kyscg/a004207.ipynb

## a004207.ipynb
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      "source": [
        "# OEIS A004207\n",
        "\n",
        "See discussion on [Twitter](https://twitter.com/kyscg7/status/1704947958045909345), [GitHub Gists](https://gist.github.com/kyscg/9f5f8ce7b8e40444bc34cb49c3aff55b), [Mathstodon](https://mathstodon.xyz/@kyscg/111104902901516055).\n",
        "\n",
        "---\n",
        "\n",
        "Playing around with the integer sequence [A004207](https://oeis.org/A004207), where $$a(0)=1, a(n) = a(n-1)+\\text{sum of digits}(a(n-1))$$\n",
        "\n",
        "## Log\n",
        "\n",
        "- Plotting the delta values seem to indicate that the max delta across the range when we generate $n$ numbers is approximately $10k$ where $k = \\log_{10}(n)$\n",
        "- The delta values seem to exhibit periodic behaviour, and the change in period corresponds to kinks in the otherwise linear curve when we plot the numbers themselves.\n",
        "    - The correspondence is trivial to understand\n",
        "- Why is there periodicity? (if there is) and what is the period?\n",
        "- Computed `mod 10` because, well, decimal, and also the duodecimal and hexadecimal bases because they're my favourites\n",
        "- Modulo 12 exhibits interesting behaviour, there are no numbers in the sequence that are ~~`(2, 5, 6, 9) mod 12`~~ `(0, 3, 6, 9) mod 12`\n",
        "- Consistently, there seem to be slightly more odd numbers than there are even numbers (found by taking base 2)\n",
        "- Something is up with 3, taking base 3, 6, 9, 12 give zeroes in the `counts` arrays.\n",
        "- There are $b/3$ zeroes in the `counts` array where $b$ is the base.\n",
        "\n",
        "**A Month Later**\n",
        "- First thing, my histogram calculation was completely wrong, so I fixed that.\n",
        "- I find that not only do bases that are multiples of three give zeroes in the `counts` array, but the indices that have zeroes are also multiples of three.\n",
        "- There is another way to get zeroes in the array, and that is to have a base much higher than the highest number generated in the sequence, but for the purposes of a mathematical proof, we will be assuming we have an infinite sequence.\n",
        "- Proof done for $k=3$ (I'll put it out as soon as I type it) but there are some more questions that I came up with...\n",
        "    - Is there a closed form for the $i^{th}$ term in the sequence\n",
        "    - Prove there are no zeroes in the `counts` arrays for bases that are not multiples of 3."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iWHONTHyGSYB"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RYzEzPnSGxDM"
      },
      "outputs": [],
      "source": [
        "def sod(n: int) -> int:\n",
        "    \"\"\"\n",
        "    Computes sum of digits given an integer\n",
        "\n",
        "    Parameters:\n",
        "        n: int. Number of interest\n",
        "\n",
        "    Returns:\n",
        "        sod: int. Sum of digits\n",
        "    \"\"\"\n",
        "\n",
        "    sod = 0\n",
        "    while n != 0:\n",
        "        sod += n % 10\n",
        "        n = n // 10\n",
        "\n",
        "    return sod\n",
        "\n",
        "\n",
        "def genSeries(n: int) -> list:\n",
        "    \"\"\"\n",
        "    Generate n numbers of the sequence and the delta, a(n) - a(n - 1)\n",
        "\n",
        "    Parameters:\n",
        "        n: int. Number of terms in the sequence\n",
        "\n",
        "    Returns:\n",
        "        a: list. Array of numbers\n",
        "        d: list. Array of changes\n",
        "    \"\"\"\n",
        "\n",
        "    a = [1.0]\n",
        "    d = [0.0]\n",
        "\n",
        "    for i in range(1, n):\n",
        "        d.append(sod(a[i - 1]))\n",
        "        a_i = a[i - 1] + d[i]\n",
        "        a.append(a_i)\n",
        "\n",
        "    return a, d\n",
        "\n",
        "\n",
        "def modN(series: list, modulo: int) -> list:\n",
        "    \"\"\"\n",
        "    Takes the modulo of each element in a list of numbers. Also returns the\n",
        "    counts of the numbers.\n",
        "\n",
        "    Parameters:\n",
        "        series: list. A list of numbers.\n",
        "        modulo: int. The modulo to take.\n",
        "\n",
        "    Returns:\n",
        "        modulos: list. A list of modulos\n",
        "        counts: list. A histogram array of the numbers in modulos\n",
        "    \"\"\"\n",
        "\n",
        "    modulos = []\n",
        "    for number in series:\n",
        "        modulos.append(number % modulo)\n",
        "\n",
        "    counts = list([0] * modulo)\n",
        "    for m in modulos:\n",
        "        counts[int(m)] += 1\n",
        "\n",
        "    return modulos, counts"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "n81N6qwHGayu"
      },
      "outputs": [],
      "source": [
        "n = 30000\n",
        "series, deltas = genSeries(n)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZIrMRXXiL8NA"
      },
      "source": [
        "- Plotting the delta values seem to indicate that the max delta across the range when we generate $n$ numbers is approximately $10k$ where $k = \\log_{10}(n)$\n",
        "- The delta values seem to exhibit periodic behaviour, and the change in period corresponds to kinks in the otherwise linear curve when we plot the numbers themselves.\n",
        "    - The correspondence is trivial to understand\n",
        "- Why is there periodicity? (if there is) and what is the period?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 958
        },
        "id": "dhenYNRTGvtw",
        "outputId": "acfc142b-ebb9-4655-91bb-e0c88fcd47ad"
      },
      "outputs": [
        {
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50Yle/6irLf/5TjlWmnae9NZc6d1bvM9G+TzejewUl0oHv+2dK+3bp/jlkPckJaSSEVLHMql2mjT+YGne/0qvf8+fMpp2krb9H6n1X9KzvYlQG53oz7wPn+89PervW3vTEw4vfJ5j9vSO5+ffK710qffZxCPym9c210ij9/DGUJc/59X1LS6QEj3S3zbu/VKe+9ojFklrP+5f9kyJq5mUjuh/37CdtMPc/ja6fiupe62XzHnvzMLii5LDPvb2jXdv7t88NzrJv3kBBpAIBgCIn5JyqTmARx5WjJKae0+E9r1Wjc18FTiyxEEMIq6oxGsvSnw+w17Z0t8ONfXetau0Wqpo9Lec0hH985eGvmINQDiKiryk9CCu8O67o0jyyddmnxNBi0u9flpxmb/zlaTazb1HdPchETPFo2ulExdJ87q828d/tUG6vEkqpzsWPeX1Uvk2/s+3YrQ0Ypz3vqn3ZGn9ltKKHn/LGblR/wWJkn/tRUllf//JTzVTUx+JUsxwLAyomx7MfOu39F4rk44DfB9vKfL6GyVVPs9XUvXE1Glf7lpS3HuM58MdmQdrVzuWFj5vuCeofnLl6P5629e3L6lMrdd+KKtJvUNhRZNPMy7y6sf7t/o0v17ldVJjUtJ8eUP+8xqsrSz4DuG9y/5udYHzgS+qJ0mJhP/zHTml/33VGO+1aQf/nzbUsLV3sWcfvxKNKxpTxyMz3eE3H43bSov/3T+db7zlTf1tX19bWD25sNj6VDSltnX53Jm5cszANrq0ysc2NCL6+kt+CmJcCggRIw8AAPgmgAM9APHg+0AR7REQe0EMQCOSlndLly2V5q709h4bl0m/GSPtEsD5dgAAABSI8QPLsP4At9leh22PD4CtSAQDAAAAjOE2KwCQKsx2kTb4r2ukz7VKrd3e9Om10rWjpJpis3EBgytKe3WFa/EiUnh0IBAR1GUAAABkh0QwAAB8w4AMAFvQHgEABvdRp3TxUunW1d70tDLpJ6OlvUeYjQuOI9kEAPxFu4pQsJ0BiDPb20Db44sy1j3cRiIYAAAAAACwS2CPtoz3YxU6EtKPV0hXLJXaEt6w5kUN0lWNUgV3AQMAWM2xfXiQj+nmEeBABi7WC79idnHZYSUT+5eCymTbB4DBkAgGAAAAmBK1K7yjtjyAkxyvh4G1IxnmG7M267426cuLpTc6veldKqUfjpK2rzQbF1Awm+tyxtgsjhewkmOPjba5TYLjorZt+bQ8odU5C9c/7Y1FXP8tQozfj+029G3f9vbK9e0PQBBIBAMAAACM4wo2AH6jXYHnnQ7pgiXSX9u86dEl0jVN0km1UjHjxQAAAI6hn28XOtQwhLtDAgCGQCIYoo/OEAAAAAA4JqDjuBgdH67ukb6zTLp2hfdIyFJJX6yXLmuU6koMBwcAQK6c24cHGa9r6wIYil+JVA7Wi+HatazbPQeXHZZybVtyLV4ACA+JYAAGYdOVLDbFAgyB23EHxKb1alMsiIao3RKcOgKYRz3MKEaPZ+tKSL9dJX1tqbSw2/tsnxHSD5ul6RVmY0PUhVCnnKvLOcTL8SQC4/i25dxjo/2M1/HfDv6K3CPF/Co3pPit3E/bGFNcGfgt/NwmQ92+08rKq+yQl9239ZPHfEKND0CUkAgGAAAAGMcBOwCgMF0J6derpO8sl97t9D6bWiZd2ywdVM3YMAAAAAAAABAHJIIBAAAAAADLBPWIh+g9OqIrId2+WvrWcun1Du+zUSXSVxqkc+ukimKz8QEA4A/X9uE8GhIIlXOPj5V8q8tOLjvs5Ni2xLYPAIMiEQwAAAAwpu/2LFEZuOB2M4BxRVFrV/zi2uPkhteRkH6zSrpmufRO7x3AmoqlrzdKn6uTqkkAQyS5VpeDevQckAvXt7mA4g/sUbOur2/YK2LblslHrVldTi5sjCmmTPTvfE2CMvhoSGPzMFFe1B7xC8BmJIIBAAAAAAA4Yl2P9ItV0veWSx91eZ81FUvnNUhn10n1JWbjAwAAALJHAsPguLgHAADkh0QwAAB8k8XABbcrBhAG7jQxNNpiwH6B1VN36/+iLuknK6Sfr5IWd3ufjS2RLmrgDmCwBf0PAEFybB/uS19mkHaV4xn4yfj4gV/bs6l6UUi5ri87Ise5/UuA+1pr2B4fAFuRCAYAQCjosAPIwPiAq8+itjyAk6iHmbn7eLa3O6RrV0i/XCW1945zTymVLm6QTq6VKkkAQ6w4VpcDe/QckAOb60hWwnyMkg9lOb++Ya3IbVs+LU9o68XE+h+mzMhtEy4z8Fv4+vuHGL8fcYe+7dveXtEWBII2Fo4jEQwAAAAAAKCPJVdBz+uULlgi/WlN/3XOO1dKF9ZLh4yUyhiTBAAAAAAAAJCGRDAAAADANEuSDgBEiPPtSkDxO7BeehLSDSulry6R1vSGe+AI7xGQn6riolQAQEw5sA9PFWS8rq0L+IvfPzMH18uw7Vq2y+TgsqNwgewXXduWXIsXAMJDIhgAAH7hrByAnEXtluC0g4B51MOMHHk82zsd0smLpMfWe9O7VEo3jpZmVJiNC8hKGMdDjtTlfq7Fi2hyfJsL8zFKvpTlY7yMMyEUpscPCi0/pPitrI82xhRXjv8WoW7flu1rs5mXb+snn/mEGR+AKCERDAAAAAAAwKCehDS39y5gaxPSyCLpmmbprDqpmDFdIF6cu+sRAAAAAEQMx2VwHIlgAAAAAAAAhrzZIZ26SPp3713AdquSbhkjTSkzGxcAAAAAAAAA9xSbDgAAAABA1HD7GgCFCurKS3uu6OxISN9dJm09z0sCG1kk/XSU9PB4ksCA6LGn7QHc5Vo9CjJe19YFEAIn79ziU8xOLjvs5Ni2xLYPAIPijmAABmHRCVyebw3Em01tgE2xICKitk1FbXkAB7GvGkSm9WJmXSUS0p/XSF9ZKr3b6X227wjp56OlySSAAcMIsy77Md8M86CdRuhc3+YCij9jXQyo3gMYyLf9YVh1brBygix/mCQX+hT2MPFb+FpmmPG7uK+1vb2iLQAwEIlgAAAAgHFcwQbAb7QrNnq9Qzq3VXponTfdUiJd3SydVMN5HEQBGzEA+It2FRlwBxwAEm0BAGBIJIIBsB8dWgC2oD0C4DvaFSCjoPa5hvbla3ukK5dJ1y6XuiRVFElfaZAubpCqi42EBCBMHEcAhXOtHgUZr2vrAhiKb1dDuFgv/IrZxWWHlZzbv7gWLwCEh0QwAIOwqQNlUywAQmfVAahNsSASNgx4RuRKb2duZ0NdRpRFrF3pU3B/wMzj2RIJ6W9t0nmLpfe6vM8OqZauGyVtzGMggTyEWJfT55tPOxTYo+eAHDh/zBHmY5R8KMuZYyI4KzLbWO9yFNrPD2192LjebYwprnp/izDrp6uPhgysjx0kn8oL67gFAEQiGAAAAAAAgO9ebvcSwPoeAzmxVJo7Sjp4pNm4AAAAAAAAMAQS7OA4EsEAZMBdMgDYgvYIQBBoWwD7BVVPg6//b3ZI310u3bJK6pH3GMjz66WvNUojeQwkEFP0PYDCuVaPgozXtXUBhMFUvSig3OHuhJT1nZJoE+AX17Yl1+IFgPCQCAZgEDZlOtsUCzAUttVAWHXlhU2xAEOwqt4AMIMB0eH521a+3yl9fal06+r+zz49Uvpus7QRj4FELITQ/6CPA+SBeuMufjtkUPAj09OxnQEwyHT/3nT5w7E9PgDWIhEMAAAAAABYJqjBTv/n+98Oae4K6aZVUnvCK+GAEdLXG6XZVb4XB0CSeyetXYsXsJFr9SjIeF1bF8AQfEtycLBexHnZYSnXtiXX4gWA8JAIBgAAAAAALGP/oyGfXCd9e7l0d1v/Z3tWSf/TLG1b6VsxACKBuzQChXOtHvFoSCBcDtYL3+7u5uCyw1KubUuuxQsA4SERDAAAADAmaleuRW15ABdRDzPKeLV97uuqOyE9sFb6wXLpoXX9czm4Wjq3Xtqriic3AOGz+Q6C/rQ9QKwFtmPNMF9fyqKOA1lx7W5YRjr5wyW50N7Yw/HfItTt28F9rfXtlePbH4BAFJsOAACA6KDDDcAWtEcA4KeOhHTzSmmzD6QD5ntJYKWSTqmV/jtZ+us4ae8RJIEh5qgAAOAv2lVk4vd2wXYGINZsbwNtjw9www033KCZM2eqtrZWtbW1mj17tv7+979v+Pv69et19tlnq6mpSSNHjtSRRx6pRYsWpcxj3rx5OvDAAzVixAiNHj1aF110kbq6ulK+88gjj2i77bZTRUWFpk6dqltuuWVALHPnztWUKVNUWVmpnXbaSU8//XTK37OJJRskggEAAADGcStzAH5zvV2x49GQq7qla5dLU9+XTm+V3u2UGoqlL9VLb02RfjlG2qw8iDgBRIvrbTJgA8fqkW+PfAt53rAfv39mTq4Xn2J2ctlhJ8e2JbZ9AFmaMGGCrrnmGj377LN65plntOeee+rQQw/Vq6++Kkk677zzdNddd+mOO+7Qo48+qvnz5+uII47Y8P+7u7t14IEHqqOjQ48//rh+/etf65ZbbtFll1224TvvvfeeDjzwQO2xxx564YUX9OUvf1mnn3667r///g3f+eMf/6jzzz9fl19+uZ577jltvfXWmjNnjlpbWzd8Z7hYssWjIQFkZtOVQDbFAsAAi9oA2iP4LmrbVNSWB3AQ+6pB5Pb4p/c6pRtWSj9bKa3q8T4bUyJ9pUE6s06q5rI6wJAwH7UY0GNraKcRNue3uYDi9+mx0cHMA4iDorTXQucTNAvrtvPte4Q4/1uYfDRkHmWHvr55NCTguoMPPjhl+tvf/rZuuOEGPfnkk5owYYJuvvlm3Xrrrdpzzz0lSb/61a+0xRZb6Mknn9TOO++sBx54QK+99pr+8Y9/aMyYMdpmm230zW9+UxdffLGuuOIKlZeX68Ybb9RGG22kH/zgB5KkLbbYQo899piuu+46zZkzR5J07bXX6owzztApp5wiSbrxxht1zz336Je//KW++tWvauXKlcPGki2GLgEAAAAAQOwlEgnd2yYd+OTt2uR96fvLvSSwzcukm0ZL70+Rzm8gCQxAUDiBAwAAAABAkLq7u/WHP/xBbW1tmj17tp599ll1dnZq77333vCdadOmadKkSXriiSckSU888YS22morjRkzZsN35syZo1WrVm24q9gTTzyRMo++7/TNo6OjQ88++2zKd4qLi7X33ntv+E42sWSLO4IByMymW6raFAsAAyxqA2iPgGigLgP2C6qeDjLf9q52nfz8ffrDfEl6R5K07wjpnDrpwGqpmPwMAIWg7wEUzrl6FGS8rq0LIAym6kUhBwrDxJx1u0ebAJ8Y2dcWUibbPhB3q1ev1qpVqzZMV1RUqKKiIuN3X375Zc2ePVvr16/XyJEjdeedd2r69Ol64YUXVF5ervr6+pTvjxkzRgsXLpQkLVy4MCUJrO/vfX8b6jurVq3SunXrtHz5cnV3d2f8zn//+98N8xgulmxxHSsAAH5x/hbQAEIXWLthqD2iHQQsQD3MbPDHP61uX62DbjtIf5j/pkolnbfJDnpzsnT/eOngkSSBAdkLo7KE+KhFP+Yb2KPngFy4vs2FeMwUWL3Pe2Y+zgsYjKntzKdywxqHsHK8w8aY4srx3yLM7duXssLe1xpsr7L5P1a2T1HAenXB9OnTVVdXt+Hf1VdfPeh3N998c73wwgt66qmndNZZZ+mkk07Sa6+9FmK04eKOYAAAAIBxXMEGwGfO3TXDjNa2Vh3w+wP07IJnVV1Spj+P6dS+M/aWXvuP6dAAAACADOjnAxDH/AAg6bXXXtP48eM3TA92NzBJKi8v19SpUyVJs2bN0n/+8x/96Ec/0tFHH62Ojg6tWLEi5U5cixYtUktLiySppaVFTz/9dMr8Fi1atOFvfa99nyV/p7a2VlVVVSopKVFJSUnG7yTPY7hYssUdwQAAAAAAgGWCGtTun++7y9/VLr/cRc8ueFbNI5r1f7OP1L7VARULIOY4UQcUzrV6xKMhgez4dccVU/WigHJ9S+ShTYBfXNuWXIsXgN9qampUW1u74d9QiWDpenp61N7erlmzZqmsrEwPPfTQhr+98cYbmjdvnmbPni1Jmj17tl5++WW1trZu+M6DDz6o2tpaTZ8+fcN3kufR952+eZSXl2vWrFkp3+np6dFDDz204TvZxJIt7ggGIDObbiVqUywADLCoDaA9gu+itk1FbXkAF1EPM0rbhz+/Xjrglt20cM1CTa6brAdOeECbvX+DtGiQ/w+gAD62S6E+ajGox9bQTiNsjm9zgR2HB1U/HV/fQFh8q9th1Tkb67aNMcWVgd/C2UcRp5eVT9khr2/r2yvaAmA4l1xyifbff39NmjRJq1ev1q233qpHHnlE999/v+rq6nTaaafp/PPPV2Njo2pra3Xuuedq9uzZ2nnnnSVJ++67r6ZPn64TTjhB3/ve97Rw4UJdeumlOvvsszckn33+85/X9ddfr6985Ss69dRT9fDDD+v222/XPffcsyGO888/XyeddJK233577bjjjvrhD3+otrY2nXLKKZKUVSzZIhEMAAAAAADExh9WS6cuktYlFmrmmJn6+3F/17iacdL7piMDAAAAgD7c7QgAAD+0trbqxBNP1IIFC1RXV6eZM2fq/vvv1z777CNJuu6661RcXKwjjzxS7e3tmjNnjn76059u+P8lJSW6++67ddZZZ2n27Nmqrq7WSSedpKuuumrDdzbaaCPdc889Ou+88/SjH/1IEyZM0C9+8QvNmTNnw3eOPvpoLV68WJdddpkWLlyobbbZRvfdd5/GjBmz4TvDxZItEsEAAAAAAIBl/D/pkUgk9M0n5+ryhd70nE321R+O+qPqK+t9LwuIJe6eOzjfHv0ExJlj9ciPej9Yu0qbAgzkZL3wKWYnlx12cmxbYtsHkKWbb755yL9XVlZq7ty5mjt37qDfmTx5su69994h57P77rvr+eefH/I755xzjs4555yCYskGiWAAAACAMb0D+5EZuOAEMGDchhOGUWlX/LG2u0en/ukY/fHVP0qSLqiXvnvM3SopKTMbGIAcReDRkCTMIWzOb3MBxR/Yo2ZdX9+wX1T6+T7VldDaOAvrtvPte4SY+C18HUs0+WjIfGYR9vrm0ZAA3EMiGAAAAAAAiKyPOqXDXnhCz65ZqdLiUs1t7tLn6iQVl5gODQAyiMoJfgAAskAyEwAAgO+KTQcAAAAAAACQwqerm59YJ23/ofTsmpVqqmrSPw6/yUsCA4BQkdwFFMy5uygHGa9r6wIIg4v1YriYs10mF5cdVmJfCwCRwR3BAAzCpitxbIoFGArbajBsWq82xYJICOrKV1NX1HIlL2AB6qHkjV/ftEo6d7HUkZC2qq7RX0/7jzYqWiu91Pct1hXgrzDqVIiPWvRjvoE9eg7IhevbXIiPUQqs3uc9M0P/F/Fialux/VFr6cXYWKdsjCmuDPwWfm6TYW7f6WXlVXbIy+7X+glqWa1snwCYxh3BAAzCpkx6m2IBED6b2gCbYgGQP+oy4J7s6+3qHunohdKZrV4S2GHV0uPb7qKNGjYKMD4A0Uf/AQAA3zl3ByIAvqINAIBAcEcwAAAAwDSu3AIAX7zc7iWBvd7hDXh8p1m6oF4qLmH4AwAAAAAAANlgvB5uYyQUAAAAMI2r3wD4zvV2Jbf4EwnphpXS+Uuk9oQ0tkT681hp56rC5gvAVq7VZdfiBWzkWj0KMl7X1gV8xfjBIBxcL379lmwT8RTI7+7atuRavHAL2xfcRiIYAAAAYEzUriyK2vIALopfPVzWLZ22SPpLmzd9wAjpljHSqOQRj0x3XuRujIB7MtbboOqyH/MNM15gMI5vc4Htr4Oqn46vbyAsfXW74DoeVp2zsW7bGFNMOX9sGWb8Lu5r/SrP5uMWAFFTnMuXr776au2www6qqanR6NGjddhhh+mNN95I+c769et19tlnq6mpSSNHjtSRRx6pRYsW+Ro0AAB2osMNwBaG2yPnB8AAuOKf66St53lJYGWSrmuW7h6XlgQGICTs/wHAX7SrCAHH7wVi/QFus70O2x4fAFvllAj26KOP6uyzz9aTTz6pBx98UJ2dndp3333V1ta24TvnnXee7rrrLt1xxx169NFHNX/+fB1xxBG+Bw4AAAAAAKJq6FvwdyWky5dKe3wkfdQlbVomPTlR+nLDcOeyuLU/EA2O1WUe2QT4wLF6FGS9p00BBjJWLwop16+YaRPgF8e2JfaHADConK6Rve+++1Kmb7nlFo0ePVrPPvusPvWpT2nlypW6+eabdeutt2rPPfeUJP3qV7/SFltsoSeffFI777yzf5EDCJhNWeY2xQIgfDa1ATbFgmiI2jYVteUBHBSDK/rndUrHLZQeW+9Nn1wj/WS0NHLIS92iv16AeIjAoyFj0E7DMs5vcwHFH9SjZp1f37BeZLYxn5YjtPVh4XqPzLYQBQZ+C19/f8ceDRn6tm97e0VbAGCggh6WsHLlSklSY2OjJOnZZ59VZ2en9t577w3fmTZtmiZNmqQnnngiYyJYe3u72tvbN0yvXr26kJBgwup3Uqc/vlta9V8zsQwmPUYMbX2r9MpVpqPot+Il0xEA/mlf4tUxZKd7nfTIfqaj6Df/HtMRILK4gi1U92xpOoJ+ix8zHQGiKoJXxnYnpBtXSl9fKq3skWqKpRtHScfW+lzQksd9niEA5GDNu6YjAADYLIL9fAB5oC0AAAwhp0dDJuvp6dGXv/xl7bLLLpoxY4YkaeHChSovL1d9fX3Kd8eMGaOFCxdmnM/VV1+turq6Df+mT5+eb0gw5f4dUqcfPVh6/iIzsQzmAe5GlxPbEvkQH007mY4geM9faDoCt6xfZDoCxFXz7HDKKcq7O27eiAn978fs5b1u9gUzseRq7YemI0AclTeGU07TDsN/xwVbXOy9Tj5GkrR03TLt8ZF0zmIvCWynSun5iTkkgU05znsdMWn477Y+mnu8gCta9jEdQWE27e1rFJX0f1bVUvh8S0f2v594lPe6hQ/Hbpuc5r2W1yeVVTP0/1n6VOHlAskmHmk6gsJUjvFeNzrJe63f2p/5Tjt/4Ge10wqfb0m19zr1c97rqF0Kn2e6hm38nyfyN+qTpiOwX/3M/vcN23qvfXW60DvZ1G7hvU7q3X8nj1Xkq/kT/e9rNvNepxxT+HzTTf+q9zr52Mx/Hy7Rpy+2SZ/xXqun+BIW8rD5l01HUJiW3hu8jN7N3/mOO7D/fcUo73XCoYXPt7l33zp2jvdaXFH4PIcyckru/2f8If3vyxt6PzvYl3A2KO3tc4w7wN/5umbaBaYjAKyU9x3Bzj77bL3yyit67LHCrmC/5JJLdP75/QddH3/8MclgrulYbjqCYSS8O/AAsNeoT0rbfl9KdEsPBjh4csArUuXo4Oafza192z4IrnwA/tj3SW/w7E4fTioO5uC3peJyd28Jvt+zUs3U/und75aWvyQ1bR9suYCr9n/ea1f+tyG4Mg6f7x2bjdw4uDKCdODrqYkSM7/pDRA3bKv3V7yv/X57gN5YL9UWS1c3SWfWSSXZNHU73uSdLG2c5U2X10kHvxX8QDGQiz3u906MPH6ctOr14MrZ9ympYebw38tXkI9o2eIiL0Grr69RVCwdOk/q6ZDKhkmsGs7+L0jVSUmin/i9tPxCqbGAfs3WV0ste/XPo6RCOuS93vfl+c8X0dG337tzbHBl7HaPlyjZuF1wZQTp0Pe9caKy3kTNKcd5iVp1WxQ23ynHSZudm1rHD/tY6lotVY3Jf76HvOu1TX11fOrnvISX+hn5z3OwdrV64sC+E8I3YqL0ydulimbprk2DK+eg/0plft8CN1nA4wdz/pNab/f5l7TytcL2s5J02EdS15r+hPCx+w0cq8jHvk+l1tv9npVWvyE1BNCWzvxW7zHPYPMeJBHssA+lrrVSZW9izfiDpP2e6U8Mg+fQeVJPe7D1c+NTpKlnuntB1oGvSj1d/ccIddOlA16WKgscEy0qlvZ5PDVx+eC3vDvfNm6b/3wP+1DqWCnV9SZuN20v7f9igQmgQ7SBh30oda/vT+TKRkmltNcjqct+yLtS2/v5JXIPdYx12IdS2zypwackeT8d9rHUuUq6p8B+21Ba9pVmXln4/gSIqLwSwc455xzdfffd+uc//6kJE/ob15aWFnV0dGjFihUpdwVbtGiRWloy7zQqKipUUdE/ALtq1ap8QgIAuKxilNS8s7TkyWDLqQ/6UWA8ix1wXuUYqXknb1AhSDWbBDv/IE/ESgNPJpVUSs07Blsm4LIw7tpQNdb756q6tDtwFJdIzTvp+QXP64BbD9DCNQs1sVS6b5w0PZccrormgUmqhZ4cAvxW0VzYCZGsymgKYV8dYP+jonlg/NUT/Zl3+omTknKvP1iIiuaBJwTzuZMAoit9vxeEimZ3k8AkqXpy6nRRkT8XnlQ0D6zjI8YVPt+RG6VOFxX50O4O0a6GsQ1haJUt3nhm27xgy6ndPNj5Bz2emV5vS6v9SZoZMT51uqjIhzYvQ70tG9l/UYnfiku8bShX6UkvRUXBxegyv/qKQ8m0T3FJxWipsjn1s0ISmPtUjR+4XsrrCj/mqRwzcPsv9EKXocZQ80kwqxybYdnrpfJtcp+XpCHb6PKG3JLUwjRinCQf+ldDqRyVXxsKxEROz6JJJBI655xzdOedd+rhhx/WRhulHtzMmjVLZWVleuihhzZ89sYbb2jevHmaPTukx+sAAAAAAADn/fn1P2vXX+2qhWsWaqtR0/XExByTwADAT8M9ngkAAOSB/evgWDcAACA/Od0R7Oyzz9att96qv/71r6qpqdHChQslSXV1daqqqlJdXZ1OO+00nX/++WpsbFRtba3OPfdczZ49WzvvTEYmAGAYzg+sZ3MFnevLCESdqTrqd7ncoRCAu32ORCKhqx69Slc8eoUkaa+N9tKfDv256u7J526K7q4HxEki7TWIIsKoC0H2P1yry67Fi2hiO8zIqbEnjuvsFpHxg6DvKO4Uy9oHp9qruHL9NwoqfpfWi+1toO3xGRR4G8m6h9tySgS74YYbJEm77757yue/+tWvdPLJJ0uSrrvuOhUXF+vII49Ue3u75syZo5/+9Ke+BAsAiCqXDgyGwMAJAGvQHgFw07rOdTrtb6fptldukyR9eacv6/v7fl+lHSvMBgZgeBwPFYj1ByAN7SpCYXo7M10+gHjzuw0iWReAHXJKBEtkkVlZWVmpuXPnau7cuXkHBQAAAAAA4mXhmoU67A+H6amPn1JpcaluOPAGnb7d6abDAgAAAAADInLxNAAACF1OiWAAAATL9YNbrs4AYAmuFgPgmP98/B8ddcdRmrdynhoqG/Snz/xJe2y0h+mwAOSE/gcA+It2FSFg/ABAnFnfBtoeHwBbkQgGAAAAAACM+cVK6axffkJdPV3arGkz3X3M3dq0aVPTYQEAAACAQa5fNA0AAEwpNh0AAAD9OLgFAACIi9U90pmLpDNapa6eLh25xZF68rQnSQJDjLl+PMTV6v1c/y0B2IF2FbBeIsB9fpDzBoLEtgsAxnFHMAAAfMMAHQBb0B4BsNv7ndKB86XXOrzpK3e/Ut/41DdUZP1jGQAMivoLWI466hzaVUe4nvBgejszXT7gqKjsI3JajiCW2fb1aHt8AGxFIhgAwB5cKQIAABB5d6+RTlwkLe+RxpVIv2uR9tjtMtNhAYCPOGEDAEAsBJqMw1g5HBWVJDUAcBiPhgQAwC8c4ACwBu0RAPt0JqSLl0gHL/CSwHaokJ6cKO0xwnRkAPxB/wMA/EW76gTnL2xlO7OX69sWkAXTbajt53Rsjw+AtbgjGAAAvqFTDiBfPrcfDBIAsMw7HdIxC6X/tHvTX6yXvt8sldNcARFChQYAf9GuIgSMHwCINdvbQNvjA2ArEsEAABZIpL1GmOkrXAAMzVgdpW0A4DNL+hyJhPS71dIXWqU1Cam+WPrFaOnImpznlG8Eef4/IESh1FfH64IVbVouMdgQL8B2mBnrBX4xNZ7JNhwbVvR/MCSTv5EvZQcUf06xRW07j9ry2Ix1DQyFRDAAAHwzxNUZG66uo3MKIAxcLQbAvPldXgLYX9u86V0rpd+1SJPKzMYFICDcUQQA/EW7ilCwndmLcWQgeLa3gbbHF2H0w+C4YtMBAADQz/GDWzqGAKxBewTAnERCunmlNP0DLwmsVNJVjdL/TSAJDBiS83d9oP8BAP6iXXUD+28AyJ/hNsj2czq2xwfAWtwRDAAAAAAA+OLdTumMRdLD67zpHSqkm8dIW1WYjQsAAAAA3OJ6kiEAADCFRDAAgD24Ah4A/MHVYgBC1p2QfrxC+vpSaV1CqiqSvtUkfaleKqFJAmKCyr6B88e2AOxAu4pMfN4uGD+wF/0JOMulbdf2NtD2+ADYikQwAAD8wsAJgHz5PrhHewQgvIHXZ9ZLZ7ZKz7V703tUSTeNljYpDy0EADbgeAgA/EW76obQk3UYPwAguZVsZTPb20Db4wNgKxLBAAAAAABAXm57+Tad+pG0PiHVFks/aJZOq+W8JYCYoxEEACA77DOHQKIPXEW9BgDTSAQDAFjE9YNbDnAA2IL2CECwehI9+sbD39B3HvuOJOmgaunm0dJoRhmAAnA8BABIRrvqBvbfAOAs25NRbY8PgLUYogUAAAAAAFlb3b5aJ9x5gv76xl8lSRc3SN9ukkoYnwQAAAAQJ0E+GjT0x44CAICoKDYdAAAA/Qe1rh/cZnP20/VlBKIuInWUq8UABOS95e/pE7/8hP76xl9VUVKh3x7+W13TbHESGCdP4IQQttMw6sKg/Q8/GgjH6jJtD2zAdjgIh9YLx3V266tjrtc1tjOLOb5txYLjv1Fg7VcO882pDQoiXp/bQN/XKW304AKuf67v3xF7JIIBAOAXBk4AWIP2CID//vnBP7XjL3bUK62vqGVkix49+VEdP/N402EBAAAAyBvjBwDizPI2kHNOAPLEoyEBAPYgwx5AbNH+AfCbv+3Kz1dKZ/9mL3X1dGnW2Fn6y2f/ogm1E3wtA4g9jocAAMBw6C/ECL81hsL2AQAYHIlgAAD4hqszAFjC+NVipssH4Jf2HumLi6Wfr5KkLh295dH65aG/1IiyEaZDAwAAACzgejKG6eN30+UXKMjxF5L+gOAZH0Mdju3xRZj12wYwNBLBkL/uDunpz5mOYnhda0xHACA26BgCsAXtEYDCvdMhHb1Qerbda1W+tee3dcknL1ERg2EAAABANNC3BxBrtreBtscHwFbFpgOAw965SXrv16ajAOC3GZeFU055o1Q7zXs/5bjeDwO4yqlveRq283/e6Vr2Dr4MIE5mfjO8ssYf4r1u/uXgyuhbntKa4MroM+VY/+e5+Xne6+TP+j9vxFdJZbjlbfGVEMu6yHvta1+CMP3iwGb9v6ul7T70ksCaiqV7djpSX9v1a/4mgW11pfc6chP/5ilJ4w/uf984y995I/omHhlOORuf3P9+5MbBlTPhcO912nnBlRGUxh2k4nLvfcs+/s57+le917H7+TfP0bsnvd/Vv/kiWFNOCK+svv1ezabBlbHRif3vgyxHkkZOHfxvZXX5zXOrK/L7f8Op2VSqHOO9n3CYf/Pd6irvtYjr7Y3r+y3CMOqT3uvUM3o/CGA8s295qif7P+90ftaJPlPP9F43/YK/893y6/7Or8+U473XII4XR0zK//8G3Y6HpXaaVNEUTllhnNuo3cI7tyEFe7wflM2+2P++PM/99WDGHei9bv7Fob+XbKj+hCRtcWH/+6KS3GMaTsPW/s5vs3P8mU9f2zHpKH/mF4bplwRfRmVL/xjSpKODLw9wGEcoyN/6VtMRANGz65+lfx3hvT/gJSnRLf192+DK2+oK6eUrest7xbsCrHYLafxB3t30HtozmHLn/EeqmeoNlK36r38n6GZcJr3SO1CSvjx10/0pYyiNAf5WQNg+9Vfpn4f2v68aKz1+nLT6rYDK+5v0z97BkwNeknq6vDo1/mDvBOA9AdXh/Z6TqsZJ5fXS8hekph38mW/y+ktfnuoCBgGzNbHAQYIxe0qLHvbeH/CSVDrSG4CYfLTUQFsXCWV1UufKcMvc6KT+C0kmf1ba/EvSylelp04PprwdfyY93XsCYrvrpObZXh2feoaXgPaXif6VNfEI6cM/e+8PeEkqqfISOyYeKTVs408ZO94kPd17smnWj6Smnbzl2eR0XxPq2nukC5dI1/duHrtUSn9okSbs+8fCZrz9XOmZs733B7wsKSHVzZDGHyjVbJb/fOu3kla87L1v2E7aYa7XTnWskDqWSSOnFBZ3XO18i/TkyeGX27STtPQp7/3+L0pltdLfNgqn7P2e8/o75Q3S8ou8O6CveMmfeU/6tDTvDu/9xCO8RNHGWdLMb0lda4M5MZayPC9Ijdv7X0ay4jL/5lVSJe31iFQ/Q+peL639SGqYmf/8phwvvf877/0BL0vFFVLNJt6J73xP/BSVSoku7/2ICdIn/1eqnyl1tUnrF4Zz/Om35H2ZCZWjvWOCjhXSIz4m6CUbf4j08d+892P3l7a6zNt3bHONNwZy9+b+lTXrx9KzvSdB/dzvJZtwuPTRnd77cQdKMy712patr/aWp7LZn3IGs+v/Dv63EROklcP0NXe7R3q094TxPo977UjjLK//VNniX5xznvaSEBI90pp3cxu7qRzdPwa++9+lR/b33u//gjdm17CtNOFQb3n9Vlzh/zyDstvd0qMHee/n/Mcbj7svwP3OTjdLT53mvT/gZe+3rd/Kq1+Jbun+HYMpd79npOopUskIr//p1/hBcj8/fXlqhkmQ8EPLXoX9/5FTpTVve+/3f8FLkKka6yW9F9L/SB4n3+UPUvVG3jqfcrw3hpOv8gapY3lvvM9LFaOlimZps7O9JHS/7fqn/P9vcjs+9UzvGLq8ofCYJG+MZ+08f+Y1lH2f8vpFiS5pzXvSfT5erJ08lrjH/d66adzeG7uqCGgfmL48QZ8PKDQ5cfol0mtXe+83P0+a/BlvO592nqSEf2MJ+z0njRjvjTXlOr6afCy03bXSc+d772d+y7vwvnF7aernvfHhogDub1PIPnzKcdL7v/feH71OWv6if/uGA1+WVr9t7zjsJ26VHu+9EHmnm71+btP2XttfOjKYMuc87fWji4ql1W+Gc/MHwGEkggFAJlVjpXULwi83ueNdv1Xw5fVdXS1J9Vv2v2/aQVrydDBllozwOoQbyvJxYGio5QGQm7Kku1Y1bN17FWqAt6IerP1r2Fpat9DfspJP3CUP2DTv5F8ZQy1PRj5fQVzoHXtS2tOk+P1cRzCrpCr8RLCqpBN6jdtLzTtLq94Mrryy+v73Ddv2b79BnEwJo84kn+zIZnkSubcrL7ZLpy6Snmv3pr/aIH2zSSotklRc4JW3JUknM+tn9L8v9IKAEZP7E8GadvS2K0mqGuP9Q37yvZNLoZLrUiGJP9kqGSF1r/Xep/cJ/DzJUDWu/31f+yd5J0v8VFLpJU5JwfVxBlNVYBJEcZnU0+m9b9pJau49iV86QqpoLHDeyW10UvtTyHqpmepd1CT1tj298yqtCj75JijJ6yksIyZKaz/03jf2rsfWfwZYXlKda9ohqS6Oy/z9Qgy23fl5p8rktiXo5clkyESlLPohpdX97xu29uq7lLq+ClWzWeqYUCEn7Euq+t/Xz+w/5vJjf5XpIo0gksuC0vfbSd66KQm4PRm0fm0nrXojuHKT62+zj8lmg/aTBzvBHcAdyAqRPP6RPObR1yblq6w2ab7bSLW9ybp10wqbb0mVpOX98+1TaLyDludTok15vVS3hT/zklLb4KDUzUitK34nTZUlJZvUb91//BdUQn79zGCXJ5Oh7tiVzTF/ckJc46z+7dzvC6b8OvZITnRs3C5p3MOHu4gHcUFk8v6opNLf466y2iH2AxZIHjNo2LZ/G6j16YKHdOWNaX067v4ODIdEMAAAAAAAYiyR8O4AdsFiqVNSY7H02xbpgBDODQAAevn56F0AAJzB/g+AqyxLzAWAJCSCAQAQpjzuzgEgDhj4BGDGR53SFxZLd7V504dVSz8dLY1ltAAIH4lAAAAAyIh+IgAAyB5DuwAAi3BAC8ASnIgFEAN3rJbOaJVW9khlkr7fLH2xniYQBsV+44v78gMAkA3b9pe2xQMAAIC4IxEMAGItanenitryAAgGbcXwWEfRx2/sK8fu+Lm8W/rSYum3q73pnSqlm0dLW1YEWKhj6wiGhL6dRGy7pJ4NgvWSFbYfn7E+I4F6YamI/S7Ob2euxe9zvKH9fq6tZwAAYBKJYACQEVdyBSb2V/kDLqLeBo8BPcRB0SDvgyquKPN7Z+W6DJnblbvWSGe2Sgu6pWJJX22QrmiSylxdRZH7nS3BuvT5pF7I7Z+TXKvL/Kb+CPt3j9jvVmTx8uTchgYUf1Dble/ztez3K4QTbbjr4jJ+YHEbh+wE3h6Y7EfYIIu2wLnj5SDrfRDL78I6DUjY25YT2y9gFxLBUIC4HHAACA/tCmA36igAuOrDTun8JdL/rvGmp5VJvxoj7VxlNq7ssQ8CYBrtEBA/3OkH2eD3A4D8sa8FgCCQCAYACJfztzsH4oh6C8APiUHeB1VcIvN7Z+W3DF0J6ccrpMuWSm0J7y5gFzRIVzZKVcW+BmheJH5nS7AufRZy+2eCn1doO7f9uRavpUL53SNWFxOGl8eFOzM4154kc2D9AqGhLjsp8DY47GN+E9thgduPc+MiEeurxUUY25aR7TfG7TcigUQwALBK2B2LqHVkorY8QIyEehIhjreLz5Xr8WN4/Ma+svRE6J1rpK8tkf7b6U1/olK6YbQ0s8JAMJauo1QuxAh/DfGbO7HNpnEx5lCwXrLC9uMz1mc08DsiBDm3v7Ztl7bFMxzX4gVgL5LVANiLRDAAAAAAACKks7tTZz9xs25a4E03FkvfbZZOrZWKOe8BAABgGU4kAxgOB3JAYdjXAogXEsEAAAAA05y4PTsAFyxbt0yfueMzeui9R1Qs6eIG6asNUm2J6cgAx5jYN3NHJgCRwfGNcexTIoz6ZRXqGoyhLQAADI5EMBSADi4AAPHCvh8AbPZK6ys6/I+H6+1lb2tkaaX+MHq9Dqw2HRWQA06kAQCAYdFfiBT6fwAAAL4rNh0AAADxwpU6AADAf7e9fJt2+sVOenvZ25pcN1n/3v9SksAAAAAAAAAAIGZIBEMBSGYAos1EHaddAexGHQXgN9qVQnV2d+pLf/+Sjv3zsVrbuVb7bLyPnvncM5rZMMl0aAAAAED0mXicNAAAADAEHg0JAAAAAICDFqxeoE/f8Wn9+8N/S5K+vuvXdeXuV6qkuMRwZAAAAAAAABFGIjAAi5EIBgAIGZ1jwDkc1IaAdYy4CXubj1odS+hfH/xLn/nfz2jhmoWqrajVbw//rQ7Z/JCkr0RtmbMRx2VGcILanthOh+fYOoplexsE+gYFsW47zDUe2lwga9bV9xDEcZkHKDIdQB7C/N3CKMuy7TDnemFZ/MOh3jskhvUPcACJYABgFRcP6ADADxFr/4oitjwArJFISD9+6X914RM3qKunSzNGz9CfP/Nnbdq0qenQgsUgcDzwO8NmbJ9ADFHv7cTvEguujKvQPzDIkW0EQ6MOOYr6B9iORDAAyIhOTHBYt4BzXBl8A+CQsNuVaLRjq7qlz7dKt739E0nSMTOO0U0H36Tq8mrDkZlUNMh7wFZR3U4LXS7H6nJy/5i+cv6KTP7uEfvdjGyHfpYZVPwO/87Oti2uxg2rOVsf5HbsBQtz2cMoi31tqGJdd1xD/QNsRCIYAGAQXIkBAABgi/9b8IpOnCd91CWVFpfoB/teq3N3PFdFDI4iSmK/Pcd9+QEAyAb7S6Bgkeh3c/4CAIDBkAgGAAAAAIClOhLSNcukK9++Sj0JaZMy6dcH/li7bP0F06EBAAAAAAAAACxDIhgAAABgXBSuxATgt6fXS6ctkl7pkKSETqyRbhgtjRi7lenQAAAAAACh4e5XAAAge8WmA4DDEnQ8gWgzkJQQi3YlDssI+I0kKQDx0tYjnb9Ymv2hlwTWXCLdutuXdMsYaQRH8UCEcawA0PcPUCQeAwYMx8R2zv4bAAAAdmEIGQAAAAAAS/xjrbTVB9J1K6QeScfXSK9Plo7Z+JOcvwUAAAAQMRzkZIf1BAAAssejIQEgI67kCm4dsG4B58Tibn0AwhV2u2J/O7asW7pgsXTLam96Uql042hp/+pM37Z/ecxgvcAFQ22nLp/gK7T+JQZ57wD6yvlLmPzdI/a7GdkO/SyTMagBaFuAfi7XB5djL1iYyx5GWexrQxXruuMa6h9gIxLBkD8uRwf8F3q9ilg9pl0CfJSpPgVZx0Ksv0VFIRzHud4euR4/hsU+02f5r89EQvrdaunCJVJrtzenc+qkbzdLNZG6hzfbHCwUubYwasvjk8j9zkFhPfmK7W54rq0j1+INFeumMI6vv8DqhmvzRfj4Lc0qEokyAGAvEsEAAAAAADDg9Q7pi63SP9Z501uUS78YLX2iymxcgDmczAEAAMMgKQ82YXsEAAAWIhEMADLiSgYAcUc7GC7WN2Ig9Nv621uvVnZLVy2TfrxC6pJUUSRd1ihd2CCVD3oeIdflsXf5/RWX5Qwb69XXdcBjTbLg2DriN/VJyOsxcr+bxcuTzbp27fdwLd5QsW7CFZf1HZflRP7ivo1ks/yOrSP2tQ7htwJsRyIYAAAAAJ9xRSyQyfoeae5K6epl0tIe77NDq6UfNEublJuNzX4MMiIO2H/aLeh2iN8fiC1OfAMAYiukfSD7WgAxQyIYAGTEACwdYwAAAP+8v+J9Hf6R9EK7Nz2tTLpulLRftdm43Ee/HUFh28pNoevLsfXNY6B8wnp0G79foGhnMCi2DadQl1EQth+7cQ4t2qh/cBuJYMgfSSKA/2L/yKQC46FdAgIWkTpGW5EF1lHkWVMPbImjUEMvx2PzHtORtx+p1nZpVIl0TZN0Yq1UGqsxpaj81ghW3B8TV2g8ti2PJaz7nW3FevIV211E8Dtaybr6FfP9t3W/x3B8jjes5SehDNZxre4DQLyQCAYAGXFghYA4NzgCAIBPQh+4tqM/9/Nnf65z7j1HnT2d2qZC+ttYaWJZPnOyY3mswwmRgLBefcV2mgXX1pFr8Voq7LoRuboYteWJsUhtm1FaFpjFtoThsI0Mz7F1FOT+MFL7WhuwPgHbFZsOAACQJKYnSH1DZx7wUYRPyoRSVq5l2JYkSnsaeewzfTZwfa5uX63j/3y8zrz7THX2dOrT0z+txybkmwSWD9oVYFhDtoUm6lBEH69oep9junxnsJ58FfvtLos21LV15Fq8oWLdFMbx8YPA6oZr8wXCZrotoC4BgM1IBAMAAAAAwEevtr6q7X6+nX7/8u9VUlSiq/e6Wn886o+q5ggcAAAAAJKQTAIAAOA3Hg0JABiE6StKAAAA3PO7l36ns+45S2s61mhS3STdduRt+sTET5gOC3AEJwIBAMAwuDsbAAAAMCQSwQAAAAAAKNDaHum8xdLP3zpBkrTHlD10x6fvUNOIJsORAQAAAAAAAADiggdTAEBG3A0LQWHbgivYVgH4LBF2uxJeec+vWqZZ86Sfr5KKVKQrd79SD5zwgM9JYLTLGYW+XcUF69VX2W6nsb7DiWvbnGvxWirsNjxy+wzHl8e138O1eEPFukEQ2K4wHLaR4Tm2jtjXOoTfCrAddwRD/mI9QAkAQByx7w8MAx2Ak3oS0nUrpEveflCdCWlsifSbYx/Q3hvvbTo02hWgUNQhAMhfZNpQjoFho6jULwAFicy+FgAQBBLBkD86GQD8RrsCWI46CsBnDu/7P+6STlkkPbhWknp0aLX0izFSsw1JYADc5HCbCABAbLH/Lgw3HAAAAPAdj4YEAIQs7oMjcV9+uIntFoDPHH5MZCIh/WaVtNUHXhJYVZF047QddOdYqbnEt2KGDwIZsF7gAOpvFlxbR67FayseE1kY15cnoPhd+Z1diRMwhjripjB/txDKcr6tdi1+n+N1/vezGfUPsBGJYACQkakrkUIud8grrlzsWNl8BZnNsQGZhL3NhlleCGW5fkWr6/EjC/zG+fiwUzpwvnTSIml5j7R9hfTcJOnMCZtSbYYV0ApixaMglm0/BW/PJpfH5tgt+52tZWA9RboNj/Ky9SlwGV37/QONN9MYnEvrx6VYbeT6+gsq/qgcP9j6+9oaVy6isAzDsHlfaXNsGbl4vgtGObeNA6lIBAMAIExcuQAgEw4sAat1J6SfrZS2nCf9fa1UUSRd3SQ9MVGaVm46OiBK2B8CAIDh0F+ARRjPAQAAFio1HQAAIBmPQiiMC8vjQoxA1FlYD21rj22LBwHgN87WQ2ulCxZLL3Z407MrpZvHSFukJIDZuD5ti8m2eGAnmx4b6+I262LMYWC9ZIf15K+4r8+oLH9UliNqova75Lg81h2v2xbPMPxef9b9HogPw9se2z7rAIDVSAQDgEy4kidArFvAPdRbAD5I7l+F0tcqGuR9duZ1Sucvkf60xpuuK5auaJTOrZdKjDSLtMWZFfY7YzCsS1+F3v45qMi1uuxavLYKeT1Gri5GaTuMyiPg8uVKnFlwZp3DHoNsM871DYLm4joIM+aQ+xHOcKweBVrvHVh+pxjsxwPIColgAAAAAAD06kxI/7Nc+uYyaV1CKpb0hTrpiiapqcR0dL0YAAMiiroNAAAAAACAwpAIhgJwy0tEGLd0NbQOYrDe2bbgjAzbaqDbL3UDiLyMbYhd7cqja6VzFkuv9D4G8lNV0k9GSTMrfA4tL7STmbFegsF69VXWfagYr3fnjpNci9dWIa9H57az4Ti+PK79Hq7FG6q4r5u4L39AqHMYFtvI8BxbR9R7h/BbAbYjEQwAAAAAEGvvdkpfSXoMZHOJdG2zdHwNN98CAACILzqCAAAAANxDIhgAIGRcKQC4h3oLwGehX+WZubxFXdK3l0k3rpQ65T0G8nN10rdsegxkJlwlOwjWCxxA/c2Ca+vItXhtxd3BCuP68gQUf+R+ZwckEuTPIQDUZTeF+buFUJbz+xTX4nct3jij/gE2IhEMAKwS8khJ5G5xEbXlAUwKuz6FWV4YZeVahmUHs5HbP2CgeP/G7V3turBV+vkqqaO3+u0zwrsL2Iy8HgNp4/q0rF2xch3BPjb1P2yrQ9mgnmXGeskO68lfcV+fWbShrh1zuBZvqGzaf7vI8fGDoH6PoOocdTlC4v5bGm4LiopIzgEAi5EIBgAAAACIjfmr5+szd3xG/17pTe9U6d0BbO8RZuMCAE5mAQCA2CExC4CzSIQDYC8SwVAAOuhAtJnoxMahXeHgAA6L1eBcnJYViI+737xbJ9x5glasX6G6YunWFumAatNRITv0oRA2E30B+h92ox0C4iesek/74jYTd0SL0DbDHYWyRD8RERVaG0BbAyBeik0HAABWilWyA8LFAQcAAGHrSfTomseu0aF/OFQr1q/Q9uO211MTSQKLBvrtgBUKPYZ27hjctXhtxXp0mnP11jGsXyAiqMsoBNsPYA71D27jjmAAAAAAgMha1i2d8Pev6955T0mSTtv2NN1w4A0q+2O54cgAAAAAAMgGFxcDAIDskQiGAtDxRIRxS2pDWO+A1WLVNoa9rHFat0CyYLf9f62Tjl0ofdT1lCpKKnT9AdfrtG1PU1Ec7rAQqzYbCAJ1KCeFtjm0WYrnFef87k4bqt5SpwvHOnQI4wcYCr8XCsG+1m5x7L/HCXUMbiMRDACAMHWuMh0BkL+OpaYjABA1ie5AZtuVkL7zwp905UdSj6RN6ybo9s/epW1atgmkPERFj+kAAABALAVwInnFK/7PEwhCHC7SAWAB2hoA8VJsOgAAsNImp0v1M8Mvt35GuOW17OO9FmXKC/Yx271ytDTpM977aRf6N990Y/f1XovLgisDCFv1ZGnikeGXWze9/33laO+1Y3lw5dVuEdy8021xkfc66ejgyghzeYIw5QTvtW5Ls3EgOJt/Mfwyxx8kFfUegrbs7b3O+5PvxbzeIe32kXT5C3eoR9KJNdKzJ/9fsElgk3vbk+qNgiujcfv+97XTgisnKKN2CWa+U46VqsZ57yccUdi85t9beDxR0bidmXI3Ptl7bQip/GkXeK9B97UmHCoVV3jv+45ZgrBF77GWib5joTb9vNQ4y3u/8Sn+zrtvffS1FX7Y+JT+tnjKsf7Ms7vNn/nka3KAfePBbHyaVNc7DjLleO+17f3gypt4uFRa7b0fd0Bw5UjSqF2Dnb/kLU/JCO/9uP2DL89vtUnHnH1tpB9a9pbG7OW93+wLhc2rorn/fRDHeBVN3uuEQ/2fd/da/+c5mOTjxqIQTjk17xR8GX02PSv1NQjNOwc37zBMPdN79bvdSz7mGTHev/ludq73OtandrNhG3/mExXjD5HG7OG9n/r5YMtKbnvKG4IpY8Jh0