{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cell-000",
   "metadata": {},
   "source": [
    "# 量子計算の基礎：ベクトル・ゲート・測定\n",
    "\n",
    "Qiskit Fall Fest 2026 @ Keio · Leona Quantum\n",
    "\n",
    "## 目次\n",
    "\n",
    "| セクション | 内容 |\n",
    "|---|---|\n",
    "| 共通0 | 準備 |\n",
    "| 共通1 | ベクトル・量子状態 |\n",
    "| 共通2 | 行列・演算子 |\n",
    "| 共通3 | X・H・Zゲート |\n",
    "| 共通4 | 固有値・測定 |\n",
    "| 共通5 | ブロッホ球 |\n",
    "| チャレンジ | 1つ選択 |\n",
    "| 復習 | 位相ゲート・回転・CNOT |\n",
    "| 任意 | IBM Quantum実機で測定 |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-001",
   "metadata": {},
   "source": [
    "## 開始前：環境の準備\n",
    "\n",
    "次のセルを実行して、必要なライブラリを準備します。導入済みのライブラリはそのまま使います。\n",
    "ネット接続はインストール時のみ必要。Python 3.12を想定する。環境によってはインストール後にカーネルの再起動が必要。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cell-002",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:26.865106Z",
     "iopub.status.busy": "2026-10-16T04:32:26.864933Z",
     "iopub.status.idle": "2026-10-16T04:32:27.336420Z",
     "shell.execute_reply": "2026-10-16T04:32:27.336079Z"
    }
   },
   "outputs": [],
   "source": [
    "%pip -q install \"qiskit==2.5.1\" \"numpy>=2.2,<3\" \"matplotlib>=3.9,<4\" \"scipy>=1.13,<2\" \"ipywidgets>=8.1,<9\" \"pylatexenc==2.10\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-003",
   "metadata": {},
   "source": [
    "## 共通：準備\n",
    "\n",
    "`QuantumCircuit`：回路。`Statevector`：回路から振幅・理想的な確率を計算。\n",
    "`sample_counts`：その確率に従う有限回の測定を模擬する。\n",
    "\n",
    "セルの実行：Shift + Enter。設定を変えた場合は、そのセルと後続セルを再実行。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cell-004",
   "metadata": {
    "annotated_original_cell": 4,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.338068Z",
     "iopub.status.busy": "2026-10-16T04:32:27.337940Z",
     "iopub.status.idle": "2026-10-16T04:32:27.589749Z",
     "shell.execute_reply": "2026-10-16T04:32:27.589483Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "# このセル：使う道具を読み込みます。NumPyはベクトル・行列計算、Matplotlibはグラフ、Qiskitは量子回路と状態を扱います。\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, Markdown\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import Statevector\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cell-005",
   "metadata": {
    "annotated_original_cell": 5,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.590894Z",
     "iopub.status.busy": "2026-10-16T04:32:27.590807Z",
     "iopub.status.idle": "2026-10-16T04:32:27.593033Z",
     "shell.execute_reply": "2026-10-16T04:32:27.592849Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Qiskit 2.5.1\n"
     ]
    }
   ],
   "source": [
    "# このセル：図と数値の表示設定です。量子状態や計算結果は変えません。\n",
    "import qiskit\n",
    "plt.rcParams.update({'font.size': 12, 'figure.dpi': 110})\n",
    "np.set_printoptions(precision=4, suppress=True)\n",
    "print('Qiskit', qiskit.__version__)\n",
    "\n",
    "# 図のラベルは英語、説明は日本語。数式と文字の表示設定です。\n",
    "plt.rcParams.update({\n",
    "    'font.family': 'DejaVu Sans', 'mathtext.fontset': 'dejavusans',\n",
    "    'axes.unicode_minus': True, 'font.size': 12, 'figure.dpi': 110,\n",
    "})\n",
    "try:\n",
    "    from google.colab import output as colab_output\n",
    "    colab_output.enable_custom_widget_manager()\n",
    "except ImportError:\n",
    "    pass\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-006",
   "metadata": {},
   "source": [
    "### 図の表示用コード\n",
    "\n",
    "以下は共通の表示関数。実行後、次の課題へ。\n",
    "折り畳み対応のNotebookではコード部分を閉じてよい。図はスライダーが動かない環境でも表示される。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cell-007",
   "metadata": {
    "annotated_original_cell": 7,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.593820Z",
     "iopub.status.busy": "2026-10-16T04:32:27.593734Z",
     "iopub.status.idle": "2026-10-16T04:32:27.595140Z",
     "shell.execute_reply": "2026-10-16T04:32:27.594956Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：回路を図で表示する補助関数です。量子計算そのものには関わりません。\n",
    "def show_circuit(circuit):\n",
    "    figure = circuit.draw(output='mpl', style='iqp', initial_state=True, fold=18)\n",
    "    display(figure)\n",
    "    plt.close(figure)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cell-008",
   "metadata": {
    "annotated_original_cell": 8,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.595902Z",
     "iopub.status.busy": "2026-10-16T04:32:27.595858Z",
     "iopub.status.idle": "2026-10-16T04:32:27.597088Z",
     "shell.execute_reply": "2026-10-16T04:32:27.596933Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：グラフの色を決めています。\n",
    "BLUE, PURPLE = ('#0f62fe', '#6929c4')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cell-009",
   "metadata": {
    "annotated_original_cell": 9,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.597816Z",
     "iopub.status.busy": "2026-10-16T04:32:27.597771Z",
     "iopub.status.idle": "2026-10-16T04:32:27.599885Z",
     "shell.execute_reply": "2026-10-16T04:32:27.599735Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：行列を色付きの表として描く関数です。各マスの値は行列の成分です。\n",
    "def show_matrix(matrix, labels, title='Matrix', selected=None, ax=None):\n",
    "    if ax is None:\n",
    "        _, ax = plt.subplots(figsize=(5, 4.4), layout='constrained')\n",
    "    a = np.asarray(matrix)\n",
    "    ax.imshow(a.real, cmap='coolwarm', vmin=-max(1, np.abs(a).max()), vmax=max(1, np.abs(a).max()))\n",
    "    for i in range(len(a)):\n",
    "        for j in range(len(a)):\n",
    "            ax.text(j, i, f'{a[i, j].real:g}', ha='center', va='center', fontsize=11, bbox=dict(facecolor='white', alpha=0.85, edgecolor='none', pad=1))\n",
    "            if selected is not None and i in selected and (j in selected):\n",
    "                ax.add_patch(plt.Rectangle((j - 0.48, i - 0.48), 0.96, 0.96, fill=False, edgecolor=PURPLE, linewidth=2))\n",
    "    ax.set_xticks(range(len(labels)), labels)\n",
    "    ax.set_yticks(range(len(labels)), labels)\n",
    "    ax.set_xlabel('Input column')\n",
    "    ax.set_ylabel('Output row')\n",
    "    ax.set_title(title)\n",
    "    return ax\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cell-010",
   "metadata": {
    "annotated_original_cell": 10,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.600575Z",
     "iopub.status.busy": "2026-10-16T04:32:27.600530Z",
     "iopub.status.idle": "2026-10-16T04:32:27.602083Z",
     "shell.execute_reply": "2026-10-16T04:32:27.601949Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：測定確率を棒グラフで表示します。\n",
    "def show_probabilities(probabilities, labels, title='Measurement probabilities', ax=None):\n",
    "    if ax is None:\n",
    "        _, ax = plt.subplots(figsize=(6, 3.2), layout='constrained')\n",
    "    ax.bar(labels, probabilities, color=BLUE)\n",
    "    ax.set_ylim(0, 1.08)\n",
    "    ax.set_ylabel('Probability')\n",
    "    ax.set_title(title)\n",
    "    for i, p in enumerate(probabilities):\n",
    "        ax.text(i, p + 0.025, f'{p:.3f}', ha='center', fontsize=10)\n",
    "    return ax\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cell-011",
   "metadata": {
    "annotated_original_cell": 11,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.602777Z",
     "iopub.status.busy": "2026-10-16T04:32:27.602737Z",
     "iopub.status.idle": "2026-10-16T04:32:27.604094Z",
     "shell.execute_reply": "2026-10-16T04:32:27.603951Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：指定した状態を shots 回測定したときの出現回数を模擬します。seed は結果を再現しやすくするための設定です。\n",
    "def sample_counts(state, shots=1000, seed=2026):\n",
    "    state = state.copy()\n",
    "    state.seed(seed)\n",
    "    return {str(bits): int(count) for bits, count in state.sample_counts(shots=shots).items()}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cell-012",
   "metadata": {
    "annotated_original_cell": 12,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.604877Z",
     "iopub.status.busy": "2026-10-16T04:32:27.604838Z",
     "iopub.status.idle": "2026-10-16T04:32:27.606629Z",
     "shell.execute_reply": "2026-10-16T04:32:27.606482Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：理想的な確率と、有限回の測定から得た頻度を並べます。\n",
    "def show_sample_comparison(state, shots=1000, seed=2026):\n",
    "    labels = [f'{i:0{state.num_qubits}b}' for i in range(len(state.data))]\n",
    "    counts = sample_counts(state, shots, seed)\n",
    "    frequencies = np.array([counts.get(b, 0) / shots for b in labels])\n",
    "    fig, ax = plt.subplots(figsize=(7, 3.4), layout='constrained')\n",
    "    x = np.arange(len(labels))\n",
    "    ax.bar(x - 0.18, state.probabilities(), 0.36, label='Ideal probability', color=BLUE)\n",
    "    ax.bar(x + 0.18, frequencies, 0.36, label=f'Measured frequency ({shots} shots)', color=PURPLE)\n",
    "    ax.set_xticks(x, labels)\n",
    "    ax.set_ylim(0, 1.08)\n",
    "    ax.set_ylabel('Probability / frequency')\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "    return counts\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cell-013",
   "metadata": {
    "annotated_original_cell": 13,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.607342Z",
     "iopub.status.busy": "2026-10-16T04:32:27.607306Z",
     "iopub.status.idle": "2026-10-16T04:32:27.608632Z",
     "shell.execute_reply": "2026-10-16T04:32:27.608479Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：スライダーを使える環境で対話的な操作を表示するための補助関数です。\n",
    "def optional_sliders(function, **specs):\n",
    "    try:\n",
    "        import ipywidgets as widgets\n",
    "    except ImportError:\n",
    "        print('Optional: install ipywidgets, or change parameters in the code and rerun.')\n",
    "        return\n",
    "    display(widgets.interactive(function, **specs))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cell-014",
   "metadata": {
    "annotated_original_cell": 14,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.609281Z",
     "iopub.status.busy": "2026-10-16T04:32:27.609223Z",
     "iopub.status.idle": "2026-10-16T04:32:27.611078Z",
     "shell.execute_reply": "2026-10-16T04:32:27.610945Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：振幅と確率を別のグラフで表示します。確率は振幅の絶対値の2乗です。\n",
    "def state_panel(vector, title='Quantum state'):\n",
    "    vector = np.asarray(vector, dtype=complex)\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(9, 3.4), layout='constrained')\n",
    "    x = np.arange(len(vector))\n",
    "    labels = [str(i) for i in x]\n",
    "    axes[0].bar(x - 0.18, vector.real, 0.36, color=BLUE, label='Real amplitude')\n",
    "    axes[0].bar(x + 0.18, vector.imag, 0.36, color=PURPLE, label='Imaginary amplitude')\n",
    "    axes[0].axhline(0, color='black', lw=0.7)\n",
    "    axes[0].set_xticks(x, labels)\n",
    "    axes[0].set_ylim(-1.1, 1.1)\n",
    "    axes[0].set_title(title + ': amplitudes')\n",
    "    axes[0].legend(fontsize=9)\n",
    "    show_probabilities(np.abs(vector) ** 2, labels, 'Squared magnitude = probability', axes[1])\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-015",
   "metadata": {},
   "source": [
    "## 学習の地図\n",
    "\n",
    "ベクトルは表現、量子状態はその使い方、演算子は作用、測定は結果。4つを区別してつなぐ。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-016",
   "metadata": {},
   "source": [
    "![ベクトル → 量子状態 → 演算子 → 測定。行列の作用と測定は別の操作。](data:image/png;base64,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    "\n",
    "ベクトル → 量子状態 → 演算子 → 測定。行列の作用と測定は別の操作。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-017",
   "metadata": {},
   "source": [
    "**進め方**：説明1つ → 短いコード1つ → 出力の確認。セルは上から順に実行。図の表示関数は編集不要。\n",
    "\n",
    "P・回転ゲート・CNOTの資料は復習用。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-018",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 共通1：ベクトル・量子状態\n",
    "\n",
    "### ベクトル＝順序をもつ成分の列\n",
    "\n",
    "$$\n",
    "\\boldsymbol{v}=\\begin{pmatrix}2\\\\-1\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "上の成分が2、下の成分が−1。まずは普通の数の列。まだ量子状態ではない。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1884c5e",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**コードの見方**  `np.array(...)` はベクトルをPythonで表す方法です。`print` は数値を表示します。これ以降、表示のためだけの補助関数はそのまま使います。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cell-019",
   "metadata": {
    "annotated_original_cell": 19,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.611774Z",
     "iopub.status.busy": "2026-10-16T04:32:27.611733Z",
     "iopub.status.idle": "2026-10-16T04:32:27.613191Z",
     "shell.execute_reply": "2026-10-16T04:32:27.613029Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2. -1.]\n"
     ]
    }
   ],
   "source": [
    "# このセル：v は普通の2成分ベクトルです。array は数を順に並べたNumPyの配列です。\n",
    "v = np.array([2.0, -1.0])\n",
    "print(v)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-020",
   "metadata": {},
   "source": [
    "### 基準ベクトル\n",
    "\n",
    "$$\n",
    "\\boldsymbol{e}_0=\\begin{pmatrix}1\\\\0\\end{pmatrix},\\qquad\n",
    "\\boldsymbol{e}_1=\\begin{pmatrix}0\\\\1\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "添字0・1は成分の名前。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cell-021",
   "metadata": {
    "annotated_original_cell": 21,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.613925Z",
     "iopub.status.busy": "2026-10-16T04:32:27.613881Z",
     "iopub.status.idle": "2026-10-16T04:32:27.615303Z",
     "shell.execute_reply": "2026-10-16T04:32:27.615165Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "basis 0 [1.+0.j 0.+0.j] basis 1 [0.+0.j 1.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：zero と one は、量子状態 |0⟩ と |1⟩ の基準ベクトルです。\n",
    "zero = np.array([1.0, 0.0], dtype=complex)\n",
    "one = np.array([0.0, 1.0], dtype=complex)\n",
    "print('basis 0', zero, 'basis 1', one)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-022",
   "metadata": {},
   "source": [
    "### 重みをつけて足す\n",
    "\n",
    "$$\n",
    "\\boldsymbol{v}=2\\boldsymbol{e}_0-\\boldsymbol{e}_1.\n",
    "$$\n",
    "\n",
    "2は上の成分の重み、−1は下の成分の重み。ベクトルの和は成分ごとの和。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cell-023",
   "metadata": {
    "annotated_original_cell": 23,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.616005Z",
     "iopub.status.busy": "2026-10-16T04:32:27.615969Z",
     "iopub.status.idle": "2026-10-16T04:32:27.617350Z",
     "shell.execute_reply": "2026-10-16T04:32:27.617213Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.+0.j -1.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：2|0⟩−|1⟩ を成分ごとに計算します。assert は期待どおりの結果か検査します。\n",
    "print(2 * zero - one)\n",
    "assert np.allclose(v, 2 * zero - one)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-024",
   "metadata": {},
   "source": [
    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)\n",
    "\n",
    "独立な基準0・1に重みをつけて足す。重みは負や複素数にもなる。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-025",
   "metadata": {},
   "source": [
    "### 量子状態＝確率振幅を並べたベクトル\n",
    "\n",
    "$$\n",
    "|\\psi\\rangle=a|0\\rangle+b|1\\rangle\n",
    "=\\begin{pmatrix}a\\\\b\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "$|\\psi\\rangle$は状態の名前。$|0\\rangle,|1\\rangle$は基準状態。$a,b$は確率振幅。記号 $|\\ \\rangle$はベクトルを表す。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-026",
   "metadata": {},
   "source": [
    "### 振幅から確率へ\n",
    "\n",
    "$$\n",
    "P(0)=|a|^2,\\qquad P(1)=|b|^2.\n",
    "$$\n",
    "\n",
    "$P(0)$は0を測る確率。$|a|$は複素数の絶対値。$a$が実数なら $|a|^2=a^2$。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ade14c9",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**振幅と確率の対応**  $|\\psi\\rangle=a|0\\rangle+b|1\\rangle$ とすると、$P(0)=|a|^2$、$P(1)=|b|^2$ です。このセルでは $a=\\sqrt{p_0}$、$b=\\sqrt{1-p_0}$ としています。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cell-027",
   "metadata": {
    "annotated_original_cell": 27,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.618029Z",
     "iopub.status.busy": "2026-10-16T04:32:27.617993Z",
     "iopub.status.idle": "2026-10-16T04:32:27.619419Z",
     "shell.execute_reply": "2026-10-16T04:32:27.619279Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amplitudes [0.8367+0.j 0.5477+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：p0 は0を測る確率です。確率の平方根を振幅にして psi を組み立てます。\n",
    "p0 = 0.7\n",
    "psi = np.array([np.sqrt(p0), np.sqrt(1 - p0)], dtype=complex)\n",
    "print('amplitudes', psi)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-028",
   "metadata": {},
   "source": [
    "振幅を2乗して確率を計算。$\\sqrt{0.7}$が振幅、$0.7$が確率。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cell-029",
   "metadata": {
    "annotated_original_cell": 29,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.620088Z",
     "iopub.status.busy": "2026-10-16T04:32:27.620054Z",
     "iopub.status.idle": "2026-10-16T04:32:27.621333Z",
     "shell.execute_reply": "2026-10-16T04:32:27.621185Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probabilities [0.7 0.3]\n"
     ]
    }
   ],
   "source": [
    "# このセル：np.abs(psi)**2 は各振幅の絶対値を2乗したもので、測定確率になります。\n",
    "probabilities = np.abs(psi) ** 2\n",
    "print('probabilities', probabilities)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-030",
   "metadata": {},
   "source": [
    "### 正規化＝確率の合計1\n",
    "\n",
    "$$\n",
    "|a|^2+|b|^2=1.\n",
    "$$\n",
    "\n",
    "「測定で0か1を得る」確率の合計。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cell-031",
   "metadata": {
    "annotated_original_cell": 31,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.621979Z",
     "iopub.status.busy": "2026-10-16T04:32:27.621944Z",
     "iopub.status.idle": "2026-10-16T04:32:27.623182Z",
     "shell.execute_reply": "2026-10-16T04:32:27.623044Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum 1.0000000000000002\n"
     ]
    }
   ],
   "source": [
    "# このセル：sum() で確率の和を確認します。量子状態では合計が1になります。\n",
    "print('sum', probabilities.sum())\n",
