persistence.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "from platform import python_version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 27\n",
    "temp = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def persistence(number, step=1):\n",
    "    temp = []\n",
    "    for i in str(number):\n",
    "        temp.append(int(i))\n",
    "    number = prod(temp)\n",
    "    #print(number)\n",
    "    step+=1\n",
    "    if (len(str(number)))>1:\n",
    "        return persistence(number,step)\n",
    "    return step-1\n",
    "def prod(lis):\n",
    "    a = lis[0]\n",
    "    for i in lis[1:]:\n",
    "        a *= i\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod([3,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "ename": "MemoryError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mMemoryError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-54-9634e4cff325>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m9\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[0;32m      5\u001b[0m     \u001b[0mtemp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpersistence\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m     \u001b[0mplist\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mtemp\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtemp\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      7\u001b[0m     \u001b[0mplist\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mtemp\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[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mend\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\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;31mMemoryError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "m = 0\n",
    "plist = [[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]],[[],[]]]\n",
    "for i in range(0,10**9):\n",
    "    temp = persistence(i)\n",
    "    plist[temp][0].append(temp)\n",
    "    plist[temp][1].append(i)\n",
    "end = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "oeis_current = [[0,0], [1,10], [2,25], [3,39], [4,77], [5,679], [6,6788], [7,68889], [8,2677889], [9,26888999], [10,3778888999], [11,277777788888899]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "oc = p.DataFrame(oeis_current)\n",
    "pdf = p.DataFrame(plist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'pdf' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-044d52b80dc3>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mpdf\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'pdf' is not defined"
     ]
    }
   ],
   "source": [
    "pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(14,14))\n",
    "for i in range(0,10):\n",
    "    ax.scatter(pdf[0][i],pdf[1][i],s=.1)\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = np.polyfit(oc[0][1:],np.log(oc[1][1:]),7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.73966076e-05, -3.28607142e-03,  5.27447543e-02, -4.70986611e-01,\n",
       "        2.49788298e+00, -7.36653437e+00,  1.11829745e+01, -3.59260347e+00])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "yfunc = lambda x : z[0]*x**7+z[1]*x**6 + z[2]*x**5 + z[3]*x**4+z[4]*x**3+z[5]*x**2+z[6]*x+z[7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "63.79005932281376"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yfunc(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'long' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-86-84c0bd824201>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mlong\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0myfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m12\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[1;31mNameError\u001b[0m: name 'long' is not defined"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "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-51-6a2651d730d6>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m40\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m41\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      2\u001b[0m     \u001b[0mtemp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpersistence\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mtemp\u001b[0m\u001b[1;33m>\u001b[0m\u001b[1;36m11\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[0;32m      4\u001b[0m         \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "for i in range(2**40,2**41):\n",
    "    temp = persistence(i)\n",
    "    if (temp>11):\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.302585092994046"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomp(number, primes):\n",
    "    a = number\n",
    "    const = []\n",
    "    prime_iter = iter(primes)\n",
    "    nextp = next(prime_iter, 0)\n",
    "    while(nextp!=0):\n",
    "        while(a/nextp==int(a/nextp)):\n",
    "            const.append(nextp)\n",
    "            a /= nextp\n",
    "        nextp = next(prime_iter, 0)\n",
    "    if (a == 1 and a != number):\n",
    "        return True,const\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decomp(1,primes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, [2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primes = [2,3,7]\n",
    "decomp(32,primes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "decomps = []\n",
    "start,end = (1,10**3)\n",
    "for i in range(start,end):\n",
    "    temp = decomp(i,primes)\n",
    "    if (temp):\n",
    "        decomps.append([i, temp])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2, (True, [2])],\n",
       " [3, (True, [3])],\n",
       " [4, (True, [2, 2])],\n",
       " [6, (True, [2, 3])],\n",
       " [7, (True, [7])],\n",
       " [8, (True, [2, 2, 2])],\n",
       " [9, (True, [3, 3])],\n",
