simple SABR

test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from SABR import SABR_swaption, SABR\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.offsetbox import AnchoredText"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uXKhy8YLw8HC4u7ujffv2mDZtGl6+fIkff/wRffr0wT///COtFxISIrPmLlD67+DTTz+FtbU1Hjx4UC9tbNS4mHaJNA8FBQUsISGBMcbYzZs3K5x+7V1u3brFALA1a9bU6PUPHTrEALB9+/bJlJdNYZeSklLhlHfVlZiYyACwL7/8Uqbc29ubdejQoVbHLhMQEFBu6rvk5GSmo6PDxo0bV+X+Pj4+TF1dvU5i4dqNGzfKTQ+Yn5/PbGxsmLu7e5X7r127lgFgoaGh0rLIyEgmEAjYkiVLZOoCYDNnzqy74OtRYWEhu3r1arnylStXMgDs3LlzVR7jvffeY6ampiwzM1NaVja15ZkzZ9657+XLlxkA9s0331Q/eAVAl3mbsdjYWIwaNQoaGhowMjLC9OnTUVhYiA0bNsDCwqLWx1dRUYGJiUmN97e2tgZQ+SojNd2/rLyulF1C09XVlSlPSUmps2XMDh06BGNjY4wcOVJaZmhoiDFjxuDYsWNyr5AiFouRlZVVJzGVHe/LL7+EgYEBlJSUYGNjg99++63Ojl+RQ4cOQSAQYNq0adIykUiEqVOnIiQkBHFxcVXu36VLF3Tp0kVaZmtri379+uHAgQMV7pOfn1+tS6WVsbGxQZ8+fWTKZs+eDQsLi3KXUqtLKBSiW7du5cpHjBgBAIiMjHzn/llZWTh37hwmTJggXYgeKF24XUNDo9L3psxff/0FHo+HDz/8sAbRN300A1IzlZ6ejp49e6KgoADLly9HRkYGfvzxR+jo6ODatWsYPHiwtK5EIkFaWppcx9XW1oaysnKN43r9+jXEYjFiY2OxatUqAEC/fv3k2pcxhtevX6OkpARPnjzB4sWLIRAI0Lt37xrHI+/rvi0lJQWhoaEYOHCgTHlxcTEyMzPlOq6enh74/NK/d+/cuQMnJyfp8zKurq747bff8PjxY3Ts2PGdx8vLy4OWlhby8vKgq6uLcePGYe3atTILaFfXRx99hN27d2PGjBlo27YtDhw4gE8++QRKSkqYMmWKtF5qaqpcx9PU1ISKiso769y5cwdt27aV+cEHSt8LoPRSpaWlZYX7SiQSREREyMT25v5nz55FdnY2NDU1peW7du3CL7/8AsYY2rdvj6VLl9Y4YXh5eeH3339HTk6O9H1fvnw5tm3bhl27dmHWrFkASj+rvLy8Ko8nEAjK/RH3tsTERACAgYHBO+vdu3cPJSUlcHFxkSkXCoVwdHTEnTt3Kt23uLgYBw4cQLdu3er8j9Umg+MzY8KRVatWlbv089lnnzFDQ0MmEAjYyZMnpeVlK2TI83hzJZE3yXuZV0VFRXosfX199vPPP8vdpoSEBJlYLCwsWEBAQKX16+oy75urkmRkZLALFy4wV1dXBoCdPn1apm7ZSiXyPN5cUUVdXZ1NmTKl3GufOnWKAWCBgYHvjHHx4sVs0aJFLCAggO3bt4/5+PgwAKx79+6suLi4Ru0uuwy/bt06aVlhYSFzdHRkRkZGrKioSFoub5vluQ3QoUMH1rdv33LlDx48YADYtm3bKt237DNftWpVuW1btmxhANijR4+kZd26dWMbNmxgx44dY1u3bmX29vYMAPvll1+qjLMiR48eZQDYsWPHZMq7d+/OevToIX1ettpPVY+3V+qpiKenJ9PS0mLp6envrHfw4EEGgP3777/lto0ePZqZmJhUuu+JEydq9b4oAjozbaYuXLgAMzMzmbO+IUOGYOPGjVBTU5MpNzExkbunpIODQ63i+ueff1BQUIDIyEjs2bMHubm5cu+rp6eHc+fOoaCgAHfu3MGRI0dqfemsun766SesXLkSANC1a1e4u7vLbHdwcJD7vXzzEnl+fn6FZ2wikUi6/V3WrFkj83zs2LFo27YtvvrqKxw6dAhjx46VK6Y3BQQEQElJCZ988om0TCgU4pNPPsH06dMRFhaGrl27AoDcbZanU09t3ouybfLuf/XqVZk6U6ZMgbOzM7788ktMnjwZqqqqVcb7pr59+0JZWRmBgYEYOnSotLxFixY4e/as9PmkSZOq7EgFoMrX//bbb3H+/Hn88ssv0NHReWfdqt6bd72vf/31F5SVlTFmzJgqY1ZUlEybqfj4eLRu3Vrmnl7nzp0BAJ6entIfFqD0H5Knp2eDxFV2P+m9997DsGHDYG9vDw0NDenlr3cRCoXSOAcPHox+/fqhe/fuMDIykrlsXZ8mTJiAdu3a4e7du9i5cyc6dOiAf//9FzY2NgBK76vW5L1UVVWt8L5o2X286v6oA8Dnn3+OZcuW4fz58zVKps+fP4eZmZlMT2kAaNu2LYDS3txlybS6bRaLxeWGNenp6UEoFNbqvSjbVtP9hUIhZs2ahU8//RRhYWFyJbw3aWpqwt3dHWfOnJEpf/78uczl2latWqFVq1bVOvbbAgICsHTpUkydOhXTp0+vsn5V701l70tOTg6OHTsGLy8vmZ7QzQ0l02ZKJBKV6xyjpqYGoVCIXr16yZRX9MNWmbIfvLpgY2ODzp07Y+/evXIl07d169YNpqam2Lt3b4Ml09atW6N169YYN24cpk2bhrZt22Lt2rXSTjlFRUVy3382NDSEQCAAAJiamiIhIaFcnbKyqoYOVURVVRX6+vpyx/O26uxXdt+uKtra2lBVVUVcXBxatmwpsy04OBi9e/eGqalpheMY5Xkv9PT0oKKiUqv3sux+bE3ftwEDBmDp0qV48uQJ2rRpg8jISISGhsokvJycHLmuqggEAhgaGpYrP3fuHCZNmoRBgwZh27ZtcsVlamoKAJW+N5W9L0ePHkVeXh7Gjx8v1+soKkqmzZSlpSUePnwoU3bmzBkUFRWV+6Gq6IetMmU/eHUlPz9f7p6qFSkoKJC7w09da9WqFSwsLBAfHy8tu3btWrnenJWJjo6WduZwdHTE5cuXIZFIZDoh3bhxA2pqatKzwerIzs5GampqhT/G8pBIJIiPj0dubq7M2enjx48ByPaaLvuhrkrZOOSKbi2U3UJwdHREcHAwsrKyZDoh3bhxQ7q9Mnw+Hx07dsStW7fKbbtx4wZatWol0/moImWTO9T0ffPy8sLSpUtx5swZtGnTBgsWLICqqioWLlworfPjjz9Kbxe8i5WVVbmJTW7cuIERI0bAxcUFBw4cgJKSfD/z9vb2UFJSwq1bt2Qu1xYVFSE8PLzSS7h79+6FhoaGzGXr5oiSaTPl4eGBU6dO4fLly+jZsycA4NdffwXw/x+lMvV9z7SkpATZ2dnleiWGhobi3r175XpOPnr0CGpqamjRogWA0vUweTwe1NTUZOodPnwY6enp5Xon1peIiAiZ569evcKrV68wbNgwaVlN75l+8MEHOHToEI4cOYIPPvgAQGkP2YMHD2LIkCEy97nKBtOXXVouKChAcXFxuSSxevVqMMbK9TiujpKSEvz666+YN28egNIf3l9//RWGhoZwdnaW1qvuPdN33Vr44IMP8OOPP+K3337DggULAJRemty5cyfc3NxkevLGxsYiLy9PZqanDz74AIsXL8atW7ek342oqChcuHBBejygtEf22wkzOzsbGzZsgIGBgUz7qsPJyQkGBgYIDAyEtrY2Tp8+DX9/f5k/Pmp6zzQyMhKDBg2CtbU1Tp48+c5L1m//O9LW1oanpyf27NmDZcuWSb8vf/75J3JycjB69Ohyx0hJScH58+cxbty4cv/+mh2ue0ARbqSnpzNdXV1maGjI1q5dy2bMmMEAsFGjRkl7Oz579qzWr7Np0ya2evVqNn36dAaAjRw5kq1evZqtXr2aZWRkSGMp6626bt06tm3bNjZz5kympqbG9PT02OPHj2WOCYB5eHhIn9+5c4fp6+uzGTNmsJ9//plt3ryZTZ48mSkpKTFra2uWmpoqs//u3bvZ6tWr2ZIlSxgA1qdPH2lMMTEx0nplPW+r6u37Zm/nAQMGsG3btrF169axtm3bMqFQyB4+fFi7N5ExVlJSwrp27co0NDTYypUr2ZYtW1iHDh2YpqamTO9TxhizsrKS6eUZHR3NdHR02PTp09nGjRvZxo0b2fvvv88AsIEDBzKxWPzO/Svj4eHBzMzMmJGREZs9ezbbtGkT69GjBwPAfvvtt1q3+V1Gjx7NlJSU2MKFC9mvv/7KunXrxpSUlNilS5fKxfj2z1xWVhazsbFhRkZG7Pvvv2c//fQTs7S0ZGZmZiw5OVlaz8/Pjzk4OLClS5ey3377ja1cuZJZWVkxHo/H9uzZI3NMeb8rZcaNG8dUVVWZmpoamzhxYs3ehLdkZWUxS0tLxufz2Xfffcf+/PNPmce1a9dk6r/974gxxsLCwpiKigrr3Lkz27p1K/vqq6+YSCRiAwYMqPA1N23aJFdv8uaAkmkzdvv2bda7d2+mqqrKNDU12aJFi1hJSQmbOnUqU1FRqdZsRZWxsrKqcuhHYWEh++yzz1inTp2YlpYWU1ZWZlZWVmzq1Kkyw0PKvP0jkJKSwqZNm8ZsbW2Zuro6EwqFrE2bNmzu3LksJSWl3P5lP7AVPd4c2lPW3f9dQy0Y+38yHT16NHN3d2eamprM0NCQ9e3bl12+fLkmb1uF0tLS2NSpU5m+vj5TU1NjHh4e7ObNm+XqvZ0M09PT2YQJE1jr1q2ZmpoaU1FRYR06dGDffvutzPCVMgYGBqxr165VxuPh4cE6dOjAbt26xdzd3ZlIJGJWVlZs8+bNtWqnPPLz89mCBQuYiYkJU1FRYV26dKnwB72iZMoYY3FxceyDDz5gWlpaTENDgw0ePJg9efJEps7Zs2dZ//79mYmJCVNWVmY6OjpswIABLCgoqNzx5P2ulNm1axcDwHr06MEKCgrkbPW7VTWEzcfHR6Z+RcmUsdKZjLp168ZEIhEzNDRkM2fOZFlZWRW+ZteuXZmRkRErKSmpkzY0ZTQ3LyGV+OKLL7Bv3z48ffr0nRMJlM1B/MMPP8hcJmyKHj58iA4dOuDkyZMYNGjQO+v27t0bqampuH//fgNF13jJ+10hioumEySkEsHBwVi2bFmz+nEMDg6Gu7t7lYmUyGqO3xUiizogEVKJmzdvch1Cg5s5cyZmzpzJdRhNTnP8rhBZdGZKCCGE1BLdMyWEEEJqic5MCSGEkFqiZEoIIYTUEnVAqkDZNGmampp1trgzIYSQpocxhuzsbJiZmZVbT/hNlEwrEB8fX+niwoQQQpqfuLg4WFhYVLqdkmkFyuakjIuLk5lImxBCSPOSlZUFS0vLKhdAoGRagbJLu1paWpRMCSGEVHnLjzogEUIIIbVEyZQQQgipJUqmhBBCSC1RMiWEEEJqiZIpIYQQUkuUTAkhhJBaomRKCCGE1BIlU0IIIaSWKJkSQgghtUTJlBBCCKklSqaEEEJILVEyJYQQQmqJkmk9YoyhWCzhOgxCCCH1jJJpPTkW/go91gZjzr47CHn2GmIJ4zokQggh9YSWYKsHgfcTsPzYA2TmF+NVRj7+uZ8IU20R/IbYYaC9KdfhEUIIqWN0ZlrHAu8nYPqe28jML5YpT8wswPQ9txF4P4GjyAghhNQXSqZ1SCxhWHniISq6oFtWtvLEQ7rkSwghCoaSaR0KjU5DQmZBpdsZgITMAoRGpzVcUIQQQuod58l0y5YtsLa2hkgkgpubG0JDQ+Xab//+/eDxeBg+fHi5bZGRkRg6dCi0tbWhrq6OLl26IDY2to4jLy85u/JEWpN6hBBCmgZOk2lAQADmzZsHPz8/3L59Gw4ODvDy8kJycvI794uJicGCBQvQs2fPctuePXuGHj16wNbWFhcvXkRERASWLVsGkUhUX82QMtKU7zXkrUcIIaRp4DHGOLuB5+bmhi5dumDz5s0AAIlEAktLS8yePRuLFy+ucB+xWIxevXphypQpuHz5MjIyMnD06FHp9rFjx0JZWRl//vlnjePKysqCtrY2MjMzoaWlJfd+YglDj7UXkJhZUOF9UwAw1RbhyqK+EPB5NY6PEEJIw5A3H3B2ZlpUVISwsDB4enr+Pxg+H56enggJCal0v1WrVsHIyAhTp04tt00ikeDUqVNo27YtvLy8YGRkBDc3N5lkW5HCwkJkZWXJPGpCwOfBb4gdAKCyVOk3xI4SKSGEKBjOkmlqairEYjGMjY1lyo2NjZGYmFjhPleuXMH27dvh7+9f4fbk5GTk5OTgu+++w8CBA3H27FmMGDECI0eOxKVLlyqNZc2aNdDW1pY+LC0ta9yugfam2DrBCSba5S/l9mitT+NMCSFEATWZSRuys7MxceJE+Pv7w8DAoMI6Eknp1H3Dhg3D559/DgBwdHTEtWvXsG3bNnh4eFS435IlSzBv3jzp86ysrFon1P52JgiNTkNydgGSswrxzelI3HuVhaISCYRKnPf7IoQQUoc4S6YGBgYQCARISkqSKU9KSoKJiUm5+s+ePUNMTAyGDBkiLStLnkpKSoiKioKlpSWUlJRgZ2cns2/79u1x5cqVSmNRUVGBiopKbZpTjoDPg7uNPoDSe6m/XX6OlOxCXH6Sgn7tjavYmxBCSFPC2SmSUCiEs7MzgoKCpGUSiQRBQUFwd3cvV9/W1hb37t1DeHi49DF06FD06dMH4eHhsLS0hFAoRJcuXRAVFSWz7+PHj2FlZVXvbaqMgM/DoI6ll3eP343nLA5CCCH1g9PLvPPmzYOPjw9cXFzg6uqKDRs2IDc3F76+vgCASZMmwdzcHGvWrIFIJIK9vb3M/jo6OgAgU75w4UJ4e3ujV69e6NOnDwIDA3HixAlcvHixoZpVoWGOZth1LQbnHiYhr6gEasImc4WdEEJIFTj9Rff29kZKSgqWL1+OxMREODo6IjAwUNopKTY2Fnx+9U6eR4wYgW3btmHNmjWYM2cO2rVrh8OHD6NHjx710QS5OVrqoIWeGmLT8nA+MhlDHcw4jYcQQkjd4XScaWNV03GmVfnhzCNsCX4Gz/bG+N3Hpc6OSwghpH40+nGmzdFQB3MAwKXHycjMK66iNiGEkKaCkmkDameiCVsTTRSLGf6hpdgIIURhUDJtYEP+u1dKvXoJIURxUDJtYGUdj0Kev0ZyFq0eQwghioCSaQOz1FND5xY6YAw4EUGXegkhRBFQMuXAsLJLveGvOI6EEEJIXaBkyoFBnczA5wF3X2YiJjWX63AIIYTUEiVTDhhqqqB769LJ+qkjEiGENH2UTDkyzLF0zOnR8FegeTMIIaRpo2TKEa8OxhAq8fE8JRcP4mu2GDkhhJDGgZIpRzRFyvBsbwSALvUSQkhTR8mUQ2WXeo+Hx0MioUu9hBDSVFEy5VDvdobQFCkhMasAoTFpXIdDCCGkhiiZckhFSYD37UsXDT8WTpd6CSGkqaJkyrFhjqUTOJy+l4CiEgnH0RBCCKkJSqYcc2ulD2MtFWTmF+NiVDLX4RBCCKkBSqYcE/B5GNKp9Oz0GPXqJYSQJomSaSMwvHNpr97zD5OQXUCLhhNCSFNDybQR6GCmBRtDdRSWSHDmQRLX4RBCCKkmSqaNAI/Hw/D/xpweo5VkCCGkyaFk2kiUTeBw9WkqkrNp0XBCCGlKKJk2Ei301eDUQgcSBpy4S4uGE0JIU0LJtBEp64h09A5d6iWEkKaEkmkjMqijKQR8Hu69ysSzlByuwyGEECInSqaNiL6GCnq1KV00/BidnRJCSJNBybSRkV7qDY+nRcMJIaSJoGTayPS3M4aaUIDYtDzcicvgOhxCCCFyoGTayKgJlTCwgwkA6ohECCFNBSXTRqjsUu+Ju/EoFtNKMoQQ0thRMm2Eutnow1BTBel5xfj3cQrX4RBCCKkCJdNGSEnAx1CH0pVk/qZLvYQQ0uhRMm2kRvx3qfccrSRDCCGNHiXTRurNlWQC7ydyHQ4hhJB3oGTaSPF4POnZ6VFaSYYQQho1SqaNWNlKMteevUZiJq0kQwghjRUl00bMUk8NXax1wRitc0oIIY0ZJdNGrmzMKfXqJYSQxouSaSM3uKMZhAI+HiVm42F8FtfhEEIIqQAl00ZOW00ZfW2NAFBHJEIIaawomTYBI5xKL/UeC38FsYRWkiGEkMaGkmkT0KedEXTUlJGUVYhrz1K5DocQQshbKJk2AUIlPgZ3MgUA/H2bLvUSQkhjQ8m0iRjR2QIAEPggEXlFJRxHQwgh5E2UTJsIpxY6sNJXQ16RGGce0PSChBDSmFAybSJ4PB6G/zcj0hG61EsIIY0KJdMmZOR/vXqvPk1FUhZNL0gIIY0FJdMmxEpfHc5WupDQ9IKEENKoUDJtYsrOTg+HvQJjNOaUEEIaA0qmTczgjmYQKvERlZSNhwk0vSAhhDQGlEybGG01ZfRvbwyAxpwSQkhjQcm0CSq71Hs0PB4lYgnH0RBCCKFk2gT1amsIfXUhUnMKcfkpTS9ICCFco2TaBCkL+BjqaAaAxpwSQkhjQMm0iRrlVDq94NkHicgqKOY4GkIIad4omTZRHcy00NZYA4UlEpyOSOA6HEIIadYomTZRPB4PI/87O6VLvYQQwi1Kpk3YcEdz8HlAaEwaYl/ncR0OIYQ0W5RMmzATbRG6tzYAABy+/ZLjaAghpPlqFMl0y5YtsLa2hkgkgpubG0JDQ+Xab//+/aWrqQwfXmmdTz/9FDweDxs2bKibYBuZD5z/u9R75yUkEppekBBCuMB5Mg0ICMC8efPg5+eH27dvw8HBAV5eXkhOTn7nfjExMViwYAF69uxZaZ2///4b169fh5mZWV2H3WgMsDOBhooS4tLycTMmjetwCCGkWeI8ma5fvx4ff/wxfH19YWdnh23btkFNTQ07duyodB+xWIzx48dj5cqVaNWqVYV1Xr16hdmzZ2Pv3r1QVlaur/A5pyoUYFBHUwB0qZcQQrjCaTItKipCWFgYPD09pWV8Ph+enp4ICQmpdL9Vq1bByMgIU6dOrXC7RCLBxIkTsXDhQnTo0KHKOAoLC5GVlSXzaEpG/Xep9/S9ROQXiTmOhhBCmh9Ok2lqairEYjGMjY1lyo2NjZGYmFjhPleuXMH27dvh7+9f6XHXrl0LJSUlzJkzR6441qxZA21tbenD0tJS/kY0Al2sddFCTw05hSU486Di940QQkj94fwyb3VkZ2dj4sSJ8Pf3h4GBQYV1wsLCsHHjRuzatQs8Hk+u4y5ZsgSZmZnSR1xcXF2GXe9Kx5z+t84pXeolhJAGp8TlixsYGEAgECApKUmmPCkpCSYmJuXqP3v2DDExMRgyZIi0TCIpXTVFSUkJUVFRuHz5MpKTk9GiRQtpHbFYjPnz52PDhg2IiYkpd1wVFRWoqKjUUau4McrJAhvOP8GVp6lIyMyHqbYq1yERQkizwemZqVAohLOzM4KCgqRlEokEQUFBcHd3L1ff1tYW9+7dQ3h4uPQxdOhQ9OnTB+Hh4bC0tMTEiRMREREhU8fMzAwLFy7EmTNnGrJ5DcpSTw1uLfXAGPD3HZoRiRBCGhKnZ6YAMG/ePPj4+MDFxQWurq7YsGEDcnNz4evrCwCYNGkSzM3NsWbNGohEItjb28vsr6OjAwDScn19fejr68vUUVZWhomJCdq1a1f/DeLQB84WuBGdhkO3XmK6h43cl7kJIYTUDufJ1NvbGykpKVi+fDkSExPh6OiIwMBAaaek2NhY8PlN6tYuZ97vaAq/4w/wPDUXt2Mz4Gyly3VIhBDSLPAYYzRtzluysrKgra2NzMxMaGlpcR1Otcw/cBeHb7/EONcWWDOyI9fhEEJIkyZvPqBTPgVTNr3gybvxKCimMaeEENIQKJkqGLeWerDQVUU2jTklhJAGQ8lUwfD5PIz6b53TQ2E05pQQQhoCJVMFVJZMy8acEkIIqV+UTBVQC/3/jzk9cpvGnBJCSH2jZKqgyjoiHbwVB+qwTQgh9YuSqYJ6v6Mp1IQCxLzOw60X6VyHQwghCo2SqYJSV1GSrnN68FbTmrifEEKaGkqmCmy0S+lScqciEpBbWMJxNIQQorgomSqwLta6sNZXQ26RGKfvJXAdDiGEKCxKpgqMx+P9vyMSjTklhJB6Q8lUwY1ytgCPB4RGpyEmNZfrcAghRCFRMlVwptqq6NnGEADNiEQIIfWFkmkzMPq/S72Hb7+EWEJjTgkhpK5RMm0G+tsZQ0ukhITMAlx5msp1OIQQonAomTYDImUBhnc2BwAcoDGnhBBS5yiZNhNj/htzeu5BEtJziziOhhBCFAsl02bC3lwbdqZaKBJLcDScJr8nhJC6RMm0GfHuUnp2GnCTJr8nhJC6RMm0GRnmaAahEh+PErPxID6L63AIIURhUDJtRnTUhPDqYAKg9OyUEEJI3aBk2syMcSkdc3os/BUKisUcR0MIIYqBkmkz093GAOY6qsgqKMGZB4lch0MIIQqBkmkzw+f/f/J7utRLCCF1g5JpMzTapXTy+2vPXiP2dR7X4RBCSJNHybQZstBVQ4/WBgCAg2F0dkoIIbVFybSZGtulBQDg4K2XKBFLOI6GEEKaNkqmzZSnnRF01ZSRmFWAf5+kcB0OIYQ0aZRMmykVJQFGOpV2RNofSpd6CSGkNqqdTP38/PDixYv6iIU0sLLpBS88SkZydgHH0RBCSNNV7WR67Ngx2NjYoF+/fvjrr79QWFhYH3GRBtDWWBOdW+igRMJw5DZNfk8IITVV7WQaHh6OmzdvokOHDvjss89gYmKC6dOn4+bNm/URH6lnY2nye0IIqbUa3TPt3Lkzfv75Z8THx2P79u14+fIlunfvjk6dOmHjxo3IzMys6zhJPRncyQzqQgGiU3NxIzqN63AIIaRJqlUHJMYYiouLUVRUBMYYdHV1sXnzZlhaWiIgIKCuYiT1SF1FCYM7mQGgGZEIIaSmapRMw8LCMGvWLJiamuLzzz9H586dERkZiUuXLuHJkyf45ptvMGfOnLqOldSTsa6ll3pP30tAZl4xx9EQQkjTU+1k2rFjR3Tt2hXR0dHYvn074uLi8N1336F169bSOuPGjUNKCo1dbCocLXVga6KJwhIJ/r7zkutwCCGkyal2Mh0zZgxiYmJw6tQpDB8+HAKBoFwdAwMDSCQ0q05TwePxpB2R9lNHJEIIqbZqJ9Oye6Nvy8/Px6pVq+okKNLwRnS2gIoSH48SsxEel8F1OIQQ0qRUO5muXLkSOTk55crz8vKwcuXKOgmKNDxtNWW839EUAM2IRAgh1VWjM1Mej1eu/O7du9DT06uToAg3yi71noiIR05hCcfREEJI06Ekb0VdXV3weDzweDy0bdtWJqGKxWLk5OTg008/rZcgScNwbamHVobqeJ6Si+Ph8fjQrQXXIRFCSJMgdzLdsGEDGGOYMmUKVq5cCW1tbek2oVAIa2truLu710uQpGGUdUT69vQj7L8ZS8mUEELkJHcy9fHxAQC0bNkS3bp1g7Kycr0FRbgzyskCP5yJQsTLTNx/lQl7c+2qdyKEkGZOrnumWVlZ0v/u3Lkz8vPzkZWVVeGDNG36Girw6mACANgXGstxNIQQ0jTIlUx1dXWRnJwMANDR0YGurm65R1k5afo+dC29vHssPB651BGJEEKqJNdl3gsXLkh76gYHB9drQIR77jb6sNZXQ8zrPJy4G4+xrnTvlBBC3oXHaLqbcrKysqCtrY3MzExoaWlxHQ4nfr30DGv+eYROFto4PqsH1+EQQggn5M0Hcp2ZRkREyP3CnTp1krsuabw+cLbAj2epIxIhhMhDrmTq6OgIHo9X5ZytPB4PYrG4TgIj3CrriHQyIgF/hcbi2xEduQ6JEEIaLbmSaXR0dH3HQRqhD91a4GREAo7deYWv3m8PdRW5R1IRQkizItevo5WVVX3HQRoh91b6aGmgjujUXBy/G49x1BGJEEIqJFcyPX78ON577z0oKyvj+PHj76w7dOjQOgmMcI/H42Gca+mMSH/diKVkSgghlZCrNy+fz0diYiKMjIzA51c+NFVR7plSb97/S8stQtdvg1AkluD4rO7oZKHDdUiEENJg5M0Hck3aIJFIYGRkJP3vyh6KkEiJLD11Id7vWDoj0t7rNCMSIYRUpNpLsO3evRuFhYXlyouKirB79+46CYo0LuO7lt4zP343Hpn5xRxHQwghjU+1k6mvry8yMzPLlWdnZ8PX17dOgiKNi4uVLtoaayC/WIyjd15xHQ4hhDQ6dbY4+MuXL2WWZSOKg8fjYbxb6dnp3hsvqhxvTAghzY3cybRz585wcnICj8dDv3794OTkJH04ODigZ8+e8PT0rFEQW7ZsgbW1NUQiEdzc3BAaGirXfvv37wePx8Pw4cOlZcXFxVi0aBE6duwIdXV1mJmZYdKkSYiPj69RbKTUCCdzqCoL8DgpB7depHMdDiGENCpyj8IvS1jh4eHw8vKChoaGdFvZ4uCjRo2qdgABAQGYN28etm3bBjc3N2zYsAFeXl6IioqSdnqqSExMDBYsWICePXvKlOfl5eH27dtYtmwZHBwckJ6ejs8++wxDhw7FrVu3qh0fKaUlUsZQBzME3IrD3usv0MVaj+uQCCGk0aj2RPd//PEHvL29IRKJ6iQANzc3dOnSBZs3bwZQ2lvY0tISs2fPxuLFiyvcRywWo1evXpgyZQouX76MjIwMHD16tNLXuHnzJlxdXfHixQu0aFH1WEkaGlOxiJcZGLr5KoQCPkKW9IW+hgrXIRFCSL2q06Exb/Lx8amzRFpUVISwsDCZy8N8Ph+enp4ICQmpdL9Vq1bByMgIU6dOlet1MjMzwePxoKOjU+H2wsJCWuRcDp0sdNDRXBtFYgkOhr3kOhxCCGk0qp1MxWIxfvzxR7i6usLExAR6enoyj+pITU2FWCyGsbGxTLmxsTESExMr3OfKlSvYvn07/P395XqNgoICLFq0COPGjav0r4o1a9ZAW1tb+rC0tKxWO5qTCV1Lz+z/uhELiYQ6IhFCCFCDZLpy5UqsX78e3t7eyMzMxLx58zBy5Ejw+XysWLGiHkL8v+zsbEycOBH+/v4wMDCosn5xcTHGjBkDxhi2bt1aab0lS5YgMzNT+oiLi6vLsBXKUAdzaIqUEJuWh3+fpHAdDiGENArVXgZk79698Pf3x6BBg7BixQqMGzcONjY26NSpE65fv445c+bIfSwDAwMIBAIkJSXJlCclJcHExKRc/WfPniEmJgZDhgyRlkkkktKGKCkhKioKNjY2AP6fSF+8eIELFy6881q3iooKVFTo/p88VIUCfOBsgZ1XY7Dn+gv0bGOI0Og0JGcXwEhTBNeWehDwyw+dIoQQRVbtZJqYmIiOHUvXttTQ0JBO4DB48GAsW7asWscSCoVwdnZGUFCQtLewRCJBUFAQZs2aVa6+ra0t7t27J1O2dOlSZGdnY+PGjdLLs2WJ9MmTJwgODoa+vn51m0neYUJXK+y8GoOgR8nouiYIKdn/nxHLVFsEvyF2GGhvymGEhBDSsKp9mdfCwgIJCQkAABsbG5w9exZAaY/ZmpzdzZs3D/7+/vjjjz8QGRmJ6dOnIzc3Vzqb0qRJk7BkyRIAgEgkgr29vcxDR0cHmpqasLe3h1AoRHFxMT744APcunULe/fuhVgsRmJiIhITE1FUVFTt+Eh5NoYasDXRBGOQSaQAkJhZgOl7biPwfgJH0RFCSMOr9pnpiBEjEBQUBDc3N8yePRsTJkzA9u3bERsbi88//7zaAXh7eyMlJQXLly9HYmIiHB0dERgYKO2UFBsb+86Vat726tUr6TJxjo6OMtuCg4PRu3fvasdIZIklDIlZBRVuYwB4AFaeeIj+diZ0yZcQ0ixUe5zp20JCQhASEoI2bdrI3Mtsymic6buFPHuNcf7Xq6y37+OucLehS+yEkKZL3nxQ7TPTt7m7u8Pd3b22hyFNSHJ2xWelNa1HCCFNnVzJtOyyqTyGDh1a42BI02CkKd+kHfLWI4SQpk6uZPrmRPLvwuPxaIHwZsC1pR5MtUVIzCxARfcIeABMtEuHyRBCSHMgV88eiUQi14MSafMg4PPgN8Suwm1l3Y38hthR5yNCSLNR7aExhADAQHtTbJ3gBBMt2eFQJtoibJ3gRONMCSHNSo2S6aVLlzBkyBC0bt0arVu3xtChQ3H58uW6jo00cgPtTXF1cT9M6W4NoHTChn8X9qFESghpdqqdTPfs2QNPT0+oqalhzpw5mDNnDlRVVdGvXz/89ddf9REjacQEfB7mDWgHDRUlJGQW4Hr0a65DIoSQBlftcabt27fHtGnTyk3QsH79evj7+yMyMrJOA+QCjTOtPr9j9/FHyAv0tzOG/yQXrsMhhJA6UW/rmT5//rzCyRmGDh2K6Ojo6h6OKIiJ7lYAgKDIJMSl5XEcDSGENKxqJ1NLS0sEBQWVKz9//jytA9qMtTbSRPfW+pAwYM+NF1yHQwghDaraMyDNnz8fc+bMQXh4OLp16wYAuHr1Knbt2oWNGzfWeYCk6fBxt8bVp68RcDMOn3u2hUhZwHVIhBDSIOROpmlpadDT08P06dNhYmKCdevW4cCBAwBK76MGBARg2LBh9RYoafz6tTeGuY4qXmXk43h4PMZ0oSsVhJDmQe5kamZmhuHDh2Pq1KkYMWIERowYUZ9xkSZIwOdhorsVvvvnEXZdi8FoFwvweDRxAyFE8cl9z9Tf3x8pKSkYOHAgrK2tsWLFCrx4QffGiCxvF0uoKPHxMCELt16kcx0OIYQ0CLmT6cSJExEUFISnT5/Cx8cHf/zxB