    "assert np.isclose(probabilities.sum(), 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-032",
   "metadata": {},
   "source": [
    "左の棒：振幅の実部・虚部。右の棒：絶対値の2乗。負の振幅も、確率は0以上。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cell-033",
   "metadata": {
    "annotated_original_cell": 33,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.623878Z",
     "iopub.status.busy": "2026-10-16T04:32:27.623847Z",
     "iopub.status.idle": "2026-10-16T04:32:27.706401Z",
     "shell.execute_reply": "2026-10-16T04:32:27.706213Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 990x374 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：psi の振幅と確率の棒グラフを並べます。\n",
    "state_panel(psi, f'{p0:.0%} / {1 - p0:.0%}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-034",
   "metadata": {},
   "source": [
    "**確認**：`p0=0.2`に変更。状態を作るセルから図まで再実行。0の確率が20%になるか確認。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-035",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 共通2：行列・演算子\n",
    "\n",
    "### 関数の入力と出力\n",
    "\n",
    "数：$y=f(x)$。ベクトル：$\\boldsymbol{w}=A\\boldsymbol{v}$。\n",
    "演算子：ベクトルに作用する規則。基準を決めると、線形な演算子を行列で表せる。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-036",
   "metadata": {},
   "source": [
    "![入力 → 行列の作用 → 出力。Xは上と下の成分を交換する。](data:image/png;base64,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    "\n",
    "入力 → 行列の作用 → 出力。Xは上と下の成分を交換する。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-037",
   "metadata": {},
   "source": [
    "### 行列は各行の積と和\n",
    "\n",
    "$$\n",
    "A\\begin{pmatrix}a\\\\b\\end{pmatrix}\n",
    "=\\begin{pmatrix}A_{00}a+A_{01}b\\\\A_{10}a+A_{11}b\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "$A_{ij}$：行$i$、列$j$の成分。添字は0から。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "cell-038",
   "metadata": {
    "annotated_original_cell": 38,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.707348Z",
     "iopub.status.busy": "2026-10-16T04:32:27.707297Z",
     "iopub.status.idle": "2026-10-16T04:32:27.709059Z",
     "shell.execute_reply": "2026-10-16T04:32:27.708894Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.+0.j 1.+0.j]\n",
      " [1.+0.j 0.+0.j]]\n"
     ]
    }
   ],
   "source": [
    "# このセル：X は0と1の成分を入れ替える行列です。\n",
    "X = np.array([[0, 1], [1, 0]], dtype=complex)\n",
    "print(X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-039",
   "metadata": {},
   "source": [
    "Xの上の行：$0a+1b=b$。下の行：$1a+0b=a$。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b731cbfc",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**ここで確認する式**  $X(a,b)^T=(b,a)^T$。`@` は行列積、`X[0]` はXの上の行、`X[1]` は下の行です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cell-040",
   "metadata": {
    "annotated_original_cell": 40,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.709893Z",
     "iopub.status.busy": "2026-10-16T04:32:27.709804Z",
     "iopub.status.idle": "2026-10-16T04:32:27.711263Z",
     "shell.execute_reply": "2026-10-16T04:32:27.711106Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "upper row (0.5477225575051662+0j)\n",
      "lower row (0.8366600265340756+0j)\n"
     ]
    }
   ],
   "source": [
    "# このセル：行列Xの各行とベクトルvの内積を、個別に計算します。\n",
    "v = psi.copy()\n",
    "print('upper row', X[0] @ v)\n",
    "print('lower row', X[1] @ v)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-041",
   "metadata": {},
   "source": [
    "`@`は行列積。`*`は成分ごとの積。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cell-042",
   "metadata": {
    "annotated_original_cell": 42,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.711926Z",
     "iopub.status.busy": "2026-10-16T04:32:27.711887Z",
     "iopub.status.idle": "2026-10-16T04:32:27.713343Z",
     "shell.execute_reply": "2026-10-16T04:32:27.713196Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input [0.8367+0.j 0.5477+0.j] output [0.5477+0.j 0.8367+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：X @ v で行列とベクトルを掛けます。v[::-1] は成分を逆順にしたものです。\n",
    "w = X @ v\n",
    "print('input', v, 'output', w)\n",
    "assert np.allclose(w, v[::-1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-043",
   "metadata": {},
   "source": [
    "行列の行・列を図で確認。赤い1が入力の成分を反対側へ送る。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cell-044",
   "metadata": {
    "annotated_original_cell": 44,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.714028Z",
     "iopub.status.busy": "2026-10-16T04:32:27.713982Z",
     "iopub.status.idle": "2026-10-16T04:32:27.738832Z",
     "shell.execute_reply": "2026-10-16T04:32:27.738648Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x484 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：X の行列を図にして、左右の成分が入れ替わる理由を確認します。\n",
    "show_matrix(X, ['0', '1'], 'X matrix')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-045",
   "metadata": {},
   "source": [
    "### ゲートと観測量の演算子\n",
    "\n",
    "**ゲート**：量子状態を変える操作。正規化を保つユニタリ行列。\n",
    "**観測量**：位置・エネルギーなど、測る量。エルミート行列の固有値が測定値。\n",
    "\n",
    "同じ行列Xでも、ゲートとして作用させることと、Xという観測量を測ることは区別する。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-046",
   "metadata": {},
   "source": [
    "### 回路図の読み方\n",
    "\n",
    "左から右に実行。横線は量子ビット、箱はゲート。線の始点は初期状態0。数字0は量子ビットの番号。測定器の記号は測定、二重線は古典ビット。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-047",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 共通3：X・H・Zゲート\n",
    "\n",
    "### 空の回路\n",
    "\n",
    "1量子ビットの操作から始めるため、最初はゲートなしの1量子ビット。初期状態は0。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2979b872",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**Qiskitの基本パターン**  まず `QuantumCircuit(...)` で回路を用意し、`.x(0)` や `.h(0)` で操作を加えます。`Statevector.from_instruction(qc)` で、その回路が準備する理想状態を計算します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cell-048",
   "metadata": {
    "annotated_original_cell": 48,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.739650Z",
     "iopub.status.busy": "2026-10-16T04:32:27.739606Z",
     "iopub.status.idle": "2026-10-16T04:32:27.807350Z",
     "shell.execute_reply": "2026-10-16T04:32:27.807168Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 215.962x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：qc_empty は1量子ビットの空の回路です。初期状態は |0⟩ です。\n",
    "qc_empty = QuantumCircuit(1)\n",
    "show_circuit(qc_empty)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-049",
   "metadata": {},
   "source": [
    "回路から状態を計算。`Statevector`の成分の順は0、1。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "cell-050",
   "metadata": {
    "annotated_original_cell": 50,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.808299Z",
     "iopub.status.busy": "2026-10-16T04:32:27.808242Z",
     "iopub.status.idle": "2026-10-16T04:32:27.809938Z",
     "shell.execute_reply": "2026-10-16T04:32:27.809744Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：from_instruction は回路を状態ベクトルへ変換します。data は振幅の配列です。\n",
    "empty_state = Statevector.from_instruction(qc_empty)\n",
    "print(empty_state.data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-051",
   "metadata": {},
   "source": [
    "### X：0と1を交換\n",
    "\n",
    "回路を作り、量子ビット0にXを1回。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "cell-052",
   "metadata": {
    "annotated_original_cell": 52,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.810641Z",
     "iopub.status.busy": "2026-10-16T04:32:27.810602Z",
     "iopub.status.idle": "2026-10-16T04:32:27.821946Z",
     "shell.execute_reply": "2026-10-16T04:32:27.821773Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 261.948x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：x(0) は量子ビット0にXゲートを作用させる命令です。\n",
    "qc_x = QuantumCircuit(1)\n",
    "qc_x.x(0)\n",
    "show_circuit(qc_x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-053",
   "metadata": {},
   "source": [
    "$$\n",
    "X|0\\rangle=|1\\rangle.\n",
    "$$\n",
    "\n",
    "行列と回路を比較。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cell-054",
   "metadata": {
    "annotated_original_cell": 54,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.822715Z",
     "iopub.status.busy": "2026-10-16T04:32:27.822675Z",
     "iopub.status.idle": "2026-10-16T04:32:27.824400Z",
     "shell.execute_reply": "2026-10-16T04:32:27.824231Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "circuit [0.+0.j 1.+0.j] matrix [0.+0.j 1.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：同じ操作をQiskit回路と行列Xで計算し、結果が一致することを確かめます。\n",
    "x_state = Statevector.from_instruction(qc_x)\n",
    "print('circuit', x_state.data, 'matrix', X @ zero)\n",
    "assert np.allclose(x_state.data, X @ zero)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-055",
   "metadata": {},
   "source": [
    "振幅と確率の図。成分が0から1へ移る。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "cell-056",
   "metadata": {
    "annotated_original_cell": 56,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.825140Z",
     "iopub.status.busy": "2026-10-16T04:32:27.825062Z",
     "iopub.status.idle": "2026-10-16T04:32:27.878486Z",
     "shell.execute_reply": "2026-10-16T04:32:27.878286Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x374 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：Xの後は |1⟩ なので、0の確率が0、1の確率が1になります。\n",
    "state_panel(x_state.data, 'X |0>')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-057",
   "metadata": {},
   "source": [
    "### Xを2回\n",
    "\n",
    "予想：0に戻る？ 新しい回路で確認。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "cell-058",
   "metadata": {
    "annotated_original_cell": 58,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.879358Z",
     "iopub.status.busy": "2026-10-16T04:32:27.879305Z",
     "iopub.status.idle": "2026-10-16T04:32:27.880990Z",
     "shell.execute_reply": "2026-10-16T04:32:27.880821Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：Xを2回作用させると |0⟩ に戻ります。\n",
    "qc_xx = QuantumCircuit(1)\n",
    "qc_xx.x(0)\n",
    "qc_xx.x(0)\n",
    "print(Statevector.from_instruction(qc_xx).data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-059",
   "metadata": {},
   "source": [
    "$$\n",
    "X^2=I,\\qquad X(X|0\\rangle)=|0\\rangle.\n",
    "$$\n",
    "\n",
    "$I$は何も変えない単位行列。図でXが2回並ぶことを確認。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cell-060",
   "metadata": {
    "annotated_original_cell": 60,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.881765Z",
     "iopub.status.busy": "2026-10-16T04:32:27.881683Z",
     "iopub.status.idle": "2026-10-16T04:32:27.891786Z",
     "shell.execute_reply": "2026-10-16T04:32:27.891630Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 353.921x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：Xゲートが2個並んだ回路図を見せます。\n",
    "show_circuit(qc_xx)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-061",
   "metadata": {},
   "source": [
    "### H：和と差を作る\n",
    "\n",
    "$$\n",
    "H=\\frac1{\\sqrt2}\\begin{pmatrix}1&1\\\\1&-1\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "上は和、下は差。その後、両方を$\\sqrt2$で割る。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d75a815f",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**Hゲートを行列で読む**  $H|0\\rangle=(|0\\rangle+|1\\rangle)/\\sqrt2$。振幅は約0.707ずつ、確率は0.5ずつです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "cell-062",
   "metadata": {
    "annotated_original_cell": 62,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.892464Z",
     "iopub.status.busy": "2026-10-16T04:32:27.892425Z",
     "iopub.status.idle": "2026-10-16T04:32:27.893952Z",
     "shell.execute_reply": "2026-10-16T04:32:27.893791Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7071+0.j 0.7071+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：H_gate はH行列、plus は H|0⟩ の状態です。振幅はどちらも 1/√2 になります。\n",
    "H_gate = np.array([[1, 1], [1, -1]], dtype=complex) / np.sqrt(2)\n",
    "plus = H_gate @ zero\n",
    "print(plus)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-063",
   "metadata": {},
   "source": [
    "$$\n",
    "H|0\\rangle=|+\\rangle=\\frac{|0\\rangle+|1\\rangle}{\\sqrt2}.\n",
    "$$\n",
    "\n",
    "振幅は$1/\\sqrt2$ずつ。確率は1/2ずつ。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cell-064",
   "metadata": {
    "annotated_original_cell": 64,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.894683Z",
     "iopub.status.busy": "2026-10-16T04:32:27.894606Z",
     "iopub.status.idle": "2026-10-16T04:32:27.903486Z",
     "shell.execute_reply": "2026-10-16T04:32:27.903317Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 261.948x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：h(0) で量子ビット0にHadamardゲートを作用させます。\n",
    "qc_h = QuantumCircuit(1)\n",
    "qc_h.h(0)\n",
    "show_circuit(qc_h)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-065",
   "metadata": {},
   "source": [
    "Hをかけた回路の状態と、行列の結果。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "cell-066",
   "metadata": {
    "annotated_original_cell": 66,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.904182Z",
     "iopub.status.busy": "2026-10-16T04:32:27.904144Z",
     "iopub.status.idle": "2026-10-16T04:32:27.958191Z",
     "shell.execute_reply": "2026-10-16T04:32:27.957987Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x374 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：QiskitのHゲートの結果と、行列による H|0⟩ が一致するか検査します。\n",
    "h_state = Statevector.from_instruction(qc_h)\n",
    "assert np.allclose(h_state.data, plus)\n",
    "state_panel(h_state.data, 'H |0>')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-067",
   "metadata": {},
   "source": [
    "### Hを2回：振幅の和と差\n",
    "\n",
    "$$\n",
    "H|+\\rangle=\\frac12\\begin{pmatrix}1+1\\\\1-1\\end{pmatrix}=|0\\rangle.\n",
    "$$\n",
    "\n",
    "0の振幅は強め合い、1の振幅は打ち消し合う。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cell-068",
   "metadata": {
    "annotated_original_cell": 68,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.959020Z",
     "iopub.status.busy": "2026-10-16T04:32:27.958970Z",
     "iopub.status.idle": "2026-10-16T04:32:27.960835Z",
     "shell.execute_reply": "2026-10-16T04:32:27.960651Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：Hを2回作用させると元の |0⟩ に戻ります。\n",
    "qc_hh = QuantumCircuit(1)\n",
    "qc_hh.h(0)\n",
    "qc_hh.h(0)\n",
    "print(Statevector.from_instruction(qc_hh).data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-069",
   "metadata": {},
   "source": [
    "$$\n",
    "H^2=I.\n",
    "$$\n",
    "\n",
    "Hを2回。1回目の重ね合わせを、2回目の和・差で0へ戻す。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "cell-070",
   "metadata": {
    "annotated_original_cell": 70,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.961665Z",
     "iopub.status.busy": "2026-10-16T04:32:27.961617Z",
     "iopub.status.idle": "2026-10-16T04:32:27.971295Z",
     "shell.execute_reply": "2026-10-16T04:32:27.971130Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 353.921x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：2つのHゲートを回路図で確認します。\n",
    "show_circuit(qc_hh)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-071",
   "metadata": {},
   "source": [
    "### Z：下の成分の符号を変える\n",
    "\n",
    "$$\n",
    "Z=\\begin{pmatrix}1&0\\\\0&-1\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "$$\n",
    "Z|+\\rangle=|-\\rangle=\\frac{|0\\rangle-|1\\rangle}{\\sqrt2}.\n",
    "$$\n",
    "\n",
    "符号は振幅の情報。確率は半々のまま。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "cell-072",
   "metadata": {
    "annotated_original_cell": 72,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.972014Z",
     "iopub.status.busy": "2026-10-16T04:32:27.971970Z",
     "iopub.status.idle": "2026-10-16T04:32:27.973497Z",
     "shell.execute_reply": "2026-10-16T04:32:27.973329Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.7071+0.j -0.7071+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：Z は |1⟩ の振幅の符号だけを反転させます。minus は |−⟩ 状態です。\n",
    "Z = np.diag([1.0, -1.0]).astype(complex)\n",
    "minus = Z @ plus\n",
    "print(minus)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-073",
   "metadata": {},
   "source": [
    "負の振幅と確率を区別。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cell-074",
   "metadata": {
    "annotated_original_cell": 74,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:27.974233Z",
     "iopub.status.busy": "2026-10-16T04:32:27.974193Z",
     "iopub.status.idle": "2026-10-16T04:32:28.029643Z",
     "shell.execute_reply": "2026-10-16T04:32:28.029441Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x374 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：Zの前後では確率が変わらないことを図で確かめます。\n",
    "state_panel(minus, 'Z |+>')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-075",
   "metadata": {},
   "source": [
    "### H → Z → H\n",
    "\n",
    "1ゲートずつ追加し、途中の状態を確認。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8161243a",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**今回の山場：位相と干渉**  Hの後もZの後も測定確率は半々です。ただしZは符号を変えます。最後のHでその符号の違いが0/1の確率差になります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "cell-076",
   "metadata": {
    "annotated_original_cell": 76,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.030509Z",
     "iopub.status.busy": "2026-10-16T04:32:28.030456Z",
     "iopub.status.idle": "2026-10-16T04:32:28.032365Z",
     "shell.execute_reply": "2026-10-16T04:32:28.032184Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7071+0.j 0.7071+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：H → Z → H の1段階目で |+⟩ を準備します。\n",
    "qc_hzh = QuantumCircuit(1)\n",
    "qc_hzh.h(0)\n",
    "print(Statevector.from_instruction(qc_hzh).data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-077",
   "metadata": {},
   "source": [
    "Zを追加。確率は変わらず、下の成分の符号が変わる。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "cell-078",
   "metadata": {
    "annotated_original_cell": 78,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.033166Z",