       " [12, (True, [2, 2, 3])],\n",
       " [14, (True, [2, 7])],\n",
       " [16, (True, [2, 2, 2, 2])],\n",
       " [18, (True, [2, 3, 3])],\n",
       " [21, (True, [3, 7])],\n",
       " [24, (True, [2, 2, 2, 3])],\n",
       " [27, (True, [3, 3, 3])],\n",
       " [28, (True, [2, 2, 7])],\n",
       " [32, (True, [2, 2, 2, 2, 2])],\n",
       " [36, (True, [2, 2, 3, 3])],\n",
       " [42, (True, [2, 3, 7])],\n",
       " [48, (True, [2, 2, 2, 2, 3])],\n",
       " [49, (True, [7, 7])],\n",
       " [54, (True, [2, 3, 3, 3])],\n",
       " [56, (True, [2, 2, 2, 7])],\n",
       " [63, (True, [3, 3, 7])],\n",
       " [64, (True, [2, 2, 2, 2, 2, 2])],\n",
       " [72, (True, [2, 2, 2, 3, 3])],\n",
       " [81, (True, [3, 3, 3, 3])],\n",
       " [84, (True, [2, 2, 3, 7])],\n",
       " [96, (True, [2, 2, 2, 2, 2, 3])],\n",
       " [98, (True, [2, 7, 7])],\n",
       " [108, (True, [2, 2, 3, 3, 3])],\n",
       " [112, (True, [2, 2, 2, 2, 7])],\n",
       " [126, (True, [2, 3, 3, 7])],\n",
       " [128, (True, [2, 2, 2, 2, 2, 2, 2])],\n",
       " [144, (True, [2, 2, 2, 2, 3, 3])],\n",
       " [147, (True, [3, 7, 7])],\n",
       " [162, (True, [2, 3, 3, 3, 3])],\n",
       " [168, (True, [2, 2, 2, 3, 7])],\n",
       " [189, (True, [3, 3, 3, 7])],\n",
       " [192, (True, [2, 2, 2, 2, 2, 2, 3])],\n",
       " [196, (True, [2, 2, 7, 7])],\n",
       " [216, (True, [2, 2, 2, 3, 3, 3])],\n",
       " [224, (True, [2, 2, 2, 2, 2, 7])],\n",
       " [243, (True, [3, 3, 3, 3, 3])],\n",
       " [252, (True, [2, 2, 3, 3, 7])],\n",
       " [256, (True, [2, 2, 2, 2, 2, 2, 2, 2])],\n",
       " [288, (True, [2, 2, 2, 2, 2, 3, 3])],\n",
       " [294, (True, [2, 3, 7, 7])],\n",
       " [324, (True, [2, 2, 3, 3, 3, 3])],\n",
       " [336, (True, [2, 2, 2, 2, 3, 7])],\n",
       " [343, (True, [7, 7, 7])],\n",
       " [378, (True, [2, 3, 3, 3, 7])],\n",
       " [384, (True, [2, 2, 2, 2, 2, 2, 2, 3])],\n",
       " [392, (True, [2, 2, 2, 7, 7])],\n",
       " [432, (True, [2, 2, 2, 2, 3, 3, 3])],\n",
       " [441, (True, [3, 3, 7, 7])],\n",
       " [448, (True, [2, 2, 2, 2, 2, 2, 7])],\n",
       " [486, (True, [2, 3, 3, 3, 3, 3])],\n",
       " [504, (True, [2, 2, 2, 3, 3, 7])],\n",
       " [512, (True, [2, 2, 2, 2, 2, 2, 2, 2, 2])],\n",
       " [567, (True, [3, 3, 3, 3, 7])],\n",
       " [576, (True, [2, 2, 2, 2, 2, 2, 3, 3])],\n",
       " [588, (True, [2, 2, 3, 7, 7])],\n",
       " [648, (True, [2, 2, 2, 3, 3, 3, 3])],\n",
       " [672, (True, [2, 2, 2, 2, 2, 3, 7])],\n",
       " [686, (True, [2, 7, 7, 7])],\n",
       " [729, (True, [3, 3, 3, 3, 3, 3])],\n",
       " [756, (True, [2, 2, 3, 3, 3, 7])],\n",
       " [768, (True, [2, 2, 2, 2, 2, 2, 2, 2, 3])],\n",
       " [784, (True, [2, 2, 2, 2, 7, 7])],\n",
       " [864, (True, [2, 2, 2, 2, 2, 3, 3, 3])],\n",
       " [882, (True, [2, 3, 3, 7, 7])],\n",
       " [896, (True, [2, 2, 2, 2, 2, 2, 2, 7])],\n",
       " [972, (True, [2, 2, 3, 3, 3, 3, 3])]]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decomps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "primes237 = p.DataFrame(decomps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "primes237[0].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0.0001,10,100)*1j+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ζ = lambda x : sum([(1/(n**(x))) for n in range(1,10**8)])\n",
    "ζlist = lambda x, n : [(1/(i**(x))) for i in n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = [ζ(i).real for i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "plt.plot(abs(x.imag),y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(630.9935963847154+0j),\n",
       " (156.9904348041871+206.16826892613054j),\n",
       " (86.98784166498862+108.32298812064596j),\n",
       " (69.54597383528869+63.56202930746658j),\n",
       " (60.71067674397936+37.45696854716214j),\n",
       " (53.982518712287614+19.854217084228317j),\n",
       " (47.78419130823748+7.049719393534789j),\n",
       " (41.65516111613271-2.611063912149546j),\n",
       " (35.44900802989491-9.990150017097998j),\n",
       " (29.093083454839665-15.561972756396285j)]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = np.linspace(1,10000,10000)\n",
    "yi = ζlist(.5+14.135j, xi)\n",
    "yreal = [i.real for i in yi]\n",
    "yimag = [i.imag for i in yi]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(10,10**4)\n",
    "y = []\n",
    "for i in x:\n",
    "    y.append(sum(ζlist(.5+13j, range(1,i))))            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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alSJmepYdbe4ZpDHzdBb3vsDX/vdPvNRWDkBKYgILJ+fypdOnsmxKAUun5LuvBokCrt7f779wgtflrzulysnIAHBIq4MOdxdstXbFcPC948KYG4l13XJPWMbcIrYY7oOGT+CUW52ePto1wNr97aw90MbaA+3sb+mjgBw2pMHypG3MOW8FJ04tYMGk3JgdrGA0zIXpvvfxh5cscHrPnU+u576Mj1SFSWGYDWzBNBWXP/hvVQo6gXlybX20d8EULGNuEVvUfwi2EZqLTubddYf5+EA7aw+0c6hdJSuzU5M4YWoBVyyr5KRphciX5nN5xj44a3qUd9w7rjXMT996ul/vm12aya4mJb713OZj3DdpLVSeFP5WeyGUd37g3QkfN//+P7fZ76fEsYKBZcwtYoKGjn4+qGuj6MNnOJ0klv99kEG2kJeRzInVBXzx1GpO0mZSOnVUTluhGoiG+1UcPUa56S+fOD32t038iZtOZcl/vwFAAd3QthdqrzZ9/9xSfbqaLzrB4+aGMZ88dK330FcsYxnz4wEpYagH0nKivSd2WnuH+GBfGx/ua+X9uja75/182gYOp83me+ct4aSphcwoyVJjzTwx7SzVKXroQ5h+ToT2PnDWHeq03w8kwWaM9y9N2KPuREo1slq7ejiwZsIac9crphWzPSelYx3LmE90hnrhsf+Awx/BSTfD+fdE5ZK5Z3CEtfvbeX9fKx/ua2PXMaWBkZ2WxMnTCrn+tGpOm5rDjD/WIxbfSM0p1f6teMopajJ9/QcxbcyNBJpg0xOhSxP2MCwTSalYHJ4dc6VgGmRXqLj5CV/2vXwccutj66K9C6ZhGfOJzuqfqqG/NefA2gdUWGLWBWHf7ODIGBvqO3hf87y3NnYxZpOkJiVwQnUB3z6vgtOmFzG/IoekRC1Q2bgBxoYCE3hKyYSy+dDwcXgOxAR+9kpoI3H1ROiyhD1sldOYOpxIQXBNr4EhhPLO96+esHHzjw502O9/Y2Vs5118YZoxF0IkAuuARinlRWat1yIEhnpg/Z9h4eVKYfC3J8D7vw6LMZdSsqeplzV7Wlizt4WPD7QzNGojMUGwaHIut66o4ZSaQpZU5XuuNmnQvKRJAar1VZ4EGx+HsdHxOi4xwB/WHLDfX1IZXKgrmVEWiP38Zew8fvLntTzrodnIdKpP0+Lm+6Aovo2dL25fOSvauxASZn7zvw7sBGInMHu8s+N5GO6FE25Q+iUnfBn+9QNo3WtKDLSjb5h/17WyZk8L7+1t5Vi3mlU5oySLq0+q4vTpRZw4tcB51Jk3GtdBVmngOuWVJ6kkaPN2h1RujPLIdcFNef/2omFSd4+y2VbDhsPdvt9gFpVafP7w2glnzF/c1BjtXTAVU4y5EGIycCHwE+AbZqzTwgT2/kvFPCdrGfp5lypjvvsVKPp6wKsbHbOx6XAna/a08O7eVrY0dCIl5KYnc/r0IpbPLOKMGcVU5KW7ff/SH71G28CY/bGuFGinYZ3a10Av5/XjO/xxzBnzDfUdTo+DbWC6aXoX7IbNcpoZu+U/RTMhLU/lXBZ/PrLbDjN3Pr3Zfj+eSxJ1zPLMfwV8B8j2tIAQ4ibgJoCqqvgSfY9LxkZh32o1Xk03jrmToWwB7H4NTvPPmB/rGuSd3c28u7uF9/e10jM4SoKA2so8vn7ODJbPLGbR5DyPAxh0zvnF206GHAwt6qDkVtv3BWcw8qogq0wZ8xNvDPz9YeRLfzYpln9kI+0yiwZZDDBeSTFcJCRA5Ynqs51gjBpqEuO5JFEnZGMuhLgIaJZSrhdCrPC0nJTyIeAhgGXLlklPy1mYxJGNMNQFNS5jxaavhA/u91iXbbNJNjd08vauZt7a2cyOo+qSviI3jQsXlLN8ZjGn1RT5HjZs4Ddv7nbS6DZy4X2refnOFdC0XT1RFoRnLQRUnqA6R2OMToMWy08vnR/8iho3skNMB9RJc5ySYjipPFFd5U1gffN4LknUMcMzPw24WAixCkgDcoQQj0kprzFh3RbB0qglE11rkqtOgX/fp2Y8anXEPYMjvLe3lbd2NrN6dzNtfcMkCFg2pYC7LpjN2bNLmFGSFbQ41b1v1jk9TksAfVra9qY+2vuGKdCNeem8oLZBeS3sfBEGu5R8awwStPEd7oOWndQs+hpEY36CPW7+Ccz8VBR2wHweWbMv2rtgOiEbcynl3cDdAJpn/i3LkMcAjRtU6CGnwvl5Lb7cvvNdnj1cwdu7mvn4QDujNkluejIrZhVz9uwSzpxZTF5G6AJV+1p6nR5fuWwS91xW66TXfeUD7/Ov6VshoxCyy4LbkD4L89hWR7NLlHGNlwfN0S0gbZTPOQXWRuGidtISVct/eO2EMeY/eWWX/f6U/LQo7ol5xF4dl4U5HNmohgxo2GySLY1dvL69mSsSKjnwwev8eKSWmaVZ3HDGNM6ZU8LiyjxHzbdJXOMy7VxvmFk5q4g3d7cCsKelH7K3Q+n84GuZ9cTnkU0xY8y/bGjhD6lC+8gGdTtpCbDe/vRv3twdmXK6lEwoX6iM+QTBeEr805eCqzCKNUw15lLK1cBqM9dpEQSDXdC2l7EFl/NRXSuvbz/Gv7Y3cax7kKQEwSl5szkpaSPv3XkWlQXh1TM5qo0/A+c29keuP8nunSdgY6xpB4mhdBlmFUPOJDi62feyEaKjf8R+/zdX1ga/oiMbVVVSdhm3LJ9qr1u/9826yNVGV56kZq6OjQQ9pi9W8VcnJ9aZAAU5cUTdW/Da3dDXFrZNDAyP8fFHawD42mrJ5x9Zy9PrDrOoMpd7L1/E+h+cy/IzziZjuJXK5J6w7Yc7XNvYdW91qjhK4tig6uQMhfJFMWXMjTiVYAZK4wbNK4/iOLPKE2GkH5q2+V42xpmI8XKwwiyRo7cFnroaRgehvx0++6Bpq+4bGuWtXc28suUoq/c08x+2tzkxGcpnLObB2oUsn1FMeoqh67Jsgbpt2grZpabthyu+2tj/59L53P3cNmaLw+qJUhOM+e5XVcIwJTO0dYWIq4BT0Ax0qpJND0qJ7X3DkRm+oSdBD62FSGnDhAljvPz0moIo7om5WJ55pNjyd2XIp50F25+DwdC6+AaGx3hl61G++vgGlv74DW5/ciMbDnXwuaWVfHX+GDIli/939bmcN6/M2ZCDwwM+Ft65h8Y2dnfTzvXqjjkJ9YzIRCgOMWRQvgiQYT8uf/j2M5vMWdFRbT2aZw7O8ffbn1hPRMidpEI9jRHaXhgxxst/c/VSj8uZTvsB+MNpcPB938sGgeWZR4r976huuhV3wZ/Og31vw7zPBLSKwZEx1uxp4aUtR3lzZxP9w2MUZaXwuaWVXLSwnBOqC5Rc7F8PqXZ9T8nE9HzIrYJjkbtk9hYemCUOs1+W889/7QstjKAnQY9ujpxMrAfe2tVivx9Sfbl+YjLU339/1Wx+rHmX/97XHvy6A2XSkglhzI1EdKTgoY9UmCo9Lyyrt4x5JBgbVRN0aq+CiiWQlKY66vww5qNjNv5d18oLm47wxo4meoZGyc9I5pLaCi5aWMFJUwvGV6C07Iapy72vuHSeo1EnDPgbZrhl+VRqPjrCDjmFP6w5EJoxzy5XJ6rm0FQKzSak5p6m7arENLPQ/tQNy2vsxjyiTFoKu15SYcKM+AxPRHVE3OGPIDUXiueEZfWWMY8E7ftgpE+pASalKIN++COPi0sp2X6km+c2NvL8piO09g6Rk5bE+fPLuGhRBafWFJLsqYRwsBt6jvgOWRTPhH1vgW0MEsyfmelvmOG7n6phbG0TL9pOCX2jQkDJPGiKLWMeEk3bg2+kMhu91PXIxrjRjnfFOCIu4vXlhz5SieQwjfyzjHkk0D3FEu2MXFEL6x4Fm83pH3usa5B/bmrkuQ2N7G7qITlRcPbsEi5dPJmzZheTmuSH0W3dq259GfOimTA2DJ31agiByRjDDD9YNdvzgu37SRSSfbYKz8sEQulc2PRkVPW3TVPjGxuFll1Kg94Lj6zZxw3La8zZpjcqagGhqmvi1JgbR8RFtL68v139Lxd8LmybsIx5JGjeCSLBYWCLZ8PoAHQeZCBrCq9uO8qzGxp5f18rUsKSqjz++zPzuWhBOfk+Ynrz/vNl+rRy5sL0RNZfonUdFs30vk/66617w2LMjXg1NK1qFNo+qUr3QjZMJXNguAc6D0F+hLRLXPiGQY1vWqF7BUm/aKtTJ1w3nvk5s4vtJ8wfv7IrMsY8LVd9byZI3Dyi9eV6w1WVCVegHrCMeSRo3qEMZrL2wy5RceHHXnydn+2fRs/QKFUFGdx+9gwuXTyJ6iL/yuquffhDuyEHaBsY4833P2IlAvJ8GLJCTZu6dQ/MPC/QIzKPFmXM90vVxh+yYSrRDF/zzqgZ8xGD+/fwdScGv6Jmz3o1v/hcrX3Qc0SZtBTq3ozLyUNR1S8/9CEkJDtVJZmNZcx9MTIIb/+3ms4TbJt4234onEH34AgvbDrC82vbeQZoqtvEufNP4YoTKjlxakHAQlZr3FQydB2rg4LJKjbvjYwCyCy2e8Zm4qrH4pXWPYzlTGZg0KT4pR7Kat4Os843Z50hEJL317RdaaK4ucqKaBWGkUlLYPMT0NUAeZXR2YcgMeqX56aZnyfyyqGPVH1+cghXaj6wjLkvNj+ppr9vfgq+XRewNyJtNmwd9XwwOpubfvIWAyNjzCnPoT+1mNtmCFICHO6r40nEqUo0+/bKdYpmOmLsJvKVvzqG5Kb5+oa17iaxeBY0m7TxtBxVdjkRkqBNO9T/KCnV56Ib6jtYMiUC8rR6ErRxfdwZc6N++aPXRzBePjKoksYnfSWsm7Gahnyx91/qtr9VJTD8ZHBkjGfWHeaq+18jcaSXD1oz+cziSbzwtdN45fbTySidTkrP4aB3y9PQg0rRwpY+PyVgi2aoMkaTqWvps99/4Bovov82mzbCztnzDLl7smRO1MoTTb2Ub9quEroeyEh2/HyvfzRCIlil8yExJe7j5hE58ekc3aRyH5Xh7X2wjLkvjm1ztL8f2eRz8cbOAX7+2i5Ovedtvv2PLRQMHwXg65edw08/u4CFk/NUOCVvCnQcDHq3jEMPfrBqNtedUkUqw5SJDv511E/xrIIaGGhXQwfChFfR/54jSu+jaAbJhklF33p6Y2gbLZ2rwkejJrXUB4Ax+Xn2rKLgVzTYBV2HvJYl/v7zju7FrsExj8uZSlIKlC1UFS1xhGlyxMGgT2mqDCF/4geWMffGUK/6Qc2+CJLSPbaJSyn5+EA7N/9tPWf87G0eeHcfy6bk88QNJ/G7VarZI63YpZ09vxq6G2F0aPwKA+SG5TX88JIFTBaquuGwNlrMJwXaPoVwUgkJ/aqgeBb3Xu7ocHxbk8YNmpJ5YBtV1SARxpj8/OXlIWiYNO9Ut170aqI2HWfSUhU2sEXoBGICN/7VJDniYGj4WDlvWeH9f1nG3BttWjy5ZI4yvi5Gz2aTvLbtGJ/9wwdc/uCHfHSgjRuXT2PNd87ioWuXcer0IkSXFkpxjWPnVwNSJZJMolKowPNh6eeXJl8z5u0HvC8XLvR4fdHM0FQFXbEnQaMbNw8pSamrE5ZESSXRG5OWqia4MITowkWboewrJDniQJFSTWiqDH+M3kqAeqNDa/0tmOZkzAdHxnhuYyMPr9nP/tY+KgvS+e9L5nHZ0srxoladh1QLr6seg14213EACgMrxfPUkjxFM+aHZKl/A3+N+2ASxpixz3qB1t2qdjnTzysJfymaoer648jYjKNph/re5E72+y0RG/JsT4Ku8xrTj1VMdRx80XUYeo+FPcQCx6tn3r5fzcEcG/W+XI+Kd5NdAfnVyI6DPLC6jjN+/g53P7uVjNREfnv1Yt755gq+cEr1eEMOyvPOdfPlya9Wt0GEOIwtyUYRp8umjdIvU2klh7uf80NEKzVbGVITwyzfeMYRM75okY8RcG37VL272fXKSanq822NrDFfvcuskhwcyU8fn805sx0nQr/+52ZQMA1SsmNWO94V0+SIg0GPl0/2UghgEsenMX/+a/DmD5WSoTd6jkJiCv1JObzflokY6eOh1z5hdlk2j99wEi9+7XQuWljhfdRab7P7WFlWKSQkQfeRgHff2JJs9MQWZHZp8fIAjGP+VFPDLCNjjp37r4sXeF+4/YBT96khBxq6IFLRLHtDUqT46hOOpOCM4hAmOEmpQkR+aLL84nO1wW8nWBISlEKlHwUBsYBpcsTBcPhjSM4IXavfD45PY657FA2feF1stOsI3clFnPHz1Ty2Q8XcHruiir99+SROm17kscnnhkfXUn3Xy1Tf9TINDfWQ6caYJyQqlb8gjLlHOutp8Df5qeMmF2AWXmPGo0PQ3eBkzH/yGccXPmQvs3im1g7v4+rLRPqGHQnBB64NwRPrOgxD3X7Fy6PWPFRRq+L6Efx8g8VvnaBw0PCxEtZLDH9EO2RjLoSoFEK8I4TYKYTYLoT4uhk7FjZGBmBY61D04JGOjNn420f1bNy+k939WcytyOHrn1Hdn3OzBnxu4k17NYakkC4+OObBU84uVxUtZtHVyFEZoDRpwVQVCop0GV/nIZA2RxKWEKViXSmaBbaRqFXqhNb5qSVuI+DNBU15rRq2EkDvRSwQEQ0bnZEBVQFXGf4QC5jjmY8C35RSzgFOBr4qhIjdrIixesTlhy6l5F/bj3Her9bwn//cRkVCJzXTpvO3L5/E7BlaY0vvMb83lcEQ6WKYd494+JhzKgL2zI3xP6e1jgzAQDtHpEP32q+2+vypgFTGNZLoJ9JwiXzpomYRjpubgr2SxT/da6OrELH5lhW16lafhGQxniMbVYlsBCpZwARjLqU8KqXcoN3vAXYCEUwXe8FmG/+cvVSwypHgBLY0dHLFQx9x09/WI4CHr11GRWIXBaWat5ilJfN6vBtzY6y3SHQB0Co9dGTmTILuoypG6ic/esExUCLNeIWtnRT6Uh0hna89tg6f2BOxocfNjZUsPi8q2/