{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "F_Xa8rkzH9dG",
        "outputId": "ac2a16c5-4920-4b8b-9ba4-17983ebddfca"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "    ╔════════════════════════════════════════════╗\n",
            "    ║     KAORU-RSA: SIMPLE SCALING TEST         ║\n",
            "    ╚════════════════════════════════════════════╝\n",
            "    \n",
            "============================================================\n",
            "  KAORU O(1) READOUT TEST: 1 to 256 bits\n",
            "============================================================\n",
            "\n",
            "    Bits    Readout (ns) Status\n",
            "----------------------------------------\n",
            "       1           228 ns  ✓\n",
            "       2           135 ns  ✓\n",
            "       4           132 ns  ✓\n",
            "       8           135 ns  ✓\n",
            "      16           138 ns  ✓\n",
            "      32           140 ns  ✓\n",
            "      64           212 ns  ✓\n",
            "     128           225 ns  ✓\n",
            "     256           216 ns  ✓\n",
            "----------------------------------------\n",
            "\n",
            "  Mean:   173 ns\n",
            "  StdDev: 42 ns\n",
            "  Min:    132 ns\n",
            "  Max:    228 ns\n",
            "\n",
            "  Bits: 1 → 256 (×256)\n",
            "  Time: ×1.7\n",
            "\n",
            "  ★ O(1) CONFIRMED! ★\n",
            "\n",
            "============================================================\n",
            "  TEST CON REGISTROS GRANDES\n",
            "============================================================\n",
            "\n",
            "        Size    Readout (ns)\n",
            "-----------------------------------\n",
            "       1,000           204 ns\n",
            "      10,000           204 ns\n",
            "     100,000           244 ns\n",
            "   1,000,000           241 ns\n",
            "-----------------------------------\n",
            "  Size ×1,000, Time ×1.2\n",
            "\n",
            "============================================================\n",
            "  FACTORIZATION TEST\n",
            "============================================================\n",
            "\n",
            "           N   Bits              Factors      Readout\n",
            "-------------------------------------------------------\n",
            "          15      4                  3×5       1554ns ✓\n",
            "          77      7                 7×11        914ns ✓\n",
            "         143      8                11×13        372ns ✓\n",
            "         437      9                19×23        270ns ✓\n",
            "       1,591     11                37×43        251ns ✓\n",
            "      10,403     14              101×103        258ns ✓\n",
            "      25,217     15              151×167        303ns ✓\n",
            "      41,989     16              199×211        244ns ✓\n",
            "      95,477     17              307×311        284ns ✓\n",
            "     410,881     19              641×641        383ns ✓\n",
            "   1,022,117     20            1009×1013        456ns ✓\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 3 Axes>"
            ],
            "image/png": 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SggYNGgDI7l98/PjxKotoOX2258gp9ueW0xUHALEYDWT33z1u3DilR+5+vXMrX7485s+fj3HjxqFChQoAgNjYWHTs2BHHjh1TOY+3tzeOHj2KFy9e4M8//8T06dOVujnJ6aIlx86dOxX6pu/du7f4vE+fPuLz9PR0bNy4UeVyCyvv9si7vdRNMzY2LpFiuTq5C81F1aRJE8ybNw+ffPKJ+H64ePEiPD098fTpU4XYFy9eaNxuTlH/8ePH6Nq1a4EFdCD7CxMg+7OTm4ODg8Jwzvstr7z55Y3LO5z7fZVb7tc1J6eyVJjXHXjz2o8aNQoDBgyAgYEB0tLScOLECfz8888YO3YsWrRogfr167NPdCIiIqI8eCU6ERERvbOmTJmCixcvYtmyZQCy+3b28vLCsWPH4O7urhB77tw5hRsj/v3332qv1oyNjcX+/fvFK27btGmjUEDetm0bhgwZojTf77//rjDcpk0btbl/+umnqFKlCsaNG4eWLVuK/W/Pnj0b/fv3V8jf3t5eYd6oqCjUrFlTHE5KSlK4YjlvfGFYWlriq6++AgAMGzYMDRs2RHJyMrKysjBixAhcu3YNhoaqT0GtrKzg5+cHPz8/TJs2DUOHDhX7VE9MTMTTp0/FgmfuLzQA4MMPP1Sb05o1a/DFF18UeZ1y5N0e27ZtU9luREQErl69Kg63bNlS7Ac87005X758me+XJUWRu7ha1G1Zp04dsV/vdu3aiV9MxMTEYNKkSVi1apUYm/sLgjp16uTbB3tOH9p79uxBSkqKOP7777/H0KFDYWVlhRs3bqBOnTpK81pbWysMx8bGKgznLe6ryi8nLvfV+nnny+nvO/fNYYHsL5rKlSsHALh9+7bKZZWmvOsVGBiYbx/lVapUAZD9q5V169bh+++/x5kzZxAREYGIiAjs2LEDL1++xLVr1/D1119j7dq1JZk+ERERkV7hlehERET0zpJIJFi6dClGjRoljrt//z68vLxw69Ythdi8RduC5I4fNGiQwtXgM2fOVLrS8/r161iyZIk4bGdnh4CAgAKXY2pqqnCVdnp6OmbNmqUQ07x5c4XhH374QeHK82+//VbhKtvc8dOnT4cgCEqP3F2rqFOtWjWxoA5kF5fzXhUeGBgo3gQzL3Nzc/G5VCqFhYUFgOyrmHPf6LIgly9fVihqA9kFRYlEAolEovGNN6tUqaJQrD99+jQ2b96sEJOeno7Ro0crdEvz+eefi88rVaqkcKX/gwcPNF4PTeVuM/evLYqqd+/e8PLyEofXrl2Lu3fvisO5u/V58uQJ+vTpg6+++krhMWrUKLi7u4vvrefPnyssY/DgweJNN/N+mZTj/fffV/jiKvd7KSMjQ+18ebsdyl0czsrKwoYNG8RhGxsb1KhRA4By0f7s2bMAALlcrnADYFVyf1GU+8sCbapRo4bClwGvX79Wet2/+uorDBw4EO7u7uIvZyIiIpCSkgJ7e3t89NFHGD9+PFatWoVvvvlGbCv3zUXz/pKlpNaHiIiISJfxSnQiIiJ65y1cuBAymQxz584FADx69Ei8Ir1WrVpITU1V6H/bzc0NzZo1U2rn33//xY0bNwBk98X97Nkz2NnZoUqVKpgxYwYmTpwIILs/7rp166J3796oXLkyIiMjsXnzZrGwLZFIsGzZMoUicn68vb3RsmVLse/yDRs2YPr06WIf5A0aNFCYfuTIEbi4uKBWrVp4+PAhoqKixLYsLS3Rv3//Qr1++fnyyy/x/fffIykpCQDw3XffYcCAAeJVvuvWrcO6devg7u6O1q1bo2rVqpBIJPjnn3+wfft2sR1PT0/xKuB169aJfdMDQOfOncVpOeRyObZu3SoOh4aGKnUJUxQ//vgjWrRogYSEBADZ/XJv3rwZzZo1Q1JSErZv365wlXKnTp3Qs2dPcVgmk6FJkybitrh06ZLK99Ly5ctx584dAFDqkz73FxPDhw9X+tXExYsXxef5/ZqhMCZPnoyTJ08CyC48f/fdd/j5558BACNHjsSKFSuQmpqKFy9eoGHDhvj444/h7OyMpKQk3LhxAydOnEB8fDyioqJQvnx5sVCdo2PHjvD398fVq1exbds2lTk4OTnB398f+/fvB5D9Pk9MTETDhg3x559/4vr16yrna9CgAdq1a4ejR48CAObNm4e7d++iTp06OHTokEKf6V9++aX43mzcuDEkEon4BVP37t3h4+Oj9EsDVSpVqiR26fP999/j+fPnMDU1RaNGjbR23wKpVIoxY8Zg8uTJALK/fLh79y4+/PBDWFhYICYmBhcvXsS5c+fQunVrdOvWDUD2/m79+vVo164d3NzcUKFCBbx48QLr1q0T2879BUKlSpUUlhsUFARfX18YGhqiS5cueO+997SyPkREREQ6razuaEpERERU2o4fPy4AEB+hoaEK06dMmaIw3cHBQbh69aqwefNmhfEbNmxQ2f7Ro0cV4hYtWqQwffbs2YKBgYFCTN5HuXLlhHXr1im1PW3aNIW4qKgohel79+5VmD58+HCF6Xfv3hWqVKmS77LNzMyEffv2Ffp19fLyEttwdXVVmv7VV18pLOe3334Tp+WXT87DxsZG+Pfff8V5atasKU6rXr262rzatGmjsC0zMjLEaa6uruK0wMDAQq3v+fPnBRcXlwLz7t27t5CUlKQ0f+5tOXDgQJXLyP2a5vc4fvy4wnyvXr0SjI2NBQCCRCIR7t27p/F65W5X1WvStGlTcbqxsbHw4MEDcdqOHTsEMzOzAvPNed+mp6cL9erVUxkTGBiodh3v3r0rODg4qJwv72uW25MnT4TatWvnm1tAQIDCe0QQBKF///4qYzt06JDvvmT06NEq5wsKCtJ4e2iyXbKysoQBAwYU+Lp7eXmJ83z22Wf5xkqlUmHHjh0Ky2nUqJHK2K1btxZ6fYiIiIj0EbtzISIiIvq/mTNnYubMmeJwbGws2rZtq9A1i5WVFbp3765y/rZt24r9DgPKXcBMnDgRERERGDt2LBo1agQrKysYGhrCxsYGLVq0wNSpU3Hnzh0MGDCg0Ll37NhRvMkoAKxevVqhyxg3Nzf8888/+O6779CyZUuUL18eBgYGMDc3R7169TBq1ChcvXoVHTp0KPSyCzJ27FjIZDJxePbs2eLVvZcuXcL8+fPRsWNH1KpVC7a2tjAwMICFhQUaNWqE8ePH4/r162Jfz2fPnsV///0ntjV48GC1y809LTY2Fvv27dPK+jRt2hT//fcfli1bBl9fXzg6OsLIyAhmZmaoXr06Bg0ahFOnTmHz5s0wMzNTmn/QoEHi1c67d+9GRkaGVvICsvsaT09PBwC0b98eLi4uWms755cUQHa3NfPmzROHu3btimvXrmHMmDGoV68ezM3NYWBgAFtbW3h4eGDcuHH4+++/xc+HkZERjh07hkGDBsHW1hYymQx169bFzz//nG9XQW5ubjh79ix69uwJa2trmJqawsPDA3v27Mm3Wx5HR0dcuHAB33//PTw8PMTPnr29Pfz8/LBlyxZs27ZNqb/+X3/9FV999ZXYDc97772HefPmYdeuXfm+Vt9++y2+/PJLVK5cWewPvyRIpVKsW7cO+/btQ0BAACpXrgxjY2PIZDK4urqic+fOWLRokUK3Q0OHDsWECRPg6ekJZ2dnmJiYwNjYGM7Ozvj4449x8uRJdO3aVWE527dvR7du3WBjY6P2XhBEREREbzOJIOTqAJOIiIiIiEpcx44dxW5Jdu/ejc6dO2ul3Y8++gi7d+8GkH3jU0361SciIiIiovyxiE5EREREVMouXryIZs2aQRAEtGvXDkeOHCl2m3fu3EGNGjWQlZWFhg0b4tKlS7xqmIiIiIhIC9idCxERERFRKWvSpAk+/vhjAMDRo0cVbgZaVD/88IN4w9U5c+awgE5EREREpCW8Ep2IiIiIiIiIiIiISA1eiU5EREREREREREREpAaL6EREREREREREREREarCITkRERERERERERESkBovoRERERERERERERERqsIhORERERERERERERKQGi+hERERERERERERERGqwiE5EREREREREREREpAaL6EREREREREREREREarCITkRERERERERERESkBovoRERERERERERERERqsIhORERERERERERERKQGi+hERERERERERERERGqwiE5EREREREREREREpAaL6EREREREREREREREarCITkRERERERERERESkBovoRERERERERERERERqsIhORERERERERERERKQGi+hERERERERERERERGqwiE5EREREREREREREpAaL6EREREREREREREREarCITkRlIjo6GhKJBAsWLCgwdvr06ZBIJKWQFRERkX7z9vaGt7d3WaehNXK5HHXr1sW3335b1qmUiBYtWmD8+PFlnQYREWlo0KBBqFKlyjuzXF0lkUgwffr0sk6D3jEsohPpgaSkJEybNg1+fn6wsbGBRCLBmjVrNJ4/JSUFS5cuhY+PDypWrAgLCws0atQIy5cvR1ZWlkJsTnFb1WPLli1KbcvlcixfvhwNGzaEqakpbG1t8cEHH+Cff/4p7mrna/bs2di5c2eJLoOIiEremjVrIJFIcPHixbJORSty1ifnYWhoiEqVKmHQoEF49OhRWaen0pkzZzB9+nTEx8eXdSpKNm/ejAcPHiA4OFgcV5jzIm9vb9StW1dp/NGjR1GuXDm8//77ePHihcp5z58/jxEjRqBx48YwMjJS+4V+7nOnWbNmqYzp168fJBIJzM3NFcZPmDABS5cuRUxMjMr5iIjeBnmPjbkfX3/9tVaX9fjxY0yfPh1XrlzRarulQRdzz1sfkEqlsLGxgb+/P8LCwso6vRK1bNmyQtVd6O1nWNYJEFHBnj17hhkzZsDFxQUNGjTAiRMnCjX/3bt3MXLkSLRr1w5jxoyBpaUlDh48iBEjRuDs2bNYu3at0jx9+vRBhw4dFMZ5eHgoxQ0ZMgQbN27EwIEDERwcjOTkZFy+fBmxsbGFyjE/U6ZMUTq5mj17Nnr06IGuXbtqbTlERETaMmPGDLi5uSE1NRVnz57FmjVr8Ndff+HatWswMTEpseUeOnSo0POcOXMGISEhGDRoEKytrbWfVDHMnz8fvXv3hpWVlTiuuOdFx44dQ+fOnVGjRg0cOXIENjY2KuP279+PX3/9FfXr10fVqlVx69atfNs1MTHB5s2bMWXKFIXxycnJ2LVrl8rt/tFHH8HS0hLLli3DjBkzCrUeRET6JufYmJuqLzqL4/HjxwgJCUGVKlXQsGFDrbYNAL/88gvkcrnW2wXyz70kl6uJnPpAVlYWbt26hWXLlqFt27a4cOEC6tWrV2Z5laRly5bBzs4OgwYNKutUSEewiE6kBypWrIgnT57A0dERFy9eRNOmTQs1v6OjI/7991/UqVNHHPfZZ59hyJAhCA0NxTfffINq1aopzPP++++jf//++bb7+++/Y+3atdi+fTu6detWqJwKw9DQEIaG3F0REVHhZWZmQi6Xw9jYuFSX6+/vjyZNmgAAPvnkE9jZ2WHu3LnYvXs3evbsWWLLLe31zE9KSgrKlStX5PkvX76Mf/75B99//73C+OKcF508eRKdO3fGe++9l28BHQCGDx+OCRMmwNTUFMHBwQUW0Tt06IDt27fjn3/+QYMGDcTxu3btQnp6Ovz8/HDs2DGFeaRSKXr06IF169YhJCSE3dcR0Vst97FR3yQnJ8PMzAxGRkZlsvyyWm6OvPWBNm3awN/fH8uXL8eyZcvKMDOi0sPuXIj0gEwmg6OjY5Hnt7OzUyig58gpfN+8eVPlfMnJyUhPT1fb7g8//IBmzZqhW7dukMvlSE5OLlJ+CxcuhKurK0xNTeHl5YVr164pTM/bJ7pEIkFycjLWrl0r/qws59vhV69eYdSoUahSpQpkMhkcHBzw4Ycf4tKlS0XKjYiIyl56ejqmTp2Kxo0bw8rKCmZmZmjTpg2OHz+uEJf7fhuLFi2Cu7s7ZDIZbty4AQA4ceIEmjRpAhMTE7i7u2PlypVq77uxYcMGNG7cGKamprCxsUHv3r3x4MGDIq9DmzZtAAB37txRGP/ff/+hR48esLGxgYmJCZo0aYLdu3crzX/16lV4eXnB1NQUlStXxqxZsxAaGgqJRILo6GgxTlWf6D/99BPq1KmDcuXKoXz58mjSpAk2bdoEIPsYO27cOACAm5ubeFzN3aYmr0VOtynh4eHw9PREuXLlMGnSJADAxYsX4evrCzs7O5iamsLNzQ1Dhgwp8DXbuXMnjI2N4enpqTC+qOdFp0+fRseOHVGtWjUcOXIEtra2+cZXqFABpqamGrfv4eEBNzc38bXNsXHjRrHrGVU+/PBD3Lt3T6d+vk9EVJru3buHESNGoEaNGmIXoR9//LHCsShHfHw8Ro8eLf6/V7lyZQwcOBDPnj3DiRMnxC9WBw8eLB7TcnfJsXXrVvGYZmdnh/79+yt1tzZo0CCYm5vjzp076NChAywsLNCvXz9xWu6+yb29vdV2VZOz3BcvXuCrr75CvXr1YG5uDktLS/j7+yt0gVpQ7qr6RE9OTsbYsWPh7OwMmUyGGjVqYMGCBRAEQSFOIpEgODgYO3fuRN26dSGTyVCnTh0cOHBA002kRN15TXx8PEaNGiXmVK1aNcydO1fpKvoFCxagZcuWsLW1hampKRo3boxt27YpLSctLQ2jR4+Gvb09LCws0KVLFzx8+FBlTpcvX4a/vz8sLS1hbm6Odu3a4ezZswox6s77crocynnPValSBdevX8fJkyfFbfE23XOGioaXdhK9w3L637Szs1OaFhISgnHjxkEikaBx48b49ttv4ePjI05PTEwU+wqdNGkSfvrpJyQlJcHNzQ3fffedxlfZrVu3Dq9evUJQUBBSU1OxePFifPDBB/j3339RoUIFlfOsX78en3zyCZo1a4Zhw4YBANzd3QEAn3/+ObZt24bg4GDUrl0bz58/x19//YWbN2/i/fffL9TrQ0REuiExMRG//vor+vTpg08//RSvXr3CqlWr4Ovri/Pnzyv95Dk0NBSpqakYNmwYZDIZbGxscPnyZfj5+aFixYoICQlBVlYWZsyYAXt7e6Xlffvtt/jmm2/Qs2dPfPLJJ4iLi8NPP/0ET09PXL58uUhdnuT8U1a+fHlx3PXr19GqVStUqlQJX3/9NczMzPD777+ja9eu+OOPP8Qvux89eoS2bdtCIpFg4sSJMDMzw6+//gqZTFbgcn/55Rd88cUX6NGjB7788kukpqbi6tWrOHfuHPr27Yvu3bvj1q1b2Lx5MxYuXCieE+S8LoV5LZ4/fw5/f3/07t0b/fv3R4UKFRAbGwsfHx/Y29vj66+/hrW1NaKjo7F9+/YCcz9z5gzq1q2rlavv/v77b3To0AFubm44evSoynMfbejTpw82bNiA7777DhKJBM+ePcOhQ4ewfv16tcWKxo0bizk2atSoRPIiItIFCQkJePbsmcI4Ozs7XLhwAWfOnEHv3r1RuXJlREdHY/ny5fD29saNGzfEXzUlJSWhTZs2uHnzJoYMGYL3338fz549w+7du/Hw4UPUqlULM2bMwNSpUzFs2DCx0NuyZUsA2YXSwYMHo2nTppgzZw6ePn2KxYsX4++//1Y6pmVmZsLX1xetW7fGggUL1P6yavLkyfjkk08Uxm3YsAEHDx6Eg4MDgOzuVXfu3ImPP/4Ybm5uePr0KVauXAkvLy/cuHEDTk5OBeaelyAI6NKlC44fP46hQ4eiYcOGOHjwIMaNG4dHjx5h4cKFCvF//fUXtm/fjhEjRsDCwgI//vgjAgICcP/+/QK/VFZF1XlNSkoKvLy88OjRI3z22WdwcXHBmTNnMHHiRDx58gSLFi0SYxcvXowuXbqgX79+SE9Px5YtW/Dxxx9j79696Nixoxj3ySefYMOGDejbty9atmyJY8eOKUzPcf36dbRp0waWlpYYP348jIyMsHLlSnh7e+PkyZNo3rx5odZv0aJFGDlyJMzNzTF58mQAUFufoHeIQER65cKFCwIAITQ0tFjtpKWlCbVr1xbc3NyEjIwMcfy9e/cEHx8fYfny5cLu3buFRYsWCS4uLoJUKhX27t0rxl26dEkAINja2goVKlQQli1bJmzcuFFo1qyZIJFIhD///DPf5UdFRQkABFNTU+Hhw4fi+HPnzgkAhNGjR4vjpk2bJuTdXZmZmQmBgYFK7VpZWQlBQUGFfTmIiKiMhIaGCgCECxcuqI3JzMwU0tLSFMa9fPlSqFChgjBkyBBxXM6xxdLSUoiNjVWI79y5s1CuXDnh0aNH4rjbt28LhoaGCseY6OhowcDAQPj2228V5v/3338FQ0NDpfHq1ufIkSNCXFyc8ODBA2Hbtm2Cvb29IJPJhAcPHoix7dq1E+rVqyekpqaK4+RyudCyZUuhevXq4riRI0cKEolEuHz5sjju+fPngo2NjQBAiIqKEsd7eXkJXl5e4vBHH30k1KlTJ9+c58+fr9ROYV8LLy8vAYCwYsUKhdgdO3YUuH3VqVy5shAQEJBvTEHnRV5eXoKNjY1gYWEh1KlTR+l9oamgoCClc5EcOe+7+fPnC9euXRMACKdPnxYEQRCWLl0qmJubC8nJyUJgYKBgZmamsg1jY2Nh+PDhRcqNiEjX5RwbVT0EQRBSUlKU5gkLCxMACOvWrRPHTZ06VQAgbN++XSleLpcLgqD+uJCeni44ODgIdevWFV6/fi2O37t3rwBAmDp1qjguMDBQACB8/fXXSssJDAwUXF1d1a7r33//LRgZGSmcn6SmpgpZWVkKcVFRUYJMJhNmzJghjsvvmJZ3uTt37hQACLNmzVKI69GjhyCRSITIyEhxHADB2NhYYdw///wjABB++uknteuSkycAISQkRIiLixNiYmKE06dPC02bNhUACFu3bhVjZ86cKZiZmQm3bt1SaOPrr78WDAwMhPv374vj8m7z9PR0oW7dusIHH3wgjrty5YoAQBgxYoRCbN++fQUAwrRp08RxXbt2FYyNjYU7d+6I4x4/fixYWFgInp6e4jhVtQVBePMezX0uVKdOHYVzKiJ250L0jgoODsaNGzewZMkShf7GXVxccPDgQXz++efo3LkzvvzyS1y+fBn29vYYO3asGJeUlAQg+6qzXbt2Yfjw4ejbty+OHj0KW1tbzJo1S6M8unbtikqVKonDzZo1Q/PmzbF///4irZe1tTXOnTuHx48fF2l+IiLSPQYGBmJf33K5HC9evEBmZiaaNGmisruugIAAhSvMs7KycOTIEXTt2hVOTk7i+GrVqsHf319h3u3bt0Mul6Nnz5549uyZ+HB0dET16tWVupBRp3379rC3t4ezszN69OgBMzMz7N69G5UrVwaQ/dPuY8eOoWfPnnj16pW4nOfPn8PX1xe3b98Wf15+4MABeHh4KFxxb2NjI/60PD/W1tZ4+PAhLly4oFHexXktZDIZBg8erLR8ANi7dy8yMjIKtfznz58rXOFWVMnJyXj16hUqVKgAS0vLYreXnzp16qB+/frYvHkzAGDTpk346KOPCuwbvnz58kpXZxIRvW2WLl2Kw4cPKzwAKHSdlZGRgefPn6NatWqwtrZWOM7/8ccfaNCggcr7cRV0T4mLFy8iNjYWI0aMULjRc8eOHVGzZk3s27dPaZ7hw4cXav1iYmLQo0cPNGzYUKGfcJlMBqk0u/yWlZWF58+fw9zcHDVq1Chyt6P79++HgYEBvvjiC4XxY8eOhSAI+PPPPxXGt2/fXvz1NgDUr18flpaWuHv3rkbLmzZtGuzt7eHo6Cj+GuD7779Hjx49xJitW7eiTZs24jEt59G+fXtkZWXh1KlTYmzubf7y5UskJCSgTZs2Cq9HTk0g7zqOGjVKYTgrKwuHDh1C165dUbVqVXF8xYoV0bdvX/z1119