{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 種々の一次アルゴリズムを試す\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "学習アルゴリズムを実装するための基本的な仕組みを前の章で見てきたので、本章ではその大事な一部である最適化法に焦点を当てることにする。具体的には、一次情報だけを用いる直線探索アルゴリズムを対象とする。その理由は、現代の機械学習では、この類いの最適化法がしばしば使われるからである。\n", "\n", "表記について述べておくと、観測データ$z_{1},\\ldots,z_{n}$を所与として、データ点および制御対象となるパラメータ$w \\in \\mathbb{R}^d$に依存する損失関数$L(w;z)$が中心となる。その勾配を\n", "\n", "\\begin{align*}\n", "\\nabla L(w;z) = \\left( \\frac{\\partial L(w;z)}{\\partial w_{1}}, \\ldots, \\frac{\\partial L(w;z)}{\\partial w_{d}}\\right)\n", "\\end{align*}\n", "\n", "と書いて、これは任意の$z$で定義されるとする。さらに、経験期待損失最小化(ERM)に従い、以下の問題を解くことになる。\n", "\n", "\\begin{align*}\n", "\\min_{w \\in \\mathbb{R}^d} \\frac{1}{n} \\sum_{i=1}^{n} L(w;z_{i}) \\to \\widehat{w}.\n", "\\end{align*}\n", "\n", "このERM解$\\widehat{w}$は一意に決まるとは限らない。また、ERM解によっては、目的関数の値が一緒でも、汎化能力を示す指標では大きく異なることもあるため、注意が必要である。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__目次__\n", "\n", "- 直線探索のクラス\n", "\n", "- 勾配降下法\n", "\n", "- 差分法を使った勾配降下法\n", "\n", "- 確率的勾配降下法\n", "\n", "- 各種アルゴリズムの性能を丁寧に観察\n", "\n", "___" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 直線探索のクラス\n", "\n", "まず、ベースクラスとして、直線探索(line search)を行うアルゴリズムを実装しよう。この範疇の特徴は次の通りである。初期値$w_{(0)}$を所与として、反復的に以下の更新則を実行する。\n", "\n", "\\begin{align*}\n", "w_{(t+1)} \\gets w_{(t)} + \\alpha_{(t)} u_{(t)}\n", "\\end{align*}\n", "\n", "重要なのはサブプロセスの順序で、$w_{(t)} \\mapsto u_{(t)} \\mapsto \\alpha_{(t)}$という順番に求めていくことが一般的である。つまり、__探索方向__$u_{(t)}$を計算してから、\n", "ステップサイズの$\\alpha_{(t)} > 0$を決める一般的な`Algo_LineSearch`を以下のように用意する。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "class Algo_LineSearch:\n", " '''\n", " Basic archetype of an iterator for implementing a line\n", " search algorithm.\n", "\n", " Note that we assume w_init is a nparray matrix with the\n", " shape (d,1), where d represents the number of total\n", " parameters to be determined.\n", " '''\n", "\n", " def __init__(self, w_init, step, t_max, thres,\n", " verbose=False, store=False):\n", "\n", " # Attributes passed from user.\n", " self.w = w_init\n", " self.step = step\n", " self.t_max = t_max\n", " self.thres = thres\n", " self.verbose = verbose\n", " self.store = store\n", "\n", " # Attributes determined internally.\n", " if self.w is None:\n", " self.nparas = None\n", " self.w_old = None\n", " else:\n", " self.nparas = self.w.size\n", " self.w_old = np.copy(self.w)\n", " self.t = None\n", " self.diff = np.inf\n", " self.stepcost = 0 # for per-step costs.\n", " self.cumcost = 0 # for cumulative costs.\n", "\n", " # Keep record of all updates (optional).\n", " if self.store:\n", " self.wstore = np.zeros((self.w.size,t_max+1), dtype=self.w.dtype)\n", " self.wstore[:,0] = self.w.flatten()\n", " else:\n", " self.wstore = None\n", " \n", " \n", " def __iter__(self):\n", "\n", " self.t = 0\n", "\n", " if self.verbose:\n", " print(\"(via __iter__)\")\n", " self.print_state()\n", " \n", " return self\n", " \n", "\n", " def __next__(self):\n", " '''\n", " Check the stopping condition(s).\n", " '''\n", " \n", " if self.t >= self.t_max:\n", " raise StopIteration\n", "\n", " if self.diff <= self.thres:\n", " raise StopIteration\n", "\n", " if self.verbose:\n", " print(\"(via __next__)\")\n", " self.print_state()\n", " \n", " \n", " def update(self, model, data):\n", " '''\n", " Carry out the main parameter update.\n", " '''\n", " \n", " # Parameter update.\n", " newdir = self.newdir(model=model, data=data)\n", " stepsize = self.step(t=self.t, model=model, data=data, newdir=newdir)\n", " self.w = self.w + stepsize * np.transpose(newdir)\n", "\n", " # Update the monitor attributes.\n", " self.monitor_update(model=model, data=data)\n", "\n", " # Run cost updates.\n", " self.cost_update(model=model, data=data)\n", "\n", " # Keep record of all updates (optional).\n", " if self.store:\n", " self.wstore[:,self.t] = self.w.flatten()\n", "\n", "\n", " def newdir(self, model, data):\n", " '''\n", " This will be implemented by sub-classes\n", " that inherit this class.\n", " '''\n", " raise NotImplementedError\n", " \n", "\n", " def monitor_update(self, model, data):\n", " '''\n", " This will be implemented by sub-classes\n", " that inherit this class.\n", " '''\n", " raise NotImplementedError\n", "\n", " \n", " def cost_update(self, model, data):\n", " '''\n", " This will be implemented by sub-classes\n", " that inherit this class.\n", " '''\n", " raise NotImplementedError\n", "\n", " \n", " def print_state(self):\n", " print(\"t =\", self.t, \"( max =\", self.t_max, \")\")\n", " print(\"diff =\", self.diff, \"( thres =\", self.thres, \")\")\n", " if self.verbose:\n", " print(\"w = \", self.w)\n", " print(\"------------\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "今の段階では、このベースクラスは基本的な要素を明示しているだけであって、これ自体が何かの役に立つわけではない。このあとの節では、「肉付け」の作業に取りかかる。参考として、重要なパーツを羅列しておく。\n", "\n", "- `update()`で反復的に行う更新則のすべてを含む。\n", "- `monitor_update()`で終了条件にかかわる処理を行う。\n", "- `cost_update()`で計算コスト等についての処理を行う。\n", "- 終了条件にかかわるパラメータは`thres`と`t_max`である。\n", "- パラメータの更新は、上記の数式と同じように、まずは`newdir()`を呼び出して探索方向を求めてから、`step()`でステップサイズを計算する。この2つが揃えば、直線探索の更新を行うことができる。\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import math\n", "\n", "import models\n", "import dataclass\n", "import helpers as hlp" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Prepare the risk function and some data to test the various\n", "# algorithms to follow in a simple 2D setting.\n", "\n", "# Data-related parameters.\n", "n = 15\n", "d = 2\n", "epsilon_sd = 2.0\n", "X_sd = 1.0\n", "X_cov = X_sd * np.eye(d)\n", "w_star = math.pi * np.ones((d,1), dtype=np.float32)\n", "\n", "# Put together risk function.\n", "def risk(w):\n", " return hlp.riskMaker(w=w, A=X_cov, b=epsilon_sd, w_star=w_star)\n", "\n", "# Generate data.\n", "data = dataclass.DataSet()\n", "X = np.random.normal(loc=0.0, scale=X_sd, size=(n,d))\n", "epsilon = np.random.normal(loc=0.0, scale=epsilon_sd, size=(n,1))\n", "y = X.dot(w_star) + epsilon\n", "data.init_tr(X=X, y=y) # all for training" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 勾配降下法\n", "\n", "探索方向を決めるにあたって、「降下方向」を求める手法がほとんどである。降下方向とは、ステップサイズさえ正しく設定すれば、現時点よりも良い候補が必ず見つかるという方向のことである。例として、まず一次元の目的関数$f:\\mathbb{R} \\to \\mathbb{R}$を考えよう。この場合、「方向」は「左」か「右」しかなく、$u_{(t)} \\in \\{-1,1\\}$ということである。このとき、\n", "\n", "- もし$f^{\\prime}(w_{(t)}) > 0$ならば、関数$f$は増加しているため、「左」の方向に行けば(つまり$u_{(t)} = -1$と設定すれば)、ステップサイズさえ正しく決めれば、目的関数は減少する。\n", "\n", "- もし$f^{\\prime}(w_{(t)}) < 0$ならば、関数$f$は減少しているため、「右」の方向に行けば(つまり$u_{(t)} = -1$と設定すれば)、ステップサイズさえ正しく決めれば、目的関数は減少する。\n", "\n", "どのケースでも、$u_{(t)} \\, f^{\\prime}(w_{(t)}) < 0$が成り立つ。\n", "\n", "この性質は多次元の関数へと拡張できる。たとえば、目的関数が$f: \\mathbb{R}^d \\to \\mathbb{R}$のとき、$\\langle u_{(t)}, \\nabla f(w_{(t)}) \\rangle < 0$が成り立つならば、$u_{(t)}$が降下方向である。幾何学的にいえば、負の勾配ベクトル$(-1)\\,f^{\\prime}(w_{(t)})$と探索方向が急角度をなすことが条件となる。\n", "\n", "勾配降下法とは、単に探索方向と負の勾配ベクトルの角度がゼロというスペシャルケースである。これをユークリッド空間での「最急降下法」と呼ぶことも多い。その名付けは自然である。関数の特定の方向における「急峻さ」を示すのは、方向微分であることを思い出そう。我々の考えている変数等でいえば、チェーンルールを使うと、\n", "\n", "\\begin{align*}\n", "\\frac{\\partial f(w_{(t)}+\\alpha u)}{\\partial \\alpha} & = \\sum_{j=1}^{d} \\left( \\left.\\frac{\\partial f(x)}{\\partial x_{j}}\\right|_{x=w_{(t)}+\\alpha u} \\right) \\frac{\\partial(w_{(t),j}+\\alpha u_{j})}{\\partial \\alpha}, \\text{ set } \\alpha = 0\\\\\n", "& = \\langle u, \\nabla f(w_{(t)}) \\rangle\n", "\\end{align*}\n", "\n", "と表せる(内積は通常のドット積)。最急降下法では、これがなるべく大きな負の値になるように$u$を選ぶ(つまり、最小化)。$(-1)$をかけて、最大化問題に置き換える。コーシー・シュワルツの不等式を使うと、下記が成り立つ。\n", "\n", "\\begin{align*}\n", "\\langle u, (-1)\\nabla f(w_{(t)}) \\rangle \\leq \\|u\\| \\|\\nabla f(w_{(t)})\\|.\n", "\\end{align*}\n", "\n", "単位円上のすべての$u$を考える($\\|u\\|=1$)。角度がゼロとなるようにしてみると、\n", "\n", "\\begin{align*}\n", "\\left\\langle \\frac{(-1)\\nabla f(w_{(t)})}{\\|\\nabla f(w_{(t)})\\|}, (-1)\\nabla f(w_{(t)}) \\right\\rangle = \\|\\nabla f(w_{(t)})\\|.\n", "\\end{align*}\n", "\n", "つまり、$u$を負の勾配ベクトルそのものに設定することで、先述の上界を完全に満たすことになる。同様に、$\\langle u, \\nabla f(w_{(t)}) \\rangle$を最小にする方法でもある。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この背景を押さえた上で、あとは勾配降下法を実装するのみ。これは簡単である。更新則は次の通りである。\n", "\n", "\\begin{align*}\n", "w_{(t+1)} = w_{(t)} - \\frac{\\alpha_{(t)}}{n} \\sum_{i=1}^{n} \\nabla L(w_{(t)};z_{i}).\n", "\\end{align*}\n", "\n", "`Algo_LineSearch`を踏襲して、この更新則を実装した`Algo_GD`を下記のように実装している。." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class Algo_GD(Algo_LineSearch):\n", " '''\n", " Iterator which implements a line-search steepest descent method,\n", " where the direction of steepest descent is measured using the\n", " Euclidean norm (this is the \"usual\" gradient descent). Here the\n", " gradient is a sample mean estimate of the true risk gradient.\n", " That is, this is ERM-GD.\n", " '''\n", "\n", " def __init__(self, w_init, step, t_max, thres, store):\n", "\n", " super(Algo_GD, self).__init__(w_init=w_init,\n", " step=step,\n", " t_max=t_max,\n", " thres=thres,\n", " store=store)\n", "\n", " def newdir(self, model, data):\n", " '''\n", " Determine the direction of the update.\n", " '''\n", " return (-1) * np.mean(model.g_tr(w=self.w, data=data),\n", " axis=0, keepdims=True)\n", "\n", " def monitor_update(self, model, data):\n", " '''\n", " Update the counters and convergence\n", " monitors used by the algorithm. This is\n", " executed once every step.\n", "\n", " For GD, increment counter and check the\n", " differences at each step.\n", " '''\n", " self.t += 1\n", " self.diff = np.linalg.norm((self.w-self.w_old))\n", " self.w_old = np.copy(self.w)\n", "\n", " \n", " def cost_update(self, model, data):\n", " '''\n", " Update the amount of computational resources\n", " used by the routine.\n", "\n", " Cost here is number of gradient vectors\n", " computed. GD computes one vector for each\n", " element in the sample.\n", " '''\n", " self.stepcost = data.n_tr\n", " self.cumcost += self.stepcost\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "要点:\n", "\n", "- `newdir`では、目的関数が$n$個のロス関数のサンプル平均であることを前提としている。`axis=0`の上で`np.mean()`を呼び出しているのは、そのためである。\n", "\n", "- `monitor_update`では、更新前後の差分ノルムを取って、ステップ数`t`も記録している。\n", "\n", "- `cost_update`では、計算された$d$次元勾配ベクトルの数を毎回のように足している。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Initialize model.\n", "mod = models.LinearL2()\n", "\n", "# Initialize learning algorithm.\n", "w_init = np.random.uniform(size=(d,1))\n", "def alpha_fixed(t, val):\n", " return val\n", "def make_step(u):\n", " def mystep(t, model=None, data=None, newdir=None):\n", " return alpha_fixed(t=t, val=u)\n", " return mystep\n", "al = Algo_GD(w_init=w_init,\n", " step=make_step(0.25),\n", " t_max=15,\n", " thres=1e-03,\n", " store=True)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Iterate the learning algorithm.\n", "for onestep in al:\n", " al.update(model=mod, data=data)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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LPV4uDrg72ePqYNM4WrHBxcEWZzvriyMaWyvLZh29aHV66pRqahpHYRU19ZRV11Fe3fCzrLqO4spaCsqqKCivoaZe9Zfz7W2sCPB0xt/DmQBPZ4K93ejg646/p7PJdrCmxJnSEt7bs4u9OVl0cHXjrcHD6O3nf/UTjYBGr6VWqzZaqPgF0qr3sjHvHdrZhDPBb+4VhalViFKDID0PCKMJ0pHSdF5ObFhg8/1ud9PTLaTFbWgKJ4oK+e+u7RwrOE+0tw9vDR5GJw/jzCebMkIIiitrOZVVSEp2Iam5xaSfLyWvpJIL/+qWCnP8PJwI8HTB38MZ/8ZO3MfNEU9ne6wsWk/9tJp6FYXl1eSXVpFdVEF2UQU5xeVkF1VQUFaNvvFNK8zNCPJyJdTbjTB/DzoFtCMiwBMHW7mk1OUIIdiemc7be3aSW1XFhPAIXuk/EE87e2Obdl1o9TriS9OxNFMQ7Xa9q9n/O2nVcWzMe5d2Nh25zW8uluZ/F0qTF6VyVQ7Ls58DBJMCPsbNCIK05XwS/z2+jABbNz6Jvg8/W9OrzlCpVPLpwX0sSU7CxdqGV/oPZGLHTvIUTSO1SjXJmedJSs/nZFYhp7MLKamqA8BMkghs50KorzuhPm6E+LgT4u2Gn4dTq8nuvxFUGi3nCspIyy8lPb+EtPxS0vJLKCirvniMv4czEQGeRAZ50TXYh4gATywU8ogKGnL9vk04zPwj8Viam/N0777cF9W9VSTfXkqNVsmuwhQWZ+xmZofhDDeQD+pqwmTSolShzmN59rPohY7JAZ8YRZAAsmpLWJC2jZc73Ya9hWk9MYrG0NV39uyiXFnPvV278UzvvjhamZadLU1xRQ1HUnNJTM8nKSOftLwS9EIgSRDs5UanwIYRQERAO8L8PLCxkv1sl1NeU8/p7CJOZReSklXIqewizpdVAWBlYU6nQC+6hfg0bKG+ONgYJ/TYVDhXUc5bu3eyOyuTju4ezBk6olUmoZ+rKeI/x5fxXtSdBiuPdrZqD5vy32sQJv/3/xKVZ7KiVKUpZFnW0+iEulGQgpq9/QsIIVrliCKvuorXd2xjd1YmXdt5MWfoiJt2qq66XkVCai6HTmdz+HQ2mQVlANhZW9KlfcPTfbcQHyKDvLC/yTvPG6Gkspak9HwSM/JJSs/ndHYRWr0eczOJToFe9I4IILZjAF3be9+UIykhBFsy0nhr1w4Ka2u4v1sPnu/TH1sL03zoudD36YQeAHPJDL3Q89DB+bwSeRsdHAwnqmer9rAx/118baOY4PfexTwmkxSlWm05y7Oepk5XweSAjw0W9q0XeswkM3RCf/HDMFZ0yrWgF4IlyUl8uG8PeiF4vu8A7uva7aaYarqAEIL0/FL2nsgk7kQmxzPy0ekF1pYKuof6EhseQEy4P+H+HjfVfWlp6tUaTmQWcPh0NofP5HDyXAF6IbCxsiA23J/+ke0Z0CUYT+fW6We5XqpVKj7aH8cvyUn4OToyZ+hI+gcYZ6bn31DqNFibW1ChrqNSXYuZZMbC9O1YmCl4udMEg9ftPF25jc3n3yfYvg+3+P4Xc0lheqKk1FWzIvs5KtT5TPT/AB/bzs3eLjREpLya+DveNs5ISEwN7IuPrYvJC9O5inJe2raZ+Pw8+vsHMmfYCPwcnYxtVoug0ek4ciaX3cfTiUvOvDiV1NHfk36dg+gdEUiX9l5YtqIAhLZGdZ2ShLN5HEjJYu+Jv35G/SPbMzgqmIiAdq1yZuJ6OJyXyyvbt5BZUc6UTpG8NmAwjlbGH6lfqNW5IG070a7BlKiqqNEo8bZxwc/WlamBffGwdgQawsrrtSqCDJSAeyHBNtxxGKO8X8LMzNx0REmtq2NVzosUq9IZ5/cugXbRzd7mBZ4/+jO+Nq6M9O7K/pJU1uQe4fPoBwhxaGeSwqQXgl+OJ/LBvj0ozMx5Y+BgJkd0bvNfbpVGy8GULHYkprH7eDpVdSpsrCzo1TGA/pHt6R/Z/qZ7Cm8tCCHIOF9KXHIme5IzOJ5xHr0QeLs6MrR7KMO6h9K1vU+bT/RVabX879ABFhyNx9POng+GjzKJUdO5miKeSVjMMK9IngwfTa1WhZ3Cigp1Hbl1pWw5n4SXjTPbzidzsjKXb2MforurYXJD40t/ZX/xIro438ow72dMQ5S0ejV/5r5GXl0SY33/S4hDv2Zv71I+OPkn4/16EuHUUMvqj6z9/JC+iy96TifM0bSck3nVVby0bTP7c7IZGBDE3GEj8XYw7YKvN4JGq2N/yjk2xZ8hLjmDOpUGR1srBnUNYWj3UHpHBLaqcGyZBipq6tmTnMG2o2c5dDobjVaHu5Mdw7p3YHRMOF3be7fph6zEgvM8v3UjGeXlTOsSxUv9BmJnabxFSAHO15fz8rFfGe/Xk8kBvdhdmMIHKX/ySIcRmEtmxLiFMCt+Ef09I3gq3LArMOwtWkBC2R88HbHd+KKkFzo25r9HWvUeRnq/RITTiGZv61K0eh3zUjdjq7Di4dBhF19fnn2Q3YWneCdqqtETzaDhSXPl6RTe2rUDgeC1AYOZ2rlLm/ziCiE4nnmeDYdOsSUhlcpaJc521gzt3oFh3TvQM9xPTupsQ1TXq9ibnMm2Y2fZfzITlUaHn7sTt/SKYGyvCPw9nI1tokFQajV8vH8fPyQmEODkzCcjx9DD23irxkJDUek/svYzM3Q4+fXlPH54IV/FzCDCyZen4hfRzsaZ1yMnAYYNChNCcLRsKT3d7zSuKMXHx7O7aB5J5asZ4PkoPVxvb/Z2LrCtIBlva2eC7D1R6tQ8dHA+4/16Mj1kMHqhR6PX8cmpdTzSYbjRl56oUql4fcdW1p09Q6yPHx+NGI2/U9vzHZVU1rL24En+3H+S7KIKrC0UDI4KYUxsR3p3CpSF6Cagpl7FzsQ01h86RXxqDkJAVLA3E/pFMio6vE2G6x/Oy+W5LRspq68jbvrDuNoY9yFYrddihoTCzJy06gKeP/ozVmYKYt1DeS5iXIva0tRAB4PNlRwtW0pS+Wq6u9xuUEGafeRHzCUzBAJ3KwcGenbi+96P8uDBb9DotdwZ1A+tXkdSRRb59eVGFaXEgvPM3rSe/Ooqnu/Tn0eiY9pUBJlOr+dAShar9iazJzkDnV7Qo4MvD46OZWi3UDlk+ybD3saKcX06M65PZwrLq9l4+DRrDqbw9s9b+WTZbsbEdGRi/0giAtrOWl+xvn5suPs+EgvON1mQlFqNwepWWpr9fxcf6uCFm5UDJypyeKTD32etTCWFxiAjpcju4eLh3/wJcxjMaJ9XkQwUXJBalc9XqZv5oud0SpRVnK0uYHn2QUb7dKOXewfePbECRwtbUipyGe7dhQdDhhjEjquhF4L5CYf57OB+vOzt+d+osXQ38tC+OSmrqmPlvmRWxiVTUF6Ni70N4/p0YmK/LgS2M92lAGRaHiEEien5rNqbzNajqag0OiICPLl9QFdGx3bExrLtjZ7+jeLaWubFH6SThyd3dDZste+3k5ej0ml4IGQwwN9yldR6LefrKzhaloGThS1DvSKbtX2jhoQHRDqJzzY8xAS/uU1eAOp6SK06z4cpf/J5zwewV1ij1GlIqcxhRfYh7mk/gFAHL+q0akpUVYQ6eBnMjn+juLaWZ7dsYF9ONmM7hPHe0BFtpirDyXMF/L4rkS0JqWi0OnpHBDCpfxcGdQ25KRMsZa6NqlolG+JPs3JvMml5JTjZWXNbv0imDIzCx83R2Oa1CDVqNQn5eXx6cB/D2ocwq1cfg7VVp1VhZW7xl8VKL4yOMmuKOFCSSlzRKSKc/NhXfIbhXl3+4pu/UYwqSsFdPMSpxEyszA0T0lunVWHbuOrip6fWk1dXyttRU7FTWFGlqWdl9iEkSeL+4EEGab+pHMrN4alN66hRq/nvwCHc0QaCGXR6PduPneWXbUc5ca4AWysLxvXpzNRBUQR5me7aUzKmixCCo2fz+H3XMXYmpgMwKCqEacN60D3UtFeEvVEuiIJap+PR9X/yzpDh+DoYVpBrtSqyaovp5NSwKnV2bQmbzyeh1mmJdQ8lxi2EImUlX6du4eXOE7A2b56BhVF9Ss6WvgYTpI9T1lKhqQXgnqAB3BPUj1W58cw9uYqXO92Go4UNPd1CWJy5m3qtGhtFy4dmCiH4/lgCH+zbQ6CzM79MnEKYm3uL29GcqDRa1h1M4aetR8gtriTA05kX7xjMrb07yb4imRtCkiSiw/yIDvPjfFkVy/ccZ+XeZHYmptEtxIfpo2LoH9l2VlLWC3FxIc4L72lrehpl9fU4Whr+u2RlpmDr+eM4KGzwt3PjZGUO9Vo1g9t1pqtLAAC/nduHRq9tNkG6Foy+ntK1sCL7EJvyE/m4x738lLEbrdDjb+tKlEsgOwtPsrvwFDM7DOfnzD1Eu7bn8bBRzW7D1ahVq3l5+2bWn01lVEgHPhw+CgcTyPS+XmrqVSyPO86v249SUlVH58B2TB8dy+CuIW0+OVLGeNSrNfy57wSLtyVQUFZNB193po+KYXiPMBTmrTs4qKCmoUp7dmUlqaUllCvr2ZedzcPRPanTaCitq+N0STFvDBxisHynC4UE6rQqHjo0n+nBgxnh3RWA7QXJJJafY5xvNGGOPuTXlQPgY3tj/mGTKzPUHPyUsRud0F8MWNh6/jinKvNob+/JOL9olmYdQKPXodSrmREytNnbvxoZ5WU8tn4N6eVlF6PrWuvTXXW9it92HGPJ9qNU16voHRHAAyNjiAn3b7XvSab1odHp2Bx/hh82x5NZUIafuxMzxvRibK+IVidOQgh+SjrGB/viuKVDGGaShEavo4eXDyOCQ/nuaDwZ5WXc0iGcs6WlJBbks2jCJIP6oM/VFPFV6mY+7nEv8P99ajsbJ4a2i2Rp1gGSKrIAaG/nwSuRE6+7LaOHhBuCXm6hzEvdTJJrMFEugYzw7opW6NhbdJqR3l25I9BwTsKrsfNcBrM3rcfSzJyfbptMP3/jlxu5HqrrVfy+8xi/bGsQoyFRIcwYE0unQOMEisjc3FiYm3Nr707cEhvB7uPpLNx4iLd+3sL3mw7x8JhejIltPeIkSRJjw8LZkJaKtULBe0P/Pyz7+2MJbElPY8Pd9+FkbY1eCGZvWodO3/yDhksJsHOnVFXNeydWUq9VYyaZ0d01iAhHX1bnxnO6Ko853e7C3cqBRw8t4EBxKn08wgxqU6sRJSEEAXbuxLiFsq/4DArJjM7O/ozx6c7OwpNszE/kNv8Yo9j13dF4PtwXRycPT769dYLBHZWGoE6p5tedx/hlWwJVdSoGR4Uwc2xvOvrfnEtmyJgWZmYSQ7qFMjgqhD3HM5i//iD/XbyFhRsPM3Nsb0bHhLeKnD8PWzuWTJzC4xvW8OzmDXw66hZ2ZGbwY+JRfp10B07WDaOitLJSNDo9Kp3WoPaYSWYs7P0oy7MPotZruc0vBgcLGxambSerppj3ut2Fo4UN5eoaLMwUuFoZvh6lyYvShegUSZKwVVjR1yOMHQUn2F5wgrz6MkZ6R6EXAgsDl2L/J9Q6Ha/t2MqKUycZ2yGMD4ePxsZE11e5Elqdnj/3n2D+ugOUVNUxsEswj9zau00lNMq0HSRJYlBUCAO7BrP7eAbfrjvAGz9u4udtCTw9aQC9I0x/hsLC3JwF4yayOOkYmRXlHD2fz1OxvQl0/v8STM9s3sCI4FC87A2f7G8umTE1sO/Fv/84t58dhSf5OuYhHC1sUOo0nKk6j4+NMwG27gZPsjVZUUoozSDaLfhvbz7UwQsLMwWnKnP5MX03m/KT0AodY317tKh9ZfV1PL5+LYfzc5kV24fZvfq0Kl+LEIK4E5l8sSqOjPNlRAV789Ej44gKbjtJvTJtF0mSGBwVwsAuwWw9mspXq/fy+Bcr6dspiNmTBtDB1/SjXe+L6g5AlUqJs3XDQ6BeCO5dtYwQV1ee7t334msStFj/UqmpY1b4GJwtbanRKEmraShKMNa3Bxqh44+M/VRp6tEKPc9GjG329k0y0OF0ZR73H/iamaHDmBH614CFS1W6XqumTF2Dr23L5sdklJcxY80qztdU8+HwUYwPj2jR9m+U0zlFfLp8N0dScwnwdGbWxAEMiQppVaIqI3Mpao2WpbuTWLBIZ2JiAAAgAElEQVThELVKNeP6dOLxcX3xaAXLn/yUdJTfko8zPDiUnKpK1Dod34wdDzQEelxaJ3JfThZ6vWBAYJDB7Pnk1FqKldU8FjaSwyVnSSw/xwDPCPp6hPPwofn0cw+nh2t7VufG087aiRc6jW/SdVt19F1eXRmvJP6KSqch2i2YFztN+NsxWTXFBNp73IiZ18WR/DxmrluNuSTx3a23tapyQeXVdXy1Zh+r953Ayc6GR8b2ZtKALnJxVJk2Q2Wtku83HuL3XYlYKMx5aEws9wztYfILRG5OP0tJXR2BTs4X12RSabVYKRrs3n0ukx3nMjheWICjlRVmkhk/TJhkMHvePL6McnUtnZx8iXELIczRh/v3z2OUdxQzOwwH4HBpGvuKzvBME0dLrVqUAJZkxjHcqwtvJi+jo6MvHRy86ejkQ7B9OxLLz3GgOJXHwkY2k8VNY8PZVJ7dsgEfB0d+GD/pL3PApoxWp2fp7kS+XXcQpUrD1CHdmHlLLxxs20a5IxmZy8kpruCzFXvYlZSOn4cTz08ZzMAuwcY2q0no9Pq/BG1sz0jnUF4Obra2PBDVAyuFgkfX/clzffrTwc3NYHZUa+pxsLBBrdfy0rEldHDw+kvu5/dpO9AKHTNDG0TqajMtTRUlkwlXyaktJb26AK1eB0B2XSnJlTl8E/swe4pO8VbycqzMGoIIOjh4t7ggLU46xlMb19LFsx3Lp9zZagQpMT2Pu+cu4eNlu4kM8uL316fx3O2DZEGSadP4ezjz6aPjmffUJBTm5jz99Z88882f5JdWGtu0f0Wn17PqdAqb088CkF1ZwdGCfDzt7LmjUxesFApOFhVyuqQYGwOP/hwsbAAoUVbjamnPgyFD0As9ACuzD7E6N54xPt0vBqI1FyYxpt2cn8RvWfsQQhDh5MsjHYYzyjuKgvoKjpVlAhDp7M/XqZsv1rhrKYQQfHZwP1/FH2R4+xC+GDPWYGXmm5PqOiX/W7WXlXuT8XJ14ONHxsl+I5mbjj6dAvnjtWks2XGUBRsOcfvbi3lsXF/uGtLdJPObzM3MGNY+hEqVEoCzpaVklpcztX8XXGxsKK6tZXtmBlMju+Dn6ERxXS0qbUPYuJ+jYdZlK1JVkllTdLHk0OqceL49u5Uvek4nwM79YnWI5qJJoiRJkjOwEIgEBPCgEOJAcxhwuCSNRek7+LjHfXhYO/JO8nKWZR1kUkAvXj62BIBFfR7Dz9aNuSdXoxf6v1S5NSQ6vZ7/7NrObyeOM7VzF94ZMhxFK8iF2H7sLB/8sZOyqjruHR7No7f2aZMLqsnINAULhTkPjIxhdM+OvP/7Dj5bsYdN8ad5Y9oIk8zDc7GxwcXGBp1ez76cLAYHtSfAyZlKpZI1qaep02oY6BPEmdISZm9cRzcvb3aey+TjEaMNEgDRzSWIQDsPHjzwDeGOPqRVF/C/ntPp6OSLzgD9cZN8SpIk/QTECSEWSpJkCdgKISqudPy1+JR2F6ZQo1VeDOlOry7gh/RdvNvtTnYVpuBv60aIg3FyZubu3c2Co0d4JDqGF/sOMPlRRlFFDR/8voOdSel09Pfk9XuG0ylQzjeSkbmAEIJtR8/y4dKdVNTUM214NDPH9jbZdZy+S4hn17lM5g4byScH9+Jj70B3bx/cbGyZF3+Ifv4BPNSjJ3FZ5/glOZGPR4wxWK3NPUWnCLB1w05hjYe14zWPkJqtzJAkSY7AQOABACGEGlA32ZKr0NcjDJW+Yfipa5yvzKsvQ6nTMLhdJyrVdWj1OhRGSI6d1qUbPg4O3B/VsjlQ14oQgj/3n+TT5bvR6vTMnjiAe4b1MMnpCRkZYyJJEiOiw+jVMYDPV8bx05YjbD92lv/eO5LoDn7GNu9vzIyOoaC2hq/iD+Jha8ejPWNRarW8F7froiABFNTW4G5rZ9DizwM9/z/1RQjRrFN2l3LVkZIkSd2A74AUIApIAGYLIWovO24mMBMgICAgOisr65qN0Qs9Feo6/nt8KV/GPMgf5/aTX1/OU+GjjSJKrYHSqlre/mUrccmZ9Azz441pI/D3aB1BGG0ZnVaPWq1Fr9f/bZ+ZmRmWVgrM5YcGoxN/Jod3ftlKXmkl9w6P5vFxfU0yfPzSJdOf3LAWe0tL3h/eEAlXVFvDr8nHaWdvz12RXVFptZTU15lcubNmCwmXJKkncBDoJ4Q4JEnS/4AqIcQbVzrnRkPC/3t8GW5W9hwry+T9bnfTzsYwnayprEl/vexMTOOdJduoV6l56rb+3Dm4u7ycRDOjVmkpLalu3GooKa6mrLSG6qp6aqqVVFfVU12tpKZaiUqpQaXWolZp0en+LkaXo1CYYWllgZWVAmtrC+wdbXBwsMbR0QYHRxscHK1xcbPH3cPh4ubiYo+5Qhaz5qRepeHTFbtZEZdMqK87700fY7IVISqVSl7ZvoUvxtyKwsyM4rpaNpw9w4GcHD4ffQsrT6VwsriI9LIyvB0c+GzULQa3Kak8C3crh6sWMWjOKuG5QK4Q4lDj38uBl5tw3jUjhECp05BQmo6VuQVfx8wwiCBdutrjheS01kStUs1HS3ex5sBJOvp78u700QR7Gy5foa1TX6cm61wxeTll5OeWk5/XuOWWU1Fe+7fjFQozHJ1scXC0xsHRBo92jgSHemJtbYmlpQJLq8bN8p9HQzqdHpVKg0qpRaXSoFZpUSrV1FSrqK6qp6iwkuqqBsHTX1Yl2sxMwt3DAR9fF3z8XPHxa/jp5++KX4AbFhbyjMK1YmNlwWt3D2dgl2De+nkr097/lScn9OOeoT1M7iHPTJLIra5ic9pZvBzsScjPJ+F8Hm8PHs7KUyksSkzgo+GjCXf3YNbGdcxPOMwj0bEGs0ep0/By4q84Wdjwfe/HmiUyuqmBDnHAQ0KIM5IkvQnYCSFeuNLxNzpSWp0TT3fX9gTaGeZp5fktG7FSKNDq9YwMDmVYcAjQOkZOKVkFvPz9BvJLqpg+KoaZY3tjoZA7oqYghCAvt5yzp8+TmV7EuYxiMjOKKMj//5gdSQJ3T0d8fF3w9nXBy8sJNw8H3NwbRipuHg44OFi3yP+JXi+orKilpLj64lZaXE3B+YqL4llZUXfxeHNzM/wD3AgK9iAoxJP2IZ6EdfTG3cPwRT3bCuXVdby7ZBs7k9KJDffnnemj8XAyrVJFSQXnmbt3D3aWlvT1D+CW0DBOlxbzwpZNrJp6D/5ODaHh3yXE4+vgyNiwcIPac7g0jdlHfqSfRzgfdr/nir6mZq3o0OhXWghYAhnAdCFE+ZWOv1FRMqQ4fLgvjozyMmb37svZ0hLm7t3D3V268lRsH4O3fSPo9YIlO47y5eq9uDva8e700fQwQcesKVFeVktKci6nT+WReuo8qafPU1PdkP/xlw482IOgYE/8At3w9nbG0qr1jJ5ra5Tk55WTk1VKZkYR59KLyUwvorDg/5NE3T0cCI/wIbyTD+ER3nTs5IutXetdDdnQCCFYve8EHy3dhY2VBW/fP4p+ke2NbdZfqFE3xJrZW1qSV1XFI+tW859BQ4n1begTNDod96xaxoPdohkd2sHg9vyRtZ9PTq3jgeDBPH6FwgbNusifECIRuOrFrpV6rRobxd+X+zWkKFiYmzEqpAMR7h5EuHvQw9uH+1evoLi2lreHDDdJQaqoqec/P21m74lMhnQL5T/TRuBkJ1dkuJyK8lqSjmWRdDSL48eyyMosARoEqH2IJ4OGRhAW4UNYR28CgtyxtGw94nMl7Oyt6RDuTYdw77+8XlurIjO9iNRT5zlzKo/TKfns23MGADNzifCOPkRFB9KtRxCdu/pjbW2aIdHGQJIkJvbvQlSID698v4Gn5q3mgZE9eXx8P5OJaLW/ZJn00vo6Ynz9LgoSwH2rl+Pv6NQiggRwR0Af0qsL+TFjF2GO3gz36nLd1zJa7buN+cf4JnUr38Q+1KJVvleeOklcdtZfHIA1ajXPbt7A3V2iGBxkWk9EyZnneWnBekqr63h28kDuGBRlksJpDLRaHSeTc4k/kM7hA2lkphcBYG1jQZeoALp2D6RrtwBCwtphJScPU1VVz5mUfJITs0k6msWZU/nodHoUCjMiIv2I7RNKr76hBAV7yP9jjag0Wj5etosVccl0C/Hh/YfG4mlilce3Z6QzL/4Qv98+lbL6Oubs3U15fT0/T5wCtNzsj0av5dHDC0mrLmBR70cJcfjratUmXZA1rbqA6Qe+obOTH1/FPGjwcO/SujpUOi0etnYozMyYtWkdBTU1/D556sXCh98cOYSztQ13RXY1qC1NRQjBir3JfPjHTjyd7fnw4bHykuRAZUUdB/amcnh/GgnxmdTVqjA3N6NLlD89YoOJ6hFIWEdvFLKf7arU16k5cTyHxIRzJBzOIP1sIQAeng7E9gkltm8HomPby4IObDh8ivd+3Y6NpQUfPDzW5HKa3ty1nfj8PLp5eaPV6/mgMVxcLwRmLfiAUays4r4D87A1t+Snvk9gr/j/GR2TFaUajZL7D8yjXqdmcd8ncbcyrBO2uK6Wpzasw9xMIsjZhWAXV2Z0j+btPTvZk5XJ24OH4+PgwGs7tjIkKPhiMpoxUWm0fPD7TlbvP0HfTkG89+CYm3q6rqS4mv17zhC36zTHE7PQ6wRu7g7E9gkhpk8oPWLaYyf7SG6YkuIq4g+mc/hAOkcPZ1BXp8baxoLYPqEMGNyRXn07YGP79+n2m4WM86U89+1a8koqeWbyQO4c0s2kRpQniwoJcnbBSqFAYWbW4oJ0gWNlmTwe/z2DPCOY2+3ui/fIJEVJCMHLib+yp+gUX8fMoLur4afKZm1cR7CLK4/1jOVwfi7bMtJRarW8PXgYG9NSicvOQqPXYW9hyZxhLVt5/J8oKKvmhe/WcjKrkBmjY3l0XJ+/lLG/Wagor2XX9hR2bj3JqRO5CAH+AW70H9yR/oM70iHcy6Q6hLaGRqPj+LEs9u4+zd5dZ6gor8XC0pyYXiEMGdGZ3v3Dbko/VHW9ijd+2MSe5AzG9org1buHmWSJImMHbP2SGccXZzbydMdbuDuoP2CiovTbuX18dno9s8PHcE/7Ac3e7j/x2cF9RHq0Y0RIKBqdjqLaWpalnKBcWc9bg4dRo1ZjZ2FhEh1cYnoez327FrVWx9v3j2JIt1Bjm9SiaDQ6Du0/y5b1xzl8IA2dTk/7EE8GDo2g/6COBLZ3N4nP6WZDp9Nz8ngOcbtOs3fXaUqKq7G1s2LwsE6MHNuVTpF+N9XnotcLFm48xPz1Bwj38+Szx8bTzsV0w+6NIVBCCF5KXEJc0Wnmxz5MV5dA0xOllMpcHjo4/2Ise0vdpD/PnOLzg/uZM3QEffwDAEgtLeGr+IPM7BFDpKdpFCxdf+gUb/28BR83Rz57bALtvVp2iXdjkpNVyvrVR9m66ThVlfW4utkzbFQkw0d3ITjUND4fmQZ0Oj3Hj2WxdVMycTtOoVRq8PV3ZfSt3Rh9axTOLnbGNrHF2JOcwWuLNmJjqeDzxyeYpM+3sKaGpzev57+DhtLRvWVX6q7RKLl3/1fohJ6f+z6Js5Wd6YhSjUbJtP1fIoTg535P4di4eJShOFlUSEFNDT19fHGytmZjWipLT55gQngEt3VsKCo4J24X7rZ2zIyOMagtV0MIwXfrDzJ//UF6hvnx0cxxN4X/SKvVsX9PKmtXJZCYcA6Fwoy+A8MZNTaK6JhguZROK6CuVkXcrtNsXp9EcmI2FhbmDBwSwbjJ0TfN6Ck9v4RZ8/6kvLqOOTNuYXBUiLFN+gv51VXcvvQ3BLD8jrtavB7ehcFIX48wPom+zzRESQjBq0m/saswhe96zaSLc0Czt3cpW9PTeC9uF5Ge7ShXKhkcFERXTy+UWi3fJhwm2MWV0aEdeGX7Fj4cPpq+/oa1599Qa7S8s2Qb6w+dYlyfTrx+9/A2X52hvKyWtSuPsH7NMcpKavBs58jY23owZlw3XFxNK9RWpulkZRazbtVRtmw8Tl2tiuBQT8ZP6snwMV3afPReaVUtT3/9JynZhTx3+yDuHmpaqwqcLinmjuW/423vwNLb78TJumUfei+4beLHzDUNUVqdE8+ck6t4ImwU9wcPava2LkWj0/Hqjq3c1jGCfv6B7MvJ4lBuLgADA4MIcnbho/1x+Dg44GVnz1Qjhn9X1ip5fv5aEs7m8vj4vswYHdumnyyzMotZ/vshtm9ORqPWEdMnhPGTehLTO0Sult2GqK9Ts3PrCdasTCD9bCFOzraMnxTNuEk9cXFtu1N79WoNr/+wiZ2Jadw5uBvPTRlkUgFKB3KyeeDPFfT08eWHCZOxNG+5h18hBJ+cWscLnccbX5SyaoqZtv8ruroE8GXP6QZbf+MCQghe27EVa4WC/wwaCkB6WSnrz6ai1et5tk8/g7bfVPJLK3nyy1XklVbx1n0jGR3T0dgmGYwTSdn8/vN+Du1Pw9JSwcixXZl0Ry/8A+UCsm0ZIQTJidks++0gB/eexcLSnJG3RDHl7t74+rVNf6leL/jfqjh+3pbAwC7BzH3oFpOKzFt9OoVnt2zk9k6d+WDYqBZ/CDZ6oMPBw4d46NB8cutK+a3fbDysW2YuM6+qiq+PHKKnty+3hoVjYW5OdmUFM9eu5rk+/RkRYtyItozzpTz+xUrqVRo+e2x8m61fd/xYFou/30PS0SycnG2ZcHtPxk/qiZOzrbFNk2lhcrJKWf7bQbZuPI5Op2foyEimPTigzYrT0t1JfPDHDqKCffjfE7fhYGM6OXSfHdzHl4cP8mr/QS2ek2l0UZr52/ssTN/B3G53MewG6iBdK0qthrWpZzhTUkKgszOjQkLxtLNnTtwuwtzcub1TZIvZcjkpWQU8+eUqFOZmzJs12WTXbLkRThzPYfHC3Rw7cg5XN3umTuvLLRO635Q5LTJ/pbSkmuW/HWLtyiNotDpGjO7KPQ/0x9vXxdimNTtbE1J57YeNhPq489WTE3F1NI2HMb0QPLVxHZvTz7Jg3G0MCQpusbaNKkqdu3cVju+PZ6R3FG91ndLs17/ApfH3F96HJEmotFq2ZKSRUlzEvpxs+vr5s/J0Cuvvug8PO+PMax9JzeGZb9bgZGfN17MmE+DZtlaHPZOSz6L5Ozkan4mzix133tuXWyf2aPNObplrp6y0hj9+2c/aVQnodYJRY6O4Z3p/PNs5Gdu0ZmXfyXO8MH8tXq4OfD1rMl6uppHLVKfRMHX572RVVrBiyt10cGuZqXSjipJLR38x4Nun+LXfLOwtDBfpkVNZiZO1FWqdHnfbhicRrV6PotHBWKlUklRYQLmyni6e7Qh2Mc50we7j6by0YD1+Hk58PWuyyRV0vBHyc8tYNH8Xu7en4ORsy9Rpfbh1YjQ2NjdvORqZplFSXMXvP+9nw5/HQIKJU2K5675+2Du0nZSIY2l5zJ63GntbK76ZNZnAdqYxKsyvruK2P5ZgZ2HJyjvuxsXGsGk6YGRRsgvzFnsO7CPazXBDw8N5ufxn5za6e/uQXVnJHZ0jmRDekIOk0mqxUiiMVvvpUjYfOcPrP2yko78nXz45EWd7w3/4LUFVVT2/LIpj7cojKBTm3H53b6bc1Vtep0fmmikqqOTHBbvYtikZewcbpk0fwPjJ0W2mqO7pnCKe+GIlkiTx9axJhPm1bBLrlTh2Pp+7Vi6lp48vP02YbPBoQaOKUkBkB5F94myzX/cCNWo196xcypMxvRkQGMiR/Hye27KROzpH8lyfhjpLeiH4/OB+pnfrgbN1y6wUejlbEs7w6vcb6Rbqw/8evw0769Y/etBp9axdlcDihbuprVUxZlw37p0xEDd305iakGm9pJ8t5LuvtnE0PhP/ADcemTWCXn3bRqmtcwVlPPq/Fai1Or57+nZCTcSfvCzlBC9t28wTMb0u9p2GwuiBDjey8mxTeGv3Dm7r2Imodg2lPYpqa7h/9Qr6+Qfy+sDBVCqVJBacZ5CR1kfadjSVV77fQNdgH7584jZs24AgpSTn8sXHG0k/W0iPmPY8OmsE7UM8jW2WTBtCCMHh/Wl8++VWcrPL6DcwnMefHomnV+v3N2UXlfPwp8vQ6vQseHYKwd6mkRbx8rbNLE05wYJxtzGsveEqUrRZUSqurcXZ2povDh+gsLaGD4ePvrivoKaauXv38Hyf/hfXqTcGOxLTeHnBeiLbe/HlkxNb/QipsqKOhd/sYNPaRNw9HHhs9kgGDOnYppN9ZYyLRqNjxe+HWPJDHAD3TB/A5Dt7YWHRuqf0zhWUMfOzZQjgu2emmESNS6VWw+1LfyO3uoq1d95rsL6zqaJkOinHTWDu3t28umMLszatJ9bHj9K6eib+sQSlVgOAl70DWr2e9PIyo9m4Kymdlxesp1NQO754onVP2en1gg1rjjH9zm/YuuE4U+7uzfe/PsrAoRGyIMkYFAsLc+68ty8LlzxCdGww33+zg0fvX0DS0XPGNu2GCPJyZf4zDRHJj3y+nKzCciNbBNYKC74eOx4h4IkNa1BptUa1p9WI0sKjR0gqKOCrMePo7OHJT0nH+GbseCI92zHxj19ZlnKChUePcKa0mLAWCnG8nLjkDF5csI6OAQ1BDfYmlDR3reTnlvHCUz/z2fvrCWrvzjc/PsTMJ4fLgQwyLUo7b2fefH8K73w0FbVKw/NP/sKnc9dRW6sytmnXTXsvV+Y/fTs6nZ6Zny0ju6jC2CYR4OTMJyNHc6K4iLf37DSqLa1i+q6svo6Xt23hidjeF31Iz23ZyMSOnegfEMja1NPkVFZSUlfL6NAwYn1bvkrCsbQ8Hv9iBcHebnw7ezIOtq0zrFWvF6xblcCCedsxMzfjkaeGM2acaa2wKXNzolJpWLxwD8t/O4i7hwPPvTaOHj2N4zNuDtLySpj52TJsrS354fmpeJhAqsgH+/YwPyGe/40ey7iw5i1/1uZ8ShnlZXjbO2Bhbo7CzIw5cbswMzPj5X4DAciurCDAyTgJqWfzSnjok6W4Otiy6Pk7cHEwjezta6WooJKP56zl2JFzRMcG89yrt+Lh2bKl7mVkrkbKiVw+encNudllTLi9JzMeG9pq8+JSsgp4+LPl+Lk7sfDZKUZ/mNXodNy14g9Sy0pZf9d9zepfanM+pfbOLthYWFxMjI1q531x3/Q/V5BcWGgUu/JLq3jyy5VYWyqYN2tSqxQkIQRbNx7n4WnzOXUyj9kvjmHuZ3fJgiRjknSK9OObHx9m0tRY/lx+hEfvX0DKiVxjm3VddAr04pNHxpFZUMYz365BpTGuP8fC3JzPR48F4NktG9Dq9S1uQ6sRpcunj0JcXSmrr+OFrZtwt7VjbFh4i9tUXlPPE1+sRKnWMu+pSfi4tb5OvLZGydw3V/PhO2sI7tCO7xbP5NbbouXpOhmTxtragsdmj+Tjefei0+p55rGfWPLjXnS6lu9Eb5TeEYG8c/9ojp7N49VFG9EZQQguxc/RiXeHDCfhfD5fHT7Y4u23GlG6FCEE1goFK1JOUlpfx0cjRl/9pGamTqlm9rzVFJRX8fnjE0wmGe5aSEnO5dH7F7B7RwoPPDyIj7+6t00Wx5Rpu0R1D2T+4ocZOCSCH7/bxYuzfqG4qMrYZl0zo2LCeWHKYHYmpjH3tx0Ywq1yLYwPj2Bix058FX+QI/l5Ldp2qxQlSZIIcnbhlf6D+HzU2BZvX6vT8/L3G0jJKuT9GWPpHurb4jbcCHq9YNmvB3j28cUAfPb1/dwzfYC82J5Mq8TO3ppX35rIC6+PI/X0eR57YCHxB9ONbdY1c9fQ7jw4OpaVe5NZtCne2Obw5qCh+Dk48vyWjdSq1S3WbqvuhWZ0j8bRquVDlD9bsYe9JzJ5+c4hDIoyXAa0IaitVfHWK8v47qvt9B0Qxjc/PkynLm1zTSeZmwdJkhh5SxRfL3oIVzd7Xn32N378blerm857YnxfbontyLw1+9h85IxRbXGwsuLDEaPJqapkzt7dLdZuqxClsvq6f3zdGH6P5XHH+W3nMe4e2p3bB0a1ePs3Qva5Ep6asYiD+8/y2OwRvPHe5DZVkVlGxj/QjS8WTGfU2CiW/LiX/7y4lJpqpbHNajKSJPGfaSPoFuLDm4s3c/JcgVHtifX14+EePfntxHF2nctskTZNXpSSCs7T/4cF7DyXYWxTOHw6mw9+30H/yPY8M3mgsc25JvbtPsNTDy2iuqqeD7+YxqSpveRgBpk2ibW1Bc+9eiuzXhjD0fgMnpjxPZnpRcY2q8lYWij45JFxuDna8cy3aygsrzaqPc/07keYqxsvb99MpdLwAm/SoqTSanlx22ZcrK2J9jau3yarsJwXF6wjqJ0rcx4cY/Ay782FXi/48btdvPnKMvwD3Zn3wwyiugca2ywZGYMiSRLjJkbz0Vf3oqzXMGvmD+zZccrYZjUZFwdbPn9sAvUqDc98s4Z6lcZotlgpFHw8cgyldXW8G7fL4O2ZdM/69ZFDnC0rZc7QkUbxHV2gpl7FM9+uwczMjM8fn9BqygcplRreemUZS37cy+hbo/j06/va3OqeMjL/RmRXf+YtmkFwSDveeX0FPy/aY/TItqYS6uvO3Bm3kJpbzJs/bzGq3ZGe7XisZy9WnDrJnqxzBm3LZEUptbSEb48cZmLHTkZbfgIaRhpv/LiJnKJyPnr4VnzdW0enXl5WywtP/syBvak8/vRInn3lViytFMY2S0amxXH3cOCjr6Yx4pauLF64h0/mrEOr1RnbrCbRP7I9T07ox9aEVBZvTTCqLU/E9CLYxYXXd26lTmO4kZtJipJeCF7dvgV7S0te7T/IqLYs2nSY3cczeHbyIKLDWkeUWm5OGbNn/kBGWhH/nTOFiXfEyv4jmZsaS0sFL7w2jvtmDGTz+iRef/4P6lpJUdf7R/ZkRI//Y++8w6Mouz58T7LphfTeKyVAEkLvvUiRoqCIKK/w2rBj7wVRbNgFFFFBFESkCNJL6CEhQICQQgLpCUYwsHEAACAASURBVOk92cz3RwKfvoIkmN1nNsx9XVwh2TK/7GbnN+c85zknmE/WRXPoTLowHWYaDfOHjCCjtJRFhw/o7DiKNKUVJ+OJzcnmxf6DcbQU17bn0Jl0vth4gNE92jNtcLgwHS3h9MkMHp2zjMrKWhZ+ehd9B+q/04WKihKRJIkZ/xnAk8+PJe7YeZ548DsK8sUWETQHSZJ4ZcYI/N0ceP6bzeQUitPcw9OLO8K68HXcMU7l6aa1m+JMKae8jIX799HP25db23cQp6OwjOe/2UyAmyMv3jnMICKN6D1nmTf3B6ytzVm0+B46hhlGZKeiok9GjQ3nzYXTyMxozCikpeaLlnRdLM1NWThnLLV19TyzdBN1AtOPz/Ttj6OFJc/v2KqT3niKM6XX9+yiXm7gzSHijKBe28BzXze+8QvnjMXCzESIjpbwx6Z4Xn9+DQHBrixafA+eXuInWqqoKJXuvQL54PO7qa9v4IkHlnP2tH5b6dwIfm4OvDJjBCfPZ/PJumhhOmzNzHll4GBO5eexPD6u1Z9fUaa0Nz2NLSlJPNS9l7AxFABfbjxIfGo2L945DD8FjCu+HhvXHeO9tzYQ2T2AhZ/chZ29lWhJKiqKJzjUnY++momVjTnPPLKChJMXRUu6LsO7hTB1UDg/7Igl+pR+NrNejdFBIQz09WPRoQPklpe36nMrZp5SrVbL6BXLkYHNd96NmUZMpdjhM+k8+Mlabu0Txkt3DReioSX8+vMRPv9oKz37BPHyW1PUCjs909DQQElBGcW5xVSUVlFVVkVVefWVfw31f0pvNAX+GhMNFtbmWNiYN321wMrWAns3O2zsrQ0iVdyWyM8rZd7cH7hUUMZb702ji8L38dXU1TPz3VXkFZfz0wt3CRsOmFZcxKgflnNLSCjvjxh93fsb3JC/JbFHeTt6L1+Pn8hgv4BW19QcLpVWcMdbP2Bjac4Pz92Jhamy03Y/rzjIks920HdgKC+8PgkTE2PRktoc2notOWl5ZCblkJmUTWZSNjlpeRRmF1GYU0xRbgkNrdhfzcTMBAc3Oxzc7XD0cMDd3wWvEA88Q9zxDHbH0d1eNS0dcKmgjHlzfyAvp4TXF05V/ETb8zmFTH97BWF+7nzx6CRhm/nfOxDN5zGHWX3btOs2ODAoU8qrKGfod9/Qw9Obr8dPbHU9zUGWZR75bB0x5y7y3TN3EqzwURQ/LNvH8iV7GDS0I8+8MgGNRjWkf0tFSQXJcWkkx50nKS6VlLg0LiZmof3TorKljQVuAS44ejjg6GaHvZsdDu72OLjZYdXOsjHysTbHvOmrxqQxcv3z56y+tp6q8moqy6qoLq+msqyaipJKinKKuZRVyKWcIgqziynILCTnfB51f9rNb2Ftjm9HL4Ii/AmODCAo0h+/MB9MDWDdU+kUFZbz9CMryMoo4tUFt9G9l7KbLa8/mMCr323lwfF9uG90TyEaKmprGf79MpwsLfl16vR/NEeDMqV527awIfEsW+6aiZ+dmHk+P++JZ8GqnTwzdTBTBym7/HvFt9F8u3g3w0Z15qkXxqkjJ26Qotxi4ncncHxXAif2JHAxMevKbY4e9gRF+OMf5oNniAdewW54Brtj59JOr5GKVqsl/+IlMpOyyTiXTca5LNJOXSAp9jwVJY2NijUmxgSG+9F1YCfCh4QR1q89FtYWetPYligpruSZR1dwIa2A1965XdHGJMsyLy7bwtZjiXw7bxqd/NyE6Nhw7iyPbtnE20OGMzWsyzXvZzCmlJCXy/hVP3BfZBTPCdooezG/mKlvfk9EkCefPjxR0emR9b/E8Mn7Wxg6Iox5L41XDakF1NbUEb87gSObYjm+6xRpCY0L25Y2FnQe0IEOvUII6RZAUIQ/9q7iCm2agyzL5JzPIyk2lXMxKZw+eI4zh85RX6fFWGNM+55BhA8Oo9fYboREBWJkIL0alUBZaRVPzf2BzAuXeOfj6XTq7C1a0jUpq6zm9je/x8rclBXPTcfMRP9ryrIsc/uaVVwoKWHn3bOwMjW96v1a1ZQkSUoDygAtUH+9J26uKcmyzF2/ruZsQT67Zv4HWzP9j1FoaJCZ/eFqkjILWP3SDFztbfSuobns3HqKBa+to2ffYF6ZP0VN2TWD0sIyjvwex4H1R4nZcpyq8mrMLc3o1K894YPDCB/cieDIAIzbwGtZXVlDwv6zHN95iuO7TnEuJoWGBhkHd3t6j4uiz4TuhA8JU1N9zaCosJzH7l9OaUkV7382g4AgV9GSrsmB02k8/Mmv3DMiikcm9heiIS47i8mrf2Ruj1483qvvVe+jC1OKkmW5oDkCm2tKO1JTmL1xHa8OHMLdXSOa89Stzoodsby/Zg+v3T2Ccb07CdHQHA7tT+KVZ38mrIs38z+4AzP1xHJNKsuq2P/rEXas3EfcjpM0aBsaT8xju9F7QncihoRhan71q7m2RGlhGYc3xXJwQ8wVQ7awNqf3+CiGTh9At+Fd2oQZ64qc7GIev385Wm0DH345U9F7/95YsY3f9ifwzVNT6RLgLkTDI5s3sv18CjvvnoWb9d8v7hVvSnVaLaNXLgdg850zMTHW/4cjLaeQO+b/QI/2Pnz0wATFpu1OxKXz3OM/4hvgzMJP7sLKyjC6lOuT+rp6Yv6IZ8fKfRz87Sg1VbW4+TkzaFo/+t7a/aZPYdVW13J8VwL7fz3Mvl8OUVZUgZ1LOwZN7cOwuwYQEhWo2L9/kaSfz+eJB7/D0tKUD7+ciZOzrWhJV6W8qobb3/wecxMNK5+/C3NT/afxLpaUMPz7ZYwLbc/C4aP+dntrm9J5oAiQga9kWV78T/dvjin9cOI4L+/eweKxExgWEHRdDa2NtqGB/7z/M2k5hax++W6c24mp9b8eKUm5PPHgdzg6WfPhFzNpZyeuF6ASuZRdxMYvt7Jp8TaKckuwdbRh4G29GXrXADr2DlFPtFehrraOo5uPs33FXg5tOEZdTR2+Hb2Y8PBohs0YgIWVOo34zySezmLeIz/g6tqOD7+cqdhpzYfPpPPAx2uZMaybsCGkC6L3sCQ2ho13zKCDs8tfbmttU/KQZTlLkiQXYBswV5blvf9znznAHAAfH59u6enX7mZbVVfHoOVf42tnx0+Tpwo5cazafZx3f9rF6/eMZGzPjno/fnMoyC9j7n3fIEnw0Vf3qLOQ/kTi0WR+/fh39vx8AG19Az3GRDBm9jC6jwrHROH7y5REeXEFe9ccYuNXW0k6loq1nRVj7hvK+IdG4errLFqeYoiNOc8LT/xIWBdv3v7oTsWu5761cju/Rp/iu2em0dFX/9V4pTXVDPz2ayLdPf62vUdn1XeSJL0KlMuy/N617nO9SGlpbAzzo/ewavJUenjqv2loXnE5k179li4BHnw2V5nVdtXVdTzx4HdcTC/goy/vITBYuQut+kKWZQ5tPMaqBb9y+uA5LG0sGHnvYCY8PArPIDF59LaCLMskHEjk149/J3rtYZBl+k7swbRnJxLSTbll0fpk2+YTvPvGesaMj+CxZ8Yo8rxRVlXD5NeW42hjyffP3olGQHXu50cP897BaH657Q4i3D2u/Ly5pnRdxZIkWUmSZHP5/8AI4NSNCq6oreXLmCP09fYRYkgA763ejbahgefvGKLIP6yGBpl331hPcmI2z7828aY3JK1Wy57VB7k/ch4vT3iHwpxiHlo0i5UXv+TBj+5VDakVkCSJsL7teemnJ/g+5VNue2o8sdtP8lD3Z3lh7HxOH0wULVE4w0d3Ydrdffh9fRy//nxEtJyrYmNhxjO3DyYxI59Vu48L0TCzawSOFhZ8cGj/DT2+OTbqCkRLkhQPHAE2ybK85YaOBnwbH0dhdRVPXKNsUNdEnzrP9tgk7hvdCy9nZe5FWb5kN/t2nWH2Q8Po3S9EtBxhaOu1bP9hL7M7P8mbUz+grrqOp799mGVnF3Hr3NFY2arra7rAxceZ+xbcxYq0z7n3zTs4eziZR/u+yNPDXyd+T4JoeUK5d85g+g1qz1efbOfwgWTRcq7KkIgg+oX588WGA0JmL1mZmvLfbj3Yf/EChzNa3uRWr5tnS2tqGPDtEqLcPVkqoJ1QdW09U15fjpmJhlUv3IWJAvPCO7ee4u1X1zFqXDhPPHuLIiM5fXD491gWz/uOC2cy8e/sw/QXJtNvck+MBVRp3uxUlVex8avtrH7vN4pyS4gc3oX737sb/87KblyqK6qqannywe/IvFjIosX34hegvLW3zIISpry+nL6d/Hnvv+P0fvzq+qa6gXZ2rGqqG2i19F1r8v2JOEpranisVx99HvYK322LIetSKc/dMUSRhpScmMP78zfSOdyHR54afVMaUvrpizw/5i1eHPs22voGXl79JF/GLWTg7X1UQxKEhbUFtz05ju9TP+P+92eSFJPC/RHz+PjBJZQUlIqWp3csLEx5/d3bMbcw5ZVnf6a8rFq0pL/h6dSO/4zuyc7jyRw+e0HvxzfXmPBAVA+OZmVyJDOjRY/VmylV1NbyTdwxBvsFEOai/zWS7MJSvv3jKMMjg4kKUV7bkNLSKl57fjXt7Cx46c2br+N3aWEZn879mjldn+LMoSQe+OAelpx8n/6Te93U+4uUhJmFGZMfH8u35z5h3AMj2bRkO/eEPMLajzZRV1t3/SdoQzg52/LSm5PIzS5hwWvraGho/YzTv2XGsG54Otry3s+7qW/FTvbNZWqnzjhZWvLp0UMtepzePu0/njpBUXU1D3cX0832o7X7kJF5dJKY+v1/oqFBZuEb6ynIL+Olt6Zg76DMPVO6QJZltn2/h1ntH2XDF39wy5zhfHvuYyY9dota2q1QbB1tePiT//DV8fcI7RHEF098ywORT3Nq/1nR0vRKWFcf7n90OIcPJPPTDwdEy/kbZiYaHp8ykJTsS6zZd0LvxzfXmDA7Mor9Fy8Ql511/Qc0oRdTqq6vY3HsUfp6+/ylRFBfHDuXwbZj57hnRHc8HJW3I3v1yoMc2p/Ef+cOp0Onf55J0pbISMrmmRFv8O7MT/EMdufLuIU88tl9tHNS3nuk8nf8Onnz9uYXeP23Z6gqr+bx/i+x6IHFlBdXiJamNyZMjmLQsI58u3g38bFpouX8jcFdA+kR6s2XGw5QXF6l9+PfGdYVO3NzPjt6uNmP0Ysp/ZxwioLKSh7u3ksfh/sL2oYGFq7ejZuDDXePuO4am945FX+Bb77axYAhHZgwRXn6dIG2XsvK+WuZ0+VJEo8m88hn9/Hhvjdu2oVzQ0aSJHqPi2LpqQ+Y/Ngt/L5kO//p+BjRvzb/JGTISJLE48/cgoeXPfNfWUdRYeuOBv+3SJLEvNsHUVFdyxcb9B/NWZmaMiu8GzvTUpv9GJ2bUn1DA0tiY+jm7kFPL/2v5Ww6fIZzGfk8Nqm/4ibJlpVWMf/Vdbi52/HEc2NvisKGjKRsHunzAste/JFeYyP5+vRHjHtgpLpuZOBYWFtw/wf38Mnht7F3s+O1ye/x9l2LqChp+1GTpZUZL781hfKyaha+tQFdVDT/GwI9nJgyoCtro0+Smn1J78e/u2sE1ibNb4Cs8zPB1pQkMstKmRPZXdeH+hu1dfV8ufEgHX1dGR6prP0+siyzaOFmCgvKef7ViTdFk9Vt3+/hwW5Pk52Sw4s/PcHLq5/CyUO5nZdVWk5It0A+Pfw2d796O7t/OsD9kU9z5nCSaFk6xz/QhTlzh3H0YArrVh8VLedvzBnTEzMTDZ+v13+0ZGtmxvsjRjf7/jo3pa/jjuHbzo4h/gG6PtTfWLPvBDmFZcy9tZ/iopA/NsWzZ8dp7pk9kNCO+l9n0yeVZVUsuPtj3p35KUER/nx5/D0G3tZbtCwVHaEx0TDj5dv4cO/ryA0yj/d/iVXvrKOhQf8VYPpk/KRu9OobzJLPd3A+JU+0nL9gb2PJjGHd2Hk8mYS0HL0ff3hg85tu69SUYrOziMvJ5t7wyH+c3a4LKqprWbr5CD3b+9CzvY9ej309MjMK+ezDPwiP9OW26W375JwYk8IDkfPYtTKau1+9nYU7X8HF20m0LBU90LF3KF/GLaTvxB58/dwKnhv9FoU5RaJl6QxJknjiubFYW5sz/+VfqalRVpn8XcO6YWdtwSfrokVL+Ud06hTfxB3D1syMyR30Pzzvh+3HKC6v4uEJYtoZXQuttoF331iPRmPM0y9PaNPjzDd88QeP9X2Butp63tv1GjNevk3dAHuTYW1nxYurHufxr/5LQvRZ/hs+j/jdbbdVkb2DFfNeHE/a+XyWfblbtJy/YGVuyn2je3Ak8SKHz1x7ioNodHZGzCorZUtKEtM6db7mzHZdUVJRzYodsQwJD6KTn/7bt/8T61Yf5fTJDB5+YiTOLm2z9Flbr+Xjh5by8UNLiRzehS/jFtK5fwfRslQEIUkSY2YP47OjC7BxsOaZEW/w+9IdomXpjO69Ahk3qRtrfz7M6ZMt62aga6b074Kbgw1fbDyouIKMy+jMlFadOoksy0zvHK6rQ1yTlTtjKa+u5b9jlZUay84q4tvFu+nZJ4ghI8JEy9EJ5cUVPH/LfDZ88Qe3PTmO1397BluHv49GVrn58O3ozScH3yJ8SBgfzvmSxfO+Q6vVipalE+57YAhOLrZ8sGAjtbX1ouVcwdREw6xRPTiRms2hM/pvP9QcdGJKMrAq4QSD/QLwbqffwXSlFdX8uDOOoRFBBHsqZ+1ClmU+eud3jIwkHpnXNvvaZaXk8EifF4jflcATS+5nzsK71XSdyl+wamfFWxufY9wDI1n9/gZem/weVQI2deoaSyszHp03hvTzBfz0vbK6PUzo3Qk3exsWb1JmtKQTUyqprqagspIZXfQfJa1oipJmj9H/Rt1/YtvmE8QePc9/HhjSJifInoo+w9xez1OcV8I7W19i9H+GipakolCMNcY88tl9PPTxLA5vPMZj/V8iP0P/+2d0TWNGpBMrl0eTfj5ftJwrmGiMuXdkd+JTszkioFnr9dCJKRVWVeLbzo7+vn66ePprcjlKGhIeRIiXctrJFxWW8+WibXTq4sXYid1Ey2l1Dvx2lGdGvIGtozWfHJpP10H6L2xRMTxufXg0b258jpzUPB7t8wLpZ5S1/tIaPPDoCCytzPjg7U1oBTRFvRYT+nTC1d6arzYdUly0pBNTqqirY3rnrhjpOUX18554yqtrmXOLsqKkrz7ZTnV1HY8/OxYjo7aVttv5YzSvTXmPgC6+fBT9pjoFVqVFdB8Vwft7XqO+rp6nBr1C6gnlVoXdCHb2Vtz/yHBOn8pg84Y40XKuYGqi4Z4R3TmeksWxJGVdDOjElCRgUoeOunjqa1JTV89Pe47Tp6OfoqKkE3Hp7PjjFLfd2QtfP+WscbUGW5fv5p0ZHxPWrz3vbHtZbaSqckMEhfvzwd43MDEz4akhr5IU2/w+aYbAsFGd6RLhwzdf7qa0pFK0nCtM6BOGg40l3207JlrKX9CJKdmameNgod9R1ZuPnOVSaSUzhisnPabVNvDZR1txcbXljpn9RMtpVTYt3sZ7sz4nfEgYb216HksbC9GSVAwYr2B33t/zGpY2Fswb+lqbak0kSRIPPzGKiopqvvlqt2g5VzA31XD7wK5EnzovpCfetdCJKblYWeniaa+JLMv8sOMYIV7O9AhVzgC/LRuOk5qUy5yHh2FurqxmsP+G3z7bwkf3L6b76HDeWP8s5pZtv2+fiu5x93flgz2v0c7JhmdHvNGm5jP5B7owYXJ3Nq+PIyUpV7ScK9w2oAtmJsas2BErWsoVdGJK5hqNLp72mhxISCM1u5C7hkUqptS6vKyaZYt307mrNwOGtJ2No78v2c6nc7+mz4TuvPLLPEzN9bsxWqVt4+LjzPu7X8PRw57nR7/VpiKmGbP6Y21jzheLtiqmuMDexpKxvTqy6fAZLpUqo6N7m+hxs2JnLM7trBjZLVS0lCv8+N1+SksqefCxkYoxyn/L3jUHmyKkCF5Y9TimZm0n+lNRDk6ejry74xXsXdvxwpi32kxVno2tBTPvG0h8bDoH950TLecK04dEUluvZc1e/U+nvRoGb0ppOYUcOnOB2wZ0xUSjjI2aebkl/Lr6CENHdiYoVFltjm6UE3tPs2DGJ3ToHcIra55UDUlFpzh5OLBg60toTDU8P/otCrIKRUtqFW6ZEImXjwPffLVLMSXifm4O9Onoxy/RJ6lTQIcNgzel1XtPoDE2YmI/5bTt+f7rvSDDzNkDRUtpFc6fusDLE97Bzd+FN9Y/g5mFuoakonvc/V15a9PzlBWW88KY+W1iYKCxxoh75wwm/XwB27ecFC3nCrcN7EJBSQV74lNESzFsU6qqqWPDodMMiwjG0Va/xRXXIv18Plt/P8G4Sd1wc7cTLedfk3exgBfGzMfM0oy3N7+g9rFT0SvBkQG8vOYp0k9n8Ork96irVdY4iBuh/+D2hLR3Z/nSPdTWKKMvXr8wf9wdbPl5T7xoKYZtSr8fOUN5VQ23D+oqWsoVln21G3NzE+5sAyXgFSUVvHDLfCpKK5n/+/O4+ipn/5fKzUPUiK48ufQBju88xXuzPldMkcCNIkkS/3lwCPm5paxfGyNaDgDGRkbcNqALMecySMkqEKrFYE1JlmXW7D1BiJczXQOUMbn17OlM9u9N5LbpvWlnp999Wq1NQ0MDC2Z8wsWzWbzyyzwCu/qJlqRyEzP87oHc++Yd7FwZzcr5a0XL+ddERvkT2d2fH7/bT2VFjWg5AEzoG4apxpjVggseDNaUzlzIIzEjn8n9Oiumum3FsmhsbC2YdHsP0VL+NasWrOPQxmPc/8FMIod2Fi1HRYU7npvI4Dv68t0rPxG7QznrMTfKvf8dRGlJFevXKqOjgr21BUPCg9h85CzVAsdtGKwp/XbgFGYmxozqrowy8JSkXA7tT2Ly1B5YWhl2IUDs9hMsf3kVg+/oy4SHRomWo6ICNKa9Hv/qv3iFevD2nR9RkKmcLgQ3QvuOnnTvFciaHw9RXa2MtbIJfcMoq6phd3yyMA0GaUo1dfVsPprIkIhgbCzNRcsBYNX3+7G0NGXClO6ipfwr8jMuMf/Oj/Bu78njX/1XMVGoigqAhbUFr/wyj5qqWt6Y+iH1dcooFLhR7ri7LyXFlWzZcFy0FAC6h3jj4WjLuv2nhGkwSFPaHZ9CeVUN43srY0RCxsVC9u48w7hJUVjbKMMkb4S62jreuP19aqvreHnNU1hYq/3sVJSHT3tPnlz6AKcPJLLk6R9Ey/lXdA73IayrNz+vPEhdnQL2CBlJjO/diaPnLpJ1qVSMBiFH/ZdsPHQaN3sbuocoo8/d6hUH0WiMmTzNsNeSlj6zgjOHknjy6wfxae8pWo6KyjUZeHsfbp07mrWLNrFv7WHRcv4V02b0JT+3lF3bxEUnf2Zsrw7IMvx++IyQ4xucKRWVV3HoTDqjuocqYjZRSXEl27ecZPjoztg7WIuWc8PEbj/B2kWbmPDQKAbe1lu0HBWV6zJn4QxCogL5cPYXBr2+1KN3IH4Bzvzy0xFFlLt7OLYjIsiTP2IShRzf4ExpR1wS2gaZUd3bi5YCwKbfYqmtrWeiAVfcVZRW8v59X+Ad6sHsd+8SLUdFpVmYmJrw3A+PUFtdx4f//UoRJ/QbQZIkJt7WndSkXE4cV8Z48pFRoaRkXyI5U/97lgzOlLbGJOLnak+wp/iBefX1Wtb/coxuPQLw9TfcjaVL5n1PQcYlnlr2kNpCSMWg8ArxYNb8OznyexzbvtsjWs4NM2RkZ2xsLfj15yOipQAwNCIII0kSEi0ZlCnlF5dzLCmDEVGhiqgK27vzDJcKygw6SordfoJNS7Yz5YlxdOwVIlqOikqLuXXuaML6tefzx5YZbBrP3NyEW26N4MDeRLKzikTLwdHWiu6h3vxxLFHvEahBmdL22CRkGUZ0U8bJ89fVR/HycaB7r0DRUm6IqvKqK2m7u1+7XbQcFZUbwsjIiCe/fpC6mjoWPbjEYNN44ydFIRlJ/LZGGa2HRkaFkpFfwpkL+h1KaFCmtPN4MkEejgS4O4qWQnJiDmcTMhk/KUoRBRc3wvevrSbvQgFPfv2gmrZTMWi8gt255/VpHNpwjIPrlXFSbynOLrb0G9ierb+fUESj1sHhQRgbSew8rt/O4QZjSkXlVcQlZzI4PEi0FAB+Xx+HqamGYaMMswVPWsJF1i76nVGzhtCpjzK6Yqio/BsmPjoGv07efP7YMqorldFPrqWMGR9BWWkV0XvEj4JvZ2VORJCX3rs7GIwp7TuZSoMsM6ir+FRZVVUtO7aeYsCQDtjYGt4GU1mW+fihJVjaWnDfgumi5aiotAoaEw1zP7uP3PR8fjTQpq0RUf64edixeX2caCkADO4aSGp2IRfy9LfOZTCmtDs+BTd7G9p7u4iWQvTus1RW1DB6XLhoKTfE9h/2cnLvGe57ezrtnGxFy1FRaTW6DOjI0Lv6s/q99WScyxItp8UYGUmMHhfO8dh0MjPET9sd2BQE7Nbj8D+DMKWq2joOnU5nUNdARVTd/bEpHg8vezqH+4iW0mKqKqpZ+uwKQrsHMuo/Q0TLUVFpdea8OwNTC1M+f2yZaCk3xIgxXTAykvhjo/iBex6OtoR6Oaum9L/EJF6kuq6eAV0CREshL7eE+Nh0ho/uogiDbCm/fbKZwuwiHvjwXoyMDOLtV1FpEQ5u9kx/cQpHtxwnfk+CaDktxsnZlsju/uzadkoRlYQDugRwIjWbkopqvRzPIM5KB06nY26qISJIfD+2vTsb+0ENGqaMZrAtoaKkgp8X/kbPWyLV4gaVNs34B0fg4G7P8pd/UsSJvaUMHt6JnOwSzp4Wn4Ls08mPBlnm8Nl0vRyv2aYkSZKxJElxkiRt1KWgq3EgIY2oEG/MTDT6PvTf2L39NMHt3fHydhAtpcX88uEmyooqmPnaVNFSVFR0ipmFGXc+P4mT+84Qu13sJNUbNVjKLgAAIABJREFUoe+AUExMjNm9XXyk18nXDVtLMw4kKMyUgEcBvbeNzcgv5mJ+MX06+ur70H8jK6OQxDNZDB7WUbSUFlN6qYxfPtxI/8k9CY4UnwZVUdE1o+8biouPE9++tMrgoiUra3N69A5i947TaLUNQrVojI3o2cGXA6fT9PI6NsuUJEnyAm4BlupWzt85dKbRnXt1EG9Ku3ecBmDgEMMzpZ8X/kZVeTV3v6pGSSo3B6ZmJkx/cQpnjyRzaKMyRo63hIFDO1JYUM6pExdFS6FPRz8KSipIztJ9G6fmRkofAU8D17RsSZLmSJIUI0lSTH5+fquIAziaeBFXe2t8Xe1b7TlvlH27ztIxzAsXt3aipbSIsqJyfvtsC4Om9cGvkzJmUKmo6IMRMwfiHuDKyvlrDS5a6tUvGFNTDft2iZlr9Gd6tm+sND5yVvddzK9rSpIkjQXyZFn+x0sNWZYXy7IcJctylLNz63TMlmWZ2ORMugV7Ca90y8stIflcDn0GKKPvXkvY8MVWqitqmPr0raKlqKjoFY2JhilPjOPs4SRORYvvktASLCxMiezhz6HoJOGG6uZgg6ejLXHJmTo/VnMipb7AeEmS0oBVwBBJkvQyg/hCXjGXSiuJDPbSx+H+kUPRSQD07mdYplRbXcu6T36n24iuBHb1Ey1HRUXvjLhnEO2cbPj5vd9ES2kxvfuFkJtTwvmUPNFSiAz2IjY5U+cGeV1TkmX5OVmWvWRZ9gOmATtlWdbLJLhjSRkARCqgFPxg9Dm8fBzw8RM/x6klbP9hH0W5Jdw+b4JoKSoqQjC3NGP8g6M4tOEY6WcyRMtpEb36BgNwcN85wUogItiT4vIqzufottOEovcpxSZl4GBjKXw9qaKihuPH0gwuSmpoaGDNBxsIivAnYkiYaDkqKsIY/9BITM1NWPP+BtFSWoSDozXtO3lysClTI5LIoMaMVayOU3gtMiVZlnfLsjxWV2L+l+MpWUQEeQhfT4o9ep76+gZ6Nl21GArHdyVw8Wwmkx67RfhrqKIiEjvndoyYOYgdK/ZRVlQuWk6L6NU3mMQzWRQVitXt7dwOJ1tLjivJlPRJYWklWZdK6ezvLloKcUfPY2FpSqfO4te2WsLWb3dhbWfFgCm9REtRURHOmNnDqKupY9eP+0VLaRFRPRr3FcbFpAnVIUkSnf3dSUjT7dA/xZpSQnoOAJ383AQrgWNHU+kS7oNGYyxaSrOpKKlg3y+HGDytrzrAT0UFCIrwJ6CLL398u0u0lBYRFOqGjY05sUfPi5ZCJz830vOKKNVhHzzFmtKptByMJIkOgkdV5GQXk5VRRGR3w+qCsGvVAWqr6xh572DRUlRUFIEkSYy8ZzDnYlI4f0r3+21aC2NjI8K7+REbc154afjlICEhXXfRkqJNKdDDEUtzU6E64mIar04iovyE6mgpf3y7C79O3oREiR+KqKKiFIZM74fGxJg/lhlWtBTR3Z/83FIyLoidsdTR1xVJglNp2To7hiJNSZZlTqfn0slXfOouPjYdO3sr/AJaZ0OwPsg4l8XZw0mMuGewWuCgovIn7Jzb0WtcFDtX7kOr1YqW02wiu/sDcPxYmlAdNhZm+Lk66HRdSZGmlFdcTklFNaHe4o3g9MkMOnUR31GiJexdcwiAQVP7CFaioqI8Bt3eh6LcEhL2J4qW0mw8PO2xd7Di9Cnx+6xCvZw5l9l6reT+F0Wa0rmMxl84xEusKRUVVpCdVUzHMMOquotee4gOvYJx9nIULUVFRXH0GBOBqbkJ+345JFpKs5EkiY5hXpxJ0H2bn+sR7OVETmEZZZW6KXZQqCkVABDkKbZ7wuU/gI5h4jtKNJfs1FySYs/Tf5JaBq6icjUsrC2IGhlO9NrDNDSIHQvREtp38iTzYiElxZVCdYR4NgYL5zILdPL8ijSlpMx8PBxtsRFcynwmIQNjYyOC24vfK9VcotceBqDf5J6ClaioKJd+k3pSkFnI2SPJoqU0m8sXx2cFR0vBTRmspJvLlAoIFhwlAZxNyCIw2BUzMxPRUppN9LojBEX44+7vKlqKiopi6T0uCo2JMfubLuIMgeD27hgZS8JTeM7trLCzMidJR+tKijOlem0DF/OKCXAXux4iyzIp53IIDhVfAdhcyosrOHvoHD1viRQtRUVF0VjbWRHWrz0x2+JFS2k2Fham+Pg4kZKk244K10OSJPzcHEjLKdLJ8yvOlLIulVDf0CC8CWt+XillZdUEBBlOxBG38xQNDTLdhncVLUVFRfFEDutKanw6RbnFoqU0m4BgF1KSxZoSgJ+rA+m5N4kppTX9oqJN6fLVSGCI4ZjSsa3xWFib06GXYTWOVVERQeTwLgDEbj8pWEnzCQx2Iz+3lNLSKqE6fF3tKSyr1EkFnuJM6bL7+rk6CNWR2mRK/gFi2xy1hGPb4gkfEobGRCNaioqK4gmK8MPW0YZj2w0nhRcQ1Hg+ShWcwvNrChrS81o/ylScKaXlFmJnZU47K3OhOlKS8/DwtMfSyjCamWan5pJzPo/IYV1ES1FRMQiMjY2JGBpG7LYTwnvKNZfA4MbMTargFJ5Pkyml5bZ+2yPFmVJWQSleznaiZXAxvQAff/EVgM3lzKHGyZSd+3cQrERFxXDo3L8jl7KKyE3XXYeC1sTewRobWwsupF8SqsPT0RZoPF+3NoozpezCUtwdbIRqaGiQycoowsvbcDoiJB5NwczCFL9O3qKlqKgYDO17Nq6/Jh5NEayk+Xh5O5B5UWxjVlMTDU7trMgubOOm1NAgk1NYhpuDrVAdBXml1NbW4+Utdl2rJSTGJBMY4Y+xAc18UlERjX9nHzQmxpw7ajibaL18HMi8KDZSAnB3sCX7Uhs3pcKySmrrtbg7ijWljKY33MvHMExJW68lOfY8oeqYChWVFmFqZkJAVz/OHTOcSMnTy4H8vDKqq+uE6nB3sCGrrUdKl0NB0em7yzNLPA0kfZd+OoOaqlpCuweJlqKiYnCERgVyLibVYPrgefk0npdEp/DcHW3JLSqnoaF1i0QUZUr5JRUAuNhZC9WRm1OCiakxjk5idTSXtKYpmgFdfQUrUVExPALD/agsqyJfASmx5uDm0VgIlptTIlSHq501dfVaSipad8+UokypsLTRlJxsrYTqyMstwdnZ1mBmKF04m4mRkYRnsOE0jlVRUQre7RsbnV44K34sRHNwdmlc3sjPa/3UWUtwsLUE4FJp63YtV5QpXf7l7GwshOooyC/DyUVsCrElXEzMwi3AFVMDahyroqIULptSRmKWYCXNw87eCo3GiALBpuRo0xg8XCprw6ZUWFZFOytzTIzFVpAV5JVeuRoxBDISs/AO9RAtQ0XFILFztsXazoqLBhIpGRlJODnbKCZSKmzLkVJhWQUONpZCNTQ0yBTklxmMKWm1WjLOZeEdajiDCFVUlIQkSXi39+BiomGYEoCTiy0F+WVCNTg2navbdKRUXF6NnbXY1F1ZaRX19Q04OBpGkUNRTjG11XV4BBpO41gVFaXhEeRGdmqeaBnNxsHRmsKCcqEabCzNMDaSKC5vw4UO5VU1WFuYCtVQWtL4Atu2E2uOzeVSVmMDWycvwyhfV1FRIk4eDlzKKjSYHni27SyEdwqXJAkrc1PKq2pa9XkVZ0qiR6CXNuVHbduJTSM2l4LMxr0Kjh5iR32oqBgyjh4O1NdpKdFBLzddYGtrQVlpVavvEWopNhZmbdyUqmuxFm1KlyMlW8OIlC6bkpOnYXSfUFFRIpc/P5c/T0rHtp0lDQ0ylRWtawgtxdrCjPKq2lZ9TsWYkizLTek7hZiSwaTvCjEyNsLOpZ1oKSoqBotjkyldTocrncvnp9KS1i0yaCnWFmaUtdVIqbquHm2DjJW52L02FeWNkxStbMTOc2ouxXml2Lm0w8hIMW+liorBYe/aeFFXlCu2S0JzsW46P5WVtf7k15ZgZW5KZXUbjZRq67QAmAmemnq5yaG5YHNsLpVllVgZSKpRRUWpWDXtuakqE1s80FzMms5PtTX1YnWYGFNTr23V51SOKdU3vrimgk2pproOIyMJExPDGAFRWVqFpWpKyqaiAqZPh0qxqRaVa2PRFHlUCq5oay5mZo3nSdGdwk1NNNTVta4xKseUmiIlU8HzgGpq6jEzNzGYvneVZVVYCG7LpHIdDh6ElSsbv6ooEhNTE0zMTKg0lEjJTBmRkqmmDUdKNU1ua6YRHCnV1GFmKlZDS6gsrVLTd0pn+/a/flVRJJY25gaTvru8vFBTIz5Sqm2rkVK9tnGWiUYjVlJtTT0mZoZjStUVNZhbGUZRxk3Lpk2NXzduFKtD5R8xtzKnulJsiXVzMW26cBZuShpjattqpHR5J7WR4LSZrAANLUGWZSQjw9Hb5pkwASTpr//OnWu87dy5v982YYJYvSpXkIwkg+noQBv+yCvGlFRuEEP5EN0szJ8PPj5g/qfotbb2r1+h8XZf38b7qygGgzGlNoxqSm0AQynKuCno1AlOn4bx48HyGq2qLC0bI6SEhMb7qygC9XOkDFRTUlFpbays4Kef4PXXweJ/ilAsLBp/vmpV4/1UVFT+guJMSQnBs0GF8JJEQ0ODaBUqVyMlBbTaxrUjS8vGr1otpKaKVqZyFQzqc29AUluKYkzJpGl/Ul0rV3K0FFNTDbW1YjW0BHNLM6oFN2VUuQrZ2bB0aeP/fXxgxQrw9m78fskSyMkRp03lqlRX1GBuaRiVrLW1Tc0GBG9fqa3Xtvre0uuakiRJ5pIkHZEkKV6SpARJkl5rVQVNmCrElMzMNNQKLrNsCRYGtLfipuKNN6CuDiZObFw7uvXWxrWmW29t/Pkbb4hWqPI/VJVVYWkgPS9rmjbNmpqJbYdWW1+vf1MCaoAhsix3BcKBUZIk9WpVFfx/e6GaVt6I1VLMzEyuvOGGgIWNBVXlYpsyqlyFykr4+uu/rh1dXmv6+uvG1kMqikFbr6WmqtZguqNc3p9kJnhPZV2dFpNWbnhw3WeTGxOtl+fumjT9a/WMplLSd2ZmGrTaBurrtWgEtzxqDpY2FhQaSLv9m4pvv732bbNmNf5TUQyXL+wsrA0jUrrcXki0KdWISN8BSJJkLEnScSAP2CbL8uGr3GeOJEkxkiTF5Ofnt1iIWdMvVi06UrrcvkNwo8PmYmlrQUWp2uhTReXfcLnnnaXBRErKSN/V1WtbvXl1s0xJlmWtLMvhgBfQQ5KksKvcZ7Esy1GyLEc5Ozu3WIi5qQmSBJWCzeDynJJywXNKmoudczuKc0sMq3JIRUVhXJ6jZOdqGMMyy5tM1EbwGlh5VS3W5qat+pwtqr6TZbkY2A2MalUVgJGRhJW5GRXVYivJbJqulMpKDcOUHD3sqautp6yw/Pp3VlFRuSqXshrHoDt6OAhW0jwun59sBDdjrqhu/Wnhzam+c5Ykya7p/xbAMOBsq6powtrCtNXnvbeUK2OGDSQldvlDdPlDpaKi0nIuj0F39LAXrKR5XB6Dbn2TRkruwC5Jkk4AR2lcU9JJu2Nrc1PKW3nee0u5fOVhKJGSk2ejKRWoxQ4qKjfMpaxCjIykK2PRlU5ZaTXWNuYYG4vdalpeVYOVReuaUnOq704AEa161GtgbWFGmUIipZJiQ4mUGq/sCjIuCVaiomK4XMosxM7VDmNj5VfcQmMmx1Zw6k6WZcqra/WfvtMndtYWFFeI3Qjarp0lRkYShQayRuPk6YCxxpislFzRUlRUDJbMlBzcA1xEy2g2hQXl2DuK7Z1YWVNHXb0WO6vWNUdFmZKDjSVFZWIjFGONEQ6O1hTklQnV0Vw0Jho8Al3JOJclWoqKisGSkZiFd4iHaBnNJj+/DGdnW6EaLjWtuzu0chm9Ak2pCq3gBqNOLrbk55UK1dASvEI9yEhUTUlF5UaoKKmgKLcEr1BP0VKahSzLFOSV4uQi1pQuBxAOtq0bsSnMlCxokGVKK8QWGTg721CQbxiREoB3iAeZyTlotYbTSLatsmIF+PmBkVHj1xUrRCtSuR4Xmy7ovEMNI1IqK6umpqYeZxcboTouNZmSo+015obdIMoypaZf7pLgcuzLkZKhbEj1CvWgrqaOvPQC0VJualasgDlzID29cSBwenrj96oxKZvLpuRlIKZU0JTFcRKcvissbezf6GjThk3JuZ01ALnFYosM3NzbUVVZS2mJYXTf9u/sA0BKfJpYITcxhYWFPPxwCZX/cz1VWQkvvCBGk0rzSI1Px9TcBI9AV9FSmkV2ZjEArm5iy9dzi8oxNpKwb8um5O7Q6Pw5hWLXczy9Gvf+ZFw0jDLrgC6+GGuMSTyaIlrKTcuCBQsoLr56OuXCBT2LUWkRiTHJBIb7oTER29y0uVw+L3n5iO0+kV1YirOdNZpW3iulKFNytrPC2Egiu1Dseo6nd+ObnXnRMLokmJqb4t/Zh3PHVFPSN2lpaYSGhrJy5Urg4lXv4+OjX00qzUer1ZIce56QboGipTSbzIuF2NlZYiW4o3l2YdmVQKI1UZQpGRsZ4WJnQ7bgSMnNww4jY8lgTAkgpFsASTEpBrMOZsgcPXqUhQsXMnPmTKKjoxk/fjzx8fEsWmSFpeVfX39LS3jrLUFCVa5LxrlsqsqrCYkyIFPKKMRTcJQEkFNYhptD6xdbKMqUANwdbcgRHClpNMa4uduRYUCmFNo9iLKiCrJT1U20uqSiooL4+HieeeYZQkJCmD59OgsXLsTR0ZFHHnFi8WIJX1+QJPD1hcWLYfp00apVrsW5ppS3IZlSxsXCK0sMoqjXNpBXrJtISXFJVE+ndhw6nS5aBj6+Tlw4bzjVbB16BQNwct8ZPALdBKtpW+zevZuvvvqKuLg4zMzM2LJlC5s3b2bkyJF/u+/06aoJGRIn9iRgbWeFd3vDqLwrK62isKAcbx9HoTpyi8rQNsh4Orbx9B2Ar4s9+SUVVFaL7YEXEOTChQsFVyY8Kh3fTt7YubQjdvsJ0VLaFPX19Wi1WlatWoWFhQU7duzA3d39qoakYljIssyx7SeIGBpmMD3vzqfkARAQLLZSMC23sQG0r2vrd1VXpCkBpOeJ7XodEORKg1bmQpphREtGRkZEDutM7PaTNAjuiGHIFBcXs2bNGubNm8eAAQMICAjA0dGRZcuWsWPHDpycnERLVGklMpOyyb94iYihXURLaTapyU2mFCTWlC7o0JQUl77zafolL+QW08FH3At/+U1PSc4lKNQw0mGRw7qwc2U0509eILCrn2g5BomVlRULFizg2LFj2NnZsXPnTsLDwwkPDxctTaWVObatMavQbbghmVIu7ewscXSyFqojPa8IawszHFp5jxIoMFLydrZDkiAtV2yRgYeXPWZmGlKTDadwIHJY44crdpuawmsp2dnZ/Pzzz7z99tvMmTMHZ2dntm3bRkSEXqa2qAggdvsJ3PxdDGoNNjU5D/9AFyRJEqojPbcIP1d7nehQnCmZm2pwd7AlNUesKRkbGxEQ5ErS2WyhOlqCs5cjfp28Ofx7rGgpBsHGjRuZNWsWwcHBeHh4MHv2bMaOHcucOXPYsWMHUVFRoiWq6Ija6lridpyk2/CuoqU0m7o6LedT8ggUvJ4EcD6nUCepO1CgKQEEezqRnCl+Lad9J0/Onc1GW284azR9b+3Byb2nKc4vES1F8QQGBrJy5UqSk5MxNzdn48aNREZGAtC5c2fB6lR0SczWeKrKq+k3qadoKc0mNTmX2tp6OoSJ7WZeXF5FXnE5wZ66WV9VpCmFeDmTnltETZ3YyrcOnTypqam/UvFiCPSb3JOGBpkDv8WIlqJYKisr+eOPPzh69CjDhw9Ho9Gwdu1a+vfvL1qaip6I/vUw1nZWdB3UUbSUZnMmIRNoPC+JJDmrMWAI8XLWyfMrrtABGiOlBlkmJesSHX3FhaqXr0jOJGQaTLFDYFc/3ANciV57iDH3DRUtRxE0NDQQFxfHtm3b2LZtG9HR0Xh4eHDw4EFGjx7Nzp07GT16tGiZKnqivq6eQ+tj6D0+ChNTE9Fyms3ZU5k4OtngLHiO0rmMfACdRUoKNaVGB07KLBBqSq5u7XBwtOZMQgbjJnUTpqMlSJJE/0k9WbtoE+XFFVjbiR2ZLJrCwkImTJhAdHT0lZ85ODiwefNm3NwaLzSmTp0qSp6KAI7vSqCsqIJ+Ew0ndQeNF8cdwjyFFzkkZRbgYGOJYysP97uMItN3Xs7tsDAzIfGi2LSZJEl0CPPkVPzVG20qlX6Te1FfpyV67WHRUoTj4ODA/ffff+V7c3Nz1q9fT/v27QWqUhHJnp/2Y2FtTrcRhlMKXnipnKzMIuGpO4DEi/k6i5JAoaZkbGREBx8XEtLFl2N3CfclO6uY3Oxi0VKaTfseQXiHerB1+W7RUoSSmprKokWLMDExYdy4cUiSxIoVK+jbt69oaSqCqKqoZs/qgwyY0hszCzPRcppNXMx5ACKi/ITqqK6tJ1nHGSxFmhJAJ183Ei/mUVcvdsR3ZHd/AOKOpQnV0RIkSWLEzEGc3HeGzGTDKWn/t2i1Wg4ePMhzzz1HWFgYgYGBREdHM2XKFD7++GMWLVrEpEmTRMtUEUj02sNUlVcz8t7BoqW0iLiYNGxsLQgMFru2nZiRR31DA2F+utOhWFMK83Ojtl5LkuDScF9/JxwcrYk9el6ojpYybMYAjIwkti3fI1qKTpFlmU2bNjFr1izc3d3p06cPCxYsICEhgcjISJYvX46RkRG+vr7MnTtXtFwVwWz9dhfuAa6E9TOc9K0sy8TGnCciyg8jI7HrSQlpOQA3pyl1avqlL78IopAkiYhufsQdPU9Dg+HMKnLydKTbiK5s/W43Wq3YaFOXSJJEUFAQSUlJ5OfnX/m5u7s7v/32G5aWllfup3Jzk5OWx/FdCYyYOcig/h4yLxaSn1sqPHUHkJCWi4udNc52umtzpFhTcnewwcHGkpPnxaefIrr7U1xcSWqS+DWuljDynsHkX7zEsa1tu+1QSEgIFRUVV743Nzdn3bp1eHl5CVSlojS2fL0TSZIYfvdA0VJaRMyRVAAio/wFK4GTadl00nFFtGJNSZIkwgM9OJ6SJVoKPXoHIklwcP850VJaRJ9bu+Pgbs/aRZtES9EJNTU1rF+/noceeogXX3yRu+66C4BvvvmGHj16CFanoiSqK2tY/8Uf9BrXDVdf3Wz61BWHopPw9nHEQ/Bgv/zicjLyS4gI0m0FoGJNCSAiyJOMghJyi8ROorV3sKZ9R08ORScJ1dFSTExNuPXh0RzbGk/qCfGDE1uDuro6Nm/ezD333IOrqysTJkxg+PDhTJo0iSeffJIXX3yRO+64Q7RMFYWx9dvdlBWWc/tT40VLaREVFTXEx6bRu3+IaCnEJjd2lLipTSkyuPGXj2t6MUTSu38I585mU5Av1iBbytj7h2NuZcbq99eLlnLD1NfXs337dmbPno2bmxtjxoxh+fLllJSU8PTTTzNx4kQAOnbsyGuvvSZYrYrS0Gq1/PLhBtr3DKZTX8MpcAA4djiV+voGevcLFi2FuORMLMxMCPV20elxFG1KIV7OWJmbKsOU+jVeqRzeb1jRko29NaP/M5RdP+4nP+OSaDktZunSpXh4eDB8+HCWLl1KYeH/d48fNGgQb7311pXvTU1NMTJS9J+0igAOrDtKVkoutz05zqAKHAAORp/Dtp0FHcLEr4/GJmfSNcAdjbFuP2OK/gQbGxnRNcCDmHMZoqXg6++Eu4cd+/clipbSYiY9dguyLLPm/Q2ipbSYWbNm8c477/ztZOLh4cGqVavQaBTZKUtFIciyzE/vrsM9wJW+Ew1rnbG+XsvhA8n06B2EsY6N4HqUVFSTklWg89QdKNyUALqHenM+p5C84nKhOiRJov/gDsQeOU9paZVQLS3Fzc+FoXf1Z+NXWynIEjunqqUYGRlx8eJFZPn/y/E1Gg2rV6/G1VX8XBkVZXN4UyyJR1OY9uxEjI2NRctpEXExaZSVVtF/cAfRUjhy9gKyDD1CfXR+LMWbUu+OvgAcOiN+oX7QsI5otQ1E7z4rWkqLmfHSbWjrG/hx/lrRUppNTU0Nq1evxtfXl6FDh16ZAvv+++/Tp08fwepUlI4syyx/5SfcA1wZMdOwysABdm9PwMrajKieAaKlcPB0OtYWZlf2j+oSxZtSsKcTjraWHDot3pSCQtzw8LJnz47ToqW0GPcAV0bdO5jNS3eQdyH/+g8QyPHjx3nkkUfw8PDgueeeY9KkSWzfvp3Jkyczbdo0tTODSrOI/vUIyXHnmfHybWhMDCvNW1tbz/69ifQZEIqpqVjtsixz8EwaPdt763w9CQzAlCRJoncHXw6dSUfbIHYCrCRJDB7WiePH0igqrLj+AxTGnS9OBmDFm78IVvJ3CgsL+fTTT4mMjCQiIoJPPvmE0tJSVq5ciY2NDQBjxoxhyZIlBrdYraJ/Ghoa+O7Vn/AO9WDI9H6i5bSYmMOpVJTXMGio+CGEqdmXyC0qp09HP70cT/GmBNC7ox/FFdWcVkDX8IFDO9LQILN31xnRUlqMi7cTY2YP449vd5ORJL5ThlarZevWrUybNg13d3fmzp1LXFzcldtff/31v2yCjYiIwNpad+1NVNoOu386QNqpi8x45XaDW0uCxtSdja3FlYbQIjnQlKXqrZrS/9Onkx/GRhJ7TqSKloJ/oAsBQS5s3RQvWsoNcecLkzA1N2HJ098L05Cfn8/LL7+Mv78/I0eO5KeffqK2tvYv9xk0aBBPP/20IIUqhkxVRTVfP7eCwHA/BtzWS7ScFlNRXs3+PYkMHNoBjUa8oe45kUKQpxNuDjZ6OZ5BmFI7K3MigjzZE58iWgoAI2/pyrmz2ZxPETuE8EZwcLPnzucnceC3oxzdEnf9B+gAR0dHunXrds3qOXt7e77//nuDvMJVEc+P89eSd6GAhxbNMsi/oV3bE6itrWfULeGipVBUXsXx5Cxq7FvqAAAgAElEQVQGdQnU2zENwpQABnUNJCX7EhfyxA/bGzIiDI3GiC0bj4uWckNMfmIs3qEefDr3a2qra6//gFbGyMiICRMmXOlV978sXbpUbaaqckNknMti9XvrGX73QDr3F19KfSP8vv44AUEuhHRwFy2F6JOpNMgyg7qqpvQ3Lr8oe06Ij5bs7K3oMyCUbZtPUltTL1pOizExNeHhT/5DVkouPy8U137IxMTkbz+bPXu2OohP5YaQZZlPH/kGUwtTZr9z9QsepZOcmEPS2WxGj4tQREHP7vgUXO2t6eCj29ZCf8ZgTMnDsR0hXs7sOp4sWgoAY8ZHUFZaRfQew9uzBBA5rAsDb+/Nj2+vJStFvzOrUlNTefLJJzExMWHevHlX+tWFhoby4Ycf6lWLStth75pDHNsaz71v3IG9q51oOTfE7xviMDXVMHRkmGgpVNXWcfBMOgM6B+rVIA3GlACGhAcRn5olvLsDQESUPx5e9vy2Jka0lBvm/vdnojHV8MHsL2nQcbm9LMvs3LmTCRMmEBQURHR0NLNmzeLdd9/lgQcewNTUlB9//BErKyud6lBpm5QUlPLp3K8JivBn3AMjRMu5ISrKq9m+5SQDh3bAxtZCtBz2nzpPdW09QyKC9HpcgzKlEd1CkGXYdkz8XCMjI4lbp3Tn9KkMEk+Ln/l0Izh5OnL/+zOJ353Axi+36eQYlZWVLFmyhC5dujB06FDWr1+PRqPhm2++ubII7ezszHfffXelY4OKSkv5/LFllBWWM2/ZQxgroGLtRtiyMZ6qylom3q6MHn1bj53DwcaSbsH6Xd+9rilJkuQtSdIuSZLOSJKUIEnSo/oQdjX83BwI9XJmqwJMCWDELV2xtDTl15+PiJZyw4yaNYRuI7qy5JnvyT7fevvALly4wLPPPou3tzdz5szh1KlTV257+eWX6dSp01/uP3Xq1FY7tsrNxYHfjrJzZTTTX5xMQBdf0XJuCK22gXVrjhLW1ZvgUPEFDhXVtew7mcqwyGC9dHH4M805Wj3wpCzLHYBewEOSJAnbZjwiKoST57PJulQiSsIVrKzMGDk2nD07T3OpwLDmLF1GkiSeWPxfjIyM+OC+L/5VGk+WZfbt28eUKVPw9/fnnXfe+cuoCYDw8HCeeeaZfytbRQWA0ktlLHpgMQFdfbnjuYmi5dwwh/cnkZNVzMTblBEl7T2RSk2dlhHd9D9c8LqmJMtytizLsU3/LwPOALrvX34Nhkc2vkhbY5QRLd06JQqttoENa4+JlnLDuPg489/37ub4rgTWfbK5xY+vr69n2bJlREZGMmDAAH755ZermpuxsTHffPPNVavuVFRaiizLfHT/V5ReKmPesocMrr/dn/n15yO4uNrSd0CoaCkAbD2WiIudNeGB+j/VtygukyTJD4gADl/ltjmSJMVIkhSTn6+7hp9eznaE+bnx+5EzfxlnIAoPLwd69Q1h/S8xVFXqf89PazH6vqH0Hh/Fkqe/58zhlg0y1Gg0hIWFERYW9o+G8+yzz6rrRiqtxm+fbmHfL4e59807CAoX347nRkk8ncXx2HQmTOmOsUb8Mn9ReRX7E9IY0S0EIyP9l6U3+xWQJMka+AV4TJbl0v+9XZblxbIsR8myHOXs7NyaGv/GuF4dSc66xNmLyuioMO3uPpSVVbPpt1jRUm4YSZKYt+whnDwdeOP29ykp+Ntb/I90796d5cuXM2fOnKve3qFDB1566aXWkKqiwulD5/jqqeX0GteNKU+OEy3nX7HqhwNY25hzy62RoqUA8MfRs9RrGxjbS8wqTbNMSZIkExoNaYUsy8IH8oyMCsVEY8yGg8oYIdExzIuukb6s+fEwtbWGt5n2Mjb21ry0+kmKc0tYMONjtFptix7/7rvv8tlnn/3t55Ik8c0332BmZtZaUlVuYkoKSnlz6gc4eTny9LcPY2QkPrq4US6kFbB/z1nGT+qGlZUyPh/rD56mvbcLIV66DS6uRXOq7yTga+CMLMsf6F7S9bG1MmdQ10A2Hz1LbZ0yTGDajD5cKihj+5aToqX8K0K6BfLQx7OI+SOelW+27Ppj2rRpBAcHAxAVFXXl54//H3vnGRXV1YXhZ+i9IyIiTQEFRQFFbCh27DVq1MSu0VhSLLHFHqN+1tiiJrbEEo2x965YQEARpCgoUqRLLzNzvx9EEhO7TMHMs9Ys5c6997zAcPcp+7x70iQaN658xpgqlA+JRMJ3g1aRnZrDrL1fYmhauV3jd+24ipaWhtKkgUclpHIvIZWuTdxef7KMeJMuRlNgEOAvEolC/3wFyFjXa+nWxI2n+UWcVwLbIQCvRo7UcrVm9/arSMSKrfv0vgSMaEPbwX5sn7uXmyde7++Xnp7OjBkzmDZtGocPH2bx4sWcPXsWdXV1nJycmDdvnhxUq/gv8Mv8/QSdCGPsyiHU8lR8Rdb3ITkxizMn7hDQzRMTU+XYNP7H1btoaqjTsaGrwjS8SfbdZUEQRIIg1BMEof6fr6PyEPcqfFxrUNXMkP2XlGNkIhKJGDikOUmJWZw4WjnLWjxDJBIxfu0IHOrWYGH/FTy6l/jC81JSUvj666+xt7dnyZIlzJ07F2dnZyZPnoyhoSFeXl5s3rwZPT09OX8HKj5ELu27xrY5e2gzqAUBI9ooWs57s33LRTTU1en7sa+ipQBltkJHrkfSysMJY30dhemotJOx6mpq9GpWjxtRCcSlZL7+Ajng26wWtd1s2L75IsXFpYqW817o6Gkz58BkNLQ0mB6wgMyUrPL3EhISGD9+PA4ODixdupT8/Hy++OKL8qm7Z2zYsAE/Pz95S1fxARJ+OZJFA1dRx9eZietHKoVZ6fsQdz+V08fv0L1PQyws5VOn6HWcuBlFbmExffw8FKqj0gYlgB5N3dFQV2PvBeUYmYhEIoZ95k96Wm6l9sR7RlX7Ksw/NJXs1Bymd1pE5J1IRo0ahZOTE6tXr6aoqAgAGxsbpk+f/q/r69dXfD0YFZWfh5GPmdVtMVZ2Fsw7OBVtXeVICHgfftpwHj19bT4a1ETRUoCyPV97LoRRs5o5njUVtg0VqORBycxIj7aezhy+FkGBAuoCvQiPBnY09HVi17Yr5OUWKVrOe+PSsCZDln9EbGgcAz1G8ePGHyktfX4UuGzZMlWZchUyISM5i+kBC9HQ0mDhsekYmSvHqOJ9CL+dQODlaPp+7IuREhivAtyJS+FeQip9WngofBRaqYMSQF8/D/KKSjh6U3lKSAwd1Yrc3CJ277yqaCnvRXh4OP3796fP6O5ESIMww4raeD13TsuWLenbt6+CFKr4kMnPKWB6p4VlKeCHp2Ht8OJKxZUJQRDYvO4spmb6SpNxB7D3Yhj6OloE+Ci+MGKlD0r1HK1xqW7JrnMhSuHwAFDTuSr+7dzYv+sGqSmK9+h7F+Lj45k0aRK7du1CKpWSRDz3hbtUE9njTNmcs7q6OqtXr1Z4z0rFh0dRQTEzu35H3J1HzNr7Jc5e8qt8KkuuXowmPCyBgUOao6urpWg5AKQ/zedkcDSdG9dBX0fxmip9UBKJRAzwb8CD5EyuRjxUtJxyho32B+DHtWcUrOTdsLe359SpU8THx1O3bl0A4ojkkRBDDVEtnHBn7NixuLsrvhiZig+LooJiZndfTPile0zdPp6GHT4Ma6qSEjEb15ymhr0FAd2U53vacyEMsURC/1bKsQYsk6AklnHBuH/SoaErFsb67DyjPKaoVaoa0+fjxpw/HUH47QRFy3knpFIpK1eu5M6dv9LuownjsXAfB5ErTlJ3pRmdqvgwKMwrZEbnRYScCefLzWNo1a+poiVVGAf23iQpMYvR49uioSQ1nwpLSvntYhh+9ZyoUcVU0XIAGQWl1Hz5VobV1FCnX8v6XIt8RPRj2ZnBvi0fDWyChaUha1ecRCqtXA/v0tJShgwZ8lx5cnNzcwDuEUItfzsO/XCStRN+UgUmFRVCQW4h3wQs5M7FCKZs+5z2n7ZStKQKIyM9l50/XcKnSU0aNlaeqcgj1yLIzi9iYGvl8N0DGQWl7KIiCkvlu0+nV/N66GhpsPOM8pii6upqMWJsa2LuJXP8UIii5bwxhYWF9OrVi23btpUfGz16NHv27AHAx8eH1ScW02tiJw6sOcbK0RtlXk5dxYdN/tN8prafR0RgNN/8MpHWHzdXtKQK5ccfzlBaKmH0BOUp1S6VCuw8E4KbnRUNFJwG/ndkEpQkgsDRWPnWOzLW16F7E3eO3bxHSqbyFNxr1daNeg1qsGndObIy8xUt540oKCggJuav8hUzZ85k7dq1NG/eHBMTE9asWYO6ujqjln1CvyndOfLjaRYPXk1pSeXeMKxCMWQ9yeYr/znEBD9g5p4v8OurHHt3KoqwW/GcORFO7/6NqW5rpmg55ZwLjeVhahYD23gpVbKSTIKStro6O26/3jOtohnUtixd+acTN+Xe9ssQiUSM/zqAosIS1q08qWg5b0RkZCSzZs3Czs6OFStWMHfuXEQiEZqamuzcubPcbFUkEjF04QCGLhjA2V8uM7PrYvJzChSsXkVlIiEqkYnNZpBwL5E5B6bQrIePoiVVKMXFpfzvuyNUszFlwKfNFC2nHKlUYOPRa9hbmdLGs9brL5AjMglK5np6hD1J4faTFFnc/qVYmxnR1deNA1fDeZKlPKMlO3sLBnzajHOn7nL9ytsV0JMnUVFRdO/enT59+tC1a1fu3r3LhAkTnjsnIOB5L16RSET/aT34ctMYQs+GM7HpDFLilaPOlQrlJvRcOON9p1OQU8j3p2fRqKPyZKRVFDu2XCLpcRYTpwSgo6M8FZfP375PTGI6wzr6oK5kpT9kosZERxc9TU123JH/aGloh4YIUkGpRktQlvRg72DJyiVHKcgvVrSc53jy5AmfffYZbm5u/PHHH8yYMQN9fX309d/cubjDUH8WHptOemImn/tM4+7VKBkqVlHZObb5DFPbz8e8mimrri2kjq9ylAGvSGKjU9jzSyAdOnvQwFt5KuMKgsCPR65ha2lCe2/l+7nLJCipi0R0c6nNoagosgoLZdHES6lmbkwX3zr8fiWc1Gz5ZgG+Ck1NdSZN60R6Wi5bNpxTtBwA8vPzmTdvHjVr1mTdunVIJBIcHBwYMWLEO93Ps3VdVl5dgJ6RLl+3nsPZXy5VsGIVlR2pVMqPk7fzvxHrqe/vzsor8z8Ip4Z/IhFLWf7dEYyM9BgxTrkczS/efkDU4zSGd2yEhrpyjZJAhptnB9arT7FEzN6IcFk18VKGdmiEIBXYcvyG3Nt+FXXcq9Otd0MO7gviTugjhemQSCRs2rSJWrVqMWvWLPLy/grec+fORUvr3Xd113C1YfW1Rbj61GTRwFVsmroDifjtKtiq+DDJzcpjdvfv2bP0IF3GtGfB4WnoGytHHaGKZt/u60TfS2bcF+2Vxt8OytaSNhy5RnVLYzo2Uryl0IuQWVCqbWFJYxtbtoaFyH0zrY2FMd2aurH/8h0S05XL5mfoqFZUtTbh+/kH5T6NJwgCR44cwcPDgxEjRpCcnPzc++7u7vTv3/+92zEyN2TxyZl0GtmW3d//wdet55CakP7e91VReQm/co/RDb7m5vFQxq0exvgfhqOuJBtIK5q4+6n8vPE8Tf1caOGvXA/+0yHR3EtIZWRAY6UcJYGMbYaGNvAkOS+X43JODwcYEdAYdTUR6w8Hyr3tV6Grp8XkmV1JTXnK2hXyy8YLDg6mdevWdO7cmbt3777wnAULFqCuXjEPCk0tTSauH8mUbZ8TGxLH6AZfc/UP5VrnUyF7JBIJvyzcz5ctZ6Ouoc7KK/PpNraDomXJjJJiMQtn/46BoQ4Tvg5QqlTrUomEtQev4mRtTsdGiqss+zpkGpT8HZywMzZhc0iw3Hf9VzExoF+rBhy9EUlMonL10t09atBvUBNOHAnjwtkImbd36dIlevTowblzL1/L8vX1pUuXLhXedpuBLVgb/D1VHaowu8f3rB63iRIlKTOiQrZkJGcxtf18fprxKy36+LLu1ve4NKypaFky5ce1Z4h/kMbXM7piaqZcU5OHAiN4lJrNuG5NlS7j7u/IVJmaSMSQ+p6EPUnhVkqSLJt6IZ+2a4i+jjZrD16Re9uvY9CwFri62bBi8VGZO4k3b96c+Ph4rl69ipXVixeVFy5cKLNeXfVa1qy8Mp9ekzpzcO0JxvlMI/5u5fQDVPFmXDsczOj6XxEZGM2Xm8bwzc4J6BvpKVqWTLkRGMuBvTfp0beRUlkJARSViNl45Br1HK1pUc9R7u1HZ7z5wEDm4bJ3HXeMtXX48Zb8K7Ea6+vwSVtvLtx+QEhsotzbfxUaGupMm90NiUTKd3MOIBHLft1ty5YtPHny5F/H27VrR8uWLWXatqaWJqOXfcL8w9PISsnmM6/J7Jj3m8oF4gMjO+0p3w1excyu32FmbcoPQYvpMNRfqaaxZEFmRh5LFxzC3tGS4WP8FS3nX/x67hap2Xl83q2Z3H8XxWIxnx7Y98bnyzwo6WlqMtijPifvx75VtKwoBvg3oIqJAUv2nEeiZP5s1aqbMf6rjtwJS+DnTedl1o4gCIwdO5ZNmzaVH7O3ty///8KFC2XW9j/xCfBk4+1l+HZryNbZuxnjOZnwK8pToFHFuyEIAie3nmdYnUlc2H2Vj2f0Ys2NRdjVrq5oaTJHIpGycPbvFOQX882cHmhpayha0nOkPc1j87EbtKjriJez/H8fv9+LIOUtTLrlMrH4qYcnepqarAuSf4q2rrYmE3o0515CKgevvniBX5G06VCXjl3qs2vbVa5fja3w+wuCwPjx41m/fn35scmTJ7N7924AevfujZeX18sulwmmVibM3P0F8w9NpTCviEnNZ7Ji9EbysiuHN6CK50mMTWZKu3ksGfIDtq7VWB+yhE/n9kNTS3kcDGTJ9s0XCbv1kPFfd8TBqYqi5fyLNQeuUCqR8kVvP7m3LZZKWRd0g7pV3mIvmiAIFf7y8vIS/smiS+cFp1XLhLiszH+9J2ukUqkwZMkuwf+rdUJOfqHc238dRUUlwshBG4Qe7ZcKT5KzK+y+UqlUmDhxogCUvyZNmiRIpVJBKpUKtWrVEiIjIyusvXehILdAWPfFz0I79T5Cb6thwpGNpwSxWKxQTSrejLyn+cLGyduFjtr9hK7Gg4SD604IEolE0bLkyo3AWKFtk3nC0gUHFS3lhdyJSxYajP6fsHL/RYW0vz/iruCwcqlw6n6MAAQJbxA/5JaCMayBNxpqaqxXwGhJJBLxdd+WZOcXsvHodbm3/zq0tTWZuaA3ErGEudP3UVIsfu97CoLA5MmTWbFiRfmxzz//nGXLliESiRCJROzZswdXV8Wmhuoa6DJ62SesufEdNrWqsnzUBj7znkJ6YoZCdal4ORKJhGObzzDEZTx7lvxBy/5N2RK5ki6j26GmxFldFU1yYhaLZv+OvWMVxn6hfGnuUqnA97vPYWGkx7CO8je6lUilrA26jou5Bf4Ob574IbdPkKW+Pv3c6rL/XgSJOTnyarac2jWs6N7End3nQnmQrHwPvOq2Zkye2Y2oyCRWLT32Xin0giDwzTffsHTp0vJjY8aMYeXKlc8tctavrxzljwFqeTqy/OI8ZuyahJWdJaZVTRQtScULCDl7h899pvG/EeuxdrRizfVFTP5pHObWylG1VF4UFpbw7Te/IQDfLuqtVGarzzh6I5Lw+BQ+794MfZ13d2l5V07cj+F+ViZjG/qg9hbJFXLt1oz0aogaItbcvCbPZssZ27UputqafLfrrFJWS23q58LAoc05cSSM3359vxFdRsZfgXfkyJGsWbNG6TOgRCIRfn2bMPfAlFdu4g09F86yYWv5tuf33DxeVjxRGX+fHwqCIBB8Kowv/GYxuc1cnqbnMm3HeFZcnv/B7zt6EVKpwOI5fxB/P5Vv5vSgWnXlqZH0jJz8Ipbvu0hdB2s6+dSRe/sSqZSV1wNxMjWjY03nt7pWrmki1QyN6F+3HjtuhzLKqyH2JvLtXZkZ6fF5j2Ys/OUMR25E0lkBv6zXMWhoCx7Fp/PjD6exsTWjSfO3+4UCpKenU69ePUaPHk1JSQnr1q37YKZVJBIJy0eu55M5H6GuqcGO+ftQ11DHs009RUv74BAEgRtHb7Fj/j7uXY/BwsaMsSuHEjCiNVoK6HkrCz9tPMeVi1GMmdBO6fYjPWP1H5d5ml/E2vH+qKnJvzN6OCaKmMwMVnXo9NYbdeX+pBrj3QgNNXVW31DMaKln07rUdbBm+W8XyckvUoiGV6GmJuLrGV2p5WLNom9/537Mv/cVvQypVMrmzZtxdXXF2tqatWvX8uOPP34wAQkgKyUbfRN9/Ac0x6+PLza1qpIQlYREUmb6+mzElJGcpUiZlRpxqZhzu64wtuEUZnT5jqyUbCasG8nW2DV0/7zjfzognTp2m13brtKpWwN69G2oaDkv5E5cMvsv36Ffq/q42Mo/G1D85yjJxdyCgFpvXxpD7k+rKvoGDKrnwR9RkdzPlP/ajpqaiOkDWpNTUMTKA8pZWkFHR5O53/fFwECHmZN3k5nx+hz/u3fv4ufnx/DhwzE3N6d79+6IRKIPKiABpCdmYu1oRe8qQ1ky9AfEJWJqeTmWT/eJRCIirkWzYvQGhtaewLJhaylUws6HMpKTkcuvi35nkONYFg5YQUFuEV9uGsPP0avoPKotWtrKt24iT8JvJ7D8uyPU97Jn3JcdlHI6vFQiYd7O01gY6TOmi2LKyh+4F0F8dhYTGzd5q7WkZyjkiTXKqxE6GhqsuH5VEc3jXN2SAf6e/H45nOCYxwrR8DrMLQyZ9/1HuNaxQfsVi6gFBQVMmzaN+vXrc/nyZQC++uqrCjNWVSYe3Utk1+IDBAxvzZIzs8lKyabD0NbUaexcPlIKu3CXg2uP07JvU1ZfW4hEKuVR5F9uHpkpqhHU3xEEgaibsfxvxHr6245iy/RfqFHbhvmHprIlcgUdhvqjoalcm0EVweOETL6duhdLKyNmLuiFhpI6nG8/FUxsYjrT+rdWSHJDiUTC6hvXcLesQjvHd1tvVMinzVxPj6H1vVhz8xrDGyTjUdVa7hpGd/blbEgMc7afZPf0QegqYS+wpktVZi3o9dL3jx07xtixY4mLiys/VqVKFQYPHiwPeXInIjAabV0tvNp6AGUZe/dD4qjfyq38nGObz1CzvgPNejZCW1cbfSM9go6H4uLtxPUjwRzeeIqY4Af49WnCyCWDPtjyCa8jOe4JZ3Zc4szOizyOTkZbV4u2g/zoPj4AezdbRctTKtJSc5g6YScAC5b1V6r6SH/nQXIGG45co41nLVp6KGata/vtUBJynjKvW693HkkqbG5npFdDzHX1WHj5gkIyp3S1Nfl2cHsepz1l9YHLcm//fUhKSqJPnz4EBAQ8F5AAJkyYgI6OjoKUyRYtbQ2KC8pqUOVk5iISiSjMK0JNTQ11dXXEpWJib8XRuIs32rraAISdv4tHKzeigu5zctsF2gz0Y9fjjWSlZhN5Pab83llPshXyPcmT9MQMDq49wcTmMxjsNI6ts3djXs2ML34cza7EjUzcMEoVkP7B0+wCpk78hdycQhYt7091W+XLtAMQS6TM2noCfR0tpn6kGO+97KJC1ty4RvMadrSws3/n+yhsXG6gpcWkxk2Yce40Jx/E0t6pltw1eDlXp3+r+vx6LhT/BjXxdlbuP0iJRMLatWuZPn06ubm5AOjrWaGtaUjm01gMDAwYM2aMglXKDvdmrlz54ybD3SdhamWMq48zfh/9NW9++0IENrWssbKzAMpGAyI1ETVq27Bj7m94tq5Lo4AGAKQlZJCXVWZrtHfZISICo7h9IYJekzrT+4vOH8RiviAIxIc/4uofQVw9eJPooPsA2NWpzrCFA/Af0IwqNSwVrFJ5KcgvZvqXu0hOymLR8gHUcpH/jM6bsvVkEBEPn7B4eCfMFOTG/sPN6+QUFzG12fvZGSl0srivW122hoXw3eWLtLJ3REsB6yDjujXjcng83247yZ4Zg9BT0ofRrVu3GDVqFEFBf7mti0RqGOlXw6lGGx4lXaV3fx9MTT/cTYxValgyc/cXpCdlcj8kDp9OXhxYc4z0xxk07NAAQRAwtTKhpKgUTS1NTv58HteGNcnJyKMov5gataujq69DVupTLG3NMTI3IDY0jmObTrPo+AxMrYz5JmAhfn19sampvA+gV5GV+pSwc+GEng0n+PRtUuJSAXD1qcXQBQNo0r0hNVxtlHKRXpkoKRYze+peYqKTmb2wDx4N7BQt6aXEJKaz4Uggbb2caev19ltIKoKH2dlsCwuhdx13alu8X0dHoUFJQ02Nqc1aMOzg7+y8E8aQ+p5y16CrrcmcT9oxbNkeVuy/xDcDWstdw+sQBIHMzExatmyJWCwmNDT0z+NSktNCsDJ3x0DPkokTJypYqXywqGaGRbWyaZQ2A1uQk1E2aqzTxIV9yw9z90oUhmYGBJ0MY9yqoWQmZ2FoZoCZdZlLRGRgNGZVTSkpKuXu1Wia9vDBys6SgtxC9I31KMyrHNl6UqmUpNgUYm7FEXktmtBz4cTdeQSAnpEu9fzq0G9Kdxp38f7POS68D2KxhIXf/k5ocDyTZ3Z9p72C8qJUImH21hMY6ekwtZ/iSmYsuXoJDTU1vmjc9L3vpfC0mpZ2DjSztWPV9UC6ubhipiv/oWd9JxsGtvZi++lgWtRzpJm7g9w1vAqRSESbNm1o06YNv//+O7169Spfh6tlV+a55d3UCFtbWyLvJuLgVEUpbU9kgYGJPgYmZRU+tXW18B/QnO1z96JvrMfg2X1waViTuPBHRAfFMmLxQACCToZh72aLSCQi9WEavl29gbJ0c1uXaqTEpVKzvvJ8BgRBIDsth8ToJB5HJ/Pg9kNiQ+KIDYkrD6Daulq4NXPFv38z6vu7U8vT8T+bxPE+lJZKWPyiOwMAACAASURBVDT7d65cKNsc27ajcm/K3nj4GvcSUlkysjOmBopJwLiR+JijsdGMb+SLlYHBe99P4UFJJBIxo0VLOv2yjWWBV1jg31YhOj7r2oRrkQ/5dttJdk0fiIWxcpUyBrh69SoDBgwoD0i2VX0wMbIjNHI72/deJyU5mysXoliz7DhfftMZx5pvYRf/AaCmpkabgS1oM7AFhflF6OqXJXzo6Gmjpq5G5PUYSopKCDoRSv9pPUh7nEHmk2xcfcrWM9MfZ5CTkYetS7UX3j/k7B22zt5NNaeqmFubYvbny9zaBNOqJugb66FroIOWjtYbTY9JpVKK8ospyC0k/2kBWSnZZCRlkZmcRUZyFhlJmSTdf8Lj6CQKcgrLr9PW1cKpvj1tB/tRy9ORWl6O2NWprkrdfk9KSsTMn7GfwMvRjJnQjp4fNVK0pFdyMyqBLSdu0NXXjdYN5L8mD2UbZb+9cBZrA0NGeVXMZmKl+BQ7m1swyKMBW0NvMcC9Hm5vU3ujgtDW1GDRsAAGLvqFmT8f54fPeyrEnuNlREVF0aVLF9TQB4po3DAAK1Nfzl5ZS7v2rXBzc0MQYPhn/ly5EMXSBYf4anqX/1xgesazgARQxc6Cdp+0Ysmna6jt68yopYOxrG7O3Sv3yHqSjZ6hLrlZecTdeYSRuQF2dV6c8CJIBdTU1Qg5c4esJ0+RiCUvPE9NTYSOgQ66BjovHK2IS8QU5hW9cppQR08bM2sTrJ2q0mZgC6o7V8OmljXVna2xsrNUjYIqmOLiUuZ88xs3A+/z+Zcd6NrLW9GSXklWXiEzfjqGXRVTJvdtqTAdu8Jvcy89jTUdO6OrWTGzM0oRlAAm+vhy8F4k3144y57e/RSyEOtobc7XfVsyb+dptp66yZD2ytFTSklJoUOHDmRn51LfdSBa2uBR24c+H/tw8tJCvvrqawShrOetpqZOUz8Xrly8R1GRqtQ4gLq6Oq0/bk7rj5tTUlxa7kxgV6c6JpZGxIbGEXo2nOjg+/Sa1AUomzL752fQs029co89qVRKTkYumcnZZKZkk5WSTUFuIYV5RRT9GXAKcguRvqDasbq6OnqGOuga6qJnqIuOgQ76xnqYVTUpG3lVM0XPUFeVjCAniopKmT1lDyFBcUya2omArg0ULemVCILA7K0nyM4vYtXY7gpLzsoqLOR/167Q2Mb2rU1XX4XSBCUjbR2+btKMaWdPceBeJD1qK8YstXtTd67de8Tag1fxrFUdD8cXT+XIi7y8PDp16kR8fDwACanH6NN1DsmJubRuV5/ly5fj59fiT0shdcRiCSFB8ZSWSFRB6QX83SrHzs2Wen5uLBnyAzUbOPDR5O44edgDvDYgqKmpYWJpjImlMY71lDczS8WrKSwoYebk3dwOechX07vQLsBD0ZJeyy9nQ7gcHsfkj1opxNvuGUsDL5NbXMwsv1YV2oESyWLjqre3t/D31OU3RSoI9NrzC49zcjg16FNMdBSzcJdbWMyABTuQSAV2fvOxwhYQS0tL6dq1K8ePHwdAR0eHs2fP4uvry+plx3GvZ0vVaiakp+aQ+iSHhIfpJCZkUqWqMfaOVegzoLFCdFdGSopKPoi9SSrenMyMPGZ8tYv7sU+YMrMb/u3cFS3ptdyJS2bYsj00dbPnf6O7Kmw0fSs5iT57f+XT+p7MbNHqja4RiUTBgiC8dl5UqYISQGRaKl137aBnbTcWt2lfwcrenIiHTxiydDfeztVZNbb7W9uvvy+CIDB8+HC2bNkClPXM9+/fT7du3crPuXzhHovn/oG+vg6jx7dBEMDYVI/6nvaIRGW9fYlEirr6h2XKqkLF+5LwMINvvviF7KwCZszvhU8T5a8LlZVXyMcLd6KmJuKXaR9jpK8Y55YSiYSuu3aQW1zMiYGfYqD1Zp25Nw1Kr31aiUSiLSKRKFUkEoW/UcvvSW3LKgz39GZvRDiBCY/k0eQLqWNnxeS+LQmMeMgmBZRQnzNnTnlAAli1atVzAQmgmZ8r3y7qg7GpHvoGOrRq64ant0N5goYgCM8FpFs3H3D2ZDg3r92XzzehQoUSEn47gQmjfqaoSMzSHwZVioAkkUqZ8dMxMnIL+H5EZ4UFJIAfbwURnZHO3Jat3zggvQ1v0oX+GZBrAfrxjXypYWTM9HOnKRaL5dn0c/RsVpfOPrXZePQal8PjXn9BBbF582bmzJlT/vWUKVMYO3bsC8/1auTI5Bld2fnzJY4fDi0/LhKJyof26Wk5HPo9mOWLj5KWmsPSBYc4ffyObL8JFSqUkEvn7zF5/A6MjHVZtfFTXGords34TVl/KJDAiId83bcldewUl1Ebl53F6huBBNR0prWjbExfXxuUBEG4CGTKpPWXoKupyXz/tsRnZ/HDTfmPUp4hEomYNqA1zjaWfLPlGI9SZW/aeezYMUaNGlX+9ccff8zChQtfeY1TLSsWLuuPg9O/Fz2zs/IJvBRDZPhjps7uxkcDmzBpaici7jxGIv53ZpgKFR8igiCwf/d15k3/jVrO1qzc8CnWNpXD5eJsaCybj9+gexN3ejWrqzAdgiAw4+wptNU1mOX3ZutI70KFLTaIRKKRIpEoSCQSBaWlpb33/ZrVsKOnax3WB98gMi21AhS+G7pamiwb3QUNNRGT1v1BbmGxzNrKy8tj0KBB5bWB/P392bJlyxsV6tPT18aldjUK8ov5YfkJ8vPLdD64n0rk3cf4t3PHra4tRUWl3LoZh6WVEeoaqrUmFR8+JcVili08zLqVp2jSwoXvV3+MsYliTEvflpjEdGb9fBx3+6pM6VexWW5vy567dwh8nMCUps2pov/+zg0vo8KeSoIgbBQEwVsQBG9Ly4pxHp7evCUmOjpMPn2CUsmLNyrKg2rmxnw/sjMJqdlM3XQEsUQ2IwwDAwM2bNiAiYkJdevWZf/+/Wi95Zytnr42Xo0c0dcvK92we/tV7B2r4O1TNtSOikhEEAQ8vR2QiKUEXb/Pgb03efxI/lWAVaiQNalPnvLFZ9s4cSSMgUObM2tBb7SVsHbai8jMKWDi2j/Q19Fi6aguaCvQsSM5N5cFly/gW92Wfu6ytV5S6q6yqa4u81u14W5aKuuCbihUi7ezLdP6+xMY8ZDl+y5W+P3FYjFz584lMjKSK1eucPToUYyNjd/pXo2bllmOpKXmoK6hRt+PfQGICH9M8I04DA11cHK2YtaUPZw6dpvEx5nMnLybiHDlrMKrQsW7cDvkIWOHbiHhYTrfLurDJ8P9lMql5VWUlIr5csNBsnILWD6mK1VMZDcyeR2CIDDl9AmkgsCi1u3eqcT526A0m2dfRjunWnR1cWXNzWu0cnCkrgIsiJ7Ro1ldHqRksvPMLRyszejdvGJ6DPfv32fgwIFcv36duLg47OwqZjOmgYEOuU8L2fHTJYyMdImNTsHYVI8uPb3YvO4cUqmUad/2AGDD6tNERSRRx716hbStQoWiEASBP34LYv2qU1SzMWX2D4Ows7dQtKw3RhAE5u88TdiDZBYP70Qdu6oK1bPjThiXEx4yr1UbahibyLy9N0kJ/xUIBFxEItFjkUg0TOaq/sEcv9aY6+rx1cljCs3GA5jYsznN3B34ftc5rt97v5R1QRDYvHkzHh4eXLt2jfbt21dYQALQ1dNi7vd9SU7MIvpeMq3buzNstD8XzkZyJ/QRcxb3Bcp2taupibC0MqqwtlWoUAT5eUXMn7mfH5afoKGvE6s3DalUAQngpxM3OXw9ktGdfRVWH+kZ8dlZfHf5Ai1q2DNAxtN25QiCUOEvLy8voaI5H/dAcFi5VJh34VyF3/ttyS0oEvrM3So0n7hGiEpIfad7pKamCt27dxeA8te+ffsqWOlfiEslgiAIwoPYJ8LgPmuExwkZ5e/dvZ0gjB/5k5CSlCWkpeYIYbfihT07A4WSErHM9KhQUdFE3n0sDOq1WmjXbL6wa/sVQSKRKlrSW3P4WoTQYPT/hG82HxWkUsXqL5VIhF67dwoe61cLybk5730/IEh4g/ih1GtKf8fP3oFB9eqzJTSYSw/jFarFQFebVWN7oK+rxbjV+0lMf/pW1x87doy6dety4MCB8mNWVlZ06dKloqWW8yzTTl1dDW8fJ2yqm1FaKiE5KYu1K07Su39jCgtL+WH5CU4fv8P96BTGDdtMZkaezDSpUFERSKUCu7ZdYeKorUgkUpb9MJiPBjapNOtHz7hyN545207S0MWW2YPaKtyQd/WNQG6lJDO3ZWuqGhjKrd1KE5QApjVrgbOZOV+dOk5GQYFCtVQ1M2TNuB6UiCV8tmo/mTmv11NQUMDYsWMJCAjgyZMnz7336aefollB1u+vQiKRcu1yNKeO3ebowRA2rT2LX+s6eDSowaI5B2je0pXhY1sz9dvuODlX5UnK2wVcFSrkSeqTp0yZsJPN68/R1M+F9VtH4F7vxaVHlJk7ccl8vfEQTtXMWTaqC1oKro0VlJTIDzev08O1Dl1dasu17UoVlHQ0NFneoRNPi4uYcvpEebE7ReFUzYKVn3UnLTuP8WsPkF9U8tJzg4OD8fT0ZO3atS98f/jw4bKS+RwOTlWYMb8XF85EkPO0gLYd69G7vw9L5h/Cz782/u3cMTIqM6DNysijIF92+7JUqHhXBEHgxJEwRgzcyL2IRL6Y1okZ83piaKQY8+T3IT4lkwk/HMDCSJ/V43pgoKutUD05xcVMOnGU6oZGfOsn/xLrlSooAdS2sGRK0xacjX/A9tuhr79Axng4VeO7EZ2ISkjl642HKP1H4TeJRMLChQtp3LgxUVFRL7yHv78/NWvKz3+rtpsNsxf1YdDQFjRuWouQ4HhMTPXo9rfCZmtXnKSoqBSvRo5y06VCxZuQmZHH7Cl7WbrgEE41q7Bx20g6dmmg8OmudyE1O4/PVu9HTU2NNZ/3VHjFa0EQmHnuNCl5uSxvH4ChtvwDZKULSgCfejTAz86BhZcvEKFAt4dntKjryMyBbbkW+YgZPx17bnNtREQEaWlp+Pj4oKv74l7ciBEj5CW1HE3NvyqX5ucVo62jib5BmcnjwX1B3L2dwPS5PYGyKT8VKhSNIAicOXGHEQM3EHTjPqPHt2XpD4MrjV3QP8nMKeCzVfvIyS9i9bju1Kgi+3Tr13E0JppD0feY4NOEBtaK8QVUutIVb0p6QQFdf92Olro6B/sPxEhbca65z9hxOpj/7btIe28X5n3aAY2/OXQXFhbStGlTQkJCnrvG3NycxMREtBXQI3nGhbMR/PLzZUaOa0NSYhbbNl1kwbJ+OLtav7ACqwoV8uZxQiZrlh0n+MYDarvZ8OX0LpUu1fvvZOUVMmrFbzxOzWbVuO54OyvHOliRuJQdt8MYUt+zwsv1vGnpCqXfPPsyLPT0WB3Qmf779vD1qeOs79RN4Q/PgW28EEukrDpwGXU1EXM+aY+6mhqCIDBmzJjygKSpqUlpaVlV2MGDBys0IAH4+dehIL+YA3tvUtOlKrMW9FIFJBVKQUmxmF3br7Brx1U0NTX4bGI7uvbyrtQ1wp7mFzFm5T4SUrNY8ZnyBCQoW7cf7vnauCFTKm1QAvCytmFq0xbMv3SejbduMsqrkaIl8Wn7hoilUtYevIq6mhqzB7Vjw4b1bN26tfycX3/9lQULFhASEqKQqbsX0bFLA1q3r4uWVtlH4kUBSSKWsvp/x+nRpyF2DhXjb6hCxcu4ee0+a5YdJykxi1Zt3Rj1eRvMLeSXmiwLcv4MSPEpmSwf0w0f1xqKlqR0VOqgBDCkvie3kpNYcvUy9a2s8amu+F7H8I4+SKUC6w8Hkp6exo/TJpa/N2XKFHr16oVUKmXlypXUri3fdMtX8SwgAS8cIT16mM7FMxEcPxRKz48a8fGnzcrXoVSoqCiSE7PYsOY0Vy5EUb2GGYtXfYynt4OiZb03uYXFjF29n/vJGSwb1QXfOhXn3vIuKOtMiEzWlGrWqy3E3o6s8Pu+jLySErrv3kFOcTGH+g3CykBx5oV/Z8mvJ/n14l3SIwJJuPQbbVq35tixY2hoaCCRSLh8+TJ+fn6KlvlWZGfls3ndWU4cCcPYWI9Bw1oQ0K0BGhrqr79YhYpXkJtTyK/brnBg703UNdToN6gpfQY0fq6zVFnJyS9i3JrfuZeQypKRnfGrJ5sCea/jfmYGxjq6WOiVle6QCoLMDVaf8aZrSjIJSobO1YQ7t0KxN/h30TlZEZ2RTs89v+BibsEvPfuiraHYD3JpaSmt/P15UGxIVa+2FCfd48zGeVS1kt/PRJbERCWzftUpboc8wsbWjGGjW9GspatS9rxUKDclxWL+2BfEr1svk5dXRNuO9RgyqhUWlpV7qu4Z6U/zGbt6P/FPslg8vBMtPRQTkKafPUV0RjqOpmbkFhezrF1HdDU15RaYFBqUjFxshB4/fcPmxqPRUJNfD/pYbDRjjx6ip2sdlrTtoNAH5IQJE1i1ahUA1bzaYtWwY5mR64jO6HwAPT8oG/5fvxrLprVneBiXTm03Gz4Z4YdnQwdVcFLxWsRiCSeP3mbnT5dIfZJDw8ZODP/MH8eaiqsEUNEkZeQwZuU+0p7msXx0V3xqK2bK7mhMND/eusme3v3IKS5mxfWrBD5+xO5e/TDX05NLYFJoUHLxcBOMF3djuJM/I2u1qfD7v4qV16+y8nogU5u2YKRXQ7m2/YwdO3YwaNCg8q+3bNmCUU0vFv56hgY1bVgxppvCd21XJBKxlBNHw9ix5SJpqbm4e9jyyXA/6nvZK1qaCiVEIpZy5uQddmy5RHJSNq51qjFkVEs8G35YG7XjUjL5bNU+CopKWTWuOx6Oitn3AxCZnsbu8Nt827J1+bHvLl/gTNwDdvbsI9NKss9QaFDy9vYWOm2ZwsnkMDb5jMLNRH7JB1JBYPyxwxyLjWZjl+60dpDvUDksLAxfX18KCwsBGD16NOvWrQPgxM0oZv58nJo2FvzweQ9MDStHSeY3paREzPFDofyy9QoZ6bnUa1CDwcP98Gig2AVdFcqBRCzl/Jm7bN9yicSETGq5VOWT4X40alLzgxtZ30tIZeyq/aipifjh8544V1dstmpiTg4TTxxhaAMvOtb8qxzGd1cuYqilzdiGPjJPfFB4UDofeJkBV1ahqabOjiafo6vxdmW934fC0lI++m0X8dnZ7O3bHxdz+Wyyy8zMxNvbm7i4OAAaN27M+fPnn9uHdDk8jq83HsLa3Jg143pQzfzDq2FUUizm6MEQft12hcyMPNw9bOnTvzGNmzlXOudmFe9PUVEpp47eZu8vgSQnZeNYswqfDPfDt7nzBxeMAIKiE/hi3UEM9LRZP6EXNaooxnHi9INY7qWnU7eKFfWsqvIo5ymfHtjHrBat6FG7DgAXH8Zz/mEcs1q0krkehQeloKAggjMe8NnNzXSr7s037j0qvJ1XkZybS/fdO9FUV+P3vh9jqS9bTymJRELnzp05fvw4AFWqVOHWrVvY2Nj869zgmMdMWncQHU11VnzWTeGVJWVFcXEpxw6GsveXQFKf5GBja0avj3xoG1APHR3ZO6KrUCxZmXn88VsQh34PJudpIa51qvHRoCY0ae7ywXZODl+LYO6OU9hamvDD5z2paqaYZI0j0VEsuXqJnrXdSC3IJ7uwkOGe3uhpajLkj330d/egYTUbtt8OxURXl/mtZL/MohRBCWBt9Al+fnCBRfX707pq3Qpv61XcSX1Cv992UdPMnF97fYSeDEtDzJo1i3nz5gGgrq7O2bNnadGixUvPf5CcwedrDpCVW8DCYQEKy8iRBxKxlIvnIvnt12tE30vGyFiXgK4N6NTdk6rWivf7UlFxCIJAVGQSB/cHc/70XcSlEpo0d6F3fx/c6tl+kCMjKPu+Nxy5xsYj12joYsvSkZ0x1FPcHr61N69T3ciIri61Sc7NJSQlmb0Rdxjt1Qg7ExN+Dr1FiVRKfkkJi9u0l7meAwk36VGjkXIEJbFUwojrG3iYn872JuOw0TOr8PZexekHsYw+cpCWdg6s79wNjQr2cwI4ePAg3bp1K/96+fLlTJw48RVXlJGRk8/EtX8Q8egJX/TyY4B/5XQ6flMEQSA8LIF9u64TeDkaQRBo5FuTLj298fZxrNTWMf91iopKOXcqnEO/3yLmXjK6elq06VCXnh/5UN1Wvn/z8qakVMy8nac5cj2SLr51mDGgDZoK3re35sY1QlOS2dS1bIYqv6SEwMePOPkglm+a+WGopV3h3nYv42JqJF/d2s7NjouUIygBJBZkMujqGuz0LdjoMxJNNfmmRO+4Hcqs82fo51aXBf4VW9ExJiYGb29vcnJyAOjfvz87d+584zYKS0qZ8dNxzoXG8lHL+nzZ2+85I9cPldSUpxw9GMKxQ6FkZuRR1dqYjl0b0LZjPSyrfHjrbB8qsdEpnDgSxunjd8jLLcLe0ZKuPb1p3d4dPf0PJ8P0ZTzNL+KrDYcIjnnMZ12aMKxjI4V1LPNKSigUl2KpV7ZUMf74YYy1dZj359RcSl4u8y6e5yO3urSws5eLppTCbAZeXY21rik7mn6uPEEJ4EzKHaaF/srH9s2Y4BpQ4W2+jqVXL7M26DqTGjfh80a+FXLPvLw8GjduzN27dwGoW7cugYGB6L/l+pVEKmXV75fZfjqYJnXsWTSso0KH/vJELJZw5WIUh/YHE3brISIRNPB2oF1APZq0cEFXV34JMirejMyMPM6dusvJY7d5EPMETU11mvq50LWnN+4eH+4U3T95kJzBpHUHScnKZfagtgQ0UpxlWExGBtPPnQKgjoUlAbVcMNXR5ZfwMHKKi1nUuh1a6urMPHeaGsbGjPCU/XYZsVTCmBubiMlNZluTcdgZWCpXUAL4PuIPfnt0ne8bDKSlVZ0Kb/dVCILA5NMn2Bd5l3mt2vBxXY/3vl+/fv3Ys2cPACYmJgQFBeHk9O5rQ/su3WbxrnNYmxuxbFQXatpUXmv+dyHpcSanjt/h1NHbPEl5io6uJk1buNDCvw7ejRzR0v4wNh1XRp5mF3D1UhQXz0ZyKygOqUSglqs17Tt50KqtW3m14v8KZ0NjmfXzcXS0NFk6qjP1nf6d0CQvSiQSRh/5g061XGjrWJPNIUEUlpbiZGaOt3U1tt8OJTg5CU/rapyLf8CBjz7GTFf221FWRR1jR9wl5tbrS4dq9ZUn0eHvlEjFjLi2gUcF6WzzHYetvnmFt/0qSiUSxhw5yLn4B6zq0JlOzi7vfC9BEFi7di0TJ05EIpFw+PBhAgLefwQYEpvIlB8Pk19cyreD2tHWy/n1F31gSKUC4WGPOHMinIvnIsnLLUJXTwsf35o0a+VKo8Y10dVTjaBkTVZmHpcvRHH5/D1Cb8UjlQhUtTamVVt3Wrd3/086xUukUtYfCmTz8Ru42VmxZGQXhWXYPaOgtJRxxw4x2qsRjWyqUywWczD6HjEZ6fja1qCVvSNnHtxHT1MTexNTrA1lr/f8kwgmh+ygl60PU9zK1tuVMigBJBVkMThwDVY6JmxuPBoddfmmBheJS/nkwD5CU5L5sUuP955bvXLlCkFBQUyYMKFiBAJp2Xl8/eNhbj9I5pN23ozt2vQ/sc70IsRiCaHB8Vw+f48rF6LIzi5AS0uD+l72NGpSk0aNnSpt5VFlQyoViI1O4UZgLDeuxnIvIhFBgOo1zGjesjbNW7lS07nqf2Z67p/k5Bcx/adjXLkbT7cmbkzt54+2pnKM3nffvUNIchIjPL1xMjNHIpXyc1gINxIT2NC5u1y1JORnMDhwDTX0LPix8Si0/swhUNqgBHAlLYpJwVvpbOPJTPdecv+Q5xQXMWDfHh5kZ/Fzt140sqku1/bfhFKxhCV7zvPbpds0crFlwdCOmBvJdq+VsiORSAm/ncDl8/e4ERhL0uMsAGxrmNPItyZePo641a3+n1hgrygyM/IIDY4n+MYDbl67T1ZmPiIRuNSuRiPfmjRr6Yq9o+V/NhA9I/LRE6b8eISUrFwm921Jr+b1lOpnEp+dxf7ICDTV1WjnVKvcMGDg73v5ppkfdSzlYwRdJClh2LUNPCnKZpvvOKrp/dVhVOqgBLAh5hSb759jcp2u9K7RuMI1vI70ggL679tNSl4u23v0oX5Va7lreBMOXA1n8a6zGOrpsGhYAF61lC+AKorHCZncDIzlRmAsYSEPKS2RoKYuwsW1Gh6edtRrYKcKUv8gMyOP8LAEQm/FE3brIY/i0wEwMNTB28eRRr418fZxwtTsv90BeoYgCOy7fIele85jaqjLd8M7KdTD7p/83Ug1ODmR8/Fx5JeW0qCqNc7mFow8dICt3XthbyL72QRBEJh9ey8nksNY7jWYJpbPL48ofVCSCFK+urWda+kx/NBwGJ5m8i/i9SQvj377dpNZWMj2Hr2pZ6WczgrRj9OY8uMREtKyGRHgw/AAH7ntMagsFBWVEnEngdDgh4SFPCQqIgmJRIpIBDXsLXCpXa385VCzygdRo+d15OcXE3MvmajIJKIikrgXmUTak7KtC7p6Wrh72OLRwI76nvbUdK6KuobqM/V3cguKmL/zNKduxdCkjj3zhnTA1EDxCR2JOTnoa2liolOmpVQiQVO9bF9UbGYGMZkZbAkJxlxPjw5OznR3lU9W4M64S6yMOsaoWm0Y5uT/r/eVPigB5JYWMiRwHTmlBWxtMhZrXfmvDSTm5jBg3x6eFhdxsN9Aahgrp8NAflEJ3+06y5HrkXjWsmHBkI5YmX4Y9WZkQWFBCRHhj7l7O4GoyGSiI5PIzi4AQENDDVs7C+wdLXFwqlL+bxUr40ppf1NSIibpcRbxD1KJu59K3P004h6kkpKUXX6OdTUTXOqUBeU6davj7GqtKsz4Cm4/SGba5qOkZefxWbcmDG7jrRSfjelnTxGbmYGdSdlz6vs2HYDnAxNAsVhMiUSCobZ8ZgmupkXxRfA2Wlq5sbB+P9RE/+7gVIqgBPAwL40h19ZR08GSaQAAIABJREFUVdeETT6j0NOQ/1RLYk4OeyLuMMGnidyqML4rh69HsOjXs2hpqPNN/9b/yey8d0EQBFJTnpYFqHvJxD9IJf5BGk9Snpafo6mljnU1U6rZmFKtuinWNqZUtTbBwsIQc0sDjE30FfJgEoslZGbkkZ6WS0ZaLinJT0lKzCTpcRZJjzNJfZKDVFr2d6ymLqK6rTkOTlVwcLTEuXY1nF2tMTb5sBzpZYVYImXzsetsOnYdK1NDFg0LoK6Dckzt/x4ZwY47oezs2YeMwkK+u3yBhJwc9vbuVx6QcoqLSczNobaF/DIjnz3DrXVN2eQz6qXm25UmKAEEpkUzKXgro2q1ZYhTywrX86HxKDWLGT8dJz4lkz/mDVWKKYXKSn5+MQ8fpBH/IJXEx1kkPs4kOTGLpMQsigpLnztXXV0NMwsDzMwMMDLWxdBIB0MjXQwMdTA01EVHRxMtbY2yl5YG2toaqL1gmlUikVJcLKakuJSiolJKisUUF5eSm1NEbm5h2b85heQ8LSQzI4+szDz++WdqaKSLTfWy4Fmtuhk21c2wd7Skhp2Faj/XO/Ls7yo8PoWARq5M6eePoRLVPQtOTuR4bAzTm7csPzb59HGi0tP5pWdf9LW0OBoThUQQ6OLsKhdNz2a7csWF/Oz72StnuypVUAIIzniAh6mdXCvVvg0SqZT47CyczOS7t+pllEokPEjKwMX25Vk1giCw8cg13O2r0tRd/mt2lRlBEMjKzCf1yVPS03LLRinpZSOVzIx8cnMKycstCx55eUX/Chrvgpq6CCNDXQyNnr10MDM3wNzSEAsLQywsDTG3NMSqqjGG/7HNqrLkWTLD/367UDYDMaA17bzefQ9jRfMwOxt1NRG5JSXMPn+GyU2a413tr826M86dxtHElKENvCgsLUVXhsbTf0cslfDlre3czLjP2kbDqG9q/8rz3zQoKU2XystceatOSqRSwtNSmXfhLE1s7fjCt6miJaGprv7KgARlvlx6Olp8vfEwQzs0YniAj5zUVX5EIhFm5gaYmb++IqdUKlCQX/znqKeUkhIJxcVlIyDpC6KVupoILW1NtP8cVWlra6Kto4menpZSpRn/F0jOzGH+ztMERjykce0afDu4PVVMZF+F9U3ZcTuUIzFRZBUW8ml9TwJqOjPi0AFWdehE8z/3WDa1rcHd1FQAuQUkQRD4373DBKZH841bj9cGpLdBaYKSMqOupkYdC0tWd+zC7PNnmH/xPDNatFS0rNdiYqBLXz8PTt+Koa6DcmYWfgioqYkwMNTBwPC/4Vf4ISCRStl7IYw1f1xBKghM/qgVfVt4KEUywzNO3I9h550wdvbsQ1ZhId9eOMvwBt6saB/Al6eOMb6RL/WsqnI4OooqMq4X9092xl/mt0fXGejQnO62FeujV2mCklgqISjzAVpq6niayX9UJQDWhobMaNGSeRfPkVtcLLfMlvfhl7O3MDXQxad2WUny7LxCLt55QFxKJj2a1qVGFeXMNlShQlbEJqYzb+dp7sQl41vHjukDWlPN3FjRsp5DEASe5OXxWUMfzHT1MNPV49P6npyLf8C3LVuzrlNXDkdHEZWRjp6mJrP9/p2CLStOJd9mVdQx2lStyzjniq/FVGmCUpGklLSiHLbHXWR0rbb4V3WXa/taf2a3rL15vXx3dGJODmkF+Uq78TYtO49TwTFM/qglUJa5Fx6XQqlYQhUTA77eeIj+/g3o3kS+P0sVKhRBSamYzcdv8NOJmxjoaDF/SAc6NnRVyilTkUhEr9pu5dO/UkFAR0ODmMwMBEHAy9oGM109HOSwKfbvhGTG8e3tvXiY2jG7bu8Xpn6/L5UmKBlo6tCluhduJtX59vZeahlay9zQNTz1CdlFRdxNe0JIcjI5xcU4m5vjbGbB5NMnMNTW4lZyEl2cXZng00SmWt6FPRfCsLU0pr6TDbkFRew+F8qgtl7li7g9m9UlKTNHwSpVqJA91yIfsnjXOR6mZhHQyJUve/thaqjcafL6Wn+lVquJRNgYGqGnqYlIJGLp1cuIRPClbzO5aorNTcFGz4wlDQahLSPfUqUOSoIgIBKJkAhSANRFajgaWKGppkGhpESm7a4PvsHSq5fp514PF3MLWtjZ4+/giIWePgE7t/KRez0+rluPvJJSRh8+QO867tgYKr44XUmpmMPXI2noYsv1e4+YNbAtAL+eCyW3sJjwuBT2XbrD2K5NqedojaUSLeqqUFHRJGU85X+/XeRsaCy2lias+bwHTerYK1rWO1HVwABDLW3mXTxHeOoTtnTtKXcNfex86VrdW2YBCZQ8KBVLxeioa5IvLuZpSQFqIhGbYs9ip2+Bg4HsNoeJRCKG1vciOiODrMJCBns0KH/vkwO/4VbFimENvJBIpWipS3EyM0cN5ZgCKBFLCIpKYMmec1QxMaSmjQVFJWLuxCXTr1UDejZ159jNKC7cvk89xxdPOyZlPCUmMR2/eu9eG0qFCkVSWFLKzydusu1UECKRiM+6NGFQWy+lcfV+WwRBoEQi4fzDOKz0Dfi1V9/nRlLyRJYBCZQ0KAmCwMHEYDbHnsXTzIG04hxyS4uw1jWhmq4p/eyblpdUTyvKoVBSQo3/t3fe8VHX9x9/fm4kl733nmQnhLBBUAQRJ0uw2tbRUjvVal2tWn5aW1ddVavinq0IiCggQ2WHBAiE7EH23rnMG5/fHwlIKSqWJHcXv8/HI4+7Sy53r88l3+/r+/l83sNpZBvi2Ws0PHXJIh7bu5vF/3qXN65ayuflpRjNZp66ZKhvklql4qOCPGq6usY8+uWbcHaw55GbF1Fc08wTH37FCxv3cdnUeCL8PZmdFIGdVkNyhD8vfbqfX1w2DbszDtKN+/NYtycXR3stz2/cxyM3XvqDazaoYLuYzZLPsgp44eN9NLR3szBjArcumW3zJbmEELja6/j9tJlcGB55qu7dSHNydcqSWKUpCSFIcQ9FJQTe9i78OWU5ekM/zlodXYY+anpb+aBiL746N3Y05JLbUc1LU38+orHyJ7lr5mwO1dfSazAwaDJxWczXSXUHa2t4NnM/HyxbgVqlwmQ2W02h1NhgH16+fRmdPf24Oelo6tCTU1ZHkLcbr3yWydyUKOy0Gowm86leTZmFVXx1tIxbLp/OtPgw/r72K7JLahRTUrAJDhZW8fS63RRWN5EQ5sfDNy4k3caq6m8oLKDHMPiNnbGvS04dVdPoNvbjqv3a8CxhUlZpSgARzr48P/lm7st5nw3VWVwdMpldTQU8mvcxP4u+iHBnX6Z5x7Ch+iArw2aMiiGdZFLAUPZ0U4+e2q4urklM5nB9HX/YtoUH51zIBC9vjGYzmtMMqaKjnda+3lO/ayncnIZyZ5ZfkMqzG/awJasQIcSpvaaT/291rV0cKq4hPtSPafFhGE1mBgxGnB2Glgjauno5UlqLzl7LzMRwSwxFQeGslNe38vS63ew5foIAT1ceuelSFkyaYFU5R9+FWUqeydzHcwcPMCMklGuTUs5ah3M0DeK1si842FJKgnswATp3lodNRwgx5sZktaYEEOToyUOpK/h35X66DX342LvSZxokyT2EGJcAbs1+g0T3EG6PvwwYfVf/xaQp/G7zJq796F/Eefvws/QMro5LQJ7W06S6s5OsuqEZVJKvH3d+voUPlq7Az9myAQWTYoN5866V1LV24ePmhFajprlTj4/bkK7mDj21rZ387NKhqg9VTe046exwc9TR3KHnwbc+J8THndwT9ew4XMJdKy5E9wNo/6BgvVQ1tfPKZ5lsPliIo86O25bMZsXcNJvbN+o1GLhr2xY+Ky1meUISD1148ZgXht5Sl8MXjXmsTllOc38XzxRupn2wh1UxFyszpTMJdfLmtxMWohYq4t2CeGHyzfzh8Dvo1FomeUbyh4QrTz13tD88R62WNVcupqytlUgPz1PvZ5ISjUpFS28vn5UW0dLby5/nzmNueASP7t3FnupKlsYnjqq2cyXQayhC0GAy8cy63VwzJ42UyACyiqtRC0GEvyeDBiMltS109vQTF+rLU2t3ERngyZ3L59Ku7+Phd7dbeBQKP2SqmztY81kmnx0sQKtWc928dG68ZDLuNliYuLa7i1s2fUx+cxP3zLyAn6dnWGRPx93OienesUQ6+xHp7MfTGb7ctP9F3LSOrAgf23QXqzcl+M9ojzi3ILzsXTjeUc0vYxb813PN0jwqCV2nc9KQ6ru7aerRk+ofgMls5qvKE7T09nJBWDizQ8MByG9uItAKQsXPRKtW8/CNl379DcmpaLz9+ZUcr2hgUmwwzR16Sutb+WD4uX0DgzjYaWjt6sHXw5ni6mb25VewcHIcIT5KdQiF0aOqqYPXtx5k04F8NGoVKy+cyE/nZ+DtZh1BRt+XfdVV/G7zJgbNJtZcuZgLwy1X/9NOpeZYeyV9xkEcNHb46tx4OuMG7j/6LxLdQ0hyDxkzLedkSkKIhcAzgBpYI6X826iq+hb+fOxDfHWuvD79l2jOYj5mKanva+NIewVuWkdm+458CfeTVzJqlWBLWQmJvn5oVCqONtST4ON7ypC2lJYQ7u7BZTFDPY+ONtRTr9ezMDpmxDX9r5xc8pwSF8odL20k90QDRTXN3LAgg4WT4/jd8xu4bEr8qfX58vo2mjt7CPJ245+b9lPd3IGzzp5fPLWWu1dcyJxUJYxcYWQpqm7i9a1ZbD9cgkat4po5adxwScappWdbQ0rJK4ezeWzfbqI8PHnxsiuJ9PAcUw1Gs4nni7dip9Iw1TuGdM9IEtyLuOXgK7w549cARLv4M9cvgfbBnjHV9p2mJIRQA88D84EaIEsIsVFKmT/a4s7GnfFXoFNr/6PFxckTa4W+iQMtJXzZmE+Mqz/7mosp1zfy08g5o6LF18mZu2bMRghBfnMT+2uq+fPceQBk19VytLGecHcPzBL+sG0LbX19qAS8cjiLNVcsxsPB8ssNJw02JTKAdQ/+lK+OlbN8TipJ4f5UNbXT2N7N9RenA0OJue/tPMLKuWnszCmluKaZ3149iwh/TxLD/Wjs0FtyKArjjMMlNby+NYu9eRU46ez48fxJXHdRus3OjAD0g4PcvX0rm0uLWRQdy6MXXzLm+UYGs5FfZL5ConswziodOxpy2d5wjLsSruLBYx/yu+zXeTB5GV72LpzQN+GqHdvKF+cyU5oClEopywGEEB8AVwHfaEqSke/RdBJn7VA0WY9xgJreVia4BiKEoLqnle0NufSbDNwUdSFTvKNZGdbGq2U76TcZ0I1SwtfJk7pOo8HTwYGugX5K2lrZUFhAkIsrE/0DWFeQR2tfL2uuWIxKCH67+RP211SzKMa6usa6OOq4fFrCqceeLo4khPnR3TuAvZ2GT/YPLZtcmBbNdX99l99cNWRIMLS00tbVaynpCuMEg8nEzsOlvP/lEY6V1+Pu7MCvrpzBijmpuDjadhX20rZWfvXpRso72rlv1hxunjjJIvtHBrOJUCdv7oi/AoDKnhY+qsrk7wWfsjplOY/lf8xzRVto6OtAq1KzLHRsW96ciykFAdWnPa4B/kulEGIVsAogZIInZmlCJUavYZ9WpebT2iM4aewJdvQit6OKXuMgc/0SSPEYqoi9tuoAA6NoSKcT6eHJ/MhofrJ+LXZqNcsSkrg0Opa91ZUcqK0+FVFT1z1Uay7Y1fr2mc7EwV6LnUbDTU/+m2BvN8L9PLh96QV8ebSMYB93psaFAmAwmtiaVcijPx+KgjSbpU2F4ypYntauHtbtyeXDXcdo6ewh2MeNu66Zy1Uzk3CwG5seQaOFlJK1BXn8+csdOGq1vHX1MmaEhFpMj0BQpm9kbdUBloVOI8zJm2WhU/mgci/b6odmTM39XdT3tZ86l44l52JKZzu7/NdUSEr5MvAyQGiSq9zZ8DTz/H8/alcCdioNt8Zdilqo6DMO8m7FHm6InHPqQ9zZcByD2cRPI+cC0NTfCYCvbvRK1P8sPYPFcUMzDS9HRxr1ep7Yv5f/mzuPIBdXBk0mqjo7UatUhLq5UdPVSXNPD7lNjf9RyshaUKtU3HvtRZTWtlDT0snc4f2izIJK4kN8MZpM2Kk0rNmcSUK4Pwlh/kPh8YohKZwDUkqOlNaybk8u2w6XYDCamJ4Qxv3XXczMxIhx8X/UPTDA/V9uZ2NRIdOCQvj7JZfi7zz21SWKuuqo7GnGT+dOqkcY9yRcxbNFmwly8GS6Tyy+OjeinP3J66xhfkAKPjpXfHSWuXA+F1OqAU4PvQgG6r7tF5w0nuR1bsZZ68M075+cj75vRT0c6FDX106AgzvzA1IA2N6QS35HDSFOXnjaO/PPkm3ktFVgkmYS3IJP5TWNBl6OX6+/5jU3MT04hFmhYQwYjZzoaOfd3BzmR0bTM2jgzs+3kOjry4mOdraWlfDiZVfhaoU9mqKDvP+jqoO7swOZhVXYaTWcaGjjw13HeOX2ZcDoh+Ur2D7t+j4+PZDPur3HqWhow1lnx5JZyayYk0q4/9hu+I8mRxsbuG3Lp9R0dXLH9JncMmmKRSq+ZLeWcU/OeywJmcKrZV9wWWA6Ez3DWRE2g3cqdqNVqcnwiiLNI5w9zYWnqudYinMxpSwgRggRAdQCK4EffdsvOGm8iXe7hMyWt3DW+JDkfum3Pf28CXXyoqGvgycLPqHL0AcIUt1DiXcL5uPqLI61V7I69Rp87F1YlfkyWa1lTPYa/Sgxd52OQ3W11HR1sreqksLWFmK9vFkUM4EF77zBT1LSuCFtKIhg1ScbqO3qxNXn21ucWwOxwT58tDuXax5+m+QIf358cTpRgd5nXbYrqW3BbDYTG+yjGNYPGJPZTGZhFZ/sz2dnTikGo4nkiAAe/PECFkyKxcHetpfoTscsJa8dOcRj+3bj6+TE+0tXkBFomcouUkqOd1Rz24RFXB48ibl+iexqKmB/czEzfCawJGQK/5f7EUtCprCxNpurgidb1JDgHExJSmkUQvwG2MpQSPhrUsq87/q9ef6302tsZWfDUzhpPIhwnjYCcs+OVqVhzbRb+KjqAO52TiwNmYarVsfr5V9Spm/kkbQf4W7nSMdgLw5qO9y0YxP1lh4QyLKEJO74fDMhrm4siIpmQVQMt2z6mIzAQG5IS8csJVJKnO3sGDSbx0TX+RIZ4MUrv19OVlE1E4J9cHEcmt2dzXP+uWk/X+SUEh3oxaIp8VwyeQIBnta/n6Zw/kgpKappZvPBQjZnFdLS2YOLgz1LZyWzeFYyMeOwpmJddxd3b9/K3uoqLomK4W/zFuCms9xJXgiBVqVhR+Nx5gekkOAWjFqo2NGQS15nNSvCZuBh50SPcYBfxiw4tdpkSYSUIx8pl5GRIbOzsxk09fJR9Z20DVSyOOQxAh3HrqrBvyr2sbH2EP+YfCMeds70mwzktFfwRWMet8ctQqceuzDMlt5evIeX9baXl/LW0RzeWrzs1M9fOnSQz8tKWbv82nE3m+jQ97HtUDGbMgvIPVEPwMToIBZMiuWitGiln9M4Q0pJeX0rO46UsjW7iBMNbWjUKmYmhnP51ARmJ0f8V2X68YCUknWF+az+aidmKfnj7LmsTEy2iuO5qb+Td07sIdbFn8uDJwGwr7mIl0q282zGjbjZjX7Id6U+i3CXKYeklBnf9dxRNSWAXmM7H1bdTq+xnWWhf8dHNzbJlS8UbyXDK4opXtHojf2Udzfy9ondLApMY7JXNBtrs+kY7EEtVPwiZv6YaIIhU8pvbuZ3U6cDsLuyglu3fsra5dcS6eGJ+bQ6euON6uYOtmYVsTmrkBMNbQgBqZGBXDQxhovSok+VQFKwLaSUFNc0s/1wCTtySqkY/tumRQVx6eQJXJwea5MlgM6V5p4e/rhzG9tPlDE5MIjH5y8k1M16qpsYzSY21+VQ2t1