er23AZ86IZ6jZCFS0B6dH4omm7+n6m5fi1+PcNoYOIDa0oqIGUrJhPgpqalA6UCCY/weSYuRCiGlgMjOstFkLcJIRYJ4RY19LSMu69pvPBb+FX89VwXyO92j+3dAH0tdDRO8Tdz27lkt+9z/6WXn78mfm8fsdyzp2RixjugUytiy85TZXR9TZ53ayx0qQIzZjjyZhXqHrdwS6/D+vlrQ5P/vdXG74k2hXH5z91qv2pPU0ux+4OExuHjJUs9/mq5W3fr4xBpucuyZCqENJyVRgrDEJi7rj1MUd7e3pyiCtr3hFQiCWioQOdhATVCRrjSdBbH3f8X/LTI1yJ3fCJcla8fMfNxDRjLoTIAv4PuENKOW5asZTyISnlMinlsuJik+uK3fHOT1Q82nU0mjZIWRbUwOggF/3vazy97jBfPm0q73xrBdecPEVVpwxoioTG8VhZZU7evDuMlSbFBs/crWZHTrm6DSDUMmq42HDqANTWMXOGw0vzqz8vq1R1t5pQ0WKsZPFZy9txQJ1IXJLImYbyzu89G6LXVzQzYp757iaHZ/6Hz4fgiY0OqWaqWGwWcqWiVsWEYzgJ2j/i+MH8MRQ54kCRUnnmkyO3TVOMuRAiGWXIH5dSPmvGOkNmpF/dunqcQ8rAPqg50LUFI7x8++n84KK5ZKcZXKp+zZinG4x5din0ePfMjZxZoYxbi8zlzqc2jV8gRzN4Pf4b8wSXWzvdWi4gJ8CJPUIo9buuSMfM97sNsfzuaofe82vbQ7xELp6lDGMAYSwzCKnNvmU3yLGQRsVFrK66vFYNWYnQ1U+oRFRcq+Mg9DVHLPkJ5lSzCOCPwE4p5b2h75LJ9DlCOmM2yZa6wwzKZLb0qGqD+y+uZHaZm9ikO888sxj62/ze9GdmqqB2O9m49V10wxuAZ56c6Hxrp6sRMgqD00vOrYTO4BUcA8Y2prprDZUsOqbqjRTNVFOHfFxNxRT6lWSAlSzGGv2Qr2j8xUqCekYve44zz/w04AvA2UKITdrfKhPWGxhrH4Rdr6j7UmLP8Wsedn1bH1c+9CHb9h9mKCmLH39+BQAJA+NFnS773Xvc/PBbALxaZxDCyihSUrheMHrOGcNtdMgsRkly38ajJ1XNqDXvPmL39PVt+d06lFflSAxHgq4GVTYY5nF1dmndeGrrb94OiakBfzbGGv2Qr2j8pXA6JGfGbBI0YpU97jj8scoJRTBcZkY1y7+llEJKuVBKWav9vWLGzgWwE/Dqd+Dv16jHo4OAdmk90M5LW45w4W/+za5jPZxRlUpOXiEFRaXa653jVrfucDf5ogeAH75lqF7JKFTJyrGRce8BVdGgR+hSkoC+Ztq05Geyu086KUU1FAUSMx9zvrXT3Wg35mnJDjPul/RnXqW64nBNFgeAsZrD55fKXsky3jM3FXt5YnjDAKa38ZfMDrjJJCKaLK4kJCp56BhNgv7EUNkTlWahSZFpFtKZGB2guh631CycwSht23uArz2xkZmlWbx2x3IqM0YQqTmQlqcWGOx0u8p8lHHqxND8oYdc9Hi6C3f+fZP9/oySbOhrpdWmjPmYmypJQMXhfVTI6Kze1WxPaqa6Nv4ZNGBmlKqwkQRuMVRZeERXdAwh1GI89kJfXYkd3mvMjVcUIcV/s0qVWFWYPXPT2vhBM+bBx8sjTkUtHNsSk3K4xkxJRCt+hvvUHIQIhlgg3o35UK8Sa+p18YyGeux3O9pb+Mryafz9K6cwKS9dvZaaDak5gBhXFqh7WXmil36ZyhAGw6SXGHmIm9c1q+0mCPjVVUugt5k2oQxrkicJwSz/jfltTzmGNjiVJQ73qZOS5pnfd0Wt/aWufj/00nO18V8hhFr2NqkqIQE8eO0y7wu371ehhGz3ydqMVJMqWoRQbf1h9sxNa+Pva1XfhRCSnxGnvFYVG4Rh/GDccmSjciwjoJRoJL6N+ds/hvuXOIcHbDbqGh3GcUFxInevmkOyLoY12K2aMRISlEF3Mea6wcynhw5cWrIztO5KD8Zcak1KqYlaO3dfC+1CZdCHxzyEPLLK/K6QGRlVadS0JPdliboxrynOssvPjvjjMOmzHDuDF7caHHH4QT6rBtoPqGalBPdfv99dZWJFS9GsiMbMQx7gDEHLypoqVOYvMZoEjYnJQhFqFtKJb2O+9g/q1qBvsmbnIf7fM6pnaSw5i7xEF890qFtdegOk546LmesGM0/00iXVD9MeD7Ybc/dJ0NTkJMftyCAMdVNUqvSoPYY8skpUCZO7blV/0Y/fILWrn7u8CTo69qEMEpJDCrMElHR1UUt0xdSKluKZ6vMN42g809CHaQSpyWKqUJm/FM1UfQoxlgQ1ThaKuJFr+EQlh42VcBEgPo35yCC8+wvHY4Nx/fYTHzItR3mJiTnlKhRjRPfMQXUJeui+zBe9dGjG/I4ntZhohvcwy7CWlRweHVMGBDhj8VySNAvXM+gm/ptdpvQbBtzH4f2iSzPmOQ5jrsfoPcbqjSQkqCEIIeizJCU433pESq1hKMyVLDp6RUtr5EfIBUzTNlX+GuR4MSsJ6sA4WejXEZ8s9HHE9FiMxKcx3/USvPNjx+NeRy15bVkKd6+sUg+yy1SdscYFv3wThnt4aG2LSqyl5Y1LgOqeZYHosSc/97Xqnrl2pu1zb8xTtMB4SlKifZ+yCsrJSktyet0J/YfrR9zco/ere+aGhiF9Ux5j9a7kVYYUM9cb7UZ8nTx6m1SMNdyVLDp2Yx6eUIsxnOHvR+2Rph3x0fnpij0JGsLVZRiJ6GSh9v3KuYxwiAXi0ZjbbLDpcaenjjQ6flD3XTqLTKnJ1GaVKs9c6wBsbFXeb9NwqkqsufHM01OU4c0XvfQlKg8+JVH7mSYmqxBNAJ45mSUMjajQjX7rhJ8CXuASxjHS3ag8uqRU+1N6l7zfQ3zyqoIOs7T3DdsrB3xuLlJliTp5UyAxJWxJUKMWz69C8QBtY2qIcyzL3nqivFbJSkdhgHbMoTcLRTj5CfFozLf9H+x72+mpzXv22+9nMORIiGaXqazyiDLu2agW/24yVGItLW+cMU8QAoGNHHppt2UCDiMNQGahR2OeprVlpiUnOjpPs4q9W1a7Z+470Tek7ceQa5F5V6NTiAUgOUkZ/MFRP+ugc6uUvO/IoO9lXTAqOfosS9Q1YNx0fxoxhmtCquNOTFIKf2GqtjBq8YTkAbYfUK3xJs7UdKsHFA5iLAkadaXElGwojnBdO/FozJ/7yrinihMMcfGRPkdoJVvzerVhFIWJyqj3yAzSElFDlt00DWXTTyKSvkSVKE0zesIZhR4ToAmasU4QwmGcM0tI196f7upRg7p6AJ866e19w4zYK0ZctEa6xxvz+69cbL//1Sf9kMLNq3KsK0Be3eZol/erLFEkOrbngQsXOEJGtz7hfSKUTyJQnhgyzXolS2hlicaZoHe40wMKB0WzICktZuLmRqXEaYVByFuEQsPHMHmpyiVEmPgy5qNDjsYgA/PyDeGLkQHlmYtER8JyqIcN9R2k2pRn3kM6GanJKswy0jeuozNPKM++W4uZG0u+lDEf75lvqO+wJ11SkjTPPDVHSefiwQgDpGaptl8fnvk9r+6067tML852frG7cdzQ6BWzS9BC9YyNudmuK/byxMCToEI7rtREf8oS9ytDnuhdJ/a/LnYYNXd544Aomql5vlEc7OuLpu0gEkL26IwzQSPWxpOYpMJDMVLRYlRKfDiSSolDver/GOFmIZ34Muavf8/t0+kjhlDJcB/vbNlPly2VBz/UvN3hXm57cgPZQjPmMkMZ6DStRNEQahEIctGMuXBTM5xR5DYBetuTG5BAYoLgt1erhiEylZc0qBV7D3oq+s4q9Rkzf3mr8n7tDUk6Q71q/wNVS3QlN3hjHhC69K0PjLMtQ06rFc1UTkD7ft/LRoum7SocFIxQmoGozgQ9ujnmkqAh1f0HypENahRiFCpZIN6M+SePuH/eWNY30k9LWzt9pLHmsFZjPtTL8IjNHjPvQWu5trf0K2O+ob6DroFhcu2eeeb4bWUUqO25yKoOaYY6Pz1Jead9LfZ4eEaK7oUmuG9Pzyr16ZnbxtT67Q1JOvaGocle3++TnEnqaiaIihaPejHu8CB9G1b0qUMmh1rMrWTZHl+dn66U16rwpgkTq+IWe7PQ0qhsPr6MuSdGDUm74X4yxCB9Mp0+qXk5w73kZyaTLRwx8wQhDJ55JwBff2ojwzYoTlTGvE+ocEaCMXGZUai250uUyuCZVxWqk0f/yBj3vLJj/LJZJT5j5h4rWXQt9FA988QktY4gKlr8blDqb1cnzkgb80LdmJtbnmhaJctQr9K/DoMxj1gnZPkidXtko/flwkxUlRIbPlH5g/QI6qYbmBjGHOzdmf19PWQxSB+p9JKmXhvqoWtglBwcMfOirJRxYZZ0TdqwOlN5z0mZeep1YRB88tHSb6fPYcx/8blF9pK9l7e50dbOLvPpmTuVPRqxe+bl3vfHH3Irgwqz+N2g5Gcli45pglupWerKxeSKFtMqWVp2AdI0Y26c1nTjX0JMHvtLyRyltxPlipaoKSXam4UiX1+uM2GM+b5eFStcX9dIhhikX6aRkKqFU4Z7KcxMJlv0MywTGUILe7gY864BlWJM1qthtCah5p5hHlit1dD6Y8zHRlT7uBZmqSnOIj9DbTM10c0FeVaJkhkY7ve4SqeGJCN69YkH0aqACELXfEN9hz3RluI9pxnwEGej4JbbK5pAKJoRuxUtTZqHb1LDkHFaU1u/e7lm00lMViejKCdBo6aU2L5fhV+jlPyECWTM+0llQKbQ3tFBJoP0kU77qBZmGeolKTGBbPq1eLlQlScuxrwwU1mjkuR+SErjR/+xjMwU9RF9tF8z3nZj7tx+LzQ/UiCU+h3YPXNwVMQ4Vcbo6I1DXrpAvXrmGYVa1YwzidqJY2g0AF3z7kaPeu3uuNUg//rphX7M/QTI96/t3Ci49eKWEGumi2ZGZYScXzTtUBVNef59Lr4wVdsmEMoXKWMei59xuNHj5VFoFtKZMMZ8gFT6SSXZNqgZ81TaR7WOSK3OPEsM0KslP4WAdpvmubvUmmfLXkjLo6Y4iwwtRn20U4vLe/DM87UTQX5msqP701+NDXutuWdj7tSQZKT7qEev/MIFKvQiga8ZjK5H8qpUNj6AYRmdfepzSUqAu1b58Czb96tEq58VGytml9i/oEOhOpjFM9X3wIypTmbTtF2FKTyoSMYNFbXKMYpSEjRis0/d0fCxKkUumhW1XYjzb4+DQZnCAKmkMUimGGQkMQMbCQyLNLu+eTYD9AtlwI91D/HA+0cgIcnumdvrxEe6VUMRbpo3M90b807tcrazf8ShFZPppzHP9m3MPSqzdDd6TH7edcEc0rV86aA7KQFX9EaeAOLm+mqlzY+yuCAqWWwut0Fj12gxJ9RiWiWLlKphKJ4rWXTKa9VtlEIt335mk/1+VJQSJy2N6gnZlC0LIc4XQuwWQtQJIe4yY52BMkQKQ6SSzhCZDNJrU155n0iHYS3MIvoZScqmIleFJNYd6nTSZ9HDLAWJ/fayxaKsFKdbUnNVCZ+LMbdpl5Y2KQ2eeTF+oXvmHnTNN9R30K6dLIZdJ7p0H/FozI3GdWA4PMY8IEEvXcc8GtiNuTlJUNMqWXqOqvyKyZosUdE2L5mjpJSj1An61i6H4F5ElRL1ZqEohljABGMuhEgEfgdcAMwFrhJChEf67YrHPb40SDKDIo28xCEyxBCDicoDH0B55tNLssimn4T0XLthHh2zORnzJK22Llv2eS4vSkhQiVEXY+4UMze08vtFRqE6QXjwzPW4tBDw2ysNNayjQ0paIMdzrNpL7+l4ciYDIjyNQ0M96iQXoGce8HBqT2SVqstgkzxz0ypZ9IEUJqslRkXbPClVacvEgEZLRJUS9WahKCglGjHDMz8RqJNS7pdSDgNPAZeYsN7x1Jzl8aVBmUKPLYWEAWVke8aUZz6YkAFDvdQ195ItBmgeSXV+oxvlxEzZaw+z6KEXoz6yqz7LvpZe+rV4Q3lemmoYSs5QJXH+kJCokqUeas27tdFv6UnCObnVo5U5mlGWCGrAdE5FQMbc74ahjoPqNkC1RL3KLkGEGBMVQkuCRm7qkF+EOF3IE1HRNgcVajnekqC6UuJkH7pEYcYMYz4JMNazNWjPOSGEuEkIsU4Isa6lpcX1Zf9IGd+ROSQ1dUBS6JepFKIMc2Kapl+SkgXDvYyO2cihn15ckm9uNM2zZY89zJKrBZ31W0Az5o5qlm8/s5m+YRXVPXlaoVPDkN9ke+4C9Zz89N0wJLRgv/BXCzfAWnO/wywBliXqpGgJ6DEJP3pha0DvHYde0RJLNG1XV1ZRajQxnfJFKmwUblkIF6I7Ju4T9d2K8v/QDGPuzkqMOy1LKR+SUi6TUi4rLg7Q0BnYcclrTo+7NDGsQVIYIIU82QlA05AyAh1jqTDUQ3ICZDHAYIKLt+zimScyRoYcsHvmeu25fguMC7M0dqjO0qzURG5eMV155i7GXA/h9AyOOsbQGckq86LP4in56Tz70x2pmpVN9XdKRV4VdPn3Q1y9q5khzSNPSvJxsgiwYUjHqP748mbfmu9eKZqhrmYGu0Nbj5k075gYyU+dKMnhfuVvDmXQtCQvC5qNlJpSYnRDLGCOMW8AKg2PJwNhq/+64TXnxpo2qQZIKGOeRpJW95CSoTzzxLRsGO5lblEiCUKSkZNvN6xJiQlOxlx571qbvuaZ60lR/RYYp5yoe+0VuWkq6WjQZdH51FxVSz40JvnW05vGH1i2Z2OuV6KMq0jRjXm25zCLXpfeNzTqX5gir0rpo4/5Tpjqw68BfneVH9K3GUWOkX1+smJ2if0UFrIKYLFWNhaid27UCQ/JboyNqGHTEZguFDHPtWSeqhCLcEVLS6/ju/3ANRE0rB0HlC2YIMb8E2CGEGKqECIFuBJ4wYT1umV4dIwLh/7H/rhbqxsfkCrMotOuxcZbR1JgqJemZpVcrO9LZnqJ8s6nl2Q5GfO2vhG7yJbXSyY9zKIpxI3z3t2EWe44dyYZKcosNbQPjF9ndrk6Cbhp2PEaZknJ9mogczLU5zBi87OLMq9KKQz2+D4fD2snl9REPxpVQhDY0lQW7LdBY1J54jeecRiqCxeVBb+i1r1gGwnbdKHiLEc1U8Ta+pPToHhOVLXNI9o0dTh6k4VcCdmYSylHga8BrwM7gaellNu9vys49rX00tE/wnZZzTGpjK1uwIe0MIuOLUUZ7OT0HORwL8O9yjMZTMyirlmFOeqae5UxHx2kvUtdeuvytz4ToHIMhtRJwCmubhtTyVEXz7wgM8XegCTd1ZZklwHSbdzcaeiFES815jq/N7R2u9WFcSWA8sSA1BI7DgY9Km7U5nwbNPnVymsM0ZiPGPTh/+viBcGvyJ78DE+Y5cEvOK6WItbWD1CxSIVZjockaEP0Jgu5YkqduZTyFSnlTClljZTyJ2as0x3fe3Yr+u/otuHbeHXsBDpQ4ZSR5EwGcHjm9X3KcDYPJSNG+hnqUdUnVy1foEoSMZQmAn9bvYWmniH7YArvYRZt6IWWBHVqGOpvU2VKeu24v+ihEjehFr0Mzub62+g56rOSZcmUfPK0k02yPw0NARhzv5Ofo0PQ1RC0Z25a41BistoHEzVaQtIPb9qm6rJ1iV6T8TkoJFyU16rfQRBTq4IhusnPj2HSkqhMFnIlrjpARwyyfJ/I2dwycidJWiQ1NyvLKcySlaO+yNm56rYMZXgrylwui7VwSl19A+BQTNQ98zRtwHPX4KhH5UTdAZESR624v638OvqIu57x3rPXmLmX5KeO14HSruT6X2vu99DojnpABpz81NG/pAITWraLYmiEXPMOFcf3MXUp7tA7QSMUarnxr44QUn56BLOfw33aZKHox8shzoz5/IrxseFeTbO835ZKPw6xKb1tfyhB3VYILWGpi2vpaI/TRlXLf1mKpsGieebLqpVyYmPnIL96Q6tR1tQUdUEtJ10WPUzixjP3GC4Bg2fubMw31HfQr83+zE4zeIFjo8qL90fH3G+ri2r8yC4zt7QsyLJEnaJsdZKWmFSe2L4/IDGxsNG0PSLJT52IaZeUzVdNcBGqaDGGQP8YyTFxRzaqcGsMxMshzoy57iUbeWrsLD4cm8vqkdkMGmLm9V3KYz/YowyYw5jnja9mATKlCq/k2rQyRc1g33xmDdlp6hLqzZ2aoXbxzJ0SoPbuz/Hll3maDK5+60RmkfoBuIRZ9O7PxATBH64xdH/2NasvkpdKFp2gyhN9GPN9Lb0Mao6+z1OELrwUZMz8AcNxh16eOBNso44mpgAxTn4P6cJ6oEOFIcJclpic6PjvfO/ZCFWYJKerK44oaLRENLRknyxkeeYBk+6mnGGLrOGqkR+QmVNAu3QMOi7NUd6cHmYp1415as74aha0rk80Y56WZ7/0LchMoTJPef967NnVmDslQO1hlvGeeYfmQXT0ufEKExLdzgLVuz/HDUvu1rs/TQ6zgF/G/M6/b7Lfz0lP9bwgKE84NcfxuQXIkin55pUn6hUtLcF1gn71SYf65MxSN2MF/aVJqywKszG/93OL7Pdf2+59AIqplNeqMMtEToI2rFNzW/Ur9SgTV8b8zJklpLlpTqkuzGB2WQ5N0vGh9mndLId61CGWizbV2p+YNL6aBYNnLruUl+yNlEw1VcWTZ56c6baVX69icVvNAlqtuXOYxXNZopZc8iPMEpA+Cyhj3u291ryuWYWlBDhfMbijfb/yyv3tQnWDeeWJoc0D7R9ynE5+e00I7dvNmjEPc5gloholRipq1dWjmxyQmRivlCKK3iwUIyEWiDNjfu8buxkcdTZJyYmCg2391LX02ssVu2U6OZq3XFSiEovTxDG6hTKwztUseQBkaZ55jq3LUa2iMa48UQinln4nz7yvOfDkp052+bgvv9eyRPDLM0/QqljGpPC/ccg26vWHaNNq7FOT/Li0bT8QdPJTx7TyxLQc9TkH2Thk/PaFNPn92FaVfA91dmusos8EDXOo5dbH19vvTyv0TyffFDoOqr6QGAmxQJwZ82lF4388es3v4MgYbeTwl4RLuWXkDjo1w9ubpLz1VDHCQIobjzs5DRJTybR59sy9dYFuqO+grlm9d2DEpsIsHoy5bpAHRmzujaobz9xjWWLnYSXm5ccl3vQSrXxzTPrfOATmJEHHRqGzPuQhzqaVJ0JsjJBr2q6ahUK4WolpyhaASAh7RUv/iOMb8XAkk592cS3LmAdFvpeaXmUcBX/PuZ73bQvQ03KbWgWjWqrq2JiqhknXEqkd/SPqfWm5ds8819Y9LrbrlDDV0fRZvv7URmxAUoLg11cuVmEWD8Z8coGqrOkbHnNUxhjJLleJsZFB+1MeyxK7DilRLD+MwX1X1Nrvv7TVD6WFXBONeXeD8vKDTH7qGPJ47rVtAkEvT4xWPNc2pmmyhKfz0xsRC0ukZKrPOYIaLSFdKQVKwycqnBrBaiRfxJUx/+Kp1U7ZeSM5dnUd9XpehnpcVZRFV0IeAF0JKhzwP59dQGV+Ooc7BtSg5sxi8mydCGxky+5xnrlTWEYnswj62+xJ2WlFGSrc0NvksWHoF59bRLK2+69vd6NdrjcAGaRwPcbMOw9rNeG+qSnOIl3bsF/2S1+vF2PuVFvvjRDLEnVmlTnKUr/22DovS/pB0Sw1QNvrZKfxGJtTQvrhdByEkX5VwhcBZpU6jNwtj0eorR8cM0EnInqzUGIkVb28E1fGvCAzhUIP3nm3Vid3qEMJcfUNq0TVxwfaGU1SHvFYjjJSNcVZFGu1y+vqOyC7jAJbO3n0kojNd8wc7JrmTsnP0WHlWXsw5jXFWeRqZYljNjcBA3vjkLGixYNiYtdhNYDZTwIqT0xOUyqOXtQT/W7lD1It0ZX7r3aoJ+5p6gtpXcEmQW9+zBGf9fQ99ItjWq18hNQSf29IUA9Esry+vFaFDT1M0AoVo+BZRBnuV927MRRigTgz5gC///xSktzsdUGG+nH1atUG58wuoTI/nYNt/WwZUUZvw5Aj2eTkbWeXkS/bKROa5+XSIu82Zp5VAoNdFKdpHajpSY54d6Ct/DoujUPtfcP0aL++wVFDmGW4T1XS5PpvzM0sT9zX0msvEUz25Zi074ekNL/q4b1hvIQ2rTwxQGPe2jNkv//gtSFUsjRtV/Hk4jnBryMAIhp+MBJmOdxvPO3w+s+e5aMCzUyOblKhwxiqZIE4NOZLpuSTmTregiQZwi9LqvK449xZVGj14feNXcYDo59mc8qSce8DIKuUPFsnk4Q2PSjHj/BFtjoxJPerGGRn/4ijwiQ3yHIwF32WX72xB635kxpj8rdLSQ/YE5V+EFR5ogdjbqwxn1GS7XYZO617oXC6KYNuTRshl1Ohhpa0BGbMjddSITWnNG2DwhnqCmgiU6blrsIUahkxVAX88vLFXpY0mRhrFtKJO2MO8Osrxv/jBg3X+8mJCRRkpjClUIVX+rOncc/oVVSXevgBZpeTxBjzxEH12MUYuw2zaN57iTTos3Tp5YL+xbLHkZ6v6tc1nfLXth/Tjkfwq6sMJ6JObbBTAJ55wBOH8qrUScN1gDSwt0kpTCYInPfLHW2aMTcB02rNhYhuRUvTtojFy90RcgLZX1Kz1f8+AhotIQmeBcrhj1XY0Fc/SoSJS2NuHFig09Dh0AjXjbjeHNTcM+j0eBzZKixSm1CnKl9cwiRuR8dp9d3Vqar9Pz8zWVVuQPCeuRDKa9Q8795BVb6YnOByqazHssMVMwdHrXn3+OqXYe1yQUgfl/Cjw0pkyyRVQNNqzSF6I+QGu9QVT4SnC2WmOP7vN/81gknQitqwhFkipjPjipRw+COoOiU62/dCXBpzgO+vmo3AUbI2YviFuxptqZVcOFWjGOhKU570WYmbaU4oGSdnqcfhj3UPOb5EWkgkc0jNM+3sH1GeeWqu8kiCxRDe8FjJ0tWgdLkDiEPripPdnsbWuaKXEurVKAb8lr7tOKD0YwrNMeb6RYUNE2RPi2aok++Qf16qaZUs9jb+EHTQg+B3Bl37vS39XpY0mfJFKvzYG+TcXw98/9ktpq7Pb9rqVL6q6qTobN8LcWvMb1hew4F7LrSXxo24sdO6Bss4Y+jCAzuSGJXajM6cmeNeXzlHeerdg6OO+vC0HEjJpliqOLtNSvWlDdYr18mrUpUqgMcocedh5cEHoKFco8W2bRLuMOiLeKSgRt227xv3kt8ijLrnW2ROmMVYnniLobIkKIq0EXJt/nnnplWyNG1TtxH2zCM6fceILodrctz8NUNp708vjWDI6tBH6tbyzM3Hna9dma8Sn7qHPjjivf7h/QPd1EtlsCsXnjHu9TvOnTleOREgp5wSqTw2gVAesx/t9V7Jq1L1zyODnhuGOg85Gnv8xNg4VNfS4/sNOZNU/N6NZ+53jbluKE3yzI3liV39Q16W9AN7RYt/xty8SpZtE7uN35Xyher26EbvywWI8at31UlTTF23Vw5/pP5/Jn2nzSTujfk3Vk5HAOU5DuW+tQeUZooeVhnW9FycOjgNNHUP8fPRK9kpashY9vlxrxdkplCeoyoPslIN3nB2ORWJalv5GUkqPpzv/Yvls6Vfr1DpaiBFi2OkuMYz2vcF3FFZU5xln1ruV+NQQoLaRtt4Y+53jXlrnco/BDjE2RM1xVn2L+xwqPWJBVOV5LCfSVDTKlmObZvYbfyupOWqhrGJ0jx0aC1UnmRKdZbZhLRHQohfCCF2CSG2CCGeE0LkmbRffnP7ylkcuOdCJ3W4nkFnI6mPmlvm4UdYmJnM67YT+GbufR49pnFDm4Gu9MmUjaoEYfJQu5oJ6uOM7bOl366LUs+wZi2HjVZzsFsJ/BTWeN2OOwKuaCmoGeeZb6jvsNd5p/gakNO213QPxjSNlqRUNRM0SCncoLDZotbGD87Buog23JTXwhHzjHnEqnFc6WtV3+mqk6OzfR+Eenp5A5gvpVwI7AHuDn2XguPmMx3GrW94fMKzLCeVm1c4YrduW/S94K6i5f8OZZAvesmnm89WadU0PsrwfLb06+WGnYfce+YhtMcHXNFSOE0lMQ3dqsbY8acX+ggpte41LV4eFopnRbaipeOAauOPcLxc5/x5jiqtO57aFLkNly9SFViaymiofOWvDjmHiPrHh9eq28oJaMyllP+SUuqu6kdAkAXWoeOuztRYF26zSadljLXjrb3Kk9dv3eFusMTmfjVNaF5KE1fUaO/14THXFGeRrZ0QRsbcxAqyyyEhiY6j++xXASPG1n+7MQ/cMw+4C7RgGowOOg3mbe9VseME4K5VXkSG+tthoD0mY4t2imaokJUX3XZw9gRDCo7obfxRqjH/yWcX2u+H3EUbCBVaruOIH4l3P6hrccg5/PrKWlPW6ReHPoLEFMfxxBhmnti+BLzq6UUhxE1CiHVCiHUtLeaWKencsnyq063Ri7a5BIqNnrY/CT13FRwHUSGZWYlHyerYpVTU/OjK1BOybhOziUmQM4nN27bakzwXzjeUIOrVJUGoEAbcBWqvaHGEWhK0409K8NGoYa9kMdeYG6UcQlYALJoJY8M+R8jdargaKQqlkuXoZlVSGiWlvYg21hipWAwIaAixAskNER2+cegjdSwx2rnr05gLId4UQmxz83eJYZnvA6PA457WI6V8SEq5TEq5rLh4/HxMM/juqrkcvOdCvqt5jG0GT9tVD9wYA3cayOwBd/M7j1JEj0xnDvugcb36R/tRLpimCZqkeRI2ya+mYFCVJyYnCmcPuP2A8t5TQhhZ5i+F48sT9aiUz+hUyy51a7Ixv3CBI6dx6xMhNr/oRrV5u9fFdjc5PPOQKlmOboKSOSpefzyRlgPFsx0a4PHIyKD6/1XGXn25jk9jLqVcKaWc7+bveQAhxBeBi4DPSxlbA//6hx0hka5+Z7m4SVr5YufACC1a6KDTZRkj7sIsNpHIJ7ZZrJCfKK9rsn8/dN27TfB0zV40k6kcASRJwjk8RFtd0HKyyUnq5DE46qdXm12hRLLaHMbc74ah5p3alUp1UPvqif+62BFvHgy1CbBkjhK8avJuzI0EXckipfqO6HXXMUDIjVeBMHmpcnhCNBER3WcjRzaqq7gYTX5C6NUs5wPfBS6WUkawrcw/kpIcnq9rQOMXn1tESgIMjdro6Fde+ui4cT4O3M3vtEl4x1ZLEZ1gG4HZF/m1X3rIxzX0Y6doJtligBI6STV671JC8y7l5QTB/Vc6Yn1ffdIPTfCEBKVBocvYBkLzDiiZbXoJl/HEFnJFS3K6SlgHYMyDpqtBdQ7q49SiRHGW4/O78S8R9JQnLVM5FDd9C4Fwo0GKID/dw5VtODisNQvFs2fug98C2cAbQohNQogHTNgn0zAaL1dqirPISnP+MoxrzvHB4MgoT4+t4A15Apx8q9+eudeYOUCxamipSTjCkLEssatBlT+WBhdzXTG7xF5rPjbmp4dUWGOvxW7vG2bI3xrz5p3K8411Suc5EpPhRK+zjnLy7MEvOL6jbV6uRE1H/200hhY3NxY1/DGSY+IOfaSS+TEmrmUk1GqW6VLKSillrfZ3s1k7ZgYrZpdw/5W1pCcncL+brPfAsLPxzvRSOO2u2SctOZEhUvhu4rfh/J/63QjisRlIR+tOnC4acYpc2Se6R7C0rWSO8qZGh/jRCw4P1msyra9VDbaOoZFaHimdp2aUDna7fdl4WR9SJcvRzapJKUpliTohNTyFQvEcNbO2IcQpUQYidiw2mypLjEE9FiOx18ZkMp+uncTO/77Abdbb1Te9YEGZx/UYm30cQ5GDU9jWwzk9nkSvssvplelMFy6NHXo4IASP1+9WfJ3i2Uosq3UvLxvmh3pNBNpPOuHxzI2fdsjqebrglb7PLtxsWiXLJlXXnhzBCfKxRGKSuippNM+YR4y2vWqCWAzqsRiZ8MbcG8bybQHcce4sj8v+4nOL7Ebk5W1H2dfSS0e/mylAfrBqgSo1HPMkeiUEe6hkbkK98/NN21RTUXpeQNsz4ncrvo7uXbfssn9eCfjwipp3Or/XZDIMkgo/eiHEEInuKesCWC6YpskSY8lPnYh2U05aqkJao8Hp6kRtTFz9++rWMuaxy7DBmEu8hw5qirPstenJCQnc+fdNds/eaQqQH9x1wRz0aL070avVu5rZOFbDAnGA1ESD1T38id9xeU/4XY2iUzhd1UY377DXeLsb2+dE8w5ILwh+fJ4PfmcYiPHy5mNelvSD3MlKP8RDEtQUTZbuo0o8LcrJT52oaZtPXqYqQoLMUdxpGBM3rTCCVzgH31czcUMcSh5ujmtjHijGDsq6ZmWE/Zq240JBZgp6oY27cMdtT21kk62GNDHCH8/TtNG7j6iW6BCz6X7L1+okpajmoeZddplhd3LDThzbprzyMIlJGeVcA7smcoMQSivlmHvP3BT05GeMGPOoaZtP0hyRIOPmxmqzhyOV/JQSDv4bqk+LeXG049qY652iAPNKfTfhGDsobVrMISUxuIG53kSvRkZH2ShVs82yRK2Tsv4DdRviEFljrbnfl60lc6Blp38dpGMjKmShD/ONB0rnqasJW8jFju45ugkQ2kzM6BM1bfPcSarhzYS4ecSGVLfvh95jUH16ZLYXAse1Mdc7Rg/ecyEv37nC5/LG5GHAiUQXfIleNcgiDspS2POaemL3q5BRFHLc1Viu+Q3DYGavlMxBth8gDYcui0dadik9lxjVr3BL6XwY7lVVLQaMjVUh/VAa1qkTYmqEDFAsM2lpUJ551MbEHfy3up1iGfMJhV4WPjLm0NMOVld7UCuLHBweHyhQJwjBW7ZlcGCN6sDc8xrMOj+g6ULuWDG7hBTtv+73VWPJXASSWUJJDHidtHNEG0IQT8ZcF7465jyK7KtPOJLTs/y4cnOLlKqNPcRcRziJqKGcvEypR/a1BfS2bz+zKTz744v69yGzxHRZinBgGfMgsBGEaJULxhODK/oJ4onRFaos8MEzled4wg1Bbs0Zv/VVdLSQyYIE1QnqtarjyEY1BzU/cCGwQDCeh0IW3CqZp5K8+olIo89wpv7tNUEa47Z9MNjpiBfHCMkGLYnvPRvBwRH65xBg89BbuxzifBEbE6fHy6ecGvPxcrCMeUAUZZsnkKR36YuE8Z6R/rU5ICfB2T9QBn35t03zdvWBSx4GL40nt5JWmcMioTRavFZ1HNmkRoWFeRKLUZs7ZMGt5DQVN3cx5kaCjtHq4lKTTwju/WHi3ssdydjXtod4MgyESUtU85SuDR4EERsT13FQyT/HQbwcLGMeEA9cs3TcczOKM4JaV16mktEctTnXSu9r6bWXw6UkAmd8E753RBl1kxi1Od/6RAi22KaxMMGHrsbIgJb8DH+IxajNPWBGlKBisTLmZmvFNXwCKdmqYSiGiKh0rJGUTFXVow9GjmX0+nLLmE883HmkD1wbnMf1+6vd10rf9oTDO8zN0K4ETL7ECyZEtEVOY4ZoJJMBzws1rld1xFNOC2X3/MLYE2CK+a1YAoNddiEo0+LIjeuUNxpirmNCUXWK+lxG/fuMQw6jBcvB9yGjMGhhu0hjGfMQCfby23hiMKZAdx9zaIT8wc2VgBmkaxlQif8/lM22GhKEZL446Hmh+g8AEfMaFm6xT8NRJ9PvP+tIhgZthof7Vf16DCc/dSKaBK06WVU8Hd3k1+K3Pu6Ir+emRfCkWB8/8XKwjHnAXLnMcXm6rNKcqfNGjGKG4RISumhhYAMeXtzUyAbbDGxScErCTs8L1r+vyvzSoyTmFAolc5R2e6OqYHnNMJ/1V8GOJju6SeU7YixermPU049oElTXBD/0oV+L9xu61B69PkKOQuch9RcHJYk6ljEPkHsuq7XXpv/jq2dEe3eC4q4LHAJY/gx4+MYzm+kii+1yChfl7HG/0OgQHP5YeTIRItFgjEK+FE9MhrKFds/cGLoJOr6sx4VjrJJF5yefcVSFRDQJmlWiuoqDiJtHTCnxwBp1GyfxcrCM+XFJoAMeRrTLhfdt86kZ2gnDfeMXOvCemjw/faVJe+mbWWWOK6NbHjdBY6RisWq9t5k07rj+fSiaBVnhGZMYKhGrCnFH1SnKmPvouo1as9D+1ZBZHHXJ4kCwjHkUMV7mPrJmH0+urfe8cAzwgW0ewjaiEkOu7HlV6VVPXR6x/bn/akfVzIAZcxYmL4ORPnMmD42NwqG1StPDYjxVJ6vJQ217vS72dXeqouFGSmXMp62Im3g5WMY8qhgvc3/8yi6+/0+H2FOwJY/hZK1tDqTmwI5/Or9gG4Ndr6gvfwQnl5uuz6HFcteteTn0dR3bAsM9EansMYvIJkE1OVkfcfP36hydohFrFmraDn0tMO2syGzPJCxjHkVcL3ONI0iDLXn0F3/jzUa96yFS1JzTnS+qaeU6+9+BniOw8PJw7GrkyKuCnMkc27ba/lTQBiROapSNV4ffetpz05TpFNYoraEA4uYRCwvtX61up50Zme2ZhGXMY5Rwq8L5G2++1TBpJwmUwR7qhq1POxb6+GGlXz5rVRj21H9M8SynnMIJCbvQU6BBG5CD76skX7bn6VWxgPHq8O3drZHbsBDqSsjPipaIsn+1mveZOznaexIQphhzIcS3hBBSCBG7004tnPA33ry7yeGZ33dlrQqllNfCml/CUK/SrtjzGpxyKySZJ3fgL8mJJmuMVJ1MqeikSoRQ3WEbg0MfxEW8PKpJ0Cmnqpb5rga3L0clhzQ6pK6qauIrxAImGHMhRCVwLnAo9N05/jBqqutcd0pV2LcbjOf/6dpJyqP61I9VDe6fV8HT1ypRrZNuCcNe+ubez5msMVKlSitPTNgV/DqObFLdpNWRSwbHJXqy/MB7bl825pBOrymIxB4p+YWRfuW0xBlmeOb3Ad/BpK7q443vrho/J/OHl8TGEAOPTD0DLn0QBjrV5ejn/xE1rW6zNUaePJBOp8zkRBGCMa97ExBQc7Zp+xUpNtR3RG5jJfNUu7xe0+2CMYf0m6vD0w09jv2rlfpdjOc63BGSMRdCXAw0Sil9Xt8KIW4SQqwTQqxraWnxtfhxxf1X1pKEChncH2y3YYi4+xF7Hfa76Aq4Ywt8+XUomh7GPYss339+Bx/Y5nF64lbOnxtkfXjdm0qPJbPQ3J0LExnJDjPw5T9/HLkNJyRA9Rlw4F2fAmfe5vOayr531ACNtNzIbM9EfBpzIcSbQohtbv4uAb4P/D9/NiSlfEhKuUxKuay4ODabKKLFp2snUXfPhez9yaqIqtn5+hHf8GdHYvR4yZTbJLxrW0SFaOdnZwZRZtnfrkSkpp9r/s6Fid9/3uH1dgyEPFU