ITEzUaD2J8sMiOtFbJCEhATExMeLjxYsXKuPmz5+PX375BTNnzkSHDh0KbNfGxgaDBw9GRESE2P9YzkHPzc1N4adR5ubm6Ny5M86fP4/MzMwC265evbrSuPfee09l/3eamDdvHq5duwZnZ2c0a9YM06dP1/jEgIiIdNfatWtRv359mJiYwNbWFvb29ti3bx8SEhKUYt3c3BSGY2Nj8fr1a6WbaANQGnf79m0IgoDq1avD3t5e4XHz5k3ExsZqlG9OoWDbtm3o0KEDnj17ptD9SmRkJARBwDfffKO0nGnTpol5A9l9xWqSuyoTJkyAubk5mjVrhurVqyMoKAh///23RutQ2NeiUqVKSjc29fLyQkBAAEJCQmBnZ4ePPvoIoaGhSEtL0ygHIU+/rkWR0x/rsWPH0KdPH2RlZYnTkpKSFM6d4uLiir28vn37YuvWrYiMjMSZM2fQt2/fAucRBIE3FSWit16zZs3Qvn17hQcAvH79GlOnThX70bazs4O9vT3i4+MVjvN37txB3bp1i7Tse/fuAQBq1KihNK1mzZri9ByGhobiF9+ayMzMRM+ePZGVlYXt27crHPPlcjkWLlyI6tWrK6zf1atXVZ7HaLo+Tk5OsLCwUBhfq1YtcXpuLi4uSm2UL18eL1++1Gh5w4YNw+HDh7Fnzx6MHj0ar1+/VjieAtnnDQcOHFA6Z8jZzrnPG/bu3YsWLVrAxMQENjY2sLe3x/LlyxVej3v37kEqlSoU/wHlbRgXF4eUlBSV27ZWrVqQy+XFuq8NUQ72iU70Fvnyyy+xdu1acdjLywsnTpxQiFmzZg0mTJiAzz//HFOmTNG4bWdnZwDZV85VrlxZvJJPVb9gDg4OyMjIQHJyMqysrIqwJkXXs2dPtGnTBjt27MChQ4cwf/58zJ07F9u3b1e62pCIiPTDhg0bMGjQIHTt2hXjxo2Dg4MDDAwMMGfOHKUbWgEo1M0g85LL5ZBIJPjzzz9hYGCgNN3c3Fyjdpo1a4YmTZoAyP7VVevWrdG3b19ERETA3NxcvMHWV199BV9fX5VtaFIkL0itWrUQERGBvXv34sCBA/jjjz+wbNkyTJ06FSEhIfnOW9jXQtXrLpFIsG3bNpw9exZ79uzBwYMHMWTIEHz//fc4e/Zsvq+nra2txv/cF2T8+PF4/vw55s2bh08//RSrVq0Sb0Kb+3VwdXUt8hf5Ofr06YOJEyfi008/ha2trcI9ZdSJj48vsX7aiYh03ciRIxEaGopRo0bBw8MDVlZWkEgk6N27t9INKUtL7qvHNTFu3DiEhYXhyJEjSsX32bNn45tvvsGQIUMwc+ZM2NjYQCqVYtSoUaW2fqqO44DmX1ZXr15dLIZ36tQJBgYG+Prrr9G2bVvxfEcul+PDDz/E+PHjVbbx3nvvAci+0XeXLl3g6emJZcuWoWLFijAyMkJoaKjSzbm1Td0X1nm/ECBShUV0orfI+PHj0b9/f3E470+gd+3ahU8++QTdu3fH0qVLC9V2ztXcOT+Pd3JygqOjo9KdzAHg8ePHMDExUfpWXJXbt28rjbt165bSncfzyu9qrYoVK2LEiBEYMWIEYmNj8f777+Pbb79lEZ2ISE9t27YNVatWxfbt2xX2/zlXbBfEwcEBJiYmiIyMVJqWd5y7uzsEQYCbm5v4z15x5RT827ZtiyVLluDrr78Wf25sZGQk/lOqjqurq0a5q2NmZoZevXqhV69eSE9PR/fu3fHtt99i4sSJMDExUXtM1eZr0aJFC7Ro0QLffvstNm3ahH79+mHLli1KN2PLrWbNmoiKiirWcnObO3cuXrx4gV9//RXly5fH999/j4EDB6J169ZiTHG+gMnh4uKCVq1a4cSJExg+fLhCt3mqPHr0COnp6eLVg0RE75pt27YhMDAQ33//vTguNTUV8fHxCnHu7u64du1avm2pO6a5uroCACIiIvDBBx8oTIuIiBCnF8WWLVuwaNEiLFq0CF5eXkrTt23bhrZt22LVqlUK4/N+gVqYXyS5urriyJEjePXqlcL/3f/99584vSRNnjwZv/zyC6ZMmSLeONvd3R1JSUkFntf88ccfMDExwcGDBxWu2A8NDVWIc3V1hVwux507dxSuMo+IiFCIs7e3R7ly5ZTGA9mvh1QqFS8KzKmRxMfHK9xINu+V+0Dhtge9G9idC9FbpHbt2go/jWvcuLE47dSpU+jduzc8PT2xceNGtd+qq/oZ86NHj7B69WrUr18fFStWFMf36tULDx48EPuyA4Bnz55h165d+OCDDzT65n7nzp0Khfjz58/j3LlzBRa8zczMlE6qsrKylH4O5+DgACcnJ41/Nk5ERLon5+qp3FdLnTt3DmFhYRrP3759e+zcuVPhnhmRkZFKfYZ2794dBgYGCAkJUbo6SxAEPH/+vEjr4O3tjWbNmmHRokVITU2Fg4MDvL29sXLlSjx58kQpPvfx2NfXF2FhYbhy5Yo47sWLF9i4cWOBy82br7GxMWrXrg1BEMQ+ys3MzABA6biqjdfi5cuXSvPm9O1e0LHZw8MD165d0+oxfOXKlejRowd++OEHzJo1C1WrVlU4d2rVqpVWljNr1ixMmzYNI0eOLDA2PDwcANCyZUutLJuISN8YGBgoHSt++uknpauDAwIC8M8//2DHjh1KbeTMr+6Y1qRJEzg4OGDFihUKx5U///wTN2/eRMeOHYuU+7Vr1/DJJ5+gf//++PLLL1XGqFq/rVu3Kl2Qpi53VTp06ICsrCwsWbJEYfzChQshkUhK/AIya2trfPbZZzh48KB4ftKzZ0+EhYXh4MGDSvHx8fFid68GBgaQSCQK2zc6Oho7d+5UmCdnHX788UeF8YsWLVIYNjAwgI+PD3bt2qXwa7KnT59i06ZNaN26tXhPlJyuYXL3z56cnKzwi/4cqmoO9G7jlehEemLJkiWIj48X//nfs2eP2D/5yJEj8+025d69e+jSpQskEgl69OiBrVu3KkyvX78+6tevDyD7avY7d+6gXbt2cHJyQnR0NFauXInk5GQsXrxYYb6JEyfi999/R0BAAMaMGQMrKyusWLECGRkZmD17tkbrVa1aNbRu3RrDhw9HWloaFi1aBFtbW7U/AcvRuHFjHDlyBD/88AOcnJzg5uaGGjVqoHLlyujRowcaNGgAc3NzHDlyBBcuXFC4qoGIiHTP6tWrxSuZcvvyyy/RqVMnbN++Hd26dUPHjh0RFRWFFStWoHbt2uKNrgsyffp0HDp0CK1atcLw4cPFfzzr1q2rUJx2d3fHrFmzMHHiRERHR6Nr166wsLBAVFQUduzYgWHDhuGrr74q0jqOGzcOH3/8MdasWYPPP/8cS5cuRevWrVGvXj18+umnqFq1Kp4+fYqwsDA8fPgQ//zzD4DsY/OGDRvw4YcfYuTIkTAzM8Ovv/4KFxcXvHjxIt8rpXx8fODo6IhWrVqhQoUKuHnzJpYsWYKOHTuKV67lfOk+efJk9O7dG0ZGRujcubNWXou1a9di2bJl6NatG9zd3fHq1Sv88ssvsLS0LPC+LB999BFmzpyJkydPKnWJUtTzIqlUio0bNyIhIQHffPMNbGxsMGLECJWx9+7dw/r16wFk35AOgHjjdFdXVwwYMEBt7l5eXiqvRlTl8OHDcHFxQaNGjTSKJyJ623Tq1Anr16+HlZUVateuLXaLYmtrqxA3btw4bNu2DR9//DGGDBmCxo0b48WLF9i9ezdWrFiBBg0awN3dHdbW1lixYgUsLCxgZmaG5s2bw83NDXPnzsXgwYPh5eWFPn364OnTp1i8eDGqVKmC0aNHFyn3nBtqe3p6YsOGDQrTWrZsiapVq6JTp06YMWMGBg8ejJYtW+Lff//Fxo0bFW6CCSDf3PPq3Lkz2rZti8mTJyM6OhoNGjTAoUOHsGvXLowaNUqpH/GS8OWXX2LRokX47rvvsGXLFowbNw67d+9Gp06dMGjQIDRu3BjJycn4999/sW3bNkRHR8POzg4dO3bEDz/8AD8/P/Tt2xexsbFYunQpqlWrhqtXr4rtN2zYEH369MGyZcuQkJCAli1b4ujRoyp/iTdr1iwcPnwYrVu3xogRI2BoaIiVK1ciLS0N8+bNE+N8fHzg4uKCoUOHYty4cTAwMMDq1athb2+P+/fvK7TZuHFjLF++HLNmzUK1atXg4OCg9CsGescIRKQXXF1dBQAqH1FRUfnOe/z4cbXzAhCmTZsmxm7atEnw9PQU7O3tBUNDQ8HOzk7o1q2bEB4errLtO3fuCN26dRMsLS0FU1NT4YMPPhDOnz9f4PpERUUJAIT58+cL33//veDs7CzIZDKhTZs2wj///KMQO23aNCHv7uq///4TPD09BVNTUwGAEBgYKKSlpQnjxo0TGjRoIFhYWAhmZmZCgwYNhGXLlhWYDxERlY3Q0NB8j1EPHjwQ5HK5MHv2bMHV1VWQyWRCo0aNhL179wqBgYGCq6ur2FbuY4sqR48eFRo1aiQYGxsL7u7uwq+//iqMHTtWMDExUYr9448/hNatWwtmZmaCmZmZULNmTSEoKEiIiIjQaH0uXLigNC0rK0twd3cX3N3dhczMTEEQso+jAwcOFBwdHQUjIyOhUqVKQqdOnYRt27YpzHv58mWhTZs2gkwmEypXrizMmTNH+PHHHwUAQkxMjBjn5eUleHl5icMrV64UPD09BVtbW0Emkwnu7u7CuHHjhISEBIX2Z86cKVSqVEmQSqVK5xaavBZeXl5CnTp1lNb50qVLQp8+fQQXFxdBJpMJDg4OQqdOnYSLFy/m+zrmqF+/vjB06FCl8ZqeF6nLKykpSWjRooUglUqFjRs3qlx2fudPuV/jgt53OQIDAwUzMzOFcVlZWULFihWFKVOm5DsvEZE+y+/YKAiC8PLlS2Hw4MGCnZ2dYG5uLvj6+gr//fef4OrqKgQGBirEPn/+XAgODhYqVaokGBsbC5UrVxYCAwOFZ8+eiTG7du0SateuLRgaGgoAhNDQUHHab7/9JjRq1EiQyWSCjY2N0K9fP+Hhw4cKy1C1v849Lfe5R37Ho5zlpqamCmPHjhUqVqwomJqaCq1atRLCwsKUjtn55Z53uYIgCK9evRJGjx4tODk5CUZGRkL16tWF+fPnC3K5XCEOgBAUFKS0Lqpe37wKOsYNGjRIMDAwECIjI8WcJk6cKFSrVk0wNjYW7OzshJYtWwoLFiwQ0tPTxflWrVolVK9eXZDJZELNmjWF0NBQlf/3v379Wvjiiy8EW1tbwczMTOjcubPw4MEDpTqGIGSfc/j6+grm5uZCuXLlhLZt2wpnzpxRyjk8PFxo3ry5YGxsLLi4uAg//PCD+B7NfQ4RExMjdOzYUbCwsFA69tO7SSIIWrjlPRERERGRHuratSuuX7+u8h4dum7UqFFYuXIlkpKS1N4wTN+tX78eQUFBuH//vkLfpW+LnTt3om/fvrhz545Cl3lEREREpFvYJzoRERERvRNev36tMHz79m3s378f3t7eZZNQIeTN/fnz51i/fj1at2791hbQAaBfv35wcXEp9A3R9cXcuXMRHBzMAjoRERGRjuOV6ERERET0TqhYsSIGDRqEqlWr4t69e1i+fDnS0tJw+fJlVK9evazTy1fDhg3h7e2NWrVq4enTp1i1ahUeP36Mo0ePwtPTs6zTIyIiIiJ6q/HGokRERET0TvDz88PmzZsRExMDmUwGDw8PzJ49W+cL6ADQoUMHbNu2DT///DMkEgnef/99rFq1igV0IiIiIqJSwCvRiYiIiIiIiIiIiIjUYJ/oRERERERERERERERqsIhORERERERERERERKQG+0QHIJfL8fjxY1hYWEAikZR1OkRE9I4RBAGvXr2Ck5MTpFJ+v11YPI4TEVFZ4nG8eHgcJyKisqTpcZxFdACPHz+Gs7NzWadBRETvuAcPHqBy5cplnYbe4XGciIh0AY/jRcPjOBER6YKCjuMsogOwsLAAkP1iWVpalnE22d/Ex8XFwd7eXuevZGCuJUef8mWuJUOfcgX0K19dyzUxMRHOzs7i8YgKR9eO4yVJ19677zpuD93C7aFb3qXtoYvH8VOnTmH+/PkIDw/HkydPsGPHDnTt2lUh5ubNm5gwYQJOnjyJzMxM1K5dG3/88QdcXFwAAKmpqRg7diy2bNmCtLQ0+Pr6YtmyZahQoYLYxv379zF8+HAcP34c5ubmCAwMxJw5c2BoqHmpQZvHcX1+3+lz7oB+56/PuQP6nb8+5w7od/76nDug3fw1PY6ziA6IPxmztLTUiX++5XI5UlNTYWlpqfNvZOZacvQpX+ZaMvQpV0C/8tXVXPkT5qLRteN4SdLV9+67ittDt3B76JZ3cXvo0nE8OTkZDRo0wJAhQ9C9e3el6Xfu3EHr1q0xdOhQhISEwNLSEtevX4eJiYkYM3r0aOzbtw9bt26FlZUVgoOD0b17d/z9998AgKysLHTs2BGOjo44c+YMnjx5goEDB8LIyAizZ8/WOFdtHsf1+X2nz7kD+p2/PucO6Hf++pw7oN/563PuQMnkX9BxnEV0IiIiIiIioreIv78//P391U6fPHkyOnTogHnz5onj3N3dxecJCQlYtWoVNm3ahA8++AAAEBoailq1auHs2bNo0aIFDh06hBs3buDIkSOoUKECGjZsiJkzZ2LChAmYPn06jI2NS24FiYiIShmL6ERERERERETvCLlcjn379mH8+PHw9fXF5cuX4ebmhokTJ4pdvoSHhyMjIwPt27cX56tZsyZcXFwQFhaGFi1aICwsDPXq1VPo3sXX1xfDhw/H9evX0ahRI5XLT0tLQ1pamjicmJgo5iWXy4u9boIgFLudsqDPuQP6nb8+5w7od/76nDug3/nrc+6AdvPXtA0W0YmIiKhI5syZg+3bt+O///6DqakpWrZsiblz56JGjRpijLe3N06ePKkw32effYYVK1aIw9roT5WIiIg0Exsbi6SkJHz33XeYNWsW5s6diwMHDqB79+44fvw4vLy8EBMTA2NjY1hbWyvMW6FCBcTExAAAYmJiFAroOdNzpqkzZ84chISEKI2Pi4tDampqsdZNLpcjISEBgiDoXfcE+pw7oN/563PugH7nr8+5A/qdvz7nDmg3/1evXmkUx/9OiYooKysLGRkZJda+XC5HRkYGUlNTdX6HxlyVGRsb6/xrQVRcJ0+eRFBQEJo2bYrMzExMmjQJPj4+uHHjBszMzMS4Tz/9FDNmzBCHy5UrJz7XVn+qBZHL5UhPT9dae2VFn/a3+sTIyAgGBgZlnQYRUanIueLuo48+wujRowEADRs2xJkzZ7BixQp4eXmV6PInTpyIMWPGiMM5N3Szt7fXSp/oEolEL2+Up8+5A/qdvz7nDuh3/trMvaRrNKrI5XJkZmbqZb/i+pw7ULj8CzrXz30/kPywiE5USIIgICYmBvHx8SW+HLlcjlevXunUTYpUYa7KpFIp3Nzc2BckvdUOHDigMLxmzRo4ODggPDwcnp6e4vhy5crB0dFRZRul0Z9qeno6oqKi9Panirnp0/5W31hbW8PR0ZGvKxG99ezs7GBoaIjatWsrjK9Vqxb++usvAICjoyPS09MRHx+vcDX606dPxWO6o6Mjzp8/r9DG06dPxWnqyGQyyGQypfFSqVQrhRyJRKK1tkqbPucO6Hf++pw7oN/5Fzf30qrRqFu2XC5HUlKS3p1D6nPuQOHzz+9cX9P3HovoRIWUs3N2cHBAuXLlSmxnIwgCMjMzYWhoqPM7NOaqSC6X4/Hjx3jy5AlcXFx0/jUh0paEhAQAgI2NjcL4jRs3YsOGDXB0dETnzp3xzTffiFejF6U/1cL0pSoIAh4/fgwDAwNUrlxZL/+xyCsjIwNGRkZlncZbQxAEpKSkIC4uDoIg5Fv4yUvf+5J823B76JZ3aXvo2zoaGxujadOmiIiIUBh/69YtuLq6AgAaN24MIyMjHD16FAEBAQCAiIgI3L9/Hx4eHgAADw8PfPvtt4iNjYWDgwMA4PDhw7C0tFQq0BMRlZTSqtGook+1kLz0OXdA8/xzzvVjY2MBABUrVizyMllEJyqErKwscedsa2tbosvSpx0ac1Vmb2+Px48fIzMzk8UueifI5XKMGjUKrVq1Qt26dcXxffv2haurK5ycnHD16lVMmDABERER2L59O4Ci9adamL5Us7Ky8OrVK1SqVOmt+GWIIAgAAAMDA53f3+oTKysryOVy8QpKTb9s0fe+JN823B665V3aHpr2pVqakpKSEBkZKQ5HRUXhypUrsLGxgYuLC8aNG4devXrB09MTbdu2xYEDB7Bnzx6cOHECQPZ+cejQoRgzZgxsbGxgaWmJkSNHwsPDAy1atAAA+Pj4oHbt2hgwYADmzZuHmJgYTJkyBUFBQSqvNC9pgiAg5VkKXj14BXOpOczszXisJHrLlWaNRhV9qoXkpc+5A4XL39TUFADEL32L2o0ji+hEhZDTv1bu/nyJVMkp1mVlZbGITu+EoKAgXLt2TfwZeI5hw4aJz+vVq4eKFSuiXbt2uHPnDtzd3Yu0rML0pZqamoqEhASYmJi8VTcq5X5F+8zNzfHs2TNYW1tr3C+iPvdB+jbi9tAt79L20HSfUZouXryItm3bisM5x83AwECsWbMG3bp1w4oVKzBnzhx88cUXqFGjBv744w+0bt1anGfhwoWQSqUICAhAWloafH19sWzZMnG6gYEB9u7di+HDh8PDwwNmZmYIDAxUuA9KaUiNT8WVtVdw/qfzeHnnpTi+vHt5NBvZDA0DG8LEWve2EREVH2s0pKmc90hGRgaL6ESlSR+/paPSxfcIvUuCg4Oxd+9enDp1CpUrV843tnnz5gCAyMhIuLu7F6k/1cL0pSqVSsV+Ft+Gz6UgCOJ6vA3ro0tyv1cKU/DT5z5I30bcHrrlXdkeurh+3t7e4q+X1BkyZAiGDBmidrqJiQmWLl2KpUuXqo1xdXXF/v37i5xncUUejMTvAb8jI0X5ZoIv777EwdEHcWzyMfT8oyeq+VYrgwyJqDTwvJgKoo33iO4d7YmIiEgvCIKA4OBg7NixA8eOHYObm1uB81y5cgXAm77oPDw88O+//4p91AHsT5WIiIgKFnkwEps6bkLG6wxAQPYjt/+Py3idgU0dNyHyYKSKVoiIiDTDIjoREREVSVBQEDZs2IBNmzbBwsICMTExiImJwevXrwEAd+7cwcyZMxEeHo7o6Gjs3r0bAwcOhKenJ+rXrw9AsT/Vf/75BwcPHizT/lSJiIhI96XGp+L3gN+zr7Yv6L6u8uwv/n8P+B2p8akFBBMREanGIjrRO2LQoEGQSCT4/PPPlaYFBQVBIpFg0KBBpZ+YBrZv3w4fHx/Y2tpCIpGIV7LmiI6OhkQiUfnYunUrAOD58+fw8/NDpUqVYG5uDhcXFwQHByMxMbEM1ojo7bB8+XIkJCTA29sbFStWFB+//fYbgOx7Axw5cgQ+Pj6oWbMmxo4di4CAAOzZs0dsI6c/VQMDA3h4eKB///4YOHBgqfenqmvy22d/8cUXkEqlOrnPzsjIwIQJE1CvXj2YmZnByckJAwcOxOPHj8WY6OhoDB06FG5ubjA1NYW7uzumTZuG9PR0MSYiIgJt27ZFhQoVYGJigqpVq2LKlCliv5dERPRuu7L2SnYXLgUV0HPIgYyUDPyz7p8SzYuISBP6XJ/J7fPPP4dEIsGiRYsUxt+6dQsfffQR7OzsYGlpidatW+P48eMKMV988QUaN24MmUyGhg0bll7SxcAiOtE7xNnZGVu2bBGvEgWyb7q3adMmuLi4lGFm+UtOTkbr1q0xd+5cldOdnZ3x5MkThUdISAjMzc3h7+8PILuvyo8++gi7du3C9evXERoaiiNHjqg8aBGRZgRBUPnIOeFzdnbGyZMn8fz5c6SmpuL27duYN2+e0s0/c/pTTUlJQVxcHBYsWPBW3QS0qNTts7ds2aKz++yUlBRcunQJ33zzDS5duoTt27cjIiICXbp0EWP+++8/yOVyrFy5EtevX8fChQuxYsUKTJo0SYwxMjLCwIEDcejQIURERGDRokX45ZdfMG3atLJYLSIi0iGCIOD8T+cLDlTh3I/nCuwrnoioNOhrfSbHjh07cPbsWTg5OSlN69SpEzIzM3Hs2DGEh4ejQYMG6NSpE2JiYhTihgwZgl69epVWysXGIjrRO+T999+Hs7Mztm/fLo7bvn07XFxc0KhRI4VYuVyOOXPmiFcKNmjQANu2bROnZ2VliVcSlitXDnXq1MHixYsV2hg0aBC6du2KBQsWoGLFirC1tUVQUFChryQcMGAApk6divbt26ucbmBgAEdHR4XHjh070LNnT5ibmwMAypcvj+HDh6NJkyZwdXVFu3btMGLECJw+fVpsZ/r06WjYsCHWr1+PKlWqwMrKCr1798arV6/EmG3btqFevXowNTWFra0t2rdvj+Tk5EKtDxGRJtTts52dnYu1zzY1NUWNGjVKZJ9tZWWFw4cPo2fPnqhRowZatGiBJUuWIDw8HPfv3wcA+Pn5ITQ0FD4+PqhatSq6dOmCr776SmE9q1atisGDB6NBgwZwdXVFly5d0K9fP4V9tib5Llu2DNWrV4eJiQkqVKiAHj16aLwuRESkm14/f42Xd14q94FeEAF4eeclXr94XXAsEVEJK6n6jKbn+nZ2dvjiiy+K9EvPR48eYeTIkdi4cSOMjIwUpj179gy3b9/G119/jfr166N69er47rvvkJKSgmvXrolxP/74I4KCglC1alWVy1izZg2sra1x8OBB1KpVC+bm5vDz88OTJ0/EmJMnT6J58+YwMzODtbU1WrVqhXv37hV6fTTFIjqRtiQnq3+kpmoe+/q1ZrFFNGTIEISGhorDq1evxuDBg5Xi5syZg3Xr1mHFihW4fv06Ro8ejf79++PkyZMAsnfilStXxtatW3H9+nVMnjwZkydPxu+//67QzvHjx3Hnzh0cP34ca9euxZo1a7BmzRpx+vTp01GlSpUir48q4eHhuHLlCoYOHao25vHjx9i+fTu8vLwUxt+5cwc7d+7E3r17sXfvXpw8eRLfffcdAODJkyfo06cPhgwZgps3b+LEiRPo3r07r2Yh0kd6us8ODQ1FYGCgUlxh9tk3btzA1KlTMWnSpFLZZyckJEAikcDa2jrfGBsbG7XTIyMjceDAAaV9dn75Xrx4EV988QVmzJiBiIgIHDhwAJ6enoXKnYiIdE96UnrBQfnN/6p48xORHtDTc31t1Gc0Pddfs2YN1q1bV+hzfblcjgEDBmDcuHGoU6eO0nRbW1vUqFED69atQ3JyMjIzM7Fy5Uo4ODigcePGhXh1sn/lumDBAqxfvx6nTp3C/fv38dVXXwEAMjMz0aNHD3h6euLq1asICwvDsGHDIJFICrWMwuBvpUtA582dizW/BBI4GzjjQdYDCIX+ev2NPX32FBxE2vP/K55V6tAB2LfvzbCDA5CSojrWyws4ceLNsJsb8OyZclwRC7f9+/fHxIkTxW/n/v77b2zZsgUnci0zLS0Ns2fPxpEjR+Dh4QEg+6rAv/76CytXroSXlxeMjIwQEhLy/1QEODs74/z58/j999/Rs2dPsa3y5ctjyZIlMDAwQM2aNdGxY0ccPXoUn376KQDAzs4O7u7uRVoXdVatWoVatWqhZcuWStP69u2LXbt24fXr1+jcuTN+/fVXhelyuRxr1qyBhYUFgOyr4I8ePYpvv/0WT548QWZmJrp37w5XV1cAQL169bSaOxGVkpLaZ1epUuL77PXr1ytckV3YfTYAuLm5ISwsrMT32ampqZgwYQL69Omj1I1PjsjISPz0009YsGCB0rSWLVvi0qVLSEtLw7Bhw5T6ys8v3/v378PMzAydOnWChYUFXF1dla7qocLrXLzT3BIlkQDOzsCDB0X+yJW4PTw9Jyo2Y3Pj4s1vUbz5iUgPlNK5vgSAEQBBrukNGhSVRH0G0Oxcv0aNGvD398exY8cwbNgwAJqd68+dOxeGhob44osvVE6XSCQ4cuQIunbtCgsLC0ilUjg4OODAgQMoX758oV6fjIwMrFixQswpODhY/H8gMTERCQkJ6NSpkzi9Vq1ahWq/sFhEJ3rH2Nvbo2PHjlizZg0EQUDHjh1hZ2enEBMZGYmUlBR8+OGHCuPT09MVChBLly7F6tWrcf/+fbx+/Rrp6elKN4SoU6cODAwMxOGKFSvi33//FYeDg4MRHBystfV7/fo1Nm3ahG+++Ubl9B9++AGTJk3C3bt3MWnSJIwZMwbLli0Tp1epUkUsoOfkGxsbCwBo0KAB2rVrh3r16sHX1xc+Pj7o0aNHoQ8ERESa0ud9dkZGBnr27AlBELB8+XKVMY8ePYKfnx8+/vhjsVCf22+//YZXr17hn3/+wbhx47BgwQKMHz9eo3w//PBDuLq6omrVqvDz84Ofnx+6deuGcuXKaZQ/ERHpJlNbU5R3L4+XdwvZpYsEKF+1PExtTEssNyKiwtCFc/3r16+LwwWd64eHh2Px4sW4dOmS2iu+BUFAUFAQHBwccPr0aZiamuLXX39F586dceHCBVSsWLHA1yVHuXLlFIr6ueszNjY2GDhwIPz8/PDhhx+iffv26NmzZ6HaLywW0Ym0JSlJ/bRcOykAwP8/9CpJ8/SyFBWVfWmVFg0ZMkTcMS5dulRpetL/12Xfvn2oVKmSwjSZTAYA2LJlC7766it8//33aNGiBUxNTbFw4UKcP694k5+8/WNJJBLIi/gtrSa2bduGlJQUDBw4UOV0R0dH2NnZoW7durC1tUWbNm3wzTffiDva/PI1MDDA4cOHcebMGRw6dAg//fQTJk+ejHPnzsHNza3E1omISkBJ7bOjo4uckjq599lLlixRml7YfbaHhwcsLCwwf/58nDt3TiFeW/vsnAL6vXv3cOzYMZVXoT9+/Bht27ZFy5Yt8fPPP6tsx9nZGQBQu3ZtZGVlYdiwYRg7dqx48p9fvhYWFrh06RJOnDiBQ4cOYerUqZg+fTouXLiQb9cyRESk2yQSCZqNbIaDow8Wet7mXzQv0Z/6E5GOKKVzfUEQkJmZWaziqrbrMyV5rn/69GnExsYq3Pg0KysLY8eOxaJFixAdHY1jx45h7969ePnypfg/wLJly3D48GGsXbsWX3/9tcbLU5Vv7u50f/31V3z55Zc4ePAgfvvtN0yZMgWHDx9GixYtNF5GYbCITqQtZmYlF6vlEz0/Pz+kp6dDIpHA19dXaXrt2rUhk8lw//59pf5nc/z9999o2bIlRowYIR447t69q9U8i2LVqlXo0qUL7O3tC4zNOVikpaVp3L5EIkGrVq3QqlUrTJ06Fa6urtixYwfGjBlT5JyJqAyU5D5by/Lus/Peh6Gw++wcd+7c0XquwJsC+u3bt3