2 - Activation Functions.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training of neuron with various activation functions."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Part 1: A college professor believes that if the grade for internal examination is high in a class, the grade for external examination will also be high. A random sample of 7 students in that class was selected, and the data is given below:\n",
    "\n",
    "          Input:  0.1  | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7\n",
    "\n",
    "          Target: 1.2 | 1.4 | 1.55 | 1.75 | 2.01 | 2.2 | 2.35\n",
    "\n",
    "Write a python program for linear regression using a single neuron (with proper activation function) on the above dataset, and find the coefficients w1 and b. Predict the external marks if internal marks are 0.15. Draw the scatter plot between Internal Exam and External Exam .Draw a straight line with red line using above w1, w2 and b."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    " # Training a neuron to learn \n",
    "import numpy as np\n",
    "def neuron_training(x,target):\n",
    "    #initializing the weight\n",
    "    w=np.random.randn(1,2)\n",
    "    eta=0.1\n",
    "    epoch=0\n",
    "    Etotal=1\n",
    "    Erequired=0.1\n",
    "    while(Etotal>Erequired and epoch<100):\n",
    "        Etotal=0\n",
    "        epoch=epoch+1\n",
    "        for i in range(len(x)):\n",
    "\n",
    "            #forward pass\n",
    "            input=x[i]\n",
    "            d=target[i]\n",
    "            new_input=np.append(input,1)\n",
    "            y=np.dot(w,new_input)\n",
    "\n",
    "            #Gradient descent\n",
    "            error = 0.5*(d-y)**2\n",
    "            Etotal=Etotal+error\n",
    "            # print(\"Error: \",Etotal,\"\\n\")\n",
    "            delta_w=eta*(d-y)*input\n",
    "            w=w+delta_w\n",
    "        Etotal=Etotal/7\n",
    "        print(\"Error: \",Etotal,\"\\n\")\n",
    "        \n",
    "\n",
    "    return w,epoch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:  [0.72099977] \n",
      "\n",
      "Error:  [0.28869293] \n",
      "\n",
      "Error:  [0.11581014] \n",
      "\n",
      "Error:  [0.0483952] \n",
      "\n",
      "Final weight:  [[1.07777397 1.19181212]]\n",
      "Epoch =  4\n",
      "Problem solved with one neuron\n"
     ]
    }
   ],
   "source": [
    "# Defining the input and output\n",
    "input_array = np.array([[0.1],[0.2],[0.3],[0.4],[0.5],[0.6],[0.7]])\n",
    "output_array = np.array([[1.2],[1.4],[1.55],[1.75],[2.01],[2.2],[2.35]])\n",
    "output=neuron_training(input_array,output_array)\n",
    "weight=output[0]\n",
    "epoch=output[1]\n",
    "print(\"Final weight: \",weight)\n",
    "if epoch == 100:\n",
    "    print(\"Epoch limit reached\")\n",
    "    print (\"Problem cannot be solved with one neuron\")\n",
    "        \n",
    "else:\n",
    "    print(\"Epoch = \",epoch)\n",
    "    print (\"Problem solved with one neuron\") \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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dLhfjx4+nY8eOBAcHU6NGDebMmeO+T1JSEi6XiwMHDriPJScn43K52LFjB0lJSdx5552kp6e77z1kyJB8vT8RESk6Sm48KDsb+vaF063Kf/JYv36F10U1a9Ys6tSpQ+3atbnjjjuYOHFiri0CPv30U/773/9y3XXXsW7dOhYuXEjz5s0BSEhIIDo6mmHDhpGWlkZaWlqeX/fgwYP06NGDZcuWsXLlSmrVqsV1113HwYMH83yPxx9/nA8//JApU6awdu1aatasSYcOHfj999/zdH3Xrl155JFHqFevnjv+rl27up9/9tlnufHGG/nuu++4/fbbufXWW9m0aVOe7n3FFVcwevRoQkND3fd+9NFH8/zeRESKlexsOHrU0RCU3HjQ0qWnVmz+zhhITbXnFYYJEyZwxx13AHDttdeSnp7O4sWL3c8///zz3HrrrQwdOpS6devSqFEjBg4cCECFChUICAggJCSEypUrU7ly5Ty/btu2bbnjjjuoU6cOdevW5e233+bIkSO5XvtsDh8+zPjx43nppZfo2LEjl1xyCe+88w7BwcFMmDAhT/cIDg6mXLlylCxZ0h1/cHCw+/mbb76Ze+65h4svvpjnnnuOpk2b8vrrr+fp3oGBgYSFheFyudz3LleuXJ6uFREpVrZvh9atoU8fR8NQcuNBeS125KMokmebN29m9erV3HbbbQCULFmSrl275koOkpOTufrqqz3+2nv27OHee++lVq1ahIWFERoayqFDh9i5c2eert+2bRtZWVm0bNnSfaxUqVI0b948z9WVc2nRosUpbU/dW0Sk2DMGJkyARo1g2TL44ANwcNyndgX3oKgoz56XHxMmTODEiRNUqVLFfcwYQ1BQEGPHjiUsLCxXJSOvSpQoccru11lZWbnaPXr04LfffmPMmDFUq1aNoKAgWrRowfHjxwv2ZgoYx/ncG8h1f0/dW0TE7+3dC/feCx9/bNtxcTB1Kvzt+6ioqXLjQXFxEB0Nf45xPYXLBTEx9jxPOnHiBFOnTmXUqFEkJye7H9999x1VqlRhxowZADRs2JCFCxee8T6BgYFk/2NAUMWKFdm9e3euL/7k5ORc5yxfvpw+ffpw3XXXUa9ePYKCgti/f3+e47/ooosIDAxk+fLl7mNZWVl88803XHLJJe44Dh48yOHDh88Yx+niP2nlypWntOvWreu+N5BrnFF+7i0iUmx9/DHUr29/BgbCyJHw1Vd2irCTTDGTnp5uAJOenn7Kc0ePHjUbN240R48eLfD9P/zQGJfLPmydzj5OHvvww/OJ/vQSExNNYGCgOXDgwCnPPf7446Zp06bGGGO++uorU6JECTNo0CCzceNG8/3335sRI0a4z23fvr35z3/+Y3755Rezb98+Y4wxGzduNC6Xy4wYMcJs3brVjB071pQvX95Uq1bNfV2TJk1M+/btzcaNG83KlStNXFycCQ4ONq+++qr7HMAkJiae8T307dvXVKlSxXz22Wfmhx9+MD169DDly5c3v//+uzHGmN9++82ULVvW9OnTx2zdutW8//77pkqVKubvv8Lvv/++KVu2rFm3bp3Zt2+fOXbsmPu1IyIizIQJE8zmzZvNoEGDTIkSJcwPP/xgjDHm+PHjJiYmxtx8881my5YtZt68eaZ27doGMCkpKcYYY5YvX24A8+WXX5p9+/aZw4cP5/0/0HnyxO+liIhHZWQYc9ddf33JNWhgzHffFepLnu37+5+U3PyNp75EPvzQmOjo3MlNTEzhJDbGGPPvf//bXHfddad9btWqVQYw3/35S/fhhx+axo0bm8DAQBMREWG6dOniPnfFihWmYcOGJigoKFfSMH78eBMTE2PKli1r4uPjzfPPP58ruVm7dq1p2rSpKV26tKlVq5aZPXu2qVatWr6Sm6NHj5qHH37YREREmKCgINOyZUuzevXqXOckJiaamjVrmuDgYPPvf//bvP3227niPHbsmLnxxhtNeHi4AcykSZPcrz1u3DjTvn17ExQUZGJjY80HH3yQ697Lli0zDRo0MKVLlzZxcXFm9uzZuZIbY4x54IEHzAUXXGAAM3jw4DO+F09TciMiXmXJEmOqV//r/9wffdSYP/9nsjDlJ7lxGXO6icv+KyMjg7CwMNLT0wkNDc313LFjx0hJSaF69eqULl36vF4nO9vOikpLs2Ns4uIgIOC8bikF5HK5SExMpHPnzk6HUiCe/L0UESmwzEwYNAheesn+f3u1anZszVVXFcnLn+37+580oLiQBATY2XAiIiI+b/16uOMO+P57277zThg9Gs6RZDhFA4pFRETk9LKz4eWXoWlTm9hEREBiIkyc6LWJDahyI8VAMet5FRHxjJ9/hh494OSCrP/+N7z7LlSq5GxceaDKjYiIiPzFGJgyBRo0sIlN2bLwzjt2urcPJDagys1p6f/0xZvo91FEisy+fXD//bbrCeCKK+yg4YsucjaufFLl5m9KlSoFwJEjRxyOROQvJ38fT/5+iogUik8/tdWaxEQoWRJeeAGWLPG5xAZUucklICCA8PBw9u7dC0CZMmVwnWm5YZFCZozhyJEj7N27l/DwcAK0loCIFIZDh+CRR+Dtt237kktg2jRo0sTZuM6Dkpt/OLkb9skER8Rp4eHh+dqlXUQkz77+GuLjYds22+7f31ZsfHxNLSU3/+ByuYiKiiIyMlKbJ4rjSpUqpYqNiHje8eMwbBgMHw45OXbjw8mToW1bpyPzCCU3ZxAQEKAvFREpVFrJXByxcaNdkG/dOtvu3h1eew3Cwx0Ny5McHVA8fPhwmjVrRkhICJGRkXTu3JnNmzef9Zp33nmHuLg4ypcvT/ny5WnXrh2rV68uoohFRDwjIcFunNymDXTrZn/GxtrjIoUiJ8euKvyvf9nEpkIFmD3bzobyo8QGHE5uFi9eTK9evVi5ciULFiwgKyuLa665hsOHD5/xmqSkJG677Ta++uorVqxYQUxMDNdccw27du0qwshFRAouIQFuugl++SX38V277HElOOJxO3dC+/Z2TE1mJnTsCBs22F84P+RVG2fu27ePyMhIFi9ezFV53IgrOzub8uXLM3bsWOLj4895fn423hIR8bTsbFuh+Wdic5LLBdHRkJKiLirxAGPg/fehd29IT4cyZWDUKLuWjY/NBvbZjTPT09MBqFChQp6vOXLkCFlZWWe8JjMzk8zMTHc7IyPj/IIUETkPS5eeObEB+12UmmrP0+a7cl5++w0efNB2PQE0bw7vvQcXX+xsXEXAaxbxy8nJoV+/frRs2ZL69evn+bonnniCKlWq0K5du9M+P3z4cMLCwtyPmJgYT4UsIpJvaWmePU/ktD7/3C7IN3u2LQEOHQrLlxeLxAa8KLnp1asXGzZsYObMmXm+ZsSIEcycOZPExERKn2FO/sCBA0lPT3c/UlNTPRWyiEi+RUV59jyRXA4fhl697JiatDSoUwdWroRBg+yqw8WEV7zT3r17M2/ePJYsWUJ0dHSernn55ZcZMWIEX375JQ0bNjzjeUFBQQQFBXkqVBGR8xIXZ8fU7Nplu6D+6eSYm7i4oo9NfNyqVXZa908/2XafPjBiBAQHOxuXAxyt3Bhj6N27N4mJiSxatIjq1avn6bqRI0fy3HPP8fnnn9O0adNCjlJExHMCAmDMGPvnf47nPNkePVqDiSUfsrJg8GBo2dImNlWrwv/9n/1FK4aJDTic3PTq1Ytp06Yxffp0QkJC2L17N7t37+bo0aPuc+Lj4xk4cKC7/eKLL/Lss88yceJEYmNj3dccOnTIibcgIpJvXbrAnDn2O+jvoqPt8S5dnIlLfNCPP9qdu4cNs1PxbrsN1q+3076LMUengp9pU8pJkybRs2dPAFq3bk1sbCyTJ08GIDY2lp9//vmUawYPHsyQIUPO+ZqaCi4i3kIrFEuB5eTAG2/AY4/BsWNQvjyMHw9duzodWaHJz/e3V61zUxSU3IiIiE/btQvuvBMWLLDt9u1h0qRTS4F+Jj/f314zW0pERETO4YMP7BTvBQvseJqxY+GLL/w+sckvr5gtJSIiImfxxx92iveMGbbdrJldkK92bWfj8lKq3IiIiHizBQtstWbGDDsoa/BguyCfEpszUuVGRETEGx09Ck8+Ca+9Ztu1asG0aXYbBTkrJTciIiLeZs0auyDfjz/a9kMPwciRULass3H5CHVLiYiIeIsTJ+C556BFC5vYVK4Mn30G48YpsckHVW5ERES8wU8/2WrNqlW2ffPNdu2aCy5wNi4fpMqNiIiIk4yxSUzjxjaxCQuzY2s++ECJTQGpciMiIuKUtDS4+27b9QTQti1MngwxMY6G5etUuREREXHCnDlQv75NbIKC4NVX7bRvJTbnTZUbERGRonTgADz8sO16AmjSxP75kkscDcufqHIjIiJSVL76Cho2tMlMiRLw9NOwcqUSGw9T5UZERKSwHTsGTz1lu54AatSw2ydccYWzcfkpJTciIiKFad06O8X7hx9s+777YNQoKFfO2bj8mLqlRERECkN2NgwfDpddZhObSpVg3jx46y0lNoVMlRsRERFP27YN4uPh669tu0sXm9RERDgbVzGhyo2IiIinGAPvvAONGtnEJiQEpkyx076V2BQZVW5EREQ8Yc8euOce2/UEcNVVMHUqVKvmbFzFkCo3IiIi52vuXLsg37x5EBgIL70EixYpsXGIKjciIiIFlZEB/frBpEm23aiRneLdoIGjYRV3qtyIiIgUxJIldkG+SZPA5YInnrAbXyqxcZwqNyIiIvmRmQnPPgsvv2wHEMfG2rE1cXFORyZ/UnIjIiKSV99/D3fcAevX2/bdd9tVh0NCnI1LclG3lIiIyLlkZ8PIkdC0qU1sKla0g4jffVeJjRdS5UZERORsUlKgRw9YutS2O3WySU1kpLNxyRmpciMiInI6xtjBwg0b2sSmXDmb1Hz0kRIbL6fKjYiIyD/t3Ws3uPzoI9u+8kq70nCNGs7GJXmiyo2IiMjfffKJnc790UdQqhSMGAFJSUpsfIgqNyIiIgCHDkH//rbrCeyKw9Om2YX5xKeociMiIrJ8uU1i3n3XLsj36KPwzTdKbHyUKjciIlJ8HT8OQ4bAiy9CTg5ceKFdkK9VK6cjk/Og5EZERIqnDRuge3dITrbt+Hh47TUIC3M0LDl/6pYSEZHiJScHXnnFLsiXnAwXXAAffmhnQymx8Quq3IiISPHx88/Qs6ed/QRw3XUwYQJUruxkVOJhqtyIiIj/Mwbee88uyJeUBGXLwltvwbx5Smz8kCo3IiLi3/bvhwcesF1PAC1a2EHDNWs6G5cUGlVuRETEf332mV2Q78MPoWRJeP55WLJEiY2fU+VGRET8z+HDdq2aN9+07bp17YJ8//qXs3FJkVDlRkRE/MvKldC48V+JTb9+8O23SmyKESU3IiLiH7Ky4NlnoWVL2LoVoqPhyy/h1VchONjp6KQIqVtKRER836ZNcMcdsHatbXfrBuPGQXi4o2GJM1S5ERER35WTA2PG2C6ntWuhfHn44AN4/30lNsWYKjciIuKbUlPhzjth4ULb7tABJk6EKlWcjUscp8qNiIj4FmNg+nQ7xXvhQjueZtw4O+1biY2gyo2I+InsbFi6FNLSICoK4uIgIMDpqMTjfv8dHnwQZs2y7ebN7crDF1/sbFziVVS5ERGfl5AAsbHQpo0dR9qmjW0nJDgdmXjUF1/Yas2sWTZzHToUli9XYiOnUHIjIj4tIQFuugl++SX38V277HElOH7gyBF4+GG49lr49VebzKxYAYMG2VWHRf7B0eRm+PDhNGvWjJCQECIjI+ncuTObN28+53WzZ8+mTp06lC5dmgYNGjB//vwiiFZEvE12NvTta4dg/NPJY/362fPER33zjZ0JNXasbffqBevWQbNmzsYlXs3R5Gbx4sX06tWLlStXsmDBArKysrjmmms4fPjwGa/5+uuvue2227j77rtZt24dnTt3pnPnzmzYsKEIIxcRb7B06akVm78zxk6oWbq06GISD8nKst1OLVrA5s12oPAXX9gkp0wZp6MTL+cy5nT/z+OMffv2ERkZyeLFi7nqqqtOe07Xrl05fPgw8+bNcx+7/PLLady4MW+eXGr7LDIyMggLCyM9PZ3Q0FCPxS4iRW/GDDvG5lymT4fbbiv8eMRDtmyB7t1h9Wrb7toV3ngDKlRwNi5xVH6+v71qzE16ejoAFc7yC7xixQratWuX61iHDh1YsWLFac/PzMwkIyMj10NE/ENUlGfPE4cZY6d0N25sE5vwcJuZzpypxEbyxWuSm5ycHPr160fLli2pX7/+Gc/bvXs3lSpVynWsUqVK7N69+7TnDx8+nLCwMPcjJibGo3GLiHPi4uz2QS7X6Z93uSAmxp4nXu7XX6FjR+jdG44ehXbtYP16ldykQLwmuenVqxcbNmxg5syZHr3vwIEDSU9Pdz9SU1M9en8RcU5AgF15H05NcE62R4/Wejdeb9YsqF/fjqkpXRpee83+OTra6cjER3lFctO7d2/mzZvHV199RfQ5fpkrV67Mnj17ch3bs2cPlStXPu35QUFBhIaG5nqIiP/o0gXmzIGqVXMfj462x7t0cSYuyYMDB+xml127wh9/wKWX2v2hHn4YSnjF15P4KEd/e4wx9O7dm8TERBYtWkT16tXPeU2LFi1YeHIfkT8tWLCAFi1aFFaYIuLlunSBHTvgq6/sEI2vvoKUFCU2Xm3RIrsg3/vv20Tm2Wft2jV16zodmfgBR1c/6tWrF9OnT+ejjz4iJCTEPW4mLCyM4OBgAOLj46latSrDhw8HoG/fvrRq1YpRo0Zx/fXXM3PmTNasWcPbb7/t2PsQEecFBEDr1k5HIed09CgMHPhXf2LNmnb7hMsvdzYu8SuOVm7Gjx9Peno6rVu3Jioqyv344IMP3Ofs3LmTtLQ0d/uKK65g+vTpvP322zRq1Ig5c+Ywd+7csw5CFhERL7B2re16OpnYPPAAJCcrsRGP86p1boqC1rkRESliJ07Aiy/CkCH2z5Urw4QJcN11TkcmPiQ/39/alENERArP1q12Qb6VK237xhvhzTchIsLZuMSvaTi6iIh4njHw1lvQqJFNbEJDYcoUmD1biY0UOlVuRETEs3bvhrvvhpObGrdubRObCy90NCwpPlS5ERERz0lIsAvyzZ8PQUHwyiuwcKESGylSqtyIiMj5S0+HPn1g6lTbbtzYTvHWTFZxgCo3IiJyfpKSoGFDm9iUKGHXsVm1SomNOEaVGxERKZhjx+CZZ2zXkzFQo4ZNcFq2dDoyKeaU3IiISP4lJ9sp3hs22PY999gkJyTE0bBEQN1SIiKSH9nZdkG+5s1tYhMZCR9/DO+8o8RGvIYqNyIikjfbt0OPHrBsmW137gxvvw0VKzoalsg/qXIjIiJnZ4zdLqFRI5vYhITAxIl22rcSG/FCqtyIiMiZ7dkD994Ln3xi23FxdtBwbKyjYYmcjSo3IiJyeh99BA0a2MQmMBBGjoSvvlJiI15PlRsREcnt4EHo1892PYFNcKZNs2vZiPgAVW5EROQvy5bZsTUTJ4LLBY89Bt98o8RGfIoqNyIiApmZMHiw7XoyBqpVs2NrrrrK6chE8k3JjYhIcbd+PdxxB3z/vW3feSeMHg2hoY6GJVJQ6pYSESmusrPh5ZehaVOb2EREQGKi7ZJSYiM+TJUbEZHiaMcO6NkTFi+27X//G959FypVcjIqEY9Q5UZEpDgxBiZPtgOEFy+GsmXt1gkff6zERvyGKjciIsXFvn1w//226wngiivsoOGLLnI2LhEPU+VGRKQ4+PRTu15NYiKUKgUvvABLliixEb+kyo2IiD87dAgeecRucAlwySV2Qb4mTZyNS6QQqXIjIuKvvv4aGjf+K7Hp3x++/VaJjfg9JTciIv7m+HF4+mm7yeW2bRATA4sWwSuvQOnSTkcnUujULSUi4k9++AG6d4d162y7e3d47TUID3c0LJGipMqNiIg/yMmxqwpfeqlNbCpUgFmz7GwoJTZSzKhyIyLi63butFsmLFpk2x07woQJEBXlbFwiDlHlRkTEVxljZz41bGgTmzJlYPx4O+1biY0UY6rciIj4ot9+gwcfhNmzbfuyy+C996BWLWfjEvECqtyIiPiazz+3C/LNng0lS8Jzz8GyZUpsRP6kyo2IiK84fBgee8x2PQHUqWO7pS691Nm4RLyMKjciIr5g1Sq7+N7JxKZPH1i7VomNyGkouRER8WZZWTB4MLRsCT/9BFWrwv/9H4wZA8HBTkcn4pXULSUi4q1+/NEuwrdmjW3fdhuMGwflyzsbl4iXU+VGRMTb5OTA2LG2G2rNGpvMzJwJ06crsRHJA1VuRES8ya5ddkG+BQts+5prYOJE2x0lInmiyo2IiLf44AM7xXvBAjueZuxYO+1biY1IvhQoualRowa//fbbKccPHDhAjRo1zjsoEZFi5Y8/oFs3uPVW++dmzez+UL16gcvldHQiPqdAyc2OHTvIzs4+5XhmZia7du0676BERIqNBQtstWbGDAgIgEGDYPlyqF3b6chEfFa+xtx8/PHH7j9/8cUXhIWFudvZ2dksXLiQ2NhYjwUnIuK3jhyBJ5+E11+37Vq17IJ8zZs7G5eIH8hXctO5c2cAXC4XPXr0yPVcqVKliI2NZdSoUR4LTkTEL61ZY6d4//ijbT/0EIwcCWXLOhuXiJ/IV3KTk5MDQPXq1fnmm2+IiIgolKBERPzSiRMwfDgMG2b/HBVlZ0Jde63TkYn4lQJNBU9JSfF0HCIi/u2nn2y1ZtUq2775ZruVwgUXOBuXiB8qUHIzbNiwsz4/aNCgAgUjIuJ3jIE334RHH7XjbMLC7CrD3bppJpRIISlQcpOYmJirnZWVRUpKCiVLluSiiy5SciMiApCWBnffDZ99Zttt28LkyRAT42hYIv6uQMnNunXrTjmWkZFBz549+e9//3veQYmI+LzZs+GBB+D336F0aRgxAh5+GEpo7VSRwuaxv2WhoaEMHTqUZ599Ns/XLFmyhE6dOlGlShVcLhdz58495zXvv/8+jRo1okyZMkRFRXHXXXeddkFBERFHHDhgx9bccotNbP71L/j2W+jbV4mNSBHx6N+09PR00tPT83z+4cOHadSoEePGjcvT+cuXLyc+Pp67776bH374gdmzZ7N69WruvffegoYsIuI5ixZBw4Z2vZoSJeDpp2HFCrjkEqcjEylWCtQt9dprr+VqG2NIS0vjvffeo2PHjnm+T8eOHfN1/ooVK4iNjaVPnz6AnZJ+//338+KLL+b5HiIiHnfsGDz1FLz6qm1fdBG89x60aOFsXCLFVIGSm1dP/gX+U4kSJahYsSI9evRg4MCBHgnsdFq0aMFTTz3F/Pnz6dixI3v37mXOnDlcd911Z7wmMzOTzMxMdzsjI6PQ4hORYmjdOtsN9cMPtn3//fDyy1CunLNxiRRjPrXOTcuWLXn//ffp2rUrx44d48SJE3Tq1Oms3VrDhw9n6NChRRiliBQL2dl2VeHBgyErCypVggkT4PrrnY5MpNg77zE3qamppKameiKWc9q4cSN9+/Zl0KBBfPvtt3z++efs2LGDBx544IzXDBw40D0WKD09vchiFRE/tm0bXHWV7YrKyoIuXWD9eiU2Il6iQMnNiRMnePbZZwkLCyM2NpbY2FjCwsJ45plnyMrK8nSMbsOHD6dly5Y89thjNGzYkA4dOvDGG28wceJE0tLSTntNUFAQoaGhuR4iIgViDLzzDjRqBF9/DSEhMGUKzJkDFSs6HZ2I/KlA3VIPP/wwCQkJjBw5khZ/DphbsWIFQ4YM4bfffmP8+PEeDfKkI0eOULJk7pADAgIAO6hZRKTQ7N4N994L8+bZduvWdkG+atWcjEpETqNAyc306dOZOXNmrplODRs2JCYmhttuuy3Pyc2hQ4fYunWru52SkkJycjIVKlTgwgsvZODAgezatYupU6cC0KlTJ+69917Gjx9Phw4dSEtLo1+/fjRv3pwqVaoU5K2IiJxbYiLcdx/s3w+BgfDCC9C/v9atEfFSBUpugoKCiI2NPeV49erVCQwMzPN91qxZQ5s2bdztAQMGANCjRw8mT55MWloaO3fudD/fs2dPDh48yNixY3nkkUcIDw+nbdu2mgouIoUjI8Muvjd5sm03amTXsKlf39GwROTsXKYA/TnDhg3jxx9/ZNKkSQQFBQF2yvXdd99NrVq1GDx4sMcD9ZSMjAzCwsJIT0/X+BsRObMlSyA+Hn7+2W5w+fjjMHQo/PlvnogUrfx8fxd4b6mFCxcSHR1No0aNAPjuu+84fvw4V199NV26dHGfm5CQUJCXEBFxRmYmPPMMjBplBxBXr24HDcfFOR2ZiORRgZKb8PBwbrzxxlzHYrTLrYj4uu+/hzvusNO6we7o/eqrdlaUiPiMAiU3kyZN8nQcIiLOyc62lZpnnrHr1lSsCO++C//5j9ORiUgBFGiof9u2bTlw4MApxzMyMmjbtu35xiQiDsvOhqQkmDHD/szOdjqiQpSSAm3awBNP2MTmP/+BDRuU2Ij4sAIlN0lJSRw/fvyU48eOHWPp0qXnHZSIOCchAWJj7fd9t272Z2ysPe5XjIFJk+wu3kuX2r2gJkyAuXMhMtLp6ETkPOSrW+r77793/3njxo3s3r3b3c7Ozubzzz+natWqnotORIpUQgLcdJP93v+7Xbvs8Tlz7E4DPm/vXrtuzUcf2faVV8LUqXbwsIj4vHxNBS9RogQulws4/YrAwcHBvP7669x1112ei9DDNBVc5PSys22F5pdfTv+8ywXR0bYX58+FwX3Txx/blYb37oVSpeC55+DRR338TYn4v0KbCp6SkoIxhho1arB69Woq/m0vlcDAQCIjI93bIYiIb1m69MyJDdhqTmqqPa916yILy3MOHoQBA+xAYbAL8U2bZhfmExG/kq/kptqfe6jk5OQUSjAi4pwz7D1b4PO8yvLl0L27LTu5XPDII7ZiU7q005GJSCEo0FTwk3s9nUl8fHyBghER50RFefY8r3D8OAweDCNHQk4OXHihXZDPJ0tPIpJXBdp+oXz58rnaWVlZHDlyhMDAQMqUKcPvv//usQA9TWNuRE7v5JibXbtOHVAMPjjmZsMGW61JTrbtHj1gzBgIC3M0LBEpmPx8fxdoKvgff/yR63Ho0CE2b97MlVdeyYwZMwoUtIg4KyDAfveDTWT+7mR79GgfSGxycuCVV6BpU5vYXHABfPih3fxSiY1IsVCg5OZ0atWqxYgRI+jbt6+nbikiRaxLFzvd+58rOkRH+8g08J9/hquvtmNqMjPh+uttBcfrAxcRTyrQmJsz3qxkSX799VdP3lJEiliXLnDDDXZWVFqaHWMTF+flFRtj4L334OGHISMDypa11Zt77z21DCUifq9Ayc3HH3+cq22MIS0tjbFjx9KyZUuPBCYizgkI8KExt/v3wwMP2K4ngBYt7IJ8NWs6G5eIOKZAyU3nzp1ztV0uFxUrVqRt27aMGjXKE3GJiJzb/Plw112wZw+ULAlDh8Ljj9s/i0ixVaB/AU6uc7Nv3z6AXIv5iYgUukOH7KrCb71l23Xr2m6pSy91Ni4R8Qr5HlB84MABevXqRUREBJUrV6Zy5cpERETQu3fv0+4ULiLiUStXQpMmfyU2/frBt98qsRERt3xVbn7//XdatGjBrl27uP3226lbty5gN9GcPHkyCxcu5Ouvvz5lHRwRkfOWlQXDhsELL9jp3tHRdnr31Vc7HZmIeJl8JTfDhg0jMDCQbdu2UalSpVOeu+aaaxg2bBivvvqqR4MUkWJu40a7IN/atbZ9++0wdiyEhzsaloh4p3x1S82dO5eXX375lMQGoHLlyowcOZLExESPBScixVxOjl1Z8NJLbWJTvjx88IHd8FKJjYicQb4qN2lpadSrV++Mz9evX5/du3efd1AiIqSmwp13wsKFtt2hA0ycCFWqOBuXiHi9fFVuIiIi2LFjxxmfT0lJoUKFCucbk4gUZ8bA9OnQoIFNbIKDbRfUZ58psRGRPMlXctOhQweefvppjh8/fspzmZmZPPvss1x77bUeC05Eipnff4fbbrNjatLToXlzWLcOevXSSsMikmf52hX8l19+oWnTpgQFBdGrVy/q1KmDMYZNmzbxxhtvkJmZyZo1a4iJiSnMmM+LdgUX8VJffGEX5Pv1V7tE8qBB8NRTWpBPRID8fX/n61+N6OhoVqxYwUMPPcTAgQM5mRe5XC7at2/P2LFjvTqxEREvdOSIXVV43Djbrl3bLsjXrJmzcYmIz8r3/xJVr16dzz77jD/++IOffvoJgJo1a2qsjYjk3+rVdor3li223bs3vPgilCnjbFwi4tMKXO8tX748zZs392QsIlJcZGXB88/D//4H2dl2oPCkSXDNNU5HJiJ+QJ3ZIlK0Nm+21ZpvvrHtrl3hjTdA1V8R8ZB87y0lIlIgxthxNU2a2MQmPNxO+Z45U4mNiHiUKjciUvh+/dXOhPriC9tu1852Q0VHOxuXiPglVW5EpHB98AHUr28Tm9Kl4bXX7J+V2IhIIVHlRkQKxx9/2NlP06fb9qWX2j2h6tRxNi4R8Xuq3IiI5y1cCA0b2sTm5IJ8K1YosRGRIqHKjYh4ztGjMHCg3ckboGZNuyDf5Zc7G5eIFCtKbkTEM7791k7x3rTJth98EF56CcqWdTYuESl21C0lIufnxAm7GN/ll9vEpnJlmD/frl2jxEZEHKDKjYgU3E8/QXw8rFxp2zfdBOPHQ0SEs3GJSLGmyo2I5J8x8NZb0LixTWxCQ2HqVJg1S4mNiDhOlRsRyZ+0NLjnHtv1BNCmDUyeDBde6GhYIiInqXIjInn34YfQoIFNbIKC4JVX4MsvldiIiFdR5UZEzi09HR5+2E7rBtsd9d57duVhEREvo8qNiJxdUpJdkO+996BECXjqKVi1SomNiHgtVW5E5PSOHYNnnrFdT8ZAjRo2wbniCqcjExE5KyU3InKq5GS7IN+GDbZ97702ySlXztGwRETyQt1SIvKX7Gx48UVo3twmNpGR8Mkn8PbbSmxExGeociMi1vbt0KMHLFtm250726SmYkVHwxIRyS9HKzdLliyhU6dOVKlSBZfLxdy5c895TWZmJk8//TTVqlUjKCiI2NhYJk6cWPjBivgrY2DCBGjUyCY2ISEwcSIkJCixERGf5Gjl5vDhwzRq1Ii77rqLLl265OmaW265hT179jBhwgRq1qxJWloaOTk5hRypiJ/as8eOp/nkE9u+6iqYMgViYx0NS0TkfDia3HTs2JGOHTvm+fzPP/+cxYsXs337dipUqABArP4RFimYjz6yic2+fRAYCM8/D/37Q0CA05GJiJwXnxpQ/PHHH9O0aVNGjhxJ1apVufjii3n00Uc5evSo06GJ+I6MDLj7bjumZt8+u4bNN9/Ao48qsRERv+BTA4q3b9/OsmXLKF26NImJiezfv5+HHnqI3377jUmTJp32mszMTDIzM93tjIyMogpXxPssXWp38d6xA1wueOwxGDbMbqUgIuInfKpyk5OTg8vl4v3336d58+Zcd911vPLKK0yZMuWM1Zvhw4cTFhbmfsTExBRx1CJeIDMTnngCWrWyiU1srF15+MUXldiIiN/xqeQmKiqKqlWrEhYW5j5Wt25djDH88ssvp71m4MCBpKenux+pqalFFa6Id1i/3q5bM3KknRnVsyd8950dPCwi4od8Krlp2bIlv/76K4cOHXIf27JlCyVKlCA6Ovq01wQFBREaGprrIVIsZGfDyy9D06bw/fcQEQGJiTBpEujvgYj4MUeTm0OHDpGcnExycjIAKSkpJCcns3PnTsBWXeLj493nd+vWjQsuuIA777yTjRs3smTJEh577DHuuusugoODnXgLIt5pxw5o29aOqTl+HDp1sisOd+7sdGQiIoXO0eRmzZo1NGnShCZNmgAwYMAAmjRpwqBBgwBIS0tzJzoA5cqVY8GCBRw4cICmTZty++2306lTJ1577TVH4hfxOsbA5Ml2BtSSJXbLhHfesdO+K1VyOjoRkSLhMsYYp4MoShkZGYSFhZGenq4uKvEv+/bB/ffbrieAli1h6lS7m7eIiI/Lz/e3T425EZEz+PRTaNDAJjalSsHw4bB4sRIbESmWfGqdGxH5h0OH4JFH7AaXAPXqwbRp0Lixo2GJiDhJlRsRX/X11zaJefttuyDfgAGwZo0SGxEp9lS5ESlk2dl2YeC0NIiKgri489zl4PhxGDoURoyAnByIibGbXbZp47GYRUR8mZIbkUKUkAB9+8Lf15iMjoYxY6BLlwLc8IcfoHt3WLfOtuPj4bXX4G8LW4qIFHfqlhIpJAkJcNNNuRMbgF277PGEhHzcLCcHRo+GSy+1iU2FCjB7tq3YKLEREclFyY1IIcjOthWb0y20cPJYv372vHPauRPat4f+/e0eUR072gX5brrJkyGLiPgNJTcihWDp0lMrNn9nDKSm2vPOetK0aXaK96JFUKYMvPmmnfYdFeXxmEVE/IXG3IgUgrS08zzvt9/ggQdgzhzbvvxyuyBfrVoeiU9ExJ+pciNSCPJaWDnteZ9/bqs1c+ZAyZIwbJgt8SixERHJEyU3IoUgLs7OinK5Tv+8y2VncMfF/e3g4cPw0EN2TE1aGtSpAytXwrPP2iRHRETyRMmNSCEICLDTveHUBOdke/Tov613s2oVNGkC48fbdp8+sHatnR0lIiL5ouRGpJB06WJ7lqpWzX08Otoe79IFyMqCwYPtJpc//WSfXLDAZkbBwY7ELSLi61TrFilEXbrADTecYYXiH3+0C/KtWWNP7tYNxo6F8uUdjVlExNcpuREpZAEB0Lr13w7k5MDr4+Dxx+HYMZvMjB8PXbs6FaKIiF9RciNSlHbtgjvvtF1PANdcAxMnntp3JSIiBaYxNyJFZeZMqF/fJjbBwbYL6vPPldiIiHiYKjcihe2PP6BXL5gxw7abNYP33oPatZ2NS0TET6lyI1KYFiywC/LNmGEH3wweDMuXK7ERESlEqtyIFIYjR+DJJ+H11227Vi27T1Tz5s7GJSJSDCi5EfG0NWvgjjtg82bbfughGDkSypZ1Ni4RkWJC3VIinnLihN0HqkULm9hERdkBw+PGKbERESlCqtyIeMKWLXZBvtWrbfvmm+3aNRdc4GxcIiLFkCo3IufDGJvENG5sE5uwMDu25oMPlNiIiDhElRuRgvr1V7j7btv1BNC2LUyebLf7FhERx6hyI1IQs2fbKd6ffw5BQXaL7wULlNiIiHgBVW5E8uPAAXj4Ydv1BNCkif3zJZc4GpaIiPxFlRuRvFq0CBo2tMlMiRLw9NOwcqUSGxERL6PKjci5HD0KTz1lu54ALrrIbp/QooWjYYmIyOkpuRE5m3Xr7IJ8Gzfa9v33w8svQ7lyzsYlIiJnpG4pkdM5cQJeeMFul7BxI1SqBPPmwZtvKrEREfFyqtyI/NO2bRAfD19/bdtdusBbb0FEhLNxiYhInqhyI3KSMfDOO9CokU1sQkNh6lSYM0eJjYiID1HlRgRg9264917b9QTQurVdkK9aNSejEhGRAlDlRiQx0S7IN28eBAbaAcMLFyqxERHxUarcSPGVkQF9+9oKDdjuqGnToH59R8MSEZHzo8qNFE9LlthkZvJkcLngySdh1SolNiIifkCVGyleMjPhmWdg1Cg7gLh6dTto+MornY5MREQ8RMmNFB/ff28X5Fu/3rbvuQdeeQVCQpyNS0REPErdUuL/srPhxRehaVOb2ERGwkcf2WnfSmxERPyOKjfi31JS7IJ8y5bZ9g03wNtv2wRHRET8kio34p+MgYkT7S7ey5bZLRMmTLDTvpXYiIj4NVVuxP/s3Qv33We7nsAOFp461Q4eFhERv6fKjfiXjz+2C/J99BGUKgUjRkBSkhIbEZFiRJUb8Q8HD8KAAfDuu7bdoAG8955dy0ZERIoVVW7E9y1fbpOYd9+1C/I99hh8840SGxGRYkqVG/Fdx4/D4MEwciTk5Ni9oKZMgVatnI5MREQc5GjlZsmSJXTq1IkqVargcrmYO3dunq9dvnw5JUuWpHHjxoUWn3if7Gw7hGbGyFSSLnmI7BF/JjY9e9pF+pTYiIgUe44mN4cPH6ZRo0aMGzcuX9cdOHCA+Ph4rr766kKKTLxRQgLExhratIFuT8TQZtu7xJbYScLjK2HSJAgNdTpEERHxAo52S3Xs2JGOHTvm+7oHHniAbt26ERAQkK9qj/iuhAS46SaDMbmP7zJVuOmlqsy5DLp0cSY2ERHxLj43oHjSpEls376dwYMHOx2KFJHsE4a+9xzGGAO4cj1njG3362e7rERERHwqufnpp5948sknmTZtGiVL5q3olJmZSUZGRq6H+JD9+1l69RB++aMsZ/p1NQZSU2Hp0qINTUREvJPPJDfZ2dl069aNoUOHcvHFF+f5uuHDhxMWFuZ+xMTEFGKU4lGffQYNGpC2ZEueTk9LK+R4RETEJ/hMcnPw4EHWrFlD7969KVmyJCVLlmTYsGF89913lCxZkkWLFp32uoEDB5Kenu5+pKamFnHkkm+HD8ODD8J118Hu3URVC8rTZVFRhRyXiIj4BJ9Z5yY0NJT169fnOvbGG2+waNEi5syZQ/UzLK8fFBREUFDevhzFC6xcCd27w9attt2/P3HPvUB0Hdi1i1MGFINdty86GuLiijZUERHxTo4mN4cOHWLryS8xICUlheTkZCpUqMCFF17IwIED2bVrF1OnTqVEiRLUr18/1/WRkZGULl36lOPig7KyYNgweOEFu25NdDRMngxXX00AMGYM3HSTTWT+nuC4/hxfPHo0BAQ4ELeIiHgdR7ul1qxZQ5MmTWjSpAkAAwYMoEmTJgwaNAiAtLQ0du7c6WSIUhQ2bYLLL4f//c8mNnfcAevXw9/WMerSBebMgapVc18aHW2Paxq4iIic5DLmdIV+/5WRkUFYWBjp6emEatE3Z+XkwOuvw5NPwrFjUKECvPkm3HzzGS/JzrazotLS7BibuDhVbEREioP8fH/7zJgb8TOpqXDnnbBwoW136AATJ0KVKme9LCAAWrcu/PBERMR3+cxsKfETxsD06dCggU1sgoPhjTfstO9zJDYiIiJ5ocqNFJ3ff7dTvGfNsu3mzeG99yAf6xaJiIiciyo3UjS++MJWa2bNsn1LQ4bA8uVKbERExONUuZHCdeQIPP44nNz5vXZtW61p1szZuERExG+pciOF55tvoEmTvxKb3r1h7VolNiIiUqiU3IjnZWXB0KHQogVs2WIHCv/f/9lp32XKOB2diIj4OXVLiWdt2WK3T1i92ra7drWzoSpUcDYuEREpNlS5Ec8wxiYxjRvbxCY83E75njlTiY2IiBQpVW7k/P36K9x1l50RBdCuHUyaZPdGEBERKWKq3Mj5mTUL6te3iU3p0naHyy++UGIjIiKOUeVGCuaPP+zsp+nTbfvSS+0U77p1nY1LRESKPVVuJP8WLoSGDW1iExAAgwbBihVKbERExCuociN5d/QoDBxou54Aata01ZrLL3c2LhERkb9RciN58+23dor3pk22/eCD8NJLULass3GJiIj8g7ql5OxOnIDnn7fVmU2boHJlmD/fTvtWYiMiIl5IlRs5s61bIT7ejqcBuPFGePNNiIhwNi4REZGzUOVGTmUMvPUWNGpkE5vQUJg6FWbPVmIjIiJeT5UbyW33brj7btv1BNC6NUyZAhde6GhYIiIieaXKjfwlIcEuyDd/PgQFwSuv2GnfSmxERMSHqHIjkJ4OffrYriew+0NNmwb16jkaloiISEGoclPcJSXZBfmmToUSJew6NqtWKbERERGfpcpNcXXsGDz9NLz6qh1AXKOGTXBatnQ6MhERkfOi5KY4Sk6GO+6AH36w7XvvhVGjICTE0bBEREQ8Qd1SxUl2NgwfDs2b28QmMhI++QTefluJjYiI+A1VboqL7dvtgnzLl9t25842qalY0dGwREREPE2VG39nDEyYYBfkW77cVmgmT7bTvpXYiIiIH1Llxp/t2WPH03zyiW1fdZVdkC821tGwRERECpMqN/5q7lxo0MAmNoGBdgfvRYuU2IiIiN9T5cbfZGRA//4wcaJtN2wI771nf4qIiBQDqtz4k6VL7diaiRPB5YLHH4fVq5XYiIhIsaLKjT/IzIRBg2zXkzG262nqVIiLczoyERGRIqfkxtd9/z10725/Atx1l111ODTU2bhEREQcom4pX5WdbSs1zZrZxCYiAhIT7bRvJTYiIlKMqXLji3bsgB49YMkS2+7UCd55BypVcjQsERERb6DKjS8xxi7A17ChTWzKlrVJzUcfKbERERH5kyo3vmLfPrjvPrt+Ddjdu6dMgYsucjQsERERb6PKjS+YNw/q17eJTalSdvPLxYuV2IiIiJyGKjfe7NAhGDDAdj0B1KsH06ZB48aOhiUiIuLNVLnxVl9/bRfke+cduyDfgAGwZo0SGxERkXNQcuNtjh+Hp5+2C/Bt3w4xMbBwIYwaBaVLOx2diIiI11O3lDf54Qe7IN+6dbYdHw+vvQZhYc7GJSIi4kNUufEGOTkwejRceqlNbC64AObMsbOhlNiIiIjkiyo3Ttu5E+68ExYtsu2OHe0qw1FRzsYlIiLio1S5cYoxduZTw4Y2sSlTBt58Ez79VImNiIjIeVDlxgm//QYPPgizZ9v25ZfbXbxr1XI2LhERET+gyk1R+/xzaNDAJjYlS8Jzz8HSpUpsREREPMTR5GbJkiV06tSJKlWq4HK5mHtya4EzSEhIoH379lSsWJHQ0FBatGjBF198UTTBnq/Dh+Ghh+yYmrQ0qFMHVq6EZ56xSY4DsrMhKQlmzLA/s7MdCUNERMSjHE1uDh8+TKNGjRg3blyezl+yZAnt27dn/vz5fPvtt7Rp04ZOnTqx7uTUaW+1ahU0aQLjx9t2376wdq2dHeWQhASIjYU2baBbN/szNtYeFxER8WUuY4xxOggAl8tFYmIinTt3ztd19erVo2vXrgwaNChP52dkZBAWFkZ6ejqhoaEFiDQfsrJst9MLL9iySNWqdlfvdu0K93XPISEBbrrJjmn+O5fL/pwzB7p0Kfq4REREziQ/398+PeYmJyeHgwcPUqFCBadDOdWPP0KLFja5yc6G226D9esdT2yys23h6HQp7clj/fqpi0pERHyXTyc3L7/8MocOHeKWW2454zmZmZlkZGTkehSqnBx4/XXbDfXttxAebge1TJ8O5csX7mvnwdKl8MsvZ37eGEhNteeJiIj4Ip9NbqZPn87QoUOZNWsWkZGRZzxv+PDhhIWFuR8xMTGFF9SuXXDttdCnDxw7BtdcAxs2wK23Ft5r5lNammfPExER8TY+mdzMnDmTe+65h1mzZtHuHN08AwcOJD093f1ITU0tnKBWroT69WHBAggOhrFj7bTvqlUL5/UKKK/rA2odQRER8VU+t4jfjBkzuOuuu5g5cybXX3/9Oc8PCgoiKCio8AOrV892O9WqBe+9B7VrF/5rFkBcHERH2yLT6cbduFz2+bi4oo9NRETEExxNbg4dOsTWrVvd7ZSUFJKTk6lQoQIXXnghAwcOZNeuXUydOhWwXVE9evRgzJgxXHbZZezevRuA4OBgwpzeYDIkBL78EmJioFQpZ2M5i4AAGDPGzpZyuXInOCdnS40ebc8TERHxRY52S61Zs4YmTZrQpEkTAAYMGECTJk3c07rT0tLYuXOn+/y3336bEydO0KtXL6KiotyPvn37OhL/KWrU8OrE5qQuXex073/2mEVHaxq4iIj4Pq9Z56aoFOk6N14uO9vOikpLs2Ns4uJUsREREe+Un+9vnxtzI54TEACtWzsdhYiIiGf55GwpERERkTNRciMiIiJ+RcmNiIiI+BUlNyIiIuJXlNyIiIiIX1FyIyIiIn5FyY2IiIj4FSU3IiIi4leU3IiIiIhfUXIjIiIifkXJjYiIiPiVYre31Ml9QjMyMhyORERERPLq5Pd2Xvb7LnbJzcGDBwGIiYlxOBIRERHJr4MHDxIWFnbWc1wmLymQH8nJyeHXX38lJCQEl8vl0XtnZGQQExNDamrqObdjl4LT51w09DkXDX3ORUefddEorM/ZGMPBgwepUqUKJUqcfVRNsavclChRgujo6EJ9jdDQUP3FKQL6nIuGPueioc+56OizLhqF8Tmfq2JzkgYUi4iIiF9RciMiIiJ+RcmNBwUFBTF48GCCgoKcDsWv6XMuGvqci4Y+56Kjz7poeMPnXOwGFIuIiIh/U+VGRERE/IqSGxEREfErSm5ERETEryi5EREREb+i5Cafxo0bR2xsLKVLl+ayyy5j9erVZz1/9uzZ1KlTh9KlS9OgQQPmz59fRJH6tvx8zu+88w5xcXGUL1+e8uXL065du3P+dxErv7/PJ82cOROXy0Xnzp0LN0A/kd/P+cCBA/Tq1YuoqCiCgoK4+OKL9W9HHuX3sx49ejS1a9cmODiYmJgY+vfvz7Fjx4ooWt+zZMkSOnXqRJUqVXC5XMydO/ec1yQlJfGvf/2LoKAgatasyeTJkws9Tozk2cyZM01gYKCZOHGi+eGHH8y9995rwsPDzZ49e057/vLly01AQIAZOXKk2bhxo3nmmWdMqVKlzPr164s4ct+S38+5W7duZty4cWbdunVm06ZNpmfPniYsLMz88ssvRRy5b8nv53xSSkqKqVq1qomLizM33HBD0QTrw/L7OWdmZpqmTZua6667zixbtsykpKSYpKQkk5ycXMSR+578ftbvv/++CQoKMu+//75JSUkxX3zxhYmKijL9+/cv4sh9x/z5883TTz9tEhISDGASExPPev727dtNmTJlzIABA8zGjRvN66+/bgICAsznn39eqHEqucmH5s2bm169ernb2dnZpkqVKmb48OGnPf+WW24x119/fa5jl112mbn//vsLNU5fl9/P+Z9OnDhhQkJCzJQpUworRL9QkM/5xIkT5oorrjDvvvuu6dGjh5KbPMjv5zx+/HhTo0YNc/z48aIK0W/k97Pu1auXadu2ba5jAwYMMC1btizUOP1FXpKbxx9/3NSrVy/Xsa5du5oOHToUYmTGqFsqj44fP863335Lu3bt3MdKlChBu3btWLFixWmvWbFiRa7zATp06HDG86Vgn/M/HTlyhKysLCpUqFBYYfq8gn7Ow4YNIzIykrvvvrsowvR5BfmcP/74Y1q0aEGvXr2oVKkS9evX54UXXiA7O7uowvZJBfmsr7jiCr799lt319X27duZP38+1113XZHEXBw49T1Y7DbOLKj9+/eTnZ1NpUqVch2vVKkSP/7442mv2b1792nP3717d6HF6esK8jn/0xNPPEGVKlVO+QslfynI57xs2TImTJhAcnJyEUToHwryOW/fvp1FixZx++23M3/+fLZu3cpDDz1EVlYWgwcPLoqwfVJBPutu3bqxf/9+rrzySowxnDhxggceeICnnnqqKEIuFs70PZiRkcHRo0cJDg4ulNdV5Ub8yogRI5g5cyaJiYmULl3a6XD8xsGDB+nevTvvvPMOERERTofj13JycoiMjOTtt9/m0ksvpWvXrjz99NO8+eabTofmd5KSknjhhRd44403WLt2LQkJCXz66ac899xzTocm50mVmzyKiIggICCAPXv25Dq+Z88eKleufNprKleunK/zpWCf80kvv/wyI0aM4Msvv6Rhw4aFGabPy+/nvG3bNnbs2EGnTp3cx3JycgAoWbIkmzdv5qKLLircoH1QQX6fo6KiKFWqFAEBAe5jdevWZffu3Rw/fpzAwMBCjdlXFeSzfvbZZ+nevTv33HMPAA0aNODw4cPcd999PP3005Qoof//P19n+h4MDQ0ttKoNqHKTZ4GBgVx66aUsXLjQfSwnJ4eFCxfSokWL017TokWLXOcDLFiw4IznS8E+Z4CRI0fy3HPP8fnnn9O0adOiCNWn5fdzrlOnDuvXryc5Odn9+M9//kObNm1ITk4mJiamKMP3GQX5fW7ZsiVbt251J48AW7ZsISoqSonNWRTksz5y5MgpCczJpNJo20WPcOx7sFCHK/uZmTNnmqCgIDN58mSzceNGc99995nw8HCze/duY4wx3bt3N08++aT7/OXLl5uSJUual19+2WzatMkMHjxYU8HzIL+f84gRI0xgYKCZM2eOSUtLcz8OHjzo1FvwCfn9nP9Js6XyJr+f886dO01ISIjp3bu32bx5s5k3b56JjIw0//vf/5x6Cz4jv5/14MGDTUhIiJkxY4bZvn27+b//+z9z0UUXmVtuucWpt+D1Dh48aNatW2fWrVtnAPPKK6+YdevWmZ9//tkYY8yTTz5punfv7j7/5FTwxx57zGzatMmMGzdOU8G90euvv24uvPBCExgYaJo3b25Wrlzpfq5Vq1amR48euc6fNWuWufjii01gYKCpV6+e+fTTT4s4Yt+Un8+5WrVqBjjlMXjw4KIP3Mfk9/f575Tc5F1+P+evv/7aXHbZZSYoKMjUqFHDPP/88+bEiRNFHLVvys9nnZWVZYYMGWIuuugiU7p0aRMTE2Meeugh88cffxR94D7iq6++Ou2/tyc/1x49ephWrVqdck3jxo1NYGCgqVGjhpk0aVKhx+kyRrU3ERER8R8acyMiIiJ+RcmNiIiI+BUlNyIiIuJXlNyIiIiIX1FyIyIiIn5FyY2IiIj4FSU3IiIi4leU3IiIiIhfUXIjIl6lZ8+edO7cuUhfc/LkyYSHhxfpa4pI4VFyIyIiIn5FyY2IeK3WrVvTp08fHn/8cSpUqEDlypUZMmRIrnNcLhfjx4+nY8eOBAcHU6NGDebMmeN+PikpCZfLxYEDB9zHkpOTcblc7Nixg6SkJO68807S09NxuVy4XK5TXkNEfIuSGxHxalOmTKFs2bKsWrWKkSNHMmzYMBYsWJDrnGeffZYbb7yR7777jttvv51bb72VTZs25en+V1xxBaNHjyY0NJS0tDTS0tJ49NFHC+OtiEgRUXIjIl6tYcOGDB48mFq1ahEfH0/Tpk1ZuHBhrnNuvvlm7rnnHi6++GKee+45mjZtyuuvv56n+wcGBhIWFobL5aJy5cpUrlyZcuXKFcZbEZEiouRGRLxaw4YNc7WjoqLYu3dvrmMtWrQ4pZ3Xyo2I+B8lNyLi1UqVKpWr7XK5yMnJyfP1JUrYf+aMMe5jWVlZnglORLySkhsR8XkrV648pV23bl0AKlasCEBaWpr7+eTk5FznBwYGkp2dXbhBikiRUXIjIj5v9uzZTJw4kS1btjB48GBWr15N7969AahZsyYxMTEMGTKEn376iU8//ZRRo0bluj42NpZDhw6xcOFC9u/fz5EjR5x4GyLiIUpuRMTnDR06lJkzZ9KwYUOmTp3KjBkzuOSSSwDbrTVjxgx+/PFHGjZsyIsvvsj//ve/XNdfccUVPPDAA3Tt2pWKFSsycuRIJ96GiHiIy/y9I1pExMe4XC4SExOLfFVjEfFeqtyIiIiIX1FyIyIiIn6lpNMBiIicD/Wsi8g/qXIjIiIifkXJjYiIiPgVJTciIiLiV5TciIiIiF9RciMiIiJ+RcmNiIiI+BUlNyIiIuJXlNyIiIiIX1FyIyIiIn7l/wFRgS2ZntP9uAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the graph\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Predicted output\n",
    "x = np.linspace(0, 1, 100)\n",
    "y = weight[0][0]*x + weight[0][1]\n",
    "plt.plot(x, y, '-r', label='Predicted output')\n",
    "\n",
    "# Actual output\n",
    "plt.plot(input_array, output_array, 'ob', label='Actual output')\n",
    "\n",
    "plt.xlabel('Input')\n",
    "plt.ylabel('Output')\n",
    "plt.legend(loc='upper left')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output for input  0.8  is  [2.0540313]\n"
     ]
    }
   ],
   "source": [
    "#predicting the output\n",
    "def neuron_predict(x,w):\n",
    "    input=np.append(x,1)\n",
    "    y=np.dot(w,input)\n",
    "    return y\n",
    "\n",
    "#predicting the output\n",
    "input=0.8\n",
    "output=neuron_predict(input,weight)\n",
    "print(\"Output for input \",input,\" is \",output)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part B Generate 51 points for \n",
    "                  \n",
    "                  t = 11 + exp(-3x) , where x ∈ [-2,3].\n",
    "\n",
    "Use this dataset to train sigmoid neuron using gradient descent learning algorithm. Draw two curves with different colours, for target and output (y) of the trained neuron."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0: Loss = 0.5861\n",
      "Epoch 100: Loss = 0.0169\n",
      "Epoch 200: Loss = 0.0116\n",
      "Epoch 300: Loss = 0.0105\n",
      "Epoch 400: Loss = 0.0099\n",
      "Epoch 500: Loss = 0.0096\n",
      "Epoch 600: Loss = 0.0094\n",
      "Epoch 700: Loss = 0.0092\n",
      "Epoch 800: Loss = 0.0091\n",
      "Epoch 900: Loss = 0.0089\n"
     ]
    },
    {
     "data": {
      "image/png": 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0DBN7zSYpKTZcyQMjNGJAhEYO8gSP5IERGmwNI3AACFiEEXSZQL/artPl1qHKOk/oKKvR/mPf3Fef4UyVmPBgjRoUqZEDIzRyUKRGDorQqEERGhYboZB+DKkA6HsII+iw9ixWFghriDQ5XTpYUasvS2v0ZdmpW2m1DpTXtnm2itkkDYsN1+i4SI0a5LmNHOQJH7ERId38EwBAz0YYQYecban33uik06WvKur0ZWm19pZWnwof1Sour23zEvSWYLM3bDQHj9FxkRoxMJzVRQGgnQgj8FtbS72X2Ou1cFO+z1LvPZHL5dbXx09ob2m1vjh121tSrQPHats8ayU8JEjnxUVqdFyUzo+P1HnxkTovLkpDYpjLAQDnijACv/i71LvRKmsbtafEob0lnsCxu6RaX5ZWq66NM1fCgoN0fnykzo+P0vnxUZ7QER+lRM5YAYAuQxiBX3rqUu+NJ13aV1ajPSUO7bY5tKekWntKqnWsuqHV9iFBZo2Ki9SYU2FjTHyUxiTQ0wEARiCMwC89Yan3ipoG7bZVa7fNEzyKbA7tP1bT5ryOpNgwjYmP1thET+C4ICFKIwZEsBgYAPQQhBH4pTuXene53DpYWaeiow59ftSuIptDRUcdKmujtyPK0k9jE6M1NiFKFyRGa0yCZ6glMpRfcwDoyfgrDb901VLvDSed+qKkRkU2uz4/6gkdu22OVlclNZmkEQMidEFClCd8JHp6PYbEhHEVWQDohQgj8EtnLPV+otGp3SUOfX7Ers+O2FV4xKEvSqtbveBbaD+zLkiIUspgq1IGRyslMVoXJEQpgt4OAAgY/EWH3/xZ6r2u8aQ+P+rQZ1/bVXjErsKjdu0rq1FrF5qNCQ/Wd04Fju+cCh8jBzK3AwACncntdrd9/fEewuFwyGq1ym63Kzo62uhycMq3V2AdN9SqvaXV+uxru/77tV2fHalqM3gMjAzVhUOilTrEqu8Mtip1SDTDLAAQYNr7/U3PCDqkyenyLBRWXqP/Hrbrv0fs+qK0Ws5WkkdCtEWpQ6y6cIgndKQOsSo++twnuAIAAgNhBGfldrv1VUWd/vt1lQoOV+k/h6v0+VGHGlq5LsvAyBCNGxqjC4dYNW6oJ4DEETwAAGdAGEELlbWNyj94XK9/ZlORzaHDx+tU29DyrJZoSz+NT4rRuKFWjRvquU+ItjDUAgDwC2Gkj2s86dJum0P/PnRcBYer9O/DVTpYUddq25EDI3TZ+YM0ISlG45NiNGJAOMEDAHDOCCN9TKmjXrsOHlf+wePKP3RchUcdamxluKU1xeW1unvmmB59ETwAQO9DGAlgTU5Pr8eug8eVf6hK+QeP60jViRbtYsKDdVFSjMYPjdFzO75SZV1Tm6/Zky6CBwAIDISRAGKva9KuQ5X611fH9a+Dx/Xfr6tU3+Tb62E2SWMSojVxeIzShvXXRcP6e4dbduyv0OrcL9t8faMuggcACGyEkV7K7XbrcOUJ/etgpXZ+dVy7Dlbqi9KaFu2sYcFKG+YJHhOH99e4pJg2r9XSEy6CBwDoewgjvYTT5daeEofyij09Hzu/qmz1gnEjB0Zo4vD+mjSivyYOj9XIgREyt3NIpTsvggcAQDPCSA/VeNKlz45U6dPiSu08FUCqG076tAkOMil1iFWThvfXpBGxmji8vwZGhnb4PbvqIngAAJwJYaSHONHoVP6h4/r0QIXyvqrUvw9VtVhULDK0nyYO76/05FhNGt5f45NiZAkO6rQaOuMieAAA+IswYpC6xpPadfC4Pj1QqU8OVOg/X1epyenbHzEgIkSTR8RqcnKsMpJjdUFCVJdfNM6fi+ABANAZCCPdpK7xpP711XF9cqBCnxyo0H+/tuvkt67jkmi1KCM5VhkjB2jyiFiNGhRhyKJiM1MTNT0lwecieOnJsfSIAAC6BGGki9Q3eYZdPtlfoY/3V6jgcFWL8DHYatHFowbo4uQBunjkACXF9pyr1gaZTZy+CwDoFh0KI08++aQeffRRlZSUaPz48XriiSeUnp7eatumpiatXLlSGzdu1JEjRzRmzBg98sgjmjlz5jkV3tM0OV3679dV+nifJ3zsOnS8xcqmQ2LCdPHIAbp4ZKwuHjlAQ/v3nPABAIBR/A4jmzdv1pIlS7Ru3TplZGRo9erVmjFjhvbu3au4uLgW7e+//35t2rRJ69ev1wUXXKA333xTV199tT7++GNddNFFnfJDGMHlcmtvabU+2leuD/eVK6+4UnWNvheTi4sK1ZRRA3TJqAG6ZNRAJcWGG1QtAAA9l8ntdrd2FmebMjIyNHnyZK1Zs0aS5HK5lJSUpNtvv1333ntvi/aDBw/Wfffdp0WLFnn3XXPNNQoLC9OmTZva9Z4Oh0NWq1V2u13R0dH+lNupjlSd0EdfesLHx/vLVV7T6PN8//BgXTzSEz6mjBpo2JwPAAB6gvZ+f/vVM9LY2Khdu3Zp6dKl3n1ms1nTpk3Tjh07Wj2moaFBFovvIllhYWH68MMP/XlrQ9hPNGnH/gp9uO+YPtpXoeLyWp/nw4KDlJ4cq0tHD9QlowdobEJ0uxcYAwAAHn6FkfLycjmdTsXHx/vsj4+P1549e1o9ZsaMGVq1apUuu+wyjRo1Srm5uXr55ZfldDpbbS95AkxDwzerizocDn/K7LCTTpf+87VdH3x5TB98Wa6Cw1VynjbpNMhs0vihVl06eqCmjh6oi4b1V0i/rj3VFgCAQNflZ9M8/vjjWrBggS644AKZTCaNGjVK8+fP17PPPtvmMStXrlR2dnZXlyZJOlRRp/e/PKYPvyzXR/vLVV3vu8rpyEER+u7ogbr0vEHKGBmraEtwt9QFAEBf4VcYGThwoIKCglRaWuqzv7S0VAkJCa0eM2jQIG3ZskX19fWqqKjQ4MGDde+992rkyJFtvs/SpUu1ZMkS77bD4VBSUpI/pZ6V2+3WT9d8pM+O2H32W8OCdenogfrueQN16XkDNbR/4E06dbrcrCECAOgx/AojISEhmjhxonJzczVr1ixJngmsubm5uu222854rMVi0ZAhQ9TU1KR//OMfuvbaa9tsGxoaqtDQjl9jpT1MJpMGx1i02+ZQ2rD++u55A/Xd8wfpwiHWgP5izim0tVhdNZHVVQEABvL7bJrNmzdr3rx5evrpp5Wenq7Vq1frxRdf1J49exQfH6+5c+dqyJAhWrlypSTp008/1ZEjRzRhwgQdOXJEK1asUHFxsfLz8xUTE9Ou9+yqs2m+Pl4na1iwovrI0EtOoU0LN+W3uAhec/RaOyeNQAIA6DRdcjaNJM2ePVvHjh3T8uXLVVJSogkTJignJ8c7qfXQoUMym7+Z1FlfX6/7779fBw4cUGRkpH70ox/pr3/9a7uDSFcKxCGYtjhdbmVvLWr1arxueQJJ9tYiTU9JCOieIQBAz+N3z4gReso6I73Zjv0Vun79J2dt97cFF7MMPACgU7T3+5vzUvuIsur6szfyox0AAJ2FMNJHxEVZzt7Ij3YAAHQWwkgfkZ4cq0SrRW3NBjHJc1ZNenJsd5YFAABhpK8IMpuUlZkiSS0CSfN2VmYKk1cBAN2OMNKHzExN1No5aUqw+g7FJFgtnNYLADBMly8Hj55lZmqipqcksAIrAKDHIIz0QUFmE6fvAgB6DIZpAACAoQgjAADAUIQRAABgKMIIAAAwFGEEAAAYijACAAAMRRgBAACGIowAAABDEUYAAIChCCMAAMBQLAcfYJwuN9edAQD0KoSRAJJTaFP21iLZ7PXefYlWi7IyU7giLwCgx2KYJkDkFNq0cFO+TxCRpBJ7vRZuyldOoc2gygAAODPCSABwutzK3lokdyvPNe/L3lokp6u1FgAAGIswEgDyiitb9Iiczi3JZq9XXnFl9xUFAEA7EUYCQFl120GkI+0AAOhOhJEAEBdl6dR2AAB0J8JIAEhPjlWi1aK2TuA1yXNWTXpybHeWBQBAuxBGAkCQ2aSszBRJahFImrezMlNYbwQA0CMRRgLEzNRErZ2TpgSr71BMgtWitXPSWGcEANBjsehZAJmZmqjpKQmswAoA6FUIIwEmyGzSlFEDjC4DAIB2Y5gGAAAYijACAAAMRRgBAACGIowAAABDEUYAAIChCCMAAMBQhBEAAGAowggAADAUYQQAABiKMAIAAAxFGAEAAIYijAAAAEMRRgAAgKEIIwAAwFCEEQAAYKh+RheA9nO63MorrlRZdb3ioixKT45VkNlkdFkAAJwTwkgvkVNoU/bWItns9d59iVaLsjJTNDM10cDKAAA4NwzT9AI5hTYt3JTvE0QkqcRer4Wb8pVTaDOoMgAAzh1hpIdzutzK3lokdyvPNe/L3lokp6u1FgAA9HyEkR4ur7iyRY/I6dySbPZ65RVXdl9RAAB0IsJID1dW3XYQ6Ug7AAB6GsJIDxcXZenUdgAA9DSEkR4uPTlWiVaL2jqB1yTPWTXpybHdWRYAAJ2GMNLDBZlNyspMkaQWgaR5OyszhfVGAAC9FmGkF5iZmqi1c9KUYPUdikmwWrR2ThrrjAAAejUWPeslZqYmanpKAiuwAgACDmGkFwkymzRl1ACjywAAoFMxTAMAAAzVoTDy5JNPasSIEbJYLMrIyFBeXt4Z269evVpjxoxRWFiYkpKStHjxYtXXsy4GAADoQBjZvHmzlixZoqysLOXn52v8+PGaMWOGysrKWm3//PPP695771VWVpZ2796tZ555Rps3b9Zvf/vbcy4eAAD0fn6HkVWrVmnBggWaP3++UlJStG7dOoWHh+vZZ59ttf3HH3+sqVOn6oYbbtCIESP0gx/8QNdff/1Ze1MAAEDf4FcYaWxs1K5duzRt2rRvXsBs1rRp07Rjx45Wj7nkkku0a9cub/g4cOCAXn/9df3oRz9q830aGhrkcDh8bgAAIDD5dTZNeXm5nE6n4uPjffbHx8drz549rR5zww03qLy8XJdeeqncbrdOnjypW2+99YzDNCtXrlR2drY/pQEAgF6qy8+meffdd/XQQw/pqaeeUn5+vl5++WVt27ZNDzzwQJvHLF26VHa73Xs7fPhwV5cJAAAM4lfPyMCBAxUUFKTS0lKf/aWlpUpISGj1mGXLlumXv/ylbrnlFknShRdeqNraWv3qV7/SfffdJ7O5ZR4KDQ1VaGioP6UBAIBeyq+ekZCQEE2cOFG5ubnefS6XS7m5uZoyZUqrx9TV1bUIHEFBQZIkt9vtb70AACDA+L0C65IlSzRv3jxNmjRJ6enpWr16tWprazV//nxJ0ty5czVkyBCtXLlSkpSZmalVq1bpoosuUkZGhvbt26dly5YpMzPTG0oAAEDf5XcYmT17to4dO6bly5erpKREEyZMUE5OjndS66FDh3x6Qu6//36ZTCbdf//9OnLkiAYNGqTMzEz9/ve/77yfAgAA9Fomdy8YK3E4HLJarbLb7YqOjja6HAAA0A7t/f7m2jQAAMBQhBEAAGAowggAADAUYQQAABiKMAIAAAxFGAEAAIYijAAAAEMRRgAAgKEIIwAAwFB+LwePruF0uZVXXKmy6nrFRVmUnhyrILPJ6LIAAOhyhJEeIKfQpuytRbLZ6737Eq0WZWWmaGZqooGVAQDQ9RimMVhOoU0LN+X7BBFJKrHXa+GmfOUU2gyqDACA7kEYMZDT5Vb21iK1dqXC5n3ZW4vkdPX4axkCANBhhBED5RVXtugROZ1bks1er7ziyu4rCgCAbkYYMVBZddtBpCPtAADojQgjBoqLsnRqOwAAeiPCiIHSk2OVaLWorRN4TfKcVZOeHNudZQEA0K0IIwYKMpuUlZkiSS0CSfN2VmYK640AAAIaYcRgM1MTtXZOmhKsvkMxCVaL1s5JY50RAEDAY9GzHmBmaqKmpySwAisAoE8ijPQQQWaTpowaYHQZAAB0O4ZpAACAoQgjAADAUIQRAABgKMIIAAAwFGEEAAAYijACAAAMRRgBAACGIowAAABDEUYAAIChCCMAAMBQhBEAAGAowggAADAUYQQAABiKMAIAAAxFGAEAAIYijAAAAEMRRgAAgKEIIwAAwFCEEQAAYCjCCAAAMBRhBAAAGIowAgAADEUYAQAAhiKMAAAAQxFGAACAoQgjAADAUIQRAABgqH5GF9AXOF1u5RVXqqy6XnFRFqUnxyrIbDK6LAAAegTCSBfLKbQpe2uRbPZ6775Eq0VZmSmamZpoYGUAAPQMDNN0oZxCmxZuyvcJIpJUYq/Xwk35yim0GVQZAAA9B2GkizhdbmVvLZK7leea92VvLZLT1VoLAAD6DsJIF8krrmzRI3I6tySbvV55xZXdVxQAAD0QYaSLlFW3HUQ60g4AgEBFGOkicVGWTm0HAECgIox0kfTkWCVaLWrrBF6TPGfVpCfHdmdZAAD0OB0KI08++aRGjBghi8WijIwM5eXltdn2e9/7nkwmU4vbj3/84w4X3RsEmU3KykyRpBaBpHk7KzOF9UYAAH2e32Fk8+bNWrJkibKyspSfn6/x48drxowZKisra7X9yy+/LJvN5r0VFhYqKChIv/jFL865+J5uZmqi1s5JU4LVdygmwWrR2jlprDMCAIAkk9vt9uvc0oyMDE2ePFlr1qyRJLlcLiUlJen222/Xvffee9bjV69ereXLl8tmsykiIqJd7+lwOGS1WmW32xUdHe1PuT0CK7ACAPqi9n5/+7UCa2Njo3bt2qWlS5d695nNZk2bNk07duxo12s888wzuu66684YRBoaGtTQ0ODddjgc/pTZ4wSZTZoyaoDRZQAA0CP5NUxTXl4up9Op+Ph4n/3x8fEqKSk56/F5eXkqLCzULbfccsZ2K1eulNVq9d6SkpL8KRMAAPQi3Xo2zTPPPKMLL7xQ6enpZ2y3dOlS2e127+3w4cPdVCEAAOhufg3TDBw4UEFBQSotLfXZX1paqoSEhDMeW1tbqxdeeEG/+93vzvo+oaGhCg0N9ac0AADQS/nVMxISEqKJEycqNzfXu8/lcik3N1dTpkw547F///vf1dDQoDlz5nSsUgAAEJD86hmRpCVLlmjevHmaNGmS0tPTtXr1atXW1mr+/PmSpLlz52rIkCFauXKlz3HPPPOMZs2apQEDmMgJAAC+4XcYmT17to4dO6bly5erpKREEyZMUE5OjndS66FDh2Q2+3a47N27Vx9++KHeeuutzqkaAAAEDL/XGTFCb19nBACAvqi9399cmwYAABiKMAIAAAxFGAEAAIYijAAAAEMRRgAAgKEIIwAAwFCEEQAAYCjCCAAAMBRhBAAAGIowAgAADEUYAQAAhiKMAAAAQxFGAACAoQgjAADAUIQRAABgKMIIAAAwFGEEAAAYijACAAAMRRgBAACGIowAAABDEUYAAIChCCMAAMBQhBEAAGAowggAADAUYQQAABiqn9EF9HZOl1t5xZUqq65XXJRF6cmxCjKbjC4LAIBegzByDnIKbcreWiSbvd67L9FqUVZmimamJhpYGQAAvQfDNB2UU2jTwk35PkFEkkrs9Vq4KV85hTaDKgMAoHchjHSA0+VW9tYiuVt5rnlf9tYiOV2ttQAAAKcjjHRAXnFlix6R07kl2ez1yiuu7L6iAADopQgjHVBW3XYQ6Ug7AAD6MsJIB8RFWTq1HQAAfRlhpAPSk2OVaLWorRN4TfKcVZOeHNudZQEA0CsRRjogyGxSVmaKJLUIJM3bWZkprDcCAEA7EEY6aGZqotbOSVOC1XcoJsFq0do5aawzAgBAO7Ho2TmYmZqo6SkJrMAKAMA5IIycoyCzSVNGDTC6DAAAei2GaQAAgKEIIwAAwFCEEQAAYCjCCAAAMBRhBAAAGIowAgAADEUYAQAAhiKMAAAAQxFGAACAoQgjAADAUIQRAABgKMIIAAAwFGEEAAAYijACAAAMRRgBAACGIowAAABDEUYAAIChCCMAAMBQhBEAAGCoDoWRJ598UiNGjJDFYlFGRoby8vLO2L6qqkqLFi1SYmKiQkNDdf755+v111/vUMEAACCw9PP3gM2bN2vJkiVat26dMjIytHr1as2YMUN79+5VXFxci/aNjY2aPn264uLi9NJLL2nIkCE6ePCgYmJiOqN+AADQy5ncbrfbnwMyMjI0efJkrVmzRpLkcrmUlJSk22+/Xffee2+L9uvWrdOjjz6qPXv2KDg4uENFOhwOWa1W2e12RUdHd+g1AABA92rv97dfwzSNjY3atWuXpk2b9s0LmM2aNm2aduzY0eox//znPzVlyhQtWrRI8fHxSk1N1UMPPSSn09nm+zQ0NMjhcPjcAABAYPIrjJSXl8vpdCo+Pt5nf3x8vEpKSlo95sCBA3rppZfkdDr1+uuva9myZfrjH/+oBx98sM33WblypaxWq/eWlJTkT5kAAKAX6fKzaVwul+Li4vTnP/9ZEydO1OzZs3Xfffdp3bp1bR6zdOlS2e127+3w4cNdXSYAADCIXxNYBw4cqKCgIJWWlvrsLy0tVUJCQqvHJCYmKjg4WEFBQd59Y8eOVUlJiRobGxUSEtLimNDQUIWGhvpTGgAA6KX86hkJCQnRxIkTlZub693ncrmUm5urKVOmtHrM1KlTtW/fPrlcLu++L774QomJia0GEQAA0Lf4PUyzZMkSrV+/Xhs3btTu3bu1cOFC1dbWav78+ZKkuXPnaunSpd72CxcuVGVlpe644w598cUX2rZtmx566CEtWrSo834KAADQa/m9zsjs2bN17NgxLV++XCUlJZowYYJycnK8k1oPHToks/mbjJOUlKQ333xTixcv1rhx4zRkyBDdcccduueeezrvpwAAAL2W3+uMGIF1RgAA6H26ZJ0RAACAzkYYAQAAhiKMAAAAQxFGAACAoQgjAADAUH6f2tuXOF1u5RVXqqy6XnFRFqUnxyrIbDK6LAAAAgphpA05hTZlby2SzV7v3ZdotSgrM0UzUxMNrAwAgMDCME0rcgptWrgp3yeISFKJvV4LN+Urp9BmUGUAAAQewsi3OF1uZW8tUmsrwTXvy95aJKerx68VBwBAr0AY+Za84soWPSKnc0uy2euVV1zZfUUBABDACCPfUlbddhDpSDsAAHBmhJFviYuydGo7AABwZoSRb0lPjlWi1aK2TuA1yXNWTXpybHeWBQBAwCKMfEuQ2aSszBRJahFImrezMlNYbwQAgE5CGGnFzNRErZ2TpgSr71BMgtWitXPSWGcEAIBOxKJnbZiZmqjpKQmswAoAQBcjjJxBkNmkKaMGGF0GAAABjWEaAABgKMIIAAAwFGEEAAAYijACAAAMRRgBAACGIowAAABDcWovAAQIp9OppqYmo8tAHxIcHKygoKBzfh3CCAD0cm63WyUlJaqqqjK6FPRBMTExSkhIkMnU8UVBCSMA0Ms1B5G4uDiFh4ef05cC0F5ut1t1dXUqKyuTJCUmdvxSKYQRAOjFnE6nN4gMGMCK0eheYWFhkqSysjLFxcV1eMiGCawA0Is1zxEJDw83uBL0Vc2/e+cyX4kwAgABgKEZGKUzfvcIIwAAwFCEEQAAYCjCCACgW5lMpjPeVqxYYWhtW7ZsMez9+yrOpgEAyOlyK6+4UmXV9YqLsig9OVZB5q6Zh2Kz2byPN2/erOXLl2vv3r3efZGRkX69XmNjo0JCQjqtPnQ/ekYAoI/LKbTp0kfe0fXrP9EdLxTo+vWf6NJH3lFOoe3sB3dAQkKC92a1WmUymbzbtbW1uvHGGxUfH6/IyEhNnjxZb7/9ts/xI0aM0AMPPKC5c+cqOjpav/rVryRJ69evV1JSksLDw3X11Vdr1apViomJ8Tn21VdfVVpamiwWi0aOHKns7GydPHnS+7qSdPXVV8tkMnm30fUIIwDQh+UU2rRwU75s9nqf/SX2ei3clN9lgaQtNTU1+tGPfqTc3Fz9+9//1syZM5WZmalDhw75tHvsscc0fvx4/fvf/9ayZcv00Ucf6dZbb9Udd9yhgoICTZ8+Xb///e99jvnggw80d+5c3XHHHSoqKtLTTz+tDRs2eNvt3LlTkvSXv/xFNpvNu42uZ3K73W6jizgbh8Mhq9Uqu92u6Ohoo8sBgB6jvr5excXFSk5OlsVi8etYp8utSx95p0UQaWaSlGC16MN7ruyyIZsNGzbozjvvPONS9qmpqbr11lt12223SfL0YFx00UV65ZVXvG2uu+461dTU6LXXXvPumzNnjl577TXva0+bNk3f//73tXTpUm+bTZs26e6779bRo0cleeaMvPLKK5o1a1bn/ZAB7ky/g+39/qZnBAD6qLziyjaDiCS5Jdns9corruy2mmpqanTXXXdp7NixiomJUWRkpHbv3t2iZ2TSpEk+23v37lV6errPvm9v/+c//9Hvfvc7RUZGem8LFiyQzWZTXV1d1/xAaBcmsAJAH1VW3XYQ6Ui7znDXXXdp+/bteuyxxzR69GiFhYXp5z//uRobG33aRURE+P3aNTU1ys7O1s9+9rMWz/nbq4TORRgBgD4qLqp9X8DtbdcZPvroI9100026+uqrJXkCxFdffXXW48aMGdNijse3t9PS0rR3716NHj26zdcJDg6W0+n0v3CcE8IIAPRR6cmxSrRaVGKvV2uTB5vnjKQnx3ZbTeedd55efvllZWZmymQyadmyZXK5XGc97vbbb9dll12mVatWKTMzU++8847eeOMNn6XKly9frp/85CcaNmyYfv7zn8tsNus///mPCgsL9eCDD0ryzEfJzc3V1KlTFRoaqv79+3fZz4pvMGcEAPqoILNJWZkpkjzB43TN21mZKV02ebU1q1atUv/+/XXJJZcoMzNTM2bMUFpa2lmPmzp1qtatW6dVq1Zp/PjxysnJ0eLFi32GX2bMmKHXXntNb731liZPnqyLL75Yf/rTnzR8+HBvmz/+8Y/avn27kpKSdNFFF3XJz4iWOJsGAHqxczmbpllOoU3ZW4t8JrMmWi3KykzRzNTEziq12y1YsEB79uzRBx98YHQpAa0zzqZhmAYA+riZqYmanpLQbSuwdpXHHntM06dPV0REhN544w1t3LhRTz31lNFloR0IIwAABZlNmjJqgNFlnJO8vDz94Q9/UHV1tUaOHKn/+Z//0S233GJ0WWgHwggAICC8+OKLRpeADmICKwAAMBRhBAAAGIowAgAADEUYAQAAhiKMAAAAQxFGAACAoQgjAIAeyWQyacuWLUaXoXfffVcmk0lVVVVtttmwYYNiYmK6raZAQxgBAHS7Y8eOaeHChRo2bJhCQ0OVkJCgGTNm6KOPPvK2sdls+uEPf2hglR6XXHKJbDabrFbrOb2OyWSSxWLRwYMHffbPmjVLN9100zm9dm/HomcAgG53zTXXqLGxURs3btTIkSNVWlqq3NxcVVRUeNskJCQYWOE3QkJCOq0Wk8mk5cuXa+PGjZ3yeu3V2NiokJCQbn1Pf9AzAgDoVlVVVfrggw/0yCOP6IorrtDw4cOVnp6upUuX6qc//am33beHaT7++GNNmDBBFotFkyZN0pYtW2QymVRQUCDpm+GUN998UxdddJHCwsJ05ZVXqqysTG+88YbGjh2r6Oho3XDDDaqrq/O+bkNDg379618rLi5OFotFl156qXbu3Ol9vrVhmg0bNmjYsGEKDw/X1Vdf7ROizuS2227Tpk2bVFhY2GYbl8ullStXKjk5WWFhYRo/frxeeukln/f+9pBQ82fRbMWKFZowYYL+93//1+cCdocOHdJVV12lyMhIRUdH69prr1VpaWmL4/76179qxIgRslqtuu6661RdXd2un6+j+mwYcbrc2rG/Qq8WHNGO/RVyunr8xYsB4KzcbrfqGk8acmvvReAjIyMVGRmpLVu2qKGhoV3HOBwOZWZm6sILL1R+fr4eeOAB3XPPPa22XbFihdasWaOPP/5Yhw8f1rXXXqvVq1fr+eef17Zt2/TWW2/piSee8La/++679Y9//EMbN25Ufn6+Ro8erRkzZqiysrLV1//00091880367bbblNBQYGuuOIKPfjgg+36OaZOnaqf/OQnuvfee9tss3LlSj333HNat26dPv/8cy1evFhz5szRe++91673aLZv3z794x//0Msvv6yCggK5XC5dddVVqqys1Hvvvaft27frwIEDmj17ts9x+/fv15YtW/Taa6/ptdde03vvvaeHH37Yr/f2V4eGaZ588kk9+uijKikp0fjx4/XEE08oPT291bYbNmzQ/PnzffaFhoaqvr6+1fbdIVAvlw0AJ5qcSln+piHvXfS7GQoPOfvXSr9+/bRhwwYtWLBA69atU1pami6//HJdd911GjduXKvHPP/88zKZTFq/fr0sFotSUlJ05MgRLViwoEXbBx98UFOnTpUk3XzzzVq6dKn279+vkSNHSpJ+/vOf6//9v/+ne+65R7W1tVq7dq02bNjgnZ+yfv16bd++Xc8884x+85vftHj9xx9/XDNnztTdd98tSTr//PP18ccfKycnp12f08qVKzVu3Dh98MEH+u53v+vzXENDgx566CG9/fbbmjJliiRp5MiR+vDDD/X000/r8ssvb9d7SJ6hmeeee06DBg2SJG3fvl2fffaZiouLlZSUJEl67rnn9J3vfEc7d+7U5MmTJXl6ZjZs2KCoqChJ0i9/+Uvl5ubq97//fbvf219+94xs3rxZS5YsUVZWlvLz8zV+/HjNmDFDZWVlbR4THR0tm83mvX178k53yim0aeGmfJ8gIkkl9not3JSvnEKbQZUBQN9xzTXX6OjRo/rnP/+pmTNn6t1331VaWpo2bNjQavu9e/dq3Lhx3uEGSW3+T/DpgSY+Pl7h4eHeINK8r/k7a//+/WpqavKGF0kKDg5Wenq6du/e3err7969WxkZGT77moNDe6SkpGju3Lmt9o7s27dPdXV1mj59urcHKTIyUs8995z279/f7veQpOHDh3uDSHPdSUlJ3iDSXEtMTIzPzzpixAhvEJGkxMTEM37Hdwa/e0ZWrVqlBQsWeHs71q1bp23btunZZ59ts9vJZDL1iIlITpdb2VuL1FpHoluSSVL21iJNT0lQkNnUSisA6NnCgoNU9LsZhr23PywWi6ZPn67p06dr2bJluuWWW5SVlXXOZ5YEBwd7H5tMJp/t5n0ul+uc3uNcZWdn6/zzz29x6nJNTY0kadu2bRoyZIjPc6GhoZIks9ncYkisqampxXtERER0qDYjPi+/ekYaGxu1a9cuTZs27ZsXMJs1bdo07dixo83jampqNHz4cCUlJemqq67S559/fsb3aWhokMPh8Ll1hrziyhY9IqdzS7LZ65VX3Po4IQD0dCaTSeEh/Qy5nT6BsiNSUlJUW1vb6nNjxozRZ5995jPH5PRJph01atQohYSE+JxS3NTUpJ07dyolJaXVY8aOHatPP/3UZ98nn3zi1/smJSXptttu029/+1s5nU7v/pSUFIWGhurQoUMaPXq0z625R2PQoEGqrq72+ayaJ/GeydixY3X48GEdPnzYu6+oqEhVVVVt/qzdxa8wUl5eLqfTqfj4eJ/98fHxKikpafWYMWPG6Nlnn9Wrr76qTZs2yeVy6ZJLLtHXX3/d5vusXLlSVqvVezu9S+lclFW3b55Ke9sBAPxXUVGhK6+8Ups2bdJ///tfFRcX6+9//7v+8Ic/6Kqrrmr1mBtuuEEul0u/+tWvtHv3br355pt67LHHJOmcQlBERIQWLlyo3/zmN8rJyVFRUZEWLFiguro63Xzzza0e8+tf/1o5OTl67LHH9OWXX2rNmjXtni9yuqVLl+ro0aN6++23vfuioqJ01113afHixdq4caP279+v/Px8PfHEE97TgTMyMhQeHq7f/va32r9/v55//vk2h7dON23aNF144YW68cYblZ+fr7y8PM2dO1eXX365Jk2a5Hf9nanLz6aZMmWK5s6dqwkTJujyyy/Xyy+/rEGDBunpp59u85ilS5fKbrd7b6enuHMRF2U5eyM/2gEA/BcZGamMjAz96U9/0mWXXabU1FQtW7ZMCxYs0Jo1a1o9Jjo6Wlu3blVBQYEmTJig++67T8uXL5ckn3kkHfHwww/rmmuu0S9/+UulpaVp3759evPNN9W/f/9W21988cVav369Hn/8cY0fP15vvfWW7r//fr/fNzY2Vvfcc0+LEzoeeOABLVu2TCtXrtTYsWM1c+ZMbdu2TcnJyd7jNm3apNdff10XXnih/va3v2nFihVnfT+TyaRXX31V/fv312WXXaZp06Zp5MiR2rx5s9+1dzaTu73nYskzTBMeHq6XXnpJs2bN8u6fN2+eqqqq9Oqrr7brdX7xi1+oX79++tvf/tau9g6HQ1arVXa7XdHR0e0ttwWny61LH3lHJfb6VueNmCQlWC368J4rmTMCoFeor69XcXGxz1oSfcX//d//af78+bLb7QoLCzO6nD7rTL+D7f3+9qtnJCQkRBMnTlRubq53n8vlUm5ubrtnEjudTn322WdKTOz+U2iDzCZlZXrGxb4dNZq3szJTCCIA0AM999xz+vDDD1VcXKwtW7bonnvu0bXXXksQCQB+D9MsWbJE69ev18aNG7V7924tXLhQtbW13rNr5s6dq6VLl3rb/+53v9Nbb72lAwcOKD8/X3PmzNHBgwd1yy23dN5P4YeZqYlaOydNCVbf9JZgtWjtnDTWGQGAHqqkpERz5szR2LFjtXjxYv3iF7/Qn//8Z6PLQifw+9Te2bNn69ixY1q+fLlKSko0YcIE5eTkeCe1Hjp0SGbzNxnn+PHjWrBggUpKStS/f39NnDhRH3/8saEzd2emJmp6SoLyiitVVl2vuCiL0pNj6REBgB7s7rvv9i40hsDi15wRo3TWnBEACDR9ec4IeoZunzMCAADQ2QgjABAAjF5RFH1XZ/zudehCeQCAniEkJERms1lHjx7VoEGDFBIScs4roQLt4Xa71djYqGPHjslsNiskJKTDr0UYAYBezGw2Kzk5WTabTUePHjW6HPRB4eHhGjZsmM/JK/4ijABALxcSEqJhw4bp5MmTPtc5AbpaUFCQ+vU79+sSEUYAIAA0X53221dcBXoDJrACAABDEUYAAIChCCMAAMBQvWLOSPMisQ6Hw+BKAABAezV/b59tsfdeEUaqq6slSUlJSQZXAgAA/FVdXS2r1drm873i2jQul0tHjx5VVFRUpy7m43A4lJSUpMOHD3PNmy7E59x9+Ky7B59z9+Bz7h5d+Tm73W5VV1dr8ODBZ1yHpFf0jJjNZg0dOrTLXj86Oppf9G7A59x9+Ky7B59z9+Bz7h5d9TmfqUekGRNYAQCAoQgjAADAUH06jISGhiorK0uhoaFGlxLQ+Jy7D5919+Bz7h58zt2jJ3zOvWICKwAACFx9umcEAAAYjzACAAAMRRgBAACGIowAAABD9ekw8uSTT2rEiBGyWCzKyMhQXl6e0SUFnPfff1+ZmZkaPHiwTCaTtmzZYnRJAWflypWaPHmyoqKiFBcXp1mzZmnv3r1GlxWQ1q5dq3HjxnkXh5oyZYreeOMNo8sKaA8//LBMJpPuvPNOo0sJOCtWrJDJZPK5XXDBBYbU0mfDyObNm7VkyRJlZWUpPz9f48eP14wZM1RWVmZ0aQGltrZW48eP15NPPml0KQHrvffe06JFi/TJJ59o+/btampq0g9+8APV1tYaXVrAGTp0qB5++GHt2rVL//rXv3TllVfqqquu0ueff250aQFp586devrppzVu3DijSwlY3/nOd2Sz2by3Dz/80JA6+uypvRkZGZo8ebLWrFkjyXP9m6SkJN1+++269957Da4uMJlMJr3yyiuaNWuW0aUEtGPHjikuLk7vvfeeLrvsMqPLCXixsbF69NFHdfPNNxtdSkCpqalRWlqannrqKT344IOaMGGCVq9ebXRZAWXFihXasmWLCgoKjC6lb/aMNDY2ateuXZo2bZp3n9ls1rRp07Rjxw4DKwPOnd1ul+T5kkTXcTqdeuGFF1RbW6spU6YYXU7AWbRokX784x/7/J1G5/vyyy81ePBgjRw5UjfeeKMOHTpkSB294kJ5na28vFxOp1Px8fE+++Pj47Vnzx6DqgLOncvl0p133qmpU6cqNTXV6HIC0meffaYpU6aovr5ekZGReuWVV5SSkmJ0WQHlhRdeUH5+vnbu3Gl0KQEtIyNDGzZs0JgxY2Sz2ZSdna3vfve7KiwsVFRUVLfW0ifDCBCoFi1apMLCQsPGffuCMWPGqKCgQHa7XS+99JLmzZun9957j0DSSQ4fPqw77rhD27dvl8ViMbqcgPbDH/7Q+3jcuHHKyMjQ8OHD9eKLL3b7sGOfDCMDBw5UUFCQSktLffaXlpYqISHBoKqAc3Pbbbfptdde0/vvv6+hQ4caXU7ACgkJ0ejRoyVJEydO1M6dO/X444/r6aefNriywLBr1y6VlZUpLS3Nu8/pdOr999/XmjVr1NDQoKCgIAMrDFwxMTE6//zztW/fvm5/7z45ZyQkJEQTJ05Ubm6ud5/L5VJubi5jv+h13G63brvtNr3yyit65513lJycbHRJfYrL5VJDQ4PRZQSM73//+/rss89UUFDgvU2aNEk33nijCgoKCCJdqKamRvv371diYmK3v3ef7BmRpCVLlmjevHmaNGmS0tPTtXr1atXW1mr+/PlGlxZQampqfFJ2cXGxCgoKFBsbq2HDhhlYWeBYtGiRnn/+eb366quKiopSSUmJJMlqtSosLMzg6gLL0qVL9cMf/lDDhg1TdXW1nn/+eb377rt68803jS4tYERFRbWY7xQREaEBAwYwD6qT3XXXXcrMzNTw4cN19OhRZWVlKSgoSNdff32319Jnw8js2bN17NgxLV++XCUlJZowYYJycnJaTGrFufnXv/6lK664wru9ZMkSSdK8efO0YcMGg6oKLGvXrpUkfe973/PZ/5e//EU33XRT9xcUwMrKyjR37lzZbDZZrVaNGzdOb775pqZPn250aYDfvv76a11//fWqqKjQoEGDdOmll+qTTz7RoEGDur2WPrvOCAAA6Bn65JwRAADQcxBGAACAoQgjAADAUIQRAABgKMIIAAAwFGEEAAAYijACAAAMRRgBAACGIowAAABDEUYAAIChCCMAAMBQhBEAAGCo/w+6xNuT3GKeQgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.         0.01010101 0.02020202 0.03030303 0.04040404 0.05050505\n",
      " 0.06060606 0.07070707 0.08080808 0.09090909 0.1010101  0.11111111\n",
      " 0.12121212 0.13131313 0.14141414 0.15151515 0.16161616 0.17171717\n",
      " 0.18181818 0.19191919 0.2020202  0.21212121 0.22222222 0.23232323\n",
      " 0.24242424 0.25252525 0.26262626 0.27272727 0.28282828 0.29292929\n",
      " 0.3030303  0.31313131 0.32323232 0.33333333 0.34343434 0.35353535\n",
      " 0.36363636 0.37373737 0.38383838 0.39393939 0.4040404  0.41414141\n",
      " 0.42424242 0.43434343 0.44444444 0.45454545 0.46464646 0.47474747\n",
      " 0.48484848 0.49494949 0.50505051 0.51515152 0.52525253 0.53535354\n",
      " 0.54545455 0.55555556 0.56565657 0.57575758 0.58585859 0.5959596\n",
      " 0.60606061 0.61616162 0.62626263 0.63636364 0.64646465 0.65656566\n",
      " 0.66666667 0.67676768 0.68686869 0.6969697  0.70707071 0.71717172\n",
      " 0.72727273 0.73737374 0.74747475 0.75757576 0.76767677 0.77777778\n",
      " 0.78787879 0.7979798  0.80808081 0.81818182 0.82828283 0.83838384\n",
      " 0.84848485 0.85858586 0.86868687 0.87878788 0.88888889 0.8989899\n",
      " 0.90909091 0.91919192 0.92929293 0.93939394 0.94949495 0.95959596\n",
      " 0.96969697 0.97979798 0.98989899 1.        ]\n",
      "----------------------------------\n",
      "[0.5        0.57444252 0.64565631 0.7109495  0.76852478 0.81757448\n",
      " 0.85814894 0.89090318 0.9168273  0.93702664 0.95257413 0.96442881\n",
      " 0.97340301 0.98015969 0.98522597 0.98901306 0.99183743 0.9939402\n",
      " 0.99550373 0.99666519 0.99752738 0.99816706 0.99864148 0.99899323\n",
      " 0.99925397 0.99944722 0.99959043 0.99969655 0.99977518 0.99983344\n",
      " 0.99987661 0.99990858 0.99993228 0.99994983 0.99996283 0.99997246\n",
      " 0.9999796  0.99998489 0.9999888  0.99999171 0.99999386 0.99999545\n",
      " 0.99999663 0.9999975  0.99999815 0.99999863 0.99999898 0.99999925\n",
      " 0.99999944 0.99999959 0.99999969]\n"
     ]
    }
   ],
   "source": [
    "def generate_data(n):\n",
    "    x = np.linspace(0, 5, n)\n",
    "    y = 1 / (1 + np.exp(-3 * x))\n",
    "    return x, y\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "def sigmoid_prime(x):\n",
    "    return sigmoid(x) * (1 - sigmoid(x))\n",
    "def mse_loss(y_true, y_pred):\n",
    "    return np.mean((y_true - y_pred) ** 2)\n",
    "n = 51\n",
    "X, y = generate_data(n)\n",
    "w = np.random.randn()\n",
    "b = np.random.randn()\n",
    "learning_rate = 0.1\n",
    "epochs = 1000\n",
    "for epoch in range(epochs):\n",
    "    y_pred = sigmoid(w * X + b)\n",
    "    loss = mse_loss(y, y_pred)\n",
    "    delw = np.mean(X * (y_pred - y) * sigmoid_prime(w * X + b))\n",
    "    delb = np.mean((y_pred - y) * sigmoid_prime(w * X + b))\n",
    "    w = w - learning_rate * delw\n",
    "    b = b - learning_rate * delb\n",
    "    if epoch % 100 == 0:\n",
    "        print(\"Epoch {}: Loss = {:.4f}\".format(epoch, loss))\n",
    "plt.scatter(X, y, label=\"Target\")\n",
    "plt.plot(X, sigmoid(w * X + b), label=\"Sigmoid Neuron\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.         0.01010101 0.02020202 0.03030303 0.04040404 0.05050505\n",
      " 0.06060606 0.07070707 0.08080808 0.09090909 0.1010101  0.11111111\n",
      " 0.12121212 0.13131313 0.14141414 0.15151515 0.16161616 0.17171717\n",
      " 0.18181818 0.19191919 0.2020202  0.21212121 0.22222222 0.23232323\n",
      " 0.24242424 0.25252525 0.26262626 0.27272727 0.28282828 0.29292929\n",
      " 0.3030303  0.31313131 0.32323232 0.33333333 0.34343434 0.35353535\n",
      " 0.36363636 0.37373737 0.38383838 0.39393939 0.4040404  0.41414141\n",
      " 0.42424242 0.43434343 0.44444444 0.45454545 0.46464646 0.47474747\n",
      " 0.48484848 0.49494949 0.50505051 0.51515152 0.52525253 0.53535354\n",
      " 0.54545455 0.55555556 0.56565657 0.57575758 0.58585859 0.5959596\n",
      " 0.60606061 0.61616162 0.62626263 0.63636364 0.64646465 0.65656566\n",
      " 0.66666667 0.67676768 0.68686869 0.6969697  0.70707071 0.71717172\n",
      " 0.72727273 0.73737374 0.74747475 0.75757576 0.76767677 0.77777778\n",
      " 0.78787879 0.7979798  0.80808081 0.81818182 0.82828283 0.83838384\n",
      " 0.84848485 0.85858586 0.86868687 0.87878788 0.88888889 0.8989899\n",
      " 0.90909091 0.91919192 0.92929293 0.93939394 0.94949495 0.95959596\n",
      " 0.96969697 0.97979798 0.98989899 1.        ]\n",
      "----------------------------------\n",
      "[0.5        0.57444252 0.64565631 0.7109495  0.76852478 0.81757448\n",
      " 0.85814894 0.89090318 0.9168273  0.93702664 0.95257413 0.96442881\n",
      " 0.97340301 0.98015969 0.98522597 0.98901306 0.99183743 0.9939402\n",
      " 0.99550373 0.99666519 0.99752738 0.99816706 0.99864148 0.99899323\n",
      " 0.99925397 0.99944722 0.99959043 0.99969655 0.99977518 0.99983344\n",
      " 0.99987661 0.99990858 0.99993228 0.99994983 0.99996283 0.99997246\n",
      " 0.9999796  0.99998489 0.9999888  0.99999171 0.99999386 0.99999545\n",
      " 0.99999663 0.9999975  0.99999815 0.99999863 0.99999898 0.99999925\n",
      " 0.99999944 0.99999959 0.99999969]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(\"----------------------------------\")\n",
    "print(y)"
   ]
  }
 ],
 "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": "3.10.1"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}