assignment2_ee19b025.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "assignment2_ee19b025.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/antonson-j1/nothing-just-my-personal/blob/master/assignment2_ee19b025.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bXzoxhKVArPQ"
      },
      "source": [
        "# ***EE4371 Assignment-2 by J Antonson (ee19b025)***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WZeD_gvhvWa_"
      },
      "source": [
        "# **Problem 1**\n",
        "![Code_AZGRc7NrPA.png](data:image/png;base64,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)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nFF-9yP_g4Bw"
      },
      "source": [
        "## ***Solution:***\n",
        "- $4nlog(n) + 2n = O(nlog(n))$ <br>\n",
        "- $2^{10}   \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;= O(1)$ <br>\n",
        "- $2^{log(n)}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;=O(n)$ <br>\n",
        "- $3n + 100logn\\;\\; = O(n)$ <br>\n",
        "- $4n \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;= O(n)$ <br>\n",
        "- $2^{n}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;= O(2^{n})$ <br>\n",
        "- $n^{2}+10n\\;\\;\\;\\;\\;\\;\\;\\;\\;= O(n^{2})$ <br>\n",
        "- $n^{3}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;= O(n^{3})$ <br>\n",
        "- $nlog(n)\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;= O(nlog(n))$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tvrY1QWKrfVl"
      },
      "source": [
        "## ***Answer:***\n",
        "$2^{n} > n^{3} > n^{2}+10n > 4nlog(n) + 2n > nlog(n) > 4n > 3n+log(n) > 2^{log(n)} > 2^{10} $\n",
        "\n",
        "<br> <br> <br> <br>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S8HkUhiCtaFb"
      },
      "source": [
        "# **Problem 2**\n",
        "![Code_XPg93ItIaG (2).png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABHIAAAF2CAYAAAAC4r9dAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAhdEVYdENyZWF0aW9uIFRpbWUAMjAyMDoxMDowMiAwMToxOTo0NQ78R8sAAMWpSURBVHhe7N1/aFNn/wf8tw/7QoV9ofLsC6ewgREHa5lgyj0w4fYPU3qDEW8wxYEp3uDiBi5usKUOtnb+4VJvcKk3uNbB1k6YJMKkESaNPJPGP7xJBEciOJqB0ggTElBoYEIDE85znZMrP3vyq0m1ad+vkXl6kpOcH9e5fnzOda6zRRVARERERERERETr3v8j/yUiIiIiIiIionWOgRwiIiIiIiIiog7BQA4RERERERERUYdgIIeIiIiIiIiIqEMwkENERERERERE1CEYyCEiIiIiIiIi6hAM5BARERERERERdQgGcoiIiIiIiIiIOgQDOUREREREREREHYKBHCIiIiIiIiKiDsFADhERERERERFRh2Ag5yXIppNIPpV/dKQsMo/iiD7Kyr/bKJtB8lFa/EKnWZt9ks0kkXiYkX8Z0X43gWStjxARrcbzLNKPksg8l3/TutFJ9YjOr/MQEdHLUL8dtP5o65x8/GJasgzkvAhPQxj5xwAGbH3o2bIFW3t2YMe3UflmJ8kgcW0cQ29uxTZTP6wWFwKP5FstiH97AANi/1jf3IItW7dhh8mN4GP55rrX7n2SRuhTkVb+YcUOLa1s24G+wzOIy3d1aZmeLDuwZYv2u30YulT2CSKiVUlfHynmx/+zFT2mHZj6Vb5JL08n1SM2TJ2HiIherCQCH9RpB607cUz9s3ydd3waFC26tddgICeNwLuiUidWrurrw5Bo0pKh1+zwBiYx+r4d/XJWx3kUxIitF32OSSTesKFXEfPSAQyfa/24m9+fxfQ5N4YsZjmnQ6zJPlFgPzMN34khWHbLWW/2oEdO6hSRnr7zwf2uBfk9ZlLKPtFZ0nGE7yQ25VX/9L0wor9vvpxzs253fRkk74QRf0FXcowo+73wXxjFyUN2OaeWl7++m0Yn1SM2Qp2nbcQ5cmMKJ/+ZC2r17DqA8ZvM+2j9yzwMYerDA+jrEW28nj4c+Crccn2fqD4TnOfrtIPWHTPcgYp1fkEaDOQocP6kYjkZg/9zi5yXY/l8FgupZagX7eiW82ilrtd6YTsyDNsLPsDtkL03gQOWIUTensLicgoL4XlxzFWofy5i4TNb68f9lS6YdjvgOmyVM9a/Nd0nr5pgPuTBSYf820DXdjMcn5zEkPy7Yz2cwYGefgxY+tD76eYKBicvHUCPeQDW3l6cvLF5tnyzbnd9WYS/6MUOywD637Bh6jc5+0UT+bHylg1OR738eJ2s7ybSSfWITq7ztM2zOKbe7Yf16xTsF2NIqUuY2RvC2D/cCL6IS7XtlE0jfm0GYx8OYWBXT+Eibs+uAQx9OIXQGgTmM/cCGPmsjVe1f53A8NdhpHmraB1ZxL8ZQv/eCaQOziAm6rZL39kQOj0A99V1nnCfZ5C4IdOp3ms93+GgB322ARz/bAqBO2s7fAPTbRs00A5ad/R1dmG4PEyy5pq6tUprPDo/OInifnXg5IcO9Cpd8m+qrQc9b8rJTvEsCu+xEYS2+zB1wQFT6aEWibZ3e+PHPlsn5+z+vw7pVdLGfbLpPU0jJCfTtxNIyunNIP24sOWI/F57y+udO+vG82zdClIz2725ZJB+mK/6RZF42QNfvW4qKeuNrLP1rdQxJ02z1lE9ou4+7sA6T7uIesL4P+04+YcLwZ+9sL8u6gXZBCI3AWWfFSatB28neJ5G+Oth9JnMGL6aQf8HPszeTUFVVah/LSPyvROm37040LsN1o+DSLajsfksgcCnA7CeTcH+qQNt21V/c2GkawrW3iFM/cqLCMayiP77AOwfp+C6NgfvfgVdYl7irii3FRusb67XhJtB/NJxDLyxDX32cSR6huC9EsOylk6113ICs6dEifarVzS0e7D1zSFM3GpzUIrpduOrW8ftxrYX3ZQVCbw5f/hVcSqo2qKAV43I2dSIlOo/LPfdmc7Yc4s/2PX1dQRScs5qLKnzn1vqb3PUK9OVQ/X/IeetQ+3ZJ/VFzsi0ctgvUo6RiOrV99far8vaWVRnj5lUUUFQPaFO3YZVSs6qrp1QlX0eda5qem/w3FkPnsyro3ugeqPy72oa2u7NaVnkgTYFqunwpBoTNdCXqqSsr3ZM19X6llhOTKtOZX2XI6u3PuoRje3jzqvztMeyKL9Fvg2zOnp7HZ0YTVq6O6k6RF4Nxa767i7JuQb+FHURkfdrx1k56helegtkOWIR6aXGL7Zk6baWbymq87sFcaSolJanW8RxNH8Z6Zx982dM9R1UcvlMvbQqUlXkrE1VtM+Kl+Xz+fakM6bbNVG/HfQCNVjHfdHr3Pxgx6+beM/zphFH8IJ29dwG+zurjS2nEXyvHwP/3igDHbZjnzSm69V6YwZ1oavju62b4PhhEWpqHr796/VKzxrZ7sD0AxWpsA/21+W8Mh107jwO4rhlAON35N+11N3uzatrzyjmUyoWf3LD3AEd+9bj+mZ/ncCBfccRWOd3AHQy7uM67k3Bc1rk2/vdcP29M3voJq8cR/87JxF85oQ/OgfP32rcMP6qBZ4zHr0HQvqyBxPXV9lrQOvFdHAAM2/64f/SsmbDNXT/fRRz104i+YENrivsFVoUx9QnY4jCDve/LKKG2QFkz7eR61pmZIH32mzttCpSleXzOQTP5O5/if57APavoq3dasV0u/E1U8d9wfjUKqruYQyhe9pEL3pe0+esQhKJSxsow2nLPmlMj2KSU9Vs4m7rm0IHnTuPE5h5KKeJXqLMgwjCDDCsKe7jWtIInB0RjWHAcfQA6pXi61Hy8jCszhlRAlngu+GHc7t8o4auwSG49Kk0pr6dXcVt0kkEPnRg7JEH/ovONd9vXXs8mDhjQsA5LBpnG/U2zOakr3gxojVUDw/jwM7cvPUti+h/PBiTt0gpp7zw7Gkk/NQFyyfis/LaYfS0AyOrDT4y3a4pZXvtG7xfmHVcx2Ugh6p7mkZYn+jBtlWHmE0wHZaTG0Fb9gmtX1kkroxg6MMZJJ7JWS9NB507dcdTIXoxFBP7DK817uPqsjd98FzVplwYHuy8XqaZ6ydh/VcAWtPY8aMfnoZ7/ZrQly+vboQQfSSnG5S8PILhy2nYz7hhe1XOXFOiMX9iDG4lirETXkRfenn/kj0Lw/dpUJ90HbG3b3yXtfTQD6/W801nxojT1ngvoldtGP403+s9jamzfiTkX81gul1bW1+REy/bOq7jbtHur5LTDYpifIsVY9rkIT8WgxURyOdZZJ5pUcIsUr/HEL8rTo29bjh3y9PrWRLx21FEfltA4m4U2e12WPY5MLTf1HJ3tOxTbSA57VGoKSS1333LBqt9CM49dbIkbTT+G3MIP0wgcTOJrj0NLqfRRki/HUL419z2pF6zwNrbB+shByza4HZltMe492BYK+TPRKB+KYe2zorvuBdG5HYSiUQIyS7xHe9Y4Thkh6nlYEEW6XshzIntSiYjiD7tgeUd0UDcaYNt0AyTUcaTjSNwReyH5BSGvtLCFi5Mhp3ozb2r69llQ2+9HimPoggmUoj9ZwjjN8Xf709i/kjpt4iT9I1+WHbKjbwzji0WLWU54P9jFk5520X2URzhaETsG3F872RhEuvdv7eR4yPS4u8RhG7GkXqSROR3oHevFQcOO2FptpRa9T5Zxf6X0leG0OMUBethP1I/OQ0K1mJ6cgRSmD1SZ6PE+RHWzw+RzsQ+wW47et/ogXnQDutb3RUFYBKhr4NVCrZeOE6JtCn/0onvjmdNMJel+Qyil2YQeSr/LNCWt2FbpjyfWH7HBdeekgQvzgv9I1hCMh5H7NcUTEdEYZlPF9pv3o4g0uR5m74X1I9H4fpLV49IF+J47O5G6pIL1vdylVjL2RjCn5sbrxgIue/WtkfmBSZxrEWas/2tF935Aim/XdkUEtp2/baM/mMuWErTTqPnjthU/bHtmSRicfG7j00Y/shWnlYKebK2H8W++q0iTzaSTyuFc84C26Eh2PPnaonkf0U6ScUw8e64HuR0XZyH863cezlbYTJbYOpqYLtXaP78yWYyYinxbzqh75MErHAfkcdR7Ivkb2FEbyewkBDfJ9KsXRz7mnntc1E+XBflg1jnyJ0UevZYYRLH1WqxwSLOm7Z4JvZN2XHsgeN9sU75Q7SG5Wrm97DII7XyJ4rEq2axP0R6FXmCGUEMvTEs/g94oypG9+Q+r6u3vkbK0lRuP/b2WjF0yIKaz0toOC1mRTkewtKjEAY+nBF/2zD60yhspekruw19+80r81I9XYhyXMsXniQQetpdP12sUC2/03TD+r5I66XfpdU7HnXBXJGGktcnEBRlVbnS5degHqGlH7GPww8zSIllM69VSz/N7uOXuK41zxntkeB+THwrytZ9U/B/0lw+b0hLQ7cncNI5hpBWgBybxdIPjrrn37ryKIBhy3Dulrn901gMucrL+ZpKjrWwIs+o5WkIJ3cdwFTajukHc3C9sN4g2pP3TBj4dxqW8zFERDpou0L7QpRhpfWCQRvsb5vQtaKhKtJtruIjzjORbkW5k9o+DPc+eUbdCWDmu0lEXh3D5AVxvuhzW5N9FMbEx8MY029PcmH2yTQcNcvl9SH+n370fyrqsrpRaKNGyhymMf8dw5a94/IPM3yiLGs8cCls5HSbL3cbai8Ia5TfGrWDso/jep0lKcvablEfPHBQlDmNBH2aPh+bqOPKzD761RZYT4uJ0rabXseoqHua+2FdTXu0kj5STlOKA6waDuSTmtMHstTfly9HYFFdis+q3iO9hQGmKl+i0bT6wZv+XFD9nxQHrzLtsam2t+XAV9rfx6bVhT/lZ8ssqZFzDlVkhIXPlr7ECSI/Z2zpti83EJzBstpLHwCy7HfLB/5bejCnTp6wV/197PGptdegtsJAdfr3KWrvPrFf9phKfsOkOi7EVgzMtXBBG6Qv/5mVr8YGs0ups0eNly+89njVSOn+KR3sOJlSIwGv6iw5juUvRXX/XH1IseWEX/Xsyy9rUi2DNrVXyS9rUl0/NDdY2Gr2yWr3f14q4Mh9ruqAWcX0VHOw478W1dmS8wM7LaqtbH/kBp6dTcrP65bUheCk6irsQ+2lqLb3fao/tLBinRe/s6k4Mbdi/tL9OdV/zqUPnpf7HZc6GYypqT/mVHflsa0cDPOur2wdtZf39rKaCk+q7v2l+7H0pajOn6rsi6WSAfHEPnCd8qm+U2Ld5DFS3u4V56JIK4fdqueEQ7Xsn1QX5KL1LapzH8k0stOuur8s/+7SbUv97F65XWWDpzV+7iz+WJl/GQxAL9JhYT3kq2p6qchLy18G51xqVnUafrb40gb/0861+ttdbnXnT0qde78ibYjzZ/FJTJ0941zx+4WX2J+Gg/UmRTqVg3ia9rvV0XM+1XPMUtjn9Qa9a1RM5C/lx7FiENm1KFfF+TB5uNp5JLZX7G9RPdSnK7ez7vqWqV3O5o/jivVsNi3e9RbW1/gl8gaxzyqVleNKr8gbS7ZNsamjv1TmatWIvOm2X/VW7FPTYY86reV5FRu4/ItHxe6VZfxyMqLO/uBR7fm0utOhegPz6mJhNdpZjyg/Nsrb5eeYsm9UnX8iP6ppeh+/xHX9IzeoeuG7xUvP97QBK8vKNYvqvVv1LKlveV71lPzGipdBuVhbSR17ta9VDbK5pM6dyO8XRfX80uw+WVSnB4vr0EzeGDsvy87B6aYGSl7+I6L6z7jK08Hbovy9MK+m/pIfqkM/D7VlFbc6V5p+WrYk8smSfE/PW2zlZbE4tydXDMwr6ilGdSORH05rD4YozK9R12nIsjp/quQ3VrzE/mgq4Zac66t+NfMAnYp60mrSfNnDe1CzTWFkQ6bbVbUXhDXKb0vbQQv3RX2nWp1lp0u0G+VChlZ5PjZRx80rHex4MaUd6xp1zzYcv/YHcqTl+KRql59TFEUkUqfqueBX58Lz6rz+mlWnT5XuVFGRlss2pXS0/INedb5khZZEQzBfGVJWFKaLqv+olrgU1X5WnDzyKCyLCv+0Pj+3TtUylcWfXHLdRSX0nKhk5QMSTxbU2S+LJ4EiKtJFFRmdOEEcJ0ZFJS+/T+bVuYC3pPFiU6cfyEWblB95vrB9pZnDkqgg5xud4lWZCAsKgZWS/fDXsrrcYEaTU16RK1heUpcqf7Twe9pLa7i5VqSZyfdLMphT84brXX3bxYl83i6Xrx0IqqrBfdKO/d+eQE4+nYvP7XGr/vvl25wKe4sNBsW5MiP8UzRktfe019+rBTbyFbhqBf+yOveR9r5Lna3IsJZFQeqS32/7zqgoXFaXfvYUzyeRl+gN6h9mC+fMfMiv+krTxdFZg/0l1nG//A4t6FZ6PErykKoN+joWv8s9yQz7RUOkNDgpCkV9/39ZmZOIRl/AlVum6nne4Lnz15I6q+9f7VU9z1q+O6na9M9USS+F/WBR3YGYuiT30XJyTh+pX//+ammxyhOOlpeWKtJ2I9stPtXq+fNnTJ2Uxxta+SMKbeepSdUfyucl83pjuTRQ5L0rly0ophn7+YpAQ9KvOsV5M3pb/t0OIh+JnDXL9fGo8wbpsG3lqnz6Qn7bbe9PqrPxRXVJHK+lpUU1pn3PJ/m8skqjrIH11fah/lQ67TOikuQLLxbyyqXEbEkFr2L/t5IWC3l0eXBpeUWBI9Yu4JTbqP1OSYBaq8wW0phF9cXl/IYsqJOFBq3IE8su5uTlG1Hmqt+9cFH7faP321WPqFE2JGcLAUzD4ErD+/jlr6v2dK183uS46NfTlRZcmwzMiTzAp46esKuulhrEJcR+yaWnWoHN9UnLcwtBOoMAY11lAS2x/TUbVaViqm93brny+nItxbqcFsCbTcj0sJxS588W863Sl7nahdmSsssVNKzArEL+qWXiexW76g2Xp6+l+/5imtUattGVedPyksij83WzL/16+tcuhGl1n7nApOo75VTt51q4AF5G5Lfyt6rXJdebirylRnu0qopATnPbvhHTbYvtBaHd+W2hHaTVd7SLpBdE3V+vq6TUhWhFm7BqUKT187HxOm5JIEf/vV7Vdiy3/fkyb77iInnzQfNyaxbIKf2c44fqscqFiza5Mc1EYvPEwflSViQre3dIek8B/fvtZRWEwu8aRVIfTMsGT5XCWFTi8wfUXqXxmU805cGCkoznc+MghC7uq3oltCFPRONbnmzG66cRJ2whE6xSUS1U1lZzbPKqNEaNlFQOqzXwtIxw9pj8PqP0JxoAozJzNQ6QlFw12t9cFF3XyD5p0/5vRyCncMVAEQ0twwaFSK23RwvpbWXAU7tKl3uvaqCmJL0aB8diuUqC4ZXJknyiWiFakoGOhuW8FfLBIvEy2F9LwdrBg+XwaKEwaD7AVyzQDbdB2z9Gx7AkvRtX+hs/dwpppVa6LNmPK9dT7L9PZMFiECAtXP2p9v1VCjlD9ba7TedPoTA9VOM8TxSDWyvWu5Cujdczds7cZMWvvvrHsR3lqnYlM1+JMKvuYJXvaeCY1ltfrcdY7v3y8regELApzVtaTIt1zyupUI4b99QpbZgqtcprA7Hz+QBXlUDNkkjj8ruNK+ryarNhg7o99YjCsalWIS/sZ0XkuxW/0ug+Xg/rWnLO6Md6DR/dW6hvriYQ8lKV1KvEy14jb6mq5BgCo8bnppGS5RrrYVLSKNstfmdFvaa8Z1D+Vb2xVJI+mu49ZWzpZ7esT1TJ9zQl7Qjjnmgl5454te0x2UYKbZ7qgeX1p3z/vPBAzgZMt623FzTtzW8LdYyq9bhlUd/J1zPEOhnUGdpyPjZRxy2re5ZehCz1ZLZwEbvVeuSLGey4a6ucWKl3l0VOrYI20NVX2v2Riv7oQ4vBeAmmXSJ70oUQTxRHJe/d74JTHFns6Vt5j6lY3+r3NWcRvujRxw3Abi/Gjq5YWuiC5dQEvINeOPZV+aatW6vfI/haT0v3vcYvjWFKu9VVGYXHcP00Jji/8EGckEIUvutr9YhjBaayewkbs7XqzulGT42dk7zqxbj2VCnFA+8nRo9PNKFvr5y8EUdJkmibdbP/nwYx9Wnue+1nqw/E1vX3EYwdy02nv51B6HFuOqcb/XtF9qWbQuQ3OVkifsuP/F3KUzcixbFn8h7G9CecOPb2tzxegDhtquhC7zv59ayURviaNp6DsNuOfoP7mLvMVgzJ6al7xiMDVZdFVn+SmUh/j1O5iVK7hzHz2WoGD1zduVPV66bCmE79psq16YLt3ZP6/eWOXaYV503X/26TU1WUfHer2n7+vLIVVZPNW/3V76nPZmW6TiJlMO6J+cgMxl7mYKarLVfviXLzsraDxS4+5YPvUCulTQ3Pwpj6LDd4pvnMGIaNxg/QHlv8tRe2Mw7YCplDi2lRaWRQQlGOfyfL8f1eeI8Y7IOuPvTLwVvTWlmRm2yI2TIkz/c4IvdXPr8nczskctOc+I/hQv5ZkF1A5LLYFIdVpvEqVluPyIZFnpQ7NvYzXsOnEnX19sv9mEaoMk9saB9XeFnrWko71u/3Vl+PlqQRvZl7FELd47bePA7Bf0lOiz05PNh8npC8K+rYchonrA2XB8n7kcJyfW/Uz0+zdybg1ge4VeA+M2JQ7y+p4x2dhWgiaRes4RusdtRNxYcKfBtZ1YC35eKYOT0lUoNYw889xvmeZrsTY+dkKrnjQ6jWY41FWeg9bVuz8ZbS4tjpKVcZgrWZMWJeqi50l47jk1nGspxcrd4G0l/ehku3bWkvVGhnflu1Hifq/id8mN6f+yv99RSCZevUpvNxNXVcbZ2rjdvTYju/VGuBnAcpGDRbmiM2dLXi16cQ0qeGYd/bpQ9ymSl7pZFIFCtRS6JiXiAOmv9+DHP/bPLQZMIIfi0rwQ4bLNVSaJcFo7+MvqBRzEtFETqfy16UDw/AVusM2m2FXU6m48lVPC6yQf8j/11zcQQv5FIEjtph7dIGjatIE+kEFv7IfUQb/LU0SbTH+tn/6Zt+5MIX9Spm3TDvy1fLg1ioeNqEsneoUGkP3c0XXXlxhH8smfdtEOGKRm8mIT4jttT+jlFhV1IYtajW6PaF4/xmD3rkZJnubcX5ouGVO8Mb1YUuWfmJf+bG2I3KpRWY/2ZQBWtkFPw2nzu1ctuuPaMIJ+bh3mu4h+pqOCevud0v/vyput5dXbIxFsfICTmAaanXzTC3eUDItj0NqEa5Gr/hkxXQJp/yYaDW+mZuBTGh7zMFQ4NGQfWcrr+PYv7L8vVoKS02MuChVo7/O3dAbYdsMGkDkFeWFY8WsJCPSqebLCj22HBSZnfBaKIiuJ1B5EY+jCPc8yMsA8EFv2t5pgLX39cmHJC5GcS4vvk2OPaZDOpOGSQTC4X1TlVufiP7uE1aXtcS5sH+tlWeV8jEEJED/Q7v6agwDjLxSC6oqRm0wyIfKNA4Ufe6mAtiaef76OHGgw7pR/lftkGpm59mRH1jLJd/KS44Bo1+JY3UAzl5OdFAuVAaEBCfb/JpWyvcCcGnn88KTv6zdv5qthRKMMQe1FjTQ1b0t5JR15RB7LY8BkctHRSA7EbvO/n9J9wUx67Z+rzI4wvpHm5Y35aTDdho6bZd7YVSa5rfljHhwNHiOkXiJSVuG8/H1Ucr1lZrgZx7WVQ/b9rXQDOWRiKab0BOYGDrFmzdtg3byl496HsvlzSVo354D1c0JF8zw27QwMo+qxHX/S1SuJI2tLtd16Db6F4Es7LBUX/9Sh4Xea3Zxus69DiBSL5C/PUAtv7P1or0IF49fTj+vfYBBc6AF47GA/CNWTf7v6RwFg3e3joVM9ObxQZZ4o+KNXndAvtgbjIuGiVl794Lw3/PjNEzHrFHNTMI3S5vtiTuijNm0AHbakf0Fw3/F/qw27dMclsaZcbwF/mnikUxbu/Bjncn9F5InabrLRts21cWddmlVq91NaiN549pZ90wWW27hzF2VKaEO+M40LMDQ1+Hkdae1vTStFquinIznt9T9jW9+qqf97ohmFfRs2xN0+Lv8UI5Hv5gB7ZsrSgntJdpIPfEOFjgveZpsoFjhuWonLxW0ZvnaRjBbwHXGa8MRMbh154KUiJ3tXcYtqpXilqTuFfYehx/06jutA07/pF7Qgf2eBH86OU171pf12Kg3aSsLkjdiOzdsExTDvT3tnLctCfDbsGWVl7v5p682Kjkb7NySjDqpV5HVjSW/Pm61+4RDO1rdPvTIq3LSdFArN4TOy+J+DU5ubcPfUafl73ZdIcaKcu7Rb1QTopGYLLFcjsenZX7voF8b3tf4aJG8FHlD5c01Hu2NRwYa1o2hrDIjzQOc1/Nhm5t2lPLDNJiU69xkfobZzrogktOA36Eo81FcuJ35YVfQfm8tFdoPRst3baxvfCC8ttKSm+xF+Tsb8UgTPvOx/XrxdxatSaSSMqrH/h8DktLS/prWXZHq3ylfqx4THpBVn+c39RnxzFgERU6kZls7T1eEqUtl/6jWCXr+b81y1pXr3A7QGPr11UjA0onY3KqQzxOFo7baCiXHpZEpd8oPahqCn6j7vR11N0nbdz/rckik+8ZU60XSqlXtNBWNSb075dZ5NUYFkrKyvhNP+KiwTv0+TBGZOY9cz0sioW8OCLXRbNm/4uKzBtRYNolt65i/QseLuQaAoKjt/k1VQ7PIBzwwCZ/Jnl1BAM9PRj4NLAmt++tqecZJG7MYOzDIQzs6snlifb8IzrX2Lo5fzQKHBfD8H+Sf5y7yF8+G0DPGwMYuVLZy6JTLIvjKyfX9PqSqOgWHqHdg22rLSrXKC0W83EHpu/LsuJPo3JCe0UwuqfZhNaF/r3u3GQ6jIWHuUmNdlvVjGh+2E+44ZJd1OOB0turxDZHRUl2wrZGV+FLGiGHprGQrzv9ZbTt4hUdNbxt/cVox7qK8u9NObmG4nf8uYlV9WgpZcGo0bY188o/8rZB2efFRovjzWaW1GQQ+k72NhBcp11r2qujK7962xXD4EZWnF/ySMB+0PLC6x3ZZ4USrH6+94po9MrJlUob6mvoXlTuL1uVXtONUuD8ySAtNvUS56/8toa85sDoj/mmdxozV0vrnnU8E2X7OXmsFCemPmytd2o96zvdtrO98GLy2xVKblVKPy9W8tt3Pq5fHRzIKfEwg2x3N7rFq5mDkP19Bsff3IoeyzC8N5ZhdnoxF55H7PZ0ISrXcZabuVop9ln+bBT/dmICriaRyerpobv7BW/VWux/0fCq+63PKz+xjOVncrIRYkX65GSXQbd5875hWTnzI1q4DSCOcCAO+8cOmF8xw+aU1bdLoeLtVXovKTOG961l1a4+8+BJuf4TmLpa2WUyi+iPU7lAjuKB+2D1Iqq6LvQe8WE+sYi5cw5ZoKQR/s8w+noHMH6nuStFL0vm5hgG3tiGPvtxBB71wPLpFObDESwER+Un1th6y79e7YXz/DwSD+bgOyyrCaJhPuHsQ69tHNFmzrF1YesLvS2mFS8mLQaRfparO3S3OVjRbbHJq8VhhO7mG8oZhK/PQPncCftr3bAdlNeTy26vSuhXb12DVsMKf1tdSyOTrzut93Sxrtc1jkgwd4yVfS/zokUbNDncQfa/Pnjz4+vsn8booeZSbXPB+JJ6xk2DcaueRTFxekKUvOI4HPVj8tiLPxLNFWHdhUazIhqRL0Ohx4JiMxw/cL0zHZ1B5Ewu/JP+1gX3lfo3JWn5cPQ/Y7lbf8V2e6/NwNFk8HVjpdv2thfWRL12UJWe0p12Pq5GBwdyFCjydo/VDHKVvTMOW+9xzDw0wfXDAhL3/fB9JCpX+2wwb88XZEEkKwZy6nq1GKtc+nMdNs5KRoON1e1rl0IyX3k8ZK5R+Wh2774krynID22dqXV7XFtU+f612P8N3Ha1shvgVmzNN0yu1h8/JJtMyB4pZvQbXZHbbcWQPjuNcH7wTv22quL9tOZDbnmrQPH2qmwihuA6GECva48HU7KwD/5rGMe/CSGRziD9exgzH9tg1QZN1wt0b2vjWnWbYD81i8XUPHxHenNXLUTDf+zQCEIGA+a+LKknK69bJa8Mo1e/RcGG0VAKi6FJeI85YNtnQW9PPl3HVuSJbbUm+Vfrunfa4flpEamwD863c+dH+tYYHJ+FGr8CuO4sYXnNirDS+/eb/521TovdrxVTy5qV469ZYZO3wQXjC7nb0J+GEbpUvFe/e78To3pyKrm9SusdmBbb+s5ahXG6oRQGDF7LNNAOHbKuD2MIybxo+G/r8Jb7OhRR9hWsuChUg9YAPTWe642jOOG/6GoyH1ZKrt5HGro9xHxiCt594qS5NwL3x6KOLtNE5vcgxv7pwNgd0bg/No3wxWq98A38Jf+FAyueA9CkYhHWQP70OFnoyTT09lqWYNUkEbsh1+CoyFtzUx2mG5YvQ4hd0C6gpRFwWnHg3yEkqxTM2cdRTL3XD6s28PAeN/y35lbR43Kjpds2txfaaDkfoKnTDso+EG0NOe18q7gHO+t8XJ01DOSIwqBKhKxU5slqh0vugSnfOLwZQrSpCl0cUyfG9HsxzedmMX2st+ErX9295kKwINz0021egJKnSRQqj9WIDC2kjwEgsoGaTxRKrG3jrV1eN8leF+LY3IzWDX60pso+aeP+T6XrZaep4uBoK5Q+8ai8a7+RQrfwqkGX4pgP4dtxfd9Gr/sQPzYMe/5Kxs4DGJYNl5krIf0ziV/F9zY6gF6NCmQjVcva+6tLFPaRXEN8dxQzHx9AX8829PQO4PgNbbwKPyLx+VUU6Dnp35Plx1pUjD2BBUR+kKkhPSUqDDVSZAN5ZTulnlWkzKdBjDtz4yq4Ls7Cu39tC+eCyu1u4/lTqADUklmqPmD/8zQSj8rXQNnngT8ewbRM5+lv/Ws0FlK1FN9quaqg15w/tmHEC7c/tapyfbvF7xRKyuZ+5wWkxS5Tb6Ec99/JV93aTYFlUP7K5ah+FVYfUHL3COx7crPRZcOBD3PbFz8v6jHi33Q8jHDLt+fU0gXTm4WtL+lhuR61Y12XsbzG0dbCU3/g0R+80WlM79gLZXTwfkVZVlUW0f949AZobhypGcMnitWjbM/n+OnGAnWvag8SiWP+nAu4MYQdW3Pjq/Qfm0L6b17MJZaw+IMLvQ1fkCm9DdQEpcXsprg9QcQStTeomG4csJorS7Aslv+Uk2ulpAz1DFr14HKniP5bBhB13TB/lLuANnmiH8kLB7DjA4NxotJBuN6wYiJhgze4gKXopGj0l2z1f8cwXuvpYSU2VrptZ3uhvfltcVDpWrKI3MrfmObAAUtxZ7TvfFy/mg/kpFNYkJPVK5sakcjk4E5JsUw12Wf591JYaurgd8G6f1QkP00Qvu+iDRY+wqPioLim15u8CXWnDU75mLP4eV/FY86a0OCTcRpqjJTaboFdrh++DtTsBRC/OpmLYK76dpJGlNzj/udyg8doZU8oQ2LflKXALivsn8vtuOrD5H8bThHt08b9X7y3s5riY6+NmPflz48wpq7V+K6nIfgv5lKj/Yyzyj3KJWM+XI5g4VkUYbGM54i9pAGtwH5E3ipwdRbhx0nEbonP1KwgFINRVQcXE9+TD5ka9STJK+yvqk/Ty2JJfxS6E/5kyX3ZD0TD/Eux3as+BaKY6Z1A2GDVTMdGkL8RJFt5Lj9NySsf1QaqW825UyNPLsu7K/wek08sEOvcs4oCTDvWcrJuD4da293G86dQAaj1dMVnmcJ7K9LWrzPoO2dwz/0rJrg+LhzVlce1BcUATLXgeevlau8el8wX4qLcrNGjqHCcqqu1vqZ9zsJgvr7zwYbKO10b0mLuyGeqV7BLyvH0aR8CrT6ppopCAzkdRuxhGuFrQdg+dJQFti0HR+RnJhG+k8XC3QBsh22NXZVdZT2ieGzSGDsfqHucV2hkH1d6WesqlkvLxmrkUfVzZvVKBgpds3GN1thuV+GRwvXy3ZysaEgfgEN/nLLWQA2t+iKIaVdxkNKVA6dW8YqCvr/1os/swXQ0pY+NuRidx7RoJNvfajbPKLkgdrjfeCDaJpgsdplegYkrtXpsxuG/kEs3yim3wa09GVGGyUlRhjWcfzah+LQyN2zvdFjCfT4J3/dxZErzC8UG98U5LFzzGpf7z0V5vduH2ah2C2DFBfynccx8ly956tto6bZ97YW1zm8NPPRjQj6F0nxmpOxcatv52EwdN6+B3k26ZnpBGmg+kKOdCHKyemWzXLzy6q+hFDJNjjfQtc8Fbz6o8pUDru+rDED5NIHQtWjxvZJ7+iKVV32fZxC/FSns/JUHzIThT+QTetIBDB02eCytLov0rSmMXys9jOJgNVLpL/lMwxlEgQlDJ9zyhJyB95xxwtVuLXN/qhXCCpwXRurfTtLIehsq6Rp9L2mQscp/NY0m5nx3whVd7bpge6/4JJDxwy7M/GZ82mZ+DyF4p/op3RDDfbIW+38BqXrJwKCg79o3hBF55Tf+mRdTvxudh0kEPnVhSlt4jxfeo9WbD9177aK414QR/z6MSYyuuPpYvFUgiNmrQcRv1qsglASjCt1Eq1vRk8SI4dP0soj/Zwi2DwLoP+Nd1ZXDqvQAyRSCtwyO9LMlefzNsPbmUkVBycC+xgHbxs+d4i2fM5i8XHFF9VkaiRtTOPneCAJy1opzrWRchEj+1rm8rGiA3ozIP6o03F5TCg3PeGXhXbltNbd7Dc6fmk9XLKpMW+k/Fgwfp6/J/inXquIJD9l7Uzhus8L6zxEEVxEcKAZgBMM0UbTaclUrNycKPYpcGP6PKBsrfkvrfj7zw2zhOFULoNZc353D8JzKHcn05SE4vggZP/FLS1/fjCOYvwrYhrSY68MRRqLyebSF3y8px0VeNXykRjl+J4Dwansu7bZhWL9iKfLM636RJ9rh3FeRx+52wK3XY9KYvDkl8kwz7O/UCuO0oR5RcmxwdRjDNY5N9IrYj/LPgob2sWYdrGuJ0kEw26bkqT/u/S9gXKM10Q3HaT+c+m4W+e6FGhdGn6cR+sIG6xdhQOuhmAjDa/g45QYVzhFxJiYaafaI3//Yih5bEo4ffHDtUVrrSZIWDTRZB3Ecyg9sn5O5NY4Db27Blp4+DH8Tb6gcwc4huE/Ib7kk6lQ3DEswRL9yY0Tr/aENtPtxnYF2RZnZflnEbssnwp2ww9pxCTeNwAf92PY/+SdelbwsY8blvjjWkXsj6K/8vPb6v34cv2xYCBjbYOm23e0FTXvz2yq31maiGD96HPrzx8Q6TX1iKd+v7Tofm6njNtCW0eRr4S0/IUttwvKTBXX2c4uqLZZ7KarzQkRd/FN+oMRyfFIVBX3uc4OTamxZvlHqryV17pRS+C7Pz0vyjSYk51T3nvz6iNdOi+o65VN953zq6AmHans79/2Wj2bVxb/kMmpM9ZUsY9rjUj365+1q706b6glMqqLBqr+nHPSqs+E5dTaakstqltXIWZsqkob8DkXtPehWR8V3aL/rOWZTRZtNhWJTR38p2aYns4XvheJR557I+RWWgm75veL3T82pS4X1bpRYvzPF42Q67FX9oZi6uLSkphLzqv+MQxUJUrynqPbzMfFpA8ulxwaqK5Ay/lwDFn+wy+9RVNv7o/o+8n3pVu07odp/WJSfWlZjF2yF37NfXKiyXjF1cjD3GcCuTt5f+anFn92qRX6P9sofX9+5UdV9WB4bWFR3MP/bDWp4n7Rj/y+q04dzywM21Xd75bmx/GBadcjfwKBPjRilp6RfFZWz3GdEenRdmFUjiZS6tLSoxoKTqmuf3J49bnUuKZepKqX6C+sE1XwuJueXWlbnPy/uIxz2i6Wq0/IJe/6zVbah9HyAOI8Nz4flBXVyv/yMQbpYjnpVs/wO+5k5dSG1JPZBxcv4YNYnjoOe1+0W53RZNrGozn6USwfK0dny/fCXSO8X8+cFVNu5iOF2NXbuCGIdCvtReym9qm3QplrE53J/a/narOrLnzsyLczfXlT1lPVE5KP5dFKSn3mOWVTTTofq+9FXSGuWj6bVubBYNl66w0R6ze9/7bu/zOfBdpHW7er0A/mxhra7HedPaT5hUyfL1rVo6WdPIR+vzGsXv8vlR2YxP1Uyf/mByMf18kOUfz+VHtWUOns0/5vitccnSpomNJC/tK1cTc6qrnza0F4yvegvvcw0qa4fplVPPk2INOC54Ffn7pasUyP54Z8R1ZvPY+Tv2E/IdHzOI/KfXn3/K/tG1fn8ud9qWlyeV0dL11v/LbH8Ee23xO8UjqVIi+ftVcpxsW6D4ve0+Ypd9d1dRd1Eipwp2f5jIv+S80sVz3Pt97xqRM431K56xJ+iHnSwyrE55VJte0y5ZQ+KdFy50o3u43WwrmXnzH5xzhjUV1siypZcGhJl6OqTyfog8oV8fVo7tyLJ4nm1LOoMkYBXdWj5xk67KE8WDNPyahTS/+4G8sy7+f0t6nCBmJpq9XjeHs39NlzqbFn6FHWK0raFyB/cjbZRtHyvsKxJdZwReWdclLVLKXUh7Fe9h3PpVc9bqpRNK8+dKp9bNbGO8hxueLvWkcgZuW+qvgzyUXGuGn+2+PJG5WcbsOHSbRvaC+3Nb0V74pT8LphV59n8eSTq66kFdT6fH9VZp7acj43WcRtoo2oq99NCC6d3g4EcUYiWVvoMXoqooOhV2j8qKoglL9P7okKsf5/4xnO5CtyKz4kC2ndXfqhRSwvq7BmnbKCXvrSKmUedLgvC5CwnpivW06TaT/nVBZnetaBCYf3EQSsLyEipsE91ykBR2UsUcu4L82qqcGDE/jP6nHgpbxczgOXbXoNt0F5iO0SDpVmp8KTq3i8TaOX3if3iv290covGyDGjZeRyho33OkQlbDJ/osiX8rZT9QZzFYFU0CUbZpUv0Zj4OX/sFlV/xXcUXjtd5Q1oYen+rOrVK5UVn9UqgKdEBWVlkqhhdftkdfu/elrR1n30F5Go7vqqpBNtv4pKdGXGWfX8EC8t8HlOpNXKinMV+catlqn64nJmpbivEDRxiMadkeppXdsGUQBr61N1O0vPhxrHpiRdLP1cEgyq9dL2x5nZQj7QkAdzxeCt/j0m1SIbFtoxc2rBCvlRseWiAlIl79O262xF1aPOuVOkBULzAY7Sz2p50Zy6KD+8FHLrn1HeFg32Yx7V90Nx3ZZ+GVVtpftbX/d82hCN9o9K1kPs2+lEecmjFUyFQlV/ie054lVn9XTe5HYLbc+/SvOJBtLW4s/FQENueUshMKYdA6Pgaux86YUOh+qvGxzV1MjbRFpyBhbXplwV+YL/k9ILEtqr9JiJNQs49fdNe2yqQ2s4/6wFDxtY31J/pdT5c8b5j2m/W50MrwwAtZoWtWNXtrxWvp+YVOcNsqOq6UzPG4vnzmot/+IpfKcrWOXLRKPNJT+jnKkWxlmDeoR2bC7kAsOVn9cugPhCMtBroPY+XgfreneyGMiufIn05C7ULVoTO2/Wv1P5fH5FOu5Ify2JRpuv5KKX9hLHY59ovIi602y82gWsFhSCt7Zig6iaskZZ7qWVZ65Tk6o/LMrFJlcuH2hdeWFKu+iQK1O1fMqlBRJPzFU9H1aokV619Ffa3iiTEvuiWh1Qq1tcqFzPVcrX0xRRZ+zAhFs/kCPK3z/kh6XUT06Dz5W/mgnkbMh0u9r2whrlt0uifj15wlH1u3N13AbaMKs9H0vUruM2WPd84K/4juKrtC7XjC3a/8QXbBjZTKbYjayrG7WfPp1FJpP7dNerKx9pmf8uo/fKPMuUdE3vwgt/5HU9WbF+pV3S6u6XtVE8Ni9wHz0Xx7jkFoQu7dGlcvqFWSf7X1N2fqzmOMj9WW8/6r/zErfTSPrWDHzfTCCY6oHpf+XMgmUkb0aL97NqT+CI+pu+Bat8/7YvvTV87pSmtVfE/m944Dyp5HwxWvf8elTfrmKe2rZ0/tLPn5Jt0tU+Bvo+uuvDtn8k4E/Otvc2vrVQun/XeN+WnR/1fqvVtFi6fL0yXFOWztpZRuXST7110LdnNedsm5Qdm0bXo9l93CarWtc1kcTMP3bg+E0zfPEYPIYPCqBGJC8PYce/ghANU8RO5UcfqaDfhjmGQNYGx9+AxPVZzN4MIlo2OKsC2/tj8J51w1J4cl4V2TDGTAMYhwfzD3w1b9FNXxlCz41hpH50lN3G0oiy9Cq0q17QiuT3A9jxQbj2/qa6Nk+6fYHttipy67OEZDyNrt5e9HStbp1aOx9L6oPrpY2jh3OIiDY4/Za7/dNq9RvqltSF73I9ELSsccNcYaUXbFmNfGmue1shEXW4P/y52/xqlivUmEXVf1TrZWDck1HvAbbTuaL3nUa77SsW8quTp0p6Eiielb2TKyx+p90aY1G90Xolfe4Wj7LbmTta/jb5kltCaJWYbunlYiCHiDa8xZ+02/dq3A5WIArlQ7JAZUOcVkEPGCrOBm+rIqJOlQo4RFlhbqBBRQ3J335yeLpkTEvRHP0lN5ZZ1VsTS/1VHF+w5m0y+rhyyspbQQ1oY+xZ9njVSKvjmqwXMgBpPhPhxap2YLqll6j5p1YREXWSRwGMvDuD5O5h2Jrp+t61HvpMUsfIJBE8PYCB/3RhZBW35RFRJ0li7nIQyikfPKt89DZVeNWC0RsReJ+OwfpeAEl9yII0QpcnxP8dsJkbeLTSKyYcOOQQE+bqRbioEwzvHQPOhzBzxCRnGkvfGsfwmSWMXRmF5aXdwtdeyRt+BBUPfJVP+KHVYbqll4iBHCLa0KKXPQhqE2/2IP+Q7qoehuG/pk0ocB8uf6QjUS3JaAhZux+LYR8cDOIQbRyPgjj+5hbsOF18LHfyyhjGlrwInq7z6GhqTrdoFP8Sx8z2GQz8YwTBR93ofl0riYOYvd3AY56fxeHXAmwnvHCtuHCTQeLKCAYG/ei7msDcJ6LRLN9ZKYHAv05iJuPATMgHe0fm6UkE39uBLW+OIZpPuI8CGDu9BO81b82xVahJTLf0kmy4wY6JiIrSCLzbg+Gr2rQLs0+m4ag2kNzTMMYODmD8DmD5aA7BC3YGcoiINrn01WH0vBuA44dFzB7dhvjlEQx914XJK5NsKK2hzG9BTF0TJfcnPZj5pwNjt6APCOv5dAjW7UpxoFFt0O3HCYSvz2DmQghdH/gxc8qCFf0gfp3A8K1eeN+3w9RAJ4mOlw5iuGcIgUPTWAy6sO3eDEYOz6DrvB+TB2v36KDVY7qlF4mBHCLa0LRKuFlUwtNiWjnohf+iB7bXS65nZDOIX/Ni5NMJhNMK7GeD8H9uUJgSEdHm8yyBGdEIG/s+Abxtx9AHHoydsEF5QU/pIk0W6XshzAVCCPwawcKthF6ma5S3beh7xwzHoB22QRt66z31Z9PIInHpJIa+mEECvbAfcsNz2g0br1C9QEy3tLYYyCGiDS99awKej30I/JYvQk2wDJqwNbWAsDZPkZWcL1zlQR4iIiIiIqJ1hoEcIto0spk0kr8vILUsZ2AbTGYTerq7Oc4BERERERF1BAZyiIiIiIiIiIg6BJ9aRURERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5REREREREREQdgoEcIiIiIiIiIqIOwUAOEREREREREVGHYCCHiIiIiIiIiKhDMJBDRERERERERNQhGMghIiIiIiIiIuoQDOQQEREREREREXUIBnKIiIiIiIiIiDoEAzltlM0kkXyclX+tT52wjkREpbLpBKK/ZeRfRERERESbW3sCOU+jCP53M1ay45j65wAG/mHFji1bsHXbDuz4NIi0fHd96IR1JOocmV+DCD+Sf9CaSt+awnFbD7b29MG6y47xOwxCExERERG1Hsh5FMDwLivc34WQfC7nVUrHEb6TQKba+x3LDHdgGr4TQ7DslrPaIH0vjOjv7QqMrc06UvtkHoYw9eEB9PVswRbRYD3wVRjse7BOPU8idMGNAcswZn5fq6BCGoF3RVrYUuP1Yajz0kgz5UAmjql3d6DHdhLh5T5Ydmozoxg7MYW4/gEiIiIios2rtUCOFsQRDZoAnJg664TpFTm/1MMZHOjpFw2fPvR+2oGNj3peNcF8yCX2g/y7RclLB9BjHoC1txcnb7Rpb7V5Haldsoh/M4T+vRNIHZxBLKVi6TsbQqcH4L66zvtMPc8gcWMGYx8OYWBXTyHA0LNrAEMfTiBwK9nauZ5NI/z1MCZ+lX+3LI3gZyMItHp7zismOC/64RG53vF9rjUK5ihw/qRiORmD//PSk1aB/ewcFlLLUC/a0S3ndoRmyoFHIZzc3w9v1o3IExWL0XlEHqhQl5ewcNUFs/wYEREREdFmtfpAzrMoxo8MI5BW4PlxBo7X5fxKT9MIycn07QSScnpj6ca2HjnZovTjwt5C5Pd27q32rSO1QxbRfx+A/eMUXNfm4N2voEvMS9wVx1+xwfqmIj+33mSQuDKCA73bYPs6ip6DXvijKaiqaGiLV/L2NEbeScH/wQ5se3MIE7eaD0hl/juBoXeGEXp9DK6/yZktU+D40IrYx/0Y+DRYvfdgI161wXt1FOZ0LpgTWKPbrLq2m+H88CQc8m/AhbHP7ehVuuTf60e2Xjyr4XIgicBnBzD1yI2ZHzywvCZna7q60buzo8JXRERERERrYpWBHFHZ/tCBsTuieXRiBmODNRoWe5yYPWbSG6ees8O8mlqH5egsXDvF7trngfcw99ZGlb0zAc8XYfR8Kf7dkz9/umA5swg1NQ/3erwN7lkCM+/1o885gaXD80iEp+He3wvlVfm+0NVtguWYD3N3Y/D1RjBiM2PgdKO3imWR+H4YvYdjGLo+D9+R3vb2OtnugO+XebgyI9ixdwzhp3L+KnT9fQTeEwqQDsBzOvCCAtRb5b/rSQbhL6zY+nVU/l1Fg+VA9tYMPFfFxz4chr00iENERERERAWrCuSkr47Bc1m70m6H99N6XfxNcPyQa5z69q/XXgbriGhsTj9QkQr7YK/Wy4k6XBxTn4whKs4f978sWH/9KwxoPfD+acPxS0koR/3wn7XVPu+7zfD8MAO3kkb4qwH0vxesG+xIXnHB9kESJ6/NwLldzmw37daoH+bhf3MGAwfHEX0m5zetG/ZPveIIivzw8jBGLq9RKOfVbqzfjnRpBN/rx8C/6wRxdI2UAxmELo/rA7EP72EQm4iIiIiomuYDOc/C8H0c0CvbOObCkD4IJRE1Kn3Fi5E7YuLwMA50xPkjGtifOTCm3yZlh/e0UzTLG/CaHWPnczcGJS8N4eT31YMd2TvjGHYG0P+dH6OFHkprxQTnmQk4H43B8WELvWl2DsPzeS4oEfxsAqEWevhU1b1tHQdykkhcamMAKxtD5JI2YUbP/3VEeJOIiIiI6KVoOpCTvDqBCT2Ko2D0aIcNuEn0smmB0E+D+qTriF2cRetf9pYPrm/1k77p4K1yyA2PnA59MILAY/lHqWdReE+MIap44DnSUIioddudGPnM0mJvmi7Y/nkydwzTU5i6vka9ctYtE0yH5WQ7PE3LoJoJPbytioiIiIioqi2qNkJpw+KYMPdj5J6YVEYxn/TCVvXCaRaZjDYCZhap32OI301g+R0XXHuKoZ9sJiPeFTJJxOLiM49NGP7IJhu3Yvnf4whHI0gmEgg96oJlrxUHDjthaab1+zCEiWsJ+UeFtxzwHCxvOGq/md1uRtl4opkoZr6PrBzno2T56FdbYD0tJg77kfrJmduG51kkfwsjejuBhUQE0awJdrH/rEbbkM0gt7tSSMTjiP22jH7RaC4b7LOS9uSg2yGEf11A4m4UqdcssPb2wXrIAcvrKw9My+vYrCbXryCbRvzGHMIPE0jcTKJrjw1W+xCce2qs0HOxzHWxjNh3kTsp9OyxwmQywWqxwfJWjXCjvv1iHcXvZJ6IdPa0G/a9NjgO2WFqc5Qy+yiMiY+HMXZdC4q4MPtkGo5132DNIPjeNgzpPSUARyCF2SPacUgjcDkJ51GjR6FFMf4VMPql9l4GoQ+34cC3uXfM52KInSq/bSb+Hyv6P41C+XweybO2F3ermfYkpTePI6S4MXd/cpVjsoht7bFiTDuku30iH/O0eRww8f1bxPfr015E1FGU7vF8Hrr0SOSfIu2ntg/Dva/iPHkm8hZtcGctnxV5aeI3wPqRE2ajHd3oefQoimAihdh/hjB+U/z9/iTmj/Tm3pO2vtEPy86uuuWAlpbCl8LIZsM48OGM+NuG0Z9GYSscjyy2/b/bEPv/DPJgoXtvyfdVyat7D3lgrxGATF6fQPB3+UeZXjhOibxA/mX4udescB2zrLiokfk9jNBNcUz+EPmKKDPNg70wvW6GbdCK3tdW7vz2HMt8uWv8Pek7Acx8N4nIq2OYvFDcrqY8TYj8Moy4+P3InSxMgxbYDg2J/VuxB/JlGpaQFOsR+zUF0xE3bPKW4az4nvjtCCLN5PNiu8M3Qvp2FfdpL6wizzbrZUoG0UsziBj2juuG9X1RppauplbWiLqFuaKMME4PBstrGi1DxOcyz8rPBex1w7k7t97JG35MfCvK5n1T8H9i7oxbbomIiOjl0QI5DXswrdrEItpiODWvLsvZhlJzqvttJffZ/OtMRL6ZEzvfq4oqW8lnvGpkOaXOX3CrotJdMr/kpTjV2T/kFzTiyYI6e8Gl2pTS77CprnN+dS6xJD+Ut6hOD0J1/1w5f0ldCPlV3zGL/A5Ftb0/qc7GU/J9VY2ckd992K8upiKq/4xT7S39zdKX4lbnnsgFpdTP7hWf90blmwaWbvtUR7V9JF6mw5Nq7E/5YanVdWzGatZP28+Rcw5VNC4Ml7Gcj8nPVUiKtLYn9xnTfrc6es6nesSxyn9Ptf1Yto5Kr2obLC6jpZHRXyrTwWosq/On5HcavsR+bupnUqr/sNH3NPMS55n8trqWxL4tLKeo3rtyvrYep6bFGWNAW6bkXF/8zlb87d0+tewoPhGflWnQ80vNHKWcOK/nRD7h2FeSh+y0qK4zs+pCw/szd75ry1ZNW3WVHl+z6ovL2W0TUb357Vtx3BZFWjDJ9+SrIo/VxC6UpGv95VD9Rnlow+dRSp09Wvp9Bq89Yl2187uBcmAp5K4oBype2nc9SamRgLc8T9Hy8Quz6nxpPi7Kj1hwUnXtk78pP7NQJy9bSsyqk+/bytbDdNir+kMxNVWSLJcScyLfLOZR+mdup8rLwuSs6sn/vvaZPTbVVppOtfLjk1l18S/5eV27jmVM9Rnt7z8X1Oljpd+vqM6fiuVXQ8R3+D8p30el37ei3LzrW1mm3V5WU+FJ1b2/YlsLr+rrtRz3qXb9+xS194hH9Z0bVd0H8/s1vx/E99/2q96KfWk67FGng+XHUrP8i2dlniQsJyPq7A8e+XvitdOhegPz6mLFJjZVhvwxq7oqykRHQGzrk3l1tCS9ABaRzzaRFxIREdGm1FQgJ/WTs1gB+dGwCbfC8h9+1SWXsX1nsMzykjp3Kl+JUVRFMan2E6Oi0jWvzodzr7mAr1gxF6+mK6DCsmgs5Je3XFyQcyvkA1Un5lTDtuCfslF7bHbF+4UgifbSKnTHPOpkYK6wDfOljQvxMm60ikpowCU/Y1OnH8jZFRZ/csnKokl1nBOVy3xARAtafVmsaCtny6un7VnH+la3fqIhc1T7bUW1n50vVLiXn8TUaX2+ts5GAQjRGN+f+z67aIyXrXHSrzpFRXz0tvy7xGLAKdfDoroDC8Xj+deiOvtRPmBnaXPDXDTKZcNAr8B3gqhX7gvtVdpo1AJKotH144K6XNogFQ3puc/F/itphOqNpcJ3ONXZkk1fCubTe/n8WhaDbtWiLbPTpU5GZSP6ryU1FpDzK1/VzmehcE4YNOYalQo4Cr+1mryptlqBHOnJbDHYZtD41/21rMYu5ANqRoGc1ZxHJUHF0t8VefpSRdZRtxzQiM84Vqzfsrpc+l0ij7bL76l1XJd+zuX37lDFitSkBeXy+V+toFxM9e0WnxmcVFeUJHJfad9h+chfHlT8K6XOn7UX87+jfrHXK7TlWGqHYF4dzQchvvTreauyz6WO/jArytNJ1XfKqdrPVRznWv4U6VAP8mn5ZUxdkuf8cnJOHZXBP+0CwcrUvyyOhae4zYqSCxKK9SiUO9pFktIg2tHZld/z57zq0bdHUd3B8qO+dNsrznuxH5Jyhm5BnZRBWj1YvuKigSYfhK1+rBcuamWB8furLUOWE9MynYty4KJf369aoEkri2d/8KmjJ+yqq+35CBEREW00TQVyYmeLjXyjxrGxYkOkWuO12BAaVefLrlKWyAdRanxPTaU9C6o0AGLnzXI9qvSSuOvVK24re+yUNAgPTVdcaS0hKun5xkzVbSg0nI0r6FpDIV8JtBs2iJbFuuQqkZXr2bZ1rGWV67dwUTZMBg16eRR6ghnsk7hPNVd7T4idM6/cjsI6KqozYLCOy6LRoL8vGh6f1+l51ozCdqxFz421URq8Ld/HdXoGlTZCy4JBpQHKJXXuhJyveBsKpBQbT5UNN41x76eqgQOhmPe0cExKt69a43vVGgjkVAuoVChua5vOowZ/N6d+OWAcyKlUGmyp1pstnw486nyzJ29JoMhcrZeWPI9XpquY6pNBDaVqj1WR/32ZL2cMerG041jqys9Pi8jHDHdVQ5bVuU/kPjfYrmKgtkr6LBxXUW8Iy3kriN/4SK6vQUAoH5gz/o0ldfbYyp6XxfK8yrldUicwPtay55lRkLelMqT0nBbLf7ewYp8SERER1dPUYMfZZTngqbD1FTnRVlurf++rvbAektOr0a2N+yKnv41g5ag5cYR/jMvpKYRurxyNIRkPIw0HrObKm+RLvFJjG17rWd2YBAVZhC96oA+Vu9uLsaNG39YFy6kJeAe9cOyrsp5rto6rX7/e/S44RQsde/pW/n7X1uqDamez4shpkkgZjItgPjKDsUHti/PEOn4n13G/F16jwXW7+tAv00r6RtwgraxO+m4IYW1CGYJ1tz5r/XueG2+jfcQ5VDhOCUTk2DnYa6r/dKbHAYw4c0/Ms5wfM3hEeRf6zKJ5pVG8EI0vLVCN+ferp2jF1C+n4ojcX+VgxV1dxXFxUkuG47isB8ob+TFs+mGS45QUNH0eaRSY3pKTL0wXbM4Rub+nEL5rkD6zEYQvi39P2WFtdqCRnUNwHctNxm/EDJ9olrwdFKnYBue+8nSVuTaVexqd9mS3D6qN9STyv4/H4NKn05i6HNLTc7NqHstKyii8p20tPJhA7PN3T+pjMzl2mVZsV9f/bpNT9W3dKidW6ELvO/LcNZB9lpJTRumzG7YvYnC+Lf+UzJYhOd6e8bmduR0SKSgn/mNYpv8S2QVERDpSHNaKca/aWIZoy7/fWyWtEBEREVXXRCAnjaThYJD1tOvJJqIG2FLwSIHtUL6iGEJEG7C51L0w/CXzpq6FKxpkGSTiohm+3w5LvYpzK143oWp1NhNG8OtctV9x2GCpVvvrsmD0l1HYXpV/vyitrN92J/z3Y5j7Z/mAqXUVGtFxjJwYQ6iyVfS6GebSQWy1dfx37kO2QzaYtAE5MxWvRwtYyB/8dLsCGRnERANQd9TS5gFx107Xq+1++LUDpnw84HGy2MDZrtRtaMav+nKNJ9FQdh003oOpR5HcRDqGhNETsiqVBGGCD1bTpBZKg59P5QDua0Hst5YafK9UbUU3fx7l/Y/8t642PuFqtw3DMhA6cTOyYn9no2HMpBWM7reuYn91i3zBnZu8GUD4YW6yKInw1ZAoB5ywlQ2enEboijZQs3B4GAdqPdntNbP4DTl9dcEwWFRXrWNZ6ZAV/S1GCrr2jCKcmId779o9DL/WxaFiPjQD96czSFRES7t3mmGqLO/22HBS5jXBaGJFeR65kQ/jCPf8CFfWCbSHLYiTzvX3irymjWWIebC/hQsnREREtJk1EchZu6uvxavia0t5xw6bPhVHJFHeUonf9CO+exTeU7LmdymEcNmVv1zvAb3iJue8cL9FClcQh3Y3GfB4EVpdP9HAsf9tZXM++2xZThnYPYyxo/KY3RnHgZ4dGPo6jLT2ZBcjonKeX8fwBzuwZes2bNtW8TIN5J7EAwu819r0FKJsDGHZ+8Rh7muhQZ5G4N0t2LKlldc4ovLb6unu6ZFXtaWy/arA+eMClv/K9XzRX8spzH1e+lylSj3ozh/ix0kZmBH+d2udfZLWn3yTY0WfYUM5idit/HmtPc1GTtZSGoT5Pbmq3hHl+2QNNdJrabWaPY9eKjMcH9tzk5fDiJS1k7OI3JxBWnHBVjWSXFv3oAOj+q4QDfbbFWGWh2LeDcB+uKIcyMQQuZqbNFt6y8+ZFUwwFTKVBJKNBByb1oXufOCtZ1sLvXGKut6ywbZ95T7NLtXInzWvm9BqCd896IJ3T246ffk4+noHMHKlMjhTyQzLUTl5raJXzFNxHEV+7DrjRS4lxeG/Wd4nJ3k/IuYOr0xHLZchXeiSgUiTsnaBMSIiItrYmrq1qvGrr+vUzn7YZQUqGF8ouZIbRzgQh9k5hNFCt/2Z8tur7kUQEu/Y33l518/SfxSroj3/146qeXu1Z/2y+iNypz47jgGLqCRv2YKtvceLDf4VFDguhuH/JP/Y+iSCnw2g5w3jin46GZNTDkzfX8LSknj9WRKIKHtFMLpn9SGXMvei8OsTNpGGajfzalPg/MloXZt5lT/CuqadZgzJSXHWYKG00bndC+/RXnSVXknvUmD/bAyyT4OuuM+FQTN6V5U0ROMnf8V9UDFuKGuNbL3xJPbS57aKxtMaSpcEpHaZ6jTi16vmzqM1URrYq8M0OJzruZieQThaEsnJinz632mYPx2CbbWnbpcNBz7M7YXQ1XBZj5nkrYAoB1xwHawoB55lkL/5p5HGedcra51KurFtLWIEzzNI3JjB2IdDGNjVk8uf7ePyzTXUZcbo9Qh8h+V+T4cx4ezDtjeHMFEI3lbqQv9emROJzy+U9K7SbquaEcfRfsJdvJUuUHp7ldjOqEiNJ2wrejO1Xob0oOdNOUlERES0Sk0Fckw7izf9LPyxqmvXL5kZNqds3l2OFitt+m1VdrgPifdKuu3PXC/eXpVORBDfPQxbp4xt0oGyv8/g+Jtb0WMZhvfGMsxOL+bC84jdnq5+u5nm1V44z88j8WBuRUW/1zaO6LPcrHJBpJ91o7tbvF7ALWjx6Gyut4ciGga1brtYb7qtorEjp4XQ3ZKr1rsMxjPSdG8r6zmSTBSb5/YjJT0ZXtHCB43qhnUwN7IIbopzd8U4GUkEzoyJRrawx4vgF9XGKGm/zJN8Ex6wKZ0ZxtGt6jx6SV63YUi/VSuNmf8W02RWNNAnRD4/PNhaGM8yeDKXNm+EEC0EL7XbqsLAMTtslbeZZZebuqWu+7U+OdVVHghdxzI3xzDwxjb02Y8j8KgHlk+nMB+OYCE4Kj+xxl6zwPPTIlLRaXj2yfPsYRAjth7seC9YFnDL67bY5HhEYZF35essGYSvz0D53An7a92wHZT5StntVQnErwGuQWuN3kwvtgwhIiIiKtVUIEd5s7/Q8Ao/LDZeOol5rxwAseQKnX5bVWFcg5Ju+4Xbq7JYiAcNBj18sUrHK1n6s5lmw4vRyvpl74zD1nscMw9NcP2wgMR9P3wfiYr2PhvM2/PjQYjKeo3bELp32nMV/bAPzrdzKTV9awyOz0KFgFz3a8XQw4vbh0nEbsjG5lEL1uFNcTV0w/6Br5DuiwPAKnCKbTFmweiX+feiCH8vJxU33KU9GRQTrHISD1J1b2vqPjSK2WPa8jNwvzeBqAzmZB9HMfXeAIYvp6HsG8X89VFYGm1Yld469NbqetMkH8pxecTStl0l27dupbBUo4tNI+fRmqt7S5cC+xE5ZPDFsLxVUDTQr00Ag244Wg2477FjRP+OIGZvy5R5L4ipm4DniH1l476reGtg8GG9UW+ySD7Qhz0HdvcXx4xaldrHsl2SV4bR+49xfZDn0VAKi6FJeI85YNsn8rOefP4s8oY1uU2snLLHBV84gYWAB3YZFE9eGsLwf0qCzHmvWWGTYzMVeuE+DSN0ScHJf+aCvd37nfJWupLbqx4uIJwW2/fOyjDOyylDiIiIiMo1d2vV2xa4ZKUzfcv4iR41Pa9yL321+WVSSD2Qk63YbcGwPhFGOK5V0KMInY/DJSrn+fp0odu+aDD6b2qfSSB6GRje84LDOBWNme5esxzjR6z9varPwXhpVr9+cUydGNMbY+Zzs5g+1lvjKmiF52kkHpVXppV9HvjjEUznnxryrV9UynPTXabewjr67xhU/NfCY5HG5C0/nsHVDMD6ku12w5cfO+rmGGZuNd54yVz3Y1Lf9wqc50XDq7Qnw+umYlDrWRb1cwETHD/E9AZcf9IH6//lxvwx7R9DuMsNfzSFZNi7srdELSW3RdneWE2LWqS/aD4dDcOylj32utqVclLIVPauafI8aknd/D6IZAO/073XnuttkZ5EWHtaVCaC0LcVvb5Wrdh7M3hNe1qhyKVu+RFXRmHfa3AcStPy7XoDGMf18kTT+sUBg2OpE+fTn3KyVU+DGJdPi3NdnIV3f/PnSUMlvDgXq8okkSzrhdeN3iM+zN2dx6g856LnQiW3RuUpsAzKHP9yVB8nJ33Tj5ndI7DLMXdKb6WLnw/p5VA6LuoHg8YPNmi9DFnG8guLiBIREdFG1Vwgp8sK27F8g660y3ktxQBM8JFx7bw4tkqtq4tZZGW352S6hd5AXf2wyVtFAncXkL0TFg1ND5z7S0IHr9sxLO+b1yvxD2OiASMaoUYV+EpXRYVTTtZUrTHzVDRG9QmDxsxOm1jP3GT8vA/B1V79bHUdq1nt+j1KFJ4iZnq9yYEdfp1B37nKJ4wJr5jg+jjf5V+knXxQrGQd06d9CDzKTa+ljGgM54IFbtje6bgwjtAF2+mgHGw0jfEvJhBvJJbzLArf6Sm9AWg5E8TMisf09sKav23rWqMDDXejZ1c/ensPwBdawNJfKlL35zF7UZzDe5Smg2TF26JW2ZvmaQRhOcit0Xgammymhav2j5MojDD0ZsXA00b+kv8aSP+xIKcMNHse6dJI3peTf9a7tah+OdC012yw6/l0GpM3o0jfCmLKaPyaVTIPDueCLFdnEX4UR/jHeI2xd8ywfZ4vG6cQrHwCUolicNMO75Eao1Wt9ljqMkjn87YGervV9HsM8nlcMPU0HGIvKnk6XepJ9QhG9pkMioj1rSzh0zdGMHTZIGjSbYPrU3njrdhIozRoeseeO47pMGIP0whfC8L2oaMsgGY5KMfG04OCWSzcDcBWOaB1XstlSBppGdiPPKpfl2kp/yAiIqINq7lAjtagezc/GHBJl/OaigGYWhXTnGpXF8vFn7VSsemGdX/+8bJxTN2cBD63w1pWOe+G/ehortEkKvH+66ISX6WRVlB323LyoZGqjZlstnBVcXnF7QUmDH/iya1XOoChwwaPCdZlRaNmCuOicVymXetY1SrXr2SMiEjZINTC8wzityKFwFNlV3a9QfNtsOIJYznZP2WjYbcVvYUrqyXrKNLw8JEa63gngPCqHrlfKovYbfmMkxMina2iHbQuvGrB6PV5jGrBnDtjGPowgGSt218ycUw4HRi/p8B+PobQlxaDIEvJuDfabRl1G0Ti3PjmAHp3zcB0Zhqe/b3obnF8keRvs7kJ5SRs+Sv0TcgNmqpRMCoafuWHN4voV1Zs3bYVPbYGg181ON+qFqAoeULR95MIPCz/oWw6gdA3J+H6IiDnCBXHrvnzSNMNZbucvJdc0fgu/41mygGjvM9IcXyTdHAWvuviSJzSxj3RZ7WuMF6a2C8X/PDfs+XGUTOUKxtzYZk4Rs5OIWFUlj0KwP2BDG6e9WJ4xXhZrR/LFUSZ0pKSR51H7leUKdk0wjfztxZmsFznp1KNlN33RFqRk3mpRxHEfywdjLgo+0ymz2O9xretFo6jWP66H7NX7XDuqziXdjvg1oMzWlBwCvGbtR5s0L4yJP281v5ob/5BREREG4zatEV1ej9UbVHsnxZ/1bYcn1Tt2me116BPjTyRb+T9taTOfiTfFy93cEm+UW75fsn37J9UF5blG6vxh1915L8LZtUXl/NLLc+ro0r+M1AdgZR8w8ByTJ0czH/Wrk7eN145bV/Y8r9rtA1/Lauxi/bCb9rORdSlv+R7Bctq5KxNFZVI+TlF7T3oVkfP+VSfeHmO2dRebb0Vmzr6S8m+bNc61rWa9Yupvj35z0M17XGpHvHZ0RN2tXenTfUEJlW3fE856FVnw3PqbDR3PBa/s+nzzafm1FTJvlp+MKu69e9UVOdPlcdO7Ofz9irr6FFdgxZVVOHFOtpV313j9Ni4iOqV6cj9c6vftQ78tajOnrLr+0fZ51InQwtq6k/5nrC8tKhGfvCoNrHNyttO1Xe7zjaXnGd1909qVnXK42U/O68uLrWSCWgWVf+h3G+bz8XkvGaU5IV7fCIVVxLHXl/f3MsblbObEfepZn15mzr9QM4zsPhDMd/QXsrbNtWWT8fa3/s8qv8nX+Hc1o9dcF6NPMjt89WdR6W/q6i290f1c9z3pVu174Rq/6FYOtQvBxrJ+ww8mVVd+e8V6zAabjVNlIudMxfWqZHybjHgLOQruX0cURdSS+pSMqbOXnDp54X2nuWjuarf1eqx1In9ks8zoXjUuSct7Jcnc6pbrndpXuk5JtZpp0P1/egrlKeWj6bVufCsOh8v/t5S0C2XFa+PZo2P6/KCOpk/l1aUT8vq/Knce46LC2ppLrEU9al2fd0sqvdu9W2MnFHkd4vXMbEOcn6psv2ueMXZW8vqy5DKMjZWkn+Wa0P+QURERBvWKgI5oiIS9crGRfWK8/Jtb67BXlIRyb+Ut0UlSVTmYud6SypCJS+lV1R+5Bf9ISrqolGw4jPiZXpfNDrkx5ojGmD5oMZuowZYTrES71D9f8iZZVLq7DFTYX3KXjtd6lx+5R74VUfNbVgWFc0q+0KrIJ5dWaVMhX2q8+2Symn+tdOuui/Mq6nCYWnXOjan8fXLWU5MVxxnk2o/5VcXZB04dqEkOFQSBFr8WVSa95Xsu50W1SK/p14gIRWeVN37DfaN+A7XOdHQqr5o4/INcWVUna/ezug8TxbUuR9GVfdhGZiT+860x6Y6TvhUf1RL1Y2Jnbfklj81X2eZRdV/tCJNiWPlODGqTgdj6mLVBlEVhYCuS52tDCw0oDQf9PxitOZL6twJub57vGpsNcf/9mhu+Rr5lO7PmDp5uDIt5xqXk6FF2XAV6/OR9hkxf59NdZ3yqdPRFs8jg9/VPu8N5hrcLZUD4mUSje7aec+yuhDIBQ7r7qPVeBJRfXL7XFUuMlRauj+reo8Yb5MWpPaF6+SmrRzL1JzqNsp39ZdJtVxY3R5a+mW0EITSX6KMdp4T+bgelMmvi3xPlCvTCZHY7/qqHHuxzufz69FI+bSkRi66Vcee4ueUty2F7zbt96h+7fdqWP7FU1i26nEsCQoqZ2qHcfKaKkPuThbOqRUvsT/dP1emizbkH0RERLRhbdH+JyoKTcoietoK61dxYP80FkMu43vJ17NnGWSed6G7u8b9Us+zyDzLoqu72+C2kHVC3w45rXXLr7U9L0NT6yf2txwPoOtVsc8rbpvJZjJ6l3uj90qXzWliX2TFOhYWbe8+TH4/gB0fhGE+F0PsVLXbMja5Z1GM7bVi/J4Ls0+m4TC6NUa7xe6qD1PRHtgP9WDpRgiBG3MI/1Z+T4PpsBe+Mx443qp/DJOXDmDHeyHYv1vE3PvN5mBpBN7twfBV0Sw9MYfERYMnGely6dI4zdaXTz/2H8Q66k/sqi1/jmhW95urO4+Kv/sy8qA4Jsz9CH/c2D5qVubacWz7UMF80ltlfJwqZPlR8Epzj6lu/Vi2Wcn2GJWJhfx5LcvLVe/Txs5DfRuaPE66NStDGltvIiIi2nxWGcgRRONrfNCKsTsKnD/F4T+syDeIKCff2Ldj+sEcXCvGw6A8/fHzljFkv4wgcqZ8PJ3svSkMH/aj92II3sGKcMmzNBK/iWVCYQSvTCH0UJvZwP5+FsbImwPwD/oR+dHZdCA6c/0kev85hfQeLyI3m3jceVOSmLHvwPG4G3P3J9s39ssGk701BpMtjalqQcCW5I7B1D4GYomIiIho/Vh9IEfzKIjjg0OYeeaEP+qHMz/wJREBjwMYemMYyTMRRAwH+6VSySvDsDoTcIXD8O6TAZuHMzjw5nGkGurRlEH4tA0DX8XhCKQwe6RacDmL8GcmDNw+ubogzKMAhi3DCKDN+Z7Wc63kqnv2v2Ow7p1BLwPlNeQCLWO755E8a2v7OZYLEsXhZSCWiIiIiNaRJp9aVWG7A9M3Z+F6VTRsjkwg3tCTRog2h+QNP4KKB75PGMRphOmIH5FAPwI2O8b/m3sSTfzqGELiX7ulkd4Q3bDZh/Spnler7fEMol/ZMHB7CHNXVhHEeR7HxHvDCLzqanvwOv6fHejZdQAnT09g7MMD6D88ji7tse0M4lSVuS721Q07vO+1P4ij3bI19cU48LnH4OlSREREREQvT2s9cvIycYQf9cK2m81V2oySCL43gKHbTkTue2HRTgO918Yk+q6FMbqH50UzMr/NYOTQOJY+nsXpV8ew+70QzAa3XK2UQfDDXgzFRxCLerAi9JMOY+Lj45hVvJg560TvKm+Hyt4LIf66HZZ238bzOIjhd4YQ0If9UWD70o/ZM5WPNKcC2TMq8eFa9HjTHv1sg/V0D/x/zMJZ9th1IiIiIqKXqz2BHKLNLC0a4D2iAX5oGotBF7bdm8HI4Rl0nfdj8mDHDQO+PjxPI/ztGBKWUfRcHMDQpaQ+kLH3Uyfsb5tKBiPNIpNOInYriJmzM0gPejF5xihIk0bwMx+WHCNw7VnHPVweBTHxQwo99iE41/N6vhRZpB9l0NXdhaXf/Rg/ehIzz9o4ftDTNJKvdGFbNoXwxZNwfxWG6XwMkU84Ng4RERERrS8M5BC1LIvEpZMY+mIGCfTCfsgNz2k3bGyHt03m9zBC14OYvRlD/GYUSTkfOy2wmfth2W/D0KAd5tfZ+2nDygdM5Z+ABd5o+3q8xf/dj/4v4vIvQDm6uoGwiYiIiIjWGgM5RETUEeL/saL/06iYssD9c5t7vD0N4eSuA5hKA8pBH0IBD8yrvP2OiIiIiGgtMZBDREQdIoPknQSyOy3oXYvHsafjCKd7YN2tcIByIiIiIlq3GMghIiIiIiIiIuoQrT1+nIiIiIiIiIiIXhgGcoiIiIiIiIiIOgQDOUREREREREREHYKBHCIiIiIiIiKiDsFADhERERERERFRh2Agh4iIiIiIiIioQzCQQ0RERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5REREREREREQdgoEcIiIiIiIiIqIOwUAOEREREREREVGHYCCHiIiIiIiIiKhDMJBDRERERERERNQhGMghIiIiIiIiIuoQDOQQEREREREREXUIBnKIiIiIiIiIiDoEAzlERERERERERB2CgRwiIiIiIiIiog7BQA4RERERERERUYdgIIeIiIiIiIiIqEMwkENERERERERE1CEYyCEiIiIiIiIi6hAM5BARERERERERdQgGcoiIiIiIiIiIOgQDOUREREREREREHYKBHCIiIiIiIiKiDsFADhERERERERFRh2Agh4iIiIiIiIioQzCQQ0RERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5REREREREREQdgoEcIiIiIiIiIqIOwUAOEREREREREVGHYCCHiIiIiIiIiKhDMJBDRERERERERNQhGMghIiIiIiIiIuoQDOQQEREREREREXUIBnKIiIiIiIiIiDoEAzlERERERERERB2CgRwiIiIiIiIiog7BQA4RERERERERUYdgIIeIiIiIiIiIqEMwkENERERERERE1CEYyCEiIiIiIiIi6hAM5BARERERERERdQgGcoiIiIiIiIiIOgQDOUREREREREREHYKBHCIiIiIiIiKiDsFADhERERERERFRh2Agh4iIiIiIiIioQzCQQ0RERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5RJtc5mEIUx8eQF/PFmzp6cOBr8LIyPeIiIiIiIhofWEgh2jTyiL+zRD6904gdXAGsZSKpe9sCJ0egPtqWn6mCdk0wl8PY+JX+XdL0gh+NoLAbwwpEVFny9wLYOSzoMjVWhf/j8hjb7Xjm4iIiKiTMZBDtCllEf33Adg/TsF1bQ7e/Qq6xLzE3RCg2GB9U5Gfa0zmvxMYemcYodfH4PqbnNkSBY4PrYh93I+BT4NIPpeziYg6xbMEAp8OwHo2BfunDpGrtc58bARd31qx490pxBnnJiIi2rS2qIKcJqJNIntnHDbLGLJfRhA5Y0GXnN+8LBLfu2A7DUxE/XBul7Pb5XkSgQ8GMJxwYv66F7bX5HwiovXsaRhjBwcQtkcQ+tKCbjm7PTKI/nsIjgsKvLdm4Hpr9Tk4ERERdSYGcog2nTgmLP0YuWPH9IM5uHbK2auQvDIMqzOJk9EwRvesVWMiicC/rBh+cBKRm6OwvCpnExGtR8+iGB+0YvJNPyI/OmGSs9sri+hXNlgvmuBfiyA6ERERrWsM5BBtMukrQ+hxBoHDfqR+cq66u3++V8+27xYx9/7aNFUKHgUwbBlGeHAtG0ZERK2Sgeebw5h/4INtLQPPMmA0Bi+D3ERERJsMx8gh2kyeheH7NKhPuo7YVz9mg2hAeE+MIap44DnyAsIq250Y+cyC9OVhjFxOyplEROtL8vIIhi+nYT/jXtsgjuZVC9xfuKHcGYP7XBRZOZuIiIg2PgZyiDaJ7KMwxp3DmNAfeOKCfe/qR22If+/B+D1AOWaH9QVdBTYfFOss/g1+NoHQ09w8IqJ142kIE59pgXI7HPteTL/B7kEHXIrIk7/yYErkyURERLQ5MJBDtKFlEf5sC7Zs2YKtpgGMXc8/tnYGQ/+nzT+JULNPPhGNlZlzUX1yeJ+19kDJ2Qwyj+IIX5sRDZzjGLANYeahfE/zLInQ18dhfVOsS88ARq7X6G2z0wbHoPg3PQXv5XhuHhFRk7KPowh8JfIjyw49b9RePbsO4OQ3YaRbeEJe/LIXU1oWO+iArdbYY8+zyKQTiN4IYOr0SQz9w4qxm6X9aTKIXxrBgV09Yt12YOibePXeNl1W2I5qE1H4vguJJYmIiGgzYCCHaEPrgu2cCm0oLFWNwCvvpXIEUnLeJOxNdszJ3A7mGitwwrqrVhgnjol9Vgy9N4xhx3GMfD2D8Cv2YgPnURDHzTtw4LMZRLXgTjqMiQ8CYqlqTOjbm5uK/hiu8TkiIiMZxP9zAKY3rPDcUuC+FMvlg8sp+J3A7McD6PmfXGAn/+r/T6M5TRzhH3MBbmVff41xvDIIfdwH+79cGLYP4+RXUwjetMK2V+al2rg3tl70vzeB0G9aRptE8GMfQvkY/Apd6DM79Kn0t0GE2VuRiIhoU2Agh2izeLiAsN4YMMPau9rRcTKI3JzJTSp9MNX8GjM80QXMhxfg/1zO2S8bOPrgxSPAxxGk/hINqfCo/j6U2k++Mu3MNVhwz48wbyMgooZpT3myo//TENK7RxH82QvHWzKK3aXA9vkkvFqPvwq2t3vlVB33wvDLPMm2syc3Yagb9ouLiPwSwfwP2s2iwgkb+rWsTx+82IHw36ewuCTyxeQ0cjneNnTVyBoVU7+cmkE4yj45REREmwEDOUSbRPpuCGFtQhmCdbc+axUSiHwrJ/eaUKu5UhRH/Ib2r4IhiznXWHnPj/4bC5j+yALlFdHEei5vHBg0o1azqdhgiSNyn4MeE1Fjsncm4D6t9ZhR4D4zYvCEp2KPPxydRUrvsajCN1g7uJyXvB8p9BLse6ORQHkG8dshfcqxtx/d2tOuPhxD6osI5s84YNJiTM+1Twlavlir5+TrJhnwAabuJuQUERERbWQM5BBtChnEbueeVoWjFphzU817nEShmbBdEY2PBtwJwadfqR6G5e1cYwVnZ+HZnW8gZRG55den3KJBU7PZ1NVVWPfgg6r3GhARlcgg/ONYLtCiuOAYNMq50kg9kJOXE2g2TJx+JPNX2KC8JidreRyC/5I2YYP9nW5EvzqOuf3TmDxYvCkrKfJsLfhe6MlYzavdxaD6b8mm152IiIg6DwM5RJtBNoaw7EnjMPfVDpbU8jiJfHMF/7u1oe+JR2dFE0k4YcW26+MIi8bK6J6SJbMRhC9pn3DXf5LWaz3FBs3vydz3EhHVlET8mpzc24c+o4wru4DIZTl9yITmbj5NI3lfTqIbWxvIGDPxSC4v3W1H39MJ+ODFzJHScE0S4atajx0zhvfVCb13bysGcq4xXyQiItoMGMgh2gzuRZHr86Jd/V3t+DirkUTsRu6GA2dXBCNxJybLGiui/RQNY0ZreZyww9pQFx8iouZ05bO9Kj0Js7dDMo8E7ActtXvAtCyL2O0pfcq8N4WZcwp8X1rKA+MPwwhqt6TuHoZt1bfCEhER0UbFQA7RJlDoFaPY0F/rsbj1vKKNMNGEx1GEbuYmA1eA0dO2il48WX3wZL0/zn5rY7dqERE1xQybU/ZquRkv3h6a9yyKidMTej6kHPVj8ljzYZxagxGvFEdU9v6Jf5OA5ZxrReBIu61K74/zL9vqb4UlIiKiDYuBHKINr9grRhsfp8FnsBhTTLDKSTxI1e3Cn7kblrdiKXB/NwZb5QCjzdxWpXku/9W81eztD0S0WZlPTMG7T+QY90bg/jiIpBxfPfN7EGP/dGDsDmA6No3wRecqeuMo6HlTTiKCZL2M8V4Es/IzlvNeuFYE15u4rUpalv82f1sYERERdSIGcog2upJeMZ5B6+rHx9G8bioGgp5li40HQyWPKt/vhefgykBN07dVpYtj9NgaejIMEZHwqgWjv8Qxf84F3BjCjq1bsGXLFvQfm0L6b17MJZaw+IMLvSueZtUYZXv+uVFpLMsgUTXxW3458PIovCcMAjXN3lZVOgj9TqXBpwkSERFRJ2Mgh2iDKwyqCTds77QUxhF6YT0hJ+sNqlkYYFnB6Klhg6vcxduqXIO526oyaf1hu1VlnqTklALbrrUdxYKINphXFPT9rRd9Zg+moyksqyoWo/OYPueC/a3Wbuw07bIWboFK/FErZyz2kLSfdcFmkCUXbqty5m6ryqbTIres4WlKfGtOS4PZExERUcdgIIdoQysOqtmewYS7YR10yekYko/kpJH8AMuKaKxYDJoWhduqRCNqbzeyd8bhvV37Unbyt9nchHIStj25SSKi+tIIfWxFjy0Jxw8+uPYo7Q147LZhWPaeCSZqPAC80EPSDsdeo2B0yW1Vg2bgUQBjl/MBbGPpB7FcDx84MLSXPRWJiIg2AwZyiDa04qCa7RpMuHu/E6N6WyGIyP3qPWgKAywftcFq1GL6PY6QvHCdujuFibt2eA/XaoQkkbibW8D8qR0WfYqIqAG/zsD1TVRMxBC6Hkf6WW52+5jh+Niem7wekYGVlQo9JAcdsBkNPJ9JIK7dVoVtWHoQwMTlbrhPmWsGnZL3A7mJY8Owv56bJCIioo2NgRyijSw/qKYyCsdgO8I4QpcNQ5/lwihTt2NVuvwXbx9w7+03boS8ZkKvIlbt7WVku4Yw+lHtxop2JXv2mjbhwtixxgYAJSLSvWXDSb0XXxRTzn70/O8W9OwawPHPphC4lUCmzrg2jTAddMOtxaLvhRB7mJtXruSx4/v7jQdV7upBj7aeO7uQfW6G60t7ncGXowh/r/1rhu9jB5/8R0REtElsUQU5TUQbTPL7Aez4IAzzuRhip9oY/HgWxdheK8bvuTD7ZBqO1+T8NZS8dAA73gvB/t0i5t7n+DhE1KBsGuFvxhDI2uD4G5C4PovZm0FEy4ItCmzvj8F71g1LC/lZ8vIQdvwr2P48t4rsrTGYbOPAqXkkz9k4Pg4REdEmwUAO0YaVRuDdHgxftWP6wZzBI25bo41pY7OMIftlBJEzlrVtQDwLY+TNAfgH/Yj8uJrHAxPRZpS8PoLjn6bgvD4D11vluVQ2k0QiGkXk1hymLgeQ0HsvejD/wAfbKp9epfVGDPzLiuHLVviTs3Bul7PXRBIz9h04vuRF5OYoLKteZyIiIuo0DOQQbVSPAxh6YxjJMxFEvlybQEvyyjCszgRc4TC8+9aqU38W4c9MGLh9ko0VImpY9uYITP+YwIHgEqYP1cmfnicx49yB41cBb1TFaCuDqT+LYnzQirE3prEYcMH0ipzfZsnvD2DH6W74o/41DhgRERHResMxcog2qOQNP4KKB75P1q63jOmIH5FAPwI2O8b/W/vR4auTQfQrGwZuD2HuCoM4RNSoNEKXJ8T/HbCZGwgyv2LCgUMOMWFGV6sZ5qsWjN6IwPt0DNb3Akg+l/PbKHl5GNbTgO/GDIM4REREmxADOUQdL4ngezuw5c0xRPMDdmqPrD29BO81bwu3CDTGdGQasfsuJI/1Y+ibONoWzkmHMfFuPzxPTmLh5iTsbKwQUcO60f26NvJwELO3azwOPO9ZHP7LQSgnvHDJx4i3pNuC0V/imNk+g4F/jCD4SM5vVSaBwKcDGLjah+D9OXh2r+lNrURERLROMZBD1OnSccxeEg2VXSYook6fuTeD44OT2PadH6N7Xkwlv/ttF6YTEbgxBf+vcmZL0gieD6H70wgiF5zoZU8cImpKF2xfBOHdpyD4LysGPphC6Pd0+dOpnmeReRRH8JuTOGAeQmRfBImL9vY9+ekVBfYz84hdsCJxOShytdbFL3mRGpxG7OfRlgZlJiIios7GMXKIOl4WiUsnMfTFDBLohf2QG57Tbti0i9FERJtaFul7IcwFQgj8GsHCrUQhoKK8bUPfO2Y4Bu2wDdrQy8AIERERdQgGcoiIiIiIiIiIOgRvrSIiIiIiIiIi6hAM5BARERERERERdQgGcoiIiIiIiIiIOgQDOUREREREREREHYKBHCIiIiIiIiKiDsFADhERERERERFRh2Agh4iIiIiIiIioQzCQQ0RERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5REREREREREQdgoEcIiIiIiIiIqIOwUAOEREREREREVGHYCCHiIiIiIiIiKhDMJBDRERERERERNQhGMghIiIiIiIiIuoQDOTQppe5F8DIZ0Gk5d8t+XUCw1+HkX4u/6amZR9HEfjqOKxvjiMq5zUmg/ilERzY1YMtW7agZ9cBjFyKi7mNanV5IqLVyCB5Ywon37Vih8h7tPxnh2UAx78KINpEwZT5dQYj/+xDj/YdPX048NkM4k/lmw1odXkiIiJ6cRjIoc3rWQKBTwdgPZuC/VMHFDm7JX9zYaRrCtbeIUz9yhBAw7JpRK9M4KR9B7a+YcXw6RlEH8r3GpGJYtzWi/7vsnBdS0JVVdEwcqPru370/nMC8Wfyc9W0ujwR0WqIcmjmvX7ssJ/E1NUoknJ28k4YM6eHYe2x4uT1/NxqMoj+ewC978wge2wOSZF/qckw3K/MoH/XAUzcy8rPVdPq8kRERPTCiQYL0ebzZF4d3QPVciaiLslZ7bR026vaFEV1fregLst5VF3svF11f+lTfaccqklkS1rWBHjViHy/tpjqE8cSsKvTD+SsvAfTql18l3LUry7KWSu1ujwR0WosqXMnFBV73Op0dFFd/is3d/nJgjp31q4qhbzQonqj1UuS2HmL/jn7d5W51KI6vV8srzhVf1LOMtDq8kRERPTiMZBDm8+fEdUrGu5r3ThfjnpVCxTVGWAIoHFawybfeGkskJNvhODYrEFQbkmdPZb7PsePxseh1eWJiFYl7lPNe0Q+96f8u8JiwFkM5uyZVBfk/DLiOyz6Z1zq7BM5r8RS0JVb/nCV8q7V5YmIiOil4K1VtMkkEfjQgbFHHvgvOmGSc9dC1x4PJs6YEHAOY/wOu6Y3phvbeuRkI56GMHMuN5KO+5BNLF2pG9ZBhz4V/GwG4crD0OryRESrFL0egfvyKCyvyhkVTEe88O6Xf9wJI/5YThdkEPrOlxtL7IQDttf0mWW637FBz8GuejBzqzIDa3V5IiIielkYyKFNJXl5BMOX07CfccNWpfLcPl2wnBiDW4li7IQXUY6z0nbpmzOY0gcDtcHcuzIMo1F6rTBrE+lxBG+Wj1vU6vJERKuTxMJfwxjaKf80ZILtkE1OG3gcwsy3udGQbeZeg0C08HovrLu1iTTGr4ZRloO1ujwRERG9NAzk0ObxNISJz4Jiwg7HvrXsi1PiNRscxxTg3jg838flTGqPDGK3teOp6UWPwdVknWIS7+ZM3Y6heE251eWJiFbLBNcZh3HwpMTWV/OfMEGpyKMy8QgKOZiyTU5V6oFpl5z8NoxYSQbW6vJERET08jCQQ5tG/LI31/ti0AFbzaugRioeD9vTh+Gvo7mrk08TCH1zEhP/NarhdsG6b1ifip6bQajdj3LNZpB5FEf42gwmPjuOAdsQZkqf9vQsidDX2qO8tXUewEjdp590kgTi38pJ0djYVq1FpPSgT07iXhIpOdn68kT0Uj3PIpNOIHojgKnTJzH0DyvGbpbmwxnEL43gwK4ebNmyA0PfxDsuELv8LNcHRvncDmuXPlmQuDclp0QO9n9VMzD0vCknEUey5PasVpcnIiKil4eBHNok4gj/mBsLRdnX39zYOI+CGLH1YuBSFo5zYSzqj2adw1DSDdf3Mxj5vz4c+Bjofbuili119fbnxhhITyF4u50d0+OY2GfF0HvDGHYcx8jXMwi/Yi8GqcR6HzfvwIHP5KO802FMfBAQS20Qj5OIyUkMKo09Pv5mGrkbCYRWlyeilyiD0Md9sP/LhWH7ME5+JfLXm1bY9sp8+FkU4yLf7n9vAqHftLM2ieDHPoQ66gROI3ozLP41Y+RdG8pLmDSS9+UkbCt66xgLI124mNDq8kRERPQyMZBDm8O9MPz3cpO2nY2Pppu5OQaryY34YBCxnzywbZdV6S4THJ+6kfngOCa0vw9b0V/tgubrJvTLyZmbkVwvnrYwwxNdwHx4Af7P5Zz9Mkj1KIBhywjwcQSpv1So4VH9fSjGwaaO170VW+VkbTHjK8qtLk9EL1g37BcXEfklgvkf7LlZJ2zo17I4LYgz6ED471NYXNIC79O5YDq2oauTssCHc/BfFdn2CS9c+jg11XRja4PbFUsaRbJaXZ6IiIheNAZyaFNI3o8UeqL0vdFQ3wtk74zD/o9x4EwQc59bVo5l0LW1MM82aKnRo8ME02E5+W0ECTnZPnHEb2j/KhiymHONmPf86L+xgOmPxHq9IrblubyhYNBcGO+lujQC727BFu0WslW/xnNPQiEiWlMZxG+H9CnH3n6RJ2tPJhxD6osI5s84YNIy6efapwQt/6sWcC+RvjJkkKc19xq/I79s1bKIXplCSHFi6gv7yvKHiIiINjUGcmhTSD/KD+nYYBfyRwG4Do0huseHqS8tFV3aJdE4yDHD/k6tm7W60F34zQSSj+Rku9wJwaf3NhqG5e1cIwZnZ+HZnV/rLCK3/PqUWzR06l94VeD8SYWq3UK26tcoLPLb1pcedLf0tLJWlyeitnocgv+SNmET+XA3ol8dx9z+aUweLObJydtB6Dco5Xss1qEcmTXI05p7je6RX7ZaD/3wngZGr87A8bqc1wY9rzbY9aaKVpcnIiKi9mAghzaB0rEAGulCnsTMh8MIpM3w/sede/S0geyDWO6JH8qQfDxrNd3YVribK4h290yPR2fFFgonrNh2fRxh0YgZ3VOykdkIwpe0T7hh37vZr+vWGNS4Ia0uT0TtVHjy0m47+p5OwAcvZo6UhmuSCF/VeuyYMbyvWm6+3sQxcXQM2bNTGPt7ewMn1Qc1bkyryxMREVF7MJBDVCFzfQJj2q1Kx8bgLg2IlMkiLD6nO2qpGuxZe0nEbuRuGnN2RTASd2KyrBEj1jQaxowWxzlhh3Uj1cFfLz4WHA9S1Z8mlVkqvnfIVLwFrtXlieglyyJ2O/fkJfPeFGbOKfBV9qB8GEZQy893D8NWM+C+XmQR/cqNWXvult7qYRwFprfkpCgHUlUHIc5gqZCBOWAqZGCtLk9EREQvEwM5tCk0PsBlErPfTuk9XDxHaoxL8NCPqW9yk55BawO3K62Rx1GEbuYmA1eA0dOVTzbJInJzRt8e937rBhtnwYT+o3Ly3pLY0iqeZQqBGMVsKrm1otXliejliiN6WU59k4DlnGvF+andVqX3x/mX7SUG3BuXvOKCKzkCf7VbekuYdjnlVBxLz+TkCllk8kEapR+m7XJaaHV5IiIienkYyKFNQEHPm3ISkdq3Nj0MI6APHOyG7Z1q1egkAl8c1xsHtT9X4i/5b5uvaGbuhnO3FYhtdH83Blvl+C0b+rYqBeZ98mk1tcYeepyU+wgY3lPalGt1eSJ6qe5FMCvzc8t5L1w7c9NFnXVbVfL6SRy/cQBzP4hyQs6rRTHbUMjBkkk5VSmJ5FU5WdF7tNXliYiI6OVhIIc2BWV77uGz2ng5y1W7Xoh342F9UMzqY6Fo3d5H4H8mb8qp9djxgjSSv8tJUT1X2hbIyei9bXT7vfAcXLkiG/a2Ksl00AWXPhVE5L7xg92TD2K5CWUU9r3lQbdWlyeilyd+yw/9xlJxbnpPGIQYOui2Ku0picevmjF50dl4r7+dQ3Ady00Go4nck7kqPUoil4MpGN1f0Xu01eWJiIjopWEghzYF0y5r4Upi4o8aXXLyj+nGkkHAJ4Pw6SHM7BzB8Ku5h4jXfux4XgqpB3LycD/62lUTzsYQ/labEBXsU8MGlf/ibVWuwdxtVZm0cbCiY73mgPt87vlYU7djBrdHpRG9nutP4zh/ErbKfd/q8kT0khTHB7OfdRmem4Xbqpy526qy6bTBOf7yaUGcA18A3osu9NZ4Kl72zgSmyh5r3g3Hx77cEwK/DSNmsHHp6GyuR+HhCZzcV7mTWl2eiIiIXhYGcmhz2G3DsLwiG0xU60IOdL2af7zUBMbOhJDWHzGeRfrODEZsVgR2TWJ6XwpzeldzBbZdJmRvjmPiV+3vKtKiwaE/HhxwHLI1EPhp0L0o9IeKK6IRYzGoYBduq3Lpt1VpjQXv7fXYjKkmhuRjOVmD+f0JeLVH/X49hWDF7VHZX2cwKY6VctQP3xHjPd/q8kT0EhTGB7PDsdeoD0vJbVWDZuBRAGOXC6P2rhuZ/8ogzs+jsFQL4mQzSNwYx9AngLXysea73Zg4o4ViJjB1taJsy8YxcyEoMjAn/OecxmVPq8sTERHRy6ESbRKLP9hVLcljt0+NyXkr/DmvehTxGe1zpS/Fpo7+spT7TNQr5zvU6dtz6vTPi7n51dwelZ93qbNP5Lw2iJ0357731Ly6LOeViftU0XzRf3cyNKl6L8SMP7eOLCfnVM9ubZ21l6I6f1xQl/+Sb9aSnFVdO6Eq+0bVuVRu1lJ8OjfvoDjef+bmVdXq8kT0Qi397M7lE4PTqmEOvDSnuvV8ROTdP/lV35k548+9REu/jKoWfR0be9l/qLYFi+rsMVOunArJDOxJTJ3W59lVX7xezt/q8kRERPSisUcObRqmg264tUuK90KIPczNW+FVG3zRWXgO9upXH5W3bXCdm8NiYh7eQTnIzOu9+qCayttdyPzVD9fB2iMaRG/lxrExn3PD8Zo+2QbF2wrce/uNxy14zYResRHK28vIdg1h9CPz+h3f4M44tmzZgq2mA5iQvZe025oC/+rD1v/Zgi3vBvRbxKra7sD03QVM7UvDu1d8fksPrJ9G0XthEYmfPTDXuF1B1+ryRPQClTx2fH+/8ZgyXT3o0Xqv7OxC9rkZri/tjY898wJkbo3B/o9xROXf9VXreaQxwfFDDAsXbUifsep5ac++EUR7J0XZNQfP7no5f6vLExER0Yu2RYvmyGmiDS95eQg7/hWE+VwMsVMGg2O2WzaMMdMAxuHB/APfyqdKERERERERETWBgRzaZJII/MuK4ctW+JOzcG6Xs9dI8vsD2PHBErzRMEb38KomERERERERtYaBHNp8nkUxPmjF2BvTWAy4YHpFzm+3hzM48OYYugMR+I+sp079RERERERE1Kk4Rg5tPq9aMHojAu/TMVjfCyCpP5mqzR4FMLx3DDgfwgyDOERERERERNQmDOTQ5tRtwegvccxsn8HAP0ZWPHZ69TJIXBnBwKAffVcTmPtkHQ8wTERERERERB2Ht1bRppf5LYipa4DrS4f+pKqW/DqB4Vu98L5vh0k+5IqIiIiIiIioXRjIISIiIiIiIiLqELy1ioiIiIiIiIioQzCQQ0RERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5REREREREREQdgoEcIiIiIiIiIqIOwUAOEREREREREVGHYCCHiIiIiIiIiKhDMJBDRERERERERNQhGMghIiIiIiIiIuoQDOQQEREREREREXUIBnKIiIiIqHM9TyP89XFY39yCLVu2YIflOMavJZCVbxMREW00W1RBThMRERERdZAkAv+yYvhyWv6dp8B2Noi5zy3oknOIiIg2CvbIISIiIqKOlLk2jsnuCcSeLEO7NqkupzB/1g4FaYS/8ML/UH6QiIhoA2Egh4iIiIg6UAaRRzb4Lzhhfk32u+lSYPt8Fv5TivgjhNDdyp46REREnY+BHCIiIiLqQN2wf+KESf5V1AXbP11ymoiIaONhIIeIiIiINpTssjbUsRnWXq1nDhER0cbCQA4RERERbSiJe2Hg8AiGd8sZREREGwifWkVUQzaTQepRDIlEAol4HKFfAfeP03C8Lj9AJGUzaSR/jyF+N4LI7SiSe32Y+8gs3yUiarPnWWQeJxCLi3wnGkXodjc8N3ywd8v3N7NsGGOmMWy7EYGHgRwiItqA2COHNr3MvQBGPgtixXCId8ZheqcfVvMADjhPYuTrGYS7LDDXCuL8OoHhr8NIP5d/vwSZ30OY+vAA+v4VWLlNtTxLIvT1cVjf3IItW7Zgh+U4Jm4koXVOb0iry3cyLa3steGA5QCGPx7H1NUl2PYyiENELXoaR+CzEQQfy78L0gg4+2A9aMeA43iufOq1wrpBgjjx/wxj4tbqBymOfzuO5Hk/gzhERLRhMZBDm9ezBAKfDsB6NgX7pw6suIt+zyhSDxaR+nMObjnLdshmMKhiib+5MNI1BWvvEKZ+zciZL8DTBEKXRjC8qwfbeg/g5LchJJqJoDwK4Lh5B1y3ezERVfVHuMa+tSD23g7YPg4hKT9WVavLdzotrdxfwOKTWejDaypDsLIBQUSrlkXiyggG9nmR2j9i0AtUgfOnRSzcTyF2rlef4xi0YqN0xjEfG0HXt1bseHcK8SaL0uydcXifeTFzpGZpTURE1NEYyKHN6WkYY4N9mNzmReQnD2y1xkJ8lsWSPmGG/Z16FcNumD+aRexSP4IHezH8feIF9EhJI3jai/DTHpgsfSsDUvU8DeGkZRgzzzzwBzywvJab3b3bhZkfPUh+cwDDX0Wrb0ery79ojwMY2jKEwIor3K3L3o9hTps4ahGphYg2tDvj2LJlHFH5Z/tkEP7Chr4L2+C9PQvPvlq5ehKxWwnxr02UTxtoUN9uM9w/xeA3B2HvFeXL7w2WII8COPmdCb4vLZAPIyciItqQGMihzedZFOMHBzDzph9+UdmrdwUzez+CgDaxexi2BntZdP99FHPXTiL5gQ2uK2vdH0WB46IfvlMeeL/zYaSpniAZhE67MJUGzJ+K7XtVzpa6Bof174uedsP7X6OKdKvLbyRZRG6M67ezuff2sxFBRKuQRfQrOwYumeC/MgpLvQLqYRiBG+Lf3Xb078zN2ji6Yfl8DsEPkzi+z4XAIzm7mowo2y8Ao99VPo48i+xLvN2ZiIhoLTCQQ5tMEoEPHRh75IH/YmVlz4honN+c0KfMTltTvSy69ngwccaEgHMY43deVBCjBz1vyslG3JuB91st9GDG8KDR1plhdWhXeeMYP+tfeYtUq8tvKHFEL2v/umHfy9FGiah5ySsuOE4n4flxBs7tcmYN6bshhMW/5n81Vz51ji5YPpmAd3sAw0fGEX0mZ1fSgjgfhmE7I8r1V+Q8TTaN0BcjCGrFFBER0QbCQA5tKsnLIxi+nIb9jHtF7xFj+ca5gqGmB68VFdATY3ArUYyd8FavgL5E0es+eVuAaAS8pU+s0Lt7KDdxYwrBe7nJvFaX31DuhDGpNRYOW9HPOA4RNetRACPOANL7vXAPNtKnL43wtaD4V5RPlo0ZxtG9aoH7CzeUO6I8PWdwm652q/R+K8aujMH6v7nB9guvrT04cM8MC580SUREGwwDObR5PA1h4jOt0muHY1+DgyDei2BWa5wrLlhWM3jtazY4jinie8bh+T4uZ64XcUTylyl392BblXZDd0+PHHcnjtDd0j41rS6/scSjs/ptVfb9Frm9RESNyiB0zgO9hDpcZ1D9vEwMkavi39WWTx2ke9ABl8hY4195MFV6QSATwohlAON35N8GGt6fREREHYSBHNo04pe9+lguEBVCW4NjCcRv+aGHX47aYO0SdcZfZzDyzz70aFf63rTi+FchJGvee98F675hfSp6bgahp/rk+vA4gUi+QvxmD3rk5AqKCVY5GX5Q8jjxVpfXZDPIPIojfG0GE58dx4BtCDMP5Xua0kea9wxg5Pp6DQQlEbuhpRQbHHsbaDJk04heGcfxf1ixQ79y3IO+f57EVCOP29WeUPbNSQzZZDospMUgErWe7rJh9jWRgU5P34XbVBvMQ4Ts3TCmtAlZPtWT+T2EqQ+HMLCrp/F8Q5dF+k4A4+8N5PZfo3nW8ywy6QSiNwKYOi3yLJHfjd0sLQEyiF8awQF9fXZg6Jv4yt42eV1W2I5qE1H4vguJJaVuO3wPck9KrPaaO8YwDhERbUCikCPaBGKqbzdULckrZ2NyXj2L6vRgbhnPL0tq7LxdVcS09nfpSznqF5+s4Q+/6pCfdQWX5My1klL9h+W6HfaLv2qIeovbcWpeXZazVyhZ/7LvbHV57Zjs6VVt+3qL+3Vwurgvk7Oqa6ecn38pXrFUi/T1caj+P+Tf7fBgWrVp67fbV2f9ltSFgEe1KVAtH02rkT/kXltOqXOfW8Q2KqrtbKTqvlwMulWL9js7XepkNJX73F8ibQbk/MrXiTnxi5qXtK+JXoiXlL71PNCrRuSfrYidMze5Xsvq/Knctrh/rlOupOZV32GT+G676g0tqEt/5WYvxadVp8iLtPxkNpmbt8KS2LcHFfE7Im/6clZdeJKbvfzHvOrV58v9WXiZVV9c+8SSOnfCpFoGLaqp8J5Hnc9nbn9GVO++yuWd6myNQisVcMjPifWV60FERLRZsUcObQ73wvDL3iO2nVX7jpR7GEbwpjbhQPb6MHzP3Qg/Wc5d5XsSw/RR0WQQ0pc9CNTo1o3XTeiXkzM3I8UrievJ/25t7ClLV5PGAxavankzPNEFzIcX4P9cztnfn+sC/yiAYcsI8HEEqb/E/g6P6u9DaehXXrjCgKO1BsR+nkTgvX70OSew/GEE4QsuWF6X29OlwH52Al4ljfAXbkwYDI6dvDIMq2MKUZEe/Ten4d6j5Pb5K90wH/HBe0r/WBmbuVc+lW3j7GuilTo9fccRDshbbwd7q/duLJMfv80FW41HW2X+O44B8wBGblvgj85hdL/IE+RgwN27XZg47xBl3QyGPgvot4aW0Z7wKPbjyPU0zF8GMXfGgd7Xcm91vW7D6HkvbLk/S+THS+uG/eIiIr9EMP+DXX8HJ2zo13a79r2DDoT/PoXFJXFMktMiV9NsQ1eNw6KYCiUpwtF1WZISERG9MAzk0KaQvB/J3SIl9L2RC8DUozXOQ/pUCj3OWfhP2UUlVtYyXzPDddqLXPU0jViy1i0xJpgOy8lvI0jIScqLI649Pjc/YKdWyX/Pj/4bC5j+yAJFNDqyz2VgY9CM3txUDWkE3s13/zd4vTGMoPhv+A2D9wqvcTmIcyMyiN2WA45WHRBbC+JYMXwpCeVo7rH3K9srIp3s1f6NY/JmxXhKj+UgqGLScn7M4Gk2Xegz55pCULyIyVsK5t+vvKWg3fuaaD1pd/oWyxvmD/JlGROfGYPV6L38612DAEmlR+W3qTZUQuXHbztsg1UGVypl74zDvncM4bQF3mvGT8EqBEeuziL8ODeZk0X0P26MaRcpFDe8HxvkWTv7CoEc508peSuTD7ayD2YQv50rSR17+9Gt5YUfjiH1RQTzZxwwaTGo59qnBO2Y1Boo/nWTDPgAU3dZkhIR0ebGQA5tCulHWkNbY4NSpdJbLt841xrOUxjdY3CZUFRi82O/1NaF7sJvJpB8JCc70e4ugwBEE4yWvxOCT2/EDMPydq6Sj7Oz8IjP5mQRueXXp9yiIVD/9xXRqMgFMgxff/hFY8AB/x8G7xVeo7DIb6srE0HoW21CrH+VAUfzT0vTendNnK3/2Pv0/WRZ4y9+1acPgqoN1O06aBwsSj2K5CbSMSTKGmQl2r6vidaRtqdvC0YN8wf5inrFZ7yIGL2Xf/3krB+YSSfl+S1KKKWxCw358dtsg1UGV38WhffEmB6QNp+ZgMeoDCsTRLI038iE4T+dCygrxxywGZWb6RQW5GTg9ypjDj0OwX9Jm7DB/k43ol8dx9z+aUweLOaCSVHW6j0a872oqnm1u9hb6bcqvUOJiIg2CQZyaBNII3lfTqIbWxtpnRYa59UbzqW6ZFd1Y93YVqh9ispy3cuz61itQY0bYbB8/mlPOGHFtuvjCItKflngLBtB+JL2CTfse9ffc70LA47mbxuoVHhammionBuDs+pjcFNIPZCTZfcXiPQbz/fQsaLPcKDuJGKFQUd7YaryG52+r4lq6dT0nU7G5JQoLV7dKqdqyQ+ubob9HePQR/x7D8b1oJYLYyeMegDmZJ6k5JQClJZjD+OYlZPWXX2Gy2fvRxCQ047txgGoTDySC1LttqPv6QR88GLmSOk6JxG+qvXYMWN4X52ytntbsfy4Vh7sJiIi2mwYyCEyUGic76/xhKtHojKtT9hgMzd2FXVdUYrd1JFaqj52z9NU8crnW6bi1d9Wl9flGySAsyuCkbgTk2WVfHEsomHMaDX2E3ZY12FsIX5HXuHfb5Xj0ZRLXp/KPS0NdrgP1WiolDwFzGwu3U9d6HpVTg4qxlffC+M5icPyebVxejp/XxNVt4nS9+MoQtr5vnsYNqNegNkwZs/lbg5VPnfCXqMXauJePlwzBHNpWfdKVyFoYnrNaGdlEbmZy/u0vM1uMQooZRG7rZekMO9NYeacAl/lbaVa3qXdDldtW4iIiMgQAzm0KdQaQNFIvnFuO2Sr2tU7c19eadzvbPhx5uvK9l7056MC6QyW5OQK2azehV/j6C3ZG60ur8k3SITAFWD0tK3iyq/WWJjRr7xWC5S8XHFEgtraOWA1G61dGtEbufEh6j32PnNXNGj0KTm+R0E3rIOu3OTNKOIrHmGfRODMWG48pz1eBL+o3IdSx+9roho6OX2/0lwBlc8rFIfVOGh7L5oLWAnD+6zG+YEun38Jh63oL90pu20YloGV8L2V49Fk70xg7GttWQXOwCRchnlbfkBmMfVNApZzrhXlqXZbld4f5181BoonIiKiFRjIoU1AQc+bchKRBm5tiiJ8UftQ9W7roiqN8DXtSqMC94mhumOe4C/5r2jwmwy7VLwMvbAckytzbaFqN/Vit39tjIPSlW91+fLghfu7MdjyPU/y1vutPvmnoe23w2J4O1MSyau5KWVfrfEfkpj9fiY3uWcE9j25ybzuQ6OYPaYtPQP3exOIymBOVjRep94b0MffUfaNYv76KCyV+1Dq+H1NVEMnp2/ljT45JUqoR/lbnarJ6AEpbTtdfzcOfWh5bi4/dsK6q3oYJ3vTL8cUEvvsqF38v5QZ7m+9sImZ8c/cOHktCX2Y6OcZJK6N4cAhbfwdE1w/hCtulSqRH5BZsJz3GgR7mritSlqW/+JQZe9OIiKizYWBHNoUlO35m4DSWF75ZOdy+cpnra7e92bguyS+9+gEPAfrNQrSSP4uJ0XFt8GxLF+ALtjeHZFXQUPFp6ZUSCZyzaOVPY9aXT7fIBH2ew3343q/FSJ5N6T3NqrVcyvPur366EKZ6xMYk0/b8Zxxy31aygTHDzEsBDzoT/pg/b/cE3FM+8cQ7nLDH00hGRaNrqq3UHT+viaqrsPTd8ltqul6BVQ2hrAcXN1mqdeTpw89VcubOKZOT+QCPlX2WdeeUczH5+E7JnJ4xw5s1Z7C9T/9cH2bhvnsHBaeLGL6WG/VHj/5AZmhjMJ7wiBQ0+xtVY+Txac+7lRaG6+NiIiowzGQQ5uCaVexC3riD73qWlW+cW52Vh9rJHB2BFHFiYkz9Z9AVDaI7eF+9DXXi35t7XaJCrZW048jdNfoGSBRhL/X/jXDe3p45ba2snyhQaJg9JTBd5fcCuEazN0KkUlXHYnnJUgifE1/1kqh51by+5OYeahPSl3oqtdAeRaG94MpfTstZ4LwDlZLIN3o2dWP3t4D8IUWsPSXitT9ecxe9MC5R6lx+4TQ8fuaqIZOT9/be2HN5xO/1x7EVwtI6Tf+5gdXF/nH2BfhXG8ZqevV+iGO5PdjGNEfLe6E/+LKW54KXuuDuVe8Tk0j8scyVHURkV+m4TtmR2/NJ0AWxyyyn3VVPJI8p3BblSxrs+l02XasUDLemsNsPAAzERHRZsFADm0OJff7BxNGAYc8rau31jhXMLTXKIyTQfiLYQzfFpXfqB/O7XJ2LWlRoZW9VRyHbOKbX5CrjTyetRv2zybgFCsVvjiD6DM5W0pfncSkaFVYzkxVeXxtC8vfi+YaJIqo5BtdWS7cCuHSb4XI3hmH93a97lQvUDqOsHY1WRnKNcIeBTDziqfi9gEzHB/a9algNLaykfJce0TyMCa0ffTRHPyVA4EWZBH/5gB6d83AdGYanv296K75pLQKnb6viWrp+PRths0py5urCzXz7cSdXEDKsbdf5L5ZRL+JwlYxLlb3Pgc8ekETRqzQG7Qo899xDH8QEvvLDt+Nmerl2OMQTu7twcAfDvjPuWB53Th3MlQYs8gu1tUoTFRyW9Wg2HaRf45drn1bWfpBLNfDBw5RPr+wkpSIiGh9Uok2icUf7KqW5LHbp8bkPCNLv4yqNkVR7Z/71UhyOTfzr2V1MTqtevYpqunwpBpbys1uyO3R3O/Cpc4+kfPWxLK6FJ9UHfpvaS+L6g0vibn1LUe9Ypuhmo5Nqwv6ti2rqZC2H6BaPppTF/VPVbea5WPnzbn1PDVvvI5xnyqq9/p+mwxNqt4LsYa25YXJH9fdHnU2Oqv6LkSqrN+i6j+qiM8qqvO7mLr0V27uUtyvpycoNtUTrLOHU7OqU98XIl2enVcXl5rbEx2/r4lq2BDp+8G0atfX0az64nLeCiIvOaR9Bqrj4rw6f8GnziblWxW0PNmifd+eUXXuD7m1yyl1/pxDNYn5jZRjsbNavqV9h1v1x1Pqssy7GrH0szu37OC0cfmxNKe6tfdhU0d/8qu+M/XLmciXuW3HsVm1mSKYiIhoI2IghzaPJ6LiqOQqjtMP5LxqlhbVuQtu1bHHlKs47rSojhOi0hxvvvoYOZOrDJvP1QoftSYVcOTWs9rrTER+sobUvDp5wq726vvIpFoOe9TpaEq+2YCmll9Upwdz6+b+uco+/WNWdYrvUt52qr5wE+vxoiSmVcdOsQ077aonsFCnYbikLgS9qiufnvT941Z9gYiaaqhxlA8G5faZ/tLT5Kg6HYypi3/KjxnaAPuaqKqNkr6X1LkTuXPc9l21kMaSOv+5TVWgqL1HfGqk3oWBsjxZ236b6jo1rc49aKwcKwSDCi/xu/tcqueCX51P1LpIsKzOn8otYz5fpdxbjqnePeIzMv+sv0YR1atvR61AFxER0eaxRfufKGyJNoXk5SHs+FcQ5nMxxE7JruxrKRvGmGkA4/Bg/oFv5ZNUiOp5nkH8qg9T0R7YD/Vg6UYIgRtzCP+m3WBRZDrshe+MB463mrj9gYjWj0cBDJmGEdztQyzu0ceNeVmyj8OYOhNAdp9DrEcCoWuzCF2Nlt/2pdjg+kLkOx9Z9HGH1lL21hhMtnHg1DyS5yofLU9ERLT5MJBDm0wSgX9ZMXzZCn9ytrExblqQ/P4AdnywBG80jFHDMWaIqsvem8LwYT96L4bgHaxoKj1LI/FbBJFQGMErUwjpgyzbMf1gzuAxv0TUCZJXhmF1BmD9cRGzR6sOQbyGkgh9ehwnnzoxd9GF3rKLD1lkHiUQiUYQvj4F/5WEPl6PsubBlSRm7DtwfMmLyM1RWHhBhIiIiIEc2oSeRTE+aMXYG9NYDLhgambQ2GY8nMGBN8fQHYjAf+RlVMipo+np5zhSDfUeyyB82oaBr+JwBFKYPcKBQIk6UxbRr2ywnu7BdHIWrjW+2FAui/BnJgx8fQCzT6bhqPlUKuHRDIZMxxGEFxF1FBY5u930CyKnuxt/wAAREdEmwKdW0ebzqgWjNyLwPh2D9b0Aks/l/HZ6FMDw3jHgfAgzDOLQKsSvjumP5rVbGrnBohs2+5A+1fMqe34Rda4uWL4MIXI2gzHLMAKP5OwXIS3Kq6/TwCEbzPWCOJrtBzB0WPy7u2vNeuMkLw/Dehq1n65FRES0CTGQQ5tTtwWjv8Qxs30GA/8YQbBtleUMEldGMDDoR9/VBOY+MfNeflqVbqVf/zf0SxT1H5ScQfDHSWCPD66Daz1aBRGtrW5YPp9H/AcTZgYHMHKt1gPJ26i7GyatM9+1WUQbKBOz9/zwX1XgPuNq/3g+mQQCnw5g4Gofgvfn4NnNkpSIiKgUAzm0eb2iwH5mHrELViQuB/V7/Vv26wy8j22YvjuH0b+zQU2rZzo2idljJsS/sqLv3XEE7iSReSbf1GWRSScQvjKO4V39mOqawMLNlztAKhG1j7Lfi/m7k7D+FkDwsZy5lrpsGLvmhU0JYtgygOPfhJBIZ8oDyc8ySN4LYurDA+g7HIHtdgKTaxA8jl/yIjU4jdjPo7A00juIiIhok+EYOURE61jm9zBC14OYvRlD/GbJU2N2WmAz98Oy34ahQTvMr/OKNRG1QTaN+I05+K8HEL+7UPKEPAW9+/pg/ZsDNpHv2Pf2onutxpgjIiKimhjIISIiIiIiIiLqELy1ioiIiIiIiIioQzCQQ0RERERERETUIRjIISIiIiIiIiLqEAzkEBERERERERF1CAZyiIiIiIiIiIg6BAM5REREREREREQdgoEcIiIiIiIiIqIOwUAOEREREREREVGHYCCHiOj/b+/+Q9u88zyBvw2ZO5fNsQ5kmcdHZzcKybE2DWuZ9tYSDZwfrwcsX3pExj0ikx6JMgVHzrBTOYFGarlz5QwkcgcSu4WJlcIEKdAghZ2sFa4eq39kkbybWcnQwQok+DGXcBIkhwX1YkECzz2/ZMu2ZDuOk1jW+wWqvv7qx/M8avt5vs/n+f4gIiIiIiKqEEzkEBERERERERFVCCZyiIiIiIiIiIgqBBM5REREREREREQVgokcIiIiIiIiIqIKwUQOEREREREREVGFYCKHiIiIiIiIiKhCMJFDRERERERERFQhamSFUSaiHSify0K6n0TqXhzxuwlIh/0YO2M2XiUiqgLP88g9TiOZUmJhIoHo3Tq47/hhqzNeJyIiIqog7JFDVS83FUL/uQiyxt+b8sch9FyKIfvc+Hu7mByE6bCITksnen45iJGbcxAPb88kTnYyhMGTbWisr0FNTQ3qD7Wh6/QIog9zxjuIiDYji5CjEdYjNrTZT6H/UgCxBiusFZnEyUG6M4K+D63Yr8RJNVbut3Sh78o2PP8QERHRK8MeOVS95tMIfd4H32Mbhi+7IQpG/abkkLriRNdlwH0jANe72+wK4WkEp/6iCwHBh3jGA4tRvT3kEPu8Cz1fKBciRs1yAmxfRhH+lRm1Rg0R0WakLjWi+Vwa9lAG4WMvFfTfAAmRk23o+kYy/l6hRYnv40p83238TURERDsWe+RQdXoag7e9EcN7lIbvty+bxFHVwXwmjOQ3zYgcaUDP1TTyxivbQf6HJMbUwnELtlt/nNRvbGi7Wou+6DTmFmSouWX5xxnEr7mMhFMW0U9scN4oc/FCRLQhEpLfp5VnEbb3Ki2Jk0fiix744caENIcFNU4qj4VHcYyeMVLzk17YB2Lb6txDRERErwYTOVR95hMYPNKGwMEggp9ZsJV9Z+re92DsVh+kj8VtlHjII35nUOvt4jrcvL16tTyNYOSiCcHEGDwdDagr7NxuEywnhhFL+BaTOaFPhhCt4lFW9f/xP+Gf/yVp/EVEL+xhDKE7ynOTDc0H9KpKkZ8cQlAIIHbNBXFf3WIcr33bAudl5Vx2XE9MZS9FEONoVCIioh2PiRyqMhJCp+3wzroR/MoBk1G7lWpb3BgaMCHk6MHg5Ha4N5pC4rr67ILt8PYa8pUdD6PudwE49hkVK6i/pe9T4855dgSp+3qxWnnO/y8mc4g2KXsvipjybP5I3HY9E9dT+64Hw79oKJOIN8HxsdMozyHPLjlEREQ7HhM5VFWk6/3ouZ6FbcAF8ZXNI1ALS68XLiEBb68PiXmj+k2ZjGFY7Y7TbUXztsrj5DH9sBk97Wv1EaqFtbXHKNMf/vAPTOYQbUoWsVsR5VlAl6UCV+3bZTyX83Yj7OpzhwhzpY0aIyIiohfGRA5Vj6dRDJ1TG/I22FtfRV+cIntF2E8orempQbivpozKNyOVCGvDqmwdFuUSZjuphfiZe90747X/YY9REiHsNYpVjMkcok3IJRG/qTwLTlia9KqdJP8giQgs8F9wvpKepkRERLS9MJFDVSN13YcRNaPRbof4ovMj5LNI3BjEqZ8XlnytR+MHfQj8sdxkBEs9SRIXA4g+1YpvgITkHTWRJMJ+eAPN+zLHOfJ96fWklnmaRvRKH7rERtQby+LWHLTi1BcRpF9izob8j3N6ocNR8t9bPpeDNBVD5Jsh9J9sQ9uHAeWol+Rnoxg6qR9PvdiP6KzxQgVjMofoxeTvxTCiFo6LsG5gorDc/ShGTneh7VD9C8ayPLKTIQwqsch60IiDLxJHN0VC5Gocrt8H4V4jSZXPZZGejCJ0xYu+D5X9+3z5xMi5PwbQ/4Eev/d/OILUm+5NSkREROWpy48T7XxJ2d8Edal9WbiQNOo2YkGeDrllURBk8RfD8oQ0p9To9cnLovJ9djn4SKtY7VFQtivbU7fpjMwZla/Zg1FZVPehya/8AmuZM44TsuXMqBx/pB+lvJCRxz61KMegHP+FuHHsq81EXLJF3c4BpzycyOjvezYnJ0NG/cpH75iyxY2JDwjaZ0r+him/bHlHlMV39PeoD/G3M8aLyn5965RNhW0ajxf79799CPUHjdKStrYP5Ml//lfjLyIqbUGeOKv//+/6/TqRJzMh+7tNMgSb7ItOy3PP9Oq51KjsUOKjGuPCkl63ypxynjmixiIlXn4Wlqef6NULjyZkn1a/PBYBZtmf0t+zac/UGG2T3esc19zvXbKpRZQtB5a27/6uENEX5PgFURaW7Rtkx7cZ43UiIiLabpjIoeqgXPCbX7hxOiOHTygNelhkz3crG8lKw/cz8zrfF5d9xjZfJHGxlTIhu7Z988U1khfPZuSgdpyQLQOlkjXKcagXMMpFhy+x+tWZkMO4ALDLwVUXOEsXUMWP4mTLmhYmZI+67ZZ1ElHPlPdp3710YaTtl5FYUk18qm/b/OXOSeSomMwhWk8hhjnlsJFcKWXurk9LZkNwlIhlS/EU3UF5VdT/UdlGixFjPisRRwtJ9WUPtzyxOqRuzI8zcjLil+2LiRmTbL8YX/88I43KNu39LnlMe7NyLhuwyEKrRw4/UCtm5NGj+neum/QiIiKiN4aJHKoKM78zGuDKw5cwKtc0IweP63dWHaESSYfFxJCwxvdl5GC3vk3Ao1xKvG5z8ljvevtYOE7IwvGg8lcpS8chDKw4iqJeR5YyCZLFix/Bt06voNX0z1pk3711rnYK/z6Ubah7uJBQLsiO+OXkj/rLxQmlpbvQlaVcIkfFZA7RGgrxoVQCxqDGDL33oBJvSiSsNcp7tFi2qiemmgzRE/sQXPJYyWTRUmL/pXu6LO7H6kf5OK6bizj19xq/hZrwFs+MFX1mRh5tV79LlEcfGFVERES07XCOHKoK2Vl1kmPVxibMla72aatbCWeDCBwrMbfMXhOaDwCmEyNwtBh1q9SibnFbaUive26WXBzRr9VCT9nJPQureCkXJhi6sP5y7NkfJG3i5ILUTT/0X9YG55HS0xZnZuN6IZtE+rFe3JD5GPyfRGD/XRCed9ee1CJx2w9tSunjFphnQ3CeB3whN8yFlcnyccSMJdjF9zYwQUaFGYuGOWcOURmp74NafBDby0z4Pp+Ar9eLhFI0DwzB3bJejIhAKo5luRiCn+uT2gsn7BBLnWOyGUwbxdD94lm8NqHFo96Ew8LcDOIhH+xFc4dlr/dg8Fa5iXyyiN4IaCX1t6ibHMSpO50YvWxbiv0PY4iMK89NNu0cR0RERNsTEzlUBbKQfjCKqMNb67XRH4fQ/3FUKdjg+1hEybe/bcfoAxkz1+xrJD/qsKfeKKoN/1c1z2UZi5N79opoLnUQi6t4KRcvF71wvK0VS8gg88Ao1hZ/kfK7pgorclnRWLLRLyG5OMFnA0xlt7FSDtFzPYh0hOE/vl56KYV4RN+Gy7IHkYEYOq95YClaXj6fiCGgvqXXBuu2WoJ9a/z7f7cL4XCQyRyiVQoTvpthe690LElddWNwSi054e21lI75ityTjFESli8H/jCFsFG0Hmos+fn8D3GEjLJ939asH1hbZ4LlmAfh9AyCx5e+M3Ajuizhvqiwcpf6WzRkMfQl4PtqeQJfuhuBevYzfySuu6IgERERvTlM5BCtkLph9DI54URXBd+RTE0GtWdXhxWlchfS7RF9FS/Y4Dq6RpP9cRpx7SJHadybTUV3tGtRW0iWtAul73QX7u4qhE83fmEg3XChb34IE2smygwPk4hq++dA7d1+JI8Nw7FPe8WQR3w8oF3YlPstdoI///PdCAZHmcwhKvY4gajWw6QHYqmeifkYwhfVvjhqjHLAtkaPzfRUIV3TBXPxuWFXLQo5e9PeUhFGjUF6PFbjrc2yblR7MbtMcHwVhLsQhG9Ky1buK1hM7jdZkbnmh3BhecJbTXrFbmppHPS0Mo1DRES0nTGRQ1VhWUeSNaUQC+m9TOxKQ7ZyL/oLvVTssJpLHUUWiTtqg12xznLsOaXxr/fbEdBlKW7c18Ha7tSL4wmkVi2xLiE04NXu7qLFh8j5Mr2bVsir3f2vNiK44k5xOdl7UcS0UgjBXR742ldsRR1W9Y2WxoHt8E5N4+h++tO/wLVrI1oyh4iW4pdgt5ZOJE8l9N56ip5W6xoxaqnnH7qtaC4OJU0ieowkUWwqrReK5CeH4L2kflaAIzQM56u4QbBb2YdP1k6+FJL7mBpB2uJfvR9q4v2O8lwu6UVERETbBhM5VAUE1B80ioivPcSpqPeJSVgcF7V5z4xn2JXvM4qvw1QMQfU4OmywlBzOJEHSutgrv05r8xoJEwnhq/qcCmjph23FfEB1Rz0In1A/HYDr5BASRjIn/ziBkZNt+jxDrR5M3F5557e0/NQQutT5bX6/sferQ7Di43qaCYILgXOrk0U7dVjVv/1b3igBf/d3/23xcfKky6glqnZqfFDjlwDn+6WTHFkpaQxDcsB6qHwaJz8ehF87NwhwHbcp/yxmhutrH0SlMnXOhb5bErT/O5/nkL7lRedRdf4dE5zXlFhUas61LWK22PTC0eKekwVFiagWP3y/WL0fHFZFRERUOZjIoaog7LMbpSwWlq5/15TPr/XGHBI3y8xDsCgL6b5RVBrxwmtM5Ej3okqzHRCPiuv2arHuK5+wyt0egle9Q6tcFrgHXCUa9ybYryUxHXKjWfLD+hc1qKmpganDi1itC8FEBlJMucDZwATTUCcp/mQO7m83msRR5NTeNnrRdsFdYljEzhxWpSZxfvpTE/5xbEL7W/3N//7vT+MPf/iHxQdR1csnETMmfBct6/UHbER92RidwsjnQ3q87/DBfWR1JKlt8WAiNQH/CSBq34+3lP8na37SDOfXWZgvjGH6yQxGTzRsqFfiy7IdsayO+4XkvhLLPRdKxXIOqyIiIqokTORQVTAdWupWn360RvplV+1iQzt8J46Sa388lxD5pROxn4kl7noWK5okuLsZja+jBa9RGuS31MFGS5N7qqtwBR5qRYNynOt1nZ+PwffxiHbxYhmIrB6ytKgO9Yea0dDQCX90GnPPZGR+mED4KzccLcLGLlxmQ+g5EkPXtXWSPrMRDN1c+ve3OOeD4IG71J3uxWFVTuVCTr34yiG7aghYZSkkcSZiYzj/qVerCwSGcf78/9TKRKRTe+Npg4kKE74rMc17Pqb3ljHU7l6/56V01Yv+SaUgOBD8ylk+Ob63EeYG5XF2FPFHC5DlGcS/G4X/hA0NG0lmv6RUIgo0eeDtXr2HheS+mohytpaIyiuHVc1nkZ3XXiEiIqJtiIkcqg5FcxhE0mss/SqYIXboxezXTvT8Ogap0Jh9noc0GUD/B31IO4LwrLdEbVZC0himZT+6XtJnC2VTiKkNcqELVvWYZ0MI7HKvmA/BDPtpvRt+JJFcdmGjeS4hdLoHQ1nAcmYMwc/KreSSR+pKJxoOBWAaGIW7owF1xau5bEQhiXN7FPZlkxQXMX77vmNRmFqXfsnCnA/CCRHWEju4OKxKuZAS9+aR+LUP8Q32yNqOipM4f/ufm/FXf/VXuHv3X/CXf/m2Vv7Hf/zfxjuJKK3EDPV/f/vhZtQpsSpxJQFxxVxdda12Y5LgGJKLPSiX5P5pED3qKoaCDf47gRUTqRd5HEXf4Xq0PbIjeNEJy9vrnB9eiBJnL7Whvr4RPVdSpW8wKHHU9+Ue+L72lujRmEViXJ9JzNZdupfm4rAqhzqsSon/nweRedFYTkRERK+PTFQlZq7ZZPU/eTT55aRRV8rCPb8sCsr71PeufBxwyqPpBeOd67jrMT7nlMNPjLrXobDdJrccToRl/+W4XHqPZ+TgcUF5ryA7fpuU557ptXOpoOxuVeoFUXZHZvTKcjJh2aEdoyDbLkzIM3Mb/G0MC+lR2VHuty7xED6dKDqWpOxv0uvd35XebvJLs/7ZXwzLY5d98nDqxfZvO2lr+0D+sz8T5Ml//lejRtbKf93wnlaenr4v/83fWLUyESnx7ageH+xfTcgTl/1yWDJeWmEh4ZMtapxo8chjj4wYsZCRJy7aZZNSb+oelpNzenU5yQtqLFW/wyUHUxl5wYinWyMjh4/rx6I+hCM+eUIy9vPZnDwd9cn2DrccLHdumhuTXdpnRXn0gVG3zJw81qt/t/hZWA5e9MljZX4rIiIi2h6YyKHq8URpzGpJg3KN2SKZCXm41yY3GEkGU4tddl2ekDMv0DiPD+gNe/PFtdJGr0B6VLYfUPb7gE12h6bLJHEKlIuAiE92tpi0fQVMsqXbJftD8Q0eayEZpP9O2uOARbb3euTRSFKe+dF4WykPRmXbCyRx1GSRJ1Z0NMrnRa3eJY+VucjKfOuQBeVzDcf88kTGqNxh/ut//e9aEkf17rv/RXsmojl54lNx8f//+HrJ9BUxX3hHlJ1nR+WxB+tkcAyLyaCieNXQ6pTdl4PyRHpunTi8AU/isv+EuLh/6sPUIiqx1i8HE5k1v3/hO7f+mbI3MRbk5AWL8h6TbDsblKc3dshERET0BtWo/1BO8ERVQbrehf0fRWC+mETy7Cuc0DEfg9fUhkG4MfHAD3Gjk/dWkuc5pG76MZKoh+1oPebuRBG6M4bYn5bmsFGZun3wD7hh/+utHGpABf83k0Vb2wewWv4WfWc+hrnpkPEKEb0O+ccxjAyEkG+1w4w0orfCiN5MYNkgXkGE87wSC89Ydsyk60RERPTmMJFDVUZC6CMreq5bEZTC5ec7eEnS1U7s/3gOvkRs/bl0KlB+agQ93UE0fBWFr33FZcl8Fuk/xRGPxhC5MYKoNsmyDaMPxlbM00NEVMkkRD85hb6nDox95UTDsoR9HrnZNOKJOGK3RxC8kdbm6xHOTkC6uHyeHiIiIqIXxUQOVZ/5BAbbrfD+bBQzISdMWz2h48MAOg96UReKI1hqJaVKpx3fKWQ21Ksph9jnItq+SMEeyiB87LVN+UxE9ArlETtnQtulToSfjMK+3qpUswF0mU4hAh/isgcWo5qIiIhoM7hqFVWf3RZ47sThe+qF9WQI0nOjfiuoKzAd9gJfRhHYiUkcReqmV1vdxGbZyNC0Ooi2Lq1Uv5v3oIloh8gqMf5SFjgqwryRpcX3daKrW3luqmVvHCIiInppTORQdaqzwPNdCoF9AbT9vB+RWaN+03JI3+hHW3sQjTfTGPuVecc21uuEZu05+l0C66/knUPkd8NAix/OI5wZgoh2iLo6mNQOhrfCSGzg/JGfCiJ4U4BrwIlXODsbERERVQkmcqh67RJgG5hA8rIV6esRbf6CTftjAL7HIkbvjcHz/s5OWJhODCN8woTUF1Y0fjiI0KSE3LzxoiaPXDaN2I1B9BxqxkjtEKbH3bx4IaKdo1aE95YPohBBj6UNp65Ekc7mlie353OQpiIYOd2Jxu44xLtpDDOhTURERFuAc+QQ0abk7scQvR1BeDyJ1HjRCi0HLBDNzbB0iOhqt8H8NgcSENEOlc8idWcMwdshpO5NF63aJ6ChtRHWd+0QlVhoO9yAuq2ej42IiIiqFhM5REREREREREQVgkOriIiIiIiIiIgqBBM5REREREREREQVgokcIiIiIiIiIqIKwUQOEREREREREVGFYCKHiIiIiIiIiKhCMJFDRERERERERFQhmMghIiIiIiIiIqoQTOQQEREREREREVUIJnKIiIiIiIiIiCoEEzlERERERERERBWCiRwiIiIiIiIiogrBRA4RERFRhcv9KYT+DxpRX1ODmvpGdJ4eQeKp8SIRERHtKDWywigTERERUYXJTw5CtHiRMP5edMCJ8Pgo7PuMv4mIiGhHYI8como3LyF1KwDv6U40fhRC1qh+Efn7IfTb9qOmpgb7bf0I3c8br5SwBdsjIqKCFEZ+FUdnbAYLz2So9+fmUkG4WpSXHgbg+m0Ma0RkIiIiqkBM5BBVtQQGPxxC4MYgBr+OIr2J1r52J7hhGLVn4toFRPL8Hgw3iBicLPVlL789IiIqMpUELoXhaTWhdpdeVdfkwPD1UdiUcvbXCaT0aiIiItohOLSKiBQJeGusGOwOIvOtA4JRu658CoOtzRg+PAHpoohavRKx8ya0fd+PZMINs1a30ia3R0REGyQhZN+Pnls+xGUPLEYtERERVT72yCEizVvG84vI3RmBdxLoabcaSRxVLaytPcBkPwK3c0bdapvZHhERbdzCvPKPXjMa9D+JiIhoh2Aih4g2KYf4eEB5FtFgWkrjqGoPNsOuPI/cTXJuBiKiN+FpColxM3wfiagzqoiIiGhnYCKH6CXlcxJS30cRuuJF34dtaLu0at2QHUqdtFh9FrBnt1axxJinAeMppI0iEVHFep5HbjaF2K0Ahs6dQpulH9HyHQ63Bel2AGO9PrhalifaiYiIqPIxkUNVLzcVQv+5yKZWT8re6ELj4U7YxE70/HIQIzfv4f/9nwVknxtv2MlyGWS0H60R9SsnuXnbhGb1eSrPHjlEVOGyCDkaYT1iQ5v9FPovBRBrsMK6nbu5PI1i6LoVkYs29sYhIiLagZjIoeo1n0bokzZYL2Rg+8S+qQl3hWNhzPwwjcxdj1HzP3DaNAJrQxdG/rjNb9e+rPkcMkaRiGjnEuD4dgbTP2SQvKjPNmNvt27jBImE0LkIrNc8sKzsLUlEREQ7AhM5VJ2exuBtb8TwHh/i37ohvuSySVLaGE7V24EPPwkj+U0zIkca0HM1vXN7pOyuQ71RXCWbwbRRJCLaGSQkv1cHi4qwvbdd19rLI/FFP6SPh+HYZ1QRERHRjsNEDlWf+QQGj7QhcDCI4GeWLbirmkViPKaV7Iebte+re9+DsVt9SmNahPOGpL2249TtMRI5c1hYma16bgypahe4tDgR7QwPYwjdUZ6bbGg+oFdtN9J1L2KtAXhWzouT5yBXIiKinYSJHKoyEkKn7fDOuhH8ygGTUftSHscQvqkWbMvu0ta2uDE0YELI0YPByZ3YiG6AuVd9lpBdOcHQ04xSq2gyle+1Q0RUQbL3olBT9uaPRJj1qm1Fun4Kg7UueN5ffnsiNxXAqd+kjL+IiIhoJ2Aih6qKdL0fPdezsA24IG7R3AG5VBwRtdBuh7jsLm0tLL1euIQEvL0+JOaN6h2jDtZ2p/IcQfLB8kRV7pGEFAR4OqzKr0BEVOmyiN1SI72ALst2S+Pkkb7aA+tHAQQ+3I+amppljz1mL4SW7Zh6IiIios1iIoeqh7qKxzm1IW6DvXVL+uIo8kjeHdFK5o7m1T189oqwnxCAqUG4r1bAHdHnwIJR3Ii6Did8TUDw+3jRXEB5xMeV36SlH12t66RxXnB7RERvRC6JuNrzUnDCosS87ST9dSfEj0PlV15U9lm0MKVORES0kzCRQ1Ujdd2HEbWlu6rnzEbkIN0ZQd8HjahX73Ie7ET/DXUi4xQS19XXy92lrYW1tUcrJS4GEH2qFbdOPofcbAqxWwEMnTuFNrELgYfGa6p5CdFLp2A9qOxzfRv6b5eZr2d2Gkn1+VYcqZL7mEP0l/u17xiZMqpUtRa4v/bB9Gsvhv5JX6VLutUP300Rvt+4yg8/WHd7REQvL59TYvdUDJFvhtB/sg1tHwb0YZ+G/GwUQyet2K/E9XqxH9FZ44UV8vdi0FL2x0VYN5ATyd2PYuR0F9oO1es9Yw5aceqLCNLrLmaYR3YyhEFlX7W4rfWqqUfjB30Y+b50qqahdwIZWYZc7pHxQSy1z8/zyGXTSNwJYeTzPnT93ArveHHvyhxS3/SjUzuG/ei6kipK2BMREdEbpZzkiapAUvY3QVb/kxcuJI26jZn7ISi7WwXZ1O2XJ6QFvXIhI499KsqOMy7ZrHwn4JYnjJdWeRSU7dp7IDsjc0blVlCOqaVBFlsbZMH4frSPyjPGq7IUlp0HjPrCQ/ApnyqWkYPdK96jPrqDyivF