AvFsQCwPTALgv532WhU4l3XN0K0kUdG7j8/pHuS1+h3WYEkCXoZEPK2/DJA0sD3saD7vRLyf/1+PrMUozN0ddRGZrCdmtZczwmcAc3wRWZb7MZK8okj1C2VCdRYJbEL+KvWTUNQGsK8jjtSOH+MtF86nq6uTpA/u4Y/osFsXEjmtDOpOhq+kSdhwZSsIFiAvxZXZyBLOTI0kI9RsX0VfjlQGDkUMlNezOPcGe3HJqW7tQCcGk2GDmTYzhwrQom624cK5IKfm0pIgHv9xBj8HAndNncWNaukXb15R01xPj8nXzzpOFBfTGfrbX55LfWYMZSYp7KC+XbOelqasIchy94JKy7r18WruaIMdUloU9YT2mBNA+WMOHlbehFlqWhz2Nq9ZvxN/3TO7NeQ+9YYB4t0AyvKJIcgvhx/v+wcX+yfwydqhu3t7mIrJay7gtbtGo6znJq0cOsaW0mAvCwony8GRRzASraK5lKaqaOtiZU8KuY+UcK6/HLCVero7MSAxndlIEUyaE4upk24mT44G61i4OFFSy5/gJMgur6BswoNNqmBIXypyUSOamReMxjmdEp9Oo13P/F9vZfqKMFD9/npi/kGhPL4tqeqPsS14s2cYb039FvFvQqXPKydt+0yB6Qz9vn9iNEIKFAanEuY1eAEZVzyE21vwJH/soFoc+jr3a0bpMCaC5v5S1VXfgoHZnedhTOGlGP/yzY7AXdztHBs1G7jr8DtEu/vxmwsJTP3+1dCcAN0dfNKbG0DXQj6v9N59o67q7qOrsZFrw2BVCtAY69H3sy69gd+4J9uVV0N03gBAQH+rHlAkhTIkLJTUq0OYTKm2BDn0fh4prOFhUxYGCKqqbOwDw93RhdlIkFyRHMCk25AfVwsQsJR/m5fLInl0MmkzcMX2mxWdHJ9lUc4iXSrfjqnXk/qQlxJ1mTGcy2oWr6/vyWV91F652ASwLfRKd2hUhhPWZEkBdbx7rq+/GTevPktAncNSMzdprVU8Lb5Z/xV0JV6JVqVEJFRuqs3i1bCf/mHwzYSPcTv27+C4D/OPObbx//BjLEhK5d+Ycq6iTN9YYTWZyT9RzsLCKzMIqjp9oGGqmqFaREOZHamQgqVGBpEYG4OVqu/XQrAEpJdXNnRwtqyWnvI6jZXWU17cB4GivZVJsMFPjQpkaF0pkgNcPclZf1tbKH3du52BdDVODgvnrvAWEu3tYWtYpyvWNVOibaR/s4aOqTF6euoq6vjZiXQMBWFeVSaSL36g2RAVo7C9mXdUf/mvyYbWmBFDdk8PHNffhYRfCktDHcFCPXpWFk2S3lvFy6Q5enroKgI012TxXtIVnMm4gwS14TFpefB/6DAaePbifNYezcbPXcdfM2SxLSPrB7Dmdjd7+QY6U1ZFdXM3RsjryKxsZNJoACPZxIzkigPhQP+JDfYkL8cVJN7aFLm2J1q4eCqqaKKhqJL+ykeMVDbQO1y50drAnNTKA1KhAJk8IISHMD6169EqGWTu9BgP/OHiAV49k46i1455ZF7DcCo7FtgE9RV11BDp4EObsQ1l3I88WbeaZjBt4qWQb/6rcT7iTD69N/yX9pkGOd1Qz0TPiVNGB0aCpv4T1VXehVTmyLOzv/7FNY9WmBFDZk80nNffjaRfK4jEypnuOvEvHYC9RLn4UdNZyR/zlJLqHYJLmUf1DnQ8FLc088MV2DtXXMdE/gNVz55HkO/r7cbbAoMFIQXUTR8vqOFpeT35lA43tQ5XKhYAwXw/iQnyJCvQmOtCLqEAvAr3cflABFAajicrGdsrqWimta6G0roXC6qb//Jz8PEkM8yM1KpC0yEAiA7x+UJ/RNyGlZEtZCQ/v+pJ6fTdL4xO5e+YFp9I7LElpdwP35bxPvFswJV313Bg1l/kBKfyzZBu3xMznodyPONJ+Aj+dOy9O+dmYaGruL2Vd1R/QqhxYGvokbnYB//FzqzclGIpd/6T2ATztwlgS+hg69eiHBG+rP0a4sw+uWkf8dG5WN0M6G1JK1hfm89c9u2jv7+O65FR+P22mRZPyrJUzZwBFNc00tHWf+rnOTkNkgBdhvh6E+LoT4uNO6PCtm5POJpelzGZJS1cPVU3tVDV1UNXUTnVTB5VN7VQ1dmAcTspWqwShw0YdH6bMKL+NEx3trP5yJ7uqKojz9mH13IuYHDj6UcPnQmNfB3ccfpsfhc9iUdBENtcd4f2Kfbw27RYeOv4ROxvymOMbz8NpK7nz8NtM8ozk2vCZo6rppCFpVDqWhT6Jm13gfz3HJkwJoEJ/kE21D46pMZ3kbPs6jX0d+DlYT47B6XQN9PPUgX28fSwHD52O26fN5JrEZDRWsMlqzej7Biivb6OsroXSulbK61upbu6gvq2L0//9He21+Hm44Ofhgr+HC34ezvi6O+Ph4oiHswMeLg54uDjirLMbE/MymyWdvf20d/fS3t1HW3cv7fo+mjr0NLR10dg+fNuhx2j6uhqIVqMmyNuNUB93ogK9iA70JirQi3A/j3GZuDqSdA8M8Hx2Jm8cOYydRs3vp83k+pQ0qzrGeo0D7Gsp5iK/xFMX1LcfepP7EhfTZejlQEsp10XMGjM9zf1lrKu681sNCWzIlOBrY/KwC2VxyKNjFvxwJl815nNvzvv8bsJCVoTNsNqr5vzmJlZ/tZOsulpiPb24Z9Yc5oSFW61ea2XQYKSmpZPq5g6qmzqob+umsf3rr5Zv6A+lUalwcrDDSWeHs4M9Trqh+3YaNXYaNVqt+tR91VlOZiaTmUGjCYPRxIDBiMFoot9gpKd/kJ6+QfT9A/T0DdIzMMjZDk+1SuDj7oz/sHn6e7rg7+lKqO/QrM/Pw8UqosFsCaPZzPvHj/Fs5j5a+/pYGp/IH2bMwtfJOnOtTrYtP7n1cNP+F7k1bhGpHmEYzSY0KvWYbEs09hezvuputCodS0OfxP0bDAlszJTg5B7TA7hrA1kc+tiYhIufSbehj9W5a9nVVMAC/xTuS1qMo8b6qnbD0Cxva1kpj+7dRWVnBzNDQrlv1hzibaCgq61a+YUJAAAMbklEQVQwaDDSOjxLadf30a4fut+h7xsykOEvfd8g+r4BBo1GDEYzBqOJweGvsx1fQgjstWq0GjX2Gg1arRp7jfprk3Oww1lnj7ODHe5ODni6OOLu4vD1bM3ZEY1aMZ2RQErJzopy/rZnF2XtbUwNCua+2XNJtpF9W4PZiFal4dbsN7g/aQm9pkHeKP+SVdEX4z/KKz71fflsqL4Xe5UzS0Of+K89pDOxOVOCoai8T2r+hKPGiyWhj41Jgu2ZmKWZt8p38c+SbYQ7+/DoxOvHPFz8+zBoMvFu7lGeO7ifzv5+ro5L4LapMwhxG/3AEQUFWya7rpbH9+0mq66WCHcP7p11AfMiomxyxeHx/I24ah3Y21zMNWHTuTwofVTfr7rnCJ/U3P+9ztU2aUow5L4fV9+HVuXAktDHx6Qk0dk42FLKn45+gMFs4oHkpVzon2QRHedKZ38/L2Zn8ubRHMzSzLVJKfx6yjR8HJX8HQWF0ylsaebJ/XvYcaIcH0cnfjNlGisTk2067P2m/S9Srm/kyfSfMMlrdGvZlesP8Fntatztglgc8ihOmnOrZGGzpgRDkRzrq+8BYHHIY/joRvdD/iYa+jq4J+c98jtruDZsJr+ZcAlalXVvFDfou3nu4AH+nZeLvUbDjWnp/Dw941urRygo/BCo7Ojgmcx9fFxUgLOdPb+YNJkb0tJx1Fp3dZC2AT3vVezhlpj5aFRnN85t9cfwd3An2X1026wXd33B1rq/4a2L4uqQv36vVB6bNiWAtoEq1lffjcHcx5XBfxnTthenM2g28kzhZ3xYdYAEt2AeTl1BsKNla1ydCyc62nnqwF42FRfhbGfHT1MncmNaOp4Ols+xUFAYS8raWnkh+yAbiwrQqNTckDaRX0yajLvO+qukHGwt5cFjH9Jt6OOlKT8n0d1yZcdy2zexs/EZghySuSL4IezV328VxuZNCaBrsIH11XejN7awKOgBIpynjoC6/40vGo7z8PF1mKXknsSruSQw1WJavg8FzU08d/AAW8pKcNRquS45lZ9NzMDHSVnWUxjfFLY080JWJp+WFGGv0fCjpFRWTcqw2oi60zGaTbxcuoM3y78izMmbh1NXEuv67YEEo4WUkqzWd9nf8gbhTlNZFHQ/WtX3X3kZF6YEQ/2YPq6+j+aBMub5307iKLdW/zbq+9q5/+i/ONZRxRVBk7gj/nKrjc47k+LWFl7IzmRTcRFalZqVScncPHESwa5KQITC+OJIfR0vHcri8/JSnLRafpwykZsmTrKKSgznQl1vOw8cGzrPXBmcwR1xl+OgsUyCs1ma+LLxOXI7NhHnejEXB9yJWvxvWxjjxpQABk29fFb3f1T2ZDPN+6dM8breYhEyRrOJV0p38Eb5VwQ7erI65RqSLDil/r6c6GjnxexMNhQWIKVkUcwEVqVnkGgjIbAKCmfDLCVfVJTz8qEssupqcbPX8ZPUNG5MS7eJZToYLmtUn8Nj+RtBwr1JV7MgwHIrMkbzAJvr/kK5fh8ZniuZ4XPzeZ13x5UpAZikkR31T1LQtY0k98u40O93qITlomUOt5Xz52NraR7o4uaoC7khcu43bkJaI/Xd3bxx9DDv5x5DbxhkZkgoq9InMys0zCZDYhV+mAwYjXxSXMiaw9kUt7US6OLCzRMzuCYhCSc72ymf1GXo49G8DWxryCXVI4zVydcQ6Gi5CuR9pk4+qXmA+r585vr9mlSPq8/7NcedKcHQlcT+ltfJan2PCKdpXBr0R7Qqy10FdRv6eDz/E7bU55DkFsKDKcutOqfpbHQN9PNe7jHeOHqYpp4eoj08uT4ljSXxiTjb0EGt8MOivrub944f5YPjx2jt6yPO24dV6ZO5LCbW5kK7M1tKeOj4OloHulkVfTE/ibzAogWiOwfr+bjmProMDVwScC8xrheMyOuOS1M6ybH2jXzZ+A987KO4IvghnLWWNYJt9cd4NP9jBkxGfh27gGvCplt9kdczGTAa2VRSxJtHj3C8qRFnrR1L4hO4PiXN4h01FRRg6KI0s7aGt44eYVt5KWYpmRcRxY9T05gVYnsz/B7jAP8o2sJH1ZlEOPnwYMpyEtwsW/S1rjePTbUPYpYmrgheTZBjyoi99rg2JYAT+gNsrvsLdipHrgh+CD9d7Ki+33fR3N/FI3nr2dtcRKp7GH9KXmpzsyYYOvCPNjbw9rEcPi0uYtBsYmpQMCsSU7g0OgZ7jXXnaSmMP9r6ellXkM+/8nIpa2/DXafjmsRkrktKtdnKJQdaSnjk+Hoa+ztZGTaDX8YuQKe2bL5UYecOtjc8gbPGl6uCH8bDfmT3yse9KQG09JezseZ++kwdXBJ4D9Eus0f9Pb8NKSWf1h3hqYJNDJqNrIq5mB+Fz7LaXk3fRUtvL//Oy+XfeblUdXXirtNxdVwCKxOTifWyPcNVsB3MUnKgppoP8o7xeWkpg2YTE/0DWJmUwhWxE9BprDvh9ZvoNvTxTNFmNtZkE+7kw5+SlpLiMboJr9+FlGYOtLzFwdZ3CHZMZVHQA6PS387CppQms7NzRvx1z0aPsZ1NNQ/Q0F/ADJ+byPC81uLT+Jb+Lv6W/zG7mgpIdAvmT0lLiXKx3eg2s5Tsr6nig+PH+LysFIPZTJpfAEviE7g8doLNRDcpWD9VnR2sK8hnQ2E+VV2duNnrWBwXz4qkFCbY+IXQnqZC/pa3gZaBbq6PmM3Po+dhb+HZkcHcz7b6xyjp3kWC20Iu8r8VtRgdTZY1pfQImX34xIi/7jdhNA+yreFxKvQHuT5iDS5anzF7729CSsn2hlwez99IjGsAz0++2dKSRoTW3l7WF+aztiCP4tYW5oRF8PpVSywtS2EcYDCZmPrqP+ns72dGSChL4xNZGB1js7Oi0+kxDnD1V4/jZe/MA8nLLL53dJIK/UE21vyJmT4/I91z+ahe0FvUlIQQzUDliL/wueMNtFjw/Uea8TYeUMZkK4y3MY238YDtjClMSvmdM4ZRMSVLI4TIPhdHthXG23hAGZOtMN7GNN7GA+NvTLa5A6+goKCgMC5RTElBQUFBwWoYr6b0sqUFjDDjbTygjMlWGG9jGm/jgXE2pnG5p6SgoKCgYJuM15mSgoKCgoINopiSgoKCgoLVMK5MSQixUAhRJIQoFULcY2k954sQ4jUhRJMQ4riltYwUQogQIcQXQogCIUSeEOJWS2s6X4QQOiHEQSHE0eExrba0ppFACKEWQhwRQmyytJaRQAhRIYTIFULkCCFGvw7aGCCEcBdCrBVCFA4fU9Mtrel8GTd7SkIINVAMzAdqgCzgWillvkWFnQdCiAsAPfCWlDLJ0npGAiFEABAgpTwshHABDgFX2/jfSQBOUkq9EEIL7AFulVIesLC080II8XsgA3CVUl5uaT3nixCiAsiQUtpCouk5IYR4E9gtpVwjhLADHKWUHZbWdT6Mp5nSFKBUSlkupRwEPgCusrCm80JKuQtos7SOkURKWS+lPDx8vxsoAIIsq+r8kEPohx9qh79s+mpPCBEMXAassbQWhbMjhHAFLgBeBZBSDtq6IcH4MqUgoPq0xzXY+MluvCOECAcmApmWVXL+DC915QBNwDYppa2P6WngLsBsaSEjiAQ+F0IcEkKssrSYESASaAZeH15mXSOEcLK0qPNlPJnS2SoJ2vTV6nhGCOEMfATcJqXssrSe80VKaZJSpgHBwBQhhM0utwohLgeapJSHLK1lhJkppUwHLgV+Pbw8bstogHTgRSnlRKAHsPm99PFkSjXA6V2pgoE6C2lR+BaG910+At6VUq6ztJ6RZHj55EtgoYWlnA8zgSuH92A+AC4SQrxjWUnnj5Sybvi2CVjP0JK/LVMD1Jw2K1/LkEnZNOPJlLKAGCFExPCG30pgo4U1KZzBcFDAq0CBlPLvltYzEgghfIQQ7sP3HYCLgULLqvrfkVLeK6UMllKGM3Qc7ZRSXm9hWeeFEMJpOLCG4SWuBYBNR7VKKRuAaiHEhOFvzQNsNmDoJOOmt7WU0iiE+A2wFVADr0kp8yws67wQQrwPzAW8hRA1wINSylctq+q8mQn8GMgd3oMBuE9K+ZkFNZ0vAcCbwxGgKuDfUspxEUY9jvAD1g/3C9IA70kpt1hW0ojwW+Dd4QvxcuBGC+s5b8ZNSLiCgoKCgu0znpbvFBQUFBRsHMWUFBQUFBSsBsWUFBQUFBSsBsWUFBQUFBSsBsWUFBQUFBSsBsWUFBQUFBSsBsWUFBQUFBSshv8HD/9KmLDwfuAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "# Visualize the output (in 2D case).\n", "mypath = al.wstore\n", "\n", "def risk2D_helper(w1, w2):\n", " w2D = np.array([w1,w2]).reshape((2,1))\n", " return risk(w=w2D)\n", "\n", "risk2D = np.vectorize(risk2D_helper)\n", "\n", "if (d == 2):\n", "\n", " tmpdel = np.linalg.norm(w_star-w_init) * 1\n", " xvals = np.arange(w_star[0]-tmpdel,w_star[0]+tmpdel, 0.1)\n", " yvals = np.arange(w_star[1]-tmpdel,w_star[1]+tmpdel, 0.1)\n", " X, Y = np.meshgrid(xvals, yvals)\n", " Z = risk2D(w1=X, w2=Y)\n", "\n", " myfig = plt.figure(figsize=(7,7))\n", " ax = myfig.add_subplot(1,1,1)\n", " CS = ax.contour(X, Y, Z)\n", " ax.quiver(mypath[0,:-1], mypath[1,:-1],\n", " mypath[0,1:]-mypath[0,:-1],\n", " mypath[1,1:]-mypath[1,:-1],\n", " scale_units='xy', angles='xy', scale=1, color='k')\n", " CS.clabel(inline=1, fontsize=10)\n", " ax.plot(*w_star, 'r*', markersize=12) # print true value.\n", " ax.plot(*mypath[:,-1], 'bo', markersize=6) # print our final estimate.\n", " plt.title('Trajectory of GD routine')\n", " plt.show()\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__練習問題__\n", "\n", "0. データを生成する確率分布の設定やサンプル数を変えることで、アルゴリズムの性能がどのような影響を受けるか調べること。\n", "\n", "0. 反対に、データの設定を固定して、アルゴリズムの設定を変えることによって、アルゴリズムの性能がどのように変わるか調べること。最良のアルゴリズム設定がどのようにデータ分布に依存するか。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 差分法を使った勾配降下法\n", "\n", "基本的な技法と概念を押さえたので、学習アルゴリズムの理解をさらに深めていくために、勾配降下法の種々の改造を試してみることにする。\n", "\n", "正真正銘のGDだと、当然ながら学習の対象となるすべてのパラメータについて偏微分を求める必要がある。自乗誤差ならば勾配は普通求まるのだが、ほかのロス関数では、勾配が定義されていても容易に計算できないケースがある(例:ロス自体が陽に表せないときなど)。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "このような状況下では、ロスが十分滑らかであるなら、差分法で勾配の良い近似は簡単にできる。この方法は遅くてもオイラーの頃から知られている。座標軸を一つずつ動かしてみる。\n", "\n", "\\begin{align*}\n", "\\Delta_{j} & = (0,\\ldots,\\delta,\\ldots,0), \\text{ such that} \\\\\n", "w + \\Delta_{j} & = (w_{1},\\ldots,(w_{j}+\\delta),\\ldots,w_{d}), \\quad j = 1,\\ldots,d \n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "このように差分の比を取ることで偏微分の近似が得られる。\n", "\n", "\\begin{align*}\n", "\\widehat{g}_{i,j}(w) & = \\frac{L((w+\\Delta_{j});z_{i})-L(w;z_{i})}{\\delta} \\approx \\frac{\\partial L(w;z_{i})}{\\partial w_{j}}, \\quad i=1,\\ldots,n \\\\\n", "\\widehat{g}_{i}(w) & = \\left(\\widehat{g}_{i,1}(w),\\ldots,\\widehat{g}_{i,d}(w)\\right), \\quad i=1,\\ldots,n.\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "次に実装したいアルゴリズムは、偏微分が解析的に求められない状況下での近似的な勾配降下法である。勾配の代わりに、差分法による近似を使って、通常の更新式に代入するだけである。\n", "\n", "\\begin{align*}\n", "w_{(t+1)} = w_{(t)} - \\alpha_{(t)} \\frac{1}{n}\\sum_{i=1}^{n} \\widehat{g}_{i}(w_{(t)}).\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "具体的には、下記の通りになる。" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "class Algo_FDGD(Algo_LineSearch):\n", " '''\n", " Finite-difference gradient descent.\n", " '''\n", "\n", " def __init__(self, w_init, step, delta, t_max, thres, store):\n", "\n", " super(Algo_FDGD, self).__init__(w_init=w_init,\n", " step=step,\n", " t_max=t_max,\n", " thres=thres,\n", " store=store)\n", " self.delta = delta\n", " self.delmtx = np.eye(self.w.size) * delta\n", " \n", " \n", " def newdir(self, model, data):\n", " '''\n", " Determine the direction of the update.\n", " '''\n", " out = np.zeros((1,self.w.size), dtype=self.w.dtype)\n", " loss = model.l_tr(w=self.w, data=data)\n", " \n", " # Perturb one coordinate at a time, then \n", " # compute finite difference.\n", " for j in range(self.w.size):\n", " delj = np.take(self.delmtx,[j],axis=1)\n", " loss_delta = model.l_tr((self.w + delj), data=data)\n", " out[:,j] = np.mean(loss_delta-loss) / self.delta\n", " \n", " return out * (-1)\n", " \n", "\n", " def monitor_update(self, model, data):\n", " self.t += 1\n", " self.diff = np.linalg.norm((self.w-self.w_old))\n", " self.w_old = np.copy(self.w)\n", " \n", " \n", " def cost_update(self, model, data):\n", " self.stepcost = data.n_tr\n", " self.cumcost += self.stepcost\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "前とまったく同様な数値実験も行なうことができる。通常の勾配降下法との唯一の違いは、精度を定めるパラメータ`delta`を決めないといけないことである(これは引数の「差分」である$\\delta$のこと)。" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Initialize model.\n", "mod = models.LinearL2()\n", "\n", "# Initialize learning algorithm.\n", "w_init = np.random.uniform(size=(d,1))\n", "def alpha_fixed(t, val):\n", " return val\n", "def make_step(u):\n", " def mystep(t, model=None, data=None, newdir=None):\n", " return alpha_fixed(t=t, val=u)\n", " return mystep\n", "al = Algo_FDGD(w_init=w_init,\n", " step=make_step(0.15),\n", " delta=0.05,\n", " t_max=15,\n", " thres=1e-03,\n", " store=True)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Iterate the learning algorithm.\n", "for onestep in al:\n", " al.update(model=mod, data=data)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "# Visualize the output (in 2D case).\n", "mypath = al.wstore\n", "\n", "def risk2D_helper(w1, w2):\n", " w2D = np.array([w1,w2]).reshape((2,1))\n", " return risk(w=w2D)\n", "\n", "risk2D = np.vectorize(risk2D_helper)\n", "\n", "if (d == 2):\n", "\n", " tmpdel = np.linalg.norm(w_star-w_init) * 1\n", " xvals = np.arange(w_star[0]-tmpdel,w_star[0]+tmpdel, 0.1)\n", " yvals = np.arange(w_star[1]-tmpdel,w_star[1]+tmpdel, 0.1)\n", " X, Y = np.meshgrid(xvals, yvals)\n", " Z = risk2D(w1=X, w2=Y)\n", "\n", " myfig = plt.figure(figsize=(7,7))\n", " ax = myfig.add_subplot(1,1,1)\n", " CS = ax.contour(X, Y, Z)\n", " ax.quiver(mypath[0,:-1], mypath[1,:-1],\n", " mypath[0,1:]-mypath[0,:-1],\n", " mypath[1,1:]-mypath[1,:-1],\n", " scale_units='xy', angles='xy', scale=1, color='k')\n", " CS.clabel(inline=1, fontsize=10)\n", " ax.plot(*w_star, 'r*', markersize=12) # print true value.\n", " ax.plot(*mypath[:,-1], 'bo', markersize=6) # print our final estimate.\n", " plt.title('Trajectory of FDGD routine')\n", " plt.show()\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "余談にはなるが、上記のアルゴリズムは*“forward difference”*と呼ばれる差分法の一例である。正の値を足しているからforwardというが、当然、引き算でも問題ないし、点をまたぐような形でも良い。