1MKYuVzKz7c6KnFER1+prVWJxNedEftsm4PM3KqVcKaWc7/oH7AemApuFEAeBycAGIURsp+8t7Pj6ER9ocwz7/XWUrhj8wdjWYUbSbM2YktfNbXw38DfvfwekLaKdsKEStZmg4IhNH3D+rG+JhrhW3VuAhJmfisz2TCZoh0tKuVVKWSKlrJZSVgMNwBIp5TEfb7WIEQL5EUdN/9oPjIMq7n5um5clvaOHlY5SyG7bZC32HSC7XlZx4ElLfC9rAQXTIGcS7Hc25gPRENfa+7oaEVceRyMPDRwvV88WfmCs045oIixEjIMqQuErf3UMGn7XtkhJ+g71+L+CkQHY/RrM+XRc65dHtCRQCBVqOfieR52WiIhrjY2qk/eMc8M+JStcmLbXmocewa4DCzMwhihu+LNjlNf1j0YwERYiZiXH6locAmLTTrtMDdrY83oAK3hLabvMvcSU/Ykk04sdA6tDuboJiqlnQn8bNCtNnKg4Eg0fq3LSGfEZYgHLMz/u+f4qxxSVDYcdgzG6Bh0x9B+sio9JK2ay8rzPQHYFbHvW/zdtf051wlbHnzSy1yHd4UZvm9/3NgBfMiTjIyZztfdfaqh3HDYL6VjG/DjnhuU1To/3tfSOqyRwXSYWMf7of/Pm7tBXmJAA8z4DdW8oj80XA52w6yXllScmh779CBNu+Qiv5FSooSZ73wCg05CM/02kEu97/qXEv+KwJFHHMuYWTnzm/ne54a8maINHGOMVxr1v1gX8/kfW7Bv/5LzPqlDLjud9r2DrM2oU2tIvBrztWCTipYEzPqV0WlxOnBFJvHceViGeOA6xgGXMLXAehdczDKOGPJQ7uYFYJNSrh5+84uj4tLeOT14GJXOVkJi3phYpYf2f1aSiivishABIN/Qd3PxYhE/oMz4FtlG2v/fPyG4XlAoowOwLI79tE7GMuQX3XFbr8TV3cgMTEaOptreOCwEn3qi0yQ+vdfs+QFVBNG2DE28K6z6Gmz8Y+g4GI9w7xOQTIC2XXe85chQRi5fvfFFJCxTGfjjRG5YxtwBguRsho0sXxW//VyjldU7VMQsuVwOq3/2Z+4WlhHd/DrmVsPCKoLcZC0S1eSgxCWrO4QyxCaENM4xIvLynSYV35l4c/m2FGcuYWwDw1xtPYZZhutGiiizuuypC4kYmMbXQsf+BlNd5TZimZsEZ31KVFnVvjX99y9OqrG35tyApQvohEcKrNk84mHkeJaKTeeIgEKF4+e6XAQlzLGNuMYF4/ZtncfCeCzl4z4U8f3t8TVkBeOS64KYzGROmbqVWT7xRdSq+cBv0OcaY0X4AXvsuTFoGi68NatuxhnHy0Jf+5CW0FAae7ZqFTQrOTYzg3M8dL6ghIiVzIrfNMGEZc4sJgxnldW6lVpNS4bI/qbmQf/k01H+ovPS/XKzCLJ99KG67Bl0xTh6q7xj0sqT5fOvVI3wsZ3N+wseR0WPpb1edp3MvjqvBzZ6YGN9ACws3/OyVHT6XcS3B89hNWrEYrv67mnX66Pnw2GdBjsG1/4z7xJmRaE4eskl4ZexEZiU08OSlEZAP3vE82EbjsmPXHZYxt5hQnDzVoePxhzUHfC7/lcfW+VzGTs3ZcPsmuOxRuOJxuG19XJci+kOk4+avjZ0IwNzO1eHf2JanoWiWGoM4AbCMucWE4vfXBNaWPjTqKEr86aXzvSypkZ4H8z8Lcy6C5PQA9y4+MMbNv/jIRxHZpn4V1Uw+n9hm+teoFQod9WpO68LLJ0SIBSxjbjHBcA2TeAu1uJYvRnW4cQxhjJs3dA1FZJvGq6ju6gugaSu0uenKNYstT6vbhZeHbxsRxjLmFhOO3LQk+31voZbvRVodME6I9kntnP/4CiAcBtdspIQtf4cpp0Fe+IenRwrLmFtMOB69/kSnx0addiPGrk+/QizHKeHWaXlxU6PzE7mT1ASizU941DgPiUMfQdveuG/ycsUy5hYTDtdhBp/97XvjlrnhUeca6mh7o7FGkiFwflOYhdfufNrNPPjaz0PnIaj/t/kbXPcnSM2BBZeZv+4oYhlziwmJUYrgoJt66Td3O+ao1BROzERmKNx3+SL7/eEwOMdGRm2Oa6T79Rb+ORcpg7vpCXM31tcKO/4Ji66ElEyfi8cTljG3mJC4ShGc97/vuL0P8Mytp0dkn+KJSM18dS19tG83OV1VDe14XmnFm8Wmx5Ws8bIvmbfOGCFkYy6EuE0IsVsIsV0I8XMzdsrCwgyWVebY7+9u6efahz/k2oc/ZHdLv/350sxk08bOTWT8acAKhmu8lT4u+xKM9MPGx8zZ2NgIfPwIVJ06Idr3XQnJmAshzgIuARZKKecBvzRlrywsTOAfX3Ue37ZmXztr9rU7PffqN1ZEcI/ii0AbsILhqKH08Rsrpzu/WL4IppwOax9UA5dDZduz0HUITvt66OuKQUL1zG8B7pFSDgFIKSM8nsTCwjur5nmWdV01r8Tyyr0QaANWoLhWGd2+ctb4hU6+RRng3S+HtjGbDf59nxo2EucThTwRqjGfCZwhhFgrhHhXCOFRtk4IcZMQYp0QYl1LS0uIm7Ww8I/ff+EEFlWMF+BaVJHF778QnMri8YLric7taL0QuP5RP1QZZ10A+dXw3r3epz35YvfL0LITTrtjwoiiuZLkawEhxJuAuykF39fenw+cDJwAPC2EmCbl+E9dSvkQ8BDAsmXLQvivWFgERjzK+cYKuWlJdGljh378yi5Th3tvbui237/uFA/NOwmJsPw78PytaiJQMEMkxkbhzR9B0UyY/x9B7m3s4/MUJaVcKaWc7+bveaABeFYqPgZsQFG4d9rCwiIyuDZgmYVrFcsPL1ngeeGFVyhD/PaPwTYW+MY2/EU1Ca38kZpoNEEJ9Xrjn8DZAEKImUAK0OrtDRYWFvGDawOW16lMAXD1QwEIeCUmwdk/gNbdarh2IPQ2w9v/rRKpsy4I7L1xRqjG/E/ANCHENuAp4IvuQiwWFhbxS2qSoxvUOJUpFJp6HFUstyyf6vsNcy6G6SuVYe5q8G8jUsIr34LhfrjovgmjjuiJkIy5lHJYSnmNFnZZIqV826wds7CwiA0eNLmqxdW7/+6qub7fJARceC9IGzx7k6oZ98X6R1XT0YrvQvHMIPc2fpiYaV0LCwvTWDHbubzzrn9sCml9QXv3+VPg07+G+vfh1e96r27Z9w688h2Yfq6qYDkOsIy5hYWFT2aXOnRMnlrX6GVJ77gmPu1aLP6y8HI49XZY90d46U4YdaO3vuN5ePJKlTT9j4dVRcxxgGXMLSwsfPLETac6PR4nW+snlz/wgdPjoDRgzv3/VBfn+kfhoRWw8XE4thX2vglPX6v+SubCF1+E9Hyfq5soTNw6HQsLC9NwbSC67alNQRnitj5HrNuobBkQQiiDXnkyvPGfqgZdJyUbzrwLzvgmJB1f3b2WMbewsPCLW5ZPddJo2dfSS03x+O5aT1z78IdOj12VLQNm9iqYeT4c2wIdB5UXPvkESMkIbb1xihVmsbCw8AvXqpOLf/NuQO83ipxV5qaask8kJEBFLcz7DEw787g15GAZcwsLiwAwCpf1jcCG+g6/3nfZ75ynPT1/+3JT98vCMuYWFhYB4CpO9h9/+MDDkg5W72pm3WGHDktFdoqlVhkGLGNuYWERECtnOeSXJHDr37zPCP3SX5xff+kOS/gsHFjG3MLCIiAeuf4kp8evbG/2WKp4zi/exjDik1Oq8yyvPExYxtzCwiJgXPVUbntqE6t3Oc+mOe9/32Ff24DTc0/efFrY9+14xTLmFhYWAfPdVXOZVexcOXLdnz/hkt+8y76WXqrvetlp1ioE0e1pERCWMbewsAiK1795FvlpziZk85Fezvnf8SWLly4qC67b08JvLGNuYWERNBt/eAG5qd6lZVfNKwm9QcjCJ5Yxt7CwCInNP1rF8pqCcc9nJsPBey60Zq1GCKud38LCImT+euMp0d6F4x7LM7ewsLCYAFjG3MLCwmICEJIxF0LUCiE+EkJsEkKsE0KEZ5S3hYWFhYVXQvXMfw78SEpZC/w/7bGFhYWFRYQJ1ZhLIEe7nwscCXF9FhYWFhZBEGo1yx3A60KIX6JODKd6X9zCwsLCIhz4NOZCiDcBd/Odvg+cA9wppfw/IcTlwB+BlR7WcxNwE0BVVVXQO2xhYWFhMR4hpfS9lKc3C9EF5EkppRBCAF1Syhw/3tcC1Ae52SKgNcj3xivWMR8fWMd8fBDKMU+RUha7eyHUMMsR4ExgNXA2sNefN3naGX8QQqyTUi4L9v3xiHXMxwfWMR8fhOuYQzXmNwK/FkIkAYNoYRQLCwsLi8gSkjGXUv4bsBR0LCwsLKJMPHaAPhTtHYgC1jEfH1jHfHwQlmMOKQFqYWFhYREbxKNnbmFhYWHhgmXMLSwsLCYAcWPMhRDnCyF2CyHqhBB3RXt/QkEIUSmEeEcIsVMIsV0I8XXt+QIhxBtCiL3abb7hPXdrx75bCHGe4fmlQoit2mu/0er9YxIhRKIQYqMQ4iXt8YQ+XgAhRJ4Q4h9CiF3a//uUiXzcQog7te/0NiHEk0KItIl4vEKIPwkhmoUQ2wzPmXacQohUIcTftefXCiGqfe6UlDLm/4BEYB8wDUgBNgNzo71fIRxPObBEu58N7AHmooTK7tKevwv4mXZ/rnbMqcBU7bNI1F77GDgFEMCrwAXRPj4vx/0N4AngJe3xhD5ebX//Atyg3U8B8ibqcQOTgANAuvb4aeC6iXi8wHJgCbDN8JxpxwncCjyg3b8S+LvPfYr2h+LnB3cK8Lrh8d3A3dHeLxOP73ngXGA3UK49Vw7sdne8wOvaZ1IO7DI8fxXwYLSPx8MxTgbeQjWX6cZ8wh6vtn85mnETLs9PyOPWjPlhoABV9vwS8KkJfLzVLsbctOPUl9HuJ6E6RoW3/YmXMIv+JdFp0J6Le7TLp8XAWqBUSnkUQLst0RbzdPyTtPuuz8civwK+A9gMz03k4wV1JdkCPKqFlx4RQmQyQY9bStkI/BI4BBxFyXv8iwl6vG4w8zjt75FSjgJdQKG3jceLMXcXL4v7mkohRBbwf8AdUspub4u6eU56eT6mEEJcBDRLKdf7+xY3z8XN8RpIQl2K/0FKuRjoQ11+eyKuj1uLEV+CCiVUAJlCiGu8vcXNc3FzvAEQzHEG/BnEizFvACoNjycT59rpQohklCF/XEr5rPZ0kxCiXHu9HGjWnvd0/A3afdfnY43TgIuFEAeBp4CzhRCPMXGPV6cBaJBSrtUe/wNl3Cfqca8EDkgpW6SUI8CzKFnsiXq8rph5nPb3aHIpuUC7t43HizH/BJghhJgqhEhBJQReiPI+BY2Wsf4jsFNKea/hpReAL2r3v4iKpevPX6lluKcCM4CPtUu5HiHEydo6rzW8J2aQUt4tpZwspaxG/e/ellJewwQ9Xh0p5THgsBBilvbUOcAOJu5xHwJOFkJkaPt5DrCTiXu8rph5nMZ1XYb6zXi/Ool2EiGAZMMqVNXHPuD70d6fEI/ldNQl0xZgk/a3ChUTewulPvkWUGB4z/e1Y9+NIbMPLAO2aa/9Fh9Jkmj/AStwJECPh+OtBdZp/+t/AvkT+biBHwG7tH39G6qCY8IdL/AkKi8wgvKiv2zmcQJpwDNAHariZZqvfbLa+S0sLCwmAPESZrGwsLCw8IJlzC0sLCwmAJYxt7CwsJgAWMbcwsLCYgJgGXMLCwuLCYBlzC0sLCwmAJYxt7CwsJgA/P89yaaCqDUDPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.scatter(xi,yreal)\n",