     "iopub.status.busy": "2026-10-16T04:32:28.033125Z",
     "iopub.status.idle": "2026-10-16T04:32:28.034636Z",
     "shell.execute_reply": "2026-10-16T04:32:28.034472Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.7071+0.j -0.7071+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：すでにある回路にZを追加します。|+⟩ が |−⟩ に変わります。\n",
    "qc_hzh.z(0)\n",
    "print(Statevector.from_instruction(qc_hzh).data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-079",
   "metadata": {},
   "source": [
    "最後にH。$H|-\\rangle=|1\\rangle$。\n",
    "位相の違い → 干渉 → 確率の違い。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "cell-080",
   "metadata": {
    "annotated_original_cell": 80,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.035375Z",
     "iopub.status.busy": "2026-10-16T04:32:28.035331Z",
     "iopub.status.idle": "2026-10-16T04:32:28.097432Z",
     "shell.execute_reply": "2026-10-16T04:32:28.097247Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 445.893x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x374 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：最後にHを追加して状態と確率を描きます。|1⟩ になることに注目します。\n",
    "qc_hzh.h(0)\n",
    "show_circuit(qc_hzh)\n",
    "state = Statevector.from_instruction(qc_hzh)\n",
    "state_panel(state.data, 'H Z H |0>')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-081",
   "metadata": {},
   "source": [
    "<details><summary>確認・解答例</summary>\n",
    "\n",
    "Xを2回、Hを2回で0へ戻る。HとHZの途中の確率は同じでも、最後のHの後は0と1に分かれる。\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-082",
   "metadata": {},
   "source": [
    "### 回路と振幅を対応させる\n",
    "\n",
    "同じ3段階を、回路図と状態の両方で確認。H → Z → H。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "cell-083",
   "metadata": {
    "annotated_original_cell": 83,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.098295Z",
     "iopub.status.busy": "2026-10-16T04:32:28.098239Z",
     "iopub.status.idle": "2026-10-16T04:32:28.107256Z",
     "shell.execute_reply": "2026-10-16T04:32:28.107092Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 261.948x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：同じH→Z→Hを、途中の回路図を見ながらたどります（Hまで）。\n",
    "interference_circuit = QuantumCircuit(1)\n",
    "interference_circuit.h(0)\n",
    "show_circuit(interference_circuit)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "cell-084",
   "metadata": {
    "annotated_original_cell": 84,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.108059Z",
     "iopub.status.busy": "2026-10-16T04:32:28.108010Z",
     "iopub.status.idle": "2026-10-16T04:32:28.117984Z",
     "shell.execute_reply": "2026-10-16T04:32:28.117822Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 353.921x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：回路にZを追加した段階です。\n",
    "interference_circuit.z(0)\n",
    "show_circuit(interference_circuit)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "cell-085",
   "metadata": {
    "annotated_original_cell": 85,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.118746Z",
     "iopub.status.busy": "2026-10-16T04:32:28.118699Z",
     "iopub.status.idle": "2026-10-16T04:32:28.128531Z",
     "shell.execute_reply": "2026-10-16T04:32:28.128364Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 445.893x128.761 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：最後のHを追加した段階です。\n",
    "interference_circuit.h(0)\n",
    "show_circuit(interference_circuit)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-086",
   "metadata": {},
   "source": [
    "$$\n",
    "|0\\rangle\\xrightarrow{H}|+\\rangle\\xrightarrow{Z}|-\\rangle\\xrightarrow{H}|1\\rangle.\n",
    "$$\n",
    "\n",
    "中間の確率は半々でも、振幅の符号が違う。最後のHで違いが測定確率になる。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-087",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 共通4：固有値・測定\n",
    "\n",
    "### 固有ベクトル＝形を保つ入力\n",
    "\n",
    "$$\n",
    "A\\boldsymbol{v}=\\lambda\\boldsymbol{v},\\qquad \\boldsymbol{v}\\ne0.\n",
    "$$\n",
    "\n",
    "$\\lambda$は固有値（倍率）。一般の入力では、この形にならない。行列を掛ける計算と、固有値を探す計算は同義ではない。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "cell-088",
   "metadata": {
    "annotated_original_cell": 88,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.129245Z",
     "iopub.status.busy": "2026-10-16T04:32:28.129206Z",
     "iopub.status.idle": "2026-10-16T04:32:28.130819Z",
     "shell.execute_reply": "2026-10-16T04:32:28.130649Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X |+> [0.7071+0.j 0.7071+0.j]\n",
      "+1 |+> [0.7071+0.j 0.7071+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：X|+⟩=+|+⟩ を数値で確認します。|+⟩ はXの固有ベクトルです。\n",
    "print('X |+>', X @ plus)\n",
    "print('+1 |+>', plus)\n",
    "assert np.allclose(X @ plus, plus)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-089",
   "metadata": {},
   "source": [
    "$|+\\rangle$の固有値は+1、$|-\\rangle$の固有値は−1。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "cell-090",
   "metadata": {
    "annotated_original_cell": 90,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.131544Z",
     "iopub.status.busy": "2026-10-16T04:32:28.131460Z",
     "iopub.status.idle": "2026-10-16T04:32:28.132963Z",
     "shell.execute_reply": "2026-10-16T04:32:28.132823Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X |-> [-0.7071+0.j  0.7071+0.j]\n",
      "-1 |-> [-0.7071-0.j  0.7071-0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：X|−⟩=−|−⟩ を確認します。|−⟩ のX固有値は−1です。\n",
    "print('X |->', X @ minus)\n",
    "print('-1 |->', -minus)\n",
    "assert np.allclose(X @ minus, -minus)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-091",
   "metadata": {},
   "source": [
    "`eigh`はエルミート行列の固有値・固有ベクトルを求める。エルミート：複素共役して転置すると元に戻る行列。ここでは実対称行列。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a884be1a",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**固有値の意味**  `np.linalg.eigh(X)` は $Xv=\\lambda v$ を満たす $\\lambda$ と $v$ を計算します。結果の `values` は固有値、`vectors` は列ごとに固有ベクトルです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "cell-092",
   "metadata": {
    "annotated_original_cell": 92,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.133695Z",
     "iopub.status.busy": "2026-10-16T04:32:28.133655Z",
     "iopub.status.idle": "2026-10-16T04:32:28.135076Z",
     "shell.execute_reply": "2026-10-16T04:32:28.134928Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eigenvalues [-1.  1.]\n"
     ]
    }
   ],
   "source": [
    "# このセル：eigh はエルミート行列の固有値と固有ベクトルを求めます。\n",
    "values, vectors = np.linalg.eigh(X)\n",
    "print('eigenvalues', values)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-093",
   "metadata": {},
   "source": [
    "戻り値の列が固有ベクトル。全体の符号が違っても同じ物理的状態。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "cell-094",
   "metadata": {
    "annotated_original_cell": 94,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.135791Z",
     "iopub.status.busy": "2026-10-16T04:32:28.135752Z",
     "iopub.status.idle": "2026-10-16T04:32:28.137136Z",
     "shell.execute_reply": "2026-10-16T04:32:28.136970Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eigenvectors: columns [[-0.7071+0.j  0.7071+0.j]\n",
      " [ 0.7071+0.j  0.7071+0.j]]\n"
     ]
    }
   ],
   "source": [
    "# このセル：vectors の各列は固有ベクトルです。A v=λv の関係を assert で検証します。\n",
    "print('eigenvectors: columns', vectors)\n",
    "assert np.allclose(X @ vectors, vectors * values)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-095",
   "metadata": {},
   "source": [
    "### 測定＝1回で1つの結果\n",
    "\n",
    "ここからは0・1を測る。状態を用意し直して100回測ると、回数の分布になる。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-096",
   "metadata": {},
   "source": [
    "![70%・30%の例。振幅を2乗した確率で、測定結果0・1のどちらかを得る。](data:image/png;base64,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8yIbQhttderUscsvv9z38yuvvJIkuJwaBSn9r//QQw9FPGDX888///jO16tXL+j11KpI26+qiZo1a1pmoWDyiBEj3OuuZITaHP3+++8Zuk1K1HjVGdpn77//fpIKBvX+1xwOtZPy5gCofZOeRzB6rb0V8KVLl3aVFDnFd999l+TnaA1czuj3444dO1zyTAk+zXJQUjC1Shz9vlGjRr6qG80oSen+x4wZ484r4XLmmWeGvG1AuEhEAAAAAACALG/xrB32ylV/2JCef9nqv/e4y4qUzGsXP1DdHvvqVGvSpZzlznO07dKS2TttwuCVviqJbvdlrlXAL774olWuXNn3s+Yz6LLUVsP36tXL+vTp47vspJNOchUMaeVfAZHSkGa1Y9LAZbXI0Qr+zOS6667zzbXYvXu3dezY0dasWZNh26PH9mZuKLkTbKh2fHy8awmUJ8/RMa/33nuvbd68Ocl1tOL96aefttdee813maopIp3T8fXXX9snn3ziOyWfj5EZ/frrr0l+btiwYZZ/P+p1VSWEBpirwmHUqFFu1kgounfv7juvofKHD/83G8ffoEGD3PtB2rRp4wa9A7GSKzGldw0AAAAAAEAmtmrBbhvTb4Ut+Gm777ICRXK7odMtr6poBQonDfDu23XY/tdljm1Zc8Dy5M1l93x8klWpe7T9TWaiVkIaRusFCaVu3bouoK5ZB1odrVYxWjGvOQLDhg1L0g++WrVqrl1NhQoV0rwtt956qw0ZMsSdv/jii+3TTz+1zEDPbf369XbyySfb7NmzQ7qN9t9bb73lzqty48cffwwasPeGVas9kpc0iBa1ESpatKirIlH1ghITKSUObrzxRl81xEsvvWR33XWXO6/WTnp9Jk+e7LvuVVddZe+++27E29akSRObMWNGkmD1bbfdZpmZqgy8+Q0K2ut9Eyy5k1Xejw8++KA9++yz7rwSe6rsCdWePXusRo0atnHjRvdz27ZtXULLSzQoHKxklRJbXmhYLcs0swSIFRIRAAAAAAAgy9mwbK+NG7DSfp/03wr9vAXirOWVFVwSonDxwMOS37p3kc38cpM73+3+6nbu1RUts9KAaLVlUZ/3cJxyyikuWRCt9kg///yzG/bsP9tA1QXqdx+JTZs22TfffONawjz22GOu/U16JSIULFYCQsFiUYBdgfb0TkR4SR2vbY8CwDofrG3PtGnTXMBbateu7eYOvPHGGy547L/GWIOMVRnhVVDkhETEihUrXKDfc+KJJyYZ2p0V34+fffaZr6qhb9++9uqrr4a9vd9++62rcvDmtahiSduigdSqWtq+/b/k7T333OMqJ4BYivyvEgAAAAAAQDrbuvaATRiy0maM3mgJ/85DjsuTy87qVs7a3lLZipcNPnD6l7EbfUmIes2K2zlXpr1aIJbUXkatjhT0V3B57969KV6/ePHibqX8/fffn6ZAdKDAtFZ+v/nmm+7n119/3a24b9++vesprwCrkgKFChVywU71s1cLJ520St07rwCuEgb+K8W1ej/SREQkTT4KFizoZi2oh74qEvxb2KQ3VTYoWKx9pBkHav9z/vnnu9XrmhdRvnx5t71ahb9hwwa3f3UMqFWPWvb4UwJD7ZmUJMpp5s2bl+TnWrVqZen3oxIHSjTJueee646TSOi2qsK44YYbXGJG1TfJW1gpKaE2U3p/A7FGIgIAAAAAAGR6u7YesknDVtkPH623w4eOBqBz5TJr1KGMtb+tipWJL5ji7Tet3GefPLXUnS9aKq9d/b9aFhd3dGZEZlayZEm3UlnBTA03Vv/+ZcuWuaoCtfKpWLGiC2C3a9fOBbEjnQuQmsGDB7skw9ChQ93PCsJq1bZOabFq1aqIb6se+pEkJFRB0b9/fxeoVQJF/fMDBYpVbRFLSjao0kHJEAWKNUhbVSLe8OBQlC1b1nr06OGODwW+o0HHk//q/UgrX9LL2rVrk2yvKl6y8vtRLaXUMkxVCkpCpKXFlPaFkidKvmlAu1pHqbpHVSMNGjSwK6+8MuS5E0Ba0ZoJAAAAAABkWprp8PXba+zbd9bagb1HA89y0rklrWPveKt0QuFU7+PIoQR7+ao/bPm8o/3dbx1S105sUTKm251dqT2NVoNPmDAhomHP+fPndwF4tdKpXr26G/zbokWLiLZFgfcdO3akqRXPBx98YNdee63bFm2TKgvUikkDodWWyWuFtHDhQosVJVSU0Pnoo49cyyr/OQTJqUJCQ49PPfVU1yaoVatWUZ2FAACxQiICAAAAAABkOgf3H7HvP1xvk4evtj07DvsuP6FxMbuwb1Wr3rBoyPc1tv8Kmzj0aDsgtWPq/mCNmGxzTrN06VJbtGiRWxG+bds2N3/h4MGDblhw4cKFfScF9rVK3Gs3lEulLGmkKgitNlc1g5II2pZIqGWUhkWn5I477rBXXnnF0oOe18qVK93cAyUk1E5HLaRUlaA2OtqHJB4AZEUkIgAAAAAAQKah6oXpIzfahCGrbMfGg77L408sYhf1rWq1mxQLK5C9aOYO63/tfFP3noonFLL7PmloefPHxWjrkV5UsVCmTBlflUBq/fpToqHU69atc4F/JTZUoaA2VGp7pPY6SkSokgMAEDlmRAAAAAAAgAyXkJBov03YbF8OXGmbVu33XV6+RkHr2KeqnXxeybBX0u/dcdjevm+RS0Io+XDdi7VJQmQTmunQr18/38/B5jyEYtSoUVHcMgBAIFREAAAAAACADKNWNPO/3+baJ635+79V7SUr5rcOt8fbGR3LWFzuXBHd74g7/rbZk7e4ny99tIY1v7RCVLcdAACEhooIAAAAAACQIdQ2aWy/FbZ09i7fZceVymsX3FLFzrq4nOXNF3kLJbV38pIQJ7UsaWdfUj4q2wwAAMJHIgIAAAAAAKSrlX/utjH9Vthf07b7LitYNLe1vq6StbyqouUvlDtN979t/QH77H9HhxcXK5PXrny6ZlQGJAMAgMiQiAAAAAAAAOli/dK9Nm7ASl+lguQtEGctr6xgba6vbIWKRSdMsXbRXju4L8GUe7jmuROsSIm8UblfAAAQGWZEAAAAAACAmNqyZr9NGLzKZozZaIkJRy/LnSeXNetezi64uYoVK5Mv6oOvf/xkvZWJL2D1zioR1fsGAADhIxEBAAAAAABiYteWg/bV0NX20yfr7fChxKOBiFxmjTqWsQ63xVvpKgXY8wAA5AC0ZgIAAAAAAFG1b9dh+/qtNfbtO2vtwL5/SyDMrGGrktaxd1WrWKsQexwAgByERAQAAAAAAIiKg/uO2HcfrrPJw9fY3p2HfZfXblzMOvWtatUbFmVPAwCQA5GIAAAAAAAAaXL4YIJNH7nBvhqyynZsOuS7vFqDIi4BUadJcfYwAAA5GIkIAAAAAAAQkYQjiTZz/CYb/9oq27xqv+/yCscXtI59qrpWTLk0FAIAAORoJCIAAAAAAEBYEhMT7Y+pW21s/5W2dvFe3+WlKuW3Dr3irVH7MhaXmwQEAAA4ikQEAAAAAAAI2d+/bLex/Vbasrm7fJcdVyqvte1Zxc7qVs7y5ItjbwIAgCRIRAAAAAAAgFStmL/LxvRbaQunb/ddVvC43Nbm+sp2zhUVLH+h3OxFAAAQEIkIAAAAAAAQ1Lole23cgJU2Z8oW32X5CsZZy6sqWuselaxQMUILAAAgZXxaAAAAAAAAx9iyZr8bQv3L2I2WmHD0stx5clmz7uXtgpsrW7Ey+dhrAAAgJCQiAAAAAACAz87NB23i0NX24yfr7cjhRHdZrjizxp3KWrtbq1jpygXYWwAAICwkIgAAAAAAgO3dedimvLnGpr631g7u+7cEwsxObl3KOvaKtwo1C7GXAABAREhEAAAAAACQgx3cd8Smvr/OJr+x2vbtPOK7vE6TYtapb1Wr1qBohm4fAADI+khEAAAAAACQAx0+mGDTvthgXw1ZZTs3H/JdXu2kInZh36pW+8ziGbp9AAAg+yARAQAAAABADpJwJNFmjt9kXw5aaVtWH/BdrtZLnfrE20nnlrRcuXJl6DYCAIDshUQEAAAAAAA5QGJios39ZquNG7DS1v2z13d5qcr5rcPt8daofRmLy00CAgAARB+JCAAAAAAAsrm/Z2y3Mf1W2PJ5u32XHVc6r7W7tYo17VLO8uSLy9DtAwAA2RuJCAAAAAAAsqnl83a5BMTfM3b4Lit0XB5rc0MlO+eKCpavYO4M3T4AAJAzkIgAAAAAACCbWbt4r40buMLmfr3Vd1n+gnHW8uqKdl6PSi4ZAQAAkF745AEAAAAAQDaxefV+G//aSvt17CZLTDx6WZ68uazZJeXtgpsq23Gl82X0JgIAgByIRAQAAAAAAFncjk0HbeLQVfbTpxvsyOGjGYhccWaNO5W19rdVsVKVCmT0JgIAgByMRAQAAAAAAFnU3h2HbfIbq23q++vs0P4E3+WntCllHXrFW4XjC2Xo9gEAAAiJCAAAAAAAspgDe4+45MOUN1fbvp1HfJfXPau4deoTb1VPLJqh2wcAAOCPRAQAAAAAAFnE4YMJ9tNnG2zi66ts55ZDvsurNyxqF95R1U44o1iGbh8AAEAgJCIAAAAAAMjkEo4k2q/jNrlB1FvWHPBdXvGEQtapT1VrcE4Jy5UrV4ZuIwAAQDAkIgAAAAAAyKQSExNt7jdbbVz/FbZuyT7f5aWrFLAOt1ex09uXsbg4EhAAACBzIxGBTOWrr76yvXv3uvMdOnSw/Pnzh3S71atX25EjR/uiVqxY0fLmzRv1bbvpppts0aJFdv7559s999xjefKk/vZZsmSJjRgxwp1v1aqVnXfeeZaTHDx40GbPnm2NGzcO+TZ33nmnLViwwC6//HK74oorLHfu3L7fLV++3AYNGuQuP+WUU6K+vVdeeaU1atTI2rVrZ7Vq1Qp4nc8++8w+/PBDd37IkCFWvnz5Y64zdepUGzBggDv/0EMP2emnnx71bQUAAED2t3D6dhvTf4Wt+GO377JiZfJa255V7Kyu5Sx33rgM3T4AAIBQkYhApqKgrQLXcXFxduDAf+XGqWnfvr3NmzfPnV+5cqVVqVIlqtu1bNkye+utt+zw4cNWtWrVY5IQf//9t9WuXfuY2yk58txzz7nzwQLbyf3+++926qmnWrSNGjXK5s6dayeddJK7/2rVqlks6bkrmTBy5Ejr0aOHvfTSS1aiRIkUb7N582YbOnSoS0bt37/frr76at/vEhIS7Nxzz3WvxW+//eaC/dGk4+aDDz5wpzlz5rjXO5Bdu3bZ6NGj3XldN5BDhw75rvPII49EdTsBAACQ/S2bu8vG9lthf/+yw3dZ4WJ5rM0NlazF5RUsX8H/FusAAABkBSyfQKZSrlw592+ZMmVCqjjwqArCU6FCBd/5119/3e699940b9cTTzzhkhDarldeeSVJUFqVDvXq1XOB/uSKFy/uO59aEH7mzJnuvk477TS33dH27rvvuufRtWvXgNsabUp6/Pjjj66U/M0337QGDRrYN998k+Jt+vfv75IQeu379euX5HdKTj388MPu/HfffWfffvttVLd32rRpvvOXXnpp0OsVKlQo4Plg1ylcuHDUthEAAADZ29rFe+z12/+yFy+b50tC5C8YZ217VrYnJ59mra+vTBICAABkSSQikKkULFgwyb+h8gK/BQoU8CUwBg8ebD179rQXX3zRtVKK1NixY+2dd95x5wcOHGilSpXy/a5o0aLWokULt1pfq/8VePeXL18+3/lA7aK06v+jjz6y5s2b2xlnnOELrvfu3dutyo9mdYIXaNc233jjjRZrqrpQpYhaWsmaNWtcW6sXXngh4PX1e6+d0e23324nn3zyMde56qqrfK2Q1BYpmrx9r+SRKi+C8Y4v/5ZRwa6T2vUAAAAA2bxqv7193yJ75qI5Nu/brUc/U+bNZS2vquASEB17VbWCRWloAAAAsi4+ySBT8QL34QZvvSC/fwLjlltucYmBjz/+2LUFUgLh/vvvD+t+161bZzfccIPv/i655JJjrvPoo4/aqlWr3CyITp06uYC/KiQkV67/hsZ557du3eqC3uPGjbMxY8bYjh3/lVtXqlTJtTFSoiA+Pt6iZfLkybZp0ybfHIQiRYpYelBQX62WtF+URNi2bZvdd9999s8//7hEgv/rfPPNN9vOnTtdBYHOb9iwIeB9duvWzc2J0P7T/Six4lFCSHMpVFWhNk+qLglWteBPbcC++OIL32wSHU9qkaXZI6qC0XGl5IJeQ73Wnj///DPg/S1dutR3fvHixe7+VRmilk06r9dC1T9KPgEAACDn2rHpoE0Yssqmfb7BEg4nustyxZmdeVFZa39rvJWsGNrMPAAAgMyORAQyFS9Y7x/AD4f/cGu18nnvvfds+/btNnHiRHvggQfcfIfLLrsspPv69ddf3VBkBY01bFitgtSeScFyJQ8UVFewe+PGje5+FbzWY1188cWuzVLyALjaDj344IP2xx9/uKC0p2TJknbhhRe6dkAaZq3tjjb/Vk+9evUK6TZr1651z0PJHCVy0kIzPH755RcX5NfAbyURnn76aStbtqxv1sL48ePd+T179ljdunVTvU8F9FObu6FExfHHH5/qfemx9XqKXnPRNj7++OMpVpmceOKJqd63Bl8Hcvfdd5OIAAAAyKH2bD9kU95cY1PfX2eH9if4Lj/1/FLWoVe8la+R+mIaAACArIREBNKdVqt/+umntn79+rArFILxAvtqzeRPq9j1WM2aNXPDrFXdoGqFhg0bpnh/aut02223+X5W8uC4445zq+1Ts2DBAnfb5MOOp0yZ4juvwdZt2rSxjh07WsuWLZO08lGAXXMo1J4ptfkC33//vUsYaEaGEhqqdNDqfSVkVG2gpMaKFSvsyy+/dNc/55xz3O80v0HJFCVOtmzZ4qoPdD+qANHQ5oULF7qEi+fJJ58MqbIgJUoa/PTTT+45K7HhJSFUeaBqE9G2pdSWa/fu3S4ZFOx6Og60/7wKhFApYSWVK1e21q1bJ/mdjiklmbQvlSDzKi6SzwDxp23UtooqNvRaaHt0uW6vyggAAADkPPv3HLGp7621r99aY/t2HfFdXq9ZcevUp6rF10+fymUAAID0lisxnGgdEAWPPfaYC2wrwKvWN/4zF1StoFZKNWvWdC1tQtW9e3f77LPPrE6dOvbXX38d83vdl2YWKDh8wgkn2G+//ZZie6JZs2ZZo0aNAv5OAXAF/XXStqt1j4Lqml2gQLMGQovmSqjSwQtW67lpO5s0aeIbyh2IKjB0f9q+n3/+OcVV91pV//LLL1usqdVQ9erVo3Jfap/kVX0sX77c7Q8lpbzno5kewSiJoaRKatfTYyjBogHhqQ09V9WEKjD02uk+dd+iRIxumzwBoxZOag+l3wVLKKj648wzzwxaleElVIIlMgAAAJC9HDqYYD99st4mDlttu7b89xmyxilFrVPfqnZCo2IZun0AAACxRkUE0p3mHzzzzDNuUPObb76ZpkHS/m1yJNiqfa3G16BpzV9Qa6Dnn3/ennrqqaD3d8opp9irr77qkgtKCuikpIOSD/7tnwJZsmSJTZgw4ZgWS2r5oxZFqfFmIyhYrSqMlCiYHQ1a8a/5FKoI0KlKlSq+fxVE1/lwjBo1ygXjFdQvXbp0kt95+0WzFi644AJfEiKa9BhKEIVCiSPtR13fq8yQ1PZ9WqTXjA4AAABkrIQjifbL2I02/rVVtnXtAd/llWoXcgmIE5uXiLgtLQAAQFZCIgLpTkFtzQrQoOa33347KokIteKRlFoZXXvttfbJJ5+4gLNmNaRErXTUXkkr3sNpSaSWPar4UJWCkhdeCx//ZElqFMAXPa6SAynRc9JcCQXSldjR9nqtf1QVoOoSzXjwhmqffPLJrlWQguz+/+oUrS9AGoyteRfajtdee83N5rjzzjuTtM1SRYqqG9QKSs9RVSpTp051t9GMiNQSL4Gup+IuPWcdC6qGUHVMalQ98+GHH7rzffr0IUEAAACAqNBn0zlTtti4AStt/dJ9vsvLVClgHXrH22ltS1tcHAkIAACQc5CIQIa48sorXSJC8xTmzJnjAuRp4QX8ixVLuaT5888/T3Xugmf27NnWuHFjF6BXGx5vRkAgCoAr+K8vHJp78eyzz/qSCaqq0Kp/BeV1P6oy0Ir4fPnyuYSHl6TQzAa1hHr44YfdZZpr4f0+GO23YPtO7ZSUABA9D69lVKzpsZR80JyLXbt22UMPPeQqX0aMGOFmVGgAtuZiKJGgBIhaLek6MmDAAHdKTSjXU9Iitf2npJFeO9Hr5NEMDVW+qHWS/+skXgJEr7Ves0D0vD3ecHPvNnqtdazoflT9otZUrIIDAADIHvR576/p221s/5W2cv7RmWFSrGw+a39rFWvSuazlzpu0choAACAnIBGBDKGKCCUEFIwdO3ZsisF0DVRWex+tqFdQOFDQ1gv0KngcLDjs2bp1q1s1r9ZHWpHfvHnzgNfzWvPoy4QeO7WgtoLPCjJrLoE/tYNSYkKVAjqF2irJC85Hqm/fvr5KEbWiSi9KBj3++ON2880321133WUfffSRa1d17rnnup+VEPFmPYwfP9699t5g57QMq/aSQaqWCKX6RMkGJaYCuf32291g7ZToMUKZ8aDZJGlNmAAAACDzWzpnp43pt8IW/7rTd1nh4nns/BsrW/PLylu+AnzmAwAAOReJCGQIBfa1Kl7BaJ3UNiiQ9957zwW1Q6VBwjqFKqWBw0p6+FdHJB84HGiuhKo7ks+Q+N///udmVIwbN84F5JUI2bdvny9YrsSKEg9KfGgORYMGDeymm24KOiw7FJpRoceTyy+/3Fq0aGHprUKFCq7tkQY76/moXdLw4cPt1ltvddURmtWhfSbea9CrV6+QhlWndj1VIaQW3L/33ntdkgkAAABIizWL9tjY/ivsj6nbfJflLxRnra6pZK16VLSCRfjaDQAAwCciZJjWrVu7oPLvv//uqhhSa6uU3pIPmw5VoAC4qiJ0Sg+aFaF5B6Lh2hq6nfz3SpakVzugLl262Omnn24XX3yxa1tVvXp1d7mXhJBoJwRSGzQ9dOhQV52iigbtD538DRo0yLXV0jGpJJF3LGhuyAcffOAuV1uxUNt8+T9PVUB4FTkbN26M+DgDAABAxtq0cp99OWiVzRq/ybyPs3ny5bLml1VwVRBFS+blJQIAAPgXiQhkmKZNm7p/VRnwww8/uNXuyZ1//vlWo0YNN2BarXgCBdAV1PVf8a++/23btg36uF4gWK2U1JopGP/H8e/zH4x/hYNn0qRJ9vrrr7vzGsrtPeeUtk3BagW/I6Vg/z///OO246233nLzKPr16+daYGkGhZ63guwaEK3AuhIkobYGUmWIfwIhVPHx8fbzzz/7gu5r1661ihUrHnO9aAyrVlJBVSfBhlWrKkUtokTVGdo3yTVs2DBgm7BPP/3Unb/xxhsDbn+4ateuneb7AAAAQPravvGAfTVktU37YoMlHD6agYjLbdakczlr27OKlayQtEIaAAAAJCKQgRTs1dwABXUvuOCCgNc588wz3SklavHjb/PmzW5gcjSl1uc/peTE6NGj3fkHH3ww6PUURFc7pfvuu8/q1atnH3/8cUQr5adMmeIb4qxB1UpIaP9q5X3y4d5qI6XfqSpl1KhRQSsktm3b5gLw77//vpuboAqWSJIR3vOZOnWqde7c2X755ZdjAvGxHlatRMU111zjkhhKaqnF00svvRTS9mu2hVpIacC22joBAAAgZ9m9/ZBNHrHGvv9gnR06kOC7/NQLSlnHXvFWrnqhDN0+AACAzIyKCGQYrfr/5ptv0nw/WuHu77vvvrNo00BlzbVIybx581yA35+C1oHOe1QZ8Mknn9iQIUNs8eLF7rI///zTreZ/8sknw9pGVQFce+21LqmhBI8GQS9cuND9TgH/yy67zE488US3kl+r+zW7Qu2FxowZY4MHD3bVEf4Be7Uuevvtt10ixRt6LS+//LJLSkTixx9/dJUvSgTo+anNkb9YD