2xsbNC/f38EBATQwtsEAKCrLsRwR3MAwK5rMdwGQwghDaTavXlbtmyJlStXIjo6GoGBgTAyMsKUKVNgamqKOXPm1EeMpInx6WYNAAi8n4jETFqGjRCi+Go1N6+npyf27t2L3bt3AwC2bNlSJ0GRps3OTAuu1noQSxj20jAZQkgzUONk+uLFC6xYsQItW7aEt7c3nJycsHfv3rqMjTRhZWenf92IRUExrSZECFFs1RpnWlhYiMOHD2PHjh24ePEizM3NMXnyZPj6+sLa2rqeQiRN0YAOxjDVFiEhswAnIxLwgbMF1yERQki9kfvMdMaMGTA1NcWUKVOgr6+P06dPIyYmBitXrqRESspRFvClUwzuvBqNak4BTQghTYrcyfTKlSvw8/PDq1evEBAQgAEDBtAYQvJO47q0gIoSHw/is3AzhobJEEIUl9yXeSMiIuozDqKAdNWFGNHZHPtvxmHXtWi4ttTjOiRCCKkXterNS0hVJv+3cPiZB0l4lZHPbTCEEFJPKJmSemVrooVuNvoQSxh2h8RwHQ4hhNQLSqak3vl2bwkA2B8ah/wiGiZDCFE8lExJvetra4QWemrIzC/GkTsvuQ6HEELqnFwdkI4fP17tA/fv3x+qqqrV3o8oHgGfB59u1lh98iF2XInGuC4twOdTT3BCiOKQK5kOHz68Wgfl8Xh48uQJWrVqVZOYiAIa42KBn849xrOUXPz7JAW92xlxHRIhhNQZuS/zJiYmQiKRyPVQU1Orz5hJE6QpUob3f4uFb78SzXE0hBBSt+RKpj4+PtW6ZDthwgRoaWnVOCiimCZ3swafB1x+korHSdlch0MIIXVGrmS6c+dOaGpqyn3QrVu3wsDAoMZBEcVkqaeGAXYmAEqnGCSEEEVBvXlJg5ras3SYzJHbr5CWSwvKE0IUg1wdkEaOHCn3AY8cOVLjYIjic7HSRScLbUS8zMTe6y8wu18brkMihJBak+vMVFtbW/rQ0tJCUFAQbt26Jd0eFhaGoKAgaGtr11ugRDHweDxM+W8Sh93XX6CwhCZxIIQ0fXKdme7cuVP634sWLcKYMWOwbds2CAQCAIBYLMaMGTOo0xGRy6BOpvjun0dIzCrA8fB4jHax5DokQgiplWrfM92xYwcWLFggTaQAIBAIMG/ePOzYsaNOgyOKSVnAl06Av/0KrXVKCGn6qp1MS0pK8OjRo3Lljx49gkQiqZOgiOIb59oC6kIBHiVm4/KTVK7DIYSQWpF7PdMyvr6+mDp1Kp49ewZXV1cAwI0bN/Ddd9/B19e3zgMkiklbVRljulhi59UY+F9+jl5tDbkOiRBCaqzayfTHH3+EiYkJ1q1bh4SEBACAqakpFi5ciPnz59d5gERxTeneEn9ci8HlJ6l4lJgFWxO6504IaZp4rBY3rLKysgBA4ToeZWVlQVtbG5mZmQrXtsZmxt4wnL6XiA+cLfDjaAeuwyGEEBny5oMaTdpQUlKC8+fPY9++feDxSlf/iI+PR05OTs2iJc3WRz1LF0M4Fv4KyVkFHEdDCCE1U+1k+uLFC3Ts2BHDhg3DzJkzkZKSAgBYu3YtFixYUOcBEsXm1EIXzla6KBYz7LoWw3U4hBBSI9VOpp999hlcXFyQnp4uM/n9iBEjEBQUVKfBkebh4//OTvdcf4HcwhKOoyGEkOqrdjK9fPkyli5dCqFQKFNubW2NV69e1VlgpPnob2eMlgbqyCooQcDNOK7DIYSQaqt2MpVIJBCLy08B9/Lly2qtLENIGQGfh4/+mwB/+5VolIhpvDIhpGmpdjIdMGAANmzYIH3O4/GQk5MDPz8/vP/++3UZG2lGRjlZQF9diFcZ+Th1L4HrcAghpFqqnUzXrVuHq1evws7ODgUFBfjwww+ll3jXrl1bHzGSZkCkLIBPN2sAwG//PqcpBgkhTUqNxpmWlJRg//79iIiIQE5ODpycnDB+/HiZDklNGY0z5UZ6bhHcvwtCQbEEez9yQ/fWtMA8IYRb8uaDas+ABABKSkqYMGFCjYMjpCK66kKMcbHE7pAX+PXf55RMCSFNhlzJ9Pjx43jvvfegrKyM48ePv7Pu0KFD6yQw0jx91KMV9lx/gX8fp+BBfCY6mNEauYSQxk+uy7x8Ph+JiYkwMjICn1/5bVYej1dhT9+mhi7zcmvWX7dxMiIBQx3M8PO4zlyHQwhpxup0OkGJRAIjIyPpf1f2UIRESrj3qYcNAOBkRDxiX+dxHA0hhFStRnPzElKf7M210bONASQM8L/8nOtwCCGkSnLdM/3555/lPuCcOXNqHAwhZab3tsHlJ6k4cCsOn3m2gYGGCtchEUJIpeS6Z9qyZUv5Dsbj4fnzpn8mQfdMuccYw/AtV3H3ZSZm9WmNBV7tuA6JENIM1enQmOjo6DoLjBB58Hg8fOphg+l7b2N3SAw+7W0DDZUajeQihJB6V6t7powxmqmG1JsBHUzQ6r8J8PfdiOU6HEIIqVSNkun27dthb28PkUgEkUgEe3t7/P777zUOYsuWLbC2toZIJIKbmxtCQ0Pl2m///v3g8XgYPny4TDljDMuXL4epqSlUVVXh6emJJ0+e1Dg+wg0Bn4dPPEqXZ/O//ByFJdRbnBDSOFU7mS5fvhyfffYZhgwZgoMHD+LgwYMYMmQIPv/8cyxfvrzaAQQEBGDevHnw8/PD7du34eDgAC8vLyQnJ79zv5iYGCxYsAA9e/Yst+3777/Hzz//jG3btuHGjRtQV1eHl5cXCgoKqh0f4daIzhYw1RYhObsQh8NoiT9CSCPFqsnAwID99ddf5cr/+usvpq+vX93DMVdXVzZz5kzpc7FYzMzMzNiaNWsq3aekpIR169aN/f7778zHx4cNGzZMuk0ikTATExP2ww8/SMsyMjKYiooK27dvn1wxZWZmMgAsMzOz2u0hdW/75efMatFJ1nPtBVZcIuY6HEJIMyJvPqj2mWlxcTFcXFzKlTs7O6OkpKRaxyoqKkJYWBg8PT2lZXw+H56enggJCal0v1WrVsHIyAhTp04tty06OhqJiYkyx9TW1oabm1ulxywsLERWVpbMgzQeY10toacuRGxaHi3PRghplKqdTCdOnIitW7eWK//tt98wfvz4ah0rNTUVYrEYxsbGMuXGxsZITEyscJ8rV65g+/bt8Pf3r3B72X7VOeaaNWugra0tfVhaWlarHaR+qQmVMKW7NQDgl+BnkEio0xshpHGp0ViD7du34+zZs+jatSsA4MaNG4iNjcWkSZMwb948ab3169fXTZT/yc7OxsSJE+Hv7w8Dg7pbUWTJkiUycWdlZVFCbWQmultj26XniErKRtCjZPS3M656J0IIaSDVTqb379+Hk5MTAODZs2cAAAMDAxgYGOD+/fvSejwer8pjGRgYQCAQICkpSaY8KSkJJiYm5eo/e/YMMTExGDJkiLRMIpGUNkRJCVFRUdL9kpKSYGpqKnNMR0fHCuNQUVGBigrNsNOYaasqY0JXK2y79Axbgp/Cs72RXN8xQghpCNVOpsHBwXX24kKhEM7OzggKCpIOb5FIJAgKCsKsWbPK1be1tcW9e/dkypYuXYrs7Gxs3LgRlpaWUFZWhomJCYKCgqTJMysrCzdu3MD06dPrLHbS8Kb2aImdV6MRHpeBa89e03qnhJBGg/MpZebNmwcfHx+4uLjA1dUVGzZsQG5uLnx9fQEAkyZNgrm5OdasWSMd0/omHR0dAJApnzt3Lr7++mu0adMGLVu2xLJly2BmZlZuPCppWgw1VTDOtQV2XYvBz0FPKJkSQhqNaifTgoICbNq0CcHBwUhOTpZeZi1z+/btah3P29sbKSkpWL58ORITE+Ho6IjAwEBpB6LY2Nh3rqFakS+++AK5ubmYNm0aMjIy0KNHDwQGBkIkElXrOKTx+cSjFfbeeIEb0WkIjU6Da0s9rkMihBD5Jrp/0/jx43H27Fl88MEHMDY2Lnffys/Pr04D5AJNdN+4LTlyD/tCY9GzjQH+nOrGdTiEEAVWpxPdv+nkyZM4ffo0unfvXqsACampGb1tcOBWHC4/SUV4XAYcLXW4DokQ0sxVe5ypubk5NDU16yMWQuRiqaeGEZ3NAQCbgmjOZUII96qdTNetW4dFixbhxYsX9REPIXKZ0dsGfB4Q9CgZ919lch0OIaSZq3YydXFxQUFBAVq1agVNTU3o6enJPAhpCK0MNTC4kxkAYPOFpxxHQwhp7qp9z3TcuHF49eoVvv322wo7IBHSUGb3bY0TEfEIfJCIyIQstDelzmKEEG5UO5leu3YNISEhcHBwqI94CJFbG2NNvN/RFKciEvBz0BNsneDMdUiEkEZALGEIjU5DcnYBjDRFcG2pBwG/fk/8qp1MbW1tkZ+fXx+xEFJtc/q2wel7CfjnfiIeJWbB1oTOTglpzgLvJ2DliYdIyPz/+tWm2iL4DbHDQHvTd+xZO9W+Z/rdd99h/vz5uHjxIl6/fk1LlxFOtTPRxPv//QPZFET3TglpzgLvJ2D6ntsyiRQAEjMLMH3PbQTer78lHKs9aUPZbERv3ytljIHH40EsFtdddByhSRualqjEbHht+BcAcGZuL7QzoaFbhDQ3YglDj7UXyiXSMjwAJtoiXFnUt1qXfOtt0oa6nOiekLrQzkQT73c0wel7ifj5whNs+dCJ65AIIQ0sNDqt0kQKAAxAQmYBQqPT4G6jX+evX+1k6uHhUedBEFJbc/q1wel7iTh9LwFRidl0dkpIM5OcXXkirUm96pI7mUZERMhVr1OnTjUOhpCasjXRkp6dbjj/mHr2EtLMGGnKt5CJvPWqS+5k6ujoCB6Ph3fdYlWUe6akaZrr2Rb/3E/EP/cT8SA+Ex3MtLkOiRDSQFxb6sFUW1TlPdP6WmlK7mQaHR1dLwEQUlfaGmtiSCczHL8bj5/OPcHvPi5ch0QIaSACPg/LB7fH9L13ym0r627kN8Su3sabyp1Mrays6iUAQurSZ55tcDIiHucjk3A3LgMOtKIMIc1GQmZhheUmDTDOVK5kGhERAXt7e7kX6X7w4AHatWsHJaVq928ipFZsDDUwvLM5jtx+hfXnHuOPKa5ch0QIaQC3YtLw7elIAMCywXawM9Vq0BmQ5MqOnTt3xuvXr+U+qLu7O2JjY2scFCG18Vm/NhDwebj0OAVhL9K4DocQUs+SswswY+9tlEgYhjqYYUp3a7jb6GOYozncbfTrPZECcp6ZMsawbNkyqKmpyXXQoqKiWgVFSG1Y6atjtLMF9t+Mw49nHmPftK5ch0QIqSfFYglm7b2D5OxCtDXWwJqRHTlZgEWuZNqrVy9ERUXJfVB3d3eoqqrWOChCamtW39Y4cvsVQp6/xtWnqeje2oDrkAgh9WDN6UcIjUmDpooStk1whroKN7cX5XrVixcv1nMYhNQtC101fOjWAruuxeD7M1E4aqNPywUSomCOhb/CjqulI03WjXFAK0MNzmKp9kT3hDQVM/u0hqqyAHfjMnDuYRLX4RBC6tCjxCwsPnwPADCjtw0GdDDhNB5KpkRhGWqqYEoPawDAurOPIZZUa00HQkgjlZlXjE/+DEN+sRg9Whtg/oB2XIdEyZQotmk9baAlUkJUUjZO3I3nOhxCSC1JJAxzA+7gxes8mOuoYtO4zg3SW7cqlEyJQtNWU8YnHjYAgPXnHqNYLOE4IkJIbWwIeoLgqBSoKPHx60Rn6KoLuQ4JACVT0gz4dreGgYYKYtPysD+Uxj8T0lSde5iEn4OeAAC+HdER9uaNZ/5tSqZE4akJlTCnX2sAwMagp8gtLOE4IkJIdT1LycG8gHAAgI+7FUY5W3Ab0FsomZJmYWyXFmihp4bUnELsuEKLNhDSlGQXFGPa7lvILixBF2tdfDXIjuuQyqFkSpoFoRIfC7xKe/z9+u9zvM6peEJsQkjjIpEwzD9wF89ScmGiJcIv450hVGp8qavxRURIPRnc0RT25lrIKSzB5uCnXIdDCJHD5uCnOPswCUIBH1snOMFQU4XrkCpEyZQ0G3w+D4sG2gIA9lx/gbi0PI4jIoS8S1BkEn46/xgA8PVwe3RuoctxRJWjZEqalZ5tDNGjtQGKxQzrzso/3zQhpGE9Tc7B3P3hYAyY0LUFxnSx5Dqkd6JkSpqdsrPTo+HxuP8qk+NoCCFvyyooxrQ/SzscuVrrYfngDlyHVCVKpqTZ6WihjWGOZgCAb05FgjGaZpCQxkIiYfh8fziep+TCVFuELeOdGmWHo7c1/ggJqQcLBrSDUImPkOevERyVzHU4hJD//HT+MYIeJUtnOGqsHY7eRsmUNEuWemrw7WYNAPj29COU0DSDhHDuVEQCNl0o7Wm/ZmRHdLLQ4TagaqBkSpqtGX1aQ0dNGU+Tc3Dg1kuuwyGkWXsQn4kFB+8CAD7q0RIjnRrXDEdVoWRKmi1tVWXM6dsGQOkk+Dk0zSAhnHidU4hpu0uXVOvZxgCL37PlOqRqo2RKmrUJXa1gpV86zeC2i8+4DoeQZqdYLMH0vbfxKiMf1vpq2DzOCUqCppeaml7EhNQhoRIfS/77K9j/8nO8TKeJHAhpSCuOP0BodBo0VJTwu48LtNWUuQ6pRiiZkmbPq4MJ3FrqobBEgrWBNJEDIQ3lz5AY7L0RCx4P2ODtiNZGmlyHVGOUTEmzx+PxsGywHXg84MTdeIS9SOM6JEIU3tWnqVhx4iEA4AsvW3jaGXMcUe1QMiUEgL25NsY4l05XtupkJCQSmsiBkPoSk5qLGXtvQyxhGNHZHJ96tOI6pFqjZErIf+Z7tYW6UIC7cRk4dvcV1+EQopCyCorx0e5byMwvhoOlDtaM7Agej8d1WLVGyZSQ/xhpijCzb2sAwHf/PEIuDZUhpE6ViCWY9dcdPE3OgYmWCP4TnSFSFnAdVp2gZErIG6Z0bwlLPVUkZRXil4u05ikhdemb05H493EKRMp8/O7jAiMtEdch1RlKpoS8QaQswNJBdgAA/3+jEZOay3FEhCiGvTdeYOfVGADA+jGOsDfX5jagOkbJlJC3DLAzRs82BigSS/D1qYdch0NIk3ftWSr8jj0AAMzv3xbvdzTlOKK6R8mUkLfweDz4DekAJT4P5yOTaVUZQmrheUoOpu+5jRIJw1AHM8z6r1+CoqFkSkgFWhtpwLe7NQBg1YmHKCwRcxsQIU1Qem4Rpuy6icz8YnRuoYPvP+ikED13K0LJlJBKzOnXBgYaKohOzcX2K9EQSxhCnr3GsfBXCHn2GmIai0pIpYpKJPh0TxhiXufBXEcVv010UZieuxXhMcboF+EtWVlZ0NbWRmZmJrS0tLgOh3DocNhLzD94F0IBHzpqykjOLpRuM9UWwW+IHQbaK979H0JqgzGGRYcjcODWS2ioKOHw9G5oZ9I0pwqUNx/QmSkh7zDSyRytjTRQJJbIJFIASMwswPQ9txF4P4Gj6AhpnLZeeoYDt16CzwM2fdi5ySbS6qBkSsg7SBiQkVdU4baySzorTzykS76E/OdkRDy+/2/BCL8hHdCnnRHHETUMSqaEvENodBpScypOpkBpQk3ILEBoNE2OT0jYi3TMO3AXQOkEKD7drLkNqAFRMiXkHZKzC+q0HiGKKvZ1Hj7efQtFJRJ4tjfGV4Pacx1Sg6JkSsg7GGnKN92ZvPUIUUQZeUWYvCsUablFsDfXws/jHCHgK+YQmMpQMiXkHVxb6sFUW4TKfhZ4KO3V69pSryHDIqTRKCgWY9ruMDxPyYWZtgjbfbpATajEdVgNjvNkumXLFlhbW0MkEsHNzQ2hoaGV1j1y5AhcXFygo6MDdXV1ODo64s8//5Spk5OTg1mzZsHCwgKqqqqws7PDtm3b6rsZREEJ+Dz4DSmdq7eyhOo3xK7Z/RVOCABIJAwLD0UgNCYNmipK2OnrCmMFmry+OjhNpgEBAZg3bx78/Pxw+/ZtODg4wMvLC8nJFU/fpqenh6+++gohISGIiIiAr68vfH19cebMGWmdefPmITAwEHv27EFkZCTmzp2LWbNm4fjx4w3VLKJgBtqbYusEJ5hoy/5I8HjADx90onGmpNn64WwUTtyNhxKfh20TnZvFEJjKcDppg5ubG7p06YLNmzcDACQSCSwtLTF79mwsXrxYrmM4OTlh0KBBWL16NQDA3t4e3t7eWLZsmbSOs7Mz3nvvPXz99ddyHZMmbSAVEUsYQqPTkJCZjw3nnyA2LQ8jncyxfowj16ER0uD2XH+BpUfvAwDWjXbAKGcLjiOqH41+0oaioiKEhYXB09Pz/8Hw+fD09ERISEiV+zPGEBQUhKioKPTq1Uta3q1bNxw/fhyvXr0CYwzBwcF4/PgxBgwYUOmxCgsLkZWVJfMg5G0CPg/uNvoY6WSBjWMdweMBR26/wtWnqVyHRkiDOvsgEcuPlSbSzz3bKmwirQ7OkmlqairEYjGMjY1lyo2NjZGYmFjpfpmZmdDQ0IBQKMSgQYOwadMm9O/fX7p906ZNsLOzg4WFBYRCIQYOHIgtW7bIJNy3rVmzBtra2tKHpaVl7RtIFFrnFrqY2NUKALDkyD3kFZVwHBEhDSPsRTpm77sDCQPGuVpiTj/FXAWmujjvgFRdmpqaCA8Px82bN/HNN99g3rx5uHjxonT7pk2bcP36dRw/fhxhYWFYt24dZs6cifPnz1d6zCVLliAzM1P6iIuLa4CWkKZuoVc7mGmLEJuWh3VnH3MdDiH17nlKDj764yYKSyToa2uE1cPsFXYVmOrirP+ygYEBBAIBkpKSZMqTkpJgYmJS6X58Ph+tW5f+JeTo6IjIyEisWbMGvXv3Rn5+Pr788kv8/fffGDRoEACgU6dOCA8Px48//ihzSflNKioqUFFRqaOWkeZCU6SMb0Z2hO/Om9hxNRqDOpnCqYUu12ERUi+SswowaUco0vOK4WChjc0fdoaSoMmdj9Ubzt4JoVAIZ2dnBAUFScskEgmCgoLg7u4u93EkEgkKC0snIC8uLkZxcTH4fNlmCQQCSCSSugmckDf0aWeEkU7mYAz44lAErXtKFFJWQTF8dt7Ey/R8WOmrYfvk5jmW9F04fTfmzZsHHx8fuLi4wNXVFRs2bEBubi58fX0BAJMmTYK5uTnWrFkDoPTepouLC2xsbFBYWIjTp0/jzz//xNatWwEAWlpa8PDwwMKFC6GqqgorKytcunQJu3fvxvr16zlrJ1Fsywfb4d/HqXianINNQU+xwKsd1yERUmcKS8SYtvsWIhOyYKAhxO4prjDQoCt5b+M0mXp7eyMlJQXLly9HYmIiHB0dERgYKO2UFBsbK3OWmZubixkzZuDly5dQVVWFra0t9uzZA29vb2md/fv3Y8mSJRg/fjzS0tJgZWWFb775Bp9++mmDt480DzpqQqwe1gHT997G1kvPMNDeBPbm2lyHRUitSSQM8wLu4vrzNKgLBdjl6worfXWuw2qUaHHwCtA4U1ITM/aG4fS9RLQ11sCJ2T2goiTgOiRCaowxBr/jD7A75AWUBTzsnOyKHm0MuA6rwTX6caaEKJrVw+yhry7E46QcbDj/hOtwCKmVDeefYHfIC/B4wPoxjs0ykVYHJVNC6oi+hgq+HdkRAPDrpWcIe5HOcUSE1Mwf12KwMaj0D8JVw+wxxMGM44gaP0qmhNQhrw4mGNHZHBIGLDh4F/lF1LuXNC3Hwl/B7/gDAKWzG5VNTkLejZIpIXVsxZAOMNZSQXRqLtYGPuI6HELkduFREuYfuAsAmNzNmmY3qgZKpoTUMW01Zawd1QkAsOtaDC49TuE4IkKqFvLsNabvuY0SCcNwRzMsH2xHsxtVAyVTQupB73ZGmOReenlswcG7eJ1TyHFEhFTublyGdJrA/nbG+GG0A/i0Rm+1UDIlpJ4sea89WhtpICW7EIuP3AONQiON0eOkbPjsDEVukRjdbPSxaVxnKNM0gdVG7xgh9URVKMAGb0coC3g49zAJ+2/SAgqkcXmekoMP/W8gI68YjpY68J/kApEyjY+uCUqmhNQje3NtzB9QOr3gqhMP8Twlh+OICCkVl5aH8b/fQGpOIdqbamGXbxeoq9B8uzVFyZSQejatZyu4t9JHfrEYs/66g4JiGi5DuJWYWYAPf7+OhMwCtDbSwJ9TXaGjJuQ6rCaNkikh9YzP5+Enb0foqQvxMCELa05Hch0SaYbEEoaQZ6/xZ0gMRv5yFXFppSvA7P3IjSaurwN0Tk9IAzDRFmHdaAf47rqJP0JewN3GAAPtK1+3l5C6FHg/AStPPERCZoG0TMADpvVsCWMtEYeRKQ46MyWkgfSxNcK0Xq0AAF8cuouX6XkcR0Sag8D7CZi+57ZMIgUAMQOWHn2AwPsJHEWmWCiZEtKAFgxoBwdLHWQVlGD2vjsoKqFF60n9EUsYVp54iHcNylp54iHEEhq2VVuUTAlpQEIlPjaP6wxNkRLuxGbgW7p/SupRaHRauTPSNzEACZkFCI1Oa7igFBQlU0IamKWeGn4a4wigdLrB43fjuQ2IKKznqfINxUrOrjzhEvlQMiWEA552xpjR2wYAsPhwBJ4kZXMcEVE0r3MKse3Sc7nqGmlSJ6TaomRKCEfm9W+Lbjb6yCsS49M9YcgpLOE6JKIgUrIL8aH/DcSl5eFdU+zyAJhqi+DaUq/BYlNUlEwJ4YiSgI+fx3WGsZYKnqXkYv6BcEioIwippcTMAnj/FoKopGwYaaqUrv6C0sT5prLnfkPsIKBJ7WuNkikhHDLQUMHWCc4QCvg48yAJP194wnVIpAl7mZ6HMb+G4HlKLsx1VHHgE3dM7t4SWyc4wURb9lKuibYIWyc4YaC9KUfRKhYeo6UsysnKyoK2tjYyMzOhpaXFdTikGThwKw5fHIoAAGyb4EwTOpBqi0nNxYf+1xGfWYAWemr462M3WOiqSbeLJQyh0WlIzi6AkWbppV06I62avPmAZkAipBEY42KJyIQs7Lwag3kHwmFt0A22JvSHHJHPo8QsTPg9FKk5hbAxVMfej7qWOxMV8Hlwt9HnKELFR5d5CWkkvnq/Pbq3Lu2Q9PHuW7SgOJHL7dh0eP96Xbr6y/5p7uUSKal/lEwJaSSUBHxsHucEK301xKXlY9qfYbTCDHmnK09SMeH3G8jML4azlS72T+sKQ02atJ4LlEwJaUR01YXY7tMFWiIlhL1Ix4KDd6mHL6nQ6XsJmLLrJvKKxOjZxgB/TnWFtqoy12E1W5RMCWlkWhtpYNtEZyjxeTgZkYD15x5zHRJpZP4MicHMv26jSCzB+x1N8LuPC9SE1AWGS5RMCWmEutkYYM3IjgCAzcFPceBmHMcRkcaAMYb1Z6Ow7NgDMAaMd2uBTeOcoKIk4Dq0Zo+SKSGN1GgXS8zq0xoAsOTvezj/MInjiAiXSsQSfPn3Pfx84SkA4HPPtvh6uD0Nb2kkKJkS0ojNH9AWo5wsIJYwzPzrNsJe0OoezVFOYQk+2n0L+0LjwOcB34ywx2eebcDjUSJtLCiZEtKI8Xg8fDeqI/raGqGwRIIpu27hMU2K36wkZxXA+9cQXIxKgUiZj18numC8mxXXYZG3UDIlpJFTFvCx5UMndG6hg8z8YkzaHoq4tDyuwyINICoxGyN+uYYH8Vkw0BBi/zR39Lcz5josUgFKpoQ0AapCAXb4dEFrIw0kZhXgw9+vIyEzn+uwSD0KfpSMUVuv4VVGPloZqOPI9O5wtNThOixSCUqmhDQRuupC7P3ITTqpw3j/G0jJplmSFA1jDDuuRGPqHzeRU1iCrq30cHh6N7TQV6t6Z8IZSqaENCHGWiLs/cgN5jqqeJ6aiwm/30BabhHXYZE6UlQiwVdH72PVyYeQMMDbxRK7p7hBV13IdWikCpRMCWliLHTVsPcjNxhpqiAqKRsf+l+neXwVQEp2Icb/fh1/3YgFj1c6V/N3ozpCqEQ/000BfUqENEHWBur462M3GGio4FFiNsb+dh3J2QVch0Vq6N7LTAzdfAU3Y9KhqaKE3ye54ONerWjoSxNCyZSQJqq1kSYCPukKYy0VPEnOwdhfryMxkxJqU3M47CU+2HYNCZkFaGWojqOzuqNfe+qx29RQMiWkCbMx1MCBT9yl91DH/BpCw2aaiIJiMZYcuYf5B++isESCvrZGODqzO2wMNbgOjdQAJVNCmjgrfXUEfNIVlnqqiE3Lw8it1/AwPovrsMg7xKXlYfS2EOwLLb0/+rlnW/w+yQVaIlr1pamiZEqIArDQVcOhT7vB1kQTKdmF8P41BNefv+Y6LFKBwPuJGLzpCu69yoSumjJ2+briM8824NMcu00aJVNCFISxlggBn7jD1VoP2YUlmLQjFP/cS+A6LPKfgmIxlh+7j0/3hCEzvxgOljo4OacnPNoach0aqQOUTAlRINqqytg91RX97YxRVCLB9L23sfXiMzBGC4xz6WlyDkb8cg27Q14AAD7p1QoH/7vXTRQDJVNCFIxIWYCt450wyb10MvS1gY+w4GAECkvEHEfW/DDG8Me1GAz6+TIiE7Kgry7ELt8uWPJ+exo/qmBoaXZCFJCSgI9Vw+xhY6iBlSce4PDtl4hLy8MvE5xgoKHCdXjNQlJWARYeisC/j1MAAD3bGODH0Q4w1hJxHBmpD/SnESEKzKebNXZM7gJNFSWExqRh8M9XcDs2neuwFBpjDH/feQmvDf/i38cpUFHiY8UQO/zh60qJVIHxGN1MKScrKwva2trIzMyElpYW1+EQUmtPkrLxyZ4wPE/JhbKAh6WD7DDJ3Ypm2KljCZn5+Orv+7jwKBkAYG+uhQ3ejmhtpMlxZKSm5M0HlEwrQMmUKKLsgmIsOhyB0/cSAQBDHMzwzQh7GttYByQShv0347DmdCSyC0sgFPDxmWcbTOvVCsoCugDYlFEyrQVKpkRRMcaw/Uo01vzzCGIJg7mOKn7ydoRrSz2uQ2uyHsZn4auj93AnNgMA4Gipgx8+6IQ2xnQ2qggomdYCJVOi6MJepGNuwB3EpeWDzwNm9G6NzzzbSM+ixMUleHTgFPJjX0K1hQVsxwyCQJn6K74pu6AYG84/wa5rMRBLGDRUlDCvf1v4dLOGgCZgUBiUTGuBkilpDrILirHi+EMcvv0SAGBroonvP+gE8aHDMPNbDOOsVGndJC0DxK/8Dp3nTuUq3EZDLGE4cCsO685GITWndC3ZQR1NsWywHUy0qYORoqFkWguUTElzcjIiHsuO3kd6XjH4YJgS+jfmXtkLjeL/r5Eq+e//7/70e7NOqFefpmL1yYd4lJgNAGhlqI7lg+3Qu50Rx5GR+kLJtBYomZLm5nVOIVYef4DjEaXTD1pkJOKr4B0Y+Pgayi5YSgAkaxvCMCW+2V3yDY/LwA9nHuHq09L5jrVESvi8f1tM6GpFHYwUnLz5gL4FhBDoa6jgExaHnQdXwCwrGS91TDB9xJf4cOw3iDS0BlD6Y2GSmYJHB05xGmtDuv8qE9N238LwLVdx9elrCAV8TO5mjUsL+8C3e0tKpESqef15SQipVH7sS/R5fgvnf5+ObW6j8KvrKIRYOWDQ5I0Y+eACPru6H5aZSciPfcl1qPUu7EUaNl94iuCo0tmL+DxgpJMF5nq2gYWuGsfRkcaIkikhBACg2sICAKBWXIh5V/7CmIhzWNPbF6fa98Khjv1x1K4PRt87hwEmFhxHWnfEEobQ6DQkZxfAQF0FmQXF2HUtBqHRaQBKk+jgTmaY3bc1DXUh70T3TCtA90xJcyQuLkGqgSkMs1Jl7v/cMW2L9T0n4HJLJwCAEp+HIQ5m+KhnS3Qw0+Ym2DoQeD8BK088REJmQbltygIeRna2wKe9bdDSQJ2D6EhjQR2QaoGSKWmu7mzYDofPPwIg26FCAiDUogO+9l2F+0X/nyjfvZU+JrlboV974ya1CsrpiHjM+OtOpdvXjLDHODerBoyINFby5gO6zEsIkeo8dyruAOXGmSZrG0Jl/uc4OXck7sZlYPuVaJy6l4CQ568R8vw1dNWUMbyzOT5wtoCdqVajnPNXLGG4FZOGkxEJ2HvjRaX1eAB+vvAUY7q0oMkXiNw4PzPdsmULfvjhByQmJsLBwQGbNm2Cq6trhXWPHDmCb7/9Fk+fPkVxcTHatGmD+fPnY+LEiTL1IiMjsWjRIly6dAklJSWws7PD4cOH0aJFC7liojNT0tzJMwNSfEY+9lx/gcO3XyIp6/9jUlvoqcGrgzG8OpigcwtdThNSZl4xrjxNxb+PU3AhKhkp2YVV7/SffR93hbuNfj1GR5qCJnGZNyAgAJMmTcK2bdvg5uaGDRs24ODBg4iKioKRUflB0BcvXkR6ejpsbW0hFApx8uRJzJ8/H6dOnYKXlxcA4NmzZ3B1dcXUqVMxbtw4aGlp4cGDB+jatWuFx6wIJVNC5FciluDyk1QcDItDUGQyCksk0m1aIiW4ttSHu40+3FrqoZ2JZr0OJ0nKKkDYi3TpI+JlBiRv/MJpiZRga6ol7WD0LhvHOmKYo3m9xUqahiaRTN3c3NClSxds3rwZACCRSGBpaYnZs2dj8eLFch3DyckJgwYNwurVqwEAY8eOhbKyMv78888ax0XJlJCayS0swaXHKTjzIBEXHiUju6BEZrtQwEcbYw10MNNCayMNWOqqwUJXDea6qtBWVa7yLJYxhqz8EsRn5iMxswAvM/LxLDkHj5Oy8TgpWzq935vaGGmgV1tDeLQ1RNdW+gh7kY5x/terbAudmRKgCdwzLSoqQlhYGJYsWSIt4/P58PT0REhISJX7M8Zw4cIFREVFYe3atQBKk/GpU6fwxRdfwMvLC3fu3EHLli2xZMkSDB8+vNJjFRYWorDw/5d/srKyat4wQpoxdRUlvN/RFO93NEWJWIL78Vm4/vw1rj9/jbCYdGQXluBBfBYexFf8b0xTRQlaqspQFQrAA1B26zW3UIycwhLkFJZALKn8738+D2hnogVnKx04tdCFWyt9