H8+HHY2toqxTx69Aht27ZF48aNERoaCmnef1BUkMvlyMjIgFwuV7iCJj+GhoZo37492rdvj2nTpsHa2hrHjh1D9+7dC71eRESkOxoGNsSxyceQ8ToD0KD+I5FKYGhqiAYDG5R8ckRU9krrXF8QgMxMzedXQdv1mRwlca4/YMAAtG/fXmGcr68vBgwYIPblnvL/rnHynt9LpdISuaCyUaNGeP/99zFx4kR4eHhg06ZNLKITkfYYGBjg5s2b4vO8LCws8NVXX2H06NGQy+Vo3bo1EhIS8Pfff8PS0hKBgYGoXr061q1bh4MHD6JKlSpYu3YtLly4UOgrspcsWYIdO3bg6NGjamNevHiB+/fv4/HjxwCAiIgIANlXlTs6OopxkZGROHXqFPbv36/Uxv79+/H06VM0adIEJiYmiIiIwPjx49GqVSuNb5J37tw5HD16FD4+PnBwcMC5c+cQFxdX4v1ulYbi3ssB4P0ciEpK3n12Zp4T9cLus93c3LB+/foS2WdnZGSgR48euHTpEvbu3YusrCzExMQAyP7JpbGxMR49egRvb2+4urpiwYIFiIuLE+fP2adv3LgRRkZGqFevHmQyGS5evIiJEyeiV69eSlekqLN3717cvXsXnp6eKF++PPbv3w+5XI4aNWoUap2JdBn7qC8e9lGvv0ysTdDzj57Y1HETBKmQfyFdCkAC9NreCybWJqWVIhGRRrRdnynJc31bW1ulC2SMjIzg6OgonmN7eHigfPnyCAwMxNSpU2FqaopffvkFUVFR6NixozhfZGQkkpKSEBMTg9evX+PKlSsAsr80MDYu+N4VUVFRWLFiBbp27YpKlSohIiICt2/fVtsrgTawiE70jlJ3g7ccM2fOhL29PebMmYO7d+/C2toa77//PiZNmgQA+Oyzz3D58mX06tULEokEvXr1wvDhw3HgwIFC5fHs2bMCvyHdvXu3wh2qe/fuDQCYNm0apk+fLo5fvXo1KleuDB8fH6U2cnbco0ePRlpaGpydndG9e/dC/ZTI0tISp06dwqJFi5CYmAhXV1d8//338Pf317gNIqKiyNln570KPUdh99l9+vTBiBEj8OeffxYqj4L22Y8ePcLu3bsBQKkPxuPHj8Pb2xuHDx9GZGQkIiMjUblyZYWYnPUzNDTE3LlzcevWLQiCAFdXVwQHB2P06NEa52ptbY3t27dj+vTpSE1NRfXq1bF582bUqVNH4zaIiEh3VfOthr77+uL3gN+RkZKRPTL3YfL/P+Y1MjVCr+294O6j+Y2xiYhKk7brMyV1rq8JOzs7HDhwAJMnT8YHH3yAjIwM1KlTB7t27UKDBm9+DfTJJ5/g5MmT4nBO/+5RUVEaXehYrlw5REREoEePHnj+/DkqVqyIoKAgfPbZZ8XKPz8SQd1/Y++QxMREWFlZISEhocA3riaKe0WnPl3NKZfLERsbCwcHB41+il2WtJFramoqoqKi4ObmBhOTkr2KQexby9BQ5/vtY67KtPFeKc3P17t2Jbqu7bu0fRx61+T3+pXmfrs06NP+Vt8U5b2ia/uS0qDbVz7L4ewciwcPHCAIurk9tH3lM7dH8Whre/A4XjzFff1S41Pxz7p/cO7Hc3h556U4vrx7eTT/ojkaBDaAiZXunwPo+zFFn/PX59wB/c6/uLmX9bm+Pp+b63PuQOHzz++9oulxiFeiExEREREREZFeMrE2QfMvmqPZyGZIfpaMJ9FPULFKRZjZmellYYiIiHQTi+hEREREREREpNckEgnK2ZaDRZYFytmWYwGdiIi0Sr9+50FEREREREREREREVIpYRCciIiIiIiIiIiIiUoNFdCIiIiIiIiIiIiIiNVhEJyoCuVxe1imQjhMEoaxTIKJc+JmkgvDYTkRERKSfeB5HBdHGe4Q3FiUqBGNjY0ilUjx+/Bj29vYwNjYusRvWCIKAzMxMGBoa6vxNcZir8jLi4uIgkUhgZGRUIssgIs0YGRlBIpEgLi4O9vb2Or+PKog+7W/1hSAISE9PR1xcHKRSKYyNjcs6JSIiIiLSQGnWaFTR53Nzfc4d0Dx/bZ7rs4hOVAhSqRRubm548uQJHj9+XKLLEgQBcrkcUqlU53dozFWZRCJB5cqVYWBgUGLLIKKCGRgYoHLlynj48CGio6PLOp1i06f9rb4pV64cXFxcIJXyh5pERERE+qA0azSq6PO5uT7nDhQ+f22c67OITlRIxsbGcHFxQWZmJrKyskpsOXK5HM+fP4etra3O/0PPXJUZGRmxgE6kI8zNzVG9enVkZGSUdSrFpk/7W31iYGCgt1fhEBEREb3LSqtGo4o+n5vrc+5A4fLX1rk+i+hERZDTTUdJdtUhl8thZGQEExMTnd+hMVci0nUGBgZvxRdb3IcRERERESkqjRqNKvp8bq7PuQNlk7/+vUpERERERERERERERKWEV6ITEZFe6by5c7HbkEACZwNnPMh6AAFCkdvZ02dPsXMhIiIiIiIiIt3GK9GJiIiIiIiIiIiIiNRgEZ2IiIiIiIiIiIiISA0W0YmIiIiIiIiIiIiI1GARnYiIiIiIiIiIiIhIDRbRiYiIiIiIiIiIiIjUMCzrBIiI3ladN3cu1vwSSOBs4IwHWQ8gQChWW3v67CnW/ERERERERERE7ypeiU5EREREREREREREpAaL6EREREREREREREREarCITkRERERERERERESkBvtEJyIiordDcjJgYKA83sAAMDFRjFNHKgVMTYsWm5ICCGruXyCRAOXKFS329WtALs9+LpdDkpKSnZf0/9dCmJmpjlUld2xqKpCVpZ3YcuWy8waAtDQgM1M7saamb9YzPR3IyNBOrInJm/dKYWIzMrLjc+TdHjIZYGioOjav3LGZmdmvhTrGxoCRUeFjs7Kyt506RkbZ8YWMlQhyGGe9VhuaJTVCplTDWIkhMg1k2QOCAFlWSpFjJRI5jDNSIMtMRhaMkGHw5nMvy1T/WZZLDDSOFSRSpBuYFi02KwVI1v4+wjjrNSSC+s99mqFZkWKNslIhFdR/7guKzb09UqXm4ufeMCsNBoL6z32aQTmNY9MNTCFIsj/3hvJ0GMjVf5ZVxqrbfIXdRxAREdFbj0V0IiIiejs4Oake36EDsG/fm2EHh+wClSpeXsCJE2+Gq1QBnj1THdukCXDhwpvh2rWBe/dUx9auDVy//ma4aVPgxg3Vsa6uQHT0m2FPT+DiRQDZPyGskDvWzg6Ii3sz7O8PnDyput1y5RS/FAgIAPbvVx0LKBbwBgwAtm1TH5uU9Kbo/tlnwNq16mNjYwF7++znY8YAy5apj42Kyt4GADB5MrBggfrYa9eAOnWyn8+eDYSEqI89fz57GwDA4sXA+PHqY48fB7y9s5///DMQHCxOUtoee/cCHTtmP9+4ERg8WH27v/8OfPxx9vMdO4CePdXHhoYCgwZlPz94EOjUSX3skiVAUFD289OngbZt1cfOmweMG5f9/NIloFkz9bHTpgHTpwMAnJNuYunJumpDt1f9CqG15wMA7F/fx6pjbmpj97mOwIp6SwEAlunPsPGwg9rYo5UDsajhGgDZBeltB8zVxv5VsQfmNt4qDucXe8GhA2Y0e7OP2HDYASZqivn/2nhhUssT4vCqY1Vgla56H3HbqgnGtHmzj1h6ojZgrv19xHdnPFE94aLK0ARjO/T3ebOPmH7OH/VeqN5HpBqUw8f+b/YRE8MD0DRW/T6ic6c3+4gxVwag9RP1+4gefkli0T3438/Q7qH6fUS/D2ORKMveR3xyYww63lO/jxj6QRRiy1UBAAz4bzK631W/jwjyuob7Ftn7iI9vz0bf2yGAurdFYfcR77+vfjoRERG9FdidCxERERERERERERGRGhJBUPc7wXdHYmIirKyskJCQAEtLy2K313lz52LNL4EEzgbOeJD1AAKKvnn29NlTrDw0IZfLERsbCwcHB0iluv2djD7lCuhXvsxVNV3ZFwAF7w+KmytQevsufcpVU9o+Dr1rxNfv8WPVr99b1J2LXC5HXFwc7O3t3+zD2J1L4WO11J2L0vZ4B7pz6dxZt7tzqVw5Dg8f2utsdy7btmp3H9G5s25355KzPXS1Oxe1P7Ap5D4iMTmZx/Fi0OZ5kD79X5KXPucO6Hf++pw7oN/563PugH7nr8+5A9rNX9PjELtzISIioreDmZli4Te/uMK0qancBTBtxuYu1MvlEJKTs/NSdbKYO7YghenHtzCxMln2Q9uxxsZvCr5lFWtk9KZADeS/PfLG5sfQ8E1BXZuxBgaav4cLEStIpAoFVG3FQiIpVqxEIke6UTLSDM0gCIrbQ+N2SzLWoBygaXgh9hG5C/XajM39xUJRYnNvDwgScXymgQyZ0OxzX6hYqbH45Y3GsZpsj8LsI4iIiOitpX9fNRARERERERERERERlRIW0YmIiIiIiIjeIqdOnULnzp3h5OQEiUSCnTt3qo39/PPPIZFIsGjRIoXxL168QL9+/WBpaQlra2sMHToUSUlJCjFXr15FmzZtYGJiAmdnZ8ybN68E1oaIiKjssYhORERERERE9BZJTk5GgwYNsHTp0nzjduzYgbNnz8LJyUlpWr9+/XD9+nUcPnwYe/fuxalTpzBs2DBxemJiInx8fODq6orw8HDMnz8f06dPx88//6z19SEiIipr7BOdiIiIiIiI6C3i7+8Pf3//fGMePXqEkSNH4uDBg+jYsaPCtJs3b+LAgQO4cOECmjRpAgD46aef0KFDByxYsABOTk7YuHEj0tPTsXr1ahgbG6NOnTq4cuUKfvjhB4ViOxER0duAV6ITERERERERvUPkcjkGDBiAcePGoU6dOkrTw8LCYG1tLRbQAaB9+/aQSqU4d+6cGOPp6QnjXDde9fX1RUREBF6+fFnyK0FERFSKyvRK9Dlz5mD79u3477//YGpqipYtW2Lu3LmoUaOGGJOamoqxY8diy5YtSEtLg6+vL5YtW4YKFSqIMffv38fw4cNx/PhxmJubIzAwEHPmzIGhIS+0JyIiIiIiIspt7ty5MDQ0xBdffKFyekxMDBwcHBTGGRoawsbGBjExMWKMm5ubQkzO/+kxMTEoX768yrbT0tKQlpYmDicmJgLILuzL5fKirdD/yeVyCIJQ7HbKgj7nDuh3/vqcO6Df+etz7oB+56/PuQPazV/TNsq0ynzy5EkEBQWhadOmyMzMxKRJk+Dj44MbN27AzMwMADB69Gjs27cPW7duhZWVFYKDg9G9e3f8/fffAICsrCx07NgRjo6OOHPmDJ48eYKBAwfCyMgIs2fPLsvVIyIiIiIiItIp4eHhWLx4MS5dugSJRFLqy58zZw5CQkKUxsfFxSE1NbVYbcvlciQkJEAQBEil+vXDe33OHdDv/PU5d0C/89fn3AH9zl+fcwe0m/+rV680iivTIvqBAwcUhtesWQMHBweEh4fD09MTCQkJWLVqFTZt2oQPPvgAABAaGopatWrh7NmzaNGiBQ4dOoQbN27gyJEjqFChAho2bIiZM2diwoQJmD59usJPy4iIiIiIiIjeZadPn0ZsbCxcXFzEcVlZWRg7diwWLVqE6OhoODo6IjY2VmG+zMxMvHjxAo6OjgAAR0dHPH36VCEmZzgnRpWJEydizJgx4nBiYiKcnZ1hb28PS0vLYq2bXC6HRCKBvb293hWF9Dl3QL/z1+fcAf3OX59zB/Q7f33OHdBu/iYmJhrF6VR/JwkJCQAAGxsbANnfkGdkZKB9+/ZiTM2aNeHi4oKwsDC0aNECYWFhqFevnkL3Lr6+vhg+fDiuX7+ORo0ale5KEBEREREREemoAQMGKPyPDWT/Dz1gwAAMHjwYAODh4YH4+HiEh4ejcePGAIBjx45BLpejefPmYszkyZORkZEBIyMjAMDhw4dRo0YNtV25AIBMJoNMJlMaL5VKtVLIkUgkWmurtOlz7oB+56/PuQP6nb8+5w7od/76nDugvfw1nV9niuhyuRyjRo1Cq1atULduXQDZ/agZGxvD2tpaIbZChQoK/bDlLqDnTM+ZpkpJ9sEGABIU7ydxklx/xVEa/RrpUx9K+pQroF/5MlfVdGVfABS8P9DGMkpr36VPuZZ2O0REREQAkJSUhMjISHE4KioKV65cgY2NDVxcXGBra6sQb2RkBEdHR/H+ZLVq1YKfnx8+/fRTrFixAhkZGQgODkbv3r3h5OQEAOjbty9CQkIwdOhQTJgwAdeuXcPixYuxcOHC0ltRIiKiUqIzRfSgoCBcu3YNf/31V4kvqyT7YAMAZwPnYrdhJ7WDAKFYbeT9+V1J0Kc+lPQpV0C/8mWuqunKvgAoeH+gjVyB0tl36VOumtK0DzYiIiIiTVy8eBFt27YVh3O6TwkMDMSaNWs0amPjxo0IDg5Gu3btIJVKERAQgB9//FGcbmVlhUOHDiEoKAiNGzeGnZ0dpk6dimHDhml1XYiIiHSBThTRg4ODsXfvXpw6dQqVK1cWxzs6OiI9PR3x8fEKV6M/ffpUoR+28+fPK7RXUD9sJdkHGwA8yHpQrPlzro58mPWwWAWevHdTLwn61IeSPuUK6Fe+zFU1XdkXAAXvD4qbK1B6+y59ylVTmvbBRkRERKQJb29vCILm5zjR0dFK42xsbLBp06Z856tfvz5Onz5d2PSIiIj0TpkW0QVBwMiRI7Fjxw6cOHECbm5uCtMbN24MIyMjHD16