6vWXIlp06a589ddd52VL18+6IwQfxMnTnTzSqR3795ufkhqFTLBqjXWr19vNWvWTLV9FAAAADKH/XuO2NT31tqUN9fY/t3/fc6sf3YJ69Qn3qrUK5Kh2wcAAJAVkIhAlqdV/6JBzwoOK5CvYK+CzNHy+eefhzys2p9/iyUNxlaQfObMma4VlSogFBT35iMosN6+fXu78sorrUOHDmFtn4Lzl156qUts6HH0GGrBpFZQzz//vDVr1izJ9Zs0aeKqUJTwUAWJWjgpEbFixQp744033M+rV68+pqJBsx4qVarktjncGRNqzdSuXTuXhFBSRi2kkovGsGptmwZjB2o3peHZUrlyZZeIUXIgtfkUa9assauuusp3vWeeecad0kIJIBIRAAAAmZuqHn78dL1NHLradm/9b/HK8acWtQv7VrWap2euGXcAAACZGYkIZHleayZVLWzfvt1+++03F+TXiveM5h+sv/DCC13SRMkIj1bWt2nTxiUR9HvNc4iEAvNqy+QlJXS/77zzjgugB0sYKHFz+eWXuxZH2mfnnXeea5uk4LxHSQ1tX9euXV0SQLM6IqHEiBIfqmjQfarVU4MGDSwW9HxLly4d8HeqPtFxMmLECDeo2r/SIxDNBunWrZtL1kSTHhsAAACZ05HDifbLmI02/rWVtm39f5/dK9cubJ36xlv95iXCXpQDAACQ05GIQJbntdrRbAUF0RVU12DmaCYiVFGgAHpKNmzYkOoqeLUUUjWC7q9Vq1bu38KFCx9zXbUsUiulUOZEqFWSNxDbm2fxxRdfWLVq1VK8nZI2CrR7/Ntk6T40S0EJkrJly1paqPpDSRY9ljdAO9hMkFhTBYhad3lzR7zh14GoqkLbqQHfHlXbBKqMefrpp92pefPmrqVVIJqJ4Q1V13EAAACAzCUhIdHmTNli4wautA1L9/kuL1u1gHXoHW+nnl/a4uJIQAAAAESCRAQyjU2bNtnff/8d9lyEuXPn+lojqeXPa6+95oLBatNUrFh0yqXVTihQqx9//pUEgWggtFoTqVohJQqOqz2TBiJrPkOjRo2CXlfthR566CHfz1dccYVb7Z/SPAvtM7U10n5S+yaPWgUp+aEB1qeddppFw9ChQ121huYwKAmhWRh6bsl5Mx00QyGl2QvePIeUrufNitBzU7Il+XNJbfi5aF7HRRdd5JJH/pRACJRE8JJUShwFSzL4Xx7JIHIAAADEhlpw/jVtu43pt8JWLdjju7x4uXzW7tYq1uSispY7L5/fAAAA0oJEBDLFB3+1Ebr77rvdKvRwaHW7lwBo2bKla3mjhMG+ffvcfWqwcDTMnj07ohkR/tSKKLUkhKxbt879q3kPKSU/Xn311SRJCM14GDhwYNAyce3nYcOG2X333RcwiP/CCy/YzTffbNGg1/GOO+7wDXhWEP7dd9+17t27p5hgGDRokDulJtTraSi0NwQ8VKouueuuu3yDx3UMqX2VlyQKNAjbOwa1j4MNyvavvqCUHwAAIHNYMnunjXl1hf0z679K4cLF89gFN1W25pdVsLz5SUAAAABEA4kIZHhbJQWsNUMgEhMnTnT/qg2R14pICYmvv/7aBg8e7FbjRxr0TW2IcbhSm0fgUWspb9V8rVq1gl5PlQWqftCqfSUQUgrML1u2zLWqUuLGo/2kqou2bduGtX2p0facc845rsJFVJWiyg5dllKVRmbw8ccfW8+ePX37XwkIzYjwEhFq7ZSS77//PtUWXgAAAMh4qxfusbEDVtj877b5LitQOLe1urainXtNRStYhM90AAAA0cSnK2QIBdsfe+wxGz9+vO+y888/37XcUTA31HZJGj4saqPjuemmm1wiQm2eNPdAQ5gj4b+yPXnbpYULF7qAc6VKlaxgwYKuDdDSpUt9Q6A9JUqU8J3XKvtrr73WqlSp4uZCeNUOehwNsFaVggZvv/TSS745DWo1FYwGR+v59e3b1/r37x/0etOnT3czGryBywqmq5pC8w/8B2dr30dD7dq1LT4+3iUitH+ULDrxxBNTvM1XX31lhQoVcs9X+yYtySNVHiipotfEfwZGKDQTQ/tr+PDh9v7777sh3f6zP7R9gapUtO900jERbOC4tkvDugEAAJBxNq7YZ18OWmm/Tdhs3rqjPPlyWYvLKtj5N1W2IiXy8vIAAADEAIkIpKuVK1fa1VdfnSTZoGD9888/72YTaEZBqJSE8ALNSj54lJTQgOWNGze6OQiRJiL8KwT8A/beAGavjZEC00pUKAiuVfRq0eRRRYOC8PPnz3cBea+CIzW6n0cffTTV65UvX96t4g9m6tSpbi6FguS6zzvvvNOeeuop3wwJryVSNNsFaX+88cYb1qNHDxs3bpxLRqRGg8Y9r7zyik2ZMsWd10yJ1IZuB6JkgH9CKBzPPfecXXXVVQFncwRr0fXEE0/Y448/7oaPa58HG1YdynwKAAAARN/2DQdswuBVNn3kBkv4d71RXG6zJl3KWbueVaxE+cBzvgAAABAdJCKQrhQ49wZSK/CtYLUCv1rdHy6tWpcWLVpY3bp1fZfnzZvX3a+SG2PHjrV58+bZSSedFPb9exUEoqHH/po2bWqVK1d2syi89kMKUCshoooAj57jzz//bP369XMr7ZWIUeWDbqdKCP1eCQKtpNdqe+0HzZLQ9qc1aK3H0kwGJSE0o+Gjjz6yzp07J7mOfyIi2JDlSDRs2NC120ptwHcgmo3hJWxUHZHeVJmR0oBwAAAAZB27tx+yycNX2/cfrrdDB/6rcj69XWnrcHu8la1WMEO3DwAAIKcgEYF0pWHNt956q40ZM8ZVKzRu3Dii+1HrpRkzZrjzgQYsq8+/2g+pkkGti7799tuwH0PthTS4WNROyZ+qHFatWhXwdkowKPjvBdG1Ov/hhx+29Pbggw/6kil6HsmTEMkrPaKZiJBIkhDiVWt4SQEAAAAgXPv3HLZv31lrX7+11vbv+a/lav3mJaxTn3irUjdwO00AAADEBokIpDvNSnjooYdcJUAk1AZJ9yGlS5e2Ll26HHOdqlWrugTFwIEDXaucL774wvX7D4daAgVKcsjevXtdpYOoisGruNAMAM0Z+OOPP9yw7Pbt24f8eOvXr3cVI9GgtlTe/AwlezSbIticjbQmDgJVqqxZs8a1RtL8DFV7hNP2SW2sPB9++KFLXoXDm7mxbds2lxBS26Ro0dyLQDMgvNkPelz/mRL+tmzZErXtAAAAQGCqevjh43U2adhq273tsO/ymqcdZ536VnX/AgAAIP2RiEC6S+sq9zfffNO1WxK1Qgq2kl9VCLqugu29evVy/fvLlSsX9uNpZsGsWbNchYE3dFnzI7zZE6rwUHWHzJkzx37//Xdbt26ddejQwbVGGjp0qBUvXjzo/S9btsxtnwZPa3bGGWecYWmlRIiGI4tmRATj33JKyZVoUPVJSnMrwuE/+yMSNWvWjGoiokmTJin+Xu23opVMAgAAQOiOHE60GWM22oTXVtq29f9V/VapW9glIOo1Kx61mWgAAAAIH4kIZCnLly+3+++/351XUuG+++4Lel0NrL733nvtsccec4kBDcJWS6dwKjE0gFptjRYvXuxmLvz000++Adtaqa8V8P7JDSU7/vzzT9cO6t1337VPP/3UfvvtNzerwn8gs7+SJUvawoUL3er9Cy+80CU9QhnwnBL/1ffeav1ANM/ir7/+clULkczpSIm+6ClJpFM4X/q0H3TyZm+Ec1u9Xpp7odurcibaNMcjUOWIt83aj4EqJkSJoZReCwAAAIQvISHRZk/aYuMGrrCNy49+hpSy1QpYx15V7ZTzS1lcHAkIAACAjBZZbxwgA6iyQYF6L8j+7LPP2nHHpVxa/cADD9ipp57qzqtFU0qJi0C+/PJLl4QItDrfq8RI3jpISYp33nnHtShS0HrJkiUuQeEN6ZZBgwbZiBEjXPsgBds/++wzNxtB7ZkuueQSXzVDpNSayjNp0qQUq1Pq1KnjKge0HdHw8ssvu9dIiQAN5VbVhZ5nqCcv0SRqcxTObfVYOk7Unmnnzp02ZcoUi6bZs2enuM16nYNtm5JgAAAAiA4tQPnzh232/MVz7Y27/vYlIYqXz2dXPFXTHhl7qp3WtjRJCAAAgEyCRASyjB49evhaMl1wwQVB5x74y5s3r6tM8JIGL730kquQCPXLzaOPPurOq1rg4osvTvJ7b2V8sBX7N9xwg5tNoQSD5ljUqlXL9zu1b7rxxhvttNNOcz+fcsop1r9/f3d+2rRp9vjjj1taNGrUyA3bFu2zPn36uHZSkVL7qAEDBrjqidRUrFjRVXlkNFUvaM4HAAAAspclv++0V6+eb6/dssBW/XV05lmREnms2/3V7YmvTrOzupaz3HmoggAAAMhMaM2ETE8Jgd69e7uqAalQoYJLLoTasqd+/fpuaLVX0fDkk0+61fpPPfVUirdTYkAzH+Tuu+92g5fDpQoOraJXCyT/7VUrpuSVC9q+yZMnu+TFCy+84IZeezMpwqX2U6pM8JInSiJoeLV+btq0qR1//PFuloGek7ZLlQSqYtBp69at7l9VI2jWhLZfw6e94dF169a17HRsZab7AQAAQHCr/tptY/uvdJUQngKFc9t5PSrauddUtAKF+XoLAACQWfFJDZlK8oCuBihfd911LojutRJSoD7ceQaqPtCMh6efftr9rH8XLFhgb731VsD2TgrAazi1VKlSxW677bag962ZBClR66Pk1QUzZsxw5xs2bHhM8kPJiF27dtnNN9/sZlJEOlSvW7dublC2kjiqhlBiQS2hdIrUqlWrLD2PgVgH+EOZI+F/nWDbo1ZQqd0fyQoAAIDIbFy+z74ctNJmTdjsuyxv/jhrcXl5a3NDZStSIi+7FgAAIJMjEYFMRcOfvcCuAufnnXeezZ8/3zeLYdSoUdakSZOI7lsVEBpa/cYbb7ifR44c6e5bSQHNdfBs2rTJOnbs6OYbyODBg61w4cLH3J8uUyWBhlmL2gBpULEGFnvJAwWmlahQIkBzAlQJoUSKF5RWiyl/GlL98MMPu1kW06dPd3Mmks+mCIdu26FDB7eNo0ePds83nIC4WlqpxZMqNzRH4uSTT7b0OgZE+06trdLjsYLN5fC/PFiiwRuu7Z+UUiWJ5lVo/6nyRDNKPMnnigAAAOBY29YfsAlDVtnPIzdYwtF1HxaX26xp13LWrmcVK17uaPtVAAAAZH4kIpCpeHMM9G/ZsmXdrAMFzxXg//TTT61NmzZpun8F9nVf3jwGBen9kxCiZIVmS0jPnj3ddQLRtqllkU6PPPJI2NvSokULO//884+5vFevXq6VkpISZ5xxhqWVZjaoHZVOaru0aNEiW758uUuiKNmiQLsqTZRY8U6a8aDkg9o3RVqRESkvqO8dB5r1ECsaaB3ocf3t3r07SYVOIJs3H12d5w1Sl6VLl7qqlORUYRNJmy8AAICcYve2QzZp2Gr7/qN1dvjg0UU0+kh6ervS1v72eCtblc9SAAAAWQ2JCGQqqkbwArtaua9qBAXNX3nllaisxldQvV+/fla5cmX74IMP7Pnnnz/mOieddJLNnTvXXe+uu+4Kel+qrNCwaVUuKBmxY8cOX2Bf2+5VHmhegxIbCj4r6VGjRg1r3ry5G2YdKMiv633zzTduuLVuG01KMJx55pnulFl5QX0vsF+6dOmYH2/JkxLJE1OejRs3BryOZoAo6eCfYDj99NPd662qCFELsBNOOMHXHgwAAABJ7dt92L59Z6198/Za27/n3xIIMzvxnBLWqU9Vq1z72CplAAAAZA25EmlcjkxECQe1MJIHHnjArdSPFa10V3UEMpeLLrrIvv/+e3d+zJgxLmkTK5obMm7cOHf+1FNPDdj2S8eJN6xb1SWxrNAAAADIiQ7uP2I/frzeJg5bbXu2/9cWs+bpx9mFfava8aceO9MNAAAAWQuJCAAAAABAujtyONF+HrXBJgxeZds3/De7q0q9wi4BUfes4uneJhQAAACxQWsmAAAAAEC6SUhItN8nbrYvB660jSv+m9NVrnpB69g73k5pU4oEBAAAQDZDIgIAAAAAEHPqCvznD9tsbP+Vtnrh0TlaUqJ8Pmt/W7w1vrCs5c5DBQQAAEB2RCICAAAAABBT/8zaYWP6rbQlv+/0XVakZF674ObKdvYl5S1vvjheAQAAgGyMRAQAAAAAICZWLdjtKiD+/HGb77ICRXJb6+sqWcurKlqBwrnZ8wAAADkAiQgAAAAAQFRtWL7Pxg1YYb9P3OK7LG/+ODvnygrW+vpKVqR4XvY4AABADkIiAgAAAAAQFVvXHbAJg1fajNEbLeHI0cvi8uSys7qWs7Y9K1vxsvnZ0wAAADkQiQgAAAAAQJrs2nrIJg1bZT98tN4OH0p0l+XKZXZ6+zLW4fYqVia+IHsYAAAgByMRAQAAAACIyL7dh+2bt9baN++ssQN7E3yXn9SypHXsE2+VTijMngUAAACJCAAAAABAeA7uP2Lff7jeJg9fbXt2HPZdXuuM4+zCvlWtxsnHsUsBAADgQ0UEAAAAACAkRw4l2PSRG23CkFW2Y+NB3+XxJxZxCYg6TYpZLvVkAgAAAPyQiAAAAAAApCghIdF++2qzfTlwpW1aud93efkaBa1jn6p28nklSUAAAAAgKBIRAAAAAICAEhMTbf7322xs/xW25u+9vstLVshv7W+vYo07lbW43FRAAAAAIGUkIgAAAAAAx1g0c4eN7bfCls7e5busaKm8dsHNla1Z9/KWN18cew0AAAAhIREBAAAAAPBZuWC3S0As+Gm777KCRXNb6+sq2TlXVrQChXOztwAAABAWEhEAAAAAAFu/dK+NG7DSZk/e4tsbeQvEWcsrK7gkROHiedlLAAAAiAiJCAAAAADIwbauPWDjB6+0GaM3WmLC0cvi8uSyZheXs7a3VLFiZfJl9CYCAAAgiyMRAQAAAAA50K4tB23isNX248fr7fChRHdZrlxmjTqWsQ63xVvpKgUyehMBAACQTZCIAAAAAIAcZN+uw/b1W2vs23fW2oF9/5ZAmFnDViWtY+94q1ircIZuHwAAALIfEhEAAAAAkAMc3HfEvv9wnU0escb27Djsu7x242LWqW9Vq96waIZuHwAAALIvEhFAOpg3b57lzp3b6tevz/4Gxw0AAMls2rTJ3nrrLbv77rstLi6O/RNlRw4l2LQvNthXQ1bZjk2HfJdXbVDELuxT1eo0Lc4+BwAAQEyRiABibNWqVXbWWWfZRRddZO+99x77Gxw3AICwfPzxx9a0aVOLj49P9z03d+5cGzFihDtfo0YNu+OOO6L+GJMmTbLu3bvbzp07rVChQnb77bdH/TFyqoSERJs1fpN9OWiVbV6133d5heMLWsc+VV0rplwaCgEAAADEGIkIBPTbb7+5fwsUKMAq/jTq3bu37d69O0OCB8i6OG4AADJgwADr06ePFS9e3N544w3r0qXLMTvm5Zdftvfff999blMFZqDAcmJioiUkJNjBgwfd5xJVa+bLly/Vnbx161YbNGiQO9+pU6eYJCKaNGninp8SEQ888IB7HD43pY1e7z+mbrWxA1ba2kV7fZeXqpTf2t8eb2d0KGNxuUlAAAAAIP2QiMgAjz/+uD3xxBPu/KhRo9xK+czm/PPPty1btliLFi3su+++y+jNybLGjRtno0ePtkqVKtn999+f0ZuDLILjBkjZV6+vstUL99hZF5ezuk2Ls5o3BA8++KAtX77cjhw5Yps3b3bB6OQB6rx589r3338f8eF33nnn2T///GMlS5a0/PnzBw2IR5u2X6dDhw7Zrl273PObOHGinXbaaZbV6XWZPXu2O799+3br2rWrPfLII+5zpP++PXDggM2ZMyfk+9Xr45+EUNXD22+/7c7Xq1fPbrzxRt/vypQpE/B8NB133HEuydK6dWuXJHnsscdcmyZEZtGvO2xMvxW2bM6u//Zxqbx2wS1V3N/NvPlofQUAAID0RyIiA1SoUCHFL3Q7duywtWvXWpEiRaxo0aJWuHBhFxyI9AusvpzqPjds2GANGzYM6XYVK1Z0iQj9G4h+V6tWLfdcVEKvL7OR9PNV4EBBEX3pXLdunU2bNs1q165t2cHevXutV69evtWMei0BjhsgbRKOJNqXA1daYqLZ7MlbrPrJRa39bVVISKRCwWwF51NStmzZNL02+jywYsUKd8popUuXtuxAn60UkNfCkFtuucV9pnvqqafc58Thw4f7khGqhPDceeedQSsdvv76a5s1a5b7bJm86qFfv37u/HXXXZckEVGwYEHf+eS3iyYlstq1a2cTJkxw1R1KRlSrVi1mj5cdrZi/y8b2X2l/Tdvuu6zgcbmt9XWVreWVFSx/odwZun0AAADI2UhEZAD/gLS+tCc3c+ZMtyIsFl/KNQgwnG30/2Kb3LZt29wJgWm1ooIx+lIdqI1CsMSMKlC0IlWzJVavXu2CCUpYnXLKKdamTZuYJGquvvpql7TS8ahghBJNhw8fDvt+lFRSAsZr46DWCsi+x00w2oapU6faL7/84v7m6HjS6tsSJUrYiSee6FpwNG/enGGkiIhaiXR/uIaNfnm5Hdib4Fb8DrpxAQmJKChVqlSabq/3uKdZs2au1U560mIG73OJqjKiTf9P6jPaggUL3OKOjRs3un+VLNDfW53UTkhJg8qVK0f1sa+99lqrWbOmq6LV31RVDyhBMHDgQPf7PHn++0j/5JNPBk0Y7N+/3yUiVK3iz39hTLly5ZL8zj+pkdrCmLFjx7r9ocU0um64VTH63KBEhD6DPPzww74FHaG+PrqdkjWqHjn11FPdTIucYN2SvS5Bq+SsJ1/BOGt5ZUVrfV0lK1SMr3wAAADIeHwqzQAKyPleAL8vjp70/uIeiLddwaoc9KX05ptvdhUR+iKsL5tprYhQ8FVfXLOD+fPn2yuvvOL2jddXObUvz/3793eVE2qdEYjXoqBVq1b2zDPPWOPGjaO2vT/++GPQx42UWmQgex83ySm4pdZz48ePT/W6Ctbdfffddtttt5GQQNhaXFbBTmtb2r55e6199/5aEhIh0Pvt1ltvdQF6nbyFENdcc42vHVNaExH+n2+0uj69WyOdffbZ9tNPP6W6kCIcCmyrxeKXX37pAuShLug44YQTrG3btta3b9+orepXcmfy5Ml2zjnnuBZU+n9C/1+88MILxyQWUpP8M5v//kq+7/yTD6klFfR/gNdKKq0++OADd4qUXq/snojYsma/jX9tlf0ydqMlJhy9LHeeXNase3m74ObKVqxM6jNAAAAAgPRCIiID+CcfAgXv/b8Aqvy+ZcuWET+WApUK9OsLazjVC952BfvCqYqJ119/PeLtys6UXFH7BAUv9PpVr149xetrNeWVV17p2iWE4ptvvnGr3zWYUsMrkT1k9eNGATEF3PT3JvnfEq3M1d8gfytXrnQDuT/99FMX4CtWrFjUtwnZW5Hiee3CvlWt1bUVSUiEQMnIQPzb7qS1hWAog4/TS6QtLf3pb9M999xjCxcuDPu2ixYtcqfXXnvN/a2OVpshrfIfM2aMS3Jo5X+wFpqpSf75zv+1S/7ZNJyKhsz0tzwzLOyJlZ2bD9rEYavtp0/W2+FDie4yvUxndCpj7W+Lt9KVo5OIAwAAAKKJREQm5P8FsG7dunbWWWdl6PYgPGqXoPYQGvZ41113pXhdBWe1stE/yKEgg26nlY9qj6D5HlrtrsHmWt2uALSCvQr6qg3SAw88kOaXSL2gjz/+eKtfv76rStFK2XBWVyqIrlW1Wn0oSp4pSILsfdx4lNzQamuPkigK3qkllM7rb9qePXts2bJlNn36dHvuuefcedHqZR0rqsoJd0UvICQkose/oiESgao8M0Ja/5bob2ePHj1c8tafKjz0mezkk092bag6d+7sa32pYc/r16+3P//80yUwdNLfWiWXNQRaVRXvvfeedejQwdJK/8d++OGHropOf9Ojvc/SMmBcQ6e9BNeUKVMsvY0bN86ef/75qCWjMpu9Ow/b12+tsanvrrUD+/4tgTCzhueVtI69qlrFWse2fAUAAAAyi8zxjRFJpOULYEa46qqrbM6cOW7Vs4IQ4Wy/rqu+xF988YVlB5s3b7b77rvPnR8yZEiqX4IV6PCCydp3Dz30kOuJ7B/M0fBQnc444wy799573f72Wt/o+gpcX3jhhWna7gcffDBNt1frBC8Job7Yn3/+ecD5J8hex42XSPC2XXSfn3zyyTEBTf190HwInTQIVUkTtZSSn3/+2VVUUOGDtCAhkfGJiMzy+SUt26GEgpKj69at891X+/bt3d85JXo9/kH2WrVqucoEnZQU1t9bJSGUdFVQ/ODBg25mgeYfqEVeNBLBmiEU6hyhjFhMo8RGRiyk8U/QZ5bjMRoO7jti332wziaPWOOSEZ46TYpZpz5VrdpJaatmAgAAANIDiYhMKD2/OGklu1Ysqy+0AhD6AqnH/+OPP3wry9RzWddTmycNOVRAUauXPbpcq/IilZ3692pVuAY1K1CsYbwpUUsa/wTMiBEjXFVBSrQCU4MgtdJcrXb0utx+++12wQUXpDmAFCm12FGff49WfsZiSGh2lpWPG1U+eO2YNEj1448/TvU+lTDRLIx58+b5Vhyr1RuJCEQDCYmsX9GQUb799ltX5bBz5073s6rLlFj3T0B4/vnnH995/e1LTsl4DY2+9NJLXdWhqsH0t1eJ/0qVKtnVV18ds+fRunXroFUhS5cujdnjIvoOH0ywaV9ssK+GrLKdm/+bvVWtQRG78I6qVvvM7Nt+CgAAANlPzv7GmQ7Uv1eBdg119gL9W7Zs8f1eq+b0ZVWl+xqAqMC/fyLCWxn94osvujJ8JQFCTVQoQaDH37hxo/3111/utsnpvvSFW4OiA1E7F538JR8+6fWXVu/jl156yUKlIbtKaATarqxIwz7feecdl9TR4MjUeK0D5Iorrkg1mOzRMaQKhNq1a7v2O6tXr3bBaP9kQHrxWjJpO0TBlmB9yJH9jhslLGfMmOH7Wat8Qx0QqyBZr169fIkIrWJdu3ZtxP3OgeRISIQvO60gD5cWVKht0r59+3yfddROSVV+gSxZsiRJRUQwqj7T3zlVWSgRLDfddJNrvdmoUSOLBVWZZZTkc4IyUmbalnAlHEm0meM3uUHUm1ft911eoWYh69Qn3k46t2SOfr8CAAAgayIRkQ4UXNMpkNmzZx8T2PXnJSKULFD7o1hQIkGDrNUyQG1cvH716uGuL+JeD+QffvjBJk+efMwwSm8FpYYCdu3aNeTH1Rd8JSKyQw9ftV3o2bOnO69gsvpFp+S3336z33//3RcgfvTRR8N6PK3SvPbaa10yR0aOHJkhiYjhw4f7AslqAxRKIB3Z57hp0KCBW107c+ZMmzVrlnXr1i2s259++ulJfl6zZg2JCEQdCYnMRQsr9BlDswT0/3/ywciB6LPRoUOHbPfu3XbKKafY+++/H9VtUvLhkksu8SUhlDRQ5Zn/IO+UWgCdcMIJKd6/nqfur2nTprZgwQK3SEQVYKqSSI3+zutv/9ChQ4MmRZJT+6dglWkadO1f1Rptem6Zhf6Pzao+/d9S++Gj9b6fS1XObx1uj7dG7ctYXG4SEAAAAMiaSETEmL5gqwWKKiK0UlirgLWKWF/CRT2Hy5cv774sqTWLWqjoX48X9FdCQNfVl2LdRyiroLQSTF8I1ec4pcGN3u/atWtnN998szv/9ddfu0SEvvCrn7yXcFAiInnQIK0rskIJQmR2qgRR1Yn6Iau9Tmq++uor3/mGDRumGsQIRCvhvYCyhhyrbVaoq9GjQck1zR7wKJCuZBRy1nGj1m46de/ePezbJn9c5ooglkhIZA563//9998R314zGGLRHk8JAlFVloZKp5SEECVgg1WKBlKsWDE3wLpOnTruM5+qFjRbSZ+9glGru6eeesqd13ydwYMH2+WXX57qYynJEazaVNVwsUxEaOZR8soRfZbUftU2KUGS1mHiXnJK1cTal1pMo/tO3iY0+bZkJVvXHk3oHFc6r7XtWcXO6lrO8uTL+p+XAQAAkLORiIgxrYIbOHDgMavRvESEWjPVr18/ye/Vosn/9nLRRRe5UyyEmwhInnhIXsWR02hF+NNPP+0SNepzH0piZtKkSb7zLVq0iOhxTz75ZNfOR62+lHBSUDk92yIp0OG1ZFL/7Fj2u86OcupxEyyQp791VatWtczgr+nbbcLgVXZwf9Zt64HUlapcwHZtPWS7tx6yxASzZXN22aAbF1iRknns/s8bWsny6ZfYzUn8A/yquNS8hNQo4Ky/kxLthLsWXQwbNsz3eUhJCP2NTG02ktpeihaQBJoREYiStpoZ8e6777qfX3755RQTES1btnT7aNSoUe7/W7XjU3unIUOGHFOdmlno/ykthPH/P23Xrl1pSj6FwnsNlKhRiy0v+ZNV9XjhBFv+x26rcXJRy18o7YkbAAAAIDMgEZEJ+fe0TY+2RWmtaEhrD96s3MNXVPGidg6qWNGKxdQocePfkivSgLJeNyUAlNgSBSfSK6CsNl0a4Cla2fjaa6/RqzhMOfG4Sc4LLHqtUIoUKWKZwXcfrLUlvx8dVoucZ/fWw/bTxxusU9/MkRjLzgOxldAO5W+Zkqbe34torKb399xzz7lEh6hV3bnnnpvqbX799Vffea+lZaj0nL1EhCoT1G4q2N8+tdNTC723337bbdvevXvtzTffdMkTXZ4ZqxCTtxjU63X88ce7ymA9T1VE6BgI9tlTFRTe/3VKxARLCun/RFVD6LR9+3ZfKyolulKrZskKChbNY3WbZr7XFwAAAEgLEhGZkH9P28y64s2f+jaLWsxo+GKovLkZWbmH72effeba5Wgld6j9+letWmV79uzx/aygcKQ0BNMLKKvlV3rQl/8777zT97NmDpx00knp8tjZRU48bpJTixG1KREFpcKddxFLbW+pYvkK5LYD+7J2khQpO7D3iG1asd+2b0j6f1C56gWtVQ+GpmfWxQ/RHNCrqgYF+T29e/cO6Xa//PJLxIkItZZSqyIF2/X56dtvv3UzulKi/2c1U0cr/VesWGFTp051Lf3U2imzVJIFU61aNfvnn39Cvr5mYdxyyy3u/LPPPmuNGze2nGj39kO2esEeO/604yxvfloyAQAAIHsgEZEJqWd7LCoidL8KZKbWciBcGqTtrVj0H94YKq+9T1aj5923b193Xu23Qu1v79+eQCv4UhtQnJJatWqley/kTz/91A3O9Lb/scceS5fHzS5y6nHj39Lk+eefd4kIrxWKZlaE0mM9vVRrUNSuf7l2Rm8GYmTjin02cehqW/DjNkvwyzWd0qaU68VeuXbg3vrIfiZOnOhbDHHOOeeE3GJpypQpaUoKa9GGt+r/999/TzURIaqcmzFjhmvlpNtqpsVbb71ljz/+eNiPj8xvWO+F9s+snVayYn678I6qdlrb0hYXx5BqAAAAZG0kIjIhBfQ9alng38Yg0hXsXhLiyiuvdP2Po0kr17RaT4MCta2hDNNOSEhwKwG1XVk1EfHII4+4qg71b+7YsWPIt/MP/KY1KVS5cuWAs0ViRceSNzjTay9UpUqVmD9udpITjhsNu1frEW2nenTrfa6Vx3PmzLG5c+e697/UqFHDBgwYYO3bt4/6NgDBEhC/jttIAgK+RITn+uuvD2mvrF+/3ubNm+ebV9G8efOw96b+9nk2bNgQ8u3Kly/vKijOO+8899gPP/xwwOu1bt06aAsrzSdC5leyQn7f0Oq37llk37671rreU81qnp51514AAAAAJCIyEbVeUVDXvyJCfW8zuzZt2lhOoxWMmoug5ItWc0dSQRKNgHLRokXTNRHxxRdf2J9//unOKwii+QYIXU45btQ6JFjCU8lKrejV0NUuXbpkifZzyNpIQCClpKlHwf1QhzErKe9VUUQyPFtDqyNJRIjmQmi7NS8i2EKVn3/+2TKjV1991VWgqJ3VmWeemS1mOcTKVc/UshqnFLUvB62y3VsP2Yo/dtsrV8+3hueVtIvurGblqrHvAAAAkPWQiMgE1q1b51ZJq9ReLW80wNajPvJe0PDFF190fd3j4+Ptww8/9F3nsssuc0kM9e1XYM+fvizrpOqDbdu2udXJ0aIvk2qrktaKDY++VIfapiYjaTX3zTff7IZsP/nkk2FXBGgwpadEiRJp2hb/AZcKVOt1juWA8xdeeMF3XoHkMmXKxOyxspucfNz401BYzYbQ3zqt7NWKXv1NA6KNBARS+5vqJWKVTNBg6FBoLoPn/PPPj2gn+39u8uZshZuMSGlQ9TPPPOMb3pycPkdqSHZGGDt2rH333XfuvFpLhTNXLKfJnSeXNb+0gjXqUMamvLHGvnl7rR06kGBzv95qf3y3zZpfUt7a3VrFipRIn/+7AQAAgGggEZHB9GVRXwoVhD/55JOPqYI499xzfSuG33//ffevgvUaUug/+FCJCJXh+18ea59//rlr9aTV3frCG+kASQVm9fyVcEmPVf1pNWTIEJs1a5Yb0BzqYEt//skWBWXTwn94sfZ/sFYM0TB9+nSbOXOm7+dInntOlpOOmyZNmtibb77pAmVKfirZob9ROinhqtW8SsAOHz7ctXC699577YknnojqEFrkXCQgEAr/SgQNfA7l78+uXbtcItUTaVs5LQzxlCxZ0qKtT58+7rNZIKtXr86wRIRa9HnJ9Dp16mTINmQ1BYvksU59qlqz7uVt3IAV9uvYTZZwONG++2CdzRiz0S64ubK1vLIiA60BAACQJZCIyAD+LVY++ugj96++kHmrzb0vqKo2CKVtScOGDV0y46+//gpaudCzZ08X/NR1o0VfJFVtoVWF/qu1I6VAQKxnb2gFdtu2bSO+DwVPH3roIReweP311yOqBvGvIlBQIy385wZolbuOmVjp16+f77x6YiugnhNw3ISvXr167hTMH3/84Sq81L5J+1dzRzQrJtx2VYA/EhAIh2Y9hPv5QwswtHBC1F6oVq1aEe30hQsX+s7nlMpCfRb9559/3PnGjRuHlPhR8rp06dJBf6/PoLpftTRVYqlChQq+RT3ZcWbENc+eYC2vqmgjX1xui37ZYft3H7HRL6+wHz5az0BrAAAAZAkkItKJvixpFfCgQYOSrKbTF1AFtm+99VZfaxQvEZFS2b0/VUR4/eeT05cztWtSiyeVxH///fcpBgjD4V/2r+cUaHuHDRvmVjzrS+fLL78c8H6860TSZzlUSpRceOGFblW/hkxGGjy44447XMBULXa06jsS/kGHtM4A2bJli+/8cccdZ7GiYMDIkSN9P6sSJifguImNBg0auPe8eoTfdttt7jINrdZ7VFVgQDhIQCAS/oFwb+ZDavR3y3P11VdHvON/+eWXYz7DZXf67KWkgYT6+eniiy8O6zEef/zxbJuI8MTXK2J93qxv83/YZqNeXG7rl+5LMtC6yz3VrBYDrQEAAJBJkYiIMZXAazifgrjLly8/5veTJ08+5kuTt8o91IG0zZo1c1+o165da4sXL/YF2VV5cdFFF9nUqVN9X/zC7UufEv9qAAUUA23vxIkTfdUTwdpGedeJ1qyJQMF6VUF4bYWURFBlRLj0Wn3yySdWtmxZe/bZZyPeHv9ExJo1a1yyKNIkjH9FRPny5S1WVLmjFlqihFnXrl0tu+O4iT0lYNVvffz48e7n//3vfyQiEDISEFlTqEH/WN3e4794Qp/VQgmkazGH9//gJZdcEtHjzp0717Wo82ihRrh0+3HjxrmFLF5rvXD3S/LrR2u/BjNt2jTfeQ35RuT0mb9Bi5JW76wSNv2LDfbloJW2a8vRgdavaqB1q5J20V0MtAYAAEDmQyIixrR6/pVXXvH9rKGsp59+um91eaABsStXrnT/hjo4UQkAtcnRl1t9MdXQap3v1q2brwxePdgVPI9m655o95WPRVshBRfatGmTpG2VEjPqX3/dddeFfD9KFihoKqrsSMuw4EqVKrkvkfrSrwHGeo1OPPHEiO5rzpw5SVaZx4rXQky0P2PR0zoz4bhJPzfeeKMvEaEgnxKosazuQfYwbuAKmzRstSUczY86p7QpZW17VrHKtQP3xkfm4D+cuVevXm6OTGr0f2W0ZuR4tDDD+79YVX+pUQs5L1ivz1cptQwKtc2h/t8+/vjjw74PLYp4/vnnXaWtFnNohpD/PgpF8uv7vy6xSEp4nyO0rVq8EoqhQ4da/fr1U3wO2m61+FPrzBNOOMFy2kDrsy8pb406lHYDrb/WQOv9CTb3m632x/fb7Ozu5a39bQy0BgAAQOZBIiLG1AZJX1arV69ud911l/vyqjZG/m1uklu2bJn7N5wvVOedd55LPuh+Vfr+2GOPuX81rFBB9+7duwe9baxXwWUUVYe0bt3aVqxY4apB1M/Z60F/9913uyGToSZ7tFJ7yZIl1rJlyzS3JVLQxUsceS21Ik1E/PDDD77zsZrZ8PfffydJeHTs2NGyM46b9OXflkQBRlWO5ZT5I4hMwpFE+2rIfyvYSUBkLXv27EkyLyYtt0+LokWLus9Z+j9Obfh++uknV2EayPz58+2LL77w/XzfffdF9JiaY+Cf2L/mmmsiup/PPvvM/asEigL7yRM0+uwTbLHI0qVL3b9elaPHa5uU/L6i9f+q146qadOmIc0/E801i6RiJKcpUDiPdeztDbReab+M2egGWn//4Tr7ZSwDrQEAAJB5kIiIMa2201yCUGcS6IuhtzIvnESEEg1aqa/Sd6/8XYF3DYNN7X5S+8KpwKAqAPQFOqtQ4Pz888+3jRs3uhX8StCo+mTKlCm2YMECN4ejT58+9vHHH6d6XwpSaOWhvjgPHjw4KtvXqlUrXyLim2++iajXtBIsOnli9WU9edJMSa/siuMm/SWvfvCfewIEEpc7l13xVE1b8/cea9q1HBUQWYw+T2hRhpLy+n9V1ZApDS7WYgl9TtHK9127dlm1atWiti36/0z/x8s777wTMBGhz2Wq3PIWbXTu3NkFyCPRt29ft3rfq2a94YYbwr4Pfab0kgmXX3657/J9+/b5zv/888+p3o//9UX7NtD5aNBnUY8SEvo7H2r7UYSuRPn8dvX/alnLKyu4gdZ/+w+0/vDfgdbtSltcXOqDwgEAAIBYIBGRDsIZjPznn3/6yuPDSUQo6VCjRg335VSzFh5++GHXOziUuQveKrhglRFqI+BVEnirCJNTdUGgNlNeoHzGjBl29tlnB7x//2B6NPz4449u1b7aYmnQ4fvvv+9bfTdixAgXaFA5v1obXHXVVW7bU9KzZ0+3jx555BGrU6dOVLZRA3m9ll2TJk1yr3mg/ZcSJTA8FSpUCLnVQbj852lUrVo1ojYSgV5ztSlLKfiU3jhuIlvlqnZKqup57bXXIno9NdvGX6TtTpCznNU1tGo2ZD6qAoi0EiDaVOGov13ywQcfuP/vkw+Pfvrpp91nGNH/01qYEAlVqvovfnj00UdDakuVnKpcPZdddpnvvP5vvummm1wlrD77BaqIUFJl7969Lgmhf/VZyGuLqdZGnvXr11s0ad/6JznU5sq/RRWiq0q9Itb7zfr2pwZav7Tc1i3ZZ1vXHbC37l1k37y71rrey0BrAAAAZAwSEZnMr7/+6jsfbq9bfYG+55573BfQa6+9NuThz/oymlJlRM2aNX3nNVTZm5Xgzyu5D2b79u2u7