mOuoytRxbakHU20REjMLUNGReABMtEW0kg6pFs6SaWpqKsRiMYyNjWXKjY2N8ejRo0r3y8zMhLm5OQoLCyEQCPDLL7+gf//+AIDk5GTk5OTgu+++w9dff421a9ciMDAQI0eORHBwMDw8PCo85po1a7By5cq6axwhBEoCPhwtdeBoqYNPPWzAGMPL9Hw8iM/Cw/hMxLzOw8v0PMSl50vvZWYXliC7sKSKIwO6asow1VaFmY4ILQ3U0dZYE22NNdHaSAPqKu/+WRPwefAbYofpe26DB8gk1LLzYr8hdtT5iFRLk+vNq6mpifDwcOTk5CAoKAjz5s1Dq1at0Lt3b0gkpfdqhg0bhs8//xwA4OjoiGvXrmHbtm2VJtMlS5Zg3rx50udZWVmwtLSs/8YQ0ozweDxY6qnBUk8NA+1NZLYVlUiQVVCMrPxiZOYXo6BYAgaG//4HNaEAmiIlaKgoQ/u/M9faGGhviq0TnMqNMzXRFsFviB0G2pvW6vik+eEsmRoYGEAgECApKUmmPCkpCSYmJpXsVXopuHXr1gBKE2VkZCTWrFmD3r17w8DAAEpKSrCzs5PZp3379rhy5Uqlx1RRUYGKikql2wkh9UuoxIeBhgoMNBru3+FAe1P0tzORzoBkpFl6aZfOSElNcDbKWigUwtnZGUFBQdIyiUSCoKAguLu7y30ciUQivd8pFArRpUsXREVFydR5/PgxrKxoADYhRJaAz4O7jT6GOZrD3UafEimpMU4v886bNw8+Pj5wcXGBq6srNmzYgNzcXPj6+gIAJk2aBHNzc6xZswZA6b1NFxcX2NjYoLCwEKdPn8aff/6JrVu3So+5cOFCeHt7o1evXujTpw8CAwNx4sQJXLx4kYsmEkIIaQY4Tabe3t5ISUnB8uXLkZiYCEdHRwQGBko7JcXGxoLP///Jc25uLmbMmIGXL19CVVUVtra22LNnD7y9vaV1RowYgW3btmHNmjWYM2cO2rVrh8OHD6NHjx4N3j5CCCHNA+czIDVGNM6UEEIIQIuDE0IIIQ2GkikhhBBSS5RMCSGEkFqiZEoIIYTUEiVTQgghpJYomRJCCCG1RMmUEEIIqSVKpoQQQkgtUTIlhBBCaomSKSGEEFJLTW4904ZQNsNiVlYWx5EQQgjhUlkeqGrmXUqmFcjOzgYAWiCcEEIIgNK8oK2tXel2mui+AhKJBPHx8dDU1ASPV/P1DbOysmBpaYm4uDiFnjC/ubQToLYqoubSToDaWhOMMWRnZ8PMzExmFbO30ZlpBfh8PiwsLOrseFpaWgr/xQWaTzsBaqsiai7tBKit1fWuM9Iy1AGJEEIIqSVKpoQQQkgtUTKtRyoqKvDz84OKigrXodSr5tJOgNqqiJpLOwFqa32iDkiEEEJILdGZKSGEEFJLlEwJIYSQWqJkSgghhNQSJVNCCCGkliiZVuHff//FkCFDYGZmBh6Ph6NHj8psX7FiBWxtbaGurg5dXV14enrixo0bMnXS0tIwfvx4aGlpQUdHB1OnTkVOTo5MnYiICPTs2RMikQiWlpb4/vvv67tpMqpq55s+/fRT8Hg8bNiwQaa8KbQTqLqtkydPBo/Hk3kMHDhQpo6itBUAIiMjMXToUGhra0NdXR1dunRBbGysdHtBQQFmzpwJfX19aGhoYNSoUUhKSpI5RmxsLAYNGgQ1NTUYGRlh4cKFKCkpqe/mSVXVzrc/z7LHDz/8IK2jKJ9pTk4OZs2aBQsLC6iqqsLOzg7btm2TqdMUPlOg6rYmJSVh8uTJMDMzg5qaGgYOHIgnT57I1GmotlIyrUJubi4cHBywZcuWCre3bdsWmzdvxr1793DlyhVYW1tjwIABSElJkdYZP348Hjx4gHPnzuHkyZP4999/MW3aNOn2rKwsDBgwAFZWVggLC8MPP/yAFStW4Lfffqv39pWpqp1l/v77b1y/fh1mZmbltjWFdgLytXXgwIFISEiQPvbt2yezXVHa+uzZM/To0QO2tra4ePEiIiIisGzZMohEImmdzz//HCdOnMDBgwdx6dIlxMfHY+TIkdLtYrEYgwYNQlFREa5du4Y//vgDu3btwvLly+u9fWWqauebn2VCQgJ27NgBHo+HUaNGSesoymc6b948BAYGYs+ePYiMjMTcuXMxa9YsHD9+XFqnKXymwLvbyhjD8OHD8fz5cxw7dgx37tyBlZUVPD09kZubK63XYG1lRG4A2N9///3OOpmZmQwAO3/+PGOMsYcPHzIA7ObNm9I6//zzD+PxeOzVq1eMMcZ++eUXpqurywoLC6V1Fi1axNq1a1f3jZBDZe18+fIlMzc3Z/fv32dWVlbsp59+km5riu1krOK2+vj4sGHDhlW6jyK11dvbm02YMKHSfTIyMpiysjI7ePCgtCwyMpIBYCEhIYwxxk6fPs34fD5LTEyU1tm6dSvT0tKSaX9Dkeff6bBhw1jfvn2lzxXpM+3QoQNbtWqVTJmTkxP76quvGGNN8zNlrHxbo6KiGAB2//59aZlYLGaGhobM39+fMdawbaUz0zpUVFSE3377Ddra2nBwcAAAhISEQEdHBy4uLtJ6np6e4PP50svBISEh6NWrF4RCobSOl5cXoqKikJ6e3rCNqIREIsHEiROxcOFCdOjQodx2RWlnmYsXL8LIyAjt2rXD9OnT8fr1a+k2RWmrRCLBqVOn0LZtW3h5ecHIyAhubm4yl9LCwsJQXFwMT09PaZmtrS1atGiBkJAQAKVt7dixI4yNjaV1vLy8kJWVhQcPHjRYe+SVlJSEU6dOYerUqdIyRflMAaBbt244fvw4Xr16BcYYgoOD8fjxYwwYMACA4nymhYWFACBzFYXP50NFRQVXrlwB0LBtpWRaB06ePAkNDQ2IRCL89NNPOHfuHAwMDAAAiYmJMDIykqmvpKQEPT09JCYmSuu8+UECkD4vq8O1tWvXQklJCXPmzKlwu6K0Eyi9xLt7924EBQVh7dq1uHTpEt577z2IxWIAitPW5ORk5OTk4LvvvsPAgQNx9uxZjBgxAiNHjsSlS5cAlMYqFAqho6Mjs6+xsXGTauub/vjjD2hqaspc6lOUzxQANm3aBDs7O1hYWEAoFGLgwIHYsmULevXqBUBxPtOypLhkyRKkp6ejqKgIa9euxcuXL5GQkACgYdtKq8bUgT59+iA8PBypqanw9/fHmDFjcOPGjXL/OJuqsLAwbNy4Ebdv367VknRNxdixY6X/3bFjR3Tq1Ak2Nja4ePEi+vXrx2FkdUsikQAAhg0bhs8//xwA4OjoiGvXrmHbtm3w8PDgMrx6s2PHDowfP17mjEaRbNq0CdevX8fx48dhZWWFf//9FzNnzoSZmZnMGVpTp6ysjCNHjmDq1KnQ09ODQCCAp6cn3nvvvSoX8q4PdGZaB9TV1dG6dWt07doV27dvh5KSErZv3w4AMDExQXJyskz9kpISpKWlwcTERFrn7d5lZc/L6nDp8uXLSE5ORosWLaCkpAQlJSW8ePEC8+fPh7W1NQDFaGdlWrVqBQMDAzx9+hSA4rTVwMAASkpKsLOzkylv3769tDeviYkJioqKkJGRIVMnKSmpSbW1zOXLlxEVFYWPPvpIplxRPtP8/Hx8+eWXWL9+PYYMGYJOnTph1qxZ8Pb2xo8//ghAsT5TZ2dnhIeHIyMjAwkJCQgMDMTr16/RqlUrAA3bVkqm9UAikUiv57u7uyMjIwNhYWHS7RcuXIBEIoGbm5u0zr///ovi4mJpnXPnzqFdu3bQ1dVt2OArMHHiRERERCA8PFz6MDMzw8KFC3HmzBkAitHOyrx8+RKvX7+GqakpAMVpq1AoRJcuXRAVFSVT/vjxY1hZWQEo/bFSVlZGUFCQdHtUVBRiY2Ph7u4OoLSt9+7dk0lG586dg5aWVrlEzbXt27fD2dlZ2qehjKJ8psXFxSguLi63iLVAIJBeiVC0zxQoXW/U0NAQT548wa1btzBs2DAADdzWmvWraj6ys7PZnTt32J07dxgAtn79enbnzh324sULlpOTw5YsWcJCQkJYTEwMu3XrFvP19WUqKioyPcwGDhzIOnfuzG7cuMGuXLnC2rRpw8aNGyfdnpGRwYyNjdnEiRPZ/fv32f79+5mamhr79ddfG0U7K/J2b17GmkY7GXt3W7Ozs9mCBQtYSEgIi46OZufPn2dOTk6sTZs2rKCgQKHayhhjR44cYcrKyuy3335jT548YZs2bWICgYBdvnxZeoxPP/2UtWjRgl24cIHdunWLubu7M3d3d+n2kpISZm9vzwYMGMDCw8NZYGAgMzQ0ZEuWLGk07WSstKe9mpoa27p1a4XHUJTP1MPDg3Xo0IEFBwez58+fs507dzKRSMR++eUX6TGawmcqT1sPHDjAgoOD2bNnz9jRo0eZlZUVGzlypMwxGqqtlEyrEBwczACUe/j4+LD8/Hw2YsQIZmZmxoRCITM1NWVDhw5loaGhMsd4/fo1GzduHNPQ0GBaWlrM19eXZWdny9S5e/cu69GjB1NRUWHm5ubsu+++a8hmvrOdFakomTaFdjL27rbm5eWxAQMGMENDQ6asrMysrKzYxx9/LNNtnjHFaGuZ7du3s9atWzORSMQcHBzY0aNHZY6Rn5/PZsyYwXR1dZmamhobMWIES0hIkKkTExPD3nvvPaaqqsoMDAzY/PnzWXFxcUM0kTEmXzt//fVXpqqqyjIyMio8hqJ8pgkJCWzy5MnMzMyMiUQi1q5dO7Zu3TomkUikx2gKnyljVbd148aNzMLCgikrK7MWLVqwpUuXlhvO0lBtpSXYCCGEkFqie6aEEEJILVEyJYQQQmqJkikhhBBSS5RMCSGEkFqiZEoIIYTUEiVTQgghpJYomRJCCCG1RMmUkDrUu3dvzJ07V/rc2toaGzZs4CweLl28eBE8Hq/cvKiEKCJKpqRZS0lJwfTp09GiRQuoqKjAxMQEXl5euHr1qrQOj8eTWePzXY4cOYLVq1fXU7Sl/P394eDgAA0NDejo6KBz585Ys2ZNvb5mVd7+IwIoXVczISEB2tra9frakydPBo/HA4/Hg7KyMlq2bIkvvvgCBQUF1TpORW0gRF60BBtp1kaNGoWioiL88ccfaNWqFZKSkhAUFCSzGLg8ioqKIBQKoaenV0+RltqxYwfmzp2Ln3/+GR4eHigsLERERATu379fr69bE0KhsMFWGBk4cCB27tyJ4uJihIWFwcfHBzweD2vXrm2Q1yeE5uYlzVZ6ejoDwC5evFhpHSsrK5k5Qa2srBhjjPn5+TEHBwfm7+/PrK2tGY/HY4yVTjL+2Wefyez/5hzG/v7+TFtbm50/f54xxti9e/fYwIEDmbq6OjMyMmITJkxgKSkplcYzbNgwNnny5Eq337t3j/F4PJacnMwYK51vlsfjMW9vb2md1atXs+7duzPGSif5njJlCrO2tmYikYi1bduWbdiwQeaYPj4+bNiwYWzFihXMwMCAaWpqsk8++UQ6B6qPj0+5uVOjo6Ol86qmp6dLj3Xo0CFmZ2fHhEIhs7KyYj/++GO59/ubb75hvr6+TENDg1laWlY5kXxZfG8aOXIk69y5s/R5amoqGzt2LDMzM2OqqqrM3t6e/fXXXzLHqKgNZe9pdT4j0jzRZV7SbGloaEBDQwNHjx6VLpn3tps3bwIAdu7ciYSEBOlzAHj69CkOHz6MI0eOIDw8vMrX+/7777F48WKcPXsW/fr1Q0ZGBvr27YvOnTvj1q1bCAwMRFJSEsaMGVPpMUxMTHD9+nW8ePGiwu0dOnSAvr4+Ll26BKB0/c43nwPApUuX0Lt3bwClywVaWFjg4MGDePjwIZYvX44vv/wSBw4ckDluUFAQIiMjcfHiRezbtw9HjhzBypUrAQAbN26Eu7s7Pv74YyQkJCAhIQGWlpblYgsLC8OYMWMwduxY3Lt3DytWrMCyZcuwa9cumXrr1q2Di4sL7ty5gxkzZmD69Onllol7l/v37+PatWsQCoXSsoKCAjg7O+PUqVO4f/8+pk2bhokTJyI0NPSdbajJZ0SaKa6zOSFcOnToENPV1WUikYh169aNLVmyhN29e1emDgD2999/y5T5+fkxZWVl6RlgmcrOTL/44gtmamoqszTf6tWr2YABA2T2j4uLYwBYVFRUhfHGx8ezrl27MgCsbdu2zMfHhwUEBDCxWCytM3LkSDZz5kzGGGNz585lCxcuZLq6uiwyMpIVFRUxNTU1dvbs2Urfk5kzZ7JRo0ZJn/v4+DA9PT2Wm5srLdu6dSvT0NCQvu7b7WaMlTsz/fDDD1n//v1l6ixcuJDZ2dnJvF8TJkyQPpdIJMzIyKjSZdPK4hMIBExdXZ2pqKgwAIzP57NDhw5Vug9jjA0aNIjNnz9f+ryiNtTkMyLNE52ZkmZt1KhRiI+Px/HjxzFw4EBcvHgRTk5O5c6WKmJlZQVDQ8Mq661btw7+/v64cuUKOnToIC2/e/cugoODpWfIGhoasLW1BQA8e/aswmOZmpoiJCQE9+7dw2effYaSkhL4+Phg4MCB0sWfPTw8cPHiRQClZ6F9+/ZFr169cPHiRdy8eRPFxcXo3r279JhbtmyBs7MzDA0NoaGhgd9++w2xsbEyr+vg4AA1NTXpc3d3d+Tk5CAuLq7K9peJjIyUeV0A6N69O548eQKxWCwt69Spk/S/eTweTExMZBZurkifPn0QHh6OGzduwMfHB76+vhg1apR0u1gsxurVq9GxY0fo6elBQ0MDZ86cKdfOt9XkMyLNEyVT0uyJRCL0798fy5Ytw7Vr1zB58mT4+flVuZ+6urpcx+/ZsyfEYnG5S6c5OTkYMmQIwsPDZR5PnjxBr1693nlMe3t7zJgxA3v27MG5c+dw7tw56aXc3r174+HDh3jy5AkePnyIHj16oHfv3rh48SIuXboEFxcXaWLcv38/FixYgKlTp+Ls2bMIDw+Hr68vioqK5GpbfVBWVpZ5zuPxpH8oVEZdXR2tW7eGg4MDduzYgRs3bmD79u3S7T/88AM2btyIRYsWITg4GOHh4fDy8qqynbX5jEjzQr15CXmLnZ2dzFAYZWVlmTOn6nJ1dcWsWbMwcOBAKCkpYcGCBQAAJycnHD58GNbW1lBSqvk/RTs7OwBAbm4uAKBjx47Q1dXF119/DUdHR2hoaKB3795Yu3Yt0tPTpfdLAeDq1avo1q0bZsyYIS2r6Izr7t27yM/Ph6qqKgDg+vXr0NDQkN4bFQqFVb5H7du3lxlyVPb6bdu2hUAgqH7DK8Hn8/Hll19i3rx5+PDDD6GqqoqrV69i2LBhmDBhAoDSe8WPHz+WvneVtaGuPiOi+OjMlDRbr1+/Rt++fbFnzx5EREQgOjoaBw8exPfff49hw4ZJ61lbWyMoKAiJiYlIT0+v0Wt169YNp0+fxsqVK6WTOMycORNpaWkYN24cbt68iWfPnuHMmTPw9fWtNDFNnz4dq1evxtWrV/HixQtcv34dkyZNgqGhIdzd3QGUnsn16tULe/fulSbOTp06obCwEEFBQfDw8JAer02bNrh16xbOnDmDx48fY9myZTKdrMoUFRVh6tSpePjwIU6fPg0/Pz/MmjULfD5f+h7duHEDMTExSE1NrfBMcv78+QgKCsLq1avx+PFj/PHHH9i8ebP0j4u6NHr0aAgEAmzZskXaznPnzuHatWuIjIzEJ598gqSkJJl9KmpDTT4j0jxRMiXNloaGBtzc3PDTTz+hV69esLe3x7Jly/Dxxx9j8+bN0nrr1q3DuXPnYGlpic6dO9f49Xr06IFTp05h6dKl2LRpE8zMzHD16lWIxWIMGDAAHTt2xNy5c6GjoyNNUm/z9PTE9evXMXr0aLRt2xajRo2CSCRCUFAQ9PX1pfU8PDwgFoulyZTP56NXr17g8Xgy9y0/+eQTjBw5Et7e3nBzc8Pr169lzlLL9OvXD23atEGvXr3g7e2NoUOHYsWKFdLtCxYsgEAggJ2dHQwNDSu8F+nk5IQDBw5g//79sLe3x/Lly7Fq1SpMnjy5Zm/oOygpKWHWrFn4/vvvkZubi6VLl8LJyQleXl7o3bs3TExMMHz4cJl9KmpDTT4j0jzxGGOM6yAIIY3X5MmTkZGRIfcsUIQ0R/SnFSGEEFJLlEwJIYSQWqLLvIQQQkgt0ZkpIYQQUkuUTAkhhJBaomRKCCGE1BIlU0IIIaSWKJkSQgghtUTJlBBCCKklSqaEEEJILVEyJYQQQmqJkikhhBBSS/8DSgyKQXfHvhQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here I am using Deribit Option data, the smile looks good!\n",
