{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MDAnalysis PCA Tutorial\n",
    "Author: [Kathleen Clark](https://becksteinlab.physics.asu.edu/people/75/kathleen-clark) ([@kaceyreidy](https://github.com/kaceyreidy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Principal component analysis (PCA) is a method of converting one corrdinate system into another where the data as represented by the resulting coordinate system is uncorrelated. The resulting coordinates are ordered such that the first principal component (coordinate axis) accounts for the most variation in the data, the second prinicpal component accounts for the most variation that it can while being perpendicular to the first, and so on. ([Wikipedia](https://en.wikipedia.org/wiki/Principal_component_analysis))\n",
    "\n",
    "In this tutorial we use [MDAnalysis](https://mdanalysis.org) to show how to use PCA to analyze and visualize large macromolecular conformational changes. As example we use the closed -> open transition of the enzyme adenylate kinase (AdK). The AdK trajectory is included with the MDAnalysis test data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conducting PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's import all of the necessary modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "import MDAnalysis as mda\n",
    "import MDAnalysis.analysis.pca as pca\n",
    "from MDAnalysis.coordinates.base import Timestep\n",
    "from MDAnalysisTests.datafiles import PSF, DCD\n",
    "\n",
    "import numpy as np\n",
    "import os\n",
    "import glob\n",
    "\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm\n",
    "import matplotlib.ticker as ticker\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's define our paths and some our analysis preferences.\n",
    "\n",
    "- save data in the _PCA_tutorial_ directory\n",
    "- use the protein backbone atoms for the analysis (selection \"backbone\")\n",
    "- analyze every step in the trajectory\n",
    "- visualize the first 5 principal components (`npc = 5`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "datapath = os.path.join('PCA_tutorial', 'AdK')\n",
    "selection = 'backbone'\n",
    "stepsize = 1\n",
    "npc = 5\n",
    "\n",
    "\n",
    "os.makedirs(datapath, exist_ok=True)\n",
    "for dirname in ('pcs', 'variances', 'cumulative_variances', \n",
    "                'mean_atoms', 'transforms', \n",
    "                os.path.join('trajectories', 'PC'),\n",
    "                'images'):\n",
    "    os.makedirs(os.path.join(datapath, dirname), exist_ok=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make a universe object of our trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = mda.Universe(PSF, DCD)\n",
    "ag = u.select_atoms(selection)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's conduct principal component analysis of the trajectory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[pca.PCA](http://www.mdanalysis.org/mdanalysis/documentation_pages/analysis/pca.html#pca-tutorial) creates a pca object which has all of the properties that we will need to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Mean Calculation Step   98/98 [100.0%]\n",
      "Step    98/98 [100.0%]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<MDAnalysis.analysis.pca.PCA at 0x11b89c860>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc = pca.PCA(u, select=selection, align=True, verbose=True, step=stepsize)\n",
    "pc.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PCA object computes the eigenvectors of the corrdinate matrix in our protein universe (using numpy.linalg.eig); this calculation may take a few seconds. Let's save these principal component vectors themselves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "pc_pc = pc.p_components\n",
    "np.save(os.path.join(datapath, 'pcs', 'pcomponents.npy'), pc_pc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We should also save the variance and cumulative variance data for later analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The corresponding eigenvalue to each of these eigenvectors is equivalent to that eigenvector's variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "pc_vars = pc.variance\n",
    "np.save(os.path.join(datapath,'variances', 'vars.npy'), pc_vars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cumulative variance of one of the prinicipal components is the variance or eigenvalue associated with that component summed with all of the preceding variances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much of the total variance is capture by the first `npc` PCs?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9995688529548218"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc.cumulated_variance[npc]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Save the data for later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "pc_cvars = pc.cumulated_variance\n",
    "np.save(os.path.join(datapath, 'cumulative_variances',\n",
    "                     'cumulativevars.npy'), pc_cvars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's save the average position of the atoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/oliver/anaconda3/envs/mda3/lib/python3.6/site-packages/MDAnalysis/coordinates/PDB.py:892: UserWarning: Found no information for attr: 'altLocs' Using default value of ' '\n",
