{
"cells": [
{
"cell_type": "markdown",
"id": "617fe864-a317-42a2-926e-544e96026286",
"metadata": {},
"source": [
"# Filter Networks #\n",
"\n",
"### Approach ###\n",
"\n",
"Analysing simple RC networks for the purpose of producing phase shifts of sine waves which in turn might be useful later for producing oscillatory networks."
]
},
{
"cell_type": "code",
"execution_count": 152,
"id": "693e7655",
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import Image\n",
"from sympy import Matrix, symbols, Symbol, init_printing, Function, dsolve, checkodesol, sin, cos,exp, pi, Eq, \\\n",
" solveset, collect, cancel, simplify, lambdify, acos, atan, sqrt, I, integrate, factor, factor_list, Matrix, expand, \\\n",
" conjugate, Rational, sympify\n",
"import sympy\n",
"import matplotlib.pyplot as plt\n",
"from scipy.signal import find_peaks\n",
"from scipy.integrate import solve_ivp\n",
"import numpy as np\n",
"from sympy.abc import phi\n",
"from functools import reduce\n",
"init_printing()"
]
},
{
"cell_type": "code",
"execution_count": 153,
"id": "a16c4a3f",
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import display\n",
"from sympy import Function, Equality, Mul, Add"
]
},
{
"cell_type": "code",
"execution_count": 154,
"id": "d8541032",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'1.13.1'"
]
},
"execution_count": 154,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from system_eqns import systemEqns\n",
"import sympy \n",
"sympy.__version__"
]
},
{
"cell_type": "markdown",
"id": "0a699a5b",
"metadata": {},
"source": [
"## The simplest RC network\n",
"\n",
"A network containing only one capacitor and resistor"
]
},
{
"cell_type": "code",
"execution_count": 155,
"id": "effe33dd",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"![](\"https://images.kiwiheretic.xyz/RC-filter0.jpg\")
"
],
"text/plain": [
""
]
},
"execution_count": 155,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(url='https://images.kiwiheretic.xyz/RC-filter0.jpg', width=600)"
]
},
{
"cell_type": "markdown",
"id": "6057575f",
"metadata": {},
"source": [
"This is the simplest RC filter I can think of. It only contains one current path for $ \\textit{i} $.\n",
"\n",
"Therefore:\n",
"\n",
"$$ V_{in} = V_c + R \\textit{i} $$\n",
"\n",
"However $ \\textit{i} = C \\frac{d V_c}{dt} $ and we want to think about the case where $ V_{in} = A \\sin( 2 \\pi f t) $ and so we have:\n",
"\n",
"$$ A \\sin (2 \\pi f t ) = V_c(t) + R C \\frac{d V_c}{dt} $$\n"
]
},
{
"cell_type": "code",
"execution_count": 156,
"id": "ec4b6463",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left( V_{in}, \\ V_{c}, \\ C, \\ R, \\ i, \\ t, \\ f, \\ A, \\ \\tau, \\ \\omega\\right)$"
],
"text/plain": [
"(V_{in}, V_c, C, R, i, t, f, A, τ, ω)"
]
},
"execution_count": 156,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Vin, Vc, C, R, i, t, f, A, tau, w = symbols(\"V_{in} V_c C R i t f A tau omega\", real=True, positive=True)\n",
"Vin, Vc, C, R, i, t, f, A, tau, w"
]
},
{
"cell_type": "code",
"execution_count": 157,
"id": "cd33a7be",
"metadata": {},
"outputs": [],
"source": [
"def multiplyIt(x, y):\n",
" return sympify(x)*sympify(y)"
]
},
{
"cell_type": "code",
"execution_count": 158,
"id": "aa2552f8-b13f-44dc-b39c-ceaaa24040b6",
"metadata": {},
"outputs": [],
"source": [
"def getSym(expr, symbolName):\n",
" for sym in expr.free_symbols:\n",
" if sym.name == symbolName:\n",
" return sym\n",
" return None"
]
},
{
"cell_type": "code",
"execution_count": 159,
"id": "0fb16257",
"metadata": {},
"outputs": [],
"source": [
"# Define the voltage across the capacitor as a function of time\n",
"VC = Function(\"V_c\")"
]
},
{
"cell_type": "code",
"execution_count": 160,
"id": "2ff1f3dd",
"metadata": {},
"outputs": [],
"source": [
"# Define \"driving term\" of the differential equation\n",
"dt =A*cos(2*pi*f*t)"
]
},
{
"cell_type": "code",
"execution_count": 161,
"id": "ba8ccfa4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle A \\cos{\\left(2 \\pi f t \\right)} = C R \\frac{d}{d t} V_{c}{\\left(t \\right)} + V_{c}{\\left(t \\right)}$"
],
"text/plain": [
" d \n",
"A⋅cos(2⋅π⋅f⋅t) = C⋅R⋅──(V_c(t)) + V_c(t)\n",
" dt "
]
},
"execution_count": 161,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Present the differential equation of the circuit\n",
"eqn1 = Eq(dt , VC(t) + R * C * VC(t).diff(t))\n",
"eqn1"
]
},
{
"cell_type": "code",
"execution_count": 162,
"id": "d0b3ec67",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle V_{c}{\\left(t \\right)} = \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + C_{1} e^{- \\frac{t}{C R}}$"
],
"text/plain": [
" -t \n",
" ───\n",
" A⋅C⋅R⋅ω⋅sin(ω⋅t) A⋅cos(ω⋅t) C⋅R\n",
"V_c(t) = ──────────────── + ──────────── + C₁⋅ℯ \n",
" 2 2 2 2 2 2 \n",
" C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 "
]
},
"execution_count": 162,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Solve for the voltage across the capacitor wrt time\n",
"dsoln = dsolve(eqn1, VC(t)).subs(2*pi*f, w)\n",
"dsoln"
]
},
{
"cell_type": "code",
"execution_count": 163,
"id": "b6f3dac6-c950-48b4-bae6-c95b000191fa",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left( C_{1} e^{- \\frac{t}{C R}}, \\ \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\ \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}\\right)$"
],
"text/plain": [
"⎛ -t ⎞\n",
"⎜ ─── ⎟\n",
"⎜ C⋅R A⋅cos(ω⋅t) A⋅C⋅R⋅ω⋅sin(ω⋅t)⎟\n",
"⎜C₁⋅ℯ , ────────────, ────────────────⎟\n",
"⎜ 2 2 2 2 2 2 ⎟\n",
"⎝ C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 ⎠"
]
},
"execution_count": 163,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"terms = dsoln.args[1].args\n",
"terms"
]
},
{
"cell_type": "code",
"execution_count": 164,
"id": "b5b073b5-e7db-4e75-aded-d8fa32a51d87",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
"A⋅C⋅R⋅ω⋅sin(ω⋅t) A⋅cos(ω⋅t) \n",
"──────────────── + ────────────\n",
" 2 2 2 2 2 2 \n",
" C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1"
]
},
"execution_count": 164,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nonTransient = sum(terms[1:])\n",
"nonTransient"
]
},
{
"cell_type": "markdown",
"id": "4a3c5e39",
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"### Find value for $ C_1 $\n",
"At this point we want to find $ C_1 $ by setting $ V_c(0) = 0 $. This seems reasonable that the capacitor starts off with no charge on it."
]
},
{
"cell_type": "code",
"execution_count": 165,
"id": "a93838da",
"metadata": {},
"outputs": [],
"source": [
"c1 = Symbol('C1')"
]
},
{
"cell_type": "code",
"execution_count": 166,
"id": "e7608c5e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 166,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c1 in dsoln.free_symbols"
]
},
{
"cell_type": "code",
"execution_count": 167,
"id": "804836bb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAAfCAYAAACRWJ0AAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAII0lEQVR4nO2bfZCVVR3HP5AvARqovaGlMrwlRAJrhcP4mlAwNiGWjY0UNlkMpaBApdZ8/UqFEraoU0j5x5JTYzVMVGYJgzQkigLykgnUggyUOhYL4ktki9sf5zz47LPP3Xt3ediF5X5nds695/ye7/Pbe3/3nN/5nt/TrampiSqqOBpxXGc7cLhh+xxgPbBF0vBOdqeKAtG9sx3oANwD/AAYYvuEznamiuLQpYPX9kTC/zgXOB4Y0rkeVVEkumzaYLsHMA+4UtJe288DI4ANnerYMQLbi4BxQD9Jr7WTowZYC1wn6f7seJcNXuAbwGOS1sf3fwWGd547Rw5sXw38HFggaWoZ2wXAFGCepFkV8n8YmATMzAtc2+8Dbgc+AZwGvAAsASxpT2InaZ3tJcBs2w9KejXN0yXTBttnAzcAt6a6nyHMvFXAxth+sDUj2yOALwP/BNwG/u8C+4AFOZz9gXXAtcBTQC2wHZgGPGH7tMwlc4D3Er7PZuiSwUv4QE4BnrPdaLuR8OF8yHa3znWtGNiebLvJ9sXtuHwrsB8YVsbuXkKMzMjOeq34NQi4DPilpP/kmPwIeDdwg6QJkr4p6VLCdzaYEPgHIekpYAvwFdvN4rXLBa/tscBFQA0hTUj+Pgv0Bvp1kmtHDCQdIKRRfeIS3gK2rwFGA8sl/aIN9F8EugEtromz7lhgB/DDrFvAa8Ak270yYw8CZwJj0p1dKue1fTxwN3CXpKczYzvjyxGEZepYx0bCD3wY8I/0gO2TgDuB/wFfayPvZcABYHXO2CWxXSrpzfSApFdsryIE9yhgeWp4VWzHAI8knV1t5p0GvIug7TaDpH3Ai1Q3bQmSvDcvdfg2cDpQK2lLpYRxxhwObC6hMAyO7d9KUPw9toMy/Wtie2G6s0vNvJLmEeSxUuN9O9CdIx25m7aYs04nzMa3t5HzDOBtBPUgD71j+3KJ8aS/T7pT0su29xNSh4NoFry2dwBnVe4rP5N0TRvsq2gHynwvK+wWQsAiSZPL0G6KbXbmnQ+cANzUDn02UQr2tGrVPjQA70l3ZGfebYRdaKV4/lA9qqIizCczGxGW508BiwgboDQ2lCOUtMf2LuAc28dJarT9ScLBwjJJv2qHn4m68PYS48nM2rvEeNK/N2esR4ofyASvpI+V968lbFdL0wqApFwZT9L8bJ/tyYTgrZP0p3beciNwOTDQ9naCXPUGcH2pC2yfAXyHEOR9gHrCLL0UeCmaZbXaBFtjm81pEwyMbbOcOEpkfYDn0v2F5LylPvQqjngkwTsMmAj0B+6QtDXPOMpqqwlHthMJwTqacCABIdf9F29tzLJYEduxtrunFQfbJ0eu12mpVAwmyG8b0p0dvmGz/X7gAYJQ3QjMbusSVQTH4eA6CpFs2sYBVwG7gNmt2C+M11whKVlt65NBSU22VwJX2h4gqT59saRttpcS5LCvEg5BEhjoBSzMybVHxXZFurMzpLJGYLqkIYR/Yn6OKN0RHIeD62hDEryTgZ7AjZJezzO0fRYwHlAqcPOwOLYfLzE+lTBj32N7ie05th8FbiSkC7fmXDOWoB3/Jt3Z4cEr6QVJG+LrF4F/A6d2NMfh4DoKUU9YpgEekbS4FdvhhB/6ujKciwnB+fm8QUnbgPOAOuCjwAxCunI3MErS7rS97d7ABOAhSbvSY92KfgzI9nBgFuGI9p2EPGgtMFfSmoxtDUHWyWqNy4FL49tGwm56rqSf5Nwvl6OdvhfGleG9EJhJONE6HbhWUl2R9zjcsD0e+D3QOx74tGZ7M/A9YGSqqq+9972ecOh0gaTH0mOFzrxxB7wW+C+hlmAQ8IX4fkrG9lTgp4SqpSxGArcAfYEBhLPthbHKqVKOtvreZi7bdbZvq8D0JEJV2zQycs9RhCcJ+u19tofa/oDtL9k+N8e2FthJ2w85miHWZN8MLM4GLhS4YbN9PnA/MEtSbWpoJ7AyBkdieyKhfvMOSY9nePoTZJE/xmUc2wuBbwFDCc+jtcoRx2uBC4CPZM/Rba8l1PpOr4TrUCHpYeDheK+6ovk7ApJ2Rx14LkENOEA4tn0ox3a/7UnAJbZ7tbcYHTgb+DEhxWiBItWGu4AnM4F7EJIaAGJJYh3wqKQHckxrCNLLxmjfl3Dk+ybwdCUctgcTtMox2cCN2Eys7a3AnyoiJK0iyFmV2K4EVh7i/TYDt5UaLyR4bQ8EzgeursB8NCGl2GR7QuybJOkv8XUNYZndF8XpHgThfIakZyvkmAlslNRMWkmhgbBZqISriiMURc28I2O7tpxhzF1ay7VHEtKP7wPvICT+9elTptY4YsB/mrC8JX21wHZJia54MqF2tBJ/0ty3EHLxBCcCTbZnpvrGSfpzJXxVHBqK2rD1jG1F1fZlMBJ4XFJ9rMmdAky1Xa7qP0E/Qs6cnjmv4i1JCOBc4FnajvtoXuD+25y+sj/gKopBUTPvM7G9iPwK+p6lxO+MXT+Cxnow8CTtsL2e8EDf1yvw5ZTYvho5LybIU2/E9wMJQTanAq5miHl7Q8rfV4CG7ElSFR2Domob1tj+A3BvlDdWAU2EWfQ6wtFfC6kjBzWEjVl2VlxGOEuvJHh3Ro7P2d5L0Ah/B1xueyPhGapNwK8r4CoE8cmEAfFtd+DMqIc3SNpZ8sIqWkWROu8VBFXgJkIBxRrC4+dPUPlSWgNsk5Qty1xGqHwaWo5A0ksEbfAzwFLCefxMgrqwGtgNjI/PcXUUziNIfOsJG1DH14ekgx7rKPyErYoqOgpd7Rm2Ko4h/B+pLRgp25XKIQAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle - \\frac{A}{C^{2} R^{2} \\omega^{2} + 1} + V_{c}{\\left(0 \\right)}$"
],
"text/plain": [
" A \n",
"- ──────────── + V_c(0)\n",
" 2 2 2 \n",
" C ⋅R ⋅ω + 1 "
]
},
"execution_count": 167,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Solve for C1\n",
"c1eq = solveset(dsoln.subs([(t,0)]), c1).args[0]; c1eq"
]
},
{
"cell_type": "code",
"execution_count": 168,
"id": "bc4fa20e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAfCAYAAAARB2hWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAERUlEQVR4nO2ab2hWVRzHP7NMNIuUCgz6M2r9mYT7I4VEGUFC4QuT/lAk1YtCglJqFknw7VtQYdksIRr1YiRB4QujwCKxoJYVG66ZWS+mjAUmQUOmWcl0vThncHd5tuc+erc7n/aFh3vPOb/7fb73/s75/c4959YMDw8zjamDs4sWMNGwfR3QDfwqqaFgOWUxo2gBk4C3gDeAetvnFC2mHKraIbZXEu5xAzATqC9WUXlUrUNszwZeB1okHQYOAo2FisqAqnUI8CzQIak7ln8GGoqTkw1VmdRtXwE8CSxKVO8FFhciqALUVOO01/Y2YAVwIlFdAxwB5kmasjdddSPE9jJgKdAMHE80XQtsBWqBAwVIy4SqcojtmcCbwEZJu1Nt/fG0kSnskGpL6muAiwjvHqMgaRA4xBRP7FWZQ85kjApZtvuAyyu4/gNJD+aq6H+OdA7ZD/xTwfUHc9QyDXIKWban414OkFQznUOmGCZ92mv7UmALcDEwBLwkaetkc0wEVx4oYto7BKyVVA8sAzbZPrcAjongOm0UHrJs9wDLJf1WJMdEcJ0Kcg9ZthuAdYTliwuB34EuYIOkzpRtM3BW+uZt7wRui8UhoC9e/26J/yvJcYrac+NK8d4CtBCWcy4BHpHUXso215Bl+2HCw/8XuA+4GngollenbOcD7wOPlaBqAtYDC4CrgA+BNtuj9jPKcFSqvWIu2+22X8hgOpew2rwG+Hs8w9xGiO0lwHvAOkmtiaZ+4Ot4wyO2s4CPgVcl7UrxXAlcAHwu6VCsawOeBxYS9sfH5YjtrcDNwA2STqbaugh7JWuzcJ0uJG0Htsf/ah/PNs+QtRH4IeWMpKiBKKgGaAe+lLSlhGkzMAj0RPsFhJ2/k8DuLBy2rwGeAG5POyPiF+LuYQY9k4pcHGK7DlgC3J/B/CZCONtje0WsWyXpp3jeTBjig7ZnALMJy+hPS9qXkaMF6JH01RgaBoAbM3JNKvIaIU3x2FXOUFIH4+euJkLoew04H3gZ6JW0KQtHdOLdhA8bRupagQOSNseq84C/MupJcq8n5LYRzAKGbbck6u6Q9E0WvlLIK6nPicejOXA1Absk9cY9jdXA47avz3h9LSEHJXv4vcCxRHkRsI/K8Q5h+X7k90mJurKdcjzkNUL2xuNS4KN0o+05ko6l60vY1QLzSTxMSX22u4FVwDMZtMyLx6OR81bCVPN4LNcRHtwrGbhGIebBgYTeI8CApN5KucZCLg6R1Gn7M2Bz/PzmW2CY0NsfBQx0ZKBqJiTvdO/dAawkm0P6I8cDtg8TNqs+BZbHl763gT3AtgxcucD2XML0HUJUuiy+rw1I6k/a5vkechdhNvQU8CPQSfgU5zuyD+NmYL+k9BbADqDO9sJyBJL+AJ4D7gG+ANoISb4R+B74E7hT0okxSfLHYsJ0vZswSXE8fzFtWPjSyTRGo9r21M94/AeLy6s/4wQ9ywAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle - \\frac{A}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" -A \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 168,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# We will assume VC = 0 at t = 0. No charge on capacitor at start. \n",
"c1eq.args[0]"
]
},
{
"cell_type": "code",
"execution_count": 169,
"id": "e61d4d03",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + C_{1} e^{- \\frac{t}{C R}}$"
],
"text/plain": [
" -t \n",
" ───\n",
"A⋅C⋅R⋅ω⋅sin(ω⋅t) A⋅cos(ω⋅t) C⋅R\n",
"──────────────── + ──────────── + C₁⋅ℯ \n",
" 2 2 2 2 2 2 \n",
" C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 "
]
},
"execution_count": 169,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn1 = dsoln.rhs; eqn1"
]
},
{
"cell_type": "markdown",
"id": "2aa9fc95",
"metadata": {},
"source": [
"At this point I am going to try and ignore the transient part of the solution"
]
},
{
"cell_type": "code",
"execution_count": 170,
"id": "8e6be21a-fffe-43c0-8f72-b8802214579a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
"A⋅C⋅R⋅ω⋅sin(ω⋅t) A⋅cos(ω⋅t) \n",
"──────────────── + ────────────\n",
" 2 2 2 2 2 2 \n",
" C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1"
]
},
"execution_count": 170,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nonTransient"
]
},
{
"cell_type": "markdown",
"id": "544e0b9c-be81-4713-a933-18b10137b76f",
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"### Computation of phase and magnitude \n",
"\n",
"We might like to find out the amplitude and phase of the above formula given that it has both a sin and cosine term in it. The result will be a superposition which will have a different amplitude and phase of any of them separately. \n",
"\n",
"If we remember that for $ C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta + \\alpha ) $. The constants $ C_1, C_2 \\mathrm{and} C_3 $ have nothing to do with the constant of integration $ C_1 $ mentioned above. It is simply because I am running out of meaningful variable names.\n",
"\n",
"Then:\n",
"\n",
"$$ C_3^2 = C_1^2 + C_2^2 $$\n",
"\n",
"and\n",
"\n",
"we can try to reduce this formula:\n",
"\n",
"$$ C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta + \\alpha ) $$\n",
"$$ \\Rightarrow C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta ) \\cos (\\alpha ) - C_3 * \\sin ( \\theta ) \\sin (\\alpha ) $$\n",
"$$ \\Rightarrow C_1 = C_3 * \\sin (\\alpha ) \\textrm{ and } C_2 = C_3 * \\cos (\\alpha ) $$\n",
"$$ \\Rightarrow \\tan( \\alpha ) = C_1 / C_2 $$\n",
"$$ \\Rightarrow \\tan^2( \\alpha ) = C_1^2 / C_2^2 $$\n",
"$$ \\Rightarrow \\tan^2( \\alpha ) + 1 = C_1^2 / C_2^2 + C_2^2/C_2^2 =\\frac{C_1^2 + C_2^2}{C_2^2} $$\n",
"$$ \\Rightarrow \\cos^2( \\alpha ) = \\frac{C_2^2}{C_1^2 + C_2^2} $$\n",
"$$ \\Rightarrow \\alpha = \\cos^{-1} \\left( \\sqrt {\\frac{ C_2^2 } { C_1^2 + C_2^2 }} \\right) $$"
]
},
{
"cell_type": "markdown",
"id": "5750b889-b0d4-4def-b879-7de0b4f15a12",
"metadata": {},
"source": [
"### Compute V_out "
]
},
{
"cell_type": "code",
"execution_count": 171,
"id": "9d2e8ec0",
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"$\\displaystyle \\frac{A \\left(- C R \\omega \\sin{\\left(\\omega t \\right)} + \\left(C^{2} R^{2} \\omega^{2} + 1\\right) \\sin{\\left(\\omega t \\right)} - \\cos{\\left(\\omega t \\right)}\\right)}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ⎛ ⎛ 2 2 2 ⎞ ⎞\n",
"A⋅⎝-C⋅R⋅ω⋅sin(ω⋅t) + ⎝C ⋅R ⋅ω + 1⎠⋅sin(ω⋅t) - cos(ω⋅t)⎠\n",
"────────────────────────────────────────────────────────\n",
" 2 2 2 \n",
" C ⋅R ⋅ω + 1 "
]
},
"execution_count": 171,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Find the voltage at the output\n",
"vout = simplify(A * sin(w*t) - nonTransient)\n",
"vout"
]
},
{
"cell_type": "code",
"execution_count": 172,
"id": "96b9d83f-50e8-4974-b9bd-be0e4e0e6b17",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAcAAAAAjCAYAAAADgtrrAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAM1klEQVR4nO2de7Bd0x3HP4moSkPr0Sqj2pTQRknca2IwHmWKmkw9xqO0xmPQlLYUYSj99qczHtE0wZRmqm0wpjpqKFPP8agiSIiggknIRL3JRIQWkfSP37rXyc55rH3OPvfsc+/6zNw59+y99m//zv7+1lp77bX2WsNWrVpFOzCzTYFNJD1pZl8GHge2lvT+QNpoh61EIpFIdD/D2lUBZjGzecBESS930kYztsxsJrCxpIlNnmsD4DlgF0kLm7FRxeYNwCOSphZhbyhSRl2D3SGjbdJgaFE2vUbUMPZNYC7wnKTxNdKMByYDewAbA68Bc4ApkmZn0vYCa1VWNmZ2D7BX+LoCWBSO/UON861ho1masHUKMKyFU54D3NaK4GZ2CbC9pH3DpvOBf5rZVZLebcG3QmgUMzHxkjcmCqCMukLJtI0hpsyoQdJggGhBoyJpWS8orjwcXmP7ZcBvgbFm9pkqJz8GL7w+BA4HtgaODt8nZdJuCFwDnJgx04NfjE2BrYDrgRlmtkOV89WykZtmbEl6V9LSJs83Ejge+GMzx1cwAXiswqengReBH7ZotyhqxkyOeImOiSIoo67Br7JpG0PdMqMWSYMBpSmNiqJAvaCg8nCNFqCZHYxXjFOAs4GxwJMV+3cGrgImS5pWcehi4IFQwfSlXQe4GbhI0sMV27cEvgDcIen1sG0GcC6wLX6XUtdG2DcN2A2YIGllZt8c4EFJp0b4s3v4vd8CPgGeB46T9EzYP5OKxzRmdj/wLLAUr0hX4pXqmVk/gP2BVcBDzfgeAnU5sDawu5mdC8yXNBa4BTgC+B0dpF7MxMZLzpiI1r2etu3QNdY/4Exq6wol0TaGiDIjadBhIjQaBpyG35BuAbwFXCvp7FBuXoxfi8+H486Q9GDF8XXL0EBLerWjPFytBWhm6wK/CT9uKfAqkL37ngo8minM+pG0JNgaBswE7pV0bSZZL7AMmBfSbhrOuxJ4osKfmjbMbBvgp3jBms0YAPMrfa9ly8xGAH/HM8Q4YCdgOi5iPX6AP6bbBfgJcCreusmyG/C4pP7O1py+rwB2Dv/vhLeOdg3fHwMmBN06QkTMRMUL8TERfe2a1LZpXXP6V09XKIG2MTTSP2nQeSLL9QuA84AL8RvOQ4G+LqIp+PU/Lhz3NHBHyKN5NG5VLyi4PMy2AM/Ca9q+u+1/A+MrHB0TTn5EhO1d8Yv2lJkdGLYdFZqqvcAoYJmZDQfWBT4CTpf0bKSNM4B5ku6rcf4l+AWqawt4BW953FrxXPq5iN/3rKRfhv9fMLMTgL2Bv2TSfRUPuEqifZe0MgTae8DsTPC8it8JbQYU1qGck5oxkzNeYmMij+7rk1/bVnSN9q+BrlAObWOoW2aQNCgDjcr1UcDPgVMl/SlsXgDMMrPPAT8Gjpf0j5B+Et5XfzL+hCZW45b0guLLw/4K0My+BvwMr8H7eAbYseJ7T/ic08hwaB7X6mPswR+LXYJfvAuABZKmx9gIBeQh+J1J37ZpwIuSLg+b1gP6X3Go5094DHNnGIRxD/A3SYsb/MSnMt9fBb5UJd26wBut+I7f/cyrkkH/W3GOASciZqLjhYiYyHvtJC1pQtumdG3GP2rrCh3WNoaYMiNp0Fkiy/WxwDq4Nlm2xCuV/seWkj4xs1nhuDwaF6EXFFgeVlYI04ANgJfMbIWZrcBHaG0fHh8CjAyfy2NPUIMe4GFJCyQ9gT93PsnMtos8fjR+x/F0xbbDgA8qvo/D+xIaIulY/A7jAeB7wPNmtm/9o/g4830V1SvYt/Hr2kczvo+nog+sgr7+1rca+NouGsVMnniJiYnc164JbZvVtRn/xlNdV+i8tjHElBlJg84SpVGT9FdAkRoXoRcUWB4OBzCzffDh6b3BeN/f4Xin5+iQvq9Dc49qxsxH+dTFzEYHR/t/sKRF+A86KtLvvou4PNjcE2/2fhS+jwn+3xRpD0nzJF0saU/gfnyUYhHMJdwpBZrxfRxr3hWDdzi/IumNKvvaSmTMRMVLjphoSvc2aZvVtRn/aukKHdQ2hhxlBpA06AQ5NJqPj8jeu4qZhfi16+8bNbO18K6N1RoYERoXoRcUWB6OMLO1gUuBqeHOux8z62vC7oA3SWeb2e3A5aGj8SH8LqAHOAEwvCO0Hr34wIZs6+xu4GB8ZFYjFgcbR5rZUnx4763ARPMX3K/AL1DDCjAUvj/CRxC9Anwd2B64MsKPGO4ELjazjSS906TvI4BvmNlmwAf6dNj4bsH+gBIbM5JujIyX2JjIde3arG1W19z+UVtXKEBb89dP/gx8W9L9rdjK2I0uM4a6Bp0iZ7n+npldClxoZh/irbiNgF5JV5rZlfh1fht4Ce8v3AS/lnnyWRF6QYHl4XC8OfzFcOLVkLQMeJ3VO7UPwkcUnYYPh52Nd7LOIq6vpxdYKOl/me13A2PMbNtGBiS9iQ/lPRS4C5iBd6TuADwCvAPsL6nRSE7wpvbWwA3AC8DVwHX4sN+WCQN2HgO+34LvvwjH/wcfpYWZfRbXol0vidcjT8zExEtUTDRx7dqmbVbXJv1bQ1fouLYx5NE/adAZ8pbrZ+OanIe3CG8ENg/7zgL+it9MPYlXbvtJei3sj9K4IL2gwPJwwKZCG8qY2X743djYyEo5xubJwAGS9inCXiI/7dA12C1E23a1AMtE2TVIrE7Z9Ko1SjNRIJLuwF/O3LxR2hx8jL87k+gQbdIVkrbRJA26i7LplVqAicQgZSi0ABOJVkgV4BDCzBbhL6PGcp2kwTQX4qClCW2vlnRMe7xJ1CLlwXJRdTWIxKBlIZAdaFKParM2JMrJdPx9qkrGAwfggxIWZfY92WZ/EtVJebBEpBZgIjFISY9AE4n6jAAws1QLDiIktTrDQ0NSzAw8SdfuIWnVHXSkBWhmXwGuxef3WwH8WtINA22jHbYS8aQ4aC/tbgEm/bqHpFV1OvUaxAp85vGxwD7AdPNZxwfaRjtsJeJJcdDdJP26h6RVFUrRBximvJko6eWGidtoox22EvGkOCiWge4DTPp1D0krpy2jQM1sPDAZn4h1Y+A1fNqrKZJmZ9L2Amtlf7j5shp7ha8r8FFsUyStMdVNLRtN+l6YrYzd3fEpfnrxyV6PlTSzyHOUjVbjIE8M1LLRgu9dHwfBbtO2Uz6uareU+Tjltap2G2pV+CPQcNc5B59d/HB8jrijw/dJmbQbAtcAJ1Yx1QOcg6/4uxVwPTDDzFZbybiBjby+57ZlZjPN7FcRSUfhqyOcwqfrVg1aCoqDqBhoYKMZ33PZyhED0CVxkPJxTUqnX8prNWmoVaEtQDPbGV/UdLKkaRW7FgMPhB/bl3Yd4GbgIkkPZ+xsib/TdIek18O2Gfjqw9sS1oKqZyPsn4bPED5B0srMvjn4KsmnxthqFUm3AbeFc80s2n6ZKCIOYmOgno2wLzoGGtkqgm6Ig5SPa1M2/cqU18L+rtKq6EegU4FHM0JUOrQkODMMfzRzr6RrqyTtBZYB80L6TfEVBVYCT8TYMLNt8LnhvpMVIjAfn3E8xp9EPoqIg4Yx0MhGnhiI8GcokfJx91CKvBb2d51WhVWA5gsX7gwcEZF8V7yp/pSZHRi2HSVfLgNckFHAMjMbji9x/xFwuqRnI22cAcyTdF8NH5bgKxjH2EpEUmAcxMRAIxt5YqCRrSFBysfdQ8nyGnShVkW2AHvCZ8M1ASU9SP3+xx68WX8JsD5wAbBA0vQYG0HEQ4ApFdum4Ys/Xh42rQe8H+lPpe1z8GflfawDrDKzMyq2fVfSv2LsDUKKioOGMVDPRt4YiPCn0vZgjoGUjz+l7BqWIq9B+7Rqt05FDoIZGT6XF2CrB3hY0gL5asaTgJPMbLvI40fjz7Qr7yYOwxdu7GMca65AHsPv8TkW+/5uqbItZmHgwUpRcZBioDOkfNw9GpYlr0H7tGqrTkW2AJ8Jn3vgqwevhpmNlPRBdnuVdKOBDam4kJIWmdlc4CjgzAhfNgify4PNPfFhsB+F72PwC3fhmofWJzxTX1Lh73vAEkkL8toapLQcBykGOkrKx91DWfIatEmrdutUWAUoabaZ3Q5cbmbrAg8Bq/C7ixMAAx6MMNWLd75m7xTuBg4mTpDFwcaRZrYUuAy4FZho/sLlFcBTwE0RtgrBzEbhw4vBW95bmL+7s0TS4oHyo90UFAeDMgag/HGQ8nF9yqRfifIadKlWRb8HeBA+eug0fLmV2cBZwCzim6m9wEJJ2SVD7gbGmNm2jQxIehM4GzgUuAuYgXfQ7gA8ArwD7C/pk0ifimBHfDjxXLyT2cL/5w+gDwNFq3EwWGMAuiMOUj6uTdn063heg+7VqhRToSUSiUQiMdB0ajLsRCKRSCQ6SqoAE4lEIjEk+T950Fy3ilnj3gAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} - \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 2 2 \n",
"A⋅C ⋅R ⋅ω ⋅sin(ω⋅t) A⋅C⋅R⋅ω⋅sin(ω⋅t) A⋅sin(ω⋅t) A⋅cos(ω⋅t) \n",
"─────────────────── - ──────────────── + ──────────── - ────────────\n",
" 2 2 2 2 2 2 2 2 2 2 2 2 \n",
" C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1"
]
},
"execution_count": 172,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vrsterms = expand(vout)\n",
"vrsterms"
]
},
{
"cell_type": "code",
"execution_count": 173,
"id": "f64e2cea-1fbf-4842-bda5-a1d2e7d5fd6e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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SQ5JWm9k3gcVmNg64F1+5bAg4HzBgVYtMDeOdFNKtopXA6RQL3OZg44NmthVfJ/UOYJb5OPabgIeBrxawVQtmNgEfBgH+ZONN5uMkt0ja3PTALqWLYg0x3pWJ8cyn1+I5VtSkI4j1QCs7HwO+ImldXroi7wM+ibeUGpyG35FfCjwErAYuA+6n2COFYWCjpPSSdyuByWZ2VCsDkn4KXA6cCXwbWIJ3ZpgBPAA8B5wq6eUC+amLt+PDHtbinTEs/H/1XsxD3Yx5rCHGu0ZiPJvTi/EcK6rqCGI90IrNkm5vlWjUVKqRSCQSiUR6g0I98iKRSCQSiXQXsQKPRCKRSKQH+X/t1kYRgVWQtgAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle \\left( \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\ \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}\\right)$"
],
"text/plain": [
"⎛ 2 2 2 ⎞\n",
"⎜ A⋅sin(ω⋅t) -A⋅cos(ω⋅t) A⋅C ⋅R ⋅ω ⋅sin(ω⋅t) -A⋅C⋅R⋅ω⋅sin(ω⋅t) ⎟\n",
"⎜────────────, ────────────, ───────────────────, ──────────────────⎟\n",
"⎜ 2 2 2 2 2 2 2 2 2 2 2 2 ⎟\n",
"⎝C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 ⎠"
]
},
"execution_count": 173,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vrstermslist = vrsterms.args\n",
"vrstermslist"
]
},
{
"cell_type": "code",
"execution_count": 174,
"id": "fdd288fe-941d-42f7-bc45-2dd64c7cfcb8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A⋅sin(ω⋅t) \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 174,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get cosine coefficient\n",
"coscf = reduce(multiplyIt, (filter(lambda x:type(x) not in [cos],vrstermslist[0].args)))\n",
"coscf"
]
},
{
"cell_type": "code",
"execution_count": 175,
"id": "653a6ade-b6ed-4039-a3e0-a2d9be144ce2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
"-A⋅cos(ω⋅t) \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 175,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get cosine coefficient\n",
"sincf = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],vrstermslist[1].args)))\n",
"sincf"
]
},
{
"cell_type": "code",
"execution_count": 176,
"id": "1833b696",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A^{2}}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}}$"
],
"text/plain": [
" 2 \n",
" A \n",
"───────────────\n",
" 2\n",
"⎛ 2 2 2 ⎞ \n",
"⎝C ⋅R ⋅ω + 1⎠ "
]
},
"execution_count": 176,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c3_2 = simplify(sincf**2 + coscf**2)\n",
"c3_2"
]
},
{
"cell_type": "code",
"execution_count": 177,
"id": "e441c722",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\operatorname{atan}{\\left(\\frac{\\cos{\\left(\\omega t \\right)}}{\\sin{\\left(\\omega t \\right)}} \\right)}$"
],
"text/plain": [
" ⎛cos(ω⋅t)⎞\n",
"-atan⎜────────⎟\n",
" ⎝sin(ω⋅t)⎠"
]
},
"execution_count": 177,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now compute the phase shift at the output\n",
"alpha = atan(sincf/coscf)\n",
"alpha"
]
},
{
"cell_type": "markdown",
"id": "7cd8ac2e-1864-4af5-ab3f-fb810d6c8a52",
"metadata": {},
"source": [
"This results in a phase shift angle of $ \\alpha - \\frac { \\pi }{2} $"
]
},
{
"cell_type": "markdown",
"id": "68fba51d",
"metadata": {},
"source": [
"### Find magnitude of voltage across $ V_c $ and phase shift ###\n",
"\n",
"The phase shift is in relation to the input voltage and I am not even sure that is quite right. I have to check if this is valid for a sin(w*t) driving force as \n",
"opposed to cos(w*t)\n",
"\n",
"We do this initially by comparing the coefficients of the sin and cos terms but later on we have at doing this\n",
"using complex analysis."
]
},
{
"cell_type": "code",
"execution_count": 178,
"id": "54b227ef",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left( \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\ \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}\\right)$"
],
"text/plain": [
"⎛ A⋅cos(ω⋅t) A⋅C⋅R⋅ω⋅sin(ω⋅t)⎞\n",
"⎜────────────, ────────────────⎟\n",
"⎜ 2 2 2 2 2 2 ⎟\n",
"⎝C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 ⎠"
]
},
"execution_count": 178,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nonTransient.args"
]
},
{
"cell_type": "code",
"execution_count": 179,
"id": "5b88db11",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A⋅cos(ω⋅t) \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 179,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get sine coefficient\n",
"sincf = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],nonTransient.args[0].args)))\n",
"sincf"
]
},
{
"cell_type": "code",
"execution_count": 180,
"id": "620dff99",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
"A⋅C⋅R⋅ω⋅sin(ω⋅t)\n",
"────────────────\n",
" 2 2 2 \n",
" C ⋅R ⋅ω + 1 "
]
},
"execution_count": 180,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get cosine coefficient\n",
"coscf = reduce(multiplyIt, (filter(lambda x:type(x) not in [cos],nonTransient.args[1].args)))\n",
"coscf"
]
},
{
"cell_type": "code",
"execution_count": 181,
"id": "dca40fff",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{\\sqrt{A^{2} C^{2} R^{2} \\omega^{2} \\sin^{2}{\\left(\\omega t \\right)} + A^{2} \\cos^{2}{\\left(\\omega t \\right)}}}{\\sqrt{C^{4} R^{4} \\omega^{4} + 2 C^{2} R^{2} \\omega^{2} + 1}}$"
],
"text/plain": [
" ______________________________________\n",
" ╱ 2 2 2 2 2 2 2 \n",
"╲╱ A ⋅C ⋅R ⋅ω ⋅sin (ω⋅t) + A ⋅cos (ω⋅t) \n",
"─────────────────────────────────────────\n",
" ___________________________ \n",
" ╱ 4 4 4 2 2 2 \n",
" ╲╱ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + 1 "
]
},
"execution_count": 181,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c3 = sqrt(cancel(sincf**2 + coscf**2))\n",
"c3"
]
},
{
"cell_type": "code",
"execution_count": 182,
"id": "ebe53008",
"metadata": {},
"outputs": [],
"source": [
"from sympy import Mul, sympify, re, im\n",
"import math "
]
},
{
"cell_type": "code",
"execution_count": 183,
"id": "8475e93c",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} - \\frac{A e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" -t \n",
" ─── \n",
" C⋅R \n",
"A⋅C⋅R⋅ω⋅sin(ω⋅t) A⋅cos(ω⋅t) A⋅ℯ \n",
"──────────────── + ──────────── - ────────────\n",
" 2 2 2 2 2 2 2 2 2 \n",
" C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 1"
]
},
"execution_count": 183,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simpeq2 = dsoln.args[1].subs(c1, c1eq.args[0])\n",
"simpeq2"
]
},
{
"cell_type": "code",
"execution_count": 184,
"id": "ee48e2dd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"cos"
]
},
"execution_count": 184,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(simpeq2.args[0].args[-1])"
]
},
{
"cell_type": "code",
"execution_count": 185,
"id": "03cfa076",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 185,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simpeq2.coeff(simpeq2.args[0].args[-1])"
]
},
{
"cell_type": "code",
"execution_count": 186,
"id": "2e9fd9f3",
"metadata": {},
"outputs": [],
"source": [
"u = symbols('u')"
]
},
{
"cell_type": "code",
"execution_count": 187,
"id": "66f6c8ec",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A⋅cos(ω⋅t) \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 187,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simpeq2.args[0]"
]
},
{
"cell_type": "code",
"execution_count": 188,
"id": "2baf1a6a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A⋅cos(ω⋅t) \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 188,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get sine coefficient\n",
"c1 = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],simpeq2.args[0].args)))\n",
"c1"
]
},
{
"cell_type": "code",
"execution_count": 189,
"id": "99628c59",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{A e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" -t \n",
" ─── \n",
" C⋅R \n",
" -A⋅ℯ \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 189,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get cosine coefficient\n",
"c2 = reduce(multiplyIt, (list(filter(lambda x:type(x) not in [cos],simpeq2.args[1].args))))\n",
"c2"
]
},
{
"cell_type": "code",
"execution_count": 190,
"id": "36345ddc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
"A⋅C⋅R⋅ω⋅sin(ω⋅t)\n",
"────────────────\n",
" 2 2 2 \n",
" C ⋅R ⋅ω + 1 "
]
},
"execution_count": 190,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get third coefficient (of exponential term)\n",
"reduce(multiplyIt, filter(lambda x:type(x) not in [ exp],simpeq2.args[2].args))"
]
},
{
"cell_type": "code",
"execution_count": 191,
"id": "07f2f49c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A^{2} \\left(e^{\\frac{2 t}{C R}} \\cos^{2}{\\left(\\omega t \\right)} + 1\\right) e^{- \\frac{2 t}{C R}}}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}}$"
],
"text/plain": [
" ⎛ 2⋅t ⎞ -2⋅t \n",
" ⎜ ─── ⎟ ─────\n",
" 2 ⎜ C⋅R 2 ⎟ C⋅R \n",
"A ⋅⎝ℯ ⋅cos (ω⋅t) + 1⎠⋅ℯ \n",
"──────────────────────────────\n",
" 2 \n",
" ⎛ 2 2 2 ⎞ \n",
" ⎝C ⋅R ⋅ω + 1⎠ "
]
},
"execution_count": 191,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute c3^2 using pythagoras theorem\n",
"c3_2 = simplify(c1**2 + c2**2)\n",
"c3_2"
]
},
{
"cell_type": "code",
"execution_count": 192,
"id": "907ce05a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\sqrt{e^{\\frac{2 t}{C R}} \\cos^{2}{\\left(\\omega t \\right)} + 1} e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ____________________ \n",
" ╱ 2⋅t -t \n",
" ╱ ─── ───\n",
" ╱ C⋅R 2 C⋅R\n",
"A⋅╲╱ ℯ ⋅cos (ω⋅t) + 1 ⋅ℯ \n",
"────────────────────────────────\n",
" 2 2 2 \n",
" C ⋅R ⋅ω + 1 "
]
},
"execution_count": 192,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# find c3 by taking square root\n",
"c3 = sqrt(c3_2) \n",
"c3\n"
]
},
{
"cell_type": "code",
"execution_count": 193,
"id": "56dcb8dc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - e^{\\frac{t}{C R}} \\cos{\\left(\\omega t \\right)}$"
],
"text/plain": [
" t \n",
" ─── \n",
" C⋅R \n",
"-ℯ ⋅cos(ω⋅t)"
]
},
"execution_count": 193,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute the phase\n",
"c1/c2"
]
},
{
"cell_type": "markdown",
"id": "4b24e8dd",
"metadata": {},
"source": [
"The tan function can be equated to the fraction of $ \\frac{\\sin( \\theta )}{\\cos (\\theta )}$ "
]
},
{
"cell_type": "code",
"execution_count": 194,
"id": "05abad5c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\operatorname{atan}{\\left(e^{\\frac{t}{C R}} \\cos{\\left(\\omega t \\right)} \\right)}$"
],
"text/plain": [
" ⎛ t ⎞\n",
" ⎜ ─── ⎟\n",
" ⎜ C⋅R ⎟\n",
"-atan⎝ℯ ⋅cos(ω⋅t)⎠"
]
},
"execution_count": 194,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(atan(c1/c2))"
]
},
{
"cell_type": "markdown",
"id": "8f32d128-ddcd-41a1-a055-e3a5207888f6",
"metadata": {},
"source": [
"### Complex Impedance Analysis "
]
},
{
"cell_type": "markdown",
"id": "61093af9",
"metadata": {},
"source": [
"I wish to compare this with the complex analysis of the circuit"
]
},
{
"cell_type": "code",
"execution_count": 195,
"id": "3bfdd494",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{C R \\omega - i}{C \\omega}$"
],
"text/plain": [
"C⋅R⋅ω - ⅈ\n",
"─────────\n",
" C⋅ω "
]
},
"execution_count": 195,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z = R - I / (w*C)\n",
"zc = cancel(Z) # express as fraction\n",
"zc"
]
},
{
"cell_type": "code",
"execution_count": 196,
"id": "f3db2138",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{i}{C R \\omega - i}$"
],
"text/plain": [
" -ⅈ \n",
"─────────\n",
"C⋅R⋅ω - ⅈ"
]
},
"execution_count": 196,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now we try and work out Vout as R/Z\n",
"rzc = (-I/(w*C))/zc\n",
"rzc"
]
},
{
"cell_type": "code",
"execution_count": 197,
"id": "01ccfae6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{1}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 1 \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 197,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sympy.re(rzc)"
]
},
{
"cell_type": "code",
"execution_count": 198,
"id": "b5d08d9b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{C R \\omega}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" -C⋅R⋅ω \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 198,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sympy.im(rzc)"
]
},
{
"cell_type": "code",
"execution_count": 199,
"id": "18c46477",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{C^{2} R^{2} \\omega^{2}}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}} + \\frac{1}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}}$"
],
"text/plain": [
" 2 2 2 \n",
" C ⋅R ⋅ω 1 \n",
"─────────────── + ───────────────\n",
" 2 2\n",
"⎛ 2 2 2 ⎞ ⎛ 2 2 2 ⎞ \n",
"⎝C ⋅R ⋅ω + 1⎠ ⎝C ⋅R ⋅ω + 1⎠ "
]
},
"execution_count": 199,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sympy.re(rzc)**2 + sympy.im(rzc)**2"
]
},
{
"cell_type": "code",
"execution_count": 200,
"id": "0436eb4f",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{1}{C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 1 \n",
"────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅ω + 1"
]
},
"execution_count": 200,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# This is the square of the magnitude of voltage dividing impedance across R\n",
"c3_2 = cancel(_)\n",
"c3_2"
]
},
{
"cell_type": "code",
"execution_count": 201,
"id": "225bcd4b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAAUCAYAAABLTIm0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAGA0lEQVR4nO2ae4xV1RXGfwNqRUnFdy2WV0BoQgiiNdgWxYCg6YvWVzClPNRobUoNtbEmxm8+0Zao4aFRCNEWpFpFkaho1X+k2lpHUUGNWCspSqqtJr5tfTAd/1j7wHHPucPAvXptOl8yWfestffaa5+199pr7TMtHR0d9OD/D72abUAPmoPdmm3A5xW2lwMnAoMlvddse3YFto8A1gFnSbquLGtpZqi3PQj4O7Bc0oymGZLB9teANuB8SfNrtBkGzAImAQOAfsCbwAbgdmCZpH+X2t8PHJ+peQ14Hlgk6dbGzmLbuKuBscAwSe8W/J4dX43LgLeBxbnAdgtwCXABsDvwMHAb8BYwkFgIE4CpwLhS1yOADmBuorsBI4ApwDdsz5G04FOYy6+JRTwb+FXB7HF8BtuHAROB6yT9p6LJb4AZwLPA6ZI2ZP37AHOAoSXeEGA/4K+SlLU/h1hgPwMa7nhJj9p+Djjb9jxJ/4UGO972DOA7wOHAIcBHwNPAYkm/y9q2AsVLmG57ekk8U9KyndGXdA4iHR1AKzCPcGJf4BmgVdKaHUxjFtAC3FKhfw7h9I3AWEnv5G3SYrksLYACRyb6eMV49yZ6UJUxts8GlgDzJf28ltG2NwFDgC9J+lcmvpl4H8cD90Hjs/rFRLh7EFiYBhwIrLA9N2u7FliUfm8AXPpbvwv6yhgIPAoMAlYQThwJ3GH7uB3MYSLQDjxSZto+hDgCtgKnVjm9jCxadOX4IjJszAW2DwYuB/7J9k1SC4Xur1fI/pzothyj0aF+pKRNZYbtPYA/AL+0vUTSPwAkrbW9mQhx6yW11qMvw3hid7vU7yZid/0CeKDKeNt7A6OBjRWZ/HnAnkTS9kxV/y5QOH5dNt4BwJXpcV5Fv4uBLwIXlROzGtic6IgK2WOJHlMwGrrjcycl3ofANcQim/AZ6XsRuDTrdx/wEnBUF0P2B3oDr1TIpiR6Q5dGZ0jJ4Jj0+F3brbbn2r4BeIEIz+fmWX1aFGcQSeb13RiqWKj75gJJbwHvE9UHkO34tAMHdmdCCTdK+mGp/wAi252QBumTte+/E7rr0bdeUnsFfwtwdBdD7p/oG5kdfYHDiGy8bQdm5xgG7JN+52f0e8DJku6lM04FvgCszMrCo4jk8SpJD5fa75XoBzXseB04uHjIQ/0mYmV0Fy+XDBpCnKv7Ag8B9xMlTjtx1k5PE+kW6tT3Zg3+VrqOcsW5vGfGPzDRt8tO6CaKMP9bSbMAbO9H2D8f+L3twZJym8cn+seM/23gNOCKjF/kCn+rYUcfts/vk46XtFOhOMMcYsfMlLSsLLA9lZhoM/V1B68mun/GL8JoH9u9a0STWuh0vkt6HVhg+2jgFGAacHXWb3iiz2X8yYm+VDBs9wK+mR7zhVLI+xEVD9DYM75YcasqZMfW6FO8wN4N0lcvXiFu04aXmZJeJfKGPdi+EyuRXnIZXWX0xTXq1ApZcTxsS+psf5XtOUo5pE8kysE2SS9W6BpOlKjrC0YjHb850fFlpu3JwJk1+rxBnJsDKmS7oq8uSOogSscDbA/NxMXlyrW2O2XOtltsn0iUnAWvF3EHsZUoWXM8QBxLY21/OZO9luioQj9R2j2R+MMTf6/Eh7ilq8LY0nhAY8u5a4GZwK22byPO/5HACcBK4lz6BCS9a7sNGGf7RuLeuh24c1f0NQirgJOIkPpCiX8V4YRZwNPp7v154lLpK0SoPRS4qdRnBHF5tEFSp9xJ0ke27wFOB75PVCsFVhPRYqHt0cQCOpKoxdcCy23fBXyPWARLJd1RY06TiPe6Td6wHS/pKeA44u76W8CPiRr0B8TNUy1MA+4mHCriLntMHfrqxSrirP9RmSmpQ9IZyZY1RL3/EyL6jAL+QtzqzS516yrMF1id6EkZ/wri0qodOIfYpJMktaXnvYk7kA+BcxOvE2zvQ5SiayRtKfhN/Tr3eYXtC4kPGmMkPdlse+qB7Z8S0WqcpD8V/J5/xKjGAiJrvqTZhtSD9L3gQmBV2enQ4/hKpPN4GrAuXeP+r2IQsBQ4Pxd8DFJEJqq+3vTWAAAAAElFTkSuQmCC",
"text/latex": [
"$\\displaystyle - \\operatorname{atan}{\\left(C R \\omega \\right)}$"
],
"text/plain": [
"-atan(C⋅R⋅ω)"
]
},
"execution_count": 201,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phase = atan(sympy.im(rzc)/sympy.re(rzc))\n",
"phase"
]
},
{
"cell_type": "code",
"execution_count": 202,
"id": "26cdf8e7",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAD0AAAAkCAYAAAA6uzK6AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAC60lEQVR4nO2ZX2hOYRzHP+8ohGJKWSgipZatiSKSIpYL5V+54sId2cVckPr6kiY3k5W4W+RKodES4cIsF8qGuJELyiSWMlbCXJwznZ295rzv3p0tZ586ved5nvf9/X7f93ee3/N0nlxfXx9pYHstUA/UABXAXknNqTiPUZair2nAc+Ag0Jui30Hk0sp0FNs9wP4sZHrMMC46K4yLzgqpVW/b04BFYbMdOAW0AN2S3qQSREiamV4OPAmvKYDD++MpxgCM0jo92mRyTo+LzgoTAWxnZmJLyo0XsqyQSdETk3zJ9lzg7QjHkgqScolEA7VAhaSukQwoLZI+3nP+F8GQ4PG2PZlhvNOyPQ+4BMwGfgAnJF0p1l4pSJLp9cD9Yfj4AdRJWgpsBM7YnjoMe8Mmiega4HGxDiR1SeoI798DH4HyYu2VgiSic5JKsoOxXQNMkDSqK8GQc9p2JfCsFI5slwMXgX2lsBezXdBBwp9M215g+2RsfANwpwRBTQKuA6cktSf8TbPtYwldFHSQEM10JbDHdoOknn5jkftoQI3AGmCFpF+xscdAm6S6sJ0DmoF7ki4lFFEQklqB1tBf87++/yfTklqAmwQVFtuzCIrOAGwvAQ4Ah+KCQ14C1ZH2amAXsNV2R3hVJhU0EsTn9A1gG3AV2ATcyvObeqBT0t+WsW5gZX9DUhtjbI8fF30XaLJdBiyUdDk6GPZvB05H+hqB15Kawq7pwNdCA7F9BDgS6ZoE9Nmuj/RtlvSgUNtxBmRAUi9BQVhFsKmIswCYwcCKvhP4FmkvA14UEct5oCpyteTpK3q/ECXfknUDaACO5hmbGX72ANheR7BEfA/bi8PgGgoNRFI3wdQgtPWF4J34q0Jt/Yt8om8SBP0wz9gb4Bew2/Zn4CzBn7TFdidwDngKXCt1oEMRO0goA+bbruIvBwmDCoykdwR75UGPt6QPwGFgB3AbuEBQ2KqBR8AnoFbSz5KoSU5BBwmZfEf2G1l//7wdGFt8AAAAAElFTkSuQmCC",
"text/latex": [
"$\\displaystyle \\frac{1}{\\sqrt{\\omega^{2} + 1}}$"
],
"text/plain": [
" 1 \n",
"───────────\n",
" ________\n",
" ╱ 2 \n",
"╲╱ ω + 1 "
]
},
"execution_count": 202,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u = sqrt(c3_2).subs([(A,1), (C,1), (R,1)])\n",
"u"
]
},
{
"cell_type": "code",
"execution_count": 203,
"id": "75116894",
"metadata": {},
"outputs": [],
"source": [
"f1 = lambdify(w, u)"
]
},
{
"cell_type": "code",
"execution_count": 204,
"id": "25585a9d",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1, ax2) = plt.subplots(1, 2)\n",
"fig.set_figwidth(13)\n",
"\n",
"f1 = lambdify(w, u)\n",
"t1 = np.linspace(0, 4, 8000)\n",
"y = f1(t1)\n",
"y2 = 1 - y\n",
"\n",
"ax1.title.set_text(\"frequency vs phase $V_c$\")\n",
"ax1.set_xlabel(\"Frequency ($ \\omega $)\")\n",
"ax1.set_ylabel(\"cos(Phase)\")\n",
"ax1.plot(t1, y)\n",
"ax1.grid()\n",
"\n",
"\n",
"ax2.title.set_text(\"frequency vs phase $V_R$\")\n",
"ax2.set_xlabel(\"Frequency ($ \\omega $)\")\n",
"ax2.set_ylabel(\"cos(phase)\")\n",
"ax2.plot(t1, y2)\n",
"ax2.grid()\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 205,
"id": "0b7c1ec1-c6d8-448f-9bc8-970f3c457ebe",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\omega$"
],
"text/plain": [
"ω"
]
},
"execution_count": 205,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w = getSym(simpeq2, \"omega\")\n",
"w"
]
},
{
"cell_type": "code",
"execution_count": 206,
"id": "f30ac994",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{e^{- t}}{1 + 4 \\pi^{2}}$"
],
"text/plain": [
" -t \n",
" -ℯ \n",
"────────\n",
" 2\n",
"1 + 4⋅π "
]
},
"execution_count": 206,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expdropoff = simpeq2.args[1].subs([(C*R, 1), (A,1), (f,1), (w, 2*pi)])\n",
"expdropoff"
]
},
{
"cell_type": "code",
"execution_count": 207,
"id": "cc21b169",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{2 \\pi \\sin{\\left(2 \\pi t \\right)}}{1 + 4 \\pi^{2}} + \\frac{\\cos{\\left(2 \\pi t \\right)}}{1 + 4 \\pi^{2}} - \\frac{e^{- t}}{1 + 4 \\pi^{2}}$"
],
"text/plain": [
" -t \n",
"2⋅π⋅sin(2⋅π⋅t) cos(2⋅π⋅t) ℯ \n",
"────────────── + ────────── - ────────\n",
" 2 2 2\n",
" 1 + 4⋅π 1 + 4⋅π 1 + 4⋅π "
]
},
"execution_count": 207,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fn = simpeq2.subs([(C*R, 1), (A,1), (f,1), (w, 2*pi)])\n",
"fn"
]
},
{
"cell_type": "code",
"execution_count": 208,
"id": "d89afff6-a5d4-4917-a29e-0021b7bc6b59",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 91, 490, 890, 1290, 1690, 2089, 2489, 2889, 3289, 3689])"
]
},
"execution_count": 208,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f1 = lambdify(t, fn)\n",
"f3 = lambdify(t, expdropoff)\n",
"t1 = np.linspace(0, 10, 4000)\n",
"y2 = np.sin(2*np.pi*t1)\n",
"y = f1(t1)\n",
"pks = find_peaks(y)[0]\n",
"pks"
]
},
{
"cell_type": "code",
"execution_count": 209,
"id": "fdb9e294-92b9-4159-a301-be102ee9c31d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle \\left[ \\left( 0.227556889222306, \\ 0.137477913308612\\right), \\ \\left( 1.22530632658165, \\ 0.149921241439572\\right), \\ \\left( 2.22555638909727, \\ 0.154507038654254\\right), \\ \\left( 3.2258064516129, \\ 0.156192708863905\\right), \\ \\left( 4.22605651412853, \\ 0.156811503428512\\right), \\ \\left( 5.22380595148787, \\ 0.157040065852002\\right), \\ \\left( 6.2240560140035, \\ 0.157125672595519\\right), \\ \\left( 7.22430607651913, \\ 0.157157701014392\\right), \\ \\left( 8.22455613903476, \\ 0.157169778691948\\right), \\ \\left( 9.22480620155039, \\ 0.157174273430905\\right)\\right]$"
],
"text/plain": [
"[(0.22755688922230558, 0.1374779133086123), (1.2253063265816453, 0.14992124143 ↪\n",
"\n",
"↪ 95722), (2.225556389097274, 0.15450703865425375), (3.225806451612903, 0.1561 ↪\n",
"\n",
"↪ 927088639046), (4.2260565141285324, 0.15681150342851222), (5.223805951487872 ↪\n",
"\n",
"↪ , 0.15704006585200167), (6.224056014003501, 0.15712567259551935), (7.2243060 ↪\n",
"\n",
"↪ 7651913, 0.15715770101439216), (8.224556139034759, 0.15716977869194848), (9. ↪\n",
"\n",
"↪ 224806201550388, 0.15717427343090454)]"
]
},
"execution_count": 209,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[(t1[ii],y[ii]) for ii in pks]"
]
},
{
"cell_type": "code",
"execution_count": 210,
"id": "054c609f-9af7-41ce-afbd-96518bff30bc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1, ax3) = plt.subplots(1,2)\n",
"fig.set_figwidth(12)\n",
"\n",
"f1 = lambdify(t, fn)\n",
"f3 = lambdify(t, expdropoff.subs(w, 2*pi))\n",
"t1 = np.linspace(0, 10, 4000)\n",
"y2 = np.sin(2*np.pi*t1)\n",
"y = f1(t1)\n",
"\n",
"ax1.title.set_text(\"Amplitude vs time from $ V_C $ formula\")\n",
"ax1.set_xlabel(\"Time (RC units)\")\n",
"ax1.set_ylabel(\"Relative Amplitude\")\n",
"ax1.plot(t1, y)\n",
"ax1.grid()\n",
"\n",
"\n",
"t1 = np.linspace(0, 10, 4000)\n",
"y = f3(t1)\n",
"\n",
"ax3.title.set_text(\"Exponential drop off component\")\n",
"ax3.set_xlabel(\"Time (RC units)\")\n",
"ax3.set_ylabel(\"Relative Amplitude\")\n",
"ax3.plot(t1, y)\n",
"ax3.grid()\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 211,
"id": "fbf1e1a0-5d37-42f5-8f84-5a0e7231ba11",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([], dtype=int64), {})"
]
},
"execution_count": 211,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"find_peaks(y)"
]
},
{
"cell_type": "markdown",
"id": "fdae93cf-493c-4aef-89cd-3844b6285fb5",
"metadata": {},
"source": [
"## Two RC Filter Network"
]
},
{
"cell_type": "code",
"execution_count": 212,
"id": "c42e81ff",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"![](\"https://images.kiwiheretic.xyz/RC-filter1.jpg\")
"
],
"text/plain": [
""
]
},
"execution_count": 212,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"Image(url='https://images.kiwiheretic.xyz/RC-filter1.jpg', width=400)"
]
},
{
"cell_type": "markdown",
"id": "c3e5d823",
"metadata": {},
"source": [
"I am assuming that the voltage in the direction of conventional current produces a positive voltage above ground.\n",
"That means $ R_1 ( i_2 - i_1) $ is considered to be a positive voltage above ground because the current is flowing to ground. However the same must be true of $ R_2 i_2 $ if we look at $ R_1 ( i_2 - i_1) $ being the voltage source of the last stage.\n",
"\n",
"There are two equations:\n",
"\n",
"$$ V_{in} = V_{C1} + R_1 (i_1 - i_2) $$\n",
"$$ R_1 ( i_2 - i_1) = V_{C2} + R_2 i_2 $$\n",
"\n",
"These can be rearranged so that all the i's are on the right and everything else on the left.\n",
"\n",
"$$ V_{in} - V_{C1} = R_1 i_1 - R_1 i_2) $$\n",
"$$ V_{C2} = R_1 ( i_2 - i_1) - R_2 i_2 = (R_1 - R_2) i_2 - R_1 i_1 $$\n"
]
},
{
"cell_type": "markdown",
"id": "c914fb13",
"metadata": {},
"source": [
"In matrix form this looks like:\n",
"\n",
"$$ \\begin{pmatrix}\n",
"V_{in} - V_{C1} \\\\ V_{C2}\n",
"\\end{pmatrix} \n",
"=\n",
"\\begin{pmatrix}\n",
"R_1 & -R_1 \\\\\n",
"-R_1 & R_1 - R_2 \\\\\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"i_1 \\\\ i_2\n",
"\\end{pmatrix} $$"
]
},
{
"cell_type": "code",
"execution_count": 213,
"id": "e91de147",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(R_1, R_2, V_{in}, Vc1, Vc2, C_1, C_2)"
]
},
"execution_count": 213,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A_0, A_1, A_2, B_1, B_2, R1, R2, R3, Vin, C1, C2 = symbols(\"A_0 A_1 A_2 B_1 B_2 R_1 R_2 R_3 V_{in} C_1 C_2\")\n",
"Vc1 = Function('Vc1')\n",
"Vc2 = Function('Vc2')\n",
"Vc3 = Function('Vc3')\n",
"R1,R2, Vin, Vc1, Vc2, C1,C2"
]
},
{
"cell_type": "code",
"execution_count": 214,
"id": "14c67acf",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}R_{1} & - R_{1}\\\\- R_{1} & R_{1} - R_{2}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡R₁ -R₁ ⎤\n",
"⎢ ⎥\n",
"⎣-R₁ R₁ - R₂⎦"
]
},
"execution_count": 214,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m = Matrix([[R1, -R1], [-R1, R1-R2]]); m"
]
},
{
"cell_type": "code",
"execution_count": 215,
"id": "34ec4cdb",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\\\operatorname{Vc}_{2}{\\left(t \\right)}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡V_{in} - Vc₁(t)⎤\n",
"⎢ ⎥\n",
"⎣ Vc₂(t) ⎦"
]
},
"execution_count": 215,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = Matrix([Vin-Vc1(t), Vc2(t)]);v"
]
},
{
"cell_type": "code",
"execution_count": 216,
"id": "a6128b46",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{- R_{1} + R_{2}}{R_{1} R_{2}} & - \\frac{1}{R_{2}}\\\\- \\frac{1}{R_{2}} & - \\frac{1}{R_{2}}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡-R₁ + R₂ -1 ⎤\n",
"⎢──────── ───⎥\n",
"⎢ R₁⋅R₂ R₂ ⎥\n",
"⎢ ⎥\n",
"⎢ -1 -1 ⎥\n",
"⎢ ─── ───⎥\n",
"⎣ R₂ R₂ ⎦"
]
},
"execution_count": 216,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.inv()"
]
},
{
"cell_type": "code",
"execution_count": 217,
"id": "eb0fd76f",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R_{2}} + \\frac{\\left(- R_{1} + R_{2}\\right) \\left(V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\right)}{R_{1} R_{2}}\\\\- \\frac{V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R_{2}} - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R_{2}}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ Vc₂(t) (-R₁ + R₂)⋅(V_{in} - Vc₁(t))⎤\n",
"⎢- ────── + ────────────────────────────⎥\n",
"⎢ R₂ R₁⋅R₂ ⎥\n",
"⎢ ⎥\n",
"⎢ V_{in} - Vc₁(t) Vc₂(t) ⎥\n",
"⎢ - ─────────────── - ────── ⎥\n",
"⎣ R₂ R₂ ⎦"
]
},
"execution_count": 217,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mtmp = m.inv()*v\n",
"mtmp"
]
},
{
"cell_type": "code",
"execution_count": 218,
"id": "7f06d9c5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -Vc₂(t) \n",
"──(Vc₁(t)) = ────────\n",
"dt C⋅R "
]
},
"execution_count": 218,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn_1 = Eq(C1 * Vc1(t).diff()/C, mtmp[0]/C)\n",
"eqn1 = eqn_1.subs([(R1, R), (R2, R), (C1,C)])\n",
"eqn1"
]
},
{
"cell_type": "code",
"execution_count": 219,
"id": "1fdca3e2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)}$"
],
"text/plain": [
"d \n",
"──(Vc₂(t))\n",
"dt "
]
},
"execution_count": 219,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Vc2(t).diff()"
]
},
{
"cell_type": "code",
"execution_count": 220,
"id": "8e3d540c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = \\frac{- V_{in} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -V_{in} + Vc₁(t) - Vc₂(t)\n",
"──(Vc₂(t)) = ─────────────────────────\n",
"dt C⋅R "
]
},
"execution_count": 220,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn_2 = Eq(Vc2(t).diff(), simplify(mtmp[1]/C))\n",
"eqn2 = eqn_2.subs([(R1, R), (R2, R)])\n",
"eqn2"
]
},
{
"cell_type": "code",
"execution_count": 221,
"id": "8ae391f1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -Vc₂(t) \n",
"──(Vc₁(t)) = ────────\n",
"dt C⋅R "
]
},
"execution_count": 221,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn1"
]
},
{
"cell_type": "code",
"execution_count": 222,
"id": "03271341",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sympy.core.mul.Mul"
]
},
"execution_count": 222,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(eqn2.rhs)"
]
},
{
"cell_type": "code",
"execution_count": 223,
"id": "c7d7558d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sympy.core.add.Add"
]
},
"execution_count": 223,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(expand(eqn2.rhs))"
]
},
{
"cell_type": "code",
"execution_count": 224,
"id": "68e3840e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 224,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"isinstance(eqn1, sympy.Equality)"
]
},
{
"cell_type": "code",
"execution_count": 225,
"id": "13085f87",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sympy.core.function.Derivative"
]
},
"execution_count": 225,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(eqn1.lhs)"
]
},
{
"cell_type": "code",
"execution_count": 226,
"id": "428b07d4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 226,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"isinstance(eqn1.lhs.args[0], sympy.Function)"
]
},
{
"cell_type": "code",
"execution_count": 227,
"id": "15a87aec",
"metadata": {},
"outputs": [],
"source": [
"def fn1(t, y, R, C, f):\n",
" \"\"\" y is an array of size 2\"\"\"\n",
" #print (t,y,R,C,f)\n",
" yp1 = (-y[1]) / (C*R)\n",
" yp2 = (y[0] - y[1] - math.sin(2 * math.pi * f * t))/(C*R)\n",
" return [ yp1, yp2 ]\n"
]
},
{
"cell_type": "code",
"execution_count": 228,
"id": "93d7f0da",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left[ 0.0, \\ -0.0628318489376257\\right]$"
],
"text/plain": [
"[0.0, -0.06283184893762572]"
]
},
"execution_count": 228,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fn1(0.0001, [0,0], 1000, 0.00001, 1)"
]
},
{
"cell_type": "code",
"execution_count": 229,
"id": "8217b134",
"metadata": {},
"outputs": [
{
"data": {
