4.nurual_network_back_propagation/ex4.nerual_network_backpropagation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 神经网络反向传播 NN Back Propagation\n",
    "\n",
    "此Notebook是配合Andrew Ng \\\"Machine Leanring\\\"中[神经网络](https://github.com/loveunk/machine-learning-deep-learning-notes/blob/master/machine-learning/neural-networks.md)部分学习使用。\n",
    "\n",
    "测试用python版本为3.6\n",
    "\n",
    "* 机器学习路径：https://github.com/loveunk/machine-learning-deep-learning-notes/\n",
    "* 内容正文综合参考网络资源，使用中如果有疑问请联络：www.kaikai.ai"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib\n",
    "import scipy.optimize as opt\n",
    "from sklearn.metrics import classification_report#这个包是评价报告"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data(path, transpose=True):\n",
    "    data = sio.loadmat(path)\n",
    "    y = data.get('y')  # (5000,1)\n",
    "    y = y.reshape(y.shape[0])\n",
    "\n",
    "    X = data.get('X')  # (5000,400)\n",
    "\n",
    "    if transpose:\n",
    "        X = np.array([im.reshape((20, 20)).T for im in X])\n",
    "        X = np.array([im.reshape(400) for im in X])\n",
    "\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, _ = load_data('ex4data1.mat')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 查看数据集（10*10的图像）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_100_image(X):\n",
    "    \"\"\" sample 100 image and show them\n",
    "    assume the image is square\n",
    "\n",
    "    X : (5000, 400)\n",
    "    \"\"\"\n",
    "    size = int(np.sqrt(X.shape[1]))\n",
    "\n",
    "    # sample 100 image, reshape, reorg it\n",
    "    sample_idx = np.random.choice(np.arange(X.shape[0]), 100)  # 100*400\n",
    "    sample_images = X[sample_idx, :]\n",
    "\n",
    "    fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8))\n",
    "\n",
    "    for r in range(10):\n",
    "        for c in range(10):\n",
    "            ax_array[r, c].matshow(sample_images[10 * r + c].reshape((size, size)),\n",
    "                                   cmap=matplotlib.cm.binary)\n",
    "            plt.xticks(np.array([]))\n",
    "            plt.yticks(np.array([]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gF/mSbIui/pw+7EIiHQkhZbNq0Mq4NWrUqJyg5eSTTwb8Hie2lD62TteX7bq07p+Ys+qeGqIjdrf33nu7zw76rfxDz63Y89SpU7MmjtJ6/vXXX84vpU0Ry9TzJh3AsGHDnOZG7xHpMjSqNbiu2dCOGCM1GAwGgyED1IiRBqPF999/3ymj1CirCEFqNb39v/76axf96vfo/xTVSO2muk3dunVDUQuKRUi9dswxxwA+368IJi8vzx3cLPVu3KPSgggOfSgpKYndRtnSunVrVy9RTUhDu1VTlFq0efPmLkIM1vR0v8S4pKJdsmSJq0FGCa35smXLXMZF7SPKrkR1KL0+54MPPnBqT42GVCuLWE/6AHIdVafhHTroQGxKGSb9/qi0AGJmUg+rvenSSy+NRQktyKfXX399p25988033b+BrzNLD7Bw4ULXiqafP++88wDPqFZVTwxLIa17qK+yV8enjRkzBkgNxFFtXHYK8gft5dIItG/fPmvqYvnp2muv7bKFwVq9/OSUU04BUnoFZSx0NF1wb1QGIZswRmowGAwGQwaoESPVm13q1ksvvdTVOxWZq1dHuW33gQUFjlkEo3VFHVLjqfYRRmSWTCZdNHPttdeW+T/9XTWEtdZay9mmaCdXBjAIii6luCsqKoqdkSrK3mmnnVzdRQ3pWlvVWMQuO3bs6Oog6smcPn064AdmaCyYxpbttdderiYf5oiy4ECD9FF8jz32GOBrearzauReWLXR4BjDoUOHugyL6pti/6rrpzMSjarTvRL71++TXiAqTYCuR4xYmQqt47HHHhvr+EX5V4MGDZxqW3uCfDp42MJnn33m6qbqy5R/pA9giBq652KkYntipl999ZWrRap3Wvb+/vvvgPd39Sy3bds2lL0xOCZU0H4nBf+SJUtcxiI4KjNMGCM1GAwGgyED1IiRKnpSVHXGGWe46FfTPYKHpqo+s2TJEldLuPnmmwHPPPTvYqJhR2lBZq3RXsq3a+LHWmut5VSXioDiHpUmpEfI4BV4cUbtgmxr1qyZU0bLT8Sa2rVrB8CNN94IpPouVdsQA1SEK5YidqRezWuuuaZcP2o2oSg4eBiz8MILL7jB2LJD/W6qk4XN5MQkmzVr5nxUrFLMPZihSPcR/VkTxJSB0fi9qPxJ91w95erR1Pq2bds20r7RipBMJp1fSiUatEt++tFHHzm/EHuVpiQXDsqWX2gSmiYcDRs2zI3D1JQg+YEOVdcRdhq/l0gkIrkm+bsG7kvBn0gk3DjaKLOGxkgNBoPBYMgAGU020hu/adOmXHXVVYDvY1SPqXLnYptz5sxxQ9Q1PUVRjthE1FFacMqOjtsRmwB/rbnCRIMQC1GkO3369JxgpVD2fipaDM7jfOKJJ4BUHVRRZvBIKUWhqtt07doVSN23MAdli4GqDiplrmz/9ddfXa+mFOfqXQs7Kg4e43fmmWe6I7mGDBkCeCWusgC6ruLiYpeN0fBxranqTOmHgKf/bLah3yu1s6bsqPYtJhf1vOiqIOh7WrPffvsNSGVhdLC36pD6nlzQWmhP0x4iNfIhhxziZjBrToD8XP693XbbAT6TENXerfV74YUXAD9xrkePHuW0AFEgoxdpuqHaINUyogcvKNAoLS11KeG4R9cFkWsnuVQFQWeReKe4uDhnXqTpqGhttZF26dLFpdEreij1YguOLcs2tH56aHUAg3xbDfldunRxm09Q9BTG6MJVQZthUVGRG6GnTVsv0ODzVrduXZeWVEpXm1BwbcO2PzjqUgHhUUcdBZQ99zJuEV1lUMAnAUyTJk3cODoRi1wMyIP3un379m4/D47LDA5qiJr8yD91zuvpp58OpNrntP5R7n+W2jUYDAaDIQNk5TxS8NGuGGiQiaaPJcs1JlqbEUztSTCVTCZjHw1YHaSP31P0WxHziProOkW/Gk4gIUy6T1eUzYiKPaUzBrEDsU21LqwKsls/E5fPpDffgx/2L4SdWs4mZKsG0GuoBHj/yMVskSDbli1bljPHRAYhG5W50LjOlStXxiLgMkZqMBgMBkMGyBojFSqLBnI5ElsTkIu1l+oi13wkWB/KhZaFqqC22ZuONcmPa5PmorYhV3zcGKnBYDAYDBkgUZ3oP5FIzAamhmdOjdAmmUw2r+g/zeasYbU2Q+20uzbaDLXTbrM5azD/iA6VrjVU80VqMBgMBoOhLCy1azAYDAZDBrAXqcFgMBgMGcBepAaDwWAwZAB7kRoMBoPBkAHsRWowGAwGQwawF6nBYDAYDBmgWpONioqKkqub2xkHxo0bN2d1fT7FxcVJHRyeK6jM5qKiopyzefz48au1GWrvWofh06s7RLsyVGYzpOxu3bp1zYwLCRMmTFjj/Lo2+jRUz+5MfLU6WBP3aqFaL9I2bdq4syJzBY0aNVptA29JSYk7jzEd6c4TdS9tw4YNK7W5quusI76E4BDybKFx48aVNkpXtNZxorK1zrZP6/CA999/H/Dnax522GFV/h2V+TRA69at3XmjNUVeXp47ciqI4HFZVRkWX1xcnDW/jgqV+XVJSQmfffZZVOZUCfXr18/Ks6h7/9133wGwcOFCAHbZZRf3Pdkcsl+Vfa+27R+CpXYNBoPBYMgAWR9an+tQZJ1MJmvFkUwVQdHkn3/+CXhmqmOo6tWr59hEbRoAnp+f7w7u1jUqKs7l4/fq168PwKeffgrAiSeeCMDuu+8OwMEHHwx4xhrHRDF9po44nD9/Pvfccw8A77zzDgBbbrklANdeey2QYr4Q/1BwQ/ag+//rr78CcP755wMwadIkAPbbbz8A+vTpw0477QSUz1DUJmif176io+Gy+QwaIzUYDAaDIQNExkgVFeTl5bnoJsqoXOxGdYA77riDLl26ALDzzjsDVTvuSIxC1xPXQchiQLfeeisAo0ePBmD77bcHUlGlosnGjRvHYGHVoHVUlDxv3jxXR5szZw4A7dq1A3ztJtcOG87Pz2fs2LEAXHPNNQAUFxcD3vZcQN26dQHPPC655BJ++eUXALbeemsAvvrqK8Az1PPOOw+AxYsXR2prbURUop1METxEvVWrVgBMmTIFgNdeew2AwYMHc+655wLw3//+F/B+HffRcNrPg1mrdOh+/PPPPwCMHz8e8L7epEkTIDvZltBepLoIvXjmzZsHwB9//MG6664L+AuJwuGU+hw2bBgAd999t7NDL9LVQdeh1N3s2bMBOPTQQ4HoHxp9nk6G14v066+/BuDNN99k0003BXyaTteZCy8i3Q89AFrXp59+mldeeQXwQp2NN94YgIceegiA3XbbDYj/OtKDs3POOQeARYsWAfDiiy8CsN5665X53ij9RJ+llJZekldccQWQStM98sgjALRt2xaAfv36AbggLK5AsTYimDLUi2pVwkalSPV3fU8ULyh9drNmzQC46aabgNTeDPDAAw8A8NZbb7lAfcGCBQBcdtllAKy11lpA9Cl/PUdTp6Y0QD/99BMA++yzD1D2+dKercBRfv/0008D/vqzcQ2W2jUYDAaDIQNknZEqstLX9957D4B7770XgOHDh9O7d2/ARz6K4qOIbhTJ5Ofnl2sdWR0U1b/77rsAvPTSS0BKsAFeXCKEzTwU/e67776Aj7KUDl1//fVd+lfsuaJWhyghG8R0rrvuOgDuv/9+ICWB79OnD+BZ0bPPPgvAM888A3hGmi4ciwO6lltuuYW//voLgCeffBKA7bbbDvAMI0qRRlBUJJ/Xunbo0AGA/v37OzHRtGnTADjzzDMB2GyzzQB/n+IW5qULRnRd2i+0xnqe9Wzo76WlpeUYYDYgxqP1PeOMMwCYO3cuAFdddRWQKsPoc7XXTZ48GfACug033BCAbt26AdE8q1o3ZebkC5tvvjkA06dPd+0o+qrMS7169UK3b1UIMvf+/fsDqf0OUpmV4LMm25UBbd481RaazfdN/DurwWAwGAy1GFljpEEm+thjjwFw2223AdC5c2cgFZEpmvniiy+AFAsBX8gO1hGyGTmoTrQqm1cH2aQod8aMGYC/hp49ewKeuYbNkmSH8v8SUelaFi5c6JicIrE420cUYetePvroo4Cvex511FEAXHjhhU6go2vR5KGLL74Y8AxAEXTUwgfdY9V1n3/+eScyat++PRDvWss3VNe64YYbAGjYsCHgswDFxcWuDq0ofZ111gH8fYqbiepaZOegQYMcw2jZsiXg2bPaOVQvk5CqTZs2jnVJeJeN51O2zZw5E4AJEyYAPkt1xBFHAKuukUr4pb+LkR5yyCFAqgYZVaYlOHRj+PDhQEp8JDuPPvpowPtJXG0w2ke05mr/U0Zlq622KvfeGDp0KAAbbLABAI0aNQKyW/83RmowGAwGQwbIGiNVveCpp54CcLJpNaJfeeWVQKo9QExJ39ugQQPAK8EktdbXxo0bZ411iEkmEolyLK4qNTfV53QN06dPB7wqWSrNsOu9slEsQ5GarmH27Nnuz1L2xqlylX98/vnnAAwYMADwUfvtt98OpO71kiVLyvyM7pN8IC62pDVWHfrqq68GoGPHjnTv3h2IX0kMnjGPGTMG8ApiMdEWLVoAsGTJknI+H2W9WYzu999/d8ynqKgI8Pdeay3l+auvvuqeNWUk9tprL8CvvXQMEydOBFIs5aSTTgLgyCOPBLLLqIL1TO0BYpfpWgzZquyb/F6ZpTigtZYCVn4yffp0Z6/28bh1CfLtUaNGlfn3bbbZBkjZpfVW5kojEHUtqrFn81k1RmowGAwGQwbICiPNz8/n+++/B/yAAEUIYhxSo/3666+OIaleoZqpahrqZRs3bhyQUkUqis40kjz77LOBlIJRPXRBxZwYj77m5eW5KFj5dtmhKO6bb74BfHNz2JBtisq1hmJz6bapriHmr9pAVFFlIpFw6/XWW28BvhYnpqG6xbJly1ykqEhZ7F+MVP8fNSNVpPvCCy8AvsF74MCBTiEdtC1oY9iZikQi4Wqjzz33HOBVmKpzaR1Xt35RDBeQT6h+Cf6eaziAVJlvv/22s0sKebHMTp06AZ4ZfvnllwB07drV/f4DDzww69ch+8V8VRvVEAv1XKZn04LsT3VV7YlR+rT8WXZr3xWD22STTdzzKZ1CZSwukUi4a8iqKjaQDVKdXF0LYvhz5851tfPffvsN8Pd8k002AcLRVBgjNRgMBoMhA2TESNOjJ/XPiVVKtavIS4zjpZdecuxJdRExJtUvVdtRNPTQQw+5qRQ1zdErOtpzzz2BVF1LqkvVutTbJQVpuir07rvvBlIKzXQ7VL9T7W///fd3/x9HHUFR8ooVK7jgggsAH4mJjSuCj3KAuuz6/fffAT/KUGxE0XEymXQTVpSR+OijjwBfh1YNTNcV1VpLiavJS2I5u+22W4W9jFIXqv6vGmBYSCQSTsH4wQcfAL43dFWKy6AaXdC16rnRs5pIJEKpUcsXg4PUNYlM63fOOec4/UWwl1H34IcffgD8dVanX7yqSCQSbo3kj1oPdSjInnR1qJiVanxi3qqnap3DhNZaTFT6FfmLsiv9+/dnhx12ACpWuAa1Gclk0vXRytezwUxV11TmU36x0UYbAX7C3Pz5892/6frUR//zzz8D4fhDRi9S3ZDRo0fz+uuvA76gqxME9DJSird9+/YVikZUpN9xxx0Bn4o855xzOPbYYwHc2LvqSpf1UKkVpG/fvs4J1MJy1113AX7WZLpwSC/Z4IatG6zBE0o7bbjhhqFKxLWGahWRQEDtRpMnT3YOpM1c6RDZqAdIgqUw7dU6aUzhfffdB+D8RuPUfvnlF5fK1ZorXa2NSy/aqAIVbW5KL2qzv/TSSwHvp+DTimqHUYCl8oH8pHnz5qGkedM3eL1oNP5PQo30ubl6BjSP9PHHHwf8pqrfpfNUTzvtNHcvs7X+iUTCBR56SWresgItpUmPO+449/ny12+//RbwAY6Cer18O3fu7Hw8WwKTZDLp1lO2HX744QBsscUWQNkUova44OAOEQyJefQ7w2qfSk+9vvHGG4APBATtD126dCnno1p72anr0X48YsQIN6f55ptvBvyznQmCQ0YUiOt+6jO22247t+46R1bXoBd7GPuGpXYNBoPBYMgAGTFSUeQvvvjCFXaVjpU4KJijFmFmAAAgAElEQVTKWt0pEookFEkril+5cmXWCsSKYvfYYw83DP3GG28E4MMPPwS8bFrMA3zkrmsW0xY7CqYPNt1001AZXrD95ZhjjgH8eZJjxoxxY7OU6pNwY+DAgYA/BeG4444LzU7ZqqhQ6dD333+/zGdrXZcuXeqYRHq6F7yQSy0MyohE1XKidJLEOxphmEwmna9IaKK0ktiJBBwqBSjNGgbEOMRqJNBYFQMW2xZDUjbg+OOPX+X/d+jQwZ2xmq11z8vLc+lYMXqxaGVaxNgWL17shqqINb/88ssA/Pjjj4DfPy688EIgxUjDEJjo+RY7UiZtVeddiknJD3TIhEZJyqfCHnSQn5/vSmdqvZE4TSMktU80bNiw3BhGrb3uk7IBSuf+8ssvrpynddHoxEygNVUGTqLF4D5Yt25d9+zJNu2J2mvCOMnIGKnBYDAYDBmgRoxU7Ozvv/8GUoxUIh4V2pUzr04dSAxDg501yDyZTLqILltYtmyZk0nfcsstQKpuCj5qVEuLbADPihTla7CA/l8iq7Zt27rvDXOEXXB9NaKuY8eOjtF9/PHHgK8ZKXq84447AN/2E+ZYMkXaGgf54IMPAr5Oozro4MGDXV1R0PqpTqfIP+zRgMERcGp3kY8r27Js2TLXOiCbVAMWW5IITXX3sNY5mUy6VgDV38RANMYyvcapaxQj1JmvGrguP1f9ce7cuVkXayQSCSdCE5vW3jJ48GDAj60bPXq0q52L3es6Tz31VMAPchGrzc/PD5Xp6XdX9Bl5eXluT9PhEtofZav2irBHS9apU8cdFqIsonQjYv3Krr399tsu06L1F+vXHiJ7xRgLCwtdFkPZumwO4Jd/VCQ0A++zug49r9r/wshgGSM1GAwGgyEDZMRI9eYfOnSoq0coSq+KqlbRhSJkKcCknlUe/LzzznNMJpssRL9LkYo+Q83HauhOR3DUnaJzRaNqqfniiy+c0jjKoepa9xUrVrioTXVb1QZ0DbNmzQLKDq0OWwkbPLpJ9ROtY/fu3R1zGjt2LJAa8Qa44/f0vWEfOi3/FFuWslUD1OW3EydOdC06BxxwAOAPS5bKXMpOqR3DYkilpaVOn9CjRw8A7rzzTsDXdHv16gWkInPZIZavWqiGToj1iVE1atQo67aXlpa6epqeRbEJZXjSWZ8ySVJNq51LrRq6L3EcYbcq5Ofnu5qolN9iSRqSEVWdf8WKFey9996AV8yLVeq50x6wePHicsfo6dnT2mrPlN5iiy22cHVfHdeXPiQmW1hdpjPYlqX9I8y9zRipwWAwGAwZoEaMVG98Reb//POPGwlYUZN2ekQjRqtIceTIkYCvVWoMnwYKnHfeeY5FhRFdBkcCrg76/KDiVWpHRXdRR8GKthT95eXlufqcas3BJvsuXboAvt4Q5QCJYF1J/rFo0SKX6VCtT/2uUjZGFb1rPcSSVItTr6Wi8okTJzrmNmjQIMBH95dccglAqP4bhNZSgxhUC9P4TtW3evbs6TJIUlOr11isVepi+cjzzz/v1l/q3Uz1C8lk0tXpVOfU+E79brGKxo0bO9W2/Deo3g47U1FVpB9CLaW8mP0pp5wC+OuLyubly5e7AxbEjqWhCDLHunXruh7p9HGp4NmmVOrSZjRu3Ng9N3FkBPLz852mQVkNdS+ECWOkBoPBYDBkgBoxUkUcilbWW28914tUERSJ/fnnn46BinmqvqTBzRrHp2lIDRs2jPzw5oqgyEwRuiJoTWLR6K8FCxZEMoA6qKDWaLXRo0e7fiqtvaJe9WKprq26XRyRvNiEWNJ5553njqZTf+9BBx0ERH+AtyJpsTKxy3vvvRfwKt68vDznq5oKo2HawZpSFNBnadqL6rVSSj/xxBNASouguql8Vex12223BXxdWqrjFStWuHumr5kimUy6z5dyXmw6qKPIy8srN9koF46uWxW0Pp999pmblqaJb7vuuisQT+ZKe4aOsdRkN40r1JpvueWW7jBs6VeaNWsG+L1f+6D2xaVLl8Z2xBqkrk/vFekwlD0M88AIY6QGg8FgMGSAGoWUiqKknrvuuuvckWgVRd7KV3/77bdORapIX7XQffbZB/BHsKUPYM81yDaxaNmuQert27ePhOEp+lP9TrW