week2.ipynb

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    "# BL40A2030 Wireless Communication Networks\n",
    "\n",
    "## Week 2: Monte Carlo simulation and validation\n",
    "\n",
    "## Author: Pedro Nardelli\n",
    "\n",
    "### References \n",
    "\n",
    "#### Markdown syntax for writing in the notebook\n",
    "\n",
    "[Markdown syntax](https://help.github.com/articles/basic-writing-and-formatting-syntax/)\n",
    "\n",
    "#### Library for numerical calculation in Python\n",
    "\n",
    "[Numpy](http://www.numpy.org/)\n",
    "\n",
    "#### Satistical functions\n",
    "\n",
    "[scipy.stats](Statistical functions)\n",
    "\n",
    "#### Plot in pyhton\n",
    "\n",
    "[Matplotlib](https://matplotlib.org/tutorials/introductory/pyplot.html)"
   ],
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    "execution_start": 1606462428815,
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   "source": [
    "import numpy as np \n",
    "import scipy.stats as ss\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import style\n",
    "style.use('bmh')\n",
    "#style.use('seaborn-paper')\n",
    "#style.use('fivethirtyeight')\n",
    "#Not to show warning messages (to keep the notebook clean)\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ],
   "execution_count": 2,
   "outputs": []
  },
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   "source": [
    "## Experiments using random variables\n",
    "\n",
    "Let us make a computer experiment to simulate when someone throws a coin.\n",
    "\n",
    "### Defining the function of throwing the coin"
   ],
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    "execution_start": 1606462432602,
    "execution_millis": 2
   },
   "source": [
    "def flip(p):\n",
    "    return 'H' if np.random.random() < p else 'T'"
   ],
   "execution_count": 3,
   "outputs": []
  },
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   "cell_type": "markdown",
   "source": [
    "**Consider indendent trials, leading to a memoryless process. If the simulation was set that $p$ as the probability of being head (H) and tail (T) $1-p$, therefore the frequency of outcomes H and T shall coverge to the respective probability values.**"
   ],
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   "source": [
    "### Monte Carlo simulation\n",
    "####\n",
    "#Probability of H\n",
    "p = 0.92\n",
    "#Number o realizations\n",
    "x_max = 100000\n",
    "count = 0\n",
    "#Experiment\n",
    "for x in range(0, x_max):\n",
    "    a = flip(p)\n",
    "    #print a\n",
    "    if a == 'H':\n",
    "        count = count + 1\n",
    "print('Number of heads:', count)\n",
    "print('Number of tails:', x_max - count)\n",
    "#Probability from experiments: Number of Heads or Tails diveded by the number of realizations\n",
    "print('Empirical and analytical')\n",
    "print('Head:', count / x_max, 'Analytical:', p)\n",
    "print('Tail:', (x_max-count) / x_max, 'Analytical:', 1-p)"
   ],
   "execution_count": 4,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of heads: 91941\n",
      "Number of tails: 8059\n",
      "Empirical and analytical\n",
      "Head: 0.91941 Analytical: 0.92\n",
      "Tail: 0.08059 Analytical: 0.07999999999999996\n"
     ]
    }
   ]
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   "source": [
    "#### Try yourself:\n",
    "- set different number of trials: smaller (10) and greater (100000)\n",
    "- run the experiments and check what happens\n",
    "\n",
    "## Validating Poisson random variable generator\n",
    "\n",
    "- Analytical formulation: $$\\mathrm{Prob}\\left[N = n \\right] = \\dfrac{{e^{ - \\lambda } \\lambda ^n }}{{n!}}$$\n",
    "- Simulation using numpy\n",
    "- Formula implemented using scipy.stats.poisson"
   ],
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   "source": [
    "### Drawing a histogram (empirical distribution)\n",
    "mean=2\n",
    "samples_mean2 = np.random.poisson(mean, 100000) # this is the simulation. Mean is lambda and the other number is how many trials\n",
    "n_bins2 = np.max(samples_mean2) # set the number of bins in the histogram based on the highest value in the outcome\n",
    "##\n",
    "plt.figure(figsize=(14,5))\n",
    "plt.hist(samples_mean2,n_bins2, density=True)\n",
    "plt.xlabel('$n$')\n",
    "plt.ylabel('Frequency of $N = n$')\n",
    "plt.title('Poisson distribution empirical')\n",
    "plt.show() "
   ],
   "execution_count": 5,
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00008-780e504b-7c10-4c7b-a2d6-9c245d416504",
    "output_cleared": false,
    "source_hash": "8bc0f284",
    "execution_start": 1606462445132,
    "execution_millis": 158
   },
   "source": [
    "#Analytical formula for Poisson\n",
    "x = np.arange(0, ss.poisson.ppf(0.9999, mean)) # set the range from 0 to the 99.99% of probability of outcome\n",
    "analytical = ss.poisson.pmf(x, mean) # creating a array with the values; check documentation and examples\n",
    "plt.figure(figsize=(14,5))\n",
    "plt.step(analytical,'r', where='post') # plotting as a step function which gets the previous value\n",
    "plt.xlabel('$n$')\n",
    "plt.ylabel('Probability of $N = n$')\n",
    "plt.title('Poisson distribution analytical')\n",
    "plt.show() "
   ],
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1008x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00009-a794d29d-49b4-4d2b-a4de-a5c39c675d0d",
    "output_cleared": false,
    "source_hash": "e91f108b",
    "execution_start": 1606462448734,
    "execution_millis": 163
   },
   "source": [
    "plt.figure(figsize=(14,5))\n",
    "plt.hist(samples_mean2,n_bins2, density=True)\n",
    "plt.step(analytical,'r', where='post')\n",
    "plt.xlabel('$n$')\n",
    "plt.ylabel('Frequency and probability of $N = n$')\n",
    "plt.title('Poisson distribution analytical')\n",
    "plt.show() "
   ],
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1008x360 with 1 Axes>",
      "image/png": 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Xd8ptWt18TZ68aoq+zuT2fZ1csmqaPZPLGJsOzl0xwz1jnWxeMcOKjmPrdz68jKnDcHbPYe7e38mWlTN0RnLX/k4uHphmx6FGO3/T8sPcOdrJE/qnmc7g/vEOLuqfZvvEMrqWwYazDh99zIMzweDBDi7sm+ahgx30dSZru4+tH5sOdkws44K+GR480MHa7sOs6jpW076pYM/kMs7vneG+sQ429Rye9zZ1L0u29k231Ta18joBHDp0aEmzd6b9P/X39zM4ONhW29SOr9NiblNXVxf79u1rq21qx9dpMbdpZmaGkZGRttqmdnydFnObent7GRwcbKttqvLrdDKRufTfckfEC4DnZOYrm9dfAjw1M689zm2fBbwTuCwz9zSXPSozvxsR3wd8Brg2M784+3633HJLbt26dbE3Zd4GBwfZvHlz6TKKWL1mDQBP+Z3PFq6krGesm+QLu+s50s1t120DYGTv3sKVlFXn/YAazIDMgMzAmeWOO+64fdu2bcc9lecRd72LiB+OiCe1eLftwDmzrp8NfPc4j/1vgfcAVx5pJAFk5nebv3cBf02jK98Zrbe3t3QJKmznww4yWXfuB2QGZAZkBqrjtD65RcT7IuLBiPgosAJ44qnuM8dtwJaIOC8iuoEXAjfOeY7HAB8FXpKZ981a3hsRfUcuAz8M3H0627GUOjo6SpegwqYOl65ApbkfkBmQGZAZqI7T/Yr7Y5l5PvDfgSuAi1q5c2ZOA68BPg3cA3w4M78WEa+OiFc3b/YrwFrgnXOGAd8A3BwRXwW+DPyfzPzUaW7Hktm/f3/pElTY2T22lOrO/YDMgMyAzEB1nO5gDjMAmXkLcMvpPEBm3gTcNGfZu2ZdfiXwyuPc75u0fgSruPXr15cuQYXdvd95lOrO/YDMgMyAzEB1nO4RpadHxEcj4qqIGFjQitrU3pqfxC7YstJ5lOrO/YDMgMyAzEB1nG5D6bvAHwBPoTFM9xnf9a20EqML6szSGWag7twPyAzIDMgMVMfp9gX6ErA+M98EEBE9C1dSe/Iwq+6y613tuR+QGZAZkBmojtM6opSZd2Tmp2ddn1i4ktrTzp07S5egwi4emC5dggpzPyAzIDMgM1AdTuyyRI7MKqz62nHIf7e6cz8gMyAzIDNQHS1/couIHz/eZUmSJElqF6fzFffTTnBZJzE+Pl66BBW2abnzKNWd+wGZAZkBmYHqOJ2GUpzgsk5iw4YNpUtQYXeOOphD3bkfkBmQGZAZqI7TaSjlCS7rJIaHh0uXoMKe0O9gDnXnfkBmQGZAZqA6HukRJc1ThH+2uptOM1B37gdkBmQGZAaqw2G4lsiaNWtKl6DC7h/vKF2CCnM/IDMgMyAzUB2PtOud5snDrLrIrne1535AZkBmQGagOhzMYYn09/eXLkGFbZ/wAG7duR+QGZAZkBmojtP55PbHJ7isk5iZmSldggrrsp1Ue+4HZAZkBmQGqqPlj26Z+c3jXdbJHThwoHQJKmzDWc6jVHfuB2QGZAZkBqpj3g2liHj6YhbS7jZu3Fi6BBV2+z7nUao79wMyAzIDMgPV0coRpV+KiJ5Fq6TNDQ0NlS5BhV2yysEc6s79gMyAzIDMQHW08hX3OHBVRKwEDgP3Al/KzMlFqazNdHV1lS5BhR2cceyTunM/IDMgMyAzUB2tNJRen5k7j1yJiMcBr4uIZwI3Z+ZvLnBtbWVgYKB0CSps8KDzKNWd+wGZAZkBmYHqmHfXuzmNpCcB1wP/L7AT+PjCl9Zedu/eXboEFXZhn13v6s79gMyAzIDMQHXM+4hSRHQAPwG8DtgC/CFwQWbuWqTa2orfHughjyjVnvsBmQGZAZmB6mil690gsB/4n8AHM/PQolTUpiYnPZWr7vo6s3QJKsz9gMyAzIDMQHW0MurdV4EPAj3AkyLi6H0j4lELXVi7mZiYKF2CClvb7TxKded+QGZAZkBmoDpaOaL0lsy8tdlAejLwqogAOARsA16yCPW1DcfMl/Moyf2AzIDMgMxAdbQymMOtzd+HM/MrmfmuzHwX8GdA72IV2C4cM1/OoyT3AzIDMgMyA9XRSte748rMacChwU+hu7u7dAkqbGzaeZTqzv2AzIDMgMxAdTzihhJAZt62EI/Tzvr6+kqXoMJ2TCzIv5sqzP2AzIDMgMxAdfjJbYns2bOndAkq7IK+mdIlqDD3AzIDMgMyA9VhQ2mJrF69unQJKuzBA86jVHfuB2QGZAZkBqrjlA2liHjNrMv/ZnHLaV8OBSmHB5f7AZkBmQGZgeqYzxGl35h1+Y7FKqTdHTrk/Lx1t6rLCWfrzv2AzIDMgMxAdcxnYpcHI+J3ga8BXRHxiuPdKDPft6CVtRnHzJfzKMn9gMyAzIDMQHXM54jSC4EB4EVAF42JZef+/JfFKrBdOGa+nEdJ7gdkBmQGZAaq45RfcWfmfcArASLis5m5bdGrakPLly8vXYIK2zflPEp1535AZkBmQGagOlrqC5SZ2yJiC42jS48GvgP8RWbevxjFtZOenp7SJaiwPZMOMll37gdkBmQGZAaqo6VPbhHxY8DtwFZgL/A44CsR8eOLUFtbGRkZKV2CCju/13mU6s79gMyAzIDMQHW0enb5W4ErM/NzRxZExDOBPwBuXLiy2s/atWtLl6DC7htzHqW6cz8gMyAzIDNQHa32BTob+Ic5y25uLtdJjI2NlS5BhW3qcR6lunM/IDMgMyAzUB2tNpTuBH5hzrI3Npe3JCKuiIh7I+KBiLj+OOv/c0T8c/PnHyPiifO975locnKydAkqrK/TeZTqzv2AzIDMgMxAdbTa9e7ngI9HxOuAbwPnAAeAls5RiogO4B3A5cB24LaIuDEzvz7rZv8CPCMzRyLiucC7gUvned8zjmPmy3mU5H5AZkBmQGagOlo6opSZ3wAuBH4S+N3m78dn5j0tPu9TgQcy85uZOQncAFw557n+MTOPnO32JY517zvlfc9Ejpkv51GS+wGZAZkBmYHqaPkr7sycpnFe0iPxaBpHpI7YDlx6kttfDXzyNO97RnAoSDk8uNwPyAzIDMgMVEepvkDHm3nzuCdwRMSzaDSULmvlvrt27eLqq6+ms7OTmZkZrrrqKq655hqGhobo7e2lo6OD/fv3s379evbu3Utmsn79enbu3MnKlSsBGB8fZ8OGDQwPDxMRrFmzhuHhYfr7+5mZmeHAgQNs3LiRoaEhurq6GBgYYPfu3QwMDDA5OcnExMTR9TMzM6xYsYI9e/awevVqJiYmOHTo0NH1y5cvp6enh5GREdauXcvY2BiTk5NH1/f09NDd3c3o6Cjr1q1jdHSUqampo+tLbFN3dzd9fX2n3KbVzdfkyaum6OtMbt/XySWrptkzuYyx6eDcFTPcM9bJ5hUzrOg4tn7nw8uYOgxn9xzm7v2dbFk5Q2ckd+3v5OKBaXYcajQ8Ni0/zJ2jnTyhf5rpDO4f7+Ci/mm2TyyjaxlsOOvw0cc8OBMMHuzgwr5pHjrYQV9nsrb72Pqx6WDHxDIu6JvhwQMdrO0+zKquYzXtmwr2TC7j/N4Z7hvrYFPP4Xlv02N7p5lO2mqbWnmdAA4dOrSk2TvT/p+WLVvG4OBgW21TO75Oi7lNmcm+ffvaapva8XVazG0aGRmhq6urrbapHV+nxdymmZkZBgcH22qbqvw6nUxkLv0J5hHxdODNmfmc5vU3AWTmb8653b8F/hp4bmbe18p9b7nllty6detib8q8DQ4Osnnz5tJlFLF6zRoAnvI7ny1cSVnPWDfJF3Z3ly6jiNuu2wbAyN69hSspq877ATWYAZkBmYEzyx133HH7tm3bfuB460r1BboN2BIR50VEN/BC5szDFBGPAT4KvORII2m+9z0TrVu3rnQJKuyeMQdzqDv3AzIDMgMyA9XRUkMpIn4vIi5+pE/aPM/pNcCngXuAD2fm1yLi1RHx6ubNfgVYC7wzIu6MiK+c7L6PtKbFNjo6WroEFbZ5xUzpElSY+wGZAZkBmYHqaPUr7i7g0xExDPwp8OeZuf10njgzbwJumrPsXbMuvxJ45Xzve6abmpoqXYIKW9HhPEp1535AZkBmQGagOlodHvxa4FHA9cDFwD0R8XcR8dKIWLkI9bUNx8yX8yjJ/YDMgMyAzEB1tHyOUmbOZOYnMvNFwNOA9cD7gaGIeE9EPHqBa2wLjpkv51GS+wGZAZkBmYHqaLmhFBH9EXF1RHwO+CJwK/DvaUxEO86x+Y40S29vb+kSVNjOh51Hqe7cD8gMyAzIDFRHS32BIuKvgOfQaCC9C/hYZj48a/0bAc9QO46Ojo7SJaiwqcOlK1Bp7gdkBmQGZAaqo9WvuL8EbMnMH8nMD81uJAFk5mFgw4JV10b2799fugQVdnaPLaW6cz8gMyAzIDNQHadzjtL3dKxsHkk6sv7gIy2qHa1fv750CSrs7v0O5lB37gdkBmQGZAaqo9WG0q+cYPkvP9JC2t3evXtLl6DCtqx0HqW6cz8gMyAzIDNQHfP6ijsint282BERzwJi1urHAmMLXVi7yXQOnbrrDDNQd+4HZAZkBmQGqmO+fYHe2/y9HHjfrOUJ7ASuXcii2pGHWXWXXe9qz/2AzIDMgMxAdcyr611mnpeZ5wF/fuRy8+exmfn0zLxxkeusvJ07d5YuQYVdPOA8SnXnfkBmQGZAZqA6TvkVd0T8UGZ+sXn1/bO64f0rmfn3C1pZm1m5cmXpElTYjkPOo1R37gdkBmQGZAaqYz59gd4JXNS8/N4T3CZpnKskSZIkSZV3yoZSZl406/J5i1tO+xofH2ft2rWly1BBm5Yf5r7x0lWUtXrNmtIlFLXssss4fKM9levM9wKZAZmB6phP17vjdrWby653J7dhg/Pw1t2do/UdzOHmrZdy2TduLV1GcQM338xI6SJUlO8FMgMyA9Uxn09uJ+puN5td705heHiYc845p3QZKugJ/dPcvKe7dBlFvOEVby1dQnG3XbetdAk6A/heIDMgM1Ad8+l6Z3e7BRARp76R2tp0mgGp7nwvkBmQGagOh+FaImtqfm6G4P7xjtIlSCrM9wKZAZmB6jhlQykifmjW5Wef6Gdxy6y+4eHh0iWosIv6nUdJqjvfC2QGZAaqw+HBl0h/f3/pElTY9gkP4Ep153uBzIDMQHU4PPgSmZmZKV2CCuuynSTVnu8FMgMyA9XR0ke3iOiOiLdExP0RcaD5+9ciYvliFdguDhw4ULoEFbbhrMOlS5BUmO8FMgMyA9XR6sQu7wIuAF4LDAKbgTcBjwZesbCltZeNGzeWLkGF3b6vvvMoSWrwvUBmQGagOlrtDHQl8KOZ+cnM/HpmfhJ4fvNHJzE0NFS6BBV2ySoHc5DqzvcCmQGZgepotaE0BKyYs6wH2LEw5bSvrq6u0iWosIMzzpsg1Z3vBTIDMgPVccq+QHOG/v5T4FMR8b+A7cA5wDXABxenvPYxMDBQugQVNnjQeZSkuvO9QGZAZqA65nPSxPGGBP+lOdd/FvjtR15O+9q9eze9vb2ly1BBF/ZNs+vh7tJlSCrI9wKZAZmB6pjP8OAOCb4A/PZAD3lESao93wtkBmQGqsOZXZbI5ORk6RJUWF9nli5BUmG+F8gMyAxUR8vjFUfEBuCpwDrg6Nnpmfm+Bayr7UxMTJQuQYWt7XYeJanufC+QGZAZqI6WGkoR8Xzgz4D7ge8HvgZcBNwM2FA6CcfMl/MoSfK9QGZAZqA6Wu169+vAyzPzScCB5u9XAbcveGVtxjHz5TxKknwvkBmQGaiOVhtKj8nMv5yz7APASxeonrbV3e1oZ3U3Nu08SlLd+V4gMyAzUB2tNpR2Nc9RAngoIp4OnA84nNcp9PX1lS5Bhe2YcOwUqe58L5AZkBmojlY/uf0xcFnz8v8APgd8FXjnQhbVjvbs2VO6BBV2Qd9M6RIkFeZ7gcyAzEB1tHR2eWb+9qzLH4yIzwO9mXnPQhfWblavXl26BBX24AEPvEp153uBzIDMQHW0dEQpIroj4i0RcX9EHAA+C7w4IpYvTnntw6Eg5fDgknwvkBmQGaiOVscr/kPgccBrgUFgM/Am4NHAKxa2tPZy6NCh0iWosFVdTjgr1Z3vBTIDMgPV0WpD6fnA+Zm5r3n96xFxK/AANpROyjHz5TxKknwvkBmQGaiOVgdzGAJWzFnWA+xYmHLal2Pmy3mUJPleIDMgM1Adp2woRcSzj/wAfwp8KiJ+JiKeGxGvAm4CPtjqE0fEFRFxb0Q8EBHXH2f91oi4JSIejohfnLPuoYi4KyLujIivtPrcJSxf7mlcdbdvynmUpLrzvUBmQGagOubTF+i9x1n2S3Ou/yzw28e53XFFRAfwDuByYDtwW0TcmJlfn3WzvTTOhXr+CR7mWZm5e77PWVpPT0/pElTYnknnUZLqzvcCmQGZgeo4ZUMpM89bhOd9KvBAZn4TICJuAK4EjjaUMnMXjQluf2QRnn/JjYyM0N/fX7oMFXR+7wzbJxwiXKoz3wtkBmQGqqPU2eWPBr496/p24NIW7p/A30ZEAn+Ume+ee4Ndu3Zx9dVX09nZyczMDFdddRXXXHMNQ0ND9Pb20tHRwf79+1m/fj179+4lM1m/fj07d+5k5cqVAIyPj7NhwwaGh4eJCNasWcPw8DD9/f3MzMxw4MABNm7cyNDQEF1dXQwMDLB7924GBgaYnJxkYmLi6PrMZHx8nD179rB69WomJiY4dOjQ0fXLly+np6eHkZER1q5dy9jYGJOTk0fX9/T00N3dzejoKOvWrWN0dJSpqamj60tsU3d3N319fafcpiOzBTx51RR9ncnt+zq5ZNU0eyaXMTYdnLtihnvGOtm8YoYVHcfW73x4GVOH4eyew9y9v5MtK2fojOSu/Z1cPDDNjkONIzSblh/mztFOntA/zXQG9493cFH/NNsnltG1DDacdfjoYx6cCQYPdnBh3zQPHeygrzNZ231s/dh0sGNiGRf0zfDggQ7Wdh9mVdexmvZNBXsml3F+7wz3jXWwqefwvLdpZcdhtvZNt9U2tePrtFjbdMTg4OAj+n9qx31EnbZp2bJl7Nu3r622qR1fp8XcpsnJSUZGRtpqm9rxdVrMbVq+fDmDg4NttU1Vfp1OJjJbG7I4IrYAL6LR2PkOcENm3tfiY7wAeE5mvrJ5/SXAUzPz2uPc9s3AeGa+bdayR2XmdyPi+4DPANdm5hdn3++WW27JrVu3trRti2nHjh1s2rSpdBlFrF6zBoCn/M5nC1dS1pNXTXHHvq7SZaiQ267bBsDI3r2FK1FJdX4vUIMZkBk4s9xxxx23b9u27QeOt67VCWd/DLgd2ErjHKLH0Ti/6MdbrGk7cM6s62cD353vnTPzu83fu4C/ptGV74w2OTlZugQV1tfpPEpS3fleIDMgM1AdrXa9eytwZWZ+7siCiHgm8AfAjS08zm3Alog4j8ZRqRcCL57PHSOiF1iWmWPNyz8MvKWF5y7CMfPlPEqSfC+QGZAZqI5Wh+E6G/iHOctubi6ft8ycBl4DfBq4B/hwZn4tIl4dEa8GiIiNEbEdeCPwyxGxPSL6gQ3AzRHxVeDLwP/JzE+1uB1LzjHz5TxKknwvkBmQGaiOVr/ivhP4Bf71UOBvbC5vSWbeRGMOptnL3jXr8hDHb4DtB57Y6vOV5lCQcnhwSb4XyAzIDFRHqw2lnwdujIjX0Ri17hzgANDqOUq1093dXboEFTY27YSzUt35XiAzIDNQHa1+xX0vcCHwk8DvNn8/PjPvWejC2s3o6GjpElTYuStmSpcgqTDfC2QGZAaqY95HlCKiAxgHVmXmzYtXUntat25d6RJU2D1jDuYg1Z3vBTIDMgPVMe8jSpk5A9wHrF28ctqX3x5os0eUpNrzvUBmQGagOlr9ivvPgU9ExNtpzIV0dGKYzPz7hSys3UxNTZUuQYWt6HAeJanufC+QGZAZqI5WG0o/1/z95jnLE3jsI66mjTlmvpxHSZLvBTIDMgPV0dJgDpl53gl+bCSdgmPmy3mUJPleIDMgM1AdLX3FHRHdwC8DLwIeBXwXuAH4jcw8tPDltYfVa9awunQRKm7nw86jJNVdb29v6RJUmBmQGaiOVvsCvQu4AHgtMAhsBt4EPBp4xcKWpnZy89ZLS5dQ3NTh0hVIKq2jo6N0CSrMDMgMVEerDaUrgfMzc1/z+tcj4lbgAWwondDI3r38xsdu5Qu7nWCszs7uOcyDB0pXIamk/fv3s3q1fQzqzAzIDFRHq32BhoAVc5b1ADsWppz2dfd+T+SvOzMgaf369aVLUGFmQGagOlptKP0p8KmI+JmIeG5EvAq4CfhgRDz7yM/Cl1l9W1Y6h07dmQFJe/fuLV2CCjMDMgPV0epX3D/b/P1Lc5a/uvkDDhV+XJ3hHDp1ZwYkZbofqDszIDNQHS01lDLzvMUqpN3dZber2jMDkuxyIzMgM1Adjle8RC4ecA6dujMDknbu3Fm6BBVmBmQGqsOG0hLZccg/dd2ZAUkrV64sXYIKMwMyA9XhJzdJkiRJmsOG0hLZtNzZRuvODEgaHx8vXYIKMwMyA9VhQ2mJ3Dnqifx1ZwYkbdiwoXQJKswMyAxUxyk/uUXEW+bzQJn5K4+8nPb1hP5pbt7TXboMFWQGJA0PD3POOeeULkMFmQGZgeqYz1fcs1/J5cBPALcBg8BjgKcCH1n40trLdEbpElSYGZAU4X6g7syAzEB1nLKhlJkvP3I5Im4AXpSZH5m17CrgBYtTXvu4f7yjdAkqzAxIWrNmTekSVJgZkBmojlbPUXou8LE5y/4GeN6CVNPGLup3Dp26MwOShoeHS5egwsyAzEB1tNpQegC4Zs6ynwceXJhy2tf2CcfNqDszIKm/v790CSrMDMgMVEerw3C9EvjriLgO+A5wNjBF47wlnUSXn5FrzwxImpmZKV2CCjMDMgPV0dJHt8z8J2AL8CLg95q/t2Tm7YtQW1vZcJZz6NSdGZB04MCB0iWoMDMgM1AdLR1Riohu4GXAxcDK5uJXRgSZ+dKFLa293L7POXTqzgxI2rhxY+kSVJgZkBmojlY7A30AeD0wRuO8pNk/OolLVnkif92ZAUlDQ0OlS1BhZkBmoDpa/Yr7CuC8zNy3CLW0tYMzjplfd2ZAUldXV+kSVJgZkBmojlaPKH0LOGsxCml3gwedQ6fuzICkgYGB0iWoMDMgM1AdrTaUPgj8TUS8KCKePftnMYprJxf22e2q7syApN27d5cuQYWZAZmB6mi1691rmr/fOmd5Ao995OW0r4c8mlB7ZkCS3yTLDMgMVEdLDaXMPG+xCml3fZ1ZugQVZgYkTU5Oli5BhZkBmYHqcArMJbK22zl06s4MSJqYmChdggozAzID1dHyxC4RsQF4KrAOODqMV2a+bwHrajvOoSMzIMn5U2QGZAaqo6UjShHxfBpzJr0F+CPg2ubvlyx4ZW3GOXRkBiQ5f4rMgMxAdbTa9e7XgZdn5pOAA83frwJuX/DK2szYtHPo1J0ZkNTd3V26BBVmBmQGqqPVhtJjMvMv5yz7APDSBaqnbe2Y8HSwujMDkvr6+kqXoMLMgMxAdbT6yW1X8xwlgIci4unA+YDjHp/CBX0zpUtQYWZA0p49e0qXoMLMgMxAdbTaUPpj4LLm5f8BfA74KvDOVp84Iq6IiHsj4oGIuP4467dGxC0R8XBE/GIr9z0TPXjAtmTdmQFJq1evLl2CCjMDMgPV0VJDKTN/OzM/0rz8QeAC4JLM/G+tPE5EdADvAJ4LPB54UUQ8fs7N9gKvBd52Gvc94zg0tMyAJIcFlhmQGaiOR3TSRGZ+KzPvOY27PhV4IDO/mZmTwA3AlXMee1dm3gZMtXrfM9GqLicbrTszIOnQoUOlS1BhZkBmoDpKTezyaODbs65vBy5dyPvu2rWLq6++ms7OTmZmZrjqqqu45pprGBoaore3l46ODvbv38/69evZu3cvmcn69evZuXMnK1euBGB8fJwNGzYwPDxMRLBmzRqGh4fp7+9nZmaGAwcOsHHjRoaGhujq6mJgYIDdu3czMDDA5OQkExMTR9dPHoZNZ81wQd8MDx7oYG33YVZ1Jbfv6+SSVdPsmwr2TC7j/N4Z7hvrYFPPYfo6j63fM7mMseng3BUz3DPWyeYVM6zoOLZ+58PLmDoMZ/cc5u79nWxZOUNnJHft7+TigWl2HGq0iTctP8ydo508oX+a6QzuH+/gov5ptk8so2sZbDjr8NHHPDgTDB7s4MK+aR462EFfZ7K2+9j6selgx8Qyt2me29S9LNnaN91W29SOr9NibdMRg4ODx91HdHd309fXx549e1i9ejUTExMcOnTo6Prly5fT09PDyMgIa9euZWxsjMnJyaPre3p66O7uZnR0lHXr1jE6OsrU1NTR9SX2e27T925TV1cX+/bta6ttasfXaTG3aWZmhpGRkbbapnZ8nRZzm3p7exkcHGyrbary63Qykbn033JHxAuA52TmK5vXXwI8NTOvPc5t3wyMZ+bbWrnvLbfcklu3bl3cDWnBb3zsVr6w2+Eg6+wZ6ybNQI3ddt02AEb27i1ciUoaHBxk8+bNpctQQWZAZuDMcscdd9y+bdu2HzjeulYnnP29iLh4AWraDpwz6/rZwHeX4L7F7JtyDp26MwOSli9fXroEFWYGZAaqo9VzlLqAT0fE3RHxXyPi7NN83tuALRFxXkR0Ay8EblyC+xazZ9I5dOrODEjq6ekpXYIKMwMyA9XR6qh31wKPAq4HLgbuiYi/i4iXRsTKFh5nGngN8GngHuDDmfm1iHh1RLwaICI2RsR24I3AL0fE9ojoP9F9W9mOEs7vdQ6dujMDkkZGRkqXoMLMgMxAdbQ8mENmzgCfAD4REd8P/G/g/cA7I+IG4Fcz8zvzeJybgJvmLHvXrMtDNLrVzeu+Z7r7xpxDp+7MgKS1a9eWLkGFmQGZgepouS9QRPRHxNUR8Tngi8CtwL8HLgTGgU8ubIntYVOPc+jUnRmQNDY2VroEFWYGZAaqo6UjShHxV8BzaDSQ3gV8LDMfnrX+jcDoglbYJvo6nUOn7syApMnJydIlqDAzIDNQHa12vfsS8Jpmt7jvkZmHI2LDIy+r/dy+r9SUVTpTmAEBrF6zpnQJxUxdfjnjH/pQ6TKK2rhxY+kSVJgZkBmojlYHc3jbiRpJs25z8JGV1J5mTzipejID9Xbz1vnOqd2+uj7zmdIlFDc0dNK3UNWAGZAZqI5Wu979PnBDZv7jrGX/DvjJzHz9AtfWVhwaWmag3t7wirdyUf80d++v55HFIxPu1p3DAssMyAxUR6uf3F4EfGXOstuBFy9MOe1rbNrJRuvODMgMqLu7u3QJKswMyAxUR6sNpTzOfTpO43Fq59wVzqFTd2ZAZkCjo453VHdmQGagOlpt4PwD8OsRsQyg+fvNzeU6iXvG6tndRseYAZkBrVu3rnQJKswMyAxUR6sNpdcB/wHYERFfBr4LXA5cu9CFtZvNfpNce2ZAZkB+kywzIDNQHS19vZmZ2yPiycClwNnAt4EvZ6YzaZ7Cig7n0Kk7MyAzoKmpqdIlqDAzIDNQHS33A2k2im5ZhFramnPoyAzIDMj5U2QGZAaqo6WudxHRHRGvioh3RsQHZ/8sVoHtwjl0ZAZkBuT8KTIDMgPV0erXmx8Angh8HNi58OW0r50POzBg3ZkBmQH19vaWLkGFmQGZgepotaF0BXBeZu5bhFra2pRncdWeGZAZUEdHR+kSVJgZkBmojla/3vwWcNZiFNLuzu7xE1LdmQGZAe3fv790CSrMDMgMVEerR5Q+CPxNRLydOV3vMvPvF6yqNnT3fk/irjszIDOg9evXly5BhZkBmYHqaPVd+zXN32+dszyBxz7yctrXlpUz7Nnr+Ql1ZgZkBrR3715WrFhRugwVZAZkBqqj1XmUzlusQtpdZzh/St2ZAZkBZZqBujMDMgPV0fJXmxFxeUS8NyI+3rx+SUQ8e+FLay932eWm9syAzIDsciMzIDNQHa3Oo3Qt8IfA/cAPNRcfAn59getqOxcPOH9K3ZkBmQHt3OnMGnVnBmQGqqPVI0qvB/5DZv4WcGT4pm8Aj1vIotrRjkOel1B3ZkBmQCtXrixdggozAzID1dHqu3Yf8O3m5SMdLLuAyQWrSJIkSZIKa7Wh9EXg+jnLXgt8bmHKaV+bljt/St2ZAZkBjY+Ply5BhZkBmYHqaPXM4muBj0fEzwB9EXEvsB/4sQWvrM3cOepJ3HVnBmQGtGHDhtIlqDAzIDNQHS0dUcrMHcBTgJ8EXgz8NHBpZg4tQm1t5Qn9nsRdd2ZAZkDDw8OlS1BhZkBmoDpa/nozG4O/f7n5o3mazihdggozAzIDijADdWcGZAaqo6WGUkS85UTrMvNXHnk57ev+8Y7SJagwMyAzoDVr1pQuQYWZAZmB6mh1MIdz5vw8BfhF4PwFrqvtXGSXm9ozAzIDssuNzIDMQHW0dEQpM18+d1lEXAG8aMEqalPbJ5w/pe7MgMyA+vv7S5egwsyAzEB1LMS79t8Cz1+Ax2lrXX4+qj0zIDOgmZmZ0iWoMDMgM1AdLb1tR8Rj5/xcBPw6xyah1QlsOMv5U+rODMgM6MCBA6VLUGFmQGagOlod9e6BOdcPAnfSGCZcJ3H7PudPqTszIDOgjRs3li5BhZkBmYHqaHUepWVzflZm5mWZeftiFdguLlnlSdx1ZwZkBjQ05LSDdWcGZAaqY8GGB5/NocK/18EZx8yvOzMgM6Curq7SJagwMyAzUB2t9gPZAvwEcBswCDwGeCrwEeBQ8za5YNW1kcGDzp9Sd2ZAZkADAwOlS1BhZkBmoDpabSgF8KLM/MjRBRFXAS843tDhOubCvml2PdxdugwVZAZkBrR79256e3tLl6GCzIDMQHW0Oljtc4GPzVn2N8DzFqSaNvaQ3yTXnhmQGZDfJMsMyAxUR6sNpQeAa+Ys+3ngwYUpp331ddojse7MgMyAJicnS5egwsyAzEB1tNpQeiXwxojYHhG3RsR24Beay1sSEVdExL0R8UBEXH+c9RERv99c/88R8eRZ6x6KiLsi4s6I+Eqrz13C2m7nT6k7MyAzoImJidIlqDAzIDNQHS2do5SZ/xQRW4CnA5uAHcAtmTnVyuNERAfwDuByYDtwW0TcmJlfn3Wz59IYPGILcCnwh83fRzwrM3e38rwlOX+KzIDMgJw/RWZAZqA6Wj2iRGZOZeYXM/NDzd8tNZKango8kJnfzMxJ4Abgyjm3uRL4YDZ8CVgVEZtO47nOCM6fIjMgMyDnT5EZkBmojpYbShFxeUS8NyI+3rz+AxHx7BYf5tHAt2dd395cNt/bJPC3EXF7RLyqxecuYmza+VPqzgzIDKi721EP684MyAxUR6sTzl4LvA54D/CfmosngN8H/l0rD3WcZXPPcj7ZbX4wM78bEd8HfCYivpGZX5x9w127dnH11VfT2dnJzMwMV111Fddccw1DQ0P09vbS0dHB/v37Wb9+PXv37iUzWb9+PTt37mTlypUAjI+Ps2HDBoaHh4kI1qxZw/DwMP39/czMzHDgwAE2btzI0NAQXV1dDAwMsHv3bgYGBpicnGRiYuLo+oHOw2w6a4YL+mZ48EAHa7sPs6oruX1fJ5esmmbfVLBnchnn985w31gHm3oO09d5bP2eyWWMTQfnrpjhnrFONq+YYUXHsfU7H17G1GE4u+cwd+/vZMvKGTojuWt/JxcPTLPjUKNNvGn5Ye4c7eQJ/dNMZ3D/eAcX9U+zfWIZXctgw1mHjz7mwZlg8GAHF/ZN89DBDvo6k7Xdx9aPTQc7Jpa5TfPcpk1nzbC1L9pqm9rxdVrMbTowBc9YN9lW2zTf1+mIwcHBo/vF5cuX09PTw8jICGvXrmVsbIzJycmj63t6euju7mZ0dJR169YxOjrK1NTU0fUl9uXd3d309fWxZ88eVq9ezcTEBIcOHZr3Ni1btox9+/a11Ta14+u0mNs0Pj7OyMhIW21TO75Oi7lNy5YtY3BwsK22qcqv08lE5vxHYYqIB4FtmflQRIxk5urm+Ua7MnNtC4/zdODNmfmc5vU3AWTmb866zR8Bn8/Mv2hevxd4ZmbumPNYbwbGM/Nts5ffcsstuXXr1nlv22L7jY/dyhd2+w1CnT1j3aQZqLk6Z+C267YBMLJ3b+FKyhocHGTz5s2ly1BBZkBm4Mxyxx133L5t27YfON66Vrve9XGsO9yRFlYX0Oo4h7cBWyLivIjoBl4I3DjnNjcCL22Ofvc0YDQzd0REb0T0AUREL/DDwN0tPv+Se/CA86fUnRmQGdDq1atLl6DCzIDMQHW02lD6IjB3KO/XAp9r5UEycxp4DfBp4B7gw5n5tYh4dUS8unmzm4Bv0pi76Y9pzNcEsAG4OSK+CnwZ+D+Z+akWt2PJOSywzIDMgBwWWGZAZqA6Wh2r9lrg4xHxM0BfszvcfuDHWn3izLyJRmNo9rJ3zbqcfO/ktmTmN4Entvp8pa3qcqLJujMDMgM6dOhQ6RJUmBmQGaiOVhtKO4GnNH820+iG9+XM9GvSU3D+FJkBmQE5f4rMgMxAdcy7611z0IYDQHdmfjkz/zIzv2QjaX6cP0VmQGZAzp8iMyAzUB3zbihl5gxwHzDv0e10zL4p50+pOzMgM6Dly5eXLkGFmQGZgepotR/InwOfiIi305gA9miH+8z8+4UsrN3smWx5bl+1GTMgM6Cenp7SJagwMyAzUB2tNpR+rvn7zXOWJ/DYR1xNGzu/d4btEw4NXGdmQGZAIyMj9Pf3ly5DBZkBmYHqmFdDKSI2ZuZQZp632AW1q/vG/HBUd2ZAZkBr19p7ve7MgMxAdcy3H8h9s69ExEcXoZa2tqnHMS/qzgzIDGhsbKx0CSrMDMgMVMd8u97NPQP5mQtcR9vr63T+lLozAzIDsHrNmtIlFLXssss4fOONpctQQZOTk6VLUGFmoDrme0TJd/dHyPlTZAZU5wzcvPXS0iWcEQZuvrl0CSrMOXRkBqpjvu/anRHxLI4dWZp73VHvTuGSVdN8YXd36TJUkBlQnTPwhle8tXQJxd123bbSJegMMDQ0xObNm0uXoYLMQHXMt6G0C3jfrOt75lx31LtTcFhgmQGZAUkODS0zUB3zaihl5rmLXEfbG5t2osm6MwMyA5K6u+t5VFnHmIHq8OvNJXLuipnSJagwMyAzIGl0dLR0CSrMDFSHDaUlcs9YfU/iVoMZkBmQtG7dutIlqDAzUB02lJbIZr9Jrj0zIDMgyaMJMgPVYUNpiazocIT1ujMDMgOSpqamSpegwsxAddhQWiJ1nj9FDWZAZkCSc+jIDFSHDaUlcsmq6dIlqDAzIDMgaWhoqHQJKswMVIcNpSWy82H/1HVnBmQGJPX29pYuQYWZgerwXXuJTB0uXYFKMwMyA5I6OjpKl6DCzEB12FBaImf3+Amp7syAzICk/fv3ly5BhZmB6rChtETu3u9J3HVnBmQGJK1fv750CSrMDFSHDaUlsmWl86fUnRmQGZC0d+/e0iWoMDNQHTaUlkhnOH9K3ZkBmQFJme4H6s4MVIcNpSVyl11uas8MyAxIstuVzEB12FBaIhcPOH9K3ZkBmQFJO3fuLF2CCjMD1WFDaYnsOOSfuu7MgMyApJUrV5YuQYWZgerwXVuSJEmS5rChtEQ2LXf+lLozAzIDksbHx0uXoMLMQHXYUFoid456EnfdmQGZAUkbNmwoXYIKMwPV4bv2EnlC/zQ37+kuXYYKMgMyAwJYvWZN6RKKmrr8csY/9KHSZRQzPDzMOeecU7oMFWQGqsMjSktkOqN0CSrMDMgM1NvNWy8tXcIZoesznyldQlER7gfqzgxUh0eUlsj94x2lS1BhZkBmoN7e8Iq3srb7MHsm6/sd5W3XbStdQnFran5EUWagSuq7t15iF/U7f0rdmQGZAZkBDQ8Ply5BhZmB6rChtES2T/inrjszIDMgM6D+/v7SJagwM1Ad7rGXSJd/6dozAzIDMgOamZkpXYIKMwPV4S57iWw4y/lT6s4MyAzIDOjAgQOlS1BhZqA6bCgtkdv3OW5G3ZkBmQGZAW3cuLF0CSrMDFSHe+wlcsmqab6w2/lT6swMyAzIDDTUeS6p0csu4/CNN5YuQwUNDQ2xefPm0mVoHoodUYqIKyLi3oh4ICKuP876iIjfb67/54h48nzveyb6yuc+WboEFWYGZAZU9ww4lxQM3Hxz6RJU2Mc+9rHSJWieihxRiogO4B3A5cB24LaIuDEzvz7rZs8FtjR/LgX+ELh0nvc94/zT5z/JBU+4snQZKsgMyAyo7hl4wyveWrqEopxHSgAf/ehHed3rXle6DM1DqSNKTwUeyMxvZuYkcAMw953jSuCD2fAlYFVEbJrnfc84PZ4NVntmQGZAZkDS9LTzqVVFZObSP2nEfwKuyMxXNq+/BLg0M18z6zafAH4rM29uXv8s8F+Bc091X4CbbrppbMeOHUffkvr7+4fXrFmze3G37MT27t27ruTzqzwzIDMgMyAzIDNwxtm8bdu29cdbUWowhzjOsrktthPdZj735XnPe17fadQlSZIkScUaStuBc2ZdPxv47jxv0z2P+0qSJEnSaSvVW/o2YEtEnBcR3cALgbljZd4IvLQ5+t3TgNHM3DHP+0qSJEnSaStyRCkzpyPiNcCngQ7gfZn5tYh4dXP9u4CbgOcBDwAHgZef7L4FNkOSJElSmyoymEOdRMQVwNtpNOrek5m/VbgkLaGIOAf4ILAROAy8OzPfXrYqldCc2uArwHcy80dL16OlFxGrgPcAF9E4t/YVmXlL0aK0pCLiDcArabz+dwEvz8xDZavSYoqI9wE/CuzKzIuay9YAH6IxQNlDwE9m5kipGnViDlS6iGbN+fRc4PHAiyLi8WWr0hKbBn4hMy8EngZcYwZq63XAPaWLUFFvBz6VmVuBJ2IeaiUiHg28FviB5gfmDhqnD6i9vR+4Ys6y64HPZuYW4LPN6zoD2VBaXJWc80kLJzN3ZOYdzctjND4YPbpsVVpqEXE28CM0jiaohiKiH/gh4L0AmTmZmfuKFqUSOoGeiOgEVuBgVG0vM78I7J2z+ErgA83LHwCev5Q1af5sKC2uRwPfnnV9O35Irq2IOBd4EnBr4VK09P4ncB2N7peqp8cCw8CfRMQ/RcR7IqK3dFFaOpn5HeBtwLeAHTQGqfrbslWpkA3NAcpo/v6+wvXoBGwoLa55zfmk9hcRK4GPAK/PzP2l69HSiYgjfdNvL12LiuoEngz8YWY+CTiA3W1qJSJW0ziScB7wKKA3Iv5L2aoknYwNpcU1n/mi1OYiootGI+nPM/OjpevRkvtB4Mcj4iEa3W+fHRF/VrYkFbAd2J6ZR44o/xWNhpPq4z8A/5KZw5k5BXwU+HeFa1IZOyNiE0Dz967C9egEbCgtLud8qrmICBrnJNyTmb9Xuh4tvcx8U2aenZnn0tgH/H1m+i1yzWTmEPDtiHhcc9E24OsFS9LS+xbwtIhY0Xxv2IYDetTVjcBPNy//NPA3BWvRSRSZR6kunPNJNI4mvAS4KyLubC77pcy8qVxJkgq5Fvjz5hdn36Q5P6DqITNvjYi/Au6gMSLqPwHvLluVFltE/AXwTGBdRGwHfhX4LeDDEXE1jQb0C8pVqJNxHiVJkiRJmsOud5IkSZI0hw0lSZIkSZrDhpIkSZIkzWFDSZIkSZLmsKEkSZIkSXPYUJIkSZKkOWwoSZIkSdIcNpQkSZIkaQ4bSpIkSZI0hw0lSZIkSZqjs3QBkiQtloi4BHga8CjgSzS+IHx+Zr68aGGSpDOeR5QkSe3s+4BvAN+fmR8HbgSeWbQiSVIl2FCSJLWtzPwkcDnwZ81FTwe+Wq4iSVJV2FCSJLW7ZwOfbV7+aeCDEXFFwXokSRVgQ0mS1LYiYgWwLzNHmosOAKuA4WJFSZIqITKzdA2SJEmSdEbxiJIkSZIkzWFDSZIkSZLmsKEkSZIkSXPYUJIkSZKkOWwoSZIkSdIcNpQkSZIkaQ4bSpIkSZI0hw0lSZIkSZrj/wf5MgDOzmzpDwAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Validation many times requires statistical tests.\n",
    "\n",
    "#### Try yourself:\n",
    "- set different number of trials: smaller (100) and greater (1000000)\n",
    "- test different mean values: 1 and 20\n",
    "- run the experiments and check what happens"
   ],
   "metadata": {
    "deepnote_cell_type": "markdown",
    "trusted": true,
    "cell_id": "00010-3abe8227-c53f-46ec-983f-e20ff0e86b7e"
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Example of simple queue\n",
    "\n",
    "- Packets or persons arrive following a Poisson distribution with mean $\\lambda$ in a given period of time\n",
    "- Packets or persons that have arrived service rate follows a Poisson distribution with mean $\\mu$\n",
    "- Probability that queue is empty: $1-\\rho = 1 - \\lambda/\\mu$\n",
    "\n",
    "### Experiment from last week"
   ],
   "metadata": {
    "deepnote_cell_type": "markdown",
    "cell_id": "00011-328228cf-90ac-4573-9205-cbf40ff912b1"
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00012-538511d9-5e9a-4c98-85c7-8c97961e0e4b",
    "output_cleared": false,
    "source_hash": "7b3f88bf",
    "execution_start": 1606462453969,
    "execution_millis": 415
   },
   "source": [
    "#time periods\n",
    "size=100000\n",
    "#Arrival\n",
    "arrival_rate = 10\n",
    "arrival = np.random.poisson(arrival_rate, size)\n",
    "#Service\n",
    "service_rate = 15\n",
    "service = np.random.poisson(service_rate, size)\n",
    "#\n",
    "queue_size = np.zeros(size+1)\n",
    "\n",
    "for i in range(size):\n",
    "    if ((arrival[i] - service[i]) + queue_size[i]) > 0:\n",
    "        queue_size[i+1] = max(0,(arrival[i] - service[i]) + queue_size[i])\n",
    "\n",
    "print('Idle ratio:',(size - np.count_nonzero(queue_size))/size)\n",
    "print('Empty queue probability:', 1 -  arrival_rate/service_rate)"
   ],
   "execution_count": 8,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Idle ratio: 0.82922\n",
      "Empty queue probability: 0.33333333333333337\n"
     ]
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Why is it wrong?"
