{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(chap:9-solow)=\n",
    "# ソロー・モデル"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div name=\"html-admonition\" style=\"font-size: 0.8em\">\n",
    "<input type=\"button\" onclick=\"location.href='https://translate.google.com/translate?hl=&sl=ja&tl=en&u='+window.location;\" value=\"Google translation\" style=\"color:#ffffff;background-color:#008080; height:25px\" onmouseover=\"this.style.background='#99ccff'\" onmouseout=\"this.style.background='#008080'\"/> in English or the language of your choice.\n",
    "</div><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import japanize_matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import py4macro\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# numpy v1の表示を使用\n",
    "np.set_printoptions(legacy='1.21')\n",
    "# 警告メッセージを非表示\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## はじめに"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "前章では差分方程式について説明し，簡単な経済モデルを使いコードの書き方を説明した。本章では，差分方程式の応用となるソロー・モデルを考える。ソロー・モデルは1987年にノーベル経済学賞を受賞した[Robert M. Solow](https://www.nobelprize.org/prizes/economic-sciences/1987/press-release/)によって考案された経済成長モデルであり，マクロ経済学の代表的な理論モデルの一つである。今でも盛んに研究が続く経済成長のバックボーン的な存在である。モデルの説明の後，`Python`を使い動学的な特徴を明らかにし，線形近似を使った安定性の確認もおこなう。また理論的な予測がデータと整合性があるかについてもPenn World Tableを使って検討する。本章の内容は次章で議論する所得収斂の分析の基礎となる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## モデルの説明"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ここではモデルの具体的な説明については教科書に譲るとして，簡単にモデルを紹介し，重要な式をまとめることにする。\n",
    "\n",
    "＜記号＞\n",
    "* 産出量：$Y_t$\n",
    "* 消費量：$C_t$\n",
    "* 投資量：$I_t$\n",
    "* 資本ストック：$K_t$\n",
    "* 労働：$L_t$\n",
    "* 貯蓄率（一定な外生変数）：$0<s<1$\n",
    "* 労働人口増加率（一定な外生変数）：$n\\equiv\\dfrac{L_{t+1}}{L_t}-1\\geq 0$\n",
    "* 資本減耗率（一定な外生変数）：$0<d<1$\n",
    "* 生産性（一定な外生変数）：$A>0$\n",
    "\n",
    "＜一人当たりの変数＞\n",
    "* 一人当たり産出量：$y_t\\equiv\\dfrac{Y_t}{L_t}$\n",
    "* 一人当たり消費量：$c_t\\equiv\\dfrac{C_t}{L_t}$\n",
    "* 一人当たり投資量：$i_t\\equiv\\dfrac{I_t}{L_t}$\n",
    "* 一人当たり資本ストック：$k_t\\equiv\\dfrac{K_t}{L_t}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "全ての市場は完全競争である閉鎖経済を考えよう。この経済には一種類の財（ニューメレール財）しかなく，消費・貯蓄・投資に使われる。財は次の生産関数に従って生産される。\n",
    "\n",
    "$$\n",
    "Y_t=AK_t^aL_t^{1-a},\\quad 0<a<1\n",
    "$$ (eq:8-production_level)\n",
    "\n",
    "両辺を$L_t$で割ると一人当たりの変数で表した生産関数となる。\n",
    "\n",
    "$$\n",
    "y_t=Ak_t^a\n",
    "$$ (eq:8-production)\n",
    "\n",
    "消費者は所得の割合$s$を貯蓄するが，このモデルの中で消費者の役割はこれだけであり，残り全ては生産側で決定される。貯蓄は$sY_t$であり投資$I_t$と等しくなる。\n",
    "\n",
    "$$\n",
    "sY_t=I_t\n",
    "$$ (eq:8-syi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "$t$期の投資により$t+1$期の資本ストックは増加するが，毎期ごと資本は$d$の率で減耗する。即ち，投資と資本ストックには次の関係が成立する。\n",
    "\n",
    "$$\n",
    "K_{t+1}-K_{t}=I_t-dK_t\n",
    "$$ (eq:8-kk)\n",
    "\n",
    "ここで左辺は資本ストックの変化であり，右辺は純投資である。$I_t$は粗投資，$dK_t$は減耗した資本である。式[](eq:8-syi)，[](eq:8-kk)，[](eq:8-production)を使うと資本の蓄積方程式が導出できる。\n",
    "\n",
    "$$\n",
    "K_{t+1} = sAK_t^aL^{1-a} + (1-d)K_t\n",
    "$$ (eq:8-kkdot)\n",
    "\n",
    "両辺を$L_t$で割ることで一人当たりの変数で表すことができる。右辺は単純に一人当たりの変数に直し，左辺は次のように書き換えることに注意しよう。\n",
    "\n",
    "$$\n",
    "\\frac{K_{t+1}}{L_t}=\\frac{K_{t+1}}{L_{t+1}}\\frac{L_{t+1}}{L_t}\n",
    "=k_{t+1}(1+n)\n",
    "$$\n",
    "\n",
    "従って，$t+1$期の一人当たりの資本ストックを決定する式は次式で与えられる。\n",
    "\n",
    "$$\n",
    "k_{t+1} = \\frac{sAk_t^a + (1-d)k_t}{1+n}\n",
    "$$ (eq:8-kdot)\n",
    "\n",
    "この式は非線形の差分方程式だが，前章でも述べたように，考え方は線形差分方程式と同じであり，数値計算のための`Python`コードに関しては大きな違いはない。また式[](eq:8-kdot)を資本ストックの成長率を示す式に書き換えることもできる。\n",
    "\n",
    "$$\n",
    "\\frac{k_{t+1}}{k_t}-1 = \\frac{sAk_t^{-(1-a)}-(n+d)}{1+n}\n",
    "$$ (eq:8-kgrowth)\n",
    "\n",
    "この式から資本が蓄積され$k_t$が増加すると，その成長率は減少していくことが分かる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "産出量の動学は生産関数[](eq:8-production)を使うことによって$y_t$の動きを確認できる。例えば，産出量の成長率を考えてみよう。式[](eq:8-production)を使うと\n",
    "\n",
    "$$\n",
    "\\frac{y_{t+1}}{y_t}-1\n",
    "=\\left(\\frac{k_{t+1}}{k_t}\\right)^{\\alpha}-1\n",
    "$$ (eq:8-ygrowth)\n",
    "\n",
    "となり，一人当たり資本ストックの成長率と同じような動きをすることが分かると思う。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "次に定常状態を考えよう。定常状態では資本ストックは一定なり，資本の成長率である式[](eq:8-kgrowth)の右辺はゼロになる。\n",
    "定常値は次のように確認することができる。\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{k_*}{k_*}-1 \n",
    "&=\\frac{sAk_*^{-(1-a)} - (n+d)}{1+n} \\\\\n",
    "&\\Downarrow \\\\\n",
    "k_*\n",
    "&=\\left(\n",
    "        \\frac{As}{n+d}\n",
    "    \\right)^{\\frac{1}{1-a}}\n",
    "\\end{align*}\n",
    "$$ (eq:8-kss)\n",
    "\n",
    "この値を生産関数[](eq:8-production)に代入することにより一人当たりGDPの定常値を求めることができる。\n",
    "\n",
    "$$\n",
    "y_*=Ak_*^{a}\n",
    "$$ (eq:8-yss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "{numref}`fig:8-solow`は資本ストックの動学的均衡を示している。\n",
    "\n",
    "```{figure} /images/solow.jpeg\n",
    "---\n",
    "scale: 30%\n",
    "name: fig:8-solow\n",
    "---\n",
    "一人当たり資本ストックの動学\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## 動学"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "差分方程式[](eq:8-kdot)を使って資本ストックの変化をプロットするが，以前と同じように`DataFrame`を生成する関数を定義しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def solow_model(k0, A=10, a=0.3, s=0.3, n=0.02, d=0.05, T=100):\n",
    "    \"\"\"引数\n",
    "            k0: 資本の初期値\n",
    "            A: 生産性\n",
    "            a: 資本の所得比率 (a<1)\n",
    "            s: 貯蓄率 (s<1)\n",
    "            n: 労働人口成長率（％）\n",
    "            d: 資本減耗率 (d<1)\n",
    "            T: ループによる計算回数\n",
    "       戻り値\n",
    "            資本と産出量からなるDataFrame\"\"\"\n",
    "    \n",
    "    k = k0\n",
    "    y = A * k0**a\n",
    "    \n",
    "    k_lst = [k]\n",
    "    y_lst = [y]\n",
    "\n",
    "    for t in range(T):\n",
    "        \n",
    "        k = ( s * A * k**a + (1-d) * k )/( 1+n )\n",
    "        y = A * k**a\n",
    "\n",
    "        k_lst.append(k)\n",
    "        y_lst.append(y)\n",
    "\n",
    "    # DataFrameの作成\n",
    "    dic = {'capital':k_lst, 'output':y_lst}\n",
    "    df = pd.DataFrame(dic)\n",
    "    \n",
    "    return df "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "引数に使うパラーメータには次の値を使ってプロットしてみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = solow_model(k0=200)\n",
    "df.plot(subplots=True)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "異なる初期値を使って資本の変化をプロットしてみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAHECAYAAAAwOIA0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOydd3hcxdm379O276pLVnPvFbANpncCTiAhEAihp1IC6YQQ3kACaQRIeUPIB4QSILy00AIhlNAxxZhi414lWVYv2/fsOWe+P85qJVmyLRfZxsx9XXNNn509K2l/euaZGUUIIZBIJBKJRCLZB1H39AQkEolEIpFIhgspdCQSiUQikeyzSKEjkUgkEolkn0UKHYlEIpFIJPssUuhIJBKJRCLZZ5FCRyKRSCQSyT6LFDoSiUQikUj2WaTQkUgk+xwPP/ww2Wx2T09ju2loaKCjo2NPT0Mi2aeQQkcikewzxGIxli9fzgMPPMDpp5+Obdt7ekoDaGlp4b777uP000/nyiuv7Fd3xhlncPfddw/r6+/KM2IXLVrE1VdfzbvvvrvLxpRIdjVS6Egkkn2G//znPxx11FFce+21NDU1ceedd261fTabZfny5aRSqWGf2ze/+U1qa2upqKjg8ssvp6ysjEMOOSQvPB555BEWLFjAD37wAxRFQVEUPve5zw061rp16/jGN75BIpEgm83S1ta2xZBOp/P9GhsbmTx5Mk8//XS+LB6PoygKhYWFA4Kqqqxfvz7f1jRNfv7zn3PKKadQVVXFvHnzeP3111m6dCmPPPJIft6bh/vuu294HqpEMgT0PT0BiWRfxrZtHnzwQQ455BBGjx69xXZ/+tOfiMVi/PSnP+1XbpomyWRySK8VCATweDw7M91hI5FIUF9fv812qqoyceLEQeuWLFnCjBkzttq/vr6e73//+3z5y1/mxRdfpLy8fECb22+/nVmzZnHggQeyceNGpkyZwmuvvcZhhx02tDcDWJbF448/zn/+8x/WrFlDPB6nrKyMgw8+mAsuuICampoBfc444wxOPfVU3n77bRYuXMitt96ar1u3bh2XXXYZCxcuZPbs2WSzWSZPnszZZ589YJx4PM4pp5zC3LlzCQaDPPvss5x00klbnOutt97KRRddBEBVVRWXX345p556Kn/84x+5+OKL8+3a2trQ9f5fCaWlpf3yHo+HQCDAMcccg2maTJ8+nRtvvBFwhdpBBx3EW2+91a/PUUcdtcW5SSS7Ayl0JJJhpL29nYsuuojjjjuOf/7zn1ts98ADDxAIBAYInX/84x9ceOGFQ3qtu+66iwsuuGBnpjtsvPbaa1v9Mu4hGAwSj8cHrZs4cSLLli3bav8RI0bwox/9iEMPPZTKyspB2/ziF7/gsssu48ADD9z2xAfhrbfe4pxzzkFRFM444wzee+89Ro0axcknn8wTTzzBr3/9a37729/y7W9/u1+/4447DoAVK1b0K1+3bh3HH388qqrmhcWtt95KRUUFZ511Vr+2TU1NnHbaaRQXF/PXv/4VgBNPPHG7lqMuvfRSIpEITz/9dF4A9fD222/3E1ednZ0D+v/oRz8CYPny5UN+TYlkTyKFjkQyjJSXl3PVVVfxk5/8hFdffZUjjjhiQJtoNMqiRYu46qqrtjjOpk2btvo6W/pS31vY/Mt4+vTpnH766Vx77bVDHsPj8TB58uQhtT300EO3WGfbNoZhDPl1+/Lcc89xyimncOWVV3LVVVfh8Xj417/+xSGHHMJXv/pVvvrVr/Kf//yHU089Fcuy+O53v5vv2yPgTNPEtm3i8TipVIpDDjmEc889l7KyMg477DD+8pe/8Lvf/Y6XX36532uvW7eOww47jCOOOIK//e1vLFiwgEQiwfz587f7fZx77rmce+65A8pTqRSjR4/mhRdeAAZadDo7O7nnnnsAWLx4MV6vlz/84Q9EIhEikch2z0Mi2R1IoSORDDOXX345N954I9dddx3PP//8gPp//etfmKbJF7/4xS2OMWLEiOGc4qeKVCq1Q0t8TU1NnHHGGVx33XV5q4Zt26xevZpJkybl233mM5/ht7/9LT/60Y8455xz8mIhHA73Gy8cDjNu3DheeumlvIDLZDJ88Ytf5Nlnn2XcuHH92o8aNYrf//73nHHGGSQSCc477zzOO+88Zs6cuc25l5SU4Pf7B5Q7jkN3dzcA3d3dxONxLMuiq6sLcB2Xo9Eotm2jaRrpdJoPPvgAgGXLllFVVcUHH3xAaWkp8+bN45133sHn8/V7DdM0+frXv77NOUokw4UUOhLJMBMIBLj44ou566676OjooLi4uF/9bbfdxsyZM7fpf7I3sWbNGrLZLFVVVdv8T77HKbYvpmnS1ta2xeWPkSNHEggEALj77ruHvHzXl/r6+kF9ZRKJBIWFhdvs7zgOqtq7X+OGG25g7Nix/OAHP8iXffzxxySTSebOnduv74UXXsh3v/tdnnrqqfzceyxaM2fOZOTIkfzrX//q1+fRRx/ltttu4/bbb2f69OkD5qOqKmeccQYAl1xyCaWlpZx77rnU1tZu8708/PDDnH766ZimieM4AGiaxsaNGxk7dizjxo3joIMOyrefM2cOAEVFRcyePZsFCxYwZ84cKisrufvuu2lra+P+++/nxBNPzPvo9DwziWSvQ0gkkmGnu7tbJJPJAeULFiwQgLjnnnsG7XfXXXeJofyaAuKuu+4adOztDZuPMxijRo0SgLj33nu32fanP/3pds/hpZdeyvfv6uoSy5YtGzR4vV7x4x//eNC6bDY7YC5dXV0CEP/5z3+EEEKsW7dOAOK1117r166zs1MceuihoqOjI182duxYcfPNN/drd9NNN4kJEyYM+r4rKirENddc06/s448/FoCoqakRa9asEUII8eqrr4oTTjhBTJkyRXz44Yfi0EMPFd///ve3+DxvuukmAYg777xzi20uvfRScf755w8onzVrVv4Zn3/++WLdunUiGAwKIYRIJpMiFovlQzqdFkK4n/W7777bb5xbbrlFAOKwww4b9OdaItmbkBYdiWQ3MJjVw7ZtLr30UqZMmcJXvvKVXf6a++233zaddwdjV/v7XH/99Vx//fX9yrbHR6egoICCgoIB5bFYjEwmw4wZM4bsu7Nq1SoAxo4du8U2juNwwQUXsHr1alKpFEVFRQDU1dX1W6IC+Oc//8nnP//5AWMIIUgkEnmrVA9/+tOfGDNmDJ2dnRx88ME888wzXH/99Xzuc5/j4osv5nvf+x5vvPEGb7zxBjfffDMAF1xwAXfddRcA//u//8u1115LQUEBiqIM6T335eWXX8ayLG644QZaWlr61Z100kk0NTURCoVob2/n2GOP5Y477hh0nHvvvZfa2loWLFjA5z73Oa677rqt+kWB63D/5S9/ebvnLJHsLFLoSCR7iKuvvpr333+fl19+ecC23l2Bz+cbsgDYXvqerbKn+PDDDwGG5KPSwzPPPENxcfEWhY4QgksuuYRnn32WF154gaqqqnydz+cjFovl80uWLOHNN9/k9ttvHzDO22+/TTweZ//998+XrV27lkceeYTLL7+cd955h/33358vfOELrF27FkVR+O53v8tjjz3GqlWrGD9+PG1tbcyaNYuvfvWrADz//PNcd911PPfcczu8u65nyW5zAdbDHXfcwWGHHcbdd9/N66+/Pmib5557jvXr1/PZz34WTdN48803uffee/s5m3/7298mFArxm9/8ZofmKZHsSqTQkUj2AH/+85/5zW9+w3XXXTfoTizJtnnwwQcZOXLkkH2bEokEt912G6eddlo/35seMpkMF1xwAY899hiPPfbYgHN1Dj30UN544w3OPPNMAH7+858zf/58pkyZ0q+daZr86Ec/YuzYsRx99NH58ksvvZSvfe1reeveL37xCw4++GBWrFjBt771Ldra2ohEIqTTaTKZDGeffTbnn38+hx9+OADHH388K1asyFuYhoPLLruMgoICmpqaBj1XyHEcfvSjH/Htb3+b+vp6QqEQDz74IO+9996wzUki2Vmk0JFIdiOmafLTn/6UG2+8kYsvvpirr756SP12ZJlib0ZRlJ1yXH3llVf461//yh/+8Ich9/ne975HR0cHP/7xjwfULVq0iEsuuYTGxkaeeeYZjjnmmAFtrrjiCj772c/y5S9/mcWLF/PMM88M+IJfuXIl3/zmN3n33Xd5/vnn85a6xsbGvEWnxwKkKArz58/nggsuYP78+VxxxRU888wzHHXUUYwfP57JkycPWPIbTpHj8Xi49tprmT17NuCe9/Pf//6XaDSa//l74YUXaGpq4vLLL8/vPJs6dSpTp05lzpw5A57Hb3/7WwCqq6tpaGgYtrlLJFtDCh2JZDfx7LPPcsUVV7B06VJ+8Ytf8D//8z9D7rstX5vNrQp7O2VlZTz11FMcf/zx+V1omUyGrq4uZsyYQVlZ2aD9hBDcfvvtfPe73+WUU07hkksu2eZr2bbNj370I26//Xb+9re/Ddi2DfCd73yHAw88kIULF27xBOtjjjmG3/zmNxx11FEEg0EeeughJk+ezLp163jooYd4/vnn81vFX3nllX67mKqqqnjrrbcIBoMDxu17t5Wu64RCIWbNmsWtt946qOVpZ0kkErzyyiusXLmS888/P1/+3HPP9Wt333338bvf/Y5AIMCoUaMAOProo3nooYcGbJUHWLhwYT4tl64kexNS6Egku4H33nuPU045hcmTJ/Pyyy8P+bqBAw44gOuuu26bvjbXXXcdBxxwwK6Y6m7h+uuv58orr+SLX/wi3d3d2LaNz+fD7/fzyCOPDHptwOrVqznllFNYsWIF3//+9/n1r389JEtXW1sbzz33HLfeemve36WH2tparrjiCsrLy/nud7+LpmlbHes73/kOX//61/F4PPlDB4uKinjiiSeYMGECjz/+OPPnzx90nC1ZY6LRKI8//jh33nkna9as4aabbspvI98ebr/9dtra2iguLh4gtHpYtWoVZ555JuFwmG9/+9ucdtppfP/73+eNN96gurqacDiMpmlks1nOO+88zjjjDKLRKEuXLmXu3Ln4/X6OPPLIAeP23bYOrri0bbvfPVuapu3wQY0Syc4ghY5EshuYPXs277//PlOmTNmu/9Jnzpw5JGfboS6B7S0ccsghvPrqq9vVZ/z48Xzzm9/khBNOYOrUqUPuV1FRwUcffTToc9c0Lb+8MlQ2t8oUFhby5ptvbtcYfbn88stZunQp3/zmNzn33HPxer07NE5bWxuPPfYYiUSCcDjMeeedN6DNzTffTDgc5qmnniISiXD88cdz++23c9lll1FXV0dnZ+eAJUVN06isrNyqA/oxxxzDG2+8MaC87xk7xx57bP7EZYlkd6IIsR2XpEgkEolklyKE2G0+WF1dXfj9/i2KKSEEpmliWRaKouDxeIZlR6BEsjuRQkcikUgkEsk+y673dJNIJBKJRCLZS5BCRyKRSCQSyT6LFDoSiUQikUj2WaTQkUgkEolEss/yqXendxyHxsZGwuHwPnf6rEQikUgk+ypCCGKxGFVVVVs9tuNTL3QaGxupra3d09OQSCQSiUSyA9TX11NTU7PF+k+90Ok5yry+vj5/2Z5EIpFIJJK9m2g0Sm1t7aBXkvTlUy90eparIpGIFDoSiUQikXzC2JbbiXRGlkgkEolEss8ihY5EIpFIJJJ9Fil0JBKJRCKR7LNIoSORSCQSiWSfRQodiUQikUgk+yxS6EgkEolEItlnkUJHIpFIJBLJPosUOhKJRCKRSPZZpNCRSCQSiUSyzyKFjkQikUgkkn0WKXQkEolEIpHss0ihI5FIJBKJZJ9FCp3homMtPP8zEGJPz0QikUgkkk8tn/rby4cFMwl3HA/JNigcCXO/vqdnJJFIJBLJpxJp0RkOPAE44kdu+rmfQce6PTsfiUQikUg+pUihM1wc+E0YdRhkE/DEt8Fx9vSMJBKJRCL51CGFznChqvD5P4MRhA2vwzu37ekZSSQSiUTyqUMKneGkeAyc8As3/cK10L5mj05HIpFIJJJPG1LoDDdzvgZjjwIrBY9fAo69p2ckkUgkEsmnBil0hhtFgVP+DJ4w1L8Fb/1lT89IIpFIJJJPDVLo7A4Ka+HEX7npF38BTUv27HwkEolEIvmUIIXO7mL/c2HiSWCb8OjXIZva0zOSSCQSiWSfRwqd3YWiuLuwguXQugyev2ZPz0gikUgkkn0eKXR2J8FS+MKtbvqd/wcrn9uz85FIJBKJZB9HCp3dzYTj4KCL3PQTl0C8dc/ORyKRSCSSfRgpdPYEx/0cyqdCohWeuFRe/CmRSCQSyTAhhc6ewPDBaXeA5oVV/4G3/7qnZySRSCQSyT6JFDp7ioppcMJ1bvq5/4GN7+3Z+UgkEolEsg8ihc6e5MBvwpSTwcnCwxdCqmtPz0gikUgkkn0KKXSGEcvexo3lPacmF46Erg3w5Lelv45EIpFIJLsQKXSGif97p46T/vga3cns1hv6C+FLd4NqwLKn5C3nEolEIpHsQqTQGQaSpsWfX1rNqpY433/oAxxnG1aa6tlwwvVu+rmrYeOi4Z+kRCKRSCSfAqTQGQYCHp2/njMbj67y4vIWbnlp9bY7HfQtmPw594qIh8+HZMfwT1QikUgkkn0cKXSGienVBVz/hekA3PzCSl5ZuY2DAXuuiCgaDV117n1Yjj38E5VIJBKJZB9GCp1h5Iw5tZx14EiEgO/83/vUdyS33sFfBGfeD7of1rwIL/1q90xUIpFIJJJ9FCl0hplrTp7KzJoCupJZLrl/EensNqw0I6bDKf/rpl+7EZb9a/gnKZFIJBLJPsoeFTp33nkn06dPp7q6msmTJ3Prrbfm6x5++GFqamoGBFVV+e1vf5tvd/LJJ1NSUtKvzeGHH74n3s6g+AyNv5x9AEUBg8Ubu/nZE0sQ29pCPvNLMO8SN/3YRdC2avgnKpFIJBLJPogitvmtOzzce++9XHXVVTz77LNMmzaN5cuXc8wxx/C73/2Os88+e9A+r732GqeccgqrVq2itLQUgP3335/f/va3nHDCCTs0j2g0SkFBAd3d3UQikR1+P9vitVWtnH/nOzjCtfJceOiYrXews/D3z8OGN6B0Inz9RfAN3/wkEolEIvkkMdTv7z1m0Xnrrbe44YYbmDZtGgCTJ0/mrLPO4tFHH91inyuuuIL/+Z//yYscgIaGBmpra4d9vjvL4RPK+MlJUwC47l9LeW3VNpyTNcM9XydcCW0r4Z/fkM7JEolEIpFsJ3tM6Nxyyy2cddZZ/coWL168RVX2+OOPU1dXx6WXXpovy2QytLW1UVNTM+TXzWQyRKPRfmF38fXDx3DaATU4Ai69fxHr2hJb7xAqhy/fD7oPVj4LL1y7W+YpkUgkEsm+wl7hjJzNZrnssstYsGABP/zhDwdt86tf/Yrvfe97eL3efFlDQwOBQIC//vWv7L///owdO5azzz6burq6Lb7Wr3/9awoKCvJhd1qDFEXhl6dOZ/+RhUTTFl+/512i6W2cnFw9Gz5/i5t+80/w/v3DP1GJRCKRSPYR9rjQ2bBhA4cffjgvvvgir7/+OtOnTx/Q5r///S/Lli3jW9/6Vr/y7u5uSktLqaqq4s0332Tx4sWUlpZyzDHHkEgMbi35yU9+Qnd3dz7U19cPy/vaEj5D4/+dO5vKAh9rWhNc/sD72Ns6OXnG6XDEFW76qe/AhgXDP1GJRCKRSPYB9pgzMsB7773HSSedxHnnnccvf/nLftaavpx++umEw2HuuuuubY5p2zYFBQU88sgjnHjiidtsv7uckTdnycZuTv/rm6SzDhceOpprTp629Q6OA49cAEufgEAJfOMlKBq1W+YqkUgkEsnexl7vjLxhwwbmz5/PLbfcwo033rhFkdPa2sqTTz7JeeedN2i94/S/IVwIgeM4KIqyy+e8K5leXcDNZ+wHwF1vrOfO19dtvYOqwhf+CpWzINkO/zgTUl3DPk+JRCKRSD7J7DGhc/HFF3PJJZfwpS99aavt/vnPf+Lz+QY9G+e1115j8uTJvPvuuwCk02m+853vUFNTw1FHHTUc096lzJ9RyU9OmgzAdU8v5bmPm7bewROALz/g7sRqXQYPngOWuRtmKpFIJBLJJ5M9tnSlKArl5eUYhjGgrqGhIZ8+5ZRTAHjyyScHHefuu+/mT3/6E83NzWQyGQ4//HB+//vfM3r06CHNY08tXfUghODqx5dw/9t1+AyVB795MLNqC7feqWkx3HkSmDGYeSac+v/cu7IkEolEIvmUMNTv7z3qo7M3sKeFDoBlO3z97wt5eUUrpSEPj11yKLXFga13Wv0i/OMMcCw4/Adw7M92z2QlEolEItkL2Ot9dPZ1LEewJLaNSzxz6JrKn79yAFMrI7TFTc6/6x06EttYkhp/LJz8Rzf92k2wcNuO2hKJRCKRfNqQQmcYyDgO3/h4PScvWsXbXfEh9Ql5de68YC5VBT7Wtia48K53SGSsrXfa/xw48ko3/fT3YfkzOzlziUQikUj2LaTQGQZUFLJCkHIE5y5ey8fx1JD6jSjw8fevHURRwODDhm4uuu89TMvZeqejroT9zgHhwMMXwPrXd/4NSCQSiUSyjyCFzjBgqAq3TRvNQQVBopbDlz9cw7pkZkh9x5eHuOvCAwl4NF5b1cYPHv4QZ2sHCiqKu4Q1aT7YGXjgLNj04S56JxKJRCKRfLKRQmeYCGgqf58xhmkhH62mxRkfrqEps43rHnLsV1vIX8+ZjaEpPPVhIz9/6mO26jOu6XD6XTDqMMhE4d4vQtvqXfROJBKJRCL55CKFzjBSYOj836xxjPF7qE+bnPnhGjqz2/C7yXHExDJu/NIsFAXuWbCBm59fufUOhg/OeiB3oGAb3PsF6N64829CIpFIJJJPMFLoDDNlHoP/mzWOER6DFYk0X/lwLTHLHlLfz+9Xzc9Pca+G+N//ruaWl7ZhpfFF4OxHoWQ8dNe7YifespPvQCKRSCSSTy5S6OwGRvm9/N9+YynSNd6PJTn7o7Ukhih2zjt4NFfmTk/+3X9W8LdtXRURKoNzH4dIDbSthL9/HhLtO/kOJBKJRCL5ZCKFzm5ictDPg/uNo0DXeKc7wTmL15K0t7GjKsdFR47ju8dNAOC6fy3l/rc3bL1DYS2c/6R7VUTLUrj385Ds2Nm3IJFIJBLJJw4pdHYjM8MBHpg1lpCmsqArwQWL15Ieotj5zrET+NaRYwG4+vElPPJew9Y7lIyD856EYLl7ZcR9X4R0986+BYlEIpFIPlFIobObOSAS5IFZ4whoKq92xrlwyToyzrbFjqIoXHniZC44ZDRCwI8e+ZCHF9ZvvVPZRDjvCQiUQOP7cN9pkI7uoncikUgkEsnejxQ6e4C5BUHunzkWv6rwUkeMCxavIzUEy46iKPzsc1M5Z95IhIArHv2IB9+t23qniqmu2PEVQsO7cO+pkOraJe9DIpFIJJK9HSl09hAHF4a4d+ZY/KrKSx0xzv1oLQl72w7Kqqpw3eenc/7BoxACfvzoYv7x9jbEzogZrtjxF8HGha6DsvTZkUgkEsmnACl09iCHFYV5YNZYgprK611xzv5wLfEh7MZSFIVrT5nGhYeOBuCqxxZz71vbcFCu2g/Of8pdxtr0AdxzCiTadvo9SCQSiUSyNyOFzh5mXmGIB2eNI6ypvNWd4MsfriE6RLHzs89N5RuHjwHgfx5fwh2vrd16pxEz4IKnXQfl5sVw9+cg1rwr3oZEIpFIJHslUujsBcwpCPLwfuMp1DUWRpOc/sFq2sxtn6CsKApXzZ/CRUeOA+D6p5dx03Mrtn5dRPkUuPAZd+t56zK4ez50bWPpSyKRSCSSTyhS6Owl7BcJ8Mh+4yg2ND6KpfjC+6toSJvb7KcoCj8+cRI/+swkwD1B+donP976RaClE1yxU1AL7avhzhOhdcWueisSiUQikew1SKGzFzE9HODJAyZQ7TVYncxwyqJVrEqkt9lPURQuPXo8131hev5urB88/CHZre3kKh4LX/0PlE6C6EZX7DS8twvfjUQikUgkex4pdIaJZHIddXV/2/oy0iCMD/h48oAJTAh4acxk+fz7q/ggmhxS33PnjeL3Z+yHpio89v5GLr7vPVLmVvx9Cqrhq89C9WxIdcA9J8Pal7drvhKJRCKR7M1IoTMMWFaCDz74KqtW/4oVK3+G4wztxvIeqn0eHt9/AvuFA3RkbU77YDUvdwztoL8v7F/N/ztnNh5d5YVlLXzljrfoSGxlCSxQ7J6gPPYoyCbg/i/Bkke3a74SiUQikeytSKEzDOh6kNra8wGFjRv/weIll2DbQ7PK9FDi0Xlkv3EcXhQiYTuc89FaHtg0tMs5j5tawf1fP4gCv8H7dV2cduub1LVv5fW9IfjKQzD182Cb8MhX4Y0/wXZaoyQSiUQi2duQQmeYqK29gBnTb0FVvbS1vcii98/BNLfv3JqQrnH/zLGcXlGEJeB7y+v53bpNQ1oOmzu6mEcvPpjqQj/r2hJ88dY3WNywlbuudC+cfhccdLGbf/5/4JkfgTO0W9YlEolEItkbkUJnGCkv/wz7738vul5INPohCxd+iWRy3XaN4VFV/nfKSL4zqgKAm9Y3893l9WS3tqsqx/jyMI9dcghTKyO0xU3OvG0BLy7byrk5qgYn/QY+8ytAgXdvhwfPAXP7rFESiUQikewtSKEzzBQWzGbO7Ifx+WpJpet4d+HpdHa+tV1jKIrCT8ZW8rtJNWgKPNjUwVc+WkNXdtu+P+URHw9+ax6HTygladp84+8LueO1tVu3Ch18KXzpbtC8sOIZuPuzEN20XXOWSCQSiWRvQAqd3UAwOJY5cx4hEpmFZXXx/gfns7Hxwe0e59yqUu6ZMZaApvJaZ5zPvreKNcltbz8P+wzuvGAuZx1YiyPcgwWvemzJ1refT/sCnP+kez9W4yK4/Rho/GC75yyRSCQSyZ5ECp3dhNdTygH7/4OK8s8hhMXy5VexctUvEWL7fGCOK4nwVO6snTWpDPPfW8WrHbFt9jM0lV+dOoOrPzsFRYEH3qnjgrveoTuZ3XKnkfPg6y9C6USINbpn7Xz8+HbNVyKRSCSSPYkUOrsRTfMxbdofGDvmuwDU19/Jhx99E8vatlDpy7SQn2fnTGROJEC3ZXPWR2u4a+O2HZ0VReHrh4/l9nPnEPBovLG6nS/85Q1WNW/l9UvGwddfgPHHgZWCh8+HV26QO7IkEolE8olACp3djKIojBlzGdOn/y+q6qO9/WXeXXgq8cSq7RqnzGPwyH7jOb2iCFvAT1Y28IPldWScrSxH5ThuagWPXHRIfkfWF255g/983LTlDr4COOtBmHeJm3/pl/DQeZDZPoEmkUgkEsnuRgqdPURF+XxmH/B/eL2VJJPrWLjwNFpa/rNdY/g0d0fWT8dWogD3b+rgC4tW0ziEO7KmVkV48tuHMm9sMQnT5lv3vsfNz63Y8h1Zmg4n/hpO/hOoBix7Em4/Ftq2T6BJJBKJRLI7UcT23lGwjxGNRikoKKC7u5tIJLLbX98021m85DK6ut4GYNSoixk39nsoirZd47zcEeWijzfQZdmUGDq3TRvFoUXhbfbL2g6/emYZd72xHoBjJ5dz85n7UeA3ttyp/l146FyIbQJvBE79fzB5/nbNVyKRSCSSnWGo399S6OxhoQPgOBZr1txAXf3fACguOoxp027G4ynZrnE2pDJ8bcl6lsRTaAr8z9gqvlVbhqIo2+z7z0UNXPnPxZiWQ22xn798ZTYzagq23CHWDA9fAHVvuvnDfwhHX+WexSORSCQSyTAjhc4Q2RuETg9NTU+ybPlPcJw0Xk8F06b/kaLCuds1RtJ2uGJFPY80dwJwYmmEP0weSaGhb7Pv4oZuLr7/PRo6U3g0lZ+dPJWzDxq5ZaFkZ+G5q+Htv7r50YfDaXdAeMR2zVkikUgkku1FCp0hsjcJHYB4fAWLl1xGMrkGRdEYO/YHjBr5DRRl6O5UQgjubmznmlUbMYWgxmdw29TRHFAQ3Gbf7mSWHz7yIc8vdU9Q/vx+Vfzq1BkEvVsRSosfgae+A2YcgmXwxdth3NFDnq9EIpFIJNvLUL+/96gz8p133sn06dOprq5m8uTJ3Hrrrf3qb7rpJkKhEDU1Nf1CU1PvDqGNGzdy5plnMnr0aKqrq/ne975HJpPZ3W9llxEKTWLunMcYUfF5hLBZs+YGPvzoG5jm0C70BHdn14XVpfxr9gRG+Tw0pLOc8v4q/l99yzbvySoIGNx27mx+On8KmqrwxAeNnPzn11mycSv3ZM04Hb75MlRMh0Qr3HsqvPQreU+WRCKRSPY4e0zo3HvvvVxzzTU8+OCDbNy4kccff5zrrruO+++/P9+moaGByy+/nIaGhn5hxAh3acQ0TY4//nhqampYvXo1H3/8Me+99x7f+9739tTb2iXoepCpU29i8uRfoaoe2ttf5u13Pkt7x+vbNc7McIDn507ic2UFWAKuWd3IOR+to9XcyiGBuELpG0eM5cFvzmNExMfa1gRf/Mub3PHa2i3vyiqd4J63M/sCQMArv3Wvjuiq2645SyQSiUSyK9ljQuett97ihhtuYNq0aQBMnjyZs846i0cffTTfpqGhgdra2i2O8dBDD9Hc3Myvf/1rdF2nsLCQ3//+9/ztb3+jrW37bgrf1QghhnTL+JZQFIXqqjOZM+cxAoHxmGYrH3xwPqtW/QrHGbrFKqJr3D5tNL+aUI1XVXixI8rR76zghfboNvvOGV3Mv79zOCdMrcC0Ha5/ehkX3v0urbEtvL7hh5P/CF+8AzxhqFsAtx7mLm1JJBKJRLIH2GNC55ZbbuGss87qV7Z48eJ+62wNDQ3U1NRscYz//ve/fOYzn8Hj8eTLZs+eTUlJCS+++OKgfTKZDNFotF8YDhYtWsQ//vEPYrGdO1QvHJrMgXMfp7r6bADq6v/GuwtPJ5FYPeQxFEXhqzVlPDt7IpODPtqyFud8tJafrmwgvbX7roCioIf/d+5srv/CdLy6yisrWznpj69u/Rb0mV+Ci16DmrmQ6YZHvwb//Bakh+dZSyQSiUSyJfaKAwOz2SyXXXYZCxYs4Ic//GG+vKGhgffee4/DDjuMMWPGcNxxx/HGG2/k6xsbG6mqqhowXnV1NRs3bhz0tX79619TUFCQD1uzGO0opmny4osvsmrVKv7yl7+wZMmSnRpP0/xMnvQLZs74fxhGEfH4Ut559xTq6u9CiG2fhNzDlJCff8+eyNdrSgH428Y2Tli4kg9jya32UxSFc+aN4qnLDmPyiDBtcZOv3bOQHz/yEbH0FpbBisfAhc/CkT8GRYWP/g/+eiise23I85VIJBKJZGfZ40Jnw4YNHH744bz44ou8/vrrTJ8+HXCXfrxeL+l0mieffJLVq1dz4YUXcvzxx/PRRx8BYBgGqjrwLWzt3Jif/OQndHd350N9ff0uf08ej4cLLriAyspKUqkUjzzyCA8//DDJ5NYFxbYoKzuOgw58muLiw3GcDKtWXc+i988hlRr6e/BrKtdPqOH+mWMpNXRWJtPMf28lN6zbhLmN6yMmVoR5/NJD+cbhY1AUeHBhPSf98TXeWrsFR2lNd8/WueAZKBjp+uvc8zn495Vg7tyzkEgkEolkKOzR7eXvvfceJ510Eueddx6//OUv8Xq92+xz0kknMWvWLH7zm99w8cUXE4vFuO+++/q1qa2t5cYbb+TMM8/c5njDub3ctm1effVVXn31VYQQhEIhTj75ZCZNmrRT4woh2Nj4AKtX/xrbTqJpQSaM/wlVVV8e0uGAPbSbFleubOCp1i4AZoT8/GnKSKaE/Nvs+/badn7w8Ic0dKZQFPjqoWP44QmT8Hu2cGBgOuqeubPoHjdfMh6+8Feo3b5zgiQSiUQigU/A9vINGzYwf/58brnlFm688cZBRY4ziIXBtu38l/mJJ57Ic889h2VZ+frly5fT0tLCscceO3yTHyKapnH00Ufz9a9/ndLSUuLxOA888ACPPvooiURih8dVFIWa6q9w4Nx/UVAwB9tOsHzF1bz/wXmkUkPf5VTi0bl9+mj+OnUURbrG4niKExau5KZ1Tdu07hw0toRnv3sEX55bixDwt9fX8Zk/vMqba7bgBO6LwCl/grMfgXAltK+GO0+A//xUWnckEolEMmzsMYvO/PnzOeigg7jmmmsGre/o6GDOnDn88pe/5Mwzz0RRFP7+979z0UUXsWjRIqZMmYJlWey3336cfPLJXH/99cTjcU477TTGjx/PX//61yHNY3cdGJjNZnnppZdYsGABQggCgQAnnXQS06dP3y4rzOYIYVNXfxdr196M42RQVT/jxn6f2trzt+u+rJZMlh+uqOe53G6syUEfN0+qHdIhgy+taOGn/1xMY3cagLMOHMlP5k8m4tvCfVmpTvj3j+GjB9180Wh3t9bYo4Y8X4lEIpF8utnrT0ZWFIXy8nIMY+CXYUNDAwALFizgZz/7GUuXLiWTyTBhwgR+9atfcfTRR/dre+mll/Luu++iqipf+tKX+M1vfjOkZTDY/Scjb9y4kSeeeIKWlhYAJk6cyPz58yksLNypcZPJ9SxbflX+ctBIZBZTJv+aUGjoy2RCCB5v6eKnqxroyNoowDdqyvjx2BEEta2Lplg6y2+fXc59b7kWpRERHz///DQ+M20r10Gs/A/86/sQdT9v9jsHPnM9+IuGPGeJRCKRfDrZ64XO3sKeuALCsixef/11Xn31VRzHwTAMjj76aA466CC0bQiKrSGEQ2PjQ6xa/WtsO46iaNTWfpUxoy9D17dtmemh3bS4ZvXG/H1Z1V6DX06o4cSyrVzymeOtte1c+ehHrG93l6OOm1LBtadMpaYoMHiHTAxe/AW8czsg3CskTrgeZp4JO2HpkkgkEsm+jRQ6Q2RP3nXV0tLCv/71L+rqXCtIRUUFn/vc53Z6y3s608TKlT+ntfU5ALzeSiZNvIaysuO3a5z/tke5YmU9Dbkt5CeURLh+QjUj/Vu3lqVMmz+/tIrbXl1L1hb4DY3vHT+BCw8dg6FtwS2s7m148jJoW+HmRx0Gn70Jyidv15wlEolE8ulACp0hsqcv9XQchw8++IDnn3+eVCoFwP7778+xxx5LKBTaqbHb2v7LipXXkk67ZwqVlh7LxAlX4/ePHPIYCdvmD+ububW+BUuAX1X43ugRfKu2DO8gW/v7sqo5xk8fW8I76zsAmFQR5ppTpnLIuNLBO1gmLPgzvHIDWClQdTjkMjjiR+AZukVKIpFIJPs+UugMkT0tdHpIJBK88MILvP/++wB4vV6OPvpo5s6du1PLWbadYt36W6irux0hLFTVw8jarzFq1MXbtZy1IpHmypX1LOhyd4uN8Xv4+fhqji+JbNWZWgjBI+818KtnltGZdC1Dn51RyVWfnUJ14Ra2sXducJ2VV/7bzYer4PhfuJeHyuUsiUQikSCFzpDZW4ROD3V1dTzzzDP5G9rLyso46aSTGDt27E6NG0+sYtXK6+jodE+W9npHMH7cj6moOHnIu76EEDzS3Ml1axppMd0t/UcXh/nF+GomBH1b7duVNLn5+ZXc99YGHAE+Q+WSo8bzzSPG4jO2IOSWPwPPXgldG9x87Tw46TdQtf/Q3rREIpFI9lmk0Bkie5vQAXc56/333+fFF1/Mn6Y8ceJEjj/+eMrKynZ4XCEEbW3Ps3LVr0in3dOUCwoOYML4qygoGLp4iFs2f9jQzG31rZhCoCtwYXUp3xs9gmJD32rfpY1Rrn3qY95Z5y5nVRX4+NGJk/j8rGpUdRDBlU3Dgv+F126GbBJQYP+z4eirIVI55DlLJBKJZN9CCp0hsjcKnR5SqRQvvfQS7777LkIIFEVhzpw5HHXUUQSDO+6zYtsZ6urvYP36W3Ec1y+ovHw+48b+kEBg1JDHWZfMcO2ajfynzT17J6KrfGfUCL5WXYpvS07HuILrqY828ZtnluXP3plZU8DVn53KgWOKB+8UbYTnr4HFD7l5I+D67xxyOXh3zpdJIpFIJJ88pNAZInuz0Omhra2N559/nhUr3B1JHo+Hww47jHnz5vW7uX17yWSaWbv2DzRuehgQKIpBTc25jBl9CYYx9LNsXumI8Ys1G/k47oqWGp/BT8ZUcmpFEepWlsXSWZu/vb6OW19eQzzjLoUdP7WCKz4ziQkV4cE71b/jXiVR754XRLAcjv4J7H+ee7eWRCKRSD4VSKEzRD4JQqeHdevW8dxzz7Fp0yYAQqEQRxxxBAcccAC6vuNf8rH4clav/g0dHe7N4poWYuTIrzOy9kJ0fWjWElsIHmnq5DfrNrEp4zodTwv5uHJMJcdtw2G5LZ7h98+v5IF36nAEqAp88YAavnvchMHP3xEClj0JL1wLHWvdspLx7gWiU0+FbewGk0gkEsknHyl0hsgnSeiA67+zePFiXnrpJbq6ugAoKiriqKOOYsaMGYPe5j5U2ttfZfWa3xGPLwXAMIoZPfoSqqu+gqYN7aTppO1we30rf65rJma792XNjQT5ydhKDinaumha3RLjxv+s5NmPXUdsj6ZyzrxRXHzUOMrCg7y+ZcLCO+HVGyCZu0F9xAw45mcw4Xi5Q0sikUj2YaTQGSLDJXTsuIliaKjeHd8avjUsy2LRokW88sor+QtCS0tLOfLII5k2bdoOCx4hHFpanmHN2t+TSq0H3B1ao0ddQlXV6ajq0ARPR9bizxtauHNjK2nH/RE7sijMD8eMYO427s96v66TG55dwYK1rnjxGxrnHjyKbx0xlpLQIK+ficFbt8Kb/wsZ11+I2nlw1JXu/VlS8EgkEsk+hxQ6Q2S4hE7HwytJL2sndFg1oUOqUH3D4z9imiZvvfUWb775Jum06yNTVlbGkUceydSpU3dY8DhOlk2bHmXd+v8lk3EtLDsieJoyWX6/von7N7Vj5X7SjiwK84PRFRxYuGULjxCC11a1cdNzK/iwoRtwBc/5h4zmm0eMpTg4iG9SsgNe/z28cxtY7rOg9qCc4DlaCh6JRCLZh5BCZ4gMh9ARlkPznxZhtbg7mhSfTujQKsKHVqEGtnCj906STqd5++23WbBgQT/Bc9hhhzF9+vQdPnTQtjM0bnqIDRv+2k/wjBr5DaqqzkTTtnDo32ZsSGX404ZmHmzqyAueI4pCfHfUCA4uDG7Rh0cIwUsrWvj986tYvNEVPAGPxlcOHMk3jhhLRWSQ83tiTfDGH91lrR7BU3Oge8KyXNKSSCSSfQIpdIbIcFl0hC1IfdRK9KW6XsHj1QjOqyR8aDVaZMd3S22NVCqVFzyZTAaAwsJCDjvsMGbNmjXobfFDYTDBYxjFjKy9kOrqczCMoT27wQTPnEiAy0dVbPWUZSEELyxr4Q8vrOTjRnd5yqOpfGlODRcdOY7a4kGclgcTPBUz4LDvwrRTQR2eZUWJRCKRDD9S6AyR4XZGFo4gtaSN2H/ryTa5vjRoCsEDKggdUY1RtoVbvXeSdDrNu+++y4IFC/KHDoZCIebNm8fs2bPx+4dmidkc286wqelRNmy4LX/ooKaFqKk+m9ra8/F6K4Y0zoZUhlvqWniwqYNMzodnStDHt0eWc0p5EcZghwfiCp6XV7Zyy39Xs3CDe7u6pip8dkYl3zxiLNOrB7lhPdbk+u8svAuyuc+gaAwc+h2Y9WUwduxZSCQSiWTPIYXOENldu66EI0gv7yD2SgPmhpzDrAL+qSWEDq/GM2rrW7B3FNM0WbRoEW+++SbRaM4S4vFwwAEHMG/ePAoLC3doXMexaGl5mvUbbiWRWAWAohiMqDiZkSO/Tig0aUjjNGey3NbQyt0b20jkdmlVeQ2+VlPGuVUlRPTBrS5CCN5e18EtL63mtVVt+fJDx5fwjcPHcuTEsoHPM9kB79wOb98KKVckESiFA78Bc78OwS1cNiqRSCSSvQ4pdIbInthenlnfTeyVBtLLOvJlRk2I8GHV+GeUomzlVOEdxbIslixZwptvvklLSwsAiqIwdepU5s2bR01NzQ4JLSEc2tr+S13dHXR1v5svLy4+nJG1F1JcfDiKsu3305W1uHtjG3/b2EZr7h6tkKZydmUJX60pZZR/y87PSzZ2c9ura3l68SbsnHVoUkWYCw4dzan7Vw+8SysTh0X3uDu1ul2rFLrPte4cdDGUT97OpyCRSCSS3Y0UOkNkT56jk21OEHttI8kPWuhxWNEiHoIHVxKcOwIttOv9eIQQrF69mjfffJN169bly6uqqjjooIOYNm3aDh8+2N39AXX1f6Ol5VnAtc4EAmOoqTmPyhFfHNLhg2nb4Z8tnfy1rpWVSdevRgFOKI3w9eoyDisKbVGQ1XckueuN9fzfu3UkTRuAwoDBWQeO5LyDR1FZsNkSlW3B0sdhwZ+h8f3e8rFHwUEXwYQTpB+PRCKR7KVIoTNE9oYDA+24SeLtJuILGnHi7qnCaAqBmWUED67EUxselmWtTZs28fbbb7N48WJs2xUGoVCIAw44gNmzZ1NQMIi/yxBIpeqob7iXxsaHsO044PrxVFaeRk31VwgGx29zDCEE/+2IcVt9K690xvLlEwM+Lqwp5fSKIsJbWNbqTmV56N167lmwnoZO1xFcUxVOmFrBOfNGcci4kv7PUwjY8CYsuAVW/huEK9IoGu0uae13NgS2cAeXRCKRSPYIUugMkb1B6PQgLIfkh63EFzSSbYjny43qEMGDRhCYVYbq3fXn8SQSCRYuXMi7775LPO6+rqIoTJw4kblz5zJ27NgdOo/HsuJsanqMhoa/k0yuzZcXFh5ETfVXKCs7AVXdttVqVSLNnRvbeLCpg2TOjyegqZxWUcR5VSXMCA/u0G07gueXNnP3m+t4a23vMuHYsiBnHzSK0w+ooWDz7f6dG+DdO9ylrbS7nR3N6+7SmvNVqD1Qbk+XSCSSvYBhETrd3d07/F/+3sreJHT6YtbHiC9oJPlRa35ZS/FoBPYrI3jgCDw1W7j0ciewLIvly5ezcOFC1q9fny8vLCzkgAMOYL/99tuhZySEQ0fH6zRsvJ+2tv/Ss6xlGCVUVZ5GVdUZBAJjtjlO1LJ5cFMHf29sY1Uyky/fPxzgnKoSPl9eSGgLVp7lTVHuf6uOfy5qIJFb1vLqKvNnVHLm3FoOGlPc38pjJt2b0t+9A5oW95ZXTIcDzoMZX5JWHolEItmDDIvQGTlyJNlsllNPPZWLLrqImTNn7pLJ7kn2VqHTg53IknyvmcQ7TVhtqXy5URkkMKeCwH7laMFdfwhha2srCxcu5IMPPsifx6MoCuPHj+eAAw5g4sSJO3QIYTrdSGPjQ2xsfBDTbMmXFxbMparqS5SXn4SmbX3LvRCCN7vi/L2xnWdau8nmfoQDmsopZYV8pbKYuQWDH0IYz1g8/v5G7ntrA8ubepfExpQGOWNOLacdUE1530MIhYCNi9yzeJY8ClbuM9C8MOVzsP+5MOZIeZGoRCKR7GaGReioqsqCBQt48MEHufvuuznmmGP4wx/+QE1NzS6Z9J5gbxc6PQghMNd1E3+nidTiNrBzH5um4J9STGDOCHwTCnf5ji3TNFm2bBmLFi1iw4YN+fJAIMCMGTOYNWsWlZWV2+1D5DhZ2ttforHxYdraX6bHyqNpQcrLT6JyxBcpLJy7zR1brWaWBzd18MCmDtakeq084wNevlRRzGkjiqjxDVweE0LwYUM3//dOHU9+2Jh3XlYVOGJiGacdUMPxUyv679hKdcJHD8Gie6G5j5WnYCTMOhNmnQUl47brOUgkEolkxxgWoaNpWt5ptbOzk5/+9Kc89NBD3HfffZx44ok7P+s9wCdF6PTFTmRJfdhK4r1msht7fXnUoEFgVhmB/csxara8O2lHaWtr4/333+eDDz7IXyQKUF5ezqxZs5g+ffoOLW2mM000bfonjZseJpWqy5f7fNWMGPEFRlR8nmBw6wJCCME73Qn+samDJ1u6SDlOvu7QwhBfGlHEZ8sKB3Vgjmcsnv6okQffrWdRXVe+POLT+ezMKr6wXxVzRxej9hxiKARs+sAVPIsf7r1IFNyrJmZ92fXpkUtbEolEMmzsUqGTSqXw+/39hE4PDz/8MBdccAEPPPAAp5xyys7PfDfzSRQ6fTE3JUgubCL5QStOIpsv10v9BPYrwz+rbJefvmzbNmvWrOHDDz9k+fLl/X4mRo0axcyZM5kyZQqBwPa9rhCC7u732LTpUZpbnsnv2AIIh6ZRMeIUKso/i89XudVx4pbNv1q7eLipkze6esfwqQrHlkT4YkURxxZH8A1i/VrbGuefizbyz0UNNHan8+VVBT5O3q+KL+xXzeQRfXbBZVOw/Gn48P9gzYu9O7ZUHcYfB9NPh0kngXfbW+slEolEMnR2qdA57bTT8luRNxc6APfddx+XXnopCxYsYOrUqTs3893MJ13o9CBsh/TqLpLvt5D+uB2R7bVoGJVB/LPKCMwsQy8e5BLMnSCVSvHxxx+zePHifktbqqoybtw4pk2bxqRJk7b7ygnbTtPa9jxNTY/T0fE6Qli5GoXCwrmUl8+nvOxEvN6yrY5Tnzb5Z1MnjzR39HNgDmsqJ5UVcHJZIUcWh/Fs5mPjOIK31rbz2PsbeXZJE7GMla8bXx7iszMq+dzMSiZU9HEKjzXB4kdc0dN3acsIwMQTXSvPhOPllRMSiUSyC9ilQqezs5Nbb72VG2+8kc985jPccccdBIPBfm2uvvpq/v3vf7Nw4cJhOfNluNhXhE5fnIxF6uN2Uh+2kl7VBU7vR2xUh/DPKMU/vRSjdNd+4XZ1dbFkyRIWL15Mc3NzvlzTNMaNG8fUqVN3SPSYZgctrc/S3PRkv9OXXdFzIOXlJ1FedsJW79kSQvBxPMU/m7t4oqWTjZle61dEV/lMaa/o8W4metJZm5eWt/DEB438d3kLpt0rIidWhJg/o5ITp49gUkUfS0/rClf0LH4YOnsPZsQIwsTPwLQvuBYfT//fI4lEIpEMjWHx0Wlububiiy9m6dKl/Otf/2L8+N6D3xKJBBMmTOCGG27gnHPO2bnZ70b2RaHTFzuRJfVxG6mP2sis6YI+n7YxIoBvWin+aSUYlYPvUtpRWltb+fjjj/n4449pbW3Nl6uqyujRo5kyZQqTJ08mHN6+bfLpdCMtLf+mueUZotEP+tVFIvtTXnY8ZWUnbHW7upPz53mypYunW7toNnutNUFN5diSCPNLCzi2JDLApyeazvLC0mae/mgTr65qJWv3PtDRJQE+M30EJ04bwayaQtenRwhoXAQfPwYfPwHdvT5I6H4Yd4y7e2viidKnRyKRSLaDYT0w8Oc//zl33HEHr7zyCmPHjs2XP/fcc8yZM4fi4k/OH+zhEjr1H3+EEFA9eSraDl6psKux46Zr6VnSRmZNdz9Lj1boxT+1BN/UYryjC1D0Xbd7q6WlhaVLl7Js2bJ+lh6A6upqJk2axKRJkygvL98usZVKbaSl9d+0tDxLNPp+v7pgcAKlpcdSVnoskcgsFGXwrfA9ouepli6ebu2myey19HgUhUOLQpxQWsDxJZEBu7e6U1me+7iJ/3zcxKur2jCtXktPWdjLcVPKOW5KBYeOL3V3b/UVPUufgK4+okfRYPShMPEkmHQiFI9FIpFIJFtm2E9G/sUvfkF7ezt//OMfd3iSewPDJXQe/PmVNCxdgscfYPSsAxh7wFzG7DebQEHhLnuNncFJZkkt7SC1tJ3Mqs5+Pj2KV8M3sQjfpGJ8k4rQwrvuzq329naWL1/OsmXLaGho6FdXUFDApEmTmDBhAqNHj8Ywhn4+UDrTRFvrC7S2Pkdn19t9fHrAMIopLTmaktKjKSk+DF0f3IrkCMEH0STPtHXz79buftvVAaaFfJxQ4lp69o8E0PqIsnjG4uUVLfzn42ZeWt5CvI9Pj89QOWx8KUdPLueoSeVUF/pd0dO8BJb9C5b/y033pXSSK3gmnAC1B4G2689Kkkgkkk8yu+UKCMdxduhqgL2J4RA6Qgiev+1/Wb3wbVLR7t4KRWHE2PGM3m82o2fNpnL8RNQdOHRvV+OYNpnVXaSWtpNe1tFv9xaK69fjm1iEb2IRntoIirZrlrhisRgrV65kxYoVrF27FsvqFQe6rjN69GgmTJjA+PHjKS4uHrK1J5vtpr39FdraXqS94xUsq/dgQEXRKCiYTUnxkZSUHEkoNHnQcYUQrExmeK6tm+fboyzsTuD0qS/SNY4qDnNMSYSjisOUeXqFSMayeXttBy8sa+bFZS1s7Er1G3tSRZijJpdx5IQyZo8uwqtr0LEWVjzr3rW14U1wep8F3oh70eiE412/nkjVkJ6DRCKR7MvIu66GyHD66AjHoWntKtYuepe1771Ly/o1/eq9wSCjpu/HqJn7M3LGfhRWjNilr78jCEeQ3Rgntayd9IrOfuf0ACg+Dd/4QrwTivCNL0Qv2TUOzaZpsnbtWlatWsWqVauIRqP96gsLCxk3bhzjxo1jzJgxQ3ZodpwsXV3v0tb+Eu3tr5BM9v8MPJ5SiosOo7j4UIqLD8PrLR90nHbT4sWOKM+3RXmlM0rUcvrVTw/5ObI4zJFFYQ4sCOa3rgshWLopyssrWnlpeQuL6jr7rhjiNzQOHlfC4RNKOXxCGePKgijpbner+sr/wOoXINnefzJlk13fnrFHu8td0qFZIpF8CpFCZ4jsTmfkeEc76z9cxPoPF7Hho/dJJ/qLiILyCkbO2I+R02ZSO20mwcKiYZ3PULCjGdIru0iv7CCzugsnafWr14p9rvAZV4B3bOEuWeYSQtDa2poXPXV1dTh9DgBUFIXKykrGjBnD2LFjqa2txeMZ2uumUvWutaf9ZTo738Jx+ltbgsEJFBUdTHHRwRQWzsMwBv5MWI7gvWiC/3bE+G97lMXx/mP4VIUDC4IcVhTmsKIQM0MB9Nxhg50Jk1dXtfLyilZeW9VGW7z/8lhFxMuh40o5ZHwph4wroSrihU3vw6rn3bDxPfp5lKuGe9HomCNhzBFQPRv0XbfUKJFIJHsrUugMkT2168pxbJpWr2LDR++zYfEHbFq1HGezM4qKq2upnTaTkdNmUDNl+h737xGOwGyIkVnZSXpNF2ZdrPcqihx6uR/v2JzwGVOAFtr5L91MJsOGDRtYs2YNq1evpr29v4VD0zSqq6sZPXo0o0ePpqamZkjCx3EydHe/T3vH63R0vEYs9jH9RAQq4fA0igoPpLDoIAoL5g4qfFrNLK91xnm5I8orHbF+u7jAPbNnXmGIg3NhRsiPrio4jmB5U4zXVrXy6qpW3l3f2c+hGdydXAeNKWHeuGLmjS2h0kjBuldhzX9hzUv9d3GBu3195DzX0jPqUKg6QAofiUSyT/KJEDp33nknN998M52dnYTDYb7zne9w8cUX5+tN0+Tqq6/moYceIpvNUlNTww033MCRRx6Zb3PyySfz5ptv9lvKGDNmDK+99tqQ5rC3bC830ykali5hw+IPqP/4I1o3rBvQpqiqhpop06iZMp3qSVOJlG3fLqVdjZOxyazvJrOqi8yaLrJNif46AdDL/HjHFOAZHcE7ugCtyLvTc+7u7mbdunX5sPkyl6qqVFdXM3LkSEaOHEltbe2QTmk2zQ66ut6ho/NNOjsXkEyu3ayFQjg0lYLCORQWzqGwYM6ApS4hBCuSad7ojLuhK0631V/AhjSVuQVB5hWEmFsQZP9IAL+mks7avLehkzdWt/HGmnYWN3T1W+YCGFkcYO7oYuaOLmLu6CLGai0o616Fda+4AmjzZS7dD7VzYeQhrgCqmStPaZZIJPsEwyZ0nn76aZYsWcIJJ5zA/vvvv8MTvPfee7nqqqt49tlnmTZtGsuXL+eYY47hd7/7HWeffTYAX/va16ivr+eBBx6gpKSExx57jHPOOYePPvqIcePcu4/2339/fvvb33LCCSfs0Dz2FqGzOalYlIalS6hfupj6jz+irX7DgDahomKqJk6hatJUqidNoWz0GDR9z+3OcZJZMmu7c6GLbHNygPBRwx68oyN4RkXwjoq45/fsxFZ2IQQdHR2sX78+H2Kx2IB2ZWVljBw5kpqaGmpraykpKdmm4EpnmujqfJvOrrfp6nqHZHKg+PT7RlJQeAAFBbMpiOxPKDSx31Z2WwiWxFO82RlnQVect7sTA4SPoSjMDPuZWxBkTiTInIIgI7wG0XSWhes7eHttB2+tbWfxxu4Bwqck6OGAUUUcMLKI2SMLmOVpxNvwJmx43XVq3lz4KBqMmNEremoPhIJa+AQd8imRSCQwzELn3nvv5fnnn6e6uprrrruOz3/+89s9wUsvvZTDDjuMs846K1/2gx/8gHXr1vHPf/4T0zQ5/PDDefjhhxk5cmS+zezZszn//PO5/PLLAfcL7NVXX2XKlCnbPQfYe4XO5qTiMRpXLKVh2cc0LFtCy7o1A5a6NMOgYsx4KidMpHLCZCrHTyJcWrbHrD5OMktmQ5TMuijmum7MjXEGfFPrCp7qMJ7aMJ6RbqwV7rjVRwhBZ2cnGzZsoK6ujrq6ugFLXQB+v5+amhpqamqorq6murp6mw7OmUwLXV3v0NW9kK6u94jHl7G5ktO0IJHITAoi+xGJzCIS2a/fNRW2ECyLp1jQleCd7gTvdMcHLHUBVHsN5hQEmR0JsH8kyPSQHytrs6iui3fXdfDO+g4+qO8asNSlqwrTqiLsV1vIrJoC5gZbqIkuQql/G+reHrjUBRAa4Vp9aua6Pj6V+0mrj0Qi2esZ9qUry7K4//77+clPfsL8+fO57bbbdnqr+QknnEBVVRV33333oPWxWIzRo0dz0003ccEFF5DJZPD5fESj0e0+YbeHT4rQ2ZxsJk3TmlU0rlhG48plNK5YNsC5GcAfKWDEuAm5MJGKseP3mJOzyNqY9XEydVHM9VHMuugA52Zwb2H31IQwanICqDq0U07O8Xic+vr6fGhsbBz0zraSkhKqqqryYcSIEXi93i2Oa1kxursX0d39vhtHP+x3EWkPXm+lK3rCM4hEZhAOT8cw3FvehRDUpU3e7k6wsDvBe9EEy+JpnM3G0BSYGvSzXyTArHCAmWE/Y70GKzbFWLShi/c2dPJeXSetscyA1y/wG8ysKWBGdQEHFieZKVZQ1L4IpeFdaFrcfys7gKK6O7uqDoCq/aBqf6iYDsauvSdNIpFIdoZhFTodHR2sWrWKgw46iJaWFk488UTmzZvHX/7ylx2abDab5fvf/z533303CxYsYPr06QPatLS0cPrpp9Pe3s7ChQvx+/2sWbOGmTNncu211/KPf/yD7u5uDj74YH7961/3swL1JZPJkMn0fhlEo1Fqa2s/cUJnc4QQdG5qpGn1ChpXrWDTquW01a0fYPUBd8mrfMw4KsaOp3zMeMpHjyFcsvstP0II7PY0mfoYZl0Usy5GdlNioNUHUCMePFUhjOqQG1cFd9jyY1kWTU1NNDQ0sHHjRhoaGujs7BzQTlEUSkpKqKyspLKykhEjRlBZWblFy48QNonEarq7FxGNfkR39AMSiVUMWL/DXfIKh6cRDk8lFJ5KODQtb/mJWzbvR5O8F03wfizJomiS1kGsPh5FYUrIx8xwgOkhP9ODPiJZWNYY5YO6Lj6o72RJY3SA1QfcJa9p1QXMqvBwsL+eydYyijoXo2xcBNGGAe1RdSibApWzoHKmG1dMl5YfiUSyxxg2ofP973+fv/zlLxx//PE89dRTAGzcuJH999+fBx54gGOPPXa7JrphwwbOPPNMotEoDzzwALNmzRrQ5qWXXuLss89mzpw53HXXXZSUlACwaNEiTj31VH71q1/xxS9+EcdxuOqqq3j66af58MMPB1w8CnDttdfy85//fED5J13oDIZlmrSsX0vTmlU0r1lJ09rVdDQ2uKfyboYvGKJs9FjKRo2hbORoykaNobimFsOzZYvGcCCyDuamONmGOGZDDLMhjtU60NcHQPHpeKqCGJW5MCKIURFAMbb/EMZkMsnGjRtpbGzMh8F8fcA9wbmiooIRI0bk46KiokEtmpYVJxZbQjS2mGh0MbHYYlKpQZaPcM/0CYWmEApNJpyLA4GxKIpOYybLomiSD2Nu+CiWGuDrA6AC4wM+poV8TA35mej34olbNLYkWLyxm48aulnRHMMeREwGPRpTKiPMLTWZ513PJHs1pbGl6E0fDPT1AUBxr6oYMR0qZkDFNDctfX4kEsluYNiEzj333MO8efOYNGlSv/K//OUv3HvvvSxYsGDIY7333nucdNJJnHfeefzyl78cdJngjjvu4IorruDmm2/mggsu2OaYtm1TUFDAI488woknnjigfl+16AwVM52idf06mtetpnntalrXr6V9Y/2glh9FUSmqrKK0dhQltaMoHTmKkpqRFI2o2q0nOjumTbYxTnZjHHNjnOymhOvoPMiXNQropf686NErAhgVQfQSH4q2fUursViMTZs20dTUxKZNm9i0aRNdXV2DttV1nbKyMioqKigvL6e8vJyysjIikcgAq1M2200stoRYfCmx2FJisY9zO7wGvh9FMQgGxhIMTSIUnEgwNJFQcAJebzV1GYsPokk+jqdYEk+xOJaiLTvQ8gPuSc6Tgj4mh/yM83rwJyySXRnWNcVZ2tjNsqbYoJYfgJFFfg4uS3GIv57JrKM6tYpg51KU2KbBH5w3AuVTcmGaG5dNhmCpFEASiWSXMaxLV62trdxxxx3MmTOH448/HoB0Os3FF1/MnXfeOaTlhA0bNnDggQfy5z//mS996UuDtnniiSe45JJLeP7555k6deqgbTa/hsKyLCKRCI899hif+cxntjmPT6qPzq7EymZpb6ijdf1aWjaspa1uA61160nHooO213SdospqiqtrKa6upaSmluKqGoqqqnebBUhYDtmWJNnGhCuCmhJkmxKD+vy4k1ZcAVQeQC8P9Malvu2yAKVSKZqbm2lubqapqYmmpiZaW1v7XV/RF6/XS1lZGWVlZZSWlubD5hYg204Sj68kHl9GLL6ceHwZ8fiKQX1+AFTVRzA4jmBgAsHgOAKBcQQCY4lqVSxL2iyNp/g4F9YkMwN8fnoo8+hMDPgY7/dSlHEgmiXWlWZDc4LlTbEBBxrmH6eqMKvI5IhIE/t5Ghhrb6AsuQpf12oUJztoH/zFruApnwylE3tDpBo+4VfJSCSS3c+wCZ0VK1Ywd+5cDj/8cK644op+Z9psD/Pnz+eggw7immuuGbQ+Ho8zbtw4HnrooS2+xmuvvcbXvvY17r//fubOnUs6neYHP/gBzz//PIsXL96qI2kPUugMjhCCRFcnbRvW0dZQR1v9BtrrN9DeUE82kx68k6IQKS3Li56iymqKRlRRVFlNuLQUVR1eK5AQAieWdUVPc4JsU5JscwKrJYkwt/BVr4BW4M2JHj96mR+9xI9e6nd9gNRti3bHcejo6KClpYWWlhaam5tpbW2lvb2dLf16aZpGcXExJSUllJaWUlJSQklJCcXFxQSDQRRFQQhBOt1IIrHCFUGJFSQSq0gm1+A45uBvR9Hw+WoJBsYSCIwhEBiD5hvDRqWatZkgy5NplsVTrEymaUhvQZDgnvUzLuClRtUJJx2UeJZEV5rm9hRrW+LEMoMLOwOLuaF2Dg43M8PYyBinjvLUWnyJBpTB1h8BjACUjO8NpROgZBwUjwN/4VafvUQi+fQyrBad5cuXM3ny5J2aoKIolJeXD3pDdUNDA6+88gpHH300VVUDLzA8+OCDefjhhwG4++67+dOf/kRzczOZTIbDDz+c3//+94wePXpI85BCZ/sQjkO0rYX2jfV0NNTTvrGB9o11dG5sGHTXVw+arlNQUUlhxQgKR1RROKKSwlw+UlY+rOf/CEdgd2XItiSxWpJu3Joi25JEpLZgAQLXClTsc4VPiQ+91I9e7EMr8aMXerd5/o9lWbS3t9Pa2kprayttbW35MNiurx68Xi/FxcX5UFRUlI/D4TCKIkil6kgkVpNIrCKRXEMysZZEcu0WLUDgWoEC/lH4A6Pw+0chvKPYpIym3illrelnTcpkdSLD+nRm8wOv+1Gia4xUNArSDp6kTTaWJdqdZlN7io7E4ALMR4aJ2iYOCrUw09vEOKWRSquBgmQdqtjKZ+AvzomesW4oGgNFo6F4DATL5FKYRPIp5hNxMvLegBQ6uwYhBKlYlI6N9XQ0bqRz00Y6NzXSuWkj3c2bsLewtAOAohAuKaWwfASR8goKyiqIlJVTUO7GoaKSYfEJEkLgJLJYbSlX+LQmsdrSbr49NeB6i/5zBi3iRSv2uWKoyItW5EMv8qEV+9Aini1agxzHoauri/b29nxoa2ujo6OD7u7uQfv0oGkahYWFFBUV9YsLCwspKChA12Mkk+vckFpHMrmWZHId6fRGhNiyuFIUHZ+3Cp+/Bt07knZ9PJuUGjY6JdRbQdZnFNYkTdq34APUQ8gWVFgK4YzASFpkY1li0QxtXWkyg/gA6VjUKq2MUxqZ6W9liqeFMUoTI7L1hLKDOUD3wQhC0SgoHNUbF47MhVrwFUohJJHsw0ihM0Sk0Bl+HMcm1tZKV1MTXc2NdDZtort5E11Nm+huad7yUlgORVUJl5QSKS0nXFpGpLSMcEkZ4dJSNy4pxRsI7tLt8T1WIKs9hdWe7hfbnektL4X1oOaEUJEXvdCHVuhFK/CiFXrRc2nFpw3iqJyls7OTjo6OfOjJd3V1bXEprAdd1/Oip2+IRIL4fHE0rZ2MWU8qVdcnNCDE4JaYHhTFg883Ats7hnZtAi3qSJqoYJNdwEbLS31GZdMgW+B7H6iAjEM47VCYFfjSDiQtMvEs0WiGtDlQhAVIM0ppZrTSxBi1mcmeVsZobVSLJoqsli0vhfXgCbuCp6AWCmr6h0gVhKvkPWASyScYKXSGyHAJnfeeXU+8M0Ow0Euo0EuwwEuw0Euw0IPHr+/RO6r2JoQQpKLddDU30d28ie7WFqKtzXS3NBNtbSHa1opjb92KAGD4/ISKSwgXlxAuKSVUXEKwqJhQcQmhXBwsKNollqG8Jagjjd2exupMY3dmsDpz6a7M1q1BORSP6oqfAi9axOMKowJPbzriQQ15UDT3Z8W2baLRKJ2dnXR2dtLV1UVnZyfd3d10dXVtcTv85vj9fiKRSD6EQkHCYQuvN45hdIHSjm03k05vzIVNsEV35l4crZguzxQ69LG0KzW0KuU0O4U0WQEaLZ2uLX2MQkDWQUnZqCmLcEbgyzioaZtswiKZMLE3e54GFjVKK7VKC7VKK7VKK6PUVkbr7VTSSqHTNaRnQbAcCqpd0ROphPCIPulcXlqGJJK9Eil0hshwCZ2HfvUurXWDf/FohkqwwEMg4nXjAi+BiIdAgceNIx78YQ+BsAfN+HTvRnEcm0RXJ9HWVmJtrvCJtrUSa28l1t5GrK2VdHxoX/AoCoFIAcHCIkJFxQSLigkWFhEoKCJYWESwoJBAYSGBgsKdshAJR+DETKyuDHZXGqszg92dwe7Khe7MlneHDZize1K0Fvaghj1o4ZwQChluPuRBDRtoIQ+2LohGo3R3dw8aotEo2eyWHZD7omkaoVAoF/xEIg6BQAqvN4lhRFHULoRow7JaMc0mLGvbn0EaH+1KOV3aeLr0kXQolbRTSqsopMUO0GIbWGKQZy4EmK4QUtI2StrCSDt4Mw5qxsZOWZjp/hYhHxmqlTaqlTaqlHaqlDaqlXYqaadW66CCdjwM7Vmg+yBU4YqeUEVvCFe4QilUlovLQd+9505JJJ9mdovQ2bRpE6WlpYM6FH9SGC6hs/ytTXQ1J0l0ZUh0m27clSEz1C+4HN6Ajj/swR82cnEuHfLgDxn4+qaDxqdSGGUzaeId7cTa24l3thNrayXe2UG8o51EZwexTjcWzratEj1ohkEgUkigoIBApAB/pIBAQSH+cCSf701H8PgD2yWMHNPGjpquAOrOYHeb2NEMdtTEiebSMXMohpQ+k1ZcARTyuOIoZKCGDLSggRo0UAI6puGQcFLErRSxVJxYLEY0GiUWi+VDMpncjhcFj8dDOGwQidiEQiZ+fwavN4Wux1G1KNCJ43RiWZ1s7Q05KMSI0EEJ7ZTSpVTQrVXTpZTTQTEdIkKHEyAuBvl7YwuUjA3pnBjK9MZGxkExHZy0hci/vKCYGJVKB5VKOyOUDiqUTkaQi5UOypUuCpXEdj0LfAWuk3SwzD03KFgGgVI3HSjJxbl0oFgKI4lkJ9gtQueoo45izJgx3HXXXTs6xB5nd/voWKZNMmrmBVAymiEZNUl2m255d4ZULEsqZuIMYfljcwyflhc9vqCBN2jgCxn4Ajq+kIE30FOu4wu4sdevo27nYXqfNBzHJhWNkujqJNHZQbyzw013dZLs7sqlO0h2d2Omtu+LHkDVNPzhCP5wBF84jD/kxr5QGH8o7KaDIXwht8wXDOELhtC9W77GQjjuEpkdM7FjOQEUN3FifcpiJnY8i8hs2dF4i2gKakBHDeTEkF9HDRoIn0JKs0gqGZJkSNopElaaRCbphmSSeDxOPB7f6u6xgTh4PGkCAZNQ2CEQyOL3mXi8aQwjiaYlUJQYQnQDg5/fA5DGSxdFdFJMN4V0UUg3hXQrpXQrpUSVIrpEhC4RwKHPz3XPElnGcUVRxs6nFTNXZrpWIiz3d8+LSZnSRQWdlCndlCu5mC7KlC5KlW430I1H2f7PQHhCEChGCZS4O8wCxX3iov7BV5iLC0DTt/u1JJJ9jWEXOv/4xz+46KKL+PDDDxkzZswOT3RPs7c6IwshyCQtklGTVNQkFXfFjxuypOI9cZZ03CQdzw52s8OQMXwa3oCO12+4ccAVQN6Agcev9cZ+N/b4dTw+HY/fbbcvWZKyZoZUdzeJ7k6S3d2kot0ko90ku7tIRrtJxaKkcnEy2o2V2fKX8rbQdB1vTvR4QyF8gSDeYAhvIIg3GHTjQBBvIJArD+DxB/JlhteHoqqIrI0dz+LEs64YSmTzeSeRxU64cU8Q2e0xFW0+aQXVr6P4NCyfIG3YpHWLtJYlhUkKk7TIkLIypKw0STNNKpMimU7hDNGqpqpZPJ40hpELnjQ+n4nfb+H1mBieDLqeQtNSKEoCRRloKXVQSBCimwKifYKbjxDriZUCYkSIE0T0CCMnt1xm5sSQaefybsB0xRHZXJntUECCUqWbEqKUKG4oU7opJkqxEqVEiVFMlCIlRhFxdGXHPwPbCCF8BSj+IlS/G+MrcE+l9hWAL9InH+kt78lLS5JkH2BYhY5pmowfP55rrrmGr33tazs10T3N3ip0thfhCDIpi3Q8SzrRI4CyZJLZfFk6kSWTtNw4YZFOZsmmd8ASMAiqrrjCx9crggyfhserYWye9mp4fL3pfN6roXs0DJ+G9gmyMGUzaVKxGOl4jFQ0SirWTSru5tOxGKl4jEwiniuLu+Xx2HYtpW0RRcHj8+MJBPD6A3j8fjz+gFuWz/sxfG7s8bnBMHwYeNDxoNs6qqWiWipkBCJl4SQtnGQWJ2W5IWnhpLLbt5S2GQJBFpuUYmJ6bEzDJqPbZDSLtGZhkiVDlrTIknZMMrZJ2sqQsba+IwwEqmphGBkMI4NuZDD03rSuZzB0E8MwMTxurGsmqpZGUXr//DmoJAgQI0KMMPFccEVQmDgh4oRI5OI4YRIEySh+1/k866DkhE9PGtN2y7K99WQd1KxFOBunhBjFxChU4hQRd0WQEqOQBAVKnELiFCoJCpU4BSQIK6kd/wD6YKsGthHC8YQRnjCKN4Tii6D5wmi+MIo3DJ6Qe2mrJ9QnHcyFPmkjKHevSfYIwyp0brnlFu655x7eeeednZrk3sC+InR2FMd2yKSsvPDJJC3MlEUmaZHpkzdTFpmUnYstsumeeNcIpc1RNaVX+Hg1dI/qiiKPht6T97j1ukd12/VJ68ZmsUdFM1R0I9fGcPN7avebEIJsOkU6EScdj5NJxEknE2QSbkgn4mSSccxkknQigZlMkEkmyaTc2EwmBr2fbKdRFAyPF8Pnc4PXl8t70T0+vJ4APiOARwvg0Xx4VK8rlvCgCx3V0dAcDdVWUSzAUlBMAVmByDiD30+2DRwEJhYZJYuJhalYZMhiKlau3CKrWZiqjanY+XKTLKaTxdzigYQCTcu6YmiwWDfRdBNdd9O6ZqLl0pqWRdezKIrAQidBgARhEgRIEiRBKBcHSRLIhWAu5PLCT8oOkLE8KFZOCFk5kdQvL9zYctCzFpFsjCI7RsSOU0CSAhJElGROCCWJ5ARRTz5EirCSJExqlwmlzbEVHUvzY+sBHN2PYwQRegAMP3iCKB4/qieI6g2geYPo3gCaN+TW63437gm6Hwyf6wRu+PvHcvebpA+7VOjU1fXetmzbNkceeSS//e1vOfTQQwe0HTFiBB7PJ0fdf9qFzs7iOIJs2t31YqZd4WOmNsvn6rMZm2zaIpux3XzaIms6ZDNWrs7eIb+knUHTewTQ4LGma33SCpqhoekKuqGi6qrbPx+UXDs3qFqfvKaiGQqqlmunq/m0qqtomoKiKkMWXkIIrKyJmUxippKYqZQrgFK9eTOdcuNUEjOdIptKYWbSmKkU2VSSbCbjlqfT2zzLaFehKTqG6sXQvPg8IbyeAF4jiFf349F9GJoPQ/WiqwaG6kHDQEdHQ0cVOhoqqqOhOAqqMzSrX48lKYuFqfTElluWE0Vu2q1zYzdYSt86GwsbO7/k5FqSND2LrmV7456Qy6ua1afc6hermoWi2ZiaTkbzkcJPigAp/KRzIZULbtqXL0/jI+X4SFl+0paXjOUhaxk4tgJWThzZwhVNubSWzRK0U4StJGE7SdiKE3JShJwkIZEiTIogKYJKmlA+ThMgTVBx44CSIUQKPxm8gywZDidZxUNW9WCpPmzVg6N6cTQPjuYF3YfIxejefFB0L4ruQzW8qIYba7qb1jxeNMOLZvhQda9rmdK8oHlAM9wxNKN/meZxg6pJ4bWH2aVCR1XV/N07W0NRFF566SWOOOKI7Z/xHkIKnb0L23LIZmwsMyeM8unecsu0yZpObzrjYGVtrD5lVtbpk8/VZx1s08HZAavCbkEBTXMFkqorvWlNyQsntU9ZXihpKqqq9CnfSllOUKma0qdeRVEEjp1FOCaObWJbJo6dwbGzbj6bwbHcctsysbMmtpXJxW7eyrrtrKyJbfbk3dgy3fSuRlcMNMVAVz3o+VhHU418XlP0Pu2MXNptk69T3Tot31dHRUNTBjr9OjhYOGSxsBQnL4Cyihtb2FiKjYXTJ53L58ptbCzFyZfbOVHlaCZCy6DmxZCFqlloat/Y3mJeVW2EKshqOqamk1V1sqqRCzpZ1UMGby74yODFxIOJl7TwkrZ9pG0fGdtDxvZg5kLW1rFsDdvWsWwV4SgotsCwTAJ2mqCVJGCnCNhpAk7aLXNS+EUGv5POxRkCZPBh4ieDXzEJ5GbgU3JlubSP3rAzvkzDiYOChYal6FgY2IqGpbixrRjYio6t6jiKjqMaOIqOUHWEauCoBkI1QNXdoBmucNIMUA0UVUfRDBTNjVVVR9UMN+g6qqqj6R4UTUfV9Fx7PV+v5NtrqLqBlmuj6jqaqqPqBihq7vU1ULQ+abVPWd947xN1Q/3+HpLr/lAdCCWSnaXHGkJw+I4scGwnL4Rsy8kLIzsXLCsXZ23srMDO5W3L7dc3n48tt51j9eR7y9xygW33SVvOQOuVINeerW062gNoQCAXthMFFA8YHtCFACwQFmADFopig2KjKDYKuXLFztX3KcMCYSOwQbh1Qlj5tC1sbGGRFj3lGYRtISy3vRA2wrFysQ3bOlW577tXdDRFR83F/YPWW67qaPTmVUXDo+j4FA1N0fJlbr0XNZd3y1XXaqVoqIr7ZSMUECgIFYSiYisONm6wFCcvuGwcnJxoshE4OBiKgxe3jY2T7+tg46hZHNVEaFk3qCaoCYSWBbUnuJ8JmoWqWiiqg6raueAgdIGlqdia6n7Baxq22ietaFiqhqW4QqBb1WlXfFjoZIROVnjI2D4yjgfTMcg6BlnbIOvoWI6B5WhYjiuusAWG7aDbFh47i8exMGwLj2PidSx8jonPyeBxsniFiVdk8TkmHuHmPSKLjywe0RtceWf1BiWLkUsbWHg3y7tl/a1XKsLtKywgvT0/Up9IXGGn4qBibxa7QcmXCUXJ1wkUbEWl8cjrOPLIL+6Rucs9ipJPHaqm4tFUPL49Ow8hBI4j8sKnR/w4tiuSHNvN59M5seS26a137Nw4m9XZ+bRA9G3j9Cl3RD4/IG07OE5um3tuTCHc5cr8eI7btqevsAWOEIhcv764y3IGKANFrBB9vieG+oWh5MLWi7bw7B1cAeX0EU6Om8+LKTcvcgLLFq5Y6Okj8uncGHYujePWCQsw8+P0r3N6y3HcB5B/PSf3EPr3UwBVAUWoqIqCqigoCqioaPTkVVTICyYFNSe4VNRcWlVUFHKxoqPi6dNWzdWrKIqKgoKiuP/NC0Vx/6tXFITiLhsKNffEFcUVZYpAKEqvSFNELnbfUW/s4CgCoWYRqgNKFqGmc3kbodgIxUJobozqCmCh2KBaoDoI3cZRbBxFkNVcQWipYKtKPrYVnZhq0K0oOSGm4KjuF6+F6lpkhEoWHVvo+byN7sZCwxKa+6XtqCAUVMdBcQSqA5pw0GwbVQg0x0ETDqoj0IWNKhw0x0F3HDRhu22Fg+HY6Ni5MhsjF+vCQRcWGg56T12unU4uCBt3lu5raNgYOfmhCweN3rYajjsWNprSm1bzsci1cdtuy3LmCruef0K29Qs2MP/c++9KoSOR7OsI20ZYFiJrIbImWJabtyyUrIVmZdEsy22XtRBWFmwbYdl90tZmeRthW2DZCNuGnBVD2Nbg9U6uzLHdsnzsuH1tp7e9435552Pbdsd0nFy8Wb1ju87GuTZu6COEhOLGKOA4uS9A1d3SnfvyHJBHyVk31D55BZH7r5GtlPWv798Ohc3aAz15+nyRK8pm5X1j1+rSI6/693HbCPSc8lLyr98/3ad9v3o2a9t/DNEj57bQRgiBo/R83wh6DpwWPSVKTw2gCERvTe/Pa76tRZ+RBtS74+fqhegdQxk4Jn1eKSd5+pUrKO7TVEBxJRuK4skLWEVRcu9cQVF62+u5Ok9P/9yorlDLPSah9Onv1qGI/HgA7o9Gz7MVbrGwQe0Rn7m2/RR17mdBVfN9Re4TckWcANXJfVQ2qO7zV1QBipN//ooiQBVuexxQRU44gqUqmJqDoyg5gahgK67QdBTIaTAc1ZXHQlVcya6AlbOoOIpbZimu9cXOlQtc26ktet93z+coAEX0fkY9aSWfFrny3E+tcN+3Ipxc7NarQlDauedWhqTQkexTCNtGmCYik8HJmAgz0yefQZjZ/mWm6aaz2VxdT9rsn85mB6b75i2rf3kuT0/asuBTvASs4C6A7QhC7WNJUHtjoZCzHvQs7+T+7Obq3C96gaO4lgUH8rGj5upyQahg575sHSVXlhsDyL9Wz9ddz59+J1dHX4uF0mcufdKwlbqtlW2rvu8ct1AOm80h307J1w95jD5pMUi657LVvBbopwvyEm0L9XnZlm8DruBQRW/bfv170oro0ycvPwcpY7Pxe+YhUBz3feTFTv5Nub16RJHI5/rOuk8/XAGiCAUhQLH7PoHe8YRwe/RKqF4x3fdh5+RDrm3PZ9bz7lQUpe+T7U0rKOi50P8d0+/JCLbwZPr87A7+5HLzUDYft7dVz9ha5RT2FFLoSIYdkc3ipFI4qTQilcRJp3GSKUQ65aZTKUQ67danUzjpDCKTy2fSbj6dxsmkEelMPs6Ll1xwTBOGeJfTXoGioOg66DpKn4Cho+gGiqb15rVcnaa6dbqOommQa6PomjuO1tNGR1E10DUUVUMxdLdt3zJdA01H0VznQ0V3fUMsVeR3HZm427WzwiKD5eYd97wbE4uMyJIRFqZwyzJO71k4GcfM1WdJC5OMMEk7WTIiQ0ZkSTmm6zfS899ojzhRev877f1S6EtfqbFLPxD6/wHvjyZcsaYLgY5wYyEwBGgINEGuHAwhBpTpwj2OUBciN06uX0/ZZuOoAgzX/tSvrifuGUvFLVNz89Ny42v5OtylFcAWKgjXaiZQEULFQUMINy3QED1LNWg4wq2z0XCEu+jhoCKElltA0bAdDZFbBhK45e6iiuusa+fHU7EUt52jqFiKW26r7kKKrai9+VzabafiKJpbpuTqVLeuZxxHcf2DHKVXADuuWQih5ixvOeuIoigINWetUMlbbhTFtaqoqoOqOGiKu7yj5JZ9VMXJPbVcWrjlCiJfp/XxWOl5ypoQKDi5z8TJfZ5O7+fS5zPUhPtZqz3GHQdUoaD0zTub1zmotpIzBim99XZPXoBQUZ0eA5KSWynVcudiuYKLXB1CQTiKu0LVo3wd3DIBImekEn2NXDlrTs+yq8j9jgrhPlMhHCYee8gu+03dXqTQkfRDmCZ2IoGTSOIkEjiJeC7uCUmcZE/cJ6TcWCRTvWU5EbPHxIeqovh8qB4PiseD4vW6sceD4jFQPX3zveWKYaB4PKgeDxiG2z9Xhq735g0DjJzo6CnTDRQjl9f1XFlOzOT69JQpO3mTuhCCtJ0mkU2QyCaIZ+Mks0kS2YQbW26czCZJWkmS2VgudvMpK+XG2RQpyw1pO40jdqHlaevaoV+loep4FQOPquNRVLyKhoGCFwWPAA8CwxF4hMDj2BiO7ca2hce2MBwTw8q6Dqs5MWII8AiB0RNwxYFH5AQJvWLFbd8rSoxcf1fY0PcyiUFxUMgIAxOdDB43FgYmBpmeMqFj4rYxMciiYwqdTK7MzRuketK52ELDFD1tNKxcnSl667PomIqW32FlqQZZRSerumWWqiM0lZwTTz6IfnlXJPSkyVvQ3LSm2OiKu8tLV210xUJXLQzF3QFmKFmMXKwrWTxqFkPJ4lFNN1Z6ZmrlfFQsdCeDgevPojp23s9F7Ykdd+lDdRzXVUcI10fGzgk9W0WzQXVUVKGjOBqK0FGcPkFoqEJHtQ0UoYGtgaOiCBVs97gCxVHBdoWgYveYtHLf6E5uOSfvTCZyZTnvKaH1fNfn71MTjpP78s8FJ+dzlVvSdZ3k3SVfgY2Tc5p3cr5jQnHcJUHFzj1/gdAEQhUoGgjd/UyEDrZHwdFVFENFNVQUQwOPhubRUDw6uqGC14Pi1dG93ty2eg+6149uuGdkaR4PuseH4c0dKGp40TUDXdUxVDfuSffNq8ref7jrLhM6q1evZvz48btqOMkO4JgmTnc3diyGE426cSyGHY3hxGPYsThOLIaTiOfTdo+QiSdw4nHETlxnsE00DdXvR/H7UH1+VJ8PJeDvTft8buz3oXp78l4Urw/V73NjnxfF50PxePN1itfj9ssJGbVH1Oh7r44XQpDIJoiZMboz3cTMGDEzRjwbH5BOZBPEsjESpitmekRNIpvYtaJkMzyqB7/hx6f58Ot+fHou1nz4dB8+zYsPFR8KPiHwCoHXsfHZFl7bwmdn8VoZvNkM3mwaXzaNJ5vAaybxZhJ4M3E8ZhxfTmgMx59LU/VhKj4yipc0XpJ4SQmDhOOh0/EQdwxSwkMaN6SElzRGPp8WHjJ4yPSUid60KXTSuboMHrJobK7qhKqA5gah9Umrg6TVPm3UgXVuPX3SSl5EeLUMHiWLT0njJUMQEw8JejaTezDx5GNXank2C7qTdZ1o7ZwDrW3nxIdAtVxh4Tg6jq3hOBqOreM4rkXHcXSErYFjoDgGim2gOh5Ux+OmbQ+a40V1Imi2B93xoKGjCw0NFUW4YgZHoLie7CiOcP2+RM63rCcIC8excYSD43bBQmAL19XbFgq2cJdMbJRcm5wwcRxUYaM4lms5cRx0R7gCy+5xUHd3+jmKhVBtbCWLrVrYapasmsXRLGzDQRggPIBHBa8KXgXFb6D5vaheH5rPj+b3u2LCH8DwRTACQTy+IIY/iM8TwGv48GrefPBoHnyaD4/myec/CUJib2eXfBMsXryYI488kptuuokLL7xwVwz5qUU4Dk48jt3V5YbubuyubjfudvNOT1k0ih2NuqImGt2lIkXx+VCDQTeEgqiBAGowiBYMovj9bnkggBoIoubzfrfM70fxB3L1PYIm4Foy9sKzGHaGrJOlO9NNd6abrkxXPh01o/l0t9lNNBMlavaGmBnbZSJFQSFoBAkYATfWA4Pn9QABI4Bf9+PX/fl0AA2/ZRLIpvFn0/jNJL5MDC3dDakuSHVCugu6uyC1yU2nusCM7ZL5AwhVxzJCWHqQrBYgrQZIKX6S+EjgI+Z4idpeumwPnZaHjqxBZ9YgIbwk8ZESXhL4SOElKVxBk8kv/AzhGSqg6iqKR0VoCo6mYPeIE11xLSF6jxBRe4WL7ub7iZg+6Z5lNwUHv0jRcySgL3/0Xwpvn9hHOpd3Y7csMyCt21k0CxxbwzYNbNvAtvV87OTTuXJH71eObaDYBWiWF9XxodleDMeLgYYuNAxyQejoqO6xjUJDEwqKY4PjoAg775QuHAvHMbGdLFlhYjkmlshiOVksYWIJE1sITHCFCO5WZdtRcBQdFMN1OhYKmgOaI3I7lgS6Y6NZNrrtbis37CyKMEHJIJQMlprB0kxMzSSrZchoJhnDDZZXIAI6wu/+s+T+TQqgBUIYwRB6IIQ3FMEbiGAEI/iNAAE90O/3o2/w6T50de/9B0oyOEP+xFavXk1lZSXBYLBf+YYNGzjxxBM5+eSTpcgZBMc0sTs6sDs6sNo7sDs7sDo6sDs6sTs7sTo7XEHT2YXd2Ynd3Q07c7S/oqCGw2ihEGpBgRtHIm4cDqOGQ2ihnjhXFgyhhoJuPidu9mZryHAhhCCejdOZ7qQj3UFHuoPOdCedmU43zqW70l10ZdwQz8Z36jV1VSfiiRDxRAh7woSMEGFPOJ8Oedx80AgSMkIEjeCAvF/39wpIx4FUByTaINkGiVY3He+A5Dq3LNmeCx1usHbyWgAjmL9IUngjWEaYtB4iqQSJEyQq/HQ5fjotL22Wj1bToCnjoTlt0JAyaM8aZDDYxhrXll9eV/HkrvlQdBUMFSMnQjIqmD0CxFB7hYmRi/WcWFF7RcnmeMgSJE2QOD4RI5i78CFAEn8u9Fzy4OZTuXQKn0jhJ4kH03XMFAqW5cGyDCzLg215sOyetIFl98RGri6CZRlkbD1fp1pePHjwCve2MkPkLuEQGj50PPm8nq830FDzu+Wy2I5J1smQdTKYuTjrdJF1MliOielkSIssWSGwhEJWuP49jmKgKF5QvCiKBxQvKB4UDDRHRXc86LaGYRuuKLFMvFaaoJVCt9LodgqbNJaWxlRTZPQ0GSNDykiT8mRIeB0SAYWMV4VgAEK5f7DCYTzhAjyRQrzhUoKBAsKG+3tQ5AkTMAJu3hMkqAcJeUL4db+0hkiAIQod27Y58MADEULwjW98gyuvvJLi4mLS6TRf+MIXOO6447jnnnuGe66fKOq+8U1SH3yAE9ux/3qVQACtoACtsLB/XFCAVhBBKyhADUfcdCSCGnHL1WAQRZW/3D30iJfWVCvtqXbaU+20pdpoS7XRnnbzPXFHuoOss/3+RAoKEW+EAk8Bhd5CIt6IG3siFHgLKPAW5MVMxBshbISJeN28V/Nu28rlOK4wiTe7oWV9Lt0CiZZcnBM1ybZeJ4HtQdXBXwyBYvAXuWl/IfiLEL5CklqYLhGgwwnSbvtpNn00pr00pL20JGza4iZtXRk6Eib2Dpw8rakKYb9OwKvj9eloHg0MFcdQyGoKaQ2SKkQVgaWrYCiInKhJq9sWSCqCsGoSJpm7kjNKwOkkIDpzN1PFCYp47naq3tgVKQN/Jmzbg2V5MU0Dy/JiZd181vJgZb1krTApy5MTNW6dZXmwbR1Q0ISKFwOvMPCi4xNuOoSBV+h4MfDkYq/Q8eRiVYBlpzGdNBk7hem4adOO59MJJ02nkyaba2fmxIpQvCiKD1S/Gys+lFxAKUJRvGiO4vo+ZS10K43fSqFbSYxsAsNKome7MawkOEkyWoqMkSRpJEl4TRJ+QacP4kGFhA8SPgURCqBEwhgFhRgFhfgKiokEitzfC08BEW+Eip7fjZ7fD08Yn+bb56y/kj3HkISOEIKuri5effVVrr/+eqZMmcJNN93Eiy++SElJCXfeeedwz/MTh0ilekWOpqEXF6MVF6MVF6EX5dJFhWhFRW5dYZGbL3SD6vXu2TfwCSCZTdKcbKYl2UJLsoXWVCutydZ+6bZUG2l7++5x8ut+in3FFPuKKfIVUeQtcuNcutBbSJHP/WNd5C0i7AmjqTvgWCyEuywUbYTYplxoyuWb3HyPoBHbaeXzF0GgFIKlECjpjQM9cTHCX0xMLaDZCtCY0mmOZWiJpmmOZmiOpmnuyNAaTdMaz5Dtd4qzAFK5MDhhn05pyEtBwMDvc2+zVzwqjqFi6gpJDWIadCkO7UKQ1iCxHV9sIdWhUMtSqCSJECdEF0GnjaDdTNBpJUyUMDFCxAgTw08SdQv3qAmh4ThBslkfZsZDOm2QzYbpzJbRYnnJmj5XxGTdYFkehOj9vBXAhwefY+ATBj48RHKxT/SWefNpAx0NIQQZJ0XGTrrBSZGxY2TsJEknRWeuzLRT+dgSAtQAiuJHUfy9adUPShhFKXfTmh9V1zEsi4iVxDBjeLJxjFzwZJtd8ZKNo2UTmFqChDdB3G8RDSh0+iEWhphfIRqAaACyIR96YRFGUTGhSDVFfvd3pOf3YVQuLvQW5oX+Dv1eSCS7mCHddWXbNh6Ph0wmg67rvP7665x99tm0traybt06Kioqdsdch4Xhuusqs2YNKAp6cTFqJCKtLNtJ2krTlGhiU2ITTYkmmpJNNCeaaUo00ZxspjnZTGw7fERCRohSfyml/lJK/CVu7CuhxF9Csa+YEl8Jxbk/3H7dv/NvQAhId0N3Qy7UuwImutGNuxtcIWNthwgLlEKoAkLlvSHYE5e5IVTuChnNIJ6xaOxKsbErRWNXik1daRq73bgpmqapO00qO3QBVRQwKA/7KAt7KQ15KAx60H06eFRMQyWpQ1SFDsWh2bJozGRJ2EO3LhVoCqWGQ4maoVCJU0AXYdFKyG4iaDUQsOrdMqKDWln6YyBEBNsKkjF9pFMGiaSOmfFimn5X1Jg+slmf67Oy2bKZgkJA9eIXHvy2gd/x4Mfj5kVv2ic8eDFQe84jEQ4ZJ0XKipO2EwNCxk7m0klMJ5XbhmugqEFQgyhKAEUNoCjBnIhx8yhBFDWAKsBrRvGYMTxmdy6OuiEbx2NGMcwYejZGwpuiKwTdQYWuIG46oNAdJBcUzIgff0k5xYHe340Sn/v7Uewrzv9+FPuKCRg7cAWIRDKM7NJLPYUQ6LpOIpHA53PPzW9vb+crX/kKlmXx1FNPEQh8Mn8J5KWee4ZkNklDvIHGeCMb4xvZFN9EY6KRxngjmxKb6Eh3DGmcgB6gPFBORaCCskAZ5YFyygPllPpLKfOXUeYvozRQumvES1+EcP1butZDV12fUO/G3Q1Dd9YNlEC4CiKVEO4JFRAaAeFcCJa5F/7lX17QncrS0JmioTOZi3vTjV0poumh3SxdGDAYEfFREfFREfHmYh+hgIHtUUkbClFNsDFr0ZA2aUhn2Zg26bSGJpIKdI0RHp0y3aZUS1GsRCkUbUTsTQStOkLZVfjN1Rhs+9JPBQNFLUI4BWSzQdJpL4mEQTSqkkq5IsY0/YOKlx6Cup+g6iPgePCbBgHbQwAvAeEhILwEhBcfRp/D39yTQbJkSFoxEmY3KStGyo6TtuJubCdI2XEydpL8yb+KgaKEciImlE8raignZHrSBopj4TW78Wa68Ga68Zg9cRRvphuv2Y3H7Ea1UkSD0BGGjrBCZwg6QwodYegKuunOEGQjfspDIygPlLu/F343LguU9f5e+EuleJF8otmlQgfcG8yj0SihUChfZlkWxx13HJFIhCeeeOITuaYqhc7w4AiHlmQL9bF6GmIN+XhjfCMN8YYhCRm/7qcyWEllsJIRwRFUBCrycUWwgopABSFPaJvj7DCW6YqWzvXQuQ461uXS66FrA5hDcEQOlEBBDURqoKAaIj2hys2HK0EffJkyazs0dqXY0J5kQ0eSuvYEdR1J6jtS1HckiWW2LWQKAwaVBX6qC31UFvgZUeCjqtDHiIif8ogX26vSbNmsS2XYkDbZkMpQlzapS5l0DUHIRHSVaq+HKq+HSo9DqRqnRLRTKDYRsdYTMlch0mvIZJrJnU62RRTFQNfLUJRibKuATCZAIuGhu1ujo1OQTvnIZr1szWk55A0Q0gIE8RG0PATSOkHLQ1D4XBGDB3WQnVhZ1SQtEsQzXcRS7SStGEk7SsqKkbRjpK04Tp/5K6qBqoURIoSihkENo6hhV7ioYRQllHPYVVCEjTfThS/dgTfTiS/dmRM0nfgyXXgzXRjZOAqCziC0RaCtwBUvbRGF9pyoaQ+7VhnD42dEcET+96InVATc34nyYDlhI/yJ/HsskWwPu1zo6LpOW1sbhYWF/co7OjqYN28e5513HldfffVOTXpPIIXOjiOEoC3VxvroetZH11MXrWNDdAN10Toa4g1k7K1vdw97wtSEaqgKVVEVqqI6VE1lsJKqUBWVwUoinsjw/7G2LVe0tK+B9tXQsQY61rr57vptO/aG/z975x0eVZn24Xt6ZjIlZdJ7gUBC7x1EiqJgb4u69l6xrL3squja6+q31lUUGyrSVEDpndBCSALpvc8kM5l+vj8GAjETCAiI+t7Xda6QyfOe856QyfnlqTEQknjwMCVASAKYEv0CR334v5i9PonK5jb21bVSXG+juMFOUb2N4gYb5U1tR0zsNes1JIRpiQvREh+qIz5US1yolvgQLTEhWnRqBZVON4V2J4VtzvaPxW1OStpcuI/w9g9XKUkIUrcfMSovEbIGwn2VhHj2IXPuo81egr2tBI/HcthzyeVBBGnikCsi8flCcTr12Fo1NDcrqKvz0dzs43AiRiaTYdQZMKqCMci0BHs0BLep0NmV6KUggiUNigAiRkLCq/LQhp1WZyPNthpaHI3YPVZsHit2rxXfr3Kg5AoNCnUIkmRAkgzI5MZDDgPIDla6ySUvQa4mglpr0Doa0TgbCHI07v93ExqnBRn+2VMNRhk1Jqg3QZ0J6kwy6vYLmwYDeJQyDCoDcYY4YoNj298bscGxxOhjiA2OxaQxCREjEHCChE51dTVms7nT11asWMGUKVPYuXMnPXv2PPZd/w4IoXNkXF4XJdYSiixFFFoKKbIUUWwtpsRags1t63KdQqYgVh9LgiGBBEMC8fp44g3xxOnjiDPEYVSfxO+3wwL1BVCXB/X5/n83FPi9NIertFLpIDQFwlIgNHn/kQKhSX5Ro+reCHSb00NhnY29dS3sq7Wxr67VL24a7Lg8XYspjVJOYpiOpHAdiWHBJIZpSQzXkRCqIz5Uh1btT/a0e33sszsosDspsDnY1+Zkn91Bod1J22HEklomI1GrJilIQ7JWTZJWTWKQimh5E2GeEnAWYrPvw27zf3S7D++J06ij0GoTUapi8HnDaWsLxmrV0Ngop7a2DYvFyuF+5Wg0GkL1JkxqA0a06F0a9DYVOqucYJ8moDcG/F1i3Wo3bVILFkc9DZYKLLYaWj0W2jzWDt4YAGQy1EEhKFSh+HxGvF49MnnIfiFj2l+RdFBMaKQ2tM4GgiwVaO31BDnq0bbVo3U0oHZZ26cOOYLk1ITIqAzxURMCNSEyavd/bDCCVyFDLpMTExzjf08Y4ju9N0wa02G/xwKBwM9xFzrbtm2jX79+yLtIqp0+fTo9evTgpZdeOrYd/04IoXMQl9dFkaWIfc372Nu8l33N+yi0FFLWUoa3i6ofuUxOnD6ORGMiSYYk/0djEomGRGL0MajkqoDrThhtzVC3B2pz/R/r9vjFTUtV12uUQRCWBuH7j7A0CEv1/1sf1WV/lUC0Oj3k17Swt6aV/JoWCmpb2VvbSkVz1xVKaoWcpHAdKeZgUszBJJuDSQ4PJtmsI8oQhPyQ8mmb10uBzUmezdF+FNgdlDlcXU5/UslkJGnVpGo1pOg0pGr9R5JWRaivGoe9AJutAJttr/+w78Pn6zpJWq2ORKdLQadNRqGIwekMoaUliIYGObW1zdTX19PW1vX9ajQawkPDCNGaMMl1GN1a9HYVwU1yVDY65Mb86kbw6iQcchtWZwMN1gpq6gtpcTbg9AW6nowgfRhKTRhgwuUyIEmm/YLGhEzWsSJII3cR7G4kqLmcIEs5Onsd2rY6tI56lId4J11BCmrDlZSY3FSGSlSHyqgOk1EdCi1a/DPMkBGrjyXJmNT+fjjw3ojVx57894VA8CfkuAudI1FaWorZbP7DJSX/FYWOJElU2irJa8yjoKmAguYCCpoKKLGWdClo9Co9qaZUkk3JpJhSSDGlkGxMJsGQgFqhPsl3AHjdfs9MTQ7U7IKa3X5xYy3veo0hBsw9wNwTzBlgTofwHv6cmaOsivN4fRQ32Nhd1UJetZW86hb2VLdQ3tT1A96sV5MWoSctUk9ahJ7UiGDSzHriQrUoftULxidJFLU5yW11sNvWRm6rg1xbGyVtXQuaMJWCHrog0nUa0nVBpO3/mBikxudporV1D622PP/H1jxstr34AgoEkMnU6HTJBAeno9OlolEn4nCYaG4Ooq6uhZqaGmpra7Hb7V3eb0hICBHhZkJ1JkJkeozOIAwtSpS1HqTWrvOLZEYlXp0POy00t9VS21hMRXUedlfg0JhSrUFrikKlNuPzheBo0+Pz7Rc0so6CQi6TCFa2EeyoQ9tQTFBDMcH2GnT2GpS/akPQEq6lMlzOvhAH5WESFeEyqsL8Sb8HxK9OqSPFlNLhvZFsTCbRmIhGIVpECAQnku4+v49b+9vExMTjdSrBccTtdbO3eS97GveQ25jbLm5a3IErggxqAz1CepAakkp6SDppIWmkmlKJ0Eb8fnkBDgtU74LqHVC1A2p2+r003i6qdIzxEJEBkb0hotf+o6e/e+8xYHN6yK2yklNpJafSQm5VC/k1LTi7CDlFGDRkRBlIj9TTM8pAzyg96ZF6QnSBBWGb10euxc7O1jZy9h+5Ngf2Lkqzw1VKMoKD6BUcRM/gIHrq/B/NaiWS5KOtrYSW1s20WHZjrdjNupZcXK7agOeSy9UE63oQHHzgSEMmi6WxUUFNTR17Squprq6msXFXlyGnsLAwIiIiiAg1EyrXE+LWobcokGqceHLth+Qge/BPJfKjCNUgGWXYFTaa22qoaSyirDwHW1FTwOuogrTow2JRayOQpFAcdgPONiPIDLg9MtwHtJMMlCowaJwYXBVoG4oIqshF11qJ1lGP/JC8K0kmwx6hpyhJS34IFIa6KDfLqAwDp9rdfsJglZ70kHQmhqSRZkojPSSd1JBUonRRIl9GIDjFOWqhU15eTnx8fIfX8vLyyMjIOG6bEhwbLq+L/KZ8cupz2N24m9yGXAqaC/D4Ov/1rJQrSTOl0TO0Jz1Ce/iPkB5E6iJ/31/cbU1QtR0qt0Fltv/fTUWBbTVGiMryH5GZ/o8RvfwdfY+RFoebnEoruyos7Ci3sKvSQlG9jUDPeJ1aQUa0gV7RRnpFG+gZZSAj2kBYcNceLpvXS05LG9tb2tjRamdnSxsFdgeBetlp5TIygrX01gfROziITL2WjOAgItR+L4Uk+bDbC2lpyaGxfhclLbtoadmN1xu4GkyrTUSv74Ve3xt9cE/0+gw8nlCqqmqorKykqqqKqqodtLSsCbg+ODiYqKgooqKiiDCFEyrpMbaokWocuEta8W534hcz1g5dbuQ6JcooHZ5gLy3eRmqtpZRX5VK7cx8ed2exKpPLMUXFEWyKRa4y43aF0Nqkx+3S0dYm49ComEwO+mAwylvQt5QTVJ6DtnI32ra6DoIGwGPUUZcSQaHZy06jlaJwL+VmcKoPnlAhU5FiSuH0/e+LnqE96RHSg+jgaCFoBII/KEcdujIajVit1vbPLRYL6enp/N///R/nnXfecd/gieaPGrry+rwUWYrYWb+TnfU72VW/q0tRY1AbyAzLJCMsg15hvegZ2pNUUyoqxe+cJ+Bu83toKrYcPLoSNaYEiO4HMf0gqg9E94GQpKPKn/k1To+X3KoWtpc1+4/yZgq7EDVRRg1ZsSayYo30jvEfSWG6DvkznW7PJ5Fra2Or1c42q53tLXbybI6ARdZmlZK+Bi199Fqy9h+pOg0K2YFGdBJOZxUW63ZarDv8H1tyAooauVyDPjgDvSETgz4TvaEX+uBeuN1yKisrKS8vp7KyksrKSlq6GFFiNpuJjo4mOjqayPBIwrzBaBp8uMpbcZW14G0OXFGnDA9CFavHo/dicddT1bCXipJcaksL8bo7J32rtVrC41PQGWNBGYHTHoK1QYsrQERNrpARGgJGLOibiggqykZburNTyAnAFWumNj6YPLOLzcYG9kV4O4ScwB+OzQjLoHdYbzLCMsgIzSAtJO33CcUKBIKj5oSFrn6ti+677z569er1hxQ5fySaHE3sqNvB9rrtbK/bTk5DTsCKpxBNCFnhWWSGZ5IZnknv8N7EBsf+/n+NSpJfxJRtgvJNUL7RH44KlBMUmgwxAyB2gP9jTH//DKbfdHmJSouDrSVNbC1tIru0md2VVlwBwkNxIVr6xBnpFx9CVqyRrFgTEYYj51vUON1sstjYbLWx1WpnZ4s9YMVTlFpJf4OO/gYdfQ1a+hl0RKmVHf6PvN42rM2bsFqzsVi3YbFsCxh+ksuDMBgyMRj6YDT0wWDog06XBsipra2lvLycsk2lVFSso76+vtN6mUxGREQEMTExxMbGEhMTQ7jCCJUOXKUtuDZbcdfU4JDg13JCGaFFHadHFqHG4q2nqnEvFftyqV6Wj9PW+WdTowsmMiUNfXgiCmUUjrZQmqqVNNW7aPrV1hQqOWFmJSFyK/rmQrSFW1DnbULu+9XPi0yGJzGGukQDeZEe1htq2R3ehkPTDDS3mxnVJkaEZ5IVnkXv8N5khmUSZ4gTQx8Fgr8ARy10Dv1lPGfOHJYsWcKGDRuO66b+6kiSRLG1mOzabLbWbGVb3TZKrCWd7LRKLZnhmfQz9yPLnEUfc59TQ9SAv9le1XYoWw+l66Fsg3/o5K8JjoT4IRA3COIG+4XNbxQ14E8Wzq1qYXNJI5uLm9hc0kiNtbMXIlSnYkBCCP0TQugfH0LfeBNm/ZFFjU+S2GNzsMFiY9P+o8zROQxjVMoZaAhmoFHHAIOOAUYd0ZrOnjSns45my2Ysli1YmrfQ0robSeronZPJlOj1GRgN/TAa+2Ew9iNYl45crsTpdFJRUcGePSWUlW2gvLwcl6vzfkJDQ4mLi2s/osIjocaJs8SCK7cF1w8VNNk7/6wpTBrUiQZU8XrcwW5qLMVU7NtOxabdNFSU8Ws3mFKlJjIlDXNiGmpdHB63maYaJXVlrdRVHrD1AS5kMgiL0RGmd2Gyl6Mr2YZyy0po6Zx8LIuJwpoexb4YGetDGlhjqMKprgMO/mwFKbQMCs+kj7kPfc19yTJnEa+PPzXeFwKB4KRzzMnI8+fP57HHHmPJkiWMHz+e/Pz8oz7H+++/z0svvURTUxMGg4E777yTm2++uf3rTqeTxx9/nK+++gq73c6QIUP4z3/+Q1xcXLtNRUUFs2bNYsOGDbjdbi6++GKeffZZNH+goZhen5f8pnw212xmc/VmttVtC9g5OMWUQv+I/vSP6E9fc1/SQtJQyo9bPvlvw2X3e2lK1vqP8k2d5zgp1H7vTPzQg4cp/jeFnw7gcHvZXtbMxqJGNhY3sqWkCbur41//CrmMzBgjgxJDGJQUyoCEEBLDdN16ALp9Ettb7KxrbmV9s41N1lasv0pGlgO99UEMNgYz2BjMIKOONJ0G+a/OL0kSDkcZzc2baGreRHPzRtraOosLtToSk2kQJtMATMaBGAxZKBT+URZ2u53S0lJKSpZRUlJCVVVVJ2+rWq0mLi6OhIQE4uPjiYuLQ6vQ4Cyx4iqy4NzWRF15KZ0ShJRy1Al61IlG1PF6bEor5aW5lOf+TOWqHFqbOv9shkTFENOzF2FxacgVMbRa9FTvayF/y4GqrIOxKK1BRVRiMKEKC4b6PQTlrMazagd4fiXstFqkXmlUpxjZHuVgmb6UYmUD0HCoFUnGJPqZ+/nfG5H9SQ9JP3XeFwKB4HfnmEJX//73v1myZAkrV64kLi7usD0zuuLjjz/m8ccfZ8mSJWRlZbFnzx4mTpyI0Whk5syZANxyyy3s3buXzZs3o9fruf/++znzzDPJzs5GoVDgcrmYPHkyZ555JnPmzKG1tZUZM2Zw991389Zbbx31nk4WPslHflM+G6o2sKl6E1trtnaqglLL1fSN6MugyEEMiBxA/4j+p1YjMXeb30tTtAqKV/nza36dH6QNg8QR/iNhhF/kdLPB3pFweXxsK2tm7b561u1rILusuVPjPUOQksFJoQxNDmNwUij940PaG+wd8fb2C5s1Ta2sa25lo9XWqQoqWCFniDGYoaZghpn8XhuDMvD529rKaGraQFPzOpqaNuB0/rqvjwy9vhcm02BCTIMwmQYTFBTXLsLa2trIzy+muNh/1NTUdLqGyWQiMTGRhIQEEhMTiYyMBLcPZ5EV514LrT/m01TRyq/r0+UGFZpkE+pkI+oEA1ZfI2W5OynfvZPyr3fR1mLtaK9QEpWWTlxGJmGx6UhSFHUVPirzmyja5QBs+w8/YbHBRCXqCPPVYajYAdkrcS3Y0+4FOvBTo4yKwtunB6UpwWwwW/hJlU+TZ0+Ha6vkKrLCsxgYNZCBEQMZEDmA0KDQgN9zgUAggG4kI0+fPr3DX7wLFixAp9MxdepUFAr/L/VFixYxceLEdpv58+cf8cK33norY8aM4bLLLmt/7Z577qGoqIh58+ZRWlpKSkoKGzduZPDgwQC4XC5iY2N5//33mTFjBp988gl33nknVVVVqNX+BMItW7YwatQoKioqAnZx/jUnIxlZkiRKW0pZV7mOjdUb2Vi9EYuzo1s+WBXMwMiBDIkawuCowWSGZ55aSZFej78KqvAX/1G+sXN5tyEWkkdD0v7D3OO4eGsAfD6J3VVWVhXUs3ZfPZuKG3G4OwoPs17N8JRwhqeGMTQ5jIwow2GThQ9FkiRybQ5WNbWwqqmV9c2ttP5K2ISpFIww6RkREszwED1ZwVqUXZzf5WqgqWkdjY1raGxai8PRsb+PTKbCaOxLiGkoISFDMZkGo1IZD1nvorS0lKKiIoqKigJ6bMxmM0lJSSQlJZGYmEhISAiSx4er1IpjbzPOfRZcZS3wqzwhRXgQmmQTmhQTmhQjrR4Lpbu2U5azg9Jd27FbmjvYKzUaYnv2JqF3HyJSMvC6I6jaZ6NsTyOW2o5/5MjkMiISDcSkGginDn3JVjyb1uDIyQFvRw+bOikJaUAmRala1pib+Nm9i0Znx9JyrVLLgIgBDIn2vy/6mPuI/jQCgQA4jsnIl19+eYfPFy9ejE6nIz4+nvHjx+Pz+Vi+fHm7F6a7vPnmm51e27lzJ7GxsQD88ssvREVFtYsc8Lvip0yZwuLFi5kxYwbLly9n6tSp7SIHYPDgwYSHh7Ns2TIuueSSo9rT8cTitLC+aj3rKtexrnIdlbbKDl/XKXUMjhrMsOhhDI0eSkZYxqnnbm8sgn3LYN/Pfs/Nr8QZhhhIGQfJYyF5jD+J+DjmQVQ2t7GqoG6/uGmg0dZRWIUHqxmZFs7ItHBGpIaTag4+qjyMWqebFU0trGhsYUVTC3Wujh6pUKWCUaF6RoX4j4zgoE5hqAP4fE6am7fQ2LiKhsbVtLbu7vB1mUyJ0diP0JDhhIaOxGQaiEKhO2S9j+rqavbt28e+ffsoKSnB+ythYDabSU5OJjk5maSkJAwGA5Ik4alrw7GrifqCcpyFFqRfCUBFWBCaVBOatBA0KSa8ai9lOTso3r6M0k+yaarq+LOpVGuI65VJQmZfYnv1ASKoyLNSltvIlqVNIB0UIzIZRCQZiesZQmSwHX3JFlwb1mCfuwXJ4eDQmjBVUiLqoYMp62FibaSFn9u2Udbyk/+L+w2DFEEMihrE0OihDIseRu/w3qKLsEAg+E0c8cn6a7Fw/fXXs337dq6//nra2tp44403uPvuu3+TqHC73cyaNYt169axbt06ACorK9tFz6HExcWRl5fXbtOnT5+ANhUVFQGv5XQ6cToPJqUeWip/vJAkifPnn0+t/WCVjFKuZGDkQIZHD2d4zHCyzFmn3i9wdxsUr4a9S/1Hw96OXw8yQcp4SB0PKRP8IxKOo7BxerxsLm5iRX4dv+TVkl/TsXRar1EyIjWc0enhjE430yNSf1TCxuOT2Gy1sbzByrJGKzmtHXOItHI5I0KCGRtqYGyoniy9tkthA9DWVkp9wy80NKykqWl9py7Den1vwkJHERo2ihDTUJTK4F+tb2Pfvn0UFBSwd+9ebL+qVDIYDKSmppKamkpKSkr7Xyw+pwfn3maa8qpx5DXhtXRMspbrVWjSQghKD0GTFoIiVEN9aTE521ZSNH8zlXm5+A4RUTK5nJj0DBL7DiCxTz8M4cmU51kpzWlg+4o63I7qDucPjQkmoVcosUlBmOpycW34Fturq3HX1HCoP0YRYSZ4xEis/ZPZFOdguXMH22sX45E8sP+toZQp6RfRjxExIxgeM5y+5r6/f9sDgUDwp+KYXAgxMTF8//333HPPPUyYMIGzzjrrmDdQUlLCJZdcgtVqZfXq1e3CRaVSBZyrdeiDrTs2v2b27Nk8+eSTx7zf7iCTyRgePZzcxlxGxIxgZOxIhkQNQac6BcdjNJdBwQ+Q/yMUreiYQCxX+nNr0k7zHzEDQN69HJfuUtvi4Jc9dSzbU8OqgvoOCcRyGfRPCGFsjwjG9TDTPyEEleLoyoEb3R6WNVj5qcHKisYWLJ6OXpJ+ei0TwgyMDzMwxBSM5jCjIHw+N82WzTTU/0x9wy/Y7fs6fF2tjiAsbAzhYeMICxuFWt0xdCpJEnV1deTl5ZGfn095eXmHcJRKpSI5OZm0tDTS0tIwm83tP8vu+jZaVlXgyGvEWWTpmECslKFJNhHUMxRNj1BU0To8Lielu3ZQ+NVXFGZvorWxocNeQqJjSOo3iOR+A4nr3Yemag8lOxtY83U9DRWbOtgG6VUk9A4jITOMKF0L0pY1tC78BfuWLdQdKpg0GnRDh6IeOYyCdB3LlPmsqlhNbdtiKD14vmRjMqNiRzEydiRDo4cSrOooAAUCgeB4csyxEplMxksvvcRNN91ETk4Obrcblero/hLbsmULZ555JldeeSVPP/10h0qp+Ph4KisrO62pqqpqr7rqjs2vefDBB5k1a1b751arlYSEhKPad3d4cvSTp57HBvwJoFXbYM8iyFvknxN1KMZ46DEJ0if7w1JBxzdvSZIk8mta+TGnmqW5NWwv7xgOizBoGN8zgvE9IxiTbib0MF2Gu2Kv3cEP9VZ+qrew0WLr0KAvVKngtHAjE/eLmwNdhrvC42mhvuEX6uuX0dDwCx7PwaRxmUyByTSE8PDxhIeNQ6/v1Ulke71eSkpKyMvLIy8vj+bm5o73GxFBeno6PXr0IDExEaXS/5aUfBKuYittuY04chvw1HX0FinCg9BmhKHJCEWTYkKuVmBrbmLP5lXs+98GSndu79B1WKnWkNinH8n9B5EyYAi6kAjKchsp3l7PirnZOGwHm/nJZBCVYiKpTxgJGSHoGwpoXb6AlseXU1Na2mEf6pQU9OPG4h7al3WRFpbVrmJT1du4ig9eW6vUMjx6OGPixjAqbhQJhuP/fhMIBIKuOOrOyAaDoUM3Va/Xy+jRoxk0aNBRVTqVlJQwbNgw3njjDS666KJOX6+rqyMuLo7NmzfTr1+/9mslJSXx1ltvMWPGDL777juuv/56Kisr2x8Qe/bsoX///qdUMvLvjtcDJashdwHkLe44+FImh/hh0HOq/4jMPK7hKACvT2JLSRM/5lTz4+4aShs7DoLsH29iYq8oTu8dSVas8aj7nUiSxLaWNhbXNbO43kKBvWMoJzM4iClmE5PCjQw06tq7DXeF01lHXf1P1NX+QFPz+g79bFSqMMzhEwgPn0BY2NgOCcQHcLlc7Nu3j9zcXPLz83E4DnrJFAoFKSkpZGRk0KNHD0JCQg7eh8eHY28zbbvqceQ24jtEfCCXoUk1EdQrjKBeYajM/jLzpqoK9m5az95N66ks2NOhn43BHEHa4GGkDhpGQmZf3C4o2l5P4bY6ynOb8B5SpabRKUnMCiepTzgJ6cF4t22kZekyWn/+Ge8h4kymUqEbNgz9+PE0DU7jZ99ufi79mR31Ozp8D+L0cYyPH8/4+PEMiR5yaiXWCwSCPwUnrDPy9OnTO3yuUCh45513mDt37lGd5+abb+aWW24JKHLA/5fu1VdfzaxZs5g3bx7BwcE8/PDDhISEMG3aNADOOussIiMjefTRR3nqqadobW3ltttu4+qrr+6WyPlT43H5q6Nyv/N7b9oO6X2iCob0iZBxFvSYAsHhx//yXh8bixpZtKuKJbtqqG89KD7USjlj081MzoxiYq9IIo1HX3LukyQ2W2x8X9fMojoLFc6DokAlkzE6RM8Us5HJZhMJQUd+yDocldTWLqG2bgkWy1YOrcHW6dKIME/CHHE6JuMAZLLO4Tun00l+fj67d++moKAAzyE9YXQ6HRkZGfTs2ZPU1NQOnkvJ7cWR14R9Zz2OPY1IzkNCQUFKtL1CCeodTlBGKPIg/9u1obyU/K/WkL9hDfWlxR32EZ3ek/QhI0gdPAxzQhJ2i4t92XUseHMXlfnNHfr6Gc1BpPSPIKW/magYNfY1q2j5/D1Kf1mBdMhUcoXJhH7CeIInTqQ6K4oF9Wv5qWQeezd3zOHqZ+7HaYmncVrCaaSaUkWDPoFAcEpw1B6d43ZhmYzIyMiA4a7ycr/Hwel08sADD/Dll1/i9XoZNmwYb775ZoehouXl5dx6661s2rQJuVzORRdddFQNA/9UHh2vGwpXQM48v/fm0CopXThkTIPe0/0Jxcepn02Hy/skNhQ18P32Kn7Iqe5QJWUMUnJ67yimZkUxtkcEwZqjj5r6JIlNFhvza5tZWGeh2nVQ3OgUck4PMzItwsTp4UaMXfSzORSHo4rauiXU1izEYs3u8DWjsT+REVOJiJiCTpcScL3T6SQvL4+cnBz27t3boUoqJCSEXr160bt3bxISEjrkkrWLmx11fnHjOuhZkRvUaLPC0WaFo0k1Idufk9RQUUbe2pXkrVtNY0XZQXuFgoSsfqQPGUHakOEYws3YLE4Ks+vYu6WWyr3NHfrmmBP0pA2MIGVABCEhcmwrV2FdvJjWFSuQDvE8KWNiMEyehOH0SVSlhbCk7Ed+KP6BYmvxQRu5kuHRw5mYOJEJCROI1EUe8XsuEAgEx4vuPr9/N6FzqvCHFzo+H5SsgV1fwe75HT03+mjofTb0nuHva6M4/uXrkiSxtbSZ77dXsnBnFXUtBz03oToVU7OiOaNPNKPSzKiVRz9XSJIkclrbmFfTzHe1TR08NwaFnKlmE9MjQxgfaiCoG4nKLlcjtbWLqa6Zj8Wy+ZCvyAgxDSEy8kwiIiYTFNS54g/A4/FQUFDArl27yMvL6+C5CQsLIysri8zMTKKjO067lrw+nHubsW+voy2noYPnRhGiQdvXjLavGXW8Adn+3jyW2hr2rF1J3tqV1JUcHHYqVyhJ7j+QHsNHkzZkOFq9Aafdzb7sOvI31lCZ39TBcxOVYiR9cCSpAyIwGBW0rl6NdeEiWn7+uYPnRpWYiHHKZAxTplCXFMKSkiUsLlrM3uaDnhu1XM2ouFFMSZrC+ITxGNV/wPeMQCD4U3BcQ1eXXHIJ5513HpdeeikLFixgzZo1zJ49u5OdzWbjiiuuYN68ece+c0H3qMmBHZ/Dzq875twER0DmOZB1PiSOhMNUEf0WCuta+XZbJd9mV3TIuTFpVZzZJ5qz+8UyIjUM5VFWSR2gzOHi6+pGvq5p6pBzo1fIOcNsYkZkCOPDDIetkjqA12unrm4p1TXzaWxc1SHnxmQaQlTkNCIjz0CjiQq43ufzUVpayvbt29m9e3eH9gShoaH06dOHrKwsoqKiOoobScJV1oI9u5a2HXX4bAevqwjRoO1nRtc3AlX8wTL5ttYW8tetZveqn6nMO9iLR65QkNx/ED1HjCFtyHCCgvV43F6KdzRQsKmY4l31+DwH1c0BcZM2KBJ9qIa27G1Y3vyA6kWL8VoOevpUsbEYp52J4cwzcaTG8kPJDywo/Dfbs7e32yjlSsbEjmFqylQmxE9Ar9Yf8XsuEAgEpwrdEjqFhYW8/PLLGAwGvvvuO7xeb4fKJYDExERCQ0Nxu91dnEXwm2mthR1fwPbPOlZLaUyQOQP6XghJY06I5wag2e7i++2VfLW1gu1lze2v69QKpmZFM71/DGPSI47JcwNg9XhZUNvMlzWNrGs+2FNGI5cxKdzI+VGhnB5m7JbnRpJ8NDdvoqp6HrW1i/F6D57PoM8iKnoGUZFnERQU0+U56uvr2b59Ozt27MByiDgwGAz06dOHPn36EBvbeYiqp9GBPbsWe3YtnvqD1VLyYBXavmZ0AyJQJxrbPTdej5vC7M3sXrGcouxNeA94iWQyEjL70mv0OHoMG4XWYESSJGqKrOxZn8fezTU47Yd4lGKD6Tksih5DojCatbjKy7HMeZea+fNxlx0MdykizBjPPBPTWWehyOrNyoqVfLfvbVZvWe3vcQPIZXKGRw/nzJQzmZg48dQaPyIQCARHQbefiAsXLqSgoIAVK1Zw9dVXU1dXx+LFixk8eDAZGRnMnTuXkJAQ7rvvvhO5378eHhfkL4Ftn0LBjyDtD3ko1P5E4n6X+D+egJwb8CcVryqo56st5fy0uwbX/rEICrmMcT3MnDswjsmZUejUxyaufJLE2uZW5lY1srCumbb94wpkwOgQPRdGh3JWREiXM6R+TVtbOVVVX1NVPa/D2IWgoASio2cQHTWD4OD0Ltc7nU5ycnLIzs6m7BBxoFarycrKol+/fiQlJXXq3yS5vbTtasC2uRrnvoOiSKaSE5QVTvDASDTpocgUB0VRXUkRu35ZSu7qX2izHlwTkZhM73ET6TV6HIYwf1K9rdnJ5sXF5K2vprnmoAdNH6qhx9Aoeg6LJjwuGMlux/rDEkq++Qb7poP9cOQ6HYbJkzHOmE7w8OHssRTw4b7vWPjVbTQ7m9vteof15uzUszkz5UwidBHd+ZYLBALBKU23n047duzg3nvv5f3332fDhg2cfvrpZGdnM2zYMMaPH88XX3xBfX09p59++onc71+HunzY+pHfe2M/pNlb3BAY8DfIOg90YSfs8mWNdj7fVMYXm8uoPSTvpneMkQsHxzOjfywRhmOfOVTpcPF5dSNzqxopcRxMWu6h03BxdBjnR4US141qKfCPX6irW0pl1Zc0Nq7mQPatQqEnKnIa0THnE2IajEwW2BMkSRJlZWVs2bKF3bt3t3slZTIZ6enp9O/fn4yMjICJ866KVmybqrFvq0VyHMy70aSa0A2KQts3HPkhiddOu509a35h5/IfqSk8mPsSHBJK77GnkTn2NCKS/MnPXq+Pwm115K6ppGRXQ3vejVItJ3VgBL1GxBCXEYpMBo6dO6l+50usCxfhO5B3I5MRPHIkpvPOxTBpEjaFhwWFC/l68SvsaTw4LDNCG8H0tOnMSJtBWkhat77nAoFA8Eeh20Ln0ksvZfLkyQwbNowNGzZ0+rrP5+OBBx44rpv7y+F2wO5vYctHULr24Ov6aOh/qV/gRGScsMu7PD6W5tbw2cZSVhXUt78eqlNxzoA4LhoST1bssYcwvJLEz40tfFxZz0/11vZGfgaFnPOiQrk0JoyBBl23y5Lt9iIqKudSVTUPt/tgEnZo6ChiYy4iImIyCoW2y/VtbW1s376dLVu2UFdX1/56eHg4AwcOpH///hgMhk7rfE4v9u212DZU4644OKZCEaIheEgUukFRKMMOetgkSaJmXwHbly5hz9oVePbn+MgVStIGDyNrwiRSBgxGvn9IrrW+jd2rK8ldW4XdelAExqSb6D0qhrRBkaiDlHitVpo//ZTmL7/EuX8sCvhnSoWcdz6mc2agjI5me912vtryND8U/4DD66+sUslVTEycyDlp5zAyduSpN2dNIBAIjhNH/O32zDPP0NDQQG1tLW+++SaXXXYZo0eP7mRnMpm47rrrTsgm//Q0FsLm9yF7zsGqKZkcekyFQVf6Q1MnKO8GoMrSxmcbSvlsU1mHqqmxPcxcOjSRyZlRx5x3A/7hmXOqGviksqFD1dQIUzCXx4YzLSIEXTeTln0+N/X1y6io+JTGpjXtr2s00cTEXEBszIVotYmHPUd5eTmbNm0iJyenvWpKpVKRlZXFoEGDSEhICCi2XFU2bOsrsW+rO1g1pZCh7WMmeGgUmtSQ9rwbALfTQe7qFWz/cRG1xQfHRYTFxtP39KlkjpuIzmjaf18SxTvq2bWygpKchvaScK1BRa8RMfQeHUNotH9UgiM3l6pPP8OyYAFSmz8HSKZWY5g6lZCLLkQ3dChtnja+KVzA55s+J78pv/3a6SHpXNDjAs5OPZuQoJBufc8FAoHgj8wRn549e/ZEr9fz6KOP8s9//pPVq1ezbNkyMjJOnGfhL4HP58+52fh//gnhBzAlwKC/w8CZYAxc4nw8kCSJNXsb+Hh9MUtza/Huz42JMGi4eEg8lwxJJDH82GdzSZLEVqud9yvqmV/bjHt/3CVEqeCS6DAujw2nR3D384qcrnoqKz6jouIznK6a/a/KCA+fQFzcZZjDJwRs5HcAt9tNTk4OGzdu7DA2JCoqisGDB9OvXz+CgjrvR/L6aMtpoHVdJa6igwNglWYtwcOi0Q2OQhHcMaTVWFnB9p8WkbNiKc79gzoVKhUZI8bQd9IZxGVktgspR6ub3Wsq2bWigpbGg31s4nuF0mdcHMn9zSgUciSXC8v339M051Patm1rt1OnpxF68SWYZkxHERJCoaWQuRtnM3/ffGxu/7WDFEFMTZ7KhT0vpH9Ef9HITyAQ/KU4otC58MILOffcc7nzzjvJzc3lqquu4rzzzuPWW2/tYNfS0sLMmTOZM2fOCdvsnwKHFbbNgQ3vQNOB3igySJ8EQ6+DHpOP++DMQ2lzefkmu4IP1xZ1mA4+IjWMK0YkMyUr6qgHZx6Ky+fj29pm3i2vY0fLwYqjwUYdV8WZOTsiBO1RnN9q3UFZ+UfU1CxCkvxhHJUqnLjYi4mNvRStNv4I661s2rSJLVu2YN+fu6JQKOjTpw9Dhw4lLi4u4IPf2+rCtqGa1g1V+A6Ej+SgzTITPCLG38zvV6XkJTuy2broO4q2bWl/PSQqhv6TzyTrtMlo9QfDYPXlrez8uYy8jTV43f4gniZYSe+RMWSNjSMkyi8yPfX11H3+OU1z5+Kt2x9OVKkwTp5E6GWXoR0yBAmJNRVr+GTTJ6ytPBjyTDImcUnGJcxImyGqpgQCwV+WbsVDVq1axZVXXskNN9zAv//9bx588EHg4JRwmUyGXq8nPz+flStXMm7cuBO34z8qjUWw4W3I/gRc+wVGkAkGXgFDr4Ww1BN6+SpLGx+tLWHuplKa7f7wkU6t4IJB8VwxMomeUZ1zUY6GBpeH/1XW80FFPbUufzhII5dxXmQoV8eb6W/ovndIkrzU1S2ltOzd/eMY/BiNA0mIv5LIyDOQyw+fqFxRUcH69evJycnB5/MLCZPJxJAhQxg0aBDBwYEnZrtrbLSuqcS2tRb2z4KS61UED4tGPzwGhaljArbb6SB31S9sXTyfhvL9Ay9lMlIHDmHAlLNI7j8I2f4KLcknUZLTwLalZVTkNbWfw5ygp99p8fQYEoVS7Re5jj17aPzgQ6yLFiHtT45WRkYSetmlhFx4IcqICOxuO5/nfc6c3DntHYtlyJiQMIFLe13KiJgRyLtIwBYIBIK/CkfsjGyz2ejfvz9z587F7XZz9dVXM3PmTP7973/jcDhQqVQolUp69erFXXfdxYIFC/j0009P1v5/Mye8M3L5Flj7GuTOB2l/+q05A4bf6E8wVgd+4B4vcqus/HdlIfO3V+LZH56KD9Vy1ahkLh6agDHot01Y32d38HZZHV9WN+LYf/4YjYpr4sz8LSac8KMoO/d4bFRVfUVZ2Ye0OfyiQSZTERV1Fgnxf8do7HfY9T6fj4KCAtasWUPpIVO2ExMTGTFiBBkZGSgUnb1lkiTh3NdMy8oKnPkHBYgqXo9hdBzavmZkv8pRslstbPthAdk/LMTR4g9pqYK09D1tMgPPmE5I9MH+PB6Xl7wN1WxfVkZTtd+rJJPLSBsYQb/T4olO83uHJEnCtmYtje+/j23tQc+Mtn9/Qq+4AuPUKchUKurb6vlsz2d8nvc5lv1jPvQqPef1OI/Lel0mpoMLBIK/BMetM/Lu3bu56qqrGDJkCAAjR47EZrN1mGB+gJaWFm699VZsNluXfzH/JfD5/L1v1r7esXoq7XQYeSukTTzuE8IPRZIk1u1r4O2VhazMP1hNNCwljGvHpDCpdxQK+W+7/laLjTfLallUZ2kfpdTfoOXGhEimR4SgOorzu1wNlJX/j/Lyj/F4/A9upTKE+Li/ER9/JRrN4fu5eDwedu7cydq1a9urp+RyOX369GHEiBHExgbOdZJ8Em276mlZUX6wekoG2sxw9GPjUCd1nqTeXF3F5oXfkvPLUjwuf+K2MSKKQWdOp89pk9HoDv7cO+1udq6oYMfyMtpa/F4ZdZCCzLFx9DstHsP+yizJ7cayeDEN771/sHpKocA4dQphV12Ftp9f4BVbivkw50O+3/c9Lp8/nJZgSODy3pdzTvo5BKv+wu85gUAg6IIjCp2hQ4cydOjQ9s8feeSRLieVGwwG3n777b+2yAG/52bJP6C5FOQq6HuRX+BE9zmhl/X5JJbm1vDmL/vaOxfLZXBmnxiuH5fKgISQ33R+SZL4pbGF10prOnQunhJu5JbESIabgo8q0bWtrYLSsneprPwCn8+fiKvVJpGYcA0xMeejUBw+3OVyudiyZQtr165tF94ajYYhQ4YwfPjwLhW+5PFh21JDy8pyvA3+68pUcnRDojCMiUMZ3rkkva60mA3ffEH+utVI+z1zUanpDJ1xAT2GjWovDQewWZxsX1bGrpUVuPf31tGHaeg/MYHM0bGotf63nc/hoHnePBrfex93RYV/HzodoRddSOgVV6KOjwNgT+Me/rvjv/xU8hPSflnZz9yPq/pcxcSEiShOYE6XQCAQ/NERQz1PVOhq6/+gYS8Mv+mEVk+Bv3vxwp1VvPXzPvJq9j/wlXIuGZrAtWNSSAr/bcJTkiR+bLDycnEN21r8oReVTMb5UaHckhhJxlFUTwHY7cUUl/yH6upv2+dOGQx9SEq6iciIKYetngJwOBxs3LiR9evXtycYGwwGRowYweDBgwNWTwH4XF5sG6tpWVnenmAs1ykJHhmLflRsp+opgKq9eWz45gv2bT7YOyplwGCGTL+AhKy+HYRdS6ODrUtK2L22sn3uVFhsMIOmJpE+JBLF/iRsb6uN5rmf0fDhR3jr/QnGivBwwq68ktBLL0Fh8icOZ9dm898d/2VVxar2a4yPH8/Vfa5mUOQgUT0lEAj+0hzXoZ6CY2DQlSf8Eh6vj++2VfL68gKKG/wPfL1GyRUjk7h2TApm/bF3Lgb/eIYFdRZeKa5mt22/x0Uu44pYMzclRBDbzc7FB7DZCikueZPq6vmwv11gaOgokpNuIjR01BEf3G1tbaxfv57169e3D9YMDQ1lzJgx9O/fH6Uy8I+zz+nFtr6SllUV+Fr9ISSFUY1+XDzBw6KRqzsLq8r8XNZ++SklO7L9L8hk9BwxhuHnXkRkcsfEcWt9G1uWlLBnXRU+r1/gRKeaGHxGEkl9w9vvy9tqo2nOHBrff799sKYqNpawa68h5IILkO8XaFtrtvLW9rfYUOUXV3KZnKnJU7m2z7VkhIm2DgKBQHA0CKHzB8Tj9TF/eyWvL99LUb0/hBSqU3HN6BSuHJWMSfvbEowlSWJRvYXni6rZs1/gBCvkXBNn5oaECCLUR3d+u72IwqLXqKn5ngOd8MLDJ5CSfBsm08Ajrnc4HKxfv55169a1Cxyz2cy4cePIysoKmGAM+z0466toWVHWPjlcEarBMCGB4MFRnRKMAaoK8lj75RyKt/urvWRyOZljT2PoORcSHtcxydda38bmRcXsWV+NtD8ROy4jlKHTkonLCG2387a20vTJHBo/+KBd4KiTkwm/6UZMZ52FbP9oiV8LHKVcyTlp53BNn2tINB6+CaJAIBAIAiOEzh8In09i4c4qXv4pn8JDBM7141K5cmQyes1v+++UJImfGqw8X1TNzlZ/DxyDQs71CRFcHx9BqOrozt/WVk5R8RtUV89D2j+M1GyeREryrUesoAL/gM0DAsfh8AuuyMhIxo8fT+/evTsN1my/D7eP1o1VtPxShm9/ErAyPAjDxER0AyKQBejjU1O4lzVffEJR9mbAL3Cyxk9ixPkXY4qM7mDb2uRky5Jidq+ubPfgJGSGMWRaMrHpIe12PoeDpjmf0vDf/+Jtbgb8Asd86y0Yp01Dtl+g7arfxWtbX2Nd1Tr/XuVKzks/j+v6Xkes/sSGPQUCgeDPTreeXDNmzKC5uRmLxYLT6cTn86HT6YiLi2PQoEFcdtllZGZmnui9/mWRJIlf8up4/oc8dlf5S5mPp8ABWNPUwtOFVWy1+kNgwQo5N8RHcGNCBCFHKXCczlqKit+ksvJzJMkvNMzm00lNuRODIeuI6z0eD5s3b2blypXtOTgRERFMmDDh8ALHK2HfWoN1aQleiz8HRxEWhHFiIrqBkR0mhx+gsbKcNZ9/Qv761cB+D864iYw4/1JCojoKnLYWF1t+KGHXior2Jn/xvUIZPiOV6NSDDfkkl4vmr7+m/j9v46mtBQILnL1Ne3lj2xssK/V3xlbKlJzb41yu73u9EDgCgUBwnOjWE2zkyJFERkYSFhZGUFAQSqUSm81GaWkpv/zyC4MGDeKhhx7iscceO9H7/cuxubiR55bsYVOxv7+LQaPk+nGpXDMm5bgInF0tdp4urOLnRn8Ss1Yu59p4MzcnRB5VDxwAj6eFkpL/o7TsA3w+v0coLHQMqal3YzINOOJ6n8/Hjh07+Pnnn7HsD/GEhYVx2mmnkZWV1bXAkSQcOQ1YfijGU+e/rsKkwXD6/hBVAA+Otb6OdV99Rs6KpUg+H8hk9B4zgZEXXkZodEeR4XZ62b6slK0/lrZXUcWkmRg+I7VDiEry+bAuWkzdq6/iLisD/Dk45ttuwzRjOrL9OUSVrZW8ue1Nvt/3PRIScpmcs1PP5ub+NxNvOHynZ4FAIBAcHcel6mr16tWcddZZvPjii3+4wZ4nvGHgMVJY18pzS/bwQ45/rpNGKeeqUcncND6N0OCjSwIORJnDxezCKubV+AWUUgaXx5qZlRRFpObocnB8PiflFZ9SXPxW+xRxk3EgaWn3ERo6/IjrJUli7969/Pjjj+19cAwGAxMmTGDAgAFd5uAAOAstNC8uwl3mF2pynRLDxET0I2IC5uA47TY2fvslWxZ9h3d/x+G0IcMZfckVRCQmd7wvr4/da6rYtKCofYq4OUHPyHPTSMgM65A8bVu/gdrnn8eRkwOAwmzGfNNNhFx8EXK1///L4rTw7s53mZM7B7fPf+1JiZO4beBtpIWkHfH7JBAIBIKDdPf5fdzKyz/77DNuu+02ysrK0OmOfRjkyeZUEzr1rU5eXVrApxtL8fok5DK4ZGgid03qQZTx6Mq4A2H1eHmtpIb/ltfh3J9Ae25kCP9IiSFFd3RVWpIkUVu3hH17/93eyVinSyM97V7M5sndKn+urq7mxx9/pLCwEICgoCDGjh3LsGHDUKm6Flzu+jYsi4tw5DQAIFPL0Y+JwzAuHnlQZ0+U1+Nhx9LFrPvqM9r2dzKO792HsX/7O7E9e3e6r5JdDaz9em97J2OjOYjh56TSY3BUhwnlzoICal94kdYVKwCQBwcTfv11hF15JfL97wOX18XcPXP5v53/197JeHj0cO4afBd9zCe2t5JAIBD8WTlh5eWNjY088cQT3HfffSQkHKxCueyyy/j4449paGj4QwmdUwWnx8uHa4p5ffleWp3+CqFJvSN54MxepEf+tjlUAB6fxMdVDTxfVEWj2x9+GR2i5/H0WPodxRyqA1itOygoeIZmyyYA1OpIUlPuJCbmQuTyI/9YtbS0sGzZMrbtn8StUCgYNmwY48aNQ6vt3LDvAD67G+uyUlrXVYFPAhkED4vGOCkJhaGzp0uSJAq3bmTFx+/TVOVvyhcaG8/4y68mddCwTmKsoaKVNV8VUJbr93QF6VUMmZZMn7FxKFQHPUSepibqXnuN5s+/8HfCVioJveQSzLfcjDI8vP3ay8uW8+LmFylr8Yey0kPSuXvw3YyNGyv64AgEAsFJoFtCp6ioiLCwMEwmE2FhYYwYMYJJkyYxdepUbrvtNnr27AnAokWLTuhm/4xIksTS3FqeWribkv29cPrGmXhoWm9GpoUfl2usamzhkb0V5O0vFU/XaXgsLZbJ4Z1HHBwJp7OGvfuep7r6GwDk8iCSEm8gKen6I3YyBn+i8fr161m5ciUulz8clJWVxemnn05YWFiX6ySvhG1jFZYfS5Da/EIwKCMU07QUVFGBGyI2lJfxy//+214qrjWaGHXRTPpOnILiVz132lpcbJhfyO7VlUgSyJUy+p+WwOBpyWi0B20lt5umTz+l7s238Fn9niHD5MlEzLobTUpKu11BUwHPbXquvVQ8QhvBrQNu5Zz0c1B2QwgKBAKB4PjQrd+4l19+OevWrUOv1xMREYFCoaC5uZn33nuPAQMGtAsdwdFRUNPCPxfsZlWBvztuhEHDP87oxfkD45D/xllUAKVtTp7cV8nCuv2JvSoF9yZHc0Ws+ahmUQH4fC7Kyj6kqPgNvF5/aXt09Lmkpd5LUFDMEVb7BV1+fj4//PADjY3+PJ64uDjOOOOMDp7BQDgLm2meX4i72n9dZZSOkLNSCeoZGtDeYWtl3Vefse2HBfi8XhRKJYPOOpfh516M5lfeRp/XR86qSjbML8Rp9wuotEERjDwvHVNER89S66rV1DzzDK6iIgA0vXoR9eCDBA8f1m7T7GjmjW1v8GX+l/gkH2q5mr9n/Z3r+l6HTiU8nQKBQHCy6ZbQWbNmDS0tLVRXV2O1WlEoFJhMJhITEw+bKCoITKvTw2vLCnh/dREen4RaIee6sSncclr6camkavP6eKO0hjdLa3H4JBQyuCrWzH0p0UddKg7Q0LCK/IJ/Yrf782iMxoH07PkoJmP/bq5vYPHixezduxcAvV7PpEmT6NevX5eVVAAeixPLwkLadviFoEyrxDQlieBhMQFLxSVJYvfK5az45H3arH5xlzZkOOOvuLZTJRVA5d5mVs7Np6HcP9DTnKBn7MU9ie0R0sHOXVlJzexnafnpJwAUYWFE3HUnIRdc0F4q7pN8fFPwDa9sfYVmZzMAk5MmM2vwLFFJJRAIBL8j3X7qGQwGDIbfnivyV0aS/A3/nlqQS7XVH0aanBnFo2dlkhh+fP7aX95g5cH8ckoc/rDQ6BA9T/WIo7e+67yXrnA4qsgv+Bd1dT8AoFKF0yP9H0RHn4dM1rVAOYDb7WbNmjWsWrUKr9eLQqFgxIgRjBs3Do2m68RnySvRurYC60+lSC6vPw9neAzGyUkB51EB1JcWs/S9/1Cxx1/1FBYbz2lX3UBy/0GdbO1WF2u+LiB/w/6KNp2SEeekkjm2oyfN53LR+MGH1L/9NlJbGygUhF1+OebbbkVxyHshtyGXpzY8xY66HYA/D+eBYQ8wPObIFWcCgUAgOLGIZIGTRHG9jUe/29UepkoM0/HEjEwm9oo6Luevcrp4tKCCBfvDVDEaFf9Mj+PsCNNR5+H4fB7KKz6msPBlvF4bMpmC+PgrSU25E6Wye2J37969LFq0qD1MlZaWxrRp0wgPP3zekbPESvO3e3FX+cNU6iQjIeekoY7VB7R3OdpY++WnbF30HZLPh1KjYeQFlzH4rHNQKDuKIsknsXtNJeu+2ecPU8kgc0wsI85JRavvmMhs27iR6sefaA9TaYcMJvrRxwjKOBimbXW18nr268zNm4tP8qFT6rhlwC38rfffUMl/2xgOgUAgEBwfhNA5wbi9Pv5vZSGvLSvA6fGhVsq5eXwaN09II0j128N+Xknig4p6ZhdWYfP6UMjguvgI7kuORq88+vNbrTvYk/cILS1+z4jJOJBevZ5Gr+/eMMnW1laWLFnCrl27AH+Y6owzziArK+uwgsvX5sGyuAjbxmrA3w/HdGYKul+Vcx9K4dZNLH33LVoa/L13egwbxYS/X4fRHNnJtqGilV/m5FFd6BeC5gQ9E2b2Iiq5Y0mit7mZmuefx/L1PMDfDyfq/vswTp/eYf/LS5fz9IanqbX7Ox+fkXwG9w65l6jg4yNcBQKBQHB8OG5Cx+fzYbFYCA0NnCD6VyS7tIkH5+1kT7W/md2YdDNPnduHZHPgKqGjZY+tjVl7ytrHNgwx6nguI4GsYwhTeb129hW+RFnZR4APpdJIetr9xMZe0q0wlSRJbN++nR9++IG2tjZkMhnDhw9nwoQJBAUdvv9P2656mr7bh6/FH27TDY7CdGYyCn3gxoi25iZ+/vD/yFu3CgBTZBSnX3MzKQOHdLL1uL1sXlhM9o+l+HwSKo2C4TNS6TshDvkhHZMlScK6YCE1zz6Lt8HfmyfkkkuIvGcWikP6M9Taa3l247P8VOLP10kwJPDoiEcZGTvyiN8jgUAgEJx8jknofP/990ydOhW1+uCDaNu2bcyYMYPy8vLjtrk/Kg63l2cX7+GjdcVIkn8u1aNnZ3LewLjj0jvF6fPxakkNr5fU4pYk9Ao5j6bFckVsOPJjOH9j41r27Hm4velfdNQ5pPd4CI3a3M31jSxYsKC96V90dDQzZswgNvbw85q8LS6av9tL2y6/sFCatYSe3wPNIXOjDkWSJHJ+WcqKj9/DYWtFJpMz+OxzGXXh31AFEFPVhRaW/y+3velfSn8z4y7tiT60o627upqqxx/HtmIlAOr0NGKefBLd4MEdrv11wde8uPlFWt2tKGVKrupzFTf2u5Eg5W9v5CgQCASCE8MxCZ0bb7yRDRs2dCgLjo2NpXb/AMO/OmqFnJ0VFiQJzh8UxyNnZRJ2HMY2AGRb7dyZW0q+3Z/MPNVs5Nme8cRojv78Hk8LBXtnU1n5OQBBmlh69XqK8PDx3Vrv8/nYtGkTS5cuxe12o1QqmTBhAiNHjjxsNZ4kSdi31tL8fSGSwwNyGYbx8RgnJiJTBfYetTTU8+P/vU7xti0ARCanMeXG24lKTe9k63Z6Wf/dPnb8XA4S6Ixqxl3Wk7SBHUNakiRh+fprap59Dl9rKzKVCvMtNxN+7bXIDhHxla2VPL72cdZXrQegr7kvj498nIyw7oXzBAKBQPD7cUxCR6lU4vF4Orym1Wrxer3t1TV/ZeRyGc9d0Jdqi5MxPbrnFTkSTp+Pl4preKO0Bq8EZpWSZ3rGM/0Yko0BGhpWkrvnQZxOf05MXNzlpKfdh1IZOOn31zQ2NvLdd99RUlICQHJyMtOnTz9isrHX6qJpXgGOPf4kZVWcntALenSZbCxJErt++YlfPnoXV5sdhUrFqItmMuTs85AH+DmrLGhi2Ue5WOv9QrDXyGhGX9iDoF9Va7krKqh67HFsa9YAENS/H7FPP40m/aBw8kk+vsr/ihc3v4jdY0ej0HDHwDuY2XsmCvlf+2dcIBAI/igck9AJDw+nsbGRlEM6wTY0NBAcHPyXFzkHSI80HJfRDQA7W+zckVtK7v7OxudHhfJUjzjCjqEnjsdjY+/e2VRUfgaAVptM716zCQ0ddoSVfnw+H5s3b+ann37C7XajUqmYPHkyQ4YMOWxPHEmSaNteR9N3+/ydjRUyjJOTMIyND9gTBzp7cWLSM5h6812Ex3duMOhxe1n/XSHbl5WBBPowDafN7EViVkfhJUkSlnnfUPPMM/hsNmQaDRF33EHYVX9v74kDUNVaxaNrHmVDtb+z8cDIgfxr9L9IMiZ16/skEAgEglODbj8p9+zZww8//MCdd95J//79ycnJYfAhOQyff/45I0aMOCGb/Kvi8Um8VlrDS8XVeCQIVyn5d0Y8Z0WEHNP5mpo3kbv7/vZcnPj4v5Oedh8KRfeSl61WK99++217Lk5SUhLnnHPOYUc3AHhtbpq/KWjPxVHF6Qm7qCeq6K6TsvesXcnSd9/EabOhUKkYffHlDD77XOQBPCm1JVaWfrC7PRen9+gYxlzYA7W244+3p6GBqscep3XZMgC0AwcS88zTHUY3SJLEgsIFPLPhGVrdrQQpgrhz0J1c1usy4cURCASCPyDdFjpBQUG888473HnnnVx11VXticgej4dzzz2XHTt28P3335+wjf7VKGlzcuvuEjbvr6g6O8LEsz0TMKuP3ovj87koLHyZktL/AhJBmlh6Z/6bsNDuVwrl5OTw/fff43A4UCqVTJ48maFDhx7WiwPgyG+i8ct8f0WVXIZxYgKG0xKQKQKvc9haWfbef9izxj8NPCq1B2feOiugF8fn9bFlSQmbFhYj+SR0RjWnXdGL5L6dw4Uty5ZR9ehjeBsbQaUi4o7bCb/mmg5enGZHM/9a/y9+LPkRgH7mfjwz9hnhxREIBII/MEd8am7bto3HH3+ccePGtedjTJgw4eAJlEoeeeQR+vfvf9ip07/G5/OxceNGvvjiCz788ENeeuklrrrqKgC+/PJL7r777k5rKisrmT17Nv/4xz8AmD59OmvXru1w3ZSUFFatWtXtfZxqSJLE59WNPFxQgc3rw6CQ82zPeM6PCj