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4fUoNfp8Gh9+j1MjkPvl8PowePVqfA/MNPvcbD79PqcHv0+Dwe5QafO5PHz73Gw+/T6nB79Pg8HuUGmbP/VzZZCCaC21JSUlKi47X60VJSQl/AQaA36fU4PdpcPg9So1s7lO+hhHwud94+H1KDX6fBoffo9Tgc3/68LnfePh9Sg1+nwaH36PUMHvuz78Aaw6Hw+FwOBwOh8PhcDgcjmlwZROHw+FwOBwOh8PhcDgcDscwuLKJw+FwOBwOh8PhcDgcDodjGFzZxOFwOBwOh8PhcDgcDofDMQyubOJwOBwOh8PhcDgcDofD4RgGVzZxOBwOh8PhcDgcDofD4XAMgyubOBwOh8PhcDgcDofD4XA4hsGVTRwOh8PhcDgcDofD4XA4HMPgyiYOh8PhcDgcDofD4XA4HI5hWFLZ9M477+Bzn/scRowYAUEQsG7dukF/s3XrVsyYMQNutxvjx4/Hs88+2+uYp556CmPGjIHH48GsWbOwc+dO4xvP4XA4HA6Hw+FwOBwOh5PDWFLZFAgEMHXqVDz11FMpHX/ixAncdttt+OxnP4t9+/bhBz/4Ab71rW9h48aN+jFr165FXV0dVqxYgT179mDq1KmoqalBc3OzWd3gcDgcDofD4XA4HA6Hw8k5LKlsuvXWW/HQQw/hC1/4QkrHr1q1CmPHjsWjjz6KCRMmYMmSJfjyl7+M3/72t/oxjz32GO655x4sXrwYEydOxKpVq+D1erFmzRqzupExjV1hbDjYgGA0RrsppnOowY+POgTIskK7KaYiSjLerG/C0eZu2k0xHV9YxGsfnkdHIEq7KaZzojWADQcbEY3JtJvCyXNOtAbw4ZlO2s0gQkyS4Q+LtJthOl1BEV2h3O8nAISiEnafaoei5LYsoBGT+JrBsS6SrCASk2g3w3SC0RjqG315MS/FJBlv1TfnhezuD4uQcnzfCQBt3RE8+LeP0dYdMfU6DlPPzgjbt2/HnDlzenxWU1ODH/zgBwCAaDSK3bt3Y9myZfr3NpsNc+bMwfbt2/s9byQSQSSSeEA+nw8AIIoiRHFgAVD7frDjLuR4SwD/vOYDtHZHMXaIF6/edy2K3Ln5GP+y9zx+/OpBAHa0rzuIh784mXaTTEFRFPzozwfw2v5GCALw5B1TMXdiVVrnyHQ8kaatO4IvrNqBhq4whha58H/3XovhpR4i1yZ9j/5xrA3fen4PYrKCGy6txNNfmw6bTSBy7WzI5D6xPu7ynd2nOvDV1e8jEpPx/DevwWcuG0q7SaYQk2T8bN1B/P1AA0JRCS99+1pcPaaCdrNMoSMQxS2/fQddoSiuGmLDDZEYypxO2s0yhY/Od+F7L+7F8dYAvnvjOPx43hW0m2QaK1/7CP9v33l0BqP47cJpuH3aSNpN4nDS4j+3HMFjb3wCRQG++amxWP65ibSbZAqKouA7L+zGu0dacUV1MR7+4mRMv6icdrNMocUfwZIX92DHiXZMHF6C1753PewWkGcz4c+7z+L/e+VDOO0Cbp00HE/cMQ2CkJt9/c83j+LZbSex/2wnvjbcvOvkppbiAhobG1FV1XPzXlVVBZ/Ph1AohI6ODkiS1Ocx9fX1/Z734YcfxsqVK3t9vmnTJni93pTatnnz5pSO0/hDvQ2t3apD2om2IH78zBv4p4tyzwIWjAEP7bUDUF/wP+9twJjYGYwuotsuMzjYIeC1ejsAQFGAZX/eh8gMCfYM/A7THU+k+ctJGxq61I61dEex9Lmt+Op4suOXxD2SZOCX++yIyer4fftIK/7jxQ2YXGEdS0k69ykYDJrYEk42NPvCuOf5XYjEvet+/Of92PiDz6DUm3uKibcOt+DlD87ofz/xxhH8z7dmUWyReaz5xwm0xq2R25tt+N2bx7D885Mot8p4IjEJd63ZidZu1Zr+h3dP4CtXjcaYykLKLTOe+kYfnvnHSf3vx984gs9NGWEJIwWHAwDdkRhWvX0MmqPPC++fxHc/Ow6VRW66DTOB7cfb8O6RVgBAfaMfP/rfD7HlRzfkpGLi5+sOYseJdgDAxw0+rNt7Dl+aOYpyq4xHkhX855tHAACipOCvH57HPZ++BJNHlVJumfGcbgviTztOAQD+5cZL0HW4xbRr5YWyySyWLVuGuro6/W+fz4fRo0dj7ty5KCkpGfC3oihi8+bNuOWWW+BM0RrZ0BXGR++/AwD415vG4XdvHsOHvgI8Oe8zOSeMrN11FoEPPsYllV6UKt3Y22bDEdtofKc297yb1r+0D0Az/vma0djwURPaAlG4L5mZlndTJuOJNIFIDD/59VYAMv71s+Pwu7eOYXebHf/17ZtR7DG/zSTv0btHW9G6Yw/KvU780+RqvLDjDPZHKvGT2qtNva4RZHKfNK9ODnv8v33n0R6I4vKqYkQlGSdaA/jNxnr84gu5N5e+uucsAKB2cjU2ftSE94624sDZrpwTFLtCIp6NKyVunzoc/+/DBvztQCP+/Z+uzDlr87ajbWjtjmJYsRvjhxVh27E2PPz6Ifz316+i3TTDeWWXOn4/fWklPjzTiROtAbxZ34w5aXo6czi0WLf3HAJRCZcMLUSxx4kPz3TilV1ncd+N42g3zXCeeENVSnxh+kisP9CA460BfHTeh0kjc2u96Y7E8Ga9mr94/rQRWLfvPB7ddBi3TRkOj9NOuXXG8lZ9M061BVHicWDWJUOw+eMmrN11GpNH5Z689OjmwxAlBZ++tBKfGjcE6w+bd628UDZVV1ejqampx2dNTU0oKSlBQUEB7HY77HZ7n8dUV1f3e1632w23u7e23ul0prxJS+fYTYfOQFaAa8ZUYMlNl+GZbafQ7I/gw/PduGZsboUKbKlXNazzp41ArKEee9tsePtIK2x2R04J076wiLcOq5aRf752DIoLXFj19jGsP9iM26ambzVIZzyRZteRdoRFGaMrCvDDuZfj7wcbcawlgPeOd+LzU0cQaweJe/RGvfpMb508HN+5cRxe2HEGu051ICjCMh4l6c5jHDZ567AqJC68ejTGDSvCXWt2YuNHTXho/qScssB2BqPYckjt6/duuhRuhx1/2XsOz2w7gce+Mo1u4wzmb/vPwx+J4bKqIvzi9onYdPA8mv0RfHCyHddeMoR28wxlw8FGAMC8SdX451kXo+bxd/DGoWYEIjEU5lAKgWhMxl/2ngMAfOO6Mdh5sh3//fZxPLPtBFc2cSzDn3acBgD886yLUeJx4MMznXhx5yl85zOX5JRR/GxHEDtOtMNuE/DjeZcjLEp4/WAj/ra/IeeUTW/VNyMqybikshC/+tIU7DzRjvNdYWz8qDHnwnxfeF/19LnzmovwmcuGYvPHTfh/+87jZ7dNzCnFWliU8PoBdW39/+Zebvr1LJkgPF1mz56NLVu29Phs8+bNmD17NgDA5XJh5syZPY6RZRlbtmzRj2GB94+3AQDmTBwGl8OGWyaoAsiW+qaBfmY5ApEY/nE03tcJwzCmGCjxONAZFLEvxxLc7jjejqgkY2xlISYML8bNE4YBUJ91riVF3/qJuhG88bJhEAQBt0xUFblvfJxb41dRFGz6SO3TvCurMarci/HDiiArwHtHWym3zvo89dRTGDNmDDweD2bNmoWdO3cOePwrr7yCK664Ah6PB5MnT8b69et7HXPo0CF8/vOfR2lpKQoLC3H11Vfj9OnTZnWBGN2RGD44qbq+f/aKYZg1tgIuhw2t3RGcaA1Qbp2xbDjYiKgkY8LwEkwYXoIFcRf/HcfbKbfMeD6IhzPcOmk43E47psTDc1/78DzNZhlOTJKx+VBiLr28uhgjywogyQr2nu6k2ziD2X68De2BKIYWu3HDZUNx59UXAQB2nmhHWMz9RMsc69PkC+NQgw82AfjSjJH4pykjUOx24Ex7CPvPddFunqFo6+qkkaUYXlqAz8UNpn/bfz7nkoVrCv+aSdXwOO2YN0lN7rPrZAfNZhlOTJKx44S69/zijFGYfckQjCwrgD8cw9bDuVWZ/sMznYhKMiqL3JhCwPPbksqm7u5u7Nu3D/v27QMAnDhxAvv27dM3B8uWLcOiRYv04++9914cP34cP/7xj1FfX4/f//73+N///V/88Ic/1I+pq6vD6tWr8dxzz+HQoUO47777EAgEsHjxYqJ96w9JVvR4Wc1yOXuc+t+9pzppNcsUtJdgZFkBxg8thF0APhXv63tHcmuzvuuU+kxnja2AIAiYOqoMBU472gJRfNLsp9w6Y9Fi22+8XE1OfEM8SfGuk7m1GTzdHkRrdwQuuw2zLlE9DrW+vnfUvJjofGDt2rWoq6vDihUrsGfPHkydOhU1NTVobu5bENi2bRvuvPNO3H333di7dy/mz5+P+fPn4+DBg/oxx44dw/XXX48rrrgCW7duxf79+/Hzn/8cHg+ZxPVmsu1oK0RJwcVDvBhbWQiP045po8sAQF9PcoXdp1TB9+YrVIX9lNFlsAnAuc4Qmnxhmk0znF3xvmrJz6cOUTc32461UWuTGew704n2QBRlXqfuvX31GDUB7wc5tm7siyvPrh9fCYfdhouHeDGk0AVRUvBxAw9T5rCPpgC+rKoYZV4XClx2zLhYfV8PnO2k1zAT+CCuaLkmPh999vJhcDtsONsRwvEcMuTIsoK3P1Hl1porVQPxjIvLAAB7TueWsqm+0Y+wKKPY48Clw4pgswn6fmVvjjk6aOuntvc0G0sqm3bt2oXp06dj+vTpAFRF0fTp07F8+XIAQENDQw+r9NixY/H3v/8dmzdvxtSpU/Hoo4/iD3/4A2pqavRjFi5ciEceeQTLly/HtGnTsG/fPmzYsKFX0nBaHGrwwR+OodjtwMThaj4obRL/8GxnTpVW//CsagGZNrpMfwm0ye3AuU5KrTKH3fEFa2b8WbocNlwVX7xyySLfEYjiVJuaRPqq+AZpyqhS2ATgfFcYzTm0GdS87yaOKIHbobrdapvCD8/klnWPNI899hjuueceLF68GBMnTsSqVavg9XqxZs2aPo9/4oknMG/ePCxduhQTJkzAgw8+iBkzZuDJJ5/Uj/n3f/931NbW4je/+Q2mT5+OcePG4fOf/zyGDRtGqlumoSkfbkiqPndtfNO+M8eUTQfilnPNSlfkduCyqmIAyCkvmMauMM52hGATgGkXlQEALi5SlU0nWgPojsQots5YtGd61cUVcMQrZmjrR64pm/bHN+Pa+BUEQVcM78uh8cvJXTTZRxu3QGI87z+bW7KPZiTV5qMClx0T4nuzj8/njnL4ZJu6pnicNkyOhwfOiFfcq2/0IxjNnfVmb1x5Nm10mR7yqfX5YI555u08qRmsyFRPtGTA+4033jigm+Kzzz7b52/27t074HmXLFmCJUuWZNs8U9Am6mkXlelC1yWVhSjzOtEZFPFxg6/HBG9lPowvWFNHJ1z7Jo9QJ/EDOfTCR2KS7lp8VVJ57mmjy/DukdacWrA+ivfl4iFelBao+X0K45vB+kY/9p3pxNwr+8+PZiW0jW3y+6glKP6kyY+wKOVU7DcpotEodu/ejWXLlumf2Ww2zJkzB9u3b+/zN9u3b+9RxAEAampqsG7dOgBquPTf//53/PjHP0ZNTQ327t2LsWPHYtmyZZg/f36/bYlEIohEIvrfWoJ0URQhiuKA/dC+H+w4I/jofFwBM6JYv96Mi9SxuON4G5E2ZEo69ykUlfBJk+oJOqG6UP/N1FGlqG/0Y/fJNtx8eW7kMtpxTLUyX1FdDLdNgSiKKHICVcVuNPkjOHCmHVddnBvltzVviORnOn2UpkDsQDAcgTOFsq0k37lMUBQFH8b7emV1kd7OSSOKsaW+GXtPt0MUza/8lMl9YvWecsiz70xis66hbdZzSXbvDEbxSVM3APSYayeOKMG+M534uMGnh9VZHU12v6K6RM+XO6KsANUlHjT6wvjwTJceZWN19sRld02ZBkDPv3XwnA+KouREnktJVrBH844mlO/ZksqmfKS+UX3hNa8mAHrY1duftOCj8125o2zSLXxl+mcThhfDJgBNvgiafGFUlVg/xOVYcwDRmIwSjwNjhnj1z7VnnEuu8wfjm95JI3rGBk8dVZZzyqa+rHsjSj2oKHShPRBFfaM/Z95VkrS2tkKSpF7eplVVVaivr+/zN42NjX0e39io5iBobm5Gd3c3fvWrX+Ghhx7Cr3/9a2zYsAFf/OIX8dZbb+GGG27o87wPP/wwVq5c2evzTZs2wev19vGL3mzevDml4zJFUYCDZ+wABDQf2Yf15/cBAMIxAHDgfFcYf/7rengZlwJSuU8n/ICsOFDiVLD73TehyYO2DgGAHW9+eAKTpKPmNpQQr56wAbBhiNLVI/9YpSOEJtjw5zfeR/Pw3MgZsuOwOn6D549g/fpPAACyAhTY7QiJMp59dQNGFqZ+PrPfuUzpiACt3Q7YBAWnPtyGhniUb7RTHb/bDzdg/fqzxNqTzn0KBoMmtoRjFSRZwYEko7iGJsd/0uRHKCqhwGV9Q5sm411SWYghRYkiURNz0LNJUzZNHNGzwvqMi8uw/kAj9pzuyBllk+bZNCNJgXhZVTFcdhu6QiLOtIdw0ZDU5DuWOd7Sje5IDIUuO66oLhn8BwbAuJjJ0ahvVK22Vwwv7vH55dXFePuTFhyJa9mtTnsgioYuNaRK1SirQrPX5cD4YUX4pKkbB852oWqi9ZVNR+I5mS6rKu6hLddccQ83+RGTZN2TzcpoLqhXjuw5sU0aWYK1u4DDjbmRn0qWFb0vyRVJBEHA5JGlePuTFhw4lzuKYasjy2r48e23367n8Js2bRq2bduGVatW9atsWrZsWQ+PKZ/Ph9GjR2Pu3LkoKRl48RZFEZs3b8Ytt9xiahW/hq4wQu+/A4dNwKIvzIPbkZhHHjv8Npp8EYybdh2mJ20MWCKd+/Tc9lPAwcOYeclQ3HbbDP3zS5u68dKT29AQceDWW+fmhFVy7TO7ALSjdvZk1M4Yqd+nz0wai4/ePQVUjEZt7STazcyaaEzG/7dzCwAFX/+nGzGyrED/7vlzO7D3TBdGXDEDtZMHN1KQeucyZeNHTcCeD3F5VQnmfy5RlOZTIRH/degttEYEXHfjLSgzuZJpJvdJ8+rk5DfHWroRiEoodNlx6bDEPqWqxI2hxW60+CP4uKELMy+2fuXso83qfuvC/ZimkMklQ7HWlysvUDZNHqkqm3JFdveHRZyMp/qYluTo4HLYcMXwYuw/24UD57pyQtl0JD5+x1cVE6vuzpVNFkBRFNQ3JFwZk7l0WBGA3NmsH2tRX4KRZQUocjt6uGhfUV2CT5q6cbSlG3PARi6tbNDCPi6r7rlgXVThRaHLjkBUwonWAC6tKu7r55YisWD19GwaHxdKjrbkhrL0fFcIIVGCwybg4gsWpQnDS+KK4dx4V0lTWVkJu92Opqae1QubmppQXd33hrO6unrA4ysrK+FwODBx4sQex0yYMAHvvfdev21xu91wu929Pnc6nSlv0tI5NhOOtapWukuGFqKooGdbLx1WjCZfBCfbw7hmHHub72RSuU8fN6rzx5RR5T2OHV9dCrtNQDAqoT0ko7rU+kaK462qQHz58NIefZ00qgzAKRxq6GZSoZIun7R0QZQUlBY4cXFlT4PMpVXF2HumCyfbQ2n11ex3LlMON6sJhaeOLuvRvkqnEyNKPTjfFcbpzgiGlpLZ6KQ7j3Eywx8WIQgCitzW34ppCphLL9jAaoa2N+ub8dF5X04pm8YPLerx+RXVxRAEoMUfQbM/jGHF1l5vFEXBx/GohAtl90uGqi6lx1tzQ3Y/3qLOwUOL3Si9QKl/5YhS7D/bhYPnu3DblOE0mmco/Y1fM7G+y0Qe0NAVhi8cg8MmYNwFg+PyuKLiSI5ULjsWfwnGDev9Emh9P54jionD8Q3SZRf01WYT9Od6OAcUEzFJxum4xWD8BX3V/j7THsyJ8s7H4gvWmMrCXrlE9MW5JXcqlZDE5XJh5syZ2LJli/6ZLMvYsmULZs+e3edvZs+e3eN4QA0R0Y53uVy4+uqrcfjw4R7HfPLJJ7j44osN7gFZNG/Yy/twk9beu1xR8mrv1OUXKO5dDhsuqlA36LkgFHdHYmiMF1O4UBbQQjiONPtzomCIFooycXhJL480re+a0Gx1tOpVF66PADA2vm6cyKEKVxygbu0+TL5/E/686wztphiCNj41OSeZcfHPTrbmRsilZhS/cJ/idTkwtlLt66EG68vuLf4IWrujsAnA5RcYvbVneqIlMGAOZaugyQeXVPYev5dXqc/5WI6sN7qyqY/1xiy4sskCaANjbGUhXI6ej0wbLK3dUbQHosTbZjT6JN7HgqUtYsdyZLOeHEZ3IWMr1ed6MgcEzLMdIcRkBR6nDcMvyLVVWeRCaYETspIbSpiBLAbjdGVTbixYNKirq8Pq1avx3HPP4dChQ7jvvvsQCASwePFiAMCiRYt6JBD//ve/jw0bNuDRRx9FfX097r//fuzatatHIYilS5di7dq1WL16NY4ePYonn3wSr732Gr773e8S75+RHG7UvGF7zy+akJwrm/WTbXEl75De64Ym/OfC/KIJu0OL3XqhBY2RZR4UOO0QJQXnOkM0mmcomiL0sqrec6km9+SKLKCt8wON3xM5oCzlJKgodAEAznRY/10FErJ7X5v1i+PjWpunrY62bl6o8AeS0mA0Wj+UTlOCj67w9sq1dVFFIew2AYGohCZfpK+fWwpNPrikj2c6Jj6mtYraVocrmzh9cqpdHeAX9yGIeF0OjCpXcxnkwsZBEx77msS1z47lwGY9LEo4HX+u4/sQpsdWatZ46y/OmsVgzJBCvZyohiAIeihoLnhZDDSJXxJXIJ7vCudUuViSLFy4EI888giWL1+OadOmYd++fdiwYYOeBPz06dNoaGjQj7/uuuvw4osv4umnn8bUqVPx5z//GevWrcOkSYmcNl/4whewatUq/OY3v8HkyZPxhz/8Af/3f/+H66+/nnj/jCSxWe9D2RRXfObCmtEZjKIzqIZbj6nsHWaU2Kxbfy4dyBgjCILuxXUqBzZ1mjdsX3JPspezLFvbqq4oij42x/SxUdcMT7kwfjkJtNwvZ9pzYwOb8GzqS57VPJusP4bbuiPoCIoQhL73KWPj89XpHHiuA83BLocNo+N7z1wwoB7X9569+6oZAU61Byy/3siyou/JSCqbrB8onAec0q1efcfrjxlSiLMdIZxuD+IaQmUMzWKgzfrYykIIAtAZFNEeiOqWIStytiMERQEKXXYMLeqd+2VMDi3OCYtB32WDxg8rwq5THTnhonpsgPFbXujSK9Idbwn0SCDOSZ0lS5b08ExKZuvWrb0+W7BgARYsWDDgOb/5zW/im9/8phHNY4aEoNh73dDDVzvU8FWP07oVgrRNTlWJG15Xb5HmkhwKQ0oom/oWEi8a4sXhJn9ObHRODTB+R1d44bLbEInJONcZwugK6yZtbfFHEIxKsAnQlYXJXJJDnnmcBKPL1WedC++qoij6+Bzbh8JUk2dPtwctX/RGM4iPLCvos7Ke9g6fbre+x5rmiXZxP/PrJUOLcLItiGOtAVw3vpJk0wxnoLV1ZHkB7DYBYVFGsz9i6dyP5zpDCIsyXPaEspAE1n3j8wgtQ/7FfUziAHRBy+qLlijJONuh9qEvV9wClx0jSnNDk65Zs0ZXePuskDRGdzu29jMFEpu8voQQIDF+z3RYv6+n2vu3UANJG4cc2Phy2KUrKMIXVr3ntE1NMkOL3CjxOKAo1g9tGCiEDkgOo7P2mgEAx5r79/wFEpsCq7v7K4qiyzN9WdXtNkF/rlb3ztPWx1Hl3l5pEoAkr5A261vVOQlGV6iyrGp4tPZz7QiK6Aqp3qV9yXnDSzxwO2yIydYP8R1M4T8q/lxzwWMtEVXTt7IpV1JDyLIyYM4xp92mRxBZ3WilebyPrSwkqvTlyiYLcGoQ7bI2EZy2+KahoTMMWQHcDhuGFvf29gESVgOrKyY0QbovSyaQUFa0B6LoCop9HmMVEsqmvhdnTdl01uKWoEgsEbven8VA2zjlgiDCYRdtfhla7O7T+ioIQs68d1rS2f6U2Vr46pmOkOUTZ2uKtbH9eIlqoTlWNzy1BaLojsQgCIlN+YWMrcyNcJWBQugAYFR5ARxxq3qTP0yyaRwTGRU3AnRHYnoYsFXR8omNLCvo00vWllSd1+oGVG2+6S/SRJPpz3WEIFlcOTxQGB2QCJm0utfl+a4QIjHV22dUH8Y5IHEPrB6ifjaeI460NzBXNjGOLCu6drk/y+1FOeLZpCmQRpUX9Onto30HWH+DdHoQi0GR26Er3KzueaA91/4Ua5pixurj91x8Eve67P2GeOrjN0eSgnLYZDBlNpAYi1a3NOuu/v2sj2p4nR2SrOies1ZFm2P6U2brsoDFN3SaZ5bqEdF3iOfIHBm/JzQFYj+ygMNu05WIVt/UcRJ4nHYMi8t4Vjeenogr/PvKmaehe+tb3DNEm4P7U0oML1WVw1FJRpPPusphRVGS1taBHR2svq6eadeeqRou1xdjc0RZejZpn00SrmxinCZ/GNGYDIdNwIiyvuNEc0XZpL0EA2lctQne6pv1dDaD5y0sTEuygoZOdcEdOcgGqckfRiQmEWub0ZztSCxYgypLLb44c9hmMAUvAIwsi1tgLTy/AAnhb2w/Gx1BEDCyTJtLrSv8d4VE+CNqaOSIsoE9J0+3By0dmnM6Ho58UT+bHCBxD85ZXRYYxHsASLzHfN3ILXIlBYYmo44qG0DZlCOFGrR3sD951m4T9O+s/Fw7gyL88VD8/uSI5HXVyuuNJgP1t64CuePZdC5pn0ISrmxiHG0DO7zM0298pSaQtXZHEYhYt8rV2RReAj3OvdO6kzjQM2dTf2gTuZU3g83+MGKyArtNQFU/oZEVhS54XXYoirU3DtoGv68cORqastTK/eSwz+lU5pccUXwOZmkGEkKklRX3Wj/V+bLv2i4jywpgE4CQKKHFb91y1Hpy8Ir+FTDa+njWws8USIzJ/javgOotoR5rXWUppzdaDsdPGv2UW5Id51PYrGtrkZXlWSDR/pED9DUXHAA0r6bqEk+/BUS0RNkhUbJ0KOj5FJ6p5sVl9XyIqeyzzYArmxhHn8RL+x8YJR4nSgucAKzt8aMpYAbaNOSCZ5OiKHmjbNI2SNUl/StLBUHIicosqUziumdTZ4gne+WYhj6/pDAWraz4jMQktHarSpWBNjqaV7Cl59IUBGKXw6YrJqw8l2phDQN5NuWC5y8AnO+Ke/4O8FxHxsdvQ5e1+8rpyZRRakXaD892UW5JdiQ8Q/qv0jW8xPpjOBKT0BxX4g9sFNfyIVp3Dtae6UD9dDvseroPS6+tHYMrS7XvrDx+gWQ5guds4iShWbIGegkAYHip9SdyPXHZgMqmhIBp1eR7vlAMgagaLjaggJkDm8FzKVhtgZ6VWaxKKgrE4aUe2G0CojEZrQHreh5w2CaVMN1cUGY3xjfqbocN5V5nv8eNKLW+YuKcFr4xiCygzbWaEsOKNPoG37xqMlGLP4KwaM3w60gs4YE2fIBy2tyzKTeZMqoMAPDh2U5LhyGl5J0Xf5cbLTwvNXSGoSiAx2nrNy8ngJwwnmrPafgg682IHJAjznel4l2qjt+OoGjZ9Sac5PHMPZs4PTifgsVA/V7Tulp3Ik/FM6SqxAOHTYAoKWi0aPK9hrggXe519uueCiRtkCysQNStI4MqS9XvrSyIaON3oM2gw25DddzCZ2XFGoddFCWRJ23AsIbyRPh1KGpN4SnZGNNfnjTte8Da62Oqinttfmm08Lqhjd/qkv77Wu51oiC+flr1uTZ1qYK/2zHw5lUPA7XwM+X05orhxXDZbegMiro3n9VQFEWfhweSfTR5trU7atncnMnepQOvN5rx35rzEpC0tg6gBAcSXpfWNuQMLruXFlh/vdGeUaHLjrIBjHNmwJVNjKN5Kg0fIIwOSMTONlj0hRelRFnfgTZIdpug99WqwrQ2UQ32THPCs6kjxQ1SqfUX51QtQbnwXDns0h6IIirJAFTlfH+UFDhQ5FZz/1jVKplYHwcWiIfngkCcQhgdkLgXjV3W9JxUFCVpjez/uQpCIhGvVZ9rcmLaVDav5ztDlvaA4fTE7bBjwvBiAKp3kxXpCIoIxT09qgd4X8u8Tnic6pbTqkbFVPIDAgmFv5Wr0WnepQM9U8D6XsOKoqS0tgqCYPkIorNJ+7GB1hsz4MomxklYbgd74a29WW/xR6AogNMuYMgAFj4g2XJrTWFas9oOtkHSBOmOoIhg1JqJ39PeIPmsOYlLsoKW7sHDIYDcEEQ47KJ5fFYWueFy9L/EC4Jg+eqIqSSmBXqGDFp1s56u4t6qc6kvFEtp8wokPVeLKu61Tctg8p12H8KibOlEvJze6KF0ZzqptiNTtDl4aLEbbkf/nvqCICQpJqwp+wxWiU4jMQdbt0rb+RT3KYniG9Z8pm2BKCIxGYIw+Hpj9VDQVBKhmwVXNjHO+a7UhGnNS8aqyiZtgzSs2AObbWCNa1XSRG5FNI+swSa2Eo9T9zyw6kSeqreP1T2bWrsjkOJV9yqL+q66p5HwzLNmXzlsoykxq0sHHodAsheMNceilpdoMFd/7Z2LxGS0B6Kmt8sMzqUQqgIklNlWnUs1maei0DVgmDmQkIusWpEuVS9nt8OurytW9ULk9M3kkWqS8HqLVqRLpWy8htUV4dqeY7D1RvMoDosyfCFrGoobU5ybrJ6zSTNUDCse2DgHJMK6rbq2NuqyIVc2cZIIRmO6FWuwF17bNFg1pr8p/vJWlQy+QbK6Z0gqIQIa2v1o9luzr1rljsGea3LOJitagrSFeWiRG/ZBlKXD4tU7rKos5bCNNr9UDxBCp6EJxdp7ajW0sPHBlNnJVXOsKCiKkoy2eEGBwYwU2vdNFuwnkJhLUxm/wy3e13Q26rmQB4bTG+3ZW1WeTVTMTuV9tbYXTJNPnYOHDTI3eZyJnDgNFlSsxSRZ33MMGoFhcWVTqgp/IHkOtmZftfGbyj7baLiyiWG0l6DQZUeJxzHgsZqwrVZLsOBmXde4Dr5gJcLorLlgpTO56ZtBn/U2g5GYpHsRVBWnFloWjErwha1nCUpr/GobJIsKlxy20TbeqYzFYXmkuNc2Q1YUilu71TBzh01AhXfgMHNtXWnyRyxZsTWfjDENaWzUrZ4bhdM3w/QxbD0ZD0hsYFNZb6y/WdeM4rm9T2n2RyDH15tUPfVbuyOIxXNFWokWfxqODnpuZOs9UwBoTmP8Gg1XNjFM8sQ2WDIvTTALiRK6QtaL6W9M4yWwehhdqkltgcT9sOJmUFOQuRy2QSsfFCRVR7Di4pyONV4XQiz4TDnsk45nk+Zl12RBZTaQnuJ+mIW9uLS5dGixe9Aw88oiF2yCmkeutdt6fU01zBxQw+4Baz5TAGhMY6POjRS5iWaI6wpZs6R6c1IKjMHQ031YdbOeoqe+eox139eGrsR+bLD1ZkihC3abAEVRKw1aDd1bLYXxOyJH0tVwzyZOD1r8msvm4APD40x4P7VYUPBqymCzbsVJHEgoJqpS8jyw7mawOclikErlAysrYdLxbEoIIRFLeiFy2CaduHxtLLZY0DMknGRYSUV40sLoLLk+ahu6FNZHh92mC85WVNyfT8OzaajFlaXae5fKRkfrq1UVa0bw1FNPYcyYMfB4PJg1axZ27tzZ77EfffQRvvSlL2HMmDEQBAGPP/541uc0g5ICh54rxopzkzYeNcPFQCSqeVlvXkrHUx+wdlXQdAziNpuAyiLV29aKHqbNmXg2WdYzL3XFmtFwZRPDNKc5MKxsuc0kjK7Bgvl9ApEYAtF4pZ1UvLjiz77JgpO4Hh+c4vhNJM623kSeTuiStsGPxmR08MpCHIPRE4SnlLPJupt1bWPmcthQWjCw5ySQ2AxZUbHWpFnUU9jQAdYuuJBOqIp2TFvAeiEcMUlGW3zzOjSF52plZakRrF27FnV1dVixYgX27NmDqVOnoqamBs3NzX0eHwwGcckll+BXv/oVqqurDTmnGQiCoM9N1t6sp64wtaLHpb7e2Af31AcS98OKxtNmPbdPinvPYs1oZb3nmo4CRpOpOoIiIjFreSGmk/fRDLiyiWGadatXagKmlRespjQmN83bJxqzXhlgbTL2uuwodA+chwtIztlkxWeaXnzw0CJNELGeK25jGht8l8OGIYWqJciKngccttHD6FKoRqcLid3Wy+/TEt+wDC1KzXNSD7myoGJND1VJ0f3dyt6/CY/uwefS5BCONotVGWztjkJRALtN0NeDgRiW555Njz32GO655x4sXrwYEydOxKpVq+D1erFmzZo+j7/66qvxH//xH7jjjjvgdvf93qR7TrNI9na2Gs1pRGBoY7gtELXcepNIDp6ip76Fw171tTXtvWduj9/SAiecdvXZt1lsn5JO3kczGHy3y6FGOi8BYG3LVzqKCa3SQ2dQRLM/gvIUBDVW0J5pqpO4lT0PGtPcIFl5/KbjSg6o47wtEEWTL4yJI0rMbBonjwhFJfjjCfZT2axXFrkgxPP7tAeiKc9LLJCcxygVrByG1Jyml6iVPQi0Nqcyl2ohHE2+CJp8YSqJTzNFMwpWFrkGzYsCJK+P1tu8Zks0GsXu3buxbNky/TObzYY5c+Zg+/btRM8ZiUQQiSTeK5/PBwAQRRGiOLDxU/v+wuMqC+OVyzqDg56DJSKipBt8yz32Qdte7BL09aalK4Ah/SSf7u8+0eR8RwCAOi+l0q7KQnV73dAZMq0fZt2npnh0wRCvI7W+FrE7fge7R03xaoEVBan1dUihC42+CBo6AhhaaB0Vyrl2dfwOLXZDkmKQLnDMymQspXOsde5UHpJ2GJ0mTFtMMRGIxBCMh5alulkfWuRGZ1BEa3cEl6PYzOYZiqZIGTpIhQeN5CSDiqKkZFFhhfRdca3rmdeSphKxstgNNCQsSByOEWgbdbfDhuIUPCcddhsqi9xo8aubdSspm1rSUEokH2dFZXZTGqEqAPQKQlZTNqUbWgao96TJF7Gc3JO+fKeFDEYRk2Q47PkTmNDa2gpJklBVVdXj86qqKtTX1xM958MPP4yVK1f2+nzTpk3wer0pXXvz5s09/g622wDYsH3fx6hsP5jSOVigLQwADjgEBf94azNSEU8LHXZ0iwJefX0LRhYOfOyF94km7zQIAOyQu9uxfv36QY8/0w0ADpxr86V0fDYYfZ8OnVDH4/kTh7E+MPj71dmoHr/7oyNYHzpsaFuMoq97JMlAe0CVkw7sfBcnBo+OhFOyAxCw4e1tOFtuHe+8/e3q+HVJoQHHYzpjKRgMpnwsVzYxTPphdNbM2aQJxAXO1ELLAFWYPtLcbbmNg54QNE1vn0hMRldIRBkF98dMaUqz8sFQi8Z9R2KJRMUpe1lYdDPIYZtk9/dUFdPDilVlk7relJrYOmNpSdNzUjuutTsCWVZS8iZhBc2zdWiOe4m2BRKhZeUprnVWDeFIN1SlolCtMijHQwat5MWVSyxbtgx1dXX63z6fD6NHj8bcuXNRUjKwl7Ioiti8eTNuueUWOJ2Jne3pt4/j3cajKB42CrW1k0xru9HsPd0J7N2J6tIC3HbbZ1L6zX8d34b6pm5cMf0afHp8ZZ/H9HefaPLxpiPAyROYctkY1NZeMejxjb4wHjnwDgKSDfPmzTVlvTHrPq06sR2AHzdfdxVuuGzooMd37DyDjWcPoaC8CrW10w1rhxEMdI8ausLAjnfgsAn48uduTekZ/aVtD8580ooxl09G7VWjzGq24bTvOA0crsdlo6tQWzut1/eZjCXNqzMVuLKJYfIljE5rb2Vx6ooUq4YJJOcZSQWtyqAvHEOLP2IpZVPCiyu90A+rjV8tdttpF1JKVAwkxrrV+sphG30uTXF+AVTPkI/O+6znGZLm/DKkUL0nMVlBezCa1j2ijWakSDWMTqsO1GKxvBLa+NVyMaWCZqSwWm6UhGdTauPQbhNQWeRGsz+CFn8kr5RNlZWVsNvtaGpq6vF5U1NTv8m/zTqn2+3uMweU0+lMeZN24bHVZapHVGt3lBnlSiq0BRMh26m2e2iJB/VN3egISoP+Jp17ajatAdWgWF1WkFKbqsvsANSQwW5RwZAi82R3o++Ttm5UlxWmdN7h8fHbEhCZeV4X0tc9ag8lQiPd7tSeT1WJWuW3PRhjtq990R5/V6tLBx6/6c5jqZI/frgWIywmcm8MTTeMzmJhSK1pKmCAxGbKapv1dPOMAPGQK1gvcbYWDpGqEtGqyiZt/FammKgYsHYydA67JI/FVLGsZ0iaxhiXw4aKQuspeZNDy9I1PLVaqJ9A+uHIQMJz1mrjN13PdSA575i1ZLxscblcmDlzJrZs2aJ/JssytmzZgtmzZzNzzkzRFBHtFktyn8hVmbriU5fzLGYoTndtdSZVrbOSnKfmb8wwRN1yCn+1vUPTUNzny/g1Gksrm5566imMGTMGHo8Hs2bNws6dO/s99sYbb4QgCL3+3Xbbbfox3/jGN3p9P2/ePBJd6YWmlHA7bCjxpOaAZtUEqJoWPZ2XwKovfLqu84A182/EJBkdwfSeq3ZPAlEJgUjMtLYZTSbeJFbdDHLYJpPNurbRabPQ/AIkezbltmKtPaiGltkEpBxaphtjuiNQFOvklchk/Fo1cbY+ftPY6Fg571i21NXVYfXq1Xjuuedw6NAh3HfffQgEAli8eDEAYNGiRT2SfUejUezbtw/79u1DNBrFuXPnsG/fPhw9ejTlc5KiIu51aTVlU7oKfyBpn2IxT9rEZj2NCAwLyu5tgQjk+HrTXwL3C9GKkVhtvdGUgOnIENY1iqt9NdPDbiAsG0a3du1a1NXVYdWqVZg1axYef/xx1NTU4PDhwxg2bFiv41999VVEo4mJvK2tDVOnTsWCBQt6HDdv3jw888wz+t/9lUw1m8xyb6gvvD8cQ1iU4HHaTWufkWQnYFrrhW/JxBJkwQWrPZD+BqnQZUeB046QKKG1O5Jy/i7atGagQBxaZE1lKYdtEl6iqQsUujI7TzY69Y1+3aJpBVr96nOpSCu0TL0n0ZgMXziWcngvbdINMwcS4ZFtFhu/6VYwBay7UTeChQsXoqWlBcuXL0djYyOmTZuGDRs26Am+T58+DZstYT8/f/48pk9P5I955JFH8Mgjj+CGG27A1q1bUzonKYbEPS7VnGXWKQTTFtDCXnNf9mnLwCiu5Za1kuyurasVhe7U15v4PRElBR1BUfcgZp22TBSIFt170vZsssZurg8ee+wx3HPPPboFYtWqVfj73/+ONWvW4N/+7d96HV9RUdHj75dffhler7eXssntdmccA24kbRkMjJICB1x2G6KSjNbuCEaVp1YZgzaZvAR6TgqLvfDZeR5YR5jWtOjpbJAEQcDQYjdOtwfR4o/g4iGDlCphhIRnUxobfIvmHOOwTWbzS3yzbqGxKMtKVkpeK4U1ZLKh8zjtKHY74I/E0NodsY6yKYPxW2nB9RHIbqNjJc88I1myZAmWLFnS53eaAkljzJgxKXlZDHROUmib82hMRjAqWcbQpr1zFRlt1q2j8FcURZ+H09qnWFAxkckc7HLYUFrgRFdIRHsgYhllkyZDpOPtY9WomoS8xD2bUiYajWL37t09XGZtNhvmzJmD7du3p3SOP/7xj7jjjjtQWNhzQ7t161YMGzYM5eXluOmmm/DQQw9hyJAhfZ4jEokgEkkMOC0zuyiKEEVxwOtr3/d3XLMvBACo8DoHPVcy5YVONPkiaOoMoqrIIgJm3Mpc7nX06mt/96m8QPXaau2OpHV/aCLLim59LfXYUm53eYH6mjb7Qv3+ZrDxRJrGLjXx3pBCV1ptqixy4XR7EOc7AhBHFhvaJrPukZaYdkga72qZR7XAdgZFBEIRuBzsRDRncp9YGXf5Tmsm1tdC623W/eEYYrK6kUxHsE3kRrGOoKhb1NMUEocWu+GPqIUlxg0tMqNphpMvylIgETJVkYYScYhFw604A+N12eF22BCJyWgPRC2jbNLG4ZA05mAreob4QjGIUvrrjaZItpJxozmDORhQx0BXSERrdxTjewcXMUmrPn4zMFhZaPwCCTkinb4aiTVmtAtobW2FJEm9XF2rqqpQX18/6O937tyJgwcP4o9//GOPz+fNm4cvfvGLGDt2LI4dO4af/vSnuPXWW7F9+3bY7b1D0h5++GGsXLmy1+ebNm2C15uaV9HmzZv7/Hz7WQGAHYH2Jqxfvz6lcwGAU7IDELDx7W04W26N2NkjZ9Q2nz58EOtbD/R5zIX3qSsKAA60dUfwt7+vhxWqWAdEQJLVV27nO28iVf1CY5M6Fj4+fgbr158a8Nj+xhNpPmhR26yEfWmN31i3DYAN7+7cC+W0OePX6Ht04Ija5qbTR7F+/ZGUfqPGxNshKwL+/NoGlDFYGCud+xQMBk1sCSdVEpU909+sW8nLTrMyF7sdcDtSDxfXNvZWUqzp1tc0hcTKIjeOtwYs9VwzyX+nKRADUQmhqIQCF/vpA8KihGBUApCZsrTNQspSzuAIgoCKQhcausJoC0QxusIaUQkJhWkmeYysMwdrXizFHkda6UmsWMhIN26k6Z00pMiF460BSynC27LwbNJyy1pBMRyMxvT1Jh3Z0EjYv0sm8Mc//hGTJ0/GNddc0+PzO+64Q///yZMnY8qUKRg3bhy2bt2Km2++udd5li1bhrq6Ov1vn8+H0aNHY+7cuSgpKRmwDaIoYvPmzbjlllv6LB+4++/1wJnTmHbFONTOvTTlvv25ZTfOHm3DJROmoHbGyJR/R5P/qH8XQAg1N8zGjIvKenzX332KSTJW7HkDiiJg1mduTlsLT4PjLQFg1z9Q5Hbg8/80N+XfuQ41Y+3xfbAXlqO2dlafxww2nkhz/r2TwNFPcPnFI1BbOyXl320TP8b+9rMYPuYy1N40ztA2mXWPXji/E2jrxA3XTEft5NRDcH/18dto8kUw5ZrrMWnkwPMFSTK5T5pXJ4cumVT21AStjqCImCTDYWfHy64/tOID5RkIxIC18vtk4q0GWNODIJNQlWJ3In1AWyCCUS72N+rahsxhE1IuAAMk5aey0EadkxqasslSXpcZeDZpiilf2DrrTab5boZaMF1CJgoYIHluslJf008QXuh2wOO0ISxaxwtR66fHaUMhJWMM+3epDyorK2G329HU1NTj86ampkHzLQUCAbz88st44IEHBr3OJZdcgsrKShw9erRPZZPb7e4zgbjT6Ux5k9bfsR0htRrX0BJPWhvjofHE051hiQmlQypoL0J1mbffNl94n5xONfF0eyAKf1TBCAv01R+VAaiTeDrPZlipKjy3BaKD/i6dsWcmnfHxO6ykIMPxGzOtH0bfo/agGkI2rLT/8dsXQ4vdaPJF0GFiX7Mh3XmMQ5dAJDPrVbnXBUEAFEWtfJZO8QJatHWnb1EHkvL7WGhDl0leCcCauYz0zWsafRUEAUOK4l4h3VFL5KrUlE3lha60kkEnwkCt80w5qaHNZe0Ba4SkxyQZXSG1renMw6UFTn296QyJ1BIWp0MiOXiaocwW9BrOJLwXSOTtspLHWmJtTbOvXhfOd4XREbSGF2JLknc0reID7KuU+8DlcmHmzJnYsmWL/pksy9iyZQtmz5494G9feeUVRCIRfO1rXxv0OmfPnkVbWxuGDx+edZvTJZME4UBi0reKdjkUlRAS1Q1Sui98mVfd4FpF8NIE6VSrs2kkL1hWKSvakuH4tWIy9I4MNkhAYhx0WES45LCNNg+6HOlZr+w2ARVea713mYRvqMfHc95YpJ9AYi1Px/oKJLy+NC8w1olJMjqD6W9eAeuFl2WS6yb5+PZgFJJsDVmAkxr6s7XIGO6Iv6uCAJSlIdM67Da9YEGHRWT3TD2bKi2obMpE4Q8k5X60yPiNSbI+htOW3QutpfRvzSC9gtFYUtkEAHV1dVi9ejWee+45HDp0CPfddx8CgYBenW7RokU9Eohr/PGPf8T8+fN7Jf3u7u7G0qVL8f777+PkyZPYsmULbr/9dowfPx41NTVE+pRMe4YvvJ4s0yIvQXtcEHbZ03fv0zZIVhGmOzLcIGmJYcOijEDcc4F1NOtGuuO3wmILliQrunUvXSVihcU2gxy20cZRhTc9bwkgIRRbRtkUzGwu1TZ0rfES41YgU+G/3GrrY9LmNd25VAvhsIpVPVNlqbbJURSg0yLPlZMaej45q8ju8XaWFThTrjisocnultmsZ+hdqnn7dAREC603mhdMZntPqzxTTYbIZL2xmuyuzSlD0xy/RmLJMDoAWLhwIVpaWrB8+XI0NjZi2rRp2LBhg540/PTp07DZeurSDh8+jPfeew+bNm3qdT673Y79+/fjueeeQ2dnJ0aMGIG5c+fiwQcf7DNUzmxaM8wcbzXPkA7dndyZ9gbJatplbXJLd2LzuhwocNoREiW0dUdQZIkY4fTLOgPWq7bjC4nQDMyap12qlFtM4OKwjbZZTzePERBfN5qsY4FtzzCMTlsfozFVcW+FuVSzSqbr+Wu59TGLzavV5J62pDC6dHDaEyXG2wLRtMcEh10qCuOe+pYZw+q8lEmZ+/JCF9AasMxmPdO8eeVxmTAqyQhGJUvk92nXDcWZRdVYReGvh+J7XWmvNwnZ3RpRCboMQakSHWBhZRMALFmyBEuWLOnzu61bt/b67PLLL+9Xu1xQUICNGzca2byMkWVFd6VNd7NutZwUHRkqYIAkzyaLCNMJz6b089tUFLpwrjOEjqCIi4cMfjxtEmECua0s1RSIxR4HnGkmukxYR6yxYHHYJpv5xWoV6TL1bLKa4l5RFL08c7qyQIXFwnR1i3oGCpSEZ541xm9HhmF0gLpGdoVEdY2sGvx4jjWosJihLVMZD7DeZr09Q2+fAqcdbocNkZg1kkkripJR0ncgWXa3xhzclqECEUiS3a3yrmryEkXPJsuG0eUynUneEmlX27FYTgo9UWYGyqbypPwFVkBbWNNNvAckvGasYAlSFCXjMIEhSe6psgVyUmQaGgkkrF5WWbA4bJPNXDrEYlbJTOcXwFoV6QJRCdFYvLBEmutGueYpYYE1A8g86TuQGL9WeKZAop3Z9NUqSglOalRYTp7NfAxrBhEryLNAQmGf7n5MEAT9/nRawKgYiEqIxNeb9ItvWEtZmpVnntda76o29srTjL4wEq5sYhBNM1xa4MzYW8IqOSmy2axrC5YVJnEgYR3J1LMJsIZiIiQmFqx0F2fteDleqYR19NClPFCWctimI0Nvn+TfWCUPjL5uZKJYs1B+Kq2fbocNBenmNEx6plaQBTJNmg1Y0DMvi42OXmLcIt7rnNSwWqVBXTmcgbeE1UJ8s4nAKLOQYkJzUvA4bfBmuN50BEXEJNnwthmNIcpSi4zfbAyRRsGVTQySyNeUudU2GpPhj8QMbZcZaJv1dPPdANbLedOehWKizJuYyFkn06pYQCInBWANd1w951gG49dqYaActsnKS9RCnpNAkmdIBhsdK1V9ykaBqI0DUVLQbQFZIBtvH6t6SmTUV4uFmnNSQ/dssshzzUo5bCHjKZBlug8LKSYSycHd6efQ9bqg/cQKirXkfMHpUm4xT9rOLMavUXBlE4PoAyODSdzrcsDjVB9rpwXioY2wxltHwMw+5MoKnge6IJ1BVSzAWiER7Vm8q1YrTc5hm4RAnL7wZCVlNpClZ5OFQgYTxpj0++lx2lHgVJX9VsjblGleFCBp/Fqgn0B2IRxWKzHOSQ1tLvNHYojE2K86nI1niLbptYKMpyhKIgwpA8VEYm1lv69tGVaRBgC7TbCUA0A2UQlWMxRns08xCq5sYpCOLOMrrVTy2JCcTRZ54bNTNlmnr5oQnOnEVmGh55rNpjfZ7dgKYS4cttHn0izmFysos8OihEBU3YxlE8Jhhb52ZqFABKyVByabnE1WGr9AQsbLxshmhfWRkzqlSVUYrZAaIhuFqZUMxf5IDLF4/tBcV0xko0AEknLLWkDpr429TAw5VjMUa44nPGcTpwfZvATJv7PCi5CNxcBKk3hyWGN2nk3WmcQzyU2l/s46Vq+OLCwG2sIsyQp8YfbDXDhsk01oTqIAAfvziyYQO+0CijOo7mPFvmbq/l5uqRCOzEpuA4n1MTmhOqtIspKVR3eZrlhjf/xyUsdmE/RxbIUQyayq0VlIYarNnQVOOzzO9NJCAMkh6uy/r3rVskzXm/jvukLsP9dskmYnG4pZL2SU7d7TKLiyiUG64omRywoy9Wxy9jgPy2SXZ0T9TSAqISyy7XasCZc2ASjxZB4jbAUFYnsgc/fU5N915Xhf3Q67ntPKCptBDtu0ZxGXn+ztw7qXXfKakUmYbrmFNusdWRhjAGt5OWeTV6LY49TzhXQyvtFR3zH1/zPL32idzSsnPazktZZVgmULGYqzjjSxkHdp1o4OBdaZm7JL+p4wFPsZNxRr62Gme0+j4MomBunIIhwCSHZltM7klsmCVexxWMbtOHmDZLNlvkGyghDSoVu8shu/rD9TIHsvLisJIizx1FNPYcyYMfB4PJg1axZ27tw54PGvvPIKrrjiCng8HkyePBnr16/v99h7770XgiDg8ccfN7jV5qHmlcg+J5woKXqIGqtk7epfYJ38d9km9rTUupFFsRC7TdALS7C+bmhrRonHkXa1YcBaxhhOeiS8utnOxyXLiv6+ZpLfR5N7rGQozlQBY6VK0l1ZKtasFFWTzT7b7bCjKO5Vzbrsrnm8lxY4M9p7GgVXNjFINkKX+jvrJHvNRruc7HbMujCdrQLRStb4bJPRWWr8ZhnmYiVBhBXWrl2Luro6rFixAnv27MHUqVNRU1OD5ubmPo/ftm0b7rzzTtx9993Yu3cv5s+fj/nz5+PgwYO9jv3LX/6C999/HyNGjDC7G4bSHYlBlDLPK1HgtMPlUMUB1sdiNgYKwGICcRYJwgHr5EZRFCWx0clyjWR9/CaS8KYffgRwz6ZcxiryQFdIhBQPH8pkn1JiIUNxNrlWAYvJs7piLbuoGtafKWCEx5pF9p4MJAcHuLKJSbK3ZlrDchuKSgiLan6FrAVMxvvanvUGyamfh/Uwl+wXZy0MlO1nCmQ/kVvJ84AVHnvsMdxzzz1YvHgxJk6ciFWrVsHr9WLNmjV9Hv/EE09g3rx5WLp0KSZMmIAHH3wQM2bMwJNPPtnjuHPnzuF73/se/vSnP8HppOdunAma9arAaUeBK/28EoIgWEZQzCaRNJAQElnvJ5CszM4ujK6d8YStwaiEqKTKApmmD7CKEiabqpFAYvMaEtn3CuGkh1XC6DR5ttjtgNuR6Xpjjb5ma/y3YshgpsYNqxTfCIsSQvG5M2NDjkWea7b6BKNIP7smx3Sy1y7HX3jGczZpC5bLbtNz16SLVXIZZVO1DEgIIdGYjJAoweti99Vty9LbxyoJFSVZ0d+xrD2bGB+/rBCNRrF7924sW7ZM/8xms2HOnDnYvn17n7/Zvn076urqenxWU1ODdevW6X/Lsoyvf/3rWLp0Ka688spB2xGJRBCJJEIdfD4fAEAURYjiwONW+36w49Kh2RcEoL47mZ63rMCJJl8ELf4gRNFrWNsypb/71OoPAwDKChwZ9bXQGbeoh0REo9GM8j6Roj0eTlPitvXb14HGU6lHtSe2dYcNHW9G0+ILAVCTvjsFOaO2lnrUNbHNH+r1ezPeuUxpjvc103e1wK7AbhMgyQpafUFUlXgMa1sm94mFe5orVMSTbbNeHEUPZc4ghE5jSKELrd0R5pVN2YSnA8lKcNVQzPJ6kwijy6yvpRbJ2aQZmuw2ASWezPZSVkmBkW0OXaNgd8eax3TmyQuvKWDKvM6MJ2CraJfbsgyj87rscNltiEoyOoIi08qmbHM2lRZYwzrSFRL1RK/ZKoZZ9zxghdbWVkiShKqqqh6fV1VVob6+vs/fNDY29nl8Y2Oj/vevf/1rOBwO/Ou//mtK7Xj44YexcuXKXp9v2rQJXm9qiprNmzendFwqfNQhALDDFgsNmI9qIKSQDYANW7d9AP8n7HhPXnif9h1X29l67iTWrz+R9vlUZ1oHJFnBq6+9jgJ2p1I0tNkBCPh47wcIHB342L7G08lWdVwcO9OU8bggwdkAADhQYJPx+uuvZ3SOQIc6Lt7fewBFzfv7PMbIdy5T3j+rPpNAe+bPxGOzIyALeG3jmxhRaGz7gPTuUzAYNL4BecoQi3g2ZetdCiSFITEu57Xr+5TsDIoRCxiKDXN0YPyZ6v0syP29Z7aetEbB7qjPUxQle28Jq73w2S1Y1tisJ0LLMnvhBUFAeaHqedARiGJkWYGRzTMUTclZmmUsNOthLpoQkmmiV8A6Ia+5zO7du/HEE09gz549KQsey5Yt6+Et5fP5MHr0aMydOxclJSUD/lYURWzevBm33HKLYeF6kb3ngfqDGDO8ErW1MzM6x/qufTj6cTPGXHYlaq+9yJB2ZUN/92n9S/uApmZcO+1K1M7KrJ0/3/MGQqKMq6+/ERdV0Pfi6o9lu7cAkFB7y424uJ92DjSeyo614dkju2ErKEJt7acItDgz/nGsDdi/G1Xlmbdz3+uH8UHLKVRdNA61NZf1+M6Mdy5T9qyvB86cxpTLL0Ht3MsG/0EfPHHkPRxvDWLyVddi1tgKw9qWyX3SvDo52ZNIEM62PNCepUERsE5+qs4sc/skG4rbA1FmlU1qkZHsQgatEpWQbQ7d5N+yrizNNq2JUbA56vMYfySWVeI9ILFZZz00pz3LcCsgobxhvq/xyVdzk86Ecq9LVTYx3FdFUfRcS5k+1zLNsykkMu123GlA4r1yi1gyWaGyshJ2ux1NTU09Pm9qakJ1dXWfv6murh7w+HfffRfNzc246KKE4kKSJPzoRz/C448/jpMnT/Y6p9vthtvd+112Op0pb9LSOXYwfBE1/0BFoTvjc1YUefRz0d6QJ3PhfeoIqaWGK0sKMm5nmdeFUFcYAVFhqq/JhEUJwXhlwKEl3kHb2dd4GlqiKqg6gjFm+wkA3VEtd2Pm41dLuO0L999XI9+5TOmMj9+hxZmP3/JCN9AaRHdUNqU/6c5jHGNIVBpke7OuhfdmZSi2TM6m7DbryYbizqCIUeVGts44QmIib17GsrtFChllmxwcsI6yNNs8XEbBE4QzRmfcQ8fjtMHjzCyPkVVeeN1ikKG3D2ChBStLzybAGglQg1FJr4qVeTVF9XeSrMAfiRnWNqMxRlnKczalg8vlwsyZM7Flyxb9M1mWsWXLFsyePbvP38yePbvH8YAaJqId//Wvfx379+/Hvn379H8jRozA0qVLsXHjRvM6YyDtBlivrJIg3Ii+WqFCkBF5JZLnF5YLS+gCcYbJwQFrPFPAoPFrkVQJnPTQZJ9Oxouj6HlgjPBsYlz2yTaMDrDGPkWbS5x2Ad4Mc+iWJXnqs73eGPlM2Z6DeRgdp086DMgcr/3WH44hJslwZBjiYzb5tFk3tK8ML1hdocSCVZChstTjtMPjtCEsyugKiijxsGk5NSQM1AJCCGvU1dXhrrvuwlVXXYVrrrkGjz/+OAKBABYvXgwAWLRoEUaOHImHH34YAPD9738fN9xwAx599FHcdtttePnll7Fr1y48/fTTAIAhQ4ZgyJAhPa7hdDpRXV2Nyy+/nGznMsTIdYP1udQIt3ArhK8mC4mZencmK+594Ziez5E1ugwcvyw/U8BYZSnrimFOemjvJ+vPVZPzNC/0TLCK7JNtGJ36W/bX1s4kBUym643Wz5isoDsSQzGjsnunAQoYq0TVZFsx2yi4sokxjNC4JltBO0MiKosyD90yE2NzNrH9whtrjWe3r9rCXFqQ+YIFqItWQ1cYHcEoRjOaU8WIKg8JZSnbwiVLLFy4EC0tLVi+fDkaGxsxbdo0bNiwQU8Cfvr0adhsCQX7ddddhxdffBE/+9nP8NOf/hSXXnop1q1bh0mTJtHqguF0BLQw3dz2nJRlxZB1o8wCXlxGyAIepx2FLjsCUQkdgSizyqZsy4sDeZYvxALKUk76aOM/EpMRFqWMoxvMRkuVkM37agVDsaIohhhyrGAo7jTAu7TAZYfbYUMkJqMzKDKrbEqE0RlgnGP4mQJJ6w2vRsdJxggtusNuQ4nHAV84hs5glGFlU/axpFZ44RVF0ZPIZTe5xYVphvvaaYAQAqgWvoauMNObQSOsI4lk6FHIsgKbjc38VKyxZMkSLFmypM/vtm7d2uuzBQsWYMGCBSmfv688TSzTboD1ygqeIf5wDLJWATILq7oVFPcdgexlAUDtayAaQkcwijEwoXSZAXQaIAuUWWD8AsleIUYohtnuKyc9itwO2G0CJFlBV0hkVtlkhGJCW6u0ynYsEhIlRGJaPrnsjRvtDMuzRijVtN83+lTZfbRxtQsMxQhvnwqrJAgPZm+INAI246vyGMNe+EL23ayNyGOkl59kuJ/BqIRofMEaUmREmAu7fe0yQAgBrOF23G6AhVrbMMsK4Auz+1w5bKPPpdkosy3gFq5t1L0uO1yOzMUXK+SnMkoWsIIHQSKEwwjFvchsvhBRkhGIJ33Ppq88jC43EQTBEqF0WsXsTCsOA4lKdizPS8l5jAozzGMEJOZglhXh2Vai07CCIjzh7ZO9srQrJCIWT6zOGjFJ1vcVPEE4pwfGvfDsKyaMyGOkCZghUUIoLsSxhtZPt8OWcR4jwBoKGG0zmG24hjb+tfOxiBHhPC6HDcVu1cGU9VBQDrsYYanTPZsYTnipe07mgTK702DDE8uJTLXNqxF5UbR8ISySvJ5lE2JihTBQTmaUFSS8nVnFkJxNemgZu8rh5BCkbNNCAGzLeEYo/JN/z/LaakRUjfaeKgq7+5SukAhF9wTnnk2cJIwSMBPVSth94Y3oa5HbAaddXQRY7WuyAjGrBcsCngdGWLyAJGUpwxskI5SlQJLQxfBz5bCLmsdIc5U2oLBEJAaRUUudNpeWZCk4WcF7QBeIs3R/r7BA+LU295VmsXnVCksA7D5Xffx61HCpTLGCspSTGZrs1MnoBlZRFN2DPRs5T9ujRCUZQUYNxcZFmrC/3nQakMco+fds9zX75+qw23Q5glUlYkfSekO7UBhXNjGGEYkyAWskkGw3wDNEEATmrQZGWIGA5PxULE/ixvTVCiWAjcivBljD84DDLv5wDFI8kVE260ZJgROaLpxVQVGfS7NeH9kPazAqsaemuGc5t4S2eS3PUrHGuhImkVjZqPWRzfeUkzmaEqaL0Tk4JEqIxo0R2XhLeF12OOIKV1Y9QzoMnpdY3aMAxnj7JP+eVRkCMC6PEesRGKxUogO4sok5jKhAk/x7Vl/4UFRCWMw+8R7A/gtvVGgZ64I0YGRf2bcEGaEsBayR+J3DLto7V+C0w+3IPEzXbkvkC2F1juk0an7RvUTZnV/0MF3DLM1sPlNFUZLC6IyRe1h9rsaFmSeeKashSJzM0J4tq/JsZ1IeI28WeYwEQWBedjcslNkCsnu+hNEZmcdIm8dZHb+sVKIDuLKJOQzzlmBc6NImomwT7wHsv/Bau7IN/dCUcsGohEiMTbdjI0riAgnPKFY3SFq1GMAAxTDj45fDNkZtYAH2q3v6DPISLWV8fgGM83IuLVBzwrE6v/gjCc+8rJUwjOe7MSonpyYfipLCbAgSJzP0EF9GvboT6012eYyAhEzM6tykeSJlK+PplcsYXVcBY/LmJf+e1TnYyDxGrO89E2GgdPM1AVzZxBzGeTax/cInT+LZLlis598wajOYnOeB1b4aX9GCzX76w4kFK9vnyvqCxWEbI5VNrL932nqWbU44TfjyhWPMVpIxygW+lHXvgUDCMy/bUu+6xxqjmzqjDE8FzkQ1RlY9CDiZwbo8q7VLU2Jng1X6mm24lTYHR2IywiKbymHDo2oYXW802abYgDxGJYyPXz0MlHs2cS6kyyDPJtZdGX0GbpBYt44YtRkUBEHXxLNqITE6TID1Z5os9GcKVzZxskGzgBvp2cSqkcKo+SX596y+d0aUZwbYn186DfKGVc/Btkd3IqehcbIAqxsdTmawno/LqLxjQGJu8jHaV10Bk6UnbZHLAa0eAKt9Nc7rkvU52LjQMubXVgMS+RsFVzYxhCjJ8MdL9uZ6RQAtZtaIDRLrL7w5ngdsbgYTVi9jPA9Y7aeRz5R1ZSmHbYzylgCs4NlkzHvnsNtQ7FEt8yz2VZIV+MKqLJDzeSUMSkwLWCOEAzBGsca6jMfJDD2PEaPP1SiFKcD+3GSUnGezCUzLebKsGFcJnfE5uMMghw4gf8avEXBlE0Nok7ggGJDfh3FBxMiXgPUXPuHFZZzbsS8Uy/pcZmBUHqPk0A9ZZi8Bqnb/ubKJQxtzNrBsCopm9LWLwdwoydZvw8J0GZUF9MS0RuYcY7Sv+WR44mSG5kXDqjygj2EjPBEZl32MNOSwvE/xR2KQDUoLwXrBm0QofvbGjTLGPfOMjCDKFksrm5566imMGTMGHo8Hs2bNws6dO/s99tlnn4UgCD3+eTyeHscoioLly5dj+PDhKCgowJw5c3DkyBGzu6GjvQQlHqeemydTWBdEzFA2sfrCG7k4s9xXUZLRHffMy3bjoAlcipLwgmOJfFKWctjG2AThbIfmmNHXjgB7fdX66XXZ4cwyr4SWDN0fiTGpuNeLomSZFwVIDqNjU+7pNCgsB2Dfg4CTGXoeGAaV4IBxFUGTz8Gq7JMvcp5miDAib542B/vCicIPLKF5DOf6MwW4Z5MhrF27FnV1dVixYgX27NmDqVOnoqamBs3Nzf3+pqSkBA0NDfq/U6dO9fj+N7/5DX73u99h1apV2LFjBwoLC1FTU4NwOGx2dwAY695XlpSQLsRgtRLdYuAxztuH1RfeyJwqLHvBJCvAsrUEuRw2vUohixtfMyxeLCoQOeyTj/nvjNislzKsmDBjk6MogD/Mnkesdv9LDXim5YwnQzdy3WDde52TGWWMK/wTYXTZv68JxRqbfTVybWV5n2Jk1bJkQzOLfU2srbm/9+TKJgN47LHHcM8992Dx4sWYOHEiVq1aBa/XizVr1vT7G0EQUF1drf+rqqrSv1MUBY8//jh+9rOf4fbbb8eUKVPw/PPP4/z581i3bh2BHiV7wGQ/iRe5HXDEvaNYFKaNDEPKpxdeV0ww6O2jCQzFSVXzsoFlK3W+WLw47JMv8wtgXM4mgG3FhJE5DV0OGwri1moW+9qZRzk0tDUyH5KhczJD26z7Ga2U2WVgQn+W31dFUQyNSmDZkNNhYGiZw25DsVvLh8ie7J4vCkTAWDkiW7JX7VEgGo1i9+7dWLZsmf6ZzWbDnDlzsH379n5/193djYsvvhiyLGPGjBn45S9/iSuvvBIAcOLECTQ2NmLOnDn68aWlpZg1axa2b9+OO+64o9f5IpEIIpGI/rfP5wMAiKIIURx48GnfJx/X3h0CABS77YP+PhXKvE60dkfR6gthaCFbj7ojoN63okH62td9upBCp6rY6AxGDblvRqO5qHodQtbtK4p7+3QEIj3Olcp9Mps2nzp+SwuchrSjtMCBc51Amz8EUSzK+nxG3qOOgOrtWOy2ZX0+bfx2hUREo1EIQvaKumzI5D6x+N7lC0YqYFgWiCMxCaF42WgjhP9yCyizjfCAAdSxERIlJp+rHlpm4IaOVS/RLoMqPiWfg4fR5RbJ87gvHENFIf2y5ckYmTeP5c16SJQgSmoYWK4rJrQ2GaHwB4CyQif8kRiTc5MZxX1Y9cxjybOJLQ1EirS2tkKSpB6eSQBQVVWF+vr6Pn9z+eWXY82aNZgyZQq6urrwyCOP4LrrrsNHH32EUaNGobGxUT/HhefUvruQhx9+GCtXruz1+aZNm+D1elPqy+bNm/X/f79BAGBHoKMF69evT+n3A2GX7AAEbNz6Hk6UshU7e+yMDYANJz/5GOs7Pxr0+OT7dCGNQQBwoM0XNOS+GYmsAP6w+hx2bXsHn2QpN5w/r46RQ8dOYf36E72+H+g+mc1HHWrbhKgxzyEWVMfI1u27EDhq3Pg14h4dPKa2rfHMCaxffzyrc0UkAHAgJitY97fX4c4uZN4w0rlPwWDQxJZwBiJfvOy0NtkE6JbTbGBZsWa0kFha4ESjL8xkXxPePgaWUg/HoCgKdcV9Mj08JYxIEM74RoeTGZpniD8SQ1dIZE7ZpBk3jKl+Gs/vw+AY1t5Vu03QUzpkgxXWViPXmzMIMVnIKJHCJbflJVlWmEoQbkllUybMnj0bs2fP1v++7rrrMGHCBPz3f/83HnzwwYzOuWzZMtTV1el/+3w+jB49GnPnzkVJScmAvxVFEZs3b8Ytt9wCp1MdCEffPAqcPI4rLrkItbUTM2pTMs+d24mm052YMGUGaq6sGvwHBFlzZgfQ2YVPz5qJOROG9XtcX/fpQpr9ETz84dsIyQLmzbsVNgNCuIyiKyRCef8tAMAX/mke3I7sIlcDu89h3amPUFQxDLW1M/TPU7lPZiPuOw/UH8To6iGorb0q6/Nt9H+IT7qaMOayiaidfXH27TPwHm1c+yHQ3ISrpmTfNkVR8NNdbyAmK7j2MzdheKln8B+ZSCb3SfPq5JDHUFd/D7ueIV1Jmxwj5ngtXyDLArGRwn/yeVnCUEtzfPxKsoLuSAzFBmwojCIQlRCLJ8w1JOcY415cnMwp9SZ7hhTSbk4PEjmbjNuss+gBk5zqwwilNdNzsIHe0UCSHMFgOL6hxrm4zBWNyQiLUtbJ1Y2kO5qoMGiUh3Q2WFLZVFlZCbvdjqamph6fNzU1obq6OqVzOJ1OTJ8+HUePHgUA/XdNTU0YPnx4j3NOmzatz3O43W643e4+z53qJi35WH9Ejc8uL3QbojDQXqagqFBTQPSHlqi0vMiTUtsGuqdDilUFjqIAYVlAqZudvgZ96sTmcdpQVNB7rKRLRZGqiPCHY33ej3TGntH4o8aO34oi9X75IrKhfTLiHvlVdyRUpDh+B6O0wIm2QBTBGDvvarrzGIcOZng2aZXLWFPcA8ZscgDGhX+DlU354sXlcdrgstsQlWT4wmwpm7R+uuw2eJzZp0vVQwYZ3NBxsqO0wImzHSEmvda68sQT0SyFP4vKYW0OMTJsG8j99abYreanlWTVa5UlZZOmQHQ7bEy0y5IJwl0uF2bOnIktW7bon8myjC1btvTwXhoISZJw4MABXbE0duxYVFdX9zinz+fDjh07Uj5ntmiTkNEvPIvCiJGJyzxOu+4xxNpEnk8WaiMtXgDbi7Npz5Une+WkgSQruuLemBwEqv2JxcplRuamAtjerPsMdPUH2F43jCwWIghCQrHG2FzaqSfhzX1PCU52aPmQWBvDoiSjO6K+r0Z6NmmeiCxhRt685POyhOHGDYY9pI3cZwuCoHtIs/ZcWcrXBFhU2QQAdXV1WL16NZ577jkcOnQI9913HwKBABYvXgwAWLRoUY8E4g888AA2bdqE48ePY8+ePfja176GU6dO4Vvf+hYAddD84Ac/wEMPPYS//vWvOHDgABYtWoQRI0Zg/vz5RPqUL9ZMo3MXJJ+Htb4aWaobSGwGfYxtBAFjE0cC+aVsYvVd5bCNP0lRYsRYdDvsutcFa0oYI6u1AuyuGYCx5ZnV87DZV0VRDDeyJdZItvraZbAxJrGhY08W4GSHJi+yFl6WLIsZ8b56nDa44oZi1uYmsxQwrPUTSMwhhinWGK70mi97T5byNQEWDaMDgIULF6KlpQXLly9HY2Mjpk2bhg0bNugJvk+fPg2bLaFL6+jowD333IPGxkaUl5dj5syZ2LZtGyZOTORG+vGPf4xAIIBvf/vb6OzsxPXXX48NGzbA4yGTQ8XoMoWsapeNrvKgnafZH2Huhc+XiQ0w0TrC2KYByK/nymEXzdvH67LDaTfGdlRa4ERYVOfS0Yac0Rg6zZpfGNys694+BivuWZtfIjEZ0Xh591yfS81aM0KihGhM1jftHOuT2KyzNTdpc3CxRw0fyhZBEFBa4ESLP4LOoIhR5Vmf0jDyScZLJM02RiXAaj7EsCghEouvN0avrYx5IbLm2WRZZRMALFmyBEuWLOnzu61bt/b4+7e//S1++9vfDng+QRDwwAMP4IEHHjCqiWlhWowwY14wyVUevAZUeQDYncjNcsVlMSGdXsLaMC8uNp9pcpWHfHCx5rCLGQJFaYETTT52FfeGhel680mZrQn/bPXV6IpPALseBImqe8Y806KkjaEvLKKyKPuckBw2SFQaZMuzSU+VYNAYBqArm1idm3LduxTIH8WaNsYEAShyGaRYY7SvrCmbuCmEIYwPzWEzltToKg/auQD2+mr0My10OaAZlJhdnA0SRFj1PAgkVXnIh+SRHHYxQ6Bg1SO2S8t5Y5hnk7o+aop7ljBc+PeyuXlN5KZyGC4LMDd+9WdqjDHGbhNQ7GFTicjJDla9JXy6wt+YMQywK7sbHYaknScsyojE2FpvjE4Qzmo+xIQHlzEVbYGkioqMjV+ubOL0S/KLYATMbhpMssYnn5sVjO6rzSYwq0k3PMyF1dwbWlUhA6s8sDp+OWyTj3OpYZ4hbgso7nPc0my05y/ArrLJ6AT3ALteXJzsKPOyuYHVlNVGezYB7I1ho/djxR4HNH06q33N9Ryk+SgvGbm2ZgNXNjFCJCYhLJqTu4DVzbqRLwGf3OjTZbCLNaubhnx6phy2yaex2GnwutGjchlDfZVlJW9KURudpxJg16O7y8SNOmupEjjZUcpognBNYWqUAgZIhAyy974abygudrPniSgnVQI03NGB0b2nkeuNNp+z9EwB7tnE6QctVEgQoLtGZwuLgjSQXxukhCuucenRWOyroiiJnBRG5WyKL1iBqIRYPIksC+TT+OWwjSlhdIwbKYzK2QSwaZDxR2JQTArTZS0sx2jvAYBdBYw57yqbijVOdrA6ho2uWpZ8Lta8uEyR8xis0uYP5896Y4Zxg1XZnSubOH2iDYxit8OwWFJWc94k52kwCuZfeAOtmSxaDQJRCVI8kZFRltviHglQ2RnDZpQU5ZsGTiaYqWxibSx25UkYkja/eJw2uB1GhemqBgB/JAZZSzjHAMn5G42CxWcKmBNGx6r3Lyc7ShhN6O/XPS7zSHY35X1lR57V+lngtBtW0VIbH6ytN2bIEPk0frOBK5sYwczcBVppXFYwdxLP/ReeRauB5u5tZB4jh92mVyhi6bnm0wafwzZGh64CycITOwIxYI7inmXh3wxvH0VRLdmskJB7jN+8srRmACaFDDKqWONkB4sGRSApkbQJcxNrY9jMPRlLffWZoEDUxoeiqAonVujSPfNyX1lqhlE8G7iyiRHMGBgXlsZlhXwKQzJXMcHOJG6G1Tb5fCyOX3M889h5phz2MacaHXtWdUVRTNnosOhRaIYs4HLYUBA3ArDY11zf0AHJIUgmKNYYWh/N5KmnnsKYMWPg8Xgwa9Ys7Ny5c8DjX3nlFVxxxRXweDyYPHky1q9f3+P7b3zjGxAEoce/efPmmdmFlNDmuLAoM2UoNiOMjlXlcL7sU8zop8dphzvuJcXSc83LfMEGGueygSubGMGMF97OaEI6M4RpFmOhgYTHjxkhVywJmJq13Ghlk54/hiEljBmhH8kCl6Kw43bMYZt8sb6GRRmipL4Xub7RMcv9ncXnaoYXF6vCv98UZSl749cs1q5di7q6OqxYsQJ79uzB1KlTUVNTg+bm5j6P37ZtG+68807cfffd2Lt3L+bPn4/58+fj4MGDPY6bN28eGhoa9H8vvfQSie4MSLKh2M+QnJdQ+BunMNUr7zHkqR9OigYxw5OWpbnJZ8IcDLDZVzMViCyNX8CctTUbuLKJEcxwsQaSk70ytFk3uNIOwObEJsuK7kKa633VnqlRye01WHQnN3PBikoyIgxZMjlsky8hydqGyyZAD601AhbDkPJJ2WRmwlaW1gzVM0+VBYqNVDbpXojsyHdm8dhjj+Gee+7B4sWLMXHiRKxatQperxdr1qzp8/gnnngC8+bNw9KlSzFhwgQ8+OCDmDFjBp588skex7ndblRXV+v/ysvLSXRnQHoYirnsThytLTYBKHIZGF7GcF/N23vmdl/LvGo+RJYMxcnrDSthdMbuDDkZ02VCSVFAfeHPdYZyfnJL3iDJsmJYkvVsMKPKQ/K5WHqmfhMEaYDNMBczvEmK3A7YbQIkWUFXSDQs7xUntzGzYg5LQmJCme2EIBg3t+eLQJx8vlyfS5NDkCIxybAk69kQTCqgYWgYHaMe3UYTjUaxe/duLFu2TP/MZrNhzpw52L59e5+/2b59O+rq6np8VlNTg3Xr1vX4bOvWrRg2bBjKy8tx00034aGHHsKQIUP6bUskEkEkEtH/9vl8AABRFCGKAz8H7fvBjgNUw50/EkO7P4RRpcZU+M0WbZ9S6BBS6kMqeJ3qfN4Viva6P0ZdI13afCEA6lwiSTFIkjHnLY4bSjoCEUP6ZsR96gioY7nYbTf0fmuK8HZ/mNpzBHreo86g2tcip8248RufzqOSDH8wggIDjWGZ4g/H9PXG60htfGQyltI5liubGMGs+EoW82+YqWySFaA7GmPCdVDrp5FVhYDkKoPsPFMzKgyq52Ovr2aMX0EQUOJxoCMooiskoqrEY9i5ObmLKZURk7x9FEUxVLmTKWYk9lTPx95m3QwFTPL5WOqrGSHJxR4HBEFNTtsVEjGsmA3hHwAcNkHPnWUELHr+mkFrayskSUJVVVWPz6uqqlBfX9/nbxobG/s8vrGxUf973rx5+OIXv4ixY8fi2LFj+OlPf4pbb70V27dvh93e93N6+OGHsXLlyl6fb9q0CV6vN6X+bN68edBjFNEOQMAb72zD2TI2PCba/Gqb9u7choaDgx6eEl1RAHDAFxLxt7+vR7KdOJX7ZAbHfGqbHHK0V56vbDjdJACw48jJs1i//rRh583mPu05bQNgQ3vTOaxff8awNoV96nn/8cEeSKfoj9/NmzfjXIs6fusP7AXOGNMmRQFssEOGgL/8fSPK3IacNivaIwDggF1Q8ObmjUhHhEtnLAWDwZSP5comRjDbmsmSMGJWQjqXw4ZoTEZXUGRK2VRWYKxVikULtXmeTfkxfrXzacomDmcwZFlBd9S8MF1RUhASJXgNDCPIFDPy3QBsV6PLK88mA40UtngIki8cgy8Uw7Biw06dMclh5kYqb1kMebUSd9xxh/7/kydPxpQpUzBu3Dhs3boVN998c5+/WbZsWQ+PKZ/Ph9GjR2Pu3LkoKSkZ8HqiKGLz5s245ZZb4HQO/H6/cH4nGk51YsKU6bh1UnUavTIHRVHww/fVjehtc28yzCAWFiUs370FCgTccPNcFHscad0nM9hS3wx8tA/DK0tRW3utcSc+0Ij/Pb4fntIhqK29OuvTGXGfdrz2MXDuLKZcMR61N4/Puk0aWwIH8HFnAy6+dAJqPzXGsPOmS/I9evijbQAimPOZ6zBlVKlh11i5/y10BEVcdd2ncVkV/QXn4wYfsOd9lBe6cdttN6b0m0zGkubVmQr0pUgOgPyyZpopTLf4I+gKiRht6Jkzw3QFIkPP1G9C+VT1fOxtBs2ooAQkbQYZSzTIYRN/JBGma2SuNK/LDodNQCwe0smCsimR78Zoz0l2w3TzQdlkZq5KXzjGTF/NWjNYlO/MoLKyEna7HU1NTT0+b2pqQnV134qY6urqtI4HgEsuuQSVlZU4evRov8omt9sNt7u3+4LT6Ux5k5bKsVoumKCoUFG4XEh3JIZ4ZA6GFHvhNMhDz+FwwGW3ISrJCElARVJf07mnRhKIqh0t87oMvX5Fsaqg84djhp43m/vUHVFzhJYVug1tU1mhOn4DUZmJ8et0OnU5YkhxgaFtKokbikMxMNHXgKiO39KC9MdFuvNYqvAE4YxgmtDlYWuzHolJCIvq5GaelZoNwct8bzU2nikAU8qSq+djr/Ke2cn8c33jwDEGTcHrchgbpisIAnNKXrMr5rA1vxjvraaeT51LWaluJcmK7hFrluKeleeq99O08RtjJjmtGbhcLsycORNbtmzRP5NlGVu2bMHs2bP7/M3s2bN7HA+oISL9HQ8AZ8+eRVtbG4YPH25Mw7OAtRBJbQ522gV4nMZtHQVB0I0IrMnuphkUGeknkD/GDVGSEYyqybdM22cz866ylRwc4MomZtBzUhhsuWVN6NJeAkEw3krN2uRmtrdadySGmMRG5TK/WZ4HjD1TRVHyZnHmsI1ZG1iAvbFollKCtfkFME/4L/awZaToTmpHrhuezK7WKskKAlGDshgzSl1dHVavXo3nnnsOhw4dwn333YdAIIDFixcDABYtWtQjgfj3v/99bNiwAY8++ijq6+tx//33Y9euXViyZAkAoLu7G0uXLsX777+PkydPYsuWLbj99tsxfvx41NTUUOljMqwp/JPXG6Pz+Gl99TMyN5llPGVtXQXMM54yNwcntcM8Qw4b49dvQtXIbKHvH88BYE6iV4C9al5aO4rdDsMrxrE2kZtWUjRJYPWFY6gopF+pxDzPJrYWrJAoQZQSLqpGwtr45bCNWUn5AfaUMGZt1kuTFPesVDE1TRbwsOXZpI2tgni+RSNJTnLPAj6TFMMep00PQfKFRBS5c1ekX7hwIVpaWrB8+XI0NjZi2rRp2LBhg54E/PTp07DZEuPouuuuw4svvoif/exn+OlPf4pLL70U69atw6RJkwAAdrsd+/fvx3PPPYfOzk6MGDECc+fOxYMPPthnmBxpihnz6vaZuIFlzbMpoVgzRzkcjEqISTIcdvr+HqYZxRmdg7XKz0ZS7GZrn+IzKYduNuTuymQxzFNMsPUSmFV1D2Bvs+4zKY+Rw25DkduB7oiak4IFZZNZnk2shQxqY8thE+A1uMQpa+OXwzZmvXMAe1VMzQqj086nKOr9NGNdShez8t8VMyYLmGVRTz4nM30NmfNM1ZBXB1q7o+gKiRhRVmDo+VljyZIlumfShWzdurXXZwsWLMCCBQv6PL6goAAbN240snmGos1NrHhLmGrc0PoaYeN9NcszpCjp3vnDMZQzILubFXJVwpjs7jNJgQgk5nVW+uo3yTiXDfTVqhzEJBndEXNeeNY262Z5wKjnZMwSZNIGST0nW5tB88Jc2OpnslLYaFdy1jZIHLbRBHMzLM2sKT7Nml9cDpteip6ddcOsyp5sufp3maSAST4nK+M34ZlngizA142chDXZx0zPpkRf2ZibEnOwsXOT055Yb1iYhxVFMbF4AVtzsFkVs5PPyYoMYWaKhUzhyiYGSJ50zMpJwcyCZZIHF5B44VmYxAHzNkjJ52RlIteeq1k5KVjpp1Ypzozxy5oliGWeeuopjBkzBh6PB7NmzcLOnTsHPP6VV17BFVdcAY/Hg8mTJ2P9+vX6d6Io4ic/+QkmT56MwsJCjBgxAosWLcL58+fN7kZWmCUQA+wpm8wKowPYEorDooRoPA+fWXMpKwKxmbIAa+PXTOGftTWSYwzsva/mjWEtDImVEF/NkGPmesPCcw2Lsr7e5HrOJrM8hgF2vRC5ZxOnB5qQ4HXZ4TQ4hpc164hZ4YJA4sVi5oU3cYPEkjCtKIppVgNNAROJyQiL9BOg6rHQZuYtYEAIYZm1a9eirq4OK1aswJ49ezB16lTU1NSgubm5z+O3bduGO++8E3fffTf27t2L+fPnY/78+Th48CAAIBgMYs+ePfj5z3+OPXv24NVXX8Xhw4fx+c9/nmS30kZ3lXbnvuLeTC9RloRi7X4LAlDkMknZxIj3QBeBZ8rC+giYF0annpMbKXIR1hKEmzuGWQtDMlGxxpASUWuD3Sag0OC0EKwpwc31bGJrn21WzrFs4MomBjBTAZNcjY6F0rhEPEOYe+HN9IKh39dILGEdMXpyK3Y7oEWrsbDxNVdZytYGn1Uee+wx3HPPPVi8eDEmTpyIVatWwev1Ys2aNX0e/8QTT2DevHlYunQpJkyYgAcffBAzZszAk08+CQAoLS3F5s2b8ZWvfAWXX345rr32Wjz55JPYvXs3Tp8+TbJraZHwnDRP+GfG0mxmXxkSirX7XWRCAQ1NIFaLHNCvYmpmzibW5lIzE7aypljjGANrxiczU2Awl09O9wzJbaN4sgeM4WkhvGwZiv0RE3NcMlZN0cwUC5nCjtorjzFzA6stDKKkICRK8BpsLU0XEhUtWHnhzUyoyJKAqT1TQQAKDR5fNpuAYrcDvnAMvrCIocV0q8SYmySTrQ0+i0SjUezevbtHiWubzYY5c+Zg+/btff5m+/btqKur6/FZTU0N1q1b1+91urq6IAgCysrK+vw+EokgEonof/t8PgBqSJ4oDvz8tO8HO24wOoPq9b1OW9bnuhCv0xa/RtTwc6dK8n3S3juvQzC8PcUe1aLbEQhT66tGe3cYgKpkT7UtqY4njz1hbGr3h6gXlujoVsdvodtu+H0vcKobJ19I7PFO0nq+vlAUAFDoNH78Frni76oB4zeT+0T7nclV2AvNMb8gBSt9Nbf4BjvP1UwFYpFLNRQrinodj9NYz6l0MTeUmTHFsInvaqaw05I8xswX3uuyw24TIMkKfKEYfWWTSZUPALbcUwFzczaxpGzSF2YTrPGAev984RgTVi8znylr1j0WaW1thSRJerlrjaqqKtTX1/f5m8bGxj6Pb2xs7PP4cDiMn/zkJ7jzzjtRUlLS5zEPP/wwVq5c2evzTZs2wev1ptIVbN68OaXj+uOTEzYANpw5/gnWhw5nda4LOdYiALDj5LnGHvmtaLB582Z0BOwABOx+/z2c8hh7fn+beh937D2Awqb9xp48Teo71fuuiKG073sq48llsyMqC/jbxjdQafB9TJcDx9X73nzmJNavP27ouY/5AMCBxvauHvcx23cuUxpa1fH78b5diJ4w9twt59X7+OGho1gf/sSQc6Zzn4LBoCHX5PREkzG6IzHEJBkOg1NspIu5CcLZkd2T00KYaRRnQc7zmegx3MNQHIphWLHhl0gLn4kKRNZkd7+JBSkyhSubGCBRlcX4gSEIAkoLnGgPROELi6gupSthmprolTHriJl9ZcmLy0yXY0BTwoaYUKyRGL/dkRgURTHcrZkzOKIo4itf+QoURcF//dd/9XvcsmXLenhL+Xw+jB49GnPnzu1XQZV8jc2bN+OWW26B05n5O/Pnlt1AWxuunTEVtdNHZHyevvB+0oIXju6Fu6gMtbXXGnruVNHu04033Yzo9rcBAJ+fdwvKvMbOMx/87RB2tZ7ByDGXonbOeEPPnS7CwUbg0H6MHFqO2tprUvpNOuPplx+9jSZfBDNmXY9JIwcep2az5ZUDQFMDpk++ArWfGmPouQ83+vG7j7ZDsrlQW/tZw965THnowFYAUcy58XpMHG7sfT/zzgm8ce4IhgwfhdraSVmdK5P7pHl1cowlWcbojsRQ5qXriUgmjxF9eTY5LUSuh1zpsrsJeR+BhKGYBW/9blMrgrKzHwPM9czLFHZakseYGUYHqJvY9kCUic26mS8BS55NMUlGMKrGKZtZgYaFyc3siY2l5JF+AnkLZAUIRCUUufn0fCGVlZWw2+1oamrq8XlTUxOqq6v7/E11dXVKx2uKplOnTuHNN98cUGnkdrvhdvcO6XQ6nSlv0tI5ti/8EXV+KSt0G76BLi/0xK8Ro7I5TyYsJZSu5UUewy38pfFNXFCUqfc1KKqhbqUFrrTbksp4KvE40eSLIBRTqPc1EF8fy80Yv8UFANRNusORmEezfecyRcsXUlFUYHxfi9R5KBCRDDt3uvMYx3icdhu8LjuCUQm+EH1lU8KzyURDMQN7lOS0EEYXaQDYysVltuxeHDcUs7RPMTPvIwvPVFEUU6OlMoUnCGcAj8OOUeUFqC41Jx8NW9V2zHsJkj1DZJluMvTkybXIROsIC8/UTPdqgLXxa16VB4/TBqddiF+Hfl9ZxOVyYebMmdiyZYv+mSzL2LJlC2bPnt3nb2bPnt3jeEANE0k+XlM0HTlyBG+88QaGDBliTgcMxExXaZYSLGttKHTZTQklYclIYb7inp2++sy0NMfvnygpiMToJkOPxCSExXgBjTxIH8AxDpYUE2ZWBGXJs0mbg4tcJqWF0NdW+s/UzHBBgK3xm0gQbp7xPyzKiFJfb2SIkrr/5Z5NnB588/qx+Ob1Y007P1sCpokvfLyfigIEojGq8araJO512eE0ZYPE0CRucplNlqwGZm6QBEFAsSce8hqKYXip4ZfICerq6nDXXXfhqquuwjXXXIPHH38cgUAAixcvBgAsWrQII0eOxMMPPwwA+P73v48bbrgBjz76KG677Ta8/PLL2LVrF55++mkAqqLpy1/+Mvbs2YO//e1vkCRJz+dUUVEBl4uuRbk/SFWjox3SaWbJYoA1L1FzFfeJRKYs9NU8xVrhBclpyz30ktP2MDyZ4K3KUkg9x1g0T0Q2ZB/zFBMJ73X6/TRbAcNSug8z00IAjPXVxKTZyQ4F/rCIIUX0ChmZWbApG9hpCcc09NLOQRYmcvMmN7dD9QwRJQW+MF1lk/mTOIMbJLM2g7pnEwt9NdvtWA15ZcHqxSoLFy5ES0sLli9fjsbGRkybNg0bNmzQk4CfPn0aNltCwXvdddfhxRdfxM9+9jP89Kc/xaWXXop169Zh0iQ1v8m5c+fw17/+FQAwbdq0Htd66623cOONNxLpV7qQKEUtSgrCoowCF73NupnhGwCbCVvNDWtgo69m5oCx2QQUuR3wx5PTsqBsKnY7YDfFU4KdDR3HWFiRfRRFIeLZFI3JCIsSaNYtS+QgNXkOZkDGMzuRdDFLXlwR84zi9vh60x2JwR+O0VU2hRLrjRmeeZnClU15QMKzib4wYqZ1JNkzRJ3cCgy/RqqY6QGjnpehDZLJZTZ1ZSkDfTXf6sWOEpFllixZgiVLlvT53datW3t9tmDBAixYsKDP48eMGQNFoRt2my6iJOuhOeZ4hthhE9T8Yf6wSFnZZJ5SAmDLM8TsdYOlRKZmb+pKPE749eS0NIV/c73VWNrQcYyFlZLqIVFCLJ6awgylf7E74YnoD8dQ5qGX4YWEQTH5OjQxPyqBnb52myxHlHhUZRPtd5XFSnSAxXM2PfXUUxgzZgw8Hg9mzZqFnTt39nvs6tWr8elPfxrl5eUoLy/HnDlzeh3/jW98A4Ig9Pg3b948s7thOtriQHuzHhYlPZ411902NQWMWZN4KUMVLcye3EoZcrE23+rFTl857GJ2aI4gCPp5aRspyCQxBfwR+u8cqb7Snl9kWUF31NzwSFY2dSS9nK2mNOcMDCu5OTV51mETUOA03vCgeSIC9OcmUp76tOel5DaYZ8hhY/wqirk5m5LPS9sLkcVKdICFlU1r165FXV0dVqxYgT179mDq1KmoqalBc3Nzn8dv3boVd955J9566y1s375dL1N97ty5HsfNmzcPDQ0N+r+XXnqJRHdMhZWEdNpLYFaVB4Cdyc1891T1/oVECaJENyFdwlvN5KS2LHk2me2xxoAgwmEX7V0wK2k2wE6uP1J5jNgQ/k3e6DDiOdkdjUHTi+R6qDmpNSMmKwiJkinX4NCBFXkguQiMWfn7WHlfzVYOsxWVQKavtJ9pVAYk2dyk2cl5LmlidvRFplhW2fTYY4/hnnvuweLFizFx4kSsWrUKXq8Xa9as6fP4P/3pT/jud7+LadOm4YorrsAf/vAHvYpRMm63G9XV1fq/8vJyEt0xFVaEae0lLDIxlpSVyc3McEGgpzcD7b6arVhLJAin28+wKCEqme2Zx4ZimMM2ZifNTj437fnF7DC6ZEszbc8Qs0OSWdnoaNd3OWzwmOApAbDjJZoIozPnmXpddj0XFO13lWMsrMgDZislks9Ne24iWZCC9npjdl9ZqTKoORvZbQK8JqUEYMVrOJHLky3PJrZakyLRaBS7d+/GsmXL9M9sNhvmzJmD7du3p3SOYDAIURRRUVHR4/OtW7di2LBhKC8vx0033YSHHnqo3zLYkUgEkUhE/9vn8wFQqxuJ4sADTvt+sOOMoMCp6hS7glEi1+uP9u4wADU+O9V2pHufitzqRNIZCFPta1dAHReFLptp7Sh02RGISmj3h+ApiSf0pdBnLTyz0CmYcn2vUxWksx2/2b5z7X71mQoC4BIUU/pa6Iq/qwF672om94nmu5aPJLx9zBf+aW90SOXQkGQFwaiEQhPCElNFC+UzL2cTGwKx2blCAHbGr9l5uLSQ166QCH9YRFWJx5TrcMjDSoJwM4tRaLDi2WRmlVcgMS9FJRmRmGyasj0VzJYjWJmDw3GHz2KPw0TPPDYcHVjN2WRJZVNrayskSdKrD2lUVVWhvr4+pXP85Cc/wYgRIzBnzhz9s3nz5uGLX/wixo4di2PHjuGnP/0pbr31Vmzfvh12e+8J4eGHH8bKlSt7fb5p0yZ4vd6U2rF58+aUjsuGTzoEAHacaWrD+vXrTb9ef9R3qu1QxFDa7Uj1PnW12ADY8MGHH6G87WD6jTSID0+q7Wg5dxrr15805RpO2AEI2LBlK0YXqZ+RGE8Xcq5Zbceh/XuhnDbeUnM+AAAOtPoChozfTO9RU0hth8emYMOG17NuR180nlHHzcFPjmF97Igp10iVdO5TMBg0sSWcCzF7AwskeRRSz0FgbhhdgVP1DJFkBf5wjK6yKS6olpou/NN+puZ75rGSG4WEYq2kQFU20fYg4BhLCSPeEmYrYJLPTbuvCS8uc+amQlciGbovLFJVNvnM9uJiZA4OJSmbzIKdFC7mrzeZwFZrCPGrX/0KL7/8MrZu3QqPJ2EFuuOOO/T/nzx5MqZMmYJx48Zh69atuPnmm3udZ9myZairq9P/9vl8ei6okpKSAdsgiiI2b96MW265BU6nuRrIYac68HT9B7C5C1Fbe72p1xoI4WAjcGg/Rg4tR23tNSn9Jt37tHd9PXa0nMaIi8ehtuaybJucMe/85SDQcB7TJl6G2hsuMeUaTx77BzqbA5g8cxauvqiE2Hi6kN8cegcIhnHTp2dj2ugyw89/vjOEX+9/FxHZhtramozPk+07t+9MJ7BvJyqKC1Bb+5mM2zEQTdtOYcPZwygfNgK1tVNMucZgZHKfNK9ODhl8Jnv7AMmWOtqeIeaG0alVTB3oDKqeIdWldDxDFEUhFsJBe0PnJ+Dqz4pizexqdABQ7HYCCFHf6HCMRVfAMBL2SsKziXpfTV5bbTYBxW4HfOEY/OEYhhWbcplBkWQF3RFCYdu0qynGVG8mU8evrixlY73hnk0GUFlZCbvdjqamph6fNzU1obq6esDfPvLII/jVr36FN954A1OmDLyZu+SSS1BZWYmjR4/2qWxyu91wu3uX1HU6nSlv0tI5NlPKi1ThuTsSI66ISCYoql4vpQWutNuR6n0qK1SfR0CUqfa1O6Kq0suKPKa1o7TABSCAUEzRr0FiPF2INrlWFBeYcu2K+GIsSgokZJ/jI9N7pDl4FHvMu8f6+I1KVMcvkP48xiEHCeGflc06ieoqJR4nOoMiVaE4GJXMT2LKyDMl4ZnHiqWZhGKYlXeVYyys5LwxW+EPsDOGzS7SAKjP1ReOUZ2bNEWT2p7cXm/CJD2bqBtyeDU6w3C5XJg5c2aP5N5asu/Zs2f3+7vf/OY3ePDBB7FhwwZcddVVg17n7NmzaGtrw/Dhww1pNy1YSUhH4iVgRcAk4zpPP8xFJmAd0dyOAboTOYkqDyUeNqwjHLYhOZcy49lkpmcIA++d9kzNKi8OsJMMncz4pf9MAXKbV/VafN3IJZjxLjU5yb16bjY26/miHNaeqdthg9thbtLs7gjd9SaYZCg2C1ZyjpGQlzLBksomAKirq8Pq1avx3HPP4dChQ7jvvvsQCASwePFiAMCiRYt6JBD/9a9/jZ///OdYs2YNxowZg8bGRjQ2NqK7uxsA0N3djaVLl+L999/HyZMnsWXLFtx+++0YP348amoyD91hgQsT0tHCZ3LuDYCNSRwgk1CRBRfVQFIJa7P6qrkdA5QXZyKhH2xs8DlsQ0TxyYhbeL6EXCUSe5qXxPTCZOi0IOWtpl6L9kadnJGCdl85xpIwKNJWwOSTJy2BfIgM5DIiU9GWjfVG82wiEkbHyLvKmmcTW61Jg4ULF6KlpQXLly9HY2Mjpk2bhg0bNuhJw0+fPg2bLaFL+6//+i9Eo1F8+ctf7nGeFStW4P7774fdbsf+/fvx3HPPobOzEyNGjMDcuXPx4IMP9hkqZyUKXQ7YBECmnJCOjIDJhtBFUpimuRnUru2ym1fCGmDD7ZiIEMKIdYTDNiQEClYUn2SEYvp9JRFaVuC0w2ETEJMV+MIitWTo+RQGSuJdZWHzyjEeXR6IxCDLCmw2c5TQg0FGYcqGYs3sIg1Asgc7fXnWTG81VtabkKS+N2TC6GgrS82XlzLBssomAFiyZAmWLFnS53dbt27t8ffJkycHPFdBQQE2btxoUMvYwmZTS+Oqm3V6CelIVlCiLXSRSNKmezYxoYAxdyphYeNAslw3bYGLwzYkFJ8shCHJirrRAswVilmYX0iEb2jJ0DuCIvzhGIaXmnapATG7ClLyuf0RNjavue7lzDEe7bkqCtAdjZk6hgbCR0AxwYLCVC3SQHKfQtO4Yf4czMp6o2UaMTWtCTOODuZ7gmeCZcPoOOmRmMgpTm4hEkIX/bjv5KpCub44k7B4JZ+fhRh3Ehv8QFKyYA7nQojkhGPA0hyRYHqYbvK56SruzV8fATZCc0gYKXTvAYo5DdXr50/6AI6xeJx2uBzqNo3m+0rSE5FuWggJmthFJJ8cxbmJlFKCBa/hRILwPChIwWg1Oq5syhNYcPEjIWCyIHSFRRkxvapQbi/OpDyb2HA7JuFhkRgv3XzjwOmHfMmhEYoLiWaH6bJQNSchJOa+lyiJJKbauWkmp5VkRffMy4eQV47xsOCtT+R9ZWCzrr0/ZhZpANh4X0kZN1jwkNY9m0w1/qvn7o6HvNJAURIFm7hnE4cKxQy4+BHJYxRfDINRCTGJTjJ0bSNoE4BCl5kbpPxZsFjoK4kwUJfDBo/T1uN6HM6F5Es1OhJCIsBGX0nlWihhwPuXpOGJZnJaEuXFATbyN3LMgYXEw/liKNY8jcws0gAknik3bpAhrOdsMl9ZKitq4SQaJHvm8Wp0HCqwYR0h504O0Otrcsy3mQsWC664pCofsNFX8zf46vnpbwY5bEOyGp2foqUuRKCKDMCGQEwiYSvARl44EsrSAqcd9nhCZX+EznPV7rHHaV55cYCNZ8oxB9qKREVRkpQwBCq0RWLUUgiQyNeUfH6qCn8CHpcAGx5r2rbBzL66HTa47KpKhZYcod1jp12A28GWeoet1nBMo4QBYYREnhGnPeEZQuuF79LzGJk8ieuLM/1nSkoBw4LnQT5sfDnsogr/JHLeOOPXo2epC8fMryKjnp++8E/CcxKgv3kFyOSA0ZLTAoCfkpGC1DPla0buQjvHWiQmIxqPEiBRHAUAApSUwyRSJQBshJb5CYTiA8myO/1wfLPXG90LkZIckewdbaajQyZwZVOeQDvBMqkqDwD9MAG9n26z+8mAtw+BTQOQX27HLHghctiFVE44t8MGpz3uGUJpLOpCoukFCOjPLySMMQAbijXi4de0N695YIzhmAPtFBjaPCEIQKHLTM8Qu+6NQUsJ4yMmu9OX8ZJDBs2E9vgFkhOEE1pbKe3JWK1EB3BlU95AO5l0j1hSYgnpaC3OhDybkgRMWglQSZRPTT4/G3lGCI1fHhLB6QNtHJqdE071DKH73pFwf1fPT1/4J+UlSluxJkoyQqIq/ef6RodEJTogsbmgmQydYw60PRG1eaLI7YDNZq63BG2jOLlUCfRlPHKetHTXG0lWiORsApL7SlcxzFolOoArm/IG2m7WyVUetDA3s6C9cSDmwVWQnJCOTgJUUnlGaAtcspxU5YGgEpHDuZBkgcJsV2nagiLpnE0sKLNJefvQ2ugkj6WiHE9OS8oYw4IswDEHTd7oovy+mj0vAfTn4YQ8Syq0jAHvUtO9hukarAKEijSo56cdVUNGWZoJXNmUJ9DewCa/BKZvkGhbR0JkFmcWwlzIeTbRtQQFojFinnm0PQ84bEPK+qpeg+66EYrnbDJf+KdftphEEl71/GwYnrwuO5x2MoYnel4hZMIakmUB7hGbW9CW3UmlDwDoh5eRCi3TZDyq6w3h4j7U1pu4skmt9GyeJzhAX3b3EVQMpwtXNuUJtGNJSbmTA/QVEyTKxALxhHTUlYiE8hhRViBq1yVR5UHf4FPKM8JhGyqWZkrrhubZVOwm402oKEA3pWTopOfSfLC+srJ5NVvuSQ555UaK3IK2dynJ9Ya+nEc2r6xMsfhGvhT30ftpsgyhXoOu1zBJxXC6cGVTnsBOlnwSAiZt7TIFxRrlUpu5HuaSLHCZ7ZmnLYrcQs3pCzqWZjpjUZvWzJ5LPU479bLFpMIaaFuaE+OX3PrYTUlxT8p7IPkaPPw6t6AfmkN+DNOX88z3RKS/3pCV3Wnvx4jIS5Q9m/yEIk0ygSub8gTaVi9SVR4A+hskUgsWwIIliGxCRVpux3Q2DdxCzekNSYGCtjI7qFejy+3NuiQruicjqWqX1KyvJNdH6l4hZDZ0ydfg60ZuQVseyCdPRFLvq+qJSE+xFo3JCIsyABLKJjZyBJJZb9hQDJOQl9KFK5vyhBLKFgNSFdoA+oszSc8D2ptB7R6Xml5tJxHmQsPtmFTiyORr0ExWzGEXkgIFbSOFlrOJhJGC5rrRTTCJKSsbOjLKUrpzKakwOoC+VwjHHOgbFAnKPrRld6L5EOn1NdmgYnaRBtrPtFurpkhyP0YrXQ33bOLQRht8tDxD8knAJBrjrj1XCn0lWcI6OcyFhmKNVOJI9Rp0k9py2MZH0FuC9gY2rHs2EVw3KFhgtfXR7bDB7SCTxDQkSojGZFOv1RdEPSWoJ2wlkyAcoG944pgD7RykJBUwumKNUtgryX1KQolIY72JK2DcDthtJqeF0PYoUVpRCeRyNtE2FJMMeU0XrmzKE7TBRysBKtnNOhsCZq6HufQoYU1kIqcX5uInGAbKc29wBoLsZp22Z5PWjtxWTJAMjUyeq2nMMWRzGiaMbDQgm8yffjl1jvEkeyIqCs0UAuQ8m7poh1wRjMCg4QVDUoagvfcklQsRoG8oJrnepAtXNuUJHqcdLge9hHR0chfk/oJFMyRCs7QVuuxwmFzCGqBbUZFkGCjtMBcO29CoRkdjLlUUJVGNjkRf3fTWjUShBfPnF4fdhkKX6j1FV7GWP4anfEgfwDEH7blGJRmRHPdE1JXD1FNg5Ph6Q9ADhnbxDT0XIgmDuDYHU65GR0KOSBeubMojSii649IQMGlXaCPpikvTs4lUfDDNjS8VbzVejY7TB2Sr0dEbi5GYDEkRerTDTFjwEiXl/k4z1Jyk4Ym2pZmoLMA9m3KSQpcDWgFcmu8rSdmHRhidJCsIRMmkhQCSK4TTM/6Tlt1p7j3J5Gxiw7OJ52ziUIWqFwwFAZOG0BWTZH3BIrlBohlaRqryAc3xS6MiSyQmU8mpwmEbkgIF3TVDvaZNUDdcZkNVARMhF1oG0PWCIRlSTzM5raIoVLwQaSWn5ZiDzSboXhk0ZZ9cr66c7E1FNjcnDeMpuWcK0H2uCeNGbu/Hkq/Lq9FxqMKCdplk7g0a2uWeVYVyfTNIyTpCMaEiiU1DsgWGW6k5F0I2NId+mG6R2wGbyUlMgfxRwACUk9NGyBueAtEYSOemDYkSYvGLki0bz9eMXINm8QIaXt005VkSRRoANlJg5ENUAo0cl5GYjEhMMv16ySQ7OnDPJg5V9I1DJNddcdVrRGMywiLZF16b2DxOm54jy0xohn6QrFICsLI4m99Xu03Qk/jy/BucCyHp2URVwRuhpYChGNZAoAABkJ/JaSNkRQG9n3abAK/L/M0rz9mUu9B8tiQ9m+h6++RfaBm5sG2K41fP2US6+AbZvvZ0dOCeTRyK0Ky2Q9JyS/OF7yJsMaC5QUoko8uHxZlOmAutEqocdiGZ3FMb78GohJhENqSzm6BSTb0Ofesr6ZBkKps6gmtkcnLaEGFlU7KBQhDM98yjXTmSYx60Sqonh4KSNG6IkgKRcAYB0nMwEwpEUvKsm+Z6Q+650jQUa9crcNrhJFCwKV3YaxHHNPQXnuZmncCCZe8R4062r/QsBrlvHWEjGXruCyIcdpFlRbdgkcwDA5AvH0/ec5J+CAd5xRrNjQ6pdUO9DmknLtLjl6SBIhQKmX4NTgJac1NIlCDFQ0FJvK9FScnQib+v1AzFuV2NLvk6VHJxxeWWIgLV6IDkd5Xsc+0iGH2RCVzZlEfQ8mzqGUtKWvAirV0m6+2jh5ZRqN5B3DpC0duHZIL75Ovw/BucZLqjMSjx3DMk5lKn3QaPUxUTSIdc6QpeQkIi3bwo+VGNjrSnRPJ1wsTD6EiHRpLzbLr++ut7ffbJJ5+Yft18hZY8kBwKWuA0PxTUluQZQtoTkWS4IEC7+ikdxRrdaoqk5QhK8lI+KZt27Nhhxmk5WUJLwCSdNDv5OqQXZ1p5jMKiDNKFy8hbR+hXoyMfMsimZ1MoFMK5c+d6fX7o0CEKrckftHHostvgISD8A/TWjUQi6dzPCUd6fqFleIrEZETj4ZikDU8hyfxQtmRoheV0R2K6N4rRvPbaa/j1r3+N7u5unDlzpsd3ixcvNuWaHHryAOlQUCBJpiU8DVMzFFMteJPbnk2iJCMk0llvyCuGyab6SBdTlE0LFiww47ScLKHn7UM2aTZAT5gmvWAlVy6jZrkltjjTmcRFSUaQuGcePUvQYPz5z3/GpZdeittuuw1TpkzpYVz49re/TbFluQ+N0ra0QjjyKySZluKetDFGvZ4gqCEzJNDuKenNK63QSMC8kNdJkyahuLgYra2tWLRoEcaNG4dbb70VAOBwsGlRzwXyxXiafC3SyuG8KnhDeJ9Cy1CcfD1SHtK0cuf5CHsMp0vGd/8rX/lKn58rioL29vaMG8QxjxJKYQKkha7ka5HuK2lrppaQrjsSQ5B4jDtp6widZ9qdtGgUkRJEKCbzH4yHHnoIu3fvRlVVFXbv3o277roLP/zhDwGo8z/HPBKFFsjPpbRCOEi9c9omIxBPhu4gmGSTeL4QSp4S+jN1O2CzkfWUoBWWQ2rz6nbY4XbYEInJ8IdFlJpg4R47diy++93vYtKkSfjMZz4DAKivr8eECRPw2muvGX49joomD9BKC0EqFBSg+b7SyWMUjEoQJZloUmdahhzy+zH1ei6bQmw9p5Xug/T4TZeMW/XGG2/ghRdeQFFRUY/PFUXBO++8k3XDOMZDy5WRZCU6DVp9Je3tA6gbh+5IjPziHCHsdkzNW029ntdFrsoDzZDBwRBFEVVVVQCAmTNn4p133sHnP/95ACDmap+v0BAoaHvEkvb2AVTPkDKvi8h1AQrFFvRcf4QNT4QrmAJJnhI5HpYDqGM40h1RZa5y867z+9//Hu+99x4mTZqEMWPGAABKSkrMu2CeQ1vhT9KTlpYnIq1UCYBq0CwvJL/ekAq5ohWVoFdoI5NxAAB9eYnkepMOGc8gN954I4qLi3XrRjJTpkzJqlEcc6BV/YCG0EUrHlpXrBFy2QTU53q+K4xwLLdzUtAq1006N1XytVgMoxs2bBj279+vz/MVFRVYt24dhg4dio8++ohy63IbGgIFvXWDbF9dDluSZwgdZZMZ3ih9QSsHDI0kpokE4ZTWR4J9LfE40NodMf1d/f73v48DBw7gjTfe0MOo58yZg507d5p63XwlIfvQel/Jrzekjaek5TyH3Qavy45gVIIvLBJTNimK0iMXFwlohQxq/SSoK6W49ySb4zJdMm7Vq6++2u93mzdvzvS0HBOhrXHNC2t8hJ5igvjiTDz0I5EMPRqTieX/ohkGymI1uhdeeAFOZ8974XKpgtL69etpNClvoKH4pJazKUJHcd/ijxBV8qpJTOnkhMt1BSKQP+ujei0y7+rs2bMxe/ZsAIDP50NpaSk++9nPmnrNfIZWGBJNQxst4ynp9zUYlYiurWoxISV+/dzO2aTt/zxEPZvo5qdiNYwu493aCy+8gOeff97ItqTNU089hTFjxsDj8WDWrFmDWlVeeeUVXHHFFfB4PJg8eXKvjZGiKFi+fDmGDx+OgoICzJkzB0eOHDGzC0ShpnGl5E6efG1SkHZPBZJi3AnObT1LWJOZ3JJzt5Acw7Qs1MnXZom33noLGzdu7PO7a6+9lkgb8nXup+kZQjzfAmHra/K1SL53ydcqIpbENNFPknnW6ChLya+PAJ13VfdCNDk8squrq9dnZ8+eNfWaQP7O+7TTQuSFcpii7E5yn6I9U5sAFLpIVbSlm8eowEFujaOWn0pLa5Jr1egeffRRfO5zn+v1+Z/+9Cc899xzWTUqFdauXYu6ujqsWLECe/bswdSpU1FTU4Pm5uY+j9+2bRvuvPNO3H333di7dy/mz5+P+fPn4+DBg/oxv/nNb/C73/0Oq1atwo4dO1BYWIiamhqEw2HT+0OCCz1DSEEz7puW2yYNaybJxTkkSrp1hJQgYrcJ+uJI8rnSeKa0QgZTob+5HwBefPFF06+fz3M/DcU9bc8mUgnCATpWSU0gLnTZCSYxVfsZkxXdq4oENHOOka/WSsdTIvnaZnHTTTfh0ksvRW1tLX7+858DAA4cOGDqNfN53tc2kLSMpzSMG8RzkFI0bpAMZ0721CeVYzM5GXpMIrf31BSINHI25UNu5HTIWLKx2WwoL++dgfDzn/88fvvb32bVqFR47LHHcM8992Dx4sWYOHEiVq1aBa/XizVr1vR5/BNPPIF58+Zh6dKlmDBhAh588EHMmDEDTz75JADVwvH444/jZz/7GW6//XZMmTIFzz//PM6fP49169aZ3h8S0PIMobJZp5xnhIY1k6TbsdZPu02Al5B1BKBTVpRmGCiLnk2CIPQ59wNq4lizyee5n2o1OsLJpKnkp6JglaTxTAtddmjF4GjMpSStr/rmlXBYDpUQJDcZL8Tdu3ejvr4ejz76KGbMmAEAeOmll0y9Zj7P+9oY6o7EIMvkvDTozMGaPEvskgCSS8fTMG4QXG8o9hNQxzAptPtKUv9Cyrv0QmhUjkyHjB+BzWZDR0dHr01HcXGx6W7Z0WgUu3fvxrJly3q0Z86cOdi+fXufv9m+fTvq6up6fFZTU6MvKidOnEBjYyPmzJmjf19aWopZs2Zh+/btuOOOO3qdMxKJIBKJ6H/7fD4AarUmURx4oGnfD3ac0RS67QhEJHR0h1HiJmNF7QpFAQBepy3t/mZ6n7zxkd0VHPxZGIkmYHodArHrFjrV5xiSyI2ndn8IgJpPJRYjt3gUuVXFVnt3CKLoTeu3mY6lzmBEvzap++t1qBsjX4js+AUGv082mw3Nzc095n7tWD73mzv3+4LxudRFbn7xOtWx2BmMErumoii6UFpgV8jNpXHFeWcwQuyaHQF1Ls10fsl0PBV7HOgKxdDuD6GCkOm3Mz5+CzOQBTLFG5e9wwTXRyCh8PE6CcoCLlUWyPRdTXUsiaKIl156CS0tLbj44osBAKNHj077eqnCyrwP0Jn7vfHXU1GAzkCYmKJAk31IjmFtvQlJ5K4JJDbrJGV3TZ7tCGS23mQynjq7Va+9YreDWD8FAB6nDWFRRnt3CIVOMor/rvh6U2AnN/drsjvxvWeW600mYymdYzOesZYsWYIvfOELWLt2rV4GGwDa29szPWXKtLa2QpKkHtcFgKqqKtTX1/f5m8bGxj6Pb2xs1L/XPuvvmAt5+OGHsXLlyl6fb9q0CV5vahth0snUnYodgIDXt2zFRUVkrnnkhA2ADWeOHcb6YN/PZzDSvU8n/ADgQHOHj2jS4q6Aen93bX8XJzxkrnnunADAjpBEbjxp99cuR4ne31hIvb9vb9uJzsOZKTbSvUf7T6rjt+XcaaxffzKja6ZLZwQAHOgKRfH3v68HIW/nHvR3nz71qU/hpptuwtKlS1FWVgYACAaDRNqU73P/8bPqWDx5+GOs7yBT+e9wuzq/nG1sI/auhyVAVlTxZOc/3gEp58muFvX+7t7/ESrbDw56vBF82Kbe31ioO6v7m+54ssvqXLrxrXfwSXHGl02L+qPq/T138ijWryeTG+dMNwA4EIqRlbc6utX7u2fHP3BuP5lrNpxRx9LHnxzHeuloxucZ7D796le/QkVFBUaOHIk33ngDAHDkyBHMnDkz42sOBCvzPkBv7rcLdkiKgP/3+iZUuNP+eUacPq+O4SOHDmB9M5lBXN8Rl2cJvq8xGYjE1PXm/Xff0o3VZtPRrM6Hew58jKrOzNfzdO7Tnlb1/opBsnsjF+wIQ8Drb2zFqEIy1/w4vt4UOBRiY6khCAAOtPuDRO9vi099V/d9sB0tH2d+nnTuUzpyf8qv1IVeTN/4xjcQiUQwefJk3HTTTZg2bRpkWcaLL77Yy5qQqyxbtqxHX30+H0aPHo25c+eipKRkwN+KoojNmzfjlltu6VXZyUyeOrYNnc3dmDJzFq4bN4TINdc27wLa23HtzKmonTYird9mep+ONHfj8YPbINlcqK0lUyUlEpMhblcFr8/feguxMta+D87ir6c/RigGYuPpnSOtwME9qKooQW3tbNOvp/Fq2x6c8Ldi/MQpqJ05Mq3fZjqW3v3LR0DDOUydeBlqb7gk3SZnRHckhhV73oSsCLjplhoUEAxVvPA+XTj319bWYvXq1Vi6dCluvPFGTJ06FaGQ6p1x7733EmsnTWjN/c+c3QF0duFT18zELROHZdT2dKk82Y4/HN4Fu6cQtbXXE7lmQ1cY2PkObIKC2po5erVDs9m/4TC2N5/C8IsuQe28y4lcM7TnHPDJR7h4+FDU1s5I+/eZjqdVJ7ajvdGPyTOuwWcurUz7upnw1z/tBVpbcPW0yai9ehSRa55qD+KRA+8hJJFbH2VZwQ/eV4X2f5p7M4YWk9EOtGw/hdfPHkb5sBGorZ2S9u9THUsrVqzQPYR8Ph8qKyvxr//6r/jHP/6RadMtA625f+X+t9AeEHH17E/j8moy2uH/Or4N8HfjM7OvxqfHk5kjhp/pxKr6nQgTfF/buiPAjrcBAF/4p1tht5Gx7n206RNsazqprje3pr/eZDKefB+cBY58jItHDENt7fS0r5kpTxx5D77WIKZedS1mja0gcs2/v7QPaGmGx05uLDX6wvjVh+8gIttw661zieXFWvrBGwBk1N7yWYwsK0j79xmNpbhXZyqkrGy67LLL8OCDD+I73/mOfvO+853vYOHChfjLX/6CgwcPorCwEKtXr9ZLoppFZWUl7HY7mpqaenze1NSE6urqPn9TXV094PHaf5uamjB8+PAex0ybNq3Pc7rdbrjdvYUIp9OZ8sNK51gj0OJJg6JC7LqBiJrpr6zQk/E1071PFUXqy+aPxOBwOIi88F1JrtXlRQXEFqzyInUMhiWB2HgKiPHk4AVkx29pgbrpDIoysbEUiKrjt7zQTayvZQ4HbAIgK6qXRwnBe6yh3acrr7yy19z/3e9+F1/96lf1ud/hUJeSr3/966a2Kd/n/u74XFpelPlcmi7lhYm5lNQ1QzHV1b/ADrhcLmLXLfWqzzQQzXx+SRd9LvVm1890xxMNWaBblwXIzaWaLBCVBQg2O5Hr+sMitIjiiuICOJ1kjAVlhao7tT8qmTqWSkpKcOrUKYwfP14/rrOzM+PrDQYr8z5Ab+4vLXChPSAiGAOxd8evrTdZyO7pUlGkjuFQjNz+KCSp4VZFbgc8bjKGDSCx3nRHzH1fkwmKcvza5NZVACgucAEIkt17xmX3Aju5sVRRpMrIMVlBDDZ4nea7yYVFSS/6pa43ZMZSOtdJOWlPXV0dfvzjH2P69Ol499139c/LysqwePFiPProo3jggQdMVzQBqvA5c+ZMbNmyRf9MlmVs2bKl3+vPnj27x/GA6i6mHT927FhUV1f3OMbn82HHjh1E+kQKmqWdSZaO1/opyQqCUTJlLbR+FrkdxBRNQHICVGKXTKoqRFYJklyymxQ+Cn0VBCFRcp5ykvBU5v5///d/J9KWfJ/7fTQr5lCo0EayigxAa30k/0zV65GvcEUnOW3iWpqyy2y08eO0C3A7yOTGBJLHrzHPtKOjo8/Pn3zySdx+++1YunQp/ud//geAuTmb8n3eB4x/tqmgXYtGQv+wZH4OSA1aczCNgjc0Ktqq16O39yT5WL0uu77/I9VX7TqCABS5LF6NbtmyZTh8+DCmT5+Oz372s7jzzjtx7tw5M9s2IHV1dVi9ejWee+45HDp0CPfddx8CgQAWL14MAFi0aFGPZILf//73sWHDBjz66KOor6/H/fffj127dmHJkiUA1M3dD37wAzz00EP461//igMHDmDRokUYMWIE5s+fT6OLpkCjhCqNzTqdF57SghW/HslSsTSqlAB0Nkg0qtElX490ueML4XM/O1CpDhRfM6IxGWGR7GaddBXfEorzC3Hhn4Linsbm1Wm3oSBeRIPUc03e0JEKowCMV5ZedtllWLVqVa9N/5QpU7Bnzx5cddVVOHPmDADg2WefNeSa/ZHP8z6QmB9Iva+yrMAfoVBdOd5PGQIxQzGtsvElFGQ8WvJsCY3KeyHNaEWugqNqKCarGNauU+RywEbQ0SEd0jK5DB8+HM888wx27NiBs2fP4vLLL8dDDz3UozIDKRYuXIhHHnkEy5cvx7Rp07Bv3z5s2LBBT/Z3+vRpNDQ06Mdfd911ePHFF/H0009j6tSp+POf/4x169Zh0qRJ+jE//vGP8b3vfQ/f/va3cfXVV6O7uxsbNmyAx0Mo0zMBaFipaVgzk194YgImrQWrgLxnEw0PC4C8wJV8LZIbJCC5LC5dzyaAz/0sIEoyQnFlj6YoIEGRO3EtUmPRFyYvJAJ0PJvoz6U0FGt0vLhIW5qt/kz782oF1HCyhQsX6gqeVJNjZ0q+zvsapOXZQDSmh4KSVIR7nDY4NENxhKyhmLzxlGakCZ2+kvWQ1iraErskgERfuwhtymjtUdIho5Vw5syZePfdd7F27Vr827/9G9asWYNHH30UX/jCF4xu34AsWbJEt1JcyNatW3t9tmDBAixYsKDf8wmCgAceeAAPPPCAUU1kDtICZnIsKfnNugOdQZG4dpnWJB6WVGsUCegpYOILVoi8dYSW1YvkZnAw+pv7b775ZqLtyMe5P1kgTVYAmY3dJqDI7UB3JAZ/WCSS7FgTSD3EhUSank2UPCcJCcSKolALvy5yO9Dsj6Cb8OaVeJi5wUq1ZcuW4Rvf+AZ++tOf4rOf/SwWLFiARx55BCNHplecwyjycd7XIK2YoBUKqhmKO4Ii/IQ361ZXDqcCLXmWThgoHQ/pYrcTQIhYX32UomrSIasZZOHChaivr8fdd9+Nu+66C7fccotR7eKYhC5ME57EAbIbJCA5JCI/FiwFgp4Qz2wSYQK5H+OeeK6UQgZJuqylyIVz/+233067STmPJrh4XXY47OSEf4B8vgU9ZxNpIZGGpTlCPrQMIL/RCUQlyBQ8JQDyIYO0Q6+DUQmiJBtyTpa8WvMZXZ4lZGhLlntIhoICib0CKc8mGqk+kq9Hw9uHVl9JzcFhUUI0Pgd6CRut8mW9SYeMWhaNRlFfX4+DBw/q/woKCvDmm28a3T6OwSReAsKxpISTZgPkvWBoLVgepx1OuwBRUi3HFcXpl71MF9rCNCnPg+QFi7hijbAl6FxnCAfOdqGqqP/x29/c/8477xBpYz5Dy/0diM9pXWFi7x0t93eaoWX0LM1kFYgOmwCPk6yytNhNOqSejpdzUXIy9HAM5YXGVdZixas1XyGtmPBTMigC8X1KB7l5mEaqD6DnfkxRFCJKPd1QTNiSQ9pgpfVTEABXjntI04qqSYeUR9vKlSv1zcWxY8cQi8VQWlqKSZMmYcqUKaitrcWUKVPMbCvHAMi/BHRCBADymnRtwSI9iQPqJNMWiBLfOOR6RYvkBauQcJUH0l5c7x9rw49e+RCfHj8EXx6a+DyVuX/cuHGYO3cukXbmK7Tc35OvSey9i/eVeILw+NwdFmWIkgwnAQ+yxHMl7e1DVhZIzmlI2lOC+PiltHlVk6HbERIl+A1WNmksXLgQ8+fPxyOPPIK77roLM2fONPwanN6QDkOiZTwFkpXDhOVZSnk5RUlBWJRRQEArQtuzifTes8jtgE0gGx1AXl7KIc+mV155BZMnT8aiRYswefJkTJkyBRdddJGZbeOYAHmhi96CRTqZNK08Deo1HWgLRIktzonJLbdDP3osWLQ88yjHfacy9/t8PiJtzGdobWCBZMUnac8msgnCL0yGXmHCZv1C8s2ziUYSU1r5bqjIPQUOhETJ8HWDe7XSJaEczv3QHOKGYkqb9UKXHTYBkBV1fiShbKKV34d0gnCajg7k9yn09p6pkvJTOHjwoJnt4BCCvAKG5oJFdrNOs6+6xw/p6h2EvbiSXclJuB3TDV1iI+6bz/1swMJmnVyuPzo5mxx2G7wuO4JRCb6QaLqySU2aTas6UD7JAmpfyScIp9PXJl/EELmHe7WyA3nPJvqye64bitVk6E50hUT4wiKGlZhbBVGWFX0OpLfekA1lLiacKxigEYFBL6omVdhtGccUSogrYOhtkEjnvKEVDgEkcjX4ieWnouTZFJ9MJVlBSJTgNTm0jWboElXrCJk885w0oPXOqdckneuPTjU6QO1rMCoRERQjMVnPCUer2iXxnIbu3A/LyZWNOvdqZQfyCcLp5YGhZWijk+7DEVc2md/X7mgMipK4LkloPdMiisaNXM8XnA5c2ZRnJOeBIeEZQjOWlHTOGybcNglYbqUk6wjp51rgtMNuEyDJCnyhmOnKJupJmUHOm0R/V90OIEjkkpw0oOktQauyJ+kE4UDCM4SEYo1mTjjd2ycagywrpocJ07S+5lfIoHFyD/dqZYd8CgUt1qvRkd2s05Dz1GuGiDxX7Rouuw0eJ9nFtZR4KH7+5Li0QjU6siVBONTRBqMkKwhGzXdfYOGFJ2YJitC3BJFQTCSHIpB+roIgEPVYoxUumHxNYl6IEXrvKmdwWFB8ks7153GQzdkEkPX+1YVEijnhFIWMkYJmXgnSYQ10DU9k5R4OGUinwKDq1U3JUJzr+xSa8qzWz7AoIxqTTb/e/8/emcdHVd39/zP7ZJtsJAQkiIAaXFCKiiCuIGJs68