UF6UNsG9ZnXF/IhQ4YkmT2hFk3qSe0lVrTPVCFRpEiRoKv4NFNCX/AffPDBqG1j8+bNXXJECQ5VmqjNgv/KxlAMHDjQd17Do2MxY0Pb5z9gMhrVEF7AXxUr7777ruXPn98yA46b8Gj1sP7OeJT0U+uycHnD6kWBMyW7ACA9KIGvhQFKuCs436lTJ5fkr127tvv/74knnnCtGf2TB+EsLvEPxD/55JO+n1u0aGG33XZb2PejBRaffvqpO695Y/5tHS+99FJ3Ev8Egz8tOAmWML7gggvcZzUJ9fNjqC0kvQoOb8HMoEGDXFVMsFZYSDu9zie2KGl1zyphP4/cYOMGHh1ovXL+0YHWJ51b0jrfzUBrAAAApK/oRy6RJl45vVYF161bN6zbKvCu1XUarBxq/2J90fb6LSt4H4gCjArGa0Wghvh26NDhmOuoukABxeQnb7XeaaedFvD3/teJFn2Znjx5shtyGOiL+DPPPONr7aA2WKocCUTtmzRLQrRiUkmYaFFVif+wbFWw6PFC9dZbb/nmNmiFZu/evS0WlGDyb9+ggE1aKyGUgPCCKepjrfOZAcdNeC666KIkCTyt9g23r7iOB70fPeeccw6DqgGkKy1M8OYsrFmzxgX3NaemZMmSSZIQSrTef//9Yd23Zk/o/2f/9osVK1Z0lRHBZjikRIsrvLZJ+swXyG+//eaqN/UY/pWuK1eudIsJ9PkhEH2W0GdInVRVES1K5ni0TVo4ocoMJX1UBYzYD7TW7IgnJp5qbW+pbHkLHP1cPO/brfZUp9n2ydNLbdfW/waVAwAAADGViHQ3evRofTN0p/nz5/suP3LkSGLZsmXd5VdcccUxt7vlllvc7+rUqRP0vp966inffY8fPz7VbTl06FDiTz/95E7Lly/3XX7OOee4+7jhhhuC3la38R5r8+bNAa/z8MMPu99fcMEFQe/Hu87pp5+emF4mT57s2/a4uLjEGTNmHHOdm266yf3+kksuick2rFq1KrFw4cK+7TjvvPMSd+3alertpk6dmligQAHf7Xr37p0YK08//bTvcXRauHBhmu+zf//+Se7zjDPOSNy+fXtiVsBxk9RDDz2U5LXs0qVL4sGDB0PalzrW9Z73v/2YMWNi8roBCK5169a+9+Dll1+epl3Vt29f333NmjUr3Xd7s2bN3GPnyZMnrNuNHDkyMV++fEn+HiX/f2rbtm1h3eeECRMS4+Pjk9yPfl68eHFiJPbt25dYrlw5dz9FihQJ+nnh4osv9n228X+sVq1aucsLFSqU+Oeff4b12OvXr/c9h7vvvjvk202aNMl3Oz2+bNiwIbFUqVLuskqVKiXOmTMnyW1ef/11320CfTZD2mxdtz/xnQcWJd5a76fEnnWPnu5o9HPipOGrEg/uP8LuBQAAQExREZGJqHWRhitL27ZtI7oPtWbyWilp/kFq8xdUfn/WWWe5U05qiaKV+F5bGbUw0CBKbzaHV5kyfPhwtzr71Vdfjck2VK5c2bV+8tokfP31167VgtpCBJrXoVWQWlmpQdeqepGTTz7Z9VoORjMxdCx5pwkTJoS1jTNnzvSdL1iwYEQtKZLTc3j99dd9z1vtyFQloZWjmR3HTVJqU6KVw/6DzU855RTXcsv//eRPx656g6vd2axZs3yXq02HVsgCSF/e8GT/mVE5jQZQ6zNY48aNk1yuyoA77rjDvvvuOytevHiq96NWi/rMoGHW7dq1c1UI/rO81JrQv91lOFTJoPuXm2++OWBLSVVKfvHFF+682jT5P5aqRFWNqXacl1xyie9zRKzocfxbeWrOlpQtW9Z9NlEFhipQtM+1z4LNKUNsBlrf/3lDq33m0RklbqD1KyvsiXa/26/jNlpCAq8FAAAAYoMZEZmIvpiJArRt2rQJ+/Zqi6J++8OGDXPl91u3bnXtUxTYVosBJKVh0V999ZX7Yv/HH3/Yiy++6OZAaD/ecsst7kux2sZoEHQsgx/qlazgvFoV/P333+61q169uvtyrhYOmzdvdu0L/vrrL988D1EgV62tlCwJRvfn34Nfx0M4/APFahUWrTkUCqLoWL3++utdIkgtoNSia/To0RG1q0hPHDf/0ZwTHV9q16aB1aJjVYNo1dZMx4yOZbWaUxu0JUuW2KJFi3ytRTxKRGmoPICMTUT4n89pGjVq5FpQ6v/NxYsXu8UCDRo0SPH/JC32UPBfCXXNQtDtk7eo0/919957r0vcRjp7QZ8P9BlF1CbSaxvpT/+X6rOL/tU2q+WjP31mUGsnDeieP3++azMVy4HRWhijv/lei0/NxfD/LKIWmkpAb9myxe6880732VX7KScfg+mpSt0i1vuN+rbgx+028sVlvoHWb9+32L59d611ube6ndAo/GHqAAAAQEpIRGQSWhWm3rneqrkyZcqEfFt9EdYKc62004o+9THWUER9CdUXZK2g12r7UqVKRXWbo716Lb1Xw5UoUcLNftAXYVFlgb4sjx071ubNm+fmWgQazB1tegxVGigor2CtLFu2zJ2CUTWHVhCGskIzUgoO6LiMdHh6avQctCJSlTt67b/88ksXjPAGiWdWHDdJKVGnAJyCWqoi8oJImzZtcif9LhitNlb/8L59+2b6BBSQXSnZ7f93P1r/jyvBH+7cmLQKNusqHBpUrVOoiekBAwYETdQqKatKgCpVqqRpm1TN4H0mUAVn+fLlj7mO/pYqqS9a3BBoztgVV1xhU6ZMsXfeecdtt6rQ0jr7KRAlFQYPHuz7O+8lUfxpJpASOBdeeKFLjCxcuNDNzvJP1qxdu9YdQ+EmcHQcav6Zjgftq2gtoshutPCpfvMSVqdpcTfQ+suBK22nBlr/ucf6XTPfTmqpgdZVrVz1ozNUAAAAgLQiEZFJPP/8875WJj179kz1C7baJyhw++abb7pV/VoBd+aZZ/p+r5X9SkJ8/vnn7t+zzz7btU3RAMNoJQW0Qs/Tvn17F1ROzmsNpVWC2oZAvOv431960dDELl26uH2jNgVaKagV3frSGmzYdaxa/mgFpl7Pzz77zKZNm3ZMiwy1M9D2KnDfpEmTmG/T3Llzk/wcjbZMgYIi//zzjz3++OPuZwVGlIjT5ZkZx01SCjQNHDjQJSN0DH/77bfuPR+o9YeSZ1p5rBWxep01GBVAxtD/9atXr/b97CXDI6XPIp4ePXqk6b6itR2x9Oyzz9pHH33kkq4etVhUol1VftGoRlWiyGtrpOSGqgaSe/vtt90CFKlWrVqSAdHJKdk/adIkW79+vaugUMJIVRuiqkudT54Y9n9+qSUF9Nn0tttu8/2shESw1p81atSw2bNnu889L730kqus809e6fOZPoepqk7/d+j/Gm2f99lMn5t1ff2r0759+9xnZZ10DKh1YPLPMgg+0Pr09qVtyptr7Ou31tqh/Qk2b+pWm//DVjv7kvLW7tZ4K1ry2M/5AAAAQDhyaVBEWLdA2PRlyD+g/cYbb9gNN9zgzntBb5X/68tUuXLlXE9hfdn0p4Be/fr1benSpVaoUCHXr99/5aKqHRTMvf32232XKZCt1W76winqDazH1qr/1KiEXiuZtUrfaxmVnKosFECPFj0/rYpLb/oyrpWD27dv913Wq1evoKsc04Ne73Xr1rkAhPpAa9V5JNUPy5cvT1LVoNYMgVZSBqJ5JUqO+AcMYtGmSn+CdEx6fa0VaFBLqFCTZhmF4yZl+numv1E6qRWTjmNVk+gY8uaDAMj4zyeaieTR55G0JLpV4af2P5nluaXH35r//e9/7v9KLbZQm7lKlSpF7b4VXNd9Tp061dfWUBWw/lTZqQoIPV99Npw+fbqbH5WSDz/80JfwV8soL3ExZswYVyWqv9P6e63Pm7pftdTzPiOpnaR/osHf+PHjXfLAW0hx9dVXu+qLUCmJraSKnoPX1iktXn75ZVdpifBs33DAxg1YaTNGbzTvW2KBwrnt/JsqW8urKli+AlQwAgAAIDIkItKBVv4qsKp2S6oaUPLB6/WvIJ0CsPpyqYCsVhX7JxM8mlWQvN+vvmA3b97crTrU4EH1DU5Oj6OydyUNRF/I9MUsNQpEaEWz2groS2GwL5zqDS9ayRZocGIoPvjgA9dWSr3klWjJCBoCqZYAoi/gahGQ0uwFRJdWLypw4rWe8A+MZGYcNwDwH30e8T4zaBFDeieUVVGqFf6i1jwKpGdlanV3+eWXu6pNVQJofoV/dYEWjHizF1TFoBafXrvJUD/n6X5VmaqFMKoo0GefYC219Du1rgxW4aCEiD7HyllnneU+ewb6bBrqYgglybSNSoSoTdO2bdvc51olaJQg8a98URJN+0Cfs72TZg+pzSYis3rhHjc/YuHPO3yXlSifzzr1rWqNOpSxuDgWFQAAACA8JCLSgXrjBiql10Bqr1pBQ3oVfP3tt98CtjhSYLxevXouWaHV+1rJppNK8FOjlWlqOaT2C2r5E8oKQT2WhiNrmLK+AAeiL3hqEyRauR/pDAoFDrTCTxUb0ejvHCkNidZg708++cS6d++eYduRUyngoMTaTTfd5FZcZpVV8xw3AHCUqjDHjRvnzmsBRnoHgVWVoFlZouB6fHx8ln9pFGxXgF+VsppJEWgegz5HqS2eFo+ESvtJi0l0O1Ux+A+ZVoWHkhIK+CtRoYpMzYnSZ76aNWumeL+at6WKC33ejEZrKmQsfe9Y8JMGWi+3df8cXUQl8fULW5d7qtsJZ9BeEQAAAKEjEZEO1B5HX8rUnkRJAQXcNQhRfeb9WzCpHU9KK8cUnNUcCPUfjuSL7IYNG0JuraPqhN27d9spp5xikydPDngdVTF8+umn7vxzzz3nWupE4t133/W1HdAKyowaWqvV+HfddVfQxAtiT6s7lYzISjhuAOAoBcK1Yt6rdtSihvSuyNBcLG+xhFo+ZhcpfUZUFYhafIZLsx9UrRttqvaNdHEKMqcjhxPt51Eb7MsBRwdaezTQ+qK7qlr5Glm7+ggAAADpg0QE4EcDszMqEYKsi+MGAABkd/v3HLGv31xjU95a4wZaS1xuc8Ou299axYqWSjrjDgAAAPBHIgIAAAAAEPpA64ErbcaopAOt29xY2c69moHWAAAACIxEBAAAAAAg/IHWLy23hdO3+y5joDUAAACCIREBAAAAAIjaQOsq9Qpb13sZaA0AAID/kIgAAAAAAKRpoPWM0RtsnAZab/5voHWDliWs813VGGgNAAAAEhEAAAAAgCgNtH5rjTsd3MdAawAAAPyHiggAAAAAQNRs33jAvhy40n4eyUBrAAAAHEUiAgAAAAAQdav/3mOjXlpuf01joDUAAEBORyICAAAAABAzC37a5gZar12cdKB1l3uqWe3GxdnzAAAAOQCJCAAAAABATCUcSbSfR2+0cf1XJBlofeI5RwdaVzi+EK8AAABANkYiAgAAAACQbgOtv3l7jU15M+lA67O6lbcOt1exoqXy8UoAAABkQyQiAAAAAACZY6D1DZXs3KsrWr6CuXlFAAAAshESEQAAAACADBtoPfrl5bbgp/8GWhcvn8869alqZ3QsY3FxuXhlAAAAsgESEQAAAACAjB9o/dJyW7vIb6B13X8HWp/JQGsAAICsjkQEAAAAACBTDLSeoYHWA1bYjk0MtAYAAMhOSEQAAAAAALLEQOv2t1Wx40oz0BoAACCrIREBAAAAAMh0dmw66AZaTx+5wRKP5iMsf6E4a3NDZWt1DQOtAQAAshISEQAAAACATGvNoj026iUGWgMAAGRlJCIAAAAAAJnegmnbXEJizd//DbSuXKewdb2XgdYAAACZHYkIAAAAAECWGWj9y5iNNrZ/soHWLUpY57uqWYWahTJ0+wAAABAYiQgAAAAAQJZyYO+/A63fWGMH/h1onStOA63LWYfb4xloDQAAkMmQiAAAAAAAZN2B1oNW2vQvGGgNAACQmZGIAAAAAABkaWsXa6D1Cvvzx22+y4qXy2ed+lS1MzqVsbi4XBm6fQAAADkdiQgAAAAAQLbw1/TtNvLFZccMtO5yTzWr06R4hm4bAABATkYiAgAAAACQ/QZaD1hpOzYe9F1ev/nRgdYVazHQGgAAIL2RiAAAAAAAZM+B1u+stSkjVicdaN21nLW/Pd6KlcmX0ZsIAACQY5CIAAAAAABk64HW4wettGkMtAYAAMgwJCIAAAAAANne2sV7bdTLy+3PH/4baF2srAZax1vjTmUtLjcDrQEAAGKFRAQAAAAAIMdY6AZaL7fVf+/xXVa59r8DrZsy0BoAACAWSEQAAAAAAHLeQOuxG21s/2QDrc8uYZ3vZqA1AABAtJGIAAAAAADkSAf3HR1oPXk4A60BAABiiUQEAAAAACBHcwOtX1tp0z7fYIkJRy/LXzDOWt9Q2VpdU9HyF8qd0ZsIAACQpZGIAAAAAAAgpYHWveOt8YUMtAYAAIgUiQgAAAAAAPww0BoAACC6SEQAAAAAABBgoPWv4zbZ2P4rbPuG5AOtq1rFWoXZZwAAACEiEQEAAAAAQGoDrUestgN7jw6QyBVn1rRrOetwe7wVK5OPfQcAAJAKEhEAAAAAAEQ60Pr6Stbq2koMtAYAAEgBiQgAAAAAAEK07p+jA63nf89AawAAgFCRiAAAAAAAIEwLf95uI19cbqsX7vFdVql2IetyT3Wr27Q4+xMAAMAPiQgAAAAAACKQkPDvQOt+SQda12tW3LrcU42B1gAAAP8iEQEAAAAAQBoHWn/77lqbNDzZQOsu5axDLwZaAwAAkIgAAAAAACAKdm7WQOtVNu3z9ZZw5L+B1uddV8nO68FAawAAkHORiAAAAAAAINoDrV9ZbvO/8xtoXSavdexd1c68qKzF5c7F/gYAADkKiQgAAAAAAGLg7xlHB1qv+uu/gdYVT9BA62pW76wS7HMAAJBjkIgAAAAAACCGA61nfrnJxmig9fqkA607313NKp1QmH0PAACyPRIRAAAAAABk0EDrJp3LupZNxcrk4zUAAADZFokIAAAAAADSc6D14FU27bP/BlrnKxhnrRloDQAAsjESEQAAAAAApLN1S/ba6FeW2x9Tkw607tC7qjVhoDUAAMhmSEQAAAAAAJDZBlrfXc3qNWOgNQAAyB5IRAAAAAAAkIEYaA0AALI7EhEAAAAAAGQCB/droPU6mzx8te3fcyTJQOsOveKteNn8Gb2JAAAAESERAQAAAABAJrJry0H78rVjB1qf16OSOxUonDujNxEAACAsJCIAAAAAAMgiA62PK53XOvaOtyady1lc7lwZun0AAAChIhEBAAAAAEAm9vcv/w60XuA30LpWIet8dzWrfzYDrQEAQOZHIgIAAAAAgCwy0HpsvxW2bf1B3+V1zyruEhKVaxfO0O0DAABICYkIAAAAAACy0EDrqe+ts0nD/AZa5zI7s3NZ17KJgdYAACAzIhEBAAAAAEAWHGg9Ycgq+/GTZAOtr61k513HQGsAAJC5kIgAAAAAACCLWr90r41+eYXNm7o1yUDrDr3irWkXBloDAIDMgUQEAAAAAABZ3KJfd9jIF5fZyj+PHWhdr1lxy6X+TQAAABmERAQAAAAAANlkoPWs8ZtszKtJB1rXaVrcumigdR0GWgMAgIxBIgIAAAAAgJww0Pqifwdal8uf0ZsIAAByGBIRAAAAAABkQ7u2HrIJg1cy0BoAAGQ4EhEAAAAAAGRjG5bttVEaaP2t30DrUnmtQ+94a9K5nOXOw/wIAAAQWyQiAAAAAADIARbN3GEjX0g60LpCzUJufkS9sxloDQAAYodEBAAAAAAAOWyg9dh+K23rugO+y+s0KWad765mVeoWydDtAwAA2ROJCAAAAAAAcuBA6+/eX2cTNdB6938DrRtfWNY69WGgNQAAiC4SEQAAAAAA5OiB1qvsx0/WWcLRfITlLRBn511b0VpfX8kKFM6T0ZsIAACyARIRAAAAAADkcEEHWveKtyZdGGgNAADShkQEAAAAAAD4b6D1i8tt5fzdvj1S4fiCbn5E/eYlLJf6NwEAAISJRAQAAAAAAEgy0Pq3CZttzKsrkgy0rn1mMetyDwOtAQBA+EhEAAAAAACAYxw6kGBT319rE4ceO9C6Y+94K1E+P3sNAACEhEQEAAAAAABIcaD1V0NW2Q+frLeEw4nuMgZaAwCAcJCIAAAAAAAAqdqwfJ+Nfnm5zf3mv4HWRTXQ+vZ4a9qVgdYAACA4EhEAAAAAACBki2cdHWi94g8GWgMAgNCQiAAAAAAAAOEPtP7q34HWaxloDQAAUkYiAgAAAAAARDzQ+jsNtB622vbtYqA1AAAIjEQEAAAAAABIk93bDtmEwckGWuePs1bXVrQ2N1SyAoXzsIcBAMjBSEQAAAAAAIDoDbR+ZbnN/TrpQOv2t1Wxs7qVt9x5crGnAQDIgUhEAAAAAACAqPpn1g77ItlA6/I1Clrnu6vZiS1KWK5cJCQAAMhJSEQAAAAAAICYDLT+feJmG/1KsoHWjYtZl3uqWZV6RdjrAADkECQiAAAAAABAug+0PqNTGevYu6qVrJCfvQ8AQDZHIgIAAAAAAKTPQOshq+yHj5MOtD73mqMDrQsWie5A64QjibZz80ErXo5EBwAAGY1EBAAAAAAASDcbNdD61RU2Z8qWmA60fvfBxTZj9EbrcHsVa3drfFTuEwAARIZEBAAAAAAAyBQDrcvVKGhdojTQemjvv2zu11tdG6g73m1gNU87LgpbDQAAIkEiAgAAAAAAZKqB1if8O9A6Pg0Drdf9s9ee7TbHDh9MtNJVCtiDI0+2AoVzR2nLAQBAOEhEAAAAAACAjB9o/cE6mzh0lW+gtWigdac+kQ+0/ubtNfbFC8vd+bMvKW+XPXZ81LYZAACEjkQEAAAAAADIFHZvP2QTBgcYaH11RWtzY/gDrVVx0b/HfFs8c6f7+fZh9axesxIx2XYAABAciQgAAAAAAJDpB1oXKXl0oHWzbuUsd964kO9r8+r99sxFs+3A3gQrVjafPTLmFCtULLyEBjK/uXPnWpUqVaxkyZIZvSkAgABIRAAAAAAAgEzpn9922sgXltnyZAOtO99VzRqcE/pA62mfr7cPHl3izjdqX9p6vFg7ZtucU6xZs8aOO+44K1q0aEZvih06dMgaNGhgW7ZssRdeeMF69OiR0ZsEAEiGRAQAAAAAAMi0EhMT7beJm23MKytsy5r/BlrXOuM463pPdYuvXySk+xhy6182//tt7ucbXq1tp55fOqbbnd21bdvWJk2aZFWrVrXrr7/eHn744QzblldeecXuuusud75Tp042ZswY3+9efPFF+/jjj61IkSKWN2/ekJNXyY+fw4cP2549e6x9+/b2+OOPR3X7ASAnIBEBAAAAAAAyvUMHE+z7D9bZVxpovdNvoHXHfwdaV0x5oPWOTQft6U6zbc+Ow1a4eB57eMwpVqxMPsvMVqxYYffcc48VK1bMduzYYdu3b3dBcdG/CQkJFhcXZ5deeqndcMMN6bZdely1QNI2yY8//mjNmjWzjPDnn39a48aNXZKgUqVKrkVTqVKlfL9/+umn7ZFHHona4z300EPuPjMDJUd0HCjBktNt3rzZvv/+e/vll19s06ZN7me9N3ScVqtWzc4880x3jBYuXDhqjzlz5kz3mKtXr7ZVq1a590XZsmXt+OOPt9atW9vJJ58cUeJL9Lp+++239tVXX9nKlStt//79Vr58eWvevLlLtqkaKa3HTrdu3ezqq6+2Ll26pOm+gFDRFBEAAAAAAGR6efPF2Xk9KtmZncvaxNdX2fcfrrcjhxPt13GbbPbkLakOtFbS4dJHj7c37vrb9mw/bB889o/1fK1uxIHC9LB792777LPPUr1emzZtLD399NNPviTESSedlGFJiJ07d7ogqpIQCjq///77SZIQUqBAAd95VTIUL1487MdRYPuZZ55x51VZkVYTJkywChUqWIkSJSxPnjwu6HzkyBEXHD5w4IDt27fPnfbu3Wu7du1yJz1X7fOtW7fatm3bbN26dS7p0rlzZ3v99dctp/rtt9/sySeftHHjxvmSdMEoeH/llVfao48+auXKlYvo8ZRs0P4eMmSIzZ8/P+j17rvvPpeQeOyxx+zyyy+33Llzh5VcU3sxJTqSGz58uJUuXdr69etnV1xxhUXqjjvucJVDY8eOdceRWpsBsUYiAgAAAAAAZBlFiue1bvfXsOaXVbAxr65wSYhDBxJs0vDVNu2LDSkOtD6tbWmb+80WmzVhs83/bpv9PHKjNe0aWUAyM1FgMj0pGOrp3bt32LdX0D2cwGwgCtorqLxo0SL3s6oezjnnnGOu5/84qhpR1US4lixZ4ktEKHGQVjfddJObsRENQ4cOtZYtW9oll1xiOYmSDkosKQkRKiVzBg8e7Fp1vf3229axY8ewHnPDhg3umPv6669DPm5UcfDuu+/ap59+6hJPqVFyQ8ex5p14VNWh2+r+RNUe2g49n549e1q43nzzTRs0aJA7r5ZqJCGQXkhEAAAAAACALKds1YJ2Y786tuT3nfaFBlrP2227tx6yT55aat+9v84631XVGrQseUzFwyUP17DFM3fYjk2H7PPnllntM4tZqUr/rZrPTLRqXgFTBSK9YKQC6wq+qz2LJ3kVQCxpJb6Cql4CRKu9UwoWK6C6dOlSW7hwoS1YsMBVU+TLl8+1nUnLcOrLLrvMrYIXtcEJ1n4p2hUv0bg/rcyPJBGhqg+t5Ndr4FFiZO3atZbT3HjjjfbGG2/4ftYxpWSMjoUTTjjBvVcUsF+2bJk79pQ8UyJBVFXStWtXVxGgWSeh0D5u1KhRkn2t953aoqldkt6rqmZRGyW1a1Ilk6paRImLpk2b2rRp09z7OKXk2lVXXeVLQpx66qkuiVGvXj133On5PPHEE74kgqoalLSoW7duyPttxowZduutt7rzSsTo/oD0wowIAAAAAACQpSng/fvELTb61eW2ZXXqA63nf7/VBvf8y3edPm+eaHFxmbdFU6DWLSeeeKLv52+++cbOPffcNN3nl19+6QKclStXdgFWBcsLFSrkWhsp2K0EiALhkydPto8++sjdRi2ZFMz0WgdphoWCvGplpGD5+vXr7eDBg8c8lgLFf//9d0Tbqfvr3r27byC1grDTp08P2nKpf//+1rdvX3devfwjrYioWbOmO//SSy/5BmNHSkkUBZUVlNbMAu1n76SfixYt6jtpPoiC6kr66KTB4GpB5QXflRS68MILLSdRVcNtt93m+1kB+y+++MLNgghGSYEBAwbYAw884GvhpJkLSlJoH6eW+GrRooX9/PPPvstuvvlme+GFF4LOatB7Qdfxknai96gGvAerqlHyQse21/JMiYtArcDuvPNOe/XVV915VVy88847Fgq9J0877TT3b506ddw8jbTOmgDCQUUEAAAAAADI0rRaWG2XTmpVMslA68W/7rTnLp57zEDrE1uUtGYXl7OfPtvgrqMKCs2YyKry5095UHcotApbQdJwqLpBp3BosLIC7pHQanOtQPcCwtWrV3fDfEOd+3D66adH1FpJK9WjyUvkhNvO6pprrrEPPvjA/awE0ciRI0Ne0Z9dKMmlAe4eHQNTp05NNaBesGBBN7dBCbP//e9/7jIlykaMGJFqYknti/yTEKq+Sa0llI7JTz75xCVHlLAQVQG9/PLLbjsC8RJMcu+99wadR6JkipIxqsBQ8kLVHkpKpZbA0zwVJSGUeFEijyQE0huJCAAAAAAAkO0HWv8+abNLNpx/Y2UrWDSPdbm3mv3183ZXQaFZE/WaFbfyNSILkGeHRIQC3ZFSENR/Fb+CsBUrVnTVFd5JlQj6V5dHMh9CbZiuvfZaV3EhqggZP368xcfHJ1n1roBzMAo8Z0Vaka/BxN7gciVyNGS4VatWltMMGzbMDfH2qDIgnID6U0895ZI5K1ascD+PGjUqxUSEEnReKyTp0KFDWO2MlPRQ5YHaNcmLL77oWiPpfZKcWpeJns/FF18c9D7LlCnjWrN57Z/0XGrVqpXidugx1ZZJVU0ffvihq0oC0huJCAAAAAAAkO0HWh8+mGiTR6yx6W6gdbyriLjmf7Xs1Wvmu2HX7zyw2O7+4CTLnSfrtGjyRGOAstoFde7c2bWt0UprraDWSdUAOqn9klbfa0W52gepbYwSCwqoprYaO620TVpd7iUhNOy5X79+SZIOqoy45ZZbXOukYEFcVSIoiBsuzXNQNUJGUNC9W7du7vmJVskrAaO5BDmRElpa2T9r1iyXoAl34LQC8Y0bN/YlIhYvXpzi9VV54CU+lEDTcRfOnBDdRu3BTj75ZF9iQ8eyBqf7S0hIcBU/XpVHau8p/8SDZrCklIhQIsWbp6Gh6+3atQt5+4FoIhEBAAAAAACy90Dr2Ttt5AvLbdncXbZ722H75OmlNvX9tdb5rmp27jUV7Zu319qKP3bbpOGrrV3PKpbVRGOAsoL6KVUTaDCukhBy9913W8OGDS09n997773ntu/88893gfnkQdzHH3/cBXLVY/+HH36ws88+2/3OmwcguizSGREZQYkXBdo1A8NbKT9x4kRr0qSJ5VSqitFJlCBQYiFc9evX9533julg1P7Kvxri+OOPD/vx9F7Ra+a1d9JMl+SJCM0v8eapKMGXGv/raCB3MKrE0HtX9N64//77w95+IFrCf7cCAAAAAABkIcefcpzd/WEDu/7l2laq8tE2RhuX77ehvRbasnm7fJdNGLLKVv65O4O3NvOZN2+erz2NBvwqEZHelIxQL/zkSQjRivNff/3VndeAYC8JkTwREQ1paWEVDgWm9Ty8JIQqOTRjICcnIZKLdNaIKgg8ahWWUiuvuXPn+n4+77zzLFL+A8X1OiY/LjW83BNsNoQ//9ZOmpsRiBJzqg5SRZOSIW+99VaEWw9EBxURAAAAAAAgRw20/uHDdTbh9aMDrZf+vuvf35slHE60d+5fZPd/frLlzc/aTc9tt93mG9g8YMCAkAKl6Zkkeeihh9z5GjVquGHAwQZNa9C1hjyHy38mgdoBxdrChQutTZs2tmrVKvezBh5Pnjw51TkA0dK7d2/766+/fD/ffvvtSQLpWZ3/4Okzzjgj6PWSJwxatGgR8WO2bNnSd37jxo32xx9/2EknneS7TAOkPRoonZq1a9cGvK1HsyMuuugil6QoVaqUjR49OuLEDRAtJCIAAAAAAECWsGrBbhvWZ6Ht3nbI8hfMbfkK5bZ8BeMsf6Hclr9gnOUr+O+/fj8nuaxQnLtd5bqF7YZXatsvYzfZrPGbLOGIVs4ffYx1S/bZqJeWW/eHamT0080U3n77bfvpp5/ceQWj/ecvqCXStm3b0mVORCCaW6HtUdBVLXq0rZpf4W/Pnj2+897zSOtjxtKPP/7oAsjePIwGDRq4dkwprdyPtpkzZ7rBxh5tT3ahmQ+LFi3y/ZzS7I8///zTd75kyZJuQHqkTjvtNPce8dovKcnhn4goW7asS5Yq8aFqmNR4SSrvtsldf/31Nnv2bDc/5tNPP3XJLCCjkYgAAAAAAABZwtI5u2zLmgPu/IG9CWZbYrM6/bsP1lnN04vaqeeHP9g4O1Frl759+7rzVapUsREjRrjV+hp8qz73qkZQqyIN5I2Pj3dBXbVtSp4MSMnvv/9up556akTbp6HVXlBZffD9WzJ5TjnlFDc/onjx4i4QnDdv3rBmaigwrKoKBZC3b99uderUsVjREGPtQw0LFz2fsWPHum1H2mnAun9bsU6dOtkFF1wQ9Pr+VSGqnEjLLBa9R1Sxo/dPoLkOSubVrl3b/X758uWufZSuH8zUqVOTbJu/F154wQ1mF1UInXvuuRFvNxBNJCIAAAAAAECW0KRzWUtISLQtq/fbgX0JdnDvEZeQOLDviB3c99+/7vJ/z0c6ImDWhM05OhGhaoerrrrKduzY4doZvfrqq3brrbfaZ599dsx1lYxQYFUBfwVANa9Bg5WDUT98rdJ+55133Op7BXwVhA3HkCFD7OOPP3bnVS3w9NNPB7yeqjiyQluhF1980e677z5fKyANZB46dGiGVJpkN3///bc7Xl577TVfq66mTZumOjNh8eLFvvPlypVL83accMIJvkREoLkOrVq1cr/Xe2/gwIHuPRfI119/7avWUKWDf8Ji0qRJ9sADD/iOIbXZAjILEhEAAAAAACBLUJullleG3qJGQd1DBxKOJin2Jk1W6F93mX8iY+8RW/P3Hjt8KMEufThnt2ZSYPyHH35wgfDLL7/cevTo4WtLVLlyZevataurDqhUqZJLQvTr18/9q6CvBkZ7K7L9kxVqMaTg77hx43wtauSVV15xQfdwqihUAeHfmiaS2Q+ZgQLjvXr1stdff939rBZTzz33nN1zzz1JrqNqDCWFVC2hCokSJUpYwYIFY7JNev06dOjg+7lx48aW2Wn/KbGlod7aNzq+1N5KVTsaOu1Rtc6dd95pDz74YKrHjNqO+bdmSisNevcESkRoFotaR+nvlhInzZo1c+8zf6qU6Nmzp+9n/0TDP//84+agKJGhKgnvmAIyCxIRAAAAAAAgW1IrlXwFcrtTkRJ5M3pzsozvv//eHnnkEV/wVMkDBUfPPPNMd/n555/vWs34U0uhunXrukG7n3/+uQ0aNMgNyVWbGbVyevPNN5MM2PVogO6aNWtc8FRB+NRoJXjbtm197YuSU8Jj7ty5Llmiqgz1yE9LSx1/GlSteRQKUG/YsMGaNGmSpvtToLx79+6uzZUX7H733XfdPAEFotVKaM6cOW6VvJ5XcloJ36hRI2vXrp1169YtasOItZI+q9myZUuSuRbJab7DddddZ1deeaVLVoRi586dvvM6ltNK7ZdSSkTo/dOnTx+X1NPxrWPj6quvtubNm7vkyi+//OLeRxp2LZoxccstt7jzShKq8kcJK71nR44cafnz53e/03tLrZy++uor125t//797jpq/aX2VIGGXQOxQCICAAAAAAAAvlXVXbp0cUF3UeBSgVut0ldVRLCgvoKZmieh9kJawf/QQw/ZihUrbPLkyS4Q6k9VFBqA3LlzZxdk1dyGUMyfP9/1u1cQV9tRpEiRY4ZHK8iqQH6sqSVO8j7/4VByoWPHjm5/i4LCWv3+/PPPuwRE8n0WiFbH66TZEqqquPfee10lBe2cAh87mg/x4Ycf2o033uiGOSdPpiW3e/fuqFZE6Hj1b08WrBJJA9Y1j0XHgAaw65ScKh70uqsqRklCJSwWLFjgXvsvvvjCvcfkjz/+cO/b33777Zj7GD58uEuwaI5ESkO7gWghEQEAAAAAAAC3mlotebRS36P2MJoL4d9WJhgNhvYkb7Wk1eBKcGjuRMuWLUOqfvCndk7ezAp56qmn3Hap+iGrUYsqtdDxnosC1KoW8QaDS4UKFVxLJK2SV+WD2jGprZCSMEoOKcmjQd1KWqhaQqv3H374YRec1pwA3T4n0TGluQqqHNBJQXztEyVqZs+e7faJAvyzZs1yJ81fUKWOZkUEoyD/3r173flAFSnh0uN7giVBVMEzbNgwV7lx//33u21Xck30ntGxoHZMauPkvYeeeOIJGz16tDuvORjec9J7Q/sleYsp7Z8lS5b4KklUAaN9pWQWEEskIgAAAAAAAHI4BSTV8kgzHjwKTGq1dGoVC2q/9MILLwQc/quV2zfddJMLvCuQHgkFmNWyxhvkrPtSxYVmAiSnFeGaOaEB1grwa9tTW/kezKOPPmrTp093swSUCFEwWpUiSiB4AepwadtUueAf2NbKe500zFhVIqoWURIilJZSaoWl++zfv7/bNq2Ab9Gihdvu0qVLW06h4HtKSQW9Xgrwa6C6Xj9VpLRp08YlKM4666yAt1ElkBI+krzyJtL3mCe1dkiqFNJrqONESQMlCurVq3dM+y0lIJ588kl3XsPkb7jhBndex4ISd14SQlVCavul+/AqMpTAUAs1UbWIhmV7vwdigUQEAAAAAABADqbV+K1bt3atXTwvvfSS3XXXXSneTkFOzYxQixf/4dNy/PHHuxYxDRs2TPP2qSpD/e61Mlw97b0ERKA5EUo8+A+yTgsvSKtV6uedd16a7kuBcLUEUmsgf1rVroCxkhORBIFV+aB2PmrrpFkRek0WL17sBjIr8IyjFMBXxYnmmyjgrgSOKhRUeaDjPtDgb/9EhFe9Eq1EhOaXhEJJNCWoAtF2qyWTEnRKXGi2hEdzWpSUEr0Hv/vuuyStoZSkUoJPx7Zup/fvs88+a++9914aniGQsvDq4AAAAAAAAJCtzJs3zwWvPYMHD041CTFq1CgXOFcrGC8JoeSDWghJ2bJlo5KE8Fo+KYis1d5KbngzEKLRLic9qEWOKhySJyFU+aBgsWYApHUlugaJf/TRR76fFVDWYG8kpVZXGvjsX82jRFogOob9r5dW/i3P0jpzQm3UNJxalRpVqlRxbcr8K5fef/9933klufyTEP4eeOAB31BrJS+CDYEHooFEBAAAAAAAQA52wQUX2AcffOBWX6uaoGfPnkGvq6SDBttq3sP69evdZZUrV3bBXbW7UVBUvL720aI2MgoYawW3J1Ai4ueff3ar2LWCXUFVXSfSkzcwWivO9bOGcGsVvdraKIGQWnBat/nf//7n2lNpWLJHP8+YMcOXzIkWrfZXZYvn448/jtp9Z7fj/aSTTvL9rORWaokIzeNIK28wudSvXz/i+9FxqfZkuj9Vcqg9k/+2yl9//eWrvOjWrVvQ+9LtNDTde89GI+ECBENrJgAAAAAAgBzu4osvdjMcUmpBpFXYWsX//fffu5+VuLjnnnvcLAWvtY03x0FB+2jyqiBSo/ZE2s5oUvLBPwHiee655+y+++5L8baaLeHftuqWW25x8xxCfT7hUoJoypQp7vzMmTNj8hjZgdozqRJIfv3114DXOf300121imh2io7pQMdBKHR7L3EnDRo0sEhpiLVmW4iSc6eeemqS32s7V61a5c5Xr1491WPNv/XTsmXLrHbt2hFvG5ASKiIAAAAAAADggvjBgpYaftuhQwdfEqJGjRr2008/ub7y/v31dT2JdEB0dqJ9oHkWmk+ggdca5j1kyJAUA8OaI6D5BV41RrjUHsuzZs2aiO4jJ9Awc48qAQIlr5Ss8J/xkZbEjve+8fhXZIRD7bc0E8QbMH3FFVcccx0lIbxEYKVKlVK9T//rKBEBxAoVEQAAAAAAAEiRKh+mTZvmW82tVfflypU75nre6n+v73x6UyskzakoWrSoC/j7J0RUrZErV66Q70uVHtOnT3dJhC+//NLdXokWtXxSe6ZQVrVrtfmwYcNcCybNughEbZqeeuoptzJf9yvq99+oUSO7/PLLrUePHi6ZEQoFzD2xqrrIaHoNlDjQMOm0VLn4C5Q4q1OnjgvSewmdr7/+2po0aZLmRER8fHxErZlmz55t119/vTvfpk0bV5ETyKZNm8Iaiu1/He/4A2KBRAQAAAAAAACC0swFDaUWBfnHjh0bMAnhXxGRUUHwYPMtBgwY4GYBqFVSKMFZGTRokPtX7Xj8V8eHK9CqdU+fPn3ctgXaj0qC6PTqq6+6GRzNmzdP9bG8dkNStWpVyy40b0OVAN99952rxGnWrJlNnDgx4vvzH+StlmRKXAVy7rnnusHfon8ffvjhsJJZXtLDf1s1syHc+1ByQW3R9u3b56peNP8jWNVRsWLFfOdVXZOatWvXBrwtEG20ZgIAAAAAAEBQ6kPvtXrp3bu3VatWLeh1d