5uSxMybl86I8nDKqiszdG5adLcrrEOSGY8rvtPzDRTa6PSKil5Tyy5Z3RFl8R1iMNeJvFyOkPPOtUzYVxyHlUfr8sCBPnNVfd/1+nRiemZD93WqstMm+6LQ890yvnkuNyg5B+Y4DTjks6XWrzCkx/Yi6r4IsfhaWp5/o1QuPJmSfVr98XwGz7C8RjzdGiem9JtnSbin6DYrOYz/GZZ9y3lu+PYccZqAmIiLaFpjIoeqgNOj1hAtkx7cbb4nOhPSGvmUgrjR7V3gSlp2FBm7v2OrXFykN4g29b/MmPtW/3/ylcREiBZWLBpPsvByXM+qFRMyjb7/JvyKRQ0S0wz2bkD1aDF5KfMyEHLJwwCkPJ/TzwaoYuowSw9UkDJxy2EiulDJ31yeL6vsEhxwskazJhOx6HC6VuFYTJy3GPnwWl1fdF3gwKovaMRQ/1riB8AJmrtn07yucn7R90ZNJM2qFNGrcjHDJY6/iBEZEREQvjEOrqCpIP8RRmKGm8WcbWxBbutEDqyOAheNllinfXbdY5+qwrrGMuQmmbqP4dRxpo7h1UkipS+IWhnepy6ufDKL5zjRGz1gg7ALyz40O8e1mNOglIqLq8KcUouqz0AVrkxIPJwdx6kYzoqlRuFrU84ESH5+rbwDEd0pEyKk4wuqopm4R1r161Urqd9oOexHLWuC7FYBjn/FCEcHUrBduhhF7rBd1eSR+44J3UikKLvh+aVk9SfyBRohG0fFtxhg25S89ZOqF5JC6q/06sB9uVs5j6sqOXmTOxzExYIdJPbEpv402Ikw9f5Q/0REREdFrxEQOVYXsrLaulEKEUKYhXkxtlPc4Qsi2+BApt0z5/ZS2FK3S/IXVvFbrthZ1i9tMQyozB8OmTUbh1+at6YHlHb0RjgthuJsKLfw84t8HtZJLaai/dLufiKiCJG779UT+cQvMsyE4zwO+kBvmwsqF+Thi2lxnLojvrY6QKSV+qp8X2y0oeRtgPgFfrxcJpWgeGIK7Zb0oG4FUnMjJxRD8XL/VIJywQyx1jspmMG0UQ/fLzHW2GY+jCH6jFkTY3qtD4otTGOsYxfCRpbOedDeiL7teakJ/IiIieiOYyKEqkIX0g1FEHd5ar4292CgX4B5ww1JmmfLUuN64R7sNlre1qjLqsKfeKKoN+LJLi2xOKhHWVyvptWLP7UHElEa4p/hCQr1I+UZ9hwu2w7ydSkTVJIV4RA+6LsseRAZi6LzmWRbX84kYAupbem2wrgqREpJ31Ehvhu290mmM1FU3BrVkuhPe3hK9aQy5JxmjJAC7jKLqYQpho2g91Fjy8/kf4ggZZfu+jfUq3YhcKq6clRRNNjQ+HYIfPgSOFR+nhNhNtceOGT2tZaevJyIioteMiRyiFaQbPr1R3uGDq71Mk/xpFIEv9Tuob/YuZeEiA3DUxtGfcmB4WSN8vYsUIqId7GESUS3J4kDt3X4kjw2vGPaUR3w8oCXDSw6RfZxAdFx5buqBWGrZ8XwM4YtqXxxA+NQB2xo9PtNThXRNF8zFKyfuqkUh12/aWypIq/uo96oEbLBZtuqMk0fyrrYWF8yHMwhcFOD/bEUi6mEMEXXobrnjJyIiojeCiRyqCrXlbpGupDTKA5/r8wU4f9FVJkGTR+KyV1/KvOyy469J4SJDEboBeD4XV9zNXecihYhoB8veixpDYEMI7vLAtzI5v06Pxdy9mNZjRbBbUTLSTyX0RLmip9W6xtDVpZ5B6LaiuXhTTSJ6jCRJbGr1LGr5ySF4L6mfFeAIDcNZnAR6KSkktCFlSulKGpaLzlXnPHVYldYf5yOx9PETERHRG8FEDlUBAfUHjSLiaw9t+lOhUW6HWGbem/y4F95xo7ku9EFs0YtremY8K99r2rpe8YsXGeoxun7rhbhyGBiHVRFR1cohPm7Mjya4EDi3MtGthMg1eyyqnw8ozwKc75dOY2SlpD60FQ5YD5VP4+THg8ZcZkqsPm5T/lnMDNfXPohKZeqcC323JGjT0z/PIX3Li86j6lBfE5zXlH1d0ePypRQmcVZYvvSVSBBxWBUREdF2xUQOVQVhn90oZbFgLOBUSvZBoVGuKJ7DoGA2hL4bzXB/9Jb+tzp5pl5aQxbSfaOoNMaFLUvkFC4yFB0+uI+sTtRwWBURVa2cmsjWi7YL7hLDntbpsZhPIva1WuiBaCmfpNE1or5sbE9h5PMh/dxSJlbXtngwkZqA/wQQte/HWzU1qPlJM5xfZ2G+MIbpJzMYPdGwRo+fF1eYxBmCB77eEmcyDqsiIiLatpjIoapgOrTULT79aDFVszZjOdpFsyH0nJTgvGxB5rbeWX9jq0BlkHlgFLub0bhVLfHFiwwBnrM9JYaBLV2kONv1i5RcVltElohox8vfi0GbAUbwwF2qJ8tij0UnRIsWIZF9qr2iURPh2sw0vSKa1bg9H4P3fEzvLWOo3b04k31Z0lUv+rWlxR0IfrV6+NKivY0wNyiPs6OIP1qALM8g/t0o/CdsaNjAaosvZml+NdsF5fhLnJcWh1U59GFV+Wx22bETERHRm8NEDlWHojkIIunyS7fW7S00sSMY/m0UWTWZ8zyH1I1+tLWP6audzKcQU+9SasuO1yJ1aQixtVq3WaXBrHWpVz5xVFzRpf4lTCX0iwxBvQgp0QovukhRh1WpS6r77rIZTkTVITWpTxAsnBBhLRUiCz0WT9gg7s0j8Wsf4kUhMj2pJ8Lth5uhRFAkriQgnl8+PKuu1Q63FtRjSC72vFyS+6dB9HwcVXbCBv+dwIqJlos8jqLvcD3aHtkRvOiE5e0SO7yVFudXsynHVyq1VDSsqt2s3cjwXi+sukVERERvGhM5VCXMsP/Sphdvx/Xu5CXUtvfAb8x5k/h1J+p/onZv3wPbVcA9HtQb4bNpYxnYeuCHAOKHXSXvZi56mDTe71QaxFuWxlladvx46YsU3E8hqr0ByNwbwdA9G3zdW7d9IqLta2ly4XKTEKenonoM3ZVB/MoQkh0+2N/WXlJISN8zAmhuGrErI8gc86yeh2y3CN8tHyyIoe+EF9HHRiYon0XsUheaD3uR7R5GMj0Gd1P5E0XquhMjaq+de1FEprLIr+wRusUWlx1vt0MsNXlyLo2UdsNiD+YehDB0vQ6us+YtHdpFREREm8dEDlUN0xEXXGoeQ2m8Jx/qdauZ4b4dh/9Yg9ZzRnjHBtflCaS+88NWuJN6wAyX0vA1dShNWpMTrpa1m7aJ7/V5bMwXXbBvWff4pW7xZYd37TWhQTkI4Z0F5Gu74DnDRjgRVYnFZcddEN8rHfnq31bjvICG+Txquz1wLUu07IHw12oPSgHpuym8dcwNe5neNOr8NvHMBIbNKfS/9xZqampQ/14PQk9sGH4wh5lvXSgzd/6ihtY+WNTC5Ah6zPV46yf1aBRPof9KCLH7uS0e0lS07HhHc+mhXrX1qFdvahyoRf65Gc7PbOWHhBEREdFrVyMrjDLRjidd78L+jyIwX0wieXb9aYpfWj4Gr6kNg3Bj4oF/9d1cIiKqavnHMYwMhJBvtcOMNKK3wojeTGDZIGBBhPO8D/4zltWTMhMREVHVYSKHqoyE0EdW9Fy3IiiFy89XsEWkq53Y//EcfIkYPOv03CEiomoiIfrJKfQ9dWDsKycaliX688jNphFPxBG7PYLgjbQ2DEw4OwHp4upl1ImIiKi6MJFD1Wc+gcF2K7w/G8VMyAlTqWXGt8LDADoPelEXiiNYasUUIiKqUnnEzpnQdqkT4Sej6w+7nQ2gy3QKEfgQlz36MCwiIiKqWpwjh6rPbgs8d+LwPfXCejIE6VVMKqkuVX7YC3wZRYBJHCIiKpZVzg2XssBREeaNzJ22rxNd3cpzUy174xARERETOVSl6izwfJdCYF8AbT/vR2TWqH9pOaS1pcqDaLyZxtivOMEwERGtUFcHkzqj/q0wEhs4/+SnggjeFOAacOI1zO5GRERE2xwTOVS9dgmwDUwgedmK9PWIvgzty/pjAL7HIkbvjcHzPqekJCKiEmpFeG/5IAoR9FjacOpKFOnsitWp5nOQpiIYOd2Jxu44xLtpDB/heYWIiIg4Rw4RERHRm5HPInVnDMHbIaTuTSP2p8ItBQENrY2wvmuH2CHCdrgBda9qPjciIiKqOEzkEBERERERERFVCA6tIiIiIiIiIiKqEEzkEBERERERERFVCCZyiIiIiIiIiIgqBBM5REREREREREQVgokcIiIiIiIiIqIKwUQOEREREREREVFFAP4/KZPYUOzkQ7UAAAAASUVORK5CYII=)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kKjdPd0suEjr"
      },
      "source": [
        "## **Solution:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cnmSim088Eb-"
      },
      "source": [
        "### **Solution 2 (a):**\n",
        "$f(n) = n-100$ <br>\n",
        "$g(n) = n-200$ <br> <br>\n",
        "\n",
        "- **To prove** $f = O(g)$:\n",
        "<br> Let $c = 5$\n",
        "<br> Showing that  $ \\exists m \\; \\; s.t. \\; \\; n -100 ≤ c(n-200)$ <t> $\\forall$ <t> $n ≥ m$.\n",
        "<br> <br>\n",
        "$n-100 ≤5(n-200)$ <br> \n",
        "$\\Rightarrow$ $4n ≥ 900$ <br> \n",
        "$\\Rightarrow$ $n≥ 225$ <br>\n",
        "$\\therefore m = 225$  \n",
        "<br> Thus $5(n - 200) ≥ n - 100$ $\\forall$ $n ≥ 225$ \n",
        "<br> $\\therefore$ <t> proved that $\\exists$ $c,m $ $\\; s.t. \\;$ <t> $n -100 ≤ c(n-200)$ $\\forall$ $n ≥ m$. \n",
        "<br> $\\therefore$ $f = O(g)$\n",
        "<br> <br>\n",
        "\n",
        "- **To prove $f = Ω(g)$:**\n",
        "<br> Let $c = 0.5$ \n",
        "<br> Showing that $ \\exists m \\; \\; s.t. \\; \\; n -100 ≥ c(n-200)$ $\\forall$ $n ≥ m$.\n",
        "<br> <br>\n",
        "$n -100 ≥ 0.5(n-200)$ <br> \n",
        "$\\Rightarrow$ $0.5n ≥ 0$ <br>\n",
        "$\\Rightarrow$ $n ≥ 0$ <br> \n",
        "$\\therefore m = 0$ <br>\n",
        "<br> Thus $0.5(n - 200) ≤ n - 100$ $\\forall$ $n ≥ 0$ \n",
        "<br> $\\therefore$ <t> proved that $\\exists$ $c,m $  $\\; s.t. \\;$ <t> $n -100 ≥ c(n-200)$ $\\forall$ $n ≥ m$. \n",
        "<br> $\\therefore$ $f = Ω(g)$\n",
        "<br> <br> \n",
        "\n",
        "Since $f = O(g)$ & $f = Ω(g)$ $\\Rightarrow$ <t> $f = Θ(g)$\n",
        "<br> <br> <br> <br> <br> <br> <br> <br>\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mh7qjrZICcO-"
      },
      "source": [
        "### **Solution 2 (b):**\n",
        "\n",
        "$f(n) = 100n+logn$ <br>\n",
        "$g(n) = n+(logn)^{2}$ <br> <br>\n",
        "\n",
        "- **To prove** $f = O(g)$:\n",
        "<br> Let $c = 100$\n",
        "<br> Showing that  $ \\exists m \\; \\; s.t. \\; \\; 100n+logn ≤ c(n+(logn)^{2})$ <t> $\\forall$ <t> $n ≥ m$.\n",
        "<br> <br>\n",
        "$100n+logn ≤ 100(n+(logn)^{2})$ <br> \n",
        "$\\Rightarrow$ $100(logn)^{2} ≥ logn$ <br> \n",
        "$\\Rightarrow$ $logn(logn-1/100)≥0$ <br>\n",
        "$\\Rightarrow$ $logn-1/100≥0\\;\\;\\;\\;\\;$ and $logn≥0$ <br>\n",
        "$\\Rightarrow$ $\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;n≥-2\\;\\;$ and $n≥1$ <br>\n",
        "$\\Rightarrow$ $n≥1$ <br>\n",
        "$\\therefore m = 1$  \n",
        "<br> Thus $100n+logn ≤ 100(n+(logn)^{2})$ $\\forall$ $n ≥ 1$ \n",
        "<br> $\\therefore$ <t> proved that $ \\exists m,c \\; \\; s.t. \\; \\; 100n+logn ≤ c(n+(logn)^{2})$ <t> $\\forall$ <t> $n ≥ m$ <br> $\\therefore$ $f = O(g)$\n",
        "<br> <br>\n",
        "\n",
        "- **To prove $f = Ω(g)$:**\n",
        "![msedge_7JB0cTrCeY.png](data:image/png;base64,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        "<br> Let $m = 0.3$ (taking any value in right of the intersection point of the curves for $n$ & $log^{2}n$)\n",
        "<br> Showing that  $ \\exists c \\; \\; s.t. \\; \\; 100n+logn ≥ c(n+(logn)^{2})$ <t> $\\forall$ <t> $n ≥ m$.\n",
        "<br> Given: $n ≥ m$\n",
        "<br> <br>\n",
        "$\\therefore n ≥ log^{2}n$ <br> \n",
        "$\\Rightarrow$ $100n ≥ 50(logn)^{2} + 50n$ <br>\n",
        "$\\Rightarrow$ $100n + logn  ≥ 50log^{2}n + 50n$ <br>\n",
        "$\\Rightarrow$ $100n + logn  ≥ 50[(logn)^{2} + n]$ <br>\n",
        "$\\therefore c=50$ <br>\n",
        "<br> Thus $50(n+(logn)^{2}) ≤ 100n + logn \\;\\;\\;\\; \\forall$ $n ≥ 0.3$ \n",
        "<br> $\\therefore$ <t> proved that $ \\exists m,c \\; \\; s.t. \\; \\; 100n+logn ≥ c(n+(logn)^{2})$ <t> $\\forall$ <t> $n ≥ m$ \n",
        "<br> $\\therefore$ $f = Ω(g)$\n",
        "<br><br>\n",
        "\n",
        "Since $f = O(g)$ & $f = Ω(g)$ $\\Rightarrow$ <t> $f = Θ(g)$\n",
        "<br> <br> <br> <br> <br> <br> <br> <br>\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fd__MqReC4At"
      },
      "source": [
        "### **Solution 2 (c):**\n",
        "$f(n) = log(2n)$ <br>\n",
        "$g(n) = log(3n)$ <br> <br>\n",
        "\n",
        "- **To prove** $f = O(g)$:\n",
        "<br> Let $c = 1$\n",
        "<br> Showing that  $ \\exists m \\; \\; s.t. \\; \\; log(2n) ≤ c.log(3n)$ <t> $\\forall$ <t> $n ≥ m$.\n",
        "<br> <br>\n",
        "$log(2n) ≤1*(log(3n))$ <br> \n",
        "$\\Rightarrow$ $3n > 2n$ <br> \n",
        "$\\Rightarrow$ $n > 0$ <br>\n",
        "$\\therefore m = 0^{+}$  \n",
        "<br> Thus $1.log(3n) ≥ log(2n)$ $\\forall$ $n > 0$ \n",
        "<br> $\\therefore$ <t> proved that $\\exists$ $c,m $ $\\; s.t. \\;$ <t> $log(2n) ≤ c.log(3n)$ $\\forall$ $n ≥ m$. \n",
        "<br> $\\therefore$ $f = O(g)$\n",
        "<br> <br>\n",
        "\n",
        "- **To prove $f = Ω(g)$:**\n",
        "<br> Let $c = 0.5$ \n",
        "<br> Showing that $ \\exists m \\; \\; s.t. \\; \\; log(2n) ≥ c.log(3n)$ $\\forall$ $n ≥ m$.\n",
        "<br> <br>\n",
        "$log(2n) ≥ 0.5.log(3n)$ <br> \n",
        "$\\Rightarrow$ $2n ≥ \\sqrt{3n}$ <br>\n",
        "$\\Rightarrow$ $\\sqrt{n} ≥ \\sqrt{3}/2$ <br> \n",
        "$\\Rightarrow$ $n ≥ 3/4$ <br> \n",
        "$\\therefore m = 3/4$ <br>\n",
        "<br> Thus $0.5log(3n) ≤ log(2n)$ $\\forall$ $n ≥ 3/4$ \n",
        "<br> $\\therefore$ <t> proved that $\\exists$ $c,m $  $\\; s.t. \\;$ <t> $log(2n) ≥ c(log(3n))$ $\\forall$ $n ≥ m$. \n",
        "<br> $\\therefore$ $f = Ω(g)$\n",
        "<br> <br> \n",
        "\n",
        "Since $f = O(g)$ & $f = Ω(g)$ $\\Rightarrow$ <t> $f = Θ(g)$\n",
        "<br> <br> <br> <br> <br> <br> <br> <br>\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yJPU0gUSLPZ4"
      },
      "source": [
        "### **Solution 2 (d):** <br>\n",
        "$f(n) = n^{1.01}$ <br>\n",
        "$g(n) = n(logn)^{2}$ <br> <br>\n",
        "\n",
        "$\\displaystyle{\\lim_{x \\to +\\infty}} \\frac{f(n)}{g(n)} = \\frac{n^{1.01}}{n(logn)^{2}}  = \\displaystyle{\\frac{n^{0.01}}{(logn)^{2}}}$ <br> <br>\n",
        "$\\hspace{26 mm} = \\displaystyle{\\frac{0.01n^{-0.99}}{\\displaystyle{\\frac{2log(n)}{n}}}  = \\displaystyle{\\frac{0.005n^{0.01}}{logn}}}$ <br><br>\n",
        "$\\displaystyle{\\lim_{x \\to +\\infty}} \\frac{f(n)}{g(n)} = \\frac{0.005*0.01*n^{-0.99}}{\\displaystyle{\\frac{1}{n}}}$ <br> <br>\n",
        "$\\hspace{26 mm} = 0.00005*n^{0.01}$ <br>\n",
        "$\\displaystyle{\\lim_{x \\to +\\infty}} \\frac{f(n)}{g(n)} = +\\infty$ <br> <br>\n",
        "\n",
        "$\\Rightarrow f(n)$ is the upper bound of $g(n)$\n",
        "<br> $\\Rightarrow f = Ω(g)$ and $\\therefore f \\neq O(g)$ $\\Rightarrow f \\neq Θ(g)$\n",
        "\n",
        "<br> <br> <br> <br> <br> <br> <br> <br>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uOZRf1nfwTA6"
      },
      "source": [
        "## **Answer:**\n",
        "(a) $f(n) = n - 100$ and $g(n) = n - 200$ <br>\n",
        "> $f = O(g)$ and  $f = Ω(g)$ and $f = Θ(g)$\n",
        "\n",
        "(b) $f(n) = 100n + log(n)$ and $g(n) = n + (logn)^{2}$ <br>\n",
        "> $f = O(g)$ and  $f = Ω(g)$ and $f = Θ(g)$\n",
        "\n",
        "(c) $f(n) = log(2n)$ and $g(n) = log(3n)$ <br>\n",
        "> $f = O(g)$ and  $f = Ω(g)$ and $f = Θ(g)$\n",
        "\n",
        "(d) $f(n) = n^{1.01}$ and $g(n) = n(logn)^{2}$ <br>\n",
        "> $f \\neq O(g)$ and  $f = Ω(g)$ and $f \\neq Θ(g)$\n",
        "\n",
        "<br><br><br><br>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8SD8050kuEqi"
      },
      "source": [
        "# **Problem 3**\n",
        "## *Describe an efficient algorithm for finding the ten largest elements in a sequence of size ​n​. What is the running time of your algorithm?*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7MjLfpihEoPt"
      },
      "source": [
        "def find_ten_largest_values(input_arr):\n",
        "    output_arr=[]\n",
        "    for i in range(10):\n",
        "        flag1 = 0 \n",
        "        for k in range(len(output_arr)):\n",
        "            if (input_arr[i] > output_arr[k]) and flag1 == 0:\n",
        "                output_arr.insert(k, input_arr[i])\n",
        "                flag1 = 1\n",
        "        if flag1 == 0:\n",
        "            output_arr.append(input_arr[i])\n",
        "\n",
        "    for i in range(10, len(input_arr)):\n",
        "        flag2 = 0\n",
        "        for k in range(10):\n",
        "            if (input_arr[i] > output_arr[k]) and flag2 == 0:\n",
        "                output_arr.insert(k, input_arr[i])\n",
        "                del output_arr[-1]\n",
        "                flag2 = 1\n",
        "\n",
        "    return output_arr            "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3r_zrY-2wrfj",
        "outputId": "b2e7f31d-f956-493d-a700-daaaea98f795",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "# a = [1,2,3,4,5,6,7,4,3,6,9,6,2,3,4,6,3,1,0]\n",
        "a =[1,2,3,4,5,6,7,8,9,10,11,12,13,8]\n",
        "b= find_ten_largest_values(a)\n",
        "print(a, len(a))\n",
        "print(b, len(b))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 8] 14\n",
            "[13, 12, 11, 10, 9, 8, 8, 7, 6, 5] 10\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FaXoykLmCvkq"
      },
      "source": [
        "# **Problem 4**\n",
        "## *Use the divide and conquer integer multiplication algorithm to multiply the two binary integers 10011011 and 10111010*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vNZv4uw2h2f1"
      },
      "source": [
        "def make_equal_length(str1, str2):\n",
        "    len1 = len(str1)\n",
        "    len2 = len(str2)\n",
        "    if len1 > len2:\n",
        "        for i in range(len1 -len2):\n",
        "            str2= '0' + str2\n",
        "    elif len2 > len1:\n",
        "        for i in range(len2 - len1):\n",
        "            str1= '0' + str1\n",
        "    return len1"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0sXJp6--i8IH"
      },
      "source": [
        "def add_bit_strings(str1, str2):\n",
        "    length = make_equal_length(str1, str2)\n",
        "    carry = 0\n",
        "    result =''\n",
        "    for i in range(length-1, -1, -1):\n",
        "        bit1 = int(str1[i])\n",
        "        bit2 = int(str2[i])\n",
        "        sum = str((bit1 ^ bit2 ^ carry))\n",
        "        result = sum + result\n",
        "        carry = (bit1 & bit2)|(bit1 & carry)|(bit2 & carry)\n",
        "    if (carry):\n",
        "        result = '1' + result\n",
        "    print(\"##add##\", end=' ')\n",
        "    print(str1, str2, carry, result)\n",
        "    return result"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "foEVVDMymGhU"
      },
      "source": [
        "import copy\n",
        "\n",
        "def binary_multiply(str1, str2):\n",
        "    n = make_equal_length(str1, str2)\n",
        "\n",
        "    if n==0:\n",
        "        return 0\n",
        "    if n==1:\n",
        "        return int(str1[0])*int(str2[0])\n",
        "\n",
        "    fh = int(n/2)\n",
        "    sh = n -fh\n",
        "\n",
        "    #Xl = copy.deepcopy(str1)\n",
        "    Xl = str1[0: fh]\n",
        "    Xr = str1[fh: n]\n",
        "\n",
        "    #print(str1 + \"    \" + Xl)\n",
        "    #print(str1 + \"    \" + Xr)\n",
        "    #print(len(Xl), len(Xr))\n",
        "\n",
        "    Yl = str2[0: fh]\n",
        "    Yr = str2[fh: n]\n",
        "    print(Xl, Xr, Yl, Yr)\n",
        "\n",
        "    P1 = binary_multiply(Xl, Yl)\n",
        "    P2 = binary_multiply(Xr, Yr)\n",
        "    P3 = binary_multiply(add_bit_strings(Xl, Xr), add_bit_strings(Yl, Yr))\n",
        "\n",
        "    print(\"@@@@@@\", end=' ')\n",
        "    print(P1, P2, P3)\n",
        "    print(\"$$$$$\", end=' ')\n",
        "    print(P1*(1<<n), (abs(P3 - P1 - P2))*(1<<sh), P2)\n",
        "    return P1*(1<<(2*sh)) + (abs(P3 - P1 - P2))*(1<<sh) + P2"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HgMy4EgFn50V"
      },
      "source": [
        "a= \"01110101\"\n",
        "b= \"10110100\"\n",
        "c = binary_multiply(a, b)\n",
        "print(c)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NvZo9WSbDyMW"
      },
      "source": [
        "# **Problem 5**\n",
        "## *You are given a unimodal array of ​n​ distinct elements, meaning that its entries are in increasing order up until its maximum elements, after which its elements are in decreasing order. Give an algorithm to compute the maximum element of a unimodalarray that runs in $O(logn)$  time.*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ehdHp0hREnN7"
      },
      "source": [
        "def find_max_value(arr, left, right):\n",
        "    if right>=left:\n",
        "        mid= int((left + right)/2)\n",
        "        if (arr[mid] > arr[mid +1]) and (arr[mid] > arr[mid -1]):\n",
        "            return arr[mid]\n",
        "        elif (arr[mid] > arr[mid +1]) and (arr[mid] < arr[mid -1]):\n",
        "            right = mid -1\n",
        "            return find_max_value(arr, left, right)\n",
        "        elif (arr[mid] < arr[mid +1]) and (arr[mid] > arr[mid -1]):\n",
        "            left = mid +1\n",
        "            return find_max_value(arr, left, right)\n",
        "    else:\n",
        "        return -1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wy6yrN7ZoWdM",
        "outputId": "57393aa6-1c3a-46a9-cff2-4267238972de",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "input_array = list(map(int, input(\"Enter any unimodal array with distinct elements: \").split()))\n",
        "left_index = 0\n",
        "right_index = len(input_array) -1\n",
        "\n",
        "max_value = find_max_value(input_array, left_index, right_index)\n",
        "print(max_value)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Enter any unimodal array with distinct elements: 1 2 4 5 6 3 2 1\n",
            "6\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UeUoV2xuDySz"
      },
      "source": [
        "# **Problem 6**\n",
        "## *You are given an array of n elements, and you notice that some of the elements are duplicates; that is, they appear more than once in array. Show how to remove all duplicates from the array in time $O(nlogn)$*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fgK6r6w2GOSA"
      },
      "source": [
        "def merge(arr, l, m, r, index): \n",
        "    n1 = m - l + 1\n",
        "    n2 = r- m \n",
        "\n",
        "    L = [0] * (n1) \n",
        "    R = [0] * (n2) \n",
        "\n",
        "    for i in range(0 , n1): \n",
        "        L[i] = arr[l + i]\n",
        "  \n",
        "    for j in range(0 , n2): \n",
        "        R[j] = arr[m + 1 + j] \n",
        "  \n",
        "    # Merge the temp arrays back into arr[l..r] \n",
        "    i = 0     # Initial index of first subarray \n",
        "    j = 0     # Initial index of second subarray \n",
        "    k = l     # Initial index of merged subarray \n",
        "  \n",
        "    while i < n1 and j < n2 : \n",
        "        if L[i][index] <= R[j][index]: \n",
        "            arr[k] = L[i] \n",
        "            i += 1\n",
        "        else: \n",
        "            arr[k] = R[j] \n",
        "            j += 1\n",
        "        k += 1\n",
        "\n",
        "    while i < n1: \n",
        "        arr[k] = L[i] \n",
        "        i += 1\n",
        "        k += 1\n",
        "  \n",
        "    while j < n2: \n",
        "        arr[k] = R[j] \n",
        "        j += 1\n",
        "        k += 1\n",
        "\n",
        "def mergeSort(arr,l,r, index): \n",
        "    if l < r: \n",
        "  \n",
        "        # Same as (l+r)//2, but avoids overflow for \n",
        "        # large l and h \n",
        "        m = (l+(r-1))//2\n",
        "  \n",
        "        mergeSort(arr, l, m, index) \n",
        "        mergeSort(arr, m+1, r, index) \n",
        "        merge(arr, l, m, r, index) \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q-hdRfIfEc7c",
        "outputId": "290bc2a6-4518-4911-878f-21ccad12e574",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "arr = [12, 11, 13, 5, 7, 7, 9, 5, 7]\n",
        "\n",
        "def Remove_duplicates(arr):\n",
        "    for i in range(len(arr)):\n",
        "        arr[i]= [arr[i], i]\n",
        "    # print(arr)\n",
        "    mergeSort(arr, 0, len(arr)-1, 0)\n",
        "    # print(arr)\n",
        "\n",
        "    init= arr[0][0]\n",
        "    final_arr=[]\n",
        "    final_arr.append(arr[0])\n",
        "    for i in range(1,len(arr)):\n",
        "        if arr[i][0]!=init:\n",
        "            init = arr[i][0]\n",
        "            final_arr.append(arr[i])\n",
        "    # print(final_arr)\n",
        "    mergeSort(final_arr, 0, len(final_arr)-1, 1)\n",
        "    # print(final_arr)\n",
        "    for i in range(len(final_arr)-1):\n",
        "        print(final_arr[i][0], end=\" , \")\n",
        "    print(final_arr[i+1][0])\n",
        "\n",
        "\n",
        "Remove_duplicates(arr)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "12 , 11 , 13 , 5 , 7 , 9\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}