   ],
   "metadata": {
    "deepnote_cell_type": "markdown",
    "trusted": true,
    "cell_id": "00013-9e424981-bd07-4cab-b83f-c7332ea86303"
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00014-6ad4ff09-1018-4280-856d-d1f5139844cf",
    "output_cleared": false,
    "source_hash": "49492844",
    "execution_start": 1606462457693,
    "execution_millis": 91
   },
   "source": [
    "#time periods\n",
    "size=20000\n",
    "#Arrival\n",
    "arrival_rate = 10\n",
    "arrival = np.random.poisson(arrival_rate, size)\n",
    "#Service\n",
    "service_rate = 13\n",
    "service = np.random.poisson(service_rate, size)\n",
    "#\n",
    "queue_size = np.zeros(size+1)\n",
    "\n",
    "for i in range(size):\n",
    "    if ((arrival[i] - service[i]) + queue_size[i]) > 0:\n",
    "        queue_size[i+1] = max(0,(arrival[i] - service[i]) + queue_size[i])\n",
    "\n",
    "print('Idle ratio:',(size - np.count_nonzero(queue_size))/size)\n",
    "print('Empty queue probability:', 1 -  arrival_rate/service_rate)"
   ],
   "execution_count": 9,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Idle ratio: 0.65415\n",
      "Empty queue probability: 0.23076923076923073\n"
     ]
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00015-fb2c8ce8-34ea-4f1f-bc20-74ac2f7f5a5e",
    "output_cleared": false,
    "source_hash": "c7e144f2",
    "execution_start": 1606462461783,
    "execution_millis": 1
   },
   "source": [
    "arrival"
   ],
   "execution_count": 10,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 6, 10, 11, ...,  6, 11,  5])"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00016-5576a3b0-f4b6-4550-9c3f-1497f80ec502",
    "output_cleared": false,
    "source_hash": "22a64dc4",
    "execution_start": 1606462463112,
    "execution_millis": 2
   },
   "source": [
    "service"
   ],
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "array([10,  9, 13, ..., 11, 14, 12])"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00017-5a3b9769-2880-42cb-978b-8db63ff631bf",
    "output_cleared": false,
    "source_hash": "236d5ec2",
    "execution_start": 1606462464043,
    "execution_millis": 2
   },
   "source": [
    "queue_size"
   ],
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0., 0., 1., ..., 0., 0., 0.])"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Packing too many things together\n",
    "\n",
    "## Not capturing the actual dynamics...but how to solve it?\n",
    "\n",
    "## Simulation based on events!"
   ],
   "metadata": {
    "deepnote_cell_type": "markdown",
    "cell_id": "00018-dec0a605-2d91-41e1-9487-d5bebd5d0b04"
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00019-92479b60-e57e-4e9a-ba3c-2deba2b49860",
    "output_cleared": false,
    "source_hash": "ffd1c64f",
    "execution_start": 1606462469416,
    "execution_millis": 1
   },
   "source": [
    "#Code adapted from: https://github.com/sarthak0120/M-M-1-Queue-Simulation\n",
    "#New libraries needed\n",
    "import queue #https://docs.python.org/3/library/queue.html\n",
    "import copy "
   ],
   "execution_count": 13,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "- [queue](https://docs.python.org/3/library/queue.html)\n",
    "\n",
    "### Steps (in simple)\n",
    "\n",
    "1. Define time-granularity of \"checks\": 1 second\n",
    "2. Arrival process: Sequencial of exponential random variables until reach the total observation time\n",
    "3. Generate a service time for each process arrived as another exponential random variable\n",
    "4. Run the queue for every \"second\""
   ],
   "metadata": {
    "deepnote_cell_type": "markdown",
    "cell_id": "00020-6379bfca-e0e2-4837-8c57-c832b3e1ed74"
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "scrolled": false,
    "cell_id": "00021-07c186da-8560-4e20-9108-4573f46c7800",
    "output_cleared": false,
    "source_hash": "d9890a",
    "execution_start": 1606462472621,
    "execution_millis": 94463
   },
   "source": [
    "# Input Parameters -- Long one\n",
    "total_time = 100 #hours\n",
    "IAT_rate = 10 #elements arriving/hour\n",
    "ST_rate = 13  #elements served/hour\n",
    "rho = IAT_rate/ST_rate\n",
    "\n",
    "\n",
    "# Initialize Parameters\n",
    "qu = queue.Queue()\n",
    "curr_process = None\n",
    "IAT = []\n",
    "ST = []\n",
    "AT = []\n",
    "wait_time = []\n",
    "server_busy = False\n",
    "list_wait = []\n",
    "list_delay = []\n",
    "num_processes_served=0\n",
    "\n",
    "IAT.append(0)\n",
    "i=1\n",
    "while np.sum(IAT) < total_time*60*60 :\n",
    "    i = i + 1\n",
    "    temp = np.random.exponential(1/IAT_rate)*60*60\n",
    "    IAT.append(int(temp - temp%1))\n",
    "num_processes = i\n",
    "        \n",
    "# Populate Service-Times (ST) (where ST[i]!=0)\n",
    "while not len(ST) == num_processes:\n",
    "    temp = np.random.exponential(1/ST_rate)*60*60\n",
    "    if not int(temp- temp%1)<1:\n",
    "        ST.append(int(temp - temp%1))\n",
    "\n",
    "# Save a copy of ST\n",
    "ST_copy = copy.deepcopy(ST)\n",
    "\n",
    "# Get Arrival-Times (AT) from IAT starting at t=0\n",
    "# and initialize Waiting-Times to 0\n",
    "for i in range(num_processes):\n",
    "    if i == 0:\n",
    "        AT.append(0)    \n",
    "    else:\n",
    "        AT.append(AT[i-1] + IAT[i])\n",
    "    wait_time.append(0)\n",
    "\n",
    "# Simulation of M/M/1 Queue (i represents current time)\n",
    "queue_size = np.zeros(total_time*60*60)\n",
    "empty_system=0\n",
    "\n",
    "for i in range(total_time*60*60):\n",
    "    queue_size[i] = qu.qsize()\n",
    "    if server_busy:\n",
    "        for item in list(qu.queue):\n",
    "            wait_time[item] = wait_time[item] + 1\n",
    "        ST[curr_process] = ST[curr_process] - 1\n",
    "        if ST[curr_process] == 0:\n",
    "            server_busy = False\n",
    "            num_processes_served = num_processes_served + 1\n",
    "\n",
    "    for j in range(num_processes):\n",
    "        if i== AT[j]:\n",
    "            qu.put(j)\n",
    "\n",
    "    if not server_busy and not qu.empty():\n",
    "        curr_process = qu.get()\n",
    "        server_busy = True\n",
    "    #after some transitory\n",
    "    if not server_busy and qu.empty():\n",
    "        empty_system = empty_system+1\n",
    "\n",
    "\n",
    "    sum_wait = 0\n",
    "    sum_delay = 0\n",
    "    for i in range(num_processes_served):\n",
    "        sum_wait = sum_wait + wait_time[i]\n",
    "        sum_delay = sum_delay + wait_time[i] + ST_copy[i]\n",
    "    \n",
    "    if num_processes_served == 0:\n",
    "        list_wait.append(0)\n",
    "        list_delay.append(0)\n",
    "    else:\n",
    "        list_wait.append(sum_wait/(num_processes_served*60*60))  \n",
    "        list_delay.append(sum_delay/(num_processes_served*60*60))\n",
    "\n",
    "###Analytical\n",
    "QWT = 1/((1-rho)*ST_rate) - 1/ST_rate\n",
    "WT = 1/((1-rho)*ST_rate) \n",
    "\n",
    "  \n",
    "time_hours = np.linspace(0,total_time,total_time*60*60)\n",
    "    \n",
    "plt.figure(figsize=(14,5))\n",
    "#plt.plot( arrival, 'o',label='Arrival')\n",
    "#plt.plot( service, 'x',label='Sevice')\n",
    "plt.plot(time_hours,queue_size, 'ok')\n",
    "\n",
    "plt.figure(figsize=(14,5))\n",
    "plt.plot(time_hours, list_wait)\n",
    "plt.plot([0, total_time], [QWT, QWT])\n",
    "plt.ylabel(\"Avg Wait Times\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(14,5))\n",
    "plt.plot(time_hours, list_delay)\n",
    "plt.plot([0, total_time], [WT, WT])\n",
    "plt.ylabel(\"Avg Delay Times\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(14,5))\n",
    "n_bins = np.max(queue_size)\n",
    "##\n",
    "plt.hist(queue_size,n_bins.astype(int),density=True)\n",
    "x = np.arange(0, n_bins+1)\n",
    "p_analytical = (1-rho)*rho**x\n",
    "p_analytical[1]= p_analytical[0] + p_analytical[1]\n",