JTq6WLPoi1gn0Un+dXad3QqrVabfWh+lit1haktWqrGJEIKIoICIbdyL4kJCHLZJJMMuv9/XHn3pmQZe7M3OWcme/79fLVMrlz55xzz/2e7/me72KkvqT//GW/Gh0ZmzIMyTME0OdF8Bj5wmdIkkFA3w2StCg6rGY4rPq7HuhZ1cLQiiwGzV8jNkhEfFioRqd3/jsjPJv0TMRrZOi102aB3SqqgLp4cRm4PuYZdqqe/usGoQ+SgaA7EEIgpN9m3Yj3VSrUkAmeiHoaJowq7AOcWHxDT909/fUlHqrRkbEpw9DbMySTNussuM7rkQBVPjEwoJ+AvlUtmDjx0nmDZESMOxEfQ70ldNysx4bpGpHvUs98C0a7v+vp8WNoDhi9czYZmj5A3/xqhD6cWClTazIlZ5MgCEzkWNPHk9Y4A4zVYkZOpNqeniGDRiQI133v6TNu76kUMjZlIHp6hkQNE+ktxGOrChnriquHt5qx4VZ6eqwZ6oobY0AMh7UPJzKyr0R8jFQo9FT+Yw3mhng26WqAMfadyxTDmv5hdEbngNHvkILQh9jNup7va7rnWOsOhBCK6FfGRmDo+EwNXm/0iaqJ7FOMSIFhkGcTy1EJZGzKQKK5YNI8T4OO7qk9gTCCkQXL0JwUOno2GVX5QM8YdxZClwRBTOKrNUYbEYnBybQwXbvVDKsBGko0jC69T5qBzPFsin2mgqCt4T4UFtAVyYdp6LuqU2EJQj/03Kwbqefpqc9K74nFbEK2Xf/TDT3fV6N1PD3zkEYL3hgbaaL1QbHo6EA5mwgGkV4+fTbrxnv7dPqC8smFVkjC02yCfPqkJ9EwAR2TDBq2YOl5OmKcwtU7p4qefSVjE4sYm2DZCG9CY+ahEV6i+YaFJEtVTPUIqTfOU0IKQQqEBPg0Tk7bGfOOGHnIRp5N6UfU44dy3qhFrMFf6+rc/aFniLrxYdt6etIat0/R86C4yx+CtL01ygFACWRsykCiMf06bBwYqNAG9FYAtSB2I2jEgiW5imrdTyC6UBjnimuAYc2I5DHQr7JQTyAkVwhh2RU3k2GlGp3WniGyLDUg1wJgTFiD4SfNOhjWjDSW5tgtMEGct1qvG9L9HVazfFigJ3oXRiH0Q1+vS+MO2iTZ3+UL6XZQbJQM1jNk0GOwB4yeuruRh6d6HhRL66rNYoLTxq5Jh92WEZqhazUvA2NJHVYLHJEXXnsF09hNg+ytpqfngUEGmDwdN4NGejbF/q72C5Z4f5MJyLGTsYk1xCSmxp80h8ICvJEQIa0w3gCj5/pobGJPad1Id8Oa2WyS839pbVgzsiiK+Lv65gsh9EOv4iixRRoMqUYX8+5oXfTGyIrZgDH7MaNkk55RCayEqGt9UBz7TI1wdFAKGZsyEL0s6YIQu2CltyA3soQ1oK+3mtHKtBF5RoxesLTeDMqV6BxWmM3sLliZii8YRiAk5YTTfy5m2y2wROaF1u+dJF+Mqoqobw4Ngw8p9DxVN9gjVhpirXUBow9jZGOpDqEqhL7oFYYUa+AxQjY5rGbYTBFPRM0368bKJX1D1I3WZ/VM4WK0F5deB8XGpjVRChmbMhC9wgS8/pgqD4YpXvoo04bnGYm4HfuCYfQEdPI8MDjMRdeKLOluLKVKdEzTOyec/u+dyWTSLV8IK++cHnmMjE7sqZcXl9FJs4FoZUO9dAHjDmP0C3kl9EUv47CkWzmsZjisBpQERdQ4rN/7anSOQD0rDBp7KK61Z144LMjJ5dP9oNjow3+lkLEpA9ErAar0EljMJmTZjFmw9A5DMuqFz3VY5ZwUuhnWDF6w9PDMM/rUQD9jKVWiYxlJVhvpeaZXSXWj52K+jnmMjA5r0Cssx+ik2QAgnXdpvaljZc0IhgV0a3zwROhLpuizQKxxWJ/NunH6rJ4Fb4zOT6WPDtHlD0KysxtXaEQvfclYT1qlkLEpA9Gr+kHsiYFRsaR6xc0arWCazSY4dV6c03/BMr7Kg16VI6O51dg+HclUjEyuLKGXYYIVz8mOnoDmniHRjY7R+e/0OXhy2oxJmg0AWRZ9DmOiIfUGeXDZoiGvehhMCf3Qq3S80fosEDUOZ4pnU4cOVbON7ms0KkGfPFx2ixkOwxwd9PVClPYKrELGpgzEpdumwdgQgdjfTvfTEQCysUnr52p0yJVeMe4sVHkgzyYCMN6bENBReYrc36icTZIBJixADv3SCqNDBnVLYsqAsVT2bErzMFCTyaRbCAehL3oVRzHaKAEATotO1SMNz+0TUzVb42ToRu/JdDeWGujto9c+xUOeTQSr6LVgRUMEjHsJdD+NZ+IkSGNBbvDJrV4x7ixUeYh6caV3aCQxOEZ7EwL65UrzGHyq7rSZYbNIniF6FZYw2rMpEzav4v9q7uVscK4QQN+KioR+6FW8QMpXZ6Q+oFeONaOLNPSqmp3mHux5eukQDHjq61UVlIWDHCWQsSkD0c/iysAGyYCQQaPQr7QzG3lGumIS0GsBC94++i9YbJ+OZCpGFyAAjMgXYkxfRc8Q7Tfr4bCATr+xRl69Xf2NVP71C8sxXvnXKy8noS+y7q5x8QIWDop1OzxlICpBj7U1EArLOdyMT5qd3qHM4m/rEzJotCetUsjYlIHo5RnCwksg5f3QT7gZqUxLOSnS20U1dow7NXyuLMxf/UIGjVcuiYFhaQOrl3wxMgeBHkaYDl80ialxydD1TWJq7GGMXmE5xvdVr2T+hL7oZRxmQQbrlhZCNoQbeSiu/drau0iDUcULdFpvGPDM00tfYsGwpgQyNmUg0gvY5Q8hGApr9jssuPfpJtwYMExEF2ft+uoLhuALinPGqOdqt5rlHEpa9pUFbx/9QgaN9zwgBkbawOYbqDzpLUtZ8IjV8r2TlFAjy4tLY9wTCMMf1E4XMDpXCKBfNTom9B6dwq8JfdFDLgFsyGD9Dk+N1931SJcgyaVsuwVWi0E5SCP97PQFEdYwKoEJg79OVQZ5SYFBxqYMRK+EdCwsWPoltTXeMKFHmIB0b5PJuGpRgD4nt0bH8gP6hYEaHRpJDI7ReYxifzsTXOB1kS/dxiuJuTEyXEsZw0ISU71ywLAR8qrPIQWhL7H6rJaVMlnQB7J0K3hjvBeMHgn9WdqPCQLkEHItYOFwg1Jg9IaMTRmIzWJGVqQcpLaGCeOFuN4JltnI2aTlBkm8d67dCrPZmKTZgD45KdhasNLfWEoMjOx5xoRbePrLUj36ysI7Z7WYkWPXTxfIjGp0xveVEoSnJ9KcCoYFOf+OFhidKgEAJLGYCV5cehTf8DCgzzptFth1SIbuYcDbR299ifWoBDI2ZSjSi9CuqWHC+BM++cRArwpKRlbvkN2O09tbTfx97T1+YqvRGYVLh36K9zd+cSYGxsOAQqGHQsxCElNAn76yoiTqkZxWXjcM9IaVczbpVkDD+Pmr9UaH0JccuwXSGZ+2hnDjdR89PBEDoTC8fnG9MXRtzdLhcIOB0DIgdm3Vsq9SzjEWZDDlbALI2JSx6JIAlYGTWz08m8JhQQ5HZKK0sw6uuEYbJaInt+k9f6UFS6+cKqwvWJlK1LPJeFmq5ZoRm8Q010hFMUt7j0JWlMRoX3U4VTf0MEb8X90KaLDgEUthdGmFyWTSpXw8C/qAZBzWK2l2LhP7FD2eqcG6u44hg8aGRupbjc7IfJ5KIGNThqJHLhgWTm71UKS7/NGqQmwkQE3v0I/Y30/3BStWAdLWi8v4DRIxMCy4wOvxzsUmMbUZlMQU0MdzkoUwc0CvvrJzGKNlYZRAKIyegHhvIw3DehzGEMaghyGcifdVhxykzKw3OlTNZkGfBYA8HWQTC/sU6be7AyEENFxvWPAEVwKXxqbW1lbMnj0bLpcLBQUFmDNnDjo7Owe9/q677sLpp5+OrKwsjBw5Ej//+c/R3t7e6zqTydTnv2XLlmndHUPQs/qBseW6xd/2B8PwBbWJcZeEuN1ihsNq3CuVpYtnk/Gb3tjfT/ecKhazSfbw0KqvsZ55Roa8EgPDQjJpfbwJjd/kANH3QFvDPRvvnB554VgKywG0K4zSwYpnnk5ltwn9yXPoaAhn4H3Vw1Pf8PVGh8plLOizQOzaqkPOJgYO54DeHnRqwsp6owQujU2zZ8/Gzp07UV1djeXLl2Pt2rW4/fbbB7y+vr4e9fX1ePrpp7Fjxw689tprWLFiBebMmdPn2ldffRXHjh2T/7vuuus07IlxZEr1g97VdrR54WOFuMlkXNLsqNtxJsR9a79gsVBVCNC+qkWXPwipCq3RLtZE/7Dk2dTpCyKkUdliFg4oAH0SLLOwoYv9fT3CcoyUpRaz6MEAaGdElMbQyPLiAHQJtSKMQQ/jMAtRCZInYk8grJlnCCse3XpULmNhPwbotLYyUFDFajFH1xuN+ioXbHJYDV1vlMC2Kawfdu/ejRUrVmDTpk0477zzAADPP/88Kisr8fTTT2P48OF9vnPWWWfhrbfekv89ZswYPPbYY/jhD3+IYDAIqzU6DAUFBSgrK1PUFp/PB5/PJ//b4/EAAAKBAAKBwSeX9Pd412mFVIGmrcunWRtkF1Vb8v1UY5xyHVZ0+oJo7ehGvkP9F7Kts0f+HaOeZyAQ6FVtR6t2uL3ifM+xWwzrq/j74nNs7/Yrbkeic8nT7QcAZNtMhvY1z2HFMYjzTIt2SPPXZjHBghACAVEpSeS3jByfdKdXElNDczbFnNT5gprkCGBGIdbD85cBbzVAp8p7DBRbAERZ6vWHNFP+mZm/OoRaEcagdQqM2PWGhTA6QHyvinLsqv8GC8n8AX3WG3YONzKj0qv0+15/SLO+srLeKIH9Fp7A+vXrUVBQIBuaAGD69Okwm83YsGEDrr/+ekX3aW9vh8vl6mVoAoB58+bhtttuw+jRo3HHHXfg1ltvHdBb5YknnsCiRYv6fL5y5UpkZ2crakd1dbWi69TmeL0ZgBnbdu9BVXet6vcPC0CXTxzbDZ99gl0pyrdUxskqWACYsGL1Jzg5N7V29MfONhMAC8K+LlRVVan/AwqRToI6ewJY/n6VXLVETbYfEOdNU90hVFUdUP8HFHK4QRzzbw4cQVXVoYS+q3QuNbnFebPtyw1o+zrxNqpFoFtsxyefb4S7Vn2PknovAFhhN4XxwQcfyJ8n8s55vV7V20WIsOIq7bBa4LCa4QuG4ekOaGpsMlohlg0wOpSiNlpR1KcaHSt9taKxw6ehsYkRzzydKiER+hNN/q7N+8pK0myLSTzU7PKH4OkOaGRsMt4DBtBpvWGgOrj4+9p7XcphdEYXMnLa0OjRbr1hweNdKdwZmxoaGlBaWtrrM6vViqKiIjQ0NCi6R3NzMx599NE+oXePPPIIrrjiCmRnZ2PlypW488470dnZiZ///Of93mfhwoVYsGCB/G+Px4Py8nLMmDEDLpdr0DYEAgFUV1fjyiuvhM2m/0Q59Ml+rK7fi5Lh5aisPFP1+7d3B4Av1gAArrtmZtK5jNQYpz/u/xzuxk6MnzgJF40pTuoegxHYegz4ejvKhxajsvK8+F/QgEAggKoPReOAABMunXalJgrvx29tBxqO4dwzT0flxaeofn+lBGrq8c8DO5BTOETxmCc6l365eRWAEGZOuwwnFyszHmvB2y1bcKCjGWPPGI/KiSepfv8vD7UBWzdhiCsHlZVTk3rnJK9OQn0kpSzH4NAcQNxE+zp92oUkM1OhTY8wOjYMa1oX0fAFQ/AFpaTZRvdV2wpBrOThiq1i6guG4LBa4nyD4AWtDYmSXMqyGZs0GxCNXV06eIYYL4N18GzyMWII13ht7QmE5MrNRusRWhuGWdGXlMBMC++77z48+eSTg16ze/fulH/H4/HgmmuuwRlnnIGHH364198eeOAB+f9PmDABXV1deOqppwY0NjkcDjgcjj6f22w2xZu0RK5Vk4Icsd2dvpAmv9/dIb4EDqsZuVl9xyhRUhknSbh5A4I2fZWrz9gNeZYSNjNgt5rhD4bhDQJFGrSl0y/2tTDHaWhfC3OdAICuJOavkrkUDIXRFXElL8rLMrSvBdniiZ43ENZm/gZFbylXVu9xSVSOEdrAyukrIG6imzt9mm902FGIM8HVX5/NK2B8ElOp6lO6ezb1rmIahCOXjE3pgtZhSNH1xvjtoctpRaNHu/WGlc26njmbjH6uWodtS/c1mYBcuxWhkHGhxHqtrSzohvEwXppEuPfee3HLLbcMes3o0aNRVlaGpqamXp8Hg0G0trbGzbXU0dGBmTNnIi8vD++8807cDdKkSZPw6KOPwufz9WtU4hmtq3mxkug1tg2aLVgMxc2Km0F/2nseaF1NMbZakfF91Tb/BitJ34n+YeX0FYiWLdZOUTQ+kTQQfRf8wTB6AiE4bepv1llRFLXevEr3zXVYYdEitjsBtN7osKILWMwm5Dms6PAF4ekOYEhueumvmUxU90lvg39sG7Tuq+EyOCtaNVur9Saquxu93mj7TOW9p8MKs9mEkDZFyBWhdZVBVg6slMBMC0tKSlBSUhL3usmTJ8PtdmPz5s2YOHEiAGD16tUIh8OYNGnSgN/zeDy46qqr4HA48O6778LpdMb9rZqaGhQWFqadoQnQ3pLOihUd0L6MNSsLFiAK2OZOv2bx0KwkpJPmldYnBk6b2XBXcu3d5vmJ+85E5Io5LMnSNFf+c+1WmEyAIIh91VL5N/q901r5Z8WACMSEDGq2PrKxoRPbIBqbtMzFRehPVPdJ/w1s1BMxvfsau9509AQ1Pdwwuq9RGaz1gTgbMhjQ/nDDaB1CCWzXyuuHcePGYebMmZg7dy42btyIdevWYf78+bjpppvkSnR1dXWoqKjAxo0bAYiGphkzZqCrqwuvvPIKPB4PGhoa0NDQgFDE7Pnee+/h5Zdfxo4dO7B371688MILePzxx3HXXXcZ1lct0dziytQLr7VnExsLFgDkaVyFhpWQnmhpZ437ydD81TrPCAvzl+gLW3MxMzY65ohnCKBNXwVBYKavmj9TRirRAUCeQydPCQZkqR55xwj9ieoDmeDZpLVsYmNtNZtNyLVrd4AqCAIzHtJ65Rwzeo8CaO/UwUqkiRLYb2E/LFmyBPPnz8e0adNgNpsxa9YsPPfcc/LfA4EAamtr5QpJW7ZswYYNGwAAY8eO7XWvAwcOYNSoUbDZbFi8eDHuueceCIKAsWPH4plnnsHcuXP165iORBOXZYLSpa0BhqnF2aGxYS0yX7SoRJUI0rzyh7RxO2YptCyqcGltLDV+/hJ9kavIMKA86aUosvHe2eDpCWqyRvqCYQRC0VxpRqL1wRMrlehi26B5GChD76pWhxSEMWidAoPF9zXdPfUBUWZo5YnoC4bhD7GSNFvbFBisHOIAmWVYiwd3nk0AUFRUhKVLl6KjowPt7e3485//jNzcaE37UaNGQRAEXHbZZQCAyy67DIIg9PvfqFGjAAAzZ87EV199hY6ODnR2dqKmpgY//elPYTZzOURx0brcMUuhOdrHfbMk3LRbnMNhAR0+Nk5HciJux4A2z5WlcAjtN4PshLwORmtrK2bPng2Xy4WCggLMmTMHnZ2dg36np6cH8+bNQ3FxMXJzczFr1iw0NjbKf9+6dStuvvlmlJeXIysrC+PGjcMf/vAHrbuSEB6GwpC0zh8mv3cOdt47LfoqyWdzpLy3kcRu6ARBUP3+LCnEWm9eM+mQgjAGrZ8rKx4wgH6etEzJJg2eq3RPk0nUnY0kNpRZi/VGPpxjYP7qlcyfhfUmHulpSSHicqJniNqwFJqTKa64gLbx/B2+IKS1wWjDhNlskisbadJXFjdImrviGt/XwZg9ezZ27tyJ6upqLF++HGvXrsXtt98+6HfuuecevPfee3jzzTfxySefoL6+HjfccIP8982bN6O0tBR/+9vfsHPnTvzqV7/CwoUL8b//+79ad0cx0ZxNxj+fTKqu4tJwU+eJ8YY1mYxOmi2OdTAsoCdSWVVNWFKINc855mOorxRGl5ZoXzCEocMNh16GNeP7qqXHmuzBFUmabSSumPWmW4O9Z9S71PhnqpejAwt7z3gY/zQIQ8jROAEqW94+Om2QGOhrroalnSUlxGkzw2E1vpSyy2lDR482bsdsbZB08mxioK8DsXv3bqxYsQKbNm3CeeedBwB4/vnnUVlZiaefflrO1xdLe3s7XnnlFSxduhRXXHEFAODVV1/FuHHj8MUXX+DCCy/Ef/7nf/b6zujRo7F+/Xq8/fbbmD9/vvYdUwBLSSBdWm90GHrvtMyVxlJ58Ry7BWYTEBbENTJLZU8rlg6e9PISZcIzT+PCKIQxSHO40xdEKCyoXuGRpdAyraufspgPUQuvS5YOFLPtFljMJoTCYh6pbJU9rVh8ptrnQzT+XY0H+y0kNEFKgOqJbNZL89S9P4uuuFpXo2NBkGtpmGhnyIML0HZxZskAo/VpPA85m9avX4+CggLZ0AQA06dPh9lsxoYNG3D99df3+c7mzZsRCAQwffp0+bOKigqMHDkS69evx4UXXtjvb7W3t6OoqGjQ9vh8Pvh8PvnfHo8HgJgvMBAY/DlJf493nYTbK/5Ojt2k+DtakW0TnaHbvX5N2iIZJrKsiY+T2uQ5xL62dfWo3oa2zh4AYhWiVO+txjjlOa1o7w6ipaMbhVnqGpvaI/M3124x7FlKvyt1rb07/nuaDNJalG1j4F21S++qT3FbkplLRvcz04jdWHb2BJGfre66zVRomYaHp7FJs1nQfbQ0hLNkQDSZTMhzWuH2BuDpDmCoK35l+ERgSnfX+nDDx867Gg/jnwZhGFomQGXphFp+4X0auzIycEqtR9y30cnBJbRdnNkxrMX2UxAE1cNuWFqcB6KhoQGlpaW9PrNarSgqKkJDQ8OA37Hb7SgoKOj1+dChQwf8zueff46///3veP/99wdtzxNPPIFFixb1+XzlypXIzs4e9LsS1dXViq47VG8BYMKeXdtR1bhN0Xe04ptWEwALjjQ0o6qqStV7B8OAPyjOwfVr1yA7Mh2VjpPatDSYAZhRs7MWVR27Vb33lmZxHAPedtXGMZVxsoTFObZyzVp8o/LB0+694jjWHdyLqqo96t48QbZv2QjAitYOr+rzFwCa28VxrNm0Hsd3qX77hKivF+fY7n2HUFV1IKHvJjKXpEI8hD44rBbYrWb4g2F4egKaGZtY0PO09Azx+kMIhaUiDcbrPlrq7iyFpwOiXu32BjSNwGDBgKhXjkCWdXcJ9ltIaIaWgpypEwMNPZuCoTC6/GLcMUt91SS0jKHcMYC2Hj8suadKbQhFYtzVdjs2soLSfffdhyeffHLQa3bvVnejPxA7duzAtddei4ceeggzZswY9NqFCxdiwYIF8r89Hg/Ky8sxY8YMuFyuQb8bCARQXV2NK6+8EjZb/DFfvO9zoKMTl025AFPGFCvrjEYUH2jFy7VfwuLMQWXlVFXv3dLpAzZ8AgC4/ttXIxwKJjROavPNqr1Y27AfpSedjMrKcareu33TEWDPbowaPhSVlRNSulei86k/XjywHq0NHTjrWxfgklOHpNSeE1m+tAY43oTzzjkLlReUq3pvpUhjNPOKS/DE1s/REzLh6quvVtVwLwgC/nvjRwAEXHPl5RhekKXavZOh88uj+PehXcgrLkVl5bcUfSeZuSR5dRL64XLa0NzpS3sPdi3z5kljZzWbkKVyGpFk0HI/xlKREUDbCuFy2gEmDIjaHYiLnnnsvKvxMP5pEIahpWeIhyFLemzOJrU9Qzp90bFjwTCRq2ncN1tWdC2TFUcTvRo/f7Ns0Rh3T7cGMe4GGtbuvfde3HLLLYNeM3r0aJSVlaGpqanX58FgEK2trSgrK+v3e2VlZfD7/XC73b28mxobG/t8Z9euXZg2bRpuv/123H///XHb7XA44HA4+nxus9kUb9KUXitVgCzKzTLE6BJLUa64gfb0hFRvizcohlvlOa1wOuwIBEQ5nciYqklhjvh8O/0a9DUgnqjnZztUu3cq4ySt096AoHpfO33iYUxhrtPw+VsYmb9hAfALZuSqKEu7/SEEQuJzLcoz/l0tyBHDUzp9ic/fROUYoS8upxXNnT5ND9rY2KxraZSIRl8YXaQBiO5T0r26MhDNaadNCgx2DDAnFuJSMzdylz+EiGMeM891MIyXJoRhaOkZ0tEdFeRGIynSYUE0Dqn5YkqGuiybBTaL8cUd9cjZxIJ7NaCtF1cHQ6cjJpMJLqcVbRG347J89WLcA6GwXBHEiAWrpKQEJSUlca+bPHky3G43Nm/ejIkTJwIAVq9ejXA4jEmTJvX7nYkTJ8Jms2HVqlWYNWsWAKC2thaHDx/G5MmT5et27tyJK664Aj/5yU/w2GOPqdArdYl6FBo/F6WQDalssZpKOksn6oC2stTD0PoIaHsCy1JIvdNmhs1iQiAkngpLBTXUQJq/ZhNUvW+yaFmZljAWLRNnsxVGp91BsZEe3f2hZUEK1lIlaOrZ1M1OVI2Whbik+WuzmOC0Gb/3jAf7LSQ0Q8sqbSxVoHHaxBh3IKoQqkU7c5sG7XM2sbc4axj3zUBVISCq+Kk9f2PHjhVFpD/GjRuHmTNnYu7cudi4cSPWrVuH+fPn46abbpIr0dXV1aGiogIbN24EAOTn52POnDlYsGAB1qxZg82bN+PWW2/F5MmT5eTgO3bswOWXX44ZM2ZgwYIFaGhoQENDA44fP25YX2OJDdNlwQgTe1LnC4ZVvTdrxmxNqwMxJkujyn96F1sQDffabOpinylTnhIa5QshjMOlkWwKh4Xo4QYD640kgwMhQfX1hqVUCUCscTi98xgB2u49Wcqhazab5IMHtQ3DsUY1FtabeJCxKYPRskobS66MgPabdVY2SFrmp2JJCQG0PbllqXoHEN2Utnu1MZbmOqywMuCZNxhLlixBRUUFpk2bhsrKSkydOhUvvfSS/PdAIIDa2tpeCWufffZZfPvb38asWbNwySWXoKysDG+//bb893/+8584fvw4/va3v2HYsGHyf+eff76ufRuI2LnNwlzMdVghVdpWXZYy5E0IRN+5dDfAAFofPLG1bmh1IMOssZQ8m9KOaH4fdedwlz8oh+awYAjPsVvk9UZtwxp7cklabzJHn9Vkn8JQJXRAOw/p6B6bjWcaDz5aSWhCNGeTukLcFwzJpxDsvPBWHO/waebZxI6CKbZDixhhVvuaCV5cWhlLWXumg1FUVISlS5cO+PdRo0ZBEIRenzmdTixevBiLFy/u9zsPP/wwHn74YTWbqSrSPMyxW5gwBppMJriybJqULWZtLuoRRsfS+gio39dYTwlmnqtGeg+r/ez0BREKC7CY2T/9JpShlWySZLDdalZVd0wWk0n0DPH0BOHpCaJ08NobCcFS9AWgbTJ01tZWrQz+obAg59Fl5blq5SEdDU9n45nGw3jtlTAMrU6+YhfAXEZe+HyNLOmsCfEcuwWSR6Xagpw5zwONToIEQWDuuWrlZSHnyWGkn0Rvosla2Xk+GeMlmqVdGB1LOeEA7UKSOxnzlAC08+hmLedY7Gark7yb0gqtNuvSO8GKDAa0031Yi77QMi0Ec/qsVutNL09wtvqqvmcTWzpEPMjYlMFoVc1LzmPksDJzmhY1NqW3Z4jZbEKeRjHCrPVVqxOD7kC0qhArfdXes4mPBSvTYM3VH4iRpRp5hrDSV2l97PKHEAypnC+EsVNJrcpuS8/UwYinBKBd1SfWjKUOqwWOSK5KLbx/CePQ2rOJpdAcrQwTLCWSBqJj3ukL9vHQThXWdHetKqFLcs5pM8t5eo1Gq3yIrOWVjQcbT4MwBK08Q1j0ltB6s85SX7U6IWFvM6itUc1qNiHbzsYGKVO8SYjesFSJTkJ6/9M9pLOXZ4hPo1NJRmSpVso/i+ujdht19k6atcw7pietra2YPXs2XC4XCgoKMGfOHHR2dg76nZ6eHsybNw/FxcXIzc3FrFmz0NjY2Osak8nU579ly5Zp2RVV0MyziaFKdBKa6T4MJZIGelfNloqCqAVrcljr+cvKugrE5FvVKMclK+GC8SBjUwajlWcIa5sGILNy3mh9asDKgqVV7o3YZ8pKlQftFC723OaJKKx5wADahSSzJl9sFrNsbFa9r4wZETMlaTagfQ4NVuYvoG3BED2ZPXs2du7cierqaixfvhxr167F7bffPuh37rnnHrz33nt488038cknn6C+vh433HBDn+teffVVHDt2TP7vuuuu06gX6pGntWcTQ3NYq6iEaNJsNvrqsJphs4j6playiRU5rLW3GovzN9MPitnQdAhD0Ow008veS5BJxqZM2TjInk2+IMJhAWaVQjZZnr9aGYZZOgkiosjKE0OnV5KBJFNkqdcfUlWWBkNh+eSalY2Odso/e8806u2T3jmbgPTwbNq9ezdWrFiBTZs24bzzzgMAPP/886isrMTTTz+N4cOH9/lOe3s7XnnlFSxduhRXXHEFANGoNG7cOHzxxRe48MIL5WsLCgpQVlamT2dUQqs5zJr3OqCd7u72+nvd32hMJhNcThtauvzw9AQwHFmq3NcXDKEnECnYxEhftaokHT2cY0hfyhBP8Hiw80QI3dHaKFGQzc5LoJUrI4svvBZhAr0WLEYUEakdgiCW7FVr48by6Z7q85dBwxoRhUlvCY0Mn0wmp3Xa0OjxqbpGdvRKYsqGCqbd6SuDxlLNkiuzJ0u1TDqsF+vXr0dBQYFsaAKA6dOnw2w2Y8OGDbj++uv7fGfz5s0IBAKYPn26/FlFRQVGjhyJ9evX9zI2zZs3D7fddhtGjx6NO+64A7feeuugHs0+nw8+n0/+t8fjAQAEAgEEAoOPs/T3eNfFQ3KI9Hj9Kd8rlrYusV95Douq902U2HHKdZjltqnZpvaIsSnXZjK0r7HkOa1o6fKjpaMbgeL4xiYl86mlQ3ymJhPgNAtM9DXbGvHg6on/ziSCu6sHAJBrt/QZG6P6Lc1ft8rzV3pXcx1mVe6bzDglci07GgChO3kxCelU9QxhUOnS2pWRqc2gBmECsW74rFQYdNossFvM8IfC8PSob2zKhPkr95UhwzARhcWTZq1P6lgJLQNiDWvqGe6lfubYLbBZ2MhkIMmXLn8IgVBYtXaxKEu1MsCweEjh0iivoZ40NDSgtLS012dWqxVFRUVoaGgY8Dt2ux0FBQW9Ph86dGiv7zzyyCO44oorkJ2djZUrV+LOO+9EZ2cnfv7znw/YnieeeAKLFi3q8/nKlSuRnZ2tqE/V1dWKrhuIui4AsKLZ04WqqqqU7hXL9gNmAGY01R1CVdUB1e6bLNXV1Wg4agJgwY5vDqAqvE+1e9e3WACYsGvrl/AZ31UAgOAT27Tmsw1o3qU8Sfhg86nBCwBWZJkFrFjxQcptVANvEACs6AmE8e7yKqiVy/uLY+Jc6Wo73ue9SPWdS5aDx8U27T9yDFVVdardd/9R8V3d//VOVLXsUO2+iYyT1+tVfC07Wh2hO1p7hrCkYGaUZ5MGrvOx7qmsVBgEoidBYt4mddyOWXymmRQGSkRhsbxtJs1FLbx/WexnrIHE0x1Aca5Dlfuy3Ff1QzgY9MxjOIzuvvvuw5NPPjnoNbt379a0DQ888ID8/ydMmICuri489dRTgxqbFi5ciAULFsj/9ng8KC8vx4wZM+ByuQb9vUAggOrqalx55ZWw2ZKfJ0fbuvHbbZ/CJ1hQWXlV0vc5kTX/3A40HMO3zqpA5dRRqt03UWLHqW3LMbx/5Gu4hpShsvJc1X7j4a1rAAQw8/JLcOrQXNXumwpvNW/GoT0tGHvGeFR+66S41yuZT1sOu4GtG1HsykZl5cUqtzg5QmEBCzeJRo2LLp+O4hy7Kvfds2ovcHA/KsaMRGXlGQDUe+eSxfF1E5bsrYE9twCVlRfG/4JCXjywHvB04NLJ5+HS00pSvl8y4yR5dSqBHQ2W0B2tPUNYOuHTrFw3gwqmFlXaWPSwAMQ51tLlV9XzgMVwiEyqpkhEYbm6ipqyNBwW5ET/TPVVg5BkFt85i9mEPIcVHb4g2tPd2KRxGB1LIYN5DCcIv/fee3HLLbcMes3o0aNRVlaGpqamXp8Hg0G0trYOmGuprKwMfr8fbre7l3dTY2PjoPmZJk2ahEcffRQ+nw8OR//vgMPh6PdvNptN8SYtkWv7oyhiG/EHwwibzHBY1ama2+ETc8kV5jgM2ZifiM1mQ2GuEwDQ6Qup1iZBEGTdvdiVxURfAaAgW5xXnf5wQm0abD55A6KHVH52anNOTWyAvN50B6Fau6T5W5Tj7HPPVN+5ZCnOEw/BPT1BVX9fmr9FeerO30TlmFLYWRUJQ3BlWdHcmTmeIWq6zguCwGRftUj2ymI/gVjDWnr3VdqY9gTC8AVDqimXLPaViMJ2dRX1NrCd/iDCkagBlvoqeZSpKUvdjL5zriybbGxSCxZzjmkVRsfiIUXUWMqeZ1NJSQlKSuKfyE+ePBlutxubN2/GxIkTAQCrV69GOBzGpEmT+v3OxIkTYbPZsGrVKsyaNQsAUFtbi8OHD2Py5MkD/lZNTQ0KCwsHNDSxQmwqA093ECV56ugDrFUtA7Q5aOv0BRGKLDgs9jVTdPcOXzDt+6p1CpcChvo6GGwkDCAMQ86/4c2cF14QlMdCD0aXP8TkgqVFpQcPg+E8gLaeByw90zyHFVLOUi02gyz1lYjCpGeTJjnhxHvZrWY4bepsnNRANkxoYMxmqYAGoI1SzKIXlzTuauoCobCADh97hmGWw+iUMm7cOMycORNz587Fxo0bsW7dOsyfPx833XSTXImurq4OFRUV2LhxIwAgPz8fc+bMwYIFC7BmzRps3rwZt956KyZPniwnB3/vvffw8ssvY8eOHdi7dy9eeOEFPP7447jrrrsM66tSLGaTfNCW7u+rlnKJtfVGy76ypuNpIZtY7Gs0qiaoyXrDUl8Hg62dI6E7WuQyYvGET2pLICSgOxBCtj31qS8vWBYznDZ27LZabpBY2vQCmZNTxRwJc/H0iCdBpXnOlO8ZCguykY6lvhJRogUI2FmqM+n0VQvln8X1EcicjY4WukCs5xBLa6RLA4OEESxZsgTz58/HtGnTYDabMWvWLDz33HPy3wOBAGpra3slrH322Wfla30+H6666ir88Y9/lP9us9mwePFi3HPPPRAEAWPHjsUzzzyDuXPn6tq3ZMnPsqGjR2VPRAYrgtJ6kxqs9jUagZHeIerSuIfCAjp96qSriX0XWOrrYLCjwRKGIJ3yudNcuGXbLbCaTQiGxdA3VYxN3qhgG6xUrt5o4e3D6gZJPqXWwDOPNSGen22DR0XlktUNEhFF9ihk6PnICZYjoQhqFAxgcc0AaKOTKiz2Ndtugc1iQiAkwO1VSReI9DPLZoFdrdJKKhCdv+zlbEqEoqIiLF26dMC/jxo1qo/XgNPpxOLFi7F48eJ+vzNz5kzMnDlT1XbqSUG2DUfbujWRTSytN/larDde9uQSEG2PFvsxlp4pEBOiruJBsTRuLHkNOyNrgj8YRnt3QBVjE4sVbePBRysJzZDiPbXYrLP0wptMJtWV6agizZbNNk/DMBfmDDBZYhWLdDeWAupvHFjdIBEiwVAYnSyG5sQoS2rlgpFzUzGUXBmIro9uNddHxjc6auoC0efKTl+10AVY9AgBtMsXQhhP1DDhV+V+/mAY3QExwTJLnrQnVspUA2Z1vGz131fmdXdV1xtGn6tme0+2+jkYtMPIcAqyxRderZfAHwzD6xcXLNZeBJfKyjSrL7wWpZ1Zze0je+apaizNjI0Dq/OXEJEMTUDUgMwCdqsZWZE8F2oZPplVEjVQ/qXNYX62OuWe1aJA5b4KghB9rgwdPAExG/U01wUk/c7tVccgQbBDQWSzrpY+G+tholZlajWwWczIsYvrjdq6D2vJlTPFuxTQZr1hta9a6e6sGRAHg4xNGY5L5dOR2JeJpQULUD8/FasbJLlCW0zFjVRh1fMgKsTVmb88bJDI2JQZSO9cNoOu0qp7hjBYtQzQNqyBtfdO7fWxJxCGPxQGwF5ftZu/bK2P0ma6yx9CIPIsiPTApbJskvSePIdVlVA1NckU3Sczw7bV0d29/hACIfYKNgHqF1Vh9ZkOBlsaLKE7aocJSC9BnpPdBcujkscPq9blWC+IWO+IVGC1r2rP30zaIPG4YGUSLFaik4jK0vSei7Lnr1e9ymWZ5jlpMZtkzwRWiHp0q3vIxtozjV2vKZQuvVDbM4RVHQ9Q3xDOal+1qJrNqmxSOypB6qfNYkI2Y+sN6e5kbMp4tFqwWHwJMuWFd1gtcERy8KhlSWc1jC5f5QT3LG+Q1PfMYy8fEBElqhCz5S0BRNuU7l6iUnv8oTB6Aup4hrDeV9W9fZxWpgpoABr0ldEkvBazST58UjPUnDAetXOsycUoGJNLgHbGJlZlsFQpUw3Yzdmk3TNN9/WG1fk7GFwam1pbWzF79my4XC4UFBRgzpw56OzsHPQ7l112GUwmU6//7rjjjl7XHD58GNdccw2ys7NRWlqK//mf/0EwyHcVj3iobV1mVZEGoom8M+GFlxYWtT0PWFuwClROMijnU6EFizCYtkielQLGcvsAGuYgYGyznhOpYgqoF2ou5c9h7b3LJPmiVc4m1tZHQP0DRYINCjQymLJW8AbIHNmUHbveqGxEZK2vmSSD1S7uw/I+eyC4NDbNnj0bO3fuRHV1NZYvX461a9fi9ttvj/u9uXPn4tixY/J/v/3tb+W/hUIhXHPNNfD7/fj888/xl7/8Ba+99hoefPBBLbtiOFJFgHQX4oD68dAs91XO26RSyCCrJ7dRRdqvitsxq5WigMxRuAgRSQljLYkpEJUD6S5LTSaTqpv1QCiMrkgBDdaeq+rrYwbJUlZzjgHq50Yh2EDtfHKsGvyBzAnbVrtSZmxFW9b6qnZxKncGrTcs93UguDM27d69GytWrMDLL7+MSZMmYerUqXj++eexbNky1NfXD/rd7OxslJWVyf+5XC75bytXrsSuXbvwt7/9Deeeey6uvvpqPProo1i8eDH8/vRdpKPW5fTOXQBkloKp5mZQEARmT0ekjWAgJMhVEFOBh9MR9fMWsHeSScRUzGEsUT2gQUinHMLB3lyUE/GqcAIbK49ZkzGabV4Z6ycQ49GtWl/ZXB8B9b1/CTZQu1Imq6kSgMw6aFPzucbmp2WtuE+ByntPaW1l7RAH0DAMlEHdcCDYmn0KWL9+PQoKCnDeeefJn02fPh1msxkbNmzA9ddfP+B3lyxZgr/97W8oKyvDd77zHTzwwAPIzs6W73v22Wdj6NCh8vVXXXUVfvazn2Hnzp2YMGFCn/v5fD74fD753x6PBwAQCAQQCAw+qaS/x7tOa3Ijc9XTE0SPz59yUu/Wzh4AQJ7Dokrf1BynHJtoW23r8qlyP0lI5trMhj/HE8cpP7KwtHT2pNy2zpiqdllWwfC+xmKFAJvFhEBIQEtHN+xm54DXKplL0vx1qTR/1USav+1evzrzt0uUXbn23vM3mXeOtbFKB9wMh9FlSpguoG4RArmABsMVn7yRymWpVkBk+TBGbS+uqOcveyq12kYJgg20CkNirYo0oGFUAoObdTUNa9I9ch1WWBmtaNul0nrDtAExg4ylA8HeyhiHhoYGlJaW9vrMarWiqKgIDQ0NA37vBz/4AU4++WQMHz4c27Ztwy9+8QvU1tbi7bfflu8ba2gCIP97oPs+8cQTWLRoUZ/PV65cKRux4lFdXa3oOq0QC2+J0+Dt9z5ATopzd+tBMwAzWo4dQVXVoVSbJ6PGOO1tMQGw4NCx46iqqkr5fvXHLQBM2L31SwQOpnw7VZDGqbNNfA5fbNmG7IatKd2zzQcAVlhMAtZUrwRjqYyQZbYgEDJh+crVOCkn/vWDzaUv6sU50tWmzhxRk0OdAGBFY1uHKm3bd1ScIwe/2YWqtp19/p7IO+f1elNuD9EbOYyOYYVY7Vx/TIdwqKAouhk2qp1YuWxIriOl+7GsEGtVCYnFvqr9rhJsIB1CeCKVy1LNMSmFvRYyvN5kwmZdC2MTi0bwTFpvtItKYK+vA8HMDLzvvvvw5JNPDnrN7t27k75/bE6ns88+G8OGDcO0adOwb98+jBkzJql7Lly4EAsWLJD/7fF4UF5ejhkzZvQK0euPQCCA6upqXHnllbDZjJ0wD9SsQpcvhPOnXopRxQp264Pwyds7gGP1mHDm6ai85JSU26bmOBXub8Gr32yG2ZmLysqLUm7bI9s+BuDHjMsvRkVZXsr3S4UTx2nz+19jc/NhDDt5LCqvPDWle+8+1gFsWY/8bDuuueZylVqsHs/vXQfP8S6cPfFCXDi6aMDrlMylb1btBQ7tR8WYkaisPEOrJifFoRYvntn+GfyworLyqpTv96dDXwDtHlx84Xm44vQS+fNk3jnJq5NQjzY5ZxN7nk1qJ6dlWVGUNnVqJAhnOTRSqlzW0RMk5T9BWK34BKj/rhJsEFspszsQQrY9te1ctCAFe3NYzfc1HBaYDrlS83CDZblkMZvgclrh6QnC7U19vYkt7sMamZQveCCYMTbde++9uOWWWwa9ZvTo0SgrK0NTU1Ovz4PBIFpbW1FWVqb49yZNmgQA2Lt3L8aMGYOysjJs3Lix1zWNjY0AMOB9HQ4HHI6+L4jNZlO8SUvkWq0oyLKjy9eNrgBSbkuHT8ybU5jrULVfaoxTUW4WADFpdqr3EvMYiS98cV6W4c9QQhqn4lwxnKy9J5Ry2zr9Ysnvwmw7M/2MpTDHDhzvQqc/rKh9g82lTmn+5qg7f9WgOE+cv15/CDBbVAhzEeP5i3Od/fY1UTlGqIuU0JdF5b8wRz1viZ5ACL6gKGNYDmtQM2cTq0pifpZNNjalCtsJh6U8RipVGOyWvEIYNAxTGF1aIlXKDIYFtHcHUjY2RT1p2ZvDahqbOv1BRLJCMGmE0cKzidX1piDbDo9q600kbx6L81ft/GoMG0sHghljU0lJCUpKSuJeN3nyZLjdbmzevBkTJ04EAKxevRrhcFg2ICmhpqYGADBs2DD5vo899hiamprkML3q6mq4XC6ccQZbHg5qk59lQ527WxXFK1Mq0HQHQgiEhF73ZYlomEDqz7TNy64iDcRsHNJ8cVbb7ZjlhKAE29XopA1JmwryReqnxWxCnoMZlUQmk5T//CwbjrZ1q5OcluGk2VKbOiL5CFPJnxUOC/I6y3IIklqGNYINpMplLV1+uL0BDMvPSul+LIdtq5lgWdqjOKxmOG2WlO+nNmoebvCw3gDqVMpkua+xOkSqIa+hsIAORisMDgZbGcMUMG7cOMycORNz587Fxo0bsW7dOsyfPx833XQThg8fDgCoq6tDRUWF7Km0b98+PProo9i8eTMOHjyId999Fz/+8Y9xySWXYPz48QCAGTNm4IwzzsCPfvQjbN26FR9++CHuv/9+zJs3r1/vpXRCzZMvpl/4SD99wTB6AqlVLpP6aTWbkG1nb8FSMyeFu5vdRMVA5izOsZvxVN/VWFdyFvtKRI2nLHr7qJk0Ww7fyLKlnHdEC9SsXMZ6yWItQjhY7KvUJkEAOlJMct/RE/WUYPFdlQ5jyLMp/VDTY0LS81g8VMyPVCltT3MdD9AoZxOjfVVzn8Lyc5W8e4Ph1Ktms1zRdjC4MzYBYlW5iooKTJs2DZWVlZg6dSpeeukl+e+BQAC1tbVy0lq73Y6PPvoIM2bMQEVFBe69917MmjUL7733nvwdi8WC5cuXw2KxYPLkyfjhD3+IH//4x3jkkUd075/eZMoLn2u3QjrATFWZjhXiLG6QCjXwPGDx1BaI3Qym9+kIEFMFLMX5y7oreaYjCIKsWLNo5JXkS6cviIBYZSJpWM4VAqhrgGFdvqi50WE5h4bdapYPiVLtqzR/s+0WOKwMHzyRsSntUOugTRCEaI5ABuWwpKN0+IIIS4pLkrBsBAfU9eJi3XtdVcOal931JjsS8gqk3lfp+zn21FNp6Al7PusKKCoqwtKlSwf8+6hRoyAIUYFUXl6OTz75JO59Tz75ZOYqUOlBNH9BeivTZrMJriwb3N4A2rsDKHU5k74Xy+GCQHQzqIrnQVfkxCuHvU0vEJMAVdX5y2ZfpZDXlBcsxl3JM53uQAj+kJQrjT0ZIxrZRc8QtzeAkrzkvX/djIfpanIYw+AzBdT1EmV58wqI64bXH4LbG8DJxcnfh+V8TUDMho6q0aUdBSoZwrsDIfgjefNYPNyQimQIgmhASaWNbob3KIC6Cf3bGQ7FB7SJSmBxvYkNeW3vDmB4QfIhryzvsQeDH7MYoRlqWZf9QbEqRuw9WUNyZ1TLusyqV4ia3j7MbxpU3QyyHQut1rvK+vzNdKR3zm4xI4tBY6BYSUadfAssJ6YFYnPCpb/npFryRRBi8hgxekihlgcB6555sWkSYg9hCf6RN+sqyWCbxYQcBtNC2K1muV1tKep5vMhgNTxpWyMHxQWMymC1UriEI0nyAXafq1r7FF51dzI2EaoZJmIFRh6DFWgA9TfrrAu2nkDq+ancck4VNhesfJVKkwtCTB4jRjcOaikirLuSZzrSO5efzWaYLhD1uEpV+W9jOLkyoK5nCOsesWoZYLr80QIaRcwaEdUJL3OzbmyKrNvBsICuFPOFEGwhGejVMpjmZ9mZXW/UKkrBuu6uah6uyHrDqgwuUKkqaGxaCFafq1qpTVifvwNBxiZCtTCkaKlja0rVXbQkU4xNuQ6rHCOcqnBjfTOoVrLinkBYDl1i9bmqNX+joR9s9jPTYd39HYhR/rtSPVVn2wNGMiJ4esTKZanA+rqhlnyR5oTDakYWg54SgHqn6m1dbHvmOW1m2CO5PagiXXrhUkn3afeyrw8U5qhTVZGXUGY1PBFZ191V249JnuAMp4XIFGPpQJCxiVAtgSTrQhyIbmhSPY2Pnhiw2VeTyaSa2ybrYS5qbRqk71vMbLqSA9F3K9VnKrlXs5pnJNORZDGr3hKAeutGG+PePrHtUquwBKteotFcf2odULDZTyDWYy1FYynjhnuTyaSqtwTBDmrl92ljPG8eEOMZ0pXeB8WxnoidkRL3yRIN8WXzuearvPdk+XCuKEclwzDj83cgyNhExCQIT03p4iE0RzIOpXoa38r4aTygniVdVqZz2HyuBSoluI+tnsSqK3nUFVcdzwOWlctMhnUDL6CeYcLNuGHCZonmC0l3j1j1QiN5MJaqE4LE+vwF1C2iQbCDap6IMWHbrKJWGFI0LQSbfc2yW+C0SZ6IyT9XMW9e5FCc0X2KWnKJh71noUqe4NJBMavPdCDI2ETELFipWdFZLnUsISmYrame3HLwwheq4AUTDgvMK9OSgtQdCMEXTD4nBQ9CXDodST00UjIgstvXTKaNcYUYiBoS1PISZdUzBIiuG6mcwPqCIeYLaEjyIN0NiIB6lZBY98wD1C0xTrCD2l7dLMvgqCE8Vd2dfd1HyrHUmoJhosMXRDAS9s2q0V8tj0vWKwwCKu49OXB06A8yNhExC5Y/pRjh1i7Jip58GWytKVJJmeYhDClfBY+fjp5o4j1WF6w8hxVSirBUFi1JCWE1mSIQnW+pKCFAdMEqYtRbLdNhuYyvhFoehay7+gPqJM6WxsliNiHPaVWlXWpTFBNmHk4hP5XsOcmwfFEt/x0HhjW1Ql4JtlDNYNrFvgwuUMur28v+oaJkSEjFMCE90yybhd08RlnRQ5xU9p5uDjxp1Qqjkx0dGH5X+4OMTYT8ggZCArwpVCuJvgTsvvCyEE85qS0PMe6pnwRJ3822W+Cwsrlgmc0mVSpGRUMj2Z2/0c1g+htLMxk3BwYYtRK2yrKU4fcuWoQg+b5G3zkbzIwW0JB0gVBYQEdP8p7OPOSAUasaXRsH64YaB08Ee0Tzcqrj6cz2Zj1zDorVCFFv48JjOLrepJKfigcDolppTVo5jUogYxOBLJslWq0kBcWLhzxGRXLcbIoJljlQMNUIieAhnAdQZ+PAQx4j9Yyl7Pc1k3FzFJqTcl6JbvYNE2qEq/AgXxxWC3IdotdVSqfqHMgX9XKOsZ9fjcLo0hPJiNjhCyIYqaSbDO3d7L+vkgxORfcRBIELw0RUz0thveFgP+a0WWC3invPVGSTbEBkuK/yQXGqUQlyug92dcP+IGMT0btaSSqeIZ08CPHIgpWCgikIAhc5m9TYDPKgSANAfnbqJ7dcLFiRfnb0BBFIQbnkwTCcyfBQjU6NhK2eniBCkXCtdDestXAgXwB1NnU8eUqksqEDYtZIhuevWh4wBFtIXiuCkOJBGwdzuFAFHa/TF0QgJPS6H4uoUciIlwPFAhXWVh5Cy1QrvsHBoVV/kLGJABDrGZJCmAAHJwax1uVkY4RjE++x/MKrUblMmg8se3AB6oS5yCdeDD9TV5ZNzk+VUniknF+N3b5mMjwoimoo/1I/Wc4rAajjUSi9r8WMv3NqhKvwMH9jQ5KTzU/lD4bl8A+W+6pGsRCCPawWs6y7q2GYYPlQUY3DDUnvybJZkGXnYL1JKWybfYM/EGsIT++DHOnd8vQEkvZC9AfD6OBgvekPMjYRANQpQcmHdVlsWzAsyC9torhjFiymN0gqnGa2dfHh2aRGmAsPnk0Wsyka+53kiXzvDRLbikgsra2tmD17NlwuFwoKCjBnzhx0dnYO+p2enh7MmzcPxcXFyM3NxaxZs9DY2NjvtS0tLRgxYgRMJhPcbrcGPVAOD2F00aTDqWxy2M8rAUQNRKkYm3iQL4A6RQh4yGMktS2V/FTS3DeZoknkWUSt8GuCPdSQTTwkWC7MiXqGJHtQzMOBOKBOiK+bk75K7Wvp8iV9Dx4OcqQ9tiAkv0+RnqmZ8fWmP8jYRABQp1oJLzHC2ZETjWRPgnhZsPJVeKbRE2q2BZsqrricVGgrTDHMpdeC5WS7r7HMnj0bO3fuRHV1NZYvX461a9fi9ttvH/Q799xzD9577z28+eab+OSTT1BfX48bbrih32vnzJmD8ePHa9H0hIjNY8Sy8i+1rScQRk8gucISPFSiA9RJzM/DYQygVl/Zz8MVm58q2Y1Oe4xR2MJo0ndAnQ0dwSapGhJ5yZsntc0fDCddyIiHKpmAup60rK+txZHq5el+kGO1mOGKVKFNNtqkLSatCcvrTX+QsYkAkHq1knBYkF8E1o0wqYaXcbNgqVrRgu1nKudsSsHLgocNEpD6ZrA1JsSF1apYJ7J7926sWLECL7/8MiZNmoSpU6fi+eefx7Jly1BfX9/vd9rb2/HKK6/gmWeewRVXXIGJEyfi1Vdfxeeff44vvvii17UvvPAC3G43/vu//1uP7gxKTyAMf1B0s2ZZUcx1WGGNzJ9k5yIPleiAqBLb0plKmDkfVWSiOZtUOHhieP4Csd4SyT1XHnLdAOps6Ag2KUox5KrDF82bx/LhRrY9Wsgoad2Hk3w3ahQyiuqz7D5TIEYGp2JY4+QgJ9WiTbEVbXnDanQDCDZINYFkRw8fCxYgCrc6d3fynk2cLFixOVUEQYDJlLhhgZfTETU8m6TnyouxNNmNAw+nQCeyfv16FBQU4LzzzpM/mz59OsxmMzZs2IDrr7++z3c2b96MQCCA6dOny59VVFRg5MiRWL9+PS688EIAwK5du/DII49gw4YN2L9/v6L2+Hw++HxRLwGPxwMACAQCCAQGn4PS3we67rinBwBgNZtgN4Xj3s9I8rNsaOnyo9nTjSHZiasTzR3d4n2c1j79jDdOepLvEDc5LV2+pNvT0tkj30vNPqk9TvmR09eWzp6k7umL8TzItZuYeH4DjVFhtg1HWrtxvL07qXY2eyLzN8vGRD8HwuUQ1353dwA9Pv+Ap+LJzCWW+50JSBvs1iQN4VJaCKfNzHRaCJPJhIJsG5o6fHB7AxhRmPg9eDOCq1ERlHV9tihiCG9JUp/tCYTQFVlvWNdpC7PtONTiTVp35+WZ9gcZmwgAsZVZUvOWyHVY4bCyu2ABqW/WeVmwJKNfMCyg0xdEXhIhUzxU2gFSTzLYEwihO8DHgpVqCVVe8uTE0tDQgNLS0l6fWa1WFBUVoaGhYcDv2O12FBQU9Pp86NCh8nd8Ph9uvvlmPPXUUxg5cqRiY9MTTzyBRYsW9fl85cqVyM7OVnSP6urqfj+v6wIAK7IsYXzwwQeK7mUU1rAFgAkfrvkM+/MTz6Ox6YgZgBntx4+hqqqu32sGGic9afUBgBXNHT14//0qJGG3x6Fj4ljt3bkVVfU16jYQ6o1TXYMJgAVf7z+CqqpDCX+/3Q8AVpgg4NPV1WDJefLEMQp2ivPv4y82w3cg8fm7vlEcq0BnG6qqqtRppAaI+WitEATgrfc+QG4c0Z/IXPJ6vSm1jUiNVJNJy0VgGNdnAbGNTR2+lD2bWN+sx0YlJH9QzEe+1VRzjklzwWo2yWFqrJJqoQZeHB36g+0nQ+hGqpUeWjkJLQNSD0PixbrstFngtJnREwjD7Q0kZ2zipBpdqjHusQtWnoNtsZiqcsnSgnXffffhySefHPSa3bt3a/b7CxcuxLhx4/DDH/4w4e8tWLBA/rfH40F5eTlmzJgBl8s16HcDgQCqq6tx5ZVXwmbr+16t398CbNuM0oJcVFZelFC79Oav9RvReMiN08d/CzPPHJrw979cvhs4egTjK8agcvqpvf4Wb5z0xOsPYtGW1QgJJlw6fYac6ycRntj5CQAfZlw2BWeflK9a29QeJ9OOBrx5YBscriJUVl6Q8PdrGzqAzetRkG3Ht6+5POX2qMFAY/Rxzw7s+qoeI8ZUoPKSUxK+b91nB4D9e3DaySehsvJsNZusOou2rUZ7dxATJl+CU0tz+70mmbkkeXUSxpD6Zp39YhQSssdPin1lQfcZDKl9gVAqB8V8hFxF88ml7qmfjFFOT1LdZ7cxpLsnCtu7KkI31HrhJZdIlkk9DImPBQsQ23isvQdtXj/Ki5R5XMTCSzW6VBUunhasaDx/agsWC8bSe++9F7fccsug14wePRplZWVoamrq9XkwGERrayvKysr6/V5ZWRn8fj/cbncv76bGxkb5O6tXr8b27dvxz3/+EwDkKjdDhgzBr371q369lwDA4XDA4egr62w2m+JN2kDXtveI+ZqKcx2GG1niUZAtjkGHL5xUW9t7RG/C4lzngN9PZEy1It9mkw33HT4BhfFcQ05AEKI5DUtc2Zr0R61xKnGJ60SbN5DU/Tr84jtUlGM3/LmdyIljNCRXnL/tPcGk2uqJvKuFHLyrxTkOtHcH4VHwriYqxwjjSPWgzc2Jpz7QOzVEMkR1H7bnbJbdgiybBd2BENq6kjsoZulQcTBS9dSX9iis52sCVDgo5qAI10CQsYkAoMYLLyVoY1uIAyp4NnGyYAGikehYe0/SizMviohsQEzS7ZjHBUuNihZGU1JSgpKSkrjXTZ48GW63G5s3b8bEiRMBiIaicDiMSZMm9fudiRMnwmazYdWqVZg1axYAoLa2FocPH8bkyZMBAG+99Ra6u7vl72zatAn/+Z//iU8//RRjxoxJtXtJISmJLJfxlZBOTVP1EmVdT2kMmAABAABJREFUvgDiZr3O3Y2WLh9GFidmuPf6Q/AFJSMi232NLTGeDDw90yI5cXZ6r4+AqPfsb+6iJOFpRqoHbbwUaQCiOkvKxVE4WFuLcuyoc3ej1etPeL3pjllvWO9rqilcpAqbPMxfOYwuyfWGp73niZCxiQCgXs4m1gUboF7IFQub9XhIuZaSWZz9wXA08R7jRkRpAye1OdEwl+j8ZbufQHShST0MlP2+SowbNw4zZ87E3Llz8eKLLyIQCGD+/Pm46aabMHz4cABAXV0dpk2bhtdffx0XXHAB8vPzMWfOHCxYsABFRUVwuVy46667MHnyZDk5+IkGpebmZvn3Tsz1pBctnaLyxLpRAojK0vbuZDfr/Gx0ZOU/iXVD+o7DakYWw0l4gajB3e31IxwWEq5YydP6WCSH5fjiXNk/bZyEqgCp63gEmxSmelAcmcNSRWqWSTXnDS9VywAxD2mduzspPU/6js1iQo6d7fWmOObwP6n1Rj6cYz+qJlVjKS9hoP1hNroBBBtIioinJ4iAmE0yIXgS4nIYUoontyyEIcVD2sQlszhLp7ZmE+BKwo1XT7JsFjiskbK4SShdLIWWxUO1anQcvKuxLFmyBBUVFZg2bRoqKysxdepUvPTSS/LfA4EAamtreyWsffbZZ/Htb38bs2bNwiWXXIKysjK8/fbbRjRfMS0chSRLifkzwXCfyiFF7JrBepiu9CzCAuDpSWbd4KcAgezZlLTnLzteovEgY1N6Im3WW7r8chh4IvD1vqpU3IcDPS+VaBNpfAqy2V9vpGcRFsRqmYnSytmBFZD++YL7gzybCABickCzSXzh27x+lOY5E/o+T+XU5dCPDMjZVJBCjHts4shETxv0xmQyoTjHjvr2HrR0JZ6fiicDTOrV6PhcsIqKirB06dIB/z5q1Kg+yrbT6cTixYuxePFiRb9x2WWXJaWwqwlPYXSphnC0c3RSl0pfeZIvdqsZeQ4rOnxBtHb5EzaktHGkC8heoimGIBVkwEadYBPpPfMFw+gOhJBtT9CrmyPZlIpnSDgczZvHg+6TyqGiJJd4OPy3WcxwOa3w9ATR2uVL+Nnw5OhQkJ1aiDpP++wTIc8mAgBgMZtkQZ7qyS3rFKZgXRYEgavNemF28mECPOWjAICiXGn+Jt5XHudvlz+EnkAo4e+3cuRNkom0dEaMTRyE0UmeIckUlgiEwujwBQFEw31ZJpXNOk/yBQAKUgjVbePKACPlbEoxfQAHsjTVIjAEm+TYLbBHvLqltSMR5MMNDtabVMLoOnqCCIXFgyQ+ZFMqB8WSjsd+P4HYtTUZzyZ+DDCFMSHqycCTYe1EyNhEyBSmEBLB0+lI1JUxgHA4MS+GDl8QQY4WrOIUNoO8LVjRk6AkFiyO5m+ewwprxNMsKUWki5/TvUxESnjJw/ORNihSnqlEaIsN0+XI2JSMLJW9YTl4pkBUmU1GlsqGNQ5kqdTGTl8QvmBihvtwWIjmC+Fgo16cwmEMwS4mkykmNUTisqlZzhHIQ9h28v2UjBI5dgscVrbzGAExIepJ9JW7g+Kc5GVTayc/Bzmxe89EPeh7AqGYHLrs9/VEyNhEyBSncMrHk3uqJMRDYQEdPcGEvispl9l2C5yMJ3oFYhXMZJQQSZFmXwkBYsNc0tuzyWRK3gvRHwyjM+JNwsNmMBOJhtGx/96lElrWIiuJDlgYD9MFUgtf5alaK5Ba0mGe8nDlOa3y3GtL0LDm6QnIB088rBupVt4j2CWVfHI8hW2rkceIG4N/Sn3l7HBDhUNxHmRw7N7Tk+DeUzpYtphNyHPylwGJjE2ETGEK+QskQc7DC++wWuRqZYmeGvDkAQPEeDYl4V4tfWcIB6e2QKzClYxnE2+Lc3JhLrFJ33lcsNKdYCgsG+558JaQ5L3XH0K3PzHPEDlckJt3LgXPJo5c/QGk5CnBU8Jhs9mUdG4U6TAmz2nlwlMi6q1Gnk3pRrJGf0EQuNLdpTnc5Q8l7InIUxEYILWcTTxVyQRi5m8KYaA87MkcVotcHTDRfXa0n+zn0O0PMjYRMslalwOhsFz6mhtBnpNcyCBPVnQgJswlCQVT+g4PHhZAip5NnMVCJ6uIxOYY4XHBSnckQ5PJxIfylOuwRvOFJPjeyfKFA6MakJoXVxtH3gNAjOE+zcNygKjhPmFZ2iUdxnDSzxgvZ6OLIBDqkqxnk6c7yJV3nisrmkIg0QNUnvKrAanlbOIujC43ufVGEATu9mRFuckdWvH2TE+EjE2ETLJKlztmg5TPQe4NIGpUSDRRWxtnHjCxYXShBPNTScKQl81gsp5NgiDEeB5wMn+TTHLPmyt5piGXLM6ycRFaJlWBBJL3DOHHKJF8WEMLZ+9dshVbfcGQHJrOi0dsUZKGNSlPGS+bHOk9DYQEOTE/kR4kLYMjBv9ch5WLtBAmkykmT2CiujtfRolUcjY1c1RkBIj1ukysrx2+IAIhfoylQPTwvjnBPJe8eUefCBmbCJlkk0nLORo42SAByZ8E8eaeKgnxsJC4Ya2FsxPqZD2bvP4Q/MEwAH4WrGTnL08lcTMR3t45ICa8LEHlX+4rJ++c1M+OJJJJc+c5maR8keaA1WyCy8nJGimHcCS2bjRz5q3mtFmQnWQIB8E2hUmGvfJUiU5C3qwnqOe1yeG9fPQ19nAjUU9EyZDBjddlsvsxznLoAtFnkrSxlJP5eyJcGptaW1sxe/ZsuFwuFBQUYM6cOejs7Bzw+oMHD8JkMvX735tvvilf19/fly1bpkeXmGBIXkSIdyRoceXs1BZIPicFT/HBAGC1mKMnJEluHIZw8lylDXpzou7VkXFxWM3I4mTBkudvos9Uflf52AhmGi2cnb4C0fcu0UMK3nLCuZy2pJNJt3F2KikZUJJ9psW5/ITpRj2bEnumPBqGJb0lmbxjBLsUJentw5t3HpD8PiXq2cSH7iM9k2BYkNOUKIU7z6Yk5y9v+zEgqu8k7NkkR9XwMX9PhEtj0+zZs7Fz505UV1dj+fLlWLt2LW6//fYBry8vL8exY8d6/bdo0SLk5ubi6quv7nXtq6++2uu66667TuPesINkVEj0JeDR4lqQpNIVPTHgp6/F8nNNzjDBizI9JDc599TYmG+TiY8NUmGSG6TjHXydeGUaPFUGkkjWozCas4mPuRibTDqR/FThsMBVtVYgeVnazFmePyB5w300ZxMfzxSICatPIhEvwS7JHp7KOh5H7+uQJA3hvIUhOawWuCJFXBKRw6GwIK/FJZysrcmGgfKWrwmI9WxK1NgkXs+TYS0W7soR7d69GytWrMCmTZtw3nnnAQCef/55VFZW4umnn8bw4cP7fMdisaCsrKzXZ++88w5uvPFG5Obm9vq8oKCgz7WZgnxikGziPZ5e+LzkLOnS2JTk8SHEAXEzt+94V0IbJLEqFl+nI5LS7/WH4PUHkW1XJt6kOcCTEJc9DxLdDHLmXp1pRL0l+JmLyYbRNXNWjQ4Q29rc6UvIs6mjJyjnyyvgJPxaNjZ1JPhMJWM2R+tjsiEc0nznaaOTbF8Jtkm2UiZvFUGB5D2bJN2Hp0PxIXkOeHqCON7hx9hSZd9xe/2Q0rPyIpti8+YJgqD40JdHGVwsezal/94zFu6MTevXr0dBQYFsaAKA6dOnw2w2Y8OGDbj++uvj3mPz5s2oqanB4sWL+/xt3rx5uO222zB69GjccccduPXWWwec+D6fDz5fVOB5PB4AQCAQQCAwuDIq/T3edXqS7xAd3dq7A+jq9slVhuLR2N4NACjKtqneH63GqTBLnPpNnu6E7t3k6QEAFGRZmXp2g41TUWSD09SuvK/NnT4Igpj0PddmYqqvA+EwC3DazOgJhHGsrQsji7J7/X2gMTrm9gIASnLtXPQTAAqzxHC/4x09CbX5eGT+FmYPPH+Teed4GTfWiYbR8aNQJKs88VaNDoi6sCdiuI9Nwuuw8hGmKym03YEQunxB5DgUGu4lbx+OlP9k81PxVnUPSN4oQbBNssUL+MzZlFpUQqmLn/d1SK4D+493JeTZ1CwfntpgtfARvCTNX38wjC5/CLkK1xuePZsS9RrmPSqBO2NTQ0MDSkt7m3itViuKiorQ0NCg6B6vvPIKxo0bhylTpvT6/JFHHsEVV1yB7OxsrFy5EnfeeSc6Ozvx85//vN/7PPHEE1i0aFGfz1euXIns7Ox+vtGX6upqRdfpQVgAzLAgDBP++d4KFCic05v3mwGY4W44jKqqg5q0Te1xOthmAmDBvrpmVFVVKf7e0WYLABNqt25Czz5Vm6QK/Y1TR7P4fDbU7EJx6w5F96nvAgArsi0CPlzxgapt1JJsswU9MOG96o9xSl7/15w4RuuOinOh292U0FwwknovAFhR39qZUJv3HBHn7+HaHahq3j7otYm8c16vV/G1xMDwGEaXrPLUKp+q86M8SW1NxDAhKYmlHJ1I5jisyLJZ0B0I4XiHT7GxiUfPpmhhlORyVfJkWJPkSqLhVgTbRKvTBhAIhWFTaGRo5jBnU3ES640gCLIcLsl1atIuLShJoq88eq9n263yQXFrp1+xsamZa8+m5DzzyLMpRe677z48+eSTg16ze/fulH+nu7sbS5cuxQMPPNDnb7GfTZgwAV1dXXjqqacGNDYtXLgQCxYskP/t8XhQXl6OGTNmwOVyDdqOQCCA6upqXHnllbDZ2HGtf2LnJ2jq8GH8BVNx1kmD90Fi+dIaoLEJkyecicoLylVtj1bjdHK9B//39RcIWJyorLxU0XcEQcB/b/wIgIBrZ1yO4QVZqrUnVQYbp72r92Jd434UDh+JysozFN3v830twLbNGFaYi8rKi7Rosib8+cgGtB5tx2lnn4crz+htlB5ojDa//zVw5DAmVIxB5YxT9W5yUrR2+fHk1o/RFTThyqtmKlYun/r6UwDdmHHJhZh4cmG/1yTzzklenURqtHCW2BOIGlGOJxDW0O0PocsvVnTjqa/JhCEd59AAA4ih5kdau9Hc6cOoITmKvtPCobG0JIn5C/CX0xCIenElGvJKsE1Rjh0WsymSr8ePoS5lBhXZAMORbBqShCdtpy+InoBYcVhKocEDJXmZYWwCRKN/nbsbLV0+jCxW5qzB40FOSZIFVXh8V2Nhxth077334pZbbhn0mtGjR6OsrAxNTU29Pg8Gg2htbVWUa+mf//wnvF4vfvzjH8e9dtKkSXj00Ufh8/ngcPR9wA6Ho9/PbTab4k1aItfqwZBcB5o6fHD3hBS3S3ppyvKzNeuL2uM0rFBUnlu6/DBbrHKVocFwe/0IhMRg6LLCHNgYDInob5yG5ouCu6UroHgM3T3iRrAkz8nU/IxHSZ4TQDvaeoIDtvvEMWqJJO8dmp/FTV9LXFZYzSYEwwI8PgFl+Qrf1YiCNqwwJ25fE5VjROpI3hU8ndRJyk9TApt1SSG2W82KTzFZQFLgEzFM8KokluQ6ZGOTUngMLZM2Km3eAPzBsKL0AYFQmMsQpCE5yXkhEmxjMZtQnGNHU4cPTR6fcmMTh94SySRYlgxTOXaL4lyeLCAb1hLIncdbJTqJ4ly7aGxKwIgoG5s4Co2U1kZ3Al6IPYEQOnxBAPwZESWYCegsKSlBRUXFoP/Z7XZMnjwZbrcbmzdvlr+7evVqhMNhTJo0Ke7vvPLKK/jud7+LkpKSuNfW1NSgsLCwX4NSuiKdvh5PQJBHFyx+hJtYeUys3KDUpVxS0FxOfnJvAMltBps8/AlxIDoHE1mcedwMms2mhDe+Xb4gugOiEZHXBSvdaeWwOpD03rR2+eRE2PFokkMaHNxUgASi8jARWSqvj5y9c7J8SUD5lzY6PFVoK8i2wWYR56BSI4x0ndVs4irhcEkS85cFWltbMXv2bLhcLhQUFGDOnDno7Owc9DsvvfQSLrvsMrhcLphMJrjdblXuyyqSbDre2aP4O8clPS+Pn9AySS61dvkRVrje8KjjAbEyOP09m0qT2ad0iHOdp9DIgiyb7Nyg1ENamr92q1muUMgbzBiblDJu3DjMnDkTc+fOxcaNG7Fu3TrMnz8fN910k1yJrq6uDhUVFdi4cWOv7+7duxdr167Fbbfd1ue+7733Hl5++WXs2LEDe/fuxQsvvIDHH38cd911ly79YoUhCcaT8hoLbbOYZSVR6Wb9eMSAwVs4hBzm4lGuhESFOF99TSrGndPEe3L4h0LlUhqTLJtFcQ4WQj/ECpCilx1Pp5LFOQ6YTWLOP6V5b45H5AtvxuxkQga53egk0dcWDjc6JpNJXjeU9lU6jBmS64BZgVc0K0Tnr3JdgAVmz56NnTt3orq6GsuXL8fatWtx++23D/odr9eLmTNn4pe//KWq92WVROdwtz/qLcGTbJK8foMJHBRzK4OT0GejMpgfHQKQohKiew8l8PhczWaTPIcV7z07+Tyci4XLHceSJUswf/58TJs2DWazGbNmzcJzzz0n/z0QCKC2trZP0to///nPGDFiBGbMmNHnnjabDYsXL8Y999wDQRAwduxYPPPMM5g7d67m/WEJOZ5U4Wlmlz/EZSw0IAryli6/YkF+nENFGgBKIy7Vxzt9isuKNnHongokt0Hi0ZUciCoTSvsqn3hx9p5mCpKhyWQCCjnylrCYTSjOdeB4hw/HO3yKTsll+cLZO1eaIQoxkPhGJxQWotXoOFsjS/IcqG/vUXyqzuv6KM3fli4/gqEwF9Wqdu/ejRUrVmDTpk1yFernn38elZWVePrpp+VD5hO5++67AQAff/yxqvdlFdmD3aPU4C9e5+DMW8JuNaM4x46WLj+aOnyKQnYl4ypvcknSZ5sT0Gej3qV89TVRzyZ/MHo4x58eIepLoh6RH/d6HgtvnAg/EiaGoqIiLF26dMC/jxo1CoLQ173y8ccfx+OPP97vd2bOnImZM2eq1kZeSTQ0R7ou12HlKhYaEBfn2sYO5Zt1TjcNkgExEBLg9gbkJKGD0cShezWQ+AapJxBCRw9/p3tAbPLIxE73eFNCMgXJpTrWzZoXSnIl5cmHMxVcz6t8kYwLzZ1+hMKCoufEYxJTIEa+KFwfWyJhlGYTj6fqCXo2SZ55nD3T4phE0s2dfpTls//+rV+/HgUFBbJBCACmT58Os9mMDRs24Prrr9f1vj6fDz5fdJ5IxTECgQACgcCgvyn9Pd51yVCcI+ZNbPR0K7r/MXcXAKAk145gMKh6e1Ih3jiV5IrGpvq2LowdEr9QT6OnG4A4RlqMvVYUOEVj8PFOH/x+f5+D4v7GSeprYbaVq74W54j7x8Z2ZfO3oV2UwTaLCdnWgeeKlu9cspRE1sdjbV6FfRUdZ4ZoOH+TGadEruXLOkBojqRMNyoMueL11BZI3DOE19wbdqsZhdk2tHkDaOrwKTM2capMR0PLEjOW8hgLnegGiYxNbNPCYXJliZI8B3AsMzbrUq6/1i6/onWPV89JSSFWKktjQ8t48JiJJdEQDqmvJZwZS81mMWSwwdODpo4eLoxNDQ0NKC3tXVnWarWiqKgIDQ0Nut/3iSeewKJFi/p8vnLlSmRnK6uiVV1dnVhjFdB0zATAgu17DqGq6kDc62taxOutwW5UVVWp3h41GGicTD4zADM+WrcJnXvi5236ap94fWv9QUVjwwpi0IgVgZCAf777AXIGqMMSO05HjlsAmLB32yb07NOjlepwuFWcj3uONCmaj4c6AcCKHEsYK1Z8EPd6Ld65ZPG5xfn42ebtyG3aFvf6z4+IY+NtbdT8XU1knE6MHhsMvnZXhOaUuSSlK7ENLG8GGCDxzbpkgOPNdR4Q+yoam3pwelle3Ot5DRMYGlH+G9p7FIUM8hwLnWiOhobI/C1TWKmG0Jcm2RjIl1cIkHguI17li9UihnA0d/rR1NET14AUCguyEZE3Y5MUfq00LEdaH5VWwmKJxD2b+PRWA8R3rsHTo/i5asV9992HJ598ctBrdu/erVNrlLNw4UIsWLBA/rfH40F5eTlmzJgBl8s16HcDgQCqq6tx5ZVXql7B1byzEW8d3ApLbhEqKy+Ie33LF4eBb77GaSOHorLyXFXbkirxxmmtbwd2b6lH2ajTUXnZ6Lj3e+evW4CmZlz0rbNRed4ILZqsGY9tX4M2bwDnXHgxThvaW3c/cZwCoTDu/uIjAMANV0/j6mBxxNF2vFy7AX6LE5WVl8a9ftXXTcD2GpSX5KOy8sIBr9PynUuWvav3Yn3TfuQPOxmVlWfEvX7De7uAo0fxrTPGonLaWE3alMw4SV6dSiBjE9ELSVFUulmXTgJ5zAMj9bUxQWMTj5v10jwnvmnsVKRM9wot4yjpOxDdvPqCYbR3B1AQJ/dNE9cGxMRO4xsjmwseTrMzkWMRt/Dh+fHDAlgj4c26XO2Sv7lYkueMGJvihwy2dPkQFgCzia8Kg0B0nWv09CAcFuImwpbky1AOZWmi+UKkHDC8GRCB5Ko+acG9996LW265ZdBrRo8ejbKyMjQ1NfX6PBgMorW1FWVlZUn/frL3dTgc/VaottlsijdpiVyrlGEFoldVc6df0b1bvaKON9SVxcwm/EQGGqdh+WJfW7wBhX0Vw32G5mcz29eBGOpyos0bQLM3hDMHaLs0Ts3ebgiCWCVzaH4OV8ULhhflABDnr8Vijdv2tm6xsvJQl1PRM9XinUuWYQXRvippU3OnNH+1f1cTlWNKIWMT0QvJANMdECtVuJyDT6aotwR/GyTZ2NSubLMuxQjzaWxSrmD2Ci3L4ktEOG0WOWSw0eOLa2zi+ZmW5YvPtEFhyCvPngeZwLF2MdfCsAL+nk9GeYbkObD7WLRs+GBI41GU4+AvD1eeAyaTWPWpuSt+4veo52/6z19e83AByVV90qQdJSUoKSmJe93kyZPhdruxefNmTJw4EQCwevVqhMNhTJo0Kenf1+q+RiG9n8c7lBWC4TWUGYgatJWm+5D0PB4PFcvynfi6oUPRPqXRE5VLPBmaADH8Wlpv2rz+uOkEoqHM/D3T6PxNf0cHCb4C6wnNybJb5Nw1SoSbvFnP5++Flzw8jkUS6sWjkefTeJfySiWxSghvoWVAjHeeAkXkGMcGmLKIB0xjuw/hcPy8BTwb1jKBY7Is5c9wL80pyWA2GMFQGC1dfCYIB2JCBhXkMpINMBwqxDaLWQ7VbWxXvm4M5fiZNincvEbDQDnuq8GeTUoZN24cZs6ciblz52Ljxo1Yt24d5s+fj5tuukmuGFdXV4eKigps3LhR/l5DQwNqamqwd+9eAMD27dtRU1OD1tZWxfflCWnT3R0IwdMTP+E3z/lWJYOpks16IBSWZfUwDtdWOTWEAtkUNarxJ5dsFjOKIofDSmSTtN7wmMKlVJ6/ytYbSTfkcf5KkLGJ6INkhFEiyNNhg9To8fVbvTCWTl8QnT5xAecxDEkWbgpOMxva+T21BRLzWGuUhTiPz1Q8CfKHwmj1xq9IJ3shcmgYzgQkQ81wDueiJBMbFLxzLV1+CAJgMZtQrKBYAWskUkRDDo3k0FsNiHmuCvrKcxidpMQ3dogV9QYjHBa49mwqTeDgiRWWLFmCiooKTJs2DZWVlZg6dSpeeukl+e+BQAC1tbW9Eta++OKLmDBhAubOnQsAuOSSSzBhwgS8++67iu/LE1l2CwqyxUgEJXI4enjK3xyWZIwST8SmDh8EAbBH8u3xxtAEZLBkgOH1QLEkAUN4A8d7z6FyVdv4602ssZTHvacEXzEyhC4MdYn5fZQpmPxu1iWjhD8YRps3gKJBFiKpn7kOK3Id/L020gb2mDu+50E0nIc/IQ5EF1pFJ0GyAYa/+WuzmDEkUnK+ob1n0GSQXn9QzsPF46lXJnDMze9cHF7Qe7M+WMhYtGqZnTtXfyCq3B5TsKGTnimvJ5LiGtmekC7Ao5doSZ4DVrMJwYghabB3sNXrRzCyQeApAa9EdH1U5tHNAkVFRVi6dOmAfx81alSfA8OHH34YDz/8cEr35Y1h+VlwewOob++OWwhG1vM4lE2SjGnqiJ9bVtJ5h+bzF1oGxByKJxBpwqPBH4iGDDYo8JCulw6KOTzIKc51wGwCwoJYhXgwnVwyltosfB7OSZBnE9EHpS5+giBEPZs4VDDtVrNc+Sle+Ecj50JcMhwp2SDVu6VExfw9UyCxk6Do4sxnX+WNQ5znKp1iZtstyOPQWJru9ARCaOkSvdN4TBA+JFfcrIfCQtxcMPURWcvjmgEAJ0WU23pFhnt+DYhAYhsdnj0lLGaTvAbUx9EFpOdemueA3cqfCi0ZhiVDKJE+RA8VB3+23f4Q2iJJs4dzeKgoecAEQgJauwb36pZDkDjMKwsklpuT51QfQHQu1imQTVFPcP6eq8VskudwvAgiyfA21OXk0lgqwd9KSWiOJNziGZvc3gD8wTAAPhVMICbkKk5fefaAAaJKSKOnB8FQeNBreT7xAqIGwXj5NwRBkJ8rj555QGzesTjzN8YozGMernRHkj8Oq1kOheCJ2M16PIO2tFk/qZBP+TIsEc8mWZbyLV/ibXQCMXm4eDXcD1O4UZfmL4+bdCC6OWvp8qMnEDK4NYSaSF4e8Q5PJYNqTkyOVp6wWczyZr0+zvvawLnBX+keJfYaXg9ylEZgdPtDcEeMpTx6NgHRZxTvcOMYx6k+YiFjE9GHMoWbBunvxTl2OKwWzdulBbKCGaevkrLNY/JTQPQ8sFlMCAvx46Hrec8zonD+erqD6AmIhjfeN0jx3I55DnHJBKK5fbK4NQYmvFnn1JgtGRlau/zo9g++WW/gPLGn0o1Oo6dHdvUvilMBlFWi3r+Dy1Lp1P0kTo1NriwrcuyivqbEO4/gB6WG8FiDKa/rzUmyF4x30Ot436xL+mxzp18+3B8I3vU8aW2N610a+Xuuwxq3YjqryF5cbYP3lefcVLGQsYnog3TiHPcliMT883piAChPJs37aaa5l+dBPOHGt2fTcIUhg1IVwoJsG5w2Po2lcuW9ONWi6jifv+nON40dAIDyomyDW5I8spdd3DCkqGGNR1zOaN6+wZTi2DBz3jc68cJ0j0Z0hZMKsrh19ZdO1eN5SvDumWcymaKbOgqlSyuGKZTBxziXwUDU2HRU4T6FVxlclGOH3SJu1Qcz+guCIMsmXvdkSuWS1E9enykAjJD22XEM/tFUNXxGD0mQsYnow4hCccNztG3wE4N6N9+KNKA8Rlha0EZwqmACUU+CwQR5IBSWPZ94dU+VNgGtXX50+QYuASwZU3n1sACUK5fSu8zz/E1nag67AQATygsMbUcqKDXyHk2LzXp8L6727gC6I2FK/Cr/Yrvr3N2DVmyNro+ZYCzlt2qkRHRTR55N6YTs2RRHn40ePvE7h6X1I75hgm/PkNj1ZjDDmtsbQFfE05ZXPe+kGLk02HojF95IA2MpeTYRGYv0Enh6gvD0BAa87oi8geVXwZSE8pE4hrW6NFCmlcTzx4ZDDMnh05LuctrkPASDnRpIC3d5Eb9CXOnpnux5wKkSku58dcQNAJgwssDQdqRCmULPSdkzhGNFcVh+/M26ZHQryrFz6zl5UmEWTCbA648msO+PdDBmy880zb2cgdhDNjI2pROSUaK+Pc5mnePkyhJKw+gaOPcuBaIez4PtU6S/leY5uF1vhrqcMJkAXzA8aOL3+nb+Df4nRfaS8WQw73llJcjYRPQhx2FFYSRJ7WBW16Ot/Hv7SMajwfopCEJaeDYNU+DZVB9Tfp3XcAhAmXfe0TQwlo4sji5YgyV+l42lHG+Q0pW2Lj8ONHcBAM7l2rNJ8oIZWL74giEcj3hOpsNmfbAwOt6TgwOAw2qRjYhHWgeWpXVpsD5GvdXi5QtJhxAkKWSQjE3phBRW3xMIywmU+4P3UGYg1tg08BwWPfX536zL+uwgMvhIGuzH7FYzSnLjJ36XPZvSwlg6uAyW1l2e31WAjE3EACjJ2yRt1nnOMyJ5tRxr70ZggM16a5dfDofgNbQMiD7TwQwwhyOCrZxjAwwQXXAH8/iRFudyjhfnoXlO2C1mhMLCgOFLgiDICxrPhrV0peaoGwAwuiQHBZwmVwaic2swo4SkJGbZLPKBBo8o2axLayfPCjEQXQuODKoL8C9fJOX/eKdvwCptscZSnj3zlCbiJfjCabPIVdoG84KRc96kgT47+B6lG2EBcNqi1et4RNqnDC6D+d+PAcq8LmXPpjSYv61dfnj9/af76PaH5LQmJ3P+XMnYRPTLiIL4niGS4OPZMFGS64DDakZYGHjjICnSQ10ObqvuAcCoiBfMwZZBjE0toofFycX8PlMg1rNpkMXZzb9nk9lskhetgZTL450++IJhmEz85o5JZ76K5Gvi2asJiMqM1i7/gOHX9TG5QnitggREFWLJYN0fkpw9ZQi/8gUARkgbnUGMiFFZyq8BpijHjjyHFYIwcF+lkJwsmwUFHBtLhysMvyb4I56eJwhCTBgSv++rpPe0eQMDbtYPRfTZUcU5XK835QoOco6kQSgzEJsaYjAvLvFvPKeFyM+yIU8qNDLA3lM6/Hc5rVyvNwAZm4gBOCmOZ0iXLyjH1I7gOOeNyWSK5m0aYOOQLl4hJxflABAFWDjcfzy/JNxGRq7llREKvLiiOZv4fq5yXweav5F+lrmcsFtJ5LOGFEJ3xjCXwS1JjTynDUNyRc+swwNsdI6mQb4bABg1RJSPByObmf44JBvu+ZalI4sG3+gEQ2HZY41n5d9kMuHkIYNv1A/HbHJ43rxKhuGjbQN7dBN8IsmbQ839y6ZGjw89gTAsMQdVPOJy2pAn5eYcYJ9yKPIe8354Kumogx6epsHhPxB9VgOtrYFQWHZ0GD0kV7d2aUG8fXasDsHzegOQsYkYACm06NAACqZkRc/PssHl5NviGi/5nqRg8n5iMLzACavZBH8wjMaO/kOupOfN++Icz4DY0ROQcxrwrHABmTN/05XWLtFNekguv27+EtJGZyBF8WBz9KSZZ0ZHjE3H2nvQ7e8/5EoyWPDe12gYXf/ypbHDh2BYgM1iQmke356T0rM6OMBGff9x8fNThvD9TIfmOZFlsyAUFgb1liD4I55n0/7mTgCiEdlm4XsLKBnCDwzwvh5ME4O/pLs1dvTAF+x/vTnSyr+nPhCVrQM90yOtXoTCArJsFgx18a0zxUs9kC7GUoCMTcQAnFIiWowHeuGlk2ueK3lJSMr04QFe+P3HxcWZdwXTajHLi9bB5gEMEy2SZxPfwm1UzILVX1UWSYgX5diRG3Fl5RXpWQ00f/dFNki8nwKlK61dotGzMIfffE0SklJ0aICNzr6ILB1TwrcsLci2y27t/RnWQmFBlqW8K4qyMXsAw31sAlMLx0UlgBhj0wDGUkkXGM35/DWbTb3WSCJ9kD2bBpjD0vPmXZ8FgDGRfcr+AeZwumzWi3PsyLJZIAj9e3HFFjHifU8mydaB9igHY1J98O7tI+lBko5+Ioda0yOtCUDGJmIApJPbQy1d/Va5SqcNrLToSorkiUinmaNL+O/ryGIplK6vcOv0BeXy1rwLt5OLs2E2iX2SErrGIm16x6bBM5USBw50Gi8pl7xvkNKVtsg7V8RxcnAJKVR3oLm4L41k6WAnsA2eHvhDYdgsJu5DBiVjdp27/5CrvU0RA0wabF7jhUdKm9oxaaD3jCZjU1oSNZj2v1k/kCbeeUDU2LSvqX/dPTZnE8+YTKZBw8uaOsS8nGYT/wUppGdV5+7ut1BDdD/G9zMFYubvAHtP2VjKeVoTgIxNxACcVJAFh9WMQEjoN55UUjDHlvKvdEl92DvAgiUpmGmhTA/iYi1tEIty7MjjPDTSYbXIm6S9/QhySTkZU8r/Mz11qDh/9zR19uvFFT2N5/9dTTcEQZBz3xXl8m9sGjVkYM+mYCgsK/9j0mDdGMzYJOVLKS/K5t7bZ6jLgVyHFaGw0G9f9zR2AABOHZqnd9NUR14fBzhVT6eNjnzIRsamtGJkZA43d/rQ6eubODudPJuk97C/OSyGiIp7F94PT4HoPuWbxr767J6mqFGN97ycRTl2uCK5uPozrB1MEwMiENWDBtp7potnHkDGJmIAzGZTjDLSz2ZdDofgf9MgbdYPtXjhD/Y+uXV7/fJmMB0UTMlgtqefBesbadOQBhtBIGpc6c9FVfosHebvycU5sJpN8PpDqG/vnYtLEIS0Ui7TjS5/CP6It0haeDZFFMAD/SiJR9q6EQiJuRaGufjO7QMApxRLHrF9+yr1/5Q0UIhNJhNOi6yRtQ0dff6+J6Iop8O6Ic3f+va+p+o9gZBcxSsdZKlsLB0ghIPgk/wsG4oiIdn9eZgeSKPDU0l/29vPQdux9m7Zu5R3bx8AOD1izP+mHxks6e6nl/Fv8DeZTNE0Lv2trWmkz0phdMfae/oYhgOhsFycivecYwAZm4hBkE8NTnjhBUGQPUPSwbOpzOVErsOKYFjoE+cuGSWG5TuRbec7tw8AnF4mVryqbfT0+VttGi1YQFSQ9xcemU7GUpvFLId/nHhC0ujxwesPwWI2cZ+Hq7W1FbNnz4bL5UJBQQHmzJmDzs7+T4Qkenp6MG/ePBQXFyM3NxezZs1CY2Njn+tee+01jB8/Hk6nE6WlpZg3b55W3eiFFELntJmRZbfo8ptaIr1zxzt8aOnsHb4qrRmnDMmBmXNvHwA4pUTybOo7B6VN3sg0OJEEomvCoMamNPBsGpJrR57TCkHoq/eI+f96b+Z5Jjp/ydiUbkhyeE9T7/c1EArLuR1PSYPD01OG5MBkAtq7A/KhsIQkl04uzuHeuxQATovI4G+a+jE2Rfp6WhrIYAA4JbJu9ndoJXmdpoOxqSDbLlfwPdGwtrepE6GwgDyHFaV5fCdCB8jYRAyCtBGXrOYSTR0+dPiCMJuiYRM8YzKZ5MX5xM261Pd0MKoBQEVkwTrS2t3Hki6dmKTLghV76hVLMBSW3a7T5blKXgV7TnhXv24QjYonF2dz7149e/Zs7Ny5E9XV1Vi+fDnWrl2L22+/fdDv3HPPPXjvvffw5ptv4pNPPkF9fT1uuOGGXtc888wz+NWvfoX77rsPO3fuxEcffYSrrrpKy67ISDnSinP4VyYAIM9pk5XAnfW9DdqygTdN3rno+tiJcLj3qfqOOrHvFWliuJdO1WtPkC9ur1/OiZcOstRkMuGMYeKBzI769l5/iw2h4z0xLRDNO9Xg6UF7d8Dg1hBqcubwfABROSRxpNWLoFTJi/PKkQCQZbdgeMRr6cRQup114vt71nCX7u3SAkkv39MoGiFikULr0mW9kdaSr4/1Xm86fcG08i4FohEYe4/37qukP40b7kqLwzn+XTUIzRhowdp1TPz3qOIcOKz8n8YDwNjSPGw92o7axg5cffYw+fMdkQVLGgveKcyxozTPgaYOH2obOjDx5EL5b9KClS7GporIpmFnvaeXi/W+413wB8PIsVtwEufJeyVOLc3FB+gbHiktWGdxPn93796NFStWYNOmTTjvvPMAAM8//zwqKyvx9NNPY/jw4X2+097ejldeeQVLly7FFVdcAQB49dVXMW7cOHzxxRe48MIL0dbWhvvvvx/vvfcepk2bJn93/Pjxg7bH5/PB54t67ng84jgHAgEEAoNv3KS/BwIBHPeIp3QF2da43+OFcWW5ONDchW1H2jD5lAL589qI4XNUkVNRX2PHiUVGFTrgtJnR6Qui9phbVpDDYQHb6twAgDPLcjVvvx7jNCZyqFTb4On1O7vr3QBEz1+HWWD2WSUyRmcOy8OGA63YdqQN159TJn++M/JMRw/JZrafiZBtA8oLs3CkrRtbDrZg6tjipOZSOoxFunHWSZLu3ttguj3y79PK8tJiAwuIaTDq3N3YfcyD80cVyZ9L+5Z00d1HFmXDYTXDFwzjSKtX9mYPC1EvrtPSxNh09ogCAMC2o+5en28/2g5BEHMKF+emxwHd2NJcbDzQ2icX1856ae+ZHsZSMjYRA3L2CFFIf9PYgZ5ACE6baFjadkR8CcaPSA8hDgBnn+TCW1uArUfcvT6XFuuzTkqPFx4QQyJONDa1ewNyfLCUn4N3xg3Lg81iQmuXH0fbulGWJyY93y4ZYE7KTxuF64yIQrX1hMU5Xebv+vXrUVBQIBuaAGD69Okwm83YsGEDrr/++j7f2bx5MwKBAKZPny5/VlFRgZEjR2L9+vW48MILUV1djXA4jLq6OowbNw4dHR2YMmUKfve736G8vHzA9jzxxBNYtGhRn89XrlyJ7Gxl3p7V1dXYeNwEwIJQVzuqqqoUfY91LB6xT6u21KK8c7f8+bqvLQBM6Knfg6qqbxTfr7q6Wv1GqsRwpwX7Ayb8repTXFAqGrQbvECXzwq7WcA3mz/FPp1EjJbj1BkAACuOtHrxzntVcETOmNY1is+6wOTlYv4qGaNA5J38bOdhVJkPyJ9/tMsMwAyL+wiqqg5r10gdKTGbcQRm/HP1Rni+iR7IJDKXvN7+k6kTxiGt97vqPQiHBVnPqYnotxPKCwxqmfqcW16Aj2uPY8uhNvx48ij5853HIpt1znUfCYvZhLGludhZ78HXDR2ysanVB/QEwrBbzWmRNBsAzonsLQ+2eOH2+lEQyWcp6bfptPccf1I+lgLYcqit1+fSQXG6GEvJ2EQMyPB8J4pz7Gjp8uPrhg6cG1mgJGvzOem0YI0UjS41R9wQBAEmkwmBUBi7I6FlvHuGxHLm8Hx8uqcZW4+48YNJIwEAWw6Lgu6UITmyYOcdh9WC08vysKPOg21H21E2bgiA6OleOi1YE0YWABANw52+IHIdomiXQkGkk05eaWhoQGlpaa/PrFYrioqK0NDQMOB37HY7CgoKen0+dOhQ+Tv79+9HOBzG448/jj/84Q/Iz8/H/fffjyuvvBLbtm2D3d7/u7Bw4UIsWLBA/rfH40F5eTlmzJgBl2tw5TYQCKC6uhpXXnkljm2sA/Z+g9NOPgmVlWfHGwYuyNvbjPf+sgVtyEVl5VQAQJvXj8b1HwMA5t4wDYUKZEzsONlsbFbH3Gqqxf7PD8E0ZBQqK8cBAN7+qg7YuhPjywvxnWsu0LwNeo3T77/+GMc7/Rhx9mScP0pcLz9+azuAY7jk7DGonHGqZr+dKomMUcXxLvz1uXVo8Fkw46orYbWYEQoL+OXm1QBC+NHVU9MmXKWx4BC2fFCLnpwyVFZOSGouSV6dBDuMKcmF3WpGhy+IwzFeMJKx6dw00t2lA9PNh6Ob9XZvQK5Ely6bdUD0ctlZ78FXR9ow8yzR67KuSzQknlqamxa5qQAxl9HJxdk41OLFtqPtuOS0EgDpufc8L7KWbj3qRiAUhs1iRjgsYLdsbEoPYykZm4gBMZlMOOukfHzyzXFsO+rGueUFEAQBW49Km/UCYxuoImcMc8FuNaPNG8ChFnFx/vpYB/zBMPKc1rQoPSlxwSmFePETYMOBFvmzzRGr+rdGFg70NS4ZP6IgYmxyY4ZsbPLIf0sXhrqcOKkgC3Xubmw74saUsUNwvMMXVbiGsalw3XfffXjyyScHvWb37t2D/j0VwuEwAoEAnnvuOcyYMQMA8MYbb6CsrAxr1qwZMHeTw+GAw9HXjdtmsynepNlsNrT3iBWvivMczBpUEuWccjGU4WCLF90hwOW0YXt9KwAxcW1pfmKnr4mMqd5MOLkI+PwQttd55DbuPCa6w59bXqhru7Uep0mji7F82zF8caANU04thSAI2HBAXDemnlbC7DOKRckYnVqWj1yHFZ2+IA65fagoc2HvMQ+6/CHkOqw446TCtNnUTYyEHW096oHVGt0OJCrHCLawWcwYVyamhthe145RQ3LgD4Zlb4l02qyfW14Ak0nMQ9rk6UGpyymHII0sykZ+VvrMzyljhuAfXx7Fur3N8mfftIuySDpwTBfOGVEQMTa5ZWPT1jSMqhk9JBcF2Ta4vQHsrPfg3PICHGnzosMXhN1qTotciAAlCCficF7k1ODTPaJw29vUieZOH+wWc9pYXAHAbo32Z9NBcWO0ds9xAMCkU4rSIiGoxHmjimA2iZvBRk8PAODLQ62Rv6WXsUkynn2+TzSsdQWi7qnfOjm9+iopG19GDIeSQnLmcBfys9lUuO69917s3r170P9Gjx6NsrIyNDU19fpuMBhEa2srysrK+r13WVkZ/H4/3G53r88bGxvl7wwbJuZnO+OMM+S/l5SUYMiQITh8WPtQmSG5Dpx9Un7aJLsEgOJcB0ZFjPNrvxFlqDQnJ6bZO3dOxGC9+5gYag5EQ7HHp9GGDgAuOVVU+NdGdIFDLV7Ut/fAZjHhvJOLBvsqV5jNJjkMad1ecd2QPH/PKc9PG0MTIHp9WM0mNHf6cLSt2+jmECoyIaL7SDL46wYP/MEw8rNssnxOB/KcNrmAgfSert8vvre8pw84kSljigGIOqzb64cgCNjlFuXRZaeVDvZV7pAMol8ddgMAmjt9qHN3w2QCzubcUz8Ws9mEiZF39Ut57xnV3W2W9DDTcNeLxx57DFOmTEF2dnaf8IiBEAQBDz74IIYNG4asrCxMnz4de/bs6XVNMmW1M4HLK0QBtm5vM3zBED7aLW74Jo8plnM4pQsXjxU9X1buEkujS4u0ZFVPF1xOG84YLinTzXB7/fjyoLhITzolfTYNAHDpaSUwmcTQuQZPD75uNyEsiHmp0iU5uMSUMeL8rZbmb8RYevGp7M7fkpISVFRUDPqf3W7H5MmT4Xa7sXnzZvm7q1evRjgcxqRJk/q998SJE2Gz2bBq1Sr5s9raWhw+fBiTJ08GAFx00UXy5xKtra1obm7GySefrEWXezFn6il4766pvXJNpANSkYX3tx0DAGyIKP/pZJQAgPKiLJxUkAV/KIwVOxpwuMWLbZEw3W+l2UnzxaeJ8mXbUTfcXr+8oZswshBZ9vTSBa46UzRGv7u1HgDwecTolG6ev06bRQ6pkvpKpAdSmNWHOxvgD4ZlvUD0BEofgykQPcRYu6cZ4bCAd76qAxB9j9OFUpcTpw3NhSAA6/e1YH+zF60+E2wWE6aMLTa6eaoiGdY+3dOMti6/rEtUlLmQ52Tz8DRZJkYO+ddHDsX/HZm/18QUq+Id7oxNfr8f3/ve9/Czn/1M8Xd++9vf4rnnnsOLL76IDRs2ICcnB1dddRV6enrka5Ipq50JnDnchaEuB7z+ENZ+04wVO8VcJ9PHpZcVHYhukD755jj2NnXKoWWXMLxZT5ZpFUMBAP/cfBQf7mxAMCygoixPLsOZLpTkOWRl+qPdTdjaIipZkhE1nbjqzKGwmE3YXteO3cc8+CiiXF4S2STyzLhx4zBz5kzMnTsXGzduxLp16zB//nzcdNNNciW6uro6VFRUYOPGjQCA/Px8zJkzBwsWLMCaNWuwefNm3HrrrZg8eTIuvPBCAMBpp52Ga6+9Fv/1X/+Fzz//HDt27MBPfvITVFRU4PLLLzesv7zz7fGiLF39dRPW1DZhy2E3rGYTLjqV/7kYi8lkwo3niYnk39h4GH/bcAiCAFx86hCMKEwf7wEAGJafhVNLcxEWgA92NODNL48AiG4K0olvjx8Oi9mErUfcWFPbhA92iBuddNu8AsDNF4h5G5duOIxgKGxwawi1OH9UEUryHPD0BPH+9nq8uu4gAOCm8wcufMErlRHd/Z0tdaje3Yijbd3IdVgx44z0e1+lQ8X3ttVj1dfi4f/5owqRbU+vrDjjhrlw1kku+ENhvLXlKF5dJxZr+MEF6Td/p48T92Ora5uw9pvj+PJQG0wmcR1KF7gzNi1atAj33HMPzj5bWTJVQRDw+9//Hvfffz+uvfZajB8/Hq+//jrq6+vxr3/9C0C0rPbLL7+MSZMmYerUqXj++eexbNky1Ndn9mmPyWTCd88RJ/zc17/E1iNu2K3mtFS6RGOLGNs+/ZlPEAwLmHRKkZxcMZ248fxymExieNkv3toOAPjOOekj2GKRBPai5V9ja6so8q479yQjm6QJxbkOeeN39R8+hacniFHF2bjwlPTYDC5ZsgQVFRWYNm0aKisrMXXqVLz00kvy3wOBAGpra3tVR3r22Wfx7W9/G7NmzcIll1yCsrIyvP32273u+/rrr2PSpEm45pprcOmll8Jms2HFihWUiyQFzhjmwilDcuALhjFvyRYAwPfPL087b0IAuPH8ETCbgA0HWvG3Lw4BAH6SZp5qEtIa8ct3tmPLYTdyHVbM+tYIg1ulPiV5DlwU8XSev2QLwgIwraKU+0IL/XHN+GEoyrGjzt2NNbXN8b9AcIHFbEJlxLtp4dvb0ekLoqIsLy119yljinHGMBe6AyH89z+2AgAqzy5LO49LAPiPieJ6U7W9Ab9ftRcAMD0ND08B4PuRg5xnq7/BwRYvXE4rbkjD9ea0oXmYPq4UggBZX7rwlGKU5TsNbpl6pJcptB8OHDiAhoaGXuWv8/PzMWnSJKxfvx433XRTUmW1AcDn88Hn88n/lqpyBAIBBAKBQdsl/T3edSww56KTsXTjYXT5xJwUN503AoVZFl3arvc4/ff0U3HnGzXyv2+/eBQXzyjRcSrNseI7Zw/DuxHX1CG5dtw0cTgXfU2U739rGP782X7UuUVPxukVQzB2SFZa9vXnl4/Gur3NCEeqWN82dRRCoSBCIeX3SOad02Msi4qKsHTp0gH/PmrUKAiC0Oszp9OJxYsXY/HixQN+z+Vy4ZVXXsErr7yiWlszHZPJhJ9PG4t7/7EVXn8ITpsZP5/GbrWyVBiWn4Xp44Zi5a5GeP0hnFycnZaekwBwx6Vj8HHEUw0AnvqP8SgvSi8PLonbLxZlaZdfFJ53pen8ddos+P755Xjh433424bD+P5Qo1tEqMWPp4zCv2rq0d4trs93Tz8N5jTKOSZhMpnw00tH47+W1aDDFwQA3BTx2Es3zjopH7ddPBovrd2PQEjA+KIwbjo//QwwAPDdc07Ckytq0RnzTHMc6Wm2mHf5WHy0uwkdviDMJuC2i08xukmqkp5PLQapxPXQob1X0Njy18mU1QaAJ554AosWLerz+cqVK5GdrUwBq66uVnSd0fznWOCDIxYMyxZwdng/qqr26/r7eo7TDaNM+KrFjAtKwujcsxFVe+J/hxUSGaeLnUBDiRmdAeDqci8+W8PHXEyG2SOB92BGlgWYlteAqqoqo5ukGT8ca8JnDWZUFISR27gNVVXbkrpPInMp1puIIADg+gkjcNbwfLz6+UFMHTsEQ13pc0p3Ik/feA4+qT0Ot9ePi8YOSask0rHYrWYsnv0t3P/ODkw9dYgcep6OTD11CNbcexne/uooSvOcaVUu/kRmTxqJg81d+MH5I9D6dVP8LxBcMKYkF6vuvRT/u3ovHFYzrjozfS2J3xk/HMc7fAgLAi47vRSnRZKGpyMLrjwNjZ4e5DutOEfYnzZJpE8kP9uG5XdNxad7jqOly4+5F482ukmaMWFkIR67/iw0enz47jnDMLY0veYvE8YmpeWvKyoqdGqRMhYuXIgFCxbI//Z4PCgvL8eMGTPgcg1eBSEQCKC6uhpXXnklN+EaPzfgN40Yp0pdfkVdkh2n67RrEnPcwuE7lwypzt9k5pLk1UkQsZw6NA+PX68s5J1nXE5b2oYhn8iw/Cy8csv5RjdDF0YWZ+Pu6acZ3QzNGVGYjRd+OBGBQABVXxvdGkJNhuQ68PB3zzS6GZpjNptwWxobI2Jx2iz4w00TxPdV54N/vRk1JCctU5n0x+xJ2helMQomjE333nsvbrnllkGvGT06OSEilbhubGyUy1xL/z733HPlaxItqw0ADocDDoejz+c2m03xJi2RazMZGidl0DjFh8ZIGYnKMYIgCIIgCIIgCAkmjE0lJSUoKdGm4tcpp5yCsrIyrFq1SjYueTwebNiwQa5oF1tWe+LEiQDil9UmCIIgCIIgCIIgCIIg+sJdoOfhw4dRU1ODw4cPIxQKoaamBjU1Nejs7JSvqaiowDvvvANATBx3991349e//jXeffddbN++HT/+8Y8xfPhwXHfddQCUldUmCIIgCIIgCIIgCIIg4sOEZ1MiPPjgg/jLX/4i/3vChAkAgDVr1uCyyy4DANTW1qK9vV2+5v/9v/+Hrq4u3H777XC73Zg6dSpWrFgBpzOasHTJkiWYP38+pk2bBrPZjFmzZuG5557Tp1MEQRAEQRAEQRAEQRBpAnfGptdeew2vvfbaoNecWP7aZDLhkUcewSOPPDLgd+KV1SYIgiAIgiAIgiAIgiDiw10YHUEQBEEQBEEQBEEQBMEuZGwiCIIgCIIgCIIgCIIgVIOMTQRBEARBEARBEARBEIRqkLGJIAiCIAiCIAiCIAiCUA0yNhEEQRAEQRAEQRAEQRCqQcYmgiAIgiAIgiAIgiAIQjXI2EQQBEEQBEEQBEEQBEGoBhmbCIIgCIIgCIIgCIIgCNWwGt2AdEIQBACAx+OJe20gEIDX64XH44HNZtO6adxC46QMGqf40BgpI5lxkmSeJAMzDZL96kPjpAwap/jQGCmDZH/ikOxXHxonZdA4xYfGSBlay34yNqlIR0cHAKC8vNzglhAEQehPR0cH8vPzjW6G7pDsJwgikyHZT7KfIIjMQ4nsNwmZehyhAeFwGPX19cjLy4PJZBr0Wo/Hg/Lychw5cgQul0unFvIHjZMyaJziQ2OkjGTGSRAEdHR0YPjw4TCbMy86m2S/+tA4KYPGKT40Rsog2Z84JPvVh8ZJGTRO8aExUobWsp88m1TEbDZjxIgRCX3H5XLRC6AAGidl0DjFh8ZIGYmOUyaeakuQ7NcOGidl0DjFh8ZIGST7lUOyXztonJRB4xQfGiNlaCX7M+8YgiAIgiAIgiAIgiAIgtAMMjYRBEEQBEEQBEEQBEEQqkHGJoNwOBx46KGH4HA4jG4K09A4KYPGKT40RsqgcdIWGl9l0Dgpg8YpPjRGyqBx0hYaX2XQOCmDxik+NEbK0HqcKEE4QRAEQRAEQRAEQRAEoRrk2UQQBEEQBEEQBEEQBEGoBhmbCIIgCIIgCIIgCIIgCNUgYxNBEARBEARBEARBEAShGmRsIgiCIAiCIAiCIAiCIFSDjE0asnjxYowaNQpOpxOTJk3Cxo0bB73+zTffREVFBZxOJ84++2xUVVXp1FJjSWSc/vSnP+Hiiy9GYWEhCgsLMX369Ljjmi4kOp8kli1bBpPJhOuuu07bBjJAomPkdrsxb948DBs2DA6HA6eddlpGvHeJjtPvf/97nH766cjKykJ5eTnuuece9PT06NRa/iDZrwyS/cog2R8fkv3KINmvLST7lUGyXxkk++NDsl8Zhsp+gdCEZcuWCXa7Xfjzn/8s7Ny5U5g7d65QUFAgNDY29nv9unXrBIvFIvz2t78Vdu3aJdx///2CzWYTtm/frnPL9SXRcfrBD34gLF68WPjqq6+E3bt3C7fccouQn58vHD16VOeW60ui4yRx4MAB4aSTThIuvvhi4dprr9WnsQaR6Bj5fD7hvPPOEyorK4XPPvtMOHDggPDxxx8LNTU1OrdcXxIdpyVLlggOh0NYsmSJcODAAeHDDz8Uhg0bJtxzzz06t5wPSPYrg2S/Mkj2x4dkvzJI9msLyX5lkOxXBsn++JDsV4bRsp+MTRpxwQUXCPPmzZP/HQqFhOHDhwtPPPFEv9ffeOONwjXXXNPrs0mTJgk//elPNW2n0SQ6TicSDAaFvLw84S9/+YtWTWSCZMYpGAwKU6ZMEV5++WXhJz/5SdovOomO0QsvvCCMHj1a8Pv9ejWRCRIdp3nz5glXXHFFr88WLFggXHTRRZq2k1dI9iuDZL8ySPbHh2S/Mkj2awvJfmWQ7FcGyf74kOxXhtGyn8LoNMDv92Pz5s2YPn26/JnZbMb06dOxfv36fr+zfv36XtcDwFVXXTXg9elAMuN0Il6vF4FAAEVFRVo103CSHadHHnkEpaWlmDNnjh7NNJRkxujdd9/F5MmTMW/ePAwdOhRnnXUWHn/8cYRCIb2arTvJjNOUKVOwefNm2eV2//79qKqqQmVlpS5t5gmS/cog2a8Mkv3xIdmvDJL92kKyXxkk+5VBsj8+JPuVwYLstyb1LWJQmpubEQqFMHTo0F6fDx06FF9//XW/32loaOj3+oaGBs3aaTTJjNOJ/OIXv8Dw4cP7LNjpRDLj9Nlnn+GVV15BTU2NDi00nmTGaP/+/Vi9ejVmz56Nqqoq7N27F3feeScCgQAeeughPZqtO8mM0w9+8AM0Nzdj6tSpEAQBwWAQd9xxB375y1/q0WSuINmvDJL9yiDZHx+S/cog2a8tJPuVQbJfGST740OyXxksyH7ybCK45Te/+Q2WLVuGd955B06n0+jmMENHRwd+9KMf4U9/+hOGDBlidHOYJRwOo7S0FC+99BImTpyI73//+/jVr36FF1980eimMcXHH3+Mxx9/HH/84x+xZcsWvP3223j//ffx6KOPGt00IkMh2d8/JPuVQbJfGST7CdYg2d8/JPuVQbJfGWrLfvJs0oAhQ4bAYrGgsbGx1+eNjY0oKyvr9ztlZWUJXZ8OJDNOEk8//TR+85vf4KOPPsL48eO1bKbhJDpO+/btw8GDB/Gd73xH/iwcDgMArFYramtrMWbMGG0brTPJzKVhw4bBZrPBYrHIn40bNw4NDQ3w+/2w2+2attkIkhmnBx54AD/60Y9w2223AQDOPvtsdHV14fbbb8evfvUrmM10ZiFBsl8ZJPuVQbI/PiT7lUGyX1tI9iuDZL8ySPbHh2S/MliQ/bRSaIDdbsfEiROxatUq+bNwOIxVq1Zh8uTJ/X5n8uTJva4HgOrq6gGvTweSGScA+O1vf4tHH30UK1aswHnnnadHUw0l0XGqqKjA9u3bUVNTI//33e9+F5dffjlqampQXl6uZ/N1IZm5dNFFF2Hv3r3yggwA33zzDYYNG5aWCw6Q3Dh5vd4+C4u0UAuCoF1jOYRkvzJI9iuDZH98SPYrg2S/tpDsVwbJfmWQ7I8PyX5lMCH7k0orTsRl2bJlgsPhEF577TVh165dwu233y4UFBQIDQ0NgiAIwo9+9CPhvvvuk69ft26dYLVahaefflrYvXu38NBDD2VMCdRExuk3v/mNYLfbhX/+85/CsWPH5P86OjqM6oIuJDpOJ5IJVSkSHaPDhw8LeXl5wvz584Xa2lph+fLlQmlpqfDrX//aqC7oQqLj9NBDDwl5eXnCG2+8Iezfv19YuXKlMGbMGOHGG280qgtMQ7JfGST7lUGyPz4k+5VBsl9bSPYrg2S/Mkj2x4dkvzKMlv1kbNKQ559/Xhg5cqRgt9uFCy64QPjiiy/kv1166aXCT37yk17X/+Mf/xBOO+00wW63C2eeeabw/vvv69xiY0hknE4++WQBQJ//HnroIf0brjOJzqdYMmHREYTEx+jzzz8XJk2aJDgcDmH06NHCY489JgSDQZ1brT+JjFMgEBAefvhhYcyYMYLT6RTKy8uFO++8U2hra9O/4ZxAsl8ZJPuVQbI/PiT7lUGyX1tI9iuDZL8ySPbHh2S/MoyU/SZBIF9YgiAIgiAIgiAIgiAIQh0oZxNBEARBEARBEARBEAShGmRsIgiCIAiCIAiCIAiCIFSDjE0EQRAEQRAEQRAEQRCEapCxiSAIgiAIgiAIgiAIglANMjYRBEEQBEEQBEEQBEEQqkHGJoIgCIIgCIIgCIIgCEI1yNhEEARBEARBEARBEARBqAYZmwiCIAiCIAiCIAiCIAjVIGMTQXDELbfcguuuu87oZhAEQRA6QrKfIAgisyC5T6QDVqMbQBCEiMlkGvTvDz30EP7whz9AEASdWkQQBEFoDcl+giCIzILkPpEpmASaxQTBBA0NDfL///vf/44HH3wQtbW18me5ubnIzc01omkEQRCERpDsJwiCyCxI7hOZAoXREQQjlJWVyf/l5+fDZDL1+iw3N7ePS+1ll12Gu+66C3fffTcKCwsxdOhQ/OlPf0JXVxduvfVW5OXlYezYsfjggw96/daOHTtw9dVXIzc3F0OHDsWPfvQjNDc369xjgiAIgmQ/QRBEZkFyn8gUyNhEEJzzl7/8BUOGDMHGjRtx11134Wc/+xm+973vYcqUKdiyZQtmzJiBH/3oR/B6vQAAt9uNK664AhMmTMCXX36JFStWoLGxETfeeKPBPSEIgiCUQrKfIAgisyC5T/AGGZsIgnPOOecc3H///Tj11FOxcOFCOJ1ODBkyBHPnzsWpp56KBx98EC0tLdi2bRsA4H//938xYcIEPP7446ioqMCECRPw5z//GWvWrME333xjcG8IgiAIJZDsJwiCyCxI7hO8QQnCCYJzxo8fL/9/i8WC4uJinH322fJnQ4cOBQA0NTUBALZu3Yo1a9b0Gwu+b98+nHbaaRq3mCAIgkgVkv0EQRCZBcl9gjfI2EQQnGOz2Xr922Qy9fpMqngRDocBAJ2dnfjOd76DJ598ss+9hg0bpmFLCYIgCLUg2U8QBJFZkNwneIOMTQSRYXzrW9/CW2+9hVGjRsFqJRFAEASRCZDsJwiCyCxI7hNGQzmbCCLDmDdvHlpbW3HzzTdj06ZN2LdvHz788EPceuutCIVCRjePIAiC0ACS/QRBEJkFyX3CaMjYRBAZxvDhw7Fu3TqEQiHMmDEDZ599Nu6++24UFBTAbCaRQBAEkY6Q7CcIgsgsSO4TRmMSBEEwuhEEQRAEQRAEQRAEQRBEekAmTYIgCIIgCIIgCIIgCEI1yNhEEARBEARBEARBEARBqAYZmwiCIAiCIAiCIAiCIAjVIGMTQRAEQRAEQRAEQRAEoRpkbCIIgiAIgiAIgiAIgiBUg4xNBEEQBEEQBEEQBEEQhGqQsYkgNGDTpk2YMmUKcnJyYDKZUFNTY3STCIIgCI0h2U8QBJG50BpAEL0hYxORdtx6661wOp0IhUIDXnP11VcjOzsbR48eVf33A4EAvve976G1tRXPPvss/vrXv+Lkk09W/XeM5uOPP4bJZOr3vy+++CLu91977TWYTCZ8+eWX/f79sssuw1lnnaV2swmCSFNI9usDyX6CIFjAaJl/IrQG0BpA9MVqdAMIQm3GjRsHn8+HAwcOYOzYsX3+/umnn2LFihX4xS9+gREjRqj++/v27cOhQ4fwpz/9Cbfddpvq92eNn//85zj//PN7fdbfuBMEQWgJyX59IdlPEISRGC3zT4TWAFoDiL6QsYlIO8444wwAwNdff92v0Fu4cCGKiopw3333afL7TU1NAICCgoK413Z1dSEnJ0eTdujFxRdfjP/4j/8wuhkEQWQ4JPv1hWQ/QRBGYrTMPxFaAwiiLxRGR6Qd0uKze/fuPn97//33sW7dOixcuFDRYpAot9xyCy699FIAwPe+9z2YTCZcdtllAICHH34YJpMJu3btwg9+8AMUFhZi6tSp8nfr6urwn//5nxg6dCgcDgfOPPNM/PnPf+7zG5999hnOP/98OJ1OjBkzBv/3f/8n39soOjo6EAwGNf2NgwcPDui2a2TfCYJgA5L9+kOynyAIozBS5p9IsmuAUvkPZOYaQPKff8iziUg7Ro0ahaysLHz99de9PhcEAffffz/Ky8sxf/58TX77pz/9KU466SQ8/vjjsnvp0KFDe13zve99D6eeeioef/xxCIIAAGhsbMSFF14Ik8mE+fPno6SkBB988AHmzJkDj8eDu+++GwCwfft2zJgxAyUlJXj44YcRDAbx0EMP9fmNgQgEAmhvb1d0bVFREczm+PboW2+9FZ2dnbBYLLj44ovx1FNP4bzzzlP0GwDQ3t6O5ubmftsaS0lJCf7617/2ueaee+6B3W5X/HsEQaQnJPsHhmQ/QRDphpEy/0SSWQOUyn8gtTVAC/kP6LMGkPxPAwSCSEMmTJggTJ48uddnb7zxhgBAePXVVzX97TVr1ggAhDfffLPX5w899JAAQLj55pv7fGfOnDnCsGHDhObm5l6f33TTTUJ+fr7g9XoFQRCE6667TnA6ncKhQ4fka3bt2iVYLBZByesstU3JfwcOHBj0XuvWrRNmzZolvPLKK8K///1v4YknnhCKi4sFp9MpbNmyJW5bXn311bhtOPPMMwe9x5133ilYLBZh9erVcX+PIIj0h2T/4G0j2U8QRDphpMw/kUTXAKXyXxBSWwPUlP+CYPwaQPKfL8iziUhLzjjjDHzwwQfyv4PBIB588EGcffbZ+PGPf2xgy4A77rij178FQcBbb72FG2+8EYIg9LLyX3XVVVi2bBm2bNmCCy+8EB9++CGuu+46jBw5Ur5m3LhxuOqqq1BVVRX3t8855xxUV1cramdZWdmgf58yZQqmTJki//u73/0u/uM//gPjx4/HwoULsWLFCkW/s3jxYpx22ml9Pr/33nsHrTDy+uuv449//CN+97vf4fLLL1f0WwRBpDck+/uHZD9BEOkIyzL/RGLXAKXy/6KLLkIoFEppDVBT/gPGrgEk//mDjE1EWjJu3DgsWbIETU1NKC0txauvvoo9e/Zg+fLlfdxDm5ubsWjRIvzrX/9Ce3s7ysvL8ZOf/AT33nsvXnrpJfzpT3/C9u3b8atf/QoPP/xwym075ZRTev37+PHjcLvdeOmll/DSSy/1+52mpiYcP34c3d3dOPXUU/v8/fTTT1e04SgsLMT06dOTa7gCxo4di2uvvRZvv/02QqEQLBZL3O9ccMEF/brdFhYW9uteCwA1NTW44447cPPNN2PBggUpt5sgiPRADdn/X//1X/jZz36Gjz76CG63G2eccQaeffZZTJ48OaW2kezvDcl+giBSJRGZnwyCICAvLw/79+9HaWlpSveKXQOUyn/p2lTWAK3lP6DPGkDyn0/I2ESkJbFJA/Pz8/Hoo4/ikksuwTXXXNPruqamJlx00UW47LLLsGHDBgwfPhxbt27FAw88gP/5n//BsGHD8PDDD2Pp0qWqtS0rK6vXv8PhMADghz/8IX7yk5/0+53x48fL16WC3+9Ha2uromtLSkoULRYnUl5eDr/fj66uLrhcroS/H4+2tjbMmjULp512Gl5++WXV708QBL+oIfvnzZuHUaNG4bPPPsOIESPwj3/8A9/5zndw8OBB5ObmJt02kv2pQbKfIIgTUSrzk+XAgQPIzs5O2dAE9F4DlMp/NdBD/gPargEk//mFjE1EWhJbDnXLli04cuQI3nzzzT7XzZ8/H9/61rfwpz/9Sf7snHPOwbvvvgsAuO666wBA0clxspSUlCAvLw+hUGjQk4dQKISsrCzs2bOnz99qa2sV/dbnn3+u2O30wIEDGDVqlKJrY9m/fz+cTmdKm7KBCIfDmD17NtxuNz766CNkZ2er/hsEQfCLWrL/wQcflD+/6aabsGDBAtTW1mLixImqtZVkv3JI9hME0R9KZX4wGMSiRYvwyiuvwO/348c//jF+97vfwWQy4a677kJpaSkeeOABAGIlu9/+9rd48cUXMWHCBIRCIeTm5mLcuHHYtGmTKu1WKv+la1NZA/SQ/4B2awDJf74hYxORlowdOxZ2ux2bNm3Cu+++ixtuuAGTJk3qdc2+ffvw1ltvYdeuXQa1UsRisWDWrFlYunQpduzYgbPOOqvX348fPy6fNFx11VX417/+hcOHD8tx27t378aHH36o6LfUjNuW2hXL1q1b8e677+Lqq69WxX35RBYtWoQPP/wQH3zwQZ+QFIIgCC1k/549e9Da2oqxY8eq2laS/coh2U8QRH8okfmAmAfoyJEj2LlzJwDg0ksvxZtvvokbb7wR27Zt6xWWtX37dowfPx7jxo3DQw89hGPHjuG5555Ttd1K5b90bSprgNo5m/ReA0j+8w0Zm4i0xGKx4LTTTsNrr70Gk8mExx9/vM81q1atwqmnnorTTz/dgBb25je/+Q3WrFmDSZMmYe7cuTjjjDPQ2tqKLVu24KOPPpLdXxctWoQVK1bg4osvxp133olgMIjnn38eZ555JrZt2xb3d9SM2/7+97+PrKwsTJkyBaWlpdi1axdeeuklZGdn4ze/+Y0qvxHL9u3bZffopqYm/O1vf+v19x/+8Ieq/yZBEHyhtuzv7u7GD3/4QyxcuBD5+fmqt5dkf3xI9hMEMRBKZP7Ro0fx+uuv4+DBg7Icv/rqq7F582bceOONsnFJYvv27bj00ksBANu2bcMVV1yhSduVyn8gtTVA7ZxNeq4BJP/5h4xNRNpyxhlnYMeOHbj99tv73VQ0NTVhxIgRBrSsL0OHDsXGjRvxyCOP4O2338Yf//hHFBcX48wzz8STTz4pXzd+/Hh8+OGHWLBgAR588EGMGDECixYtwrFjxxRtONTkuuuuw5IlS/DMM8/A4/GgpKQEN9xwAx566CHVPQAAoKWlBYIg4JNPPsEnn3zS5++04BAEAagn+wOBAL73ve9h7NixvcLq1IRkf3xI9hMEMRjxZP7atWsxadKkXgcGra2tGDduHI4ePYpgMNgrdGz79u2YP38+ANHYdPfdd2vSbqXyH8jcNYDkP/+YBEEQjG4EQRjB66+/jscee0xRvPMdd9yBsrIyVarRacHDDz+MRYsWgV5ngiCIwVEi+8PhMH7wgx+gq6sL77zzDqxWNs/mSPYTBEEMzvPPP49169Zh2bJlAMSDhDFjxmDZsmXo7OzEQw89hPXr1wMAGhoaMGLECLS1tcHhcCA3NxdtbW3IyckxsgsDQmsAwTrqB9YTBCd85zvfQXt7Ox577DF4vV6Ew2Fs2rQJ99xzj3xNMBhET08PQqFQr/9PEARB8IkS2f/Tn/4Ux44dw5tvvsmsoYkgCIKIz8SJE7F27VrU1dXB7Xbjpz/9Kc4991xMmTIFJpMJHR0dCIfD6Onpwbx581BeXo68vDx0dHQAEKu5EQSRHGRsIjKWwsJCrFq1Cp999hlGjhyJIUOGYN68eTj77LPla379618jKysLL7/8Mh577DFkZWXhr3/9q4GtJgiCIFIhnuw/dOgQXn75ZWzcuBFDhgxBbm4ucnNz8emnnxrccoIgCCJRpkyZgjvuuAMTJkzAmDFjYLfb8cYbbwAQE4WfdNJJGDduHK699lqMGjVKXguKi4tx8803Y+TIkbjwwguN7AJBcAuF0RFEGkButARBEJkHyX6CIIjMhdYAgnXI2EQQBEEQBEEQBEEQBEGoBoXREQRBEARBEARBEARBEKpBxiaCIAiCIAiCIAiCIAhCNajEioqEw2HU19cjLy8PJpPJ6OYQBEHogiAI6OjowPDhw2E2Z94ZBsl+giAyEZL9JPsJgsg8EpH9ZGxSkfr6epSXlxvdDIIgCEM4cuQIRowYYXQzdIdkP0EQmQzJfoIgiMxDiewnY5OK5OXlARAH3uVyDXptIBDAypUrMWPGDNhsNj2axyU0TsqgcVIGjVN8khkjj8eD8vJyWQZmGiT71YfGSRk0TvGhMVIGyf7EIdmvPjROyqBxig+NkTK0lv1kbFIRyYXW5XIpWnSys7PhcrnoBRgEGidl0Dgpg8YpPqmMUaaGEZDsVx8aJ2XQOMWHxkgZJPsTh2S/+tA4KYPGKT40RsrQWvZnXoA1QRAEQRAEQRAEQRAEoRlkbCIIgiAIgiAIgiAIgiBUg4xNBEEQBEEQBEEQBEEQhGqQsYkgCIIgCIIgCIIgCIJQDTI2EQRBEARBEARBEARBEKpBxiaCIAiCIAiCIAiCIAhCNcjYRBAEQRAEQRAEQRAEQagGGZsIgiAIgiAIgiAIgiAI1SBjE0EQBEEQBEEQBEEQBKEaZGwiCIIgCIIgCIIgCIIgVIOMTQRBEARBEARBEARBEIRqkLGJEY62efFxbRMEQTC6KQRBEESaEQ4LONTSpXiN2XK4DV83eDRulTIEQUBLp8/oZsjQOp1+sPRMd9S1o7XLb3QzCM441NKFz/c2G92MpDjQ3IWtR9xGNwMA4AuGsO94p9HNACDKpSOtXmbkU6OnB6EwG23x9ATgC4aMboZMIs+IpXbrARmbGGHqk2twy6ub8OWhNkXXd/tDil/4wy1e/Hr5Lhxr71Z0fWuXH8c7tFPsg6Gw4pdyT1Mn/n3IjDav8YqXpyeA51btwYHmLqObAkEQ8Oq6A9iscL5ozQfbj2HFjmNGNwOAuEn+6xeHmFicmzp68I8vj6AnoGxh8fQE4A+GNWtPS6ePiXEh9OfR93fh0qc+xpINh+Ne29zpww1//Bwzf/8pE/PloXd3YuKvP8Ka2qa41/YEQlj49nZ8tKtRk7ZsPtSK8x/7CP/6qi7utYIgYMHfa/Dwuzs1aUu7N4Dv/O/n+PCoSdH1z1Z/g+//33rF8igRBEHA3Ne/xD1/r1F0/b++qsNVz67VbD19ftUe3PzSF4r6un5fCyY8Wo1/18R/psmw/Wg7fvXOdkUG061H3Pj285/h0t+u0aQtBF8kog9c+tTH+MHLG7Cjrj3uteGwgM2H2jSRBclw+dMf49rF69DQ3hP32i5fEG9vOYr27oAmbfnJnzdi2u8+UbzePPjvHfjkm+OatOWPH+/Dxb9dgz9+vE/R9Y+9vwv/94myaxPli/0tmPT4Ktz1xhZF17+67gAW/L1GE+OU2+vH+IdX4uo/fKro+hU7G3HTS+sVza9kWPCPGsz8/aeKjEhraptw1kMfYsmGQ5q0JRwWFO/39YKMTQzQ7Y9OztqGjrjXt3T6cP5jH2HOXzYpuv8PX9mAlz87gP96oybuteGwgG89Wo3zH/sIXn9Q0f0PtXQhGFK2IDa092Dirz/CL9/Zoej66174Aqvrzfj1+7VxrxUEAU+u+Bpvbzmq6N6J8sh7u/BM9Tf43oufK7r++VV7sPDtbZps1lbsaMCi93Zh1gvK2vLOV0fxo1c2oN2r/uLc3h3Az5ZswR1/29JrLg/EpoOtuPHF9dhZH18hSoYb/vg5HvjXDnysYPE/3OLF1X/4FG9+eUSTttz80hf4f//chj+s2hP3Wk9PAOc9+hEqn1O2eAJAp0/ZOwoAH9c2YeKvP8JvP4z/LhHs4wuG8OM/b8QfPoo/twDg1XUHAQBPfvB13GtjFbKegPrGT18whAX/qMG7W+sVXf/6elEpe2blN3GvfWPjYbyx8TBue/3LhNqkVE7/9K+b0dzpx90KjCr17T14+6s6vPb5QUWyMVFe/mw/vm7sRNURi6Lr/7BqDzYcaNXEqLK/uQvVuxrxzld1ijawd/+9BrWNHbjvrW2qtwUAflf9Ddbvb8GKHQ1xr52/dAvc3gD+a1mNJm35zv9+hiUbDuOx93fHvfbTPeK61ZGAbE+Ebxo7MPXJ1fiHRmseoR5f7G/BWQ99iFc+O5DQ95ToVq99fhCzXvgc85cqMxwkypbDbZj+zCf4WIHBJnb/cKglvvH50eW7sOAfWzFviTZt/2J/KwBg2cb4BzNLNhzG6+sP4Sd/3qhJW56K6GtPKdDbDjZ34U+fHsATH3yNgMI9WSK8GDFiVW2PL1MBYNF7u/D2V3VYuVPZ9Ymwfl8LAGD/cWWHFXct24ov9rfiwX8r23smgiAIeHtLHWobO+S5Mxg/X/oVAiEBv1K4D06UB/69A5OfWK3IASAUFnQ5UCRjEwPsOhYNVSjItsW9/p2v6tDpC+LjWmWW9MOtXgDAxoPxX4LuGCVRyUv8+b5mXPrUx5incMH63zV70N4dwBsKhDgQPdX5SoF77daj7Xjh431Y8I+tCCuwpDd3+jBvyRbMeW2TIsu7tGg2dyrzsvpd9Td4Y+MRRcLH6w/igX/twMK3t6FLgZK5XcHJVSz3/H0rPt3TjN9+GH+jKQgCnllZiwX/qMHRNm/c65tjTms7euIbs/7ztU3YeLAVN7/0RdxrAeDvmw5j3tItCbtYH1RwYv77j77B7mMe/M8/lW14/l1Th9kvf6HYVX1f5B1SstjWHHbDHwpjb1OnotPMf9fU4ayHPsSr65QpotLC9oLCEzKCbf5dU4+13xzHsx/FN8DE4rDFX/bNpqinjEfBO93o6cGSDYcUn5K/uu4g3t5Sh5+/8ZWi6yUc1vhtb1EonyXCYQGzX/4C1//xc0XrRlsCBvvY+yn1zv37psOY+/qXisYy2VArpX3YesSNn/1tM+rd8U9JY9ctXwIGSqVe1C2dPvzyne3YflSZ14aEgPjPNJyEsr31iDvhU3IloTk2S2JqeSgswJ2A5/fdy2pwtK0b/0/hmkcYx51LtsAfCuPR5bviXhs7563m+HPo9fUHAQAf7Y5vDJLun4iX1U0vfYG9TZ245dX4h+Kxh2ZWBfP/7S2isfwzjUMG7db4RvymDm08ZZIhGDMHEl0HlZCIXI/lmAbeRL6YuZiIseRQS/w9TaJ4Yw6S7ArmrxIdLBUk7/Vnq+MfRL74yT6M/mUVHnovvoxJBTI2McD2o275/ys5RU7WDdCkwNO+K8abSYly/NEucaH6cGejIqWx3p1c25UoYKFwdOzqFCjHf/n8IN7ffgyrvm5SdJqSiKCNPVVQEiaw9pvj+OsXh/DGxiOK3HF9SYZa7aiPn4PlSGs3nlu9F29vqcOyjfFPP5tjnrunJ76hrCNyjZJrAeAXb23H+9uO4SEFoSixSovTpuy0PxH+9Ol+rNvbgh+8vCGh7+U6rHGvybJH29voif+eLI0sKIve26XIa+I4QzlviL50+oJY83WTIoMHABxtTU5pcihQoGMPHTwKQhX+a9lX+NU7O/DQv5WFi+1SIIf6Q4mSlhPzrikZyx317Vi3twU1R9xoVbDmJRISEGswUmIY6vaH8Iu3tqN6VyNWKggDTNZbyqvwe9cuXocPdjTg+dV7417r6Y7K3u4EQnOUtuX7L32BpRsO4943a+K3JcZAmqVgHUh0rfh3TR2uXbwOdy7ZnND3cp3x14FYXUeJd8L//HMrzn2kWlHoFAAcUXCARLBBIsbkjl4Gm/jKfp4z/sF2LPPf2ILzH/tIkW4CJBb+Fys7lHxPyaG8GigxHLhixlFphIdWxI6dFqlQ/An0L9YApNQDPxGjUezamsh+SGlbGj09ivMqxb6n/5+9f42WtLrOQ+Gnqvalae4IcQchCSQBEiCBQCDJAomLVD7J8BgnY+jkJJE+5VhjHNs6x3YnJzYnXyTLdoxkybJyYsVy5BApcXIkf4njOGYLaBqai2jU3Jp7NzR9g6bv9L177127qr4fb73vO9dtrmfu7r17A7XG6LG7qlatmrVqXeZ85jPnZOxsRgeT7Xf+5vlZhSOeenx+nxye7qLfB1oEQH0kbQg2LYB2UChbjJK2TRwiliRjI838LpDKK4NGv/PE8er/zwjQLNUYD2msjRKX5/RMvRFf2pYPR9w/aVOOLQeaPAiZ7yxlOUCAMHJ8y6W+hZBFHsYMU0kyvZj+px0/lu1TNnn5MOCnvGCZg/mMkxZV/2dkX09SdgFX9sVjeSND7r3Xdud/p3effrzonzcg5jIX1LAdeft/lr2ML/3wMfz2X3GMg52zZLWMEewguRYZULhkb/6EDM2ZrSLMKGmLBWjLsLLuX12D+0d7j0jnEWM43vtiDTAxhg4L1ADueciwpmRIP0O2kUCdJQ8Mc/cenJrB2u0FK4g5G3eJuWbsIwaQKluv16/C7Z7ctId+HwAcT9wDEihggN6S5fHP/5oLydhPOnmG7c3VpP7C6D4nEsCnbBPPbsXewx0qnEs2ho0qz2nm7Dh1Ma9DAsC/e3g9PvYHy/DLP8qHVksHBXNXyvtmF3HG/+DBdfj0Hy3H7/zN8yZwhTDfnLOUYVz9lydewxVfvwf/5C+fpkAYi70p7SVm7Mc3vIEPfu1u/H/+/Uoq35BcJxanCyPLa7sP4fpv3IcbvrWc0q13G+8+6VjOtamZLn74yAb81VObsdSYh5Kxtco1c9wcs63esmDTgw8+iL/zd/4OzjnnHDQaDfz1X/919j3Lly/HRz7yEYyPj+Oiiy7CD3/4wzmXEwB+7caL8HevOAcAMMWATcKzcGjKAjblf+6DYrwtBAtJbiyGlbVdGBk5r7NDCybAJinLS9vydHVX9vw8WlB9eegznsRJcTAzyrfsw4AkZdtOGHmTMzbwc4e41BhF9iwB8OQuLznnzL0sjVhGFmlEMfTacWGU5BQF6WlcTFwu0nBkAEppGOf23kJI8jxsevvBQ+sAAH/5OJdzTjIKLb8vo/zLfH0MYCM9zYwsltAD6S1mZJeGFhPy/MBLdRjJbBmjqSbPTwYsf1CwWhlWi4VBJM9aJh/jz0SIygnjeQ/pbmFoTRqMEsZQeEaEzl31rlNtshBzNG4Amw6IuWMcePLzGYarPNctCZAXSiWvYTs2TbKDGBBagk0WxgSbvqNsp58wnu0jQVVGdsnYyJ2Tk50ufu9vX8DWfZMOmJ9qcn8z943cr9v35fXrHz+2Cet2HMQPH9mAdYbiCIyjRZ41jEPnwZd2YO/hDv7rk6/h/tVMMnT+fpSRIIyN8vjG3Tg43cXyNTuqHI1ak6CR5R5kwKYNOw+h2+tjy95J3E7kuJRh6cwcWZwbUidhipLIuT6FAGXLuZuLSBDZ3rJg08GDB3HFFVfge9/7HtV//fr1+MVf/EXceOONWLVqFX7jN34Dv/zLv4y77757jiUtWmmMMoqXzI2Q2zhS8aeYTZ16PCu6bK1qkTsgpJHTomSvx9tEhJjITXx4+ih7tMV4DIghQUbm4JTK9NH2VMpL4jBxcMrwLOYglwr3q2/oa0we3EzuDRdsyl9wUrHZQIRSylWYM0y3C1C4Sxjgcu8xYaDSoMsZdzKWn9lLwzb/7Rcufmf1f4aZKXOl5dZi1+ittYbRve+ME6v/Mwq0hdkkmVVW2Rk2kfRGH+1yxPJOZHJoyPOIAb6kvpAzumRfxqCT88jMi5xri6eZceLI842Zl11G4GuR8OrmQmGkccmE90tZmP5WVqE0XLaTIU4AF+4xbMeuSd2dYSFJfYfZf5JlZwnX23lgKuuAkDbK6ScSYNOkBJtsOmTuLvHTX+ScIbKIDuM4kToq40Rx7Q7+nGRCyCcdZlP+jpVnGTPvlvvRcbQczOsQHSELk7d2j/idLGATA6xOdyXpIq+LW50b8r7JrQH5Gz34ch7olWl2GFV/crpkNs0t2GTjUb6J2uc+9zl87nOfo/t///vfx7vf/W780R/9EQDgkksuwcMPP4w//uM/xq233jpXYlatRBUZxcg9IHKATb1pWwQ76JAxjM4BmwjZ5eI/OD3j5Nfwm2MEEKDH4WmbcjxpAHj8S6fb66tG+2EjCGe9gHYc8Bg8J6cRbKvsDohByL5zvy2MbtLgYZe/Y7fLgE02ltWkwxCzgXaHp7uqN2C7kWUl9x6TF0EqObnfSZ4Zc1GGdtiOvEkv6opXduF9Z56o9HZZO1OdnroW5b5kwrOsBq8Egp/bvBfvfecJan85Zr/fR0OxfKVSybB9phyAx6ZwH+0wOiuzSd4DzB12SADUk50uFi9K95XsWaYqqXVe3FCCozuPHWdeCFmMwJfce3sOd1Q2hpwLZj3uNKY9OCTWDMNsOnHRSLXONuw65ISG+006g95hCGcftvlv8txjwmHkmcqAyR2hB+zYP+WkxIi1kWajclq9cWDayVXkN+ksGyfuG8nKsurLW/ZO4pxTjkv29cHsTrePsZH0fSP3nDXKYBvBbJJnRg5ol7oaw7KSsjAOHfn5zBkv7bBer48maQMx+UKlLMy5uuewDVy1NOfuI2R5wwg2SX3njUPTOHdMWb+evZ+bd2m3U3bzPIXRvWXBJmtbsWIFbrrpJue5W2+9Fb/xG7+RfM/U1BSmpkRy5H1F0tNOp4NOR1cSytfLv2WUzcHJ/HulwrL34CQ6nbRysX1v7WWe7HSzY+87VH+fg1N5WSRYwMkuFN6Dkzh1kWKs760ZQfuIsQ9MCuNrOv9dDwvZDxyeUvv7IMruA4dx8nHpy3bfIbnh87IcmqpfZ+Z9jzjcdh88jE6nkCX2Pv8SOXh4So0ZPni4HvvQ1ExWlt1izew5qM9jOWb1WZPTav8Dh+uxDxPzuPug2I+Hw7H9fXdQ5u0i5l1egvsPT+GEsfShf0isx/2HifV7WBpI+XmX6/dg5LvKdnDSNXQPT04lq774c8Q0S99hizd5NuYUln6/7wCSxZ2QPo+k4TJDgI3SWGEAZIsDxDegTco/oVRKUIXJoSH3dA7IkJ/PeAKtCcKtyr8Me88BPFJ2JhG6ZV4AO5tIthzgaJ0Xl62W798Rjow9h6ZpsGmm1886b3aJO4kB4RyglwCb5NzkWFnSS2+tejds89teF5EFTJS0E4rWsTnacmBAt9d37o0cGCDz3DAAq8tssjmKcwWTfLBguttTGbL7HLCJYF0a8yRZQHzHSWTMtWiWhXDmTnmgv2ZHHMm8MGf2Hid0LacvuY8PTulEB/n5nZn8vEhHC5X/12F9TeNcBSz156LT62G8mZ53uR8miXmcrzC6Idg0aFu3bsWZZ57pPHfmmWdi3759OHz4MI47LlwMt99+O77+9a8Hz99zzz1YvHgx9blLly4FALz6agNACy+t24CJiXXqe/YdaKEM6Ln/4RXYckp6M2w8AJQ/82Snh7/52wloZ9ZjOwo5AGDHrt2YmJhQZVm3sYkyGvOZ51/AxB69GtHkVC37Pfc9gPOOT/d9YXcty+4Dk1lZnnq97r9p8+uYmNBzn2zeWsu+8slVaL6WLsO9vwPI7fI3P12Kdyhe5Jf31rLs2X8wK/uLG2pZ1qxdh4muXv1n/8F6Hpf/bCV2v6NYA+V6ku3QjCv7nXfdjcXKzn9crIHXt+/Myr55Sy37k8+txll79RKab+yrZX/okUex/fn0+t16qJb94OR0fh431bK8smkzJibiCYvLeVr/at3/6eeexzve0JOsHhLr9+5778MZ6TsCz7wh9tKe/VnZn36t7r9h02uYmNik9t+yvZZlxWNPYGp9eh73TgNyDfz1nXepawCIr6VUO3RoWOHoSJuFMbH7UCdQ/LQmARvG8+aG0TH0el52n7U3NdNVFek9juw25Z8JXXPmMTO+VCqZsHQ5HsNsMjN4DErupKfg5pqZ2STBpozB6OdrPDTdVZV/1xCxhZlT613IuzvD+vLX93TG6JIMRAaEc1mFebBJrrGcF14yTo52frJhO7pNGo3MmreG0Vny+/j7P7fO5HjMmW3N2eSESmfO1UD2mR6gkLhcxowRtDOGruXuSsdJRIBBElywykIxm7x8rtq557Oscg4FV4fIf9e9h3kmrT/czgNT9H3DsKysrF65xnNOKP936XT70FL/ucwm/r4ZhtEt4HbbbbdhyZIl1eN9+/bh/PPPxy233IKTTjpJfW+n08HSpUtx8803Y3R0FJsfXo+fvvYyzjz7XLTbH1Lf+/Vn7gemi0Posis+glsvOzPZ94mNu4FnH6seX3/DZ1Sv3d7HXgXWvggAWHzCSWi3r1Nl+dv/vArYWSSWe9d7Lkb7Mxcl+/b7ffzGo7UB++GPXoePXphO9jn24nZg9SoAwGS3gVs/+znVg7h++TpgYwHSnHr6O9FuX6XK/qPNK4F9ewAAF3/gMrQ/dkGy75a9k8DjD1aPr77uk7jk7HSYy/1rdgAvFOBVa2wc7fYNqiyP/e2LwJYCGDnznPPRbl+m9v+dp+8HBmyS9112OW7+0BnOepJt675J4LFa9l+48TM4Q6FMH3ziNWBtARgdR6yBv9z+BLB7FwDgrPMvRLv9AbX/15+5HxgwuT581dW44X3vTPZ9/vV9wNOPAgCmew187nOfUy+s5+5+Cdi8oZD95Heg3f6o87q/7/5/O2rZ33PR+9G+4T3JsXu9Pn59Rb1+r71eXwN4diuwpqgs1m2Oot3Ww3Gfv+cl4NVC9tPPPAvt9pVq/z9dvwI4UOT2ueSDl6P9kXOTfV/dfQh44uHq8cc/9WmcfXIcLfXniGklq3PYZt+kIpfzMvo5DXLGyB5raIDR4LUorT6gMzXTgxYwaA1rcNlE1rAGffw3jOydw0bgy8Lgmen2HGMkB5QdCcvKmrMpNzc+0PHGwWlV+e8YmU3W/FEWIM6XPQ82ScPbtmaYMDrLmpFhdNYcm8M2v83NmUYANsYwOnleWMGmHBhgBYel7My6lAZ9JzM3oey8Y8Z63zD9LfvVem9LkJ9aA4bQtemZnjPvWeeG+PzJTg/dXl8t9OTOS152S84mPyXv7kMdvOsdSn8jq1fmpLKGXuacUMH6zYClB0SUDCN7uX4XjbXAZ/yztyHYNGhnnXUWtm1zKxVs27YNJ510UpTVBADj4+MYHw9/9dHRUdpIK/uesKiIyZ7q9rPvlbS+yS7U/r2G6zGe7DbU/tKG6fTyskyJS2emp8vS6fYcOuNUTnYvf/1Ur4GTlao40kCbJuZRbsTpjOxouErfoRl9/E6vPlSnZ3r531ScT8wakF6Ow0KW2Nqb6buHWQ9NWvYpQnZJrz44ne8vL6xuX1+PM333cuo1WirdUzJeD0x1k2OX8yTXQLevrwHfaOlkZO+KdOIHpmYwMjKS8ezwewnwvC8ZWXpw5yy73mE/xxZS+973vodvfetb2Lp1K6644gr863/9r3HNNddE+/7VX/0V/uAP/gBr165Fp9PBxRdfjH/yT/4J/tE/+kfzKrNFCfUVw5w3bc8hm/HthtFZmU0ZQ8STPacQ7TGysuRc7DQyeHKAjZs/qo+Zbi8ZjlrIYsvZ1DEAPHs8ICIH8Mh52Tc5g063p4ZSWcPoHJZVpuCGr5DvOdTB+ael+1tDLKwhffJ32pNhNgXrt6uHsEqQkQqjM7AKu4MwvrLl9p71Nx22Y9fkb8Wce/uswITYFzszYXRTHgifAybkOqSAMiOzSc7HTM92V+buVmvYtpzr3P7r9fpOnzyzyXZvS1mYXEMWJ5EPfOfk8c/dmV4fWkG9aYMOAdiAOF9USxEIhtn0hpNf+Og6N3wHmGXvWZwbx4025xRsGgZtD9p1112HZcuWOc8tXboU112nszqOVls02IWMMiLR6FyCZX/T5haqPOgZD6KlGl2QOygru+2ScA5aihIqUPpcRQBvw+e+q9UrJQ9m5lJx10BGFu/13CU05SQIz8veMazHfr9vmhv/83PzbpGl6CNkMcwLkL9UpCy9fv5CPJK9l5PFH+/AVH6NvVnbT37yEyxZsgRf+9rX8OSTT+KKK67Arbfeiu3b46V9TzvtNPzzf/7PsWLFCjzzzDP40pe+hC996UvzVom0bBLoyJ3Tft6lHDBhNURkZUQmb4wljC4EynR59hqrzsjxcomwu70+5FTmziM/ZCOXE8FaGc8GfHl52Ax3EpAHv6YMhkgxHg8K+q/nQmGsslhDL4/E05z7nazFQuR9nWM2WVkbUh/s9vpZo+vN2L73ve/hwgsvxKJFi3Dttddi5cqVav89e/bg137t13D22WdjfHwc73vf+7Ih7/PRpFN5aqaXrYwmnQJWNl/u/vDXeI5NZAU17TmbeGAiYCIaQte4nE0GlpXR0SL3/9RMLwg/DmWRwJdNd88zvry7L3ffTNvm3QJ89ft9527PhW37vg+TLMQ8yvXL6CiWqrMxJrjWrKysYc6mI2wHDhzA2rV13pv169dj1apVOO2003DBBRfgtttuw+bNm/Ef/sN/AAD87//7/44/+ZM/wT/7Z/8M//gf/2Pcd999+Mu//Evceeed8yLvogENO3dJ9Pt9ZyPkSs37h19uE8vEglx1Ah6Y8Mc7lDF4/U2e82DIw48qp2wCynzQTj/0fQ9DLl7ZcvH3+33TJeEffvlwCwHCGWnBzMUvdaZsyI03F4c7XZyi9JcKGhPj7gBfhnnx3xtrsVwBi5WiMrIKEQU2GRJK+/vhEFFa9s3avvOd7+DLX/4yvvSlLwEoKo3eeeeduOOOO/Dbv/3bQf8bbrjBefzrv/7r+NGPfoSHH344WYn0aBaHqMaU5d07eoL4Q17C91yi/V1eKE9ORpk4f28m+Tzg0t4nM8ntD0+5r6WS25fPyVC4w0ThBwkyT83o/f379lCmSMABT+Hef2gS4800p10WfmBkd+9TfR59WaxFAnIFOqam3ftRG9vXS3LzuP+Qy6QoCp2k+08aflPAnUcpS+p9rqdZL3Lhr99Dk9NVgY5Ym+7w8wi463fvIV2Wg16I6+Fpfd4np93XDhx2c5e82YtDlI6G73//+7j22mvx3e9+F7feeivWrFmDM844I+g/PT2Nm2++GWeccQb+y3/5Lzj33HOxceNGnHLKKfMvvC+buLP7/XwhBRewYXIN1ePndKVYkm2tOWATxcoyVqMz6ErRnE2aLGIeOSYtz7KKVcbTZXF/x8mZLhaPpc12qZMy+q+FMeoznK3ODUu4YxYM6vacPjlZfNU+u96dBOE20I4p7uL8ThkA0XeCZx2RVrBpgMQNczbNsj3++OO48cYbq8dlbqUvfvGL+OEPf4gtW7Zg06Y6Ae+73/1u3HnnnfjN3/xN/Kt/9a9w3nnn4c///M+TxsbRbosGCVJzlG//cMohuv7CzC1sCQBxgI3YZMY8DVZmU64qgDQcmJKPDrPJwFIB8jRMmViQURQsLKtur+8ANlmwychscmLQmRK6DsBztGXxWRD8ZU6t32l+vfuXSF6Wvvc4A/QKACjHsvLlsQK9DIj4ZmzT09N44okncNttt1XPNZtN3HTTTVixYkX2/f1+H/fddx/WrFmDb37zm8l+R7M4RNn2isIPr6zfiImJ9cn3btgPyOv74RUrsXt1+nx8TiTO73T7+B9/OwGtGJVMnL9l556sp/+wSJy/5uW1mJh+Kdn3eVH4AQDuf/AhrD9RkWXjq5Us+w/lC0Vs2VbLsmPnG2p/v3jCk08/g+O3PZ3s/9RWV/af3rNMLRSxen09j1Odmazscg2sNa6BRx9/CoeVIgErt7uy33f/AzhLWaqvvl7LnisWUhxXtSzPvrAGEwdeTPZ/7aDb/7EnnkJ/U1r251+tZZ/qdHHnnRNQfDfYs7eex02bt2Dp0s0A4kUP+n3gcKeWZc3Lr2Ci83Jy7Oe89bts+QNYrRQ62SD2HlMsZNtOcQ68ugUTE5uTffd5hR+eevoZLN6aXr9Pb3Flv/Oue3BCBCd7sxaHsDoa7rjjDrzxxht45JFHqlDwCy+8cD5FTjZfl8oVUth3BAnCLUwPgAmVNobRWYGymdkDPJacgvZ5zISxGoEvv//haR1smjSwo/3Pt7AiS1m05uvLOdvTlq/Qk8UINmXzUxntCDd0LedA75nsN+vec0JYDWDpEGyaZbvhhhtU2ukPf/jD6HueeipdkWwu23EksylAxg0bGDj6YXQWirg/Xg5dDg5mA4OHOSCmDKBKENKXBVXC/pqiYEkyGDC+DCwrIH8A+SBcjpXlsqysstgAHsv+YEIELGwiH0y1Mptyc2PZe/1+/4hCWJmY+Ddj27lzJ7rdbrSy6OrVq5Pv27t3L84991xMTU2h1Wrh3/ybf4Obb7452f9oFoco2+88XRd+OOvc89BufzA5xuMbdwPP1YUfLr9SLxTxzF1rgM0bq8c33HQLTlyUvv5l0v/+yCK0259K9vULP5z/Lr1IwOgLdeEHALjqmo/h2neHCXvKeTrz7HOA7VsBADNoZhPt//mmR4H9BdPsxJNPRrv9sWTfnQemgMceqB5f/P5L0P74hen+j24C1tfr6GOf+AVcfMYJyf4/++vnga0FWNBFA+12W5X9Xz73ADBgzJ1xll4sxF8DH7jsQ2h/5Lxk/90/3wS8Ust+3cf1Agd/tetJ4I2dAIBFx5+Advvjyb6Hp7vAz5dVj8+78N1of/b9yf5PbtoDPFOHN33w8svR/nC6wMHqpS8DrxXAWx8N3PLZz6r5pv74pYeBwwUIctKpp+Pmm69IFj2Y7HSBR2vZc+u3+fw2YHUN6Fxz3cdxxXknJ/vf85NngJ3F+m2MjKHdvjHZt5J9AOAcf/JpaLfjueYA4LXdh4EnHqoev/8SvdDJ1p9tADbUQPAnb3ALRbyZi0PMxtHwN3/zN7juuuvwa7/2a/jv//2/453vfCf+1//1f8Vv/dZvodWKG19zwWqNtcmOC7ocODwFhYjoOM4OTumsyGJ8oW9kGHc+K/LwlM6inBKA0Uyvj8OTU2puO6mfSNljnzHT7bnGfY5Ja5R9ekYmWs/Po9RJpzNsVH8eJzNMxClvDew/PIWTxut59OdJMmk73V6eAeqkzMgxkl3ZDxiZtIcmp9E5Lr2AJ52omgwj2WdHK8zuTqeD6Z5rv+TmXZIFOt0+pqendRtIzGOO1bvPC9OeMjLBs3uv47IE2TXQ6Bd/54rV+pYFm95srYyXzMZjBoCNDY3OUQKlV8GesymHFnu0ymxiP1u+KRlfzTCbJg3MJqux7o+XK7dqCV3zGV4WEI7p7wMXUzM9NZ7XyadxlGXx90N+bnjgC/AUhTnMHwUQrC8H+MozHCXOnGMV+nsv5w18u7UTTzwRq1atwoEDB7Bs2TIsWbIE73nPe4IQu7IdzeIQZZPrNZcgvu+lW5zJJoh3FaUZ6P0nPY+npfBDLul/z1PaupmCBV3HC9gHmi0VaPCTleuyuMp8bh77/jxm+ktPd78PNFsjakVVeWbM9HXZ+17xj05mzXQ8hRvNzLyLIyI3j4c8MkJOFr/wQz+3Brx57zdaGB1Nq6/Siy4LbsT258GOe0/0kCtc4hWtMKzfyY6xgEamSEuv4YYj9gxFK4rHcdnfjMUhZuNoWLduHe677z78g3/wDzAxMYG1a9fiV3/1V9HpdPC1r30t+p65YLXG2nObXRbaXUuX4TRFh9z5Rs2Ie2PfgSyD7pBgo762+XVMTLyW7PvKPsDCRHxpQ83mA4D/MXEXxhWgbN/+WpatO96o5ic2T5NdV5aXX1mPiYlXkmOv2uXO40OPPIptz6dlf3VzLfvBqU52HncJFuX2DJN256Qr+9PPPY93vPFcsv/z3hq4+977o2zUcp4kI/kwIbtcAxs2vYaJiU3Jvi96jM4Vjz2Bzob0PD79mtv/3vvuxxnxWlsAgG3bxfrds0+V3Wd0Pr9mLSYm02xqH2xa+fiTmFFkf3m9t37v/CkUrgD2HxJ7acs2VfbdU67sa9bqTNrHPEby8ocexkaFCS7X775Dh1VZiqibQpZHHn4IJ43NHat1CDYtkFYnCD+6oIeVkXPICys6mrmGfOAgFxZnZWVZQqL8HBPWnDdZWQLAhp+bbLK7I5gXgMmTFIIqGthkyh9llCWYR8PvlFsD3V7f+a75JJl+GJ11r9r2ntZ8cMkaRsdQrN+M7fTTT0er1YpWFj3rrLOS72s2m7jooosAAFdeeSVefPFF3H777UmwaS6aXH/2RKP6WvTZj5O5amFiLeaYk8G5bkwQntvTgeydrgo2OblIMsxff55zzp4gjN2Y563T7aHVTJ+llgThgSyGZOWx96uyZMMawnAPVRa/sqcxlGBqpofjFcPbkkPDnxdLPo/YY1WWmTxT+JDnVTfJks3nYSss8FZvvV4PZ5xxBv7tv/23aLVauOqqq7B582Z861vfSoJNc8FqjbVX7nsF2FSDKNd/4lN4zzvT8Zp/tmEFcGB/8SDDoOv1+vj1FbVR+Y4zzkS7/eFk/5+9sgt4/onq8aUfuhztj6SZiI/fuRrYUgMXN3zmJpyqJKz85gsPAlNFLayxxSfg5puvSc7TrgNTwMqajXru+Reg3b40OXbn6S3AS89Wjz9y9UfxCxefnuz/t3tWAbuKYiLdfgO33PpZlZUl2agnZJi0L28/ADz1SPX4vRe/H+1PvSfZ318D11z3CXzw3HqN+evpr3bWbNR+I88C/qcrlwIozoR3nnk22u0rkn3HV7uM5Es++CG0r0ozaV9c+jLwah0G/vFP/AIuPjPNAr7j1Z8D+/cWn3Xc8Wi3P5Hsu2XvJPDEg9Xjc85/F9rtS6J9O50Onvrxvc5zH7r8CrSvPCc5/qN/8wKwtQZfP33zLThhPA2XfP2ZmpV+wik6G/WVHQeBJ39WPc4xafc99hrwygvV46sTTPCy/bddTwK7B2ugOaKugZluD3i0mJvP3HgDHvvZ8jljtQ7BpgXSRlqF8pFPsGxT0oK8R0ZGTi7XkJuk2MjKysVaG40YN9mzDfiyGhlHG1RxEsMalFdgFmF0RoAnm5TbCV3jq2UUsmTivo2haxbgy5clH0Z3ZMwmP8m832wsKxvwFQICb80wurGxMVx11VVYtmwZfumXfglAYVAsW7YMX/nKV+hxer2eEyox181aEjk0Gm1nhiW5Z46BajV4/bWXBTI8wOhwp4sTFymsLCdJ6tEG7WY/j4Axb4UhESgwixwaOVapIdGo/71yd5h/rlsrSlnA1exvZMwjaF0zMtVBv1+8f1ypAe6Cpca9ZzwHmEp9b5Y2G0fD2WefjdHRUSdk7pJLLsHWrVsxPT2NsbEQIJkLVmus+Qy6LANU/JSHp3UGnb/mu32dodbt+2y+DIPO2849tDKsS7lfeyoTcQZu6E6OzdfzZM8xb33Zu40WjlNYlG5S7hwr0gWtsixgbw10Ev3LeXIZyX2MjIwkge2i0BDPpobHpJ3OfFf/Ouo19PXr6z9a30bTL66iM0D9KyDHRg2O0Ya+fuV9k5PFZ/Vm2ajeeuxn5lH2n57R57GLemKOW1ScdXPFalWIYcM2n210ADYdbQDG2t9XQDXFq9szsoOOkJVlrQCntaCU6xyDdhY2kfU3tbDVGFkCb3yOgWaQ3SqL+XeacRX7rmLcHWl4IZMIULbc3raU9/aZKUNmU92WLFmCH/zgB/jRj36EF198Eb/yK7+CgwcPVkljv/CFLzh5PW6//XYsXboU69atw4svvog/+qM/wn/8j/8R//Af/sN5k/lIqv0AdhZMzgCX7Aor08N6rluBMkueNyszJD+PNsDZAvD4yr/1N82BHlbgq2M4j/zX8/NiOxtD4J7vb60yerSZTf5vrp3VM123ypK1Spgl8S3AJZB9szTpaChb6Wi47rrrou/5+Mc/jrVr16In1t9LL72Es88+Owo0zWcLzposqFn3P9zpoqfs7/BcMp7xxsTWFhDfenbk1rxfbMV6t+ZA/CkLOGyVxRsvd29bknJbZfGTnx/OnKtH5mixnXs554ZP5LY6FCwONLsDyiaLxT7sdPuqDSTHGlXC+49GGzKbFkhrNQvcr2v08GWTbBsZOf6BoOUa8i+QnNFwpOEWFqZKp9tHr9dHM7GB/IvbblDZDloLmyj/m8418GU7DOXnm3M2HW0PeGTNpMJWzMwmq7FmXL9ynq3zklPmrEnl38zt85//PHbs2IGvfvWr2Lp1K6688krcddddVS6PTZs2odms/SwHDx7Er/7qr+K1117Dcccdhw984AP4i7/4C3z+85+fN5mtZ6OZkeMrrRkFWoLCM72+GvoTsG2PtiESYTZpzVKRx678hyF9uiz8+XWkv+lsQvq0JuWx/kbW0DUzKGhgIpvD6I46ky8C8BwX9wgH85JzUBh/Uysj8s3WlixZgi9+8Yu4+uqrcc011+C73/1u4Gg499xzcfvttwMAfuVXfgV/8id/gl//9V/H//F//B94+eWX8Qd/8Af4P//P//NYfg0AMWDQ9ttOzqQrl/n6g9X4PtoOBSm775D0W6C3ZR2QR2Z3aOdHt9d3Pt96juXuyqDqWnZuwu+aCjm35vO1snrDu48/V3M5S63z4oNNWcaz1aEgzuncfRM63OcubBso7u7UOSDnUQsVPRptCDYtkDYyAEWyIQv+oW80ePMLNQI2JZo1YfIRJze3hkV1e1iUABoCJc1a1c8IrJnAJusamMXhozV/bjRQpd/3L1urLDZlOgt8RQyBVL4pq+IdAr3WC0tfY10DaBdL4m6R5a3MbAKAr3zlK8mwueXLlzuPf//3fx+///u/Pw9SpVsYHq2vlTCPkdEQmYWHtGTf+s26tgJGjpFNpCmWvvJvztmUnUfbnWdh8FjDC4+UZWUxjHLOG+u8+Iyao84m8lgeWrPOy5GyCrW9as4f5RddMcqe+53ebM3qaDj//PNx99134zd/8zdx+eWX49xzz8Wv//qv47d+67eO1VeomlVv8/fgoWkFbArYfDY9zBwqndsjBlaWNZVI4FAwAjwa+GV1WFpz6FrPVQuIf6T53uz3Da+jHu1zzF9+RzMXns9Izv5G075uZbM7cqwvX+eZ6vSQSpdW7rtGA2rhkqPRhmDTAmkl+nzU6aw+oyGjfAdhdCrYZFReg4PW2D9jrMcuuBTQEDKbbPOYOzi73gFiSRDe6epMAmvuK/+7ZYEvw2Xuz3lu/fqUTivLynoJafL482bJq1W83yhLDijruWtAZeYZlUVrqNOwzW87Gt4rS3/NAPeVJ6DYR6kaAaEyxK/z2Pv9FngxFdmP1BDJz6PR0xywvgzKv9ExlM2TZMzZFDOMUs4bfx6teZKsYXTa7xRT/vv99Lxb5yVgWRkYq4AeDhUylY6eUVSMZ9t7b8ZmcTQAwHXXXYdHH310jqWyN3NePp8BagBJZsMYV2UxhgBavutch70G86icZUfKiszfTzZWbwg2pcc3O4mM7Ggze9UJo8udqbZ58avRmUkdijwhq/fo2pJWm9/CAi73zmhz7jMqDXM2LZA2UuVs6quKkTnJthkk8cCALn9h+QBLIIuV2WQ8DH3ZpxTZA8ZMDsTwZckCDTyoMtPtBQeWHmfr/0ZGpNvKJlLGtx6cASCYZfC4r2vzAtjWu+U3isliNWStIQ7ahRvuPZvCldt7wza/7YgrumWZHrwhEltL2j0TgE3ZMDqbh9Si5FoNkSPJBQQQFeD8qmvKPFpDxewhFr4sRy+flZVpZw2PDkHB9Pj++u319fGtuUWCHDBHcb1bHRRhhV/j/fsWBJveKi3IS5Ot2snfIUfCOmH6W9h//X7fpKOaE/obmSH+HjqaoJ39jLcBPL5D1AI25c8xm0MhmBsDSNLt8bmGgPy8+B+dy0NrqZxuZXz538taHONohoGWso8kWOtHsw3BpgXSRgSDQdtk1oPTjuobUFFPTquH4WjnvLFccIGye5RD1ywMnpjBos1NMC9Go8SaD0gP/bCtLwtzDpiFN96w3gNw0ixLbr3zl0pM4dKUKGveLivwNWzz2464opvRm6bt6djZo631IzZEjOeXxYiyeprnGuCxAPd5ANHWPwzRMs6N4rwJ80cZwwutsijfNXYWavIcadGVfDU6f274OymXw/PI995bK4zurdTMVTu9/podEYb35gxea7iYL7t2doSfrTmuLcx7YBZhdAYmojXvkTX3lZXBY7HJfCLB0WYT+evvaLK+rNV1/SVmz8un3B+R6CGL7NaKuda8y+pdOZiHkTkOoQOGYNOCaTI5l6WCgD38KxdGxxvIQd+cF84Yr2zN2RSystL9zcwma6J1g+EQqwijeiTMh49t3i1Ufmt4lpllZRzfB18toJ01R4qlukbs/bLFFEOVDXekF3lG9mGb3zbXRqN/vmlrN/aaysgx3jGhQ+PoyR7zNKtMYYNRBISyW5mcWv8wz58tB6J5Hq1sIgUkseQlKvobAR6DwRhbq0woQepxMP6RsuFUZpNRpzrCMLrc7zRsx66FhRRse0Q7J83hxmY9zAIOh69p+onZ0Wa8W/39r+WPCthk1v1qDH/PnU0WdryZkRyck7b+GjHCz/1a9OfP7Kxt6H20mQ2nMpvCsXJJ5WXLMps6tnPAUoClCqOb4+TgwBBsWjBNIosW6mM+/Mu2KS2hRYEXLucdsXpWDZeKZIaUU6nJ7iPV1jCkLBXXEkYX9ewYAJ5sHi4bC8IHLnTviK/g2EC4bNUJM6jCK1Fh5cWcoWmTxRIGGlsDeuglb4AD9nCLYZvfZqFtA3ajsexfno3anpZsCqa/hboPhN+NZfCUCSwZoEw66lTnjVHhrmjngw/I3Rul7NU8GoyovAfelSXLFB683iKKkViV/1L2cuyeAvBJWct5MYf0kWcjMzczwbwYdQHjmmFCAJl9F5fFppcMmU0LtwXMRZLV0iDWTvka0xc4GrnBOIC1XPfauRqCw0cPqAbqc7E6m9S8nzbgwAra+edqLlWJv2aOas4mT4fI3X0Bs8mQ0iImnzOWf69m5tEXNadfmYAv7/4Acmwim01udeb5tqmmG5afPQyjexu12YfRHV0P4oxHq2M8iMcNMsfmvcg2oMxyGMpD//hBBQ5GIV002syOHXs9d8GVv+HxY8XcMIfVmECXtQPFHEYXyMIpLeXcWCoo5dZAOfbiUpZsOGLPkSV/ORtAvkHfcv3m9lLXnxdz6Br3m5brgLlsZytLzjAdtvlt5W9dK7icU6D8/fOMHHetq6CH2O9lgQUL4MzeSeMjA9nJal6LBv01hdvf0/I5TZaxUhaSpcLMo3y96k8o/1IW9SztlmdAMXZe+fdk1wDHXh/lR48Rv5M/71lPc7V+8/MixyvPRs3wlkZRVXhFDRsdzONIeZZyXm8GPCrkcedGW7+dnvubZnN4GvU7f/3m9t6wHbtWGo1lFVBtnfX7dY6b+mzK65zsfrXnBnNBEv3siNw3ylnm62HmVCKkM+Q44lwtXxuv7qa+yoSaLVDN3De9Xr8CVcZH8nqhXZbQ3tOaf7daojWy/Wf4eQFqZlM1L9ZIAI24MHhttNUQoGD+3mbmpRjf6MwLdJp8COvIMEH426e1HGaT4kUOlF0OFS0vrKxB3fXAAAWY8A99IESQHVlmXNlZo6TV6DuPNVkAYJxQ6mpAhTusfAWTrdxw3AD4yiUIBwp0ebRKFE+g0aQslWJByALEDIH8hSXLojOeoMUEICjHYmQp+rvy6B7tou/x4y1KlhlPFvrQb+UvFfm9jiMAyq6/fkkDiQVXh21+W6kQnDDO7dHy9zthfHTwflJRHMufjeXaajUb9RmjJQgfGBInDmRn98WJi8ozgAslKGXXzpfK4BqrwSYmKXcpO3sejROGSE8ANosIBb3c76Usuf4+4JhlWRkcLPLsKeVhmE2sLL6jinU8nbCIl2W01aw8tgxTolwzLHBfrl92ry4a4w1pBywljNcTjHuvnMdclbBhO3at4/22OsAq9AcDSMKCTdZ1Vu6hE4hzVTJDmKrcvuOElb2yO0gm7SLCxvLvpkI+oj9rAwWOX45lxeiQ054s+fB395xkmU31d+WAL+Z3mum5855jfJUfXesQxjVDkAVGm02KfR2Cwtzdt5iUfcbTIxigd3TIbHr7tEaDAxrKhVcayGy4RWncZ/tXBnhekao91K3gOV32YmwWOBhrlo85ZgjD9rB6dup55A5m3+PBXBIjzUaFMKuX7eA3rOYxa2S4hkA+3GLQf8Rw2Y5ya8CXhb2wGFl6vTqU8nhCKfLBo34/E58fzAt5SVR7VZlH8b2oy7brzwtprJHK4rDNb/N/HxaItwKl5VnNnKUjzUaVS5BhNlV7jgzlYQwRIHQMqFVqepE7ibjDWODLZxSqiUAjDDG1vweo5OSpAR4by4pZA/LsKeVhjF1WFh8sZ0PXTqAU6JIR0qzD6AiAspqXrNd7sH5JsMly5/m/aU72QB8kGZHHk8DasB275gODOmATO2sIXcYI9tbrjANk6zM+f46NCOeG6gwJQBL2rmTvVt7BGQOHmXPVfnbkZZmJ6JAMq5ex9aQs44QuXrzugSqEbTjSbFB3q6/P5O6b8mUWWJv29h5j04y0Ghgt16/BScRWo+Mdke79pDkUpivZh8ymt1VrEYpReWhXin0ub4ynXLAeiRIBZvILSFSf8cKxilGJhA+60/mjJKU13d942ZbzSF5Y/jwyTIIR4YlVE8mWlwQZiuZfnrRHggDWfEMT4EA+BoSTrzMHs/xNFpeXCuFRK2UB9P0UypJbv+XvlAcFyzkfbTWokJ4w1JH1jnBA77DNb5ua4ZWb4nVXkaOZJIRXsl6LTYo96SvQrPLPnkc+KMzso7GRJpUnyZ/3bD47w7zL15iQ5CnvvJDyRWWpgHgulNY/11Xlf/BaoyFCrqiwXvI3DUKSOV2AAWOrVACtBlrN/PnY8QBEltlUswq5ENZFBMgXY4szyfnreeEceOzvNGzHrpXrhmGvyjXFgJoByzGb2Npj3lrZqyw4TDHSB7KzTMTKWM/rhMV4FnA4AjapuWKtwIG/X/P3gZSHurfHa/aOFrLb6fr3R+6Md3UORpaxkWbFbtPWe8XKImWpmE2zZPLp+X+L10Zbktmk2Xs2sNTC6pW5FiuCCQHaDavRvc3aKKEYWY3GipFTsWD0hVrn9ykXav7Cksa6huhOebLnvJnloV2CTapXWHxu7aHkZc8mew6YTewlQSi7ZbigpBFr/Wfc3zSbH8NXpmkPeH5uKrqpAByZKhK8oclftnIeFjNGSYQCrRqPRtl9+iszLyNNoXARBhUb0jfd5WUZtvlvPuuz17cxIKwhVPp5VLwmzyNt/NkaIscRYUVALOSKU55GiPBVn/mb3dMG2WNhDSqjTIS6MiCfdR5nfCWX0DPGWs3qHtBZziEIx+SbYual+OzBGiOM15J5JMFS5lznQywKWZjwQjke43jy70f5XKyVbLOKsWo0XnN6z7Adu9bx9Ac1B5PD7M8z9CwORSAESdgiEJTuI8BhhtnvM2aylcU8lgobusacq9K5USZbZ8K2+bBX97uq940DOObnxne0yM+Ly+Ldw6TOwbCJynQtYyNNkcso/11ZZ1v58myZfIzuXoClBoCysuHJ9ctEaziAI7OXaqBsrtsQbFpAjTEyq01gjD2tWTCcclyj+vmFPS5RfeqgzRsNQP3dxpuhfH6r2EHNOhyRkV1etmoiTmMIoE/N10C4ikkgc6QQRgbNVjPKYskzIvMSMbmJwgSoOaDMVb6ZHCYAFyZQMwM4Zl4VomPMH7WYCC+SVSFK0JnxTDK5Y4BQyRkymxZW8wEbgAQaaMVvsO9G8mevZNmNGEK7rXljGPCoeN0FytR9ISrXjTEhgDNHNo9s1SQmrCHmIWUAx3Eicbr8bIZNJD3NlQKter3deQS4+5oJjwZCsFyTpVKgmw0bU4JgHgG2UJjYfcrIMtoSzDyCgcayCq1G2rAdu2bJgybzHlX7Vc175O5XNrE1G3IVAqza2LWjjTn3ytdYx+9UZQMZ2UTVGZ/XZ4t8q3mQZMoAYgDSqcgDB40GME70n/bmJSeP5R4u5OFB/Cnh3JhVgRxjziaWHVSRLohQfJkgnMorSYbR+b+TZkfEcr8ywNcwZ9PbrI0wrBbfgGUNXoJS54aiMah+eUBwWfj9pNmsUTLeKsZk8keNCFmsQAOj2FcX1lFkNlWKQqtB5ZiwsttCVkP+EHf6M2DTCBcC2PUvrCwVl5ddxn0zlR5mKvCIY+YFlwRZ0aICVwnw06Xi5hULNoTGVxaHOZsWViuVrRMX2RQ/NkGmJbmnZFqOEMqTT69nK0Zacw1ZjPUREijzGat0+BehQEvlf8zAEh0b4Rg5VuDAMo/lbzRGAl9VPg95ljIADw3cuwamznAt1wA5j164R57l7K53Rl8DOBaiTNhasjw0BlpgSJNecjZkcNiOXQtBecJZ1azzxnAV3ThHsV9FmGVSU6B8T6x5Ahz22Xk5Np/FGWJ1tpb6YqspnK2GMLp8SJ/h7iuBg2ZTAF95WaTOweQVpe9tb/0yYXSjrSalu/s6RK+v51u1hNE5xTGoghS2+8ZPaXA0oxLkaxY23DBn09usMUBDdejTyfGK/kyepFiSbQYVbTUlopsHsxh6nxyfCaOTFQFGiHDErqd05fpbw+h8NpFOga49OxbA0ewdoQDE+jUmdE1eEoxnxwf5+OTmvMIlZWEuibFWTYFmDma7gcSE9EnPJGMgubJkc7f1vPU79GgvqFZXhhFgE6G00kn/KxYMoUD36vOIqQ7ke5q7vT4FZjEgiQwnZCovduVZ2iw9pHngnq3uWim5VF7AUhYBHJAsUQZw9hVutmgFE3obA74YWVhmk3+W5ipvBmuAWF+upzmvO1R3NQncLybWb8dR/vkQIXkPMGGj1blOGq9s6OWwHbtmybUpQ3mYvDH+2HKMWPP3Xy43WLW/KUC2ln2EkN1aXMCSaN0MDkdZlPlzlU9W7uq/bBXZUcLxW1coblUsSkZfZisgWxwKpSzjImcTQy5YRN435UucHVG/djxB6qjCQMk1YC3u44e8MpVYARHJQgK9c92GYNMCahUzhDpoucSaFmaT3IBMqJBjlFjYRKSBXG6quhqdNi8Db7xkNhmM9dz45eXK5kkKKjEQG36EVDCnPRCDBRypak4y7pupWiQAG8ab4rOJaFYDJUttIFmMZKsHvJaF86hxIX210kKVT/UYYrlKehaDfdjmv5W/59gIpyjONmcTlTdG5tAg7iT/rLPKziiJbH9Z2ZOq7hrMC2e4UDmbBIA8agiRd0LXmPOIDGsI5p3MoVEzm/JrxjVemf58SB8gAE0in0dhvM4iWbLR06ye6/I+JQBNmUODYRWW4YQsCGDZe8N2bJslVDp2ZjMFco4jwSYrqGlxKMhqXlRCf1+Wrp7Y2hICGMuzR0UliPyGmnOjdhTbKosxefYkq5dy/IpzkgF4fKaSVefQ83bVspTMJirfqli/6nrvN3hZuuF9wwCUhWOGd0ItMjoImL0nHS0cS7C24ee6DcGmBdRGDcnx6JLBAQVPWXgy5pdKdCYvOIZNVHoQS7oppxjVzCZu09SXbf5w40sMD6oAspUYvLACJjyr1WxQSeJ9ZpP0/mvjM3Hc1gpK5cE3OtKkjOSQHaQftAG4SrOsGFlqkM/CzGOMO6cqBAFQxqm4Sn8rDd5oUA3b/LaY0srE5jMhFoBU/omw3uos5RK2+pU95efFWg3w5HMNyY89jth3MmdTHdabN0TmIvdVjG1L5a0QAA/D5GSV/4BZrJ6lErBhZHHPl2L8/D3DzLs1NKBjNrx5WQDBCGBCUgeyNBuoc4jRAGV+vfd8fZB0PtZrZngPLNRmcSjIvEeWJNuyuE+OXQhwYUi9Xl1oiGGMynNydBZAWT+j/1qiQaQhX6coyOtVo2TO0q4nS76qtbdfVfBIOK2J+0bqHAzA45/xNCOH0DljrCymIIV73yhrciDqYsLuiKWToXR30lFcEUBI0kXNHOcJI27ex7wNNGQ2vc0aVTYxoM5zysViItGZjPml2BVOmABBHzRcQFLWslgYcxk6shCgSnlBAPqmr8MR8/TXXq9fHW5M7qtYnhGG/rpYJPbTDk8/hIYx1poizwjFJiK9KRaWVaw/lT/KkYUFePiwUUvOE4BL5O5695i9Z/NM+gnrcyE3wza/LRa6xsTms4n2LZT2GUcWpjJiBPgklGIGKHPBJj4EUHprmbOxdMbkGIKWfD2SbTtKnKWxcBLmPBonlVb/d1LDC0VIcos6G8vzyyY7VaUvAjYxTKXC8Dbkv2Mr6QVh6eQdQyRulnuP0QUsSXilPCxIPWzHroVnDcOII3VxsS4ZBmi15ol1Js8hS45ANt9qLASQCXNict5I2Rn2fTTs9ShWAaydirwsI60mxkbyZ0evX9tMDFAWOyd12Q33vAN8MQCPldlU/GXmvWSLykTrHJuIc8xY10BAMCHsMTckVXOG1PfNXLch2LSAWsUOMjCbcqi+X8KRRZeZcK5ORDGyeMBzFNJy41TV6IjDh6Xi1pdtg/KmWHI2xar6MRd/S+ZsIpTvEsQAdMaaz8hhGDAjRllYNlG5BsZHWO+Iu2aYC0iG0XG5aTjKqSXnyYyjcOXjvmP5XbjQDy5mvbxAWaNk2Oa3yfAvLkEmz2rp92eX80Yq/xqDtgLuBSPnaMkut0xdeZE5S2uWKMNsWjTG7SM/DJgBVNykvZyXkXE81aAdWR0oCMvJn9Ou8Zo/j2S+KY4lynuamw1bERUn9xURTnLcGGe8lqKOEXm7qt+0Sc5j5B5Qw0zLeSRDu/0w0GE1uoXbLMymjtBnLRUYefaqC1KyVYGZAiYS+GL2iG+sA7pOW75Uhy3lZZEJ+hmW1WiLC6Pzz71cfkM/Zylz9400bWF0TclsIkAVlt1WJVonQL7qjG82MEYwmypmHgk4llPM6O5SFx8jHH+zzZd2HOnc8B3LzG80Kuxgig03ZDa9vRrjYYgxGhj2BkPBi3oYtIO2W3tuqaTcg5fGCYOn3+/XnttBNTreWOe9mexl67OJ1AtLekcINlF1YZFGSZVMWDCbGPCLUVrckD4+4aGbIDwPUM62EhVFJadlkWvAkLPJ4Kkp+vPzIsv/MonWJQ2eMdgWkUlwh21+m2TBUF5GA8PGUf4NiUal0sqEJMs8SRQFnjB4yymY1bluyDc1TlcldRVFjvnbpEL6SkC42bABE0yiUcm25c4vVLK0DM4Y/iwtZTd47JtcaIAT3t8knD2eLLn+JSOAcZhUyv8IZ4hI5Z9hFdZOhNq41AyXYc6mN08z5WxyGA186LNcZ0xOncrgZUPRiDPeSbLNONq8c8//TL/5ug8LHFgKIzjh7wSbyGq/cfkKw3NPBVUGsrQatkgACvwUZ9zi0XzV7K5kWRmcbex9UzGbDGBTs8HpYrF0Msx6Z4Gymr1qA74sTqLy95/LNgSbFlCjvHAeSwXIbISA2ZQfm06sGWOGEKwWrpRr/RpTjc6lqw8OHypemaOr+8wmRnkFuO8ao+IywJqVScAADW5In40dRCUIr0L66vWlo/ruemcYFtLoZQz2EdIj4ec9Ug0S8RIT9+2WvM4bVHINlJVEGEWkNkqGzKaF1OyAjccOIsIIAG4fxfKHceWfWaXVO48IJXGkxYVHu2dp3ugqlf8xEmgIk2wzdwwpi3Of8g6QRWP8XS1lp1nOBqPLPUvzxjETllPOS7MJkwLt6AKELKzyX4ckW9htNtaGXAOMLExIkXTgsaEww3ZsWtcBh/n9zabAiLFgLKE/6t0kcr8yecqmq/3KVmAsAdwGdT/VLJj8PE4LEKNF2TT1WcOFI7qyyM+MtaAgBRmCW4bRabL3xBlf6xzEmW1wtBSyG3I2CeBLS8odO+OZnE0SlE/2HQzTatbh73qCcCPA4wG3xRj5uTmOIIy44e+Ek0g45+a6DcGmBdSY5NAx5UKvKsNTH2NoMetxtCiB5eU53U1XkZByltXodFqlTfY6t4e4bDXPsHfx61UbpGLPh0SNOLIQRkxDsuF4wIaqDNIkQY/SG+8APITSQsZaWxKKS2YARSN22HD2EFYmT0DRn8/Xwhpr5f5wDFltDXjzmMvvMmzz22rjns3Z5O0Lba0IBbIEeNiCBZbQbjf3Q37tMqE85TCjMqyXOtebFR2fMRYkQ5A5j6xVlqgwugpUsbKDZse0ZOaxJZKeMtXoZL48hkFrkb3VaHAKdLeWhekfU/6ZNTPGsLJkWA6RsykG9FJl4AXLI3VuWMP7h+3YtVieMiadgZsUn2CjsixwD2hgHL+S7U6FmhrD6FgHZ+VQMLBORltNU7EeKQsTRidzxWo5An3WJZerTsjCOmYG37WnsiLLc9Lm3DCxiZo16UKXpT7jqXDHEmyinERCtzZEPDjh70To2nEyuTnDbDIkuLeGv4+I9ThXbQg2LaBmSQgpGQ2mECot8aU4rFrEhRXLM8MojYsIoEFukHJPUiwrunxqeKBYkuMxQEOjUdMTqZKlTS7HhOORaDKx1r5hamV85UEM9uKPJXekkrcSsf89sQYsLCs+KTd/8cskg5YqJWwVomjYqOEcGIbRLazmMpsYQNtlqrGUdgsdf1SG8hCh3TyzyVWe1LFLsGmEDaEKFWgq35RQtrhk0pbwL5KlIsIaLCFX8jdNOW+cHHKM8i9k4ZhN5VnKsW0tia0rWViWVcQJxqwBN9SNWDPEPWBN2NoVTjML40TmHEuFFFkTrQ/bsWvOb8WEolnZqM7ZxOdYsxi8Ts40gjFOFyMQ+5vLE+qDwwxjhgOqu7GzhgG+RvL3Ta8Xy7XIgiQ8CCcdCswZz5zZ8swaJ2ymOll5E63G7Ji0lpxNGgjXs943UWYT4SAYzTsIZH8uZ5PYSwzoLCIq5roNwaYF1Jh4z5jXOaVIycSwVDJL4e2wKZhcJYaoB1E5aMtW7gMGKGuJQ5811hmlrvxaDHVeVvVjvExSwaRyX0UAIUaBZXJMRAFEmtlEADyeLPIz/RbLM8LkXymYTbzBM0qGW1i8exUVt8HFoFu9I+ZQJ++CG4bRLazmhqLxnj2qtLQDCPPKf0uU0aYZgkT+j9IYYZiWVRidA6pyxnplRBH5PBg2kTUMKZ6zSTszBvPe4jyqsfLPqe4u2zYPOEuHBpNo1ElQzHiDDYxrh2XFVHRznAiWULdadk2h71Y5m5i9Fzo0GFnckHrCkBbGQkpPknuYyQM0bMeuOWkkmHUm8h5ZqkdKB4El9EfLDebmTLOF8nDgcD0+UzE5DHtNdhVMJQ44cFi9jJ7XleeqPjexqn6Uc6PVwCgRRidzE1nYcMzdJ6tajxvmpSnOPSY1gNRpKGYTkQalFNNh0jKsQsG+pu4bIvRS2vBUjkDBzGNs+CqEdViN7u3VLDkpZMhC6kCRa2yMYIZYlbRYfgGO2ZSPV5YKU4lL6LLUly1TGc8B1gwlSy3eEcdjQNJZqaSgVX9Uv5NKxQ1C0TgAcZSYx8ooaTTQrC7PZPd4FbXE+LE8I2z51JZBFteDwXskGAaE62ViDB4WLA094FzITV6WYZv/Js91C9hYeg17/fQZEA+xyK9d9ywlziO27L2BJVoxm1pcGJ2jcBMhyXE2Uf48soSlt4i7Wo7PyCLHd5038fHlOIzyb83ZVFddqz2qzO9kDemzJj3lwsxthrfPhtONooEspPEqw0CptAoidDxrvIrfuyrrPrwHFmRzzo4RHqR09DZiDTtVhJkk2+KsSQ0vdRlL/ijW6efqbfxZVjvc88yQsRFxjqk2U3n3kU7ryH2TjO4wOghkJWmmEqu035oN5ruWjmKCSStkGWNsw2pe6jA6jVwgK08z7Llyiqt7m0jJ4jhaVKJD7Si2pnDJRQTJtVGe2ZqtJ8PoGBt+yGx6m7Ya1edCFnKeL2ehtvIxuXHFiENoLV6AcQJokApmGS7IMT3IXEMRoIHx3o+1auMuF7JQ5OowMKGEQXU0qxbVxt3sAEQq9KPJzXu1BoiEvG6eEYJNFL3Ij5430Fe4usplK5MMUnlDuvKSsISKGGnwBAV62Oa/uQoOz7Jzcp8lz6P6XG9llBvZX55f1D1gBMqYUJ7yJdZLXp/rNsafc36lwO+I8s+cF1Kp1Dz2PUcWHkAeJ3I/RPOckAAPl2i0/q7MnRcA92YnQvr8mo6cpcw8jpIJii05mypZRhqU8dox6HeAGzrOgk2OkaPIPmzHrkmwiUkLIXMN1WdwHlRhw41nvDUvP9NvsRA95i5zi0AQjPRms2LwMGG4pe7OgOYjTVJ3dyrp5Vm90fvGADZZHZCMLJLVS+VsEiG7KXm64lwaIWSx3n2uc9aes4lNEM7oHNPCfrPobk5idiLP3jhRUCVukzN335DZ9LZqDDI+E9lkqY0jDw5GMZKHPkMfdMO/DOFcrXy+qZriiaovG7LQIi7PTuRgtlYtyuWbkocPc5EXOZh47ydrCFQ0TIqRE16GXI4nkk0k5ib3u8aSbLOyUx61XuRgJgwBtxJk4rKN5DxhDB5pZFBgKV050mWTDD3aC6vFmE2MZ4/Kf2dNVC090xSQGbL4UkqrzEMxToQAlh/LgqoShB2t2Ly2szTl7LHnvgr3NFvgYPbMJh1oYCs+mR0aM+X4xgqpRHh09RuRssTy1+jVrSRAmdGpHOWfdyRJtgEDljp5BAlguEncM7Gy2NodM2zHrvXkuUcZsCGYTAMThnNSOglTS0c6IE3ODekMofXlvEO03LNMKpGO0AktOmSr2azmkQ4JzuQmkmdixUYlWFl0GJ2B1VuMb79vJKDCpLRoSZYVAwqKc5LK2TRW3zcpR7G8+5rUfTM7sHREFINhmE3M+i1ld/RIMpJlrtsQbFpAzZKcsqDm65t4xrpQpUfCdNBygI2rfOsHs5SlheL/jPHFhoq4ua8YRlkINjEHrTlnk6GimwPwJObGyTNSVqIikzVyuaxCcIpJSCc9HsmwFaNnJyaLyuRzvIfE3itDl0byYSuVAd6SyfaZC8um5Mg1wwCUVZLBIbNpQTU7eBgq/6mz1FyWXnglR5vE2hVrMaecyXOKMda7/WI810AmjCghO5OYtNXM50yU1PtFRBiSAzQQrJY4I4AAbEYMnmZCwfVloRKNVk4EmwOkPNf7fUV2kReQYyqFjFUqrKGZz2kW06kYQ2RsFuc6FQZqMV4dvWTIbFrIzQVsbACreZ0R4HAVQiVZlDndhwXKROgPk38nXtglfzZReWsl+4/KbyhkJ8Bh5yzLnKuykiWVl0ie8UwYnYwGocLryzM773B3wzTzIJyTlLvMWUnIMsrae4OXjmPuG6FDWKI1juSMZ2z4Sl9SbJrY3mNDWOe6DcGmBdQYj2McsOFRUYZaKy8sBphgLzhJrcwZApLiyTCbHOPb4BGUFTAYUEVWLcoetE1bWIkDwFhDPzKyAKSBFAnn0T01qPpzXoD6Qsz9TjHFniufKmQhjEH3Ms/vPUkjThrV5bw08kaAfG1UsEMYg8pJqkmsd9czOTQ0FkqTvz+zdmOe5hxDkM5nFzFKzaFoRGgsZawPXnLOaRqEzXuDJasld1ZHnSvMHiXD6OT5RbFaqvwiDTQGDpkcSOKEjZMghqVYiMy7wvxO0kueOtt78jcl1oCsAMcYafHQtXh/6bxgGCTTRidYfa5zYRBORanM+L2Y13t4ByzIZgZsYnljGDZfq5ld8/KzOf0XlewMGFSH4HLVmF0mVAlMxPtKHWeM2K9uZTGbA53J7+MwdavfNSWLPAts4e8U4C8ZPETOphibOg1sy3nhgTKW1Ts9I+4bYo2VQzGsrGiCcEIWmSeSBUtzbG25hyuwVN2nxd8mmUpERvjMdRuCTQuoUQkhe6HCoIUslK08aDXdImrA0gitja6e28SS4lnuA64qBEcRd6o/GaiPThhdpuoLW1WoVuybVJiLzE3UzIwv1xIT+tGN/KYMk4APF+O9UjLnyShx2caYeRxAafNILDLkSHHi4Qklhy3l6sTEZ8CpXq+Pcqm6rKyhobFQmtW4mA3TckQq0BTw2TQ5QEaccz3etxdhNvX76b1RPu0mvuXuGKrAgSHctVb+OXBaAjZc4QdU/S0G5kizmc1rKKtdWhwaTWlEMbIYjTTnLM3cYTSz6YicYLpTTn5uXR3I5pBjqjKx4f2VscuE0cUAxGE49YJsMYNXBWwk2Gs64zkGXVT/zTg32HMsGoZE6cuEDplIJZKtpGe8h4v9DaJ/rS/nZI+mNWHmkTwn60iAGmygQvelDpk5J0et89isnbO87p4PReujGHPcwMpiKtQWstT3sOW+caJHcrI0WHwgXL8sI3Ku2xBsWkCNqn4QOWgZoIG6UGSiM3OJ4Tw45YYJ5A1kwE0QzsjSEln4daAsDF1TN3FV7lgcVhmgYVTmgCBBu0p2Nhwxc6DEwCYq9r/FyW4PcagBJNa4c3KeEJWlClQ/72WKMQ84irU07vTL1g0t4ujYDFjqllvNeEck6Ewoi8M2/y3qlVTWrkM7z+6j2J5jvN5cgvBoWK8hDEkbvzwGRwnmkZTFYcFQbEhklX/nfmQMukhIMpP7ykm0ztwbrQbKlAtJXUA6VwjgS7JgTHT8Zn6NyXLO0kueqhAkK56aKuO1OFDFYdtmdAE3rIEvAT7aZBMOi/vXkCDczXWi30lM5bphO7YtVs2WqXrorGEi36pkaXZm8ucqkwS5SrBMslRklAFTOj62v1MO9xg4XPRPyVLreIxN4xbH4FOVNAlQxZ0XQoeMOk+ZKJkmJXvNpM3nW63YoqQ+E2X1mvVl/sz2n4/JwqQFkP0ZWYBEPqvE3ef8pi1mHou/RZgmHyExrEb3NmtccmihkGYOK2mQMPQ+p+y9xSMowSMyBJAFyhywiTisZKgIdTk76HJeqZOxrelcQwKEY8Kz5LwT/XuReUwxA+QcMJ5YJ3zC4I2X65ExSuQFlz/0RXleKpwHlFESK9HLgHxuiE7KSK4V+9kmCLfuPUuSQSnjsB37JtmNzD6Ke3d1oEEq84whIs9SJrknA5I4CZZbRK6hwdNsNTqnEmhVBUf5rv36DGDBbxrEcPY0EY44eKk4M/j7erTVrMAm5iy1OEAcYEItnlDfp7k14BuAg+WeDOvrRkPF8mE5I6wR5XiDdVCwFzlLGUOaz70TysI4wSwh9ayDbdiOXYtVs2UBVitQnQur7ff77jrO3E/umjTYHQ6wbbMjzLpPxjHjhr0S9hjJyipfkmdZlpFMA/41wJML0QPE79TI68tyDTD5VqXDnbk/4gV10rI7TvGcg0AMxKSRiOnuav6obgiUMek+RgUxIjePNOPd6CSSNtBctyHYtIAao5BalJdqoTYaKNeSNUSPUerc8K+8EcMAZY7sGRQdkDHCXK6DWMgVM+9NAWSkvClyXhijJKYE6kZJfbjlvmusokWvnz48peLNJZIN2Ud6Yr9YKEpKFqkQ8SyFkWazDi+kQ9EIUFAClNXvqnuRHWCVYVmRBpJbujjnja9lHCOYecM2/80BbCqwPK38V0qrVM4Sv2dHKMSMIeKc65YzgACEHKCBSTZbgU0kSOKEITFgefld8wU6XE8wofhFzjrGoUEbmNIDW92RKQ9p6NDgqiZxwL0DkpDneiFPMxsibQ3/kolvqdBLx/GUMV6dnE1FXzUM1DHQeKeDI7v2O8ncKJnx4+EhikU3bMesOYANk3dMgiSMLhNh8zFnNhOiJXVCDiir95+pvyEdB8DlN4wzY7n7hspzG2GsJUGPiCyMA13mfTxaTmv5tCXknNV/nSqcjMM9Ck7lQ58ZNrX1Ho4BPKytWoVeJuZG3gdNYTMnK+kN5p0POa/1grluQ7BpATUGSY8pL7nDSh5smmIkPYIcu0J6U2bn5Uttsp4AVMpFystCAGWxyiyppKDicxlqcFwWZl5kvD2jKBA5myQoQbGyQsVeTyRb/GUT+83ISyXjBYiCcASA6CjTTAVD0tMbA2MZKi7j2ZHJyi1gKZMgUT7tJPgcMpsWTIt6sBI/j9zrTN6KWFJ+a5gCk2SbM0SK5xsNlyWa7l/8HW1ySqhzlhr2NMMmijNDtDumNqJqxkxeFteLmWbYlNtXsn9T47thdHkjKqZws/mpct/VAZvkXGbuX4YRLcdn+7tsXv3+jfX1v1NMFnk/sjmbTI6nRt6B5yYIz+trw3bsmhmwiSSWZ9NI5JxbM959k3coiL6GpPijYk+x7NWcHSF1Lhdo0MOWrGcNk68QsIUYxkPLWDtC1yH8/nlHS/2lWhbdnQi7LOQMzzHq3hZOotQ52fHvm5zNNOv7QzDHrXsvycwL2W1AOgy0HIYOOa/siCHY9LZqFoZNq9kUMfp5sKklFmoSRXVyMNnYFRYvsnsw55W6ymurVkoQIBxx2UrDIef9lPPlyJ463GKKPQUcNLKeVcCW1DbGJNL6SxCDMkqkAksk9nMrbPDekVoWxtsBTlGIGIOp/jLPCGOwWRWFaCVIkuGYk0Wu69FWowpb0QzlYZvfFgtFS56N4jxqEgq6o7AYwuKYMAX5uRTbNlL4QetfSkmzWsRZmguJAmxezBig0uuTnmlDonXLPJb9qzvSIAu7BrjwEB4ok+eawywmcg0xYTmx+5FjSuRZzpJxLZX/LEObMHKknG4yfyKMnWAtynAPZi8N27Fr1mIBsRB/Vn/I5XtzmU3NbB6bOFCWtwuaxP6T/SnnRqR6pNa/F9mvFGhHOrmdu9KQBoXKWSruPkaWaIJwwmFJ2R2RM1U9syN3nxYhEQsLZ87ghiyqlMnzZWUYy3BEBpxyci1mmE0tkbOpeD51V0ogy0K6GIbRva0ap1zwm7hGi0EpRk5uD2KTybhcxgtXbRwiplgqdbkNWYwtQAzDZct4neV8MYlkY/HKTCUR6S1lLluGKukmtc0fVrHcQYxRIqsWscAazw6q1yNj3Fnz3jhMJcIb7673xOXsGDxN57m4LLOLz2eMDP+yZS7EYZvfNiNp56QTAeBYdi5wwCcClfnsKOVJ7tOM7E1yLZZPO6G0jOInlVb13gjPu1xyc995w8x77dAgQZJM3kHnThJ3ZDqcuv6NGAeIlIVJNGpR0CWoxIDlLiPH4vVmGdcyxFAHKGMedTlGSna59xhZXAde/t5w7hkC6GWcMcN27NqM+F0ZHTIGkrDMaAuzSTpz00m5UcmeC/GW4zPgEeA75nTZy3lhbSAH2KbyrdbnKsNssqVBQdWXOTuioWvaGnAK6ticGzkGTyz8i723qfVbnatAjsEsdSsA2TUZ1d0ZoKzFFTGReZJy+lgMtNP6ywThDJu6XNpy7LlqQ7BpATVGuZCbMhdCVYfc+UCDrgSyh77ViImHIeWYTagrf7GeHcNly3id/bCVbM4mCR4Rl20MQGQBx9kYmv53cse2rYG6UlB96GvGXcewZmI5m+Tzqf7yAtIuiU4U4CHWAGH4usaXLnchS0xp4ViCOVahXAPy79DQWDjNAWzI8GiAS0A/W0/dbFgwOcXSV25ydPxyGFf514Cy8PyiWKJEf7fgBqP41eGITYL1aWFDyjOWydkkE9nK/Z/M/SBksdynjhc+xw4aAI45XWAmIgurZ3BrJtx7OdklsKqNX3u98zmV5GujIgkv63jKMU56jvGa1zOG7di1XgRo0NdN8Zet5iXZ9zn9xNF9Gvlzshs7UxkdsskVyInry3n9t0GArFFwmAXKGnnZY2ylXP5UCdppaVC6UVmIc1LcCUdL54gVOmCAL6tzw5VFvz/KPKvVGsiyiWahLxnst9FWnUuZ0d1KHULrH3PMsIDjXLch2LSAmoUZ4jCbMptGItdyjGDsSCgay67IUeH9MCSW/sqECBSyDPrTOZvkpWJD9XO/UywvERtrTSXkFfms8l4pafDUzyfjmyOsBsrIIFF96VHLGbIzDuOL8CJHL4m8V0qyvpJArJDRCb2kEoQTTLvIXtLBKQlo6omT5ZkBgFJEhm1+m0XBcSjtBmCiRaxb+VpRldR4J2WTQ9cKdPkerX/5NL2nIw4WpoopExoQu780edw7xuaMYYF4oCyj7X6mJktLKJYpcSyhKoCrtOaA+Bn/PKoMHV0WluVhBcpiXvVkiIVgizMOPCvjRIY1MNWJy6G4XCQhg7qnGK/DduyaGbARRibHRg1TZuRAj2aDY9N3I7qJfnZgMH4tix4hUY+fA/ElKFG+pxjj6AINjk1D3DfNBu+YaTUbTghVysaKpWKgGKAEs8nJWyu+a1J3F6A8A7I7ujvBhIrp+ky+QvlXy4foj02xeht527CQk98frsOdcG7EQqVJJ9FctyHYtICaxRBwN0KeHdQiUFEruyJ6oBC0fyrWWmxgCTblPLEyxEnfZKGnN4nqi+9UHCjF/3Pez1EiF1AxjgCEiMNNJhnMAo7Ca8uErcSMDIrV4CQo5QBHiywSbEqGO0oFjQBU3BCaXKI+d/3mvM4xg0cNAxUJwlsM4Oj0L/fekNn0Zm3S25Wt1Nl3z6M6/0oKtLUp0LGzVD8D5J2UCWsQQHn5Hk2e8tlWo5GtWiY/V54BenVMfm5cYEowLQkWTM6DKV+jmE1S+W+Aztk0KnKuMP1ZpVUy1rKeZuH1BvKe5sqQJiu6xcLFmFySDANNGiIMU0KGwphkIe4YQAIBNtaG43wcFopYcM0FbPKsltg6YPS2EVERi0lnUMoEKIBsbM2TwEGuQrEcSxawYJgeQN7R5pzxFiYtIYt8jTknXQCfObMFm4hg9lt0cce50UAW0HRyWVl18Yw9BsSdG1k7ouU7uBJjx3R3dh4zdjAg128za++lHVwZG8hh0nIswbluQ7BpATUmIZ08+Gna/yApWrme0lWL5MHJlP0U+QVIb2bZnwWbZDW64jvFZYmhxRz9tU60nvNm+uMnw+gcD6IBsJkFGp2bRx9oyCUatB76tQKbV0Kk0uzms9JlHxE5mDR54h5wm6LArl82X9pIMx/eIF+TlUSYsLti7+WM5IRx9xYGm773ve/hwgsvxKJFi3Dttddi5cqVyb4/+MEP8MlPfhKnnnoqTj31VNx0001q/7loFsCm7NtokMBEJAeB9ts7oa4M8CmUuXyyWVRjF+/JKIr9uj+zp2WFyfo8Snb3mCec0irvUk2eaIiF5vWeZTnnAljjZPGV1mTelWh+HxZw5NkD8m8anAqNLsZ4ZZPTdiIM2uy8eIZ37uwtDGlb0RUGnIqHxiXmPcLmzskzbMemOYANwWoxJxSPsC5Ta95nhuTPpkgaiaMEsrvy5CudyRBcV/bEXRnVxTnQrtLzjlIxjdjdpPW35kmSQEM2BFcA1Q1Cv45WqFXuPkuhDkd24YDIp4cp5rCeG/1uteYIZM5gq8NdFnhqCOJF2gYK9x6zHqUDaq7aEGxaQK1mNBDABJGoT/YF8kamRFxNHvBWHlRxmSH5S8KtciZl1MdnvB1AXPFKbWCZZNBy0LKyOIdbQ/9N5ecylFPJmio+I5eQLpJnhAlDIarLOWuglTfuYpU+NHkcjwTh2Ymt9xw9tVUd+jnvXsxw1GSp5z2nzMmxinBErtR4bSC9tcte/+QnP8GSJUvwta99DU8++SSuuOIK3Hrrrdi+fXu0//Lly/H3//7fx/33348VK1bg/PPPxy233ILNmzfPm8xVCLNgE6UV4uJvHYqWA0kG/ZuuYpZmidZrkQnlcUAVQy4z+TelEJUiOl5DSgklc5/NIklqq1ncAzkvfOWMIdizchwLy6q8k5rV84wjKQ80uIANAzhiIE8eoJRnFyDZBvGxXUYOX/xDVmrk9BhR4TcbklE8zuVktKwvXxaGERtzamSZTV5ahbfaPWBxNMj24x//GI1GA7/0S780twISzU38zu/XlnnN54EJn/2QA1XkWdAy3h8cwBNxKBDzAtS2UO6Mb9LnngA9DPu1SdxnMccvkD5rJAhnyZMkQXzGkQsgC2RInbOcezXfVOScpNhEhDPEX7+so7h5BI6WXP4oYMAyZu2Iwe+ZzxWLShZr5da5bkOwaQG1HL2veE0oF9mYX3chWQxqRrGP5T1iaJhUfxF7KvdBqn8n4u1gk2znUH1rGFLsoKUSzBG0SsBTvrNJBhPGHdG/ZViPrWZeCfGrELGgXQnwlOsgd2ExRm/xWugFSHkOpYJTvkeVpTJ43PWSMvA7EbCBYWW5e0lnBrCX7Zu9fec738GXv/xlfOlLX8Kll16K73//+1i8eDHuuOOOaP//9J/+E371V38VV155JT7wgQ/gz//8z9Hr9bBs2bJ5k1nuu6zy74Wi5dZLzNtVPJ8/S5nzqOsouTpYnlJa0wZy8dct184ZLpaQ5BEC5JXfs/ir3zMuCDc7D2lOIS7HLX/WHOAs9QZNHgnYMMq/E+qW+a6SSVR+hjZ+jLXB5K9xS3rH+/f7/eidl1q/vnKeWwOl7LNhWeXuGOklZ8K1Y/MI6MDdm61ZHQ1l27BhA/7pP/2n+OQnPzlPkuotlvAbIO4EJ6yaW2f5RNWDNe+HIWWcFUwOP8DOvI0CPIRO6MhO2Ewmdjx5TsbsNyaEStpBaR216D/azCeeBnw2EeckKsdl777RFrl+o3dl3n6T5x6bs4kPXcvbS0A8hDyXPxWwRVSwUQmSpGFxzjXnAQkamfuPGDa25VgtvmLEVi2qKaRNAD1lk4lLwrDhGXaFy2zKM0McL5wAm9KbUjBDGGM9FlOcY8z4CmbycBvIQqLLbh6u4jmN2WShbcok2EDeIxEL02Rk4SpU1M/LBOG5JNujzVr2Tref/p0EQEnFiXfr8dmcY/ZD3wsB7MNZz7Hxc2FUgOcNbOmXbYpN8lYEm6anp/HEE0/gtttuq55rNpu46aabsGLFCmqMQ4cOodPp4LTTTkv2mZqawtTUVPV43759AIBOp4NOp6OOX74u+1XnbK+LBor/T890o2NNTU8DGOyHTqdaT1PT8c+enukCABroo9ftVs8fnprGotFWKF/Vv4d+r1vJl/pepez93gzKLEtTnZm47IPnmg04sk9OTwf9O50OehgoiOgLWfpJWUrZ0etVWuBMNy97r9utAJuU7NOdmUqWTqdT7aPJqfi8l7JI2buK7N1qHrso5zG9Bsp5JNdAKXsD6HVnxDjT6ES0wJlynfT7QL/4f0ebx249j42B7J3UGhjI3vLW73Ri70wPnms4ayAvC3o9oF/vpUKmTrwvgH63i0a/nHdd9uZA9vI+mEzMe2emnOtadmYeG/0e+gPZU/3l+d3rzlTrdzohi9x7cg0cnp7G4tGBvJGzKdcsfee6SUcDAHz/+9/HnXfeiTvuuAO//du/HX1Pt9vFP/gH/wBf//rX8dBDD2HPnj3zKHG8zTi6uKginEqZEdEHuBCqppnZlNNPLAxN2b9JyN7v9x0nd9ZRLEJw5V8mjYQlf9QIwY6XrzEhwT6wXem/ye9aM2kru4MJ2yaAcKnPAvnw91huYTlOIEsEPNIKZZYfK5Ny5yN2OMBR7g0mlUiVL60pKuklC3XEHe65fME00UHaQMzem0dm0xBsWkAtb8DW/2eYTSkDmfOOMHT1SHxohhlS5hnJoa7SsyPOqjSFVF62FvqrBFVyh77nHcmFL/rxxP1+H43Ipo6FodAU0gyo0hGgmvwOyQpKUUood2HlYrPlGmCAMpk7BigVhX6+5C5JxZW/Uy7nWCdx6GeVnKabc2Gm10OrGRr41rxdUsmxVLSQsr8VE8Pu3LkT3W4XZ555pvP8mWeeidWrV1Nj/NZv/RbOOecc3HTTTck+t99+O77+9a8Hz99zzz1YvHgx9TlLly6t/j852QLQwMMPP4j1O5sAmli/fgMmJtYF79t+GABG0OvOYGJiAvv2Fu9d+djjOPxK+Js+t6UBoIWtW7Zg2dLNKK/9ibvuxqJwKWLrtuLzn3/2GSweAYAWdu/ei4mJiej3mJ4pPv/B5cuxeXPx3jVrXsbE4TVB3/X7C9mnJg9jYmKi/t4/ewSvnxSO3esXa3vTxo14sLMewAimOzNJWXa9UYz31FNP4ECnkH3L1m3R/v0+0OsXc3H/fcuwY3sh+zPPPoeTdzwb9F+1q5jHvXv2YGJiAv3B975v+XKceVwoy7oNxXivrH0Zi3a9BGAEhw4dTsr+xu5ivCefeByvHihk37BxEyYmNgR9d04CwAjQ62Lp0qVoNpoAGnjiyafQ3xSugVVbC9l3bN+Gu376U5Rr4J6l9+LE0VCWDRsL2de+vAaHNxeyvLF7T1L2qU4h+0MPPoBNg/Xz0tpXMNF5ORx7sAamB2vgwP7ivSt+vhJ71oSyPztYv9u3bcXy+18HMIKZbi8py/YdxXhPP70KM71C9u07dgLvdPccAHR6qObivmVLseX1QvYXXlyNiX0vBmOv21f0nzx8CBMTE5gZfO/lDzyIl48PZVk7WAMb1q3DI/vXAhjBocOTSdn3DubisZWPYvPB4ntvfv11TEy8FvSdkbLfey92Dc6NJ1c9jdHXVwX9n9xRjPfGrp346U9/iiZa6KGBe5bei5PH3L7+PGnt0KFDdN+5bLN1NPzu7/4uzjjjDPxv/9v/hoceeij7OUfb0RDvV4CBDQDdmbrv5PQ0OmOhDlmCqf2+BNnjQDUQd250EsD25MC50RoA283GwKFAODf63VIuYGpqOpobpgaHu0Bj4LSeGcjkje/oOL0umiWwnQCHpwXAKh0E09Px/h0pewlsK+BwKSd6XTT6+jxK+8IBhzPOjUajXwHbnW5/4Nwo9r1cTzHnhupomSmdGzUon1wDU3En0VRiHkvZWw2gL4HtqWm0IrBDBcL0hSzE+u33umgN1mNqHic9x0ztVEqt39BBoDm4qr3U76GZkb2cRwCDvcc551rV+q2/U3T9Vk6iXrGfkFkDYt7n2tEwBJsWUMuHZ7moqCX2lBnfWkUiFiaQR4s9D0MSPBKJ0SLfKehfofr53EEAot6RXHUCK9Agw0rKcUYitBYnz4ghsR8DCPmhH7kkpVXuGLKKhPxdWZYV7yGLA2XJEIeId49hlFnWr59nJJ9gF84aSHlrrOVWpex83Pdbn9l0pO0b3/gGfvzjH2P58uVYtGhRst9tt92GJUuWVI/37dtX5Xo66aQIaiJap9PB0qVLcfPNN2N0tLD0/+8nlwHdLj594w049MxW3PXaWpx7/gVoty8N3v/KjoPAqp9hfGwU7fat+I+vr8SGA3twxYc/gs9edmbQ//WHNwAbXsIF552LX2xfhv9r5b0AgM/cdDNOPi5EGn687XFg7xu46sNX4uTjRvFvVz+JE048Ce32ddHv85uP3gMAuPmmz2Ddg+vx8LZNeM9734v2zRcHfR/bsBt47jGceMLxaLc/gX/18s+wc/IgPnrtx3Dtu10mWafTwd/8eRHK+N73vBu3fOJCfP3JB9BvNNFu3xqV5c82rAAO7sd113wUOw5M4f995Xm84/R3ot2+Kujb7fWBRwuj+tabb8ajf/siVu3aivdfcina170rHPzZrcBLz+Cdp5+Gdvuj+N1nluPQwWl8/BOfxPvOPDHo/uB/ew7Y/jou/cAH8AvvOx3femYFRsfH0W7fEJX936x7BDh0AB+79hqc+Po+3Pnqyzj73PPQbn8w6Lt+50HgqZ9hbGwUN9/8afzpC8U8ffDyK9C+8pyg/44VG4H1a3D+OefgF3/xcvyTlUvR7fVx46c/gzNOHA/6L/+vzwI7tuDSSz6AS846CX+2+gkcr6yB3378XqDbw6dvvAE7Hn8Ny7dswAUXvhvtz70/6FuugZMGa+AHGx/F5kP7cNXVV+OG970z6L/tkY3AhjU475xzcMvNH8BXn1iOPhr47Gc/FzVe/8PmlcD+Pbj6Ix/BTK+Pv1j7DE459TQAO509BwAHpmaAn98HAGh/9lY8cedq/HzHZlx08fvRvuE9wdgrN7wBPP94JfsfPP8A9nemcP3HP4HLzgn3/eN3rga2bML7Lr4In77ibHzz6Z+hNTqaXL/fWv0QMHkYn/j49Xhhy3781w0v4owzz0K7fWXQ9/B0F/h58bt/9tZbcM++Z/Hinh344Ic+hPZV54X9n9wMrH0eZ51xBtrtj+D/euxeTM/08KkbbsQ5pxRoaexsyrUSbDnWbTaOhocffhj/7t/9O6xatYr+nKPtaIi1p7aXwOCOAhhstNDrN3DP0mU4Jdyu2DwASde8+AIObOoDGMHefQeSoObk1ADkf+gBrNtRvHddwrmx8QAAjGB6qgBJD+wr3vvzxx7HwbWhDvH866Vz43Xct+w1lGbm3078FCORcJ3tg89/5pmnMdIAgBZ2vrEbOCcDDt97L157rXjvi6vXYOJg+BtXwPZA9umBc+PBhx/GpvDIrsDhjevX46HDrwAYweR0JwsOP/7Yz7HtcPG9X9+yNdrfAYeX3Vs5N55+5lmcuP2ZoP8TA3B49xu7CudGr/isZffdj3d6zo2lS5di02Au1qx+EdOvFWvgwMFDSdn37CtlXzlwArWwfsNGTEysD/puPVTI3p0p5mLvwDGy8okn0NkQcXBtLmTf8vpmLL371ep733X3PQMHlts2vVrI/vKa1dizqZBl1xtp50Zn4Oh5YPn9eLVc+y+vxcTUS0Hf1XsKWQ4fLPbDoYPFex9Z8XPsfEFfvw/cX6zfTrebdRI99fjj2JdxcO3voJ6Ln/4UW7cMHHsvvICJPc8H/Z+qHFy7MTExge7AuXH/Aw9gTeSoWbd+4Kh85RWs2P0ygBEcVBxcBwZz8eiKR7B1sB/mytEwBJsWUGNjSYGSkcPTWeXfbLwybaxLdkXG+PZkycV99wRQVjJhur00hbQOuRKlX6kQQL7yTziPOosrFq88EmESSBCm7E6V/SR+p0oWFigzAIjyNSeZHhGiV36GKosPTmXAL5lnhKnGYWETSRZf8Rnud/JbvZdqmno9TrgILKGRvV6/YjkWv5P7mUnZyTDQN3M7/fTT0Wq1sG3bNuf5bdu24ayzzlLf++1vfxvf+MY3cO+99+Lyyy9X+46Pj2N8PNT6R0dHaSNN9i1//0VjoxgdHBL9QR+/NVvF661msxhj8BiNZvyzB97ikZEWjhsXFIZmK9q/BN3Hx0YxPjaqyiLXopS912hE+zeapeyNgezN6vlY//J6GB1pYdFYPVcjIyNRlmgpy/jYKMZGB151xGXplSF3AMbHRzFWHc6JeRQhBKOjo7XjICl78fr46Igje2p9lLKPjY5gfHSk+v76Gii+W3lv9DNrYHSkeL3VaKCLfnreBy6esZERjI+NDORLy16umUXjYxgbGanG0OaxkqVcA424LGWyktGRFo4bq9dvc2SkWj+ylbfy+NgoWgPByqPO359N4ZhdND6GkXINZNZvtQbKiyA5j6hkXzReroH4b1q8Vp8D5Rro9eOyTPXq9b9ofAyjA0s+tQYa/vptNjANoNEcCfpbz7E3Y9u/fz/+0T/6R/jBD36A008/nX7f0XY0xNrBJ14DXnkBZ51ZAIP/7LF7MTXTw6duvBHnnhLSKCf2rgJ2bceHPngZLj3nJPw/z6/E+HGL0W7Hc1D9s8fuBXo93PTpG7Hvqddx92uv4LwL4s6NpzbtAZ5diROOL8b70eaV2HhgDz784atw86VnBP1ffXA9sPFlXHD+efjcrR/AbY8VYO5Nt9yCxWOhyfkXWx4D9u3G1R/5MMZGmrjjpVU48aSTAbwRzNNBDxx+7p6X8Mi2V/Geiy5G+zMXBWM/sbEAtkvZ//ilh7Fr6hCu/dh1uOpdp4bfdaIAhy+66D24+doL8HtPPQg0W0lw+I/WPAQcPoxPXH89XtlxAH+57gWcPgBz/TbZccHhB//b83jmjW245NLL0P7YBUH/qadeB9Y+hzPfWThLvrbqfkwe7uDjn/wFXHTGCQDc9fTTfS8Au7bhig9ehivPPwXfee5RjI0vQrv9qajs/+rlnwGHD+L6667Foo17MPHqWpxz3vloty8L+q7Zuh94egUWDZwlP972OF7Z/wYuv+JKtC8/O+i/Yfk6YNNavPtd5+MX25diyc8LAOPTn7kJpx0/FvS/5y+fAXZuxWWXXYr3nH48frD6SZx4ctq5seTnS4F+Hzd95tN49ZGNeGDrRrzr3e9B+9b3BX3Hnt8CvPgsTj2lGO9P1z2CrYcP4OqPXoNPXPSOoP9rD9Xr9+abLsbXnnwAfTTQbrejsvzpukeAgwdw7bXXYNeBKfznV57DaQkH17Z9k8DjD6LVbOAXf7GNB//qOTy+83Vc/L4PoP0L7w76zzy9BXjpWZxx+jvQbl+N3392OQ4cmMbHP/5JXHJ2iJY+8t9fALa9hve/72LccOkZ+NYzKzAylnZwfeOFB4GpSXzyEx/HB85YPKeOhiHYtIBaLneQn2S71LNyMb9scrxYokwq75FgBzG5gIrPYCsolX8LsIkJc6KAMgEeZJkhiaSgKSaUC2KIeHsCyCjVR6YCHJNk0E8Qnl8DpSwiObBWsjRWKShXHbEEj8icTVVC3kxZajfRpIWV1czKErKydFnq7+oymyx5DpLgp/jM2YDOOWD4zdzGxsZw1VVXYdmyZVVVoTLZ91e+8pXk+/7wD/8Q//Jf/kvcfffduPrqq+dJ2rrV60syM/W+1e+Zq14n9kVZTVMD7mNnYy70OpA9lVvEC0nOhnYP/vpn6UyvX+VgkE0mvs2djXJ7ydDbdHnxGlgH6rssXRCh/q5UovVeuAZyVWdqIN4dI5DFY7g2mwC6Gisaley5CjhF/3qNZZPHerKwia2bDTckudvrI5JyTJx3NeCXcyKUclSM1cxZWq2BVuasjrLF006wGXkn5dizgT6Yc1bWfeVfTZ43U7M6Gl555RVs2LABf+fv/J3quV6p046MYM2aNXjve98bvO9oOxqirVEs7NFWqwIGp6CA8gPNcZQEtitQc3wMYxWwnQKHS1l8gDUFbDcq2RcJ50ajFYKaxecWfwuQvfis8izw56lRR2QNAFYSHB7IWjl/E/NYgvJjI+w8Fn/Hx0YxOqKDw9MSHB6rZU86CALnxgCUb4Wyj46OVs6K0dERjJVOrISzopCzeMP46Gi1BnqI9294zo163uOy96vzsYXx8TE0GsXvHJN9MBCAgXNjlAflx8fGqnlPOzc8B8FIbv3WUSDl+u33gVZrJMqkrZ0bIxgb66myN1tleGHpbGsNPjLvKHTWQGr9lvM4OoLxgWOmqziJyjUwJvbZXDkahtXoFlBjQ6IAN79PktEg8sbI8ZmEdCZjXYRc5Y3vUhZ3jHBsl0mSLTEsZJltziY2jC7HhJLhXA6zKVsK2lYim0kymGJldTIAzyihePvj5xPvub/paKZ/R8wjgGyIoUwyaGJlEVWLZI6k4jvoa8wF4QiwKZIvLVd+G8CgrLorY1r2RvUZWv83e1uyZAl+8IMf4Ec/+hFefPFF/Mqv/AoOHjxYJY39whe+4OT1+OY3v4l/8S/+Be644w5ceOGF2Lp1K7Zu3YoDBw7Mi7ypiljJ8yVZEStzBgR523KOASKBZc9fizngwAMaMsZ6OUyr0XBCkPPhrvkkqfJ5x0lBFglgqwCOOvdjtKsjT6uJOtFoBiSpE9+Wz+dlAYgwYEPuPrcqmqUIBcdYdSrseExhbfxmg2H+1vuu0bCsX44l6rDFDXoJA1A6e49IlBvcv5k19mZr0tFQttLRcN11IUPiAx/4AJ599lmsWrWq+vd3/+7fxY033ohVq1bh/PPPn0/xnRbovy2uWhhT+TJ532RybQY5HzOgZtPbr8lzVeg+Ze7MZG7Wbhwcpiu35mwmmexZfM9UFWEnjUTGGRrcN6Qd4dsdzLmaKx4l5ZHfNXfP+8QFOl9wZUvEZXEcXGTUQNk/l8i9OlMrfUlfA05KC0Pl1pFmM2vTyHsSkA53ch5zjpyYPabeN8XfWHqXo92GzKYF1PI5m4rnyyTbLLMpZORkPLekF64j2B6sYjTiHfpZL5xXRSJ3Ibaa+aoQfkUL9qClczaJeXSV49wB0awutWR4YeDNHBycRylfT+V1buWVFn/8XGWQ0LOaUaC6rpKTW2PWUuOywkbOex9enoPnCaO60SjCI3t94kIkZE964zNrxjfwNUXkzdw+//nPY8eOHfjqV7+KrVu34sorr8Rdd91V5fLYtGkTmoIl86d/+qeYnp7G3/t7f88Z52tf+xp+53d+Z87llT/DKLHvrOB3db6IqjbTUBiFjhLqPpcauxyXzX0mGauABtpCyFKfpZ1uL1pJT56lWYeGBG2JfTfrs5S4k+RrVKUi7yytwKYUM9Moe1SWzG8EDM7SjGEcgN+Z3ylWYQfIg4KtZgPNvi57urR0tHuyWAgDZlHFQgyVaeVnSl0jb+hwesybsS1ZsgRf/OIXcfXVV+Oaa67Bd7/73cDRcO655+L222/HokWL8MEPuvnQTjnlFAAInp/v5v9Wlvys2byc/pmdAXvTDoJU/zAXJqCnBSjGl+xSXZbKBiIrctNFkoTdwTBp5bznHJD+fZPNFZvIucsUeGIciuUdwujLybMjcwbL/jO9ftIGkrYBW/Cm7J+zVXse4Fj+jLn7qSXWlyaP1GlYWSqbnIxmYiMqnCrulP3mptiYyzYEmxZQY5ULM2BDKlJuUuO810teQmz+nUo5Zg9O0qDqyUuildvw9f8txh2faL3e8GU1PQ1okCFaZZecclzKkfeuu/M+yhoCnqLQ6/WjFFL5XXNlQtNGMnnQZrwjrhdZXy9y/GYzr0BJI0D+zX7XwZSNNJuY7vaokNecp0auDQbo9efxrc5sAoCvfOUrybC55cuXO483bNgw9wIpLVX4IZt83luLHYJdATBeyYEsjXwo2qwBmzLUIgPylk8X+4IISXby33EGWilP9j71lP8ahNEBHjb/naVIgL8GyqOZmRf5PkZ3YO87wL0Hcmcpq0A7jK8g/11anlazUSVNssqSBG6DqqS59Rvej8Xz9d3g9kc1PsueZc/1rthL8u9bhdkE2B0NC7X5vxVr3DuATeZc8vsfLf1Bnk1c2LbQ23JAVsJYZ3X3bMi5AA58Jm0sZDfGgmGYtM2GIUKi5cueP/dyujjgsmNzZ4EPso/mZEkQHZK6e6ySdAZQKcdlGV9SF5fPa7I4zDzCsZwHYl27Nk8AibMKc/Yhs5di8sxlG4JNC6jlaNA+dZ6lv4ZGRp62yaCiMxEPBg+U6Ydhz+vPovoyRw7DDJGXRA4trjc8d1hJUFADGuQ8VlVgyYM2m5ckxW7LenqbjmLf7ffRRHggScUih+oHdNYMhVSyFBzZk5d58ddJVp6Yl36/74TosPTU0mvPVoBzLhUlR0rMe5+TpRx31sn53yK5Ot7szfU01zm4GMOifI8/jtPfB0kynu9Y6E/uTgJIwNn3MmbO6nL0VrMunqD1l6wZ9k4q5cnK4s17DmiIyaLlv7MULPDDbHhvLXmWivFzDg05v81m/jcNWVbkeiSdN46hU82LfpaW67G+T6Pdg/uUZRPJ+7GUp9VUCkU08sarLzsdxk4yJd6szeJo8NsPf/jDoy/QLJr/W1nAALZv2T8LJvs5AnNnfMTJ3e1prBbLuWdb8z5IwgJlPouSsTty8yjvj0Yjf99U+ztwbvBnjc5qgeifY/YP+nqhaPxdSdoGBvColCcbYlraBeUayKZwia+BLJO2kZ9H3zbMEUD8ezu73qNrIK3nV86NeWA2LXyI/23UWDor650Mk7Fy9ETJVOprSp1Y2PlE1YPLk8wbMtuDVua8Scd9u8ZdlhnSrQ8TR5ac7P5BS+SbsuZpsND4Gdklki4dgBZlmvXG58DPcpzRFrfepex51p+7BtjE6YE3PvNdzXuVWL9yzhuNfHJ+a6jIsM1vCz3Nxf+zytBAP2DZjb53LJm3TdLxDbI0m0worbsWc97acpjmILl5/h4IHSDsfUqHIw765XNF8MnKgXiet2zi6crD736nlCx+3rb0WV2Pn5uX4CzNFFuQ4ctS9rxB13Texxg6WaAsOBtdGQNZRD6a8jOK5/NntROWk8tf0xSyECAcUOtWObYayxYftmPXAsAmw9Z39F8yv1PZ38psyrNXE/lWDbpP8uwQoV/FZ2RsmgRQxuRbdVJgpO7KSKh0FmSfBVBd9OcLwVBMWqGj5s4aa1RC6qxhHKKsHVGMzwMwfESQmBeCSRt1EhHMIylT7m711zsTyVLlJ+vzv+tctiHYtIBaNndBAi3ObvgKjXbH8ZukkMpY1Szboyk92tGuYtOUCqZ++PjIeDNzWMUU9dyhX/UvFfUM/TX0fnJKYC6sT1YKqg/laFczBdrqYYjlsirkyRibxLynLk829JJV7KWRTClczfoQT4UipWRJ55sy9q/mkQFifVbDYF4IloIry9DIWAgtVfjB6jXM5uKrQtd0hSjmHcsVfhipgAB+j0rZU7JU7MPBfs6dpdJJwSqtLMvKP7/oPd3wztLc+ESRAN/DXw6fLvyAShYA2fvaXQMcg6uQhz/X/XnPK8Rw+jN6Esv64x1yrtPBwsRgmBJy3ln2rB9mnnUk+etXSSA7bMemhYANbyCz+d7K8Wd77uWAcDrXUGSPZJ3Wnk3DO9zL8aPdo/eHKnsk5CpbybIqhsaDcFL2VD6raIEnjUk7mIQmccan1kBKX06eNZY1kDr3PLKAlbjAOvRL51mJN+Xy6BZObh4UdmWJdo/Y/LosTr4psX6zldaHYNPbq+WNxnJRu4BN1pvpK1KGqhCp8WUYkuvRJhOU5rLwJy4J5rDKGSSuJzafINz3phxtqq9UFHLzGCYIt8nCJo8cFYe4Nn7ME0R7R7KVgtz1W4qTA1ddVF9fX2V/tqIFzbJK5HfJySOZAWkAcSB3EA+vG3dsjpRhm99W7q0y6WluraSo1XlFsXhcKTiMwkInj+WMdWuC5Yph02TvvHofZauc+U4Bo/Kfy9kUS8AKEJ5vwujygYbc2VjPe/E4d8+4HlJuHgGfCZUz0AayGEOS88Z0OI90PsYMYJM2XnPnupf/w7AG0pWz3HmhQQASwBi2Y9dSDDorYBOrouaHPucdCvG8MazdkT9XUY07Sobs1vNiKzSUtQ28fFO084RwEvqMTjM7iMzZJO2x1Boo5Cn+Ws7symFF5mxinUqxc5JiNjWIe9isc9j0Aglm0bp7IIuN2ZSy4ZP5pkj9bS7bEGxaQI1NLmZmNvkL20BlBOKHp/xMN79AdOikF44tMWwBbFhmSLPBofpBrixzBQxDbo9MEmz/oJ01BTpD82w2XQppVuElYtBrxR4mWfw8I5Zy3bkY9LB/njEBgGbmVcZg7rIVgAC7fq1eI38ehx7thdHC84JTzGqmB6mA+PuIuGesyefz4VzxOyy1dstnW96ZYVH+aWYIeU6zssfKaAMcmzcLIPrK/GD4tKfZepZGAJvMevT7p1hWQcJ6631qMHRGMk4tX/nPh5OgGlu+j8lTWOabSvX3QTvWeA11pGj3ZGj3Wy1n01uhWQEbGfbq6G2R7uU6KJ0bbJJt2rmRAITSep4INyZtmoDpkTmDy/50VIK3R5JnWSSiIq8rl98hxyZKsCiT5/Bg3Egxgvj4oez2CAnyd8royzEWcNqJU89jwxA2WrGJjIzRKs9XhgnOsNL9eztbZT0RBmpxWKnyeHMzl20INi2gls2j4G0C9tAPkkMTyouDikY2mRs3yx+0PBXXU6ZZY12EIPT7cXlqpkepeEOVPaXU5XNMkJeEoAazxlTgecmFFwb5plLzHuY80eSJ5xnR+/qenZyiPps8I6UsqTXgg6Usq6Eu160r9qnkrcxly8oShKFkQ504xXXY5rcFYZGs4mfMIWe+ByjPrpeLr1L8OIZrvjIMnP6WO8zKDKmcPXRVvxx7ciC7ZwAy3uNc/p0gzLx8PsdW88Bypuw2HxpQKv+5czqucGeNXXK9l99JhjXQsuTu0wQwzIRkFO9Lr/cUaGd3Pup3u1+ZaxhOvfCatey9E36Z0dt8ZnQO7PX1BxYQoplNQh7WCV3PC1kNktXdvfHpvEqNvMMyVRWWJwvw4fVyDTDs1dmeY0woPgCRcyx/lrFs0dnoBIXs5BogfydLziY7icJzLBvSz+RseD9KZq7bEGxaQM0K2NSHfip5nWcIZJQ6iaLKWNVYf3vc9+xyHVTe+xwyLqtISMU+0t/f8HmkG07/WlG3AWVMmACLurPV5fwLKweSSFkajXy8coxRlqWb0t4R7+Jv6XMTC59I9Q8Vey5nE8tsSgG9ttCPTHJgf/3m9pJPgx+G0S2IVu8htlKYUdlKnKUMOyjreUsCmdHuYVLj3L6owCbj3DTyycpTIVE5EMM/SxmF2ym2kA2TzzObAl2gPKfZNUAaF06YeV8H7o+UPZAFhPzfiXDe0Pep7xRgAUpyjTGsRfn9pR6TZZ/RuXHg9BsyXBduSwM2fNgrEF87qRykSQeBp/vkIyRsOSJjQEPe8QtSluKvz7JiWZQasNbv9+sCFt45GR3bYxhnQTtPh2SLdQRAAwHaZH8jIysyZN5yv6tjR5CAYylTOl9hymbKsNWM9htjBwfVEWkgy4tKMIB2Rf/wuzo20JDZ9PZq+UWdotbGx5OeVSAf82sp6+sv1CxQlkiYnA/l4DZZUrEnlOO84p1iHkS7B4wci2LPhhQ0SaPBV3azTCg/H1DGcJDKd5alkAIQjYAjU6Utd9n6VNxsFSLfMM2GZ6TWWD5XAJ0cONin0e7JUMohs2lhtI6RKp0ykFlPXe6eibOD4rIH53oOiPcMnZwRVT7LgCSB8k+fL6RB5yvcDff51PjybASI88thuOYNNIDIZ5cAbDjDRchOOG9yTMtgPRpDknMe/ti808ZljmUVGCJcNSxm3nueTsUmsmWBMl8XGM3IPmzHriUBG0PZeyDlKI7r+bnUDWzeGB/UtDAdaWPaZyISIU7yLxsCqDHS5RBu+g4dtPOBMrYQyGyq0aX69/v9qL7MMLikTHmGDZz+TNEISzJ8SpZKJ3BlSWHs1e/UKtcvV2RipNnI5rKyhsX5NhCbt6vVbAzsGsWGF8/JgmBz1YZg0wJqWWZIsjoXR9tkQZKQeRJBRcVObTUtlVNIhLZS6orH2U0WubCAjGenUcsvZQxlH/QjQbsks4m4bNmQgiDJYCbmN2A2Zcqem1kTArBhY/+t1ThyIQ4WhSsM6yRpwT4IlwtbMe493zsSS+6YSvabC5/wv+vQyFgYLe1NJZNvkueRb1BbQgOO2rmeUBRzzCbfQxo31uv/W2TnmSFe7j7SuC8YNmKciDw+UJYNmfDOxoqBSpzT8jswQJlURFXnDXnfpcHvaPckIzbtNEM1PluVlAZiy+9aGiK0HpNfY47y35xNOMnsqgAOczYtvGZN5h7TIVP9A6A6A5L4az6v59XMQvk5FlZ3aklWa97bfzk9jNbFDXeCnC9Z2INJ3uzKwuniLBOqSYRtz/aurCrpZVNauPOeD5cXd6XxzM7Jkqogmp13P8w78rv6oF3OfkuvgZwd0XRkYcLf5fhM3uW5bkOwaQE1S6UdII/QpnIHpTeZK8ds8gtYczalK8DF+zOJPmnPDgmoBIc+e6BU/aGOH5M96YkNgDKytHMAkkS7K79TvL9Lxc2VjS5lKR6zCesDD7jBQwbEL/+efygbwjQB+/pl8560GrV3RD6f6iv/5n5TNonzsM1v86v9ZBmrybVFKn6GQhRSkYtXNvJkaWX2kbenc3mSymEYhdv31FkAXoDPoRHcSVmluGBPlkdSLoccE5IcGIyDVOpsiWMWKBtpuizRqNLqn425MDqj0ZXMUZZJOCzvgbTXOy5LVo/xgV4yGbomTxJsosNpw3EcWXzmeuYcGLZj16yl41O5WqJnjadD1npYXBZ/zbO56maT88a9byJjp3SfrO6O6jPkZ/ot1N3T4zupRCwhuy3uNw32d6m3ZdlEeWaTfE6GACbtq6Qtqf+mfJ4vuX71nLspWVI2Ss8DbnOpRFK6u+XMzkemkLZnz12/bDgtky/NzbscHe6otrc02PS9730PF154IRYtWoRrr70WK1euTPb94Q9/OMhRU/9btGjRPEprid8kwSPvYM6CJCmAJ3dYNQwebfKgDUAPMn/BSDNfRS1QvLNju8wQmnJa9c9dzuKSyFxY4W9UPG9NSpgHSYrHlqqBbGJrmjU1y9hpfw1ooR/1Zeg+H8iS2Es54y6oOkFcQk6CT4WZ5ystyQuuYkQ2nb9Dj/bCaEknAhlClWPlBcAEy2zyDRdF+Wcrt5jZRIOnzcY6E4pWgSTlZ3BsIpa+n3YO5RQ/e6LRyqFBht6yHlUKuE85b5LzUvyl8wia2bao+rHKPKv8p50InB6j7b1g/VbOlejQ4jcdvCfr7IlX5hreAwuvmR0EAlRxk0Mruk/LZ5jbAFM2P2v2XE3cN7He6egLfWw/EsAaWh2bGt/hTjtxgvBF9swmHcuecyPObKqfszg3gkIKxnOS0Tmc+yZ6zxd//YgHxpHrysIVMVHtYG8NsHYBmzsxZQPRAKXS369+OtftLQs2/eQnP8GSJUvwta99DU8++SSuuOIK3Hrrrdi+fXvyPSeddBK2bNlS/du4ceM8SsxvSL8iVja3S7nhDR5t+Tc2fs0MQTY2FJg9eMRusqRyrFy27MGZSjKYZ/D4h2H+IM+BHmHCOFKWpl0W2d/CgmAPQgsAI99HydKUCe4jYaD+3jDEwxd/i+fZXCC5vVc+HYKliizB3shdnvVnaLIM2/y21NnIezx1BccMksiQjMxZWrFISKUyzCGnV6/rw5VZu5OSil92j3ohyamz1A9Jnq1XPQrY1P+3VCWtZXE/M9WfdfakDMDY72QNiwsU6FmGJOeYfPIs7fURZ0r4vxH9m5LglDc+72nmy5Gz6zfFzEvdYcN27JqfIJw3Ml1gWwPl2ZyPqdAc9myyhC3J+yY2fMByJCvpWYvShPpyWocE3NA1qz5LF0kiE4QHoWsKI7mUQ+sr+/tV0dioBDoZehPOfcPoHDlmf5AQn72fgjNeXwMM4JgqkGJdM0cjD6Uv+1y3tyzY9J3vfAdf/vKX8aUvfQmXXnopvv/972Px4sW44447ku9pNBo466yzqn9nnnnmPEqcZ0ukmE0M26d4n9WgVhQjM3jkeTtyCZa9A8LCmsmh+sG85Gj/ZuCAByb88pM86AFHJvrgzPxOFrqszDPiHrSZBPTePObKdbOJrdNKDrF+y4s8Qw0P2CT0JcF5nQOwVFMWgwsoOnRgVOcu/mGb32YHJn2FZfA8CZJkwYBESLJmuAR7NJdDIwBsErKU+44AJnzlv74f42OHzJDiP6mqNpYCGu74+bM35SVnABX5HWgvORk2XHrJGV0gNEYzOQ1JBTrwkiv7Q+bQaPrrVxvbd66QTjA+wavPWozpAnD6sPpgUB2RnMfc+MN27Fo3CeIbK26pug+c9+SZtMiOXTwPR2YNZJfjNJvw7ptI32RKi1wIri+7Ld9qNEG4p7tbQHD518pqYcreAzVjN1v5knBuJM9gMj+V5ZyUa0CrhO7bktn7g2Q2pcDY2Dz6oJ0ZcJxlyDnPbErbKTKctjEPzKaROf+EY9Cmp6fxxBNP4LbbbqueazabuOmmm7BixYrk+w4cOIB3vetd6PV6+MhHPoI/+IM/wGWXXZbsPzU1hampqerxvn37AACdTgedTkeVsXxd9uv3ugCKBRN7/9R08VyrUbyvP9gsnZletP/0zEw5MjqdTpXXYbozE+1fHtj9XrfoP1h/05HvU8rSbDQGshSyz3Tjskx1Clkag+/cGCz0zkw32r8zU4zX6JdGePm5cdnLg6PXLV5vNRvodfuYnO6g02klZB/Mf79bfX9tHhuDecRApumE7DPlbdvvOfM4FZlHadj0ujPoDR53+/E1MN1x572UZaZbfIdg/ME8lrI0Gpk10I2vganpUPYZT/Z+N7d+3TWQW78zM+48NjLrt7o8BrK3mg10uv2B7CPO/JTz2BrMY6+UPbF+pzvuGijXZXL9+mtgIHt6/fYH3bvoVvsWmJqaxnjTvSiqNYByHm3rt5SlMxOXJXY25Zql77C5LQSDcoAznP7WRPutjIIeC+tNjZ8GGjjFL1cFUoLZ8m9M9JTyzyrQWcaX0VsbKv+KAegV3Mj+Rt68V84V0omQZdD6obeNBrrox5V/Q54T+TybR8WiQMunfKZEbGpSrELe00w6hxrevGvh0bMInQL4ZMm+I2kYRrfw2myZTc0AQFL2q/XMpveImyDc4ih2wrajY8eBgHxOUbYwEZx+mmPGYSI2RLoMEvBnowxmG8VQyNNLANv1c04lvRQgmEoLQd6V7LkqWb2p/gHTLscE95lNpOyMA82dx2b1Gb1+4fjwQRyrc87iQJfjMECZf6/OdXtLgk07d+5Et9sNmElnnnkmVq9eHX3P+9//ftxxxx24/PLLsXfvXnz729/G9ddfj+effx7nnXde9D233347vv71rwfP33PPPVi8eDEl69KlS6v/750GgBHMdHuYmJgI+j61swGghT2738DExASe21E83rZ9e7T/yxubAJrYtHEDJibWYcvrxePnX3gRE3tfCPrv398C0MDKnz+KXS8C05PF4wcffhgbT3D77pwsZEWvi4mJCbx+qHh8eHIqKsszWwtZd2zfiomJCax5vXj86ubNmJh4Nei/YSD7+nWv4OLzgDd27QTQxFNPP43xLauC/lPThawPP/QgXjoOQK94vOy++3DauNt3/f5C1snDhzExMYHVewbzumdfVPanK9m3YWJiAhs2FbK9sm49JiZeCfrv2Fl89tOrnkLj1T727RnM62NPYGqdBxx0B/MIYNm9S1HgKyPo94E775yADzhvGMg+NVnI/vSuQradu3YDZ7vrCQBeWV/IumHdOkxMrMVrA9lXv/QyJg6vCWTfN1gDj/3859i9GpgezOuDDz2E9d4aKGUtZL8Xh2YGsk134ut3eyHrGzt3YGJiAi9sKx5v2bo12v+1zQNZVxfrdeeO4vGqp5/BcVufDvrv2TeQfeVK7FnTR79aA/fjdC/92sOPrAAwgs50sV5fPVDIfuDQ4agsL2weyPp6sV7XDeZx/fpib/lt06vF6y+vWY2J/S9Wa+CxJ55AZ0PM2CxeX37/fThxtJ7Xu+9ZiuNH3b7lej148EBxDrxRPN71xu6o7Gs3FLJs3FCs11cHsq95aS0mJl8K+pfNX0taO3ToEN132NxmZVr6LFGaYWMFVQiWXYpynvZiw5ElD5QhOn4271HDQt3nGH/mUIJE+EmW2WQIo6sqUnoyJvt7IRZs4uxmE0A3x5RwQZIUhuEzLbMe+wAsdceJjV3I7BqvsSWZ8tizbHHWY9+sAKG0Qdrz+uZAu1p2jzVlrIY1DKNbeC2sIKufq5Z8mKn7gDVga8AmU2iIBMpiCcKL7xT2DUFzDpT3AVlrzlItjK6KpqCrMftAGXfG5wq7JNdAJozOqaRHO2bc5wPZyzXgA5pZUAW0g4sNB64Yo4Nh+TM7vz+ceWy4svf69WdWYxtDUsPojkxVv7J/Kz++D37OdXtLgk2zaddddx2uu+666vH111+PSy65BH/2Z3+G3/u934u+57bbbsOSJUuqx/v27cP555+PW265BSeddJL6eZ1OB0uXLsXNN9+M0dHCmtx1YApffeIB9NHA5z73uQAVnXl6C/Dyszjjnaej3b4a3We24C/WPotT31E89tuzd78EvL4BF73n3Wh/9v14+K+fx8odm3HR+96P9qfeE/T/ozUPAZOH8fHrr8dHLjgF31r9EHZPH8bHrrseHz7/FKfvuh0Hgad+hrGxUbTbt2Lt9gP45tOPYGR0DO32jcHY21dsBNavwXnnnIN2+3LsfHQT/nrjapx51tlot68I+j/4354Dtr+O9118MXD4JZx5xhl4Yc9OXPbBD6F9dQj+3fbEMqDbxY033oB3nbYY//cTy9CZ7uIXPnUDLjjNBf4e27AbeO4xnHjC8Wi3P4FTXtmFP33xCRx/wolot68Pxt716CZg/Wqcc3Yh69r71uKezetw/gXvQrt9SdD/h6/9HNi/F1df9RHccumZ+I+vr8SGA3tw5Yc/jM998Cyn78GpGWDlfQCAz916K6Zmevjnj98PALj1s5+tkjiW7YmNA9mPL2QffWE7/v1Lq3DSyScDeMNZTwCw8n+8CGx9Fe+7+CK0P3MRHr9zNR7etgnvee970b7p4kD276x5GJg8hI9ffx2uetep+OYLD2Lv9CSuu/7juPy8k52+h6e7wM+XDWS/BbsPdfB7Tz0ENFtot28Nxj7w+GvAKy/grDPPRLv9YRx6cjN+su55vOOdZ6Dd/kjQ/659TwO7tuFDl12G9scuwP/Y/RRe2LOjWAMfDdfAd196GDh8CNdf9zF89MJT8S+eug9T3Rl84pOfwnveeTyAet9dc83HgGcex+LjFqHd/hRe2LIP3372UYyNF4/9tvGBdcCmtbjg/PPRbl+GV+57BXdvfgXnXXAB2u1Lg/73/OUzwM6tuOyyS9G+7l34f7c+hlf278YVV34Y7Q+5a6Df7+PXVxTAzi03fQanHT+G33y0ePzpz3wG7zjBRUtPeHkn8OKTOOWkk9BuX4fFL+3AD9Y8hRNPOhnt9scCWZ6aWA1s2YT3XfRetG++GKt+ugYPbt2IC9/zHrRveV/QP3Y25VrJ6hw2ewsqIxqVITbchsmpk/J4AnEjNlWiOxeeRYcwwx1fC4OojPXGIPSLDkuHI0u6qk0CmEj+TnD7K7+rD5JkFWjPsChVhZzyH4RcEaEtgJgbJXyRDW2xFk9I5V3JJYkf8YxXLWeTLwubmD0bllOt97J0tfudYmMHIFzOSB+MaWWIDcOpF26r9mt1J9gYdCobwwBKAJE0Esr9UTzvFdTJhL2WH+uzWqL7NXGm5kF5dx7Nua+I3Jm5FBhh7kRbKgY6fyoBZFjXgH0eU2tAD1Ev2UHNRgHWxO4Qq+x+YYQcKJ8CynKVzRuRHJc+ayh9f9hAPiZ3MaAzaf2w7blub0mw6fTTT0er1cK2bduc57dt24azzjor8S63jY6O4sMf/jDWrl2b7DM+Po7x8fHg+dHRUdpIk33Hx+oF0RoZDRdBo1g5o60WRkdHMT54X7eP6OeVyVVHR0aKzxlpVePE+pfrd3yskKmu1NUK+jdbxVitZqOQZayUpZ/47oXsYyPFWGMDWfpoqLKPjY4Ah4HRkUE5zITs5WZdNJC93PSNiOyN5kD2VjHW2OD1HuLzWM37QPbRkZFB/7jsvYHs44PftgSMYrI0u/X/x8dH0WjVh2tzZKT+zQLZy3kvZCmH8ddev+GugbHMGigPpbHBPJbx0IjIPtWr1+ei8TEsGgjRS6yB/mAeR8p5L+cxt35HRwbzWMqemveiVeu3rLbSiqyBwVilLOX6Tcler4FyzeiyoFy/I77s4bzLi2Z8bAxjY2NoNRvo9vpotEYi69ebx3L9ZubR33upNVA26zk2bLNrflW0LIiR8hpaPZ5KsudCnjr3nZTTkcUzePPe3bjilw2jC4CJsG8NqoX5cWKU9lRIn7XCJFu9jqlEFvRNKdBBmJs7TiBLykueZfDkWV8pIycP2mHwGZwRxeTu83NfSR1KC8uhQymTnulo92TIYGxv14bCoG9mDcw2DLQOh4Laf9iOXQsYCpnfymLE+tW8csZ3KjcYm5ONrsDo3Tfx/ZoADsh5sVaMU5m0HiCvGfZAGC7PhkQF4Yhs6BpzZpOyhOHGroy58XO5GQPHT7NIgxJlE3X5tQ7Y2NHFOPHq49qZ7Y9dfC4P8uXCOq2gs1+ARbsr56MSHYC3ZoLwsbExXHXVVVi2bFn1XK/Xw7Jlyxz2kta63S6effZZnH322XMlZtBylX9SShdLw6STtPnJMomFmkP1Q+8k62HwDsPEaWVRGoPkdfQFBGfs9GWbuBAVZLyUh41XZn4joFYgGFqllIcJt5DKiQy5yRpfrfxvBITfNUs5TVxCmhfZ6iEL4u2TChq/BnxWAyAMDU1Z9PrmEq374UIp2YdtfluqQkm+nLPNyAyZJJGxPWNdFluIhv70/X1E5psiWS3l00zIYMDGcRS/mCz+eUFS1Mn7t8xpxyTy9/NKZAGb6mwsHpffNO/h51gzqXxAWgigfx5lz9LAeNXvDfNZ2vAqe0aGt+abCkA71vD2jQXCEMkCt8He4/Q7dt6H7dg1WTAEMLBaiHWc1E1IPYxdZ0xeGr8CoyxGED+z4chS3ZU5JiLpIPAdPyqTNmED9fuZuzLI2ZRJbu7PYzKUEs74ug6ZkIUsjpFl3iYZaLbE7Cori9QhQgaabS9RdoQ356nxff2HD+ucneylChSXZXAO+LF+c9TekswmAFiyZAm++MUv4uqrr8Y111yD7373uzh48CC+9KUvAQC+8IUv4Nxzz8Xtt98OAPjd3/1dfOxjH8NFF12EPXv24Fvf+hY2btyIX/7lX543mfMlH+MKac64DzdlziMB531MRaxcwtFUdYJ8Mj24sif0oqQXQKG/WktYhx6JhCx+XhKLZ6eXO6xSh09CFmPIQljtQ5FFrAtZZrq8bCV4KscwJxOuPEf6GkiW1GYuW5KlEBhUSQMfTn/tkvANfCCXIyWRzyGn/LW8vTf0aC+IFngkjWFFeQO5+Fsr/4PPzYQhScWy1+3r94CZZeXKlFqL5bOMgZza/2X/PKXdfd5vqfs3nZQbjhwaWylZEpn0YlfndM7TbB2fAEAtyrn8TKbCICAYAcQd5oeBFgbs4E5SjNegDHziaAyA+4zHvgYoS5DPHceVxb/buYTDDGNRfiabc2zYjl0LEoTn9I2AcVeOE9sjGPSx6mEc0GHXgf8AAQAASURBVBCcHY10f7lU5XnQRT++XxNgUJaJSBrrQXVKZX+n7u3yc5toeP0RlSXlUPBZM2xiawsoz4MYruxZsoBvd2TsFP+c1JKb+/POJqDnC3sUfy3z6AOrQD7sDiDAz5TOQc67tld94Hau21sWbPr85z+PHTt24Ktf/Sq2bt2KK6+8EnfddVeVNHzTpk1oNmti1+7du/HlL38ZW7duxamnnoqrrroKjzzyCC69NMzHMlfNYbVoHkQfsCEZDTmPRMqDGK/8A0cW2rvubXhWFg0Zl3HfvgGmJ/aD8xksNTGn1FkMh/K5RsMtMV2Mk5aFVTDtIQvFX+6wqp8rkgzW+2mm18dY1rjjjGp//WaVHOJ3Ta9120WezakSeLH0efSVy3heEjh9sgwLT/nL5VQZtvlt5upAyf7x8SsvOWHEup5mVON3EpR2H8jk2Yccy64CbAijK1DMhMdOY+SYgfjBsNkqOL5Cr+St8IEANo9R3R9qf5+pxBqYIwGoosw7qQtYk80eSeJboPidZvoJ4zXJQOUSDueqKc74d5JieIfs2cHzRkCQdvhlwnWH7di1rndm25kk+fCZAGClgYbMuTd4uk7Doe3Xep85e7CbYCL6Z0fOSZjU3XPnZH5ugnNJ3DfdXh+jbgaM6ruGFQYzbKIAnOJkVx0EhjPVkcUDM1l9Ocds8s/J8j7TZYcre04Wcr37rEJtHisbxdN/AF2/8nUCa3RHdr23PD2C0Jfmur1lwSYA+MpXvoKvfOUr0deWL1/uPP7jP/5j/PEf//E8SJVuMpml5rVreYd4UlH3FaNsQtPUwo4ANtbYUyPoEYREtThjnckbEYQUZMKQrJ5bn6asXlg+cOB5R4L+xpCFMGEcqZAS3pRgXnLGXcpTk5UFWVnkOJV3RFkzqVhrlhmQY9qlykxnDSTidwq9e+7zfrMCjsM2v638GZqeEZhTnujqciVgQwCffliv/MsADSPKnSFlDBTFHDuIMLpSZ2NO9mDs3D5q2ULRQsZapK/3mzolwHshSzT0kLrjJMcngbUAJNEcT0F4tC6LfyfRyY99IJ5YA+X/Z3r9RA4YOP2zHngDezYmj8kBIpjCTBlte4iFrscM27FrqTM7x2B3mNGIn6tWdkUqKiG9zvicNw6zKTiHY2N7903mrvTZqDmHu2936Lnq4IyZi0yx6u4h+MzaWPnfKcWizNpjBIgBRHT3HEgSgDAKWNp11yMrC51offC0n/dIcxDUsshxFLvDu/tYG54lmMwmHHGu21syZ9ObtbFhdDz10XbQWoyYlAJYKkap/kzCUfmZgVIXq4jkeOPz4IHvoWZLlgZxtqSBZImfL2n/8jWnv3cZaoAKUH9Xmo7tA5SMd8SbF2v/ZGhkcHC6zyfH98NAFaOa9QqnWApsrHU1fkRbdAx8Yu+FY2eMNZ9am1HQhm1+W8DIyzDPUuEwOW9Xy082mwPuGYU7aUxHRQkdGgpwAIShaOp55AH3gmjJhX+RAAxrAAYhGQagoUmepZUh4n2n3Pg0C4ZwOvhhbq1M+FdYlUmXPVDotbvd+03l/6PGa0LPyFaA8/WYrAMkP+8p8JPtz4ZksOzcYTt2rQRs6gTh6XXW7/eTZ5nKoCOM6Vj/PDgMp7/K6hbfxzfYo+BwcHbYqvTlkptb0iUEebWE0a7dT4Eeljw7QMtS9Od12hSLkg19ph1iNEDJ309JdlDmzGZB+ZTuzugQ2RyXqX1KRiexBBMmn2fsrpzLNgSbFlDLJQhPGrAZCh5bZtpXjJh4ZVoxMlN3/QsuveHlvcGEuoVJ16zKsY5GpwCbOHDg9gGkopCWxUfGedADZP986FrKQwYkQMFkFQlb0nf2gmOYeYEylwNsAsWeq8jCgHbFuPDkUcYmvetWcGLY5rclQzr7ceDemkMj5U3TczChYlJQwGeg4Oql4ENjPdq9MjiY7xrsOXEeqV5JH1QzMwT17xqEUCmATew+1ea9lKH8qmwYe5YNZzh7UwYanag6Z0Qlxmc8zU7/yPBWnSqs6sftvYBRxjB/jYCjlRGZm/dhO3YtpcvE2Xz1/ylQ3upsNYPDXrgYwYwt5CjXcZ1o228pYz0HmodAQ7R7kjmlsbJ8539KHn9eKud/MoTc+66qLPVzFGAT3GWZ5OYJXf9ogEd9EeLMsOfMzLzq3APVP5mbUU3JIu4bwhlizrtM6hzJPF9K9d4h2PQ2bSoS6TMUzMa3Lakbh4wXjx2gTDWQ4I6dQXT9gzmqqMfivjVjPfieabmlLHTJUg+woVB6oRzrnlu3T5YWnPBK5foz3vgU0y4pe8J7z4YssBecX/o8GkoZeONJAz/YG3HZQwWNMNibjcDA19ZMnRMByb7++I4sQ7BpQbTQC9gMXnP6+6wWs6cuP3YM/FbPUlJ5qgHncmxXxkD2wdMWYz2WrFMNSSYMOjlGkBw6safLp/3ziKG050IAg3O94T4fyO6fX4rCHVP+dQ+p2zefawjOmHk9xutPhNQ763fQPzZ6EoQjARtNFjmO74VXDcAIU1gFHKvwRY7hGjrkot2H7Ri2sKhDfs0D3DpOOltT+zUAwrlK0kwOt9h+1VIUWMKEnP4EcCBlZICM1D2ckieV+4pl0mpndowhxoAe/t2U7D9L25NhZUXZ1IZ5z5/ZcGTQUlrIcZhz0o9MkXLp9zxI2RPznnHMhLaqUk1xCDa9PRtVQcuaGM1TdNgkg5onNpW8Lie773XOIbpMkja5j6icN0aUPhUOQSv2DGgXMe5iv5OfZJCV3fdK5fOMeLJkWBDldyhtpBjjJ1XGk1Xsc+GLdf/icR1iyOcck+PE+vvrly03r4GCvlIh5bGEW1hZDUNm08JolWHvgYeAnleJCbGQz8+GXp/r75+NbBLT2ljXDeTyab+SIgPC5SjtqbxtbN5BTQlVlX/mThJrgCkW0lC+pxw/AL8zxmswNxELMMxRyDGF+eIiXhJvTUfSwNLI8KHyX34nErDJMJsCBwshu888SvUPDG/SGcMmch+2Y9f8og6qs6of7lc17DVx1rBOaDaNRJCkWDknXWZI8Tc2epjbx6a7s6lELOeklJ25n+h8byk9T7mHAaG7K0CDr+dn8015d1/W4Z4Ku8ukQTGB8j6gQgIw1bykIlOSUTgcYKM6uY26eBK0I+09zaHv229z3YZg0wJrlGLPLryEJysbl+tdQoxRklOMgoNWqcwjx6AoobHDSpvHVNhKbsOTpeNTgA0ji1X2kVzct+99yRimqST0scOqTgxbHyOMIcBWRUsnycwYMYxRkgAQpZxuf5ssyfUbu2w9kAzgGBxsSKo1weewzW/z84flmE2hd9cdJzU+UzEuGtY7C+A+y/QgvLVAHUphAcpisjNliLPAQcJY1+j1gKDvK7Knqpal5PHzcFU5m0iFW1VCI/epxfFE50AkgCyn/2yZEoP/x6bGl4Vlz9KeZoMek6rwK19jxmYNl9x3HbZj1wLdhwxFY3LqhI5iNoSqeJzLGxNW83I/Nzq2OO9qplU4dmq/Hq3S8UkmFHHu5fqX+TorOyKbs4mXJXpma7q7fw+L76AX1Mmzep3xid9Jc25wjhmjzqGkEbCO79sF8n2qk5tkiAWOmdKBntx73v2UYV9LGea6DcGmBdYYUIWmkHa9w0q5sGSSQUqpU5gh0VxDSaAsKnrIslIuOEexb5R/NWPd7ZNT0sKcJ/qGr9FlL3yCAA4A7nCbdWJrFnAMPEHpZOUsCyLFJEjpupVHm82rZAEoE/MC6OvXZ1ikvXt9px+ltLBsEgPVW47BJvgctvltqXNdvub095X/jOJnYUBEw3q1s7Q0igiPpJSl3qPF88l9BHd8S5JtR3bNYULsUdmfUuajgA2S49fnRSSsQTtLK2N08Hy2qo17ftFhDepZCqdPNleWzybKsETLISimROQ+HVHumTBcPxNSZARsfKeGdm+k2LOFnPl8ITnmus/aGDodFm4LdB/F8TsT2a+Mo82/DwAdyKCdW4kQQNZB0KzuhHDs5H4i13wuBNDiDIkxQ1SnYnlXeqBHEmQ3MKGigE3VP6K7J+6y3PhBHtqMHcFEJbj2mz/v+XOPZZfW93z4udr4TFU/JzJF+67duB2RdW4Q97b8/hQzz9vXc92GYNMCa+WaZZDIXCWyIOeNqqjX/2cSYQfhWTnFyEBNlGMEVWIURb3ZiCS1jR4QXgJDEjhgQIxC9vjBrLFaBDko47mNJ188GhVo+v06z4iFvi1lZxL7MUpI8Xzxl/ECxJMMKuVTPSO5mVm/QaLXDODoA72qLBGFi/He03lGAiXHHWfYjm3zzwCnqmPs7E1R1MkzgKnmFVOe4mvXC3HKATaGsCIAkT1N7AuhO+nGvdtHAzHk+EEIFalAMyWUS9llCKB2ltbziKQsQHj/NhVDJKr8E6XUfcAm1b/KAdPiKtOGTrDB5yrzLvdQs/qdwrFDJq87TtA/4USIyeLcSYRjIMYgKa8lJpTS6nTIzfuwHbsW6D6a/msGhz2dsNUIXlP7Z854P6yWc6DXz6kJ/RO6OButwaaRYPTl+qwRzH4CDGAAQfm8BfCX486G1ZsaPxX6nAbtXFk0B7pe4ImXJcuy8plNRpspKnvMUaw5Q4yRJhaGo5SPOeMrR4vY/3PZhmDTAmsjSg6LAI1WFEY5hp9ENOfNZPr7dNOsYmQFGirQw5VJuwxjh77KDprloa/RJIEwLIYx7qTsujfek51U1C1KCBA73NJjO7Jb5j0jezKkj/bGIylLz98bQttRqwD6oZE5gJIwBKLePcXQ9L17VkpzjkY8bPPbtLL3+j3gUdpZA1nxBMaMdR34hCNDOXa/z4EkeaB/IEMrv49itHD9vPMcGhlZLMxieYZYzqMY4MywDZqDDCc5tgEXYhHKrucR9O87IadiYAYe+8RxdCSMVfl/rZT6bNni9H1KGK/+vgbkvIeyJCvpGc+B4T2w8Fo690p6PwG13qCB7NZiBPZqk6Usef3avF9T51guFI3WlQayG86auGMmzybKF1Jw+2uV9Mx5j/z7I6NzJFnAqXMyyOOnnXuRAk8EsObLkgoDTRUyYtmo2vr17WD5f0b/yTsKvdBLAviS46tsau97znUbgk0LrDEJJNl4z6DkubLhowtV6x9ZqJpiZD2skiwY1RtfP8d4U3zUvddPVCKzKsdeSIR20Pr5nQrZ3e+lyU6DTQQF2rmwWvk14OcZyY6fYKulAUf3QmTmUcqssYmCvZGjkntKS9ZDlrhU1LCSmMJFKH9WZsuQ2bSwWvkbNxqR31/1kLp9c/dAtXaJ5JsxBVplWXkllHPj0wZyKQPByosa6yalNT02YDPutQTh8YqqoexMCGDNyhrImANsKFmE8k+worv9+HpM9Q+SzZL5G6mwnOh9Wt/vaVk4ACad/y4itwQBLECZ0P01B4vViLLmehu2Y9f8BOEqeFT9rvUdoju34Izt7FdF9/GZUOn9OmDft7yzQx07PLN7/dAItuafrM4OIl+hlNFy1sSY/QwLJsdIDxycCpBV6xDhGmBZLQxAybB6i890ZdbCF8t5lLLrDq64HSHHiske5BxL5oqN3/OaHew45zTGc5JhnJnHSnfLs6OlPAwzT+p6c9mGYNMCa5rCO1tPFrXhpReO8AL4cbDy/2qCZdIjEZZ2HvTXQtFiwJeBzirHcmTxc19lLgkfhKG88UIGNeTKSzKoKdJAeHAyiaelPKrsMQopdTmXSoj7fDC+7wliZSe8gX61w1wlPcs8ys9kqLg+kJUbP9hLZmaenitg2Oa3+VRp+X/Ky5hR/FLnnZUWziRklka+2p9UtkqDw6+wo4O29XNqgszAsNCrqIXnl6bMF5u00RAsGMaRFANJCOdNUzm75Pj+naTJImVn7tPZltHOKtw++0jpH3WCKcarldkUnKUKu1wLD1H3XsxwIfTB2Rf/GN4DC62VP4nPbIrmLFWcVRZGJ8Dp1yOKLLK/v1/1im71c1rYq8YsjDmKQydh+hyL5a3V9pR21ljubTsrK9I3cm8zKS2c3IzK2ZSygbIpXAhHjp/jC+AiKiobKBsGWvwN83xFRZ9VRAWfdsDtk89/xutuThhdI/87xXS9uWxDsGmBNV2xL/5aE5oynizXCwdnfPWSiB1uRJ6RltJXfiYTlxsDvijjvhk5rJTxGUqzIzvxO8UOKw2ECfPvyMvWIEsOcPQPQ8LQBHLeeH9s1rhz35eTvVZy3HHistfPWUIWsslYfdlVA6n4Ky9bLR+bryzmmHnJfGnD8IkF0eLhX8VfDQxgz6PUPrJW81IV6Jjhoshu8dgX/VwggwXutTMjVUAjWSii650Byj7yc1Y4/VnZDYBz+baUAl2zg1y2rXYexeZRU3Jjia31PIWeAZiRnVH+fbaPlMcSlpNzJIWyxPrWnxgY3oRhLD9HYwQEhjQJlg7D6BZu85lN2m/ln0vy/+oZX4Umi9cIHTXr3Bg8PZv8O7J/bHj/LnMKu8T035STMCpL/X8GDIgCDQybiJgX+Tyjc/ppIXLja7LrRR3IsybQC7QoA7d6YVZ23wbKkAV6ns6Rq4Lt59xlIiokG1Wz96z5f8MzHklZ1AThhA4x120INi2w1lKMzCRgk9nwQQJUUrG3Vv7RlWPvwsog4ykWDOPhk/9Xw5AartxF/1CWZInsFMiXoPoyh7gzPvFd5fti0vjGnXb4yO/OKLAxw5Siv3rejnxyc6+qn2IgATYKaSzfFAOssclYW8Re8hVLIHPxe6BzTuFKyT70aC+M5isUgM0ozbIbu/w+UsN6CeVJfgd1H3lAqWZMy/7UvETvgaB7JJw6Lbf8TCYMWHOAaIYID/L5hSKQ7Cuf90MJGAZqTvYaKEPwPsuaoVmihvsRqL9r1Hj17qTcuZ7y2Mdlqf8fGhf5sd3+jPE6+E4ptnjXl103GIft2DUf8OX02XDdxJlQ7tiNRsNk3OecG36+HiszpAJ4ImP7oLx8n1bYhQG2o8x+K1CmhKhbI1PSOmeaeR/Ltcjk0M3JY2H7xPqrbOoI6KHbKXHbMCVPipmXIvbX47s5Mc25FhUHF7sGLOzVaIJwFfx09+lctyHYtMAaQzmlAZtEf01xAWpPh5abKIaKUgrsoLu1xLAKZEUOfcob781Lavww14F++JRD+Acze9AyFQRiif1iy6A63HzZFTp2THaG1SD/zzCbmspal2OE4GrYN5Zk0BoGOitmHis7Ec5j3kue4QjEFZEwr44u+7DNb5PVNMvGeCWt3jEGJNFz8fGy5PpXOTQI4AAQ4V9G5V9T0JPJylnlnwJgImcjoUA78igM13LM8l25kt5BKFpsbCtTojpfih9JVtKL5vrrurJoeU7kGBQ7NwLcasZFktlE6iVMOCIQuzfyJb1z8iQNkRxQRugxw3ZsW3KdRddwqMtY0kjI/haQJLVsgmIEhvtDfg+N2RR1tGkhV8GaT+tJxfjld3DHcccu+3DzONvwYUb/jUWaWM/J8mtoERUBOz4VSuk73K05SxWAJ2Tq1zCGBsaGdnAmZ5MlqiY2j4SOoq1HR5YgvyFnR1CswiHY9PZsHGDjbrJ+P7WJ4fRnFJdmo07SpjFyrMpxeGEVz2eZIYSHIXZhaSEOM/7YGdp/lduDSJodA2y0yzZGIVXDMzwPhmPcRabSktjPDUUbfIfSaFAOWplkUF0DifWbDQP1QtE0WRpy/RK0Y4f+SngNWCp5ILsWwhoLW2GUxQiNWM3vQgJlwza/zeodS1UHygGflsqeMVnUSookpT25FjOeurKfHtZQ/I0ym7R7gHBoyM/0ZWHDEZl7IxpCFbuTAmMUSVnk+AwjJ+q8qdZYZOxKlvo57XdN3WHZ0DVfF9A89uJg14zX2SYcZgyRaN4u1WESMbwJ5401lyQLrA3bsWtpRo7VyAzH1s4axjmbA0l8xgTDsIkBDVF9VtHdO6qjzT/jY3LXT1Zh24oeFmOG5BzRQMSOYNlB6n1T/HXvvnRuTvP95Cd9J+9KJm+tzy7Ny+LeNxIr0XSUMHwxKnqQc5eTxSZ7GGmSSIHh6UtM0ZD4XlLWjNhDc9mGYNMCa1ReB8/4BjLeUv+AINFlNWGctwnke/XDren8zRtIeeM+yg4iPDXlwSm9IyrVt1Iw830d2RnFu8XJnpoXIBFGlzjcNCNWAo46Kys0SrTkkT5go5UCl/JYGGKxJIPa+m3FwugIozqbt6syqPJhdJp3T1UWI4Ajo9ANPdoLq2kgieX3ZNeiNQ+bRdmSifYZoExb57EKqRZnDKBXC0vJ0k8pfn3//FLuuyNkq8nvQSVmV+ZcPu/n0FABxJgTgT2/GsrcBPeAvn790E41LD1yJ1UOk9jYCVmyyr8POCp3UnQ9Ek4EQOgamgFI6BnO+CRoMGzHrvmArK4/wOkLyLNGY9Ah0j9/rmo2Sr/fr0AixrkVTSMh9mBS9ojubmHe5qp51UBD+pycbdgrXYzA1/OM4VxMvqmo7JQNpAM2KcdMfD0OPt8YmcIyadM2UFx4v+CF5miJRiUYonBY55yfs5KxUYCMfhVZA3PZhmDTAmtMTGYF2GSy8PsewfqgDT/XP0zk+3TqPLj+CaAspxwzl208wRyS/QM6a5Pb8IySJr87VT41gi4zF1YdQiU/O+huMkz9g01+B/XyjIEkijLNerRD1gSS/a1JBn3gVsrFGMlsmWkmdE0zNC3zCMAUAjjM1bEwms4kySsVOS+jyVMXpYXnladoklQGKFNDLOr/M+GovvdVykWxrDKKX5BHhfieI+KAoRhiRsOlupMUuYGIh19lWirrkTBE5OdoIYBMHi4pY6D8E2CQfF/0frQq/57slGERdYKl866wCYdTCcJzxmuoC0S7D9sxbDNdN4+jztQPdR8qxDdy1jBAhu6wrP9PJQjX8vUEvSP71aq7E/Pijh++Vo9d/HXPPaWStK+7CwZXDNj2HahH9d7W1kDUQeD20cAj+ZnBvCs2invuuePEZa+f06Ik/BQuOWer79yo1gDJDrLYHdniVL7uRtjYI5H7Q7fhh2DT27KZFmpWOU5cEsTBBsz+wqIUIyUReqy/BQiQ/6dj1jXl2OAd0cpPWj0MTJlpJ15ZU6aDQz9/sDmyKGsgergR5bpznlgTK0uJn1cNHnK9J73xOdkNRknUWGM8NRmGY2CYZsCJt0L73ve+hwsvvBCLFi3Ctddei5UrVyb7Pv/88/if/+f/GRdeeCEajQa++93vzp+gqH9jeedTjgHiPOr3RQ45by0eDdAjmpvI4H1TK29G8rDprJbB50ccJjq47t5JQIoNGS9woO5R1nkTmXdtbnwAuXxbDvxmioXEARt+HuX3sOglySqACbBU0wVGIvMYG97XqRzHk7ImW14oTHRelNxXqqdZrpmW9ju5Y2YdeH5y2gzIN2zHrpU/IZdnb9A3tl8jP60WlcCEG+sOcVGBMXDOhrKouo8CTJR9Gg3BpGUYOYTxLce320BpWWo7xWUYF68F3QMQkbMj6uc0h3s0ubkWPeLfN4osMZ1DcxRr9webEL+KklCAMkZfcnLuUntvdrZkVHcnbFsqn6+UpbSzlUgTKcNctiHYtMCa7hH0DNhcFn7fk6WGFUUqYqkU7vQlwRgxmkdbPu97ATR2kLvhlXjl2AWnehDdPmxVP8aDqCW1ZS5naaDGfAy+N14LKzF7tGPeFNUD545f/u33U5eKK3uL8V5EwaOgu5okUw3V9JWWhFfYBwUtxpf8vxoCSDLz/PG1JINvhfaTn/wES5Yswde+9jU8+eSTuOKKK3Drrbdi+/bt0f6HDh3Ce97zHnzjG9/AWWedNc/S1uvNYQiq+67463tfc2G9AViuKsSk8qSwMdQKcBV4NGCdKOdus2EM640Z90bFjykVTIWiiTtaDY2NAQ0q68s3ugbPR+SWyr8lnJoFj6JrwADcMw4NQK53QuEmjVdfQc8nHHZlmW1YJ53nS10D8apfvb4eBsqGgr9Zm8XR8IMf/ACf/OQnceqpp+LUU0/FTTfdpPafr5as6EY4cgGpz+bzGMn/R/PDeVEM+n6t/+9XSWQqFMv/xzBQFcSP3jeuLE0NgBFOHz9vLZOo2pXFprdFK8wlihfQ4JHyO9mrnybsN+U3cvq3yrtSYXSSdkcUVFF1d2/eCZsGkLp73u6wppOJRiUQzjkt55i1QvwwjO5t3piF6m94gFNIKbSY3cCKQsoYMbky07VRUm748vlIX3FJ1LK7n+v2d+V15CGUOg08cg7aABlPx89L4FCPb3YvfideOapMe7JbafyGC0jKpa2x6EFLMcrSY0eVFmX9xlB9FSxNhiDE128ydMlIaWb3qmrEeL/rWz1Xx3e+8x18+ctfxpe+9CVceuml+P73v4/FixfjjjvuiPb/6Ec/im9961v4X/6X/wXj4+PzLG3cKNX3XSJZp6JUyjH1seGMKfur9PqY7Brt3NvTNMuK8EzTDEFv3nOKXzIUjfAEA9wenb3yn5Y7didR4dEkW02rYKie6wxYGlH+uWTlcg0MCqmE3fWQZEJBZ5hzrUhYp1aSPhqWTjjZXLA06B7I81asSmp1NCxfvhx//+//fdx///1YsWIFzj//fNxyyy3YvHnzPEvutqCimwrYaGdHOLb5XPXOA22/qlWBWUex0aDW2foJ/ZdgcMn+TGoQRxbVGYLgc2JAWWAzMbLHcr+SQINFR6115bQdAYSOHHY9qlXXvDNbvlcF/T2HgsYaL2Qvxx68ptrk9XMWHYUFm6p5rObFWM2UGHuu28i8fMqw0Y2iMhpRUT83kXroG8MhXG88L4tktfT7/cqTUPXvuptY8xj4CXBzsseN9SaAHvVdGTCo0YiFXAXd9ctTPZjdXCC9bj/hCar7uGPbLiAabCKU72hi614foy19fD38x/18+TnaGpgtsJYLRUsqCqyXiTDWAmOw11eTpzPMgDd7m56exhNPPIHbbruteq7ZbOKmm27CihUrjtrnTE1NYWpqqnq8b98+AECn00Gn01HfW75e/p2Z6Q5e6VfPlTrj1HQ4XpnPo9/rodPpoN8r3t/t9YO+U9Mz1f973Rl0OgD6xfs7M72g/7T4/PK1xsBM78zMRGTpDvrUYzUV2bvlRu110el00OuWsoeyTE1PD8Zr1K+pss9U8layNwrZpyK/SznvpezdmfrAnZruYFFwHg3mvdsdzHtvMAcx2eu5qF8rZQnnsRORvVwD05H+5bz3B/NYngTRNSC+V7EGGuj307JPR2Rv9NNrYLqaRyH7YBFE1295IPW9NRCRZbLTrf7f9dbvzOB3kK2cx2Zk/Xb7CPsPPhv9frAGJqemMd7se/3LvVeuAWb9Ily/MdlnBrKLeSxv+ej6rWTvDeax3uuTU9MYG3F9yeV5X6yBWnY5j/5fpln6znWTjgYA+P73v48777wTd9xxB377t3876P+f/tN/ch7/+Z//Of7rf/2vWLZsGb7whS/Mi8yx1q102rz+EHP8UsD2LKMS9OI79f+ZiqMaUBbTTqLARLOBaaTAAHdMDcRI6lWZ/rEcpzpg41a6Azg9jyoeFXFusPYbAwiFbNSwr3wuyH2lfM9YcR9admJu/PUYZ5PV7w9sJpIJbgF682F0cPpRoB3JEKsdYuFYc9GGYNMCa8xCLRdQGa/c73MHOeW9iHoYbBeWWpklATSMeCs+lcSbPXw0+mvpVXRpm+7nxmSnKoNoHm1SFi7Bbv1c8d5+PIwuherHgKnYb0rJEjlo1YMZwfsYjwTjeWHXQOyC4zw7g7EzoWgpTxAbSknF28c8cBQLIv093+xt586d6Ha7OPPMM53nzzzzTKxevfqofc7tt9+Or3/968Hz99xzDxYvXkyNsXTpUgDA2g1NAE1sWLcOExNrAQCHDrUANPDIikex4wX3d9q5s3jt6VVPofFqH29MAcAIOp0ZTExMOH0nZ4rXAGDpPfdgtAk8v70BoIWt27YF/Z/aVby2Z/fu6rWd2wv5nn7mWRy/7Rmn/8ZNxWsvv7QGEweL+e3OFPLd/8ADWONNxd79xWuPrVyJPWv62HSgkO/gocOBLDsni9f6vW712subC/k2vvoqJiY2Ov2f3Vq8tmPb1qr/vj3F56187AlMrXPncYMne7FNirm6+56lOGHUlX1yuhjroQcfwOrjgDV7BnO1d18g+/r9xViTh+vv9drg89a89DImDq9xZd9SjLVdyH7wwGANPPpzvLHalX3HYA088/QqNF/rO6zev71zwnk83a2/1733LsWiFvDCtuLztmzdGsj+yr5S9kPVa1u2FLI//8KLmNj7gtt/ffHa+vX1+p2eKuR78KGHseEEdx73D9bAyp8/il0vAq8O1sCByBqYkrIvvQfjLWDN64Xsr762GRMTrzr9nxys7V07d1Rj7dpRyNfv13uubK9tLl5b/eILmNjzfHYN7D/gyv7y3uLz9u0/EMi++WAx1sz0dPXaulfLudqAiYl1Tv/nB2t7y+v19zp0sPi8FY+uxG5vDbz62mA9rS5+EzlXEz+9C2MBWFqMtfy++3DSGPD0YK/v2PlGILs/T1o7dOgQ3Xcu29FwNBw6dAidTgennXZass/RdDTEWr/fD4BBEMB2gwS2Y86N8ryYjjkIeimANQS2Dw8AVgDod2fQ6TfQKMHhmRBgnRaAcA2wDr57FBwugWrp3BgA251pdDruhk06N2LzKIDyEGSPyD5TgrvCuVGONR1xKMy44HBXKINTEWC7AkPKee+X4HAvWEfTEZAd0GQvxmo6jpnBazFgu+fPY/F53X5kDUz5Dq6+cMwoayDq4IqA8qWDq98P14Dm3AgcXDHnXP241+2i0+nXzo2ILFOlk0is1XL9Rucxsn7lZ3c6voMgsfeUc6DVlPNYOufS67ec97l2NAzBpgXWagM5H8Nb9u90+yoIQ8Urxwze0qCOeQyiyS+VHBYJ8Kh8zV+IQWyrEYBhwpDYhHRBoj4iXpkOh1Di59nkeGpOiq4re1NdXzZZYkg6A6y1vHAIgPPsMMwj9jfVvCNquW4/7jsytiz/y1RcioVSzjbsTltjfq63tyKzab7abbfdhiVLllSP9+3bV4VgnHTSSep7O50Oli5diptvvhmjo6N44s7VwJZNuPii96J988UAgO+98gi2HT6Aj15zDa5/7zuc9/9o80pg/x589KqrcPOlZ2DL3kl8/ckHgWYT7fatTt+9hzvAY/cDAH7xc5/FSKuJqadex//7ynN4x+nvRLt9ldO/98wW4KVn8c7TT0O7/VEAwJ17V+HZ3dtxyWUfRPua853+9/2XZ4EdW3DpJZeg/YkLAQC/9+xyHDwwjY9//JO45OwTnf5//NLDwOFDuP66j+GjF56K51/fhz969lGMjS9Cu/0pp+/LW/cCT/0c46Oj1ffa+rMN+JtNL+Hss89Fu/0hp/+OFRuB9Wtw7rnnoN2+HADwH19fiQ0H9uDKD38Yn/ugm4/rfk/2fr+P33y0MLI//ZnP4PQT3JDK3378XqDbw6c/fQPOP3UxTlv3Bv7Ni49j8fEnoN3+uNP3sQ27gecew0knHo92+xMAgMfvXI2Ht23Ce977XrRvutjpv+2RjcCGNThPyP5nG1bg9UP7cfVHP4pfuPh0p3+5Bq6+6iO48eLT8N9/WoMDt372sxgVl+GBqRlg5X0AgM/deiuOG2vh0JOb8eN1z+Md7zwD7fZHnLF/vv4N4PnHcdKJ9fd68L89h8d2vI73vf8DaP/Cu93v+rcvAltfxfsuugjtmy4CAPzhiw9iz/QkPnbd9bjy/FOc/n+05iFg8jA+fv31+MgFp+CFLfvw7cQa2D/ZAVYW67f9uc9ifKSJnY9uwl9vXI2zzj4b7fYVTv+DT7wGvPICzjqz/l5/u2cVntu9HT2g2nNl++m+p4Fd2/ChD16G9rUXZNfAt1cXsn/i+uvx4QtOweMbd+NPXngMxy2uf+eyPf/6PuCZR7H4uPp7rbv/Fdz92is49/wL0G5f6vTf+MA6YNNaXHD++Wi3LwOgr4G7Stkvuwztj12AyU4X/2zlMgDATbfcghPGa62q1+ujv6L4XrfcfBNOO34Mree34YcvPY1TTj0V7fY1AMKziWkl2HKs29FwNPzWb/0WzjnnHNx0003JPkfT0RBrEvC8b9kyHD8KrBoAgzt3hcDgmgHgeejAAQrYjjk3Jg8XQOTDjzyCLc+58uwrHQQ//zl2r4bq3Ng3Xct+110/BVAD269vCYHtJ3eWzo36e23fVsjXi4DDrw7A2pfWrMbE/heL+SqdG8sfwJnHubKnnBsxYHv74eK1XncmdG5sCp0bzw9A761bXsfExGsAgN1vFPI98dRTwKseOLxZgMP7XhhEOtTA9vHedut0BoD9A8vxjkXAiwPnxu49ewPZVz72OIAWDh08WL22cfA7v7z2FUx0Xo7L/not+yHh3Nj1oufg2lW8tuqpp9Df1Mf+TiF7t9fHnXdOQKjyOCQcXPfcfTdGmsBzO4rP27Z9B7V+t75eOjcKJ4Bs6wbOjXWv1N9rZuAIeuChh/DK8e48Hhw47h5/bCV2rAZeP1TId3hyKpDlYEfKfhdaDeCl0rmxOXRuVPO4tZ7HNwZr4MmnVqH52lNO/9cHTpsXnn8eE7uKjdZECz00sPTeZTjFy+IwPVjbDyy/H6eO186Nvfv3Uw6uDRuLz1v7Sr3Xy/bCYG2//tprmJjYVD0/V46GIdi0wJpuZA7ijwOaXAJs8uNDZxmvTJe8VmO5XTBAggIMW6lpBD2s1Xb0fD1un9mGlmlJbdn44/p3EmF0CvjV82WvGDCRvtFcVmlGjlbaWc171AjXgP+76onW82td/p9m5s0ihFVbj7H+0TUQCwO15jnQGGUJltVbkdl0+umno9VqYdu2bc7z27ZtO6rJv8fHx6P5nUZHR2kjreo7+K1HR1rVe8uEmo1mKxivPI/GRkcwOjqKRWO1p87v25iqN+6i8TE0Gg2MjRbXfm8gg9O/WdAhRlr1546OFM81Gs2gfx8R2cszuxXKXi7n8bFC9vGx0cHzEdkHsrSaDSFLIXu/0QjnuVHM2WirlnNEmcd+bN6bDXR7fTRbI8l5XzQ2htHRUXUeIZKLlq+NDeYRkXms1oCYs1r2sH+vWgPFGpJMpkL2mtbSrB3NGB8fxehIC+Ol7H1lDYjPHW2VsofzXq6BsdFQdm0NlOtXWwPNTn1GLRobxUirWc1jrx9bA61K3nrNNJ3vKt9Tjj46MkKtgXr9jg7WQPF6NyI7qvUr1sBoqXIr63cktn6VvTeYx35D/Oae7B1xgTPr13qOvRXaN77xDfz4xz/G8uXLsWjRomS/o+loiLWpmR7w6L0AgM/eejNOXDSKsRe349+/tAonn3IK2u1rnf4nrt0JvPAkTj75JLTb1wHQge3HS+fGxfVr/+rln2HH5EFcc+3HcO27XVZX6SD4+PXX4ap3nao6N7bumwSeeBAjzQba7TYA4MDjr+Ev172A088Ige3O01uAl5/FGaefjnb7agDA0gPP4KldW6Pg8NK/fAbYuRWXXXop2te/CwDwO0/fj0OHOvjEJ34BF5/p0ihTzo3xCLC9dvsBYNUjWDQ2hnb7RgDA5ofX4283vYxzzg2dG5sfXg9sfBkXnFe/9pfbn8DL+3bh8suvQPvKc5z+9/ykkP1DHyzA4X6/jyUC2H6HB2z/X4/dC/R6+Mynb8Q5pxyHk1/Zhe+/+AROOPFEtNvXF/M3WE9XfuQjwAtP4+ST6teevfslLN+yARe++91of/b9ztivPljIfv7556Hd/iAA4PvrV2DL4f24+uqP4pMesP3vX/s5sH8vrrn6KnzmkjOw+9A0/r+PLwcAfPZzn3N00TcOTgOPFa/9T+3PodlsoPvMFvzF2mdx6mnvqJxYZTvx5WL9niLW7wN/9Rwe2/k6Ln5f6Nx49G9eALa+hve/7yK0P104N77xwoPYu3cS113/cXzo3JOd/rc//wAwNYXrPvYxXPmu07B2+wF88+lHMCKcWGXbdWAKePyBSvZGo4HtKzbirzeuwVln1Y6gspVr4HyxPv7Ljifw0t5d+NDlV6D9YXcN/M3up4A3duCKyz+E9tXnAQD+6cql6HX7uOHG4neWbcnPlwL9Pm76zKdx5kmL8NiGwrmxOOLceHxj4eA68YT6tReXvoxlr6/Huy68EO32B5z+65cXzo0L31U4N+ba0TAEmxZY0yuRFX/jzJOwf9LIZEESNSxOMda1/l7ct/xsR54EMKGypiIhVGyoGxPzG4TREclPi7EH4xiT2jJJBoGagRaDDgKGmBGwUauaaGtGBT0QvM//XZ0ytAZ2kCuL+7kxWdwS2QSISAC3sRK6KnOuG65fdQ1YE0p74YtvxcSwZRsbG8NVV12FZcuW4Zd+6ZcAAL1eD8uWLcNXvvKVYytcosXB78FrBHjoV6GS+e/K9zcaYUU3ay4HJnG+7K+D8cUX5PJK1M+NEAkyY/tIKxIw4sneRTz3mX/GlLIwYePy/xqAHK1IqCaPHfSNyBl77FfHpEPqiZDkmC4QrW6VCOvVnCuyvyUhMFDPI8tELtcA40zS9K8oy9mai0+ZR3/9ys/x16TjAGnl76Q3YzsSR8O3v/1tfOMb38C9996Lyy+/XO17VB0NkTbTr/OUjY+NYXR0pAYGNXC4VQOYJSDbRwykHMggANaq2ETUuVG8Y2wAsKrOjeYglEg6CAay9yMAa2MAsI4IwL8Gk2PgcKPqEwCyqnNj1AG2u7F5bIXOjbGREpBNg8MjEQcBIvNYHhFS9majkDEKbA+EHx+Aw+OjadmbMWBbWQONwT0QnceY7KWDoHISic9ujVSAfvG4PgzHBx1rYDuyBqr1Gzo3YiB76ZgZ8xwErOyLBjJ1e5F5bA3CCxuFLgmgcsz0GxFgvXIQxNZA2kFQOlpK2TvdhIPLXwNjjKMwtgZi67fUY9w5mytHw7Aa3QJrtUJKGvcGthLDrqAVIyX8S1NIY8mh/a/a69XJrkODigO+LFUh5HsZ5ZtJVu4q6k1CFqNCGl0DQffkvMd/o3QZWroEqYGVVeYcA3TluFmd3fn1xYJHMdkZgLJm2oVyxmQPDCQV/ETwPs1IjhumkfET4YuxeXwrtCVLluAHP/gBfvSjH+HFF1/Er/zKr+DgwYNV0tgvfOELTl6P6elprFq1CqtWrcL09DQ2b96MVatWYe3atamPOKotCh4SObj886gYyxs7Vi1OYTeqa5E9vwxgPLMvaMZfZB41Yz0uu/taTHY/lJYti62zFQcVBtmzNNjT4Wf7cst+TALWIwlJVteAz7jW9JJqzmuw1LI35PdQwaZGuAZMbHFFF4glbqZz8Wl6j7fe2TXgF4p4q9wD0tFQttLRcN111yXf94d/+If4vd/7Pdx11124+uqr50NUtcWcVWouTE+vku9TqzGTLHD/DvGdG7G+PoBffC6n+zSZ/Wp2bngAqxFkZ3V3LY2EPaIiIbuiz8rct5otGXNwUk6oWFSCvwZmmVPUmRcmkXv0jM/rHNR6jOjWrA6h2XvRKtgJeeLRHc2kLPG7zLZ+57INmU0LrGmJhFWljlhMlMIYMTLisrh9cuP7ipFWiSHKDGm4csb60yGAxnkMDaS43EDCW04AE1FWgxFUiUVFpcp7q0pI9LKNjB2ThVC+JchX5RxTlOPKG2+9sDQFKmaYEnupDgNNXyiuceddcARTRfbXDDAXEAg/u5IntQbeIkaG3z7/+c9jx44d+OpXv4qtW7fiyiuvxF133VXl8ti0aROaQjF//fXX8eEPf7h6/O1vfxvf/va38alPfQrLly+fc3lnyySpGA1iIXR7fY8xaAOQZw1+R1h20X1agbaDvtp5UbJ9yDtJU/7NwL2i+PlMEhaE0891JGUxAw2eIlo5QBoCsKlkD4aO34+E4ylaDYupyEOsFxrMHDwVO9ejxmvZ35E9XZm2ugcqJogrp2yzNeis9285ZqPRqJgSgfNGyFeX9E7L8mZtS5YswRe/+EVcffXVuOaaa/Dd7343cDSce+65uP322wEA3/zmN/HVr34V//k//2dceOGF2Lp1KwDghBNOwAknnJD8nLlscv+G7L+w/0xEH9ArxmnABAHYeM4N+bkzkVQfHNs9du4F3RPpO3jdXQeP3M/PyR7TlzWHaAx8TqVBiTncGbbzkaWRSI+fOrOBSFSCBnoYGMaxsYvxEchQzXsMEEo5irUz27gGWPtNiwaZk+gOpX8sdc5ctiHYtMDarCvAEf1170V6E6jgkdUo8Vgq8rXYY0s1Okd2Lbn5rMOQXKChP1DqYt+FZp1ElGPmN42FuvnDy6om/iWhey/q5ywAYlb25IXYDy6JqHLcUtavJot2YUmFS7tsDReWU/rVUxRUA5yWPWZU58Gvau8p+/St0r7yla8kw+Z8AOnCCy8MPLTz2cqfzAzYxID7QGl1x5P/j1bqNIIkWrEFPUedG84VV0LTQBmv+OX3UZQN6Y0vv4vPEuXzApa5g2x3ks4ULh5LdTEF3MfXQCQcUWG3MeWcAcn6Soc7BmXdWeXfyhAr78dQ9AS4irQ83h1mvh8Zgy72XZX+/t7rRZw3LljqOW/eQveA1dHwp3/6p5iensbf+3t/zxnna1/7Gn7nd35nPkWvWtTINALbFEt7ljqn1Jlmej20mnWusBizn2KYS1mUtBDxKAZXzpjsIWiX7yv/H2eSRO4nItKEmff4GlBYLYrsrGPGcpZpaVD8uwkgGZ20/hsBNIlzktpLMX3GyKaeLXsuWAOOzuH+Ze1ga+X0uWxDsGmBNe5SCfuri8+L0Ve9I7GQBSMCbNmU3V4/ScMs+sB5nxXRZVB6pz9xmfusrKZQ9WPekQoIiMoSM6gIqmTssPLlFm9nLlsNQNQM07iXKegulOM83duhkAb01/TYrFEdu7BUwKbrrt/yb78f5smRBhYD9FbzIpQ4JjG7q9C5r8mWTm4ejj1s899i57rFMSDXfIolGs0hR54BFUiigh4R414Fs+C8L5pzcPD2GNDAFCCQ72XCuQq54rK7d5J/n2qy1M/p3loFWFPGL8+sRkPcpynlP6qcB0MHgKAji5XdRijc2nkUDUVraWPDGVuOH8NUVOWf0AUY5pzrBBvcMda7nd17zYIp7OsODlg66K4ZIm/mZnE0bNiwYe4FMrZSf2g0hHPLeI6Z00gooIqm//p7NsZS0ViOWshVtx8awVoUA+OY0+2lNHhkzbdK58VN6OMxoIGygUhZYk4l1d5LnHux8a3hXDFwSl/vCGRnmLqBHUyCQbUDKhxbZYIbwanAUSjkO9JciyzgOJdtmLNpgTXVQFZYLRYKqepZtaLRJPClIel+fzcpaFPtK587okNfOYBCAykcq3ocNdbifYvnEMo++K92oLje+OKv311+HkMjrudFGhlpWbQk8Qy7TZPHkT0wSmwXOU+BDj+76p8AbKKyD/pKZZEyGsh5jFYwZBQufw28hTzab+amKa3MWmS8jA6Dj2HBRcAplQkVk11Zu0x4aYq5Icdx+yshg1blX/EyUrkfooANFNldeQGWzVs/V77V/53UXECqE0GOndcF4mE5Qfe6QmrDNVw0FhTLFFaLJ0SOOzOjzAO/mNxXtBNMYYWw4GrqzpP6VxBKObwGFlRTw7mO5joj1o3sHyvskjon6RBcRRfXwGH7GQ9Hrrgs7nhO/6NwZkeduSlna8S5oemnlWMmBiDSTiXefpO/byr8iwlPl8+xd6UeiqYxdd17u99XgLKI/WaNSmCB3tQd4rKp4ciu6YVRu4B0zMxlG4JNC6zNGiTRNoIfPqNtAiMazYaiRcMzEvK4rBZX9phipB2c1oNWzzHRDN4XUh/T1XDYMJTZVovyuzsXVpVjIq+EuACiZpi6Yxf9B+NHrAwL5VQCNlUVrYoZQBolBoNdk6UYA44MmsKlKYtMlStHliO84Pr9vlBEQgPpWIaPDVvRrMyQOjl0uBYZL6Mloarsr+YOsnr2KAU6ctYZlX9V8TOETahV0dRzun7OaogwIVfMGWCl18dk0RxPZpZzwnDp9cOEw7M2LiN3Uj/ClLCyxX02L+UEIw2XuPMm3d/yu8ZAYW2fDtuxa2pIFAnYjGhpJNR1E5HH038150Y0QfhsdR+jrq8b94a8n+KY0Kpgz/acjPePyyL7M6kSeGfrbG3JvI4SdYaqurVRd4+eq/x3VcHSGGBDFXiqn5s1G46I7rDa5NQ9P09hdEOwaYE1ayWyVPiMTDAXUPBoECM+tnyOTmhqONziB60GNBR/aU9NRFFXw1a8TakzCVy5gRztPz2P5txEXt+ZyGGlstUUZVcNAYwdbhFFofJgtMLvGnjj1WSNkbGjlwSjQIWXipZkkGE2qUmZyUN/tt7AQPkTD/014L8+bMemlT9xHLAJ+8+mCpU55NJMgecUv5COX6sg/r2ksqaM4BGr/FOKn3cnmQEbBUBk2bnRULfEnRc1RikwSITUm4Ey3nBxwnL68b5sEQoNVIlFDUfzqDB6jKcL0J7m8o6hDTotBJ9fvzHwU9sbw3bsWlc5l9jUCmb9gekfcbSFZ3bP+fyif7wvkNFnI8sydk5S4V+VsY5kX2s1yCO1Iwp5CBuomndGdu7MtpIFtKq2gezGe1gLOWd+U3f8oLsIxx/8VXT3qBPHbJPn7Q4nZUZqHo06h/Wej9kpc9mGYNMCa9ZKZCmkPpZgjkLpzcpuuMn4UtChrG5fwWqpZAmGjiuk6qZ0v5/8f7RMqKeouZetP3b64tcVhfq5CpwiPKvys3qe51Z+d4bdpo6tXRIRgJIOF0tdtmZWQ2T9GgFHSzUOxrvHepm0pMy0R5sJ//HYbTHZh23+W0xh4UooF4/LKlSx/rFzvQQotHAuGvyOldHWFD/fyyj3kRL6U43NKH4scKCBvMp9WimtRlnMDFdC4WbCJqy5rGLVrSzGqJSF6W9W/hWHhpYsOXbUxUIALYxYyqMeM7wV9mysvw7y1c+l8hrW66vurBkiw3bsmpqXiHZADl4z6mHMfSNt01TILmNMy/fHwu6iCf1nCWT4YUj9vsICjuWtVfWw+jnGfmNA+RjQwIHsQhZCn2XJAhYHp0XPd8fmzib93EtHPcR0DsYxY6n07MquRGAQzCYtuoMFka128Fy2Idi0wJpK2ZslMu5XgDs68cpWAykcP3XBWQ5l+f6oJ8gIrGkGkl/FBUgb90yoWEoWLSl3DHBMhRhGK9AoXiktlNJagpRJbCz/H4B23fB7ciEL9XOMN57NB6MlZQ5kN7JD4vOieMAtoJ1UWmKeycjvNGzz27T1op8BUjmLrxe1upzCVnT2hQJ+W3P9+d/Vnv/Oqvzn59HCbGo1IzlvjAUL6PtUmXdLHiaVfUafR0j2j68x3niVay11ftFAvMpOCLqbztJ4OXLjnaQar4O9R5akr5l5eTZDzeCKyDK8AxZUi6ZiYPJ+RvQHjQXDOmf9s6bRaCTPyRmvkIp8H5v3UwOHLca6M/6gj7wzk7p75C5j0ms4shjvm5TDXQINWhidtbqc7qAPuqtnPONs5UCS+jkuX2Hs3HP7yu8eTYFB3DdU+hlyHnW9wB978HoUFE6PzTsKQ1nmsg3BpgXWGGScWUzR6jkJFhSQCP3RkG6rQa0ZDinKtzM2on0L2SOKOqXskoaAZ1A1mw2UovlhfbNl5NCGgDKP/tTEKtDI91kS+9GyEGEFUdZXYh7ZXDMxz63m2dE8akwyVh1wHOyliNEQV6AQyMJ5tMP1rjEyomySmEDDNq9Ni/tnc6uljBE707IcL9x3OmAThnNZjPWo7GXIhLVohdFjzyh+Meq+Ftqth4cogM1RcDpwOeQQ7SufYx1PWuLbMDy6fhxzgDC6AJPgPiZLjClh8thH2OLyXPfzTcXZRPkciFY2XNyrHp931hgdtmPX4gw3my5eqh6qs6oZ9qeZixkGKJ8cetAnwiyM6kre/SH/H7vPfJBEdW7EzmDljNdykPIFAOKyxBnD8b7O2JFzMroGYqGaGjAR1d0R7R8PpUyDJJodoeeJrJ9LhajPOPdNXucwh1LG5p2Zx1iED7OXiPXlOtAHn0uumblsQ7BpgTV9kw36EIpRPKFp8Zg+TCh0ObbJgu5xAClplBR/2WpbtXekfq5JyEIndYvl02jED0+tUpg6j2yIg5bbw+tbJdhtIPDGy9c1WbTDLSaL5o2PrZlUPquYQqQCjt2wv1ZmOupRU3Jr+WErEnAMlRYEY5vLoRKUZqbUscNwjLFJhl7tY97K37gRVc643z+1XmarPNHh1BrwlfDWyjGdcNREf2v+KMbjKcd3AWd3LH/sGHMyBjSYk5WX9wbLaomsgQr86ibm0ZElnZ9Ov9ttxisT3q+GJPcj82I8G8t5iR11UVAw8V1jbHEt31T0TjKGxY1oezW2JlOyV2OHFZ+Gd8DCaprjN3rudRXnVlTfcMfU+scKjBT/R1QeLUG4CmzH7rKgt65fMwmWVf1XA8piZ4fmJFKANUZ2Le8nnxPXfc2RJQpO2XSOkVYcOLc6oS0MzZQs9V3prho5V7EcgYHdHGHmme3gWRIdmETrTFgnnUMssn7nsg3BpgXWjlb4TPSgbdRKV0o5jiO0oZyaUheLVdVyKYRA2QAZjwFfpMfAenCW55xe7jhyGCaQdBqNNnjXgQQFurqwiLGtij3h0WbzjOgesvjY7npRcs1USkv9HMMOYXMLRC/zlHcvsgb0xH4x2rwGTrljSlmYxMaOgTT0ah/zFlP+mbDL6HmU8tYaQQ+WAm9JbO0a6xHln5GdABpohlgEFK7OGIKlogENsT3NsD7NiapjDJ4kcF8/Z85npwGOUQMzHsYTBWzUNeDKK99nZ3wF3TPM4njfYvxm8L40O7d+zpznizB03JLhCZ2qG+6NYTW6hdmiYUiEPuCCR7aQqyQrUjxknGE6q8UGksQw0LgTMq5DZp0bCZvJ+Z6E85SvoqYU1EmAdlEGl7IGYkx9DWhgqwaqayZxZrOAYy+muys2UCykL1VQRcoWzRGYBOVZ3d2mL5VDMPOoJUIH0voSm3qknsf5gYGGYNMCa9bEwClU1NlkEcWeoVlX5VO1MAHi0AckYEMctEZkXGPkaPTXmJLG5JiQn5UuNS76qoqCdrgpCeaiayDeN7ZegEgYXQxwZDwM5OGmhTgEinrU4Bm8phpfoef2SJOVy8+MKgqJvcfnm3L7yM+xV3aMyw3UrA3tHBi2+W9xIHPwGsGyk+81sRVZ0IMAvxnlyQnt9hwgsf5WoEw/j2JnaZifKhX+Fct5I5kEDODM5W1DpH/QPQFO6bK44GS8r3yONXS0ClSpBMJyTDmnyZCM2NloXAOa8RpbvynwqBgfwftSLGcn8S2V/yyi92isEOIciIKlis4zbMeuaTph7KfSABvrOak5CGKhbozDUss/GK0GWQHVQfdZMxFjNlAy12Zk/zGpFTRZpDxMug9t7DhZwHbPW4sBzVR3SH6NzdYuMFc2jxAdNCZtfN79sV15c7LEbSZXTtnUStVEdIf8zqH9xuMD8vOkrTqXbQg2LbBmLVeZQ3SbjbCiG8AhuhRlj9yUehW1OOjBJqnVQxCC7nH6qzEPRJJRpoWtsB4DzchQLhW/u9Y3Jo/FewHoeUboeawMh1Tf+jlKFiKkIClL4jft9+tcM4zREzMEqZK4pGGqXea+gdSLnAOyetkQbDr2Lf57EoUiomA8MbaRWq0DNoqSm2B9yj5OOGpwJ7nyurKQyj9xlsbCnJizUQXKYrIrDJuYl5FhH7l3XpyVJXWBum9+bF5pRbp/ArQr5KnPozRDu/h7RGE5iftR9o+GgjNhOXINJNZ77E5i2QPVd1XCHaMVflNgKZk8f9iOXYsynRMAKGDXN6J2RGL/xZghUrYUgy6eckK7y+rnNGZTbB2nANwo2KTsV/XcM+7X+HdF0D9XRTim4/nfTT6mHZxW1mUkeiSVf06rjqjp7mbZCSeRe2Yj0t/dTzHHiQaWxgsNaazCUpb8monqeeJLMKlHqjNeSyUiFYM5bEOwaYE1CkknNqXmHQFC416j7MUz34djNpmFTYRQRT2lxLywIQiqV1j1IEaUuqSCGVMUjp7srUgOC7+7lpNEkz0WGql5GKIgHzvvif56xUDSAFf7I5SF8JAxF6JVadFZVkF3HXAkQGRn/JhGN2zz2up9UT+XYoYANi+mxn5gqdXqWowqoQnlKaL8y+/BsG05diMHksSU/1zi2xRLNDi/IrJQrJaIQsyzeYu//v2rFRRgPfZMiDGjcFvXQNSQ1s51BSyNYSoxMCvlwNPyYMbksd5JUd1Bu0+rec+zlaL6l7I3hu3YNb1yc6x/uObrqARNn62fSwHhsVA0IJ2Q2VIIyJVdsC5L/TfoHV/HKf3aZXWX+zUP2NCyx+4P5VzVWC0pBmhM34zJY2UTVfPYkmcH8v2dc5iXpfpNrSA729/AbpP9A2ZThJlH6e4RHcVaATfJEIvYKLH+0TVDOKyk7HPZhmDTAmuMcc9Q/OJer/r/KQYEg7rLz4tRGXVkvH5uNvHK1rAiswcxoqSVH0mh0ZqRodAweVaLIovXPSaLU7aWMEz1XAFpkETL7RGfd9/DUF6GnMGjATZxpl2kxHtmXoDEZZ7Ye1HKsWo0RPaS5smMsr7cvnWuDvdCGebrWDitHzlLU2tRJmylFJZI8k3Vaxgz1hlKOwGup7zkSa96BMhSGah99/MdWchE2MlcfLHqPZrhorANotXrYvdG4g5LJu3NecmN4FF8fQXd46zlhvvZvixFn4jhEvRXquSyYGm1fkPZTazlah5FwQ3xHdI5xyJg0BGGh8jxXbaSniuLAfiG7di2CpQgnHKADtjoZ3wepJTvZ84PSz4dV5b6OS1kUAP9A9nFmR/XrQjjXr0rlSTemv5L3PPx4gJ5oIHJqwXkyAWc/ZZj9ru/afxccsYmHQrR+ybFbhuM3UA/WoAlPCcRykIwvmK5Yq3V65IpECLFV2LyxMgCTBVZuTfmsg3BpgXWGOM+5rUL6YPF3xQyngpbOqI4W8VAigI2qU0WVdTdz5UtHvfNHJz5yzPl2UklctfQaFaxV0E7JZm0f5fH6KlSnhTlNO4xCESJH4aKYhEDeFIhg1HFWwXtYgCPNu9uH/n/1F7y5cl6JIj1le0fmXeLURJTQqTsMU/psM1v039/xVhn+mt0eUUBYZOVq8p/QpZGIx7WlwylPQpnqRouRoR8aMp8TJ4oaKfsOUsODfkwZkRRuUhUEANhfwZwjK0Zcg2kErOrVf1U8BNBf814Ze5rK7utXl9CFoblbHX4RZwaTD4PrZrisB27Fk0QToFH9XM6q9tiR6T0X8OZrQGsmqNF1Tn5uy/onzg/LPkH5XPm8EVi/Og9TNw3R5QjMCF7zuEenDXRim6I9pWyRCt4G+/ttD3mjpHW3TUAMRAlkwaF01GSIYAZnYNKEK7YETG7eS7bEGxaYI2ivTHIuJJYE1AOWqkYNd3XYrIwh1WSypg6rEpQIkZljChGWgxvFJyKHIYpIMPx7ESUupRCyiSdlc9FvSl0WWoMZI/39Q+TtBdZkUXL1yIToCYUi5Q3PutlIj2xR6V/Zi/JPoBNUWDAT2t/JglniiqrXebDNr/NUoo6y7IjAGQGtI2yVKLGfSh7tjJeAvhk2BhaYutYmIK1bHEu6X9MmY+Nr7INFJCEqewpz6OYPEfKWrZXx4ysseR6LP76a6B8qyXpKZ04PeGMKeRRxifWo8x/l1L+rVVyGYNOPhcNm0icG6mQjJhhP2zHpuVATQYIZ0B2il3hhKJB/D8BTChhSCxLRYKgfrMkQy/7NhpwWS2JPRJjZemVyBD0ZxiglGNGkaWQ3R07CiBqjuKqf57xLH9jJmQ3zkhOn3txRwuS/bUQw+QZ7I2Rnnf3dWD2doeaBiX2O6XWY2QvxfrP+r7xkbg5akOwaYG1cmGxCb0sFd0Y5djMxogANtphxVXAGLyeQPV9cWKKunZJzLaCEhMLq10SbIJEa+nM8v9+99j3LOTJlfeOra9AFFOeEfmQYSpE84YwgKORQhrNSxJ4dhD0ARTA0WDAFONH1gBhJDP5plJrQBt/2Oa3VeE5lJex/v9sc3ap7KAY8DlYmDz4ndjTCeCzfMjcYZqXXFUUVcWPAEkSlPOUUaeFh2iADVPVxrwGFMCRlYViiDF3e8QQUfsrAEzMARIDYDTjNZbE2yKL7J/KGWMuAW40FpiwiWpeIg6KWP9hO3ZNCx0FSCBcY9BZ7IhqjSEehuSvs1iCcE3/jeypcr/EVmT8bIrrs0lmf84xQ3xP+Xmsk1DP4eb2jYatifeF1ZsRyqJUE7ew4VyHe/28xoQCDEwlgy4u5WEYoOVX98k7qfB6zfHLppNRdXclrUGqIIUcu9EQBVWSdkf9HGUDDcGmt2djNiWT2DqWwBtIL+zYwZyqNiA/jwJsxFkXBzLyl6eO6CLof7QqkTkHrcF7b6fWhon64l6ASLWEEvhKjB0wmxrlWPl5V3NGxPKYZOis/vipJINaCVJ/PCnLSCRxuh4CGH5XLdEkE1piWV/y82J5RsyJkAngFtAN32Gb39aLnesJJTTNssOgf34tqqCt4qmLrUU1hDm1p/212NKNhZgholWGiSXNpoGynBGVAG0pCjwBIDMGYDq0O2G4xIwo1ZFU/GWLf2gsZybEwpGdYS1rYKkCfsZInL3I+rXoJZo80fuxHFurLhf9rmnZmTtJM6Rj/Yft2LUoaC70GoZNb2fQ6WOHDsuErh+ThQG+Yrk5o3pbKW/+bMrpvxST1gh6aExEk5OwssfqQ9UBGpJOxYgOqVViNTgs5fcDal07pS/HdIJ+ROfoRdaADvJFZMnclT6ekora0cLorBESuoM+dt/kxwbyyflHovkKufU4l20INi2wZqW9pfrHQAkgrWTGWVOI9pX9o0mQE7L48qSBsnBsl9l0ZIp97LDKeeOD/imDSvVeRH7TGDtIBRqKvyORQ98fPkZpdmRPKRYsUBal4pZykhdW6ZViLiypcCWMEjpvlwmwqR/Lc7+VYvJpBrtqIImxFcBR+65sGN2Q2bRwmgZ8+l5Jh9ViWLtsRZMY0MBQ2i3eWt8BknZSlGs331c+F00oTipbudx9AUiSCMmIAgdGsCml/EugIn6HeV7vCJtIBxzTzAp2HpOMr4TxmmUbRO/eQBTVYaKFk7gKuvtaJUti/eZYhazjKXq3J8YGMtXrUoBjZGw51rAd+1btP/bMVpJJq05rAqRMFhhJgfLRc8/93JgsMd09hn/GzyZEZU8xN9L6bylvRLdW7z4xNmHcx/OKxgvk+CBJKi+fhaHpyjL7JPG5uy92ZvvjObKT9lvU4Z5zEHhjpO29UF6tSl8sBYJa3Cei01Trl9Q5csn5Gbug+DxX3rluQ7BpgTUz/TVDH2SVOjVRJs2ySimM4efL/zNAg6YYqQom6WHI5eoA4pc/g0arIX2KEmhdA373WG6q4r2JijWaJ5YESZLVnMT7mXxWmte2eD0lC2ncRRSFZLJyobTEYv8ZTyMTAngkiSZTeymZIFxRioZtfptOxXb7OqwWR6nQCxY4Cq4G2sby9VBrsX4uCXpE8gjK9x6pxz6e+Bbp/iqQcXTu02jycXJPp1ilqTWQBRoSxqs/NTGmsAp+RwyXPPPXHSOXt4IG7pWzN3bSRZX/BKM7Bu5o8kTD+1vx36gYP21ERSsYRozplNdb0xtisg/bsWtRpr5ShUoDbI5aOg5Sf9AYdOYzOOid0d0J0KN4HNd/tbx50ZxpkZCoWecIJPRZV554Xj57dIcYOylL/X8mMiWXwoXS9VW7A5H+iPYvZfHJO5WjOLV+Y/YVuX7V4j6ac86oc6RsoGiuYw20G4JNb8+WSt6aKnmdQt5jBqx8r8mDSF8SCRAjpRxnKKSpw4pBxq2Hfk6xbzQ4L3WUlaUBDTFlWvNIaAwe32iIeLCK/sXfVLwykwgdSCDpGW9H2B/R/loyRSmr2l8x7mLhEymPRMxYAwglhzbubJetBXROK1zp8Ydtflv5G0STmCZ+T/88aiW8xxpjRr5ePR48ZMs/62FIbt+Y11DKk3JS0B77mCyKwh3N75NwIsSSj8vHR6pAx86MXNL/YA0M/svkbdPCcqKADeN4IpKe1mxbV/XM5YyJgaV8WGf52UF3taJbGijz1kBCZ9OBsojXO6LfMaEwTD4rTW8A4rrGsB2bFgXZG+nfyhJOKcenWJSRNSwfJ3XxaDoDdr+WsodGcMwGyskentmDz+4m9ivLjo86FNzXYv1jZ7bVfktWHCXvbY0sEJ5j8dD9lBM9mrfL0X/j35VevzEQP+EgqM9Id4yscyM2j5rOwdpvsXs+47RORiel7pvI3Rdfj+54c92GYNMCa+lE1fX/YwuVqehW9B+8zrArlE1mqSDgAA1RLx9jINWvpy9biP4K0GBhEiSAhlwVNZYCbU4wF0OvB+/1e6dypFi8Ump+jH5EliRK3w/6FP9PAJQKoBKTx37ZhrLkAJumd1rmFbT6OSY5f5xezRnVyYs/5SFTLqFhm98WU6DNFd1SIG/GyLQ4HTSldSQSSpvcFynQNgUgs3u6F5Mlfj/Kz2NAu2xIRvBd3e+Wld2gcCfXQKVwx5PHxkCPmDwxho3Z8ZQLMU4ZUYReklrrcvzYHRPDUzTAJsVuC8LoUixn491uCadOOR9TYGlMb5BfY3gPLJym5Y0pXjfo7tF1NhiT2N/pc8/9bF+22Jrv9yP5etRzLxA9DjSUZw2R7NkdPyVL/VyKKQgk9muZf1C9n/L6ctZJSDjoGSdRrGBAan01Gq5DLFeRkF6/ypphgbKc7u7jKbnvGndAKfcNIXuqInf6vknp7jm7WfTV7LfE+HPVhmDTAmtJWn4CsEn3H7yeRMbjin28jG4op2WTJStiZdBlltUSyx1U/lcrGRz3xCZYLSnZU8pxxHCM9de8n2xSt1S1nWR+jEzVQNd7EU/em5IlF1ZS9BeyJH4nLQ9XbPzZXrbx/m7ftHEX3x/RRH3Si2xgt8VBPgzGn/3e0wy2YZvfppctzp8v8rFlXxSvu7JY12IMWM2xG5M5bxKysyFUMWVLrQQa2dfJHHIJVlbSK1k6ewggy5GFARwzjNVkSIZz7ir3qZKEV/PYM9WHYr+R/Kx0rqH6Oe1u141Xd75Syn9aL4mHHaRC3WKJb+scTIHoiftUd8YUffKgQWzsRqNR3cXDe2DhtNj+05JDx/LsMWkkmHCupB1R7hEP4ImxIuX/Kceytkdi+rWR2WQJu0uxSx1ZIkA4myA8fX/od6WFuRhbA1pUQsjSdV/PjV85N5IsSnj9lXteOSdjbNTkueeNkdJRomlNEszVQj5ed5MfxejuybDtrK6fz8Ml3z8Mo3ubttxCkn2ANDCRWkhHDRmPAhOZQ5w8rGJAg7xsGWZTymhw+0e+a8KbmfRop2SJsE7keGXTqfCk7AlPUMxDJvsnAUrnIES0L6CDghpKHyuhm06wWz8nvwYju2bcabIzCXZlf9/IiFWu0hSuKLBGAI620A93DG2NDdv8triRWfxlzhf5mKqMKFktKeCeXIv/f/bePMqyq7wP/d17q7paI0IgqQVonoXUktCEQBJCM5fnF7O8HIhJbLMIOAOJExQTIC8xGPMw74k4DrbDw7EdG0NCDJixEGrNaOqWelDPre5Wz/NcPVbd6f1xpj18066uKlXju9fqVX3P3Xef7+zz7W8epPoMvFPAKLRSRgxHETHVPjMI3Bblgira68JmijYQDGV0pDCtAHI4wNWWoLpdSlGiYh1Bqoua0O7cQuvcz3FLbxl/o2cl6w7mc0O4XYONIUpUN9z765Pp/cxzcuuzSpTrvDkOxVtKEemP12dwtIbDM6oWnsU4bEmhStUj6ALhAr8h5TZangVo2qfJkPZoVGFfzHoEyPlcZD9nyGD3nY1cjNdOrhGolWQ5Hr4tyRxkUxLdSOJHgDI1K0tc99dIwV+Lg8siu3mNsgzrqzSb4/OGiC+ANgxP5ugbm6bZ4Cy6nGCkpX9ZO/+QRQkFRCW9AONMQ7IoSO58SwqgnKsqGXj8uW2G8fPeEf/78Dki76cQcipFZZFhysFcChYJ9tROemJBRSYfnk/90GGp1WqCoCAUNpaMpQYc4MJNWVjKtatrLm5aCtybwogNgoUGe9/Y9PoPqf5diCtUBCrA8wHJoJJ9z0RjkIVDbfSIrX+n8AFL2l1ydKNyLuL58ffZvZDDbhS4JSVKEFrJyGJGIA5xgGssQXlffQcIZ5wyKi6UwVGJWub2kXXGMFGibAoHER0Ugs4abBLeqfs5xYEnRotT/JQ5S4CtI7AWKUEZEfvj9RkqrbEYbCxZCQacZ43DDC0jjUGCYZsyrJWR+jHoZFaCqndwUVlsRDohE0pGO4MO1Gb4DV82Rd53W1QWyLne+hb9rSPTDgsflmQOKW1UdrgTqfsMLME2qrBba+6m7KPXKIuSlwy8zP3MyTRkWROyIQV9PiZr9I1N02xwRNwlVmTKgsEA46/v35dCbK6mUjbfX8/9Py/ocEVBQc4/rvBXxujBzWcjcop9aYQHPl+L2XfKAANIwrQOi7s+FZrfCdIEqqgpfw2tY81xdSTUvEaRogl5Piso6PieGkKqnSXecOuvTTNDXbmj01Ai0JloOM2zw8De92i/7kMylvMGG9rQYFG+3fl8C+V6NDfExV6vVyrwlLLOpcaGfEA3NNBCqyXFkDPcu78lnTeGiK9sPg2LZGgQ078MUVkcDnCw68K/jjPjbrhhNH6r9T+c6Zb6d3SEqw8312WJL8DKOZ4YWKTob8mBRzlAGP4IGPkvJw8KRsT+eH0GG9lU4AKTukbhDRVBR0aGKEYS63klC4RL55XgH8UZCVHScxBYnIQFvwnr1jK0TIou7fV4B4Sl1iabmaIYtlOjiXxaQztyAa4eYg4rt3ZiNLXZoVDggDG7IyX6mk2jU/aRK25u4cVsLWIGBzQ9ONKZNPwlo3SJSFrmbE/W6BubptnQ8v8BmxCYKtSR0RXJ4YPaAfbX0AssMwqVQcCUag2J7So5b6bRs0NZ6b0UKsbabY7IEQTSiDkzYf9anrgfnmqAhRLUjZ4areNSHMHhf1/NRzTf0kGJFtAYfDR6mdrEPrqPkVJQUTaUubCAnJ8aitsfUz+KV2ApeKkVquaKQ7OGe3Z9Yi6T4gTQgl90Lsp0K+8ym1ok1d8BKOMUAYvCMwDQnZMYuh4qLmyNpwRDvHs/SulKT+dKo18pNeQociEZBaOOpww94lI4KAXQi8oyREUXzx2Czgn/fNRGPDeDh5Y1KOORK69xaaApsMTzc6dDaJAgvN4hPP0xPUaJN5GD0y4vSxENVAfRiZIfpCYz2fc0LBZHG3deOYW6TKllHC0W2OX0r9goaOI3Bl6pOjg5I74xu0PUgRKNR7yzAuR8Dna/eYEgu5Pyb1oaXYoOJKeBxu9JW9udA/CGMlZ/Ux1cMeyi0W6KrEB9Y9M0G5zHWSO0nILMCXVcXZr0vFmd0LKpPEqOsLVdJSVMSyGkYtpdJOwyRUFZwux/H/42CiEVI3Ii0MUw4vBRUwUFybNK4YCUosOlgR6PAdGFjVMGrQKXGFFmVDJSmIRUjJXGX/ksufcX5yvGib5H+/UfKfXy2KhPJspOrdvGGAPI6EaBJ5m6qyTiotSNLvueSwHUYWGFf9aJkP2NIwR9WGNYqmuW2g+0x/M4FUDFOMVHIusCNCAb7s0RYqXB0Q4LCTsR3VYZgwK4OeGfk6nYKFEGFsoI4CreBh7JOzQq3PeV12Jt+ixZDY798foNriV5SgctS3S8G2GqRaNaabZkMHW/Lz8TOM+XhaD5DRsZQtACQDeqeLA3BFqTcF7VqBbOkMXqb4Z9NNBsC+wqDhgcBADvDEntfipFr/Kytb+GJhfwWQn+OnI5DkF2T+DzbDSqxcHF6IbS+pM1+samaTY0y3W9BlOBZbaSPac4UIU1DdZlUyijIuzyhjI67Y5TYqzMljIesBE5TLtjjuhTkQEePAlpdBwOZPDE+cpcAdRUQYFiWFJ3DQvR54rRscodF/bPMmf/e/deVAhpknKnwGLFX/69SrDzQssAmeqk74v7LJQhrj+mdlAeJlUYMkdaZn/t9T8Egw1DG4E0z16krDPKQtWNLoY7vD/gpDlZYPEMZQQsxvQvjX41CIVO9jLq/FfDAYsTwTLfpIh0q1RKin6ZDfeKgM4pr5botuIVhNvO1u1izxId3aadPU8uEZRXKbKCw99ajVO89XPtr4/+mCYjuUYk0ZCklE2IF0tFhqh19gJ9lCtTQTpba+73DJ0kUn+i8+rJPrrewcnuqszJGIdjWd9fT4LFdeqQ843ODT1zwJkrGWyIOkzJDq5x8ptYXva/z/6ff2fMStANNv4anCOaimySMlMkhwKnX4XwcB25tX23OGa4dwq4UYVTYwbqG5um2dC8aqzSyHmRE70jydFBhpA9NYyfPWQg5/O5rTHDootsUwXpmBbDrDdTI8w2QwP1rKwRzvWOEISW9ZRyRJ8JtSc9/ZTRjrTq03niWu4/HxlgwxnKmCUpd5SgwEcJMtEhGv4yAhrnpSaVZCEig6rdxkV8WRXN/pj6UbyDWo14/1YBhMMXhg+oXkwKFkF4SokmipT1mv+9BLuU1iCdacnLSBptjfyX4xttggZI7cip9tKpqS0T3QXQUsSU9dgrPMxaO0hq0Z19TxebpZVRb6pfB9MBJyVq2f1s4Rti/Q/iPfHGz3g99/PxyoP9MfnjGy9uwG9942UML9nmXVdl/QQ6Sb3WtKLGNCxqUWNHNpEbu8TzNXnWhdedz2YlWHUgQll3ZSzW0GAxenCGhtJp7U3ny6AkGIRERzGl72kyR43GAavsXny0RE5xsLh1Ik18vjDKwx+VjkWXBuDSQC0GR8s7qlFn1YCP7meLXCB1paSyZCZz9I1N02zoHoZQYIQ4n/Nk8YU73bUFQwPlcWQNB4jmus9irUvCM1v//tLcXq9H1kjh91E2NPAEBf58haBYQkg1Q0P4mrSIMpbxk90MJGIV44CFMQOCEkOs7cGToJRQAhe57+y++PcuRmoBX16R9e/v3oszqoXwpHRHdH/bVzJe/0EZeTWjR1w0EvT8cdIvquClSI8MYeS80MrVvPHXK+Aqfm5xamjFYLP5cP4vz4+NdvF6AM0fpToUSQZnhq6zOENELWfr++uFsJNdRkWeRNAvY3qIZvyknAgU7CL+wh/dUuGio8WtjUtYRxIpZ0iwE/MTHBTu59RI934a3dSPZVsO4GfLdmDtzkPedT4yxP++GJLsTjqKifU1w7M1GrWskxQ6WxOiXTm5jatTpjbHiHAe5HwKFtcRYdGxuHpTLj+gDA1WJzdv5MvXcx0nDf5sS5kAqd3BzZkszPpSurwkc9ics8X33mWePxERyR7NTsBfrpQIa/BPDXRIibKiHFzMe5qs0Tc2TbPB12rJ/h6PpVucTyC2WGOCEAI54sanIfmwFoNlWGU4vC7Y88o6ojmAFJqY/Y1CcTWDjTGElLTqK+80gycmhpEwzVjGtRx3OrKJaPtJrM8LRP56MSy6AQbgw7dT6t5oOGAOxeWEFuJsSOvTsDNrcwq+xviNHvD+mPoxHu8Y29HNaihVhP9UQwN17tioluhcxOu5n/nUn+MX/llDg9HDrzoRSJ6EaNCpBIm8XYl84LsD0cI/DTvNvwBrSgZEWKyGe24vybPEKK/cPnLp15qxiWsDT7WidterPsdpety51vkpgvky7FT0w/GOo0ePTviav0iDr9dD4zxrlKdkd2Ztz9lqMg4rNNgQ2ZTdy18vnE/ivL8EX6eseFYmpS81Ot6nHe79mfkuLExNXN5ZIdNgrkB4CEtlfHbWlvQ3IgJU1Q2jd5pKa+ish5TOrX5XdjuvDGV3HXZnrvNbk8yhGMrijtwy/0h1zFAp5NZSOJM5+samaTb4cHImHSbBygnoSixd9yg2NJBeZFYJSKt1wHYzULx8ppbXnIKUoDS4n61FCVMUB0vKAlXHJBKmFe+IqcCu81t2fcrDYPSQ8bWyZEXA1IWIUxwZYxNrKCuNR1zL9gAWJpJAE+hM+8jhL1dDLFFB6o+pH1KtCLbQfkgbuS5UShSMpW6bRrtCeDThia2hYfXsseeaEP65M6p5X4/TeSMWDqUihQl4VHoR4YD/fbk2q+jQKYCUwsjJDX6EGIUzPoyVgOtfH2/9jxgeKkWe4Y/qOw3mc4Z7Bnay8K2QkiFFOXP8lEtt4bpSTmWE6+233x5dW7ly5YTf50QdmszJGWzYWi2GiHRPfkhIoTLXPeLOa0pkkyLPAoyslBpFaZAhpcYuVLQgWxOXMTRMWBkJoTGRqL8ZZA6Of7C0JjG4QDTYMLwphEdLowsNHVwGEeVo8XAgQeawGCfd+cmOFktUb45wvZ5dt52s8boZm+bOnft63XpaD46hdAklABDS7hSDjSkkVPDCpXVQ8u9djORWmw2OMMfrm4gVBbuBmLifWQ8458EwRJ6wkQRukUFD2LHqiTWE/Yud9IjWsjwhZAyOXHcNRhnU0mIsBkTe2ER7XjSin1qXhBNELJ0gOWGRrfOlGksnXskoxtGjR7Fly5bo+rJlyybtnificKNsiqFFS8Se5vx7q2c6gVazqddMGhLXkZLriKVFK4Y0Q001JwzxkYeUTS1TjCQM/7XQDHfPQ+G/KORLdkXj9oVJVbGnNRT35nDGKW6uOAXC9StaFzg0OMN9zYc1goVpA88WICf4aWjj03i7JYJams+lgYbPVsETz+fPaa5INxj8tUa4Mvz6eMaPfvQjfPnLX8ahQ4ewadMm77sPfvCDE3afE31wRhUVLw0GG1tjBArPfFhS5Qc+elWW9S3GYb65QPG9Te9QeV9E4xmjvAS72WHpf1/BIsucFnlZchSXtCYhdc1qlNebUxlwINHZqmcl+Nc13ZMzrvJ8Pp6bHLjA6GOs3hw5QxDBLtW45J51ssbrZmz61V/91dfr1tN6lKGyRkKoVabnClVblFKxNoIUums8ZFpdEnPqmkBorZ4d3jupGGy4fWeEwJT0L86AGM5XC4SbFSreK5zBE8xPSgHM10uMzLMKxykhpO4nSqnma6R4l3lYGCKeVJxfgcVdz4PFbHSO15vI8Z3vfAeXXXYZ3v/+92P27Nmec+Gf/JN/Min3PFEHaXBWhUq6U6c1MoR1ahD0KD3NzV+rXFuJJrLUYXOfhXPIkCnGZi+j/30xkusnUMK8Qfi3dFliW0uzvN2H1bp+cg0NMooL5Py45hgj94zTG+xFChcODf+W6Yp0otKlebItKfh8xAnEtS28PVvfv/dEjGuuuQannXYadu/ejV//9V/HJZdcgjvvvBMf/OAHMTg4OGH3OdFH8ep4A0wijXdx3pPbes7/Qc7RHAqx3ObfO7yXNV1MwvlQNFELpxuN7FoGBssrQ6M8IRdysFS8zH8mPTLWn89GzVB6hPPj0FFM1ghMpHuqw91sVCHkX25fmLpdWlmTWrSP2d+Jij7y9pHbF07+USLBeUch3RyDkt1I2BmZZrLGwGQu/g//4T8kr/d6Pezdu3cyb33CDi3Nze5VUxRkwyHzhGODp5cNw2QOMEvcOK9zwoF3vSO9Xq/0vGupaJYILvcza+RjQk5taSv+dyEs9RpdZyQUFzVYuJoUbOtXg+dWDZdO9hgwDM7UkdAPIaWMcj4O+GsVgxOgtGLCHOwWj3mpIEU55cWzcQJXOF/G38lKo/v93/99zJ8/H+eccw7mz5+P3/iN38BnP/tZ/Nqv/VoU1fH3ebjdVSyF9tscXU+MEk2p/8EX8NaEoUQeZqS9enSjMzc1elb1vsKfzz5rHMkZRrVQkcMm4V8zfrNGPn++XkPOmavsY61mM37zBsfsb2pnI0vX3uKdRsorszbflVTG31ih489Hp9sTapr5c7PvaNjtKRb+99H8CeQDF110Ef7Fv/gXuOaaa3DnnXcCALZs2YINGzbgmmuumbD7nOgjNY1OrZPERqT3MINQ9FOchDGeMd2bGWcrV8Sbkn/LufCHns5F02AzfyL4sHs/Pp05ltvsEcnjk39NdbsE/Y2KEmNh4SL1WT0C5HwtItnSQdTDXyoKmNtHfxmW7qXK7mKdW2Zt1gltdHCpUYgELBTsXKTgZI1JNTY99thj+MY3voFTTz3Vu97r9fDMM89M5q1P2MFGwCQabNSObgbh2xOGU8JfUw0H1kPGKSWEMB0K8qXyzqSiaTnr1uKqWi0Q1rBmgEXvKONddjz9HM7488kUGkIhqj7HzFxtiZvsMfBhrCL5aEOZFEJaR7xPfhQEnUanRRKwyqD1WSn8LXGAyYcPFSStMCUH+yQZflqtFs455xwAwI033ohnnnkGH/jAB7BmzRrPUPr3fbioYBFYkj3HHN/IP1qM6+leQFoRScVFNiqPVah5YYtPa6BhT40U5sP3bYKfZOi31tBg+QbTcENzgFCdjay0jqPTBSycAM1GWZmNKvF8NvJXizxKVLqS0+4MZy9FQXNhO155cCLGn/7pn+LZZ5/FNddcg2uvvRbvete7JvweJ/JQ6Rgrc0Kdz9EaFy/IbswGZdqdb46k5fCSktvy/1uNwzwNzu+d6vRj+I2FV7IlMJiIZI4Gc4aJFEeOqL9RRnmOD6v77l1Odm5IsMeyeHUzU13JkmYHsCTgowV2S7AAJRMArqwPcj6X4RMHIxT3j/GRhJ3hCZM1JtXYdNddd+G0004rvRvumD179mTe+oQd4/ci++vwHd24Q5l/Txg9wvluRwtKqOMJrQ+jplCxhNZwiMMUwAHn/+F6HixsSoEPu2q040JxDQeeT6VkBEZGmNas9JyHjGL8VnjGG4prNU5Vwrd3mST6YQjpYCNf2/mdC47a7TBVyWAK4vP1Y5waKZqAYxXmEo2fEzXOPvtsLF68uKTzZ555JubMmYPf+I3fwOLFiyflnifi8IR/4tyl1+AK1s9xi2vOYDFopxvi42cD0g1llTDPpIInpCRzXW24CBtztAF7Tv3vAZ+usnwgwUNqjcjRhH++ZlN1LdUDz9LpxNSWcRdVrcX7HhmbuLOk8Ha780Y2GpjOniJTpRbhjaINmDqYEzF++7d/G0uWLMFjjz2GP/iDP8Dy5ctx1VVX4YUXXpjwe52II7UQfQpeuv93cYGrsaYp39aIOL3xAsj5VPkOzjgcGQ5UWYmbH6yfasyioom4s13KeImwH4exSdLfUgw8mgzJ66p0TUGbwcZuUJFgoephAnqjISvNpmQa/izRsHPRcOMNdGAdXA6+uzjwC5FG973vfY/9bs6cOZN56xN2sPUxiBBrwKKsB/PZQ8a33QV8xHZBa1BCnVVB5gxlmhBosYwzhLaApVZjWl4zhJYr7MfOj8KIOSOi/2wAb5jS8udDcZFV7hKIm/sKYniK+xMKEiPYc4YyTuExKwKCspbBE+NvPcABLqqQiybiaseobW4NhjU2jDjR6MwaP5mzNFHjG9/4RlSfY8aMGfif//N/4hOf+MSk3PNEHC4umAyfTESOmqZgfP8pEatqtATLwzg+wCnf3uW0VIIEo4QHizUyMwEW0cuYYLjX0gsttYDczynOm27PT0vX03ptskBKoXVvfcPeFHPDVuoc7LrBkea/nPDPOc1cvuEZASg+YIVFaXLBnqVJ4AO33XYbbrvttvLzc889h5/97GcTfp8TdRSvzhoRxyqllMHGwSEXz/zukdUaKp1MNMhaa9tRBf0147DVYVnxD8boYYjodO/Hwe7pTInO09TUNTW12pCVwOlvnMzBNdPgnD5qZH+Ck9sajaPBEppTUmtc6jjj4q9cf9Bc95Gh2Zq8ZCkQ7v70F6JA+De+8Q389V//9WTeQhx/8id/ggsvvBAzZ87Erbfeinnz5onz//Zv/xZXXnklZs6ciWuvvRbDw8NTBGk11GgJK/FRhTTQ8z3h2PmeC8WlvCPWqCxFUD+ewpocoWUFQCZlodpH/zprXWaZbQyL+yyUkc9cGLZRpK2EsIOezxhJKA+41PaTLDJYrq3Xg3J/azEeufNNUVasZwfRXECPKrS2/9XqjPBnNV6bYyghf0hJK5HWn6jx5JNPsorFu9/97km5pztOFNrPdcdU64GxxqOg+xcjsJRpUQahWCt6mhrxx9FetgOrMapFqkPB1Stgm1Cw9IWLFAYzn+ZJftFeGge0Bhp8OL6ujLr3SqnHCPiCaskDmHdkieR1YbMI0O5nS/oJ6wBh8UuuR5Nav8aSdsfX0om/d9e2plhw+Mvt+0SMAwcOeJ/f/e53Y+PGjRN+n3CcKLRfO6+cEZ9rAMA62jxDQyU/eM5WThZXZJ/0SGpDoerSOOyvoTks+X30LqvO1ki5Z3lxTPvUZhph46BEhwLnVKJTqOL7h/8n9TfunRodLZzMkSLTqM6ERFgieZk7S4n8qUvoWGwWCyuL+7CWayvBBZbC7PV6rSyO7upkHA5M5phUY9NXvvIV/NIv/VJ0/Zvf/Cb+6q/+ajJvjW9/+9v45Cc/id/93d/FggULcN111+GBBx7Azp07yfnPP/88/tE/+kf46Ec/ioULF+KXf/mX8cu//MtYunTppMIZDi1a4rg7urEKsv89kDEjiqlwClJKiKf7OTRM6CGk3mUx/9h9NhcWe7E7mfGn5zfrAiknhGjKWgBKMg6wofaMt5RU7jgFhom0Y2tSFN4UI3PWlTsH7mKtyHDrr1XOVxmQ/0xqbQ/D+mqERaoB0cicJ2r0ab9teEw/ISInnTbS3l0+urG6xtbr0QzIRh7GG0r976P1DV5GHpauDLvRy8jxDcpwzzlv3DNrMfJpOJCaBmxZPyxuXq7NGLLUKGejkSS1SLxUcDjijyws2V++2yGtLFjPKqVIccK/fk5tigvrvJlEPnD33XfjsssuQ7PZxKc+9Sl88YtfxCuvvDLh93HHiUT7kyMREwwTHK0Zr8HmeCJjfdgRzPfXC3/bJc4IV3ja2lyANTQo6/sOy6qUCNWUxhwxk8DLXNgsvNjV37i6XaZoIsZprTkIuLqilkg+Dge4FHIVlkDvSHFaA4a0cAJ/2ei2RF1yopoqeToQo8NP5phUY1O9Xscb3/jG6Pr/+X/+n/jDP/zDybw1/vN//s/42Mc+ho985CO4+uqr8bWvfQ0nn3wy/uIv/oKc/0d/9Ed48MEH8Tu/8zu46qqr8IUvfAHveMc78Md//MeTCmc4VIZijWxSQh9Ti3J3iAMfwqOFPlqr6quFZA3GKRcu15jF5c3qRgzao21p5er+3iQoKPvIWsbhD9Vox4Ydh3sDMzyaoczsrWOE45S6JFoIKesV5phtYhqKNbVECn9NjbCI5+f3NhrKJmrUarU+7TeM1Fa+qfUT2Jpz6jmynGn/+3JtTRFh5yOYb+8mNFF1KFLrU6XwDZPzhopwTXXeGFOSWQeLkpLhKy7x9+69Ug2UsZEkXy8xes6PNsjnouZ1wlTPEqu4GGFhIiso5dXDAWf9lAhEwBIpAWY+JnzMnz8fK1euxFe+8hXcfPPNePOb34wf/OAHE38jZ5xItL/O0HhVaTQYJjhaoynTPB0DPd9oCC8+cnSYK9/RIc4r6zxl5VmbrKQ7FWMZEgjpZAy3+1veEMDxbVrWT40+8nCACxbQIu1SjXxWPi/IHCG8lUHQX0NNww7mpzhaPNgN87XaVOZABCW7w4oDlOPa/W04f7LGpNZsqtfr2LdvX6R0nHbaaZPa/npsbAzz58/HZz7zGQ+We++9ly1O+MILL+CTn/ykd+2BBx7A97//ffY+o6OjGB0dLT+PjIwAyDoxtVotEcbi+3Bet9vJ//a870Zb7ew5asFvckGx3el411vtvHFoz1+nllf2GW21vevtggJ0/XXqdQAdYHSshVZrIH/u6vtOp41WK/ttL4e90+16a4xxsPdo2NsE7K1Wq4R9LIQ9PzjdAPZaLfNmZrDX8+cey2GpBfvYKffBg73dLveN2sexdofcx14v2MdaAbuPGwUB6HaqZ6r20b/nsXzfQ9h7OQ50eyBhR69Lwx7sY6eAPXh/BTHK9jGH0VHuaNhTcaCr4oAPe4vB3y6JA8dGx9Cake2b65EiYWFg53Cg1fb3sdXuluv5OFCt5+17uY8VznQ72T07wfOPjmX/bwT72CvxN6QDabADPG2SRji30Wj0aT8z3P09NuYIAO020M2QpNcr3mf4/vNzBPoctUJ6VJ6j8Exnf1NwsdvL9rdIvxjNv2/UaVhCGlDwJCsuthl6VIhGLj3yFIFOu6T35TkK+SmzjzXQ+9jq5LAH57Gu8YGQn9aATgl71rHg2Gi7gr3dRqveK38L8PSogL2iyQw/LWAHvY9jYyEfqO5f4kC7akR+bHQMjVx01OlRyE/pfeT4aYvB30J9PDam89MCBwp4aw4/K/bBg53hSS2OD+Sox8lUIf4WfMDFXw8HOm20WtU5pGApYLfKVAX+hvy0HvDTiaD97vVvfvOb2LVrF66++mr8yq/8CuphPYIJHCca7a9odoBnHVp+qNUY+TeB1pQ0O5IhaVpTyQ/he85gaUd0UpYhI/m3kF0JfgNktGYwt7BwON/rMue1gD3AeZS0Ju28uvs+1q4sJtl5rZXPkT2Xf8+CZod0snARtzj5N+KV1bO5+FY41CMc0PS3dhutHIbuBOlvFa3R6V72+xj2jkuzR8dQdPcZK/hN3Yq/2fWYz/fK70k9gpPdHdi7rMxB40CJv6D3kZXdFBwIYQ9xoFHu+1iFA2Muv890+Imk/dSYVGPTJz7xCXzgAx/At7/97bINNgDs3bt3Mm+L3bt3o9PpePcEgHPOOQcrV64kf7N9+3Zy/vbt29n7fOlLX8LnP//56Pqjjz6Kk08+2QRrWCh9zzEAGMBYq+3ljq/YVwPQwOFDB73ry3Zk17ft2OFdX7WxDqCOzZs2Ynh4fXl9547s+pIlSzG8e0l5fe++BoAaFiyYj9F1jse4k11/4skn8eaZ2bXDrQxGAJjzs0fKg7jpUHb98JGjHiwLdmUw7t2z27u+ekt2fcPGTRge3lBef219BuNra9dgztir5T7t35ddn79gIXobKxgPH85gfPGF57GteiTU0EAPNcx57HGcMZRd234kg7HbbnmwvLIng2XP3n3e9UX5/u7ZtdO7viGHcfWatRhurS6v79iVXV+6eDFmbnulvH7wQAbj3Hkv4/CaCvaxVnb9maefwpk5jCUOtH0c2Jjv79joMe/60nx/ez0fn9bkMG5Yvx7Dw6+V17dsyq6vXLUKw4er87BnbwbLKwsXoLvBJaQ5Djz1FM45Kb/Wy2ABgCcffxyn5LWgt+b7e/TYqAfjyzmM+/bu8fF6e3Z967ZtGB7eUl53cWA4xwEALA7sy/f35ZdewsHV1XUKBwoe0QlwYP3BDPZDh4/4uJHjwO4ABzZuyGB5dfVaDI9VOLAx39/Vr/r7e3CkwIGXcMiBcWwsu/7zZ57GivyMHcrPWK8H/Pgnw+UZK3BgNMCBxTn+7tq917u+cnN2fcsm/4xt2ZzBuGKlD6M7Upo4HDlyxPvcp/36mDNnDkbGgOIcPfLTn5b59a+NZNdHDh0i6dHu3T4ursvp/drX1mF4eG15feu27Pry5cswvKdKDdmf0/v58/2zfmw0u/7cz5/B6vysu/T+J8M/LXFxXX5ejh316f3ivTmMe3xaujyn99u2bsHw8KYKxs0MPcphXLpkMQa2VrT0aE7vX3hxLvasyJWebgXj4489hpNzyWbn0ez66NiYz3sOZLAcPXLYh7GkR9u966+ty2Bct9an99u3ZteXLV+O4f3LyusH8rP+8rx5OLDKMa72suuPPf4E3pSf9SPtCvY5j/4MA7k+ztEjDgfWrn4VQAMbN/v7uzHf31dXrsTwyIry+khOM+e97PP8Q/n+zn3xBezIH8nd35/+7NFyfwuePzY2Su7vgYOBvLI1u75921YMD28ur2/O8XfVqtUYPrqqvF7g74rlyzC8t8LfI0dyHHhhLnYvzw0zPaDXy3nSE4/j1JwnHXX299E5j5X7uyqH8chh/4wtL2Sq7T4OrMhp6dbNPi3dvj3HgWXLMbyvwoGCJ81/yaf3o8ey688+9xw2n5Y/j4sDP/tZGcGwkZGpluXy4KGDI971V/P9jXAg50mvrlqJ4UMVDuzdm11fsHAR6psXltePh/YX40Mf+hDOPfdcXHnllfjxj3+M//Af/gO+/e1v44orrjCvnTJONNpfyL8bA968yX1XB6t3tW9vJfvUNlX4dPBQdV53VuiHGkFrCnrY7fiy5cr9GSz79/v4tGRbdn3Hdl8+W5/LPmsCfrMj1y+WLVmMU3ZUNPtwDuOLc+dhv0MPjzmyz6qc34x1MhgB4LHHn8BQ3kWY4zeF7L47kH1KfrON5jcrVvr7u3NXBsuSVxZhYEt1Fo7ltObZ55/H9qUEjI/Nwcwcxt2F7D7WIvf3cMDPV+b7u2WrTw8L2X39a69heHhNBWNOaxYv9fn5wYOHAdTw0rwXsddB9UJ/e/yJJ3FWvr+HHH7+qKO/VTKHzxMX7iz0t10m/W3zlpyWr1yB4QPLy+sHcn7+8oIF6Dgyx+F8f198/jlsOTW7Nurs7/AjPytxYMvh7Hq7NWbC3wIHajWfphWy+6rVazA8WukX2/L9Xb50KYZ3VcrksaMVDmzLt73j8MQnHq9kjl2FzNHicOCgSeZYk8sc69f5OLAjh3FJgAMjBzMYQxzodnP97YmnShzgdHhgYmg/NSbU2BR6sn/zN38To6OjuPbaa3H33Xfj+uuvR7fbxbe+9a3Im3Aijs985jPec4yMjOC8887D/fffj9NPP138bavVwpw5c3Dfffd5XZu2HTiG31v4DFCvo9l8oLx+0qpdwMqFeOMZb0Cz+c7y+tEFW/C/XluGN7/5bDSb7yivr5izGtiyDhdfdCGazSvL648eWoxFe7bjyquvRvO2C8rrX1v3AnD4IN55y82447I3l9f/r4VPYPRYG3fc+R5c9OZTAAB7Do0CLz8NAHh/832lp3D5thE8vORFDM4YQrN5V7nGsYVbgDXLcM7ZZ6HZvLG8vvXZ9fjRxlfxlre8Fc3mteX153+wDNixBVdecTnue/d55T59e8crWDOyF9dedz2a151bzv+/lz0NjI3izttvx9vfUu3777z0GMbaXbznve/FW8/ITtmrOw4Cr7yAoaEZaDbfW84dWrETf/HqIpz2Bn9/98/bBLy2AufOmoVm8/ry+pKfvYqntq3HhRddhOaDlfD0re0vAQf24R03XI/m7ArG/7F5LjYePoAb3nEj7rv67PL6Q3PnAL0e7rn7bpz7hkwiKHGg5uPAok37gSXzcOrJJ6HZvLO83n5lG/5mzRJ0AQ+fFv10FbBtAy695GI0H7i8nD/vRyvw/M5NuOTSy9C8+9Ly+p9vfBE4NIKbb74Jd19xVnn9dxc9iaNHW7j9jjtx2dkZNxhrd4EXHwMAPHD/fTj9pOyea3YewpdfeR4Dg/7+ji3aCqxZirPP8nHg4Mub8bfrluOss89Bs3lDef35HywHdmzGFZdfhuZ7Lymvf3vHy1gzshezAxz46prngCOHcds7b8U7Lz6zvF7gwF3vfS/ecsZJaLVa+KsfZMR0ZoADS7YcwB8unYsZQzPRbL6nvL6PwYHFj6zCU9s2RDjw+N8uAXZtw9uvvgrNd19YXv/LzXOxKceBe6+qcODfv/wY0O3i7ve+F297Y4anB4628B9efjLb3wcfLL17HA4MLN+Bv3z1FbzhjW9Es3lLeX3142uATa/hogsvQLN5VXl93o9W4PkdOQ7cU+EAwNMmaYSFX/u0nx/u/u471sV/nP806jXg/e9vlnMWbtqPP1o2DzNPOhnN5h3VfV7aDLy2HOee45+XVx9fgzlbXsP5F/jv+Qd7FwL7duH62deieePbyuv/Kz9HIS397PzHgU4H733vXbjgzExxGjnawmdzXLz/gQcxI9fWX96wD1j6Ek479RQ0m7eXawyt3Ik/X7UIpwe0dP1TrwEb1+CC889Ds/n28vrcHy3H8zs3R/ToLza+CBwcwTtuuA4PXvOW8vp/W/cCth09iBtvvhl3XJrxqmOtDjD3cQDAgw/cj1OHMtFm494j+OKiZ1FvDHi09Lm1e4Dl8/GG009Ds/mu8jpHj1784XJge06P7q7o0dPfW4qXdm/FZZdfieadF5XX/2j1s8DRI7jttltxy4UVPfrs/MfRGuvgzruq/d13ZAx46SkAGT8twuQLejQ00z/rIQ4U+HTVlVfi+xtWY9ast6DZnF3Of/Tbi4Hd2/H2t/s8/2+2vYR1B/fh+htuwPuumVVe/4PlzwCjx3DH7e/GtW99A4DMS/vQ3Ixu3nPvvXjjyTMAAK9sPgAsmYtTTvJhfGn9Pvzx8pdw8sk+bmx6Zh2wYTXOO+9taDavKa/P/8lK/HzHRlx8ySVo3ndZef2H+xYCe3fhutnXonlThb9/svZ57Dh6CDfdcgvefcmbAORRFQ5PekPOkw6PtvHpl54AANx19904/eSMz562ZjewfAHOCHCgkKneFMhUa57IaOmFF56PZvPq8vqT31mC+bu34fIrr0Tz9goHOJ70h68+iz2jR3DLO2/DTRdk8vKewz4OFKkPy7aO4CtLXox40tDKncDKRXjjG/0ztuuFDfj+hlWYda6PAwVPuubtV6P5rgoHvrt7Pl49sAfXzJ6N5g1vHRftLyJ7wvHaa6/hu9/9bvl50aJF+NjHPoZnnnnGtO50HRNF+7fO3ULKv3P+d35er/bf1d/uyt7V7OuuQ/P6ih7+Pyuy83r7u9+N6972hvL6Zxc8jrHRDu58z1244E0ZrVmz8xCw6HkMzfBlnzPW7sF/WzEfp5zqn4Udz28A1q/C297q49PKx1bjsa3rcP4Fvn7x7Z0vAwf24obrfRi/vuEFbDlyEDfedBPec3klW3765ceAThd3v/cunJ/Tw7F2F78zLzvH77nrvTjztEwmemk9zW8Gl+/EX766KJJ9Njyd85vzfH7z/A+WYe6uLbj0sivQvOvi8vpfb5kHHNyPG298Bx58e2WA/Oqa57Dz2GHccss7y3N8eLQNzMtoyvseeAAnzcisIVv2H8UXFv4ctUbD4zenrt4NrFiAM95wOprNqkPjvnmb8N31K3D2Ob5s+fJPVgLbNuKyyy5B896KHj5+eAkW7NmGK6/MZMsCn4ZOOhk4dhTvfte78I7zzyjn/0dHf7v4rEx/2+3ob/+HQeY4PH8LsHYZzjnbp4fbnsv0t3MD/P3pyCvAnh249pq3o3nr+eX1/7n9Jaw9uA/XXefrRl9cmutvd9yBq87NrO+j7S4+lePAvffdh9NmZrRo2dYRYPGLOHmmTw/f+FqGvyefeiqazXeX1wscqNdi3eiZ7Rtw0UW+bvS93QuAfbtx3XWz0XzHW8vrf7T6Oew6dhi33PpO3HpRhgOjjszxwP3347SZmcyxad8R/P6iZ1Gv+zhwyqu7gBULccYZPg5wMsfLP14BbN+Eyy+9FM17K7noscOLsXDPdlx5lU8fvrLq5zwOdHwcoHT4iaT91JhQY9Pll1+OL3zhC/it3/qt0gDxW7/1W/jgBz+Iv/u7v8PSpUtxyimn4M/+7M+8lqgTPd785jej0Whgx44d3vUdO3Zg1qxZ5G9mzZqVNB8AhoaGMDQ0FF0fHBw0v6xw7swZVQiee71Wz4hZo173rs8YzF5hN1+rGL18/wcbDe96obTWav46hZ15RgBPIfjWnXXqjTw0sZa1M69gz/7f7fmw1GoZ7AMhLAONElYfllr5fXF9cHCw7LoWwl5EPoawD9RrGANQrw+U12v1gfy5gn2ckV3v9WrBvtdzWOo07Aj2sVejYSlgD+5bhP3PnFHNH8pxINrHAgca/hpDOezF/OK7Yh9nDDL7HsBeBAbPGBwIYI9xoN2r0iqGhmZgMMfDoRmD5XN5Z6BWL/fB2/cBH3bnByQsDWYfC9iHZgT4Wytgr9YpsrhCHChgj/GXw4GB8tnIszcQ7GOdwYE81GrmkIMD1fbmsDfy/9M4MGOQhh0l7DQOhLC7I4WO3XrrrQDgpcj1ab88BgcHUS/C6+s+3RlycNVbr06/z/IcoUaeiwgXFXo05DzHzG7l9nJxseJJNOwhT6poQMiTaFys6FFIS2vl/YvrYw6MM2fMKGEsznTbyk/zfexFsMc8KZtf7EUAe6/aC4qfurDXG1VKxtCMwVJ2quhRSEsZWAYLfhrKAtWzUfQI9UYAey9fr4J9wDnXLi2teFKAAzNouaTkpw2Gn4Y40GNgL/G3gr0Dhyc5fGCmU5qUgn1gwCZTlbSUkWN4/B0w4IDPT93nyPYhxIEGCUsBe4i/FR1oBPuY428teKZEOkaN0047DWvWrMGll2aK0vXXX499+/aZ1hzPONFovyb/DgV4U8juEZ5xtCanEzUHR2oNmmaX8gMYuhfhPI1nhfw7GMqQ9fi8AlVNNve81htOZLp733yNWPYZKNeiZZ86ifOo0bwyln9j2GtVlhdmDs3AYO6AGZpRpW1b6F4l/4Y4UH3vwTJA40CvpNk0raH0N6vMUcAe628FDtCwxzJHJTdQ8q+LA7V6xRNJfsPhL4MDdfjnc8aAggMR7DHNbvUcmWNosNSBCj2406X1twGjzNFj+Pwgh78Fr0zAgVCHByaG9lNjQhOoP/nJT+JTn/oUbrjhBvz85z8vr59xxhn4yEc+gq985Sv4vd/7vUlVNoBs82688UY8/vjj5bVut4vHH3+cvfdtt93mzQeycLLJhjUcVYcKX3FLLS6W3MWlLGDnw1MVO3PmKoWqrcXH+aJuxXrMszLFMgeCKrhUAWeuaCfblrNDw64Xa6TXd4vp9Xo9x/BRre++UxIHWFj862zBOLbYHeT5TJFBS0cLtoBh+U69yyrO8G1F/XXogrwx3O5ctjtMVGjS/75cXz17PozUe+UK8hb4yBVr5PCR7SYzQfWT/uW//JcAgDvuuKNP+xNG8e5r3LkI8bzDdVHL/qYWk07pMAnQRSbNeM7RRu1M+8uTRVVduNxjyp/pDLiQZ9Q5eqQUCI+KcjNd2qjitG4R0xpBA463C2ByUe78vbl7U6vVylB7qpX6QEAbS37HFCsPaSlPv3xYJdi1LrnRfLYIr8wHrPuoNejwYYlhBQwNMYzF+VM7IaUMzoD0x3/8x/gH/+Af4Hd+53fwl3/5l/jUpz6FCy64gJw7EeNEo/2pzQi0823Bs1QcZpv1sE0dGHqgFJN257u3Is8Id17Z4tA2vUOjB36jIYbWaHoEx7c5WdxIDzQ6aeHbOn7Bn18r7m3DR73xUQxLOF/lqwzfDmtgczIKp0uqHUQpvm3kH7zM4a8Xzjd3X8zPVpvYx6nqRAdMsLHpM5/5DFatWoUbbrgB733ve/GP/tE/wpYtWybyFubxyU9+En/2Z3+Gv/qrv8KKFSvwz//5P8fhw4fxkY98BADw67/+614hwd/+7d/GI488gq985StYuXIlPve5z+Hll1/GJz7xiSmFe4A7ZAoh5Fo+skyCM5IYCC1HxMsD2aFh4ZR7tkMFQ2itTIUibhwzLD5zHWWizmIqYQ4NE7EA21EYVjbfWVvplhESWrUFaaJwbCG0rNEuQSByf88ahKw4QDDE4qeWzovZfEbpZXCmOCuWs8e10HVhszBbTunluhBxxonxjoceeggAMHv27D7tTxhqRzdO+bZ2oeIcAwmdjVhcZM4c30kxN/CEtJGZ32XoV8WTYsNBuH5yh0nWaFesbeOnmmJECf/cvsTCObO28qzmTrYF/TLAXjljvKksP+UUF51+2Xl7ON/vTGtXvDnezssC/jPxTjlB+De/owJ2/54NDhburDIOk5Rx441ZWnzY+GH27NlYsGABbrrpJmzYsAGXXHIJ/vf//t/jvo9lnEi0v3hXoZ2PxYWEjljZ5xjPeLrk37uaT6/NyZCcQ4HlCb0Yj71OeoT8a+0Imiy7F7CHTmtKdnedG850Llgg2TicKC93mfNNGf05