    "forawrd_price=1603.8\n",
    "strikes=[1300, 1400, 1500, 1600, 1700, 1800, 1900]\n",
    "time_to_expiration=0.2558724912480974 # here I am using ETH-29DEC23 options\n",
    "iv=[0.4613000000000001, 0.41789999999999994, 0.3821, 0.3626, 0.3608, 0.3738, 0.395]\n",
    "model = SABR_swaption(F = forawrd_price, # forward rate, scalar\n",
    "                      K = strikes, # strikes, vector (N X 1)\n",
    "                      time = time_to_expiration, # expiry (in yrs), scalar\n",
    "                      vols = iv, # observed market volatilities, vector (N X 1)\n",
    "                      calibration=\"SLS_SciPy\",\n",
    "                      beta = 0.5)\n",
    "\n",
    "model.plot_smile()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Assuming there's another coin,\n",
    "# I use the same parameters except for the forward price and strikes.\n",
    "# In this case there's at least similar smile structure.\n",
    "# However, the smile disappears.\n",
    "coin_strikes = np.linspace(1,50,num=1000)\n",
    "coin_forward_price = 3\n",
    "y= [SABR(model.alpha, model.beta, model.rho, model.nu,coin_forward_price,k,model.time) for k in coin_strikes]\n",
    "print(y)\n",
    "\n",
    "plt.plot(coin_strikes, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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RLad5qYaIiFqOsc6EeRtP49HFe5Grr0Y7f0+smZ6AmUM62WURAVhGhLmrS/2lmi2neKmGiIhaxtmCMoyan4xFSRmQZWB8v3BseGEg4iJaiY52UywjggzpUj+Idf+FEugrORsrERE1n9ksY8meTNz34W6czjPAz8sdn0zojXmje8JLbf8jMuw/oZNq6++FToHeSC8sx46zhXggto3oSERE5IAKDNX48+qj2JVeDKB+Pqt/j+lpN3fKNAXPjAj0v7tqOG6EiIgs99PxPAx7Lwm70ouhVinwxgPdsOSJvg5VRACeGRFqSJdAfLzjPLanFaLWZIabnQ4sIiIi+1JWXYvXfziFNYcuAQC6t9HivXGx6BjoIzhZ87CMCBQb3gr+Xu64XFGDAxdKkBjZWnQkIiKyc0eyrmDmylRklVRCkoBnBkVi1pAouKsc9x+0jpvcCSgVUuPCeVs4GysREd2E2SxjwY5zeHhhCrJKKtHG1wPfPJ2Al+6JdugiArCMCNdwi+/WMwWQZVlwGiIiskcFhmo8/tk+/PvnNNSZZYzoEYKNLwxsnLPK0fEyjWADO7WGu0qBi5crca6wHJ2CHPN6HxERWceWUwX4y5qjuFJZCw83JV67vyvG9gm3q+ncbxXLiGBeahUSI/2xI60IW04XsowQEREAoLrWhP/beBpfplwEAHQN0eLDR+MQGeAtOFnL42UaOzCkYTZWLpxHRESon0n1gY/2NBaRJwe0x7oZiU5ZRACWEbtw19XZWA9nXcHlcqPgNEREJIosy1i+9yJGfrgbaQVlaO3tjqWT++Lv93WFWqUUHc9qWEbsQIjOA93baCHLwLYzvKuGiMgVXamowbRlh/Dy+hMw1pkxKCoAP828HXd0DhQdzepYRuzEXdH1l2o2c+E8IiKXk3L+Moa/vwu/nCqAm1LCyyO6YMkTfRHgoxYdzSZYRuzE3d3qy0hSehGqakyC0xARkS3Umcx4e1MaHl28F/mGanRo7YV1z/bH1IEdoFA4z90yf4RlxE50DdEirJUHqmvNSEovEh2HiIisLLe0Co98shcfbT8HWQbG9QnHD88PQPc2OtHRbI5lxE5IkoS7uwYDADadzBechoiIrGnr6QLc+8EuHLx4BT5qFT4cH4e3xvSEl9o1Z9xgGbEjw7r9bxXfWpNZcBoiImppNXVm/PPHU3jyi4MoraxFjzY6/PjCAIyMCRUdTSjXrGB2qk87v8aF8/ZnlqB/Ry6cR0TkLLJLKvHciiM4ml0KAJjSvz3+OryzU9+y21Q8M2JHlAqpcQK0X3iphojIafx0PA/3frALR7NLofNwwycTeuOVkc49d4glWEbszLDuV8vIKS6cR0Tk6KprTXjluxN45qvDKKuuQ68IX2x4YQDu7hYsOppd4WUaO5MY2Rpe7krk6atx7JIeMeG+oiMREVEzZBZX4LmvD+NkrgEAMH1QJF68OwpuSp4H+C3uETujcVM2zrbHu2qIiBzTd6k5uO+DXTiZa4CfV/2U7nOGR7OI3AD3ih1qmACNZYSIyLFU1Zjw1zXHMHNlKipqTOjX3g8bXxjoElO63wpeprFDg6MD4aaUcL6oAucKy9Ex0DlXaSQicibpBWWY8fVhnC0ohyQBz9/ZCS/c2REqng35Q9xDdkircUNiZP1tvb+c4tkRIiJ7t/5IDu7/aA/OFpQjwEeNr56Mx+yhUSwiTcS9ZKeGdWuYjZUL5xER2avqWhP+tu44Zn2TiqpaE/p39MfGFwYikfNEWYRlxE4N6RoISQKOZpciX18tOg4REf1GdkklxixMxlf7siBJwAt3dsSXU+JdZqXdlsQyYqcCfTToFdEKAC/VEBHZm82nCjDig104kWNAK083LJ3cD7Pv7gylC62025JYRuzYMN5VQ0RkV+pMZsz76TSe+vIgDNV1iIvwxYYXBmJQVIDoaA6NZcSONYwb2ZtRgtLKGsFpiIhcW4GhGo9+ug+LdmYAqF9b5punExDq6yE4meNjGbFjbf29EB3sA5NZxtbThaLjEBG5rORzxRjxwS7sv1ACb7UKHz/WC6+M7Ap3Fb9GWwL3op1rODvy0wleqiEisjWzWcZH29Lx+Gf7UFxeg+hgH/zw/AAM7xEiOppTYRmxc/dePeCT0otQVl0rOA0Rkeu4UlGDKV8cwNu/nIVZBsb2CcP6Gf3RvrWX6GhOh2XEzkUFeaNDgBdq6szYdoaXaoiIbOFI1hXc9+Fu7EgrglqlwL/H9MS/x8RA46YUHc0psYzYOUmScG/3+rMjG4/nCU5DROTcZFnGsr0XMXZRCnJKq9C+tRfWz+iPsX3CRUdzaiwjDqDhUs2OtCJUGOsEpyEick7VtSa8uPoo/r7+BGpNMu7tEYzvn+uPLiFa0dGcHsuIA+gS4oN2/p4w8lINEZFVZJdUYvSCZKw9nAOlQsLf7u2C+Y/2go/GTXQ0l8Ay4gAkSWo8O/LTCV6qISJqSdvTCnHfh7txKs8Afy93LHuyH566vQMkibOp2grLiINoKCPbzxShsoaXaoiIbpXZLOP9LemYsvQA9FW1iA33xY8vDGhcNZ1sx+IykpSUhJEjRyI0NBSSJGH9+vU33X7t2rUYOnQoAgICoNVqkZCQgE2bNjU3r8vqFqpFuJ8HqmpN2JFWJDoOEZFD01fV4qkvD+LdLWchy8Bj8RH4ZtptCNFxNlURLC4jFRUViImJwfz585u0fVJSEoYOHYqNGzfi0KFDGDx4MEaOHIkjR45YHNaV/fpSDe+qISJqvtN5Btz/0W5sPVMId5UC/xnTE/96sAfUKt62K4oky7Lc7BdLEtatW4dRo0ZZ9Lpu3bph3LhxeOWVV5q0vcFggE6ng16vh1bruqOaj2aX4oH5e+DprsThvw/l/e5ERBZafyQHc9YeQ3WtGW18PbBoQm90b6MTHctpNfX7W2XDTAAAs9mMsrIy+Pn53XAbo9EIo9HY+LPBYLBFNLvXM0yHNr4eyCmtwo60ItzTPVh0JCIih1BrMuNfG05jafIFAMDATq3xwSNxaOXlLjYYARAwgPXtt99GeXk5xo4de8Nt5s2bB51O1/gID+dkM0DDpZqGtWp4qYaIqCkKDdUY/8nexiLy3OCOWDq5H4uIHbFpGfn666/x+uuvY9WqVQgMDLzhdnPnzoVer298ZGdn2zClfWtYnGnr6UJU15oEpyEism8HLpRgxIe7cfDiFfioVfhkQm/8eVhnKBW8bdee2OwyzcqVKzF16lSsXr0aQ4YMuem2arUaarXaRskcS1y4L0J1GuTqq7ErvRhDuwaJjkREZJeW772I174/iTqzjKggbyx8vDc6BHiLjkXXYZMzIytWrMDkyZOxYsUKjBgxwhZv6bQkScI9XKuGiOiGjHUmzF17HC+vP4E6s4wRPUKw7tn+LCJ2zOIzI+Xl5Th37lzjz5mZmUhNTYWfnx8iIiIwd+5c5OTk4MsvvwRQf2lm0qRJeP/99xEfH4/8/HwAgIeHB3Q6jmBujhE9g/H5nkxsOVUAY52Jt6MREV1VaKjGM18dxqGLVyBJwEvDojF9EGdTtXcWnxk5ePAg4uLiEBcXBwCYPXs24uLiGm/TzcvLQ1ZWVuP2n3zyCerq6jBjxgyEhIQ0PmbOnNlCH8H1xIW3QpBWjTJjHXanF4uOQ0RkF1KzSzHyo904dPEKfDQqfP5EXzxzRySLiAO4pXlGbIXzjPze6z+cxJI9F/BgXBu8Oy5WdBwiIqFWH8zG39afQE2dGR0DvfHpxD5o39pLdCyX19Tvb65N46BGxoQCAH45mc+7aojIZdWazHjt+5P4y5pjqKkzY0iXIKx7NpFFxMGwjDiouHBftPH1QEWNCdvPFIqOQ0Rkc5fLjZj42f7G+UNm3tUJn0zoDR+Nm9hgZDGWEQclSVLj2ZHvj+YKTkNEZFsnc/W4/6M9SMm4DC93JRZN6I0/DY2CgvOHOCSWEQc2Mqb+Ft9tZwpRVl0rOA0RkW18fzQXD32cjJzSKrTz98S6Gf0xrBuXx3BkLCMOrGuIFh0CvGCsM2PL6QLRcYiIrMpkljHvp9N4YcURVNeaMSgqAN/NGICoIB/R0egWsYw4MEmSMLJn/aWaH45yAjQicl76ylpMXnoAi3ZmAACmD4rE50/0hc6T40OcAcuIg2sYN5J0tgillTWC0xARtbyMonI8uGAPks4WQeOmwAfj4zBneDTXl3EiLCMOrmOgN7qGaFFnlvHziXzRcYiIWtSu9CKMmr8HGcUVCNVpsGZ6Iu6/+o8wch4sI06Ad9UQkbORZRlL92TiiSUHYKiuQ68IX3z33AB0b8NlRJwRy4gTuK9n/V01KRmXUWioFpyGiOjW1NSZ8f/WncBrP5yCySxjdK82WPH0bQjw4WruzoplxAmE+3kiLsIXssyVfInIsZVU1GDCZ/uwYn8WJAn4f/dG478Px3BBUCfHMuIkGu+qOcYyQkSO6WxBGR6Yvxv7MkvgrVZh8cQ+ePp2LnTnClhGnMSIniGQJODQxSu4dKVSdBwiIotsPV2A0QuSkV1ShQg/T6x9NhF3dQkSHYtshGXESQRpNYhv7wcA2MCzI0TkIGRZxqKd5zH1y4MoN9Yhvr0f1s/oz4nMXAzLiBNpuKvmu1TeVUNE9q+61oQXVx/FvJ/OQJaB8f0isOzJePh5uYuORjbGMuJE7u0eAjelhFN5BpwtKBMdh4johgrLqvHop3ux9nAOlAoJr9/fDf/3YHe4q/i15Ir4/7oTaeXljjs6BwIA1h/JEZyGiOj6TubqMeqjPTicVQqtRoWlk/tiUmI7DlR1YSwjTmZUbBsA9ZdqzGZZcBoiomttPlWAMR+nIFdfjQ6tvbB+Rn8M7BQgOhYJxjLiZO7qEggftQo5pVU4cKFEdBwiIgD1A1UX78rA08sOoqrWhAEdW2Pds/3RIcBbdDSyAywjTkbjpsTwHsEAgPWpvFRDROLVmupnVP3nhtOQZeDR+AgsmcwVd+l/WEac0Ki4+ks1Px7LQ3WtSXAaInJl+qpaTF5yoHFG1ZdHdMG/RnWHm5JfP/Q/PBqc0G3t/RGi06Csug470gpFxyEiF5V1uRIPfZyM3eeK4emuxCcT+mDqwA4cqEq/wzLihBQKCffH1s85so531RCRAIculmDUgj04V1iOYK0Gq6YlYGhXzqhK18cy4qQevHqpZvuZIpRW1ghOQ0Su5LvUHIz/dB9