    "#plt.scatter(xi,yimag, color=\"RED\")\n",
    "plt.plot(x,np.sqrt(x)/14.135)\n",
    "plt.scatter(x,[i.imag for i in y],s=1)\n",
    "plt.plot(x,[i.real for i in y])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-6.989047421090567 -1.06943384522942\n"
     ]
    }
   ],
   "source": [
    "print(sum(yreal),sum(yimag))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [],
   "source": [
    "yreal = [i.real for i in y]\n",
    "yrpos = [i if i>0 else 0 for i in yreal]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x1008 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1, figsize = (14,14))\n",
    "\n",
    "ax.plot(x,yrpos)\n",
    "ax.scatter(ypcFrame[0],ypcFrame[1],s=1, color=\"RED\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [],
   "source": [
    "ϵ = 0.01\n",
    "xfit = np.sqrt(x)/14.135\n",
    "ypeak = [yrpos[i] if (around(yrpos[i],xfit[i], ϵ)) else None for i in range(len(yrpos))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [],
   "source": [
    "ypeakcat = []\n",
    "ypdif = []\n",
    "for i in range(len(ypeak)):\n",
    "    if ypeak[i] != None:\n",
    "        ypeakcat.append((x[i],ypeak[i]))\n",
    "for i in range(len(ypeakcat)-1):\n",
    "    ypdif.append(ypeakcat[i+1][1]-ypeakcat[i][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [],
   "source": [
    "ypcFrame = pd.DataFrame(ypeakcat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11</td>\n",
       "      <td>0.237234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>39</td>\n",
       "      <td>0.432443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>40</td>\n",
       "      <td>0.440740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>61</td>\n",
       "      <td>0.548760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>62</td>\n",
       "      <td>0.550329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>8114</td>\n",
       "      <td>6.364777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>8115</td>\n",
       "      <td>6.364782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>8116</td>\n",
       "      <td>6.364768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>8117</td>\n",
       "      <td>6.364735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>8118</td>\n",
       "      <td>6.364682</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>186 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        0         1\n",
       "0      11  0.237234\n",
       "1      39  0.432443\n",
       "2      40  0.440740\n",
       "3      61  0.548760\n",
       "4      62  0.550329\n",
       "..    ...       ...\n",
       "181  8114  6.364777\n",
       "182  8115  6.364782\n",
       "183  8116  6.364768\n",
       "184  8117  6.364735\n",
       "185  8118  6.364682\n",
       "\n",
       "[186 rows x 2 columns]"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypcFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {},
   "outputs": [],
   "source": [
    "def around(y,x, ϵ = 0.001):\n",
    "    if y<x and y>x-ϵ:\n",
    "        return True\n",
    "    if y>x and y<x+ϵ:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(2,10000,100000)\n",
    "y = np.sqrt(x)*np.sin(np.log(x))/14.135\n",
    "z = np.sqrt(x)/14.135"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.plot(x,z)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-174568.40421175    +0.j        , -177475.40342481+11773.65390954j,\n",
       "       -186813.30827016+24504.06331208j, ...,\n",
       "       -204787.04641555-39351.6396066j , -186813.30827016-24504.06331208j,\n",
       "       -177475.40342481-11773.65390954j])"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.fft.fft([i.real for i in y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.34966808399698274-0.9368736473153031j)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.e**(np.pi*2j*np.log(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def comex(base,s):\n",
    "    return (base**(s.real))*(complex(np.cos(np.log(base)*s.imag),np.sin(np.log(base)*s.imag)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1+1.2246467991473532e-16j)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comex(np.e,np.pi*1j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [],
   "source": [
    "freq = np.fft.fftfreq(y.shape[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999000000000005"
      ]
     },
     "execution_count": 274,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(freq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000,)"
      ]
     },
     "execution_count": 272,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "plt.plot(freq,np.fft.fft([i.real for i in y]).real)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [],
   "source": [
    "fourierTransform = np.fft.fft(y)/len(y)           # Normalize amplitude\n",
    "\n",
    "fourierTransform = fourierTransform[range(int(len(y)/2))] # Exclude sampling frequency \n",
    "\n",
    "samplingFrequency = len(y)\n",
    "\n",
    "tpCount     = len(y)\n",
    "\n",
    "values      = np.arange(int(tpCount/2))\n",
    "\n",
    "timePeriod  = tpCount/samplingFrequency\n",
    "\n",
    "frequencies = values/timePeriod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02400005-4.97023578e-01j, 0.03316384-3.44766338e-01j,\n",
       "       0.03070027-2.63191324e-01j, ..., 0.00034522+6.97374472e-05j,\n",
       "       0.00034519+6.98508332e-05j, 0.00034517+6.99642215e-05j])"
      ]
     },
     "execution_count": 294,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fourierTransform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "plt.plot(frequencies, abs(fourierTransform))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}