+/e7f4NN9AaSy+99JIL+P/www9uJfmuXbssMxg4cKAvCVGiRAnX+/+TTz5x7XcefPBB3yDrJUuWuCHU3lyAlOg5epLPDsjKFHTXUGbtAwX2VZ3gP/w5HBs2bLCvvvoqyfDwYDp16uQ7v3jxYpfICteIESNs69atvp8vu+yysG6v955muKxcudKKFCliY8aMccdLMP6Dq71ZESlZvXp1wNsC0UYiAgAAAAAAAEH98ccfvvMK5AejuQY7d+5057VyO7O49dZbrWXLlu78L7/84oLLmguQ0TS0WlShoe3SvI3u3bvbpZdeas8884zNmTPHtZqKi4tzLa86d+5sCxYsCHp/CtQrQC+6zTXXXGPZiX+1iyokbr755rBfR91OiQAvYSYK8qc0/Ltu3bq+n/WYoVQZeBYuXGiPPPKI72dVNWgIdjj69u3rWjspuffuu++m2tZJSYpatWq588uXL7elS5emeP1vv/3Wd17twIBYIREBAAAAAACQhSQfZBzpYONQbdy40Xc+pdkPmqGgeQe///67ffDBB5ZZaL6CZjx4K9/V3ufaa69125tRtE9V6SBKkniBY3+aE/HAAw+46ggvuXPTTTcF3G7d1+233+77WcH2KlWqWHaiFlf+czYUQFdgP9QKF1VS3HbbbTZ16lTfZRq6rmMhGCV01BLKq/BZv369tW/f3rUrS40SSUp6edundmXPP/+8heONN97wtUVTQkPJqFCogsb726DKm2CUuPLaVKmVl/+wcyDaSEQAAAAAAABkIRqWHGhAdKxUrlw54NDdQO1ztKJaweJAgfXMkIxQ4FnUAkkDojOKkgwetdxJyeOPP+5bRa+B4RMmTEjy+88//9y1YfKGKiug7M23iISC2FpV753Umisz0KyO999/38108KhVk56vZjeo5VIg27Ztc9Uneu2HDh3qu1yJAbVNKliwYIqPq8TDk08+mWRotI5x3ad/yyX/JJPabOm9oHZOokTG22+/7YaXh0pJPVXziBIaOg5CpaSUlzwZMmSIO0YCJa9uueUW38+9evUK+f6BSJCIAAAAAAAAyEKSt6NJnpiItrZt2/rOK3g/a9asNN+nWuQoqREokBsrZcqUsc8++8xX1fHEE08kmRWQnhTg92ZAKLCtljspJXj82xIpeK7kk56LWmWptZDXEqtixYpumLiGikdKbYu2b9/uO8U60RUO7TNVtPgPS1eiQa2sypcv7y5v3Lixq5TQv6VLl7aSJUu69kb+lT1KPmh4udeyKzVKdNxzzz1JHlP3WaFCBTv55JNdskKDrfX4OqnywZurooSAkhbhzIZQ+ye1hdK+V2soJWDCmbui22iei/f34ZJLLnGVH2+99ZZr4aVESdOmTX1VOSeddFLQQe9AtJCIAAAAAAAAyEK2bNmS5OdYB/M1s8CrJNixY4c1adLEbrjhBtcax7/XfiCHDh1yK9U120Ar+RUw7tq1qxuKe84559j8+fMtPalyQLMYvLY1oQyAjpVHH33Ud17zHK6++mqbOHGi22fJKdmgqg5RZYcSDponMWXKlCTPTbMmFFTOzlQd8uuvv9rll1/uWif5U7JBv9NAZ/2b/L3iVXxo7kmHDh3CetwXXnjBPvzwwyRJECUK5s6d645ttXzyT3ZIzZo1XcItnGoDJemUhFAyQgklPZeiRYtauNRSSu9T71h/55137LrrrnPtnZQo8bZVLcv0GN7xBcRKnpjdMwAAAAAAAKIueSufVatWxXQvK0Cp1eOqjFCPfK30Vu96nRQIVmBWK8N1PbUc0up8BYB1Sq1/f1q23ZuNEe6shz59+rjno2oC/2RAct6K9ljRKvVFixbZY4895p7De++9505qGaT9qRX+WrmvZI9e87179/q2yz/AruupdZCCzKqeyAni4+PdHBLNTdA+UxJg5syZAV8ztXQ68cQTXeJL+6hBgwYRP66qGi688EIbNmyYjRo1yn7++edjEkd6DyjZoQRet27dUm39lJxeQ7VMUpLuo48+irjNmbZDbbWUsLnvvvts3rx5vuopvW+VXFTVhOZmJE/oALGQKzEjJ/MAAAAAAAAgLEuXLrVly5b5flZAsXr16jHfi0pCqJ2RAr8a/JtWChC/8sorEfemL1WqlKsGUWBZQdZwaPCzAsRqU6OqCAV7q1Wr5u6zSJEitnnzZleFoESKAv1anR4rP/zwg0tGaOV8qGE6tZdq166dC4xrZX+4we6UKKDvtXqS2rVrJ5kTklkpyK5V/jom1FJKiTG1wKpUqVJU948/JYdWr15tmzZtcgkkVaooMadjO630PNRWKlr+396dwF061o8fvwehrBUlDbLE2MlaNJYmZkJZIzEkMsm+NYxKlDEhQ4x1smVKyEyhCMlOGlLCzMjYZjSUfctyfq/P9fpf538/57nPOfdZ7vOc55nP+/U6r+FZznPOfe7t+n6/1/dipsWMGTPCPk2LK2dAqNNMREiSJEmSJCk3ApkEzQmgU9FPUoSe+QT3aVWz4IILhgWF44PAPoFsFhUm2B8fyyyzTEsBWwKp/E0C5Y8++mhTz/Hwww+Havlahg0b1qMFUlFIdtx8883hNT355JNhJgTV9rTlWWyxxUJQnd7/LJRMIJnAtyT1FyYiJEmSJEmS1K9QiU6SAyxITEV6s+2dSGhUW/CbhAmLP7fSzkeS5BoRkiRJkiRJ6mdoWzNkyJDy/7M2QDOzK+iNz6wOno8ZCDwPyQn667OgNrMtJEmtc0aEJEmSJEmSJEkqjEuiS5IkSZIkSZKkwpiIkCRJkiRJkiRJhTERIUmSJEmSJEmSCmMiQpIkSZIkSZIkFcZEhCRJkiRJkiRJKoyJCEmSJEmSJEmSVBgTEZIkSZIkSZIkqTAmIiRJkiRJkiRJUmFMREiSJEmSJEmSpMKYiJAkSZIkSZIkSYUxESFJkiRJkiRJkgpjIkKSJEmSJEmSJBXGRIQkSZIkSZIkSSqMiQhJkiRJkiRJklQYExGSJEmSJEmSJKkwJiIkSZIkSZIkSVJhTERIkiRJkiRJkqTCmIiQJEmSJEmSJEmFMREhSZIkSZIkSZIKYyJCkiRJkiRJkiQVxkSEJEmSJEmSJEkqjIkISZIkSZIkSZJUGBMRkiRJkiRJkiSpMCYiJEmSJEmSJElSYUxESJIkSZIkSZKkwpiIkCRJkiRJkiRJhTERIUmSJEmSJEmSCmMiQpIkSZIkSZIkFcZEhCRJkiRJkiRJKoyJCEmSJEmSJEmSVBgTEZIkSZIkSZIkqTAmIiRJkiRJkiRJUmFMREiSJEmSJEmSpMKYiJAkSZIkSZIkSYUxESFJkiRJkiRJkgpjIkKSJEmSJEmSJBXGRIQkSZIkSZIkSSqMiQhJkiRJkiRJklQYExGSJEmSJEmSJKkwJiIkSZIkSZIkSVJhTERIkiRJkiRJkqTCmIiQJEmSJEmSJEmFMREhSZIkSZIkSZIKYyJCkiRJkiRJkiQVxkSEJEmSJEmSJEkqjIkISVLHPPTQQ8mvf/3ruX6L//GPf0yefPLJhrbDP/7xj+SZZ55J3n///bl++ykb+0epVKq7eX77298mRx55ZPLPf/6zx9efeOKJ5OKLL27L5uV1nHTSScmDDz6Y+f2///3vyfe+971kwoQJmd//8Y9/HL4/c+bMZCD797//nWy99dbJrrvumrz22mt9/XLUIM7H7733XnhIzfrLX/6STJw4Mbnjjjty/fzUqVOTadOmDegN/sADD9S8nvG9Z599tiOv5dprr02uvPLKZPr06R35e5IkDWSDSnlGrJIktcEXv/jF5KabbgpBxmOPPTZ87U9/+lPy4osvJgsuuGAyzzzzJIMGDar5HFy2CP7873//Sz74wQ+GIF5/s9JKKyWPP/54csEFFyT77rtv3Z/nPX/gAx8Iwa7Zs2cnSy21VEdep/oPAiSf+9znktVWWy256KKLkhVWWKHqz26wwQbJ/fffn4wdOzYZPXp0+BrH0zLLLJO88MILIQC01lprtfR6HnvssWTIkCHJvPPOmzz33HPJEkss0eP7HPdbbrllMnz48OT3v/99r9/nd3kOEnCrr756MlA98sgj4TPjXPb666/XPf8pvzfeeCP5yle+kmyyySYhqcW+GHH+veGGGzKvO/Eaw+9vtdVWycorr1z1b4wZMyYk3Dim7rvvvn758ZAAo0iAY7TWe1Xr2LcIas+aNSvZf//9y1//0Y9+FPbRY445JuxP0ZlnnpnMP//8yTe+8Y1kgQUWKH99xx13TK655prwOyeccMKA+2jYPoMHD06WW2655LzzzgvHYRrb8JBDDgnnTa4RRdtiiy2SW2+9Ndluu+1CIn9u8pOf/CQkyFZdddVk3Lhxff1yJEkDwHx9/QIkaaAhuHH66acnH/7wh0PwOE9wPa8YIHnnnXdC8P7AAw9Mtt1226Q/uOKKK0IS4qMf/WgYVEeXXHJJeDRj++2371gi4uWXX04WWmihZL75Wrt0Emz817/+Ff6bQGwe//nPf0ISYuGFF245CfHUU08lu+yyS7LGGmskBx98cLL22mvn/t233347/B7OPvvsXsEB9W1AG7fddluyzjrrhGTETjvt1Ovn+D5JiGWXXTZ8/hHBLv7/uOOOS04++eRk0qRJLb2ee+65J/xLELgyCYEPfehD4V8CSVnqfT+vH/7wh+XXctVVV4VjuJuQpAEB4CKTEN2+HYpAguuWW24J1x3eO7PxFl100fA9Ztp85zvfqfscN954Yzk4f9ZZZ4XzN+e9ddddN3wt7tsf//jHk/5yDUp75ZVXkiWXXDIkItMFAgNRN9ybvfTSS6H4gJ/5/Oc/H5KQ+MhHPhL+5Rofsa8df/zx4XPffPPNQ3I2Ikkbz68DEdcftin3Puuvv36v7xMUZwYg+y0zTClyKdLDDz9cTgAVif2TfYLzy8c+9rGkW2br/O53v0teffXVpD8o4jwpSWovz9CSlCTJu+++mxx++OEh+MXAh/8HAyEe++yzT7LZZpvl2lb8LgPeTvj2t7+d9AczZsxIvvWtb4X/ZhbAJz7xifL3YqCRwfmmm26a6/nuuuuu5Pzzz08WWWSRhl/Lb37zmzCoXHzxxUMQIgYP3nrrreTNN98MVbAMuHgQLOBBlTiD3sMOO6zlijACwexTVJzXqlpPi+0HGHy3ipY4VO4yuPzBD37Q0O9SkUlLKbZXOmDSV8ea/r8vf/nLyaOPPpp885vfTKZMmRKSTaeddlrYZyP2dVoy4dRTTy0H+yMqdKmu5RghYMYx0iwCuKAiPUsMEqSr1NPi16t9Py8q3//whz+E91p08J39mSpdKnn5WwQ76wU6Y+sqjoM85xaOEYJvVLFzTiKJy9/ppu3QLUjE0U5ljz32CNdkEr8333xzsthii5WrywlyEjSuRNKBhF36GkMbMRJ+yy+/fDkREc+DjWzTvr4GpZGYIXHJNYHr9EDWDfdmJEF++tOfhn2S/Y5EGeL+mD7fXXjhheGz52fTSQj2F45nfpZZcAMNxwDXJ7C/xyRN2oorrpgccMAByfjx40PyfNiwYYUlcp9++unk+eefD4mrbbbZJiny+sG9Ebh2x//uazHpteGGG3b073bTeVKS1F4mIiQpSUK1+c9+9rOaQb68YuCCASdBkCLstttu4YY7Vnd2GkEwKusJjNcb/DE4oIqMyktmQuywww49vh8H3iQh9tprr1x/nyAmiYhmgpS0oKA6uNlqNRIqDIKbRZAY6e1w1FFHhf78JGV4T5XbNCYi5syZ02M2SeU+zOCMQCUVz7V6S2O99dYLVfGN4vUxGGwmCdTuY009Mdto8uTJoeUSLWMIZBDEiccVs1hIQPEZ0tri+uuv77UJCdISdPnqV7+afPKTnwxfY59i0M8xzIyceutI8LOxfQWzlkh+EaCnepxWOPx9zl/g9WTt0xwPIHFCsJf9hgA8wRreGxXCecRkS9asjHYjQHL55Zc39bsEXGKbrEYw86XbtkOncD4kgMs+Ww3Xnj//+c+hYvqvf/1rOO+SJIuJsE996lOZ1x2ODxIR6aramJjj2h7F7zdSfdvX16BKG220UUhEcJwOZN1yb/b1r389BNBpT0fLm6wCDIKpFApwvqRtU+W5gtmJtANr9jqcB/sD53HWEmLmFg/O3cygWXrppZOhQ4eG44pjqJ0IwrN2Dtca7o2qoS0V1yL2XZI2++23X1KEmLz67Gc/G957UdItprpltin7WUxEbLzxxh392912npQktY+JCEliwZxBg8I0eYJ2BPNoU8JNMJX3aGTwwe+CAMkXvvCFQrYvg9P032oEwWqmLlPxHKuI4uO///1v+XvxX4KPtAggyEYCgq8REAQDbrZXNTwHA1UGtFRTUWVaqdM90Qm+81qY9k5wjgcJAIKdDOp5EKjgfRFMoF3N3/72t/AzBHlbGdgQwKfKC1/72td6DECpVq6H2Qj1gsD1ggIE49ox0G1m32v3saZs9BmnKv+UU04pt2eikpsAPgjqX3rppTU3H+0uslA9XQ9tHDhXUK3LrJ977703BN2a2aezkmpZFezVxEWEawWr24WqeAJn/C2C1vx/vfMblb8c/9/97ndzzXiKMyJI9hCsy5uM7eR2yCNeSyofXG+4bqQfVLzydf5Nf50Kd9otMfunFgK2v/zlL0OrHPZD9ilmNeSR/vziOS89AyV+v5HrWF9eg7LE1jdcp7lG5Zlh0x91070ZFdskJEgkZiUimNnGPs75gXUS0mICuYj3wHmCNRn4uzEZXM0vfvGL8usgYNyONlHM9KBFGJidV2vmJfcQXNM453L+JOldxP1DvGdjfYgisTYTOC/EFph9jfvFeL+f5/Nl/2l1FmO3niclSe1jIkKS/t+gkZY5aWeccUY5ONpI8KaTfUmr3fBTIca0ZIIKDGapIuZBsoEKp3aplYggwEg1KhX4LM5MhWllK5g0KtpYDDDvYLVZtP7hUQ/JFwaeDGwIKPL681Zh15oNQbU5A7pVVlml/PUTTzyxXP3I/lMZ1KIFAfvnr371q8wBKsFJEkUxOJcnEdFsdVt8bc0ONtt5rOXFNpk2bVoIxnMckHCLyTcGrQQ02K4EztNtw/qzPffcM9l1113D9uY4JQhLIJfBPRWuWaj4JBhJkLhy/4oJzHr7F5itFPdbEGBnv2M7x/2b44o2F1/60pfKP5/G10lQ3X333WER7diWgWB1IzN5YhCl2VZijSD5wMKejYgVn8wYKXLf6+R2APsLFansL7F1RrwGcfzl2Y/y4DnzGDFiRAhwcu5htg8zcRoVr+3p83MzifS+vAbVSkRwb8C5oZF1g/qTbrg3i9gHOR9WKwggqMqMtHRrvei6664L/7Z7fSxmZ9BSKlbms89xTfjMZz4T7s24rySpR5KEda6YKcC+SbszHsxIoNik2SIF8Pe5l1l99dVzHSMHHXRQcu6554Z7QrYZCcc8uOaQYOAz4PXWOo5ZYwYkMWl/mBfXzTiTj3MenyXXtXqJCLZ5Ja69zIxlvZp6+zHnW9qscS2//fbbw2eSXui8EVx/wedBQoDzOp89+wL7BG004+dEYorEEJ8h+0irSaFuO09KktrHRIQkNVDllkcnK/yr/S0CibGKqxYqH2nVQTIhVqiz6CYDYP77mmuuCYMwBlQggM6DoC0/z/T8LFTsEQhl8EU1H9X+cVAye/bszIAbg2Ae3YBBHwNGguNUXbHoaTuq/ag0zOofnbUYYxqDbAbLVPw1O6AEFdS0fIitmZpBn+Rq+x4D7laCEI0ea1kIYpD8YnFaAtk8CK7lTcARGDr66KMLq5gtAoEYKsYJZqf3Dz4Lvs46DXGBdD6/av3sY/As6/sEsPMEFu68887Q95xkAcE2UK1IMCtrkWaSk7EFVFrcjzhXZH2/0QB8q4teF4FtQNUx76/oBFintwP7IW2q4rWj3nWI60l8EPBiezBrgTY0zHpgBgjYVlTJMvOLRyMBJ1pfEayM57BGdfLaXtQ1KAvrD3CMcq4g8DhQExF9fW/GejDf//73w7aOCdkrrrgifI9EOWgZlQ52E4glmE3ijiA7ibyYtGe9LdaIyRKLE9Jt8mrhXo+2UpwnKAbgODn00EPL6zNsscUW4V8Cz6wlBIpdaF9GwpEgOq+HZD8JilpFJ7VaMjETj/MBs+TyFDtwnrnsssvCLEsKNSiw4DpYD/ehja4X0ur6InvvvXfN78e2mVmJCJJDzJzh/ZKY5zOKCRQS9HxuHL8UHVQuKk1rL+7rayGQzz6Wfl72O+6jQBKEcy/bLX1OjzNwub8iCUHLVmZkkmBn32W2Srtbd/XVeVKS1D4mIiQph1aDq51GZS4tUQgwMGihTQsDER4EeQgo8qjWx5jWFd/5zndCD26mPtNDm8FnesHEWhgskQxh0Mpzxb7kVFEROGLK/RFHHNFjsE4wlUUZ82DAyeLWRSBYP3z48BA0YFDG4JMe2q2iOo2qQbZFvVYiaQQqGQQyOG0lCQEqxkDv5cokEkELAnT19vUYxGPQyv5B4IFtRfKJ6mQCE5061hiAz5w5MwRBaP9DEC3dSqASgQ0SYxwT7PsMXBm4Uz3IDB4G3vSP5zFq1KiwlkUnq2ibwbanVRGvnSpPqh/Zf8Hnw3+zfWjRRHUknzM987PEmRCV34+zEQg21GtPwbENqmO7ocVL3BdaPXZaEROI7NvpNWBmzZoV/uWzq7X2C9ud4BKV0M0GUzu9HThPcK0heEVCgWOO5EK8BsUEOP9mXYdIvhLgJKnFeyZBSAKX/a+V1h+VAdJqa5Q0M2Oi269BtT4rZoNRMMCMEc59eXBeaDapMzciaErbulq4fsVZi2lxfZKrr7663GZt0qRJdf8m1/p6SBhyj8fzrrnmmqGivHLWWUxkUxlfWUTBfR3nfWZ2UkzCcRvbNuVFwQvtlcDMpXrFGWncG7FexPHHHx/WFOI9sDB9LXyf8xCJFs6JWTNRCeyzXbj2sb5SZYusegjYc5/E+Zt7o1oJPmYacC8FZp1Uip85z5VnUXnOkfHcy3FaD8Ua8TPOElvnxX2K/YAHrVfBNuQel32J+ybey4QJE0JyisQQM37bPRuv0+dJSVL7dPfoWpK6RLsG2yz6xkCSACgDn2rPGwN/DFxpb1JrHYYsVB83076Iv0s1OJVpINjPom9ZAwgqzQkgZVU7UU1OUIMqtXQgl4EqAy4C8gwYEaurqISvVqldrWo+T7VtIxiIEfBi2zFI5T2su+66bXluBsm8XgZx9YLtDNwIkLPt4kLVtHSqDJjxfHxmBJcZ/A8bNqzm88ZKy6z3xDR7gny0jKK3LgM7Bpfso+yL/A0efH4gUFDZwqcdPXkbOdYImND+q9o+wvukQpIHQQCSc9WC4wzwSYaxjxI04L95r/XW5OhrrNlA4oTjiYQDLWgIJHIMn3zyyeFrDM5ZE4KgL++pXhV5te+T0KyViCAZxGtBXESVY4pkJIlPPpP4+cbz09NPP12uCk5jNhUI3MWZGARjYnsmgiD19vduSUQQ1I5Jh2ozI+rtZ5xrW6no7ovtQPVsM6+ZqlZm03B+IahIxXMzVfrsWyRAWl13p5OKvAbVwrWav0Wysh6q91nbgIIAZqw0U/3ebTpxb8a5mgAt11auQxwbXGsIpNNehmsQyTaC+vG4icHseK2Nbew4n3M9q8T1kAQ0M2L5O7zOegFo7vM4txLUZfZR5QLYvK44k7IyEQG2F6+Z8zJBaILRtAJkhkUevAbaCPIaOKfHe8NGHHfccSEQTTHCzjvvHP47K6Cf3t951HLssceGz5prXmwzWJTp06eXkw1ZawWRKOTcwGfLvSDX8TjLk+sq53Vmu3Gt5B6Tfxu5l2JNEO45uU7wOrhH5Tjn/p/nZ6YKiQ2eu9qsOq5R7L8ULXFNJ/nA++K5SZrxb3pttP54npQktUlJkpRp/PjxRLnDY+bMmbm30v333x9+Z6mllur1vTvuuKP8nHkfL7zwQq/nGTx4cPjePffc07ZP74033ijtuOOO4XmXXHLJ0pQpU6r+7C233FKaZ555ShtvvHHpnXfeyfX8d999d3juBRZYoDRjxozy10eNGhW+Pnr06NKtt96a6zFmzJjwO3vssUepXaZOnRo+M553+eWXL02fPr1tz80+MWjQoPDca6yxRt2f32yzzRreT6688sq6z3vAAQeEnz3ooIN6fW/y5MkN/82FFlqotM4665RGjhxZ+tnPfhbeZyePtdmzZ5d/j+3Lazn66KNLN910U+mtt95q6rW89NJLpY022qj8vFdddVWpP3j//fdLZ599dumDH/xgeN28B47NI444ovTKK6+En5l33nlLSyyxROniiy/OfCy77LLhd9Nfu+iii0oTJ04snXPOOeH5axk+fHh5u/GZguO10f0qz+O4447LtV222mqr8PO77bZbqa+suOKK4TU8/PDDpWeeeaahB8dDtetJI7phO+QxYcKEsJ9yPB922GFNH8fXX399ab755gvXl1dffbXX97l2sj222267cI2tfPB1vp8+pw0bNix8jX064hhp17WoyGtQnr8dj61HHnmk1/fZJhz/XPPTx+Ell1xS6i+67d7svffeC/sZ+zrX5Pi8Q4cOLd1+++29fv7ee+8t/8xzzz2X+ZyLLLJI+P7bb79d9+9zfeCayc+vtNJKpddee63mduN1VvsZvPvuu6VNN900/Oyqq64a3l89DzzwQLgm8TurrLJKac6cOaVmzZo1q7TCCiuE52I7pI/TRnHeXXDBBcO5iPN22j777BPOo7/97W9L7XL11VeH173wwguXusVRRx0VXtOIESOa+v0333wz3H8wVoj77bnnntuvz5OSpPZwRoQkdVCs5KeyiOnntdBfleq7TvT05u/ssMMOoYqMqnZas1T2ZaeanrY7tE+iYpoHbTOohIvtWGpNoY794ulXm66cp8oeVG/zaETsG94qqqlol0TV4VprrRX+v10929m2VKg3MnsjziKh2rReOwCq9s4888xcLYSoTkPWc9KqgMpt2hFQnUllHBV3VGNSWUcFJ5Wv9DmmWp3KWXoW9yWq86ikpD0AFZj1+iDnQRUp1XtU17Et6OlNW6NuRwUtVZu0Q9t9991Dqwr2CaoQIyodmd1Eu4ks48ePDz2eq32/FlpxcNxwvoqzZuIsCs51zMZgH2JfYj/ka7TFYOZG3qp5Xn9clL1yzYlunhERWwlxTm10MfZYJdtKO6Ju2Q71cB5jNhj7LbNoqs12yoN9hBl2zGziusYxzcyoSmyPrKr2Tm+nIq9BeXC+o10fM3dos0cbRq5dvA5mP7DOQLrlHccsr7NaG7z+ptP3ZhzXnGeZ8UUbO2ZLgNlrtJqhWp/94YwzzijvB+nXxSyCyutdbOHG/pynxSFV6/wtzi3MsKg2IzW2W2T2a61ZqzwP6wNss802YeYH7ZaqLcYN1h+gvz/rXjBziar7VhY4ZjvxN7kvYT9mdiDXpWbOI8wM5lrDvdtqq63W43u0L6M9Eu+zXWK7pU9/+tNJt5gyZUr4l3urZo8p7j8YW3DfyOfc6oyIvj5PSpLaw0SEJHVQDCbFdRdqYbo8g91WA1B5nHTSSSFYw2CQtkmVSQgC07RbIqFAEJtBMoskMhDgdwkGZ03ZB4EKArm0yWBgyNoQaQxyWDiZQUtWn95afXcbDeplufDCC8N0cp6TQTHtJipbE7SCVgUM5Gk5wCA5jX7KLAJJcJZBb3zvManAoL9eu6oYcMgTzGXqPbLaafGe8/RlJpBNIqLd/X6bxefVbrS8OOigg0Lgh4APLQpWXnnlpD/gOKQdE/sULRzYr9MD9WbXiOB5aFPBMZLV3oY1ZThXkaikL3RE0pFkWVps2UHQud4Cnq2K7Sv6MgDfjkVyW32ObtgOtdDWi5Ys7Le0YmolCRH3MRYtZf8iYU7i/Oc//3lI0nWboq9BefG3eS0kgUgmnnfeeeG6HZFI5HpFYPErX/nKgAoAdvLejHsizpMsTE0CgmRDXO+BbUuLKFot8n3uGWizxH0PSQvuDdhPWLw4LiAdxTaOeT+Xn/zkJ+FfWj5mLZAcxTUrqt3jpdHeiesnrXO4p6yWiGDNhcMPPzxsC5IPJCFI+nN+4p4ntq7Kg8+CxA6FA0OHDg3tAUnI0/aKe0+u5aecckrucx9JGVpUcZ8Ut1FavCertsZaMygAQLfcZ1B4FBdQz7rmZ2H/5DNnX/r6179e/jrnYdYnYz9qZZt1y3lSktQ6ExGS1M8CUu1GMJz1C3htDIazquUZeDE4o/KcAQaDCiqdSUIwMDjqqKNCFWUWvn/nnXeG/+bnKrdBX1WbM3gdM2ZMeRYGQVGqswnesk0IwNDzmEA/wVQG1yz810g/bBbvGz16dAiuHXroob0SEQzAGVRRGZ7eLkXtJ7FfdKOLLmYlPnjdA1k6KUPVaLcECPJgfyNZRPKL4FF6UVPWI2hljYh0YDIeRyNHjgxBIIJr9XryE4wgyEOwjEBU0UiedEsighkrjSzGjjwLjfaX7VDrvEQym9fIgrV5e8vXE6usWcz9nHPOCdcuApZ77rln0g06cQ1qBD31CfbRZ59Huj89245ZjcxsGog6dW9G5TtV4RQn8HlSdc7MijjziX8pBGH9I2aaUsjAeZeAPskIZrrRez9rQWtmUKJyoeksU6dODet84Zvf/GbNn73rrrvCvxSe5Ln2cN1hLQvWnarEMc6+RJIF7NfXXXddWJuK6nauT63g+bgOMWOTIhcSImxDjie2KbN+amEbcs/K+2DtmKxAdzyHt7NIKBaJtGOdrXbOhuD+IatwJQv3+SSY4mecxjmr3poc/eU8KUlqnYkISZrLMdhl8EuQrFarHWZE0EKAASaD4bPOOitUBtLOhcVFCVykq+oYjDCgowo1iovnEaAnQER1FIO5ZhYDZ1BONR0BUNq00FooLyq/Gawy2GJWxdixY0NgnfYUvLZqqEYk6MrCiAx06v0NppBTgc52y1qAMFbWVRswUSFcb+YB7ZTyYluhlfYHcRAeK6wHqvTiuK0GR/oisEvgikBTZeCQ/0+3a0qjIpXKzPTivRxnsSVSDGanEbikVQX7MAlNZkrVOiYIUPCcJN+oVM2Lv01yhcrWPJW53diSKJ0Q6rRu2g6VmEHDrBrakrAPtRPXlgkTJoR2NSTTK6t7OX9SEd7KebUZnbgG5UVAj0Bf+lrN8clsEq5dtGlS6zg3cp9FS0m2KYUJcfYpLZW41sdZaSRGSDiw/Wln+cQTT4SAMK2PuAfjnJs1qwjMMK0nFkWQAMhqWRbR4igmOCpnYFQTA9dxhkYaMx1IaJCIIDB9zTXXlFuj8V45XhdffPFwTPDfVL2ToKBlFfeT1YwbNy60g4rnN+632B4UurCtmOnCosZ57tn4fNgutI7iUSneD/AemJlSiesbM4q4DtM+i88szzGIbkn00bYLjbSfYsY0su51B8J5UpLUPiYiJGkuxsCNhAADPipR6znxxBOTyy+/PLRsIIjIYI1EBNVI6SQEAUNaa9DihUEpCYdYfQfa3VS2aGoFA/W8iQgCXtttt115EENA4LDDDguBdQL0W2+9daikpQqRNQgYIPI7bCsqvgjWENDi/RPQrZZEYSBKcIFK+tNPPz1zUB6D+tWqpGmRUcSMiFbaKsVe2nFtj4GKzy5qRwuwTmHgTnsMKmYJ7FbuQ+1eI4JAD+cFgi1UI1abKUNwhnYjjz32WPh/glsxwNUIXmMzAXgCYK2gKrOZhGna448/3vC+xPbkPNSqbtoOlc9HoiDOmIvnl3ZjH6WStnI9CM7t6cRbJ3TqGpS3nUpc9wdcr+mPzznAiuL2otCD4gOKOmg/Fs8FVMMT8GWGWOXMDH4mJg1Y74Tjl0QDa3ZwH5VevyAGzfO0WIzt95i9UEv82xyXedeEijMyeF9Z5wuCwyQGSDyk732y1hqjVSi4v6x1XeKY4PhIPx9Bfe5vmY3KPl1rHS2SD8yg4DnAdYrZrLXUSrpHHOd5sH4C2C61cI7gupl3jaRmkISlvSMaaWUXEzTtul/qpvOkJKm9TERI0lwsVkASxM8znZ+KMgZ19M6fOHFi6J9L0LNyMEKlGy0ICGRQ8UZrjDQGFLR1YtBFBVveAQItcghEUq1OUIngGsH1PANvMGtj++23T+bMmVP+2jPPPBMCpCROeN21ptszOGOwPHny5JBcoFKc/s5ZGChRVUbbBYIPWYtVx79V7f03slh1PSRGYkV7vXUnaomBQtYNGcjSQfJuWkCyFnpi07udgBQtKOjXXC+w0SoCuxwPMTCSNWuCfX///fdPfvnLX4b/578rF4Ql4ER7HiqGswJSHJ9Utja6QGy7WhKxQC2BsLxVwdW2VbOLVbeqm7ZDZaCTam8+Vz7/ImVVGxPoYjHmSsySIEjfbp28BtXDtYMKY7Bfkqzh2Gy0fZjyIVFLgHSllVbqkXDgPoxCELY9yYY0rtUEhgl6E3gFiQwSEawlERMRXN9jO608MyLimgT17i9iy02SEHmThOkkfrWWV6wplEdsBViv5V9MgFfuu/x/THRWw7bjPJBeG6nWDAyOE5LK3AvHRcazzmsslJ13m8VEcb01D/ibFAKRWImtitqN5wezDtIzQ/O+h3YE/LvpPClJaj8TEZI0F4vBVnpA50XVKoNX2jJVS1bQboCEBIEcBmpxgBIxuGlkgJMOJJGIYFCa1U6jFtoZUBkVXws96ml9QH/kWpVyaQzMWDiSHub0uaf3MP2eq7U2yFtBWE0ji1XnbcvE4K2VquNYJZsONgxE6dYs/SERQYuIL3/5yyGoy75NJWi6JUEMaFP5Gfs/V5sxk/V9KlsJZjP7iSBN+vitFfhi5gwBNioTI4LOlZXpMUDP/lX5vfR+3miQox0zAUikEJDjPdC+qtn2QfRCbzQJ2K5ERDdth7RY7cr+1M7FX/MiMZO1vxXRwqovrkHVEPiOC/GSVCJoWq9/vlqXdS2h/RCqrY3CufHggw8u/38s/iARQZtMcL7n3M7+Eds91RIDvLUKUJhdF5NxLKKdF9cg0GKp1bU3YusjZt82k4ioh/sYAtssaE/xCMcShR1cO6vNwCBZRCKC2STVWhex7Tim8q4jERPFtc7PfBb8bd5jI59HI7hPjPsjM6UaEc+Z7IcD5TwpSSqGiQhJmosxmGp08WIGxUypr4ZAIckCpk8TsKxWJd0ptAegioqZGTHQSRsZpng3MzOAgTWtPFgMcfbs2WFmSFGDGyr06DGcZ9BfTxyopwNsVDdvsskmdRerTIttnQZyIoK+2AyGsdlmm7W0pkbR+Fx/+tOfhqAwlZ0Eum688cZeC0zG4AABKCoNa6n3fdaFyJNInDZtWljglsXtOe445pgJQS/pysVW+VmQwMxaiDUm0hoVA/l5AxjVgmGxhze985tVuYBnJ3XTdkhj5lyj16D+ptuuQcyUikkIAnW0CWplv1A+rKXFuZPPPAaoOWdTvc325zNNt/sh+Usil6Bquk0Q7R5ZJ4fzKudKEsGxBV/ehd7j+aDW/kc1OdcNXhtrJzR6X9nqWgEsNB0Xcd5www1bDuRXevTRR0MSglY+JEFZiyK9SHsnVb5+EhnpFppc52M7U2YyxXvrdqP1KrNdeR2NtGVCfL3NzpbttvOkJKk43nVKUgdltecp4nfyilVx7U4UVE5XT/eNp8qJCkyqnKiMbiQAEqfp06KJGRE8LwNlgpRUBFab9cGAGlS5MchpZjZGGq+b2Q4sVkirhaI00qu/njiQiwGI6dOnh0Eag/2sRATtfRioE1TgM2KmC32aY9Vys4Hh/oCBfhxM51losi/xObCAMwEtWpRRsZ6VOCGo9cMf/jAkEvkMG51ZEBesppf8Gmusket3WCyUtWGojGWWBecZEhG0aIptmipRRcqjXXjfrbaLiAt38hw777xz089Di5BG++6z3RtJFPaH7ZDVV7zI6xy4VlDBzGdAO5u8fy/9c3EbNqrbrkFxPSgWDWZ2i0mIztybcb9FlXa1/bPamgOVC6yDgC3tKWlxSbU3xyaBVxK/eZD4o5UfSfdqYpsojpu8yXgKFEiEo9VgebxGkFyv9/fjIt95Z0Qwm4R7SF4v16drr702tBfsq0RE5XmZBZp5T7wuZrByf8s9G60W86zn1gz2wdNOOy38N62qGl04O85qjDMr+/t5UpJUHBMRktRBMSBPr9N6rYViwLhdrTmykAyg1UqsRu4EBu933XVXS8/B9ksvMMpAshoq2ulHTFCdKeeVbTiolKINDzMLGHhReZenFQ9Vigxu0j1s240F9uoNBnlPVPLlTUTEpBN9qfksKvsg09uY6susqvT0gJlBI/vzQAtiESiPASH2hdiXOw+SOgTfSbZtsMEGPRYSLQqV6ewn9LknaFFtIXKCBLTTwR133BHaBBHcYYHUouy5554h0EXLKKpj48KjW221Va9qS1r0EASh7UhWVS8V3CzO2qhYeVzZHi4vgs9xf6A3eyvta3jPzawR0Y5ERDdth7S4EDdBtiL96U9/CjPMSO5yvo/X1ZkzZ2YGgPl6ZRI9njsbTUh00zWI6m8q6cGx3+ri5QNFJ+7NOLdxDoszIpiZwrFNgp/PMY1gLteQajPUOLey6DPBWl47x/VOO+3UayZcrUTE1KlTy7MXKlFFHgO3JDzyIrFFcJ+kSKvnrZiQzpP0jIUReddEojqe10kbK5L3JOX6UryPYp/ieOb6zGuKbTSZTQPWgGqltWYtnAfj/sAshCzsa9y/82BmI4VAnM94rfH8GJPLjeqm82Rf3MtJ0txkYEUPJKnLxSprgv/pQHotDJZaWVy4Fm6uCUxQhTRu3LiOBJUJfBAUYiBB9VoMkBH4qTeIpo8vlYDMqKB1DoM2Bgpsz1qoGOfvpvv1Ekwi4E4/YNpIVQ6IWLCvVl/iONhqtGqsEQzA67UsoV1KnkQE75/tzfbiMWnSpDDQS/caJlBH9SUDSmZAUF3JwpokHwjQMBiOPd0JOBDQZuHGRqfwdyP2BxaCpLoUgwcPDlWTeTAYJ6gXF3mMaPtwwQUXtK2NTTUEVwne5+1r/9hjj4WFLocOHVpoIgJZ1Zucdypn+xCUIxHBbIusmUAEpZpJRMQZCM22iyAgwr6PaouX9gfduh2GDBkS/uW8kuca0Gp1dawYj+f8+++/v2YvdGYaRXHbNdMDvVuuQeljqNU1jAaSTtyb0WYxtlrkGktylWsrn3/lug68BvazAw44IDN5ScCdczez3Fi4mufhv/OitRNJDK5x3PulUaAwZsyY8N8EYeOaFPVwrMQFgfmdVlozEQQmIJ233VSsws97raUQg2QO2znPmhpFo3If3NPSKo2AP68viude7kuKwOwLElug+KLy3MA+wWwy9rHYnq8a7gspVGEf62/nyb6+l5OkuYWJCEnqIAZmt912W7LIIouEG22qxioX8+OGPy4MS5UXP1sUepYzEKX6hwoxFpUtGgPmzTffvNcC2AxgWVSuVn/6ODBl8E+APK+sCjIGXQx6qCDnfTOQoSqXwTkBeabpMx2+2kLeVBMWtZBxUW0i2G4kIe67777kqaeeCmtExFYG/D4DfvY7+kGTaKjcbgQsWDQzBuvZb9iH6HvNzxc1SC4aiTgW/YwLYzLDhuRO3vczcuTIcByx8CdBdBICBM5pw/Hss8+Gdg+tLtpZTyOL68bPtagEZzeJ50+qNxtFUDImajjOmdnRCpJ/zbRmGmjbIY3EAL3PCbydcMIJIUDYbgSX6KHPtScmTTlWueYQACTwlT4+uf4SVOX3lllmmR4zCGl/1oxuuQalEytxNkonsE0JqtO2cdSoUcncfm/G4rskhCmsqNynOEZZ94dzelwXIAtV6ySUCc7SSqeRwC+zFcaOHRsq4LlOEWiNCDgzIwJxFl3e54wzm6pV1OfFPSG++MUv1p2tQMtAHsgbKGbfr9bOsy/EmRzcn3EfzD7I4sqVs37jbKZ2Y3FoAvb83bh+TBrJZ4LznEP5TJjVSAKH4iXWdmCdE1pyPfnkk+E+fc011wz7FOe4ylat3Xye7IZ7OUmaG5iIkKQOosqcR7fYdtttwwCcWRFMv+fme8SIER1/HfSsZ3C/6667hsFFVk/kdiK4R3UVqCZkhkVEMIzWDAxGGNwTLKispKJ9EVVfyNuTudHX1+hi1XnahTDYffHFF0MrAqRnQ7APMBBl4EWVYLXp//HrDDKpCGUAyAwXpr8zgE5vy27GduO1U+VGVXTEdH/ef95qTp6DfYUFRGlXENsJMLuCATsDV4Kr7Wivk4WWTFSr89ny2eVZA4AEUqxCr9eGJGL/IkhCX3GCEul9p1EELCr/LoN8MOsmLlCaRoVlMwg+EIiIM3kaceSRR5YD9/RiT1dpNoNAbF/ppu2QRnCfgBvBHvZlZsS0e5YOz825iuMxVj+TyCapyrFP8HKFFVYo/zzbiZlola1BaH3W369B9F6PaHNSWRRQ5Lo7scqYFiuNVO8PtHszgv8kGsC1gXMqLWnYB0h2UAnPWjzMJkvvl5VIpMUKca5DzCLIuy4DM49o80OAlX2N4Cr7AsdKTCJwXHKPmAf7bJx1xPWBY61ZvIaYCIkzM2qJswXQXyvW47mG6yBtMQn0p+/9uL/i/Bjvt9p5n8XnFmcBcU6sTPzwNzl2SaJzrqI1XxbOV8zi5b2wP/H/PChWoXglb9usvjpP9vW9nCTNVUqSpEynn346Jebh8cQTT+TeSvfff3/4naWWWqqwLTt48ODwN+65556Wn4vX+4EPfCA83wILLFA6/vjjS6+99lqpndZYY43w/LfeemvVnzniiCPCz3zoQx8q/fWvf838mWuvvTb8zLbbbtvS6/nXv/4Vnmf++ecvvf/++72+z/tfccUVw88ceOCBPb73+OOPl1ZYYYXwPX7mjTfeyPU3H3300fA7bIvohRdeCF9baaWVevzs0KFDy/te3sfll19e9zV84QtfCD+7wQYbhM/6zTffLH9vypQp4XurrrpqzefYe++9w88ddthhYdudffbZpQUXXDB8bb755iude+65pU4da3m88sor4TnZ9yZOnFjaf//9y59t+sH2OPnkk0vvvvtuQ89/8MEHh9+/8sore33vrrvuCt/bfvvtS0XhNTe6r7T6uPDCC6u+niOPPDL8zPjx43t976abbmr5bz/zzDMNbZ9TTz01/N4888xTmjp1aq7fYb+O5yMeO+ywQ6kVQ4YMCc8zYcKE0sUXX9zQg32W3+Wc34pu2A7V/Oc//yl94hOfKP+db3/726Xnn3++Lc/93nvvlVZeeeXwvJdddlmv73/uc58L14F4Lf3jH/8Yrod5j1k+I557jz326PprEDjnc2/C737mM58pvfzyy6VOePbZZ8ufA4/vf//7pU7rpnuz2bNnl8aOHVtafvnly9uEz2OvvfYK/73aaqvV/Fyvuuqq0qBBg8LxvM4664TfWWKJJUrTp0/P/VqnTZtWWnzxxTPPs5/+9KfDtbOep556qjR8+PDy72233XYNX0PTHnroodJiiy0Wnottkcctt9wSfn6RRRYpteqss84Kz7XbbrtV/ZmNN944/Az3o608Txr3U/z8lltuGf79xS9+0et8EI9b7pGPPvro0oMPPlj1nMe95Z133hnurXjOO+64o+a+OGrUqHAuefXVV3t9/6CDDgp/d/fdd6/5HnjN/Bz744svvhjujbgn5Guc36+77rpSozp5nuzrezlJmpuYiJCkKsaNG1ceXDFg64+D3byuv/760kILLVR+v7x2AlB//vOfWxpUNpKIwK677hp+bplllskMRLUrEcFAjUErz1Ut6REHVfwcwRsGQZMnTy599KMfLQ+Mbr/99tx/s5FEBMEtArnnn39+6aKLLqoapPz5z38egpsEGR944IG6r2Hfffctf8af//znMwd8BOF4XVnYBnHQd9ppp5W/zoB46aWXDl8nuNKpY62eDTfcsG5gm+DNmDFjQqCsGTFwMGvWrF7fe+edd8J+wmC4KPfdd1/pkksuCYmkG264IQT76z14v7zmjTbaKNfP8/jDH/4Q/gb749///veWEhEHHHBACCCkH9dcc034HsGAyu/x2HzzzZtKRPDz8847b/jdtddeu/T666/XDYqPHDmyvH+su+66pf/+97+ldiQiXnrppYZ/l/NvOxIR3bAdamGf+uQnP1n+e4suumjpkEMOCUFGjqNm/eY3vwnP97GPfaxXICruj8stt1z5b7z11lultdZaK3w9T1K12UREX1yDIt5X3M7sV2eccUYIKDfy2gnysW0J/nFty4Nz5CqrrFL+26ecckqpk7rx3oxtefXVV4dzcfq6VOs6OmnSpHCdJhFBUpjz43rrrVcOuP773//O/XpJSqY/k3h/Ve0eIOIzP+aYY8JxGn+PQod655Va2AfjOYDAdd7zzQUXXBB+Z8011yy16swzz2xLImL06NG5gveVxRgxcD9nzpxeP/O3v/2tfJ8VH5wD2Gacs0gefeQjHwnJqcr7nEsvvbTua3j77bczv87nzHPssssuNX8/K2HBeZ0EW3wdjRaqdPI82df3cpI0NzERIUlVMDMg3jwzAOjPg908eI/xRjz9IEFBhdOOO+5Y+t///ldoIoIKvFjBRCKkqEQEdtppp/Bcyy67bOnuu+/OfC2x0p9ZAOlqzoUXXrh04403NvT3GklEFOWkk04qv4djjz221/fjeyToWxnwJYhKsI3vE9B8+OGHe3z/scceC9syaxBX1LFWTxygVs58IGhDkJNAZLP7dLTNNtuE5yUwV4mgDEGBdgRI2ulXv/pV246jZhIRhx56aK/vkejge/x+lmHDhjWViMB3v/vdHoFXgsfPPfdcj2OdgBx/m2M7/uz666/fluB7NyQiumE75AlEMuui8pgl2EnwjwBXrSRYraAhM4cqg27M/uJ7JHzT/vGPf4RzP9e+GTNmFJKI6ItrUGXyNyam4mPJJZcMyVuq2gnE7rnnnqE4gIp3Zo6svvrqYb/hHJr+vd///ve5/y7Xh3g8cG4kudkp3Xpv9sgjj5S22mqrXvs912G+FxFgpQAgBpoJmqer2kmo8XXu12bOnNlQsJdALbMsqu3vnCeuuOKKcG5IB5ZjMp8EdSvY/2MSgoAyn1Ve++23X65AeR5sX56L/T5vIuKcc84J93VcTzlH8Tpi8Lza9SyrGChuT2bDVMN5+IQTTijfJ9d6cHzzcyNGjAjX12YxSyw+H4UvlfdM7Je//vWvy0mU8847r8f3SQ5wPiGQz31it54n++O9nCT1V64RIUlVzJo1q8d/11swL9XyLvz72muvFdYHmYUS03+rHXh/N998c+iTSl9e+kfj9ddfTx588MHQI5xFPZuRZ/0CsPgjPfvpR/vjH/+41/fpUd8uLLA8bdq00DP9s5/9bDJkyJBkvfXWCz3E6YFOr17eL4sgxv65oK/y6aef3qPXdiPrPqS3RfwafZ6b7YEfn5Pnog86PXKrrW+Qfs1ZP8OCrmyLW2+9NVlxxRWTDTbYIFl66aXDAoQs5My+gGOOOSZZbbXVevwufXXZT5rpA9zssVbP8OHDQ59tFpxl/RPeP58zCyy2C4syXnfddaF/PP2V01jwms+mXe+nP6h1Tqr1vbzniGbQS5o1QVjDhH7ie++9d/l8w5onzz//fI+f57inLzQLyg6kBb27fTtwnNKz/r777gtrCnA9ite7e+65JzxGjx6d+/no983vsNArfevT9ttvv7AuDgudVvb8ZtFfrj8sFMxiwvF11Fv8uduvQWlHH310WHSc9zllypRw7eDzr9wH8pgzZ05Da4KwDgzXFtaCoX88PfG5fhSt2+7N+NkTTzwxrPXAGllsG9b74V6A/Z/rMOtmsUAx918cr1xTMG7cuLDAcHrxZbYrC/ZyHWY/Yq0FroH1sK7QpptuWvNnuEfZd999w34ScVyxngXnh8r1VPJiO51zzjlhXQru71g8/ne/+114/ZVmzJgR1sxIr4PE62IdAHAst4oF6uPz1nrNaaznwPmFe6Q0Pk8WV84jfT9W636B+6vvfe974cFxxzns5ZdfDvsS5woWdOZczf7Atpp//vmTVg0bNizsa6zzwDpHLGDOmhXca/K3WZw6rju19dZbh/0kjWvL5Zdfntxwww1NHeedOk96LydJnWMiQpKq2G233cKgLi70mVcMLjPYPf744wvdvu+++27bn5NF2XhMnz49BFhZoI3AEIsbNisO6uK2qWXLLbcMDwbREyZMCIuKsogkA9S4yHI7FiRkEM1i0DHxwWCKRyUGvQyeWLRx5MiRYbDSDAIN6X/TiZWnn346LNLaDscdd1wIbmQhuRANHjy41/d5bwSF+H0CInGRv2iVVVYJSYi99tor8/mbSUK0cqzVQ3Dk5JNPToq0xx57JKeddlo41lnoeuONNw5fZ18iiIsY8O0WWftiu2Ql3KL4tawgXTyXVTtHxABRMwjGsD+zoOUpp5ySPPTQQ+HrBNXSgTUCFttvv30IHrGvN4rFRAmaEIDifBUTXizOC4I4jQaG4jZj8dq4wDfbigA4i8tzLBJU76bt0CqOI4KLJE0ISrJwLdcgkid5zw9s85gYJIi26KKLlve9Qw45JLn00ktDAoYAWdYC7/wuC5PecsstYTFXFu7lPM2xHBc2JvjFAqqoXCS1G69BlQjoXXbZZeE8QBCVoCbbjQQBQT2uT/xt9psFFlggbC/Oqbx3Ap0kqXk0mtjlXuKKK64IAVzuk1hEloQRAcsidcO9Ga+BhXDZ7hyLHHds43322ScZO3Zs2LZDhw4NnzXXFhISBIBJnLCoNfsc15t0EiIdzOa42WWXXcKxM2LEiGT33XcPP8/n1QoS+ex7kydPDvdnnEN4tPKZ8ZlzLHJsg8A5ici111478+d5XxwfHAscbwTdCVDzXsH+1CoSPuAYqKbyWsX5knslgvLc63K88PoIluc9NpZbbrmwGDTXuax7s75eYH38+PHhHvXUU08NYwMKltIWW2yxcL9D8jbrfMrX2B+b0anzZH+8l5Ok/moQ0yL6+kVI0kBy2223JZtttlm4MafSrQhUj7344ouhUpNBYScwwCIY0QyCFQQ4qLykCjMPgiKVVfcYNGhQCP4w2GgXLoUEmajG50EAhs+PhAfVsQx4W8Wgm2ouBvTMMMDjjz8etgcDUAKXDKTiZTn9b9bX0v8yIObzIVhJdW+1IAtBDwb+fB4EGalAroYB8cyZM8Nr5XPndZMUUm9UhFJtTpCIhAqBCAITBIsJHhPQ7CZnnXVWCGRttNFGYb9sp1GjRoVgARW7VF2nEVRmfycgf/bZZ/f43qRJk0J1NEH1888/P1S/8v8EaAjG87scl+yXHCut4FxE1TGBPQJFH//4x8MxQSCsFZzvY8CiUwgMEfzppu1QFIKDeQP+VOhSyct7479jxXbcB6mkJehZ63pEBS8V5VQoU5UOgoRU4KZxfiRhEZOp3XoN6tbzJu+T8xCJkYF8b0YhBcFOvg+uF8x4OPLIIzOD71zPuWcg2J5O4BAkrYWAOPcBzAgC77Vytl4zSFg1Oyu2EklQZjDEYP5OO+0UAs21ihnitSULMx/bUXTAtSbeV3GOyML5gOr8K6+8Mtl5552TdqH4hnsHtku33muxfbg3596QxDDnpzjTtBPnqKLPk/3tXk6S+itnREhSmzF4BMGyapXj7ah6ZzAb/1YnNJuEYODATTwDhDgAz4PKV1oNMOWcIDvPw5RzBuG1AujNILlBoJ1HUeJnFVs3xBkKrbRkahQVrXkHUiRHSARlJYPUE9WqfJYEQ6jcAwEVZpYcfvjhXbe5XnrppfBvEeeP+JxUHVeKbV+yzgMEwqlApPoRBGJIRsRqWSra2b6tJiHAjAUe7Ubg8ZJLLgmvleBIO9piVKvIJQDDdmwleFvUdihKI7MOSKbceeedoUI83TaGKm6qXpdccsm6SXHajBAkTieXaGtFIIztT6CS/ZVgcbOzwTp5Deo2tJe59957Q3uoopMQ3XBvtsUWW4R7GJJ9JCSo2ua/qyG4uuOOO4ZkIwUEXGfytEjj3EObRWaUEtw/8MADk3ZoVxIiBvMpmGBmyJlnnhmOtXrYT5g5QnKR6wuzdjjHUgVPq6B2yKrmrxSvX7yOdmKf6HZsHwL+PPpC0efJ/nYvJ0n9lTMiJKnNmLZM5R2DXabFF4FWEVQGb7LJJh0ZwKt1DF6pzGUg1Y5exupOTz31VAhSMpjls+5GBH+YVUTAfOLEiW19blo2UKlIoGL99dfv8T0CN7QTIinJTIc8SGIS8C0qqC9p7tAN92bcBzSStOL8x8zJZls3ci3q1nMnCVUq7Lv19dWa9cJr/9KXvtR0uyF1v/5wLydJ/ZWJCEmSJEmSJEmSVJj68w8lSZIkSZIkSZKaZCJCkiRJkiRJkiQVxkSEJEmSJEmSJEkqjIkISZIkSZIkSZJUGBMRkiRJkiRJkiSpMCYiJEmSJEmSJElSYUxESJIkSZIkSZKkwpiIkCRJkiRJkiRJhTERIUmSJEmSJEmSCmMiQpIkSZIkSZIkFcZEhCRJkiRJkiRJKoyJCEmSJEmSJEmSVBgTEZIkSZIkSZIkqTAmIiRJkiRJkiRJUmFMREiSJEmSJEmSpMKYiJAkSZIkSZIkSYUxESFJkiRJkiRJkgpjIkKSJEmSJEmSJBXGRIQkSZIkSZIkSSqMiQhJkiRJkiRJklQYExGSJEmSJEmSJKkwJiIkSZIkSZIkSVJhTERIkiRJkiRJkqTCmIiQJEmSJEmSJEmFMREhSZIkSZIkSZIKYyJCkiRJkiRJkiQVxkSEJEmSJEmSJEkqjIkISZIkSZIkSZJUGBMRkiRJkiRJkiSpMCYiJEmSJEmSJElSUpT/AwmdPe6R8vNnAAAAAElFTkSuQmCC)\n",
    "\n",
    "70%・30%の例。振幅を2乗した確率で、測定結果0・1のどちらかを得る。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-097",
   "metadata": {},
   "source": [
    "`sample_counts`で理想的な測定を模擬。状態ベクトルを観測して読み取れるわけではない。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c875cc3a",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**測定回数の意味**  `shots=100` では同じ状態を100回準備して測った場合の結果を模擬します。`counts` は観測回数で、振幅の値そのものではありません。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "cell-098",
   "metadata": {
    "annotated_original_cell": 98,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.137793Z",
     "iopub.status.busy": "2026-10-16T04:32:28.137756Z",
     "iopub.status.idle": "2026-10-16T04:32:28.139307Z",
     "shell.execute_reply": "2026-10-16T04:32:28.139163Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'0': 75, '1': 25}\n"
     ]
    }
   ],
   "source": [
    "# このセル：measured_state は測定する量子状態、counts は100回の測定で得た0と1の回数です。\n",
    "measured_state = Statevector(psi)\n",
    "counts = sample_counts(measured_state, shots=100)\n",
    "print(counts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-099",
   "metadata": {},
   "source": [
    "理想確率と有限回の頻度を比較。100回で必ず70回・30回とは限らない。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "cell-100",
   "metadata": {
    "annotated_original_cell": 100,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.139982Z",
     "iopub.status.busy": "2026-10-16T04:32:28.139948Z",
     "iopub.status.idle": "2026-10-16T04:32:28.168605Z",
     "shell.execute_reply": "2026-10-16T04:32:28.168401Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'0': 75, '1': 25}"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# このセル：棒グラフで、理想確率と実際のサンプル頻度を比較します。\n",
    "show_sample_comparison(measured_state, shots=100)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-101",
   "metadata": {},
   "source": [
    "### 1回の測定後の状態\n",
    "\n",
    "`measure`は結果と測定後の状態を返す。結果0なら状態0、結果1なら状態1。Z基底での理想的な射影測定。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "cell-102",
   "metadata": {
    "annotated_original_cell": 102,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.169417Z",
     "iopub.status.busy": "2026-10-16T04:32:28.169369Z",
     "iopub.status.idle": "2026-10-16T04:32:28.172117Z",
     "shell.execute_reply": "2026-10-16T04:32:28.171951Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one outcome 0 state afterwards [1.+0.j 0.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：measure は1回の測定結果と、その直後の状態を返します。\n",
    "measured_state.seed(2026)\n",
    "outcome, after_measurement = measured_state.measure()\n",
    "print('one outcome', outcome, 'state afterwards', after_measurement.data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-103",
   "metadata": {},
   "source": [
    "### 回路の測定記号\n",
    "\n",
    "古典ビットに測定結果を保存。ここは回路図の確認。上のセルで測定を模擬した。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "cell-104",
   "metadata": {
    "annotated_original_cell": 104,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.172890Z",
     "iopub.status.busy": "2026-10-16T04:32:28.172825Z",
     "iopub.status.idle": "2026-10-16T04:32:28.186777Z",
     "shell.execute_reply": "2026-10-16T04:32:28.186602Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 353.921x220.733 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：measure(0,0) は量子ビット0の測定結果を古典ビット0へ保存します。\n",
    "qc_measure = QuantumCircuit(1, 1)\n",
    "qc_measure.h(0)\n",
    "qc_measure.measure(0, 0)\n",
    "show_circuit(qc_measure)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-105",
   "metadata": {},
   "source": [
    "### 位置を測る2状態模型\n",
    "\n",
    "$$\n",
    "\\hat Q=\\begin{pmatrix}-1&0\\\\0&1\\end{pmatrix}\\mathrm{cm}.\n",
    "$$\n",
    "\n",
    "基準0は左−1cm、基準1は右+1cm。2つの検出位置に限定した模型。連続的な位置全体を表す行列ではない。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "cell-106",
   "metadata": {
    "annotated_original_cell": 106,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.187557Z",
     "iopub.status.busy": "2026-10-16T04:32:28.187510Z",
     "iopub.status.idle": "2026-10-16T04:32:28.189121Z",
     "shell.execute_reply": "2026-10-16T04:32:28.188944Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q times basis 0 [-1.+0.j  0.+0.j]\n",
      "Q times basis 1 [0.+0.j 1.+0.j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：Qは左位置−1cm、右位置+1cmに対応する観測量の行列です。\n",
    "Q = np.diag([-1.0, 1.0])\n",
    "print('Q times basis 0', Q @ zero)\n",
    "print('Q times basis 1', Q @ one)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-107",
   "metadata": {},
   "source": [
    "固有値−1cm、+1cmが測定値。行列と状態の積そのものは、1回の測定結果ではない。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "cell-108",
   "metadata": {
    "annotated_original_cell": 108,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.189846Z",
     "iopub.status.busy": "2026-10-16T04:32:28.189804Z",
     "iopub.status.idle": "2026-10-16T04:32:28.191964Z",
     "shell.execute_reply": "2026-10-16T04:32:28.191772Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "left -1 cm 674\n",
      "right +1 cm 326\n"
     ]
    }
   ],
   "source": [
    "# このセル：0の観測回数を左、1の観測回数を右に対応させています。\n",
    "position_counts = sample_counts(measured_state, shots=1000)\n",
    "print('left -1 cm', position_counts.get('0', 0))\n",
    "print('right +1 cm', position_counts.get('1', 0))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-109",
   "metadata": {},
   "source": [
    "<details><summary>確認・解答例</summary>\n",
    "\n",
    "ベクトルは状態の表現。ゲートは行列による状態変換。測定は固有値の1つを確率的に得る操作。固有状態の測定値は確定する。\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-110",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 共通5：ブロッホ球\n",
    "\n",
    "球の点は量子状態。電子の空間位置ではない。北極は0、南極は1、赤道は0・1が半々。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-111",
   "metadata": {},
   "source": [
    "$$\n",
    "|\\psi\\rangle=\\sqrt{p_0}|0\\rangle+e^{i\\phi}\\sqrt{1-p_0}|1\\rangle.\n",
    "$$\n",
    "\n",
    "$p_0$は0の確率、$\\phi$は相対位相（ラジアン）。$e^{i\\phi}$は絶対値1の複素数。位相を変えても確率は同じ。Hの後に差が現れる。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b259ad9d",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**ブロッホ球で見るもの**  球の点は1量子ビットの状態です。左右の位置ではなく、振幅の大きさと相対位相を表します。右の図ではHを加えた後の測定確率が見えます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "cell-112",
   "metadata": {
    "annotated_original_cell": 112,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.192681Z",
     "iopub.status.busy": "2026-10-16T04:32:28.192626Z",
     "iopub.status.idle": "2026-10-16T04:32:28.194867Z",
     "shell.execute_reply": "2026-10-16T04:32:28.194732Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# このセル：ブロッホ球上の座標とHゲート後の測定確率を表示する関数です。\n",
    "def bloch_demo(p0=0.5, phase=0.0):\n",
    "    a, b = (np.sqrt(p0), np.exp(1j * phase) * np.sqrt(1 - p0))\n",
    "    vector = np.array([a, b])\n",
    "    point = [2 * np.real(np.conj(a) * b), 2 * np.imag(np.conj(a) * b), abs(a) ** 2 - abs(b) ** 2]\n",
    "    fig = plt.figure(figsize=(9, 3.8), layout='constrained')\n",
    "    ax = fig.add_subplot(121, projection='3d')\n",
    "    u = np.linspace(0, 2 * np.pi, 32)\n",
    "    t = np.linspace(0, np.pi, 18)\n",
    "    ax.plot_wireframe(np.outer(np.cos(u), np.sin(t)), np.outer(np.sin(u), np.sin(t)), np.outer(np.ones_like(u), np.cos(t)), color='#bdbdbd', linewidth=0.4)\n",
    "    ax.quiver(0, 0, 0, *point, color=PURPLE, linewidth=3)\n",
    "    ax.text(0, 0, 1.16, '0')\n",
    "    ax.text(0, 0, -1.18, '1')\n",
    "    ax.set(xlim=(-1.2, 1.2), ylim=(-1.2, 1.2), zlim=(-1.2, 1.2), xlabel='x', ylabel='y', zlabel='z')\n",
    "    ax.set_box_aspect([1, 1, 1])\n",
    "    ax.set_title('Bloch sphere: quantum state')\n",
    "    show_probabilities(np.abs(H_gate @ vector) ** 2, ['0', '1'], 'After H', fig.add_subplot(122))\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-113",
   "metadata": {},
   "source": [
    "まず固定図。赤道上の＋状態と、Hの後の確率。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "cell-114",
   "metadata": {
    "annotated_original_cell": 114,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.195558Z",
     "iopub.status.busy": "2026-10-16T04:32:28.195513Z",
     "iopub.status.idle": "2026-10-16T04:32:28.259018Z",
     "shell.execute_reply": "2026-10-16T04:32:28.258815Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x418 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：p0=0.5、位相=0 の場合を表示します。\n",
    "bloch_demo(0.5, 0.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-115",
   "metadata": {},
   "source": [
    "スライダーで位相を0からπへ。動かない場合は上の引数を変えて再実行。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "cell-116",
   "metadata": {
    "annotated_original_cell": 116,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.259865Z",
     "iopub.status.busy": "2026-10-16T04:32:28.259817Z",
     "iopub.status.idle": "2026-10-16T04:32:28.366500Z",
     "shell.execute_reply": "2026-10-16T04:32:28.366291Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x418 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：p0 と phase をスライダーで変更します。スライダーが使えなければ直前の bloch_demo(...) セルの引数を変更します。\n",
    "optional_sliders(bloch_demo, p0=(0.0, 1.0, 0.05), phase=(0.0, 2 * np.pi, 0.1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-117",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## チャレンジ：1つ選択\n",
    "\n",
    "共通部分を終えてから選ぶ。上級を終える必要はない。\n",
    "各課題は「変更 → 予想 → 図 → 結果の説明」で提出する。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-118",
   "metadata": {},
   "source": [
    "### Level 1｜初級：少ない測定では、どれくらいずれる？\n",
    "\n",
    "半々の状態を10・100・1000回ずつ測る。理想確率と頻度の差を比較。提出：3つの図と、有限回の揺らぎの説明。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "577fb7fe",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**チャレンジは1つで十分**  結果だけでなく「予想→実行→理由」を口頭で1文説明してもらいます。Level 1が測定、Level 2が干渉、Level 3が固有値測定です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "cell-119",
   "metadata": {
    "annotated_original_cell": 119,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.367442Z",
     "iopub.status.busy": "2026-10-16T04:32:28.367388Z",
     "iopub.status.idle": "2026-10-16T04:32:28.368910Z",
     "shell.execute_reply": "2026-10-16T04:32:28.368729Z"
    }
   },
   "outputs": [],
   "source": [
    "# このセル：|+⟩ を測定用のStatevectorにします。0と1はそれぞれ確率0.5です。\n",
    "half = Statevector(plus)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "cell-120",
   "metadata": {
    "annotated_original_cell": 120,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.369685Z",
     "iopub.status.busy": "2026-10-16T04:32:28.369600Z",
     "iopub.status.idle": "2026-10-16T04:32:28.450861Z",