2mXBybrZCc3XfT0uLvaxMTcxE9ezzc7cZ/DoeDxYsXs3379v3rY7jgggswmw+feyS5fVgWF9G6thIAZYSWsEt7oY7rOgeoLGcHi998mZaGOmQyOcPPv5gR51/aaQAngLW+jaUf7KZqn78vTvqQSMZfmkGQvmMujs9up2b2szR/+SUAmp49if33cwT16tXBbm3lWh5Z/Qh1bXUoZUpu7H8j1/W9TgzgFAgEgj84R/wtHhcXx6RJk1i7di0+n4/4+HjOPvtszj33XCZPntze1v9o+eCDD3jnnXeYMmVKp7yeiy66iIsuuqjDa6tWrWLGjBlce+217a+Vl5fz2WefMWXKlKO+/qlIs9vDvXll7d2NR5iCeT0ziYSgo6+okiSJyqovyM//Fz5fG0plCJm9ZxMR0f3vVVlZGV9//TXNzc3IZDLGjBnDhAkTjpiH5a620fDZHjw1fm9U8MgYTGemIFcHXufzeln75Rw2fPslSBIhUTGceds9xPbsFdA+f1M1K+bk4XJ4UQUpGH9ZBhnDozvZOfbsoWLWPbgKC0EmI+yaq4m4807kh1RUuX1uXs9+nQ92fQBAiimF2WNmk2XO6tb3SCAQCASnNjJJkqTuGvfu3Zs33niDDRs28O2331JUVMT555/PNddcw/Dhxz7XJzk5mSeeeKLdoxOIkSNHctFFFzFr1qz21yIiIli5ciW9e/c+5mtbrVZMJhMWiwWj0XjkBSeIzRYbN+YUU+F0o5TBP1JiuCUxEsUxeHHcbgu5ex6irm4JAKGho8jKfAGNpntde30+H2vXrmX58uX4fD5CQkI477zzSEo6fAhHkiRsG6tp/r4QPD7kehWhF/ZE26vrHB5rXS0LX3ueyvxcAPqcNoXTrroedVBn76DL4WHl3Hzy1vsrxaJTjUy+JgujuaOtJEk0ffwxtc+/gOR2o4yMJPbfzxH8K0FeZi3jH6v+wc76nQBc3PNi7h16L1rl0TdcFAgEAsHJpbvP76P2y2dkZHD66afz0EMPUVBQwEcffcQ555xDZGQks2bNOqxYOVa+/fZbSktLufXWW9tfczqd1NfXEx9/dJOhnU4nTqez/XOr1Xrc9nks+CSJN0trebaoCq8EyVo1b2cmM8B4bEM+Ldbt7Np1Ow5HBTKZirTUWSQmXtet7sbgH+HwzTffsG/fPgCysrKYPn36Ebsb+xwemuYVtE8a1/QMJezinl12NwbI37CGH995DafNhlqrY8qNt5MxcmxA2/ryVn747y6aa+zIZDBkWjJDpiV36G4M4GlqouqBB2ld4c/x0U+cSMzTT6H8VcfuhYUL+df6f2Fz2zCqjfxz1D85Pen0w39zBAKBQPCH46iEjslk6jB1ukePHjz11FM8/vjjfPTRR3z77bcnROg888wz3H333R2uXV5ejk6n4+233+bTTz/FYrEwcuRIZs+eTWJiYpfnmj17Nk8++eRx3+OxUOdyc/vuUn5p8o+IODcyhOczEjAcw4wqSZIoK/uAvfueQ5I8aIMS6dPnNYzGvt0+R2FhIfPmzaO1tRWlUsmZZ57JoEGDjpgb5CproeGzPXgbHSCXYTojGf2YuC5nVHncblZ8/C7bflgI+MvGz7rzPkyRncNPkiSxe3Ulq74owOv2ERyiYcq1WcT2COlk27ZtG+V3z8JTVYVMrSbygX8QetllHfbv9Dp5duOzfJX/FQCDIgfx7NhnidHHdPfbJBAIBII/EEcldNavXx/wdZVKxXXXXcd11113XDZ1KMuXLyc3N5cbb7yxw+sWiwWz2UxsbGx7/tBDDz3ExIkT2b59O8HBgUuXH3zwwQ7hL6vV2qHD88liY3Mr1+cUU+PyoJXLeKpHPH+LCTumhGO328Lu3Pupr18KQGTkNHr3eqbbCcc+n4/Vq1fz888/I0kSERERXHTRRURGdh6OeSiSJGFbX0XzgkLwSihCNYRd1gtNYtcuREttDQteeZbqfQUADD3nQkZffHnAhGOXw8Mvc/Io2FQDQFKfcE6/qnenSeOSJNH40UfUvvAieDyok5KIe+1VgjI6di4us5Zxz4p7yG3MRYaMG/vfyI39bhQJxwKBQPAn5pT/Df/WW29x4YUXYjB0fGgPGjSovQrsAC+99BLvvfceq1at4owzzgh4Po1G08EzdLKRJIn/ltfxz32VeCToodPw3z7J9Ao+tryQlpYcduy8BYejHJlMTc8eDxMXN7Pbgslut/PNN99QUOAXHgMHDmTatGmoVKrDrvO5vDTPK8C+zT85XJsVTuiFPZFru/6RKty6icVvvIjD1kpQsJ4zb7+H1IFDA9o2VdtY/PZOmqrtyOQyRpyTysDJiZ28RF6rlaqHH6blJ7/IM047k+h//hOFvmN117KSZTy65lFa3C2EakJ5duyzjIobdfhvjkAgEAj+8JzSQqeuro758+fzww8/BPy6z+fr0MdFkiR8Pt9xGZx5Imj1eLl7Txnf1zUD/lDVixkJBB9DqAqgqupr9uQ9is/nJCgogb5938Bo6NPt9ZWVlXzxxRc0NzejVCqZNm0agwYNOuI6d52dhk9y/VVVcjCdmeIPVXXxfff5vKz94lM2fOOfqRWd1oPpdz+IMSKwx2jf1lqWfZSL2+kl2KRm6vV9iEkP6WTnyM+n/PbbcZeUIlOpiHzwgU6hKo/Pw2vZr7VXVQ2IGMDz458nOrhzmEwgEAgEfz66LXRWrlzJuHHj2j+/5pprurR9//33f9uu9jNv3jyCgoIYO7ZzguqqVau49tprmTNnDkOHDsXhcHDPPfcQHx/foc/PqUKBzcE1u4oosDtRyWQ8nh7LtXHmYxJlPp+T/IKnqKj4FIDw8AlkZb6EShV46ncgsrOzWbBgAV6vl9DQUC6++GJiYo6cp9K2q57GL/ORnF7kBhXhf+uNJqXr6zpaW1n4+vPtYxwGTD2L8VdchzKAx8jn9bH+20Kyf/J3bo7rGcKU6/qgM3ZOaLYuWULlQw8j2e0oY2OIf/U1tH07irxmRzP3rbyvfRjn3zP/zp2D70QlP7y3SiAQCAR/HroldEpKSrjwwgvp27cvb731FhkZGcyfP5+nn36aBx98kGeffRZJknjggQd47rnnjtvmFi5cyIQJE1AGyN8YO3YsDz30EDfeeCM1NTU4nU7Gjh3Ljz/++LuGpgLxY72FW3eX0OL1EaNR8d+sZIaYuh5/cDiczhp27LwVqzUbkJGScgcpybd1u6rK6/Xy448/smGDf4ZTRkYG55577hGbPUo+CeuyUlqW+UWIOsVI+N96ozB0XVVVX1rMdy88TXNNFUq1hik33k7vMRMC2ra1uvjhvzlU5DUBMGByIiPPTe1UVSV5PNS98goN774HgG7kCOJeeqlTVdWexj3c9fNdVLRWoFVq+efof3JGcuBwpkAgEAj+vHS7j47NZuOll17i5ZdfZtmyZVxwwQUUFhaSkJBAWVkZ4O+aW1VVdUI3fLw5kX10JEni1ZIaniuqRsLfAPC/fZKJUB+bR8Fi3c6OHTfhctWiVBrJynwJs/m0bq+32Wx8+eWXFBcXA/4O1+PGjTviGAef00Pj5/k4dvtnVelHx2KaltrlME7wl44vefNl3E4HxohIzrn3ESKTUwPaNlS0sug/O7DWO1BpFEy8sjfpgzuHtbzNzVTMmoVt7ToAwq69hsi770b2KyG8sHAhT6x9AofXQYIhgVdPe5UeoT0Oe48CgUAg+GNx3PvoBAcH8+ijj3L55Zd32TjuVM2N+T2webzcuae0vcvx32PD+VePONRHEBVdUVX9LXv2PIjP5yI4uAf9+r6DTtf9GUxVVVXMnTsXi8WCWq3m/PPPp1evwJ2HD8VT30b9/3bjqbWDUkboeT0IHtx140HJ52PtV5+y/uu5ACT26cdZd/4DnTFweKtwWx0/fbAbj9OL0RzEtFv6ER7beUyEs7CQsptv9ufj6HTEPv0UxjPP7GDjk3y8tvU13tvl9/aMiRvDs2OfxaTpfkhPIBAIBH8uuiV08vPzO3y+d+/eE7KZPws2r5fpWwvYbXOgksmY3TOey2PDj+lckuRl374XKCn9PwDM5klkZb6IUtn1zKhfk5uby7x583C73YSFhXHppZcesXQcwLGvmYZPcpHaPMiNasxXZKJO6Lpk3e10sOTNl8nfsAaAwWedy7iZVyMPMDJCkiS2LC5mw/wiAOIyQjnj+j6dZlUBtK5aTcWsWfhaWlDFxhL/n7c6lY7b3XYeWPUAP5f9DMB1fa/jtgG3iYnjAoFA8BenW0Jn6tSpyGQyDo1yCe9N1wQrFIwM0VPn9vBeVjLDQrovSg7F47GRk3MX9Q3LAUhOuoXU1Lu7nY8jSRJr1qxh6VJ/6XVaWhoXXnhht4av2jZV0/TNXvBJqBMNhF+eiSJAUvABWhsb+Pb5p6gpLECuUDL5htvoM2FS4Ptye1n+vz3t/XH6nhbP6AvTUfw6H2f/KIeaZ58Dnw/t4MHEv/YqyvCOorGqtYrbl99OXlMearmaJ0c/ydmpZx/xHgUCgUDw56dbQqeoqKjTa6mpgfMtBH6eSI/jjqQoojTHlo/jcFazY/sNtLTmIJdryOz9b6Kiuv/w9ng8LFiwgG3btgEwdOhQzjjjjCMO5JR8EpYlxbSuLAdA2z+CsAt7IlN1La5qCvfy7b//SWtTI0EGI+fc8xDxvQOXube1uFj0n51UF1qQy2WMu6wnWWPjOu/D46H6qadonusvSTedfz7RTzzeYSAnwPa67dyx/A4aHY2EB4Xz6sRX6R/R/7D3KBAIBIK/DkfdR2fFihWMHz/+ROzlT4VKLjtmkdPSspvtO67H6axGpQqnf7//w2Qa0O31drudzz//nJKSEmQyGWeccUa3hq76XF4a5+a1Jx0bTk/EOCnxsN67vZs3sPC1f+NxOgmPT+Tc+x8jJCpwj5qmahsL3tiOtd6BRqfkjBv6EB9g4Ke31UbFrLuxrVwFMhmR991H2NVXddrH0pKlPLDqAZxeJxmhGbw+8XUxykEgEAgEHei20MnJyeHGG2+ksLCQtWvXnsg9/aWpr/+ZXTl34PXaCQ7uQf9+76LVdn9waVNTE3PmzKG+vh6NRsOFF15Ijx5Hrjjytrio/ygHd3krKGSEXdQT3YDD5/Fs+2Ehyz94B0nykdx/EGff9Q80usBl8xV5TSx+ZydOuwejOYizbu1PWExnW3dNDWU33YwzNxdZUBBxL76A4fTOwzY/3v0xz296HgmJcfHjeH7c8+hUxzYIVSAQCAR/XrotdC677DIuvfRSZs2aRVBQEIGq0rtZqS7ogoqKz9iT9xjgIzR0FH37vIlK1f2S98rKSj799FNaW1sxGo3MnDmTqKiuK6QO4K6zU/9BDt5GB/JgJeFXZqFJ6vq6ks/Hqs8+YtP8rwHoO3EKp197S8B5VQAFm2pY+uFufF6JqBQj027uF7AJoCMvj7Ibb8JTXY0iPJyE/7yFtl+/DjZen5fnNz/PnNw5AFyScQkPDHtAzKsSCAQCQUC6/XTYunVrh8Z9//jHP4COgz4ff/zx47i1vw6SJFFU9BpFxa8BEBNzIb0ynkJ+FB18CwoK+OKLL3C73URFRTFz5sxu9QVyllpp+DAHn92DIiwI8zV9UJm7Tlb2uN0seetl8tauBGD0JVcw/LyLuwxvbVtaypqv/FV6aYMimHRVJkp15zwh2/oNlN92G77WVtSpqST83zuo4zt6shweBw+seoBlpcsAmDV4FldldQ5pCQQCgUBwgG43DPyzciIbBnYHn89DXv5jVFb6k26Tk28jNeWuo3p4Z2dnM3/+fCRJIjU1lYsvvpigoKAjrmvb3UDjZ3uQ3D5U8XrMf886bKdjp93Ody88RVnODuQKBVNvupPMcRMD2ko+ibXz9rJtqb+ZZL/T4hlzUY9OQzkBrEt+oPK++5DcbnRDhhD/5hsoTB1731hdVm5fdjtba7eilqt5euzTotOxQCAQ/IU57g0DBccfr7eNXTl3UV+/FJCTkfEk8XF/O6pzrFmzhp9++gmAfv36MWPGjIAjM36NbXM1TV8XgARBGaGE/a03ck3XFVl2SzNfz36c2qJ9qLVaZsx6mKR+AwLfl8fHso9y28vHR56XxsApgZOam+bOpfrJf4IkYZg8mdgXnkf+qxEedfY6blp6E/lN+RhUBl6b+BpDoocc8R4FAoFAIDhuQsfj8XDhhRfywgsvkJ6efrxO+6fF7bayfcd1WCxbkMvVZGW9QmTE1G6vlySJpUuXsmaNvznf6NGjmTRpUrc8QS0ry7Es8rcM0A2OIvT8Hocd52CpreHrZx6lqaoSrdHEBQ8+SVRq4P9jt9PL4nd2Ura7EblcxsQre5ExonMllCRJ1L/xJvVvvglAyCWXEP3Yo8h+Vf5eYi3hxp9upKK1ArPWzNuT3iYjLKPT+QQCgUAgCMRxEzqzZ89mw4YNhIV1LhcWdMTlqid729W0tu5GqTTQv9+7hIR030Ph9XpZsGAB2dnZAEyaNIkxY8YccZ0kSVh/KKHlF384ST8uHtOZyYcVR/WlxXz9zGO0NjVijIjkgof+RVhs5743AE67mwVv7KC60IJSLefMG/uSmNW5I7Tk81Hz1NM0feqfvm6+9VbMt93aaR+5DbnctPQmGh2NJBgSeGfyOyQYEo54nwKBQCAQHOC4CJ3vv/+eZ599liVLlgihcwQcjkqyt12J3V6EShXOwAEfYTD07vZ6j8fD119/TW5uLjKZjOnTpzNo0KAjrpN8Es3f7cW2oRoA4xnJGCccXjRU7c1j3jOP47C1Eh6fyAUP/xNDmDmgrd3q4vvXt1Ff1opGp+Ts2/oTndp5xpTk8VD1yKNYvv0WZDKiHn2EsL91Dtdtq93GzUtvptXdSu+w3rw16S3M2sDXFggEAoGgK36z0Pnf//7HXXfdxRdffMHYsWOPx57+tNjtRWRnX4nDWYlGE8OggR+j06V0e73b7ebzzz9n7969KBQKLrjgAjIzM4+4TvL6aPwin7btdSCDkHPT0Q8/fGO98txdfPPck7ja2ojpkcF5DzyBVh94zlVLo4P5r26jucaO1qBixp0DMMd3tpVcLiruvY+WH38EhYLYZ5/FNL1zt+cNVRu4ffnttHnaGBQ5iDdOfwODuusZWwKBQCAQdMUxC53Nmzfzz3/+k+LiYpYvX86AAQOO47b+fLS25rE1+wrc7gZ0uhQGDvgfQUGx3V7vdDr57LPPKC4uRqVScemll5KWlnbEdZLHR8Nne3DkNPgbAV6Sga5fxGHXFO/I5rvnn8LjcpKQ1Y9z738UdVDgknNLnZ1vX86mtdGJPkzDOXcOJCSqc+M+n8NB+R13YFu5CplKRdzLL2GY1HkW1sryldz98924fC5GxY7ildNeQas88mwugUAgEAgC0S2h87///Q+n00lTUxN5eXmsXr2a0NBQrr32Wq666ipUqmMbdfBXoaUll+xtV+B2N6HX92bggA9Rq7sfhnE4HMyZM4eysjLUajUzZ84kKSnpiOskt4+GObk49jSCUkb45ZloA4xcOJR9Wzbw/Uuz8Xo8pAwYzPR7HkKl1gS0ba6x8+1LW7FZXIRE6Zhx5wAMYZ3L2n02G2U334J940ZkWi3xb7yOfvToTnY/FP/AAysfwCN5OC3hNF4Y/wJqRdfl7gKBQCAQHIluCZ0PPvgAl8uF3W6noqICj8fDiBEjCA0NPeKQyL861pZdZGf/HY+nGYOhLwMHfIRK1Tl3pSvsdjuffPIJlZWVBAUFcfnllxMff+SRED6Xl4aPd+MsaEamkhN+RSZBPUMPuyZ//WoWvvY8Pq+X9KEjOevO+1F2IWIbq2x893I2dquL0JhgzrlrAMGmzoLI22qj7MYbaduyBbleT8I7b6MbPLiT3aLCRTy4+kF8ko8zU87k6TFPozqKhokCgUAgEATimBoGNjQ08PPPP/PRRx+xb98+XnjhBaZNm3Yi9nfCOZENA63WHWRv+zsejxWjcQAD+n9wVCMd7HY7//vf/6iurkar1XLllVcSE3PkoZU+p5f6D3NwFVmQqeWE/z2LoLSQw67JX7+aBa/+G8nno9fo8Zx56yzkXYjYhopWvnslm7YWN+FxwZxz10C0ARoNelttlN1wA21btyI3GEh8791OIx2go8g5N/1cnhj5BAq5ENACgUAg6JruPr9/c2fkFStW8Pe//52bb765fSzEH4kTJXQslmyyt12F19uKyTSYAf3fQ6nsfkLtoSInODiYv//970RGHn7IJvg9OfUf7Bc5GgXma/ocdm4VQP6GNSx45Tkkn4/McROZevOdyLsQGvXlfpHjaHVjTtAz484BaPWBRE4rZdffQFt2NnKjkcT33kPbt08nu4WFC3lo9UP4JB/n9zifx0c+jlwmP+J9CgQCgeCvzUnrjDx+/HjWrl3LhAkTkMlk3H///b/1lH94PB4b23fcgNfbSkjIMPr3exelMvBU70C0tbXx8ccfU11djU6nOyqR0/DRISLn2j5oEg8vcgo2rGXhfk9O5tjTDityGioPipyIRAMz7hxAUHDn8JK3pYWy666nbft25CaTX+T0yepkd6jIuaDHBTw28jEhcgQCgUBwXDkuT5XY2FjmzZvHM888w7Zt247HKf/QKJXBZPZ+jvCwcfs9OUcvcqqqqo5K5EhuLw3/241znwWZer8npxsiZ8Grz+Hzev0i55a7uhQ5TdU2vntlG45WN5FJBs65K7DI8dlslN1w40GR835gkbOocJEQOQKBQCA44Ry3J0ufPn24/fbbWbly5fE65R8as3ki/fu/j0LRudS6KxwOR3vi8QGRExUVdcR1kttH/ce5OPc2I1PLMV+TdcRw1b4tG9pFTu8jiJzmWn8JeZvVhTlBz/Q7BqDRBRA5bW2U3XxLe7gq6YP30WZ1FjnLSpYJkSMQCASCk8JxHer55JNPIpeLB9YBjmYCucvl4tNPP6WioqI98bhbIsfrLyF35jchU8kxX9UHTfLhq7pKdmzj+5dm4/N66TV6PGccRuRY69v81VUWF2GxwV2Gq3wuF+W33Y5940bkwcEkvvcuQQGaGa4qX8W9K+/FK3k5J+0cIXIEAoFAcEI5pidMTU0N48aN63wyIXKOCY/Hw9y5cyktLUWj0XDllVcSHR19xHWST6Lxi/z9fXLkhF+VhSbA2IVDKd+Tw7cv/Auvx0P60JH+6qouRE5rk8PfDLDJSWi0zl9dFSDxWHK7qbjrbmxr1iDTakn4v3fQ9u3byW5D1Qbu/uVuPD4PZySfwZOjnhQiRyAQCAQnlGN6yjgcjvap2YLfhtfr5auvvqKwsBCVSsXMmTO7VUIuSRLN3+z1j3VQyAi/ovcRS8ir9xXwzbNP4nE6SR4wmLPuvL/LEvK2FhfzX91GS4MDU4SWc+4aiM4YQOR4vVTcfz+ty5cjU6tJeOvNgH1ysmuzuX357Ti9Tk5LOI1nxj4jSsgFAoFAcMIRf07/jvh8Pr799lv27NmDQqHgsssuIzEx8YjrJEnCsrAI26ZqkEHYJRloMw7f8fjAFHJXm534zD7MmPVgl80AXW0evn99O03VdvShGs65eyDBIZ2bAUqSRPUTT9KyeAmoVMS/8TrBI0d2stvTuIdblt5Cm6eNUbGjeGH8C6IZoEAgEAhOCkLo/E5IksSiRYvYuXMncrmciy++mNTU1G6tbVlWSuvqCgBCL+hxxNlVltpqvnrmMRytLcSkZ3De/Y+h0nQe1QDgcXlZ+NYO6kpbCNKruhzrAFD38is0f/klyOXEvfAC+gDhzFJrKTf+dCOt7lYGRQ7ildNeEWMdBAKBQHDSEELnd+KXX35h8+bNAJx33nlkZGR0a13r2kqsS0sBME1PJXjI4XN57JZmvnr6UWxNjZgTkjj/wSdRawNXgnm9Ppb8dxeVBc2ogxTMuGMAodGBS+Mb3v+Ahv/7PwCin3wC49QpnWzq7HXc8NMNNDoa6RXWizdOf0MM6BQIBALBSUUInd+BTZs2sWLFCgDOOuss+gZI3A2EfUcdzd/vA8A4OQnD6LjD2jvtdr6e/TjN1VUYIyK54KF/EqTXB7SVfBLL/5dLyc4GFCo5Z93aj4jEwJ2cm+d9Q+2//w1AxD2zCL3ook42FqeFG5feSEVrBQmGBP4z6T8Y1N3vDC0QCAQCwfFACJ2TTE5ODgsXLgT8XaWHDh3arXWOvc00fp4HEgSPjMEwMeGw9h63m/kvPkVt0T60RhMXPPQv9GHhXdqv+3Yf+RtqkMllnHFDH2J7BB4A2rJ8OVWPPgpA2DXXEH7ddZ1s2jxt3L78dgqaCjBrzbwz+R3M2u5PaxcIBAKB4HghhM5JpLCwkHnz5gEwZMgQJkyY0K11ropWGj7eDV4JbV8zIdPTDtujx+fzsvj1FyjdtQNVkJYLHnySsNiuvT/bl5eR/aM/HHba5b1I7htYlLRt20bFrHvA68V0/vlE3ndvp314fB7uX3E/2bXZGNQG3p70NgmGw4sygUAgEAhOFELonCSqq6uZO3cuXq+XzMxMpk2b1q2Ggp6GNuo/2IXk9KJJNRF2cQYy+eHXrfjfe+RvWINCqeTc+x4hKjW9S9u9W2pZ/WUBAMPPSaX3qMCl7c6iIspuuhnJ4SB4/Dhi/vlkp/1LksSzG5/ll/Jf0Cg0vDHxDTLCupd7JBAIBALBiUAInZOAxWJhzpw5uFwukpOTOf/887vVXNFrc1P/QQ6+VjeqmGDCr8xEpjr8ui0Lv2Pr4vkAnHHrLBL79O/StiK/iZ8+yAEJ+oyPY/AZSQHtPA0NlN1wI97mZoL69CH+pZeQKTs31X5/1/t8nvc5MmQ8O/ZZBkUNOuI9CgQCgUBwIvndhI7P52P9+vXMmjWLsLAwPvzwww5ff/HFF9Hr9cTHx3c4qqur220qKiq45JJLSE5OJi4ujrvvvhun03mS7+TwOBwOPv30U1paWoiIiOCSSy5BGUAk/BrJ7aPh49146ttQhGgwX90HedDh1+VvWMMvH78LwLiZV9NrVOdy7wM0VtpY9J+d+DwSqQMjGHtJz4AeJp/dTtlNN+MuK0OVkEDC2/9BHty5Emth4UJe2foKAPcPvZ9JSZOOeI8CgUAgEJxojknoKJVKYmNjf9OFP/jgA+644w50Oh2KAN15y8vLueOOOygvL+9wHBiN4HK5mDx5MvHx8ezdu5ecnBy2bNnC3Xff/Zv2dTzxer188cUX1NTUoNfrmTlzJlrtkcurJZ9E41f5uIqtyDQKzFdnoQjQlfhQKvJyWfz6iyBJ9J9yFkOmn9+lrd3qYsGb23G1eYhJNzH56kzkAcJhksdDxd2zcOzciSIkhIT/eweluXP+zqbqTTyy5hEArsi8gsszLz/iPQoEAoFAcDI4JqETFxdHWVnZb7rwtddey8aNG3nqqacIDuAhKC8vJyGh6yTWAwJi9uzZKJVKQkJCePnll3nvvfeor6//TXs7HkiSxIIFC9pHO/ztb38jJCSkW2utP5X4RzvI/aMdVFGBe9kcoKmqgm+f/xcet4vUwcOYeNUNXeb/eFxeFv1nR/toh2k39UOpDjyKoebZ52hdsQKZRkP8f95Ck5LSyaawuZA7l9+Jx+dhctJk7h1yb7fuUSAQCASCk8Epm6NTXl5OfHx8l19fvnw5U6dORa0+6OkYPHgw4eHhLFu2rMt1TqcTq9Xa4TgRrFy5kuzsbGQyGRdeeGG3PWC2jdW0/OwXkaHn9yAoPXCZ9wHaWlv45rkncbRYiUrtwdl3dD2/SvJJLP1wNzVFVjTBSs6+rT9B+sCjGBrnzKHpk08AiH3+3+gGDuxk0+Ro4tZlt9LibmFg5EBmj50thnQKBAKB4JTilH0qlZeXs2XLFsaMGUNKSgqTJk3qMEi0srIyoHiIi4ujoqKiy/POnj0bk8nUfhzOa3SsOJ1Otm3bBsCZZ57Z7a7Hjr1NNH3rr4AyTEwgeEjUYe29Hg8LXp5NU1UlBnME5/3jMVRBgcc1AKz/rpB9W+uQK2RMu6kvIVGBOyS3rlpNzTOzAYiYNQvjlM5dj11eF3f9fBflreXE6eN45bRX0Cg6z8MSCAQCgeD35JQUOpIkodFocDgczJ8/n71793L11VczefJkduzYAYBKpQpYuXSkku0HH3wQi8XSfvzWEFwgNBoN1157LdOmTWPYsGHdWuOub6Nhzh7wgXZABMbJgSugDiBJEsvff7u9V8559z9GcEjX3p/dayrZ+kMJAKdd0avLhoDOggIq7r67vVdO+PWdGwJKksST655ka+1W9Co9b57+JmFBhx8qKhAIBALB78GRy39+B2QyGXv37u3w2syZM/nkk0/49NNP6devH/Hx8VRWVnZaW1VVRVxc183xNBoNGs2J9zzo9fpuixxfm4eGj3KQ2jyoEwyEXRC4AupQshfPZ8eyJSCTcdYd9xKR1Dl/5gCVe5tZ8WkeAEOmJdNrROBeOZ6GBspuuhlfayu6IUOIeeLxgPt4f9f7zN83H4VMwQvjXyAtJK1b9ykQCAQCwcnmlPTogL/8/Nd4vd72B+8ZZ5zBjz/+iMfjaf/6nj17qK2t5fTTTz9p+/ytSF6Jhs/24KlrQ2FSd6tXTlH2Zn7533uAv4w8bfDwLm1bGh0seWcnPq9E2qBIhk0PLIgkl4vyO+7EXVGBKimRuNdfQ6buXOm1rHRZexn5A8MeYHTc6G7eqUAgEAgEJ59TUug0NjaSnp7OZ599hs/nQ5IkPvroI1atWsWVV14J+IdhRkZG8uijj+L1erFYLNx2221cffXVmAOUQJ+qWBYV4sxvQqaSE35lFgrD4cvIG8rLWPDqv5EkH1kTJjHk7PO6tHU7/RVWbS1uzAl6Tv977y49RdVPP0Pbli3IDQYS/vM2ytDOoa2CpgIeXPUgAJf1uoxLe116FHcqEAgEAsHJ55QUOmFhYcyZM4f333+fhIQEIiIiePvtt1m0aBG9e/cG/L18lixZwu7du0lISCArK4u+ffvy6quv/s677z62TdW0rvGH30IvzkAdF3iy+AEctla+e+FfuNrsxPXKYvL1t3YpXCRJYtlHu6kva0VrUDHt5n6oNIGrsZrmzqX5889BJiPuxRfQpHb2+licFu5YfgdtnjaGxwzn/qH3H+XdCgQCgUBw8pFJkiT93pv4PbFarZhMJiwWC0aj8aRd11lqpe6dHeCVME5KxDjpCMnHPh/fPv8vCrduQh9u5orZr6AzhXRpv2lhERu/L0KukHHO3QOJTQ9sa9+0iZKrrwGPh4h7ZmG+/vpONh6fh1uW3sK6qnXE6eOYe9ZcQoK6vrZAIBAIBCea7j6/T0mPzp8db4uLhk9y/dPIs8IxnJ54xDVrv5xD4dZNKFVqzr33kcOKnKLtdWz8vgiA8X/L6FLkuCsrKb/zLvB4ME6bRvh1nSusAF7d+irrqtahVWp59bRXhcgRCAQCwR8GIXROMpLHR8OcXHxWF8pILaEXH7nCqmDDWtbP+xyAyTfcdthp5M01dpZ+sBuAvhPiyRwduFGhr62Nsttuw9vYiCazNzFPPxVwHwsKF/BhzocA/Gv0v8Q0coFAIBD8oRBC5yTTvLCwfYZV+BWZyDWHr/CvLy1m8ZsvATBo2jlkjpvYpa3L4WHxOztxObzEpJsYfWFgQSRJEtVP/hPn7lwUoaEkvP468gAzuPY07uGJtU8AcF3f65iaPLWbdykQCAQCwamBEDonEduWGmzrqgAIuyQDVUTgzsQHcNrtzH/pGdxOBwlZ/Rh/+TVd2kqSxM8f76Gx0obOqGbq9X1QKAP/9zZ//gWWb78FuZy4l19CFaDvkNVl5e6f78bpdTImbgy3Dbit+zcqEAgEAsEpghA6JwlXRStN3+wf73B6ItrM8MPaS5LED/95xT/eITyCs+/6R5czrAC2Lytj75Za5HIZZ9zQh2BT4KaIbTt3UvP00wBE3H0XwSNGdLLxST4eXvUw5a3lxAbH8uzYZ1HIu762QCAQCASnKkLonAR8bR4a5uSCRyKoVxjGbiQfb1n4LQUb1yJXKJl+9wPojKYubSvymlg7bx8Aoy/qQUwXyceepibK77gTye1GP+n0LpOP39/1Pr+U/4Jarual017CpOn62gKBQCAQnMoIoXOCkSSJxi/z8TY6UIRoCLu4JzL54ZOPy/fksHLOBwBMuPJaYnp0nQBsszj54b0cJJ9Ez+FR9J0QePyF5PVSec+9eKqqUCclETt7dsDk4w1VG3g9+3UAHhr+EFnhWd29VYFAIBAITjmE0DnBtK6uwLG7ARQywmf2Rq5THdbe1tzEgleeQ/L5yBg1jgFTz+7S1ueT+On9HNqsLsJig5kws1eXFVz1b76Jbe1aZEFBxL32GgqDoZNNja2G+1fej0/ycW76uZzf4/yju1mBQCAQCE4xhNA5gThLrFgWFwMQcnYq6oTO4uJQfD4vC197HltTI2FxCUy58fbDlp5vWlBERV4zSo2CM27og0odOI/GtnYt9f95G4CYfz5JUEbPTjYen4f7Vt5Ho6ORjNAMHh7+8BHL3gUCgUAgONURQucE4W110TgnF3wS2v4RBHcxMfxQ1n01l7KcHag0QcyY9RDqoM4l3wco293I5v0iasLfMgiNDg5o566tpeK++0GSCLnoIkwzZgS0e2vbW2TXZqNX6Xl5wssEKYOOfJMCgUAgEJziCKFzApB8Eo2f5+G1ulBGaAk9P/2I3pHSXTtYP28u4G8KGB6f0KWtrdnJTx/kgASZY2LJGB4deB9eL5X3/wNvQwOanj2JevihgHZrK9by7s53AXh81OMkGLu+tkAgEAgEfySE0DkReH3IdSr/RPLLex+xKaDd0syiN14ASaLPaZPpPWZCl7Y+r48f38uhrcVNeLyesRf36NK2/u23sa9fj0ynI+6Vl5EHdfbS1NnreHD1g0hIXNzzYs5IPqPbtykQCAQCwanO4Z/AgmNCplIQdmkGnvq2IzYFlHw+Fr/1cntezsSrbjys/eZFxVQWNKPSKDjj+j4ou8rL2bCR+jffAiDm8cfQpKZ2svH6vDyw6gEaHY30DO3J/cPERHKBQCAQ/LkQHp0ThEwmO6LIAdi84BuKt21BqVIz/a5/oArgdTlAZUEzmxcVAzBhZgYhUYHP72lspPLee8Hnw3T++ZjOOSeg3f/t/D82Vm9Eq9TywvgX0CgCNxkUCAQCgeCPihA6vyOV+XtYPfd/AJx21Q2YE5O7tHXY3Pz0fg6SBL1GRNNzWBd5OZJE1UMP46mrQ52eRvQjDwe021Kzhbe3+yuxHh3xKCmmlN92MwKBQCAQnIIIofM74bTbWfT68/i8XjJGjqXv6V0PzJQkiV8+2UNrkxNThJaxl3YuDz9A06ef0vrLL8jUauJefBG5rrPXx+qy8uCqB/FJPmakzWB62vTjck8CgUAgEJxqCKHzO7H8g7ex1NZgjIhi8g23HbYqa/fqSvZl1yFXyJhyXRbqoMCpVY78fGr//TwAkffeS1BG547KkiTx1LqnqLJVkWBI4KHhgSuxBAKBQCD4MyCEzu/AnrUr2b1yOTKZnGm33YNGF7gHDkBjlY3VX/iHgQ4/J5XIJGNAO5/TSeU99yI5nQSPG0voFZcHtFtQuIDFxYtRyBQ8O/ZZglVdX1sgEAgEgj86QuicZKz1dSx9900Ahp93EXG9Mru09Xp8/PR+Dh63j4TeoQyc1PUw0NoXXsRZUIAiPJzYZ54J6CEqaynj6Q3+yeW3DLiFfhH9fuPdCAQCgUBwaiOEzknE5/Oy+M0XcdpsRKf3ZMQFlx3WfuOCIurLWgkKVnH6VZldDgNtXbmSpo8/BiD2madRms2dbDw+Dw+uehCb28agyEFc2+fa335DAoFAIBCc4gihcxLZ/P03lO/ehUoTxLTb70Wh7LqNUeXeZrJ/KAFgwuUZBJsCl357mpqofMhfWRV6+eXox48PaPffHf9le912DCoDs8fORiEP3H9HIBAIBII/E0LonCRqivax5vNPAH8peWh0bJe2LoeHZR/u9peSj4wmbWBkQDtJkqh+4km89fWo09KIvPeegHa76nfxzo53AHhkxCPE6ru+tkAgEAgEfyaE0DkJeNxulrz5Ej6vh/ShI+lz2uTD2q/+sgBrvQNDWBBjL+66lNy6YCEtP/wASiWxzz0XcMSDw+PgodUP4ZW8nJF8BtNSp/3m+xEIBAKB4I+CEDongXVfzqG+rASt0XTEUvLCbXXkrqkCGZx+VW/U2sDhLXd1NdX/+hcA5ptvQtsnK6Dda9mvUWQpwqw18/DwwM0DBQKBQCD4syKEzgmmIi+XTfPnAf6p5DqjqUtbu9XFL3P2ADBwUiJxPUMD2kmSRNXDj+CzWgnq2xfzDTcEtNtUvYlPdvvDZU+OepKQoJDfcCcCgUAgEPzxEELnBOJ2OFjy1ktIko/MsafRY+jILm0lSWLlZ3n+qeRxwQyf0XkI5wGa587FtmYNMo2G2OeeRaZSdbKxuW08uuZRJCQu6HEB4+LHHZd7EggEAoHgj4QQOieQVZ99RHN1FfqwcE67+vBTyfduqfV3P5bLOP2qTBSqwP81rpISag50P75nVsCp5ADPb3qeitYK4vRx3Df0vt92IwKBQCAQ/EERQucEUbprO9lLvgdg6k13EhSs79LWbnWx8rN8AAafmUREgiGgneTzUfXwI0htbeiGDyf08sDdj1dXrObrgq+RIeNfo/8luh8LBAKB4C+LEDonALfTwZL/vAJA/8lnktx/UJe2kiSx4rM8HDY34fF6Bp+Z3KVt02efYd+8GZlOR8zTTyGTd/7va3W18sTaJwCY2XsmQ6OH/pZbEQgEAoHgD40QOicApVrD2L9dRVRqD8Zdfs1hbfduqaXwQMjq771RKLsIWZWXU/viSwBEzpqFOj4+oN1LW16ixl5DgiGBOwbd8dtuRCAQCASCPzhdt+YVHDMymYzeo8fTa9S4w5aSdztkJUlUPfIokt2ObsgQQv8WeHTEhqoNfJn/JeCvstIqtb/xTgQCgUAg+GMjPDonkMOJHICV3QxZNX/+Bfb165EFBXUZsrK77Ty+9nEALsm4RISsBAKBQCBACJ3fjcLsOvZl1yGTyzj9yq5DVu7KSmqf91dZRdx1J+qkpIB2r2W/RkVrBTHBMdw9+O4Ttm+BQCAQCP5I/G5Cx+fzsX79embNmkVYWBgffvhhh6+7XC7uv/9+kpOTiYuLY/jw4axYsaKDzfTp0wkPDyc+Pr79GDt27Em8i2PDaXezYm4eAAOnJBKReJiQ1eNP4LPZ0A4YQNgVVwS021qzlU9zPwXgiZFPiCorgUAgEAj287vl6HzwwQe88847TJkyBYWi8yTtm2++mbKyMrZs2UJ4eDjffPMN06ZNY8eOHaSlpQFQXl7OZ599xpQpU0729n8Ta7/Zh93iwhSpZei05C7trAsXYVu1CplKRcwzTyML8H1yeV08vvZxJCTOSz+PUXGjTuDOBQKBQCD4Y/G7eXSuvfZaNm7cyFNPPUVwcEcPhMvlYteuXbz77ruEh4cDcN5559GrVy8WLlzYbldeXk5CQsJJ3fdvpSK/id2rKgE47fJeKNWdxQuAp6mJmmeeASD85pu6bAz47s53KbYWY9aauXfovSdm0wKBQCAQ/EE5Jauu1Go1GzZs6PBaS0sLxcXFGI1GAJxOJ/X19cR3UWbdFU6nE6fT2f651Wr97RvuJh63l58/8c+yyhwb2+UsK4Da51/A29iIOj0N83XXBbQpbC7kvzv/C8ADwx7AqDYe/00LBAKBQPAH5g+RjFxbW8tZZ51FdHQ0l1xyCeD35uh0Ot5++20GDhxIamoqM2fOpLS09LDnmj17NiaTqf04mR6hTQuLsdS2oTOpGXVeWpd2tvXrscybBzIZMf/8FzK1upONT/Lx5Lon8fg8jI8fz5SkP1b4TiAQCASCk8EpL3R+/vlnBgwYQEhICCtXrkSr9feGsVgsmM1mYmNjWbt2LTt37sRsNjNx4kRsNluX53vwwQexWCztR1lZ2Um5j/ryVrJ/9Iuw8ZdmoNF1HsQJ4HM4qHrcXyYeetml6AYNDGj3dcHXbK3dilap5eHhDx+xlF0gEAgEgr8ip7TQeffdd7ngggt45plnmD9/fnu+DsCgQYMoKSlh5syZaLVagoODeemll6iurmbVqlVdnlOj0WA0GjscJxrJJ7Hi0z1IPonUARGkDozo0rb+rf/gLilFGRlJxN2By8Tr7HW8vPllAO4YeAcx+pgTsm+BQCAQCP7onJI5OgDfffcdjz/+OKtXryYzMzOgjc/nQ35I8zxJkvD5fKecd2P3mkqqC62oNArGXtKjSztHXj4N778PQPRjj6IwBC47f3bjs7S4W8gKz+KyXoG7JAsEAoFAIDhFPTqtra3ccMMNfPrpp12KnFWrVtGrVy82bdoEgMPh4M477yQ+Pp4JEyacxN0eHrvVxbpv9gEwfEYq+tCggHaSz0f1k0+Cx4N+0ukYJk0KaLeyfCU/lvyIQqbgiVFPoJAHrtoSCAQCgUBwinp0tmzZQl1dHTNnzuz0tZEjR/Lll18yduxYHnroIW688UZqampwOp2MHTuWH3/8EY1G8zvsOjBr5+3FafdgTtDTd0Jcl3aWb7+jbetWZDod0Q8/HNDG4XEwe8NsAC7vfTm9wnqdkD0LBAKBQPBn4ZQQOsXFxR0+Hz9+PD6f74jrrrrqKq666qoTs6njQEVeE3nrq0EG4/+WgVwR2IHmbW4+OObh1ltQxQTOuXlv13uUt5YTqYvklgG3nLB9CwQCgUDwZ+GUDF39GfB6fKz4zD/moc/YOKJTTF3a1r78Ct6mJjQ90gm78sqANiXWEt7b+R4A/xj6D3Qq3fHftEAgEAgEfzKE0DlBZP9USlO1Ha1BxYhzA3c1Bmjbvp3mL74AIPrxx5GpOpedS5LE7A2zcfvcjI4dzeSkySds3wKBQCAQ/JkQQucE4HF52fFzOQCjL+zRZc8cyeOh6sknQZIwnXsuuiFDAtr9VPITayrXoJareej/27v36JjP/A/g7xmTG5FErptMgpBqkSi/iNKGIlKSuJRupah1KyWNbpIW0UqD6km7bktUbX9b0qIs2lPHEieE/LrqGlWyCCJyT0VcMkFmkpl5fn9Ys51mVDTfmWHyfp0z58jzPDPfz3xc5u0738tz7z12Z5URERE9rh6LY3RsjcK+FWLfC8P5wxXo0sfngetubtkKzbnzkLu6wnuO6ftU3Wm4g09OfAIAmBYyDe1d2pulZiIiIlvEoGMmbdwc0Ds68IHz2uvXcW31agCAd2ICFL+4GOIvrTu9DlV3q+Dv7I+pwVPNUisREZGt4ldXVlK1ciX0tbVw7NYNbq++anJNYU0hNp3bBACY/9x8OCpMX4OHiIiITGPQsYK6vDzUfPMtAMBnwQLIWjW+6J8QAp8c/wRaocVA/4EY4D/A0mUSERE98Rh0LEzo9fh5yZJ7ByCPGvnAm3bmlObgcMVh2MntMCdsjmWLJCIishEMOhZW891OqE+fgbx1a3i9847JNRqdBn858RcAwKTuk3gAMhER0e/EoGNButpaVK1YAQDwfCsOdt7eJtd9dfare1dAdvLG9JDpliyRiIjIpjDoWFD1p2uhq66GfceOcJ840eSan+/8jP/N+18AQFLvJF4BmYiIqBkYdCxEU1iIG5vunUHl8/57kNnbm1y38uRK1Gnr0Mu7F6IDoy1ZIhERkc1h0LGQq598Ami1cB40CM79+5tcc6rqFPZc2QMZZJjfZz6vgExERNRMDDoWcPvQD7jzf98DCgW855o+g0ov9PjL8XsHII95agy6enS1ZIlEREQ2iUHHzIRWi6pPPgYAuE8YD4dA01dL3l24G/++/m+0VrRGfK94S5ZIRERksxh0zOzWjh3QXCpAK1dXeMbFmVxTp63Dqh9XAQCm95gOTydPS5ZIRERksxh0zEhXW4trq9MBAJ7x8Wjl6mpy3Zdnv8TVu1fh18YPE7uZPhuLiIiIHh2DjhlVr1sH3Y0bsO/UCe1eizW5pupuFdb/ez0AICE0AQ6tHCxZIhERkU1j0DGT+pIS3PxqIwDAZ95cyOzsTK5LP5WOOm0denj1wLCOwyxZIhERkc1j0DGTqqXLIBoa0OaFF9BmgOkbcp6/fh47C3YCAOaGzeXp5ERERBJj0DEDvUYDXW0tIJfDe57pACOEwLLcZRAQiAqMwrNez1qhUiIiItumsHYBtkju4ID2G9ZDc/EiHLt0MbnmUPkhHP/5OOzkdkj4nwTLFkhERNRCcI+OmchkMjg+/bTJOZ1ehxUn793cc0LXCfBz9rNkaURERC0Gg44V7CrchYJbBWhr3xZvhLxh7XKIiIhsFoOOham1aqw5tQYAMCNkBlwdTF9bh4iIiJqPQcfCNp/fjKt3r8K3jS/GdR1n7XKIiIhsGoOOBd1S38IXeV8AAGb3ms2LAxIREZkZg44FfZ73OWobavF0u6cR0ynG2uUQERHZPAYdCym/XY4t+VsAAEmhSZDL2HoiIiJz46ethaz9aS20ei2e830Ozyuft3Y5RERELQKDjgUU3CzArsu7AIAXByQiIrIgBh0LWPPTGggIDGk/BMGewdYuh4iIqMVg0DGzvGt5yC7JhlwmR3yveGuXQ0RE1KJYLejo9XocPXoUSUlJcHd3R0ZGhtG8RqNBcnIygoKC4Ofnh5EjR6K8vNxoTXl5OWJjY9GxY0colUokJiZCo9FY8F083OpTqwEAA0ezLgAAEUxJREFUwzsNR2e3zlauhoiIqGWxWtDZsGED3n77bbRu3RqtWrVqNB8XF4cjR44gNzcXJSUlCAoKQlRUFHQ6HQCgvr4ekZGR8Pf3R0FBAc6ePYuTJ08iMTHR0m/lgY5VHsPRyqNQyBWI6xln7XKIiIhaHKsFnWnTpuH48eNYsmQJ2rRpYzRXUlKCjIwMrFixAm5ublAoFPj4449RUVGB3bt3AwC2bduGq1evIi0tDQqFAm5ubli5ciW++OILVFdXW+MtGRFCYNWPqwAAY7uMhdJZaeWKiIiIWp7H8hidnJwc+Pj4IDQ01DBmb2+Pl156CZmZmQCAAwcOYOjQobC3tzesCQ0NhYeHB7Kzsy1e868dLD2IvOo8OCmcML3HdGuXQ0RE1CIprF2AKRUVFfDz82s0rlQqceHCBcOa4ODGZzAplcpGx/L8kkajMTqOR6VSSVCxMZ1eh/RT6QCA17u+Dk8nT8m3QURERA/3WO7RsbOzg1zeuDSZTPZIa0xJS0uDq6ur4REQEND8gn9FDz1eeeoVdHTpiEndJ0n++kRERNQ0j2XQ8ff3R0VFRaPxyspKKJXKJq8xZf78+aipqTE8SktLpSv8P+zkdni92+vY+fJOuDq4Sv76RERE1DSPZdAZPHgwqqqqcObMGcOYTqfDwYMHERUVBQAYNmwYsrKyoNVqDWvy8/NRVVWFiIiIB762g4MDXFxcjB7mwvtZERERWddj+Uns5eWFKVOmICkpCSqVCjqdDu+//z7c3NwQHR0NAIiJiYG3tzdSUlKg0+lQU1OD+Ph4TJkyBZ6ePCaGiIiIHtOgAwCrV69GSEgIunXrBn9/f5w/fx579+6FQnHv+GmFQoG9e/fi3LlzCAgIQPfu3RESEoJVq1ZZuXIiIiJ6XMiEEMLaRViTSqWCq6srampqzPo1FhEREUmnqZ/fj+0eHSIiIqLmYtAhIiIim8WgQ0RERDaLQYeIiIhsFoMOERER2SwGHSIiIrJZDDpERERksxh0iIiIyGYx6BAREZHNUli7AGu7f2FolUpl5UqIiIioqe5/bj/sBg8tPujU1tYCAAICAqxcCRERET2q2tpauLq6PnC+xd/rSq/Xo6KiAm3btoVMJpPsdVUqFQICAlBaWsp7aJkR+2w57LVlsM+WwT5bhjn7LIRAbW0t/Pz8IJc/+EicFr9HRy6Xw9/f32yv7+Liwr9EFsA+Ww57bRnss2Wwz5Zhrj7/1p6c+3gwMhEREdksBh0iIiKyWQw6ZuLg4IDU1FQ4ODhYuxSbxj5bDnttGeyzZbDPlvE49LnFH4xMREREtot7dIiIiMhmMegQERGRzWLQISIiIpvFoENEREQ2i0HHTDIyMhAcHAx/f3+EhYXh0KFD1i7pibd+/XoEBwdDqVTimWeewWeffWY0r9FokJycjKCgIPj5+WHkyJEoLy+3UrVPvuLiYri5uWHy5MmGMfZYOoWFhRg1ahR8fX3h5+eH2NhYVFZWGubZa2ncvn0bc+bMQWBgIAICAhAcHIx169YZ5tnn30ev1+Po0aNISkqCu7s7MjIyjOab0tfy8nLExsaiY8eOUCqVSExMhEajkbxWBh0z2LhxI+bPn4/t27ejrKwMc+fORUxMDAoLC61d2hNr48aNSE1NxT/+8Q+Ul5fju+++w4cffojNmzcb1sTFxeHIkSPIzc1FSUkJgoKCEBUVBZ1OZ8XKn0x6vR4TJ05Ehw4djMbZY2ncvHkTL774IsLDw1FWVobCwkI4ODhg9erVhjXstTQmTpyIU6dO4cSJEygtLcXmzZuxaNEirFmzBgD7/Htt2LABb7/9Nlq3bo1WrVo1mn9YX+vr6xEZGQl/f38UFBTg7NmzOHnyJBITE6UvVpDkOnfuLJYtW2Y0Nnz4cJGYmGilip58cXFx4uuvvzYaS0pKEqNHjxZCCFFcXCzkcrnIzc01zGs0GuHh4SF27txp0VptwYcffihiYmJEamqqmDRpkhCCPZbSggULxIABA4zGtFqt4dfstXQcHR0b9SwhIUGMGDGCfZZIhw4dxIYNGww/N6WvGzduFO7u7kKj0RjW5ObmCnt7e3Ht2jVJ6+MeHYmVlJTg8uXLGDFihNH4iBEjkJmZaaWqnnyffvopxo0bZzSWl5dnuHdKTk4OfHx8EBoaapi3t7fHSy+9xL4/ouPHj2PVqlVYu3at0Th7LJ1du3Zh9OjRRmO//F8xey2d0NBQ7Nq1C+I/l4y7c+cOcnJyEB4ezj6bSVP6euDAAQwdOhT29vaGNaGhofDw8EB2drak9TDoSKyiogIA4OfnZzSuVCr5va9EGhoaMHv2bBw5cgTvvvsugHt9/3XPAfb9Ud2+fRvjx4/HX//6V7Rv395ojj2WTkFBAby9vTF16lQEBgaiR48e+Oijj6DVagGw11Latm0bqqqq0KtXL8THx+PFF1/EtGnTMGfOHPbZTJrSV0v2nkFHYnZ2dgDQ6JbxMpnMGuXYnOLiYvTv3x/Z2dk4dOgQgoODAdzr+697DrDvjyo+Ph69e/fGhAkTGs2xx9LR6XRITU3F+PHjUVhYiB07dmDLli2YN28eAPZaSteuXcP169fRr18/hIWFwdXVFbt370ZlZSX7bCZN6asle8+gIzF/f38A/92zc19lZSWUSqU1SrIZJ0+eRFhYGMLDw3Hq1Ck8++yzhjl/f/9GPQfY90exfft27N+/v9HZbPexx9Jp3749Jk+ejCFDhkAmk6FLly5ISUnBV199BYC9lopKpcKQIUPw7rvv4rPPPsOkSZOQnZ2NoKAgTJgwgX02k6b01ZK9Z9CRmI+PD3r27Ik9e/YYje/btw9RUVFWqurJV1xcjOjoaHz66adYtmxZoxvEDR48GFVVVThz5oxhTKfT4eDBg+x7E+3evRvl5eVwd3eHTCaDTCbDokWL8OWXX0Imk0Eul7PHEunfvz/q6+sbjd//c80/z9LIz89HdXU1Bg4caDQeGRmJY8eOsc9m0pS+Dhs2DFlZWYava4F7v19VVVWIiIiQtiBJD20mIYQQX3/9tVAqleLChQtCCCG+++474eLiIi5dumTlyp5cUVFRYuHChb+5ZsaMGSIiIkLU1NQIrVYr5s2bJ7p37y4aGhosVKXt+eVZV0Kwx1K5dOmS8PHxEfv27RNCCFFSUiK6d+8uUlJSDGvY6+arra0V3t7eYvbs2eLOnTtCCCGKiopE3759xcsvvyyEYJ+l8OuzroR4eF8bGhpE9+7dRXJystBqteLWrVsiIiJCvPnmm5LXx6BjJuvWrRNPPfWU8PX1FWFhYeL777+3dklPNADC29tbKJXKRo/71Gq1SEhIEEqlUvzhD38QI0eOFKWlpVas+sn366DDHksnJydH9OnTR3h5eYlOnTqJxYsXG324stfSOH/+vBg7dqxQKpXC19dXdOrUScybN0/U1tYKIdhnKZgKOk3pa2lpqRg5cqTw9fUVSqVSJCQkCLVaLXl9MiH+c84dERERkY3hMTpERERksxh0iIiIyGYx6BAREZHNYtAhIiIim8WgQ0RERDaLQYeIiIhsFoMOEdmU06dPIzw8HP379zd5iXlzU6vVOHDgAADA09MTALBu3TrU19fj6NGjmDJlisVrImrJFNYugIhsj1qtRnV1teHeb5b097//Hd988w2uXLmC7du3489//nOjNXq9HteuXYNcLoeXl5fJ11Gr1XBycnrofXd0Oh2EEPj5558BAHV1dRgzZgzy8/MBAD/88APS09Mxc+ZM5OXlQa/XN/MdEtGjYNAhIkmcOHECubm5mDVrFo4ePYrXX38dZWVlZtmWEAI6nQ46nQ5ardbo13379sXy5ctx48YNvPnmm0bPu3DhAhYvXoycnBzU1NTA19cXdXV1GDVqFN577z2ToeZh76GoqAh9+/Y1/NyuXTvMmjULly5dAgAUFBRg4cKFAIDc3FxotVrs3bvXsD44ONgqgZCopWDQISJJnDlzBjt27MCsWbPMto3Lly+jS5cuRntFZDIZFAoF7OzsIIRAeHg4li9fDicnJwQFBRnW7dq1C3FxcUhNTcWGDRvQo0cPrF+/Hr169UJ6ejqee+457N+/H88880yzavzjH/+IgoICZGZm4tatW1i5ciUA4Pr16/jXv/4FDw8PrFmzBrm5uQgMDMSiRYsYdIjMiEGHiCTR0NAAe3t7s24jMDAQ1dXVhmBjZ2eHVq1aGeYXL16MH3/8ESEhIUbPy8/Px4wZM5CVlYWQkBBotVoUFRUhKCgITk5OmDt3LhoaGjB16lQcPny40Xa3bt2KxMREw93FAUCj0SA9PR29e/c2Wrtjxw6UlZVh5syZyM/Px6hRo/DWW2/h5s2biIuLQ01NDdq2bYvw8HB8/vnn6Natm8RdIqJf4sHIRCSJu3fvwtnZ2azbkMvlaNeuHdq2bQtHR0ejkAMA+/btw4ABAxo9b+HChXjnnXcMAejMmTPw8vKCt7e3YU1cXByOHDmC4uLiRs9Xq9WIiYlBUVGR4TF06FCo1epGa1esWIGYmBgsXboUzs7OiIiIwPjx4w17diorKwEAV65cQadOnX5/M4ioSRh0iEgS169fh4eHxwPny8vLsWDBAgD3jkuRyWRNetw/vuVhLl26hMOHD2PMmDGN5jIzMxEbG2v4OSsrC4MGDTJacz9ANfdMLXd3dxw8eBAlJSXo378/BgwYgP379+P06dOYOXMm9u7di8rKSigUCjg6OjZrW0T0cPzqiogkcfHiRfTp08fknFqtRmxsLDp37gwAyM7ORkNDQ5Ne18XFpUnrUlJSMHr0aHTs2NFovL6+HiqVyujsqi1btmDRokVG61QqFW7fvv2bYa0pJk+eDAD49ttvMW7cOMN4eno6AgMDMXjwYLi4uCAiIqJZ2yGipmHQIaJmu3v3LrKyspCQkNBorq6uDmPHjgVw73oyAODj4yPp9jdv3ox//vOfOH36dKM5e3t7+Pj44OLFi+jRowf27duHGzduYPjw4UbrMjIy0KFDB3Tp0qVZtURHR+PKlSsoLi7GsWPHkJiYCJ1Oh4kTJ2Lp0qXo2bMn5syZg02bNjVrO0TUNPzqioiaLS0tDQEBAXj++eeNxouKijBo0CCoVCpkZmbCyclJ8m1v2bIFb7zxBtavX2/YY/RrkyZNwsKFC1FWVob4+HgsWbIECsV//5+3bds2zJs3D8uXLzf5fBcXF+Tk5CAoKMjwOHToENq2bdto7Z49e/DKK68gJSUFP/30EyIjI7F27VosXboUABAZGYlbt26hX79+Erx7InooQUTUDBs3bhSOjo7ihx9+MIwdPHhQODo6CmdnZzFr1ixRX18v+XZLS0vFn/70J+Hs7Cy2b9/+m2tv374tBg8eLGQymUhISBBCCHHu3DmRlpYmevfuLTw9PcXWrVuNnlNXVyea8k/klStXhI+Pj+FnvV4vpkyZIoKDg8UHH3wgnn76aaHRaIQQQpSXlwtvb2/xwgsviMjISKFWqx/1bRPRI5IJIYS1wxYRPZlqamrQr18/pKWlYdSoUYbx6upqzJw5E9OnT8fQoUMl325ycjJWrlyJ6OhoLF++vMlnL9XV1Rn2Kl2+fBkffPABhgwZgldffbXRGWO/98rI9/3tb39DcnIynJ2dMXnyZEyYMAGjR4/Gyy+/jI8++gjjxo3D5cuXsXXrVqPr/RCRtBh0iKhZhBCQyWQW3WZhYSE0Gg26du1qtm3cDzoP+yfy/pWR7wedTZs2YfHixejZs6fhwoU5OTlYsmQJYmNjMX/+fAD3AtJbb72FgQMH4rXXXjPb+yBq6Rh0iIgkpFKpoNPp0K5dO6PxX+5NIiLLYdAhIiIim8WzroiIiMhmMegQERGRzWLQISIiIpvFoENEREQ2i0GHiIiIbBaDDhEREdksBh0iIiKyWQw6REREZLMYdIiIiMhm/T/ypSmlO0PhRgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_lst = range(100,300,10)      # 1\n",
    "\n",
    "ax = pd.DataFrame({'capital':[],\n",
    "                   'output':[]}).plot(legend=False)  # 2\n",
    "\n",
    "for i in initial_lst:                 # 3\n",
    "    \n",
    "    solow_model(k0=i).plot(y='capital', legend=False, ax=ax)\n",
    "    \n",
    "ax.set(title='ソロー・モデルの移行過程',  # 4\n",
    "       xlabel='ループの回数',\n",
    "       ylabel='一人当たり資本ストック')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "````{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "* `#1`：`range(100,300,10)`は100から300-1=299までの間の数を10間隔で生成する。100，110，120，$cdots$，290となる。\n",
    "* `#2`：空の`DataFrame`を使って空の軸を作成し，`ax`に割り当てる。\n",
    "* `#3`：`initial_list`に対して`for`ループを設定する。一回のループごとに以下をおこなう。\n",
    "    * `i`は`k0`の引数に使う値になる。\n",
    "    * `.plot()`を使い`ax`に図をプロットする。これにより図が重ねて描かれる。\n",
    "* `#4`：`ax`のメソッド`set()`を使い，引数を使い以下を追加する。\n",
    "    * `title`：図のタイトル\n",
    "    * `xlabel`：横軸のラベル\n",
    "    * `ylabel`：縦軸のラベル\n",
    "    * この３行を次のように書いても同じ結果となる。\n",
    "        ```\n",
    "        ax.set_title('ソロー・モデルの移行過程')\n",
    "        ax.set_xlabel('ループの回数')\n",
    "        ax.set_ylabel('一人当たり資本ストック')\n",
    "        ```\n",
    "      この３つを`.set()`でまとめて書いたのが上のコードである。３つに分けて書く利点はフォントの大きさを指定できることだろう。\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "図から初期値に関わらず定常値に収束していることが分かる。即ち，定常状態である長期均衡は安定的である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## 定常状態での変数の値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "次に定常状態での変数の値を計算してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def calculate_steady_state(A=10, a=0.3, s=0.3, n=0.02, d=0.05):\n",
    "    \n",
    "    k_ss = ( s * A / (n+d) )**( 1/(1-a) )    \n",
    "    y_ss = A * k_ss**( a/(1-a) )    \n",
    "    \n",
    "    return k_ss, y_ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "定常状態での資本ストック:214.5\n",
      "定常状態での産出量: 99.8\n"
     ]
    }
   ],
   "source": [
    "ss = calculate_steady_state()\n",
    "\n",
    "print(f'定常状態での資本ストック:{ss[0]:.1f}'\n",
    "      f'\\n定常状態での産出量: {ss[1]:.1f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## 線形近似"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### 説明"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "{numref}`fig:8-solow`は，定常状態は安定的であることを示している。またシミュレーションの結果からも定常状態の安定性が確認できる。次に，線形近似を使って解析的に安定性を確認してみることにする。また線形近似は真の値からの乖離が発生するが，その乖離がどの程度のものかをコードを使って計算することにする。\n",
    "\n",
    "＜テイラー展開による１次線形近似＞\n",
    "* 関数$z=f(x)$を$x_*$でテイラー展開すると次式となる。\n",
    "\n",
    "    $$\n",
    "    z=f(x^*)+\\left.\\frac{df}{dx}\\right|_{x=x_*}(x-x_*)\n",
    "    $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ソロー・モデルの式に当てはめると次のような対応関係にある。\n",
    "* $z\\;\\Rightarrow\\;k_{t+1}$\n",
    "* $f(x)\\;\\Rightarrow\\;\\dfrac{Ask_{t}^{\\alpha}+(1-d)k_t}{1+n}$\n",
    "* $x^*\\;\\Rightarrow\\;k^*$\n",
    "\n",
    "公式に従って計算してみよう。\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "k_{t+1}\n",
    "&=\\frac{Ask_{*}^{\\alpha}+(1-d)k_*}{1+n}\n",
    "+\\frac{1}{1+n}\\left[\\frac{Asa}{k_t^{1-\\alpha}}+(1-d)\\right]_{k_t=k_*}(k_t-k_*) \\\\\n",
    "&=k_{*}\n",
    "+\\frac{1}{1+n}\\left[\\frac{Asa}{k_*^{1-\\alpha}}+(1-d)\\right](k_t-k_*) \\\\\n",
    "&=k_*+\\frac{1}{1+n}\\left[\\frac{Asa}{As/(n+d)}+(1-d)\\right](k_t-k_*) \\\\\n",
    "&=k_*+\\frac{a(n+d)+1-d-n+n}{1+n}(k_t-k_*) \\\\\n",
    "&=k_*+\\frac{1+n-(1-a)(n+d)}{1+n}(k_t-k_*) \\\\\n",
    "&=(1-\\lambda) k_t + \\lambda k_*\n",
    "\\end{align*}\n",
    "$$ (eq:8-kapprox)\n",
    "\n",
    "ここで\n",
    "\n",
    "$$\n",
    "\\lambda\\equiv \\frac{(1-a)(n+d)}{1+n}\n",
    "$$ (eq:8-lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "３行目は定常状態の式[](eq:8-kdot)と式[](eq:8-kss)を使っている。式[](eq:8-kapprox)は$k_{t+1}$と$k_t$の線形差分方程式になっており，$k_t$の係数は\n",
    "\n",
    "$$\n",
    "0<1-\\lambda<1\n",
    "\\quad\\because\n",
    "0<a,d<1\n",
    "$$ (eq:8-coef_of_kt)\n",
    "\n",
    "が成立する。{numref}`fig:8-solow`の赤い直線が式[](eq:8-kapprox)である。従って，初期値$k_0>0$からスタートする経済は必ず長期的均衡に収束することがわかる。\n",
    "\n",
    "式[](eq:8-lambda)は$k_t$の係数だが，その裏にあるメカニズムを考えてみよう。特に，$a$の役割を考える。$a$は資本の所得比率であり，目安の値は1/3である。そしてソロー・モデルにおける重要な役割が**資本の限界生産性の逓減**を決定することである。この効果により資本ストックが増加する毎に産出量も増加するがその増加自体が減少する。この効果により，{numref}`fig:8-solow`の曲線は凹関数になっており，生産関数[](eq:8-production)の場合は必ず45度線と交差することになる。即ち，資本の限界生産性の逓減こそが$k_t$が一定になる定常状態に経済が収束す理由なのである。この点がソロー・モデルの一番重要なメカニズムとなる。\n",
    "\n",
    "ここで$a$が上昇したとしよう。そうなると資本の限界生産性の逓減の効果は弱くなり，資本ストックが増加しても産出量の増加自体の減少は小さくなる。また式[](eq:8-kss)が示すように定常状態での資本ストックはより大きくなる。これは{numref}`fig:8-solow`で曲線が上方シフトしている考えると良いだろう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} 内生的成長\n",
    ":class: note\n",
    "更に$a$を上昇させて$a=1$になるとどうなるのだろう。この場合，資本の限界生産性は逓減せず一定となる。そして$k_t$の係数である式[](eq:8-coef_of_kt)は1になってしまい，$k_t$が一定になる定常状態が存在しなくなる。$a=1$となる極限の状態を内生的成長と呼ぶ。ここでは立ち入った議論はしないが，内生的成長の典型的な生産関数は次式となり，\n",
    "\n",
    "$$y_t=Ak_t$$\n",
    "\n",
    "この生産関数に基づくモデルは$AK$モデルと呼ばれる。資本の限界生産性は$A$で一定になることが分かると思う。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### $\\lambda$の解釈"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "上の議論から$\\lambda$が定常状態の安定性を決定することが分かったが，$\\lambda$の値はどのように解釈できるだろうか。例えば，$\\lambda$が大きい場合と小さい場合では何が違うのだろうか。次式は式[](eq:8-kapprox)の最後の等号を少し書き換えたものである。\n",
    "\n",
    "$$\n",
    "k_*-k_{t+1}=(1-\\lambda)(k_*-k_t)\n",
    "$$ (eq:8-approx_lastline)\n",
    "\n",
    "左辺は$t+1$期において定常状態までの残りの「距離」であり，右辺の$k_*-k_t$は$t$においての定常状態までの残りの「距離」である。後者を次の様に定義し\n",
    "\n",
    "$$z_t\\equiv k_*-k_t$$\n",
    "\n",
    "式[](eq:8-approx_lastline)を整理すると次式となる。\n",
    "\n",
    "$$\n",
    "\\frac{z_{t+1}-z_t}{z_t}=-\\lambda\n",
    "$$ (eq:8-kspeed)\n",
    "\n",
    "左辺は$t$期と$t+1$期において定常状態までの「距離」が何％減少したかを示す**資本ストックの収束速度**である。このモデルの中での収束速度の決定要因は資本の所得比率$\\alpha$，労働人口増加率$n$と資本の減耗率$d$ということである。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ここでは$a$の役割に着目し，なぜ$a$の上昇は収束速度の減少をもたらすのかを直感的に考えてみよう。この点を理解するために，まず$a$は資本の限界生産性の逓減を決定するパラーメータであることを思い出そう。$a$が上昇するとその効果は弱まる。即ち，資本ストックが１単位増加すると産出量は増え，その増加分が減少するのが「逓減」であるが，その減少が小さくなるのである。これにより（上で説明したように）$k_t$が一定となる定常状態は増加することになる。重要な点は，定常状態の増加の意味である。定常状態はマラソンのゴールの様なものである。トップランナーはゴールすると走るのを止め，後続ランナーはトップランナーとの「距離」を縮めることができる。定常状態の増加は，ゴールが遠くなることと同じである。ゴールが遠のくとトップランナーは走り続けるわけだから，それだけ距離を縮めることが難しくなり収束速度が減少することになる。極端なケースとして$a=1$の場合，$k_t$が一定になる定常状態は存在せず，ゴールがない状態が永遠に続いており，永遠に収束しないということである。言い換えると，資本の限界生産性の逓減（$a<1$）こそが「距離」を縮めキャッチアップを可能にするメカニズムなのだ。\n",
    "\n",
    "労働人口増加率$n$と資本の減耗率$d$の上昇は収束速度を速くする。式[](eq:8-kss)から分かる様に，$n$もしくは$d$の上昇は定常状態を減少させる。即ち，ゴールはより近くになるということだ。\n",
    "\n",
    "これである程度キャッチアップのメカニズムが分かったと思うが，今までの議論で足りないものが２点あるので，それらについて簡単に言及する。第一に，ここで考えたソロー・モデルには技術進歩が抜けている（一定な$A$を仮定した）。この点を導入してこそソロー・モデルのフルバージョンであり，その場合の労働効率１単位当たり資本ストック（$K_t/(A_tL_t)$）の収束速度は次の式で与えられる。\n",
    "\n",
    "$$\n",
    "\\lambda\\equiv \\frac{(1-a)(g+n+d+ng)}{(1+n)(1+g)}\n",
    "$$ (eq:8-lambda_g)\n",
    "\n",
    "ここで$g$は技術進歩率である。ソロー・モデルでは4つの変数が収束速度の決定要因になるる。$g=0$の場合，式[](eq:8-lambda)と同じになることが確認できる。第二に，式[](eq:8-lambda)は資本ストックの収束速度であり一人当たりGDPの収束速度と異なるのではないかという疑問である。実は同じである。これはコブ・ダグラス生産関数[](eq:8-production)を仮定しているからであり，対数の近似を使えば簡単に示すことができる。式[](eq:8-approx_lastline)を次のように書き直そう。\n",
    "\n",
    "$$\n",
    "\\frac{k_{t+1}}{k_*}-1=(1-\\lambda)\\left(\\frac{k_t}{k_*}-1\\right)\n",
    "$$ (eq:8-ks_rewrite)\n",
    "\n",
    "ここで$\\log(1+x-1)\\approx x-1$の近似を使い左辺を次のように書き換える。\n",
    "\n",
    "$$\n",
    "\\frac{k_{t+1}}{k_*}-1\n",
    "\\approx\\log\\left(\\frac{k_{t+1}}{k_*}\\right)\n",
    "=\\log\\left(\\frac{y_{t+1}}{y_*}\\right)^{\\frac{1}{\\alpha}}\n",
    "=\\frac{1}{\\alpha}\\left(\\frac{y_{t+1}}{y_*}-1\\right)\n",
    "$$\n",
    "\n",
    "同様に$\\dfrac{k_{t}}{k_*}-1$もこの形に書き換えることができる。後はこの関係を使うことにより，式[](eq:8-ks_rewrite)を整理すると次式となる。\n",
    "\n",
    "$$\n",
    "y_*-y_{t+1}=(1-\\lambda)(y_*-y_t)\n",
    "$$ (eq:8-y_difference_eq)\n",
    "\n",
    "式[](eq:8-approx_lastline)と同じ形になっているので所得の収束速度も式[](eq:8-kspeed)と同じである。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### 線形近似による誤差"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "次に関数`solow_model()`を修正して線形近似の誤差を確かめてみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def solow_model_approx(k0, A=10, a=0.3, s=0.3, n=0.02, d=0.05, T=20):\n",
    "    \"\"\"引数\n",
    "            k0: 資本の初期値\n",
    "            A: 生産性\n",
    "            a: 資本の所得比率 (a<1)\n",
    "            s: 貯蓄率 (s<1)\n",
    "            n: 労働人口成長率（n>=0）\n",
    "            d: 資本減耗率 (d<1)\n",
    "            T: ループによる計算回数\n",
    "       戻り値\n",
    "            線形近似モデルを使い計算した資本と産出量からなるDataFrame\"\"\"\n",
    "    \n",
    "    k = k0\n",
    "    y = A * k0**a\n",
    "    \n",
    "    k_lst = [k]\n",
    "    y_lst = [y]\n",
    "\n",
    "    # 定常状態\n",
    "    k_ss = ( s*A / (n+d) )**( 1 / (1-a) )    \n",
    "    \n",
    "    for t in range(T):\n",
    "        \n",
    "        lamb = 1 - (1-a) * (n+d) / (1+n)  # lambda\n",
    "        k = lamb*k + (1-lamb) * k_ss  # 線形近似\n",
    "        y = A * k**a\n",
    "\n",
    "        k_lst.append(k)\n",
    "        y_lst.append(y)\n",
    "\n",
    "    # DataFrameの作成\n",
    "    dic = {'capital':k_lst, 'output':y_lst}\n",
    "    df = pd.DataFrame(dic)\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "近似誤差を計算するために，上と同じ数値でシミュレーションをおこなう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "df_approx = solow_model_approx(k0=200, T=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "非線形のモデル[](eq:8-kdot)と線形近似のモデル[](eq:8-kapprox)で計算された資本ストックを重ねて図示してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df_approx.plot(y='capital', label='線形近似モデル')\n",