KKmrQLVSL9TP6o3sbnehYZMdYRpxUdLAW0cE+qDGZsfF4vug4ROQCZFnGe1vOYubKVNTUmXF31yCsnp6AYJ1GdDSycywjTqzh7AgnQCMia6uuNeFP36TivS3pAIBpt3fAwsd7w9NdJTgZOQKWESd2f2woJAnYf6EE2SVcyZeIrONyuRGPL96H9am5UCkkzBvdA3Pv7QKFggNVqWlYRpxYiM4DCR38AQDfH+XieUTU8s4VlmHUgj04ePEKfDQqfDGlH8b3ixAdixwMy4iTa5hzZO3hS5BlTg9PRC0n+VwxHlyQjOySKkT4eWLds4no37G16FjkgFhGnNw93YOhVilwvqgCx3P0ouMQkZNYc+gSJn6+H2XVdejTthXWz+iPjoE+omORg2IZcXJajRvu7lY/Pfy3hy4JTkNEjk6WZby/JR1/Xn0UdWYZI2NCsXxqPPy83EVHIwfGMuICxvQOAwB8dzQXxjpOD09EzVNTZ8Zf1hzDu1vOAgCeuSMS74+LhcZNKTgZOTqWERcwoGNrBGs1KK2sxdbTnB6eiCxnqK7FlKUHsObQJSgk4F8Pdsdf74nmHTPUIlhGXIBSIWF0r/qBrGt4qYaILJRbWoWHP05pXGPms0l98Vh8W9GxyImwjLiIh65eqtl5tgiFhmrBaYjIUZzM1ePBBXuQVlCGQB81Vk1LwODoQNGxyMmwjLiIyABv9Irwhcksc/E8ImqSHWmFGLswBQUGI6KCvLGOa8yQlbCMuJAxvcMB1F+q4ZwjRHQzK/Zn4ckvDqKixoT+Hf2x5plEtPH1EB2LnBTLiAu5LyYEapUC6YXlOHaJc44Q0e+ZzTL+/fMZzF17HCazjId6hWHJE/2g1biJjkZOjGXEhWg1brine/2cIxzISkS/ZawzYdY3qViw4zwAYNaQTnj74Z5wV/GrgqyLR5iLaZxzJDUH1bWcc4SI6pVW1mDCZ/vx/dH6xe7+M6YnZg2JgiTx1l2yPpYRF5MY2RohOg0M1XXYcrpAdBwisgPZJZV46ONk7M8sgY9ahaWT++HhPuGiY5ELYRlxMUqFhId61Z8d4aUaIjqRo8foj5NxvqgCoToNVj+TgAGduNgd2RbLiAtqmHMk6WwRCjjnCJHL2pVehHGLUlBUZkR0sA/WzeiP6GCt6FjkglhGXFD71l7o07YVzDKw9jDnHCFyReuP5GDykgOoqDEhoYM/Vk1PQJBWIzoWuSiWERf1cJ/6syOrDmZzzhEiFyLLMhbuPI9Z36Q2rrq7dEpf3rpLQrGMuKj7eobCy12JzOIK7M0oER2HiGzAZJbx+g+n8OZPZwAAUwe0x/vjYqFWcdVdEotlxEV5qVW4PzYUALDyQJbgNERkbdW1Jjy/4jCWJl8AALw8ogtevq8rV90lu8Ay4sIe6RsBAPjpRD5KK2sEpyEia9FX1WLi5/ux8Xg+3JUKfDA+DlMHdhAdi6gRy4gL6xmmQ5cQLWrqzFw8j8hJ5emr8PDCX80hMqUv7o8JFR2L6BoWl5GkpCSMHDkSoaGhkCQJ69evv+n2eXl5ePTRRxEVFQWFQoFZs2Y1Myq1NEmSML5f/cRGK/dzICuRs0nLL8PoBck4W1COQB81vpmWgMRIziFC9sfiMlJRUYGYmBjMnz+/SdsbjUYEBATg5ZdfRkxMjMUByboeiG0DtUqBtIIyHMkuFR2HiFrIvozLeHhhMvL01egY6I21zyaiayjnECH7pLL0BcOHD8fw4cObvH27du3w/vvvAwA+//xzS9+OrEzn4YYRPUKw9kgOVu7PQq+IVqIjEdEt2ng8D7NWpqLGZEbvtq3w2aQ+8PV0Fx2L6IbscsyI0WiEwWC45kHW80i/+oGsPxzNQ1l1reA0RHQrlu7JxIyvD6PGZMbdXYPw1dR4FhGye3ZZRubNmwedTtf4CA/ngk3W1LddK0QGeKGq1oTvj+aKjkNEzWA2y3jzpzN47YdTkGXg8dsi8PHjvaFx4xwiZP/ssozMnTsXer2+8ZGdnS06klOTJKnxNt+V+7mviRxNrcmMv6w5hoU7zwMA/jKsM954oDuUnEOEHIRdlhG1Wg2tVnvNg6xrdK82cFNKOJ6jx4kcveg4RNREVTUmTFt2CN8evgSlQsK/x/TEjMEdIUksIuQ47LKMkO35e6txd7dgAMCK/ZyRlcgR6Ctr8fhn+7DtTCHUKgUWPd4bY/vwsjY5HovLSHl5OVJTU5GamgoAyMzMRGpqKrKy6r/A5s6di4kTJ17zmobty8vLUVRUhNTUVJw6derW01OLeuzqQNb1R3JQbqwTnIaIbiZfX42xi1Jw6OIVaDUqLJ8ajyFdg0THImoWi2/tPXjwIAYPHtz48+zZswEAkyZNwtKlS5GXl9dYTBrExcU1/u9Dhw7h66+/Rtu2bXHhwoVmxiZrSIj0R4cAL2QUVWDdkRxMuK2t6EhEdB3ni8ox8bP9yCmtQqCPGl8+2Q/RwbycTY5Lkh1g2k2DwQCdTge9Xs/xI1b2+e5M/OPHU+gc5IOfZw3kdWciO3PsUimeWHIAJRU1aN/aC19O6YdwP0/RsYiuq6nf3xwzQtd4qHcYNG71M7IeuHBFdBwi+pXd6cUY/8lelFTUoEcbHVZPT2ARIafAMkLX0Hm4YVRsGwDA8r0XBachogY/HsvF5KX7UVFjQv+O/ljx9G1o7a0WHYuoRbCM0O88fnWsyE8n8lBUZhSchoiWpVzA8yuOoNYkY0SPEHz+RF94qy0e8kdkt1hG6He6t9EhNtwXtSYZqw5yEjQiUWRZxrubz+Lv351snFX1g/FxUKs4qyo5F5YRuq6GO2m+3pcFk9nuxzgTOR2TWcbfvzuB97emAwBmDenEWVXJabGM0HWN6BkCX0835JRWYfuZQtFxiFyKsc6E51ccxvK9WZAk4I0HumHWkCje3UZOi2WErkvjpmycyXEZB7IS2Uy5sQ6TlxzAxuP5cFNK+HB8HCYktBMdi8iqWEbohh6Lr5+RNSm9CBcvVwhOQ+T8isuNGP/JXiSfvwwvdyWWPNEP9/UMFR2LyOpYRuiG2vp7YVBUAGSZt/kSWVt2SSUeXpiC4zl6+Hm5Y8XTt2FAp9aiYxHZBMsI3dTEhPqBrN8cyEYF16shsor0gjKMWZiMzOIKtPH1wJrpCegZ5is6FpHNsIzQTQ3uHIh2/p4wVNdh7eFLouMQOZ2j2aV4eFEKCgxGdAr0xrfPJKJDgLfoWEQ2xTJCN6VQSHgisR0AYEnyBZh5my9Ri0k+X4xHP92L0spaxIT7YtW0BATrNKJjEdkcywj9oTF9wuGjViGjqAJJ6UWi4xA5hV9O5uOJJQdQUWNCYqQ/vpoaj1Ze7qJjEQnBMkJ/yFutwsNXb/NdsueC2DBETmDt4Ut45qvDqKkz4+6uQZzenVweywg1yROJ7SBJwM6zRThXWC46DpHDWronE7NXHYXJLGN0rzZY8FgvaNw4vTu5NpYRapIIf08M6RIEAFianCk4DZHjkWUZ729Jx2s/nAJQX/DfHhMDlZJ/DRPxt4CabHL/dgCAbw/lQF9ZKzYMkQMxm2W88eNpvLvlLADgT0Oi8OrIrlBwnRkiACwjZIGEDv6IDvZBVa0J3xzMEh2HyCHUmcx46dtj+HxP/RnFV0d2xcwhnbjODNGvsIxQk0mS1Hh25Ivki6gzmcUGIrJz1bUmPPvVYaw5dAlKhYT/PhyDyf3bi45FZHdYRsgiD8S2Qaurq/luPlUgOg6R3So31uHJLw7gl1MFcFcq8PFjvfBQ7zDRsYjsEssIWUTjpsRj8fVTxH+6K0NwGiL7VFpZg8cW78Oec/UL3i2d3Bd3dwsWHYvIbrGMkMUmJraFu1KBw1mlOHihRHQcIrtSYKjG2EUpOJpdCl9PN3z11G1I7MgF74huhmWELBboo8HoXm0AAAt38uwIUYOsy5UYszAZZwvKEaRVY9W0BMSG+4qORWT3WEaoWZ66vQMkCdhyuoCToBEBSMuvX3k3u6QKbf09sWZ6IqKCfETHInIILCPULJEB3o2ToC3m2BFycYezrmDsohQUlhkRHeyD1dMSEO7nKToWkcNgGaFmm3Z7BwDA2sM5KCyrFpyGSIzd6cV4fPE+6KtqERfhi5VP34ZALVfeJbIEywg1W592fugV4YsakxlfJF8QHYfI5n4+kYcpSw+gssaEgZ1a46up8fD15Mq7RJZiGaFb8vTtkQCA5XuzUGGsE5yGyHZWH8zGs18dRo3JjOHdg7F4Uh94unPlXaLmYBmhWzK0axDat/aCvqoW3xzIFh2HyCY+252Jv6w5BrMMjO0Thg/Hx0Gt4sq7RM3FMkK3RKmQ8NTA+rEjn+3ORC2niCcnJssy3vklDW/8WL/y7tQB7fHWQz258i7RLeJvEN2y0b3aoLW3GjmlVfguNVd0HCKrMJtlvP7DKXyw7RwA4M93R+FvI7pwwTuiFsAyQrdM46bEUwPrF/9asP0cTGZZcCKillVrMuPF1Uex9OpA7Tce6Ibn7uTKu0QthWWEWsRjt7WFzsMNGcUV2Hg8T3QcohZTXWvCM8sPY92RHCgVEt4bF4sJCe1ExyJyKiwj1CK81SpMubo0+vzt52Dm2RFyAuXGOjyxZD+2nC6AWqXAJxN6Y1RcG9GxiJwOywi1mCcS28FbrcKZ/DJsPVMoOg7RLSmpqMGjn+7F3owSeKtV+GJKP9x1ddZhImpZLCPUYnSebpiQ0BYA8NG2dMgyz46QY8rXV2PcohQcu6RHK083fP1UPG7r4C86FpHTYhmhFvXkgPbQuClw9JIeu88Vi45DZLGLlyswZmEy0gvLEazVYPX0BPQM8xUdi8ipsYxQi2rtrcaj/erPjnx49RZIIkdxJt+AMQtTcOlKFdr5e2L19AR0DOTKu0TWxjJCLe7p2zvAXanA/swS7M8sER2HqEkOZ13BuEV7UXR15d1V07nyLpGtsIxQiwvWaTCmTxgA4L0tZwWnIfpjv155t1eEL755OgGBPlx5l8hWWEbIKp69IxJuSgnJ5y8j5fxl0XGIbujnE/nXrLy7fGo8dJ5uomMRuRSWEbKKsFaeeKRvBADgnc1pvLOG7FL9yruHuPIukWAsI2Q1MwZ3hLtKgQMXrmBXOu+sIfvyOVfeJbIbLCNkNcE6DR6Pr7+z5r+bz/LsCNkFWZbx7uaz+AdX3iWyG/ztI6t65o5IeLgpcTS7FNs4KysJ1rDy7vtb0wEALw7lyrtE9oBlhKwqwEeNiYlXz478cpZr1pAwdSYz/rLmWOPKu6/f3w3P38WVd4nsAcsIWd202yPh5a7EqTwDNp3MFx2HXFB1rQnPfnUY3x6+BKVCwjtjYzApsZ3oWER0FcsIWZ2flzumDKhf0ffdLWdh4tkRsqEKYx2e/OIAfjlVAHeVAh8/1guje4WJjkVEv2JxGUlKSsLIkSMRGhoKSZKwfv36P3zNjh070KtXL6jVanTs2BFLly5tRlRyZFMHdoBWo8LZgnKsO5IjOg65iNLKGjy2eB/2nLsML3cllk7ui7u7BYuORUS/YXEZqaioQExMDObPn9+k7TMzMzFixAgMHjwYqampmDVrFqZOnYpNmzZZHJYcl87DDc8O7ggA+O8vaaiuNQlORM6u0FCNcYv2IjW7FL6ebvjqqduQGNladCwiug5JvoX7LSVJwrp16zBq1KgbbvPXv/4VGzZswIkTJxqfe+SRR1BaWoqff/65Se9jMBig0+mg1+uh1WqbG5cEq6414c63dyBXX405w6MxfVCk6EjkpLJLKvHY4n3IKqlEoI8ay6fGIyqIC94R2VpTv7+tPmYkJSUFQ4YMuea5YcOGISUlxdpvTXZG46bE7Ls7AwAWbD+H0soawYnIGZ0tKMOYhcnIKqlEhJ8n1kxPZBEhsnNWLyP5+fkICgq65rmgoCAYDAZUVVVd9zVGoxEGg+GaBzmHB+PaIDrYB4bqOszffk50HHIyhy5ewcMLU1BgMKJzkA/WTE9AhD9X3iWyd3Z5N828efOg0+kaH+Hh4aIjUQtRKiTMGR4NAPgi+SKySyoFJyJnsSOtsHHl3bgIX3wz7TYEarnyLpEjsHoZCQ4ORkFBwTXPFRQUQKvVwsPD47qvmTt3LvR6feMjOzvb2jHJhgZFBSAx0h81JjPe2XxWdBxyAt+l5mDqFwdRVWvCoKgAfDU1Hr6e7qJjEVETWb2MJCQkYOvWrdc8t3nzZiQkJNzwNWq1Glqt9poHOQ9JkjB3eBcAwPrUHBy7VCo2EDm0JXsyMXNlKurMMh6IDeXKu0QOyOIyUl5ejtTUVKSmpgKov3U3NTUVWVlZAOrPakycOLFx++nTpyMjIwMvvfQSzpw5gwULFmDVqlX405/+1DKfgBxSjzAdHoxrA1kGXv/hFBfRI4vJsoz//pKG13+oX/DuicR2eHdsLNy44B2Rw7H4t/bgwYOIi4tDXFwcAGD27NmIi4vDK6+8AgDIy8trLCYA0L59e2zYsAGbN29GTEwM/vvf/2Lx4sUYNmxYC30EclR/vScaHm5KHLp4Bd8fzRUdhxyIySzjb+tP4MNt9YOg/3x3FF4d2RUKBdeZIXJEtzTPiK1wnhHn9dG2dLz9y1mE6DTY+uIgnl6nP2SsM2HWylT8dCIfkgT8c1R3PBbfVnQsIroOu5lnhOhmpg7sgLBWHsjTV2PhjvOi45CdKzfWYfKSA/jpRD7clQrMf7QXiwiRE2AZIaE0bkq8PKJ+MOuipAze6ks3VFxuxPhP9iL5fP06M0sm98W9PUJExyKiFsAyQsIN6xaMhA7+MNaZ8eZPZ0THITuUXVKJsQtTcDxHDz8vd6x4+jb078h1ZoicBcsICSdJEl4Z2RUKCdhwPA+704tFRyI7cibfgDELk5FRXIE2vh5YMz0BPcN8RcciohbEMkJ2oUuIFhMT2gEA/v7dCa7qSwCA5PPFePjj+undo4K88e0ziegQ4C06FhG1MJYRshuz745CoI8amcUVWMDBrC7vh6O5eOLzAygz1qFvu1ZYNS0BwTpO707kjFhGyG5oNW54dWQ3AMDCHedxvqhccCISZfGuDDy/4ghqTGYM7x6MZU9yenciZ8YyQnbl3h7BuKNzAGpMZvxt3XHOzOpizGYZb/x4Cv/ccBpA/ayqHz3aCxo3peBkRGRNLCNkVyRJwhsPdIfGTYG9GSVYezhHdCSyEWOdCc+vPILPdmcCAOYOj8arI7tCyVlViZweywjZnXA/T7xwVycAwL82nsaVihrBicja9FW1mPjZfmw4lgc3pYT3H4nFtEGRkCQWESJXwDJCdmnqgA6ICvJGSUUNXvvhpOg4ZEW5pVV4eGEy9mWWwFutwtLJ/fBAbBvRsYjIhlhGyC65qxT495gYKCTgu9RcbDqZLzoSWUFafhlGL0jG2YJyBPqo8c00TmZG5IpYRshuxYb7YtqgSADA39ad4OUaJ7MrvQhjPk5GvqEakQFeWPtsIrqF6kTHIiIBWEbIrs28qxM6BXqjuNzIyzVOZMX+LDyxpH4OkX7t/PDtM4kIa+UpOhYRCcIyQnZN46bEfx7m5RpnYTbLmLfxNOauPQ6TWcaDcW2wbGo/ziFC5OJYRsju/fpyzf9bexxFZUbBiag5qmpMeParw1iUlAEAmDWkE94ZGwO1inOIELk6lhFyCLOGdEJ0sA8uV9Tgz6uPwmzmZGiOpLCsGo98koKfT+bDXanAe+NiMWtIFG/dJSIALCPkINQqJT4YHwe1SoGdZ4uwNPmC6EjURGn5ZXhwfjKOXtKjlacblk+Nx6g43rpLRP/DMkIOIyrIBy/f1xUA8OZPZ3Aq1yA4Ef2RHWmFeOjjZOSUVqFDay+se7Y/+rX3Ex2LiOwMywg5lMfjIzCkSxBqTGbMXHkEVTUm0ZHoOmRZxidJ5zFl6QGUG+sQ394Pa59NRLvWXqKjEZEdYhkhhyJJEv49picCfdRILyzHq9+fEB2JfqO61oTZq47i/zaegVkGHukbzlV3ieimWEbI4fh5ueO9cbFQSMCqg5ewcn+W6Eh0VYGhGuM+2Yt1R3KgVEh4/f5umDe6B9xV/KuGiG6Mf0OQQ0rs2Bov3t0ZAPDK9ydx7FKp2ECE1OxSjPxwN45ml8LX0w3LpvTDpMR2vGOGiP4Qywg5rGcGRdaPH6kz45nlhzldvEBrD1/C2EUpKCwzIirIG9/PGIBErjFDRE3EMkIOS6GQ8N+xMWjr74mc0irM/CYVJs4/YlM1dWa89v1JzF51FDV1ZgzpEoS1z/ZHhD+ndieipmMZIYem83DDwsd7Q+OmQNLZIvxzwynRkVxGvr4a4z/d2zjny/N3dsQnE3rDW60SG4yIHA7LCDm8LiFa/PfhWADAkj0XsCzlgtA8riD5fDHu+3AXDl28Ah+NCosn9sGLd3eGQsHxIURkOZYRcgojeobgL8PqB7S+9sMp7DxbJDiRc5JlGR/vOI/HF+9DcXkNuoRo8ePzAzCka5DoaETkwFhGyGk8e0ckHuoVBpNZxnNfHUZafpnoSE5FX1mLacsO4a2f6+cPeahXGNY+k4i2/pzIjIhuDcsIOQ1JkjBvdA/0a++HMmMdJn2+H9kllaJjOYWDF0pw7we78MupArgrFfjXg93x9sM94eHOFXeJ6NaxjJBTcVcpsOjx3ugU6I18QzUmfLYPhWXVomM5LJNZxkfb0jHuk73IKa1CW39PrHkmAY/Ft+X8IUTUYlhGyOm08nLHsifjEdbKAxcuV2LiZ/uhr6oVHcvhFBiq8fjifXj7l7MwmWWMig3Fj88PQM8wX9HRiMjJsIyQUwrWabD8yXi09lbjTH4ZJn2+H4ZqFpKm2nyqAMPf34WUjMvwdFfi7Ydj8O64WPho3ERHIyInxDJCTqtday8se7IfdB5uSM0uxeOL90FfyUJyM4bqWry46iie+vIgSipq0C1Uix+eH4AxvcN4WYaIrIZlhJxalxAtVjx1G/y83HHskh7jP92LEk4bf12704txz7tJ+PbwJUgSMG1QB6x9NhGRAd6ioxGRk2MZIafXNbS+kLT2dsepPAMe+SQFefoq0bHsRmVNHV757gQe/2wfcvXVaOvvidXTEjB3eBeoVbxbhoisj2WEXELnYB+sfDoBQVo1zhaU48H5yTidZxAdS7htZwow9J0kfJlyEQAwMaEtfpo5EH3a+QlORkSuhGWEXEbHQG98+0xi422/Dy9Mwe70YtGxhCg0VGPGV4cxZelB5JRWoY2vB5Y92Q//eKA7PN25tgwR2RbLCLmUsFaeWDM9EfHt/VBurMMTS/bj892ZkGXXWO3XZJaxfO9F3PXOTmw4ngelQsLTt3fA5tm3Y2CnANHxiMhFSbID/C1sMBig0+mg1+uh1WpFxyEnYKwzYc63x7HuSA4AYGRMKN4c3QNeTrzibPL5Yvzjh1M4c3Wa/J5hOswb3QPdQnWCkxGRs2rq97fz/s1LdBNqlRLvjI1BzzAd/rXhNH44mou0fAM+GB+H6GDnKrxZlyvxr42nsOlkAQBAq1Fh9tAoTEhoByVX2SUiO8AzI+TyDlwowbNfHUZRmRHuSgX+NDQKT9/eweG/qIvKjPh4x3ks33sRNSYzlAoJj8VHYNaQKPh5uYuOR0QuoKnf3ywjRKj/4p679hi2nC4EAPRu2wpvPdQDHQN9BCez3JWKGixKysAXyRdQVWsCAAzs1Bp/v68rooIc7/MQkeNiGSGykCzLWH3wEv7x4ymUG+ugUkh4IrEdZg7p5BDToOfrq7E0+QKW772IcmMdACAm3BcvDo3CwE6tOYMqEdkcywhRM2WXVOL1H042niVp7a3GrCGdMLZPONxV9ncD2qlcAxbvysD3R3NRZ67/de4aosWLd0fhzuhAlhAiEoZlhOgWbU8rxD9+OIXM4goAQBtfDzw7OBIP9QqDxk3szKSVNXXYeDwfqw5kY/+Fksbn+7X3w1MDO+Cu6EAoHHzMCxE5PpYRohZQU2fG1/suYsGO8ygsMwIAfD3dMK5vOB7r1xYR/p42zbI34zI2Hs/Dj8fyGi/FKBUS7u0RgqcGtkfPMF+b5SEi+iMsI0QtqLrWhBX7s/DZ7kxcuvK/dW3iInwxsmcohnYNQrhfyxeT4nIj9mZcxrbThdhyugCG6rrGP2vr74mxfcLxUK8wBOs0Lf7eRES3imWEyApMZhnbzxTii5QL2H2uGL/+7Wnn74nEjq0RG+aLrqFaRAX5WDTGpMJYh7SCMpzKNeBUngEHMkuQXlh+zTatvd0xtGsw7o8JRXx7P16KISK7ZtUyMn/+fPznP/9Bfn4+YmJi8OGHH6Jfv37X3ba2thbz5s3DF198gZycHHTu3BlvvfUW7rnnnhb/MES2VGioxsbjedhwPA+Hs0phMl/7qyRJQKCPGqG+Hgjy0cDDXQmNmwJuSgWqa02orKl/5OurkauvQmll7XXfJzrYBwM6tsaw7sHoFdHK4ec/ISLXYbUy8s0332DixIlYuHAh4uPj8d5772H16tVIS0tDYGDg77b/61//iuXLl+PTTz9FdHQ0Nm3ahNmzZyM5ORlxcXEt+mGIRCmrrsXejBLsy7iMk7kGnMjVo+xXl1SaKsBHja4hWnQJ0SI2XIf49v5oxQnKiMhBWa2MxMfHo2/fvvjoo48AAGazGeHh4Xj++ecxZ86c320fGhqKv/3tb5gxY0bjcw899BA8PDywfPnyFv0wRPZClmUUl9cgT1+F3NIqFJUZUV1rRnWtCTUmMzRuSni4KeHprkSQVoNQXw+E+GqgdYD5TIiImsoqa9PU1NTg0KFDmDt3buNzCoUCQ4YMQUpKynVfYzQaodFcO7jOw8MDu3fvvuH7GI1GGI3Gxp8NBoMlMYmEkyQJAT5qBPioeYcLEdEfsGgGp+LiYphMJgQFBV3zfFBQEPLz86/7mmHDhuGdd95Beno6zGYzNm/ejLVr1yIvL++G7zNv3jzodLrGR3h4uCUxiYiIyIFYfTrJ999/H506dUJ0dDTc3d3x3HPPYfLkyVAobvzWc+fOhV6vb3xkZ2dbOyYREREJYlEZad26NZRKJQoKCq55vqCgAMHBwdd9TUBAANavX4+KigpcvHgRZ86cgbe3Nzp06HDD91Gr1dBqtdc8iIiIyDlZVEbc3d3Ru3dvbN26tfE5s9mMrVu3IiEh4aav1Wg0aNOmDerq6vDtt9/igQceaF5iIiIicioWDWAFgNmzZ2PSpEno06cP+vXrh/feew8VFRWYPHkyAGDixIlo06YN5s2bBwDYt28fcnJyEBsbi5ycHLz22mswm8146aWXWvaTEBERkUOyuIyMGzcORUVFeOWVV5Cfn4/Y2Fj8/PPPjYNas7KyrhkPUl1djZdffhkZGRnw9vbGvffei2XLlsHX17fFPgQRERE5Lk4HT0RERFbR1O9vq99NQ0RERHQzLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQklMXzjIjQcPcxV+8lIiJyHA3f2380i4hDlJGysjIA4Oq9REREDqisrAw6ne6Gf+4Qk56ZzWbk5ubCx8cHkiS12H/XYDAgPDwc2dnZnEytCbi/mo77qum4r5qO+6rpuK+azpr7SpZllJWVITQ09JrZ2X/LIc6MKBQKhIWFWe2/z5WBLcP91XTcV03HfdV03FdNx33VdNbaVzc7I9KAA1iJiIhIKJYRIiIiEsqly4harcarr74KtVotOopD4P5qOu6rpuO+ajruq6bjvmo6e9hXDjGAlYiIiJyXS58ZISIiIvFYRoiIiEgolhEiIiISimWEiIiIhHLqMpKUlISRI0ciNDQUkiRh/fr1f/iaHTt2oFevXlCr1ejYsSOWLl1q9Zz2wNJ9tWPHDkiS9LtHfn6+bQILNG/ePPTt2xc+Pj4IDAzEqFGjkJaW9oevW716NaKjo6HRaNCjRw9s3LjRBmnFas6+Wrp06e+OK41GY6PE4nz88cfo2bNn48RTCQkJ+Omnn276Glc8pgDL95WrHlPX8+abb0KSJMyaNeum29n62HLqMlJRUYGYmBjMnz+/SdtnZmZixIgRGDx4MFJTUzFr1ixMnToVmzZtsnJS8SzdVw3S0tKQl5fX+AgMDLRSQvuxc+dOzJgxA3v37sXmzZtRW1uLu+++GxUVFTd8TXJyMsaPH48nn3wSR44cwahRozBq1CicOHHChsltrzn7CqifCfLXx9XFixdtlFicsLAwvPnmmzh06BAOHjyIO++8Ew888ABOnjx53e1d9ZgCLN9XgGseU7914MABLFq0CD179rzpdkKOLdlFAJDXrVt3021eeukluVu3btc8N27cOHnYsGFWTGZ/mrKvtm/fLgOQr1y5YpNM9qywsFAGIO/cufOG24wdO1YeMWLENc/Fx8fL06ZNs3Y8u9KUfbVkyRJZp9PZLpQda9Wqlbx48eLr/hmPqWvdbF/xmJLlsrIyuVOnTvLmzZvlQYMGyTNnzrzhtiKOLac+M2KplJQUDBky5Jrnhg0bhpSUFEGJ7F9sbCxCQkIwdOhQ7NmzR3QcIfR6PQDAz8/vhtvw2KrXlH0FAOXl5Wjbti3Cw8P/8F+8zshkMmHlypWoqKhAQkLCdbfhMVWvKfsK4DE1Y8YMjBgx4nfHzPWIOLYcYqE8W8nPz0dQUNA1zwUFBcFgMKCqqgoeHh6CktmfkJAQLFy4EH369IHRaMTixYtxxx13YN++fejVq5foeDZjNpsxa9Ys9O/fH927d7/hdjc6tlxhjE2Dpu6rzp074/PPP0fPnj2h1+vx9ttvIzExESdPnrTqgpn24Pjx40hISEB1dTW8vb2xbt06dO3a9brbuvoxZcm+cuVjCgBWrlyJw4cP48CBA03aXsSxxTJCzdK5c2d07ty58efExEScP38e7777LpYtWyYwmW3NmDEDJ06cwO7du0VHsXtN3VcJCQnX/As3MTERXbp0waJFi/DGG29YO6ZQnTt3RmpqKvR6PdasWYNJkyZh586dN/ySdWWW7CtXPqays7Mxc+ZMbN682a4H7bKM/EpwcDAKCgquea6goABarZZnRZqgX79+LvWl/Nxzz+HHH39EUlLSH/7r6kbHVnBwsDUj2g1L9tVvubm5IS4uDufOnbNSOvvh7u6Ojh07AgB69+6NAwcO4P3338eiRYt+t62rH1OW7KvfcqVj6tChQygsLLzmjLXJZEJSUhI++ugjGI1GKJXKa14j4tjimJFfSUhIwNatW695bvPmzTe9Dkn/k5qaipCQENExrE6WZTz33HNYt24dtm3bhvbt2//ha1z12GrOvvotk8mE48ePu8Sx9VtmsxlGo/G6f+aqx9SN3Gxf/ZYrHVN33XUXjh8/jtTU1MZHnz598NhjjyE1NfV3RQQQdGxZbWisHSgrK5OPHDkiHzlyRAYgv/POO/KRI0fkixcvyrIsy3PmzJEnTJjQuH1GRobs6ekp/+Uvf5FPnz4tz58/X1YqlfLPP/8s6iPYjKX76t1335XXr18vp6eny8ePH5dnzpwpKxQKecuWLaI+gs0888wzsk6nk3fs2CHn5eU1PiorKxu3mTBhgjxnzpzGn/fs2SOrVCr57bfflk+fPi2/+uqrspubm3z8+HERH8FmmrOvXn/9dXnTpk3y+fPn5UOHDsmPPPKIrNFo5JMnT4r4CDYzZ84ceefOnXJmZqZ87Ngxec6cObIkSfIvv/wiyzKPqV+zdF+56jF1I7+9m8Yeji2nLiMNt5/+9jFp0iRZlmV50qRJ8qBBg373mtjYWNnd3V3u0KGDvGTJEpvnFsHSffXWW2/JkZGRskajkf38/OQ77rhD3rZtm5jwNna9/QTgmmNl0KBBjfuuwapVq+SoqCjZ3d1d7tatm7xhwwbbBhegOftq1qxZckREhOzu7i4HBQXJ9957r3z48GHbh7exKVOmyG3btpXd3d3lgIAA+a677mr8cpVlHlO/Zum+ctVj6kZ+W0bs4diSZFmWrXfehYiIiOjmOGaEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiIS6v8DYaGFK+AV0FsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use the parameters reported in the paper for eth.\n",
    "coin_strikes = np.linspace(1000,2000,num=1000)\n",
    "coin_forward_price = 1600\n",
    "alpha = 0.42\n",
    "beta = 0.5\n",
    "rho = 0.087\n",
    "nu = 2.8\n",
    "y= [SABR(alpha,beta, rho, nu,coin_forward_price,k,model.time) for k in coin_strikes]\n",
    "print(y)\n",
    "\n",
    "plt.plot(coin_strikes, y)\n",
    "plt.show()\n",
    "\n",
    "# Use the parameters reported in the paper for lido.\n",
    "coin_strikes = np.linspace(1,4,num=1000)\n",
    "coin_forward_price = 2\n",
    "y= [SABR(2.6*alpha,beta, rho, nu,coin_forward_price,k,model.time) for k in coin_strikes]\n",
    "print(y)\n",
    "\n",
    "plt.plot(coin_strikes, y)\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.10.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}