XZLtDM3xp/wlh/oe7xT3v4/mB51bi597snuiLqk6rELZnQkuoLqCcvxGM/jHsPvPVs7nzh6nAzGOZYrGczRjMseEGpsA4Nxzz8Vf/uVfYu7cudi8eTOuuOIK/P7v/77XvWEqxgc/+EE8/PDD+E//6T/h+uuvx6JFi/DII4+UxQA3btyIbdu2lfPf9a534Vvf+ha+/vWv47rrrsN3vvMdfP/738c111zD3WJShktIOwRx4yKP2BbAicQqig4q51fXVMu4ERaO6HMthjliqB1KWln3ppafOULLtSxlWxIbImx8b3yN/L8XkcNFfOWwhOKi1oI0fNbCSMIaERnljvIiW/GxstIH7bc5LwCr3NEMsQiB9jxkBNzu51QciOfL6/ve+Hi98Lfu1nQVpdfqjefO3vGOP/3TP+3T/oSR2n6dpevMuSgj4YzeMUop5SJDeGWaU4oQre3NZ4Qni8HZfQ53uuvxtEQK89EGjAGZeU+cwVkS/mOelKaI6AZHf321XbRhb/h24YjmevONkcIlT4rwPV+fE/5dB4iLvwmRwuaIk3J+wMOYs0cp9l0GB3jDLaMAsnyguLeuSKcOLqoVyFLOPvjBD+Jzn/scfuu3fstcQHu840Si/fr59uezjjZW5kS0Puuw1IzyRjlMdfwGOF9G9nNOQkLmtMo+nLNV5ZWs/Ftdq4w7QTQq5yhOPH+pEence6UiRtVIOGtEp+IQY434nLGUdVolwMKcDS6yKdQ7VOcc59wwyEuaXsvBzgdR+M9U8gQmw8fC+yZzTFo3uhtvvBE///nP8e1vfxuf/vSn8Rd/8Rf4yle+gg984AOTdctofOITn2A9FE899VR07Vd/9Vfxq7/6q5MMlTw8YkUQt9TQRE6wjw0NduKWGmWlEYhkQ5kxKovaGzZUVvG8RGlLhaU7jOLi0u40TyxHrFwvMmMM0kJIudDdWBGI7++vryt3qQpMZaUPYGejiTjljlHYCIOQ+pxGHGA9Egn46DI716Pm/pY0OkdrI1pbhJ0RFCZi9Gm/fVTv07+u0WmzcYqjX5Thk/XUxfC681MjVllDvFVxIXCXFf4Dw33pkWeF8zoJeylAG/mplgaRYvQI6boetczNp1PdYoeJD6sL+yhoHmY1IHIKIK9407Co/JSY3+n2kqJEzbSUw19OBhMUF/PaqfuYaGRIGQ899BB+7/d+r4xq/dVf/VU8/PDDeOtb36r/eBLGiUL7S4OK1dCgyVYGA65qaJgo2Yehe5yzlYKn1enRtMbKb5QzlQ67k93BGSUcGa7T7Tn8QXZWcLBz2R18dJCOM2oZFFaGADmfd4iF8zXdwJ9fr9eAbu+4dM9SLvCXVtNAU/bR/T6ErdProQ7/t6lBGtZoajZiTeCV4VmazDHhkU3h+OAHP4iVK1fiox/9KH7jN34D991332Tf8oQeLiJaUtc4AZML+U72mFMGm4RwU29+gNd6KloiszVEfbHeDk6oyzeWzeFlI5uY92QQjj1iRew7V2ckMjaxkQFaigPH4Kpr7nO6yh1bc6wXPxugRypZIzL4CBH/2QCQdbIkWDgPtRaZx+6jpyQ7sAb7WHykagWwSrI1DJ6BfSJHn/brQ0sVMxsyFT5gUUrbDD3y0hpMwj+iue5nNsXYarBpELCwETa1aA7gnNHjTCdReV6C0GpWojSjR+itZYV/kOuzEa4JigtF6zxYGOOnWfGm+KnjxbbUQFMjm4wyFRX54H62yFS6ETlYW1MAmSgPdt8ngA9Mh6jWE2moUWtsDVJ/HZY2NWJZKbV2FyuHaZFNBjrp4pxFHtcckCy/4eryGVNNqfmaPhbCo0UwH69RPiVaiZ8bZwG48+N3FKdp+uvrpUTcz3Fpk/h8pEdTF+/Ju8yngWo8wX2nbE2leD1AN2byDnSbbJhy9jhYJnNMWmTT2NgYVq5ciaVLl5b/TjrpJDzxxBOTdctfiOGH4FXXU1IKAEHJUMIw+agZl1jl3zEHMj0VzbtsKEqYRmip2h7mqCx2X/z1IlgMHkr3/XJpK36NiXiue6+Ad/L7orwn3sATGz85HAAyg1PB5zVlzYozmmfHEmLdyT0NbLQahwNGD4MqoDHeEeo9tXs9WxixFtlkFFomYvRpv32kRp6x54KtoZF/b6ABXIHlYn4HPVp4soaFM0YPNTXAYmhghP8Bhp+mnFEf9rT5Fn7KeTCp1BNvbaPiwu8NU6cwIeWjdMYc5z6WsLMFxRl8J/hpCAtQ8aEOIXBHSr2iiLBnj1Wi9PekKaNcmnms0OUK4HHUvjqeMR2iWk+UUSfOE2CgHUYeTxmzuBprFU7611MzJFIMsu5zs9EbHfd8c2fEh7UYrEOBy6jo+c8WwWKgNV4kLaEzJTcaCt9TIq+kInj0wAV6bbbWUCLfDmkTl5VAySipkbRsGp22jwZerEW6ArTenJwaycAeO9xBw0PiAD13MseEGps+//nPl8rF2rVr0W638YY3vAHXXHMNZs+ejWazidmzZ0/kLX/hBpc+kxJ5lH2GMh+m+cXHlHDWXi+LaqkFh4hT7q3ee84yrlq7Eyzj1oivVGJFrc8ZGnyDo7vvcihuAIpAmOO1AWHfS6ElXluMJOj2IqHEatVPr+1BPyslTBc/teZ9a+lCdg+D/334fxL2bo9hcPDnasqdcR/HO/7gD/4AAHDzzTdj3bp1fdpvHHzkkf99OJ8T5mOllK55I6VzAYSgWAfQCXG3+M5Ip1VDv3c5LdqW5V/V52xvGj4sRtjVaEUj3yjpoSNwp67NG+2Ke/vXNQGa66THO3viuWbDV2Jkha68uvtIR2S58HUJgZtTuo63A1yb6RwpliZg5nZDmYrBgVQj9WSlU3/wgx/EL//yL+Phhx/Gb/zGb+BP//RPMWfOnAm9x4k+tAi61DNiMSSqNQJZxxno+YnOVq7mDWs8IKJRrTVvUqOJNMO2GzHK1ZLjm2kUzTEYGmzlH0z5jpSaqCxN5WQOLrJfkZdZnHHeqdeR2yC7p3SLc2GJ0uhY+cqHtZxPRjYVNDVc25U57Dq8Pdso//446AA3dzLHhBqb/vZv/xbXXnstfv3Xfx3XXnstZs+ejfPPP38ib/ELP+oeosY5wlaLruZVS/XCdSmGJVh0O91eZEziiBXvteMISnVNIlZSCKm1+LgW3m5VMiim4jNbkP+nvCO8oOBdFpgtU5eEIZ6kVV/Zl3D9lDpGPizcfB/GlDSXyoPlrxGmAIbGUrN3L+Hsuc/NRmUZmMRAYgj0RHu0v//97wMAPvShD+Hmm2/u037jSKFdgH7uWCeCJTXAuRfnZaSUe3Nkk2qYsPEB0lBm8TImGMtZxcVKvxIi1jSexPN2uqNqVPSUNTj76wEZ3UtSXlUDoo0/qp1mj8Pg6K5/PMJ/uS9R+QD/+3J95myTaaCsY8jB3178zlhFxIqPzLOOd/SjWu2jnuj0U43PhvmptIar96YZkzkjDCf/Ws5gajMNjVeaI/uFqCxJ/vXltnwtg4znwnK8RbmpmqipjhZO/h1g0ug4oyDp/LfggCE6SO/Q5l9PbQRCRa9qjtwQHrUWm9FBkJpKKdGBE9bYtHTp0olc7u/tGKjX0O7S6TNWb0eqF2BCvHCBRXeg4cPCMwnvskAMs7+sNz6CvXi2mGGxXfes4anMfC7PljrwXN2jWq2Gei0TLsl8ZS5SKZAXtX20e4Ly70nC6d+TLWytMU+GYZm7riV447vBd8Vw7+UaS5M7iSScPc/gaFCo2LXZbooy7KFxYrzjxRdfxBve8AY89NBDOP300ydm0b8Hgz2jmsHGmhqgrh/XA3O/Lz8TAhFbg4BJK9JTruDP54QzUnHJhUSmzkkIu7aPVuO3WqzT0N1Vc/Rk83uRw4JtEhDyAU4BJHlS/GzhZ8rIZ45uUwRuazSRBAuVGlBGCHnGUkUp4qLbjGdPV17tinR2/y4a9UyoqrpMGou+qwZEjHv0o1rHN9QUXMN57fV65Zk1ye4czVYVWB/2ZH5DpLpJkbRSClWy8choYE2LyqLhdkHzYFf0CK72a3LNXU7mJGm2N5WP6NT0MaseQcDC1Yn0YKf4fCIOhHoKWyNQld2duQrvC2HXdJrIgZ5qdE6IGub48GSOSavZ1B/jH1IVfnMh2WRDQ/4944VrE4eGI1bZeo4glWgo4581rkfge+PDQxnXpEhtv52avqh2uzNYxgvYxzrdAAfkdtpxzSaI883CNBEJVYbiBlIIVxyPFVoUZsuFEUepH6ogUu1OGU0iGEs7vV5JHFM7+ejRJ7qSka1fwRLOtxpLU9MR+2NqB1dTwI1WdKPsuBB1vlg9I5wFhtTwtxbvseat5SL+uPRSTlm3CNxSBFetlp15suZcsI9U1JQES3KhUYLeaYasYn7R1SY1tUUrys1G2yYYvy01wdz5sSKSf8/xJIZWk8pomGMMZt978j4eT9Syu/7xOBG4yDy+QxSNA3oHw/HzgX5U6/iG5qziauSYjcOUvKHQ1ImK6LTUm5Jkd6qeVXJEDme0Y6ODGL1GoDXh2kUzjU63F9S2Y5whjLFXM4TztIaGneo6G0bGFs/S69ki+8ddJJ6Qf93vq8/+etn/8+9So4OMdLL4yMrXxD6GcNdqlcyRUgonNbrteGq9nfCRTf0xMUNMn2GiWqx53FoKFSeMUAQiJFacRTc1BVCL4OGKbFsYYoohABhHsXLOMCEyLESjqJHiGdYS0+g6TJoLu+8scQMPOxNaC6ThDEtoucgDDt9ZQuvM7fnfhWtH8xUiznkkTMXKBYOjxCSOOyKDEVr6Y2qHJoAA8KLs+LSGfL3I2BivB9DnyBXM4m5ecbdDtbC11RCvpvXa6TrVyrdR4wvtcwK3tWEBl36tCf8d0vAVPqd//8GGDIvKwwwCtPtbTiFNiTaIFBdufoNOA9Yi8ywykvt7SvE2OxGUs8R2FYucYDwf4DqQZffX8Z1TuiqnhneZ5b8pox/VOr6hRWlblEzPQdCw45kVbzSFN46C8e9dzidovKmgPyFD8gWQ6X1kC1sn0hoyqpeiNbW4mQbXjVmNsjLgQLdXOVAt/KwyZMVwu/cPI/s5RwurSxqiVz3nRlIkrQ87n4adr+1PV51zpmhqBr8K2K3NfXjjp/9sEuxeVLplvuDknqxBqLn98XoPSqhLja5I9WSlhNpr1mIgVNbj77PP+VyroYwMha9uZLOMpzGs1C4ubLtuybrMMCwgLUIsdE5qedzcs6bUGuKK1Gb3pxgc/Y44ocXiBUgNJS/+K3mRLVEQlOIIOB1fWGWwuiZ5GCgFP9VYyhUUnwgloz+Of5TGIEYwA7j3768z7q5ohPBE42L2l4oqZYVEoyGei2rhIk/I+juC8C/VnDO3FVYcICE96nHvlQrHNxgcKYGbD8c3Cv9CeL0Ej6UGIut4SizKnRJ9pBkc2fnWNAUuslhz3lgUF8VZAsArCsylZJRng4n8tUZK9Mfkj9AAWwy9zh6trLPKPVFGgo10DuUwlu7FtAAQImlriOZzOkf2eyqaHuT81Bo2WmS/LZKW55VUoe3U7A5W3yOe1f0pV5fPAotrrEzJqOCi4VJqkJLziawaNiqLM35ykeOsvpd/z+mSBt4H0DKHFo1q5TckL3P5NocDBj1iMkff2DQNBy1I+d+Fc+1MAvR8xQhjMXq4v3WV9YlKQyIPsBvZZPCmqB5nzgjHRtj46+gCKbE2ybDivdFCa8M0utSUGzVc1iAcF/Wm3PtLsLBRDQmhuxZvvAdL8F04N5vvwKIZKAMc0AQ0S1RDdi37axIWFQOiVUHqj6kdmucY4NJnQiWTLtbJRVdICi8lPIlReUZaqtfuo3HX5PEUzhFl6OcEP73mjT9fMghT8JDFOrlUlcDTHP4/tf5HigMkvH/2OZ6jKUUhPHyEDSJYALdVO/es1bVUg6NWF8VqPKLqf0ieZsnQK9b/SJDBUhsL9NOpp35wEekpETaicZjABa6maJ1QpgHdKM8ZyixdgcsuZ2QkYgwPa/Cv0fuoR6Qb+Y0gi9P8Ji7fkcr7dEO4A7fzfRzxQ5QSKWlwEB3NRvYXayfSSW6+kVfSwQU6naQzAbzpaiSfSY8QGlJIhjWujIDZWaEZnRMimKmzN1mjb2yahoMSADQl0xz2zxAIrTYCaSQhDkFxyWIBHmAMDaxASh3gRIuupnxzxcqT296zkVNxQV7a0EAoVIxwXIVL07BzTCUu7ujfu1yf6sRQvCNrfQxFqbYLxwWsNA6kFMGVjKV0bY+0FMC0s4Ro0Eq1v1a5tuKt43DgeGp19Mfxjy7z/jklkz3TXBcqBhepMy0KT0TIvGZoCGlpcpRo/pEPI3fnFvQlAp2MmuH3kYadP0f+9y4sLqwx7BQsNF3n5pujshShlfIch/fn1tciqDnYzYWtS56n095Ug2NyWgObIpQol1A8yVBwmHSaGRQRIN3h1x+TP9jIfs7BmWgcFiOpGfm018siM6v5/loxLP4zpRSHliJpq4L+Duwd2pFb6UBBF86CdjDphWwUuMGoYqm1aYm85SL7Nb3D0yN68fclLIQho6LZPtysYVsx8lmDBUh8dCKPwtR9ufupDfbyLPnTWRzgHfpC4AJhsCHrISpOJXuUFa9fiesb9LHJHH1j0zQcpde5oyMH55liiRWBeKIXTkBU2aIbwxJH2Pjfx/P1dqseszUwiRTvpDffqCCxhgyKQAie2JRWzVUxRX8NPvUjXtubzwikXoSNYBkn8ZcjtFwaHet1jiM4pLpdlMGxx7wjv5siZRQEOd/MbIWzR4djU/gr1+HiFXwE8/3v++P1GVqqjTvH/T+bRmdUXMhoRYEejSsNiaOliUIrlwZMRduGRgn39yaBW0kNsNS8kemRnZ96ArRFcWFTCeL1OFjc31qMMHwdLgZ/mYgyrf5H+FopWKRoAyqSj2uIwRd91zr2xnADsUOG4r9cZFNRcDhcU3WCBWSdb/4Rw9sfUzO0yH6uSDFnHLYYYSxdDyl5g+0gyjoJvcsVDlM6DaHv0sp6fm+j4YuLihxv2itX3zAcklGQpR1G3kfRGvcVsAZKA832ZI4E3dOcDUIYyjg65sJnMVCy+Nuh3xOnN/PGUkTzuSwWQI7kS+2EzslXvMPdh4XirVx6+mSOvrFpGg6psJ9VOE7xflq8cPZ8ZYnB2aIrOO+LmAdLESvqwBs8fCbPjgI775GI50rCMaUgsdFBwRoq43fW7vV6LLOlmAoHizufVgZDwkkXhuXrHvnPlsEi1e2i8D3/TjDyWQr7afXPLIopFzXlzafoAOOtC717KemI/TH1g6NH7jmxhWLTCnJKV1LJ25USkcPRUs6ArIW0W2qRcEVP3fuZ6t9p6SQGxSWVHnE8rOhqE8LD0QDd+O1dLn9vgcW9ZsEBP60Bzv91nKFh1/FXht2fY4EldsbkayVGnKSVJohAFw2UVuU1Ne2uPyZ/TESdPc84bFCotbpHQKjc+7CGa/N4RheqJtNYCaSnutGpnfTMhoM0QwMVBWPJSqDkZVb+jWRIH9ZyPkWziXsXQwpcEA02Bth5mUOGhdKByNR9QRY3R9IykePUvkjr0/IPyLke7FSUlTGySZWvnOldgd9Q60vBApM1+samaThEoc5qpddC9pzpfnQQDUtybQ+HQPBeNZpYcd5Mst6FcGhSjB6ecOztjRZJQu87H2XlRszE947XhzO/eFZ6bigvqkKLx/jj78vPtfhZuX1055sMZYxypxayJNJ/SNgJ/C3+JyrVhgg0TuDiIvNIb3xRt0BSMqhOegwd6PbCMHhZsOh7tF/f0WMEXD/KTsdF1mDDegKpAqz8maailTjay9FSjgZIwjwJ+zgjBMlIS0b4twp+NOwOrAZ6xHnggTR+ShnVfNhpZ4+luxy3PhttUHPxt+v8X+OPNP5a6irJ0QbFe43XTjXchp5pysEmeZopxxOXpsnBk8yTmGft1+57/YYmt/FKZmywadRrRAfRGM9YGdL5rcU4zEXEsbI+IUNaDA204eA4lXUG5zmjCmloEFKoROWec24YjcOVIZxJozNEGfP4hWiODHvMP7z1DfxJ0oE0fHcHZygrYA9XZ6OJFGOWNbotBQf0KCsGdsbobJH1JT4/WaNvbJqGg/KusoJRqXz7a7DCseDNpOZLnlirUqKmITEKEtdxgPbGR6CI6VxcKke0fqHcG5QG97e8EFhd49psutcstYO4NDouZ72EnfB2ULBLBhhSUKDqwWjGT6PBUWL81PqSYU1MF6JSBq0KEosD/nouXGJRWwvDcoVFBxyNOfeVjNd3FPQgVBQA2VjOCkNhzbmOMt8QLQEwtFfxHEfzNacDQV/I9QXlO7m4uTGtKEUBTI0UFut/iPyUU0TSeJK1cChptOPSbOp0VBbnUdUMZRYFU0qlrN4rkR7NyAJx/TuaX1NnT/I0U46nat8j0GmHX3GujfVouJpQ3Pz+mPyhdiIzyJCis7VG4BmXZcAo66kRdFztPCrah4u49OaTCrI/l4sC1gxffipa1UHUEk1vMsob6twmGz0oA2L+01otLZMlhMVN2bVE5FDpXN58g+zOdS/kYNcaRgC+7M5FNqXL7oReYIiktRgo+e6nsr5Hlfqo12JZUpR/+samv9+DigzRaiOkCseUt1Ga7zOJ/DtJOCYNQswhYIpysxZd4tBQAmaSVd/5uUm544o7MkYSMiJHIFZkni23L8XawRpsZJMAC8ALsJbCsO76ZLhsaPxUutFZlJLitxSzJZWS/L+SoECmDHLGIysOEPWmJAWfZBKc0OK2rTV4D/vGpukxRCVTiBDkImw4we94DZ8UvmjeWndNb33DGfWibRnctUbkiFEwDCz2fVRgT+CnEi2l0oBZejQhCqCRHjHdp3zYKVg4uSQ0kij4TtFpiSc5y7PGUqLltvscFlg85w0TEeArjPy+F5dIQy9nhDMqr/3IptdvpEb2S8Zh0tkqGaeYGmjuHECSw+j0L90xR8AiGsos/Kb6TBblthhgBOMw9awWBwFlDIgcv4lRWanOU6neVAgLBw8bLMAZSxmdjIxIFg02MR3mZYjq/5boI4ofuL9lU9TJtdN4pZUGs4YvSr+yOKwMxs/JHH1j0zQcKWFvlMAI6CF4di+cf3/3XlalRC9UHdSZSVCQOcu1O99S88QljJTl3WTEcP4fRWURz2pRMiw4UNzKHI6tKEhsjRTiWanotpT85uQwYtK7nqgkB99psKd28uE7KCGaL0UJykp1MJcRFtmOFgQz7I+pH7LQmv014aJGSxMMn6K31uB08LyMhFeSF/5juLPvQ9gpgTtNaFXTs5KVKBssVOHb0rtL0C8pxTBK51KEfz4azsZPZSMJP79NRPBY63/oXXIJOUOApWvgSZSBz10/pRV1vRZ7miUnGNnZqEEou5oyatxHLoqrPyZ/lEZERnZnI/sNEePZ73k84/AGCBwQnKGBiwBVZH3ScSbIYSZHmwu7JSpLoB3kfMIQzvEy9xppCDfI1i48nKPYk8UZuF1YLA7IbA3E85VoOBYHmKY0fvFx/7mssIfzvagsgheHq2uGXtbJTe4LAXtC914tOymW3fz1vLmS4bYf2dQf4ZBCH63pMFwInhRSJ61vEXQ4eFK8He58Po0unkt7BAVlPSL61f/9+chh0fddSp8YIJ6Vs7pn8NiNTcU+9VAzpURUQogDi8dsfVgkw5c5IodJt2DDiBlBhCScgtBCR3H596bgSTL0soK9DgtXCN1d31Kc31PwDQJa36M9PUaXeT+ATKv5cHx/DS7yk4qC4SJgsms5LTV0mORwUTXaEnibzbekU/vfUfB4+8icOz09xMAHDMbv1DQ6yjgVheMXAm5Y9JSLghFgp4r2pgqtVDqJmtbLOs10PiAVPSW7u7KGW5Cw8IVy/fXc30pyid++3CDHEAXxuYhr8z4ySld/TP6gDCqA1Jo++2uNMC/Pdyc29sZpqdX/LfIDd/6KjynOWbEch0X24aKymPW1Onvs+aZohxiVVV1TsxKMzlbqvBZ7bi3FkBq9WqUj+nPZ9C+tC6C3tpBGJ0T2S/Npfc+fq9WbsnQ/FfXghGAB1WgXyVdxNoit/q9N5pis0Tc2TcNBGUnG3cXFImAW1t9a7IWT6yRZCYS/VjlXYbYmi67Bo23xgPsFEnWmohntLCHQojdeWJ+DBbAZYSociMN8yfWlfRQUKrJtrcFTk8GT/bV4wG1RVtW1HgOLu74lKksz9Jo84MI+yh5z+pyG81kFiQkj7o+pHaLgJxkDko0koOcblXXSaGsR/slW1/Q5Ylt6G4Rczpid3Q/x/AQPvPsc3Dmy1kOYkK42WrefEHaGX1POHtFDStBeUzp1grGU7Q7EvSejEkWlR3L1P0rnTY+L8kiQkUQeg2g+jQP5/Q38N7XDGdUwpj+mZmhlJOIzEkejmhRe591yMqcbGUIbnw3nz8FPzmBDySbmGoGsXFX930JryEYtYgdRqplGcW8bja/2nYkOYpytlk7SkvOUNKwJ0fRSFoMlutSHPaSrlOzOw05GWQkRZeT8bqXbuoMy8kmZKam8UjTyGYxwLjycQ6FL4K9VH5Mi8yZr9I1N03CUHsrUEFLSIIRgfj63Rxz45FDGGPaUyCYtDWnihDqCSRi98UmhuK6CZFAEuOgzdn3WeFT932KEkTwvIuxk9xwb0dc8Nb2e30WN895TwjFXCNK95inV5b2j6XJtLYN3D+Aj82iFvYCFgh0x7Iyg4H5O2fe+R/v1HWJkk2RsNBg+3aKnfAqzTVknBRbFcACEPCz7a/Eci3UEJbpOCtz1aH2tFhBrtGOe1eo5Tm2jTdeckw0wET9l6GMFC1GoWqwBQ8AuCtzU+jQtdWljr9djFSlKKTIZbknHUzCXc94oZ89X0Gi4AbnGEz2f7xyZ2kmvzwemz1DPa3RGsr+UXiBHFuoKr3vNZuDhz5/7vbS26NwQmiTFsk91gKnadhYnoWvw42rhWbrCuvBRhjXeaO6vwekGJOwl3BEoYqSS1aHA0ppxG7Z1vdaDxZjFQNXWqmCh16Zqs7rPJsFiCRYw8Q8muk2rb0jJBNYMCSlYYLJG39g0DQdZFFQR0gCOMBtSEFIjbBgrPVAZGsiaFEZBh2OIUvirNTKAU9ZrtVpJkKh955R7F3QvFc0Au1RjQqzVwexjCANHrKT8Yyq6TVZKjDijCMfunOz/8feAWzidCA2nYClTS+JWsVKbaUsRbw5/ucg8uc7I8TH+OruPdgWpP6Z+SEYSSiAqBejESMuQD4iKSCItDelXrVZ1IvPX5/gAFRae0yP02O4qpNIlGD0oQxlnxOj2fON3SnSjWPeI9KpLAndxf4MsQAjE7vq8A6S6VvE7oeGGwQHiz4/XTzHaUbDThdN1xcXmaY7hdf/PRrcZZJ5s/RwfjXUHaZlKlgXYSAmjgbI/Jn+UNJJ5V2wmgMEYBDAGIeG8SpEhlvPnNZkxRG9YZB9LyQz3oy+3caUbYnj9tG2dt5ocBOR8fy57XjnaRK2d/5dKfSbr7Blkd0tdMA52NVWaekdE5IKUekkXQ8/+khkVwVzJAAPwkeDtxHpTVHMMjt/ETmt6fVpHyf7Skd3E2RPkzskafWPTNBwpXjtNMLKEYUqhibIHPIadti77a5VrM5EhfD2CGHZLzq9F+XbXsBgapI4TAN0KOoKlIxBOwTvCWbqz+dV1bn2pcKsMS3XNUpCXUkq4fcngoRRZhtkaDIju8/ih5LV87Wh6klLNhr+qzLa6xinggOwJEhlcgqDQ92i/vqMSnuLvxDoXUbcURHPd85Ri+DR7GRnva/Y8dgFHcmhQslDx7JZIpeyav6Z7LzEl2UBjKBpggsVAG114LFEwbEqyQo/MdbskJcqaStDz7x3CQu2Lu1Y03xgdRMoCrDPGiZRIiC631CdzYbF67JNSWBnjUSlTMelQfafD1A/OOFyWEOA6YhHOVivtkEoOJEV1C+fP/b4YknNDLGpMKNThGeEdxfR8vftpAEtCZGE2n39WS/1Bf31/bTotzl/Lg6Vc3+golozyLP/w12CN8uTaPpzuoOrspTpnS6dV9E4Rry0458Zdl89icMzn9no2h4UUjELjY/x8kh4xWaNvbJqGg0am7G9yJ4aUCBtjWKVczNK/vzc/hJ2o2O/ei02fsAp1xHyu+GIGu31vqHx72RPrr+f+nxYwifmMYM/igKZkONsuM6AYFlM3DoMXeSARfymDTWqR7eK/VoMNX9tDZracwOUzfpBru7+3ptxIgoKlZk9/TP2w0C8Xv9ji0FR0kMFbaxEq3WtkNMZxplyRhrLizMVLi40faBoQp9GZIgQ9GkB3JSWjd8R3ykdxSVEwFkWn+NzrhVFZdsOEKbWFMGiGRgx3DfpZ/blk5IPgvCEjHyS5hCwfQCtFXLOQlFS01C5L8r5TckkOKxf1x8lUhojI/piawb0rrv4KnRJF0yWAlq9Taw1pkdF+xIyzFhfZRBnwqagWSdaXzojBEK4ZVKJIWiHiy96NmTE0uPKvQceiYO+V30WgkI5isc4eKXPIsLhOazf1OaWZht1o53/nz895K6lH+HMpXU9yzsm8LE0HErM7DEEa4z0bVufcZI2+sWkaDtlTRs8FEguKG1Kc3GupRURNDIuz6nMeRMEIl3zIkr33dsJJpaKV8zuJsFDMmdnHGB5/LQl2uXYQDwsdzmrHMa6wtVZ82FqsnPQwFN8JxlKq6xaXksoxWz4EurpmUfCpKEHJA24ylhL41R9TP6r0VSPusmca0VzfW8vQgOOIxpDOHWWI1Tx1FCyU403qpEfWESzONEEbpZRkv4uaD2sEO5XWm2iwkVPR9DNN1W3zhH9TOH4qPUpTADkPP4UvFvylCn5TsFfG2Hh9Ti4J1+eMiJKhLDWC2u5EoNNP2DRQJmKt35X09RvU3kvKulx4mqfZVGqZWf7l6B7llHMOL9+QJD6vFJ0UI6FIuY0yHijlO4wR46lRwAMUPVB0mgxena7SOBCvJcGSLC8bnNYFrfEc7gZjqWi0I/UIIZOliFbqxLCHhg4qA0dukiQYsqw0XomOdtd0YbNECYo1dKmz1zc29QegGGwEYmVBvtRIJanQmYjY5PrBXCVXlQ0jTjSUWXPWU0JI01OcCGJlgMWa0lfc0kKsUowSLuyUsmbdR4uxNMVIYhfU47WLV0AzZ54J8Smp1TUxui317BXP6kWT6MKiyWjHnL3+mNqRHtFA8wE65a76PiWkPbWDlmT49NKMi3OXYLinm1DEtLTCc74Om6l+lGv8NvA8KbXFbLQTnlWMEBMM9wV9dG0IFsP9+Hl7Ih9g8NdPS+dhF5UiUolCDoueOs7xJM6YVfHT6pqY2k3hI2NgyGAfpzyYT5cbBfjw9sfUjeLduVvvnVfOsO3MSXW2Wuqz2uokFbKJc56cB7HUt5QzJGI5T2oEI6WXceeVcs5T6cOk8YiRCd31LZFQXnMfgzGAai7AGSfd39ujgwrYdecJRWskHBh36r5VRiEj/4r1/blkfTIpEpxycIkyynhptj5f1oN5WPqRTf0RDUnJEItDGwi5hKjWcEDRo0110lMOWRj2r4URW4RXgGu1mabcaUYSe4Fd8PNTo6wEQmvad4kQSrATHgZJmE4ltKSyaWi5awsLJoQQKXzbwBAlDxkFj1SHS3qn9jzxGAbWG89EFfbH1A6JZkhdbTg+QOX8U+unRHG61zqe8UhQ7sX16bkU3SUjm/JrdMFvYj7F8woBPRLkqv+Txm9W+K+uWYpD02vbal/xjqTq/8X+iZ7mcQr/FrruzieFf4Ph3sNfzkiS6gBxFXXmnbo1YCyyhsSTxH00GhxpmcpfqxiUl1xygPT5wOs3JJkNiPE4tTmKWBjYGMGjOq0dtBHb2I/XUEacETHtjpTHmbWNsniqkT2l0LobLZ/iUHB5X/E/q9FOjg6K6TD3Xv16q11vLjVfMvJZeSWnjwEg00ZLI2LNp2+S/FOvxZHmyc19Ehw5rA7PzRedG8amRwKfn6zRNzZNw5ESoeB2/jHV9yEQ1URojSF4UvEyyyGz5PxaupxxsIsKlRDqG7cgRTTXwmypItjWTgycAQZwlLuEfbem0KTk8muwR6lo9TT8TQ4lJ58V5NrZfP/+gM74qeek5pPpQiZmW12TvFJFNxIPBzhvPIEv/TH1g6N17rUkXCQMjTVKeCo90zbaSCoihlppJJ8xdMYrlfVoZcUBYjR+c4oLJ/xrkU1tyghnNCCKXvLyWatrvAMkht2r28UY7kk6TdVgEviv5HRoG1LHJcN9rUZ4ySklyhBNlGooM0W3EVFZJjmDVOoFgyMV4coYP4FqL9sSTyL2pT+mZlBGCRf/oygYwehB4fwApXxLyroUdckqvITyLRqq40goKRojOQqGPK+xzOmu58MycbTDoqd4zg0KHoNhu5RnSdiLOS4sxb0p2d2HF+CdJx6t6cbPYEu9tOhj1TXunXrzSZyh55ozJBKc+YB8tiU92NK9To4+i0BRspPi+ZM1+samaTjEcEDRwINovkXJTI3IsSjI1CEWc1V7hXBcfW9L/TAIuxTxSbWkRwee6FBhiPgiib4xLFhk5gkGm1TmScNS3DeV8UfTZSbBFepLNSC67zSA04edf69ccWDqLAGUoAB2vliDyWqcEhQwS72W/pj60WWEIUD2jvFpCs7ahk4v1roVVSoB4vmJBme+lhlFj6KlZeO30TPNFVp375cSmdmlDMLG6AHRyJcSsUrA7hkaLN5awfEkCejWLmpa0wo3LceCv96+MEXc3TWSnRSG91Tx9upaqvNGMgLQyrH/XCHcgJtK2SO/B2je3h9TM+rE+bAYBik530r3xPOaYOBpENF2Uiqa5DiRojFoR0u8fooTnabZvB5B8koLzTYYBbkyKHxtRmLfi+7KpCzOy7Niim8irSnW9CPz6LWtvE+KGE3lreHsVD5M4qOBf5iaHtXiffTmc819jDo5aaAU5k/W6BubpuGgDDamFsMGpVTygNMehrR6PaQCzjAsyjLuegePt5uBlEYnMhWyLok/l87L5oVdmvFbwlmNDI6CvSCGYe0rSRE056Bb0uhiWCzpGXKNiTQFSSqoSOd9+/C6z2GpH5VaZ8TE+M3evQJeAnZOcHVg6Y+pH+m4S+MLpXynpnOJAktJA7rRfBp3fXhd2CwpVN3SEB8trUQHWWkpyPleG+3CAWJQAM0KXaqxXDBox+2Za9EcSfiXapGY639MUERsZZiqrlmiDai6RxNh5BMjNwzCv7y2v542XywHwPAYd03JAdLvSvr6jYoHV9dS35WsZMZrSkYVqoaq2qjFQJfc+1Fd0czycoIM6c0/TqNHqY8Rhaet9aM4oyBFs13YOYe7D0u8VjWfWJtxtGTz7d1SPVrTiXklx5/IKF3hndJpd9F0uhh6ue/03ONJpZR4JT3ff65yLocDCp936YZodBbOXt/Y9Pd8kIRcELzKQ0Z00IoMPEJeqzWtSPKApzBEv6ApkfPLMVsSlggU8ZBJniAqHD5O//K/d+8jKQ2k0c64j8kRPMx7lQgtJSjQdb7870hYzEKRz4TcZ5gM5a40ZJkVU1ppp/ZFqjNCnT0xIkM0CETT6TB4LpKAwJf+mPohK9T+HICnXy6u9EojSbGOUZmWhCfSgAwSFsDt/mVQXCgvoBDxlVocmi6qqgu5pbIuRIaQAnGiIiJGE4n0zp9LpdRLHXZS03IoHEiVHZLakXcssNh4DB2dAHa+bJyihX/zO803pkOksMpyScxn5JQMnw5I8/vp1FM/pAgFYAJkHyqqRcJLQe+wNPfhijF7a1MyITE/NZpIioTiughbU6KkTJPjdRRTNLvX6xmM8s5zBs+lzZf1FB8WF3Yust+d7xUID5Yfr05DO6yMBh5GjpCDLgj+QWampPFti8yR5pyjzqltHyVYJmv0jU3TcFCFzixMgqofFHV0Sw2tlZiEldAyh9gXjPy51PpVCGl1Ldkbnxr6yDBbKUzS6p3k1vbWp4iVtO8JxIpOL4xhIT2rFsJpNJZW6Rnd6BlinPHv78637mPpATd7JOh9l95prRbDnh5Rlv2llXBKiSHeq8E40R+v3+Ai+NxrlogGLxw/ny6m3VJFhwXDPWmwEb3B2V+qiLelFklBsylRSIpUkoRQuqC4TgMsxm9zHcEE/uiuT9FqizHLxE+JfZEUFzKdy6rscsZvgX9NSPME0tmT2AaeM5SRCp3O76w1EylY2KK9zkdKAWRTKfuRTVM+KMOgpKyLsg9BKOnzmkibGHpQrN3rOUbN1CjHxPNq6V5HGb9C2UquZWU0HFj4h/V8B/zGFcksRvnivxOxj6TMwTggpGYE9VpcJ5J2uKfhTHL33pxOhrPJKCtGPsmeJw1npOg2Cw6kZneIsCcaqSdr9I1N03BQhdFSCTnb0U1APDOipoazcmlIbhhmIRg5Dx0LpNlfe1oRwWwNBiGyvTcDu9VynR4CTShIHfu+d7s8sRLTLoUIGwoWa0e3tuClbgReAym6rUzrdL3CTBF3H5bqWvFLEgcIDwbHzMmi74YOK3YhJ05hTS3Or4bB93WM13VwUSqAYmhgOrq5a5a0jir2XIvPhakWHxWNkeiksHXHzO9LKVGkIUBP67XWLAjX94xNCdG2JCzCvqTOtxjKirk1UvhHtLYlesCPiBVSwfNLFv6bGrUx3npTlNNBihan61OFsPjfZ2vT59S9Rtbus8pUjNzjpYEGdIBygFB0oD+mZrivIkzZbdRrbFMHS/ROtoY/x1vfGHWpRaMCjuwu0o58PXM0UXH/6lqK/OvCzqYjGo0eYlaCkU62mUYt7hqUc8NSSqTYUrmebxoslMxp2fdkh7skQ4h0VVifkAtCEah6pxWC2aLVqmupmSkW55zJwTUBzg3JkTNZo29smoajQmxjd5PgkIkd3aTQRHMYpiRI2RkWqSBJXrhxMgkzgSAIUGWIoztadHso01ZSw3xTBcwU74i7jyHsyURfCq8WBAVrmkso8Iot2yWPNqWYkiGk/nfukLp0Sfn2xd5IdXLks8QLi8flwWD2ncKv/pj6YaEBtKDI1+sJjSTW6ENbZxgbDUjxZIspfdSZJg1f/n2p+fb0E56WsnWP3LWlLn2NGHaxdkmiwB16bEU6TRjuU6MHUvbR/T9nuLc6wapoWBsscl3LaLqSYqin0ckeeKoOpvCsggIo1kwcJx3oj6kZVIMcqQAylZpc0Y54fQnPxDQkMjrIILsLvEw8T0LnS0qGtBe2ls+rvUmSJHPaeJ8pzbvrz6XgIbtgF99RvFKK4jrOaGr3WkhrrGUhUh0zYkSy4BALwaneaay/WfVgsbPjeHUsIhqV62BoTt0vcIDqCkshzSSNvrFpGg7KSCLV34i8mY7cEIc+wpvr/t8c/iopyKnGLMGLzHZcSvTE0ml00XSH0FbXOG8mlbYiM/7xGY/MHTDEfQzmUoK6qJRIgvrxK3ehkU8ssi3VATHCwhlivfkJ3nh3vnhOpbMkKNVWhkUXiaaZSt/YND1GqnLPdsd0o0RD4V9UYNNSjKkC4TItNZwjqrNRwTPipRWDs01ZF4Xc4GxYip7SBl4edpK+WNO5BM90+F4lLzYpzAvz6Zpz/loULBYHi98sxI6/VieYVCtLNvRW1zj+Tr1T2UsOAXZJGU3jecW7tKRp9tPopn54MmRQr5Lu6ObPATSaXaxN0CazrETP985rIfsYaOp4I/Xd/1sN2ynn1UKDrTKnFBVpceR0PH4Tym1ELcReMZfXx6wOArrzpZ3Pj1enSa9ZajUI5Wsxc905lnqFx5MCmGKglLM7Yn5gKrZP8ad+ZNPf75FusMnn5Ahk6ehmKSLsXiNbigotTqkOAqQHI4zIsXjsrAeeCBE3RRMZ9sZV3jsBobW2ck0N3ZUIRBlNFMBCwk4I9mIxYYGRpxp4ZGE6fwYhuk3y7ln3sfifWJvG4DXwjE0F/loiuBy5PtXTaErVpJgzF9nUVzJe15Ea3cgpI+7nTiD8y0aMVFiqa6bweovRlgr1L9eOlk4W/lOF3FBAd2lHuHxKJ1j3mqUmhgsfJbRanDdy+j2itZPpS2K0AccHXPpX7HdKEXcfFiKdOuCPgE3xLmSp8dbQsDgHXVisfCDFS55a56Q/pmaQziqT/GBU1qVUHqthm5lPdT2UFF6pFpBogPHOiP+dNp/PqEA011JT1EyDx+koDveRWp8u3+E/lzdfkN2laKJUo3yxpmS0kwMdYtjH6yCg9b0QlkT8TU19JmR90TkXnD2x1mKysTSGXeJPkzX6xqZpOKhwQEmhLoQrU80bkpjk900NHxRDQinFQRd2Uom+CRYytFaChUhfTIkkoBQkAnbReCQZPQSGVUy3MCzAVaiE9K8Ej5cH+ziFIjm6zYfbDAsltBBUn4z6YhR8GgfyfRRCw83piNR8kSFKSow/l1J4+mPqh2SElRwDcWps9bmIfLEZ4m0CsQiLlAZhwHWp5bbV2GSrI1hdSxH+XVjCOipSkwCLcO7ex56K5n/nzQ8cLJIQShnu5XRERPMtHlUqrUEy3HdLnmSh69U1i5zhkjuxVlYo/Ds/5Jw3VhwYINKb0gvf8rBzNWCsdKA/pma4rzrEM2stIEtEHGmwSXXOig7L4q9+Xq0Kchipr62flLZNrg0VFvL8iTVLq2uW6MLQOEzBTjsI6LmA4oCkcEboumZxopeyuCGwwJ0vdsFOdG54ZVDy+eFrpRzFMv5SEWWpeofAn0K+LdYuFvaFwkfKOCXAMlmjb2yahoNUqAWraJjDaelAQ3VlsYa/msIwE5WY6MCbveX+fSlYPNhNhfqqa5zAS3qlEpmtjXlW10yhuME+krALUVmpiqk1Pz8lYm1SYHH2nfNQu/e0eKUoHLCklVij/mgmYYfd4o13YeiPqR9luhjB8ynhn+uw4/4+qv+RakCWcNfYrj1c38VFro5gr0fVT4iWTq6/QzkRRKG19MLDu49Ej8wpExJ9ERwmqQJ3SEtF45EHiyALUI4nYd+ptN5yLwN657XRTjGSJOIA2YHVIPy3BX6a3NJbanSS6kQw8IHU1Kn+mJrhp9EZZB/BYGPPBEh1Ksawhp/LLsKJzlMLztuN8v6aUoMc2vHL70tFx6prlqgWn8b7a7kj6n7q/C6cHgYWAFWkPmnYpoxHAu2QDY7R9IjWiDXHiHT5tlTfkKCrcvQRz59C0D1+E8gcon5ljVYT5ksGSqojtyWNTgwYIemA/91UjL6xaRqOkqAYFeowRNViFSUR1WihtYT6WouXFbcMFaTUAsi0cIwIdonBpXTjEMOIJ4DZVrDYisRLNZtsUVnxc4WwHE+R+BQPXLo3XhK4sr8e/gbfqbAzOOYZm4JoEnOXEpPCXl1LqtUhGRyJ6Lb+mPrxhpMGcf6ZJ+ONp8yIvpNogKULlaS40CHq2V9rd7mUiAn3PuI5CgRuShQKDQHu72QHSHVNFHIDpc5iPAKMCqNkLDcKre38QUzFzRNqPaqwCHTdyvM4Z5L7+yiNzqxI64pLalHg0GhHzaeirNILrftwSrC4z5EU3WY81/0xNYOie5YUJ6+mqGQ4GO8ZMdB4qri5mAoqOAjkZ43lMEnv6Ab8g4LdjXIsnBsmIx8pi0fTyaLcVVc0Xka1RNLSxaHp58zW4HHAmt1hoWWhzCnyMlI3jKYzuqqAAwSfr84HDYu7prw2kmBJTgEMHVzO76IC4aKjReDDxvmTNfrGpmk4xFotBiFQsopKIXWpIaSphTtFy3hXJ1YkA5IE7wYR+igRFIrZMsycUjJED7jAbMX6GNQ+CsQtjG6r1QhiRdR3sRiyaO/98ReJ58L+rUUykz3gPf87D/YEJuHeLtxH0YNlJPqUsSGl252lo4UL8y/C2Lt3Lz784Q/j9NNPxxlnnIGPfvSjOHTokPibr3/967jrrrtw+umno1arYf/+/VMDLIB/+d5L8cyn3ot/cdel0XeUkWR8nWHi+9L0RY9wTY2ECj2e7nNRn8PaDxTs9LnQFRdz7TOmDbH0nO76YlHuVIcJ6ezxn8uDvcbhAEVfCKeWsLZE1+k6SfG+s0V7CX4q7yMEWGz81yLHUMZSThagPPYkXac6RBX4a0w/sXRlivipAddP5JFK+/fu3Yt/9a/+Fa644gqcdNJJOP/88/Gv//W/xoEDB6YE3lqtVqb3WM5rqtGRdhLmaxlxwZT+VabR8WtTDgJLlAodSRJNjyKhREcb5dwwOFo6lDHZ6HCXaE3oQK14GS9bu1HAEj8gDTAmg1A831KqRMQByXhk5B+2Ol9FoyEnmjqYnqy/pUY2CXqERXZLdbRITmvKyCfxj8kafWPTNBxUbQRR4GUETCAmKKQXziLoEAKjrJQ461sOTsoh8wRM8LAIhjWpzTTZkjjYG8rQIHlqSgWpE8MiExT3Pv5aPjw+IZeIPlXfxVSY0uhlSlaSQyOJxGwpAcqQUuDCXvzUKthzsNdqtdhYaklvoIQ58z76a0nzLR0tgF8sr/aHP/xhLFu2DHPmzMGPf/xjPPPMM/j4xz8u/ubIkSN48MEH8dnPfnaKoLQNiX6lRBPZGxbk6wj0yJzWEAitXmRIgItUZ6NK6YpxM7W1tCzk6sK/xSjhzkstbD2RQmtoyJA77GR/ybRe0nkjwRJNj2Hp8jhA8lMxIjrHR0M9KPd5rJ5pqY5g1OHXOXdRpESi8H+8xfZd+CJjqSEN5kQeqbR/69at2Lp1Kx5++GEsXboU/+N//A888sgj+OhHPzplMBfvu9h+S6MWc0kLwuhRydcxLJKjWJT1S4eCnqJniXL01qbOtyQXGoxNZFRWCUu0tMg/7NkgNCzZGjQsknPendcjvivnBwYY9z70s/pz3PtYDB+pKedcWQB/7epaSgSzlI5I8RvLc9rTQH14gTS5wBbBRcmF0XQxFZ9af7LGwJTdqT/MgypGZjFMhCF4FgYBaIIO8rV15RuIDQcuPBbByxSl4hEfe3iqBouUvhjOL9JWuj1bVJYUOm+pu5DNN+TbB4yfhqX6v4XBUXnflrbnJIMzCFFc6Ku7trXukVQk0yzYSwakWg0d9OJuHBIDInDAWiNFLjwbKEiGUHLA38sTeaxYsQKPPPIIXnrpJdx0000AgK9+9atoNpt4+OGH8Za3vIX83b/5N/8GAPDUU09NEaS2kWok4fhAah0Ye80NsPM5AZqCnQppl2pZuWkQ4e9SDWU0n6FhkfidO9/kJadgFx1JznyTd7fgAwZ8ISOP+LVJZdfC2wV6VBjuO92eychH1S4Zv+JNrN/w8V3CX99YmilxFsMtKfwbor+9+QZDmaWJyonOA8ZD+6+55hp897vfLT9fcskl+OIXv4h//I//MdrtNgYGJl89KuSH8IyYZUKBBqdEabvXrPPDTANTulWiTEhHtUTTY+OwZ2gIZB/nczdwhsjyKZFaZjh/7m9FnSnBWZGt2UMDDg5IBhiXfxRRl8RGpsocUb3gcesRNpmjK8jLkfzr/C4Ex9XfTLonQSeTs2QsBkqDPlYGFvSy6LZareY4iWyF1iVYJmv0jU3TcJBWUYsRJiC05rxZwTglFSmWojHIQrIpXjizAca/rz8/rYNAeCh7vV6VcsUIvGOdrkmokyK+pG5O/j7ysIQh0BJRpgxlKXnZgKvEEAyrET+rVJg9ZCqmVCHCO2KtW9DLK8GkMjiW2XZi/DW3MReEkPEX28+LDEq12zyB68RWNIrxwgsv4IwzziiVDQC49957Ua/XMXfuXHzgAx+YsHuNjo5idHS0/DwyMgIAaLVaaLVa4m+L77V5hc9yrN0u55bnu9OJfl+849HWGFqtQYzl39drvWhur9su1yvhabfL+0aw9TKcajn3bXc62Ve9GJYC3cZaGezHRqvvu502WnAEd4dQjI61MLMBjI5lsNQR71Ov28nv341gQU+A3dnHsqV9V4I9e5ejY9n3jVotmtvxYB/DjHoPY/k+1oh97OWwtNvuPnbz+d1ofi3HgRaJA20P31qtVpmWU8A+lsNeqxH7mO8ZhQMU7Chh7zqwdMvn4mHPnnW01Sm/y2D3aVK9BnSQ4UCr1cBoq9j3icOBtoe/vXKtGPZsZLBUOFCrAe3ynFTPUoxjo2OYMVAXcaBgKC7srbYAe0EHWjHOiPgbwF6vx/jbDXDATpuqkTJ3ssZE0f4DBw7g9NNPFw1NE0n7C/khw7OB8rzWCZyv3lWFN2Otgk7yON/xzki3/C7Cm/xvQbM9GajTRqvly3qF6HdsLOc3Oc2ukfyGojUFzsew9IgzUuE8AXvAb0YdftOL+E1Fh46NjWGgNlCdEYHW+LDz+1hDwW+qs1nIYj2Cbxewj7Ys57WiNaNjYxisValiIs0m+DaIfSwCiT2ZoyfIHDnDKflNgdfQaU2xRxrsY859W4XMQdLsgk7mODBW7RXF/xr1GrqdXslvirNUA0HTuvFZanV4/EXA+4rn5mHPRslvSt6n4UALjXqt5Dek7EaepRj2yab9fWPTNBxSjj5p9Gj4SqYlPLWYV6/XbLnT1sgmIQzzeNv0VgYYt1CfVGckh9caElrz50ih8xnsADqV0Cq+o8AQkD2HwWtEeAGSOigxYZKFoayAuaoxYUtdM0U2Uek/BoOQLYrP+k4J2Hv+dxQsVNciPuWma2pdTEfOgZ0v1pqRvHtEGLGURufi+Yk8tm/fjrPPPtu7NjAwgDPPPBPbt2+f0Ht96Utfwuc///no+qOPPoqTTz7ZtMacOXPE77dvqwOoY9my5Rjetwy9HtDtZSz7yScex2mD/vxOuwGghieefBqzTgaW7qsBaODQyAiGh4e9ubuPAcAAxlqt8rvVG7L7bdywHsPDr3nzX92arbVx02YMD28EAOzfn91vwcsv48gaH4f27s7WWrhwEQa3LMShVnY/APjZI494EUsZ+uXfPToHpw4CC3dm96vV4n3acCibf+jwkRL29Tnsa1avwvCRlf78/Lu1r63D8PBaAMChwxnsL77wPLYv9ffx8KH8u7nzsH9VD5sPZ/drjY1G++jC/sjP5uCUQWDJtgz2nTu2R/OX7M6/2727/G7L1gy+5cuWYXiPD8y24rvlKzB8YDkAoNMtcOAJnO7UlZ8zZw6O5M/1/ItzsWdFD2tHMviOHT0SwbLzaP7d6Fj53crNGXxbNm/C8PAGb/7K/Lk2b9mC4eFNAIB9OQ4sfPllHFvr40CBv0uXLcfw/mUY7VR79dicORhq+PuOXrbWY48/gTfNBJbuze53cORABPua/LlGDh4y4cDaHPYtW7dheHgLAOBg/p7nzX0Re1b4oIwcyL97eT5G1/WwfzS7Xx29CJZjznMN//QRzGhUOLCLwAEK9gIHVq7I9sodWzZm3616dTWGj60CABw9lsH33HM/x7qA3Bw7mn337PPPY9tS4DUBB0o6MNbyvtNokzuOHDlinjtZYyJo/+7du/GFL3xBTbueSNrf6xQ0+0m8eSbK8zoqnNdR510t35Lh2dat1ZksxuKS1uwp5+/cleHSksWvYMbWRcHzZ98temUxTtr+Si5HZHj9xOOP4eRAW+zm/ObJp57GOScBr+zJ7jeyPz6v6w5max08dLjiN+tzfrM+5jert2drbdtWnZ/9+Zl8+aWXcGh1wG/2ZGstWLgIjc0LcTDgN67403ae65GfPYqTB4AFu7L77du7xwT7hk3Z/Va/ugrDh31aU9Khta9heHgNAOBwfiZfeP45bD7V38eCZr/wwlzsXt7D9iPZ/brtVgRLy4X9kUcxcwDo5qaK7dsq2laMgt/s2lXxm207crli6RIM71rszd++3Zc5AKCVv+enn3oSbxzyYT96JOc3z7+AncuANQcy+I4dPRzBvoPiNzlt27RxI4aH13vzC5ljkyNz7N2X85sFC9Bez/GbZRjeuxTH2tVe1Qk5IuQ3Jf4e2B/B/uqB7Lv9IwcrfpPj79o1qzE8+qo3f0P+3eo1azHcWg3A4TcvZnvljhIHcr5d7FW3045gOeI810+Gf4qBOrA036vt27ZieHizN39Jjts7du2K+c3ybK/cMVm0v29smoZj3MWkE9LoivXrqJkKlFpD8Oiio4JRJQwftBgaHBojRvtIdR0MobtSgWUgNmSkGNXc35GGAzKCp+s9lwi7EiYZReSIedwEDqTWJpLCawMDjynUmzTAWPfd/46CpYC91+uJOFNcijooCalF1k6NUgcMy757YcQB7EVx0l7P38vpOD796U/jy1/+sjhnxYoV4vcTPT7zmc/gk5/8ZPl5ZGQE5513Hu6//36cfvrp4m9brRbmzJmD++67D4ODg+y8p763FPN3b8XlV16J5u0XZUb2Fx8DADxw330442T/t59f/CSOtFu4/Y47cPk5p2Fw+U5g5SKc+cYz0Gze6s3duv8ovrDw50C9gWbzAQDAkp+9Cmxdj0svvgjNB6/w5u94fgN+sGEVZp37FjSbswEAf7L2eeDIIbzz1lvwrkve5M3/3p4FWHlgN95+7Ww0b3wrdh0cBV5+GgDwf7y/GT3rv33xUQDA3ffcgzefOoRDL28G1i5Ho4Zon5ZtHcF/XvIiZsyciWbzPeVeYddWXHXllWjecZG39srHVuOxretw3gUXotm8EgDwpWVPA6OjuPP223HNW/339f+tfwFbjxzEjTfdhPdcfhaWbhkBFr+Ik0+q7leMXq+Hf/vinBL2N506hJ0vbADWr8Jb31LtVTFqS7fjr1YvxhlvPBPN5i0AgB/sXQjs24XrZl+L5k1v8+Y/+/1lmLdrCy69/Ao033NxdrZfyO53/3334sxTZnj49LV1L2PbkYO46aabccdlb8bcdXuBZS/j9FNPQbN5u7f2hr1H8MVFz6LeGChxYPXja4BNr+GiCy5As3mVN3/Pixvxd+tX4pxZ56LZvA4A8KevPQ8cPoRbb70Ft1/q48Azf7cUL+3aisuvuBLNOy/CwWNtYN4TAIDmgw9gaNC3Nn12weNojXZw51134YIzT87wdxWNv/M37MNXl72Ek06unuup7y4Bdm3D1Vdl58UdO55bh79bvxpnnT0Lzeb1AID/d+XPgWNHcfu73oUbzj/Dm/83217CuoP7cP0NN+B918zClv1HgQU/x0CjOi/FODrWwb+f9zgA4L7778cpQwPY8TyPAxTswwcWAXt24tpr3o7mref783+yEj/fsREXX3IJmvddBgD43UVPAu0W7rrzTlx6tq+9/tHq57Dr2GHccus7cetFZ2Leeh4HNu/L6EAtfy4rbXJHEdkzGWOqaP/IyAje//734+qrr8bnPvc5ce5E0v7/sOAJjI62ced73oML33RKeV5PO+1UNJvv9n67kTivG55+Ddi4Bhecfx6azbd78+vLduB/rH4FZ7zxjSWt+ZttLwEj+3DjDTegee0sb/6P9i3Esn278PZrrkXz5rdlkYhzM7x+4P77cdpMX1383CtP4uiRFm6//U5cds6pqC3dDry6GG9+U3W/Yryy+QD+y9K5mHnSSWg27wQALBxeCWzbiEsvvRjN+y/35u99cT2+s+5VvOmss9FsvgMA8MdrnwOOHMZt77wFt10c8JvdC7DqwG5cc+1sNN/xVuzM+U2tBrw/4Dfdbg8Pzc1o6D333os3njwDowu3AmuW4uyzzkKzeaM3f3EO+9DMCvbH/zajNW+/+io0332hN3/lnNV4fOs6nO/wmy8seQoYG8N77rwDV846zZv/p689j+1HD+HGmzMaumr7QeCVFzBzaAjN5l3e3Hani383N5MB7r73PpwyCDzxV9nn8972VjSb13rzC37zBofffHf3fGDfHtxw/Ww0b3irN/+p7y7B/N3bSpkDAD45dw7Q6+Hee+7GOafP9Ob/8drnsOPoYdx0y6141yVvwvNr9wDL5+N0An837DmC/3vRs6gPVPi7Ys5qYMs6XHxRtVfFoGSOP9vwInBoBLfcfBPee8VZ3vwnjyzBgj3bcMWV2Ts5cLQFvPQkgCxqL6Rpn53/OFpjFb/BkgJ/z0SzebO39pvW7cWfLH8ZJ59SPdez318G7NyCK6+4As27LvbmL/3Zq3hq23pceFElS315+TPA6DHc/u53Y/bb3uDN/285DtyU48DqnYeARc9j5tAMNJvv9eYeGm3jMy9lfPT+Bx7AzMEGNv98HbBhNc4ncKC7eBu+sWYJzjzzTeVz/WjfQmDvLsy+NjvrgF0udUcK7e8bm6bhIItZWvKbiygVQ6RSMX+wAbmjm2BoEAt3GtOQxtOml4KFzuGte3Pc31qKSUsFloHYkGGp7eEbyvh9pGoplBE5gmHNkhbnw9Pzfmfdd6lI/Hi7SEQdLcQovhgWuXh+da34rwV2931ZatmYauoYI+0ms6NF8TztXs/D8+k4HnroIfzmb/6mOOfiiy/GrFmzsHPnTu96u93G3r17MWvWLOaX4xtDQ0MYGhqKrg8ODpoZtTZ3MLc29lDH4OAgurUq/H9oKP5tEZVYqw9gcHAQtfzzQKMezR2aka3V7fac7zI8GRwYiOcPZqJCr1YrvyvQZgbxHAXstXp273oju99AvUY+c1Gvp97I7108C+J9GpqR37+H8npxpIYGY9gHy5QYB/Z8/owZ8fyBEvZGto+NRg5jvI8AypTkAvZarV7uQTh/xiABe/kdBUtukKlla7WcqN6ZQzO8+YODgxHs9ToP+1D+udNzcKCAfaAR72OBA8Q+kvtewp7Nr7cqOjY0NKPEkWIU9LXcdwF/ZxQ4gJ6zj9nvZxD4O2Ogkc+JcWbGjBh/y9oX5T7maQ0E/nZr1XPUBwIcIPZxSIKdxN9Gfp/q3gUfCHEAqHhkvdxHAQdmZOkX3S4iXEqhY5M1poL2Hzx4EA8++CBOO+00/N3f/Z36PBNJ+4t3VdHs7F0NkO+qevfheR1oEHiWn1eKTkp4VpzXVq+SG2YODZbnvxiFXFEr7l3ATvEbgu5JtGbGAE9rKH4zEPGbDK85flOMYt8h8kqCZtd4Xhnuowv7EEFrKr5dD/hNDPvAgONAbDQwOFh3Gt4Q+0jQbInWFPymkDlcZytNaxo57BZaE+NvsY8zSBxolHMs+zgw4MNeG614Za0Wn89Cvi5gL3FAgN3jH4W8NEjwyoJmU7ySwoEIf3kcmNmr+E2tMZCdS4EOlDIHiQMUn58c2t83Nk3DQbeaz78zpFwlFzQtiJU1DUmMnEI0X+xQwKTRUfpxWHQ2my9F+/jwZr8tvrMY7brRd9T8KrIJAizFO40LJFo7WkiGhtA4JaXouWukFKYkI+0kHDDCHrUaVwpyu3N1WCjDbXFf6T3p0UHZfN+gmWoslQr4hgUPretHxcoZHKjnWnKx/gtr9+BvXtyAq2adivPIX7w+46yzzsJZZ52lzrvtttuwf/9+zJ8/HzfemHknn3jiCXS7Xdx6663Kr6ffiGuZOd8Z+IDc6RDeHEDuDFPS6Y7t3IX1yaSGBQXsVKF9ajrtAPHv6w7qHKW0Fi4jVqmwTxApyeW+xBtZwVJdE43lIW10ntnETw1FsM0Rq0J6dCottRjuxeLmtRgf5cYPRUHx6pqpPqRhHz2ZqpPAT4+nk54YEZs9azugG9ZCzNNpTDbtHxkZwQMPPIChoSH88Ic/xMyZM9m5kzFCmSCliLA7X+7mZTuvnCwOWJ2zdhnPg90oc9oyB7LPFvm30+1Fzlaz83ScTkKSPwWFs6XzSkWkF2KBXFrBBkskczhkQeRPKZkpRC3XZB0oQf6p1Wg5IqSrUg1dqdaxvaGKYd/DzBRBdnPniR3lST1YPh+TMQj07I/Xe4TdCQAtVSj7a6uqX/2/UpD5jm50OpdEIOKi3CJxS4mwIYlP9ldiEmQHAQNh9pQ7Q1SWDfbqmik1MjEKJjQ4UvvirmERFKji5pJQJBVal7oAVvib1+GiiH75nCjbTHcE5kwWCBdhoRkQt36BR4Vwk7Iv7n0sCjugKRmBglTCEk0F4Ci+Oeyb9h7BT5Zsw8sb9tE/mObjqquuwoMPPoiPfexjmDdvHp577jl84hOfwIc+9KGyG9GWLVtw5ZVXYt68eeXvtm/fjkWLFmHNmqy+wpIlS7Bo0SLs3bv3dXmOYkgddo7XSFLgT69HREMmGhosbbRLAVoxfke4S0wXBT9pXwjlXnKwRPyUNdqCni/ti5G3c6naHDyR0yHR+C3hDNlCWdpHxmAD2Az3JoMg5QQTBG7a2RNNJ86S3gnWXVNUjBONdqEi7a5Pwx7AYjSs9hx4TrQxHto/MjKC+++/H4cPH8af//mfY2RkBNu3b8f27dvRcYpIT+bgnH4S7aC6QYpdqIzlOMIocK1mKUeb7J30imfl64RaDWUhf7JG9kfZIIIxyFpKROpEJjeOgfcMnCEgpMOlbE05N4gOcCk4ozpbA6O/iQ9TOGDUPUWaHbwnq8xRdvCWaugKsIiyu9VAGemSYOdSzX1kQ5bvfHCfgzsfkzH6xqZpOCSrvkWwt1h/AVew99eh5rueWLlNrw+vK1SnpACSDIg0wPBCoERoJQ94aBl37+2OkBhKDEt6p5Yufe7/RUHBYHCk4DF51Eghh4eF9GibPGr+Ou5w72dRBEgFqWTOumCveuMZb4osnFXXTB5wq3EqEkJkJTk8TxLzPFHGN7/5TVx55ZW455570Gw2cfvtt+PrX/96+X2r1cKqVau8woZf+9rXcMMNN+BjH/sYAODOO+/EDTfcgB/+8IdTDr87ImVd6C4IxNFKMq2r6KuFBpDRFRZ6FylRCj0yGJskeiR2YCWiuMQOloZ9AdIcJqmpsVykUvbdxMDiG+4N+2J0PEUpyYKckV3P1wwN9yJ+VdekmoZVmnl1LaXrqcSTiu6u7priWaK6tZp4ezeaTymMobNSNJS58mAv+vqEGqm0f8GCBZg7dy6WLFmCSy+9FOeee275b9OmTdxtJnREeCY1anEcBL2AZ4sRnS6emSJP0uS2toHGk4bt8lmj6VFZiOz//lre+g0adquDwNKN2ez0y2FJrhVrOK8UPN083TE1sklq7mN3tjK8UnKgO4ZtyVkR6mPufIlOhvjI1q2N9pF/R5QeITpyxLMXwzKeTBN3noxf2V9r+Y7JGv00umk4ZCWT8gKEkSH6IfDn6147s5IRGj0Ug02KZ6cgGoU3vl6vyVEtlAdcjBDz5xfCa62mKGAGQ0NIaGs1uTC7ZNWXFM0ohYYxJ8f7nl8XmATpFU402tHeEX9NS3RQMX9AgYX0MATf+bD4gr2q3AXeFFFpEM61GBlg9ICHDFFjKJyx9EQ2Np155pn41re+xX5/4YUXRh78z33uc2pR2NdjiJFNpghBnV4U8wYbsnGSSu1OU9Y1ATqHJfBMU+SLqmcnR/z58Kqwc0Ko5iE1CIp0dJC/DglLIJxna1GeafiwGJwrxbyBRk1xauXwWoV/ThlVjN/F+lJdQJI2SrX+KGePhV8bhPnierfTI+YTcwnjUWoUl8TfOeeNZEAs5p+4lD+d9t91112vezQXR+OlRi1AdV5NXYE9I2V+XwvO539rtcygysFTpXmn8Q+TLGNUkNkSAkzqMxuVNYHOVnO6cQQL2LV9eJD/zl+HmktGBxmc4m2P3xhwwEDHCpgbNZuzwoWh5Alk9CqHj9HUYH722aRLuu+0Y+BPpJFPcBAY+E3h3Oj2qEhwmx7cj2zqDwA0gZCLIPtzJEGkyPl154kMaLyeWCIMkyL8UTSG8JyecFyurxvKUqODoloHnHckms/vy0BAaD1YDAYYfX7xrMFcLaolUAZJD0MZIVZdS/HGq7VmwvmS4uhF5hWw+OtIa7vPITEsSrlLiSgTUzOoCAursVTAyfEoSAARBcHgTH9M7Qg901pIe2mwCc6R1pXUJnD7c4G0FC3pjLrXw3o9FCqK6SHkuSPCyC0e/kDgtkZlmcLlvX0U6g4WxuxOLPxT4IQGR4tzxYVHEohFD7/kjDHsCxAb7lNTjC3GUiqyQqr3aDbcJxgoxZouIg/LPne7PTEVPEVxoehAf0zdCFO0LJGIQHxeU9P2pXqrodxmliETaIH7/+QUKoPhSzNsc/WppAgbKg1pIoxTKWVQ3OsF3yidpwY+7MIlyr9UZL/BIGSJ9nHXlbsxS7qnkHppjEgOnehSORnynfZ4WMQyKCS++3MkfHHhSU2VLobmQJuM0Tc2TcMhCXWSEhtaOSnPJ+AIIyVBEQwNhAdRQtSQqXjESjCUhZZ0ldmGhjWDIcD9P8kQw1BcJQyTTf2wwi5Yo8u1yVDcGBbOyGeNajF5vIz7GHuobYXWLfvo/j5kEtaC9cVjWNIzXAHDZFjr8WdP8jJJnkwy3cIgLGqpS+F7fT28Hf3Bj+r9F3huE0BCg40Wit0OaAB9jnKDjVsg3BIlagivd9cIjbzkuSBSLGQ+4M9x4ZHPNHxYEgU/i1KUzfe/82Gn96Veo6MNUlKSScN9svDPwx4V7dX2kVFezfuYYPx016eV4yBKUIDFhyeEhS8S7zpvxBShkA44eCzWXSkjH4R36lxz96Y/pmYk4fw4z6v7WkXDNmOwYZX1BJlTqlNmPa8pRnzN0JASBU46N6QMjBKW6ppJ1k80NhUwiIZnAnZTuY9A5uDWD0uViM58wcFFBSLQ0at2/iRFroqwS7I1KUMQa4sOhXh++KxmQ1lQK8va5EtbfzJG39g0DYeYq5pCaBk8Ci3jljQkKpRRIsxhlFX2HQ+Lxfvp1xfwn1Xy3lsZXLSPQpikB3uQ+mEJgfbmC8od5b0XU9cM++jNj2C3KhkWZa2AJV6LWj9Mu5Nym911Uw1lxf9kw1fuNVKUuzDcuy1010gubEwxCVEBq3tr6go+vHl9Y9P0GlH9ME34ZwwTKi0t379e28XqqeNqP3C0NDZ8Ztcp1CXpusFba+9qA2++JpiF9FFO/4I3x71PSpFt3mADb57FSeXOs6Tl+EKrAWcCxYUjL2y0gVDgPtWAaK3fmAILBY/oGAo86u7/ZZ7kw53BGa8f8iRJyaEaxvTH1I0UQwN1Xi3yr4tnBepY5F8t0rmSOeHBIkf7VNfEKJgGcb5FudCHITUyRM4c4fmH2F0ukMXd+/qw+IZtiRa48FTGZGltgfeJMqo/t1azybSpndClfU+NpOWcp6z8Gz6r5WyQ+ygZ/B0+b4C9NB4pkUexccq/rwaL1IF+skbf2DQNh5TfbAnxs3piQ2XdmnsqhmGGSoZiGefyxNXCaAZFQDKSWOarobiFYB8QTikH3V1XhiX7S3nvSW9mYBTUPLEljhm6qNFFtnV8DJVkbj5npZdym911Uw1lJXNOgN0cHWQ0OEaFLI0MS1aqs7+WltcZjAHDUowZ/TG1gy32rEUHJdBGb36OZqmRJJYOWlpUS+RpLnCRmFus0evZDKuhMO92x5S6osW1hkjQ4xpPosIYd2tNKbKtG5B9g3NlyOIjLYHKsSLRI5GfGrzq5g5RhmetE0Y7Cw/zjHyiYuTPkYyT7j0jw5pR8bZEt4WOIXY+A4tUTDyDpxd93x+TO1KMTe45iJR1sVA8ot9ZOmWq0fGcgdUYYSNHY/jwApCLpyc62uLO05JcRehjhvdUGI206PjQQWDtJB2m0Vmc/+76UgSPle6FeyMbPar/mxxiFJ0U5/tzVPyNzt74ahfTjpl8jtE5xzsIFF4Zwm6McNRqaE7G6BubpuEIEanXq3L0LZZLiQF56/cshwzeXHd9i4DZUQhtmLMuKdN1TzDK4RIMZWKr+YRwVs2jHacv2gQFKcVBiihLCcNMFezlsOAYFotw7HtieUIb1UghQK/Xq5pjFTPXvetUGl0K7Gr6T6Ro2gxlqaG47Y79WdXUj4aPY5o3sD+mdqTUlQAIGpCjDTXf7aBlM5JQQmv+XZLwRILOCn7Uo8rnyC6EunCS86PoARr4lJRkkh6ZeJL/DDwOZH/DGhoSLICNHomGe9Ho4cOuOcEsysJAoFy6zyDVgDGn3YUGR0UWiOqrCbBQxY+liLJQYVRTu5noBD0tvW9smuqRUmeR6sRrq78T47ylmYq9Vl1u9EiIOvHX11NBXbhoOumvqRq2A0OGtdZQVAjbQLOtxuEy/V2IjqdgN8mz1L4LUVyR81She5ai3B6/KZwbAuxi3SODI0c1lDHR1NYMH4tjptgP3cEV6JJCFJ+7hsVRTEU4tjvye52M0Tc2TcPB5ZICCoHIp1kRNTJ6GJmE6CkL185hqdWYGhMJoY90GDGvfJPtug1hnlYPQ1LaisSwKENDgAPa+pxiamW2ydFBBlhCxs/uI2uwkZlESoFwUkm2wK5EB7GGMi1lITgf1lbjxX8txlWrwdHqDeyPqR0hPZIMBwCl3PPeLm9+SqSlWfBjFJHUsHBKaHUk2Sh8PyF6FjAKfoqhLCUlmYzIET3NHCy2fZSEf9dwn0SPqPTFFNgTI/NoOo0IFjkF0J/vCf+C8mrBrwweOw9z5/bCsycYp6zR4qziQoDuGp37kU1TPypnq04nqbqfFsevPaqFNpLokSHw/lrlX4ujjY6kjedHdUKVEhhJUVmCUd7WXU4+r5Eekap3iHQsptkm2lTArhgl2G6KCg6k6G/WiDJOf1PlJcO+U/qYhDNxLdcYTm8+p0sy/CZuHsOvTUU4amd7Mkbf2DQNB5eaA2hpTn6dGbtgP97wQd0woXa0SBEwnUth6occzurC7n9HwWL1MERRWZKg7lyKvKUGI5y7vsWDYTU2tRPC/ilYxEilUCBSjB4WhuWukxaK6zDb8jsKFgSwy+GmYTqivfWr/p6ouiRSgc8wEsouLOrCX39M/QhTac1pSOWZzq6rNZ4ipZTC3Tj9S6IBYXSF5kmL61DkawtzPdgFGhN3fKLXimFPO0e2lGQiIsfCT62paExha33ffdjFlt5EWoPsUbXCHsglEj7m13o9lAYbMaWo2JeSTlffWQxl1uLmlg6Gfu1JeL9LcSSx8xOcYO71fs2mqR9xFFp+PdGYLOIwoSCL8q81qrvmr2lJ5QFi+Vfq5mU1lEVnxGpoiOgkQTsI54aYxcCszcHO0Rpu30MDZbG8xYDowmNx0Kv1oxL0N8qwbcJHBwcKeMRmQCEsjD0lRd9LbTAR8wOnSZKhrqSmv3HODWuEoxTdNlmjr1ZMw8EZbACNuMH7nWqNNgikqaGMKWsD8aGUrMu1Wo0gbgZDmZdCpTOsSDg2h2HKhJZj5oOEdh8J6l2l3XHp6Q2e02xw1GHxFaTsr4XZqlb6oL23NSInbAdu8dQAFXOmW43TrcPZtBXGiyWF1rowm/LnCcWUTDMN9t2s4EeKbJ8tTIfBpvKo0RXZZysNiKMxiLlihKuAu0YjCYe7FOhU7YfS6WCJnrUK/2alyz9HlnQPmp8Ka5c44F+P5yOYb8QZi/Gb4gMGg5A5tTs03BtgcdeVIoXDfXeFf9HBkmqwMcgOkvIqpd3FdICOFue6klrr1/TH1A2uVp1V5hRlH+K9lvKMUKbC6nwqDedhNGqyoy1eWzKUydkdvs6UKv9KNNidZ3K2BtFB7n3dMe5mBAWfF9Ym91GQC/nuyja6Z6XxnQBn7GVQ/HX8tX15SYts4oyCUipzt0c5Nyw6UPXdRGYl2AIdeB2ew7HJGH2tYhqOkOirreOThTp480QiPl7LuDUMM1hfs+rztYZ4WDyLbn4j6pCFVv1U63IqgSijVAweBk1BKvargt2HMYIlYd8LuP0IMcGLlfCO3HvG82nyFNa8sLR29kNIwcITPqta/4wz9BKPShVjlQxCyTnrnPFIE7jCugVTx3/6Qxicp04zfJYKdYFbnNAaGngkT3PAM9z/p3Tz0ui6qbMncY5KY4DBs6cJ/5xCp9bKKoR/QXEpz3SHOtN6kwBrpKU1KovjeZZi5f58HRYrfwyVV0mYd+GxRQpnn9UOqYzizSsuDCzC2tT6JvkuNUJMU14D/O2PqRusY455VyEdTpZ/DUZNi8GUhEUy9oo4z9e3LOaoNW9Ch6XxjITRqBLvc9e1GEnaASyAn+FQwhLInJr8y6VoSTJk21HgJMNEijHTvW55p+49w2ABa31DuWtn9jeUrblai1Fh9i4/n4xGFeSC0EFg1eHDUjhqynmK4ZaQ3abSsdw3Nk3DUSnT2WdXCDAJ9gqiDoSh9gKDC1P0ADkfOowOMntqjB7EOqOASXmzZM6vwQKcGjqvPitj7ZYKipsLrYfEx+whCzvWCIycVDJ0ol/hIwlKHM6qKHesIit5qF3vSPAdCXuosDOUsopAs6cjuvMstbKoIoOSsGit75KabtEfUztSise61+NaLTalVKwhV/CMAFc4eDjPG6fwRnwj/0uBTkUImlpXB7SRnR8as437HnYfogS5cB8BxdkTCcT+PeP5NM5oKcyW+nohfrk4QAnoUdSG8JwujFHNsQkw2EROMAUHuKYrqqE3cPaoUVkGA1Ky4bbw8IdpnUYZrD+mbnB1+TS5zZSGT8g+ojE5Qa6i1pci2GmDjU5rQoMKt35M95T0L3Yf47kubaui7+3OVpd/UJGIKQ1yqPnF3siplNW10lAmOWasMgdjlOfoZBzJ56/jjtCY6cm/CTqTJruHNF7Ssan5KdHRgE3W1wMdfFgkGi9GUzN0ZjJG39g0DUd1CHIFVg37Rz4/OPCad8TA4KhQRlN0RSLDMtcaSlg/rGMEyEIdGwqvGj3g3cfqBZCt9PS+cPO5bk6acmdJvaT2UWJwnBFjgKH6lbJmFaYZRdYAiwu7FIob4gDrHWGUGC4NtHgkizLIpbhw8LCGXi4MPsj914yr/TG1g8Nza0c3a6H9qGtVQmqOu4472AhX1gES0LviWRErwFTth5ROeq4hSzRQB55pjR5FRbmFJgEdgieJXUatjiQmJdlquE8pOOx1RUtxgmmKSE9/VspwL/EwzpiZfafDkpqSWvJfo9NB4gOc0Y43fMGDWZWpgppm/TF1IyoQriqZ9HkVZUJX9pEMPFxktOasMpxvMqpbqD8ZGj3cyBDJSGKN7OejLqn6UdX/benG8GDRDIi8HiFHB1UOguK+uj6W/Z83lLGplMYIGy0zJanWkORwF2SO9KyEEN/5uRTsouGL4pUWnUmLzEuIdpWafE2lrN83Nk3DwRkCADkMM7XGhElQL9eurolpdEHVfmtR0JhAKMQqIG6id8SYq8qFhHLnMSaGPowR7IyhwRKV5Yfi6kxFKoROwS4LLT7c2Xwh/DVBgaFgUYXp8D0Jhf1KfCQMZWJNFSM+Rml0xjpJZSe9HBYxFDeoTQWAThcKU5E0IYcxNkylt6M/+MEZMaxh4eZUgiAqzyKwaMo6R7/Mwn9xpjnaOw7DhCUa1oPFGm0bniMDLF6kpfBeU1PRUrosueuMJ1LCTW+QOkSl1lEJC9xrBptusO9yOrX/Trn55b5HRd9J0AmjYL6OAIu7rhwVwsglxrOUWnuyP6ZupNAOIK0JCNXRTTYmw5uv1nxknGFmA6sg+8RlIdKUdV2GhDdf0iOkwtZi7avIoUiCEsltUkfj7HpAy3r+dW9uclYCww/UFFwfH9WU88CISDa8CWR3z8FlMTgmwiIZHN01QgOoHCwADyYuui0OGMk+Wx3uckof0dxFwN/JGn1j0zQcUatbJw2JRlS6kOxEeEekUNwUpUT1ClsFI26+4cADSroFY+RTo1rKZ5VbjReRPdG+i+mLsXAspS/G3nUOllCwl1qQZnD3eq6wnn0n72OIjyQovDKoFEi0pC+GXqBer4cesmtyFy3bWYrSERVhMY5Wsuesa56d4w6DV4wT/TG1g/OO8QYYJj1aE7YMBcXDLmquocESDal2SM0vx8YjcjorbFk8/JrhK4RdMziHqeamyF/PcM/TR44G6PWjjM8aGLRFfirRI0HZtUY2xcZvYxqdgedxxklt/dDTzMkCKSnJVEqGGHE9Tq+32QlGyHj9MTWDrxNKz+ciSSSDDVVGwtJgxFqKwZK2T0d15+dbkH/JKEpRT4EHix12Oe0uTH+WjHZR91ONdjBym6Z3lOsH1725hCG5+G9SoWpFni3fk1YnMqDxUlp4iL/J8q9WL5iV9fm59HxBjzA487PrgXxllt30s0dFU2sBAJMx+samaTjSa3Vkf80GmwThhTI2FcXmLPM15hk/a37dLEjpsLedEOVCxpQJs15/x19fFxgBnrhJIc2ht0OHPVTWrII9VFjcdcfjAdcMiJb6K9R8U/vfwAvErR8KFXbDLVRY3HuG4d6S0Y6KbpOVuxwWq7AYClB9Y9O0GJzBWeMDVkM/74HlBRYyDcki+BmjrEJhizU2MfSOrrmReEYjg3AiDTDwU99wz7+niAYk8iTdyBfQALFTETwYNHrEpkwoRjtLKoxksLFE27pRy2IdlUCJshrutfcUpZkKnmwuUthscBRS+oAYB/pj6kbUAbmkNWkFliVa464rZiUEdE+tD8fRSWNUliT7cM7TbB2+02/k9DOmnEs11tx1wjpoZDRqspMIASyJNF40HvlrZ78TookCXmZ1tFhpTYXv/nuSgwVsOlCIX+Mubi7QYBeelJIs1rORqktGASZSZLdD3zVePBmjb2yahoM32GjCbtohK7tQCQJmyIAAhbgFhFY3NMCbrwpG4yAQ3V4W0eI+g8iw8mlazZtYqPOvx/NBwy4I06EQUmOE4yrVDd7v7LDzQotX3NGAY2xa50QJxwy+S9FBoYcBoL0vbP0zhdlGHi9lfixcEmcvDCPuuPgrMTg/DUXtoGRUTPtjakdq4wc+LJxeP45u5HGdW1ubbzbYhIav/C+HiSlFk0MnglpDI/S+JjpvRFhcI4kh3THZcJ/qvElYP8IBt6uflJZjpI0Rz7NGOQfwiPVoEmWquNEJOT2GRUnh4J41Lb1fkwfh/bXiQH9M3eDkB11uyz5bnH7F+q6z1WIkMfOb8LxqNN4g51VyWPbXlduo5cPIJi3lPDb2ylkJx1OY3V470SZzxpH9xX2VLmolPD6cNCx+DTFrRKcWMTMQ4K9YL5iJFnXXkeZrNJ6LvDXX7RLqUIa8zxqRHOlXWhqdIVqbim57Peqz9o1N03CwRglrpFKiYC8Jda5Q3wtyVUXLeGj0MOb8pgpGlpQFIDM4eWGYlpzfDk98gLTQeSDOnZXeK1cw1xoxo9Z3CYRdifh43TgMggUfFmxUNI0eNUsXLc6gAigMLvJKKYJ9J/DUqIqARdH002M9gUtktsjn24x21kKy/TG1oxG8TykFAhAM/WyNp0ApFQSWyPOmeBm5FAurlzG1I4/oaeaUdcUpEEadsHQ9NAob2mJT8Ije3fEa7o0OE0t0GxdNxsFetd0O+R0DS6S42DpKWZRjdh+NyqU94gTe+tY0niJaXKylY4w4idI6VZ4Eb15/TN0I5QfNwJpSk60R0BprZIjFEebCntrYJTQ0yJGIcWoyWUokMUo7igwpDTZpeodU2Dou3szJ4kE0vTEKuOLzxfV4rie7GwzhVcp59lnbRy763irrm1KfCYOjKZooEZZK34vnknW7LLJ7UG9V04OtumSsN+s6fLeHUod/PWT9vrFpGo6o9oagBGTzacRjoysC4Vg2NMTCccEsZC9c0F3DyjytzNYgqLvP3+52x909h/dmgpzPGybgzSuJoZQ/H6Q3aIzcnG7BGBylUFwPdkGw4JRktQtR6PFilersb6TECNFqZMtrCt+DAvcaLOGzdo1MxWLg4YqBWtMn0j2NU8+A+oMfKQKFO9/qHWNTCQxG2DLyqMbVEWRogBF2N5JTmh/Tu3huZZhC/lcT5MLW8bLRIw5p5+uwuWfXQgNSUq/dNawe/lhAj+EsYRHeEZ2K5itR6r4zRju7AsjPD/HFCkscyUtOZ+t2WXlepTBaFBcbPpoVl8Dw1R9TN1JlJZbGC8bhYr7qIGj4dWPMMqSVNjF4KXfGyz6bGweFhjKFf1hlTjaa3pL2Khgx3Ovj5fMV7aAcLdX/i4AB0aEQwpIoc5YGG+M+pjha3NR6UeYI+bAxMs+qZ5tKiXCRcOYUUxkWzrEoGT+zefCeoZ9Gd5xj7969+PCHP4zTTz8dZ5xxBj760Y/i0KFD4m/uuuuuvIhd9e+f/bN/NkUQ+yMk4qmRSlpOP5vvKRx4f30p5coXdpOFLqtFNyEFIVsXKrNN9exwhgNr9FFbiJwqccBQuJWCpfKQkdMjQmuBxZ1vSrmJjHY2QUEPxc2FojD0XEyh8d8pt37sjfefKYYl2EercTVkKgLztHZqrOYHaXQKg7PmiffH1I7kiBw2GoNen5svdTSxNAjI7kkr36np0Rwq8lFcPE8qzoXeZQnemtZo27ATmWS0c2GX6GMYDWBXRv2UQb5uVwCLwVBm9RxzSpQWTZTKf204QMOiRR5ZjVN83S5yOhsVIvGw1A6/1g5nIZ/pj6kbXAS7NXW0pNmC47dY1y8jwePZuFNHNQU5wVBWD/bFWu8tjg5SmvtYIx0ZQ4NcziCUxY37ohhs4m6TNRWWYr57xE1OJXOtuuyzNf1rPI6W1BpMbSGt2n2mUDfQZJS4bhfPb6yO3Hqwtqa/hZHdUjBCGE2tGRwnawxM2Z2mcHz4wx/Gtm3bMGfOHLRaLXzkIx/Bxz/+cXzrW98Sf/exj30Mv/d7v1d+PvnkkycbVHJwETC6VTT7bK11YBHSwhSqXq8iWKJgdJyGBqsgZak3VcDhGptSinKnRoaYQ04lATPBij6hsFAdkZw1LAbKmIjH61DrWwv4sl4sAfZuL67bZfGm2AseWhUkeLBbDL0h40/dx+RQ3L6xaVoMtpGDSteR/02jAbITAd5czQvI1puyGsqK+eRs3ggj8yR4a6tp6YkKYEpqQLG+1rSCj/wlQeFT5NmInDCaIYdFUkSM0bY8LDZ6pPNfBPDo3evKCNRxRourKamJyqulxXisuPj31NaWDBLe/L6xacoHKz8o7ypMz1Hrw3V66NXo74rBRVeo9XoCo6bZISqcb76WlcJvwrQlrTFR1HnapjOZ5F/D2QYI2mHV94p9DJ7Jg8V1bgQ6kFRKxJJy58FeZLIYI6FKg41gCOfwUY3QtPKbwLiqOWZS9EOOH6jNMRINtxZnSJid5M6ZysimXzhj04oVK/DII4/gpZdewk033QQA+OpXv4pms4mHH34Yb3nLW9jfnnzyyZg1a9ZUgcqOWAC0Cva2wsApHWhCQ4NvsJGKbBsNDYkCaSlgGrwGHqHt9Eplqlaj9yb2GFiVe5sikCJMc4pjsqBuDCGtYInfaZGv3O3ZQk5TamkAcQqCBEt2HeT6UhpdMd/FX2orI+9IIgNSvcgMQ5S8Uu2wHpTxXKtpnQxD5PC3P6Z2cLio06O0aKIoWlGqZxcqCqrBBqb5YWSI3sGnELb0tKUURcGDJTENyZLCHKW2KMbv1Mjf0PGULLQKOBMa+DT+GLYANztMEo2rYadR0XkTnCW9ngd82BN5u66o60pdWOvRnEZn5GHhvvfH1I0oQsFIV0216pwlOr2e143KckYq2mGD3Vwyw8DPirm9XOa0dlQcb80btTYR48wVazZZ67dFfDjtfBd0T4ts6gbyrylYwMq3IwOMbJS3GBxZvm2M0DR30jNkyQCSk1vilT7N1h1/tjp7HD5ampIU9+Bgn6zxC2dseuGFF3DGGWeUhiYAuPfee1Gv1zF37lx84AMfYH/7zW9+E3/zN3+DWbNm4Zd+6ZfwH//jfxSjm0ZHRzE6Olp+HhkZAQC0Wi20Wi0RzuJ7al630waQIV6r1cLYWPa5XqPno5chT6uTzW+18/nokfNrtQwxx1pttFqtkrghv5+/dEWcjo2Ood5tlJ87nTbC5XvdTgZ7DstYPoGFHflhbHdy2LPf13o9bx9bzjoZ7Nl3hSLe63Wi9V3h3hNJAACtXUlEQVRP3bGxMYwVns9aTdnHTg57to810LDXc9jH2tk+tnPY0Yv3MZufjdFo32PYe51srU7+TkbHlH2McKCTz6dxACHshXbCwN6o19Dt9HBsrIVWq1ESt16nHc/v5TgQwN6o07D3AtjHChyAto8BDhD7WJwlADg25sBSq6HdbiMcMf628/k07OFZKvGXOXsF/o6O+bB3OwQO5LB08rNwbHSshF3CgXaEvwwdyHGg1fJxoHwfCg1zR8rc/rCNcRtJjOkzfFSp1FraBgvXjcXs3TUamyqjrb8ONdeaLhqlOycqLpKgWK/XUKtlSlToabYYyuy1S4LCuqyADg9mSShmo20TlUvd6aAb7UR4EhQXra6ltQZTSrQt4D+rm9ZAw579NTvw2OhZGpZwb/pj6kaUPmM+3zrO12o1NOq1MoKyXKNmozXW1NEqSsW/Ho6USJVYQTbym2htW3MfzTET80q+e10qrUlvkANv3ZL3KfV6LM6NkKZaDTalzFGkrhlTAC2plFZYUiP1o9Rn6/oGeLjoNj1CzKcDajRqzz97kuG2WN+d0jc2HcfYvn07zj77bO/awMAAzjzzTGzfvp393a/92q/hggsuwFve8hYsXrwY//7f/3usWrUK3/ve99jffOlLX8LnP//56Pqjjz5qTsGbM2dOdG3nUQAYwOhYC8PDw1h/MPvcGj2G4eHhaP6rW2sAGti0aTOGhzdixabs8+bNmzA8vCGav29vHUAd8xcsRG1TD7v3NADUsGjhAnQ2xAJHDQ30UMPPHn0MQ40MFgB4fM6jmNHw567LYT146DCGh4exbF8Gy6GRERL29RsyWNa8tg7Dw2uxdl32ed1razE8vDrapyOHMlhfnDsP+1f1MJJ/nvfii9i93F87O4cZrI/OeQzt/HOt1yVhWbI7g3XXrt0YHh7Gwp3Z5727d5Hzt27JYF2+YiWGR1Zg67b88/JlGN6zNJp/yIF95NUejo1mn5999hmsPsmfuyPHgWOjYxgeHsbmw9nn9tgYCcvqbRmsW7dtw/DwFqwscGATjQPbXNgPrsDOXdnnJa8swuCWhdF8dDNYH3v8CbxpJtDpZvv65BNP4PQZ/tS1IxmsBw8ewvDwMJbszWAZOXCAhH1lDvuWrVsxPLwZa9ZnsKxfl+FEOEYOZLC89PJ8jL7Ww7792ecFL7+Mo2t9/B3tZLAAwE9/+ggOt4vPNA68VsCe4++CXTkO7NlNzt+8MYN15aurMXx0VYXPq1dh+MjKaP6xY/k7f+55bD0dOJp/fu65n2NdQDL2jmawjLXaGB4extYCB9o0DizJYd2+M8PXJdtzfN6xnZy/c0f+zpdm+Lp1e/Z51YoVuO0cmjZx48iRI+a5/WEbURcqo5HEmnrLdZiTU4z9dFROVmG92OYolewvJwpFnfQsXkZrSvI4lS6roaFRq6GdGxjcaANTUW5ztC2M84NaXAahNYLFWAy2uMegURExdxMK5kudOgs4yiYniWvzygK8edY6SWG0rdTS25J6kq3tR0KZI8T6kU1TPrgUKv7dwp+vKci1GjrQO9G516NoUSMs1po3ljMVRqRrdfZSo7Q53meJgvFKiQiwWzu0xcYpOYorrFkqRTZ5zo0wsslicDQaPaw1AlPwN3T6VEWwGQNiaJzSyk4klk2JorUNqWtRdBu3dsOn8eYu2IbSI1F0W9/YJI9Pf/rT+PKXvyzOWbFixbjX//jHP17+/9prr8W5556Le+65B2vXrsUll1xC/uYzn/kMPvnJT5afR0ZGcN555+H+++/H6aefLt6v1Wphzpw5uO+++zA4OOh9t2HvEXxx0bOoNwbQbD6A+Rv2AUtfwmmnnIJm8/ZorR3Pb8APNqzCrHPfgmZzNlY/vgbY/BouuuACNJtXRfP/dtd8vHpgD2Zfdx2a178Ff77xReDQCG65+Sa894qzovn/bt4ctDo93HX33ThlRgOY9yQAoPm+BzFjwD/4r2w+gP+ydC5mnnQSms07MWPFTmDlIrzpzDPQbN4arb3ysdV4bOs6nH/BhWg2r8S8H60Atm/C5ZddiuY9l0b79PUNL2DLkYN4x0034a7Lz8L/u/LnwLGjuP3d78L1550Rrf/QvDnodDPYR9tdYMGzmDGY7Ws4aku3469WL8YZZ74JzebNOPTyZmDtcsw65xw0mzdE85/7/jLM3bUFl112BZp3XYzv710A7NuN62dfi+aNb4vm//nGF7H58AjecdNNuPuKs/DZ+Y8DnQ7uvusuXPAm39KwYc8R/N+LnkV9IIN1yZYDwOK5OPmkmWg23xOtvev5dfje+tU46+wM1lcLHLiQxoHnf7AcL+7cjEsvuxzN916Cb2ydB4zsx43vuAHvuyZOJf3s/MfRGuvgzrvuwnlnnAS8kBki7r/vXpx5im9tWrBxP/7rsnmYefLJaDbvwMDyHcCqV/CmM9+IZvOWaO398zbhu+tX4KyzZ6HZvB7zf7IS2LYRl192CZr3XhbN/8bWeVh/aD+uuz6D9b+99jxw+BBuvfUW3H7pm7y5x1odfGre4wCAe++/H7tHjgALXsRgo0HiwKJN+/FHy+aV+HtkwRZgzTKcc87ZaDbfEc1/+Scr8eyOjbj4kgzWp763FNi1FVddeSWad1wUzf+j1c9i97EjuOWd78QtF56J3130JNBu4a4778SlZ5/qzd0+cgyfX/AMUKuj2XwAy7eNAItfxCkzaRzoLt6Gb6xZgjNz/N35wgZg3Sq87a0ZXQjHnEOLsXDPdlxx1dVovusCfG93hr/XXvN2YNdSkjZxo4jq7I+JG3Edtuy61bOn1k9IqUEQCP9VGoGtAGuqwaaqB0ROZxUji5HEGjVlrb8Teuy1FKpGvVampLtKoNTZ01rIlkvLYWHJl0ltFtJ1YE/ujmiNyDEWpw0FejoVrbrW7lapBFajnb1eXmhw5PA9X7dnaUnvK5f2DqkBzqiGNfLr/pjEESrrKo0P05xUugqgA9XIAIxDQY4iQOVUoagWrbEpjWuU5+hYlLIrGJ6zewb7aHRAtDv2UiLJxceNfJ6LKJNSrtq5g0hLo0tt1hPSDqvMETU+ImHJ/lprBA4E+6LBwncwNMooBpkjlE94PuzTbD11H948KQ3UvdTp9VBz6Dz3rJMxThhj00MPPYTf/M3fFOdcfPHFmDVrFnbu3Oldb7fb2Lt3b1I9pltvzQwja9asYY1NQ0NDGBoaiq4PDg6alTRq7swZ2edOt5d9V8/ChwYaNXLdGQPZ971a/n0tQ+jBgQY5v1QQanUMDg6WxGrG4AA5Pzs4PdTqDdTqFcrMHJoRHYahwQJ2+LA0aFhmDBTrZbD3cuQPYSn2qTistVq2XnHYhmbQe154duqNAdTytKRGndnHwQyWXi+HPb/XQKNO72O+78U+9nI//OAAvY9Fa9laue887EMBDtRyHGjUaVhK2FHgQC2Hnd73wQEfBwrYuX0siFi93kCt4eNAOL+ApZvvYwH7gBF2dR8LHKg3PPwdmhHP79Wq0Lt6Y6CEvcGcpXLfC9hV/A1woICFOUsx7NkPqH2cOaPyFvk4wOFvdq1b4ECecDiDoQMV7Nn8ggcN5e8jlY71x8QOzuOppi2Fwpkm/Fsim1xjkyO0qh2ugq6OVoNNWcBZMQgVilFb8AaHHZ+6iuDHF8q17buaMujA7qa30OH4IGHRPPyl8UhJa2CVLqX2g1u/Ua1zYqgv414PFUa9RoceieHC2HXwV4828GtoWBVGPf2kelZNeeUKhGvRA1ajc4jv/TF1I4pENBo9QqO8jGfdPCLHvcavXZwncxe1MP1LqzdlON/1gN+Mt1mP1dBgTnMKjcNUQX8GFrNhWzOEF4aGfP8KaEScyemMmrbNpXMZIr6AhLqSFgeXU7er1+tNqPPMXcfa9MSlk15jDzGVEt499K5+ASxa9KqhXlpYc9ctHtKPbCLGWWedhbPOiqNuwnHbbbdh//79mD9/Pm688UYAwBNPPIFut1sakCxj0aJFAIBzzz13XPAez+ByfiVPKWCvMZHadWKgXsNoPs/N+aWWj6zRRuITCscqszUWdWvUa0CnCJ3X5tY9WNQQ0sS0Fba4I9mBxlemzCk0kXddFnZjD7iilPSCQpOCYmr1GnFMgoW9EeyjILREIaQdfi7Ap//YQ8P9dbj5luKRxT17Pb+4ozVtxV7fxYdlKtuh9gc/YnqRXecFluxvqGTyXW2CwsMdvV5PMb860wzskSKidHVMrNnkzu9209IaNMEvvbMnvHkqzXC8npqnObWrTaoswBrKFBzo9qpUtPQmFDZYrGk53V5PNdqFkRLmlIl82dR6HrpRMIaFhZ2R15KjBI3z+2PqRrKyzsmQCp61u3LXS3eNiI4p8m/Eb7gOcJx8QqzvPo8n+1jlMHUf4cGsp39VcptKs0PnxgQbScI02YJGce9poF7DWA67tVtctC8K7agiY5Woy3BvhGcNO6Hb5VkjDjB6ikVGcfVgU3Sb0eBf7aO/Trw+/PmloYycjkY9q7nb6fUAZ+3aFEY2cZ2FT9hx1VVX4cEHH8THPvYxzJs3D8899xw+8YlP4EMf+lDZiW7Lli248sorMW/ePADA2rVr8YUvfAHz58/H+vXr8cMf/hC//uu/jjvvvBOzZ8fpJ5M9QgHTSnwsbRABQbA3FJB0DySFqOwBtnpWNYtu6B1JMGZZu5ylMyDbvnNKj2RoCKMUVE+NMQwz8oArIdAuMVRDcVONcMG+mGE3FNV0L7UdYykrcIWGLKuClAi75ey576LtnT3Z6Bzl/mvCYlTnYOoYUH/wg/N28cq9zwfU9BnW6cCf6WKeWgcmotP+PWPYq7UBx2hLznbOaVcX/HgHBb02Jyhq+x5FoCn77kbY1Gqykc/KH+N3qtT/4NJPBMNXMd/a6jxSRIzGUnuHKHg4oDkd3Mi8iXLgsfWsDLKDH9mkywJW5421lXo4vz+mbkQFws3RfCEts+OZ6jgzRiI2QtqhycsJhvNQbkutv6PBwtXC0/SUdrerG4eTI4xTaQdyWIr5xXU9RSvZ0aIayrK/Ued0Y/S1xIvdx3HlX7OxdLx1vgwGTT9CTFi72BdjGnbYkTDZaGeINNfS3ydr/MIZm4Csq9yVV16Je+65B81mE7fffju+/vWvl9+3Wi2sWrWqLGo7Y8YMPPbYY7j//vtx5ZVX4qGHHsKv/Mqv4Ec/+tHrAn+BGFVEg4Z42V/rgecEWNYD3qiEaY1YRUaSROVbK66aWuXf9SCaLddGQxaXtmIhVl4YpqDcdbo9vyCvxmwTlbtwvmVv1BoTpRCC8jcyLLRgbxWKJBwrOrIAvgdcFYiMOBB7A221QCwGSvf5vbPH8AjOWGr1BGnG0v6Y2hEZm4pumgofiDyeiqBoiRL1Pc2yVxo4DgNPaPxmUNE1lnvGb8FLbhXMkgt+s5FNWpqexZDlK5eaMTv0kI47/YSMtq3+nxls0mhdqsc+JVJCwwHP2NSxdLeqlEvA/p7s0XCVYbi4B2dw5BRAc7F947O60WH9MTUjar9ulJWSU7R6etprQa/KIsVGA0/o5NYVZHgdGClZrFarld1yLYYy1nhkNMhWz6rXIHTPCZly3qD3hTf2gobFamgo9AiVn3VV3lc5W3OYhGjnDMbQ0WKU3SMjDB8dlMGjG5s4mcPq3DDrzT099ZmLErQGjGg6EGsUNDiWtX2crHHCpNGljDPPPBPf+ta32O8vvPBC9BwvznnnnYenn356KkAzjdALN14LbXK+smrVrwitegjKWh3j82aqVvpgPlsLpFGli+mGA07YlQlzsjczIQwzm1+lXVnz53VY0rzxrqBgTVkI611wnUE4b7ymUJmF6VpWt8vijY/DglPPEkzrW4TFkA5otWbid6rNhzfPZYgd8hf9MZUjFp6y62o0US/1TOv44q7hpn9pBS+tdZK49s+8YbU6R67xW+zmZRX8nIiZ4h7ZfOVZrdGQjiEj1RCvzk9Ms2GNJEpkU6YA+muEI3qnav2o7G9crFzfdz3atvq/ayizKMbZXxvOWDpEZeu4sKS+IxvsBb3QUrv7aXSv34gKCSuyUhR1aTWadtyaTRwewFvTipelc0sp4OwacF1UkxzFnR68tCW70y+Nrlpl947jaOHW5xy/Zj5shSWgNbqT2+Kc9/HRnhJuNarQRhIpQ6KYrzpyy30vflM4rGwGHj24wIVF0YESjcJcaRuL8RPQz55L43s1/55TNX4hI5tO9OEVxzNY9VO9alzbT0vxVnMHmnFGNmnMNjLwGNdvG7yZIbPVnjW9tkcFS5In1mAkYcNZFWHXktLnwd7tGup2pb2jOOwf4vwoBVBNLUEJT1dh/KEhy5zKESj4ltxsr4WukEoJGL3xjCHWrCApz9ofUztC4Sm1eKzVU2cRFGu1WtFzwHOApEYfmlOS879cpLdnaOhU9MjS+leP9EC5NuAKfgwsUe0rm4DeTRD+w320Gr81500YWSHtTcSTyndKLh3x6lR6pPJf51k9nkQ8aq1WQ92JlEh14Flrl1QFYZWIAEchTYmIBgz4Vc7vlvcAJK939refRjf1oxHgjTkN39CBEfDPlKasl87WHA9aWjowF3FnME75aUiycp/Jy7bUZEvBZHeddAdEV6fZUd1azemTZvSIingXRkQuypjISrB2+NRLg/jzrIELsc7Ezy3gKWDS6J7ZUJZaa9GRUTSHO5eensq31ci80FhqOHsaDkzW6BubpuHwPIg9e8i3vcYEfeC1+gVZyoKWypG2dtSFyOqpMVvSs7+mDjRsSp+NWKVEHniWcaXGRDchZaGAwUqsUpmEn4oGum5XubYPi9nboUbDJcJOCVwMnY3SOhUm4daOARKKaobeeEW5c6MgrMbS1KgsDWf6Y2oH6wU0Gw8hzw/OtOb5dml1ikfdhclcULwwINPTPT5QnGkOHq/WkJuSbPV4qvPzta3KgvOs5VyDRx3QPfDj7aRncTqEBketHTmXkmyNzNTSF8PuQOF9Y/izv379O9s+FusPqvMLA48Miy9T2eSv2PipRAmW71Tz8Ps8rD+mboR7bzUOd0qFWn63VKppaoqTRSZ0n0F3zsKTfVjalP/tGrI7+GhUG87bHTkG41EOS6/nd1FTdRSjHBanDObXFZ6QpAMZ+EEGOx1Nr9bcDWjZIEHkQ75tpWMlDoyzzpdqtAv0N2r50PBlzdYIz55FhnB/p+FAu6t39Zus0Tc2TcPBeRDVFAQjkxhkC8nS8LgMTqvtw3nh7IYGK7O1WXTd1DjVsxMVPMyua3UXLF5hd52Q2WoKkqlAYrLRjmYSevoi0CqJsmacDFroJuKMtW6BViOl4RFapK1t9IBbUz9cg5DvjaeVOxces8crqkOQpphyDKs/pnawBSw5YauoFVHU3EjwTHvGb5OH1JiGZK1Fwpyjeo1WgF1lwT0XpPHbgdFmKEO5tguLNaLMujeul1ytzxGmFyYakK1KlyZwU1HOEwcLyPlaq/YIf1l8RzTfypNa5XwNFv8ZLPueWmjdXNOwhMW/rq3fH1M3wr3X68P577aM9kg4r1YHgVWuCp0hltbxmoMA8M+r1VA23s6X2ny3Fq0WYRN2UWtpzX0SndxRw4DgejgoxwxrUAmistSoyHHT7MwQJ+17mOFjrglmrNnEO1sZ3dOpxeXqNJTMUXX7ToteLd5Py+hw70TOPJ2fafrVZI2+sWkajtDYZCWEZa6q5ollag1pBCJLRVOsy4yClFo/ivdmJubZOsRT8/RzHkHNm9kKmLOu3Pstr8k6I24xVofZDhq6ZQDj98ZbQlQ7CvOson38e2iwjLvOiApPTvi7KZEEBSxaRBnKtQF7ioPbOlyc7yjhmpIRRlmp7eYZw20/sml6DM4QYG3OoEVaUpFK7nUenvToCvOZ7gTPyqAiZWjQjLDl/NIZY4NdjW4M9j3FGKAK51y4vJn/Wg1fNkOZC4818qhArVR6VBpLDelfWrRt8V0Gj8GBx/EYJWI1iszTojx6didCESnR1hoFhBGOajSc73jqj6kbUYFwBW8qh6gf2WRJNbUaMVLrQUUpgAbZypV9JtQ4HEWpaIYy+PPVZ+2qKbJ8FzWb0U6LbqsHvLLwWVoi3s1RlAEsKh0z6mMNgu4BVQBEODwDpbUmWKdb/gYwpDIbS2B4qc9GfAQQRAHrspULu+rgMupMLo3X5k7W6BubpuEIhWO1KHdgaLAKgcWhbBvnu0xCg6UUjIzEJ+6gxRDDgtl2umrNG/e6JbKJI7QcwwoZf0pNFdezQxFDlxlYiFsRhhpHNpHTWau+HmrvKCRGK70utPhdUCpPb1qReIvntsAzNWfdir9BnQNzfn4nwAGDgKYxT74QsrKPUV0Scnp/TPEIvd6aIZ5PQ0qjRxbvm7m+QWloUBTeho+LJa6Ts2lDmVZDo1i/NNwbFRc10pKJLLYoF8ke+8RORXaPaiZnFO9LV0b0d8oVm02NzLTsjRYdBFS45BrurYp3Sj0PwFV2NaOB3etdzjfKg1HEquKk6Ec2Tf3gI6MV+aEb1Hw0nClVHgj4jb1uTHC+FZxvOwYbd51wJKXsckZzg9PP/Z3uiLYbpor1i33RHMVxhgQ5na1xaind0NJoDRNlpRoxrHTS0d9M0dQOL7Z2GCyWVflNGAmuZTFQhlvFkVfMt+so/lmi0gvd+5pry+bXWx0br5yM8QvZje5EH/V6Vhuh1wuZhEYgss8paUWA7qV2FWrN2xgeMs2zynbGU4RA12OQXdc9lGbvhdlaHOyjFk3kvCdVQXIup9R16ERRVorHwBguS3liWSNcEEJq9cZbC/KGVn3NG18ZV3VBPTT0qu1T88vhWeIEC8pwC+hKjwmWRIUnnK91DOuPqR3s+1TOdLsTniNdsHRpqaWbpq4gw4NBS7Hg2t5z8hBVP4E/Q2mGezZV2xA9AKQV92x1ZOM0x2OshW9VnsfVETQIxfo7LfAXNlhYWUCO+nL5o5QCXNy268olZsO9MSXVWEPDjQhIUV4tskBU9N3INzouQ+qPKRkRD1bLQsR4k12fOMN2FNWtGgLg/U6r79N2FN5aTXCeoVpXM/hHWQnWBgABzdazR3SjXdhFraPQeB4WW/RRaXA08CetExkXZaU1GrI6uCgdSISHiCaylsDQMh44Z6ut9uv4aLZV5kit2WQ1fmXrvz7Gpr5WMU1HwxNGrG16bcp3GAWjep0JA49G2Ir56YYyzXBQeXa8Im1aKH+Cdbl4Rk0RCCNyzLnWhmLPtVrNC/u3KiVFbQmtq18ys3WiuDTviPvuLDgQdQFUIgPKfbSmLzoetSrdQsffTq/qdGVtoWs18rUd4xEgCGgN9+ylKTypdQu099ofUztSU3NSIwrdtEuLoaGiX7rnOEr/Mhruw5RkDhVdIVc3HFT/t9St4FK1tfRFs5fcERQ143TIk1I76VkVF2vR3qRis5FTwAqLzVheyDEWWAA/UiK1lpWuXMCbb210khJxDdgUHbfsgfvX2p24P6ZuRBENRiWz1bHJvz6epcm/utE8+2s1lA0661vOa/HV+AxlMl1Nrf1ad85IUmRTV9/HqAxK+Z7I6Z5DodfroYeaCLuvA6WlVetO8TQ9wqWrBa5b5o8LB4zyktWZR9Xc1WgqkOkpWkBH7EC37ju831l0IK2G32SNvrFpmg66JoWtvkBK6Lz7O7XDXEe30Iad9KwROfGB15lE11HWLd5Ps9V9HLAU95DWp4iVxGypPFsz80wULKwpERbYw+g23QgXGD+thf16fhctPu/b2Uej5xCwCQpcoXWtrpLbXU7y7lE567pB0AaLq2ha5vfH1I7QCKuF1w+G799YNyb0vPE1b2Lc1aIb7R7SAnY/JZkLVKmiJ3X+6BnunXPE8qQgPbpMU7Aq94rxK8UB4tKLDBZNgGbokaFYuZvaws/P1m919Ggil8f0HMO9tcCr1nq94ey7JvwDQCP/685X96UwICp1vrgOhin10jTFIpyv1WwKjdSWiJP+mNoR8mB7t8muSf51z1SqPKspyJwMqTtDdFkmWwfluhNdjiPWmWwd5lJqrGVwOCnnXI3AwOCo7nstfqdAWgRoaq1F1nna8PfdGjHqZsnI81HOV/c9pNkKja9gyT5buwx2DGfJj2zqms9eFZVurBVbRjblz2TQUzT5ZLJG39g0TUcVPphu9CgNE2q6RUDcUiKbDIcsxZtSVuHX6l04ebZJnp0Eb6Y1nDVSBBIYoqZ8Zd+hXDelLpELi9Ubb/WuesRKEdSBTGHQu/plf6OuW9o+doOIDAUeT0FS8AXII6G0+lFhVJb6npxQcuXcueu4sFjSc2yw+Eq1Zljrj6kdofKtC/++wms1OIcd3VR4DEZYrqsNh+uDjYB+FUYVBhavaYUSLp99V6WCT7jg5wihbt2jNC+5LSVZNZIwNECv7xNGNukFW9UOOJ7jyU6Pyn3XGj8QtFHC3wIcPw1UKTUQdeZKVNQT2mhbHCCZ00GrR5P9jaOsyOnR2TtRx969e/HhD38Yp59+Os444wx89KMfxaFDh0y/7fV6eN/73odarYbvf//7kwuoMzgab6mvlSL/WgyyXI01i9Mvewb/nhzsrqFMkn2KR+r27CUEKrpnK/Ycwq7VGrI4CIoyKMX6qmEiMHqoxmfCUO3CGK3v6kAJDWwAl2aT0yucMabuU0Z2ycHlRUJp+34c2Rru7/Q6e7bMFM+4muCYcWHXnD5hnduU8jNT3XW6b2yapsOtqZNssEk1TGhCo2dosAlpxXyrYB/VddDq7zgpUYBuKPMEdaunRvHEptb2cA1lWlqJu07HAHuZ+pELotY6I1UKYL6OwetshQXIo+E0WDgmoRHmyLOjv6eqwL2eb29SqqOitrKQ44WSKzVPXDg7BoYV1z9TYAmUDM3g2B9TO3jjIT0/NJKkpFFaotqoc2dNQ9J5DB2Rw4FTpnAYYAEqZazd6akRM2wanUEgdlNjWT5TKCJdPT3aN37rgmIYDZdiKGs5kS3cVrrKrrbvYetqc7efKJVAc/b0SoeGqLw6+25VAK3OGNbxZMEZo1xSrJuaHm1NJznRazZ9+MMfxrJlyzBnzhz8+Mc/xjPPPIOPf/zjpt/+l//yX1iFdzKH220WqAwOls6BnY6F1lR4rEZcBl2EtWifOLLfWHbCgMNAdV7bnarukbVeT1uT3ctC1T7sWr1VSxqdO7/btZTjoHkl25GQMGK495TWT3W4685Wn05aeUKn21P1VPe+bsdRS0ZFSl2+AuaWYoijsjsszjlT6mWkR2j7nv3t9vKoYasxyxDVO1mjb2yapqPuCAAaokbpE8aCyZny3VNbZ3qpP8boimJ9cw660ZvC1WxK8SJrQlqxbksTjp2UAsD1SpHTkzqDuHCaal8xlnF72LFNKbHCUqCBJX0xTLkp5yuGr3a3UhzF9YkuKKwy5Qr2TuqH7h0x7ruD71q0B+AoyV2dSVTRatlnNUow9I7kf7kOGCfCSPVu7927F//qX/0rXHHFFTjppJNw/vnn41//63+NAwcOTCHU9Gg47zPrPGRTYM01mxLoi/tdx9KNjimYrMIS0lIGHCrNXBKevNQDJSUqPNMFibE4b1I8za6hjEuPdq/73mByOl/0VHWw+HIGp3i7UdHJETkJioj7V6ut5UbbWpRXGyzVXBssAf6WjgQaFtqBR69dqyVGSgTKq7WW5Ikc2bRixQo88sgj+O///b/j1ltvxe23346vfvWr+F//639h69at4m8XLVqEr3zlK/iLv/iLKYK2Gm7dPPevidY4hm2dThoixgP+Ya8bY6OTod4B8DQ4Wz/768rLWjSftbkPlwlgqYtrc25UdDgVFv1ZK1jcVEqLblDohnpnvMA4lRiRw8OCChZDRHLDcRJZna0FHGYDTFRGQi/5YunoVuK7m8Vg6E7qw6LIV90qklqCh8xOmmLjer8b3TQd7kHQDTa+0UOrSVEQ+KhIsYGpaAWTowLLanRFUNtD86Y4h7Iq9gw+DNNJudKYBFs43WjkU9MKSIZFTgVQvacs7F8xIIZpKAmCvddCl1MynBBSW9pKLS9iqSslUYFwowej0zF69xyjSvmcBvx1javW0N1KeVQU2Y7NQ0bV7dLy7UNjg9VIbTE4TPfx4Q9/GNu2bcOcOXPQarXwkY98BB//+MfxrW99i5y/detWbN26FQ8//DCuvvpqbNiwAf/sn/0zbN26Fd/5znemGHp/cFGiHO1l6ZEpukLP4284nj2NTnOGg9TIEM0obHEihPBYhfnCI21NMQ47ullSPqzGaSA3UGs1XRihVVdEnNQTyWjn7LtmLPfwN6VmTGkst+17q9NTFV0AXncrDd+jmmNa0wpHpur1HAeeoX6N5hws4CzSwK01YKyNIn4Raja98MILOOOMM3DTTTeV1+69917U63XMnTsXH/jAB8jfHTlyBL/2a7+GP/mTP8GsWbNM9xodHcXo6Gj5eWRkBADQarXQarXE3xbfF397ZfmITvb7HOd7vQ65Vi3vJDXWauPY6BiA7L22223yfgVKjbVaGG1XjjZq7W6nk/3tAWNjY2i1O+U9yefqFUXNu2i1WiX96HVk2EdbbRwba4mwtFqt0sA61mpjLH++OgNLAXunm30/lsOOXpeGJYe91c5gLXmmAvtYu43Rlgw7UO376NgYxlodcX6t3Mfs3u38WTgc6BWwd7o4Nlp93+u00erFZ7ygEqOttsdXybXzewPAsbExtEscoPex1+3ksOc4UBYf4/Y9u3+r3cGxsQx/B+o1dh8L+jw61kKrwAEWf6szMDo2hlaO7+W7Dn5TnL1y3wv87dL7Xnfwd1TBX6Cit8fGxjDWkvG3gqWb04FOCTt99vJ97HRKOlDsQatF4IBDB7qdOgl7SJssI2Vu39g0TQdljU4v7KdYOTuVN9M03zFOaYaGTBitBB0t/DWMDuKU9VJI67iw6NFBaemImcBoVUqsniAqUskCe6ujRxKwKX0Jlm4JHnffrUpJK6+nYjbCBUUGLYJ6sS+12sRZ9Rv1GoqUO6tXymqwoSLzxKK2Hh0oYJfnlmHwRny3KtXTfRTe7ZdeeqlUOr761a+i2Wzi4Ycfxlve8pboN9dccw2++93vlp8vueQSfPGLX8Q//sf/GO12GwMDNIucSIWDG67wdGysEkLRY4T/biWEegJ0ty0LLO1OKbQ2BMHPFVgq4UkWWru58F8oLj1WCC2E/+z7ghZw6xfCvyu0NgTBrzi/x8Yq2DklqtZllChGCC0VxnY3FvwQpya5wn+vm8HFCv8ObT42WimAcGB3/5ZKVyG0tgvhn4Yd5b63TTjgCv+FAsjtY6ddPfuoCzuDv6XAHSiA3L43apXirSmArVbLwd92qQBysBdnr1BeNeG/wN+xli/8c7C7StfomKxEZd/VAPTyfe+Ua0h0oJ2fpSIFiT17OY6OtTsRTllGytzJGtu3b8fZZ5/tXRsYGMCZZ56J7du3s7/7t//23+Jd73oX/sE/+Afme33pS1/C5z//+ej6o48+ipNPPtm0xpw5cwAAr+ypAWhg9+69GB4exoEDDQA1vPzSSzj4amz8W7+xDqCONa+tw2NH1wIYQK3XxfDwMHmfvXuy+fMXLkJ2HBvYs2snOf9IGyhUwh8P/xSbt2S/XbViOYb3L4vmL96Vwb5z1y4MDw/j6NEM9ueffxYbT4lh2Zavt3zFSvS29QAMoDU2ysLeqGUl/V98cR42H8lg37plC4aHN0Vzdx/LYB8ba2F4eBg7dmX3Wrp4MWZueyWa/+q2DPZNW7bgJz/ZhG4ve+6nnngcpw7GsGx1YD+4MYPl8KGDLOy9brYXjz/xFFbvyH67Yf06DA+vjeauHclgPzByCMPDw9i/P/vtgpdfxpE1MQ6s2p7BvmXLVjz+5GYU7+yRR35KwrJ/X7be/PkLckN+A/v27iFhP9ZBud5Phh8p8W31q6swfHhlNP+1HPaDhw5jeHgYR3IceIHBgY0bsvVeXbMGT+5/FcAAOu0Wu4+j+Xo/f+45bDiUPfeO