Colab_17_L'algoritmo_di_Shor.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOWybU5StmVYj45QN3ET4bJ",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/EmmanueleVilla/quantum_computing/blob/main/Colab_17_L'algoritmo_di_Shor.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "g_FoRSIhRflf"
      },
      "outputs": [],
      "source": [
        "!pip install qiskit --quiet && pip install pylatexenc --quiet && pip install qiskit-aer --quiet"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from qiskit import QuantumCircuit, Aer, transpile, execute, assemble, QuantumRegister, ClassicalRegister\n",
        "from qiskit.visualization import plot_histogram, plot_bloch_multivector\n",
        "from qiskit.visualization.state_visualization import array_to_latex\n",
        "from math import gcd\n",
        "from numpy.random import randint\n",
        "import pandas as pd\n",
        "from fractions import Fraction\n",
        "from qiskit.circuit.library import QFT"
      ],
      "metadata": {
        "id": "YFLbY_XWRik5"
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## La funzione periodica"
      ],
      "metadata": {
        "id": "u3EvA6HZTOk3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "N = 35\n",
        "a = 3\n",
        "xvals = np.arange(30)\n",
        "yvals = [np.mod(a**x, N) for x in xvals]\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(xvals, yvals)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "IFKkKqgfTP0P",
        "outputId": "966cce5b-ad1c-4872-fa9d-ac30416778df"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7afc51bd87f0>]"
            ]
          },
          "metadata": {},
          "execution_count": 35
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "8twVjCX7TkVf"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Soluzione classica"
      ],
      "metadata": {
        "id": "H55k4-zzT24n"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = 1\n",
        "a = 3\n",
        "N = 35\n",
        "while(True):\n",
        "  y = np.mod(a**x, 35)\n",
        "  if y == 1:\n",
        "    print(x)\n",
        "    break\n",
        "  x += 1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h0Ki1X_jT4Vl",
        "outputId": "62e33add-d070-4ea8-d006-3f3d2634d11b"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Operatore U"
      ],
      "metadata": {
        "id": "1dAvpJ65XwMT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Creo l'operatore U\n",
        "a = 7\n",
        "mod = 15\n",
        "pow = 2\n",
        "\n",
        "qc = QuantumCircuit(4)\n",
        "for _iteration in range(pow):\n",
        "  qc.swap(0,1)\n",
        "  qc.swap(1,2)\n",
        "  qc.swap(2,3)\n",
        "  qc.barrier()\n",
        "  qc.x(range(4))\n",
        "  qc.barrier()\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "HzNvT850UJV1",
        "outputId": "5efd269b-0bfc-43f9-c6fa-fa1ba3074e58"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1123.61x367.889 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Soluzione quantistica"
      ],
      "metadata": {
        "id": "fJ9lcJvfYX7x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def c_amod15(a, power):\n",
        "    if a not in [2,4,7,8,11,13]:\n",
        "        raise ValueError(\"'a' must be 2,4,7,8,11 or 13\")\n",
        "    U = QuantumCircuit(4)\n",
        "    for _iteration in range(power):\n",
        "        if a in [2,13]:\n",
        "            U.swap(2,3)\n",
        "            U.swap(1,2)\n",
        "            U.swap(0,1)\n",
        "        if a in [7,8]:\n",
        "            U.swap(0,1)\n",
        "            U.swap(1,2)\n",
        "            U.swap(2,3)\n",
        "        if a in [4, 11]:\n",
        "            U.swap(1,3)\n",
        "            U.swap(0,2)\n",
        "        if a in [7,11,13]:\n",
        "            for q in range(4):\n",
        "                U.x(q)\n",
        "    U = U.to_gate()\n",
        "    U.name = f\"{a}^{power} mod 15\"\n",
        "    c_U = U.control()\n",
        "    return c_U"
      ],
      "metadata": {
        "id": "zFQ1rj_mYhpA"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "N_COUNT = 8\n",
        "a = 7\n",
        "N = 35"
      ],
      "metadata": {
        "id": "RH8NxQ7HZqWH"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def qft_dagger(n):\n",
        "    qc = QuantumCircuit(n)\n",
        "    # Don't forget the Swaps!\n",
        "    for qubit in range(n//2):\n",
        "        qc.swap(qubit, n-qubit-1)\n",
        "    for j in range(n):\n",
        "        for m in range(j):\n",
        "            qc.cp(-np.pi/float(2**(j-m)), m, j)\n",
        "        qc.h(j)\n",
        "    qc.name = \"QFT†\"\n",
        "    return qc"
      ],
      "metadata": {
        "id": "jmB5z_htZzuO"
      },
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "qft_dagger(4).draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 227
        },
        "id": "I2OGGJm4adSA",
        "outputId": "ab04ab63-5449-498f-aa5b-e585ae34addf"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1541.66x367.889 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Creo il circuito totale\n",
        "qc = QuantumCircuit(N_COUNT + 4, N_COUNT)\n",
        "\n",
        "qc.h(range(N_COUNT))\n",
        "\n",
        "qc.x(N_COUNT)\n",
        "\n",
        "for q in range(N_COUNT):\n",
        "  qc.append(c_amod15(a, 2**q), [q] + [i+N_COUNT for i in range(4)])\n",
        "\n",
        "qc.append(qft_dagger(N_COUNT), range(N_COUNT))\n",
        "\n",
        "qc.measure(range(N_COUNT), range(N_COUNT))\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 878
        },
        "id": "4cTxBPlfaeiG",
        "outputId": "e4e45d52-c215-4811-b80b-8187652317cf"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 2228.58x2290.94 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "aer_sim = Aer.get_backend(\"aer_simulator\")\n",
        "t_qc = transpile(qc, aer_sim)\n",
        "counts = aer_sim.run(t_qc).result().get_counts()\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "id": "sMHrm12da27v",
        "outputId": "afe853b5-9c87-4a76-a817-b6b6cde86c0f"
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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kPo9v6UN/4p68kswfxj15pa3TkHnck1eSB8cMIP92MqaxN3gu98yU5L8fG9d2Mqaxx4t1SrZw+PPdTmlpaXB1dUVGRoaUPUpi1Hvy9Ho93nvvPaxevRpvv/12scA2bdo0nDp1CgcOHCjxatuSODo6lrqnrujQ64MXZDzM0tKyxOcyNzeXzhksotFoDPY6Fnn4nMJ/a3/4cekfJb02arW6xMMIpW2P572dnqS9tNrLsk5UMmPbTsY09qhkxradjGnsUcnk2k7Fnu+xeslAr9djwIABWLFiBXr37o3ly5cXe2FiYmKg1+vRrFkzqFQq6b/Q0FAAwMKFC6FSqdCtWzfpd7y9vZGdnY2UlJRiz1l0Ll7RuXlERERELyqjjOZFAe/nn39Gr1698Msvv5SYZNu2bYsKFSoUa79x4wa2b9+OOnXqoEWLFvD3/+fcpODgYERHRyM8PBz9+vUz+L0dO3ZIfYiIiIheZEYX8ooO0f7888944403sHLlylIPPQ0bNqzE9oiICGzfvh3BwcHFDvEOGDAAM2fOxNSpU9G1a1fp0GxsbCzWrFmDunXromXLls92pYiIiIjKmdGFvC+//BIrVqyAnZ0dfHx88PXXXxfr061bt0fe8PhRfHx8MHnyZEyYMAF+fn7o0aMHsrKysHbtWgDA4sWLeW4KERERvfCMLuRduXIFAJCdnY2pU6eW2KdatWplDnkAMH78eFSrVg1z5szBggULYGFhgVatWuGrr75CQEBAmR+XiIiIyFgYXchbvnw5li9f/lSPERISgn+7M0zfvn3Rt2/fp3oeIiIiImPF45JERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECmSUIW/lypUYPHgwGjduDEtLS6hUKixfvrzU/vHx8RgwYAC8vb1hbW2NKlWqoG3bttiyZUupv7Nq1So0adIEtra2cHZ2xmuvvYbjx48/h7UhIiIiKn9GGfImTJiARYsW4erVq3B3d39k30OHDsHPzw8rV65EgwYN8Mknn6Bdu3Y4cuQIunbtiilTphT7nalTp+Ltt9/GrVu3MGTIELzxxhvYu3cvgoKCEBUV9bxWi4iIiKjcGGXIW7JkCa5cuYLU1FQMGTLkkX2nTJmC3Nxc/Pbbb/j9998xffp0LF26FCdOnIC9vT1mzJiB/Px8qX98fDwmT54MHx8fnDhxArNmzcKiRYuwd+9eAMCgQYOg1+uf6/oRERERPW9GGfJeffVVeHl5PVbfS5cuQaVSoUOHDgbtXl5eqF+/PnJzc5GdnS21L1u2DIWFhRg/fjwcHR2l9oYNG6J37944d+4c9u/f/2xWhIiIiEgmRhnynkS9evUghMCff/5p0J6YmIhTp07Bz88Prq6uUntERAQAICwsrNhjtWvXDgAQGRn5/AomIiIiKgdmchfwtL7++mtERUWhZ8+e6NKlC3x8fHDr1i1s2LABNWvWxLp16wz6x8fHw87ODpUrVy72WN7e3lKf0uTn5xsc/s3MzAQAaLVaaLVaAIBarYZGo4FOpzM49FvUXlhYCCGE1K7RaKBWq0ttv/+45k/wqpiOotccAFQqFczMzKDX66HT6Yq1l7Y9nu12+oeZ2f0/r8LCwsdqNzc3L7X2sqwToHnEK2e6jG07GdPYU8D3/ufC2LaTMY09Kll5bKfH8cKHvDp16uDgwYN44403sGHDBqnd1dUVAwYMQM2aNQ36Z2RkwM3NrcTHcnBwkPqUZtq0aSVezBEeHg4bGxsAQNWqVeHv74+TJ08iMTFR6lO7dm3UqVMHhw8fRmpqqtTesGFDeHl5Ye/evcjKypLamzdvDjc3N4SHhwPo9IhXwXRt375d+re9vT3atGmDpKQkxMbGSu0VK1ZEUFAQ4uPjERcXJ7U/j+304B9eaGgorK2tDWoEgI4dOyI3Nxd79uyR2szMzNCpUyfcvn0b0dHRz2SdAP/HfBVNi7FtJ2Mae0DJ742mzti2kzGNPSrZ895Ox44de6w6VOLBaG6Epk+fjnHjxmHZsmXo379/seWHDx9Gt27dUL9+fUybNg116tRBSkoKfvzxR8yePRtvvPEGfv31V6m/hYUF3NzccO3atWKPFR8fDx8fH3Tp0gWbN28usZ6S9uR5enri9u3bUkh8Ht/Sh/7EPXklmT+Me/JKW6ch87gnryQPjhlA/u1kTGNv8FzumSnJfz82ru1kTGNv0JxHvHAmbOHw57ud0tLS4OrqioyMDCl7lOSF3pOn1Wrx1ltvQa1WY+PGjdKetBo1auD777/H5cuXsX79ekRFRaFFixYAAEdHx1L31BUden3wgoyHWVpawtLSsli7ubk5zM0Ng5hGo4FGU/yDtugP+HHbH35c+kdJr41arS7xMEJp2+N5b6cnaS+t9rKsE5XM2LaTMY09KpmxbSdjGntUMrm2U7Hne6xeRur8+fO4fPkymjZtKgW8B4WGhgIAYmJipDZvb29kZ2cjJSWlWP+ic/GKzs0jIiIielG90CGvoKAAAAzOH3hQUfuDe96Cg4MB4P/PczO0Y8cOgz5EREREL6oXOuTVq1cPDg4OiIqKKhbakpKSsHDhQqhUKoPQNmDAAJiZmWHq1KkGh21jY2OxZs0a1K1bFy1btiy3dSAiIiJ6HozyIPuSJUukGxKfOnVKaiu6x13Lli0xcOBAWFpa4rvvvsPgwYPRoUMHvPbaa9KFFxs2bEB2djY+++wz+Pj4SI/t4+ODyZMnY8KECfDz80OPHj2QlZWFtWvXAgAWL17Mc1OIiIjohWeUIW///v1YsWKFQVtUVJTBvLIDBw4EAHzwwQeoXr06fvjhBxw4cADbtm2DnZ0dAgIC8MEHH6Bv377FHn/8+PGoVq0a5syZgwULFsDCwgKtWrXCV199hYCAgOe7ckRERETlwChD3vLly7F8+fLH7t+2bVu0bdv2iZ6jb9++JQZAIiIiIiXgcUkiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlKgMoe8vXv3IjEx8ZF9kpKSsHfv3rI+BRERERGVUZlDXmhoKJYvX/7IPj///DNCQ0PL+hREREREVEZlDnlCiH/to9froVKpyvoURERERFRGz/WcvPj4eDg6Oj7PpyAiIiKiEpg9Sef33nvP4OdNmzbhypUrxfrpdDrpfLwOHTo8VYFERERE9OSeKOQ9eA6eSqVCbGwsYmNjS+yrUqkQGBiI2bNnP019RERERFQGTxTyLl++DOD++Xg1atTAiBEj8MknnxTrp9Fo4OzsDFtb22dTJRERERE9kScKeV5eXtK/ly1bBn9/f4M2IiIiIjIOTxTyHvTuu+8+yzqIiIiI6Bkqc8grcvjwYRw5cgTp6enQ6XTFlqtUKkycOPFpn4aIiIiInkCZQ15aWhq6deuGqKioR94zjyGPiIiIqPyVOeR9+umn2L9/P0JCQvDuu+/ipZdegpnZU+8YJCIiIqJnoMypbOvWrWjSpAl27drFWS2IiIiIjEyZZ7zIzc1F69atGfCIiIiIjFCZQ17Dhg1LnO2CiIiIiORX5pD3n//8B1u2bMHBgwefZT1ERERE9AyU+Zy8lJQUdOrUCcHBwejbty8CAgLg4OBQYt9+/fqVuUAiIiIienJlDnn9+/eHSqWCEALLly/H8uXLi52fJ4SASqViyCMiIiIqZ2UOecuWLXuWdRARERHRM8RpzYiIiIgUqMwXXhARERGR8SrznrzExMTH7lu1atWyPg0RERERlUGZQ161atUe60bIKpUKhYWFZX0aIiIiIiqDMoe8fv36lRjyMjIycOLECVy+fBnBwcGoVq3a09RHRERERGVQ5pC3fPnyUpcJITBr1ix8++23+N///lfWpyAiIiKiMnouF16oVCp8/vnnePnllzFq1Kjn8RRERERE9AjP9eraxo0bY/fu3c/zKYiIiIioBM815CUkJPCiCyIiIiIZlPmcvNLo9Xpcv34dy5cvx+bNm/HKK68866cgIiIion9R5pCnVqsfeQsVIQScnZ0xa9assj4FEREREZVRmUNe69atSwx5arUazs7OCAwMxIABA+Dm5vZUBRIRERHRkytzyIuIiHiGZRARERHRs8S5a4mIiIgU6JlceBEVFYXY2FhkZmbCwcEBDRs2RIsWLZ7FQxMRERFRGTxVyDtw4AAGDBiAixcvArh/sUXReXre3t5YtmwZmjdv/vRVEhEREdETKXPIO3PmDMLCwnDv3j20bdsWoaGhcHd3R0pKCvbs2YPw8HC0a9cOBw8ehK+v77OsmYiIiIj+RZlD3pdffomCggJs374d7du3N1g2ZswY/PXXX+jSpQu+/PJLrF279qkLJSIiIqLHV+YLLyIiItCzZ89iAa9I+/bt0bNnT+zZs6fMxRERERFR2ZQ55GVkZKB69eqP7FO9enVkZGSU9SmIiIiIqIzKHPI8PDxw8ODBR/Y5dOgQPDw8yvoURERERFRGZQ55Xbp0QUREBCZOnIi8vDyDZXl5efjPf/6DPXv2oGvXrk9dJBERERE9mTJfeDFx4kRs3boV33zzDRYuXIgmTZqgUqVKuHnzJo4cOYLU1FTUqFEDEydOfJb1EhEREdFjKHPIc3V1xcGDBzF69GisXbsW27dvl5ZZWVlhwIABmDFjBlxcXJ5JoURERET0+J7qZsgVKlTA0qVLsXDhQpw/f16a8aJOnTowNzd/VjUSERER0RN64pA3depU5OTkYMqUKVKQMzc3R/369aU+BQUFGD9+POzt7TF27NhnVy0RERERPZYnuvBi586dmDRpElxdXR+5p87CwgKurq4YP34875NHREREJIMnCnk///wznJ2d8dFHH/1r32HDhsHFxQXLli0rc3FEREREVDZPFPIOHDiAV199FZaWlv/a19LSEq+++iqioqLKXBwRERERlc0Thbzk5GTUqFHjsftXr14dN27ceOKiiIiIiOjpPFHIU6vV0Gq1j91fq9VCrS7z/ZaJiIiIqIyeKIF5eHjg9OnTj93/9OnTqFKlyhMXRURERERP54lCXqtWrbB7925cuXLlX/teuXIFu3fvRuvWrctaGxERERGV0ROFvGHDhkGr1aJnz564fft2qf3u3LmDN954A4WFhfjwww+fukgiIiIiejJPFPICAgIwYsQIHD9+HL6+vpg0aRL27NmD+Ph4xMfHIyIiAhMnToSvry+OHTuGkSNHIiAg4ImLWrlyJQYPHozGjRvD0tISKpUKy5cvL9ZPq9Xi999/x7vvvou6devCzs4O9vb2aNq0KRYsWACdTlfqc6xatQpNmjSBra0tnJ2d8dprr+H48eNPXCsRERGRMXriGS9mzZoFKysrfPfdd5g6dSqmTp1qsFwIAY1Gg3HjxuHrr78uU1ETJkzA1atXUaFCBbi7u+Pq1asl9ktISEDPnj1hZ2eHV155BV26dEFGRgb++OMPDB06FNu3b8eWLVugUqkMfm/q1KmYMGECvLy8MGTIEGRlZWHt2rUICgrCrl270KJFizLVTURERGQsnjjkqVQqfPPNN3j//fexbNkyHDhwACkpKQCAypUro0WLFujfvz9q1qxZ5qKWLFkCb29veHl5Yfr06Rg3blyJ/ezt7fHTTz/h3Xffha2trdQ+a9YshISEYOvWrfjtt9/wxhtvSMvi4+MxefJk+Pj44PDhw3B0dAQADB06FM2aNcOgQYNw+vRpXhVMREREL7QnDnlFatasWeY9df/m1Vdffax+VapUwdChQ4u129ra4tNPP0WfPn0QGRlpEPKWLVuGwsJCjB8/Xgp4ANCwYUP07t0by5cvx/79+3nBCBEREb3QFLu7qmhuXTMzwxwbEREBAAgLCyv2O+3atQMAREZGPt/iiIiIiJ6zMu/JM3ZLly4FUDzMxcfHw87ODpUrVy72O97e3lKf0uTn5yM/P1/6OTMzE8D9i0CKbhStVquh0Wig0+mg1+ulvkXthYWFEEJI7RqNBmq1utT2+49r/rirblIevDm3SqWCmZkZ9Hq9wUU3Re2lbY9nu53+UfQFo7Cw8LHazc3NS629LOsEaB7xypkuY9tOxjT2FPy9/6kY23YyprFHJSuP7fQ4FBnyFi1ahD///BNt2rRBx44dDZZlZGTAzc2txN9zcHCQ+pRm2rRpmDJlSrH28PBw2NjYAACqVq0Kf39/nDx5EomJiVKf2rVro06dOjh8+DBSU1Ol9oYNG8LLywt79+5FVlaW1N68eXO4ubkhPDwcQKd/X3ETtH37dunf9vb2aNOmDZKSkhAbGyu1V6xYEUFBQYiPj0dcXJzU/jy204N/eKGhobC2tjaoEQA6duyI3Nxc7NmzR2ozMzNDp06dcPv2bURHRz+TdQL8H/NVNC3Gtp2MaewBJb83mjpj207GNPaoZM97Ox07duyx6lCJB6O5ESq68GLZsmXo37//v/bfunUrXn/9dXh4eCA6Ohru7u4Gyy0sLODm5oZr164V+934+Hj4+PigS5cu2Lx5c4mPX9KePE9PT9y+fVsKic/jW/rQn7gnryTzh3FPXmnrNGQe9+SV5MExA8i/nYxp7A2eyz0zJfnvx8a1nYxp7A2a84gXzoQtHP58t1NaWhpcXV2RkZEhZY+SKGpP3vbt29GzZ09UqlQJu3fvLhbwAMDR0bHUPXVFh14fvCDjYZaWlrC0tCzWbm5uLp0HWESj0UCjKf5B+/B5gv/W/vDj0j9Kem3UanWJhxFK2x7Pezs9SXtptZdlnahkxradjGnsUcmMbTsZ09ijksm1nYo932P1egFs27YNr7/+OipUqIA9e/agRo0aJfbz9vZGdna2dNuXBxWdi1d0bh4RERHRi0oRIW/btm3o0aMHXFxcsGfPHtSqVavUvsHBwQDw/+e5GdqxY4dBHyIiIqIX1Qsf8v7880/06NEDzs7O2LNnz7/uhRswYADMzMwwdepUg8O2sbGxWLNmDerWrYuWLVs+77KJiIiIniujPMi+ZMkS7N+/HwBw6tQpqa3oHnctW7bEwIEDcf78eXTv3h35+fkICQnBmjVrij1WtWrVDC7Y8PHxweTJkzFhwgT4+fmhR48e0rRmALB48WKem0JEREQvPKMMefv378eKFSsM2qKiohAVFSX9PHDgQKSkpEhXuhaFtIcFBwcXuyp3/PjxqFatGubMmYMFCxbAwsICrVq1wldffYWAgIBnuzJEREREMjDKkLd8+XIsX778X/uFhISgrHeA6du3L/r27Vum3yUiIiIydjwuSURERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRAigp5GzduRNu2beHq6gorKytUr14dvXv3RlJSkkG/zMxMfPrpp/Dy8oKlpSWqVauGUaNGITs7W6bKiYiIiJ4tM7kLeBaEEBgyZAgWLVqEmjVr4q233oK9vT2Sk5MRGRmJq1evwtPTEwCQk5OD4OBgxMbGIiwsDL1790ZMTAxmzpyJyMhI7N27F1ZWVjKvEREREdHTUUTImzt3LhYtWoShQ4di7ty50Gg0BssLCwulf3/77beIjY3FmDFjMH36dKl97NixmDFjBmbPno1x48aVW+1EREREz8MLf7g2NzcXU6ZMQY0aNfDDDz8UC3gAYGZ2P8sKIbBkyRLY2dlh4sSJBn0mTpwIOzs7LFmypFzqJiIiInqeXvg9eeHh4bh79y4GDBgAnU6HLVu24MKFC3BycsKrr76KWrVqSX3j4+ORnJyMdu3awdbW1uBxbG1t0aJFC+zYsQNJSUnS4V0iIiKiF9ELH/KOHTsGANBoNGjQoAEuXLggLVOr1Rg5ciRmzpwJ4H7IAwBvb+8SH8vb2xs7duxAfHx8qSEvPz8f+fn50s+ZmZkAAK1WC61WKz2vRqOBTqeDXq83qEej0aCwsBBCCKldo9FArVaX2n7/cc0f+zUxJUWvOQCoVCqYmZlBr9dDp9MVay9tezzb7fSPoj3ID54u8Kh2c3PzUmsvyzoBxfdqE4xuOxnT2FPAwZ3nwti2kzGNPSpZeWynx/HCh7xbt24BAL7//nsEBATg8OHDqFu3LmJiYvDBBx9g1qxZqFmzJj788ENkZGQAABwdHUt8LAcHBwCQ+pVk2rRpmDJlSrH28PBw2NjYAACqVq0Kf39/nDx5EomJiVKf2rVro06dOjh8+DBSU1Ol9oYNG8LLywt79+5FVlaW1N68eXO4ubkhPDwcQKfHfEVMy/bt26V/29vbo02bNkhKSkJsbKzUXrFiRQQFBSE+Ph5xcXFS+/PYTg/+4YWGhsLa2tqgRgDo2LEjcnNzsWfPHqnNzMwMnTp1wu3btxEdHf1M1gnwf8xX0bQY23YyprEHuD3OS2hyjG07GdPYo5I97+1UtIPr36jEg9H8BfTBBx9g8eLFsLa2xsWLF+Hh4SEtO336NPz8/FC9enVcvHgRq1evRt++fTF+/Hh8/fXXxR5r/Pjx+Oabb7BhwwZ07969xOcraU+ep6cnbt++LYXE5/EtfehP3JNXkvnDuCevtHUaMo978kry4JgB5N9OxjT2Bs/lnpmS/Pdj49pOxjT2Bs15xAtnwhYOf77bKS0tDa6ursjIyJCyR0le+D15RXvlGjdubBDwAKBevXqoUaMGLl68iPT0dKlvaXvqig69lranDwAsLS1haWlZrN3c3Bzm5oZBTKPRPPJCkMdtf/hx6R8lvTZqtbrEwwilbY/nvZ2epL202suyTlQyY9tOxjT2qGTGtp2MaexRyeTaTsWe77F6GbHatWsDAJycnEpcXtSem5srnYtXdG7ew/7tnD0iIiKiF8ULH81DQ0MBAOfOnSu2TKvV4uLFi7C1tUXFihVRuXJleHh4ICoqCjk5OQZX2Obk5CAqKgrVq1fnlbVERET0wnvh9+TVrFkTYWFhuHjxYrF73E2fPh3p6eno3r07zMzMoFKpMHDgQGRnZ+Orr74y6PvVV18hOzsbgwYNKs/yiYiIiJ6LF35PHgDMnz8fQUFBGDRoEDZt2oQ6deogJiYGu3fvhpeXF7777jup7+jRo7F582bMmDEDMTExCAgIwPHjxxEeHo7AwECMGDFCvhUhIiIiekZe+D15wP29eUePHkX//v1x7NgxzJ07F/Hx8Rg2bBgOHz6MypUrS31tbW0RGRmJESNG4Ny5c5g1axbOnz+Pzz77DLt27YK1tbWMa0JERET0bChiTx4AeHp6YtmyZY/V19HREbNnz8bs2bOfc1VERERE8lDEnjwiIiIiMsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR0RERKRAJh3yjhw5go4dO8LJyQm2trZo1qwZfv31V7nLIiIiInpqZnIXIJc9e/agXbt2sLKywltvvQV7e3v8/vvv6NWrF5KSkvDZZ5/JXSIRERFRmZnknrzCwkIMGjQIarUae/fuxaJFizBr1iycOHECPj4++OKLL3D16lW5yyQiIiIqM5MMebt370ZCQgL69OmDhg0bSu2Ojo744osvUFBQgBUrVshXIBEREdFTMsmQFxERAQAICwsrtqxdu3YAgMjIyPIsiYiIiOiZMslz8uLj4wEA3t7exZZVrlwZdnZ2Up+H5efnIz8/X/o5IyMDAJCWlgatVgsAUKvV0Gg00Ol00Ov1Ut+i9sLCQgghpHaNRgO1Wl1qu1arRUGe+VOssXLduaOV/q1SqWBmZga9Xg+dTlesvbTt8Sy304PMzO7/eRUWFj5Wu7m5eam1l2WdCvI0j3rpTNaDYwaQfzsZ09gryDPJ7/3/6u5d49pOxjT2CvIe9cqZrvT057ud0tLSAMBgm5REJf6thwKFhYXh77//Rnx8PGrVqlVseZUqVZCdnS0FuAdNnjwZU6ZMKY8yiYiIiEqVlJSEl156qdTlJrkn72mMGzcOn376qfSzXq9HWloaXF1doVKpZKysfGRmZsLT0xNJSUlwcHCQuxx6AXDM0JPimKEnZWpjRgiBrKwseHh4PLKfSYY8R0dHAChxTx1wf7A4OzuXuMzS0hKWlpYGbU5OTs+0vheBg4ODSfwh0bPDMUNPimOGnpQpjZmiLPMoJnkCRtG5eCWdd5eSkoLs7OwSz9cjIiIielGYZMgLDg4GAISHhxdbtmPHDoM+RERERC8ikwx5r7zyCmrUqIHVq1cjNjZWas/IyMA333wDCwsL9OvXT74CjZilpSX+85//FDtkTVQajhl6Uhwz9KQ4ZkpmklfXAqVPa3b16lXMnDmT05oRERHRC81kQx4AHD58GP/5z39w4MABaLVa1K9fH59++il69eold2lERERET8WkQx4RERGRUpnkOXlERERESseQR0RERKRADHlERERECsSQR0RERKRADHlERERECsSQR8+NXq+X/s2LuOlxcMwQET07DHn03KjV/wwvlUol/Zsf3lQatVqNwsJCAIZj5sHwR/QgfjGgJ/XgOFH6ewvvk0fPXFpaGo4ePYro6Gg4OzvD0tISXl5eCAgIgJubm9zlkRFKTk5GeHg4jh49CktLS1hZWaFOnToIDQ3FSy+9JHd5ZORyc3NhbW0t/Vz0sfbgFwWiB6Wnp8PJyUn6uSjsPbhzQgnM5C6AlGX//v0YM2YMoqOjAdx/kxVCwMbGBr6+vmjbti06d+6MRo0awdzcHHq9XnF/VPRk/vrrL4wdOxYnT54EANjZ2SE7OxsAULFiRbRr1w59+vRBSEgIrKysIITghzchOjoaGzZsQGpqKiwtLeHs7IzAwECEhobCxcVF7vLIyBQUFODPP//EunXrkJGRAa1WiwoVKiA4OBjdunVDpUqVpL5Keo/hnjx6ZvLy8tCwYUOkpqZiypQpcHNzg0ajQUpKCnbu3Im///4b9+7dg7e3N4YOHYphw4bBzIzfM0xZXl4e6tati/z8fMyZMwcVK1aEg4MDkpOTsXnzZvz222/IzMyEra0t3n//fYwdOxaVK1eWu2ySUWFhIaZPn45JkyYBAJycnJCfn4/c3FwAgJeXF7p06YLevXujSZMmUKvVivrQpidXWFiIMWPGYPbs2QCAGjVq4Pbt28jMzARwf2dEly5d8OGHH+KVV16BRqORs9xnSxA9I4sXLxY2NjZi6dKlJS6/dOmSmDFjhqhTp45QqVSib9++Ii0trZyrJGNSNGZ++eWXEpfr9XqxevVq0axZM6FWq0W7du1EYmJiOVdJxmTlypXC3NxcdO3aVRw7dkwcOXJEnD59Wqxfv1706NFDaDQaoVKpRLVq1cScOXPkLpeMwIoVK4SZmZl4++23RUJCgkhKShJZWVkiMjJSDB8+XFStWlWoVCphbm4uPvnkE5Geni53yc8MQx49M2+++abw9vYWFy5cEEIIUVBQUKyPTqcThw8fFp07dxYqlUr88MMP5V0mGZG3335beHl5iXPnzgkh/hkzer1eFBYWSv2uX78uPv74Y6FSqcTYsWNlqZWMQ/PmzUWrVq2kMfOwjIwMMXv2bFGrVi1hZmYmPvvsM3Hv3r1yrpKMSVBQkGjVqpX02fSwgoICsXr1auHv7y9UKpXo16+fYnZA8GQoeiYKCwtRoUIFJCcnS4fTzM3Ni/VTq9UIDAzE8uXL0ahRI8ybNw/37t0r73LJCAghUK1aNSQmJsLR0RHAP2NGpVIZHDLx8PDAzJkz0bZtW/zyyy+4efOmLDWTvNLS0nD58mVUq1YNPj4+EPd3VAC4f+K8TqeDg4MDRowYgXXr1qFp06b4/vvvERkZKXPlJJf09HRcv34dlSpVQq1atQzGjE6ng06ng7m5OXr37o3w8HD07NkTv/zyC7Zs2SJz5c8GQx49NSEEzMzM0KJFC9y7dw+ffvop7t69C+CfN94HFRYWwsXFBa1bt0Zqairi4uLkKJtkplKp0KJFCwDA4MGDceHCBQD3x9PDY0an08HCwgLNmzfH3bt3cfny5XKvl+QnhIC7uzsSEhKgVquhUqmkc+3UarXBF4OAgACsXLkS5ubm2LRpk+JvlUElK7q7w9mzZ6XxUjRmNBqNNGaEEKhQoQL++9//wtXVFX/++ad0nueLjCGPnlrRH0xwcDBat26N//3vfxg3bhyuXLli8Mar0+mkQJifnw+VSgW9Xg9vb285yycZtWjRAj179sTWrVsxatQoREVFFduLB9x/M87Pz5f2+tarV0+Ocklmrq6uaNOmDaKjozF58mSkpaUBKP5lsujfVapUgZ+fH2JjY6X7L5Jpsba2Rvv27XHu3DkMGjQICQkJJd5PsehLgJOTE15++WWcP39eEXd+ePHXgIxGlSpVsHbtWnTt2hWLFi1CjRo10KtXL2zZsgUFBQXQaDTSH9eePXuwbt06tG7dGnZ2djJXTnKxt7fHqlWr8PHHH+Ovv/5Cq1at0LJlSyxfvhypqanQarXIyMgAAGzduhU///wzXn31VY4ZE/bee+/By8sLM2bMwMSJE3Hx4sVie/GK/h0fHw+tVotKlSrBwsJCrpJJZgMGDEBAQAD+97//4fPPP8euXbug1WoN+hSNmXPnziEjIwMvvfQSLC0t5Sj32ZLnVEBSoqIT5S9duiQmTZokKlasKFQqlVCpVMLBwUF06NBBDB8+XAQHBwszMzNRq1YtsX//fpmrJjlptVohhBApKSli/vz5IjAwUBozarVaNG/eXHTv3l34+voKlUolGjRoIA4ePChz1SS3CxcuiE6dOklj5bXXXhMbNmwQd+7cEVlZWeLWrVtCq9WK999/X2g0GrFp0ya5SyaZ3b17V3z44YfCxsZGqFQq0bJlSzF37lxx7NgxceHCBXHlyhVx69Yt0atXL2Fubi42b94sd8nPBO+TR8+EKOE+VFqtFr/++itWrVqFI0eOICcnB2ZmZtBqtejcuTNGjRqFwMBAmSomY1RYWIjw8HBs2bIFx44dQ3p6OnJycqDT6fDmm2/i448/ho+Pj9xlkowKCwthZmaGuLg4rF69GqtXr0ZCQgIAwMbGBv7+/tDr9Th79iwyMjLw3nvvYcmSJTJXTXLSarUwNzdHcnIytmzZgt9//x379u1DQUGBdM5efn4+rl27Bp1OhxEjRuD777+Xu+xngiGPngm9Xo+kpCR4eXkhPT0darUaDg4O0vK0tDScPn0azs7O0n+2tra8SakJy8jIwPXr11GxYkXcvXsXzs7OqFixorQ8MzMTV69ehbu7O8zMzGBvb6+sm5TSM5GRkYHt27fjzz//RFxcHHJycpCWloaaNWtiwIABePPNN3l4nwxkZ2dj37592LdvHy5evIi7d+/i+vXrqF+/Pt566y107dpVEefjAQx59JRyc3Px/fffY8eOHTh16hQsLCzg5+eHhg0bolGjRqhfvz5q1KgBKysruUslI5GWloZvvvkGmzdvRkJCAmxtbVGzZk34+PggMDAQQUFB8PPzkz6Y+UXAtD24/c+cOQO9Xg9bW1vk5uaiSpUqBvOP3r59G+np6ahevTry8vJga2srU9VkDO7du4djx45Bp9OhsLAQlpaWqF27tsEc6hkZGdDr9XB2dpb2EisJQx6VWUFBAfr06YMNGzbA19cXtra20Ov1SE9PR2JiIszMzBAYGIi+ffvi7bffNphAnExTfn4+unbtivDwcLRq1Qqurq7QaDS4fv06Tp48KU1717NnT7z//vuoUaOG3CWTzIQQOH78OIYPH46TJ08iJycHTk5O8PLyQr169dC8eXM0b94c9erVK/HenGR6hBDYtWsXRowYgbNnzwK4fysVJycn1KpVC61atUJYWBiaNWsm7YBQ6pdJhjwqs//9738YNmwYhg0bhilTpsDOzg4pKSm4fv06Lly4gN27dyM8PBxJSUkIDQ3FtGnT0KRJE8X+MdG/W7JkCT7++GOMHj0aU6ZMAXD/m3RWVhaSkpKwc+dObNiwAadOnUK9evXw7bffIiwsjGPGhG3btg0ffPABcnJy0KVLF6jVaumcu1OnTkGn0yEgIAD9+vXDe++9BxsbG7lLJplt2rQJ77//PqytrdG7d2/Y2dlBq9XiyJEj2LdvH/Ly8uDu7o7evXtj8ODBir6NF0MelVlwcDC0Wi1WrVqF6tWrQ6fTGZwzlZaWhpiYGCxbtgyrV69G06ZNsX37djg7O8tYNcnplVdewb1797B69WpUr14der3e4NyXgoICJCQkYNWqVZg2bRrc3d2xd+9e7tEzYS1btkR6ejrmzp2LNm3aALg/i0FWVhbi4+OxdetWbNq0CVeuXMFrr72G7777DrVr15a5apJTUFAQ8vLysGDBAjRt2hTA/YsvVCoVEhMTsWnTJvzyyy84ceIEWrRogblz58Lf31/mqp+Tcr2WlxQjIyND+Pn5idatWxdbptfrDX7W6XRixowZQqVSieHDh5dXiWRksrOzRVBQkPD39//XvjqdTixbtkyaR5JMU3JysrC0tBQTJkwQer2+2HuLEELk5OSIqKgo0bt3b6FSqUT37t0N5j0m05KSkiJsbGzE2LFjhU6nK3HMCCHElStXxPjx44VKpRKNGjUS6enp5Vxp+VDG5SNUroQQsLOzQ926dXHq1CmcPn1aatfr9dJhNfH/cwSq1Wp8+umn8PPzw7Fjx6Sb25LpEELA1tYWDRs2xOnTp7Fz506p/eEpzID7U1T1798fISEhOHHiBFJTU8u7ZDICFy9ehIWFBTQaTamH621sbBAUFIRFixZhxIgR2LRpE7Zu3VrOlZKxuHbtGiwtLVFQUCBNfVcSLy8vjB8/HtOnT8fx48exefPmcq60fDDk0RNTqVRQq9XSYZTPP/8cly5dktoBGEwCDdz/0Pb29saNGzeUcRdxeiJFb7Rt2rSBXq/H559/jqNHjxpMYVY0NVXRuNFqtfD09MTt27d5CwwTVbduXXh4eGDTpk1ISkqSpkJ8eB5avV4POzs7DBs2DDY2Nti/f79MFZPcfHx8ULNmTaxbtw4xMTEASp5DXa/Xw9raGu+//z6cnZ2xf//+Eqc7e9Ex5FGZDRs2DKNHj0Z4eDgCAgIwevRoHDhwAHl5eVLge/DWB+fOnUPt2rV5OxUT1qNHD8ybNw8XLlxAkyZN0Lt3b2zfvh05OTnS1FRFY+b06dM4duwY6tevzyuzTVSFChXQoUMHnDx5El988QWSk5OhVqulL5MPf3jn5eXBzc0Nd+/elatkkpm9vT369OmD5ORkjB49GjExMcXmUH/wiNPNmzfh6uqK3NxcZV7cJddxYnqxFZ3ncOvWLTF58mRpqpiXXnpJ9OzZU8yYMUNERESIGzduiE2bNonWrVsLKysrsX37dpkrJ7llZWWJBQsWCE9PT2laqsaNG4tPPvlEbN68WRw6dEgsWLBA+Pn5CVtbW7Fjxw65SyYZ3bt3TwwePFioVCphbW0thg8fLvbu3VvieXezZ88WGo1GbNiwQYZKyZhMnTpVWFpaCpVKJbp16ya2bt0qTaP4oGnTpil6zPDqWioT8dAtLa5fv46lS5diw4YNOHHiRLH+Tk5O+Pzzz/HFF1+UZ5lkRB4eMzqdDj///DN+/vlnREZGFuvv6emJsWPH4sMPPyzPMsmIFF19fe3aNcyfPx+zZ89Gfn4+rKys0KhRIzRv3hwhISHIy8vD3r17sXjxYvj6+uLIkSNyl04yKXqfuXv3LlauXIk5c+bg8uXLAAAPDw+EhIQgODgY2dnZOHr0KNauXYugoCDs27dP5sqfD4Y8emb0ej1SU1MRFxeHQ4cO4fDhw7C1tYWPjw+aN2+O0NBQuUskI3Xt2jXs2rULMTExcHV1ReXKldGkSRP4+fnJXRoZkbS0NCxduhSrV69GbGxsseVdu3bF559/jhYtWpR/cWSU8vPz8euvv2Lp0qXYt2+fwfmcarUa/fr1w8iRI1G/fn0Zq3x+GPLoiZ04cQLx8fG4cOGCdAGGt7c33Nzcip3TkJ+fzwstCPv27cPJkydx7NgxODk5ITAwEDVr1oSnpycqVKhgMFPBw3v8yPQUjYGH76P4oIsXL2L37t1ITEyEl5cX3Nzc0LZtW94M2cQ9+JmTl5dncA74zZs3sX//fty+fRtVq1aFg4MDmjZtqripzB7EkEePrbCwEIsWLcKXX36JW7duGSyrXLky2rVrh969eyMsLMxg2aPeqEnZCgsL8e233+LLL79EQUGBwTInJyc0a9YM3bp1Q9euXVGpUiVpGYOeadPpdFixYgXOnj2LixcvombNmmjcuDF8fHxQtWpVuLi4GNx4vQjHjenKzs7GggULcOTIEVy6dAl169aFr68v6tSpg9q1a6N69eomeQEXQx49tnXr1mHQoEHw9vbGwIED4efnh5iYGMTGxuLYsWM4efIk9Ho9mjdvjkmTJqFt27YMdyZu1apVGDx4MJo2bYpPP/0UtWrVwokTJ3DhwgUcPXoUBw8exK1bt/Dyyy/jiy++QK9evThmTNzx48fx5ZdfYsuWLbC0tER+fr60zM3NDSEhIXjjjTfQuXNnWFhYAGC4M3XR0dEYN24c9u7dK10pa2lpiYyMDFhbWyMgIABdunRBt27dULNmTQCmM2YY8uixNW3aFHq9HqtXry4219/ly5exd+9e/Pbbb9i2bRscHR2xePFi9OzZU6ZqyRg0bdoUarUaK1eulN5ci9y8eROxsbHYtm0bli5dinv37uHbb7/F559/LlO1ZAw6d+6MqKgoDBkyBP3794dOp8PJkydx9uxZREdH4/Dhw8jMzERoaCimTJmCli1bmswHNpWsffv2iI2NxZgxY9C/f39kZWUhISEBly9fxoEDB7Br1y5cvXoV/v7+mDx5Mjp37ix3yeWnPC/lpRfXzZs3hbOzs/jkk0+ktsLCQqHT6Qz6FRYWit9++024u7uLSpUqif3795dzpWQsUlNThZubmxg4cKDUptPpShwzu3fvFvXr1xe2trZi69at5V0qGYnExEShUqnEuHHjSlx+9epVsX79evHmm28KlUolKlWqJCIjI8u5SjImiYmJQq1Wi//85z8lLr9z546IiooSY8aMEdbW1kKlUok1a9aUb5Ey4nEReiwZGRmws7PD9evXAdw/Z+bBm5KK/5/STKPRoEePHvj+++9x69YtRERESMvJtOTm5qJChQrS7QuKblr78KwoGo0GoaGh+Omnn6DVarF7927ZaiZ57dq1C5aWlmjUqBGA++fzigdmz6latSp69uyJZcuWYenSpcjPz8eHH36Imzdvylk2yWj//v3QaDTw8fEBUHzMuLi4ICgoCJMnT8a6devg5eWFESNG4MqVKzJWXX4Y8uixeHt7o2rVqvj777+xZ8+eEueSVKvV0h/WG2+8gRo1auDw4cMoLCzkoRQT5OnpiVq1aiEiIgJr166FRqMpdr6dSqWSxkxQUBB8fX0RExMDrVYrR8kkM1dXVwghpC8GRR/YD8+HbWNjg/79+2PkyJE4d+4czpw5I2fZJCN3d3dYWFjg5MmTACBNe/fgmAEAKysrdO7cGZMmTcKtW7ekKc+UjiGPHtu3334LtVqN9u3bY+rUqTh//rz0YVz0B1X0c1xcHDQaDaysrBR9eTo92owZM1CrVi306dMHQ4YMQVRUFHJzcwH8M2aKrrqNi4tDQUEBnJ2dDW6pQqajadOmsLa2xtKlS3HmzBmYmZkZ7PkF7o+bwsJCAEBwcDBsbW1582MTFhAQAHd3dyxZsgR79uyBmZmZdOX1g3v0isZMnTp14OTkVOJ9FpWIIY8eW5MmTfD111/Dzs4OU6ZMwYcffoh58+YhKioKSUlJ0Ol0sLCwgFarxS+//IKEhAT06dNH7rJJRnXq1MHXX3+NatWqYdGiRXj//fcxZswYrFu3DmfOnIFWq4WlpSXu3r2L+fPnIy4uDu+++67cZZMM9Ho93NzcMG/ePMTFxaFZs2b4+uuvcerUKelowMNHBC5fvoycnBzF3siWHk2v18PBwQE//fQTNBoNXnnlFQwePBj79u1Dfn6+NIc68M9pIufPn0dmZiYCAwPlLL3c8OpaemLnzp3DDz/8gK1btyI5ORmVK1fGyy+/DEdHR9ja2uLq1avYu3cvOnbsiK1bt8pdLhmBzMxM/Pjjj1izZg3Onj0La2trvPTSS3BwcICLiwuuXLmCixcvomfPnli7dq3c5ZKMsrKy8NNPP2Hq1KnIyclB48aN8eqrryIwMBC+vr6oXbs2gPvnYo0YMQI3btyQzhUm06TVarFmzRqMGTMGN2/ehLu7O4KDg9GyZUs0bdoUjRo1QnZ2Nvbt24cRI0YgLy8PV69elbvscsGQR4/twXNjUlJSEBsbi4MHD+LQoUM4d+4cEhMTAQBVqlTBm2++idGjRxvc4JZMgyjldhbZ2dm4fPkyjh07hv379+PQoUM4e/YsHBwc4OXlhZ49e+Ljjz+Go6OjDFWTsYmLi8OCBQuwefNmXL16Ffb29qhUqRIsLS3h6OiIY8eOwcXFBZMmTcLgwYPlLpeMQF5eHubNm4eVK1fi1KlTAAAzMzO4uLjAzs4Oly5dQs2aNTFp0iS88847MldbPhjyqFRFH9ZarRZqtRqpqakoKChA1apVpT4FBQW4ceOGdDglMTERjRs3hp2dnYyVk1yKxkxubi7y8/ORmJgIS0tLae8LcP8q2+zsbFhaWuLevXtISkriHLUmrrRZcdLS0pCQkICjR49K98i7evUqatSogSpVqmDKlClo0qRJibNfkLLpdLpSt3tKSgpiYmIQERGBXbt2ISMjA15eXvDw8MCYMWPg6+trMhcDMuTRI50/fx4LFizA1q1bYWlpCSEE3N3d0aZNG7z11luoVauW3CWSERFC4OjRo5g2bRqioqKg1+uRm5uLSpUqoVOnTnjrrbcQFBRU4u+Zypsulez27dvIycnBlStXULVqVVSvXl1aVlBQgIKCAtjZ2eHWrVsoKCjASy+9JGO1ZAyuX7+OK1eu4MaNG6hXrx5q1qxZ4kVbaWlpMDc3h729vQxVyoshj0q1Z88efPLJJzh9+jRq1qwJHx8fnDx50uD8l/bt22Po0KFo27YtLC0tOU+tiduxYwc++ugjJCUloWnTpqhZsyaOHTuGy5cvIzs7GwBQr149jBo1Cj169ICNjQ0Dnom7c+cOfv/9d3z//fe4du0adDoddDodatasiZ49e6JPnz6oW7eu3GWSEUlOTsaKFSswc+ZMZGZmSvfg9PT0RLt27dC9e3eEhobCyspK5krlx5BHpQoODkZCQgKWLFmCkJAQaDQamJub49SpU1i/fj3Wrl2LixcvwsbGBmPGjMHEiRPlLplk1rJlS9y4cQPLly9Hq1atpPb4+Hj8/fff2LJlC8LDwwEAAwYMwHfffQcXFxe5yiUjMHLkSCxYsABVqlRBq1atYGFhgUOHDiEhIQH37t0DAISGhmLMmDF49dVXpftx8ouB6Ro8eDB+/vlnNGjQAJ06dUJBQQFOnTqF+Ph4XLhwAXq9Hv7+/hg9ejR69uwJjUZjumPm+U2mQS+ypKQkYWZmJr7++muh1+uFEEL6/4N+++030aRJE6FSqcSYMWNEXl5eeZdKRuLatWvC3NxcfPnll9JY0Wq1xfrt2bNHtGvXTqhUKjFgwACRmZlZ3qWSkbhy5YowNzcXvXr1KjblXWxsrJg2bZpo2rSpUKlUwtraWvzwww8yVkvG4MqVK8LMzEwMGDCg2LILFy6IZcuWiV69egkzMzOhUqnEJ598IrKzs2Wo1DjwuBqVKCYmBiqVCk5OTlCpVCgoKJC+Ben1emn3eI8ePfDzzz8jICAA8+bNw9mzZ+Usm2R09uxZmJmZwdzcXBozRTfCLroLPQCEhIRg/fr16Ny5M5YvX46jR4/KWTbJaO3atbCzs8MHH3wgneZRdNNaPz8/jB07Fvv27cOaNWtQq1YtjBgxAj/99JOcJZPMfv/9d9ja2kr3YC0sLJQ+j7y9vdG/f3+sXLkS27ZtQ1BQEObOnYtvv/0WgGlOr8mQRyWqV68eAEhTxVhYWEjL1Gq1wR3Fa9eujQULFiA3Nxf79+8v/2LJKAQEBMDMzAyHDh0CUHzMPPghbm9vjxkzZsDMzAyRkZGy1Evyu3nzJvR6vXTIXqfTFftiYG5ujl69emHFihVwd3fHf//7X+n8TjI96enpKCwshLW1NQBIc6YD/8yhbmZmhrCwMGzZsgUBAQFYtGgRbt++bZKHaxnyqERVqlRBjx49sHjxYnzxxRdISkoqsV/Rt261Wg0nJyeTucEkFefs7IwBAwZg8+bN6Nu3L2JjY0ucg7Zoj15+fj6cnZ1x+/bt8i6VjETr1q2RmZmJgwcPAoDBlZEPfzHw9/fHsGHDcOXKFRw+fFiWekl+oaGhuHfvHrZv3w7A8MvkgzNcFBQUwMXFBQMGDEBWVpbJ7oBgyKMSWVhYYNSoUahZsya+/fZbjBgxAjt27EB+fr5Bv6I35ZiYGGRmZiI4OFiOcskIqNVqjBgxAk2bNsWaNWvw0UcfYenSpbh48SLu3bsnHSopelM+cOAA7ty5g7CwMDnLJhm1aNECDRs2xLBhwzBlyhRcvny52CG1B3+2t7dHbm6uwQc7mQ4hBAIDA9GxY0dMmzYN7733Ho4fP17sy6QQQgp7Go0Gubm5cHZ2lqNk2fHqWnqkS5cuYcqUKVi3bh0KCgrQsGFDdOvWDc2bN4etrS0sLCyQkJCAESNGwNHREefPn5e7ZJJZbm4upk+fjiVLluDGjRuoWbMm2rRpg8DAQDg6OsLJyQlnzpzBV199hZdeegknTpyQu2SS0R9//IFBgwYhNTUVXbt2Re/evdGsWTNUqFABVlZW0iG21NRUDB8+HDt27EBaWprMVZOcDhw4gPfffx9xcXFo0qQJevTogVatWqF69eqoUKGCdPg2JSUFH374Ifbu3Ys7d+7IXLU8GPKoREUXV5ibm+PatWv4888/sWnTJkRFRSEzMxNqtRqOjo64e/cugPsnSU+bNg3t27eXuXKSy4NjJi0tDfv378eOHTsQGRmJhIQEaLVa6VAtcP92K19//TVat24tY9VkDBISEvDVV19h48aNyMrKQv369RESEgJfX1/Y2trCxsZGOpn+s88+wzfffCN3ySSz3NxcfPPNN/jll1+QmJgIT09PNG7cGLVr14azszNsbGywZs0aHD9+HGPGjMF//vMfuUuWBUMePTatVivNVXv9+nVkZWUhLS0Nr732Gtq1a4cqVarIXSIZGZ1Oh1OnTuHcuXO4desW7ty5g7S0NHTq1AlNmzblPfJMXGFhITQajTQlYmRkJP7++29ER0cjKSkJBQUFBv0nTZqEjz76CBUqVJCpYpLbg9OZpaWlISYmBpGRkYiMjMTZs2cN9thpNBrMnDkT7777LpycnGSqWF4MeWSgsLAQcXFxCA8Ph62tLczNzeHq6oqGDRsazFmbn58PS0tLGSslY5Gbm4sDBw5g586d0jmaXl5eaNWqFXx8fKR+j5prkkxXQUGBwTl29+7dw6lTp5CQkICcnBzcuHEDtra2aN++PV5++WUZKyVjkZmZCQcHB+nn/Px8XLlyBbdu3UJubi4SEhLg4uKCFi1amPz0dwx5JLl8+TJmzZqF+fPnG7RbW1vD29sbISEh6NixI4KCgmBnZ2fwLZxM0/nz5/H1119j9erVAAAbGxtplgJHR0eEhobizTffRIcOHeDo6AidTge1Ws0xY+IuXbqE7du348yZM7CwsICNjQ1efvllhIaG8ogAFSOEwIkTJ7Bq1SpcvnwZhYWFsLW1RePGjdGtWzeDeY5L+l1Tfr9hyCPJG2+8gU2bNmHQoEFo2rQpzMzMkJGRgb179yI8PBzp6elwd3fHgAEDMHz4cLi5ucldMsmsa9eu2LFjB0aPHo3mzZvD3t4e6enp2LFjB9avX49bt24BAPr06YPPP/8cDRs2lLdgkt26deswevRoJCUlQaVSwcbGBjk5OQCAypUro0OHDujVqxdCQkJgYWEBrVZb4qTzZDoWLVqEyZMnIyUlBc7OzlCr1QaHZdu0aYMPPvgAXbp0gZWVFY8aPKg8p9cg43X58mWh0WjE559/XuL0ZdevXxcLFiwQgYGBQqVSiTZt2oj4+HgZKiVjceXKFaFWq8UXX3xRap+tW7eKsLAwYWZmJho2bCiOHj1ajhWSsUlMTBQVKlQQ3t7eYvv27SIyMlIcP35cbNy4UbzzzjvCxsZGqFQq4eLiIsaNGyfS09PlLplkdvXqVeHk5CQaNmwooqOjxblz50RaWpqIjo4Wo0ePFrVr1xYqlUqoVCrx1ltviQsXLshdslFhyCMhhBA//vijsLa2Ftu2bRNCCJGfn19iv7i4ODF06FChUqnEe++9JwoLC8uzTDIiCxcuFFZWVmLjxo1CCCEKCgqEEPfnOH5wXGRlZYmZM2cKlUolOnToYNLzSJq6iRMnCjc3N7F169YSlxcUFIhly5YJf39/oVarRY8ePcStW7fKuUoyJpMmTRJubm7ir7/+KrXPtm3bREhIiFCpVCIkJEQkJCSUY4XGjTdDJgD3b2qcl5cHGxsb6eeS+Pj4YNasWRg4cCCWLVuGhISE8iyTjIirqyvy8/Olm44WjRmVSmVwqMTOzg4jR47EF198gb/++gtnzpyRpV6S34EDB+Du7g5/f38A/8yY8+Dtd/r3748NGzagb9++2LBhA3755Rc5SyaZHTt2DK6urtJFN0Xz1D44h3rHjh3x999/44svvkBkZCTnN34AQx4BAJo1awZra2tMmjQJFy9ehEqlghBC+iMqotVqYWVlhbCwMKjVakRHR8tUMcnN398fzs7OGDt2rME40Ol0BrMUFBYWQq1Wo1WrVlCr1Th69Kgc5ZLMtFotatSoIV35CECap/bB+bABoFq1aliwYAH8/Pzw888/IzMzU5aaSX4vv/wyLly4IF08UTROHhwzRfPVfvXVVwgNDcW2bduQnJwsW83GhCGPAADe3t54++23sX//fowZMwaxsbEGe2T0ej2EENLempycHKhUKl4JZ8KqVauGTz75BOfPn8eoUaPwxx9/AIB0xXVR0Cv6IL958yZUKhVq1aolW80kH3Nzc7Ru3Ro5OTn44IMPpHmuH/4yKf5/knlbW1s0bdoU165dQ0pKilxlk8yCg4Oh1+sxYMAAHD9+vNiOB+D+0QO9Xg+VSoWGDRvixo0b0o36TZ6cx4rJuBQUFIjhw4dLJ7F26NBBrFmzRmRmZhr0S0lJEcHBwcLNzU2mSsmYfPfdd8LV1VWoVCrh5+cn5s2bJ5KTk4UQQuTk5AghhEhISBBNmzYV7u7ucpZKMktNTRWvvvqqUKlU4s0333zkhTh3794V/fv3F5UrVy7HCsnY5Ofni7fffluoVCrRsmVL8dtvv5V6Xm96erro37+/qFixYjlXabwY8kgIIYROpxNCCHHz5k0xZ84cUaNGDSns2drairZt24px48aJN998U3h4eAhbW1vx/fffy1w1yalozGRkZIjVq1eLNm3aSGNGpVKJJk2aiLffflu0bt1a2NjYCEdHR/HTTz/JXDXJLTMzU7z//vvSOAkJCRErV64Ut2/fFnl5eSItLU0IIcSCBQuEg4OD+PDDD2WumIzBlClTRIUKFYRKpRIBAQFixowZ4ujRo+Ly5csiKSlJ5ObmiunTpws7OzsxbNgwucs1GrxPHpV6s8jNmzdj+fLl2L9/P+7evQtLS0vk5uaiUaNGGDVqFF577TXpQg0yLaWNmT179mDjxo2Ijo7GrVu3UFBQgNu3byMsLAwjRoxASEgI73lmwgoLC2FmZoZr165h/fr1WLFiBU6ePAng/mH9Jk2awNnZGefPn0dCQgJatGiB5cuXo2bNmjJXTnIpuk/i3bt38eeff+LXX3/F7t27kZ2dDY1GA29vb1hYWOD69eu4c+cO2rdvj59++umRN0g2JQx5BAC4fv06qlSpgtzcXGi1WoMpY7Kzs3H8+HEAQJUqVWBnZ4dKlSrJVSoZifj4eLi5uSE9PR1WVlYGY+LevXuIj4+Hra0tnJ2dYWVlBVtbWxmrJWOUn5+Pv/76C3/88QdOnDiBzMxMZGVlwcLCAn379sWHH35o8tNSkaGCggJERUUhIiICZ86cwZ07d3Djxg04OTmhV69eeO+99+Do6Ch3mUaDIc+ECSGwdetW/O9//8OpU6eQnZ2NBg0aoEGDBvD390f9+vVRq1YtfjiTJD8/H+vXr8f8+fMRExMDtVoNb29v1KpVCwEBAWjWrJl01S3Rg27duoXU1FS4uroiIyMDFSpUgKurq7T87t27SE5OlkKdg4ODSU9HZep0Oh3i4+Nx9+5d6WKcGjVqwMPDQ+qTlZWF7OxsuLu7cz71UjDkmbBJkyZh5syZsLGxgaenJ7RaLQoKCpCUlAQhBPz8/NCzZ0+88847qFy5stzlkhH47LPP8MMPP8DLywve3t4wNzdHeno6Tp8+jYyMDHh6euK1117DgAED0LhxY7nLJSNw48YNjB8/Hn///TeuX78Oe3t7VK9eHXXq1EGTJk0QFBSEBg0aSKd+lHYqAJmOuLg4jBs3Dtu3b0dBQQEsLS3h7OwMLy8vNGvWDGFhYWjZsiXs7e0B3L/7Q9H9OskQQ56JunLlCl5++WWEhIRg1qxZqFOnDm7fvo2kpCQkJCRg79692LFjB+Lj4+Hn54dvvvkGHTp04B+TCbt8+TJ8fX3RuXNn/PTTT6hYsSKysrKQnp6OGzduYO/evdi4cSOOHDmCKlWqYMqUKejXrx8/tE1YSkoKunfvjkOHDqF9+/aws7ODWq3G1atXcfLkSeTm5sLX1xdvvvkmBg4caLCXhkxTcnIy2rdvjzNnzuCdd95BhQoVYGZmhjNnzmDfvn3IzMyEk5MTunfvjg8++ABNmzaVu2TjVu6XepBR+PLLL4WLi4vYuXOnEEIIrVZrsDwjI0McOHBAjBgxQqhUKlG5cmURExMjQ6VkLKZOnSpcXFzErl27hBCi2JR2Wq1WXLp0ScyZM0dUrFhRqFSqR05FRMo3adIk4ejoKObMmSO13b17VyQlJYm9e/eKCRMmCF9fX6FWq0Xz5s3F/v37hRCixPmzyTRMmDBBODs7iyVLlkht+fn5oqCgQCQmJoqFCxeKFi1aCLVaLXx9faUp8jhmSsaQZ6L69esn3N3dRUpKihDinz+Qkv5Q1q5dKxwdHUWzZs3KtUYyLkOHDhVOTk4iKSlJCPHoN9Xw8HDh7u4uateuLfLy8sqrRDIyvr6+4rXXXpPmn314zOTl5YkTJ06ITz/9VKhUKlGnTh1x8+ZNOUolI+Hn5yfat28vjYOS3mdSU1PFvHnzhIuLi7C3txdnz54t7zJfGDzuZqIaNGiAlJQU7Nu3D4DhHcOLiP8/kt+rVy+8/vrruHjxIuLi4mSpl+TXqFEjZGRkYMuWLdIh2IenMCvStm1b9O/fH9evX8fZs2dlqJbkdvPmTQghkJ+fj4oVKwJAscP2lpaWaNCgAWbMmIEffvgBcXFx+P777+Uol4zAnTt3pPN83dzcABQfMwBQoUIFDBkyBPPnz0d2djZ++OGH8i71hcGQZ6KaNGkCW1tbTJw4UZpLtOhcO/H/VzIVBT/g/rRnubm5nEPShDVp0gQeHh6YOHEitm3bBsBwCrMHJw4HgIoVK6KwsBB5eXmy1UzyEEKgYsWKePnll3Ho0CEcPnxYai9pWiozMzN8/PHHqFevHo4cOYLs7OzyLplkJoSAq6sr/P39cejQIWzdulX6EllYWFisv5mZGXr16oWgoCAcP34caWlpMlRt/BjyTJAQAq1atcLs2bMRHx+PJk2aYPDgwdi1axeysrKgUqmkwKdWq5Gbm4tTp07BysoKgYGBMldPchBCoF69eliyZAlsbGzQpUsXtG/fHuvXr8fdu3cN5jlWq9XIycnBwYMHYWtri+bNm8tcPZW3oveQsLAwZGVl4fPPP8eZM2eKzYf94J7gzMxMeHp64tatW7Czs5OzfJJB0R677t27A7h/Jf+uXbugUqmk+a91Op3BmMnIyEDFihWRkZEBFxcXeQo3dnIcIybjkJ2dLRYsWCDc3NyESqUSbm5uomvXruKbb74RO3fuFGlpaeLQoUNi8ODBwsLCQnz22Wdyl0wy02q14rfffhMNGjSQpqXy8/MTw4YNE7///rs4d+6c2LBhg+jVq5fQaDRi7NixcpdMMps+fbpQq9VCpVKJd999V+zYsUPk5uZKy4vOudq5c6eoUqWKGDRokFylkpFYtWqVqFSpklCpVCI0NFSsW7fOYL7aojGzbds24eHhwTHzCLyFigkSD93SIicnB0uWLMG6detw5MgR6XBK0TcorVaL/v3746uvvkKVKlXkKpuMzKZNm7BkyRLs2LHDYMwIIWBubo5hw4ZhzJgxnB3FRBW9z6Snp2Pp0qWYMWMGUlNTodFo0KhRI7Ro0QKhoaFwdHTEkSNH8OOPPyIrKwu7d+9G/fr15S6fZJSfn4/ff/8d33//vTTbkpubG4KDg9G2bVtYWlri9OnT+N///gdLS0uEh4fj5Zdflrlq48SQR5Lbt2/jwoULOHjwIPbt2wedTgcfHx/UrVsX77//vtzlkREQ/3++ZtEhN+D+vdD27NmDqKgomJubw8PDA3Xq1EHnzp1lrJTk9vCXyby8PKxYsQI///wzoqOji/X39fXFuHHj0Ldv3/Isk4yYEAJ//PEHFi1ahPDw8GLn5jVv3hwTJkxAhw4dZKrQ+DHkmZhbt27h1KlTuHDhArKzs9GkSRPUqVMHFSpUMPjgBlBsmpiH37TJNDzJDbB1Op3BOOKYoZIkJiZi586dOH36NCpXrgw3Nze0bNkStWrVkrs0MgLi/u3dDN53MjIyEBERgUuXLsHDwwN2dnYIDAyUrsKlkjHkmZA///wTX3/9dbFv0S4uLnjllVfQq1cvdO7cGebm5tIyznBBDyptPOh0OqjVaqhUKhQWFkonSpNp+uuvv3D69GnExsaiUqVKaNy4MWrVqgVPT0+4uroavMcQAcW/ID7Y/uDFgPRkGPJMRFJSEkJCQpCTk4P+/fsjNDQUly5dQkxMDE6cOIGTJ08iPz8fvr6++OKLL9CzZ09YWFhwT4wJu3nzJr799luEhYWhadOmcHJykpYVvW1wbNCD0tPTMW3aNHz33XfQaDQGt0txcXFBixYt0L17d3Tp0sXgaki+z5iuh784lrQX7+F28f+34uGXyX/HV8hELFy4EHfv3sWSJUvw+uuvGyy7du0aDhw4gC1btmD16tV4++23ce3aNYwePZpvvCZs/vz5mD17NjZu3AhfX1+EhIQgODgYDRo0MDiMr9frIYSARqNBREQE8vLy0L59exkrJ7ksXrwYP/74I7p164bhw4fDw8MDMTExiIuLw5EjRxAdHY0//vgD/v7+mDhxIrp16waAXxZM2cKFCxEREYF+/fohODgYdnZ20ngouudm0VGCovYHb6tCj8Y9eSaiWbNmsLa2xvr161GhQgUUFhYa3LOqyJ49e/DZZ5/h7NmzmD9/Pt577z2ZKia5+fv74+zZswgICMDx48eh1Wrh5eUlXRXZokUL1KlTR+p/79499O7dG1u3bkVOTg6srKxkrJ7kUK1aNdSrVw8rVqyAq6urwbLk5GTExMRgy5YtWLp0KXQ6HRYtWoSBAwfKVC0Zg+rVq+Pq1auwtLSEn58fwsLC0LFjRzRt2tQg/BedBnLv3j0sWrQIfn5+CA0NlbHyFwNDngnIzs5G9+7dce3aNRw7dgw2NjYGu8gf3j0eExODV155Ba1atcLmzZt5KMUEJSUloXXr1nB1dUV0dDSOHTuG7du3Y8uWLTh58iTUajVefvlltG7dGq1bt0a7du0QFxeHLl26IDAwEFu2bJF7FaicnT9/HoGBgRg+fDimTp0KwHBPTJGCggLs3LkTH3/8MdLT07F161beMNtEnTlzBvXr10ejRo3g7OyMnTt3AgBsbW3RokULdOzYEWFhYQZfJvfv34/WrVsjKCgI+/fvl6v0FwbPZDQBdnZ2aNSoEeLi4rB27VoAKHa+Q9HPer0e/v7+aN26Nc6fP4+rV68y4JmgGzduIDMzE/Xq1YO5uTkCAwMxefJkhIeHY/v27Rg0aBAyMjLw008/oX///ujcuTPGjRuHmzdv4oMPPpC7fJKBEAJOTk5ISEgAAOl2Fw9/mbSwsEDHjh3x/fff4+7du9L82WR6Tp06BQDo06cPwsPDcf78eUyfPh21atVCeHg4RowYgTZt2qBPnz745ZdfcPfuXWmKvHHjxslZ+guDe/JMxPXr19GhQwecPn0aH330Efr37w9fX1+DQ2pFu8MzMzMxcOBAHDp0CFevXpWxapLLxYsXMWbMGPTo0QN9+vQptlyr1SI5ORn79u3DH3/8gZ07d+Lu3btwcnLiHJImrFmzZjh79izWrVtX7N5lRUcEio4ipKWloXHjxmjUqBHWr18vU8Ukp0WLFmHIkCHYtm1bsfFy5MgRrFmzBr/99huuXbsG4P4c6pmZmcjNzUV6eroMFb94uCfPRFSpUgVffvklqlWrhh9//BGDBw/GzJkzERERgatXryIvL086kfWPP/5AREQEbzBpwmrVqoWlS5eiXbt2JS43NzeHl5cX+vTpg3Xr1uGbb74BAPTu3bs8yyQjUbSvYO7cuXBwcECnTp0wcuRIHD58GHl5eQD+ubhCq9UCAOLi4pCfnw8PDw95iiZZCSHQoEEDjBgxAj4+PgbtABAYGIjvv/8eFy5cwB9//IF+/frh5s2buHnzJt555x25yn7hcE+ewj18Pl1aWhqmTZuGX3/9FUlJSahYsSLq1asHDw8P2NjYIDc3F7/++iuqV6+OTZs2oXbt2jJWT3Io6RzMf7tX1ejRozFz5kwcPXoUAQEB5VEmGSGdToeVK1di3LhxSElJga+vL8LCwhAUFARfX1/UqVMHarUa169fx6hRo7B+/XocOnSIY8aEZWdnw8LCAhYWFsWWPfxe9NFHH2H+/Pk4fvw4GjZsWI5VvrgY8kxA0R/KtWvX4OHhAbVajdOnT2Pr1q2IiIjAuXPnkJSUBABwdnZGw4YNMXfuXM4FaMKKxkxKSgrc3NwMwt2DNz4G7t+Cp1OnTkhOTkZqaqpcJZMRSU1NxY8//ohff/0VFy5cgI2NDapUqQI7Ozu4uLjg/PnzSE1NxYABAzB//ny5yyUjVvRelJCQgF69eiEjIwPx8fFyl/XCYMhTsMLCQkRFRWHp0qW4cOECVCoVbGxsEBgYiDfffBP+/v4QQiApKQm5ubm4dOkS6tSpA09PT5iZmfGqWhP08JhRq9WwtraGn58fevTogaCgoGK/c/v2bfzyyy/w8PBAr169ZKiajMWDcxvn5uYiPj4eR44cQVRUFA4dOoTz58+jYsWK8PT0xMCBA/H222/D1tZW7rLpBbB161Z06dIFo0aNwowZM+Qu54XBkKdgM2fOxFdffYWsrCzUqlULGo0GcXFx0nJfX18MHToUPXv25Px/BODfx0ydOnUwaNAg9O7dG5UrV5baCwoKYGZmxqmHqBi9Xo+8vDxYWFggIyMDKSkpPEpAksfdmXDz5k389ddf6Ny5s8FsKfRoDHkKdfnyZdSvXx8BAQFYsWIFLCwsUKlSJaSkpOCPP/7A+vXrERERAQAIDQ3FjBkz0LhxY3mLJlk9yZhp06YNvv32W55LZeJyc3ORmJiIqlWrwtra2mCZXq83mKXg4Q9zzottmh41Zv5NafPbUukY8hRq0qRJWLhwIVavXo1XXnkFQPE32VOnTmHmzJn49ddf4eXlhVWrVqFRo0ZylUwye5oxw0P7pmn69On4/fff8frrr6NZs2aoXbs2KlWqZPBB/PA8x6mpqXB2dua0VCbqccbMwzhmyo4hT6F69OiB2NhY7NmzB1WrVpXugffgOTNFfvjhB4wcORLvvvsuli1bJmPVJCeOGXpSL730EpKTk6HRaODo6IigoCCEhYWhadOmqFGjRrGpzXJycjB58mTcuXMHS5Ys4Z48E/Q0Y2bx4sXck/eEGIsVyt/fHxs3bkR2djYASN+AHpyvtmjvyyeffIJ9+/Zh9+7duHTpEmrUqCFb3SQfjhl6EhcuXEBGRgaaN2+OPn364O+//0Z0dDS2bt2KqlWrIiQkBK+++ir8/f1RpUoVODk54fTp01i8eDFCQkIY8EzQ044ZBrwnx5CnUEUTN/ft2xezZs1Cy5YtS7wPUdE5DrVr18aff/4pfcCT6eGYoSdx4cIF5OXlISwsDMOGDcNrr72GuLg4REdHY/fu3fj999+xatUq+Pr6ok2bNmjfvj127dqFzMxMDBo0SO7ySQYcMzIQpEiFhYXis88+EyqVStStW1f8+OOPIiUlpcS+aWlpol+/fqJixYrlXCUZE44ZehLr168XKpVKrFu3zqC9oKBAxMfHi99++0188sknws/PT1hYWAhbW1thY2MjnJ2dZaqY5MYxU/54Tp7CLVy4EN999x0uXboEDw8PdO/eHR06dICnpyc0Gg2cnJwwb948zJkzB0OHDsWsWbPkLplkxjFDj0MIgfPnz8PKygrVq1cv8eKbnJwcXLhwAXFxcVi2bBn+/vtvfPTRR5g7d65MVZOcOGbKH0OewgkhcPHiRSxevBhr166VJnp2c3ODubk5bty4Ab1ej969e2PGjBl46aWXZK6Y5MYxQ0+rpA/v4cOH48cff8SxY8fg7+8vU2VkrDhmng+GPBOSk5ODw4cPY8uWLUhOTsatW7fg4OCAN998Ez169ICVlZXcJZKR4Zihp1F0L7wrV66ga9euuHv3LhITE+Uui4wYx8yzxQsvTIitrS1CQ0MRGhoKrVYLc3NzuUsiI8cxQ0+j6Ara69evQ6vVYujQoTJXRMaOY+bZ4p48IiJ6roQQuHbtGlxcXDhXLT0WjplngyGPiIiISIF4N0oiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBWLIIyIiIlIghjwiIiIiBfo/wTHw/WElQ5kAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Divido i valori misurati per 2^8"
      ],
      "metadata": {
        "id": "1WWhjj5pcjyE"
      },
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "rows, measured_phases = [], []\n",
        "for output in counts:\n",
        "  decimal = int(output, 2)\n",
        "  phase = decimal/(2**N_COUNT)\n",
        "  measured_phases.append(phase)\n",
        "  rows.append([f\"{output}(bin) = {decimal:>3}(dec)\",\n",
        "               f\"{decimal}/{2**N_COUNT} = {phase:.2f}\"])\n",
        "headers = [\"Output\", \"Fase\"]\n",
        "df = pd.DataFrame(rows, columns=headers)\n",
        "print(df)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0oVBKDF8d0Nr",
        "outputId": "dac70c07-25fd-497e-d8e3-d576d322366a"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Output            Fase\n",
            "0  10000000(bin) = 128(dec)  128/256 = 0.50\n",
            "1  11000000(bin) = 192(dec)  192/256 = 0.75\n",
            "2  00000000(bin) =   0(dec)    0/256 = 0.00\n",
            "3  01000000(bin) =  64(dec)   64/256 = 0.25\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rows = []\n",
        "for phase in measured_phases:\n",
        "  frac = Fraction(phase).limit_denominator(15)\n",
        "  rows.append(\n",
        "      [phase, f\"{frac.numerator}/{frac.denominator}\", frac.denominator]\n",
        "  )\n",
        "headers = [\"Fase\", \"Frazione\", \"r\"]\n",
        "df = pd.DataFrame(rows, columns=headers)\n",
        "print(df)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JFWB8Zseen5R",
        "outputId": "7e09b2ed-0b49-4a6f-a85b-99dcb0e92ba7"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   Fase Frazione  r\n",
            "0  0.50      1/2  2\n",
            "1  0.75      3/4  4\n",
            "2  0.00      0/1  1\n",
            "3  0.25      1/4  4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "o7zbMriyfbeZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Da ricerca del periodo a fattorizzazione"
      ],
      "metadata": {
        "id": "8OXijYfGgSoZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def qpe_amod15(a):\n",
        "  N_COUNT = 8\n",
        "  qc = QuantumCircuit(N_COUNT+4, N_COUNT)\n",
        "  qc.h(range(N_COUNT))\n",
        "\n",
        "  qc.x(N_COUNT)\n",
        "\n",
        "  for q in range(N_COUNT):\n",
        "    qc.append(c_amod15(a, 2**q), [q] + [i+N_COUNT for i in range(4)])\n",
        "\n",
        "  qc.append(qft_dagger(N_COUNT), range(N_COUNT))\n",
        "\n",
        "  qc.measure(range(N_COUNT), range(N_COUNT))\n",
        "\n",
        "  aer_sim = Aer.get_backend(\"aer_simulator\")\n",
        "  t_qc = transpile(qc, aer_sim)\n",
        "  job = aer_sim.run(t_qc, shots= 1, memory=True)\n",
        "  readings = job.result().get_memory()\n",
        "  phase = int(readings[0], 2)/2**N_COUNT\n",
        "  return phase"
      ],
      "metadata": {
        "id": "RcJa5TKSgUbA"
      },
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "phase = qpe_amod15(7)\n",
        "Fraction(phase).limit_denominator(15)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cQWdYf2ZhGxn",
        "outputId": "a84cd442-9100-405d-e8b0-ca94ea59f18f"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Fraction(3, 4)"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = 7\n",
        "N = 15\n",
        "TENTATIVO = 0\n",
        "while True:\n",
        "  TENTATIVO += 1\n",
        "  print(f\"\\nTENTATIVO {TENTATIVO}...\", end=\"\\t\")\n",
        "  phase = qpe_amod15(a)\n",
        "  if phase != 0:\n",
        "    fraction = Fraction(phase).limit_denominator(15)\n",
        "    print(f\"Fase: {phase}\", end=\"\\t\")\n",
        "    r = fraction.denominator\n",
        "    print(f\"r: {r}\", end=\"\\t\")\n",
        "    guesses = [\n",
        "        gcd(a**(r//2)-1, N),\n",
        "        gcd(a**(r//2)+1, N),\n",
        "    ]\n",
        "    print(f\"Guesses: {guesses[0]}, {guesses[1]}\")\n",
        "    if guesses[0] * guesses[1] == 15:\n",
        "      print(f\"Divisori trovati: {guesses[0]}, {guesses[1]}\")\n",
        "      break"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dDYidMo9hP9_",
        "outputId": "0a0e1820-bc13-4f15-f6fb-77965a9d61c8"
      },
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "TENTATIVO 1...\tFase: 0.5\tr: 2\tGuesses: 3, 1\n",
            "\n",
            "TENTATIVO 2...\tFase: 0.25\tr: 4\tGuesses: 3, 5\n",
            "Divisori trovati: 3, 5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "CSh2veaSio7F"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}