    "df.plot(y='capital', label='ソロー・モデル', ax=ax)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`df_approx`が図示され、その上に`df`が重ねて表示されるが、殆ど同じのように見える。誤差を％で計算し図示してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "( 100*( 1-df_approx['capital']/df['capital'] ) ).plot(marker='.')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "初期の資本ストック$k_0$は同じなので誤差はゼロであり，$t=1$から線形近似の誤差が現れることになる。誤差は単調ではない。{numref}`fig:8-solow`の図が示しているように，階段のような形で増加していくためであり，その階段お大きさや進み具合が異なるためである。線形近似の値は大き過ぎるため負の値になっているが、誤差は大きくても約0.02％であり、定常状態に近づくにつれて誤差はゼロに近づいている。もちろん，誤差の値は初期値が定常値から離れればそれだけ大きくなっていく。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 長期均衡の予測"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 説明"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'myst_nb'",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mModuleNotFoundError\u001b[39m                       Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[22]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmyst_nb\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m glue\n\u001b[32m      2\u001b[39m pwt = py4macro.data(\u001b[33m'\u001b[39m\u001b[33mpwt\u001b[39m\u001b[33m'\u001b[39m)\n\u001b[32m      3\u001b[39m latest_year = \u001b[38;5;28mint\u001b[39m( pwt[\u001b[33m'\u001b[39m\u001b[33myear\u001b[39m\u001b[33m'\u001b[39m].max() )\n",
      "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'myst_nb'"
     ]
    }
   ],
   "source": [
    "from myst_nb import glue\n",
    "pwt = py4macro.data('pwt')\n",
    "latest_year = int( pwt['year'].max() )\n",
    "glue(\"latest_year_glued\", latest_year)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この節では長期均衡（定常状態）に焦点を当て，理論的な予測のデータとの整合性をチェックする。まず定常状態の特徴をまとめよう。式[](eq:8-kss)と[](eq:8-yss)を使いうと定常状態での一人当たり資本ストックとGDPは次式で与えれる。\n",
    "\n",
    "$$\n",
    "k_*=\n",
    "\\left(\n",
    "     \\frac{sA}{n+d}\n",
    "\\right)^{\\frac{1}{1-a}},\n",
    "\\quad\n",
    "y_*=Ak_*^a\n",
    "$$\n",
    "\n",
    "この２つをそれぞれ試すこともできるが，同時に捉えるために２つの式の比率を考える。\n",
    "\n",
    "$$\n",
    "\\frac{k_*}{y_*}=\\frac{s}{n+d}\n",
    "=\\left.\\frac{K_t/L_t}{Y_t/L_t}\\right|_{\\text{定常状態}}\n",
    "=\\left.\\frac{K_t}{Y_t}\\right|_{\\text{定常状態}}\n",
    "$$ (eq:8-kyratio)\n",
    "\n",
    "この値は資本ストック対GDP比と等しいく，次のことが分かる。\n",
    "* 貯蓄率$s$の上昇は資本ストック対GDP比を増加させる。。\n",
    "* 労働人口成長率$n$の上昇は資本ストック対GDP比を減少させる。\n",
    "* 資本減耗率$d$の上昇は資本ストック対GDP比を減少させる。\n",
    "\n",
    "この３つの予測が成立するか確かめるために`py4macro`モジュールに含まれるPenn World Tableの次の変数を使う。\n",
    "* `cgdpo`：GDP（{glue:text}`latest_year_glued`年;生産側）\n",
    "* `cn`：物的資本ストック（{glue:text}`latest_year_glued`年）\n",
    "* `csh_i`：対GDP比資本形成の比率\n",
    "    * 投資の対GDP比である。\n",
    "    * 貯蓄率$s$の代わりに使う。\n",
    "    * 1960年〜{glue:text}`latest_year_glued`年の平均を使う。\n",
    "* `emp`：雇用者数\n",
    "    * 労働人口の代わりに使う。\n",
    "    * 1960年〜{glue:text}`latest_year_glued`年の平均成長率$n$の計算に使う。\n",
    "* `delta`：資本ストックの年平均減耗率\n",
    "    * 1960年〜{glue:text}`latest_year_glued`年の平均を使う。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "### データ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "(sec:8-data)=\n",
    "### データ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "1960年以降のデータを`pwt`に割り当てる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "pwt = py4macro.data('pwt').query('year >= 1960')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "また、後で使うために、{glue:text}`latest_year_glued`年を変数`latest_year`に割り当てよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2023"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latest_yr = pwt['year'].max()\n",
    "latest_yr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 貯蓄率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "1960年から{glue:text}`latest_year_glued`年までの国別の貯蓄率の平均を計算するが必要がある。[ここで説明している](https://py4basics.github.io/3_Pandas.html#id33)`DataFrame`のメソッド`.groupby()`を使うのが最も簡単な計算方法だろう。ここでは異なる方法として`DataFrame`のメソッド`.pivot()`を紹介する。`.pivot()`はデータを整形する上で非常に便利なメソッドなので知って損はないだろう。\n",
    "\n",
    "`.pivot()`は，元の`DataFrame`から列を選び，その列から新たな`DataFrame`を作成する便利なメソッドである。実際にコードを実行して説明しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true,
    "scrolled": true,
    "tags": [
     "output_scroll"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>country</th>\n",
       "      <th>Albania</th>\n",
       "      <th>Algeria</th>\n",
       "      <th>Angola</th>\n",
       "      <th>Anguilla</th>\n",
       "      <th>Antigua and Barbuda</th>\n",
       "      <th>Argentina</th>\n",
       "      <th>Armenia</th>\n",
       "      <th>Aruba</th>\n",
       "      <th>Australia</th>\n",
       "      <th>Austria</th>\n",
       "      <th>...</th>\n",
       "      <th>United Arab Emirates</th>\n",
       "      <th>United Kingdom</th>\n",
       "      <th>United States</th>\n",
       "      <th>Uruguay</th>\n",
       "      <th>Uzbekistan</th>\n",
       "      <th>Venezuela (Bolivarian Republic of)</th>\n",
       "      <th>Viet Nam</th>\n",
       "      <th>Yemen</th>\n",
       "      <th>Zambia</th>\n",
       "      <th>Zimbabwe</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1960</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.292292</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.140910</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.336618</td>\n",
       "      <td>0.207003</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.239277</td>\n",
       "      <td>0.230340</td>\n",
       "      <td>0.144855</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.358695</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050083</td>\n",
       "      <td>0.189235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1961</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.334405</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.149655</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.296569</td>\n",
       "      <td>0.205342</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.241543</td>\n",
       "      <td>0.231433</td>\n",
       "      <td>0.154907</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.338576</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.046848</td>\n",
       "      <td>0.181016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.372550</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.132196</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.317393</td>\n",
       "      <td>0.187515</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.225732</td>\n",
       "      <td>0.236722</td>\n",
       "      <td>0.133602</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.349284</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.042926</td>\n",
       "      <td>0.128391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.355781</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.112345</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.309578</td>\n",
       "      <td>0.184681</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.225506</td>\n",
       "      <td>0.239582</td>\n",
       "      <td>0.122253</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.320073</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.031393</td>\n",
       "      <td>0.111248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1964</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.267336</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.137489</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.332907</td>\n",
       "      <td>0.207555</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.268017</td>\n",
       "      <td>0.240732</td>\n",
       "      <td>0.100760</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.389544</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.020332</td>\n",
       "      <td>0.114591</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 185 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "country  Albania   Algeria  Angola  Anguilla  Antigua and Barbuda  Argentina  \\\n",
       "year                                                                           \n",
       "1960         NaN  0.292292     NaN       NaN                  NaN   0.140910   \n",
       "1961         NaN  0.334405     NaN       NaN                  NaN   0.149655   \n",
       "1962         NaN  0.372550     NaN       NaN                  NaN   0.132196   \n",
       "1963         NaN  0.355781     NaN       NaN                  NaN   0.112345   \n",
       "1964         NaN  0.267336     NaN       NaN                  NaN   0.137489   \n",
       "\n",
       "country  Armenia  Aruba  Australia   Austria  ...  United Arab Emirates  \\\n",
       "year                                          ...                         \n",
       "1960         NaN    NaN   0.336618  0.207003  ...                   NaN   \n",
       "1961         NaN    NaN   0.296569  0.205342  ...                   NaN   \n",
       "1962         NaN    NaN   0.317393  0.187515  ...                   NaN   \n",
       "1963         NaN    NaN   0.309578  0.184681  ...                   NaN   \n",
       "1964         NaN    NaN   0.332907  0.207555  ...                   NaN   \n",
       "\n",
       "country  United Kingdom  United States   Uruguay  Uzbekistan  \\\n",
       "year                                                           \n",
       "1960           0.239277       0.230340  0.144855         NaN   \n",
       "1961           0.241543       0.231433  0.154907         NaN   \n",
       "1962           0.225732       0.236722  0.133602         NaN   \n",
       "1963           0.225506       0.239582  0.122253         NaN   \n",
       "1964           0.268017       0.240732  0.100760         NaN   \n",
       "\n",
       "country  Venezuela (Bolivarian Republic of)  Viet Nam  Yemen    Zambia  \\\n",
       "year                                                                     \n",
       "1960                               0.358695       NaN    NaN  0.050083   \n",
       "1961                               0.338576       NaN    NaN  0.046848   \n",
       "1962                               0.349284       NaN    NaN  0.042926   \n",
       "1963                               0.320073       NaN    NaN  0.031393   \n",
       "1964                               0.389544       NaN    NaN  0.020332   \n",
       "\n",
       "country  Zimbabwe  \n",
       "year               \n",
       "1960     0.189235  \n",
       "1961     0.181016  \n",
       "1962     0.128391  \n",
       "1963     0.111248  \n",
       "1964     0.114591  \n",
       "\n",
       "[5 rows x 185 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "saving = pwt.pivot(index='year', columns='country', values='csh_i')\n",
    "saving.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "`pwt`の３つの列`year`，`country`，`csh_i`を使って新たな`DataFrame`を作成し`saving`に割り当てている。引数は次の役割をする。\n",
    "* `index`：新たな`DataFrame`の**行ラベル**を指定する。\n",
    "    * コードでは`year`が指定され行ラベルになっている。\n",
    "* `columns`：新たな`DataFrame`の**列ラベル**を指定する。\n",
    "    * コードでは`country`が指定され列ラベルになっている。\n",
    "* `values`：新たな`DataFrame`の**値**を指定する。\n",
    "    * コードでは`csh_i`が指定され，その値で`DataFrame`が埋め尽くされている。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "1960年以降欠損値がない国だけを使うことにしよう。`NaN`がある列を削除する必要があるので`.dropna()`を使う。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true,
    "tags": [
     "output_scroll"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>country</th>\n",
       "      <th>Algeria</th>\n",
       "      <th>Argentina</th>\n",
       "      <th>Australia</th>\n",
       "      <th>Austria</th>\n",
       "      <th>Bangladesh</th>\n",
       "      <th>Barbados</th>\n",
       "      <th>Belgium</th>\n",
       "      <th>Benin</th>\n",
       "      <th>Bolivia (Plurinational State of)</th>\n",
       "      <th>Botswana</th>\n",
       "      <th>...</th>\n",
       "      <th>Tunisia</th>\n",
       "      <th>Türkiye</th>\n",
       "      <th>U.R. of Tanzania: Mainland</th>\n",
       "      <th>Uganda</th>\n",
       "      <th>United Kingdom</th>\n",
       "      <th>United States</th>\n",
       "      <th>Uruguay</th>\n",
       "      <th>Venezuela (Bolivarian Republic of)</th>\n",
       "      <th>Zambia</th>\n",
       "      <th>Zimbabwe</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1960</th>\n",
       "      <td>0.292292</td>\n",
       "      <td>0.140910</td>\n",
       "      <td>0.336618</td>\n",
       "      <td>0.207003</td>\n",
       "      <td>0.014559</td>\n",
       "      <td>0.090716</td>\n",
       "      <td>0.274124</td>\n",
       "      <td>0.039017</td>\n",
       "      <td>0.206834</td>\n",
       "      <td>0.102649</td>\n",
       "      <td>...</td>\n",
       "      <td>0.112642</td>\n",
       "      <td>0.196667</td>\n",
       "      <td>0.104302</td>\n",
       "      <td>0.098392</td>\n",
       "      <td>0.239277</td>\n",
       "      <td>0.230340</td>\n",
       "      <td>0.144855</td>\n",
       "      <td>0.358695</td>\n",
       "      <td>0.050083</td>\n",
       "      <td>0.189235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1961</th>\n",
       "      <td>0.334405</td>\n",
       "      <td>0.149655</td>\n",
       "      <td>0.296569</td>\n",
       "      <td>0.205342</td>\n",
       "      <td>0.017380</td>\n",
       "      <td>0.079419</td>\n",
       "      <td>0.294998</td>\n",
       "      <td>0.037919</td>\n",
       "      <td>0.163327</td>\n",
       "      <td>0.124339</td>\n",
       "      <td>...</td>\n",
       "      <td>0.146735</td>\n",
       "      <td>0.199453</td>\n",
       "      <td>0.117391</td>\n",
       "      <td>0.113316</td>\n",
       "      <td>0.241543</td>\n",
       "      <td>0.231433</td>\n",
       "      <td>0.154907</td>\n",
       "      <td>0.338576</td>\n",
       "      <td>0.046848</td>\n",
       "      <td>0.181016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962</th>\n",
       "      <td>0.372550</td>\n",
       "      <td>0.132196</td>\n",
       "      <td>0.317393</td>\n",
       "      <td>0.187515</td>\n",
       "      <td>0.026159</td>\n",
       "      <td>0.073334</td>\n",
       "      <td>0.280298</td>\n",
       "      <td>0.037577</td>\n",
       "      <td>0.267985</td>\n",
       "      <td>0.143526</td>\n",
       "      <td>...</td>\n",
       "      <td>0.187319</td>\n",
       "      <td>0.197619</td>\n",
       "      <td>0.099309</td>\n",
       "      <td>0.115779</td>\n",
       "      <td>0.225732</td>\n",
       "      <td>0.236722</td>\n",
       "      <td>0.133602</td>\n",
       "      <td>0.349284</td>\n",
       "      <td>0.042926</td>\n",
       "      <td>0.128391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963</th>\n",
       "      <td>0.355781</td>\n",
       "      <td>0.112345</td>\n",
       "      <td>0.309578</td>\n",
       "      <td>0.184681</td>\n",
       "      <td>0.018701</td>\n",
       "      <td>0.078361</td>\n",
       "      <td>0.269299</td>\n",
       "      <td>0.038658</td>\n",
       "      <td>0.227549</td>\n",
       "      <td>0.158613</td>\n",
       "      <td>...</td>\n",
       "      <td>0.192624</td>\n",
       "      <td>0.200368</td>\n",
       "      <td>0.088076</td>\n",
       "      <td>0.143015</td>\n",
       "      <td>0.225506</td>\n",
       "      <td>0.239582</td>\n",
       "      <td>0.122253</td>\n",
       "      <td>0.320073</td>\n",
       "      <td>0.031393</td>\n",
       "      <td>0.111248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1964</th>\n",
       "      <td>0.267336</td>\n",
       "      <td>0.137489</td>\n",
       "      <td>0.332907</td>\n",
       "      <td>0.207555</td>\n",
       "      <td>0.023628</td>\n",
       "      <td>0.076604</td>\n",
       "      <td>0.303141</td>\n",
       "      <td>0.032848</td>\n",
       "      <td>0.231306</td>\n",
       "      <td>0.195691</td>\n",
       "      <td>...</td>\n",
       "      <td>0.206365</td>\n",
       "      <td>0.197618</td>\n",
       "      <td>0.116514</td>\n",
       "      <td>0.182406</td>\n",
       "      <td>0.268017</td>\n",
       "      <td>0.240732</td>\n",
       "      <td>0.100760</td>\n",
       "      <td>0.389544</td>\n",
       "      <td>0.020332</td>\n",
       "      <td>0.114591</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 111 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "country   Algeria  Argentina  Australia   Austria  Bangladesh  Barbados  \\\n",
       "year                                                                      \n",
       "1960     0.292292   0.140910   0.336618  0.207003    0.014559  0.090716   \n",
       "1961     0.334405   0.149655   0.296569  0.205342    0.017380  0.079419   \n",
       "1962     0.372550   0.132196   0.317393  0.187515    0.026159  0.073334   \n",
       "1963     0.355781   0.112345   0.309578  0.184681    0.018701  0.078361   \n",
       "1964     0.267336   0.137489   0.332907  0.207555    0.023628  0.076604   \n",
       "\n",
       "country   Belgium     Benin  Bolivia (Plurinational State of)  Botswana  ...  \\\n",
       "year                                                                     ...   \n",
       "1960     0.274124  0.039017                          0.206834  0.102649  ...   \n",
       "1961     0.294998  0.037919                          0.163327  0.124339  ...   \n",
       "1962     0.280298  0.037577                          0.267985  0.143526  ...   \n",
       "1963     0.269299  0.038658                          0.227549  0.158613  ...   \n",
       "1964     0.303141  0.032848                          0.231306  0.195691  ...   \n",
       "\n",
       "country   Tunisia   Türkiye  U.R. of Tanzania: Mainland    Uganda  \\\n",
       "year                                                                \n",
       "1960     0.112642  0.196667                    0.104302  0.098392   \n",
       "1961     0.146735  0.199453                    0.117391  0.113316   \n",
       "1962     0.187319  0.197619                    0.099309  0.115779   \n",
       "1963     0.192624  0.200368                    0.088076  0.143015   \n",
       "1964     0.206365  0.197618                    0.116514  0.182406   \n",
       "\n",
       "country  United Kingdom  United States   Uruguay  \\\n",
       "year                                               \n",
       "1960           0.239277       0.230340  0.144855   \n",
       "1961           0.241543       0.231433  0.154907   \n",
       "1962           0.225732       0.236722  0.133602   \n",
       "1963           0.225506       0.239582  0.122253   \n",
       "1964           0.268017       0.240732  0.100760   \n",
       "\n",
       "country  Venezuela (Bolivarian Republic of)    Zambia  Zimbabwe  \n",
       "year                                                             \n",