つまり、\n", "\n", "\\begin{align}\n", "\\frac{l(w;z_{i})-l(w-\\Delta_{j} ;z_{i})}{\\delta} \\quad \\text{and} \\quad \\frac{l(w+\\Delta_{j};z_{i})-l(w-\\Delta_{j};z_{i})}{2\\delta}\n", "\\end{align}\n", "\n", "という2種類の差分もある($j$番目の偏微分の*“backward difference”*および*“central difference”*と呼ぶ)。直感的にもわかるように、後者のほうが断然、精度としては優れている。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__練習問題__\n", "\n", "0. 先ほどの`Algo_FDGD`を改造し、backward differenceとcentral differenceの差分法を生かした勾配降下法を実装してみること。ほかのアルゴリズムと比較して、軌跡がどう異なるか。収束する速度はどうか。$n$が小さいときの頑健性はどうか。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 確率的勾配降下法\n", "\n", "学習の対象となるパラメータが$w=(w_{1},\\ldots,w_{d})$きわめて数多くある状況について考える。この場合、勾配降下法を使うには、物凄い数の偏微分を計算しないといけないが、データのサンプル数が多くなると計算量に圧迫されて、通常のGDは現実的な手法でなくなる。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この計算コストを大幅に削減する良い方法として、サンプルの全体ではなく、無作為に選ぶサブセット(別名:ミニバッチ)の分だけ勾配を求める確率的な最適化法がある。まずはインデックスをランダムに取る。\n", "\n", "\\begin{align*}\n", "\\mathcal{I} \\subset \\{1,2,\\ldots,n\\}\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "このミニバッチの大きさは$B = |\\mathcal{I}| \\ll n$となって、その部分集合の勾配を求めて、経験平均ベクトルを通常の更新式に代入する。\n", "\n", "\\begin{align*}\n", "w_{(t+1)} = w_{(t)} - \\frac{\\alpha_{(t)}}{B}\\sum_{i \\in \\mathcal{I}} \\nabla L(w_{(t)};z_{i}).\n", "\\end{align*}\n", "\n", "古典的には、$B=1$とするのが主流で、これを確率的勾配降下法(*stochastic gradient descent*, SGD)と呼ぶ。今では$B>1$のミニバッチが用いられることも多い。一般化すると$i \\in \\mathcal{I}$が独立かつ一様に$\\{1,\\ldots,n\\}$からサンプルされるとすると、これらのランダム添え字について期待値を取ると:\n", "\n", "\n", "\\begin{align*}\n", "\\mathbf{E} \\left( \\frac{1}{B}\\sum_{i \\in \\mathcal{I}} \\nabla L(w;z_{i}) \\right) & = \\frac{1}{B}\\sum_{i \\in \\mathcal{I}} \\mathbf{E} \\nabla L(w;z_{i})\\\\\n", " & = \\frac{1}{B}\\sum_{i \\in \\mathcal{I}}\\left(\\frac{1}{n} \\sum_{j=1}^{n} \\nabla L(w;z_{j}) \\right)\\\\\n", " & = \\frac{1}{n} \\sum_{j=1}^{n} \\nabla L(w;z_{j}).\n", "\\end{align*}\n", "\n", "つまり、このミニバッチ平均の期待値というのは、全データ点を使った場合の平均ベクトルにほかならない。確実なことはいえないが、コストの小さい反復回数をたくさん投じることで、一回一回のばらつきが平滑化され、最終的には良い解の近辺にたどり着くだろう、という発想である。\n", "\n", "実際の動きを自分の手で確かめてみることにしよう。実装するためには、例の`newdir`メソッドのたったの数行を追加するだけで済む。" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "\n", "class Algo_SGD(Algo_LineSearch):\n", " '''\n", " Stochastic companion to Algo_GD, where we randomly take\n", " sub-samples (called mini-batches) to compute the sample\n", " mean estimate of the underlying risk gradient. By using\n", " small mini-batches, the computational burden of each\n", " iteration is eased, at the cost of poorer statistical\n", " estimates.\n", " '''\n", " def __init__(self, w_init, step, batchsize, replace,\n", " t_max, thres, store):\n", "\n", " super(Algo_SGD, self).__init__(w_init=w_init,\n", " step=step,\n", " t_max=t_max,\n", " thres=thres,\n", " store=store)\n", " self.batchsize = batchsize\n", " self.replace = replace\n", "\n", " # Computed internally.\n", " self.nseen = 0\n", " self.npasses = 0\n", "\n", "\n", " def newdir(self, model, data):\n", " '''\n", " Determine the direction of the update.\n", " '''\n", " shufidx = np.random.choice(data.n_tr,\n", " size=self.batchsize,\n", " replace=self.replace)\n", " return (-1) * np.mean(model.g_tr(w=self.w, data=data, n_idx=shufidx),\n", " axis=0, keepdims=True)\n", "\n", " def monitor_update(self, model, data):\n", " '''\n", " Update the counters and convergence\n", " monitors used by the algorithm. This is\n", " executed once every step.\n", " '''\n", " self.t += 1\n", " self.nseen += self.batchsize\n", " if self.nseen >= data.n_tr:\n", " self.npasses += 1\n", " self.diff = np.linalg.norm((self.w-self.w_old))\n", " self.w_old = np.copy(self.w)\n", " self.nseen = self.nseen % data.n_tr\n", " \n", " def cost_update(self, model, data):\n", " '''\n", " Update the amount of computational resources\n", " used by the routine.\n", "\n", " Cost here is number of gradient vectors\n", " computed. SGD computes one for each element\n", " of the mini-batch used.\n", " '''\n", " self.stepcost = self.batchsize\n", " self.cumcost += self.stepcost\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "要点:\n", "\n", "- `batchsize`は上記の$B$で、無作為に取るミニバッチの大きさを決める。もし$B=n$であれば、言うまでもなく`Algo_GD`とまったく同じ働きをする。\n", "\n", "- `replace`は、ミニバッチのサンプルを取るときに、再抽出するかどうか決める論理値。\n", "\n", "- `nseen`と`npasses`は、データ全体の何周目か記録する。上記の実装では、通常のGDと同じ終了条件となっている。" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Initialize model.\n", "mod = models.LinearL2()\n", "\n", "# Initialize learning algorithm.\n", "w_init = np.random.uniform(size=(d,1))\n", "\n", "def alpha_fixed(t, val):\n", " return val\n", "\n", "def make_step(u):\n", " def mystep(t, model=None, data=None, newdir=None):\n", " return alpha_fixed(t=t, val=u)\n", " return mystep\n", "al = Algo_SGD(w_init=w_init,\n", " batchsize=1,\n", " replace=False,\n", " step=make_step(0.05),\n", " t_max=150,\n", " thres=-1.0, # nullifies this condition.\n", " store=True)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Iterate the learning algorithm.\n", "for onestep in al:\n", " al.update(model=mod, data=data)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "# Visualize the output (in 2D case).\n", "mypath = al.wstore\n", "\n", "def risk2D_helper(w1, w2):\n", " w2D = np.array([w1,w2]).reshape((2,1))\n", " return risk(w=w2D)\n", "\n", "risk2D = np.vectorize(risk2D_helper)\n", "\n", "if (d == 2):\n", "\n", " tmpdel = np.linalg.norm(w_star-w_init) * 1\n", " xvals = np.arange(w_star[0]-tmpdel,w_star[0]+tmpdel, 0.1)\n", " yvals = np.arange(w_star[1]-tmpdel,w_star[1]+tmpdel, 0.1)\n", " X, Y = np.meshgrid(xvals, yvals)\n", " Z = risk2D(w1=X, w2=Y)\n", "\n", " myfig = plt.figure(figsize=(7,7))\n", " ax = myfig.add_subplot(1,1,1)\n", " CS = ax.contour(X, Y, Z)\n", " ax.quiver(mypath[0,:-1], mypath[1,:-1],\n", " mypath[0,1:]-mypath[0,:-1],\n", " mypath[1,1:]-mypath[1,:-1],\n", " scale_units='xy', angles='xy', scale=1, color='k')\n", " CS.clabel(inline=1, fontsize=10)\n", " ax.plot(*w_star, 'r*', markersize=12) # print true value.\n", " ax.plot(*mypath[:,-1], 'bo', markersize=6) # print our final estimate.\n", " plt.title('Trajectory of SGD routine')\n", " plt.show()\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__練習問題__\n", "\n", "0. GDの節での練習問題に、今度はSGDについて同様に答えること。「良いアルゴリズムの設定」がGDとSGDとで、基本的にどのように異なるか。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 各種アルゴリズムの性能を丁寧に観察\n", "\n", "この節では、各種の学習アルゴリズムが時間とともに、平均的にどのような振る舞いを見せるか調べていく。" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "## Import all necessary modules.\n", "\n", "import math\n", "import numpy as np\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "import models\n", "import dataclass\n", "import helpers as hlp" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "## Experiment setup.\n", "\n", "# Data-related.\n", "data = dataclass.DataSet() # Initialize one data object; will be re-populated at each trial.\n", "n = 500 # sample size\n", "d = 2 # number of parameters\n", "init_delta = 5.0 # controls support of random initialization\n", "num_trials = 250 # number of independent random trials to conduct\n", "cov_X = np.eye(d) # covariance matrix of the inputs.\n", "\n", "w_star = np.ones(d).reshape((d,1)) # vector specifying true model\n", "\n", "w_init = w_star + np.random.uniform(low=-init_delta, high=init_delta, size=d).reshape((d,1))\n", "# NOTE: Initial weights are randomly generated in advance, \n", "# so that per-trial randomness here is only due to the data.\n", "\n", "# Algorithm-related.\n", "m_idx_todo = [0,1,2] # let's us manually pick and choose which methods to evaluate.\n", "t_max = 30 # termination condition; maximum number of iterations.\n", "thres = -1.0 # termination condition; if negative, runs for max iterations.\n", "\n", "def alpha_fixed(t, val): # step-size callback function.\n", " return val\n", "def make_step(u):\n", " def mystep(t, model=None, data=None, newdir=None):\n", " return alpha_fixed(t=t, val=u)\n", " return mystep\n", "\n", "# Clerical.\n", "mth_names = [\"gd\", \"fdgd\", \"sgd\"]\n", "num_mths = len(mth_names)\n", "mth_colours = [\"black\", \"purple\", \"red\"]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# Make choice of additive noise distribution (un-comment your choice).\n", "#paras = {\"name\": \"norm\", \"shift\": 0.0, \"scale\": 20.0}\n", "paras = {\"name\": \"lnorm\", \"meanlog\": 0.0, \"sdlog\": 1.75}\n", "\n", "# Put together risk function.\n", "def risk(w):\n", " mean_noise, var_noise = hlp.noise_risk(paras=paras)\n", " return hlp.riskMaker(w=w, A=cov_X, b=math.sqrt(var_noise), w_star=w_star)\n", "risk_star = risk(w=w_star) # optimal risk value." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "## Running the algorithms.\n", "\n", "# Prepare storage for performance metrics.\n", "riskvals = np.zeros((num_trials,t_max,num_mths), dtype=np.float32)\n", "loss_tr = np.zeros((num_trials,t_max,num_mths), dtype=np.float32)\n", "truedist = np.zeros((num_trials,t_max,num_mths), dtype=np.float32)\n", "\n", "# Loop over trials.\n", "for tri in range(num_trials):\n", " \n", " # Generate new data (with *centred* noise).\n", " X = np.random.normal(loc=0.0, scale=1.0, size=(n,d))\n", " noise = hlp.noise_data(n=n, paras=paras)\n", " y = np.dot(X, w_star) + noise\n", " data.init_tr(X=X, y=y)\n", " \n", " # Initialize models.\n", " mod = models.LinearL2(data=data)\n", " loss_star = np.mean(mod.l_tr(w=w_star, data=data))\n", " \n", " \n", " # Initialize all algorithms.\n", " al_gd = Algo_GD(w_init=w_init,\n", " step=make_step(0.25),\n", " t_max=t_max,\n", " thres=thres,\n", " store=True)\n", " al_fdgd = Algo_FDGD(w_init=w_init,\n", " step=make_step(0.25),\n", " delta=0.15,\n", " t_max=t_max,\n", " thres=thres,\n", " store=True)\n", " al_sgd = Algo_SGD(w_init=w_init,\n", " batchsize=1,\n", " replace=False,\n", " step=make_step(0.01),\n", " t_max=t_max,\n", " thres=thres,\n", " store=True)\n", " \n", " # Run all algorithms and save their performance.\n", " \n", " ## ERM-GD.\n", " mthidx = 0\n", " if mthidx in m_idx_todo: \n", " idx = 0\n", " for onestep in al_gd:\n", " al_gd.update(model=mod, data=data)\n", " # Record performance\n", " loss_tr[tri,idx,mthidx] = np.mean(mod.l_tr(w=al_gd.w, data=data))-loss_star\n", " riskvals[tri,idx,mthidx] = risk(w=al_gd.w)-risk_star\n", " truedist[tri,idx,mthidx] = np.linalg.norm(w_star-al_gd.w)-0\n", " idx += 1\n", " \n", " ## FD-GD.\n", " mthidx = 1\n", " if mthidx in m_idx_todo:\n", " idx = 0\n", " for onestep in al_fdgd:\n", " al_fdgd.update(model=mod, data=data)\n", " # Record performance\n", " loss_tr[tri,idx,mthidx] = np.mean(mod.l_tr(w=al_fdgd.w, data=data))-loss_star\n", " riskvals[tri,idx,mthidx] = risk(w=al_fdgd.w)-risk_star\n", " truedist[tri,idx,mthidx] = np.linalg.norm(w_star-al_fdgd.w)-0\n", " idx += 1\n", " \n", " ## SGD.\n", " mthidx = 2\n", " if mthidx in m_idx_todo:\n", " idx = 0\n", " for onestep in al_sgd:\n", " al_sgd.update(model=mod, data=data)\n", " # Record performance\n", " loss_tr[tri,idx,mthidx] = np.mean(mod.l_tr(w=al_sgd.w, data=data))-loss_star\n", " riskvals[tri,idx,mthidx] = risk(w=al_sgd.w)-risk_star\n", " truedist[tri,idx,mthidx] = np.linalg.norm(w_star-al_sgd.w)-0\n", " idx += 1\n", "\n", "\n", "# Finally, take statistics of the performance metrics over all trials.\n", "ave_loss_tr = np.mean(loss_tr, axis=0)\n", "ave_riskvals = np.mean(riskvals, axis=0)\n", "ave_truedist = np.mean(truedist, axis=0)\n", "sd_loss_tr = np.std(loss_tr, axis=0)\n", "sd_riskvals = np.std(riskvals, axis=0)\n", "sd_truedist = np.std(truedist, axis=0)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Visualization of performance.\n", "\n", "tvals = np.arange(t_max)+1 # better to start from the first update.\n", "\n", "# Average over trials.\n", "myfig = plt.figure(figsize=(15,5))\n", "\n", "ax_loss_tr = myfig.add_subplot(1, 3, 1)\n", "for m in m_idx_todo:\n", " vals = ave_loss_tr[:,m]\n", " err = sd_loss_tr[:,m]\n", " ax_loss_tr.plot(tvals, vals, color=mth_colours[m], label=mth_names[m])\n", " #ax_loss_tr.errorbar(tvals, vals, yerr=err, fmt='-o', col=mth_colours[m], label=mth_names[m])\n", " ax_loss_tr.legend(loc=1,ncol=1)\n", " plt.axhline(y=0.0, color=\"black\")\n", " plt.title(\"Excess empirical risk\")\n", " \n", "\n", "ax_riskvals = myfig.add_subplot(1, 3, 2)\n", "for m in m_idx_todo:\n", " vals = ave_riskvals[:,m]\n", " err = sd_riskvals[:,m]\n", " err_log = err / vals\n", " ax_riskvals.semilogy(tvals, vals, \"-o\", color=mth_colours[m], label=mth_names[m])\n", " ax_riskvals.legend(loc=1,ncol=1)\n", " plt.axhline(y=0.0, color=\"black\")\n", " plt.title(\"Excess risk\")\n", "\n", "ax_variation = myfig.add_subplot(1, 3, 3)\n", "for m in m_idx_todo:\n", " vals = sd_riskvals[:,m]\n", " ax_variation.plot(tvals, vals, \"-o\", color=mth_colours[m], label=mth_names[m])\n", " ax_variation.legend(loc=1,ncol=1)\n", " plt.axhline(y=0.0, color=\"black\")\n", " plt.title(\"Variation of risk across samples\")\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__練習問題__ \n", "\n", "0. 「学習効率」とは、より少ない計算資源(ここで反復回数)で、より良い解に至ることを指す。上記の実験で、データの次元、データ分布の設定、アルゴリズムの設定といった要因が学習効率にどのような影響を及ぼすか。「過学習」が起きやすい設定があるか。サンプルごとの性能のばらつきが大きくなりがちな設定があるか。この類いの問いに答えられるように調べること。\n", "\n", "0. Numpyでは、多種多様な確率分布が整備されている。`helpers_datagen.py`のソースを開き、ここで使っている関数`hlp.noise_data`を拡大させてみること(つまり、対応ノイズの分布を増やすこと)。分布族によって、どのような違いが見られるか。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "___" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }