atan.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{3}}{2}$"
      ],
      "text/plain": [
       "sqrt(3)/2"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import atan, pi\n",
    "atan(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:10.775587Z",
     "start_time": "2020-04-14T04:32:10.133626Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 45$"
      ],
      "text/plain": [
       "45"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "deg(atan(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:42.908593Z",
     "start_time": "2020-04-14T04:32:42.525596Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\pi}{4}$"
      ],
      "text/plain": [
       "pi/4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan2(1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:55.981595Z",
     "start_time": "2020-04-14T04:32:55.973592Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{3 \\pi}{4}$"
      ],
      "text/plain": [
       "-3*pi/4"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan2(-1, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:55.981595Z",
     "start_time": "2020-04-14T04:32:55.973592Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:55.981595Z",
     "start_time": "2020-04-14T04:32:55.973592Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:55.981595Z",
     "start_time": "2020-04-14T04:32:55.973592Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:32:55.981595Z",
     "start_time": "2020-04-14T04:32:55.973592Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:33:16.133629Z",
     "start_time": "2020-04-14T04:33:15.952596Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1c88bdb0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import plot, symbols, atan, pi\n",
    "from sympy.abc import x\n",
    "plot(atan(x), (x, -5, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:34:17.454623Z",
     "start_time": "2020-04-14T04:34:17.100588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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77NaXpxVVeNIsKNu2HzmStcFhc7ka30cymeQXf/EX+fVf//VjOf+TxhOoE0wjVNxxnF2Ta/fiKEm3O118jQKusiwzNzdHPB7ft5/dDJQNl1031a+r/lsd2xxhkreHkFhA0BJWTR6j4JhoZHCph/9GlBlWjE3Kjsakb5aKs0BEOU3CrOdDlZ0cgh5GtDky9s3O8xDggT7PbOAKJfs6qhQmYy02P3exWa59m+XaDT7b+5MElb3v0/POYb/Pxy1cz4MF1S17CVehUKBQKOzW5JnAE6gTSEOYUqkUmqYRi8W6yqM46jIYjuOwtbXFwsICPp+Pc+fOEY1GD2zX7XxXI/H2sG3yzjqW3QPqZttWiQV9jQn/FQrWe82tNVdiy0pyKnAJ3fkAAEEc2MQRFutmhRHfGA6dg2PFyZNknLAySsWpL9Phk6IkzboYLej3mfC/RFCWKDotsZSQyVppKu5d/v3mf8df6f0pJgIvH/pePAonyYI6Do5LuE6aQD3NJOZCobDvy+VJxxOoE8TO5NpSqdTMn+iGbgVKCEEmk6FUKrGxscGlS5cOXTT2KALV7UKHy7XvsiZnOKtOULHrCblRdYaNWo671RIzvilqYgVNipI0658v6wucCb5Exb5N0lxpHssUVQrOKBLFjnNElQkS5iIBOcyoNkXJWSGizpBx7jX3SRgPGNAuE5D70N36HFdcnWNt+/g1N89/zPwcF8Nf5JXY30aT/Ye+Ro+96Va4qtUq9+/fJxKJEIlECIVCT71W4dMin88311V7FvEE6gSw1wKBR81NOuwclBCCZDLJ0tIS8XicYDDICy+80PW5HMfpqoxRtyHtK/oNhCQoOnEU1gEXpD4gh0CQ1AU9Pj+uPoSrtnKh5mtLzPpeIi0+6jieKg2QtvLElB4Mtx7Fp8p9QBbdrZAwbSb9c2StbEe7HnWKJX2eoByi3xnD8q1j03ndMXWK90r/nvu1a/ynfT/GqP/4q6I3eN4sqG7ZS7jee+89Tp06ha7rlMtlUqnUQxbXiRYuIeCYvtdCoeAJlMfR2E2Y2gccVVUfqgF2GA4SNtd1WV9fZ2Vlhb6+Pl5++WUCgQDf+c53uj7Xo6wJdRgs1yCh1wvCbpgbXAq/RMG8zmp5A7bHlapcZli9iCnr0BbYJBAsl0w0tQdbbYWTZ40yeTeHLA0QlhxsobNhturzWcKgYIfwKRFwt1rXSgzYpOZWSQDntVdZNz7uvB9EgQ0K9gb/bvN/4ZXof80rsS+gycdf2eAkCdRJSFxuIIQgGo0+tPBlu8V1EoVLclOo9p9gaT98bMf0BMqjaw67cu2jWFC7tXMch7W1NVZXVxkaGuLVV1995JIw3YhNg25ELVH7CEe0ap3dKa0yrcxSkztDv1Nmgbg6DKw1t/nlGOtyml65l6hkY4oyAQZY3w4pz1pbWHYPfaqfnLzecTxBmLuVBc6HXyBj3USV/GyYrXp/SFCwfQTkC9hiEVNUUAmwaS23HUOwUPuYD8tX+ev9P8R08PJhb5HHI7Lb7+kwrsLjFq5DVXkXAtX+Q3zmr6IHfv3YrCeoV7GYmJg4tuM9aTyBeoLsl1y7G0cVqJ1RfLZts7q6yvr6OiMjI49UWXy3Pnb79tzNHNRi9YOOvx3ZwfLPgn4daB0jrIxxu7rOXGCM4na18qgyiWCZrJ0jKE8iM09IGwO7lbBbUouE1Utobg5ruySS7Kqs1FYQEtyuLDPru4hfEeTtxY6+ZK0cOXuLmNrHsK8fRYpSNO43P1cJkDRXsIXJ/53651wKf4a/1vt3CanHk9x7kiyok9KPo/A4heugCD7hPCBg/gKqexVL/Tu4yvG6hD0LymNfGsm1pmk2B+XDRuQ9qgVlWRYrKyskk0nGx8ePpbL4To4S0n4Yq0sIQSqV4l7+HXZM87CmlxjyX2bTaIWElxwLW1ikrTARJYQlqhTtlr9vzdzgdPACm2bnvFJQjjJvLDGojeGXUxhumQH/aXK1liW0YCYYqJxC9mm4cv2YAaufrFx3/xXtAmVb5kxoHAkJsS2cvdosRb2VyLxQu8ndyj/h831/iyvRz3Us4fGsc5JcfMfFUYQrFAoRCoWIRCLNdrv95oSoIcxfQ3VuoIqPMKWXMLUf5bhl3hMoj11pT67d2NigUqkwNzfX1ZumqqpHEqjG4J5IJJicnOyqgGu3b+VHmYPar00jcGNxcRFfj4YSHAO3FfgQkKMs1zbZNDVOh0Yo2kn8coQ1ox4anrXz9KgzaNIGK0an2y5vC/zyBDit+ai4OkHKWiJlpRnSBgnIEpUd9zyq9LHsJBmWJwnJOapuDuwg+FpLyWtOjA/K9xlRZgmoGWoiT8XRO47To46zpN/nq1u/zQelb/Cf9f83jAdmurp3O+/VSbBcnkdx2o9uhKtcLmOaJrdu3WoKVyR4HR//AkQaTZ6mKl3GVf8TJDm2xxmPTrFYfKYF6vl5hTshNAIfDMNoWk2NqLpuB5NuLShd17l9+zYLCwuoqspbb73F1NTUocXpuMVmvzY7BzUhBBsbG7z99tvk83muXLkCY4Kb5XX6tdYgHtMmEIAlLIp2FBmVmDrZtFoAFvQEfvnCQ+dVpCgfVVYY8rXmgoptIrJpZXDcSQpOqaNdVB1GAEkzzZblp1+doah2zoHFA/V6hEknzYauEKrNsmWtdeyTa4sK3DCW+FrmD/nD1L+muKOU0mE5SQJ14iLhngIN4RoaGmJmZobLly9z4cIFhoaGmJ6eJhxJ4fAPke3/GcQ6lco5ikYZ3UixVfhrVKvVrn9LB1EoFOjt7T3WYz5JPAvqmNhv5VpN0x5aSvowKIpyqHbVapXFxUWKxSLT09MMDg6SyWS6HjSOmtP0KFF8DWFaWlqir6+PV155Bb+/nj80n7mLAFZqChFFQUgOptvy960ZaV6MXqbmPBzpuKRXGfbNkTLrLjYJiTWj7pL7sLzCi5ELVJ0t1sxkZ9/kCAXdpN+nUbDr+2+ZLQEpOxVK9jABW6Ls2w6aEBIZuxXtZ0oWVnCQHimK7iTQRZmIGCLjZlrncRXWaisscp9b5et8pud7+VzP38CnPHu5UydFKIFjH+AfFdu28fl0hPy/ofj+DXH1NRSnhCm9SiQ8jxAFSubPUy7rpFKZPV2FgUDgSC8BnovvE07DYmpf52Xng3RYodnJQRZUuVxmYWGBWq3GzMwMFy9eRJIkcrncI81dPc6cpkYbx3FYX1/fVZga3K/Uk2Q3zQJxTuGElkjU0h373K6sM6wNdWwLyTHWjBRp08dMcIScnWRAm+RerSUiH5bXeClyHugsbZQxK+TsIpYIMh4YQ0JiWd/q2MdwBSsUOK9dpGDP06ONs2K0WUtCImVuUnKKhJUQs8FRQCWjtyyoId8pVrYTfC1hcnXrL/nL9Dd4ide4EnyDWCRGJBLB5/PtOfifFGE4Kf0Aun7Bepy4QqcmfptQ7FsY5k0kIshii4p0lqAEuCaW+gV6Yv8lPQNt7Q6Y49pZOWO/e18XyMe7eOPjxBOoI7JXcu1uHHUuaS+BKhaLLCwsYFlWs4Br+0P6KNF/j9vF57oulUqFZDLJ8PDwrsIEULQKbBqtAq3zosSb/hfYMJY69hvQxlmoVRjyxai69eoQPdooCSOBIUxSpp+4GkWSIkBLaARwt1JkNDDHxraV1asOsrwtgGWnxlLNx4XwqY52ITlCYntu605llVHfGKrUGZU36JtkRa/PiVWcKh+XTaYCU0SUHsrb81/ujkFlMDTBfG2eq3yDj80PeS3zGYYTY1iGhaIozTfpRuTYcUVhHgcnqbTQSeiLEA4l89+Rq/0qSBIBpf68aOqrlOz3kJCQpWHKch8h3996qP1RgzN2CtfzgCdQXXJQcu1uqKp6JAtq53Hz+XxzeYvZ2dk9fcsnUaBc12VjY4Pl5WUURWFubm7f/Iz7lbsdfwsJMkYPqqRii7Z7KQUp2Gn61WEkyghcKk6rPzm7RFQdIWV2zvP0a0MsVbNsmTKXY3MkzQeElX6gNf9kuTY3S1vMhs6SMOrW3IBvjMz2CrwAGavEpukyFz7NmlGvrK7QOTiM+Ce5U13BL/s4H75AwVpn3VjtuLi01RLBosjzoXYLQ7nO9576Xl4Mv4herVdFSKfTLC4uNivb+/1+ZFluhjsfd5TmYThJFtTTrGQuhEPO/Co18y8w7P8HgBDncYSOLU8j2dcRlAmon6Pi3kSRz6Oqrx/6+IcRrlKpRCqV4pd+6Ze4fv061WqVn//5n+fixYtcunSJubm5Q92fH/mRH+GP//iPGRoa4qOPPnrocyEEP/3TP81Xv/pVQqEQv/Vbv1WfNz5mPIE6JK7rUiwWcV23aVY/zuKtDRp18hqBD6dPnz6wNt9Rlts4aj8PEqh2Yerv7+fVV18lkUgc+COZr9x/aFva1Bn0nWfDaP1g1vW6RbKgp7kSvUDOfsCKnupoZ7kqCsPIlHC3K5+H5V6giIPLR8UtLsdmSRmdixeO+ie4V03y3VKFFyMXWDfvULRqHfuM+Ce4XUnwQbHC5cgFSvYKa0ZncIQj6s+J4ZrcKK1yMXQe1bfF5nbi75BvnFWjNRcWUWKsGWsIBL+X/D3+wvcXfLbn87w1+jqa3LKclpeXMQyj6S6tVCo4jkMgEOiwtkKh0GO1Kk6C1dLgafRFCJec+Sekqv8K012jR9kOL5eGMVwVUzLolRSEKCLkNzGd6whRIxT4mWM5f7twDQ3V3d2/8Ru/QS6X4/u///s5e/YsN27c4Mtf/jK/8Au/cKjE3R/6oR/iJ37iJ/jSl7606+d/+qd/yv3797l//z7Xrl3jx37sx7h27dqxXE87nkAdQHty7ebmJrIsMzk52dUxjmKZCCHY2tqiWq2SSCQ4f/78gZXFGzxpC2rnwmnQKqe0vLzM4OBgR9WKwyTqbmy7yBooQmG5tsWDqsOrPTNsGIv0aoPcr7SKvn5QWuON+EWSZqf1pUphPiwleDF6jqRVXw8qbbQsJQeXpC4TU3uBlkhJtHz3N8qrvBC5zKremaxruK3r+Kic4FzwDKqaZdOq998vBUnsEKx1o0TSLHAxfA5dJFHlUMfn/doIGauVTByQw/yb5B/yx+mv8Vf7Psvn+z5LWAk3XX9jY2PNfYUQGIZBuVymUqmQzWapVqsIIToqf0cikQPnLw7LSbKgnqRAOUJnQ/8jiuZ3MO2vAxBXL+O47yNJZ5DkAQz1KggN2V3FkF7BLwmEayC0/wpNe+mx9k/XdQYHB/niF7/IF7/4xa7afu5zn2NpaWnPz7/yla/wpS99CUmSePPNN8nn82xsbBz76tqeQO3CXivXapp2pNp43fx4GzlMS0tLzUHkxRdf7Op8x10iaT92itpOYXrttdcemqQ9SAiLVoXlqo0iKTii3p+I28OmqIeEz1dMBv0RIsoA0HKVCSCpK/RpA2TbXGbrel3EbpTWeCV2gZq7xVKtM2E3pMS4UVzlpdhpVo15VEl9yBKrOgqKGCGoFCg6BUJyiOVap5CWHJflWoUXY+dZM+4x5J9gvtoStT51gHWjvmzIx5V1QnKAcMiPT/JjivqzlbM6w9wNt/4CUHbK/HH6a9wq32fYN8Ql5wyj8nDHvpIkEQgECAQCDAy0Zt6FEB3zF+1LVrTPXUQiEfx+f1fP7EmzoB63i89wcmzo/4FE7fexRYERbbr5mUINXX6LirNEVNSfzYB0mTKbOM4dgsSpymfp0f76Y+0jPN4IvrW1tY4X9YmJCdbW1jyBepwctHKtqqpUKpXHcm7XdZuVxXt6enjxxRcJBoO8/fbbXQ8AR6mPB482B+W6Lmtra6ysrOwpTIft353yMovVLG/1nWsWipXdAFAXqJxVZSwwRcnZseQ1Eg8qW4TVACEtRM2tMqANdVhZ7xfXeCN+Gugs8rqhF3ARfFBMciV+FleY3K12JvqmzRJJI0dUCTJMHz2RPtJWaymPoBxkWd/AQXC9uMZkYArX7fzeYmof60ZrAblB3wjvFxPE1DinQz3obomE0YpUjCpREnqrH0EpyGJthfvVRb7FNU6rM3w+/1muxC6jyXv/nCVJaoYuDw4ONre7rku1WqVcLlMoFFhfX0fXdRRFeUi49vo+T5IF5TjOYxPLnPkxi7WvULQ+BrEICELyKMWWTR0AACAASURBVLpzG1AIKW+w5XyMI5YY0F7AdpJU9RfQAmu4boqo+hoVsQXCJaR97rH0sZ3HuRbUbh6Qx/EMeALF/jlM7Rw12GE/GgP76uoq/f39D0W1NSIAuxWoo3AUgYJ68Mbbb7/N0NDQvsLUfp7d3IINbpeWAHgnt8HL8TFS5jol0Xnf75e3OBOeBFoWzIhvhNtGnpKjc1YdRWaRsNwDlDva3imXOBWYZVmvu9GGfEMsVOuiIYD3C+u8Fj8LtIRhQOtnpVYPtCg5NSoCrojOyeph3xi5NsEq2iYr1RKfip0jYc7jCIeU0Rms4W7PTxXtGteLNV4In+FUIMqKvohAMKiNkGtz940GxrjXZpHpwuI3Vn+PiBLirZ4rfL7vDcYCnVbVfjQCLCKRzkhE27abwpXJZFhZWcE0TVRVbUYUNv5/0iyo4+yL6VZYqX2drPkeKfObAIz5zlOy6wN0TO0BcZmsU0OliCNKyPgQbhJTehVEBZcUsjSKIZLY7goDoX92bP3bj8cpUBMTE6yutrwXiUSiw9V8XHyiBWo3Ydrv4T5quDi0rIbG8R3HIZFIkEgk9q0sfpTcpKPSjYuvIayN1Xe7KUB70BzUnW2BcoQgqWtEtAgJUaa9UNloYJi3Myle7B1jYzvsOyBHaMwh3aukuRI/Q9qsdhy7T4uzUs2xoUu80jPDsr5IWIkDLatGk1Tezq5xIXqWDXMeF5e42kt7hF8AP9/MrnAxMkfRXaPm6lR3WHSD2iBpY5n3C2uMBkaZDkS4VWnV5gtIAZbb59qExGJtk7xdYtQ/xnDAR8HuFNfqjvJJxrZwl50q/2/mW3xUnkeRFN7qeZm3el6iRzta+RxVVYnFYg8tWWFZVtNNmEwmqVQqGIaBEIL5+fmOwIynEU13HBaUEC6b5scs1r5GovZtVFlD2/7uVSlI1anPcQblOUqORd5eIqQMU3PuABBVXyJnP8ASt+lTelGkszhSP7b7HTTlBcLaf/5oF3lIHqeL7wtf+AK//Mu/zA/8wA9w7do14vH4sbv34BMqUIdJrt0NVVX3ffM/qK1t28iyzMrKSnNC8aACrkdN8j0Kh7GgXNclkUiwurrK8PAwFy9eJJ1OdyWg+7n4LNdmvtJa1iKhF3greJYVaWfgQxBbZFguC3oDYSpOhbTRKUaLlTJjwX6gVcGhT+1nhQQuguv5LV7umSapd66uOxEY5WYxxQeFdS5Epim7CVJG5z4xN8YWeW6Vkwz64pwKDnOv2jkflbda/dnQ84ToY8J3hpyzRsWpMhYY406lZXFNBEZYqtXnvTaMPI7oxxEq04FZVvQlomqUtbZovzAhknbLHdin9bC2nTu2klznm7l3iSpRXou/wKvxy/Rohwuy2Q9N0+jp6ekY+DKZDFtbW/T19VEul0kkElQqlWbE687AjMcdUXhUYdwy53lQ/QaLtW8zoPWTserRosPqHHn7uwD0a9MIkUcXEVwpQNF+H4AepQ/DTSNJF6g4SSyRI6qcwjZtcnaKcZ8M0nmQvwdJejI5bI8iUD/4gz/I17/+dba2tpiYmOBnf/Znm2Pfj/7oj/J93/d9fPWrX+X06dOEQiF+8zd/8zi73uQTJVANYVpYWGBychJZlrv6sTyKi0+SJB48eEA2m2V8fJw333zzUD+kRwlR7xZFUfYU4J3C1LCYCoXCseZOzVcSWDvceRlDZlAMkJZagQ+ben3w3zIrDPpHiClpVqqdgQ+DvgGuZdd4rW+axdoSUHe7NXAQJKou/f44aasVvSdE62dxu7zJpcg0eaclcgDltj6mzTJ9yhCzgRAL+gMEgj61l/W2uSRJyKwaWxTtKhElwIXoKLUdFpdfDnT8HVd7uFVeYsMoMKANMOYbpezcxXDr19Ar9VFoc3EO+PrYslqWYESJcLuywO3KAr+z/h94q+dlxgPDvBw7z0QXbsDDoKoqfX199PX1NbcJIdB1vWlxNaJSoTOxNBKJEAgEjmUOoxsXnytc1o2PWai9R9ZcJGt/WL8WyU/Brj8PEhK6W4/CjCiz1ByZTWsLyDCsNcLJQwhc8k4vIdkAkQBkNHmYrO8dwso44LJpZ7gU/puPfI2HpVAocPbs2SO1/fKXv7zv55Ik8Su/8itHOnY3fCIEamdybSqVYmJiousfxFEEyjAMlpaWyOfzxOPxriqLw6PnUD1qZfJ2V2S7MO3X5jDn2cvF15h/aidjGKSqLhOxCEWnTEQJsVLJtrVJ8+meGVa419Gu6rgIJK7nMnyqZ5yslWOp2lkqKa7FeW9bxBZqS6iSwkK1s7SRI/xkdT+T4RDrRooeNca6VepYWK5g1/iwlOZMZAoh5enT+ki2WV0TwRHuV+rRe2XH4G65TFgOMBUYZ0VfQ0EmoW92nLd9vmrLqnCnnKdgh7kQOUXB2aRkd1qMGbMtj0tIHQLpkzTeyX+EKT7g9ze+xtnQKcYDI1yOznEpMkdE7Qx174a9njNJkggGgwSDwY6Iwp2Jpclkklqt1pHP0x6Y0c0z7DjOvnOgZTvPYu0mi/pNyvYiWbtuwZ7yn2nuM6ydIm/XS2D1qbNossAQA5QdGd2tP2OD2gyGexOf3EdIvsCKUc8BGlB7MdwYknSOnHUdgJg6Rsr6kIj6In5l/NDX8qg863X44DkXqL0WCNQ0Dcuyus6672ahPV3XWVxcJJfLMT09zejoKAMDA127Nx41ZLyba2w/V7swjYyM7OmKPEpS8H4uvnvllY6/A7KPpWoGRwiEM4BMlSH/ECuVzhDwpO4yF5zmwbalpElqU2hs4XK7UOG13ilS+kJHu4xRwwXezaZ5vW8WB5OPijuFokTWqlEuKLzcO40qyazrrQniHjXCynaJpPvlNGHFR3+s042jSZ3W0ZhvgJulVVZqcDE6Q69P5aNya35qzD/EUq1ltQ37+ljbruX3fmGdEX8fAUcw5guxYScZ9g+wbrSE9VRwlMW2EPjJwCj3qq17K6Pw55l3+PPMO0hIvB5/gR4tyrnwKc5HTnXlDuw2MGG3xFKoP3ONwIxcLkcikcAwjK5KPe3sS8nOs6zfZUW/h+kWuVfdFhJthKpbvx+qpFFoW4zSETlUKUBEOYsuJFb0+tzSlH8WffuxDcgOfvkKq8Yqg2r9OEG5D5caRbePPhVsbIQxQUb+CFfUGPT/7UPfo+PAE6gTyF45TO1vYY8jGq9BtVplYWGBUqnEzMwM58+fR5IkSqXSkYTmUer4HcWysW2b5eXlA4Wpvc1xVp9Yq9jIyM2KD6OBQZLbrru75SyfHTyNKzrbykgsVrIYrs3l3hESepLxwDA3i60Bu+ZapHWFYV8fqe1FC3u1KMvbx3aBa9kkn+mdA1oCNezrZWk7ws8UDteyad7qmUEWEq5Uf1kZ8g2SahOssBLhG1vrXIpOY5ChaFdZrnWKXtFu5dN9XEpxNjTFlH+OsrtF1ioQViK0z531aHHW9JaF1KvFuKUvgwUDvgH61brLMGfX+6pJnVaEJTq/o8220k8Bycd7hdtYwuZP099hMjBMzTWYDY0zF5rgTGiCscAQPdruKwEfZSmZ3VAUhWg0+lBCum3bTTdhOp1maWkJy7LQNK1DuKQArNlLlMwsuY1Nam6JNeN28ziDWiuiLaaGqW57e0d8p8ha9bSDfnUW8JO2TPJOHpn6i0dAjlKw6tZTj3KWjF2iYCcY0KaouY3giDnWzBu42PSKGkHlMnnHRhUr+OVJen2PP7S8nccZxfekeO4ECmiuw7RXOaKGBXWctFcWn52d5dKlS8ciio+rEvpOHMchnU6zvr7OzMzMoVffPU4X33IlwzuZdT43PMf9ar3UkU/qrGv3nXSSl3o6w1n7RJhlpz7a3M/qDIVC7FyBQ5UUbhXThBSVoVAPaTPPkNZPoi2UXELmWnaTC7E55msL9bkkrYeltjD1Xi3CN7ZWGJf7UMMGBbtM0eqMrOvX4qzWitwqpQkpPl7vPc/7xZb7sVeNstImWJqksFDbRHdNVEnmpfhpClZnvt3mjjJM7X9vGRVuOCnylsnpyBQ9qkK6beXgiBLuSCge8w115FpNBkc6gjXCSoBVPcWWmeed/C1G/P0kjQwxNczZ8BS9WpQRf//2vwEsx0R5jIEPqqoSj8eJx+M4wiFn5khbaZK1JKv6EkvV+2RKaWpUCKNg6fUvf0ppJZKO+MbJ2fVVklVJI2u1LCYJi37tEnnLwhAhlo264IxrU6StuqU+pI1huj4s0YMj+SlYdWs3JKtURRRZmiVjL+BiM6jNoEgyS8YiI1oAVRrAr/4XSNKTHW6LxeIzvRYUPIcC1YjI288VdySxEK1Bqt3nXiwWefDgAbZt71pZvMGTrO4Ah7dsHMdhdXWVtbU1ent7GRwcZHZ2tqvzHFeQxI183Qr5VirF60NjLNfWye2o3NHvi3EjU2QwGCbv1gfxoeggy9m60JSx6XFjZIXZ0W5QRJh3atQcC0kE6QvFKO94BqaCg9wu5riW3eDlnmnWzBXSRqdQjPn7SdXWSLg1evUg52KD3Cyuduyzabaelapjkqo59CtjaKrOhpFh2D/AptEShOnQKLfL9f7bwmXLcFiuVPlUzywFJ4Nf9rHS5u4b9w+wqrf+PhUcYqGaBiTul7c4Gx5nqepyLjJNSAWfpPCx3XJtRtUwtAmU7rZe1mSkjrmwYV9dnACKdoWyXeO9QssqmQ6OsVRbJyj5mKyNEFR8RNUQMSXMsL8PCQgofgKyn4CsIUsyqqSgSSpu4z8hEAhqjo7pmjjCpewUKTsVKk4Vn6ywVFumYBVQJYWSm20uUDkXHCfhLoMEU4FJUubi9nXI5EUr4tGumjQqVw3KI5TFMgPaGSRizFfvYQkLTdIIb6/eLAEVp/6dBKVeTFdjxSgCJYa0+oH8cgSBTdGJE1UFplu3SlWpj0XjOjFlCFmsknenOOV/iyeN5+J7RjlSuLgUQdb/NbPD97Ct85QrEgsL9R/93NzcgQ/Co1hQpmkevOMu7fYTKMdxWFlZYW1tjbGxMd544w1qtRqLi4t7ttmNR12wsJ0PC/WB3gUeFFwGwzEWy52ReTERZMnOETPDBHwmumuRNzu/S0soqETQpErTtRUNxsGsl/bZsmqopSAFudiRW+WnlSD9QT7Fy/GZjiKuACWr9V3krBplY5BzoVnu15ZwhMuwv4+Vast9piCzWNmi7BgoksSV3lnKdqfF1dEJICQHsYTL+7kkiiTx6b5JLD9sbAtFTO10/wWVnUsrSNjC5VapLjTTgREG1WnimkzWyrDWJk4xJcxyrXWN08FRFmotq7JPi5IyW+cqO63AjKgSYmW7bU2YKEjcLN1vO9ZIc9mRfi1Ozm5ZfRfC09zdTjjWUNFkGd2tv4ycD08zX6tbKKokE5Q1am79uzsXnqG4LdZhOcSG0UpJ0NpeDCcCU6TMenV5n+Sn5s+g4SfKKIalsuVG2TBTjNgCy1d/fgblUfKi3mbYN4Urtoirn6JqOywb9TSHMd8UFec2iuSnR73Igv7+dtsYlqsQUa6wZnxQv3dKnHTNRfgk+nwXedKYpvnML7txMtK/j5mD/OFHXeHW8f8wEhZm+kcobP1Lzpye5ZVXXjnUW8qjCNRxWl62bbO4uMjbb78NwJtvvsns7Cyqqh7pXJIkHTpwpMFeFu7NfGuwSRtVotIE9o75Jtutf7cJo8KIb5KQ4mex0hl1N6jFuV3MMK5NIm8P/ht6pyXUF+pDdyIMtiWyrpQ73WiVmgNmlKHtuYuYGmKh0hkFWLBNrmY36JVHGPDF6VM7ff4zoSHK2/5GRwgWS2WWyxbnwqeQAJ+kslBtWSySkFiutgTBcQU3C2lu56uMqlPMBsfZMLId+6+2LeIYkDQW29yH/VqUxVqKO+VNruWSOG4flh1lNniameAk4/7hpjUCoO4ol5RqcxX2a/EO62o8MNScKwSouS3h7VWjrOot4Rvyt8LPJSBptvp8KjjaFCeAotMKlZ8KjDfFCSBrtfozHhjGof68BuUgG0Z7EIiz3Y8hxv0X8UunSJkBUo7FqkhgSTYyEnagFWnpuHXL12fHKBcVVmou96tLaG3zdz7ZJa7OUXVHydtr2+eOUXPWkaQL2DgIHCRUCrZFRdliIvBXedJ0+5s8qTyXAnUQ3YqFEILNzU3eeecd7iS+gOp/iZnhjwjwD7Dtw1kcjyI0xyFsDWG6evUqUBemmZmZjnmmo1pD3bLbeQpmtWNgBtAthTm1Myw31VZJ4f1MijPB09g7foyV7fv1QW6TucA0I/5ekkZnAVZXyKSMKpmqyqi/lzF/H1m307IpOxbrRoW1osOIiNFrB2jvdUwNNcVxvpJjvSI6KqDDw8EKI4E+smaNa5lNepRRLkVmm8VgAaZDwxTawsdPhQbJbLsMb5fS5HSFqhnifGim7lbzDVK0a237D3ccb8TfR/vdCch+1vQi7+XWeT+XIVF1icvjzAXnmA1MkTPbQuMDw2St1t9Dvs75jHZrKi6HWW0rrjsa6O8QvmxbUMZUcKyjQka7yA37+tk0Wy8cUtsxxvwj5OyWQFWdVt/G/aO4OITdOGPqGUw3gOEMc69aJWUWWdI3cITDsK/Vr3H/ZHORy7jSh+bzEVEukJOCZLQUruSi4aPgbs9dOSFyRYd7tS1kW6Hs1AV40DdFyR1gw1xFiC1kfPRor5Nzl+rnCXwPT4uTUiPxqDyXAnUYC+owLj4hBMlkkqtXr5JOp3nhhRcYHBykqvw0qC+jST7syv9ETf+3Bx7rqBbUo0bxNRKTr127hiRJvPXWWw8JU3ubJ5EUvJuL78NCgp3vfBu5HO/ms5wJ1YMiBrUomR3VIjI1wYVIa30bn6TyoM0t+E4mxbDSWYJFRuJBqT5gZkyd9RIM+vo79ompQVa385iqwmFet4kFO/fpsfy4bb2OSAH+MrXGlG+CXi2MjMzSjpyqXNt6UouVPMmqy6Q2yZi/fuyA3Lm6cHSH+y6sBtnQS7ydSZGuaoSIMx0caToJnR13Md8WbKEgsdyWBzagxVispVms5ng3t0HF9nO3ZCK5A4z5pulXB5kNTtKvxZGQyLQlAe+0pgbVeIcg5dsqso/5B0lbbVGDbWtaReQQq+0uRV8rgi8kdy5VElFaofqDWj+OcJjwzzLhP0/V8VOw+li0XHTh4051laJToVeNkzLrx5eAgt2eGwaq5GPEd46QMs2dao6FWoJR3zAO9d/qZHACV3IY1C4S858npaa3+12/Br85yUppg4KdISJ6qdkpHPc0jqhff8CZIK7N8KQxDOOZXuq9wSd2Dmo/sWhfZK+3t5eXX36ZQCDQ0Vb0/gxu9ZeRrXex9D+g5KSIhn98z2M+6SAJgI2NDebn5w9dueKoxWK7ZTcX34eFRMffChIp10Qg8XG2wnA4TK8SZYnOoIm1Wpl0rcKFvkGWammmQgPczHVaYsulGpcjp/ioXH8TngkNcivfGjDzlkGiaHM6NMx8tW4FTAX72WqbmwnIGt/cTPKp3ikS5ga6ayGHAlBuvcXHCbBGlY8KWwSRuRwa4ZbdOkafFmGpzUr0Syrz5TS6ayMhuNI3Tbkt/BwBq7Ud7ry2+S1HwHdLW1Rck2H/AHORONm2eZ5BLd4RTDETGuF+pdWfkUAvm2ZLSBoCkzGrZM0qMbXctOamA5PotsOkvxe/LBFW/ESUMFW3Rs4sUhKtF4cRXx/JNisoroVJbk/dqZLCalv9wfHAEPe356IkIGW2RG8iMELeyhJUwqiSH4HCiHaagqWj0cOdygMgzaDWQ8Fpna/qtq5pyNfH0vY9GPOPkd2O5OtVhnFEgLwVJ2msM+hrvQiYovWdapKCIs1xq5pg0h/bvgYNS00Rl18iJ2o429U8+rQe8pafrEghU0ESQezcSywYC81Q+Me9eGSDQqHwUB3FZ5HnUqCOakG1l/PZucheg3aLRgn9BE7ln6PYd7HNPyOLTm/oZ3Y9/5Oag2rkMa2srNDb23vokkrwZAWq/TxCCJa3OoMhToUHuJWtD7Yl2yKmBzF33NZ+X5jEtkAsFkxGonH8UqcFElI05ktZ7KLg08OnuFleJqh0Js32aSHuFNOoksKVwQk+Licw7E4BnQkN8IGR4np2k8lQDzFR48GOua9q27hTw6WCn2GGsOUKGbdC1NJI0eaOC/Rzu1x/IxdIFE3B/VKBl3qnKLlFArLWcY7p8CDzbX9PqHGWtvOeUkaFQV8vHxdqTIdGGA0F8SsyKbN9sO38uWfbog2DssZCpSUOc+Fh5tuSoaNaiJul1hzPqL+Xje1Q90G5nxVLJ64NEVJ89Kk9+KQ4iiShIOG4MnPB0wAEJD+GaLlSJaFxyn8aB4FfCpCz86giTNHS2ZAFq7oJmJwNjbOk188vAYZo/X4HfXEKtfp9ibkhNq3WdeTt1v2KqmGCynk2DR1ZinBre9XmycAYW9YSAAPaAFlrjZjST1iZ5MPKLQCGtGEKdn2fMd8pyo7Okr7E+dA0WxZohCjikiHNZGAKIe5StiY4F36ZWDT2UKmnYDDYkcN1XItHNigWi898BB88pwJ1EDvFoj3UerdyPvu19YX/EWblF5DtD7GNb5J2awxF/8lD7R63BdUQpmQyycTEBKdPn8ZxnK4KZz4pf3XDxdeY27v7YJ6vpVZ5bWSKj7bzcaJKiPbVbdeNGv1KFBmp6VYbC/axVq5bBAXLJFwLo7idFtZ0aIAPtoMIvpNK8dbwFBvVzoCJiVAvqVoSS7i8s5nm00PTfFjoLPzaWLYdYLVaYkaJcr6nn1vluuU3oEVYqnZaOyt6kbxVQ5NkXhs4RckxoO3UprHjJcl0cQS8n00hA58bHMYKwsr24BveIayqpOxoXn8ul6oFlqoFxgO9xKVhxkIhKk6ZpbZgimFfDwm91d+Z0BAfl1vutIDc+WK20VZ2aczfy3rb371KgIxdomY0Fla0SG8L41xomMVi67jnw2Pcq9RdbgO+aDOxGOBiZJKFbQuzX4t2uBCVtkdzMjDCutlyC2bslpUYJ0h6uzL9uH8U0y0x5T9H0XL4sLSJsf18BOTWAYNtgSEDWh+G28PdSoJzkdbvrkcNkjRhyHeOouOSMpPIyJScFUJyP6p0irR1A4CQLCi756iIIsO+OQYGBg5d6ikUCnUsZ9JtqacGz0OSLnzCBap9UG+EWh+UnKqq6kOr6vrC/xBq/ye2/me49jy52h/QG/ziQ+0exxzUTmFqWEzJZPJI4elPCtM0uXbtGtFoFPXUKFbS5VoyzcujI9wrJ6lYnfdqxBfh/VyWT4+e4sPten07jT3LhUpNIaz4qGwn7so7HvHFQo2JUJw1WpaFYbdZc0jkdTgTHOduNYEtXDRJYb7U6TZ0XIl3NtO80j/JipliNNDHRq01EM9FBrhTrLexhMudfAlVUrgQHeN2eR2fpLDuttRKEhLrVlvggID3NjcoCovZ4CAxv8RKm7tPRWbNbl1DWPExX24J0Figh0StLvAr1SIXoqNUdZvZ6Ag+xSUga2y0LZzYHi2pIHXULDwVHGC51rJEBnzRDoHKtl3HVGCA1bYw9qDSetELyj4Wqy0X42igl1y53gdFkllpE6SxQB+FSv2zgOxjpW3RxrDqh+1HezIw1DHHVFGKjPrG0aQICI0H1TywztnQRFOc+tU4ye02PkkjZa4SUeJE5THmq5uUnNL2fFXdgpSRqblZospFFmo5/FL9exj3j+GTyyQMl0m/tX0dKrrws2I84JR4c9fx5FFLPYXD4QPnl/L5vGdBnVQOeuOwbZtarca1a9eYnJzsyg2216q6vuDfxyFCRf8jqrWvoSrTRH2vNT8/qvtsr5why7JYXl4mlUrteg1HKXX0KBymMK0Qgkwm00xsfu211wiFQvzLu/X6aI6A+1s1RnriLJQ7F/brVUKsoPOdjSSfGZviRnGFpVKhY5+xQJz3N1Oc7+nDlrcwXJuVcuc+o4EYV5NJ3hyZ4kZpBb+scm+H+CgovJtOciE+TE7kGAvEuZlvDdA+SSGxPTfzfmaT0WAUacfKuaEd1s5UqI/r2XWStQoX4mMMhny8k225zGYjA9wrbbX93c/8diDHQq3EpB2lastM+3pJSSWG1CiLbRXYZ0KDfFhoDeJD/ihrtda1K5JM3jK4nq2LwHiwh7DoZywUwS9D3ikjUV+wcS48zL22uarYjkKyybYqFpPBftb0tvkmX5BVo3FOqVmjsN7HYe601VrMtUUIzoZGeVBtzUPm2sR3NjjM/HaNRVVSSLTNYcXUILI0SkCKIAs/t0sLrJgFVKlERGsb3qTWC8+Iv5clvd6vycAkDnC3ss6E36Hk1OevJgIjFJz6OSf9Z0kYG5ScBOdD06S2Q+QjSg+3qxlsYVFy6q7bIfVTLOj1PKhB+xxquLtamI9S6ikcDjcF8XlI0oXnVKD2wjAMFhcXyWazyLLcdWVx2N8SCgb/Di4qQv8a+fL/hRodJ6jVI9CO6j7b2W6nMO11DUepkXdUGuK7n8hns1nm5+fx+/1cvnyZGzduEArVB773tlqWR8E0mbGHEaKzdp3htMT22kaaz4zP8O3NzsAK26m7/u7kc7zQN4Sj6tzLd67jVDHr393VZJI3hqewJZMbudYgKiOxUKwPwLcLWcZCYUI7IulORwa5mW/1T7cdriY3eWVokjuVdUzXYbW6I6eqLcH3diGDJsa4GJ5k08qxZZYJK51zZ3VRaIl0fzjOcm6NjG7hl32cC8TRbZuN7QonuVLndaZqrUABTVI6rKvxYJy1betqQ6/wqfgYt/IVwkqUqUiMmBzlfFij5FRIGwUSbYEWU4H/n703j5EkPc/8fnFkRGRERt5VWZV1n33N9PRMzwy7Sa5E75pLabAaLSgZpi0Blrg0QIjclQGLhhaybMGwIGqxC2kBEksba2shGyJlwrIoyUuKAmXt8pjp7unp+6z7yMrMyvu+M/xHZmVGVPdMd9f0cMiW3n+6szKOL77M/J7vfd/nUj8pcAAAIABJREFUfd4Q27bXAZdOrJ9SEoCY7b0FfYzV6hA0Wzb6e1QNDAqPoQdmw/eCJGzCt62+KogsyCy5p+nQoWtJFFpNbheLfSJHkdPmJE2h952fc4+z1a+L8khuYjYPrNBOE1WnqHdU8i2L7UavQFyXJOgP0ZQVugQQrBHKHYtSn1Lf7hMoxpRT3Kmu07KaTKpR6t37BOTTNPokHpeg4W/PPpWmjXapJ7s1m00qlQqVSoV4PD4IGf7O7/zOoPXJ1atXOX78+IDk9Tj2rW99i1/91V+l0+nwmc98hl//9V93vF8oFPjFX/xFtre3abfb/Nqv/Rq//Mu//J6f82H2TALU4UX9QCGhUCgwOzvLsWPHeOONN44EGo8KuRnun0MQdFrVPyNV+d+Y8v33TyW302q12NzcZH9//12B6cB+mH2k3g2g8vk8q6uryLLMyZMnH2gt3rUsrmb3HH+TcTGtRFipx+hYFiICO9Vh+KttWdRqMrNGkM1+2w0RgY3i0GO4kc3wE5Fp1oQynX74ShNlVovDMNmFZIL/ZGwGScgMjpkzgtzPD8ElXq3QbUk874tyo9gbp3Qo9zOtB0jXElxIJpky/Ez7DC5mh+Bpyiqr5eFiLCOyWspSbjdRRJEXw9NkGs7OuQ6As2CrMgSrdrfLlUKWcrvFuBZgwecjVs9xQHAckQz2bOG7SclkzUYRP+xdNfrfk0qnxWoxx3a5NAiRLhnjVJoNptUguixhyiqapFLrNCm1qyRsob5Z9yibtloolzicJ1NyD5oxAoRVk2SrNyeq4GKzGkdAQJdUIkoQj6whCS4kZGqdBgoRkrUSYUnkXj+HtWyMD1iGsiCya1P9kG0/jSltlI36KrqoM6lOk2xmuV/JYco6Vj/U6xIkEs3eRklCxrIUtqsCAmkMV29iA7KPUjuNTz5OtWPRsnp/98oyWvc0tyrbzLh736Np7QWskvC+dhVWFAVFURx6e91ul+npab785S9TKpX4/d//fe7cucNHP/pR/tW/+lePvGan0+Fzn/scf/VXf8Xk5CSvvPIKr7/+OidPDpUwvvzlL3Py5En+/M//nFQqxbFjx/iFX/iF94XW/kwC1IFVKhXW19epVCrMzc1x4sSJAVg8zq7/YfY4uSRd+2kE0Ueq/DVipf+LSe9/fuRnaLVa1Ot1Ll68yPT09GN7fR90H6lCocDq6iqCILC8vPyOlNeVYppiy5nTq7U63MikOBed5kppixkjyP2sM1RXabVJldqMe73Ea0Vm9AArOecxiXKdY+5x7tfitK0u854Q19NO5t3VVIYFT4SdVppap4XP5cZOzpjzBFnJ5YlVy3xobIo75T3WS07God2726mUGHV5OWNOca+aoNZpMaeHudoYhqUWzTC3+yHDZrdLutpmt9LghfA0m/UUAZfuCHHOe0Ks2mq7lj0j3C72PKJ4vcqo6mMjX2PRGyGkKSiSyH5uGEpTFXXgGQDsFIZz4BFdDu9qyTPC7dIQSAxZZaWQZq/Wy8uMqB5SffbfvB5ivZRBFzz4VA0PASZdCrIooAoS3TYsu+cQ6NUwVbp1LCwsCxptgUllhkanQ9DlYb26T6lVI2dZtNsF0n36+wveSW712YQ9lYwhCCnS8Hcwr0fY7ivK93JWvfmWEHGJLsZci9wtJwnIDNiH01qYjb5C/Iw7SryxxqQ6B5aHt4s9wdhlfYp4q8f2G1MixJsudqp7PGf0IyMINLsqtyobTKlj1Lv3cIs+JtSPPDFJ6WmYKIrMz89jmiY/8zM/w8/8zJM1SLx48SKLi4sDPc5PfepTfOMb33AA1EF3BsuyKJfLBIPBJ25d9Lj2TAJUt9vl2rVrNBoN5ufnCYVCDyy4B1TzowDU4xT5upUPM2r6iBf/HfnaSfzu5wf5pMcBmGazydbWFvv7+4ii+ER5Mjh6DuoowG0HqFKpxOrqKt1ul8XFxUcyid5KO8N0PU+otzi/uZfg3OQ0gmABQ/CRBZHVfJZau41WNQipOgGX7jhGl1ysFrO0uxYvhMdYqSdwHfq6zxp+1gslMo0a814/VaVCvOL0ZPw2wLqQSPKhkSl2m9lBuwxddLFSdOaw4tUKu9WeoO2cT6PVdW4UVNHJEPW5VFY7bS4kE2iSzPOREAWlSabZy3V6Xc4Qoyo5z29aHSwEVoo5VoowpQWYkCOE3Aq5VpmN+hDsJt0+dm3e04TLy11bWK5ZH24WBGDLVnc1Z4TYsNVxeRWNbhXKVodqvUK126HQL0Q+5R3jdmkIyktmmLW+TNSsHnSI3540XWSa/XorPcxOfQiY5e6wvmrBiHCvz/J0iZJDQ1CxsfJm3WO0aCJYGplGkx/0c30iAonGEHzr1jCXbIgapjjHlWKKUx67ukrvtz6pLrHXKJNq5XEJMqnWNiISE+ppblV6zQ39LoVC202hNcaMdoyN9ub7tnA/yo5KM4/FYkxNDVXgJycnuXDhguOYz3/+87z++utEo1FKpRJ//Md//L7Vdj2TShKSJDE3N8err75KOBx+qnVJT3Ke5jpF1Ps5EtWv0+m0H+vcZrPJ/fv3uXTpEm63m/Pnzx9J8PGHWRgsiiLlcpmrV69y9+5dZmdnOXv27GPRXHcKRUf+YcYToGzbAFyMJZG7zgV53gxS689jvFJBbeuUG855nfcEaXd7Oalr6TSL2tgD4BNSjcH/14sFfB0vIk5gTh6ipLfbUChZzIlm/z5hmjYAmnB72a32wkapWpV7qSLdpsS41vMgRQQ2Sk4CyG5lmD+qd9rczGTZL7Q4ZUww5fY7wn0iAmu2cKEuyqzY+l5NaF62qwVWinneTO4jdzy4OybPe6Y44RljTD30mdiIBC5BdDALJyQPudYQILRDRBD7uBaM8ACcwNFsmIDL7dBL7G0memZIiqP+yuca5krCisdBsjhQdwBY1Meod3thSE10kWnmmNOmCbYj5BsSV3M5ruTjBJThveb1CKVO7/lCLi/xRpyIEiHqWuZSYZf1WgpVdBHvq1fookahnSUoH2OnVifVr6+a0SIAuMWlwRgAmt00ze48HUvF5/J/IB7UgR2VJPEwDb/D6+df/uVfcubMGfb29rh69Sqf//znKRaLD5z3NOyZBCjgkYvjUQHqSbrqAqiuWSaNf8LtzO+96+JvByZd1zl//jyTk5OIongkPb730qbjSTyvarVKoVBgZWWF6elpXnnllSfqQfNnK/c54x1KFYUUJ2NMFERuxLLMu4c/Nq/sTPimqjUaVfDIwxj44aLUXK2FaRnoNu8jV3eGFj2ySjxX5zlfbwEa0zxsl50/vFilRLnV5H6pzvOeCUTL+ROKqE4G1pI3zPVMmni+zoveSU54R8nb+kfN6n6S9SFwThs+4rUSbcvi7dQ+3YaCF5NT5hiSILDkCTtCovNGkJaNIh5xO0OpsiixVytzKZXkSirLVr5GVBrltDnNc+YE+/UhmWLJM0K1M9wchM3hb0gAEnb5IkEfeHgAqjCcB02UWbOFDWeN0KB2TcBi1+bRLRgjA8V5EQZdgwEm3f6BeJIpaWxW7TkmgXn3BMvueebVBdZKXS7lMuy2GqzbPKuCjQ2oy0OwmFAjhOUFbhQqdCyRtnVArojQ7BcBT2nTZBo6d8pxxtXhvOqSTMea5H41QbHdA62wHKDeHWGjts8x4wTw5J2Gn6YVCoUj9YKanJxkZ2fYPmZ3d5do1Nl/7Q/+4A/45Cc/iSAILC4uMjc3x927d9/zmB9mzyxAPcrej6aF72QebQZJmqek/H8PAE2z2eTevXsPBaYDO6pX8356ULVajZs3b3Ljxg0Mw+DkyZMEg8FHnme3+7k0mXqNS7sJXgn0wgq1lvPe82aQfKNBPNsgqvQ8nnzdWd+1YPbyRKOCbwBAu2WnOOyoanAnkyUi+vG5VAKKxnrR6cmUmy1q7TbX9tK85Jsg6nZucqYNH4naEEyuJdNkik2WzWERZq5xqJVGf4VtdS0uJpKoLTcv+SeQ+wt6UHUC8ojqJJEEFJ072QxXEhnMjpdRl9cB4p1Dm6V0fejxuATRUb816e55V2ulPBeSCVpNmb1iGx8BjusTBGSTY54IQZfeC+9VhmAxb4TI2YR6R73DxU+EQWdigKhoUO8Ov+clm5jtnDEUvwVo2RQh5o1RcjbtwHxfUFYRZBaNcRb1KRbdc0TkSa5kM7ydzXIxGyffbgzkZqOyZ0B4GVP9A6agLIjEG0lmtSmC0gwb1fIg19a1yWeJQgtDMhhzLZFptcj3SRi1fq+noBxmtVphp55hXAlS7OQQEDCkKe5WeiHNA4CCD06s9agA9corr7CyssLGxgbNZpOvfe1rvP76645jpqen+c53vgNAMpnk3r17T9RD7knsmcxBwaPbQLyfbd8fZseD/5h76f+O3fI3OGH+Is1mk42NDdLpNLOzsywtLb3jbuuoAHUUyf1HeVD1ep319XUKhQILCwuMjIxw9+7dJ76XIAhciA/zTxe2E7w8PcHdrDOf4+97S5V2G1fRxUwowFreSVJQ+t7Sai7PcjBAx91iLef0fMqNHqit5fNMmSZTAYMfVO3Fny5WCr3rWghc3EvyE2NTGLKLSru3iI6qHrZtBb7L3iC3s1mEosXZ8QmSzSLrtvCdSxBZKTrHul4qsF+rEDW8RHwa+zVnCDF56PVedQi0qWqNt9spiq0WJ4JjdFpVtmxhtjHNZKsyfL3sDXOrYGs+qJnsVIfjP1CeSNYqZOpVVNFFpd2bp+f9kzRoETXCuKS+dyoIFFo18s0q2zVbXkvysGvTv1NVBfo46RUUNmyCuVpnuGB7JY21fnhPFeWewK4whioqKLgod+oYlkSyViIutVntH/uCN0qjH1Y1JJX16jCv1BZag01BRDXJVdMYksaCe5rNaoZL5Szjqo98p/c9M2VtUFelSyoSCqm6Roosktj7LEYUH6lWnEl1nmpLJdPq9YwaVQ3iDRG/fHygzq4IykDW6YO0er1+pNSALMt86Utf4hOf+ASdTodPf/rTnDp1iq985SsAfPazn+U3f/M3+aVf+iWef/55LMvid3/3dx1KGU/TnlmAepQdqWmhzZ6Y6SZI+IUPsdq4QGE1Rmf/PLMzC+8KTPax/rAo4+9Ermg0Gqyvr5PP55mfn3+AEXkUAL2QcBIkcvkWM0aAW7Yao4ItDJdvtVjohikqLTKN4a48VhoujvezOT4anSAu16j2gcWQXawWhgvqTqnEuNtkxvCx1VcrWDCDXLP1UTJdCj+I7RExDMIGbFXyZOvDewK4+7VLFgJvxfc5F4li+nTuFHrhrWVvmFu2Gqs5j5/1Qu9+e5UygiXgEmWe80W4VUgy7jbZqQwJDFO6zxFiXPIFud8H0ZuZDEuqSaft4oXQKHWavRClLWdmp3kD7Nuo7B5Z4b6N3LHsHeG2bd5dosyN3PB1WNVJ95Xkl80I6VqFEVcIQ3ah1VucMP2IgoBLFECwOG1O9++jUunUsaxewWm3YzFFmGang9GRSXZdNLptKlaHt1sZiv1mjmcDE1zrz6PfpTn6cLWt4cZy3ghzp9ILSfkljUS3N38CvfDwjDrH7WKaoNQm3m+5Mq6Z5Ps5sTk9zHqtyLg6iimEuZDvMfaeMyfZ7Ic/o6qXruXjUm6PF33RASOy2S3gk45xv5LBK/c+p3l9EVl8uEzaD8ssy3ri9clur732Gq+99prjb5/97GcH/49Go3z7299+T2N8XHtmAepxBGNrtdq7HvNOdgAYT8LQaTQaaNkp1jzfQ/RkmDt2kdHAS+87ZfxJ7TDYHHh6mUyGubk5jh8//sDcHrWP1KV9Z/1TUNO5Gd9nKRJipZjBLckPeEuiJWK03HQVi1yzzrhuEs85yQ/ZSpNx0cu+q0Sp1WTeDHLDJt0jiyK39tNYWJwcHeF2IYVoOZ9p3gxwvZZir1xGrUl8KDrJxf2Y45jtQ0oWxVqTO7kcL4yNs1XPoRwCiJCis25jGo67Td5KxaEIs94Qc4aXeKUyyNeMHsqBmS5nMa8FlNstLid7QPJ8YJQz3gmatNgsZx3hvajbZNsGfotmiKu5IctOsdV29cJ7OduxQVZt1HpT0VgpZ8k1G0gIaIJIJd2nhQciDh3DRTM0IHUsmSFWK8MxHTfDpPpKH3Oqly2bMsaejVY/7fZzq9IDR89hj8lGnJhU/RRaIgEtRLVl8f10X85IlNi0bT6ytpowCYspZYEr+TjPeYehU6uvpWRKBoWmyN1KDAFItXr39kseml0ft8oJjhvjg3Yi9vzTB20/7r2g4G9xDuq9eFBPEh5sNBrcvXuXy5cvo7t1Fo1/SFXSiDeL3Mr+C6rtnUde46hNC49iB2DTarVYWVnh0qVLeDwezp07x/j4+EO/9EcBqJ1mjfyhfE2l3qLe7pBM15jx+FnwhgZMvAPbK5bZKRTxdXW8LpWJQ6QAVZRYzeVYyxYIWh4CioZ8iMiw6A1QabWottrc28txNhBlLe9UfhBsgNXodGhVBU6b4wMixpiskbLlezyyi5W+l3YtkaJbFVGRHQzFxCFGYNbmBW4Wi2xnK0REHy8Foqii9ED4b8cGVoogstMYvj+q6dzIpricTHIjmWVGGWFaCfKif4KI5mFMc5I37NR3CYE1GwAtmSEyzeHY7Mw6Adi2hRGXvGEqto6z9p5QI6rOuo1xaAdYn6w5lNr9+pBRGdV87NuaIeZtqhhRUR/oBpqSxlYtxbwe4bgxS64B96stLmQTKNJw87hojAzYdlHNR7KZxZA0TuiLvJ3P8nYhgVtSBx2ADUkl1ogzo03R7QS5W+ltTGb1EcqdMpqoMqLMcasvVOzuY3tEmWDRfQrgA2XwtdvtD4ze/rTtby1AHbXtOzweQDUaDe7cucPly5fxer2cP3+eUCjElHCCNgb5tki61eF27t+Qrr/1rtf6YXpQgiAQi8W4ePEimqZx/vx5JiYm3tXTOwpArVSdJAZNklnN9RbJUqNJudDGe0j+J+hS2euH87ZyRUKWh1LJuYhHFY1mv3B2K19Eqcvkqk5P2ZCGbL+OZVEstVjyhAbEBVkQWcs5CRT1dptriRR6W2PZG8J7qFPuojdIu2tn03l4czvOpOTnmDdE1G2yY6OTj6j6QFIJIKy62Sjm2CuXuRzbZ0IKMqp4CKm9PMK8J8C+rW39si9Mw8bemzKclGKXKHE9nebSXpJYtk6jBmfMKC/4x5nWfQ7dv2PeMCVbHyqP4pz3narT80rbmka6bUCgibLjutNGYABXh2uq5s3AgOAhCjj6ZI27h0SRoMtNvDv0kAWXwIjsYU4ME2n5qVQUrmYK3M/lWLPVc+03bXVztq/uuOpjWZ8nU1OpdhiQORaM8IBNOKuPMKHM8VYuS8BWgxZwKXhlL+12hGJ7+FnkWvuMKuPEaxpRrSf++qQRlqdpz4qSOTzDAPUo9/a9kCTezfuq1+sDYPL7/Zw/f55oNIog9GRPhK5ASH2OlqBR6rrJtATuF77OWun/fkeiwVEB6p2EZh9mB513d3d3BzqFU1NTjxWCPApA3UoXOekfJlbnfQFaNkWGbLVOrdgh4h7urEddTnr5Tq5ItyHisy2oQcPpUbksiUKuSUQeHrOTd4bmfC6VK7EkC1qQgKKx6AtSbg8/X7cks9oHrP1KldVEAaUjOkJ4hz86b99b2CoUuRfPs+QOE9WHC++0xwkosx4/9ksEXBpvxZLkC21Om+NM6s4Fx3XocynZqOciOMBvzG1wLbPP5eQ+b++l8FkejI7BKWOcl/wThBQDv21u7R7SvCfoAEb7XEsIDsWLZV+Iho29V7DR6RfNENnmENjqNjr7kifsODZlY/nNGkHm9RGe90xzUp9hp9JmrdTmWqVMQ5Op9fl707p3MH+jgptkX+pJEUQ2qgkCsofj+hzr5RpvZhJUO62BVBGA2Nfwm9LGqDRdvJXvhSlbDMfVpUuqqpNolNjryypF1QCa6OZeqcOCPixw/XGsgfpRtGfDDzyCvRea+cPArV6vs7GxQS6Xe8dczcF5Hwn+JF/eeIOwooDLwOrWqFe+T665ypnAP0UWndRjSZKONNYDwsO7gYy9F9bExARzc3O4XK4nqt94UoBqdjrcLBSwinB8PMzdfNrh1QCE3TrX4/uMmQYjboNUrUKn40SBpWCIe8kM034voiqQa9SJH/Koxjxe3i4mMCyZ4yMh8s06iaKzbfxOtue5rWRyhNwqYZ+be7b3F31BbuwPc1gjboPb+TITPhOXR2SrlGc17/S44odo7rF8iVShxtlolI1aziEeCzzwOt9v6dLpWlxPpphwm0QFH1G/wVY179AUDCiagwSy5AtxN2+jlxteR3ixa1lkajUytRoSAh5FodBsE9AMTgRCNK0u0+4AtW6LgEtjt1qg2e30w3tDcF8yQ9wt2aWjhp9P+BHhvdXy8DxddhFw6QQUHb+sY2Hh1gxS9RqpSpeVcgEo8GJwfBB69Mqqo3ljw6ZWPuULki/1QG5BHaHebnO3WKQi5CjIvXkwRIXNai8vpYkyqWaOeW2BG4U0mtx7RlNS2e3XVC1o01zJpah125zwjJLsd+Ydcfm5VUpT7jR43lwYjOGDBqhnxYN6ZgHq/fagDjyaA9r1AbvtYcB0YAeekCF7mNFPkG/GKLTadCQNXRTpNFP8IP0/8IL/n+JTZhz3q9frD73mu9nB/R4Wauh2u+zs7LC7u8v4+PigF9bOzs4Te0OiKD4RgF7e26PRv0csWWJxNEjmUBhuxvSRLdRIlCpEBQ9Bl0rsUJsT09UDte18kajXw6jf4F7KCRTF/rxVWm3WEwU+PDtBojjUqRvTDZKlIWBlag3WdtIs6x7u93fy1qHarCnDJFWqECuUEIvw92amecNGoJgyvOzYKutDqpv1fB4LuBJLMqrreN0qPkWl0GzgdakDivvB8Ws2wJnyDK+3Vy5z3B9EcIl0hCqxbp05M8DbNqFUQ3aCfd7Wv0yTJO4VbOw9f5A7fTDL1Rs02xZvpYbXirgN6jXwqTrLvhDVbotxs9ct16uo6JJKoVTEMAxEehJHFhYhRSfXqiHQ06tzIfOibxIsAY+kkG3WqLXbVJpNVrNlMo02cYq8HPZwuS8eHFLcrNkUzxs2NfRFM8j1fiPEsKI7qOz5doWTnmn2q00aqNzulxPMBEJc729gZlSTjX6YLtr2stOss2YlOK6H2Gn3vKc5PcRWvcyCe5FWR6TW9w49LolkG8aVURKNLsV+fZgdoD7IPFA+n/87gPpxt/fS3lyWZWq1Grdv36ZQKDwgRPtu5x2A4sdC/yn/cu1/Zlz1U+8IGCL4XB4Q2lzNfYUp4+8z7/k4cHSSxMPo391ul1gsxvb2NmNjYw80aZQk6YGGjI9znyeZyx/YKtWrrTaNYgdFde42uzZyxF6xzJLXQ0KsU7MtUqly1XHMhzzjRI0We31JI5+ispYbhqvaXYt0tsYroShvZfawgAmP1wFQkx6TvVyZVKPFc5ERNms5tg61ssjaaO1dC0qVFkFLJxjQuJVLEXEbDoCaNX1kq8MNxoRhcnk3gVuWeXksiiQJXEwOAW7G9JOpOUHCfj3dpfL2fu99RRLRvSpnAmOslbOUmk02S8NnDqlu1mze1rIvxPXskNGmHwIzOxFjzvSzUcoDAvlGk64FNzM9IBCAgKqRa/ae67RicmV/yK5b8jGoAVvyBnm7NGRsngiEudunkB/3hYmVht6pPZw4a/q5ku/rEcoqKzavyx5KnDH83C5XmJT9GILO7XyGWqeCIopotn1TxqaEISkCU/IIjZaCpboo9j1eyUb4aFTK6N0R3qwmOGYMSSbZVoZJdYKVYgtJ7j3zhDpCUBmGlz9oD+pZCfE9szmoR9lRKZi1Wo1kMsnW1hbBYJBz584xNjb2WNezA1REi/CceR5J8NMWNJqCSr4tUGgLFDsS65W/5gepf0m723gqunoHwPTGG29Qr9d59dVXWVhYeGCXdxTgftJzvre97Xgd0T3ksnXmfL0flSgIrKWd9HKv24PaEBnts71G3Dpbh3JJ5VqLZqnDnLd3nTmv35Eb0l0uVjNZrmwnOO2LoEkytabT8xuz5YnuJDMsaSHGPMOFx+tS2K7aQoQWrKUzJMsV7sQynNSDVA91Mq61nZ/dAZmi1m5zZTdBq9LlbDA6uHftkDearg3vJyCwacsvqaLEhZ0Y13ZT1AodzgcmmTMCTOi9BfVwbsv+PRWgD0A9mzP9jkLhkOYs9NytDBf4ZV9oAE696w6PC6luRwjSa8tbeV0qq7b6K901rBmacJsOQkalY5N0MoMDhYheeC+FIkgc90QQLQWaBrcKFRpdqHV6v7FlM0ytn+sa18xeSxJgxGVidTRuZMqslwps9vX+JEEg1S/EntXGiFkiG60Khuhir98aJISG3HDxdqZMWHIPJJLs3hP8HUA9LXtmAepp1wDUajVu3brF1atX8fl8RKPRxwamAzsMNMvG8zS6HeptlUZHpYNOo6tT7YhUujL5dobv7P9zitbukQGq3W6zt7fHm2++Sblc5pVXXmFpaQmX6+HFhO83QKUqFe5nnGoRdKFUb1LINJj2mIwpKuVDwJGr1MnUW8h1kTHDw5TpDGFossxaJke+1iCTrnIiEIJDQ1rw+we09Vt7KeZVv6MQGKBQc75WkNnay/NKeBxZEFjwBejaUG/BH6Bo826ThSob8TzHVA+KIKCLEis2dQxNkljJDRdvtyRzN53hyk6SdLrGy/5xOjbvMaIbbNr6XC36AmRt4d4FX4B2fzwdC1oteHsnSTxVZQwTQ1A4ExwjrOk9ZQtbKHHJF3RQ3Q8DUtzWg2vO9Dtknkxb7x9ZwHHdGdMOipaDdLHgDQxo4gKwaSNZjNu8lICiOeq4Wv3i3DHN5LR3ggV1jGZdZTtf5wf7uxT6Oby0TSrJ3o4jqpuEFA8n9BkCUpi3skksBJa8YaoHva88YZrdFsfcc7RaGum+1uCCOdQSnPFOcaPWpI3kQVj3AAAgAElEQVSFbsMfNdHhxo0brK+vs7+/T7Va/bHT4ftRtGcWoB7HHoflZgemcDjMuXPnCIfDRwKMw3mvV4MnidclBEGmi0KlI1LpStS7GvWOQrWr0ujq3K79n+xK330iOSHLsqjX69y8eZNCocDZs2c5duzYI5uKHVVW6XEB6lIs5tjRi4LAerq3SBXrDfKZOnO+kOOcgKax0Q/VJUsVqFgP1DYt+P0Denm11WY7UUQ59PWWD71WBZl6oc3JYI9N6FdV1g/Ry/eKZboWXNlKMqv4HQWtvXOczMK5QJBm12I1VyVg6bwYGHXo5UVd6qBBIPQA5uB11wKrJbAWz7OoBXgxNMa04QRir+qkgLcPzXvMFqJrtDq8sR3j+m6KbLbBi95xjhkhXg6Ns2AG8CnOse/Z1N6nPV5iNo/JDl4COMKIUy7dITJbtTEgF8ygo16saQvNLXtD5Gz1Vnb6+pwngCDAtO7nJd8kcteFr+tjK9MgWa1zLZum1mkzawPDUdlNop83lAVhoKA+qpoIXYVYocvFdJKOLYyn2zjoAZeO2xrhzXQSt+3vkthFRGDJvUCyXh/se2rSAWHD4B+/+A9ZWFjANE0qlQqpVIrt7W3eeustbt++zfb2NtlsluYh7/r9sKO22vhRtGc2B/UkIbeHLdq1Wo21tTVKpRILCwucPHlycM2jSg8dXsglQeJ88AzXCldJt1JMaj68skJXFLGELpLQpNKtYVkVFOkW30z+Fh8L/zfo8jvvjizLIpVKsba2hmVZzM/PMzExceQxPu1z/vrOBq+MRbmU6OUk5nw+NvaHHkK11aFabLMQCAxqkWZ9fq7amujlag2URJEFf4C1PntOPaRePu31cXU9ySuz41xKxREFga1DTQ8lBIr1JqWdLK/MjNMRLK6Wh/eZ9JjE8sNFO5YvkS/VeHlsnLdTcbpAsuwkblRtnl+6WiOqm8xrARRd4k42jdfjAVvIrn5IzaTaL17eyBYgC8+NjPByaJx0s8ZmKc+uLf+lCoKDPThj+tiyeVvzfr8jL9TpWFyzsRHreodZV4CArqIrLgrtBqIgkKyVGXU7VSzs3tSi16ksYS9G9iuaoz+WX9Wgf+pheSWP7Xc3rftRRIkX/VHoCtAWoK6yVqlghkyu9mWXetcY5qKqtnYXYVkl0/egls0wHdpErRES1SrfL/dktRRRGvSlEoHdegZFkFnWJ7mZyw0U2vca2cEx2VaRiDzNtVwapd9dd0Qx2G+mCbp8hMQ5DNkNMui6zsjICJZl4fV6CQQCVKtVyuUymUyGra0tWq0WLpcLj8eDYRiDf59WSPBZCvE9swAFjy8YaweoarXK+vo65XKZ+fl5Tp069Y508aOM57B9fORV/jj2V7zgnaLULpBu7hNwKRiSjNflQhG8NKw2RVLo3SD/PvnbnPZ9kmXPhx3XsSyLTCbD6uoqHo9n0K/lSb/076cH1ep0+P7GNpVmi1Pjfm4V88gt5zwG3Bq3Eyl0l4vlSIj72QzWoUsvhoKsxNK4azIno2FuZ9LsFpy0bl//M72ymeDFqQhVWqwknYvqRqbnBVgWXNlM8tHZSXyqSqFPEhkzPA6AWgoGuZNMc2UzyZiuMTri42rSpt+nKKxmh/dQRJHVTK7XuyoLz0VGHMoYsiAQbwwXWFUU2SwOn8MjSdxKpgYewktjEQSXSLvbJVOvManqrNtyRiO67gAou6cmwQDMAeZ9ftYLveffLsDLkXFuJ3vgIQoCDa3DcfcIbkXGUGTq3Q4jqkHT6hBW3dQ6LRqdDo1Oi/12A1kQ6VoWC94A17JJ3JKELIqUW02mdC+qJDOueah0m4hWT8i404QpOUS6ViMkenkr2du0+FwqFasx8DzbNo9nyRfkWuHgOI01G3Ei362jiTLLngguy8WbmV2gxNnwOKlCD2yXzRD3+qrjC54gmksg3miRqNYH4DSnB0j0ez8tGBGy9QaxWprnfRHW+117p3Qv5W6XWMnFS5FRDttBDkqSJEzTxDSdSh7NZpNyuUylUiEWi1GpVOh2u7jdbgdwud3uJ05X/B1APSNmr4V6HGA6sKephB5QTD4SfIGbhTV8ikhUmwerQZcqpXYbQxbRpDGaDYmy3kVE5Ubxm6xU3uTvh/9r3JJJJpNhbW0NTdM4ffo0ut6ro3q/w3VPes7F7RiVvodxL17guXE/1UOnzfr9XCsmqDRbxBIFnpsYGYQAD8wj9/JntVabjd0sH12Y4gdbTuHZRHEILDd29vnwzCQZd5VsreehzAcCrO4Pr6uIIlc2E7hVmePBEHezGfKH8lGaDeyT1SZTDYmXw+Pczqeottss+PwOwdnlYIhbSVudUAfu7WU4OTZCS+7gEiVup2yKDqEwN/aH5y+FwlxJDD2gRqXOvWIJsFjwefAgDKjqAEkbDd+QZUeuazkY4o4tFxbQ3FAYhun2bXVSY7qHW+nhuF6OjPN2cjiOUcNgv08UOREMcTuX4SBbUNW6tMsCbSzmvCb3EsN7aGGFm9me97LkC3Lf5oVlbeG9BX+AK9kDhXHZ4XV1GH6fF70BrhaqCMBxzyjtepNUDS6XU/jdw01nxdYm5CAvNaqaBGUf39vvEXZeDY+z198rhDWNRBlOeKag4yLW7/6rycP1wC0p3MxJFNo1zvqHJSEH9iiauaIoBINBR4say7Ko1WoD4Eomk9RqNURRdHhaHo/nXUP1fwdQPyb2OB5UuVxme3ubSqXCwsLCuwKT/byn2UvqH4TPc7O4hi6OUmiVcEsy7Y6G4RJody2atClaFlJLJqhobFU3GFNb/LvNf8ZM8RNEheOcPHkSj8fZS+hHCaBarRbfeOuq42/JXJ2F0RCbNgHVrk1NotHq0C13mQ/4uWbzVBK5oZfR7li0Kx3ORsa4nOxRr8c8HvYOCcjuZoq4WgILfj9r+TzeQz/wpVCQO/E0tXabXLXOudkob9vAQQA2c84QYaHWYC2TI+RxsxgOOqjx8KCa+EGvqvuJ3oL3kdlJToZ6HiD0PBe71Q+x/4YQIhArVpEskUa3w5ThxqfJ7NvKA+b9AW6kh+E8t+wkxcRt+aWo4WHbRqWPekxHPmrfFpKc9/kdKhWKDbRNl8JKbggmIbebjXK+/+wy923Cv15Vhf4QIm6DdVtOy04hX/KFuJbva97JMiu2wmBVlHjRO8lWoYSrq3G9LzB7zBdktV8X5XepA7FaSRBINUqc9kxxJZWi2x5uUHKt4fNWu3WWtBneSO6z6B0qmew3e8cv6eNcSmcptBsoosxzvgdD6Edh8QmCgK7rgw2m/VqVSuUdw4QHwHUQJvw7ksQzYNVqlWw2y/r6+qAeaGRk5LHc6aP2WoKHEzNO+2YYkeeodMo02ir7tTZuSafSslgv50jWG4hdg0Krxf1KDK8wzWY5jtQMEw9cYG30b7C0BwHzKAD1tEGt0+mwsbHBxYsXecvuTQATHoO31/Z4ZazXsdMliqztH6KXqyp3NvY5OzbeO8drEi86wSdfrXNtPcHZkQiSIDBxCKgjHoPdfJFMpc5essSLo2Mkis7ckXpItqhT7zKjeZn09lu7BwLkasOduClLrGd6C1amXGNtO4PYgGmvrbV71t6qHbZsNVkCcDue5v52hlnFy4sjEbZsgrUel4sVW7hwwjTZtYX/joXD/WJngb1KA7diksm3GMXNSd2PVG9h9J9JANZt4DDt9bJXHs7hlKmjiMPP3N5WJGp42LaFDYO2HkOS4JRUWgwMGYXgzFstBUI0bQK1dl3CKRuN35Rd3LcVEneF4fWOeYMseEKc8U4wKYV4M5bkYjxJslolZ2s371WHm495b4AuFm7Jxav+WTIliwvJJKOah3i/ncaIagz6W825Q+xX4FJmn1FVZ7fee74JzUu6WeKkMUu2KlLotwV53juBKj64z3+aNHNJkvB6vUSjUZaWlnjxxRd59dVXOXXqFKFQiFarRSwW44tf/CIvvfQSiUSC3/u93+NP//RPWVtbe+wN57e+9S2OHTvG4uIiX/ziFx96zN/8zd9w5swZTp06xU/+5E8+led7N/tbB1CVSoXr169z48YNfD4fs7Ozjw1MT8MeBgCCIPCSfwnJMsg2W4QUH5dzcVKNGkElQq7dYY88KgHEup+9Whqf6xi43dQslWa3zFc2/1uuFv6Gri1h8069nd7NjuJBPew+3W6X7e1t3nzzTQB8cwukq041jFqjt1O+sr7Hy6PjLIVDVA/lpPZyJSwLrq/FOaYbRD3OWH5Qd7PeV4+4tpnkhDdEvem8xoR3eE6r0yWTrTCmGoPdv2DxAIGi0eqwmc6TTVc4GxkjcIitN6ZqDjbi0kiQ23tpkokSZ8NjPD86MshlQQ/gsjaAWwgOAW83V6Jd6SLXRV4ZHSfs1lkIBBwMvXHDCbquQ2zCXJ96nqk22MxVWM1UaZS6zMpezgfHGFd1wv16JM2mjHHSn+Z/euF/4ds/9cf87PR9Im5tkJsCHpjvPZuE01IgRNHGSrMrpE+ZThZgVxg+y5zXWW/l0OzzBwc0dF2U6XYtXg5McEwbxWrK3IjnuBzfJ6i6B8eNaDob/UaRAhbbtiaOltDlRe8k1FUqjTbFvmZh1Bh6RjMeLy5B4rRnGg2T3b6Q8bQNOKO6hyX3LN9L7hPQht+Fh4X3oBfie7/roA7ChNPT05w4cYLf+I3f4MKFC3g8Hk6dOsXVq1f5whe+wPXr1x95rU6nw+c+9zm++c1vcvv2bb761a9y+/ZtxzH5fJ5f+ZVf4c/+7M+4desWX//619+vRxvYMw1QdtA5AKabN28SjUZ59dVXCQQCP9SuuvDO+avXxk/zVibDhDvA99LbBF1+NNHP/UoCj+BHq42QqBRwKV7c6iSCJBOrVTGkELfLG4wqc/z75L/l63tfIl7v6YQdpZHge/WgLMtib2+PN954g0ajwYc+9CHm5uZ4Y2WHpfAw3m64XGzZut5e3Ywzrrhx2WpXpvxeEoXhLnw9VcFjuRyssZmAM9a+mynSKDYZ8wwXoOqhFvFjpofrW0kmFIOo6WE+6PSO3LLMWj/v1Wx3ubaRQGhYA28KcAjbwhAwuhZc30ribsm8HBkbFKL6D9HDD9PFNVkiX61zZSNBMVvDJ6icCocHz5q1sf0kQWDd5o2N6O4BDR9gORSk3m4DAruFMu2OyEqiSD7XItR1E9B8fCgU5HfPXudP/8GfsOjdZ9xd5ufmbvGvz/8R055h6MvuTU17vY7Qn73I1pBl7tnCexFb+wxNlFixeXB2LyykaawWs7glmXkzgE/WeMkfZc4VZEkb5VY8y1uxJJuFAvds+oJtWy5q2vQNNgvzZoB0o0pY1XnZN8X9VIkL8X0KzaYDuA5auffGJ+O1AryRSNK0taDv9Guv/C43lYbEhVQvzFztDOfknQCq2+1+IIW6siwjiiI///M/z2/91m/xJ3/yJ5w5c+aR5128eJHFxUXm5+dRFIVPfepTfOMb33Ac80d/9Ed88pOfZHq614xydPRBcsjTtmcaoADK5fIDwBQOhxEE4T2THY4S5nune5oujY+PneKNVAK/y4OMTqyWxdsIkS3VaElguQJYko6FzL1ymlF1kquFFSa142zU4gRcJyi04vzv27/N/5v8Q1o0nxhsHpW3e5iJoki73WZ/f58333yTQqEwKAg+SBT/xbX77MULnIqMADDjM7GnbATg9laKJTOIofQWvohtlwtgyBJv3t3iZDCM29W7bvOQxzUf9LOdLtIotjgWDmGqCquHVCny1d4ueidTpJyrM3XIS1gMBWna5m3CZ3JtK0Fmv8zLkTF8qsJeZQhoIjjCeQDb2QJXNxJoTZGzY2MOWSbAwTo8nN9yCRJvbyW4t50hjMb58QmHN7UYDFK0eWdTfmetlHQoGrBbsMkkSTJW8xK/tPBH/Pz8G0iiRbKis1I0eSG8zYnADn/wE3/Kf7Wwxpymk69UUPsFpwHXMHQmCLDhCO8FadnGaO9ltRwMYlkWEbfBgjeAC5GXQ+O8HBjneU+EMUwaxS7JVJU3tvd4O5ZkI19wqFMsBYIDhQi3LLNiCwPaW4VM6F6eM6Kkcy3qzS7FfgHvnOkf1FmFVDcblSxeWeWsOc334wm2yyUUUWS931BREUU2qikWjVE6dTe3ivv9+XOx1SdNeCSVY2aEd7IPomFgp9M5UoFwLBZjamqoxj45OUks5mzQef/+fXK5HB/72Mc4e/Ysf/iHf/iex/soe6ZJErFYjK2tLRYXFwkGg0+NLn5w7lF6vrybh/LJiZf4871rHDemWSltMmr5EE0ZRQ4QL6U4IXvZqaYRhCZRbZKrpVWeN0+zW9/FK0/Tsbps1gqcMJZ4M/dtdlybjHQWOGYdQxQe70t7lB9VLpejUqmwv7/PmTNncLudigR39lLs9ENoq1tpzsxFaDScXs3CSJD1WJZMqcbMqJ+sVKdwKCQ4pmts1Crc2UkxM+qn6m4/kLOy+ornpVqTyk6GDx+b5j+uD6WVAm6NDZugbLXZYwKeGYmwUshSabYe2LWNGQbxTIl2x+rlumbG2bNy7PbHtxQOct82jtmgn810b/Eu1hpkMxVq9RZnx8a4lU4TMQy2bIC0GAo6QHQxHORWokdwyFTqzNS6xOMl5kI+Qj4dWXKOsGSbS1kQWMsOn2/W72OzLwkV0Kr883P/gfPRywD8ID6DX5UJuGNMeXuL/HbRR1uq809e+H+Y9RX47e+dxUJAEyXK+QaRroYs9MCq3ukSVr1Y3S5eFE57R+lavY1ErtlgxuWj3mqjNGVaJUiV6ug+hYv7w467y8EQyUoVEFgOBbma6RFTXKI4aG8PvS7Ig3P8Aa7n+51tFY1Mo8bLgQm2UjlWMwVi/RCdJdrU1TWNrb7jM2f6AB/3MgUqcncArEu+EPeqPULGoieAR1a4kNznuC9MutYD+QUzwGothiyIfDz8PNJj/q5+WFYsFh+gtD+OPWxTengtaLfbXL58me985zvUajXOnz/PuXPnWF5ePvJ4H2XPNEBFo1Eikcg7LrpPo+XGkwLUu4HinBLkJXWCO4U409o4Hl2iY3XZrZUZETxcysWY1r0oos5mLcW8fpJEI4VEEJfgYrUaZ1Ff4ErpDqc8L1NobVCmxr9e/x/5R5H/giXPySM96ztZoVBgZWUFWZbRNI3nnnvuocd9+9bq4P+drsXaTobFUWdozh4C29rPsxAJUG0456nd7jqOeXFmDNUrs9X3XhRJcgBWtwuFXI0XRka5n89Sa7WZCfjIl2zCrT6TeKZEvFBmxKszGTZZzzi9oVzFCZTNRptEus4L0yPsVssYhxiBQbfGpu31qGFwJZsgv57Ap6vM+XxkKjXK/fyNqTrPP+wBHQDQTqbITrpISHcz7/bhEtrgVlmxAdJyOMidfRuTTnezXcjxjxZu8s/Ofhef2gOiakumIbTJd/OYfVWO9cIEhjuGz9X7TZwdu8QvvVjiD658jBHDw2ZpGN4b9/u502c5KoLATqlKq7/InQr6Bx2KXaJIpT38TMKGzla/zbtPVVm1hf5sTYxZDoS4le9r5ImCQ9sPUcAjKyyZIbySxvf2dngrl2TEpQzAySWKjmLigx5TJ72jtBoiV7K9scu2KJzb1XsRUnRMweT7iV7Nk67I0Ac3tyzik90YVoAJddjP7EfF8vn8kSjmk5OT7NhEnHd3d4lGow8cEw6HB4zBn/iJn+DatWvvK0D9aMH/UzZRFN/VI3ivHtRRzn2YB1Wv17l9+zZXr17lw/7jjBtBBJcKlsS9Yp4pLcz1ZpZJdZS2pVBpNwnL0+RbFUoNDY9scK+UJayMcK24zbx+mo3qJrmWDpZIvVvjf936F3w99n+wV999h5E9vpXLZa5cucLKygpLS0ucOXPmXePtf2UDKIDl0TC3NtKctOWPdtNOxXCfqlHNN1ke6cke6YqLvZJTdcFqW2STJU6P98Isi+EAdRsBQJUl1hJZbm3uMyrpRL0mjUMECnuuKlWsItdhORAcEChGDJ3NjJ1WLQ7qp25tp2gUmqhIqLaVLnmIIZi2hfcK1QYbezmEapezkTEiHoOYLQQniwJrmSHgBDTNUQc2Hw6QqdbYzhRYS1cwuwqjgpuXRiI8PzLygDq56brJl376D/m5ExfpdHubqZVciFhdYSG8xaQ/Q6bV5T/sThEwt9D64LRf8ZFrC7x+4m3+s+feZNy0kzQsB6NwxmsOwAlwaBNOaCpV2yYwYSNZzPuHXXVVSeS+Lcek2ObzmD9IqdUkrOmcDY1hNaFesriymyJdqw2uEbDlxJYDoYHk0rhuoAgyS+ooa6kSt/IHtH7YKA9BLFbP87x3nHJJZL08/MyTjeHnY2HRqunczeX4UHgYErPbURm+T8OOWgP1yiuvsLKywsbGBs1mk6997Wu8/vrrjmN+9md/lu9+97u0222q1SoXLlzgxIkTT2voD7Vn2oN6VLjqaTctfNLzms0m6+vrZLNZ5ufnOXHiBGe7Hb7617cY83b4biLBT45N8939DZa0MNWmgKIKKIKfltUiXu2wZPq5WUgQUT1sV0vM6Qsk6kVa3SCTmsHdygrjnQhRzcOt8iXeLr7FKfM0Pz3ys4SecAdYq9VYXV2lWq2ytLTkKDJ8J7u5m2Qv71R5aPdB5H4sz0vzYxTbTdb3nKG6crVJqdqgvtvihbkIFnBza1iX5JJE1uJZ6s0Od9aSvLw4PmB1HdjiSJA7O71deCxTJGBoqKPOGpNs2Ql6btnFtbUE40EPit+FT1XJFKrOa8aGdPlxr8lb92KETDdjYybpao2Y7XnHTQ87NjJI1OsZvH9tI8FswIuhqwRH3NxLZXr1WDYPaCbo49ru8Ln9mpNcUW+3SJerpMtVRMCnqSwYPmZHary2/Becjgxrzwp1H9d3pnl+fAOpH/6qt2W2Kn5GAylSFZOIp8hOMYCktAkovef+L0//gH97eQbo7ajnAwHWbf2q7L+yUUNnx0Zh93u90Cd4RNxuYjaSRc4GVgv+wAA4JEFgvZjDkF3Mmn5GFTcVV5udbJFx0eRmrnecIcsOUCvaCA4HG4YlM8S4YvIf93ph3tPhUa4X+2E8b5DVau/7MWv48EpuLu+liBoe4rWelzfmNojXe/9/wYxyJZGl1mkz7jaZ9Ty81uiDVDIvFotH6gUlyzJf+tKX+MQnPkGn0+HTn/40p06d4itf+QoAn/3sZzlx4gQ/9VM/xenTpxFFkc985jPvGDV5WvZMA9Sj7KhtLODoxbqyLNNsNrl//z7pdJrZ2VmOHTs2AFNFkvlE9ATfit/mmHeUK5kU4+4g3bZIU25jNTV0t8CdQpnnfCFu5JMEVTeVtkhICVHviAh4CCgybxXWmWeSfTGOKi7iFlVGFZlL+Te4W77Dae+rfDz8cQLKuxf1NRqNQVPGhYWFJ6Ll/8Vbdzk7Nc7bO3EswOtWuR8fLvDX1xN85Ng0CaU00LELedys9YtZW+0ut1aT/L2TTrbUUiTE3a1+IaoFN1YTPD81gq64BteRcI5x0ufl5kqSM/MR7mUzmIrCVmaYCxKArXTvdTxbRsjBueVJNJdMvU/GOEzv9rt7lONMqUamVOPcwgReReXOfu8Zx70ekja5pDGvhz3b66Chc2W7t2BOBjyM6gZ7Wnmgst44RALZtYGfWxJZteXTlkaCxAoxPjJ/iRMjezw3OgzZ7JXGaIldRkP7JCoBJswsibKPUkdmPty7f66qk9yPEjJz6Mowr3UrNcfHT36T7219ikLdIKBrHNRWy4LAlk3BYsrnHRT2SgIDPUXokTmS+733PC4XOzZmYqtZZ9Sl4pNceGWVVLPBXrnK3VKGhFsl19cotHtWi8Eg1/qhuhG3m3hfh08QenVoS0qYlXgOITz8Hthxw6cqCFU4448iWy4u7PeiC1HDQ6Kft5v0mJTKZY65o3TawoCoce4dvCf48W218dprr/Haa685/vbZz37W8foLX/gCX/jCF448vie1ZzrE96hF9L2wbI4iGNtqtUilUmxubqLrOufOnSMajT4wjk/Nn2a3VEax3BRbDUbkIKluhXxNwlQUbmTyzOphbuYzuGU3imAiCS6abY2uJVFpd9go5xnXIqx3cwSlJRrdEoV2hyuFPRb156l3qmxX1/nNe7/JV2NfJde07Yj7xcStVouVlRUuX76Mz+fj3LlzjI6OPva8NVptvn11lasrcU6PR3BJIgvhoKN1uyDAynaaiKoT9vS8m5mgs4+TJsu8dXuXBY8+WKAOq4pHPSrXN/bxtGFU15BEgY2k0ys7UHq4uf7/s/dmsZalWZ3fb49nT2ce73wj7o05h8jIjKyoKsrVBoqyq3EJNzQuW37ALdQvWALLlsCSZclt8cBbY7C7HiyEJYsG2eoy3RIGYSGghpwiMyMjMsY7j2ee5z364Zx7zzmRY0RlVjYB6+nec/Y+3x6//7fW+q//KpIUQjO0d4C1VILGFDEjooV48/4R0UDhSi49Cgk9JrtUaMwWDRfqHTZ3KlyIxDmXStDqzcolVbuzHts0jb5Y7/D+dpFB3eb5ZJoXs5lTvUCA1XiU0pQ47bypnbL7VMnhpy/8kN/95T/g2y/c5NzcMQ8qS3RtlbePl1GNCmG9jqYO8aUhDyvnkVSbTHgC0I1hnKYgo8qT5/pWcYlMooihOvyXr/wtEHDUng7TRRlMvQfTtV/nErN1UtVhn7CqshqJcjWV5Woqy0vxHOeNBJWOR7XpsF3r4SFx2O7hB7CgaafgJAqwMeUxBVNFvIvhMLoo8XJyjlciC7y9X2SjViemhths1U/335pq7+EGPmtqhrcPy1TtiZc8LUCriCKpIMHNQmlGE/BG+qMB6ovspvssyRzB33MP6sexJwnxua7L3t4ehUKBeDzO/Pw8i4uLH7l9Vg/zs/Pr/MXRI76aPcter4I0NMiEQzystcjoYXbaHRRZJSrF6bgNZDQMTeRus8KqEafp1tFEk5SfYhi4PGy1eSm6QtGkWqUAACAASURBVEWoc7d1QFRZQkBgWV/kb6p/w05vj/nQIv9R5hsIgsD29jbFYpHl5WVu3LjxVNTVv767Q3vsCby/U+T8Ygr7MeLDuWySzcMqtCEZ1llJxuh0Zxl+53NJ3t8tslfusZqL0/SHbBdmwScZjXLUGFDrOmi2z9WlJO8eTDw1VRTYzE8mt0K9S1QOcW0hx3vHRbwg+ABZYTUZ53anQKXVp9Lq86Vz82zVG7THdVVLsTCH1clknQmbpx7Ydn4kgZQIG5zPJHlUqpK2jBmPbSke4bA6Cf+tZxI8GoPq/f0yLyxkMV2ZK7kUbdchrKnsThUUu0GAIrl87fxdri7s8qWVrZnj77gBr+eXeGlpn5NAnO1KbNZyJKNtBo6MKo+8zTv5ZdLpKqYgsNM4y/nkBhuVMyykiqf7vriwx3/2fJONco45wyQAQghcisbQQhqyKBAAr2TmIBh5SWpMYui4qILEbrlB33Y5pE1kTuP9sbL6pUzy1GMUBDicCgNmYzEOSyNQXw1H2BwrUMgCPKyN7u+qEUayIegJvNsp8fJc7nT/M/EY79ZGHuK5WIKH3QpRJcSVcJY3jo7wgmDUZmUMYrosn0ojvRSd53ahTtuxR2HH7kkxMB+Zf4Iv1oNqNBrMzc19IWN/HvZMA9SnXekHQfDE3tRJqO7jzPM89vf3OT4+ZnFxkRs3btBsNilOCW9+lP2ztevcrBzRs13mQjHafo/20Gfge/ieQtdpccVYoDAoE3gqyxGV1yr7fDm5ytvNTV6OrVF3S9iOguvIXAqf5e3mFles8whiBy/weLuZZ06Ns6KfYa+/g4jC//DgX7AgzPHT7tf5qRtfeaIX7fHr+G9v3p/5vtkeEBJE0mGTcnvkCZhTie1qu8+CohCyZnXjpjXudgt1LuTi1CXvpIsDkiiwW554GgPHA0fipfkcd4tlbM9jPZPk/uEEsMKKxGahRlCAxaSFrQQzYAEweKxpojPw6NQGXFvN8X6+RMo0ZgBqIRam3JwKd8Wj3NobTY5ruThzqTCV1v5pUWnaMmbGNB4DSNf3aPWG3N4ePS/nswmu5XL0fIdSp875pTf4r59/m5gxWv3fPl7ihfkDSu0IHS9BKl0iBdw+XuaF+X2OG3F6KCxmRxPwQT3OuuKw11wlmylwAkSRaJ7v75zn4vIh0xmmnUqGxfk3+DdvRQgCEUkUCCkSXccFmry0mOPW0eh8BQEiukZjXAB9bTFHz56qY6pOFhghZTINrSXibJyqrgfstyeAHDUNGAPU86kMoiBwXOtQbww5oHPap2lnqmB4WtcvooV4WZ3nYaHOUPNOyRWr0Ri3miPq+3o0Tn7YJCfF6PZ82uM6qrVInM1x590LkTRxdbaUYtq+6BzUhQsXvpCxPw97pkN8n8Y+C7LD4+Z5Hru7u6cyPzdu3GBlZQVJkj71eM+ncrwcWWav1+BeqUFYVrnXanDezHGvVeacscR+r0ZvoDBvhHmzWObF6Co/qOxxNXKBh+1jmgMVkYDioMvtepEL5hr3O1sc930GrsJFc428XafjqOj+As12g7BgcRTK80PhLX5781/yRv3tmdDGR9njEkmFRpubW7OFfgvxMIflFn7fZyUZHTHW8rOeUDZi8Wi7zMsro4S8GVLYOJrV8Atcj2bD4aXl0UpxPZucCaVJosBuvs6dzQILukUuan2gXmU9lz4FiqNqB7XnEZMExPF8bKoyW1MhQlGA3XITx/W5vVnA9EUUQZzJcj0ezutMKVjsFuqUC20WNYuXFrKEZIlKe7Z1/P6Ud6UrMlvFSThqMR5hI19j83CPpcRf8c9/+v/ln7zyo1NwAsgm6vzN9gUCzSMamYjrLmZL/GjnPJLhEA9PANQy+/ztwQViscLMcT8oLCLHh/TtCSHjuB5HMD0ss8FzqyOlknPp5Bicxuc7VY+1noyfghMw07l4PZ04bQUiCsw0iZxW2DgTj1OeEqodeh7XU3OcUWOItsitgxKlbm8k1DveZjkcpjoGFVUU2GzWkBE4HwpzWGzx9kGJjuPQdibH44uT5zYp69htifdLFczQBDij2mjxICLws7nZ9u6P209C5uij7FkSioVn3IOCT98T6qNaoH/cfo+TJHzf5/DwkIODg1MB2sdj0U9CzPj26kV2bteIJFTeLRVYs6K8Vy1xPbFCyx2g+SYxQ+FhrUFWi3C3XuNKZInCoI1FkoyhcrO2z43wKvc72zRtkbSygqX43G8fExIlzutnOeztkxJSbPkNLmgLqMMQ271t5rQF/tXuH7KkLXAt9hJfT36JhPrh8e0TgDp5Mf/0h/e4ujzHO3uj3j2SKLA/br3Q6PTpD20u5yK8n5/VwCvXOwQBvPfwmKvrOQRZ4L2tSWGnKksc1/o4rs+dh3munZsbZeOn7Fw2yaP9EagdlJpEDBXlMS277mPyR5lYjPe2C5zJRhlIHmFFnmkVMR/ROa5P8kcqAu8+yHMmG0PWJSqd7kwBcNzQ2J5q55GwRgXCQQCFWofVTJSIrmOHPYrtLmuZOFtT269nErx/OAGZ5ZTD1Ytv8MrlR4SUESg8KuS4PH+E5wscVldQrA4LixXKrSxz8RHoVNphul6MeK5FtRMhGx1d71IzSkdQmV+osVfJsJIajbVXPUssVQEENso5Xpjfp9IO01dkNHk07lefu8f7uyuElMkkHNNDM/R4awpokobG9lSt1nS907lkggdTHs/BlKp6xjAIqwqyLxJ48N7+6BglERpTreqHU+zNtGWy1xv9xoVkClWSOKx26LsS+cHYa5ckNsdFwKIAG80qKVUnK4W5U6rSGrcvKQwmocaaPZJPSgRhXozO1gc9bk9TwP9Z2bOWg/oHD+rH8KBOgOYEmF577TVs2+bVV19lbW3tQx/SJxnvHy2ewXEC7GEwUol2ZOKqju0EaILK0AvoDj0azhAVDV1S8V0FSzTR5BAP6i3mifBadY9VfY2228ENZO40mlzUV+n7LpXekL4bIWJEsCSDh90jhm4YU1jEkk1UQeFgcMS99kN+486/4F9u/QF3Wg9nRGlh1oMaOi7/z4/ucvvhMdeW55BEgQtzKWpTdUxDx6PTcri2MnnZV9Nxjqbqod7fLOA1ukRCk8XDuWyC3nCyMLi7VcTpOGSm2iKoj61elxMx3n9Q4IVcGktTR+BRnKVJn4y7X2xSLXZJW+GZ2qbkY9X5kfHkvF9ssL1b5UIszkpqMjEsJ6P4Uwujx4kfMV3n9maBWrnLlVSK+UgYSZzM3KNFVcCZhTy/9HPf5ytf/T+5dGb/FJwA5nN13tpa47CTxUhUUdThSMJL79PoRNgvn8FVJQyriSwFDFAYOgpbpRyeJhA2h6Oz1zy6Q5X3j5cIRauchPXiqTY75Qw130QLTcZNRjpcWj6ckXdaTcRnznevMVl4LMcnWnmqJM6E94zxvRWAy6kUC2aYl5M5zigRjktt7u5VeO+gNKMksZ5InJIvDGW271Vl0COqhriemiPkyLy7X6Lc7c3Uu51LJU89rvVojHN6nE7do9bqUh1rD6ZCodOi36gaIiyHGLQEDpptXkpPclwfZl90iO9Z8qCeeYD6vGqhTjyo4+NjXn/9dXq9HtevX2d9ff1jvbEnAShREPhnV65xq1Dk5UiOjX6TqG/ScPu8WyizYES4VSnzYmSRh60KMSFK0+3zoN5ERqXpDGm6cDm8RGXYZrftoCNjex7vNgosKWfwFJ+cluRH1UPi0gJnjWXKQYWGO+S12iFz6jnO6mvs9XZJhxLcbNzm/9j/v/n19/9n/vXhv+OwP1qpTwPU//fOJo2x+sLtR3kuZlLIj92HVMTgoNrjvQfHXF3MocrSiL48ZeGQzMPDFiFXZj07Ytw93l33/EKSB7tlBk2by/NpFElk57GaqmCcw7q/XcZ0RS7Pp2cm09VUjEprEkoyVIW37x6REENcnk+PWoM/lp/qOrNeeb7U5HC/waqhk7U0Gu1Z7b1Of9ZjO6m/CgJ4dFBhc6dCnBFp48J8CCPxOv/8n/4Z//k//hvOrx6hqg49P8TQHi169gpptipZoosdhq752Fhh7pWzqJE6kjS5YIZus129TCTZRZYnn4dCLm8fnSWVmT1H19XY6GYwjdnQZakZ4fz52kzYbuBO3qG15KiYeHKtJt+dSyfRFYULyQTXsllUX+SilSDiKFi+wvs7JW7vFREQOJ5SrphmDhpTC5a1ZOK0jceybpKSDdy2x+2DIptTHYRr9iTceNLC43IsTUK0uFOoM/R9FhKTiX1hXJisixKrvs6twyot2+a5cJxmrc5gMPjIyMwXTTN/lgDqmQ/xfZI9jQcVBAG1Wo1qtYqu67zyyisf2+Fy2p60ncW3z17gf3//bfbaHa6EEkiySK8d8FJqjr852OfF1By3ayWuRBYZBn326n2u53J8v7TLT6VXea+xi+1ImILJkiTwWi3PK5EVjt0ygSCy0erzajKJLoW40zrgrLmA4iVZ1Cya/S7vtXaZ17IM3BgreoqO26UwLHPBWuffFf+Kf1v4K16Nv4iOTHKYZUVf4P/6/p2Zc6jVe5iyTDpiUh6rLCwlotSqo0n8zkaB9aUk1casAsP6fJr3HuWpt/u0egMuLETYOq7ObCOfdHLtOzzaLPOl55a4uTnJfRmqzNYUYNVaA6qFDlcXszwsVenbLjFDY2/qN8+k49zZKVJp9Kg0erx6YZ79xmTynotZFKpTtUyWxnFjdC6HlT5hXSUWE1mIGBy1eliqxPZUPisTMdivTDyMM5k4u8UKq6tFls7vsbpaRBR9uvUsp139gEi4x729JVKJIUbqZHyBoezQ7YcQRZ98LYeVapA2XHbyGdYXRwuIWtOi6epY8SLHpSTzmdHxDIYqx80kifkO3W4S0xxdX9vWKA+TJDJdGu04sfBosu/0DbpyiKhRZill02yZ6LJMe2CzHIugiBJzloWhKMiCiCIIOIHPlViKdn9IyBFpVfu0qn3WUjG2pryw/BQgpSyDvXG4byUWZfeULBGwO9WfSpYErqVy1Bs9woHMrYMxoSSV4ME4jJfU9dPCYlkU6DsOz1kZ7h1VyUYnhds1e6ouS4TL0TSV+gAi+ik548uZeZrNJkdHRwyHQ2RZPm0aeNI40HXdDzQd/ElZp9P5QOPSv8v2zAPUZ+lBBUFAqVRie3ubaDSKYRhcvHjxMz2ex02VZH714sv8L3dexxl6GKaEH0Cp2UeXQtgurJpxxEBA8BTOhhO8dnzEpXiWd2rHJP0w1V6Tkj1kXrPIhMLcauXJhhIICKxbc7xWOeRabBVBH1K161TcPgfNFl+KX6bt1bADh6Y74LXaLs+Fz5JSbLpuj4yapGRX2e7uU/fb/PXmO5yVz1COdZCbOm57BNqLiQjvPTomZmms5RLsluocFmf17gTXo1PpspiwOKyNJqpSbTJheV4Ag4CLmSQb5ToDx0VXFTYOZwkU3caARctiIAbk623Wsgnu7kxyOcmwzk6hTpCHZMxgKRf5gMzS43JIzsCjUezy0rkcj0pVcpFZgFpOxqg3J0SDM9k4d8bMu4tLSZJxg9ceTYpmo6pECRAEn7n5GpdeeMiN3C7DZoj5uQmQmfEC+WKcTKpFrTHHULaJLnaplsMsWJPxFdXmwf4C2WyDcLrJSYgumWtSb6aodyT0ZB/LHAACfijAdiQcx6A00DDjI7HWph3CNKHXD1EaxAhZo89LHZ1YuM5gqJAfhNGt0fsyn94hv3eB1VyYe1Nkl25keKrefnUpy+2jE9074bRvFYxYfie2FIuw35rch5OW8jAq3D4BqLVEnN1OkyvJNBoiW0cNWmNyxkp8MjGbmnpaTLwci1Cu9MjoBpcjKX54eIAXwFIkzP44XxUPaeyMqeaWrKAHKu8cFREF6DOZH/7jC1eYN6farjgOnU6HTqfD0dER3W6Xfr9Po9E4BQvLsgiFQj8RdfMvqs3H52XPPEB9kn0aDyoIAiqVCltbW4TD4VPF7h/96Ec/kWP89vmL/Os7d+gJPd7aO+Zrq8t8/3ifry0s807jiDkljBqR2Go2OROJEgQCgSOyKIVxfJtiP+CV7DI/KO9yTVskFXbwA583ykVeiGVIKCa3GnukQ0kMOcI5NcI9+5gH7QI912PFjPF8JMWt5gaPOvtYsknFbnHBmmPdiHM4OGBBTLHnF9l2dzCXLMwXKzgNheFelN2qA4JEozOgO7D5ypVlfvj+3sw5OkOXTt9lWOry4nqOVn/I3uFsUexg4LJzXGIhG8UJB6QiJnc2J8BghGQ2D6vYrkdIlXjxbBZ7OEtIWUxGqTVGK+Vqo0dMC7EYtrAdl3bfJqKH2MzPsvf2iw1cL+DOgwIRM0RIkpAE4ZSm3H6MvdcfTCa0rYMqghOwYkWIxnU2SkXMuQLXL+0Rj7RZXKpMjRXQ7WiY1mgS73Y1WsMY/bpCONbkhHZgxnv0ehaG0aHRyNLyXaKLPUqlGEtzk9/r93WOGxEWc1UkaRKOMkybh/sLpLJdjPAk9KiGO2wf5sAI0MOTcwqnejRacUoDDSM++fzMWp533zmHPRURWE3FZnJT0w0o1zNJ7pUmx3cw5ZWmwsYpQM1FLQ6m9AmL3S6aLLMej5PSNKr1Hg/3K1zOpU7BKaIq7E+FAadb2AuCwCuJOd4/KtHRHE7qxDOWyf5YpXwlHqFW63E1kUP1JN46GhFz1uJxHo3ros5G4jPgBKMFbjwenwmr3b9//1QG7JO8rc8STL5IDcDPy/4BoGSZ4XD4kd9Xq1U2NzcxDIMXXnjhC3HdVUnily5e5vfffJ2r2Ryv7R/x8tw8j+pVFpU4hiHxzkGJLy/P84PCAS+HUzxoVUipFhEphCVJfP/4kOuZFd6u7ZPTYuRMjUuRHLcbBV6Or7CgO/S8AQ/aZcQAXgqvUBXqXAinudU4YLMlciW6jiTZ+IFHxW7xsJPnsnWGcl/FVESyQpaCXwSrSzCQUGIOitHADWpogF3Q6B8aVHoGzy2muHtUIQggF7c4KI0mF8fxuXs/z0+9eIajfBN33BhwPhkmXxxNJkfFJlpIZjUxy1ZayyW4uzVarQ9tj4P9OovpKDFTO82J1VuzSg5WSOXOxgh4nl8e1dac1B0BrM8l2TiYhBUtTeXt24fELJXcfIxiq8POFOEiZmps56fZeyFKg0MSi3XkRJv/5BtHiOP8z7Av49gqylhWSA15DFpROiWNjqNhpPqo2Q7Nokk4NtWwUPY4PI6jaCbhVI+TJ9KID+n2QpjGkP3jNErcJZztc1RIsrxQPt1/9yiDnLLp2QqWOkUT72iUgjDL1qxX6vsi90oplldmP9c0h7OrVXb3pth8pgZjfI/qIbbKE7BXpkgnZ5KxmSaLpSlB3VzE4qjbYSkSYSFs0R4MqfW6PGiVSUfN00Jpeer3FiIG9xqjz1fjMbY7DeYtiyU9wu3DEkPXA4KZ9vX1qbyUJstcNtLc2S9zdWHS4ymihTgpuPvq3EcX585eL/8UgLLZyW99mLfl+z6GYcwA19N6W77vIwjCF9KH6vOyZx6gnjbEV6/X2dzcRFVVnnvuOczHmuf9uMfk+/4TqTP8pxcv8q/eeIN22yaqagiOwLweRkCk0x6yGI5w87DAmm5yaPdISzGSpsbbpTzXklkqQp+u7XPZWkSQXW6Wi6yYMc6YKd5vHqGLOnFV5Wp0iVvNA6q2zd7AJZUUWTZS7PcqdF2Xh/Uyc3qYFyPnedDZYad3hCFpPBo2UPsaAwyUroDk++hLHqgubkFDzQ7RlvuETIFW4n38vkiuFGbYVEkKFuWqD97oehghhXfuHLCaiVK3h1RbPbJRi0Jxsiq2NJV3bh1w9XyOB/kKA8dlMJi9j2eyce5sFAibIS4vpWl0BhyUJxPUSb0UQKs7pPWgyCsXF5hPhDmujQAz9BgTMxM1yZdbNDs2zY0S1y8u0LTM0yLglXSULXmHWK6FGetx9nIVSRuBi2OL+G4IUR79H9JdBq0kipqn29GoNsKoEej0DHILE5CLZrsUjuPk5uvUq2GaQw0jN2BYNgkzmdhlxaNRztAeeITSk3yenhzQ6egoqsthNYGRHi3Iqg0TyxodS7cdpYaImRxQrcRJpUfj+z6U6/PIqS62LaNOAVqzaRBbHOLuTFbu00K5q6kY743De5IosF2dpeHvjP+dj1gU2x3OJmLEQhqyJ5BCo5BvkVMNHozzjiuJKLvN0f0Txdn6qWkvbiFsEZYV7h1XyM6ZY3CCM4k4W+PW8HFNY7tZx1IULkfT3Dko03dcIGBvqji4NKamr4aj/Ifzq3wa+yipow/ztoIgoNfr0el0fmxvq91uE4lEPnabv2v2zAPUJ9njIb5Go8Hm5iayLHPp0qVPTDg+jQrFSS3UkwBUSFH4J3Nz/MHBAdfn5tnoVJFckdVMlFu1Omd0HQKIa3Giig8BHNZarOtR3qmW+HJmkc1umbhsMOg7PBfN8X6zwDVliUuWiS94vFM7pjzUuRiaZ9+tcDEyxxuVY1aNJFfCZ9jv57kSWeBu64ie6yEQYz0cQZdF3mlsYesDvKIKWQcHAaGYwnH6RKMB/ZqCknAg0cOtqshJB1aaaDWdWuIO6csw2DXBFchKafbv9tktDIloJheX0uzlZ8N9S6kYtWqPuw/z5NIRwjmdh7uzCh2NsbfU7g5pPyrx5ReW6fbs04Lac/NJHu1OPItkROfde0eIosDVczm2yjV2Hhs3X51WZvepDco0hQJXv+oRivcwkm+T0U488gC7ZaKPAUpRfdo1i/j4/2Ffod0RKFaWiCw30DKj/cyUTbetYYYnK/yBr5AvLiHFGxjhET1cig/odUIY1hDXkaiWkwSJAV5dITkViZLkgG57Ds/vYCQn0QIz1adet3BdGdsEZezZBeOOxkEAe4UMarKLCJQrURbmR2DR64Wo+BZqqoYozeF7EivJ6Exn4IE7G967Xx6BeHyce7o2lyPwA0xZoVbtsd9pMIyYFKbEZytTbMCkpZ8C1LlUkvu10bGYiky+1+P5RJJu3+Og3DrtWDxdcxU3tFPOyWo8yhkhynahSV91x+A0kkba6o48u7ShU+x3uJ6YZ6tY52rm4+nlJ/YkLD5BEE77K/243laz2XwqJfN/n+2ZB6hP60G1Wi02NjYQBIHz589/qpXI03bVfZriYEEQeCUeJy+p3KoUMTyVRFjhje0jnkvHudOs86W5BTY7VRw74Mpcimq/j+zpnDWiVId9vL5IMqPzWqGK50W5GlvgYadI4EkkQiEuRbLcbxWx5Qj9voIRVtFEmd1elYiyRK0ncUYPEZF1mk6PF6IrvFE9AHxizSiC7BDE+vg9EcHwGYQGuGZAWQbRVlGKOhI2guwReCBIgOUQDEWEkI92povXkWlFdoitg10IIVku3aFJomth5/u4bQW/I3M0VUtTKLeYi5m8sJrl9m6RIID5ZISD4rRSecDWdgXF9XluJcP7e6UPUN8XUzHq9T6eF3D3QZ4rZ9MEisj90jGyabOwKNOyi5y51kOLD9DjQ9yGTC478WIGpQhWbng6qi04qI6IpIwmf1+x2X2URQp7qIkhQsqGvojdV1D10SQpyQGDjoHh25QKERxFRE069Boq4SntClH2qddNWi2DwAIpPUAA3FCA74mIko/vQ/4oiZjuIbUUoto03V2g1c2ipCtMlWAhGD0atTgtW0WdAjRvnASzbZnjXgzJ8IGAeK5N4zhOOmzQdRwMVcFQZFRJ5tpCDgIwFIWhHqHS6pHUQ9x+NMkdLqWjOCeh3Hj4FKCyUYv9KcCbZvlpY5WH9UScBdPi5t4R91s15qPWqZafKokzNVLFXheBUcsNBnCrOCLPqFP1a3FThzFArUcT7NWavLNf5OfOnkX5lAvKz4Jm/qTe1ve+9z0kSTrd5klTEX/+53/Or//6r+N5Hr/6q7/Kb/3Wb33odm+99RY3btzgT/7kT/ilX/qlH+scP4098wD1STYYDKjX6zx69Ihz58490QrkabvqPm2bD1EQ+C9eeJ6Nv6zg+w7H5QFZ06LctbmWnqNj20QCjWza5Ee7h3x1aZEfFg94TkkiazLzlsxbh0VenVvizfIhc1qYM1oaXZF4vXzIahDnpcgKDzvH6KLK3+aPuJFaYUiP3W4ZSRD5QemQl+PLLGoe+X6VZSPBfq9GXbIJQiDaGlZXQQ4cXHNAkFcRcg6+6SM3TToRlyAQEPY1FMXHMALcvo+yMEQQQRVkfEYTtRyzAQHHauEkW4QtnSAx8mjcSplU1MHvyfg9kaNOg6HrsLJo0uuCpfsY0Q6BJ+DbIvMpi2KpRADsdmtcfilCyz7COtdDVHykkEcz2iCRGaJFhkiGhxPZZtAMuPRzEwCSqiqR9FSNk+7hTQGQnGrSreqYybHXpHvk9+NIaoAaFvCNAV7GQ8Y/XTzJuk8zb5JeGE3Gg65Cs6XSHyyipOuojJ4VIdakUbaIpUcTcKNs0QsUJB9i+mTyVsMunVoKUW1RH5ooWQcQ6QcKJ0+37wnk8wnkTA+zbRGKTPb3fdirREitzKp8qJZLux6jYutI4Yl3lJlv0NyMkc+3aDR7NIDnV7K8tznyaEVxxKo7yR3FLf1U9DYXNdmfEsCtTckjzccs8mOwWYxHOBiTKObDFhoyC4rF7mEdc1FmMO62nJ0CqPVUgvfHgrK5sEk8pCEPYeeoji2fhCUD9pqTXFhl0COtGyyoYdodm8JYM/Lry8s8iX0eeaCP87aq1Sp/8Rd/we7uLj/zMz/DcDjka1/7Gr/7u7/7ib/reR6/9mu/xl/+5V+yuLjI9evX+fa3v83ly5c/sN1v/uZv8s1vfvMzP7ePsmceoD7qQel0OmxubuI4DrIs88orrzzxb38eOn4fZ67rMjjcJyerFF2RjjPgYjzOYb+N5AposoyNz1G1TUozuFeu8oKZouz0KB70ubG8iBv47NdavBJfYK/boGc7mIrCxUiaB60yMcVAdnSWTIOy0+ftB7aggAAAIABJREFU6iEx2SKpJ8hGdH5U2eZW/ZB0KEpxYPNyMoXSbeNYDkJBxs96NKMOoZaK0xdQPR9qMmLCpWO2oSshmD5+1sMdytR1DzQBaddClnxiERm3KCJme4haABUNxiExTxsiOAKCEiCnHNyiipobQgy8hosWdXHENgrgNMPEL4wmNH8g4EllkuP8iV1UGWTzyECKkadmzI9AJwbY+RB6bjSmZkDv2Dj9PpS0aR1ZRBbGq3TLo3VkEV8ajeXZMu2mTrejIRkinjVAmHfxuyq+0QcE5FBAp6iTMKaKT7N9ijtJPDVATtqIOZfhwEcYSMjayWJGQNIl2jUTFxM32kfBxWlLBL6AMG5C6PsCla6EKhmosakmfnGbWjFMJGpTbJnIGQcQaPQUsuOAge+KHJfjCHMug7aKNsXyC3yBjWKc+PJsi5HofIuVjMVeefL5dHjvXC7Fw8KEYDHdwHIuHiY/biGSDs92Lz4BK4ERDT1jGJTqHYxA4a2xzqMmS2xUah/YB0BRRmzL59JpwqLCa7ujfZ6bz/BeZeQ9nU3G2RrTy1O6Tlo1KJcqbAt1htLoukuCwE8tfTqCxBdhiqLwjW98g8FgQCqV4rd/+7fxPO9TiVIDvPnmm6yvr3P27FkAvvOd7/Cnf/qnHwCo3/u93+MXf/EXeeuttz7zc/goe+aVJB63Xq/H7du3uXfvHktLS1y/fv2pdbM+C5mkT2PNZpObN29i2zZXrlzhf/z2N6l0+lzLzrFZqTOvWHRcm/tHZXKmyWGzzbqVQJcUhEAgHIS4lpvjR3uHfC29MmIveSJWoHM1NUep30NwZF6OLVEYNGnbDm9UK3wlvkZcNcgZFvfqVf76YJ9XomvMG1FiaggvgDcrxww7KoNSaCQf0xMQBLBFB1+DfkKkO1CwGxZuIYRfG4U+RAnE4fjxE0U8HYYpKIZcGhq0GmGaBRMElcGejltTEOSAoDbReBMjLr49WoBIMQ87P/luoHbAHo+lBQyrk3CqmrWhOiG9KOkhYn9SkyPFbbAnz4QYdQicSchGTdn4AwW7K9MpGgw8iep+hkI1Sk3QceYCHFHHjw4RJAEEAd+TZqSO9GyfVtGkXTEoHsSp9KK0DRkp4SKM422S5tOqTI6zUzYo1TVKzTCuNcnNKGGPWn6UdGpVDGqtBEHao9P8YJinM9QpDXXk2OS5VZJDeq0Q9kCm3EwhxD1AoN+d5F99X6BaTePGRx7WtEmKT2Jx4lVG9BCbU4XJ2pRm30oqSrE1lWOa6o+1kJiE1RdiYSIhlavpLAlCHBdbvLddIF/vYOmT+7yWTZ6SIFKmfsoMDEkSqiiRFQ3u7pQoTit7TEXfYoaGALyYznA+nOTd3SJD12MtFccZn+jVbJaoNqty8u+jtVqtUx0+SZKYn/94zcATOzo6YmkKgBcXFzk6OvrANt/73vc+0MDw87Zn3oM6sX6/z9bWFp1Oh/X1dZLJ5I/thkuS9FQA9Wn3O/HyXNfl3Llz3L9/H13XsSSJ/+5rX+Z/e+0tzkXieAJUyl2uLczxg619vrK6xJv5Y85EYvQ9j3yrixcIJDSd+5UqS2qMut2n0OlQ7LS5mp7j3WqeS5EMgqvwYizGG7VjdloNqn2PBU3kQiTNw1aZan/IRqPDS2mTy1aWe50iQ9UlUKAnSSg1Ga0t4Jk2YlnEy3oE8QC3IuAkR4Ak7ShYloggOohVFT9pQ9THbJp0o10IgVsQIBdQwwFPAk0AX0bRRYJtE1EJMFQJMRBx5D6C6iFGXLyuhGR6iHrA8EghtDiavORcH7uioqZGHoGjDZBsAVENECQYNAROOihIWoBbNRCsLm5fxrMlJN+g6/bxRYFADVAcFbK9kcsF2F0J0fQ5KZL1Y0PcnoRsjMNz0QGdQxNrvsuwZiKKFi3fRg33EcIuASArPu28SXRxKteS7dM4jGErIMZdJFwCR8Sd8axANKFZzDGIdoDROUpJG6enoBgOvg/V4xh+0kNuaoT1aSkmgVrdQggD5sRj8sMevjc6n3wxQRB3EIFO1ZgJczbLJnW5CozyJavZOLfGXYIlUWB7WkT3Q8J7oiAwF7XQJZmruSzleodcyOTdcY3bfDzMYX3C4Nyf0vmbFqmfj4URuyILZhjX9nh7cyRUnLR0dsZitbIksDklXCsC63qcu7tlzs0lJz82BWL/wcpsN+ePsy+yFqnRaJBKpZ54vw875sfnxt/4jd/gd37nd37iRcDPPEAFQcC9e/doNpusra1x5cqVDwWmp2HjKYryuYT4TsC02+1y7ty506K/k9yVJEn8/AsX+P6jXerukP1qg5V4lPsHJS4kUhQaXV5KZnGlgAf5MhczMd6tVvnywiJ5u01c03lYrXBtbo4fHh+ALfJyfIGOP+Sw3aHY6fJCOMnGoMmVWJY388ecDce4GpvnVuOY5+NzvFsuoDkSdGQE3UdsCfgZHzse4NUFPFFGBaQ8SJmAwPLABWTwrICG7hGIImI/wKhYCI5LV7KhL4AeQM4l1A0xNIcQ8aEgQ87FUQPQJEh42HgQuGgDAzs0SuZLVZnAcUahQDGgv6mghUfN3z03oL+vYuoKvb5DMABR9wlpo5buwUMVKeEh6AKu7iLUIiO2oQHdoI/UlJATzoiIQJ+grKKkRxO6Zw4Y5nWM+bFHIPv0Kxpho4vTVnDbOj0XunUZKeLDmB7uVyNIUxp44tg7C0SPVsnE1gVCqooSmyo8VXw6xwaxpTa+KzCoxOiYDkFbIBKdIlFIQD+GT4f6wMBPjUJ6Q0Fiuty0U9FpaQpxZZamHyge9ZJFP1AhPnGbhu5k2mhXDVq6Auk2I7QWqE4V2Z7NxNiYUmmv9waspeNYIZWoNhJhPa628LoebxQPT7cLqROPNxszT7X4zqbjbI7p5aosslmpIYsiS4aG7AhUS10qQZcXVyY5muV4lEp+dF/WU0nu1iucjcXIhgze3BqBWDikslkbeX2SKJy2qp+zLH76CQDqixaKXVv7+FYgH2aLi4scHEyUTg4PDz/gfd28eZPvfOc7AFQqFf7sz/4MWZb5hV/4hR/voD/BnnmAEkWRubk5Ll269JEA9HiriE9rTxvi+yiShG3bbG1t0Wg0WFtbI51OzxzzyXiqqiIIAv/NN77Kf/UH/4ZswqJY6xDVdGKySj/w8L0A3/VJGwb3inVeXZzndqmIiUwyqxP48PZhnq/klni9dMiyEcUOPK5n5nmrdEzf8bF8AwEwZYXtdoNryjxLSoqQICEiMFA8FFegr4oow4BQTWYYdxHUAAIBOwpaPUSn76C3BSKKSivWBStAyku4OR9fFxgUA9wsgIRUlBE0H9Vl1MMpEMHyEVIe4lDCC3mQ8E4BC0Fg0HMRx9EsL+lAVUZIuScXjU7Y5uQyGg2DptUFayQiK3ZFvMgIZAJdABUE2UdARFYlgsBBEEYrStcXp14YAV8MCPzJKl6Oe2DLBLZMtyHhBgLdbRV53oHEaIK38yH08JSqe7iPMVQgNAIHcWDS7Rn0I02EdIBIgMMAt6ihZyf5FSk7pLYXwY8KBPERaAYpB2wF1NFvBT60+hIDW0eOTsBHinp4TQsp2sGuJmnro+vjdyKI8UloznMEqp0IkcVZ4Vsh6uG7Ar22Rl1REcRRODIxB2EniiSLXMyGwA8I+QFnTJ2h46MrCrsHkxzTYibCwViE98JC6rRYNxM12a18eBFvxAzBGO+ey2VGpJd8nWbDZr9aJGDULHGa7t5xJl5h3NB4Pkjx4KhCcmUStjuTinGrNMpLnUsl2O+1eCWdo991WXoC4tQXDVBPIxR7/fp1NjY22NnZYWFhgT/+4z/mj/7oj2a22dnZOf37V37lV/j5n//5zx2c4O9JDiqRSHysd/TjKJp/Fh6U4zhsbGxw8+ZNotEoN27cIJPJfOCYHwe2uViY//bnvkq51iVtmSwYFu2BzaBlo8kyj/IVoqKKIop4ts/lWJqVZJx3dvJcTWcZuh6243HJSpEwdI7bHXZKjVHdR7+NJavcPCxwNTpPVrfY6dQ4brd547iAeiwR6ki4cRCGAk5YJHAlvJqMOlAwm6MVcD/mIrVFejEoaDa0TEJVg0AIEHqj83NTHtLJ35kAL5DoJgRq8YBuWaPdCNErhVDqJkFeJahJYPiI7vjxTfqQP4EOAZTgVPXcCzuQn6zG+2YfYTDaTxAFcKYgxwjwipNtXdNGKk/yOGLCxT6eyoFZPv1dA6ESobNr0ijr5HcsqrLEIAVuOsAJiTAVQRGzQ4Tu1G+oYFdN2vsW1ZJFRYFapIs4nM15uIpA4I9qkzpHBpVamKYfItCnwnwy2I1RzmpYV6lWozTCLoPOB4WM6x2RdjFFVXc4Qe8mw0mezFao1CK4KR+/N7uOFWRoFWPUxRDC1Fee2SApa+zt1tnaqbN30GS32OWg3KfUGGJOqdUnDOUUnIBTEWEYhfSm/z4J7wnA0PW4NpdjUTXxhz63twq0ekNSVuj0Mq9lEtTHZImYHmKzWudcMsFziRQPDso8GDfAnFZcd8YPjCQKZAwDdSBya7fI19c+vfcEX7yS+dP0gpJlmd///d/nm9/8JpcuXeKXf/mXuXLlCt/97nf57ne/+zkc6RMc2xc6+k/IPm3Twic1WZbp9XqfvOGH7Od53kxL+KWlJW7cuPGxxbsf5nl947l19kp13tw9xPV8/J7PQjrCDx4dcGNtkdf3D7kUj1LsdpF9kYgZImOa3Nw95ktz8zxs1IhIIYrtLlfTWW6Vi5x1BTK+Rs6y2Gk1eOP4iJSikVEVQuEw7zUrdMMgugJKTSKsytRCQzqWh1IXaMYChKFPumnSCnoE4/YGggSSC3XTA11BKYOo+ER0lX53AEaAIEBIFumPO/a4ER8EATsGRWzUpoKtiUBAtKTSF20kFwQvIFIOMXBsVFOEkoobH4zAKubCUEAIBQRKgFeSERfGRakJBy+vIM2NPZg5B78pIRg+wVDAISA4VlEklUAQ6Tsu/SMFT/cJjADiAn3Bg+zoHAPfh5YMkdHzJMS8ESEjNZqABVGg3xGQPZlhQ8XXJYZhB6UrIY33QRDotAWmeyxKlo+dT9M3HezESPEAy8Vvq4hTTLuBMaC9G8HNeAhj8AoSDl5fRNLHXlxDoSuEUAJ3ZgIQDJ9+SUfWXBqegWcFgEDQM8GYeCRBWyffU7Dis7JR6mKf9q2p1hqLKe4djguhBSg2J+/KUi5JdW+UY0paGof1CbMvPyWBlI7oWIaKKcngwa2xlJUiizSm2n303Ml7Yerj7reCwOVMinKrx/ZBjXO5JM3+aJ9sxDrtWaUrMpu1Oi9kMtTqXe4elmmNt/uZc2d4Evu7CFAA3/rWt/jWt74189lHESL+8A//8KnGeBr7e+FBfZI9rQf1tCQJQRCo1+szLeGXl5c/UVnio0KDv/L1a8RUHcGBuYjFGw8OeHVpnjv7Ra7n5qgNhzgtl6VElHtHZZb0CAlDx/UCDFthKRah3hvQbA54NTXPo2aVruPy1u4R12NZBCCmhnjY7LFZahJuS6CA3IGhJVCRXRI1DbUhEMgBBBCERPo9j4Eq47syyqGIOIS2ZaOMQzROGnxRohxyacdFgl0F4VBGciUizfFqWwe5Orku3imFTKAZcfAkkUFSoJ8R6Q5kmjGZsiJSCUF3aNAcaDRtje6BTrdq0C3pdCSJ3rZOp6gxrJq4skG7ZNCs6rS7Jq2aRtPVaEkh6qZIu6dRi/jUwy6DFEjoBMboGAiBV5l4XYIo4HRn72M/ZCMMJcSGSVCO0fRV6g2dQRpsy0MQRNz+7KQmpB3skgoDmc6eSbmpU5Q9bHn6eRPod6c8wHqUWt+g66unTEAAQRZwGiNPsHNo0JAVXDPA7nywULzTValh4IYmC7q+Msk/OTWdvCfjRAMCd9bDVxI2e62Jcvz0MZzNxWda3JemPKal9GRSzUZNVFXl+WyS9UiY4nGTrZ0qtzeL9PoTQDyXS56qPyQsjXx3Ev6sdHu8PJcjJ+k0WoPT5pSGNrlWc1PK589nMyyGwtzbLWGF1FPvazUeZS35ZCGzp6mL/KzsWeumC/8AUMDTe1BPSpIIgoDj42Pu37+P4zi8+uqrnDlz5lOvuD4KoGRJ4r//ha8TEiTqzVG9016hzgu5DLbrYngiZ1Jx3t445KX5HLeOi6RFg6Hrossyb28d86W5BfbbLQIHkoLBckjHD2C/0SIjhhEVmYyk0ws83E6A1VLwJZB7gCjQsl3skITkyISKQADtiIvUBccQsC0J31aQCxJiD8a1uGjq6GUWBBFXF+jFRSpqQMXzEGoaSimEIstIFQF88OIBcuGEng6hqYR9J2YjdkaTYqAKqA2ZUchPwMkGiIKEY4EbEbFVCTcq0Dd9OqaL2FPxDQFXDvCyAUJlck+8rAutyavStfqIvcn3Qc4haE3dw4yLe6ziFhXEYoRuQ6O8a1IKQdVy8MJA6DFwSLv4lUkozi2HGPQsSq5KPwNoAoER4ExR6QGCpIOXt+jUYpQ0l0ADN+6DPftqB4ZA7cCinxRG1HfAjfmnNH2A3pFBIyIj+LMTrB1yGdZUekWNsqyALCDIAnZtNnQoDlX85GihF5KlGVV4S59su5iKcDz2mCJ6CFkUubaU43IqxWo4Sv6wxYOdKq4L5e7IkxEEKHUnHlO3PwG4jKURAGeTMX5qdZF6qcvtzQK247FZmrR2355SWW8MBlxMJTkfjtPvO+yNc17TFPaffkLvCb74HNSzJnX09wKgPomd93kX3J70kXr99ddpNpun4rNPInX0SePFLZ3/6Z/+LGfiMWzHYz2ZIHADcMD3Aqr1LjFNo9bocX1uDk8I2DiosBgJ43oBlUaPlxJZCt02+UabR7UOX8rMU7WHzFth7h9VaRX7iMOAQQzsgYenikQcFaUFdgzUBgx18MMyclUiVBKQxotmLwSRgcIwKtJLSkjHEqGSjN1yCTdGE6IXgdg4X+LrAl7Tpx0OqJvg9BQGXQWvKCP6MvKRhFQW6SsO1rjvFBKI3cm97sRtxOb4f1FA6E++8xM+ZmOqbipmI59O6gK+xCR3JAoEvalXRRZw65P/ZVvBqyn4xzqDI512xaAZqHTCMrWIgxsHN+Of5r4AHNNFq08LEAtIhBjs6zSrBm1Lpp30oDILAiPPZfR3UFPoHJkUezJ9fRIBEGRQu5M8jliNUPEUHG8W3AQF7GoIPJHmkUk3LiJIIk7jg89lq2pQ15WZGUOSJr/ntmVKPR0vNzq4tcUkw7GHI4pQbvU4k4nx/FKGM4kYl9Mp0pJGNFB59+4xdx4W2NivUJgK9aWik+tzNhunMdZQ1BSJQm+sSmFomLJCWlDYP2xQLNUYOqNF3HzcPG2JspadhPeez6aQHYHNvSr5WpuNseK6IDCjsP4z63+3AMr3/S/Me/u87Nk6m6e0z5MkUavV2NjYwDCM0z5Sw+HwM2X/nVg6avLr//gr/K9/9hq13v/P3pvHSpJdZ36/u0VE7plvq1dbN6u6qtnsZrO5uKUmJUiANR5JxIDDoce0ZBgYQCYEQrIhGDYMzcgYwxrLtmZseTwSJI2HNGBIlGV7xpYgjagxDcsCJFukuDab7K2qa696+8s9Y7mL/4h4mfmavVRVN9kzbJ6/KuvFjYjMuHG/e875zndSdgZjklgT8sC4yLiwscpBkRIKMF7y7pMn+IsXb/JDDz3AF7fuYKwlT3Ped/IEX7i9xWzmOZ/0uHM4QFrIW5L6EAo83gQEkr6xJBOJ3PFlFttDoQIrIuKgXYB1xDdAr2kOkoK4kGTGU7TBavBKkU4d0R1Jo25IZYEoIBjI10BnAhsH8jWIB5KsEyiAaFuRl+x73DSgsxgTBHlRoK4qah3DzOaQhpJVGAlm3RLMJlXOZiJzcJQ1L5FA72rsRvk33w10hnXG8QyykrHX3i1bP4QgyEWgcbtGv5GDEbAe6GQxaX2pId+wxqRThaWMoDZImCaLMNc0soiBxA0Mrq7pNx2NPMEvtVi3BpbhQtQC2fUE2TKMmxZqAIH6LKKoLXJR/Sgl3jOMc0PRLedMZgK1Mq20mFNRwnSUkPcW8zFPAnM6Q4DZnTrTJjTE8QrdaWJpeRDTmEOXYHVAblieOLdBXUc8dmKNyTSj00h45loV+hOw1m2yOyg9oCcudOfKEmfW29w4WBAnlpXR60se2IXNFZRSzCY5g1HKV6/uEkIJhAf54h7H+VJNV5FysdtiNnGoAl7aKsN+D22u8PRWeW8X1ld4/vCA0+0Wj6ys8s6NpbqouzRr7VsCUN+NvaDgbQJQd+NBzWaz1zzm1ca9GtAMBgNefPFFtNY89thjx1TR71eLTyn1ukB6otfiP/4bP8Sv/+H/h7Oem4cDhIBH1tfYGo0xQqJrghtbA3qNhNOdFs/f3qZpQbUiZqMZz9zY4dF2k2f3dliXNbbSCfEolDmTSOC1xHiB3nOkawIvwSaSIALrw4g+KQetjLjQZAZUSzFxFj0SiNSjTgpcEoi2A9mGwNcVYRTY65QKBvXbCm8C6EArMhzEOQgIcvES5qsgZ+BrkLcEYisw3QzQUCQTyV7iAQ1NMHtQrAI+UAw80sVoKcgyi94G1xZorTj0Bep6hG1B0DAtHFIl+ChABOnQ49YWXhb9UIJT9TlNHSyJN4y1RRwBIDBszdBDCbnAzzSjWCCmGn/aA2WR7yy4Yy9laAfClkGcKHBbhhSFawqievlbHV27GMoKrEAUkmw7YuoCnF4s2L4JftsgN8s5VNyM6bcFydCXmk+VucTjdg2qa5ns1kmrqFEyqZEuKVh4FZhdrzNsK4KpZJZk4NJ4C3dbzXt5dS7U5mPesdnjylI35TuHi6Lk1U59DlDvONHlpUr2SEoYTDPed3aT2SRHZPDMzZJg8cRDm+xcL0H/wuYqz2+XCue9ZsKNwYRmHPHw+gpbB2O2KsBzS0A7nC5Chd16zHv1Bt+8vsNHLl7kfsw5RxR9K2vy221HdZzfTb2g4G0CUK9nWuv78qCO6qeW7eXqD68UE34jAJUutcx+NWvXE/6jj/0Q/+SPPk+iFFuHBxSFI/aK1V6dzz9/kw88dIov3rjDhU6ddqNBLY75+s0tnjx/hj+/doNs5mhMFAfZBNGW2CYkux6XBNpOM0gcSguiXQhRIE4h6wkORA4oon2PLCyclExjR7wL2arE1sHsBhqRhthhZx5XE+SrAp2BjQXTVYisJI8CaSiIr0ukDKCgkwsGqx406APIq7Wv6DD3vNKGpzswDKraH5XIkkYsBUVPkewEppsejJwrdBeRBxRiF3xSMfK0wNwGf7o6ph2ItiX2RPnM064j2pG4jaoBYccRbUncZsVArHm6/TozkWNsxKhwZBm40wGq6JXQAl0VMAP4ToA7Ck5W82MmULbGbBiTdhZzRuxowuZizs66lmQkcQNN2jYUKwExhdj744F8YwhTx/QwJu9VuahCojk+H4uZJle1Y9dMp8ASs9BtGw5zg3xZgW9yXjC4Uf4GRkteur3IRbUaC6r5g5tdru5WYCXg1sHCY+q2ajwcKRraoIPgy5fvcIuyD9gsLDaFu0s1UnG0WM4unlglLSwv3tgja1i2+iUQnl5pcaMq+m3GhpvjGeuNGus64rmru0yqsOQjLcPW1hbNZpN6vX7XrXHeqhDfZDJ53dZA/yra2wKg7qblxv2E3Jbt1dQf7ud+Xs3uBdiMVvzMRz7Er/3vf8aNmztELclKvcaXn7/JE6dX+fKl27zn9CpbWYrbm/LAZkLdRHz5ym0eNE2uj8bETuKMIN5zZKuKJDaMlSWfWKQAVxPUUpgZQYLAjx1FU1A/EEw7Chtg5UCVobaOQjhHUIJarBnGHpB0x5p0YEmamtk4x54QZS5p38O6AKHwKpD1ygUin0E4hKgQRFJQ24OptNgmRHuQnSy//0gUCF/W+aYNT7QNeSUuELoSrAMN3sDKKOEwKoG/WA+YfbBVdCdfC8gUQrWuioYsxeiq9crppdBKAS4XiJuKWpwwsAV3tEfUNSGpZJBCIBoKfLsCwRrIbY0/vZh/LhaYHU2WSWY9wbDtSfYCLLUj8s2SNELJuIcdw2gmS/CrkmehDvEgJltq0y6cYbgPfml6Fr2ATgUcAfO25tBoEn18rk1qlnrVJkXvNzloOIQJ5bClKd1vj4AmAsGFs2t843oZQpNScHVrqRFjM4GKhX5+s4fSkjPdFpNJxo3rhxyOy2fy6PmN+Zhzp3p87XpJNT+9uggJKln2P3vPmRNMxzl7B5M5+Gm9AJe1bmMOUA9vrlI4z7PXdjhxujEHp8dOrvHI2VOMx2P29/eZTqdzJfFms0mr1aLZbL5ivuetAqh+v/9d16wQ3iYA9Xp2vyQJKBOTzz777KuqP7yZdj/3+e9/7AcZ723z5y/tIyPF2STh+u6IJx84xUGWwsxz8cw6f/HiDU4kNTIX2BuOkTLgrUV0JD6WxAce15G0nGZcdyQHHm88RUdivGRqAvE+qEkoQ1CFIDeBSV5g2wpSz5qNGNcdw8QR7weyFUm/7mlmmoHw+ERQv1Z6MG5FYAaBoiMoeoLoIJCvCFwNkm1BekKQAp2JIk0AG/CRp71rSLMCGUDuBURHIhNBHrm5h5VFgeQOZJVndNhI0ROwDQBBFClsRTMMkaC+p5kkBSIFW3iSGwpZl0ipmM4s8lCQdcHWgJ6gtg/jFUu5agvqO4L0yCMSgnqIGLPwhF0PRA5yIHEzxayryCYee2IBflaLZQwgjz3xHYWQgiwypO2AbEBsA1YvvHorj+KLknxiGLUD8VAzp1ECSIHf06hNS347YtIr7zvsK9hYOi4ShD2D9YaDVgm4IYJkGpM2FiBYRBbV9Kixwi9VKV84s8rzN/dp1iI2Og0iKXnPmQ0OD6d0ZMTTlfbexbNrc3BKIs2lJQ9ski+8tbVenZujIefXutQJXN2b8M29bU6uNLlV9Y5KjOLFJeHaO4MxD633qKGZjPPF8K1EAAAgAElEQVT535RagNiPPX6R1dVVVlcXOSjnHJPJhNFoxPb2NpcvX8Y5V2pjVs0DW63WvDvCd9q+Gynm8D2AAu6PJFEUBVevXmU6nXL+/HkeeeSRb3v8935Dgx96ZJ0H1pr8L39xnUMbsM5x1R4wSjNa9Zi/+MZ1al6w7WeoqcfXJHEQpIkg2vO4VUUrKPppgZ945Ioibwt0KjAzQVQEhl3IuxKVgQvQnUqyGow7EB968q7kQFhMJmjNFC4tEDYQtOAouiSNIihP3lSEPBAPPHoc8AlEDUMeLAhIeyCzgI8Fg4YjOYB0ReBrinzXk66Xi7LIAkoLrABiTXsXxu2AzAOZFKibgAaJQIwdsi7KhSox6JegaJQe2MiUXoVtCTBgWwKrPUF7qElqhcKaxXMJzeNeVtYLiBxClZroNzPiA0FoQWMag1OMBhn5aarQX0BFgmUJCtuF5CicWIDcVky9wJ5kfpxXUBtGjFYW4DeLCrrbLXbqOaFdzs+8E0o1pCX2hVeSdHcR9gOwQnDMF5gJxgODPXU8IZ9NmIcslZVMdyPqpxQPDrpIIXji3Cb4QGIM6yahfzAjaTb56tdLxWytBKPZAuBMtLjqQ6dXeKbywFbbNS5XgPLAWhsTJBu6xrVrfR480WCalWC6sQRQF06u8vStHZQQvOeBTYazlCs3Dllr19mtiuwbkeH5nTJ3paTgr7zrPC83pRTtdvuYlxJCYDabMR6PGY1G3L59m8FgwHg8ptvtHmvXfi/ds+/H+v3+dx3FHN4mAPVm0sxfrv7QbrdfUZbobu7Je39PE/deAWo4HPLCCy+Q5zkf+as/wI/+yA/yn/yjP+D63oDRIKUWG/aGMzqxYRIs0ThgGoaJt6gsoNsS3VAw8GRxwASBbSqiHY9sKbSRjJTDikBtyyM7Cpd7fCwZGI869LQThfeQ+wBaIHcd01UFkaZ+xxG3NBNfEM0gX5VkPUkn0wxiS76miA48RU1SWM/KvsIngpkviIJktFEulFYtYkzTVdDjgG0KQiyIdkIZNgRG9YAJkqIWygLgbU+6Uj23lioLj9uCKZaoLiga89OSHIKtmNt5FEi2IKv0NGfGUd+BWRWCS2NPsi3IT5b35wwkdwT5ZkAfCIw1FDPPLIKJ8WA8SgikK4kHUFLu4x2B3ViAgSsEjf06e8oSqvtu9yWTpZ5P/ShHVfyJZj9hH4cdOUJzMT+DFsSHEdlGDgEaBzX2jKcVFDkL5lvRCSS5oogctXFM30lcL2C8wy8RVmy95IHoqWY6i8gaAd/O6E1jvv5s6RXVYo0TzCngeqkFx0MPrPHs9TLWl0SaF5c8prwiWkgpeOjkKqfzgq2dIYlTfPm5Uui1mRhuHla5KAG3lqjqSMH7H9jk9vYQrOfKnTLEeHqtPSdXPHRyha/d3ubdJ9d5eG217Kp7FyaEoF6vU6/X2dgow5BPP/00586dm7dsv3HjBpOqQ3Cj0ZiHB5vN5j2XmbyWfc+D+i42pdS3kB1ebt57bt26xfXr1zl16hRPPfUUSin29vbeUFfdbwdATadTLl26RJZlPPzwwzz33HMkSUJTaz71n/7b/OI//hf8v89ep7CONRMzzHLqUhI05JljNYk5SHKiA4/qGigcmRHEs0DoCGxdIEPAjwraDcPQOJCQBmhoRZQKxolHCJjqEpg2xxH9LCXtSfTEYxsS21UlZT1SyJGndtsjWpI0FBBXbSsMpYMgBcOklCoKWpMFT3yrrF0RAWpTmHXKxbKF4bAKYU1XQU0Dri4IkUDdcRSnyt88XROYVFAkAYRApgGqDXLeFCRbnvSkqI4FMwRb/T2rwnJHXlHaYEFZB0JHYfqO2GnSqSNV4PqCrFEBRUcSDQO2WlNcLIi2fOlFVabrGu8tcqcUqh21Bb56Bkc2K47PB58IzDVF1hDsNsswXGYCUSrm5A8AmwjEQFBMNDvtivSxb4+xEEFgdwP1pM5O5KACT7EnYAk4c+OpXdcMWgZXsfmKlcD+9QWB4fwDazzzUpk7qieGSzf3ly8zt4fOrvL1ipK+0W2QaMW7T29w49Yhd7YG3Norc04n1haezAMnOnyj0tc7v9nj0t4h5zd6rNZqPHN1m6xwGC2Z+sUmdGtQelhKChpxxJl6i2ev7PK3Pvhe3ohZa0mShFardSwP7b2fhwh3d3e5cuXK/NjlEGGSJPcVifkeQP0rbG8k9BZC4M6dO1y9epX19XW+7/u+79jO5402LbyXXdTrNTpcVkO/cOECa2trCCGOsQ2FEPxnn/wx/unnvsJn/ujLpLlH5aBiwbRwmETSn2Q0kUxrEjuxJEoSHOSJoD4E04yYjFKKlsKPC1Ziw2E9UJsFpjUwI0fXasbCE/UdeVexF3J0ojCTgB47kAJbE9T2HOmqwrckYteTSYnIPPVrDr1iGNehNRCMugFfEyTbjvSEQgpJ3UgGzWpjkQu888hhYDKz9IYSVVdMZjkUAduDUJek66LMkzUEKEFrojhIqk6764L4MJBVYa6iJRAOggKkoOYEo0ojMMSC+HZArSjsuMxvyS0wKxEjZ5nUoXGgOdwEaiVqJduBdL45F4gUlsN4WUcgbSDIkhpvrcBvK6abi02M9ApYkh7qCuIDgV0J1A8N0ywwiwS+ubThkoLWNGKQVKE/C2JUtkm3q4tz5x3QS6ArJ2CzmJ3Oos8VgA9L71MAdVsxcxLXXQr9CbjMIbUKsafZwss7d2ZlDlaNejQHq24zoZlEvPfBE+zvT1hvNfjac6UH9sBmh6t7pXZebI6rVAwrTb5OPeZkt0U2c1y/ekj3Yjz32C6eXuOZ21UX3c0et4dj3nt2k3Sa8/nnbhACrLXqfOjhN9Y599VIElJKWq0WrdaigDqEQJqm8xDh1tYWaZqilDrmaTUajdclXiw3K/xusrcFQN2PhRDY3d3l8uXLdLtdPvCBDxDH8bcc90ZabtzruFcb45zj6tWrbG1tce7cuW/Jh72S5/U3/4338eg7Nvmlf/I5ZIB+mtNINJOppVM3TGY5xkmSWDMSjlouSBLFhJxZmlPTCnIoapJZPyduKiILaRwoWhJ5WBDaikSBGHuypkTuO+yKougaWplkNirwgJp5XE3ierLMS8WSogkZAZkKNJLanRzbEKQrElNAYWDQ9DRTyTjxJfFhx5NuKGwL/EwyiDxEGgIlDV4BDsx+SSiIlGKcWhqHELUjhIBZPyepSnNqtYjsToarCRBgI0FyFVxPU6jArAkiA98sNxkqDUyMI9QqD60dFnk2oFgT6AJs5WVka6X6hu2WFPlmFlHcLpitCYpGeQ5zeNzDHjUtSR+Kai0SHuJZhN8P9BMgKq/VmRhGjQUoDLQFD3pXYKNyQxHvL8tlVLT6A0m+6dFbklmsCF1BNAC7lN7I2xDlZTsUu6eYtiUqDcfOBZBtemo3FOu9BleWwnbTrKAWG06utjjRazCcZOztjgl54MtfvYE/Kjpd0vJrt2tQAdSFs2t8vcpLnVxpUo80D3Wb7BzO+Nrzd+ZguD1Y1DgVoeq626qz2Wqyszfm6y9u8Z6HNucK7h9+30XUG8wVhRDuOioihKBWq1Gr1VhfX1/caxUeHI/H3Lp1i/G4nJD1ev0YcC3XWw0GAx544IE3dO//MtrbBqBeT9F8OSf0SuoPr2b3Kxh7P8D2ck9wOex4+vRpPvjBD77iy/FqocFHL57k03/vJ/k7v/IHPHt9F2cDvTjGFo6GUQghGRWOXmw4VAV6P6PTjphOcmZNRTQJNIJm0gJXBKZGsDExDGxGkQikh6mB9lTBniXIBRhZEbANCUIQHThMTZBrTwPJoAm+Jmn2PeOuZBgFOqlhqCCZBdRBgY5FWT/lXdnAEMg6EpkHfCQY1XxJj19TIKCBJsMilCRbC9QKyTQJUNPIXcdhXHkcG5pa3zPrCVI8UmiCgVAV5MZpIDcAAiR0R4qDuPxtXSKobXtmVVjQxYLalic9XX1WkNx22DMS4aGVRdi9HKaCrCk41CDbqhTcrazoCaJ9T766KMplGtA1kDuQ1SUHjUDdSZY9K+FfNg+mAbWtj3ljWVegs4Bf2nepyCBvOaadxXFiJqCz3DNEILcUeUtTVKU3LhGYocC1l0J/a55Gy3Du9AobaQslBFoIbm0PKPoZ1w8z/BnHjTslHfzdj5xk91IZFnzwVJcrOyUgaS15acljssHz6Nl1lBfEWvGVqnPuYw+dmIcHz53scrnS11tpJYQAj51Y5/rWIV+d3GGWW7QSXNkrc1JCwF97/zv5l8GMMfR6vWO9nbz3TKdTRqMR+/v7XLt2jTzPGY/H/OEf/iHD4ZDz58/fc177j//4j/m5n/s5nHN84hOf4Od//ueP/f0zn/kMv/zLvwxAs9nkN37jN3jiiSfenC96F/a2AajXM601h4eHXLlyBaXUt6g/vNa4b4ds0WvZkbbf5cuXWVtb+5aw471cK4kNv/K3P8an/9c/5w/+5JvY4MmKss4px5PEitEkp6UUaQzjrJRyqWUwqwtM6tCRQE0sWU9zGAq0VjScwI8tsxXFMPJEaHIZaOaQjR1pT9KZKQZ1T95TqClYJbEzz+pAM9GOaVMis5J0MawHVFXIa1cNehbwRiJ8oPFSQYgEpq5RCA67niDBRQJ8ACk4qFniQ0fWUyAFJodZVduUriuaU8G4XhEUlt5vnwiSHUe6WYHgqiQ68OQr5UGHNVvlsapzdSSiCHNAy7rlZ5lDPBH4QpBch7QrGepA2NA0CkmmSnDxNUlt15Eu1TxRtV3Hl1R+nwnEWDNdWYCBGARYaiHVrxVEQ0oShEs4jC2NuuIYvVwJumnCQZyWx+1rRoYqnLQEks2j37H02Gr7hqAkhT4+71sipl/R500mCX3BQGRcu7zP/mHpzbz7XSfZ3auKZjc7c3BCwJ2l/lDNZgIVQF08u8r1/SGPv+MEsVQ8d22HWWpRStBoLdB1mYLeaMQ0xxEXTqwQS8kXXixB7PGHTszrqB4+s8Yzt3fp1hN+6JEHOb3yxuuIvl1MXinl3HM6shACBwcH7O/v89u//dt85jOf4Vd/9VdpNBr8wi/8Aj/+4z/+mud0zvGzP/uzfO5zn+PMmTM8+eSTfOQjH+HRRx+dH3Pu3Dn+9E//lF6vx2c/+1l++qd/ms9//vPflu/4Sva2EIuF15444/GYyWTCpUuXuHjxIu973/vuuir729X2/dXMWssXvvAFdnd3ef/738/DDz/8unmsuwHDf+/jP8Df/ZkfoxPFtJTB2kBTKYpJQUca8qklFNBB4yToAjqpJHWOwntsTdPse1QeaARFKgJFooh3LdHYw6hcPMYGcKAmkA1zzLTU8Jv/FjXJbJRjhSCZQbLjiA4dQULbVXF4KUhCOXWDFLiGIu9oJpFgqAP1gaR2AGYcaFx39PqSeM8h0lBy4IFhKxANqrwc4LPF75O3Jd0l9fK8p9B2yYNZ5tNogT4ox8o8UPeK9X7EyqGmdjNgDgXxNYFDM20o0jWDyAVUxaMCgesfnwehrRFLDotX0L4pkX1F1jDkKwbRf5kuXjuUJI+j2xqA2hLkSnEYl7S+SeKoT18WMhQWfQhqWzFKBF4J1PB4pMFHguRQYoYgdhXjBCaRQ75MHazvSwZgexiRTyV5XSIuRHNwEhJubC1kjnrdBSPjobOr7FbHRVpydavPuZM93nt+k0QosoOM557dwlvPLC1/r4sPrNGv6qXWOjVeunOIEHDh5ArCgh8XfOOFLS4vSSsdThcU/CQ2vPf0CbJhzg9efOPhse+0Hp4QgtXVVT7+8Y/T6XT49V//db7yla/w2c9+lqeeeup1x3/hC1/gwoULnD9/niiK+Imf+Al+//d//9gxH/rQh+ae3FNPPcXNmze/Ld/l1ext7UEtqz+0Wi0uXLhwz7UEWmvyJVHKexl3Lx7UeDyeU8bf//7335OsiZTyrq71/sfP8j/80k/yn//DP+KZF2/hi0DHRPjCY4wk8jCyllVnOAw5auxQNYUeOtK2xCoBUjAdZuhIYBuKehIzVI7IQ3JgSXsKU9dY6bFtTTcTjCYFtZqhGHqmbUG+ojEjR95SsGKI8gATwXSckQygaCvGTUmnUAyMwzZLIMzWdKlavl9QbBiIJSaHsQyEmoEa1G5bbFsg8kCUQtMrpBBMxhmNgSUYiBNDNs6pjQAESglaJiKVjqxaHJs3BVNKZQwrFY19QVqTpEAmHUIJXK9qJRKHikJe/s6zFYkqSvo5QLomicaBvKKCp8bTuOYRWlI0FHkkCCnHWHhpV8xrwaDMH0W7oWThTUX5PFZAe1HR8MvvEmWSab0EN50C++ClxK4shf5aLMghAA6aNmFHZ1CvjhMC0w9kS9HvYASNG5p+10OVd9tr5ZxUIJ3gwjvWef5aSSfXSnLl1iJsF9c07zjZo12PaUSGZ17Y4ubeAbOVBvvjaak1JwU3dheNE92Sl3dytcnp9S53toc0tZ4X/b7zHet8s2L4PXiiy9X9Po+cWqNpDF997g4+BE6ttPjgu944QN1reO3NtMFgMAeSZSLGa9mtW7c4e3ZBCjlz5sxrekef/vSnX9cre7PtbQNQyx7UMtvtSP3h+eef/4521b3b3FWaply6dInJZMLDDz9MlmXU6/XXHffya70ejf7IGvWIv/93Pso//M1/zv/zlzfwwKSwREaSek8Hw8DnaCEwQjLzARspVnLNqMjQ04Bta3TqUXuWUcvTEoaRdGgP0SDgbEG7bhgmgb7xKCcZi4B0gdWJZuIKnK8WHwEqC+SxwHcM0YFFCEncD9hJSj0ShI4pSRgevIR0TaNHDttSFBF0RoJB9c7KmsJrwEhmDQiHJWjSM0QjR96RZSVQLSLetaQb5Ssysw7lAq5XokoYOvLOkue6W0CtPDbEgnjLMju5+Lw6Vey1qudtBNG2Y3aqKigWAn3oUEMBAXxbUxhB0REctWMfNQN67LHNagHUktYQBrFHuEC8B84JnFT4o0iVhsZIMuguNif92KImAdMX5K2yJ1Z8KJYDf4RI0p1K+i1LdADeSnYSiyzEsXyVW9JEjQ7AeUlkIliqpfIS0nWobzGP10gheNeFE1jv0UJS5JZrl/eYzcq7ePDBFaaz0uM+eaLN7qj0rC4+uMZzN0qwWenU2B9OeeLcJv39IddvDBjNyuuaZKmXV/XaN5KI06st8qzg0ku7vPvi5pyM8Tc+9ChSvvHQ3FvdC+peWXyv5PG9WqTpT/7kT/j0pz/Nn/3Zn93X/d2vvW0ACsow0pUrV9jZ2fkWttt3uqvu6ymoF0XBSy+9xP7+PhcuXJhLKH0766eW7aM/9hjvf/ws/9P/9jRiNCHzjp6OmBWWulJoIRgKR8crxnnBWDqCUUhvUTOHrSk6UuOsJxukyLbCNjVx31K0NZkP1PcsvmtweYGrSXwicWOLbUiUFdRu5tiWZNbWmL6l6GryniYaWIqOxkWGaL+gaASMk3RmglGa440AF7CtcrEYxh5VCJwRZDVBsluQbpTgIpKlUF5L0ZtJDqtW6UVDIlwgKAFaYPYtrmLo5W1FbyI5bFQ1RKt6Xt8FkK2oOWED4HDeRkSgPOiaonarDL35hiJrG3S+GE9Lkuw60o1qwRMCPQzYJcc5zT29XcEoluSt8jorqWa/vpjHY+nmeTjlIdoVhELMc2oAWYe5NNWRuQKSW6UnJkwps2T6kC1k8bANQX0icINA1pIIBMOiWGgEVqYeinmis4r1gXesddjZGZIOM166XtLLH3vXyTk4nTrR4erNkrggFVzfXmj3BQEnVppsdpskRvGX37hJf2vC+bMdRgflJvHc6R6XqzHrvQaFdbzn7Al2dod86dlbFNbRSAwv3C6vXYsMH37yzSFHvJXddO+1ZAVKj+nGjRvzzzdv3uTUqVPfctzTTz/NJz7xCT772c8ek3/6TtjbBqC2t7d5/vnnOXv27Cuy3b7dTQtfbq8GGt57rl27xu3bt3nwwQe5ePHisXs9Gncvk/F+AEpKybkHevzj/+Yn+Qe/+n/y+a9eKc/hAgTHyAiaQTAylpbUpLnFZRbb0kSpQ4fARFi0kNimId4v8MYhWwYVSiKCLAJFEagrTTwKjJuCcQIy87hYorsRAoj6HjX1CF9QdDRxIyppw0KUgOEDTgkOvMM0DK6a1c07DisDwgVE4YjWamTSE1qm/B5KMKsJ4t2CbL38PafeVguswNcl3bHgsFUu3OmaJs4hqzyHcZEzf4WkKBUsKsmfEAlqdwp8SyOmZZ2UyD1+1ZBGMNWShoPx2tKzXRoPpW7gsqWrisZE4PsWryVFU2EPPb6x2PUO8xzqi8+uJuiNFArJSHqyNsSFgOAXpU1S0pgpclOAD7T7mrHySF2Czvxc8fHddWOoSJzioOXmRzkjaE4l4+Zivg3TlMJannu2JCdsnmjPwQkBOwcLOnivV58X4148t8ELN3Z56MwKvUaNO7sj9rdHDLbH1JrxnMcxyRfvX1IztBsx5zZ6GCX50vMlOeI97zzJzkt3AHjo7Bpfv7bFu06v8QPveuBYt983Ym+VBxVCuK/815NPPsmLL77IlStXOH36NL/7u7/L7/zO7xw75vr163zsYx/jt37rt3j44YffrFu+a3vbAFS3252rP7ySGWPIsuwV//Za9maRJI7awV+9epWTJ0++6r3eD9jcTR+pVxujteJv/4c/zv/9p9/kf/yf/4LRLGNceHooRt7SsopZniMSTRCwYhWHUSAOkuAdapQjuwbb0agiUNhAdFgQrUTMuho9dczqisQK6lPwUwshkK1HZAra48CoLrFRRHRYEAzYaUbTBdxazKyu6E6g3wCMRO7ksF515VVgm0d9LDQ+c2XfqgCru4KiIcgnOaII1G7lJPWINLXUd0s9QqklaEW977HeIwLUvQTpET5AgJ4tvTYRQGrF5qFm5B2ZCuSJQSPLXBogMl96IxUmTRugHdjqMWcrilohmB2pMbQVtYOA1QE9CqhE48eOfLPy/oA8XjAVAWxLEu9ZsjWFngaiQ08aPNnG4lXPTKAzlgxaS32RKIi3PUGXJAiQxH3PdCma7GqS1kwwDRbTF8zakFt37PoAxdRBE9QsoAeCoql5dqc/B7HVtSZ39ks5ovMPrnHpRglWkVFcuXnAqY02q+06WkvqXnHtxX2aj57iznYJXBfObfDNKyXYPXCqy9XdAUZLLp5eJRSBrJ/x0ngXH5U/tNaSK5VX1UwMkZSsJ3WuXNvn7/2tv3JP78Vr2VsJUHDvDEKtNb/2a7/Gj/7oj+Kc46d+6qd47LHH+M3f/E0APvnJT/KLv/iL7O/v8zM/8zPzMV/84hff3C/wWvf4HbvSW2xJkrwmkGit55pZ92Jv1IMKIbC3t8elS5fo9Xo8+eSTr9nw7H4B6m76SC3by3td/es//CgfeN87+K//28/y7OVtfBFoSIXwIJVCZ54gA4WQmJkndQW6ZXANQ3RoSdoxKBgIT9E0qL6lHgkkMAZSDdF+gesZfIDuIWS+YFyTyFzgI4lramQA2zS41MHUk4hyjx9v57iGIlszRKknTyR5Q9GdCfq1cgGV4wKS0isb1wLBeXy7XOzj3ZxRDMQRcubwsQQlyIF4x+E3y2cyCgE9BdssF6LR2FJ0zHyBFvtZ5Y2V91UfwqAqZwmxJNkrmJ6oclORxOwU2JOVqyQFYTtHririQaAZx3gbOIwDRRcKAH08dOjqkmTPLkKBlNJOK4eagbHkXUMA6lPBtL6kWpFaaJULeGcsSacB6SRZc+HRpTUxz+sBZbhzx0NHUrRlyX6MSjHgbHWxOOZN6A00w+DmObPdrmWDEoReur43PzaKNQ+ersgRScTzL26zc72PPOG5XYFYCVwLaaRJmldzVLC51kLh2dmdEgnF05cqL+nCOl97qSJKnFtnMst5oNdBKcGXni1Faj/8wXey3n3zeii9Vd10Z7PZPeelj+zDH/4wH/7wh4/93yc/+cn5vz/1qU/xqU996g3d3xuxtw1A3U1PqG9X2/dXGzebzfjiF79IHMevWxC8PO5+wnV3S5I4slciVrRbNf6Lv/tRfu/3vsQ//YOvMskLUu+pSUEGtKRiOsyoJYZpLNEDS70dkTU1k8wSgKYLpE1FEJCrslB3bQSjPCdvKGTuIZJYFSgijfAQHWSEWOK7EY1C0FeBkCjivZxsNWIEtIRmJCRm5ElmrlSyMIKJAhFHBAn5WoQeWmxb47Ug3slJT5RZf78SoVxZTOtrivqhZbpSvh5ZT8/rsRCCptT0q/iSbeoyRFjltGarZn4NgFHNowuBreqi0pY6XidVafbpmaceRYy9Qg0leUNyQNmYMTqw5NW9oAW9VLEfLeaA14K4EMgdi4sUeSdC5h4RHVHZwY8s1JfyTl1J7bYDrZg0gIZCDo7PqxALGoPAuAfxrkdEirQOIoTjmhFL08QMA9oqstzDEjMw7wpkV/Po2RNkhUMEcIXjyvPbFLnnFrB5qsNwVG6kVlYbc4C6cH6dZy6XHtPZU13iSPP4uRP0D6d89elbWOuJjeKlWyWISSm4tT+kmUQ8tNljMim4drOkoG+caM2P+ckfeXMLTp1zb0kO6rtVyRzeRnVQr2f3CzT3s/hPJhOef/55RqMRjzzyCO95z3vuCpzg/iWS7gfUjsaEEHDO4ZzDe89f/+vv57/75Y9z8cwqTSFJlKatFHioJzGFCzQduJqmOMxgUNBBIpQgEyBGjm4ck4zL8w+CRxiNtpJ2KjATS2oEtbFDSEHRSzBa47PAZJTRGjiiPJCvlt4OwKgm0FNL0JJpyyCQuHpEiCNaW5Z4O6e1a+kGTXsGemTJugZVjS8U6L1FiDdva0RRPVcj6eSLV6VfC9Smi2fuGmXB8Pz3XqpHwkjMbpnbMRNHbRpYPQj09qG+49AzSXIQsK2IYQy+pYmHx5/v8rkBDoVFOpCpp77lqBeael9QdAy+VuaNjt0DJSCpmQcfqO95kt2AyhaSSqRIVCcAACAASURBVAB5R5K8jLdjp55oB2xdU+iSLHJUP7b4rSTxBJKtgJeSIhKo5Fs9iUHXsXdnxPNfv8Nzz9whMoYiL891/twqd3bKEF6jHvHCld35uLSwPHZug0fPrtGJI156fodnn91idaWJtYvx41mOFPDEwyc52WqUhBvruXyzpLO/89w6d/ZH9Jo1/s0ffDen19/cRf2tCvF9twrFwvc8qLm9kaaFd2tZlnH58uW5LElRFHdds3Bk9xviu1+AOgKnEMJceBZgfa3F3/+v/i1+7/e+xD/7P77MuPKQciwayL3EpBbTMBQCRoWnPnaIToRPLcPcEpSkN4Vh8IjCQTtirCGaAnmBzx3SCHyicD4gEIRmRNHP8UYRpx41sRQzR9HSJFJTyeih64YilCrl07pEBsksksyAxthDXaMKiPZSzIoin+TgArWbKaZu8CFQN5phsHggVRJz4EpdPQG1oCkGFuEDWko6aMZFQZGWJIuNvmA0yQhK4KSkPhLkRpHHUGQeacAl5etnuwblFwoWWc/M9QaPPidDT9qW6LGjkUvsnZzZZkTeKsOQpm/nNHeASVMcYxVGXtCbakY2kNWq/lEJGCcojlTKEcQZpLVAfQKmEIzrisRLZks+k6gtFmHpoTcz2Kll1JHzPFOqA2boKdqVF2cDZjXi1qVBSXyJFFeuL8J2yizu/dy5NSaTjEYcobXg6W+W9UqrKw32xyWCJrHmUkU5FwK8D7zn3Ca3bh+yszvm9s4QBAyrcKAQUIsNj53e4MqtAz76Qwu1hDfL3ioPajgcfs+D+m63+w3x3Y1Za3nxxRf50pe+xMrKCt///d/P+vr6fUkdfScBajKZMBgM5uD0SiD/0Y9+gH/0K/8Oj54/QSIkbalItEZNLa16TJEHEgtNKcmNJBsWyCBJZqV3NJ3lSKFIkghzkEEIJQsv0rhWTDeXxHs5YmbpFhURoBNhhjlWS7J2TE0ZVC7IJwW1mzOi/ZzMO9pH3oCR6OHi2aa+TOwLoFhNKFKLbUfYXoJ0glmsyBLNAZ7gBT7SWFWGD1EapGaoSqWKEBkKrTiY5aSS8jzdiDRzFL0I2zaEpkb3F7VBIZZEB0st3jWYnSWCjhIkw0qdIvP0JgK1VxDtOYJUTBJB0TaIJUcm75ZU/CMTUqCHjvZMUrtt8SkchFL1Y34fEtTu8SLzLLPUblryANOqmWMYHn8vskgQHTqSHYceBAY4ppqSLLFkpnpe8Z5HjwR945mtl0vOxYsnmEzK77yx3sQ7xxMXN3nnmVXuXO9z9dIe3/jGbUaTfF6vdGKzja+ucf7cGt1GzOPnN3hos8ELL+zwjefusLHeKsEJuHh+neEk44lzm/xrF0/x1W/e5rkrO/zoBx/m5Pqb3x79raKZfzeH+N42HtTr2RvRxgPmi/iyee+5ceMGN27c4IEHHuCpp556w5Xm9wtQdxuGDCHgvadWq9Hr9XjppZeYTqcYY2i1WvOuovV6ff59e6sNfum//Jv8X//iaT7z259nnBVESCbTgsh6XN1g91KSmkZpySQEhINOBi6JKKY5ad0QJRFi6MA5jHak7YihLhUPXD1imDpaM4+INBPBnD2WO4fQilAz+CAIsUI6QTYtSPoWGUmol3mkNJa4piHay8jX4lLz1S4JnK7GqLHFNTVCSaJRwawKV+UrEbUcZhWHZbnrhE8U0W5KdqIUxJs2JLWxY1aRKWYdg5o6XJUHmrUUIveEKk+Udw0y86jUU0eRjSyNzJN1DBMCYS0myvw83eMTSXywoMcLKFmSgB47zNDhIkWWeVzXlJ6NhOhgUQMGUDQVuEBzIrCppWhokqnFLtHLi7Y6plrRmUryQSBfX5wnRKLUOlxdeFdaS+Jth2su/m9yRnFBNkiM5vELZR6p22vwjW+WdPB3PXaKg0ry6MyZHpevll5SsxnzwpVdHjjZpdeqcTiYsX17yPadISurFUFAwGiWowScP7NKJCTZIOObgy1W10syRBJr/t0Pv+/VX4A3YN8L8b359rYBqNcL8b0Rkccj0DjaPYUQ2Nra4sqVK2xsbPDUU0+9aTsrpdQ90+HvRuroCJiOgEwpxblz5+Z/L4qC4XDIcDhkd3eX6XR6rA12q9XiR/7q4/zgDz/Cf/8P/phvPLeFTHNEpElHObW6xtlAimdFaWa6BBAXKTQSPcjIWxF1IZnVFEUIxNspPhaoZoTzAWkkbmhLNXGl6Q0dM+cITYM5yChWE3xd085Cmc+pG8zMUdRLIkQ8siS5IKQFWE97ZJkVDhsrzH5GsVoCVhTgyPmadQx6VGBbBiEExpb9lgBs29AYeSYVGy7vRMjC40352eaLDoZCCTqF4oCSDacyjxkUqJrBWY+XAjnz5JsxE4CVmGgvQ1QbYwEwsdBYMDxDq9TsCwL0xGG8RN4syFYMRbe8bnRQ4JYBqaHmNWDCBuK+Q+wG0o0IGhoB2IY6Th2XgujQErRAS8U08oSORk09rr7YcOmaJqNUvNBpYFZXdFREH7d0fcE4yvnKX14FoNmK2a7IEEIK9g4XTNpGMyaJNQ+e6tHt1nnh0g43rx7QfvQkN26VtPGHL2zwXJWvevc7TyICzAYZRiq+8WJJrHj04RN889oOj5xd44c/cI52I57P8zdTmuh7APXm29sGoOD1W27crx3lr7TW7O/v8+KLL9Jut1+1h9Qbvda90uFfy+s6AqajYr9XC+UZY1hdXT1WSX4EWkddQo9A66Mffyffd/MM/+x3v8b+4RQrBNoL0sLR1YbBNEc7SBLNbJhi2zGJMeRTj4okcpJDI0JGCm8UdupZ0ZLMwKRlUKMc14oYGUliFJmDIBXxnRk+EmTtGG09VkuKXoyaFri6Iatr9GGK65VeTuhn0I3LOLcLJAOPzyzOe3oFiFgzGadgHTL1CC3IlSTetrhEAgJjDPUMfOFwhacpBBNXkiKEh24fRtOUIARjKehlEaNYIKTGdzQIKCoHwMX+eF1UL0LnAVsBYr4SEQ0teVuDD0Q56NszXEtjG4asBo0gWA7a2Y5B2YCrtPFCLKlt59SbCYPgsE2DyjxU+TooVeDjg0rbMASSvicUYGuSfC5sIWgFRX+5xYcQrOzDoCax9RJUh8FWOoSLOXXQlhzB7ObpFi9eKnNRJ082uL095OR6k5Veg9kkx08tt2/2uX7zkFlaoI3gaqWtJ2QpBfXeiyfZ2xtzsDfhzs4QrQW7w1JZYqPXIDaabpwwHmX8tR9+dD7ngfl7cTTvl/Os92pvFc18MBi8ogLEd4O9rQDqbuyVQnWvZ8YY+v0+N2/eRGvN448/TqPReP2B93G9NysHdQTUr0SAuFt7NdAajUbEccxP/wcf4HP//Dm+/MUtZmlBS0pm04IYgY4k09RCbOhYKCTo3DGTAuEEZn9GSDStIBhpwdAHVL8gjhSJ0kynBUXdUAwyaMeIRKNtIKsZbAHqYEZkJFHDEMWGI1lSHy+8g7QdkdhAqgU0DGJ/hl8r2ZTTcYFLArQTAhCNCvJG1ZgweIQpl9gJYLZn2PUaKFXWSRUCG1d1UpOCohPPF//iMENUmxYvQe+lsFH1yTCSZGQZdyuRWSVQexn2RAw+0CwEfr9ATjy2rsm0RDYMrqbmAblxXaJHpaIHlMXK8V6OWIv+f/bePLqurL7z/ex9pjtqsmVbnkdJNQ92FQWEPEI6/dIJISngZSU0j+SxilQ6LFI0TRrSCYSQLKqzqjIwFkWT1yRZ0PQiNK+b6hogkApDVck1m6qyZXkeJVuydOcz7b3fH0fn+kqWLMmWbFPl71paXrq+wzm65+zv/v1+39/3hz0aYaREOA4lqc4Skidpq0G5pSXIytq0l0BZEt8T4CXikmrLuPmKo5GBRsaGfGxTtRS6oaeIKHAEHZHFGUvhTigcy+aMp+gqCLpwOTlcZeO6LooFD2MEE6d8Th0tk3EtDh1JjGHXdGc4eDSpK61b20atYdiytoDr2jy7K7Hque6aHn4ylPQ9XdPXQ6w0HRmPXMHl+ZeTvqePvO8t5PNn1bLpxqz1X7hw0rpcIomrEdSrBHNFUGkktBAboXq9zsTEBLVajWuvvXZBxcoL+bwLFTy0nndrOq/1JlwMOI5DV1cXXV1dANx4442cGSvz+fsf5eWXTuIag7AFQWjwBJhQUbMElm2hYoNV8tFtHq4QBELi1yJyAqKcjSIZr1FHUFQ29YpGhxo5WifuyhLkHQqxoWoLdFcOqxzgSws/MrRXYpQrCesxBSMpaZXUxioBTEZUqiODCBXGtVAFB2esQbQ8iwCEI5tRhiq6uGd8wq7kdXHBRUQa4yR9UqIcQneyEKq8gzvmEy5Pnht0etilkLjdbf5u1WNULrkVa1mZpP+EIKslxnGxRyL8nI1vgVmWxa5FzXEdOmvjjQUE3QnpCcDyNXERRKRxx2M8yyGuJFL2FN5YSLD87O+NOAZsMpGAsYA4O1mz6zi7RMSenJL6s2sKq6QIljvU7ERlGRUs8pGk5pyNrBrVCK9qUDmLYFINaPry9OlOfvLiMY6M1dnW38PeyZRcz+oODh9NyKlYzHB8pMqKTo/2QoaJCZ/RMZ+J0xW8QnL8nmtxdGSCLeuXUcx5HDxyhlLFZ/Wqdg6MjJPNOPyrO7Zx2w1THctT0mmNelrJqjXlPR/SupriW3y8pghqLiyEMMIw5MCBA4yPj1MsFlm7du2ClTSXylcvxfQ602IS0/nQtayNj9376+wbPMGDf/1dhkeq6CDEciz8UGM7FroRIHIOwnFwGxpjNHlPUrMtoiDC1BRZS+JpwTiaihTIWoTJZxBKk6tD3GgQaoXVlkFlbKy8i1IaLDkpqgAKGcrGYEUCfIMwko7xKBkTLiGXdfGlwTeGuOA0iSfMWDijdaLuyXxce6ZpJGs8i0I1ojJZe4qWZ8k0FH4aSeRdpAE9+acWk1+f9BXSV9jVCK9d0qiHGEciGzHRyhwVDLgCu6KgeFYMkXUcKi1/X5VzmsQhG4q86yKP+ISdHirvUge88ZCg+ywhqZZIEm2wfIN7NCDo8hCTRCaFnJL6Cy3wzii0BXnHpSLAFCWOFs20pADwNThQbAgkkpoD+VAk5zOJcSfm2aGTiChRc1aqZ51OCh1Zin7AquUFDBEnT8aMDTdYdWMX+w4ns516+1bx0uAwq5bn6OjwOHayysEDo2zc2E6p4iMEdK8o0tGRY2y8xm+/4/Z5XatzkVZrpBXHcfP+kVJO+f1S4kKczH9acJWgWpBKzc/XNKuU4tChQwwPD7Np0yb6+vo4cODABZHGhfReXQhBpb1MpVKJXC6HlPKy3Ehb+1Zz3xd/i39+ZBff+PsnKdeSwYQOmsCxcBXU/QCZtQmkJPRjHD/CbvcwyhBYkjBQFA3EWhFFMSZjYyyJExuiXBKlOGfquG0CE0R05V1KcYzybIqBpmKTzDJSBi0EJuNQ8yNM3gNLUjUGpxRhZx2kkdjjAbLoEdQCjDZ4J2o4WZsoULiRwm3PYLkWsQZ3uD65mBscKZMaFyTTal2butIIRyI8h2IZyrYFrkXU6SCVQXVMRnJZB8dXRJPqwajLw65GxIWEpKouiSiky0PEhoKwcCY0vgN1y6IqJhumW/zxwoJ9NsojccvIj0YYKYhcic45uCpxiUgJybfAHY8JuxykBmc8Bm3QRZuq0AkZWYJ2bTFmTUYYBlQjJlvWNDpdmBRI1KTGUoJ05mR7ZDHRFtNxCvr7ezh8dIxtW1fQVvQ4OVymPlZnNNZU/KTZtrMrx+D+ZJz7+rWd2EKysj2PULDvUIk41mzcsIwzpTp9G7pAal74STJc767/63rKE6MYVaRYLC44ypmNtIBm8/rw8HCTwKIowhiDlLL52qWcE3WVoF4luJhmXa01x48f58iRI6xZs2aKI/rF2B0tlGwW8lmtu74NGzZMkYynyrvpkvFLgZ/7Nzfyhrf08bd/8zADPz5EEEB2UtWXzzjUIoMMfHIdOaKsRPnJeRSMoWbAx4C0EJkMhWqEHyt8KbCkQLVlUO1ZZC1A5z0qscH2Fa6SxGGEMxGhPZsw71AINVVXYjIOmUqIX3STFF6ciAa0EARFj4wy6GJCHvaZBoHnggdGaYJIJeM9bJucBfXJVJ0PWBM+cVey2anFGrRGTzbn1moh5BMPPyEEroZUmymkQJQiyJydFyUDDYUk6spGoCoxMk7k93VpQGmMLRCTrY21jMAuh8Rtk1GTI2lraHxtyPiGSAiEmzirp3J534I2X1Bu2Z+5lk22pKlL0UxDFnxNpcUx/YyKsUKN3TCQsVAZG6mnXaO2wCopLAnCklQdBe02bTcWCMshYTlg/8RJVm/s5OTxJL3X3dPJ+NAIUgq2bOnGb0ScPDFBPuuya1dCPhu3rcBuBPRuWoEymuqET9ZxGK3VWdGV5+ff2Mv/+eZrqVQqnDhxgmq1itaafD7fvP6LxeKCR1Wk934QBOzevZtsNsuOHTuwbXtKpNVa402/y4sVY0zH1RTfawQzLf7GGE6dOsX+/ftZvnw5t99++zkXs+M4FzRVdylti6Y7QKxZs4Y1a9YASXqyUqlQLpc5derUFNJKf7LZ7JKQltaaI0eOMDw8zDt++w289/d/mb/77Pd56gd7EbbEjzQFCSrnocqJ+i2fc6kKSSMyOFrjuDZSa6rG4Ds2GSHwLQsdKwr1CN+P8Noy1LXBSIHjWATKgOPgSptQgggFfiPAjTVGQGwJijmXmjDogod9pk68LCHuqBbAZHQTdWZx/Zgwk/RJZSNDqqmsZ23cakg4WRuxCh5q8hiwJfaZgGiSoHTexRk7mzKsugLnjE80WdeK2j3a6zpx56hGKAOZYw3irmyipOvKY5d89OQUXjwLb9zH705eLwBHWsSAXQqxGxqTz6BjRc07Gwk4Y5P9YJOoxTEitshUFEoZgrxDu5YY+2x6riZpRmNuZBClGKMN8bKzKUSds/HKiqDNQipDh3aoO8mwwkbLex20fSaO1bG1Yc2GNo4dS8hp85ZubCm4ZusKjDE89/QhjIGtvSvZs3cEx5Fcf90a6n6ECTTSEryy5xSOI1m7toPcuEMu6/J/v+N2bNuakn7XWlOv15stEwcOHCCKInK5HMVisUlc51PgGmM4evQoJ06coK+vrznNFs6NlhZbjDEdYRiSyWQW/LqfBog5ZNeLr8m+jFBKnZcQDh06hOM4zYV8fHycvXv3ks/n2bp166wXwalTpyiXy2zdunVBx7Nv3z6KxSIrV66c92uMMTz55JO84Q1vmPX/L6TOFIZhs8+pXC7TaDRwXXcKaWUymQsmLWNMczFYuXIl69evn5IyadQC/t+//g7PDRyk1oixbEHVj8gXPKqxxjMGO+sQG0Njsq6UM1D3Q4zQyEKWWApkI0RnnCRNVa6T7cgQx5qwEaKWJzK1XBBT9xKisCbqqI6EJETFRxc8LK1xpMASUK8FIMBojd2VI4gVIohRXVkQAgNYEw1UZxJ2eKEicGUzTdYWaEqTtSgD5LShjkFGGtmIyBQ8grKf1MeUxm3P4CuN9mysaohqP3vNZSJNw5PNOU5OrAkdcdZJ3YBRCgTYlYiM4+LXg+RYJ2FPTCUkQg2eQFvglGJkqCnkPCZaDPVFpNEumElhBsbgjoY4RY+6lRyOAbJAvWXv5vka4ydilNQR3Y3B95Lal9AGr2agoek8FtLbvwpLWpQn6kRGc/JECcuWLF/VxvBwGde16L9uDYEfUSo3GK/51OshW7Z0YwRkHAfpSnbtOUH3sgKf+fP/i86O+bl8G2NoNBrNjVulUiEIAjzPa0ZZxWKRbDZLrVZj9+7ddHR0sHnz5gsSRkwXY0xfh+dLWsYY3vSmN/HCCy9clrT9ImLGg79KUC04duwYSimWLVvG3r17Aejt7aVQOL8l/9jYGKdPn6a/v39Bx3Pw4EE8z1twD8MTTzxxDkEthQAiCILmzXoxpFWpVNi7dy+ZTIatW7eed2daLtX58n2P8uIzhwlChbYEOohwCxkaVR+d8fAsCMII5dpkHBvfAI0A0Ahbki1kqAgBBkS1gSlkwRicKAJbEAVx8r7FDFiSvCERUQDWeA3VmbQIWOUGqn2SvGKNwWCcZDGS4zVMZw4TxTgGpGdhpCCsh4h6iMm5OBmbwI8RWmMyDtK20PUQ00o6tZBGi7rOGq8TLT+7qNrjDaJlrb9P/X9nvIEuuuSUAKURsaacd5t3uxPpZGbU5HdkjMFRmjBjgTHYlZgOx2FcJ+pFAGKNsGg2HAMUIgg8yIWChjbEgGcJGtbZJUI2YuKCRS4UxPWIOGPjNhRB+9REjV1JNiDKsZrCkdXGJdiVNN9ed/NaXnopkYbfeOt6okgRRwon4/DSyycQUrB+83LCKGblsgLHRsqcOl3huut6CGJFMedx9//zJtav6Zr1OpsPjDEEQUClUmneA6VSCaUU3d3dLFu2rJkiX4x03fRIa/ogQmMMlmVNEWakBPXiiy9e9OdfZsy4iLymUnxzLaTGGI4fP87w8DC9vb1Twvbz4VJP423FUirzPM+ju7ub7u7u5mMpaZXLZU6cOIHv+81dZvrjeR5CiKY5bqPRYNu2bbS1ze1/1tae40N//nYqpTp//+nv8vxTB6nFGhHEaCEpSgiVIec61GJD6NcTT7pilpww1I2g1lDkVYzMOAS2RRjG4NrgOMQAWSdxuahrbKEIaj6OLbGLHmHew1aK2LJQbVnkRB3dkcPYknysmma0dOQgTPq4IiBTD/ALHuQ8yLpY2hBaEpG3kBMNlOckLa3FDNZYDbUsIcFGzsFpRETZJPTQ7VlkqNCTZBFnnYQc7URRZ6TEGW2Q9RyCRoSSElHXSURoWRjLwqmETUl55EiKDUVl0mJJqKSfql4JUJ6FcWzGjcZSCekAYEusCR+9PIOINXY5wtcCO+9MikySp0XVCCbJR8QGu6ETl/iuDGQTe6UwZ+NWFWHBomiScSpVW2IZiFou0+HYJ9dm0eN5VCoNrr9uDVIKXvlJMk5jW98qXnr5BD097axZ08mx42cYO1PFsiS2Jdlxy3r2HR4limI++Im3XzQ5QXIvZTIZMpkMjuNw+vRpNmzYQE9PD9VqlUqlwsGDB6nVakgpm1FWsVikUCgsuhgjJazWx9Ka2qsVrymCmg1RFHHw4EGGh4cpFArccsstC1rkL4agFjpIMMV8HSAWGzORlu/7zUjr+PHj+L6P1po4junp6eG6665bcI682J7j/R//VRqNgL//y3/i2SeGMLGPCiJ0EGNcBzsM0RkX25PEtRDtWeQtgS8EATKxBnJt8togI0Wt4gMauoqQcWkXUDZAMQ+lGlGcuHFbtQDbsVBBjFEKrxEShIqaYyFrProjjxYCT5mmsKGRdRG1AJP3MELgKk2cDvPtyFKIk4UZQOcz2NoQTwokdKBgkqCMNlhn6uSWFxCRwkIiaorIhYYyCNfDLjVo5CwoJA26XiOiMRmUChIPvDhV4xlDpAzuSB2kROddqkIgI42ZrJUJIRCBOuuGrhL/pI6SomIJzORIdF2PoWg3ozGds/FO+WTaMlSVQWcdjIGcEtQnIytLG0RdkY00jezZya+RMUhfI7Uh5zhUtaHR41EPJGf2j2E7knynh4oVPT1FXE+ycnmBYt7juRcO096W4cab1nNyuETGs5moNLimdxW//a47WLcI5JQijmP2799PtVrlhhtuaA4G9DxvSoN6HMdUq1XK5TLHjh2jWk22Mvl8fkqKcKGNvLOpALXW7N69m/e///1s2bLlYk7xisZrKsWntZ7iWK615vDhw5w4cYINGzZQKBQ4duwY119//YLeNwxDdu3axY4dOxb0ulOnTlEqldi2bduCXvfEE0+wY8eORW+yvVikgpIDBw6wfPly2tramqmRIAjIZDLnRFrzRRwrvvHg4/zwsZcolfxk+uzkAh8rjYoU2nPRxmD8EMuzyeQcfAQRAlGuYYrJ4iLrDZxChnrNT+xy2nNoKcmqmIY1GRFM1DAdSZTjhiGhN5mGixWoZMdqlMKzBE4xQ+RH+DUfbEmuPUu97INSGNsik3cJqj52xsXJJJ5+qh7iKw1CYHs2cdVP0ol2snu2aj6qLdP8u0o/Qhe85u+e0gTu2dqWF8b4WRuhDVY9QtRCjGMjcm7i81cOiLtaNgmhQmQkKq1fxZpCZGj4MTrrICyZ1NoyFrTYFGVDnTQHh4bAJFGXDQQt664IFBhD1naoa42wBB7QkIkHoAXklYVSGmULgha7JKuhyFY1t29dQ70ecurkBHbOYXi4QmeXR3tnlsBX5NuzjI37rF/fxcnTFbZs6uYDv/NmisXFEwuMjo4yNDTEunXrWLNmzYLvM611M9JKf5RSTTFGSlznm6A9E6Io4tOf/jQPPfQQX/jCFxa87lyhuFqDMsYQhiHGGE6cOMGhQ4fo6elhw4YNWJZFvV5ncHCQW25ZmNux1pqdO3dyxx13LOh1Z86cYWRkhGuuuWbex6+15uDBg4yMjDTTCumCn8/nl7Tf4nwol8sMDQ2RzWbZsmXLOeRjjGlGWq1F6Gw227xR29vb57xZjTE8+t8H+P63nufk8XFiI4jDGJHx0HGcLIxtGWIEvjIIP8DKuhitCYMQ0ZZPFnQBASIhHK2xXRsTRbh5Fz9URFLgORbBZLrFqTWIConYQJTqmLQ2pTVGafCSCKgoDOW03hPGCEtgJklHjNfQy87WM+26T5yfVN1pgzEa7U6u9I0Qk7XBmpynVA3QbWctk2TFR+UccgjCiUZyHp6DziXpVZTGsgXRJLkYoE0KSi2XRzGI0Ri0kQQyIQ5hiSn9U14jplG0kb7CqkVYXjJny7TMnkqJzJYCUQoxUpD1XKqWbh4vQCFORnzUtEk2BgCxBgx51yHSJpnhBVh1hTcacsst64mjRO12fKREFCk2bl3O6bEqubyNkJqbru/mjh0bmtfRhaTXWhGGIXv37kUpRV9f36Iq5Iwx1Gq1KaQVhiHZU9X6FQAAIABJREFUbPYcBeFMhPjyyy/zgQ98gH/9r/81f/RHf7ToXp+XEVcJSmvNiRMn2LdvH52dnWzevHnKghiGIS+++CK33Xbbgt97JuHCXCiVShw9enTOiG22OpNSqhmhlMtlqtUqlmWdQ1pLGWEFQcC+ffvwfZ/e3t4FDWCcTlrlcrl5s7ZGWrOR1stPH+C/P/A4xw6cJlKGKFJYrkUQG2JlyHkSY0sa1QAKWTDgYgjCCK0UuDaykMFGEE4qA2kECdlIiWUMKgwxymC7FkYaIgMy45CxJLXJRVCU681oy2iDCALMJPHktaJqnY10slrTmCQs/AgrY6PSHplyvSnQAMhHCt+TmHoEYYwIFXbOJY402Ba21oT5swtUQWkq7tmFORMr6i2Tba1qgIk10ghk3iNGIOv+FKWgrIXE7cl7ykZERguiRkTcnmmuIM3IypagDHY1Ip9xqUgzZZmx/Jgoa+EGGqUMuDaONviOAAkFaSMiQz1W2BhCT+IagaPBV4nE3q7GdLgOGzcsJ/ZjvIJHrBQ9azq59eb1vP72zUjJFCFDml4rFApTIpW5SMsYw8jICAcPHmTz5s0LUtdeDNL7oFVB6Ps+rutSLBb58Y9/zE033cR3vvMdHnvsMR544AFuvfXWS3JslxBXCUopxa5du9i0adOMbhFaawYGBnj961+/4Pe+EIKq1WoMDQ1x8803z/j/FyKAiON4yoJfr9exbXvRe5yUUhw5coSRkRE2b95Md3f3ohBhKvdtPYe0R6X1HFp70cZHK/z3z3+P536wlyBShIHC8eykv0kZfAU5V+D7EQoQto1xHFwJQaRAKyQar5gjEqAaIWrSlULU/CbZ4IfgOpNRjcE0AqRjYzsSW0CsDUEjwGgNtiRbzCTkqBS4DpmCi9AGJQSRH+NlXRrjVZhUBmYLWRoTtaTmY0lwHUTdxxSz6R8HV0CQRskGLB0TTUZdBpD1AF3MII2BaojwQ3BsZM5DCZFEXh1nr30TKayMJJ60PMoqQ1RqYDIuZjIqTFR9BjV5nMIYOpCE2tDQZ50nZD3xGBTGIKsxwoCXcZJG4snnuIDwY6TnNKf0SiAnJBJBI1ZEwlB0kzEkgVJ4SGxLkHFs+ras4G3/5iZuuWmqr950pOm1dMGvVCrNBt3WmlB6Hfm+z549e3Ach97e3gU37i4FgiDgzJkzfOpTn2JgYICxsTG2bt3KLbfcwtvf/nbe/OY3X+5DXExcJSigmeKbDRdCNBf6Ot/3efnll9m+ffuUxxdbANE6yyklrQvtcWqtM/X09LB+/folTysaY6jX61OixZlIy7Ztvv+tZ/jePz7D0QOjGCOoB4pC3sEPI4wBZTvJiPBGgLEmSYRkdEZWaBomke7mnGS6rJtzqJcbmJwHrkMWTUOmabjJaMtKXiMaYZPMCtJQnbznjFI4UhDJyR18+Wx9K4mqFI20eK50QmiTwgQThAmBpVFXPThLYAA1H2NLsraFqocIATLj4qfXjDF4tmzOtwIoCkFZAsaQEwI31kQCfC0wIvl7u0YTuGfTeF6siYIIFJiMk7hd1ENU22QEpw2yEVHIulTM1NSebERkixnqtRDjnHVeL7o2ShtqUeJh50mZmAQrhYjBy9hYUtCzsp2ffeNWfvkXb8R1LlzX1dqgm15LqX9eEASsX7+eNWvWLLgmtFQIw5D777+f733vezzwwAPcfPPNlEolXnjhBXK53AVleq5gXCUoWFqCev3rX78gIonjmGeffZbXve51zcemO0AsVXqutTG3VCrNKBefnnsvl8vNxuUtW7Zc1hs5Ja1W4o3juLlDNpHkn772LC/8eC9nRmsYIDYWjiMJ/RDpOViuTajAsyCKFG7ORSuNjwTLIoPCnxw4aAUBsetiS0NYqSNdGy/vYduSAAhDhTFMytmTRVRW6+i2pFZlK0UkJaT2WPWzNS2jNNJotJvs2u04JnYTtZzUGjeMCAETJF54uYxDPVQgJca1KUhB1Tq7SXDjmCDTEgH4ib0TImmmDSYaiedeMds8HlFtNBuWIYmSjB8iY4O0LJRjJVL/nH32NcbQ7liEsU5ScmmqshFBwYF6DBqMZ2MLgWtLtISwmtSpsCSuFGQdm0YjQgvIZRy0MvSsaOOWm9fzzndsp1hYGpeEWq3GK6+8Qi6Xo7OzsyloaK0JpdHWbDWhpcKLL77IPffcw6/8yq/w0Y9+9IqI6JYYV/ug5osLmQk1faruQl6TfualdBp3XZfly5ezfPny5mOt9aBjx441lXf5fJ5KpYIxhr6+vgXVmZYKQgjy+Tz5fJ6enh7gbAG6XC4zUZ+g981dbHnTbVRGQnZ97zBHh8bwGzFOziWKDUEthCCE9hwZx6Jej0AI8o4hChXaaGjUEsLJZfCEITQSq1DA1OqEShAqg6nUsNoKyTRebQjKDcykeCJbbRBGyfdqKYXXnseyJEpaWOU6kdK4noNfC5GWn6jnbAt5uopozyOkJMZC1uro9kRgUQfyGYuaTGTxVSATRPiTKbnQtpFjVUTWwTYQBwpZCaAtRyQEMpeFSCENzVm3ppDFrfhI20IKQYwE4SCzyQBEAZBxaBOCWiVIiCfjUA5jhB8lvoJa40Qax3GIfYO0LQIhkJHChJrYTZpM814iR280QrRjoY0iZ1t0debYvn0jv3bnrXR1nb85/mKQqndPnTpFf3//OVMIWmujaZ14uqvExTqrzIYgCLjvvvt4/PHH+fKXv8yNN964qO//04bXHEHNNRNKSpksJgtUAbVO1V3IscBZR+T0scslG0+bElesWAGc7QEZGRmhra2NOI556aWXzlsPupwQQpDL5RgfH6dUKtHX18eKFSuo1+vc9n/cSLlc5pl/foVd3z/I6PEKMlaQc7GMplGPkdrgehYmlqi6j3Y9pOeRdSSNICaMFQQB0nXItmUwRhEZiDIest5A57KECoQfIApJCk8xqVibVFuZRkjD8wCJURLHc4iExCrYOHFE6DhJLam9AJU6tE+mAnNZZK2BzifzqWqapA+MJLIKlaatDaq1CGFbGMcjq6FhWc2mWcePCCdTh8KWyFqQpAA9lyDWaNuGWkjUErHI2CAaAUIb3KxHzYCIQWbsRGJuNJmMgw4MkVLETiIfF0GM6zk4k8a+kSdRjQhpW4SxwRaGgiXo6shw401r+JVfu5XVa7qXPF1cLpfZs2cPy5cv57bbbpvx84QQZLNZstlsUyjR6ipRLpc5efJk01mlVX13McbLzz//PB/84Ae58847+Zd/+Zcr5r66nHjNpfiiKDpv5/Wzzz57QY2lL774Ilu2bJnTFilFGjHt3LmzWQ9qb2+/Ihb8VjXT6tWrWbduXfNGnknEEMfxjPWgS40zZ84wNDTEsmXL2LRp06ybDK01tVqNp/7pRX74zWc5eXCCStlHILHcxPEhUmDbAm0gjmJ0rLCzHtJzkIJkzLzWEISIbAaNIe8kEVXkR+TbMtTKSRO2MZpsZwGkSDp+YkWkwXIswmqjKVH3si7+eDVRFwpBtuAlNSmZevsJdBwTGoFGJGk4o2GyR8vECoyGzOTv2kAYQs5Lohg/xMQKr6NAECfEaSmFapHCg0HWQ6Rj47jJsEcBZDMWVWUQxuAag/IjdKyT2pxIjsWzJI4lUCrxSxSxxrUlwpJopclmHFzHZuPGZWy/YxNv/lfXEIZnm7yr1eoUR4a2tjYKhcKikJZSiv3791Mul7nmmmvmPfF6LrQaL1cqFer1+hQlbbFYnLP9IwgC/vN//s/86Ec/4sEHH1xwH+arBFdrUJBEBedzA18o0aR45ZVXWL169Zy299MFEJCk1kqlUnPBV0o1aynpz6Wa1Fkqldi7dy/FYvEcGf5saE2tpTeqUopCodA8/guZwzNf+L7P3r170VrT29vb7PZfCI4MneT/e/D7HHz5KKdPVAgjhZgkBsuxUUbg2IJGmKTuTBiRX1ZIUnBxTBDqZC6VhNhKCCdrGRqTLqkmDDGWjbATDzxHKKLJ57lCE2Ml0RBArQ5tqWxdQxRDdnLDFMUIKTCpWCCOsTwbZcAyBttopCPRkUJrUAgsSxCKswtkzoLa5FgOB4OtFMoYhG0TxMmU5awlqKtEfecKiP0IHStkzmvWmjK2RCpNEMZoJxmA6NkS27IIwpisZyOlZMXKNjZvXcHP/5sb6Lvu/L6Tra0TKWkB55DWQq6lM2fOsHfvXtasWcPatWuXPEMRRdGUPqfpxJs252azWZ599ln+/b//97zzne/kwx/+8GXZ2F0huEpQMDdBvfLKK/T09Mzbhy/F4OAgy5Ytm1LTmY75CiBaF/xSqdSs/0xf8BczHeL7Pvv27SMMw3kZ5M6FNEppJS2t9ZQerYs9B6VUs5awdevW8/7tF4Ioivjht57jqUde4Nih00ycriFEYr2HANe10EikFASxQSNwpSHCSlR5tsEPFVIKHM+mXg1wMi6uZ4FtEytNGMSYOMbKJXWMuN4A10VaEulY2FqhnSSSsiZ73pQ2oJOIJqyHyQgPz03cUaSFmIzEzGTzMZmzzhM0fNyiR1RN6keJWavbFDxAIlnXtkV2kmyMMkjHohYmzhC2AO1HKG3IFLOEscZzJLZIJPyeY+F4NsuWF1i3cTm3/cwWXvemXpyLUN7BWc+51n4/mLvPKYoihoaGCIKAa6655rKOpEiJN51L9e/+3b8jDENqtRp33XUXv/zLv8xNN920aJHdTyGuEhTMTVB79+6ls7NzitfcfLB//37y+TyrVq065/8WQwChtT6nKVcI0bxB29vbL6gpN50QfPr0abZs2cLy5cuXbIfZ2ptSKpWm7I5bz2Eu0mod3bFq1aoll7pPjJZ5/JtP89KPhxg+PMrEmRpIgYqTxtQ41ghpYTsCrRPncMe18SMF0kok5johMhNFIEC4buJoIQ3BpFLQkaCFQU1OEHSMIpKJms9ojSshTCXuSuFlbILJbLWFxvVslNJIwJICYyBSSdOyJhkK6RuBmRyQYU+O5pCWIGzEIAWeZye9YZZF1rMxsUJrg2UJYg2WEFiWJIoUti3I5zzau/Js2rqCm+7YzOt/rh/LWto6Eky9ltL7QWvd3MTFcdycer1q1aorxg4M4JlnnmlGTW95y1vYtWsXzz33HNu3b+euu+663Id3uXCVoGDukRsXOgLj8OHDWJbF2rVrm48ttTJPKTWlFlSr1bAsqxmhtLe3z9qUa4xheHiYQ4cONVMfl8MmaSY3DCnllPRmK/HWajUGBwfxPG/O0R1LBb8e8NTDL/CTH+/l6NApzgyPE0UapQ1aG8IgRthWMhrBEknkFcfoOMbKuGSyHpYlibVBq2TqqpP1kn4rY5ASch0FoiBCWgJp2Ug7qeMIQGmDsCRhqLCMJpRWs+dJxDHGc4FEDCTjZFRJ7EeJkaxrgYFGfHaOUz4jMVJilCaOFLEGKcxkpCWxbIkwiQltW0eOFas66LtpDdt/tpct/Qu7T5YSWmvGx8cZGhpqKmqNMRc9PXex0Gg0+NSnPsUzzzzDgw8+uODxPK9yXCUomJugjh49ijGG9evP36k+HcePHyeKIjZu3HjJJeOtOF9TbirCaDQazWGJW7ZsueyijOmI43gKaaXjDFKH9K1bt7Jy5coraldcGqvw/PdfYfCFQwwfGmXsxASViTr1RgQmqesYKZEYpG1jEMkdadv4tTDxA8w4CMdGa4PnSIJ40pdOCnSsJutJEpQiihUgyBYyBHUfpTSWY+FmXPxqABjIJPZERmlsC6RrEwcRUgi8bNJvFJtkyq0lBdICIWRigo6mvSvHqrWdrNrYyfreLord9oyp5ktVHz0fUn/NI0eOsG3btma6t7U5t7U+mop6UuJa6ntgYGCAD3/4w/zbf/tvueeee66Iv9kVhqsEBec6mk9HKh/dvHnzgt43dSbfvHnzJR+BMRfSGU6pOW0cx7S1tdHZ2dkkrSule346jDGcPHmSQ4cOsXz5chzHaRJvOqY+PYel6Eu5UDQaDQYHBwlqEfEZwdHdw5w4dIqJ0QpnTpVo1ALCICYKNNKWCCnRyiQEJCVKGaRMYpwoTq4l2xEEfoxB4HgOAoNSJolyHAsVxsmoD9cmjjVxrHBcC4NMxBYIXM9CSoGXcXE8m1zBo2tFkZXrlrF643LaVjloJ5nfNVOaezYLoctJWvV6nd27dzcnX88lNGg1bE3Po9WZJCWtxbgnGo0Gf/7nf85zzz3Hl770Jfr6+i76PV+luEpQMDdBjY6OMjY2tuALaWxsrGkyebFuyouNtM40OjrKli1bWLZs2YwmrblcrrnYXy6peCtSRWFbWxubN28+Z5c705j62YYnXiporTl06BCnTp2it7eXrq7zzybyfZ/9Lx1m365DnDoxxpmT4zSqMSZOFONGJROAAcJAISdVg8YkkZhly8RmyJZkcx7CEkhb0taRJ1vMkstn6OgusGJtJ91rl7F60zIyuXPFApVKhT179tDe3s7mzZsX9N2ngphU0HOpSEtr3fSD7Ovrm1NBez5Mt9NqdZRoJa2FpJSffPJJ/uAP/oD3vOc9fOADH1i083/ve9/LQw89xIoVK3jppZdmPJd77rmHhx9+mFwux1e+8pWmueyjjz7KPffcg1KKu+66i49+9KOLckyLgKsEBWdHbsyGiYkJjh8/znXXXTfv90tTTydOnDinjpIu+BfTwHehaK0zrV27ljVr1sxaZ5rJOuhSSsVbEYYhQ0ND+L5PX1/fghSFrRN/y+Uyvu9f1ByqhWBsbIyhoaGLFm7MlOJcKpd6pRQHDhxgYmKC/v7+RXMJmU3FmV5PFzrAL0WlUmH37t3NnrelqJ+mPX+tpNU612y20Rj1ep1PfvKT/OQnP+FLX/rSgue9zYUf/OAHFAoF3vOe98xIUA8//DCf/exnefjhhxkYGOCee+5hYGAApRS9vb1897vfZe3atdx22238t//237j22msX9fguEFcJCuYmqGq1yr59+2Z1GG99n/PVmVpdxUul0oy1oKWUvU5MTDA0NDRr9DEftC4yqerOGDNloVysRsr0844ePcqJEyfYvHkzK1asuOhFOHUASM9h+kiP9vb2Cxoa14q0Dyu1glqK7zXtrWmtLbYKYi5kEzQ6Osq+ffsuWX/Q+UirVcRwPtJSSnHw4EHGx8e55pprLrodYqGYPhojHcZ5+PBhnnzySVatWsX/+B//g7vvvpv3v//9S7ahO3ToEG9961tnJKi7776bN7/5zfzmb/4mAH19fTz++OMcOnSIT3ziEzz22GMA3HvvvQD84R/+4ZIc4wJx1YtvPnAc57wiivkKIGzbpqura0qKJwzD5iKZet21LpSLUaxtNBpNFdO11157UX0Vrc2Fa9asAab2pBw5cmRO1d18MTY2xr59+1i+fDm33377ot3YQohzLJxa3TDS1GwURVOao+ej9kpTTMPDw4vahzUTHMc553pKBTGVSoX9+/c3R6u0biBmIq0gCBgcHATg5ptvvmT9QTNdT62kNTw8zNDQ0KykNT4+zuDgID09Pc2J0pcarTZIrdfTypUr+e53v8v//t//m5UrV/K3f/u3PPTQQ9x7773nTCtYahw/fpx169Y1f1+7di3Hjx+f8fGBgYFLemwLxWuOoOa6qFNPvelYjBEYruvS3d3dLD6nu7FSqdRcKFsdudPd/XwW6ziOOXToUHNmzLJlyxZ0bPOFZVm0t7fT3t7evNhbo8UDBw6cM4Oqvb19VgFDo9Fg7969ANx4440zzulabKSefblcrtm31priPH36NPv37z+vo0dqq9Td3c3tt99+WST6juOwbNmyKd91q4rz1KlTU8QkxWKRer3OyMjIrCKIS425SGtkZIShoSHq9TpCCNasWUNbW9uCjZmXCsYYfvSjH/GRj3yE973vfXz1q19tXgvDw8OX5Hqe6ZimYzYP0itFVDQbLv83fBlwPsNYy7LO8eqb7gCxWItR626sdaFMC84nT55spo5ma2ZNVW6HDx9u5pUv9WI5W7RYqVQolUoMDw+fI2AoFAqcPHmS0dFRtm3bNqeYYKkxkzt6q0Q53d2nbQq2bTcFJ5eDnGbDTKQVhiEjIyPs27cPIQSWZXHkyBEmJiYWPA/sUqCVtE6fPs34+Djbtm2jra2NSqXSPJfWDUR6f1xK0qpWq/zJn/wJQ0NDfOtb32LTpk1T/n+mpv1LgbVr13L06NHm78eOHWP16tWEYTjj41cyXpMENV9cjn4mIQSFQoFCoXBOWq1UKnH48OHmaHfXdalUKnR2drJ9+/YrSiruuu45C2WqHDx58iRjY2PNdNTExATGmCvCKLcVUsrmd7Fq1SqOHTvG8ePHWb9+PZZlMTo6ysGDBwGWrC53sUjtoCYmJrj55pubIohWBWSrM/eFDLFcCoRhyODgIMYYbr311qawpVgsNhfV1g3EqVOnzol6l4q0jDH88Ic/5KMf/Si/+7u/y+c///kr5vsGeNvb3sbnPvc5fuM3foOBgQHa29vp6emhu7uboaEhDh48yJo1a/j617/O1772tct9uOfFa04kAXM7mj/xxBO87nWvuyJGYMyEtMcmDEPa29vxfb8pwmiViV9O77GZUK1WGRwcJJvNsnXrVhzHOa8zeprivNypnImJCfbu3UtXV9eMLunTveIqlUozCmity13qRSxNVc5XBDGTAvJSy/ZbMwJbtmxp1nkW8vqZjItb3SQuhrQqlQof+9jHOHToEF/60pfYuHHjBb3PTJhLAn7ffffx1a9+tblJjeOYnp4e/uzP/oz/+B//I5lMhu7ubizL4o477uDRRx8ll8vxX//rf2XHjh1AovD74Ac/iFKK9773vfzRH/3Roh3/ReKqii/FbASVRky7du0iCIJmraW9vf2S99PMhLnqTNPVaqkIo5W0LkeEEkUR+/fvp1Kp0NfXR1tb26zPnb7AlMvlZtE8PY/FNsqdDancPQgC+vr6FiQ4abVwKpVK50jF29vbl6z1IFUVQqLguhhZ/XTF2lKSVqPRYM+ePXiex7Zt2xbtWp2NtFpHxMwlijHG8Pjjj/Of/tN/4v3vfz933XXXol6DC5WAf/vb3+av//qv+f73vw/Axo0beeaZZ5ZUqLPEuEpQKaYT1EwCiLTYnC72vu8vuuJuvmi1cVm3bh1r1qyZ14LQqlZLzyPdTbYu9kslhTXGcPz4cY4ePcqGDRvo6em5oIVsujFopVJppkLT81jMCMUYw7Fjxzh27Niiyd1hZql4q5ikra1tVu/EhRz38ePHl0xV2Crbb5VZX0yvmTGm2V4wn+bmxUAraaXfyXTSymQy5HI5yuUyf/zHf8zx48d58MEHF2yDNh88+eSTC5KAv+td7+Lnfu7neN/73gdcJahXFVodzRcyAiNV3LUu9mnjYXt7+5I4SKTmlx0dHWzatOmiSXF6b1OlUgEW7ig+F9K0WEdHx4KdCeaDmUxmL7YvCBL3isHBQTo7O9m8efOSNyafzztxIbWg1Aki/XtfSieT1hHp6XcyX9KqVqvs3r37shz3dEy3QPrTP/1TXnzxRXzf541vfCN33303O3bsWPAonvngH//xH3n00Uf58pe/DMA//MM/MDAwwOc+97lznluv11m7di379u1rkvmmTZvo7OxECMHdd9/N7/zO7yz6MS4xrvZBtWKhAoiZFHetFi/Hjx9v7uyLxeKUnf2F7Ijr9TpDQ0MAXH/99Rc0hG8mzNbblN6UrSKMVpn4fHf2QRAwNDREFEVcd911SzbfxrIsOjo6ptjbtEYo+/btW9BiH0VR8zXXXnvtJWsAnUl11xqhnDhx4py0WppyhrOTYkul0qI6QSwEs41IT0lrYmKCI0eOnGMdND4+3nSwOF/a91KhVaCUy+Xo6uri2muv5UMf+hAnT57k4Ycf5gtf+ALf+ta3Fv2zFyIB//a3v80b3/jGKZHmj3/8Y1avXs2pU6f4hV/4Bfr7+/nZn/3ZRT/OS43XJEH9wz/8A21tbWzfvp3ly5dfcLTQutinSEdglEolDhw4QK1WW5CDRBzHzU75rVu3XpJ0x2yL/fR+mtkWSZjatLrUc6Vmw0zNrKlarVQqNRf76Tv70dFRjhw5wsaNG+nv77/stUbP887pl2slrbTJW0qJ7/usXLmSG2+88bKMHpkNs5FWo9FgeHiYV155BctKRpIcPHhwSi3ocqpRjTH80z/9Ex/72Mf40Ic+xHve857m+vDud797yT53Nmn4TPj617/edIlIkT53xYoV3HnnnezcufNVQVCvyRTfQw89xOOPP87TTz/NxMQEvb29bN++ndtuu42bbrrpouoAM6HVQaJUKs0oXrBtu1mvWb9+PatXr77sC+V0BEEwZTR9EATkcjksy2JiYoJVq1axefPmK0pyOx2ti/3p06c5deoUQgg6Ojouu5hkvvB9nz179mCMobu7u1lnTA1/W8n3SjoPpRT79u2jWq3S399PPp+fUidNf1qdxS/leUxMTPCHf/iHnDlzhi9+8YvNDMOlQBzH9Pb28r3vfY81a9Zw22238bWvfe0cT9BSqcSmTZs4evRoMztRq9Wa06prtRq/8Au/wMc//nF+8Rd/8ZId/yLgag1qJsRxzCuvvMJTTz3F008/zQsvvAAkFjDbt29nx44d9PX1LWpuPL0p08V+bGyMRqNBNptl9erVdHZ2XjKl2sWgVquxe/dutNbk83nq9fplM5hdCKIo4sCBA01VYaFQmNEo90IcPZYSrWKCmUQQsxn+Tl/sL4dsPzXSTU2Lz7f5muk8Wh1W5mtFNV8YY3jsscf4xCc+wYc//GHe/e53X5Z7byYJ+Be/+EUAfvd3fxeAr3zlKzz66KN8/etfb77uwIED3HnnnUCynr3rXe+6kuTj88VVgpoP0kLps88+y8DAAE8//TSDg4MsW7aM7du3s337dm6//fZFGSPdWmfasmULWusp4oVWj7ullCUvFK1pyG3btk0pGrfW5WZT3BUKhctyHq1ko5kwAAAdjklEQVTu7nOpCtMm0NbzaB3Wl4piLtVCVi6XGRwcXLCY4Hyy/UuxiYiiiMHBQeI4pr+//4J785aKfMfHx/noRz9KpVLhC1/4wqI7K8zV2/T444/zq7/6q00Xire//e18/OMfn9drX2W4SlAXCmMMIyMj7Ny5sxlpDQ8Ps3nzZnbs2MGOHTu49dZb573wRlHEwYMHmZiYOGeBb8VsjujpQj+9DrTUmD6+Y74O2LP1BLXW5RY7rTodaZNwLpdrNgkvFFrrc5SDiyWKmQ1xHLN//37K5fKiuXdP30SkLvXTSetiyDe9Z9IZaYsl1Z/+GbM15baex0ykZYzhkUce4ZOf/CQf+chH+M3f/M1F32zMp7fp8ccf5/777+ehhx5a8GtfZbiq4rtQCCFYtWoVb3vb23jb294GJDf53r17GRgY4Nvf/jaf/OQnCYKA66+/vkla11133ZSFUGvNiRMnmnWmbdu2nfemncnjrrUZNy2WX4pBg5VKhcHBQfL5PDt27FjQAj+XCGO6V196LotBvnEcc+DAAUql0pxNwnNBStls3G59/5S0Dh48uKjke/r0afbt28e6devo7e1dtAV+JnFPK/keO3asSb6tEeN82w/SGpnjOAu+VhaCVtVdq/1RKhVPjWbTiDE9v/7+fv7sz/4M3/f5zne+s2SeeTt37mTr1q3N6dy/8Ru/wf/8n/9zXiRzMa99NeEqQV0gpJT09/fT39/Pb/3WbwEJeTz//PMMDAzw+c9/npdffpl8Pt+Mrh566CEefPBBbrvttgsmkZkUXq1+ZPv27WsWTBcjFRWGIfv376dWq9HX17doMuaZ5NWpLLlUKjVlya22RwshX2MMp06d4sCBA6xbt27OzcCFwrZtOjs7p0TBreQ7MjKyYBsq3/cZHBxESjnFh24pMRP5ztR+cL7RKmlj9rFjx9i2bduSOerPdR4p+U4nrYGBAR588EFefPFFstksb3rTm/jGN77BnXfeydq1axf9WOY73uLJJ5/kpptuYvXq1dx///1cd911P5WjMZYCVwlqEeF5HnfccQd33HEHkNywzzzzDL//+79PrVZjw4YN3H333axdu7YZZW3fvr3ZYHchmM2FOzWXPXr0KJVKZcF9TVrr5mKzadOmSyK/nmlu00wjMFp39TOlomq1GoODg3ied1lMdOfqbUoj30wmc45yMBVBXK4FvhUzRb5pxJi2UaSDE7PZLOVymba2Nnbs2HHZ/RNbIaUkCAK++tWvUiwWeeGFF+jq6uLll1/mmWeeoVarLcnnzqe36dZbb+Xw4cMUCgUefvhhfu3Xfo2hoaGfytEYS4Er5yp6FUIIwSOPPMJ9993Hz/zMzwDJwn/48GGeeuqpZv65UqnQ39/flLrfeOONF2X02rrLTZE2sZZKpXP6mqan1NJZR8uWLVvU4YELxWzkO1tzdJrGSdV5rQvr5cZMkW8aMY6Pj7N//36q1WqzEVwI0RzrcSVhesSotebAgQOMjIzQ1dVFGIY8/fTTV4wzujGG//W//hef+tSn+OM//mN+/dd/vXkcN99885yTsy8G8+ltar1Hf+mXfonf+73fY3R0dEF9Ua9mXBVJXAGIooiXXnqJp556ip07d7Jr1y5s2+aWW27h1ltvZceOHWzbtm3RiaI1pZb2NaWL4qZNm+ju7r7iFsiZoJTiyJEjHD16tBktzXdg4uVGKoJISVVKOUXJeSXL9svlMnv27GH58uVs3LhxSiTbOs6jXC6fMw/sUjijnz59mg9/+MNYlsVnPvOZBTujXyzm09s0PDzMypUrEUKwc+dO3vnOd3L48OGmSGKuvqhXEa6q+H5aYIyhUqnw7LPPNlWD+/bto7u7u9mbtWPHjuaFfbFIZwaNjIywbt265iKZSpJTldpi+fQtJur1OoODgziOw7Zt25pR4HSz33SBbFVAXu75WekMo/M1Zs8k24fF905cCJRSTeFJf3//vJWF6YZosUxmZ4Mxhm9961v8xV/8BX/yJ3/CO97xjkUlwrnk31/96lf5i7/4CyC5DlNT4Pe+9738l//yX4iiqCm8+u3f/m0eeOABbNsmm83yV3/1V7zhDW8ArujRGEuBqwT104zU0Xznzp0MDAywc+dORkdH2bp1a7OWdcsttyxI5myM4fTp0xw4cIBVq1axfv36cxa6VN3VKkm+1BLxmaCU4tChQ4yOjtLb2zungWerg0R6LqkIY6kVkNORqtxs26a3t3fBRNk6wDL9Ti5Vz9yZM2fYu3fvvGdMnQ+tac70Z7obxkKtj06dOsV/+A//Ac/z+MxnPrPo7t7zkX8/8cQTXHPNNXR2dvLII4/wiU98oilweBW4ji8VrhLUqw1KKfbs2dMkrOeffx6lFDfccEMzyrrmmmtmXHRTIYHrulMij/mgVaVWKpUueXQyOjrKvn376OnpaUZ8F4JWEcb0lNpSzJ7SWnP06FFOnjy56CKI1p656aM8Wj0gL5RQoihqzsbq7+8nm80u2rG3Yjbro9beppk2EsYYvvnNb3Lffffxp3/6p9x5551LQtALHYsxPj7O9ddfz/Hjx4GrBHUeXCWoVzvSm/u5555j586d7Ny5kz179lAsFpupwd7eXh544AHe+ta38vrXv35RhARpdNLqN5guKq3RycXWTlL5tRCC3t7eJZkY3Dp7qlQqLVozbjrGY7apvEuB89WBFtJrlqYiN27cuCgOKgtFupFoTXMqpfB9nx/+8If09/fzjW98g46ODv7mb/5mSRf/hYzFALj//vvZs2dP8/mvgrEYS4WrBPVahDGG0dFRnnrqKb785S/zgx/8gGuvvZaOjo4pUvf29vZFXXhau/zT6MQYc0G1k1T5ODIyclnk16lDfaujx3yjkziOpxikXqoxHrNhpjrQbFOXgyBgz549SCnp6+u77DW7VqRtEH/5l3/Jk08+SRRFFAoFbrjhBt797nfz8z//80vyud/4xjd47LHHphDUzp07+exnP3vOc//5n/+Z3/u93+NHP/pR85o9ceLElLEYn/3sZ18VruOLgKtOEq9FCCHo7u5m586dbN68mb/7u7+jra2NAwcOMDAwwHe/+13uvfdeGo0G1157bTPSuuGGGy6qYD1Tl39r4+ehQ4eargutqcHpC31a81i5ciW33377ZRFoWJZ1TjNua3QyfYxH2p9VKpWaIoi+vr4rQkU4U69ZmlIbGxvj4MGDRFHUHOWxYcMG1q5de8WpOU+dOsUf/MEf0NHRwb/8y780Je4vv/zykhLpfOXfu3bt4q677uKRRx6ZsqF6tY7FWCpcjaBeI9Ban3dxD8OQXbt2MTAwwMDAAC+99BKu63LLLbc0I60tW7YsOkG0qu1KpVJzoc/n85RKJWzbXtKax2KhNc155swZRkZGMMbQ2dnZHOUxmy/clYR6vc7u3btxXZeOjo5mFNzqTrLYtbmFQGvN17/+dT796U/zqU99ire+9a2XlPjnIx0/cuQIb3nLW/j7v//7piIPXjVjMZYKV1N8VzF/GGMol8s8/fTTTRHGgQMH6Onp4dZbb+W2225j+/btdHd3L+oCoZTi4MGDnDx5kra2NqIoao5aaBUuXCm9QK1oFUGkysLW2sn0hf5SO6KfD8YYjhw5wsmTJ+nv7z+nNnm+2lyr7dFSnsvJkye555576O7u5q/+6q+WZPT6fDDXWIy77rqLb37zm2zYsAFIevKeeeaZV8tYjKXCVYK6iotDOo8oJaynn36aM2fOTBn4ePPNN1+w7Hx8fJy9e/c2Gz9TEkrrWWmUlfYCtcqqF9tFfKFIRRDLli2bcuzT0WpDlRb8L/dYlUqlwp49e+js7FzQwMnzudSnP4txLlprvva1r/G5z32Oe++9l1/6pV+6pH1NxhjuueceHn74YXK5HF/5yle49f9v78xjorraMP4MshRi2bTguIGssqrAGGpbSgpKVarVWpcapTG4VAvaVi3GtBJbFVu3KgqmUpeaaNFWaCpYNampuDCQiooKEmCKMgOEXZBlmDnfH+beb4bNgVmgw/tLTATOZc69xvvee87zPk9AgEbHEhpDBYrQPR0dHXj06JFa4CNjDJMmTVILfOxtaau9vR2PHz+GXC6Hp6cnrKysXvq53M2Ru9E3NzfD1NS0SxSJvm/0nAiiubmZT4ntz+9QPZfnz5/DzMxMrWjp41w4m6K6ujpMnDhRJ0bAqpZa3Lmo2h719VykUiliY2MhFAqxd+9endtXadLXlJGRgUOHDiEjIwPZ2dlYv349srOzh2Ikhj6hAkXoH04SzAU+isViPH78GHZ2dnzgo0gkwujRo6FQKHD16lXY2NjA1dVV6+VCTrjA3RxbW1thaWmpprbTZQor55b+svDD/tDduXQ2l9VGDFBfX4+CggIIhUKMHz9er4W8vb1dbZlTVVDSU9+cUqnE6dOnkZSUhN27dyMiImLA+ppWr16N0NBQLFmyBADg6emJa9euQSKR9KkniugVUvHpmtraWixatAgSiQTOzs5ITU3tcV1coVAgKCgIY8aM6RJOZkxwBq8hISG8Oom7mXMuGCdOnEBxcTHa29sREBCAVatW6aSnydzcHCNHjuT7YDingoaGBtTU1KCkpKSLG/rw4cP7vJ/V0tKCgoICmJub680tvadzaWxsRG1tLSQSCTo6Oro4YbzsXLg3vufPn2PSpEkGEZ+Ym5t3McrlBCX19fV8tEpjYyOuX78OT09PpKamwtXVFX///bdaBIiu0STWorsx5eXlFIlhAKhAaUFCQgLCwsIQFxeHhIQEJCQk8B5cnfnhhx/g5eWFxsZGA89y4BEIBHB0dMR7773HOzYzxvDZZ5+huroamZmZ2LFjB1pbW+Hj48O/Zfn4+Gh18xcIBLC0tOQdwoHe3dBf1oirVCpRVlaGiooKeHh4qAVJ6hvVc3F0dASg3mtWUVHBxzSoOmGoijC4AEQnJ6cBlb0LBAJe7q56LlKpFJcuXeKbXuvq6rBu3TpERUVh+vTpepmLJrEWPY2hSAz9QwVKC9LT03Ht2jUAQFRUFEJDQ7stUE+fPsXFixexdetW7Nu3z8CzHFwMGzYMH3/8MYKDg/n/zMuXLwfwojE0Ly8P2dnZSE5ORn5+PiwtLREQEMAXrc6u2X2luzRZrhGXyzhqbm7m9024G31bWxsvghiofqzO9JQoywkXysrKeLUd51LPKfQG24306dOniImJgYuLC27evIlXX32V39/UpzRfk76mnsa0t7dTJIaeoT0oLbC1tUV9fT3/tZ2dHerq6rqMW7BgAbZs2YJnz55hz549Rr3Ep0sYY6ivr0dOTg4vwpBIJBgzZoyaq7u9vb3Ob7jcvkldXR0qKyshl8thY2MDe3v7Lo4LgxXGGCoqKlBaWopRo0bBxMSE907kRBiqlkcDUbSUSiWOHz+OlJQU7NmzB2FhYYOur+nixYtITEzkRRKxsbEQi8UaHUtoDO1B9Yfw8HBUVFR0+f6OHTs0Ov6PP/6Ag4MDAgMD+bctQjMEAgHs7OwwY8YMzJgxA8D/l9mys7Nx/fp17Nu3D42NjXzgY1BQkE72VszMzKBUKlFTUwNXV1eMGjWK38+qrq5W28/Sh7GstnD7ZBYWFhCJRF2KqapwgUv41ZegpCf+/fdfxMTEwNPTE1lZWQNiA2VqaorExERERETwfU0+Pj5qfU2zZs1CRkYG3NzcYGVlhePHj/d6LKE76A1KCzg1j1AohEwmQ2hoKAoLC9XGbNmyBT///DNMTU35Te758+fj9OnTAzRr46OjowP5+fm8avDu3bsQCASYMmWKmkmupmIIVRGEu7t7j/tgnZtXVXuauJu8oXuauF41qVTap30yVUEJp7bjGqRV7Zt00SCtVCqRkpKC48ePY//+/QgNDdXbNdJEyPTkyRMsX74cFRUVMDExwapVq7B+/XoAQHx8PH788Ude4LFz507MmjVLL3Md4pDMXNds2rQJI0aM4EUStbW1+O6773ocz0W80xKffmGMoampSU3qXlRUhJEjR/IFSyQSdQl81IUIQjX2gjOWNTc379KfpQ+amprw6NEj2NrawsXFRetiotogzTUV99fwl6O0tBQxMTHw9fXFrl27+tU31hc2b94Me3t7/v9oXV1dl31imUwGmUyGgIAAPHv2DIGBgUhLS4O3tzfi4+MxfPhwbNy4Ua/zJKhA6ZyamhosXLgQZWVlGD9+PM6dOwd7e3tIpVJER0cjIyNDbby+CpS2T4lDAW4/hvMaFIvFqKqqgpubGwIDA2FlZYXU1FQcOXIEHh4eOl2q6xyU2NbWptOgRKVSyYc3Tpw4EdbW1jqbe2e6C0vUxD1CoVDg2LFjOHXqFA4cOICQkBCDvFlqssrRmblz5+LTTz/F9OnTqUAZDipQxoq2T4lDFYVCgdzcXGzZsgUlJSUYP348mpqa4O/vz6sGvby8dL4X0zkoURuPvoaGBhQUFMDBwQFOTk4DsgfGvTV2do+QSqVoaGiAk5MTEhISMGnSJOzcuVMjpxBdoamQiUMikSAkJAT5+fmwtrZGfHw8Tpw4AWtrawQFBWHv3r0D5gFo5FCBMla0fUocymzcuBGTJ0/G0qVLIRAI0NLSgjt37iA7Oxs5OTl4+PAhhg8frqYa1CbFtye68+hTfTOxsbFR8zhUKBRqOVP6XirrK21tbbh16xaSk5Pxzz//wMLCAn5+fhCJRFi6dCmcnZ119lm9CZmioqI0LlBNTU14++23sXXrVsyfPx8AUFlZiZEjR0IgEOCrr76CTCbDTz/9pLO5EzxUoIwVbZ8SiZ5hjKGmpkZN6v7kyROMGzeOd3QPDAzUS29Rd28mFhYWMDMzQ0NDA8aOHQsnJ6dB19MEAEVFRYiNjUVQUBC++eYbWFpaorS0FGKxGCKRCK6urgaZh6YPb3K5HJGRkYiIiMDnn3/e7e+SSCSIjIxEfn6+vqc9FKEC9V9Gn0+JRN9QKpUoLS3l97Nyc3PR3NwMLy8v/i3L399f52IIuVyOR48eoaWlBTY2NmhubkZ7e3sXpd1AZk4pFAokJSXhl19+wcGDB/HGG28M2FwAzYRMjDFERUXB3t4eBw4cUPuZTCaDUCgEAOzfvx/Z2dk4e/asweY/hKACZazo8imR6B9yuZwPfBSLxbh//z5MTU3VAh/d3Nz6tTSoakzr4uICBwcH/q2J289SlYer2h31R2nXXwoLCxEbG4vg4GBs3759UIRMaiJkysrKwltvvQU/Pz/+OnFy8mXLliEvLw8CgQDOzs44evQoX7AInUIFyljR9imR0D1c4GNubi6/n1VcXAxHR0c+8DEoKOilDu6tra0oKCiAmZkZPDw8NBJsqNodceGC3H4Wpxzsb2ZXd3R0dODw4cM4f/48Dh8+jODgYJ383u7Q1KDZ2dmZ79viAgP7cjxhcKhAGSvaPiUShoExhvLycn5pMCcnBzU1NXB3d0dQUBACAwMxZcoUWFlZQalU4tatWzA1NYW7uztGjBih1WfL5XK1/qyWlhZYWFio9Wf1x5i3oKAAsbGxePPNNxEfH68TV/re0ESxCrwoULm5ubwbfF+PJwwOFShCP2iTSDrUUSgUaoGPd+7cQUtLC1pbW+Hv749NmzbB29tbL/tKnLMJtzwol8v5/qyXOUd0dHTg4MGDSEtLw5EjRzB16lSdz687NF3O7qlA9UfxShgEKlCE7tEmkZRQhzGG3bt34/z581i5ciWampqQnZ2NwsJC2NraqgU+jhkzRufqPdX4Ds66iXOOsLGxQU1NDby8vHiFXmhoKLZt26Y3Z4zu0FSxOmHCBNjZ2UEgEGD16tVYtWpVn44nDA6ZxRK6RywWw83NDS4uLgCAxYsXIz09Xa1ApaenY/ny5RAIBAgODkZ9fb2aOop4gUAggJubG27evKm23MYYQ3V1Nb80eOrUKUilUjg7O/MFKyAgANbW1loVre7iOxQKBb+ftXPnTty7dw8NDQ2YPXs2Jk+eDJlMptOeJkB7g2YAuHHjBkaPHo2qqipMnz4dEydO5AM0if8OVKAIrdAmkZQKVFcWLFjQ5XsCgQCvvfYaIiMjERkZCeCFEKK4uBi3b9/GpUuX+MBHb29vvmj5+vpqnfY7bNgw2Nraory8HFVVVVi2bBnWrl2L+/fvQywW4/Llyzh27JhWn9GZq1ev9vgzR0dH/uFGJpPBwcGh23FcgXVwcMC8efMgFosREhKi8fHE4IAKFKEV2iSSEv3HxMQE7u7ucHd3x7JlywC8iNC4e/cubt++jaNHj+LBgwd45ZVXeFd3kUiECRMm9ElyLpfLsW/fPmRmZiI5OZnfOxQKhXwEiiGZM2cOTp48ibi4OJw8eRJz587tMqa5uZm3jmpubsbly5fx9ddfa3w8MXigAkVohTaJpIRuMTc3h0gkgkgkAvD/wMfc3Fzcvn0baWlpKC0txejRo9Wsm0aMGNHtA8P9+/cRGxuLmTNnIisrS+u3MV0QFxeHhQsXIiUlhVesAlBTrFZWVmLevHkAXog5PvroI7z77ru9Hk8MTkgkQWiFNomkhOFhjPGBj5zUvaGhAR4eHnzB8vHxQWJiIq5evYrk5GRMnjxZb/PRpC+psLAQixYt4r8uKSnB9u3bsWHDBsprMh66X1JhjPX2hyBeysWLF5m7uztzcXFh3377LWOMsaSkJJaUlMQYY0ypVLK1a9cyFxcX5uvry3JycvQ2l8zMTObh4cFcXV3Zrl27uvz89OnTzM/Pj/n5+bHXX3+d5eXl6W0u/xXkcjnLy8tjR48eZdHR0UwoFLKYmBjW1tam98/etGkT/++0a9cutnnz5l7Hd3R0MEdHRyaRSBhjjG3bto19//33ep8noXe6rUFUoAijoaOjg7m4uLDi4mLW1tbG/P392YMHD9TG3Lhxg9XW1jLGGMvIyGBTp04diKkOapRKpcE+y8PDg0mlUsYYY1KplHl4ePQ6/s8//2TTpk3jv6YCZTR0W4MMHx5DEHpCVfJubm7OS95VmTZtGr+EFBwcjKdPnw7EVAc1hhSwVFZW8mpOoVCIqqqqXsefPXsWS5YsUfteYmIi/P39sWLFCuppMjKoQBFGQ09y9p5ISUnBzJkzDTG1IU14eDh8fX27/On88PAy2tvb8fvvv+PDDz/kv/fJJ5+guLgYeXl5EAqF+OKLL3Q9fWIAIRUfYTSwPsjZ//rrL6SkpCArK0vf0xry6KKvCQAyMzMREBAAR0dHteM5Vq5cyfeJEcYBvUERRoOmcvZ79+4hOjoa6enpWpuwEtrB9SUBeGlf0pkzZ7os78lkMv7vFy5cgK+vr34mSgwIJDMnjAZNJO9lZWV45513cOrUKUybNm0AZ0sAmjnxA8Dz588xbtw4lJSUwMbGhj+e8pqMBjKLJYyfjIwMbNiwAQqFAitWrMDWrVuRnJwMAFizZg2io6Px66+/wsnJCQDUsoIIghgwqA+KIAzNy/qyOMRiMTMxMWHnzp0z4Ox0S2pqKvP29mYCgaDXXreerklNTQ0LDw9nbm5uLDw8nG8HIIYEJDMnCEOiUCiwbt06ZGZm4uHDhzhz5gwePnzY7bgvv/wSERERAzBL3eHr64vffvutV9fw3q5JQkICwsLCUFRUhLCwMCQkJBhq6sQghQoUQegJTfqyAODQoUP44IMP/vPO2l5eXvD09Ox1TG/XJD09HVFRUQCAqKgopKWl6X3OxOCGChRB6AlN+rLKy8tx4cIFrFmzxtDTGxB6uyZ9bdoljB/qgyIIPcE06MvasGEDdu/e3WO0+mCjtzBBTaIrNLkmBMFBBYog9IQmfVm5ublYvHgxAKC6uhoZGRkwNTXF+++/b9C5akpvTbea0Ns1oTBBojO0xEcQekIkEqGoqAilpaVob2/H2bNnMWfOHLUxpaWlkEgkkEgkWLBgAY4cOTJoi5Mu6O2a9KVplxgaUIEiCD1hamqKxMREREREwMvLCwsXLoSPjw+Sk5P53ixj4sKFCxg7dixu3bqF2bNn86pEqVTKZzT1dE2AF2GCV65cgbu7O65cuYK4uLgBOxdicECNugRBEMRA0+1G5Mv2oGj3kiAIghgQaImPIAiCGJRQgSIIgiAGJVSgCIIgiEEJFSiCIAhiUEIFiiAIghiUUIEiCIIgBiX/A7Fe8gAzdgL3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1cf95d30>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# complexplot3D\n",
    "from sympy import *\n",
    "from sympy.functions import *\n",
    "from sympy.plotting import *\n",
    "from sympy.abc import x, y\n",
    "plot3d(\n",
    "    Abs(atan((x+I*y)**2)),\n",
    "    (x, -1/2, 1/2), (y, -1, 1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:34:30.199587Z",
     "start_time": "2020-04-14T04:34:30.103590Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x - \\frac{x^{3}}{3} + \\frac{x^{5}}{5} - \\frac{x^{7}}{7} + \\frac{x^{9}}{9} - \\frac{x^{11}}{11} + \\frac{x^{13}}{13} - \\frac{x^{15}}{15} + O\\left(x^{16}\\right)$"
      ],
      "text/plain": [
       "x - x**3/3 + x**5/5 - x**7/7 + x**9/9 - x**11/11 + x**13/13 - x**15/15 + O(x**16)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import series, atan\n",
    "from sympy.abc import x\n",
    "atan(x).series(x0=0, n=16)  # 此处 Mathematica 是 Series[atan[x], {x, 0, 10}]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:35:04.348732Z",
     "start_time": "2020-04-14T04:35:04.202702Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{1}{5 x^{5}} + \\frac{1}{3 x^{3}} - \\frac{1}{x} + \\frac{\\pi}{2} + O\\left(\\frac{1}{x^{6}}; x\\rightarrow \\infty\\right)$"
      ],
      "text/plain": [
       "-1/(5*x**5) + 1/(3*x**3) - 1/x + pi/2 + O(x**(-6), (x, oo))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import series, atan\n",
    "from sympy.abc import x\n",
    "atan(x).series(x0=oo, n=6)  # 此处 Mathematica 是 Series[atan[x], {x, 0, 10}]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:36:04.069695Z",
     "start_time": "2020-04-14T04:36:04.021702Z"
    }
   },
   "outputs": [
    {
     "ename": "PoleError",
     "evalue": "Cannot expand atan(_x + I) around 0",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mPoleError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-15-fa0d1531946d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msympy\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msympy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mabc\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0matan\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mseries\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mI\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# 此处 Mathematica 是 Series[atan[x], {x, 0, 10}]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\core\\expr.py\u001b[0m in \u001b[0;36mseries\u001b[1;34m(self, x, x0, n, dir, logx)\u001b[0m\n\u001b[0;32m   2824\u001b[0m                 \u001b[0mrep2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2825\u001b[0m                 \u001b[0mrep2b\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2826\u001b[1;33m             \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrep\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mseries\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdir\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'+'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlogx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2827\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m  \u001b[1;31m# lseries...\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2828\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0msi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrep2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mrep2b\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0msi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\core\\expr.py\u001b[0m in \u001b[0;36mseries\u001b[1;34m(self, x, x0, n, dir, logx)\u001b[0m\n\u001b[0;32m   2834\u001b[0m             \u001b[1;31m# replace x with an x that has a positive assumption\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2835\u001b[0m             \u001b[0mxpos\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mDummy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'x'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpositive\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfinite\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2836\u001b[1;33m             \u001b[0mrv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxpos\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mseries\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxpos\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdir\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlogx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2837\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2838\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxpos\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\core\\expr.py\u001b[0m in \u001b[0;36mseries\u001b[1;34m(self, x, x0, n, dir, logx)\u001b[0m\n\u001b[0;32m   2841\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2842\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m  \u001b[1;31m# nseries handling\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2843\u001b[1;33m             \u001b[0ms1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_eval_nseries\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlogx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2844\u001b[0m             \u001b[0mo\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ms1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgetO\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mZero\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2845\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mo\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\core\\function.py\u001b[0m in \u001b[0;36m_eval_nseries\u001b[1;34m(self, x, n, logx)\u001b[0m\n\u001b[0;32m    712\u001b[0m                 \u001b[0mterm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mZero\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    713\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mterm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_finite\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mFalse\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mterm\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNaN\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 714\u001b[1;33m                     \u001b[1;32mraise\u001b[0m \u001b[0mPoleError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Cannot expand %s around 0\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    715\u001b[0m                 \u001b[0mseries\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mterm\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    716\u001b[0m                 \u001b[0mfact\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mOne\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mPoleError\u001b[0m: Cannot expand atan(_x + I) around 0"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import x\n",
    "atan(x).series(x0=I, n=3)  # 无法在 I 处展开"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scope"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:36:38.878695Z",
     "start_time": "2020-04-14T04:36:38.870701Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.463647609000806$"
      ],
      "text/plain": [
       "0.463647609000806"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import atan\n",
    "atan(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:36:56.179694Z",
     "start_time": "2020-04-14T04:36:56.171701Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.32581766366803$"
      ],
      "text/plain": [
       "1.32581766366803"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import atan\n",
    "atan2(2, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:37:08.236694Z",
     "start_time": "2020-04-14T04:37:08.228771Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.46364760900080611621425623146121440202853705428612$"
      ],
      "text/plain": [
       "0.46364760900080611621425623146121440202853705428612"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import atan, Rational\n",
    "atan(Rational(1, 2)).evalf(n=50)  # 和 Mathematica 一致"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:37:27.643701Z",
     "start_time": "2020-04-14T04:37:27.637697Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.463647609000806$"
      ],
      "text/plain": [
       "0.463647609000806"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import atan\n",
    "atan(0.50000000000000000000000000000000000000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:37:36.493698Z",
     "start_time": "2020-04-14T04:37:36.482699Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.23342585568312 + 0.123674060459027 i$"
      ],
      "text/plain": [
       "1.23342585568312 + 0.123674060459027*I"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import atan, I\n",
    "atan(2.5 + I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 没有测时间函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:38:03.181703Z",
     "start_time": "2020-04-14T04:38:03.171700Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\operatorname{atan}{\\left(\\left\\langle -3, 1\\right\\rangle \\right)}$"
      ],
      "text/plain": [
       "-atan(AccumBounds(-3, 1))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(AccumBounds(-1, 3)).simplify()\n",
    "# 没化简"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:07:37.873986Z",
     "start_time": "2020-04-17T13:07:37.862988Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.099668652491162 & 0.197395559849881 & 0.291456794477867\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[0.0996686524911620, 0.197395559849881, 0.291456794477867]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Array(atan(i)for i in [0.1, 0.2, 0.3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:38:52.611698Z",
     "start_time": "2020-04-14T04:38:52.601738Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\pi}{4} & \\operatorname{atan}{\\left(\\frac{1}{3} \\right)}\\\\\\operatorname{atan}{\\left(x \\right)} & \\operatorname{atan}{\\left(\\frac{1}{2} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   pi/4, atan(1/3)],\n",
       "[atan(x), atan(1/2)]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Matrix([[1, Rational(1, 3)], [x, Rational(1, 2)]]).applyfunc(atan)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specific Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:08:22.499636Z",
     "start_time": "2020-04-17T13:08:22.488634Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\pi}{4} & 0 & \\frac{\\pi}{4}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[-pi/4, 0, pi/4]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Array(atan(i)for i in range(-1, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:04:35.544058Z",
     "start_time": "2020-04-17T13:04:35.528059Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{3 \\pi}{4} & - \\pi + \\operatorname{atan}{\\left(\\frac{1}{2} \\right)} & \\pi & \\pi - \\operatorname{atan}{\\left(\\frac{1}{2} \\right)} & \\frac{3 \\pi}{4}\\\\- \\pi + \\operatorname{atan}{\\left(2 \\right)} & - \\frac{3 \\pi}{4} & \\pi & \\frac{3 \\pi}{4} & \\pi - \\operatorname{atan}{\\left(2 \\right)}\\\\- \\frac{\\pi}{2} & - \\frac{\\pi}{2} & \\text{NaN} & \\frac{\\pi}{2} & \\frac{\\pi}{2}\\\\- \\operatorname{atan}{\\left(2 \\right)} & - \\frac{\\pi}{4} & 0 & \\frac{\\pi}{4} & \\operatorname{atan}{\\left(2 \\right)}\\\\- \\frac{\\pi}{4} & - \\operatorname{atan}{\\left(\\frac{1}{2} \\right)} & 0 & \\operatorname{atan}{\\left(\\frac{1}{2} \\right)} & \\frac{\\pi}{4}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[      -3*pi/4, -pi + atan(1/2),  pi, pi - atan(1/2),       3*pi/4],\n",
       "[-pi + atan(2),         -3*pi/4,  pi,         3*pi/4, pi - atan(2)],\n",
       "[        -pi/2,           -pi/2, nan,           pi/2,         pi/2],\n",
       "[     -atan(2),           -pi/4,   0,           pi/4,      atan(2)],\n",
       "[        -pi/4,      -atan(1/2),   0,      atan(1/2),         pi/4]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Matrix([[atan2(i, j) for i in range(-2, 3)]for j in range(-2, 3)])\n",
    "# 因为 Mathematica 和 sympy 的 arctan 是反的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:46:12.831318Z",
     "start_time": "2020-04-14T04:46:12.825298Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\pi}{2}$"
      ],
      "text/plain": [
       "pi/2"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:46:16.221308Z",
     "start_time": "2020-04-14T04:46:16.213305Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left\\langle - \\frac{\\pi}{2}, \\frac{\\pi}{2}\\right\\rangle$"
      ],
      "text/plain": [
       "AccumBounds(-pi/2, pi/2)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(zoo)\n",
    "# 这缩写简直了\n",
    "# 和 MMA 不同"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:48:28.837298Z",
     "start_time": "2020-04-14T04:48:28.830303Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan2(1, oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:48:28.837298Z",
     "start_time": "2020-04-14T04:48:28.830303Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\text{NaN}$"
      ],
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan2(+oo, -1)\n",
    "# 和 MMA 不一致"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:48:28.837298Z",
     "start_time": "2020-04-14T04:48:28.830303Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:50:37.246296Z",
     "start_time": "2020-04-14T04:50:37.222309Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left\\{\\sqrt{3}\\right\\}$"
      ],
      "text/plain": [
       "FiniteSet(sqrt(3))"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "f = symbols(\"f\", cls=Function)\n",
    "x = symbols(\"x\")\n",
    "f = atan(x)-pi/3\n",
    "solveset(Eq(f, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:52:54.095581Z",
     "start_time": "2020-04-14T04:52:53.888583Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x12397990>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.plotting import *\n",
    "f = symbols(\"f\", cls=Function)\n",
    "x = symbols(\"x\")\n",
    "f = atan(x)-pi/3\n",
    "plot(f, (x, -2, 2))\n",
    "# 不会加点"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:53:11.292659Z",
     "start_time": "2020-04-14T04:53:11.105693Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x20935f90>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.plotting import *\n",
    "plot(atan(x), (x, -7, 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:53:43.468654Z",
     "start_time": "2020-04-14T04:53:39.153694Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\plotting\\experimental_lambdify.py:165: UserWarning: The evaluation of the expression is problematic. We are trying a failback method that may still work. Please report this as a bug.\n",
      "  warnings.warn('The evaluation of the expression is'\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x20a3e2f0>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.plotting import *\n",
    "plot3d(atan2(y, x), (x, -7, 7), (y, -7, 7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### sympy 没有等高线绘图函数，等大神补充"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### sympy 没有极坐标绘图函数，等大神补充"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{\\sqrt{3} \\sqrt{\\frac{1}{2} - \\frac{\\sqrt{2}}{4}}}{2} + \\frac{\\sqrt{\\frac{\\sqrt{2}}{4} + \\frac{1}{2}}}{2}$"
      ],
      "text/plain": [
       "-sqrt(3)*sqrt(1/2 - sqrt(2)/4)/2 + sqrt(sqrt(2)/4 + 1/2)/2"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(pi/24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{\\frac{5}{8} - \\frac{\\sqrt{5}}{8}}$"
      ],
      "text/plain": [
       "sqrt(5/8 - sqrt(5)/8)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(pi/5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.assumptions import *\n",
    "m = symbols(\"m\", integer=True)\n",
    "atan(pi*m).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:48:28.837298Z",
     "start_time": "2020-04-14T04:48:28.830303Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\pi}{4} & 0 & \\frac{\\pi}{4}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[-pi/4, 0, pi/4]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Array(range(-1, 2)).applyfunc(atan)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function Properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:58:47.353739Z",
     "start_time": "2020-04-14T04:58:47.305739Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left\\{x \\mid x \\in \\mathbb{R} \\wedge \\operatorname{atan}{\\left(x \\right)} < \\pi \\right\\}$"
      ],
      "text/plain": [
       "ConditionSet(x, atan(x) < pi, Reals)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "# 好像没定义域函数\n",
    "solveset(atan(x) < pi, x, domain=Reals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:59:06.530789Z",
     "start_time": "2020-04-14T04:59:06.524775Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(\\left\\langle -\\infty, \\infty\\right\\rangle \\right)}$"
      ],
      "text/plain": [
       "atan(AccumBounds(-oo, oo))"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(AccumBounds(-oo, oo))\n",
    "# 没出结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:59:46.156741Z",
     "start_time": "2020-04-14T04:59:46.149778Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\operatorname{atan}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "-atan(x)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T04:59:50.327739Z",
     "start_time": "2020-04-14T04:59:50.314763Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(\\overline{z} \\right)} = \\overline{\\operatorname{atan}{\\left(z \\right)}}$"
      ],
      "text/plain": [
       "Eq(atan(conjugate(z)), conjugate(atan(z)))"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Eq(atan(conjugate(z)), conjugate(atan(z)))\n",
    "# 没出结果"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:00:08.250375Z",
     "start_time": "2020-04-14T05:00:08.237376Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{x^{2} + 1}$"
      ],
      "text/plain": [
       "1/(x**2 + 1)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "diff(atan(x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:09:41.871480Z",
     "start_time": "2020-04-17T13:09:41.849474Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{x^{2} + 1} & - \\frac{2 x}{\\left(x^{2} + 1\\right)^{2}} & \\frac{6 x^{2} - 2}{\\left(x^{2} + 1\\right)^{3}} & \\frac{24 x \\left(1 - x^{2}\\right)}{\\left(x^{2} + 1\\right)^{4}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[1/(x**2 + 1), -2*x/(x**2 + 1)**2, (6*x**2 - 2)/(x**2 + 1)**3, 24*x*(1 - x**2)/(x**2 + 1)**4]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "Array(diff(atan(x), x, i).radsimp() for i in range(1, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:10:20.254285Z",
     "start_time": "2020-04-17T13:10:20.018293Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1e4a4b70>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "from sympy.plotting import *\n",
    "plot(*Array(diff(atan(x), x, i).radsimp()\n",
    "            for i in range(1, 5)), atan(x), (x, -1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:01:39.446376Z",
     "start_time": "2020-04-14T05:01:39.437378Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "n = symbols(\"n\", integer=True, positive=True)\n",
    "diff(atan(x), x, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:01:46.466372Z",
     "start_time": "2020-04-14T05:01:46.182408Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x \\operatorname{atan}{\\left(x \\right)} - \\frac{\\log{\\left(x^{2} + 1 \\right)}}{2}$"
      ],
      "text/plain": [
       "x*atan(x) - log(x**2 + 1)/2"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "integrate(atan(x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:01:54.959369Z",
     "start_time": "2020-04-14T05:01:54.748370Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "integrate(atan(x), (x, -1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:02:07.713371Z",
     "start_time": "2020-04-14T05:02:07.355407Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x^{2} \\operatorname{atan}{\\left(x \\right)}}{2} - \\frac{x}{2} + \\frac{\\operatorname{atan}{\\left(x \\right)}}{2}$"
      ],
      "text/plain": [
       "x**2*atan(x)/2 - x/2 + atan(x)/2"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "integrate(atan(x)*x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:02:43.365387Z",
     "start_time": "2020-04-14T05:02:29.165380Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int z^{k} \\operatorname{atan}{\\left(z \\right)}\\, dz$"
      ],
      "text/plain": [
       "Integral(z**k*atan(z), z)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "integrate(atan(z)*z**k, z)\n",
    "# MMA 算出来了"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Series Expansions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:03:03.927373Z",
     "start_time": "2020-04-14T05:03:02.571373Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x - \\frac{x^{3}}{3} + \\frac{x^{5}}{5} - \\frac{x^{7}}{7} + O\\left(x^{8}\\right)$"
      ],
      "text/plain": [
       "x - x**3/3 + x**5/5 - x**7/7 + O(x**8)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(x).series(n=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 画不来批量的图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 不会级数系数列表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Invalid limits given: z",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-38-8491f8cacd39>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msympy\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msympy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mabc\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mz\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mfourier_series\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mz\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mz\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[1;31m# 不清楚\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\series\\fourier.py\u001b[0m in \u001b[0;36mfourier_series\u001b[1;34m(f, limits, finite)\u001b[0m\n\u001b[0;32m    637\u001b[0m     \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msympify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    638\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 639\u001b[1;33m     \u001b[0mlimits\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_process_limits\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlimits\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    640\u001b[0m     \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlimits\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    641\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\series\\fourier.py\u001b[0m in \u001b[0;36m_process_limits\u001b[1;34m(func, limits)\u001b[0m\n\u001b[0;32m     83\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     84\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mSymbol\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mstart\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mstop\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 85\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Invalid limits given: %s'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlimits\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     86\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     87\u001b[0m     \u001b[0munbounded\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNegativeInfinity\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mInfinity\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Invalid limits given: z"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import z\n",
    "# 无法在 I 2I 展开\n",
    "# 和 MMA 不一样"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:04:31.612441Z",
     "start_time": "2020-04-14T05:04:31.420450Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x + O\\left(x^{10}\\right)$"
      ],
      "text/plain": [
       "x + O(x**10)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "tan(x).series(n=10).subs(x, atan(x).series(n=10)).expand()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integral Transforms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:05:24.331971Z",
     "start_time": "2020-04-14T05:05:18.098035Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathcal{L}_{t}\\left[\\operatorname{atan}{\\left(t \\right)}\\right]\\left(s\\right)$"
      ],
      "text/plain": [
       "LaplaceTransform(atan(t), t, s)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "laplace_transform(atan(t), t, s)\n",
    "# 没算出来"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:06:23.716971Z",
     "start_time": "2020-04-14T05:05:58.770977Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathcal{F}^{-1}_{t}\\left[\\operatorname{atan}{\\left(t \\right)}\\right]\\left(k\\right)$"
      ],
      "text/plain": [
       "InverseFourierTransform(atan(t), t, k)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "inverse_fourier_transform(atan(t), t, k)\n",
    "# ？？？\n",
    "# 没出来"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:08:35.701132Z",
     "start_time": "2020-04-14T05:06:36.344977Z"
    }
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-85-63419b3bb790>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msympy\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mmellin_transform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0matan\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\transforms.py\u001b[0m in \u001b[0;36mmellin_transform\u001b[1;34m(f, x, s, **hints)\u001b[0m\n\u001b[0;32m    362\u001b[0m     \u001b[0mhankel_transform\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minverse_hankel_transform\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    363\u001b[0m     \"\"\"\n\u001b[1;32m--> 364\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mMellinTransform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdoit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mhints\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    365\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    366\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\transforms.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m    121\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    122\u001b[0m                 return self._compute_transform(self.function,\n\u001b[1;32m--> 123\u001b[1;33m                     self.function_variable, self.transform_variable, **hints)\n\u001b[0m\u001b[0;32m    124\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mIntegralTransformError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    125\u001b[0m                 \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\transforms.py\u001b[0m in \u001b[0;36m_compute_transform\u001b[1;34m(self, f, x, s, **hints)\u001b[0m\n\u001b[0;32m    305\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    306\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_compute_transform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mhints\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 307\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m_mellin_transform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mhints\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    308\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    309\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_as_integral\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\transforms.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m    206\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    207\u001b[0m             \u001b[0mnoconds\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'noconds'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdefault\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 208\u001b[1;33m             \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    209\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mnoconds\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    210\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\transforms.py\u001b[0m in \u001b[0;36m_mellin_transform\u001b[1;34m(f, x, s_, integrator, simplify)\u001b[0m\n\u001b[0;32m    230\u001b[0m     \u001b[1;31m# convergence of the integral.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    231\u001b[0m     \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_dummy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m's'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'mellin-transform'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 232\u001b[1;33m     \u001b[0mF\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mintegrator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    233\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    234\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mF\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhas\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mIntegral\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\transforms.py\u001b[0m in \u001b[0;36m_default_integrator\u001b[1;34m(f, x)\u001b[0m\n\u001b[0;32m    220\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    221\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_default_integrator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 222\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0moo\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    223\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    224\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\integrals.py\u001b[0m in \u001b[0;36mintegrate\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   1520\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1521\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mintegral\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mIntegral\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1522\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mintegral\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdoit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mdoit_flags\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1523\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1524\u001b[0m         new_args = [a.doit(**doit_flags) if isinstance(a, Integral) else a\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\integrals.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m    574\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    575\u001b[0m                     antideriv = self._eval_integral(\n\u001b[1;32m--> 576\u001b[1;33m                         function, xab[0], **eval_kwargs)\n\u001b[0m\u001b[0;32m    577\u001b[0m                     \u001b[1;32mif\u001b[0m \u001b[0mantideriv\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mmeijerg\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mTrue\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    578\u001b[0m                         \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtry_meijerg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxab\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\integrals.py\u001b[0m in \u001b[0;36m_eval_integral\u001b[1;34m(self, f, x, meijerg, risch, manual, heurisch, conds)\u001b[0m\n\u001b[0;32m   1030\u001b[0m                     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1031\u001b[0m                         \u001b[1;32mif\u001b[0m \u001b[0mconds\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'piecewise'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1032\u001b[1;33m                             \u001b[0mh\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mheurisch_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1033\u001b[0m                         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1034\u001b[0m                             \u001b[0mh\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mheurisch_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\heurisch.py\u001b[0m in \u001b[0;36mheurisch_wrapper\u001b[1;34m(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations, _try_heurisch)\u001b[0m\n\u001b[0;32m    134\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    135\u001b[0m     res = heurisch(f, x, rewrite, hints, mappings, retries, degree_offset,\n\u001b[1;32m--> 136\u001b[1;33m                    unnecessary_permutations, _try_heurisch)\n\u001b[0m\u001b[0;32m    137\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mres\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mBasic\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    138\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\heurisch.py\u001b[0m in \u001b[0;36mheurisch\u001b[1;34m(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations, _try_heurisch)\u001b[0m\n\u001b[0;32m    733\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    734\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mretries\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 735\u001b[1;33m             \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mheurisch\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmappings\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmappings\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrewrite\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrewrite\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhints\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mretries\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mretries\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0munnecessary_permutations\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0munnecessary_permutations\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    736\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    737\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\heurisch.py\u001b[0m in \u001b[0;36mheurisch\u001b[1;34m(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations, _try_heurisch)\u001b[0m\n\u001b[0;32m    716\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    717\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mF\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfree_symbols\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mV\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 718\u001b[1;33m         \u001b[0msolution\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_integrate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Q'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    719\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    720\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0msolution\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\integrals\\heurisch.py\u001b[0m in \u001b[0;36m_integrate\u001b[1;34m(field)\u001b[0m\n\u001b[0;32m    707\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    708\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mPolynomialError\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 709\u001b[1;33m         \u001b[0msolution\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msolve_lin_sys\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcoeffs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcoeff_ring\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_raw\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    710\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    711\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0msolution\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\polys\\solvers.py\u001b[0m in \u001b[0;36msolve_lin_sys\u001b[1;34m(eqs, ring, _raw)\u001b[0m\n\u001b[0;32m     33\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     34\u001b[0m     \u001b[1;31m# transform from equations to matrix form\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 35\u001b[1;33m     \u001b[0mmatrix\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0meqs_to_matrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meqs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mring\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     36\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     37\u001b[0m     \u001b[1;31m# solve by row-reduction\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\polys\\solvers.py\u001b[0m in \u001b[0;36meqs_to_matrix\u001b[1;34m(eqs, ring)\u001b[0m\n\u001b[0;32m     15\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0me_j\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meqs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     16\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx_i\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m             \u001b[0mM\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0me_j\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_i\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     18\u001b[0m         \u001b[0mM\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0me_j\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\matrices\\dense.py\u001b[0m in \u001b[0;36m__setitem__\u001b[1;34m(self, key, value)\u001b[0m\n\u001b[0;32m    488\u001b[0m         [2, 2, 4, 2]])\n\u001b[0;32m    489\u001b[0m         \"\"\"\n\u001b[1;32m--> 490\u001b[1;33m         \u001b[0mrv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_setitem\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    491\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mrv\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    492\u001b[0m             \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrv\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Program Files\\Python3.7\\lib\\site-packages\\sympy\\matrices\\matrices.py\u001b[0m in \u001b[0;36m_setitem\u001b[1;34m(self, key, value)\u001b[0m\n\u001b[0;32m   2728\u001b[0m         \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mj\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mkey\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkey2ij\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2729\u001b[0m         \u001b[0mis_mat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mMatrixBase\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2730\u001b[1;33m         \u001b[1;32mif\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mslice\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mslice\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2731\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mis_mat\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2732\u001b[0m                 \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopyin_matrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "mellin_transform(atan(x), x, s)\n",
    "# 等很久都没出"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function Identities and Simplifications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:08:50.963136Z",
     "start_time": "2020-04-14T05:08:50.942172Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x + y}{- x y + 1}$"
      ],
      "text/plain": [
       "(x + y)/(-x*y + 1)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "expand_trig(tan(atan(x)+atan(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:09:31.505160Z",
     "start_time": "2020-04-14T05:09:31.491140Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{i \\left(\\log{\\left(- i z + 1 \\right)} - \\log{\\left(i z + 1 \\right)}\\right)}{2}$"
      ],
      "text/plain": [
       "I*(log(-I*z + 1) - log(I*z + 1))/2"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(z).rewrite(log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:09:53.040136Z",
     "start_time": "2020-04-14T05:09:53.028134Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{i \\left(\\log{\\left(- i z + 1 \\right)} - \\log{\\left(i z + 1 \\right)}\\right)}{2}$"
      ],
      "text/plain": [
       "I*(log(-I*z + 1) - log(I*z + 1))/2"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(z).rewrite(log).rewrite(atan)\n",
    "# 变不回去"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{re}{\\left(\\operatorname{atan}{\\left(x + i y \\right)}\\right)} + i \\operatorname{im}{\\left(\\operatorname{atan}{\\left(x + i y \\right)}\\right)}$"
      ],
      "text/plain": [
       "re(atan(x + I*y)) + I*im(atan(x + I*y))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "x, y = symbols('x,y', real=True)\n",
    "expand_complex(atan(x+I*y))\n",
    "# sympy failed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(4 x \\right)}$"
      ],
      "text/plain": [
       "sin(4*x)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "expand_trig(atan(4*x)).simplify()\n",
    "# 好像没有 TrigReduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(x \\right)} + \\cos{\\left(y \\right)}$"
      ],
      "text/plain": [
       "sin(x) + cos(y)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "# 好像没有 TrigFactor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{i e^{i z}}{2} + \\frac{i e^{- i z}}{2}$"
      ],
      "text/plain": [
       "-I*exp(I*z)/2 + I*exp(-I*z)/2"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "atan(z).rewrite(exp).expand()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function Representations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:11:13.034138Z",
     "start_time": "2020-04-14T05:11:13.028132Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "atan(x)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "acot(1/x).rewrite(atan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:12:43.132561Z",
     "start_time": "2020-04-14T05:12:43.128558Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "# no InverseJacobiCS\n",
    "# no InverseJacobiCS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - i e^{- \\frac{i \\pi}{4}} e^{- \\frac{i \\pi}{4}} \\sin{\\left(i x e^{\\frac{i \\pi}{2}} \\right)}$"
      ],
      "text/plain": [
       "-I*exp_polar(-I*pi/4)*exp(-I*pi/4)*sin(I*x*exp_polar(I*pi/2))"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "# no Hypergeometric2F1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "# 没有球面谐函数？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:14:24.056923Z",
     "start_time": "2020-04-14T05:14:24.052919Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "# 没有约化函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 没有 DifferentialRootReduce 微分根约化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:11:20.353081Z",
     "start_time": "2020-04-17T13:11:20.340080Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}36.869897645844 & 53.130102354156\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[36.8698976458440, 53.1301023541560]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "Array(deg(x).evalf() for x in [atan2(3, 4), atan2(4, 3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-17T13:11:54.906906Z",
     "start_time": "2020-04-17T13:11:54.898906Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 90.0$"
      ],
      "text/plain": [
       "90.0000000000000"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "sum(list(Array(deg(x).evalf() for x in [atan2(3, 4), atan2(4, 3)])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:19:22.728953Z",
     "start_time": "2020-04-14T05:19:22.678954Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "atan(x)"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "integrate(1/(x**2+1), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:19:47.920053Z",
     "start_time": "2020-04-14T05:19:47.912059Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x + y}{- x y + 1}$"
      ],
      "text/plain": [
       "(x + y)/(-x*y + 1)"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "expand_trig(tan(atan(x)+atan(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:22:31.537493Z",
     "start_time": "2020-04-14T05:22:31.165476Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x13090a70>"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.plotting import *\n",
    "plot3d(re(atan(x+I*y)), (y, -2, 2), (x, -2.5, 2.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Properties & Relations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:24:08.753522Z",
     "start_time": "2020-04-14T05:24:08.742527Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{i \\left(\\log{\\left(- i z + 1 \\right)} - \\log{\\left(i z + 1 \\right)}\\right)}{2}$"
      ],
      "text/plain": [
       "I*(log(-I*z + 1) - log(I*z + 1))/2"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(z).rewrite(log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:24:23.536665Z",
     "start_time": "2020-04-14T05:24:23.527668Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{i \\left(\\log{\\left(- i z + 1 \\right)} - \\log{\\left(i z + 1 \\right)}\\right)}{2}$"
      ],
      "text/plain": [
       "I*(log(-I*z + 1) - log(I*z + 1))/2"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(z).rewrite(log).rewrite(atan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:25:47.423703Z",
     "start_time": "2020-04-14T05:25:47.415703Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.14159265358979$"
      ],
      "text/plain": [
       "3.14159265358979"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "(16*atan(Rational(1, 5))-4*atan(Rational(1, 239))).evalf()\n",
    "# 无法识别 pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\csc{\\left(x \\right)}$"
      ],
      "text/plain": [
       "csc(x)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "# no Hypergeometric2F1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:27:52.123871Z",
     "start_time": "2020-04-14T05:27:52.047869Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\sqrt{3}, \\infty\\right)$"
      ],
      "text/plain": [
       "Interval.open(sqrt(3), oo)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "solveset(atan(x) > pi/3, domain=Reals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Possible Issues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:28:51.142642Z",
     "start_time": "2020-04-14T05:28:51.127653Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 - \\pi$"
      ],
      "text/plain": [
       "4 - pi"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "atan(tan(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:29:07.156003Z",
     "start_time": "2020-04-14T05:29:07.149007Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "(atan(tan(4))-4)/pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neat Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-14T05:30:18.918056Z",
     "start_time": "2020-04-14T05:30:18.659057Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(\\pi \\right)} + \\frac{x - \\pi}{1 + \\pi^{2}} - \\frac{\\pi \\left(x - \\pi\\right)^{2}}{1 + 2 \\pi^{2} + \\pi^{4}} + O\\left(\\left(x - \\pi\\right)^{3}; x\\rightarrow \\pi\\right)$"
      ],
      "text/plain": [
       "atan(pi) + (x - pi)/(1 + pi**2) - pi*(x - pi)**2/(1 + 2*pi**2 + pi**4) + O((x - pi)**3, (x, pi))"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.plotting import *\n",
    "atan(x).series(x0=I, n=3)\n",
    "# 不支持在 I 展开"
   ]
  }
 ],
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   "display_name": "Python 3.7.0 32-bit",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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   "version": "3.7.0"
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  "latex_envs": {
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   "autoclose": true,
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   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
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   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
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   "labels_anchors": false,
   "latex_user_defs": false,
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   "user_envs_cfg": false
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  "mimetype": "text/x-python",
  "name": "python",
  "npconvert_exporter": "python",
  "pygments_lexer": "ipython3",
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
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