    "p_analytical[0]= 0\n",
    "plt.step(p_analytical,'r')\n",
    "plt.show()\n",
    "\n",
    "print('Idle ratio:',empty_system/(total_time*60*60))\n",
    "print('Empty queue probability:', 1 -  rho)\n",
    "print('Wait time in queue',QWT)\n",
    "print('Delay time in system',WT)"
   ],
   "execution_count": 15,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1008x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1008x360 with 1 Axes>",
      "image/png": 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ImOpImC+8egUrG91W21NuxIVyIy6UG3GR79yMxpK8+0db6MtMtf/B20874esKiZtEyrK9e5TH9w/y2P4hxhLJF5yeUF9RwsUn1VNeEuJNp8+n9hgjSX56v5nuHKPgLojuc+3t7TPvNMdMzGWF9AmLEwMsX35g76z/roHMtQBWNeZveciVjZW8ft3hObMjsSQdwzE+cMc2Bsfczp1SbsSFciMulBtxkc/c9I7GecO3n842RR976RI1RR4qCRlOmV/FdS9awL+8fg03X3UKd75zPR+7aCmLatNNTl80wU+f7eK2pzp4063PcO13n+GWRw/y1MGhI35WUN5vCnWO0ZwThHmUhRZPptearC1Ln8j34QuX8K8P7qNzOMYz7cOcMr+KklmYjpZMHW7AzlxYc8I/bzofeskSbjx3EYlkiru39mTPa/rcfbu49owWzllcQ2k49+8flBtxodyIC+VGXOQzN3//27bs7TMWVLNhdf4uqC5uKkrDXH5yI5ef3MiBgXE2dwzz6L5BHsicQ94XTfD9pzr4fmYV4GX15axpqmRBeQqfLEo3LY0Y5Uk4PDureBSTRKZhKQmnm5+Lls8D0n+J/uxn27l10wtP+nMxscZ/ScgU5CrR5SUhqstKeONpzazNrBazpXOEz9+/i3u2Tb9e/tGUG3Gh3IgL5UZc5Cs31lqeyIwyvHZtI//42tVEjuOLRSm8RXVlXLqmkc9sWMG9N5zJJy5extvPamV5fXl2n7a+Me7f3ssfD0an+Un+oRGjPBkcHKS+PrcT0uaCWCLFh+98HoDSUPqNrra8hOvOauWhtn529Y7xvSc7uGBZHSc3n9i3Uc8cSl/0LFXg8+dKwyE+/+qTuHXTIbZ1jbKjJ8r3n+rgwT0D3HjuQhoqSme8RoByIy6UG3Gh3IiLfOVmX//hRZPed/7sr1Yr+WWM4VWZEb53nr2AeDLF5o4RdnSPEjIGO9rvbYE5UiueJ83NzV6X4Ctt/WPZ1dzWtRxufN5x9gI+/6qTsvc/fOfz3LrpEKOxpPPvmlje8/KTG51/hqvGylI++tKlvOucBQB0j8R54uAQN/10G2/7/mae6xyZ9vnKjbhQbsSFciMu8pGbg4Pj3PiT59I/v6q0ILM9JL9KwyHOWljDNetbuPr0+bzm9GA0u0penvT29npdgq/EEunzixbVlvHJlx85yXRBbRkff9nS7P1vb2rnx890Ov+uiebjREeeTsS5S+r4+tVrueq0ZpbXl1NTFsaSHlKejnIjLpQbcaHciIvZzs3AWIJ3/XBL9v4Fy7y9kKrkR1Deb9QY5UmxLIM+WyZGi5qrS6e8FsElaxr5jzeenP2W6NYn2tncPuz0uybmJK9pclsye7Ysr6/g/ecv5utXn8IrV6aHl//p93sZGj/2inXKjbhQbsSFciMuZjs3G9sGsrc/cuESPnhBMEYW5PgE5f1GjVGeaIrCkfb2p0dKRqaZIreysZKvXLE6e/9vf73nuH+PtZbhzO9YPM8f6+UDLK47XMtn7911zDcI5UZcKDfiQrkRF7Odm4kFk05vreaKU5oI6UKuRSko7zdqjPKko6PD6xJ8JZxZhvukhumvK7S6qZK/u3wlcHiU6XiMZabsAb5azeZ165o4Z3F66fAtnSM8fmBoyv2UG3Gh3IgL5UZczGZu/rCnn5096cbo5GZvZ3lIfgXl/cY/nxyLTHV1tdcl+MrExV2bqyIz7nvWpGsPTYw05Wpze/r8orpjXHnZKyFj+MtXLM/e/9Q9O+kcjr1gP+VGXCg34kK5ERezlZvO4Rh/9cvdPNeZboxOma/rahWzoLzfqDGSgpi4hlFpeOYh8snnIB3vqNHEkPzA2LHP4/FKTVkJn9uwInv/utue5bc7+zysSERExBu3ZS4A2lRZynvPW8R5S2s9rkhEjVHeDA+7LRxQrLIXdw3lNnd4YtpZPJmaYc+pf891Z7Ue1/MK5cLldbxq1eHrP/zf3+zh0m88wSXfeIL9A2PKjThRbsSFciMuTjQ38WSKze3D/Oy5bgBWN1fyptPn+2r6u8y+oLzfKIV50tLS4nUJvjLRsIRzbIwm3iDv3tpzfL8n00jlMjLlBWMMn3j5cm5+49rsYxPLMHzqnp3KjThRbsSFciMuTjQ3f3H3Dv70Z9uz9ydPM5fiFZT3GzVGedLV1eV1Cb4ysQpbru1KY2UpAA+1DRCbYtRocCzB4FHT5ay1xCam7OXYgHnlpMYKvn3tOj5x8TIuWjEPgPahGA89f9DbwiSQ9H4jLpQbcXEiuRkYS7C5I30ucFlJiJsuWKyLuc4RQXm/URrzZKpr9cxlE6MiuS7D+a5zFmRvP7Rn4Iht27tHedOtz3D9D57NNkedwzGu/e5m7tic/otXEoAh+daaMl61uuGIb8v+7pEBfrOzj1SO6/3v6x/jbd/bzBd/tTtPVUoQ6P1GXCg34uJEcvPtxw9lb9/1zvVceWowlnCWExeU9xv/f3oMqIaGBq9L8JXMQA65/r2oKSuhKTNq9OUH2rIjTr/Z2cdNP90GQDSe4oM/3cpoLMnDewfozzRJtWVhTmsJzuo2JSHDX7x8Wfb+l36zh//64wGe6xzhuc6RI5Ygn2xH9yg3/Pg5ukfjPLC735cLTkhh6P1GXCg34sI1N9Za/jdzXtFFK+YF5oOyzI6gvN+oMcqToAwZFsxEY3QcT/nLVy4HIJa0fOSu57nkG0/wpd/sOWKfzuE4P3qmk4cyV87esKqeH1+/nlVNwboewoZVDfz9a1Zl7/9kcxcfvet5PnrX87zrh8+yt38s+6djKEbKWj6YaRAnfPNRTcObq/R+Iy6UG3HhkpvRWJL33741e/995y2azZIkAILyfuOvi70UkdpaLTs5WSrTGR3PN0SntVRRVhJiPJFiW9foEdv+7GVLuf2ZTnb3jfHdJ9qzj68L8HUQzlpYwz9fsojvPDvIaCzJcCzJ/oFxekcT3Pjj547Y9/wpljX9xbYedvVGCRvD1afP56IV87DW6lu5OUDvN+JCuREXx5OblLXcuqmdWyf9O33WwmrmV898TUMpLkF5v1FjlCfJZNLrEnzFHudUuvS+hu9cu47vPdnBA7v66I0muOKUJm548UKqImFObq7kvT85/A1UyMC5S+pmufLCaqkM8XeXHx45+n9/2McTB4ey9/cPjAPw8N5BAMpLQtzy5nW89XubAbIN5JYpzjl6w6nNtFRHeP26JkoDcA6W5E7vN+JCuREXx5ObHd3RI5qicxbX8DeXrMxHWeJzQXm/UWOUJyMjIzQ1NXldhm9Yh6l0APMqSvngBYv54AWLXzD6sby+gp+/+wx29kSxQHNVKU1Vwf4W6ujcfPjCJUds7xqJ8dl7dzEwlqAkZLjx3IU0Vpby/beeRudIjM7hGH/76z1T/uyfPpsexu4eifG+8xfn7Rik8PR+Iy6UG3FxPLmZuEj7ivpybnrJEtYvqM5naeJjQXm/UWOUJ62t/rzAqFesw1S6o0313NJwiLUBnj53tJly01wV4ear1r7g8caqUhqrSjllfhWj8RT//cgBwiHDSQ0V1JSFGU9aNmbOw/rJ5i6e6xzlgmV1XLN+fs4rBYp/6f1GXCg34uLo3PSMxBmOJdjTN8ZwLEk8aRlPpPjOpkPEkul/+xfVlakpmuOC8n6jxihP2tvbWbZs2cw7zhGuI0ZzzWzk5vKTG7n85MYXPN41EuPt338WgC2dI2zpHOH7T7ZzyzXrqM+sACjBpPcbcaHciIuJ3HQOx/jzn2/n0FBsxuesX1BTgMrEz4LyfqPGKE9KS/VBc7LD1zHytAzfy2dumqsi3PGO9TzXOcKn7tkJwGg8xZ/9fDvfvGZd3n6v5J/eb8SFciPH6/muUXb0pnior51bHjt8TaLSsGF1YyULaiNURcKUhgyl4RAvWlTDKfPTCynJ3BaU9xs1RnlSVxfsRQBmm83xgqVzXb5zUxUJc87iWu694Uz+4Xdt/GpHH/sHxklZqyl1Aab3G3Gh3Mjx+N2uvknnsPZnH794xTw+9crlWgFVphWU9xu18HnS3d3tdQm+cnjESG+c0ylUbowx/PnFh4e0X/PNJ+nIYTqE+JPeb8SFciO52j8wdsTCPuctqeXSNQ18/eq1fHrDCjVFMqOgvN9oxChPgtIZF0pKA0Y5KWRuQsbwqlX1/HJHHykL1//gWW66YDEXLKvTNSYCRu834kK5kVx9+/HD0+b+8VWLOGP5fA+rkSAKyvuNRozyJBbTt+9T0TlG0yt0bj7x8uV88uWHR46+tnE/1932LF0jym+Q6P1GXCg3kqvO4fSy25etaWRBpcfFSCAF5f1GI0Z5cE/rS7wuwXfOyvyJAfd4XIu80J8edf/xz3hShoiI+NBlmT8Am7wsRALtsvaHvC5hRhoxEhERERGROU8jRnlwWftDtLW1BWK99kL5m1/t5ve7+/n0K5dz8Un1XpfjW17nxlrLNx45yI+e6QTgzIXV/MNrVntWj+TG69xIMCk3MpXdvVHed/vW7P2VjRW8cmU9r1nbRFUkrNyIk7a2Nq9LyEnBGiNjzGXAvwJh4BvW2r87avvbgb/I3B0GPmCtfSqzbQ8wBCSBhLX2nELV7SoS0cnrk2Uv8KpzjKbldW6MMfyf8xbx2P5BdveN8eTBYW59op3rzgrGFavnKq9zI8Gk3MjRfvZcN1/9w77s/V+850zCR50crNyIi6DkpiCNkTEmDHwNeDWwH3jUGHOXtXbLpN12Axdba/uMMZcDXwfOm7T9FdbaYKz1B9TU6CrPE6y1PLinHwCDOqPp+CU3N1+1lkv/+0kgvRpRJGx48/oWb4uSY/JLbiRYlJviNJZI8ZudfQyNJ8CmL5eRynw7GU9axhIpyktC1JSFCRlDPGVJpFKMxFL84KmO7M/50mUrX9AUgXIjboKSm0KNGJ0L7LDW7gIwxtwGXAlkGyNr7eQzsh4GFheotrzo6emhurra6zJ8YWAskb29qLbMw0r8zy+5Mcbw7WvX8Y4fpP+KfuORg1xz+nxdq8Kn/JIbCRblprhYa7ntqQ5ueezQzDvP4H+uXceCmqn/vVZuxEVQclOoxmgRsG/S/f0cORp0tBuAX0y6b4H7jDEW+E9r7dePfkJnZyc33HADJSUlJJNJrrrqKm666Sba29upqqoiHA4zODhIc3Mzvb29WGtpbm6mo6Mj+0INDw/T0tJCV1cXxhgaGhro6uqitraWZDLJyMgIra2ttLe3U1paSl1dHd3d3dTV1RGLxYhGo9ntqVSK4eFhenp6qK+vJxqNMjY2lt1eXl5ORUUFfX19NDY2MjQ0RCwWy26vqKggEokwMDBAU1MTAwMDxOPx7HYvjikSiVBTU3Pcx1Ra2wikl+puCI/T1tYZ+GPK1+sUj8fZv3+/L45pfGCAb73xJN51xy4APnPPDt67LqLXyYfHVF5ezsGDB4vqmIrxdfLbMY2PjzM4OFhUx1SMr1Oux3T/tk5ueWIg+7loTUOEk5sqiMXGqayoIDY+TiqVYl5tNX2Dw4zbMJFwiGQiRm11FfHxMSpKDOuXNBLrbacnNvUxVVRU0NbWptdJx3RcxzQ+Ps74+Lgvjmk6xtr8X3nTGHMNcKm19sbM/euBc621H55i31cA/w681Frbk3lsobX2oDFmPnA/8GFr7QOTn7dx40a7du3afB9Kzjo6Omhp0dQjgI6hGNf/4Fmaq0r57ltP87ocX/Njbj59z04e3T8IwKtXN7Csvpw3ntpMaViLWvqFH3Mj/qfcFI9H9w3y6Xt3Zu9/59pTaanJzzkdyo248FNuNm3a9PiGDRumXK+gUJ9s9gNLJt1fDBw8eidjzHrgG8CVE00RgLX2YOa/ncAdpKfm+drY2JjXJfhGMtN8l+jqrjPyY26+eOlJ2dv3b+9NT6u79Rmi8aSHVclkfsyN+J9yUxzu395zRFP0xUtPyltTBMqNuAlKbgrVGD0KrDbGrDDGRIC3AHdN3sEYsxS4HbjeWvv8pMerjDE1E7eBS4DNBarbWWurVvGakEilG6OpTuKUI/kxN8YY/ufN63jvuQtpqiwFYDSe4v/9Yd8Mz5RC8WNuxP+Um+D7i7u384+/25u9/6cXLeXcJXV5/Z3KjbgISm4K0hhZaxPAh4B7geeAH1prnzXGvN8Y8/7Mbp8DGoF/N8Y8aYx5LPN4C/CgMeYp4BHg59baewpR94lob2/3ugTf2NY1AkBYJ+7PyK+5WVBbxpvWt3DrW0/llPmVAPxyR5/HVckEv+ZG/E25CRZrLXv7xnjtLU9y5f88xSXfeIInDg5nt3/96rVcdnJj3utQbsRFUHJTsOsYWWvvBu4+6rGbJ92+EbhxiuftAs7Ie4GzrLy83OsSfCEaT2a/zSov1TkpM/F7bkLG8OcXL+M9P3oOgAd29/GyFbpgr9f8nhvxJ+UmOJ4+NMTHf74jez+ePHx++MnNlfzL69YUbFaGciMugpKbgjVGc01FRYXXJfhCNJ7K3r7hxQs9rCQYgpCbxXWH39y++Ks93HejGiOvBSE34j/Kjf8lU5Zn2of5xN07jnj8MxuWc86iWkIhQ3lJYb90VG7ERVByo6/w86SvT9OMACYWPWyoLOHMhcG4uJeXgpKbf37d6uzt99/+HM91jnhYjQQlN+Ivyo1/Pd81yi2PHeTybz55RFP0z69bzX03nsXLVtRTGQkXvCkC5UbcBCU3GjHKk8bG/M/zDYIU6c7IoPOLchGU3JzaUk1laYjReIpdvWN89K7nueKUJj5y4ZKZnyyzLii5EX9RbvxlJJakcziGtfChO7cdsa21JsI1p8/n1BbvL5Cp3IiLoORGjVGeDA0NBeIKv/k2MWKkdRdyE6Tc/ODtp/PbXX185YH0OWQ/e66btc2VXLImGG9+xSRIuRH/UG7843tPtPOtxw+94PGrT2vmkjWNrGjwzzQk5UZcBCU3aozyJBaLeV2CL0w0RlqpOzdByk1ZSYhL1zTyipX1XHHLUwB8+YG9PH5giI+/bKkuAFtAQcqN+Idyk3/WWvrHEtSVlxCa9A1hXzTObU91APDHvYMcHBzPblteX44BLlw+j3ecvaDQJc9IuREXQcmNGqM8Ccp67fmmqXTHJ4i5iYRDfP9tp/HW76UvL/abnX209UX5tzes1UV9CySIuRHvFWturLV867FD7BsYxxioKg1TVx4madPb4inLKfOrqIqEOamhgvnVs3cxVGst27pGaR+K8Z1Nh+iNJhiJpS+GXRIyrF9QTXNVKfc+3zvl829722k0ZK4X51fFmhvJr6DkRo1RnrS3t7Ns2TKvy/CeptIdl6DmprGylJ9cfzrv+8lWukfj7Ood4zXffJKbLljMyc2VrJ1f5XWJRS2ouRFvFWNu+qJxrv3uzNeAv2tLd/Z2WUmI/3vZStY2V57wSPen793JY/uHptyWSFk2HThy2ytW1rOmqZLSsOG1a5sCcSH0YsyN5F9QcqPGKE+CsixhvqU0le64BDk3NWUlfOctp/KJu3fwTHv6ooNf27gfgHXzq1hWX84HL1hMmQerKBW7IOdGvFOMuZk45xFgVWMFl53cyEgsiTEQwtAbjdPWN0Y4ZHhk3yAA44kUf/az7QCUhgxrmitZUBPh9AU1lIYMKWuJJS0DYwkAasvCvGT5PBqPGtnZ2TOabYqqImFevLiGl66Yx0XL59E5HGfj3gH6RuPEkinGEinefEYLC2rKCvG/ZVYVY24k/4KSGzVGeRKJzN7QfJBZTaU7LkHPTThk+MoVq3niwBC/39PPz55Lfyu7pXOELZ0j/GJbD29eP58bz13kcaXFJei5EW8UW25GYslss5PrKpm3b+7ktic76M80PfGU5dmOEZ7tGOGXO469vPD/e2g/FaUhKkvDJFKWlLUMjScP/9zrT8dMmirRUhPhDac2ux6arxRbbqQwgpIbNUZ5MjAwwLx587wuw3MpTaU7LsWSm7MW1XDWohrec84Cnu8e5Y7NXfwx84Hlh0938uCefr5+1SlENHo0K4olN1JYxZSbofEEV3/nmez9XC8oftVp87nqtPkAdAzF6B6J8eShYQbGEgyMJQgZMMYQIv3FT9gYHmrrpzeaIBpPHXER8wl/9eqTjmiKik0x5UYKJyi5UWOUJ01NTV6X4A8TjZG3VQRGseWmuqyEFy2q5UWLahkcS/CmW9MfXA4OxrjiW09xyeoG3nhaMysbKz2uNNiKLTdSGMWUm59vPXzO0HvPW0RVJHzcP6OlJkJLTYRTW6dfUvgjL11CMmXpGokRDhlKjEk3TSFDJGyKfkXOYsqNFE5QclPcf3s9NDAw4HUJvjCxKl2oiL89m03FnJva8hJ+9q4zOHtRTfax+7b38oE7tvGG/3mKscQLv3mV3BRzbiR/iiU30XiSbz6avgbQ6a3VvOn0+Xn/neGQobWmjOaqCPWVpdSWl1AVCRd9UwTFkxsprKDkpvj/BnskHo97XYIvTFzHSENGuSn23ERKQnzp8lX8/eWreO95h88zGo2neP23niIxMfdSjkux50byo1hy8+l7dmZvv9OH1/0pNsWSGymsoORGjVGeBGW99nzLXuDV2zICY67k5qxFNbzp9Pnce8OZR3y7+5l7d2KtmqPjNVdyI7OrGHLTH42zuWMEgA2r6lm/YPppcHLiiiE3UnhByY0+r+ZJe3u71yX4QnZVOk2ly8lcy40xhveet4hFteklazcdGOLS/36SL9y/64grwcv05lpuZHYUQ25+u6s/e/sTF/v/GinFoBhyI4UXlNyoMcqTqipd0BIgqVXpjstczc1/Xr2WmrLDJ0s/1DbAx/73eY0e5Wiu5kZOTDHk5t8z10o7e1GNvoArkGLIjRReUHKjxihPwuHjXxGnGPWMpOeUjuvE+pzM1dxEwiF+cv16fvD207h0TQMAfdEEl/73k3z23p0kde7RtOZqbuTEBD03Q+OJ7O136Nyiggl6bsQbQcmNGqM8GRwc9LoEX5hYoEeNUW7mem7qK0r58IVLWNl4+ArZf9w3yHt+tIVDQ5padyxzPTfiJui52dh2eJWrU+YH49voYhD03Ig3gpKbnK5jZIz5U+DX1tonjTHnAz8EEsDbrbUb81lgUDU3F8cVrk9UMtMPndRQMf2OAig3kB49+o83rmU0luT9d2ylfSjGoaEY7/zBFhbWlnH2ohru297L6sYKyktD/PnFy6ivKPW6bE8pN+IiyLkZGEvw5Qf2AnBSQ7nH1cwtQc6NeCcoucn1Aq8fA/47c/tLwD8BQ8C/AOfNflnB19vbS2WlLlqZzJwjEgpp7nculJvDKiNh/ufN6/irX+7mocw3wwcHx7OLMkysRHXtdzezqrGCN57WTHlJmHAI9vaPsenAENeub+HsxbWeHUOhKDfiIqi5sdZy3fc3Z+/feO6iafaW2RbU3Ii3gpKbXBujOmvtgDGmBjgDeJW1NmmM+Uoeaws0nTSelsqcGxLWSbE5UW6OZIzhC68+iWTK8uTBIQ4MjvNsxwgdQzG2dI5k99vRE+Uff7f3Bc9/8uAw37j6FOoqSqgrz/XtLniUG3ER1Nw8cXCI8czKPpeuaeCcOfDlh58ENTfiraDkJtdPCvuMMS8BTgUeyDRFtUAyf6UFW1CGDPNtYlW6OXAx8Fmh3EwtHDKcvbiWs4HXrzv8/ygaT3L/9l729o8xNJ7kkX2DjMSOfFu68SfPAVBXXsKLl9QyOJagKhKmrryEt57ZUhTT8JQbcRHU3ExMoQP404uWeljJ3BTU3Ii3gpKbXBujPwd+DMSAqzOPXQE8ko+iikFHRwfLlumaChOriYU0YpQT5eb4VJSGj2iUAFLWEjKG+57v4b8fPUhfNL1y1cBYgl9u7z1i358+28W1Z7Tw7nMWBDqjyo24CGJuekbjdGdWO/3Excu0RLcHgpgb8V5QcpNTY2StvRtYeNTDP8r8kSlUV+vq25vbh/nj3vS5IWGdY5QT5ebETTQ4l6xp5JI1jVhr+f2efjYdGGJ3b5TykhDReIqtXaMA/OCpDn7wVAc/fPtpzAvo6JFyIy6ClhtrLW/93uFzi161usHDauauoOVG/CEoucl50r0x5hTgTUCLtfZDwEogAjydp9okwFLW8ul7dxKNp5elqyzVXDrxhjGGl62o52Ur6o94vD8a5/13bKV3ND2i9ObvbuZNp8/n7EU1nN5aTaREmRXxi+c6R7JftAF84HwtuCAisy+nf/mNMdcADwCLgHdkHq4mvTqdTGF4eNjrEjyVSFmi8RQhA289s4U3r2/xuqRAmOu5KaR5FaXc9rbTeeOph6fi/fiZTv7ynp1c8a2n+Mid2zys7vgoN+IiCLkZS6R4/+1b+ehdz/O9JzsAKA0b3njafI8rm7uCkBvxn6DkJtcRo78GXp25jtG1mceeIr1CnUyhpWVuNwIT5xaVhgzvPufoWZhyLHM9N174wAWLOa21mgODY3z78XYSmexu7Rrltbc8yetOaeI95yz09QiSciMu/J6b5zpH+Ohdzx/x2EUr5vGm09UUecnvuRF/Ckpucv2Xfj7pRgjATvpvMNbe80BXV5fXJXgqlV2NTucWHY+5nhuvXLRiHm85o5W733Mm995wZnZp73jScvvmLq6+9RnGEimPqzw25UZc+Dk3I7HkEU3R0nnl3HvDmXx2wwpOmV/lYWXi59yIfwUlN7k2Ro8D1x/12FvQqnTHNNdXypkYMVJjdHzmem78wBjDD95+Gv/2hpOz58aNJ1K8/ltP8Z4fbfFlg6TciAs/5+Znz3Vnb7/7nAX819VrfV3vXKLXQVwEJTe5NkYfAb5ojPkdUGWMuRf4G+Bjuf4iY8xlxphtxpgdxphPTrH97caYpzN/HjLGnJHrc/2ooWFur5aT1IVdncz13PhFyBjWNFXyk+vXc9maxuzj+wfG+fQ9Oz2sbGrKjbjwc242HRgE4EWLanjrma2B+VA1F/g5N+JfQclNTo2RtXYrsBb4GvAZ4BbgdGvt9lyeb4wJZ557ObAOeKsxZt1Ru+0GLrbWrifddH39OJ7rO0EZMsyXiaWQNWJ0fOZ6bvwmHDL86cuWcuc713Naa3r6zjPtw1z73Wc4MDDucXWHKTfiwq+56YvGeeJg+kTtC5fVeVyNHM2vuRF/C0pucj6b2Fo7aq39obX2H621t1lrj2d5iXOBHdbaXdbaGHAbcOVRP/8ha21f5u7DwOJcn+tHtbW1Xpfgqf965AAAaouOz1zPjV9VlIb5u8tXZe/3RRO8+0db2NMX9bCqw5QbceHX3OzsOfz36qIV87wrRKbk19yIvwUlNzmtSmeMWQp8HjiL9DLdWdbaNTn8iEXAvkn39wPnTbP/DcAvjue5nZ2d3HDDDZSUlJBMJrnqqqu46aabaG9vp6qqinA4zODgIM3NzfT29mKtpbm5mY6OjuxFp4aHh2lpaaGrqwtjDA0NDXR1dVFbW0symWRkZITW1lba29spLS2lrq6O7u5u6urqiMViRKPR7PZYLEZpaSk9PT3U19cTjUYZGxvLbi8vL6eiooK+vj4aGxsZGhoiFotlt1dUVBCJRBgYGKCpqYmBgQHi8Xh2uxfHFIlEqKmpyemY4pnzMN60qozx8fGiOKZCvE4dHR2MjIwU1TEV0+v09VfV82h/hP96LL1s8Ht/spUzm0v5+IULCZGa8Zj6h0f53MYhhscTrGsq45MXL2aov++EjykcDhONRvU66ZiO65ja29uz2fHTMf2xLX1tsbPml1IRStHW1janXye/HZMxhsHBwaI6pmJ8nfx2TAMDA1RWVvrimKZjrJ15YTljzB+BrcCPgCO+IrXW/iqH518DXGqtvTFz/3rgXGvth6fY9xXAvwMvtdb25PrcjRs32rVr1854LIXS1tbGsmXLvC7DM2/73ma6R+Pc+pZTmV8d8bqcwJjruQmKX+3o5e9/23bEY2ctrGHDqnoaKksJG8O6lirKMkt8R+NJ7nu+l69t3P+Cn3X1ac2cu6SOMxdWO59HodwUzlMHh3h47wDN1RHqK0pYOq+c5fUVgZw27NfcTPz7cf7SWv76kpVelyNH8WtuxN/8lJtNmzY9vmHDhnOm2pbrdYzWAhdYa12XY9oPLJl0fzFw8OidjDHrgW8Al1tre47nuX7T2trqdQkFF0+mGIklAYgl01EpDeCHBS/NxdwE0YZVDZy/tI7/++s9PLo/fZL4EweHeOLg0BH7NVeVYgx0DseP+bN+srmLn2w+PPf6zy9eyqtXNx5z/6koN/nVPRLj/u297OqJ8rvd/VPus6y+nHnlJaRsevrXqsYKTmutnnJfv/Bjbqy1dI+m/768fl3zDHuLF/yYG/G/oOQm18bof4GLgd84/p5HgdXGmBXAAdJLfb9t8g6Z6Xq3A9dba58/nuf6UXt7u28640IYS6R4zw+3ZP9Bm1ASVmN0POZaboKsKhLmby9byb7+MR4/MMQf9vQTDhm6hmPsyyzM0DVy5N+HpfPKee95CzlncS2/3N7LgcFx7ny2i9H44e+c/vF3e/nF1h7+7vJVOV9UVrnJD2stn7pnJ48fGHrBtlesrKc/msg2w219Y0yMIT7TfvgU3JMayikvCfP6dU28cpW/VmXyY262dI5kb5+9qMbDSuRY/Jgb8b+g5CbXxugjwEPGmJ1Ax+QN1tr3zPRka23CGPMh4F4gDHzTWvusMeb9me03A58DGoF/z0wnSVhrzznWc3Os2zOlpaVel1BQXcMxukfjhAzUlKVjdVpLFdWRsMeVBctcy00xWDKvnCXzynnDqYe/3R6JJYknU2ztGmVv/xgpa1lcW86Fy+uy0+UuySwD/u5zFhJLpDg0NM7/+clWADZ3jHDFt57iYxct5fyltUTCIaqm+buk3JyYjqEY//HwfkrDhvqKUkpChnjScueWI1dRWt9azavXNHDmghpaatJThBMpy7auEeJJS+dwjMcPDLHpwBADY+nzZHb1jgHpD/z/8/ghbjh3IRcum+eLqXd+zM3Ewgvp0Vbv/x/JC/kxN+J/QclNrucY3QmsIr0gwtHnGH02P6UdH7+dYzQyMkJV1dy5Ovfu3ijvu30ry+vL+frVp3hdTmDNtdzIkcYSKT51zw42t4+8YNvLVszjhhcvZEFt2Qu2KTfH74dPdfC9J9sJhwxD48lp9z1lfiX/8ro1x/VBvW80Tm80zub2kSnPLbtyXRPvOmfhtA1vvvkxNx+8Yys7eqJcsKyOv3r1SV6XI1PwY27E//yUm9k4x+iVwEJr7QvnE8iUuru7fROAQohnLuha4oNvQYNsruVGjlReEuKfrljDz57r5o7NnQyOJ7MjDw/s7ueB3f1cua6ZV66qZ2VjBZFweqqdX3LTMxLnaxv3EzbwoQuXUFee6z8xhdU9EuMbj77wVNVLVjewdF45mMy1LIzhRQtrOKmx4rh/R31lKfWVpaxsrOR165r43hPt/HJHHwcH09Ms79zSzZ1buomEDcmU5RWrGljdWMHZi2vTNRSAH3IzMJbgd7v6iCUtA2MJdmRGjF68OBhL+85FfsiNBE9QcpPrv1pPk57mpsYoR3V1c+uidEk1RrNiruVGpnbFKU1ccUoTAINjCb6z6RB3bukG4M4tXdkpXs1VpTRVlbKoKsy7m2I0V3m3AmTvaJy3fn9z9v7vdvdTXhLiJcvqOKmxgkvXNHreKKWs5cE9/dz+zOEpct++dh01ZSVUlIYI5WnqVsgYrnvRAq570QKGxxP80+/38uCeAQBiyfR75y+39/LL7ZA+lRZCBl61qoHXrG1iXUtuHyaSKUvKWkLG5DRVz+v3m3gyxTW3PjPltlet9tf5WHKY17mRYApKbnL9V+rXwH3GmFt44TlG35z1qopALBbzuoSC2po5YVaN0YmZa7mRmdWWl3DTS5ZwzfoWvvqHfRwaHD9icYeukTjPAb/c/SwVpSFed0oTbzi1maYCNUmdwzH+7jd72Nzxwul/Y4kUv97Zx6939vGNRw6yuqmCd529kDMWVOe8sESuRmJJ7t/ey1giibXp5rIqEmZ4PMn+gXEe3NPPj5/pPOI55yyuobXmhVMT86m6rITPveokrLXEkpbukTh3b+3muc4R9vaPMZiZ1peycN/2Xu7b3svJzZW0VkdorCrl1JZqltWXE0ukaOsfo3c0zuBYggf3DHAgMxoF0FRVyvyqCElrWTqvnJcsq+PC5fOOqMXr95ufbz18PZFzl9SyuK6MsDFcuqaR8lnOh8wer3MjwRSU3OTaGL2U9NdYlxz1uAXUGE0hGo3OvFMRiWe+9eyNHntZYpnZXMuN5G5+dYQvXpq+psvweIKe0Ti/29XPls4RNmVWTYvGU/zw6U5++HQn1ZEwi+rKqCkLU1NWwoXL6zh7Ue2sntOyf2CM9/zouSMe+8iFS3jt2kae7x7luc5RHtzdz9OZVdq2d0f59L07AVhcV8aKhgo+dMFi6itP/KTcmx/ez73P92bv3/LYoWPuW1ka4tWrG3jLmd4tH2uMoazEsKiujP9z3qLs4+OJFH3ROD98upOfPZceJdzWNcq2rlEAbt/cNeXPO1r3SJzuzKqI27pGuX97L3XlJaxqrCBpLWctrGGgv5/KfUkW1EY4c2FNQUccf/R0B//1SHo648rGimy2xf/075S4CEpuclp8IQj8tvjC+Pg4ZWWF/SbSS7c91c43Hz3Etevnc8O5i2Z+gkxpruVGZkd0bIytvXFuf6aTJw8OMZ489vv6WQtrePnKejasqs+eo+TqmlufyZ4D9d7zFvGSZXUsnGJxCGst//LgPnb1RrMf8Cc7taWKv3r1SdRmptrt7R/j2Y4RzlxYTWt1ZNpFD/64d4B7n+/JTk0DqCsvydY1YX1rNeEQvO3MVs5YGIxloBMpy8NtA4wlUmw6OMS2zhGSNj3NLmQM88pL0uealYRYVFvGmQuraamOsLt3jGg8yVgixZbOEX70dCdjiZkvQ9hcVcpJDRW8Zm0T5y2tnfWphYmU5Z5tPezujfK/maYP4D+vWsuKhuM/j0u8oX+nxIWfcjPd4gvHbIyMMcZmNhpjjvmv5wlc9HVW+a0x8tMVfgvh+0+2c8tjh3jLGS2858ULvS4nsOZabmR2HJ2bWCJFx3CMvmiC3+7qY//AGE8eHH7B8169uoG3n9VKdSScbUpy/p190ezy4u8/fxFXnTY/p+dZa+mPJvjW44f4xbaeI7adt6SWofHkEdeyAThjQTXvP38RjZWljCcsBwbHuHtrD891jrzgWlG3vuVU5ldHSKYsnSMxKkpC1JWXzPmln/tG4+zpH6Otb4yekRgW2NvVT+d4mF29U3+Te+maBt52VisLJk03jMaTPH5giFPnV+U00peylu9samdjW3926fLJfnzd6cedPfGW/p0SF37KjeuqdAPAxLIwCdLT5iYzmcd0oZopRCLenQTthczaC8zxzx4nbK7lRmbH0bmJlIQy11eC9QuqAYglU/xx7yB3beniqUPpJun+7b3cvz09/aypspSTGitYO7+KC5bWsrKxctrfuX/g8Pksb5x0DaeZGGOoryzlYxct5UMvWcyPn+nMTnv7477BKZ/z1KFhPnDHtml/7rXr53PN+pbsh+xwyBzxgX6um1gl76xJo2WHDoVYsGAByZSlZzTOpgNDfGfToWyzee/zvdz7fC8hk26iy0pC3LXl8EjPsnnllIQNp7VUc9aialY3VdJUeeT1h/7+t238ZmffEbWsqC/nRYtqeP2pzWqKAkj/TomLoORmunekU40xi621+4EVhSqoWNTUBGOqxmyZGHnM16pOc8Vcy43MjlxyEwmHuGjFPC5aMY/BsQR/9cvdtA+NZz8Ed4/G6R6N88i+Qb79+CFaqiOcsaCa1poIa5oraa6KZBdXeeLgEP/2UPraPK9YWe88GlMaDvHWM1vZsKqBnT1RukZibO9OT7W7YFkd6+ZX8e8b97O5fYThWJKykhClYUN1JExjZSmL6sp4+Un1nDK/yhcXTA2aidyEQ4b51REuO7mRy05uZCSW5Av37+LpQ8NY0l98TT5/a0Jbf3oEaGdP9IiL4Z6xoJpIOITF8tj+9PlvZWHD5199EmuaKtUMBZz+nRIXQcnNMd+drLX7jDGDQK21tq2ANRWFnp4eqqurvS6jYLIjRt6WEXhzLTcyO443N7XlJXzlitVAeqrT7t4ow+NJdveN8e+Zi5F2DMe4b/sLPwwf7axZOF9nfnWE+dVTf5v4qVfqe7l8OVZuqiJh/vG16Xxs7x5lc/sw27pGMSZ9ra2VjZWc3lpFz2iczuE4j+8f5JmOYXpH0+d1TYxITvbj69dTppXmioL+nRIXQcnNTF/b6HOuo/r6eq9LKKjUxIiRvrU9IXMtNzI7TiQ3IWOy0+bOWFjDleua+MOeAYbG0+cnlYRC9EXjLzh5PxIO8clXLGN5vU6aD6pccrO6qZLVTVNPq1yWee0vO7kRSJ9/tLt3jPFEingqRV80QTxpOXtRjZqiIqJ/p8RFUHIzU2NkTXqOxDE/7fpl8QW/iUaj1NbOnSt3T6zhoX/6Tsxcy43MjtnMjTGGl66YB8Dla5tm5WeKP832+01FaTjni9FKcOnfKXERlNzM1BhVk154YSpafGEaY2MvXH2nmE10xzrF6MTMtdzI7FBuxIVyIy6UG3ERlNzM1BiNAqcWopBi09rq3YUDvaDFF2bHXMuNzA7lRlwoN+JCuREXQcnNTDOfUtbatun+FKTKAGpvb/e6hILSct2zY67lRmaHciMulBtxodyIi6DkZqbGSB9zHZWXl3tdQkFlF1/wuI6gm2u5kdmh3IgL5UZcKDfiIii5melz7OUFqaIIVVTMrZWanjiQvlaFVqU7MXMtNzI7lBtxodyIC+VGXAQlN9M2RtbaBwtVSLHp6+ubeaciksxMpZuYUidu5lpuZHYoN+JCuREXyo24CEpuNPMpTxobG70uoaAmBorOWuj/i3f52VzLjcwO5UZcKDfiQrkRF0HJjRqjPBkaGvK6hIJKZIaKSkOK1ImYa7mR2aHciAvlRlwoN+IiKLnJ6VOsMearx3j8X2a1miISi8W8LqGgkpnGKKxzjE7IXMuNzA7lRlwoN+JCuREXQclNrl/vv+sYj18/S3UUnaCs1z5bknaiMfK4kICba7mR2aHciAvlRlwoN+IiKLmZ9mOsMeY9xpj3ACUTtyf9+SLQXZgygyco67XPhkTK0jkcB6BEI0YnZC7lRmaPciMulBtxodyIi6DkpmSG7RMjQhGOHB2yQAfwznwUVQyCsizhbPj1jt7s7YiGjE7IXMqNzB7lRlwoN+JCuREXQcnNtI2RtfYVAMaYL1prP1OYkopDJBLxuoS8iiVT/Gp7L0PjSZ44mD6hrr6ihNrymXptmU6x50byQ7kRF8qNuFBuxEVQcnPMr/eNMZPnRH3OGBOa6k8BagykgYEBr0vIqz/s6eefH9zHNx49yOOZi7u+/axgzB/1s2LPjeSHciMulBtxodyIi6DkZrqv9weA2sztBOnpc5OZzGPhPNQVeE1NTV6XkFf3bEtPnzu5uZL1rdVURcJsWNXgcVXBV+y5kfxQbsSFciMulBtxEZTcTNcYnTrp9op8F1JsBgYGqKqq8rqMvLDWZqfPXbxiHm9a3+JxRcWjmHMj+aPciAvlRlwoN+IiKLk5ZmNkrd036XZbYcopHvF43OsS8mZHTzR7+zVrg/ENQFAUc24kf5QbcaHciAvlRlwEJTc5nylvjHk9cDHQRHoaHQDW2nfkoa7AC8p67S42th2eJ1oZ0UzK2VTMuZH8UW7EhXIjLpQbcRGU3OS0eIIx5vPAf2b2vwboAS4F+nP9RcaYy4wx24wxO4wxn5xi+1pjzEZjzLgx5uNHbdtjjHnGGPOkMeaxXH+nl4KyXruLHT2jAFynxRZmXTHnRvJHuREXyo24UG7ERVByk+uqcu8BXm2t/RgQy/z3dcDyXJ5sjAkDXwMuB9YBbzXGrDtqt17gI8CXj/FjXmGtPdNae06ONXsqCPMoXUXjKQDKSrQo4Wwr5txI/ig34kK5ERfKjbgISm5y/WQ7z1q7OXM7ZowptdY+QnpqXS7OBXZYa3dZa2PAbcCVk3ew1nZaax8FgjEJcQbhcPFOMSsNp2dSLp1X7nElxaeYcyP5o9yIC+VGXCg34iIoucm1MdppjJlYpW4z8AFjzPVAX47PXwTsm3R/f+axXFngPmPM48aY9x7H8zwzODjodQl5k0ylV24vKzEz7CnHq5hzI/mj3IgL5UZcKDfiIii5yXXxhc8AjZnbfwl8F6gGPpjj86f6BH30dZGmc6G19qAxZj5wvzFmq7X2gck7dHZ2csMNN1BSUkIymeSqq67ipptuor29naqqKsLhMIODgzQ3N9Pb24u1lubmZjo6OqiurgZgeHiYlpYWurq6MMbQ0NBAV1cXtbW1JJNJRkZGaG1tpb29ndLSUurq6uju7qauro5YLEY0Gs1un/h5PT091NfXE41GGRsby24vLy+noqKCvr4+GhsbGRoaIhaLZbdXVFQQiUQYGBigqamJgYEB4vF4drsXxxSJRKipqWEkOgbAQH8/bYm+ojgmv7xOyWSS/fv3F9UxFePr5Ldjqq6u5uDBg0V1TMX4OvntmOLxOIODg0V1TMX4OvntmGpqamhrayuqYyrG18mPxzQ+Pu6LY5qOsfbY/Ykx5hPA74DHrbWJaX/SdL/EmAuAL1hrL83c/0sAa+2Xptj3C8CwtXbKc42OtX3jxo127dq1riXOuv3797N48WKvy8iLj/3v8zzbMcJXrljN6a3VXpdTVIo5N5I/yo24UG7EhXIjLvyUm02bNj2+YcOGKdcsmGkq3auAXwL9xphfGmM+a4y52BhTdpw1PAqsNsasMMZEgLcAd+XyRGNMlTGmZuI2cAnp6Xy+Nl3DGXQTU+nCRlPpZlsx50byR7kRF8qNuFBuxEVQcjPtVDpr7SWZFeXOBi7K/PkoUJVZNvt31trPzPRLrLUJY8yHgHuBMPBNa+2zxpj3Z7bfbIxpBR4DaoGUMeZPSK9g1wTcYdIfwkuA71lr73E62gJqbm72uoS8OTA4DkBYi9LNumLOjeSPciMulBtxodyIi6DkZsaPttbapLX2EWvtV6y1bwBWAZ8HVpM+3ygn1tq7rbVrrLUrrbV/m3nsZmvtzZnb7dbaxdbaWmvtvMztwcxKdmdk/pw68Vy/6+jo8LqEvPjDnn6GxpMAlIQ0YjTbijU3kl/KjbhQbsSFciMugpKbGRdfMMY0Ai+b9GcBsBH4B+D3ea0uwCZOHCs2e/vHsreX11d4WElxKtbcSH4pN+JCuREXyo24CEpupm2MjDHPAhWkF2B4ELjZWrutEIWJP40n0hd3vf5FrYQ1YiQiIiIiRWKmqXQHgSpgGbAEWGyMqcx7VUVgeHjY6xJmXedwjO89mR4KLdMJRnlRjLmR/FNuxIVyIy6UG3ERlNzMtPjCqzOLL7yI9DS6DwPfNca0kZ5G93tr7Z35LzN4WlpavC5h1j28dyB7e8m8cg8rKV7FmBvJP+VGXCg34kK5ERdByU2uiy88OmnxhbXAT4DrgNvzXF9gdXV1eV3CrOqPxrn54QMAXLRiHhcsq/O4ouJUbLmRwlBuxIVyIy6UG3ERlNy4LL6wnvQUu1+RPvdIpmCK7Bo/v9jWQyJz/aLTWqo8rqZ4FVtupDCUG3Gh3IgL5UZcBCU3uSy+sBbYDTwAfBV4wFq7uwC1BVpDQ4PXJcyqg5lrFy2dV85lJzd6XE3xKrbcSGEoN+JCuREXyo24CEpuZppK9zfAYmvtKmvte6y1/6OmKDdBGTLMxYGBce59vheAN5zaTEVp2OOKilcx5UYKR7kRF8qNuFBuxEVQcjPT4gu3FaqQYlNbW+t1CbPmkX2HF104Z3GNh5UUv2LKjRSOciMulBtxodyIi6DkRmsu50kymfS6hFlz6xPtAGxYVU9rTZnH1RS3YsqNFI5yIy6UG3Gh3IiLoORGjVGejIyMeF3CrCkrScdkw6pgzA8NsmLKjRSOciMulBtxodyIi6DkRo1RnrS2tnpdwqyJJ9Or0a1srPC4kuJXTLmRwlFuxIVyIy6UG3ERlNzk1BgZY046xp9Fxhg1V1Nob2/3uoRZMzCWACAS1kudb8WUGykc5UZcKDfiQrkRF0HJzYzXMcrYAdjMbTPpNkDKGHMX8EFrbcdsFhdkpaWlXpcwK5Kpwy91eYkao3wrltxIYSk34kK5ERfKjbgISm5y/aT7f4DvAmuAcuBk4Fbgg8DppBusr+WjwKCqq6vzuoRZEUumsrfDoWBcnCvIiiU3UljKjbhQbsSFciMugpKbXBujvwLea63daa2NWWt3AB8APmut3Qq8C3h5fkoMpu7ubq9LmBUT5xfVlOnaRYVQLLmRwlJuxIVyIy6UG3ERlNzk2hiFgOVHPbYUmPi0PEzu0/LmhKB0xjP5zc4+AErDGi0qhGLJjRSWciMulBtxodyIi6DkJtdm5l+AXxtjbgH2AYuBd2ceB3gtsHG2iwuyWCzmdQmz4t7newAIocaoEIolN1JYyo24UG7EhXIjLoKSm5waI2vtPxhjngauAV4EHAJusNbek9n+U+CneaoxkKLRqNclzIqJxRc+9crl3hYyRxRLbqSwlBtxodyIC+VGXAQlNzk1RsaYpkwTdE+e6ykaQVmvfSbxTGNUW66ZkoVQLLmRwlJuxIVyIy6UG3ERlNzkeo7RXmPM3caYtxtjKvNaUZEIynrt07HWsn9gHNA5RoVSDLmRwlNuxIVyIy6UG3ERlNzk2hgtBX5GeiW6DmPM940xrzPGaBjhGCKRiNclnLD24cPzQWvL9FIXQjHkRgpPuREXyo24UG7ERVByk1NjZK3tttb+u7X2pcCpwFPA35I+10imUFNT43UJJ2wsnr6GUchAVUTLdRdCMeRGCk+5ERfKjbhQbsRFUHKT64jRZC2ZP01A/6xWU0R6enq8LuGETSy8sLy+wuNK5o5iyI0UnnIjLpQbcaHciIug5CanxsgYs84Y8zfGmJ0cXn3uDdba1XmrLODq6+u9LuGEJTKNUUlI5xcVSjHkRgpPuREXyo24UG7ERVByk+uI0R+ABcB7gcXW2o9Zax8xxriMOM0JQVmWcDpJNUYFVwy5kcJTbsSFciMulBtxEZTc5HpGfYu1NnsmvjHmdOCdwNuAhfkoLOjGxsa8LuGEDY4nAQirMSqYYsiNFJ5yIy6UG3Gh3IiLoOQm18UXYsaYZmPMR40xm4AngXOAj+azuCALynrt0zGZfmhvfzDCXAyKITdSeMqNuFBuxIVyIy6CkptpGyNjTKkx5mpjzP8CB4D3AXeQXnThzdbaH+W/xGAKynrt00nZ9FS6tc26dFWhFENupPCUG3Gh3IgL5UZcBCU3M40YdQD/CWwDzrfWrrPW/g0Qm/5pUl5e7nUJJ2xi8QVd3LVwiiE3UnjKjbhQbsSFciMugpKbmRqjp4F5wHnAi40xzktKGGMuM8ZsM8bsMMZ8corta40xG40x48aYjx/Pc/2ooiL4S1xPLL6gc4wKpxhyI4Wn3IgL5UZcKDfiIii5mbYxsta+HFgJ3Ad8HGjPTKurAkpz/SXGmDDwNeByYB3wVmPMuqN26wU+AnzZ4bm+09fX53UJJ0zLdRdeMeRGCk+5ERfKjbhQbsRFUHIz4+IL1to2a+3fZK5ZtAE4BKSAp4wx/5Dj7zkX2GGt3ZVZ3e424Mqjfk+ntfZRIH68z/WjxsZGr0s4YY/tHwLUGBVSMeRGCk+5ERfKjbhQbsRFUHKT63LdAFhrHwQeNMZ8BHgj8I4cn7oI2Dfp/n7S0/Nm7bmdnZ3ccMMNlJSUkEwmueqqq7jppptob2+nqqqKcDjM4OAgzc3N9Pb2Yq2lubmZjo4OqqurARgeHqalpYWuri6MMTQ0NNDV1UVtbS3JZJKRkRFaW1tpb2+ntLSUuro6uru7qaurIxaLEY1Gs9uj0SiLFy+mp6eH+vp6otEoY2Nj2e3l5eVUVFTQ19dHY2MjQ0NDxGKx7PaKigoikQgDAwM0NTUxMDBAPB7Pbi/EMfUPp9ecHx5P0NbWRiQSoaamJtDHdPTr5Ldj2rt3L7W1tUV1TMX4OvntmKy1DA4OFtUxFePr5LdjamtrY8mSJUV1TMX4OvntmJLJJD09PUV1TMX4OvntmPr6+li1apUvjmk6xmZWHssnY8w1wKXW2hsz968HzrXWfniKfb8ADFtrv3w8z924caNdu3Ztfg/kOLS1tbFs2TKvyzghn7l3J4/sG+SvLzmJ85fWeV3OnFAMuZHCU27EhXIjLpQbceGn3GzatOnxDRs2nDPVtpyuYzQL9gNLJt1fDBwswHM9E5T12qcTT2ZWpdNUuoIphtxI4Sk34kK5ERfKjbgISm4K1Rg9Cqw2xqwwxkSAtwB3FeC5ngnKeu3T0XLdhVcMuZHCU27EhXIjLpQbcRGU3BzXOUaurLUJY8yHgHuBMPBNa+2zxpj3Z7bfbIxpBR4DaoGUMeZPgHXW2sGpnluIuk9EUJYlPJbnOkd4pn0YgJJQofpnCXpuxBvKjbhQbsSFciMugpKbgjRGANbau4G7j3rs5km320lPk8vpuX4XiUS8LuGE/GFPf/b2gtpgH0uQBD034g3lRlwoN+JCuREXQcmNhgLyZGBgwOsSTkg8M43u+he1Ul+R8yWr5AQFPTfiDeVGXCg34kK5ERdByY0aozxpamryuoQTksw0RjVlBRtUFIKfG/GGciMulBtxodyIi6DkRo1RngSlMz6WicZIF3ctrKDnRryh3IgL5UZcKDfiIii5UWOUJ/F43OsSTsjEinRhNUYFFfTciDeUG3Gh3IgL5UZcBCU3aozyJCjrtR/Lr3f0AaCVugsr6LkRbyg34kK5ERfKjbgISm7UGOVJUNZrP5bGqvSCC3XlOseokIKeG/GGciMulBtxodyIi6DkRo1RnlRVVXldwgmZmEq3oiEY684Xi6DnRryh3IgL5UZcKDfiIii5UWOUJ+Fw2OsSTkgiqcUXvBD03Ig3lBtxodyIC+VGXAQlN2qM8mRwcNDrEk5I0qox8kLQcyPeUG7EhXIjLpQbcRGU3KgxypPm5mavS3CWspah8SSgVekKLci5Ee8oN+JCuREXyo24CEpu1BjlSW9vr9clONt0YCh7u1TL0hVUkHMj3lFuxIVyIy6UG3ERlNyoMcoTm5mKFkQ9o4fXmo+EFZFCCnJuxDvKjbhQbsSFciMugpIbferNk6AMGU5lYkW6y09u9LiSuSfIuRHvKDfiQrkRF8qNuAhKbtQY5UlHR4fXJThLZhojnV9UeEHOjXhHuREXyo24UG7ERVByo8YoT6qrq70uwdnEiJFWpCu8IOdGvKPciAvlRlwoN+IiKLlRYyQvsLFtAFBjJCIiIiJzR4nXBRSr4eFhGhuDcY6OtZav/mEfz3ePArC9OwpAWYn65kILUm7EP5QbcaHciAvlRlwEJTdqjPKkpaXF6xJy1h9N8POtPS94/E2nz/egmrktSLkR/1BuxIVyIy6UG3ERlNxoSCBPurq6vC4hZ8nMEop15SX825Un829XnsyPrzudqkjY48rmniDlRvxDuREXyo24UG7ERVByoxGjPDEmOOfnZNZaoDRsWNNc6W0xc1yQciP+odyIC+VGXCg34iIoudGIUZ40NDR4XULOJq65pbUWvBek3Ih/KDfiQrkRF8qNuAhKbtQY5UlQhgwBLOnOyKDOyGtByo34h3IjLpQbcaHciIug5EaNUZ7U1tZ6XULOJkaMAjLKWdSClBvxD+VGXCg34kK5ERdByY0aozxJJpNel5CzlKbS+UaQciP+odyIC+VGXCg34iIouVFjlCcjIyNel5AzTaXzjyDlRvxDuREXyo24UG7ERVByo8YoT1pbW70uIWcpTaXzjSDlRvxDuREXyo24UG7ERVByo8YoT9rb270uIWfWTowYideClBvxD+VGXCg34kK5ERdByY0aozwpLS31uoScZQaMCGnIyHNByo34h3IjLpQbcaHciIug5EaNUZ7U1dV5XULOtCqdfwQpN+Ifyo24UG7EhXIjLoKSm4I1RsaYy4wx24wxO4wxn5xiuzHGfDWz/WljzIsmbdtjjHnGGPOkMeaxQtV8Irq7u70u4QhPHBzin3+/l6/+YR/buo48AS6V6Yy0Kp33/JYbCQblRlwoN+JCuREXQclNSSF+iTEmDHwNeDWwH3jUGHOXtXbLpN0uB1Zn/pwH/EfmvxNeYa0Nxv9V/NUZdw7H+Iu7d2Tv7+ge5WMXLWVZfTkhYyaNGKkz8pqfciPBodyIC+VGXCg34iIouSlIYwScC+yw1u4CMMbcBlwJTG6MrgS+bdMrATxsjJlnjFlgrT1UoBpnVSwW87qErP6xxBH3t3aN8r7bt3JSQznvOHsB27ujAETjKS/Kk0n8lBsJDuVGXCg34kK5ERdByU2hGqNFwL5J9/dz5GjQsfZZBBwivT7AfcYYC/yntfbreax1VkSjUa9LyEpm1uNe01TJ0nll/HJHHwC7esf4wv27s/sdHBz3pD45zE+5keBQbsSFciMulBtxEZTcFKoxmmqOlj2OfS601h40xswH7jfGbLXWPjB5x87OTm644QZKSkpIJpNcddVV3HTTTbS3t1NVVUU4HGZwcJDm5mZ6e3ux1tLc3ExHRwfV1dUADA8P09LSQldXF8YYGhoa6Orqora2lmQyycjICK2trbS3t1NaWkpdXR3d3d3U1dURi8WIRqPZ7aFQiOHhYXp6eqivrycajTI2NpbdXl5eTkVFBX19fTQ2NjI0NEQsFstur6ioIBKJMDAwQFNTEwMDA8Tj8ez24zmmqKkBIJWI8aFzl3D1Mrhjd4Ke0TiJZJLRVJjtPWO8cmkFIyMjxzymSCRCTU2NL45ptl4nvx1TKpVi//79RXVMxfg6+e2YamtrOXjwYFEdUzG+Tn47pmQyyeDgYFEdUzG+Tn47prq6Otra2orqmIrxdfLbMSWTScbHx31xTNMxE9ewySdjzAXAF6y1l2bu/yWAtfZLk/b5T+C31trvZ+5vA15+9FQ6Y8wXgGFr7ZcnP75x40a7du3avB7H8Whra2PZsmVelwHAUweH+PO7d3B6azVfuWL1lPskUpaw0XlGXvNTbiQ4lBtxodyIC+VGXPgpN5s2bXp8w4YN50y1rVCr0j0KrDbGrDDGRIC3AHcdtc9dwDsyq9OdDwxYaw8ZY6qMSQ95GGOqgEuAzQWq21kkEvG6hKxEZipdyTSvdknIqCnyAT/lRoJDuREXyo24UG7ERVByU5CpdNbahDHmQ8C9QBj4prX2WWPM+zPbbwbuBl4D7ABGgXdnnt4C3JH50F4CfM9ae08h6j4RNTU1XpeQ9bWN+wEIaz1u3/NTbiQ4lBtxodyIC+VGXAQlN4U6xwhr7d2km5/Jj9086bYFbpriebuAM/Je4Czr6enJzpH0UjyZYv9AelGFFfUVHlcjM/FLbiRYlBtxodyIC+VGXAQlNwW7wOtcU19f73UJADyybzB7+8ZzF3pYieTCL7mRYFFuxIVyIy6UG3ERlNyoMcoTvyxL+Ltd6aW5S3UOUSD4JTcSLMqNuFBuxIVyIy6Ckhs1RnkyNjbmdQkATCw6+KELl3hbiOTEL7mRYFFuxIVyIy6UG3ERlNyoMcqT1tZWr0sAIJnpjKojYY8rkVz4JTcSLMqNuFBuxIVyIy6Ckhs1RnnS3t7udQkAJFPp/2pBumDwS24kWJQbcaHciAvlRlwEJTdqjPKkvLzc6xIASGVGjLRUdzD4JTcSLMqNuFBuxIVyIy6Ckhs1RnlSUeGPpbEnptKFtfBCIPglNxIsyo24UG7EhXIjLoKSGzVGedLX1+d1CQAkU+nGSANGweCX3EiwKDfiQrkRF8qNuAhKbtQY5UljY6PXJQDwxMFhQFPpgsIvuZFgUW7EhXIjLpQbcRGU3KgxypOhoSGvSwCgrrwEgHkVJR5XIrnwS24kWJQbcaHciAvlRlwEJTdqjPIkFot5XQJweCpdY2Wpx5VILvySGwkW5UZcKDfiQrkRF0HJjRqjPPHLeu2JlBZfCBK/5EaCRbkRF8qNuFBuxEVQcqPGKE/8sl77xKp0JTrHKBD8khsJFuVGXCg34kK5ERdByY1OPMmTQi1LaK2lP5ogMzAEBjqHDw9XxpO6jlGQBGU5S/EX5UZcKDfiQrkRF0HJjRqjPIlEIgX5Pf/5xwPcvrlrxv3UFwVDoXIjxUW5ERfKjbhQbsRFUHKjqXR5MjAwkP/fMZY4ZlN0cnNl9nZTZSlG5xgFQiFyI8VHuREXyo24UG7ERVByoxGjPGlqasr779jePZq9fcs1pxBPWTYdGOLcJbUsritnLJHi6UNDrGgIxvClFCY3UnyUG3Gh3IgL5UZcBCU3aozyZGBggKqqqrz9/O6RGJ+6ZycAqxorWFRXDsDy+sNNUHlJiHOX1OWtBpl9+c6NFCflRlwoN+JCuREXQcmNGqM8icfjs/4zU9byHxv3MxJPMa/88Ev3okU1s/67xBv5yI0UP+VGXCg34kK5ERdByY0aozzJx3rtj+wb5M4t3Uc8tqapkve8eOGs/y7xRlDW+Rd/UW7EhXIjLpQbcRGU3GjxhTzJx3rtX/rNnhc81lITIaSFFYpGUNb5F39RbsSFciMulBtxEZTcqDHKk3zMo8xcq5WVjRVMtEJvOLV51n+PeCcI82/Ff5QbcaHciAvlRlwEJTeaSpcn4XB41n9mMtMZ/evr1hApCZFMWV24tcjkIzdS/JQbcaHciAvlRlwEJTcaMcqTwcHBWf+ZyVS6MZpohtQUFZ985EaKn3IjLpQbcaHciIug5EaNUZ40N8/uFLeUtWT6ItQPFa/Zzo3MDcqNuFBuxIVyIy6CkhtNpcuT3t5eKisrp93nmfZhfvx0J5s7hnn7Wa3UlZfw0uXzKCs53K+OxJKUhk12gYWwAaPFFopWLrkROZpyIy6UG3Gh3IiLoORGjVGe2ImVEqbxw6c6+OO+9NDizQ8fAODvaaOyNN0YjcZT2X1XN6Uv3Jqc+cdKgOWSG5GjKTfiQrkRF8qNuAhKbjSVLk9yGTIcTx5ufOomXbB1NJ46oikC2N4dnb3ixLeCMtQs/qLciAvlRlwoN+IiKLnRiFGedHR0sGzZsmn3SWSGf7782tWsX1BNLJEinjmRaGvnCN99op3GqlJWN1ZycGicvX1jXLRiXr5LFw/lkhuRoyk34kK5ERfKjbgISm7UGOVJdXX1jPskMk1QaTh9zlCkJEQks+3sxbWcvbg2X+WJT+WSG5GjKTfiQrkRF8qNuAhKbgo2lc4Yc5kxZpsxZocx5pNTbDfGmK9mtj9tjHlRrs8NqkNDMUDLbouIiIiIeK0gjZExJgx8DbgcWAe81Riz7qjdLgdWZ/68F/iP43iub8STKUZiSbr6hxiJJaf9MzCWAKBUjZFkDA8Pe12CBJByIy6UG3Gh3IiLoOSmUFPpzgV2WGt3ARhjbgOuBLZM2udK4Ns2vWzFw8aYecaYBcDyHJ7rG7/Y1sO/PbQ/c68vp+fMr47MvJPMCS0tLV6XIAGk3IgL5UZcKDfiIii5KVRjtAjYN+n+fuC8HPZZlONz6ezs5IYbbqCkpIRkMslVV13FTTfdRHt7O1VVVYTDYQYHB2lubqa3txdrLc3NzXR0dGTnPQ4PD9PS0kJXVxfGGBoaGujq6qK2tpZkMsnIyAitra20t7dTWlpKXV0d3d3d1NXVEYvFiEajkCqjPAwWCJkQ1qYwxmABrMWEQthUCozBAGsbSkiNj3KoZ5hYLJb9+RUVFUQiEQYGBmhqamJgYIB4PJ7dXshjmtgeiUSoqamhp6eH+vp6otEoY2Nj2e3l5eVUVFTQ19dHY2MjQ0NDOqbjPKYdO3Ywb968ojqmYnyd/HZMiUSCioqKojqmYnyd/HZMu3fvZtmyZUV1TMX4OvntmGKxGOFwuKiOqRhfJ78dU09PD2vWrPHFMU3HFGJdcWPMNcCl1tobM/evB8611n540j4/B75krX0wc/9XwCeAk2Z6LsDGjRvt2rVr834sudq/fz+LFy/2ugwJGOVGXCg34kK5ERfKjbjwU242bdr0+IYNG86ZaluhRoz2A0sm3V8MHMxxn0gOz/WdhoYGr0uQAFJuxIVyIy6UG3Gh3IiLoOSmUKvSPQqsNsasMMZEgLcAdx21z13AOzKr050PDFhrD+X4XN/p6uryugQJIOVGXCg34kK5ERfKjbgISm4KMmJkrU0YYz4E3AuEgW9aa581xrw/s/1m4G7gNcAOYBR493TPLUTdJ6K2VtcgkuOn3IgL5UZcKDfiQrkRF0HJTcEu8GqtvZt08zP5sZsn3bbATbk+1++SyaTXJUgAKTfiQrkRF8qNuFBuxEVQclOwC7zONSMjI16XIAGk3IgL5UZcKDfiQrkRF0HJjRqjPGltbfW6BAkg5UZcKDfiQrkRF8qNuAhKbtQY5Ul7e7vXJUgAKTfiQrkRF8qNuFBuxEVQcqPGKE9++tOfel2CBJByIy6UG3Gh3IgL5UZcBCU3aozy5Pbbb/e6BAkg5UZcKDfiQrkRF8qNuAhKbtQY5UkikfC6BAkg5UZcKDfiQrkRF8qNuAhKbkx6lezg+9WvftUFtHldx4Te3t6mhoaGbq/rkGBRbsSFciMulBtxodyIC5/lZtmGDRuap9pQNI2RiIiIiIiIK02lExERERGROU+NkYiIiIiIzHlqjGaZMeYyY8w2Y8wOY8wnva5H/MkYs8QY8xtjzHPGmGeNMR/NPN5gjLnfGLM98996r2sV/zHGhI0xTxhjfpa5r9zItIwx84wxPzbGbM2871yg3MhMjDEfy/wbtdkY831jTLlyI0czxnzTGNNpjNk86bFj5sQY85eZz8nbjDGXelP11NQYzSJjTBj4GnA5sA54qzFmnbdViU8lgD+z1p4CnA/clMnKJ4FfWWtXA7/K3Bc52keB5ybdV25kJv8K3GOtXQucQTo/yo0ckzFmEfAR4Bxr7WlAGHgLyo280LeAy456bMqcZD7rvAU4NfOcf898fvYFNUaz61xgh7V2l7U2BtwGXOlxTeJD1tpD1tpNmdtDpD+kLCKdl//J7PY/wBs8KVB8yxizGHgt8I1JDys3ckzGmFrgZcB/A1hrY9bafpQbmVkJUGGMKQEqgYMoN3IUa+0DQO9RDx8rJ1cCt1lrx621u4EdpD8/+4Iao9m1CNg36f7+zGMix2SMWQ6cBfwRaLHWHoJ08wTM97A08ad/AT4BpCY9ptzIdE4CuoBbMlMwv2GMqUK5kWlYaw8AXwb2AoeAAWvtfSg3kptj5cTXn5XVGM0uM8VjWg9djskYUw38BPgTa+2g1/WIvxljrgA6rbWPe12LBEoJ8CLgP6y1ZwEjaPqTzCBzTsiVwApgIVBljLnO26qkCPj6s7Iao9m1H1gy6f5i0sPOIi9gjCkl3RR911p7e+bhDmPMgsz2BUCnV/WJL10IvN4Ys4f0VN1XGmNuRbmR6e0H9ltr/5i5/2PSjZJyI9N5FbDbWttlrY0DtwMvQbmR3BwrJ77+rKzGaHY9Cqw2xqwwxkRIn1x2l8c1iQ8ZYwzp+f7PWWv/adKmu4B3Zm6/E7iz0LWJf1lr/9Jau9hau5z0+8uvrbXXodzINKy17cA+Y8zJmYc2AFtQbmR6e4HzjTGVmX+zNpA+H1a5kVwcKyd3AW8xxpQZY1YAq4FHPKhvSsZa34xeFQVjzGtInwMQBr5prf1bbysSPzLGvBT4PfAMh88V+RTp84x+CCwl/Y/SNdbao09oFMEY83Lg49baK4wxjSg3Mg1jzJmkF+yIALuAd5P+clS5kWMyxvwVcC3plVSfAG4EqlFuZBJjzPeBlwNNQAfweeCnHCMnxphPA+8hnas/sdb+ovBVT02NkYiIiIiIzHmaSiciIiIiInOeGiMREREREZnz1BiJiIiIiMicp8ZIRERERETmPDVGIiIiIiIy56kxEhERERGROU+NkYiIiIiIzHlqjEREREREZM77/7gWhsaxAL3+AAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1008x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1008x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Idle ratio: 0.19091111111111111\n",
      "Empty queue probability: 0.23076923076923073\n",
      "Wait time in queue 0.25641025641025644\n",
      "Delay time in system 0.33333333333333337\n"
     ]
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "deepnote_cell_type": "code",
    "trusted": true,
    "cell_id": "00022-5983dee4-7049-4cb6-b903-7466239af1b7"
   },
   "source": "",
   "execution_count": 14,
   "outputs": []
  }
 ],
 "nbformat": 4,
 "nbformat_minor": 2,
 "metadata": {
  "kernelspec": {
   "name": "pycharm-942acabf",
   "language": "python",
   "display_name": "PyCharm (wireless-net)"
  },
  "language_info": {
   "mimetype": "text/x-python",
   "nbconvert_exporter": "python",
   "name": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6",
   "file_extension": ".py",
   "codemirror_mode": {
    "version": 3,
    "name": "ipython"
   }
  },
  "deepnote_notebook_id": "d11c4cbf-c151-4313-861b-3dd40f19474c",
  "deepnote_execution_queue": []
 }
}