     "shell.execute_reply": "2026-10-16T04:32:28.450657Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：10回、100回、1000回の測定を比べます。回数を増やすと一般に揺らぎが小さくなります。\n",
    "for shots in [10, 100, 1000]:\n",
    "    show_sample_comparison(half, shots=shots, seed=2026)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-121",
   "metadata": {},
   "source": [
    "<details><summary>確認・解答例</summary>\n",
    "\n",
    "頻度は揺らぐ。回数が増えるほど典型的な揺らぎは小さくなるが、1つの乱数例で差が必ず単調に減るとは限らない。\n",
    "種を2027・2028に変更して比較する。\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-122",
   "metadata": {},
   "source": [
    "### Level 2｜中級：位相から最後の確率を予測\n",
    "\n",
    "H → 位相 → Hの位相を0から2πまで変える。図の曲線を式と比較。提出：曲線と、位相π/2で半々になる理由。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-123",
   "metadata": {},
   "source": [
    "ヒント：最後の0の振幅は $(1+e^{i\\phi})/2$。\n",
    "絶対値の2乗を計算すると $P(0)=\\cos^2(\\phi/2)$。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "cell-124",
   "metadata": {
    "annotated_original_cell": 124,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.451769Z",
     "iopub.status.busy": "2026-10-16T04:32:28.451715Z",
     "iopub.status.idle": "2026-10-16T04:32:28.453187Z",
     "shell.execute_reply": "2026-10-16T04:32:28.453022Z"
    }
   },
   "outputs": [],
   "source": [
    "# このセル：0から2πまで81個の位相を用意し、確率を記録する空リストを作ります。\n",
    "phases = np.linspace(0, 2 * np.pi, 81)\n",
    "observed = []\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "cell-125",
   "metadata": {
    "annotated_original_cell": 125,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.454011Z",
     "iopub.status.busy": "2026-10-16T04:32:28.453966Z",
     "iopub.status.idle": "2026-10-16T04:32:28.460817Z",
     "shell.execute_reply": "2026-10-16T04:32:28.460606Z"
    }
   },
   "outputs": [],
   "source": [
    "# このセル：各位相に対して H→P(phase)→H の回路を実行し、0の確率を保存します。\n",
    "for phase in phases:\n",
    "    trial = QuantumCircuit(1)\n",
    "    trial.h(0)\n",
    "    trial.p(phase, 0)\n",
    "    trial.h(0)\n",
    "    observed.append(Statevector.from_instruction(trial).probabilities()[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "cell-126",
   "metadata": {
    "annotated_original_cell": 126,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.461607Z",
     "iopub.status.busy": "2026-10-16T04:32:28.461522Z",
     "iopub.status.idle": "2026-10-16T04:32:28.490161Z",
     "shell.execute_reply": "2026-10-16T04:32:28.489990Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 704x528 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：Qiskitの計算結果と、理論式 cos²(phase/2) を重ねて描きます。\n",
    "plt.plot(phases, observed, label='Qiskit')\n",
    "plt.plot(phases, np.cos(phases / 2) ** 2, '--', label='Formula')\n",
    "plt.xlabel('Relative phase (rad)')\n",
    "plt.ylabel('P(0)')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "cell-127",
   "metadata": {
    "annotated_original_cell": 127,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.491044Z",
     "iopub.status.busy": "2026-10-16T04:32:28.490995Z",
     "iopub.status.idle": "2026-10-16T04:32:28.492372Z",
     "shell.execute_reply": "2026-10-16T04:32:28.492175Z"
    }
   },
   "outputs": [],
   "source": [
    "# このセル：計算した確率と数式が一致するか検証します。\n",
    "assert np.allclose(observed, np.cos(phases / 2) ** 2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-128",
   "metadata": {},
   "source": [
    "### Level 3｜上級：Xの固有値を実験で読む\n",
    "\n",
    "Xの測定値は±1。Hを入れてから0・1を測ると、Xの測定に対応する。＋、−、0の状態で結果を比較。提出：入力ごとの±1の確率表。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-129",
   "metadata": {},
   "source": [
    "基底の変換：$HXH=Z$。Hの後の0を $+1$、1を $-1$ と読む。これはXを状態変換のゲートとして使う操作とは区別する。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "cell-130",
   "metadata": {
    "annotated_original_cell": 130,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.493125Z",
     "iopub.status.busy": "2026-10-16T04:32:28.493082Z",
     "iopub.status.idle": "2026-10-16T04:32:28.573645Z",
     "shell.execute_reply": "2026-10-16T04:32:28.573425Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plus P(+1), P(-1) = [1. 0.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minus P(+1), P(-1) = [0. 1.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zero P(+1), P(-1) = [0.5 0.5]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：|+⟩、|−⟩、|0⟩ のX測定を、Hの後の0/1測定で模擬します。\n",
    "for name, vector in {'plus': plus, 'minus': np.array([1, -1]) / np.sqrt(2), 'zero': zero}.items():\n",
    "    before = Statevector(vector)\n",
    "    after = Statevector(H_gate @ before.data)\n",
    "    print(name, 'P(+1), P(-1) =', after.probabilities())\n",
    "    show_sample_comparison(after, shots=500)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "cell-131",
   "metadata": {
    "annotated_original_cell": 131,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.574512Z",
     "iopub.status.busy": "2026-10-16T04:32:28.574460Z",
     "iopub.status.idle": "2026-10-16T04:32:28.575894Z",
     "shell.execute_reply": "2026-10-16T04:32:28.575719Z"
    }
   },
   "outputs": [],
   "source": [
    "# このセル：HXH=Z を行列計算で検証します。\n",
    "assert np.allclose(H_gate @ X @ H_gate, Z)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-132",
   "metadata": {},
   "source": [
    "<details><summary>確認・解答例</summary>\n",
    "\n",
    "＋：+1を確率1。−：−1を確率1。0：±1を半々。\n",
    "固有状態では固有値が確定。一般の状態では対応する固有値が確率的に得られる。\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-133",
   "metadata": {},
   "source": [
    "## 確認して終了\n",
    "\n",
    "- 振幅と確率を区別できる。\n",
    "- 行列の作用を、入力 → 出力として読める。\n",
    "- 位相だけでは変わらない確率が、干渉の後に変わる。\n",
    "- 固有値の計算と1回の測定を区別できる。\n",
    "\n",
    "次のSQDでは、エネルギーの最小固有値を求める。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-134",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 復習用：位相ゲート・回転・CNOT\n",
    "\n",
    "上級や、次のSQD実習に進む前の確認用。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-135",
   "metadata": {},
   "source": [
    "### P：下の成分の位相を調整\n",
    "\n",
    "$$\n",
    "P(\\phi)=\\begin{pmatrix}1&0\\\\0&e^{i\\phi}\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "Sは$\\phi=\\pi/2$、Tは$\\phi=\\pi/4$、Zは$\\phi=\\pi$。符号反転は位相πの例。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c22ba777",
   "metadata": {
    "added_explanation": true
   },
   "source": [
    "**以下は時間が余ったときの復習用**  Pは位相、Ryは重ね合わせの割合、CNOTは2量子ビットの条件付き反転です。共通部分の理解には必須ではありません。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "cell-136",
   "metadata": {
    "annotated_original_cell": 136,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.576616Z",
     "iopub.status.busy": "2026-10-16T04:32:28.576572Z",
     "iopub.status.idle": "2026-10-16T04:32:28.578101Z",
     "shell.execute_reply": "2026-10-16T04:32:28.577956Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7071+0.j     0.    +0.7071j]\n"
     ]
    }
   ],
   "source": [
    "# このセル：Hの後に位相ゲートP(π/2)を作用させた状態ベクトルを表示します。\n",
    "qc_p = QuantumCircuit(1)\n",
    "qc_p.h(0)\n",
    "qc_p.p(np.pi / 2, 0)\n",
    "print(Statevector.from_instruction(qc_p).data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-137",
   "metadata": {},
   "source": [
    "### Ry：重ね合わせの割合を調整\n",
    "\n",
    "$$\n",
    "R_y(\\theta)|0\\rangle=\\cos(\\theta/2)|0\\rangle+\\sin(\\theta/2)|1\\rangle.\n",
    "$$\n",
    "\n",
    "$\\theta$は角度。π/2なら半々、πなら1。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "cell-138",
   "metadata": {
    "annotated_original_cell": 138,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.578875Z",
     "iopub.status.busy": "2026-10-16T04:32:28.578818Z",
     "iopub.status.idle": "2026-10-16T04:32:28.632976Z",
     "shell.execute_reply": "2026-10-16T04:32:28.632769Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x374 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：Ry(π/2) により、0と1の確率が半分ずつになる様子を描きます。\n",
    "qc_ry = QuantumCircuit(1)\n",
    "qc_ry.ry(np.pi / 2, 0)\n",
    "state_panel(Statevector.from_instruction(qc_ry).data, 'Ry(pi/2) |0>')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-139",
   "metadata": {},
   "source": [
    "### CNOT：制御が1なら、対象を反転\n",
    "\n",
    "2量子ビットの表示順は$q_1q_0$。右端が量子ビット0。\n",
    "`cx(0,1)`：0が制御、1が対象。01を入力すると11になる。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "cell-140",
   "metadata": {
    "annotated_original_cell": 140,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.633805Z",
     "iopub.status.busy": "2026-10-16T04:32:28.633747Z",
     "iopub.status.idle": "2026-10-16T04:32:28.650296Z",
     "shell.execute_reply": "2026-10-16T04:32:28.650111Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 373.974x220.733 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 1.0}\n"
     ]
    }
   ],
   "source": [
    "# このセル：Xで |01⟩ を準備し、制御ビットが1のCNOTで |11⟩ に変えます。\n",
    "qc_cx = QuantumCircuit(2)\n",
    "qc_cx.x(0)\n",
    "qc_cx.cx(0, 1)\n",
    "show_circuit(qc_cx)\n",
    "print({str(bits): round(float(p), 6) for bits, p in Statevector.from_instruction(qc_cx).probabilities_dict().items()})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-141",
   "metadata": {},
   "source": [
    "### HとCNOTでBell状態\n",
    "\n",
    "$$\n",
    "|\\Phi^+\\rangle=\\frac{|00\\rangle+|11\\rangle}{\\sqrt2}.\n",
    "$$\n",
    "\n",
    "00と11を半々で測る。1回に両方の結果を得るわけではない。この状態は1量子ビット状態2つの積では表せない。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "cell-142",
   "metadata": {
    "annotated_original_cell": 142,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.651123Z",
     "iopub.status.busy": "2026-10-16T04:32:28.651061Z",
     "iopub.status.idle": "2026-10-16T04:32:28.666247Z",
     "shell.execute_reply": "2026-10-16T04:32:28.666075Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 373.974x220.733 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# このセル：HとCNOTを組み合わせ、Bell状態 (|00⟩+|11⟩)/√2 を作ります。\n",
    "qc_bell = QuantumCircuit(2)\n",
    "qc_bell.h(0)\n",
    "qc_bell.cx(0, 1)\n",
    "show_circuit(qc_bell)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-143",
   "metadata": {},
   "source": [
    "準備した状態を繰り返し測定し、00・11を確認。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "cell-144",
   "metadata": {
    "annotated_original_cell": 144,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.667020Z",
     "iopub.status.busy": "2026-10-16T04:32:28.666970Z",
     "iopub.status.idle": "2026-10-16T04:32:28.698426Z",
     "shell.execute_reply": "2026-10-16T04:32:28.698239Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x374 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'00': 100, '11': 100}"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# このセル：Bell状態を200回測定し、00と11だけが現れることを確認します。\n",
    "bell_state = Statevector.from_instruction(qc_bell)\n",
    "show_sample_comparison(bell_state, shots=200)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "cell-145",
   "metadata": {
    "annotated_original_cell": 145,
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.699260Z",
     "iopub.status.busy": "2026-10-16T04:32:28.699208Z",
     "iopub.status.idle": "2026-10-16T04:32:28.700726Z",
     "shell.execute_reply": "2026-10-16T04:32:28.700538Z"
    }
   },
   "outputs": [],
   "source": [
    "# このセル：Bell状態の理想確率が [0.5, 0, 0, 0.5] になっているか検証します。\n",
    "assert np.allclose(bell_state.probabilities(), [0.5, 0, 0, 0.5])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5523b46f",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 実機実行：IBM Quantumで測定する（任意）\n",
    "\n",
    "この節は、IBM Quantum PlatformのアカウントとQuantum Computeインスタンスを利用して、**実際の量子プロセッサ（QPU）**へ回路を送ります。実行枠の消費や課金が発生する可能性があるため、利用プラン・残り枠を確認してください。\n",
    "\n",
    "APIキーはNotebookのコードや共有ファイルに記入せず、入力欄から渡します。**デフォルトではジョブを送信しません。** 実行する場合に限り `RUN_ON_QPU = True` に変更してください。\n",
    "\n",
    "IBM公式ガイド：[アカウント設定](https://quantum.cloud.ibm.com/docs/en/guides/initialize-account) ／ [Samplerの実行](https://quantum.cloud.ibm.com/docs/en/guides/get-started-with-sampler)\n",
    "\n",
    "\n",
    "「すべて実行」ではこの節をスキップします。実機を使う場合だけ、次のセルの `RUN_ON_QPU` を `True` に変更し、接続から順に実行してください。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "5473fa3a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.701515Z",
     "iopub.status.busy": "2026-10-16T04:32:28.701433Z",
     "iopub.status.idle": "2026-10-16T04:32:28.703051Z",
     "shell.execute_reply": "2026-10-16T04:32:28.702889Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "実機セクションはスキップしました。接続・ジョブ送信は行いません。\n"
     ]
    }
   ],
   "source": [
    "# 実機を使うときだけ True にし、この節を上から実行します。\n",
    "RUN_ON_QPU = False\n",
    "service = backend = isa_circuit = qpu_counts = None\n",
    "if RUN_ON_QPU:\n",
    "    %pip -q install \"qiskit-ibm-runtime==0.50.0\"\n",
    "else:\n",
    "    print(\"実機セクションはスキップしました。接続・ジョブ送信は行いません。\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5062dfaf",
   "metadata": {},
   "source": [
    "### 1. アカウントに接続\n",
    "\n",
    "IBM Quantum PlatformでAPIキーを確認してください。利用するインスタンスのCRNが分かる場合は入力します。CRNの欄は空欄でも自動選択できます。\n",
    "\n",
    "`getpass` で入力したAPIキーはセルの出力には表示されません。Notebookを共有する場合、念のため実行出力を消してから共有してください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "91e26b9f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.703748Z",
     "iopub.status.busy": "2026-10-16T04:32:28.703704Z",
     "iopub.status.idle": "2026-10-16T04:32:28.705311Z",
     "shell.execute_reply": "2026-10-16T04:32:28.705146Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "実機接続はオフです。認証情報の入力は不要です。\n"
     ]
    }
   ],
   "source": [
    "if RUN_ON_QPU:\n",
    "    from getpass import getpass\n",
    "    from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "    \n",
    "    ibm_api_key = getpass(\"IBM Cloud APIキー（画面には表示されません）: \")\n",
    "    ibm_crn = input(\"インスタンスCRN（自動選択する場合はEnter）: \").strip()\n",
    "    \n",
    "    service = QiskitRuntimeService(\n",
    "        channel=\"ibm_quantum_platform\",\n",
    "        token=ibm_api_key,\n",
    "        **({\"instance\": ibm_crn} if ibm_crn else {})\n",
    "    )\n",
    "    del ibm_api_key\n",
    "    print(\"IBM Quantum接続を確認しました。\")\n",
    "else:\n",
    "    print(\"実機接続はオフです。認証情報の入力は不要です。\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83229745",
   "metadata": {},
   "source": [
    "### 2. 実行する量子プロセッサを選ぶ\n",
    "\n",
    "利用可能なQPUから、必要な量子ビット数を満たすものを選びます。`backend` が実際の計算機、`pass_manager` は回路をその計算機の命令へ変換する処理です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "e5aaf7d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.706003Z",
     "iopub.status.busy": "2026-10-16T04:32:28.705952Z",
     "iopub.status.idle": "2026-10-16T04:32:28.707538Z",
     "shell.execute_reply": "2026-10-16T04:32:28.707383Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QPUの選択・回路の変換はスキップしました。\n"
     ]
    }
   ],
   "source": [
    "if RUN_ON_QPU and service is not None:\n",
    "    from qiskit.transpiler import generate_preset_pass_manager\n",
    "    from qiskit_ibm_runtime.executor_sampler import Sampler\n",
    "    \n",
    "    backend = service.least_busy(\n",
    "        operational=True, simulator=False, min_num_qubits=2\n",
    "    )\n",
    "    print(\"QPU:\", backend.name)\n",
    "    \n",
    "    qpu_circuit = qc_bell.copy()\n",
    "    qpu_circuit.measure_all()\n",
    "    pass_manager = generate_preset_pass_manager(backend=backend, optimization_level=1)\n",
    "    isa_circuit = pass_manager.run(qpu_circuit)\n",
    "    print(\"回路の量子ビット数:\", qpu_circuit.num_qubits)\n",
    "else:\n",
    "    print(\"QPUの選択・回路の変換はスキップしました。\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1b284fd",
   "metadata": {},
   "source": [
    "### 3. QPUで測定する\n",
    "\n",
    "`RUN_ON_QPU` を `True` にすると、実際に量子コンピュータへジョブを送信します。初期設定は `False` です。`shots=128` は同じ回路の測定を128回行う指定です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "663de87a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.708348Z",
     "iopub.status.busy": "2026-10-16T04:32:28.708305Z",
     "iopub.status.idle": "2026-10-16T04:32:28.709823Z",
     "shell.execute_reply": "2026-10-16T04:32:28.709645Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "送信していません。実機に送る場合は RUN_ON_QPU = True に変更してください。\n"
     ]
    }
   ],
   "source": [
    "qpu_counts = None\n",
    "\n",
    "if RUN_ON_QPU and isa_circuit is not None:\n",
    "    real_sampler = Sampler(mode=backend)\n",
    "    job = real_sampler.run([isa_circuit], shots=128)\n",
    "    print(\"Job ID:\", job.job_id())\n",
    "    qpu_counts = job.result()[0].data.meas.get_counts()\n",
    "    print(\"実機の測定結果:\", qpu_counts)\n",
    "else:\n",
    "    print(\"送信していません。実機に送る場合は RUN_ON_QPU = True に変更してください。\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6831cbd6",
   "metadata": {},
   "source": [
    "### 4. 結果の見方\n",
    "\n",
    "Bell状態の理想測定では `00` と `11` だけが約半数ずつ出ます。実機ではノイズのため `01` や `10` が現れる場合があります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "7e1ee3f5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:32:28.710511Z",
     "iopub.status.busy": "2026-10-16T04:32:28.710474Z",
     "iopub.status.idle": "2026-10-16T04:32:28.711887Z",
     "shell.execute_reply": "2026-10-16T04:32:28.711753Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "実機ジョブは未実行です。\n"
     ]
    }
   ],
   "source": [
    "if qpu_counts is None:\n",
    "    print(\"実機ジョブは未実行です。\")\n",
    "else:\n",
    "    total = sum(qpu_counts.values())\n",
    "    for bits in (\"00\", \"01\", \"10\", \"11\"):\n",
    "        n = qpu_counts.get(bits, 0)\n",
    "        print(f\"{bits}: {n} 回 ({n / total:.1%})\")"
   ]
  }
 ],
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  "qff": {
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   "challenge_levels": [
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    "中級",
    "上級"
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  "qff_repair": {
   "date": "2026-10-16",
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