{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "
\n", " 数値計算による常微分方程式解法(python版)\n", "
\n", "\n", "
\n", " ordinary differential equation(ODE)\n", "
\n", "\n", "
\n", " cc by Shigeto R. Nishitani\n", "
\n", "\n", "\n", "* /Users/bob/Desktop/maple_ode/python_ode.ipynb\n", "* origin\tgit@github.com:daddygongon/maple_ode.git (fetch)" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true, "slideshow": { "slide_type": "slide" }, "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Euler法による落下運動\n", "\n", "## 重力場中の運動\n", "重力場中のボールの落下を考えて,1軸で考えた運動方程式を立てます.\n", "\n", "$$\n", "\\begin{aligned}\n", "v &= \\frac{dx}{dt} \\\\\n", "a &= \\frac{d^2 x}{dt^2}\n", "\\end{aligned}\n", "$$\n", "質量を$m$, 重力加速度を$g$として,働く力が$F=-mg$であるとすると,ニュートンの運動方程式$F=ma$は,\n", "\n", "$$ \n", "-mg = m \\frac{d^2 x}{dt^2}\n", "$$\n", "となります.\n", "\n", "\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Euler法\n", "1次の微分方程式の一般形は\n", "\n", "$$\n", "\\frac{dx}{dt}=f(x,t)\n", "$$\n", "と書けます.この微分方程式を簡単な近似から求めるオイラー法を示します.\n", "$x(t+\\delta t)$をテイラー級数展開すると,\n", "\n", "$$\n", "x(t+\\delta t) \\simeq x(t) + \\frac{dx}{dt} \\delta t\n", "$$\n", "となります.これらを代入すると,計算アルゴリズムはつぎのようになります,\n", "\n", "$$\n", "x_{i+1} = x_i + f_i\\,\\delta t\n", "$$\n", "ここで,$f_i$は点($x_i, t_i$)における関数の値です.このアルゴリズムを適用して,$t+\\delta t$の座標$x_{i+1}$を一つ前の時間の座標$x_i$から導くことができます.これを重力場中の運動方程式に適用します.\n", "\n", "## 重力場中の運動をEuler法で解いたら\n", "Euler法は一階の微分方程式に対する定式化をしています.ところが,重力場中の運動は2階の微分方程式です.このようなときには媒介変数を導入して1次連立方程式に置き直します.\n", "\n", "媒介変数として速度$v$を使って,2階の運動方程式\n", "$$\n", "\\frac{d^2x}{dt^2} = -g \n", "$$\n", "が,1階の連立方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv}{dt} & = -g \\\\\n", "\\frac{dx}{dt} & = v \n", "\\end{aligned}\n", "$$\n", "で置き換えられると考えることに相当します.アルゴリズムにすると,\n", "\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} &= v_i - g\\, dt \\\\\n", "x_{i+1} &= x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "なる連立方程式を解くことに置き換わります.これをpythonで関数にして,さらに計算結果を表示させてみます." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def euler(x0, v0):\n", " v1 = v0 - g * dt\n", " x1 = x0 + v0 * dt\n", " return x1, v1" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Eulerは$x_i$, $v_i$を受け取って,先ほど導いた簡単な計算によって,$v_{i+1}$, $x_{i+1}$を順次計算して返します.結果は," ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def my_plot(xx, vv, tt):\n", " plt.plot(tt, xx, color = 'b', linestyle='--',label=\"height\")\n", " plt.plot(tt, vv, color = 'r', label=\"velocity\")\n", " plt.legend()\n", " plt.xlabel('time')\n", " plt.ylabel('height and velocity')\n", " plt.grid()\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#g, dt =9.8, 0.01\n", "g, dt =9.8, 0.1\n", "tt,xx,vv=[0.0],[10.0],[0.0] #for compare rain_drop\n", "#tt,xx,vv=[0.0],[0.0],[9.8]\n", "#tt,xx,vv=[10.0],[0.0],[0.0]\n", "\n", "\n", "t = 0.0\n", "\n", "for i in range(0,250): #250 for compare rain_drop\n", " t += dt\n", " x, v = euler(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "# print(xx)\n", "# print(vv)\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "位置(height:$x$)と速度($v$)の時間($t$)変化を表示させています.\n", "\n", "\n", "時間とともに位置は放物線状に変化し,速度は一定の傾きで増加していく,等加速度運動を再現しています.Euler法ではこのように非常に簡単なcodeによって微分方程式で表される現象をシミュレートできることがわかるでしょう." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## 空気抵抗がある水滴の落下\n", "ballの落下ではわかりにくいですが,より小さな質量の水滴では,速度に比例する空気抵抗が効いてきます.この様子を見ましょう.微分方程式には,\n", "\n", "$$\n", "F_x = - C v_x\n", "$$\n", "\n", "項が付与されます.そうすると運動方程式は\n", "\n", "$$\n", "m \\frac{dv_x}{dt} = - C v_x - mg\n", "$$\n", "となります.これにともなったv_xの時間変化に対して,今までは単純に重力加速していたのが,v_xに比例する空気抵抗を記述する項が付与されます.この変化をEuler2に入れ込むと少しの修正ですが,結果は劇的に変化します.\n", "\n", "\n", "![image.png](attachment:image.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "その前に,ここで示した修正がどれほど普通の微分方程式の解法としてややこしいかを少し示しておきます.\n", "$$\n", "m \\frac{dv_x}{dt} = - C v_x - mg\n", "$$\n", "を整理すると,\n", "$$\n", "\\frac{dv_x}{dt} = - \\frac{C}{m} v_x - g\n", "$$\n", "です.右辺を$v_x$の係数でくくって,変形していくと,\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv_x}{dt} & = - \\frac{C}{m}\\left(v_x - \\frac{m}{C}g\\right) \\\\\n", "\\frac{1}{\\left(v_x - \\frac{m}{C}g\\right)}dv_x & = - \\frac{C}{m}dt\n", "\\end{aligned}\n", "$$\n", "これで変数分離されているので積分をとって,\n", "公式$\\int \\frac{1}{x+a} dx = \\log |x+a| + C_1$を使うと\n", "$$\n", "\\log \\left|v_x - \\frac{m}{C}g \\right| = - \\frac{C}{m} t + C_1\n", "$$\n", "なんですが,両辺の指数をとって「適当」に変形すると\n", "$$\n", "\\begin{aligned}\n", "\\left| v_x - \\frac{m}{C}g\\right| & = \\exp(- \\frac{C}{m}t + C_1 ) \\\\\n", "v_x &= \\frac{gm}{C} + \\exp(- \\frac{C}{m}t + C_1 )\n", "\\end{aligned}\n", "$$\n", "となります.最後の絶対値の変形は怪しいんであまり信頼しないでね.\n", "\n", "これをpythonが用意している数式処理libraryのsympyを使うと次の通りとなります." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle v{\\left(t \\right)} = \\frac{- g m + e^{cc \\left(C_{1} - \\frac{t}{m}\\right)}}{cc}$" ], "text/plain": [ "Eq(v(t), (-g*m + exp(cc*(C1 - t/m)))/cc)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "v, f = symbols('v f', cls=Function)\n", "cc, t, m, x, g= symbols('cc t m x g')\n", "# dsolve(f(x).diff(x, x) + f(x), f(x))\n", "dsolve(v(t).diff(t)+cc/m*v(t)+g,v(t))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def euler2(x0, v0):\n", " v1 = v0 + (-cc * v0- g) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "g, dt, cc=9.8, 0.01, 1.0\n", "# tt,xx,vv=[0.0],[0.0],[-10]\n", "tt,xx,vv=[0.0],[10.0],[0.0]\n", "t = 0.0\n", "for i in range(0,500):\n", " t += dt\n", " x, v = euler2(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ちょっと気をつけたいのは,$-Cv$の向きです.vは例えば自由落下の時には下向きのベクトルなんで,抵抗は反対向き,すなわち上むき,数値的には正,になります." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# 高精度計算\n", "\n", "## バネの運動\n", "今度はバネの運動です.空気抵抗との違いはほんの少しで,\n", "$$\n", "F_x = -k x\n", "$$\n", "と今度は,位置xに力が比例することです.そうすると運動方程式は,\n", "\n", "$$\n", "m \\frac{dv_x}{dt} = - k x\n", "$$\n", "となります.\n", "\n", "連立方程式は\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv}{dt} & = - \\frac{k}{m}x \\\\\n", "\\frac{dx}{dt} & = v\n", "\\end{aligned}\n", "$$\n", "となるんで,アルゴリズムに置き換えると,\n", "\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} & = v_i - \\frac{k}{m} x_i\\, dt \\\\\n", "x_{i+1} & = x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "なる連立方程式を解くことに置き換わります.これをpythonで関数にして,さらに計算結果を表示させてみます.\n", "\n", "\n", "![image.png](attachment:image.png)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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okO9nZXw5OfaWhHrT2bWLk7yaNrXHQG6/nRMIK1Zk4cJJH4k9e/hz8cW8AdapYz93YMECTnxdsABo25Zp2dWcT50CfvsNuPBCXgNONsOICPYbKfc1bhzPE7uNpRTfDOBv9rOjOasj+4g41N7ufjFvHs/zZ59lWrm5rJGUL2+PXijg+kAkodZAnJoX1q1js0dqqm/C2nUkqm3dANCpE3D33c5oVazIDOTnn+1X5PV4WI1X7m/UKM5xsAu1TTkhgRmd3XyXtDRfWZUuXdifFR1tL45abUJR/re7USQmMtMORdjt1Kks6RcXM70DB4DHHrNHKzWV/QGKJL5ypf1y51u2sGak+LOcQAieC8q8iItjjcROEENBAQthyjts25bXkV1GuXGjT0NWyqvYZWzqOZaaygLG2LH2aIUKLgORRKtWrJZWqsQSZkYGmxjsYPVqDhnMzWXpqVIl+8xIYTxKWHFBgX3Tjo+B8O46diw7rO0gM5OlJfXm6sTWrbYpK//bNcl07swmBYA1v6efBipVshc6pdaynDqr58/nTHuAn11iov3eJ+npbBoKhZSqTmRzCnWgAMCVGFrY7Oizb5+v9L2app0QV2UuKTS6dQM++8x+LauuXbkBF8AbPuCMgWjnmOtE/5ehVy/+KHDiIFM7SwGWUJxI04Bvo65Uyf7kionh5MFatdho7iQssriYfTNK8cPKlVnCs2NTLinhxacsHkWis/vM1BJdcTH7LnJy7Iman3ziC+d2qoGMG8dRXTfdxNJ1SYl9WmqNDeDGTeHhXE9MFmrtGwA+/pj9W19/LU9LO/fz8uzXldu9m6MPr7ySgwbUz182Tysx0dcfRoGS3CurhRQV+UeaKQzE7nzNzvbN+chIFgycVJsIBVwNRBLZ2f7VZJ991n6THmURKZOiRg37qnJiIvtOQhEL37gxO6cbN84ppWV3A1O6ECoOTSebq7JYlE2nRQuugWSHiStJccq1e/ZwRNCKFfa81c2bs7kDcM7YtJt+bKx9qVW96QBsNrVb6DEjwxf2DHBCohLuKgs94amoyF5OlfJslA3aiaQfHs51w5RNf+1atg7MmydPSztfK1dmn0idOsbXmCE21j+YomJFX8XgMwVXA5HEsGEsKSkJVF99xdE2dspgZGbypFBC8/7+2/64rrmGPwri4py3z1SgJMY5CZlV4MQOHB/P0qAiEbZpw1FZdlBYyFqHMh6fk9/ekhg/ns2bHTvyJrRtm/0w6sxM//BMJ5ppTo5vQwV4M7NbHr5NG3aiK6hY0T5j02MgAN+nbMSZsokqWsPFF3PHxIYN5ce1Zw/ngdx+O1C3ro+mnftUR9Mp/zspfaTN1I+JOfMMxNVAJKE2ewDOpMNQx4ircemlQL9+9q794guuBHvqVCQA3lyJ7NmU58/nDHmlLWvnzhxxYzd+PSyM1XeAx5SXZ09q1W46ygaWn29PBRwxwr9d73nn+c8TGSjlLxQ4mWMvvcQ2fAVONp2bbvJ3miu07GRW33wza0La52+HUWrfZZUqHN2lZpxWsW0bh8IrFaSdMBAtkww1HnnE/hoPFVwGIgm1IwvgSWpXOvzyS67tr+C997ivsx289BJHXikYPtznvJNFVhZvzNHRHMB+xx1c/sJOk55TpzjyRzHNKQlQdvIatm/niJgdO/j33buZ0dnpsx4ZyQljSjOp8uXZ32AnD6S4mJmYesMaN85+1WGtYHHDDWzftwOlfIaCUJo9Klb0MXFZVK/O1Y+VSLOmTbkagyIcyEC5H+X5Z2SwFmGnEZqWGTkxh9WuzZqpOuqwSROe/7I4eRK47jrOJVHwwAMuA/nXITvbf3E7UePDwvyddWvX2rO1Ahxfru1Noq7bJQPlfqKi2FYUH8/qvB3/jHZBFhSwNmLHP7NnD2tHSsSZE6dkbCyXhlAWtxA8RjsMRHuPAPDRR8CECfLjArhPhjrq7bHH2NdjB/PmcckdBfXrs6PZDq65hhP+FFSvzpqWndyj337z9x12784Vde3kBz34IEcyKoLdiRPcUXC5jRbr2nfpRANJTORxqH0eRUX2ohDT0jg5Vb3G09Kc9yNyCpeBSCInx3+jqFjRfjHFN99kH4oCJ7burCx/CfjTT3nDt5NXkp3Nkr3CMPbs4RwJO13elIWnPLMdO9j5bafaqTbE0onZIy+PNSN1F7x33wUuuki+AqX2HpWf7QoW1av7h40S2e/Wd//9HCGm4IknOH/DDjIz/X1gt9zCJh87Fak/+4wDUEIBIXwaJOBs09cykIgIZuDnny9PKyWFzXS5ub5jdi0WekLKLbf4+z3PBFwGIolRo1iVVDBvnv2olgkTOKtXgRMGkp3tz0CionjjsWOu0NLau5cXu53+76E0CSjPRmEcFSrwhmbnma1axb4Z9WY6YgTQurW8aqS3uO1qpvn5bI5Uaw333We/tlZ2tv+4nEArPDlBXp5/bsqWLazZ2zH7TZ7MeSAKlDlmZ+5rzWEAlxDp3VuelpJpr3Z+250XenPMdaL/C/HYY1yoUIGTqCStrVvpS2FH2tRu+spEszPBLryQK8oqcLIgmzbljGPFtu2EgSi29goV+H8h7C9IbegnwAzy0CH5jLt69bj+kloatDuuzEx24qoj8mJiQheFNWcOJ7fZKfWvZSD//MMRT+vXy9PSMpDoaL5HO4Eaixaxz0OBEw3k4Yd9HQkV5OTYG5cyX9W0QjlfnZjPQwU3jFcCHg8nGSUm+jax6dN5An/xhTw9JYxXQfXqbJ/Oy5MvLHfBBf7XOFlEN93E/yvNgpxs+oMG+decckKLiJ+7OgHxqafsFabTkzRvvRXIy2uKm2+WoxUVFZhFbXdxK5uO+h5jY1moKCqSczKXlLD5RL3pp6ezdpORwTk6MtAykLw8Dpe1U+48L8+flhNzpFbLCg/n52dH4ImICIye69qVfT2yIbh6DKRPH3vjCg/nsGRtAM+Z1kBcBiKBU6fYmfzRR74+FOvWcSbu55/L1y7SLsg77/SX/GXwxhv+vzvRGvLzOWFMSysU0k50NGttdmg9+GCgM/nJJ+2NQ89vUbEicOqUvBN99252cA4Z4sv9+Ogje+MykloBHrNM+LNie9dKrYC9eXHrrf79wZ3OMW1SHGDfP6AN2V21yl4ezpQpnD/13HO+Y3ZNRUpwgVoYeOgheToAF9fUmpAVP5vdYqKhgMtAJGBk61bCOGW0huJiliYVTSbUqF+fN1s71WAvuYQlQsWu7MQcNmwYT/wVK/h3Ibi2lpK17RRpafzsZTcLPQ0kJgbIz5e3Sa5bx76xSy7xjcNuDoiy6agZiFo6l2Eg5ctzvTX1HHCimb72mv/vTgSLH37w3/Sio/l3tcPZKvR8M3bnl+LTVDMQp9qktg5ZKBJyATaZVq9+ZhmI6wORgJEdUv2dVURE8AR75hnfsbVrOQHQToXSevX8u7A1aMBZ2uedJ09L609JSGCbuZ3qvqmpgVFqd9zBGduyGDeOW4yqMWAA50nI4qKLgPff9zchVqwYujDepUs54knJmrcKvU2nQwc21ck6sCMi+DnXrOk7ZlcYUMqHq8PCnTCQ+vV5zioQgueXnbbCRIHJetOn2+uJo8eM7DKQG24AZszw1+Yff9xeMcrvv+e9QZ1z060bW0JCwYzswmUgEjDSQIDQFDXLyeHIDVmbstJnQL1ZKQs+FA75sDA2N9hN8tIuyM2bOepGFqtWsalIjZgYe1Jr+/ZsTlD3xnDKQNTPbPVqjt6R3ai7dGE/hbpgZ4cOnBcim3yZksLJqgcP+o4lJfHGI6v5pqfzs/7wQ9+x2Fh+jnY2xE8/9fnY1Mf695en9fvvgfPinXeYniz05qvdkOymTYHrr/fXDsqVYyYgm5+1cyfvDWpmlJnJJZXshniHAi4DkYDeRhEXxxK67EtMSWHzjmLaAXyLWnZDzMtjtVgtTZ86xRPfTr8GLQMBgFdesVfHR88+feut9npSaCN3AH5mdhjIgQOBtcJuuQV46CH5AmJmgoXsxhMeznNKvVEUF7MmJzvHdu5kjU0pIwNwJYDlyzlxTwZ691ihAkdiDR0qRwtgjUrdHhfgTdVODw892HUw6zGQQYPsZY9v2AAsWeJ/rEIFFvTUBVmtIDubzXzqZN758zmAxE54fajgMhAJNGzIyWZKaXKATSipqfKmotRUrnh74IDvmF0Gomg/emG8dkMGtZv+55/bq7yql4dgd3GHkoG8+CKbBNTo2hXo2TNFmpZyL2qp3i4DWbeOmataC/3rL9Ycfv9djpaeydUu9BiIE+i9y9atORBBFsOHcy6IGna1hoKCwHvs25d7AMniww9ZSFRDuWfZOWtkWlO+O1NwGYgE6tXjOHG1Tdku9GzdygSRnVx6G0VUFEsrdmzdjz4auLnatQMPGMARJFpadrPHtZuOXROWHpM8dgxYty5eurLAI49wsphaOrTLQDZtYvOLOu/ArmChF2mWm8uRVLKd7IwYyBVXcFM0GSgSuPZdRkfbe5fffRfoN7Q7X//+O1Azyszkagyy4Hpy/sfsvksj05ry3ZmCy0AkcPIkl25Qq9kHDrCdU7bujlG4Zps28kULo6O5s55aC1JqO8lOLiHYXHXFFf7H7WoNr7/OGd5q2N30K1UKjCq7/nrO3JaF3oKcPRsYNaqddJJdxYr+DmHAvqSpNy+cMhCtYLF5M3DkiBwtIwayfbv85moUnWRHm1R6iGjHZVczBQJrvn30EednyZqd8vMD77FdOxY4ZJup1azJ/iY1FNp2ilmGCm4YrwQmTmRbaGqqr/5Pfj6HJA4YIGdX1ltElSvby+qtVQv45pvA43bUeMXerg0XtSvRlZQELsjy5e0tbr2+7NoOkVahp4HY1RpmzOACfiNH+o+roEA+8CCUDERv0w8PZ9qy91irFod1awsx2tmo9ZIlFVqyhQaNGNsbb9gTLEaO5HDsgQN9x9Qbtcz71NOYu3bljyz0WkqfDQzE1UAkoOdEt7u4lV7XobBPG0V0PPqorxOgVezZw7Hl06f7H7ejNRQVcZSTdvLfey/7VEKB9HSO6JINl9VjIHbf5ZQpwJgx/sfCw9kRLhufH0oGMnQoPxttxnmFCvKbTsOGnAfSoIH/cTvCQEICV3RQ+tE7GZfemgS4GKWdyr5ffcWBAdpxAfL3qde22eNhk5isNqOHunU5tN1O6HOo4DIQCeTk8IaojpCxO7kuu4xNYlq1tFcvtoHLYO5cloy0E//hh9kBKAM9uznAMfWrVsnRUha3Vgrr3Bm46io5WgBn6b/7rv+x774DWraUb5H70kuBWcF2JTq9QIGUFC6C+OefcrSUSCv1xlOxIvcuka0IGxfHrXYjNHYGO5t+Tg7fk8cTSEv2eSltY7Wm2n79OBJOBkoSqVZjXrGCTbHa8ZqhqIg/2ndpd1689x5/1Fi6lN+LrMl76FBez2rEx3NOVf36crRCCZeBSEBvo7DLQIywaZN8WF5eHpuetNJOerp8TolyH9r7jIiwV6pFj9bevRzRJRsLv3Ah2+/VsPv8+/QJDBQIZYRMbi5rJdrxBsPzz/Mmpk4OK1eOE067dJGjtWSJfkmVyy8PrN0VDOPHA1WrsqlOja5dOXpKBkeOcBSc0hhMwS23sNYsgwYNOPhBbXICgGXL+FnK9Cox0mbsMpD27f2bvAH25+uGDf4RmwBr3atW2WuzECq4DEQCejkNUVHsQJVNzPr5Z/abaCVnO45vI6fk4MH+peetQK+UBsBmGq0EFAxG2syUKcDVV8v3UQllVMuKFYE9plu1Al59daN0cUY9BuJEsNBqDAAnA2o372D48Uf/khwKvv5afqM2EgbefVe+L/2BA6wBagWlwkJ7zZb0YGfTN7rHjh2Bjz9mBiqDOXP8y/IDznK9tGuyoICLqE6aJEcrlHAZiARuuy3QvCQEb0SyHeO2b+feB1op3I5TUjlfy8RC6eBctYrtrTIwWpB2JX29qBa7C7J3b94U1EhMBLp3T/Vr5mQFeoKFXal1/HhOstOiQwd5p7De87ILozlmB3pFBgHWSmRrmq1fz0KSVtOzM8cKC9m8pH2XjRuzOVK2evF99/n3owd8z092XugJT8rvrhP9X4ILL2SpPhQIZSijES079ulmzTiCpW5d5+NKTGStRZtkaWfTV3pvh4KBGNHKywNWrkwM0EyCYe3aQOZql0kuWgRMnRp43O680GMgQ4bI+8aUCs3aiLqnn2YpWHZcgP67VPwQVnHkCPsAtXlFdhh4gwZsEdAmM+blcckQ2TbMes/fifCkZSBhYXzMZSD/EmzcyHkgWtxyS2A59WDIy2PtRVvBt0sX3sRl0K4dRzZppUM7DKRJEy6RrlXXK1RgP4tMqYl69djE0bx5IC1AbmwlJfxctEmcLVtyUlzDhtZpFRWxc1W7uNPTgaefbo1ffrFOC+D70WpZ4eEsydoppqiXIxBKBpKZyVFQoRhXRkZgSRgrtABjYUBmXoSSlhG2beP8LG3trmDQe/7x8cALL8hHTl1wgf6+YGeNhxJuHogERozgyJGFC/2P//WXfJ0iZUFqHdPacFAruPTSQIcwYC/aJi2NP0aJcXl51hMdle6KMTH+TmE7WkNEhL5DumZNLmUhAzONTf29VTzxBHfmu/pq/+N2su2NzE6hZCB2Np1rr9WP9rETemtkwlJL59rqukYwepfXXMPzWCYpd9Mmzqp/8UX/IAMnYbx6c0xdNdsq5s3TP243pypUcDUQCRgtSDuLu1IlrtYZCuTn6zukBwzg8E8ZjB/PyWLaFp4VK/JilIlqmTWL73P7dv/j3bszE9bmFNhBQQGXn5BxMIdaan33Xf+imE5gNsdkgysmTtSvX2aHgVx6qX4zJGUDk4mou/FG1lwaN/Y/bmejNmJGUVEs7WtNbmY4fJjzn7SBLXYEi6Ii1j713uXRo1zsNBT48kvgnntCQ8sOXAYiAbPFLbsgn3+eC+dp8cwz3KtCBg89BNSpE3j8kkvki8AZba533cVMRcbBbLS4q1XjUFIZ6fDIEWY8Cxb4Hz9xgs1+2nLeZoiLY+amLdcSGQmEhZHUBma2UTz5ZKCjPhgiIvTLo48aBTzwgByt+Hj9yCE7Uuvhw/rhosqmL6OBR0SwYKHd3Dt04NwNq9qH8vcbNQo0IR4+zJqhTBi1Fc3IKsLDuaS/NlkSYJ/gK69Yp5WRwfeo7vuu4Jpr7PXWCRXOKAMRQlwphNguhNglhAhoTioYH3m/3yCE6KD6bp8QYqMQYp0QYvXpGK+ZSSBUauSpU/p+lmDj0ouOSU/nBSRjh1cWkWxPdqNxAfq+hunT5eLX09NZytdKh3ak1vLlOWlN6zcRAihXziMlDBhtOgCHamvLeQfDggX65ooBA3jMMvjkE32H/Pnns0lKBvfco39N8+Y8Npk5tmgRhxFrtebWrYFnn5WLdhoyBNi1K7BXyqlT3I9FXco+GEKpmYaF8caulw0vK3Dm5HCFCL05vnp1YKjw6cQZYyBCiHAAYwBcBaAFgCFCCG1601UAmng/IwBoguJwCRG1IyJNuk7ZwIiBnHeefDboM8/oq552w3j1xjVhAuc2yGRpG/lm1q3zLVYZWkDg2A4dYjOGTGZ7sMUt88zS0nhz1yuaOHr0Br+aVnbHpRwLlYPz8GG20cvgk0+4TpsWd9whX43XaO737ct9YmTKvK9cyWY/bSe9wkLOdwmFMGZn0zfTQL7+Wq56QmYm8MUX+utFVuA0E1IefZS7HJ4pnEkNpAuAXUS0h4gKAUwBoA0u7AtgAjFWAYgXQtTQEjpd+PprfYftJ58E9iMIhjVrOPxTC4WByNiUjTQQO7Zbo43i5ElOADx61DqtUJoEjDZqhbYMrc2bWfXXe/5t22YEFAw0Q34+M9tQ+cZGjtTf3F98kXNXZGD0Lu1AL4zULvLy2IylTZhcu5bDx2WinT7/PNAUCdibY+XKscagXUthYcDtt7MwZhVHjnCL3tU6thFZDeR0CSl2cCajsGoBUDXbxCEA2jqVeufUAnAUAAFYKIQgAF8QkW7vPSHECLD2gmrVqiFZNhbPi+zsbMTGJiMzUz6cTw9Hj7ZDWBghOdm//O7x43VB1BALFy5FVJS1Qj5HjrRFcbFAcvI6v+P79lUD0BxLlvyJOnWszbImTeIwfHh5JCcfQ3Z2dunz2rq1EoAOWLVqPUpKrKULV6gQh2HDKmPFin1+Gk1qajkA3bBu3XbUrWuNI61eXRlAW2zduhaRkf4B+dHRF2L79sNITrZWV1yhtW1bIK3ffy+PdevWoV27dEu0AGDxYmb42nmRl9ca6emRSE7+R/c6PUyZ0g2HD6egSRP/2NhTpxojM7M6kpP/sEwrM7Mb0tJSkJzsT2vWrFr48suG+OGHFShfvsTvPRvhxImOqFy5EMnJG/2Or1qVgDfeaI4PPliHBg2sefl37myEcuVqBNzLnj0xADrj7783oUIFazX1Fy9uhD/+CKSVlRUBoAc2btyF5ORAW6nePdesyYEHW7cGmr62b49FTEwxate2to527qwIoBN27dqE5GT/eykp6YCDB4sCnqURtm+PBdARu3ZtRHJyqt93OTktkZJSHsnJwa34Vt6zNIjI9ANgJoBrAIQFO1fmA2AggK9Uvw8D8LHmnHkAeqh+Xwygo/fnmt7/qwJYD+CiYH+zY8eOZBeLFi2h+fOJ9u0L/O6994guuUSOXufORFddFXh81iyivn2JsrKs0/rqK6KxYwOPz5hBBBCtWyc3NgVLliwp/XnNGqY1a5Y9WmqkpzOt996zfs0ff/Az27Qp8LuZM4nWr7dOa/Zs/vurVwd+16RJJvXpY52WGW67TX5exMYSjRoVePzJJ4kiI+VoVayoT+vjj/n+T5zg39Xv2QgtWxINGBB4/OefmdaqVdbHddddRFWrBh7fuZNpTZgQ+J0R7r5bn1ZeHtN6/XX966zcsxo1ahANH279/OXL+e//8kvgd5Mny62jrVuJrruO16AWQ4cSNWpkjY7sPasBYDXp7KlWNJDPANwO4CMhxHQA3xKRpJtXF4cAqGOHagPQtrkxPIeIlP9PCCFmgU1iS0MwLl3k54ejTx8uZfLII/7fHT0qX6nWyLzQr5+8s/TOO/WP27ED79rFSXbaEGM7tE6d4sRDbSSQHfNC9+7GzsIBA6zTAcxNArJO9J07gTff5DmhTZjU69FiZWxG5rCiIn6eerWy9GCWUwLIPf/nnuOoLi3slgzRM4cptGRCxY2eV1QU/x2Z/h3ffsvBHT/9FOgDlDUVmc0x2ba9zZpxszM9nGkTVlAfCBEtIqKbAHQAsA/Ar0KIFUKI24UQku1y/PA3gCZCiAZCiHIABgOYozlnDoBbvNFY5wPIIKKjQogYIUQsAAghYgD0BiDpYpRDQQE/KjM7pEzp6MaN/XurO8GJE/oNglq3Znu6TL7Fgw8CN90UeDwmhvuEyMTVP/54YLl6gBf1ihVsVw4F/vwzsJS9GcwWd3R0idRmePAglzGRLXSoByXTX39c/L/M5pqZqV9M0Y5vbNAgfV+DHcHi66/1uxjaqe1klCEvhHwzry1bgN9+0686LevPMnN8Hzkin71vhFGj9ButnS5YcqILIRIB3AZgOIC1AD4EM5Rf7f5hIioGcB+ABQC2AphGRJuFEHcLIe72nvYzgD0AdgEYC0CJj6kG4A8hxHoAfwGYR0SSBSjkUFjIO6dRmQlAPslu9OjA4z//zHkSMvHrHTro5wjUrs1Of5kCdUYSXZ06rGndeKNzWkJwaQaZ3vJTp3LJltTUwO/uuUcuu/eKK4Bffw1sjwsAUVGhC+P99tvAMuNmKChgJ662twXAWe4TJ/r3ogmG8uXN56vMfa5dq98G1272vp4gEhsLvP8+15yzirp1gbZt9b978kl+ZlZhFnQgK+n37Mnh+Hql7h95RK7R26xZvIa15e8BLuUj87xCjaDKsBDiBwDNAHwH4FoiUryeU53mXxDRz2AmoT72uepnAhCQCkdEewAYTJuyQWGhsQaiNgk4rVZKxNKsTNaxURRWfj73EWjQwHoCoEypEiu0jBbk1Kms0Vx8sTVaR45w5VW9jUe2oFyNGvrMA2ATlkxPdDNtZvt2Y9ODHmJijHNjWrbkj1VkZHCy6uDBgcUOGzYE/vc/fZOUEbp356TUt9/2P16lCjBsmFz3v7ffZiFCW1K+XDn9bPdgtIwwaRInrN58szVaZtWLZRlITExgEVEFsvM1M5P3BD3T5bZtHGJ/442BYdGnA1b+5FdE1IKI3lCYhxAiCgDoNOVfnA0wM2HVrcvZ4zKhtxdcAHz6aeDxUIbeHjrEDX9kigMa0SListl62bBGMFuQTzzBpgyZcQHG5h0Z7W/jRmDaNH2T4/Dhe/Djj/LjMpL0Fb+FU5w8yd3srAoWaWncTEovka51ay6BYdW0SWT8LqtX53wjmW6Js2frl1gBeEPU03TswI7fwihU+dVX5coCrV3LuS5670t2vprN/R9/ZJ+KDL1QwgoD0XtsK0M9kLMdNWvmYcECoFu3wO/69gV+/926lO/xsNNdr1ugrB1YKU1e1nkgQnCWtIxpzUwDkbUpK9WL9Uw45cvLLaCpU1ky17N116qVH+AMD4aKFc01U6vP/8ABNlUtWxb4XXIya2t6vgM9GDUGU+DxWPfZFRbyPAtVHohZTknXruZahRZDhrAfQA+yCXvVqxt3arzwQqBHD+u0li1jDUtvXsrO12BCivqc0w1DBiKEqC6E6AigvBCivRCig/fTE0AI2sr8uxATU4LeveW7kunBbHHLRqJYoSUzud55x7h+luymP3Jk6GgpzEhv07cj0RnR2ro1Fp9/HnjcCDffzFV39WqRyUYopaayZK7n55F9l2ZS65YtbAqcMcMaLbM5VlDAz1+mnYGZYCFr3tmwgQMZ9CCrgbzzjnFNtY0buQSLVZg9M9l7DPUaDyXMfCBXgB3ntQGoW8NnAXi6DMd0ViIlJQozZgCXXRZoO165kiOKJk4M7IGsB7PFXaUKMHSosY1ei7Awnvh6jjQ70olZjSTZBWnmQJal1bAh27P18OyzodGyAGDFiiRMmsTFI2V7wGtRpQpH2lk1YZlJmrJRWMGyl9XnOKFVrhxrKHaEAT3ICgNmZtK4OOfvUMGHH3KAi1Xzmtm7HDCAw+SJrI2veXPWtPTq0521DISIxgMYL4S4nohmnsYxnZXYsqUSXnyRJR4tAykpYYep1ZpTZguydm25HsdRUYF5KervhJCbXL//zr1A9Gp7yW76O3ZwZdXq1fVpaUvGm2HkSBjWqNILFTaD2QYWFVUCIt4UrRSUnDaNo2QmTw7cDAYOlIvCCqWkWVjIwoUZLaubfqVKfH96wpFSxkVm04+O1q84rIwtFHkgQGDl5mAYPpzH9e67+uOSqTicl8fMVc+x3amTNUFTgVlumJ08nFDCkIEIIW4mookA6gshHtZ+T0Tv6Vx2ziJYHghg/SWGhbE9W8/sIT8u7sleu3ZgQTshOEbcyK6rh8suAx57DHj99cDvzjtPrlLqZZdxHwm9hDrZYn5m2LgR2L3begKmOQPxlJ5jhYGsXcvFBEMh6QYLFACsb649exprPrLMqEIF8+Q3WcFiyxbj72TNO2aOb1msWWO8Ju2aSfVw4gQn7HbqJBeWrYeePTkPKlQ5ZbIwc6Ir21FFALE6n/8UrDAQqxOsZk12iupV98zKYkbw/vvWaG3fzpmqRtLWjTdaLwJnlsgGsAr/wQfWaAHm5oV69QK7Hpph+HBj89qECWz2s4rXX+eMYz1ERXFdcqvCgNk9rlnDC3zDBmu0oqKYSev1w2jUiCNuunSxRgtgpqbH2GQZSEYGl6U3aoIku7ma4aWX5PqedOsWWAFAwdixwP33W6dl5txX7tFqpOVrrxmXkp89m8OiU1Ks0br7buPmc4mJPCecpg/YhZkJ6wvv/y+dvuGcvTBjIHYyaI0QHc2bl9VwTWWjM7bpc5RQmzbBaZlJwHZgJh0uWsRaw113WaN18CBvZHpQL24rmoBZ/3S1BmIFZveYnc0mQat5JZddZtwLJi6Oo/2sYtkyTmR8881ArTEyEnj4YevMaPNmoFcvDgfXy0a/807r3TU9Hs5qHzoU6N8/8HuZewSMW70C3Kly7lzrTb2C+WY8Hg7LtqI1VKzIHyNagHWmm51tHDF38iQzpMsukxPIQoWgYbxCiPFCiHjV75WFEBIR/OcGzDLRK1VibcKq4/vPP3nB/f134HcREWziknWWGkkgt92mn/GuB7OsagB46injultGYzNakDNmcKJbKGiVL49Sv4UVzJplnBvTo8dJ7NrFuT1WECz5TDnHKQoLWQO0Gsa7ZQvn2eg9EyHYzm8UlKBFMMHipZf0y9/ooaCA371eVjXAx/XK7NuBrGnNTAMZOpTLnFgt5TN5MvDZZ/rfyTIQs3EdPsza+Zo11miFGlbyQNoQUbryCxGlAZB0W/770bv3MSxfrr+IkpJ4cVvt15CWxrVw9Lq4KU5JqxM/mAYiQyvYRrF9u/XuZ8XFxq1elb8RKpuy7IJ87TVjqTQmpgSNGlmvoxQba8xsZDXTqVM5ITUrK/C73FzuYWI1sz3Yu8zJ0a+fpodggkVxcWiiwwBOML31Vmu00tNZmzRKbpVlIO3aGWtSDRpwi2gZBvLVV/rfyc6LUM79UMNKXc8wIURlL+OAECLB4nXnFJKSCnWTCO0g2CIK5aYvk0yVlMQqv5G5S3ZBjhvHdbr0YMcpabSBqW36RtE9WlrGDs4ovPkmm1msdJk0M4/ILu59+9j0ZFSuRYaWWRgpwH4DowAHI1pGz6xnT/47VvIkgo1LZl7k5AB79xrPyeho1sBKSqxt/GYVG/bt43D9a681Nk2pYaY1yGqmwbRv5ZwzASuM4F0AK4QQStrRQACvld2Qzk5s3FgJR4/qR6MQsRR6//3W2ksGW5B33GFcIE6L9u1ZVa5dW/97mU2/QgXzIm8ytCIi+D6MILu4e/UytvH268fPISHB2tjMFuTx41F48kmWRmXbFGsRG8vjslpbzGxzVSLCrD7/YFqDzLsMRksmcsqKwBOKJFqA50ONGjzPnPr1li/npNHt2635e8zmWJs2HMRhVCtLi+uuM/7urGcgRDTBWzSxl/fQACIyCcQ7N7FgQXX8848+AxGCIyr0Moj1EGwRvfmm9XE1agTTFqwVKlgvNZ6aygulWzf9cF3ZTWfdOg4vTEzUpwWwTdxKBMlHHxl/Z1YcUQ9Ww3itYNQoHv9rOiJVjRryZeajovRzB4SQk87Dw7lqglFQgcym37MnMGeOccHE6Gg2y1qBx8PCjlEhx1AyowcesB7RlZcHdOzIAuBtt+mPC5DTGowEmqpVgRtusEYHMC8weaZNWFbrN0YCEKqf/3MoKAg3jTeXWdy1arE920gyJeJoDys4coQ3KT1/CsAOTqtRKBs2cBTMJoPOKo0bW9eM9u/ngpFG4cV3381jD0UM/6FDbIqxGhZp5viWZSDLloXO6Rssp0GGgT//vH6tNTu0atdm040Ro5eZ+02bckSdUUi2DK1g5jAZ5OZy2K1RcmsoHd85OdxOwGpWe0GBcfhwTAyvVzNtvyxhJQrrQQCTACSB28dOFEJIRFefGygoCDNVg2UW5JVXctczIynsggvM1VY1vv2WJScjhtOpk/VKqcEkugcf5HyAUNCqVIkldKslqGvUAF55Rf87ZQHt2mWN1urVHFGmByUPREbTMrrHkhJ+/l98YY1WrVpcTNAIP/4olyNhBhlT0fbt7BszElJkAyLMcOut1nt4xMaywGOkGS1dyiZZoxL5agQzh8kykLVrgfHj9b87epQDbhYvtkaraVN9rQjg9dOypXXzbahhZfneCaArEb1ARM8DOB/A/8p2WGcfCgvNGUgok6lk1Pj8fDZTGGVNr1/P5gertJS/7xTBpMNNm7gJlJUcCSLg2LHQZVY3aqRfXgWwlwdiNC/Cw9mMZ1TsT4snnjAvv3HRRdYzjt9919z0cccd1qXWqVPNBZq+fVmjtIK//+aQ9+3b9b9v29Z6LkizZsxUjUrZnDjBeSJWzGvB5qus4zsqylhjs1Mw1Wzv+fxz68wo1LDCQAQAtexRAp856z+DYAykf3/riVmvvGLei0HW1xAdbWzrHjfOelhkMK1hyhTuJWGl5lcwiW7rVjavmZlZrNKSkQ4LC4G33jKOm4+LK8KxY9bzXYKZnUIpWCxYwBUMrGD5cvNNZdgwY6lWi/x8Dms2Cna44QYuf2MFhw9ztJNRZOCBA1yR2KoJ1wwygkWwOda6NYewm2mIajz2mLHgZsefYrb3PP+89crKoYYVBvINgD+FEC8KIV4EsArAuDId1VmIJ57YZqiSAsB77wH33WeN1smTxmUhAHk7cKjs5sGksMxM1hysZMkHY0Yyi8hK5I76PDNkZrKkv3y5/vdhYdw+1KoW1rChedKhzPO/5x7z7nlPP82Vl60g2KaTnm7NtKPQMnseubnWBAEguJY7Zw73RLEipPzwAzukjUyXMvMiOpqz7I3aLMfGAp07WwsTBzjoY8UK478FhMafAsiH14cSQRmIt2ji7QBOAUgDcDsRfVDG4zrrUK1agWkJDBkEW9x2NBAzWgUF1poH9enD2bZGPdRlFmT79mz6MDK5yCRTnU5mBLBmZNQxT4s//jDPqJcRBrZv53yDUNAKNscefdS6xhzMhPLGG7zxWqkTFcp3mZHBgRN6rV7Vf8MKrcaNWTMyyvXKzubaWkalZtQoKTEPHVbMzVbGVVLC2liw/eKsSyT0Jgwq2Of9lH5HRCYy9LmHn3+ujoIC/VpAANuIs7N5Aw6GYIu7b1/OQ7CC//2PJTYjqBdRsHDZ6tWNfQNqWlY2/Ro1uJCjlXEFQ7ly3G/FqGhevXocQWal/IgVBvLOO/xc9YpdyqJHD96crCAvzzxJTWajyMsDKlcOHa1g/j+rdaKsapNWxhbM7BQXxwKM1aoCZsjMBEaM4ICIZs2sjctIsIuI4MoVVvJJPB4O+DDrhngmNRCzPJA1AAj+/g7ldwIQInn834EJE+rjxAljBlJSYr2/RbAFOWiQ9XEFkyLVkn4wBrJuHfsmjNq9yjCQAwe4rtGFF+o7+GUkzSpVzPunR0WxjdoKrDAQqwuyoIBzJO6/37ga8PffWxsXwM/CrC2yTL5FUlJwYcDqpvP00+ZOcvWmH4yBxMZyAp1ZSDAgp5kabdQtWhjX3NJiwQIWGubP56gmo3GFgrEB1oWTyEj91grasZ11DISITNy8/z2EMoy3e3dzqTQ/n7UZK703lBwEo0iUgQPZ8adXIlyLadO4H7VR74fq1bnqp5XEv9mzOeQ0JUWfgbRrxyYIbQ8TPQSrsltczNn4XbsGZ6ihZCC5udzbXobhBxtbqCL9zKrUAj4NxIrZKZikrN5cg82zYcP4YzYuhVYwhLJ6dHo6R8uZJV5aHVd+PmsZZuP6+WcWFjp3NqdVXMxjq1TJmDnPmuW8r4hdWMkDEUKIm4UQz3l/ryuEkOhKcG4gGAORWdyjRplXyH31VfZDWFncjz1m3vOgZk3OA7GixgfbwDp25AQoK/1FrKjxlSpZK2OydCmfbxaB9MAD1jrQdezICVyXXGJ8jlUGYmUDu/lm671KunY1N12OHm3cx0QWMhv1woXmda5CmQ3dpQv/PStlPlq25CrARnM7I4M1RCsRSsHmq4zfolYtNucNH258zt13G1frVWPPHmY0Zu+9evWzOw/kUwAXAFCWQRaAMWU2orMUBQXhIdNAgqF8eZ9NORiCbfoHD3KWtpV8i2C0ZBBsc83KYkeuUTSUllZJibGUFRHBHyuLOzKS/TOhcEpayZs5ftzcMa7G+PHGCY4Aa61Wu0tef735BnXZZdzn20oi56uv6pdqUdC5M5ffsaLlfvghJ9IaISmJy8xbiXbq14+TDo20hrAw7sdi5fkHm6/h4Tx3ZJikmdZs1exkRUj54Qfr1SZCDSsMpCsR3QsgHygt536GFKYzg6IiwOMRphtFz57WeyJ07WreIlRWXTYb18aNnDC2e7dzWnv3cv7KrFnBaeXlmecOFBVxspuVPgahNDtt2gS88IJ52OmKFbwoQzWuUEXI/Pkn5/VYwcKF5pn5nTqx1malbW8wwaJ1a64hZVRZQY0dO8zfeUYGS9tWky/NIONPsSIMbNjAjbiCYdcuDvowKgkEWJ8XVsq1/PCDXKfQUMIKAykSQoSDHecQQlQBYCEo9NxBRAQwffoKU1PRTTex/8AKMjLMzVMyzmoriWwytMw2irAwlubMclgUBGNGoQ69tWpC3LgRePllc2d0+fLWTGuRkWweNAp7VsYlkyFv1sr4hx+s5xoFe/5KTk8ohJS8PN40rbQNCDbHjhzh6D0rmun//mfun1EEGCv32KgRa21m/r1mzaz5JQ8f5hJDZkVMrc5XK4wtlMmqsrDCQD4CMAtAVSHEawD+ABAkLuDcghDcDySYhFVcbD0WPthmqJwXDMFi9GWY0VtvATNnhobWXXeZ0wplHojyXSgyjgFuBBQs8gXgzWvlSuDii43Psbq4i4vZ3m2WpGm1L7fS295s01mwgDUHK/XDgs3XlSs5XFavw6YerVAJFjk5wZ+F1Xlx7bXsKzHTyL7+OnhwAhDaTd/KfD1bw3gBAEQ0SQixBsCl4BDefkS0tcxHdhYhLQ0YP74eEhKMmy2NHs326/z84GaBYAuyUye2OVuxKY8bZ246kHGWBuupLMNAmjUzj5cPC2OfhpVxNW/OkrdZXsPy5dYiuqyYBH75hVvCPv10cHrB0Lmz9QAGwJpgUVBgPn6rm47675rBSrKq+u+awUoSrVVawcYF8POXKfVvhjff5AZp11xjfp6VdzlmjDX/U+PGLMyY9aY5qxmIEOJDAFOJ6D/nOFdw/Djw7bcN0Lu3MQNRN/xxykDatDH+O1qYRRMBchvFjBl8vtECkaG1fDkv8EsvNT4nOpo3w2Do1s04Q1iBUUMtLaxIh1bt00uWcIXiqVONkxzNzJ5qyDCQYBtncTHPH7M8EBkNcMECc+YsozU0amQu8Mhq38EYiJXEXoADOmbNMvcVhtLxbSWSEWAGYhZYofwdRTM1c9yXBax0JPwHwLNCiKZgU9ZUIlpdtsM6u2BFapVZRHfcwbkgRigo4JLP1aoFj4qaPZtDHo2k/fr12e5fp07wcY0ezX/TiIFERAADBljLoH3zTXaEmvXKOHXKmq9BYTJmjHnCBP7/llvMaYXSJHDyJD9bK2VigsHKHLMqncfHcxVmM6iFgWACj15inRoyc//dd0NHK5j5VgYZGcHfuYyvIS7OfGzLlvEaN6vWoIwrPZ1Dg41Ktjz5pLVOqGUBK7WwxhPR1QC6ANgB4E0hxM4yH9lZhJK9B1ATh0NjEsjNxYcP7MaA/sbG21WrONpp5UpzUpSbh2f7bcTUSQZ1zsGbQ6tWFsIi8/PR6NTfiIswr5Q4cyZnqpuiqAgNjy5HjQjzDk9WmAdKSjD+zqVoHbPH9LSvv7YQoeTx4PHzf0fOsn9MzUqWGAgRYtctw6VYhPJRxhzkvfc4jj8Yk4lZvwJvdZ2JxnWMVbJBg4CdOy04clevZi+uSaSAVWZE69Yj+cZPseGnA4bnWN70t21jDmLC3aKiOAouaAXpffvwSoU38GBL80bsN91koYfKkSO44q9XcGPJZFOniiUGkpqKIbteQfpLH6JedeN3+dVXFjb9rCxsH/Yqvq3/Ak7uNH+XMTGnX/sAABCRpQ+YgbwLYDeAuVavO5s+HTt2JDs4eN09RAAdHHA/kceje8733xMBRFu2mBBasYI8SUl84jXXEOXn65725598yk8/mdDavJk8tWoTAXSsRluikyd1TysqIvroI6ZpiEOHiJo2JQIotXwtou3biYhoyZIlJhcZID2dqGNHIoCyw2OJkpMNT33hBaIxY0xo5ecTXXopEUBFCCf67jvDU6+8kqhzZxNaJSVEN97IDxYgeukl3dOWLFlCTz5JFBdnQouI6IEHSmnl9B9qOC/eeINPy8szofX6675xdesW5OQgGDeulFZuzYZEJ07onpaayqfu22fynufOJU94ONOKjifavFn3tKwsfo9bt5qMa+VKouhofpdhkUQLF8rdlxrbtxPFx/ue2ZdfGp7atSvR5ZcHHi+956NHiWrV8tF69FFDWr17Mz1DZGYStWjho9W3r+G8uOsuomrVTGgVFBD16FFKq6h1O8N58eefRA89RJSWZkCrpIRoyhRK/vVXkz9oDgCrSY8v6B30OwF4E8BOAL+Aq/LGB7vmbP3YZSDJYzbRp7ibH9dnn+mes3490WOPER05YkDk1CmimjWpqH4jehVPm07WDRv46xkzDGgVFBC1bEklVarSI3ibiiKiiPr10z21qIhpvfyyAS2Ph6hXL6KYGHqq0ieUGZ1E1LYtUXGx7sbSsSNPfkMMG0YUHk6j63xCB2LOI6palSgjQ/fUtm2JrrvOhNaTTxIBNP38d+iPyJ5EUVFEu3bpntqvH1Hr1ia0PvmECKBN1z9Ha1sP44eiw9wsMc0ffyQCaF2Pe+llPMu0xo3TPfX99/lrw8X9559EQhANGkQ0diyf/PTTuqfu3k305psmc2zvXqKoKErvchldhXlUHBnFTDMIdO85PZ0oIYGK27SnrlhJ2RWr8ss32BBNUVhI1LgxUf36dE2d9XQgriVRjRpE2dm6p0+eTLRsmQEtj4fowguJEhOp4J9N5Ol9BTOmAwd0T+/Zk/dhLUrvecgQovLl6YHuq2lG0l38/Fes0KWVksKM1xCPPUYkBCU/s5DGt3mHaU2apHvqgw8SVapkQuvDD4kAmnPjd9QHc0yFnvHj+evduw1oTZ/Oc/+FF0z+oDmcMJC7ASQFO+/f8LHLQIqLiebO+Z1KLu5JlJRkuCGa4vnniQA69OPfBBBtv/BOoshIoj17Ak7dsYPfjKHA7d1oUr+ZTQDRyn5eMff333VPj4ggeuopA1q//MLXjhlD8fFEX105jX//5hvdjaVZM6KBAw1obdzI1z71FLVoQfRYr9X8+7PP6p5+/vks1eni6FHeGG6+mW65hahzrcNEFSrwgtfBkCG8R+kiN5fFvZ496c47PNSwRi5R7dosTmo2xKAMpKSEqFUrombNaMaUIrrsUg+VdO7KUqyORvnZZ/wIjh41oHfFFURJSbTs50xKSCA60XsoUfnyuhcor2r5cgNaw4cTRUXRqhkHCSDac/NzfME//wScWlTESsGhQwb3/OKLRACdXLiGAKJFw75lWj/8EHCqx0O0di3R4cMG4/rqK752zhyqVYvo9auX8e9vv617eo0aRP/7nwGtBQv42k8/pfr1iR7qv4/X0T336J5+1VVEnToFHl+yZAnRpk3MvJ96it5/n2j0c9lEVaqYTEoTHD/O723YMHrmGaJwUUKe1q1Zsy8uDjj9iSeIypUzoJWfz4JXz570wvMeAog8ffuy1qWz90zzLtlNm3RoeTwsWTVvTksWLZK/Ly9sM5Bz6WOXgRB5J9yqVfzIPv444PviYpYyCwp0Ls7K4pffvz9t3swkfhxziHf2hx8OOP3gQT5n7FgdWiUlRI0aEXXqRLt38eT67stcnvgGWkhsLKu4urj4YqI6dYgKCmjvXqLjxzysGrRpQ0t++y3g9Pbtifr0MaA1bBhRxYpEqam0bp3XpNGvH1Fioq763bMnC5O6ePpporAwoh07aOBAZlz0yCNE4eG6O9XttzNP0MUXX5Cicdx0E1HDhsQ2F4DfqQpLliyh334juvlmFsIDMH8+XzdxYuCxyZMDTv/Wu+/qyAlUOhneeIPmzuUf10/bxj+8+mrA6b//zl/p7gNpabyRjhxJCxfyeSvnpxHFxBDdcUfA6enpfM477+gwkOJiourVifr0oX37vPLE2CKi+vWJLrkkgJbHw+cYCridO/Oc8ngoIYHo3nuJX379+jyfNWjQgJ+/LgYO5M21oICqVycaMYL4/ipU0N1cBwwgatkykMySJUt4PkVG+pt/X32Vb2bHjoBrZs8meustg3F9/HHpLv7ww/zYafJkPqZjrvPyZ73b5z8EEP38Mz3xBCvepXvP558HnD7Hq6D8/bcOrbVr+csvvrBnkvbCiIFYSST8z2P5cuDzzxsis7m33OsnnwQ429as4TyFX3/VITB7NodSjBrlc87WqsW9QMeNC0jhTUjgmkEXXKBDa8UKjjV86CHUqCmwbBlw2bXluXLbnDlcR10DQ6fw/v1cLOjuu4Fy5VC/PlC1mgDuvRfYsAFxOrUYDGnl5LCH/aabgIQEtG3rjQy77z4gNZVL/Wpg6JQkAiZP5qJITZqgf3/u1od77uGiWGPHBlzy0Uecu6GLyZN5MBdd5IvcGTaMm2/oFIzavZtrLOmW5//+e45IuOEG37Hevbk14eefB5zepAkXVNSNrpo6lT2ft91W+kxFs/OAXr34HktK/E43dVb/+CPXh7n11tLvI6vEc82cKVMCbsbUib5sGTehv+WW0nFFxURw6veSJezJV0EIdn7r0tqzhzMMb7oJEML3/EeM4LIGOnG2hvMiOxv46Sd+9uXK+cJ4R4zgNTR1asAl7dpxXlUAiHhOXnEFkJjoW863384JGjr9A+bNM4kimzaNo1VatvTd44ABvJh1ojvuvpvnq67je9o0vu6yy3Dddd7qBF26MH2dcZkG8EyfztEqAwYYDNwZXAZiAWvWAFOn1uXihnfdxa3j/vrL7xzTxT1lCsfRdu/uHyN+110cpzd3rt/pFSpw5Ihu+OSUKXxx374oX54bzVSvDl7cHg9vlhoYxq8rm/rgwSgs5M5yf/8NLh8bE4NqCxcGXGLIQObN40XsDdGaMIGDgdCrFwf/T5wYcElcnEGBxL/+4s3FS2vIEG8kTaNGnFgycWIAA69YkXtNBODIES7n621yUrrpxMbysZkzA27IcEEWFPBG3b8/EBWF557jxDKEhXET9aVLmSmr0K0b8N13OslsRLzhXXwxUL26f3jx8OFM548/dMelO8emTuXQvc6dERvLfzc+3ksrNzegLEBkJA9b911OncqT8Oqr0bAhM9Q+feDbXL/7LuASwzmmlJEdOBAA14xr3hz8DCtXhl6faNM5lpdXWj+/9F126cKLRYfWc89xQJoWlbZu5Thzbxxty5be+nQ1a3KHtu++CwidM8wPOnyY35WXVmmeV1QUr6VZswIYeLVq/BwCGEh+PguCAwYAkZHo1s0rPAnBz/+vv3j/0YwL0MmpUphkr17WarDYgCEDEUIkmH3KZDRnKfw2/QEDeNfTdAoyXNynTnEm1qBBQFgYatbk8L1GjcDdlmrW1O06tGkT731+KC7mBdmnD1CxIo4d44362DHw5nH++cxgNFi+3KDY2pQpvPgaNkRODmdeL18Ojgm87jpUWbo0oCTwVVcZVFOdMoV3yQsvBMBC4fTp4Ik/aBCweHFAcaApUwL2SMbUqfyM+/UDwD1FMjK83w0ezPU3NAkmixZxafsAzJjBC8m76fiV+Bg0iKXan3/2u8QwmW3BAt4IvLSOHfM+e4WW8vesYMMG3gi81/nNsWuv5UFoangbjis1lR/AjTcCQqBnT36PjRqB32+9egHjEsJgoy4uZmZz7bVATAzKlWPlKjYW/H4vuki3Ro2h1jB1KlcP9aZSz5vHeVCIjubWm3PnBux8prRq1AC6dweRioEoc2zFCk6usIAqS5bwHLvuOgC+4p8A+DkePhxQm8VwXDNn8hzzMsm4OF6OAHhchYUBc2zzZtYssrI0tBYs4INeWvv2qZpieY9pq5lecAHzussu09Bav57XinJdWUDPrsUmL+wFsMf7fwmAkwBSvT/vNbpO5gPgSgDbAewC8KTO9wJci2sXgA0AOli9Vu9j1wfywgsae2W/fmwjVjnHDhzgc776SnOx4kBcvVqf+KhR7E3ThOmUK8dBSH749VemNXMmEbEt3M937o3cMI8l9kLx1L/7LhGxW8HPxKqywwZFRgYbah94gIh8NvHnn/d+r4SVffppcFolJeyQvvba0kPt23PUMxFxGExEBNHjj/td9sor/CcKCzX0LriAqE0bv0OlfvOiIvYdqSKVlixZQvPmeX0IKzW0hg5lf473j5T6UxR07EjUpYvfJX/8wbEAAe6kp59mf443zHbxYqJbbuFIUCIiuv76gDlWVMS+9QBfvRK9tWYN6UKx9WvmWFIS+579bOPKHPM6y/fsIRo9mv1yRFQazaYN6a1Xj8fvB2WOvfee/rh++om/nzfP7/Du3TpBVZmZPMfuv5+I+LE8/bTKH6T4kzRx4W+/TXTeeRpaJSWUn5TkFwJYvbrKca/4kx57zO8yZR8ICETr3j1gjpWiuJgDODSRJ4pvLCBySjPHBg3SjL9LlyDx6io89RTPsZQUIrIZlu8FZH0gRNSAiBoCWADgWiJKIqJEAH0AWCh2bQ5vhd8xAK4C0ALAECGEttvBVQCaeD8jAHwmcW3IwNKJx1e7ZsgQFj1//730HEOzx/ffcz2CDh0AsASTlqbSjgcPZglFI1XomgSmTGFR0NsPMyCreuBAlsY0Gs133+lo94q9WKV2+9G64goUx8ToajQa6xGr3AUFfqYFP1qtWnEjCw2tb79lrdwPy5ez9KfKVvQr/ZKQwL6RqVP9BqKrAR44wNmYmpaBpWaDiAi2p8+d61fFMDaWNX4/C0Zenp9pQflbfr6NG29kE8PevaWHlD4lfu9SMV/16lXaw7ZXL35HpWa4gQN5jqlUtIgINlcGZI5PncpzzNuWcsIEfuSlWtvAgaxJzpnjd9nXX7PlM4BWxYqlaubWrZzpfPiw9/v+/fkBarSQDz7QaXurmEi9/qITJ7hvfen0vOwyLvimodWwoU7lBM0cCw/nenGlpXJatGA/l4ZWVhYren5zduVKRJ086ZcG7vcu4+OZsKJZeKGuRVaKQ4d4zhqllIeH8zP7+We/SaBr8rYyxwYMYM1I5es8dYo1/mXLVOedBvMVYM0H0pmISvUvIpoP4OIQ/O0uAHYR0R4iKgQwBUBfzTl9AUzwMsFVAOKFEDUsXhsyFBQA5cqpdpM+fdjMo3LaxcYCL72kaal67Bg7HVVNxqdO5T2w1FTeuTOvGI0DMMC8UFjIE7pfv9LdMqD8RY0abFPXbK7jx+v4nadMYQeKt4hUQI2oqCikXHgh2/xVs/yBB9jqFkCrbl02oUGHGSkmhmXL/OxyGzfqWHymTuVBXHtt6aGA2mGDBvEDVJkYdM07ygamYiBPPQV8+aWGVl6eX5nVCy9ks5lf/a2ff2Zzl4pWQCkNxVSguildxvbPP+xYUG06AUz5mmv4YpUZq6gIeP55P7mFd+XffuNxeefY0aNsIik1yXTpwjuyxiR27bWaVshFRVwzvm/fgDlWep81a3IdHg2tfv10gj6mTuVzvdwgJ4fdDoWF3u+jongQSgCAF7/8ouMrnjaNA0+8f6SkhN9RKS2AN9fff/frnqb7/KdNgycystR8pXzv9y4HDOAAAFXW/KhR7E7yY+DKu1aZiUaNYqbrRysnx69lpu58/eUXnmNGjA1gZgT4CZyFhby+N29WnbduXcAcKwtYqYV1UgjxLICJAAjAzWBTllPUAqBuG3MIQFcL59SyeC0AQAgxAqy9oFq1akg264tqgH79gEsuyUZycsXSY83PPx8JU6ZgxcCBIG+Rmosu4gmm/Ilas2ahiceDvxo2RK734Pr1NQE0xdq1K7B/P8/+Buefj7pTpmDFjz+iyFtpToiu2Ls3A8nJ2wAAiStXonV6Oja0aIFTXlpr11YD0Bzr1/+J1FSeiTXat8d5yclYPW4csr2N13NyWiM1tRySk7mTT8zevei8eTN2PPAAjnhpbd8eC6Ajdu3aiORkfr3lzz8fNX75BRvfeQepPXoAAI4ebYTMzBpITmbJOCIzE90WLMCh66/HnqVLAQAnT5YD0A37929HcjLbpCvUr48uRNj5xhs4fP31AIDjxxsgN7cukpO9O2JJCbpNnoyMLl2wWdV1KDOzG9LSTiI5mY3BEYmJ6BYZicPvvIPdI0cCAPbvrw6gGX77bSWqe0tIdPjqK4imTbHm4MHSDkXjx3dFq1YZaNp0W+nfvCAhAZljxmBz1arIzs7WnSMtPv4Y8ZUrYyUA8n5fvXpdxMWFIznZp3F0aNYMGDcO/3ibXR88WB5AV6xZswUJCewDavj556gdHo4VVaui2Evriy8aYu7cmvjpJ5/G0bJzZ8RNnowV/fsD4eEoKRF45ZWLcfDgXhCxBFJz9mw09Xjwd8OGyPHS2ratHoAGWLkyubRcTKPzz0etH3/Eip9+QnFFnsdbtsQiPByoVYvvOeGvv9Dm1ClsbN4cqV5a//xTFUALrF//J06d4jlWq21bNBkzBn9OmIC8unUBALt2xcDjEWjaNJvf9/796LJxI3bedx8Oe2nt21cBQBfs3r0Zyclc5iapWTO0mjQJ6z/8EGnecKn33muGTZvi0LDhnwCA8OxsdJ8/H4f79sVu7xw7diwKQ4ZcgMcf34arrmJHVMX69dGppATb33wTR70F3Q4dqgWgCX799Q9UqlTM73vSJJzq1AnbVXOsb9+GiI9PR3IyN7uJrFIF3cLCcODdd7H3zjsD5oOC9mPHIqxxY6w5cqRUOPrllw6oVKkIyckbAQBCCHSrVAmpn36Kbd71vWNHZQBtsXLlP8jKYgd7808+QeW4OKwUonSOHT3aDkIAycnrSv9mp4YNUfz111jXti0AIDs7AkAPbNy4C8nJhwAADcaORd2wMKyoUgVFXlpGc9sR9Oxa6g+ABAAfAljr/XwIICHYdRboDgTwler3YQA+1pwzD0AP1e+LAXS0cq3ex3EeiBqKj2D+/NJDhw5pKop0785JZyq89x5f5pdjsG6dxgGhk7B3001ElSv7JZoopm8/e3FKCts9VQ6UG24gat5cdc6zz3KOxbFjpYeKitgcr07XSP71V7bHqpL3nnqKXRCl0PHxFBaySTqgukqbNlyqw4uXX+ZLi4q8BxYv5gPTp/tdFhvLmbt+uPZazl/xOqaUkPtt27zf795Neslquklq993HjoqsLFqyZAkdPUrUv7/Kb5GVxUliI0dSULz1FqkTP/bv1/jGPB52GFx1ld9l99/PqUJ+mDqVlPwVBQFJoT178mRRGeaffJJN+H5YuZJpjR9feqhrV86ZK53bt93GNVxUThbdOXboEB985RW/Yfjl9Lz4IifpqXJ2VnvzSmfPVp2Xm8u5Q6qXMnw4v6dSKKnWKqfU1q0UmHrj8XCOlCoR8PPP+bxDh7wHvMk0m597joKiVy9OBPQ+29WreR56XQpUmiTz+ut+l7VuzfPHD3fcwann3mcbkNOTm8vJI5oyD126cK6pH156iZ+ttyRBfj7Teu011XNo2DAgIfKM5IEQ0SkiepCI2ns/DxKRhZ50QXEIgNrSWRuANu7I6Bwr15YtrriCwy1Udv1mzVS9o/fvZ9uopvKgbqnnNm34YhWtN97gdAwArNb8+CO3TFPFvQ4YwNYQv7LdSUlsW1aZsfzMYURshL7kEr9WehERbI5Xq8uklN+dM6c0V6V8eV/DIgABPh6ATSctWgCJiZpnduONHCnj1QYCzAvff8+mwauv9rvs5Zf9rA0+WgcPcuVJ76/FxVyZGIDvWWoiUHQbGt14Iw/ip58AsDXFr7T33Ll+4aOmUP6e18QTH8++gdJx/fknzw0NLd0S/zpmLL93efQom2xU5ivAoMx5164BZiy/sNSCAr7pvn39bDS65e9r1QowY/lFKCk+nosu8rN36s798uXZjDVrVumkCjDfTp3KJtKuPiODblVlIfj5L17MkWngqdm/v6qS7bRpQHQ0UlX2No+HfSWatBumtWNHaW/anTs5P6vUQqaYrzRmIt05dsMNHMHnTRTr0oWngVexZxNpTk7AfH3hBS41H0CLqNSMVa4c33rp81+7ls1vZRl95UVQBiKEaCqE+FIIsVAI8ZvyCcHf/htAEyFEAyFEOQCDAczRnDMHwC2CcT6ADCI6avHaskVUFG+us2aVvjm/BalsYEOH+l2Wl8eh9H7VYBUfwe+/l4Yh9uun6nT30088uTS0EhLYhh1QWXbQIHbken0Efgvy7795Z9Q0cN+8GXjmGZ0oyEGD+G97wxD9bLeKj2fIEL8N7OhRdqpqUiJ8m6Z340lI4D2tsBC8gc2cyatd01f0oYfYF+iH667jd+D1c4SHa6r7Tp7Mq1PTJUt3c+3enf1HXloBARGTJ7OvqHS1M7p04fQPP9Svz194aVWqxLmKpZdOnszjVmzZ8P2tAAYSE8NMZMaM0t3N710qQsKQIX6XNW2qE2qtbK4LF5Z61/0CNX75hY9r5tjw4dwPJ0AYGDjQF4oMzdzfsIG97xomGR/PMlBATszAgbwre80rfszo5EkeszdEWYFhX5eBA/lZzZ4NgH3hP/zglZWKi/m99OmDEtXDTknh9xTgJ+zfnxerl1EEOL6//x7o2NEbL+2D7ru89FIWOFW06tZV8eopU4CqVQPaW159tU54bosWnETipcUdU1WP5/vvmWNq5lhZwIoTfTrYdPUsgMdUH0cgomIA94GjvLYCmEZEm4UQdwshlHiOn8GhxLsAjAUw0uxap2OSxuDBLFX88gsAzYKcPJkdfqUB4YxLLwVefVUngWjQIN4MvJvr1q2sXZTSqlmTJToVVq3izSnAAdu/P3MVr2P+3XdVycPff+9jfips2sSdzwIqgF98MU9sL63OnbmJUlgYeDF6PAEb2K5d7EjUJCz7NBUvrTvu4GCShASwgzEtLYBWSQnvUaURRQoqVeJotOnTAY8Hu3axpL91K9g7v3lzAC0i3pMDStuHhfHG8/PPCM/N9Wcgqan8fgcPDmghd/JkQJoMY+BAzj7ds6f0HoqLwf9MncpBGJp2k4atXgcO5B3cG43lt7lOnswbWKl6w7jnHt3Ef6ZVWFgajeXHjCZPZhVU0wEsOppff0D3PK8fS5mvAeOKiAiQgFu14j0voJnSlVdy5JeXlrpBEmbM4OemEXgMGUj79rzmNE5+AKyZpKQE0DLsxVKtGq851T2Wnr99O79jDS2Aqw8EdBAsV461u9mzgcJCpKfzPrBuHXgPmTuX9wBN049VqwyaXN1wAwuc3tyqEyc4iAceDzMjb4Z9mUPPrqX+AFgT7Jx/yyekPhAiNt4nJXHMPrG5dPBg8tWtMa1VroM2bUpjvK+5hqhDB2LjbUSEbuXeAH+EGtdey/kUpQ4GYgeHarxqfPMNBcSll97zyJHsA1A7bjweHm/79gG0lFpMuhVVR4/mL3fu9D/erx+PTZPIceIEn65Tfszn+Pjtt1IT/88/E9cXi4gwLGWuiz/+IAJoyxNPUEkJ03rxRfLVONLJsfDLHVBDsY17fQTh4UTPPENUmmCiU2Z57Fgu/R6A7Gx+9t4/lJ3tfaVbtjCtd96xfo8eD1HduqVG9aFDuQDlsrlz2Qd0330Bl8yfb1Ljqls3Ll/u8dDtt7NLioqLuShZaeKORQweXFozLS2NzfseD7Ef0fs31Ni7l10PukV4H3+c3/+xY7RsGZP94w/iWm1eH496PSv+lO+/16Gl5L2sW0dLlpRON05y0vh4gkIpWjV7tn+9O2XxBSQecdkv3erX69fzNZ984n9cca7oVAEuCx+IFQbyIljyrwF2qCcgBE70M/EJOQMh4skaFka0cye1aeOtZzh0KDvMSrPCfDh2zKQct7JZLV3qc3w/8wxPVJ1azaNGsf9RF4qTf9IkWryY99SSseNUK8AfStVY9dhK7/mff/jL0aOppIQoJ4eoeNES8vcOB/5p3dzJw4fZw3vvvbRiBe9l+5bs4WeoUzI4wAmtRk4OM51rry2NQ/hxYhZvEoMHGzwYA5SUEDVvTpmNGxN5PNSkCdE7b5WwVKBJDlQQH1+aOxmIyy9nT3B+PsXEcC4fXXEFH9OtuGmCO+9kJqKOSrjnHk6sO3484PTbbuP+KLp46SV+UFu20Pr1vLHuutvbqmDt2oDTTeeYsvH9+iv98w/nINLMmXzMm+yqxqRJHAeyb58OLSUr9uuvfceUeWdQtdcQ27wFKV96SZELaMnU45yd663aq17PSr3BWbN0aKWm8rO/805auZKX4oK5BSw9BHi3g6CwkKhmTaLevenkSf6bH33o4XLBKme9GpUq6QSQEPG5HTvyJuHx0KhR3nzNwYN5/mdlBVxyphjIXp3PnmDXnY2fMmEgR47wQr7pJpo0iej3D9fyZmjQ62PQIKImTQz+SE4OZ0b37Em33FxCnWof5RCkAQN0T7/7bj5dF94NkZo3p7dfK6Ao5FFJvfpE7drpTlQlOkydrOx3z5dfTlStGv00MY0AD2W168HiUW5uAC0leEi3vDQRR6SUL0+LvjlAANGJa25jplKa7uzD9u2lfFAf3vTgfbP+YUHxBm9KuqbKLhHvBQMGGFSzJfJFlM2dy78rGo7BH4+ODkiI90EpO/7ZZ5SYSPTWDd4uYTpVdon41auVRT9s2sTXPvMMffQR0dcvHeBNTafKLhHva4aNj06c4Pl66638e3Y2Z2VffLHu6ffcwzxaF3l5PAcuvZTnVEkJa9D16+uWMFeEFF2h3ePhiMUWLeifv4ro+eeJCgYM4sgknWYqGRkc6Gb4zK66iqhaNVq7NJMAou3XP0XqMD313F6xgrQBlf646y6i6GjyHDrMS0dp2qVzQUEBP4IJEwLJEFFptd/cletY67lrCZlZK8qV49LvulCi037+mVq1Irqr9x5Wdx95RPf0M8JAzqVPmTAQIg6LBZhpNGnCu/qpU7qnXnedcdUDIiqNO1zS/B5aFdmDZ5BOaWkiljTr1DGh5S0VsbXTzTQF3m58ixfrnqo0xVOH8frd899/E4WH0/Eu19A7eJhPNugEZ1imQcGePUQxMZTWsjuNwrt8ssFOrGgWOm0oGKdOEVWrRgVNWtDNmEBFkdG6JjoiNnsALDjrIj+fsuvWZRPMrFm8OXbooLsZEnG4qWHTL4+HN+W4OBqW+BMdim/JUquOVkpkobnWkCFEkZH0dKvZ9Ff85cy99u7VPfXiiw35AePxx4kAOvjmJNrdazg/lD/+0D016Bzzls85/uxHtPlm7yRShQqroQgpBkujVHtZd+2zNAAz+GSDcNuvv+avDR4BKerCqRuGUyf8xc21hg4t/Vo9t/ftY4uUQa8y/iIqis3Ce/dyaZKuXXVrsStl8o2qt1BqKlFiInnOv4CScIKOVW3FDzgnJ+BUP1OqHvLzOWy5aVO6tH0q/ZV0FZe1L41Z9scZYyAAWgG4EcAtysfKdWfbp8wYSEEBJ1sAVByfaNJOjQV507aYHg83OQAoD1EGhlnGoEGs+ZriOW4qVAJBaU/oGdkZJSWsTKiVk4B7/vhj8ghBBNDhK+8w7E6Xk8OLMqAulRpTp1JJeAQRQKltLzFs16n4NgylQyKiRYvIU6ECEUBp1c4z9H2Y2rq9+PuLL0rbpWZXSLJWV8wIu3ezyQKggrAoE9WH36Np88ATJ0rbDhvb9BhduwaxruTksNnES2vfYP0mXURsETHUmImYufbuXUqrpP8AgyYX+kKKHzwe9lN4aeW26qyr4RJxWTXApFEXUSmjJICyEur4nSy9mX7wQSmtovIVub6bDo4eJUXxNMaUKb7nJcIM683l5pJiOTbGb78RRURwy+cgftczZcJ6AcASAMcBfAPgGIAZwa47Gz9lxkCIiDwe+l/vfdSlVaAkoUaPHpx0FQxb5u2hBZP1+5wrSElhH0Ew/PjebqqHvUqrc8vQu+d1s/ZQG6yjn+bqMw8ZbPxpH3XHMvpxpr6ET8QL8vPPda1b/jh0iLmMjiSnwNTW7cWSJUuIjh6l+2r9QLdfm2J4nsdjsbtrSgrNvel7mv2+kTrGqFPHZ1UyRHo6vd/xOxrY0KAwpxdt2xr2FvMhO5vm3DCeeuMXWvBLsuFp/foF0ZiJiPLzad6N39IQTKLsdCObEssyQgR5bsXFtPqh72gkPqG1ywLt+Ap0E3K18Hgoe9wUmtruNVo+05/TqOd2Tg5bog3NYV6kfTOLXsNTNPk5Y6Fizx4y13IVLFhAeXc9SIWL9LuIErEANns2BV+3S5fS3Np309ONp5qeVhYMxEopkxsAtAWwlohuF0JUA/CV/bivcxRCICuhHtL2mp+Wl8dhkcHQ/OoGaB7kHKs10orrNsR+GJSi9mLKFI5+LU2ENEB44wbYACDPhNbSpVz26oknAqIS/RB9Xj2cal4P0THG51Svzm1TgqJWLf6YQDeRzeCPrqjWHzU8xqccO8Z/7osvdAoSqpGUhD4TB5ucwAioxaSHuDj8fd7N+OdP89Muu0ynXpkWMTHY3f0WLJwB3FeoV1OfMWOGQaiyGlFR2N3jVnw/Dfi4GDB6ne3acei2bhMlBeHhSL3qZnz6ATDU5DzDMF41hEDMHYNw4x2mo8fs2Zz+sm1bQES0P7n+/fDM7f3wXmXjcyzPsd69Ed27t+kpmnJdxrjwQsy87EJfa4HTCCt5IHlE5AFQLISoBOAEgIZlO6x/Jwwbzqjw2GPeBjFBsG8f5w+aLd7x43WL5Qagf3/ORWjTxvicRYv0G+9oUb06JxyaLbTffgOefVYnd0CDxo25K9sVVxifk5rK4fbBnivAlX11+mmVQghO3tJtPKWBYVMjL5Q8hYAkTh1kZ3NDSjPoJp8ZjMtjwtgA4J13gIcftkYLAAoLjV9UeHiQTdoLw14lKgwYAHxlQfQ0bc4G/+90G5JJwhIzsjiuyEjOS/WrDmGAN980n6/Z2VzjM6AvkA6++QaYPz/4eaGGFQayWggRD07kWwPgHwB/mV7xH4VhwxkVBg3yKzRriDlz+DzdtqpefPqptU0/LCz4Zm51A0tK4gSo1q3NaUVFBf+bVjB/PrckPXgw+LkzZwb0APLD+edzdrxflV0DWGEgynnB0L9/QHWWADz2GHfGDYaxY0vzEx3D18nO+EW9+SZrWcFgZXNli3hwXHABJ4727Gl8ztVXc2dpU23Gi9hYrmJsBKsMJKBkiA6aNOGcT01CuS6+/jqgwr4fDh7knFO/Mu1nGazUwhpJROlE9DmAywHcSkTaLg4uEHzTATjj20rTNNM+x15YMnuAN8277uIKE05pEXHWa0AnNRu0srO5dLpOQ8ZSWDYJwNrzt4pmzQKKCOiOy6p0HkyweP55g06PGljZMGvWZC0xGK66ijOdk5IKDc+ZPNmaZHv55VyJxMx0dvPN3na2QRAZyYn6fqVpNOjaVVUrLgiISku56cLquxSCk/VDIRgpf8+KlmVljn3+eWnbldMKqUdBRPuIyGQb+m9j0CAuLWKGCy8ERo8OTsuqGm9lcmVkcA+MXbuMz7GqgeTnc4WHTz4xp2VlXBERLK0F1MzS0AKsjS3Ygly0iM1lVkwCH38MTJpk/L3M4g42Lo+HhQorZro5c4BbbzWX5k+eDG7mAngz7NpV0+tGA6vCQPXqLHVrypj5IS/P3Cem4NQpLiD4l4mdY/9+9llYgWG/di9ktMnjx7nAoRF++41LVW3ZEpyWVS3XyhzbsaO0otJpRYh4qQuAa+jdfLP5OTK2buV8p7Ss2Kc9Hq4TFQpaVjcdpZBcsHsEQqOBHDjAdflKKwk7QLVqXBPMTEtRj8uMOZw8yZJ7QBMlHWzaxB0HCw2UhpIS9ptZ2XSOHQPGjVP6t+jDqpBy4gQzXDNHrlXBIjeX67epejkF4LnngpsFFQSbF716AW+9Zc2fFQypqVyPzQoDD6UGYsX/WhZwGUgIcewYV3A32qA8Hi46K8NAQqGBWKH1yy9cWDcYhAgu0X35paoQZBBaUVHm45IxFdWsyTX5jCAjab79dkBdQT80asQVh5s2DU4r2POS1bIA42emtFu1Qmv3bq62u2+fseRgVUjZsYOFJ2/lc11YFSxCqX0DwRnI+eezD8qKefDBB7mkuxFkBZ5Qzf3y5X3Cw+lEUIVSCPEdEQ0LdswFhzzefz8X/NQLsZXZwLp25eKhZtFOO3ZYs8da0WZkEGxBRkeHbnFffz1v0lbu87cgTQZkFuSRI+YmlMJCFhTKlw++8fTvD7RsGXxcspppQFVhyPtmAHMnutVxWdn0jcZs9PeCablW59gtt5j7Zo4cYXoNLcSWLlzI1YQffFD/e5l3OXducD/P4sXW/EZqy0AoNCmrsJIH4jf1hRDh4K6ALjQINvFlJldSkk4PDA283TEtjatCBXO7+aOP8kY9YoQ1emaL+9NPeWFYyd84//zStuy6aN3aPOJLBqE0CUybBgwbxiXrvZ2DDXHVVfwxgl0GooeICM5LsfLMrERheauFB4UVBnLjjXJm0lBpIM8+a/79iy9yuOzhw8FpBZsXMnMsmD8oMTH4HqCgenUWUkJhnpWB4cwRQjwlhMgC0EYIken9ZIHzQGafthH+ixDMP1ChAtuvAxrE6CAjg3M8DhzQ/764GHjySW4JEAwxMdwT6v77jc+ZOrW0uV9QPPececTHpEn67Rj0MH8+8Pjjxt9v3sxN/Kzg1VeBBx4w/r5yZV5kVhy5AZ0XNZDZKDIz2VxkxMBltIbYWO6fYmSqiItjE+IllwSnZSUPxCqs+MYeftiaUBEezlK0Yo7Tg1V/CsCmnWCaUag05tq1OVDDLJhAwaRJbDozwq5dvC7NIsgUKObDhITg54YShjOHiN4golgAbxNRJe8nlogSieip0zjGfw2CSYfly7PUakUlPXqU+yEtX67/fX4+x+ib5T3IwKqtG+DGTWYStYx0GAxvvBHQJM8Qa9ea+3FGjuRFZsXWHexdyjCQTz9lLcWIVt267MRt1iw4reuvZ0etke9FKbJkBcrYCwv17Sh5eTxfFywITsuK2Sk727qEnJdnXhXh2WdZgLKCPn0CerH5IZT+lOuvZ3+iFXrLl5vncS1cyH3MzELmzzSs5IE8JYSoJYToJoS4SPmcjsH926AsIiOJISuLw1YDuv6Z0DKSnGSkVoBNU2ZRPjJS2JEjxpqRQssqMxo2zFwqlaEVyjyQBg04LNUomkbWwam+RovatVkS1XTftYV//mF/kbe9uymqVGGG2quXvp0qJweYOJF9bcFQtSqwerWvUaEeGjQw1xDVMPMNACzlW0m8BKyF8Vqd+7VqhU7KD2UY7x9/cIKst8PwaYOVnuijASyHf0tbbZt3F+BurTNmGEuHmzdzHsjKlcFphVICBjh/wMgURCS3UQ8Zwo5JI8gsyP37zTcoq5E7QPAF+eqr1ttEX389J8YZOX1l/Snqa7TIyGBfipUImm3beGxGIa7K3yjttW2CiAg26VWsqK8WyAR9REZyd12zLqoyQsqzz5qXPfnzT52WyQaw4rewOq7x49n5bYRnngHatrVGK5RhvNnZvK+cOmXtb4cKVoyf/QGcR0RXE9G13o+VEl//OVSrxovbaBHZCdcMxkBCsbkWF7M0KuOUN9uorYYqW6Elw9iCLcht27hgZCjQowdvclb9KYDxfc6ezUKHmVanIDMT+OEH4NAh/e9lNdOPPwY2bNDnkrK0vvzSWDiSFVJmzODETyPccAObN60g2BwbNYoLf4YCJ05wFKbVcZmF3ubns7nVSr2vUEdaWoUVBrIHwGkMDPv3IieH7cVG0RyhjLaR1UDMFlFkJGfYPmpRrwy2IA8dCp6Rb5WWzKZTuzZQv745LavPa8kS3tSN8houuQR45RVrtKxG54VCm5GdF08+CaxYoS/xyNJ68EFg1iz974qL2RwYKsEilH6Lq6+2WPUWwJgxwMCBxt/LzNeKFTkowuxdRkdb89lZiVwrCxjKT0KIjwEQgFwA64QQiwGUxkUQkUVr5n8HR49yPaMJE9i2r4UMA4mM5KiounX1v2/VinMRrEwu5W+erjwQIYLbsK3Sevdd67SeeMJckpTZdAoL2URiVMwyLY03RDOTjYIOHbj0i1GFVhlt0qpmKrO5FhToP+CSEg4nt1K9WKEVihB2wJp5x+o9XnklWweMsH49196yUlVg5052bodiXA89xB8jPPggl0eygjOlgZgp4Ku9/68BYFIz0oWCUOaBAJxIZAQh5BKGzLK0jx3jyKqHHjKvgKrAbKPweNgpbqUCLQC0b29+H1Yq51qFrD8FML7Phx/mJC8rZqeGDc0L/9nRTI0210aN2CRjtmGqER1tnAfSrp11c4wyNrP8lBdesP4+rWggVt9lnz78McL113M+0sSJwWkFY2wyGkgwWGhxU4q4ON4vKlUKzd+2CkMGQkTjT+dAzgUEi8K6+GIuOW51UkyezOfqlYbetIkrcD76qLnZRoGZ4+/UKbbDDx5sbVy33GKcZ1BQwM7PRo2sMRCzHBCA80Rq1TLvZaLghx+A994Dfv5ZfyE1a2ZdY7Mi6VvdKPLyWHKtW1ffzyRjwqpQgekYOcnbt+ePVbAGEpqKRmbRThUqcMKeVcTHc3CBHpT8HKuSfn4+0zKqpCubB1JYyNqZnmbcowebsq1g5Uoui/Luu/p7wqJFrOmamcwU1KtnPY8rlLAShbVRCLFB81kmhHhfCGFBgf/vQEkeMlpEdepwUx0r2bgA26eN4sR372Z7bCiiLmQd8hdfbFw0UlbLCoZbbmFGaQUnTnBsvdECHjPGvIqwGlZ8UFY3ne3bOTLHKEelTx++RyvMLSGBI9f0TKTKuHJyrOeC8Iaovw2sWsWa5N4gXTbVtIyk88JCDv82Sw5U44cfWMPTgxAs8FjZWAH2x1WvbmyOlPWnKNfo4amnONrPCo4e5UTB1FT977/80rzy79kAK6LHfADzANzk/cwFsAzcG/3bMhvZvxBRUTy5jTYdpeSylUqdgLm6LLtRv/22cetVWVrHj3MCo94mJWuD/+ADlp7MsrRl7ObKNU6RkABcc41x+2FZqdVsXJ07W2zbawGffMKmSivZywAHfTz+uH7ywP79wI8/Wn+e8+Zx0qQeNm9mKTsUXfPCw9npbSXxEgitMFCzJpeJCUXJECtaroyW1aaNtY6PoYQVBtKdiJ4ioo3ezzMALiaiNwHUL9vh/bsgBC/I227T/37yZPMMbi3M7MCyG/WmTcCvv+p/J8tAvv6aS9frSZOytHJz2Y+gV55cNvQzmHR42WXB6yIpqFWLk/GMOsuF0p+yZw9vsFZx7bUsnepB+RtW8kAAoEYNIDbWeR4IwIKAke9FltZXXxkz1dxcfjdWalep/6bevCCS26hvvpkbsxnlB3XoANx5p/NxKcetjisykkPUrfS6CSWsMJCKQohSd64QogsAxR17mkt3nf24/HLjqp65uTwhrHY0s8JAQhEWGRHBEShWHXBmG2JREUvAVmoBWaElG/ppRAvgTdpqccBguPtua73trYzr+eeth5ECwNKl3HNCD/n5/D6t5KcAXG9tzhz9UrWyeSA//MC9uc1oWX2X69ZxLogejhxhJmql/QAQXNKfMoULPYYCp05Z106Chd7KMBClftjZmAcyHMBXQoi9Qoh9AL4C8D8hRAwAi6k8/x3Mn2+cTCUboWFmwiop4QQjGTOKEa2ePVkKtppBa7YhNmvGJVusttc0oyW76VSpwuYgo6gumQVZUMDmig8+0P9+8ODQhVjm5VlnuIC5s1q2DtnUqcDs2foMRFbLnTDB+HmFMozXTqiyegxqCMG+FCtBGgAz7/PPN66eIJsHUqOGse9L9l2GMlTfKoLKKUT0N4DWQog4AIKI0lVfTyurgf1b8cADQKdOwAUXBH6XmyvHQMaPN86BuPde6z2hgdDngQChoWdGq0IFrvFjtUbUBReY9/CQMTuVK8dOTqMghd27OT/CyEeiRoUKLJl37qz/vey8MBMGZHwzgHkYb4UKHOEXCi1XloEotIgCN1hZBtKyJbeRrlEj8LuCAmYKLVua9wxRkJ3NZVTS0/W/l2EgrVubm5yMNDAjBAsxLguYlXO/2fv/w0KIhwHcCeAO1e8udFChQugkzXr1zHtlyKBmTaBJE30H/uzZ7B+wGtFlZhJYv55rZVkpwAdwuO8NN+iXa4iMBLp3D80zkLV1K50XjRZkr17Wq8GGhbFfzKiplKxmarZRX3118NBoLS2jRMIRIzgCKxQZ361accVhK5s0wH+TSL/MhywDadSIE0z1/vbx41yU0apz34o2GaoIxLp1jROJ9XDZZdY6ZIYSZiYsJdg01uDjQgdmi+iZZ8zLN2vxyy/AF1/of/fdd2yHt4r77mMfgJ7/Ze9eDpm0miNx/vm+HBUtDhxgm7JRyKQWPXpw7xA9JnHqFGthBw9ao7VnDye//fJL4HfFxRzAYNbhUYtgErWMpP/XX6ExewDm0nKfPuY9JrQwC+OVhdnzataMx2W1km1iIoe9mwVqyFQV2L1bvyy6rC/RTHgiAu64wzwBWI2MDH5fcwzStD/7zLwemBaTJnGC6+mEWSLhF97/Xzp9w/n3w2wRmbU11cP06RzVpReNsnIlJyVazZEwg6x5wUwykl2QZti9myX3uXN5MwkGItaA9BzlkZGcYCiDYEEMMgzk2muBfv30BYJXXpGrKmBm2khJYSHBSokVwJyBfPghNyz74QfrtIye18mTnBTXqJG1IJK77zYWkDp2ZIGnVStr49q5k8+dOjXQWR5qf4qRwGeEefOMuw4+/zyP10oDujMFK4mETYUQi4UQm7y/txFCWAyG/O+hfHnjGPyFC9neKkMrVKry/PlsDjp6VJ8WYD30MyuLI2D0ylzISod//82dAvWSxpTnGKooLFlcf72x30JWAzF7l717W+sgaAU338z5K1bx8svADz/ody3bvFkuu/n5541Lu4wdy+YVKyXrgyEhgTddmerRgP7zl2Ug8fHsa9OLWCSynuOlHpeZP8vqmgQ4GMBqNYlQwYruOhbAUwCKAICINgA4zcP89+Ddd9nsoodnnuEuglZhtunk5sr5U9LSgBUr9E1LymZo1YS1axcvYL1uibIaSHg4OySzs/XHBYQmJHjPHjaT/fijNVoA8NFH+tqfUkojVH6LpUut97YA2BRk1I9FVrCoUAEoX15/15PVsipVMm9lYLU0OQAsW8Ymx/37A7/btYvNpFaTJc02alkGUr8+r6NLLw38bv9+ns9WzdSRkfxMjPJTZH2mp04Zl/kvK1hhIBWISBvb4uZ/GKB5c2NTld1oG70sbdnJZba5Vq3KZgGrMLMDR0Zy2YhQaA12Qj8B/QWZnc2JZyUl1mgFw5dfykn6ZgykXz/uy2EVe/Zw50E9yM6L5cuBMWMa6ZZ/kdWyVq3iUh56G7sy960KKSdPsi9Lr3vnokUcqGHVz2Y2X1u2ZDOS1RB2M8hq30IYzwvZHCjgzITxWmEgJ4UQjcCl3SGEuAGAjiHEBcCLaMIE/e/sbPpE+lna5ctbr7iqnK+MQYvHHuNwWVlaehv17bezmaxyZefjUjYiq88sOppzWvQc8rK0AI5o0mubGhHBZWE6dLBOK5g2GaowXllaGzYAM2bUMXQwy9Bau5bDZY20XNl7VK7TIpSmzcREfs9WfUa5uexPGTcu8Ds7deBattRfK3Zomc2LsoKVfNV7AXwJoJkQ4jCAvQAMSum5+P57NmHpmRhkF/e993JUh57aP3Wq3LhCWSfqdOWBXHMNb0pW80CEMM5OtrMgPR79zTA/n8tGNGpkParojTf0c3o8HrkOjoB5ImEoNVOj6sF2aNlJlgT0N0RZ02ZUFGt4erlZ+/fzHLv8cmtFTsuVY9+QXv6GnTlmlLcUG8ttFmTf5dmYSLgHwGXezPMwItKRVVwoMHOiy0phlSqFrr5/YiI7hPX+/iOP8GSdNMkaLbONYtw4dthbTYKKjeVIK7349fh4DssNBexoIOXL6wcd7N/PtcAmTQKGDrVG66KL9I/biVozkzSffloub8bsXY4ZY51OMFq33qrvN7BDKzfXV7rDCoTgMHY9/PYbC2n79lljIBER/LdDYXI1Q1iYnIUB4PB6q5W+Q4WgDEQIEQXgenDhxAjhNWIS0ct2/6gQIgHAVC/NfQBuJKIAa6cQ4koAHwIIB/AVEY32Hn8RwP8AKHFATxORZJBm2aB8ebZf6vUL+P1366YdgKXcadO40ZNWxb7rLo6tHzXKGq3WrY2lnS1b2OZsFTExHLuu5+tZv54XpVUoWdp6+Ptv/owYYb22U48eHG2mDVaoWpWjVKxkjiswkvRlJWCATUUpKYGbqB3Gdt55XO1AD8OHW6cDnD5t0qgopREqVWJ/ol4Ukp1kvS1beN5qtVlZc5hyrt491q7NeRgyyX933ME+w9df9z9+7Bgz8KFD+TlYwciR1v9uqGDFBzIbQF+w4zxH9XGCJwEsJqImABZ7f/eDECIcwBgAVwFoAWCIEKKF6pT3iaid93NWMA/AvCdIu3bWzTEAF8x79VXOltVi/nxmMKGArK07PJzzGvSKRspGhynQCxSYN4/NeFaLTwKsMeiZFzp3ZmZspfmWAqONws6m/957+lVaY2M5P8WsY54W993H+UF62LzZuL+EHsxMRTfcwJGDVmHmG9uyxXp1AoA3zS1b9LWWhx8GkpOt0wLYRKXXw96OMGCkATZrxlGYMmt840YWurQ4dIjX/q5d1mmdCVhZmrWJaBARvUVE7yofh3+3LwAl2HU8gH4653QBsIuI9hBRIYAp3uvOahhJYQUFnFm6aZN1WmZ+C1l/yokTzMCmTw/8zo5E98svXDFVb1yyDCQxUT+DVomDl2EgZv4BWfTqpW+ismsO0xtXVBSHq1rpxx0MRUXs4DXqyaGHyy4DfvstGd27B363Zo31KgAA57Lk5+u3rb3rLrnKCWaoXVsuahAILgzIzP/evfUrGuTnc46U1WZegHG5HDtz7O23ucy8TC6KU1gxDKwQQrQmohDJuwCAakR0FACI6KgQQs+wUAuAevoeAqAuEnCfEOIWcO/2R/RMYAAghBgBYAQAVKtWDcmyoosX2dnZlq6tWzcC48dHYsOGfISH+2ZSWlokRo7sjgcf3IF+/awV7d+xozKAtlixYi2ysvz7e+bkXIjU1MNITt5jiVZGRiTWr++OpUt3okoV/0YKKSmdEBGRj+Rkf+5mds9DhnTDRRelYNQo/wSGAwdaweOJRnLyakvjAgCPpxt27z6J5GR/EXXnzsaIjKyG5GT9RDc9FBd3xOHDhUhO9p+uP/xQC998Ux/ff78KFSsax/Kq77l2bf5oH8GffyYCaI0tW1ajuFgngUUHJ082QnZ2DSQn+4e7ZWVFYP36eLRokYGEBGtZdr/+Wg3ffVcPn366xu9ecnLCAVyIo0d3ITnZekJATo7+e87I6Ib09MD3YgcnTnREQkLgezFCdnY4nn66NQYMOIyePf0zVv/6KwF5eWG4+GLrdlePpxMOHsxDcvJmL32+523bGiIysjaWLbOe4auYCbWPbPbsmvjgg6aYOXMFEhJ0Qid1kJfXBmlp4UhOXut3/K+/eO1v3foPwsOtxSvv2lUHmZmNsHDhUkRHB3IRq3uYFIhI9wNgI4ANALaAkwi3e3/fCGCD0XWq6xcB2KTz6QsgXXNums71A8F+D+X3YQA+9v5cDewXCQPwGoCvg42HiNCxY0eyiyVLlti+loho714igOjrr61fs2wZX7Nwof9xj4ePP/+8dVrZ2XzN6NGB391yC9FzzwUeN7vnunWJbr018PiIEUQ33GB9XAqtW24JPH7nnUQ1a8rR6t6dqFevwOOvvsr3X1Bgfr36nj0eosJC/l+NQ4eIJk8mOnXK+rieeoooIiLw+IoVPK75863T+uwzvuboUf/jx47x8TFjrNM6epTommsO06pVgd/FxhKNGmWd1rFjRPfdR/TXX4HftWghNy8yM/le3n478LtrriHq0ME6LSKiTp2IrrzS97vynvftI/rjDzlaRnj3XR5zerr1a/r0IWrfPvD4Dz8wrX/+sU7rgw/4mpMn9b93socBWE06e6qZBiJhldVlTIYVXIQQx4UQNYi1jxoA9Nr8HAKgroBUG8ARL+1Sr4AQYiyAn5yMNZTYu5drB910EzvHFNixtRrZpwsLOWrJTh6InrpslDkfjJ6eSUC2FpAZLTumNaOSIHl5bAqTqTn1xhvsA8jP93fm1qrFiWwyKF/el8GuDgiwE7ljZNq0Y/bIzQXmzauJgQP9iwASyZsjc3K4pW7HjoElYOz0wgGMw3hl54XRHKtXT85nAXCJm8hIzoZXw445rEUL7guihV3fDHB6c