7dswPLwlmjvmwP7TR36Gbfm+r1yxHLeeXZ25Yizbma+3MzsPrXZ2r2eeehJnDMWw7NqZrffKkiXYuTbD32NHjrCwd/P1nnzqaazanf1244YNGB5eF83ddCiD/fCRoxgeHsaevdlvFy6Yj7F1MQ6s2ZzBvmHDRgz/dH353I/PmYOZhMi6f192/5fmL8RAHQAaGNm/n4Q93CdpHDlyxDy3b2yapsMNk0stVN1KMHp4xiZDhxuzF7mbGSVUb2ZQpM0amu9G2Aj2miSjXZSyoKVbOAaY4jeAobaHsc4I1SpWLWjaTYfFUmTbNZJosGSw13EMXT8iw5CD7v7loyBifNSMn8X8UolVDDyd3LCqhe5yhl6LgdJS1JYuqKikxISdQbgUHaZjGBdiPd3HeL3b4Thw4ABOP/101tAETKzCwY1RR3ga/ukjWJcLamtXr8LwkVjwW7YvE0D27N3vCX7PP/cs1hMgrcsFybXr1uPpw69BE/4PH87Xe2EuNh8GgAa2b6OF/z2F8N9qY3h4GFu3Z/dasWwphncviWHPBb9tO3ZgeHgY7U52r3qN3qfNm3JBctUqjG7NYDly6BALe6uVrff008/g1VLwW4/h4deiuVsOZ7AfOXoMw8PD2JcL6wvmz8foa7Hgt2JHDvv27fjZo1tRvLOfPfIIGZlVKIALFy3KDccNHNi3l4W9hgZ6qOFnjz6G9ZsKHHgVw0dXefPmzJmDjbnQeigXWg8fyWB/8YXnsJkQ/jdsqJTXJw5nymuv3eZx4FCuTLw4D7tHM9h37txBzs/ISa4IPTqnxIHly5ZgeNfiaP7i3bnyuns3hoeHMZa/s58//RSWEcJ/oQAuW7ECo1ty4f/oURb2eq68vvDiXKwZqQGoY/OmjRgeXh/N3Xk0g310bAzDw8PYvSeD5ZWFC9DdEOOAp7z+dBM04X/b1kJ5XYGdMwFJ+Adc5fVJvJb/9rW1qzE89mo0d/WBDJb9I5kyvH+kMGDMwwhhwFi3KZv/2rr1mDMnOw+TpXCkjk9/+tP48pe/LM5ZsWLFuNb+4Q9/iCeeeAILFy5M+t1nPvMZfPKTnyw/j4yM4LzzzsP999+P008/Xfxtq9XCnDlzcN9992FwcBCDy3fiL19dhNPPOAPN5q34r2ueA44exrveeStuvejM6PevPr4Gj215DeedfwHufPcFwIJnMWNwAM3mA+T9vrt7PlYd2INrZ8/GsVYXeG0Fzp01C83m9dHcQ6NtfOalJwAA99//AB4ZWQLs2YnZ116D5i3nRfN7S7bjG2sW441nvgnN5s34/OIngVYL77njDlwx67Ro/twfLccLOzfjkksvx22XvxlYMhennHQSms07yX16eHEGyztuugkztx0ENq7BhRech2bz7dH8LfuP4gsLfw7UG2g2H8A3t70EHNiHm95xA5rXxhFr++ZtwnfXr8BZ58zCAw/OBl58DADwwP334Q0nxdam53+wHC/u3IxLL7scV7/ldGDlQpx5xhvQbL4zmgsA/2nREzh2tI077nwPNr+0Cdi2EZdfegma910WzV24aT/+67J5GDrpZDSbd+CP1z4HHDmMd956C951yZui+fvnbcJ31mWw337HpcD85zFQr6HZbJKw/M/tL2HtwX2Yff31mWNxzTLMOvssNJs3RnOPtTr49/MeBwDcc9/9ePbHK4Bd2/D2q69C890XRvMXbdqPP1o2DzPz91jiwJ134PJzYhxY/MgqPL19Ay686GLcNvtc4JUXcPLMITSbd5Gw/9Hq57B79DBuvvWdOGnLCLD+VZz31rei2bw2mjvW7uJ35mXv8Z5778MP9y4G9u/B7GuvAXYsKc9cMVqvbMM31y7BG9/0ZrzvfTfit1/IaN59996Ds06LGc6jhxbjlb3bceVVV+OKc04Dlr2M0087Fc3mu0nYv7DkKRw+NIZ33X4H9izeBmxZj0svvgjN910RzV2x7SAeXvICBmdke/H/rX8BOHwQ77zlZtxx2Zuj+Ruffg3Dm9bgLW97G+67/0pgXnZW3vfgAzhpRiOa/51d8/HqgT24dvZ1mDFQB15djDe/+Uw0mzdX+xHQJssonKyW0Tc2TdPhKo7W2gWVocFes8lS94iaL0aGOMXxVENZEMKtFVgu5rccw4EpssmQhuI+f7urF1RM7f7kpSMajCSF4afV0aOsBhshLBDnU7AA/Ht1i0lrsLiwuwZHraNFWLPJUiReS7Vw1/Fh0fG34xZyV85eYeDV0ovcfdSMcO46ln13cb3ndVxSIpu6ttpt032M17vtjt27d+MLX/iCWlh2IhUOboy1u/iUIzw995OVouB32prd+PrKBTjltNPRbN6G3130JNBu4a4778SlZ58azV/zxBo8uuU1nHf++XjnDW8FFs/FqSfTwj8AfG3dC9h25CBuuvlmzNw6kgn/59PC/7YDx/B7C59Br1ZHs/kA/nbXfGD/Hrzj+uvQvCGOMOMEv3oN5D69/OMVeG7HJlx8yWW44fw3ACsW4o2C8P/FpU/jUGsU77r9duxatA3YugGXX3oxmvdfHs1dveMQ/p/Fz6MxOAPN5nvxtXWy4HdkwRb8r9eW4U1nnY277n478PLTqNeA/+P9tPD/vT0LsPLAblxz7ezsLK9einMY4R8A/t28OWh1enjPe+/GoifWADu34qorr0TzzouyvXPwafXuo/jKkhcxY2gmms334PcWPwW0xlgFcOVjq/HY1nU4/4IL8e6b3gosegEzZ2bPTY0/3/QiNh8ewQ033YRNe48A61bhbW85F83mdeT8f/viowCAu++5B4/sXwrs34MbrqNxoL5sB/5q9Ss4441notm8BQ/NnQP0erjvnrtxzukzo/nP/2A55u7KlNdbLz4TWPoSTj/1FDSbt0dzW60W/t9ceb3x5pvRWbcP2LIOl1x0IZrNK6P5G/cewRcXPYtaI1Pk//vGF4FDI7jl5pvw3ivOiua7yut9918DzM3u9eCD9+PkGbGY/dz3l2Huri249LIrcOGbTgZeXYyzAuHfHf/XwicwdixTXlc9ux7YsQVXXXEFmnddHM19ecM+/PHylzDz5Gwv/surzwJHj+Ddt70TN1/4xmj++qdewyOb1+Bt552H++67fFIVjtTx0EMP4Td/8zfFORdffDFmzZqFnTt3etfb7Tb27t3Lpsc98cQTWLt2Lc444wzv+q/8yq/gjjvuwFNPPUX+bmhoCENDsTI6ODho3rNi7syhDDc6vexawYNnMGvNyB0gXdRQq2f/b9Rq7H0HG5niWas1gFqxRoOcP7NXCWi1xgC6eUrW0OAADctgdv9e/jxFBtXMIRn2Xq0G1DO4Bhp1FvZCDKnVM2M7AAwysA/NyKIDu71eBkuvuE7DPjOHvdurodYYcNahYR8cqBfAoFbL/t8QYC90g3qjgn0Gs48zZ2TXOt0M9m4JO7OP5b7XUM/fb6PO48BAgQP1OopAWw4HavXKUOHBPkDDPlTA3vNxYGjGDHL+wECxfq28l4QDZYZLrYFevu8cDtQbPef/A+U+FvsVns9yH3s1NAaq6ycN0bDPyGHvoV5GOEiwF7qBh7+DzNkb8vfRjAMh/g4NYnAgNjYVsKNWz/AAGW0gcT2RjllH39g0TUdK2/uoC1FCzSavoxunlBJ1kix1HUx1GgqDijWyyal5U0WdsKCQ9TE0g00Bh711Zm7kM3aRcAuaShE2g6UhrqsaMeJ0Lnl9L2ImochgBos9IqfdddPo9MJ7xW+k+QOOEU4r6ueu47b/1dLogCL10tiFqOPjr1Y/yisaKNXtciL5VGNp0Go8JarQLbQuGRFfjzGZ3m13jIyM4P3vfz+uvvpqfO5znxPnTqTCwY2GIzzVGgOVAK0IrZXAnf2AF6ALobVeCv+NuiD4FQJ3vZ79Brzgd9JQdR4GBgYcIZSDvRD+M0GxfG7Q+1QKrbUaUNOF1gKn6/UBdBUBuhD82lbhf6AS/ksBWtrHRqW49PIzOygqLllKsqZ0DQ4OEkpXr3wmCQeASgGUYCmUV9Tq2T9kyowEe6fby4T//BqHAzMGKxwYGBgoaelMRvgfGsyF/1q9xAFJASyoWq1e7TunAA4FCmCFv/Q+DjnKa91TXmdgcDAW/gcc4R+K8A9U/KfeaFT4q9CBAn8LusEaAQYLg0elsE6WwpE6zjrrLJx1VmzcC8dtt92G/fv3Y/78+bjxxsxo+8QTT6Db7eLWW28lf/PpT38a//Sf/lPv2rXXXos//MM/xC/90i8dP/CGUTqrog6izHyi5iMXjQ74DXJS6sO59VYtZScA11GsR99XjmIB9vwr3znLrM10btVh8UuJaB2WrY7iOpGZklysXJX19fIa/ny3aYyOA62OnoHB1Sy1NA5JrRGoO62r/4dF5eN4ThoWQMruoGBJcxQnd+RWsjsiHd5QeqRh0N8mY/SNTdN0pBC3MI3OXJuo04WlowXVtcgSjeESQzVqKrVmU9fW0aJBRPBosAB+PSs9wiaIJmLmu0Vqtcgjdx0Xdq2LRBHVorXQdWHxi2zLhjivZpNobHLny4SWY7ZslJXXhUg3fnrpiIbUNbpOEocDdCpaEsOyRDYZCoqHrcatUYWuUOHec7qMyfRuF+PgwYN48MEHcdppp+Hv/u7vJlWBso56PUsj6/Z8Iy+f1ktHWpq6qyQJ0E70rBLBl83XlQXO+M2B4wqKluLmldJVdaTU6qqZnQgNYh8lBdDhSVU0oZ6SbOnsGSpdVTdNZd+dSEhLpLClFl/xXUGL1EjL8p3Co0eqktbRC6dn32V/bU1X8ncadLcaZHGmknkcvUWXewwRqBns7tmzOc2q4uZpNT9PxHHVVVfhwQcfxMc+9jF87WtfQ6vVwic+8Ql86EMfKmv1bdmyBffccw/++q//GrfccgtmzZpF8oXzzz8fF1100ZTA7eJN9tdGJ83yg0MnU1rHu85cNg0/scGI52xVGg0BfkF/ayfLbg95K/icxrOwO/qVy2+06HtD7VcgfFYt2t3n22qdW4JO2up+dlX8qtVqZc1dk85U8D5j11la5hB4n+PM1cpI1Gq1qgRGADtVPr8Qo1xYMngUPbujl4dx51s6yoc02Eqz3QZM2TPJsGew1MS5kzX6xqZpOlyrvlU4DmsHWYwk7oFkO7p5xMrQtcixpOspfUEakplhdU2GL68FqeJNidLoFOHbFXaz3yiFrQlLuiyoV3ujGQ4GA9jNSkkPHrHSUgxdnBGNfIRRkG3XzQj2lsLWpnREAhaJzpLGJoWIF+l8qlLiGIa1rkLJsDjX3bpgemRT2EVLCLV6HcZkereBLKLpgQcewNDQEH74wx9i5sw4Zef1GgONOsbaXS+tl8Mtrli91n7dXdtqhG0p9CikpS2FDzQYwydrbHIMPBbhn6qXxxruS6HSN9pp3l1L503AF9B7PRkWFx6L84bDAdVL3rHt46BDv4poH9HxRHSDZWEh3inA00dPYTQoXQWYFjkmdIC0NBmsEZ8lwOLJTuVhLt/Q+GMBu2LACDrZnqjjm9/8Jj7xiU/gnnvuQb1ex6/8yq/gv/7X/1p+32q1sGrVqkmtMZU6Bhq+7F7IEdq77RiM5gB9piydpH3jsBylHUZlmZr7mJwbPQA1k0MhjOrWOiZ7MqSpo3G+ttFIkpJREeoRmlHweJxEFudsIzc2uY2JND0ichRr/KbXU6Os3O/8yDx2Ohq1GjoIjE01zthUGflaDg6oerZBFvdg9yLE9Ei74h4iLF6Jleps8Dp8BfuAwUk0GaNvbJqmgxKO9cimoouaTZCyKLDuOtkhgzrfCyFVCEqYima16LY82FlQfGFXgcW16lsieFwPeK/XK9Mt2NQ1wgNuEuwNRhUvBNogfDcSrO4hLJbQXcqqr3pqAoaledTcd2RR7trdbhXxZcVfKyw5DlgNQu1O5fGypqSmhMGb0kAdIaftCVxTy4QmaozHuz0yMoL7778fR44cwd/8zd9gZGSkrEFy1llnodGIU2CmcgzUaxhDECFowC1A70hZ0saerXU8xTf4c1ER5ZaDX5xRhYriBPTIprYBFh92qEpUYcwraEsVDSmv3TVEfAGOcarTKw0gVv5r7ewZ0lI1DcJQGzJbx01JTnE86Q4T6p1K63sOEEtaTv7XVbq0s9HrwaPrat1Mp0turaY7b1xYLNEJ3a4uI7kGwQymrnc9hr3i1SfyOPPMM/Gtb32L/f7CCy8sjbvc0L6f6MGVkeAMNh4tMETH+2fKEpFeK+mMGkHnyA+2M+LIhEq0aPZd9rfr6B2aPAsEBtmJiqQlDA1iVFZRBsXbF47f0NHxWnMfcw1SBxYtygrIcG+0na2t8Zt6wG9U3TOxbq1rjNUitUs4O4Fuyxpus78urkvrp+473dxHgBtVdkxHoQNedkdH59updZcnY/SNTdN0NAhk0kLhw/la/nFqKk/HETAth8xkKHM8DAVMAE+YG4U301qvhyhsrSlUhXfSal3OmLOzhuLNtFrG/fRFLbqtum6J+PHC8k1d0dKs+q7iazWUdXPBXmO2br6yJfXDS+lT6gq4cLr4yzP+uB6UtL4rtJSCpQF2l/FrRd+L+Zpw6e1jPldSkE6EkerdXrBgAebOnQsAuPTSS7211q1bhwsvvHDKYKdGZVx3DTZahIIfZWdJpTXVT3AjMxXPccSTjMK/q0QBlYEggsXx7mr80YXdV0R0emRZnzYI617vbq+HopiENSVZo0eu8QjQhf8Bbx9tyihQ0Jf8nhZjk0EWoN6pe52Dpe1EJ4gKoBcpkea8scpgbfecmnmM3UBpwTG3LmAGkyJTBZHx/TF1YzDY+5ZyBhtONJ+l7qd3ppLkX0u9SjoyhMN7N1Jfy3gAKsOPxVDmRTa5qaasc4OWZ/nIkOyv1UjiOrlVflMaHH0nkRbd5jdgSsOB1ChKvoxEtbbrcLcYpywyB5UuZivhYki9rMWw1Gr8fNfJbSvHEcv6Fv5R/EZa343MK2iGxG/caNeBupxiOlmjb2yapiOFuLlChCmiITH3lEqhSg991EPh3b96rmp14KWsH9qSLuUIZ1Z9z0hi6OpXHHhpPh2Ka1MytMiAUDhuaczZYRIdRXF052fCdELNpm5PDeMPYbeGEZvTVrz3ZI+CcPFXV5KD3GlDnQMtZN6DxcEBSzdFi3BJGQQlhnUijFTv9l133TXl3uyU4dJHDV+4SEvt/fueN0FB9iIzbfQFyEO9NSXKNRw474OTK1OMGO58V0DX9rFYX6sH5EYPaEY4D3bHSWFNSdYii6t3lL0nq/Bv4dUAzX/FyOLxCP9BwVYtstin07ry6qcjGniSKbqccIBYCjcb0xfHU/+jjJYxGoZP9DS6E3G46TAAdIeCozRaimyPl066zlxN5oyKbGvRqx1bhkTxjUWWCc+r1qWYkn1EncaJAracV8+ootVscuYCjqHB4FCwBQtQhjVDnSSDUZByoGfry+/JrT0nyxyEs9VgoDSlXhLyj3w2xudwt+g0cc0xjd/E/MMW2dRFJ+86OdUZDCe2ZvELPBqe1dWmNAL+QdDDpvU87mx+PZovCnUJhjJXme4ZCHnDPTQG45GXjmiJ4HFr6hhrNrm5zdJ8yjspWemp+j7WGilaMWHfG2/ojEcSN5uCpIXxe4WtDTjgGmxSUmhazj5KNVJc/NXqtfiF010ckPHXWm/KNwjIzNO9bEkvorzx0tnoj6kfNL5oYd42wa9O8AFT+pfBMFGkJGfz9fpkPo9xouw4Y1MCf3Rhtwih7nmxGAM8w32C4mJObfFqNtk8/O2ub7Tjuzhlf63KqM8f9SjRes1Ov6hUSinawBe4LdFByNfXnVpRZJNae7KCRXP0AL7ymhIpYUkBdHkSAB32X5CaTSfiiFIe1dp2Di1IKixvMzSkRGm6MqHbzVY18Di0wFTQ33BG4qhu2Xk24BlUUg02qRGgNqNd4STSeAht8Nf30TXaiTUCEwxxrn7lOVsV/tR1ajZZ9tF1tsr6W/aeXF7MZiW4BkTD2inFyt21UkpaAEYDpRvhqOh62XdpZ28yRt/YNE2HV9jaqDQCmddAQ1RKKUn1joihu54XwFpYM2xBKhsastDd1GLldmu0G0bMw1IdeK/IYEJhdmtUi/aearVanibgEysLg7N5yGKrvlVBainE0F2na3hPVRc1Xfly72tPA80ZlsHw5RFxQ92jAS9SJc1opwkWRTeOEnYt9YNIMZ1qb0d/yMNVHFvKO/K8tV6HHVnY6hgEXPc7a9c10hhgUHjL+lGWxg/jMNi0lHPhG+67ZmO5Z7Qz0HVraosbzVDwvBkDjEPD8ZB6qWhqSoYV9ti4Lisu2d/0tAY7PrrOFS4iBEiLlAiVV2vqpRUWOuJLMNpR+K5GnGTKa6XUKY6nE7xm04k43Oh1y7uiZEhrhE01X4KnwgU9gq6Qw/y0V61AuKXRAVBFtbrPytZD9WRIu4PAWoOUykqQU3Yr3qqmUP3/7b15mJxVmff/raqu6iXp7GSDQCAsYQkhgIQlIGuAxvWdAZcMP0QUVHBecN5RVCTuKMNvfo6OyoiDwvvioOOo71wakbAphEACGNYQIAkkQBJIQrZOuruW5/dH9VPPOU89dc737lRVd5L7c11cobtOV9996jz3OedeY5kprFOJLhBuGhCJmk2SMitJRjVGdvoeITRQJkVaUTrbM+e1xrsy0ZKeJSYyT7IG8oQDynyf8udU/TubgRqbhih29BFnPALs6A1fzSY2lcdSKJLQXeKBjy72sPK+mfoCjEU38uxwnqCWhMM0Y7QzPTtU6hpxwIxaonKbc1jKmOkikXywJ0JrifcG7AuSb/2aB/sCoTyTQ6C51A+mxlP4axkjn1k3pCD07jGbRFIkH9XqWPDsWcV+m5zHrbixDIK+NDqh4d6styCp5cC3f05ILfLIIk0vZSI9zNckz3Qoj2+fSU5H9B/++QN3goGaqN/YV2T2JPMz8usjM+WjrxAa4Vy61zzkuo1ZlgFG4PUuGxCZmmPlf5n0kCoHCGm4p2UZ4KWrSOxhpvHPXAO1I921ZtNgUSsVrXYjBeN5CvizD3vOk0RjZI01H+oOV80bqbM1fBvGqFLdSc/9DCZ1snTVsJFGAUt0mZWZYtw7an1MSQZExvnPposllVnxRUeXAjsykokCpmo2Wc19mH2+/C/jsLDvY35ZTMdfSfgsSYxNxZLR7ZdokiQtDTJYZ301Ng1R0gIFYaYsMN5Vs127yKJbDLwd3czXqBRAQ8aefDH6PnEpqbQCpzYJiHLcRWlIxZK1odQK+0/aJKRWfTb9K/I6+y9IkRGu5lvHLo4yS7qk3lSpBH+tmcQC4cxnWqoocSaMuMSENPfLko9tKLULTVavGcYDbv6trkOR5Nmz5oUosqw0H8l6STJKmN+Pk07QL2z6F6UDjEMrG13B7klJXkPXc5Q19Rdp9CjL40+LSqo1xBpspNGNvkuUeenoLUT7qe8CKI0msjyqDtnNrkxskW0rbY1xaJCe6VAlF4m0iXh0m28NJDmpqPR+Uq8nR0q49yQA6OnzO0DM9aU0l5pp+EQ3umgd1H5/ieNXOt68F1TOVc5mPdUGHmc3uv5/WUNZ4h3II3uedOJJHQqZBF3G3IEKpZK365rk7zTfXzqPlJHEmLPQ+eAab9eyYmQxHaK8g4s5u1sRX4Jng332kuadStumGmtV38eYhhSmLK5nrxHozWKIIlUQ5mGd9dwy6Vb2eC6qJdFQRngQewSHY/OCTHkEiZQ+IBbBQ6ZbWCl9ZIQY88C3JFivnWug/18mxTD5UEHk/JIFTW3F7K7tYW5YvUXT4Og7cHHr0Uy9ZOqMmJ0gfRuW2f5XLAu1eRqfE2EsTTJQUmmgxGarNB/bSMKnRxeIiAaz9S9V/8PySsoim3zGcrsGAWFYr1y+ucgmy8HiSSWIO2/yHiNfouGAKHpavugQxqmEqNKan2mtw7+n7hFTE8yUvWg2rSAMlEx0QlJkntMIZ8nCrBnQspTT0sv/T51jEvYYxqHB1BAz35+JQqx1pvI5ntTY1HzMdWM1mWHObYSuSSwmzToJPftN1tRjRHSFGe1OpX8lPX+kjvfpsop+J40YScZe/hzm1tmmjFRkkyGLr6ao+RqrmywDjyeayDSQm1GUtcRJjG6j5tEfZQVEc8YYysw1wGW9JOxPxD3CzByonQZqrwFZRoUgsqnoL1beKNTYNEQx69IwD6XpIWFD9gq0ZzW6NETRQYRhouQ32Jjv05snOtBYhzreK0ynIRkboqRmU+USwG78lOGgOnea2Zzt7nU1ohoSZKHS4shIgpYEo52r5kn4kZgXpFpTaRq+mIgvsxU0p5jL/0pSWEuBv22xKUuBvCAlGb5cBspsS6Q32MimPDkvSvNJ8qb5Gj8EAdBbiNZizUhLYXh9ooHamUIVPadsJIm5JzERf3Rnz4QIAibyxNx//V2ZpGkKcsM9GyEGRLo0nXIccs2aYAKHCX92qF6/3ssrOS9ZoSzhK7Ys/jT2PkKXmod/al7MZ4/Yf+1aJP17EuPAY6LFjXQopbmY58Ue5vxr6hoqUr/8L5sqbV7WfemapkM8TzhyE8/ijLGJbWKTEL1a+xmpPluzkUqMgSdpv6mla8y3sQ2OhHODMtiEspAlMBLvbzX2vgTnhuvMkeQopvZK0sElcW4k7U1MNLW5ZtyNtaI14/tbzW+bd6Daz160fvOEAz1p3l2yNwI1Ng1RssZiknidTU8WU7OJqxsDYzxx4TUOjayF1pTdnYZkKnGBB7wU1SRwhasnRnsQlwxfeoM5vuyVch8YgWTrtVvRol8eM8XBfcCkOyglKE7OC2AWNvYfvilFm3SoYGVh0u6Mi0Do7K19UK8+LLKRSsy8DNQTxHj37K5+fj2gNJ+kSEvf4R8AdvVfMt2GA+PATdVD4A9P5u/OG2lI3uiKYok02hqyMJ1kkrySxD5gpqJ5O3uS+ihrHv6ZTjJWSjJXHLosu/8QmjgvlOGrRO2/tlHQ47wxGz8I06MrshCXV9ZAWTE2FUoIKvsAsyf516+0BoxdH4e7RAGRHoh/P1F2rdnUdGqVkfAa5Yus87Q6ulTaeZpyVhEOguQUwNqyhK+Uzyf2eyRhOdqKbn1gGzFk5zZZBLv/eU2lUpXxpsGx1udqR0X6DQdmNL0omkgQuABEZ3fXvOSMz4ipHWTe95iInOS9OHlN5jLVz4a7flS0b8v2yihIwxVNHb5mpb8L6nMyTmt2DTQCNTYNUcKFw0c29S9U0zvirdnEbRJWZBNzUE8wCLnyZsOXxJd1KmWh/7DLRhMZFyRJuHrlYC/tQMOk0ZHKMBTHKhpX05tiGsqYzbM6IoeJ4GEuSEC0WZqhuL4cd+YCbr6PfUFyeMCNzdwfSl59WOQOXCXOQGkZhEJjqd8bb3nUPBfTfNGs2aTGpqFEi2G490WemM9AZS06n4vyv/bl2792rToXhM4QG+6pQ2jCeEavF7nLffj+u4yaN77UtRKZEhVFzAiNdlYaXQ3DV4KnmfmM+orSSxRXL09Wayi65DBrwFxfTJHU8NeyKfXhe5kGGy6Njr94FwMuHSp8LvuIC6CZBhqeqVzRBuazpDSXJGNTNuOKDKnWqW4HASrjRXVpin6dbe4t4QWZiS4tlrgMifDXms4w5m7QVyj5634aRjumlmtyvVUiKrJAOooFhobEz4jQ8Xky6tKMmqk4oTy6A+D2G7ODIXN/Syo74Qp0SIq+rvWnVs5WBbZ5VPTe4T2FLj8juKeIIhytefTvZXbaaHPNP2psGqKYlwzmYBQtVElRUK5zitiq31JtdWXCPKMLkl8WqyU1cdg1FbNbWUUpV/4ONNH3dxGyJ6ahEJszYzwCosM004HG9Dgzm60VWiu5lJCFsM2DQlzGWmNZD5kZwSPdVHwF8ZMiCbgQZTOXX+gNpAyU/mcvyRjgkkVpPsk6w59CFR5YQm9vEpYhgDE4h17JgqxuhXXIrRlll2A4ICIhS0RrafP9mZpNpuxMpLA46tPQjVRhdvOQW3Abs0wPdx/hFEjqPETVszOMn641lqTvfJF5TEfdsizmgZtwIliXV/6SxqSimREnzJmqcnkVGhwLhMHRHN/DRDga+6PSXEyDTSUaVdjhyt2BMdKTXM0m86zkKYpvGcr8z591lin6I3JSxvPKRf8lRKMykYiELEn7jbPeakJEGeOg7y34DQ3iz9TY+xhnSFLUcM2oXtO5UYwyU2rLkrTfMMZP4x5BnmnYmk1MYEFZduNOLkwh9xm+gCjSirvDJ0TSiqMKa8vSCPRmMUTJJj2UREpED6OsEhae2wOeYC0mFC1r1Y8fjNjLep7ZbEPvPVnYz0wr8HegMTfb8FDHXZAkdZLY4njhNOzqExgc6Tbm1UY7VtFS+fwJaXS1htv1yfi6R2xtIquWjedzsmsu+L17Zlgw45GIZClRYcSRR01au83/GSnNxwzH90c2JegjxttFXr6jsHPOYBN5a2V7Uvh35tiUZCbaNqGmIXNZN3Wpz3DPy1K9/1JpDcbBkrnUhVHOTNr4wGo2+bvgmDU0fJGW4foKAtZLHj0bjEMjfIVPdwzPJX4HSFK9GGZe2MLNOdNYyjQ66f/du4gIR3MeleZi1qsMdQ2jO9iSFtL0maxlmPAYhxPOPqzRvJJW5DhuhG/FG1Wqn1cqErH/vXPkebbinGV0PNvxOyGK0teQQqrH2BqBSWeOWnNjdz8VNLsQ7n1Fa7+RnmncDi6mrpYpuymLa81YTuvA//5JkbS17tnJznzm2SsZKX0a2aQgVr+AeBDiBpvyeLdV1HxoWM+XqKMb8cCb71UJ+WZS+sx0LmK8VdiP2FSselNEfYxIdv8DXzAiZtiaKlRxx/6XzMtdzQLhltVdEP46gE2CUYaVNDqiyKCdFjcwbx0TgWYeclzt48O3Yg5c2SRZyMsdU9gvOSLDbyhjDgpK80lqqV7r4miuxfDi4o70kB1aK9GH5AG64mlm0pDMQyu1D1TrF0b2PK0z7Mt6xqmPyv/aEWJslJUgrYFMe49Skv0Gx6TLJefs4brgJKef1LoAGlEefXxajunQcI03IyUoB15iZFONC6DpBKPqN5b/pYv8GmmglbODaw+rlFXga7eF76s0lyrDIGX0YKNUyv9atTmdafjhOjP0pMdgY8oubS7ARCJKa3NKnK2FYimKACWdG9R+kxAFQ+03/bKnU34nIe38F9TQLb9/tUM0zFZJlt0+u1NNFwpczSarjADhJMpYZ5qoQUayLMbZWtBBNF/0ByKUxw/M0Bs+S+lU7bN+UlQvW/uVyZBoBGpsGqJYhwvB5Z7pQpSxHjJJlEoJ+UK/F8ARyhhZjNmUKzv8lU5xqly+HA98qvohYx545gJmvs8uKqql34hBeqXs6Da/lzp8iQr7t7o22PIlYXas8aWWlV8zN1teGYbrV17wkEvliC5IXHoGE3JauZQQBpvKhlUqcYXTM+aa8W+ISRf8moeWhHoRrnlRmo8VvcFckCsRrv7Dv31oJUL9W6qjgxgnhelp9nlrAe7ikk6SnTFM0DXnQtmjOiq1x0Z7hiQ9mq3HKE17j0eJMnqdTiVIOuSy3l3BfsqsX1MW6hzT/1Yl2ijYf3ntXwMpxwXQdiIwe0x1mo17z0tyPkqMpYSDraTGpsEgrieZkhPFImmwSYqCqZNhIimSlsmQMFNNnSlR/f+WSlxx6Phl3TU+cihGepLqfkrX5YsME0wB5/C9dvb5z2Gmc4PJkLAjlfy6ycruIM7u4RqLykjUHGo50KlaQ+beVyDWjGFUCdUZ49zg6gUbQRoFf0pfksPd3U2xfx6JdFqrgRixvjLmvbby7KmxSYG5mGSHC0l0RcEIyWbqJBUND6JTcRpFR6m88spDxodJmsqKUcyWZ4coMMd0oLE6CBAKwiw8zdRJMqOsKh5tomaTpKtJkdw8rcJ+gs22KPSAU3VGhKlophdL0uXILN7qzs+3L6aMx4stnG55Awv+w2ViKHnNMPjo9zL1ppTmYzdz4I0kTGSTeYCWhOPnizLDBNMRK2sd/AjDvaDwdPn9zT2Pj+CJ9iTWmypNa+DTEc00YCYtiutGV21AdBsmjENuZU9y6PXQ8GW19PavgXD9MkYS1jMdqnCxp5mIsjINt0y6hzi9PyENlHHeRLV0/GtdazYNDvHzAxfZRNZMSzD2MqnSjFHTLkQviKArcWlI4a+19ar/Ak5ldyTsN9S8F0lHcUJNHUkpEXdKn8y5YUev8vuNqVed8qSic0FZFr8Bn60RaGZUUGl0aVuW8t+T/P6mTmSCBaLo6IC6N1eCOorcfS98jpksmcQIY6a5i3Fncn2mjUCNTUOUrLFQOW+pbfTgLhllg5D588njq63RVDtlshhrpTZCGNlEXb5L1AHT7izGX0qsNCTCUNZTIA51lY0fZCc9PsoKqI5scnU1Cd8nMNaA06CSsEnQG5Yg/JUxepjhrFwoeUK6BVNbyzKuEpc7STc6YUhzkZQlybvHRBL0Eput0nzMKJiKp45YX1SUnRH1KemwkzdqpUkcIC557JRk5sAtu0SZXdckhfm5KCsYsvBRVnkzOpeIVrSjZvx7XtQh1a/XTWOmWxbDqCKIEu0lGj9k0kZKMrF+zWhbJkrUjJQQXQCpCLEEYylbF1BwLukjC5CLCoQb5zWl+cT3bC7C3CyKT6wzYd2jXiIN33wvrgRGtN8w3bzCX8sah6vWfNrV1c8wNPQR+41Rb1XSUMdKlSaMAbuYSNoE54aztIKp44WGbabLZ3UaHbH3CRsjFMk0unC99zJ19kznhujZMyLzqKjeEmWgjK8B2gElSgMtGc+eGpsUmNFBXEHIuCeLuQQAZk4/Gw7o96aYIX7UhbpqkyCs+obyYZQ4myoiuSCZrzHzGG0SJSqU0TSsMRFilYN6JRzbL0t5fP9my4aECi5rdk4xcWghNv6kVEe65hjhjbe9h3zaKPPsWSmpTL2WBE8mU5hSfsH3HxaV5hPX64DnUJGxnyPK6VDivLWm4Ys6QCekhzCHf0n9O9brbRrLmWjITGwfcD+j5dfoCLFEWfyfU95sWkHMDXP4l6ZnmYZ+ySG3zyoS73ew9PQRh//E+o3+/VHcja7Pfy6xUwCZ9MLqNAg2DXQg9T/ckXDRfqo0n3gzAuZ5Mjt8io3yhGGbqXtkjSecVZahuuA/+1SMwwFnVMmm+XOYtN6UlY4Y6mxiHtmi3C2xeXfOi+XcIHRBRU9G+zar4xnDRJVzg1gDVpQVYcjKG2l07PMRfc/93gDrKE4ywsmiEHOO+148Mo/5TAF5YfY8kTbaCPRmMUQxQ+2L1MGeX6hJtVqcofAJhgMm1c3sRseEnHI569FDwx0wzYeM2JwT0pAkRQldspsbFtXNwIhuYwyO6VTQLztxaMkIFa0Z1SAokGilW1AecEYWcw0QF82EKCtms7Xqgglk52uC8cXKi0Vu/bbEnqVUqvYBLTEMXiObhhTx2ivl7/kv4IyHNLE+B2HIZKMbJZ46MyWZawFe/ld84Cajj+L1etz7I4z3lqY18OmIZmo3UxulT3IIFdePinQvc9llIpsAI8qZqpVV7RRgIyW4dEf7TMXsGYCRwuocX/63VDL2U8c8StKbzNcoB4ixnyrNJ15nj0mRLZYCqtZQOL5ssGGMz6HeY43D/PnBdrT5ZU/1n2f5iNGYzibOSfz46jOhuyN3ZCSR1GwKZWHOeGyXvtChXSDPs1F0W7QGGB3fR9VbjfbhKEuGO4uH65eRhWnqkHT+ZQyUVgorlcnCGXiqIxz9n5EpO9soi5G9EaixaYgirdkUpXPxRbYBLqLBemgIw4Epu6SQLFUg3IxSIRRnrlLU1uw64ZA9ZjgASCMfYyQxDsd9hAHRuiAJajZRXU2MjZK5mGYTlD53KZFF5lVkISK+AO5CZRamLBCRAemEDYtJc5FENuUH4h0RXJJZ41GUKuJ/9pTmE4+cLH/Pr2OYA0hSEVMuCoaNKExbsvs8afGDIuOBpwsmm2kNgvSvXcxBrl+XBgGZHm3oAEk6l9UW2xFpWZ2STDgRjL2dGc/qo3ixct/48O9iDtxJraipNDqiyyiQdHn1r0fALG7u2qv7ZTeK/HL1QthaJ7beYKNnleZT2YOJyCbr+RNEnVg12ZxNaRKcGwIjCWPgKRZNZ6tLd5T/NQ08TOQtm4YUvhUTTW+W42CifUI9li8MrGaTuzRI+d+CYXB0ZyWUXys7/yVZMrJSIpyhrPrMwRbCjjrjMft2tN8weltSs8mMEHM7oaPzUnjfc2dIxPQA4VQ0ZWe7WjPZGo1AjU1DlEoaXUHmdY4KQvofeIDMETYUrSSVJ1/kuiVEKQuCMEmrU0Lt8aZHkLHoxmUBarfONOVhZLdCa4k0OitlgTE4hpsnYfQw52CnIOWGbR2ebFTxb7YVWYgLD0AWxBdGWcUPUN7xgjTQpLROZuMvGc8ek8LKzIspKxNVqDSf+NoCOF3N6PXWlkg3SiNyJF5yxnhk/m7m4pJU9JTXvfzlvpcqsFytj6iaGLTXOzTacQYbUaSldfhn9sfowM10o4vL4oq0LMvK6yM7pc9/EQkjJejIJsHl1XwpSmH173d0zSbr8iqXnfXAB4EanJpNdX041vFLnCGNWkNcMxXbQWC+h3s8f3a3aza5ntfyv0Xrguw668fPYdx+s5NJX6yUwABl4DE7ujEp5+G9g0mjM50bTHRbcvdmwmjXx51/Q3kqta+oTuVc+rC531CO5ZS9BnKZdM3UfcBwKPTx9abY9Ws63KkaT4L9xopsItK8zQgxrdmkWJjtKrnLPX/JTCrGylyQrdxT4qFhOroBSdEYfiu9qWjd3vt+WYqc7HFZXEW2y/LEDgoO2UMlbBb5ZGRhaxNVjE2VcGz3Ggj/rJ2EZyepZgSjOM1QXJcBKXwvxvCVZCylQ3GJi2ZOutlKogrN55pI/TAPaEzaSnU6rVvFx6MKtWbT0CLpwsscnpgOO3akEu99zRdLVKRl5QBNHv7jkU0u/ZVrMWQnLlHSKK547T5n9GyS8Zs0fElqNvWQxu9cVXSQX5ZyowjegGgb7v1GEtaYHU9fZGSnU5LDy6swbZSpgZhKpUTjzQLhVNHemNHON75idBZ6ybVuU/OJR0az9SQrRg/GSWiefx3GgNCYEz5/aZ9xWHJ2T9QdLiNG+d+i9bdmar+/wGkNJDlm/GfOUombx8RC2HWOEDPHMzVO2XqFyc5W/5pkGntYDqtwvyF0sKXjBWl0vuidyrNHnH/NOrSSeoXss5rL8OtXWuMy6Q6vxiYFgH0g5WpSxA86tcea9TFkxVi5osaSFqTma1TNpkz1Q+banCOPIOf9lNQ6MOVhwl8rhq9CNI9snSSmq1/4EpNCk0qlKsqtu7dg/S2JsiQYbJgNy0r/cbx/uCns7CvLwqbR9VLFWCPvCJNGF66PHf3zkk55Lj2CQ45VZFCQDmFHEvB6wB/ZxD97SvMR66Oqz5MwxBe4yKZQX/A1b8JDq18WUx4mtTsnlN1soczogHgKFaO7AMNLTuxhfWydpJgsKY8+qhxaBbIAbDRRZOBhOtNGhvtC/8/Xbz9NKpbs3gfK//aRXXLjUR4+2atTL/3vzUa4StOboq66/mfPvOypsan5SHRN0tmHMTznjcgQrtkJ56ySpCElRUW6zuLhW+WNaAy3gYc3fAHV5zYqHdHo5sXUW2WNw/Har670QvPPYvRkUm1GxphlGqpdDq6qNDriM2IbI5ipaMydSRLZbf5uJhrOrtnE1E+N7kycgTKmB9g7PFHCJfHZ05pNCmB7kRmvc1XoPGnV52oNmZ5Y/0LNxh748nsQl3VpvSnCGp0zDvZUrnXc0u2LDKkKI/YfvM0uD6yRr7JJODvMISaLew2E8lDRRAmRAczBosfYbJl57+7lFSfAbhLRJTlPRGTE58UX7SMpkml794hnyUoD5Ys79hApNEC1J0hrNg0tqi7fXmNTPCLHbyTpM9YW48W2DDyEwYZNo6uKxiBkt1OMXfqlX38VSgjv00zYOdchNVVVL4+KDhJ6vaM14LlE9RvqdxId3az2z5XxpHeXSLurODSIUH9TnkgfcYd5RpbQf0EbKAVGACD6XKjoBONcwnV2rHbgMRHgzLNnzkFejU1Np7qpA3f2YcYnnTlbifo+u0jnhkRnJ16+qee1aBRY9usy9iyTqTzfBfq982ajFleEmNDhXq1ruMimnYSBx0yVHkiNQF8ETDwd0X03jN6rl7hjJdXlYxwQO4mUvvJ78Wsmig7iHL8ZU8cTRj6poTduoGScbWYnSJehrBGosWmIkk1Hm4SkkFrkAfdZ9fsPsMRCzSYcjJiIHGlkUy9xMDLfp5e4UNmXdb6DgNSbyRgarAsSZfiq9gK4Qk7jkU3+S4kd2cQowqJRGJar18LVGYlHWblkt7tI8HWP2HTEXGxefEq5RfDsJRU3d1+SQ4OA2QnSP34XcdEsyxP37qmxaSgRv8D6DJ+SwtZJhgYqHJ+MbIqndrOHVsYBIo3Kijdy8Mkev3T5notK6prg4Fcw2z8T87hL6kQQFFovvz9f38eqReL6nGJpOT59FO8AJ3UiuA0w5X97C1xpgkpUFpsGKnA6VAy9pCxJ+6mk4DBTVwvQyKbBIF4YmNFLAHe5N9cZk4oWPq/Sukc9RJSVXfOGibAp/5svBuhlIkMEkYXl8bbOZo12vcTZPW4IMH+fSxaJkwjgnLMtCfs2FWVFRgdlY2d3JnoHENboLXJ1jyJHsf9OU37d1quUwabIpaLF9zLz97llIffKypmGzwiy0ui0QLgCwGpXGSoIl+1AUhTUHE9FBxkbFvWQZWzrsm98vNUmo5QB7hBoy06EYcaUDx2GSbW9DxVnQIXiZgyDI7NJVIxNZHRb/HNybRKm0mdCceMXTfM9kojS6Po3OEcaHWCuGT582zTyMd4U5jBn/m6JLAD3OUXrt2ikgRLePWIDMn830wlSaT5VdYx8azH0SjIXEeP5DVNGXV5vs+5R9BzV7/BUJTvrAJF0u+zjDn4VvU5G5MQNE4wBOW/VkPN7phnHkPn+PUSkklm7rxHtn8OLLWOEM9+fKpKajmRhamiEapN14MUNNj4HXnU0kf9SZBoB3M+efTEu/z5i/RIRkeb7aEe65hOPbGIiLgGuLk0UvcoVFM/GDDAu5yaQFI3BOf2YVvBmJCLVdS32jLCGMipCzLxHCGSxnK3EfsNGt4XrgHGI2vs2k24cP0N49r5Y2Qnmrme+P2NcZTuhh7Js7/EbvsryxNYMYZQ3myQxxqMdvZHO5lJYZTXHegjZzWdPC4QrFqbVPSyy3eoqjidMWYgrQ6YYa1+hFLU7JrylZhg/c2hkNiz7cMwXCM8XS9QGF2627OU7mndCFqFHotLRosh1rAk/EkZxAkYET78XgEl1NIs7Sj9TV953qJi7WY+E4GCfGNnk9GhnLFm8aXSVaDim4KFhLJV6JglDWdUlmY0mIUN3leYS97zRNZtCXUc0LACigyJzGDKLnnJFtknDZyWd2r/H2FGifCc9aVpDJcrKc2iN15zjnA5k84+4LKReZ+pHAYYuZbr9GCn1TGpAfF5Yby0TUWY2foguIq71WP6XjSZqiclCR3kQZyqzEyR3kbYvo96uflXRtrXHmvU/NLKp+VSnLXGGQcYYEEWAFivOXCZ6daBNHZjLut3Ny/+8hucwwH0HqnSjIyLGy7KG804YzRPOYVSUihlJy3RFI+pHAdFnKNm32fq/8cwUdr9hIpuywmCB8DXbye3/nNisBMl6N+eR6QKYa8lYsgDu81jc6OzfK229wRUr15pNSozo8m14Yomiyb1kRINkk2iteEdKVL5ndWcxzvDFPmRVXjs211rQ2pkpsFseH1fMLiNG9F6VS4mz5klo+OJS0SqRTcRhtyxr/+fE1EkyPNqSmk1s6kdcFu+8V0XD+efRCiN2rZmw5kmvP7XIlF1SJBPg1li8fpRPnhbBIcT83azeUJqLuLtgrKix7wASftxUCHxCajcT4coeWuOeOiZcvhREa5epTWSn9RJGW7JWVryDJWPEsDt78oZ73zy2Cg08FcMaEQmVTTj8uw33/bqU9JKH88CksZsHd6q2VrjWzctr1r/GIsM9d6ZiUliTLq+yws3SMxL37IURYkrzqGrq4Pis0obOZozJZl0+iVGTT+XpX/NU+nD0Wi9T1Lh/+I4e47LuugNl7L2PjUjfRTg4wznrNdK5qNpX/fOS9hmHK+P99aNMeborZ1S/IYt2blTpMW7v20EYeNLpVPXdk4gutTrjEbWy2POvJPraNJbmCcdvJeKrJ3JAudZApRMkHZkXu3sShqx8gStu3gjU2DREiSsfQNby3F8bgfemVAw2Ba6bV/gaXfMmFhlCX0oIZWXmWjMPmTj1I66YifQJwEhdIyJyrI4Wrs25/1+m0Lr5u8PDN1NksFAsiWo29RKK0PzdkSwyRUulW5AtS+Pz4tv4q1NY/Z+pKTvjqTGNTW7Zw8sdFyFWdbjUmk1Diuo6RrILr/9yX369Enbu8hy37N6hVa5L/c8FwEVDJh1aXeJkYl5Gr7E8Fr7vMmKY3trw0MrVj2LTo/tlIVIjzfESD2kPuSfFD9w+WUQpRWb9DyIlOfzV5uWV2X/ZZgvVxlWhEUBwLvEanQWfafn9oouU0lyqjCS+c1vMmMwUqmaNmtV1yrjnlXn+TP1M1RpKh2PZO5Ds7C7ZK5PSXp2Olhahk6gqSoU7L1Opa1Y5Dj79vdJdjo5s8qd1mr+7l4hgju8HABetzawvUxbGiG/q80qUoOOeEv+MWMevdP0yz154HukjM3wagRqbhiiV4s2GZZxJFaIjcirGAL/ySToYcTWbZHmzrJGkKj2DiFLpyRe5tp8xWdhDWi8Z9h/vlkB1FiOLbIcvsUY7SbpFOC+lAFwnBkE3HKA6gkdc2I8KITXT6PwbFtuNrjrVqfZYM2Whlwj3jh8sy7/Pv37ZbhzVekONTUOJyPtKptEJajYBMk9gvPOmKV+yLLaeZutNMdEY5ms7CANPkiGASetlog2AaB4jA4/LaFcea0eJ8vsAXUOjxy9L+f34A3e0vqI1wBhVtrMH7tj6ZTvThvI4L6P9w7cbl1dndIIgWs18ndGlkRMsoGrvSNObpOnRZqq50lwk6TCAqbMJI4nRuCAsx8EYbNiOxnF9wMhSlp0wkqTssb47UFUzDTKyn9mfzDnj0sX48ylgGL4IPWa+zjiKw7GFUoAiUbOp4mghPlPzd2/vyVPjJU1s4vNS/nliv+mXRZqV4KtvGCIJdGDWuvk6G40qOaMkGZ21QLgCIFJWO8mFKml1mzzev1DNwtZMRywmeqcsi+zCK7mUxFsvmz/fCFnYotyRAvJb9emufv0v8bKEXgD/GrO7APJd11hPjUQWUx7GCxB19StRtT2ksoSfE2vgqU5hZWQxPDtEVGEoS6s3sknmgVOaS6YqNUDoqaO9knzth12kPgr3sF5ybUkM1KZe3kEYeKT1EKoKs5MXlx1EYdKkYp1UNJGwQHhlXhxGuPL78XMTT9M0v+eUpWIQdBu+4i3D2TXQS6z3lnRgyZLLpJ0Gx1zcCODr7lolu+zizRh6Kw4N0gnGn2OiC6nSXKojF93rLHyGdvT6L/fxCy/A6Xg6BbdKx7uf1/DlSE+6xgeW7FJDtX+/iTtmuOe1m8lKqDJieHS2oByHKQ9jcKw0dSjKutHRjuJYYASbusbVSbJlAbhGQ6EsPoOKxOCYXG+19vuH+y57j4jPi9+x2C870VAllKW3UNSaTYpNuJDYB7jK6CEOIXU8ZMbvrjyUzk3Cvnz7HnipcpOFPkYW3fj3mPf2FRmsuiCRXYsqEWJMUVCyA034EitLJdWNkMVcH0zURJU3nrwgVWQhDWVMy/bwM+qzal/5D2hRQU3PsxSP5HOkIpV/d+zZI2QxN2ZnREaa93gBZgqgRjYNRSoeUjLSMp7+xXrTwkMok8qzw4oMqb3WM/FDJVtDg5A9lUpVRSC6o1QGFukhNdqFsjMRMwAXWRwV8JbJQjt7BM6bpDQ6xtNcmRdWFqpYueFpZjqB9r/EfEZlWULDmrA7kCCNDgBVuDm8lEcF6IVOBPLZy2vNpqYj6cIJROuWuiD3jzVtiM51FjNOtXmiIqsyARyyp1Kpyn7B6PjwihHKTkeGEOlZpuySbnQAyAwJ3qACJO2V3D2iSOzboSx051ZhKYbWmCz+0g38nSl+T/U7CPh5KcvCO63N15h7c2vsbMWms3eTxtL4eclphDMCRkpEhGMjUGPTECW+iOnoIKJYavn97QMpc/m2fx9nmKj189Z7xUJ3/QYe/lKSdNl2F8LmLzBA0gWJ8wJUZCGig3YaYfYuRRt+5Kws8XlwGVXM9RQaMtyRBPFLMndBqiVbrfdnjCrxz6gsD2dcLY/1bBKx1Eg+dc1/EZDOS/iZB4H9tW+81mwamrQYhwTAfwAJPViVCD7fPhBzGrhT0eyDXDrluegYHSwBJiInvPBy4+P7iktX5+LzSF5EmHbLUlnMOesjajZVWi4TUZmJsngim+Jzw1xEzM+IOfyzsoTz3kekGKdSKcNIQlwAYy+xDryoCyi3ZqhU7QQ53XW+7M+ozRutlrJkYS/q4fsrzSPqgEym7MbWLWM8CvGW44g9377ntUpne6Oy+PNM/CX/Zb3/eSXvQPHUUbYEBiNP3KnMdgVmjSRVa8Dh/DfvGMzeGr7GGiXin6H3c4qXkSCiiZjPCJDNi/n+VKMh4zXGAFp9dvftH/b69er4DK/jkyKKtWaTAiDBEEBeYKOOE26PRFwhMAWTfd8Lkcver5iJLg/l18t/W/jAs0UJgeRNwxofV/rkBhfJIlPMTIRYKIvPK5xJBSJZqtaAswtR9Fr4/q7PKbwkhEYP/8XRfp1No2NkaYkZYHzyxNc2200xhPWYl4i5icvCXpIrP++NbLI322Z7OxQ38bXhe47inmjWQ1rra/u94oftjNPQEB/vk6UtdiCSHiydxu/4PuCQuzw+ro+ksvD7Y63v1ZLFq0vjspDOnsrPOw02Mn0kuRgnve6NKo0/H65o29hLPt1YbUDkIlYZWVKpVPX7OyJi4+sj/qxUySJcM5WOwwWNbGo28s8qpicJo0flazK6IsQX2RQ3BrP1pmr9Puu94s+r12DDn2fLr8vOnCLZhft2XFax09p1H0v4zJlU6crXYllkZ1Q2ejXpZ6tkEZxngGpZXe9v1luNxtfTUSzU8YLPKWke1NikAEg4AJIX2BC/wYZ/ENLpVMJDyV8yWMNBLdnixC2+kigrtpsTK0t845deBCSXDH/tDftrNnWt8rXjbzVb7oa41qTEmJkki3S86yKQNMfugviy9VsVyUcahitfC7wj0s3TZ3SOrxHfeleaS7XBxmNsqvIcS58j/uLCRlewslQZysg04BCmA1zld3kOcu3Z3ZSFiPpk5ak2wgmNJMJDq2seq9YXmTbOvHdZFtnnVHWOcUYKu3/WJ4tP9vjZgS2sW+tr+73i8yK7uPgiVs0mMEpzkRgpAdkZcqCR0SHedRZf82TkbUU+QSSiv/6OzMBTdf6t4/MaP9OxXYFr/XyVLAIjonS/kd7fdveM6pKl+v4mk4WttxrSkZM5FNypz1JDr+zZqzZouvePuH9NazYpAOSKMH7Q8S3s+AG0nopZ7k3ZTQNPA63LUqOddB6ZGinMWACI6yY2lTJ6f5n3xTU3kqgpQL5hSdZ70mbmLii+e7L41kxcVrbdKkBENgk9ZNWyuzdbpblUf54y3djIA7Q30qMqqlTmRKinoazaa+iTZXejrGq/v5n+xcgjNjZJD/+x8XFDm0uWekc2xddMu+fwL5FHGtlUJYvQ8CV1PDGFm0P8EScyI0CURqfGpmZTHekhO3OytcGSfjbObkfQefSB5OwujmwS6/jd22/c3VLt9/IZMSTOf0AY2ZTwmutzlURwJcoiXGMuvVo95/XTqUD1+vPWKJM4ioXzKNXxkujrcr20tDXWFZXeCNTYNESJHw6k1mJvdNBuKzdXZNPuHTC9hjLJZV14WZNGlFUfdmUKxd2FSGi0i70szf33Fx0duIGnnht50vs5ZYm9lkkFojojUgOPdM3U1TO5m4dLn+xKcxGn0cWjPoVpDfWMrqiKbPLKLkwBFKXRySJm4jpDGmkpSVdJp9x7ZFWUldQIJ4xOcM1NtSwy/eIzUFatMc/4uDHK3b3O/losizAaThKJ4Uvvl67f+GfKGgU1ja75SFN243u6uzmKHZEuN9gI0+jIdM0QZ80mqXE49rt9huq4w93vyBHcgdKyeYy/7nP8Soz4mbQd1ZJrSTt1TVtOdnaXpq5JdNnuRvVKx8f/9jjVa4Y39Nbb0VJ9l+T/1man0AFqbBqySI0e0voCVZFNAoXiKwpaFWpIFoyryOaRXaKA0mnbi+zNJxbKItmAAFltIqks8TuF2MDjre/DR1qJjXC7Gf7q6/5kzqUvelQqizQCLX5JZ1q50rIIPiOget40jW5oEdfL/uigmG4kIxpCJLX4/JFN0hTAuOz1M5TFx/qiVKqMGMLITMnctGXdta8kaePJssgO/5LIJu9nFJdFmP7lNwry6116eZVGw8XXjDfF0Pj99S7CK03jiRc0VppHvKaatNamxFFc71QeSc2bpN8vSaPz3oFaZLqjyjgsnEenw7KF16nAABwtwogf82/zytLA6Gigev9yGVUaGWEMyPa+pNcljmL/HV7mUKiqH+Uz9Brvp8YmpYKkaCdQ/cDKo4N4hVLvMP64Ndl3IN2dekB1l11Y22N3wl/FkU3eehoyj5o5F5l0yrkhSlMK4gcutnNDRTbBevcZm6SeGmkEWvVmLonM882L7CAaNzr7nj2luUjDyKtSA3zdWHYnlccb2RQ3qvrWokyvm7K2CCNDpOlZ0v1UYsiQXkSkDg25UaW2PJlY/UZpyoTU692ek50dXPJURzbJDDbeKKvdcODV8zNKGu9Lqd8bajZt3rwZ8+bNw4gRIzBq1ChcccUV2LFjh/fnFi9ejLPPPhvDhg3DiBEjcMYZZ2DXrl1NkLhMR2uL9XU9C4QDsogGsUNhdyObnA1y3LL5ZPGlrknT6KznVSiLb7/ZHcNX0tdxTKeA2NFSx0i7pNdd8uzuvEjXjH8v5t8/3vDBH+ggM5RVZWAInHNqbFIqSOsexQ8f8gLhgsgmYXSQbzOMP+DeaAyhp9f826TGo0YavnzyVM2L0NgkjWySzI10Hv3pX3zEV9L7S+Tx6OTq9MI6X+6kkXnm51jPVEegeo1pzaahRfXBr87Gb8E+Ew/H9xWelu4xUo+q+bq/2LPsEiVt/CCOPDHeT1ysvI7phYDciGjKK71c+lP6ZAaeqnRHV2cjaWSTMC1H7oU39lNhipBvHuMXbXb99hUC57ihzLx58/D8889j4cKF+P3vf4+//OUvuPLKK50/s3jxYlxwwQWYO3culixZgqVLl+Kaa65B2qM360n8s6pnOhcgjWySPa+SyzcgqymYBuz9psFRKhK9Kq0FJDdiyKJ6/eVBDOeG0PDlNR5JDTyC6Llsxk4DlT4b8mg4z3nZmLtUqs5ZCcLIvCodL7g3+9I0G4Eam4Yo1REKshQEf0e33VC0Qu9IvQ08ksgQwD7U+R54qaIVG1UEn2t8U/BfYGJfC0NOfWvAlMdvULFflxYrl35Ovouv+Tl50+iEslRF5nnTQGWbiuWREHo7vMamnGz8UGcg3u2rrroK06ZNQ3t7O/bbbz+8//3vx4svvtgkid1IL43yi4gsglZi4BkW89hLDch+w330uu/5j8+D33Ag043SrmvmXPgOuPH3kqau+b3wsvB983V5pLAs9dJXQ6Mqdc11eU3Zf6u0np1vje1O6qW0qYT0IsJe0vbUAuHLly/HPffcg5/+9KeYPXs25syZgx/84Ae4++678eabb9b8ueuuuw5///d/j+uvvx5HH300jjjiCFxyySVobW1tmuziiLjdiCQRp9F5zjJxHS+NgnHtZ6mULJpIWmNN6rC0sztk59lGpvQlfV0tD+/ckBoQpWdOScRoKpWy5sZvhJPN4+50qW1k9BklSy5+vhJENg3COb/FP0QZDKR1j6ojFGQWYEnnFHmxVPf4agOPx+ssvggYkSEe2cXpiDFZpIdGd1e0cmpIsRRQsuTStlfSd1CQpuiYn5O0Y6DPsyMpnJ70fpLaRJ7MDLFHQhqBFr+0eOsitKSBvmL5vYVRhdKUvj29ZtO8efOwbt06LFy4EPl8HpdffjmuvPJK/OIXv6j5MyeccALmzZuHAw88EJs3b8ZXv/pVzJ07F6tXr0bGo4sazbDYgULcnUtQsymXcdehAMoHor4avytO/MIbv5jEqTrkei/rvD6qPuDKnmnv5UJ4AZQc/qUXEXGBcGN8KuWfS1Oeuhcr343UNZ+nGSjrw0KoS4U1x6RrxnvxFhgBqus3ygy9rId/T02jW7x4MUaNGoUTTzyx8r1zzz0X6XQajz/+OD74wQ9W/cxbb72Fxx9/HPPmzcOpp56KlStXYvr06fjWt76FOXPm1Pxdvb296O3trXy9bds2AEA+n0c+n3fKGb5ujmuNLcNUEDjfp+oRKhWd4811mE2nnGNTJfvzz6bhHB/fjlJBySO7IUsmhUKhkDgufI9cJo3e/jpiGY8sCGzZWzPuvzU+j6nAM4/G+Gwm7ZalVLRlaXHL3hI7u6fhnsf445zyrQEzkrbFPS8tqZgsKfd6TEMme8Z4/9aWNIrFAorFmsPRls2gu19nZzzrNw37jTKG7Ek/F5c96/lbrY5uHlmA8rwX+u9vLSn3Gkgh9ux5ZGmL36tL7nk37+EtCbK75qkWkrFqbBqiVBtsZJcMaZqAvxBgOvH/k5DWm5KnAAoNGYJ6U9K0ovhh2CdL3FPjutyFVv0dvYWqn00irnu8ETPCC5L5t0lrmPguyWJZxEZBwyPhsafEL5a+i2b8Uu1d7/Fnz7PG7OL8sku1dB735DS60Lu9dOnSyqXjBz/4Abq6unDLLbdg8uTJiT9nplpMnToV3/zmNzFz5ky8+uqrmDZtWlNkr0V8bXV6DDa7U8+DiWozDZ/SC69Pdmlkk2l4lXrs6220q45s8hkyovHy4rGyFAtJnaS2Fnex8rI8vD6St17nUyzKr5t63b9+c5k0doJbv82MTvAaJ4WRTfH13dnmfvb29ALh69evx/jx463vtbS0YMyYMVi/fn3iz6xatQoA8NWvfhW33HILjjvuONx5550455xz8Nxzz+Gwww5L/LmbbroJX/va16q+f++996Kjo4OSd+HChZX/f/6dFIDo81r+3DNYsOHpmj/7xpo0zKSU+xfeW2V8MOnblQFQfq62vrMJCxYsqDn2rV2AeS1c9fKLWLBjec3xKzfYsj+/7CkUXq2divn2hkj2dFByygIAQTFfkX3jhvXO8S9vtWVZ8cKzWPD2MzXHr15nj3900cNY2V5blq2bI9n7du10yrKrAJjzuG7tGixY8Cot+3PPPIO2dbXXwNrX7DXw8J8fdJ5r873RGuje9o5I9rWvvYoFC1bVHP/8Rlv2J5Y8hk21lww2vR3JnkHRvwYKA1+/L734AhZueR6A/cyFrH7dln3xI3/Gi46gxq2bItmDUsErexqR7OvXvYEFC9bWHLs8pgeee/qvwNraz1JcDyxe9DBWO9RP99ZIll3dO2rKnjRPtdi5cyc9Vo1NQ5SwZWm/UVQUdQLIc63jIXlxdqfIoNfAs5vFzSVRMxKDCiVLPCXK264ylfj/tWgzjE3eVJGYqD5ZqgrMCdLFfPOSTqeQy6QrnlLfpUGagy5NMWyz8pWdQxMK+/lkkXmRLVla0kgLogol7bQZWeJrak9OoxuIdztOd3c3fvazn+Hggw/GlClTao6rt3e7FvFoxfas26OajY33eWvNpZ31eIIB20Oa84yvjrSUeVRT/Z7qWj8jkaWykZLjW1L2pTsl8NYCQDooIp+vfVA0HQM5z7wAtoc0HfOQxtdTXJaMx0Nqqow2z/oC7AifFk+0QTqo7WlOIhXzNLd4xsejlmuNDb9vGtZ8sqeCeJSHJ+Ikvq94ow2i//eu35jr3xdx0hpT4+2+Z69//K6+8lmjUd5tKddffz2++93vOscsX+642Too9UfxXHXVVbj88ssBALNmzcL999+P22+/HTfddFPiz33xi1/E5z73ucrX27Ztw5QpUzB37lyMGDHC+Tvz+TwWLlyI8847D9lsFgAwdvVm/OTFJypjzjjlRJx5+H413+PF+17GA+tWV75+70UXOg3E//bqYqzftR0AMHnieHR1HV9z7Ovv7MK3lj1c+fr4mTPQdeIBNceXnlmHu1c9W/n67DNOxcwDRtYcv/i/X8CSt18HALS35tDVdVbiuHCehne0Yce28j479cAD0NV1TM33fvK1d/CvLyytfH3yicfj/KMn1By/dela/PbVaO2cc9aZOHBM7dv6f7/zV7y49W0AwJiRnejqOrXm2F19RVy/9P7K10cdcSi6zjm05vinX9+Kf33h8crX7zphFi48ZmLN8a888AruezMyAF0w91y05nI1x3/vpUewqbdsGDhg4gR0dc2qObavUML1S++rfH3EYdPQdW6y4RUAsi+8hTteXlb5+t1z5uCY/Ws/B/dufwbPbC4bgEd0tKGr6901xwLA919ZhM1vdwMAJo13r983tlSv3/OOnVD1zIW8/vBq/GHty5WvL5x7LsYMqz2P93U/g2ffKcve0daKrq4znbLPX/Yg+naV9eO0qQehq+vImmNHr9qEW198svL1aaechNOmja05fu1fVuPeNyLZ33P+ORjfWdtS9qu3nsTK7ZsAAGNHj0RX18nW60m6yUd47mVQY9MQpiWTrniavKHt8dorwkJq3ogcUb6yNJVH5v0UpyFZuaoer63QiLE76WJM3qz5uXq9n/EDprCOiTeCx0qj80fAtGZNY1PjUvoA2Xr3RjYJi5VLU1jNufClZgAxQ6+w9pXUuLonp9ENxLsd8qMf/Qif//zn0d3djSOOOAILFy5EznF4q7d3uxZBAKSQQdDvkVqzcgUW7KxdT+qVrYC5rT+x5HG84yg/9ebayDtWKvR5PXWFvsg7tuHN17FgwZqaY7vztiyvLHd7ml/YZHv2ljy2GBM7as+T6SXvcXjqQsx5XPvqKixY8ErNsRt7bNlfePYZLFhf29O88s1I9hQC3HvPPXAFCHXviOZx2+aNXtkzqQwKoew1PM3hPL0U85IvWbwIbwyr/d7r3jC8tcQa6N5mepo3O8fvjHnJVzz/HBa8/WzN8S+tt2V/5KEHMMxx7l3/uiF70e9pLuV7K7L7og1e3W7L/sxTT6J3VW0D4stvxSIlHv4zlju85Js3RrLv2LbVKXsxsGV59ZWXsGDXiprj1+6wxz/71BLseLnmcLzerwdefmUVph/UOO+2lH/4h3/Axz72MeeYQw45BBMnTsRbb71lfb9QKGDz5s2YODH50j5p0iQAwFFHHWV9/8gjj8SaNbX1Wmtra2JNp2w2S1/SzLEjOuz3GjO83fk+HbnotWwm5dynADsroi3b4n7vNtuo2dHq/ps6223ZRw9vc443HXMtmbR3vsy7Q1vOLXt7qz0PnR2tzvHD2+zxHW055/i2bCR7azbjlj0dSyFvc8/j8HZblvZWjyzGGkinArTm3OPNNdDR6p7HlpbAKt/R6lkz7W32a755zBlnzg7PZxqOMX9Wsn7bctG8Jz2frVnbBDKiow1Zx11lWGv08znh+vXNY1vsOR7umcfhsXkv643asts1d2vPo1SPsaixaQiTM4xN/su0LLIpbrCRGJu8qTzCVvC7E9nUnvWH/eesaKL6RjaJiz0L5jEuj7QbnSS9EJClXDERMG3ZDLb3FChZdqdOUjaT8kYH2ekW7o47UsNXVRqdYM341kv8/erd+nVPMDY10rsdMm/ePJx33nlYt24dbrnlFlxyySVYtGgR2traEsfX27vt4oa/PlCJbjxp1rHoOn7/mmOXrd2CH7ywpPL16aediuOmjKo5/pl7VuAv618DAIwc3oGurtOdstzy4sPY0lduC374tIPRdeERNcf2FUr40hORh/S02SfirCNqe+zbV7yNn73018rXZ5x+Gl56clHNefrzb57DkxvLxX/Hjx2Nrq6TnLJ/6an70d1bPozOOPIIdJ1xcM2xb23vxTf++ufK1z5P88bH1uD/vla26rVmM7joovOdstzxxhKs7d4CADho/8no6jrWOf7rzzyE3u5ytawjD5uGrvMiT3N8PU147R380PDwn3Pmu3HIfrWtTUt/vxyL3yqH94/uHIaurtr1agDgvzZGHtL9PZESu/qK+KLh4T/x+OPQdeykmuO7n3wd/7n6hcrX77nwfGfK4/KFL+PP68tRHiOG1faSh3M0YngHNvf2r99DD0HX+YfXfO/n3tiG/++5xypfn3HayTjhoNE1x6eeW4+7VkbG1A9eNNe6KMVZuCPy8E/cbyy6uk6sOTYIAnzuscgAdNyMo9F18oE1x6/e2I1bnl1U+fq8M0/H4RM6a45//t6X8Od1r2L/KQcCeLVh3m0p++23H/bbr7bOCDnllFOwZcsWPPnkkzjhhBMAAA888ABKpRJmz56d+DNTp07F5MmTsWKFbbR76aWXcOGFF+6+8CTx88PIdk+WgeA8EB8vrQ0mrcvnTde0Ukf9kf2SrIT47xanJwtSgpnC09lMCvmylXgAnfH4VGmP/xyAfeb0yRIv3+FtLiBuZiU7/1p3IK8ssrO4NM3b6sQqfPZ8gQ7SAvfm3pLNpPzZI4KAkUagxqYhzLBW/oGX1l6JP1SSNCdfvYt4Yet610myjE2+nCjINolsJm2lLDQysonZbE1PkLfGROxlScRX0tdxTOUX32CSiBsF3bIIo4mMz52JsjLrIvkKhLf0t3gP+m1Ski59gKxmk3T9+ozIw4WFYeNrpGyEHlrtrxvp3Q4ZOXIkRo4cicMOOwwnn3wyRo8ejd/+9rf4yEc+kji+3t5tFx25aB8Y6fPWxjzNfg+pqV883lrY68nnIc1mYR24vbLHPM3D2lr73yd5nkzZ23J+2Ue159Ddb2gY7vU021+P7XRHG7TnZB7P0R3R3+qbx/L7Z4DuUJbk6IFwnuIe/mHt7jUweli0ZnzRA2VZonkf64lkSGdsfeTzeo8eZht3h7e3Oh0JHYanecww9/oC7OYj7Z6ojZHD7GdpeLvv2YvmPZdJY0RHm9MRZj17vkiJ/vcMI4V9EScjOux5HOWJlgkjJQpBWd5GebcbxZFHHokLLrgAn/zkJ3Hrrbcin8/jmmuuwYc//OFKrb433ngD55xzDu68806cdNJJSKVS+Md//EfMnz8fM2fOxHHHHYc77rgDL774In796183Tfa4QXJEu3s+W6XGJklHN+G9oCN23hjR5pPdcPoJo7p9Z5mRsXnzG5tkzlaJLKlUCiPbc9i4o5eURXaGtJzWhN1gpLHfMGfOtmwa/aKLZEn6ukqWdpks5plX2qnR93yY67Ut6y9pYcrLGGyss7uw/Izv2TNlGdGW9QZdWM8eoTfqzV5pbPrWt76FP/zhD1i2bBlyuRy2bNni/ZkgCDB//nzcdttt2LJlC0477TT8+Mc/rlkksBmUC6yWn3hpNzr/JdM4dDHRQcb7xS+0cVKpFIa3tmBrf66qxFoMMPWmbNl9SLwjQPkhDiNypJd1SQSPrwZT+f2M8XWObIq/n2/erW50vlw0xNLFBIXTy+N5WZgoK1Nen+ipVApZI6pwmK/99m7U+fIVBwfs9et79qRdiBLTEQNHa5BBoJHe7SSCIEAQBFZNpsFkWGsLsL0sy3CP5zj+nI121B8AYrqReY6sDnD+tduRi/YBn+xxfeiqnQDILlEAMHpYFm9sKRubpO2ffbKYB09Gr5ufC+PdNceMHe5Lm5Ed/k3DVzuh102dMcaV44bq2pNeWYx5aSXq2Ulkif9+3346NmZskrRSH9nhP/xLIk4AoKM1g76dXFp6R6zFmW/fCOeir1gyMwH3KO666y5cc801OOecc5BOp/E3f/M3+P73v195PZ/PY8WKFVba37XXXouenh5cd9112Lx5M2bOnImFCxc2tTFEPDrIa7ARtIIHZDUfq5zQHh3fEbt8S7pgi6OyfIaDuLFJ2ATCG3livM7IPrK9JTI2SWURGHgYu8EoY26YO5MdwSMz8Pg+p1EdMlnsLIb6Gr4aKQsgq3Uc19G+85X57PkiCuOyMOeletP839gE+vr6cPHFF+PTn/40/TM333wzvv/97+PWW2/F448/jmHDhuH8889HT09PAyV1Y3bvkRiPACYiRxgdJLjwxsdIImbivysJU3afUSL++5mH0jKqCCOb2jxhM7ndkMW3BjIpWHVC/MXKzQ0r5Q/1FdSPAmLhssJudJ2eA5eV0sfIIohsAmwvhO+SHD8simo2Ees3J5Elm7HWgPdZirUOH4zw2nphereXLFmCRYsWJXq3p0+fjiVLyqlmq1atwk033YQnn3wSa9aswaOPPoqLL74Y7e3t6OrqGsw/p4K5vny6N76exgkME8yFd5xRgJJZu8MGKHtnW4v3ObINB4SBR+DdjT83XsOXwIgRfz9m/zV1s/l3+GQpy+N+f9N4JTV8+YyZcXn8Bh65Bz5klGdepLKMaG+xW4YLHCCjPNEpQDxSwv+37jecf/Y6Yp+j79kL9X5+D+1GBwBjxozBL37xC2zfvh1bt27F7bffjuHDh1denzp1KoIgwJlnnmn93PXXX4+1a9eiu7sbjz76KObMcaeR1pv4Opc45uod2dTakrHWis9wHt+b/NEVMtnN84i/42jakqf+HUdlDs5RlhFf5rD0ncOkaXRm1Jc4dU2YiuY18EhlEZTvyKTLWTWV8Z41Zu6l0nnxRSACsfXu2/tiZzVJx1FKlqzs2as3e6Wx6Wtf+xquu+46zJgxgxofBAG+973v4YYbbsD73/9+HHvssbjzzjvx5ptv4ne/+11jhXVgXix9iyPT3/0rxJ+KJosOMh/yYa3+8aYhRVqzSVJvylUTIURsbBKkaJmHvnSKCFPeLVnc751K2QWnJSl9nW3+g4JVqE8YBSGRJZTHhTzKio9sAuyNobPVY/iSRhWa0SFMZJ4ZVehZ7+l0CsMEn1PcsOpbA0Odu+66C9OnT8c555yDrq4uzJkzBz/5yU8qr8e9221tbXj44YfR1dWFQw89FB/60IfQ2dmJRx99tKrY+GBhfp6+58JcW52tLV79JfV2md1OGANPu8jYFI01L9a1sKOJZId/30Eu/hz4DDytQqOddcil6t9FYyQRX3HZfLJIvd6+eYnL41szpvGKORCbsoyhZOEvr6lUSrRmzLVuesxryiI0UO5nPnseWeKp3xlfx9OMEdmkNBVplIH00pgVrrNxlvHZY9Q09ibmLG7pSWlUFvG3mnuMxMDTns34DTyCKCvANvAwpUfMR1Ti3GDKbFoRPJQR34ikHebei6WdpKWymJ/TOOJcIEl3lEY2mU5znyMv/vulkU2SZ08a2cSksNabvTKNTsrq1auxfv16nHvuuZXvjRw5ErNnz8bixYvx4Q9/OPHnGt3+2vRO+VoAA+XFGR4W0vC03TVaOzPtjs12yh3E+OGGQSoDT+vlWIvhdFCqmh/z57OGLK1E22jzmWVkNw//aV/La0Syt2czKBQKzvc253FYLuOVpdXYADOp2usl/H6uJY1d+bJMWV/La0P24a0tonlsSftbHpuy5zxto1Ox1K22jKfNtFHkO5tmWocbP5vxy24ePNpa3OOTWra720xH433t4AF73tuz/vFmrTff+s2mozWQy6Qt3TVU2l9LCL3btQi92yGTJ0/2drAabGyDjS/FQmbMlqbRTRghi2wyiad4xmkTHiqzGdklanSHzKNqwnjVI1n8722mfPmiPgGZgUea1jBmN1L6KGOT4LJrer17+vzpvLYsfgOPdM0Mb81g447q35WEeVmJ149JQnIpAmxDL5N+LeHDJx2ID846ABkUcf/CN+r63oob07DtsQkCsPULs26k62zc8Fa8uqnfGSOIbGKiok3ZqeYoQtmtmoKCyKYJI1rrnvYqSV1LpVKVVGMAGN+Z3Jgk6fczwegjhWl05hjTyJ1EVQdkSc0mYTkOnyzh79+VLybKFsd0JjB+1naBES6UJen/k0ilUujIZbCzf9+TPHu+1FsgbqTWAuGDQtgWe8KECdb3J0yY4GyZ3ej211uM1rivvbwcC7a+UHMsAKCYQdjWd9Ff/owXHM+C2Rq3b6e/bfTa1yJZ1q1Jbr1ssnNrNP6VF57GgnXL3LIbS/HB+xYivk+Y87R8S9RieMcWd+tlANhmzOPrq9wtgwGgpzuax6eWPo4tjuE7zPbeJX/r5VeN1s5b317vHf/WOmMeVyzHgm2+NZBHtAYewvOONbB6eyR70LvTK8vKDZHsb617EwsWvO4cv/WdSPbnnv4rgjW1C0+X9Wu0Bv58/0Lnwes1Y/32EOv39TWRLLl04G3tXDRavD/9xGPY5Gh2Fm9Lfd+f3G3Pn98czeOWTW97Zd/0diT7yhUvYME7zzvHIx/JvmzpYrzlGL6l15C9mLdkGSrtr/d1zFQeb80mM7KJOYAIvd4TRkSHYOayYNj1/Omlxuu+ukSAPI1OktYgRRqlYkc2yebRXz/Kjrb11T2y6iSJazZJI5vc729G5IQXBlYWaUofVSfJLEIviBJl0hqkkRJ2ZFN9PdNt2QzashkMEZ/BPou0jtHB42p3mYzGy2oNWetMUI7Dp2cAe926uiOGSJ0hEl1jOkvGj3Abd+Lvx1zWRwjTxUy8ad7iyCY+Wg2wP6fxHgNPfJ7jHQ2rZRl4/Sgm4llU58s4T/USKcS7FWVFrJmOXEvF2CRprMVFNkXjDxjN2SfqyR5jbGLbX0+fPr1JEjW+/fUTv1+OpW+vBQCcc9q7cMZh45zv+U8vPoxt75QLoF5w3jkY63gYXt6wA7c8+ygAYOJ+Y9DV9S7ne698YCXuf3MlAGDmMUega07tttEAcO+OZ/DClrKh7sIzT8Mx+7vn438uvrfy/++76MLKxpU0T2NXb8aty58AAEyZPBFdXcc53/vl+1/Bog1l49js42eia9Zk5/j/WL8Ur+14BwDw7tNPw4z9R9Ycu6O3gC8/8QAAoK21FV1dZzrfO/P8Bvx69dMAgCMPnYquLvd6feaeFVi0odyafNbMGeg68YDEceE8DWtvx9a+cp2xiy44z+lhfW3zTnzvuUcAAPuP96+B/LI38ctVzwEADj34IHR1Hekc/8dtT+P5dzYAAOacchJOOWSsc/w/LonWwHsuctfLeXnDDvxz//pl2p6v+fMq/OmNVwCUI4V8rZ3vfGMJNq7ZAgC44JwzceAYt3L+3GOR7Bd5ZO98eSP+fcVTAICDDvC3Pf9L73NYtqnc4v3Udx2PC46e4Bx/6+rF2LBrOwDgf1x4rvNCuGVnHvOfehAA0NFebh3O6KY4jWx/va9TCsyoUvfhzDzwMweQE6dGrdw3d/d5x5seV8aoYpqXfZ7jNuHhyZSFS12THXIlmLIzskijiXb2RRGzPo+9+bmUiMaSZvpZifgBO6VPaFQRhO8XKFl2x/Dln3dzrn1dSdsEKaOA3EBprvd6RzYpQwPGGGSulZkH1D6bhrRnZeUPJDXcTJ2eIUJDTNmPnuy+E8THS9PufPuNHaUi0x1czSZZupgEs6ZoI2o2FYqR7vVFE5lzkU75532UMMJYEmUFAN290V6Z80yOKWtPnjA2GQVfGYeYuYcxzj8zktaHuTf5osYB24B4/IGjuF9SR/YYYxPb/noghG2xN2zYgEmTJlW+v2HDBhx33HE1f67R7a9HGIfAiaM6vO+50wg7L7e6rf0gDzNCGTuIdseTDEuor4U1YD9YE0f7ZTdpba1+iM15Mtt7+1pYA8CEkVEf69GeVs0AkDYKBU4Z2+kc35mO5jidTnnfe+Io2TwOM9JmDhw73DvePJ53drQi6ziUThoVecUyaX+7bnPep4wd5h1veoV9baPjeNdXhyHLGP/6ajfmMZf2P6OmoXaMp220CdP2fFib+ez51+/+xpoZRbT37jXqbowf2eHc/Ds77Dxu8733tPbXeyvmnZvxHocwBptDx0fe5Vfe8p9yzDQ6pt6YaSjzYV4sfOmCADD74DGV/y8ShonRQu9uCBN1ctSk6OK0kpjH0VYhbP/77zIOwv7aegP3ou8kUtdMowuTRjd94ohKWg5j4JFgzh1TIPyQ/aI9j/lc463dXVi1+IjLqLSj6n7C4vzKngeXihZ99jMOGOUd/4FZk3H7otUAgAJRk6uzTWYMCPHVBQPsdX4UYWzqOmYifv9s2WnN6A5J4WOreyQRiXjA6Hbj//2RIdIOcBJMXTe5w7/3SaOJtvdGIY5MrbpcplzC5VhiPY4y7p7M6aBNEGUFAAeNHYbl67Yhl0n3n525OnS9RCStqeOZmk0btkUNxs46wl8DlDEahVg1dIl1v9Mwwh03ZRT9e+rFHmNsYttfD4SDDz4YEydOxP33318xLm3btg2PP/64qKNdvTEXE2PRNT3Tkja9zOF0/1GRomW8dqZFl8ltDZFutsxmaBoOmAvY+q2RgvApFPPgzVwDxwllMTfPaeOHO0aWMevR+BSQqdh6CkTKgrFODiHCt83LaL03W1OWg8b6ZTHXCXNOt+rkEJ9TCLMBmbIwHq9JxrPHbEY7e6PPUtIdZioxj0rzkRhsTBhPGgD84hOzcdX/eRI3vvdo71gzja6VOOBIRDd1KfPMmYf/F970R9ZJPaohzDNqPpebiAgxM5oo4+mCBAC7+ty1AE1SqRQuPGYi/vhc7RIANX8PceDuNfYK5pJ28YkH4J7ny7JIIpsYzAsoUyD8w+86AD98qBzlzCzNYQLDnVXnj1hf5x41Ab/56xt49vUt1OHfNjZpZNPeiC96DgDyRtTJsY6o+8qYA0bha+87Gj99ZBXmHj3RO948lzLNC0IYY9OmHZFuZNLozjtqPG65eCb+9Px6vPtw//1Pol/Ms89Iot7b+UdPxN1XnoxCMcDJh4zxjh/eNjBjE3MvOHJSJ34873jkMsC2l5Z4x48SFCsHgB09/H7T2pLBv116Arb15HHBMf71ZRqPGAOPeZdkUte+9r6j8cRrm/F3Jx+E9lwGeSJiCeDuQGb0qitzKOSasw/DdxYsxy0XzxSfI7yyGPPIPHuvb9lV+X/GMVNv9hhjk4Q1a9Zg8+bNWLNmDYrFIpYtWwYAOPTQQyutUKdPn46bbroJH/zgB5FKpXDttdfim9/8Jg477DAcfPDB+MpXvoLJkyfjAx/4wKD9HeaDKDHYMAvPXNRvGouwFubBfhjRdaLHkF2yATAXXlMZF0t+RWKGyDKF1N4w5kPSnYtRFGbrcF9uM2BfXCYReeXmIVQiOxNCah48DtnPb/gyN3Nms02l+Mup+X77j5LNCxFIYL2/xFs2jjAKm7IwXYsmjYz+vk7G2CS8mIYcNt5/+FOazwBtTdShFQBOPXQcnpk/l9IX5oWXiYIJqCt9Ncw6T6VSOGz8cLz81g7M8aSYA7GaTQIjAhspdMfHT8LHf74UnzvvcO9Ys55HD3HgZoxAJl9739F45vWtOONw/7yYMJ/pLmMMczk+84jxOP2wcQgC+9JTD6S6dOKINnzlPUfhoRVvYc6h/rlhOmyFmM8PE9m0/6h2/N+rT0O+WKL2GDNtg3l/Zc+DORMeMbETw3IZTB7VTtUpA4DLTp2Ky06dSo01nRTM810ZS8g+qz99p7OthTaY/u0JB+BvT0guHxFHUvjYfF4Zo3k6ncLJnlIQJtb5V7DfMHeUVCqFC2dMQj6fx4KX/e9pGtOYCLHtAmMTAJw1ne/ca847UyfJlIWZx5MOHoOTDvYbA+OYRtxaSFMv3zdzMt430122xUTi3DDnkXlOP37awbjnufX41Lun0b+jnuyVxqYbb7wRd9xxR+XrWbNmAQAefPBBnHnmmQCAFStWYOvWrZUxn//859Hd3Y0rr7wSW7ZswZw5c3DPPfegrc1/kW0U5gGTMSCFMB6A4a0tOOPw/fCXl97GGcT4yUZ0RYEw8DDGiySOP3C0d8wBoztw2qFjseiVTc56SiHSyKa8sP3vVWccgruXrsW82Qd6x5rKhFG0W3ZGxiYmhebjpx2E7z+wEu+bub93rAnjYTDXo6+GEQCcd9QE3PPcehw5qRNTiPFtLRn6UmUeVCYaaZK1OGXaWOw/qh3jhudw6MhN3vEDzbFnPC+TR7Whs7UF7bkMPnKSf81YUYXE+pVeTEPM+j3K0GGgkU2HEpGQIaxh2rwUMxedgRrKxo/gnCt3X3kyHlzxNi6aMck71jQaSSJDWGPTuw/fD89+dS5loDD3812EgYcxApmMH9GGR75wlsjhwMrCjDHJpFP431fMpse3pFNUvaYy0TimZhMAXDHnYFzhqTkZYnbVlSBJF2SdGebeopFNeydMxMHI9iwevf6cutcBCmEM/Ukw59NDx3fij//zdCtCtp5IHIMmjIFHirQmWwjrJJJgGtOY+9v2XpmxaaAwd6AdvUOna4G5nTKOZSmSyCaTLPHsHbP/SDwzf67IgFxP9kr3yM9//nMEQVD1X2hoAsrpRmYNqFQqha9//etYv349enp6cN999+Hww/0eykbCpM6Z/O8rTsL5R0/AzX/rLjgccvtlJ+Jnl78LVxGWTmlb6okjZbL/8yUzcfph4/BFT8HskDs/Phu//+wcfHT2Qd6x5iGUSQH88d+dgDHDcvj55e6C2SFf7DoST8+fi0+c7q8ZZh7+GcXyqTOnYXhrC647l1uLH3nXFDxxw3m48b1HUeNDTGNiLU6cOgbjO1tx7pETqGi10w4dh8e+dA5+dvlJlLF0+iQ+siaTTmHWgaMweWSbVbulFvuPasei68/Gr6+ajU7iXDFF2K3h1Glljxdzielsy+LhL5yFv3z+LOrQNdGIbGLWzNGTywZYxtMPADf/zbG4Ys7BuIAIsVeaj/RgfuvfnYB5sw/EPEI3DoS7PjEbX3vf0TjhIL9xcqJQ9q+85yi859hJlPEIKDsS/vaEA6iLl6njmEjLGy46Eu3ZDG65eCYlCyCLhJnWXz+IqeXwT39bluELF/ANUCSGpr87uWz0ZqKyPtxvID/riMaUNfini8vnl/811y9LWM8um0mJa1UxXPXuaehsbanMD0sjDPfjhrfi+gun4wsXTBddSpiUd2Vw+d6HjsNBYzvwz5dwumZkR7buKakhZ00fj2G5TOVMw8Lq+iMnjaANw1IYp6bJuUeOx8j2LN5zLLffSDDvb4wu/h+zyg7ia8mzvgTT+M1kpvxD/z7w/5zSmDNECPN5dR1T/mwkzjMJR/bXW5xFFM22yqAM0DDk4qP9AQvSmkqsrWCwDE0AgECpG1u3bg0ABFu3bvWO7evrC373u98FfX19Ncfs7C0En/vlsuBPz62rp5gDZtErbwc/e2RVUCqVvGM37egNPvW/nwgeWL5ht34nM08MX/7tM8EXf/MMPZ75GwfKLx5/LfjkHUuDXX0Fanyh6JdloPO06JW3g8tufzx4bWM3Nb6vUGzY3Ly2sTu4/GdLgsdWbqTG5wvFoDdfFP0Odp568oXg7//jqeA3T62l3ndXXyF4ecN2kSwSfrl0TfCLx1+jxq7Z1B38r18tC15av21Av2sga0mi+/ZG6q37TTZs3RVc+u+PB/cMkX1Awqq3dwSX3Ppo8NCKt8Q/Wy/dH5dnzSZO1wVBWcc0il19hWD91l30+K27kuehHvNUKpWCDdt4Wd7p7g2KxL40UDbt6BXJsqMn7xyzO3Mk2WNe29gdPPzS2+Lf0QiefG1zcNntjwcvb+D3AdX9chqp+weLXX0F6twZBEHwx2ffDD70b48Gb27ZWbffP9B52ryjN7ji50vpvbJYLNHncCmlUim4acHy4P889io1vlAsifamIJDN06+Wrgluvmc5dX4vlUrB8nVbG7b/LV65Mbjxd8969XYoy/NvbA221dj/fPjm6M0tO4Pv/nE5vX4fX7UpeO6NLQOSheHlDduCnb3cmvzPJ9YG193916CvDp9To3X/XplGt7fQnsvg/yU9Hc3g1GnjcOo0rgbEmGE5/PjvTmiwRDzf/MAM0Xhp+oGEj5x0IJU+FSJJoZQi+UyBgYcpMxw4tgO3f4yLJgMaa6VvbcngXz48ix7fls00zPMCAJecOIUeO2VMB/5JEI2hDG3Gj2jDnR8/abDFGBAHjxuGX151ymCLUeFgYZRHI3VMWzYjSodqRKpHSCqVwvhOPgqt0QVGJZEPjZZFEkFy4NgOHDhWFl3RKI4/cDR+fvmeqTeUwUWily44ZhIuOKb+kUEDYfSwHH562Yn0+HQ6hbZ0Y9IRU6kUrr+Qj0TNpFPiyCwJFwvOkKlUCtMn+rsFDpSTDxlL179KpVJU58KBMmlkOz4viBgeSD0oCYcKaqdK6pkNNntlGp2iKIqiKIqiKIqiKIoyOKixSVEURVEURVEURVEURakbamxSFEVRFEVRFEVRFEVR6oYamxRFURRFURRFURRFUZS6ocYmRVEURVEURVEURVEUpW6osUlRFEVRFEVRFEVRFEWpG2psUhRFURRFURRFURRFUeqGGpsURVEURVEURVEURVGUuqHGJkVRFEVRFEVRFEVRFKVuqLFJURRFURRFURRFURRFqRtqbFIURVEURVEURVEURVHqhhqbFEVRFEVRFEVRFEVRlLqhxiZFURRFURRFURRFURSlbrQMtgB7E0EQAAC2bdvmHZvP57Fz505s27YN2Wy20aLtseg8ceg8ceg8+RnIHIU6L9SB+xqq++uPzhOHzpMfnSMO1f1yVPfXH50nDp0nPzpHHI3W/WpsqiPbt28HAEyZMmWQJVEURWk+27dvx8iRIwdbjKajul9RlH0Z1f2q+xVF2fdgdH8q2FfdEQ2gVCrhzTffRGdnJ1KplHPstm3bMGXKFKxduxYjRoxokoR7HjpPHDpPHDpPfgYyR0EQYPv27Zg8eTLS6X0vO1t1f/3ReeLQefKjc8Shul+O6v76o/PEofPkR+eIo9G6XyOb6kg6ncYBBxwg+pkRI0boA0Cg88Sh88Sh8+RHOkf7olc7RHV/49B54tB58qNzxKG6n0d1f+PQeeLQefKjc8TRKN2/77khFEVRFEVRFEVRFEVRlIahxiZFURRFURRFURRFURSlbqixaZBobW3F/Pnz0draOtiiDGl0njh0njh0nvzoHDUWnV8OnScOnSc/OkccOk+NReeXQ+eJQ+fJj84RR6PnSQuEK4qiKIqiKIqiKIqiKHVDI5sURVEURVEURVEURVGUuqHGJkVRFEVRFEVRFEVRFKVuqLFJURRFURRFURRFURRFqRtqbFIURVEURVEURVEURVHqhhqbGsgPf/hDTJ06FW1tbZg9ezaWLFniHP+f//mfmD59Otra2jBjxgwsWLCgSZIOLpJ5uu2223D66adj9OjRGD16NM4991zvvO4tSNdTyN13341UKoUPfOADjRVwCCCdoy1btuDqq6/GpEmT0NraisMPP3yfeO6k8/S9730PRxxxBNrb2zFlyhRcd9116OnpaZK0ex6q+zlU93Oo7vejup9DdX9jUd3PobqfQ3W/H9X9HIOq+wOlIdx9991BLpcLbr/99uD5558PPvnJTwajRo0KNmzYkDh+0aJFQSaTCW6++ebghRdeCG644YYgm80Gzz77bJMlby7SefroRz8a/PCHPwz++te/BsuXLw8+9rGPBSNHjgxef/31JkveXKTzFLJ69epg//33D04//fTg/e9/f3OEHSSkc9Tb2xuceOKJQVdXV/DII48Eq1evDh566KFg2bJlTZa8uUjn6a677gpaW1uDu+66K1i9enXwpz/9KZg0aVJw3XXXNVnyPQPV/Ryq+zlU9/tR3c+hur+xqO7nUN3Pobrfj+p+jsHW/WpsahAnnXRScPXVV1e+LhaLweTJk4Obbropcfwll1wSXHTRRdb3Zs+eHVx11VUNlXOwkc5TnEKhEHR2dgZ33HFHo0QcEgxkngqFQnDqqacGP/3pT4PLLrtsr990pHP04x//ODjkkEOCvr6+Zok4JJDO09VXXx2cffbZ1vc+97nPBaeddlpD5dxTUd3PobqfQ3W/H9X9HKr7G4vqfg7V/Ryq+/2o7ucYbN2vaXQNoK+vD08++STOPffcyvfS6TTOPfdcLF68OPFnFi9ebI0HgPPPP7/m+L2BgcxTnJ07dyKfz2PMmDGNEnPQGeg8ff3rX8f48eNxxRVXNEPMQWUgc/Tf//3fOOWUU3D11VdjwoQJOOaYY/Dtb38bxWKxWWI3nYHM06mnnoonn3yyEnK7atUqLFiwAF1dXU2ReU9CdT+H6n4O1f1+VPdzqO5vLKr7OVT3c6ju96O6n2Mo6P6WAf2U4mTjxo0oFouYMGGC9f0JEybgxRdfTPyZ9evXJ45fv359w+QcbAYyT3G+8IUvYPLkyVUb9t7EQObpkUcewb//+79j2bJlTZBw8BnIHK1atQoPPPAA5s2bhwULFuCVV17BZz7zGeTzecyfP78ZYjedgczTRz/6UWzcuBFz5sxBEAQoFAr41Kc+hS996UvNEHmPQnU/h+p+DtX9flT3c6jubyyq+zlU93Oo7vejup9jKOh+jWxS9li+853v4O6778Zvf/tbtLW1DbY4Q4bt27fj0ksvxW233YZx48YNtjhDllKphPHjx+MnP/kJTjjhBHzoQx/Cl7/8Zdx6662DLdqQ4qGHHsK3v/1t/OhHP8JTTz2F3/zmN/jDH/6Ab3zjG4MtmrKPoro/GdX9HKr7OVT3K0MN1f3JqO7nUN3PUW/dr5FNDWDcuHHIZDLYsGGD9f0NGzZg4sSJiT8zceJE0fi9gYHMU8gtt9yC73znO7jvvvtw7LHHNlLMQUc6TytXrsSrr76K9773vZXvlUolAEBLSwtWrFiBadOmNVboJjOQtTRp0iRks1lkMpnK94488kisX78efX19yOVyDZV5MBjIPH3lK1/BpZdeik984hMAgBkzZqC7uxtXXnklvvzlLyOdVp9FiOp+DtX9HKr7/aju51Dd31hU93Oo7udQ3e9HdT/HUND9ulM0gFwuhxNOOAH3339/5XulUgn3338/TjnllMSfOeWUU6zxALBw4cKa4/cGBjJPAHDzzTfjG9/4Bu655x6ceOKJzRB1UJHO0/Tp0/Hss89i2bJllf/e97734ayzzsKyZcswZcqUZorfFAaylk477TS88sorlQ0ZAF566SVMmjRpr9xwgIHN086dO6s2lnCjDoKgccLugaju51Ddz6G634/qfg7V/Y1FdT+H6n4O1f1+VPdzDAndP6Cy4oqXu+++O2htbQ1+/vOfBy+88EJw5ZVXBqNGjQrWr18fBEEQXHrppcH1119fGb9o0aKgpaUluOWWW4Lly5cH8+fP32daoErm6Tvf+U6Qy+WCX//618G6desq/23fvn2w/oSmIJ2nOPtCVwrpHK1Zsybo7OwMrrnmmmDFihXB73//+2D8+PHBN7/5zcH6E5qCdJ7mz58fdHZ2Bv/xH/8RrFq1Krj33nuDadOmBZdccslg/QlDGtX9HKr7OVT3+1Hdz6G6v7Go7udQ3c+hut+P6n6Owdb9amxqID/4wQ+CAw88MMjlcsFJJ50UPPbYY5XX3v3udweXXXaZNf5Xv/pVcPjhhwe5XC44+uijgz/84Q9NlnhwkMzTQQcdFACo+m/+/PnNF7zJSNeTyb6w6QSBfI4effTRYPbs2UFra2twyCGHBN/61reCQqHQZKmbj2Se8vl88NWvfjWYNm1a0NbWFkyZMiX4zGc+E7zzzjvNF3wPQXU/h+p+DtX9flT3c6jubyyq+zlU93Oo7vejup9jMHV/Kgg0FlZRFEVRFEVRFEVRFEWpD1qzSVEURVEURVEURVEURakbamxSFEVRFEVRFEVRFEVR6oYamxRFURRFURRFURRFUZS6ocYmRVEURVEURVEURVEUpW6osUlRFEVRFEVRFEVRFEWpG2psUhRFURRFURRFURRFUeqGGpsURVEURVEURVEURVGUuqHGJkVRFEVRFEVRFEVRFKVuqLFJUfYgPvaxj+EDH/jAYIuhKIqiNBHV/YqiKPsWqveVvYGWwRZAUZQyqVTK+fr8+fPxL//yLwiCoEkSKYqiKI1Gdb+iKMq+hep9ZV8hFegqVpQhwfr16yv//8tf/hI33ngjVqxYUfne8OHDMXz48MEQTVEURWkQqvsVRVH2LVTvK/sKmkanKEOEiRMnVv4bOXIkUqmU9b3hw4dXhdSeeeaZ+OxnP4trr70Wo0ePxoQJE3Dbbbehu7sbl19+OTo7O3HooYfij3/8o/W7nnvuOVx44YUYPnw4JkyYgEsvvRQbN25s8l+sKIqiqO5XFEXZt1C9r+wrqLFJUfZw7rjjDowbNw5LlizBZz/7WXz605/GxRdfjFNPPRVPPfUU5s6di0svvRQ7d+4EAGzZsgVnn302Zs2ahSeeeAL33HMPNmzYgEsuuWSQ/xJFURSFRXW/oijKvoXqfWVPQ41NirKHM3PmTNxwww047LDD8MUvfhFtbW0YN24cPvnJT+Kwww7DjTfeiE2bNuGZZ54BAPzrv/4rZs2ahW9/+9uYPn06Zs2ahdtvvx0PPvggXnrppUH+axRFURQG1f2Koij7Fqr3lT0NLRCuKHs4xx57bOX/M5kMxo4dixkzZlS+N2HCBADAW2+9BQB4+umn8eCDDybmgq9cuRKHH354gyVWFEVRdhfV/YqiKPsWqveVPQ01NinKHk42m7W+TqVS1vfCjhelUgkAsGPHDrz3ve/Fd7/73ar3mjRpUgMlVRRFUeqF6n5FUZR9C9X7yp6GGpsUZR/j+OOPx3/9139h6tSpaGlRFaAoirIvoLpfURRl30L1vjLYaM0mRdnHuPrqq7F582Z85CMfwdKlS7Fy5Ur86U9/wuWXX45isTjY4imKoigNQHW/oijKvoXqfWWwUWOTouxjTJ48GYsWLUKxWMTcuXMxY8YMXHvttRg1ahTSaVUJiqIoeyOq+xVFUfYtVO8rg00qCIJgsIVQFEVRFEVRFEVRFEVR9g7UpKkoiqIoiqIoiqIoiqLUDTU2KYqiKIqiKIqiKIqiKHVDjU2KoiiKoiiKoiiKoihK3VBjk6IoiqIoiqIoiqIoilI31NikKIqiKIqiKIqiKIqi1A01NimKoiiKoiiKoiiKoih1Q41NiqIoiqIoiqIoiqIoSt1QY5OiKIqiKIqiKIqiKIpSN9TYpCiKoiiKoiiKoiiKotQNNTYpiqIoiqIoiqIoiqIodUONTYqiKIqiKIqiKIqiKErd+P8BsTAERwqUHqAAAAAASUVORK5CYII=",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axs = plt.subplots(2,3)\n",
"fig.set_figwidth(14)\n",
"fig.set_figheight(10)\n",
"\n",
"farr = [1,5]\n",
"\n",
"start_idx = 8\n",
"for ax1, ax2, ax3 in axs:\n",
" freq = farr.pop(0)\n",
" res = solve_ivp(fn1, [0,5], [0,0], 'RK45', args = (1000,0.00001,freq), first_step=0.0001)\n",
" ax1.title.set_text(\"$V_{{C1}} $ freq = {} Hz\".format(freq))\n",
" ax1.set_ylabel(\"$V_{C1}$\")\n",
" ax1.set_xlabel(\"Time\")\n",
" ax1.plot(res.t[start_idx:]/(math.pi*2), res.y[0][start_idx:])\n",
" ax1.grid()\n",
"\n",
" ax2.title.set_text(\"$V_{{C2}} $ freq = {} Hz\".format(freq))\n",
" ax2.set_ylabel(\"$V_{C2}$\")\n",
" ax2.set_xlabel(\"Time\")\n",
" ax2.plot(res.t[start_idx:]/(math.pi*2), res.y[1][start_idx:])\n",
" ax2.grid()\n",
" \n",
" vr1 = np.sin(2 * math.pi * freq * res.t) - res.y[0] - res.y[1]\n",
" ax3.title.set_text(\"$V_{{out}} $ freq = {} Hz\".format(freq))\n",
" ax3.set_ylabel(\"$V_{out}$\")\n",
" ax3.set_xlabel(\"Time\")\n",
" ax3.plot(res.t[start_idx:]/(math.pi*2), vr1[start_idx:])\n",
" ax3.grid()\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 230,
"id": "1db9ef88",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -Vc₂(t) \n",
"──(Vc₁(t)) = ────────\n",
"dt C⋅R "
]
},
"execution_count": 230,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn1"
]
},
{
"cell_type": "code",
"execution_count": 231,
"id": "d8c3b4e9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = \\frac{- V_{in} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -V_{in} + Vc₁(t) - Vc₂(t)\n",
"──(Vc₂(t)) = ─────────────────────────\n",
"dt C⋅R "
]
},
"execution_count": 231,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn2"
]
},
{
"cell_type": "code",
"execution_count": 232,
"id": "184ca226",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[(a_2*omega, -a_1*omega), (a_3/(C*R), a_4/(C*R))]\n",
"[(a_4*omega, -a_3*omega), (-a_1/(C*R), -a_2/(C*R)), (a_5/(C*R), a_6/(C*R)), (a_3/(C*R), a_4/(C*R))]\n",
"[a_1, a_2, a_3, a_4, a_5, a_6]\n"
]
}
],
"source": [
"sysEqns = systemEqns()\n",
"\n",
"res1 = sysEqns.extractCoeffsFromDiffEqn(eqn1)\n",
"print (res1)\n",
"res2 = sysEqns.extractCoeffsFromDiffEqn(eqn2)\n",
"print (res2)\n",
"print (sysEqns.symbols_used)\n"
]
},
{
"cell_type": "code",
"execution_count": 233,
"id": "71203e92",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & - \\omega & \\frac{1}{C R} & 0 & \\frac{1}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & \\omega & \\frac{1}{C R} & 0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 1 ⎤\n",
"⎢-ω 0 0 ─── 0 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ 1 ⎥\n",
"⎢ 0 ω ─── 0 0 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ -1 1 1 ⎥\n",
"⎢ 0 ─── -ω ─── 0 ───⎥\n",
"⎢ C⋅R C⋅R C⋅R⎥\n",
"⎢ ⎥\n",
"⎢-1 1 1 ⎥\n",
"⎢─── 0 ─── ω ─── 0 ⎥\n",
"⎣C⋅R C⋅R C⋅R ⎦"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"M, syms_used = sysEqns.orderedMatrix([res1, res2])\n",
"display(M)"
]
},
{
"cell_type": "code",
"execution_count": 234,
"id": "eed5dd94",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left[ a_{1}, \\ a_{2}, \\ a_{3}, \\ a_{4}, \\ a_{5}, \\ a_{6}\\right]$"
],
"text/plain": [
"[a₁, a₂, a₃, a₄, a₅, a₆]"
]
},
"execution_count": 234,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"syms_used"
]
},
{
"cell_type": "markdown",
"id": "cbb4a6e8",
"metadata": {},
"source": [
"The rows of M1 are in order of a1, a2, a3, a4"
]
},
{
"cell_type": "code",
"execution_count": 235,
"id": "9c052a4c",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\omega & 0 & 0 & \\frac{1}{C R}\\\\0 & \\omega & \\frac{1}{C R} & 0\\\\0 & - \\frac{1}{C R} & - \\omega & \\frac{1}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & \\omega\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 1 ⎤\n",
"⎢-ω 0 0 ───⎥\n",
"⎢ C⋅R⎥\n",
"⎢ ⎥\n",
"⎢ 1 ⎥\n",
"⎢ 0 ω ─── 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ -1 1 ⎥\n",
"⎢ 0 ─── -ω ───⎥\n",
"⎢ C⋅R C⋅R⎥\n",
"⎢ ⎥\n",
"⎢-1 1 ⎥\n",
"⎢─── 0 ─── ω ⎥\n",
"⎣C⋅R C⋅R ⎦"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"M1 = M[:4,:4]\n",
"display(M1)"
]
},
{
"cell_type": "code",
"execution_count": 236,
"id": "798afa00",
"metadata": {},
"outputs": [],
"source": [
"A,B,D,E,F,G,H, w = symbols('A B D E F G H \\omega')"
]
},
{
"cell_type": "code",
"execution_count": 237,
"id": "82281ff1",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\- \\frac{A}{C R}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 0 ⎤\n",
"⎢ ⎥\n",
"⎢ 0 ⎥\n",
"⎢ ⎥\n",
"⎢ 0 ⎥\n",
"⎢ ⎥\n",
"⎢-A ⎥\n",
"⎢───⎥\n",
"⎣C⋅R⎦"
]
},
"execution_count": 237,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"amat = Matrix([0,0, 0,-A/(C*R)])\n",
"amat"
]
},
{
"cell_type": "code",
"execution_count": 238,
"id": "1be85e38",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\frac{A \\left(C^{3} R^{3} \\omega^{2} - C R\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}\\\\\\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A \\left(C^{4} R^{4} \\omega^{3} - C^{2} R^{2} \\omega\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ ⎛ 3 3 2 ⎞ ⎤\n",
"⎢ -A⋅⎝C ⋅R ⋅ω - C⋅R⎠ ⎥\n",
"⎢─────────────────────────────⎥\n",
"⎢ ⎛ 4 4 4 2 2 2 ⎞⎥\n",
"⎢C⋅R⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω + 1⎠⎥\n",
"⎢ ⎥\n",
"⎢ A⋅C⋅R⋅ω ⎥\n",
"⎢ ─────────────────────── ⎥\n",
"⎢ 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω - C ⋅R ⋅ω + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ 2 2 2 ⎥\n",
"⎢ -A⋅C ⋅R ⋅ω ⎥\n",
"⎢ ─────────────────────── ⎥\n",
"⎢ 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω - C ⋅R ⋅ω + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ ⎛ 4 4 3 2 2 ⎞ ⎥\n",
"⎢ -A⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω⎠ ⎥\n",
"⎢─────────────────────────────⎥\n",
"⎢ ⎛ 4 4 4 2 2 2 ⎞⎥\n",
"⎣C⋅R⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω + 1⎠⎦"
]
},
"execution_count": 238,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"coeffs = M1**-1 * amat\n",
"coeffs"
]
},
{
"cell_type": "code",
"execution_count": 239,
"id": "08cf3dfa",
"metadata": {},
"outputs": [],
"source": [
"d,b,f,e = coeffs"
]
},
{
"cell_type": "code",
"execution_count": 240,
"id": "c2603919",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\left(\\omega - \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A⋅C⋅R⋅ω⋅(\\omega - ω) \n",
"───────────────────────\n",
" 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω - C ⋅R ⋅ω + 1"
]
},
"execution_count": 240,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Do a sanity check - should equal zero\n",
"simplify(b*w+f/(C*R))"
]
},
{
"cell_type": "code",
"execution_count": 241,
"id": "60c8e5ae",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\left(\\omega - \\omega\\right) \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ⎛ 2 2 2 ⎞\n",
"A⋅(\\omega - ω)⋅⎝C ⋅R ⋅ω - 1⎠\n",
"─────────────────────────────\n",
" 4 4 4 2 2 2 \n",
" C ⋅R ⋅ω - C ⋅R ⋅ω + 1 "
]
},
"execution_count": 241,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(e/(C*R)-d*w)"
]
},
{
"cell_type": "code",
"execution_count": 242,
"id": "6f02f484",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A \\left(- C^{4} R^{4} \\omega \\omega^{3} + C^{2} R^{2} \\omega \\omega - 1\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}$"
],
"text/plain": [
" ⎛ 4 4 3 2 2 ⎞\n",
"A⋅⎝- C ⋅R ⋅\\omega⋅ω + C ⋅R ⋅\\omega⋅ω - 1⎠\n",
"──────────────────────────────────────────\n",
" ⎛ 4 4 4 2 2 2 ⎞ \n",
" C⋅R⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω + 1⎠ "
]
},
"execution_count": 242,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# This reduces to -A/(C*R) but simplify doesn't do much of a job of reducing it. If you look carefully you can see why.\n",
"simplify(e*w-(d-f)/(C*R))"
]
},
{
"cell_type": "code",
"execution_count": 243,
"id": "69e5d7b8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\left(\\omega - \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 2 2 \n",
"A⋅C ⋅R ⋅ω ⋅(\\omega - ω)\n",
"───────────────────────\n",
" 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω - C ⋅R ⋅ω + 1"
]
},
"execution_count": 243,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify((e-b)/(C*R)-f*w)"
]
},
{
"cell_type": "markdown",
"id": "919c4009",
"metadata": {},
"source": [
"This is a little bit at variance with the results downstairs but not by much. It indicates that I may have a sign issue somewhere."