5GTNmuN48qRmlsBO7UJ9dHOurqFh12xtuuAFIZSnUW3fCCScA/hrDPoKsImh9pHaUMjcdsjFdNZ3+NUqk1+bA+4bYnnx14sSJZfr/wPuvvmqCV7ovh8E49Dtluwanrwq5uB+kQ9egNXvqqafcn3Ughu5JGIrWyhA8qEDz0eXfQmlpqXvmpFcIHgCfK/Vo7SfTp093vel6jygzE+b+kVFqV8Z37969UsGOGo5btWrlTjrQzwcbdnM1VZOOYIr34osvBvxDVLdu3UiuI7gBKXXUoUMHly6VkEPpGKVygw9FlAgeGKCG765du7oRZQrOcuVhjfPlWBPIJ4KCLrWL7LbbbuVOUwoGrwp0ojonM860YLag50vlnvfee8+190iglQs+nWsvw0ygoODDDz904wLPOeccwI+5DPM6LbVrMBgMBkMGyEgtEJQ5rw6KGNKb/nM5dVtVVDSyKuo0ZHBNmzZtWu48wCADjTP61z1XhK5h2OnnXa4JkXIuIMgmlSmpSsYkKia6JkBZFg0+eeaZZ4DU4BMNmdGIyLBHAf5fg/aK448/npNOOgkg0n3EGKnBYDAYDBkgO/r1amBNqIGsCnEJYSrCypUrYx+NVhVUJ6thMOQygqI4ieaOPvrockesGcJBMpmMRzwZ+ScaDAaDwbAGIVEdhphIJGYDU8Mzp0Zok0wmKzwl2WzOGlZrM9ROu2ujzVA77Tabswbzj+hQ6VpDNV+kBoPBYDAYysJSuwaDwWAwZAB7kRoMBoPBkAHsRWowGAwGQwawF6nBYDAYDBnAXqQGg8FgMGQAe5EaDAaDwZABqjXZqKioKNmmTZuwbKkRxo0bN2d1fT611WYdeZYrGD9+/GptBiguLg7Vbs0yrc6s4MrWOmyba4LKbIaUj+iIs1zBhAkT1rhnsTb7R67ZXdkeUht9WqjWi7RNmzbuaKBcQaNGjVbbwFsbbS4pKXGnvOcKmjZtWmmjdElJCZ999lloNug4pOoMo65fv36laz1ixIgsWJc9NGzYsNK1bt26NR9//HEU5lQZRUVFa+SzWBv9o6SkhGHDhkVgTdXRpEmT1drdunVrhgwZEpU5VUJxcXGVBkREPmvXYKgq0k8MAnj11VcBaNGiBeDP1YxqprDsCJ6jm0wmy81ZtUEnhtVBvi0fkt/UhvnYhvKwGqnBYDAYDBnAGKkhVgRPf6lTp46L0v/55x8Arr/+egC++OILAO6++27AR/NRRfFKJcuuefPmuf9be+21AVhnnXUAn4bWz8jGKM/31GeJ/QTPrK0O9Dtq+vOGFAoKUlvu3LlzAZg9ezYATZo0AaC4uDgew/DPU506ddzfdW6q3fPVwxipwWAwGAwZIGuMVBFr8GtQaQm+HqCz+XLlLM8gW0j/e3WUolGisLCwzNd01iGWV5nNcV5TcF0LCgr4448/ALjooosA+PLLLwG47777ANh+++2BqomNaoqCggLnl2IRH330EQA333xzGbsKCgrYYostANhvv/0AOOKIIwDYbLPNAGjUqBEQTWQvv9Vn/fLLLwA0btwY8KynKs+dfteff/4JpDIHqlEbqg7thz/++CMA55xzDoATFT7wwAMA9OrVCwjXtwXdW+0dCxcuBHAipblz57L33nsDsN566wHkLENNf+/ItihtzMqLNJlM8s033wAwePBgAMaNGwfAr7/+Cvh0AcB2220HwBlnnAHAJptsAsR3uHNQPLJkyRLAO01hYSENGjQo8zNROPqqIOfX5v7OO+8A8NxzzwF+s+zUqROHH344APXq1Svzs4KuV4jjhSobZOOCBQu49NJLARg5ciQA999/PwAHHngg4O9LGNDLZdCgQay//voAbL311gB8/fXXgN94JNVfsGABU6ZMAeDOO+8EvDDq+OOPB/zGqRRwmA+57vOzzz4LwEMPPQRA27ZtAR+QrLXWWpXec90f3YNZs2Zx0003Ad7XMg2EE4lEmdRx+jUERVy5EnRXB+nP3QsvvAD4F+huu+0GeN+O4hnUPdV++9ZbbwHw6KOPAn7vXr58uRP0bbDBBgCcfvrpAGy11Vbue+KA1lTvFb1/xo0b5w5RVxAbFAmuqrwSJHfVhaV2DQaDwWDIABkxUgkqhg4dyrnnngvgmJuK52rAFuusU6cON9xwAwAbb7wx4CPlqBlpUKzy2GOPAfD4448D8O233wIp5iF2p4hMbCRqmxWBjRkzBvDpT6XeFFE988wzfPDBB4C/Lol0pk+fDsA222wDwEknnQSk1iNqVhqMFu+66y7ee+89AO655x4ADj74YMBnCsKAPv/ff/8F4MEHH2TzzTcHcAzs1FNPBaBPnz6AF4wsX77cCZDGjh0LeGaqNLAyM7fffjsADRs2DGWt69at65joddddB3hxlFLmSt0deuihFbJ7PdsSeIlJ/fvvvxx33HGAZ1M1ZYny5SVLljj/lT36qv2kqKgISK2bfEafq2cwV9lqYWGhy648/fTTgPd7pU41PGHRokWh26Ns1vPPPw/AJZdcUsaGzp07A3Dssce6vVF+e+GFFwLw5JNPAl5cF9XaB7NoYtEPP/wwkHrOunTpAsATTzwB4LJFM2bMADzrl48lk0nWXXddANq1awdUn2kbIzUYDAaDIQNkxEj11t54441dsVy5c0WQQcHGqFGjGDhwIOBFI3HVRmWT6rqXX345AL179wbgzDPPBFJ1IdWV3n77bQDef/99AFdHi+IaEomEi2QnT57sbANo1aoVABdccIGzR7Vo3YOXX34ZgJ9//hnwTO/EE08M3faKIOYzfPhwIMUEDz30UAC6desGlI0co0IymSxXx5RgSEivm+u+7LTTTkCKOQH07dsX8IyuY8eOQEofsHjx4jI/mwn0OxYtWsSbb77p/gw+ilfNaNNNNwVW7bOqVSqKv+aaawCYOXMmAPvss4+rGdeUhegzXnvtNSD1TIktyGatjTJbes423HBDl+WS6KlDhw4ANG/evMx1xS0MTK/zKjs0bdo0IHUdAP/5z3+AcOv+6cjPz+eHH34AoH///oBnxdrj5NcFBQVltC3ga/3jx48H4KCDDgLCt18+/PfffwOegar+n/6emTBhAuD3b+13P/30E+AzkPKxlStXuqyosnfKoFbZvupekMFgMBgMBo+MGKne7C1btixXM1Rkqejzt99+A6Bfv36cf/75AOy+++5AuLWvipBIJJz93333HQBnn3024GtL6UpC1Q2kruvevTuAq+eJrYRZK8jPz2f06NGAr73JxmOOOQaAs846C0jdB9nyv//9D/A1PbFARflBxWQUUIS5YMECwNczkskkF198MZBSlUK0ysB0FjNnzhzA102lLF5dK5S+96ijjgJ8Dalfv34ALhtz4IEHuvXPhoJXtr344otOEao1FgNV1kitOukKRfnA/PnzAZzmQS0+yjT169fPscSa3hcxNWkREokE++yzD+DXQraLTUyaNAlIZbT0ubJftWxlY1S7lZ/HxUx1nbNmzXLKWPm0skG6F1Ex0mQy6e6f7Pvrr7/KfI9sXLx4cbk2Rq2pMi5R1UallP/+++8Bz56DNdM99tjDMW49a7JZGUi9o/T3Jk2aOL+XxkEMtaowRmowGAwGQwbIiJGmq+eC/TdBFeR5550HwEYbbeSYnyLL4ODmKJBMJt3niV0qcgk2HScSCVf7uvHGGwHPXqWAVcQe5jXk5eU59qyalfq7FOFKoZlIJJxKU7UoMX9FZKqhqg5S0x6qmkCRroYFqIbYs2dPx6CCY/XCZBb63VqLFi1a8NJLLwGeTapuUhU79D1SEH7++ecA3HLLLe7vUr/qGckEWqN//vnH3Wcxi1133RXwUbZ8dFUDRyZOnFjmq5iulMs77bRTxn6i+6oa3TrrrOP8OMjOtTfoM6dNm+b0AXoW1OMqRb3UqDvvvHOZn40a8qXXX3/dDWIQkzvssMOA6JXGyWTSDeTQ+l9xxRWAV+Tq61ZbbeX2aDFq1afVXxqVvkV2aJ9VXffDDz8E/H6y6667ctpppwGpdQc/ylO+JF/T/dlqq60cS9czUl2fMUZqMBgMBkMGCG1ovSKEO+64A8Cd6XfJJZc45Zf6ltSjqTFUQtjRmqJw1aoqGuqdfkyWWJ4isSiHkKd/nuxRfUiKTLGQZcuWOSWs6kz62S233BLwasc4xx8GJ9cccsghLjOgkWXyJUWQYagy9btU6952221dz5/O0FxVbbEyKLux1157Ab6/9Ntvv3XMMZuMe1X1bili1Ues+7711ls7xil2pwMCVLsWg5IqPJlMus+oaW1X17nDDjsAqXtfUY1QTEQ93cXFxe55/eqrrwCvMtUAeCnZ46qNivlIJzJy5Eh3rzVCUs9g1KP20jNxPXv2BPz6aV/WXr3//vs79jZo0CDAZyaizmLJ5mbNmgFeg6B+evnrgAEDOOCAAwDfH6seUfmS1N7pfcjBY+yq++4J7UUqJ65fvz7gRRevvfaae2F++umnAFx11VWAT81cdtllgL/BYb9Qq+LMejiUytULSzcpqhRNcNyfNnmlt5RyGTp0qGtW1iall8SVV14J+JdwVEKHdMh+pYw22mgjIDV2TiknHVyttgalbPbYY48yvyOMDXPdddd1a63gqSZBk3yrffv2gN9Av/76axcoaGxgJtehe9i5c2cnjNPzJfGRNkP57CabbOL+LBGHUroSd+j3Snx02GGHuZYHPdM1tXt1aUF9/lNPPQXgxkYWFhY6kYjaF/TsadPXoBd9X1RiNfmHvr7xxhtAqr1OvrTnnnsC0LRpUyCeIRK6X7JTbWZKaz744INAavyoSkhqedL4vTgEiuDvuXxQ91zlq1deecX9WQGVhknIL/TcZROW2jUYDAaDIQOExkgVbarVRU3/BQUFbliDJMdqghUT0aAGNSvHJRYQ0k8kGTVqFACnnHIK4KPyKFjdihUrXMuQIjJFvUq5pLcPKAoOStejZtHpUBSs9RJL0t8vu+wy1yolZvXZZ58BfjiAhEktW7YEsit40O/acsstnbAieKhBdaAUmAZ5SF7fvXv3cif2ZALZvdFGG7nMjlL6v//+O+DtVwpUbAPKnwQSTJ+rTLBw4UKX9ZAfhZGe1O8UA5IgpmHDhi5NqkyFRCXyEwkCJRJr27ZtJL4ulqZxkErjz507l3333ReAI488EohGQFcZggcBBA81mD17NkOGDAFg6tSpAJx88smAzyLqusT6w7qeik4T23bbbQFfduncuTMDBgwA/HjLa6+9FkiNTQ0LxkgNBoPBYMgAoTFSQdGOWGgymXTsQ5JjsbtHHnkE8JGDJOJxDFNPR506dXjllVcAP5rvxRdfBKIVC5SWljoGrDqnagYa1KC60JZbbunqXpJ/y1bVCKIWSkHZc0fTbVLEu/nmm7tIXi1HGt2o0XfpLT7ZRjqz0xg3ta5osPrqjg9TxCxmp6yLbFedulu3bk7Ik82My9KlS91wA9XNNcRe16HsSkFBgYv0dS1iForwdaCBfGivvfZyg73D9H3Zo5YjHbBQr149Z6PWWENSdJSgRFVqUfvf//5X42HkVYH8UL9bgwBUb958883LCV/iGou6KgQPjtA4w0mTJjnBnbJZEqPpeECN6lOGLIz1zcvLc1kqZbAk3pN/SLNy4IEHuoyFGKmOP9SIQD3X2bwHxkgNBoPBYMgAoTNSYVXRq/5NDFWRkZRYwWg5aijiHTNmjGOAd911F+AVr9lopq8OtFYayajmcyk0xfS22WYbx+QUVWq94xjJGERwfJ0YdZ8+fVwjvQ4GEJuT4lGq7zAYkRjz2muv7WTyYjpax/SDAdKvBTxbVr1OY/B0n4499lgglW0Ju/a/yy67AH4Upw5slop3xIgRjqVKIS99gvxdNSiNl2zSpEkkbErPvuyQ2rlHjx5uP9DzqWdQowE1tFxjJ0eMGOFU02EwJtXBxZZUY9SzeMIJJzjfjesg7NVBa61nUOy5Z8+ebqCIfFz3QZqXW2+9FcBlQQoLC7OePVxrrbXcXqaRrMpQaKiJ9ox0PYvWX76r51hdIdmsUxsjNRgMBoMhA0TGSFcFRTmqI6kOo4ZaRRRRq3aD4w0vuugi1zyu2kDcrE5sTF81Bk4oLS0t00Sfjjhqo0GIVUj9pxpI37593XB1DQnQ+EMpN8WewmRGy5cvd36o4+dUc1QEr9rc5MmTy9VjpM5VNKxajg4HDzPLovut9dFXRfFibjfddJNrvtczph5dKTiVAVGva1S1vWDdToNdXnnlFfd/YoI6Wiu4j6jGvvvuu4eyh2h/+uijjwA/Wk9Zif333x9I7Rm633Ef7bYqaD3VkaB73atXr3KHp0spL4avoRhh7inJZNLda33VYHrVw3XQeCKRcHuzvlc6EtVIgyM0jZEaDAaDwRAzYmWkinY0tUTTMxRJRj0+S5BCTfWj8ePHuwk8qsvE3dsaRNCeevXqOQYSHP6eC5BNGm0otnfzzTe7SLFPnz6AH6sW7HEME8uXL3cHjOtoOkW/OuZNCsbly5e7cXCKgtWDKp/WYfGq5cRRK9OaiyX/8ccfbvJYr169gFQNEsrXj6JmUrJVPYDKuAwePNitsaYDSU0tyO+VRWrXrl0o6y1GqrVR/6jsE7svLi6ObS+rCmS/Dh1XJqZ169YuK6dnT5kX9XJfdNFFgGd3YTybS5cudT3B6iuW5kCdCZpilJ+fX67fW9en94qU89nMKhojNRgMBoMhA0TOSPPy8lzEpghfg4c1pUfH/EQdtSsKF7tTP1jnzp3dkWO5qLpbFZLJpGMbwUN4c4mZqganvkUp66B8jS+u3jv1I6oXWtNedOh18+bNXRSv/jbVIaWuVu9pnJmM4OSd4cOHu15u2a8+5bg1AMFj7Y444gjADytP/56gPwcHkIf9zAbnzupYRtXD0w+9yEUE9z3VfHfZZRe3h2h61Lvvvgt4tb30C2FmLkpLS90sbh3HqalnI0eOBGDKlClASq+g69GAe03iUoYpjCl0ob9IdVFKfY0aNcoJMjQcWWc0Snof12ajVI3SBbpJzzzzjHOoOAa81wTLly93TeiSsEs0ozNAlTLNBWjTkzAgF6BNQS/QM888E0i1M4AXtRQWFro0o4Qa8nu9/IMtXnFAa6zRen379nVBa9QD3qsK3QPZlUv26Z4qhSxCoGBE6c5cTuuCX2O1ZilA7N+/vxMsas/QgHuNClQrWthBroIjvUdUElLpRCno9IH0KtHpmdT9CkPoZ6ldg8FgMBgyQOiMNL3BHVJRwpw5cwCfxtP5iLki4FHUq/aG9u3bx57qqi5WrlzpiuoSxyjNqGESuTSmLJcRFGtpXZUWhfIj9oLIhXS6nkW1DynVBeXbqQyVQ+upwyHEkmrbWmofELvT0Yzp9kvAIz8OtsVEjWCGQnbpPZOOKLJcxkgNBoPBYMgAkYmNFLnsvvvu7ugd5axzpe4hG3UArEbBLV26NKfFAhVB66phAGrXEPPPlXWvLQgKKuIaXZkpggMbDJkhWMetrVgdk851X4+rTUswRmowGAwGQwZIVOcNnkgkZgNTwzOnRmiTTCabV/SfZnPWsFqboXbaXRtthtppt9mcNZh/RIdK1xqq+SI1GAwGg8FQFpbaNRgMBoMhA9iL1GAwGAyGDGAvUoPBYDAYMoC9SA0Gg8FgyAD2IjUYDAaDIQNUayBDcXFxsqSkJCxbaoRx48bNWZ08uTbaXFRUlBWbg+fyZdJUPX78+NXaDP+31zqbWJPXWue05gqqYrNGa+YKJkyYUKl/ZMuvNRpVe4kGwdek26Myv66NPi1U60VaUlLCp59+WnOrQkCDBg1W23dUUlLCiBEjojKnSmjYsGGlNg8dOjTjz9GJNYJmTtbkIWjatGml/V0lJSV89tln1f7dYaJ+/fqVrvWwYcMisqZqaNKkSZXWurY9i23atHFzXHMFjRo1Wq3NrVu3dseK5QqaN29eJf/I1K8TiQTfffcd4PcSHWdWkznClfl1bfRpIfLzSGsDNAB5Vecd5nrfrWxdunQpt99+O+Cd/owzzgD80PVcH/ula9ERX7qOXLe7NiN4tmauDV5Pfxb1Z32tKAOTa9eQ69B6zps3j/PPPx+Aq666Cig/mN+QgtVIDQaDwWDIAMZISR3MDD6iVSRbp04dIDXkXf+mw3o1cD/XBn+LUfz888/ccMMNgD94+LTTTgNy40iv1UH2aQj4tGnTAH8gte5BrmcHahPk+3PnzgX82jZr1qzM98U2FPz/25efn+9s0CHPOtT5n3/+Abzf6LD15s2b58xzqusIsmcxvPT11fdof4rqmEnte6+99po7Im7PPfcE/L5Xm6E1Vqarbt265fbz6u6RxkgNBoPBYMgAoTHSYH1Raq+8vLxyope4GJIivsmTJwPwxhtvAD7qWn/99QGYOXOmU69tsMEGgI/Q9PdcqdvJjgceeMAxuOuuuw6A4uJiIPePe1IEPnr0aACOO+44AO68804ADjvsMGDNiI7jhp49ReJnnXUW4A9/v/rqq4H4/Du95g/w8ccfO7+YMmUKAL/99hsAP/zwAwALFy4EYJdddgFSz8KGG24IxJNBSiQSLlMkFj1z5kzA70Hrrrsu4Nlgfn6++14JtNq3bx+qnbJlwYIFQIqR6lnL9SxWdSAm+scffwDwwQcfsM8++wApwRNU399De5HqpugBGDBgAABTp051KccmTZoA5dNFQbFPWNDnPP300wC8/PLLADRo0ADwKaNEIuEWVovfq1cvAO6++24g/hepnENBwfDhw11Kd6eddgJyLw29KuTn57uN8PHHHwe82liBQdxrvSpoowyWB4I+nGu2K3X32GOPATBkyBDAi0riThLCXf0AACAASURBVJ8rqPrmm28AuOKKK9wLUyl+fdXLSM/1+PHj3VcFBlE+A7Lj33//5a677gJSzyX4NPTaa68N+ADmqKOOAuC7777jvvvuA3BBQKdOnUK1V2v91FNPATBjxgxnT64H31WBgpT58+cDcM455wDw4YcfMmjQIKDmxMhSuwaDwWAwZIDQGenff/8NwHPPPQekUhqKBCRkUKFdEZFSC4Ki5rBs3HXXXQEfjRx//PGAj8IKCwuZOjXVTvSf//wHiK7wX1Vo7cRIFy1aRJ8+fQAfidWGqDIvL485c+YAMGrUKMDfl+222w7IHWYttlZYWMi8efMA+PPPPwFo3Lgx4BmH2Il8vrS01EW9KhtEnT4rKChg1qxZALz66quAz8Z07doV8Ew7rjXX52qQQ69evZw/r7POOkD5dNwpp5wC+CxNu3btYvF97S/Tp0/n0UcfBbwvH3300QDsvvvuAGy77bZAKs0IcNNNN7lUbu/evQH/HIdl5+zZswF45plnADj11FMdy8+1/a46kA9rb7zyyisBXH/wGWec4da/pm09xkgNBoPBYMgAWWekQWmxpgpJENCyZUtatGhR5nsVib/11luAFw2oXSMsKNrda6+9Vmm7Ipk6derw+eefl7mOe++9N1Tbqor0OgzgJiIlEolaVRtNb6r//vvvAR9B7rHHHoDPTMQVHQf9VfaMGjWKvn37Aqm2I/BsqaioCPBRvybDtGnTxj0HPXr0KPP7w0b6oAv59eDBgwHo3r07AB07dgS878RVKxXL1BCR8847r9z3yB8kqlP2aO+99wZSwqm4REaQqjWK6cj+//73vwAuI/Dss88CcPPNNwNw+OGHc+211wI+2xTWEATtc19++SXgmenhhx8ee408E4jBax9Rhk516ssuuwyAvn37uslN1v5iMBgMBkMMyDojVXSjSEvMTRH6jTfe6OpEeuunK/IALrzwQsDXl8KKJtNrXOlQFJxe45DqeJtttgFg6623LvO9cUHr/fvvvwNeebzjjjuWG/dWG7B8+XJefPFFwN93SfDjjo7lr1rXN998E4ALLrjARfHyXbHob7/9tsxXfV/r1q2Je0D30qVLy81jPeSQQ4DohwBUBt379JYnZY40ROK9994DvN+ofa2wsDCWGml6647WU1mMH3/8EfB73ocffgh41nTWWWeFzkSDdmrv6Ny5M5Cq51bUYhYczxj3PpgOrZt8+4ILLgB8pvPUU08FPCMtLCysMRMVjJEaDAaDwZABss5IFQ3cf//9AHz11VcAHHzwwYCPdsAzvpdeegnw9aQDDjgAiI6BVPQ5GiLx5JNPurqLBr9LlZkrw5tVI9XXnXfeudyRRxX1NsYJ+UB6PUPR+SabbALEz0j1uepXlG+LfR588MHcdNNNgLdZay1mGvxd6deSaTRcXehzFi9ezJgxYwCvJpVSNG6GUdFapK+bvueFF14APONQD6x6M+Ma3CH71LcI8P777wO4AyU0mEG1UXUFJJPJyJio+rZ1ctPFF18MlB1jqO/V/q5hEWL6UnvHvbfUrVvX1UQvueQSwGeDTj75ZAA3x0D74/LlyzN+9oyRGgwGg8GQAbLGSBW9KPrSOXaaXqS+qSZNmpQbkP3xxx8Dnnmst956QHyRpNiR1KMvvviimxKUHjGmf40bqjNrzTp27OiYzsSJEwFfM9Iw76gmSK0KqjNOnz4dgLFjxwKpAfXqxdxvv/0Az/7jYkmqxWmNL7roIgC22GILAG677TbHRDWFqTosM+r+UT1/EydOZMKECYDvZ1RWKC6/1lrr89N7uSHlN1ovPZ8PPvgg4OuP6lNv164dEF+dN70HV5kiTVHTlCL9ffvtt3ffC9Gsv/Y59RDL3gMPPBBI7SX6N/m1mLQ6LHR/NIVphx12iCVLJ7/5+uuvOffccwG/pxxxxBEA9OvXD/D7iWzPxvOXtRdpcESdZPUyUvLuadOmuQEIGrenoQ0S8ARfUlGnvOQ8SjHOnDnTSdElmsoVEYZs/uuvv4CUiAVS4qP9998f8AIXraf+XWcMxpmm1lprKMEXX3zh0kRHHnkk4Fsf9DBHjeA8WqU/lUrca6+9nKChW7dugPeTuFOk6QgKQ5599lk3qk6zozWPWfcjKmhT//XXXwE/FED7iV6K+++/v0tDq91FP6OS0EEHHQSs+kSVKBAkFePHj3e+c9JJJwHedvl2nPuJWhQ1RlEB94oVK1xgrrSo7odm0yoQ0B4S9VorPSth0dlnn+0CLImKNIBBz2Q2X6CCpXYNBoPBYMgAWWOkiv7UZH7MMccAfjSgBgUMHjzYRb1BJiQ2pb9HnfJSVPzKK68AcMsttwApltGlSxegfDQTtDE9XRpl+lcZAZ3dedVVV7l0tCT2En4pPaO0u1IeUUL3WKPfNOhiyJAhzg/EQuIeKKF7royJTglSyvyTTz5xa6hUqQ4zUEoyF0oAQUY6depU5zd6FuNAQUGBGzCvwRZff/014LMQWvOBAwc6Rjpy5EgAWrVqBXiRjPaXqDMsWkvZLCY0cOBAd+CCsix69qJm/lDeD1Ri0zjAdKiMMWnSJAAeeughIFXOAD9OVYNGws7A6DnSXq3nTfd+ypQpThDav39/wPt2mKI+Y6QGg8FgMGSArDFSve0lFJLEWOPPlLdetGiRi8J0tJB+VkMcFPlHFVEqulEUrOhGxxf179/f1e1U/5BkXDaKtajW0bBhwzJnsKZ/TzahCE0CIuGcc87h9NNPL/N/Yn9ipM8//zzgG5br1asX+Zg6rZ/Yxbx589zQ8TjPkExHsEYqQY4Gu3ft2tVdh2pGqlkrQ5MLbVLB61iyZAlbbrkl4MdkxjESsLCw0I0oVGbiySefBFLPEcAdd9wBpAaN63t0PRIpSsATdZuXnm+1hOgMV+lCmjdv7tiqvjfODEVwEI0Gg2j/lWhrxIgRrl1H7TliooJ0FrqusPw8aLPq4qqDStzau3dvrrnmGgA39i+MmmgQxkgNBoPBYMgAWWOkwVYKRShSOOprnTp13Cgv1RLEiBQVRzXOS1GiVK2XXnop4FmlmuwbNmzo2Kok1Tq1Xt+ro79Ub9hss80cOz/22GMBX/MLAzoGSEMD3nvvPTfuTYc166BsZQQkcw8ObogCUuuqIV219Dp16jgFqXwoSkaafnBBcHSkbNZwDikY3333XWe/fDhXGtShfEZEAyW+++47zjzzTMC38qhNIwqk1/Xlo7vssguQGpgOfsC4fDYvL6+cPkH7iZ6Bnj17lvmcsO5B0I4nnngCwB2ZJhXxAQcc4Bi26re5oOaWDcqaDBw4EPDHiz333HOuFU31Rq3xiSeeCPj9Tv4eFuQrUpmLIau2fvbZZwNw7bXXlhm0ANFobYyRGgwGg8GQAUI72FtRYJBNLF++3Kli1a+kCDLsPHtFNj711FOAP0pKB0ir0funn35ykZAiNKnUdA2qz4ihzp8/nylTpgBewakhydmE1qply5aAr0k/+eSTrqdRjFu1Ug3gl7JaTCvKKFlRonqIpYBt1aqVq5HHURtVNDt06FDnF/JL1WWUfdBh3v/++68bRyfFoOpMucA8ZL/W+vXXXwdSz6KU3XEMdRfjHzVqlGMWO+64I+Dr+NJRKHPRqlUr1wetQS6rGtoA4fuPWJJsf/jhhwE/olC1ujvuuMP1aOprHOsdhHpEe/XqBfg6o5S4+fn5Tlch35faWKxbTFBK6rD2bu0XYs2qP4sZX3755UAqoxX1yE0wRmowGAwGQ0YIjZEGoah45syZTgmmUU6qJUYZpSUSCfd5GtYs9a4Ulz/99BOQirY0wkvRsEbCKfoNjjZLJpOOjYjNiu1kE8GB6uoZ3WabbVwdV1G+Jr7IdkWPucCaZEunTp1cHSmO+qKi2bZt27pMiXrVNt54Y8DfR43Va9u2rVMIxlHXrSqkNF+wYAGQYs1bbbUVEK8PJBIJxx4eeeQRwLMlPaOqN/br18/pLdQzLT9Jn8iT/u9h2SzbVP/UuEsxfmWCxo4d646TzIWauaB7ruMqVTuXn+Tn5zuWrzXVfdFeqcxLmFnEgoICN2VOvf3ah1UrFVNetmxZ5PMHwBipwWAwGAwZITJGqihh1qxZjj3pkGyxuigZaTKZdCxSc3S7d+8O+Hy/GMg666xTjmkEI/hgRJZIJNzPaJ5mmNFosMexd+/e7pBg2abvyYX6jKB7IJbXtGnTWCJKQWtVVFTEvvvuC/jot6LvLS0tdf6QC+w+CPmdWHPbtm2BVN1rxowZgM8KRQn5YYcOHVytVnVPPTNS9Pfu3RtITd+RDkETjYSo+0f1PKlHXoxYDO/8888HUocv7LzzzkBuPXvBCUf6+6qmXOn5DKpzw2b9kGLBmqikNZbOQ7qPKBW6q0Lkqd1vvvnGpQs0RDiuZnU5kNJbShll48UT99mZuTJUvyIEB3iMGzcO8JtQXEhv45If5MIwhUwgP9eYugceeABItZQoJRbHNcoHWrRowWOPPQb4sooCLA0LULCdfiJU3PdFNql0ItuCIrWePXvGGhxWF7mUfobUXqZ9QQMYVJ7Smse9vpbaNRgMBoMhA0TGSBXlrLvuui6qkLQ6bmGGGGcupV3WdKQPPgAfYZaWlsbONNY0BI8jFAtNJBKxHTWWjpUrVzqBmbJUgvaGuPeIIJLJpFtPlYYEral8e+XKlTmfIcpFyCfr1avnhl0IWs+4mahgjNRgMBgMhgwQGSNNl7GrDUNjv4LFbsP/HSjqtGxA+NBa5yLjr8316IrYsvl09pDrfmGM1GAwGAyGDJCoTm0kkUjMBqaGZ06N0CaZTDav6D/N5qxhtTZD7bS7NtoMtdNuszlrMP+IDpWuNVTzRWowGAwGg6EsLLVrMBgMBkMGsBepwWAwGAwZwF6kBoPBYDBkAHuRGgwGg8GQAexFajAYDAZDBqjWQIbi4uKkhkjnCsaNGzdndfJkszk7qMxmgKKiomTr1q2jMqlKmDBhwhq71rlm9/jx42Ndaw10CZ5qsjqsqc9idezWcH0h/UzlbGJNXWuo5ou0pKSETz/9tOZWhYAGDRqstu+opKSEESNGRGVOldCwYcM1zmaA1q1buwN4cwUtWrSodK11sHuuoH79+pWudUlJCcOGDYvAmqqjSZMmsfi1NnwdNq0Zt5qctroXwpr6LFbFbr1AdaylAhDNsV2xYkVWX6ZVWeva9n4RIhsRaIgWiUTCbShB6OHItUHgawJ0tFaujzRbk1CvXj0AhgwZAsD48eMBOOmkkwBo2LBhzhwNppeX/KQirFy5MrSzbfXZs2fPBuCZZ54B4J9//gHgkEMOAaBdu3ZuD8mV9asOapKhqCmsRmowGAwGQwYIjZEGj25SJFZYWOgiIqUQFL3b8PrMkb62L730EgCPP/44APPmzQPgkksuAeDQQw8FcAet18aoM04oWs/Pz3cHDM+YMQNIHRcI4dWbagL5huwuKCgo96zJzsWLFwPhRvE1hWxUSnLs2LEAXHTRRQD88ssvQOqADIDNN9889gyB1v7vv/8GPBsM7pNCcXExjRo1KvM92YKe92+++QaAyy+/HPB+oUPW+/Xrx2mnnQZ4P8gFP14d8vPz3fUtWrQI8Jm3Bg0aAL4EoGtaunRpxtdljNRgMBgMhgyQdUaqN7siMP1dkdioUaOYPn06ALvtthsALVu2BFK1DMi9+lIikahyxKJoKJ2lRBHFab3//PNPAG6++WYGDhwIQMeOHQEoKioC4IorrgBgs802A6B9+/ZAPMc+KRJXlJhIJFymIhfZEPjI/ddffwVS7ELsQYc877333oCv00WFRCJRrg6nr2LLP//8M5BibgsWLHA/Bz5qV7YiF59J1URVC+3duzcAkyZNAmCjjTYCCI3RVRcFBQV88sknANx3330ADB48GPCCqGAd7/zzz3e+pPuZjetIJBL8+++/ALz++uuAf/b0VWz5r7/+yvjzwkawDjpz5kyGDh0KwFdffQX469A+qMPjdcB9p06dXHajpsj6i1Q3Y+rUlNjpnXfeAeCVV14BUg/xnDlzAGjbti0AW221FQBXXXUVAJtssgngnSouUYw2oOXLl7vNMygV1w3URiPnHDp0qEuhKs0XxotB9uiBvOGGGwD46KOPeOqppwDYddddAf+A6DzYjz/+GIDtttsu63ZVBtmth/r2228HUjaeddZZALRp0waIXxSlDaxu3boAPP/88wDceeedAMyaNYvOnTsDsPPOOwN+w5Rv69/DClbkh8lk0r0wpUb+9ttvARg5ciTgX6Tz5893wV4w7Ttr1iwA+vTpA/hrjzu4KSwsZMKECYBP5erveumff/75AKy//vpAfOeCai0nTpxI//79AZ+GFnnYc889y/yMbC0uLnb3pn79+kD2XqQLFy4EcKUf7dkKYHfccUfAi46y9dnZgOwQYRHULXDrrbe6F6jWT/dB7yI9K/L5yy67zO05wc+pKiy1azAYDAZDBsgaI9XbXdHuxRdfDHjWo0grLy/PRQg//vgjAD/99BMA3333HeDTYQceeCCQ6i+KMhIWW/roo48AePbZZx17bt481Zsre3TdSjO9/PLL7vsU5YQpngpGTmION910E4cffjjg115fmzVrBsDo0aMBH4nm5+dHFnmKwV999dUAPPHEE8422XX33XcDsO222wLxMQtF7GPGjAHgyiuvBHzKqFu3bmy44YYA7mvPnj2BVIQM8MgjjwB+7bOVKpX/yZYLLrjA9Q9KbCGf0LAMMY4OHTqw3nrrAf5ZlJ26HxLsbL311oD3laihezBlyhSOPPJIwKeqlVHRfdl///2B+DIZYku//fYbkBLtiInuu+++ANxxxx1Aam+D8kw/mUy6fSibe19+fj6jRo0CymYxwO97nTp1AmDTTTfNGSYqBMsqDz74IAAPP/wwkGKh8gft1a1atQLgueeeK/O7lMVbsmRJubWoLoyRGgwGg8GQATJipOm1ozfeeAPwLEJRj6IzvfE32GAD93OKKvR/kydPBnx7xqBBgwB44IEHXOQcpuhBUa8iyeuvvx5I1WDeeustoLyYSl8VNaqe0bdvXzbddFMg3Mg4WL9Ll7Kr/igbVRvRuovx6x5FISjRZ6le9+qrrwKw++67A6no/Z577gFStQuA//3vf0DKd6KyE8oLQJ588knAr5/qh/fccw/z588HfM23Q4cOALz33nuAr0fpZ7Jto9jn5MmTnYhvjz32AHxE3q5dO8BrEADGjRsH+BqTmvIlRJMgI67aqHx3+PDhQMoXfv/9d8Cz5Pvvvx/wa16ViUZhIOgvuucjRoxwgr5LL70U8IIo7Q1B7QWEY38ikXD1b9mp50lixG7dugGp9qJgBiJYX1xV+5R+Xxj2i5GqDqrWPvnpoYce6tZYojR9j9ZaNp9wwgkAnHLKKWXsrwmMkRoMBoPBkAEyYqSKDmbOnOne+p9//jngowG94SU9vuKKK1z0oDqMmOfMmTMBH51J+fvXX3+5qDoMNqIIZdq0aYBXA0pOv/POOzvVnZjx999/D3j2LCVyv379AOjRo0ekLQOKLtMl/8Fmb8nCNZhBqlitdxT2KpKV0lIR72GHHQak6ltirT169ADghRdeAPxaRwWty9y5cwHf6C/FpSLaRCLB2muvDfj113UefPDBAC5jc/zxxwOp5yMbEbvuWYsWLYCUOl7q1aZNm5a5DkGtaI8++qhjc2IpuraTTz4Z8MrXqNtf5AOqLapla+TIkS4zoWdyp512AvwzEEZtsSpQVui1114DfCalTp06nHrqqYCvT2vvDA6jiQJBFhlk0spugLdT90PPq/Y/1da1/+27775OJyBNQzavTUpcKYpll+r/7du3d60sAwYMAOCaa64BPGsVA73ggguAlNo706yhMVKDwWAwGDJARoxUkcywYcOcojF4AsMZZ5wBpGqGkMq7K1pX76CiCzVWq0lcSsRJkya5+k42ITtUF1IfqxiyFIt33323U9cpghRrVSQvlbJqYNk+OaGqWF30pzqY6l/KEkSJYH1c/iJV9OLFi92/KcIXIz366KMBr4wNmyUFGakGiag3dPvttwfKKlmDNWvVwqTqViN+t27dsqJCDiouW7Zs6XxAv1/rJEYtheNz/4+98w6Qqjrf/2d2AZGuYEFwMYo1FhJUDGpiib13Y4lfo9GoEU0s0dgVRewmxt6xEkuIYomxYewFUGNBESOKIopdKe7O74/5fc6dvUtZmJk7s8l5/hnYnZ1577nvOfd93nrLLS3W0P2q1W68MStG6nW8+eabAOy3335AIvuSSy7JGWecARBqd42XTZkyBUhYnxnSlWZ7nnXmeFx22WUAIW7eo0ePECtXVln0TjvtBCQevEqvc319fQtvkOe4sXPzFRobG0M82oqKZ599Fkjiv+aT+BmrrrpqOOvTORjlhGeE66feTJs2LTBRzw0bMHhG77777kBSd1yOHJbISCMiIiIiIkrAQjFSn/7G2q699tpgffmU16I1g0oLvbGxsVlNKSStAvVlW1tozPTKK68MLdeM+5RqZeZyufAZV199NZAwto022qiZHL179w7XakzJLEKtN+N51WpSXtya0O/XStSa1Gsg+9NSq0Z8RraQ9mAUwzXUSs+6LlBZzcTVUyIjbk1sOc3obOFY7tri4tF46e5EWui2qTMXoFhH/PubbroJSLohye722WcfoHDNldDt9FrK6iZNmgQkMeChQ4eGTl1mqI8ePRpIPAfGpa3h7dq1a8UyYCFp8O84MjPSxeeffx66TKn3dkAzD8SYdLpOvdzI5/OhDWRaB9Ub2fEXX3wR2KW1yXrv0q09xauvvhrOTT025mKUE+nvV7dPOukknn76aSDxWFhfrC5X4jxZqAdpep7dE088EQ5yky1UZh+sKlsul2sR3DZRQ5fjnHqE+vcqYqmoq6sLBbqW7Ph9RxxxBJCUCzQ1NQWXhglSuuzczG70rA77dBq6rjDdjx07dgwPTA8lDRPLelzLLBsdeM9tsuB9dUj15ptvHg5xXXW6nEyEyTqJxEPeV42nOR3O3hcPHJPvdKOZNFepa8jlckEHzzvvPCBx5Sqv+23JJZcMh6c/80FvWZKv7u999903fH45H07qsQlxPmg09s4++2ygkGxiyMWHrAejSSa6HT04Dz744Io0knDtPLh9kCrPaqutBsBWW20VXJCGiCQauqnVLd2PlUJTU1M4u9IJRL6a0DN69OhALrwmr3luhmB9fX1IBuvVq1f4znLBdVJGw3BHHXVUkFPD8Te/+U0zmSvZTCS6diMiIiIiIkrAQjHSdPOBvn37hnZdWgoGqdPJEMVWbDpNXTeH7jA/a4cddghlJ+W0brQkLUSWXco4/K6vvvoqWMSWDlxxxRUADBw4sJmslUaazd94440AXHTRRUBipXfq1Cm0yrKMxxKTrbbaCqhOCzXZr23IbOZuI/hp06bxr3/9C0h0xaSzl19+GUhCAVkxaV26NrRQ9mKkm2mryyaZyERWXnlloLKs2vvqusno1dVNNtkEgBVWWCHI6x7QHazO6B5V3zfccMOKDBPwsx588EEgYcY2NZEZ3XHHHeG9hmD0gqUnqqgvlWrRKUvTk2ZLUM9FXYvF81BNsvN89L2eb5Uu3Wlqago6mJ6cYgmLIbb7778//F1rE4by+XxgvHo5yrFPiweIQHLe6XVRTy699NLQ/MI1nBsTnZNexIYMERERERERVUBJjNTxYHvssUeIM2q1n3XWWUAS17JdWbEVq+/aQPHw4cOBhPVZZDto0KAWTKxUNDU1hUC61qKWVLp11oknnhisW0tkvJ6sm3hrmdkc35FRNgdwXN21114brDYtQwuQLUzOikUXIx2ncxSZ7QBvuummYP16P0z0kuU5eiorRqpOm3Rk7Fbk8/lwX9Rv74+emv333x9oqWPlRj6fD+tnY3QZtYl63bt3DzJ4P5THRKrBgwcDCVOyDOXcc88NLNWYZDmuRTm8p16D62eTA9cZkhyNdOs39duzpxKJRvX19eH8MkFoyJAhQJIA4/kxY8aM8F49SOYBmFux5pprAnNuFVhONDY2htIbm4M48k+WbIvOXC63QExUGA8uF+rq6oJeGP/01TwWhy2sscYaLc6FdD6Jr+ZnpL9roWRcqL+KiIiIiIiIABaSkabjQXvttRcPP/wwUEh/hmQ0mk0WLKZfe+21A9M0FiZz0voUpmn/4Ac/KHsbu3w+H+RIs12tRy2zW265JZS3OB6rGmUuxdPtZXLGQc3ENS42YcKEFgN7HWyr9Vvq6KBSIIuQ8dhO7fXXXw8eCa1NLWfLCtSlSsvv58oizUY0fqhOtm/fPljBZkjroZFxOBowiwxC5TZj3hii+j2vpu7pJurGoy1fe/fdd8PfWyZRDvh9sknXxzOmmCm4hmaq61kxdmujF2OU5Vxr2czUqVNDJv+WW27ZTFblUeZOnTqFvScjde232WYboGUT+0qh2GNhyY2Z5Z7dnhu5XK5Fm9E5fR4kcg8ePDhkK5ejRBEK6+kzYtiwYUDS7MH/u36ej8Xwntk8wjJAPaEzZ84M55CtKBf0ORMZaURERERERAkoqUWgVkj//v1DwwSbGWupGE+SMTU0NIT4mBaC1ryWgxakY5KWWGKJirTO0mLS8tGClInK+g488MAQw1P2dFwmK6TbvdmuTpmt+5s6dWqQ35F2sj7/Zvvtt89I6rnDdTR7sTge7qsMWo+FVqcei0oxUmWTiSqHzNjm3lOnTg1xJmsJ1WkzwfUcZBHXlbGlY/0L4kWZm15XWt+NxRq/ksHpaamvrw/71DpRa9bNW/DcSI84LAV+p7p32mmnBT3w+2TErq9euZtvvjkMLbAZhjFzG9boNcgik97zVY/P7bffDiTng2ve1NQUdEeWndYd9cE2r2eeeWbZWjPKjMeMGROyxr0PVifoAfK509jY2IJFF3sRILkH3stVVllljpn4C4LISCMiIiIiIkpAWQZ719fX9eo9MQAAIABJREFUhwxYu+loaWlJanFNmzYtWAZBiP9vQcswZLfGOpZYYomKZDmmY6PW/GmZmcH461//OmQ8apllzUSFmZLGN2644QYgidvZOefCCy9k7733BmC33XYDkuzTM888E0iyDY2DVaOuVKSzNiHRC+NIdn2ZOHEiQIt6sUrJpF7usssuABx++OFAUm/82WefBZ02I1ZmZWzda6m0J6O+vj6Mtrr55puBZE3dm3bV+f7771uw1bQ3wDiS1vsiiyzSLHO2XPAeyuqs21ZHzafo2LFjaD2nXsgI/QzXuBJ64Tp16NAhZLmaN6E+WgNrnfr06dNDrNx9a0ejanQXE36na27VhCPfXnrppXAtxoPTLS/1tHj+d+nSJXxuqZ4i9eyDDz4I+8t9ZDz3lVdeafZdXbt2DfF8cy30dtlNzTp6PRmrrbZa2OML6/mMjDQiIiIiIqIElGWMWmNjY2Ccds+xg4cWbXEjZ1mVlqUxu8033xxIYlH22azUaCEtnkceeQSAI488EkisHuO6/fv3r0rNZRrF9YoOuba7i1a4a9e3b98gs9aWdYXWsNkNJOveta2FVqb6oR5ohao/lYYxJT0lNnAvjkfboUnGIXtN15dWkolCoWbUzEObuQvXUcbQsWPH0HHJvqgyjlGjRgFJvMwM4L333jvkCVRCb9J7XS+EOQrF73FNs9ib6W5uQ4cODeeYgyysNVdvrQr45S9/GbpJ6f0x47kaTDQNZUiPU1t55ZVbxBlF8dkPyT0oZ4a0n7nBBhtw2GGHAQnbT3fKcz032WSTwP5lsT6bjIPqNSq+hlKfMSU9SEUulwuCSKttFGBQ3Un3kASRDXbbnszN6o2t5OGTy+XCTb/mmmuApCBZ16fJDFk3XZgX3NAqg+4J4ZoVu2lVNt1klgVUYoJ9OZF2reqadJLGnnvuCVRuIolwfdyQtlBzc3/77bfhQZROtHBfVDoU4EH39ttvB5dWOulGqO/t2rULDwb3rXpjswP1TENhiy22KHtzlHmhFgzYYnjNXbp0CVNFdJULddEHbZ8+fcKZl54RW0tIT1uqtox+f9++fTn99NOBubuLfbB27ty5xZCJdKvASlxXdO1GRERERESUgLIw0mJorWrh2kYwzZwgsRS0MnQrpT+rEiiexahsJhdZFlLuJhDlRLq4vjWoFUuztUiP2XNUUrrgvdINJebWsEPXXfHv0mubVVKa1vaAAQPCaKn5FdHn8/n5WvjpphflcIP9N6CxsTGweZvWp1G8ZrXGrNsaZPfzQ7W8h5GRRkRERERElICyM1KRLv6uxTic1rbt24wlyfKq1XQhojmMKxmz9n5UK1Ej3RatlpDP58siVy3u11qDaxTXqvKo9TWOjDQiIiIiIqIE5BYkvpTL5aYB/6mcOAuFfvl8fom5/TLKXDbMU2Zom3K3RZmhbcodZS4bon5kh/muNSzggzQiIiIiIiKiOaJrNyIiIiIiogTEB2lEREREREQJiA/SiIiIiIiIEhAfpBERERERESUgPkgjIiIiIiJKQHyQRkRERERElIAF6mzUq1evvGOXagVjx479ZF51Pj179swX90QtF+xFKhak88b48ePnKXNbXGcorHWtyT1u3Lj/yrVui3JH/SgP4l7MDq1Za1jAB2lDQwNjxoxZeKkqgK5du86zgHfZZZfl4Ycfnudn2OjYh2G6QXI+n28xmufCCy8ECPMcd9ttN6B1bet69eo1T5kbGhr417/+Nd/PyRKdO3eeb6F0Q0MDjz322AJ9bro5enE7xnK0YOvRo8d817qt6TQU5H7iiSeyEKfV6NKly3zX2vnEC4vikXm+2tozbdzaXH9e+tO9e/e4F+cB19Q1To9aW5A+BK3Zi21Np0V07UZERERERJSAijWtT6OY0TliLT2iKT11/bvvvstENsdipa2rYotX+R966CEAzjrrLABWWWUVAAYPHgxA7969gdoeVeaQYa9pQUaxlYo0i/jmm28A+PLLL8P/1Y/FFlsMSAa+13rj6rYMvTDpwQ21osfq7Lvvvhv24BZbbAHAc889B8Cf/vQnIBlcf+SRRwLQqVOnqDsLgQ4dOvDee+8BiQdur732ApJB7+pJtde3eJi657nIQpcjI42IiIiIiCgBFWOk6ZiizGPq1Kk88sgjQGLFpAcnmxy05ZZbAvMeQFxOWef289mzZ3PLLbcAMGzYMAD69+8PJCPYevbsCVTfMpsXvB4t+OnTpwOw8cYbA9mMi9NafOeddwA4++yzAXjxxReBAuNwLddee20Adt99dwB22mknoPrjy1yn4viRTE6kB30vTEyp0sjlckGeBx98EEjui8Pul1pqKaB6eu26/uc/hVDVvffey4YbbggkHgs9GD/4wQ8AuOKKK4BkrU844YQW3q+sMb8h67UAZXTNv/rqK8455xyAcP55dhx//PEAbLrppgC0b98eqJ6e+P0PPfQQEyZMABIvxtZbbw3AkksuCVRGxrI/SD1cPv30UwBGjRoFwKOPPgrA5MmTef7555v9TVrJlliikCQ1fPhwAHbdddeqbAQP/REjRvDHP/4RSFwayubmTRsDWc8wdd3npCRuDN2nJ510EgATJ04EYOzYsUDBLVLp9XVdfIg/9dRTAHzyySdA4XD0GtQZN4bGyxprrAFk/0BNG1zvv/8+AI899hgvvfQSkOinsq633noA/PjHPwZa6kk1UV9fz4cffgjAGWecAcALL7wAwNJLLw3AjjvuCMDMmTMzlc2D8dVXXwXgoIMOAmD//fcP99813GabbZq9nnjiiUBy+G+zzTbBKDOxsJJIhy9yuVwIU6mzXp8u9Wq60NVJzzvduRdccAEjR44ECu5xSPbib3/7WwB+//vfA3DooYeGz6qGceBD89Zbb2XEiBFAssY+/C+66KJmPy+nnNG1GxERERERUQLKzki1DEy9PvbYY4Ekcahv374hQUd8/vnnzd4jc7ryyisB2GyzzVh88cWBbCw3LRbLIs466yxWXnllAM4//3wgYRzp0pmsmWg6OWROFq4yFbvXAb799lugueyVtia1yNdcc00A7r77bgCefvppAAYOHBhcMCY46KqTocrusmKkrvHXX38NJO79e++9F4CPP/6YVVddFUjcjZMmTQLg5ptvBpIEGF1iHTt2rDorraurC2EWmahudd2lWUNddV+pA/586623bsHqffXs0S192223AQXv2NzCN+VEmolaCjdq1CguvfRSIPEC/fCHPwSS61tppZWafUaWUF7DK8cccwwA48aNCx63IUOGAEmy5VtvvRXeA8n98uzMGq51u3bt6Nq1K5DojLpdSRkjI42IiIiIiCgBZWekPvUtBznttNOAJMYycODAYLVrCWnVGIeUacgCO3funIn1rjzGjQy0z5gxI8SQVlhhhfAzmHMjgSygVfXss88CcNNNNwGJNdm3b9/AStNxSRM3LCupBlxrmb33ul27diHh5ZlnngESnTKOmgW7gGTd1Merr74agKuuuqrZz9u1axdiRPvuuy+Q6Mett94KwMknnwwksaZjjz22agkwxbrqNfjauXNngMCws45Dq9d6Kmymcu655wKw3HLLBU9KGspqCVq6zKvcSJftyeLdZybS3XTTTcGb4XvU7b/85S9A4umaWyleJZDWP2OLL7/8MlDIRTjiiCMA2HPPPQHYaqutgOQa9R6lS06ygvf2q6++AhLvJiTX517US7TWWmsB5dXtyEgjIiIiIiJKQNnNCJmjVqEWTTG0FMUbb7wBJBaCbMU0906dOmWSbacFo2Vmu6qDDjooyCLLW3TRRZvJ7GvaSq0UtNyV0Tii8ecjjjgixJyVZfz48UASKzUzU6uuGvEZ11MZvvzyy2CdK69rv//++wPZN+p49913AbjrrruAxMKVtR1//PEhm1u25N/6c9n/P/7xD6DQLEB2UkslEOYidOvWDchOtnRzkL/+9a8AbLDBBgDssMMOwLzvfToXoDUtAktBmum6F/VkPfnkk0AhZvub3/wGgAceeABI9qt/89prrwFJ/L81rUZLhfJ/9NFHQMKS/fkOO+wQmKh63atXL6BlKYmv1fKuqDczZsxoIYPPDtlqJc7myEgjIiIiIiJKQMUc22mroLhg3Zq7v//970ASD9Gq0NrRH1/pOI2yvf3220ASCxswYABQYHcyQGsHzXBbccUVgaSetLiesxKWT7rWSwu3R48eQMKScrlcYP5e3yWXXAIk98Yax2plaEJyPa7r8OHDAxtxzY07Gk9Nx6crBe+lWc7KKGs74YQTANh5552DjqbjqsZTZbXbb789ULi2ajPR77//PsTYlVvmZx5DFp4gSHTQTHkztNUFfz8vedT3a665BkjuQffu3Suy1u4rm1lYU/nBBx8Aib5uscUWoZbxnnvuaSbbZ599BiR5GVnCNTEu7j2XyY8YMSLkhDiUQ49AFoy5NfAeuDcnT57cosG+1+V5XonnSWSkERERERERJaDsjFTL9osvvgCSmJCZYLlcLtQiyQCF8aSDDz4YSCylSlvuWjCTJ08Gkgzj7bbbDoDll18+ZF9efvnlALzyyisA9OnTB0haZZl53KVLl4rKLRO1/tJWbtOmTQMK2Y5mv77++utAYrVpudth6uOPPwYKMdOsWZJrrxX/9NNPtxjVZG1slrLlcrlgucqS7NZlHNpOOvX19UFWsxlvv/12IMnaVXZZdtZZ3sXQC/Dvf/+b0aNHA4lOmD2d5VrX1dUF1n/eeecBsP766wOw+uqrA/NmEenMeXMu1llnHaBQs1xuBlXcrejPf/4zkOwj2bNn4AknnBD0w+sxA13G58+zXHfjmsbDzYz2jLvvvvtCByPPCgcBWG9c7Xad6ZF6xUh7hypZ+VG2B2lxX1pIitYNqs9JkVU4Xy1a33nnnYHEjZNV2zpb5fkgVcnHjBkTkqb8nQXUHq7XXnstkCRHbLfddmVXsvbt2wc3uG3+fBDpIjrssMPC+9PNItJtBG335YNir732ysyVl5Zx4MCBQMGVp5GgEWby109/+lMgcdVUWi9cr379+gHJA92khfvuuy/8XFe/rjuNRGW07EXXbrt27TJ3j3k9Jo6MGDEiHP4bbbQRkDzAsmwW0aFDh1Dm4uzPoUOHAgW3LMz7wNYIcO19kHr2VCJZMZ/PB6PIh6CJQ+kpVuuvvz5HHXUUkISENICXWWYZIAkXVKNJh2tr60Vb6e23337hPLFMxzPDtTWkVK0HqjotsZkyZUqLhh2SnXSSa1nlqNgnR0RERERE/A+gbIw03R5Ldilja2hoAAoWhO8xYUaWZeKD7jFdDpVqC6jlIjOwfZcMWffF8OHDQzmPrlsbTui6O+WUU4DKplhDYmVpYWsJzmm6iOus1eZ1mThgKrtWcRbW8PyaEPTr14+jjz4aSOQ+/fTTgYQB/upXvwIqO0c1n8+HNXV6xHHHHQckgxh+8YtfAIV169u3L5AkmMheLRS3abqfVQ0LXovcRJ4RI0aE8Mmvf/1rICmJyqLESBfzpEmTQiKc7K54bWHO+qJ+e8bYUlRPkmteqbVWPy1tse2f54k6semmm4a9ZyN9ZdKzpcciyz1Y3FS/WG6x7rrrBjev55slPa61jNVywKwYdboRg96AmTNnBj1XZ5xuZQlaazxBC3p+R0YaERERERFRAirGSJ1ebzG9FksulwvvMRhvXERklYihzFo3WoVpLLroosGi9HqWX355ILHAjJeYYl0Jy+z7778PCS5ahJZVGN8Q+Xw+xDr++c9/AkmJjgxPlq2sWbCkNHNOp6q3b98+xKptgJBm3VnBdVF3TbywHEfPSXGykc0kjIEZzzVGpp5kGR91jU3ocQTg9OnT2WOPPYCk7KWSLD8N9920adNCIpz7x5nEDrCY0995X4zXpZsd6FGq1Ag477kxdNll+vf5fD40FzHu7/mx3377AS09NZU6A4s/94477gCSdTPJc9111w3ym/Oh/h5wwAEA3HDDDUByzttIIqtxe16HHkCTWdu3b98i+SzdLKc1nzsnvZsXIiONiIiIiIgoAWVhpHV1dS0ao5vNpdVYbGkZ37vzzjub/U21SgK0cB2/ZOmCjRn23Xff0Az+kEMOAeBnP/sZkIzJ2meffYCkNKIS7Cmfz4e4kgOX0yhumSXzdO1trK61n2WGrpaqMZeddtoJSMotlPv111/nd7/7HZCk3C+33HJAZQuq5wWZqWufji1/+umnoSzAeL96r96oL9UY4CwjlSXbHKBXr16hxMu4UpYDvF2L5ZZbLsRm0/c23Qy9rq4usAXZnTrlGpufUWk9SWfnzq2ZfocOHUJjCUvS3Ivqtnux0mdgLpcLXge9J5bMHXjggUDilWhsbAxMT6+We6HS7RdLQTpTXrbcGqSzgFv9dwv07oiIiIiIiIhmKImR+vT+7LPPuO6664AkE9fi3uLWgFAYjjxy5EggqRXTwjSrKusm6sarBg0aBCSZaA7dnTBhQsgO0wp+/PHHAdh1112BJKvN662UpeaazC3GZrbolVdeGWrWlEmLPesG08XNDS6++GIgGQwss7Zp97333hvG6i2xxBIAnHrqqUD1GKlIx8ONOR533HEh3qQV7ABv407p2rYs4D7S46M+yzgOOOCA4BnIun44DddUnVVPbKrg+n322WfBU2T2sfv2zDPPBJgru80aXtOdd94Zxhzqzdhyyy2B7IZcFMPvMn5vIxq9J8aW6+rqwu8cQWYlxeGHHw4ksd5qr/WcGjOkm4y0BjJt69pbi8hIIyIiIiIiSkBJjFT28+ijjwZ2aau6tIWiFTRx4sQQozGOZNcg6wOtbcsqnqQVowVjhpoN6UeOHBnYkJaK9W7Wqmn9p4dpZwW/z/q/MWPGBNaq7DL+rNsA5vP5oCvWUTqwwJrM4lo2Y49avXYDqkZ8sRjeY9mbOn/bbbcFK/7YY48FWjLRasguIzIr3niX+nDwwQe30NssUdyizri4mebGnNP7qKGhIey9M844A0jqou2CVG12rczGTK+99trA7PRU2Ekq63XP5/PhnHOt7QhllrweoU8++SSwe9u36tWy7lgdy/o60lnO84rtL4xsnletRWSkERERERERJaAkRirjWWmllUKmnD0zzWbVYvAJv9hii4X4gJak2bJaN1n72+cWv9pll10A2GOPPcJ1pLPW0tlr1co8Tjd/t0sTJLVfdlqpRjzDe2umoDWtjzzyCJDExpZccsnQBDw9TL1aY8fS1q/xO/MCOnbsGHofO3w83Xi/GjDjVSb69ddfA4RhzauuumpV2Vvx/XSvWcN4//33AwnT8B6sueaaISaaPi+qzUSFclmf+corr4SOV5tvvjkw/w5flULx91n3qjfAWmIzi997772wT/XEmbdQnNlbDaQb7ls1cd1114WRdKXUai/ofSnLg3T11VcPDQIuu+wyIHEX/OhHPwISl96aa64ZGjSnG1JXO2CdhtdXK7P35gUVy7KjNdZYI7hyPXiyTuIqhhtOd76b14e8TfcXWWSRUJ6TdVLU/KDbXCNR4+Wkk04KhfVpg6ua8MFiUb3NPHbffXegsN9qZW09mHUlWmaWNkxnz54drqtWHpxzw6uvvgoUZo26Bw191cK6p2foGspypnF9fX14j2dgFq0jWwP3l8l9thUdMGAAl156KZCstWdiJfdkdO1GRERERESUgLI0ZGhqagqp1CeeeGKz1zTy+XyLxusRpcM1NVHr+uuvb5HokmWxfRpp97lsziQdywKg9jwTwiQN2bSsYq+99qpq0s7cIIvQRZ5uClFLsgpl+uabb6osycJDvZDZLbXUUsFjoYu3lrxc6ZK6WpJtfkh7gDbbbLPgPvd3WcwjjYw0IiIiIiKiBJStaX0tW7n/S0hbYbWKWkjGaS3SDfaN64oZM2bU9HXEvZktZHQ2dL/rrrtqkon+N6Ha515kpBERERERESUgtyDZY7lcbhrwn8qJs1Dol8/nl5jbL6PMZcM8ZYa2KXdblBnaptxR5rIh6kd2mO9awwI+SCMiIiIiIiKaI7p2IyIiIiIiSkB8kEZERERERJSA+CCNiIiIiIgoAfFBGhERERERUQLigzQiIiIiIqIExAdpRERERERECVigzkY9e/bM9+vXr1KyLBTGjh37ybzqfHr16pVvaGjIUqT5Yn4y9+zZs+ZkHjdu3DxlhsJa15p+vPTSS/91+gFtcy+2Rb1uizJD29Trnj175p38VCsYP378fNcaFvBB2q9fPx5//PGFl6oC6Nat2zwLeBsaGvjXv/6VlTitQufOnecrs3M6awWLL774fAul+/Xrx5NPPpmFOK3GoosuOt+1HjNmTFbitApdu3Zt1Vq3xb1YazJ37979v05maJvn3rLLLhvmWdcKevXq1aoGEWXrtVsOOEHDSSHFr/ZQrHYDCWVSVl/TA78jSoe9bV3zWu8f3JaR1msR9TnivxUOvm9sbCz5uRJjpBERERERESWgJhiploHT17/66qtmr7Nnz0bfeceOHYHsmamWevv27QH47LPPmr0uvvjiQDIPtJKz71qDurq6sK6+yuiymM9XClzrTz/9FEjkdHZptb0SabRv3z7ohTNfa5nJuX7FOjJjxgwAPv74YyDRmSWXXLLZ37RF5HK5oFNeR61dj+utF6aas4OLpx05g1f98Hd6MNoi3KvvvfceAF26dKF79+7Awp+JkZFGRERERESUgMwZaV1dXbAItMLeffddAIYNGwbACy+8ACTWwQorrMBZZ50FFILokK3FX19fHyzEe+65B4Drrruumawbb7wxAH/+858B6NatW1UYnxbtl19+yYQJEwDC60orrQTAGmusAcCiiy4K1NaMxPr6er755hsAjjjiCACmTZsGwOjRowFasItqQT2eMGFC0IMNN9wQgD59+gC1xUzTc1VnzJgRktr+8Y9/AIl+ex2XXXYZkDCQaq85zJ8NeX2+zp49my+//LLZ36r71YYyTpw4EYD//KeQ2/LTn/60ajK5vz7++GNeeuklADbffHOgbTNRnzdPPfUUAOeccw4Aw4cPDx7FhT2zM3uQeuh8+umnXHnllUDyAFWJPv/8cwB22mknALbeemugkM3VrVs3IFt3pAv/+eefh0P9gQceAKBXr15A4SEPhAPJDaurICu4IXU1n3jiiTz66KMATJkyBUiMkLXWWguAE044AYBVV10VqI1knvr6ej788EMAXn75ZSBx5yuf7qas4QGjXpgVefrpp/PEE08AcPbZZwMwZMgQINHX9OFeDB+2lV5/11HDZNiwYdx5551A4kZXvtdffx1I9uiKK64IVN/oyuVyzR6QkDzcXevx48cD8MwzzwDw9NNPM3nyZCAJwXifKoni5Mm0QZVOoDvppJOA5B5tttlmVXPvur6vvfZa0OO//e1vQGKEV1sP0ihOTJzbPlpkkUWAxDjs0aMHUDgPDSMuLKJrNyIiIiIiogRUnJFqvcsyjj76aJ5//nkA1lxzTSBxG2y11VbNfi4aGxuDtZmFayld0nLkkUdyxx13APC73/0OSCzK5557DoCrr74agL59+zb726xk1ULUPX7TTTex3HLLATBgwAAAJk2aBMD9998PJLLrvunUqVPVE5ByuVywDr/44gsABg8eDBTkg+yt4TR7UH9PP/10AB5//PGgs7rk1HshI5ItzZw5M6y1HoLll1++LPIWJxMVy/LKK68AcNFFFwEwcuTIYJX/6Ec/AuCdd94BEu+QbvZqu/T0aNXV1fHXv/4VgPvuuw9IvED//ve/AXj//feBZC8OGDAgJKqpS0ssMd8a+4WG6+2+evHFF9l3332bXYdelb///e8Aof76T3/6E1DdRED1p0uXLkFvDV38+Mc/BmDWrFlA9fVCJjp16lSgsK8Mq6Tfo3fF9x533HFAkuRaCiIjjYiIiIiIKAEVY6Raw1ouBnYfffRRbrrpJiBJ0NGCk2mkYx9ZQetKa3HkyJFAgcEdc8wxQCH2CPD2228DcMABBwBJIk86TTwrmbWqjDdvsMEGIUFr6aWXBmDXXXcFCrEPgJVXXhlI1r+aiSReR1NTU4ht6cVYd911qyqTFu2IESMAwrqqp9tuuy2/+tWvAFh77bUBGDduHAC33HILkLB/2Wy7du2Cda9u9e/fvyxyu/dk9nogLrjgAiDRkX79+oXYnLF+mVO6dKpae9HvN2Z7/fXXc+ONNzZ7z+qrrw7Az3/+cyDR60GDBgGFuJ7vNQbpuVQJmY2Hes6NGzcurGv63txwww0ArLbaagBsscUWQHXzFWTD/fv3D0lZeihqrfzFs/ruu+8GCvvr8ssvB5J96z03j8XcC71I5WD/kZFGRERERESUgIoxUi1J4xh33XUXAKecckqIhRp/qYVs0WJoUY4dOxYoNFkwa9frMntNa+af//wnAKussgpQyOrNIs7hd3Tp0gVIWM1dd90VstSMexk70mI3nprOiq0mZs2aFTKjvRb1JWtWpEXruskuzXo9/vjjATj00EMD07j44ouBpAzqgw8+ABKvwO9//3ug4B3o3bs3kNy7cumLVros+JBDDmn2PX/4wx+AQna8enzhhRc2u9bddtsNSO5BVroh0zGWaDa08ax33nknMM00m5Y9eZ3u42L2WclMWGWWPctIhw4dGmTz+mRQ9pa97bbbgKShSzUbMoji7Hg9cHq+ql0O5d60gcitt94KFPQ13e7SXIt7770XSHR7scUWA8pzDZGRRkRERERElICyM1KtAWOFZthZV9m5c+cQ+7IW01hTtTNGtWDSWYADBw6ka9euQGIJWZtpTdKzzz4LJJZ9JbMCi6E1ZUbr+uuvD8DNN9/MscceCyRWpHEO4zBm9dZCkX1xW0AzGM2+q1Y8RplkRd7jX/7yl0CSwT158uQQOzceKSs6+OCDAdhjjz0AWGeddcLnq+/lzkiXiTlmba+99gISb8qWW24JFGKLtkmz2YXsTfn1alSakabvsTW61jHIPiLhAAAgAElEQVTK3seMGdMilpxev2+//baisqaRzlMwK9ozYJNNNmlxLlpLb638BhtsANRWfWY+nw/nnRnQ6kO1GbNeNFm/enzyySe3qDPXM/P0008DcPvttwO0aH9YCiIjjYiIiIiIKAFlZ6RavVrvtmOS5R177LFce+21QOKr3mWXXYCkQbYWdbUZqlhqqaVaxGzOOOMMILGCzzvvPCCJP2ZtWWoNG08cNGhQiNvKrIwlKbusoxZio8V6o4VoVp1drarFnOemj86pvOCCC4LV+5Of/ASAgw46CEgYRyWzRdPwfsrcjNu+9dZbzV7XW2+98G/zAfRSyKCz2oPefzOKjT+/8cYbQML6brnlFnbYYQcgyUfwb6t1XshsHnvsMSCJxR1++OFAQU6ZnVm6tgI85ZRTgCQ2moV+LAjUWxmp15F19m66taPraIeqQw89FCjsN89CZT3zzDOBZG+aF1DOtS7bgzSdrv7iiy8CycXousjn8+Fg0i1qurJKte222zb722ptEL//gQceCGUulmb84he/AJIDc6mllgKq55pJT0jp2rVreIDqFjvqqKMAWGaZZYDyuDRKhTLqjrvmmmuCm3r//fcHkrBA1vL6QNpmm22AZLNafmF7ve+++y5sUo1EH0heVzUOyHRjBo08W0K+8MILIYnn66+/BpI1N0SQlQsvPc/Xxhbqrvtq1KhRwZ03fPhwgPBgzToBxrPOhDLl8Vps/jBlypSQFHPJJZcAiVGrq7+WHqCu49SpU4MRa5jAPZFluKX4uwydDR06FEiMGMuHJk2aFP7tXrTXuC53r6mc50l07UZERERERJSAsjDSXC4XLEZduLq0LKbX8srlcsHCMPirpX/kkUcCiUWnyzefz2fq1tOdYXr05MmTQ2s3rZrNNtusmazVtihlcTaqHzt2bGAiFv7vuOOOQPVlLYZW/ZtvvhleZSFa7dWaoOK9tdG5iUMmFNk+DZL2Y3/84x8B2H777YFEh2tlviQkrOKSSy4JbQNloAceeGCzv023OmxqaqqIh8h7rDtadpeWY8yYMcFDoAvV5DkTYbIOAVjKYhjLdf7tb38LFDwqnnnqubrtfjUBLO06rQaU4ZVXXgnnuWdJteDzxWYye+65J5A0ttCz0rt3b372s58BSQMGGahndiX2YmSkERERERERJaAkRlpc+Gr7MRsw+P+NNtoISGIwxZbWJptsAiRj0wwca7Vl3WZPq8siaa3Frl27cu655wJJg30D2tUuHdF6tGDakowpU6a0iFtXW9ZipONZrvXkyZNDK0NjudWe6ekam1D0ySefAEmz+c033zyUjzhuSh2yeYNML8vhC36HcST3oIkaY8aMCe8xnmdSiQMOtPidU7r22muHPV1OqA++usZ6h7wHAwYMCF6uarUSFd5L8yPce7YqNJnvww8/DMlbxqD1vjk0oFZm7BbL0Llz56ozUSjI4xmmp0KdVgemT58OFFoE2o7WRDWHS5ioVInzpPqrFBERERER0YZRFkY6a9askD5vrCjd/q84XVprwlZashEzw7TotEIrzUi0drwG2wF+9NFHQMGyNF5qfLEWLEdI4kIWeBtD6NChQ2gisd9++wHVy36dE7R0tSQdU9euXbswcFw9qXZ5jvph9p/3/uijjwYK7f5cY5nbqaeeCiStMbfbbjsgaRWYxTVZsiW7NDv+uuuuAwr3QMZnWZeF7f/4xz/CewB+8IMfAIWSpPSYwVJRnDfhesmezY4vHsdoBqwNXarVsMPr16NmPFzIgE455ZRw3x1u8MMf/hBIPFu1UupXjFmzZgVdr5XzzlwQ5VEvGhoagIJH5YorrgAS76EVF5VEZKQREREREREloCRGqhXVuXPnkHVmay8LjoXMqbGxMYyYcnyU79X/nY6BVApaM8axHI/ldWk9jh49uqZad0Gyng4G9nXZZZcFCkzPhgaVzFZbWMhqzHzVO7HtttuGAdfVjo2mm17b0F1mP3DgQKAgp94UM9CNpxq7du2zYE/KLauzgb71r8Uxcy17676NK5nFa0asOrT00ktXhD25PtYHGic349JhzLfddlto3eloMllKtTwX6qmv6eYS99xzT/CyGVe3vrhWmF4xirN2/bferWrLm9a9NDN94403wlliIxLj0OUY4D03REYaERERERFRAspSRzpz5kz23ntvIInRpTOnrCN97rnnGDVqFJDUUl111VVAEhtNx1UrBa0tWZFtDe2MYdbdV199FRhgtZFmNNY02pDe9lfTp08PHaJEta1JaD7AG+Dqq68GEovyyCOPDLHRate7pkfU2a3IzFwZ3o477hje8+mnnwLJPrAG1XhZpWNh7dq1C/WV559/PpBkwctUZU6dO3cOHZk23XRTIGGetus0hioqxfrUC9m+WdB+v9f0xhtvBNZvC76szovWwnV2YMekSZO4/vrrgZa1vLWMb775JmTO14qXKA3X2vPv5JNPDjrt+ZdFTkhkpBERERERESWgLIw0n88HxmY/1xVXXBEo1KoBjBw5Eig0DrauZ+ONNwaSTMZqZcTKhrR+7YhhtuPpp59e9S47QsvduJ0MyP8boz7kkENCjLfazK4Yym9Wt0O89Vgsv/zyYY1rhWG4frvvvjuQxHMdjH7jjTeGWkI7wTgq0F7MaR2vFNq1axfW9PnnnweS7Gf7MDsGbtCgQWFItsw5XZuZBXPK5/NBRvMkrEO3r65M9eKLLw5d02pNT2RHxuJeeukloFBLb9Zztc+PBYXnnrHqWs0V0YPx2muvhR676VrTSqJsTetVEF0Bul9MCLDAevHFFw8b2gSDaiXBeKjZzNtpKSYCOJGhb9++LWZHVgvFCV6QHIqWHZlgdMwxx9TcQQOJLG4AD303ao8ePWrO7eU6rrTSSkDSJtKkuFGjRgWDxjIpE+ksjcjqAJo5c2aYjWoZl7AcxqYLHTt2DHtA91e1S0l8sOvyN2FK2ZdYYokWyT21hvQ82A022CAY67X2IJoTvBd9+vRpNmyk+LVaepKGeuuQg/vuuy+se5ZrHV27ERERERERJaDs80jTY3ZMstBKaGpqynyC/dyQbuZt6Ui64LyxsbGmWB0kVq/JIZYpFP++Fi329GgvXUfpMVq1CNmbrHPIkCHNXovhdWbtFWhqagqJQrqT01Cm4iSMWmEYsghLWkzicv1mz55dc3tRqMO6FG3KAW2DiQr1/OCDDw56ofy1oidCXbA8p3v37lXxaEVGGhERERERUQLKzkhF2qde7djivJBlYkW5UevxormhmGG0NdRKvHxOyOVyNS1fa/HfcA1tbU+KdIla8c9qFdXWl8hIIyIiIiIiSkBuQeINuVxuGvCf+b4xW/TL5/NLzO2XUeayYZ4yQ9uUuy3KDG1T7ihz2RD1IzvMd61hAR+kEREREREREc0RXbsRERERERElID5IIyIiIiIiSkB8kEZERERERJSA+CCNiIiIiIgoAfFBGhERERERUQIWqCFDr1698g0NDZWSZaEwduzYT+aVntwWZe7Zs2fNyTxu3Lh5ygxxrcuF/+a1tlVoKbC9ZLrpy8Lgv/H8gMJa2/K0VjB+/PhM9KOcaM1awwI+SBsaGsKYrlpB586d51l31NDQwBNPPJGVOK1Cly5d5ivz448/npU4rUL37t3nW9/VVtf6sccey0ia1qFHjx7/lWvdr1+/kvW6rq4u9OG1J2wpo+m6des2X/1oa2ceFPqGP/zww1mI02r06tWr4vpRbsxPP0TFWgTODXV1daHdlK+10ppPS9cm9sVIW79ttf1XrSGtC8WtyNJrHmuey4u6urqg87WyB+cG5Xz//fe54oorgGRgw0YbbQTU/jW0ZcxpfxajLbdyLAdijDQiIiIiIqIEVJyRasEUT4//4osvgKRh+XLLLQdUr5G5Mn7zzTcAnHTSSQA8+eSTQIGh7rPPPgBsvfXWAG124n2tQNbvyClH63311VdhTbt37w4kQ8BlHJGZlgb1/euvvw7r7ui1WmUWyvztt99y3XXXAfDRRx8BsN566wGJLtXqNbRFuKa6z7/77rtmv/e++L5qNbf3+dKuXbswBD7dfN+xgZXQj8hIIyIiIiIiSkDFGGl6OPb9998PwN13383LL78MwOeffw7AMcccA8D6668PwMorr9zsbysNkxfOP/98AC6//HIA+vbtC0Dnzp0ZOnQoAKNHjwbg4osvBmDFFVcEsmGmuVwuWFmtYWW1yNxkonol/va3vwHwyiuvADBhwoQg94ABAwDYfPPNAdhggw2AOY95ygLzixMVI732tXAvlFtdPe200xg3bhwAN910EwC9e/cGai/eWDzAuUePHgAsv/zyQLJ/s/Rk5fP5FnowN72Y1733d7U0pkxZ2rdvz5tvvgnAzTffDMB//lPIvXEfy/5OOeUUoODZyHJftmtXeITpWXnzzTd54YUXgJZDv7faaqtm/y/nniz7g1SK/8knnwBwySWXAMmN+Oijj1q4AY466igAdtxxx2Z/06VLF6DyDykPDVOvzzrrLAA22WQTABZddFGuvfZaAC677DIATj31VABuv/32isuoUQKJwrh2uj2FCl6c1JWGB06Wh7v3/PXXXweS9XvooYeA5uvn5nj++ecBuOuuuwA46KCDAPjVr34FJBuiUmuvHMIDwnswr/Xzbz1o/H8tPKCK3emusdmS++23H1AbchZDPb/jjjt49913geQ6skTxg8+9pttz5syZzd5bvEfTJTvK7meoW37WnB7UlYY6qoy33357SOx68cUXm/1OdOvWDYA//OEPQOHcyeJB6r4y/CYJmjhxYtAP19JzfY011gBg9dVXB8qr49G1GxERERERUQLKwkhzuVywZsaMGQMQXKHPPPMMkFgQHTt2DBZLmlU98MADAAwfPhxIWEsul6soe9KS3GWXXYDEMtNarK+vZ8iQIQA899xzAMElNnXqVAAWX3xxoLzuxrQL84YbbghrIxvbdNNNm12D7ugePXqEZB0TSXSJrbXWWs0+t9LMNJfLhUSuW265BUhc/R07dmz23n79+gVr/e233waSNT7zzDMBgrtJz0H37t3Ltu7e81wuF7wqH3zwAZC4oe+44w6gkKwDzT0GwiJ+rd/jjz8eSFyn1UhS8z67F3v16hWs9mnTpjV7z4KEECoJ78fHH38MwIMPPkj//v0B2GabbYBsy6OK18Uwj27xp556Ckj21aKLLgrA4MGDWWyxxYCEBQ0cOBBI9GSJJQo1/4Yz0uy2kvC8+/TTTwG4/vrrgYJn8KuvvgJgnXXWAaBPnz7N3mtI5s477wTgsMMOq2jSl/rg2XDkkUc2k2ePPfYIIaC//OUvQHLGVDIMFxlpRERERERECSiJkWqdzZ49OwR4DznkECCx4mWbWgEdO3ZkmWWWAZI4qoknwvT2Y489Figk+2QJrUZfO3ToEOJishB/99577wEF6x7Ka4Vpfb300ksAnHPOOeH7v/zySwCuuuoqoCV7bWxsDMzD9ZOhuq577rlns++plEXfvn37wOKMKWu1ytB83WuvvYL1q3fD+PTEiROBQsIawE9+8hOgEDM1tX1hIauU+bz44ovByjbmohciHeOf07q99tprACGxTkZuklrnzp2rVqYxp6YiWXknWot0Ypcs6amnnuIXv/gFAKussgqQ7MX031RifWVvEydO5OSTTwbg3//+N9DSuyKbu/POO1us6zXXXAMk620cz8/cd999AyutVKxUPZ48eTIAxx13HAD33HMPAIstthiHHXYYAAceeCCQeFiMrf/mN78B4KKLLgIKeu17K+HVcJ/67PB10KBBQOFs8yyRtZpzYycwkxdL6YjVQq6yfVJERERERMT/IEpipFpnb7/9NkcffTSQMFFZjlavfutDDz00xAGMG8lWtOjmFHOqBrSovvvuu9CkYdKkSUASK9CqqWSGnWy3S5cuwQL72c9+BsC2224LJMzY2Oknn3wS2JWvxnDuvfdeIMmSrlT2a/GaaLVPmTIFKMQyAP7v//4PgB/+8IdAwYNhOcOaa64JJIzjnHPOARJ2Z5x10003DfdjYTPx1FdjuBdffHFgBFrU6QxpGc+cvjOdlWk8zTjNySef3KK4PWvk8/mgW7K74t9VE54tb7zxBpB4Xjp16sQBBxwAtGxer77pnTBGWc6yGPfIMsssE/behhtuCBRYJDTPnAcYP3588CR5PhrnN8b4/vvvA3DuuecCBYZlLLjcGdTqpgzttNNOA2Ds2LFAEg8dMmRIaEDjtRiLlEHrYbFhzWWXXcZ2220HUPKenBO8l2uvvTaQrPltt90GFNi/Z6PZ/p4nyhxjpBERERERETWGkhipFnmPHj2CpW1syAxRa/5kHssuu2z4Oy2F4rgewKqrrgok2YXVRlNTU2BzxnfPOOMMoLKZYH6mlt2ee+7J2WefDSTsyPVNW+eQWMYTJkwACJaisUbZ4WqrrVaRa1CmadOm8eyzzwKJdWpNl7W6sr+mpqZgdSrPoYceCiTZuxdeeCGQWPPvvfdeyH4s1fo1XvTll1+2iO/76hrL5jbbbLMQhzY+I4PSg+DfqkdTp04NmZxZZ/AWewqU23rAarfXK867ABg2bBiQeFyOOuoofvSjHzV7r2zP2N4///lPIPG4bLvttmVbY9enQ4cOwUsl5nZeDRgwoEXjAD00Xp9x+KWXXhooeOcq4RWor68PXrXTTz8dSOKdrqs1mQMHDgzsPr1+XutKK60EJPrz5ptvBk9LJb10fvYJJ5wAJN6r7t27h+YQnnuusY1+yhkbFZGRRkRERERElICSGKlWylJLLRWYkqzHuqjBgwcDzTPptC5lr8W1e5DE/YyZVqsxvFbXQw89FGSzbsma02ImVW5okWrN7rfffiGT9a233gLgnXfeAZJ2acWMTJnS62vsyFhJpeJhft/MmTODFajlmm5Fl2Z7xfIrp83JZYK2mHz//fdbZGwu6DX5fmM999xzT/iZ37vFFlsAycACPSqrrrpq0BUzo405yqa10q1Dfuihh0J8R5ZSaeghMMb89ttv19zQBb0Ao0aNAuC+++4DkpFpQ4YMCetut50TTzwRSNbWjHYrCRoaGgLbKpWNFJ9jacYli043cp8xY0bwyBjLM76vB8S8EdlTnz59WmQjl0tuM6BdP+vKZaI//vGPgZYN6ouRzvzOutVh+mxwlN4RRxwRsvrt0rX33nsDle3WVZaGDN9//314cPqAcWEVvnj6i+nIr776arP3WqS86667lkOsBYYy+qDRBXLaaaeFCTU///nPgeS6snCF+V1LLrlkaErwyCOPAPMOoCubTRpWWGEFIHkAVSqpy82kATB69Ohwrz1sTLpoDbx+N7jXoVHx4YcflryB/Q4PFd1dkOiDhp3X5frOnj076LAPKT/Hh649Sj/88EOgcA+qlVSn8Td9+vQQgllqqaWA6rl2NfamT58OJE0OXCMNkr59+wYX7h//+EcgMURsU2eCkgleU6ZMCckp5cKc5uamW0r6YL/qqqtCM4/0ZKO99toLSAx0y0vK7X7U0Lv77rsZMWIEkITfLHExyag1pWQaPLb4NEy05557ZtJ0JG0w//WvfwUKpYI+XE2inFPYq9yIrt2IiIiIiIgSULam9Vof6fZ/Wmla4ueff35wLQgt/u233x7Ifjai1tpnn30GwMMPPwwkRdMffvhhaCSgC7U1VlvaEirVIvr+++9Dko6uqnm1Eku3hNMq1yNg0pEMr1Lo0aNHYHPFTbmhpdt5TmvkzxxikC58L6el6Wfpgi7+mWx6XuUUvjedfJRu5tCpU6fMS0xca70Bn3zySdhrepSq5er1nHCogc3I3W+67u64447AoNRbGZZJeZ4jxVNiKuHWSzNR3bSW89nwfdq0aSHEZTMJZdfL4h4t3s/lcJOm3fkPP/xwSIAzVKEHsDVtCZXT8JxDPEz42mijjUK7VL+zEkg3ULnxxhuBAgs1AUk3up4rdagSuhAZaURERERERAkoGyMtnmEHyVPfgL/xjOeff75FjMnkIttNFQfpKwm/Z/z48UBSmGx8TIbarVu30G7KOEK64YQoTjSw9WF6dl8pSJdipOH3d+zYsYVXYNlllwUSS9HWg8Z9yzUcIB0fX3fddQOzcK1tv2f5i+nr9fX1LRIXXLdbb7212Wf4meuss84ck5VKwYJ6Q9JrbQzM2Los2qSSwYMHZ9qYHBJ9d0++8847wUpX3ixnes4J3kd1Z+ONNwaSZgGHH354SP668sorgWTNLXuw2YFt61ZZZZWKXJd6aZmF7VFdXz1tu+yyS5AtnRSoXOVMLCqGn2e7wldffTXogU1QlFNWOSd4hpmA5P61BabDM9Zee+2Kn9uQMFKbShgXv/jii4POeF7Imv15ReSp2CdHRERERET8D6AsjLSurq7FmCzLMyyONn5QzMq0KrTgTP22AbHtqSCJrZXLv11fXx+Kom0WYWalFpuZl2+99VYYPq6sjjMzFT8dR3vmmWe44YYbAMIINps3VAJanq7Tgw8+GMoAZENPP/10M5ktLbB5fZ8+fcoat5Nd9OvXL5SVuMayBod1e+9tRF8Mh8LbPk2mb6nV4MGDq8qkiocZGx9T/42NWr7haMB+/fpVbXi2OjJ79uzARtyX1VjHOTWIMOPS9TOe37Nnz9CO1BGNf/rTn4DEk+R4PdtQVuqavOfGmfVWqduywPvvvz+85+CDDwYS71A6p6RSMvbs2RMo6KEs0sx/yxAt2Sper+JqC0hikVYPWIqmN6+hoSFTHZJtmouwzjrrhAx0G/vYfrGSiIw0IiIiIiKiBJTESLVWvv3222CR2Bot3ejbOEYx49EKk63alNw2WcUDqH/5y18CCQspNbuwQ4cOwZrRgjQr1HFCthh77LHHwvX5NyLNoKw9vfbaawOjTluflYD3QrY2dOjQYHnKQLUU/b+sSWu/uH1jOeC9bmpqCozUBhKORpOhWgO4zDLLBPm0gm0F6LXJVoobaleD3am/33zzTahjkx0ZU7cNYHGLTKhOdmyanXTt2jW0XfQ+uF/NWq5kZrHr99lnnwWviW3cdthhByDJfPX+9uvXL2TtyjSM3xmHTBfgV+oa0jWhZot6bhiju+OOO0Jzd9fZzPlKt2b02vWy7brrrmFohUxU3TSj2LpzaDkgwhaXslc9LGYhZ+3R8NwrzlHwnEgPUKmoHBX/hoiIiIiIiP9ilCVG+t133wU2p4VlfE6LyAzF9u3bt+joks54tLuJVtCsWbPCqCL/tlSLftasWWEck51RrKvaaaedgMSKO+CAA0INppblo48+CiS1psplJ5udd945tC7LotVh8XgnKGRCG//SIvP///rXv4Ckrsqa1EpZxU1NTYFlHnPMMUBimdt9RiY/adKkFo3LZRbWCTr82GzjasVHi/V45MiRQOJdcUSgnb6UvVw1xQsD18nM4f79+4ccBuONDkFw+Hsl19Y16Nq1a4sM7aFDhwKEYQTG85ZeeumwX832N8ZvDoJ6XOk6dGVWP43vrr/++kCyzj//+c9DXNe8BOtkt9lmm0xkNS7ev3//IIvnk13HZPTFDM575N/beUkmarZuJRrBtwbpLO+pU6fywAMPAImnUaZdSURGGhERERERUQLKMkatZ8+ewboxBvTYY48BSd2UjGPQoEEhBqq14wghrWMzY43l7L333my++eZA+VhdY2NjqF00u1arxtdiK8sMMLsy2UdTS142bcbxSiutFH6WZTxMmU8++eTQnzTdF9jBt8Y/ZKqVZEkyG7ueqC8yDrtJvfPOO0EOGYaszl7MWsEi6/6w3le9LKNGjWrRN9pYvhZ8ekh4NVCcRQ3w05/+NHhY3KfG97Jc02IGpIz+7IgjjgDg97//PdB8/dKZ8tXKgpaZpmu83Verr756i6xouwtljaamptD5SS/igw8+CCSewOL74Zpac+recy9mXQudxm677QYkWf/HHHNMiP36nNl9992Byu69srh2iych7L///kCSem7yggvetWvXFo0J/J1/ayMED6w+ffq0aPRQDqjw85pykH6vDx/doeuuu26z9xWX6VRztuOMGTNCEoQbw2b1thl0IoWJMauttlrFD6P0xnSuqyVCxW3FdJWZ/JAu8alWiz1dR7r3n3jiiVCErqzKXumElwVBcfIXFNzPhjcMyWTdnnNuSIeE2hI883wwnXrqqSGUoSHpHM+skc/nwz4ylGXYbE5NIbwPhmbm1MqwGvA8NlHKpLnRo0cHnXYggEmrlSQ00bUbERERERFRAsrWIjBtcacbFRSXYKQTGLSAtNYs8i2eeVctt83cICuqVpC9NUgPErCJt65dE31seHDWWWct9DzPBYU6IMszSWpO1rDvrTarM7nIchzLL/r37x+SiUzYmNd4u2pDfejWrVsoz0m3dYxYcKjLhnsscRk1alQ4J0yM0jVaDf1IJxDJMk2unNffVJuJivQ8UssTfYW5z0ytBCIjjYiIiIiIKAFlY6Ribun987IG0pZDLVrxbRnp9XVskglUJnVVo4wkq1KFckC25vpZJtWxY8fAVo2RViuOuyBoampqE+veVuC91vMj+9xnn30CWzXBMZ3zUakWga1BNUuySkXaa1UtREYaERERERFRAnILYoXkcrlpwH8qJ85CoV8+n19ibr+MMpcN85QZ2qbcbVFmaJtyR5nLhqgf2WG+aw0L+CCNiIiIiIiIaI7o2o2IiIiIiCgB8UEaERERERFRAuKDNCIiIiIiogTEB2lEREREREQJiA/SiIiIiIiIErBADRl69eqVd1pHrWDs2LGfzCs9uWfPnnnbtdUK5idzW1xnaJty9+zZs+ZkHjduXFzrjDC/te7Vq1fNnR8vvfTSfPWjra51rcncmnMPFvBB2tDQwJgxYxZeqgqga9eu86w76tevH48//nhW4rQK3bp1m6fMDQ0NPPHEE1mJ0yp06dJlvvVdDQ0NYWh4raBz587zXWunuNQKFltssVMR5csAACAASURBVFatdVvbiw0NDTW3F7t37z7f8+Opp57KSpxWoWPHjq3Sj7a21m313IMKtAhsKyiun7W9W/Ecvrm9f24t7arZ4isi4n8J7ldf07XwbaHFqDLP7ez5/vvvw3vi2TJ3ZDVkY36IMdKIiIiIiIgSUBVGqhXmAFytMVle8XDsSiGXy4XB4ePHjwfg6KOPBuDTTz9t9t6NN944NKB2oLdj4bR+/SwHPDc2NtaMJam1tuiiiwLJeru+tTIaqS3D++9YJ9e2lsbsed+Vtb6+PuxFkdaJalv6adTX1/P1118DMGzYMABuvfVWALbddlsALrzwQqB22EoxlMWm9TZbd/C3Z2CfPn3Ce8qNWlyXBUV6nxU/QzyTszx/IyONiIiIiIgoAZkxUq2Ddu3a8c033wDwj3/8A4CJEycC0Lt3bwB+8pOfALD00ksDlYt5aP3985//BOCFF14AWsYvrr322jAEe+eddwZg/fXXB5Ih5O+88w4AW265JQDdu3dvIXe1GKqW7b333gvApEmTAPjhD38IwHrrrQfQgp1kiWKWJFwvrfZai30pX/v27Zk8eTJASFxyRN2AAQOA6lr/3tfPPvsMgLfffhso6Oznn38OJPKtuOKKQDL8fW5xyKyhHDNmzODQQw8FYOrUqQCceOKJQGGcXa3D6/joo48AuOmmmwA488wzgWQv3njjjWG8YTlG3bmv6uvrW8ReffV73Ge1NGIvzaJNAPvb3/4GFBKVAPbee28WX3zxOX5GekxnOXW64g/S4gcowOOPPx6U58EHHwTg448/BgoPH4DBgwcDcN555wHwgx/8oCKHqEq91lprAdCtWzcApk2b1kxmgPfeew+Aiy66CIBrrrkGINy0Dz74AID9998fgJNPPpnFFlsMqJ5CKr+b9uyzzwbgmWeeAWCllVYCEmVcbrnlMpNVvdBF89hjjwEF48oHp27yfffdF4CBAwcClXX5twbpUMQDDzzAOeecA8Czzz4LQP/+/QEYPnw4ANtssw0A3333XWZyakApkw8c3YiffvppWGvX1FmaQ4YMAeB3v/sdkFxz1g9U9UT5jj/++HA96q16kdabaj/8RT6fb2Z0QWJ4exZqcPkgbd++fVnk976NHTsWgD//+c/hrPLs0qBebbXVANhggw2AAkmolTV0/S6++GIA/vSnPwHJ2WbY6sUXX2SLLbYA4JVXXgGSc1A9+elPfwokul6O8Et07UZERERERJSAijFSrQAtmj//+c8AXHrppcEikhFqGcg6n3zySYDgLlthhRXKzkjz+Xz4TC2U3/72t82+X7ZUDC2j999/H0jcpLLZ2267DSgkCxx11FFllXlBUFdXF5jHqaeeCsCECRMAWGqppQDYfPPNgcQyzdL61DK/8cYbAfjjH/8IwGabbdaCyb/44osArLHGGkD12JHf+9VXXwFw/vnnA3DLLbew3HLLAUlY4tVXXwXgkksuAQpeFSjoMmTjpfA7lliiUE+uq1DLfPnll2ejjTYCYNSoUQCcdtppQLIHDj74YCDxFmXtXncPuq+uvvpqbrjhBiDRB+9HrSKXy4V78cUXXwBJotSXX34JJJ4u2WBTU1NZ9NvzyvP3iy++CG7Qb7/9FkhCa5dffjkAgwYNCv9Xd6oZVmnfvj0jRowA4KyzzgIK5wTAXnvt1ey95513XlhTn0GvvfYakCSluVf1eK622mol78fISCMiIiIiIkpA2RmpVrsp6saOtCg+//xz+vTpAyRW7rvvvgsk1pNM1VhlJZJ0iq1Ev++4445rdg1z+zuAt956C0iYh5azcd/HH3+cgw46CEjYapax0vbt24cuIffccw+QXGffvn0BOPDAA4GEkWZRqqGVeP311wOJhWls+eijjw7yuF633HJLs79RblFpZuq6qdMnnXQSUEhCg4Inw/ijsbxf//rXQJJ8ZGzH0oy6urqKyy2LkIHI5NTVDh06BBlcY+XXau/cuTOQPft3zWWb3vsBAwaw3XbbAbVVWtRa3H333QA8/fTTQLK+xneLy2LK0ZDB++k+69mzJ126dAGSvaiOmqegvnTv3r2qMVLP4cmTJwdGvc466wBw2WWXAUmyZ/F7d9llFyBZS3NwfJ788pe/BOBXv/oVUIhTr7zyykByHxYUkZFGRERERESUgLIx0jQTPfnkk4Eku1WraqedduKwww4DknIXY5P2adXSvO+++4CCH7wS1mfa0mtNYwIttGWXXRYoxJmgpfVz6aWX8sknnwBJDDgLRup9GDNmTLA002UtxsiyjH9o/Zr9LEOTif7hD38ACutr7MZyhiWXXBJIMvUsvF9mmWWAymfxun5///vfgYS97bHHHgAce+yxwbvi/Z8yZQqQ6JSfUY0SKHU2nW08derUcE0333wzkDDRffbZB0jY68Ja6gsL10uPj5nmV111VdALZVJG/0Z9Vi+qxar83g4dOoRSHb0CnpNHHnkkkOQreE3Fmb7lgKWETU1NIXNcfbjqqquAJPPV8qJZs2aFn6XLT9KlJJWAZ8aECRPC+uk1NN7vtSjffvvtFxr9qA++d/XVVweSe6CODxs2LOQyeL0LelZHRhoREREREVECysJIi9vt3XnnnUCSAaY/ftdddwUKFtgqq6xS+PL//zdmzTqtQMtBi6Ec1nBr4g3p4vNiSzb991q7Wi7KaNOD4t9lAeXTWr/33ntDnZ0yb7311gCcfvrpQBIbzYKRura2XzReYTarrGLWrFnhGt58800g8W6kWxxWmmmkWfQVV1wBwNprrw3ABRdcABQsXvVBL4p1gtZEH3LIIc1kr0YWpOulxX7uueeGbFFbXl566aVAIrc1mVlDfTGz0mzobbfdtsVeNN6oB0idKtatarBS5fv222/DXjSTXm+Q3qH02VNuz0WxvqXZpeevrF9PS+/evUNNptnE7gnzLKwAqERLSb9r4sSJ4dyQXc6tDWDHjh3nOmDEM3rjjTcGkpaww4YNY9y4cUDSaCcy0oiIiIiIiAxRNkZqh4m//vWvhQ/+/9aE9T7nnnsuUMhgTcc7tXrOOOMMIKm10tqpBLNr165di9ia9a3GNLXc27dv34KJen3KZiz4kUceafb7rKCsL7/8MlCw0mU/dtUxc09ruBodgtKN061bNDtz5ZVXDl1YzIB+7rnngCSeasy00oxfWY132lrPWlC70qy55ppBZuNNdqgp7s4FtdHm0HVba621QuzMVoHW4FVLTveZZ4A1xA6N6NGjR4ibWnvs/60r1YPg/88+++xMMufTbNI9+cwzzwSviszq//7v/4DkfJTRZRFDTzM2PX8//vGPAbj//vuBQq38lVdeCRBeZc56szxbDj/8cKDACMutO7NmzQpscn7r0xpG7HtkphdccEE4a2TeC4qynPb19fXhIFHxTaE2mG4yxpwSelQ4F0m3nwHm1VdfveSbk06nv+eee3j99debfY/NFTyodTGuu+66QWG8LpXwuuuuA+CUU04Bsk/JTx88I0eOBAoBepXdchFlz7JNnXBdbMdokwgTzUxwWHzxxcOhvu666wKE1HQn7+gGrvR1aGjY7s+SFjed17DIIosEvfbBpIFgGMMEqlqA92L33XcPD3yTOCzP8YBXZ7J6sGq82CTAfabL7cMPPwzlC4aNNN5teWm51wknnADA9OnTM0n4S7tMP/zwQwCGDh0a+ourDxoBJil6T7JMRks/dNZcc00gMUAaGxvDWWzYzb1pcpp67hl6xhlnhHOz1LVW51ZYYYVwlmnM2gu6lM/VPb366qsHErWwiK7diIiIiIiIElAWRtquXbswyUVmpCtGd8GCJAylpxKUA1q6WlhHHHFEi6kH6e/TYhs9ejS33347kCRCyYYsYvb/Wpg77bRTRV3TwusyWK6LubGxMVi/sopaKGCX5akfegh0J22//fZhvWRFWu9ZN//XctUaNvRgMoZM/6233gr3wYQXXbw2H8myBKq1aGxsDCzOIvYxY8YAiV57jVl5MfQcyXBcV70S55xzTtiXMlHvj4lRNj3QTde/f/+K6n66vEgdt/3lyy+/HEIZtrSTDfneas4uVv40K66rqwthIPerv9NDZ8jOZKpddtmFDTfcECh9zrHPjAEDBoQzTCasvuqyX5AwlXtQj8ZSSy0VwgMLmywVGWlEREREREQJKAsjraurC+n+Wt6yCeOf87IItXaLC5ghYXflTKkuLihWtnQ5xZyYqYzPmaXpMWD+rVbwueee28JaqqTV6Rpa6N2pU6fQ+EJrLuui+jkhbb0bGzXhoVu3bsF6T3sMqlVYn/7+6dOnA8l8z+7du4cYo8leWugW2u+www5A6VZ6OZHL5cIap5ONHEGV3hOVvgfqhbGwNHsYN25caN5hLoNNMI4//nggST6y0X2l4ruuhfqqt0uW5vfPnDmTI444Aki8GenmGNWEsniG6337/e9/P9czzLm1v/nNb4Ak8W7ChAkhiadUXfe+9e7dOyRneY9t6KIueJa35oxLNw+aMmVKGJSxsIiMNCIiIiIiogSUhZHm8/kWLdB86qdZWC6XC5acjNM2ZVpnxvYcOFtOq83vnj17drAklT39PcWt9YonzHsdxdB6MibWu3fvYPFkgfS6f//996GxvuVFtYR0Cn7Xrl3D/7Vk02udbnWYFdSTf//73wCBXfjzM888k9122w2Ap556CijE1SFpKjGvQQiVRlpXXcd27dqFBirGdGUeWuhZl8GoD+YXeEY8/PDDQKGhgRmb6reVAWbdmydgXLVS8VHXUW+Qa2m835LAHXfcMTTk8LrS7QurGSP1u40xqwsTJ04MMV1jpebAWGJkuz1bpq633nplX+/vv/8+ZMy7By3lMzPaoRENDQ1BZ9OeJPeg902v0XPPPRcGUSzsfYiMNCIiIiIiogSUrWuAsUJjLWb9aT3agiyXy4X3PvDAA0BivYuf//znQHmt4vSQ4z333DNkGlvjNzfWUFdXF+KMshCvU6tT37yvTU1NmVqZ6djAIossEjLbqtF4obWYUztGkbaUrfXKIq5ULI/6KtMwo9RmC7vuumuQNa2r1WAaae9EWibHFo4YMYKrr74aSOJ7ei/23XdfIPv4tGzGdpaOX5RxNDU1hexpWaoZsGbr2ni/0lnqrq819OqDLMma6WOOOSYMWFCXK1GZsLBQPxzAYYx32LBh4YzUY6T8snB/fvbZZwMFL0C5czGKPZ7WrdqXwFip/Qu22morVl11VSDxbJrV7YBv27gaw95oo41CjsbCPmsiI42IiIiIiCgBZWGks2bNChmiMlEbfGutOYx30KBBwcJ36Pf48eOBlt1uymkNa2mYhXbNNdcEH7nj27Rk0oynvr4+NN23a8fzzz8PFKw2SDI4052PssLw4cOBhH2uu+66gdFXczhvKdBa1+rVg+FAXplHORl3MQtOx2T9v/prx6NOnToFK1zL2PtvdmNWscZcLhfWQ4ZmM3JZpy0X33333RDTP+aYYwD43e9+ByTeoKy9GeqqAwpkzDKeyy+/PFyPbel+8YtfAInXK6t6adfGbmK2ktx0002BpK3e0ksvnWkLwAVFulpi9913BwrexCeeeAJIWp8aC/Ua3YMO2K6Unqdruq0t18PoaMO//OUvoYuUQ9PTnkZ1a8cddwQK9eHKv7D6HhlpRERERERECSgLI21sbAx9UPVZm/llFuOzzz4LFKwzrXUtBXtiDhkyBEgso0pa8Y2NjYElb7nllkBiwcwJab+/Y52uv/76Zr/X2sm6XjAdu9hmm20WqLaqlmGsSavYxt82jy8naypmROmOL9ZGm2WuR2XkyJEhzq5HRkvZzNGsmF19fX3YczI24/myIVnECSecEK5p0KBBQHL91Y6ru/cdm+W4t0033TT0B3aNvT9Z67nnmN25/P69994bSNjbzJkzayI7d35I63vPnj1DnoVZ6XMbUVZpfUkPDfFsM2Pb7OKnn3461BEbl9aLaAa4+m9P4TkNMFlQlK38RWFVIg8/W47dddddQCEQL402gWCjjTYCKjt1fU5NFtJNFVrjfklvCDf6nCbIZ7lpVA6//+GHHw4BeZsBVPtwXFB4LbqRLC/IYh5p8We7brr+HVRg8/qHH36Y999/H0iSZExe8GGflWu3qakpuGt1XWlcOXfSZL5ll102HC6VmCdZDnhQK9/2228fDvpqN7dIz0zVPe7ggmL5avkBOjc0NTXVRMOIOaG4jBES1/LOO+/M9ttvD9CivLH4bC7+23JcY3TtRkRERERElICylb/4VNf6NclC15YFtcVIWwhZWj/FFuKCuF3S75mbzFlZoLIl23oVl2Fk5XapFIrHKEESNlhttdWA7Jvwqyeyf9uj+Tqn92a99k1NTUG+yy+/fI7vKd53hgTaCmpJXtfRtqh6p7zncxuGEVF+zMmbmeXei4w0IiIiIiKiBJSNkYo0y8y6xdj/Ktoq65wX1CXLX0zwqnbyVK2vdToRJKIySA9VSK93ZKL/O4iMNCIiIiIiogTkFiRLL5fLTQP+UzlxFgr98vn8EnP7ZZS5bJinzNA25W6LMkPblDvKXDZE/cgO811rWMAHaURERERERERzRNduRERERERECYgP0oiIiIiIiBIQH6QRERERERElID5IIyIiIiIiSkB8kEZERERERJSABWrI0KtXr3y/fv0qJctC4aWXXvpkXunJvXr1yjsjtFYwduzYecrcs2fPmpN53Lhx85QZ2uZat0WZoW3K3RZlbqt7sWfPnnmnz9QKxo8fP9+1rrXnS2v2Iizgg7Rfv348+eSTCy9VBbDoov+vvTOP8qn+//hjZsyIGYSWkzCtsqVIWrQ6nTotTiulU6HNadFGnKhIyJSkOkol2jdtorToWI6jldIeoZIktIiamjGf3x+f83y/79yx9f187r0fv16PfxzGZz7v+77v+76v52t719li3VHz5s1zbsx169bd6phnz54d13C2iQYNGmy1vqt58+bukPRcobi4eKtzrcOLc4WSkpJtmmudrJQr1KtX7//dXDdv3twd35crNGrUaKvro1mzZjk37saNG29x3KWlpTm379WvX3+b6lqz3iJwa+Tn59c4sVzkylmIYfLz891RPMGm8ODHbPW4hmEE0Z5RUFCQeFvLbKH9b0t/qlXif6k9rMVIDcMwDCMDYlOksljKy8tZsWJFtZ9JzdWpUwfwJ5uHfx4XsiR16HF5eTlr1qwB/DFxOry3bt26gD/SK5eUqZS/rkNjS/pAZMOIA+0nlZWV7vmMo5H8DjvsAMDrr78OwLJly9xRe7m4T2wJzZf2EHkL//zzT8DvJV9++SUA8+bNc8fJXXjhhcB/Q5maIjUMwzCMDIhckUrdyYIpKytj7NixgFdMslh22203AO644w4AunbtCsRnvWmssro+/fRTACZPnsyMGTMAWL58OQCnnHIKAGeccQYAXbp0qfY7krY4CwoK3Fg//vhjwFvo4bEmaTHK4q1VK70UCwsLXYxF1m7SByRrndauXRuoeVRgKpWqcb/DsfRcOtIseJC9rk3zH34mdQ+Cn0mS4Pdvbs61rl9++WUgva8cdNBBQLRH8On7pTqVWHX//fezzz77AHD00UcD3pMVPm4yl+KLBQUFbi+cP38+AK+99hoAixcvBuDHH38E4KOPPgLSe0zv3r2BaNdK+Hdval3EuQdH9iLVhelinnnmGQAmTJjgHtrwhf7www8ADB48GIAjjzwSSJ9AH+VGpLFq0xg1ahQATz/9NABr1qyhffv2gH8QdD3vv/9+tb+3atUK8A9TXGgu5YL55ptvuOKKKwD4+uuvATjwwAPdzwCOOOIIwI85iXGWl5cD8MILLwDpeVS5wZAhQwDYeeedq/3fuNAYZ82aBcCYMWMAaNSoEQDHHXcckHbl1a9fv9pnfvvtNwAOPfRQAHbddVcg2Q1Scx98WS5cuBCAl156CfDG4yGHHALg1pCMsKQMRD2jwUTEcNKi9pUJEyYAMHz4cADGjh3rrieOF+kff/wB+OcslUrRp08fwD9rRUVFAO4F265du2p/tmrVKjHjS4bIypUrGTp0KADvvPMO4IVEgwYNgHR2MMANN9wApM8M1jVGsdY1Nv2pPUF7d2FhIcXFxdU+E0eil7l2DcMwDCMDIlOkshhWrVoFwAMPPACkLYiSkhIA9t57bwBnzQupvqit4HDqthSHXMtKKBo9ejRnn302APXq1QNwCvXXX38FvOs6affjhg0bgLSqXrZsGQD33XcfAC1atADg2GOPBbyL96GHHgL8PYsSKTYlnPXt2xeATz75BIC2bds6l9xee+0FwMknnwzAHnvsAcSnisKuQrm3lHj26quvAum5l8IIJtUBHHzwwYBfU/vttx8QrzLVfEmxSdWVlZUxbtw4wCfRybJfsGAB4NeIFF3cnpZwuOXaa691Y+nVq1e1//vFF18AcOeddwJw5plnAnD66ae764sS3XspSa2BFi1auLWr61i9ejUAS5cuBeCtt94C/FofMWJE7B6YsMobPHgwM2fOBHBeoh49egA+tLXvvvsCPsEq6A7OpqIOh6EefvhhACZOnAjA559/DqQV8mmnnQbgErykmqMsqzRFahiGYRgZEHmMVArp22+/BdIWi6wa+dWlSGVtyLoPNz2Iaoz6HilgWVsXXHCB+7uU1M8//wx4Cz5YdJ0kUhtTpkwBYPr06YwcORJIW+SA6zr0yy+/AD4GrSSaKGMJmid9t+79e++9B3jV3LVrVwYNGgTg4jOy1qdOnQrE17BD89GxY0cAbrrpJsAnbykGtnjxYrdGZc1rbb399tvVPtOmTRsgHkUaVqLyDt1+++1A2orXs9iyZUsAvvrqK8DHxOQ9Sio2qrEr2W/OnDlOcQitrWnTpgGwfv16wHs74lL/uufr1q0D4IMPPgBg3Lhxbp61puSRUV6IPiv1FGeJWjjhT/O4YsUKHnzwQcArzz333LPaZ8PJUlHNtcamvUB5NJdeeingY/mrVq1yXhbtF9OnTwdg9913B6LZP0yRGoZhGEYGRF7+Ek6vr6iocFaYskk7deoEeCUal+IIp/TLpy4rRwq1oqLCpXkr1qVrkNUriz7uVmBh5S8F1LBhQ1c+pDFJbSjjTlZmHHFdKfpFixYBvlhd6uiss84C0nEVZRfrmhSTjDv+rPUhxX7RRRcBfn1K+fz1119OrSpuqrEqtiRLPs5MTI1B9/+6664DfKnCpEmTOPzwwwH/7KmsQeNUc5S4s401Hu0R/fv3B2D//ffnqKOOAvz9USbpU089BeDyGdQAPa79RPOtdaHM7fr169dYu8q/UEa6SKJcSnuzFLTijwMHDnQxW8211lKcsfK8vDw3L4qDa9+99dZbgeoeQWXTn3TSSQB069YN8KU78oBmNYabtd9kGIZhGP9BIo+RyloMKjX5rN98803AW5tXX3014K3RqOMyYUWqzLNwDeyYMWOYNGkS4GMbqv+6/PLLgXjijJtCltj3338PeKXXu3dvdtxxR8Bfj+LUrVu3BrwijVNthK1AeSOkGlKplLsPstbDDRDiJtwQQutzl112AdKxRp20EY6Vn3feeYCv4Y3zQAaNRZ4ItXG7/vrrgXR9trJGpTzVREC1s6ozVaZ31LE7jVlxxhEjRgC42sBhw4Y5T5H+r053Upa6vBvhLOW4uOeeewAf78zPz2fy5MmAf06VeaxGEXFn6GpcAD/99BMAt912GwCXXHIJkM6t+O679OEnqi9WDbX2kDiUcyqVct8jdan9VutRe0NeXp6bW+WISL3Ki9i2bdusj90UqWEYhmFkQNYUaVjF6W2/0047AenYBqRjMOF6pdGjRwPe/y1LomnTpkD0FmW4pVS4vnTRokUu21QqT3VgTzzxBOCtHqmpuLuSPPvss4C33Lt16+bGIhWt+kxZweq2k2T7urDXIT8/31mZ4ViT4qtJ1GJCzXUiRTR37twazcilpk899VTAr4s4PRaaH9XjKjb0+OOPA+n6YcXLtRakrPXsxRUj1Z6g+VEuwrvvvlttzG3atHEZ86od1P9Vdro8LVo3derUiTXrWOpNjBw50sV61fVIMVLFrdXgPY71oX1N6/fRRx8FfGa5vG0zZ85041aOiJTggAEDADjnnHMAv4dENc/6vcq83ZyXKtiuU2PW+yPKHIusvEjz8vI22X4M/KanQG9FRYW7GUqMufHGGwG/0at/bbiIOW50TePGjXP9gZU0oySN8ePHA3DiiScCvlFD1C4wbTxaLHqhq3SnY8eO7kUkQ0VudqWK6z7E6VYK9tQFn1Ck61m7dq1rzag1pM1FxkzSPYL1QGruZ8+eXaNUS+0XZUAmcR6lxqK+rioLUOORgoKCGm5SPWvHHHMM4J/BKOc6uMGpmYJejipBU8LZkCFDnItaL1m57GTcav+QG7Bv376xJMeET0rRel2/fr178cglquvr168f4J8DPZtRznfYIJQ4kBH+xhtvAGljUG5QhSj0bMrlrqY6cbRghG2bF+0PWhcyYmW8RCEczLVrGIZhGBmQkSINptfL9XLYYYcBNS1xJWgUFRW5z0nFyb0kC1KuXQXrO3TokEhLNVFYWOjGLxUnl/Xvv/8OxO8elbJTs3HNj1K+CwsLXXOGRx55BPDJMWrBGKdKktKRy1CeCjUY17qZNWsWc+bMAWqWTiXdHCDsEtNBBTNmzHA/a9iwIeBLqJIk3OhdakjtOouKipwSGjhwIOBdvCr1CSvVKNxj+fn5fPbZZ4BP1NHz9MorrwDeW1VaWuqSY+RxUemRXJJ6NqNUSUEvnBSQVLO+T16pAQMGcM011wB+7Urpn3/++YAPWwSTZqJY5/n5+e6e6vfrXnfu3LnaGJo1a+ZO5NJnpFovvvhiwDfuUCvMpKlVq5bzFKmcR2PV/heFt9AUqWEYhmFkQEaKVJbYhg0beOyxxwCvfmT1ysceVJRSGIpbSOVJ9SkGImXSqVOnrCnSYKmLrOytWaypbCZoPQAAB09JREFUVMpZZGpOr3iMiKPhO9Qsslezd1nhxx9/PJBOPiorKwP8vEr5qzlAnCpf36XklSuvvBJINyEHX0a0dOlSl6ij1nxqbahr7dChAxB/7Fz3WOPQmq+qqnL3RQk9us5cQipP15GXl+darukYOylTHXAg6z3qZhiK0x9wwAGAP35OZTfyZCxfvtypuKuuugrwilSxyc2dpZpNKisr3b6l+dS+pVaMUsQ9evRwa1Vjk+dCz204WSfb860xrl692jXdUMywcePGgN8XguWHKodSfoUSuRRX1XpP+pxaUVRUxPPPPw94la9EzCj3O1OkhmEYhpEBWcnaTaVSzhqUBaMGBsrukqKrqqpiyZIlgG/pJcteMQ9lGapYPxuWhCwyqeBp06a5tn5bK6coLCx0BeJqSaVCdh3VlFQrNX2frktNpocPH+5aHqoIXA3ig/cibmSZa97UJCJ4aPawYcMAnxWrtntJZL4G0bxpbWsNFBUVOUWlNaVYUpKlRWHCamfdunXuWtTKUO31grG6qNm4caPzMihjVOi5VcnL0KFDXTmPMlw1x4r3Rom8aUuWLHGKR5nyuvfK2Faj+qZNmzp1rCxpZfvrmDLFUMPxy2yhzNUZM2Y4749KSRRb1tikUCsrK92eIdQ0R4cvKDaatCLV+2f+/PnOQ6FKC+3v8iZGgSlSwzAMw8iAjBSpLMEGDRq4ei+1FFOrOlltwYYNK1euBLzfXZaCfPOymJTJmY1YmCxbHYPWr18/LrvsMgBatWpVY4zB7124cKGrdVXBumI5Os5HrbOiVqThel1Z58pqHD58OAA9e/Z0xd6yInMJza3ugTKJS0pKnLX73HPPAT6GLoUat8rT2lFjC2UqBmumdR801zoAPqka6E0RXt/jx493eQg333wzgMvSjFv9h5uih4/2Us7F1KlTXa2pMoyTOHKsvLzc5SDo36RM7777bsDnJFRUVLjre/HFFwGvlhQD7tmzZ7Xfle01Lo9V586dXYtIeQLVYnFTa1Xj0TOohvZqI6g60qTWuZ5NvUP69+/vGs4olh5HnbwpUsMwDMPIgIwUaVAdde/eHfAZUrJ0FZ8LHqIdbvek+jYd2aN2e9lE3ynV26ZNG9ekWUpHtV2yihcsWAD4Q4XBH4atbkHKYtNn4qpxlMUqRSeLTGque/fu7lqVYSfrPhcI3w/FWoItvhTXkbWr+sG4kfLUQd7qWKM1/c8//7gYo2J9SXVd2hThuVbHlylTpnDCCScA3nqPOnt0W9FalYdLMfRevXo59RbnUV5Cz3n79u1dd7M+ffoAPjaqOLPi5HPnznWxX3k15G279957AZ9jEZUnQM9QaWkpgwYNAnDH0Smv5cMPPwR8a8XatWu72m1l0MvzGM4JSaq2W0p53rx5QLrNoWqPFTeNY52YIjUMwzCMDMiKRKmqqnIZX6pDU5adLEpZRC1btnSqTj0xpUgVV5Ilkc04gX6XuluUlZVx1113AV5FK34qdDBwnz59nLWp47BU6xi3EhX6PtVxSV3rOisqKlz8QMpfWY06Gkm1ebnQtD5oNYa7SEmdKKa+du1awMeg4hq/FPKmaoZlmevP8HFqSaKxqPOO4v1r1qxh1KhRgK9n1H1ISokGY5CAy+DWOu/fv79bH0koUlFRUeH2OuVYaDzKAdHabtKkieuuo/pRqUHFeeOKSQc9JRqD4rTaH7QPFhcX1zh4XPt40rH/oDcI4MknnwTSh3prj44zzp81X59ukJJGdP6e3ARaVCUlJS69Wi/f8KnwUWyM4Rdd69atXcBfCUNKWtD3yzXTtGlTt5nr5iS9kISua1MJF1pkXbp0AbyrWidQJJ2yvjk0/3Ir6e9KhNF9ict40T3XA6pCeyWOVFZWuuL2uBpz/Bs0JpWLzJ8/H0gnxchADCf5JI2eLxkvcp82adIk8TIoSK89vRRVZratnwP/vCa5j4RfihIwClOkUqlEjZUtof1YZ+0GTwlS+WScSWi599QbhmEYxnZE1rNPpC7lKpIrVVRVVTmFkYS1E3QlynUoF+7m/u/GjRsTD6r/LwTd6QATJ06s9u+5lBATJHyWrYrVu3btCnjXb9zWvKxgNeVQyUtlZaVrUi/1l0uNGDSWdu3aAXDuuecC6XKN8DmqSStSjUPPpo4HFMFkxaSJsxFEHITL/rYH5J3QYR3t27eP9VhIYYrUMAzDMDIgsnqIcPJFLhJlTDYXCBd3by/XqTWjJtq33HIL4D0YScXzgsdLgT/uD3xyXS7OscY9dOhQwCuOYAwpaSW6ObYndWTEh9aFGkKo+czff/+diMfCFKlhGIZhZEDev3l75+XlrQa+i244/xOlqVRq58390MacNbY4Ztg+x709jhm2z3HbmLOGrY/42Opcw798kRqGYRiGUR1z7RqGYRhGBtiL1DAMwzAywF6khmEYhpEB9iI1DMMwjAywF6lhGIZhZIC9SA3DMAwjA+xFahiGYRgZYC9SwzAMw8gAe5EahmEYRgb8H8cd4+lBJz62AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_100_image(X)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 代价函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 401)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_raw, y_raw = load_data('ex4data1.mat', transpose=False)\n",
    "\n",
    "# 增加全部为1的一列，\n",
    "X = np.insert(X_raw, 0, np.ones(X_raw.shape[0]), axis=1)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 10, 10, ...,  9,  9,  9], dtype=uint8)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_raw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expand_y(y):\n",
    "#     \"\"\"expand 5000*1 into 5000*10\n",
    "#     where y=10 -> [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]: ndarray\n",
    "#     \"\"\"\n",
    "    res = []\n",
    "    for i in y:\n",
    "        y_array = np.zeros(10)\n",
    "        y_array[i - 1] = 1\n",
    "\n",
    "        res.append(y_array)\n",
    "\n",
    "    return np.array(res)\n",
    "# from sklearn.preprocessing import OneHotEncoder\n",
    "# encoder = OneHotEncoder(sparse=False)\n",
    "# y_onehot = encoder.fit_transform(y)\n",
    "# y_onehot.shape #这个函数与expand_y(y)一致"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., ..., 0., 0., 1.],\n",
       "       [0., 0., 0., ..., 0., 0., 1.],\n",
       "       [0., 0., 0., ..., 0., 0., 1.],\n",
       "       ...,\n",
       "       [0., 0., 0., ..., 0., 1., 0.],\n",
       "       [0., 0., 0., ..., 0., 1., 0.],\n",
       "       [0., 0., 0., ..., 0., 1., 0.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = expand_y(y_raw)\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 读取权重"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_weight(path):\n",
    "    data = sio.loadmat(path)\n",
    "    return data['Theta1'], data['Theta2']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 401), (10, 26))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1, t2 = load_weight('ex4weights.mat')\n",
    "t1.shape, t2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "序列化2矩阵\n",
    "在这个nn架构中，我们有theta1（25,401），theta2（10,26），它们的梯度是delta1，delta2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def serialize(a, b):\n",
    "    return np.concatenate((np.ravel(a), np.ravel(b)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10285,)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = serialize(t1, t2)  # 扁平化参数，25*401+10*26=10285\n",
    "theta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 前向传播 Feedforward\n",
    "> (400 + 1) -> (25 + 1) -> (10)\n",
    "\n",
    "<img style=\"float: center;\" src=\"./img/nn_model.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def feed_forward(theta, X):\n",
    "    \"\"\"apply to architecture 400+1 * 25+1 *10\n",
    "    X: 5000 * 401\n",
    "    \"\"\"\n",
    "\n",
    "    t1, t2 = deserialize(theta)  # t1: (25,401) t2: (10,26)\n",
    "    m = X.shape[0]\n",
    "    a1 = X  # 5000 * 401\n",
    "\n",
    "    z2 = a1 @ t1.T  # 5000 * 25\n",
    "    a2 = np.insert(sigmoid(z2), 0, np.ones(m), axis=1)  # 5000*26\n",
    "\n",
    "    z3 = a2 @ t2.T  # 5000 * 10\n",
    "    h = sigmoid(z3)  # 5000*10, this is h_theta(X)\n",
    "\n",
    "    # return的这些均是后向传播所需要的\n",
    "    return a1, z2, a2, z3, h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sigmoid函数的定义为：\n",
    "$$g(z)={\\frac{1}{1+e^{{-z}}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deserialize(seq):\n",
    "#     \"\"\"into ndarray of (25, 401), (10, 26)\"\"\"\n",
    "    return seq[:25 * 401].reshape(25, 401), seq[25 * 401:].reshape(10, 26)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.12661530e-04, 1.74127856e-03, 2.52696959e-03, ...,\n",
       "        4.01468105e-04, 6.48072305e-03, 9.95734012e-01],\n",
       "       [4.79026796e-04, 2.41495958e-03, 3.44755685e-03, ...,\n",
       "        2.39107046e-03, 1.97025086e-03, 9.95696931e-01],\n",
       "       [8.85702310e-05, 3.24266731e-03, 2.55419797e-02, ...,\n",
       "        6.22892325e-02, 5.49803551e-03, 9.28008397e-01],\n",
       "       ...,\n",
       "       [5.17641791e-02, 3.81715020e-03, 2.96297510e-02, ...,\n",
       "        2.15667361e-03, 6.49826950e-01, 2.42384687e-05],\n",
       "       [8.30631310e-04, 6.22003774e-04, 3.14518512e-04, ...,\n",
       "        1.19366192e-02, 9.71410499e-01, 2.06173648e-04],\n",
       "       [4.81465717e-05, 4.58821829e-04, 2.15146201e-05, ...,\n",
       "        5.73434571e-03, 6.96288990e-01, 8.18576980e-02]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, _, _, _, h = feed_forward(theta, X)\n",
    "h # 5000*10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 代价函数\n",
    "先回忆一下，不考虑正则化的代价函数为：\n",
    "$$J(\\Theta)=\\frac{1}{m}\\sum\\limits_{i=1}^m\\sum\\limits_{k=1}^K{\\left[{-y_k^{(i)}}\\log\\left({h_\\Theta}\\left({x^{(i)}}\\right)\\right)_k-\\left(1-{y_k^{(i)}}\\right)\\log\\left(1-{h_\\theta}\\left({x^{(i)}}\\right)\\right)_k\\right]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在这个例子中，$y$ 和 $h_{\\theta} \\in R^{5000 \\times 10}$。\n",
    "\n",
    "如果忽略m和k维度，代价函数可以写作 $y*log(h_{\\theta}) - (1-y)*log(1-h_{\\theta})$  \n",
    "需要做的是把所有维度的代价函数计算后加起来。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(theta, X, y):\n",
    "    \"\"\"\n",
    "    y: (m, k) ndarray\n",
    "    \"\"\"\n",
    "    m = X.shape[0]  # get the data size m\n",
    "\n",
    "    _, _, _, _, h = feed_forward(theta, X)\n",
    "\n",
    "    # np.multiply is pairwise operation\n",
    "    pair_computation = -np.multiply(y, np.log(h)) - np.multiply((1 - y), np.log(1 - h))\n",
    "\n",
    "    return pair_computation.sum() / m\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2876291651613189"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost(theta, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 正则化代价函数\n",
    "\n",
    "神经网络正则化的代价函数写作：\n",
    "\\begin{align*}\n",
    "J(\\Theta)=&\\frac{1}{m}\\sum\\limits_{i=1}^m\\sum\\limits_{k=1}^K{\\left[{-y_k^{(i)}}\\log\\left({h_\\Theta}\\left({x^{(i)}}\\right)\\right)_k-\\left(1-{y_k^{(i)}}\\right)\\log\\left(1-{h_\\theta}\\left({x^{(i)}}\\right)\\right)_k\\right]}\\\\&+\\frac{\\lambda}{2m}\\sum\\limits_{l=1}^{L-1}\\sum\\limits_{i=1}^{s_l}\\sum\\limits_{j=1}^{s_{l+1}}{\\left(\\Theta_{ji}^{(l)}\\right)^2}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularized_cost(theta, X, y, lambd=1):\n",
    "    \"\"\"the first column of t1 and t2 is intercept theta, ignore them when you do regularization\"\"\"\n",
    "    t1, t2 = deserialize(theta)  # t1: (25,401) t2: (10,26)\n",
    "    m = X.shape[0]\n",
    "\n",
    "    reg_t1 = (lambd / (2 * m)) * np.power(t1[:, 1:], 2).sum()  # this is how you ignore first col\n",
    "    reg_t2 = (lambd / (2 * m)) * np.power(t2[:, 1:], 2).sum()\n",
    "\n",
    "    return cost(theta, X, y) + reg_t1 + reg_t2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38376985909092365"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regularized_cost(theta, X, y, lambd=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 反向传播 Backpropagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "读取数据和权重过程与前向传播相同"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5000, 401), (5000, 10))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape,y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 401), (10, 26))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1.shape, t2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10285,)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sigmoid函数梯度\n",
    "Sigmoid函数梯度函数的公式写作：\n",
    "$$g'(z) = {\\frac{\\partial}{\\partial z}}g(z)=g(z)(1-g(z))$$\n",
    "\n",
    "梯度函数的计算函数如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_gradient(z):\n",
    "    return np.multiply(sigmoid(z), 1 - sigmoid(z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid_gradient(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\Theta$ 的梯度\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在我们准备好实施反向传播来计算梯度。\n",
    "\n",
    "由于反向传播所需的计算是代价函数中所需的计算过程，我们实际上将扩展代价函数以执行反向传播并返回代价和梯度。\n",
    "计算的公式如下：\n",
    "$$\\delta^{\\left(3\\right)}=a^{(3)}-y$$\n",
    "$$\\delta^{\\left(2\\right)}=\\left(Θ^{(2)}\\right)^T\\delta^{(3)}.*g'(z^{(2)})$$\n",
    "$$\\Delta^{\\left(l\\right)}=\\Delta^{(l)}+\\delta^{(l+1)}\\left(a^{(l)}\\right)^T$$\n",
    "$$\\frac{\\partial}{\\partial\\Theta_{ij}^{(l)}}J(\\Theta)=\\frac{1}{m}\\Delta_{ij}^{l}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(theta, X, y):\n",
    "    # initialize\n",
    "    t1, t2 = deserialize(theta)  # t1: (25,401) t2: (10,26)\n",
    "    m = X.shape[0]\n",
    "\n",
    "    delta1 = np.zeros(t1.shape)  # (25, 401)\n",
    "    delta2 = np.zeros(t2.shape)  # (10, 26)\n",
    "\n",
    "    # 前向传播\n",
    "    a1, z2, a2, z3, h = feed_forward(theta, X)\n",
    "\n",
    "    for i in range(m):\n",
    "        a1i = a1[i, :]  # (1, 401)\n",
    "        z2i = z2[i, :]  # (1, 25)\n",
    "        a2i = a2[i, :]  # (1, 26)\n",
    "\n",
    "        hi = h[i, :]    # (1, 10)\n",
    "        yi = y[i, :]    # (1, 10)\n",
    "\n",
    "        # 第3层\n",
    "        d3i = hi - yi  # (1, 10)\n",
    "\n",
    "        # 第2层\n",
    "        z2i = np.insert(z2i, 0, np.ones(1))  # make it (1, 26) to compute d2i\n",
    "        d2i = np.multiply(t2.T @ d3i, sigmoid_gradient(z2i))  # (1, 26)\n",
    "\n",
    "        # careful with np vector transpose\n",
    "        delta2 += np.matrix(d3i).T @ np.matrix(a2i)  # (1, 10).T @ (1, 26) -> (10, 26)\n",
    "        delta1 += np.matrix(d2i[1:]).T @ np.matrix(a1i)  # (1, 25).T @ (1, 401) -> (25, 401)\n",
    "\n",
    "    delta1 = delta1 / m\n",
    "    delta2 = delta2 / m\n",
    "\n",
    "    return serialize(delta1, delta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1, d2 = deserialize(gradient(theta, X, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 401), (10, 26))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1.shape, d2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 梯度校验\n",
    "假设你是用函数$f_{i}(\\theta)$计算$\\frac{\\partial}{\\partial\\theta_{i}}J(\\theta)$，那么可以根据如下公式来判断$f_i$的计算是否准确。\n",
    "\n",
    "$$f_{i}(\\theta)\\approx\\dfrac{J\\left(\\theta^{i+}\\right)-J\\left(\\theta^{i-}\\right)}{2\\varepsilon}$$\n",
    "\n",
    "梯度检验函数如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_checking(theta, X, y, epsilon, regularized=False):\n",
    "    def a_numeric_grad(plus, minus, regularized=False):\n",
    "        \"\"\"calculate a partial gradient with respect to 1 theta\"\"\"\n",
    "        if regularized:\n",
    "            return (regularized_cost(plus, X, y) - regularized_cost(minus, X, y)) / (epsilon * 2)\n",
    "        else:\n",
    "            return (cost(plus, X, y) - cost(minus, X, y)) / (epsilon * 2)\n",
    "\n",
    "    theta_matrix = expand_array(theta)  # expand to (10285, 10285)\n",
    "    epsilon_matrix = np.identity(len(theta)) * epsilon\n",
    "\n",
    "    plus_matrix = theta_matrix + epsilon_matrix\n",
    "    minus_matrix = theta_matrix - epsilon_matrix\n",
    "\n",
    "    # calculate numerical gradient with respect to all theta\n",
    "    numeric_grad = np.array([a_numeric_grad(plus_matrix[i], minus_matrix[i], regularized)\n",
    "                                    for i in range(len(theta))])\n",
    "\n",
    "    # analytical grad will depend on if you want it to be regularized or not\n",
    "    analytic_grad = regularized_gradient(theta, X, y) if regularized else gradient(theta, X, y)\n",
    "\n",
    "    # If you have a correct implementation, and assuming you used EPSILON = 0.0001\n",
    "    # the diff below should be less than 1e-9\n",
    "    # this is how original matlab code do gradient checking\n",
    "    diff = np.linalg.norm(numeric_grad - analytic_grad) / np.linalg.norm(numeric_grad + analytic_grad)\n",
    "\n",
    "    print('如果你的反向传播算法是对的，那么差异会小于 10e-9 (假设 epsilon=0.0001).\\n差异为: {}\\n'.format(diff))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expand_array(arr):\n",
    "    \"\"\"replicate array into matrix\n",
    "    [1, 2, 3]\n",
    "\n",
    "    [[1, 2, 3],\n",
    "     [1, 2, 3],\n",
    "     [1, 2, 3]]\n",
    "    \"\"\"\n",
    "    # turn matrix back to ndarray\n",
    "    return np.array(np.matrix(np.ones(arr.shape[0])).T @ np.matrix(arr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "如果你的反向传播算法是对的，那么差异会小于 10e-9 (假设 epsilon=0.0001).\n",
      "Relative Difference: 2.144837505196823e-09\n",
      "\n"
     ]
    }
   ],
   "source": [
    "gradient_checking(theta, X, y, epsilon= 0.0001)#这个运行很慢，谨慎运行"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 正则化的梯度\n",
    "\n",
    "我们还需要对反向传播函数进行一个修改，即将梯度计算加正则化。 \n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial}{\\partial\\Theta_{ij}^{(l)}}J(\\Theta)&=\\frac{1}{m}\\Delta_{ij}^{l} \\text{ , for } j = 0\\\\\n",
    "\\frac{\\partial}{\\partial\\Theta_{ij}^{(l)}}J(\\Theta)&=\\frac{1}{m}\\Delta_{ij}^{l} + \\frac{\\lambda}{m}\\Theta^{(l)}_{ij}\\text{ , for } j \\ge 1\n",
    "\\end{align*}\n",
    "\n",
    "最后的正式版本如下。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularized_gradient(theta, X, y, l=1):\n",
    "    \"\"\"don't regularize theta of bias terms\"\"\"\n",
    "    m = X.shape[0]\n",
    "    delta1, delta2 = deserialize(gradient(theta, X, y))\n",
    "    t1, t2 = deserialize(theta)\n",
    "\n",
    "    t1[:, 0] = 0\n",
    "    reg_term_d1 = (l / m) * t1\n",
    "    delta1 = delta1 + reg_term_d1\n",
    "\n",
    "    t2[:, 0] = 0\n",
    "    reg_term_d2 = (l / m) * t2\n",
    "    delta2 = delta2 + reg_term_d2\n",
    "\n",
    "    return serialize(delta1, delta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "如果你的反向传播算法是对的，那么差异会小于 10e-9 (假设 epsilon=0.0001).\n",
      "差异为: 3.188645959632846e-09\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 运行耗时，耐心等待\n",
    "gradient_checking(theta, X, y, epsilon=0.0001, regularized=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 训练模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "记得随机初始化参数以打破对称性。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_init(size):\n",
    "    return np.random.uniform(-0.12, 0.12, size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_training(X, y):\n",
    "\n",
    "    init_theta = random_init(10285)  # 25*401 + 10*26\n",
    "\n",
    "    res = opt.minimize(fun=regularized_cost,\n",
    "                       x0=init_theta,\n",
    "                       args=(X, y, 1),\n",
    "                       method='TNC',\n",
    "                       jac=regularized_gradient,\n",
    "                       options={'maxiter': 400})\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 0.3153887919013315\n",
       "     jac: array([-1.65164486e-04,  4.04632393e-08,  9.52229821e-08, ...,\n",
       "       -3.20925145e-05, -8.30450522e-05, -8.86181724e-05])\n",
       " message: 'Max. number of function evaluations reached'\n",
       "    nfev: 400\n",
       "     nit: 27\n",
       "  status: 3\n",
       " success: False\n",
       "       x: array([ 0.00000000e+00,  2.02316196e-04,  4.76114911e-04, ...,\n",
       "       -1.07493708e+00,  1.36602285e+00,  6.60932712e-01])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 运行耗时，耐心等待\n",
    "res = nn_training(X, y)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 显示准确率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, y_answer = load_data('ex4data1.mat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_theta = res.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_accuracy(theta, X, y):\n",
    "    _, _, _, _, h = feed_forward(theta, X)\n",
    "\n",
    "    y_pred = np.argmax(h, axis=1) + 1\n",
    "\n",
    "    print(classification_report(y, y_pred))\n",
    "    \n",
    "    correct = [1 if a == b else 0 for (a, b) in zip(y_pred, y)]\n",
    "    accuracy = (sum(map(int, correct)) / float(len(correct)))\n",
    "    print ('总体正确率为：{0}%'.format(accuracy * 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           1       0.99      0.97      0.98       500\n",
      "           2       0.96      0.97      0.97       500\n",
      "           3       0.95      0.98      0.97       500\n",
      "           4       0.94      0.99      0.96       500\n",
      "           5       1.00      0.92      0.95       500\n",
      "           6       0.93      1.00      0.96       500\n",
      "           7       0.99      0.93      0.96       500\n",
      "           8       0.98      0.97      0.97       500\n",
      "           9       1.00      0.89      0.94       500\n",
      "          10       0.90      1.00      0.95       500\n",
      "\n",
      "   micro avg       0.96      0.96      0.96      5000\n",
      "   macro avg       0.96      0.96      0.96      5000\n",
      "weighted avg       0.96      0.96      0.96      5000\n",
      "\n",
      "总体正确率为：96.14%\n"
     ]
    }
   ],
   "source": [
    "show_accuracy(final_theta, X, y_answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 显示隐藏层"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_hidden_layer(theta):\n",
    "    \"\"\"\n",
    "    theta: (10285, )\n",
    "    \"\"\"\n",
    "    final_theta1, _ = deserialize(theta)\n",
    "    hidden_layer = final_theta1[:, 1:]  # ger rid of bias term theta\n",
    "\n",
    "    fig, ax_array = plt.subplots(nrows=5, ncols=5, sharey=True, sharex=True, figsize=(5, 5))\n",
    "\n",
    "    for r in range(5):\n",
    "        for c in range(5):\n",
    "            ax_array[r, c].matshow(hidden_layer[5 * r + c].reshape((20, 20)),\n",
    "                                   cmap=matplotlib.cm.binary)\n",
    "            plt.xticks(np.array([]))\n",
    "            plt.yticks(np.array([]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hidden_layer(final_theta)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python (Python 3.6)",
   "language": "python",
   "name": "python36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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