FAEBAQCAiIgI3L9/Hx4eHgCy+2H79ttvERsbKxYzDh8+DEtLS9SuXVvlcku6DzZtXDUq5PorqtIqZupTH0r6lCugX/kyV2W6si8ACt4faCPXnHZKet+lT7mWdjtEREREREREpH1lWkQPCgrCpk2bsGvXLlhYWIh9mFtZWcHU1BRWVlYYOnQoxowZAxsbG1haWmLkyJHw8PBAixYtAAA+Pj6oXbs2BgwYgHnz5iEmJgZTpkxBUFCQykI5EREREREREREREZGmyrSIvnz5cgDZPzXLLTQ0FIMGDQIALFy4UOx/LS0tDb6+vli2bJkYa2BggL1792L48OHw8PCAmZkZAgMDMWPGjNJaDSIiIiIiIiIiIiJ6S5V5dy4FMTExwdKlS7F06VK1Ma6urti/f782UyMiIiIiIiIiIiIiAjthJSIiIiIiIiIiIiJSg0V0IiIiIiIiIiIiIiI1WEQnIiIiIiIiIiIiIlKDRXQiIiIiIiIiIiIiIjVYRCciIiIiIiIiIiIiUoNFdCIiIiIiIiIiIiIiNVhEJyIiIiIiIiIiIiJSg0V0IiIiIiIiIiIiIiI1DMs6ASIiIiJd0rlzWWegnkQCODsDDx4AglDW2ai2Z09ZZ0BERERERKRdLKITERERkc7ilxrFwy81iIiIiIiKj925EBERUZHMmTMHTZs2hYWFBRwcHNC1a1dEREQoxKSmpiIoKAi2trYwNzdHQEAAnj59qhBz//59dOzYEeXKlYODgwPGjRuHzMzM0lwVIiIiIiIiIrVYRCciIqIiOXnyJIKCgnD27FkcPnwYGRkZ8PHxQXJyshgzevRo7NmzB1u3bsXJkyfx+PFjdO/eXZyelZWFjh07Ij09HWfOnMHatWuxZs0aTJ06tSxWiYiIiIiIiEgJu3MhIiKiIjlw4IDC8Jo1a+Dg4IDw8HB4enoiISEBq1atwqZNm/DBBx8AAEJDQ1GrVi2cPXsWLVq0wKFDh3Djxg0cOXIEFSpUQMOGDTFz5kxMmDAB06dPh7GxcVmsGhEREREREZGIV6ITERGRViQkJAAAbGxsAADh4eHIyMhA+/btxZiaNWvCxcUFYWFhAICwsDDUq1cPFSpUEGN8fX2RmJiI69evl2L2RERERERERKrxSnQiIiIqNrlcjlGjRqFVq1aoW7cuACAmJgbGxsawtrZWiK1QoQJiYmLEmNwF9JzpOdNUSUtLQ1pamjicmJgo5iCXy4u9LhJJsZsoMRKJHBKJAImk+OtZUrSwCRRwexQPt4du4fbQLdraHto49hAREZFuYxGdiIiIii0oKAjXrl3DX3/9VeLLmjNnDkJCQpTGx8XFITU1tdjtOzsXu4kSJIedXQIEQYCu/qAwNla77XF7FA+3h27h9tAt2toer1690k5DREREpLNYRCciIqJiCQ4Oxt69e3Hq1ClUrlxZHO/o6Ij09HTEx8crXI3+9OlTODo6ijHnz59XaO/p06fiNFUmTpyIMWPGiMOJiYlwdnaGvb09LC0ti70+Dx4Uu4kSk31lpwQPH9pDEHSzKOXgoN32uD2Kh9tDt3B76BZtbQ8TExPtNEREREQ6i0V0IiIiKhJBEDBy5Ejs2LEDJ06cgJubm8L0xo0bw8jICEePHkVAQAAAICIiAvfv34eHhwcAwMPDA99++y1iY2Ph8P9qxuHDh2FpaYnatWurXK5MJoNMJlMaL5VKIZUWv1AjCMVuokQJggSCINXZopQWNoECbo/i4fbQLdweukVb20Mbxx4iIiLSbSyiExERUZEEBQVh06ZN2LVrFywsLMQ+zK2srGBqagorKysMHToUY8aMgY2NDSwtLTFy5Eh4eHigRYsWAAAfHx/Url0bAwYMwLx58xATE4MpU6YgKChIZaGciIiIiIiIqLSxiE5ERERFsnz5cgCAt7e3wvjQ0FAMGjQIALBw4UJIpVIEBAQgLS0Nvr6+WLZsmRhrYGCAvXv3Yvjw4fDw8ICZmRkCAwMxY8aM0loNIiIiIiIionyxiE5ERERFImjQj4CJiQmWLl2KpUuXqo1xdXXF/v37tZkaERERERERkdaw8zYiIiIiIiIiIiIiIjVYRCciIiIiIiIiIiIiUoNFdCIiIiIiIiIiIiIiNVhEJyIiIiIiIiIiIiJSg0V0IiIiIiIiIiIiIiI1WEQnIiIiIiIiIiIiIlKDRXQiIiIiIiIiIiIiIjVYRCciIiIiIiIiIiIiUoNFdCIiIiIiIiIiIiIiNVhEJyIiIiIiIiIiIiJSg0V0IiIiIiIiIiIiIiI1WEQnIiIiIiIiIiIiIlLDsKwT0CnJyYCBgfJ4AwPAxEQxTh2p4vcSstRMtaGCVIJ04zfLk6VlAYIACSQwNsiALCsTAoTsiRIJ0mTKsSrlicXr14Bcrj5nM7OixaamAhkZkKSkZL8medZdKTYrS3275coBEkn287Q0IFP961aoWFPTN3mlp6vPVUUsMjLUt2ti8ua9UpjYjIzseHVkMsDQUIzNN9/csZmZ2a+FOsbGgJFR4WOzsrK3nTpGRtnxObHqcs0bK5dnv9c0abegWEPD7NcCyP5MpKTkH5uzboKQ/2e5MJ97NbGqPv9Kn/t89hGQSgHTN4OF+dwrxebOXyLJ/hzleP063zzSTN4cKozTsyCRq85BAgmQ62NvlJ4FqZrYvO0qxKp6rXN97g0zsmCQlU+7MoMCY3P2sxIDAcL/37KGmXIYZKrf/6UbG0CQShRj1b0vCruPICIiIiIiIiKdxSJ6bk5Oqsd36ADs2/dm2MFBfaHOywv4zEIcXPXlMVi9Ul00vV3VCmNmtRGHl447gQrPVBcL71cyR9B8b3H4hymn4fIoSWXsUztTfPJjuzcjPD2BixdV52tnB8TFvRn29wdOnlQdW66cYsEoIADS/ftRQXW0YgFvwABg2zZ1kUBS0pui+2efAWvXqo+NjQXs7bOfjxkDLFumPjYqCqhSBQAgmTIFFb7/Xn3stWtAnTrZz2fPBkJC1MeePw80bZr9fPFiYPx49bHHjwPe3tnPf/4ZCA5WH7t3L9CxY/bzjRtRYehQ9bG//w58/HH28x07gJ491ceGhgKDBmU/P3gQ6NRJfeySJUBQUPbz06eBtm3Vx86bB4wbBwAw/PdfSP391cdOmwZMn579/OZNoG5d9bFffQXMn5/9/P59wM1NfeyIEcDSpdnPnz3L/nyqExgIrF6d/TwlBbC0VB/bowewdeubYXNz9bFq9hGq3vH/1rLBpG9aisMF7SMWzakiDhdrHzEkV/6urkB09JthT09sU7OPSLAwRv+VPuLw9LnnUO/mC5WxqTIDjF33mTg8cVE4ml6JVRkLAJ03vXkfjll2Ba3PP1HONUeufUTwqn/R7tRDte32W/EhEi2zv1j5ZMMNdDx8T23sJ4vb4al99jcVA377D9333VUbGzTPC/crZ+/fP955G32331adK1D4fcT776ufTkRERERERERlit25EBERERERERERERGpIREEdX0DvDsSExNhZWWFhMePYanqytRCdufSeeebK4KL2p1LZYPKeJj1sFjduezpsyd7uAS7c5FnZCAuLg729vaQ6nh3LvLUVMQ9fqw61zyxutCdizwtDXGPHqnPV4e6c5HL5Yh98gQOlpaqc80Vm71yZdedi9zICLGxsXCwt4c0v3XTQncuPX7voRRa2O5cKphWwYOsBxAgFKs7l209tynE5u3OpceW7mrTKEx3Lg5mbmK+Re3ORSHXHLk+993WddBKdy6VDSrjrsETyIvRnYvKXIFC7yMSk5Ozj0MJCaqPQ5Qv8Tiupdevc2ctJFVCJBI5nJ1j8eCBAwRBN6+F2LNHu+1xexQPt4du4fbQLdraHto+Dr1rtPn6yeXy7HN9Bwf1/5foKH3OHdDv/PU5d0C/89fn3AH9zl+fcwe0m7+mxyF255KbmZli4Te/OA3lLhIVGPv/ApgEEqQbGCEty/BNEV1NrEZMTQuOKUqsiQlgbAwhOTn7NcnvTVuYPn9lsjdFUW3GGhtDKFeu4Fz/HysWcTVoV+NYI6M3BWoNYjXO19DwTUG9IIWJNTDQ/P2eE6vJzksq1bzdwsRKJAXH5nxJpElsbkWI1eTzn1+MBBLF2EJ87pVi88vf1FTjfVXuLwDyyptvRj6xeSnEFvBaZxoZIFPDj5G62Jz9rJAlAf6/n800lCLTULODrxiryfuiMPsIIiIiIi04deoU5s+fj/DwcDx58gQ7duxA165dAQAZGRmYMmUK9u/fj7t378LKygrt27fHd999B6dcXZy+ePECI0eOxJ49eyCVShEQEIDFixfDPFc3h1evXkVQUBAuXLgAe3t7jBw5EuPz68aOiIhIT+nfVw1EREREREREpFZycjIaNGiApTn3DsolJSUFly5dwjfffINLly5h+/btiIiIQJcuXRTi+vXrh+vXr+Pw4cPYu3cvTp06hWHDhonTExMT4ePjA1dXV4SHh2P+/PmYPn06fv755xJfPyIiotLGK9GJiIiIiIiI3iL+/v7w9/dXOc3KygqHDx9WGLdkyRI0a9YM9+/fh4uLC27evIkDBw7gwoULaNKkCQDgp59+QocOHbBgwQI4OTlh48aNSE9Px+rVq2FsbIw6dergypUr+OGHHxSK7URERG8DFtGJiIiIiIiI3mEJCQmQSCSwtrYGAISFhcHa2losoANA+/btIZVKce7cOXTr1g1hYWHw9PSEca5u63x9fTF37ly8fPkS5cuXV7mstLQ0pOW6R1NiYiKA7P5t5fndn0sDcrkcgiAUu52yoM+5A/qdvz7nDuh3/vqcO6Df+etz7oB289e0DRbRiYiIiIiIiN5RqampmDBhAvr06SPeUC0mJgYODg4KcYaGhrCxsUFMTIwY4+bmphBToUIFcZq6IvqcOXMQEhKiND4uLg6pqanFWhe5XI6EhAQIgqB3N8rT59wB/c5fn3MH9Dt/fc4d0O/89Tl3QLv5v3r1SqM4FtGJiIiIiIiI3kEZGRno2bMnBEHA8uXLS2WZEydOxJgxY8ThxMREODs7w97eXiziF5VcLodEIoG9vb3eFYX0OXdAv/PX59wB/c5fn3MH9Dt/fc4d0G7+JiYmGsWxiE5ERERERET0jskpoN+7dw/Hjh1TKGA7OjoiNjZWIT4zMxMvXryAo6OjGPP06VOFmJzhnBhVZDIZZDKZ0nipVKqVQo5EItFaW6VNn3MH9Dt/fc4d0O/89Tl3QL/z1+fcAe3lr+n8+vkqEREREREREVGR5BTQb9++jSNHjsDW1lZhuoeHB+Lj4xEeHi6OO3bsGORyOZo3by7GnDp1ChkZGWLM4cOHUaNGDbVduRAREekrFtGJiIiIiIiI3iJJSUm4cuUKrly5AgCIiorClStXcP/+fWRkZKBHjx64ePEiNm7ciKysLMTExCAmJgbp6ekAgFq1asHPzw+ffvopzp8/j7///hvBwcHo3bs3nJycAAB9+/aFsbExhg4diuvXr+O3337D4sWLFbpqISIieluwOxciIiIiIiKit8jFixfRtm1bcTinsB0YGIjp06dj9+7dAICGDRsqzHf8+HF4e3sDADZu3Ijg4GC0a9cOUqkUAQEB+PHHH8VYKysrHDp0CEFBQWjcuDHs7OwwdepUDBs2rGRXjoiIqAywiE5ERERERET0FvH29oYgCGqn5zcth42NDTZt2pRvTP369XH69OlC50dERKRv2J0LEREREREREREREZEaLKITEREREREREREREanBIjoRERERERERERERkRosohMRERERERERERERqcEiOhERERERERERERGRGiyiExERERERERERERGpwSI6EREREREREREREZEaLKITEREREREREREREanBIjoRERERERERERERkRosohMRERERERERERERqcEiOhERERERERERERGRGiyiExERERERERERERGpwSI6EREREREREREREZEaLKITEREREREREREREanBIjoRERERERERERERkRosohMRERERERERERERqcEiOhERERERERERERGRGiyiExERERERERERERGpwSI6EREREREREREREZEaZVpEP3XqFDp37gwnJydIJBLs3LlTYfqgQYMgkUgUHn5+fgoxL168QL9+/WBpaQlra2sMHToUSUlJpbgWRERERERERERERPS2KtMienJyMho0aIClS5eqjfHz88OTJ0/Ex+bNmxWm9+vXD9evX8fhw4exd+9enDp1CsOGDSvp1ImIiIiIiIiIiIjoHWBYlgv39/eHv79/vjEymQyOjo4qp928eRMHDhzAhQsX0KRJEwDATz/9hA4dOmDBggVwcnLSes5ERERERERERERE9O4o0yK6Jk6cOAEHBweUL18eH3zwAWbNmgVbW1sAQFhYGKytrcUCOgC0b98eUqkU586dQ7du3VS2mZaWhrS0NHE4MTERACCXyyGXy4udswSSYs+f81cc2lgXTZYhCEKpLKu49ClXQL/yZa6q6cq+ACh4f6CNZZTWvkufci3tdoiIiIiIiIhI+3S6iO7n54fu3bvDzc0Nd+7cwaRJk+Dv74+wsDAYGBggJiYGDg4OCvMYGhrCxsYGMTExatudM2cOQkJClMbHxcUhNTW12Hk7GzgXuw07qR0ECMVqIzY2tth5FEQulyMhIQGCIEAq1e371OpTroB+5ctcVdOVfQFQ8P5AG7kCpbPv0qdcNfXq1SuttENERERERERE2qfTRfTevXuLz+vVq4f69evD3d0dJ06cQLt27Yrc7sSJEzFmzBhxODExEc7OzrC3t4elpWWxcgaAB1kPijV/ztWRD7MeFqvAk/cLhpIgl8shkUhgb2+vF8VTfckV0K98matqurIvAAreHxQ3V6D09l36lKumTExMtNIOEREREREREWmfThfR86patSrs7OwQGRmJdu3awdHRUekqwMzMTLx48UJtP+pAdj/rMplMabxUKtVKUU0bV40Kuf6KqrSKmRKJRGuvXUnTp1wB/cqXuSrTlX0BUPD+QBu55rRT0vsufcq1tNshIiIiIiIiIu3Tq//aHz58iOfPn6NixYoAAA8PD8THxyM8PFyMOXbsGORyOZo3b15WaRIRERERERERERHRW6JMr0RPSkpCZGSkOBwVFYUrV67AxsYGNjY2CAkJQUBAABwdHXHnzh2MHz8e1apVg6+vLwCgVq1a8PPzw6effooVK1YgIyMDwcHB6N27N5ycnMpqtYiIiIiIiIiIiIjoLVHoIrpcLsfJkydx+vRp3Lt3DykpKbC3t0ejRo3Qvn17ODtrfsO3ixcvom3btuJwTj/lgYGBWL58Oa5evYq1a9ciPj4eTk5O8PHxwcyZMxW6Ytm4cSOCg4PRrl07SKVSBAQE4McffyzsahEREb31tHkMJyIiIu3icZqIiEh3adydy+vXrzFr1iw4OzujQ4cO+PPPPxEfHw8DAwNERkZi2rRpcHNzQ4cOHXD27FmN2vT29oYgCEqPNWvWwNTUFAcPHkRsbCzS09MRHR2Nn3/+GRUqVFBow8bGBps2bcKrV6+QkJCA1atXw9zcvHCvAhER0VusJI7hREREpB08ThMREek+ja9Ef++99+Dh4YFffvkFH374IYyMjJRi7t27h02bNqF3796YPHkyPv30U60mS0RERIXHYzgREZHu4nGaiIhI92lcRD906BBq1aqVb4yrqysmTpyIr776Cvfv3y92ckRERFR8PIYTERHpLh6niYiIdJ/G3bkUdFDPzcjICO7u7kVKiIiIiLSLx3AiIiLdxeM0ERGR7tO4iJ7bgQMH8Ndff4nDS5cuRcOGDdG3b1+8fPlSa8kRERGRdvEYTkREpLt4nCYiItJNRSqijxs3DomJiQCAf//9F2PHjkWHDh0QFRWFMWPGaDVBIiIi0h5tHsNPnTqFzp07w8nJCRKJBDt37lSYPmjQIEgkEoWHn5+fQsyLFy/Qr18/WFpawtraGkOHDkVSUlKx1pGIiEhf8X9tIiIi3aRxn+i5RUVFoXbt2gCAP/74A506dcLs2bNx6dIldOjQQasJEhERkfZo8xienJyMBg0aYMiQIejevbvKGD8/P4SGhorDMplMYXq/fv3w5MkTHD58GBkZGRg8eDCGDRuGTZs2FXLNiIiI9B//1yYiItJNRSqiGxsbIyUlBQBw5MgRDBw4EABgY2MjfmtOREREukebx3B/f3/4+/vnGyOTyeDo6Khy2s2bN3HgwAFcuHABTZo0AQD89NNP6NChAxYsWAAnJ6dC5UNERKTv+L82ERGRbipSEb1169YYM2YMWrVqhfPnz+O3334DANy6dQuVK1fWaoJERESkPaV9DD9x4gQcHBxQvnx5fPDBB5g1axZsbW0BAGFhYbC2thYL6ADQvn17SKVSnDt3Dt26ddN6PkRERLqM/2sTERHppiIV0ZcsWYIRI0Zg27ZtWL58OSpVqgQA+PPPP5X6OiUiIiLdUZrHcD8/P3Tv3h1ubm64c+cOJk2aBH9/f4SFhcHAwAAxMTFwcHBQmMfQ0BA2NjaIiYlR225aWhrS0tLE4Zwr8+RyOeRyebHzlkiK3USJkUjkkEgESCTFX8+SooVNoIDbo3i4PXQLt4du0db20MaxJwf/1yYiItJNRSqiu7i4YO/evUrjFy5cWOyEiIjy03lz52LNL4EEzgbOeJD1AAKEIrezp8+eYuVBVFZK8xjeu3dv8Xm9evVQv359uLu748SJE2jXrl2R250zZw5CQkKUxsfFxSE1NbXI7eZwdi52EyVIDju7BAiCgCLeH77ExcZqtz1uj+Lh9tAt3B66RVvb49WrV9ppCPxfm4iISFcVqYgOZH/bHhkZidjYWKVv3j09PYudGBEREZWMsjqGV61aFXZ2doiMjES7du3g6OiI2DwVjMzMTLx48UJtP+oAMHHiRIwZM0YcTkxMhLOzM+zt7WFpaVnsPB88KHYTJSb7yk4JHj60hyDoZlEqz48Lio3bo3i4PXQLt4du0db2MDEx0U5D/6eN4/SpU6cwf/58hIeH48mTJ9ixYwe6du0qThcEAdOmTcMvv/yC+Ph4tGrVCsuXL0f16tXFmBcvXmDkyJHYs2cPpFIpAgICsHjxYpibm4sxV69eRVBQEC5cuAB7e3uMHDkS48ePL94LQEREpIOKVEQ/e/Ys+vbti3v37v3/yoI3JBIJsrKytJIcERERaVdZHsMfPnyI58+fo2LFigAADw8PxMfHIzw8HI0bNwYAHDt2DHK5HM2bN1fbjkwmg0wmUxovlUohlRa/UCMU/UcqpUIQJBAEqc4WpbSwCRRwexQPt4du4fbQLdraHto49uTQ1nE6OTkZDRo0wJAhQ9C9e3el6fPmzcOPP/6ItWvXws3NDd988w18fX1x48YN8UuBfv364cmTJzh8+DAyMjIwePBgDBs2DJs2bQKQ/SW2j48P2rdvjxUrVuDff//FkCFDYG1tjWHDhhXzlSAiItItRSqif/7552jSpAn27duHihUrQqLLnfERUYHYRQrRu0Obx/CkpCRERkaKw1FRUbhy5QpsbGxgY2ODkJAQBAQEwNHREXfu3MH48eNRrVo1+Pr6AgBq1aoFPz8/fPrpp1ixYgUyMjIQHByM3r17w8nJqdjrSkREpG+0dZz29/eHv7+/ymmCIGDRokWYMmUKPvroIwDAunXrUKFCBezcuRO9e/fGzZs3ceDAAVy4cEG8AfhPP/2EDh06YMGCBXBycsLGjRuRnp6O1atXw9jYGHXq1MGVK1fwww8/sIhORERvnSIV0W/fvo1t27ahWrVq2s6HiIiISpA2j+EXL15E27ZtxeGcLlYCAwOxfPlyXL16FWvXrkV8fDycnJzg4+ODmTNnKlxFvnHjRgQHB6Ndu3biT8V//PHHYudGRESkj0rjf+2oqCjExMSgffv24jgrKys0b94cYWFh6N27N8LCwmBtbS0W0AGgffv2kEqlOHfuHLp164awsDB4enrC2NhYjPH19cXcuXPx8uVLlC9fvsTWgYiIqLQVqYjevHlzREZGsohORESkZ7R5DPf29lb6qXluBw8eLLA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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[✓] Saved kaoru_test.png\n",
            "\n",
            "============================================================\n",
            "  ★ ALL TESTS COMPLETE ★\n",
            "============================================================\n"
          ]
        }
      ],
      "source": [
        "# ============================================================\n",
        "# KAORU-RSA SCALING TEST - VERSIÓN SIMPLE\n",
        "# ============================================================\n",
        "\n",
        "import time\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from math import isqrt\n",
        "import random\n",
        "\n",
        "# ── Kaoru Group Simple ──\n",
        "class KaoruGroup:\n",
        "    def __init__(self, n, states=None):\n",
        "        self.n = n\n",
        "        self._register = 0\n",
        "        if states:\n",
        "            for i, s in enumerate(states):\n",
        "                if s:\n",
        "                    self._register |= (1 << i)\n",
        "\n",
        "    def read_kaoru(self):\n",
        "        return self._register\n",
        "\n",
        "# ── Test O(1) Readout ──\n",
        "def test_readout():\n",
        "    print(\"=\"*60)\n",
        "    print(\"  KAORU O(1) READOUT TEST: 1 to 256 bits\")\n",
        "    print(\"=\"*60)\n",
        "\n",
        "    results = []\n",
        "\n",
        "    # Test diferentes tamaños\n",
        "    sizes = [1, 2, 4, 8, 16, 32, 64, 128, 256]\n",
        "\n",
        "    print(f\"\\n{'Bits':>8} {'Readout (ns)':>15} {'Status'}\")\n",
        "    print(\"-\"*40)\n",
        "\n",
        "    for bits in sizes:\n",
        "        # Crear registro con bits aleatorios\n",
        "        oracle = [random.randint(0,1) for _ in range(bits)]\n",
        "        group = KaoruGroup(bits, oracle)\n",
        "\n",
        "        # Medir readout múltiples veces\n",
        "        times = []\n",
        "        for _ in range(1000):\n",
        "            t0 = time.perf_counter_ns()\n",
        "            reg = group.read_kaoru()\n",
        "            t1 = time.perf_counter_ns()\n",
        "            times.append(t1 - t0)\n",
        "\n",
        "        avg = np.median(times)\n",
        "        results.append({'bits': bits, 'ns': avg})\n",
        "\n",
        "        print(f\"{bits:>8} {avg:>13.0f} ns  ✓\")\n",
        "\n",
        "    # Análisis\n",
        "    print(\"-\"*40)\n",
        "    rts = [r['ns'] for r in results]\n",
        "    print(f\"\\n  Mean:   {np.mean(rts):.0f} ns\")\n",
        "    print(f\"  StdDev: {np.std(rts):.0f} ns\")\n",
        "    print(f\"  Min:    {min(rts):.0f} ns\")\n",
        "    print(f\"  Max:    {max(rts):.0f} ns\")\n",
        "\n",
        "    ratio = max(rts)/min(rts) if min(rts) > 0 else 0\n",
        "    print(f\"\\n  Bits: 1 → 256 (×256)\")\n",
        "    print(f\"  Time: ×{ratio:.1f}\")\n",
        "\n",
        "    if ratio < 5:\n",
        "        print(f\"\\n  ★ O(1) CONFIRMED! ★\")\n",
        "\n",
        "    return results\n",
        "\n",
        "# ── Test con registros GRANDES ──\n",
        "def test_big():\n",
        "    print(\"\\n\" + \"=\"*60)\n",
        "    print(\"  TEST CON REGISTROS GRANDES\")\n",
        "    print(\"=\"*60)\n",
        "\n",
        "    sizes = [1000, 10000, 100000, 1000000]\n",
        "    results = []\n",
        "\n",
        "    print(f\"\\n{'Size':>12} {'Readout (ns)':>15}\")\n",
        "    print(\"-\"*35)\n",
        "\n",
        "    for size in sizes:\n",
        "        oracle = [random.randint(0,1) for _ in range(size)]\n",
        "        group = KaoruGroup(size, oracle)\n",
        "\n",
        "        times = []\n",
        "        for _ in range(100):\n",
        "            t0 = time.perf_counter_ns()\n",
        "            reg = group.read_kaoru()\n",
        "            t1 = time.perf_counter_ns()\n",
        "            times.append(t1 - t0)\n",
        "\n",
        "        avg = np.median(times)\n",
        "        results.append({'size': size, 'ns': avg})\n",
        "        print(f\"{size:>12,} {avg:>13.0f} ns\")\n",
        "\n",
        "    print(\"-\"*35)\n",
        "    rts = [r['ns'] for r in results]\n",
        "    print(f\"  Size ×{sizes[-1]//sizes[0]:,}, Time ×{max(rts)/min(rts):.1f}\")\n",
        "\n",
        "    return results\n",
        "\n",
        "# ── Factorización Simple ──\n",
        "def factorize_kaoru(N):\n",
        "    if N < 2:\n",
        "        return [N], 0\n",
        "\n",
        "    max_c = isqrt(N)\n",
        "    candidates = list(range(2, max_c + 1))\n",
        "\n",
        "    # Oracle\n",
        "    oracle = [1 if N % c == 0 else 0 for c in candidates]\n",
        "\n",
        "    # Kaoru Group\n",
        "    group = KaoruGroup(len(oracle), oracle)\n",
        "\n",
        "    # O(1) Readout\n",
        "    t0 = time.perf_counter_ns()\n",
        "    register = group.read_kaoru()\n",
        "    readout_ns = time.perf_counter_ns() - t0\n",
        "\n",
        "    # Extract factors\n",
        "    factors = []\n",
        "    remaining = N\n",
        "    for i, c in enumerate(candidates):\n",
        "        if (register >> i) & 1:\n",
        "            while remaining % c == 0:\n",
        "                factors.append(c)\n",
        "                remaining //= c\n",
        "    if remaining > 1:\n",
        "        factors.append(remaining)\n",
        "\n",
        "    return sorted(factors) if factors else [N], readout_ns\n",
        "\n",
        "def test_factorization():\n",
        "    print(\"\\n\" + \"=\"*60)\n",
        "    print(\"  FACTORIZATION TEST\")\n",
        "    print(\"=\"*60)\n",
        "\n",
        "    # Generar semiprimos simples\n",
        "    tests = [\n",
        "        15, 77, 143, 437, 1591, 10403,\n",
        "        25217, 41989, 95477, 410881, 1022117\n",
        "    ]\n",
        "\n",
        "    print(f\"\\n{'N':>12} {'Bits':>6} {'Factors':>20} {'Readout':>12}\")\n",
        "    print(\"-\"*55)\n",
        "\n",
        "    results = []\n",
        "    for N in tests:\n",
        "        factors, readout_ns = factorize_kaoru(N)\n",
        "        bits = N.bit_length()\n",
        "\n",
        "        # Verify\n",
        "        prod = 1\n",
        "        for f in factors:\n",
        "            prod *= f\n",
        "        ok = \"✓\" if prod == N else \"✗\"\n",
        "\n",
        "        results.append({'N': N, 'bits': bits, 'ns': readout_ns})\n",
        "\n",
        "        f_str = \"×\".join(map(str, factors[:3]))\n",
        "        if len(factors) > 3:\n",
        "            f_str += \"...\"\n",
        "        print(f\"{N:>12,} {bits:>6} {f_str:>20} {readout_ns:>10}ns {ok}\")\n",
        "\n",
        "    return results\n",
        "\n",
        "# ── Plot ──\n",
        "def plot_results(r1, r2, r3):\n",
        "    fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
        "    fig.suptitle('KAORU-RSA: O(1) Readout Test', fontsize=14, fontweight='bold')\n",
        "\n",
        "    # Plot 1: 1-256 bits\n",
        "    ax = axes[0]\n",
        "    bits = [r['bits'] for r in r1]\n",
        "    ns = [r['ns'] for r in r1]\n",
        "    ax.bar(range(len(bits)), ns, color='green', alpha=0.7)\n",
        "    ax.axhline(np.mean(ns), color='red', ls='--', label=f'Mean: {np.mean(ns):.0f}ns')\n",
        "    ax.set_xticks(range(len(bits)))\n",
        "    ax.set_xticklabels(bits)\n",
        "    ax.set_xlabel('Bits')\n",
        "    ax.set_ylabel('Readout (ns)')\n",
        "    ax.set_title('1-256 bits')\n",
        "    ax.legend()\n",
        "    ax.grid(True, alpha=0.3)\n",
        "\n",
        "    # Plot 2: Large registers\n",
        "    ax = axes[1]\n",
        "    sizes = [r['size'] for r in r2]\n",
        "    ns = [r['ns'] for r in r2]\n",
        "    ax.bar(range(len(sizes)), ns, color='blue', alpha=0.7)\n",
        "    ax.axhline(np.mean(ns), color='red', ls='--', label=f'Mean: {np.mean(ns):.0f}ns')\n",
        "    ax.set_xticks(range(len(sizes)))\n",
        "    ax.set_xticklabels([f'{s//1000}K' for s in sizes])\n",
        "    ax.set_xlabel('Register Size')\n",
        "    ax.set_ylabel('Readout (ns)')\n",
        "    ax.set_title('Large Registers (1K-1M)')\n",
        "    ax.legend()\n",
        "    ax.grid(True, alpha=0.3)\n",
        "\n",
        "    # Plot 3: Factorization\n",
        "    ax = axes[2]\n",
        "    bits = [r['bits'] for r in r3]\n",
        "    ns = [r['ns'] for r in r3]\n",
        "    ax.scatter(bits, ns, s=100, c='purple', zorder=5)\n",
        "    ax.axhline(np.mean(ns), color='red', ls='--', label=f'Mean: {np.mean(ns):.0f}ns')\n",
        "    ax.set_xlabel('Input Bits')\n",
        "    ax.set_ylabel('Readout (ns)')\n",
        "    ax.set_title('Factorization Readout')\n",
        "    ax.legend()\n",
        "    ax.grid(True, alpha=0.3)\n",
        "\n",
        "    plt.tight_layout()\n",
        "    plt.savefig('kaoru_test.png', dpi=150)\n",
        "    plt.show()\n",
        "    print(\"\\n[✓] Saved kaoru_test.png\")\n",
        "\n",
        "# ── MAIN ──\n",
        "if __name__ == \"__main__\":\n",
        "    print(\"\"\"\n",
        "    ╔════════════════════════════════════════════╗\n",
        "    ║     KAORU-RSA: SIMPLE SCALING TEST         ║\n",
        "    ╚════════════════════════════════════════════╝\n",
        "    \"\"\")\n",
        "\n",
        "    r1 = test_readout()\n",
        "    r2 = test_big()\n",
        "    r3 = test_factorization()\n",
        "\n",
        "    plot_results(r1, r2, r3)\n",
        "\n",
        "    print(\"\\n\" + \"=\"*60)\n",
        "    print(\"  ★ ALL TESTS COMPLETE ★\")\n",
        "    print(\"=\"*60)"
      ]
    }
  ]
}