]
},
{
"cell_type": "code",
"execution_count": 244,
"id": "bcaecaa0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}$"
],
"text/plain": [
"E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)"
]
},
"execution_count": 244,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vc2 = E*sin(w*t)+F*cos(w*t)\n",
"vc2"
]
},
{
"cell_type": "code",
"execution_count": 245,
"id": "58abd6f0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)}$"
],
"text/plain": [
"B⋅sin(\\omega⋅t) + D⋅cos(\\omega⋅t)"
]
},
"execution_count": 245,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vc1 = B*sin(w*t)+D*cos(w*t)\n",
"vc1"
]
},
{
"cell_type": "code",
"execution_count": 246,
"id": "eabd944b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Bds96sesEW5Y5zGwy/ra5I/BN/PChHSRtNj+O80V8KqvZzo+luEf2ZTyy9M3AoI3J/Iz0U4ArawPRVrpSpsNM3rWtaBPDTG+qpitlmFN+BL4kMWiOBIRljhDMcjke5b0vfrrVh4Fk/WU/vLNNt5CG9ZWjgTvNjycd8gzymMbjQakndbjdNzVdLNNmZW8qalvRVsYzTPSmarpYhpnlkvaSNKmqjhVlRE9PT7Kj4jpg+xBcMQY/Zevjkq4wsyuBJyUtaHq3mpqampqammFHEoC5M75XNwlOmYVvoUm2gu4LrKampqampqamJkUSM3E/sKv5PzMZje+TtejcgFHAxLCn9JWsw4Nqampqampqhh8jASStxbeq3IHvmV0q6Zyo3r8CnwCeoP+BKjU1NTU1NTXDmMytoTU1NTU1NTU1Rfh/BKTtSA449+EAAAAASUVORK5CYII=",
"text/latex": [
"$\\displaystyle \\frac{\\partial}{\\partial t} \\left(B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)}\\right) = - \\frac{E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}}{C R}$"
],
"text/plain": [
"∂ -(E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)) \n",
"──(B⋅sin(\\omega⋅t) + D⋅cos(\\omega⋅t)) = ─────────────────────────────────────\n",
"∂t C⋅R "
]
},
"execution_count": 246,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq1 = eqn1.subs([(Vc1(t), vc1), (Vc2(t), vc2)])\n",
"eq1"
]
},
{
"cell_type": "code",
"execution_count": 247,
"id": "ee42ac89",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle \\frac{\\partial}{\\partial t} \\left(E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}\\right) = \\frac{- A \\sin{\\left(\\omega t \\right)} + B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)} - E \\sin{\\left(\\omega t \\right)} - F \\cos{\\left(\\omega t \\right)}}{C R}$"
],
"text/plain": [
"∂ -A⋅sin(\\omega⋅t) + B⋅sin(\\omega⋅t) + D ↪\n",
"──(E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)) = ────────────────────────────────────── ↪\n",
"∂t ↪\n",
"\n",
"↪ ⋅cos(\\omega⋅t) - E⋅sin(\\omega⋅t) - F⋅cos(\\omega⋅t)\n",
"↪ ──────────────────────────────────────────────────\n",
"↪ C⋅R "
]
},
"execution_count": 247,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq2 = eqn2.subs([(Vc1(t), vc1), (Vc2(t), vc2), (Vin, A*sin(w*t))])\n",
"eq2"
]
},
{
"cell_type": "code",
"execution_count": 248,
"id": "22a2f62d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle B \\omega \\cos{\\left(\\omega t \\right)} - D \\omega \\sin{\\left(\\omega t \\right)}$"
],
"text/plain": [
"B⋅\\omega⋅cos(\\omega⋅t) - D⋅\\omega⋅sin(\\omega⋅t)"
]
},
"execution_count": 248,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq1.lhs.doit()"
]
},
{
"cell_type": "code",
"execution_count": 249,
"id": "8781faf8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle E \\omega \\cos{\\left(\\omega t \\right)} - F \\omega \\sin{\\left(\\omega t \\right)}$"
],
"text/plain": [
"E⋅\\omega⋅cos(\\omega⋅t) - F⋅\\omega⋅sin(\\omega⋅t)"
]
},
"execution_count": 249,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq2.lhs.doit()"
]
},
{
"cell_type": "code",
"execution_count": 250,
"id": "86a4b00e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAAUCAYAAACpg7gVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAMJklEQVR4nO2deZBdRRXGfwmIrEnYQSgdkCUEkBAWAYmSgmBRIsSixKJYE1Ypo7IGqoAvRzYrkYAoYAFSEgTZUlRk0aCCUoAghIQlYASKsAcRCGGLGBL/OH3n9dy5b525b957c7+qVz2vT6/3O92v7+nTPUNWrlxJgQIFChQoUKBAgcYwdKAbUKBAgQIFChQo0M5YNSvSzK4HDgC2kPRR3o0wsy7gJeB6ScfkVEdT+xTq3AV4HDhe0rXNqLOTMBCchXoL3qog7zFbcN+aKHgv0Ay0oh5U05Eh6W0+M9sNeBQ4XdKMlOxeYHyqjBXAe8ATwMWS7m+gA13kO0DL9qmfyj8FmAEcLummlOwOYA9ga0kf9nfdUT1pblYCHwGLgbnA74DfS2qLfd28OQt1DDhvzYSZrQ38E9gMmC1pQh/K6iKnMVtw3z8oM1+ncZ6k8+sos4uC95ZGDbzPlHR0s9pTL1pZDyrJsixTFwJLgasyZLsA/wMuiuLWAb6KkzfOzMZIerqejgGvA9sB79eZr1ZU6lN/YJcQzs2QXYwrxg/p+dzyaMNK4PwQDgGGASOBCcD3gPvMbIKkD3JsR38hb86gNXhrJoQvpFYCY/pYVp5jtuC+f7ALsBx/nuUwq84yC95bH9V4/3MT29IIWlkPysp6WKbMbBv8zfVaSSfECc1sS+BFYK6kXdO1m9l9wDhgiqRptfcpX1TqUz/W8RywOTAsy/IT5GviJssVOdSfcLNQ0sgM+Sa4ZWof4DZJh/Z3G/oTzeAs1DOgvDUTZjYKmA/8BdgU2AnYUNJ/BrJdaRTc9w+iOWGepL4unHNHwXv/oN14T6Md9KCcLG2ZmoRbNG7JqD9ZQD1apn1vhnBxquKDgB8Bo4D1gHeA54FbJF0Z0nSRYTqO44GpwE+B/YC1gWeAqZLuKtOeWvqU1HMi8CtghqTTKqR7EdgS2ETSW2b2U2BKlGSFmSV/HyXphvD3zaH944E5VdrbCBJuslbZSFpsZocCi4DvmtkWkl5K5Ga2O3AasDewAfAu8DSu0LfGZYVyfoD/GK8GvADchD+7/6bSVuW+DHLjLMS1Cm/NxC/xZ3oqcDbO387An+JEtXKWNWZbfbyGuMHCfTInPFZL4oL3Qct7LnN/SN/I/N8OepApS5/m2w/4DHgko21lF1NmNho4EF9QzY7iTwjfRwF3ApcA9wBrABMz6iiHLwH/ALqAG/AHvQMw28zGVclbqU+Y2cbANHwRqCplJYuVvUL4BD6BADwMWPT5a5TvoRBW819oFAk3j5dLIOlt4O/h6x5JvJkdj7d9QggvAe4GNgJOjssws4vwZ78dPoiSH+iLgDlmtlqUti/c58kZtA5vTYGZHYZbja+U9Bw+WUJqq28QjFcYPNzX/KNa8D5oec9l7g/pG9WpdtCDTFm3ZcrM1gJGA8+V8Z5PSNo7mBIB1gK2xb3u5wKTJMV76ScCnwI7Sfp3XJiZbZBRRznsg7/ddC8hzewm4I/AGUCm03sNfQI4D/ctOqcGp8NFIRwJIOlWMxsBHI2/qV1dJl+i2F+vUn6jqGiZivBOCEdA99bPlfj+9FhJC+LEZrZ59PeeuEXjVWB3SYtD/NnAHfhi+nRK+8gNcZ83Z9BSvOUOM1sH+BnO/dQQ/VQI09sAHT1eYVBxn8wJe8XjOIXp4TkXvJfQybx/JGk65D73QwM61UZ6kCmLLVObAatQ2q7rhpkNoTTxHo+vCIU/wG+HRk+X9GxGxctxp/UeqNNX42XgglT+OcArwO4V8pXtE3STeiyuUL+uoR0JwetGcclzeaJcprDAXAZ8sYY66kLEzUpgXpXkw0OYLKq+jy+oz08PJgBJr0VfJ4XwgmQwhTTLcTPxCuC4VBGNcN8MzmCAeWsipgJfACTpvRCXaZkK6PTxCh3OfWq+nkhpvo4/k1M/WAXvdDzv34qS5z33Q/061RZ6UE4W+0ytH8L36I2t8R/ihyTtnUSa2TB8y+g64HYzO1DS3VG+G3Hz3rNmdjPwt1DG2+U6UQbzJX2WEf8qsGeFfJX6BHAo8HngVkkfJ5FhH/lU4HJJD0fp1wxhvD88BleYaicY3wU2rpKmESTcLFT1U3rbhHBhCJPtvj/UUE+igPelBZL+ZWavAVuY2fCgbI1y3wzOkv4MJG89YGaL8G2SWnGjpCOqlLk9fupkAe5jAICkN8zsHeDLZrZOpDeDYbxC53OfOV9XKo+C9xjtzvuDksZWKSvPuR8a06l20oNestgy9UkIV8/ImJgO58eRkpZKuhc/LghwVEo+AzenvYxP6ncAb5nZ/WbW60RgBSwpE7+cyre4V+oTuFkanOgYB+JXCaRJ2CqEzwOY2arAjsCzWQ54KawRtac/UdVfCrpPSWwBvCHpyRA9IoSv11BPYtXKfGuI4kdAn7jPlTNoGd7SeBFf5Nb6eaOGMq/AX5hOyfiRexr3edg5iej08QqDhvvM+bocCt57od15L2txiTAihP0+90PDOtVOetBLFlumkn3N9emNaoMzybteWiBpJjAz7FPuBXwHNxvOMbORDbz91INKfQL39wI/ihnjmyF8JYkws6H4iQcokTkKJ76i8oa8I/ATL/2NWv2lkhMMV0RxS0K4Gb2fQRrJG8cm+CSQxqapdI1ynzdn0Bq89YCkffuzPDM7HPhG+HpvdGIljTHAA1E7Onm8wiDgntKc8GTFVD3bUPBOx/Bey2JqSQhzmfuhIZ1qCz0oJ4sXU28Cb0cNjlFtMZVcgLWwjBxJS3Bv/ntCYybhDlz1XhpXDyr1CUor7m5HNjPbjtL+frxy3Q8/5fCopJdD3OgQVvNV2ha3AsyvpdF1oupiysyOwJ/3IuAXkeiRkP8Aqg+oefgP7z6kBpSZbYXf2fFS4LkH6uQ+b86gNXjLDWH7fTpuyr4B96dLowvYl8gyFaNDxyt0OPcBdS+mEhS8dwTvtSymmjL3Q1061S56kCnrNr3KL656ANggPKCksUPxCXc5fmdID5jZWPwuieXA1SnZuOAUl8ZGIfw4Q9ZvKNenCMnK+CvQ7cA3jZIybhvi1wzxUNrShNIKemmVpiT7071Os5jZb8xspZkdU6WMXoi4WUHGADKz9c1sOjAT34c+OOVXdRXO27nhdEc6f3wa5LoQnmNmG0ZpVsFPiw0lcgpslPsmcAZ95K0vnDUJhr8tXirpWEnHpT/AWSFttxP6IBiv0OHcR3PCZ1T3CUnyFLyX0O68LwOeqyFLbnN/kNWtU+2gB5Vk6Us7ZwGH4GazF0LcSPzytfeBs6LtgnWB7fG322XARElP0RN3AB+a2SO4VWQIMBbYDbekNONa+6w+xe3bFbjM/K6sncP38fidE9eb2Z3AwThRV0uaHeVPrEEXmtkO+OmBBZJuS9WzPz65zaY3kgXt8rp7VuLmA+D0wM1QStzsiZs0HwKOVHRRJ4CkZ83sZNw5eZ6Zzcb3l9fHOVqK30+EpIfNbBpwJvCMmd0e+nsAfpfMg7g1JEFfuM+TM+g7b33hLFeY2Y74xXqvAD+pkHQB3reRZra6pGV0/niFDuY+IJkTlgJTKmzvXiMp8ZcpeC+h3Xl/LJyyq4ic535oXKdaXQ/KytJOgbPwfcvYkTwxHQ6n5zHLY3Fv9p8DO0j6bUalZ+F3MozBLwGbCHwO998ZJ6nXsckckNWnBNOBy/AHcxK+uNxf0qPh+1q41e1TvP0nxZklPQBMxgmZjD+X0XEaMxuOX4p2l6RXM9qwI74YujtDVg0JN+vQ87qKQ/BTD1cBX5O0d3ohFfXhGnxv+S7cjHsGcBD+FnBFKu0U4DB80B2FOxYOBc4Bxkv6NEreF+5z4yz0o6+89YWzvJE4nf9YFf7buqRPcB5XxW80hg4fr9Dx3ENpThhG9pUIAs7F+5Cg4J2O4b2WLT4g17kfGtepltaDSrIe/5svJD4bv3xrjKRq+4ptgYHsk5lNBi7HL0Z7MCUbgd/5dImkM5vZrlbHQOthOd4KzvJHwf3gRMF7AWhdPagmyzqueinVtwjaDQPSJzNbA785dlb6wQeMxZ2EZzSzXW2CAdPDKrwVnOWPgvvBiYL3AtCielDt97zXYir4ThwJPG5+vXvbYwD71IU75Z9epl13Slpd0a2yBRwDrIddlOGt4Cx/FNwPThS8F4DW1YMqMv4PEQHQvfXV/lUAAAAASUVORK5CYII=",
"text/latex": [
"$\\displaystyle \\left( B \\sin{\\left(\\omega t \\right)}, \\ D \\cos{\\left(\\omega t \\right)}, \\ - A \\sin{\\left(\\omega t \\right)}, \\ - E \\sin{\\left(\\omega t \\right)}, \\ - F \\cos{\\left(\\omega t \\right)}\\right)$"
],
"text/plain": [
"(B⋅sin(\\omega⋅t), D⋅cos(\\omega⋅t), -A⋅sin(\\omega⋅t), -E⋅sin(\\omega⋅t), -F⋅cos( ↪\n",
"\n",
"↪ \\omega⋅t))"
]
},
"execution_count": 250,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq2.rhs.args[2].args"
]
},
{
"cell_type": "markdown",
"id": "e3e1066b",
"metadata": {},
"source": [
"Afte cancelling for sines and cosines we end up with the following equations:\n",
"\n",
"$$ F + B \\omega C R = 0 $$\n",
"$$ E - D \\omega C R = 0 $$\n",
"$$ E \\omega C R - D + F = 0 $$\n",
"$$ E - B - F \\omega C R = -A $$"
]
},
{
"cell_type": "code",
"execution_count": 251,
"id": "2a239e00",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -Vc₂(t) \n",
"──(Vc₁(t)) = ────────\n",
"dt C⋅R "
]
},
"execution_count": 251,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn1"
]
},
{
"cell_type": "code",
"execution_count": 252,
"id": "e75ca38a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 252,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"isinstance(eqn1, Equality)"
]
},
{
"cell_type": "code",
"execution_count": 253,
"id": "31d5305e",
"metadata": {},
"outputs": [],
"source": [
"if isinstance(eqn1, Equality):\n",
" eq = eqn1.lhs - eqn1.rhs\n",
"else:\n",
" eq = eqn1\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 254,
"id": "6521fde3",
"metadata": {},
"outputs": [],
"source": [
"ii = 1\n",
"for eqn in [eqn1, eqn2]:\n",
" sym1, sym2 = symbols('a_{} a_{}'.format(ii, ii+1))\n",
" vc = sym1*cos(w * t) + sym2 * sin(w*t)\n",
" eq = eqn.subs([])\n",
" \n",
" #display ([sym1, sym2])\n",
" ii += 2\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 255,
"id": "c170de0f",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}C R \\omega & 0 & 0 & 1\\\\0 & - C R \\omega & 1 & 0\\\\0 & -1 & C R \\omega & 1\\\\-1 & 0 & 1 & - C R \\omega\\end{matrix}\\right]$"
],
"text/plain": [
"⎡C⋅R⋅\\omega 0 0 1 ⎤\n",
"⎢ ⎥\n",
"⎢ 0 -C⋅R⋅\\omega 1 0 ⎥\n",
"⎢ ⎥\n",
"⎢ 0 -1 C⋅R⋅\\omega 1 ⎥\n",
"⎢ ⎥\n",
"⎣ -1 0 1 -C⋅R⋅\\omega⎦"
]
},
"execution_count": 255,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m = Matrix([[w*C*R, 0, 0, 1], [0, -w*C*R, 1, 0], [0, -1, w*C*R, 1], [-1,0, 1, -w*C*R]])\n",
"m"
]
},
{
"cell_type": "code",
"execution_count": 256,
"id": "e8cd9971",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{C^{3} R^{3} \\omega^{3}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2} - 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2} - 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{2} R^{2} \\omega^{2} + 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{- C^{2} R^{2} \\omega^{2} + 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 3 3 3 ↪\n",
"⎢ C ⋅R ⋅\\omega 1 ↪\n",
"⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n",
"⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n",
"⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n",
"⎢ ↪\n",
"⎢ 3 3 3 ↪\n",
"⎢ 1 -C ⋅R ⋅\\omega ↪\n",
"⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n",
"⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n",
"⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n",
"⎢ ↪\n",
"⎢ 2 2 2 3 ↪\n",
"⎢ C⋅R⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ↪\n",
"⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n",
"⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n",
"⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n",
"⎢ ↪\n",
"⎢ 2 2 2 ↪\n",
"⎢ - C ⋅R ⋅\\omega + 1 -C⋅R⋅\\omega ↪\n",
"⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n",
"⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n",
"⎣C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n",
"\n",
"↪ 2 2 2 ⎤\n",
"↪ -C⋅R⋅\\omega C ⋅R ⋅\\omega - 1 ⎥\n",
"↪ ────────────────────────── ─────────────────────────────────⎥\n",
"↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n",
"↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎥\n",
"↪ ⎥\n",
"↪ 2 2 2 ⎥\n",
"↪ C ⋅R ⋅\\omega - 1 C⋅R⋅\\omega ⎥\n",
"↪ ────────────────────────── ─────────────────────────────────⎥\n",
"↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n",
"↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎥\n",
"↪ ⎥\n",
"↪ 3 3 2 2 2 ⎥\n",
"↪ ⋅\\omega - C⋅R⋅\\omega C ⋅R ⋅\\omega ⎥\n",
"↪ ────────────────────────── ─────────────────────────────────⎥\n",
"↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n",
"↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎥\n",
"↪ ⎥\n",
"↪ 2 2 2 3 3 3 ⎥\n",
"↪ C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + C⋅R⋅\\omega ⎥\n",
"↪ ────────────────────────── ─────────────────────────────────⎥\n",
"↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n",
"↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎦"
]
},
"execution_count": 256,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"minv = m**-1\n",
"minv"
]
},
{
"cell_type": "code",
"execution_count": 257,
"id": "2c252f1a",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\- A\\end{matrix}\\right]$"
],
"text/plain": [
"⎡0 ⎤\n",
"⎢ ⎥\n",
"⎢0 ⎥\n",
"⎢ ⎥\n",
"⎢0 ⎥\n",
"⎢ ⎥\n",
"⎣-A⎦"
]
},
"execution_count": 257,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"amat = Matrix([0,0,0,-A])\n",
"amat"
]
},
{
"cell_type": "code",
"execution_count": 258,
"id": "4a5efba9",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ ⎛ 2 2 2 ⎞ ⎤\n",
"⎢ -A⋅⎝C ⋅R ⋅\\omega - 1⎠ ⎥\n",
"⎢───────────────────────────────── ⎥\n",
"⎢ 4 4 4 2 2 2 ⎥\n",
"⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ -A⋅C⋅R⋅\\omega ⎥\n",
"⎢───────────────────────────────── ⎥\n",
"⎢ 4 4 4 2 2 2 ⎥\n",
"⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ 2 2 2 ⎥\n",
"⎢ -A⋅C ⋅R ⋅\\omega ⎥\n",
"⎢───────────────────────────────── ⎥\n",
"⎢ 4 4 4 2 2 2 ⎥\n",
"⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ ⎛ 3 3 3 ⎞ ⎥\n",
"⎢-A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠ ⎥\n",
"⎢──────────────────────────────────⎥\n",
"⎢ 4 4 4 2 2 2 ⎥\n",
"⎣C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎦"
]
},
"execution_count": 258,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Find the coefficients of B,D,E and F.\n",
"coeffs = minv*amat\n",
"coeffs"
]
},
{
"cell_type": "code",
"execution_count": 259,
"id": "7edafd6a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left( - \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\right)$"
],
"text/plain": [
"⎛ ⎛ 2 2 2 ⎞ 2 2 2 ↪\n",
"⎜ -A⋅⎝C ⋅R ⋅\\omega - 1⎠ -A⋅C ⋅R ⋅\\omega ↪\n",
"⎜─────────────────────────────────, ─────────────────────────────────, ─────── ↪\n",
"⎜ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n",
"⎝C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n",
"\n",
"↪ ⎛ 3 3 3 ⎞ ⎞\n",
"↪ -A⋅C⋅R⋅\\omega -A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠ ⎟\n",
"↪ ──────────────────────────, ──────────────────────────────────⎟\n",
"↪ 4 2 2 2 4 4 4 2 2 2 ⎟\n",
"↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎠"
]
},
"execution_count": 259,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = coeffs[0]\n",
"d = coeffs[1]\n",
"e = coeffs[2]\n",
"f = coeffs[3]\n",
"b, e, d, f"
]
},
{
"cell_type": "code",
"execution_count": 260,
"id": "15bfbe9d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle 0$"
],
"text/plain": [
"0"
]
},
"execution_count": 260,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(f + b * w* C* R)"
]
},
{
"cell_type": "code",
"execution_count": 261,
"id": "2274eae6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle 0$"
],
"text/plain": [
"0"
]
},
"execution_count": 261,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq = eq1.subs([(B,b), (D,d), (E,e), (F,f)]).doit()\n",
"simplify(eq.lhs - eq.rhs)"
]
},
{
"cell_type": "code",
"execution_count": 262,
"id": "47d3a7eb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle 0$"
],
"text/plain": [
"0"
]
},
"execution_count": 262,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq = eq2.subs([(B,b), (D,d), (E,e), (F,f)]).doit()\n",
"simplify(eq.lhs - eq.rhs)"
]
},
{
"cell_type": "code",
"execution_count": 263,
"id": "1e658941",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right) \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ⎛ 2 2 2 ⎞ \n",
" A⋅C⋅R⋅\\omega⋅cos(\\omega⋅t) A⋅⎝C ⋅R ⋅\\omega - 1⎠⋅sin(\\omega⋅t)\n",
"- ───────────────────────────────── - ───────────────────────────────────\n",
" 4 4 4 2 2 2 4 4 4 2 2 2 \n",
" C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 "
]
},
"execution_count": 263,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vc1.subs([(B,b),(D,d)])"
]
},
{
"cell_type": "code",
"execution_count": 264,
"id": "21799d72",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right) \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 2 2 ⎛ 3 3 3 ⎞ ↪\n",
" A⋅C ⋅R ⋅\\omega ⋅sin(\\omega⋅t) A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠⋅cos(\\om ↪\n",
"- ───────────────────────────────── - ──────────────────────────────────────── ↪\n",
" 4 4 4 2 2 2 4 4 4 2 2 2 ↪\n",
" C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ↪\n",
"\n",
"↪ \n",
"↪ ega⋅t)\n",
"↪ ──────\n",
"↪ \n",
"↪ "
]
},
"execution_count": 264,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vc2.subs([(E,e), (F,f)])"
]
},
{
"cell_type": "code",
"execution_count": 265,
"id": "8d622a8f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAJkAAAAhCAYAAADKxQmiAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAFXklEQVR4nO2cbYgVVRjHf2uaaBYpvRkUSa2lFrquVBZlBQmFkEn2BpJ9KCQopXaLLPj3VFRYpiVEkh+W/FL4oSjQSHqhzF40V80yxEQMUsIWWc1K1O3DOVdmx/tyZu+dvXfl/OAyd86c+Z/Hv2fOnDn3mW3q6ekhkh0zGw2cL2mzmV0A/AiMlfR3nUNrOJpiJ6sNZrYFmCHp93rH0mgMrncAjY6ZjQM6gV8lTSpRpxU4LXaw4gyqdwADgDeB14HxZnZ6+qCZjQLeBR7u78AGCrGTlcHMZuE8WgQMAcanjg8FPgRekbS+3wMcIMROVgIzGwa8BrRJOgD8AbQkjjcBHcDnklbWI8aBQpyTleYpYJ2kTr//MzApcfx64B5gq5nN9GVzJP3UbxEOEGInK4KZXQI8BkxMFG8DphR2JK0j3gmCiEsYRTCzD4CZwLFEcRNwEBgpKZqWgTiSpTCz6cA0oBU4kjh0BbAKGAPsqkNoA5bYyRKY2RDgDWCxpE2pY3v81xZiJ8tEnFP0Zj5wLm5trBeSuoF99J78RwKIc7JI7sSRLJI7sZNFcid2skjuDAYwszgxi+RGnyb+ZjYc2A6sktTWl4ZroZGHVhUxXASsBM4DjgIvSFrV3xp5aFVLX2+XzwDfVdl2LTTy0OorR4EFksYD04GlZnZGHTTy0KqKzJ3MzJpxq99r+tpoLTTy0KoGSXslbfbf9wH7gVH9rZGHVrWctOJvZpOAdtxPK+cAe4GNwCJJG3DpL+3AdcUEzewz4Ba/exTY7c99J1GtrEZGaqlVkgBfknWLZsoGelNWo4+x55K5a2Y3Am24n+AuBB6U1JGuNyh10lyccf/h0ljGAg/4/XlmdgewQ9KOMm1PBhYCo4HLgPeA5WbW4tsI0QiilloV2plLGV9Sdctlypb1JlAja+yZtcysw8yeC6g6ApedMh/4p1SlEyOZmU0FVgDtkpYk6uwBvvLBtgP3mtls38AQM+uW9LzXuBQ4G/jED9GY2XLgWWACLlf+2nIa/pwlwA3A1ZKOpwzYiMvzWhCiVS2BvhTqlsyUDfSmYrZtBm9yz9yVtBpY7dvqKFUvebtcDHyfMjIp2AU87T+Fq/vK1H9oK9ANbPF1RuNuZ8eBTV6nrIaZXQ48CtyaNtGzHZ+hWkmrRoT4EpIpW9GbShpZvGmkzN3COlkzMBW4r0q9VtyI0m1mg4BhuHSZJyT9EqjRBmyR9EWJ413ANVXGGURGXyplyoZ4U0kjizcNk7lbGMkm++3G0BOLTfC8zgrgVeAs4CVgp6SlIRre/LtwL24UypYAuyQt80VnAie9QFsinqT2i7iljnLcLOnLxH6wLwGZshW9KaeR1ZssmbtmthA3VywwFOgxs+Sa422Svg7RS1MIYrjfHuqLSILJwHpJO30+1jzgETO7KvD8Mbh5S/Jquxs4nNifCISOikmWAuMqfH5InVMrX6CxvXkbl8JU+HxUpCx4AEpTGMm2+e004P10JTMbLulwujxVZwxuHeaECZJ2m1knMAd4MiCekX57yGvehHs0PuL3m3H/4JcDtHohaT9urSgLVfvi6zW6N124W20h3oNAl6SdWbWKMdg3ssHM1gDL/Ktg3wA9uKvvIcCAdRW0WnGT2PSVtBaYRZiRe7zG/WZ2AJc8+DEww/8ZgLeArcAHAVpVUyNf4BT0BsDMRuCWYsDdFS/264ldkgqZxL3u2XfinnYeBzYDG3CvhX1L2FDZCvwm6d9U+Vqg2cwmVBKQ9CfuaXE28CmwHDfZbcH9bPQXcLukYyVFak+1vsCp680U3NJLJ+5Bxvz3Xk/4MTM2kjsxnyySO7GTRXLnf0kw4Zv6NQ1AAAAAAElFTkSuQmCC",
"text/latex": [
"$\\displaystyle \\frac{A^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 \n",
" A \n",
"─────────────────────────────────\n",
" 4 4 4 2 2 2 \n",
"C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1"
]
},
"execution_count": 265,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute the magnitude of Vc1\n",
"simplify(b**2+d**2)"
]
},
{
"cell_type": "code",
"execution_count": 266,
"id": "37d264fc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A^{2} C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 2 2 2 \n",
" A ⋅C ⋅R ⋅\\omega \n",
"─────────────────────────────────\n",
" 4 4 4 2 2 2 \n",
"C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1"
]
},
"execution_count": 266,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute the magnitude of Vc2\n",
"(simplify(e**2+f**2))"
]
},
{
"cell_type": "code",
"execution_count": 267,
"id": "096e59a0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAUAAAAAoCAYAAACPQCMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAPrElEQVR4nO2de7xWZZXHvwe8X9LSaVCRtMDMGDHQArsIODqYJodJmfIzzqjdlMoIM6W01S+JMaJwNBWLknDM6wyoDF4wwRtaUIgaJpClad6CkLC8kKc/1rM973nPvr3Hfc4+l/39fM5nn7P3s5+99nPevd71rLWetZtaWlqoKA9JO5vZn8uWo6KipyNpRzN7sZFz+nWWMBXZSBoEqGw5Kip6CWdJ2ruRE7bqLEkq0pG0KzAH+LeSRSkMSdV0oqJMdgeulTTezDbnOaFSgCUgqQmYB8w0sz+VLU8RSBoGPA8MMLPXypanom8i6UJgNvDvedpXU+By+E8AM7utbEEKpBm4qVJ+FWViZjcAAyTlmllVFmAXI2kX4Hzg2LJlKZhm4GtlC9HTCT6sK4C3AluA88zsunKl6nF8DbhG0k1m9pe0hpUF2PV8HnjMzH5etiBFEYI5g4HFZcvSC9gCTDazA4AjgQsk7ViyTD0KM1sGPAlMyWpbKcAuRNK2wOeAuSWLUjTNwG1m9lLZgvR0zOxpM3sg/P4M8EfgLaUK1TP5PnC6pO3TGlUKsGs5Do9U9bYpTTOwoGQZeh2SRgD9zez3ZcvSA5kP7AL8R1qjSgF2LR8DftZbIr8Akt4CjAIWli1LbyKM6zzg02XL0hMxs43AUuDEtHaVAuwiQt7fkfQ+P9nRwLLepNTLJrhKFgDnB39WRcdYChwafNSxVFHgruNDwDbAL8oWpGCagRvKFqK7I2kW8EHgvfWpQpJWAPeY2eSQIzoXuMPMruh6SXsVdwNNwDjcJ9iOTAUo6VvAl4HRZnZnoeL1Ld4ftqtKlaJAJG2HW7VfLFuW7oykd+LR/yMS8iQfAd4Tfn8/vjroQUnNYd+JZvZQpwva+4jG7AN0VAECI4AWYGVBQvVV3gf8xcyeaOQkSUOAU3BFMwjYFdiIK9L/A+bW5jpJug04oq6b54E1wH8XnFN2BLC20Xvqg3wJWGVmSxKOb8A/H5jZPVSuqUIwsxckPYX7qGPJM9DDgd+Y2abCJOub7Ac8nbexpCZJ5wG/As4GXgKuB74D3I5bDBcDt9adGn1hfQMvtPBN4C5gJL5OskhrrZkq+puKpH549P/6mn2zJH2+ptnOQENVTCpy8ziwr6RYYy/VApT0duDN9D7HfZcScpEGAPc0cNqPgJOA1cAJZtZm6hz6nIInIEf73o7njD1qZlbX/lTgUuALwKzG76It4cE+hvbWZkVb9sWt9top7ETarpoZhv+fK4rnaaA/8DbgN/UH2ylASf2B04BPAO8Ku4+T9FvgB3hkqsvWe0o6CfgIbvHsAbyKf5guNbP/STnvvcAZ+Px/d3ya8RAwx8yurWk3EU9OHoYHKdYBPwG+a2Yvx/R7LK5EDsCVzXpgLXCNmV2SIM6euDN2Q857noIrv0eAkXH1As3sr8A36xI9Dw7buEDLLWH71jwy5OBQYLOZPVhQf72VN4ftZgBJo/HPwyvh7yHAQcB/db1ofYLnwnYvYhRgmylwWHKzGLgI/4etCYfmAzvg06mvd5KgSVyKa++7gAuAq8PfV4QpYjskfQpYhk/RluHTxv/HH/5JNe2mA9fgiv4nwPdwRTUduFXSNnX9fhqPeB4A3BT6XQRsD5yccg87hW3mSglJe+DjvAWYmFUsNSjCiDQFGFmKj2TJkJNmquhvHp4AXgNOkHQQcCH+2TlG0oHA5cCD+DNWUTzR8xG7nLDeApwLjAHONbNpkpbg/qRTgIG44/0MSdPM7JW4DiVNxk3+vDxgZgtSjg81szaaOyimm4GzJc02s6dqjh0AXAJsAj5oZr+qO3dg2I4CpgK/x1MTngn7p+IfxmNw5/X0mtM/g39zDzOz5+r63T3lHnYI2zxLxSYD2+HBjYdztK8lUoArYmSbGf48v8E+kxiPzxIqUjCz58Jnair+pSHcyFgI3B9+P97M/laakL2b6JlLV4DBND8OWByUXxMeAFkbAiCrQ77SSOAdJFsSk3ELLS8/JsWRXq/8wr5XJF0MjAUOxzPmI07D7+u8euUXzn0y/HpK2E6LlF84vkXSGcCHgU/SVgGCW2avxvT7x6R7wH0Q4JZAFs1hOy+tUT01/y+AYyWNpdX3cSxu7U/KigJLGmJmazPaDMW/5O5tRMa+ipnNAGbU7d6vDFn6INEz1z/uYK0F+KmwvTBsBwNvwqeOEVG6ReKDbGb7NCxiCiGL+yxc0Q3Cp5u17FX398iwvTmj60hZ3FF/wMzWSHoSjx7tYmYvhENX4tPe1ZKuBu4E7jWz5zOuFY3bdmmNJO2EPxgtwM8y+qxnCL72Edz3WcuLwHFmdgsJSNoatw4nS9rbzP6Qcq3xeO2/ymqp6O5E+iI2yl7rAzwct25uD3+PCNtaf9Jg3Pp5vEABEwlRzV8CpwLP4CXkp+HTiB+HZtvWnbZr2D5FOpGySEpNifZH/WFm38WLmT4OnI5PlZ+VtETSwe16aCWXAgT+IWw3ZdUxiyG6/uVm1mRmTcBueKR4R+CqsByvHeFL5q7Qth+tVmgSzVT+v4qeQfTMxSrArcDfTAb8I/BsTUmjNgowOHAHAUvTyh4V7AOcgj/EJ5vZ3LrrfJxQWbmOjWG7F/DrlOtGVt0AYqJDeMS5th0AZjYPmBeUyaHABHw6fauk/ROswWfDNqusUfRP2l5S/wYtrHb+PzPbAMwK/s7j8YXhF8WcOxR3f3wGOBe/p9iIdvChvgvoTdWsK3ovO4ftc3EHoylwU9huI6lfSHOJEmp/GY59IWznZFxwMsX5AKPI5f/GHDss4Zz7cWVwFOkKcCU+DR5NnQKUNBgP+vw2VJVoR9i/CFgUcuJOwdf7tpPVzP4kaSOtSjWW4DB/HB+/0cBPk9rW/J8i0iLAc3AF+HFiFKCZLQp9fgufPh8madeEex+P+4n/GnOsVr7qBUkVnUaY4eRhz7B9LO7gVqGzTZKewC28cZJuxpXDunDsRDwv7V7gqgzB9skpWB5+F7aj8dQBACT9Cx6giONSfMp8rqRbzaxNgqmkgSEQ8iM8inmOpBsjyy3kQc7Ep4I/rDt3DG4B1z/cUW5d2rR1Ha15lWnMwtN9Lglvt2qjxEOwYxyedjMx7OuH50luIX6t8RLcMh4pac8k/56ZvRiW0jXjUfC4PMvmhP31feX9gL6OpB3w4Np1ZvalRs8vqo/O6KuD1y+kPH6RZfZ7YMn+PYCnk76wa4Mg0/G3KV0F3Ij7yNYHZTgOf7AmdPFLby7BH/TrJF0P/AGfro0DriXmlZJmtlrSJPxeVkq6AU9U3g04BE+PGWNmyyTNwAs9PBz6fxG3HIfiqza+Xdf9fGCzpPtx5dyEV/g4BLe8bieZFcDBkgZlrJ29EDgQtygfCgppDe573RtP7B6I5y1G7I/nGq6Kc0+Y2auSFgEn4NPbi1OuPx9XchOoU3Ty95lEi/U7g6/iFnzZfXRGXx0hKo//gKQBwC8kLbIGX/5dYD9F99WpBMNgX2ICnRGvB0HM7DI8heQZfKoEbhHuA5wDjMoR7SyUsMpgDJ7MfHSQ703Av+IKLum8H+CKYiFuPZ6Jp4I8T83Db2Zn4fe6Fq8cezo+JufglTvqcx3PBpbj1vEkXDlvjUepx5hZu/SYGqKUkaEZ99xiZp8I97sQXyXwWdziPRC4D7fGT685LW36GxEl2n407frhmlvwmUB9xP1ovKBrrhUtjRBWROxPdvS+U/vojL46ihVUHr+oforuqwsYgufgJi5BbZMIbWazgdmSZuK+oH+2kktgmReEHJtwOHGaZWb3kf2wY2ZX46tL8sgymxTFm8EduE91FO47zLrWojztQtt5ZOQNmtn1pIxXTbsNku7EswKOpG20t5kOFD8IAbQzcb/t7niEfQUww8yWh2YzQ5tDY87/Ka2fgS249T0jfNHVkthHByiyr0Ryjk1iefwGxia1nw7KXnjJfkkfwhcgjMD9d+0CoA1wUNgm6rCkajAH4Q/rAx28cEUdwe92N27RdncWhG1ztENepXgcDSrAsJZ7BfAyPnXeD4/ev4z7apE0HlhjZmsSuhkOfAX35wzGv7AukxTV0MvTRyMyF9ZXxnVOImNsQru08viZY5Ozn0Zlb6gvSXMlfT1H052Ah/Gga2qgLQdj8ZVeiTm1SdVghuER0BcSjld0jCuBiyXtZmbryxYmhQW4L/IjNek4h+Nl0XLngIb0mznAmWZWW4HmCeCu8BCBJ69/TNLx+AOwtaRNZvYNSe/A06pusdblipfhbop301qnMrGPcE6uisx5+iqCvGOjlPL4DYxNVj+NjE2nluyvnflImvsGuzsSD2AlZiTEVYMZiJviVfXn4rkSr/rxURIq1HYHzOzJ8ME/BE/tWYKnvyxosKvv4D7D2PJbkS/RzKK1spFVNLRG2YzAA1erwvE98Onpa7SmaKX2ocYqMmfJUxSZY6Ps8vi5xiatn0bHJodM3QJJw/F0stS0vXYKMKSINJzCUJFNSDP5Hh7E6LYKMDAfV4ATJC3Fg0hH5T05BBFG0RpQ6ygjcCtsU4jqbY8XpDijPsUphdwVmbuCBsYmqzx+3rFJ66fRsekpJftPBhaZWWr1o+qlSF3PLOBUSSPNrMwUiywW4KlR4/HUqJei6F9OorXWK1Jb1RHj8B6Of4t/G88AmI7np16Qpw+1VmSeUbNvFvCYmUVJ4YkVmdMc8JKm4akyaYwxs6V1+3KNjWWXx881Nkn9dGRscsgU9fMV3DcZsS3QIqk2n/IoM7s7q69Gka9sOwGvI5pK9e6BLsZ8dcVU3E/TbQnfnI/iqVDTaHztb1QCbPMbFGU4/trNdWYWrQufJOmfcp6fVJG5Nmm9oxWZL8CT29N+fh5zXl8Ym9l4MDX6uTFmX0Nfjg1wGm79ZfonKwuwHC4HJko6wsy68+sG5uO5j2OB2OKzKUS1DA/Di862QdIOllHwQdK+eI7Z6w+omf1O0kp8XfOXc8jRaRWZzUugpZVBS6IvjM0GaiqgS/ozsMHM1jXaVyPIa1+eRHLqXBsqBVgCZtYiX154naRl3TGLPhApwPV4Ck9uzGx5WEV0UUiovhdPrRqOl14T2e9IGYE79OstkMV4Mnyeh7y2IvNG2lZkXoWvNurSiszV2CQjLwkX1QDoBwwKuZIbLN/bB2cAn7OaGp9pVFPgkgirar6If9i7K8vxsmILrWO1/ybgUckpeE7pcnzVzH3km/6MwFNv6pf3LQaGSHp3Vgfmlbun4sUgbgMuwx3/78GXua0HPtzB+3sjVGMTz8F4+s5KPKij8HtmFF7+Koy7zSxx6Vs9TS0tVdGOMpH0TjN7tGw5kpD0SWB10fleFRVFI2moNfgaiUoBVlRU9FmqKXBFRUWf5e84s8XFHKwkugAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle \\phi = \\operatorname{acos}{\\left(C R \\sqrt{\\frac{\\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}} \\right)}$"
],
"text/plain": [
" ⎛ ___________________________________⎞\n",
" ⎜ ╱ 2 ⎟\n",
" ⎜ ╱ \\omega ⎟\n",
"φ = acos⎜C⋅R⋅ ╱ ───────────────────────────────── ⎟\n",
" ⎜ ╱ 4 4 4 2 2 2 ⎟\n",
" ⎝ ╲╱ C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎠"
]
},
"execution_count": 267,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now compute phase of Vc1\n",
"Eq(phi, acos(sqrt(simplify(d**2/(b**2+d**2)))))"
]
},
{
"cell_type": "code",
"execution_count": 268,
"id": "bc3d128f",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAATQAAAAtCAYAAAAgL5d4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAPo0lEQVR4nO2de5xdVXXHvwnPRCURKSUSUpAA5SWQoQjCJMRUEEzFWKRKC9VgULHVFEIxFrr6w0glgqA0khRKA2hVoJWiBmJQIOURXg7hZQsBYsIjYExDDCoBiX+sfTInZ87rzpx772TmfD+f+ZyZc/ZZd90996y791pr7zVk48aN1NTU1AwEhrZbgZqampqqqA1aTU3NgGHrdisw2JG0FXChmc2oUOZpwJVVyaupaRMjzezlRm6oDVobkTQUuBaYX7HoY4EPmdn3KpZbU9MSJO0N3CBpipmtL3tfPeVsL/8MPG5mP6pY7lHA/1Qss6amZZjZE8AVwL81cl9t0NqEpCnAJNyoVSl3b2Ctma2uUm5NTasxs+uA7SX9Xdl76ilnG5C0A/AvwF+a2e8qFj8eWFyxzH6DpN3wafrOwOvAF83s+lbLaIasKumvevWCvwW6JN1kZk8VNa5HaO3hfOBRM7u9CbI7GcAGDX84p5vZfsAxwKWS3tQGGc2QVSX9Va+GMLMVuGH+Rpn2Q+rE2tYiaRdgOXCCmS1sgvyngfFm9mzVsqtC0luB/wXeXeZbt0DWUmCyma1sp4xmyGrwda8HlpjZxf1JryqQ9HbgaVz/W/Pa1lPO1nMWbtCqDgQgaTSwsT8bs8AXgAVpxkzSwcDZwARgJ+AF4AFgtpndn2jbAWwVf0gl/Rh4T/jzdbyvZ5vZFWmKpMnoLVXKSsgdD8wAOoC3Ax83s/mJZucDd0i6Mpnq0Cy9WoWZPS/pRuBcINeg1VPOFiJpO+ATwHVm1oyh8QT6eXRT0nC8D3pEryR9DDderwJ/AewN/HX4+1OJtjsC1wCnJ8SMww3mKGAs8B1gnqRDUl4vS0bDVCkrhTcDjwKfA36T1sDMHsFHMX/VQr1ayb8DEyQdlteoHqG1lsnASOA/myR/SwgIHA9sBO6Kn5R0BJ4MfLaZXRK7tAJYHB7MqO12wI3Al83s7tj5PfH+vcXMVoVz8/Bv9v2BriIZ4doluC/yMDN7I3HtAeBOM5teRlYVmNkCYEF4rfk5TW8CPgrMaYVeLWYRsAY4Fbgvq1E9QmstJwOrzGxpk+RvCQGBTuDBlBHqxcC9CWO2CTNbAyBpCJ6I/BMzuzbRrANYBywNbUcBFwFvAD+NGuXJkLQPHlk7O2nMAj8DDom1z9On1dwHHCZpWD/Tq8+E/8WtwEckbZPVrh6htYiwKmAScHuT5O8EjDCzZc2QXyF/BDwfPyFpL+AIfHRRxJH4dPRhSR8M504JU64OfHq2LvT3MGADcJaZPV5SxgxgqZndlvH6a4B3lZTVap4HtsH9bKP6kV5VsQg4CTicDNdKoUGTdCHw98DRZnZHpeoNLg4CRgD3Nkn+eODOJsmukmHAi4lz48LxgaKbzexOsmcW4/Bp61eAHYALgGVmdmkZGcEIngjMjp27BHjazC4Lp94CvFJSn7jsWcA/FDSb2MdUnsi/NqysXlsYD4Zjpq+4zBvuwH0eXUUNa3I5Mhyb9Q25JfjPAFYDb02cGx6OpdfsZTAOuNvMlpnZT/FAwhmSDix5/x64Dy7+PzoJ+HXs74OA+GivLJcC+xb8ZPqGShL5GX/RRzn9lceA1/DPeiplppzjgKfMbF1VWg1S9g3HZ5okfzwNrntrE13AxxLnHg3HCcB3kzdIGm5mv06eT7TZA3+gNxkjM1suqQs4BZ9lFBEZ2vVB5tH49G1D+Hsv4GB6sVwtLEVr9nK0A4DnzCw5Ah4QmNmGkGe5b1abXIMm6R34P3lRxboNRsaG4/KqBYelVKPpNgz9mYXAhZLeZma/BDCz+yXdDFwmaRgeAd2If5lOA0TxdLoDd/4nR0+LgA9RzqCtCDJOlrQW+DrwfWBySEz9BvAw0NJdTCS9me7Pz1BgTMjXWxMy6SM68f4dyDwHTJS0vZn9Nnmxh0EL+3N9GjiNbkt4oqRn8NXvX86I/jSFkJv0Z3hkaRQ+5HwEuNzMvplz32F4EutReILmmnDflWHRa9TuJOBv8KnEtsAy4D+Ar5rZqylyP4DnA+2Hjwh+CTwJfNfM8pZn7A68bGav5LTpLUcC9zQpt61SzOwRSfcBHyGkFwSm4P16Zji/Ac+r+iElfGu4QXsq5UO+CDhH0v5m9liBbi9JmgnMBD6IG9JFwA+AJeH3Dzdh/W0RhwLxIIXCz9WE0a6k7fE+PLbFurWaZ4EheHDp/5IXNzNoYa3X94GJ+DfiE8CB+DdSJ/AlYHvgH5uq8uZcjs+dF+NZ42/Dc5mulbSPmZ2XvEHStHDf7/DcnCfxRbqHAmcA14V2F+Af3tW4EVsPHIc7k4+VdIyZbYjJPR2YB6zC+2l1kPtO4OPkrzcbQcyZXDFbiv8sQsDXJM2NjEP48phNzCHfCGYWGaLk+R/jD0BZOWk67N0bnaoiBAqK3sNpeNrLkuZr1FYi19fItIvJEdp83JidZ2azJN2GD/2n4lOapcBZkmbFH/Q4kqZnvVgGD5nZjTnXD0gukZG0LXAz8PnwUDwXu7YfbljWAZ3Jb+WwPChK5JwJrMQTKKNEzJm4AZ+Mh/AviN3+SXzkcJCZvZSQu1PB+3wTbgibwXhgepNkV46Z3SJpDv6Z+nm79RkgvIbnzw10okhu6kL7TQYtOEBPBBYFYzYE92E8GQICj4cs6cOBPfEEwzSm48PBslyNZzOnkrbeLzgH5+Br9ibhSzsiPo2/ry+mTTFi6xynhuOsyJiF669LOgsfBX6CzQ0a+PrA11LkFjl8h5OxbCUPSX8CPJMlP/ic9iGWOLolYGZfb7cOAwkz+9d269AiIpfC8LSL8RHatHCMPmhj8VyeH8baRJGmTB+ame3esIo5SBoDnIMbrjF4HlOcXRN/Hx6ONxeIjnKffpK8YGZPSHoW2EPSiNhi32/hGe2PS/oOcAdwl5mVCZO/iic9liKMQs/HF2pPA67KaPouPPO+1X6dmpp2sF049vBvw+Z5aJPw0Ue0mr0jHB+MtRmLj05aMk0IUdYon2gVnjQ5i26HKHS/wYiR4fgc+YwIxxcyrkfnI3mY2VfxxdI/Bz6LT01flHSbpEMLXu8V3P9YiKQRuAH7U/x/lJl3E6716wXpNTUVEk01U3MWtwaQ9BbgD4EXY1GizQxaCBOPAW5PC5dGVOxDOxMPAvTYLkXSR3HjkmRtOO6K77mVRTTq2gVI25NrVKIdAGZ2DXCNpJHAu/HI0lRgoaQ/zhmt/Qof8RZiZi9LOhUfVq/C87OyGI+P5GpqBgO5SdjRlDOKoGwraWhIy4hWCES+mc+FY1F5tOlU50OLcm/SdqfIesiX4NHM48g3aF34tPNoEgZN0ljcYf2Mma1NuzmcXwAsCEtmpuLGJWsnjZVAp6RtswIqCflvAOslLQaOk7Rbcj+rsEj3EHKWU0nq96kcNTVmVjYS/QfhuCLt4tZB2DpJK/AR2PtCkuM4fB3cOkmn4PkudwHfLlBs95KKlWF5OB6Np0kAIOlY3GGfxuX4FPU8SQsTi5KRNDoEBq7CQ93nyvcr/0W4vhW+Q8NQEpn3kibiI9Skkdg5HPOy2ZfhBm9XGlstsBg3zhOAZN5dB/BYWr5cRAMflHq//gapSr/B0GcV6rUHsNoy6nXGfWhRNO/beNRwBLBVMG7X4CkbU1qZVIunX2wArpf0TUmzJS3AHf43pN0QDNgZuP5dkq6T9CVJcyU9iHcqYX+o2XjC66OS5kiaDTwEnIDn4X0lIf57wEpJN0i6SNLFIUl0Mj41z9tN84lw3LOxLiDaECDNj1b1dkH1fv2NUZV+g6HPqtJrd7qfpR5sMmhmNg9PeVhF9zYuY4KAc4EjSkbzKsPMHsbz4u4G3h/02wFfyjI3574r8BUCP8BHd2cDH8AX7c6JtTsHf69P4hvHfRbvk3OB96ZMDT8P3I+PXs/Ak2m3waOwE82sRzpHjGiDvXfmv+sePICP/NIMWqUJtWb2gpk9FH5fhScO75h7UxNkNENWM6hKv8HQZ1XoJWlXPChwT1ab1CIpki7Clw3VWwZVhHz30LXA9WZ2aoP33opHoXexsPA4+O1WAe+wBipLN/CaHcDVZnZAO2U0Q1aK7D4XbalKvy2lzwpet6hgS6/0kvTn+MzsBDO7Ka1N1uL0g/GAwEONvGBNNmb2anDw50Uss1iMG7TxQOR3OBBY3ogxU8kCJOreh35aioxSRUjyZDRKlbIy6FPRlir6q0hOozSrz9T3gi190etwPG0sM00paz+0g/AIX6rjrabXfAvfKWGvBu+LRslxY9jQdFMlC5CoeB/6wiIkJWSUpreyJM2X9E8l2vWpaEsV/VVSTmmqlJVCXwq29FWv9wALzez/sxqk7bYxGv8mqqea1fNfeBT2w/RcUpXHvfhDFPejdeIGshCVLECign3oVaIISZGMcE+pIiRlZFVAr4u2VNFf4VyRnNJFW5rdZ9b7gi190ku+3904egbqNqOHQQspDaVD/TXlMbP1kq7Cv7lKGzQz+22Iph4laUfzgiFHkijtlkOpAiQU749fpghJrgx1FyF5b0bEPF6EpBX79fe6aIukowr0K1W0hZz32WB/5crKeP/N4j48JWqYmf2mAr1OBF4C/juvUV0kpfXMBk6XNMl8a5uyLMYfvk5JP8M391tTcE9DBUiseB/6wiIkJWSULkJSQlYV9LpoSxX9VUJOQ0VbWtRnZYgXbHmqL3qFvvskcGkwjpnUBq3FmNlKSXPxHVQbMWh34EU2xuPZ0mX9Z6ULkJSUVViEJAv1oghJWSR9AfdVRWwHbJQ0I3buODNLOpT7VLSlgP7cX80u2rKpYEsv74/zfjzFI2+/QaB/WPLByHnAAWHKUpa78SjZBBpLqK2qAAn07yIkc/HofPRzU8q5NANVF21pTtGWSgq2BN+bATPLBCnrEVobMF9O9hk8W7qHozfjnlfCSodDgd3wJN8y9LkASWjX34uQrMGnX5G+v8Kn5UV1SuuiLc2hqoItJ+MBsVL7vdUGrU2Y2Y2SOvEcpwtL3rYY95esM7OsbY+Sr1NFARIYuEVI6qItDaAWFmyRtDO+q/TxKUGbVOopZ3s5B5jQwNQzSqVpdLnTFDy6diaeLH1/eO17KO8nyitCspek/YsEmG9bPhNPW/kRXp9hBh6lW4IXnDneWrhZZYiyRUVb4vS1zwZkf+EzhK7wMww37l3EtrBSd8GWHsnDZZG0NT4q+1TCUOaSuvSppnWExM55ZnZKibYj8GnVVDO7uqh9TTkkvQ/4GrBfi43DgCS4U04ws2P6IGMmvht0Q1/e9QitzQRfTKl8suAU/QxwS1OVGmSY2S14AujodusyQKiiYMtljRozqEdoNTU1A4h6hFZTUzNg+D0ocUDJFlY9wAAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle \\phi = \\operatorname{acos}{\\left(\\sqrt{\\frac{\\left(C^{2} R^{2} \\omega^{2} - 1\\right)^{2}}{C^{2} R^{2} \\omega^{2} + \\left(C^{2} R^{2} \\omega^{2} - 1\\right)^{2}}} \\right)}$"
],
"text/plain": [
" ⎛ ______________________________________⎞\n",
" ⎜ ╱ 2 ⎟\n",
" ⎜ ╱ ⎛ 2 2 2 ⎞ ⎟\n",
" ⎜ ╱ ⎝C ⋅R ⋅\\omega - 1⎠ ⎟\n",
"φ = acos⎜ ╱ ──────────────────────────────────── ⎟\n",
" ⎜ ╱ 2 ⎟\n",
" ⎜ ╱ 2 2 2 ⎛ 2 2 2 ⎞ ⎟\n",
" ⎝╲╱ C ⋅R ⋅\\omega + ⎝C ⋅R ⋅\\omega - 1⎠ ⎠"
]
},
"execution_count": 268,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now compute phase of Vc2\n",
"Eq(phi, acos(sqrt(simplify(f**2/(e**2+f**2)))))"
]
},
{
"cell_type": "code",
"execution_count": 269,
"id": "5f98d6e5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{C R \\omega}{C^{2} R^{2} \\omega^{2} - 1}$"
],
"text/plain": [
" C⋅R⋅\\omega \n",
"─────────────────\n",
" 2 2 2 \n",
"C ⋅R ⋅\\omega - 1"
]
},
"execution_count": 269,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# I am have a bit of a guess here at computing tan (phi)\n",
"d/b"
]
},
{
"cell_type": "markdown",
"id": "038f993b-ac01-4eef-bf57-9c4dd68f21ca",
"metadata": {},
"source": [
"### Compute V_R"
]
},
{
"cell_type": "code",
"execution_count": 270,
"id": "cd55f6cb-560b-4171-b48e-8fa3850c2b27",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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gi/feCMwUEd8gOysz9q8mPyhbFD3uFRnH93bbGxP798fmJJ2d2B9FB/09gKqOB94C3CsiL5DPBrH8AKExFOgikljdG4YnFR4AzAsBFAJjgaDjwFgnaDgQqI8q65eqfgxbOwrgFym9ShHTiDWGXD4uAS5xc2vegUXFOxK4VlV3aKGXqAzRPKXNMo5v77bJsN7RgrrDSyCo6jrAv7iPUeNpEtbQyhwiFzt3EywYxDDj3cEQUi5QGyIyrjhVewQNB+okaDjQCwQdBwL10KG69Sqsh+Ql4FJs3agkW2EL26aG1wYQWzPpKuAq1zg4EgsocEW1OR7BY8CTrG30JNnYbYcDJ6jqjqydhxTv7dkXi4R3u4hEwTGmuO2ignxsj4X3XhzfOR7K30S1lYvvAy6Ph6brtI06bLWRh3/GxPkarLvwyyJyeadt1GFrLNCKIwo6HnX9SjQTdNwaQcPVEHxxd+nEj8I8Qp1IzUOoE72BYgurzhaRk1ITqO6CRUyblti/D3CDiCQbUK9x21XUiIgMqepNwL+q6rYisjSR5ElsXtXOwBJVHYeFCb8T+y7bAwtcfZrtzjkjdn7U4/R0QVbe7rYjot61uujqF7BFqtqhCht12GqV1cAMEZkE7AcMulCCnbZRh61eJeh4JFVpJui4cwQNjyb44v4m1InRhDoxxlHVtwCfwYaLnZaT9LfAy8AOagvERlwJPKKqP1bVc1R1jqrOx+bk3AH8X01ZjxP1PL0n5diVbjuotuDq9dhwwOnA88DFqnoW1jiaDFwoIj+NnX+H235VVc9W1VmqelDKdfbDyid+bvnGkKpOxOJ6X1323Cpt1GGrHUTkMRFZ7P5/HFvQatNO26jDVi8SdDyaqjQTdNwZgobTCb64fwl1Ip1QJ3qCKGjCDMlepwcR+TsWVGA81miI+Dxre4ymA0dgC6WehC38Oirkdg1cgc0d+njKsbOxQBMvA8dg+d9PRG53n18JHIutlTTd7RtGRG7C1n96zm2FtUPnAFDVjYEPAv8jbhHWiFEBFFR1CrZw0l7A5tg4v4VYt9wCbJGnmdjkq1Go6vXAO93H1ViUjNki8p1YslwbJanSViYe5RJPOwCsmyxsz7LJtdFi3iuzlbC7J3ACMIDFuz9CROa1Y9Od35YNz3uVqZsS96lndVyFhvPstJj3ynVch4ahfR23q2FnI/jiFM30moad3Ub64ioJfj2bUCdS7dbi26uibP0SkT2LUw2n3TFl3/nEwnDnnLsMm1PjtT92fG8P2y+q6iBwuqpOFZFFsWMvAce5v+R5F2NR94rsfwP4Rk6Sj2NBFs5JHhjRM+SiWyzEJip9BNgOW831BeAYVT0AeEBEHsi52DTgFGxc47bAZcAFqjrVXcPHhhdV2iq4zuHklEsi7abAJcCnUkzllo2njbJ5L21LVeep6iyPpBOAe7DW+t8L0nYEn3vloZvC+9TLOq5Cwx52yua9lK2gYSD44izN9JqGoYE6rpLg13OvczihTqTR03ViDDOX4qF+laOqGwAnA1eIyM3J4+NjCXcDLsLijc+NpXkYuMmJdibwUTcObwKwnqo+LSKnORvbYCHrrnFdn6jqBcCpwE5YlIe359lw58wF9gB2FZE1iS+0ELhZRGb42GoXz3KJ0q4P/AQ4U0YuDuVbNrk23HHfsim01S4ichUWkQRVnVe1/bKUuFeZuvG9T3k2YvkZczquQsMedrw1XGSrXXpRw85O8MUpmqlKw+548MUdIPj1bJpUJ5rk16G368RYRkSeV9XDgH1U9ZV5Q/4qZivgQjJ64+LD5OZgYermpiUUkRVYq+pkGH4b8eZExR7AIjkscWm2xLqj1uBif4tIrg1V3R4b7/fuZIVy3IcLGVhkqyJ8ygW1yBfzgF+KyKUpSQvLpshGmbLxyE8v4nWvCnRTeJ88bIxJHVehYbc/006Zcimy1aNUoWEIvnge6ZppW8PuePDFnSP49WwaUSeCXw+UQWx+z02FCau95n3ArKzj0TpDE4HdgEPavN4A9gbkabXY5Rtgk50+JyL3eto4AVgiIr/KOL4CeFub+fSiZLnsjnVR36WqH3T7DhORu93/PmVTZKNM2RTZ6ikapmEYmzquQsNFdsqWS9/ouEINQ/DFWZqpQsMQfHFHCH49m4bVieDXA2OaqGcoike+0PdESZ+INg3rsj0beBVwOrBUUlbfTbPhKuKHWRtDPOp6fUhEznO7NsKiRfjkJ277K1iIyzz2kZErAXuXi9gYxLzofIVlk2ejbNl45Cdu+xRsvHDE+sCQqsbXRHifiPzax16XKK1hSNVNKQ2n2ahLxy1qGDzLpgoN59lppVx8dRw0nGor+OLRtKVhqM8X94iGqyb4daNlv+6uX1udCH490AtEYtzQbZ/NSujJNOBWEVkqIndik/emq8VH92FrbOxq/O3AwYxcDGoyUOZNTsQgsGPB3/zEOVWVCzS7bM7HQhBGfz9L2VfqYdQFmqJhqO9eDVJew9Ccsgkazqdf/M0g3fPFTa7fvaDhqumH+z5I8OtZhDoR6AhRz9A9brsX8MNkIlXdUERyV6dV1a2xOPHDFUJElqnqIuAw4ESP/LzabZ91NvfGQiK+6D5PxMR/xuhT8xGR5Vgs+zK0XS4uXdPLZgXWjR3l9xlghYxeIbjJNEXDUNO9alHD0JyyCRrOp1/8TVd88Rio372g4arph/se/HoGoU4EOsV4ABFZoKpXA+ephZ+7BRjC3hgcBSgwKhRdggFswl2y9X8dcCB+lephZ+NQVV0JnAv8HNhfVZcA3wLuYu1KtbVSUblAD5YNgKpOwMJwgvUyvkFtvYMVIvJwp/IBjdIwNOxeNahsGlUu0JMahh68Vw3SMDSsbKBZOq6ScN+zaVDZNKpcInq1TgTqIT5m80NYBJHjgcXYSrUnAbfh1w05ADwoIs8n9l8HTFTVnYoMiMhfsOgrBwG/AC7AJuZNBX4DPAW8X0Re9shPVbRbLtC7ZbMLFnZzETbpUt3/VUfM8aXrGobG3quul01Dy6XXNAy9e6+6rmFobNk0TcdVEu57Nl0vm4aWC/R2nQhUzLihoaFu5yEQCAQCgUAgEAgEOo5XtLFAIBAIBAKBQCAQ6DVCYygQCAQCgUAgEAj0Jf8P+4VewElWJJcAAAAASUVORK5CYII=",
"text/latex": [
"$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right) \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right) \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + A \\sin{\\left(\\omega t \\right)}$"
],
"text/plain": [
" 2 2 2 ⎛ 2 ↪\n",
" A⋅C ⋅R ⋅\\omega ⋅sin(\\omega⋅t) A⋅C⋅R⋅\\omega⋅cos(\\omega⋅t) A⋅⎝C ⋅ ↪\n",
"───────────────────────────────── + ───────────────────────────────── + ────── ↪\n",
" 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n",
"C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ↪\n",
"\n",
"↪ 2 2 ⎞ ⎛ 3 3 3 ⎞ ↪\n",
"↪ R ⋅\\omega - 1⎠⋅sin(\\omega⋅t) A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠⋅cos(\\omega⋅ ↪\n",
"↪ ───────────────────────────── + ──────────────────────────────────────────── ↪\n",
"↪ 4 2 2 2 4 4 4 2 2 2 ↪\n",
"↪ ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ↪\n",
"\n",
"↪ \n",
"↪ t) \n",
"↪ ── + A⋅sin(\\omega⋅t)\n",
"↪ \n",
"↪ "
]
},
"execution_count": 270,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vr = A*sin(w*t) - b* sin(w*t) - d*cos(w*t) - e*sin(w*t) - f*cos(w*t)\n",
"vr"
]
},
{
"cell_type": "code",
"execution_count": 271,
"id": "db9bbd1f-00f1-4981-a8fb-7417eb6d69f5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\left(C^{3} R^{3} \\omega^{3} \\sin{\\left(\\omega t \\right)} - C^{2} R^{2} \\omega^{2} \\cos{\\left(\\omega t \\right)} + C R \\omega \\sin{\\left(\\omega t \\right)} + 2 \\cos{\\left(\\omega t \\right)}\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ⎛ 3 3 3 2 2 2 ↪\n",
"A⋅C⋅R⋅\\omega⋅⎝C ⋅R ⋅\\omega ⋅sin(\\omega⋅t) - C ⋅R ⋅\\omega ⋅cos(\\omega⋅t) + C⋅R⋅ ↪\n",
"────────────────────────────────────────────────────────────────────────────── ↪\n",
" 4 4 4 2 2 2 ↪\n",
" C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ↪\n",
"\n",
"↪ ⎞\n",
"↪ \\omega⋅sin(\\omega⋅t) + 2⋅cos(\\omega⋅t)⎠\n",
"↪ ───────────────────────────────────────\n",
"↪ \n",
"↪ "
]
},
"execution_count": 271,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(vr)"
]
},
{
"cell_type": "markdown",
"id": "9952df1c",
"metadata": {},
"source": [
"## Larger (x 3) RC Network \n",
"Now try the same thing with three lots of RC components\n",
"\n",
"There are three equations:\n",
"\n",
"$$ A \\sin ( \\omega t ) - V_{C1} - R_1 (i_1 - i_2) = 0 $$\n",
"$$ R_1 ( i_2 - i_1) - V_{C2} - R_2 (i_2 - i_3) = 0 $$\n",
"$$ R_2 ( i_3 - i_2) - V_{C3} - R_3 i_3 = 0 $$\n",
"//\n",
"These can be rearranged so that all the i's are on the right and everything else on the left.\n",
"\n",
"$$ A \\sin ( \\omega t ) - V_{C1} = R_1 i_1 - R_1 i_2 $$\n",
"$$ V_{C2} = R_1 ( i_2 - i_1) - R_2 (i_2 - i_3) = (R_1 - R_2) i_2 - R_1 i_1 - R_2 i_3 $$\n",
"$$ V_{C3} = R_2 ( i_3 - i_2) - R_3 i_3 = (R_2 - R_3) i_3 - R_2 i_2 $$\n",
"\n",
"However if R1 = R2 = R3 the above simplifies to :\n",
"\n",
"$$ A \\sin ( \\omega t ) - V_{C1} = R i_1 - R i_2 $$\n",
"$$ V_{C2} = - R i_1 - R i_3 $$\n",
"$$ V_{C3} = - R i_2 $$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2af0f0fe-a18d-4389-bc4f-cd993060ba27",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 272,
"id": "be3953e6",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}R & - R & 0\\\\- R & 0 & - R\\\\0 & - R & 0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡R -R 0 ⎤\n",
"⎢ ⎥\n",
"⎢-R 0 -R⎥\n",
"⎢ ⎥\n",
"⎣0 -R 0 ⎦"
]
},
"execution_count": 272,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m = Matrix([[R, -R, 0], [-R, 0, -R], [0, -R, 0]]); m"
]
},
{
"cell_type": "code",
"execution_count": 273,
"id": "989e65a5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle - R^{3}$"
],
"text/plain": [
" 3\n",
"-R "
]
},
"execution_count": 273,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.det()"
]
},
{
"cell_type": "code",
"execution_count": 274,
"id": "8e0a402b",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\\\operatorname{Vc}_{2}{\\left(t \\right)}\\\\\\operatorname{Vc}_{3}{\\left(t \\right)}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡A⋅sin(\\omega⋅t) - Vc₁(t)⎤\n",
"⎢ ⎥\n",
"⎢ Vc₂(t) ⎥\n",
"⎢ ⎥\n",
"⎣ Vc₃(t) ⎦"
]
},
"execution_count": 274,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = Matrix([A*sin(w*t)-Vc1(t), Vc2(t), Vc3(t)]);v"
]
},
{
"cell_type": "code",
"execution_count": 275,
"id": "d94e3e61",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{1}{R} & 0 & - \\frac{1}{R}\\\\0 & 0 & - \\frac{1}{R}\\\\- \\frac{1}{R} & - \\frac{1}{R} & \\frac{1}{R}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 1 -1 ⎤\n",
"⎢ ─ 0 ───⎥\n",
"⎢ R R ⎥\n",
"⎢ ⎥\n",
"⎢ -1 ⎥\n",
"⎢ 0 0 ───⎥\n",
"⎢ R ⎥\n",
"⎢ ⎥\n",
"⎢-1 -1 1 ⎥\n",
"⎢─── ─── ─ ⎥\n",
"⎣ R R R ⎦"
]
},
"execution_count": 275,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.inv()"
]
},
{
"cell_type": "code",
"execution_count": 276,
"id": "bbeeee6b",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R} - \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\\\- \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\\\- \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R} - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R} + \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ A⋅sin(\\omega⋅t) - Vc₁(t) Vc₃(t) ⎤\n",
"⎢ ──────────────────────── - ────── ⎥\n",
"⎢ R R ⎥\n",
"⎢ ⎥\n",
"⎢ -Vc₃(t) ⎥\n",
"⎢ ──────── ⎥\n",
"⎢ R ⎥\n",
"⎢ ⎥\n",
"⎢ A⋅sin(\\omega⋅t) - Vc₁(t) Vc₂(t) Vc₃(t)⎥\n",
"⎢- ──────────────────────── - ────── + ──────⎥\n",
"⎣ R R R ⎦"
]
},
"execution_count": 276,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now to calculate the currents i1, i2, i3\n",
"minvv = m.inv()*v; minvv"
]
},
{
"cell_type": "code",
"execution_count": 277,
"id": "e51811ad",
"metadata": {},
"outputs": [],
"source": [
"Vc1 = Function('Vc1')\n",
"Vc2 = Function('Vc2')\n",
"Vc3 = Function('Vc3')\n"
]
},
{
"cell_type": "code",
"execution_count": 278,
"id": "8902fcbd",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}C \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\C \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)}\\\\C \\frac{d}{d t} \\operatorname{Vc}_{3}{\\left(t \\right)}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ d ⎤\n",
"⎢C⋅──(Vc₁(t))⎥\n",
"⎢ dt ⎥\n",
"⎢ ⎥\n",
"⎢ d ⎥\n",
"⎢C⋅──(Vc₂(t))⎥\n",
"⎢ dt ⎥\n",
"⎢ ⎥\n",
"⎢ d ⎥\n",
"⎢C⋅──(Vc₃(t))⎥\n",
"⎣ dt ⎦"
]
},
"execution_count": 278,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mm = Matrix([C*Vc1(t).diff(), C*Vc2(t).diff(), C*Vc3(t).diff()]); mm"
]
},
{
"cell_type": "code",
"execution_count": 279,
"id": "28aa249b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d A⋅sin(\\omega⋅t) - Vc₁(t) - Vc₃(t)\n",
"──(Vc₁(t)) = ─────────────────────────────────\n",
"dt C⋅R "
]
},
"execution_count": 279,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn1 = Eq(mm[0]/C, simplify(minvv[0]/C)); eqn1"
]
},
{
"cell_type": "code",
"execution_count": 280,
"id": "717505e9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d A⋅sin(\\omega⋅t) - Vc₁(t) - Vc₃(t)\n",
"──(Vc₁(t)) = ─────────────────────────────────\n",
"dt C⋅R "
]
},
"execution_count": 280,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn1"
]
},
{
"cell_type": "code",
"execution_count": 281,
"id": "ea323a49",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Eq(Derivative(Vc1(t), t), (A*sin(\\omega*t) - Vc1(t) - Vc3(t))/(C*R))\n"
]
}
],
"source": [
"print(eqn1)"
]
},
{
"cell_type": "code",
"execution_count": 282,
"id": "e74d9997",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAAcCAYAAADhhWo2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAJc0lEQVR4nO2ce7BVVR3HPxepQC0ZtXxhkooPJvGKSpjiqPkiS7k+KCxNREbBKBSbZND5+tV8jC+yFBtwEiq1SAVL8pGiMeUTFVMkDdPUIDEVH5gP9PbHWvuy2Xeffc5BziFgf2bOrHPW+q29fvv+9lrrt35r7dvS3t5Ordg+BRgrqXfNlUpKSnLpUqd8KzB31atRUrLusTKd77EG6FFSss7RtVKB7VZgAjAAWAAMB3YBzm2KZiUlazm5nc92b+BPwNXACGBHYBqwPmuw22l7KjAI+IKkpTXW2R2YA4yQdE0j9SvJZ221W0tewMX2HcCrko5N5U0GDpe0WY78dcCxwKmSJhY1aPtO4CDgSEnTP6b+NWN7T+BB4AxJl+eUnwZcDnxL0vWZsukED6C3pLeboW8zKO3WIbcZsBCYKGl0pqw3cCJwMPB5oAewBHgcuBmYIumdlHzyd0rzCvAMcIWk3yaZndZ8treODU3IFH1A5VlvckxPqlCeXLsXcCCwCPh9kWwDOB94kzCb57F7TB/JKbsQ2Bz4XgP0Wp2UdgscQegLNycZtltsnwfMA84E3gVuBC4D7gJ2A64C7sjRp52wPHPUfzZhEJgWBwsgP+CyG/AhoWen6UeFzifpXkLP3s12v4KbHA60ANdKWlYgt0qxvQPh4Zkm6b8VxHYH3ibcxwpIegj4G3Cy7XqDVP+3lHbroA14ldBJEn4OnAX8HWiVtLekkZLOlDQU6BnLF6T03RbYGHhGgXMknSXpaOC7Uez7iXzemq8dWA/4FPB+vOhA4EvAjwtuYDJwCWGNODJbaHs9YFi8ficf3HZ/YCywD7Ap8BrwBHCNpGkF7dbCiYSH5zc57V4E/DCV9ZHt5Pvxkn4Zv/8aOIfgUmRHuzWZddputj8DHABcL+nDmHc6cAIwHxgg6a1svTgYnG+7eyp7j5jmzcK3x/RzSUbeaDAHeA+41PZ2tg8DfhXL5ubIJ0wldNahttfPKR8EbAXcJem5dIHtEcB9wOCYXgbMjIqOKmizVg4kzOYP5JQ9GnUntu3U596U3F9imvXn13TWdbt9DfgkMB3A9hYEV3EZMCSv46XJzMhFnW/7mM5PMjrNfJIW2R4GXAQcT9jXmwKcQc7Unqr3iu0ZwJD4mZIRGRHTSelM232AiQS/fqCkeZnynpXarAXbGxD2J+fnRcokTbPdA/gOMFXSpKxM5OGY7lulvTGERXmtzJU0ow75VUppN9qApcCd8fcYoBshkPJknWonnW9OOtP2psCl8edFSX7uVoOkG4Abstk1ND6JYMCTSBkxjiZfBRYDt2TqjIx6nJc1YNTlpRraLWIrghu9qEAmWe88WklA0hu23yVEvIoYA2xTh35TgRl1yDeCddJutrsBhwK3SXo3Zg+O6S/qUdZ2S0qfw20fQNB/G+Bwgpc5Kh3trLjJvpLMAp4F9ra9s6Rkih0W25oi6YNMnQExva3axW2PA44k7Du+R3BHxlUZoTaJ6esFMv0I0dwnqqjwGtBpqyWNpF5VrvGxsf089XXw6yR9u6C80XY7FTgZ6BWz5gE/kjSzoFoz7HYQsCHLXc4NgR0I69sHq1wzS29go/h9bKZsKXC0pNvTmas0cicpvSg/CTpGhOGEG5qcU61HTP9VQxP7EVydLxMWycuAu2xvXFAn8cm75RXa7ko4ufOUpPeqtN89db3VybPA03V8FhZdrAl2e4kQHOlHcM1mATNs9y2o0wy7HUlY7yaDwGdj+mZ6765GEpfzWkktkloIA8jpwAbADdFN7qBrvJHaX23IITaUcC1hj+P4OFMNBLYFZklakFN9SUy3IoSFi9o5JP3b9nHAG8DeVN5/WhzTTSqU9yEYuKLrEtvqQnjgnqsiN4YGr/kkfaUe+RpppN2yLut42yOBvYC/VqjWULvFKO7XCff3RsxO1pbdba+XRD9rpNN6T9JrwATbewHHAMcBP03Ku0ahdOf5WEh62fbvgKMI/nNbLKq0IH4gKj6IKkbM4dOE2bvINVlEOGGwY4Xy1phWOzC+IyHsPbeK3BjWvDVf0+wWH/pjCO7efQWijbbbvoSO3XFaR9Ji2/8k2G8/4O5KF7XdRdJHqayiSOc1hHseSrbzFbGS7/BNJhhxLLAr8B9SN5nhauAU4Gzbd0h6KtN+z4LF+xWEP+r9lRSR1G57NnCU7e1zRvFkZH2z4H5g+RrnniKhZqz5GkjD7GZ7F4KduhE2xdskVVyrNcFubcBHdA4kTSDsZ0+0fYSkFQaW6I4fSlgPD4l5XQiHU5bR+XBK0vYSYIDtLSUthNoCLq3EUcP2JUDfrPuXw53A80D/+PtKSe/nCUp6yvYo4GfAY7ZvIZwq2ATYk/DH3T9bz/blhI3dfWpwD24iPFSHkDqREElGqvNtf5HgesxLR6UiBxP2nLLGWptopN2eJjxLGwFHA1Nt71clWNYQu8UONBi4X9LLGfmfAH0JG/xPxLOazxACO1sTnrmeQPoc6U6EmfzxVNS0A0kf2P4D4RxtG+FYWk0Bl1aWT+39gYeqVcgs4CF/wZ6Wn0y4qVsJ0/0PCOHZVxJF09ieQJjCD5D0j2r6EIy4mLBvmW17NjCaYLzRhC2V1kx7GxGMdaukF2tob42kkXaT9L6kBZIekTSOMKCfRjGNstsehI50MxkktUsaDhwW76sVOJUQiOpLmL1PYMXzokUuZ0LiQRyVZKzwVoPz3+G7h/Cg3wh8InWx+ZL6FDTWEGxfAXwD2D8VEq+l3jjgAqCfpLpeCLY9mjAiDpT053rqluRjexawsMoWSEPsZvsCYBywbfbUTjPpcDtd/A7fHEJkag7hjOcLhH22pmL7KkLEaDDwuu3NY9Hbqv6qzwTCGuVcQpSr1ja7Ewx1U9nxVo54DnMm8CIhSHYsYaY8rIbqjbBbG8FFXG0dD1Z0O68EZsZT2wviBugfgcVxgbgF8BbwsKR/SyqKMDaKUQTj3U2IhiWfM6pVjL74ccCceHSpVnoRIn5V2yipyOaE88FPE2y3JzBIUtUN+kbYTdLOklrruFZDaGlvb0/e4XsB6C8pOQuH7YnAdpIOsX02cLCkgatL2ZKStYlk5qvlHb5Wyn+eVFKyykg6X/odPmCFd/iSDrcrlU8jlJSU1EkScEm/w3cxYd8i+Z8ec1OyO9neEnhH0pIm6llSstbRBcI7fIQd+0OBJ4HxhFdL3mH5O3zjgW8SDsle2GxFS0rWNnL/e1lJSUnj+R+Yg2zokMPbBAAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -Vc₃(t) \n",
"──(Vc₂(t)) = ────────\n",
"dt C⋅R "
]
},
"execution_count": 282,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn2 = Eq(mm[1]/C, simplify(minvv[1]/C)); eqn2"
]
},
{
"cell_type": "code",
"execution_count": 283,
"id": "2875b41c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Eq(Derivative(Vc2(t), t), -Vc3(t)/(C*R))\n"
]
}
],
"source": [
"print(eqn2)"
]
},
{
"cell_type": "code",
"execution_count": 284,
"id": "8066a383",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{3}{\\left(t \\right)} = \\frac{- A \\sin{\\left(\\omega t \\right)} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)} + \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
],
"text/plain": [
"d -A⋅sin(\\omega⋅t) + Vc₁(t) - Vc₂(t) + Vc₃(t)\n",
"──(Vc₃(t)) = ───────────────────────────────────────────\n",
"dt C⋅R "
]
},
"execution_count": 284,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eqn3 = Eq(mm[2]/C, simplify(minvv[2]/C)); eqn3"
]
},
{
"cell_type": "code",
"execution_count": 285,
"id": "c23c9ce7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Eq(Derivative(Vc3(t), t), (-A*sin(\\omega*t) + Vc1(t) - Vc2(t) + Vc3(t))/(C*R))\n"
]
}
],
"source": [
"print(eqn3)"
]
},
{
"cell_type": "code",
"execution_count": 286,
"id": "55da3b94",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[(a_2*omega, -a_1*omega), (a_1/(C*R), a_2/(C*R)), (a_3/(C*R), a_4/(C*R)), (0, -A*a_6/(C*R))]\n",
"[(a_8*omega, -a_7*omega), (a_3/(C*R), a_4/(C*R))]\n",
"[(a_4*omega, -a_3*omega), (-a_1/(C*R), -a_2/(C*R)), (-a_3/(C*R), -a_4/(C*R)), (a_7/(C*R), a_8/(C*R)), (0, A*a_6/(C*R))]\n",
"[a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8]\n"
]
}
],
"source": [
"sysEqns3 = systemEqns()\n",
"\n",
"res1 = sysEqns3.extractCoeffsFromDiffEqn(eqn1)\n",
"print (res1)\n",
"res2 = sysEqns3.extractCoeffsFromDiffEqn(eqn2)\n",
"print (res2)\n",
"res3 = sysEqns3.extractCoeffsFromDiffEqn(eqn3)\n",
"print (res3)\n",
"\n",
"print (sysEqns3.symbols_used)"
]
},
{
"cell_type": "code",
"execution_count": 287,
"id": "bb3c1ceb",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\omega & \\frac{1}{C R} & 0 & 0 & 0 & \\frac{1}{C R} & 0 & - \\frac{A}{C R}\\\\\\frac{1}{C R} & \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & 0 & - \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & 0 & 0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & 0 & \\frac{1}{C R} & - \\omega & - \\frac{1}{C R} & 0 & \\frac{A}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & 0 & - \\frac{1}{C R} & \\omega & 0 & 0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 1 1 -A ⎤\n",
"⎢-ω ─── 0 0 0 ─── 0 ───⎥\n",
"⎢ C⋅R C⋅R C⋅R⎥\n",
"⎢ ⎥\n",
"⎢ 1 1 ⎥\n",
"⎢─── ω 0 0 ─── 0 0 0 ⎥\n",
"⎢C⋅R C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ 1 ⎥\n",
"⎢ 0 0 -ω 0 0 ─── 0 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ 1 ⎥\n",
"⎢ 0 0 0 ω ─── 0 0 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ -1 1 -1 A ⎥\n",
"⎢ 0 ─── 0 ─── -ω ─── 0 ───⎥\n",
"⎢ C⋅R C⋅R C⋅R C⋅R⎥\n",
"⎢ ⎥\n",
"⎢-1 1 -1 ⎥\n",
"⎢─── 0 ─── 0 ─── ω 0 0 ⎥\n",
"⎣C⋅R C⋅R C⋅R ⎦"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"M, syms_used = sysEqns3.orderedMatrix([res1, res2, res3])\n",
"display(M)"
]
},
{
"cell_type": "code",
"execution_count": 288,
"id": "66d5c346",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left[ a_{1}, \\ a_{2}, \\ a_{7}, \\ a_{8}, \\ a_{3}, \\ a_{4}, \\ a_{5}, \\ a_{6}\\right]$"
],
"text/plain": [
"[a₁, a₂, a₇, a₈, a₃, a₄, a₅, a₆]"
]
},
"execution_count": 288,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"syms_used"
]
},
{
"cell_type": "code",
"execution_count": 289,
"id": "9006121e",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\omega & \\frac{1}{C R} & 0 & 0 & 0 & \\frac{1}{C R} & 0 & - \\frac{A}{C R}\\\\\\frac{1}{C R} & \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & 0 & - \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & 0 & 0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & 0 & \\frac{1}{C R} & - \\omega & - \\frac{1}{C R} & 0 & \\frac{A}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & 0 & - \\frac{1}{C R} & \\omega & 0 & 0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 1 1 -A ⎤\n",
"⎢-ω ─── 0 0 0 ─── 0 ───⎥\n",
"⎢ C⋅R C⋅R C⋅R⎥\n",
"⎢ ⎥\n",
"⎢ 1 1 ⎥\n",
"⎢─── ω 0 0 ─── 0 0 0 ⎥\n",
"⎢C⋅R C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ 1 ⎥\n",
"⎢ 0 0 -ω 0 0 ─── 0 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ 1 ⎥\n",
"⎢ 0 0 0 ω ─── 0 0 0 ⎥\n",
"⎢ C⋅R ⎥\n",
"⎢ ⎥\n",
"⎢ -1 1 -1 A ⎥\n",
"⎢ 0 ─── 0 ─── -ω ─── 0 ───⎥\n",
"⎢ C⋅R C⋅R C⋅R C⋅R⎥\n",
"⎢ ⎥\n",
"⎢-1 1 -1 ⎥\n",
"⎢─── 0 ─── 0 ─── ω 0 0 ⎥\n",
"⎣C⋅R C⋅R C⋅R ⎦"
]
},
"execution_count": 289,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M"
]
},
{
"cell_type": "code",
"execution_count": 290,
"id": "2a72d91f",
"metadata": {},
"outputs": [],
"source": [
"\n",
"\n",
"#M_1 = M[:6,:6]**-1; M_1"
]
},
{
"cell_type": "code",
"execution_count": 291,
"id": "7eca5f0f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left( 6, \\ 8\\right)$"
],
"text/plain": [
"(6, 8)"
]
},
"execution_count": 291,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M.shape\n"
]
},
{
"cell_type": "code",
"execution_count": 292,
"id": "20d74c31",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}C R \\omega & -1 & 0 & 0 & 0 & -1 & 0 & A\\\\-1 & - C R \\omega & 0 & 0 & -1 & 0 & 0 & 0\\\\0 & 0 & - C R \\omega & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & C R \\omega & 1 & 0 & 0 & 0\\\\0 & -1 & 0 & 1 & - C R \\omega & -1 & 0 & A\\\\-1 & 0 & 1 & 0 & -1 & C R \\omega & 0 & 0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡C⋅R⋅ω -1 0 0 0 -1 0 A⎤\n",
"⎢ ⎥\n",
"⎢ -1 -C⋅R⋅ω 0 0 -1 0 0 0⎥\n",
"⎢ ⎥\n",
"⎢ 0 0 -C⋅R⋅ω 0 0 1 0 0⎥\n",
"⎢ ⎥\n",
"⎢ 0 0 0 C⋅R⋅ω 1 0 0 0⎥\n",
"⎢ ⎥\n",
"⎢ 0 -1 0 1 -C⋅R⋅ω -1 0 A⎥\n",
"⎢ ⎥\n",
"⎣ -1 0 1 0 -1 C⋅R⋅ω 0 0⎦"
]
},
"execution_count": 292,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Use the method row_op on the matrix to multiply the whole matrix through by a prefactor\n",
"\n",
"# I also did a bit of fiddling with the signs of the first two rows of the matrix by also swapping\n",
"# it's signs on the basis that if I multiply any equation through by a constant it shouldn't matter. The\n",
"# same principle as for the rest of the rows really.\n",
"#\n",
"M2 = M.copy()\n",
"for ii in range(6):\n",
" if ii < 2:\n",
" M2.row_op(ii, lambda e, col: -e*R*C)\n",
" else:\n",
" M2.row_op(ii, lambda e, col: e*R*C)\n",
"\n",
"M2"
]
},
{
"cell_type": "code",
"execution_count": 293,
"id": "dc5fc471",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}C R \\omega & -1 & 0 & 0 & 0 & -1\\\\-1 & - C R \\omega & 0 & 0 & -1 & 0\\\\0 & 0 & - C R \\omega & 0 & 0 & 1\\\\0 & 0 & 0 & C R \\omega & 1 & 0\\\\0 & -1 & 0 & 1 & - C R \\omega & -1\\\\-1 & 0 & 1 & 0 & -1 & C R \\omega\\end{matrix}\\right]$"
],
"text/plain": [
"⎡C⋅R⋅ω -1 0 0 0 -1 ⎤\n",
"⎢ ⎥\n",
"⎢ -1 -C⋅R⋅ω 0 0 -1 0 ⎥\n",
"⎢ ⎥\n",
"⎢ 0 0 -C⋅R⋅ω 0 0 1 ⎥\n",
"⎢ ⎥\n",
"⎢ 0 0 0 C⋅R⋅ω 1 0 ⎥\n",
"⎢ ⎥\n",
"⎢ 0 -1 0 1 -C⋅R⋅ω -1 ⎥\n",
"⎢ ⎥\n",
"⎣ -1 0 1 0 -1 C⋅R⋅ω⎦"
]
},
"execution_count": 293,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M3 = M2[:6,:6]\n",
"M3"
]
},
{
"cell_type": "code",
"execution_count": 294,
"id": "1b70eefa",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{C^{5} R^{5} \\omega^{5} + 2 C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - 2 C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{5} R^{5} \\omega^{5} + C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{5} R^{5} \\omega^{5} + C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ 5 5 5 3 3 3 4 4 4 2 2 2 ↪\n",
"⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω - C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω - 1 ↪\n",
"⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"⎢ ↪\n",
"⎢ 4 4 4 2 2 2 5 5 5 3 3 3 ↪\n",
"⎢ - C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω - 1 - C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω ↪\n",
"⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"⎢ ↪\n",
"⎢ 3 3 3 ↪\n",
"⎢ C ⋅R ⋅ω + C⋅R⋅ω -1 ↪\n",
"⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"⎢ ↪\n",
"⎢ 3 3 3 ↪\n",
"⎢ -1 - C ⋅R ⋅ω - C⋅R⋅ω ↪\n",
"⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"⎢ ↪\n",
"⎢ 4 4 4 2 2 2 ↪\n",
"⎢ C⋅R⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω ↪\n",
"⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"⎢ ↪\n",
"⎢ 4 4 4 2 2 2 ↪\n",
"⎢ C ⋅R ⋅ω + C ⋅R ⋅ω -C⋅R⋅ω ↪\n",
"⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"⎣C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"\n",
"↪ 3 3 3 ↪\n",
"↪ C ⋅R ⋅ω + C⋅R⋅ω -1 ↪\n",
"↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"↪ ↪\n",
"↪ 3 3 3 ↪\n",
"↪ -1 - C ⋅R ⋅ω - C⋅R⋅ω ↪\n",
"↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"↪ ↪\n",
"↪ 5 5 5 3 3 3 2 2 2 ↪\n",
"↪ - C ⋅R ⋅ω - C ⋅R ⋅ω C ⋅R ⋅ω ↪\n",
"↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"↪ ↪\n",
"↪ 2 2 2 5 5 5 3 3 3 ↪\n",
"↪ C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω ↪\n",
"↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"↪ ↪\n",
"↪ 3 3 3 4 4 4 2 2 2 ↪\n",
"↪ -C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ↪\n",
"↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"↪ ↪\n",
"↪ 4 4 4 2 2 2 3 3 3 ↪\n",
"↪ C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω ↪\n",
"↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n",
"\n",
"↪ 4 4 4 2 2 2 ⎤\n",
"↪ C⋅R⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω ⎥\n",
"↪ ─────────────────────────────────── ────────────────────────────────────⎥\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n",
"↪ ⎥\n",
"↪ 4 4 4 2 2 2 ⎥\n",
"↪ C ⋅R ⋅ω + C ⋅R ⋅ω -C⋅R⋅ω ⎥\n",
"↪ ─────────────────────────────────── ────────────────────────────────────⎥\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n",
"↪ ⎥\n",
"↪ 3 3 3 4 4 4 2 2 2 ⎥\n",
"↪ -C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n",
"↪ ─────────────────────────────────── ────────────────────────────────────⎥\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n",
"↪ ⎥\n",
"↪ 4 4 4 2 2 2 3 3 3 ⎥\n",
"↪ C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω ⎥\n",
"↪ ─────────────────────────────────── ────────────────────────────────────⎥\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n",
"↪ ⎥\n",
"↪ 5 5 5 3 3 3 4 4 4 ⎥\n",
"↪ - C ⋅R ⋅ω - C ⋅R ⋅ω - C⋅R⋅ω -C ⋅R ⋅ω ⎥\n",
"↪ ─────────────────────────────────── ────────────────────────────────────⎥\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n",
"↪ ⎥\n",
"↪ 4 4 4 5 5 5 3 3 3 ⎥\n",
"↪ -C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω + C⋅R⋅ω ⎥\n",
"↪ ─────────────────────────────────── ────────────────────────────────────⎥\n",
"↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎦"
]
},
"execution_count": 294,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M3**-1"
]
},
{
"cell_type": "code",
"execution_count": 295,
"id": "2e9c93a3",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}A\\\\0\\\\0\\\\0\\\\A\\\\0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡A⎤\n",
"⎢ ⎥\n",
"⎢0⎥\n",
"⎢ ⎥\n",
"⎢0⎥\n",
"⎢ ⎥\n",
"⎢0⎥\n",
"⎢ ⎥\n",
"⎢A⎥\n",
"⎢ ⎥\n",
"⎣0⎦"
]
},
"execution_count": 295,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"col = M2[:,7]\n",
"col"
]
},
{
"cell_type": "code",
"execution_count": 296,
"id": "ad3c7583",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{5} R^{5} \\omega^{5} + 2 C^{3} R^{3} \\omega^{3}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} - \\frac{A}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3} - C R \\omega\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
],
"text/plain": [
"⎡ ⎛ 5 5 5 3 3 3⎞ ⎤\n",
"⎢ A⋅C⋅R⋅ω A⋅⎝C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω ⎠ ⎥\n",
"⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ ⎛ 4 4 4 2 2 2⎞ ⎛ 4 4 4 2 2 2 ⎞ ⎥\n",
"⎢ A⋅⎝C ⋅R ⋅ω + C ⋅R ⋅ω ⎠ A⋅⎝- C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω - 1⎠ ⎥\n",
"⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ 3 3 3 ⎛ 3 3 3 ⎞ ⎥\n",
"⎢ A⋅C ⋅R ⋅ω A⋅⎝C ⋅R ⋅ω + C⋅R⋅ω⎠ ⎥\n",
"⎢- ──────────────────────────────────── + ────────────────────────────────────⎥\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n",
"⎢ ⎥\n",
"⎢ ⎛ 4 4 4 2 2 2 ⎞ ⎥\n",
"⎢ A⋅⎝C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎠ A ⎥\n",
"⎢ ──────────────────────────────────── - ──────────────────────────────────── ⎥\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ ⎛ 5 5 5 3 3 3 ⎞ ⎥\n",
"⎢ A⋅C⋅R⋅ω A⋅⎝- C ⋅R ⋅ω - C ⋅R ⋅ω - C⋅R⋅ω⎠ ⎥\n",
"⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n",
"⎢ ⎥\n",
"⎢ 4 4 4 ⎛ 4 4 4 2 2 2⎞ ⎥\n",
"⎢ A⋅C ⋅R ⋅ω A⋅⎝C ⋅R ⋅ω + C ⋅R ⋅ω ⎠ ⎥\n",
"⎢- ──────────────────────────────────── + ────────────────────────────────────⎥\n",
"⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n",
"⎣ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎦"
]
},
"execution_count": 296,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res = M3**-1*col\n",
"res"
]
},
{
"cell_type": "code",
"execution_count": 297,
"id": "599f7599",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega \\left(C^{2} R^{2} \\omega^{2} \\left(C^{2} R^{2} \\omega^{2} + 2\\right) + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ⎛ 2 2 2 ⎛ 2 2 2 ⎞ ⎞\n",
"A⋅C⋅R⋅ω⋅⎝C ⋅R ⋅ω ⋅⎝C ⋅R ⋅ω + 2⎠ + 1⎠\n",
"─────────────────────────────────────\n",
" 6 6 6 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 "
]
},
"execution_count": 297,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(res[0])"
]
},
{
"cell_type": "code",
"execution_count": 298,
"id": "8830a26f",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAOkAAAAjCAYAAABxRC0xAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAIWElEQVR4nO2dfYwdVRnGf4ut2FoM+AHWb6KlWmpodwlCpXzFFiUkIBEFY2NN1DQ1CtGiaTE8vtUgIqWtBGMjmo3wh6YkEEpapOIHFqi0UIoVGlJWUgOiQqFlUcHS9Y/3DJ3e3nvnzJ37MeXOL9nsnZkzzzn73nPmnDlz5tmBsbExKnqLmU0GjpH0kJm9HXgAOE7Si93U6IRWRXEGqkbaGDM7CtgOzJL0eBfz3QqcK+lvvdTohFbOfFcDGyUt62a+ZWNcrwvQa8zsQ8AWYLukGTWHlwBrizZQM5sBXAacDrwV+DuwGbha0qaatEPA62obhJndBZwVNvcCT4Tzf1onv7oaLZa9bVo1uqcBi4Ah4B3AFyQN1yRbCvzBzG6QtLud+R9KHNbrApSAHwHXAtPM7PXJTjObCHwR+FkRcTObjzfIl4DPAMcBnw/bC2rSvhn4BfDlOlKD+EVjMvAB4JfAKjObmUMjb9nbplWHScA24BLgP/USSPozMAJ8rgP5HzL0dU9qZhfgF6qrgcXANOChcPgcYAy4p4D+KcANwGWSlqcO7QTuDo0gSXs4cCtwlaR7a3TeDxwJ3CHp6bBvFfBt4Hh8JNBUIxxfDswGTpK0r+bYZmCDpEtjtIoiaS2wNuQ13CTpbcDFwPXtLsOhQt/2pGY2AbgGWCTpeeApIN0rzQYekFTkpn0Z8KeaBvoqknaFsgwAw8BvJd1YJ+kQsAfYGtJPDmXfBzwYo2FmU4Gv4heMfbXHgUcJf39EebrJ/cBJ4fvqS/q5J/0W3nNsCdt/AWakjr8Xb7gtYWZTgFPwXiCLj+JD4YfN7Pywb14Y7oE30knAHjM7DJgAvAx8Q9IjkRqLgK2SftegDLuAj0RqdZOngPH4fWvXJu/KRF82UjN7H/A14ITU7m3AiantCcA/6pz7PeDyjCzOBI4JnzdnlUfSBpqPagbxYfMPgTcBVwI7JK2I0QgN+1P4sD7ZtxwYkXRd2HUE8GJkedLaUfGQ9PsYvTok96tVT9pnLAeOAv5qZsm+AeAFMxsIQ9xnQppaVgA3ZejvxHsigNHCpfVGepOkHQBmtgAYMbNVkb3bsfg9bTrtp4ErUtsnAI+QnxXExaNVkvv2fxXQOKTpu0ZqZnPxRyFD+JAx4YPAarxCj+CTMfNrz5f0DN6As/LZFj6eDvyqzvGJkv4doXMsXlFfbWCSnjCzLcA84JtZGuy/2IwGzTPw4ePLYXsKPtT/foTWAcTGowDTgSclHTSq6Rf6qpGa2XhgJbBM0oM1x5Kr/Uy8kf4a+IGZvUXSs3nzkrTJzNYB14VJj3vw2eJB4EuAARsipIbwCaLaXm49cAFxjXRn0PismT2PP3ZaA5wbFir8GHgYuCVCqy2Y2ST8URL40Po94XnyLknpnnc2/l30Lf02u3sJ8Da8kh6ApD3A04TJozCMvB+4qEB+n8RnYb+OP9rZhE9Y3UfEvWpgCHhc0n9r9q8HppjZ8VkCkv6JP2K6ELgTWIVPJM0ENgLPAudIeiWyTO3gRHy0sgW/37TweWmSwMzegMfwoAUb/US1LLAJZvZxvOed1uUKXAGY2VeA8yTN7XVZekm/9aS5kHQH/hD9Xb0uS5/yP/zZbl9T9aQVFSWn6kkrKkpO1UgrKkpO1UgrKkrOOAAzq25MKypKSu6Jo7AC5uf42tRXgJPz2mq0Q6MTWt0ivKv6KLBa0qJeaXRCq0AZ3g3cCByNv9T+XUmru63RCa2itDLcHQaukDQNX/L2Uo80OqHVLS7HFxH0WqMTWq2yF7g0fI9zgRVm9sYeaHRCqxC5etKwumWlpI+1mmE7NDqh1S3COtmr8GV501vpudqh0QmtdlL5PO3noLW7zfx4gHcCo2a2Jny+WdKVNednefFMydLIQTu16mJmi/E1slPxXnojsFjStjppZ5DtZXRNSDOrzvmxPkYNNVqgnVoNKerzlMfjqZFGgbL30ufpwOFuhB/POHzB80L8heY5ZjanRjPLiydGI5aWtcxs2My+E5H0DHwB+iy8kuwFfpO2Pgl688nwMjKz84DHJD3WIK9MH6MIjWha1coRuyT9fIr7PEV5PGVo5CavVs7YZPo8QaonjfTjmQpsTq4oZrYWX5C+PmzHePE82Uwj7Iv14snUKoqks2vynwfsxt0L1oR9sV5GJwMXmdmF+Bc03sz2SFoa62PUTCNVxtj4ZWoVJUdsGvoq5YhNlldUtMdTllY7iPV5Sg93M/14zGwTcLS5H+1u4DT8jYqETC8e/E2Qhhq234tnTpYXT5ZWhzgCH4E8l9oX5WUkaTH+NkrSu0xPNYiY2GVp5IpfllabaIfPU1RsmmnkrFel8nlKnpNG+fFI2mtmS4C7cSeDOyXdnkqS6cUToRHtxROh1QlW4q+d3Qe5vYyaEeNjFEMeL6OOkjM2zXyVYmPTTCNvXErj85T0pIPhd4wfzzpgXYPDmV48zTQspxdPRHnS2kvwe5qEw4ExM0vPZn5C0h+baFwLnAqcmnp1LTp2aepMEETFrplGK/FrUp60bquxy1Ovmvkqxdaruhot1qson6d21KsskkJMDL+L+vEMAvdK2iF3PlgALDSzD0ee38iLJ20z0qoXz0/w+9Xk57Y6+xpWpvClXgycJWkkdagssYPOxa/V2JUlNqWtVzEkPWlhPx4rvxfPLnxIk5T3BdyqY0fWuWa2Eh/6nClpe83hssQOOhS/ArErS2xKWa9iGRcyaocfz2vVi+d6vDKcDzxn/l/GAEYljZYodlCy+JUoNqWKS4JF+jylx9xF/Xheq148C/H7lbvwB/DJT/qeo+exg9LGr+exKWlcIMLnCSpnhoqK0lO9T1pRUXKqRlpRUXL+D6u74fRlvRw0AAAAAElFTkSuQmCC",
"text/latex": [
"$\\displaystyle \\frac{A \\left(- C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" ⎛ 2 2 2 ⎞ \n",
" A⋅⎝- C ⋅R ⋅ω - 1⎠ \n",
"────────────────────────────────────\n",
" 6 6 6 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1"
]
},
"execution_count": 298,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(res[1])"
]
},
{
"cell_type": "code",
"execution_count": 299,
"id": "3bd9f332",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" A⋅C⋅R⋅ω \n",
"────────────────────────────────────\n",
" 6 6 6 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1"
]
},
"execution_count": 299,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(res[2])"
]
},
{
"cell_type": "code",
"execution_count": 300,
"id": "5de8a6c6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\left(C^{2} R^{2} \\omega^{2} + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 2 2 ⎛ 2 2 2 ⎞ \n",
" A⋅C ⋅R ⋅ω ⋅⎝C ⋅R ⋅ω + 1⎠ \n",
"────────────────────────────────────\n",
" 6 6 6 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1"
]
},
"execution_count": 300,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(res[3])"
]
},
{
"cell_type": "code",
"execution_count": 301,
"id": "d393000e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\frac{A C^{3} R^{3} \\omega^{3} \\left(- C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 3 3 3 ⎛ 2 2 2 ⎞ \n",
" A⋅C ⋅R ⋅ω ⋅⎝- C ⋅R ⋅ω - 1⎠ \n",
"────────────────────────────────────\n",
" 6 6 6 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1"
]
},
"execution_count": 301,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(res[4])"
]
},
{
"cell_type": "code",
"execution_count": 302,
"id": "2a546639",
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
],
"text/plain": [
" 2 2 2 \n",
" A⋅C ⋅R ⋅ω \n",
"────────────────────────────────────\n",
" 6 6 6 4 4 4 2 2 2 \n",
"C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1"
]
},
"execution_count": 302,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simplify(res[5])"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}