ujdvPd927pLWvbqf9/kc1uzxcXe62Sf+sKSNOoT/e8btvZnnmP38143O8ef+cGTfP40qLGwkZt4dVCSpp0XTBlAhHFHMADIZOrnpOkXSStfl+7fIbxyq8ZKB/1XKqsNp7zG7aT9X5RGTAi2nG3/x0u4mHZ+6klMvzXOCmd5gDBt813vgGf5RdIDIQ4OVo6WDv1ASnT1nywJUtUY6aA3pNKRwZazyenSVldK4w+WGrYNrpygl6e0WuoK6GRhZYt3IrBmqpvJJq4Yu5+04D4zZU841EuIHL17uO3K6F2lI1qltR9LDb0DRj7eabAzIX13ufTNZVJHQqopr9FP9/mOjt9sH6l2qm/lDFBS5bUp+z0j1WwWXDkjN5IOn+/dXbRqTHDlBKV2M+mAV/qTiwtRVi91rvDeTzxKGjtHWv124clLQSY8u6Z6snTYx1LXGunuzcMps2ZTaaMTvWT05IT0oEw5XprxDS95IugTeC17evV37Yf+ndBIt9GJ0ozLvOQWF09Ibnq2tPV3pJWv+n/MOHaOtN+zXt/GLxuf4p0MXPXf/gS2QvV0+TOffBSX9+/L/vMFaenT4ZQ79Qxpi/O9sZe+9di9Lrjyxu4rHfah1DYvuLrYp26af/u9wbTsLR3+UTjLE4TKZumQd7yLE4t9PE2x5de9xJrlL0pNBY7plVT1v68cJR38llRSWdg8kx38trTmPWn5c9L7v/NvvmGrHOUtS3F5OHd3GrmxdOCrqYl6QdjqKmnLS7x9bJDjmTWbBLs8xRVST3sw826e7SXJNW4v1W9V+PzqtvT6AlLvuNQ8qafDv7HycQd4ifOjd/Ov3ayeKB34ulReL9051p95umz6V72+6IqXpaYA643ktT2Hvi8levxtm5NN/6qX8BLG8gShYRtvHGZ9q1S7qX/z3fQsaeY3vfElP8dXazeXDl8gdazw7xzPp+70+gQ1U6XXrvZnnhvE+NGBI8ZLh30kda2VKhqDKWOba7xjlOUvBLsfBiKKRDAAyKSoyDvJbqJzXxvSiZY+DSHc+ayoVCopD+eKvTCWBwhTUalUUhHuFa99qieFW15tgAkUfUoqpeKScNZnkMuT8U6OPimr9faDLg5wuSSMK+UHU1LllW+iXalo6r/zgSS/bs3/zHrptEXSSx3e9IEjpLlnvKzJ9ZN9mf+Qyuq8OuNXIsBQqsZ6/1xV79NdBsvr+xPBioq8dsvUHayibISPd0/KRmlN7/4npAtxwuwTSN7g+HAD5IWcPA97efxWVCyVjvD/9y8d2dtG+9xGFBVJZSOj018qr+/fl5XWhFhwprGXgJNIyhuCu2tIOr/2e0MJc3mCMHJj/+dZVOK1iUG0h34mlEpe3Wvc1ksEc13NJuGWF0bSeEm5l6QYxh27glyeopLg5l1a7e0/mnf0Z37F5anT1RP9mW+fkhHBHAvXhXERnSOPtSsqlkqr/NsmhlMd8DF/2MsThMpR3j8/FVcEd+xR1eL980tfn4ALv/zn590aMykqMXdeBIgAEsEAAAAA0xIRu4IsjKvAAUlre6TLl0rXrpB6JDWXSD8eJX12pFQURhKY1XJtV4ry+D9AhEVt3wxki34cfEEbCgBAsNjXAgAGRyIYAAAAAISOk6ye/NfDI2ul01uldzq96WNrpB82S6M4ykXeGEgHAPPoIwFAvNDuAwAA+I0hcgBAZlwBDwDh4c4LMcRvLimvbX9pt3TJEummVd70+FLpxlHSQSN9jg0AgFgy3EehXwwAQAjY3wIAEGUkggEALELyGQBLWJ8Ma3t8GBYnOXPWnZB+vlK6dKm0rMf77PN10nebpNoSs7EhBNa3ywAiL/B2yJZ2zpY4AAuE1f+gn+M4238/l+KzPVYA/mNfCwBBIBEMADLi5Ky/J6hZn0DeSBaJyTqwaBljsb5tYHI9u/cb/3Od9MVW6cUOb3pmuXT9aGnXKrNxSbK4ztgaFzCI0OvSMOVZW7cH4/hdnAJb367N15Sk5QnzJFnG3z1q69YmPq/bIestfd2CObcfsgXjmeFybB0ZqVeOraOCRW15TS8P+1rEmentzHT5QGFIBAMAAECM2HoAx1VpQCZvdEhfWyL9uc2bri+WrmqSzqqTSm2tztagXckdGxWScMU44orkE/iCNhQAgGCxrzWP3wCAvUgEAwAAAJzDCTrncZK1V+b1sKBLunKp9ItVUnfvtz5XK32rWWrmMZDBKCoi8QUAYAH6SAAQL7T7WWEMAQAA5IBEMABAZpwIBAAgQAzielLXw8pu6fvLpetWSGt7uyIHV0tXN0lbVoQfHQCEi30DbOD4Y0YBAAAAAIg5EsEAAAAAAEat7ZF+tlL69jJpaY/32exK6bvN0q5VZmOLD068AwAAAAAAAIDrSAQDAAAAnMNdG91H0o0kdSQSumap9KMV0rLeBLBpZdLVzdKh1dwUJFy0KwBgFHfl7sXOHwCAAegnAACAHJAIBgAAAJjGgB5i6M2lb+qYV17Rc23e9MZl0iUN0sm1UinngH1AuwIUhjrkG/o5QAxR7wHAbrTTzqOPbQEGrwDYi0QwFIBOBgCfcfACwBq0R0BQEomEfv3ir3XOveeorbNNTcXST0ZLnxkplTCGBqNo+wEAAJAjxjMLxEEgAFfR/gOwF4lgAIBB0IkFACAwMX3m4cr1K3XWPWfptldukyTtUVur3zat0niOTC0Qz20SGBx1AjCDugcAwAAxHUMAAAD5KTYdAAAAAIBcMQDovvj9hk9+9KS2/dm2uu2V21RSVKLv7PkdPTh9S5LArBG/bRJASDhxmR3Wk4f1AAAAAABAQUgEAwAAAIDQxeckZ3dCunqZ9MlfflLvrXhPU+qn6LFTH9Mlu16iEk72ImvcrRaAaXFph9g3A/3CqvdxaV+ATJK2fx6zGSLWNWzBvhYAgsC11wCQEQOfvuIkL1AA6o+/bF2fNg1G2LqOIsbovjG8sud3SScslB5eJ0nd+uyMz+rGA29UXWVdbyhR2N4sXQZOosA5IdelYdsfE3WokHVgui0aovys2qOA4g9sPxPAfI2226a2n0zlmt6Wkb1C631AItG/lKgLNuA3GJ5r68hAvJFpk7IUteU1vjxDlc++FhFnfDszXT5QGBLBUAAaQAAAAAADJRLSH9ZI57ZKS3uk6iLp+kN+pZO2PklFxgdyAAAAAAB24PgQAADAbySCAQAGwV0kAABA7t7vlE5dJP3fOm962wrpthZp821ONhoXhlFURPcPAAAAAAAAABxXbDoAAAAAAIif6F313JWQfrpCmjnPSwKrLJKuapSemCBtXj7Y/4reegAAAIWgbwAAAAAHGH20OwAMjTuCoQDs4AD4jXYFgC1oj4Bc/HuddFar9HKHN71LpfTrMdImgyaAAQAAAEAU2D5+YHt8yI7PidIksAAAEGkkggEAAABA6KJxt4uPu6SLl0i/X+1NNxVLVzZJn6+TSqKxiIgTToYAgHlFdCAAAAAAACgEiWAAAAAAEDbHT3K290g/XCF9c5nUlvDS2k6rla5plppKcpmT2+vBbrkmNfFbAKlIDPQP6zIrtvQNjMdhunz4g3oPAECw2NcCAAZHIhgAIDPuiAAAANIkEtJdbdL5S6R3Or3PZldKPxklzao0GxsAAE7jGBwAEEfGE5ABAACih0QwAAAAAMCwXmuXzlsiPbDWm24pkb7bLB1fIxUzdg8AAAAAAAAAgHEkgiF/61tNRwAA7uhebzoCAIBV3MmceqVdum6FdMsqqUdSeZF0Qb10SaNUU1zgzLn6GwD60SYCcqmPBACAs9bNNx0BAAAIUKHD9oizd35hOgL4rWkn0xFIEw73XqunGA1D5XXhlbXFhd7r2P3DK1OSNv1CeGU17RDcvKee6b1uenZwZfSpHD3wsy2/5r2O2WPo/9vT7n88CFZFs+kIPI3bhVfWpE97ryOnhlemJLXsHXwZFaO81wmHBlfGtAu815Z9giujT6Z2daurvNeq8fnNc8ye3uumZ+X3/5GbshD7Gn1Gbuy9Tv5MVl9/br101AJpq3nSL3uTwI6oll6fLH2n2YcksCCFsX7HHei9bv7F4Mpo2tl7DWN5phw78LMtv17YPDf/cu+8jytsPpJU3tj/vm7Lwudnq01O8143/1L4ZY/6pPeavK7D0PwJ73WT08Mtd8IR4ZYXlKqx3uvEw82UP2Yv77XQ/kOmY61CTDzSe512vn/zTK4bpSP8m69JYezLhlJWa6bcoGzWux6nnGA2Dr+M2mXgZ8ljSZVjcp9n3xhOQ4DHuTWb+TevvnhH7erfPDNJnr8rx2V943BhjydPOjr4MopKvNcgxyo2P897nfzZ4MroUzt94GczLvde62fmN8/6rb3XjU7M7/8nG39I//u+Y9XqyYXPN9nITXrnH/D6nvp57zW5/laNK2yepdXe6zifzx10rvR3fn36xh2C0ndsWbtFsOX0qd4onHKSNe1UWDtU2eJvPMkqmrzX5HpbqL7zYiWV/s0zk9Ka/vd9x9uFjlVM7t0nmdhOTOjbHoPcxpI1bBtOOclqNus/LxTkeQQgBNwRDDClaUdp6dOmo5D2e1a6b5b3vnlnaelT4cew71PSA72DBjMulWZ83dvZ3hHCgOAnbpMeP8Z737SztMttkhLBdzo/8Xvp8d5O5tbfkSYeJTVsHVx5FaOk9sXe+41PlaaeITVu7385W35devXb/dNHLJLal+RwAJjI7mvTL5Feu9p7v/1PpI1PLnx5tp8rPTNMMll5U//dEA+fL3Wukmo2lcYfKtVvVVj5Jm12rvTmT0xHIe31f9JDvQl1Ew6XProz/Bj2/qf0j09572d8wxuArWyR/jwq+LJnXC69cmX/9OELpY5l/g9+pdv3CemB2b0xXCZNv9jfgfN0TTv172tqp0k7/1pqyHPgcSgt+0oLH+ifPvgtac27UmOWB5CJLNujT94uPdY7ULn1t6RJn8lzeZLK2+yL0ps/HvrryQMMRy6V1n7oDeCOP1CqySGRb8we0qL/897vdre04mWpKYD9gyk73yI9ebL3fuRUac3b4cewyx+lf/cODI36pDT7t977N34YfNkN20ht87y2RJL2f0Fa/eawJ97+vU769jLp772PgCySdHi1dFGDtHNVFuXu9bD0UO8JrBmXewNjQSaW1G8trXixf3r/54O7qCB5/7Trn6TlL/if8D7naen+Hb33My6VRozPc3mS2pXKFmn9wqG/PuFw6d1bvPefWdvbHuwgTTleKq/PvthtfyA935sYu+3/eL+/Hyd7S5M2vspRXrsedJ89LJufJ71xnfd+hxu8hKjG7aU3fhR82XP+I93fuw1veamXjDMy4EHs4grv2KfveHjPB6UVrwR78UiyA17xLtIYLtk+275Asj3/IT3cOzg+/WJpo5Ok8obs/382ZY7eTVr8LynR400f+Lq05p3CLx7Y7ofSc1/O7ruVY6Q9H/K2l7IaaflLw/QfkpZrp19IT/Um/dXPlHa7S0p09Z/kLMQmZ0jv3OS9/8TvpeUX+XvcW1olHfKuVFQsFZf5N9+whbEvS5fSH9pFmv07731JxcDv+nFnvBGTpLXz+qcPfD24C/62+Z70wle899tdK005Rmqc5W8Zez4oPdx7scnm50lTP5fbvnmDtDamqLi/Lclk+iXSowd57w981RsDadzea98SXVLZyOzK2vtR6R+7ee+3usJLeq7LkJhSiBGTvGPbrjVeP8Evm57lLXPQYz5106QDXvba19KR9h6X7fmQ9HBvAvDMK6WNTwo2Qb9uhrTyFe99yz7SzG8Gc1I4ef8heeOZaz/O4dg+yz7DrJ9Iz57rvd/2+7395AKXZ6srpZcvH/o7yXXiiFZvbLNuujT+IKkuy2SaolJvfHf1m970vv+WVr7uT3s3erf+9+MOkMbul9u4Rjb2fz6rY+GCbf8Tr140bu+1oT0dXl+pEId96B3XB3nuwA+HfSR1re1PFPLTPv+WHuxNTp5xmXfBUe00f8vY/nrpmXO891XjpTlP9S5PgWMZLftICx8c/O/J7c9WV3h1oG5L7+kiaz8auh1KPnbY+1/SP3qTimd8Qxq9q1Q5trDYMzn4bWnNe9mPr2ajeUdvvGrERP/mmUlJuXTIe5ISXr9h8mcLbxPGHyzt90ywY+mmJZ9D3vJSr+/rd8LnVldIL1/RP73hvMikwuY7+Rjpg9sG//vYOdKC+733m5whbXqmVLO5lOjO7TwCYCmbr+EGomvkJuFlTA8nzDvNDCblIKbIO4As9AApWxMP639fXCqNnBL8iQ8p7QqBYql5p2BPZCUf8BeXe0l/xcPlAudx4mPK8WnljvZ/cK92i/6r3iVvAD6r5RlG352QslU1Vqrd3Bs4bd4x9eSka/quijNtzO797009Fmd08lW+RVL9DKkypDuDJV+BVFQsVY3JfkCuEClXf4bQBo+Y0P++uNyrP0G0f5uclpp4Ul4XzMFbyoFvsT/Ls/FJuX2/otHblxYVefv1bO+sMO6g/julSV471ryjt/1FxcSku70Uup/IV/LVY0V9fY0p4ZS9yRmpdzcsq/HqeIY2NpGQHmyTdv9I+uRHXhJYsaTjaqSXJ0l/GpdlEpiUepfMoiKvLavK444R2UpvKxu2yfPk6DAmfTq1T1VS4fXh/K4z6Sfj/VievrtZZGtDe1DknZisyuHYpTpp8La4xOunlZTnVn42aqam7lNcVb91MH3bbKWfZG7cNpj6k2zTz6e2TaUj+re3MJTVBncc3LJX0kRf++fzsf8mp6euv/I6f5Zn1CeG/nty/6asVqrf0msTSypz6z8k75uLSr3Bfb9OJCQnZ/W10cUl/sy7z8iNgr9QI0gTjwpnX5YupT9UEnx/KD0xoW5aalvrl4rmtOOb3v2e34mCyXcDyWffnEndlt7FbkNJ3i6Sx5Jyrbcpd20p8vo6fiR/phsxTqr1+URsUVF4Yz71M7z6afNxWe3mSRN9v2WAd0hM3s6Ly3rHTwPoV258cup0RZP/F6yVVmfoJ/uwPJnu6juUylHePryoyOsHZlsXp34urf9W7f1/P/pvKfPIcVwjW0McC/uquDSprZwo1fgw5lreYH8SmORdwFS7aTDzrp+RNNG77Q6ZjJyH5HMDxWX+Lc9w+8vkpPjiiv52taIxt3Zo9Cf73xcVeQnMfo1pFye1U+X1wYyvNmxdeNJdNvrO//k1VlEU8vlME9KPNRu39f8Ci5TzIqX+nRcZ7s6BJUn9u5LK3t9yZHDnEYCQcUcwADAijySrgooLubzARW15AAQjhLbC+fbV9fgxvKF/40RCuqvNuwPY071PMS6TdHKtdHGDtEkA51mc5nydDwHrKA8xXGdsJ5lle3IyiPU37DwNXagB/1H/fBbl9elXvY/yOoobfsuCON/+uh4/YCP62EBwOMZFvJEIBphi6m43Q7IgJqPrxVDZYS+zldsekM6G7TSG7VEoigZ5HwG0r5bj90m3un21zlok/X61N11VJH2uTrqwXprg240sWO+FCXP98VvF/uRWXPZjoS1nhNenXyey47LNIU0Iv3ukty1Dy0a9R7pQfssIjx8AyE/obU+Y/Doepb1EQMKof8b6ijEfD0IkkQgGGEFHzB78Fr5yuiOYxXwZsESQ2L785fT6jEJ7ZEt8NsRhMIYhtpOnPnpKx/75WL27WiqRdEGDdEG9NJojxCHYsD3lKZs2w/p2JaJiud7juMx+Yv2hAFm1OUFsY1Hdbl1eLlPbAmAjlxNLqMuAP6gngDnUPyAIDPMDAAAgRFxdk5Hzj4iAK7p7unX1Y1frikeuUHeiW5NKpd+1SLtWmY6sANSfzJLXC+sIgEm0QYgsx7btAXUxwPip9/BFPtsR2x4AmwTZJtHeAQAGRyIYYAwZzrAdBxIAEGmxvAuNTcJf/++veF8n3HmCHpv3mCTpszM+qxvW/kH1JaGHksSH9cC2DCAyTLZnYR3/0Wbbz/RvZLp8AMBAQbbNtPsAgCBwjhPxVmw6AAA2sWCnaPSKQQuWPwxclQkn2LCd0h4FI3mAL8rLCfvEd3tLJKSfr5Rm3jBTj817TDXlNfrNYb/RrUfcGkISWHzXuz/CXH+cgIm9uBwnhLacMVmfhYjLNueawBOs+d0L4/j6o94jJ4wfAEgTyn7E9fbG9fhhLfpxgFO4IxgAC3DSCb1s70jaHh+QF9rgzCyv77RHyNK77Z0642P9P3v3HSY3cf9x/LPX3e7O3bgbY1zAVONCL45Nx7RQklBCDyYYCDUECAQIEEroAQL8EiDUUAKExIEACcX00Hsxzaa493L7+0N3vr273T3trqSZkd6v57lnr+ikr0Yzo5H0laQnlkrSQm0+YHP9ec8/a+2ua5sOrRF12R5sC8A82mGyRbH9fYz9jY8zTS8fAApkst/0lbxLvwrXce4SAIBCkQgGmJBKyc7BqwUxRf5qn1SO703FEMXiXH+Ud0jLSPJrpaxcdxtiSmJ/FDXX+6OQlmllm3RUyoJ2ZWh7rk5L1773pE575zMtaZA6pKQLJl2u48Yep/KyKN8FGcH6R3bhhX4FYbBo20RWTwyvs+vrGVr8Bcw3qBjom5Ij8jGZ4+08imUW2v5o92jD5DmToGcdp34JiLlIxsKuXyeiv0FIwmp/oR0rFDIv2g3ih0QwAEgE7vwCALvRTyM4/1gs/eI76c0Vd0uStu0g3dRLGjp+mtnAEDH6FaA0JtqQyZPP7a1vKbHRHwF2KLAtlnSxj3YPU6h7AFzCvhYITztthBsUEHMkggEA7MHAC4A1ktAfJWEdk+XjldIJ30oPLfZ+7lrVUef37qSjqr9VGZsb7aKSAOYloR0mYR0dx3F5QsRsO1NvYVIS6p/zb5gAUDzaKKJEgiMQlDLTAQAALBXZa5YAAEii4E6kLW+Qfv29NOozLwmsQtIJ9dJHu5+rY3rWW54EZnVwAAAAcAHnsAAACAn7WABwEU8EAwAAgCeSu1g5eYAEC6GNPb5EmvqN9O5K7+cdOkhX9pRGVUuq6hT48oBY4yIygNgjARuZ2O/BdtTR9tGvA1bjGBMAYAiJYIARHKBZw9iju6M+AIhqeVGUZyqkAyjaJQxLwqsEIhVWX9Ga4/1R7E9I2dCuwonhgxXSyd9JDza+BrJ3ufT7ntIPO2d2J1G1g4RIpeTuxago24KrZWSKy/WqSE63pZD5Gg+GVX7tzJOxagSiahcm2l8B9celsUvK5bGW3/4mAM6WEdqI7baMYB8Xh/FPbLc/IHNjXcbYgELbD7e736L9Id5IBANMsXKAZ0NMBmNIzGDfhu0MtMeCemq0n7Zg/UOTsW5W7gtLEbf1iZmY1LfZq6QL50rXzpNWSiqX9LM66dfdpa7lhoPLKh7lbkwp9bbgCzVsKySlDvhcz1IvdsZkvxOMXGVJGSVTRDeQxVVJfUuUSRy0+/iLui1HtP8GYLmoEjcdkLO/cyR+OIhxPOASEsEAY9iZAW1Yf7LG9vgABMf29h5AfK6c2IIkadYq6ZzvpZsXeAlgkrRjR+myntLIKqOhlcj2tpYkbAvAOOuPhwLA+AOwQ9zaYtzWB26xff8dSHwhtjHaL2A52igAuIhEMAAZbDhoNRiD7QftgUnKesJtFtRTo32CoWVH/SrFxPS7lkqnk3Uux4b6lhmDz5Pds1ZJ182XLp0rLW789wk10rndpYkdQ4gxcFE8ht2CbRsWG+otEiQp9S2i9Yx1+w1qABHnMrKUFRfbXX19uyWC7FsKmpfl7T7WfW6SpXN8j2ZR9euUP2wRQV00tU8JbJwWdPy0fzSJc12w4TgJCBaJYIAJqZTYqWRI5OvXIl5uVAcvUWzLVCqc5VhxQhzJlpTX0xajiBjD6ivaLiiE+US4TZzY/qWwYf1yxZA/tv8tly6ZK929sPkJYGOrpd/1lLbq4HfRUbWDUriUCObYGD5lqF9xqYxskMhjQ0fW2UT/6WuZpsrPgW3mvKjKuL3lhBFHAfO0fuySyYWxVqYCxwYlrVvG/zpVRsjLhW1ZVIxRnTtwoPzycWH7I6ZcOr8X4XJpk4gNB9sf4AASwQAAAODhBAIQLh9t7Nml0gVzpEeWNP9u8xppWr20T2eaaXYUSjAoRwAAEoWBJQAAAADEEolgAAAAAGDQ6rR0zyLpsrnSi8u935VJ2rezdHJXadMao+EBAAAAAAAAAABHkAgGAEbE+V3aEYjqVZcA3BZJXxHUMgz1a/SnRi1tkP6yUPrtXOmDxvc/Vko6qFY6tas0rCqAhbCNA+ZQeRrb9g6VkTWSWGYOrLPV/afp2ApcvtVlmUSWbw/X6otT8ZYSa6H/mzG9U2WEvFzYllbHaHNsPlhdtkAMFNrGaJNAgGhPiB8SwQBTrHz8ug0xGYzBym0SBr/rycCnraTUERtYUNZG+wQL1j80GesWt3430vUJYFlxK//2WLa+D876UId9In3f4P3crUw6vl46uk7qFaujNLvK3TlR1lvL2ogZSR//JqUORLSerrWpyC4kpXJ8j2jYUOZRxGDDeoYksL4l5aPdh1GOMd42SRP5fo66k5Wf7RDItgqz/Nm2KEQE9SXQ/s3EMSZtCmFxrW4l/RwPki5WlxgAd7i2s4wztkWwXD6hS12AadTBYDlcnq5dOLaZDWXZKoYFyxfotH+dputeelCSNLBCOq7eSwDrXBb4woOeYcI5XJ6+2oLD6+e0BJa7DX2ztaK6mAvkE0Idi7reRrY8h9sjfQnQLJL2QJsDrMZ+ETCH9geEgkQwAIBFbM/Qtz0+AIGx/vHqtseHbB76/jv97JpR+nLhl5K8J4Bd0kOq5HwHrEC/AphHOwRgE/okwB/L24r15zcAAAAQNBLBAAAA0IhsFCAMs1ZJP/9WumfRG5KkdbqtoxtGbKLtvr3bcGRxQd/VLi7+AAhUgf0ud3gD9il4bEA7BgAgVIyZAYNof4ifwF8+AgCwERf/ANiC/igrkjRiKZ2Wbn71Zo38TLpnkVSulE7b4jS9fvTr2q7HQNPhxQjtJzvKBUAhQuwzGOdYJCEXOKhz2bUpF9o9LFdUPUpa3UtIvw44K8w+KWn9HVAo2giSjSeCAYAJLpwQszpGm2MDYI8I+gqr+8r2pER/Gp6PVkhHfiM98eERkqRNqqU/jhyjjSZeGHEkbONgxbk8A7qI5HS/aEgiyyyJ6+yH33ZoovyCutDMBevcotqutrc/2+NrzbV4G/l66khQ7dXRMkIWbMvSuFx+YZ4/YGyAJKP+A8bwFD7EHE8EA4xIiQGeJdjRByuS8gxrGUmuC0led4tY0R9FcVIyqvU0UZ5cILVP9GW5Ki1dMlcaPVN6YqnUoaKDLukhzRggbdS5c8TRJKUuRXRBxYp+ukguxx57Sdw2SVznIHE8BBfFtH45vX91OXbYIU51KIJ1cbq/AJKAMTZgTirH90HOF0geEsEAWCCBO2MO/ktE+QHBiXN74mRu+1yP3x7ptPTwImnTmdIp30lL09IOHaQ3jn5dv+gqVRgrarZxsCjPdjnfLxqQyDJL4joHifJDKag/wXK5PON8kw7CwbYsjevl53r8cFYij5cAACgNr4YEjHD5MdBwUqxeNxOndQGSiFfeIH4+WylN/VZ6eLH3c7cy6Xc9pENqpVS3oQYjox0EKlbjKdgjifUqiescpLDKj+2CRrG42Ep99odygu1idP6AYwkgoWj7gDm0PyQbiWCAMXE4sQYEzfaBme3xAaVi39Qs6vZe6PLoj2ywsEH67RzpsnnSsrRUKWlaV+nUrlL38mz/QRtDlOgnCkeZIRP1oYWSkoMoS8AOmW0x7HEp7R6mmKh7Juu7n7ZMewSsxRgbaCXKes15WsQbiWCAEexc7MG2yK2YAVcU5RnSMmJx1zPcRh0MlsvlyStaghPOOq5KS39aIJ35vfT1au9323SQrusljaxqHYLJck7CNo6Q02MFl2OPuyRumySuc5AsKL9S+kOn+1IULbbb3eH1KnSbxHYbAlIkbdn1NhRm/K6XDWLChnpoQwyACRbUffZFiCESwQBTbNyp2BhTXPE48BJRfrFHf4RA8HqH9rkefyFK71dWp6XbFkrnzZE+Wun9bmil9xrIPTrZ2nUlaRtHgfJsl/P9ogGJLLMkrnOQKD+Uop36Y7xPMr38QrkWrwmUUXywLUvjevm5Hj8AAEBykAgGGGPjlUIbYuKpGeGI8vH/QBBsqKcGY7AzmyQEMVvPkrZbzMrCSsWXcTotPbJYOvV76e0V3u96lnuvgJxaJ1WXBRRiHEXRnxm/YB0m+oZoJby8GX84upygmOhLXSsjBCIxfU1YAiw/I2Motn98RLEtM+oofQcAKaK+wPF9Lf0lQkP7A1xCIhgAAACAgMXjpNOKtHT7AumSedI7jQlgXcsaE8DqpU4kgAEAEiMe+/bE83NhkIuHWIO6AFiPPhtwHG0YMIf2h3gjEQwAAAAwjjuUbDJ/tXTzAunyedLnq7zfdU5Jx9RLZ3SV6stNRgf4xJ2PQIloQ8GhLAE7RPm0eNo9DGEMDCAp6O8AAHmQCAaYwJ069mBb5FHMgUQE5RnaNqMuwDQb6qANMQTE5f49qthdLiO/ClzH91dIV8+TblkgLWrcDfYpl07sKh1VK9WWnACWyvF9SFzYxkHEGNl6OlCeubhQF5IqkdsmiescIOePh9j+9mMbJQPbGVjDtVfNGRFm/K6XDWIhrH4gkcd7QIFof0AoSAQDAAAAkGivLpMunCvdu6g5DXpUlXR8vXRQF6mGV0ACAGKvgBuBePoAkDy0ewAAClfQ/pN9LRCoQtofY13EEIlgAAB7MNgCDKMNNqMs4i6dlv6zTLpwjvTYkubf79pJ+nmdNLFjGDeOpXN8n2BB7PsZPwCIDfqzRGN/5qEcALiGfgsAAACWIREMMIZHUjajLADAHPpgJMuyBum+RdLV86Xnl3m/K5O0fxfptK7S6Gqj4QEAYD9eseEwP9uOhAZkQbsHLEXbRBIkpZ4nZT2BPEyNORnrIoZIBAOQgZN9AACYwT44bCsaGnTJHOnyudL3Dd7vqlPST2ulk+qloVVGwwNCQL9SOMoMGXi6R3AoS8AOmW0x7ItdtHsYQ90DkBT0dwCA3EgEA4wgsxgOKOakXSRZ82Etg3YJwxJz10lUJylcLs+oYne5jPzy1vGpJdLPPv9Ibzc+AWxAhXR4rXRkndQn1kdESdjGUXK5PF2OPe4SuG0SM+YJi+vl53r8SRCHbcQxR/tS4gIyrBdZQmEEbdn58U+Y8bteNoiHsOoh+1qgfRntj5sJgMDE+rIHYDXnD/7gFgZPAPxg34R4+Xbxtzp5lvR/CyVpuXqWS5f1kA7oIpUbqe6pHN8nGGNiALBDuyfc6a+BxGGcBgBAuNjXAiFq5xiX9oeYIxEMAAAAQKw0pKU/LpBOvXY9zV3mXbo+smdXXdhlrrqWm44OAADAFB8XO7ggAgAOoc8GAABAWySCAYARPKGrNJQfAD+i6Ctc749cj7+t/y2XjvlGem6ZJM3VhlXS9b2k8X36SfPnmg7PgPhtY6N4RL0PlFHhElhmtKXSUH4ohfVPf3OtfrsWrwmUUXywLUvi/P7b9fjhLuoeAACFKjMdAJBMKZk/sWYpo3eeJmSbhFrGUZRhSMtI9F3PNq67BTFFXieS+Mo41/ujALU4IexY7JZY2CCd9K206UwvCaxzSrp80qV6aaA0voMS2s/bsM5RxBDRSWEjdaiUZXKy3A02tNMmUcVieJ0ja8thLcfF46Ec/VEi980w3gcEibFB4cui3cdHJNuymOPkYuq5w+czgcSJYoztSnvN1d+5Ej+cE9q+P2O+gS6DtoBkIxEMAJKgqDvOTFw8tPyCpfN37gHwzfb2Hkh88TgYTqelexdKoz6TLpsnrZa0T2fpnUHStHHHq8La1bS8jkXF9raWKGwLwDiTfWJ7yw7qhDxJIA5gf5AItEUgQLb3mwHEF2afQX+ERKP+A+Gx/UnIQLh4NSQAAAA8nHyDY15eJp34nfT0Uu/nIRXSNb2knTqZjSsn2lhIKFcAiBb9LpA8tHsAAMLFvhYwh/aH+CERDAAAAIBTZq2SzvpeummBd29XTUo6uat0elepA888BgAAyM5XUjoXQQDAGdxsBAAAgCxIBAPQzIZX8xiNwYL1j4IN2xlolwX1NIn9URTr3GIZFmxnOGXWKuniudJ186VljdXnR12kC7tLAyrb+Wcb9n8tYkjKCfsoXjVmwbYNTZzXzUI29BNGJWT9I9vOCSnPUiS+zbWSmIv5UR9zxI3j6xbrbZMwkW9L6g4AKZq+wPX+xvX4YS3GcYBTSAQDTLD25J6hnbi15RGmqNc5qm0bwXqlUiEtJ4n1EHYxVAcj74Mj6o9C6yvaLCiEWUa5Tdzo+z5dKV0yV7p5QXMC2Pga6eIe0lYd8vxjIscYGSJrB6ZFOM5xtk7Rr1grMe00k8ttyQKpsMqPk/qJ0W79iUP7jPIciKvllVKszhUhInE+fxD6QmIw/nE9frgrqmsOYWCMDbSL9geEgkQwwBgOnJLNhQGIzTHaHBsAe3CXYPvsjv/N5dJv50p3LpRWN/5ufI10TjdpUscYnEePhN3b2Dku3f1oLFaHysgaCSwzJ9qSxTEaKb8SdrpObG8LRFVO1m8P2+NrzaV4C421lME2T4KOJwe2pc19nM2x+eJ6/HBXnOseY2zAHE4sI95IBANMsfLKpQUxGS0XC9Y/ClbWPaA1C+op/VFIUjm+R+RSKWvPpT27VLpwrvTw4ubfTeoondZV2rZDkc2T/Z8hlHtpXCs/1+JFSwnZfpHtDxJSngXLKBf2zQnl6FN7rRHUuiXlidQITeTbkrpjVpjlz7ZFIRhHtM/1+GEtxnGAU0gEQ3HINI+n9CrTEQAATOJgDgal09JjS7wngD291PtdStI+nb0EsE1qjIYXDNpYSChXBGTVQtMRAEiyVYsiWAj7TACIF/p1AAAAtFVmOgA46ut/mo4AYfj0NtMRICzrTjUdgT/dNjUdQVvrn+V9dttMGvYz7/ve25mLJynmv2E6AoRl4A9NR+BPVb3pCJpV9/A+NzjP+6yskwbu433fsb+ZmAK0Oi3dtVDa5HNp56+8JLBKSYfXSu8Oku5eKyZJYK2VVZqOwA7VvUqfR7dNSp9HEmT2vxWdvM9Rpzb/rn6DaOMBolS3nukI/FnnSHPLrh2R/ff99/A+R5wg9d7e+37YMdHElDTvXmo6Ak+HPqYjKF1FR9MRuGHESW1/t/Yhzd/XjWr+viaAMRtQqLUPNR2BP52Hmo4gQ2Ni2Ohfe5+dhkhDDva+r9/QTEiAad3HmVv2gH3b/q5ulFRZ733fb1cp1Xipvs/EyMICIjNgH3PL7rtL29916OvtGyVp0H7N592bjnuBGCERDMVZOc90BM02tuREWabxt7QzQUqR3K2z59eFTb9ibvAxTPki+Hn6tbOhRJKd34x2eX6284gTSl/O2D+0P02pTzrpNNDHRGG1nZQ0fFrzj3vNlnZ5Sxp9jjT5BWnik9Lw46RJM6RtHgkphhDs+p7pCDz7zCts+pUh3A2/z5zi/7emxIsh425qf5ownhQ05fPg55nPD55tf5p+u5a+nMyLEzmVWJ7l1VJZdWnzKFpK2uZvzT/u9qG04yvS+mdKO70q7fGptNaO0o4ve/2Uo5Y3SDfMl4Z/Ju0/S3ptudQpJZ1YL30yRLqxt7RuVZ4ZTHrex1JCHm+VVP4lHor13VWq7t7ORD7Wv9PgwpZbaH/enqaEpFwyE5Vy6TggmFjau9AURD9tKjk/lZIm/Ln55y3v89rQhhdIu77vjdk79pN2eafwYwjkt8kV7UwQYj+156zw5p1Lx4Ht3zQR9Jhnj0+bvx95SvZptnus9OXs/X3p82iPr0SwkOpMTc+WP+/ytleHtrjL6y/WO0Pa5mHveMiVG42SKIikifb2za1FPR7tunHL5OWqbm2nKauUanqXvqytH2hnggDao6nzC6mUtN4vm39e70xp0nPS2Bu8ccGu73vJX3t8Ju3+UeH1Au7Z/eNol7fbB+1P05TAVIr1f+VjohLbcnWWfqjNIkIc8216ZfP3e38r7fy6t947viTt/D9p8I+kyS9Kk54JLwa4pyzfCRdJm17V/P2IE7NP4+d4vT17zCx9Hu2Z+LSPiUJqo313av6+br3GtjhD2uMT7xxfr62kvb6Rdvqf1G3jcGIAconi/M8Wf/ExUUjtr+fmzd9XdWs8l/62t2/c8SWp327N5917bxtODIBBJILBfaly+56GYctTjWy4i7NjP3PLLjf0+JBcd1KHpaJz8/e5nuSQKqK7b/0K2FRF9hOscdKU/S95JzzrRnknarpv5t1RnCqTeoyVKjqYi7FQteuajsBTVWc6Aqmqq7llpypattWoRL1/LPeROBXIyc+UlwQTttrh4S9jjVZ9bkWX5u+r6ppPBnXdyHtaWSrlPQWpsjaqAAOzsEH63VxpyKfSUd9IH62UupdJv+4mfTZEurSn1M/PC+z91LewmRprSF4d6Ldb9MuNvD8vk7qNaf6x0MS1QvTaJrx5NwniCWi+tepXyjNO9JfXSD3GeWOb2mHNY/a6EXYcQ8RJ97Hmlt0hgCSIYvT5QbTL6zSo+ftcTwgsL2b83qoNRbHPNf0K4fKMpyjVjfTqUHl1c39R0cE7Hir4+DLd/iQIRhT7staiHg+lyrybIpr03z37dJl9Q7G6blT6PNpT2aX9aYLS+jxPWXnG9xVSj/FeEl3Hft74QPJu2Ou8dunLgv06D4l2eZn75qYn47RW1H6xdd0ri6Ytm5T5RPPq7lL96MZzBpt6fUwqJXUfQ0InWmmnfXXfrPn7Xttmn6aqvZvTfOgU0I1d+ZS3k/QWphb9WGNbrOzstdumvqm6u9S1mCd0s69FiaI4/1Pm5yRvRLpt4p3XrOzi7SNTqZbn3RFrF154oTbbbDN16dJFvXr10pQpU/Teey0fpLFs2TIde+yx6t69uzp37qy9995bs2fPbjHNzJkztcsuu6hjx47q1auXTj75ZK1atarFNE8++aQ22WQTVVdXa5111tGtt97aJp5rrrlGgwcPVk1NjcaNG6cXXnih4FjaQyIY3JdK2XdywbZ4EsvwSfS8AqwjkV0sSMmag4vQ2pgl64cYsqj9hMqy/qjkvsLP/zveH0U4Zvl2lfSr76WBn0gnfyd9vVrqXyFd3sNLADuru9S9vP35NLNhP28yBp9j4HansbxvSrVu72HGG0Wbt7y8A5GEdSyEyX2JAW3abC4Rr3Mg+zsb9jtNXB5/2FSOcdTONvTTRgtuL1Fv01brkCveINp9IGMtW0W43ZwtI7QR6LaMqA5ade0gjDgiXL/QlsPYwE4WjemtacMAAFc99dRTOvbYY/X8889r+vTpWrlypSZNmqTFixevmeaEE07Q3/72N91zzz166qmn9NVXX2mvvfZa8/fVq1drl1120YoVK/Tss8/q//7v/3TrrbfqrLPOWjPNJ598ol122UXbbbedXnvtNU2bNk2HH364/vGPf6yZ5q677tKJJ56os88+W6+88oo23HBDTZ48Wd98843vWPywKA0TACSjB36m774OhJ918LmeJZdHHMoTxljRHg0neMRWxrr53s5xLo8m8V3HT1ZKl8+VblogLW08dze8Ujq1q/SjWqkqslWPbxlbzYr+3GEllV+e/2W7IKs41IsAj4dKLQ/amQ+UUTJFsd1dqlsFXtwupW/J+78Bl1nOZbm0bZBfgNvST73m/AEQrIL2JzYlYkXQxsMaxwc+X/a1iJrD43iOzxPvsccea/Hzrbfeql69eunll1/W1ltvrfnz5+uPf/yj7rjjDm2//faSpFtuuUUjR47U888/r/Hjx+uf//yn3n77bf3rX/9S7969tdFGG+m8887TqaeeqnPOOUdVVVW6/vrrNWTIEF166aWSpJEjR+q///2vLr/8ck2ePFmSdNlll+mII47QoYceKkm6/vrr9cgjj+jmm2/Waaed5isWP3giGGAEO5xki/P2ZyAIFM+GOmhDDEFxeV1cjt2TTqf1wCJpt6+koZ9KV833ksDGVEv3rSW9NUg6tC6CJDDr+nYTT8xIgiifRugql2OPOev6qVIFmYiF7Cg/wBpO9+Euxw4EzeHzmQACQhsFzKH9IXrz58+XJHXr1k2S9PLLL2vlypWaOHHimmlGjBihgQMH6rnnnpMkPffccxo9erR69+69ZprJkydrwYIFeuutt9ZMkzmPpmma5rFixQq9/PLLLaYpKyvTxIkT10zjJxY/eCIYYIxNd1HYxGC5xOIRwxY9spk6DueZrMOmlh3Fcn28xgVOW92wWtOe+q2u/rr5d5M6Sid3lXboYPJ6mQ31zYYYIhZJO49xuYZVfvS/yCoO9cKi4yHamQ+UUTIxNihJaH0L54pQqAC3ZaxfwwpYytk2FUHczpZNE9fjh70crlvOt2vksnDhQi1YsGDNz9XV1aqurs77Pw0NDZo2bZq22GILrb/++pKkWbNmqaqqSvX19S2m7d27t2bNmrVmmswksKa/N/0t3zQLFizQ0qVLNXfuXK1evTrrNO+++67vWPzgiWAokmXZubbdgWdbPNaLWXn52v4OrHPWgZElcYfWxixZP8SUrfXL1rjaE+SrI0pYRmDl17rPjWi7BNyfLlu1TPvft7+ufv1OSdLUOundQdI/+kkTOzJEClygr1CxWSrH92Eup5Rpwvz/Qpg6yRWHOhekmBwbFMTCdS6qL7T5RDHHQ8jFwvYXuJR8vW4+iDFQJGOtCLdHlBfAMpcVi/EoJDmyLbPUc2vidvwtB9aUI6Lh5ziculeQwPfDNh+vAMWiXqMwo0aNUl1d3ZqvCy+8sN3/OfbYY/Xmm2/qzjvvjCBCc3giGGIgJoNABC8uBwjt4oALsF5S2g8nHx0TbDl+v+R77X333nrqs6dUWVahP/Vapf27BLqIVmyoBwZjSEw7SMp6xkRi6iVyi3EdoH4Hg3I0LIzydyGxE21QjjAtsjoY87oeh/Mw9EcAAKBIb7/9tvr167fm5/aeBjZ16lQ9/PDDevrpp9W/f/81v+/Tp49WrFihefPmtXgS1+zZs9WnT58107zwwgst5jd79uw1f2v6bPpd5jS1tbXq0KGDysvLVV5ennWazHm0F4sfPBEMMZC275GOtsWTVFZvB5tjyyGdljVxO/8qBCSOTe0nTFH1u37Ls+R4TL5eyq3XVr0x+w1tduNmeuqzp9Slqose2+PakJPAJDvaVCkxlBh/2ucY2OrxkNR+ObRu72GuTxRt3vbtEYQkrGMhLHpVYWQsXGfr+8JCOT7+QIgK3a8WM49Sp29vdu3Mr/WxQK7pg2j3sRhrWYAyig8nt6VN1w4cf+27NeWIaFg0pqfuAQBy6NKli2pra9d85UoES6fTmjp1qu6//3498cQTGjJkSIu/b7rppqqsrNTjjz++5nfvvfeeZs6cqQkTJkiSJkyYoDfeeEPffPPNmmmmT5+u2tpajRo1as00mfNomqZpHlVVVdp0001bTNPQ0KDHH398zTR+YvGDJ4IBsAxP1iiN6ddARPXqpjC4Fm+ArKz7NsQUdQwut59C+HiNS9I5Vi6PvP+I9r9vfy1asUhD6ofowf0f1OhqSW+ajqw1t8o1Nhyrz9YJrPxazYftgqziUC9MHw9lLiYO5Rk2yiiZotjuLj1pqMCL22GNDZwqM9ghwG2ZmFfeA66yKRErgleshtXf8CREOC+KtuF6+4Otjj32WN1xxx168MEH1aVLF82aNUuSVFdXpw4dOqiurk6HHXaYTjzxRHXr1k21tbU67rjjNGHCBI0fP16SNGnSJI0aNUo/+clPdPHFF2vWrFk688wzdeyxx65JQDv66KN19dVX65RTTtFPf/pTPfHEE7r77rv1yCOPrInlxBNP1MEHH6wxY8Zo7NixuuKKK7R48WIdeuiha2JqLxY/SARDkWwa+AEA4of9jBkcEMG/dDqtK56/Qr+Y/gs1pBu03eDtdM++96h7x+7SvDdMh2cp2lg4KNf2sV8FAACZGBsAAAAASIbrrrtOkrTtttu2+P0tt9yiQw45RJJ0+eWXq6ysTHvvvbeWL1+uyZMn69prr10zbXl5uR5++GEdc8wxmjBhgjp16qSDDz5Y55577ppphgwZokceeUQnnHCCfv/736t///666aabNHny5DXT7Lfffvr222911llnadasWdpoo4302GOPqXfv3mumaS8WP0gEAwAAAIxz60LMytUrNfXRqbrhlRskSUdscoSu2fkaVZZXGo4MQDO3+hUAcUZ/ZI8YJE9zN38JomyLtHuYkrS6R58IJFfS+jsAKF7ax2uGa2pqdM011+iaa67JOc2gQYP06KOP5p3Ptttuq1dffTXvNFOnTtXUqVNLiqU9JIKhSDYdYNgUC6ySmJODYa0nBxIwKWbtNyn9UVTrmZTyDF1x5Thz/kztd+9+ev6L55VSSpdOulTTxk9TKvLtYkM9sCGGuKOM3cL2SrxY76PjvG5RohzjJ4ljwDigHGEar0hzS5jlyDYCAAAIGolgAAB/Yn1RBwDgx3OfP6c979pTsxfPVm11rW7b8zbtNnw302ElE/tlAAAAAAAAAADQColgiAnbnlzUTjyplLjTJcFSKcnHIyit1F7cUVyUTqUUTpt3eLsgAgHUDRvaT1au1ns/5VniuvnpE0LpN8Lq57Lxt5yGdIPOe+o8nff0eVqdXq3RvUbroQMe0uD6weGGF2tBbOMA2oHxfV+B7SzMeNudd0pSQ6kLKfH/ixXhPsZ4nbKNj3oVqzLzsz5R7ueaxKiMQz2ejFE5JZWvuhGDsUGLaXJNH8FYK7DlmBDl8aerZYS2XN2WNpyPCXP8Y9f5A8REEGOKwESxHK7XAebQ/oAwkAgGwDImd/gxGGz4OnHBq9vgAhvqj8EYYt1+Ujm+h60WLF+gwx86XPe8fY8kaf/199cNu96gLtVdDEdWKOqbGZR7acIqP7YLsojD+MOm4yHamQ+UUSJFlnDhiIIT7xwfG8RhX4NGQW5Lm/bfANqyKAnQ6XEE+1q4jvYHuIREMACWMXlQYdEBTbFsulPH+F3EcJsN9cdgDLFuP37u3octXp/9uva5ex99MOcDVZRV6IZdb9ChGx9qOqwiUd/MoNxLU0L55d2XsF2QRRzGH0EeD5VcHjEoz6DkLEvKKHomnsjXSslty89FnDjXrVLWLcKxQa7tHId9DRoFuS1t2n+7hgvbSJhI2rgjT+9jX4vI0f4Al5AIhhiw8TWLST8pVaDQ7lAwVS98LDfIdQ6t/LLUUWvuJgkpDmvWD/GTsrh+2RpXeyK4Y9jPNnN5H5bnVdXpdFrXvnitTvrnSVq+erkG1A7Q3fverfH9x4cfl182tCnjMSTkzvnMcg6zzCN5klAMtkdeNu/vTDG5LzHBbx2Iep0DWJ5N28nl8Ufs+0HDTLQ/I23Dz1OGg4jLkmOOMES6XNp9fET9FDAXl5WP6/tvzsfGSyGvTA1zX+sHdQQAgEKRCIbiMDgvEeWXbHHe/g5fOKBfs0wSt0cS1zlMDpen4f7ouyXf6bCHDtND7z0kSdppnZ305z3/rO4duxuNC63ZmGgRc6mUu3fWMs6xWMy2jdEk6qSg/AB7uNweXY4dCFpUN2IBsBdtFDCH9geEgUQwAAAAAJKkxz58TIc9dJi+WviVqsqrdNHEi/TzcT9XWarMdGgAAAAAAAAAAABoB4lgAAAAQMJ9v1o64f6D9OfX/yxJGt59uP6y91+08VobG44MAAAAgXH56ZYAgLZ40hgAAACyIBEMxbHqpFFa7b7PPHK2xZNUFm8Hq9pQAayJO6Q4rFk/xE/a4vpla1zt8RN3ievmZ5uFtl2j2S7pdIPuXShN/Vb6ZvWflVJK08ZP03nbnadOVZ0iiaFoBZd9CCfIS9n+Jdcdv2Ngy9t4oe0szL7U17yD2G4xZ+3+zhST+xID0n7HPFGvc4zKWHJ+/IEQBdL+CqwHgdfHQtch1/RBxGXJMYfzkrCOSeHqtrQlbtf337aUIyKRjmpf6wd1DwCAQpEIBsAyJu9iisEdVL7uAvO5nqWejOSONJTCivpjMAZj6x/FclM5vk84AxeAvlq+VD97Z4Ye/M77eVTPUfrj7n/U+P7jI48lEknvV4yJul+Jm1LWLV+/EucyQ9GC6CdN97VBHg+VfMGJdtYsV1lSRolUaj8RaDt3UQnr1uKYo/V8gi6zHO3e9H4CAQpyW9q0/wZgtUj2I2Etg30tXEf7A1xCIhhiwMXO28WYXWRrOQcdV1TracvJVgaCcJEt7SdsSeuPwhJu7KvT0s0LpJM/eVTzV61UpaQzukmnH/mKqiuqQ112oGw4sWU0hri3gyY2rYNNsRQqothtaJeuiV2ZJaVvMsnx8otdnUf029SiOuRyfXY5dsRDZHXQlrGJ422OPiOG2KYtUMcBc2h/QChIBAMAAAASYvai2dr7C+mZZZK0Upt1qdcfu87T6GpJLiWBAQAAAAAAAAAAoI0y0wHAUWTnAgBCxX4GCNqrX7+qzW7cTM8sk+rKpMvX3VjPbbqNlwQGAACABOA4CwDihX4dAAAAbfFEMBRn2bemI3BferXpCAAAQELc9/Z9OuiBg7Rk5RINr5Qe6iutO3CEtHqp6dAAAAAAAAAAAAAQEJ4IhuK8coLpCFoa/nPvs+/Ozb+r6W0mFknqNKj5+367ZZ/ms7uiiaWs0vscfW7703YaEm4so3/d/jQd+we7zEEHeJ/DM+psl2Etp+m6kfc55OBgly1Jw4/P/vu6kcEup+dW3uc6RzavT2vVPb3P/nv4nGm67c8jTmycx57Nv25db5rKfOQpPpfTyuCfNH+/1uTs0/TZofGbgO9667uj91kW08fjjDw5++8XvBvN8utGeZ+jz2n+XWVty2lSjUOTNds4YJ3Xbowhoz8q75B92l5bZfzQuj0UYeQvvM8B+2TEM7TlNAN/6H2O+EXpy2sts9wzpcqbv+/Qp8SFpKW1f+p9O/x4aeC+bScpq5J6bO59P/Rw//Nt/XNTX1G3fu5/G3GS9zlgb5/LaWXY0RnzOjH7NK33KUVrtY61owKZa0O6Qb9+8tfa5559tGTlEk0eOlnPD5DWrWqcYPCPGpc3IpDlRa5p373ucc2/a71Nuo/3Ptc+LJwYBu7nfWaONTqv03Ka+g29zyEHZfwygH6lqc/IHHu2tu5U77PPpOx/X+fIwpdbv4H3uf7Zzb+rrG85TVljJevzg3Zm1l45pJtj7LG5NPy4tpP0GCcNn+Z9P7SE7dxzi+bvq3tkn2ZAY7/WcWBxy1hrp+bvNziv/enr1ituOZLylm3t8BLm244e48Obd1O5Z+5Lbddl3ebve22TfZqmMW/TsVuQyjt6n37qW21Axyhr1ifPmLqp/27qT4LSbUzb31V0aTnmrKrzObMsbajbpt7n+mc1/666e6vldfI+++6k0Kw5LpsS7Hybjhea9i+BaVWW3cd6n6X02dkMaDxONXk+yLTMfVlNr+zTtLcv833OIMOg/b3PfOdeso6Hskj7GCP12937rOqavb4O3Eda5wjv+x4T2p9fLpllOOjA7NM0HdsUK/P80Pq/yr5sqbkf67tLCQvLUrblNd5nrvMvQSyrqlvG8joFu5imuJvGvAjGer/M/vvMetk03i9F035s+DSp9/bZp2k6Vh2cow22keX8wTpHed/2zDjPU9lqPNBUh4Ye4XM5rWSW2dqHZJ+m22bFzbs9pfZDfq3pV0NcXr5jW0Qrcz/edZO2f1/vjObj/VRAzxzJPMeQKfPcbdM1jmJlXtdoPVbp3Xg+etgxpS2jtTXXbo4Kdr65jvl7bJH998Vqus4T+DECItd0bSRTIdeQSz0P3nQ8LbW9LtJ0nmdkwNdFmo5tms4bAgnCE8FQnIYVpiNolkp5Jyt7bSt13VBaMU/66u/eBfy/BXVxtkBV9dJuH3gnU2p6S5/+Req9nfTgwOaY06uiiWXPWdKSL6T60d5Fsoou0jP7SUs+b55mypfSqkXSsz+WFn8SfAx7fSstm+VdyOq+mVTVXfr3JGnl/OZp9pgpNSwv4KS8Hylp/K1eMkK3Md5FxPlvSKsWS88f2jzZD/4rzX87+0UDyTvZ99kdBSw21bw+ndf2Tjp23Uh6eETz32t6Sbu+J1V0LnblMhcobfcPad4bXvkOOUia/463zT+9o/kCxG4fSIs+lrptXPxy1jtDWmuStz7Lv5NmTZd6btnc1lJNZf7z4k9ujL/ZW0bPLaWO/bx16LOD9MCA5mV03Uja+XWpQ98i1yWblFd+O/0v+IRE06Z8Ia1aInUZ6l10qVtPeiQjyWTVkmjimDTDSzrrtqmXkLBqofTRH6WZdzdPs9c30pIvpe+eCSeGnV6TFr7vncDovb3XTt+5VPr67xkxNPVZwSTieFLeBcO+O0tdN5aWXy7NetzbHk3bIpWSJvzZu7CXqz/a7HrpxaOz/y2XzD642xhvv/SvrZufBJUqa+yzVkiVXYpfRW9m0tjrvZOD3cZI6QYvGavbJtLMe702VlYubT9dmvem93Oxyxm0n9RlHe+kcHqlN/9BB0j3NK5DKuVdSOm7U+4E2fYMO8brZ7qs45Vfj/FS3WjpkYyLNTU9pF3flyo6Frku2aSkDr2lXd9tmyxZgMUrFuuQBw/RvW/fK0maNm6aLpl0iSrubEo0SHlJcju+JHUJMSkkNClp3I1ewl63Md6J+zmveNv+mf2bJ9vhca++1Y+WXs6SRFRqDBP+JI04oXGscYQ0/01pxXzphYwLCJOe8fbNmSc8glh2352lHV/26qjk3WjQuh2MOMHbp3bdMPtshh0tvX5mYYue9Gzz+vTd0VvfT2/zvprs+bU3Bu1aapJHqjHRfWOpfn1vfN1zK299Zj/pXQDuso608SVev1BKGdeuK+38pjdOq+wifXKbd3Hqr00nmlNen5JZ5oXqMVba4UlJaan3tl6/UlYjvXCktOCd5un2/Mor145BjXUak+ebxv25kgOCWE6XodIub+VOpivFLm9ICz/06oMrano2j/trekqf3u6Ngx7o1zhBSuo+Jrwx6J5fSItnem2m+zhvf/X8odLCDzKm+UpauSCAhHB544rM9Smv8dZ54L7SvV2bJvISkWuHBzfe2mu2d3zSeUjz+lT3kD6/31tWebW0e+OxblPSQzEmPtV87Nh3F2nF99Lnf5U+uql5mimfN5d5Mfad39yfp1dJM+/x1uHuxuSJVEpa/5fNx2VBWv9sb71CbWMpaYd/lzgWzKHPRGnHV7Jf4EiKdvdlan9f1nvbAheaksb/n3dxJXM8tHKhNCMj2S+o8VAq5Z3z2+lVqdNgL5mjaX3mveUdZzZdmO66cWlJ1RWdpN0/8i5wd+jrlV3PLaWHmm6IS0m1wxrLvMgL0zW9vHVZ/JmX4NZvN+9NDF89In1wbfN0e3wmLf40wHbfeBPWlC+9c4TF9ll+VHSQdv9YUkoqDyB5KNPWD0hz/xd8f5JUe37tnVuvHe61585rS3/PqBuZbaKsPOds/ElJW9wpzX3NW9aok6W5r3t1/LM7m/uiyS82n0sqdjnDjvGWUT/aGwt/+ZDUd1fp/saxTyolbXK5t78tdjmjf+3Nv+vG3sXt3hOlnhOkh5oudKekzoOlXd5umRwZhFL7IV9SXpJc/UbecVnQpnwurV7mXVdB9H7wX2n6li1/l3m+q2M/aZd3vO2zcoE091UvaaOsPJjjmL1me/u+ulHesUSHvtI/NvPOK0pSWYW3H0yvKv782x4zpdn/lgYf4O33vn3O2wf/u+mmuZS07cNeP9Q9x3nZYmVeuwnTXt9Iy76R6gK+2XP0OVK/Xd06Dkd2G/xGerZVYnUh15BrijzPs+fX3nX7wT+Sln/jXRfpton0aNM5w5S0+e3S3F/kvi5SrC3u8sYajBWRQCSCwbzq7tLy70ubR6rM20FJ3snroYd6J16Lsc5R0od/KC0eqeUJtbXbudsxm4rO3o61VNXdvC/JO1GcTWAXmHKo6dE8QMh1V3SnAeEsu7yquW7UjfC+Pv5Ty2kqOuUfBFTkeFpQPpnrM2i/7NPUrpv998Wo6OBdWJQa16dxsDQ0I+Gtqq6EJLBGZeXN5dmxn3eH2+LPWk5TXlXakyDKKqQhP27+ee0cT2qrH138MvIp+YJ1gPrvKX1xf+nz6div+fuBBp+gUdm5uW72bLwr+6ObW05T3d37CisRrLJL80m9Xo0nON65tOU0mX1WkFq0n/5e3V74YctpMvusrPMo4kkhmevTL8fd40H2wWWVLfuApvUZfEDz7yo6NvdZxUqlWp6YWeeI5hNEa2Ipz1+e7S6jrPnJElL2J5xJ3knXMJTwxJ6Z82dqyp1T9OqsV1VZVqnrd71eP934p20nTKUCTk6KWGZ9q13X+5p5b8tpmurb6mXhxNBirDHS+2rdt2Xum4OUSnknTpo03aHdYpqydtpBEU/XzFyfpvL/9PaW02SOQUuVSrXsM5rWp+lJnpI3fgjiSVT1GReL18ny1MLWZV6M3hlPheozMfs0HdbyvoIW9ri/SaDJ1Bkqa0svfxMyx/25nhAR1hi0qqv3JUlr5XhCXxj1LXN9svZNqWBPxNb0ak5wzFyfzHbceXDpy8k8dmzqlz5vNV7PLPNiVNa2LLOi+vYilTp28iuIsWAupR7zxkHefVkqmH1Za9nGQx/f2nKaoMdDmQlRTevTdJzZJIh+JjOxMPNcRab6EpLNJG9dmtanKeavHm05TVW9VLVRacvJJsgxWz6dQ3oLQXlNNP1WUnTo05wYPmBK9mmCTLYtr87YfuXN+4bMc+mZ55KKlXk8UdHBeyLlinktpyn1eKKsvOU54CE/yj5d0G+JSDUez5XaD/ldVlj777jdlOuazCeKZso839WUXNShT8vjmyCOYzLH8v12zT5NpyKfyr3m/wc09y2d1/a+Zj3RcprymnDqeOa1mzDV9AwnITSqYwSEL5UliTuKa8hN1+2l5usi81u9paa96yLFajHWAJKFRDCgjYBfNVc0W+KAr9cSxFJS19siKfoBa1jTD9gSR9SSsN7BrePTnz2tfe/ZV98s/kY9O/bUX/f7q7YcuGX7/4iIJaFe+2BN/xpDLcqWcgZgEH09CtJefeE4uWhRtkXaPUyh7gE+0VacR38HAMiDRDDEQExPAIWaAGLDADGCGHKWoQ3rH6DIkoVi2tasFlWZm2wTNrRHg/2RsQP2sJZLf2RSOp3W72f8XidPP1mrGlZpg94b6KH9H9Kg+kHZ/8H5ZFMb9vMGY7Bu+4W0ztatZ1hs2B8GISnby3Ghjj+SWAfi0n4jkph+PUmiPtZJSh2ib0HcRdSW2e8EhHJExCI5Z8q+FsiO9gfEAYlggBG2Hjix442Grds/CFGsW0jL4MQQjKMOBsvh8iyiP5q7dK4OffBQPfjeg5Kk/dbbT3/c/Y/qVNUp6OjgFIfbgY2cHiu4HHvcxWzb+GknTrclG1B+gD0cbo/0xUCGCNoDbQ6wHG0UMIZ9JBAKEsEAANnxaGEAtkhCf1TCOr7w5Qv64T0/1GfzP1NVeZUum3SZfrbZz5TiINpuSajXvlAO4aFsgZLQTweIskQhqC/hibJs2Y4whboHICno7wAAuZEIBgtwkRIoDY9SB2CJqPoJ+iNJUkO6QVfNuEonTz9ZKxtWau2ua+uefe/RJmtt4nMOlCPkQHuyPT60YH19AoCEi0M/HYd1sALlCMMia8txr+uchwEAAEBbJIIBAAAAphV4UvWzeZ/pJ/f/RP+Z+R9J0t4j99Yfd/+j6mrqwogOAAAAAAAAAAAADiARDBaw7fGllsQT5msobHjFhdEYCl22BeVlhM/1tqE+xVYSytaGdfQTQ1hxFjjfoNqbc+3WtXiLUMA2efj9h3XwAwdrztI56lTZSRdNvIhXQWayoX77isGCOANV7PrErRyKFUY5ULbIJcy6Ead9kd9yoq21jzKKhm3tr8jtbsNYzgphjw3Cri9sRxhCHwLERBRt2fH+gv4OBbPpmh/1FwgbiWBwX+AXPaPY+dh2ci6ubC3noOOyaT0jiCW0RAebyhHx2x4+1ocknmA5XZ7ZY5+3bJ6OffRY3fHGHZKkMX3H6O597taQrkMCXY4zbNjGRmPws2wLyihWHC5PXr1jLxv6skDRN4WP8kMOpvqT2PVjBXB53V2OHTFhUx2MIhab1rcYrscPtIP9ImAQ7Q8IA4lgAAAAgOWe/uxpHXT/Qfps/mcqS5Vp2rhpumCHC1RdUW06NAAAADiDiywAEC/06wAAAGiLRDAAaFdSH1Ga1PVOIrZ1+2wpI1viiFoS1jv7Oi5ZuURnPH6GrpxxpdJKa+2ua+uOve7QuP7jIo6vUJyMbl8S6rUPvMogPJQtUCLaUGDoj1AQ6ktoomyLtHsYQ90DkBT0dwCA3EgEQwxwoRG5JKRu8KofwAFJaT/0R0F64pMndOTfjtRHcz+SJB2+8eG6bPJl6lLdJZgFOP/Yexvit/3VkHGQlPWMC7ZX4jm/bwFcZqr9Rb1c+plgUI4wLKoxA2OTgFCOAAAALiERDObZdoeYbfGEItc6RrnuBss5Eds4SpQnSmBDezQag6llW1DuyOnrRbN14mOn6s4375Qk9a/tr5t2u0mT15lsODJX2FC/bYghYjb05y6j/BAp6lugaL9ADrSNktC3AAAQLva1SBrfdT6CtkH7A0JHIhhgK+5WsgcDEv9crrcux46Y8FMH6Y/ibHmDdP186aybd9CCFQtVlirTMWOO0fnbn6+6mjrT4SGuGOc0ivs4IO7rB3tQ15AN+5po0P6i53CZcw4EABKO8VlL7BcBc2h/QBhIBEMMBLyDsOZESJhx2LCOEcRgzbYMm+lXsSWlnE1IQNna0E6jiCHnMuL2+hb6o2I9tWi5Dp4pfbZKkhZqTN8x+sOuf9Ama21iOjSL2VAPDMZgQ/+ZKax4kvLKGNPLR8LE/VgzYrRf2MJYXYx6PESbA+LB9PmDmGAcAhSP9gPkkMDzmkAMkQgGAAAAGHTzqzfrqI+/1ypJfculs7a/QIePP0XlZeWmQwMAAAAAAEDskIQBAECckQgGtJaI1+PkWMdI191kOSdhGwfApveFI75s6HONxmBq2RaUeyFsqCchWNWwSqf96zRd+tylkqQDOks39pY6bfhjiSSwEthQX3zEELd6XfT6xKwcihVKfaBskQt1wxe/7TJu/TkQGMYGpXF9bMB2RHvCSkKh7gHwyflxvOvxI3oWXfNzvv0B9iMRDDCBR14mW9Db36r6FEUsNq1vXFCmdmA7BMvu8vx28bc64L4D9Pgnj0uSzurVWefULvK69Mj6dbvLCAGwaowQBy6XZ0JesemkJJZZEtc5QLQz5ETdQCGoL8AakexbHW9zjD8Qd9RxwBzaHxCKMtMBAED0GFQAAMx54csXtOkNm+rxTx5Xp8pOumufu/TrPl045gUAAEDIGHC6g20FhCsubSwu6wEAAIAgkQgG93HVFABKxGN4w8e+ClI6ndYNL9+grW7ZSp8v+Fzrdl9XMw6foR+u90PToQEAAAAAEB3O6QMAAACh4dWQANCupCbJJHW9gSxseWe9LXFEzv31XrpyqaY+OlU3v3azJGnPEXvq1im3qra61psgsds2yWzZ5qbjML38JjG8EEW/ApSINhQcyhIFYP8VoijLlu0IQ+hDACQF/R0AIA8SwYBEsmGAGEUMuS7o2bD+Dsp5px7liVLkqj9RXpA3WIeNHbCHtNyo7uh17M7hT+d9qr3v3luvfP2KylJlumD7C3TKFqcoZXo9TC+/VLnij7JdGd032rb9wlrnqNbTdHnGZTxluhzhS5j9pOv7lqLEpf3CfYbaX9RjssT0M/QtQDCS0meEjXJEHLGvBbKLom3Q/oCwkQiGGHDxIMTFmBGcGG//SE7Ixrj82kjKxe8E8NM2EnNBIyp29Ef/+PAfOvCvB2rO0jnq0bGH7tz7Tu2w9g4lzxfwh7oUKPpphCKB9cqZtmRrnLbGBeOcaVsxQpkDJbCp/UQQC/0FAAA5sI8EwkAiGAC0J6mP2E3qeicS27p9tpSRLXFEzb31Xrpyqc558hxd8uwlSiutzfpupnt/eK8G1g3M8R/urSNKZMt+1nQcppffJJYXZiwpW8BZtKHA2NLXw5H9HfUlNFG2Rdo9jEla3XOhXwcQjqT1dwCAQpAIBiBD3AaOHAgHi/JElOLWHyUFT7GTpI/mfKS97t5Lr89+XZJ05CZH6sqdrlR1RbXhyFqzuxzbZ0P8JmOwYf2jQL/iFsoR1AHAHFPtL+rl0s8AKIATCbAuoBwBAABcQiIYYoCDEACA7dhXJcHqhtW6csaVOvPfZ2rJyiXq1amXbtrtJu02fDcf/00dAQAAAAAkBcfAAAAAQFhIBIMFeOpLdiEeDNvweHajMRS6bAvKywif621DfYLDbKg/PmIIrZ4b6o9ca7cOxPvmN2/q8IcO14wvZ0iSthm0jW7f63b1q+3ncw72r6M7LChLX3XWgjglBRdHsfOxpRwMX4gKpZ+zpWxhH+qGP37LifJsH2UUDduSKlwfG5jm+tiA7QhTqHuAP7QVF8435ud6/IieTdf8qL9A2EgEA4zwcXKOx1aXztoytDWuIESwbtZu1xBEta5WHvTatp2jKCPb1tlxUbSfVErLVy3XBf+5QBf+90KtbFip2upaXfKDS3T4JoerLFVW7IwDDdP8csJiQ/wGY/BTx5O0z4yEw+UZVV2gzhUudmXmZ33its5Ro/yQg7H+JMl10uV1dzl2IGhRtAfH21zsxqwAAHuwjwHCQCIY3MdBCADAeuyr4ui5pWkd9oeN9c5370iSdh++u67d+doCngIGAAAARInjEgCW4Jx+MChHAAAAZEEiGNwX+JNsLHkyjpVP6EGyUAeNox+wSKnbgm1ZGrvKb8Fq6czvpavnp5XWO+rVqZeu2ukq7TtqX6WKPglr1zoiCmxzD+UQGsYRQGloQwGiLFEA2l6IeDUkEoA+BEBS0N8BAPIgEQxoIwmDp1zrmJATQgyQi5QruYHydJ7JuwdtaI9GYzC17LCWG+9XGqbTad3/7v2a+pn09Wrvd4dsdIh+94PfqXvH7kZiKkls7xy2oF+xIoaIhdWXJuaVhnGpM6bLEf7Epb5ZwobxLGAl1485DKNvAQKSkD4jdJQj4oh9LRLG9/gygrbBWBcIHYlgcJ/xizZFcDFmBCfW2z+KdYtz+RnCoDsCfuotdTtYwZbnO9++o2n/mKZ/fvRPSdKwSumaXmX6wR63BLocSTHfTyBa1KVguVyeLscedwncNuznSkP5ISfqRvQcLnP6EhhnUR2MpD1YtL4AANiEcSkQChLBAKBdCU2SITkIaGZLe7AljsiZW+/vlnyn858+X1e/eLVWNaxSVXmVTq5doTO7STXlAR6kJnbbJpg129xwHNaUQxxPOtlStoCraEOBsaavhxv7O+pLaKJsi7R7GJO0uudCvw4gHEnr7wAAhSARDECGuB04xm19DCMrH1Gyrr5xYO1LjF7hlk6ndcXzV+jsJ8/WwhULJUm7D99dl026TEMfWyf05UfDtnZWIBv6CaMxWLD+kYj3K2fjh3JMPBv6ZiCxDLW/qNs9/QyAgtBnBINyBAAAcAmJYIgBDkIAAJbjYoVTlq5cqkMfPFR3vXWXJGmTtTbRhTtcqElDJxmODAAAAACAOOA8CQAAABAWEsFgnm2PCrctnlDkWsco191kORe47ETUiWx8rndiywfBsKH++IkhpDgLbj9BxWFDuRcgwn7m8/mfa8pdU/TK16+osqxSV+x4hY4ec7TKUmUhL9mxbWIzK/ZLBvuVQgVWXsXOx5JyMJ6wG0Y5WFK2sI8V/aQL/JYT5dk+yigSxvdlrRTb19BHNXJ9bMB2RHvCqiPUPQB+ud5fuB4/omfTMS71FwgbiWCAEZadnIstW8vZ1rgCEMmJ5xiXH+wVxcUI2y7cOK/w8nzikyd0wH0H6JvF36h7h+6674f3aZvB2wS6DH94FZ4/hcYfxvra/mpI17exZZzup+Pz6t74iVuZ0TeFj/JDLqbqRoLrpNP7PZdjB4IWQXtwur+Q+/EjC7YpAFvQHwFhIBEMMcAOAgBgO/ZVNlvVsEpn//tsXfjfC5VWWhv23lAP7P+ABtcPNh0aAAAAEBwu5AOwBv1RMChHAAAAtEUiGGArTs5ZJKmPKE3qeicQ/Y0PlrSHxL4mJbz1nrN0jva/d39N/3i6JOmITY7Q5ZMvV6eqTqEtM7ukbtsks2Wbm47D9PKbxHBfmNh9BhAQ2lBwKEsUhPoSHl4NiQRgnwP4RFtxHv0dACAPEsGA1qxJiDARhy3rHhBrtmVcUJ6Ri6oOW3nQaFt9s7GMbOTWKw2fmfmM9r1nX3296Gt1rOyom3e/Wfutv18g83aC6/tJK+I3GIMV6x+ByNYzIeUZOsoR1AHAnKS8GpJ+BkABknLcFDrKEQAAwCUkgsECJV5cD/pgzsqEiIDlXMcI191oOSdgG0eK8kQpbKg/UcSQa19laP2TsK/LY3XDav32v7/V2U+erdXp1Rrefbju2ucubdhnQ9OhIRAW1O9EtrEkrnOAEllnYA71LVC0XyAH2kZpKD/EHAlaAExjHI/E8VnnI2kbtD8gbCSCwQIlHvS5OFjjQDfhHNn+RbWtCNaN9hMwytOXkvc1fv6fbZFbEeWfo6+YOX+mfvzXH+s/M/8jSdp//f110243FfcqyCD7IxfHM3lRn9sVxTZ3YZ/pVN13oDxbcKlsE8yFdhq4JK5zgJysM/RHkfBVN1yoPy7VFxfKM0OU4y6nxniIl+DOHwQrpGU4OS4AEAz2tYgL9mVAGEgEg3m2HazYFg9gC9qGAZQ5XGP3K9zuevMuHfXwUZq/fL46V3XWNTtfo59s8BOlEtu/JXW94ZaI6mli+4GAUY4AgNCxrwFQCPqMQDDOB4AYoC8HkoREMLiPgxAAKBF3D4WPfZVJc5bO0fGPHa/bXr9NkjS+/3jdtudtGtptqOHIAAAAAABIIs6TAAAAAGEhEQzm2faocNviCYUN62gwhoK3sQ3lZYLf9U5q+SAQNvS5vmIIK05T/ZEF5V6IEurJA+8+oGMeOUazFs1SWapMv9zql/rV1r9SZXllgAHCLjbUb5P9SqECiqPodmpLOZi+EBVGOdhStrAPdcMfjoeCQxlFw/S+rLUit7sNx4g2CKUcoixbtiPaY8t5FgDJ5Xp/4Xr8iJ5Fx7iM+YHQkQiGGLPtBFgmm2OLE0vLOdZPsYti3eJcfqbYWKa2xRTFgYlt6+y2b5fO18/vO0B3vnmnJGl49+G6ZY9bNGHAhACXEtY2s/sVm/awIH6j+3Q/y7agjGLF4fKMrK46XEbGxKzM/NS1WB8PRYHyQw6m2lai27TL6+5y7EDQOJ/ZPtfjBwBYK9HHE0B4SARDDLCDCAwZ2EDyWDvIjll/ZG05x8+qtHTzAumXd/5E3y2br/JUuU7e/GSdve3ZqqmoMR0eAAAAYBDHJQBsQX8UDMoRAAAAbZEIBgAAgFh44pMn9POZ0lsrJGm+RvcarZv3uFlj+o4xHRoAAAAAAAAAAAAQOhLBACNi9qSbuAv6SWnOPHnN1jhtjctR6bQoUx+sabe2xBG1/Ov9+fzP9Yvpv9Ddb90tSepWJp014Tgds93vVFVeZSwuc/OCG6LY5j6WYbx/M738Jn7upLclVp+Mb1v4k8Dt5ErdtDZOW+PKw9qyTCIXtoULMbqKskUCFLXPseTYDAAKwRgbAJAHiWCwQKmDlaAff5zkwVPc1p1HYweL8kSS2bavslRUr8BsXM7qhtW6+oWr9csnfqnFKxerLFWmn9U26NzuUtcN9pFCTQKLAedfWWpD/CZjsGH9oxBtv4JSUY6IUx2I2/Ex4s9U+4t4ueyzgZiIqi3TZwSDcgQA55E8CCQKiWCAERw4JVqcT1pGsm4xLj8T4lwfXcO2KMi/P/m3pv1jml6f/bokaYsBW+iana/Rhk9s1DiFw/0RdQGBoS4Fy+XydDn2uEvgtmE/VyLKD7n4qRvUHzSiL0bStWgDDp8/oF8HADiPfRkQBhLBYAEykGG7hNZR7g5IDra1D5aUUVK3VcZ6v7tCOv3Fh/XA7N9LkrrWdNWFO1yoIzY9QmWpMlMRli6p2zbJrNnmhuOwphzieNLJlrIFXEUbCg5liUJQX0JjzbgLCBP1HPCFfUIMsA0BALmRCAb3xfUONiPrFbOyjGvdMIbyRJQsq28lnxyxbH1CE956vr5cumyu9OeFUoM+UnmqXMeMOUZnb3u2enTsEdpy483xemnDft5kDDasfxQifuUsSkQ5wvV9C+AyU31w5MulnwFigXG+WyhHAAAAp5AIBgAAAKtd/dqfNW2mtLrx5z16r60L9v6bRvUcZTQuAAAAAAAAAAAAwCYOvz8H8VHi3STdxwcTxholPvWl9/bBhBGqXOsY5aNkfSyr9w6lLaKiS/HLzjTogNLiKFWXYWaW23OLlj932zT7dC4/RrrDWqYjgBWPsPYRw/pnlbaIrhvlWHSB69/H8D5m6BH5/17TO9DFzV06Vz+5/yc67t/nabWk3TtJzw+QHtjzj/FLAlv3Z9Etq2k7DdgzumWGobpn9t9HuV8q71R8DAP2Km3ZA/ct7f+bVHULZj7F9ueDf5T/730mFjffQo04KZrl5BRCve23a/DzzKVv47KGHx/dMl0w8IemI8iu0H5yyMH+px16WGHzttkwv/tmG8azluu6oekIkmHd48wst5TxUDbtnVcb8pPi5luoqMYgOYXQt9SvH/w8cxl5ivc5+MfRLRN26TMp/99T5eEst269lj87ca6+QH13jm5ZZZXep/E+EaEr79j8/dqHGAsjWo6P45vOp9SOMBsHHOK3zkfRNhxvf4ADSASDXaZ82fLnPhOlXtvk/5/agJNkMk9U7fmVtPHvWv597B/y//+mV/pYSIHJb0OPkLaf3vJ3m9+R/3/67Z77bzlPxmX8vrqntNOrzT+P/IW07WMtJ59wW/4Y8p3s8XNCcLu/S2OukbZ+UNr1vZZ/2+C89v+/vCrXwtv/30z995B2fEna61tp3E35p53wJx8zLHD77/yGNO6P0o6vSONvkfZbLv3gGWmz66Q9ZhY2r0LUrtv8fc8tpM6Dc0yYWZ5RPCY8wGVsckVw8wrbNn+Ttrqv5e/G/TH//4y52seMU4U93r1DP2nS8y1/1zquQvi9OLDbh83f14/22kCLGP6a//9reuULov3ljz5LmvBnafz/SVM+b/m3/ntKndfO//+dBvhYto/tUD9a2vl1ac9ZXjz5rP3T9udXqM2u8/r+HV+Wxt4g/XCx9/24m6Rd3pIqOwe2qA/nfKgJf5yg216/TSmldGF36YG1pHE1knpv62MOjvVH6/48nPlms+t73j7FphO5u33Q8uf1zmj/fyo65viDz35lz1ktf9713ZY/b3hB+/MoZayx1g+k7f4hbXKZN8bIlKqQNrww///33aX9ZfipSxUdpN0/lvb41NvXFK3IEzgD95W2eUSa+B9p7I1eWez6ntfXTHw6dyJ60Ead2v40Yb4OJYwExsyk/rBf5bLVvd74YNRp4S4nSpv/pWVSxZ6z2iaGt3dsuPElPhaUZ9vsM0cafY53XLb9423jy6fPD/L8scD6Nu5GadJz3vHxZtfnn9ZXIliB9XGvb7yxxsSnpW0flfZb6vWfm10v/XBRYfMqxPCMffPOb+SeLvIbYwJsz1HddNSxv7TLO9KeX0ezvLjot1vLn8fekH/6kSe3P0+/+4M9Z0m7vO21u/YEde6lSdcNvXHBto95xzx7fOodg21xpzdWCfNmvc5Dm7/f9tH2pw91/xpC39LiZriQxwYbXuDtO9o7b4FojL8l/9/9nGct1LYPS+Nv9Y49x93k7b8nzfD6st0+lFIhXZrq0Kf5+5pePpORIzh/EGR/sf7Z4cw3mz1nSTv9L7rjMpiz5xfS1g94+96xN4a3nPXObP5+34XhLcePsMfxqZBfyjVgb++61eQXw10OYiSjzrc+1mgxWdSJYLx+GAgDr4aEXTr2bflz93HeAds3T5mJp6aPd6fhq79o/t06R0ovHJX7f5ruksmn0AO0+g3aXqwdfID07IG5/6eyrrBltNZ7+5ZPsKlbT+o7ueU0Q34kPZcn2asy1xO5fCqrzP2ElN7bS/pVafP3K5VqPtgdepg04/Dc05bX+JlhYcsvr5aGNiZ0dNvY++y5ufcVlW5jfU7o2ImTMod2g50Gt717d+hPpRl5LraVd/Ax41RhA/ueW0o9xrX8Xb898v9P3iQsn7pknJDvPr5t/W/vyUbVPUpbfqpMGpKjv+u5ubd93ru8tGX4bT/1o73PIT+WnstzN3ypfXA2ZeVe3y9J3TZp/mz6PiD3vX2ffvrQT7Vg+QINqB2gu/a5SxP+07jNu4/L/89Nwj4ZGvQyWswr5Nir6pr3JzZIlUtd1mn5u97bSR/eIC3/Lrzldsh4gl1VV6l2eKsYSnwyqR9rTfK+JK9//fa/3vddN5KGHCT97/Tc/+un/vmto52HeJ+dBuWfriK4ZM81UimpX+Md7b229D5rerRMSI+CrwtRLp+YCjn28uq24wPX1Q6TqrtJ71/l/dyht7T2wdKb5zZP096xoZ8T//naaVVXafTZ2f82eH/p2TzJEFX17S/br7JKqUfjk7iHHia9eHTuaX31OwXWx5qebRPM1mrnKSOByIizQ9/ck0UtyPFHZW1w82pPHU8qKNjQw6QvM5K01zlCeuHI3NP7erqOz/rToXfLsVLUmsYEmQbtF/5yM9uEn/N7jA1yKytv3nfAvLUPkZ4/NPffy3PdZFOCskpv7CQ1H3/2GOt9RaXnVv6mi+L8QZBtrsWxS8ixV3fzvhA/qVTLPIyqrt4N8WErr27+PsAbSq0Udt+Sed0KKFSp15CDFMl+GEgeh66AI77aSUCI/O7aVstz+bV3OeVYp8x1DX3Ha7BcY7lNTXK4PKkLEcnXn0S1DfLEEEg9KHYe1MFMy1ct16n/OlW/n/F7SdKWA7fUXfvcpb5dLLr4Ghb6owDZUJbFxND6Tjgb1qO1sPvSJKP87JMlWT429Twu6xE2m16bEZLY1OmYcn37OBm/RTE7WX4AokH/AIdZtX+zKRYgAr7bXwRtw6q+AIgnEsFgXt7O3kAWcMnJUCHcAV1MHPn+x8+rIdvOsPAYQk3+KKVuhDnACPDpHDbxW59cu4POqYO9kPqjQrdZtunbm0fep6wUsQ2K6hMDjqHlzIv/11Dbj1t9zfvfv6/9791fr87yXkt8yuan6PwdzldFmyf3+V0vh/sjF/cTJcm2viUkQhV1IqGIvi3oGELpDwKuS6H2pS5w7PVPLSStXwlKidsljKdj+V947j+ZPuHqyn7Od7/s8KshE9F3J4nJPicbB+tXwf2jw2MDV/piRCO29cGi8wdBlnGLviqu2w7xZdP4gONwJI3P/QevhgRigUQwOMCmgaEPoZzsDyshzbUYXGDbidegWHTixMnyC0DQCaHNExU60yLmkYT+KIh9lQ3lFL10Oq1bXrtFP//7z7V45WL16NhDt+5xq3ZZd5fs/+C7LbjcH7mx7QJjw0UHG2JowdJEsKTVzdasqycFcDl2p1maCGaczbHlYlPMNsWCUAVx006p80R+Tpeny7EjeDGtD0k4f+B0PwTEHe0TFrNq/2FTLEB8kAgGC9iW6GVbPGEo5olgQYfAqyHjw+XydDl2l5i+u6SdGIzWg2TXwU/nfaqjHj5K//zon5KkbQdvq9v2vE39avsZjsyEZNeFYNlQlkG8GtJCVj0RJ2YYn1oqrtslrusVNJ/l5HT7dTl22M/F+mVRzE73LQDCRf8Al1lUf9nXInF4NSSQJCSCwW5WZST7FdGr2ML4n5YzsCAGQ/MuRVzvwLXpDjoXyy8QlryqtpjXp9nwysNQ642lT+6xuK2sblita168Rmc8foYWr1ys6vJqnbPtOTp585NVXlbezn/7XK8o1j+sZVi87cJRzJMG4xhD5qIDWrYN/W+suLz+LsduShBlZvDYwOp9ic2x5WJRzFZvW5gV1yeU28zl8nQ5dgQvrvXBovMHiXwKLJBwjNthNYvqJ20FCAWJYEAi5ci0jjQDmyfwxAflifZY/gQZo3efWLD+EXv727d1+EOH67kvnpMkbTNoG924240a1n2Y4cgM4y6oANlQlkXE0KYOWHgSJN+JGepwiSg/RKmU+mZh32Qc7RfIirFBiSg/IFT0UQDY1wI5RNE2aH9A2EgEgwXydfZxPcls+C5NXwe6tu+ESykf0+sWs3qdWZ9cu4PO+pM+UT3RKOxysCERrCy8GEqp95G3H3NWrF6hi/57kX7zn99oxeoV6lLVRZf84BIdsekRKkvl2z7Fcqw/QktBtStnY7D0SYNW9OcGhdpPJ6D8XBTJWNHAvsT0GNiZMY9Fr81oIUnHQyiIdU8od7F+FRozYwPAXZltzLUniifnXBJCZGocaNX406ZYgAj4bX+RtNOI98NAApEIBgTN18FXodOE9Uq4sOeXxJ13XF/FYNGrIZ0svyKlougHCkwEi+o1sfn+x7ZX1QbGhn47HC9++aIOe+gwvfHNG5KkXdfdVdftcp361/YvfGY2vaqWVzsExIb1tSGGMMS3XzHD5fV3OXaHGU3KsHmb2xxbDlaNJW2KBe6h/gTKqr6hQC7HjuDFtj4k4fwBAHvR7mExm/b9NsUCxAiJYDDPqjsApGTcBZBrHROSgR1qnYtxueXkcptxOXaXWP4qMV4NGZo5S+fozCfO1PUvXa+00urRsYeu2ukq7bfefkpxgNdKvOtCUYpumzaUZTEx2BB3O3g1ZHgoP/tE8tRUU+K6XgGz6m7psLgcexK4Pl52sH7Z1J5tigWIJYfbGP0DnGZR/aUtIXH8XgOOoG3Q/oDQkQgGC7T3asiIdwZRvMqn4IvfQT8JyE8iWNgxlMrhV0M6mfzgtz459ih1lwaboT0FK4L+KO9r/3Jsg7zbJqo+sYB5F1uXwnw1pMG+ZnXDat3w8g06899nas7SOZKkH43+ka7Y8Qr16NijxLn7XK8o1j+sVzs4f9GvQFnLMeL9vA0xhPF6j8DbQYiv2XWCw69/cnL8aYMoXvNq4olgpturK/XRopPkmUIbfyAZImx/Lh1vr5GkV0O60hcjGjGtD35vZIlkrMz+G/DYVH/Z1yJp/Nb5qF8NCSAMJILBbk5esAjhZL8Nr0GzIYao5l2KUBJvLOC3vJ07ceKSkJIxjSemFvP/cUpMDZOZuJ789Emd8I8T9Nqs1yRJ6/daX1fvdLW2GbxNQEtIwKsdbN3HhSboJCxXYwhj2RaMB+PE6fV3OXaXGTw2sLm+2hxbTjbFbFMscI6T7c9mLpeny7EjeHGtDxadP6D/BZKHdg+rUT+BuCMRDBZoJ+s38jsIWy8vhlnJucrUybs1i8GrIQPldL1xOXaXlPiEwtAPmoOoBy6/wi4Yr89+Xaf+61Q99uFjkqT6mnqdt915OnrM0aooY8jZLqf70mwMtisbyrKYGNr8jwXr0YZFT8SJHcrPSk60yyLY0E86waa7pUNCXbCc69vHxfhtitmmWIA4crmNuRw7Es+q8adNsQAR8Ps0zEjaKe0PCBtX5WBeuzsU04lgBbLlVWwlvxrS9ifwlMD4wYal5ZKXRa+GTOyj1MNqg1E8oTDPq8Rytsc89SroJxQG0ifYmAgWTV/z6bxPdda/z9Jtr9+mtNKqLKvUEZscoV9v9+sAXgOZRWyfUJjgV0PmWt+i22Yx/xd0mZf4asjABP1EsGL68zgJsW2GXn5J61eCkFIkx4ah7a9sTtx0pD5adZI8U1KPhxCMKNufg/Wr0PYc5jFH2H0LTylBptjWB7/7b8fOHyTi2AvxZVH95TgciWPRzU7sy4DQkQgGy7k4UIrLq9hsjCGqeZfC5MWeMFmUeOFk+QUgtNezRtAfBb7NLOuPbK2TIcf13ZLvdP7T5+val67VitUrJEk/XO+H+s12v9Gw7sNCXHISXu1gaZ0KS7ZyjLpd2RBDy4UHNBsb+t84cXj9bd1XxZ7J18bbvM1tji0Xi2KmPaMk1J9guVyeLseO4MW0PsT2RjIAbqDdw2bUTyDuSASDBSzL+k1EFjKvhgxNIk/KO1xvbK/ztsfnWxFPpIh03Q2Ws4Pb+KuFX+mqGVfp2peu1YLlCyRJ2w/ZXhdNvEhj+o4xHJ3L3KsL+ZncH9pQlrY8ESxg+Z4I5kL8VqP87BTT7eLg+MMMi+6WDo3LsSeB4+cXnOxrbIrZpliAOHK5jbkcO2BT/bUpFiAKfp+GyashgTggEQwWyNfZmzjpVerOJ6i7vn2+hiLnIop5dUWedQ/taURFKmnepl/F5uDJXF6FYkipj6kP4Ql1Qb8a0opX1UbR74e17HyC7WvS6bSunHGlTv3XqVq+erkkaaM+G+miiRfpB2v/QKnIEmEteiJYWK92iEVScSF1O9v6llAGRe2XLIghlDoQ5RPBbN+nBiDUtskrKaxU6jg3lKezBrFsw+3Vmf2cTSfJM/FqKZQg0vbnYv0qNGaHxwbO9MWIRGzrg9/9t2tPFHexfwUa2TT+5DXMSBq/5x4jaacW9QVATJEIBrRh48l+G16DZkMMceFiuVgUc6IOoEpNCohJf9R63W1LTLVWcOv8zeJvdOiDh+rRDx6VJG0xYAudvPnJ2m34birLm+gXApte7cCrIQNiw/raEENrAcTEqyED5vL6uxy7KUGUmcnXxptIMPM9kwDmETGrxpI2xQL3UH8CZVXfUCiXY0fw4lofYnojGQBH0O4BAOaQCAbzbLoDQLIvnlAU8USwOAl1GydxcO9yvbE89iT0R8U8oTCyGCJZuMFl+zP9o+k66IGDNGvRLFWXV+uyyZfpmDHHRPgEsKSwvy64w4ayTOCrIZOwzwoT5WepuG6XuK5XwPy2S6fbr8uxw34O1i+b2rNNsQBx5HIbczl2wKrxgU2xAFGw6KnX7MuA0JEIBrulUnJvMBbGXd8WPI3LuifwWJqA4GednUyesClmm2KJUlht0IX+KOxXQ5YqZeeBS4l9zcrVK3XmE2fq4mcvliSN6jlKd+59p0b3Hh1EdCVIwh29CevnstbViMeAOWMwxcVXQyaBw+vv5PgzDmx9NaRhNseWk0UxO1l+sAf1J1gul6fLsSN4Ma0PNj1RPK5lDCAP2j1sRv0E4o5EMFjAwovnVghzJ5z0Mk/6+gfMxgQYv1yOPTZs2AYGY7C0Dn405yMdcN8BevGrFyVJR296tC6dfKk6VnY0HFmc2VkXnGRFu7IhhhDkvUAS03WODOVnp5huFyv6SRf4LSeXy9Pl2GE9J/sam2K2KRYgjlxuYy7HDthUf22KBYiA7/F5FG2D9geEjUQwWCBfZ28iI7nUnU9Ad31nXmgL+mlcuXb2eQcBFj6Bp2imXw3pYKa9VRd+gyw/2webfh/Vm4vPvqaQE/SBPx3QT38UwBPBwqzDJd05aro/auv212/XMY8co4UrFqq+pl5/3P2P2mvkXgHHVoqYPhEss87H4kkfhdTtLOsbebsKOIaSL3xa+kSwfK+GtH6fGoAw22boF8vj0K8YUOp2CeXprL4XnudvpturI/Ux73g013RRCGn8AQuF0FYiHWc6WL8KbROhlmfI5ReLYw4EJrb1we94KIL1D7SMHexfgSY2jT/DjiW2fSvc5fP8cyTt1KK+AIipfGfys3r66ae12267qW/fvkqlUnrggQda/D2dTuuss87SWmutpQ4dOmjixIn64IMPgooXMKDAwVpcXsXWZj1sSwSzVUwTwWyKOakHUKG9ntXB/qioOpDEelPYOi9cvlAHP3Cwfnz/j7VwxUJtNXAr/e/o/1mWBCa7Xu0Q2jKSVl9tWF8bYghB4HU0puXkm8vr73LshgTyyliTr423eZvbHFsONh2D2BQLwhXKtqb+BMvl8nQ5dgQvpvXBpvMHcS1jAHnQ7mEz6icQdwUngi1evFgbbrihrrnmmqx/v/jii3XllVfq+uuv14wZM9SpUydNnjxZy5YtKzlYxFR7mcWR3yHQenlxzErOtU5xXNcsbLrrJBZcLk/bY7c9vgDkbI8RrnsgfUKx8zC/jdPptO556x6NunaU/vS/P6ksVaZztjlHTxz8hAbWDTQdXoKYrwv2cbddFReD42NQxlclovzs5Hi7zCku6xE2m16bERaXY08A5/etLsZvUczOb3/Aci63MZdjB2za11oVCxAFi45x2ZcBoSv41ZA77bSTdtppp6x/S6fTuuKKK3TmmWdqjz32kCT96U9/Uu/evfXAAw9o//33Ly1axFSezj6Vyv/3METxKp+C7zIK+uk3RSRehPY0oiLZ+io2P3E5eQe36cfEZkrQq1D8vo4mJ4f7o6BfDRnq65FK2FeFWQd9bNvvVktH37Ov7nvnPknSkPoh+tOef9KWA7cML66SJeDVkEm7IyvXU3eKbR85/y9PuQby5B8/MeT7n4aMRVv6akirXzUXBV7/lDxRvOY1pG1j/DUPeThTH/3umzkeQlga2p+kYBG2PyfrV6ExOzw2SNoxB9qRxDccRH0MzqshAY9N9ZfjcCSM7/PPvBoSiIOCnwiWz8zRCC0AAGizSURBVCeffKJZs2Zp4sSJa35XV1encePG6bn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            "text/plain": [
              "<Figure size 3000x2000 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots(figsize=[30, 20])\n",
        "ax.plot(deltas, label=\"Deltas\", color=\"orange\")\n",
        "ax2 = ax.twinx()\n",
        "ax2.plot(series, label=\"Series\", color=\"green\")\n",
        "\n",
        "plt.title(\"The Sequence and Deltas\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bxeb4lTFOOsC",
        "outputId": "4e34a37e-6cc2-4e58-b191-6a3c589149e3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Counts of mod 10:  [3016, 3228, 2624, 2704, 3244, 3481, 3147, 2893, 2708, 2955]\n",
            "\n",
            "Counts of mod 12:  [0, 3722, 3424, 0, 4035, 3823, 0, 3847, 3884, 0, 3396, 3869]\n",
            "\n",
            "Counts of mod 16:  [2023, 1791, 1713, 2059, 1959, 1923, 1601, 1755, 1977, 1784, 1892, 2104, 1960, 2047, 1614, 1798]\n"
          ]
        }
      ],
      "source": [
        "mod10, counts10 = modN(series, 10)\n",
        "mod12, counts12 = modN(series, 12)\n",
        "mod16, counts16 = modN(series, 16)\n",
        "\n",
        "print(\"\\nCounts of mod 10: \", counts10)\n",
        "print(\"\\nCounts of mod 12: \", counts12)\n",
        "print(\"\\nCounts of mod 16: \", counts16)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xOOqIPhCmI_M"
      },
      "source": [
        "- Computed `mod 10` because, well, decimal, and also the duodecimal and hexadecimal bases because they're my favourites\n",
        "- Modulo 12 exhibits interesting behaviour, there are no numbers in the sequence that are `(2, 5, 6, 9) mod 12`\n",
        "- Consistently, there seem to be slightly more odd numbers than there are even numbers (found by taking base 2)\n",
        "- Something is up with 3, taking base 3, 6, 9, 12 give zeroes in the `counts` arrays.\n",
        "- There are $b/3$ zeroes in the `counts` array where $b$ is the base."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 641
        },
        "id": "6TJJ_CscJo98",
        "outputId": "0cc2759c-3b3d-47d3-94ac-b478152d0c31"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1400x700 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(14, 7))\n",
        "\n",
        "plt.plot(counts12)\n",
        "\n",
        "plt.title('Mod-12')\n",
        "plt.xlabel('Numbers')\n",
        "plt.xticks(np.arange(0,13,step=1))\n",
        "plt.ylabel('Counts')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E59Y_v7CJwZW",
        "outputId": "38536bc6-7b9b-4c9a-def2-005e4f80cae9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
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4.0, 2.0, 6.0]\n",
            "[4273, 4261, 4292, 4301, 4279, 4326, 4268]\n"
          ]
        }
      ],
      "source": [
        "m, c = modN(series,7)\n",
        "print(m)\n",
        "print(c)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RjFNOPeeLHSl"
      },
      "source": [
        "- The big question now is if I can prove why this happens, I'll work this out on paper and see what I come up with.\n",
        "\n",
        "To Be Continued..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rzxekpucAzU5"
      },
      "source": [
        "$$s(n) = s(n - 1) + σ_d(s(n-1))$$\n",
        "\n",
        "$$S(n) = 1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, \\dots$$\n",
        "\n",
        "We need to do three things:\n",
        "\n",
        "1. Broadly examine the behaviour of the sequence under $\\mod{k}$ where $k≡0\\pmod{3}$\n",
        "2. Prove that $\\nexists s_i:s_i≡0\\pmod{k}$\n",
        "3. Prove that $\\nexists s_i:s_i≡r\\pmod{k}$ where $r≡0\\pmod{3}$\n",
        "4. Prove that there are no zeroes in the counts array for the other numbers(rewrite this formally)\n",
        "\n",
        "---\n",
        "\n",
        "Examples:\n",
        "\n",
        "$$S ≡ 1, 2, 4, 2, 4, 5, 4, 2, 1, 2, 4, 5,…\\pmod{6}$$\n",
        "$$S ≡ 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5,…\\pmod{9}$$\n",
        "\n",
        "there are no $0\\pmod{6},3\\pmod{6},0\\pmod{9},3\\pmod{9},$ or $6\\pmod{9}$\n",
        "\n",
        "This sort of behaviour can be verified empirically with larger numbers and bases. (In the code above)\n",
        "\n",
        "---\n",
        "\n",
        "Consider $k=3,$ we can show (via the divisibility test of three method) that if $a=b\\pmod{3},$ then $\\sigma_d(a)=b\\pmod{3}.$ This means we will never get a term that is $0\\pmod{3}$ starting with a term that is $1\\pmod{3}$. $\\blacksquare$"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [
        "nO4U9fWoa0BI",
        "dqhKIOnIGsIc"
      ],
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}