0HMiinqFBEIGeYAuBXAaO//s3XO+RtAEyFEAwCHweVThgKAwny85/UHazZnBXbsAB59lGPO1QzEzuRq354zqLXXREUB27fLjSssjGPYQ9kTpKxpffghdDOkzaDnKAV8m6HVTGjAf6NWM5D9+1lQ6N7dOkO6+WbgwgsD/77dhDEgcKOww0CMmFFJCY+3cWPn41Loy9xjZKRxuGxuLgcfyODZZ/V9aUuWsN9CpiNkWpp+TS87QopRaaPBg4G+feXrrSnjOF0ITR1neYwGcLkQYieAy72/QwhRUwjxMwAQUTGA+wAsALAVwDQiUjpHvyWE2CiE2ADgEgAWg1nLHkYv0Y5EER7OoYcyTmQz9O6t76xt1YqjhGRgtOkPHszRIzIYNoyjurRISpKXDo1gV2pVrlVj2jTWdPQqBBihQQPOkteGdjvRTLXjqlGD83CMCkDqwegeIyJ4c73tNue0AK4aLRtibORgtvMue/fWr2r78cfMXGRgpjHLCilGCAvjtW/UUE4P553HYcHaubRyJQu0e/faCI8MAovR9aEFEaUCCAjQI6IjAK5W/f4zgIAQXSIaVqYDdACjRdSxI2sNej00jJCVxRVOBwxgaVDBgQOc6f7CC3JVXOfODTzm8XDop9W6QgrGjNGXtJYvl09mMuphMH48byJWW8cC3BHy998DQyMvuEB+XEbv0o42uX8/P5trr/WXnu1oILVqcfkN7UaRkMAbiAxCafYwYyB9bcRPXnCBft8TO5F+O3ZweLM2G102mhEwZmxXXCGXZwRw2O/MmVygUY2FCzlU/623rGs0XbrwR4vjx7nE0h13hF5fOCMM5FyG0SIqX16+W1hxMfeYrlfPn4GkpfEmadRWUwbKZii7ubZvb0xPdnEXFXGYs9YWPGYMayEyDKSgQD9vxqh6rRnMGEh0tJxmuGIF+8W2bPFPDLviCn6XMoJFp06cI6PFqVO+3hdW32dUFFChQjGE8N8K9u1jqf39960XjSxXjj/agpUeD5frP+88uSS7X3/VP75okZxkDrA/a9GiwLBk2RIrgLEGcsUV/JFBSop+YcyVK3ntvyuZMKGEEKu1IGWNR0WFqJKoCmfKhHXOQtl0tOVMNm8G3nlHv7qoEYySEu1IwABLrdry5IqPQXYRLV8OzJoVeNwOA7npJn2zix3p0Ghx24mNb9mS28NqqwfYHRcQKLlWrcplTmRs3UZYupTLWciUhhcCmDfvj4D2vJmZTEfGTCcEM/DnnvM/npvLzGjaNOu0zFC3rhzDBczzQGTna7duwJVXBh5PSZGr6AAoPekD52deHjNjGSFl1So2PWoZr7Jf6IX2OoXLQEKMevVYytF2PvvzT656K2MqKleOJS2tI9mO3RzgZEJtvwC7GsgXXwSanjwe3iBDJdHZkQ5jYvietMlcl13GPggZtGrFTk6tGcXOpmOkzaxbB0ycKMfgdu7k/BRtK9RQ1mJS5lwoaNkd16BBwP33Bx5/5x256tHK3zZK2JN9lyNH6tcJu/NOzniXgSI4aFv32hlXVBTPIyOB09VA/gWIiODFrV0sdiJkhOANUdtsyQ4tQH+jjoxku7xsJrQercJCloBlHd+hDOONiWHTn1ZyViQ6GZSUsMaoXdwPPSQf+mzEQGbOZPOajOM1IoJ7m5w65X/crmb60UeNAzZEu3Pssce4V0ooxrV/f2D5EyL+GwsXytFS5phWsJg9mzO4QwEngRpai4UdWkbBFVWq8Lp0NZB/ATwebhOqLStuVwqrWDFwM6xQgX0QcXFytPQ2akWSlS12p0crOppttzKRO0a0AHtSWPv23JNEa4e3Q2vdOnZMa+tOtW4tV1kWMI/Ok2m0BPi0xVBppn/+mRjgxLXLQGbPDszQtjv3Y2IC71HRIuwITx5PYPht48Zy9dEA1kpjYwOZkZ1Nv2FD1o61tIqLQ6flDhnC6zIqKvQMxHWihxhCcC7C44/7R0jZNQkcPBhoB+3Vy7gjnRmio9mMFQqEMg+kQgWf2Um9ke7bJ+8sveoq/mgRyjDe339nLUCvfpQRWrTgysJNmvgft+NPMWIgdiX9qKiSgHtMTGTneVKSHC29WmROGIhWy7JLa+BA7jqoXUtjxrDQoVe/ywhEbBXQFiHNy5PrnwKw9q8Xwv7NN3I1tYD/Vh7IOQshWGvQmp1ycnijlN0QQ5UDAnCpc60fYMECTnjcsEGOlrpsvYJdu4A2bYyjZ4xw6aXseNUumPh4+YQxgOloaYXSb/H00xxCLYOYGI6e0mqNThibdo717cvZ0fIMxBNwj926AT/9JC+d6/XDadiQo8b0GjqZQU8DsasZNW3KFY+1bQEeekg/os0MoTQ7mUE2nyQ2lsPYW7f2P/7SS/IWBqtwGUgZoGLFwIn/4oty0TEK3nknsFfA+PEctWTUuMoIjz/OoYFqpKdz2KvVfhsK/vc/ZjrqSZ6ezuWpZXMKevXiDVnNLHNz2da9cqUcrfnz2a+zZk3gePUiZ8xgFsYru4EVFABjxwZWMM7NlQ9gCAvjyLUWLfyPn3ceO55lhY5y5QIZiF0oQQxqxMVxBKBsg6QOHdh2r4ZdDeTwYTbVqpluURGbiuxqgNr7fOIJefPtqlXMpLXz/LXXeO3LoEIFrt6gDvkHfJUTygIuAykD6GkgMTH6SVHBsGgR25XV2L8fWL1av9mOLOyG8daowZKOdtMH5DfEggJe4Gr7dHo6LyDZnidRUawVaRn4Cy+wGUMGRqG3dqLDSkq4MZbWn/LOO/rh0MEwcSJn/auxeTOwbJk8raSkggDTy8cf83yVLSVTrVpgSPLBg3yPssmqjz0GTJjgf6xhQxZ4BgyQo7VsGWto6jwQuz4jZX5r1/itt1rPmVFj//7AnK7Zszl3RhZ5efolbuz06LECl4GUAfQYyIQJ9goN6kVhKfWxZM1hL7wA1Knjf8zupr99O28yGaoq804cr7Vr+0fcKPcsOy49/wARL9DiYnlaL7+sn71sxxwmROCGXKeO9Y5zwfD++4FMxQqee24rfvzR/9ipU9ycSzY/5fvvA02Yy5bxhq/XHlgW4eGcOxMKc6QTc9jw4YGJr5s2yeeBmPmz7Gz6VaoENgFzGci/DL/9xhV51Zg40V7VWz1zWHa2fgXPYCguDlzECm3ZjXr1ara3HjvmO2Z3QSr3omaUys+y92lEq3JlVu9lEBHBvhmtGcXOgjQKyZ48mZtzyaJ798AM/Zyc0PXEzs1lbU5WSNGD3Xf5+ecsWKjDqHft4tpV+yVLveppk3aDDjp2ZHOkWhjzeFgj/+gjOVpmEXV2/Cl6ZVbsBGpYhctAygCxsYE5B9nZ9ha3kQZih4FER7MpRW0qUuzmspKmnkSXkMAhiTJ93wH9RWSXsenRsqvNAGxa00qVP//MzldZ6Gmmr7xi3BPeDCUlgWYPu/Ni5sxaAZ0X7UqtEyYEJtHafZf5+fz81e9y2zb2D6SkGF+nB70cibp1mRHJmsMA1mrVyZ8KXdnnH2oGohcd2aGDXMSgDFwGUgb4/nuOfFAjJ8fe4k5ICFzIjRtzRJUs9Db9fv04ckfW8apHq2dPNl9ozWTBoKc1KAtK9pklJHDPcHXLUbsSMMChn88/73+sSxe5MucK9KKK7GoNoRQsDh6sEJCYZ5eB7NzJyZHqKLhQmiPt0tKbrxERzERkI/22bGHNbMYM3zG7TDI2ltegtkZY+fI8l2Whx0Deeos/ZQE3D6QMsHgxRwOpQz3taiCvvhpYHl27oVmFOnqkUiV7NBSEMuZcj4FceSUnUMoytkqV2DejhhMGoi2BUVAATJrEEp1eX2wzLFgQuFnZ3fRjYri6rJZWlSrytMqV8wSYPbp0sRdCHRPjK2mjzJGcHNbIZfpkKLSU6xXYfZfNmnFyrzrEdc8eNiHeequc0FOhAjPIUDC2ChX0gyh275ajo8CoUnBZwdVAygCh9FuEEq1acblvdcjuHXfwcVnoMZD33gMaNZIvXFi9OpeTaNfO/7jSVEgWhYX+i8gpA1HfY1oa1zzSVhqwgkaNAst9O9FAtHPsk0/Y6S8LJQ9ErTXcdVdgyLcVKM9YPbaRI9kvaJeWOlzW7ruMjWUNOTHRd2zrVvZxqf14VqAXhWVXYw417rknMNqwfXvgqafK5u+5DKQMoNi61Qvy4EGOkpHF4sVA//7+dvgrrmAHtiwuvJAbDqmzizMz5TNeATbt7NnDORwKjh7lj6zWEBfHXRzVeQ2LFgH33isfRgrwJvH0077fa9dmk6I2C9wKtAwkK4v/t7NR/Pijv7+jqIiZnR1avXsH+hq6duVkRVlERZXolvmwA73NtW5dezb4unWBG27wfz52Jf38fNY21J08nQZqqOdmzZrA11/LNfNS0Ly5f2HS9HRe87IJuQAzEK0/a8+esstOdxlIGaBiRXZyqqNHypWz5xQ7coQ3HnUZ+J077fcC0WZp25WAo6O5AKP6nrKy7Jk9AL4ntSS4ejXw6af2MvG10nmDBmz2s9Pd0IiB2LnP777z7+8QEcHNwUaOlKd1++3sTFZj5kwOJZVFQkIhWrb0ZyDdu9tzLlepwpqWOmT61185q10W7doB06f799F5+ml+B7KFMXNzOflSHfFmVxiIjg4MyU5M5HdiZ47l5vqbI9PSeM0fPixPS0kMVqCUXSkrzchlIGWAihXZ9KJIOHl5LE3//rs9WkCgvdXOhFi7lheeejFnZ9vbDHNygNGjeaNX4ISBtG7tr6Hl5PAitdMnQxvtlJnJi1FbYNEKHn6YpToFTsxh2nEJwbZ32ag1BUVF/sLAkCEsZcvi6quPYdMmf0EiLc0e8+7Th0Nt1UEG778fGFRiF2Fh9k2RgL8wYPddCsEaszo/KCWFs8ntSPpagcdJ1ODtt/uXlM/PZ5NyWTGQ/7wTvaioCIcOHUJ+EM9TXFwctm7daolmr16cQZ2Swp+SEi6YVr48211lUK8eO+SJfNd+9x1v1LK0wsO5rW1Sku/aF19kSViPlvqeo6OjUbt2bUR6PaFFRWxXjYrymU2cMBC9RVSxor3+0lpa48ezyS8lRb44oNZM5MSEpWUgJ05w6fOBA+Ud8qNH8/PPy2MmW1jI7yRUG4VdwUIPdrXcAwfYVPrxx8DNN/Oxb7/lnjayfcwVQUTPN2ZnbNqopl9/ZQ1n+3b5zqPa8i9O/ClajdmJwGMF/3kGcujQIcTGxqJ+/foQJrtVVlYWYm2uqPx8/tSvL7+BZWezBNGwIfsKlOiPmjXlS6MUFvKnXj1ftE5cHDur9aJ3lHsmIqSmpuLQoUNo4G0cojwKdXmKrl0D6zNZhXZztRv2DBhLdHboHTnC0njLlvz7xRdzDbBGjZyP6+BBduK2bSvPQJQQ25wc3hyd3OO6dfF4+mkWTJT7sisM7N7NdcdefJE7LQI8turV5WlFRbFJRj3H5s3jki2yDEQIpqfeXB9/nLVLWXMYwHSKi33PyAkzCuV81VZDFoI101BVO9DiP89A8vPzgzIPWeTlsT2/Rg1+oUpUkp2IovBw/wlOxFVq7fhTlL+vNuVYYUJCCCQmJiJFlb0VHs4TXF3KRFtCQQZaBkJk37Rzxx3+zzo7m7UsO7XDnnqK+1somc8VKwZWO7WKihVZkCgu5vE43XQA3ngSE51tOgUFYVi5kjW0Ro342dtlIMXFHKE2fLjvmF1hwCiM165goZXOy5Xzj8qSwQUXsEColIBx8vz79PHv+SME05bt9wMEhp0nJfnMmto+LaHAf56BAAgp8wB4EaWm8uRUsr8Bezbl8uW5RLqCsDB7SWzqv6+MR3GoCxHcVKT3jCpVki+QZwQtAxk71j4t9eYFODOHxcX5M8m//+b2xCNGyEuuDz3EvjCFuTnZdLSbq91ENgCoUIE93sq79HhYMpfpkaHAyGdnb1yBtJxopkuW+GvaEyeyoPfoo/K0tImcTp6/9u9feqn96rmh7NNjBS4DKQNoJX2PhzevUNQVcgIhuFqqMsmJuDFVrVqsLclCy0CUngvvvSdP65ln7JkS9JCTw5u+ol05kVrj4nyhzkJwFM/zz3OehCy0yZtONh0tA6lXj0uD2zOt8URV3mV4eGAypuy41Jvrb7/ZC4YIC+MNUcuMate2NzZtntGsWVzA0w4D0Wrf2dk8f2XbIijQNlOzi2uv9U+KXLSIQ4IXLXJOWw9uFFYZQJH0FdNVXBzXozHaKPbt24dWBtl8RDzJlTyQnBzgmWc+xxdfTNA9X8G3336L++67L+B4nTrAp59ygxGFwdllbH/84V8g8tgxezklAHDddf79OvR6l1jFY4/5a22DB9uPAqpUyT/rOCuLTWGyWdUA2+6fftoXZulEA2nalO9TkagrVGAflKyPDQBiYvw1EG0Iuhwt/l/NQJo2DSzVYRV33MHFCxUUF9sXBubMgV/VYSeChdZvMWwYlzCyg4cf9teMpkzhXC87msTFFwMPPuj7PSuL79MOA7cCl4GUAfR8DVbMRHoQgieAMplKSoD+/e/G0KG32BqbxwO8/npoGEhios8Xo8Sb243cOXCAzUMKZs0C/vrLHq34eJYOFWZ2+eW8EdmBYodWpE0n97hrF/DGG774/ltuYcHAjkR93nkcCaTkHezZw0mi6nwhq6hYsRhduvjuddMm3nC0FaWtIDKSo/IU30JhIWuk2kZaVvHJJ/4l6jds4FIydvDBB/55OE4YiNbk2qqVvbwZgJ+ZEt0HcCTXwoX2NPKsLK7VpfhU3Cis0wxty1eAQzmHDeNQu6uvDvz+ttv4c/IkZ84CPpV2xQpe1BkZvNiNmEhJSQn+97//YcWKFahVqxZmz56NI0eO4N5778WBAymIiamA774bi6pVm+HLL19EgwYV8dRTj+Lvv//GnXfeiZiYGPTo0QPz58/HJm822ZEjR3DllVdi9+7d6N+/P9566y3cddeTyMvLQ7t27XDeeS3x2GOTbDOQadM46uapp1gaI7K/uY4ezfQUTSs93Z4TEWAGUlzs6/a3fTsvoFq15GldcglHJyljycpytukoNAA2d9h14hKxxhAZydrHypXs++nRw0415BL8+afvdyehyoC/IJCWBjzyCDMCrQnJKpSgAwV2TT2VKvn7FrKyAkvLWMX11/trRn/9xe+ka1d5WrGxvgjJcuXs9/sBuLfOsGFstWjSpOwZiKuBlBEqVvRJEDk57FQ3m/g7d+7Evffei82bNyM+Ph4zZ87EiBEj8PHHH2PatDV48sl3MHLkyFKtQaF1++234/PPP8fKlSsRrplx69atw9SpU7Fx40ZMnToVBw8exKOPjkZ0dHmsW7cOX33FopzdvusLFgBjxvDPTjedypWZaSiO/YwMBHTJswrlOiVbf8AAf7VeBk2acA6CuuCj3XvUjmvGDC7nbgenTjG9r77i3xUNye4zU0PZdEKRB6KMy64w0Ls3O5UB1p6HDWNTlB1oAyJyc+2/y759/efUs8/aK/EP+N6ZMjYnfV30NGbA1UBOG4xC3bKyWNIzC4VLStL/vqQkuDTRoEEDtPOKaB07dsS+ffuwYsUKDBw4UGWPLvCL6EpPT0dWVha6ecNlhg4dip9UaeaXXnop4rwzqkWLFti/fz+qV69TatqJjOT4fLutcStV8k3UiAiO/7cb4hofz88pO5ufVVGRMw0E4LHVqsUbtt2NNSeHAw2aNWM79TffBJZRtwpFM1AYyLx57Nx87jl5WopDXqGl/G/3mV1+Oddxev11Z+VaAK5uGxvLWodTBlKhgr/PaOJELg5oB1oGsnOnveoEADOf48fZqsBr0V75dWVcAI+tShXWLO0+e2VeKP6sVq24+GdZNZRyGUgZ4dAhnlg1a7IKHoyBRKl28fDwcBw/fhzx8fFYt24d9u9nqbx+fZ6oSntUCuKx1tIsLi72G0d0tP2IFoAna3Y2L8IqVTir2i6UzTUtjTeNOnXsmxc6dGBbt+JQdsJA9u7lhLhp0zhjPD7ePi0tA3GiZUVGspSqbIjp6SwI2HWWHjzo2wCdMpADB3wbs1MGot70ledm95kpUYPKshHCftTUN99w35kTJ3juZ2Rwsq8dtG4NjBrl0zqqV7dv7tNqIFddxZ+ygmvCKiNkZ/tHtchO1EqVKqFBgwaYPn066tUD6tUjrF+/HvHxvBEJAVSuXBmxsbFYtWoVAGDKlClB6UZEABERkSgqKkJxMTM3u5FTar9AcbF8GXc11AwkKYk3IbuO78aNObKlalW2K+fm2t90tAvy7be5tIwdxMezRqNUUnbi51HoqTUQJ+YrdUh2q1YcBWcnoks7LqcMRHuPTmg99JDPB1JYGIY77uBq13bHpR5TRob9cbVrx4EGSij9O+/YC2AAfGNQ3mVhof31bQUuAykjRET4JxDaCfucNGkSxo0bh7Zt26Jly5aYPXt2wGQYN24cRowYgQsuuABEVGqyMkJcHDBs2Ai0adMGN954k+3oGMBfXf7+e77HPXvs0brgAq4mazfcU43iYnacp6Y69w1oTQKvvMK+HzsQgrUrxX/lZNMB/KXz115zlmmsZiBdugBvvmnfDl+5si8arE8fFgbsltJQ8nA8HucaSFISzy8hgMzMCHzzDZux7CCUDEQJEw9FI6hq1YAvvvAVehw82L42YwWuCauMEB7uYyDBMsfr169fGjkFAI+qMpt++eUXpKSwqtyiBYeCDh78Ipo14+9btmyJDRs2AABGjx6NTt7Khrfddhtuu+22Ujpq38iYMW8CeBMHDgR37pvhtttYSwgLY6eux2N/EdWs6QuD/PNPztv44AP5wnQAR3I1a8YO/ltv5T7ddvo0AD4zTkYGM6asLPslVgDuLlmtGvuLcnKcaQ2jRvnGUqWKvW6ECuLifL6GU6d4/oZCa4iKkm9xrMZFF7E2VFzMfrEqVew//5072RQ5fDiQnR1ROlY7UDMQItZKZWvTKdi/n1sOjBvH66l3b47+s9MEqkIFrpKgID09dEUx9eAykDJCRIR/TwQnKCnhPBCPh2mqo6bmzZuHN954A8XFxahXrx6+/fZbU1oKDWV8dm3AgP+1isRpd0EWFHC5+yZN2Mwwfz6r8nagdqLHxHDkjl2EhfECzMhwLgEDHHlVty4zkK1bnc0RdcmWb75hCfvaa+3R6tLFtzHfey+X6bcrnbdqxWVQPB4OEvj7b06gtCOoXHYZfwCOxjpxwt6YABa+nn2W6YSSgQihH/5vFVoz6apVvuKddrBuHUddNW7M47PL2KzANWGVEcqV44/HwzHZdhK8FCiOb8VnoTaHDRo0COvWrcOmTZswb948VAkihmZnczJWTo5zBnLyJJf0+OMPllrj4uwnJebmcvbtjz/6ckHsStTR0b5KrikpPD47nQ0VTJ7MUp3yDp1oIGrzjhD2TJsK0tJ8vbNHj7afYAcATzzhCwlOS7MfUQSwFL1gATPf+fPZHGZXy1VMV+pig3ahNkdmZfHEt/sua9dmDbltWx7f5MkcOONkXBkZLCxmZTkTUq66ylduPj3d2XwNBpeBlBGqVWNJrLiYJ6yTdqHKJlNUxB8nm47CMIqKnDMQITjy6p9/mIE4mahxcUwvLY2lTCGcbWIJCcyIfv2VW/naXdwA2/FbtPBpIE4ZiFKi/LbbgGXL7NN65hng/PP557S00OSAAM7fpRpOx/XbbzyWP//khM4BA+wHa6gl/aKiMMTGOguuePBBNrHu3s29QP75xx6t8HCflqv4oZz4xtT+rFDOCz24DKSMoZgonGz6yrUFBbx4QmF2KinhKCW7kTYAL+zwcN7wr77av3OfLMLCeCwnTvAnKclZ8cnq1dmmr9j1q1WzT2vDBpakO3Vi6fCKK+zTUjSQo0e5jtiBA/ZpJSbyZl9YyL4sJz6QmTP5GR04wONzwkB+/51Dzv/5h9+l3XBswLeRpqdzR82FC+0nvioCSWoqcNFFJ5GZKd+HRY3t233PC3C2UcfF8T2GwkyqDq64/35n8zUYXB9IGaGggG35Sgaok02/XDmWUMLCeGN0klWq1kCc2kaVTT8lBRg61BktgMdz5Ajbf9VlIuzgxRfZobhoET8/JxLdxx9zG+CjR51n9FatykKFYst3sulXr84Cxfbt/L8TJhkZ6WPeTjWQiAh2DJ88yXPDyT0qAs7Jk86ZkTKO48dRGoTiBD16cG7QhRfy707G9uijvlJHl1ziLBoxIcHXY/3ll+3TsQKXgZQRwsJ83QQBZ6XKIyN9kpJT00JYGC/wggL2O0RFOZP0q1blhX30KC9QJ4yyVi0uNGi3VIUa113H/0+axGN0Uiq7alXeCGfPZn/Km2/al4Jfe40LKipx/k42HaXL3/r1zmkpm2tKCkfAOelgpzCy48eZnhNayj0ePeqcgURG8pgSE4GHH66JKVOAzz+3T69yZd6oQyEMqMui/PabfToAP/+tW1kzzcjg+7U7X4PhjJiwhBAJQohfhRA7vf/rbotCiK+FECeEEJvsXH8mERHBm1ZhIW/Soeh1waWs7YnAzz//PBZ5mwL89NMHAHKxZYvzhlC1a3P8es2avLE6wWuvcShjKHD8OC/Eo0edbToAX19SwiGgY8c6W4zKtcqm42RsSuJZYiJv1H362KeljOPECc6wVupPORnX4cMcyfXpp/ZplS/P2uOxY/xOnWhZAN9neDiwfn284w59NWrwuFJSmKYT4S47234OlRb33ce+ybVr+X7tJr5awZnygTwJYDERNQGw2Pu7Hr4FcKXOcavXnzEoPZhjYrhUgdNmMfv2cXiex2PPifjyyy/jMm885FdffYCSklwAzhnbTz8B77/PPztNAmzXjs1XrVuzw9QJpk/nTfChh+yHAytQNsTVq+319lZj/35g0CBO+qtUyRkDOe884LPP2MGflOTr4GcHivS8axeXA7fbDwTgOR8Xx+bIyEjnZr8XXwSuuYaflROfBQB8+y3Ph7S0co7fZY0afI8PPMCht04Ei+ef5x42Y8awY95JV8HOndnvEQr/XzCcKRNWXwA9vT+PB5AM4AntSUS0VAhR3+710njoIcPGBeWtVETUoFE+kNe0HWj8B4YM5IknnkC9evUwcuRIAMCLL76I2NhYeDweTJs2DQUFBejfvz/uvNPXESksjOtgPf7445g/fz6EEHj22WcxaNAgAMBbb72F7777DmFhYbjqqqswevRo3HbbbejTpw+OHDmCI0eO4OqrL0GlSkm4666bsWXLJrzv5QJjx47F1q1b8Z7FtoJhYcC2bfyzU7vyyZNcw2rTJmdRa4CvLlFMjM9GbRdNmvD/O3Y4ryskBGsyX37J2ftOBIvERODuu9nk9803wAsv2KcXG8tZy4cPMxNfs4ZritnFkCHMOO65hx25LVrYp6VUuQ2FM/jnnzkoIje3nCPTGsBa99y5zHydarnVq3Oo+aZNXJfMSQOolBSOWtu+3Ue7rHCmGEg1IjoKAER0VAgh+/gtXy+EGAFgBABUq1YNyRq9NS4uDlne6nFRhYUIMyrPSYRiydKdYWECJSWEU6eyUa6cfkGaa6+9Fk8++SSGebPdpkyZglGjRmHVqlVYvHgxiAiDBg1C27a/om7dyyEEkJWVhdmzZ2PNmjX4448/kJqaip49e6JDhw7YsGEDZs6ciUWLFqFChQo4deoUsrKyUFRUhLy8PNx+++14++138emnS5CYmIAaNU7g9ddfxXPPPYfIyEh89dVX+PDDD5GVlYWSkpLSZwMA+fn5Ac/v1KlyuP56rgZ88uQyJCfbLG8KYM+eGIwezSnjBQVrkJycFeQKY+TkRAG4AHfdlYk339yA2FhrGXvZ2dkB91hYGIYPPojFQw+1R4UKh5CcvMv2uEpKBMqV64Fffz2CJk1226aj4PDhaDz/fCtkZESiZ8+VtmhkZ2fj99+TcdddwLRptQE0xsGDfyAz036W46BBwKpVCXjjjTZo2fIfnDhh31aanx+GI0fKo2FDB8k8XpSUNMaBA9VBVA7Fxc7eZbNmFfH449F47LFI1K6dh3bt0m3TSkurBqA5li7NQFxcFH7/fZVtWn/9VRlPPNEWXbqkAkjE1q2/Y9cu0p3bjkFEZfIBsAjAJp1PXwDpmnPTTOjUB7BJc8zy9epPx44dSYstW7YEHNNDZmampfO0KC4Ofk6zZs3o8OHDtG7dOurWrRs98sgjVK9ePWrbti21bduWGjVqRGPHfkVpaUQxMTFERPTQQw/RuHHjSmncfPPNNHv2bHr44Yfpyy+/DPgbt956K02fPp2IiOrVq0fr1qVQRgZ/N3z4cPrhhx9o69at1KlTJ8N71ntWRUVEF1xAdOedwe8zGIqKiGrWJIqLIyoocEbL4yEqV467i1h8xUREtGTJEt3jKSlEtWsTjR/vbFxERO3b87hmzXJO64ormFbPnvZpqO956FCiKlWcj4uI6K23eGxHjjij89xzTKd1a6JNm5zR+uQTphUbW0hffOGMloLKlYnuuccZjYULlU44RBdf7IzWunVMp3JloqQk33GjuW0FAFaTzp5aZhoIEV1m9J0Q4rgQogax9lADgGyBAqfXnzZYsXrdcMMNmDFjBo4dO4bBgwdj3759eOqpp3DXXXcZXkMGJTaJCMKCHaNWLV8G7PDhw/H666+jWbNmuP3224MPWIWICO66GApERLAtGXDumxGCzRW7dzuLAlKQlMS+gVBg4EB2cIYiWa97d8767tHDOa3PPuOM6lDQmjGDa1gBzk0oSo+ZjRudPzPFzPrii5sxYkQ7R7SKith8mJZmv5S7ArVvp1EjZ7SU2nutWoUmvN4MZ8qJPgfArd6fbwUw+zRff1Zh8ODBmDJlCmbMmIEbbrgBV1xxBb7++mtkezsXHT58GCc0RYAuuugiTJ06FSUlJUhJScHSpUvRpUsX9O7dG19//TVyc9lJfurUqYC/Fxsb62ea6tq1Kw4ePIjJkydjyJAhZXinwVGnjrPie2pceql/YTmniI0NTWG6J59kZ/rFFzunNWoU56k84dwDiIED2VkdityB889nAeWhh5wHkHTvzv8nJTnPXWrbliO7Tp602UVNBY/H18LabpMrBXXqsP+vRw/n8yImhnNK6tRhH1lZ4kz5QEYDmCaEuBPAAQADAUAIURPAV0R0tff378HO8iQhxCEALxDROKPr/61o2bIlsrKyUKtWLdSoUQM1atTA1q1bcYG3JnPFihUxceJEVFV56vr374+VK1eibdu2EELgrbfeQvXq1XHllVdi3bp16NSpE8qVK4err74ar7/+ut/fGzFiBK666irUqFEDS5YsAQDceOONWLduHSqXZeEcFwB4Qw1F2XqAHdX33RcaWklJHFUXCtSuzSHUTpzBCmrWBJYsCY1gkZTE0Ulr1hwH4Ew1jYricjSrVvmYnF0IwT1sHn7YGR0FXbo412QsQc+uda5+zoQP5N+Ca665hhYtWuR3zIoP5FyDEzvxvxXuPZ972LSJ6IEHiPLzfcfKwgfi1sL6jyM9PR1NmzZF+fLlcamT7DEXLlycNWjZEvjwQ9aSyhJuKZP/OOLj47Fjx44zPQwXLlz8C+FqIDCOaHLhg/uMXLhwocV/noFER0cjNTXV3SBNQERITU1FdCg8oi5cuDhn8J83YdWuXRuHDh1CSkqK6Xn5+fn/uQ1Ufc/R0dGoXbv2GR6RCxcuzib85xlIZGQkGjRoEPS85ORktHca7P0vw3/xnl24cGEd/3kTlgsXLly4sAeXgbhw4cKFC1twGYgLFy5cuLAF8V+KPhJCpADYb/PyJAAnQzicfwPce/5vwL3n/wac3HM9Igpo2vufYiBOIIRYTUSdzvQ4Tifce/5vwL3n/wbK4p5dE5YLFy5cuLAFl4G4cOHChQtbcBmIdXx5pgdwBuDe838D7j3/NxDye3Z9IC5cuHDhwhZcDcSFCxcuXNiCy0BcuHDhwoUtuAzEAoQQVwohtgshdgkhnjzT4wkFhBB1hBBLhBBbhRCbhRAPeo8nCCF+FULs9P5fWXXNU95nsF0IccWZG70zCCHChRBrhRA/eX8/p+9ZCBEvhJghhNjmfd8X/AfueZR3Xm8SQnwvhIg+1+5ZCPG1EOKEEGKT6pj0PQohOgohNnq/+0gIiS72em0K3Y/vAyAcwG4ADQGUA7AeQIszPa4Q3FcNAB28P8cC2AGgBYC3ADzpPf4kgDe9P7fw3nsUgAbeZxJ+pu/D5r0/DGAygJ+8v5/T9wxgPIDh3p/LAYg/l+8ZQC0AewGU9/4+DcBt59o9A7gIQAcAm1THpO8RwF8ALgAgAMwHcJXVMbgaSHB0AbCLiPYQUSGAKQD6nuExOQYRHSWif7w/ZwHYCl54fcEbDrz/9/P+3BfAFCIqIKK9AHaBn82/CkKI2gCuAfCV6vA5e89CiErgjWYcABBRIRGl4xy+Zy8iAJQXQkQAqADgCM6xeyaipQBOaQ5L3aMQogaASkS0kpibTFBdExQuAwmOWgAOqn4/5D12zkAIUR9AewB/AqhGREcBZjIAqnpPO1eewwcAHgfgUR07l++5IYAUAN94zXZfCSFicA7fMxEdBvAOgAMAjgLIIKKFOIfvWQXZe6zl/Vl73BJcBhIcevbAcyb2WQhREcBMAA8RUabZqTrH/lXPQQjRB8AJIlpj9RKdY/+qewZL4h0AfEZE7QHkgE0bRvjX37PX7t8XbKqpCSBGCHGz2SU6x/5V92wBRvfo6N5dBhIchwDUUf1eG6wO/+shhIgEM49JRPSD9/Bxr1oL7/8nvMfPhefQHcB1Qoh9YFNkLyHERJzb93wIwCEi+tP7+wwwQzmX7/kyAHuJKIWIigD8AKAbzu17ViB7j4e8P2uPW4LLQILjbwBNhBANhBDlAAwGMOcMj8kxvJEW4wBsJaL3VF/NAXCr9+dbAcxWHR8shIgSQjQA0ATsfPvXgIieIqLaRFQf/B5/I6KbcW7f8zEAB4UQ53kPXQpgC87hewabrs4XQlTwzvNLwT6+c/meFUjdo9fMlSWEON/7rG5RXRMcZzqS4N/wAXA1OEppN4BnzvR4QnRPPcCq6gYA67yfqwEkAlgMYKf3/wTVNc94n8F2SERqnI0fAD3hi8I6p+8ZQDsAq73v+kcAlf8D9/wSgG0ANgH4Dhx9dE7dM4DvwT6eIrAmcaedewTQyfucdgP4BN4KJVY+bikTFy5cuHBhC64Jy4ULFy5c2ILLQFy4cOHChS24DMSFCxcuXNiCy0BcuHDhwoUtuAzEhQsXLlzYgstAXLgoI3ir4I70/lxTCDHjTI/JhYtQwg3jdeGijOCtMfYTEbU602Nx4aIsEHGmB+DCxTmM0QAaCSHWgRO7mhNRKyHEbeCKp+EAWgF4F1xmfRiAAgBXE9EpIUQjAGMAVAGQC+B/RLTtdN+ECxdGcE1YLlyUHZ4EsJuI2gF4TPNdKwBDwWXDXwOQS1zscCW4nAQAfAngfiLqCOBRAJ+ejkG7cGEVrgbiwsWZwRLiPixZQogMAHO9xzcCaOOtktwNwHRVg7io0z9MFy6M4TIQFy7ODApUP3tUv3vA6zIMQLpXe3Hh4qyEa8Jy4aLskAVuFywN4t4se4UQAwGuniyEaBvKwblw4RQuA3HhooxARKkAlgshNgF42waJmwDcKYRYD2AzzoFWyi7OLbhhvC5cuHDhwhZcDcSFCxcuXNiCy0BcuHDhwoUtuAzEhQsXLlzYgstAXLhw4cKFLbgMxIULFy5c2ILLQFy4cOHChS24DMSFCxcuXNjC/wEBk3bkKq/tCQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def euler3(x0,v0):\n", " v1 = v0 +(- k * x0) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n", "\n", "t, dt, k=0.0, 0.01, 0.01\n", "tt,xx,vv=[0.0],[0.0],[0.01]\n", "for i in range(0,100000):\n", " t += dt\n", " x, v = euler3(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "kはあらかじめ$m$で割られて正規化されているとします.これをEuler法で計算すると上のような結果が得られます.\n", "\n", "徐々に発散していく様子がわかると思います.本来,摩擦のないバネは定常的に振動します.この発散の原因は,Euler法の計算誤差が大きいせいです.そこで,より精度の高いRunge-Kutta法を導入します.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2次のRunge-Kuttaの導出\n", "一般にRunge-Kutta法と呼ばれる手法は,4次の古典的Runge-Kutta法を指します.導出は意外と面倒なので,2次の場合のさわりを紹介して,そこからの類推としましょう.$x,v,t$などのパラメータ名を変更しますのでご注意あれ.\n", "\n", "(「ANSI Cによる数値計算法」堀之内聰一,酒井幸吉,榎園茂,森北2002, p.133)\n", "テイラー展開により,$h^2$の精度まで展開する.\n", "$$\n", "y(x_0+h) = y(x_0) +y_0'h+\\frac{1}{2!}y_0''h^2 + O(h^3)\n", "$$\n", "\n", "この式において,$y_0' = f(x_0,y_0)$は既知とする.一方,$y_0''$は$f(x_0,y_0)$から直接的には求められない.したがって,この式の右辺と$h^2$の項まで一致する近似値を,$f(x_0,y_0)$だけを既知として算出する方法を考えよう.\n", "\n", "平均値の定理より,\n", "$$\n", "\\Delta y = y(x_0+h)-y(x_0) = hy'(x_0 + \\theta h), \\, 0<\\theta<1\n", "$$\n", "\n", "$y'(x_0 +\\theta h)$の近似値として,$\\theta=0, \\theta=1$の場合を考えると,\n", "$$\n", "\\begin{aligned}\n", "\\Delta y &\\simeq hy'(x_0) \\, &{\\textrm where}\\, &\\theta=0\\\\\n", "\\Delta y &\\simeq hy'(x_0+h) \\, &{\\textrm where}\\, &\\theta=1\n", "\\end{aligned}\n", "$$\n", "これらの値は単独では$\\Delta y$に対して$h^2$の精度をもつ近似値にならないが,これらの一次結合$\\alpha h y'(x_0)+\\beta hy'(x_0+h)$を$\\alpha, \\beta$をうまく定めることによって,$\\Delta y$の$h^2$の精度をもつ近似値にすることができる.実際,\n", "$$\n", "\\begin{aligned}\n", "\\alpha h y'(x_0)+\\beta hy'(x_0+h) & =\\alpha h y'(x_0)+\\beta h \\{y'(x+0)+y''(x_0)h+O(h^2)\\} \\\\\n", "& =(\\alpha+\\beta)hy'_0 + \\beta h^2 y_0'' + O(h^3)\n", "\\end{aligned}\n", "$$\n", "\n", "したがって,テイラー展開式と係数を比較して,\n", "$$\n", "\\begin{aligned}\n", "\\alpha + \\beta = 1, \\, \\beta = \\frac{1}{2}\\\\\n", "\\alpha = \\frac{1}{2}, \\, \\beta =\\frac{1}{2}\n", "\\end{aligned}$$\n", "となり,\n", "\n", "$$\n", "\\Delta y = \\frac{1}{2}hy'(x_0) + \\frac{1}{2}hy'(x_0+h)+O(h^3)\n", "$$\n", "\n", "いま,\n", "$$\n", "k_1 =hy'(x_0) =hf(x_0,y_0)\n", "$$\n", "\n", "とおこう.上式に代入して,\n", "$$\n", "\\begin{aligned}\n", "hy'(x_0+h) &= hf(x_0+h,y(x_0+h)) \\\\\n", "& =hf(x_0+h, y(x_0)+y'(x_o)h+O(h^2)) \\\\\n", "& =hf(x_0+h, y_0+k_1+O(h^2)) \\\\\n", "& =hf(x_0+h, y_0+k_1)+O(h^2)\n", "\\end{aligned}$$\n", "\n", "したがって,\n", "$$\n", "k_2 = hf(x_0+h, y_0+k_1)\n", "$$\n", "とおけば,\n", "$$\n", "\\Delta y = \\frac{1}{2}k_1 + \\frac{1}{2}k_2 + O(h^3)\n", "$$\n", "となる.これより,\n", "$$\n", "k = \\frac{1}{2}(k_1+k_2), y_1 = y_0 +k\n", "$$\n", "\n", "とおくと,$y(x_0+h) = y_1+O(h^3)$となり,$y_1$は$h^2$の精度の近似値となる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Runge-Kutta2次公式\n", "こうして得られたRunge-Kuttaの2次の公式を定義すると次の通りです.\n", "\n", "微分方程式\n", "$$\n", "\\frac{dy}{dx} = f(x,y), \\, where \\, y(x_0)=y_0\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "y_{n+1} = y_n +k (n=0,1,2,\\cdots)\n", "$$\n", "で与えられる.ここに,$k$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 & = hf(x_n,y_n), \\\\\n", "k_2 & = hf(x_n+h, y_n+k_1), \\\\\n", "k & = \\frac{1}{2}(k_1+k_2)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Runge-Kutta4次公式\n", "2次と同様の考え方で,$h^4$の精度を持つRunge-Kutta4次公式を作ることができる.\n", "\n", "微分方程式\n", "$$\n", "\\frac{dy}{dx} = f(x,y), \\, {\\textrm where}y(x_0)=y_0\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "y_{n+1} = y_n +k (n=0,1,2,\\cdots)\n", "$$\n", "で与えられる.ここに,$k$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 & = hf(x_n,y_n), \\\\\n", "k_2 & = hf(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}), \\\\\n", "k_3 & = hf(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}), \\\\\n", "k_4 & = hf(x_n+h, y_n+k_3), \\\\\n", "k & = \\frac{1}{6}(k_1+2k_2+2k_3+k_4)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 連立方程式にRunge-Kutta4次公式を\n", "連立微分方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dy}{dx} &= f(x,y,z), &\\, \\, where \\, y(x_0)=y_0 \\\\\n", "\\frac{dz}{dx} &= g(x,y,z), &\\, \\, where \\, z(x_0)=z_0 \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "\\begin{aligned}\n", "y_{n+1} & = y_n +k &\\, (n=0,1,2,\\cdots) \\\\\n", "z_{n+1} & = z_n +l &\\, (n=0,1,2,\\cdots) \\\\\n", "\\end{aligned}\n", "$$\n", "で与えられる.ここに,$k,l$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 &= hf(x_n,y_n,z_n), \\,\n", "&l_1 &= hg(x_n,y_n,z_n), \\\\\n", "k_2 &= hf(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}, z_n+\\frac{l_1}{2}), \\,\n", "&l_2 &= hg(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}, z_n+\\frac{l_1}{2}), \\\\\n", "k_3 &= hf(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}, z_n+\\frac{l_2}{2}), \\,\n", "&l_3 &= hg(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}, z_n+\\frac{l_2}{2}), \\\\\n", "k_4 &= hf(x_n+h, y_n+k_3, z_n+l_3), \\,\n", "&l_4 &= hg(x_n+h, y_n+k_3, z_n+l_3), \\\\\n", "k &= \\frac{1}{6}(k_1+2k_2+2k_3+k_4), \\,\n", "&l &= \\frac{1}{6}(l_1+2l_2+2l_3+l_4)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def runge_kutta4(x0,y0,z0,h):\n", " k1= h * ff(x0, y0, z0);\n", " l1= h * gg(x0, y0, z0);\n", " k2= h * ff(x0 + h/2, y0 + k1/2, z0 + l1/2)\n", " l2= h * gg(x0 + h/2, y0 + k1/2, z0 + l1/2)\n", " k3= h * ff(x0 + h/2, y0 + k2/2, z0 + l2/2)\n", " l3= h * gg(x0 + h/2, y0 + k2/2, z0 + l2/2)\n", " k4= h * ff(x0 + h, y0 + k3, z0 + l3)\n", " l4= h * gg(x0 + h, y0 + k3, z0 + l3)\n", " kk= 1.0/6*(k1 + 2*k2 + 2*k3 + k4)\n", " ll= 1.0/6*(l1 + 2*l2 + 2*l3 + l4)\n", " return [kk,ll]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Runge-Kuttaの4次公式をそのままcodingすると上のようになります.これを先ほどのバネ運動の問題に当てはめてみましょう.\n", "\n", "先ほど導出した運動方程式の漸化式\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} & = v_i - \\frac{k}{m} x_i\\, dt \\\\\n", "x_{i+1} & = x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "\n", "とRunge-Kutta4次公式を示した連立微分方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dy}{dx} &= f(x,y,z), \\, where \\, y(x_0)=y_0 \\\\\n", "\\frac{dz}{dx} &= g(x,y,z), \\, where \\, z(x_0)=z_0 \\\\\n", "\\end{aligned}\n", "$$\n", "とを比べて,変数の表記の違いと関数$f,g$を具体的に書き下します.\n", "\n", "| 4次の公式 | 運動方程式 |\n", "|:-----:|:-----:|\n", "|x | t |\n", "|y | x |\n", "|z | v |\n", "|f(x,y,z) | f(t,x,v) = v |\n", "|g(x,y,z) | g(t,x,v) = -k x |\n", "\n", "この変数の書き換えを吸収する中間関数としてEuler3を書き換えます.RungeKutta4の仮引数を上の表に従って置き換えて,数値を渡しています.また,関数$f,g$も定義しておきます." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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0O6LFdrn7Qs+9j8WcbiSA4krNmgHp6Sr811/dn5N/1rOtatYE+vYFOnd23sPvd88KcxvcZafTSqNGFLv4/nsVXlICzJ5N21+mD/lv+d58vu66Sw3W8uyoYJDuJY/bb3fikYc+R/v2UT2UHlf65ht6/j59VHj//u74hdWkwsNhel79vt27UyacTovvvef+nPyz7nqKx4lW3Ny4fr8Txt9Tf06+Bk89pcJr1QLOPRc4U+NGjAFpaU48v+dqvOkm9ZrcXKol2rFDzVIMhShTTf6u/JwAEIkcf3b/dwqQpQBaGIbRxDCMVACXAdByLDAZwFV2NlYvAMWMsX2GYdQwDCMLAAzDMAEMAOBSinP8RjRKFKcTHl9cPWjZsiWl8OoEM38+sGiRc6MlYxAyE5X/9nrJl64HD0tKhB82KrxIiu9YxiM/t84UMjNj6NHDPasHSM4odcZ/ySUkND/6SIXv2kUMrF8/Fc6fW99c/H76fZ95hny8+maeMIE28uuvu+PR/en8fvoan3MO8Oijzmyujz6iezz6qDsefSRTEmrWJF9+dra6Hps3U5ymalU1/iLjkedCvq/sKzcMIDPTGZNhTKTBJntmHc5jGnqwOTOTMqv0VGE+l/qa8ffUaeXWW4lWuBLBx8qVlJjAs6v44N/X8SSjlVGjiCl/8EFjBf7NN5QGO3WqOx6dJvga6GvaqxcpjatWqfCpU4E33qB7y0Oe32RxDPkd0tOB885zKgJFRaRsAKQ46c8JANHof5EAYYxFAdwO4EcA6wFMYIytNQzjZsMwbrYvmwZgG4AtAN4FYOeAoA6A2YZh/AYSRDMZY9rSH98Ri7lPFa/D0LXc0lLg+uud6XmcGHi2CR8ys5f/btMGuOoq+lsmqv37SSuuWVMwARn/hx9SPYgO1/EYBgk1wLkJL7qoNzp1EnUZfGRm0mY7+WS4Dp3p8MwdHX711cAVVyTXyk44QYUnYwq5uRR017XNmTOpcl0fXHDom1/P2JHHuHFOa5Iz6VNOcX9OfehBbz6OHgUuuIAEtZtwmDBB1TZVpiD+rl1bZPnIa1lSQmtVq5aaucWF0jXXbHcIcT70NeNWkk4rbdoQTehKCH9uN43cDc+ZZ5Kg0+fwiSeczFf+frt2Kpx/X3/+tDRKl16zRs0rXrGCuh/olmyytczNpd96kgFANMdTznU8Q4aocPn55Llo0IDKA3R4cTGlLBsGKWA6/g8/VIW4TCvl5cc/DetvrQNhjE1jjLVkjDVjjI22YW8zxt62/2aMsdvs/3dgjC2z4b8xxk5gjHVkjLVnjD1xrPscjxGJ0OR/8okKP/FEImw9W2LCBMpZ11Nd+UJHIqrGwRda1yzS00WGl0xIu3cT4z94UNU2Of60NBWPzGj0TcvrOWR4LAYcPpyG334TqY98pKXRRte1TZ6Rom9aXhehb8ZYjKyxJ59U4ZEIMeWLLlLhr7zijue776j+QH5HjmffPkoXlUc4TAxAtyhuuw048cRDjvl5803K69cFHb9OLybj76+nbDZrJoSQvPa//CI0XzdXo76WMlOQBQt32el4jh4F8vNpHeTCOj5fPAGDD/nZ9Lng2q0O56mievsTxoChQ50Fr8OHq8/Ax/r1NM86DcViwJo1TsZcXk7C4667VPhzz1E2oI5n8mTaN7GYykz5ftSVBE5rK1ao8PPOo2fJ1rrAjB9PKbl6cSnHs2CBe6bk0KGqlVOzpnAvynO9ZQvxFh1eMVr5D3sAuYzKSvQKjsaNy3DFFU53SyRCmpy+ofTPfHDtt3t31YXSqRNpdytWqESwezf1bQKSm7XyvTj8yitVbbNuXXpOytYQ8MOHhZ/aDY/+N0AC69tvndrmCy+Qf5wXFPLRt6/z+QFB3PpclZc7q9ABYo7XXSc0Mz4+/9wdD/+sp+uaJs2H2/B6mQMPz8XX3ZT8Or1gsF074F//cmrMZWVUWwEkF+hua3Dyyaq22bQpuZAOH1bTPw8cAJ5/nv5ORitu/vH332+aiAsBxMgiESpy45XnAL1/hw7O5+f/c4OHw6Qk6FbsVVdRzcLAgU64/vzys7ql9+oFrQDVr5x9Ns2VPLjSwF3SfPD7ffuten21ahTP1F3FAAlTnVZ+L4335ptVpt6yJVlXzz+vvsfRo8INJs+pPC8ynOO//HJy9/GRlUXxkuJioHnzJDnA/8GoFCAVHH36HMZddzkbyY0ZQwFQvRCoInn4MgHk5pIPWS+SW7OGLIDcXJXAkuHhBB2LOYuQ3AKHZWViU7oRpNu7DBxIbjO9gjwcJqtBd9Xw77tZIPIz8/Hqq4Rb1zYnTSIfuN4NIBke/ll//rFjqV5Ft3zGjqU063nznO8FOJljsphJr15Ur7J6tSp0pk0jZeDGG9XvJEtwSMb4TZM6Aei0UlAgmunJAeFkaynHVXQG7/MR85FprrxcMEh9rpO5pG68kbRmPTFh+3ZidiedpMKTuSn5Gutr8MorxBy54OFjwgRS9l57LRkelfUlo5V//Ys6FuhW7KefUtxEb05akX0vz1HLlmRpHD6svtv8+eQ2HTSIXMZu33WzQAC1rsjrJa+GmwA8HqNSgPyB8d577iY0AFx8sQrX3UF8nHqq6HkkE8y+fWQWG4aaZcTxTJ+utmVIRpDduonOm/I1W7dSFlGHDlC0TX7NK6+o2uaxBAi3iHRmkZtLm3bbNhUeDpNVpVfxJ2P8vXpRUFy/75NPOgW1jEevauZMzW1Tz5zp7By8cSOwZ4/pcEvw7+vPyTOCdMskFKKAad++7nRw111qoDMZI+jVS3QskOGFhURvhqEGazmeqVOpap+PZGuZmSm6P+t+9g4daD7lzr4cz7BhFLtyG/ocPfooCSEdnpdHBaNy/E5+Pt7qhI9ktNKkCbl7dGXpww+PTSu5uaqE4gLXzXPw00/OQsUDBygOqRfoyd+XBbS8HvK+Ly2lTgYdOqjuRT4PzzyjxuaSCZA2bURcVV7jkhJg9GjVKjmeo1KAVHC89VYzvP22u7sFcLZD59eNHavCW7QQ1bMyIS1dKvr8uBGJbqYL/7Uz/ZAzJ1lwHTlCzGbNGlXb5Phr1VLdRl4v0Lp1ieM5ZfxuGv/ixcC//63Cw2Fimnrm2ejR6rvwMX06md06449GKd7B54+PWIxcgDxGwsfEiWQt6c85ejThcXO3FBWlJdxAfPDnWKDWL+Lss6mKWA/GjxlDG58/m/ycAFXwu1mNV12lxtJq1hRCV8azfbsQfrJLhz+n7v6T76VnYnG6kq+xLKKTbdtUZUMOWMtMjcc5dDyASN122zcLFjizrcJhcr/q8S8+nzqer78mmnPLwlqyxNlcMBYjWh89eo0CHzOG0oR1mnvhBVIG9DXmn/Wmifw55s1Trcy+fcllp7/Dl1+KfeCmSBw65A4/4QTVAs3IELFSfd+PGuWM4RyvUSlAKjjCYZqqZALktNNUTfTUU0l43Hmnmqmxa5fwySfLvHJjLp06qdrmwIFk9oZCagbKmjWiA7CMR83GcMJHjVJTM2vUAF5/fQXWrXNqm5xwde06mcYfiRDT0+s3zjmHNujZZ6tw/vzJ/OC6thmLuWfDAJTNoreJWLTI+fzy/XSm0LYtzYHe2I4xEqbRaPIUTLc1uPBCtUFl//4Ux3nzTZUxb99Ogi4ZHv0d+N+nn662DunZk7TheFyNTxUXi6ygZJqtmwX18stiDgFilJ98QkxT7/GWk0M43BIcdPwAzZ1lOZNPunYFnn7amc3lFvORP+uZeceilWrVnCnrvF2P/vx8LnTXFqeV3r2dbkr+rslcxW6xjlNPVd+hRw9SVmfPVhNudu4UGYdutJLsnf/TUSlAKjh40C0Z06FrxN/dupFGuWqV+p1PPyVmMWKEqm0mYwoyfrkRYkoKbU7ZFQKQgOKCRg7GJxMgfj/1PNqyxWnmer1kGssuHcbcN0KydETGiOF8+aUz5rB0KQkR2XUmf1+f62R+8M8+oywfvUDv2WeJ6esdXJPh4e+gw2+9lYQa1yD5uOsueqdkMRMdV7I1btKE0ngDARX+8890WNJZZ6naZkXqhHiXVz4MwxmrCQapjxugpq8mo7+UFFKUtm93P5isTx9RJ8Kf81iJEm7w118n6+rqq1X47NmEXz8eIRmtcPeRvpbvvUc9uJ58so0Cf+EFela3wkM3PMnqts47D3joIWLmctbemDHAffcBX32lxiOS7ZtkfKV6dUqqyMxUXWSrVpHbrlEjtSNvpQD5hwwedNMJ9bTTRJBLXuj9+6mwrWtX1bcpV7DKhJSMKVxwgfDlykS1ahVpY3Xrqq4VjmfpUnq238PfooVgIvLzb94MDB7cGyefrLYx50R7xhmqtpksg8swKGWzXj3nJrz0UrLQ9Hbx/D2TxUx0PFWrUtYKPy+EjylTnO25ZTy6649n7Lj5wX/4AY4mi5EIbeg+fVTmnMya7NlT1AXJ8J07ibnUqaO2dOfP+c47qq89WR3IyScLYSbTysaNJKTr11fng+O5556NShA6GSPLzhbfl685dIhcYzqt8Gv696fsI3kkY/wXXEBzpK/xgw8Cjz2WPFFCr8VJRisApRyvXq3WgSxc6EzrPhYeWfvXn2nOHMrAkxtU8n1z7rkq3SUTICefLNyCMnzHDtozPp/6vPz5vvuOeI7+/JUC5G8ekYiBtDQy3WV3xTnnEGHTNQL+wgtCY3XTVgoL3d0DAwaoGn+VKqJDr4xn7VrazPv2qYSajGDS0kSxo/4/tzoQHg/Iz1e1TY6/b19iSDIOPg/yc8bj9KxHj7prcT/+6Ex3jURIS9Ths2bRXOh43n+fMpzcmMvPPzsP14rFKJVZ1zaffx645JLdrplEo0erbjqO//BhshLc3IJff626RNq2FfUK8j0mTBDZQm60Yhjuleh16qidj1NSxGcZz969FFjfu1cNWvNrPB41CyAlRTAh3fdvGEQ/uvUZClGtCT8XRH7Hs88W6b988HiVPtfz5pEV7RZzmDXLKSgiEUoo4DESPmbMoPu6WSAffujMwiovJzp1oxW3hI6hQ8mqANR73HefsJLc1vL779UsKY737bfV1PJmzYQVJs/R3Lmis4Ib/9A9En+1APk7u/H+fzW6dj2Cfv1qOQ4bKikRBFERE5QvaP36xMC4cDjtNCKObt3UQOeyZcInn8xsdsN/9tnkl+YbrkcP91bQq1aJE++SZY654f/ySxJ2/HAk06SMm9691ZiDZYkMlGRuADfGzxgxJVlba9zY2RMMEMWdyVxSeh1InTrJ63R8vrgDj2whRSIiSM1xXH01zTd3M515Jt3jggtUPIcOCZ/678UZ5L/r1iVByNeyd2/C06CB2gFh5UrRziWZ68wNPmZMa/TpQ9oxIOpMeN8oPnbtonvHYsmf2Q0+fz5p1LJmPGwYWW96xtsZZxDNVJRWktUMVatGSoKevsqVIbdCQoBcTPJo3Jj2d7Jea/ozyW4rt7U8/3xau1at6DP3YNx4o3Ou3WKlySwWfk379pQ8wpMQWrcm+s3IUDPqjteotEAqOAYN2o/Bg0mDkRfu1lvJD/7998nztSvC+GvWJFdISoqqbc6ZQ2bpWWepabzJNi3XNAoKRNHasUYgII6CrQjT8XjonVevptiDfM2ePWSZyNpmsneXP+tM4aefSGOWXXAABZl79nTGUn6vDkS/7yefEMO/9loVfsMNQGGh39H0MdlcJBMCAwdS/OuHH9S41eefkyUzZowqZH9P2dD/Tk8nBqS3z1m7lhhgo0bJ21noa8ktFt0a45aGHgjmFkxFaCUtjZSK776DktkWj5PbtG9fp0XBv19RAZKfT9at3vbmlVeoV9ynn7rj0QsJk9HKU08Rvd98s7pOzz9P6bf796unLVZk38vX9OxJdLhkidps9MsvyaJ/9FG1GLIiiocsxLxeUmz0CvXjNSoFSAVHNGrgxx9JU5A1+ViMFnjQIHWR3LQDgEzf6693wjdvJtwpKaKOQ8YzaZLaiTTZpj3/fHHEqgxfvJjS/Dp2VBvGcTw//EDm9+/hT0ujtMbcXPUdd+4kjfiWW0RMRcbTt6/TJcXxutWBNG/u3MyPPy46jsqDX6dbh5zBuvnBV64ULSH42LIFOHgw7ZjtIORnPeMMEZvQA9hffkk0IWeecTzXX69q3skYwaWXijRw+R22bqW5NAz16FTO4PLzk8e/ZDyNGwuBID/DihWU9dezp6qRczwvvqhmHyWbH9MkJtiunXrfsjKytEeOdM+SatLEWd2fLBbRoAFlrulC/513nMdJy3iaNFHNcR54Zsx5cNiqVVTUJwuQQ4fop1at5AkIenyKd52W4QcOkNuvd281ZZo/5/33J4+3yH+fe66IT8n49+yhedYPfzteo1KAVHCMHNkhEUTVi4X27SNidfNtfvKJqm22aSNcG/JCz5ol0vDcXGF6HQgn8pYtRWM3PrhpLeM/eJCEyOrVKjFxQjVNdSNkZwP9+xcq1wAiC0tv48D//ugjtfaFf/fii6l4TB4ffUQuBvk543HyUa9f726xjBsn2snL8DPOUP3vgDiVTsdz223EBN2yvFatysIddzhjGm3aELOVYxpXXik68cq47rkHuPtu+ttNU1+6VGV4/LvPP682wKxTR7TOkfGsWUMMEnDvsqy7dOR11avXucUq4z96lE5PXLJEdXvw569XT52HKlVEkFwXhgUFBHOjlQ8/VE/048z7yiudqePjx5Nlq6/Zyy+Tla6vcTxOwq97dxUejVJB7euv/6rAP/9cWLYyrrvvFp0P9LUMhejkSTnjrbycXHPr16uJD6edJtyL8ju89JJ7zyu+v7duVduj8Gtuukm4wQDaR7zFj/yce/dSXzC9uPd4jUoBUsEh+0z1TVJaSrn9coDy+utJCx06VDVx164Vftg/ktuflaX26bnhBiLWDRsoV5yPOXPci7qStQPn8LvuEjUHAFkAjz22Drt3U1oiH4cOEYPavz+5O8cN/7p1ziypQYOoDYycmlleTtlde/c6tU2OSz9+9ffqQPTeWbzdRzI3yeuvq5lkeXnA4MHE0GVmbFnurpXfizmccYZa03PddVQ8ed996nG3v/3mHt9JRiv8mhYtKLDPx8CB/EghlTFv2ybqKv5ITObVV1XtvmZNyhRct45Sp/nYv5+EzaZNyTVzN6Z5+LDT/dqpE2nSumXy6KN0bbK13LJFhaelqa5meeTkkLYvv/PmzU6c8t9PPaXGyE45hQRC69aqIC8pEYIm2b50W+MOHdTMuSuuIPp94w3VbbdqlUhMcHvOyiysv3nE40KAVGQz9+9PjH3OHFWDeO890prGjFGZRTI8nMBKS53psSkpztz+bdsoZz49XRVcyZhadjY956+/OiutAQr2J8NTEX9vlSpkWY0fT5q5PH78kVxq8hkPFYmZ6MxiwQLaTHKQFiCXYFaWs06Dz+mxDmqS73H//SRAHntMFV4XXkjZP7/+mnwtK0IrrVsTvWzerFqxU6cSU7jzTrWI8ffWIBh0Clm3UVxM2UpA8pok+e+qVWmtFixQlQ3G6D1bt64YTSfDbxhUs/PTTyKgz8ekSaQMcMtO/35FaWXiRBLYw4Z1Vf43bBi5k3bsUBM3/uhaXncdWVBjx6oFr6NGUVwsP19VaCoyRzK8dm2i80BA5QcLFlDm55lnqr3oKgXIP2TIAkRe3KFDRd8eGb5xI7kZ8vKcLqOsLKopqFdPhbv9/cADoqpYhs+eTT7yOnXUFvP8mg0bVG0zGf6uXWnDZmaqG2TePODss/vgwgvdYyb33KNqm8k2mmnSpurQwbmZL7iAWlnIrVU4nq5dK+4HT02lDaV3B/7uO9WvrOPRa1O6dQP8/pjjfQCKmTz+uOquiMfJfdi5s8p0ktWBnHWWiH/J+FeuJIWiZUtxKJB8zdixFUtMuO02UXMkwxcuJFqpV48sPv27o0evVqzMZGvZqBFZ1c2aqUxtzRpSZi67zJ1W7riDXIZ8JLOGPR5Ki2/b1rnG991HwlQvkIzFaA/oLUv4PfR1BMgy2ry5inKPhQvVGhwdT3q6iqtjR7Hm+nytWUP7Qz7hMxYj11b//skVMvnvIUPc41/Ll1MiRna22qCSf/fjj9XEhEoB8g8Z8Tj5U9euVRn/4MGiwaJMACNHUvET4NRcIhHSNvVgPEC+5BYtBDwzU9xPxsODwPv3V6wOpFo1cSSrmwmvxzTKy4GyMh+++Uat5Ob427RR60Dq1SMNqGpVdR54O+8jR9zdDJ9/Tpq8jv/KK4VvmI+tW2m+dTyjR9PGcdNC331X9AiS4RdcQK4POWBOJ8ZtVZ4DIK2OZ2zpG37XLvqeXixaowY1bJS1wY4d3RMo3n5bnEPhxlB0bZPD+/UTaeAAMWA3prZjB9GKnpnHr9HrQKpXF0xIrysASFi4aeMTJqgNDDm8e3f12OKsLLJIW7VyatpTptCcutHKV185D46KxymNWhZQALnN7r3Xieepp6glivx8HM/UqdTqRY5PxWIUcysrU+s0brxRZHjJeAYPFmnxOv6jRylzUU6siMfJ8powQY3XtGrljmfy5GPTSmUdyD90DBhwAB07VnP40/ftEwcmJdMm9L/LyoixTJsmzkO48kpyJXXooC72Dz8If3MynG6mb//+ZDbzYqTTTnPXxmfMIKF19OgfrwOpWVO0Ialdm7SuvDyVKRcUiKC3XPQm43V7r7IyirfICQK1alH6rX7o1ief0PPrjQJjMfrhMQ8+WrVSg9Xy8PkYfD71mWS3kv6s+/aRoOvdW7zfVVeRVTpggIp7507Rb6wirjMOz86mDshciF14IQmCmjXV5IoZM4AvvkiOJxn86afboEoVEdA+8URnc1CAnn3AAGKwsuBK9i5ce587l9aO9+HKyCDruGFDNQmgrEy4rmQlSsbrpiR4PORGk925KSkktPQ+azNnivXULaFIhP4fCon6kY4dk7do5/u0omsZi9F7T5kilMIhQyh7UO/mvW6dyMZ0m9Nk98rJoaA5D/yfcgo9v9erZncer1FpgVRwXHBBAfr1o6wJOWh21VVkas6dq2ZFVMR3qteBdOxIm1PWNqdPJy36xhvdfZv63+nptFm3bFEPIUo2AgHhQpIFV7LnrFqViHPmTIrn8BEMktusdWu1dXUyPHK6pHxNVhYFj+fNc6blPvooMR1d2/w9P7iemjlpEgnYs85Sm/adeSawZUsmIhFV26yoYsDHOecQ45o4UfWDjxtHbV0mTFCPOk7GFI7lFqxXj5ikXBm/fDm5NQYNUhlwMjx+P7mLAoEUrFGb07qO8nKhnVdkHnJzyTX344/qSX/BILllW7VS042Tuf5kvPoa804MulX9wAM0P3ra9x9dyxdfJPfYFVeoSTJ33EEZWKWlwrL/M/h79yaFYOZMehc+PvyQkkveeks9AK4iOGVFkMdK3Qohj8eoFCAVHKWlXixcSEE8vR1EjRpU5yCnNiZb3HvvJZcHoG6SpUspWJuTI7RIgJhLTg7FU+TDd5Lhv+YaQYgy/ilTyEQ+8UR3P/iaNaJFgo5Tb+b23HPEAOVrli0jrfSpp9QjXmXXHE9j5O/ldi+fj6yw2rVVOGMUL5G7zOrf13tn1a3r7tIBSLhOm6YK6507gaNHncfbJZvrq68WCQAyfPdusgYuucTZ2yotjbTNZAJKnuvhw0WQW5/rESOIOfB2GvI1335LrpTfw9+lC7lkc3LCyjVTplBt0/nnC1qV8UyeTBaoG37575wcovf27Z3zk5dHySRufdwuvFC0xdH/p69jjRq079xalhyLVjp2PKow1VathAWp49q9m1xPsqu4uJiUr4wMlTkny6q6+GKR6iy/w9atwnUmW32xGAnFm29Obu3J+G+7zf20y99+o/9VRJn8M6NSgFRw3HnnCUn94AcPkhtF1jZjMbIYvv1WLQBs1UocISsv9PffiwNhdPzcRJe1Ta+Xfs46y9lm3DBEm3E+CguJ8SxcqBZvJfORNmgADBy4D36/UzMsKqKN4sY4nn1WnG8gw/Py1OCeYVDwvlcvFU8gQH2hNm1yT3d84glny+1YjJi5rm1u3CgYkYzr3HPdc/5jMWDDhqq49lrnWp5+OjEN2YV5/fUi0C/jv/FG91TqWIwE1owZFLuS4Tk5VGkv+8Fr1RKpmjKeZcuE4HBbA30t/X4SyB06OA9AAoi+ZDwlJaKV/Pz5TvxVqqhJA3XqiGaQMp5QiNYgFEpOK3I3AA4//XTnCYNz5xIT1vGMGkUtP9ysz3HjyLKXuwHEYmRpvvLKSqXNydSpolpexnXJJaIAVl/LHTvoxEK5xiIWowSQPXtUhe/MM4WLUMY/ejQlOOjwWIz2+/LlTlpMTaV9IOPPyCCr1ONRn3PbNqIrvWHp8RqVMZAKjnjcQEoKMQDdJ7lpExH87Nmi3cioUbSQco0GQBoXL86qSNuKWIw2tMdDGtvw4QS//3760cekSXSgUzT6x/zgI0cSkXMtqVMnYMSIjfjiizqKn339eiEQ3aqdU1Lc32XdOtronOg9Hpobj0fEkAAi9DvvpE0iV2snM9E5LrdzsQFyefEz2flYuVIwcP1ZCwvT8O9/kwuEr+WFF1ISgt5X6dAhkaKt4+EC3G0uzjiDrEzOOEaNonfWi97mzv3jtAIQI7nlFuE2uvxyZ5YSQIWld98NHDqU5upnT011x//mm0QHvH6ncWNivv/6lxqHWLeOmKlhqFlkMn639yosJItYdoW2aUOptvIcRSLEgPlzynGQWIzuc/Cgeo+cHLKi3Ub16nRPWQDv2CEsD7dnfeUVog/ebuTSS+k6OdEGIK8AD57rc2oY7inlwSBlBsr7fsQIUlBkdzlAvGfOHGejy2RKxfEalRZIBUc8biQKg/QF4nCZAPr3p8X//ntV23z9dXIBvfWWONpW/66+mTlz1LUst7FlC92zZ081SyqZy6h+fXJV/PSTs14CIKYpB6eP9ZyAkyk0aEDujhkz1OOAIxGC160rGKmMMxlz0TUsgLTl9u2J4es9qaJRYsT6O3C3g5PxMwf8oYcoeHzPPaJNDECC4I03aM7leE0sJjT0ijD+Vq3Ij75ihZrNNWkSpQ4//riaSZYMj9dLMbCjR9XAf7Jx+DApNOnpUdfeWfoa1K1LVtfcuepxwJEIZdnVrKl2XZDxuD2zDq9RgxjhypXCSufjrbdoTt3a7fD9p9O4W0eG6dOJ3q+6qocScxg0iNx5q1c7zzThQilZjEZ+hxtvJPxPPEHWFx//+hdZMsuWEd3I3/0jfKVmTfJs7N6tutRmzyY6ueMOtVPDf7UAMQzjTMMwNhqGscUwjJEu/zcMw3jV/v9vhmF0seENDMOYbRjGesMw1hqGMfyvftZ43H1B776btEcdvnQpuVTOPtvZDiInx5mum4wpvPGGMJFl+MSJZP7XrSvSEuVr5s4lYtLhuoaSl0dZXvXrq/AJE4BTTumPW25xj5mMG0cpuDpcZwpZWeQGaNxYxR8MUt3Am2+q2WGcCVx4IQUpdbisbcojGCTNld+bMWIWem0Ix1W9Om1E2X992mlAmzYUJdYD/jt2ULKEHv/KzKS6CFlARaMiE03Gc/31IrdfnqP8fLIau3Z19p5KTydLoiIC5NFHKZPJ61XhkydTYL9bN7jWe4wdu8q1pkdfy7ZtKbagp9/OmSPiHW61CS+8oPYdS4bf7yd6bNjQqSTcfTe5iXnjTxnPSSdRJwWZJlJS3IU4QFbj7t3pSvxr2TJVOZDvUaUKKSeyddW/vziiWXf/bd1Ka6HXf2Vk0BrrljWnFRnPXXeJ9HkZ/vPPlPbdsKF6ciYXmC++qBZh/tcKEMMwvADeADAQQFsAQwzD0JJkMRBAC/tnGACeZR4FcA9jrA2AXgBuc/nucR3xuIGTT6ZglFzxfNFFoo5BXujhw0UdiL7h43Gntsk1nSeeULXZ1FThOtELij77THWjyPfSCaZOHSL4jh3VE8v40JkOMWkDX3yhapuym0TG064dCZUWLVQ8xcUUVNfPA+HXvPqqKMSU4WeeKcx2gBhpaak41Em+x+23i6Auh3OBM2ECMbxDh9R7DB5MGqKsbb77LnDRRXsc+Nu0EUWZTpcXWZSyoIrFSDgtXEhN9Pjo1Mm9D9qrrwp3kx738XjIny5ni/FnuPFGZ18wwBn/2raNfPybN7s3d9TrQBo2pJP1GjdWi974cKMVgGo7+Lkm/PkBmgs5dtS0KcUGeWt4PkpKRJ2EWxbWO++o6dcyrYwdq9ZAHDniHlO85RaRxae/w/z59Exy+5NYjFyt+/er7rM77qB11/GcfrpIrNDp3bJoj+iCJTeX0vXlJJCWLYXrVcY/aRIJJz1uFY3SupSXO9OOU1Pd63mOx/g7YyA9AGxhjG0DAMMwvgBwHgC5P+d5AD5mjDEAiwzDyDIMow5jbB+AfQDAGAsYhrEeQD3tu8d1XHzxHpxySguF4QAU/+DZDzpBumkWsRgxg65dSfvmfuQHHqC20XLrZoC0Lp5mq+PxepO34zjtNNLmOGO68EK1YI+Pjz4ipqwTJP87Lc2d8U+cSMyTB0EbNiQf9SmnqNevX0+bqlYttTfQ7/nxi4uJKTdrRp8NgzS4vn3JHSCP8eMFg+Xf57/Lykjoy5uqVy81JVoeqalxZGer2mYyd0IsRr7tkSPJhcafdcQI2rB6AeOaNaIHlo4nGX6Ph4TcY4+Jxo133klzXaWK+pyffir84H9kLceMaYUdO0Tyw2mnOVvpAxRUv+ACsjbcUsqTuarmziUBzuMwWVkkoJo1U+Nfe/aQoNatVX1euGDlAioeJyUqM1Odj5YtKZlBrkuaNYv2rBvOkhJaI1kh69/fGc/gw+dzHvaVzOXM8d98MykqrVsT/K67iHb1s94XLBDWrtu+d1tjr5c8CYMHi4LOIUPEufcVOd7hj46/04VVD4BU7I89NuwPXWMYRmMAJwBYfPwfUYwLLtiLLl0oe0fOurj4YtKMVqxQg7XH8m1yApMJr3p12ji7dqna5rRpJETuvlsc3sTxuBFS9epEnJs2VSx1Ty7Yc0tDdotpPPkkEfjbbwt4URG57erVE5tDxpOW5s5c9Odv0YLmd+1aVWstLaXNlp5OprusUXFGK+OV7wuo7zB5MmU39euntlFp3RpYuTILRUVq5XQyBp+MWZx3HuH+4APBrADSkv/1L9I2ZYZxLAHi8znjPtwqtSw1DXnpUrLELr/cGZPhc6H3QevRA9izx8TatfjdwV2Hev0Jp2M9gaJ5c6KRxYtJQeKjqIjidLVru7fd0GmF1/HohXs5OeS6jMXEscZ8XH01ff7kE+d58skKAN1o5fXXSWiedx7tcT7OPZdiYvG4KAbmeJKtpRu8d2+ycL7+WqWVt98mxW78eLo3H3wekgkQ3fr8q8ffaYEYLjD2R64xDCMTwFcA/sUYK3G5FoZhDAO5v1CrVi3k5+f/qYfdsSOKhQtX45FHOsDvX4Xu3akpT0lJd1SrFkRx8VrFl19c3BXUwTcTa9asR34+5eJdeqmJAQNSMXz4CdiwYTPy88mnsGRJNrZuzcQ77zTDsGFbMWQIyc19+9qivDwD55xDJcz88XfubA7Gatt/70d+PtndHTuS9nHZZb2wZ89R5OeTvTx1ah1MnFgfjRsH0bhxGa69dgcAYMOGegBa4Omnf0G1apEE/rVrawNojXg8iMOHI8jPFy/Xpw8wdWoHHDmSivz85fZz1cDjj7fDbbdtRlZWBAMGkGq5alU1ACfg3HM3o1mzMuTnHwUAHDyYCuBE+HwxhMMM+flSviiAo0ebIBptiPx8SuYvKkrByy+fhGh0MwKBffD74wlts7y8Lxo3ttC0aRkWLtyE9PQYQiEPGjXqCtOMAMjCL78swrZtoux5zpxczJvXHrNmLUWzZtRTpqDgJLRoEXPQSDDYCz5fHEA6VqxYBY+H1v6cc2qjqCgNW7Y0wcqVa1C16iGbVtJx9Ggq7rqrM+69dwPOOouyKPbubQ2vNwt+/yJs2SJcJQcPdkA06geQgY0btyI/n9b+3HN9OOMML664oie2bduN/HySdkuXZmPp0hxMmVIXZ59dgNtuI//Zrl3NwVgtDB78i0Irmzc3BNAU8biFfftKkZ9P0sLjITfM9defgMLCCPLz1yRo5f33m6Bfv4PIzIzixhvpvr/9VgNAOzz99FI0aVKWwL9yZXUAHRCLBREIMOTnL03MXatWQEpKK1hWNvLzF9l4qmH48BNw221bULeuhRNPPAyAijiBbujZcwcuvNBK7BlilHnw+WKIxbyYPXsuUlOF9rV7N9Hw3LlEw/E48PHHefB4tiM7Ww1slJX1RM2aQL16JVi1ahsOHAjbz9kRXi8DUB1Ll65AWZlgJ+vWVcHkyV3Ru/dvKCkpAgDs29cRwaBX2RcAUFzczd73GVi9ej3q1KF36NMnB82b+/HKKy2xfv0m5OcXJN65pMSHe+7pjJtu2orLLqO1Lyhog0ikKurVW4xDh8Ra7t3bCpFINoAU7NhRgPx8WvuBAw2cdpoH117bHXv2HEF+PkXwf/01C9On18btt2+BYZT+af6XdDDG/pYfAL0B/Ch9fgDAA9o14wAMkT5vBFDH/jsFwI8A7q7oPbt27cr+7MjODrPOnakaY9o0AW/dmrEBAxh74w3GNm0S8A4dGDvzTMZ++omxggIV15EjhGfsWAG76SbGsrIIPnq0gF94IWPt2jEWCDBmWQI+ciRjzZszNmwYYx9/7HzeJk0YGzpUfB49mnA3a8bYRRcJ+EsvEbyoSP3+woWMDR68m3XvzljPngIeDDK2cydjp5/OWOfOAv7554SnSxe6Bx+zZhF89mwVfzjM2OLFjF1xBWOZmQJeUEDPesUV9L14nOB799LnVq3o99Gj4jspKTQfbuOTT+h6eW06dWLspJMIvmKFgFerxtgJJxSxwYMZW7tWwOvVY+zaa8WzyGP1asIzYYKAdezIWLduBH/nHQG/4grGGjRg7KuvGNu8WcBPO42x7t3pWeX78uH3M3bffeLzo48S7mrVGLvjDgG/9VbGcnOd33/rLcZatGDshhsYe+op5/9btSpmAweKz2PHirXs00fA+RqvW6d+f8MGxp54grGTT6b78HH0KGNLlzI2ZAhjdeoI+OzZhKdzZ8aqVBHwZcsIPnmyij8eZ2zHDsYeeID+X1pK8CNHGLvzTsauuorg+/YRvLycPnfqxJhp0vPx0aABY9dcw9hsnSAZYzNm0PfmzxewHj0Y692b4FOmCPjJJ9Meu/56ekc+2rdn7Lzz6N3Ly1X8Bw8SnldfFbCzzmKsbVuCP/OMgF96KWMtWzI2Zw5jW7YI+JVXMta4MfGbOXMcr8AaN6b54OOttwh3QYH7O1d0AFjGXHjq32mBLAXQwjCMJgD2ArgMgJ6tPhnA7XZ8pCeAYsbYPsMwDADvA1jPGBv7f/GwsZiR1DQ9fJiKhD77TGRWvfkmZeboLcanTnX66/nfyfB7vZTieMcdotjpmWfoRx9vvEGVxMn84MnSYx9+mNxf/KS5Xr2A22/fgr596yuZSvPnU0yjRg33Y1OT+cHXriUfMM8QSU0l98k994imcQC53R56SMQPuMku49fnKCtLbUcuj/r1KUgvZ0mtXy/WSX/W0lIfvvqKAvPchTZsGLm33Frn8wKtiqxlNEpFdYMHkxuOx3Lefpv+p8dlvvmGisi8XmeKKi8WdYuZtG5NrhGeEXXzzaK+Rx7ffUfrXlSUqvQX+706kHfeoeA6L9Js1YrwDB+uXr9wIbl3OneuGC3yv/fvJzo78UR6H8Og/mcXXUTJINxtWFxMCQicVnT3pcfjPF+9cWM11Vge2dk0bzIt7d9P9CXj5X+XltJRBaefLlLyb7+dXGZ68sGmTcLFVhFa4XTP08f5Xn/lFXJbynsPoGSR9evdg+vAXxdE/9tiIIyxKIDbQVbEegATGGNrDcO42TAMTu7TAGwDsAXAuwButeEnAbgSwCmGYay0fwbhLxzHCo65wfv0ocykL75w+sFff518m3r2UbJ6D5/PKRCSjS1baOP26ePek0pnCm3aUCPHxYvVquNIBAiFPIkN/Ht4kvnZO3emOM6SJXQfPoqLKSW0ShViDHzIzAtwNlx022yFhRSbSU8XgcKjRym9k/vb5ZqYY8ccnHUgPI32ppuoRoEPHuc4cEBkV/FnTlab4JZY0bQpCY+5c9WYzBdfUBHZs886UzPd/OAZGSTYo9HkDQDlcfgw1T00bBh0TSnX17J1axJ6K1aomXk8UcE03Ys/kxWX6rGO9u0pnXbbNoon8vhOeTkF+CMRUqL0tdM/y/eVPwM0x6eeClx0UW9lLdu3p32zYIGzt5VbzDIZDd10E9V53Hef2qZl2DASBBs3Uruh38PDlQF9jbOzSXhs2qSmlM+YQYL9ttv+b9N4/9ZKdMbYNJCQkGFvS38zALe5fG8+3OMjf9lgzN0Cef55ytpYskSFz5hBBDdkCGlJXLuMx2nj6Ed28oCpYah4+CmEWVnO4N7KleL8a551wQlPzsfn9+WN1WT8gwbRT//+Kvytt4Dhw/vhyScpiMlrMvg1H3/sXgipC5bcXNJCf/pJhe/fT2moTz1FWh8PpvJrBg2iAkNO+HKgVv4sv5+sbYbDtIF5SxF5xGJkbXXtqlomQ4YAR46UYP36qsqzBgKUbfXOOxT85gyGCwQ9LToZUxg1ioTd6aer8K+/prW/4AJK/ZbbrHi9zrb2yQTIiy/ST+vWKvzdd0kYmaZopS4/2/33b8TFF/dW8APinBU+unaln0suUbOnvv2W5vnZZ4lWRo5U8Tz2WMWytnidxKxZ6nWWRXNnWaQktGmjWl/dulHGIU8CYYzWl3/WaaW8HDh8OC3RCZgxspDlVG/5WTMynLU+F1xAdSOvvabuy4ICsrRfeIFSjnkjRC6IdCszmeI4Zgy9b8+eKnzCBBL8TzxBtT38aGNOE8kO3PqvqwP5/23EYgY6diSNlrcwByg1Ni+PXyPgt9wimhPqmoVhULqlXhTl9ZLGOcjFltKZxfLlJKTCYedZEW7E0qIF4e3Qwdk7yw0/33Q//0wpuzJ+wNnao39/cuHVrq1uqH37iEEGAu7V8J98orZ74fDu3SmtmZveTZvSRufaG78uGiWXEC+60i2Wn3+mYsvffqPPPHuoTx/SduU+Ze+/j0TwX56Lhg1FFpGbG2PUKFoPGV69OqWEyopCp07uuf0vvkiMyK0NhddL2qZcNc3dG3ff7WxXDjjxbN1K1uWhQ87aI8BZB9KuHQmERo3UFNZIRBQqurlBZ8wgZUmH162r0lyPHrQuepPFvXupToILJ71b86RJtF6627BbN3K9cusnM5Pe1a3A95xzVGVLvs/69bQ/5LbnsRi5MrdsUTPn7rmHsgJ1/H36iJM33ebohRfofBwZ7vVSFwh+VgxA9N6unXNffvEFuceTZWEdOaJmcaalES3+V1og/z+Nm27aisGDWyomOkCWh2XR38l8mzohpaWR0JFz+998kzQj+fwLgJhLNOru7+ZEoRefeb3EWOrUEVXkV16pupD4GD2aNN6TTnJ3MyRzP3z9NRUIcm2zaVP6OeUUEUfh8zN4sFPr1t0Pem7/kSNUod6hg+q/7dqVrCHup45E6Fm4INDdGPE4MV+ubcbjVLCVvA4khgYN1NqBY7kvy8poDhs3FvGuV16hddQPP5o/Xxwi5uau0NeYz0nfvqTx8rTpMWMoe0pv0f3SSyRs3JQBbrG4CfFXXmmByZOpJgggF4h+pCxA7rqbb6Y1dlM2ktHKggVkKfOYDz+wqlkzcl/yHlbr1xN+3klYX0vdquPvFYmQ5l+jhtoTrUkTwifvqblzRUNJHT8/TVBmwBde6DxWAKB7ejykROnHIBzLJXXffbTfeNzmuefo/fWaId4pWk/LTWZ9cnj//iSseWPR224TTRz/ilFpgVRwnH9+Adq0oSIxPR/844+pylfu6ZSs9Ql3VenwqlWJ0DdsULXNadMo8H7ffWqlajJCatiQXCz79ql4ko3yciLU+vWTB8VlptOhAzGqVavU0+f27KF+PNnZ7tXCx+qHJH/u04e05F27qN04Dzzu3Uudb3m1Pg9SHou5AE7G7/XSfLZuTbUgi+3qIcao9cWiRdWxa5ezPuGP9CvibUNefZWsHD5GjyZrZf58cdAX/y5fy2TMQnfDeDw0T/IRr0uXkqvw8sudtQkejzPAWr8+WX+HD6cqfZuSDf4MVauSK0nGDzjXuEcPKm5cvVpt/Ll7N2nS1arRessNEDke+XMyOD/6lp+Pwt/h6FFi/Hv3Eo3KCQJuLqNkcTeAhPbppxM98Nb6AFnIw4eTsJEVs2S0kkwJ6dmThMdnn4nDxgBSQp57juaPdwPm33Xb91yY6mv8V49KAVLBsX17BrZsIe1PPnyHWxTNm6sunWTMZeJEsgp0pvDZZ+Ty6tFDZFrx73q9VFQkuyuSEdIDD9ABPjr+xx8npnnTTc4gnsdD2qfcDj0ZU2jenDTJWrVU+Lff0iabPNnZowcgTVB3DXD8gNhsKSkkSLm/mcMPHyYX08aNFLTWXVWtWtE9eMZMSgrNJc+40TdVMEgxJDkjLhymljX6iMVIuOhnP4wdK6qrZfy//EKKwPDhxNBlPD4fWXtyR4NkxWGff06uHp0pfPopuUlOOoncfDJ+r5eswmHDnHAd/3nn0fNVqRJV4I89RvGD0aNVFxy/5p13nHsAcNJKw4Y0Pzk5KnzxYoo3TZ9OdKev5TnnUAYaj2EkEyB86AqZZdH3d+wgmFz0GIuRS+2UUw4oJ2QOHCg63Or4w2FSjmSFjO8bfSRTHJ98UpwSKO/L2bMpeH/TTWpvOU4TZ57p7GScjFY2bHDCv/yShKmugByvUenCqsBgDLjuuu4JrVHXLCIRYvqnnCICy5zpLF6sZgA1bEi/daYwYQJl4LiZpqmp5Bf2+URVbY0ahKtPHxU/Hzr+oiIKXG/frnZq5W4SfZx0EnDllTvg8TRW3DlHj5JmF4u5WxQ//khBWt0/3LSpejBO27YUuPziC9pA/LoNG4ipJNNCv/mGmNqmTWrfLa4R8lG3Ls397NmkzfE1Ky0l9xX3Z+v4Dx5MwxlnUCpxv37if82bOzvcXnutexrv+ee7n2fNGfn48TQX3OXFmdFnnwn6AAQD1Wli3jyaB50xc/yRCNEsn8P69cmaO/lkd0bi8TAla4vH1TZscDYC5c8jj969SWlYt059nv37yS1VXu5OKzNmULLH4MEUt+DwFi3UBI06dWieJ01SaWXHDrJGucWrC6L8fIpFzp2rxp7atQPOOGM92renfv1+P1n669cTPv2kUN49V3+HYJC8DtdcIyy+WIwUDV3AcHrT9+WIEbSX3fa9x0MKRPXqauKGx0Npvbq72zCceNatI1rRU9CP16gUIBUYfNMl620ViZCJPnasIPzJk2mD6wHrf/+b4Ml8mMkI6aSTiEl+9hnB5aZ18hg1igLGFW11wOGPP06uBX5Mbb9+QDy+A3l5jRX8kyeT+0WPafxe7cC6dcTQr7yS7meaJESuvprMeN45dfNmyubhmnVF0ngbNSJ3CJ8rebPUrk2bnG+2aNQZE5HxRaMGZsxQDzp6+GH1WFE+VqwQlpKb0HeDe73kihs+XAiQqVMJrtcnvPuu0Dj12MWx/OAnn0y0yk+4u/de0YRSHm+/TYpPbq6nwrQCkIBft07E1zp0oJ9IRKXLH38k5soVL66s/J6rat8+aveSl0fz6/HQnjnlFIrDcMvh4EFx9Kv8/WTuS4Dclm4KF0AC+7TTxDkwAGVUcQtGnyPGSPHr3VsIkCefpD2vK2VLl5KQ/CP73uslOjz1VJFV+c039H76Eb6vv07WtBut6HvieI5KAVKBcSzmlYxZ8MDbBx9Qtgn/PGYMaZ+TJjljBW6ElJ5OhK37x+XvMSbM+G3bSJO65BJnvyg3P3vv3qRtrl5N3+MjEACOHHGe0pTMXSHDZfynn04a848/UsrukCH0DHv2kDvvooucsR2OR/6sw/kmyckhTXTaNHrfRYtIIG3ZQqb7Cy+oRwT/Hn63OpCHHybL6/LLgeuuo+IugO5z772kicrB21jMnXlxuL7GnKHp2uann9LaPvOMytSS0UrNmsTES0udbhi3UVREFmnv3gGYpmgYlQx/r16koHCtlguQw4fJrUhtS9TnBNS5PpYAGTCArJ6ff6bA786dZJEdOkTreNll7icY/pGaocWLyXV54ol9MGkSZSYWFVESxlNPqXEO/t1kdSBuCiV3Hd52GwkjboledRUJ2Z07VeZ/rN5WaWnOxAoee1qzhp6Lu91++IG8FPwwNhnPX5WBBVQKkAoNvoBuTOHTT2lzv/uuCv/sM3KV3HILuXO4AOELqp/fnWzTch96u3YqAT/0EAVQFy8md82UKSoe+VjZY+Hn7pZLLlHxP/ss8OyzJyYaRfKzsfl3X3vNWZwHEPHy43cNg7TFGjUoLiBft2ULpaFmZVHgfeBAtbCsf39yu3DLwTDUo1R1Bsk3CYcHgyQU5ToG+f/Z2aThcpegz0dWj98fUK5jjDJ8QiHyM/fpIwRIPE7fk+sD5LnWO7XyLCq9jfk775D1cdttqrbJ8cvJGYDIytPXctw4+n3qqWpq9xNPkOunalVyK/Gzwvl3r7tuB049VUSak9HKiSfSz513qvCPPqKYzGefkQB/5RUV/113kYWrxyp0Bp+ZSQyRu804/NAhCig3aEDr2qmTcBMBtDfGjBHBco+H/ubxMN1txxhgWb6E2y4SIbesfPStPBfp6STU5aaMN91Ewn7KFHUu1q+n63i1vuzKdLMyuVB1i2kAzu7Wb7xB8zhuHCUO8H3P27nrmZaVAuQfMDgB1q5NxCYvyLnnis0qE8BNN5E2kixbYsYMIiYeIOML/eKLcLSMB5x4VqwgzU/3qcpdS+XRrRtdW6uW6jvlxOluQjMsWWLgu++cAkQ/Y+Cii2gj83qIWIz+v3kzMQR9jvjvmTNps+zbR/PL4S1aqGmwPXqQO+Hbb4kR8+sOHKBNI/uI5d+rV5PW+sUXpG1yeKtWarDfNOkdv/jiiPL9aJQEpR7T4R1iAXJHDRokfOWcwe/Yoba04O+jz/Xzz5M1kyz+tXo1CVeeepyaSsz2X/9yujLc8G/fTvGmzp1pDmX8gLMO5KSTCEdurtrNoLTU/cAqPg9Ll1LmmS5AsrJUxnn22ZTerSsV69eTJalr/Pz/8+dTUeXKlSREOLxpU7WWqFEjmvuFC8mtzK8rLycrSq/bkgVV48Zk8Q0ZIhShGjXUQ88AyooMhah2Q56Lbt1IaUy27595hp6d13rxff/TTyqtcB6g4/nsM6LVZC6v/fvpXnXrirmXPR3He1QKkAqM1FRgxIgNGDiwtaOnzPTpQvPRF9RNs+Dwyy8nzZIz5mnTaOG5hs3HiBHE9N0IMtmxrB4PtZkvLSXTFlCzcuTxr38Rcz3zTCd+w2BJmcWUKeTK4MyiWTP6ycujbCguxPLzRRsH+fvJ3A9yHcjcuWSFyEyyXTvSRjlDKisjIcQL3nSm4PGQFcK1zbQ0mnc9NsUYZ/xxtG1b8TRhr5eYZm6uECBff02MSA6IA9R7KiPjj/vBhwwhgcdPK+RxKn3cdx+957Hwu/XUevvtZnjiCUo4AIh2Lr6Y/pbbsL/0ErV1ueuu5O5LPjeyYrN0KSkWDzxA9J2bSz9NmlC8hp9RvmwZuQR5HVEy96W8tllZdL9Nm4gG5D5W9erRnPC6j2hU1Bbxzzq+nTtFZh5jRLtyQJ+PoiJSEvR7/l679TFjKAmEC5Dx40kgyAkmAJUGcNe1myBKhn/oUMpC48L5wQfFwXZ/xahM463ASEkBBg7cn3BJyX7SQYNIK9i/X20j8HtMQYenptLmWrWKtHY+pk2jQqy77yb/++/had+etNlAgIj89wYXOI0bC3+qDNeZTl4eMbD169XzQDZsoAB7RoZ6/Gcy9x//rfuRL7mENLsDB8iNxU/6W7OGGH80KoSq/L1kDF6H5+SQwGzWjIQIr2AvLKRrf/klF2vXOk+ZTPb8bm7NQYMoQWDMGDWN97HHSNjMmaNuar6WetA6WQEgH3v2UOIDH8uXk2XKM4N0PLq12qYNvefRoylKD65o1OkilN+xevXkNUPy57POovndsIHcaLzglgfg09NJG9fnsKJ1IH36kKKRnk60y5nm9u0Uf9i5k6w7fj5NMpo7loAaN46EHK9pkeduxAhaA17xzr/Li0IrUgDYpQvhGj9e5SsvvUQJNx9+qBbmJlNM/X4RpP+rUnbdxu8KEMMwvjIM4yzDMP5nhU0kAqxdWxUFBcQ0uTnLTVyvlxiarIkkI5glS6hdib7QL71ERU+XXKKeBc7xXHml2rU2Gf4nniAGr+O/4QbKQLnnHmHCy3ieeoqElQpnrkzn+utVHzRAQvS888gH/vDDIsuJX3PllZQdxmtljrVpefBQhu/bRxkve/ZQ/ESv/m/cmLRNrvVXqUJuDc7o3E6427rV2RnZMJjjOv6ctWuLeIfXSwzlvPPU/mWMEdPctInWwjmnZEXJLUK4xq6v5YIFZLXoazB2LGX9XX45BWd1PNdc46wPccN/+eWUzOHxMAV+yy00j6++Ks79lvE89JB6hG+yrKfGjammQ89Umz2bNPvly0X2kPz/U08lZsrdOMlohQ89/lVSQoL7wAFKfuDWpywAzzqrIHGCZHo6WVzcKpXXkv8sXeqsA3FzFXN4lSpqQsF771EjSH0NvvqKBN/jj5PAkPF4PCS4ZFdusn3/ww9EazqtvPKKsCb/ilERF9ZbAK4F8KphGBMB/JsxtuGve6R/3igqAm6/vUvCZ65rLl4vaZcnnkhZR/x/Xi/5YWXfJm+8py/0l1/SdclM1t27iZA5g+RH33bv7p6ip+MvLaUg4aFD7j249HHOOUA0uh1ZWS2UgquCAnHSoZtltXgxCaO77yatiF9Tq5ZwVQDEJHbtIveTjGvhQhJG/Pxpfa4XLqQ5nj9fbb/SrJk4ixogQffTT6I6mV+3bRvFAvTz6vnvUMiLk04i197FFwvmWKWKykC8XlFEKK9ZNEpC5ckn1dYs8hx9/DH5qHkwnsM/+EBVQrgQ1WlizhzSrrOznWuQkkLWZzQqekO1aUPwk05yb+Hi9TIHHo+HAstyJT2H64O3zSkqovtwYb1lC1mqehosn5MVK2iezziDaJ9/r1499fzxrl0phjZrFrX84XhWrKCYgm4t8t/r19MafvUVXcPhdeoAZ5yxCT17UqCgZk1STvR262VltO66S43/7fVSDPTCC4XFx/erfnws5wv6Wt59NwXKk3kqZsygOT35ZBW/bJXIQ8ezbh1lQf5V43cFCGPsJwA/GYZRDcAQADMNw9gNaq8+njEW+ese758xfs+05llPw4cLQlm1ighT79s/Zgy5N/6IH9zjIb+p1yv81O+/7/6s11xDguKP+tnHjKH0yenTCX7qqYDXuxd5eS0UYh0/nrRfuaqWCyuO322ONm4kjfPaa8nUNk3SMM86ixgi18jXriWtVO4yKv92a+Xdrp040jQ9XU1jzMoii4kL3EiEGKzuYhMWCGn+XGvz+ymxgRcV8hGNkubYrJnIPJPxHGuuH3mE3HNcgKxeLY6plcfo0e7xL3mu5QLAWIye97rraB7XrSP4I4/AdYwaRcJab2qYjFY48/r8c2qC+f33NF+dO4skhvvuE9d/8w3RyYsvqnPze/upsJAUhNNOQ+J8+tRUsqAnThSu1oICsqD4+e2/h9/rJeubWzY8U5CPtDQSBtwyOZblw+foxx/FuTGM0b6U28HzMWMGKQ1uSkWyWKnXS9Z8drYQICtW0H10Qf7gg3SdW5zrb8/CMgyjOoChoDM4fgXwKYA+AK4GkPdXPdw/ZeiEpAff3DYbb+733ntEsDzA+txz5KP+4guRZshxueHhWVMFBU7THSAtKRYTzGf3btLW9JbbyfAPGkQ+4p07VW3zwAFg/34toi+9c3o6MSt+9kUyATJ0KGlYixaRr/iCC0iArF1LmuEtt6jM+Y+eB9KiBcVHVqygDfTtt2QBLFxIFsIXX6hB52TuFv6bjq4Vn/1+0hIZI6vssstImAcCxIxeekk0SJS/90fiXzwrbsYMej/uYvz0UxKOo0e75/breJo1o7k9csSdVvRRUkLXNm9eqtBistjLwIGkFG3ZQi4Tft2uXRQD1JsO/p6g0OHXXENu2qVLaY8sXUoB7C1byO17xx3q2TF/FH9WFilgBQVAvXp5ePttypbcsIHihv/+t0hUkL+XrA5EXwPDEHHKO+6gYD1PXhkyhH42bEhen+UmrHW4YdDPypW0z3v2JPgPPxCfuekmNXX9bxcghmF8DaA1gE8AnMMY44b8l4ZhLEv+zf+eITMFnkUDkMYycyb5TkePVt0Yb79NLq0nnyTtQW6H4PVSLYB+DzeC4YHBAQNUbfOaayggvGEDVeTyRmwcjxzYOxZ+7vbRT5N76CHgu+9OQDRKm+qbb9S5ePBB0UlYxy9fx+tA5PRegLTuRx+ltMoDB8gSkVtzdOlC9+TZKWlppMFxf7oeKNTvW1ZGrjo+Z1zb5P+vUoUEAncJVqtG2nK9emUKnkiE/P21a5PGracL65tTFyDyc06bRgLp1FPVuX7ySXLT8Jbkcpqp1yssFbe5lvF88gn9vuIKFT5sGNFIdjZZmTt3qnjOPbcAeXktFfy8+WI8Luauf3/64TVG/PtvvkmCdNo0eobXXqP55c9w7bVEr7wILhmDT0+nH12479lD2YqnnkrPzuuD+P8bNaL4IV8bv5+sqmR1IDqtRCIkTHWhKz+n3jLo0UdpzcaNU11zS5YQTX33HdEgFyB8rvSTM4+1730+cpHJ8EceIfz8tEqu9HE8yerL/qpREQvkPfvgp8QwDCONMRZmjLkkuP33DZkpyP2Q5M0tE0B5OWkgzz2XXAudNo2sBh6k5Ic9PfusszBNxw8QA65b191klYN3fJx2Gvmoa9USAWiAtBVuEusakMfDEtlVbnMhj9tuI/N/wwbxfYAIfPFiJ/Pgv1etEh2OZQFSu7baRO6MM8gnr9cOrF1LB1NxzU/Hf+AAze24cbSZOTw3V32v3FxarxkzAo7vt2lDLjV5DeR5uPNO0r6HDpUtGZoL2XLgp/7pa/n88/QOyWiFuy1465PsbGKSN98skhXkoePZs4cESLLeWfo45xxyF9WoQQKDC5DCQqJ/Nzel10tuyo8+onmUBYjfr97nhhuIMfLOB/y6X34hhaxLFyd+gBITRo4kN+sZZ6hKCnfxACRIVq8my0X+/t69JJy5m03HD1CcbuRIukZeSz2OwF248lxbFimGfN+7ZWE9+yztW578wOFTpqj7lscd9bX8/HOKDyWjlV27yIXNM8/q1xcutr9iVESAPAXt1EAACwF0Of6P888ctWoBjz66Fv36qQc8hMOkaXTp4s5c3Hyb3DS9915yT3ABIh+vKY8rriCiTEYwjDnhfj9pfEuWCD+4fKqd3B762mtpIw8c6MTDm7PJWii/ZuZMioeMG0fCgdeB9OxJriNez/LDD6Q1ydXV8hzpWigXpCUlZFV17w4liN+sGWm83DIpLiZ3Fa/W/j03Rk4OMTBeG8BHNCr6HvXs6eziq2uJMvyLL+j7Q4eSCyk/n55TdgsB5B9v3PiPx6fuuYf+5t2Mv/wSruOKKyiWVFH8vODxo48a4eqrhWUyZIi4Rk4HfuIJYmD6iYMcv545x3//9htZJiNHkgssJ4d+GjQg647Hv3g2Ej+F8/doxe8XVsHy5TS3cqJG9er0zJ060edw2D2DT3ZVFRUJl2R6Os29W0xjxw4S5K1bC/pMRivyHH30ESlGXIDMnUvWr96f64UXSOHwet0PjHPD7/NRfHL5cnGM9tNPO5/9eI6kqbmGYdQ2DKMrANMwjBMMw+hi/+QBSE/2vf/GkZkJ5OUdROPGpCnyfPCSEmJc06eT5H/5ZYL/HiG5CRY+li1TYxEzZ5IQuOMO99oBHU+fPuQ6i8XctVN9cIHWtKnwpwr8LKE58s18ySWUsbJhAwkQfo/Fi8nVlZJCG48H+X4v5qAzhdtuIwuOu7X42Sv5+fQ5FqO4ye+leCaDN2hANQjNmpGVw2tZ1q0jhrN4cQ4WLXKefHgsASLDU1JIa69fnywLmdmPGkWfp09Xz1JJtpYpKfT8yWiFV5jzsWoVMeSLLlLP35Dxy9Zq796ULBAOe7F/v4AHAs4WMDKe3FxinHLigOy+5Jr3tddSzGHjRnJx8c7FCxZQKnJ6OtGdXpdR0bU85xyK+aWnU6xk6lSCL11KrtFduygIrR82lrwPmqokVa1KjLx3bxIiL7xAcMaoCPKllyi2N2qUiuePxL/atSNaGT9eNEoFaH6mTiVlSU6YSYYnN1ecPPh/WQdyLAvkDADXAKgPYKwEDwD4C2sb/3mjtBRYujQbbdoQ88zIUP3MXq96wI5cpawv9MGDRKgzZqjwESMoxfKTT4iI8/MJzgWOfEAQv4dbJTo/S+Saa1T4gAGkyZx2GhGk7Af3eKhuQK4d4C4sWRB4veRbbt9eVNBzZvHBB2SNNWlCaaoPPkjaJn+G886jFFquaSXbzHzobpI9e8jtV1RErpQmTUjD5/+vVYu0V84satWigCwPUOv4DYOEFHdJylajPOS1bNlSaLjcBdaxI6Vw8+8Hg+Sf7tWLrLPevVXryOt1apsyU5C1Ta5FnnGGyhTuu4/cnBs2qE0wOZ5kfnDdTcmPUB06VE3jHTqUmO+dd1Ka7IoVot2610uCQW9q6Bb/atyYfviRyBw+fTrFfS68kKy3oUNpTjgt9exJVqWc3ZSaKgSNXtOj37eoiBSakhKim6wstV18ejpw0UW70aULaSG5ueQCbdhQ3a/xONGHadJa8KQUed/r88zhtWqpWXU//kjv+MMP6hqMG0c0xF2k8vkyXq9a3KvPtYxn/nz6fdVVTr6yb5+Ijx3vkVSAMMY+AvCRYRiDGWNf/TW3//9jbN8OjBjRCU2aJNdCn3iCtFpZsPB+/rIfnLfl0DWFCRNIc/V6KajHByeYbdvItOZxgRNOIO2tUyf1nGs+3GIjhkE4Dhxw4tfHddcBTZvuQG5uW7RoIXBt3EhZLMn84Js2UfHSTTcJAeL10nvLLUmuuoo05SVLVDxTp1JqJnez6VlYvMvu119TRheH5+aq6ao9ehAj14vUFiygegg9KUCsGUPXrvR8cmKBx6P2QzJN0oD5XPPrDh0ihuhWzCm7Mfx+IVi4MvDmm+rhR3zojH/uXHKf6HUgXMgXFZEFwVvs9O5N/+ve3elW4+8ci6luSo+H0qI3b1bbzCSjFa6gyA0HV6yg77tZn14vreUDD9B61K8v/p+drR7xOmiQ6Bgt45kxgzR1Oagv/y4qogy/N98kq5XDTRO47batyMsjAdK0qdDy5QrybdvIjfTxx+oayPv+oosoNvXAAypcPjwNEIkROuMfPpxqYZJZLD/+SGvJs89Mk37uuEPta8aHjmfDBrVbwfEeSQWIYRhDGWPjATQ2DONu/f+MsbEuX/uvHMlMU84cPB7y8fftSwIkJ4eILydHLSJkjHyqZ57pZAqyZiG7njh85EhV2xw/3v1ZTzmFGEeyM9STEeqbb1L2zLp1xEQGDAB8vkLk5bXFzTeL68eNIxfQ2LHq3CTTQmXBMmkSab21apFQTU0lRrFihQgw//YbMVhuDembVk+prFKFcGRmqtomH34/bVA9MJvMjeHxMKxdS0ISoGcdN86ZolpaSlZily4iqC3jcdP4+Vy89RbRBRcgwSBdKysaALnzkjVZPJZ79LHHSOPkx93KfnB+3jhA3QFWrgS6dWOJOeU4k62lx0OW5gsvUKyienWaAz6/cufgzz6jd+WuGXnfJMNvGKQQTZlClpdsrTVuTBo8j0ns3k0M9oknnPgBJ61kZFDRY716QEmJF+EwlMPSAFIceLJCMk+CvMb8nA+A1nTCBFLu5MEYWVodO7orFdylrdf0cFrZsUMIELnNkTyuvPLYtPJXjaQxEAA84SwTQBWXn/+ZkUyAJIN7veRiqVaNNBvO7ONx4Tf96CPRiBBI3qK7RQvy1SfzgxcVUXYJH4WFpJmcfHLyc7dlPFdfTdk8hw+TtsL/t3UrsGuXMx2M40lPV7v6JmMKI0aQ0Fu/nlKD+bPOn0//83ppw/FN+HsMXof36EHujtq1Kb7B41PffEPBzV27aM71DqzJemfp8amsLMreat6cLB9eFLdnD1kgc+YQE+YxjWQ0caw18PvpeX78Ua1D+OILstAefZTaivweni5dKDaRjFbKy9UswnCYrmvWrAxDhyaPaXBcV11F2v6BA7R+XNFZt064UOTxe4JIhz/8MFmM27dTogO3OJYsITotKSHlixfn/lFaadyYBFPv3sCgQX3x7LMEz8+nZ5kzh5QFPSFDp4lka+z3i5Yod9+tVrBffjlZzUuWUDq42xzp1uSxYqUrVohGqQBZY2vWkDXIY7Eynr9qHMuFNc7+naRo/j8fhmGcCeAVAF5QuvCz2v8N+/+DAAQBXMMYW2H/7wMAZwMoZIy1/6ueEVAJpmZNwezq1CHm1bQppefx64qLSaM/6yzS1qtVU1M8vV5nah0nJL0JGw8iy98HKCe+Vy/SlH/+WW0vIvtS3fDzVuQeDxXGAUJLjcXomrvuAtavb4uMDKoMnzxZpGZ6vWRp6edluzELnnHDg71yeu+YMUTws2fTXDVsKL7XrBklEPCYRtWq5A92OwGQz6kM521bGCOmmZKinjeSmkrZRrzPUIMG5JevVy+obNqyMmKQLVqQ4OcxEHkt9XkGhDIga5vr1pEWfP754rpolJjNOecQzezcKawEPqdyWw8ZrtPKhAn0+9571fkZOJCeu149EkQ8C4mfIdGnz6FEIBhQmZf8TjxVlrt7OPyFF2itJk6kNR07lqxg/pxnncW7O6vPr+PnVqke29u2jdxId9xBa9C1KwkD2eU1fryYp6wsEhJ6R2U+9C4E0ag7o5XX+IwzxJ5NTSXlr08ftQ7EskiQtmtHv91oRa58l3vp6bTC3cR6TOPGG8ktl59PCgdvmcLnVD858++0QAAAhmF8ZBhGlvQ522be/9EwDMML4A0AAwG0BTDEMAw9Y3kggBb2zzBQXy4+/g3gzP/0OSoyYjEgEwF4veRi4VpoWhox8Zo1VU2hqIiCyCtWJNdcpk4Vh8EAxCAzMkhrcTuuVtdENm6k6t9kWm4spprEl11GGnSnTmTucm1z/36yWpJpiXv3ErFyXNxS0sdTT5FLQ89kmTlTNI/U8QPkhrj1ViFguBujShVyo/HeYZdeShaSrn3OmkVxIW7a6xYFQLiee079v9dLrhXeR6l+fcqmqVcvpGzmDRvIypk7N/la3nOPoAn5fJUVK8htx0eDBs7jjPkxsMuXJ1/LpUvVrr6NGtHz3nijO63o7TIKCymekcylpo9rryWrq3FjYv7cFcRPu0zmpiwoIC1b7inFmabMOB95hFyaOp7vviMrVYfzOS0qIldOfj595u+Ynk7KDO/z1b8/xbp4LYTce6tOHVJYPB7mSBP2eknI3nGHE/755+Lo3LQ0SjDQ0/f376dWRjNmJKeVMWNEoots9X72mdqNNyND1M/Ia/bll06+Is/1tm0kZPlo21akMf8VoyLGTUfG2FH+gTF2BMAJyS+v8OgBYAtjbBtjrBzAFwDO0645D8DHjMYiAFmGYdSxn2MugKLj8By/O0747D5srd0VXbuoEc7Sdz/DnvZnYPuWmFIE5J86EQvQGynxsLrQP/yAuegLf7QUL7wg0gLxyy/YUr0nXniwCF27SlrEihVYV7UnPn+xQMWzejWmHeiKGtYuFb51K77e2RX1yzbi3nul+omCAvzri164qdtynH8+aXNeL4BDh1DarBOeOnN+YtPG4wCKizFmwYnobeWrm9my8K/Jp2BgZDLmzydNes8eANEoGl9+Itqv+SKhbXbvTsjq3jAQm0d95GAKZ310MW7Bmw4/9eXfXIwn0p9FaSltlkSb8RtvBJ58ErVr0/PzOWrw0t24fM0Djs3aceLDeBnDHQHcE6Y+iQXthyndcAGg/PmXUHbe5SgvN3DyyYIZ5XzzPr7B+fB61LNRqn33MWYjD17EMGOGKHBs/tvXKO52Cgb0DcPnk7Tan37C7kZ9MH96qbpms2djBU5ARuiwCl+6FHPKuqFa6ABeeEGq41m3DlP2d8dr9+xAr16USAAA2LwZ2zLa443b16t4du/G+PVd0LRstQo/dAjPze2NztZCfPVVPZimHZQtLsYV4/rh6vo/48wzSdHJzQVQVoZI9xPx0hnT1bWMRHDfjAE425qowuNx3DT1HAwp/wgbNtDy8caW1a44G3W/eg1du5Jw44dB1bt/KPDiiyotAuj+wS14CE850n0HfHc7Psy5Bx4PuZ+4FY4HHwSGD4ffT9YQd19WH/c0nth/IyIRtQNxwwljMAmDHYpX4+lvYV3rC9Cmtbrvo/8ej8BJZ6LoYAydOok+a2kzJmMWTnbu+6lTkY/+8MfKMG2aSDf2zJ8Lq3Mv3HnlEWRlSQkOy5djV50e+Gn8fse+X1jaATVKt6vwLVswu6QLapdswiuvkJsPALB3L15e2BNv3yRlfxznUZFCQo9hGNm24IBhGDkV/N7vjXoAdkuf9wDoWYFr6gHYhwoOwzCGgawX1KpVC/lcfflDDxpCi/2bsTB/Im749CTUq2fhkkv24MQ7h6F+qAyvv/Q9XnmFcvby84Eej9yG3jiIlfO/RSBwOuJxA/n5K9F55N3oiw1YvvRblJSchWiU4B1GjkT1JUuw5s03Ma/6QJSV+dCt2xG0fuoptA0swYKvP0W3K05B06apyM8/jOavv46O0RVYtuo9fNf8JoRCNZCfvwANx49H+/IVGLT3ebzlfwzl5XWRnz8PdSZPRqvFi1EwYiQ2PfxQ4r1qzJqFdsHfcMWWhzC97A306FEH8+atRb3fFqLj0YW433oQ725tBaAl5s1bgKZ7l+GEfbPxRuYqPDdjLr77rh3OP38J2kdWodvChcDChciXukeae/ei567peAPT8eKazgA6YfnyX4H923Hi6kl4E5Pw+ppeALpg5crVqBbfgT5rJ2EUJuHzKXm4/PJeuP/+DRh46m70txtaze+WhwYNYti1C9i1I468qS/hAQBvrLkYQBds2rQF+fl7kDflKXQC8OWiS+DxnIht23YhP3878l57BDUAzNl8MTp1ysO55xbg+uu3I+/+u5EKYF3nK3HnnfmJtcwbfQOaAHjzl5mIRPpi375i5OdvQL9Hr0UjxDFu3lRY1qk4cCCE/Pw16HnvHahaUIDlk/+NB38dgLS0OC64YC+63H47GuzaiPEvTcG//tUAAEN+fgztHhqBE7ASSxZPwOHwYJSWZiI/fwlaP/00urDlWPHbx5ibdhVKS6sgP38Jmr3xBhosW4atzz2HRX2uQVFRKjp0KEajjz9G0+Ba1PrxDeBf1+HWWzORn1+AupMno431KwauG40vGj6LeLwx8vPzUXPWLLQ9ugj3ZY7Ay6G3EQoBc+bMR+PVc9Fh3jwcHXYrVr4/LrGW1X77DScULcRjxTdi/L7v0apVYyxbthZHZ61Gt/0/42XkY8y61gA6YMmS5YisXYeeu6biNUzFy9M74b33OqNt25U4vHoLTvz+e+D77/GL1GrAW1aGvhs/RTd8ig+W9wPQHb/9thY5GXvRf/bbeArAG2sGAeiCdes2Iv/nPcib+QZaAZi+9DwMHNgPw4ZtxZAhu5H3zDMAgK96XYoTTihHIGCv5TsP4UYAL68cBo+nC7Zv34X8/G3I+2AE2gD4cEE+YrHe2LOnCPn5G5E38lZUA7Bg7SS0GXwGOnQoxq23bsVJtwxDlZCFZ+6biVtu8Yt9f/91OBmH8eb87xAInG4nWqxE5wfvQX9swool36KkZBDCYQ/y839FxxEjkLNyKTZ/9iZeDF2AI0dScNFFe9HmySfRcP9S/PDmpzj/7t446ywP8vNDaP7qq2jH1uDXZe9jaeNbEA7XRH7+L2j08cfoHP8V+1aOxQctHkIkUgf5+fNR97vv0HLJEux/4AFsGDkSpaWlf4r/HWtURBC8CGCBYRjcGL8YwOjjcG/DBaYnMVbkmmMOxtg7AN4BgG7durE8ro78gXG0IAi8/jraVGmA9evrIT0dyMtrDoSoZLVTbjr6SnhZ6VEAQPvsNFSvng3LAvLy8oAyyrsbPpjh+0+yUVZmw21VomxrLvJXd8WqVeTHZmOpf3yjTAOn3dpVPNBHHwEAaqcbaNiwHjweG4/dm+PkvCz84G0AwIbbLXzXbW2EtavycP/9lOlSxa5YZP6qePTR9nZvq37A9jUAgKgnDW3akCreq9eJqDdrKwAgIzsDHTtS8KBr1x7osI3keRRe1K6dhxdeoFqFVuXCJr/jjk64+mqgWrUTkLJcFDv06kXpO23bdkCfZsKfctJJlMfZokVr9G8uUmV6dDsJ6zZ40Lw5UCflUALer2c7jB0L9OvXHF07NEzAT+/RBl6vgfr1GyGvv4D3bd4S0WgKatVqhLy8Rgl4rVgp8vK0ohsAXetUQ/fuJtq3N5GXVxtgpB5f1i8T78zLRHZ2JvLy8sDsnu8NPLWxcmUzVKsG5OW1ALMr81pViePss/sk8PIQRvMqHtTJqYldu+w1s/0cN5wHzPmtFnbssOEffwwAKNhcG4tTeopsK1utzc7046LbeJOIlhQgA5CSUQVNmzamueqXB4+dP92uWy5Mk6LNvXv3Qe5eWvsDh6qiqCgPt91G1lVTXjjk8WLEiI52K4/ewNf0vnHDi86dSSB07twVPQPCOdC1a2cAQIcOnXFipkgxbN06D6+9RrGo9jm/JeCXX94dPXsCDRq0Q9XDosCqdy9yfDRv3gp5nUUGx8k2rTRq1Ax5Peok4D1atEY4Iwe5uUCNXME2ejSujaFDd+HSS5sgL0/QxJkda+JRMw01a9ZBXp7A0612QwSDVZGeXpVSf0MUROpYPRUyP2EBSnvrUN2Pjh2zEIvRmrFSyiW/9jRg+uRsFBcTPF5O+fqZgVxs2NrW7kTdIuGaaJwJnHGRFNSw1752ZgoaNqwHw7Bpwi7dH3haFfzMpH1vr/2mnY2Ql5eH/Px85XmPx/hdFxZj7GMAgwEcsH8uZIx9chzuvQdAA+lzfQAFf+Kav3xsPEKO+L0rD7pmRZiBQjz1lDhjm9k2uFlaiG+/lXybdgTY2L9PxWMHFUo2H1DgLEy2dGawEJs3Q/TjsZlR47R9GDxYStPkeZsHDqhBORteNXIY8bjIvuHwtLjUHEu6vmZ2KWrUEL5eDg+XRVQ3g330oQ8x7N9PQdaCAul5QIHH3Fzbny4dlZiWShs7FoMoVQbgjZULuISneHsR+vWzZaUEzygrxF132SmYEp7sSKGYU6m8eut8aQ2kBc0oPYwTTxS9jvjwl9BaPvWUCq8WLlTXzEc+s/2/aWtg+9KqBAsTDQcBgNk+rsxgIcaMEeejyI51JXZhJ/9H9qi0wt+5aqgQhYUUq2NMzFHTjAPo31+qlbHh8UBp4kx0eQ28iCEcJr9+ebm4PgVSYA0yPIKMDEqESEmBsjaKa0uCHzrI8PTTdmq6BPd7I4kW/TK8YVaJwCPRUGz/QVf8voP70LatnSEnrb2/+ACuvHInHb0grX0db6Hr/l778z5HkBsAMkoPYOhQ4V5kHrHvP/lEpC8b9r7PCqkuqbiH9v2+ldq+54IlWIiZM6WTP+13yI4WYvhwcfTC7+17zxGhaB3vUdEErxQIa8ClVd+fGksBtDAMo4lhGKkALgMwWbtmMoCrDBq9ABRL3YD/z0aoCgUT0kokASJVfPkDBzF1qlhQw0vT2qlOITIzRQfOuC0Qdq4uUQnVJowqoYMqAdibOcM6iNdeowZ0ABJRyrb1SxJnkANIEMz6uQdVpmNvtqrlBxMB8GhUwLPKD2L8eAryFhYKPFURwPnnU4C3dm0BDx6NqJky0mZWmAWPpgLYuYPhgQfsYLe0yVvWLcWmTbbfVmL8KcWHBB7p+rTyEld4pnUQ69fbRZUSHhw8iIcespteSs/jC0prwKsNAaSXHcHevfY8SFkIjTOkak1p7Uu2FqJuXZHSzLw0wf4SdQ1YjBY1M1iISZNEJlNKiPJqezYhPE2a2Nfbz7rt12KVVvjahA+6CpAqViHee48CpzLjb1qdaOXxx+24jL1m2xYddBUg6dFA0rWcPZtqMTZsEPgNxtCvH2WRde0KlSaMuMAjwVPCpQIurWXJtkN4+WW7j5sErxYuxC+/2FlqMv7Dha7PmWrRusbjKp6axkEUFaXQpRI8vr8Q11xj04rUEiDVKhFrKa29WXYQmzeLpo1837fKVit74xGyMw9uLU6chQMAht10Kz14SBUg0r6fNInqegDxzl3rF6JpU6nY0n6H3b+67/usiEul8XEaFcnCGg46/yMXQE0A4w3DuOM/vTFjLArgdgA/AlgPYAJjbK1hGDcbhsFZ4jQA2wBsAR1glWi2YRjG56Cmjq0Mw9hjGMb1/+kzJRthP+UDplgS05Fa2qaEA4o2a9j/S7EC+PBDUXTHGVVgTzHGjZNy/u2FTosEVKZQRIRUzShxZSIoLkZhoWiYyOGp5aXo31/Som24qTMF+7410wOwLAqIy0wHAXfLxM+CqFKFmJ3PB1Xrs50y0agK37+1DM8+ax+FqgiEAFq0sFOjJcbvswLiOWVLJigxBYmJ5KYF0LYtpcLKeAJ7SzBqlH3Ql/ycQYkxy/jLg67wap4AhgyhjCsEgwn4oW0BfPut3SoiHocnbK99WF1Lo/gova++xom5DmDmTKlHlg0PFZZg5EiJVrS11AVIti/grvEXF6OsjNpayAw1PRZAkyZB3HKLzdgSAqTEFU+2L4BAgPpulZWpc6So6PIaR8uQmWlnYklrlmyNi/cEcNdd9hEFErz8cAAnnmg3upQtHCsAj8dJc75gicgIlOD1qwVw3XXdqbecRCsHtgTw6KN2o0Pp+hSZVqTDX9LkNY5EYNhCpworwYMPilbuXKgd2FiMCROkKvWjtgegXKMV+5l0eGLuAgH8+qvUnoRbk8WlGDpUpHMn1jjqUrJ+nEZFLJDrAfRkjD3KGHsEQC8ANx6PmzPGpjHGWjLGmjHGRtuwtxljb9t/M8bYbfb/OzDGlknfHcIYq8MYS2GM1WeMvX88nsltlKdS4YcvVIpGjag6WSawxtWlhT56NKGlHNkdwHff2SGLWAyeAC1kargE9euLVhOMM2aNYDxHiGAa5WiZOzZB7llfgpdekrqFcjzRAE4/3enaSiZAMmICLjMXoyyEH3+kRnU7d0p4mIVT+sewbZtdpyExhdSIdJ6GzJgtd8ZfsjeA55+nIigZXsVTikWL7JMBJa0yxXK3QDxlEjOS8HiCpSgstGW3whRKcO21djdkCZ7tK3EVIKGDAWzYYFtQMhMMCdcISkpg2GvvC5XC77cFbCQCw7YyOzYtVaxYZuM6tD2Ar76StE3uXiwvQcuWUiW8fb1fFyA2vFZGqavlcHBbCd56i1qJB4NQBEiHDsV48037CFyOP1bqKkB8Vim8iLmuwbolpTj9dLt2SYJ3bkZCZ+BAde5SQu4CxBeSLBPp+siRUnz0kZNWPKUkxIcOVfH4y6W1lK5HICA0ddmSsUoRidhKlExzoRKcdZZ9ho+Ev1H1UnXf26OssBRr1tgCMBKBp4zeJzWkMnJPsa3w2YKIy1/D3vet66lwmVYmTRJHGLAjQhC1a0fZkYB4VjMmVY8e51ERAWIAkL2CMbgHt/9rRxQ+WPDDZwUweTIVDyl+fFkTkbTT4AF3AksLFWPqVDoBDaEQDLukN52VYuRI0acpoe0EAmprEu53Lit29Xn6I2RRHD6s+sGreQJo357qLkxTwFmgVHVJ2c/qj1s4eiiK5cttg0vWNuWSZnnTRktRtartJpEZdhLGHygI4P777Q7E0tylWAH07OkU1im2BaLjObq31FVL9AbpnUeOhOrCKivGmDF263LZFcYCrgKkaKc73BcqxQMP2JaJ8r4BTJ9uxzElF5kvKOEJhRJaa/iwKlgSaxkuxtKlTq2yCgK48kqJVvjcBdwtEH95ibrGHB4rBWOkvTMm5s4fC6JB3Rguu8wuyJPpt9yd8QcPkBV16BAqRCtei+C6i8kbDLjCWUkA11xDTTUV5SFYinPOses+5LWMSftDgu/dEIDXa9eBSDTntQLo0sUurtWUjbFjqW+VqmwERM2NRHNHdklrLK19WqgYr7xChaOwrMTap5aXYtw4qU2J/UxGaanqkrLvHStxh6eVB7B1K1WoM4YEj6oCSck5zqMiAuRDAIsNw3jMMIzHACwC8Jdp+//E0bcvgAw/clKljSBtirIDAVStanfklVxbvrDEFKTOZ6mhEnz8sZ1oI+FplE3unG7dQF+yuyoe3UMEmag6tnH5w5p/3NZy08oDeOkl8stHIuIeaeWlOOkk6qSbnQ1BqOFQwvWkB5tTyyVtUHrWtYsCGDCAXBny5mnXMIDiYlvblPAoAkTCo7gxpLmLFZfivfds/NLc+ctL8M031N1XxuMplTathMdTFnBdg4xocaIiX+ldXmrh9NPtOhYJvzdUKpiRJuiWLbOLt6Trc/0yTgE/ulvSKqV5S5G10FAIhr2oaeESfPSRXcTGy+oB1DRL0aYN9XYCxDsHCzXLwX5ns7wYXjnWYePxxy3MmpGDlBTbly/NXddWpfj8c7vOQZq7tJBkTUpzp6yl9M4HtpD7b+FCde7qZAYQDFJhq4yHCxBdGVAsFvkc4QAJ67VrVTwoIavrwgvV5/FYpTAM5qAVn+W+X7M9QgjIeMKHAujWze59Jbu0Q8n3/cKFdisT6TnrVg0kqvARjSY2emCfZmXac8ddW7ySneNKLQ/g88+p+WQ0KuYoM/43ChC7aeK1oKK9IwCuZYy9/Jc90T9wVK8OoIofKeFSDB9OKbYywViFpfjuOzuIrhCkqm3ykRaWgnLa8YBLllAPJIUJBktx5ZVUqYtIJEFRnJAAezPb3zGjAVXb5LhCIbBIFJGITXjSPZrWLMXFF9sBfwmuaJsSvGx/AD//bCs58jvI2qa8qWwBIj8nINwVOjx2NIAbb7T7/Uhz5y0rwfnnU6sTdY4kbVCbuwRjluBmNIAmTWw3gASPHA7j1Veda+yzAq5r5rVKXeE+qxQvvUT9nWR46BDFxdau1eYn7I5HccNEIsLcDASweTN1M4jHAcbjbuEATjuNrNuMDDF3vngEqYw0Xsc9okFXeLK1rJ4awMknU4W//g5ueEIHA/jiC9sNqq2NadqJF/IaJ6GJZPhRWopLLqEOyDI8fJDclD16aHiSrKWibEjwjFgJ+ve3e2RJ8MM7AnjxRTv7Mtm+l+CpIfcYqrcsgIkTqaOvDI8XU0xm82aQG9Te96lhTUmw5y4tosE5LstyppYdp5FUgBiGkcN/AOwAMB50LvpOG/Y/M7ZtA47GqiJSRMGr5cuRWLQovAnNC4CDOToIJiUFOX7LAY8ZXgQPBDB+vN2JVtpQKaEAWre2z3mwry9HCnxRS5zXEYmR89bngzdajhQmpcFaFqIgypr0IWk7mzcTPG57I0/sEMCECXaA0rIQsUuEuAWS2Mw2heqMP2aT0sFtAVx6KbWSgGUhYlDSXuNaFkIh2z9rWYgZhEeJXWjMRXl+D+GJBy1MmyY9v5066S0L4K237K6lGlPQmQVLSUE8aDngEfiQEpYYkw2PwgtfMICuXe12+hyPx4OqHieziHl8KC8KYPZsuzyDw+FBarhUaJsSPCXkwnRSUpDpcdJKFF5Ej9J6nXuurW1yARINoU2LKK6+2u4QbFkotxMnU+107cRa2il5/og7Y17ycwBVqthV9tJatm1iYdYsO/5lWYgahEexEFxohcM5rViFAQwfbqenS3iqIoCdO23LRF7joIaf90eRXbzSWhohCytWUDdbee68wQCGDt1JripZWYqUOhQ+lpKCWKmFYNCWpzKthJLseyuAZs3sUzMlmstKsu/DRaWYM4fOBNEFZrVqdgakDY/DQKqkOMbKYzAiESAlBb5yK+FJ4GvM972iDBzHcSwLZDmAZfbv5drnZcf43n/dWLgQ2H6wOiJHSh1abiFqwmtRIPj++wX8EKrDZwXw8ceaayAnB7CchHSA1Uxo0TL8IHKRGiZt87vvgHiZ7arw58AXK8fZA2N4/31yQwEAs/uX8MBZLMqAUAiHDDsVWbMoDnnsZlOathmvTtfX8AfQr59wz4WrEjw1LOEJhXDUR/Dw4VJMmCA2bWkq6RqeUBBpaXZsJBSCtzbd16u5sILp1el6TbAE/YSHBS2cdZaw0spTMxGECU8Z+cd79IAQvtWru2qVByI5CBcFHfCDqIGUcBADBtixEQnuDQbw+ut2zysbbtSoobo9bPj+eE1EjwQclk8haiIlTG6Ghx6SaMWogZRwKR5+WAjGBK0Eg4pri+PxRcNIAbk4YyHSTg+B5q5wWyl++QUIhxhgWQil09z17GBhzBhhZcZzac38duIDv8dhT25iDUpLbTeoZaHEa+uNkhsKlgVm40mPUxA3M5Pglp3+rrspA6mEP3q0FK++arspLQvFaTUT923YUODx1HTHE06rgrDhB0pLhYvXshDz+BBAFRihIE47za7Lk+bOGwzg7LP3kZuVz3X16olgtk4rZYctx74/iBrwhchKPu88gf8gcuGzAnj6aTs+xWklJwfesPu+ZyXO+x5GDlLDAcyaZSdW2PAibw34IiFcf3UUq1YBKVH7+e1974+q+/4w399uR0weh5FUgDDGmjDGmtq/m2ifm/4lT/MPHbEYUIaMhDtEXejq8JZb+OUXu2DQhue0zEU6gvB4bEXJhu+xclBe4iTIIuTAF3ES2GFUhzdajklfxnD++UCkhOBZTWgzd25l4brrAG85wdfsIybCCSseJrdHkUGbNiVmJd4JloUim1nM+6EUWVl2C23LQlptwt+ppYU5c+zeUJaFgjDh95Wrbo+jPsLjC5cp8EAK4Sk5YOH22+3MFMtKtCrN9FrYt88+4c6ycMRLeAxLxR9OqYIovPCE1OeH349oajq8EVXbZKmpYFWqAMEgHnwQCW2TGQaOIguGvZnlNTiM6vCVh1BSYseMbaaQ0SgXJpyWSZE3F9Fiysxr0kRdS2/YaeEQ/iBmz6YTHDn+Wm1zkRYpQ1aWsAABYGeAlA2P5q8/bAsKXgAaK+VKC83dz1OC6NMH2L+TXFZVG9EatG9m4d57BWPeUpRj4wkpc3rEY9NQRF2DYh9dv2W1hebNheWQUouur59jYc0au7eVZWF/lJ7HG9ZoJZWYncdSLZOyNMIfDVh46ik7ZmJZ9MCpqUAwiFWr6JwUhEIIe0yUIgMoK1P2TTTFRBDp8ITUNWaGAWRlIy1uYf/+NDpagFsm2blgZUFccw0Uy6QIOfC4MH5aSwsHDtg9uGx4RsPq8DNVwALAYZaDaCCI6tXtBqEa/9DxH0IufJEQ5syOU1t4G57bmuauVmYZOnZEIm18c2ItbZooozUtstdSEfrHcVSkDsQwDGOoYRgP258bGobR4/e+9980YjHAggmjPORY6GQE5snJhmFZ+PRTux7Dhu8oyYFhBfHSS/ZpfIoACcHrUZlFrCoRhp+phMEZ8IEdFhYtAqKloQQeAOjZ0cLo0eJ7RbbXMdUWLLFyCtJXb5ZN+EIhFBcLbfOox9Y2LZVxlthMJN2w0LGj0GaLbe3UG5GYUSiE+p3oOUNHLbzxhl18ZlkoCHPLxELt2sLCCfkyE+4HmQGX+0xaAysIwxBMwZ9lomoNP3zlFPweM8bGY5jYsMMPhEK48UYKLMKyEPX5ibnIDN5m5EeQDW8k7FjLqg2z4S0nQX3JJQK+tiAbsbIQXn/drtOw4UeQnaAJXUnwRpw0hJwcIBRC/mymaJu7gjR3w28OK7RyBLRmnFlwq9RTXYWzoP3bPiaw7GAQmzcDkSDF0fga180uxn332UqsZeGITSspMdtNa2v21VvQ88RKLWzdKlw6h1m2k1ZCIQS8BPdFLdSpI1xqpT6Ce8tVwdWwbRXA40G8zMLDD9tnjFgWiiwTZXFay44d7cw8y0LEayIMgstzGuG0oglxw+9H3WYm0uIWHnigI+68Uzzz0i3ZiJZauOkmNS5WhBx4Q0GHMnAE2fBEQo41Tq+XA295CKNH28WxNnxdYXXEyyy88IKdcSjh8ZZbjn1f4qE5SrWFO19jyn4B1q0gugsdIXhBiNbsrFMszJwJZHgIftQQ+/uvGBXJwnoTQG8A/ISJAKgN+//M4ALEE7bQogUdGMMXuvvppNHoTGHtvhzEgxbmzbPrQGSCLLeQnS02AocDQBrCCp52fWymwFRC+n4RXT/lyyB69waCh1Xm0rGFhQcfREJz5nBumXDmUqNVjgKPRajXyZItBN+wMoRWrey4j6SFNqwZwqpVdDYBLAtHuQApVy0ET3UVzjfbAasaANI2H3lEMIuwx0S5xw9YFlavtlMnLQveTBOxtHTCKW9mfsanCxMJwQQsCzt32gdZhUKIpghBdP31dnW/ZYGlpKBJh0ykRp0Mfl84G/EyCwUFaiCYKw+JIcGN8hCqVbM7rNrwPufkICXqpJUlW3IAxjDv53I8/jjALFUZqJttJeINMjw1pgqQlj3VtUzQykKC5/9goWVLYM9mzlwIXq86uWDr1bPX0mY6voi0lqEQqtlWrw5fvZfgRQUWevcWySRc2chKpbnjbsFSXxYAwKMJEL6W3B3LaaU0biIQpbUcN07QSrnPRMgg+MSJduJDKAQj3URqVROGpc41M00wv9+mIaZYJkeRBSNkoaTEzoqV17jcwjnnQHF5NeueAz9zWpl7yrIRD1rYtYsOGuOMm+/7xJDgHhaH32u3B+J85QxdcaTf89cTfPGcEO64A7CKVJqoVz2EAQMEDXBlQBHux3FURID0ZIzdBiAEJNq5px77K/9dIxYDQvDDCJEW/cknUDQOIxRyaLMrduY4mBpAJqsnGsEPU6KUxmvDWTXatLddZykaCtc4dGZRGFVNVg7nhBQsCmHHDmLQANC0K+FpWDOEESOAmlVsX25M1TY58+KEFyu1sGkTUFZK/nSuGemWyYlnCaZTr55dZ2JZWL/f1jZDqhsj5E1HyPAjboXw5JMi6F7uMRE2SCC0bSu04tqNTWTVJmYhz+n+EhNrt5tgQRUe9fnJP27R5r/9djjcG/fcIwK1hmmiQXM/vNFylekYBmYuqYZYMOTqdvSEQ3j8cXe3x7vvivcCyEIwolGkGFFN2XC3KPharloYpPPSbaHP3YuDTglh9myhbSZoxdZa+fWHWXWFhjg8oZ1a5ThyRFgmzbsTPNtv4YYbgPr1aO33ldsCRHNfFtuWTLwshEWL7DYwloUSn4v2a1noeUo6mN+fcCNy+Ja9JsqYmRDKCWXAKwTFvffSmSOwLJR7TYRtZePEE+06EMtCRnUTjdqkw7DUOFdZ3MRPv5goLwmJdu42rZDFEsLgwSJZJe7xogRVYYQs3H+/mplXr122a0wj/7dsB43ytfRGwhj3ZkzJ5uJr/ORDIQpTyFapvJY2TWw+rCoPfC25grh7s4UJE4RlUrWhy349jqMiAiRiH/7EAMAwjBoA4sf+yn/XuOgioEf/QMI9AyCxIIs2ZoNZFmrUUC2KI8iGpzwMnyfuICQA+GmKRYcc2fALrid47WqqtvnRFI2QOFOAyhR0pjPrewtNmgAHd3FLhuCNa9F96+YQvi9nqtqmzly41sTKKZbCXVWHdlvo2dM+6Miy4K9D8KqpIezZY5+IaFlYv6cKoobPwRTCHmIKSkwjFLItDWIWb75pHx4kWxrBIKZPpyNPOZ6yGAl3edOWc6ajCfGUqiaatCEmVVYm3DCxNBOHykx4wmGceabd+sQWONz61DN0jiAbRtjC5s1SbAfAJTdlwxMOib5JNvynX233nydECVC69alZmRw+b4aF224T8IFXCFrJyxPC/+2JqgUiBIgNt2MaCaZjKwm7NnqRkwMsm0fwJl0IXqNKCO++C3RsXQ4whmmLqyu0kohpeNytz6CRiajhQ/iohbPPtg9Qs4W1YZpIiYYQjVLnZlgWCo6QpWFoca5yr0nKgLaWviomUqrQGk+dKrLF4PcTrVik8N1yi7qWumsrmmImFESF8ZsmuvYxE+8rr+XO4iwwy0KPHsApp6hr6QmTK1pXNgBgy5qQEiu9arhmIdi/py92VxwTnoSYyg84/hXzLVx6KcUcAaDPuTb+v9GF9SqAbwDUNAxjNID5AJ4+9lf+u0b16kBmDS8My8LIkULbjKWkYeYCcqu8/hrDnDlwEIwfISXNMpIpTFMlz93WOH5bQr5NTjA7SohgzuhHwex0QyWktJjKFNr34QSmEuShGMFjpRZpm3YwvshmLrmZIVx3nbBM+PPrguXMy21tMxjCkiXA4UJKH160riqY4XFYJpZhIuRJh6fcEodu2Yw/7HFqmx16mKhRn7TKBx8UmSxrtpnYuIfm+uSThRsx4rVdVW4uLI/TYvFnmWjegZjUySfbrVIsC6UxE9/OMGGEI3jgATqTiNbYnbnEfKkIIh1G2Bm3yqxPc/3WS6GEoAOA2ato7kaPsqha29LWUrNAUmu5u6q4pbFns4XPPhPa5n7bQujQIoSvviIBA1BGD+AULB3y7DWOhRVa2RsUWitjslJB15uwcO65QO1cKnorMaohDiPhkuJ0fdZFJrzpfrCghe+/p3R4hEJYudFEaczvoJWwx0TEQ5aJjKdcskBkK7BeM1pLWGRNvvYawXcfMvHTwvSE9cnrQKI+WktPSHJhhUIiZqLRkCfdRJsTTHisIAYNspsXWhZiqX6M/yYdCIVw771UmKuvZSoLOzwPfI1luK8GXT/jOwvXXCPmerHtQr72MguBgFAuHO5L+3qeVJOwTGxPAucrf5sFwhj7FMAIAM+ADnI6nzE28S95mn/oWLkS2LA9BywUwtat1Cpb0VwYS1SN84U6iiwAQKYvRO4cWwMY+bxwPcmENOYDgi+cZeGOO5xaaK2qFvr1E0ygKAlTOHMIj3XYm9mGP/KKiGnk5ACrFqnaab0cC++/DzSpoxJqwuqyn7N6M3qvhGViE+qcJeROKC+2MGgQ8O03lEYYgolyr4lMI4jycjqZjmuhUZ8/4e8+ZkwjFEJJxERJhJjFN9+ImIzsB3/9dbuGxnZjNGzhdwiQqM+Pkmg6mJweywUO/PCWiy6ssCxEU82Ee6NHDxHz8aSbuGm4CSMeRwoiwp/u8+GH+VUAUKBTLi7lzEXXNhMWSFxlCnc8ZjMdTUl41F7LVYtDuOIKIFCo4q+RaeHCC4n23GiF3/fEQTazi6oC5OWP6fr924lhT5mg4s/xB/Hdd8CJJxDcgomI1y+UATuF1MwxYaRT8om8xht2irW87jqhJIQME2EvMfLDh0VavK+KCU+6UxmAaZK1ocFDHhMBG//ChSKzMJIi1vLyy3fR0bW2Vdq5twnoSkKaiX3F6YkizQSc00QslnTft25EbjUOH/E0zZ0/HlT2/YSfhGXy0UekmMlrlhoPUSPKkCaguKCw+cQNI1RXNOcfI5//m11YhmG8AiCHMfYGY+x1xtj6v+RJ/sFj1ixg3vJ6MCIR+IyYIKQU8p0CwFtjLWrmZlsmYQ8dhPPwvVbCJwzDSJxbmSAkW7As3+aeQcMJZu/WEMaPB8JHCd7pZGIuXduSz7OKj+A8FTLBLDQ83KLgBFmkZ9DYv6+/l+CZXqq7qJ5O8IW/ZSCekgqPLUA407CYHxGfCRYK4YcfgF2b6L0sgwRIAj8jf/rp55mo18xMHM7DGfC8ZSa27RNMIaGFevwI2xbF9dfbfcQsO2Zi+8HPPhvo2ZPgOfVMtO3qtEz2FJkY/7XQZnU/uLc8jAsusBvn2VorZeCV48H7Ywkt10g3UaMhrb0JK7GWEZ+Jb34kuJ8JJYEZBopBiQMzJoeUTB9PDs31FYMphdjPz2fJUQULp4kNB92VB850Sg5YmD4dKD1I8JPOJniT2hbeeosEDAAcinM8mjvEpgldeQgiHRFPmoNWrr7ZJHdS1EKvXkCtavS9RatMlMVNR+q1BbI0EArh3/+2my+GQgh5TJTba5yTI7K22nUz0aG704X16wYT85c717jca1ufwSCuvdY+w0VaS4Qs9O17KJGZZ2ab6HqiXw2620rL2x/T2qd4YooACcEPALj/TouamVoWoimU4QcAN14Zop5dlgV4PMhqWDWxlrIA+Trf3frk+/W3xRbuvlvse56SndeLlFm+L7lV6tOUhD1lf78LawWAUYZhbDEMY4xhGN3+kif5B494HAlBYcJKmL4xW6MBgK1rqDoXlgVvhom3/m03/Zc2WzzNjydfJAJLi6suLN23qVsga5dZuPJKIGAzhZsfFH7wiy8WBHjhDZqPVNNyE/5cblrH6fqdG2kTLs4neOvuVRD3elEj08LUqUCH5rbGNMWOCdhaJSfMIDMR8QpmwQVUuddEuTcd0VIy0WdMi9KE2n5qw7JQWgqMGkXPtO+oiaNhYgoygw97yBXGC+sSmUG1TdRqTNcvXqxahzyba8QIkc3FXV56hg53Y3jKyxGNMDoOwrKQkWvi6mF+5V1hWQh7Tfz8C8Gb1w8lmAjXTgHVTRlPE/DNv1kJAQgAr38qtMoqVcTc3f6Ie1aVQwvVlITt60MYOBAo2ErwoXfaMY2MIG6+GaiWRu9x4/02TWgWSDGrirjhSViZ/HmCzES5z0TJAQu1agFTJxK8ViM/vBkm/Ahh4ULgvNMJPnepiaMh4ZLibXhCklKhu4zifoI/9BAEA+ZWqWVh8WK7y7RloSRi04rlEv/ypDvg6bkm2p5A7sg9e8xESnkkxURRiGjoyqEskd4b8/md+15b4/KSEJ1BY1nwZJh46Am/MpewLMT9Jr6cQvu+djXK5NQtFl1J4Pt1+/oQXnoJKC8m+DPj7DiaYaFpUyHkr72bW5MqHq4k/J0urI8YY4MA9ACwCcBzhmFs/p2v/VcNnoUFkC9SD74BmmbBg3gAZk4JJQLK0RQT85YT/OarhWUST0lFGTISeABBADz4rVsUXDst3hfEzJlCQ+GE16S2hVdeoRRKGa5rlfc9RVqxt1wVaHOWmIj6JG2TCwrbJZUStXDSSUKbDTITEZ9gFpzp3P2giYatKEvqo4+AjSsJPmOebWmEQsjIsE+xs90YEa/TLRE2hHYqw5u0NdGjn3CHPPEEEtrpJ18R/Pzz7aaDsssrGFRiF9yFZTCGNKNcCbo3bUdrdv/wUMIPXhbzkyUDYPgw8vEfiybiaSaiPjMBZ8x2/6WkJE4cW7s8hHvuEWu5YCOt2Zn9qe4iDSJ4DzgDqSedpWqhXHkI2N0AQkeo2JLHTIriWQCAamlBPPEE0LCGbcXGTUR8ZsLK5Gt55/0mUqtRCnRhoYijzVtmIsj8CtMESOkq95nwhENo2VJoyxzOLYd4hFxBg4eaaN+VaGLsWJFAseBXEwt+pbVs1MgugQqFUO7xo9zrtEwo6C5ohSt81euZ6HcGucjGjm2ZcKfuPmTipbf8QDyOC8+JJOJWETtjD5CsSSkVXIHbArBhK4J/8o6VaGUS8Zn48EuCXzk4mHCpxVLSEvh1ZcCb655txS2NvVtDePZZYWWuLhDxr4ULgdwMW0F0q9E5jqMiFggfzQG0BtAYwIa/5Gn+oYPXgQBAm8YWnbhmWahWx8Rr79pMQRIslmHi5beJiexYb+Hzz4kAZM0lLW4lmtHJ2qkeBHvuHY1Z2Iy8cVdyYW1cRQV0R/epgqJWVQt33kkuKCC5C+vks9IBv9+hbT76LD1TUUEIdetSbAYALGYi6vUjHRbmzwdO7iWYQsRmFoBwbXHt0WNXlnP8G3eZOFhKm/z++4HJX5F2Gjb8Ce10yRJgzPPk8sptYCKnnsYUNO1UtkzCXpEOvGWLXcAYCpEF4kkHGMP1V5YnXEk1Gpi45CrNJWVR6uei3wgeOkKVx7LAoZcXjFNmLjWrhtCwId03pYqJyTPoejmjLppq4o4RdP3OjRbGjiXGHPdSOw4AyDCCaNoUCesuWUzjgTE828peSxve0Q6W795EtLtrI8FL4+mIeNNQxVuGhx8G6le3BQgzEU0xE4V+PE7VtquJlKrpibXla/nxRBNFQRPRgIUOHYCvP+UuL9sqDVvYuBG4bohtSaX6EUsRSoJOK4k1jlEs5UDAxIFiEhRvvWUfZ2xZisvrk0+Al18meE5dW+gH1QLAWIqfXFuRCHxSKnWE0woou5BXlnOrFAAGnSxc1OnVTQwfQWspC5Byr4nvZ9H1ZYdD2LCBhHg8VQgi1SMh8Gd4KTbJBcV3c7KIVhL8gH6ffy3t44KtFh54QAgQThNVfORG5N/j8L/NhWUYBrc4ngCwBkBXxtg5f8nT/EOHbIHcOSyEiROR0Dgyazg1kRBMTPnZFggSs5AFyK+/BHHPPTbB+E207ED4B/QJYds22xJJTbVLtFULhBkGjtimr85EOMGEjoawerUwfR95LhPM50O1NAtPPknFaQAwfzmlzeqWSVnctLU7ajXCtc2yuNAe5evf+MBE3aaU3dSqFVA9g/7/+Td+7DqcnmA2XFDJbow33gAWzZYEkZfw16sHZKeTe+XEU030OtnJFKbPMfHOxy5aqMe2ZEIh3HoLS7RKSfjHAQwdTG41WBaq1LQDqQD8hlAG9peYeON9WhtZsEQl5vLRuFAiYCoLkGFXksavCDqoWmU0xcSsRTY8YTmEwNKEP33XRkq9Li+mte91OlmN7ZpaWLoUyHH4wVX3ZRDpiPrS4IuoQrwsbltFoQh27QJCxfS9R542kVrFj9S4hbvuAprWoevzF4uUZhkPWZ8mEA5hzRqgeL9QNiI+p2Vy78MmOvagNa5eXSg5k6aZWL1FxKcMO6EhbJiJ+NeLLwJffglhldo01LatyMxr0dHE6eenA5GIErtYtcnEw087lYSI146vAXhsZAj9+zvX+JKzg4mgfmpVE516aYpjKITSmImXxwnrk69lVNr3P39voW9fckfGU21aB1WQHz5sFw6mpSVohSuO3PPwy7os1zXmCuKRAkqGKT1E8HOGVKFmlH+jBbIdQG/G2JmMsQ8ZY0f/kif5B4877gBuGr6bPkib4UjYxPufEsHUybIS/aIimhsDcAqQrWtJ22QWZZl8/i3B0w2q3/CESTtt29UmJC4oQhZYmvDNcm2TB6NLQP7rnRuonqRwJ8Gvuoly76v4Qhg1SqR4DrneRDBuOv3dcT8ivjQBD6vMoryENu3MyQT3Z5vwpFNW1YYNwKXnClfYgWIRLOf4eeYOZ/ycKVWvbyK9OjGdN98EJn/p1E6nTAEeHin86UG74lx2SYU9lNEDAKYkEBq2MnHuJQQv2issipIIFSQCwGknWQm3o6yFylZmRBIUJQesROylen0TU2Y641+WYeKhpwie6bVQvTqtvRyQTTALW2vl+HdtpPTxSAm14/j0a6G1dusmBI9ZJwvMMISVKbmSoikmfOUqIy+NmfQeRTE0agSsXEDwAeeYSKlqIi1GNNqmsbBKC0vdBUjU5098TiRWSMrAKacAkz5xruWuXcCDdxF87VYT+486LZOwR42ZsAilD9dsZKJOU3+iDmTKFJBiI7mQX33OSrSHSdSTgNLrZcuh3OO0KHIbmrjlLjvWUUx1Q7AoCWC+7Yru1NJKtLeRlQe+76Ht++J9ZLkzy0JalomVG5xWbCzVxNAb1X1PloxQKjicr3ExqoEZBg7soOJPLsRfHicy2P6KUZEYyNuMsUN/yd3/PxlZWUC12tQ6+r3XyPcPi3r0fDTR9m1eTEFcnZAUE9RvonZjm8BigsBk7XT3JgvPPAOUlxAh7TlMBNa6cQjLlwPZaWT6RpAC5vGIoHgoBJaSgkcf94Kl+R2uqhXrTcTTTMTKaNOGbW2TmIsfpieEO+8UgqU0biLiTXMwiw8+N1GvKWWsrF8vWqi8+aGJAwFT2QiAEDhGiDJreB2LHkjlguqKG0z0yiP4q68C074i+PufmfjsG4J37sTQpLbEXDwmEI8jzRNRBEiEMwVJgNRuYqLPaTTXI+6wqD1FKIR1O0w8/SJdf8k5VuIcj4jX3d8tu7BS4wK/x/QjPYfgP34XSrS/CBsmJn1P8LMHhHDoEOArV5mLXLvDTBOde9qCRQ6MSrRydB+19ig7RJZJCGmIpfhRs4qFH38ULikLJmKpJrwaTTzyDLX88EXCCnz+cmKoLETV0bL1GfURniuuEDGTICNBpAuQ194z0aEHrdm8eZQWDAAffmH3KdNoJQTK5ONKBadhohWhbHBa6XeGidPOMYFoFC+NiWLsGKpJ+m6Gicefo7nr3dmiA9q4APEIRU2JmXiclknVmib6nk7wZx8VBb4HAiYeGk3wgXkW3n4bDsUx4XmwLCXZJjXJvl+7nKrgw0dJceQejF6dKDaZlUppxRy/V1Ic46lpOPscD+Kp/oRlkphbnur8N2Zh/c+P/Hzg51/qAwACB0PYuBEO7VTxg0vMJdMXSvTzr1bLj58XODWLsrgfJw2g6/duoQK6SLHKXNINC1260KaKp5kADMRSTUXbNEwTjzwCeDNMeCVCYh4PuvZOQVncj8ABCkRu+FViLikm0kFB9wa5kvbo8yeyrbj/vU5T0k4NLdbx8UQThSXELAYMEBk6Ce3UIhP9qosJnlmD8OgCRCZ4GX7E8qM4YgKM4avPyzFvhsZcAIx9OoSnHiXLpGVnISjSYVFtgmWhuNzEzkIhEORitXLbYomVhRJZWLKg6NTSwgUXAAiF0LiNiYlThLbJmc7hoInnXiX44T0iM092YySLmcjuyNSqJmYt8Dvg0RQTtet6EPOl4uBuCzffTHUgLNUPwEA81Q8/Qjj9dKIZ5vUiihSKaWhuymHDTfiz/IksLL6Wl1xj4lDQRKTEQtWq1EMLIIuFWzLjxwOdWxM+HnTnNMHXzJ9twpshWRQ2Lc1damJvkZlodMktEx5Hg0Vu0ycfJHhOPRM5dU0gHIbXiAulidMKiPFz5mkZJoKM5nTJHAvz5jLJ0iD4eadvT2RzNWxtYsi1ziSZkqiJXzcIV7TsvkzEvyRXruzyqp9LaeWGZSG7nomVG1QBwiwLZczE7ffZysB+C19/TYW+slVqhEOJbt7xNBNxeBH3pSTe1bBd6ZMn076X+QHz+eBN8yX6iP0Vo1KAVGD88APw9Q9NACTXQmdOsRJFZvE00uwA4PS+tBl8kZCrHxxBwrN8HcF9khsjluJHFClgXi+K95OmYx2xYJh+Sks1TdTNpgOWqqWR1rp7NxD3C3eFEbLA/LbASTHhsZmI7EqKplKWVDAomrb9MNtE1ZoGUqLUGqGGXaE+7mMKfnOXFmc6ZXGTAqOhEBYsoGAkILRTXdt88EkTpw4i5uLzCW3zmZdN/DhPuKQ407MM4S9+9rEQvvw3t0D8CabQs6OFbu0I3raLif5nCkHhiVI7jvxF/oQrSdY2yz1CC33uMZFqWS5ZIINOoSAuLAspVUzUbCTWkguiQ0ETb33EmY4lBXAFnrXLLAweDERLSQtt0ppoqFu7EOJxu6bHNOnwlLQ0RYDE0kwcOADEUoS2aYQoVRQA4qkmwkepuWDgELlzHn8cSK1qoloqMX5uZa7elIZIigkvt0Ak11MsRaRk8zUOxv2Iuqzll5NNtO4slId6OQR/+yMT2/aZiZRsLlgSMROLUsS3rHYKkBQfS9z34qtMXHiFrQx4QglaeeMDE29+aK8xBDwRGwHwyrMWnhxF7xeWXFXtmh1OWId1m5o47Vynlbl+mx833eVuffK1/OJDi86M19yavTqFMGUKzZ0n3USVmpqVGQrBYibe/9ymFWmN46kmypEKZhgo2GrhxhuB4BHiH/36ASzNjya1KYuzRqaV4CkwVSuT+U3E40A09W8QIPKJhG4/f8nT/ENHLAZEvGkAVE1Edm8U7w9Rl1BbO1250altHgiYGHCOTUiaiRsG4ZdjHbFUzhT8KNoXwi23kMsopYqJl18GfJkm0g1yw6TFiLAbNgTKYqoLi6XRpomlmvBKjJ+lpoLBQwWRRymdds0S+n/XPia8mSlIjVr44gugRT2Cjx5LbjXdXVEWNxPMRbYcfFUo9gKLBBHXZuWK8337gAfvpvnYts/E4TKyNPyecuHG4MwFpFlzeOvO1K8IoF5OPFssEPHjiEXvff0VITzziOZPhx2wtM+gDnvtmAxUi6J9dxPvf+pcy71FJl57l66vnxtK9EOSaSItJgXdJffG0f0hfP01VRHn1DWxYp0/sVZc2yyJmmjXjja/TBNkfZKgkJWEuE0rsTQTZYfJL39wl7BKzRwT/ji5njK9Fpjfj46dDOwvFi4sj6RUxFL9DiuTLBA/4mUWMjKAn6cSvF5zE2nV/DBCIcycCfTvQfDxX5nYccBJE7KyIcOr1SaLCIzhkZHl+H6S09L48bsQXn7GtkpDJorLhTKQECDSGpuwEvPXrJ2J8y4j+IEdBhYvElbp9v0EP61vCM88A0oTltdSslZlAeIpF7GRhq1MzF7gjGkcsfwY+RjBc/wWuncnCyGaKvZ9wvUUoqA7YCCeZiJQaOG998iNmFbNxJw53NIIoUYNWpuQx0Tt2oDF/CLOFQ4BtlLB5/qvGMeyQJZDnEB4EFQDstn+e/nxuLlhGGcahrHRLlIc6fJ/wzCMV+3//2YYRpeKfvd4jliMNF1AKgCUeuhwOOX2WwrBr/81hHPOIc2+LG7i5/mkWfTpQni4H5y7H1Ikxu/LNHHFFQBMwSw8tmYRDALMNBE6QqZv+KjKXKqlWfjgA9sy4YSUKtpNeML0nNOnk4sgEesoD4H5fHj3Qx9KIukObZO7MYyQhTPPFFXHpTEzoenITGHyTBOnnEXwb79h2LuF4I8+a5I7z2bgcswk6rPdEpK2aSURIP3OMHHepXT962MsjB0t/OyPPUfXd2tn4Yx+tiDyCEFhwkpYguWaYIlHqa19Zq4fbU6g67/40Eq4I3cUmnj+Nbq+X3cr0SBPiY1I7grmN5Geo7mqQjatGAaQloYDOywMG0ZrGfGaWLcOiKeZaF6Pgv0ZhlhjypwTzMLIMDF8OODN8CfSbz1hskr37KHro6XUTy10RGitsRQ/0mJUrMbdl2GkIZZqOjLnZs430by9CYTIWuVr9vr7tkvKJf7F03W7dqXUcg6PpJiAXeHN1/L510ycfTE91zefWYl2O2PfMvHueIJnpVmJ7sMWBK34EUrMa8hQBUhC2TjBxCVXE3zW91m4figJzp8WmLj9XuGmvOE6WnvZ5SUrAxGfXyTJSPDUKn40ai1cZ3Xq0L4vskw896rAv2QJzWk0xQSDB/HUNAdNtGpFlgav6TFClmJpBAqp2LLsEHkqDhwgBbFGJh3qVSNDWKUx2Wo8ziOpAJFOHvwRwDmMsVzGWHUAZwP4+j+9sd3h9w0AAwG0BTDEMIy22mUDAbSwf4YBeOsPfPe4jXiciBIAGta0cNppACwLPfqb2HnA6b/ets/EZdcSPFBIZjqCll1IZoD5TUXbjHJLw6/6MDNrmBg/3o5pcHg4hOKIiYwMoDTqR6CQ3CGlh4QWGk8zYSKEa68l/78sWBKup3LSTs84AzCzNXeFaWLYMOBgoAqipeQHX7nQAjwehGIpiKVQMdYPPwBd2ojNHJdy+xN+ap4RE7fPPLBdUkvWmNhziDbVI/dZ+PFbSYCk0PN+P9HCEw8QvGNPEy07CwHCmVrEJ66X3RghQzCXnRss/LqQ7hs27DRkkHvxvtvp+l4nm3jqRdudwEKJjKidhSa+nGwm5r6kBAnXFhdEic0ZCiUOvgKoHXqnTvT/+i1MHDjsA3w+iVmEUHDExEkn0dqXHqIW8LFSiSbSiCZq1qT7xyWrVLZAuFXqzxIFgJ4QCaIGDYADJaRs5OVRZh6TmIsvFsa//kXuEOa3Yykp/kTmnLec1r5rrxRk5ErBcvs+Dz1lu6osC61bU2NAQHJ52YdlnTOA4GaOCV8GzV26J5Rwq8ouXllJ2FloouAIwT99z8KUiSIBJGKv/VMPWXh9DF3fvrtwX8pKQlncxOEynm0VSmj9ssvryD4La5YRXI6LdW1r4e67yGJp2cnEpKncTSk8CfuKTbzwOuGPl1nYvx8J1xZZFGriAC8sZX4TJiw0bEj7L6s2Vcn7MsnS4Gt8tNxEy5ZAyPDDKrLw9NOkDMQ1/tGuHe0/oTiaf2sQvTtjbBr/wBj7AUD/43DvHgC2MMa2McbKAXwB4DztmvMAfMxoLAKQZRhGnQp+97gN2YXVr5uFbyZQoNZIN+HLVLVNWBYKAya+/JYsDVmz4MTO/Cb2biVtMx6kzX/qqQD8JprWC6Gw0HavcI3DLzGLsCoovBKziKf6E/BoqYUFCyiby5tJgqhqLRMpsRBefhmoXZVaq3z1Fbm8uGDxhgXhRezUzMQ5BX4/YnHD1Q8eiJrofQoRateuokL91ntMLLYL8TK9gvEH48KimP6NlahQ5ymn/Hp+oM41t5i48HIuKKyEZvbIs6IQT3ZXhAyB/8t/Wxhxh3Bv8FhKt3YWLjuP4HWa2s8P6kXF8fy6wcQDTwgr04jS2kck5rJoNqVeM5sp8Ay5Hh0srFxpp1pK2qOsVZbGTCxYALA0iVmEqY0GQPCSAxZGjRJrOWQIKRU56RY2bCC3iGyVeiQlIaE8pAn3pRFWmYsnHMa6dcIy+eEHmg8jRId9NawVAjNNvPOuoWTacXxlMREb2b1b1B4l3JoAEA4nvvf9LGFpNK1jIcdP8DvvNzHVzj7K8Fiu1ucPX1uY+6NsgRC8VlUrUdt0yiB/Ig3Wj1BCaRn/tbBA/Eyscdgj8P/4jbBWw9Iad2ppYcRwsliq1DDRM88WINK+33nAxH2P2IkPMb7GoQRumCa2rqHeWbEyshCyssjSaFaXDj7zxzVakTwS5R4TmzeTIphIry8PCVd3molwMe3vYBH1axs+HDBz/joXlq8C1xwyDGMUgPGgM0GGAjh8HO5dD8Bu6fMeAD0rcE29Cn4XAGAYxjCQ9YJatWohPz//Dz/oWWd50LfTIWAYsHXNGhTMmIG+AGb+chRvLzuErwDEy3ahTZsSsI1BHCwNgzSONAQK9wIAWLAMhSWcYL3Ys3k/3v0WeLVqAOW+Ixh1Xz4iVwAlu3dg/dp89DhShG2x2uiaFsO+WgylB/fTd48eQbGXcsFLIjF4jhwEAFhFh1Bqu82Ky6OI7j6Kk04CtrU4iOq+COrVy0dZvBSs6BA6dcpH5OtdCETprJOl7crRtqQYAFB6cD9Ctl4R8vgQKw0AAAKF+xDx+RANMRRZ5YgHg6hbO4R/1ynA6SkpmDt3Lhoe2I+msRgeGvETGn62DgDwxXc+dGoWQk8AafEAAgf3AQAOBxmOeKiTqSdchOBher9ajUthpJUAAJ57bD3qHNqGqwAsWb0aaQcPohOAay5ZBn+oBFgMHCgOIxShczciJQcQKcsEABwsjeJINGbPzV7AInjjNgU4t3sVYCywbN5qFOwycC6An38pwIZt23EbgNyMLTjv9I3ARGB/cQgWqA992eECpESpGK+wxIJln6t2cNde7NoRg4EI6jbbj9lPzEFsYCr2bdqErfn56FtWhl/XlOCuvgcx0+ND6Mhe1KoVQjRQgoNlxJQsw0CgsMB+j2Icqkrw0lgcR3cexOifgLvrFSGWmYZhw/IRub0c4cJ92LcvH7UK9yEQ8KFhBrCjVQT/j73vDpOi2Pr+9eTendmcyDkjSQRJgqIoBlBEBROYMGBAUcyKGRVzxICoiGBWRFFQBgkiQXJOSw7LLpt7dndm6vvjdE1X1fTgXl+53vtd63n2md2zPae7q06dfE4lhYtiNFHqoDk4GqpGoPSoucaHUB6hOTtaVYO6lVVo1w74te1BdHY64fMFUVJdBG9ZGU49NQjH6m2ocblw/fVA3U4hnGsYABjKjxxExONBpFrDkcoQEInAxQxUHDlo0qeb4ABO67Ef13n2YjiAhcuXI3v3brQCcN/tPyNj6SrgR2D+Ug11GoZwLgCt6miMJg6V1sBbFQYARCsOo8qsKqjTtAjJWiWwEvjonfUoL3fhegDL1m1BOO0QegDo130tuqQfAdYBB44aqIjSCVauSAVgFNNallWjjNCj/MheuMMVAICchgdxx6nbgAeBTSs3YOsnQZwHYMnqAnz9aD6eAuCN5mPQeXuhzTRwuIz2fcTjQdkh2vdRZd8X7j2I1euAcKAM3tQifPllEDWXajiSn49NwSC6FRVhj7MOLu5YjGAVQ2XhQeh6GFXFRShKIRouDUdQXXjYXONC1HiJH5RU1SBUXIbbbwfOb3EY6Z5qnH9+EOEV5SjffwTl5eV/iv8da9RGgAwH8DDoTBAA+MWE/V+HZgNjtbymNt8lIGNvAXgLALp27cr69ev3LzyiNebPnQsAOJhfFzdf0xWrAVRGm+KbbxsCXi9O7x3Ahsd1wBNFUmYdAIAzORk5KToABld1FfIa10UXBniLU5GZRMzHEwmjXrNmqNevH5CRgRotBT/+2A+9oxr0jDxUVzuhZ2QiNdODLVuArLMZIll5AIDkrGx4jhIh+V0OeBrk4PnrgdwfcqBtJyac4nEhKSMXQD8EchrCu2cPsrP7IdXjB0vPAPYB/pw86AcjuP9+oOkSDzzhNKAAYL4kuMPE5DN0L9wpKTi0XUPgxTw4ngijqMCNQEMftKQkTJ3aD2O13wEAfbt1A+bNA5xORBxJCOTUBQC0bhxGwyyy5JgvE3pGLgAgXdeQodN8vP9JQ2DZIeAnYPu6XLDyQwCAZ185BS2T96EjgDN6NwWKi2n+UusgYmp7OSluhGuINFyBHHhZFgAgL1VHsoPOQDv3ovZA+/bA88CmlfXw4actMQjAhp3tMOmHEzEawMB+GRh4bg7wKZCUWRcRTwCoBPJSfLFzGfSMunB53AA8yE0hFwQANGnbFk369QP8fhhHszHurr5YWl0NZ6ARFn6TDVfdAE5qp+Pgch+QEkZyFtGKLy0d2X7uz48ip2EdnJkHBIqygBBt0yQH4GvQAP369QPy8lBdYmD58n44GV6EMzKAHYA/OwfpJZVYvBhofLsDVdFsYDsQyM5FUsFaAECa141AcibeewRoOTsX7tnV5jp44E5JRVFRP/hzvoW75ke0atUPmYEP4AqkACVAIJfWcvQ1VWhzyAPH3iSgGkgx1zjVU0Nr6XKhpMIH9mZd4Eag5KAPnnrE6CZ9cAauTitDKwA9OnUC+XqAsDsd/mzCk5sC5KR4zLXMhcdH9JztdyG1moTAQ081ByorgZnAni11sH07cD2Aj786GTvLsvAlgNN61AMaNQKeAJIy6wH7U4FiIFmridGEJy0Prqp04BBQJzUJ3igJ757926LnpV2BB4Hdm/Nw+ycdcB6Ao6FWmPBMOzzp8aD3iSnoPT4L0BHb947kZOTyfV9TjUBOPbpPSioy/UT/7nAN6jVvTvs+PR2VNSl48sl+mBUG3Kl1sSaYBt8JmWhR14PKdS6gBVCZkRPb98kh0xpyamD1cnDpSUDm4Vxo+ST8UtwupOTloVu3fvDVqw/HoUPw+/34s/wv0ahNIWERY+w2xlhn8+c2xljRX3DvvQAaCH/XB7C/ltfU5rt/6WAuF+B0glUYKDnEA68+OpLTzDLiJnq1wweHg+BJMNC2GW3QNl10rFgBOP26FCzfuldHkyYU4A0VUSEhq7R8pPCRydqiBbmqIm7TveET/N3VIfjSddx+O5CcabkxnFUGKqM6Tj0VOFBM6brt2wOHdqmxkRAefxzI1HlNAQVYtaoqAGY6ra4jKwvwptD//U4DrmrK8nr3XWDPEcJ32RADi34iUzwSQczE/u5zA6f3MgBNQ7M2HqTXFfzd3NWn5PbHznYO6TAYwRfOMbB0frzL66pLDNx1CzH4QZfoGH6N5a7groYd+31Sbj+Hiy6v6hIj1lus2qmDudyA04mG2QauMfs5DbpEp3PWdXILcgGyarOPziTRqVp/zXLa6Bw347QCxILuHO6qMeD3kx88rwklOPjSBTdllYGDxT4kJwOFlTpqygzcdRc9L4+ZMC/Fs3r0oLhcRHBrWvGvEBzJOkaOBNLr6rEzUJzVIYRdOi68EMg/SM/ZqCHDxhUGYGbycffpqxNDaJJruVv4fZIdRoxWAEBLio9pfDXbR9lZoMO15s60YiacVqa9a2DU5WZMo6sPzdrHuynFmImPGbG4lejy2rzaysyr0nwx+EntD+Lp8QQfMMhqceKJGPCabtNdh3yY/SOlUnsiFn7e4QA67Sd+bHS1U6cWLLqOdD2EK4bS9d36Ujqtw89dUgxayMCO/T5cdBEQdlMfsTlzzOwswdWt1gxxuLXvDaTm6vjoI6qtcgr7vjxCsdL8g39PFhYAQNO0lpqmvaVp2o+apv3Mf/6Cey8D0ELTtCaapnkADAPwjXLNNwCuNLOxTgZQwhg7UMvv/vVD1+GOGPDBIiQuKLatNdCvOy2eK6CjcWMAPh8aZhtYv1wgePPTFTbgQg20SASVTEd+vunbrLGYhUgwNaUGnn2WAqz+bB0PPEDMxcdCWLCANlaNmzJ3wm5dyraKcEHh02OtD5zVIUuA+HQwg/LKI+XUWmXjRqBBK7LrbxwZQrpOGT333Qds3WvFKFw1FhPh+HZvNhAqihcgMIxYq4lvZmq47FqCZyYbSDYr1Huc6otl3OgwYnUxYnB97kwDC+fE+8cbZBloVpfgp56t45wLzdgFswTF6+/puHq0FdOIMQWHjoiT4lYLfjRwzmmWYOFr3KK+gScfouvdKTpSUiya4AJk214dkyeb8LAF53EX+HQc2RfCWadT9pme5kP37sRoM5Mo3uSqVvzgsfgXdYKtrKSsKmmNBVqJVhp47z3qNuBN0/Hcc0BGXRJEX31F3QwiXoq9VER8cFRVmzQh1JOYa6k7q+EUArIxmqkwqOGnruPwYeC0swl+bn8DeWn0/DfcAPy2VohphEOxOBqnic2rjNixyxVRPZ5WADzyjI6bxloxDb6WZw/x4Za745UEkSYWzTHw0bvxSkJuShm6dyB4u646zh1qxTL5/p71s44rrqA18ESMWHsSnpkFnw/rlhlokGMF3blCmZdq4INJ1r7XNBIsrhoDbtRAYwwF5To++8yMTwnxL578wXw6jCIDw4ZRzZA3Tcc555jp+44QKitpXkVacQixkShXND1/owAB8CmAlQAeAHCX8PN/GoyxMICbQVleGwF8whhbr2naDZqm3WBe9h2AHQC2AXgbwE3H+u7/9Zn+cOg6PAJTqHJYBBMuN5C/ieBnDNKxfTviLJMla3SceCIxVHfYQGYSLWqMYHRZ2xSDb+GKEMaNo268aXV0PPaYZWn07k0ax6FSqh04VCqk69YIhOTVrcyaGisYz7x0ulq93BoczA9BS9LRujXgDpDr5PXnDOQGyDJ56ilLgCQ5KEApZXuAMwsD8PlQvz4JOgB45B4DKxfLBA8Ab71oUO8sTcPW3V4UGZxZGLECK1GA+JhVdXzeRT6cdxG937a1BlYspOt3F+jYXUDXn3KSgTtNyySkmRaFwwFv1JAsEIdTQ9TjgSdixLJrLrvGh19/tdaSd0v9dZVOPZZ0HeleA+edbikVnCYkASJYGpEy00IDZQwtWQLKSjIMytiorsbGnT40bEgtZUSaiAWlfYK2WS1YpboOVFJr+1AxHeF7xx1AWh1SHgYPYvBEQwjBh169gM17dDiiETgRlmiCCxK/k+Y6lhJqCpD2zQysW0aZfNnZ1ho/+6iBtk1IULz9NrBlt6AMhC2lggsiH0KkJHg86NDJgawGBP/oHQML58ZbGg+MNXDnaIIXV+kImVapVxEgfJ68USN2YNaAwTrG3EvwkkNRLPvFtEoP6Ph9FVkabRobePQeiyb4Woo0wT0Mmq7DJVifA4dYVqkoANdv9+H66+mdk2DgzD4yTVgFgFQ8aXkeqOZmxgxSHuo20/Htt0BSJq2lrlOQPv8gWaVHKqx976wWFEfv3ytAwoyxNxhjSxljK/jPX3Fzxth3jLGWjLFmjLEnTNibjLE3zd8ZY2y0+f8TGGPLj/Xd4z4UbTPq0alZrsIsRAZ5dL+B4ecTvKjCh99/p02e4zdivYFqBIJx1oRilkl6XdLinAGubTI4TSZy6BARZNQ8ZyNqhGKZO9zl9emngM6sgkTmo9PVHKDcez1Tx8KFQJO21iZ31pDgev55oKCcgnYwDLBQKE4LHTzAQGaSpZ3ygsUkzdy0OmWN8JTmzasMOn5V13HWWcCUGYK2aWZ5RZmlnerMoGwWTaP0YY/1nNyNccUoHVeMIvjin0P4ajrBbxqr48Y7CF433UCnlhZzcbq0OKYQArkjo14v3IK2mV5XR9OmtDZrlxnodSLBl67VqQeSrqNehoHXJlraqdNJ17tqLG3W5fehcWNiOk4BLtJKVbGBEcPInVTJqKsA8+pIchiorGBxVqnYDSCQQ1ZpUoaVZusyaw02bSLtGIzh+6+rUVMmKw8AMPlVA1lJlluTw7nryeUnPD1PE5SEGsrku/9+YMNOeS2ZTm4bnhnYtZ2BnACtfTSK2HvE1lLXMXcuMOJ6un79cgN7t4YApxNnnevCuIfpeleNEdPWK5llsfiiRqw412C+mEAVLZO+Z+m4+jon4HYjf6MnVjP08ls+XHMNrUFOwMBZfeMFiDtiwBONVxzFfe9NI2EKXcehXUbsELadB3W89RatWbrPiB0RHEsDNxVHD6qhMQZPKimajmRuUbBYej2/PlJBxzVEKmi/VlbSmjmrKZsrCYaiOP59AmSmpmk3aZpW53+1Ej02dB0ZPgMD+9FiXHcLFfBAp5gGJ6TZ83UMGULwaIWB1UstExdArDKbL2q1qIlUW3gatdbxxhuAN5UECJm+UWzM9yEvj/zgMMyW5JUKczEMDL2QydqplwdpQ3BVE1Po1QuxlvS86Cqk+TB2LLCvMA0A0Ly+gf3bhNRPk7k8Pd5AgyyCp6TI/m7OFPh7xfCbbozff7diJh9PNrB8QbzL666bDVxzKQmiYcM19Do93t9dHPLR+dqAZFEYsCyNI3tIWwaIufDN37aJgesutwTO1KkgCyRswGeuwcIVOt5+G3HMQmQiCeNfmoFe5rnhvc/QsXMnub5cwhovWK6jY0ea02ilgW8/i9dONcOA7iK3h+jeELXN9LpklfqzuZXJ4AyHcLjUhzZtEIs5DL/AkItOzc8rLzKowaDXoiGABIW7htrntGpl0Uqyw4AzTG7QJ58ENuYTfOQlBtYujXdr3n+Hgc6tCN6sGWKtPXTNtDJ9FjPltMJpaP9+4HCZ6ZKaK7gvmRUzGXymgXtuJfgFl+q4/AoqzvQKgmV/kQ/5+XQPb9RSEkRBUVFoYMPvvD7EopX6GQZuu46uP384xTLVfb90Ha0BzFRqJtAEACAp0b6nAuIuren61p11LF9O9TLOKkuwrNmqo04doNTsbfXKKxRDVfd9wwYMWpWV3su8vthpkH/1qI0AGQFyWS0GVaDzCvX/vaFT76kH77SJaQiEtOOATk30TG2Tw2MCJElHqNjAHTeaWm6eD+efT8F1HQYO55sWjo8YKmcWXGsNC8zFUV0FF2rgiNRY7g3zueZ8W4WoEUJaXR1ff025/QAw6QUDSc4QDPgwZQpiLiOyQKxitYjHE4NzbROwtFPOON1+H0pKgHOGErxza4NiJj4fzjwTsdz+WLBcERRbVhvUO0uBO6qMWAXu+PHUkh4QtEqvF2eepeHiK003RtSIdTmuZOSSgq5jwwoD70+yAqyin7pPV7q+aTvTvWgGTPlcf/OjDxMmICZAYvEvzRIUh/INDD6T4MynU28kXUdWkoEP3zJpRWCQIk0UGTq1gjeZjhUz8cW+F600cLfJHFNyqchTT6dGl/v2MriqSQs9eJAEkcYYPKiOWSD8uQCrLkJMxACAlYsN1JQZSM7UsWAB0Mos2rz7VgOZySHUuCmWsuOgoCTUGDFa4IIiXGYAVaGYshIVacWMf23ahJjV2DDLQJpOSkLPnojFv3xcgPh8iEQsi2XrGgNbVhtWLMV8jyQY1EMMwFU3+uhUQV2HR6CJsQ/oOP98mlNPtComQESa2L3JwGP3xwuWzOQQLjqP1jizng8nnIBYLJOv2bK1NEecH3BasRRHHyoLDQwwXVguPxV5ajrt+1/nxVuljmoLj8F8OHgQsUJkJ8JwRCMxpQI6WZlPPVKNaKWBpAyyDjPq0v8d1RTr+itHbbKwmtj8NP3Ln+S/YSja5pff++j8ZB+1Q+fapqidihZFTBPRfWCVBn7+juAndNPx5ZdURawZVvHcz4t8cLmIkLWQwFwUQZGGYgCIYwqXDKqEI2RAT9cxaJCl9V1+IW3+kiodV11laaeWoDCZgdsLgDYn1zYBiymMuNjAnm0hieABYOxNBprXI5fXjz9SNgsgWyaRiOXe8CFEripdx+DBQMuOhGfJPDNmYjIR5vYAmoah54Uw9BwLj9OlAT6fbIFEvZL/mjOLex7R8cwztGaVhQZ2babN+ctSH2bNIhdWnTQDl18Yz1xEbVNkLlqVgWoz1/+G23Xs2iXQiqltzlui44wzzPhXjYETmsk0oemykhDTTpNo7d83A7J1m+mYNIn6Rmk1NbHiuQ07STs9UmEyeFTCFQ7FsrMkK7A63tIYfoGBykJKoOjdmwQVAAw/34DfSUVsd94JbNhuZVu5woJS4ZOtT+bTEQiQGwYAnnvctAIVWrnpKgM9OxH899+BvUWi+zIUp1T4mOlK8vlw2WXA6QModrFjvYHF80KAy4WiUhd1DNB19Ohk4Por49fSGwlJAoQrA2JG3XW36pg+neA1ZUbsjPnl6y2rNMVtYMRFx973vEmnZtLKkb0E73+OD7t3I9aVmvOV39bo6NIFMDSiicY5slWq6TocNdVIBqXsqvzgmUcq4aiuQiBHx+OPA9kN/kYBAgCaprXXNO1iTdOu5D9/+ZP8NwxT27zuCtrky9bp+PxzxAKpzzwSz1ycggaRWV9H377cDx6y9YNHKw08bmpAVS7Km9eSyNJYu4SK2MKCdgoA6aACsbwmRNg8PTYVVBxYEfHh22+pXxUArPnNiB1mBFibf9zNRPQ8JTOWmmlmW3lTfAiFKIUVoEwcZzWdvXHJJYhVnMf84EpwvVGOgYArFBMIsUwfHizXKR3xUjP9Nn9TCHu3ExNp3Bi45lqyKJI1A0kOi7nEmAJ3S+g6IlEtXoBoGrr38aBPH4LnbzLwxgs01y9OIisn6vEgM8nAuf3j3RiithkSmIVofYqWRkWhgWsuJfieAh/mziW4jxn4bKqV/RVbY8ECyapP6bQuvw4tGkUKqA6CeX1gzKKZ5x+gjPoat3lkqjnnS2bT2kdE7dSca2c4hEC2jk8/RSw9Ntlk/AZ0vP++JYj2bzeoatojC4oLzzGQ5o1XKrgAcSb5UFoKXHUTwcsLDDqFz6ejXz/gk5kyrcRowqSVdJ+BZKcF19zUBoaUBFr7Rx4BuW91HXu3WgkaZ5wBOhBM1xFwGshJCQGahqqoW6AVS4BUIklaY74vm7enDDnoOgp2GbjndoJ/+5NOpxOa+K+9TNn35hHRfC2Z1we/n9ZY5AdqTOPS82l/Fxk6Vq40U7KrQlj9K8FFtyZg7fuMumSV8kQGrlCGPZQhF3b/jQJE07SHAbxi/pwK4BkAg/7yJ/lvGKZJyTOZRI1G1CCqnCJBhtC+KcEHDtERDFqExAnsmx99yM62LI0vpxHBVAvMBQBy3EQwMU3EhGeAmEhGPR3XXmv5qTmB7SnUcd55wN5Cgl83vAxaOBynnV41zICrxvKdchdWskaxCy1Jh9dLacqAxSxqXDo++QSxrKdXnjWwd5tVT8KZzk1XGWhejzZ5jx5Ag5aKS8o8vhcesjQkgSAIim1rDWxebTEXDu92goGLB9H1jz0G3HwzyF0RMeBFCMznw6LFGpYsoes9YcvaC4FcUlGvF+FyA4V7LabAtdMUt4FBZxD8udcoQUB1V0z/Wsfo0QTXQgYK9nCaENZMjJkIcEeVgfpmK/SO3X347DPyg4truXglPc/BUoK//0KhLU20yqHrVRdWAGVwRCPwpfkwdChiWU88KH40RPUh2/bS2t11iwGjSAium3iGDSKXkerC0mFZDiJt+TRKv2U+6ijLz2SZ+YmBjSvp+mgUgJviVpcNMXBKV1rLs84CTj6ZcHm5BaLrqK423fqmkuCzoZWCPVZMRlQq6mcW46araK7vfZTiOKqVueh3ynpSlQdRqWCVRuxccjVra7BJKyNv1KkdkGKZzFlI7xY1U7K3rDFpQlAcAcSKZkVaAYBsB+37xq19mDTJsho5P9i534fcXGDr7r/XAhkKoD+Ag4yxqwB0BMwexP9rQyEwkZCMIgNjzfTCtDqUBsuZFG8/LfnBqy1TuTyi48gRgmuMxSwHy2Sl7015gZhC49bkl0/KpP9Pe4UIpqzGh6VLLWbFCSmsaC4ZWjGAeO30wPZKoKoKWfUpA6hVpyoAwEXnEqMNaTpuuQWxQjxdC0nFahyPUWhAq7KytvinqG3++CNw/W30vQzd1DZ1KlR8aoIWYxbeSDxT2L3FQP7GeAvE7zSQ6asEdPJ1n3aauWY8c87nw913A/ffj1hMw8voJMeaqJPOVPd6cWS3geefjFcS/M4QLjrX0h65YBGZwvL1dLhPnB9cUAaiRigW/8pppGPAAHPto1F8P6NUmsvYmplryWMjmgoXXF4A8MU7BM9tTBlAuU0IPunJoth7/fgjpcICJEA8YQNhsy0G00XLRO63BADGUUpp1tN9MAzEekyd3NFAqodqkoYNIyYJmC6paCguY6/4ALn/eNYWj1vF3H+6jldeQcxV7GMh6GafuMaNESvajGXU+XyEx1ybw/kGfgvG01CSZqBJbiXgcqFXXxed5aMIipfe0nHvvRat2LkvK4pCuPU6UvhCjiTJ3Tn6mnhLw1llIAl0ff5BH374gWhCi0QQALUNUgXFfTfSvs9uSHPqNs8aWvYjwZlPl6zS2L5XXFt/lwAxGGNRAGFN01IAHAbwPxsDEVMwReaiVRmoPEKEMeZeHfPmIc4P/taHOh2LaS5o49RiAIIfXLEoqpyyJjJrKsEbtSYTmguQpulESKs26+jeHSgoUwWIzOAzHbJ2yuF3XUtwZzLVb7gC1APqyovIbx6CD6++CmzdI8Q0IqE47VQHMX7mo7qUjDyyKL6ZYeDwbkE7NQ9MGnqOgfZNKsF0HYWF1HcPOp1fwZmC6qriWuiYMZa74si+ELavI0tm5Upg2zaCN8wyMPTseCYSEywCPOr1xtwYTNPw9hR3LCGCGQY1HATwzlQ6qIkzr37d4pUKyQ+u+cxiMh8cNdXYs5n81+cOJSYSm5OjtAafzdKRkUF+cADI0uwFhSpAuGD5+HXTKq3rw3XXAel1CN6pIcEPFFMn5k35phB3FANArCCR4yGLwnJh8ed84gEDoRKySn0+yyodPMBAqodSymfMALbsEdyUEcsqdbpp7X1cSfD6cOqpoJRpXcfyhQa2rzcspcu892k9zGaHJk1wQeGJGLEGpOIaU2U50dAddwDjxhG8ujSMTStJcC1eDCxdSvA0r4HLh9ApntVRVwy/y27fm6nafI2ffEGP0ZxYM/TVbB+uvtqau1M7k4JoxUZ80lqq+37LUqKJLj19+Phjy1WFIrp+7iJSZgrKZWs1tu99f68FslzTtDRQId8KAL8DWPqXP8l/w1D83b40H7Ky4uExV4yuA6EQnnyABMuBYh07diBGSK8/bhJMAkJq3VnHXXdRdpYIL49QoSLXCn/5iuDVihvj4VtMl5dbZjqZJjNq2ErH6tXUYkWEF1eRf3n/0VR6voJSIBqNC7ye3JE2bVSJpfBApyfFh3XrgCtHkFZZesi0QHSy0F55BbL7T6d545vfBwO6Fs8UYq4tHzHHIUMA+Hw4vMvAxpV0/YUXIsbgdRiok0ZFb5IACdsIEI/HsjJ9OtLStdgaG0UGJpjtL7772ReLf7lrDFxxETEX0eXlrKmKaZtpdXR06mStPfdTq5bGq49aa3z0qMXIP3yZ1lJKBQeQafY1bdo+CU8/DSRn8bU8GsOzbBli51esmCszF25pjB1JeFSlIhUlcIAhvS6dKzJgsOm+NLOkKpmOW28lywtAbC25UqF5qA1Ms3rk8uIFiZIywEgQ/fwzMGIEwY/uN2AUkbLRqhVw++0CrYTirU93AgESq+nRqYp70CCCh45GEJxNysYddwAPPmg+T8RA68YhohXu8lIERRW8tkqCK0DClD/n6Ktp7VduongTn9M7rqI1kFLBYe3vrAYUJ+IJCByu0sr7L8hWqSOJPt97TlE2/k4Bwhi7iTFWbBb3nQFghOnK+t8bJtPp3iEE5vHgjUmOmD/dWW2Zpo8+S0FlvtCle4oByKYvgJgGwQWIwxQUWaZv86RTKGOIExLXLL6f50Pz5ojVP/z0mUkwiiXTro5pgahuD1NQ+NLJIuKWDMd/pIICyvuKUgAAz9xL8KiS5TWofwWc4Wown466dQE9lSwNH0zLgb+nOXc81sG8PmzebL6+ruP3RQaO7KmMMRfOgHt2MgsAdXKdUct7H7wRC/+ePYi5/zwRA3q0Mo6JGEcN7N5KqaUiPNUbwoBTSDudPBl45x2yQHiaLfP58MEHiGXccCYS9XgRjjqstQyFYjENMZAKAN1a0NpffRPVvqjM4uW3dUoJNa/ft85UBsy15GvPaYWf/65aq03a6hg3zlpLrgys3qKjWzcrPvX1FNm9wWmiS2MZztc43Wx750z2oV49C38yyuFiYVRGfXjlFWDzTlr7KW8YqCqxBAifo9NONpDmobXs0gXIzbVogrspY8PnM61PUhKOHjWNeJ3clzs30PUxV5XPh+b1DAw8zbI0uFXqjoRIsPh82LABsbiVJxJCEirBfDKtRMoN7NpsxMG9UQODB1Ac7dmJGp0+quz7Dz6lrCdR+AKyVQogZmWq8E4NaK7PuoA8GNxVxdd42peU2caVgY2/KkqFSRPJIdnzwBVT59+VhcUHYyyfMbbmL3+K/5ahUxHY2acasY3H4TxThjmd2LjNjVWrEMcsVIL5agoRQIsTfLjiCsBhEsCTY+n6kCOJ4mcKHk4wqmBRA6lbltD1bbqQdle/BcEvPYuuP1xG/mVu+nKmwwkvagbR0837RpSgO98IWfV92LcPGDSY0mmb5VXCFyXttGdP4Ouv6TteFoI7GorTQksPh8AqrYCslJhg1g48+igweDAsd4XJXHr3Bu68EzHh7mOkVYp+8MojlEIa8SrujbCBJrm0ls2aAc2bUwyEuyuYV8eHHwLvvYcYs/AhFDtrmuNHJILnxpeBOZ0IpLvo1EJzjq4abK898rU8VEKpnBzO1zKmVJhr/OMMgjdtq2PsWMSC64/eZsa/wrJVyteyRhE4MVpRLI09q01B1C4Jq1ZRajkADDyZri+uIqVi8w4KcqeyYqIRvma8uj9cCW80FHN5xebIXEtvKhXhDR8OwOdDlp/iX2GXDy1akBCXrExFGagoMFB+JB7urDJiPcRGjRJoJUwWDnRKWb/lFpNWIlWmkkBryYV+TZmBn2cZCLtlZcMRMtCpFdFKVhbQsKEJj4QRQBmiLje++9GFDz+MX0tVcXxrAs11ah65eDl89DDzlAzRgyHQSiXTUV4erzzE1tiklflf0X3rNtPx1FNAZstMoG9fhEWe9ReNf0mA/M8PXafjV8vKAJ0yN+64A7GF7tyoKKa5xDYOBEKCLEBKdhIBDByi44MP4rXNF97UY+4TQBBECnPh+FXB8ss3BE+rQ914uXujRaaZpXGA6lh4dlbMdxrTQilXIsPUQiNuH9xuwOVxAB4PvnxXYY7m7z3blZjPQ32kCgoQc0l5o/GCIsYskpMwciRicaL92w0U7SemUFxsaaHN6xto0zTejRGrIFfgPDDKvJTmzKuFoxWUJcV8lEX27beI9cLqcyIdyBNjLroOZ5hy75lHYC6m5ZAaLULUq+P114EFC4Q54Wv5upcsKBPeOsdaSzs3hrrG+zfQ2nQ8WcfEiVamnaecrv9mbhKaN6dECsCyMhNl7IUVwbLgK2JevnSqjOf4+XMWhcituXUbCYr0qKxUcEsgEKW1ZzpZpX4/wefPpnRglVa6tLbSgbdtA0pKzLWMhmJWZjgMuFyIUx5uvx2xOS07EsKeLeQi27XLormMJAN9T1JowueDJ0xJLExPkvYrVx6iXh2vvQZMmWKuDWMo3FEC5vPhyy+Bt96y1uyMLkUxi0hdS6ZpqGIeCe41aC1H36lLVimnlbc+1NGihZVo0DjFfn+rCiVXarcuo+vrt9Bxzz1Adt+2QDCIsrZ//aGt/wiQf2WYC/TF5KOodhBzDAYRYyJndCmCIzkpjrlkoAgRtw8ndNBw1lkWHs6w1TYOK+bQZq5y6JIgGnmevcbBCemkPj5Mnw6k5sqxlH2FFHwrDxP8yFY18Erw3u1MAWIyBc3tBFwupJnPWa85pU4OHUrPFIhYlszZZwO//WY+q7kReGyEb57cZHJ7cO2Uz5E3asAXrYTLr+O994CzzyY4z/SBTj2GHn0UMW3TWZUgKM7iXVgus+aGeX046SRLQEUrDaxaQlXZzzwDvPkmCRBHVQgt61fCkSQEaoWam6iX0pmTk+W1jFlowlp+P+0ool4fduZrErMY3MfSTu2UjTadfRg5Mp5ZVGlUX8GZy5r58lry6y8+/dhMp1l7ahfPiza5q+pQqY5XXwUOHyVLo3Q34eEZe3xOOza0lAoRnhoxtescskqHDzfXzCiDk0VQHvbhxBOBr76CZZkIMRM+F34XtVZREyhiQXGdLKJzzyV4dYmBksMhMA81ibznHotWeAaeTCv2Liwe04h6dTRvjlg2JQAsnlWEsFvHtGnAiy9a8E4Ni+BIslccI24fAika6tSx4LGYhrLv535C8IMlFCvlwv3i0621B+KtyVadyCrlwXUOr4j4sH07cBw8V7FRmzqQD2sD+58YImEo7hAAxDhtNJGmqUWIen248UZIJm4GihB1unD/w65Y+wsAKN9turAU09dVprg3FEJq2IpiLyoh/b5Rx6WXEnMALNdWTID4vICmoXGKop1qDNB1pLGj0vvz3zmzKIvQMahc6+O+2YjCFDrUt/CcfTbQrBn9rkfK4UFNHP5YnYaZmsnnovyImXuvMIV0n4EW9cmF9c47wHXXIaZVcqYwcyaweLEJD1OQOypYjVEvWV3l+4pjcHENujQugiNZx1dfwcq042vp8eGxx8yUUxPuC5FgsaUVj0eOpQCoq9McnTNUj7nOxLV8dxq1SikLE7xom5KIwfuRhexdWBkmnrQ8ajOTXscUjKYA2bY/CbfcAuzZS5bGliWyVcqflWvFEY8O86gcQNeREra3SlNqLJr7/Xcr/rVjXQVQXR0TiBxP87oGUt2kJFx+OdCtG2JKArcyi4rM0JNuJUREffL+i1QYOLSbjuSVYxohdDuBjgh+5x3EOivzNPqox4evvgJmzpTXIOrxxa1l6EARonpSHLxDg6OATnHM1ashK5QuD55/0YGBAy24u4wUxz+KlfKkmhwXwbv29mHiRGvfcwEV/I2E4I4dOG6jNhZIO/EPTdOcAE48Po/zHz5EZuGNFxQbFhaiEnTwvZiu27nxUbgD8dppBooQ8ZBWX1Oj4He4ENbcEv5962jTnnImmdeeVIJ3a04Es7dQx08/WYIhUcwkLSrHTHgrkNB+ur5TD3IZtW1LrroWGWbq51HSinnvJi5AVO3UZ5roqnbKN4InVcesWcCFF8IUUASviOpwu4HXX4fALOJjDuEyA5HKeBeWszpEB3XpVDh54okmXBAgd9wBvPoqJIuCeeU0XgDYvvwoQohf4yapR2Mpq3ZruXQpYgHW2FraMJ1NvxahxuVDp06mxWXCe7Qsohd1u+Pw260lz8JSXV4FW+j6E3vr+PhjILseBbm7NLEsjc8/B4pL6AhWvgaqoEiJ2MB9PoQLCN6otY6aGlCPKV1H/WRa+8JKynr65ReCB8I2Li9djylFKlyMf735JmJJKZ5oKGZR5OQATzwBSUlgimKnhczDwRRlwBEOwx8tgyOJUt/F/UprpuPZZ4GXXpLhKn4A2PpbUawdisdjwVtkFMHlj6cVbq1u2wYsX67QkMuDMHNK+Lcto7lrf5KO666zlIE+bS1Fs7TUSnxQYyNOJ47bSChANE27V9O0MgAdNE0rNX/KQHUgXx+/R/oPHrq1aaOeeJM1NVKEsIfSKUVLA4WFgE7pjlyTAoAcZyGiNgSZgSKEbfBHjxCz6NTdi5tuohbhAOApJfhXP+g4/XRixACQBTo7mueVOz1OwO1GepSu58yI37toOxGeK0BartNJFki2g64vNJLw/vvA/v0wtU177TRQTdc7k2lz8hbXJTsLpXnkv9fxmMzFm4Rw2IL7qkrgRDS2MUQ3BndVTZgAXHQRYtpmyOw0+9NPwJYtiFkaTXIq4E2LZ+SZKJSUAV59n4UjiPqS8NNPVhIAAIQPFyLq0/Hoo5AybhomF8Hpjxc4mShExBuvneqhowi7qV2/aGmgsBDw+XDPvRodWGUKuizNFBRmDW+cH9ysXubaafVBgjdoScVn/gBZFHoF4Vm1WcfQocDu3SQ006KKgDLpLjVspve65KB46Q77teQ0V6kl4bvvzNNqdR2BGlmAxIozqwju8JPQ53UgZXuLgWjUCiib+DN8BgJOy30pxi4oQ06OTzlYFGkoBvNR7GjMGOuZK/YeRY0nCd9+i1g2JQC0yiqCL8M+ppFov0Y8Or74Ali2zIJHjxSCeX147jlg1CgLXs9XGKf8cDxhTzyteCtojs690CvFXrhC9uq7tF/52sWUCqeQFn+cRkIBwhh7ijEWAPAsYyzF/AkwxjIZY/cev0f6Dx6c8eMwwkkB5OUB9esjjpDU66v2FaA4GkBREfEHDs+KFsCbGbAnJLeOgQOBBx6w4NkoQLU7CQcOO7FqlaVxsIICAEDImQwAcPoo976Oy4S7AwQ375ERJfhpg/zYscNyJWVG6Hz1LQcCuPNOoKDAA+g62GGC1/hkPJmM8NR46dyQWMuPKoJnNw1gyRLgzDNBAVaD8JSwAOrWBT74wHy3QiL4iBJc9xuEJ5os39dXVUIur0AA110H9O1L+LWQAWdVJSJeaso4aZI1d56SI3Cmxs91Lg4jkhyIc2FlowDhpAB8PsTOfAGA8IEClEb8+PFH2YWVXnMYvqxAnNDPwWGE9QCaNZOVh2wUIGzOm0gr1fsKYLgDqKkh/ik+J/x+RBhtWS4oOLM47WwfXn8dcCeTpZFprvG+0gB+/tn0g+t6jFaqPNacRj0eZDtNrdUt1+Kk1dD1J/QMoKQEsT5iGWFay70lAVx1FbBunYw/bNIKnwuOJ6L7JfyBEOFJygngm28sa0wvIzjzB+B0mvEvn4+i7OEwon6ZJlw1BmVDJQfkDDlzrqPJAQwcCPTubcGdJYWo0nTcdptplZpwX+lhuNPj1zIbBYgkBSQBBfB9Lws6vpZHwwH8/jtixagAkBo6DE9G/HPyfd+2LXDOOfJ9q71+MGhSxXnN/sNgmhbb9w6vG8zhQD334bg1Pl6jNnUg92qaVk/TtJ6app3Cf47fI/0HD86MUAN3uh8ffgh88okF10EtH0aNQuwoTADwsiqEXP54PzhjQCCeIDmeAQOsylkA8KEKVZ4A3ngD6NzZajCnMYYqdzKi5nJaZnoNAEUT0XV4WRUAICk3gCZNLLPbC4q2bT0YwHPPASUlbnID1BAeLij4s/Jz3V3pATorwg/TzUD4EQhIc+cAAwCEvX4cOGD5r6n0PD7o7goTXAv48eijpqAQ8CAQwNq1lpbrYFG4EbbVElFVhZA7XoAAgC/TjzlzqLCRCxAPahDR/Zg4EXj3XXkNwroNnupqMH8gTmv1oAaOFD/uuccMHJtrnAQD1b4AbroJ6NpVuJ5VwXDZ4BdoBaC6DP48NS4fupyo4cYbrXRaH2juvvoxCf37I5YOrjGaO1GpiHq9cFabLVdEq9Tni9GKKz2AlBQrG4qPAsOPKVOAAwcg0UrYJwsKvpau9ABOOcWqA3FHq21pxRUlPFwgaJp5X7PehiXJ+B0sChciSMoN4JlnLKsUABxgiCYHsHgxsHGjvJa2tFJdDcOGVpyIwpsdwCefQOoewPfrs8+Cemr5rLWp9tnTnLTvBTzQdVxzDTBjhvyc1Z4Axo2zstoAwB2tRpXbj0hUo+dzadTxt6aGmkf+nRYIH5qmTQCwCPKRtncev0f6Dx4CAfjzArbwsC+AHTuAnTtleLXXnpCOhv045RTEzi/gI1AngMJC010ktHOocguCSLh3tcdiLqJWE0nyY+jFDixbBmRmyvdYvTUJTz1lpU7G7uGRN6f4DnbwdicHsGmT1fCOjx0FAZxwgqypA0BYt8cTSZK1Vj6caQE8+KCsPQIA/H507SpnxABANCkg5fbzURq1EeIgpla/PjE1LkAAIKIH8OGHciCVP78qKABgf5kf9eoBjRqhVrRS4yWtXqz1AUhzjOH30DntAFCuEa2MH49YKxAAcKcHsH8/qPZIuIfhEiwW4Vmj0CyXl9Oq9wGA0y8IYPt2y5XEB7dKxZoVIDFNqNYqHznNApg/H1JKMwAUhMiinz4d0ppFk+xpkVulKq0gEMC111qWEh8s2Y9hw0Ct/BWas6OJwpA9rXjS/QgEgPR05X31AL7/Hvj++/j5scNzqNKPJk2sOB0fybn2tFLlFSwih7X2nFZic2HOXY3Pj169Nbz6qvmsx2m4anHNBQBaMWaqIv/LQ/DHRpP8uO0WSuWcMNJyRbizUhApMxczOTkGT0RIlY4ALr4YuPhiAGHBpZGainvuAWbNAvbvdxHBVFWhStSMYOIqK0OVIECcTutZKzQ/srPNOARgqjD0uWyFA/fdB1x+OZBqPisxF9MkdrC4TZieblosfuFZRe1ReOdKhx/r1gHl5fI7S24MAY83JxU33wy0bQtgjzB3vgAO7aGN4E+kxQnPEA2kWptNwB9JCmD2bFDG23qZYb/7OjH+eoIA8ef5EVkb/5xhn9/CL7xvjS9A8QwA2C0/5513kvY7a6qFx5EmCAqBtvgaOxwg1VvXgcpKVGh+9O1rWmIwn6mqCkhNxeuvA089ZXanTU4GCgtjFldsrrlLVdRanUBYuLc/zw+/Q8Bvju2H/HjuOQpmN0wkQAQ8zlQ/WrUyl0WkFfF3cX94/Dh0yDRGBTxcqXA6AYguv5QAnngC6NcPwBrr+nItgB1rgJwcIE94TneGIBDEtUxOtdZAWctvvjEtrgMyI3//LVqW63pbNOevk4LI4Xj8NR57QVTtIaWI/hDfKwV33QXMng2sXesG83igVVeDJSuKY3KyyQ8EWoQ5d4WFqHQG0LatuZeO46hNFtYOAO7j+xj/JUMQ5flFAfz2m5meJ8Azm6RaCy3Aqz0B9Okj+zYBcgvV1FB9IlwuMJMRHjRSLB+pcO96rRUBYm62KjdpWLNmmUSflgaAXBWrV1PhU3W1hYcLNMDEZV4fTbKYi8PBYtdHoaHPWckoKgJ69JDfbekGP/r0ATZssPDwexAeSExB0k4FPKkNUvDKK6YlI8BLIgE0bCi7kgBQTCAiPz8ARJJTbNcgrAfQsSPQuLH8PEfDfjz1FPD550BY2PxJuQKDF/DX+ALIyDAtOhHuFQSpcN/dRX7s3m2mU6ammv4YIKeJsPk9Hmkt+/UzA68AeI+wag9ZLPv3y/coiqRYzynAU+snFiADBwKLFgF161rvXOkKYPVaByZMMK1SEw9zOCSLRZy7atFaFeaiVVeySk89VYZvPRhAy5bATz/JcElQCHMnWSACXPP7cd99QM+eMrxCI6v0pZfk53SkBOxpIinFWgMBXuMjmqtbF7KlZJDr+uOP5ecP1BPWQMBT5SXLSqW5alEYejxg5v92FaeiuDgWFoRm3iOrcUBeY2F/n3aamYYM695Vbj8OHyarNJaYchxGQgtE07RXADAAlQBWaZr2E4CYFcIYu/X4PdZ/6BAJz2vPvJBCBOnxAEhOBnO5oIXD8GX5KQMEAOBE1B+Ao7wM1V4yuefPB53XnJoGlJWhKJwqC4r0dHL2BwLxzCI/HyFPAM2bUzsOAEBGBgAipB9/pFjKpZcCHvMdDhsKczGvd6X6BZOYxeAhpx9JJuMT5yICBwoqkrBwIVBRYeEBFEEhzJEvy49LLgGaNAFQKTALfwqqQzR3Dkn42jMRKbguwP31UjF7tumGKRSYgk4WQuvWQA9FsPC5DqekxOCGy2/LXNIaBPDjR+YfIeE5vX6MHk1ehOcm+mNrz61DpxOELDWV/FaBACJHhbXMyAAqK+FIDeCii0w/PgCWlgat8AiqPH48+SQxx1DImtPCmhRZCzWf1RHwy2tswkOuAPJySEsHgBJTgFS4UrFsGXDvvcBllwGp5vXlkC2W2Fw4HNCSdKSlmfQurL1kaYgM3hHA1q1AZaV8PXdrqnPtSA3g1luBLl0AlMhrtm8XoQgoeOz2peGy369ZTVPw/fccJNCK14+33wbq1AHOPVG4rxnT8Pnk5wx5ZauXOZ3QIhFkNAxQWjoAwI1oUjIclRWo9gYwdiywfTvFxlhaOrTKSpQ7bRTHw4dj1ra6xpEkEiCnnSbDQ+4APv+IOmUcPSqzqL9yHMsCWQ7qvvsNgMcgn4m+4vg8zn/4ULTrGEEKbo81u1LRtavp29Q0aOaCNu0YkFBF0zMJj8cfLygAhDwptvD8wgAuvdRs8AeYajDQqH0A69eDzqIALMbvVnykJp5Kp98WXuUJ4IoryBVSt24oBtdS/Fi6lGo3du60rq/RPILFAlmL43UmTus5ASC3eQDTp5t+alE7PZwKXQd1LhWYgpRNkpUVg0uBWpHppKXgzDOBFi1keNhHzOjTT+XniehWRkyN4ArbXWQvANMbCMxR8NdXeynjZt06AJqGSCDNhMtrHEmlZ1q/O4C+fc2+TbCetUWXAKqrY7kFsWeVBJFwveG2UTYAHKwMYOhQatHi9Vp4Mhv5sWkTtekwDCBsvnOlM8VW4FQ6FGXDxBP16Titv4ajR80MM2HNVm3WccopwMqVMlzK2EtPj4OLygwA+LIDeOklk0GKVmk0gMaNgcmTFTw+QcES1pi/g0or7qxUdO5sKjOi0uIL4OmnTUtDwMPdl2p8bdP+FPj9pntU02KWQ14Led+z2L4PID/fPHIAEPa9/Vpu2e9H//7m+Sew5qhJez+KiwWrVNj30podp5HQAmGMvX+8bqppWgaAGQAaA8gHcDFjvNxZuu4sAC8BcAJ4hzE2wYRfBGA8gDYAujHGlh+vZ5WGsBJVKdmypsDh3hQyn/ngWntWFs4/n1wD8+YhpqFpOdkKwaQBIAFi55bIL8tEvxNNAQXEiNuVm4WpU4HnnjNdVSYhlfmybZlCqSvTFr6jOANtQO+laRYePSMJe/cCX3wBPPQQYgyVwWGLBwBS0zScfrrJ88ssxi/l9iubH4hnLiF/lgUXNnM0MxtTpoDapAes64ujKfjpc6B9e6CVgKdRl0xrzQQ81SlZsTWICM8WCmRj82ZKgIJmbRUjKRO330AWzrhx1qtktMxCZHs8TYT82bKlYaZfl7gyqWqdDy6ksrIwahS1ycnPBzRTaNakqbRiChBV2TDXbEdJFno2M9O0TbwA4K6bjZ9+ohMbzz7bcmFVuOwFiOFIiikbImM2QhqsqAGkNSs6qmHBAtDZ5KIQF4tOBXhy/XQMH24mIEQtAcIys2BUkgB0CkLcnUfPoNJKVSDLwi8qG+nZmD7ddEmJzxlOwTdTyCo9uZtlfTY/OQuRL61Ehhj+FGUNzFHtS8GPP1p/M8agAQglZ+KBO8lifPVVAH6asZSmWYgUWHi4wAl5UqzeX0BsLY8gExdeaBbfQniHrCw8+ig1oSwtta6v1LP+LQKkNllYazVNW6P8LNA07QVN0zL/6PsJxj0AfmKMtQDwk/m3el8ngNcADATQFsBwTdN4SGgdgCEAfvmT9/8/DyOQg5YtTTeJMCoDudLfzGxEM3tVLioqLK3SpdGObHdqjkyQ5i9lSbm44grz9DwgJnCKfbnYutUsfAJim3lrSY4tc2nVy16AlLgyMWoUtR9JS7PgVQ4ffvkFuOEGoLzcFSPIGrhs8Wg+j8xcBO3xhBOAOXMo5Vhk2GvWUHD1228hbeaIwx2HH1BcYQIeZGVhxAigY0dIFsIh5GLoUDNtVsDjbZhrzZEYtE4T5k5w04VSyMcjeu4A4Pd9ufj5Z1O7FkajrvIaaBFyPlf6c9ClC9Crl3mhmV5dnizTCpc8P6/LkdwVWgq9f6czlDU237nUl4vLLxesUh4b8eRi40YqhGTMmrv9lWnSWnILpGHrJFurtBoeXHIJ1aW0bo0YY47Aid9+o95o+fmQ1l6iCXGN7VxhAOo3dmHaNDP+JeA5WO5HcrL5biJNpGVbeERrNTXHFl6TnoMBA0ipENd+XzgXt9xiWqWC5A80y5UVOHOEUnJsBUhFIE8GmOnMP67OxcqVVoack9HEN+meIyugDpqXsqRc9OwpWKVmYL9Mz4VhmG5iWHOxdFeu7Noy37nTgJy/1wIRxvcAIgCmmX8PA6ABKAEwBcB5f+K+gwH0M39/H0AQwN3KNd0AbGOM7QAATdOmm9/bwBjbaML+xK3/mlGncx4+e9D6O+qjls/lKXVxzjlAvXpmx85AACguxhFnnkx4XMXIk+Ga2cIinFMH55wl3NB0k5W5MjBxIjGFgwcRM6M37vUj0jRegCQnQyakPCJ0dyQEXRfig/XqAQA8kRDWr6civAEDHOQEBnBkb0jG06ABAMAXNZCWRrUMSUkWnriRazHLmhrKzIpGYVZimnMoMp26dWPwJk01vPCCyVwErbIaHqxYRO6HunlpMXhIT7fwuK38jz1V9pu/Ubc8bN1KiuYKwTlrpObhzjupzcWVV1rwipQ6EnNhDge0aBRVGTJcc9Map7fJwyO3CDc0lYEyfx2cdx5Zpb/8gtha7q7KlZ+T03lmJiIHlUwckIA90cYqZYxcMI89ZgoQc+5274xIa1llpuj5ncoam2vjixrSY/C1dCGMvXsp+eChhxCjFcCiOYcDEk2kp1MiSXY2gGwLzpiAP89ixpLAEeBFZYKykZoag7frkYL33zetUpfF3qpTszFzJlljbdsKSkJmPZkBm2NXVZ4tvEnPOlh6qzmfAJjbDa2mBuWp9TB2LD3iXXeB9n1ZGUqTFVpxu6EBiOYo+960cgKt61puKiBm/ZR7M3HjjZZVyoXgvuJk2+A6NO0/RoD0Yoz1Ev5eq2naIsZYL03TLv+T981ljB0AAMbYAU3TcmyuqQdgj/D3XgDd/9UbaZo2CsAoAMjNzUUwGPzXnxZAeXk5gsEgGo0cifqffYa9+n7sCR6K/T/louvQ4MNp+LXUhU2bylFaaiAYXI+cS4aj4cTXsNjIQGFhMTQNCAZXIeWcoWi7dgte/CkVrVtvRJ06bgSDe5HZpw/a/vILMs/RMGPGr4hENNStG0Ja585o88F0LHC2x769BxCJZCAY/BWBFi3QGkn4xdMJu3btBZCHYHAhknNzcRKAz8Id0LnzQrz/vgfz51dCT05GF48PVZf1xosvrsKyZem46qp8JDkcaOtMx7S0ESjbtBVACxhGORY6wzjRkYTJGTejcu0GAG2xfPlvOJJZjm5p6dhy4RVwOoN49llgzx5gb00NOqTVww91LsGhl1biqafa4NFH16Fl81K00evj8+gQaEtXADgR69evQUqgEE3TWuHr4jPgicHXIjW1EJ06dEAoNxebfg+iUyc6OCp4BKhT72RsPZCFiu9/xbBhPTB69DYMHboXOS37I3+LB3t++x3Aidi5cxuCwb3IOek8HF1WiKXfbEAk0hF79+5CMJiP5kOGIG3VKqzYvkpa55WnX4E6c3/Ekj2FmDw5B716HUHDhluQcv71yP1qJpYcqUJFhYHDh0sQDG5C6ohb0fi9KZgww42MjEPweqsRDG5HnSuvQMuXXkJxkwqJ7jIGnotmqzdjUXUODhwoQijkRDC4Ehn9+qHVD/OwKNoEBw4cRlWVH8HgUqR36YITPp6OF5fVR9P2q3DFFUkIBvcjpXlzdHK7kTsyB1On/obSUjfati1Fcm4u2mlJ+N53Okp37ILD0RDB4Hzofj+6wIVvU89B4ZbtAJph8eIF8DRpguYeHd81vgCtW/+CL790YtWqGnjDYZyYnIotZ1+Kb179HT/8kIdrr92BDLeB1p46eDPpVoTXrAfQDitWLMXR+iXo4MnCu45rEV65BkAHrFq1AtWtS9Ctbl0UnNIXBQVB3Hkn5RAEjzK0zGuD37TuOPzWCowZ0wnjx69H9+5FaJDVEcuPtAJb+CuAHti6dROCvx5EnQY9sXpPPRQvWA6gK7Zt24zgLwfQtm9fuCoqsGbhfDRsSF0+gkEgve05qN5wCFtWrMTIkSfh4ov34LrrdsLf9QI4l+/Ekg3bEA53wr59exEM7kDmOVciadZCTPmuGIaRhUOHChEMbkHjK69E3a+/xtrKvWCLDsTWMvXi61H3o0/wW4mGL76sQIMGlTjppPXIHXYp6j//JpaE0lBUVAyHgyEYXI3U8y5Cq/U7MP7zbKSn74LH40IwuBVZffui9eLFcPZgEq2kdemCNh99igXO1ti//yCqq1MRDP6GQIsWaAsfgu4u2L17HyKRbASDi2P7ftLBLqjbeRnuucePBQsOQdMsHvaXDsbYMX8ArAbQXfi7G4DV5u8rj/G9uSBXk/ozGECxcu1Rm+9fBIp78L+vAPCKck0QQNc/egf+c+KJJ7I/O+bNm8cYY6ymOsoO7K5mlZWMnX8+Y+PH0/8LCxm76SbGFi1irF07xi68kODRSJQBUfbQQ4z16sXYaacRvKSEMQ0RNnGizc2iUcYYY4MHM9ahgwXu1DHKrrmGsZEjGWvQwII3qBdhV13F2M03M5aebsFbNK5ml1+eGP/jjzMGMFZVReBT+0ZYnz6Mvfgiwb/+egFjjLGz+lezk09m7PPPGWvYkLH8fLr+8ssZa9LEBn8kwhhjbNYswrNkCYFvvr6aZWZE2eLFBJ89m+Djx9Pfu3Yxdu+9jG3cSPDZ30dZv350v/Xrac4YY4yFw4yFw6yggL738ssE/vhjxgAL/4svEvyX+VEGMDZnDmObNzN2+DDBD+yLsA/ej7KDBxl78EF6nnnz5rHCI1H2+fRqduAAY1lZjN14I12/YT3hmT6d5mHkSBPP/ijTEGFvvGEzF9XVjDHGLrqIsaFDCVRTHWVDhjD22WeMnXoqY717W5fn5UTYqFFEP23bWnC/t5qNG2eD3xyjRjGWm2v93atnlJ12GmN3382Yx2PBO7WrZkOGMDZhAs1RRQW98+n9o6xHDxvEJq288461RowxNuziCGvZkrFp0wjO1+ym66pZdjZjCxYwduKJtG6MMXbn2ChLSrLBb9LKb78RnlmzCPzow2GmIcK2biX4lCkEf+N1WoMtW2jd160j+KrfI2zYMMY2bKB779tnzXVlaQ2LRBjTNMYeeIDgEyeuZABj8+cz5nIxdt99BN+8ifbr1KlEJ8XFBC8+GmXffkk08cgjjL33HsHLyhh75+0o27yZsdataZ0Zs/b9+PGM9ezJWP/+BK+ooH0/YULiub74Ysa6dbPA550bZS+/zNjw4Yw1b27BmzWJsMsuY+z66+W1b9awml15ZTx6zsP+zACwnNnw1NpYINcCmKxpmh/kuioFcK2mackAnjqGYDo90f80TTukaVodRtZHHVCDRnXsBdBA+Ls+gP021/1bx858DS1buvHhh8Dvv1vWc0YG8Npr9Lvkv3ZocDgINmiQ5VFxOq0AdGkpwXgG6QVD6NwQ1d2ychWZ3ldeKcMdLsIzZox5lKc5mMuNSIRShFevRixgOy+oWS4kWLgefdwBxsyGcDDTeAHA7UY0SmePDxli4Xc66RlnzqQzpb/9lrweTHMgEkacCd2xqxtloXg4/6xTx2wFYY5DhzUEg5TVdO655I4ZNsz6goqH5lyLnX8Qw+/SYte3bGnh37DJgStH0PxMmACMHUt9uzIyNQy5xB37Tgy/08LTuLHlUXE4NTBYLgM+DhwA6td34/XXyd3I8bjcGp2nDmqfYreWF15otsc3R9RJa7l/PwVkeextzBjKNlNpZV6Q6O6ee2Q4x3P11RRA54lETpcWo5Uff6S6ArcbWL1Gw6FD8XN93fUOFBZaMT3LFUP4e/c2O83y93IS/mCQzgiZOdNs4WJuFMnlBaBBYyd69bZqGNS11HXzdEFzHCpwYPp0aiF0zjnACy/Q3LjcGlxuF0gMxdNcNCrvV5FWYsW3ALZt13DuBW58/TX1cOveHRg5kryR11yrxXDF5sGhQdMsmuOuYnHfq6NBQw1XXUWZceIZHt/MJPyLFtnTytChpsvOHHzf79hBNNhL9B/9xeMPg+iMsWWMsRMAdALQiTHWgTG2lDFWwRj75E/e9xsAI8zfR8C+u+8yAC00TWuiaZoHFHv5xua6f+uIpWJG5E3LGPn2VThAG6Z9e8rYuf12GU80Svn+AwZY1//8M7BpUzwePlS400l4mjUzi/zM4XAQfOZMyu3n48UXieGrm7Z3b0qtdTrJxSoyZjuC5/gLC0lA8c3+6KPEfNTNf+21lDqam0u/c9c4v38oREzTjD/GvqcKhLlzSVCazUhj8CFDqL7g5JNps/GMFRHPxInA0qXyfdU1KyujXkcHD8rwvDyKDXXrRoz2qadk/JEItTW/7z55fuxogg/Vz96rFzGc4cMhZWhxYX3vvULOP0hoL16MuICv2219R6UVzhxPOEFgnCZ80SIS4ly5eO01YMSIeAFy2mlEt7pO4TCeqMTxqIPDDcOaV44/M9NSojj+kSOBBQsobHP//fSs4v8rK0mxKCmR4SqtcMVpzx4Z3rZtCfbvp0LEDRssYSSu5RNPmK1JFLg4pzU1dJAafydxLSdOJIXkvfcQqwUR8VxyiazwFRdTbLC2tNKqFYUKTz+dkl7EuY5G6YC00xOq8X/NOFYh4eWMsamapt2hwAEAjLHn/w/3nQDgE03TrgGwG+SugqZpdUFuq7MZY2FN024G8AMojXcyY2y9ed0FAF4BkA1glqZpqxhjZ/4fnqfWQ9Vc+N+FhbQpX3kFOOMMoaAPwNSp1nc0jX4SMS/AYtgqfNw4Kv664w6LeQLA+vV03eLFRMjcSuCbVk035vBIxHoegDTGUAi47Tb6CQZpl998M23YWbOAl18Gpk2jTS/i4c8tzpG6mflo0ULIGAJp0/37U2bZgAFUpXzaafF4OP5t28ga4YWZMc3eZcVNe/aU3xcg5nXXXWRtdOsmb2aRAe/aBZx1FjXK9PutpJ3UVKE6HPH4IxFiaryGLhHTAUiI3norcMEFUqyXmnOCmAmzGgFIc20nEFTm8tprtGY33yxbjbNn0/2WLCFL8+abLTzRaLxV6nKRIqAKkJ076Rml1FKQpdioEVkxd99NAfamTRPTSlUV0TJXGtSgdVaW2TbfHJmZpIzt2UPMcdo0EraJaG7HDtqTl18uwz0eFov5t24tzydAzzlhAh1KNnBg4rUsKSGF5eWXyYIWrZY7JM4Zj3/fPqmELOEan3IKKRYXXWS2bjHHzJn0uW8f7Vuerp2IfxyPcSwLhKd4BxL8/OnBGCtkjPVnjLUwP4tM+H7G2NnCdd8xxloyxpoxxp4Q4F8yxuozxryMsdx/l/AAEjN+Ef7aa5alIY4uXcyDd0Abs29f0t4SMQWV8c+ZQ9k6J55IQooPn480zrffhlDtXjumI8LHjyfBoY6BA4lJ7NpFjEG0LESmoLoHcnKIQfLEkEceIY2JuxP4GDaMrArOSFVBpFok/DMtjRgU17LWr6fn37iRLJ2tWwneoQNtMq65q3gS4eebnLvVqqtJyBYUAOedh1i9j64Tk+vZU3GHHEOAHD1K2uYdd8iWhjgnZwlZeG3a0HzWdi1nzgQ++4yYd+/eFjwnh9yts2bRXHHlQWQ6/G8Rv9NJSV98jZ54wjxOVhlnnEHvVFhIqasiQ2csMa1kZ5Nw5kl5779P73z0KKweWaD01rVrrYQvFY/qUhP35/z5liApKPDg4YeJVp5/3rJK8/II/4UXynOaaC1F+IIFZmNPc2zdSs8+bBhwp9l+VtNIieG0Upu1zM8nxfDii4HRo+Pn/J57ZH6QnU1JYP8OAXKsQsJJ5ucjx/cR/ruGSDDdupnVzgpcHfXrk6mqCpxgkH5/5x17Qho7Vu5jw+HLl5M23acPwSdMIE1NJZjZs8m18Mgj9vgfe8xMv1TgX3xBjPmaawi+Ywdps+rmHzKEtMFETKFbN8LFRyhEmVSzZ5P//ddfzdRcyHPHv5+RQTUkKl7+6fXK2nV+PmmCvXoBV11FVcotWtAc1K1rdr21wRMXM0mwlgUFwEknkRtr4UIrDuH1WvU6oiUj4unfX24nwee6poZogV87cCC5JtS1XLyYPi++2H4tOdNW4UuWkBDkVsJ771nCQsTzwgv0LNxaVgXIjTfSj4p/1izS8KdNo/U6epTmWV3LXr2IiXJ6VoVs06bm+S3mOHqU3LirVpHg//JLS/nicyri0XUSKlwgckHH8TNGmjwfhYVePPooucbGjiV3ZLdupIi1b2/dw24tXS45lglYlps4TjyR9tC6dZaSApgdgUFn/dit5bnnyjEQDi8spPfgmexXX00Wmeq+XLCAPm+55W8UIHxomtYSwBug1Nv2mqZ1ADCIMfb4H3z1/8uRmkoE0L07cP31FlwksPbtSSN44QWCVVYSwz+Wb1ModkXbtqQJiRoovwdn/Lt2WcVJ06aR+SrGLQArxpBI03E67eFr1hDOa68l+L33ki+Z+1n5dwYMoJ+vv6amedwcT8SAuZtEZS4ffEDWD9f0Obx/f0pUKCggIduxo/z/0lISRh07EvNIZFEUFJBVeOqpMrx9e8LftCkJN4dDDlRGIuQeOf988leLzEK0NBijNuepqTLc6yUtv3NnOW4hzvXJJ5Nw4+6IXbvIBVbb+FdeHgmmLl3s8U+eTLhFAeJ0yi48wGzlgXhmxPGog8Pz8ylexAXDxInA00+bLUaEuT7jDPpZupQ0cl7jx/8fDssWdyLh/vPPFGPiHQA4vGtXSjCorCRLqXNn+f+GQcKxa1dyWfEEEdV1FgpR/VafPvJcN2hA927bltZInAfAopUePSyLMpFFUVpKAkiFDx9O6zhiBKTB8VxxBSlg3Fpau5asjZSUeNcffybXH3L4/9uoDfq3QWeAcItkjaZp0wD8TwqQ5GSzUEgZIiEdOWI2izOHy2VPSO3bU7Bw1Cip3o1ancCKbXAf7bFcUmpMBiA3gMdDFopoaTz5JG2Uzz+nACDXiDj+cFhoZaLcV3zXwkLSNgcPFipnQcxp3DjCf9ddVJzXqFG8m4TjKSsjnzp3P6ibITvbsoYAWoPcXGLa555LZ0iIDF5lOoWFZIWpTEtkNOIQ13L6dCtzK5H7MhKhrKxHHyUG0qYNwb1e2aWh3sMudpFojYcMIeZ3442WJQWQWxOgOa6osLTsRDSXCP+cOeQmGT9e6H4Aut8FF5CSMGMGuQY9nsQ0ocL5u1VXExM/6SSzv5Q5WrcmhhkMkpXOrdJEa3n0KNGsGnTnIymJnpcPl4uuKS0lBvzSS7IAUfHzGODzz8tzlJRkKSDiEGng55/trUx1ruvUoZ5Wp54q95/kLlFOE3b7rza0ctddJFSuv97ezfhXjj/MwgKQxBhbqsCOY4Pg/+wRiZBv8+hRYj4TJxLc7aagYffu9locD0SK8O3bqdHmiBFyNgYf110npyrm5hLBSb1ykDho9uabpHGmpkpFwmjUiNwk8+fLwexjCahIhO7drp1176eeoviCOvr0IS2UsXi3CmCTmml+NmtGwq1hQ/r711+JaS5aJDONoUOJ2fHrauuSSksjLZVreEVFlB2zbh3NMxfcublk2fDYip0bI5Gr6tNPLX83Y6RIVFcT4xSF4GWXEay2DH7FCjrj/fTT6f3V8cQTsn/c57OESG3wv/8+CQ+XS+6Y37w5xVDWriXG/0dKBf/MyaGAL09AeOklmv9YKw5znHoqCSWewl7btaxfn6wcnr66Ywcxy7lzKXPqgFnrd/rpRG/duv1r+CMRetYHHqC/Kyvp/bdtI0ucC0GPhwTr4MG1Z/B8v06caGXsiaN3b/MYaHP070+WicpXeJafCp8/n1yeHTuaRwQfx1EbAXJE07RmoNbu0DRtKIADx/7K/7+jooI00smTKf3vyBGCu1yk6Z96amJCuvZa8zwQc3AC2L9fzvm/5BLazCrhffklEWsipvDss4jVF4j4v/gCUoPHYJCeX8XzwAO0mRPh52dfc6bALZ933iFGw5lDVRUJWNWV1LkzWVyJBEjjxuQu411MysqIcQaDpJX+/ru8FnbMiwtr/v7i/xkjQcqzpA4cIKa7eDE1uluzhuC6ThuYd1+xYy6dOlkBX57Jprp6GCMr56mnyGowT2MFQILrsssSu4xuuIEUCBEejQKbN5vHsprjrrto3dQ1mzaN5iuRtfrggyQUVPgXX8gW9po1wEcfxc/1iBGknKhwPudnnkkCmbeM5/+fNo3mf/t2ea5UPA0bytlPKv70dKJHrkSUl1M8dKpURAAAW6tJREFU5rffiGnOn39s/Jpm78IS1zgpyXItFxWRkjdvHrnCeI2Lw0FxqTZtEu+bbt3kg50SuQVbt6Z3UvG8/jpZ9In4yo03Ag8/HA9fvdqKsx6vURsBMhrkvmqtado+AGMA3HjMb/x/PEQCUxf66FEr2CzCL7+cXAv33CNbGnyhBw6UmcXKlcQoausH93iIsBo3ttwnIv4vvqDgMh/TpxOjtnOp9ehBTE+0WBIRPNekCguJIXDtdMoUslb27ZPnbNAgYjqtWlG2GA8G8v+XlpImqWqF6t+LF1MWFGdCHN63LwmPa66hzcNra0RX1sMPW7Ej0b0iXsfde1u2yPDkZGKAAweSdSRah1xYn3iilXbK58POvciHyhT69iXL5PLLzaJJZa5vvZWYDB+LF1Og3K7xH8dvp/1mZJidbxX4L7+YPdzM8fnn9CyqS6pzZ3KrZWQQc1SD1iq98O/xhoB8bqZNI/rlGXP8uoEDge++o/mcMMFKi+f4i4tpDdQ6EDULa+tWCjZzYcnhDRpUorSUlLq9e605FWlgzBjz4CvlvVQPwNy5ZJmoc/3MM+Q2+/hj2dLgwrp7dzktPBwmWkxEK+oat29PQke1Svl+fe45mVaOx/jDGAijZoanm5XnDsZY2fF9pP/scSwBkpVFjHn4cMtkBmgDAMQgPR6h+vcPXEYq/KGHSCt/7jk562PhQvr89lvaQGIB3b8SM1m2jLTyhx+mH669XHcdMex336WfhQutzCHuzhHnRmX8aiCvUye5crZRI3IBzJtHdQlr19LmSCRADh6kdx00SIbz4fPJrjX+/yNHyBpo2pTuz+GqpVRWRhvy6acpEYG7V9xuWlu7wedi2zbhNDnNYswq02ncmLT0666ThfXzZnXVnj1EK6IV9Ee0Igqit96iLKYnn5TdRp99Rp/ffUfPqgZ87SwiPkcifPt2CqBffTX98DFgAM3X1KlE98uWkesq0VryAlx1Dfho0IBcw3xkZpKSs3Urad5z5hADTURzhw+T0sLrgkQa5Ue/iP0/RQHy0ktkDffvf+x9P2AAxY1at5bXkqcMq0NUvMS1SbTGAwYQHdyoqO1vvEGfXNnkVk4iPMdj/KEFommaV9O0SwHcBuB2TdMe0jTtoT/63v+vQ9Ww7BjzG2+Qe0IcjJHrS6yzGDiQYgp2WqIdg1++nOIBnTsLnVeF8eqrVkBcfJ5EWqimSWfi4M03IXcCNcfJJ1Mm0q5dpPWJ5r6YVaW6AZo3p7Yr3Kf+4ovEhIuKILVS6d+fWq+rFkkipsM/W7SguhQurHfuJGY2Zw6llubnE7xuXRLeajHZH+H3ekk75XMSjZKQ27mT5l+MHz3/PAnZ2vrBIxFimmPH2se/zj1XzvLr1IliRLVVNhYvJuuhcWOiMT6Sk+nnyy8txUbFoz4/QHQiNEjGu+/GZwkCFLO6+Waa79hhSQKeRC6jJk1oLjgNfPkluQjXrSNhFQoR/OST6d3ExBLxM9FaZmeTO5QrHaWlLowdS9bDI49YrfmdTqIbHk+yc18mWoOlS+XzYfiz9+hB9+DjnntofWu7lkVF9HPJJfSjjttuky2N+vUpO09VWo7HqA36r0Gt21dAONL2f3Vwwg+HSQDwOhD+PztXT9u2lG9u56cGyKKwI6Rnn5VPBuX458wh7bRvX4I/+6zVRkXE8/nnJCSuusoev+iqEOFvvEGblAd9t22Lb+sBUDwnL4+0PP598fPUU61UYICEaDhMabu3306MuHFj6/+qIEpPp4C82bU8Dn9yMrl7+CgsJG2zXj1yIzVrRvgdDtI2VabF/66pIcH2R26YSITScR9+mOILh6xmzDGGkyimMWyY1Y5DhB89SmvJ3/HCC+2F/owZ9HnKKfH4q6vJWhJrDXgF+fffk7Dmx+O+/z7F21T8jz9ObpannrK3QMaNs/ezv/suxdMWLiRaO3KEYnoqI+/WjZiomurNP9u1k5ljKEQu0LlziVbUmiHp3BKQgGvRQrbu1U8x1dkwnHj+eaKLRx4hptu5M71Do0a0LnZ4uPuPr5c4F+oYMoQUjS1bZIVv7FgLlx2tjBwpV7Rz+K5dtK7cYho9mgSLSnMffUSfQ4cefwukNgKkPmPMRtf43xwOBwW1TjpJOMjeHHyh/X4i+sceIzgPsNY2ptG5MzFmMRNDxH///WTKcwHyww/kW/Z6ZTy80WMiQlUHh69aRUKKC5CXXwY+/JA0YhFPt2708/HHpH3bBSJV/EA8c/nmG7oX17g5vH178snv308Mhhfuia6sTz+lbJ/s7MRabmUlBY1VP3r9+uQKycmxsm2CQev/RUUUkL3pJtIYE+EHKLCt1oEA5NLs3t1+LaNRcrUNGECMGLCSD45FK2LNUMOG5AYRXYIcP1cG9uyxBMjMmfSsXbvK+DnD0rT49hr8vip+xkgJ+PVXOaZx2232dRpdu1Jw+7rr4pUCw6B4Bhf0iWhlxQqyarkrkcMbNCBGXVJCQl6tGTpyhOaCtxlKlMYLkGXG24JweCBA7rgGDeK7TPC57t2bkgt4PDORRXHgAK2hCr/sMtrXYjxUxHPhheTKmjWL4Lt2Ea60tMR1IP8JAmSxpmknMMbWHt9H+e8Ymhbvi+SDL7RhyK06EhFS166kYT/0kHRWDt5/nz4XLyamxF0QifAkgn/4IQUbP/5YZgD33UcB4NdfJxeNWMBnp/0mwn/4MGmJl1wixwY6diThOXkyFVMePSoXOdoFyY8csdwUKtHXrStrp4EAMYHNmyljKBgkYXos/M8/Hx8odbvlnmXi+wLEmL//noQjkDjoDhDzGD6crDIx4+ahBM5eMfVadRmFQvFzPXw4ab5qVwFesPfTTwTnvZL+VVr5+WdSHLhfnY8rriAX44cfkjDn6auiMLWzWNQ5qqwkgdyrl6X4AMSoR48mS6NbN7J2mzVLjMcwKPtR7SrAR2qq3EDQ4yEGe/gwxVJmzKA1P5YyMH48zbcoyJxOs3uwzeBzumgRzZUKV+e6Z0/a90OHWoIOINcWYBUaih18E8Wn7OAPPGDVPon1aMdjJIyB8KNsAfQG8LumaZvN42w5/H92rFpFzKt+fdkN9NBDpLEmWmiVkAoKiLmOGBGvoQKkaYntzRs0IJdMbZnCZ5+RZqvrsissM5PwzJtnHvtqjkT1JFywNGwouxGmTCG3gJieCpDl8MADxOirq+NdQ4n81F27UuyCn1q7cSNlbE2dSgyGBxx79ybLQdUy/wh/69a0ObkfvKKCYkbffUduA35MsNdLzIDHsVQGbydA+Bp88YV8euGRI3TPjAy5ud6VV5LlUdu13L6dMtROP92+oO3hhy2LF6BAdnp67fHPmmUv7PLyaI3Xr4d05rc413YxkyZNSPDyvz/7jOhXrOIGaA1ffdUKPqtWbOwIaKVPWocOZH3yIs+iIhJMb79NDSm5W7V9e9pjPF7D8R7LAnE6iQYjESv+xV2+S5aQa0rcN59/blkNtYl/cfhLL8kJCDU19DwdO8rxrwEDyKo6VnxNhK9eTenMHTrI+/V4jGNZIMe5hvG/d/ToQQxg3z45i+LOO+Mzkvjv3PUk+kI5nLs/eJDyyiuJiamEx2s5TjjBHj/3k6vwSZOIMHna6YIF5LNWg2xjxxIjffFFGT8XLLfcIqeu8mvGj6dNy5mDYZBw5IKFX3fCCfR9sfW3+NmihZy6WlNDbomvvyYGtHGj3DlVTWRwu2kexQaB4v8ZszJvANLO7r6bNOD33ycmk5dH3+vZM74FOP+dMdL0eQ2CONfqaNOG6gSqq+Wz1R98kD7vvNN+LR95RLZKOfy338ia4/GUBx8kOlRpZcIE+jnjDHv8b78tx0w4/K23SFDxAPv69UQv5eUynosvJlfr3Ln2FsiQIfHt6AEqnnvzTWLqaWmJs7Dq16d7qJ2N+WdWllwkFw6ThZSdTQw9GLRqUIB4WlFbmdjNkTiiUWLqd99NAX7x2IQzzjg2noED4+tA7HpnnXIKCX5VAeW0Mn16/L6MRkl5EGmL3zcYpE/RKvqrx7GaKe5K9L//9ZFIC923TyRQC3755bQRxIAy/24kQszoggtoYwHkV3a7a5/bn5pKvl/1OHKO/9NPiZlz5v/TT8SgRL8+QMHDRo1o4/F4g4jHbh4AYga8oBIgTfX88+NdP7160c+SJTR/qh/88GEqXGvTxjrPAoif67VriTmpva1atiTXRihE2j5nwPz/O3aQkBw1iiybRPgBsq54DEmEf/kladdivQ2/pqaGfNR3321ZG4msOn5PtePyqaeSNq2mgPI1uO46csHwJpUbNpCQ1fXa0QrHI1qkIjwYJF8/FyALFpDLVrQmAHqG5s3JEuzeXcbD30vFD8Qz2jlzyPoeOVKGd+1KCtG2bfSsavfdAweIznr0IKUg0VoeOEC0wtN4ucIUCIRjVdxPPSVX3zudlCBxzTX007PnsWnl++/ltvt8PPkk4RVddoBFEzk5pCzybhaJ3Jp8qPygUyeiUVVA8LV84glScP8WAfLPSDwSCZCuXUnbuPlmOTuIt1jfu5c0DLFtQyQSbwkkMk2feoqyfz75RE6/5R1U33uPcKt1IHb4gXj/9fLlxMA5QQeD9HnlleQ2evRRcnvxlh/iprLTQrl7Qyyoq64mX7doWtevTwxz7lyKVRw8SIxYdWPwv0tL6dm4Vif2EQNobnhzQPF7u3dTi5Izz/xjAXL11eRabNXKYg5A4tYQnCYOH5ZdeoncGN27kwUjHpYEWG1Q1q0jDZ1Xu3NtMxy2Fwgqc5k6lSy3Dz+UmfnkybQe779P9S78PJBEqeOJ1nj7dqKVG26QLY0+fUj4TppE99i718IPxAsQFa4yTi6o+EhLI5fOpk2kkK1eTa6aRGtZUUHWq9pVgHcPcDotRUF856NHKd7Tty8JEE7D/DnF/XT11fRMJ58sK3F2ac4cP4+VimuTiFaGDKGYxvjxcu8snvixbBlZ9aJL91jFq3/l+MM6kH9G/EgkQJxOIrRXXpFjGoZBLoAGDaxCMYC0ul69au+n3rqVtPf27e2Dvy+9RCmyIp5jMQVdl5njF1/Ivlc+2rSh4PCePVZ1toiHtyRX4V27yv2Zpk2je65eTZohTzTo2JEYHWf6qrtCLQ7j8F69KNGA+8ELCsjt8fbbpP3t3y/PAz+VMRHzUt0DdesSoxLbiH//PQWcW7aUmwJOnBivRfPf+Vra9S8bO1Y+jZKP/v3lg5ROOolcRupaJtJaN2wgP329ekR34vWaRlbplCnxz2nXbwmgmADPTAKokHPIEKJrcbRoYZ1gKLbnScTg+WenTsQguYtx3jxi7LNmyeeKNG9OWYdcQUtEKyq8fXvaP7zZZE2NhlGjqA3PXXeRq46PrVvjT5vkRaFqTIZf43JRNpoY/1q5krLG6tSR9/3ddxOt1HbfV1WRILz4YvsTBm+8UW6A2bgx0ed/Sh3IP0MZnGAuvlhm5JwAqqqsLqAAaa12AufZZ+nz/vvjmUs0Svncoh+X458+nYiSm8YvvWTfSoEziL59ZYuFX/PRR1ZfK/G+Dz5IDJ67UbZupfiDarHw7Jx58+wF1MCB8nnMnBm99BJpp6GQnDLK3WT8ukCA5o4zFZUppKTIvuhQiBhjTQ0xzzPOICHAtUfVDy66W9LT7U+HU8dll5GbaetW0uD5uOgiKx6mCtNolNyH4rNy/Lt2WQFvgDLFVq6MX8vnnqPPr7+OZ17RKK2DmN7L8X/4IQlt3upi2jRiaqolM24cPeP119srA48/bm/VPfKI3HPpyBFKMFFjJh060DvwOJkan+rcWXa1RKNkaX7yCSlFu3fLglCNNbrdFOxXOy6L/xf3KmOkaBQWkuJ0yilWtmN6utWM0c4z0LixbLUkopXbbqP7HDwoZ0NdcQV92gmQ6moSMHYtidasIVrhtVPjxlGyh6o88GLiXr1kmjge4x8B8ifGG29QrEB0UwG0iEVFxKxfeEE+cjXR8a5A/Gbu2pUILtEZEuPG0WbjAmTpUgqu8jbbfHDXTqL2FHa5/dEoMYQ9eywBMmMGCZVhw+QN1aqVdfiRyrwAEqS8SE+FAxauX34hi41bbfy6vDzSQHfvJs2OZ2fx/2/dSm67IUNoQx/LJSVW2IsW2MGD5GPn8RjOCJ1OEsp9+lB2k5geqx6xC9Cc2bVuufdeYnyq64uvZcuWVFfAYw7V1X98LrYIb9aMBBc/BEnEzxgJ65wcS4AsWkTr2bmz/Jx+vzUPolV6LFoBqGp782YLPncupcCKjRABskzuuINiHqJyxT+LiymGWKfOsetAtm+nfcFdoGIh4YoV5Hq6806iS/F7O3aQwjZ8OLkFj0UrEyZYDF+Er11LNMir5cW5KCoiV+S991qdBZxOezz5+VZtmAi/9FJ6HvF8c/7dSIQ8Frx7MUDCb9cuWi87S0O1eo/H+EeA/Ilh104boIW28+UmEiB9+pBv9q235Owibj5/+y0JKu4jT2TiJoJ//DH50nmzPT5uuolM6Kefput5mwXRJWUncFQ/+KFDxDwuuUQ+BKdlS8rkeuMNYu5qzr4dAw6F4mMdfDRsKGc88XM81q0jn36fPn8sQCZPtrQ60S3BfePqcDrpuRculM+fF9dYxD98OGmGl10ma4/XX2+1dfd4ZDecnctIPINchF97LbmEJk+W/eCPPkqfn35KzE09ttduLXlcTIT/8gu5hiZPlmNKgwfTGk+eTC5BzrwS0UQieEUFKQK9esnHrzZoQPUPP/xA+6q09NhB8UiE8KhryUd6uhxf83hIYPB6px496O9EB0oBlMySmUnavmiVcqGkDqeT3NTr1lkV7BxuR4vDhhG93nSTbJXylN69e2kOxCSOY9WBqILi8cdJoZw82T4Y/1eOf2Igf2L89hv5wlNTycTm48EHZe2Dj0SEFAoRY7niinhrBiBcvFAMIBdCp06J6zRU+Lx51vdFQkpKIi0qGLQaMYrPlogptGljHaMLUEC6b18r1sBHgwZkvvOUWD7EQjz1wByAYgFTpljutsOHyYf/8MPkkuJz2KoVJRPwZ0lUZ6IK8f79aZ74pmWM1uyVVyjxYN066/olS6xMqtqspdNJzz11KmnffOzZQ9pvcrLsB+fV1MfK7VeF9Z49JCDUqnOAAqpib66MDKIXu7W0w79kCTFY8ShVgJhoy5YkRHgLc/HdE9FKx47k4uVj4UJKevjtNzlu0rCh1eASiF9L1Vrl8H79aA/y7CzGyIV1111U+8SVluxsmjeeHs7xqEFx9R3atKHMRp5JCNCpllOnkgD8+WcL/vHHVqqtupZ2ShHfry+/LB/4VFZGAqhlSzn+NWAAzWUiWlGVgfx82h9t28qK6fEY/1ggf2JccgkRbmmpbNqPGEEuESCeYJxOYiDiucxOJy3+4sVkafAMjhtvpFRedZPfeSf9iG07ACuQ+vvv9v7x8eOJmXPT+LffyJdeUiJ3D73+emKkN99szxTGjbMyyET4ddeR1sRdGYZBTLOkRMbTujWZ+Pv22WeFtW4tM1+AhNNHH5GmzftG8aGeK+J2k3ap9kMCrMOVxHx5TaON2qcPsGCBXOPSrp2VTaVuWo+HNr7ok+ebWR1nnWVlUonPM2oUMb3rrrNn8G+/bSUHcHg0Skyzfn3LKn3ySSvfX3zO0aPpR+xqLOL/+ef4DCCAaMXjoRRQgNyEX31FdC3iOeccslpeeYVoVcVz2WVy7ykOf/BByhrijDUcJjrhrh5OF7m5lELLEy1Ul1durpzlpGkUbC8pIdrr00c+HVCNfwGkAKqxGHGO1PHgg+RenjtXLgDs2jX+6AL+LoyRoiBapXy/VlURzfJnuPxyckmp+563fH/9dfvnfOut+H0ZiVD2WXr6P2m8/3EjkWbBTxgE5M186aVE2Ha+zaoqMusff9zKpCgoIK2ptnUg2dkULOYxAhE/rwNp29a6/8qVpPU1aGAxN4Cskqws8lfz9xPfMZEfvKJCvn7NGnIjNGggP2fbtsTwfvlF1qL5NTt3ko+ep02qFgVnLrt3k2tMZcypqTRvVVWkzanHiy5bRpvxwQct5q9aFPwd333XyiIS3+GTT2hTqu4Mp5OeKymJXHfcpSfSiig0S0vtLZm+fQm/2qGXM53LLqOfV14h+J49xDiTk2tHK7pOz6j6xvk18+bJbpv160lxqF9fbvCXl0c/ixbF11Dw+9rhVzP21q8nWlC7CjRrRhlSGzfSnIiHmAEUn/riC1I4xJYfdmm8Q4daySjie3MrJRqNL8TbuJEUxfvuk5/Nbi1nzrTcnOJcP/QQPY9otfNrKipI0XnqKauFSSJXFWP0o65lp05ERzw+J+KPRun+7dr9fyhANE3LADADQGMA+QAuZowdtbnuLAAvAXACeIcxNsGEPwvgPADVALYDuIoxVvzveHYgsRvjwguJad17r3zW9vDhpGlt3EgaP2dsx3KH2KVmvvwymdC//SZXVPMA7NNPkxbPzydPZOImcj+sXEkM5MUXiYkEgwQfOpTe57bbyAqYOfPYeBLBq6tJkPboIVti/KyDn34irVnNsLHrbbViheWrV5mh1yszQYA0tL17ieHdfPMfC5AHHqCYRteuclA5UWsIp5O0aLs+aHZrfPHFFAR9+WW5EI8nLixYQFapeGzvseJfKtP54gtyucyeLWunjz1GPxMmEB1ypUKcWzEzL9Fa5ueTInDjjXJG0oknUiX488+Ty4sfFPVHtFJVZaXKiqNNG1l7T06mfbZ5s5WqfSwBEo3SHHC3pZ2QVe/pdJLFtXq1XPybaC0feojo7fTT5ToQcV1V/HaxF7EWR4RfdRXtxbfekq3ea6+ln9mzia9wQSemdh/vIPrfFQO5B8BPjLEWAH4y/5aGpmlOAK8BGAigLYDhmqbxhgBzALRnjHUAsAXAvf+WpzbHsRi/30+ELcY0jh4l/3rbtpSCy8fgwfE9evjvdszi4EFi8i1ayG0u+HjhBerrxAcP2iaqA8nOlvH88gvVJagN2OrXJy2woEBuYf5HTGHAANktFAySJjhzpnykacOGZJ63a2cVeIl4VGuPf150EWXG8KByTQ1ppOPGkRAXg9/5+VZ6o/qsidaybVuyWsRA58yZtJHr1LG6ogLEkEVN0g6/6rZjjOZHPHwMoPU65RQ5/tW9O2mSKlPg2qbKdPbuJTeV3y8LQD6mTyd3GB9iTYzdWjZqJDPyJUvIyuLprnzUqUPWoc8nW6Uifru42IABVqoyQFasw0HKzIIFllKRkUGuGbULAf9dXUvxhMMDB+R3uPpqopMbbiC3Fx8rV8Y3jeS47NbS4SDLfc4c2a22fDm5X/1+yhbkY+xYq2BUff5wmOhCvW8kQvNqFysdOZL2Dx/NmxO9qIrj8Rh/lwAZDMDsOYv3AZxvc003ANsYYzsYY9UAppvfA2PsR8aY6QHHEgD1bb5/3IbTSVrd1VfL51lwAj5yRN48N91k1UOICzp2rHXAlF2++S+/xJ+LHYlQaqYY/J40iYhLFRTPPmt/9gP//euvyU3AB99sV14pM/5t22gjlJXJeHr0oNYeDRrY1w4MHmwxVRH+8MOyJs/PCQmHZTweD7kR1Dbs/DMtjXz84tzNnk0a8IQJcp0GYO8Hdzjo+w0byrUyXBtUx7hxxOgOHpQDzmJqqcpcfD6yaMQ+aA4HMdO1a60TDAEK3IudCvi4805yW6lMgTOXYFBupsiveeYZWiM+Pv/cCt6LeEaNIuspI8N+LV98US5S5ddce62colxURGtw+LA8Dy1akOAVOwCI+Lt3l9ukOxxEF+++K1urfKjngQCk5PBjelVacblIWRIzzD7/nOZm0iTL9QzQNWrshf/uclH8qTZ1IM88Q3HFigr5/2efbcX67BTHF16QBRGHz58vK16PPUaua1WpGDOGFMl/RyX63xUDyWWMHQAAxtgBTdNybK6pB2CP8PdeAHZG4dUgd9i/bbz8MrmQVG3A6aRK7exsYrhiRpadlssbyanwk04irUUswuPXMEaCZ9w4ai8CkDk/d66cXy8O7vcW8QCJ/dRr11oBaoDcWqNGUVBXLGysW5eqtI8csYKIIp7iYnJZ8c0mZmGJBL9pE2n7jRvLcK+XNOXduym4yL/PP5cupYyeG2+Ug5F2c3rrreT2AuR7HD5M3+WMJRi0vvvrr+RnnjzZCgg7nVZwXcSzfLmVxSXe9+676T3EbBt+TUkJFdg9/7zFPEUt124tVWbRogXRgdqZgH/3+ecpy++CC+jv9etpTlu2lPHwOcjN/ddiGmpD0dWriTnWrSvTXG4uKUP16skWF8ezfz+5u/gBbar7kq9tcTFlbPF4jCgQvvuOrP39+63/czwrVpCracwYudjQLqbx7LPk6hS/D5A16vPJsTV+zebNRL+vvmqttctlj3/LFrlLAh/DhpGwTFQHctZZRMdPP01w3rTU77enlf/qSnRN0+YCsHG04H4bmC0KGxiTLtC0+wGEAXx0jOcYBWAUAOTm5iLIOcS/OMrLy2PfdTho06ioyso6o7zcB8CLzZvXIxikKGxBQWuEwzQVW7ZsRDBIfqB77jkBBQVejB+fj4yMCgSDxJk6dCB3zr335qJFi3I0bUo7dPfuRgCaIBIB9u7NRzCYDwDYt68ZamrqIhplOHDgIILBbQCA+fOzsGRJJl5/ndKj+PPWqaPhhx+AW25phQYNKnHZZbsBANu21QHQChUVVSguLo+989ateQBao7TUgK5XIRhcBQAoLnZj48YA2rcvRfPm4Rj+8nIX7rwzCxMn1sUjj7jwwQdLAQBr1qQC6IzSUgPhsAPB4K/me+kAuqOsrAqa5kIwuMB2DebPp8+SEhc6dGiPhQs1TJqUilatfoHXGzW1xn6oqKgC4MWSJYuRlUUc6NNPu+PwYR98viiWL1+GvXtDx1zn6uruKC52orjYg0WLfkdpaSkAwDC6oqzMDcCLDRvWIBAgP9ntt3fE4cM+DBpUhOLiAwgGKVeV2oJr+OILF/z+CDweUp2LitqhrCwFgBc7d25FMLjPXMumCIcp8LFr13YEg6RDvfxyc6xZk4bnntuK7OwqBIP0/G3b0s9tt9VFkyaV6NSpWFrLcBg4fHg/gsEt5lw3BNAUpaUGCgtLEQxuRHl5OV5/fQXmzs3FiBH5SE211jIa1fDZZ2489lhT+HxR3HEH4dm4MQtAe5SXV8HjqUYwuEJa44qKajidYQSDtPahkAM7dyajfn0D3bvLtHLNNXUxbVo6xo8P4NtvybTes4dooqQkBKfTg2DwF/N6J44e7QNNozVevPgX6Hq8qcgTIKJRoFGjk7B+fQSff56Ctm2XIC8vhPLyckSj1SgrYwC8WLVqOcrN/OL33uuCbdv8yMqqwfr16xAOl8Xhl2mmM4qLdRw96sHy5evh99PNjxyx3/f3398eu3cn4dJLC+BwFCIYJNpKSSFhMGVKEjIyqpGSQlrcwYMtEArloKbGiX379iAYpLS3vXsbIxJphOrqCA4cOIBgkMyTTz+tj9mz8/D00+vh9UYQDFabz2nxsL9sMMb+7T8ANgOoY/5eB8Bmm2t6APhB+PteAPcKf48A8CuApNre98QTT2R/dsybNy/2+8KFjD33HGMOB2Nz5ljXfPstY08/TTkTn39uwa+6iudRMPbhhxb8nHMY69LF/n6GQdc/+aQFmzqVsVNPJfjDD1vwceMY83oZS05m7I47LPj999MzJhpNmzJ22WXW32+9RbizshgbNMh65ylTCH7ppYw99JB1/fffE3zBAsYikXj8F17IWNu21t8LF9L1deow1qiRBd+6leB33cXYV19Z8GiUsUCA8Hz0UTz+xx+n71VXWzCHg7GMDIIfPGjBmzWj51fHAw8wNno0YwMGMJafb73znj2MffAB4fn1V+v6zp0t/D/+aMH792esZ894/Fu3MjZzJl0vvsPnnzP22GMEf+01C37vvRatTJxowa++mrF69eLx8xEIMHb77dbfX3zBWIcOhOf66y34U08RrEkTxkaMINi8efNia7x9uz3+nj3pHfn45huLVrp1s+B8jS+6SKbRlSsJ/u67jB06FI9/9GiaVz62bbNoxeu14GVlBB8zhu4VDlv/69GDsbPPZuzFFxkLhWT8b79N39u923rn3FxrLdeuTfyufLzyCq3PyScztmKFBd+6lbEvvyQ8n31mwUeMsNZSXPvzz2fshBPi8RcUMLZuHV3/7LMW/IsvaN8B8v57+GGC+Xy0d/i47z7GnM54/CIP+1cHgOXMhqf+XTGQb0wBwAXB1zbXLAPQQtO0JpqmeQAMM7/Hs7PuBjCIMXacz9yKH3fcQT5ttRX3OedYzc7UmEZSEvmARd+/00mWzA8/yC6gu+6yXBIinssusw71sfOdFhRYVewcHo2S60AM4q1eTTGO3btlPMOHU/BVrTPhv48fb1Wti/CzzrLaZQNktv/2W3ztQOPGlGDQpIk9/rZtrQwygILp5eXkq1Zb4QPxdSAAWW7cxWAXV1LH229Tv6gff5S76Navb9+i2+Gw0mzFGhoeAFXjJqNGWSm94vMMGWKdkGhXE/Pll9bBVxxeU0PPKjb+e+kl+8Z5F1xA65yZGf/8ALkp1WaK/Hl5dTtAacIPP0wuGhHPKadQsLllS/u1vOoq+chnDr/1Vjk7KRKhBIejR+XnT0uj+GCLFvb4c3PJxSv+Lz+f3FhjxsgxSH4f8fsAudlSU+PTmhPRyquvWodKiW675s2tbDnRpeZ00s+oUZZrjsNrauJjpffdF98kEqC15Id92dHK7Nmy24s//+uvx3tJ/urxd8VAJgD4RNO0awDsBnARAGiaVheUrns2YyysadrNAH4A4AQwmTHGt86rALwA5miUsrOEMXaDepPjNRLFNDZtok0FyAt98cUUQLU763j/fmLA771ndXOtrLQKElUfpt1GyMuj7BLRdy1e88kn9D/OsHbupM2g4uH9kLp1iz8sSby3CufNI/k4dMgSlGK9R7161hnh/P1EPKtXU7xFPHGPM2bxOUtL6RkrK+NTP9esISZeUxPfn2v2bBKSb74pt4mwS6l85x3LZSbee+pUYhJiZ1p+zdKl9Pn993J2nR2tHDliFeCJc9e7NwXMBw+Or00wDEpweOopq/Hf0aMUO0gU/1IDqSkpJPgSndcRDMoB4n37LIEi4klNpbU94ww5mYBfU1MjK1hi/EvEU1BgNWkUBXJmJgXu162zL1RcvpyC+mL3WztBA1CCAw+Si3P9+++wHS4Xrf3ZZ1MqtNgl2m4tZ84EFiyIxz9uHO15NfXb6SRhl51N8TXxqOVEHSt4QogI79iRlJNevewFyz33UKKPWifyV46/RYAwxgoB9LeB7wdwtvD3dwC+s7muuQr7dw5RQxEX9LbbqNbjySflQrMzzqBFXrqUNBGu2SYKmIr4RY1myhTazBs2yPnmt95KP2PGUDokz4oRA5GJNpf4+7p1VD/w3HO0gbn2cuaZtGFHjiRti58/wr+b6LwR9ffqarJwune3mhcCxIzGjSMG/8knsjXGe0OpzHHzZgpO2zFNhyO+DiQvj9Zm+nSrCI8/n90avPoqPeupp8p1FIlaQ4jfVbOw7PCPHUtpwO+9JydLnHmm1aajfXu5DiRRK3Egfg3mzKHC1MWL5cPBbriBfm65hWpcxIJHgOhO1aLtft+3j7L4Ro2yTtIEyCL54Qcq1nzkEStxQRQsiWhFhDNGArNVK7lRpMtFdPj778QcayNAxF5wdvSiDp/PqvoXLY1EtPLaa2RxDxkiC8FWrawiQFUZ+KN9L8IffpiE6cyZMl8ZNIharUydSsJc7JkHxCerHI/xd7mw/quHXZoj/z03l7RsUUMtKKDGiN27W1otQATAC8dqs6lKS0kby8mRmRpgdV797TcLlpxMgiCRANF1uRJ97VoiVvEcB4CyVk48kTR+dUPZPSeH9+snnweycSPNy+uv0+98pKZSZkmXLokrpO2ef+xYSjEWx1lnURbQLbfImWQ//0yb0A6X3aZ1Oklz/PlnOcPp668pLTsQsJgjQMySn1+v4klUB5KURMxQdG9UV5N2es45ck1P9+7yQWHqXKj4jx6lrKFoNF6YAlTnsHSp/F3+fbu1zM6WD77asoXWlhcK8pGaSkpMRkbtnpPDhwyxCmIBshiSk0kp++knC+5wkNAdODAxrdj9PmoUuUPFRpSjRpGydfnlcs3Qd9/Z14Ecay2bNydXq1hAvGIF8QKHwyq+BYg2ec2LXU2Mel8OP/dcmVYAot0rr5TPaG/enOZHrek5HuMfAfInhtNJjPm222Tty+kkIs3PJ7OTjyefpHoGfg0fV15ppW+qhOrxkEtH7PzLr3noIVlQfPihZSaLeMaMIVeJeDyseM3cuSQwVHi/fnL9Rn4+uX0OHZLxtG9POBL5qS+80DLPRfi4cXKrjmiU0jPLy+OZwlVXJWZGfr+V98/H0qVkybz6anyFsZ2gcLuJUbVrV7vzQF54gVqVlJfLWmWXLlZ6qspc8vJIQKpnPJSVkYUg1oG88IJl5YjPecUVluVkNxdbtljHB4jw228n5YWP778nRlRYKOMZMoQYTqNG9gz+zTctASnCBwyggk4+SkupdU5+fryb9eOPye2iWmgAue5EmuDwN96IP94XsE9RPf30+LNjOC6Hg9ZZXLP582k+PvqodjETh4Pw82N0RbgdrXzwgZVyK+Lp0SNxAbHTSe5T8RhcLri++YbmlY+XX7bvxjBsGAlBXuN0PMffFQP5rx7PPWd1/xSH00lxkCZNqNDPrnhQ9W3yfjziQp90ErkWOnSIxw+QBt+qlRWM3L/f0ibtNI7cXNmv7XJZZ67b4T90SK44X7OGai3U50xLo+roW2+1P7Bq716KdfBq90QaVnGx1cdLbCAIENO8+25rnsTvfv89CdqxY+P/p8ZG7ryTXA3qvcUTFgGrIaTDQYKoWTMSkuppiYA8F0uXWpXpIvyOO8gVo54H4nDQO/XqRZXVdtZFoviXWgdy3nlkSdrVb8yZQ/TEaxN27bJ/Tj6aN49vEineW3x+gBibWLC5d6/VhVd0zQUCxNh0nepfVPybN5MLlburEu0ZgARBZWX8UbSTJlENR3FxPK398AMJ02eftd5bvEacixdftDoni/eeP5/+tos1rlxJ1ejff28fCBd/37jRPr524YWkZFxzTTx+gOJir70mn21j9/x8/Dsq0f/nBUhNTQ327t2LkGgy2IzU1FRsNP0uPh8JkPXr5dYbd9xhZUMkJ1tumiFDrOysnBwLfuQIMZcVK4gRcniHDrSRli6le3Eto0sXq/1ERoZ1fd++FjwtzYLzo3S5NsLhdeuSdXPoEFky3B3WuLGFhw4XoneuVw946SUfxo+vD6fTcpAXFVH20gUXyDEZv58OLRozhvzPwSDBaxOHsSP4evVkV5vTSQx56VJaA1GAcKagbqhFi0hg5+XVblPxa3bskAVtIiH4/PP0znfeKVulp55KzG77doKLfZv4qE386MEHSXH5/Xd5LoYMIXfXhAkUP7GzRGvz+9q19A6TJsnu1zZtSEAMGkRryV0v/yr+qipag65dZVrx+UiTfuEFUrrsijFrI0j5SEmJd++edBLR+YsvWqeAHuse8+dT9lmrVrJV6vfH30/EU1gY3wfN7vfnn6d45hNPyG7B3r1pfn77jQQ5V6oSCbpE+N95hzLgNmyQafF4jP95AbJ3714EAgE0btwYmmjfKqOsrAwB024tKyNiOXKEXB+cKTRoQEz18GHSDHmgmGviABEGJ/D8fDL5VUsDIOa/fj0xC+63LS21Kn8bNrSqwg8epHsAdD3X+PkZEi1byoFR8R7Z2ZbGWVxsbYDsbCAjg965uJihpqYQr7yyF+XlTWLfz8+nrKb33ydXG6889nhIC3355dr5wcUWKuqZ7PXq0fyOH2+5MhwO0qJvvJH8zuLg97Dzj592muxPB8iFFwyS+2b2bAv+3Xe0yceMSRxUVjdzs2YygwLIIv3mG7KigkHLNXHJJSSYJk2qHVOIROgZRR87H4ZB85OaagmQrCxKrV68ODFO0Q2zbx+976hRsgBxOolx7toV765NNA8AuWmGD7fghYVkrd53HylZnObcbooJ/PSTnG2VSFDzv4cPl88BByhZZeNGapYpumB/+MFKQa9tXKZtWzldGiDLf9Ysy4rj7tPXXqN3Gz26dmvpdNKevu8+Gf+hQ8CCBeQSnDqV0vYBcilfcw21dalNrLSigtZT9Twcj/E/HwMJhULIzMw8pvBQx8GDJDwA2afq91ubUj13AqBsGNX8ramhgCdPJQXIJaUSL0CCh29uO/ydOsnNETl861Y5SBgK0WZV21inpBAOdcNqmgaXKxNt24YkBs+vGzFCjnVEo+T22bZNxpWdTS6pOnXsN1fbtnI9CX+H7dutPHhx2HUb5f2mRJcav4edn/rLL6nn2K+/yvDUVAuH3aYdNSr+6NdQiNwz4n3GjyfhoeLp29e+PoTjnzZNPtLY6SSXxOuvy0fIvveedcSqiKdHD3s3Cf9dnVMO79+fBD8fhYVkWe/YIePv0IHWt3FjewE7alR8bQJAcRR+JjhACsvatUTzahubBx4ghchOGcjLs1KZ+SgqktOOxcGbTYr0zrPTcnNrVwcyYwYpFuvXy//nre0B+7UcOzY+Lb6ykhQwsfbo1VeteJI4p337WsLGDv/MmdaBWSL84Yfj6fqvHv/zFgiAf0l40PX2vxuG5Q8W4WlppJWnp8d/lzHazImsBPXRuIUgwnkgONF3KyvlIGE4LAdu+eDBxtRUWdARnvg5SqQBhcPWsaXiNamppB22aWN/mNHPP5O7QWWc/NnE0aQJbUDRXw/I2S7qs86bR/EC8ZpE7zB5shW0Ftflrbfo2dX7Op3EvNLSiCH+kS//wAH7mqFu3UhTPu882WXCvzt6NAVneTpnKJTYpcNrQMT7pqXFJz2I+A2DCkz5KCsj95L6/D4fKTPDhsW7FwGyZisr48/xsHtOboGLPbI8HmoWeMklZHmLg8enOnWyT+NV3+2ss8gKUfeX2GRSHE4nCek+fch6tCsoFX//9luLVsR3u+kmimuosVKHg1zLTZrQcw0YEI9TxMMTc1R4u3a0n3r2lLPLOJ5XXyUBL3aT/qvH/7wF8leOAwfIfdWggUysycm0ccvK7DUbdSQSUEePkonepo1MMBkZxBT27InvQPuv4A+FCEe9enLTxORkYogFBRQw56M2fnxxHmpqKCDfsaN8LrbbTVrjL7+Q1ikOjkvd/HYnPx5rcHeD6KY61rPOmEGa5qBBsjVTrx79iL5uFU9t3AzPP0/C4NNPZT/4SScRU5g1Sz4q+F/Fv2wZubsWL5bdOYMHEw2NGUPB+z+Lv6CAMoxGjJBTtXNz6Z5PP225YFQ84u927fsBmt9Dh2jdVKv0hhuIoYpdEcTvq7TCLTY7Bc1u8E4GCxfK65woFvHpp+SevPJK2SqtV4/WVj25NBHNJYJPmkSW4cyZ8uFQPXuSRTd9OrlK7fAc7yD6PwLkT4xEDFjTSHNSTeKaGhIsW7bI6b1paeQ22r8/HyefLFRLJbgXb3v+7rtvYurUD6TrolGyKjj+KVOm4N57b44RkIhn4kQrH1Os1q6upk2rnovtdFpMNFGQ0C6m0bKldRwnQC6Gjh3JpbN2rXz9gw+S/z5Rbr+6+V0uipdwLZ6PwYPJpSO2BgfI1XPXXfF4jsU4u3alug8xVjBzJmnKDoecqXbPPVYabW0D5B6PfFoeQFr7/Pmk2YvvdtJJ9mdgJGJqhkGCoqws3ooNh6luQMxA83ot5pfomcVY3eHD9M5r1si4vV7SeNPTayeI+P969ox3PeXl0XrOmSPDJ0wgeCJaUeEuF8VMxBomgAR1drbVqZiP118HJk6k30V6OVaBZf36FAsUCwlXrqTnTE2lpBU+Ro0iWlSf9Y/oplcv4i18RKOktI4eLbuqmjWzrPh/BMh/4OAbUvXlaxptzspK2UVz5Ih18I64mVNTZYJQ8bdtK7sxOPyss27ARRdZtjs/sErF7/NZrhQR/uyzJECaNZOPKeXXbN4stxqpqaG/o1GZsBs2pIwRt1uG8+Nohw6V25jzDTh5MhVYiWPPHhKA6ubnZ0+rjJ+3H1dba2/ZQnjU4Dp/DxU/DzL26BFfLWxnLU6dat8Wvnlzq22LCOcC+rXX4tNjq6spi01Ma/30U8qs4u/Ix1lnWYWQdsxl9Wo5aM3hI0eS646PxYutYwBEPCefbLk17fC/9ppsaXD4JZcQI+YjFCJhvXGj/PxJSeTqSUmxZ/y9e1uZigCthctFz67SSnU1CUiVOXJXkB2tiDFGPtasob0pHgzGB79efFaOd8CA+LR1O1r54Qcrq1HE07atpQzYCaX33rM/8vnDD+UuDTNmWK5MEX///hRDU+HHY/wTA1GGXd+Yiy+mwF9lJaWPqofZjBxJP0VFVr8rv582QTCY2GKJRCxtPxKJ4LrrrsPixYuRm1sPb775Nfbt249bbhmNgoICJCUlYeLEt+F0tsbEiePRoIEfDz54J5YtW4aRI6+B05mMjh17Y/ny77FxI0mT/fv349xzz8KmTdsxaNAFeOWVZ3DPPffAMAxcdlkndOjQDp9++pHtPIgCsKbGyvJS/eDdupG7Qq3fcDrJBbRvn5W2qfamEkeTJjQfomsLIOZx1VXxDMDjIUHUrJl9AZ26cR54gBiw6PoDrOaU6nA6SYPMy6N3sPOvq3UgH34YD7/hBjozRTwgSMRz5pnkbura9dj4o1HrpEjxmmbNSHDk5cUXQgK0blu2WAyruJja0qh4+D169LDvg5aoZgiQrdLKSkvoi8/vclG68eTJ8emwTicpIqtXW8eyArTGdgWDTZvSmoiuP4CSAu66K74o0OMhd93tt1vxHCBxyvebb1pCS2TwX30VH4vjeA4coPnfudPKVkvkktqwwXIfivCzz6Z1vOwye4v+tttovfl+Olamml2j0eMx/rFA/sTg2RyqHzxRLD6RADl4kFICmzUDtm/fitGjR2P9+vXIykrDokWf4+qrR+G5517BihUrMHHiRNx1101xeK666io8++ybmDz5VzgcMrWsXLkKTz45A6tXr8U338zAnj17MGHCBOi6jvXrV+Hhhz+SgunHcs3xIRJkRQXlnA8cSMxBHN98Q+4fMdVS3Cy1dT8YBlkJatB6yBBiVmKX4WPh2bCBPlVBl2hwPIcP1y71c9o0SkV95BE5dbJTJxKyq1bJjO1fjR9NmkTMfeFC2Q9+yilUm/HMM7JbMBGeRG6YHTvImnjpJUsAAFSLwBi5jcRWI4lcZyJcvFc0SvTQvj0JTXFMmkTpqzxbTf2+ygQTMX6Akj9Uq5THULhWzkciWuFuua5dE7sL7fCovacSrcFHH5Egfeklma5POIH20fz59sWWx/pdvO+sWdTNYOFCK9PveI1/BIgygsH4H175mZREf8+cSX7S556jzCHeRbd1azIrJ02iNNZgMB6/yIw5Qeo60KRJE3Qy7dYuXU7E9u35WLZsMYYPvwidOnXC9ddfj8OHD0haZnFxMcrKytC9O+2Qs84SekEAOOWU/mAsFW63D23btsWuXbti/2NMzuA51nPy3x0Oubq4pIQsro8+kgkeICZRp07tmBf/e+BA+VxsgDZ/UhLNqzhef53cY7VlLk4nJR+oaY2PPUb/69NHhk+fTkWBKp5j9UFLTiYtWCxk4z2jOne2rDiArJLzzot/1j9i/A0bxmvwhw7RvInHnaanWz28RDyiFSgy2pIScvuJLhLAUpT27ZNTTv8oEFy/Pr0jH4zR3w88INd7AFTf07lz/Frateng9zjzzPiMuyFD6Hl5FTkfr79OxwEkyjyzw5+eTpahuA/ef5+Ug0aN5Ll4+uljt1tPBL/1Vjn+deAAWUinny6navfsabk1a1Nnwhhlbnm99n3Q/srxjwD5E6Ow0CIgkcB0/dh1IGrOPIcXFQFeYaVDISd27iyC35+GX39dhVWr6GfTpo3SGezMNIE4nmbNZELiODduBBhzIix0F+RNCMXnTE62fK92z5+eLp9RwZnp449TVa04Zs2iDSG+L2+EB9gz/jZt5H5R4nXvvou4YXfmM09Z5FW8Ih47YblwIWnH4oYFrOdOFHQfOzaecVZUkJAQ3T0ffkjCSPwuQK4a3vvJjim8/bZc58Dv9cQTZLXy8eWXVnGhGpPhDNZOEM2ebSk+4n0vuIAUAj6qq63WGiL+Bg2sJAK757/5ZktAAhatfPaZ3H8NIEa9ZUv8WvLr7Bh/ZqZc0Q5YFp54zgkfdm09ePzA7jhgO1pZsIAyqnbvlhWJQMCyOu3mYvRoOTuLX7NqlZyw8vnnVr8xtebmllsS458xw4r/ANYajxlD9zie4x8B8idGIvdOZSUFtFV4Sgr5bTMyZMLj1+zfH+8OS05OQd26TfDll58CIGGxevVqqQ4kPT0dgUAAK1cuQUoK8Nln0xM+s4jf7XajpKTG9l00jZ5TDBLya6JR+/oNIF6L48ViKgMeOZJcPXfeKcOdTmrlLgZ8xXuo+Hv2tHphieP11+ld+fkMIp4tW+S6AcD6vvqcH3xAmTjqfZ9/ntxaEyfaa4ANGsh1C4m0/3377Av9OnQga2LwYDn7i+OZNEluqJdoPQCaB7WmJzWV6hLUuiHxu2LfsWjUEvqqwMzJIb+8mGbL8ezaJVulYm8ydU7PPZeyxVT4zTeT65GfXSPeY9o0WdCJeO1obsqUeFp55RWaI7ErMcdfWhpvlSaypmfPttLPxXe47DKiuRdflN2aXFfs3Fm2+BJZdaWllntSxN+yJWXC9expTyuLFsX3evurxz8C5P8w1JhHYSGZjo0bx2dDJSURIYgb/o/qFx977CO8//676NixI9q1a4dPPvkaW7eS9sU3w7vvvovbbx+FK67ogdJShkDAotRE+K+5ZhSGD++ABx64TLqGB8tzcmSCd7vJd330aO16CYl/q5t56VJyAfCKcT4mTKB7v/WWDE+Uxsu1zdrm9vMKfrEFO2DNo/r8c+fSp1jhC5DbJxCgdbZ7TkB2G4hMS/z9448pWPvpp7Im3aIFCY9vvpEZeSI8idZg2zbSSt9/Xz7lsV07wj1+vNzW5V+NyVRVUer1hRfKVqnHQ8zujTfIMhXHsVxGQLy7ZfduosO2bWU4b+ypWqWJaIUfJqXGRhINnpnI42Z8iC41URH8+WfySIweLd87PZ2C4ocPy/teXL/atMn55htyd02fLmdntW5N7vVp02SrNJHScjzGPwLkTwzOdFUGzTX4rCyZwGpqKE112zbZEvD7SbjUrdsYK1eui8FvvvlOjBo1HvXqNcE338zG6tWrsWHDBtxzz0NgDLj33vG46y5S4du1a4c1a9Zgzpxf4XKlolMnSucZOXIkXnjBUt1mzPgW/cwUsyeffBqffroRjz/+UVygs6BArlXh78UJOhHx2zGFpKR4BjxwIPmv1VYtN95IVlpt60DcbvIVq1lUw4bR86p9kh59lBipiieRBeJ0kjUxaZIMnz2bNHrePoSPm2+2utAmmiO73087zarWBsgNNmUK+ew54wOIWXBGWps1iEZJIKuCDiBF5qef5HNfROadSICI7sVolATEvHnxSlH79vGp3eKz2q1x06bU5l8cAweScFWt0jFjyFX5r9BKx47xysM999DzigWPHD5qlD0eO/xOJ8FefVX+37p1VtYUz6ADqF0Jv+e/Ev864QQ5/lVTQ9lrd98tW6V161o1O7VVsP7s+EeA/InBBYfqg3U4rACWOEpKLHNeFDpJSVYQzc4t1rq1vSspP9/ync6aNQsdOnRC587tsWrVAowbZ5VyJyVZZ0vY4W/YUA74ivjF7Kxo1DK11Qp7Xuxm56ceNsxKT+XD7aZg79tvy/Dt2ym4qjIFu3PDOZ5IJF7D4n551YUF2NeB8PlX3RUul3wgFR+8qE1937w8cik4HPaM4IUXZEHBGfa0abLAXrTI0tzFuW7f3iq0E+Ecz7x58WdIABSgFrOz9uyxmIs4d02aUCYWf3c+eMbhAw/ILen5dx9+OD7x4bXXaK5V5vXDD/Kzic/au3d8o0j+fdUqLS0l4VfbOhCPx74OZM8e+lRdWACtvYqHu/14QFt8/pqa+HssX24JaRFX/frWUQx2CgDvFyc+P4eL+5I3XhSvAaxD21T48Rj/CJA/MfLyaEOrRYCcAYttBUS4OiKRxMF4ntdv993qaivId8kll2Dx4lWYMWMdXnxxFnJysuPunZQUX+jn8cSnJR7LpcY3gkiQDgfNw0svxddvOBzUmkTN6uHfVwn7rLNI+Kqb9uqrKclAtQTcbmKa77xjj18VFE8+SY3wVPwvvUT3VdOBvV5KAlDdJ5xhq8+/YgUxUpWpXXABuThuusnetXDLLYlPeRSvD4et4k7x3g0bkrZcp07iDDGR6UQilmBU58LrJSasKkZpabWv4Aeo+aIdvHdvChSrqaVOJ7lpREEnPp861+ecQ9a8Cr/uOno/1Sp1u8kdpQbvjxX/mjw5/vkffZRohR/pzAenCbsGnnyIuHbutNxvIrxfP5qfkSPlGBXHzw91s8OvvgNXMP+xQP4Dh9tNi6cWLNWmJ6N4TUkJMeamTWViSEoi/+nhw3I2SG3qNMTfq6vJj1yvnkyQLhdpKfv3y72z7AL86u8qQb75Jmm0YiM8gDTrbdvIBy+ORG4AvklUP/jRo8Tw1LbUPMNHbXPBv69ufp5CqwqERINbC6pWyfGrzz9nDikDajZagwYU81G13ERxkkRMZ9EicpNNmyZnDbVsScWKL7wgpwknwpMollJWRsL6+uvlinCAziB5+un4Ogo+EgkXFf7112TxqVbpq69SvEeNaSRi8ImEOHcPq2vPtX3xOGkRj0pz3B1U2yaE/PvHKrYUf+dFk3ffLVuljRqRq23uXJm31Cb+JcK3bKE1/PBDqhM6nuMfAfInRkUFEYBqaWRkEKM+lmZv97vPF9/zqqSENGCRKF0u+/hLIsbPGD2rnfkejZKAEWMytRFKYqUwQJW/TzwhB3wBK9hn18MKiN/8Xi8FkNW2FZdeSkxHzfm//XYSvCoergWqTIHn9qtM6p136P3UfkjPPEPuAZUZJXIJ8PuJvb8ACm6eemq8i+yUUyxGaldBDthbLBkZ8c+0ZQtZaGLWU3KypTQkisOIQWVNIxeTWEvCR00N+fDVTEE+1OfhTFEVRGPHUnsbMeALUKxD1+PnNpEF4vEQrajW59VX0/yp1uptt5EwqK0g4mugpgN/+y3Nk6qEjBlDglcN0ieqAuf3u/RS+ZkKC0lJuOAC2Spt29Y650V81kRKiMtF+5u3sD+e4x8B8icGj3GoGofHQ5snkQARW0SIcNEsBUgb5J1YRVxer4XDjsE3aWLXhj3+3IFo1ErvUwURD5Sq1pTDQfEStTV1KEQa0xdfyHDei0rdtNxfbscUGjeOP0GNb0LuP1fvreLnG80Oj11uP6+HEQPWfNj5wfmmFftCAZbg4j3J+Pj1V7k9Oh8NGlgxBbVWBiCLQmRI/Jp77pGZy6ZNVqKCyFAyMiyLwU6APP+8pZmL3x03Lr4ANlFKNleg7GIFI0ZYR7uK73boULwls2wZ0aeKh7vC7JQNny/eKuW0olqlAAlBFQ+vA1EFAsej0gvfM+LZOvz5GLNXWoD4I2r5c6gW0apVVrdocS7q1rXSz8V7cJp79VXZKuX4r7km3oX8V49/BMifGIlcVVVV5JKKr+mgBVb7MHE86tkcx7IoOExtL8LPHEn0nOoz2Z0rApD2kp1tX8Eq9u5Sh3q9XbdRgLTNYNAqouPD46GNb5eTb4dn+HASsuo733EHvZuqhfLcfrVLb6KYyfffU5GeykRGjyYGrh5wxQU3b1TIRyIfdFERuXQAeQ2aN6eg8dCh9taIWnyWyL3B/65XT/bNe71k/YhBWkB+f/Wdf/st/hqALMN77423Sp1OigmpVimnOZVW+Jqozz9oEBV4iu3o+ffXro23ShO5zh54gALaKvymm+zjXxyPmP4sPp+6Z5YtozVTj1I45xzyIrz5pj0e8WgE/l58qJ2VFy6UvwvQGj7xBFm4dk0fI5H4s1T+6vG3CBBN0zI0TZujadpW8zM9wXVnaZq2WdO0bZqm3SPAH9M0bY2maas0TftR07TjfPKv+lz2cK4ZqpvT46EFVgnsX+2dVVUFNGrkj6tod7sprfTAATlzSPzuY489hLlmccNLL72IUKjS9hkOHKBUQfXkxObN6f14fYQ61M3PmZAKX76cGBo/n4MP3hBRxc83s4qHbxg1cJlotGhBn6r7hONV3Q28Ml2spgZok5eXxwv9RM+RSICsWUNuUDVmkptLGvHnn8tCP1Hqrsh0xN9LS0nI3nuvrGHrOvXrevFFOqmSD5EOErW/UNfgtddIi1djGh99RJaYXUdkOzyJ1jg/nywH8ZRNwOo6XFta4fEEsW3IsQZPjhE7UgOJ15JbsWrKuq7TPlAt0D9yg6q/79pFVtsjj8hZk1lZlAb+8ceyVfq/UAdyD4CfGGMtAPxk/i0NTdOcAF4DMBBAWwDDNU3jW+FZxlgHxlgnAN8CsDnw9PiNRH5FvgnFRQZoE2zbFt8DyOdL3N1TxflHo6qKmEaiA3DGj38Up5tOaVGAqFplUVH8uQnic9SG+AGrTkLNzrr5ZnIzqb523iBQxSP2CxOH203pkLzFOR8PP0zP+tprMvyGG0gIqngSCRD+HGKnX4ACyrm5svsHoGrqk06yBJWKXx0cv+oSrKykIr8xY+S1z8mRz5y3wy/+rmlkAYiuSz4OHyarorbWJB9Nmsh/T55MGUtqjI23kVGFaiIa4rUNaj3GXXdRlh+3gPgYPNg+ZsLX0I5WXK74dGAe/1ItgSuvpJ5v4lEHds/NB58vFc/WrUSjKk107UqWqp1rjg9x7/LrGjWS6TQape4Njz8ur2VSklWZfryzsFx/fMlxGYMB9DN/fx9AEIDSixPdAGxjjO0AAE3Tppvf28AYEw2zZAAJwnv/4jhG8xhdaLyUEgZaGYDHC0AggoAJd4nwTp1gPPqibU2BxwO89dbdyMhohK5dqWPj+PHj4fMFcOBAFL/88gkikSpccMEFeOSRR2IbcOdOICODYdy4cfj++++haRqGD38AAwZcAocDeOaZZ/Dhhx/C4XDglFMGYsSICbjuupEYNOhc7N+/H/v378cNN5yKnJwsXHPN5Vi3bh1eMPtcf/7528jP34i335Y70vGYjEqQX3xBefHqZkhJIR+/ynR4oDcYtKrDAavqV2Vel1xCmqwd47djgBzGtUJxGEY8U+Papppxw59DLarkWrvqGvD7yfJUmSmfL7WwkeP/6CO51fv27fZWXmYmMdRHHrG3QCZOtO+3dNddlN4qxgsuuYQ+1TX79FNKHFDXoG5dcj2qZ5Dv3Ek/8+bJvZh4cFtds1deoXdV8ScnU+xNjRHyMXeuLLCLimgtVTz9+1M8QG026XaTZc6YLJR5LNOu3YdhxAfFOVO2s0oBOltEHLyuRo2V+v1kuakKJccjniUvwidMkFOgKyut9vTiWvp8lARy443//wqQXMbYAQBgjB3QNM3OuKwHYI/w914AMTLSNO0JAFcCKAFwaqIbaZo2CsAoAMjNzUVQiRCmpqaizPQteaur4UjUnpYxhM3/aQB8OhFjWLg8GtUAOFBVBTic9I9odTVCoQqQnEPsXnQ9cOqpF+GZZ8bi3nspUjl9+nSMGXM7Vq9eih9/nAePJ4JLLrkEs2fPRvfuloP9o48+wooVK7Bw4UIUFBSiT59T0aXLKfjqq8X4/PPPMXfuXCQlJWH37lIAYYTDNTAMA1dddRWee+45vPfeXDRsmAqvtxiPP/44HnzwQbjdbsyc+R7uu28SDKMcTmck9rxlZbR7NmxYAcasd2DMjTvvzERZWRGCQYujFxV1xfLlfnz99UKkplrSs6KiOwAdO3ZsQDBoRa7HjOkEIA07d25GMHggBs/KAn74QQOdrWLpCQcPtsDhw/Xw5JNr0bNnoQBvBKAJDhzYjWBwRwz+3Xd52LevNQ4cOIBg0Oqc2KiRVekcDALl5eUIBoPYvj0HQFv071+Od99dHrt+69YsAO1RU1ONYHBxDF5Q4MU33/RAWpoMD4WceOONJDRsWIlg0CKWnTuTAZyEqVOBa64JxuD79/sAnGw+jwWPRIAFC9oAyMX8+RY8HNZw8cVN4XQWIhgsjsHJEu0HAFi0aAGSkkS6Jvjvv/+KffuqYu984EAK+vRpgM2bt6GoyMojTUnpgsLCMgSDgs9LwLNx40p4PFYK2Kuv9gbgwpYtaxAMWhHnaNSBJ59Mg65XIBi08B882A4bN2Zj2rQlqFs3JMGBbOzbtw3BoJWj/MorzQHUx/79OxEMWj7JtDR5LfnYt68hgKa49datuPBCiiqXl5cjP38LgJYoKipCMLgmdv3SpRn4/fcOaNOmFMHg7zF4VpY9/k2b0gF0xOmnA/PmWf/YsiUVQGfzegteWurCu+/2joOHQg48+2wqmjatkPZSSYkbQC9s2qTShAaAqkeXLJkPp9PaH2vW1IemNcOKFYvg94dj76zyv//zYIwdlx8AcwGss/kZDKBYufaozfcvAvCO8PcVAF6xue5eAI/U5plOPPFEpo4NGzbEwexGaWmp9HdlJWOhkHoNY8uW0Y96rR3cMAjWvHlrtm/fPrZq1SrWs2dPNnbsWNagQSPWtm1H1rFjR9asWTP2zjvvsEiEMV1PZsuWMTZmzBj27rvvMsYYi0YZGzjwcjZx4tfsjjvuYG+99Zbwfozt38/YiBEj2KeffsoYY6xRo0Zsw4YCtnIlYzU1jF177bXsiy++YBs3bmRt2nRly5bRu4nvvGwZY99/v4GtWye/w/vvMzZ5cvx8vf02YwBjP/0kw5s0IfhXX8nwU04h+JQpMryoiN5BHR98QNc/+6wMf/JJgo8bJ8Nfe43gDz4Yj0sc8+bNY4zR8wGMqSTz3XcEz8qS4UuWEPyGG+JxLlxI/xfHli10PSDDDx+2h5eUEGz8+Hj806YxdsUV8XCOp7raHl5YKL/z8OGM3X+/PX6AsY0b7fEsXSrDk5MJ/vPPMnzOHMamTo3H/9lndL36v8GDCf7mmzL8llsI/vTTMrymht4pEpHhM2fS9TffbMHmzZvH3nmH4Geeaf88dnMajcbDFiywX7PVq+3hmzYR7Mor43HNnx+/N/jaq3gYSwz3+Ri76y4Zxtf5zwwAy5kNTz1uMRDG2OmMsfY2P18DOKRpWh0AMD9tkiixF4B4jFB9APttrpsG4MK/+vmPNaqqqJeT6sdPSiKrROyMCfzxQTTnnTcUn332GWbMmIFhw4YhGmW4+up78dFH1MZ927ZtuOaaa5SsKkvbUOGaAKiuji94BKyKZIcDuPbaazFlyhS89957OO+8q2yfmbtE1ASBiROpb5Pq6qlfnz5VlxE3qdVusPygJ7VNxH33URB42TIZzmsMVHdFouwyHpfiKal8/PQTXat26R08mFw3anuNRLUD3F0junIAiif17h2f0VOvHs2FWvWtxs/48PtpTexcocGgdRqi3UjkxlDnbu3a+AaCgLW2iRIFVFcVP0aZt9Hh45lnqLWKmgbL3Zx2ricgnla4q06NObz8Mrn6PvhAhg8cSJ9qi/9ERaF8DdSans2bre4L4ujdm2JZ6qFqKh/gg8+jWuRXU0PV6OI5KgDxldomi/CRlhafBXc8xt8VRP8GAPfmjQDwtc01ywC00DStiaZpHgDDzO9B0zQxLDUIwCab7x+3wTex6oN3OomxJKrMVYNyHN637zBMnz4dn332GYYOHYoBA87EZ59NRmkpOWn37duHw4cPx9J3KRXzFMyYMQORSAQFBQVYteoXnHJKNwwYMACTJ09Gpdm97ciRojjfbCAQwPbt5IbSNKB79+7Ys2cPpk2bhpEjKcVFFSB+P72bmoq8di254tSMFd5OQt38fFOq8NxcuqdYmQtYAX21voJ7AtWNxc9LUWMvfDOrmXB8DffsQdwoLY1napwJqZucP8fGjTKcM1+11icpifz66gmJnKmpAs3hsBoYqkMNDvNx6632AumkkygWoQrBdesodVmN4/D4jbo2PNZhpww0ahSvbHCf/1bFE8aD5Opcc4as3pcnaKhxKB5rWL1ahvNGhioeHoNTj8blc6bi57Ry4ADixtGjiWMmqlLBn//nn2U4tyfUwY8DtuuikJ4erxQBtB/VfnPHY/xdMZAJAD7RNO0aALtB7iqY6bjvMMbOZoyFNU27GcAPAJwAJjPG1vPva5rWCkAUwC4AN8Td4TiORJk7jJG2b5cd0rJlPLPjTLp+/XYoKytDvXr1UKdOHdSpUwdz5mzE1Vf3gK4Dfr8fU6dORY6Zh+jxABdccAF+/fVXdOzYEZqm4YEHnkHjxnk46aSzsGrVKnTt2hUejwedO5+N0aOflO47atQo3HbbQGRl1cHy5eTUvfjii7Fq1SrUq5eOkhL70+FUTRMgoVhQIAdwAevkPzV18sYbqemfyjhDIWIAu3fLzJ8zbLX77bff0qe64S69NL7GBLDSihcskDOfOLNQGe2hQxRk3bFDhp9wgv3hRFywvvkmWU188OC1XYB45UqrmE0cn3xiD/9XR9u28YIUoGBzoippIF4B4oxU1eC7dqUTHdU029RUYqhq0Lp+fUpuUBk5z1tR98eVVxLzVQULX8tVq2TmzBm2WkT6yy/0qWrkPXrYM2wuEGfMkBtIcgGh1r2EwyQcVQGSmUlzpwpY/rd6psmxUm737rVPGnniCas55t8y7Pxa/7/+/FUxkGiUsb17/197dx8j1VWHcfz7yNu2tQ2tVtOyjaVNY0qIFEpIW40x1kQFI/3HpNFqm1T/MTEoRbu0SRubmCqiMUQlNVTiK428VCuJCaKlpKZBqYAFF1oWjF0EgaULW1peAj//OAeZnZ1lZ+/uMuyd55NM5s6ZuZP73Ds7v73n3Lk3jW1U278/4vjxut4yIiIOHEhjJ9UOHUp9n7VU9/FeyBtvRBw+3Le9uzv1t58zZ86cWL9+fa/XVGbu6YnYtKnvutq2re84RETE1q0Rjz1Wu8+4ln37IhYuTP3Y1e0PPdR3XR88GPHww/2vo2pvvhkxf37aPpVOn45YsCBtz4jz/cRnzkQ88kjEnj31vf/ZsxGLF0ds2dL3uUWL+o4TREQ89VTqP6/X8uURa9f2bV+9OmLNmtrzvP32wO97LvMLL0QsXdr3+RdfrL2N+7NjR8QTT/Td9nv3pjGc6s9vf9u+P0ePpm1W/Xd25EjEvHnpvtKxYxFtbb23/YXGA06dSuMHHR2928+ciXj88dpjck8+mT7z9VqyJGLjxr7ty5ZFrFvXt33FijT+Vq9nn+07pjQSYyCKWiW4pGbOnBmbN2/u1dbe3s6t1ddRraGnp4cr++vUHMW6u7uZNWsW06ZNY+XKlb2eq85c77oazTZs2PD/66Y0C2duDkPJLOnliJhZ3d6oLiy7REycOJFXR/q6l2ZWSj4XFr2PaLLavI7MrFrTF5CWlha6urr8BXkBEUFXVxctgz2W0MxKrem7sFpbW+ns7ORQ5QWiazhx4kTTfYFWZm5paaH13I87zMxwAWHcuHFMrnWsY5UNGzYwvfpXZSXXjJnNrH5N34VlZmbFuICYmVkhLiBmZlZIU/2QUNIh0qlPing3cHjAV5WLMzcHZ24OQ8n8voi4trqxqQrIUEjaXOuXmGXmzM3BmZvDSGR2F5aZmRXiAmJmZoW4gNSvn6sulJozNwdnbg7DntljIGZmVoj3QMzMrBAXEDMzK8QFpA6SPiFpl6TdktoavTzDQdINkp6X1C5ph6R5uf0aSX+U9Fq+v7pinoV5HeyS9PHGLf3QSBojaYuktflxqTNLmihplaSdeXvf2QSZv5Y/19slrZDUUrbMkn4q6aCk7RVtg84o6XZJr+TnlkiVFyIeQK3LFPp2/ka6HnsHcBMwHtgGTGn0cg1DruuAGXn6SuBVYAqwCGjL7W3Ad/L0lJx9AjA5r5Mxjc5RMPt84NfA2vy41JmBnwFfzNPjgYllzgxMAvYCl+XHvwEeKFtm4MPADGB7RdugMwJ/Be4EBPwB+GS9y+A9kIHNAnZHxJ6IOAU8A8xt8DINWUTsj4i/5+keoJ30hzeX9IVDvr8nT88FnomIkxGxF9hNWjejiqRWYA6wrKK5tJklXUX6onkaICJORUQ3Jc6cjQUukzQWuBz4DyXLHBEbgSNVzYPKKOk64KqIeClSNfl5xTwDcgEZ2CTg9YrHnbmtNCTdCEwHNgHvjYj9kIoM8J78srKshx8A3wDOVrSVOfNNwCFgee62WybpCkqcOSL2AYuBfwP7gaMRsY4SZ64w2IyT8nR1e11cQAZWqz+wNMc+S3onsBr4akQcu9BLa7SNqvUg6VPAwYh4ud5ZarSNqsyk/8RnAEsjYjpwnNS10Z9Rnzn3+88lddVcD1wh6b4LzVKjbVRlrkN/GYeU3QVkYJ3ADRWPW0m7w6OepHGk4vGriFiTm/+bd2vJ9wdzexnWwweBT0v6F6kr8qOSfkm5M3cCnRGxKT9eRSooZc78MWBvRByKiNPAGuAuyp35nMFm7MzT1e11cQEZ2N+AWyRNljQeuBd4rsHLNGT5SIungfaI+H7FU88B9+fp+4HfVbTfK2mCpMnALaTBt1EjIhZGRGtE3Ejajn+OiPsod+YDwOuS3p+b7gb+SYkzk7qu7pB0ef6c300a4ytz5nMGlTF3c/VIuiOvqy9UzDOwRh9JMBpuwGzSUUodwKONXp5hyvQh0q7qP4Ct+TYbeBfwJ+C1fH9NxTyP5nWwi0EcqXEp3oCPcP4orFJnBm4DNudt/Vvg6ibI/E1gJ7Ad+AXp6KNSZQZWkMZ4TpP2JB4skhGYmddTB/BD8hlK6rn5VCZmZlaIu7DMzKwQFxAzMyvEBcTMzApxATEzs0JcQMzMrBAXELMRks+C++U8fb2kVY1eJrPh5MN4zUZIPsfY2oiY2uhlMRsJYxu9AGYl9m3gZklbST/sujUipkp6gHTG0zHAVOB7pNOsfx44CcyOiCOSbgZ+BFwLvAV8KSJ2XuwQZv1xF5bZyGkDOiLiNuDrVc9NBT5LOm34t4C3Ip3s8CXS6SQAfgJ8JSJuBxYAP74YC21WL++BmDXG85Guw9Ij6Sjw+9z+CvCBfJbku4CVFReIm3DxF9Osfy4gZo1xsmL6bMXjs6S/y3cA3XnvxeyS5C4ss5HTQ7pc8KBFujbLXkmfgXT2ZEnThnPhzIbKBcRshEREF/AXSduB7xZ4i88BD0raBuygBJdStnLxYbxmZlaI90DMzKwQFxAzMyvEBcTMzApxATEzs0JcQMzMrBAXEDMzK8QFxMzMCvkf2033yt7mz/MAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def ff(t,x,v):\n", " return v\n", "\n", "def gg(t,x,v):\n", " return -k*x\n", "\n", "def ode(x0, v0):\n", " kk,ll = runge_kutta4(0, x0, v0, dt)\n", " x1 = x0 + kk\n", " v1 = v0 + ll\n", " return [x1, v1]\n", "\n", "t, dt, k=0.0, 0.1, 0.1\n", "tt,xx,vv=[0.0],[0.0],[0.01]\n", "for i in range(0,10000):\n", " t += dt\n", " x, v = ode(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これを前と同様に走らせると\n", "発散も収束もすることなく,定常的に振動を繰り返していることが見て取れます." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# RLC回路の応答\n", "電気回路の応答を考えましょう.R(resistor,抵抗) L(inductor,コイル) C(capacitor,コンデンサー)をそれぞれふたつずつ組み合わせてみていくのが常套手段なんですが,一個ずつだと面倒なので,まずは全部入れた方程式を立てます.そこからパラメータを変えて回路の挙動を観察します.こんなとこから進めていけるのが,数値計算の利点です.どんなんでも解けるから.\n", "\n", "コンデンサに蓄えられた電荷を$Q(t)$, 回路に流れる電流を$I(t)$とします.\n", "\n", "* 自己インダクタンス$L$のコイルにかかる電圧は$L \\frac{dI}{dt}$\n", "* 容量$C$のコンデンサにかかる電圧は$\\frac{Q}{C}$\n", "* 抵抗値$R$の抵抗に掛かる電圧は$RI$\n", "\n", "となります.コイルにかかる電圧,コンデンサにかかる電圧,抵抗にかかる電圧の和が,この回路にかけた電圧$V(t)$であることを使うと,\n", "\n", "$$\n", "L \\frac{dI}{dt} + \\frac{Q}{C} + RI = V(t)\n", "$$\n", "\n", "となります.ここで電流$I$とコンデンサの電荷$Q$の関係$I=\\frac{dQ}{dt}$を使うと,\n", "\n", "$$\n", "L \\frac{d^2Q}{dt^2} + \\frac{Q}{C} + R\\frac{dQ}{dt} = V{t}\n", "$$\n", "が得られます.\n", "\n", "先ほどの重力系の問題と比べると\n", "\n", "$$\n", "v \\rightarrow i \\\\\n", "x \\rightarrow q\n", "$$\n", "と置き換えれば良さそうです.\n", "\n", "そうするとアルゴリズムは,\n", "$$\n", "\\begin{aligned}\n", "i_{i+1} & = i_i + (V - RR \\, i_i -qc \\, q_i) \\, dt \\\\\n", "q_{i+1} & = q_i + i_i \\, dt;\n", "\\end{aligned}\n", "$$\n", "となりそうです.RRやqcには適当に規格化した値をいれます.\n", "\n", "![rlc_circuit](./figs/ode.005.jpeg)\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def euler_rlc(q0, i0):\n", " i1 = i0 + (v - r * i0 - qc * q0) * dt\n", " q1 = q0 + i0 * dt\n", " return [q1, i1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "コンデンサー($C$),コンダクター($L$)を1として,抵抗値を0.5として,入力電圧を1Vと設定してコンデンサーにたまる電荷と電流の変化を確かめたのが次の図です.\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dt, r, qc, v =0.01, 0.5, 0,1\n", "ii=[0.0]\n", "qq=[0.0]\n", "tt=[0.0]\n", "t = 0\n", "for i in range(0,2000):\n", " t += dt\n", " q, i2 = euler_rlc(qq[i],ii[i])\n", " tt.append(t)\n", " qq.append(q)\n", " ii.append(i2)\n", "\n", "my_plot(qq,ii,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "入力電圧を0V,コンデンサーにあらかじめ1クーロン貯めたと設定して電荷と電流の時間変化を確かめたのが次の図です.\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dt, r, qc, v =0.01, 1.0, 1, 0\n", "ii=[0.0]\n", "qq=[1.0]\n", "tt=[0.0]\n", "t = 0\n", "for i in range(0,2000):\n", " t += dt\n", " q, i2 = euler_rlc(qq[i],ii[i])\n", " tt.append(t)\n", " qq.append(q)\n", " ii.append(i2)\n", "\n", "my_plot(qq,ii,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 課題\n", "\n", "## 雨粒\n", "空気抵抗を受ける雨粒の速度の変化を自分の言葉で説明しなさい.\n", "\n", "## 大砲\n", "free fallの初期設定を変えて,x=0から鉛直方向にv=9.8で投げ上げたボールの時間変化を示しなさい.\n", "\n", "# 自由課題\n", "以下は 2021年度は不要です.\n", "\n", "## RLC回路\n", "抵抗が0の場合の電荷,電流の変化を確認しなさい.\n", "\n", "## RLC回路\n", "抵抗が0の場合にも,エネルギー保存が成り立つようにコードを改良しなさい.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "Python 3", "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": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": { "height": "192px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }