{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5dd13f3d",
   "metadata": {},
   "source": [
    "# 第 9 章　人工神經網路（ANN）基礎 — 實作 Notebook\n",
    "\n",
    "「醫學生的機器學習入門」第 9 章配套程式。建議在 **Google Colab** 執行（選單「執行階段 → 全部執行」即可）；本機 Jupyter 也可以。\n",
    "\n",
    "- 第 1–4 節：用 scikit-learn 的 `MLPClassifier` 在乳癌資料（WDBC）上訓練神經網路，只需要 Colab 預裝套件。\n",
    "- 第 5 節（進階）：用 Keras 3 在胸部 X 光小圖（PneumoniaMNIST）上訓練。**沒有安裝 Keras 的環境會自動跳過這一節**，不會報錯。\n",
    "\n",
    "本 notebook 的醫學資料皆為公開教學資料集，結果僅供學習，不構成臨床建議。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8334c925",
   "metadata": {},
   "source": [
    "## 0. 環境檢查\n",
    "先印出套件版本，並固定隨機種子讓結果可以重現。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a531b07d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:34.545585Z",
     "iopub.status.busy": "2026-09-29T20:02:34.545517Z",
     "iopub.status.idle": "2026-09-29T20:02:35.243324Z",
     "shell.execute_reply": "2026-09-29T20:02:35.242999Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy 2.1.3 | pandas 2.2.3 | scikit-learn 1.6.1 | matplotlib 3.10.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "print(\"numpy\", np.__version__, \"| pandas\", pd.__version__,\n",
    "      \"| scikit-learn\", sklearn.__version__, \"| matplotlib\", matplotlib.__version__)\n",
    "RS = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b5513d8",
   "metadata": {},
   "source": [
    "## 1. 一個神經元：加權總和 + 活化函數\n",
    "一個人工神經元做兩件事：把輸入乘上權重後加總（再加偏差 b），然後丟進活化函數。下面用 NumPy 手算一次。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "35553341",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.244583Z",
     "iopub.status.busy": "2026-09-29T20:02:35.244490Z",
     "iopub.status.idle": "2026-09-29T20:02:35.246700Z",
     "shell.execute_reply": "2026-09-29T20:02:35.246406Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weighted sum z = 1.510\n",
      "sigmoid(z) = 0.819  (probability-like, between 0 and 1)\n",
      "relu(z)    = 1.510\n"
     ]
    }
   ],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "def relu(z):\n",
    "    return np.maximum(0, z)\n",
    "\n",
    "x = np.array([1.2, -0.5, 2.0])      # three standardized inputs\n",
    "w = np.array([0.8, 0.3, 1.1])       # weights\n",
    "b = -1.5                            # bias\n",
    "\n",
    "z = x @ w + b                       # weighted sum\n",
    "print(f\"weighted sum z = {z:.3f}\")\n",
    "print(f\"sigmoid(z) = {sigmoid(z):.3f}  (probability-like, between 0 and 1)\")\n",
    "print(f\"relu(z)    = {relu(z):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bacbe19c",
   "metadata": {},
   "source": [
    "z 是加權總和；sigmoid 把它壓到 0～1，可以解讀成機率——這其實就是第 4 章的邏輯迴歸。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "24578e8e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.247691Z",
     "iopub.status.busy": "2026-09-29T20:02:35.247634Z",
     "iopub.status.idle": "2026-09-29T20:02:35.293578Z",
     "shell.execute_reply": "2026-09-29T20:02:35.293187Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zz = np.linspace(-5, 5, 200)\n",
    "fig, ax = plt.subplots(figsize=(6, 3.5))\n",
    "ax.plot(zz, sigmoid(zz), label=\"sigmoid\")\n",
    "ax.plot(zz, np.tanh(zz), label=\"tanh\")\n",
    "ax.plot(zz, relu(zz), label=\"ReLU\")\n",
    "ax.set_ylim(-1.2, 3)\n",
    "ax.set_xlabel(\"z (weighted sum)\")\n",
    "ax.set_ylabel(\"f(z)\")\n",
    "ax.set_title(\"Common activation functions\")\n",
    "ax.legend()\n",
    "ax.grid(alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "887a6a1c",
   "metadata": {},
   "source": [
    "三條曲線都是「非線性」的，這正是神經網路能畫出彎曲決策邊界的關鍵。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987f3b2c",
   "metadata": {},
   "source": [
    "## 2. 為什麼需要隱藏層：XOR 問題\n",
    "我們造一份「對角線同類」的資料（XOR）。邏輯迴歸只能畫一條直線，加了隱藏層的神經網路則可以把平面切成好幾塊。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b22e031d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.294932Z",
     "iopub.status.busy": "2026-09-29T20:02:35.294848Z",
     "iopub.status.idle": "2026-09-29T20:02:35.594920Z",
     "shell.execute_reply": "2026-09-29T20:02:35.594579Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic regression training accuracy: 0.50\n",
      "MLP (8 hidden neurons) training accuracy: 1.00\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "\n",
    "rng = np.random.default_rng(RS)\n",
    "centers = np.array([[0, 0], [1, 1], [0, 1], [1, 0]], dtype=float)\n",
    "X_xor = np.vstack([c + rng.normal(0, 0.13, size=(60, 2)) for c in centers])\n",
    "y_xor = np.repeat([0, 0, 1, 1], 60)\n",
    "\n",
    "logit = LogisticRegression().fit(X_xor, y_xor)\n",
    "mlp_xor = MLPClassifier(hidden_layer_sizes=(8,), max_iter=3000, random_state=RS).fit(X_xor, y_xor)\n",
    "print(f\"Logistic regression training accuracy: {logit.score(X_xor, y_xor):.2f}\")\n",
    "print(f\"MLP (8 hidden neurons) training accuracy: {mlp_xor.score(X_xor, y_xor):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1c588d",
   "metadata": {},
   "source": [
    "邏輯迴歸大約只有五成（跟亂猜一樣），神經網路接近 100%。畫出決策邊界更清楚："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "be720d62",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.596168Z",
     "iopub.status.busy": "2026-09-29T20:02:35.596077Z",
     "iopub.status.idle": "2026-09-29T20:02:35.678393Z",
     "shell.execute_reply": "2026-09-29T20:02:35.678019Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(np.linspace(-0.6, 1.6, 200), np.linspace(-0.6, 1.6, 200))\n",
    "grid = np.c_[xx.ravel(), yy.ravel()]\n",
    "fig, axes = plt.subplots(1, 2, figsize=(9, 4))\n",
    "for ax, (name, m) in zip(axes, [(\"Logistic regression\", logit), (\"MLP (8,)\", mlp_xor)]):\n",
    "    p = m.predict_proba(grid)[:, 1].reshape(xx.shape)\n",
    "    ax.contourf(xx, yy, p, levels=10, cmap=\"RdBu_r\", alpha=0.35)\n",
    "    ax.contour(xx, yy, p, levels=[0.5], colors=\"k\")\n",
    "    ax.scatter(*X_xor.T, c=y_xor, cmap=\"coolwarm\", s=12)\n",
    "    ax.set_title(name)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a6c4106",
   "metadata": {},
   "source": [
    "黑線是模型的分類界線（預測機率 = 0.5）。只有加了隱藏層的網路能把四團點正確分開。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59bc48b0",
   "metadata": {},
   "source": [
    "## 3. 表格資料實戰：WDBC 乳癌資料\n",
    "資料來自 scikit-learn 內建的 Breast Cancer Wisconsin (Diagnostic)，569 筆、30 個細胞核影像特徵。\n",
    "**注意：sklearn 版的 target 0 = malignant（惡性）、1 = benign（良性）**，先印出來確認。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3780939f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.679570Z",
     "iopub.status.busy": "2026-09-29T20:02:35.679491Z",
     "iopub.status.idle": "2026-09-29T20:02:35.714395Z",
     "shell.execute_reply": "2026-09-29T20:02:35.714018Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(569, 30) | target_names: ['malignant' 'benign']\n",
      "target\n",
      "benign(1)       357\n",
      "malignant(0)    212\n",
      "Name: count, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X, y = load_breast_cancer(return_X_y=True, as_frame=True)\n",
    "print(X.shape, \"| target_names:\", load_breast_cancer().target_names)\n",
    "print(y.value_counts().rename({0: \"malignant(0)\", 1: \"benign(1)\"}))\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=0.2, stratify=y, random_state=RS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e64a277",
   "metadata": {},
   "source": [
    "先切訓練集與測試集（分層抽樣保持良惡性比例），測試集要留到最後才看。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e46037a",
   "metadata": {},
   "source": [
    "### 3.1 用 Pipeline 訓練 MLPClassifier\n",
    "神經網路用梯度下降學習，對特徵尺度很敏感，所以一定先標準化。這裡用兩個隱藏層（16 與 8 個神經元）。\n",
    "不使用 `early_stopping=True`：在這份小資料上它常常太早停下來，模型幾乎沒學到東西。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e4e516f5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.715539Z",
     "iopub.status.busy": "2026-09-29T20:02:35.715449Z",
     "iopub.status.idle": "2026-09-29T20:02:35.839256Z",
     "shell.execute_reply": "2026-09-29T20:02:35.838883Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iterations used (n_iter_): 345\n",
      "test accuracy: 0.9561\n",
      "test AUC (malignant as positive): 0.9940\n",
      "confusion matrix (rows = true [malignant, benign]):\n",
      "[[41  1]\n",
      " [ 4 68]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.metrics import roc_auc_score, confusion_matrix\n",
    "\n",
    "mlp = make_pipeline(\n",
    "    StandardScaler(),\n",
    "    MLPClassifier(hidden_layer_sizes=(16, 8), max_iter=1000, random_state=RS),\n",
    ")\n",
    "mlp.fit(X_train, y_train)\n",
    "\n",
    "net = mlp[-1]\n",
    "print(\"iterations used (n_iter_):\", net.n_iter_)\n",
    "print(f\"test accuracy: {mlp.score(X_test, y_test):.4f}\")\n",
    "proba_malignant = mlp.predict_proba(X_test)[:, 0]          # column 0 = malignant\n",
    "print(f\"test AUC (malignant as positive): {roc_auc_score(y_test == 0, proba_malignant):.4f}\")\n",
    "print(\"confusion matrix (rows = true [malignant, benign]):\")\n",
    "print(confusion_matrix(y_test, mlp.predict(X_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a60a330b",
   "metadata": {},
   "source": [
    "準確率約 0.96。混淆矩陣第一列是真正惡性的病例：被判成良性的那一格就是偽陰性，臨床上代價最高。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26f31c44",
   "metadata": {},
   "source": [
    "### 3.2 網路裡到底有多少參數？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ee7ec85",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.840513Z",
     "iopub.status.busy": "2026-09-29T20:02:35.840450Z",
     "iopub.status.idle": "2026-09-29T20:02:35.842318Z",
     "shell.execute_reply": "2026-09-29T20:02:35.841970Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "layer 0: weight matrix (30, 16)\n",
      "layer 1: weight matrix (16, 8)\n",
      "layer 2: weight matrix (8, 1)\n",
      "total trainable parameters: 641\n"
     ]
    }
   ],
   "source": [
    "n_params = sum(W.size for W in net.coefs_) + sum(b.size for b in net.intercepts_)\n",
    "for i, W in enumerate(net.coefs_):\n",
    "    print(f\"layer {i}: weight matrix {W.shape}\")\n",
    "print(\"total trainable parameters:\", n_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00fb06a3",
   "metadata": {},
   "source": [
    "30×16 + 16×8 + 8×1 個權重，再加上每個神經元一個偏差，總共 641 個參數——比訓練資料的 455 筆還多，這就是神經網路容易過擬合的原因之一。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c90f2b7",
   "metadata": {},
   "source": [
    "### 3.3 不標準化會怎樣？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2d49d1de",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.843225Z",
     "iopub.status.busy": "2026-09-29T20:02:35.843170Z",
     "iopub.status.idle": "2026-09-29T20:02:35.954860Z",
     "shell.execute_reply": "2026-09-29T20:02:35.954404Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "without scaling: test accuracy = 0.9298\n",
      "with scaling:    test accuracy = 0.9561\n"
     ]
    }
   ],
   "source": [
    "raw = MLPClassifier(hidden_layer_sizes=(16, 8), max_iter=1000, random_state=RS)\n",
    "raw.fit(X_train, y_train)\n",
    "print(f\"without scaling: test accuracy = {raw.score(X_test, y_test):.4f}\")\n",
    "print(f\"with scaling:    test accuracy = {mlp.score(X_test, y_test):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c348e21",
   "metadata": {},
   "source": [
    "沒標準化時準確率明顯下降：有些特徵（如面積）數值上千，有些不到 1，梯度下降會被大尺度的特徵牽著走。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d86c0932",
   "metadata": {},
   "source": [
    "### 3.4 看訓練損失曲線\n",
    "`loss_curve_` 記錄每個 epoch（把訓練資料看完一遍）後的損失。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "910b4f5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.956014Z",
     "iopub.status.busy": "2026-09-29T20:02:35.955931Z",
     "iopub.status.idle": "2026-09-29T20:02:35.983891Z",
     "shell.execute_reply": "2026-09-29T20:02:35.983481Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 3.5))\n",
    "ax.plot(net.loss_curve_)\n",
    "ax.set_xlabel(\"epoch\")\n",
    "ax.set_ylabel(\"training log loss\")\n",
    "ax.set_title(\"MLPClassifier training loss on WDBC\")\n",
    "ax.grid(alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03c88278",
   "metadata": {},
   "source": [
    "損失一路下降代表模型在「背熟」訓練資料；但光看訓練損失無法判斷有沒有過擬合，要搭配驗證資料（第 5 節的 Keras 會示範）。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0471d0f6",
   "metadata": {},
   "source": [
    "### 3.5 正則化強度 alpha 與網路大小\n",
    "`alpha` 是 L2 正則化強度：越大越懲罰過大的權重。用 5 折交叉驗證比較幾種設定（只在訓練集上做）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "473c6948",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:35.985002Z",
     "iopub.status.busy": "2026-09-29T20:02:35.984941Z",
     "iopub.status.idle": "2026-09-29T20:02:38.543476Z",
     "shell.execute_reply": "2026-09-29T20:02:38.543138Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hidden=(4,)       alpha=0.0001  CV AUC = 0.9922 ± 0.0109\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hidden=(16, 8)    alpha=0.0001  CV AUC = 0.9943 ± 0.0056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hidden=(128, 128) alpha=0.0001  CV AUC = 0.9924 ± 0.0104\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hidden=(128, 128) alpha=1       CV AUC = 0.9948 ± 0.0084\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "settings = [((4,), 1e-4), ((16, 8), 1e-4), ((128, 128), 1e-4), ((128, 128), 1.0)]\n",
    "for hidden, alpha in settings:\n",
    "    pipe = make_pipeline(StandardScaler(),\n",
    "                         MLPClassifier(hidden_layer_sizes=hidden, alpha=alpha,\n",
    "                                       max_iter=1000, random_state=RS))\n",
    "    s = cross_val_score(pipe, X_train, y_train, cv=5, scoring=\"roc_auc\")\n",
    "    print(f\"hidden={str(hidden):10s} alpha={alpha:<7g} CV AUC = {s.mean():.4f} ± {s.std():.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15914402",
   "metadata": {},
   "source": [
    "在這份資料上各種設定的差距都很小（落在彼此的標準差之內），表示「網路越大越好」並不成立。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d1a78b6",
   "metadata": {},
   "source": [
    "### 3.6 神經網路一定比較好嗎？\n",
    "同樣用 5 折交叉驗證，拿邏輯迴歸與隨機森林當對照。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c5c1a8f6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:38.544741Z",
     "iopub.status.busy": "2026-09-29T20:02:38.544661Z",
     "iopub.status.idle": "2026-09-29T20:02:39.990983Z",
     "shell.execute_reply": "2026-09-29T20:02:39.990630Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic regression  CV AUC = 0.9935 ± 0.0108\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random forest        CV AUC = 0.9867 ± 0.0158\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLP (16, 8)          CV AUC = 0.9943 ± 0.0056\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "models = {\n",
    "    \"Logistic regression\": make_pipeline(StandardScaler(), LogisticRegression(max_iter=1000)),\n",
    "    \"Random forest\": RandomForestClassifier(n_estimators=300, random_state=RS),\n",
    "    \"MLP (16, 8)\": make_pipeline(StandardScaler(),\n",
    "                                 MLPClassifier(hidden_layer_sizes=(16, 8), max_iter=1000, random_state=RS)),\n",
    "}\n",
    "for name, m in models.items():\n",
    "    s = cross_val_score(m, X_train, y_train, cv=5, scoring=\"roc_auc\")\n",
    "    print(f\"{name:20s} CV AUC = {s.mean():.4f} ± {s.std():.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77dcf69e",
   "metadata": {},
   "source": [
    "三者的 AUC 都在 0.98–0.99 附近、差距小於標準差。這種小型表格資料，神經網路沒有明顯優勢，卻更難解釋、更需要調參數。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f4d70fe",
   "metadata": {},
   "source": [
    "## 4. 小結（sklearn 部分）\n",
    "- `MLPClassifier` 用法跟前面各章的模型一樣：`fit`、`predict`、`predict_proba`、放進 `Pipeline`。\n",
    "- 一定要標準化；不要用 `early_stopping=True`（入門階段）；看 `n_iter_` 確認有沒有真的訓練。\n",
    "\n",
    "## 5. 進階：Keras 3 + 胸部 X 光（PneumoniaMNIST）\n",
    "PneumoniaMNIST 是 MedMNIST v2 的子集（CC BY 4.0），把小兒胸部 X 光縮成 **28×28 像素**的灰階小圖，標籤為正常（0）／肺炎（1）。\n",
    "我們直接從 Zenodo 下載官方 `.npz` 檔（約 4 MB），用 NumPy 讀取，不需要安裝 medmnist 或 PyTorch。\n",
    "\n",
    "先檢查 Keras 是否可用。Colab 已預裝 Keras 3；本機沒有的話，這一節會自動跳過。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6e63fb68",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:39.992303Z",
     "iopub.status.busy": "2026-09-29T20:02:39.992194Z",
     "iopub.status.idle": "2026-09-29T20:02:42.694738Z",
     "shell.execute_reply": "2026-09-29T20:02:42.694442Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "keras 3.13.2 | backend: tensorflow\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "os.environ[\"KERAS_BACKEND\"] = \"tensorflow\"   # must be set before importing keras\n",
    "try:\n",
    "    import keras\n",
    "    print(\"keras\", keras.__version__, \"| backend:\", keras.backend.backend())\n",
    "except ImportError:\n",
    "    keras = None\n",
    "    print(\"Keras is not installed in this environment -> section 5 training will be skipped.\")\n",
    "    print(\"Run this notebook on Google Colab to try it, or `pip install tensorflow keras` locally.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "438a3c85",
   "metadata": {},
   "source": [
    "接著下載資料（已下載過就直接讀本機檔案）。網路失敗時會印出清楚的錯誤訊息，而不是讓整本 notebook 中斷。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a0f26748",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:42.695982Z",
     "iopub.status.busy": "2026-09-29T20:02:42.695852Z",
     "iopub.status.idle": "2026-09-29T20:02:42.715450Z",
     "shell.execute_reply": "2026-09-29T20:02:42.714975Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train images (4708, 28, 28), normal=1214, pneumonia=3494\n",
      "val   images (524, 28, 28), normal=135, pneumonia=389\n",
      "test  images (624, 28, 28), normal=234, pneumonia=390\n"
     ]
    }
   ],
   "source": [
    "import urllib.request\n",
    "\n",
    "NPZ_URL = \"https://zenodo.org/records/10519652/files/pneumoniamnist.npz?download=1\"\n",
    "NPZ_PATH = os.path.join(\"data\", \"pneumoniamnist.npz\")\n",
    "os.makedirs(\"data\", exist_ok=True)\n",
    "\n",
    "pneu = None\n",
    "try:\n",
    "    if not os.path.exists(NPZ_PATH):\n",
    "        print(\"downloading PneumoniaMNIST (~4 MB) from Zenodo ...\")\n",
    "        urllib.request.urlretrieve(NPZ_URL, NPZ_PATH)\n",
    "    pneu = np.load(NPZ_PATH)\n",
    "    for split in [\"train\", \"val\", \"test\"]:\n",
    "        imgs, labels = pneu[f\"{split}_images\"], pneu[f\"{split}_labels\"].ravel()\n",
    "        print(f\"{split:5s} images {imgs.shape}, normal={np.sum(labels == 0)}, pneumonia={np.sum(labels == 1)}\")\n",
    "except Exception as e:\n",
    "    print(\"Could not download/load PneumoniaMNIST:\", repr(e))\n",
    "    print(\"Check your internet connection or download the file manually from\", NPZ_URL)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef7e768f",
   "metadata": {},
   "source": [
    "訓練集裡肺炎占約 74%，類別不平衡：一個「全部猜肺炎」的模型準確率就有七成多，所以等一下要看 AUC、敏感度、特異度，不能只看準確率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b52be8f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:42.716589Z",
     "iopub.status.busy": "2026-09-29T20:02:42.716529Z",
     "iopub.status.idle": "2026-09-29T20:02:42.826423Z",
     "shell.execute_reply": "2026-09-29T20:02:42.826047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x340 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if pneu is not None:\n",
    "    fig, axes = plt.subplots(2, 6, figsize=(9, 3.4))\n",
    "    imgs, labels = pneu[\"train_images\"], pneu[\"train_labels\"].ravel()\n",
    "    for row, cls in enumerate([0, 1]):\n",
    "        idx = np.where(labels == cls)[0][:6]\n",
    "        for ax, i in zip(axes[row], idx):\n",
    "            ax.imshow(imgs[i], cmap=\"gray\")\n",
    "            ax.set_title(\"normal\" if cls == 0 else \"pneumonia\", fontsize=8)\n",
    "            ax.axis(\"off\")\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d6512b5",
   "metadata": {},
   "source": [
    "28×28 的解析度遠低於臨床判讀所需，這份資料只適合拿來學神經網路的概念。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70aeea52",
   "metadata": {},
   "source": [
    "### 5.1 建立與訓練全連接網路\n",
    "把每張 28×28 的圖攤平成 784 個數字，除以 255 縮放到 0～1，接上兩層 ReLU 隱藏層與一個 sigmoid 輸出。\n",
    "加入 Dropout（訓練時隨機關掉部分神經元）與 EarlyStopping（驗證損失連續 5 個 epoch 沒進步就停，並還原最佳權重）防止過擬合。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "02dc7b7c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:42.827720Z",
     "iopub.status.busy": "2026-09-29T20:02:42.827651Z",
     "iopub.status.idle": "2026-09-29T20:02:44.958451Z",
     "shell.execute_reply": "2026-09-29T20:02:44.958026Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">Model: \"sequential\"</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1mModel: \"sequential\"\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Layer (type)                    </span>┃<span style=\"font-weight: bold\"> Output Shape           </span>┃<span style=\"font-weight: bold\">       Param # </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ dense (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                   │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">128</span>)            │       <span style=\"color: #00af00; text-decoration-color: #00af00\">100,480</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dropout (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dropout</span>)               │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">128</span>)            │             <span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_1 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                 │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">64</span>)             │         <span style=\"color: #00af00; text-decoration-color: #00af00\">8,256</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_2 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                 │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">1</span>)              │            <span style=\"color: #00af00; text-decoration-color: #00af00\">65</span> │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mLayer (type)                   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mOutput Shape          \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m      Param #\u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ dense (\u001b[38;5;33mDense\u001b[0m)                   │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m128\u001b[0m)            │       \u001b[38;5;34m100,480\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dropout (\u001b[38;5;33mDropout\u001b[0m)               │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m128\u001b[0m)            │             \u001b[38;5;34m0\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_1 (\u001b[38;5;33mDense\u001b[0m)                 │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m64\u001b[0m)             │         \u001b[38;5;34m8,256\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_2 (\u001b[38;5;33mDense\u001b[0m)                 │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m1\u001b[0m)              │            \u001b[38;5;34m65\u001b[0m │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Total params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">108,801</span> (425.00 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Total params: \u001b[0m\u001b[38;5;34m108,801\u001b[0m (425.00 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">108,801</span> (425.00 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Trainable params: \u001b[0m\u001b[38;5;34m108,801\u001b[0m (425.00 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Non-trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> (0.00 B)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Non-trainable params: \u001b[0m\u001b[38;5;34m0\u001b[0m (0.00 B)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 1s - 13ms/step - accuracy: 0.8207 - auc: 0.8610 - loss: 0.3948 - val_accuracy: 0.9160 - val_auc: 0.9716 - val_loss: 0.2407\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9080 - auc: 0.9581 - loss: 0.2272 - val_accuracy: 0.9389 - val_auc: 0.9785 - val_loss: 0.1702\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 3/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9197 - auc: 0.9683 - loss: 0.1978 - val_accuracy: 0.9561 - val_auc: 0.9803 - val_loss: 0.1512\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 4/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9280 - auc: 0.9741 - loss: 0.1804 - val_accuracy: 0.9542 - val_auc: 0.9817 - val_loss: 0.1426\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 5/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9293 - auc: 0.9747 - loss: 0.1762 - val_accuracy: 0.9523 - val_auc: 0.9827 - val_loss: 0.1426\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 6/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9369 - auc: 0.9760 - loss: 0.1702 - val_accuracy: 0.9523 - val_auc: 0.9835 - val_loss: 0.1353\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 7/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9299 - auc: 0.9768 - loss: 0.1675 - val_accuracy: 0.9523 - val_auc: 0.9820 - val_loss: 0.1365\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 8/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9339 - auc: 0.9768 - loss: 0.1683 - val_accuracy: 0.9561 - val_auc: 0.9851 - val_loss: 0.1308\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 9/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9380 - auc: 0.9793 - loss: 0.1571 - val_accuracy: 0.9580 - val_auc: 0.9843 - val_loss: 0.1323\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 10/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9314 - auc: 0.9756 - loss: 0.1728 - val_accuracy: 0.9599 - val_auc: 0.9851 - val_loss: 0.1326\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 11/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9352 - auc: 0.9779 - loss: 0.1625 - val_accuracy: 0.9504 - val_auc: 0.9797 - val_loss: 0.1566\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 12/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9376 - auc: 0.9802 - loss: 0.1557 - val_accuracy: 0.9523 - val_auc: 0.9847 - val_loss: 0.1445\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 13/30\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74/74 - 0s - 1ms/step - accuracy: 0.9397 - auc: 0.9798 - loss: 0.1533 - val_accuracy: 0.9504 - val_auc: 0.9797 - val_loss: 0.1509\n"
     ]
    }
   ],
   "source": [
    "hist = None\n",
    "if keras is not None and pneu is not None:\n",
    "    keras.utils.set_random_seed(RS)\n",
    "\n",
    "    def prep(split):\n",
    "        Xs = pneu[f\"{split}_images\"].reshape(-1, 28 * 28).astype(\"float32\") / 255.0\n",
    "        ys = pneu[f\"{split}_labels\"].ravel().astype(\"float32\")\n",
    "        return Xs, ys\n",
    "\n",
    "    Xp_tr, yp_tr = prep(\"train\")\n",
    "    Xp_va, yp_va = prep(\"val\")\n",
    "    Xp_te, yp_te = prep(\"test\")\n",
    "\n",
    "    model = keras.Sequential([\n",
    "        keras.Input(shape=(28 * 28,)),\n",
    "        keras.layers.Dense(128, activation=\"relu\"),\n",
    "        keras.layers.Dropout(0.3),\n",
    "        keras.layers.Dense(64, activation=\"relu\"),\n",
    "        keras.layers.Dense(1, activation=\"sigmoid\"),\n",
    "    ])\n",
    "    model.compile(optimizer=keras.optimizers.Adam(learning_rate=1e-3),\n",
    "                  loss=\"binary_crossentropy\",\n",
    "                  metrics=[\"accuracy\", keras.metrics.AUC(name=\"auc\")])\n",
    "    model.summary()\n",
    "\n",
    "    hist = model.fit(Xp_tr, yp_tr, validation_data=(Xp_va, yp_va),\n",
    "                     epochs=30, batch_size=64, verbose=2,\n",
    "                     callbacks=[keras.callbacks.EarlyStopping(\n",
    "                         monitor=\"val_loss\", patience=5, restore_best_weights=True)])\n",
    "else:\n",
    "    print(\"Skipped: Keras or the dataset is not available.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ce2853b",
   "metadata": {},
   "source": [
    "每一行是一個 epoch：`loss`／`accuracy` 是訓練集，`val_` 開頭的是驗證集。batch_size=64 表示每看 64 張圖就更新一次權重。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f94becf",
   "metadata": {},
   "source": [
    "### 5.2 學習曲線：訓練 vs 驗證"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4a15b35b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:44.959731Z",
     "iopub.status.busy": "2026-09-29T20:02:44.959661Z",
     "iopub.status.idle": "2026-09-29T20:02:45.036839Z",
     "shell.execute_reply": "2026-09-29T20:02:45.036377Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yTwD7JAD/DTj8J3DmELD2HW2S/dtumBaAtx4MeNd/ZCarkv7qB5Zp0+FV2n43Fd1Na82WoLpZb+0yyInNwIElWmB+cqsWnMu0+g3AKxBoNbAyCB8CBDWDI2DQXY2WTXwR5O2G7KJy7D6Zje5xWhBORESWrfgthcSk4veFyPBsROTEVJ/bYqA4R+tzK4W55Nb4WLt1KcpCYHY6XNwqtMJV5wTF+n3pa2yw7jZLUJhzQptqQwI+PQBXwXjVID3MfL4EsXXanjLgzEHztHBpxc5Krn55V3cgrD0QqbdcV7ZiB8bYvgVfXl8P5P3OP7KHoaIC+Wlp8IuI0FpZ7UFQU6D3v7RJPr+Sei0B+L7FQGEmsGOBNkl6fsvLzraC20MAKt+hI6u1gFnSxk8fMH9ePqMSZMsFA0khr67velxfbbpyolZoTv7/KghfBhSeAfb+pE0ivIO2vrZDgbh+df/c2wkG3dWQdPfOMf5YfSgbW5KzGHQTEdXR3XffjVWrVqnprbfeUvM++ugjVXTz119/xcSJE9XoFn/88YcayUKKdK5bt07V9+jQoYMqxjlkyJAa08vld/rDDz/EL7/8gt9//10V8Jw1a5YaIYOI7IwEeyVnA2PzQFmfqns+2/y5iguPKlPnVGI92NVbOVWrp2/N99Vyfue5X/lYgiUJHvIzKqd0Lf1Zbk3n6bflxdqFAAmAawqCq/IK0gJOY6t5lRZ1dx/4Jm+HS0FyZWGzJO11qhMQc7b1Wp+atAXctZEWyIqk9T3hJm2S74qkZ0sKeuKv2kUS1Sd6OfDrU0BUl7MBuLSaN8TFD7ngJUXx9JTxo2vNP0cubkBs38rW7MFAVNe6XdzwDwe6jtQmqXh/clvlay3RWsTT92qTZAHId6zl5WeDcOnS0Egw6K5B5yg/Leg+mon7BrRs2HeFiOg8rcOFpbYZZsrHw63WVbcl0N63b58aqUKv17F79251++yzz+L1119Hq1atEBISgmPHjuHaa6/FSy+9BC8vL3z66ae44YYbkJSUhLi4uBpfY9q0aXjttdcwc+ZMzJkzB6NGjcLRo0cRGmqh9EUHMHfuXLV/pPBp165d1X6SkUdqGp5OLnZ88sknOHHiBNq3b49XX30VV199tXEZyUyYOnUqPv/8c7VOGWlELrDIRRRWZHcC0l9TCiHVNEkAKa10VYNoaWG2GBctSFFToJZ6q9/3CoDBKwB5pS7wC5FU4sq0YT2ornpfJinCZa3WT3n94Jp/w8yHlsqrDMJPV97qQXo1gbrMlxR2Sf+WSVKTqyH/q3MSkyVokZZrPS1cv2+ptG+qH+nL3by/Nl31IpCxXwvApRU8eZ3WL1ymVa9oF0r0QmzSGm7JFmD5Hh9aVdmavfzcbI2g2LMp4xIEewdZ5nVd3YBmPbXpivFAwRng0Apgf2XAn5+mpeXLJJq00fqBy3a0uBTw8IG9YtBdA2npFpuPZjbk+0FEdF4ScCdM/t0me2nP9GHw9azdYSMoKEiNRS3ji0dFaVVJExMT1a0E4UOHDjUuK0GyBIS6F154AYsWLcKPP/5YY9FOIcHeHXfcoe6//PLLePvtt7FhwwazINGZLViwQGUQzJs3D3379lV964cNG6YuZkRImmUVEjhLMC0ZBPHx8SqD4Oabb8aaNWvQvXt3tYwE4e+9954KzDt27IhNmzap7AV5vx999FEb/C/posmwPRKw5ZsGzhkmAXTV+We0YLo+ZLioyuDYPFjWg+eqzwWdu6waIsq1caUSX4iLyYUEKahVmyBdClFVbS2XW5PWdENRNop9o+EZ2wOuURJgdwSCmzee/UJAWFsg7DHg0se093ff71oQLoFw7klg03+1Sb4Xajiya4G2V10w5f4ceguzpItLcHt8Y5XhzryBFgO0lHEJcGW7GqKV3TcU6PQPbZLfrNSd2vZJEC5F6CS1Xab1753dRr0gW5PWtu8GYYJBdw0SIv3g5uqClJwinMwqREyw/V45ISJqTHr16mX2OC8vT7WeSqr4qVOnUFZWhsLCQjUE5fl06dLFeF+KrAUGBiItLc1q293YzJ49G2PHjlVBsZDgW/bx/PnzVbZBVZ999hmef/55lXUgHnroISxdulSl7UswLiQAv+mmm3DdddcZ0/6/+uordbGDbKysGK5yEl5+Sktrrq4VWgJn0yC6pirU5yOVqCWNubpJUpp9Qqppga68z1Rly5BAQvazTBL8nOcCRFZamnaRjYF24yffr+6jtKm0SCvApreCy5Bte3/UJvmOSgV0aQWPv04LPquTm1LZl1pas1dovxumpD+/CmCvBJrbQSuyq+vZYnSX/Z/W/eTQyrNBuPz+6SnweFa7wNRWbwW/TMs8sSEG3TXw9nBFQnQgdp7IVq3dDLqJyB5Iire0ONvqtS2hahXyp556CkuWLFEp523atIGPjw9uvfVWlJSUnHc9Hh7mQ4pIenOFXAknte82b96MCRMmGPeGq6ur6ie/du3aavdQcXExvL29zebJe7F69Wrj4/79++ODDz5QXQfatWuH7du3q+clwK+JrFcmXU6O1loq75Ul3i9Zh3S7cNj3XoqH5aVqJ8hyYp2bAheT+/qta2Emzs1fuDBJx1YBs48EzZXBs08TGPT76nFoZRGvJloaqZzUX4wGeI8c/vNQB9wXDrwfpDK+Xt372tfVEGQuqhDbb3CRQnnJa7RpySQYZAzwdlejos0weGRmADs2w3BwubZc1d+CllfAoIqgXamlkJuq5f6TfZ2eW4zkzEIcO1OgTZmFSK68n1dcBndXV3i4u8Ld1QUebi7qsbub3Nfmubu5wlPmVz4+O//sfXXr1hoebm3h3uEhRBYfQevstWiZtRbR2VvhlnUU2PgfNZW7euBMaE9kRF2G09GXIc0lAoP8gxHkW/+aBbX9XDHoPo8eccHGoPuGrjH1flOIiOpLAsvapnjbmqSXSx/gC/n7779VqrikMust30eOHGmALXRcGRkZat9HRkaazZfHepp/VZJ6LsHz5ZdfjtatW2PZsmVYuHCh2XsoLeQSNEv6uZubm3pO+uJLf/qaSD9x6X9fVXp6OoqKimCJE57s7Gx1oicXFhqN8hK4FqTDLT9Nuy1Ig6t+X92mafMkjbiWDK7uqPAORYVPCCq8ZQpVtwa576PdV5Px+RDt5L1W2ystY6VAbvVjIduLRvt5sALuCyC/pBwns4vgVV7o2J8J96ZAx3+pyTX3BLyProDXkeXwPLkeLjK2esY+uK95G1WTzkvDO6E4dgCKYy9DaUTXs+Njy3XS82SOSVe3k9klOJFdjJMy5ZjeL0Zx2YVGBiiHdVyiJl8Uob/rbgx03Y4rXLcjFukIz1inJuyaiROGJjha+CqiOl5W71fMzc2t1XKN48zNhkH3J2uPYksy+3UTEdWVpB6vX79eBdD+/v41Xg1u27atCu6keJpcVJg0aZJjtUg0ElL8TtLRJaCW90ECb0lNl3R03TfffIMvvvgCX375perTvW3bNlVRXgqqjRkzptr1Smu79C3XSdAuFetlGDjpElBf8lmR7ZX12cUJtQwTpbdMV7ZEuxjvy/xTWmt11VTO8zBIYBwQBfhHabcBUTDo9ytvK/wikJ5bivCICLi5usJKIw3bPbv7PNiQs+yLrIISHD1dgCOnC1Rrqtw/ejofR88UICPvbMZUXGgaujQLRpdmQejaLAgdYwIbzUXsOpHuBK2lDseTql+/atWWwmP7l6DCxQ0uepXxVoPg5heuqv1XrfhfXmFAak6Rapk2tlhX3iZX2a/VcXUBooN8EBfqg9hQX20Kkce+CPLxQFl5BcoqDCgtN6CsogKlZRUorTCgTH8st8ZlKtR8udWWqXxcce4y+n3tcQv8VXEtlpeVI6zkGDoXbEDnok3oWLIDTV1Oo7RFl2rrm9RV1QyxmjjgJ81yejTXxufeczIHhSXl8PF01kMYEVHdSdq4BGIJCQmqj7YMGVYdaV299957VepyWFgYxo8fb0xBposj+1FaolNTU83my2O9sF1VcmL+ww8/qNbn06dPq0BaWralyrzu6aefVvNuv/129bhz586qYry0ZtcUdEtFepmqkiDAUoGABBaWXF+tycWhI38B277Uxj6WgFr6TNeWBNMmgfTZKRrwj9RuA6LgIn13qxQEOqc8kARY0kJui/1gZ2z2ebBDjrAvVLpyXrEWWGfka0G1Cq7z1eOcorLz/n2gt7taJvmMpDgX4ucdp4yBYbvIAHSVQDxWAvFgtI8KUGnLDsM3BOj8DzXJRZj0yj7+8nnILSpFckquMZDW0r+1wPp4ZiFKyisuuF/jmviqQFqCarlV90N8VbdcT3d72o99Adyq7lUU5+HMrmWIa9nWIt+L2q6DQfd5xAR5IyrQWxVT23E8C31b1bESIBGRE5M+v1X7D0saeXUt4suXLzeb98gjj5g9rppuLidhVWVl1T4N19FJan/Pnj1Vivjw4cPVPDnhksfnqwivX7WXcc9lCLHvv/8eI0aMMD5XUFBwzgmGBPdOl5mQcxLY9gWw9XMgs5quEDJGswqYI6sNoo3zqgmmiZyRtKyeyi5EcmWLtWqpVvfzVTBYUHL+dGQ5X2/exLdy8kOLJn7qvgSF/p5uOJB8EqeKPbHrZA62H8vC9uNZSM0pRmJKrpoWbDqm1uPl7oqEmEAVgHeNDVIt4y2b+MFVIvRGpqSsQhWDPpapBdPJZ/Jx4FQm0goOqMA6s+D8495Lv+mmla3TpkG1HlgH+ZrXVWk0PHxR0lSC8IbFoPsCVwd7NA/GrztTsDk5k0E3ERE1GpLSLa3PUi1exuaWIcPy8/ON1cxHjx6tgmtppRbSFUDG5+7WrZu6lYryEkw/88wzxnVKFwDpwy3jp0t6+datW42ZCg6vvBTYtxjY8qlWHVcfTkcqc8twNjJUT1BTreVahrlhME1kRlJ+pQXVNKDWU8ElKDxfy6rEvBIASjAtQZ8eVLcI81MB4PmyUeV3TFpl28SFYWD7s+nEkj6tB+A7jmer+9IivjU5S026AG93lZIuAbgejEuQL3GCLVVICniupIDr6d+VLdWZBTh+pkA1GlZcoGt1Ez9PNDMG0+YBtvwfpZAZWQaD7gvoEReigu4tHK+biIgakZEjR6piZZMnT0ZKSooKphcvXmwsriZDspm2WktauYzVfejQIdUHX4YOk2HEgoODjcvMmTNH9bl/+OGH1fBskoL+wAMPqNdwWOn7gK2fAtu/1sY/1skQOt3vAhJuAjyr9ogksmxwVVRWrlp7C4rLUVBapu5L10c1r0R7rM2rcr+wED4+qXA5t0NCjdeFzh9LutTpb8rLDTiZLYF2AU5kFaoW7Zp4urmiWagWWKsW61BfNA/TWq2bWiFdOTLQG1d1jFKTnkElreyS3brtmBaI7zqRjdyiMvx94LSadOEBXloALv3DY7V+4sEWqIRtSrbnTH6JsS+1HlQfl6A6sxAnapECLqMxNQvR+lM3C/FBsEcFOjaPUNkAElz7ezEUbCjc0xfQs7Jf95bkLPXht/VVLSIiotqSVPKa0slXrlxp9njgwIHYs2fPedcXEBCgWsxlcmjFecCeH7RW7WPrz86XFPGud2jBdlgbW24h2XFKb1ZhCbILSlXlbAmIqw+Oy5Fv9lw5CkvLkF9cGUyXas+px6XWqvRsm6En9TRw1WpdeSuPpfCWmw3TuOUcv2WYn5pu6tbU2Dq/LzXX2BK+/Xi2eixDYi3dm6omnfwfVP/wykC8U0zQBetByfBZpsNqaf2pzwbX8hm6UAq49J+OlYJlIb4qsJZgWgXaoT4I9/cyxi7S4p9m0qebGhaD7gvoGBOkrqzJlSa5+iVfRCIiInIwUifg+CatVXvXQqAkT5vv4ga0G6YF2m2Hnh1ShxxeUWm5Ov/LLChBVkGpui+VsjNN7p8pKK2cV4LM/FIVRFk7aPX1dFPBnJ+nu7r1NU7uxufk1tvdFQX5+fDz9691o1F19TLOPneev6thvrxqVJD0t5YWa1/VQtyYGrCkqJrEAjLd0SdOzZOLIbtPZqsAXFrFJRjX+qFr04/bT6rl5AJC2wh/Y6E22X9a6rfez/rC/apFZKCXCqj1CuCSDq499mEKeCPCoPsCJODu0jQIm45mqvG6GXQTERE5kPwMLXV862dAuskY5qGtge7/BLrdqRU+o0ZLAklpMcysDKC1gLm0MlDWguhMk8BZC6ZLUFR6cQUCJaYM9PZQqbt6ACzBsp/+uDJw9vVyV/e1Zdzh56UtJ/dVUO0ly5qvoy4FvdiyaR3yfvRqEaomnWQ27DihBeASjMttWu65hdqqE+zrYQyiVWt1ZXAtQbak1Xt7cPQkR8Cgu5Yp5nrQfWvPZtZ/V4iIiMh6KsqBgyu0Vu3EX4GKytYmdx+g43CtVbt5fxZDa+DAuLisQrUuS7CrbstM7lfOLy6ret/kb+RxSTnO5OajsPyw1jqtWqlL1Li/F0PSd6WvboivB0L8Km/lsel99fjs/UAfD5umSVPDk0rel7UNV5MuJbuoskhbFnaeyIGHq0tl6nfl2NWVgXaAN7NnnAGD7jqM1701OdPa7wcRERFZS+ZRbZgvGVc75/jZ+THdtUC7862AdxD3/0WQ/sp/7kvHnpM5qg/y2cD5bNBcXBkY67emAbYE3NYmw0GdEzBXBssSWIf6eWi3lcFzsJ8HArzcG1U6NNkPSauPCorCsMpCbeTcGHTXsoK5SErNRU5RqUoZIiIiokagtAhI/FlLHz+06mzvUxkju8tILdiO6mTrrWyU5Jxo+d40LN6VgpX70i46HbsqaSWW/siSViuTl4crvN3l/tl56r679pyX+9l5EliXFxcgNiIUof5exiBbAukLFbUiIrIWBt21IEUfZLy65DMF2JachcvbnU0dISIiIjuUskurPr5jAVB0dsxdtLoC6DEaaH8d4OFtyy1slKQ/9NI9qfht1yk1hJLpkEWSNntZ2zCVLitBs1eVANl4XwJpY1BtHjTLrRSvuljsx0xE9ohBdx36dUvQLf26GXQTEVlfixYt8Pjjj6tJSIrnokWLMHz48GqXP3LkCFq2bImtW7eqMakvlqXWQzZQlA3s/E5r1T659ez8wGZA91FAt1FASHO+NXWUllOE33en4LddKVh/+IzZWMutw/1wTadoXN0pCh1jApmKTURUDQbddejXvWjrCWxhv24iIps4deoUQkK07j6WcvfddyMrKws//PCDcV5sbKx6rbCwMIu+FlmJwQCPkxvgsuZnYM+PQFmhNt/VA4i/Fug+Gmg9CHBlanFdyHBGeqAt5z6mw0UlRAfimk5RKtBuGxlg4TeUiMjxMOiupR5xwepW0svlCi+rUhIRNayoqIYpRuPm5tZgr0X1dHwTXBbejyZnDp6dF94B6HGX1l/bjxdO6uJgep7qny3TzhPZZs91jwvG1R21QFvGXCYiotq7+E4zTqZ9ZAD8PN2QW1yG/Wm5tt4cIiK79sEHHyAmJkb1rzR100034d5778XBgwfV/cjISPj7+6N3795YunTpedcp6eWmLdIbNmxA9+7d4e3tjV69eql0cFPl5eW47777VKq4j48P2rdvj7feesv4/NSpU/HJJ5/gf//7n1q3TCtXrlTp5XJ/27ZtxmVXrVqFPn36wMvLC9HR0Xj22WdRVlZmfH7QoEF44okn8MwzzyA0NFQF7bJ+srKgWCDzCCo8fGHoMQb41zLg4bVAv0cYcNdymK69p3Iwe8k+XPXGKgyetQozf09SAbeMeNW3ZSim3pCAtROuxKKHL8UDA1sz4CYiughs6a7tjnJzRbe4YFU0RPp1x0cFXsz+JiKqH8nxLC2wzV708K31uMW33XYb/v3vf2PFihUYPHiwmnfmzBksXrwYv/76K/Ly8nDttdfipZdeUoHsp59+ihtuuAFJSUmIi4u74Prl76+//noMHToUn3/+OQ4fPozHHnvMbBkJ+Js1a4Zvv/0WTZo0wZo1a3D//feroHnEiBF46qmnsHfvXuTk5OCjjz5SfyMB88mTJ83Wc+LECbWtkoou25mYmIixY8eqYN80sP7ss89U4L1+/XqsXbtWLX/ppZeqbSQrCYiEYdR3SPdqjvCmLeHiyraE2gTa249nq0Jov+9KwZHTBWZjUvdvE6ZSx4cmRCLM34sfXSIiC2DQXQc940JU0L3laBZG9WUhFiKyAQm4X46xza5/7iTgWbu0Uul7fc011+DLL780Bt3fffed6ictrcKurq7o2rWrcfkXXnhBFUn78ccfMW7cuAuuX9YrQfV///tfFfx27NgRx48fx0MPPWRcxsPDA9OmTTM+lhZvCYa/+eYbFXRLC7u0gBcXF583nfzdd99V/bzfeecd1QIeHx+vAvPx48dj8uTJ6v8iOnfujClTpqhl2rZtq5ZftmwZg25ra3UFDGlpVn+Zxky6xW06ckb1z5Z+2qeyi4zPebq7YmC7cBVoD46PRJAvh0UlIrI0Bt110L25VsCHxdSIiC5s1KhRqkVYglZpzf7iiy9w++23qyBVWqqllfiXX35RRcskVbuwsBDJycm12rXSQt2lSxcVcOv69et3znJz587F/Pnz1Xpl/SUlJXWuSC6vJeuWYFonLdjyf5BAX2+Zl6DblLSopzEYJBspLa/A2oOnsXh3Cv7YnYKMvBLjc76ebhgUH6EC7UHtI+DnxdNBIiJr4q9sHfSI1YLuwxn5OJ1XjCZMuyIiW6R4S4uzrV67DiRdXFJZJbCWPtt//fUX3njjDfWcpHYvWbIEr7/+Otq0aaNanG+99VYVFFvK119/rV5n1qxZKmgOCAjAzJkzVfq3NUjLuikJ0qv2aSeypuKyCizbm4rFu9OwdG8qsgtLjc8FertjSEKkGt5LxtKW8bCJiKhhMOiuA0m5ahvhj/1pediSnKX6OxERNShpba1liretSSv0Lbfcolq4Dxw4oAqZ9ejRQz33999/qz7PN998s3osrcZSwKy2OnTooPpQFxUVGVu7161bZ7aMvEb//v3x8MMPG+dJATdTnp6equDahV7r+++/VxcQ9NZuWbcE8dJnnMjW0nOLMXtJEv639QQKSs9e6Anz98TQhCjVon1JqyYqlZyIiBoef33rqCdTzImI6pRiLi3dkuIt93XS53nhwoWqQvj27dtx55131qlVWJaXAFjS1/fs2aOKs0mruSl5jU2bNuH333/Hvn37MGnSJGzcuNFsmRYtWmDHjh2qgFtGRgZKS8+2DOokaD927JgqDCdF1KTaufTdfvLJJ439uYlsobisHO+vOohBr6/EVxuOqYA7Osgbd/dvga/vvwTrnxuCGbd0xuXtwhlwExHZEM8W6qhHnJZiLhXMiYjo/K688kpVEVyCWgmUdbNnz1bF1qQlWtLQhw0bZmwFrw0pgvbTTz9h586datiw559/Hq+++qrZMg888IBqaR85ciT69u2L06dPm7V6CwnapQVehhwLDw9XLdhVNW3aVAX1MkSZFH978MEH1VBkEydO5NtPNiFZF9JP+6o3/sSM3xKRV1yGzk2DMPcf7fDX01dg6o0dVcu2m4z7RURENsf08jrqUdnSveN4lipS4uHG6xZERDWRluCqQ3DpLczLly83m/fII4+YPa6abi6BhqlLLrnEbCztqstI8TYZCkwfDkw3Y8YM430JtP/4449ztq/qaw0cOFAF3TWRodFMx+0WpmOKE1lKUkoupv+8W42mIiICvPDM1fEY3jUaGRnpcGWgTURkdxh011GrMD8E+3ogq6AUe0/loEuzYOu8M0RERESVzuSX4I0l+/DF+qOoMGhDfY29rCUevqKNqj7Oon1ERPbropppZQgWaaWQ4jWSsne+q//SZ0/S9oKDg+Hn56eGapHiN6akmI70zTOdrr76atgjuYLMFHMiIiJqCJJVN3/1YVwxcwU+W6cF3FIYbdmTA/H0sHgO90VE5Igt3QsWLFDFY+bNm6cC7jfffFP1xZP+ehEREecsL335pK9dfHy8qhL7888/45577lHLyt/pJMg2TQGUtEB71SMuGMsT01S/7nsubWnrzSEiIiIHtCIpDS/+vAcH0/PV4w7RgZhyQ4Lqr01ERA4cdEvxGyk8I4GzkOBbr0z77LPPnrP8FVdcYfb4sccewyeffILVq1ebBd0SZEdFRaEx9evewmJqREREZGEH0vLw4i97sDIpXT1u4ueJp4a1x4hesSyORkTk6EF3SUkJNm/ejAkTJpgVyRkyZAjWrl17wb+XwjRSOEdaxatWmV25cqVq/ZZqtlLt9sUXX0STJtVfyS0uLlaTLicnR91KfyZL9GmSdci21rSuzjGB6qB3MrsIJzLzER3kA0d1oX3hLLgfuB9s9XnQX0uf7I2+Tfa4bfa8L/T3s7rjlrP/3jqz7IJSvLVsPz5dewRlFQZ4uLmojLpxV7ZBoLeHrTePiIgaIuiWMUzLy8sRGRlpNl8ey9ilNcnOzlZDrkig7ObmhnfffRdDhw41Sy2XYV1atmyJgwcP4rnnnsM111yjAnlZviqpPDtt2rRz5qenp6OoqAj1JSc8ss1yQlTTGKxtwnyQlFaAlTuTMbid1vLtiGqzL5wB9wP3g60+D1IRW15Pxo92d7ev2pfy/5djgpBaHM6srvtC3k95X2UYMw8P82AqNzfXattJ9qmsvAJfbTyG2X8kIbNAGyt+SIcIPH9dAlqG+dl684iIqJ4a5AwuICBADeuSl5eHZcuWqT7hrVq1Mqae33777cZlO3fujC5duqB169aq9Xvw4MHnrE9a2mUdpi3dsbGxauiXwMDAem+vnAjJSZOsr6YT6j6t0pGUlowD2RW4o5q+7I6iNvvCGXA/cD/Y6vMgryW/nWlpaer1JECzpwBXgkeq276QAD0rK0tdRJFuVVUvLkuRUnIefx/IwPSf9iApVbvY0jbCH5NvSMBlbcNtvWlERGSLoDssLEydHKSmpprNl8fn648tJ6Vt2rRR96V6+d69e1VrddX+3joJyOW1Dhw4UG3QLf2/qyu0Jq9jqRNgOak93/p6tQjFZ+uSsSU5y+GD0QvtC2fB/cD9YIvPg6xffhNPnTpV7XjXtqSnR8s22tOFgMawL2SZZs2andPKLZz9t9ZZHMnIx8u/7sUfe7RzKhmO9Mmh7XBnnzi4u/EzQETktEG3VB/v2bOnaq0ePny4micnGfJ43LhxtV6P/I1pn+yqjh8/rlLuoqOjYa/0YcP2nMxGUWk5vD3OTYMnIrIE+e2Ni4tTqeZ6CrM90NOjpf6GsweKdd0XEmxX133K0mSIz5kzZyIlJQVdu3bFnDlz0KdPnxpb6uWCuBQ7PXHiBNq3b6/qr1QdwlOeGz9+PH777TcUFBSoi+oy+ogMD0oXlltUindWHMBHq4+gpLxC1Yi565LmeHxIWwT7enIXEhE5oDqnl0ta95gxY9TBVQ7cMmRYfn6+sZr56NGjVf9tOXALuZVlJV1cAu1ff/1VjdP93nvvqeclbVL6Z//jH/9QreXSp/uZZ55RB3HT6ub2plmIDyICvJCWW4ydJ7LRu0WorTeJiByYtIxKoFZdy6gtA03ZHkmHZtBtf/uirkN8Tpw4EZ9//jk+/PBDNczn77//jptvvhlr1qxB9+7d1TKZmZm49NJLMWjQIBV0S5eH/fv3qyKodH7lFQZ8t/kYZv6+Dxl5WsPD5e3CMem6DmgbGcDdR0TkwOocdI8cOVIVLJs8ebK6ci7p4osXLzYWV0tOTjY74ZCA/OGHH1at1z4+PupALgd1WY+QK/07duxQV9alj1tMTAyuuuoqvPDCC3Y9VrecAEtr9+LdKWq8bgbdRERkT+o6xKdcEH/++edx7bXXqscPPfQQli5dilmzZqnjtpCWb6mhIi3bOimCSue34fAZTP95N3ad0EZbaRXmh4nXd8Cg9hFO3zWDiMgZXFQhNUklrymdXIqfmZKhv2SqiQTicjW9MerZ/GzQTUREZC8uZohPyUarWsRNjtGrV682Pv7xxx9Va/ltt92GVatWqcw2ubAuwT2d63hmAWb8lohfdpxSjwO83fHY4LYY3a8FPN3tIyOCiIisz77Gn2lkejTX0um2JmeqIjrOXkiIiIjsw8UM8SnBtLSOX3755apLmNRrWbhwoVkdgUOHDqnuYZK2LsN7bty4EY8++qiqOyBdz2oK5k3ruMiII6K6McrrM5a9PY1vXlBShnmrDuHDvw6juKwCri7AyN6xeHJIWzTx17L4LL299rgfbIH7gfuCnwl+NxryN6K262HQXQ+dmgbC080VGXklSD5TgOZNOJYmERE1Tm+99ZZqsZZuYHIRWQJvSU2XdHTTkwup0/Lyyy+rx9LXe9euXSp1vaagW2q7SO2WqqSrWlFRUb23W7YpOztbnUTZuj99hcGA3xPP4N3VJ5Cerw0h17NZAB4f2Axtw31RXpCNtAIrvbYd7Qdb4n7gvuBngt+NhvyNyM3Vhnu8EAbd9eDl7qYCbxk2TFLMGXQTEZE9uJghPqUo2g8//KACYanELjVWpO+3DFmnk1FFEhISzP6uQ4cO+P7772vcFklxl5Zx05Zu6RcurxcYGAhLnEDJRQJZny2DzW3HsjD95z3YdixbPY4L9cGEa+JxVUJkg2TC2ct+sDXuB+4Lfib43WjI34iq3bJqwqDbAv269aD7lh7N6rs6IiKieqvPEJ9yAiF9tWUIMQmmR4wYYXxOKpdL9XNT+/btQ/PmzWtcnxRFra4wqiXHuZcTKEuur65m/LoX7/95SN3383TDI1e2wb2Xtmzw4URtvR/sBfcD9wU/E/xuNNRvRG3XwaDbAkG39NmSwJuIiMhe1HWIz/Xr16sxuGVUErmdOnWqCtRlGE/dE088gf79+6v0cgnGN2zYgA8++EBNzio1p8gYcN/WsxmeHtYeEYG1a/kgIiLnwKC7nmTYMJGUkoPcolIEeNvPGLpEROS86jrEp6SVy1jdUizN399fDR0mw4gFBwcbl+nduzcWLVqkUsanT5+uhguTYH7UqFFwVntOaYXh2kT4Y+ZtXW29OUREZIcYdNeTXM1uFuKD45mF2H4sGwPahlnmnSEiIqqnugzxOXDgQOzZs+eC67z++uvVRJq9lUF3h+j6908nIiLH5NydfiyYYi44XjcREZFz2XtKq1zbITrA1ptCRER2ikG3BYPuLcmZllgdERERNRKJbOkmIqILYNBtwX7dEnRXVBgssUoiIiKyc0Wl5TiUka/uJzC9nIiIasCg2wLiowLg4+GG3KIyHEjPs8QqiYiIyM7tT81DeYUBIb4eiAg4d1g0IiIiwaDbAtzdXNEtVqvuyn7dREREzldETcZ9JSIiqg6Dbkv36z7Kft1ERETONFwYK5cTEdH5MOi2kB7NK1u6WUyNiIjIKXC4MCIiqg0G3RbSPVZr6T6Uno/M/BJLrZaIiIjskMFgMAm6OVwYERHVjEG3hYT4eaJ1uJ+6v/UYU8yJiIgc2ansIuQUlcHd1QVtIvxtvTlERGTHGHRboV83i6kRERE5Nr2VWwJuL3c3W28OERHZMQbdVhivm0E3ERGRY9ODbhk2lIiI6HwYdFuhpXv7sWyUlVdYctVERERkR/aeylW3rFxOREQXwqDbglqH+yPQ2x2FpeVITNEOxkREROR4WLmciIhqi0G3Bbm6uqAH+3UTERE5tIKSMhw+na/us6WbiIguhEG3hbFfNxERkWPbl5oHgwEI8/dCeICXrTeHiIjsHINuC2MFcyIiIsfG8bmJiKguGHRbWNfYYLi6ACeyCpGaU2Tp1RMREZGdBN0J0YG23hQiImoEGHRbmL+XO+KjtIPwlqOZll49ERER2ctwYdEcLoyIiC6MQbcV9GgerG45XjcREZFjMRgMSORwYUREVAcMuq3ZrzuZLd1ERESO5HhmIXKLy+Dp5qqGCiUiIroQBt1W0DMuVN3uPpGDotJya7wEERER2cCeytTyNhH+8HDjaRQREV0YjxZWEBvqgzB/T5SUV2D3yWxrvAQRERHZAFPLiYiorhh0W4GLiwvH6yYiInJAHC6MiIjqikG3lXC8biIiIsezN0VLL+/A4cKIiKiWGHRbOejekpylKp0SERFR45ZXXIajpwvUfQbdRERk1aB77ty5aNGiBby9vdG3b19s2LChxmUXLlyIXr16ITg4GH5+fujWrRs+++wzs2UkKJ08eTKio6Ph4+ODIUOGYP/+/WjMOjUNgoebC9Jzi1WlUyIiImrckipbuSMDvRDq52nrzSEiIkcNuhcsWIAnn3wSU6ZMwZYtW9C1a1cMGzYMaWlp1S4fGhqK559/HmvXrsWOHTtwzz33qOn33383LvPaa6/h7bffxrx587B+/XoVnMs6i4qK0Fh5e7ihY0yQus/xuomIiBq/PRyfm4iIGiLonj17NsaOHasC54SEBBUo+/r6Yv78+dUuf8UVV+Dmm29Ghw4d0Lp1azz22GPo0qULVq9ebWzlfvPNNzFx4kTcdNNN6rlPP/0UJ0+exA8//IDGjP26iYjIluqSmVZaWorp06erY7UsLxfVFy9eXOPyr7zyiioc+vjjj8P5iqgF2npTiIjIUYPukpISbN68WaV/G1fg6qoeS0v2hUiAvWzZMiQlJeHyyy9X8w4fPoyUlBSzdQYFBamTg9qss3H068609aYQEZGTqWtmmlz8fv/99zFnzhzs2bMHDz74oLpovnXr1nOW3bhxo1pWLpQ7k0QG3UREdBHc67JwRkYGysvLERkZaTZfHicmJtb4d9nZ2WjatCmKi4vh5uaGd999F0OHDlXPScCtr6PqOvXnqpL1yKTLydGuPFdUVKipvmQdcoGgvuvq1izIeGU8t7AEfl512t12wVL7orHjfuB+4OeB34uG+o2w1O+taWaakMy0X375RWWmPfvss+csL/VWpDvYtddeqx4/9NBDWLp0KWbNmoXPP//cuFxeXh5GjRqFDz/8EC+++CKcRUWFAYkpuep+QnSArTeHiIgakQaJAgMCArBt2zZ1oJaWbrny3qpVK5V6fjFmzJiBadOmnTM/PT3dIv3A5YRHLhTICZS05F8s+cuoAE+k5JZg1a4j6BXb+NLRLLUvGjvuB+4Hfh74vWio34jcXC2wqw89M23ChAm1zkyTi9mSVm5Kipvq3cF0jzzyCK677jq1rtoE3Y3lQvmFHDmdj4KScni6uyIuxMfuLkbz4jD3Az8T/G7wN6Lhfytru546Bd1hYWGqpTo1NdVsvjyOioqq8e/kQN+mTRt1X6qX7927VwXOEnTrfyfrkOrlpuuUZasjJxESuJsewGNjYxEeHo7AwECL7Dzppybrq+/JU6+WTfDzjlM4lA1c2zMCjY0l90Vjxv3A/cDPA78XDfUbUTXwvRgXk5kmqefSOi7dv6Rft1wklxFIZD26r7/+WqWqS3q5o10ov5B1+7WuYq1CvXHmdAbsDS8Ocz/wM8HvBn8jGv63srYXyusUdHt6eqJnz57qQDx8+HDjhsvjcePG1Xo98jf6Ve+WLVuqwFvWoQfZEkRLFXNJbauOl5eXmqqSHWepA66cPFlifb2ah6ige+uxrEYbtFpqXzR23A/cD/w88HvREL8Rtvqtfeutt1Q6enx8vPq/SOAtqel6odRjx46pYqhLliyp04WBxnSh/HxObc9St51jQxERYX8X0XlxmPuBnwl+N/gb0fC/lbU9HtY5vVwOnGPGjFFjb/fp00dVHs/Pzzf2GRs9erTqvy1XtoXcyrJy8JZA+9dff1X9xt577z31vF75VFLU2rZtq4LwSZMmISYmxhjYN2Y9jMXUslR/MFdXF1tvEhERObiLyUyTExAZNURan0+fPq2Ow9L3W7qDCUlXlyJsPXr0MP6NtIL/+eefeOedd4x1WxrzhfLz2ZuSp24TYgLt9iI0Lw5zP/Azwe8GfyMa9reytuuoc9A9cuRIlRI2efJkVehMWqdlSBE9hS05OdnsxSUgf/jhh3H8+HHVN0yuoEtBFlmP7plnnlHL3X///cjKysKAAQPUOi2RYmdrMqyIt4crsgtLcSgjD20iWHyFiIisqz6ZaXLslYvnMoTY999/jxEjRqj5gwcPxs6dO82WlQvuclwfP358tQG3I+FwYURE1KCF1OSAXdNBe+XKlWaPpQX7QoVW5GqDjA0qk6PxcHNF12bBWH/4DLYczWLQTUREDaKumWnSrevEiRPqYrrcTp06VQXqcmFcL4raqVMns9fw8/NDkyZNzpnvaHKKSnEiq1Dd7xDV+IqiEhGRbTW+Mawa6XjdEnRvPpqJEb1jbb05RETkBOqamSZp5TJW96FDh+Dv76+GDpPuYMHBwXB2iae0QjlNg30Q5Oth680hIqJGhkF3A+gRp/Xr3pysVT4lIiJqCHXJTBs4cCD27NlTp/VXXYejp5bHR7GLGBER1Z19VgJxMHoxtQNpecgqKLH15hAREVEdsD83ERHVB4PuBhDq54lWYX7qvgwdRkRERI0Hg24iIqoPBt0NPXTYUaaYExERNRblFQYkpWp9ujtEM72ciIjqjkF3Q/frZtBNRETUaBzOyEdRaQV8PNzQvImWtUZERFQXDLobsIK52HYsC2XlFQ31skRERFQPiSlaEbX2UQFwc3XhviQiojpj0N1A2kb4I8DLHQUl5cY0NSIiImos/bmZWk5ERBeHQXcDcXV1QXf26yYiImpU9laO0d0hOtDWm0JERI0Ug+4G1CMuWN2yXzcREVHjwMrlRERUXwy6bdCve3MyK5gTERHZu6yCEpzKLlL346OYXk5ERBeHQXcD6hYbDBcX4NiZQqTlagdxIiIisk97Kvtzx4b6IMDbw9abQ0REjRSD7gYkB+z2kdqV8i1HsxrypYmIiOhi+3NHsT83ERFdPAbdDayHXkyNKeZERER2LdFYuZxBNxERXTwG3Q2sZ1xlv+6j7NdNRERkz/ZWjtHN4cKIiKg+GHTbqJjazhPZKC4rb+iXJyIiolooK6/AvtQ8dZ8t3UREVB8MuhtY8ya+CPXzRElZBXaf1K6gExERkX05lJGvjtV+nm6IDfG19eYQEVEjxqC7gbm4uKBHZYr5FqaYExER2fX43PHRgXB1dbH15hARUSPGoNuW43Uz6CYiIrLr4cLYn5uIiOqLQbcNg26pYG4wGGyxCURERFSb4cJYuZyIiOqJQbcNdGkWBHdXF6TmFONEVqEtNoGIiIjOg8OFERGRpTDotgFvDzd0jNHG/GSKORERkX05nVeMtNxiuLgA7SMDbL05RETUyDHotpEeeoo5+3UTERHZZWp581Bf+Hm523pziIiokWPQbfN+3Vm22gQiIiI6T+Vy9ucmIiJLYNBtI/qwYVIdtaCkzFabQURERFUw6CYiIkti0G0jMcE+iA7yRnmFAduPZdtqM4iIiKjG4cK0+itERET1waDbHvp1J2facjOIiIioUklZBQ6m56n7HKObiIgsgUG3DfWsTDFnMTUiIiL7IAF3abkBAd7uaBrsY+vNISIiB8Cg2w5aujcnZ8JgMNhyU4iIyAHNnTsXLVq0gLe3N/r27YsNGzbUuGxpaSmmT5+O1q1bq+W7du2KxYsXmy0zY8YM9O7dGwEBAYiIiMDw4cORlJQEh+zPHRUIFxkzjIiIqJ4YdNtQQnQgvNxdkVVQikMZ+bbcFCIicjALFizAk08+iSlTpmDLli0qiB42bBjS0tKqXX7ixIl4//33MWfOHOzZswcPPvggbr75ZmzdutW4zKpVq/DII49g3bp1WLJkiQrUr7rqKuTn5ztgETWOz01ERJbBoNuGPN1d0bVZsLrPFHMiIrKk2bNnY+zYsbjnnnuQkJCAefPmwdfXF/Pnz692+c8++wzPPfccrr32WrRq1QoPPfSQuj9r1izjMtLyfffdd6Njx44qiP/444+RnJyMzZs3O9wY3SyiRkREluJusTXRRaeYbzhyRhVTu61XLPciERHVW0lJiQqEJ0yYYJzn6uqKIUOGYO3atdX+TXFxsUorN+Xj44PVq1fX+DrZ2droG6GhoTUuI+uVSZeTo7UkV1RUqKm+ZB3SRcsS65L16C3d7aP8LbLOhmLJ/dCYcT9wX/Azwe9GQ/5G1HY9DLptrEec1tK9+SgrmBMRkWVkZGSgvLwckZGRZvPlcWJiYrV/I6nn0jp++eWXq37dy5Ytw8KFC9V6ajrRePzxx3HppZeiU6dONW6L9AOfNm3aOfPT09NRVFRU5/9bddshwb+cRMmFhfrIyC/F6fwSuLoAIa5FNabi2yNL7ofGjPuB+4KfCX43GvI3IjdXy46yStAthVlmzpyJlJQUlV4m/b/69OlT7bIffvghPv30U+zatUs97tmzJ15++WWz5SVV7ZNPPjnn4F+1gIsjF1Pbl5qH7MJSBPl42HqTiIjICb311lsqHT0+Pl4VEJPAW1LTa0pHl77dcmw/X0u4kNZ26Vtu2tIdGxuL8PBwBAYGWuQESrZX1lffE6i9+9LVbcswP8TFRKExseR+aMy4H7gv+Jngd6MhfyOqZohZLOjWC7NI3zCphPrmm2+qAFmql0ol06pWrlyJO+64A/3791cb9eqrr6qiK7t370bTpk2Ny1199dX46KOPjI+9vLzgDML8vdCiiS+OnC7AtmNZGNgu3NabREREjVxYWBjc3NyQmppqNl8eR0VVH0zKCcgPP/ygWp9Pnz6NmJgYPPvss6p/d1Xjxo3Dzz//jD///BPNmjU777bI8by6Y7qc7FgqOJQTKEusLylVG587PjqwUQaultoPjR33A/cFPxP8bjTUb0Rt1+Fq7cIsX3zxBR5++GF069ZNXT3/z3/+o64wSNqaKTkgy4mAPoWEaC3ATjV0GFPMiYjIAjw9PVVmmemxVj/29uvX77x/KxfI5aJ4WVkZvv/+e9x0003G5yQdTwLuRYsWYfny5WjZsqVDvV96f24ZXYSIiMhSXC+mMIsUYqltYZaqCgoK1BAjVYuuSIu4tJS3b99eVUyVq+zOokecFnSzgjkREVmKZKVJFy/pvrV37151bJWhveSiuRg9erRZobX169erPtyHDh3CX3/9pTLQJFB/5plnzFLKP//8c3z55ZdqrG7pZiZTYWGhQ7xxHC6MiIiswd3ahVmqGj9+vEpZMw3c5cB+yy23qCvmBw8eVEOWXHPNNSqQl/S4xlwJtTa6xwap263JmSgtK4ebVHCxE6wCyv3AzwO/F/x9aNjfSksde0aOHKmKlU2ePFkFxpJxJrVS9GO4DPVlmhYnaeUyVrcE3f7+/mq4MBlGLDhYK/gp3nvvPXV7xRVXmL2WdA+T+iyNWVFpOQ6ma+ONc7gwIiKypAatXv7KK6/g66+/Vq3app3Ob7/9duP9zp07o0uXLqqAiyw3ePDgRl0JtTaCXQzw9XRFfkk51u09irbhvrAXrALK/cDPA78X/H1o2N/K2lZCrQ1JBZepOnKMNTVw4EDs2bPnvOuT/5+jOpCWh/IKA4J9PRAVWLvCOERERBYPui+mMIvu9ddfV0H30qVLVVB9PlK0RV7rwIED1QbdjakSam11jwvB3wdO40ieKy7teG5BOlthFVDuB34e+L3g70PD/lbWthIqWdaeyv7cHaIC1XtJRERkk6DbtDDL8OHDzQqz1HQlXbz22mt46aWX8Pvvv6NXr14XfJ3jx4+rPt3R0dGNvhJqbfVsHqqC7q3JWbirXwvYE1YB5X7g54HfC/4+NNxvpbNXnraVxFNahgFTy4mIyNJcrV2YRYYImzRpkqpu3qJFC2PRlbw8bVgOuX366aexbt06HDlyRAXwUim1TZs2aigyZ9FTr2CenGnrTSEiInI6ehG1+OgAW28KERE5e5/uuhZmkaIrUvX81ltvNVvPlClTMHXqVJWuvmPHDhXEZ2VlqSJrMo73Cy+84DRjdYtuscGQbLajpwuQkVesxu8mIiIi65O+6ntTOFwYERHZUSG1uhRmkdbr8/Hx8VFp584uyMcDbSP8sS81Tw0ddlXH8/eRJyIiIstIySlCVkGpGj2kTYQ/dysREVkUO45Vp6wY3vt+AAwNM2SYjinmREREtkstbx3uB2+Pc4cqJSIiqg8G3VVJBdr/XIng5eOBPf9DQ+oRp/XrlpZuIiIiahh7WUSNiIisiEH3OXvEFYYON6q7LiteBMpL0dAt3TuOZ6OkrGFb2YmIiODsw4VF13/YUSIioqoYdFfnkodR7h0KlzOHgC2foqG0DPNDiK8HissqjCcAREREZF2JDLqJiMiKGHRXxysA+b0e0e6vehUoyUdDjfGqp5hvZoo5ERGR1RWVluNwhnac7xDF4cKIiMjyGHTXoKDDCBhCWgB5qcC6d9FQelSmmLNfNxERkfUlpeSiwgA08fNEeACH6yQiIstj0F0TN08YrnhOu//320DBGTRkv+4tySymRkRE1FCVy6U/t2ScERERWRqD7vPp9A8gqjNQnAP8NQsNoUuzIDVO6KnsIpzMKmyQ1yQiInJWZ4NuppYTEZF1MOg+HxdXYMhU7f6GD4CsZFibr6c7Eiqrp7JfNxERkXVxuDAiIrI2Bt0X0now0OIyoLwEWDEDDYEp5kRERNZnMBiwN4XDhRERkXUx6L4Q6d81ZJp2f/tXQOoeK78lLKZGRETUEE5kFSK3qAwebi5oHe7PnU5ERFbBoLs2mvUEOtwo18SBZdNhbT3igtXt7pM5KCwpt/rrEREROXNquQTcnu48JSIiIuvgEaa2Bk8GXNyAfb8BR9fCmpoG+yAy0AtlFQbsOJ5l1dciIiJy9iJqei0VIiIia2DQXVthbYEed2n3l06RjmCwFhmyRO/XPf3nPTh2psBqr0VEROSsTIcLIyIishYG3XUx8FnA3Qc4th5I+g3W9PAVbRDq56lSzG94ZzVWJqVZ9fWIiIicDYNuIiJqCAy66yIwGrjkQe3+smlAhfX6W3dqGoSf/j0AXZsFIaugFPd8vBFvLt2HigrrtbATERE5i/ziMhytzCTjGN1ERGRNDLrr6tLHAe9gID1Rq2Zu5b7d3zzYD6P6xqls9jeX7se9n2xEVkGJVV+XiIjI0SWm5Kpja0SAF5r4e9l6c4iIyIEx6K4rn2Dgsv/T7su43aVFsCYvdze8dHNnzLqtK7zcXbEyKR3Xz1mNXSeyrfq6REREjiyxcnzuePbnJiIiK2PQfTH63A8ENgVyjgMbP0RD+EfPZlj08KWIC/XF8cxC3PLeGnyz8ViDvDYREZHj9ucOsPWmEBGRg2PQfTE8vIErJmj3/5oFFDbMsF4JMYH4adwADI6PQElZBZ75fgee/X4Hiko5ljcREdHFjNHN4cKIiMjaGHRfrK53AOHxQGEm8PdbaChBvh74cHQv/N/QdnBxAb7eeAy3zVuL45kcVoyIiKg2pChpIocLIyKiBsKg+2K5uQODJ2v3170H5JxCQ3F1dcG/B7fFJ/f0QYivB3aeyFb9vFftS2+wbSAiIvs3d+5ctGjRAt7e3ujbty82bNhQ47KlpaWYPn06WrdurZbv2rUrFi9eXK912qtjmQXILymHp7srWoX52XpziIjIwTHoro/21wKxfYGyQmDVq2hol7cLV8OKdakcVuzujzbg7WX7OawYERFhwYIFePLJJzFlyhRs2bJFBdHDhg1DWlpatXtn4sSJeP/99zFnzhzs2bMHDz74IG6++WZs3br1otdp7/2520X6w92Np0JERGRdPNLUh+R3D5mq3d/yKZBxAA2tWYgvvn2wH+6sHFZs9pJ9+Nenm5BdUNrg20JERPZj9uzZGDt2LO655x4kJCRg3rx58PX1xfz586td/rPPPsNzzz2Ha6+9Fq1atcJDDz2k7s+aNeui12mv9lT25+4QFWjrTSEiIifAoLu+mvcH2l0NGMqB5dNhCzKs2Ms3d8bMW7uoYcWWJ6bh+nf+4rBiREROqqSkBJs3b8aQIUOM81xdXdXjtWvXVvs3xcXFKmXclI+PD1avXn3R67RXen9uDhdGREQNwb1BXsXRSd/ufb8De/4HnNgMNO1pk824rVesqnD+4OebcexMIf7x3hq8MLwTRvSKtcn2EBGRbWRkZKC8vByRkZFm8+VxYmJitX8jaeLSkn355Zerft3Lli3DwoUL1Xoudp16MC+TLidHC3grKirUVF+yDoPBUKd16enl8ZH+FtkGe3Ax+8ERcT9wX/Azwe9GQ/5G1HY9DLotIbIj0PV2YPtXwNKpwOgftdRzG+gYE4Sfx12GJ77Zplq8n/luB7YmZ2HKDQnw9nCzyTYREZH9e+utt1TqeHx8PFxcXFTgLWnk9U0dnzFjBqZNm3bO/PT0dBQVFcESJzzZ2dnqJEpa3i8kv7gcxzIL1f0wj+JG1x/dUvvBUXE/cF/wM8HvRkP+RuTmat2VLoRBt6UMeg7Y9T1w+E/g4HKgzWDYigwr9p/RvTB3xQHMXroPX21Ixu6T2Xh3VA/VB5yIiBxbWFgY3NzckJqaajZfHkdFRVX7N+Hh4fjhhx9UIHz69GnExMTg2WefVf27L3adYsKECar4mmlLd2xsrHq9wMBAi5xAyUUCWV9tTqA2HjmjbqODvNE2LgaOoq77wVFxP3Bf8DPB70ZD/kZU7ZZVEwbdlhIcB/QeC6ybCyydArQaJJ3dYCv6sGJdYoPx2NdbseO4NqzY27d3V1XPiYjIcXl6eqJnz54qRXz48OHGEw15PG7cuAueQDRt2lQNIfb9999jxIgR9Vqnl5eXmqqSkx1LBYdyAlXb9SWl5qnbDtGBDhec1mU/ODLuB+4Lfib43Wio34jarsO5f5Ut7bL/A7wCgZSdwO6FsAcDZVixcQPQuak2rNiYjzZgDocVIyJyeNK6/OGHH+KTTz7B3r17VTXy/Px8lTIuRo8erVqhdevXr1d9uA8dOoS//voLV199tQqqn3nmmVqvszHQ+3N3iA6w9aYQEZGTYEu3Jfk1Afo/Cqx4EVj+AtDhRsDdE7YWG6oNKzbtp934asMxzFqyD9uOZWH2iG4qFZ2IiBzPyJEjVb/pyZMnIyUlBd26dcPixYuNhdCSk5PNrtBLWrmM1S1Bt7+/vxouTIYRCw4OrvU6G9NwYfEcLoyIiBoIg25L6/cwsOEDIPMIsOUToM9Y2AMpojbjli7oHheCiT/swrLENNzwzmq8988eqvgaERE5Hkn7rin1e+XKlWaPBw4ciD179tRrnfauvMKAfSmVY3RHc4xuIiJqGEwvtzRPP+CK8dr9Va8CxVrfMXshw4ctfKg/moX4IPlMAW55dw2+23zc1ptFRERkdUdP56OwtBzeHq5oGebHPU5ERPYbdM+dOxctWrRQxVb69u2LDRs21Lis9P267LLLEBISoqYhQ4acs7yUbJdUtejoaPj4+Khl9u/fj0arxxggtBWQnw6snQt706lpEH7+9wAMah+O4rIKPPXtdjy3aCeKy7SxWImIiBzR3srU8vaRAXBztc3QnkRE5HzqHHQvWLBAFVKZMmUKtmzZgq5du2LYsGE1jnMp6Wt33HEHVqxYgbVr16phQq666iqcOHHCuMxrr72Gt99+G/PmzVOFXPz8/NQ6LTF+p024eQBXTtTur3kbyM+AvQn29cR/x/TGE0PaqSHFv1yfjBHz1uJEljZ2KRERkaM5W0SNqeVERGTHQffs2bMxduxYVak0ISFBBcq+vr6YP39+tct/8cUXePjhh1Wxlfj4ePznP/8xDjGit3K/+eabqnjLTTfdhC5duuDTTz/FyZMn1XihjVbCzUB0V6AkD/jzddgjGVbssSFt8dHdvRHk44HtMqzY23/hr/3ptt40IiIii2PQTUREdh90l5SUYPPmzSr927gCV1f1WFqxa6OgoECN/RkaGqoeHz58WFVANV1nUFCQSluv7TrtklSEHTJNu7/xP1phNTt1RfsIlW7eqWkgMgtKMXr+BryzfD8qKgy23jQiIiKLYdBNRER2X708IyMD5eXl5wwNIo8TExNrtY7x48cjJibGGGRLwK2vo+o69eeqKi4uVpMuJ0dLF5MWdJnqS9YhLfD1XlfLgXBpeQVcDq+EYflLMNz8PuxV02BvfHv/JZjy0x58s+k4Xv9jH7YmZ2HmPzpZZl80chb7TDRy3A/cD/w8WP+74ey/M9aSVVCCk9lat7X2URyjm4iIHHTIsFdeeQVff/216uctRdgu1owZMzBtWmUrsgkZO9QS/cDlhCc7O1udQJmOYXox3Hv8G2GHVwI7v8WZ+FEoaxIPe/bkgEi0CXbD6yuSjcOKPdQ7FIM6VMDNzQ3OypKficaM+4H7gZ8H6383cnO1Yl9kWYmVQ4U1DfZRXaqIiIjsMugOCwtTgVdqaqrZfHkcFRV13r99/fXXVdC9dOlS1W9bp/+drEOql5uuU/qBV2fChAmqmJtpS7cUaAsPD0dgYKBFTp5cXFzU+uodYEVcCcPem+GyZxGabH0Hhju/gb3715UR6Nu+KR75ciuOZxZi4tIUdNiVj7GXt8R1naPh4eZ8QadFPxONGPcD9wM/D9b/btTnojTVjKnlRETUKIJuT09P9OzZUxVBGz58uJqnF0UbN25cjX8n1clfeukl/P777+jVq5fZcy1btlSBt6xDD7IliJYq5g899FC16/Py8lJTVXKiY6mASE6eLLa+wZOAxJ/gcmAJXJLXAC0GwN51jQ1R/bzfXLoPCzYew96UXDz5zQ7M+mM/7h3QErf3joWfV4MmSticRT8TjRj3A/cDPw/W/W44+2+MtYPuhGimlhMRUcOq85FdWphl7O1PPvkEe/fuVYFxfn6+qmYuRo8erVqida+++iomTZqkqpvL2N7ST1umvLw840nK448/jhdffBE//vgjdu7cqdYh/b71wL7Ra9JaG7tbLJkiJdvRGMiwYpOvT8AP93XG/w1tizB/TzWk2As/70H/V5bj9d+TkJ57tm89ERGRvY/RzeHCiIioodW5qXLkyJGq7/TkyZNV8Cyt04sXLzYWQktOTja7Sv/ee++pque33nqr2XpknO+pU6eq+88884wK3O+//35kZWVhwIABap0OlWI3cDyw/SvgxCYg8Wegww1oLIK83fHIoDYYe3lrLNxyAh/+dQiHM/LxzooD+OCvQ/hHj2YYe1lLtAr3t/WmEhERnaOsvAJJqQy6iYjINi4qP1hSyWtKJ5ciaaaOHLnwUFnS2j19+nQ1OayASOCSh4G/XgeWTQfaXQO4Na70bG8PN9zZNw4je8diyZ4UzFt1CNuOZeGrDcn4emMyhiVE4YGBrdA9LsTWm0pERGQkF4pLyirg6+mGuFBf7hkiImpQ7DjWkC59FPAJBTL2Adu+QGPl5uqCqztFY9HD/fHNA/0wOD5CZcwv3p2Cm99dgxHz1mLZ3lSO801ERHZhT2V/bhkqzNXVxdabQ0REToZBd0PyDgIuf0q7v/IVoLQQjZlkKPRpGYr/3t0bS564HLf1bAYPNxdsOHIG932yCcPe/BPfbjqmWheIiIhsPVwY+3MTEZEtMOhuaL3uA4JigdyTwPr34SjaRgZg5m1d8dczV+KBy1vB38sd+9Py8PR3O3DZa8vx/qqDyCkqtfVmEhGRE+JwYUREZEsMuhuahzcw6Dnt/urZQGEmHElUkDcmXNsBayZciQnXxCMiwAupOcWY8VsiLp2xHDN+24vUnCJbbyYRETkRDhdGRES2xKDbFrqMBCISgKJsYPUbcESB3h54YGBr/DV+EF67tQvaRPgjt7gM7686hAGvLsfT327H/spKskRERNZyJr9EXfwV7aMCuaOJiKjBMei2BVc3YPAU7b6kmGefgKPycnfDiF6x+OPxy/HfMb3Qp0UoSssN+HbzcQx940/865ON2HjkDAyNZOxyIiJqnK3czZv4qq5PREREDY1Bt620GwbE9QPKioBVr8DRSbXYwR0i8c2D/fD9Q/0xrGMkXFyApXvTcNu8tbjlvTVYvCsF5RUMvomIyPJBd3xUAHcrERHZBINuW5GIc8g07f7Wz4H0fXAWPZuH4P27emHZkwNxR584eLq7YmtyFh78fDOGzl6lxv0uKi239WYSEZEDDRfGyuVERGQrDLptKa4v0P46wFABLKsMwJ1Iq3B/zLilM1aPH4RHBrVGoLc7DmXkY8LCnRjw6grMXXEA2QWseE5ERBcv8RSHCyMiItti0G1rgycDLq5A4s/AsY1wRhEB3nh6WDzWTBiMSdcnICbIGxl5xZj5exL6vbIM03/ag2V7U7H7ZLYqiMP+30REVBul5RU4kJan7idEs4gaERHZBiuK2FpEPND1TmDb58DSqcDdP2up505ICtzcN6AlRvdrjp93nFSVzhNTcjH/78Nq0nm5uyI6yFsNTxYT5KNuo4N9EB1YOS/YByG+HnBx0v1IRESag+l5KCmvQICXO5qF+HC3EBGRTTDotgeDJgA7vwWOrgYOLAXaDoUz83Bzxc3dm2F4t6b4c38Gvtl4DEfP5ONUVhFO55eguKwCR04XqKkmnpWBuTb5GO9HmdwP9fNkYE5E5AxF1KID+HtPREQ2w6DbHgQ1A/reD6yZo7V2tx4s5b7h7KSlemC7cDXppMBaWk4xTmYXIiW7CKfUVKhutceFyMgrQUlZBY6eLlDThQLzqMDK4Fxay02CdGk1b8LAnIio0drL/txEZAPl5eUoLbWvukQVFRVqm4qKiuDqxHFGRR33g4eHB9zc3Or9ugy67cWAJ4HNnwKpu7RW764jbb1Fdsnbww1xTXzVVJPissrAPKsQKTlFOJklAbkWmOuT9BmvVWDu5qqC76hAL0T6uaJTXB7aRASgTYQ/moX4ws2VKexERPY/XBj7cxOR9UndoZSUFGRlZdnltknAmZub69SZP4aL2A/BwcGIioqq135j0G0vfEOBAY8By6YDK14EOg4H3L1svVWNkpe7G2JDfdVUEwm4U3OqbynXA/P03GLVFzD5TIGaxE+7T5u1lLcK80PrCH+0Cfc33rYK91MXB4iIbG3u3LmYOXOmOgns2rUr5syZgz59+tS4/Jtvvon33nsPycnJCAsLw6233ooZM2bA29vb2HozdepUfP7552qdMTExuPvuuzFx4kS7PIk729LNMbqJyPr0gDsiIgK+vr529bsowWZZWRnc3d3tarvseT/IsgUFBUhLS1OPo6OjL/p1GXTbk74PAes/ALKSgU0fAZc8aOstclgSMNc2MJfW8uNnCrDraBpSCgw4mJ6vhjaT56XQm0ym5PsrBXtUIB7ur1rF9YA8xM+zAf53RETAggUL8OSTT2LevHno27evCqiHDRuGpKQkdUJY1Zdffolnn30W8+fPR//+/bFv3z4VUMtJyezZs9Uyr776qgrKP/nkE3Ts2BGbNm3CPffcg6CgIDz66KN2tdvlwqlkNclvcvsoBt1EZF1yUVIPuJs0aWJ3u5tB98XtBx8frQinBN7y3l5sqjmDbnvi6Qtc8Szw8+PAn68B3e4EvJkSZw+Bec+4YPSLcVdfNun/UV5hwPHMAlUZV4ajkUmCcbnNLizFsTOFalqRlG62TukjLoG4CsIlGA/3U7dShd2VqepUh2Dim03HcDAtD92bh+DytmFo3sSP+4/MSKA8duxYFRQLCb5/+eUXFVRLcF3VmjVrcOmll+LOO+9Uj1u0aIE77rgD69evN1vmpptuwnXXXWdc5quvvsKGDRvsNrW8ZRM/+HrydIeIrEvvwy0t3ORYfCvfU3mPGXQ7iu53AWvfAU4f0G4HPWfrLaJqSF9uCXJkujI+0uzqmRRy04Nx421aHk5ma9XXT+efwYYjZ8zW5+PhptLStUBcC8hlat7EV6XLE8lna9PRTHy29ih+23UKpeUGtVMWbj2hbmNDfXBZ23Bc1iYM/VuHIcjXgzvNiZWUlGDz5s2YMGGCcZ5cMBwyZAjWrl1b7d9I67akjUsALSnohw4dwq+//oq77rrLbJkPPvhAtYK3a9cO27dvx+rVq40t4fYYdHfg+NxE1ICcOXXbUblY4D3lpV974+YOXDkJ+HYMsOYdoPs/geA4W28V1eFLGR7gpaZLWpmnFuUXl+GQtIan5+JgWr4xKD9yOh+FpeXYfTJHTVWD+7hQX9Ui3rqyRTzY1wMhvp5mtzLGOX/kHZN8bn7YdkIF26ZdGbrHBaN/6ybYdCQTW5IzVWbFl+uT1SRJE12aBasW8AFtw9WyMhQfOY+MjAyV6hgZefaioJDHiYmJ1f6NtHDL3w0YMMCYfvfggw/iuefOXvyVFvKcnBzEx8erq/3yGi+99BJGjRpV47YUFxerSSd/L6SQjUz1JevQC+OY2mMsouZvkdexdzXtB2fD/cB9YavPhP46+mSP9O2y5va1bNkSjz32GB5//HHYK0Md94P+nlZ33Krt54pBtz1KuAmI6QGc3AK80wfofR9w6WOA/7l98Kjx8PNyR+dmQWoyVVpZrE1aww8YW8jz1eO84jIczshX09K9WhGH6ni4uSDIxxMhvh4qCA/21e5rQbkeoOvz9eU8VQo92af9qbn4fN1RfL/lhPocCG8PVzV+/T8vaY5OTYPMAvP1h0/jr/0ZapLP0LZjWWp6e/kBdVHmklahqiV8QNswVQCQF2moqpUrV+Lll1/Gu+++q/qAHzhwQJ04vfDCC5g0aZJa5ptvvsEXX3yh+n9Ln+5t27apEyspqDZmzJhqd6oUYps2bdo589PT09WQLfUlJzzZ2dnqhMh0+Jddx7SMomifCmMRHEdW035wNtwP3Be2+kxI6rG8llywlMneyP9fLpSKqucAkgUlxTZnzZpV79eRbkh+fn52uQ8utB9qIv8XeW9Pnz6thhAzJVXQa4NBtz2SD8AtHwCLHgRObNLSzDfNrwy+Hwf8wmy9hWRB0gKp+nmH++OqKj8KqTnFZqnq0pc3s6AEWQWl6jazoFQVdJNUYykYJFNd+Hq6ndNqfvb+2cA9SL/1dkNBSbnqty7ZzXLBoKzcoKq8y608VvMq9PsGlFXOU/dlbMQyA0rVrb6ctqxaTh5XztfWWc36KwwI8/PEwPbaGO6ynY5C/n9/7E7FZ+uOYN2hs10QWob5qUD71h7Nqk0blws60s1B7+ogVfgl+F4t04EMnMkvURdt9As3TYN9MKBNGC5rF4ZLW4exwJ8Dksrj0hKdmppqNl8ey7An1ZHAWlLJ//Wvf6nHnTt3Rn5+Pu6//348//zz6mT16aefVq3dt99+u3GZo0ePqsC6pqBbUtyloJtpS3dsbCzCw8MRGFj/uiVyIqSyjMLDjSfUMnTk0Uzt97BvfCwigrVCOI6suv3gjLgfuC9s9ZmQi4gSgEmBLpnsVdWgUcj+kamm7dYD1dr8v+pT4dvW+6Em8v+Wz44UyNNH89BVfVzjOuq8hdQwwtoC/1oKHFgKrHhZa/VeMwfY+F+gz1ig/2OAn/1VRiTLkR8/NUZ4kDcubRNW449gUWlFZQB+NhiX26zKoNz0sf68BM0VBqgAuqCkECeyChvdWyd9mSWNulfzUAyKj8CV8RFoF+nfKFtwZbi6Lzck4+sNyUjL1QIF+b8NTYjEXZe0UGnkdSm0Fx3kgxG9YtVUUWFQabYqCD+Qjo2HM9X7vWDTMTXJ7urcNEgLwtuGo2fzEGZAOABPT0/07NkTy5Ytw/Dhw40nnvJ43Lhx1f6NDItS9YRULxijp+DVtMz50uu8vLzUVJWsx1InwPK9N13foYxcdfEu0NsdzULsa9gea6q6H5wV9wP3hS0+E7JuPXi1x98c+R3Xt8t0+2SUilWrVqnp7bffVvM++ugjVYRT6nrIkJA7d+7EH3/8oS6YykXUdevWqYuyHTp0UBddpaVcJwU2JQNKTy+X1/rwww9VIc/ff/8dTZs2VS3qN954I+xpP5yP/p5W9xmq7WeKQbc9kw9C26FAmyHA/j+04PvUNuDvt4AN/wH63g/0f1Qb45uckvwA+Hi6wcfTBzF1aMmRQCynSALx0gsH64UlyMzX5ueXaOk4pmnt7q6u6lZa7GVyN943f+7sfFe4u7rAw90VHq4ucK+cZ7ac+jv9b/T5rvB0c4Gbq6tq+V+RmIak1FxVlE6mVxcnqhZcCb5l6te6iV2Ply4/+msPnsZn647ijz2pqiK+CPP3wp19YnF7n7g6vac1kWBdUtFleuiK1igsKVf766996aoVXPqJ7zieraZ3Vx5URf0kFV36gkufcCnoZ48nD3RhcmIkrc+9evVShdFkyDA5SdKrmY8ePVqd/MgJk7jhhhtUQbTu3bsb08ul9Vvm68G33Jc+3HFxcSq9fOvWrepv7r33XjsdnzuQn18isumxXur22IIcz2tz/H7rrbdUccxOnTph+vTpat7u3bvVrWQ2vf7662jVqhVCQkJw7NgxXHvtteo4IBdTP/30U3VckKEo5bhQk2nTpuG1117DzJkzMWfOHFUHRLKkQkOdJ4Zh0N0YyBem3TCg7VXAvsVa8J2yA1j9BrDhQ6DvA0C/cQy+qU6BmNbX2xMtUPuhpgpLSpGamo7oqAh4utfux9xanr0mXg3bJsH38sQ0rDl4WrXgShArk/R/ltRpvRXcEgGsJUiWwcItx9U2SmE9XZ+WobjrkuYY1jHKqi3NcpFG0vJlEmk5RSr41vuDSxcFGepOH+4uKtBb9QO/rG2YyriQiwLUOIwcOVL1m548eTJSUlLQrVs3LF682FhcLTk52ewKvbRmyHdabk+cOKFSMfUgWycnSxKIP/zww6qftPTlfuCBB9Rr2BNWLicieyABd8Lk323y2numD6vVcIlBQUEqO0qGxdK7H+kFNyUIHzp0qHFZCZKl77dOan4sWrQIP/74Y41ZVHpr+h133KHuS+0QaVGXkTKuvvpqOAsG3Y2JBDjtrwHaXQ0k/QqsnAGk7AT+mgWs/wC45EGg3yOAT4itt5QclAxfJsGstDzbQ+unpI3e1a+FmqQFd83BDBWASyAuQ7QtS0xTk4iPCjC2gnePC1GV4RvS7pPZqjDaD1tPGq96+3m64ZYezVR/7fZRAbCFiEBvtQ0yyRV5afmWvuB/7k/HhsNnkJJThO82H1eTSIgOVH3BL2sTjp5x5kUByf7ISVBNJ0JSOK1qn7UpU6aoqSYBAQGqxVwme6YH3fJ5JSKiiyOZUqby8vIwdepUlSp+6tQpVWCssLBQXcQ9ny5duhjvS5E1qefhDAUuTTHobowk2Im/Dmh3DZD0C7DyFSB1F/DnTGD9+8AlDwOXPAT4BNt6S4kajLTgDu4QqSY9eNQDcBlSSx7LJCnUUiBOWnqlFfyKdhFWG9O6qLRcjaktw31tSc4yzpe+53Kh4ObuTVVlcXshF1IkHVemsZe3UtsvQ5L9tT9dtYJL33B9en/VIXi5u6JrjB+6t8hEQoz2d1IZXboCENmKfP/Z0k1E9kBSvKXF2VavXV8SIJt66qmnsGTJEpVy3qZNG/j4+ODWW29FSUlJnYqWubi4ON3whvZztkd1J2mBHW4A2l8H7P0RWPUqkLYHWPUKsP494JJHtNZvb7ZGkXMxDR4fGdQGmfklWLUvXQXhK5PSVJ/1H7adVJO0ePeMC1EB+OAOEWhrgT7Mx84U4Iv1yfhm0zFVOVxIP/ZrOkerFPLeLULsIlPgQqRPvKSWyzRBhnjKLVbZBH/u04qySXX9Dcm5atJJarzsQ9n3kl0gLY3x0YEI9XOcKvNk3+RzKd9xSWZpG+lv680hIicmx/rapHjbmqSX68Nonc/ff/+tUsVvvvlmY8v3kSNHGmALGz/7/xRQ7YLvjsOBDjcCe37Qgu/0RGDly8C6d7X+3tLv25tpduScQvw8Mbx7UzXJMGTS6iwB+PLEVOxLzau+GFuHCPRrVftibFKcbtX+dHy+9iiWJ6WhstgzooO8cWefOIzsE4uIgNoNK2GvwgO8cFO3pmqS1sSklBws35mME/nQMglO5ahie7tP5qjJVGSgF+KjtAshHaID2CpOVqO3crcK97frYopERPZCKo6vX79eBdD+/v41tkK3bdsWCxcuVPU+5IKC1Phwthbri8Wg29GC7063AAk3AbsXacF3xj5gxYvAurlng28v2/QdJbIHkvosRctkkmJs0iotrd/LzlOMTQJwCcRlKK6qpCX7203H8Pn6ozh25uzQa1J4TPpqD46PcMh0aznYtosMQLBLOCIiIlRBLrnwcDyzUKWfJ6bkqOBHgvGjpwtU62NqTrrKONCxVZysYW+KFnTLBR4iIrowSRuX0S4SEhJUH20ZMqw6+mgV/fv3R1hYGMaPH4+cHPOL7FQ9Bt2OyNUN6Hwr0PFmYNdCLfg+vR9Y/gKwdi7Q/99An/sBL6bdEcWGnluMbVllX/BT1RRjkxT0K9qFIzsrD7+uSsHPO0+hpEy7yitjAt/WKxaj+sapVjZnrIof18RXTVd30iqgirziMiSl5FYG4RKM171VvGWYnyrgR1T74cJ4gZmIqDbatWuHtWvXms2TNPLqWsSXL19uNu+RRx4xe1w13Vwy46rKyjpb58ZZMOh29OC7y21a6/fO77Tg+8xBYNk0YO072hjffcYCnrUfMorIGYuxybTVpBjb3BUHzf6uY0wgRvdrjhu7NlXrcBppe+G7azEQfwXQtIdW5LEaUiyuZ/MQNenq3Cru5qr652rBuBaIy8S+4lQVi6gREZG9YdDtLMF315FAp38AO7/Vgu/Mw8DSKVrwfeljQK/7AE9fW28pkd0WY5M08lX7JABPx6qkNFXZ+/ouMbirX3N0iw1uFIXRLKa0EFj1GlzWvI3AijJg9XQgKBaIv14r7hh3ifa70wCt4hEBXmq4tSZ+ngjy8UCgTN4elffdqzz2QICXu3ptckzyvTyUnqfuc7gwIiKyFwy6nYmbO9DtDqDzbcCOBcCfrwGZR4A/JgJ/vw0MeBzodS/gcW6/VSJnJy2qN3dvpqaS0jKkpaUjJjpS9WV2Kof/BH56DDhzCBK6loZ3gnvWYbhkH9NGTZDJN0wb1lCKO7a8HHCvfeXyuraKp+UWq6m25NqIBN5Vg3N1660F5jXO8/ZQ/fyd6gJLI7MvNRcVBu37KhdkiIiIGm3QPXfuXMycORMpKSno2rUr5syZgz59+lS77O7duzF58mRs3rwZR48exRtvvIHHH3/cbBkZZH3atGlm89q3b4/ExMSL2TyqTfDdfRTQZQSw/Wst+M5KBn5/Dvj7LWDAE0DPuxl8E9VACqO5uzlZ4FVwBvhjErDtc+1xQDQqrnkNp0P7ICIkAC6HVwF7fwKSfgUKMoAtn2iTVxDQbpjWAt5m8EV1Z7lQq/jB9DxkF5Qip6gU2YWlyJGpqMx4X90WlaKotEJVlZfnZALOFr6rLUlzVy3olcG4HpAHeLmhXagbRkdE1HmdZPnUcqm/wIsjRETUaIPuBQsW4Mknn8S8efPQt29fvPnmmxg2bBiSkpJUBduqCgoK0KpVK9x222144oknalxvx44dsXTp0rMb5s5GeKtz8wB63AV0vR3Y9iXw5+tAdjKw+Flg9ZvAZU8C3e+y/nYQkf2SKHXX98Bv47VgWkh3lCFTAM8AIC1Nu0AXf602lZcCR1ZrAXjiz0BeKrDzG21y99ECb2kBl0DcJ7hem1Zdq/j5FJeVI6ewzCw41wLyMi1QrwzOtecqg3aTZaUFtaS8Ahl5JWqq6oaOTTC6Xv8jslwRNVYuJyIi+1HnyFZKxY8dOxb33HOPeizB9y+//IL58+fj2WefPWf53r17q0lU97xxQ9zdERV1tgWDGjj47jkG6HoHsO0L4K9ZgKSK/vYMXFa/gcDYK4D2V2j9NIOb11gsiYgcTOZR4Jf/Aw4s0R6HxwM3vKX9FojqxuaU35PWg7Tp2teB4xuBvT9qQXjWUS0Ql8nVHWg5UGsBl1R0f+u3EHu5uyE8QKa6px1LYT1pWdcDdAnEc/PyYcjYB48z++CTmYQyvwQA1Wd9UcNgETUiImr0QXdJSYlKE58wYYJxnvRnHDJkyDll5utq//79iImJgbe3N/r164cZM2YgLi6u2mWLi4vVpNPHh5PB2S0xQLusQ06wnG6wdzkJ7jEG6CIt31/AZfUsuOSchO+erwCZ5MTTPwqI7QNDsz5AbF8gugvgVvv+mo2V034mquB+cJL9IMXRNnwAlxUvwaW0AAY3Txgue0oruijf98r/d632Q7Pe2jRkOpC6Cy6qBfwnuKQnAgeXqcnw8xMqkDfEVwbgwdX/9tuMtN6fOQi/9ET4p+1FjGy7TKcPwsVQblyswO8mVFTcV++Xc9jPlZXJZ/Fs0M3hwoiIqJEG3RkZGSgvL0dkZKTZfHlcn/7Xkqb+8ccfq37cp06dUv27L7vsMuzatQsBAeceOCUgr9oHXKSnp6OoqAiWOOHJzs5WB3CnK5Kki7seGHkVPA8vhyF5LQIy98Dj9B645KWoVisXabmSkxw3L1VIqSSqB0qjuqMksjsMPqFwNPxMcD84y+fBPWMPglZNhEf6bvW4JLoXsi+fjvKQ1sDprPrtB9dIoOO/1OSWdQjeh5fC69Af8EzfCSSvhUvyWuCP51Aa3hFFLa9CUcuh2us2lIpyuOUkwz3zANzP7IP7mQPafSkUV1Fa/Z94BqAstC1Kg9sgM6QLXNPS6v2ZyM3VUqSpbk5mF6lMBHdXF7SJ8OfuIyIiu2EXHaevueYa4/0uXbqoILx58+b45ptvcN9957YaSEu79Cs3bemOjY1FeHg4AgPr349LTiSlAIusz9FOqOuqIvKfSG89DK7h4TCUF8NwcitwbD1cjm8Ajm2AS+EZeKZsVpPO0KQN0KwPDLGVreFh7QCXxr0f+ZngfnD4z0NpAVxWvgKse1e13hq8g2AYMh3u3f+JJjV8f+u1H6QGSDtJU5+ICunOkvgrXBJ/UsG3BPwyBWx4A4aw9mooMoOkoUd1sUz3FkOFVjwybS+QvldrdVfTPriUV18J3eDpr6XXh8fDILcRHbTHAdFwd3GBa0UF3NLTLfKZkIwvqjsZWk5IwC1dCYiIiBpl0B0WFgY3NzekpqaazZfHluyPHRwcjHbt2uHAgQPVPu/l5aWmquREx1InwHIiacn1NWbGfeHuB7QcoE16gaXTB1QQrqbk9UBGElxk3ukDcNn+pbacd5AKwhHXVwvCm/a8qArGtsbPBPeDw34eDiwDJMVb+lyLjjfD5epX4RJgntVktf0Q0hzo95A25WdoFdAlDf3gCrhkJAGrk1R3FwTFaX3AZZKLehcYC1z9RmUf1wLqtD1AmgTWEmgnqYsM1ZJib+HttaBaBdZyGw8XGYe8MuB3sfJnwiE+UzbAImpERLbRokULNTqVPkKVHA8XLVqE4cOHV7v8kSNH0LJlS2zduhXdunW76Ne11HrsLuj29PREz549sWzZMuNOlJYOeTxu3DiLbVReXh4OHjyIu+5i5Wy7JiegYW21qfs/zw4rdHwTcGydaglX94uytUJMejEmFzcgqrMWgMuJsxRlCmpm0/8KkVOSAFeGCtyxQHsc2BS4bhbQ/mz2UYPzCwN6jNYm+e3Yv0QrxCa3MrrCurna5BdRORb4DUCLy4CC01pgrQLsvZW3iUBJDanabl5aFo4KrqUFu/I2uIVEvQ39vyYL2JuSaxwujIiIbEe6C4eE1G5kkdq6++67kZWVhR9++ME4TzKd5bWkYdjh0sslrXvMmDHo1auXGptbhgzLz883VjMfPXo0mjZtqvpd68XX9uzZY7x/4sQJbNu2Df7+/mjTpo2a/9RTT+GGG25QKeUnT57ElClTVIv6HXfcYdn/LVmfbyjQ7ipt0gsQpezUAnC9RTznBHBqmzZteP/syb5KR79Eu5WgXKogE5HlSQvw9q+1gLvwjNZ22/cB4MqJgJcdBSySJdP5Vm0qLQQOLj87Fnh+GrD5I22SC3kmBc3MuHoA0uXF2HItqeEJQEgLwM0ueliRhbByORGRfWioEanc3NwazehXdT7jGDlypCpYNnnyZKSkpKim/MWLFxuLqyUnJ5ulxkkQ3b17d+Pj119/XU0DBw7EypUr1bzjx4+rAPv06dOqP9yAAQOwbt06dZ8aOQmcm/bQpkse1OZJuqeeji63EpRLIL57kTbpKZ6Shi4p6VL52Od8V8tqSPY8b9/P8zxX3d9JoahSH+mIep51EjUCZw5pqeSHtN9fRHQEbpwDNOsJu6bGAr9Om9RY4H9pAfjen7UAXALvJq0rg2qT1HCZxwt4Dq+wtBxHz2hdBjhGNxFR7X3wwQeYOnWqisdMY7ibbroJTZo0wfPPP68aXSU2k4bWDh06qMZVGb2qJlXTyzds2IAHHngAe/fuRadOndQ6TUmh7vvvvx/Lly9X8aWMYPXwww/jscceU8/L9n3yySfGdYsVK1aotPaq6eWrVq3C008/je3btyM0NFQ1Fr/44otqeGoxaNAgtQ0+Pj7473//qzK5H3zwQfUa1nRRl/kllbymdHI9kNbJzpDKtufz9ddfX8xmUGMlqeQydfqH9rgkHzixubIlvLJFXNJKj67WJjvgWhluGwKitWJOMlSafsuxy6kxkEB17VxAiqWVFWrp1VeMB/o/2viCUjUW+JXaJGOBSyE2+W661338bXIMBzOKVAJHmL/XRY3DTkRkFfLDVFMNEWvz8K1V8dHbbrsN//73v1UQO3jwYDXvzJkzqlH1119/Vd1+r732Wrz00kuqptann36qMpSTkpJqHN7ZlPz99ddfj6FDh+Lzzz/H4cOHjcG0TrorN2vWDN9++60K9NesWaOC8OjoaIwYMUJlRUvALsWzP/roI/U3ElBL464pyaiWbZVUdNlOGV1r7NixqkCpaVD92Wef4YknnsD69evVsNey/KWXXqq20VqYW0e2J0XVWl6uTULGqM3YdzYIP7kFKDvPUHAXuKhTudAFnj7/8wYZtzjnJFxyTwEy7f/dPAVWAnDTYFz6ijJ1lezFiS3Aj48CqTu1x/Jdu/5NrRW4sZNiapIqTk7tQIbeym1H3SOIiCTgfjnGNvvhuZO1Klwsfa9lJKkvv/zSGHR/9913qp+0tApL63fXrl2Ny7/wwguqFfvHH3+sVU0vWW9FRYVqVZbgt2PHjqpV/aGHHjIu4+HhYTYctLReSzAsI1lJ0C3dkqVluri4+Lzp5O+++67q5/3OO++oFvH4+HgVmI8fP15laest+Z07d1bdmWWZtm3bquWlRhmDbnIu8oWQgkYy9RwDe2CoqED6icMIr0iDa+ou4NR2IGUHkLpHa5WXVFeZdO7eQGRHk0C8KxCZoKXIEjWU4jxgxUvA+nnaMFnSTeOql4Bud1pm6C0iO7E/vVDdJkTXf9hQIiJnM2rUKNUiLEGrtGZ/8cUXuP3221WQKi3V0kr8yy+/qKJlZWVlKCwsVF2Ka0NaqLt06WI2HGa/fv3OWW7u3LmYP3++Wq+sX2qB1bUiubyWrFtPQRfSgi3/Bwn09ZZ5CbpNSYt6WloarIkt3US1ZPDwAyL6As1NfijKSrQqyRKAn9qh3Uof9ZI8LWVeJp30OZUWcGNqeletYJxPMN8Dsrx9fwC/PKmlXovOtwHDZgD+rJVBjmd/ZUt3PFu6icieSIq3tDjb6rVrSdLFpTuwBNa9e/fGX3/9hTfeeEM9J6ndS5YsUTW5pAi2tDjfeuutKii2lK+//lq9zqxZs1TQHBAQgJkzZ6r0b2uQlnVTEqRLa7w1Megmqtc3yFMLomXS6wXKlzbzcGWF9spAXG4LMirHCN57dogmIX3C9dZwPSAPiGJLJF2cvDRg8bPAru8rP19xwHVvAG1rLnhC1JhVVBhwIENr6WYRNSKyK9LiWosUb1uTVuhbbrlFtXAfOHAA7du3R48ePdRzf//9t+rzfPPNN6vH0mos42PXlhRe++yzz1BUVGRs7ZaibKbkNfr376+Kp+lk+GhTUvBMCq5d6LW+//57dQFBb+2WdUsQL33GbYlBN5E10uOlr6xMerE46TMufcGNQfh27b6MO5x1VJukErPOL/xsarpqEe8ChLQ8d/zg8jKtv3tZsVYcS90WAaUyr+pUrA27pC9zEfNdyooQ5u4LF0n9l/HZZSgmab2X+1LIiinLtiOfsa2fA39MBIqyABdX4JKHgUHPNYoDPtHFOp5ViIKSCni6uaB1uD93JBHRRaaYS8Gz3bt345///KdxvvR5XrhwoWoNl0B20qRJdWoVvvPOO1W1cklfnzBhggrYpdXclLyGFD77/fffVX9uCdI3btyo7psW55bnpYCbFFsLCgo657UkaJfhrKUwnPQ3l2Wl77ZUXzetzG4LDLqJGoIEo4Ex2tT+6rPzC85o6eim6elSRC4/HTi4TJt0ngFa0TbT4FoKvDUguWbojkwg94T5tqnt86+82NDWJCCvvGXQZ10ZB4CfHz9bV0Au0tz4NhBzdrhGIkeVmJKrbttE+MPDzbYnVUREjdWVV16pKoJLoCqBsm727Nm49957VUu0FFeTomRSRby2pAjaTz/9pIblkmGkExIS8Oqrr+If/6hsmALUcGIy7JcMTS2BvQwlLQH0b7/9ZlxGgnYZJatXr16qtV0fMsxU06ZNVcV1GTJMir/J/+e+++7DxIkTYWsuhguN59UIyBsvVzuys7MRGFj/Iipy9UY600dERNj8qoitcV/YYD+UFACpu4GUytZwvWBbefH5/87NUyvgJsMmyTjn6tYb8PA2ma/frzq/puXN51e4eiDzxEGEVGTA9fQBQKaM/UDmEcBwnpSfwKbmreJ6QB7Y7NzW+0bAbr4XUlNgzVvAqpna50PeL2nZlhbuBqiebzf7wQ5Ycl9Y+phmbyz9/3tjSRLeWnYA/+jRFLNG1K3ojiPh95H7gZ8J2343JH1ahsOS1lnTomH2QkI+KYIm41WbFhpzNoaL2A/ne29re0xjSzeRvfH0BWJ7a5PpGMsS3ErrtlRArxpAy2MZOsnaKipQaggFIiLMg2UJ/iTwPr1f2079VqbCM0DOCW06vMp8fRIkqtZxvVVcWsnbaLfedhRsSBq/DPsh6fZyW5IP97RTQGllETy54CDVwWWqMLlvOpnNl/uGGubry1c3T78vf1sO7PkfkLZH2wYZs/r6Nzh8Fjmdvae0lu74KA4XRkRE9olBN1Fj4OahDTlmzwXlwttpU1WSQm8aiOut42cOaanyMgSbTFX5R2ot41UDcik8p19gkOBTLkiYBsRm901vC1WwfM484339uWr+tty8QqdcbgiDnfBtAlz9ilad3ImvXFP1ZAgWqQCbkpKiUu3mzJmDPn361Li7pC/ce++9p4ZskTRCqVA7Y8YMsyv7J06cUOmFkvZXUFCgqtl+9NFHKuXPFhJTtDRHFlEjIiJ7xaCbiKzLNxSI66tNVVuPpYCcHoRLX3b9fn4akJeqTabjn+tp9N7BZ4Pi86W1W5yLGoLD4OGDChd3uLp7wEUuAEjRMjWZ3JdMgGrn6/ddaphfZTpn/S5n50vBvT4PAH5NGnAfUGOxYMECVTxm3rx56Nu3rwqohw0bpvrrSZplVV9++SWeffZZNU6q9N3bt2+fqlgr6XfSp09kZmaqMU8HDRqkgu7w8HDs378fISEhNvgfArlFpUg+o1UuZ0s3ERHZKwbdRGQb0udYr/Lebpj5c0XZWnEws3T1A8CZg1qKvQTlVUkgKmOpS3q+pOB7VHer368y37Om5/zM50kav4sLDBUVSK/sH+bi5H2ZyX5JoCyFZ+655x71WIJvGYNVgmoJrqtas2aNCqj1AjpSoEaK2ZiOkyrFb2JjY1XLts60umxDS6osohbu54FQP0+bbQcREdH5MOgmIvsjVdqb9dQmU9LPOfsYUJxTJYj21VLwmV5NpJSUlGDz5s1qeBadFBAaMmQI1q5dW+1ektbtzz//HBs2bFAp6IcOHVJVYO+66y7jMj/++KNqLb/tttuwatUqVSlWKsxKcF+T4uJiNen0qrdS3Kguw85Up1uzICx9fAD2H0+r97oaO/n/S4Eg7gfuB34mbPPd0F9Hn+yRvl32un32uh/097S641ZtP1cMuomo8ZBW5ZDmtt4KIruXkZGB8vJyREZGms2Xx4mJidX+jbRwy98NGDDAWN1Vhnh57rnnjMtIIC59viVtXebLOKqPPvooPD09MWbMmGrXK33Cp02bds789PR0VRG2vnwrKtDCr0xVJ3bmKvpy4ifVc+W9437gfuBnouG/G6Wlpeq15FYqY9sb+f/LcUE4e/Xy8jruB/29PX36NDw8PMyey83VMq4uxP4+EURERNTgZPzTl19+Ge+++67qA37gwAE89thjeOGFFzBp0iS1jJx0SME0WU7ImKu7du1Sqes1Bd3S2i5BumlLt6SoS39wSw3zKSdOsj5nDza5H7gf+Jmw3XdDAjkJwCTTKCDAfkdTqBo0OiuPOuwHeU/lsxMVFQU3N/PRgmo7PByDbiIiIgcjlcflxCA1NdVsvjyWk4bqSGAtqeT/+te/1OPOnTsjPz8f999/P55//nl1whEdHY2EBPORFDp06IDvv/++xm3x8vJSU1WyPkudAMsJtSXX11hxP3A/8DNhu++GrFuKSkoWj7yer6+vXbUo6xlMcnHAnrbLnveDLCujdMh7Ku9tdYF6bT9TDLqJiIgcjKR79+zZE8uWLcPw4cONrT3yeNy4cdX+jZxYVD150K/o6/3epNCaVD83JVXOmzdntw8iIv2ipnR3sTd6n2T5nXf2oLuijvshODi4xgvWtcWgm4iIyAFJSrekfEs6uBRGkyHDpOVar2Y+evRoVQhN+lyLG264QVU8l5RxPb1cWr9lvh58P/HEE6rgmqSXjxgxQhVd++CDD9REROTsJIiTjCAZ3UT6AdsTvU9ykyZNnDorqKKO+0Fat6umlF8MBt1EREQOaOTIkSolbvLkyUhJSUG3bt2wePFiY3G15ORksxOOiRMnqhNGuT1x4oTq/ygB90svvWRcpnfv3li0aJHqpz19+nQ1XJgE86NGjbLJ/5GIyB5JkGaJQM3SwaYEkNIH2dmDbg8b7AcG3URERA5KUslrSieXwmmmpNrulClT1HQ+119/vZqIiIiodpz3MgcRERERERGRlTHoJiIiIiIiIrISh0gv16uqytiflsr1l3H2nL3Pg+C+4H7g54HfC/4+NOxvpX4s049tjobHbOvg8Zr7gZ8Jfjf4G9Hwv5W1PWY7RNAtO07ExsbaelOIiIgsdmwLCgpyuL3JYzYRETnbMdvF4ACX0uWKxcmTJxEQEGCRcefkioUE8MeOHUNgYCCcGfcF9wM/D/xe8PehYX8r5bAsB++YmBiHzLbiMds6eLzmfuBngt8N/kY0/G9lbY/ZDtHSLf/BZs2aWXy98kY4e9Ct477gfuDngd8L/j403G+lI7Zw63jMti4er7kf+Jngd4O/EQ37W1mbY7bjXUInIiIiIiIishMMuomIiIiIiIishEF3Nby8vDBlyhR16+y4L7gf+Hng94K/D/yttGc8TnE/8PPA7wZ/I/hbae/HDIcopEZERERERERkj9jSTURERERERGQlDLqJiIiIiIiIrIRBNxEREREREZGVMOiuxty5c9GiRQt4e3ujb9++2LBhA5zJjBkz0Lt3bwQEBCAiIgLDhw9HUlISnN0rr7wCFxcXPP7443BGJ06cwD//+U80adIEPj4+6Ny5MzZt2gRnUl5ejkmTJqFly5ZqH7Ru3RovvPACHL00xp9//okbbrgBMTEx6jvwww8/mD0v///JkycjOjpa7ZchQ4Zg//79cKb9UFpaivHjx6vvhZ+fn1pm9OjROHnypE232dE5+/Fa8JhdPWc+ZvN47bzHa8Fjtn0esxl0V7FgwQI8+eSTqqrdli1b0LVrVwwbNgxpaWlwFqtWrcIjjzyCdevWYcmSJeqDedVVVyE/Px/OauPGjXj//ffRpUsXOKPMzExceuml8PDwwG+//YY9e/Zg1qxZCAkJgTN59dVX8d577+Gdd97B3r171ePXXnsNc+bMgSOT7778FkqAUx3ZB2+//TbmzZuH9evXqwOY/G4WFRXBWfZDQUGBOmbISZ7cLly4UF2svPHGG22yrc6Ax2sNj9nncuZjNo/Xzn28Fjxm2+kxW6qX01l9+vQxPPLII8bH5eXlhpiYGMOMGTOcdjelpaXJZUHDqlWrDM4oNzfX0LZtW8OSJUsMAwcONDz22GMGZzN+/HjDgAEDDM7uuuuuM9x7771m82655RbDqFGjDM5CfgsWLVpkfFxRUWGIiooyzJw50zgvKyvL4OXlZfjqq68MzrIfqrNhwwa13NGjRxtsu5wJj9fV4zHbuY/ZPF5reLzW8JhtP8dstnSbKCkpwebNm1VqpM7V1VU9Xrt2LZxVdna2ug0NDYUzklb/6667zuxz4Wx+/PFH9OrVC7fddpvqctC9e3d8+OGHcDb9+/fHsmXLsG/fPvV4+/btWL16Na655ho4q8OHDyMlJcXs+xEUFKRSfZ35d1P/7ZSUtuDgYFtvisPh8bpmPGY79zGbx2sNj9fV4zHbdsdsd6ustZHKyMhQfUAiIyPN5svjxMREOKOKigrVH0pSizt16gRn8/XXX6u0E0lVc2aHDh1SaVrS9eK5555T++PRRx+Fp6cnxowZA2fx7LPPIicnB/Hx8XBzc1O/Fy+99BJGjRoFZyUBt6jud1N/zhlJar30F7vjjjsQGBho681xODxeV4/HbB6zebzW8HhdPR6zbXfMZtBNF2zl3bVrl2rNczbHjh3DY489pvq1S5EeZyYnctLS/fLLL6vH0tItnwvpw+tMQfc333yDL774Al9++SU6duyIbdu2qYtSUoDDmfYDnZ/UwRgxYoQq2CMXq4gaCo/ZPGbzeK3h8Zrs7ZjN9HITYWFhqvUqNTXVbCfJ46ioKDibcePG4eeff8aKFSvQrFkzOBvpaiAF9Hr06AF3d3c1ScEaKRgl96WV01lIVeqEhASzeR06dEBycjKcydNPP62unt9+++2q4uVdd92FJ554QlUPdlb6byN/N80P3kePHlUX7NjKbR08Xp+Lx2weswWP1xoer6vHY7btjtkMuk1IqmzPnj1Vn03TK4byuF+/fnAWcqVHDt6LFi3C8uXL1XALzmjw4MHYuXOnas3UJ2ntlVRiuS8XaJyFdC+oOmyc9Gtu3rw5nIlUu5Q6D6bkcyC/E85Kfh/kIG76uykp+FLF3Jl+N00P3jJc2tKlS9XwemQdPF6fxWO2hsdsDY/XGh6vq8djtu2O2Uwvr0L6rEqaqARXffr0wZtvvqlKzt9zzz1wpvQ0SZ/93//+p8bq1vt/SHEkGevQWcj/vWo/dhkKSb6Uzta/XVpzpSiJpJfLD5SMhfvBBx+oyZnIeI/ShzsuLk6ll2/duhWzZ8/GvffeC0eWl5eHAwcOmBVikQtPUlxR9oWk2L/44oto27atOqDLEByScj98+HA4y36Q1qVbb71V1YCQDCHJhNF/O+V5CRLJsni81vCYreExW8PjtXMfrwWP2XZ6zLZKTfRGbs6cOYa4uDiDp6enGpJk3bp1BmciH4vqpo8++sjg7Jxx+BHdTz/9ZOjUqZMaCio+Pt7wwQcfGJxNTk6Oev/l98Hb29vQqlUrw/PPP28oLi42OLIVK1ZU+5swZswY47BhkyZNMkRGRqrPx+DBgw1JSUkGZ9oPhw8frvG3U/6OrMPZj9eCx+yaOesxm8dr5z1eCx6z7fOY7SL/WD6UJyIiIiIiIiL26SYiIiIiIiKyEgbdRERERERERFbCoJuIiIiIiIjIShh0ExEREREREVkJg24iIiIiIiIiK2HQTURERERERGQlDLqJiIiIiIiIrIRBNxEREREREZGVMOgmIqtbuXIlXFxckJWVxb1NRERkp3i8JrIOBt1EREREREREVsKgm4iIiIiIiMhKGHQTOYGKigrMmDEDLVu2hI+PD7p27YrvvvvOLJXsl19+QZcuXeDt7Y1LLrkEu3btMlvH999/j44dO8LLywstWrTArFmzzJ4vLi7G+PHjERsbq5Zp06YN/vvf/5ots3nzZvTq1Qu+vr7o378/kpKSGuB/T0RE1DjweE3kmBh0EzkBCbg//fRTzJs3D7t378YTTzyBf/7zn1i1apVxmaeffloF0hs3bkR4eDhuuOEGlJaWGoPlESNG4Pbbb8fOnTsxdepUTJo0CR9//LHx70ePHo2vvvoKb7/9Nvbu3Yv3338f/v7+Ztvx/PPPq9fYtGkT3N3dce+99zbgXiAiIrJvPF4TOSgDETm0oqIig6+vr2HNmjVm8++77z7DHXfcYVixYoVBfgq+/vpr43OnT582+Pj4GBYsWKAe33nnnYahQ4ea/f3TTz9tSEhIUPeTkpLUOpYsWVLtNuivsXTpUuO8X375Rc0rLCy06P+XiIioMeLxmshxsaWbyMEdOHAABQUFGDp0qGp51idp+T548KBxuX79+hnvh4aGon379qrFWsjtpZdearZeebx//36Ul5dj27ZtcHNzw8CBA8+7LZK+rouOjla3aWlpFvu/EhERNVY8XhM5LndbbwARWVdeXp66lT7bTZs2NXtO+l6bBt4XS/qJ14aHh4fxvvQj1/uvEREROTser4kcF1u6iRxcQkKCCq6Tk5NVcTPTSYqe6datW2e8n5mZiX379qFDhw7qsdz+/fffZuuVx+3atVMt3J07d1bBs2kfcSIiIuLxmojY0k3k8AICAvDUU0+p4mkSGA8YMADZ2dkqaA4MDETz5s3VctOnT0eTJk0QGRmpCp6FhYVh+PDh6rn/+7//Q+/evfHCCy9g5MiRWLt2Ld555x28++676nmpZj5mzBhVGE0KqUl19KNHj6rUcSnARkRERDxeEzktW3cqJyLrq6ioMLz55puG9u3bGzw8PAzh4eGGYcOGGVatWmUscvbTTz8ZOnbsaPD09DT06dPHsH37drN1fPfdd6pwmvx9XFycYebMmWbPS0G0J554whAdHa3W0aZNG8P8+fPVc/prZGZmGpffunWrmnf48GF+BIiIiHi8JnJYLvKPrQN/IrIdGad70KBBKqU8ODiYbwUREZEd4vGaqPFin24iIiIiIiIiK2HQTURERERERGQlTC8nIiIiIiIishK2dBMRERERERFZCYNuIiIiIiIiIith0E1ERERERERkJQy6iYiIiIiIiKyEQTcRERERERGRlTDoJiIiIiIiIrISBt1EREREREREVsKgm4iIiIiIiMhKGHQTERERERERwTr+H7fHFSaBhjOXAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if hist is not None:\n",
    "    h = hist.history\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))\n",
    "    axes[0].plot(h[\"loss\"], label=\"train\")\n",
    "    axes[0].plot(h[\"val_loss\"], label=\"validation\")\n",
    "    axes[0].set_title(\"Loss\")\n",
    "    axes[1].plot(h[\"auc\"], label=\"train\")\n",
    "    axes[1].plot(h[\"val_auc\"], label=\"validation\")\n",
    "    axes[1].set_title(\"AUC\")\n",
    "    for ax in axes:\n",
    "        ax.set_xlabel(\"epoch\")\n",
    "        ax.legend()\n",
    "        ax.grid(alpha=0.3)\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "else:\n",
    "    print(\"Skipped.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12bc8ded",
   "metadata": {},
   "source": [
    "訓練損失持續下降、驗證損失卻停住甚至回升時，就是過擬合開始的訊號；EarlyStopping 會把權重還原到驗證損失最低的那一刻。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d314b439",
   "metadata": {},
   "source": [
    "### 5.3 在測試集上評估\n",
    "最後才碰測試集。除了準確率，也用臨床熟悉的敏感度、特異度來看。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "68286ac4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-29T20:02:45.038660Z",
     "iopub.status.busy": "2026-09-29T20:02:45.038539Z",
     "iopub.status.idle": "2026-09-29T20:02:45.115051Z",
     "shell.execute_reply": "2026-09-29T20:02:45.114638Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test accuracy : 0.829\n",
      "test AUC      : 0.916\n",
      "sensitivity   : 0.982  (pneumonia correctly flagged)\n",
      "specificity   : 0.573  (normal correctly cleared)\n",
      "majority-class baseline accuracy: 0.625\n"
     ]
    }
   ],
   "source": [
    "if hist is not None:\n",
    "    p_te = model.predict(Xp_te, verbose=0).ravel()\n",
    "    pred = (p_te > 0.5).astype(int)\n",
    "    tn, fp, fn, tp = confusion_matrix(yp_te, pred).ravel()\n",
    "    print(f\"test accuracy : {(tp + tn) / len(yp_te):.3f}\")\n",
    "    print(f\"test AUC      : {roc_auc_score(yp_te, p_te):.3f}\")\n",
    "    print(f\"sensitivity   : {tp / (tp + fn):.3f}  (pneumonia correctly flagged)\")\n",
    "    print(f\"specificity   : {tn / (tn + fp):.3f}  (normal correctly cleared)\")\n",
    "    print(f\"majority-class baseline accuracy: {np.mean(yp_te == 1):.3f}\")\n",
    "else:\n",
    "    print(\"Skipped.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd20a8f7",
   "metadata": {},
   "source": [
    "典型結果：AUC 約 0.9 左右，敏感度高、特異度明顯較低——模型傾向把正常的片子也判成肺炎（訓練資料肺炎多）。\n",
    "數字會因版本與硬體略有不同。請記得：這是 28×28 小圖、單一醫學中心來源、未經外部驗證的教學結果，不能拿來推論臨床表現。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fee4d90b",
   "metadata": {},
   "source": [
    "## 6. 動手試試\n",
    "1. 把第 3.1 節的 `hidden_layer_sizes` 改成 `(2,)` 或 `(256, 256, 256)`，觀察 `n_iter_` 與測試準確率怎麼變。\n",
    "2. 在第 3.1 節加上 `early_stopping=True`，看看 `n_iter_` 與準確率——理解為什麼本章建議入門時不要開它。\n",
    "3. 第 5.1 節把 Dropout 拿掉、`patience` 改成 30，重新畫學習曲線，看訓練與驗證曲線是否拉得更開。\n",
    "4. 第 5.3 節把判斷閾值 0.5 改成 0.8，敏感度與特異度如何交換？"
   ]
  }
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