       "1960                               0.358695  0.050083  0.189235  \n",
       "1961                               0.338576  0.046848  0.181016  \n",
       "1962                               0.349284  0.042926  0.128391  \n",
       "1963                               0.320073  0.031393  0.111248  \n",
       "1964                               0.389544  0.020332  0.114591  \n",
       "\n",
       "[5 rows x 111 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "saving = saving.dropna(axis='columns')\n",
    "saving.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "`.dropna()`は`NaN`がある行か列を削除する。行と列のどちらを削除するかは引数`axis`で指定するが，デフォルトは`'rows'`である。即ち，引数なしで`.dropna()`を実行すると`NaN`がある行が削除される。ここでは列を削除したいので，引数に`'columns'`を指定している。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "AlbaniaやAngolaなどが削除されていることが確認できる。何ヵ国残っているか確認してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 111)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "saving.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "属性`.shape`は`DataFrame`の行の数（左の数字）と列（右の数字）の数を返す。\n",
    "```\n",
    "\n",
    "111ヵ国含まれていることが確認できた。次に，それぞれの列の平均を計算する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>saving_rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>0.340081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Argentina</th>\n",
       "      <td>0.146066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Australia</th>\n",
       "      <td>0.277670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Austria</th>\n",
       "      <td>0.272072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bangladesh</th>\n",
       "      <td>0.143379</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            saving_rate\n",
       "country                \n",
       "Algeria        0.340081\n",
       "Argentina      0.146066\n",
       "Australia      0.277670\n",
       "Austria        0.272072\n",
       "Bangladesh     0.143379"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "saving = saving.mean().to_frame('saving_rate')   # 1\n",
    "saving.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "````{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "1. `.mean()`はそれぞれの列の平均を計算し，`Series`を返す。後で`DataFrame`を結合するメソッド`.merge()`を使うために`.to_frame()`を使って`Series`を`DataFrame`に変換しており，引数`saving_rate`は列ラベルを指定している。もちろん引数を使わずに２行に分けることも可能である。\n",
    "```\n",
    "saving = saving.mean().to_frame()\n",
    "saving.columns = ['saving_rate']\n",
    "```\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{tip}\n",
    "上の計算では1960年以降に欠損値が一つでもあればその国は排除されたが，全ての年でデータが揃っている経済だけを扱いたい場合に便利に使える方法である。一方で，`.groupby()`を使うと欠損値があっても平均は計算されるので，単純に`.groupby()`を使うと1960年以降に欠損値がある経済も含まれることになる。それを避けるためには一捻り必要だが，それについては[](sec:9-saving)が参考になるだろう。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 資本減耗率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`saving`と同じ方法で資本減耗率の平均からなる`DataFrame`を作成する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "depreciation = pwt.pivot(index='year', columns='country', values='delta')\n",
    "depreciation = depreciation.dropna(axis='columns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 110)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "depreciation.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "110ヵ国含まれている。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "depreciation = depreciation.mean().to_frame('depreciation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 労働人口成長率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "平均成長率を計算するには1960年と{glue:text}`latest_year_glued`年の労働人口だけで計算できるが，上と同じ方法で計算してみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "emp = pwt.pivot(index='year', columns='country', values='emp')\n",
    "emp = emp.dropna(axis='columns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60, 91)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emp.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "91ヵ国しか含まれていない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>employment_growth</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>0.029506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Argentina</th>\n",
       "      <td>0.017632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Australia</th>\n",
       "      <td>0.019195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Austria</th>\n",
       "      <td>0.005053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bangladesh</th>\n",
       "      <td>0.021290</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            employment_growth\n",
       "country                      \n",
       "Algeria              0.029506\n",
       "Argentina            0.017632\n",
       "Australia            0.019195\n",
       "Austria              0.005053\n",
       "Bangladesh           0.021290"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emp_growth = ( ( emp.loc[latest_yr,:]/emp.loc[1960,:] )**(1/(len(emp)-1))-1 \n",
    "             ).to_frame('employment_growth')\n",
    "emp_growth.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 資本ストック対GDP比"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "{glue:text}`latest_year_glued`年の`cgdpo`と`cn`を使って資本ストック対GDP比を含む`DataFrame`を作成する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cgdpo</th>\n",
       "      <th>cn</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Aruba</th>\n",
       "      <td>4823.155273</td>\n",
       "      <td>2.274172e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Angola</th>\n",
       "      <td>225950.187500</td>\n",
       "      <td>7.037451e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Anguilla</th>\n",
       "      <td>327.047302</td>\n",
       "      <td>4.200483e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Albania</th>\n",
       "      <td>44771.500000</td>\n",
       "      <td>2.628630e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United Arab Emirates</th>\n",
       "      <td>816201.875000</td>\n",
       "      <td>5.953914e+06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              cgdpo            cn\n",
       "country                                          \n",
       "Aruba                   4823.155273  2.274172e+04\n",
       "Angola                225950.187500  7.037451e+05\n",
       "Anguilla                 327.047302  4.200483e+03\n",
       "Albania                44771.500000  2.628630e+05\n",
       "United Arab Emirates  816201.875000  5.953914e+06"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ky_ratio = pwt.query('year == @latest_yr') \\\n",
    "              .loc[:,['country','cgdpo','cn']] \\\n",
    "              .set_index('country') \\\n",
    "              .dropna()\n",
    "ky_ratio.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "* `@`を使うことにより，`.query()`の外で定義された変数`latest_yr`を`.query()`の引数の文字列の中でそのまま使えるようなる。\n",
    "* `.set_index(''country')`を使って`country`を行ラベルに指定し，`.dropna()`によって欠損値がある行は削除する。\n",
    "```\n",
    "\n",
    "資本ストック対GDP比の列の作成しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "ky_ratio['ky_ratio'] = np.log( ky_ratio['cn'] / ky_ratio['cgdpo'] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "含まれる国数を確認する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(180, 3)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ky_ratio.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "180ヵ国含まれており，`saving`や`depreciation`の国数よりも多くの国が含まれている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### データの結合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true,
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "上で作成した`DataFrame`を結合する必要があり，そのための`DataFrame`のメソッド`.merge()`の使い方を説明する。`df_left`と`df_right`の２つの`DataFrame`があるとしよう。`df_left`を左の`DataFrame`，`df_right`を右の`DataFrame`と呼ぶことにする。`df_left`のメソッド`.merge()`を使い`df_right`と結合する場合，次のコードとなる。\n",
    "```\n",
    "df_left.merge(df_right) \n",
    "```\n",
    "しかし注意が必要な点が２つある。\n",
    "1. 行数が同じでも`df_left`と`df_right`では行の並びが異なる可能性がある。\n",
    "2. 行数が異なる可能性がある。\n",
    "\n",
    "これらの問題に対応するためのる引数が用意されている。\n",
    "\n",
    "まず１つ目の問題は，ある列を基準列もしくは行ラベルに合わせて行を並び替えることにより対応できる。例えば，上で作成した`DataFrame`であれば，行ラベルが`country`になっているので，それに合わせて結合すれば良い。その場合の引数を含めたコードは次の様になる。\n",
    "```\n",
    "df_left.merge(df_right, left_index=True, right_index=True) \n",
    "```\n",
    "ここでの`left_index=True`と`right_index=True`は行ラベルを基準に結合することを指定しており，デフォルトは両方とも`False`である。行ラベルではなく，ある列を基準に結合した場合もあるだろう。その場合は次の引数を使う。\n",
    "```\n",
    "df_left.merge(df_right,\n",
    "              left_on=＜`df_left`の基準列のラベル（文字列）＞,\n",
    "              right_on=＜`df_right`の基準列のラベル（文字列）＞) \n",
    "```\n",
    "`left_on`は基準列に使う左の`DataFrame`にある列ラベルを文字列で指定する。同様に`right_on`は基準列に使う右の`DataFrame`にある列ラベルを文字列で指定する。デフォルトは両方とも`None`となっている。\n",
    "\n",
    "２つ目の問題は`how`という引数を使うことにより対処できる。使える値は次の４つであり，いずれも文字列で指定する。\n",
    "* `'inner'`：`df_left`と`df_right`の両方の基準列にある共通の行だけを残す（デフォルト）。\n",
    "* `'left'`：`df_left`の行は全て残し，`df_right`からはマッチする行だけが残り，対応する行がない場合は`NaN`が入る。\n",
    "* `'right'`：`df_right`の行は全て残し，`df_left`からはマッチする行だけが残り，対応する行がない場合は`NaN`が入る。\n",
    "* `'outer'`：`df_left`と`df_right`の両方の行を全て残し，マッチする行がない場合は`NaN`を入れる。\n",
    "\n",
    "では実際に上で作成した`DataFrame`を結合しよう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "上で作成した`DataFrame`を結合する必要があり，そのための`Pandas`の関数`.merge()`の使い方を説明する。`df_left`と`df_right`の２つの`DataFrame`があるとしよう。`df_left`を左の`DataFrame`，`df_right`を右の`DataFrame`と呼ぶことにする。２つを結合する場合，次のコードとなる。\n",
    "```\n",
    "pd.merge(df_left, df_right) \n",
    "```\n",
    "しかし注意が必要な点が２つある。\n",
    "1. 行数が同じでも`df_left`と`df_right`では行の並びが異なる可能性がある。\n",
    "2. 行数が異なる可能性がある。\n",
    "\n",
    "これらの問題に対応するためのに引数が用意されている。\n",
    "\n",
    "まず１つ目の問題は，行ラベルを基準に，もしくはある列に合わせて行を並び替えることにより対応できる。例えば，上で作成した`DataFrame`であれば，行ラベルが`country`になっているので，それに合わせて結合すれば良い。その場合の引数を含めたコードは次の様になる。\n",
    "```\n",
    "pd.merge(df_left, df_right, left_index=True, right_index=True) \n",
    "```\n",
    "ここでの`left_index=True`と`right_index=True`は行ラベルを基準に結合することを指定しており，デフォルトは両方とも`False`である。行ラベルではなく，ある列を基準に結合したい場合もあるだろう。その場合は次の引数を使う。\n",
    "```\n",
    "pd.merge(df_left, df_right,\n",
    "         left_on=＜`df_left`の基準列のラベル（文字列）＞,\n",
    "         right_on=＜`df_right`の基準列のラベル（文字列）＞) \n",
    "```\n",
    "`left_on`は基準列に使う`df_left`にある列ラベルを文字列で指定する。同様に`right_on`は基準列に使う`df_right`にある列ラベルを文字列で指定する。デフォルトは両方とも`None`となっている。\n",
    "\n",
    "２つ目の問題は`how`という引数を使うことにより対処できる。使える値は次の４つであり，いずれも文字列で指定する。\n",
    "* `'inner'`：`df_left`と`df_right`の両方の基準列にある共通の行だけを残す（デフォルト）。\n",
    "* `'left'`：`df_left`の行は全て残し，`df_right`からはマッチする行だけが残り，対応する行がない場合は`NaN`が入る。\n",
    "* `'right'`：`df_right`の行は全て残し，`df_left`からはマッチする行だけが残り，対応する行がない場合は`NaN`が入る。\n",
    "* `'outer'`：`df_left`と`df_right`の両方の行を全て残し，マッチする行がない場合は`NaN`を入れる。\n",
    "\n",
    "では実際に上で作成した`DataFrame`を結合しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "for df_right in [saving, depreciation, emp_growth]:  # 1\n",
    "    \n",
    "    ky_ratio = pd.merge(ky_ratio, df_right,          # 2\n",
    "                        left_index=True,             # 3\n",
    "                        right_index=True,            # 4\n",
    "                        how='outer')                 # 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "1. `df_right`が上の説明の`df_right`に対応している。`[saving, depreciation, emp_growth]`は上で作成した`DataFrame`のリスト。\n",
    "2. `ky_ratio`が上の説明の`df_left`に対応している。右辺で結合した`DataFrame`を左辺にある`ky_ratio`に割り当てている（際割り当て）。\n",
    "3. `ky_ratio`の行ラベルを基準とすることを指定する。\n",
    "4. `df_right`の行ラベルを基準とすることを指定する。\n",
    "5. ここでの`'outer'`は左右の`DataFrame`のそれぞれの行ラベルを残し，値がない箇所には`NaN`を入れることを指定する。\n",
    "```\n",
    "\n",
    "結合の結果を表示してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cgdpo</th>\n",
       "      <th>cn</th>\n",
       "      <th>ky_ratio</th>\n",
       "      <th>saving_rate</th>\n",
       "      <th>depreciation</th>\n",
       "      <th>employment_growth</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Albania</th>\n",
       "      <td>44771.500000</td>\n",
       "      <td>2.628630e+05</td>\n",
       "      <td>1.770061</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>669309.500000</td>\n",
       "      <td>2.916442e+06</td>\n",
       "      <td>1.471873</td>\n",
       "      <td>0.340081</td>\n",
       "      <td>0.041635</td>\n",
       "      <td>0.029506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Angola</th>\n",
       "      <td>225950.187500</td>\n",
       "      <td>7.037451e+05</td>\n",
       "      <td>1.136102</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Anguilla</th>\n",
       "      <td>327.047302</td>\n",
       "      <td>4.200483e+03</td>\n",
       "      <td>2.552850</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Antigua and Barbuda</th>\n",
       "      <td>2526.366943</td>\n",
       "      <td>2.060428e+04</td>\n",
       "      <td>2.098716</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             cgdpo            cn  ky_ratio  saving_rate  \\\n",
       "country                                                                   \n",
       "Albania               44771.500000  2.628630e+05  1.770061          NaN   \n",
       "Algeria              669309.500000  2.916442e+06  1.471873     0.340081   \n",
       "Angola               225950.187500  7.037451e+05  1.136102          NaN   \n",
       "Anguilla                327.047302  4.200483e+03  2.552850          NaN   \n",
       "Antigua and Barbuda    2526.366943  2.060428e+04  2.098716          NaN   \n",
       "\n",
       "                     depreciation  employment_growth  \n",
       "country                                               \n",
       "Albania                       NaN                NaN  \n",
       "Algeria                  0.041635           0.029506  \n",
       "Angola                        NaN                NaN  \n",
       "Anguilla                      NaN                NaN  \n",
       "Antigua and Barbuda           NaN                NaN  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ky_ratio.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "列AlbaniaやAngolaは`saving`，`depreciation`，`emp_growth`の`DataFram`には無いため`NaN`が入っている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "結合後の`ky_ratio`の情報を表示してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 180 entries, Albania to Zimbabwe\n",
      "Data columns (total 6 columns):\n",
      " #   Column             Non-Null Count  Dtype  \n",
      "---  ------             --------------  -----  \n",
      " 0   cgdpo              180 non-null    float64\n",
      " 1   cn                 180 non-null    float64\n",
      " 2   ky_ratio           180 non-null    float64\n",
      " 3   saving_rate        111 non-null    float64\n",
      " 4   depreciation       110 non-null    float64\n",
      " 5   employment_growth  91 non-null     float64\n",
      "dtypes: float64(6)\n",
      "memory usage: 9.8+ KB\n"
     ]
    }
   ],
   "source": [
    "ky_ratio.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "180ヵ国が含まれるが`NaN`がある国も多いことが分かる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### トレンド線と散布図"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここでは次の３つをおこなう。\n",
    "* 資本ストック対GDP比と次の３つの変数の散布図の表示\n",
    "    * 貯蓄率\n",
    "    * 資本減耗率\n",
    "    * 労働人口増加率\n",
    "* 回帰分析に基づいて計算したトレンド線の表示\n",
    "* トレンド線の傾きの統計的優位性の表示\n",
    "\n",
    "`for`ループを使ってこれらを同時に計算・表示する。まず`ky_ratio`の列ラベルをみると，回帰分析の説明変数に使う変数が最後の３つに並んでいる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['saving_rate', 'depreciation', 'employment_growth'], dtype='object')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ky_ratio.columns[-3:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これを使い`for`ループを組んでみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for var in ky_ratio.columns[-3:]:              #1\n",
    "    \n",
    "    df_tmp = ky_ratio.copy()                   #2\n",
    "    res = smf.ols(f'ky_ratio ~ {var}',         #3\n",
    "                  data=df_tmp).fit()           #4\n",
    "    bhat = res.params.iloc[1]                  #5\n",
    "    pval = res.pvalues.iloc[1]                 #6\n",
    "    \n",
    "    df_tmp['Trend'] = res.fittedvalues         #7\n",
    "\n",
    "    ax = df_tmp.plot.scatter(x=var, y='ky_ratio') #8\n",
    "    \n",
    "    df_tmp.sort_values('Trend').plot(x=var,    #9\n",
    "                                     y='Trend', \n",
    "                                     color='red',\n",
    "                                     ax=ax)\n",
    "    ax.set_title(f'トレンドの傾き：{bhat:.2f}\\n'  #10\n",
    "                 f'p値：{pval:.3f}', size=20)   #11\n",
    "    ax.set_ylabel('資本ストック対GDP比（対数）',   #12\n",
    "                  size=15)                     #13\n",
    "    ax.set_xlabel(f'{var}', size=20)           #14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "* `#1`：`ky_ratio`の最後の３列のラベルに対して`for`ループを組んで，`var`はその列ラベルを指す。\n",
    "* `#2`：`ky_ratio`のコピーを作り`df_tmp`に割り当てる。`.copy()`は実態としては別物のコピーを作成する。詳細は割愛するが`.copy()`がないと実態は同じで参照記号のみが異なることになり，予期しない結果につながることを防ぐために`.copy()`を使っている。\n",
    "* `#3`：回帰分析をおこなっているが，`f-string`を使い回帰式の説明変数を指定している。また回帰分析の結果を`res`に割り当てている。\n",
    "* `#4`：`data`で回帰分析のデータの指定をおこない，`.fit()`で自動計算！\n",
    "* `#5`：`res`の属性`.params`は推定値を２つ返すが，1番目に傾きの推定値が格納されているため`.iloc[1]`で抽出し，`bhat`に割り当てている。\n",
    "* `#6`：`res`の属性`.pvalues`は$p$値を２つ返すが，1番目に傾きの$p$値が格納されているため`.iloc[1]`で抽出し，`pval`に割り当てている。\n",
    "* `#7`：`res`の属性`fittedvalues`は予測値を返すが，それを新たな列（ラベルは`Trend`）として`df_tmp`に追加している。\n",
    "* `#8`：`df_tmp`を使い横軸は`var`，縦軸は`ky_ratio`の散布図を表示し、その軸を`ax`に割り当てる。\n",
    "* `#9`：`df_tmp`を使い横軸は`var`，縦軸は`ky_ratio`の回帰直線を表示。その際、メソッド`.sort_values('Trend')`で列`Trend`に従って昇順に並び替える。これはトレンド線が正確に表示されるために必要。\n",
    "* `#10`：図のタイトルを設定する。\n",
    "    * `f-string`を使い`bhat`の値を代入する。\n",
    "    * `:.2f`は小数点第２位までの表示を指定。\n",
    "    * `\\n`は改行の意味。\n",
    "    * 行を変えるので`\\n`の後に`'`が必要となる。\n",
    "* `#11`：`f-string`を使い`pval`の値を代入する。`:.3f`は小数点第３位までの表示を指定し，`size=20`はフォントの大きさの指定。\n",
    "* `#12`：縦軸のラベルの設定。\n",
    "* `#13`：フォントの大きさの指定。\n",
    "* `#14`：横軸のラベルの設定であり，`f-string`を使い`var`の値を代入している。`size=20`はフォントの大きさの指定。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "３つの図からソロー・モデルの理論的予測はデータと整合性があることが確認できる。ここで注意する点が一つある。式[](eq:8-kyratio)は因果関係を予測している。例えば，貯蓄率が高くなることにより長期的な一人\n",
    "当たりGDPは増加する。一方，トレンド線は因果関係を示しているのではなく単なる相関関係を表している。ソロー・モデルの因果関係を計量経済学的に検討するにはさまざまな要因の検討が必要になり，本章の域を超える事になる。"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}