      "  \"\".format(attrname, default))\n",
      "/Users/oliver/anaconda3/envs/mda3/lib/python3.6/site-packages/MDAnalysis/coordinates/PDB.py:892: UserWarning: Found no information for attr: 'icodes' Using default value of ' '\n",
      "  \"\".format(attrname, default))\n",
      "/Users/oliver/anaconda3/envs/mda3/lib/python3.6/site-packages/MDAnalysis/coordinates/PDB.py:892: UserWarning: Found no information for attr: 'occupancies' Using default value of '1.0'\n",
      "  \"\".format(attrname, default))\n",
      "/Users/oliver/anaconda3/envs/mda3/lib/python3.6/site-packages/MDAnalysis/coordinates/PDB.py:892: UserWarning: Found no information for attr: 'tempfactors' Using default value of '0.0'\n",
      "  \"\".format(attrname, default))\n"
     ]
    }
   ],
   "source": [
    "pc_ma = pc.mean_atoms\n",
    "pc_ma.write(os.path.join(datapath, 'mean_atoms' , 'meanatoms.pdb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating projections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now convert our original simulation data into the principal component coordinate system to view it in a new way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we need to project the original projectory onto the principal components and store the projected data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Y(t)=\\sum_{i=0}^{m}((X(t)-\\overline X) \\cdot u_i)u_i+\\overline X$ where\n",
    "\n",
    "$Y(t)$ is the projected trajectory,\n",
    "\n",
    "$X(t)$ is the original trajectory,\n",
    "\n",
    "$u_i$ is the principal component $i$, and\n",
    "\n",
    "$\\overline X$ is the coordinates of the average structure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`pca.transform()` computes the weights $w_i(t) = (X(t)-\\overline X) \\cdot u_i$ for each principal component $i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "pc_transform = pc.transform(ag, n_components=npc)\n",
    "np.save(os.path.join(datapath, 'transforms', str(npc)+'components.npy'), pc_transform)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analyzing Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's load our newly projected data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "tpcs = np.load(os.path.join(datapath, 'transforms', \n",
    "                            str(npc)+'components.npy'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to store this data into a more usable format, a pandas DataFrame, so we need to make a list of the columns we want to have."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns=[]\n",
    "for i in range(npc):\n",
    "    columns.append('PC'+str(i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's put our data into a DataFrame and set the index to be an indicator of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(tpcs, columns=columns)\n",
    "df['time']=df.index\n",
    "df = df.reset_index(drop=True)\n",
    "cols = df.columns.tolist()\n",
    "cols = cols[-1:] + cols[:-1]\n",
    "df = df[cols]\n",
    "df = df[::stepsize]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can use seaborn's PairGrid function to create a grid of principal component graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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KXRF+JElr7bwk522y76Mbra9N8vZJ+OjTJ+Gcvcq1+BnXYuK4lhu4Dj+vW69HN9bVjTUl3VtXL+nXa+h79bZe/J5q7k7d+B3V9PS6rZ5kgmrqint+AAAAAEyWbrnnBwAAAMCkEH4AAAAAfU34AQAAAPQ14QcAAADQ14QfAAAAQF8TfgAAAAB9TfgBAAAA9DXhBwAAANDXhB8AAABAXxN+AAAAAH1N+AEAAAD0NeEHAAAA0NeEHwAAAEBfE34AAAAAfa2vw4+FCxe2JBbLRCxTRt9aJnCZEnrWMoHLlNG3lglapoyetUzgMiX0rGUClwnR1+HHQw891OkS4FnTt/QaPUsv0rf0Gj1Lr9GzdJu+Dj8AAAAAhB8AAABAXxN+AAAAAH1N+AEAAAD0NeEHAAAA0NeEHwAAAEBfE37Q84bWrsmqR3+aC8/+XNauXrXZY9asXp1zvvSFrFm9eoqrAwAAoNOEH/S8e763NN8896s56//9s1z+ta8mSdasXpUrLz0/Q2vXZGhobc7/l6/m9L/881x/1RVPev/q1atz1plnZrVgBAAAoC8NdroAeC7Wrl6Vq879St54wknZcbc98/L5u2XGjIEcvuidGRkezqWLv5JHfvLjvHjrbbLyhw/kiGPfkhe/ZOu8/o2H5tFHf5obrrkmhx5+RNa3ln8+55/yl3/xyVQlJ518Sqe/GgAAABNM+EFPGVqzKg/fd2/u+NZ1+dY3LsgbFv5Sbr/+yux76NE59h3vycjwcK67/JK88djjc+uS67LLK/fIjjvvmm9dd3XeeMTRueP2W/PDB+7Pfq87MEtvvy0PPrgyC497c5LKCYtO7PTXAwAAYBKY9kJPGFqzKnfddmOWXvONvGDetnnDwl/KL//Wf8rVF5yTz/z338/l/3xmkuTGKy7J3gten9uWXJfXH3ZUZs+Zm+dt9fwcetTCDAwOZrdX7pFD3nRELrrgvHz6r/8yrz/wwHxryZK87e1vzxZbbNHhbwkAAMBk6OjIj6q6O8mjSdYlGW2tLRjb/++TfCDJaJJzW2v/eWz/h5K8d+z4322tXdiJupkaQ2tW5c5rv549Dz4m15375dxy+QU57c8/l6sWn5WbLr8w7/iPf5xD3vK2VJKD3/K2JMlr33BYbrrmmzngsKMyc9asJ51z9pw5SZK3nvjLqZqRmbNm5ahjjpnKrwUAAMAU64ZpL4e31h56fKOqDk+yKMlrWmtDVfXSsf17JjkpyV5JXp7kkqravbW2rhNFM7lGR4az5NwvZ/UjP0prLfsduShJpapy0PHvSNWMbP3yHTJ77pY58u2nPvG+OVtsmQOPPO5pz7/FFlvkHe7vAQAAMC1047SX307yp621oSRprT04tn9Rki+11oZaa3clWZbkgA7VyCQaHRnOHVdemH2OXJRtdnplXnXgEVl+87U5aNG7MnPW7Myeu2Xe9LZTM3vulp0uFQAAgB7Q6fCjJbmoqm6sqtPG9u2e5I1VdV1VXV5Vrxvbv12Sezd674qxfT+nqk6rqiVVtWTlypWTWjwTa3jNqqy4fUnuvOrC7LzvQbnrpquz5xuPzewttsxr3vSWDM588jSWfqFv6TV6ll6kb+k1epZeo2fpZp0OPw5ure2X5Lgk76+qQ7NhKs6LkhyY5A+SnF1VlaQ28/72pB2tnd5aW9BaWzBv3rxJLJ2JNDoynJvOPyuXfeZPssuCQ3P3zddkj0OO7evAY2P6ll6jZ+lF+pZeo2fpNXqWbtbRe3601u4b+/lgVZ2TDdNYViT5p9ZaS3J9Va1PsvXY/h02evv2Se6b4pKZACNrVuWe6y/L/IOOzcBYuLHs6guz1xEnJqkMzJyVvQ47vrNFAgAA0Dc6NvKjqrasqq0eX09yTJLbkvxzkiPG9u+eZFaSh5IsTnJSVc2uqp2S7Jbk+k7UznMzsmZVfrj0htxz/aV5+T5vyPevPj+joyMZGVqT+fsfmntvvib7vfVXMnP23E6XCgAAQB/p5MiPbZKcs2FGSwaTnNlau6CqZiX5+6q6LclwklPHRoHcXlVnJ1maDY/Afb8nvfSW7150VpZf8bUc9/EvZfm1F2b7fQ7Og3felAe+e0u+e8W5eeN7/2jaTHMBAABg6nQs/GitLU+yz2b2Dyd59y94z8eTfHySS2MSjA6tya5Hvn3DRlV2Pui43Pq1z+X7V56X4//bZ5OqzNt5j84WCQAAQF/q6D0/mD6+e8EXc/eV/5r9f+0jGZw1O0my18KTU7XhHh/7nfjrHa4QAACAfiX8YErsdszJSSUv3mnPJ/bNmrtlXnvieztYFQAAANOB8IMpMXPultnzhN/odBkAAABMQx172gv9b2TNqvzgisUZWfNYvrP4MxlZs6rTJQEAADANGfnBpFl+8VkZemRlVv/ogXz77z+WJHmV0R8AAABMMeEHk2bno0/O/Tdemm33PyJVM7LL0Sd3uiQAAACmIeEHk2J0zao8cOMl2e71x2Vg5iwjPgAAAOgY9/xgUtx1yZm5/n//TpZf8LlOlwIAAMA0Z+QHE2Z0zarcc8kXs+Oxp2ano05JUtnpKFNdAAAA6CwjP5gw91zyxdx31eKsH16bB268JDsvfE8G527Z6bIAAACY5oQfjNvo0OqMrn4sOxz+zux56kdzz9e/nCX/+7dz1wVndLo0AAAAMO2F8Xts+W358XdvzA+v/Vr2/M1PZP5R70pSmX/UKZ0uDQAAAIQfPHvrhlanrV+Xtn5dfvTtb+QlrzsmW+7wytTAQLbYZscMzt0yu771fZ0uEwAAAJKY9sJzsOquW7Pq7tvywKVn5o6//M08fMNFmfm8F2T+8adlcO7zOl0eAAAA/BwjP3jWttxp77T167LFjnsmMwbykv2P6nRJAAAA8AsJP3jWBmZv8cT6Dsf/ZgcrAQAAgKdn2gvP2Lq1j+WB8/4m69Y+1ulSAAAA4BkTfvCMrbzsC7n3cx/Jysu+0OlSAAAA4Bkz7YVnbN4R7/65nwAAANALOjryo6rurqpbq+qmqlqyyWv/qapaVW09tl1V9VdVtayqbqmq/TpT9fS0bu1jeeRbF+elR/9aBuZ4ogsAAAC9oxumvRzeWntta23B4zuqaockRye5Z6Pjjkuy29hyWpJPT2mV09C6tY/l4fM/nfWjw3nosi/k7r96X1Ze/NlOlwUAAADPSjeEH5vzyST/OUnbaN+iJJ9rG1yb5IVVtW1HqpsmfvL1z+eRa/85bWQoLznspGz3nv+RrU15AQAAoMd0+p4fLclFVdWS/G1r7fSqOiHJv7XWbq6qjY/dLsm9G22vGNt3/5RVO8288PBfyZyd98uPvv7FPHLtOXnZuz5mygsAAAA9p9Phx8Gttfuq6qVJLq6q7yT5cJJjNnNsbWZfe9JBVadlw7SY7LjjjhNZ67QzMOd52fKVr8+cV+yVJJk79pOJp2/pNXqWXqRv6TV6ll6jZ+lmHZ320lq7b+zng0nOSXJYkp2S3FxVdyfZPsm3qupl2TDSY4eN3r59kvs2c87TW2sLWmsL5s2bN8nfYHoYmPO8zHvzbxn1MYn0Lb1Gz9KL9C29Rs/Sa/Qs3axj4UdVbVlVWz2+ng2jPW5orb20tTa/tTY/GwKP/VprDyRZnOQ9Y099OTDJI601U14myfq1j+XH538669c+1ulSAAAAYFw6Oe1lmyTnjN3XYzDJma21C57i+POSvDnJsiSrk/zapFc4Ta0fGcpPLjsjD33xI0mSFx332x2uCAAAAJ67joUfrbXlSfZ5mmPmb7Tekrx/kssiyaobz83zD35HkuQFh/9Kh6sBAACA8enWR93SQVu+9pisueOKvPDo38gM9/kAAACgxwk/eML6tY/lkQv+b1IzstWBv5wZM2d3uiQAAAAYN+EHT3j0G5/LT774R3ns62d0uhQAAACYMJ284SldZP3Q6mz1xlNSSZ73Jvf5AAAAoH8IP6a59Wsfy+g9t2Zo+bez9vp/yvNP+h/u8wEAAEBfEX5Mc2suPyNrrzsnL/r9rySVzNzx1Z0uCQAAACaU8GMaWz+0OnMPeVeSSgZnZatjf6fTJQEAAMCEc8PTaWztN/4hP/k/b8vMnfbLjNlbdLocAAAAmBRGfkxT64dWZ84hpyRJBk11AQAAoI8Z+TFNrb38jDzyF+/I4M77ucEpAAAAfc3Ij2lm/drHMnzLxZlz6IbH2Q7uYNQHAAAA/c3Ij2lm7RVfyKOnvy/Dt1ycLY75baM+AAAA6HtGfkwj64dWZ85BJyVJZr3m6A5XAwAAAFPDyI9pZO0Vn88jf31KBnfa14gPAAAApg0jP6aJjUd9DG6/V4erAQAAgKlj5Mc0sfaKL+Snf31KBucb9QEAAMD0YuRHn1u/dlWGb70kcw45JalkcPs9O10SAAAATCkjP/rc2qvOzGN//zsZvvWybHHkaUZ9AAAAMO0Y+dHH2tCazHnDO5Iks/Y+ssPVAAAAQGd0dORHVd1dVbdW1U1VtWRs3yeq6jtVdUtVnVNVL9zo+A9V1bKqurOqju1c5b1h7VVfzKP/9z2ZOf+1mTFny06XAwAAAB0x7pEfVfWCJAuTbJekJbkvyYWttZ88w1Mc3lp7aKPti5N8qLU2WlV/luRDSf6wqvZMclKSvZK8PMklVbV7a23deL9DP2pDazL7wLcnSQa3c58PAAAApq9xjfyoqvck+VaSNyXZIsmWSQ5PcuPYa89aa+2i1tro2Oa1SbYfW1+U5EuttaHW2l1JliU5YBzl97W1V5+ZRz/9qxl8xT4poz4AAACYxsY78uPDSfbfdJRHVb0oyXVJPvc0729JLqqqluRvW2unb/L6ryf58tj6dtkQhjxuxdg+NtKGVmX4tssy5w3vTGLUBwAAAIz3nh+VDQHGptaPvfZ0Dm6t7ZfkuCTvr6pDnzhx1YeTjCb54kaftaknfXZVnVZVS6pqycqVK59BCf2jjQ5n7VVn5bEzfjfDS7+euYe/16iPHjGd+5bepGfpRfqWXqNn6TV6lm423vDj40m+VVWfrqo/Glv+Jhumwnz86d7cWrtv7OeDSc7J2DSWqjo1yfFJ3tVaezzgWJFkh43evn023F9k03Oe3lpb0FpbMG/evHF8td4zfOtFmf26E7PFiR/OrL2O6HQ5PAvTuW/pTXqWXqRv6TV6ll6jZ+lm4wo/WmtnJFmQ5PIkQ0mGk3wjyYLW2j881Xurasuq2urx9STHJLmtqhYm+cMkJ7TWVm/0lsVJTqqq2VW1U5Ldklw/nvr7zaw9D8/Ismsz59D3pGYb8QEAAADJOO/5UVW7JtmmtfalTfa/sarua619/ynevk2Sc6rq8TrObK1dUFXLksxOcvHYa9e21n6rtXZ7VZ2dZGk2TId5vye9/EwbWpXhpd/IrL2PSQ3O6nQ5AAAA0DXGe8PTv0jyR5vZv2bstbf+oje21pYn2Wcz+3d9ivd8PM9gOs10tPa6f8yaf/mfWb/ojzL30F/tdDkAAADQNcYbfsxvrd2y6c7W2pKqmj/Oc/MszHn923/uJwAAALDBeG94OucpXps7znPzDLShVVn7zTOSmpG5h/6qe30AAADAJsYbftxQVe/bdGdVvTfJjeM8N0+jjQ5n6Nqzs2bxn2To2rM7XQ4AAAB0pfFOe/l/suGmpe/Kz8KOBUlmJfmlcZ6bpzF82yWZtf8JSSqzX/+2TpcDAAAAXWlc4Udr7YdJDqqqw5O8emz3ua21y8ZdGU+pDa/JzFcekpE7r8zsg0/xhBcAAAD4Bcb7qNs5SX4rya5Jbk3yd6210YkojKc2dP0/ZviWCzP3zf9J8AEAAABPYbzTXs5IMpLkiiTHJdkjG6bCMEna0OoM3/nNzH7dv0tSGdx2906XBAAAAF1tvOHHnq21vZOkqv4uyfXjL4mnMrTkn7L23E8kJ/1Z5hzyK50uBwAAALreeMOPkcdXWmujVTXO0/F0Zi/45STJrFce2uFKAAAAoDeMN/zYp6p+OrZeSeaObVeS1lp7/jjPz0Y2THm5IrNf/w73+QAAAIBnaMZ43txaG2itPX9s2aq1NrjRuuBjgg3deE7WnP2hDF3/lU6XAgAAAD1jvCM/mCJteG1m7fvWJMns/U/scDUAAADQO8Y18oOpM7zkn7L687+bwe32Ss3eotNdidDjAAAgAElEQVTlAAAAQM8w8qPLtaHVGfnulZm1/6IkycDLPNoWAAAAng0jP7pYGx3O8Lf+OWu++pGMfPeqzD7oFKM+AAAA4Fky8qNLtdHhjNzxjcx8zcIkyczdD+lwRQAAANCbhB9dauQ738zgzgsyunxJZr3ubR5tCwAAAM+RaS9daubuB2X07m9l5h5vEnwAAADAOAg/ukwbXp2h685OakZm7XWU4AMAAADGqaPhR1XdXVW3VtVNVbVkbN+Lq+riqvre2M8Xje2vqvqrqlpWVbdU1X6drH2yDH/7axm65K8z/O3FnS4FAAAA+kI33PPj8NbaQxttfzDJpa21P62qD45t/2GS45LsNra8Psmnx372jTayNrP2OS6pZNZrj+90OQAAANAXunHay6IkZ4ytn5HkxI32f65tcG2SF1bVtp0ocLKMfPtfs/rsP8zAy/dIzfJIWwAAAJgInR750ZJcVFUtyd+21k5Psk1r7f4kaa3dX1UvHTt2uyT3bvTeFWP77p/KgifTzNe+Jalk4KW7dLoUAAAA6BudDj8Obq3dNxZwXFxV33mKY2sz+9qTDqo6LclpSbLjjjtOTJVToA2vyeiyazNz3xNTgzM7XQ5TrFf7lulLz9KL9C29Rs/Sa/Qs3ayj015aa/eN/XwwyTlJDkjyw8ens4z9fHDs8BVJdtjo7dsnuW8z5zy9tbagtbZg3rx5k1n+hGjDazK64taM3Hxu1v7r/8jITf/S6ZLogF7rW9Cz9CJ9S6/Rs/QaPUs361j4UVVbVtVWj68nOSbJbUkWJzl17LBTkzyeBixO8p6xp74cmOSRx6fH9LKRW87N0DdOz8y9j83sI38nM1/zlk6XBAAAAH2lk9NetklyTlU9XseZrbULquqGJGdX1XuT3JPk7WPHn5fkzUmWJVmd5NemvuSJtyHsqGRgVmYteFunywEAAIC+07Hwo7W2PMk+m9n/cJIjN7O/JXn/FJQ2Zdrwmox+/7rMfO0J7vMBAAAAk6QbH3U7bYzccn6Gzv2fGbn5XztdCgAAAPStTj/tZdppw2uy7q7rM7Dz6zPz1cckSWbufVyHqwIAAID+JfyYYqO3XZC25pGsf/ThjH7visw69DdSs+Z2uiwAAADoW8KPKTb46oUbRn7s9LqkKgPzdu50SQAAANDXhB9TaMOUlxsysMtBqcGZmbX/L3W6JAAAAOh7bng6RdroSEZvuzBDF34io7ee1+lyAAAAYNow8mOSteE1Wf/w3WmPPpTBV70pqWRwr2M6XRYAAABMG0Z+TLLROy7JyNVnZOAV+2bdilszuPdb3OAUAAAAppCRH5OojQ5l8FWHb9iYMTODu7+xswUBAADANCT8mESjt1+cdd+/KjPf8J7UzNmdLgcAAACmJeHHJBrc88gkyYyt53e2EAAAAJjGhB+TqGbOzcx9ju90GQAAADCtueHpJGgjazJyy7lpI2s6XQoAAABMe8KPCdbWjWR06aUZveaMjN5xWafLAQAAgGnPtJcJ1NaNZN3d1214qkslg3sc0emSAAAAYNoTfkygdXcvycDL9866+27L4F7HpgZmdrokAAAAmPZMe5lAAzvum3X3Lc3A/AMEHwAAANAlhB8ToI2szejtFyRVGdzlDYIPAAAA6CLCj3Fq60ay7s6vZ/T6L2bdnV/vdDkAAADAJtzzY5zW/eDGDOxycJJkYPc3dbYYAAAA4Ek6PvKjqgaq6ttV9bWx7SOr6ltVdVNVXVlVu47tn11VX66qZVV1XVXN72TdSdJGhzKw3d5Z98DSDOxxVGrmnE6XBAAAAGyi4+FHkv+Q5I6Ntj+d5F2ttdcmOTPJR8b2vzfJj1truyb5ZJI/m9IqN2Pdd7+Rkcs+mdryJe7zAQAAAF2qo+FHVW2f5C1JPrPR7pbk+WPrL0hy39j6oiRnjK1/JcmRVVVTUeem2sjajN59XQZ2Oywz5h+QGS/aoRNlAAAAAM9Ap0d+/EWS/5xk/Ub7fiPJeVW1IsmvJPnTsf3bJbk3SVpro0keSfKSTU9YVadV1ZKqWrJy5coJL7itG8m6712edVeennX/dksG9zjGdBfGbbL7FiaanqUX6Vt6jZ6l1+hZulnHwo+qOj7Jg621Gzd56T8meXNrbfskn03yfx5/y2ZO0560o7XTW2sLWmsL5s2bN6E1t3UjWX/vtzOw8xsysN87M7Ddayb0/Exfk9m3MBn0LL1I39Jr9Cy9Rs/SzTr5tJeDk5xQVW9OMifJ86vq3CSvaq1dN3bMl5NcMLa+IskOSVZU1WA2TIn50VQWvH7FTZnxsldl/QPfycArD3efDwAAAOgBHRv50Vr7UGtt+9ba/CQnJbksG+7r8YKq2n3ssKPzs5uhLk5y6tj625Jc1lp70siPSal1ZG3W3XNDZrx876z/4Z2ZscO+gg8AAADoEZ0c+fEkrbXRqnpfkq9W1fokP07y62Mv/12Sz1fVsmwY8XHSVNW1/q6rsu6mryYH/noGXvG6qfpYAAAAYAJ0RfjRWvtGkm+MrZ+T5JzNHLM2yduntK7R4aStz4z5b0iSzNj21VP58QAAAMAE6Irwo1u1n9yb9qO701bclBl7n+ipLgAAANCDhB9PoV64Q+r522Z9ZqReuF2nywEAAACeg47d8LRbtdGhrF/x7bR1o6nBWalZW2Rg98ON+gAAAIAeJfzYRHtgaWrerml3XZk2OtTpcgAAAIBxEn5spI0Op1726rR7b8z62/4l7e5rO10SAAAAME7u+ZENU13aT+9PfnJv1j/6wwzs+ZbMSKXmH9jp0gAAAIBxMvIjSbvnhrQ7zkvtsCAzttomqYHM2PWw1ODsTpcGAAAAjJORH0lqx9eNrQxkxs5v7GwxAAAAwIQSfiSpwdmpnQ/pdBkAAADAJJj2017a6FDW33WVJ7sAAABAnxJ+3Lsk7Tvnpt27pNOlAAAAAJNgWk97aaPDqe33S5LUDgs6XA0AAAAwGaZ1+JEVS9IeuC31ymM92QUAAAD61PQOP7bfP5UkW72s05UAAAAAk2Rahx81ODuZf1CnywAAAAAm0bS/4SkAAADQ34QfAAAAQF8TfgAAAAB9TfgBAAAA9LVqrXW6hklTVSuT/OBpDts6yUNTUE4vcC1+ZtNr8VBrbeFUfPAz7Nteoq826MR1mJK+fY4926190Y11dWNNyeTUNd3+W9utf7bjNZ2+Vz/2bC/++an52Zmq/z94NMmdk/05z1I39kq31dRt9STJnNbaq8d7kr4OP56JqlrSWlvQ6Tq6gWvxM67FxHEtN3Adfl63Xo9urKsba0q6t65e0q/X0Pfqbb34PdXcnbrxO6rp6XVbPcnE1WTaCwAAANDXhB8AAABAXxN+JKd3uoAu4lr8jGsxcVzLDVyHn9et16Mb6+rGmpLurauX9Os19L16Wy9+TzV3p278jmp6et1WTzJBNU37e34AAAAA/c3IDwAAAKCvCT8AAACAvib8AAAAAPqa8AMAAADoa8IPAAAAoK8JPwAAAIC+JvwAAAAA+prwAwAAAOhrwg8AAACgrwk/AAAAgL4m/AAAAAD6mvADAAAA6GvCDwAAAKCvCT8AAACAvtbX4cfChQtbEotlIpYpo28tE7hMCT1rmcBlyuhbywQtU0bPWiZwmRJ61jKBy4To6/DjoYce6nQJ8KzpW3qNnqUX6Vt6jZ6l1+hZuk1fhx8AAAAAwg8AAACgrwk/AAAAgL4m/AAAAAD6mvADAAAA6GvCDwAAAKCvCT/oO2tXr8rVl56f0ZGRrFm9OldesmF9c1avXp1LLroow8PDU1wlPHurV6/KJRddmOHh4Tz6059kaO3aTpcEAAA9QfhB3/nWNd/MXvsdkO8tvSU3Xn159jng4KxduyaXX3xB1q5dk1WrVuXRn/40t9x0U66+8srst2BBvvKPZ2f16tWdLh2e0tVXXpX9FrwuX/nHszMwOCtV1emSAACgJwx2ugAYj6G1a7J+3fqsX78ut15/ZfY9+PAsOOTwXHTOl3PN1y/OR//qM1n2naX5zu235qePPJIXz9smLeuz9Lbbc/nXL8tffOpv8tWvfiV/+RefzIwZM3LSyad0+ivBL/TGQw99ol+rKscf/9bMmj2702UBAEDXE37Q9YaH1mTd8HCWXHROXn/8OzNr9twnXrv3e0uzfn3L9++4NY898pP86KGVue/u5Tnl/X+QzJiRSmXXV+6ZV+y8a2689urs9qpXZd269dlp590yY2AgqcqJv/TLmTFjRk5YdGIHvyX8YsNDazIwODOp5IRFJ6ZqRhYtWpSZM2d2ujQAAOgJwg+61tCaVXng+3ekJfnB0pty6xUX5XUL3561o6uyfv263H79lXnNwYdn/br12W7n3XPr9Vdmnzcclsu/9k8ZGBzI8e/4lSfONXvOnBx29MKfO/87Tn7XE+tGfNCtRkeG89OVP8wLXvrypLWsG16bd550UkaGh9Ja63R5AADQE4QfdKXRkeEsOffLuf2b5+fUP/1stnnFbtlxz31z3/LvpLX1ueuOW/NPf/OJ/Pp/+d9ZcMSbkyQHHrnh58KNQg/oZaMjw1l6xYXZ840L84Pv3LzhBqet5UUv3Tbbzt+10+UBAEDPEH7QdUZHhnPHlRdmnyMXJUlqYCBzt3hednr1/hkeWpP1o+uz7U6vzIyBgbz6wMM6XC1Mnjuuuig773tQHli2NNvvtlfWjYzkmgvPyc6v3q/TpQEAQE8RftA1htesyoPL78gjK+/PzvselOXfvjqvX/TuDM6c9cQxs2bPTcbu73jE207tUKUw+UZHR7Lrgjfme9ddnj0OOSYzZ89J5szNkfoeAACeNY+6pSuMjgznpvPPymWf+ZPssuDQ3H3zNdnjkGN/LviA6WJ0ZDjfvfL8pLW8cJttk7i3BwAAjIeRH3Tc6MhwvnfVBdnriBOTVAZmzspehx3f6bJgyg2vWZWVy5fm0YceyCtee1DuuvGK7H6wEBAAAMZL+EHHDK9ZlYc2+oveD266Jvu99Vf8RY9paXRkOLdecFa+d8V5OfFjn83dN35T8AEAABOka8OPqro7yaNJ1iUZba0tqKoXJ/lykvlJ7k7yjtbajztVI8/d6Mhwbr/grHz/yvNy/H/7bH5w4zezm7/oMY0tv/rC7HH4iUmSgZmz8qrD3trhigAAoH90+z0/Dm+tvba1tmBs+4NJLm2t7Zbk0rFtesy6keEsv/r8vPLwE7PrIW/OwMxZeeVhbxV8MK3NP+CIrLj56uy98OTcv3RJ1o0Md7okAADoG90efmxqUZIzxtbPSHJiB2vhObr76guzwz4HZ8XNV+fVx78nM2fP7XRJ0HGz5m6ZnQ9amLuvvzTzdtojd19zYadLAgCAvtHN4UdLclFV3VhVp43t26a1dn+SjP186aZvqqrTqmpJVS1ZuXLlFJbL0xlZsyrLv7k4Ox5weO675ZrsctBCoz3G6FuSJK1l5wOPyX03X5MdX3dEp6t5SnqWXqRv6TV6ll6jZ+lm3Rx+HNxa2y/JcUneX1WHPpM3tdZOb60taK0tmDdv3uRWyLPy3YvOyjc+8YHce8Nl2eXQt2ZA8PEEfUuS3Hn+53P+h0/K8+a9LDPnbtnpcp6SnqUX6Vt6jZ6l1+hZulnX3vC0tXbf2M8Hq+qcJAck+WFVbdtau7+qtk3yYEeL5BkbHVqTXY98e5Jkh9cd2eFqoLuMrFmVFTdcmt2POSlJ8uKd9uxwRQAA0F+6cuRHVW1ZVVs9vp7kmCS3JVmc5NSxw05N8i+dqZBn67sXfDGX/rf3ZOvd9un6f9GGqfa9i87KFX/+/qxYcln2WvQbfkcAAGCCdevIj22SnFNVyYYaz2ytXVBVNyQ5u6rem+SeJG/vYI08C7sdc3JS/kUbNufx34/tFxgVBQAAk6Erw4/W2vIk+2xm/8NJ/O2gx4ysWZV/W3JpXnnce9znA7Lhd+L7F5+VXY4+OTPnbpmZc7fMnif8RqfLAgCAvtWV017oDyNrVmXl0hvy/YvPzNV//jv53vmf63RJ0BW+f/GZ+dbf/XG+f/FZnS4FAACmha4c+UF/WH7xWbn3qsU59L98Pklll6NP7nRJ0BV2PuIdaevWZecjzNwDAICpIPxgUowOrclOY3+xmzFzVl5lSD/T3OiaVbnrkjOz0zHvzoyZs7L1q/bPDNPAAABgSgg/mHDrRoaz/MLP5d+uPjd7n/pfMjh7bqdLgo4ZXbMqj9x9e3607Obc8vd/nKSy21t/I/P2eF2nSwMAgGlD+MGEu/+687PjYf8uSeWF8z3dhent7kvOzL9dtThv+MgXklR2Osr0LwAAmGrCDybcy/Y/Kg/ceEl2Oe5XPd2FaW/+Uack2TD9a7e3mv4FAACd4GkvTJjRNauy/F9PT2bMyPaHLBJ8QJLMmJEX7/qkJ3cDAABTSPjBhLnnki9m6Wf/a+65+AudLgW6xj0XfT5Xf3iR3wsAAOgg016YEKNDq7PD4e9Mkux45Ckdrga6g98LAADoDkZ+MCFWXPyF3PjxU/KiXV+bwblbdroc6Ap+LwAAoDsY+cG4jQ6tznZv2vCv21t5ugs8YfsjT0naer8XAADQYUZ+MG73XfyF3PQ/T8kLd3ltBuc+r9PlQNd46MZLMvrTh/PQjZd0uhQAAJjWjPzgORtd81gevvGSvHzsXgbP86/bkORnvxtb739Uhn/yYLbe/6hOlwQAANOakR88J+tHhnL/JV/IHX/5m3n4xkuy4/GnGfUBY+6/9It+NwAAoIsY+cGztn5kKA9dd162OfTfJZW8xL9qwxPWjw7nZW96Z7J+XV687+GdLgcAAIiRHzwHD19/Xl649yH5ya1XZrtjf82/asNGHr7u3CQtz99t/8wYnNnpcgAAgAg/eBbWrX0sD199Tl6839F55LarsvXr35wZM2d3uizouHVrH8sD5/1N1g2tzov3Ozo/ufnybLXrazMwe4tOl8b/z96dh0lZHXjf/53aurobFVQkuLAvsoMssimyg6iocUWNSUyMmcn1PPPMzPs+M5kkbyaTZJKZOEkmE5OYaIILKi6AyCY7gsi+gyyKC0oMGjX0Uvt5/6iGNAh0011V576rvp/r6qu77uqmf9387vuCU+ecGwAAABCDHzgLR5Y9oTf/+6v6ZMtitR5xIwMfQJ0jy57Qu499S0eWPqZgeQvODwAAAMBj2PMDjZKO1+jCUXdIklpeMd5xGsC9dKxKHy57QheO/YJaj7lbko6/BwAAAOAtDH6gQZlkXB8unq5P1s3RxXf/q4JR9vhA6UrHqlT79i5VH9ii9x7/liSpzbUP6HPXPuA4GQAAAIDTYfADDfp0w3ydf9UtkpEq2vdyHQdw6s/LntCnr81Sh//7jGSkC5ntAQAAAHgegx84rXSsSlVbXta5AyboL1sWq/WEL7OPAUre+XWDHSYQzJ4ToYjjRAAAAAAawoanOKVMMq6Plz6mQ7/4iqq2Llar4Tcx8IGSlYlV6eMFv1ImVqVgtIUqOvfX2z+6RR8vftR1NAAAAACNwMwPnFLVxnlqOfJWyUgtBrDBKUrbp8sf15EnvilJajX564q2763zht6klqNZ8gIAAAD4AYMf+IxMvEaVfceoevsynT/+PmZ8oKRl4jU69+o7JUnnjb5HkhSMttAFk9ngFAAAAPALlr3gM/6yfLoO/+dtCl9wMQMfKHnHzodo5wEKcKcjAAAAwJeY+YHjMrEq1WxdpHNHZV/dLmvX23EiwI1MrEpHVzymc0Z/Uedew/kAAAAA+B0zP3Dc0RWP6aNf3qfabS+r5aSv8yo3StbRFY/pkye/qarl0xWItuB8AAAAAHyOmR+QlN3X4JyrpslIKu8/wXUcwIlMrEq1WxfpnFFfkJFRi7pZHwAAAAD8jZkfkCRVr/iDPnrwFpV1uoJXuFGyqlc+pk8e+rJqty3Sucz2AAAAAIqG72Z+GGMmSfq5pKCk31lrf+Q4kq9lYlWKb12oylFfkCSF2dcAJSoTr1HlyGmSpPL+Ex2nAQAAAJBLvpr5YYwJSvqlpMmSekq60xjT020q/8ok46pd/gd9+tCXFd+6SOdM/Bte6UbJycSqlNj3mmqX/14fP3iLyjoy+wkAAAAoNn6b+TFE0gFr7ZuSZIx5WtJUSbudpvKpxKaXFB1xu2SkMl7pRomKrXxMsfUvqOXfPycZoxCznwAAAICi47fBj0skvVvv8SFJVzrK4muZeI0ifcYqsWOpysd+VYFwmetIQEFlYlVKbHtZ0bolXwpFVDnxb9yGAgAAAJAXvlr2Ismc4pg94ROMud8Ys9EYs/HIkSMFiuU/sZXT9enPblPggksY+PAAelt4sVWP6+hv7lNi28uqmPg3CpRVuI7kK3QWfkRv4Td0Fn5DZ+Flfhv8OCTpsnqPL5X0fv1PsNY+bK0dZK0d1Lp164KG85Po1feobPBNCl3GFH8voLeFF736HlXe8UNF+nFr56ags/Ajegu/obPwGzoLL/Pb4McGSV2NMR2NMRFJd0h60XEmX8nEqlSz+NeSCahiArfyRGnKxKqU2L5Y0dFf5hwAAAAASoCvBj+stSlJ35C0SNIeSTOttbvcpvKPTDKu2KrHVf3MtxRb9ZjrOEBBZWJVqlnym+x58MoTOvrwVxVb8XvXsQAAAAAUgN82PJW1dr6k+a5z+FFi6wJFh94iSYpedbfjNEBhxVY/qeqZ31bgvDbH+895AAAAAJQG3w1+oOkifcYpsWNJdqo/m5yixERH3iUpex4Eoi1UMf4Bx4kAAAAAFIqvlr2g6TKxKiV2LFGk/2QGPlBSsstdHs7uczPua+zxAQAAAJQgBj+KXCZWrcSB9YqtflJVv3tAsVXTXUcCCqJ+92ue/Y5iq59wHQkAAACAIyx7KXKxNTOU2DRX537jcckYRUdMcx0JKAi6DwAAAOCYJg9+GGPGW2sX5zIMcsvGaxUddlv2QTCiirH3uw0EFAjdBwAAAFBfc5a9PJKzFMiL2JondfShLyjcob8CZeWu4wAFQ/cBAAAA1HfGmR/GmBdP95SkC3IfB7li47UqG3qrJCl0SU/HaYDCsLFqJXYtU3T4HZLoPgAAAICshpa9XCXpbklVJx03kobkJRFyIvbqDCU2v6SKG78pE610HQcoiNjap1XzwvfU4ov/o/IxX3EdBwAAAIBHNDT48ZqkGmvtypOfMMbszU8kNIeNVyuxc5miw26XxCvfKH42Xq3Yq08rOmKaosOyMz4ivcY4TgUAAADAS844+GGtnXyG567OfRw0V+zVp1Uz6/tq8cX/Vvno+1zHAfLuWOdljMqv+TK9BwAAAPAZDe350UVSG2vtmpOOXyXpfWvtG/kMh7NjE7Uqu/IWSYZXvlES6nf+2GwnAAAAADhZQ3d7+Zmko6c4Xlv3HDzCphKKvTpDVQ9/RaH2fWXK2OcDxcvGq5U8uEmxtU/TeQAAAAANamjPjw7W2u0nH7TWbjTGdMhLIjRJYsdilQ28UZJR6JIeruMAeRVb96ySW+erxVd+K0l0HgAAAMAZNTT4ET3Dc+W5DIKmsfFqJXavVKTnNUrsXqHoyLtlQhHXsYCcs/Fqxdc9p7Khtyl6ZfY2ziYUUfmoLzlOBgAAAMDrGlr2ssEY89WTDxpj7pO0KT+RcDbi655TzZN/r8TulSobMIWBDxSt+LrnVPvivyv+2kyZskqVX/1FmQhjsAAAAAAa1tDMj7+TNMsYc5f+OtgxSFJE0k35DIaG2UStIoOzfw2RnqMcpwHyp37XsxucAgAAAEDjNXSr2w8kDTfGjJbUu+7wPGvtsrwnQ4Pi655VYttClU/5RzZ7RFGj6wAAAACao6Fb3UYlPSCpi6Qdkh6x1qYKEQxnZhO1igy6UZIUuri74zRAfth4tRKvr1TZkM9LousAAAAAmqahPT+mK7vMZYekyZJ+kvdEOCMbr1HyrS2Kr39WVb//uoKX9eGVcBQlm0oovv451Tz1/yrx+ipFr/oCXQcAAADQJA3t+dHTWttHkowxj0han/9IOJP4xheU3L5IlV/8pSSjUNturiMBeZHYvUyRAddJkiKXX+04DQAAAAA/a2jwI3nsA2ttyhiT5zg4E5uIKXLFDZIkE4woOvIex4mA3LLxGsU3zVLZoM8r0v1qJfauUtmwO7mLEQAAAIBmaWjwo58x5i91HxtJ5XWPjSRrrT03r+lwnE0lFN/wnJI7lyg66e9kIlHXkYCcsfEapf+4T6lDuxRb8KAko+jwaSrrO8l1NAAAAABFoKG7vQQLFQSnlv1P4X5lPv1AkX7XSpJCn2OpC4rDsX6n39ul5M6XVXHPf0vGqGzgja6jAQAAACgiDc38gGOJzXOU3LVEFXf9VKn9r6nsyttYAoCiUb/fUt1yruHTHKcCAAAAUGwY/PAwm4gp3D+74aMJRhTpO8FxIiB3Tu53GYMeAAAAAPKkoVvdwqHEptmqmfF/FLykJ3t8oOjQbwAAAACFwswPj7LJmML9p0hGCrbp6joOkDM2UaPkvlezdy6i3wAAAAAKgJkfHpXYNEe1T/1D9lXxsgrXcYCcSWyeq9is7yh54FWVDb2DfgMAAADIO2Z+eIxN1Ci5f60iA66ve1W8i+tIQE6c3O1w1+GuIwEAAAAoEcz88BCbSiixZa5is7+r5BtrVXbl7TIRXhWHv9lEjVLv7lBiy0t0GwAAAIATzPzwkNS+VxTunb2jS7jLMMdpgNxIbp2n5OvLVXHbj7MzPug2AAAAgALz3MwPY8x3jTHvGWO21r1dW++5fzbGHDDG7DXGTHSZMx9CXYYp/fZmRQbexKviKBrh/lMU7jFaCoZVNuQ2ug0AAACg4Lw68+On1tqf1D9gjOkp6Q5JvSRdLGmJMaabtTbtImCu2UStUgdeU6jb1TKhsOs4QLPYRK2S2+Yp3G+KTKRCkcG3uo4EAAAAoIR5bubHGUyV9LS1Nm6tPSjpgKQhjjM1m03UKnVoh5Lb5ik29/tKbp3jOkyeVj0AACAASURBVBLQLDaVVHLbS4ove0jJ7fNcxwEAAAAAz878+IYx5guSNkr6B2vtx5IukfRavc85VHfsBMaY+yXdL0nt2rUrQNTmSW6fp+TrK1Vxyw+z+yH0neI6EhzwW2/PJLX/FYV6jpNEn4tZMXUWpYPewm/oLPyGzsLLnMz8MMYsMcbsPMXbVEm/ktRZUn9JhyU9eOzLTvFH2c8csPZha+0ga+2g1q1b5+1nyAWbjCvce6LCl18jBSOKDLpFJlLuOhYc8FNvT8cmapXcs0KhzkOVfmerwgNupM9FrBg6i9JDb+E3dBZ+Q2fhZU5mflhrxzXm84wxv5X0Ut3DQ5Iuq/f0pZLez3G0gjm2NCC1d5Ui13xVJlzmOhLQJDZRq/SRN5U5vFeJFb+WrvtmdoNTAAAAAPAIzy17Mca0tdYernt4k6SddR+/KGmGMea/lN3wtKuk9Q4i5kTqwKsK9RwrSQq27uw4DdB0yR0Lldq3SuU3/ZtkpFCnK11HAgAAAIATeG7wQ9J/GGP6K7uk5S1JX5Mka+0uY8xMSbslpST9rZ/v9BLqNESpN9cr3P8G7u4CXwv3mZT9IBhWZODNbsMAAAAAwCl4bvDDWnvPGZ77gaQfFDBOztlErVI7FyrU51qFLx/lOg7QLDZRq/TB9Qr3u45BPAAAAACe5adb3fqeTSWV2rFQiVW/VWrHAtdxgCaziVql39+t1M6Fii/4sVLc0hYAAACAh3lu5kcxS7+xVqEeo7P7IvSe6DoO0GSpXS8rtf8VRW/4riRDnwEAAAB4GoMfBWKTcQXbX6H025sV6ssSAfiXTcYV6pHdrFfBsMJX3Og2EAAAAAA0gGUvBZLatUjxl74nc86FDHzA1451OdCmK7doBgAAAOALzPzIM5uoVfrtTQr1HC9JClzY0XEioOmysz7GSKLLAAAAAPyDwY88sumkUrsXK/nq7xUZ/w8K97/BdSSgSWyyVpkP31LmTweUPrBG4eH3ykTKXccCAAAAgEZh8COP0m+uU6hb9na2wfYDHacBmi61e6nSb6xR2ZR/kSQFLujgNhAAAAAAnAUGP/LAJmuVfnuzgu0HZpe89JksE2SfD/iHTdYqtWeZQj3GyITLFepZb4PTfte7DQcAAAAAZ4kNT/MgtWeZkkt/rvQ7mxXqOpKBD/hOas8ypdZOV2rPMkmSCZcr3O86mRAbnAIAAADwH2Z+5JhNxRXqfo0kKdj+CrdhgCao3+Fjm5sCAAAAgJ8x+JFjqdeXKvPmWoWG3C0TZkNI+A8dBgAAAFBsGPzIIZuKK9R1lFKSAhe0dx0HOGt0GAAAAEAxYvAjB2wypsyf35E9ckDpg+sUGjxNJhx1HQtoNDoMAAAAoJgx+JED6X0rlD64TpHx/yjJ8Io5fIcOAwAAAChmDH40k03FFexyVfZBMKRQ78luAwFnwSZjSr+7VcFuo7IH6DAAAACAIsStbpspvXeFEksflLmwE7cBhe+k961U6pVfKX1om0K9JtFhAAAAAEWJmR/NkJ31MVIyUuD8dq7jAI1mkzGlD9XN+DBS8NL+riMBAAAAQN4w86MZ0vtWKLnsp9lZH2wOCR9J71+p9OrfKP3eNoV6TqS/AAAAAIoaMz+awCZjSr+3TcGuoyRjFGh1metIQKP9dcaSUfCSfq7jAAAAAEDeMfOjCdIHVim9+mGl39uuUI8JvGoOX0nvX6nksp/LXNCR7gIAAAAoCcz8OEs2FVew8whJRsFL+rqOA5yV+v1lxhIAAACAUsHgx1nKHHhFmXc2Ktj/Fl41h+/QXwAAAACliMGPs2BTcQU6DZckmVaXOk4DNJ5NxpR5f4cCnUdKor8AAAAASgt7fpyFzBurlVr5C5kLOvCqOXwl8+Yapdc+osz7OxS8fBz9BQAAAFBSmPnRCDYZU+bwDgU6jZAkmZa8ag7/sKm4Ah2HSZICF/dxnAYAAAAACo/BjwbYdDL7qvm256WhX1aw+1jXkYBGscmY7CfvyX78ljLvblaw783M+AAAAABQkhj8aEDmve0KtB8iSQq07e04DdB4mYNrZQ9tVnDk1yUZmZaXuI4EAAAAAE4w+HEGNpVQ4HM9lPnjHgW6XC0TDLuOBDRaoOMwZWSlQFDBbmNcxwEAAAAAZ9jw9BRsKq7MR28qc3CN0mt+LVPRioEPeJ5NxZU5sFI2FZckZf64S0pUK3N4l+NkAAAAAOAWMz9Owb71mjLvbVFw2P3KsFwAPmHfek2ZnbMVkGS6jFKgbW9lYkcVaNvLdTQAAAAAcIrBj5PYVEKm3eDslJhASMGu1zhOBDSO6TA0O/DRbnC2x6Ey+gsAAAAAcrTsxRhzqzFmlzEmY4wZdNJz/2yMOWCM2WuMmVjv+KS6YweMMf+Ur2z27deUXveI1KqdTCiSr28D5JwJlUmt2im97hHZt19zHQcAAAAAPMPVzI+dkm6W9Jv6B40xPSXdIamXpIslLTHGdKt7+peSxks6JGmDMeZFa+3uXIayqYTMZdlZH+a8i3P5RwN5Z1MJmXM+p8DF/WTaX+k6DgAAAAB4hpPBD2vtHkkyxpz81FRJT1tr45IOGmMOSBpS99wBa+2bdV/3dN3n5nbw4511yry/TYGeU7KvogM+Qn8BAAAA4NS8tufHJZLqz9c/VHdMkt496fgpX9o2xtwv6X5JateuXaO+qU3FZT94XabdkOysj3OZ9YHCakpvj6G/cKE5nQVcobfwGzoLv6Gz8LK87flhjFlijNl5irepZ/qyUxyzZzj+2YPWPmytHWStHdS6desGc9p0Svad9bJbn5L94HUFOl3Fq+YouLPubSquzME1df3dQH9RcGfbWcAL6C38hs7Cb+gsvCxvMz+steOa8GWHJF1W7/Glkt6v+/h0x5vFfrBb5pIBkiTT5vJc/JFA3tl3N8q+Pk8qO0em3WBJ9BcAAAAATsdry15elDTDGPNfym542lXSemVnfnQ1xnSU9J6ym6JOa+43s6mETOuuskf2y7QfJhP02q8DOJFNxaUje2Uuy94kyVzUXSZUJtNppONkAAAAAOBdrm51e5Mx5pCkYZLmGWMWSZK1dpekmcpuZLpQ0t9aa9PW2pSkb0haJGmPpJl1n9s8hzbKbnpcpvw8Bj7gD4c2yW5/VjqyV4GOI1jiAgAAAACN4OpuL7MkzTrNcz+Q9INTHJ8vaX5Og1w6MLuZyDmfy+kfC+TNsc627u46CQAAAAD4RklPdzChMqnDcNcxgEajswAAAABw9pwsewEAAAAAACgUBj8AAAAAAEBRY/ADAAAAAAAUNQY/AAAAAABAUWPwAwAAAAAAFDUGPwAAAAAAQFEz1lrXGfLGGHNE0tsNfNqFkj4sQBw/4HfxVyf/Lj601k4qxDduZG/9hF5lufg9FKS3TeysV3vhxVxezCTlJ1epXWu9+nfbXKX0cxVjZ/3490fms1Oofx8clbQ339/nLHmxK17L5LU8khS11vZu7h9S1IMfjWGM2WitHeQ6hxfwu/grfhe5w+8yi9/Dibz6+/BiLi9mkryby0+K9XfIz+Vvfvw5yexNXvwZydQwr+WRcpeJZS8AAAAAAKCoMfgBAAAAAACKGoMf0sOuA3gIv4u/4neRO/wus/g9nMirvw8v5vJiJsm7ufykWH+H/Fz+5sefk8ze5MWfkUwN81oeKUeZSn7PDwAAAAAAUNyY+QEAAAAAAIoagx8AAAAAAKCoMfgBAAAAAACKGoMfAAAAAACgqDH4AQAAAAAAihqDHwAAAAAAoKgx+AEAAAAAAIoagx8AAAAAAKCoMfgBAAAAAACKGoMfAAAAAACgqDH4AQAAAAAAihqDHwAAAAAAoKgx+AEAAAAAAIoagx8AAAAAAKCoMfgBAAAAAACKWlEPfkyaNMlK4o23XLwVDL3lLYdvBUFnecvhW8HQW95y9FYwdJa3HL4VBJ3lLYdvOVHUgx8ffvih6wjAWaO38Bs6Cz+it/AbOgu/obPwGk8OfhhjLjPGLDfG7DHG7DLG/O+64+cbYxYbY/bXvW/lOisAAAAAAPA2Tw5+SEpJ+gdrbQ9JQyX9rTGmp6R/krTUWttV0tK6xwAAAAAAAKflycEPa+1ha+3muo+PStoj6RJJUyVNr/u06ZJudJMQAAAAAAD4hScHP+ozxnSQNEDSOkltrLWHpewAiaSLTvH59xtjNhpjNh45cqSQUYEmo7fwGzoLP6K38Bs6C7+hs/AyTw9+GGNaSHpe0t9Za//SmK+x1j5srR1krR3UunXr/AYEcoTewm/oLPyI3sJv6Cz8hs7Cyzw7+GGMCSs78PGktfaFusMfGGPa1j3fVtKfXOXzOhurVu3yR2Rj1af9nEysSjWLHlImVlXAZED+NKb3J+M8QKHRUwAAgMLz5OCHMcZIekTSHmvtf9V76kVJ99Z9fK+kOYXO5iU2UatM7V8UWzVdNlGbPRavVvKNDYqtfUo1L3xPsbVPn/A1mViVYutnKZOMK7biD6p66p8VW/mYi/hAo53Q9fiJ/2G08br/SKYSiq19+pS9P1kmXqNM9SdK7H9NsZWPcR4gZ2y8WvGt82Xj1Sdcm489d6br8zGZWJVqFv8629NYFT0FAADIgZDrAKcxQtI9knYYY7bWHfumpB9JmmmMuU/SO5JudZTPOZtKKPXebqXf3qbEjpcVGXKLbCKm+JqnlNg6X+c88HtJRtHh045/TSYZV2zV48oc/VDKpBUdfrtkpOioL7j7QYAzsPFqpQ7vlayUfnural/6D5lzWivSc5QSu1co0nu8YmueUs3sHyhw3kWKDrtDko6/ry8Tq1Js9ZOKjvqiUu/sUOqN9Ypvmqvz/m5m9ms4D9AMx7qafnenbNVHin/6gRLbF2WvzTWfKv3H/Uq9vU2JLfP+en0+VU/rrtPVM7+tUIcBSh3crPiGWfQUAACgmTw5+GGtXS3JnObpsYXM4lWJXUsU7jpCwTZdFWzfT+nDryvz5/dUNjh7AxwTiqh89H3KxKpVu/S3il59rxJbFyg69BYl9ryiSL8JSmx7WdExX1UgXOb4pwFOLb7heSW2L1KL+x5W8HNdpEBQkT7jFHt1huzRj5SwmeOdj/QaI1NWqfLR90mSMrFqxdbMUHTENAWilYqtflLVM7+twHltFOk7QaGLu0uBkBSKqGLi37j8MVEEjnf1S79Scu9qRXqMUrBdX6UPv67UW1uU3LZILe7/nWTM8euz9NmeHrtOS1KoXR+FLuuV/Qb0FAAAoFk8OfiB07PxGiX2rlLk8lFKvL5KkV7jFO44UDZRK9umi5J7X1H06i/IhCKyyYRiq59UzfP/qmDbyxXpM06JHUsUuWKKAuEyRa+82fWPA5yWTcQUGXijJCNjAjLllYpenV31Fr3y1uzMjx7XKLFn+fHOH//aet0PnNtG0cE3KDryLklSpM84BcoqpLIKVUz4uosfDUXmhK4Gwyrrf60kHb82B9tkB+5MKKLya76c/ZpYtVLv7Vbyra2qee67x3t67DodHf3l4wPT9BQAAKD5GPzwmfjGFxSb95/SHT9WWb/Jx4+bSLlMpFxlA647fiyxbaGiV96swHkXKdxpQHbgo/9kZnrAF+IbnlNy+yJFJ/+9TKT8hOdMWaXKBkyRpBM6f0z97kf6jFHNkocVvepuVYz7WkGyo7Scsat11+byUV864Xjs1aeU2DxX5/zNYwqc2+aEnkbrZjMBAAAgdzy54SlOr2zQzYpO+X8U6X51g58b6T1Wyb2vquyK6xRbPUNVv3tAsVXTT/m5mViVql97XplkPNeRgSYpG3Szwn0nKtS2+1l/7cndr3n2O4qtfqLBr8vEqnR00UPKxGuaEhklqildjQ6/U5ErrpcJRhQdfAM9BQAAyDMGP3zGlFUoOuJumbKKhj83WqmyQTfIBEOKjpymitu+p+iIaSd8TiZWpcS+tardukjRnlerZuNcZWqr9MnCX3FLRTh1Nl3/zNc2ovsnyyTjql7+B8XWvSClEvp04UPH77bB+YAzaUpXTbRS5WO+IlOWnSnSmJ4eu15Xr3gs29NMWunqT/TJAvoJAADQEJa9+IiN1yi+aZbKBt501v8hDERbqGLs/Z85XrtyumLrZqnVP83V0aWPKnP0Q3368Qf6aMa3JEktJ7HWHIXTnI6fzum6f7L4prmqGHG7Ip0H6ugrM/TJk99UWacrFHtziz584puSOB/wWbnqbGN6evx6/Q/PKdLpCiXe3aXa/Rv00VPfkQz9BAAAOBMGP3wkvmmWYvMf1Mm3sG2O8lH3KntjHaNzRt+r2q0vq7zfBIXOb6vKQZ/dSwHIp3x0vLHK+k9SfOsilQ26XuF2fWRkFGnfV5F2vRVs2UaVA6cUNA/8oZCdPX69DkVU1m2oMvEahS+5XCYY0rmj783r9wYAAPA7Bj98pGzgTZKMygbmbjO8QLSFKuvdPrFyaPYOMJUDJsnGa/TRy4+o5dh7FczRq/DAmeSj440ViLZQ+dDPZx+EIjq33qvolf0n6NMlj+q80fcoEG2hTDKuoxvnqcWACQpGWxQ8K7yjkJ09+Xp97K5FLSd9XZl4TXYJzMqnuGYDAACcAnt++Igpq1B0+LScLQc4k/hb2/Xx8sf16brZUiqhI/N/rTRrypFnhez42fh0+eM68sQ3VbXlZaVjVfro5UdU2fMqVW1Z7DoaHPNKZ7lmAwAAnBkzP3BKZR36KnLp5SrvOlh/Xvm0Dj/+L5Kk1tc+4DgZUHjnjb5HktRi0BR9tPj3OvzEtyVJF0y4z2Us4Diu2QAAAGfG4AdO6dh06sruQxVt31uSdP6Yux2nAtwIRFuo1eTsMphj58H5Y+5WIFzmMhZwHNdsAACAM2PZi0/YeI3ir86QjdcU/HsHoy3U+toH2NsAeeOy32eL8wGStztLRwEAAD6LwQ+Ps/Eapd7epsSm2YoteFCJTbOd5EjHqvQBa8iRY17pd1NwTpQum0oosfEFT3eWfgIAAJyIZS8el9g8R8ldS1Rx108lSREHd8GQpA+XPaH3HvuWJKkNa8iRI17pd1NwTpSu5J4VCve7VpLxbGfpJwAAwIkY/PAwm4gp3P86SZIJRlQ2fJqzLBeOuVvhlm3UcvC1zjKguHip301xYd1+Cheyr0LJsPEaJfetUbjbSCX3rVbkyltlQhHXsU7peD/HfsFxEgAAAG9g2YtH2VRCiU0vqGbG/1Hwkp4ykajTPMFoC513xXh9vGG+0rVVen/er5WuZTo1zp5N1Cj1znYlNs3yTL+bIhhtoTZ1+yqkY1X64/xfKx2v4fwoQsc7u3mOal/4tpL71yjSZ4JnBz6kv/ZTNqOPXp1FLwEAQMlj5odHJV9fpXDfSZKkYJuujtNkHVn2hFKfHlH8z3/U249/R5LRxVO+5joWfCaxea5Su5eq/M4HJWM80+/mOLLsCb372LdU2XmAjh7Yorcf+7Y4P4rHyZ0Ndx3hOlKjcd0GAADIYvDDo8Ldhiu5/1VFBt/imVcXW4+5W59sXqyWA8ZLJqA2Y+5yHQk+FLnieslIJhRW2dA7XMfJidZ1SwwqOvRRRbtekgznRxHxc2e5bgMAAGSx7MVjbKJG8XUzJRNQpNc4zwx8SNlp1BcMv0nB8ha6eMrXFCznNopovPrdLrvydpmw/5a6nE4w2kKfu/YBBcsqOD+KjE3UKLl/rSIDb/JlZ7luAwAAZDH44TGJLS8pvuQXSmx50XUUIKfoNvwoseUlxWZ/V4nN3rylLQAAABrHk8tejDGPSrpO0p+stb3rjp0v6RlJHSS9Jek2a+3HrjLmS2TAdZKRInV3wQCKBd2GH9FbAACA4uDVmR9/kDTppGP/JGmptbarpKV1j4uKTdQodWCtIlfcKBOpcB3njNK1VTo07zfcOQANsokaJdY/m13uMuQ2z3c7Fzg//K8Ye0svAQBAKfPk4Ie1dpWkP590eKqk6XUfT5d0Y0FDFUBy6zzF5nxPyS1zXEdp0OFlT+rg9G/rj8uedB0FHpfcOk/xpf+j5Na5rqMUDOeH/xVjb+klAAAoZZ5c9nIabay1hyXJWnvYGHPRqT7JGHO/pPslqV27dgWM13zh/lMkI4X7TXEdpUFtx9wlI+lz3DkgJ/zc24b4qde5cvz8GHeP6yh5U8ydlYqzt1y3i7+3KD50Fn5DZ+FlxlrrOsMpGWM6SHqp3p4fn1hrW9Z7/mNrbasz/RmDBg2yGzduzGtOSKnaKr2/dIYuHjtNoeK9k4Ap1Deit8XDA+dGQXpLZ/3HA908Ha618Bs6Cz/i3wfwm5x01pPLXk7jA2NMW0mqe/8nx3lQ5/2lM7TvD9/R+0tnuI4CeArnBryKbgIAgFLjp2UvL0q6V9KP6t57f2OMs2ATtUpum6dwvykykXLXcRolVVuljzYt0cVjpynS8iK1Hnqt60jwCD/2OZeOnxvj71ar3iNVcWkX15HQSKXQ3VS8Rm2vuV2SdPH4ux2nAQAAKAxPzvwwxjwlaa2k7saYQ8aY+5Qd9BhvjNkvaXzd46KR3DZP8WUPKbl9nusojXZ46ZPa8/Ov6S/7NunCwROUidXqzbkPK1Vb7ToaHPNjn3Pp8NIn9d6C30qZjKIXXqK3F/yB88InSqG7hxc/rh3/Pk2teo+UMhkdXj1bqdoqrt8AAKCoeXLmh7X2ztM8NbagQQoo3K9uc72+/tlcr+3YuyQZnddzqP5yYJv+vG+T9kz/nmSMOl33Vdfx4JAf+5xLbcfepXM6D9DRt3bpz/s2c174SCl099i1u+KSznp30XQlPjmi2j9/oN1/+C49BQAARcuTgx+lyETKFRl0i+sYZyVU3kKXXXe/JOmcTr3V4rLuMoGg2jGNuuT5sc+5FCpvoZY9higVr9E57XupVbeBOrdTH9ex0Ail0N361+5Lx07TkU1L1HrgOCkQ4PoNAACKlieXvZQSm6hVYuNzsola11GaJVRWoXCL89Tp+vulTEYH5v6W6dMlqlg6nQuhsgrJGP35wDYpk3EdB2dQqr0NlbdQ25E3KlTeIjvjg+s3AAAoUgx+OJbcPk/xZb9Scvt811Fy5q0lM/Temhf16Vu7XEeBA8XY6eZ4a8kM7Xz0/9MfNy1xHQVnQG+z6CsAAChWLHtxyCbjCveeKMko3Ld47pTSYcLdajf6Nr29fKbO69BLofJK15FQADZRq9Qb6+q6XFydbo4O46Yp2uoitRk4Vvvn/lYdx03jnPCYYr0WNwV9BQAAxYqZHw4lt81T7fPfUqBt96K6pWKorFxvL5+pQ2vm6pO3druOgwJJbl+g+LwfKvXmekUGfb6oOt0cofJKXTpyqt5a8pS2P/pdHVzylOtIOEmxXoubon5fuYYDAIBiwswPh8J9J0tGCrbu7DpKznWccLfaj75NB5fNVMtOvRUqK+3/UJSCY30OdbrSdRRP6jhumiSjjhPuUipeq4/f2KlWnTk3vKCYr8VNxTUcAAAUG2Z+OGQi5YoMvLkoX2kMlZXr4LJn9e6aucokE3r9xd8pyQZ6Ra2Y+5wLofJKdb3+KwqVlSuTTOjDvZuUSSZcx4Lo7qlwDQcAAMWGmR/Im07j79T5XfvpzWUztfmRf5UkXX7DVxynAtx7c9lMbfnD92WCIc4JeBbXcAAAUEwY/EDehMsr1brHYLXs0FPRVm102dBJriMBntB5fHYJTOfxd7qOApxW/Wu4ZNRl4l2uIwEAADQZy14csYlaJTbNkk3Uuo6Sd+HySl0yaKzeWbtQaab5F51S6nKuhMsrdfkNX1G47i4aydpq7Z7zO6Xi/A4Lie42zrG+2kyGngIAAN9i8MOR5I6FSqz8jZI7FrqOUhCHNizV5/oO155501k3XmRKrcv5sP/lp/TW6rlKJxPaNYe9FQqF7p4degoAAPyMZS+OhPtMOuF9sWs3bJL2zJuu9Y/8m4wx6jWVdePFotS6nA9dJ9ypC7r20/6lz2r9774nSZwjBUB3zw49BQAAfsbgR4HZRK1SOxcq1OdaRQbe5DpOwQTDEXWfOE3GGHWbwD4HxcImapU+uF7hftfJhMKu4/hWuLxSbXoO1vkde8pInCN5VqrX4eaipwAAwM9Y9lJgqZ0LlVj1W6V2LHAdpeDC5ZXqNfWv+xzA/1I7Fyq+4MdKbZ/nOkpR4BwpjFK+DucCPQUAAH7E4EeBhXpPUuTq+xXqPdF1FGeStdXaMfsR1osXAfqce5wf+Udvc4OuAgAAP2Hwo8BMpFzhK26UiZS7juLM64ue1mu/+55ef/lp11HQTPQ59zg/8o/e5gZdBQAAfsKeHyi4yyfeIRnp8gl3uI4CeA7nB/yCrgIAAD9h5keB2GRcNlal5JY5sola13GcCpdXqs/U+1gv7lN0Ob84P/LDJmqV2veKbKKW7uYIXQUAAH7CzI8CyRx5Q5k/7lVi9aOSpPCAqY4TAU1Dl+FHqd2LZWs/ka36SInVj0iiuwAAAKXEd4MfxphJkn4uKSjpd9baHzmO1CiB1p0VOL+dZAIK9ZrgOg7QZHQZfhTqOV7ptzYq2GGQZAzdBQAAKDG+WvZijAlK+qWkyZJ6SrrTGNPTbarGMeEymWgLhQdMZZM9SYnaam2b/YgS3CXAd+hy/nBe5I+JlCvU7arsZqd0N2foLAAA8AtfDX5IGiLpgLX2TWttQtLTkpi37EN7Fj2tNb/9nvYs4i4BwDGcF/AbOgsAAPzCb8teLpH0br3HhyRdWf8TjDH3S7pfktq1a1e4ZKdhE7VK7VmiUI9xvNJYT4+Jd6ii1UXqOHyi6yie4LXeng59zq9eU+5RRauL1H7IGNdRGuSXzkr0Np96TMze6aXn5GmOkzSOn3oLSHQW/kNn4WV+m/lhTnHMnvDA2oettYOstYNat25doFinl9qzRMk1jyq1Z4nrKJ4SKa9U+yFjtHPe40yXlvd6ezr0OX8StdXaOe9xtR8yRhEf3D3DL52V6G0+Rcor1e/G+2QzGW31wfIXP/UWkOgs/IfOwsv8NvPjfz/oPgAAIABJREFUkKTL6j2+VNL7jrI0SqjHuBPe4692L3paq3/7b5Kk/jfe5zgNGoM+5w/nQ/7Q2/yjvwAAwOv8NvixQVJXY0xHSe9JukOSp+famki5wv2udx3Dk3oemy5d9x7eR5/zh/Mhf+ht/tFfAADgdb4a/LDWpowx35C0SNlb3T5qrd3lOBaaKFJeySuEQB3OB/gZ/QUAAF7ntz0/ZK2db63tZq3tbK39ges8Z2KTtUpue0k2Wes6CtAsdBl+RG8BAABwjO8GP/wktXupkq/+XqndS11H8bREbbX2rpyrVDLhOgpOgy4XRqK2WptnPaJknP+s5wK9LRyu4wAAwOsY/MijUM+xCg//kkI9x7qO4mkH1y/TZf2Gaevcxzx/p4BSRZcLY+fCp7XvlXlKJxPaNOtRzodmoreFw3UcAAB4na/2/PAbEy5XuN91rmN4XufhE7V17mNa+dsfypiABt70ZdeRcBK6XBi9J92hNt36adfi57Xi4e9LEudDM9DbwuE6DgAAvK7Jgx/GmHMltbbWvnHS8b7W2u3NToaSEQpH1HfynWpxQRt1GT7RdRzAmUh5pS7pNUitO/VQ5fmtOR/gG1zHAQCA1zVp2Ysx5jZJr0t63hizyxgzuN7Tf8hFMJSWSHmlOg0Zoy0vPcGUaZQ8zgf4Eb0FAABe1tQ9P74paaC1tr+kL0l63Bhzc91zJifJUHK2LXxGS3/zfW1b+IzrKIBznA/wI3oLAAC8qqnLXoLW2sOSZK1db4wZLeklY8ylkmzO0vmUTdYqtWeZQj3GyITLXcfxjX6Tbj/hPdyhw+5xPjQd/XWH3gIAAK9q6syPo8aYzsce1A2EXCNpqqReOcjla6k9y5RaO12pPctcR/GVSHmlBt/0ZUXKK11HKXl02D3Oh6ajv+7QWwAA4FVNnfnxdZ20vMVae9QYM0nSbc1O5WM2FVeo+zWSpFCPMW7DAE1Ah+Fn9BcAAACn0tTBj2pJbSQdOOn4UEmvNSuRz6VeX6rMm2sVGnI3063hS3QYfkZ/AQAAcCpNXfbyM0lHT3G8tu65kmRTcYW6jlKg0zAFLmjvOo5vJWqrte6FR7lbgAN02Fs4FxrPJmNKvbFWoe6j6a9j9BYAAHhRUwc/Olhrt5980Fq7UVKHZiXysfTry5R4+T8UuLCzTDjqOo5vbVnwjBb/5gfasnCm6yglhw57C+dC46X3LldqxS+Ufmerwr2vpb8O0VsAAOBFTV32cqZ/VZbsPONg99GSxCuOzTRg8u1qccFF6j58gusoJYcOe8sVU+7Uxd376nNdSn4f6QYd626w3QDHScA1HAAAeFFTZ35sMMZ89eSDxpj7JG1qXiT/MuGoQr0n84pjM0XKK9VlyGhtmPuk4kybLig67C2ZTEaH9u5QJpNxHcXz6K53cA0HAABe1NTBj7+T9CVjzApjzIN1byslfUXS/85dPH+wyZhSuxbKJmOuoxSNzQtm6uVf/0BbFjBtuhDosDdxHjSM7noT3QUAAF7TpGUv1toPJA03xoyW1Lvu8Dxr7bKcJfOR9L4VSq1/UpIU6jXJcZricMXk22QkDZhc0ndOLhg67E2cBw2ju95EdwEAgNc0afDDGBOV9ICkLpJ2SHrEWpvKZTA/CXa75oT3aL6y8koNvflLrmOUDDrsTZwHDaO73kR3AQCA1zR12ct0SYOUHfiYLOknOUvkQyYcVajXJNaa51i8tlrbl7+keE211jz/e9aO5xEd9q5EvFa1Rz/Vas6BU6K73kRvAQCA1zT1bi89rbV9JMkY84ik9bmLBGRtmj9T1Z98pL989CfN/82/S8ZoxM1fdB0LKKjD+3fpnT1bteDhH8twDsAn6C0AAPCapg5+JI99YK1NGWNyFEcyxtwq6buSekgaYq3dWO+5f5Z0n6S0pP9lrV2Us2/cRDYZU3rfSgW7jeKVxxwbeO1t2rtuhboPuUbnXthGPUeMdx2p6NBf72vbtZcu6tBV57VuyzlwEvrrXfQWAAB4TVOXvfQzxvyl7u2opL7HPjbG/KWZmXZKulnSqvoHjTE9Jd0hqZekSZIeMsYEm/m9mi29b6VSG2covX+l6yhFp6y8Un2vmaKyikp1v/IarX1xBtOnc4z+el+krFzlLc7jHDgF+utd9BYAAHhNU+/2krdBB2vtHkk6xWySqZKettbGJR00xhyQNETS2nxlaYhNxRXsMlIyUrDrKFcxSsL6+c9q7q9+KEm66vNfdBumCNhkTOlDWxXsNor++gTnwF/RX/+gtwAAwCuauuzFhUskvVbv8aG6Yycwxtwv6X5JateuXV4DpfetUObtDQoOvJ0p13k25NpbT3hfbArZW0lK71+p9KanpaseUKjnxLx/PzSf186BQne2PvrrH/QWaB46C7+hs/AyY60t/Dc1Zomkz53iqX+x1s6p+5wVkv7x2J4fxphfSlprrX2i7vEjkuZba58/3fcZNGiQ3bhx4+mebjabjCl9YJWCXa5m8KP45W5jmwbku7cS3S0hBeltITpbH/0takV1rUVJoLPwo6L89wGKWk4629Q9P5rFWjvOWtv7FG9zzvBlhyRdVu/xpZLez2/SMzPhqEI9JvCP7wKK11Zr5XN/YP14M9Fd/6H7f0V//YHOAgAAL3Ey+NFEL0q6wxhTZozpKKmruMVuyXlt3rOa/at/12vzn3MdBSgoug+/obMAAMBLPLfnhzHmJkm/kNRa0jxjzFZr7URr7S5jzExJuyWlJP2ttTbtIiNTrt0ZOuVWyRgNvfYW11F8i/76E92nu35DZwEAgJd4bvDDWjtL0qzTPPcDST8obKLPSh9YpfSmZyQZhXqMdx2npJSVV2rU5+91HcPX6K8/0X266zd0FgAAeInnBj/8INjlaklGwS5XuY4CnDX6C7+iuwAAAGgqP+354RnZzfbGM+3akXhttVY8N51N9JqI/voTvae7fkNnAQCAlzD4Ad9ZO+85zXro37V2HpvooXTQe/gNnQUAAF7Cshf4zrApt+jc81ur71XjXEcBCobew2+GX3+b2nXvrUu79XQdBQAAgJkf8J+y8kr1HDpKK2c/pVgN06lRGug9/CaTzujg6zuVSWdcRwEAAGDwA/60Zt5zev6hH+nV+UynRumg9/AT+goAALyEZS9nySZjyryxWoHOI9l0z6ERU26RMdLwa29xHcVX6K+/lWrv6a0/lWpfAQCANzH4cZYyb6xWevNMSVLwctbeuxKtqNSYW+51HcN36K+/lWrv6a0/lWpfAQCANzH4cRZsKq5Ap+GSpEDnkY7TAI1nkzFl3t9xvLf0F35AbwEAAJAr7PlxFjJvrFZq5S9kLujA1GuPiNVUa8PS+UomEq6jeFrmzTVKr31Emfd3KHj5OPrrU7Gaai15drrisVrXUQqC3haHeKxWB3ZsKpneAgAAb2Lw4ywEOo1QoN0gmZaXuo6COjvWrlT3K67UstkzuAPGGQQ6jVBwwK0KXNzHdRQ0w+p5z2nT8oVKJZN6+dnpRd95elscUsmk3ti1Talk0nUUAABQwlj2chZMOKpg97GuY6Ce/leN07LZMzTzl/+hgAlo/K1fcB3Jk+hucRg55RZ1uLy31iyYpWd++WMZmaLuPL0tDmsWzNLMX/1EgWCoqPsKAAC8jcEP+Fo4EtGo625Vqwsu0oCr2AgRxS1aUakufQbqsq491bFHH7Xr2sN1JKBBo264jb4CAADnWPYC34tWVKrvsFFaNvtp1pSjZLy5Z6dsJuM6BtAo1rpOAAAASh2DH41gkzGl9y2VTcZcR8FprHzpea2v2wth4czHin4vhLNBf4tHrKZaC2c+plQyqfXLF2rlS8+7jpQXdLa4pJJJ7WfPDwAA4BjLXhpg08nsHQe2PS/JKNhtjOtIOIVR131eHS/vrVULZmvdskXqdHkfdes7wHUsp2wyJvvJe7Ifv6X0VvpbDLauXalPP/6zdqxfo9u//o9q16W760g5xzW3+KxaMFsbVi5R1179S/66DAAA3GHwowGZ97Yr0H6IJCnQcbjjNDidaEWluvW9Qu279dDVk2/U1nVr1DGRUDgScR3NmczBtbKHNis48uuSDP0tAv2GjdKHR45owIhrVBYtdx0nL7jmFp8xN9yqa6Z8Xm+/sU/xWG3RdhcAAHgby14aEGjbS5k/7VOgy9Uy4ajrOGhAWbRc29avUe+BQ7TohadUW8LLXwIdh8lceoUUCCrYbQz9LQLLX3pB65YvViqZ1EszHy/KfnPNLT5l0XJlMmntY+kLAABwiJkfDTDhqILtBrqOgbMw+KqxWvTCU5r+Pz+RAgFdd9s9riM5YcJRBbuNdh0DOTTmupvV+fLeWj5/jqb/4j8kqej6zTW3OC2fP0eP//JBBYLBoussAADwB88Nfhhj/lPS9ZISkt6Q9CVr7Sd1z/2zpPskpSX9L2vtImdB4VnhSERjb7hFCgQ0/oZbXMcBciZaUanufQeoc4/e6j1wiNpe2s51JKBRxk+9Rb0HDtGl7Tu5jgIAAEqUF5e9LJbU21rbV9I+Sf8sScaYnpLukNRL0iRJDxljgs5SwtPKKyp13W33KJOxmvvM46qtqZEk1dbU6Pmnnzj+GPCb2poazXnuGV3Ypq0k4zoO0CiZjNWmDRsUi9UqHuMuPgAAoPA8N/hhrX3ZWpuqe/iapEvrPp4q6Wlrbdxae1DSAUlDXGSEfyyZ+7we/e//1KZXV0mS5r/4gn79s59owYuzHCcDmmb+iy/o1z//iRbOnaPDh95xHQdolGO9XTB3tt7ct8d1HAAAUII8t+zlJF+W9Ezdx5coOxhyzKG6Yycwxtwv6X5JateueVPCbSquzMFXFeg4XCZU1qw/C26Mu/7zatepq7r16qOVixdq8g03ycho8g03uY52glz29hj6W5yuveFmGUkTptygUDjsLEeuO0tfi9vkG26SzVhdO/VmhULu/umRj2stkE90Fn5DZ+FlTmZ+GGOWGGN2nuJtar3P+RdJKUlPHjt0ij/KfuaAtQ9bawdZawe1bt26WTkzB19VZvssZQ6ubdafA3fKKyrUs98VWjDnBf3oO/+kDWtW6+Y77lJ5RYXraCfIZW+Pob/FKVJWpn4DB+vbf/8NLZj9grMcue4sfS1ue3fuUIdOnbV31w5FytwNbuXjWgvkE52F39BZeJmTl1+stePO9Lwx5l5J10kaa609NsBxSNJl9T7tUknv5ydhVqDjcElGgY7D8vltkGdrVy3TmIlTJElDRlwlSaqpqdFLc2bpuqk3qcJjAyG5Qn+LT01NjV6a/YKuu/Em3fOVr6tHn36uI+UMfS1u3Xv1OX7NBQAAcMFze34YYyZJ+r+SbrDW1t+V8kVJdxhjyowxHSV1lbQ+r1lCZQp2vYYp2D43ePjV2rF5va7//O0qr6hQMpHQ3Nkv6H9++qDWrl7tOl7e0N/is3b1K/r444/16upX1HvAQM/NYGoO+lrc1q5ZrY8//lhr1xTvNRcAAHib5wY/JP2PpHMkLTbGbDXG/FqSrLW7JM2UtFvSQkl/a61Nu4sJvyivqNBV4yYpHIlIkl5ZsVwTJl2r73z/hxo2coSeeWqGarj7C3xg2MiROq9VKw0bcZW2b93sOg7QaMNGHOvuSNdRAABAifLc4Ie1tou19jJrbf+6twfqPfcDa21na213a+2CvGVIxZU5sFI2Fc/Xt4BDw0ZepS2bNmj0mHGaO2eOli55WQf273Mdq9nobfGbO2eOli1dogP796v/gIGu4+QM3S1+r65Zo08+/kSvrlnjOgoAAChRnhv88AL71mvK7Jwt+9ZrDX8yfKe8okJjxk9UMBTS1Jtu1oM//W/t2rXb97M/6G3xO9bX3bt3K5FMuo6TM3S3+A0fMULntmyp4SNGuI4CAABKlNdvdeuE6TBUgbr3KG7RaFSzXnhBP/vpgzJGuuPOaa4jNRm9LX7F1Nf66G7xmzNnjn7+s58qEAgUTW8BAIC/MPhxCiZUJtNllOsYKJCpN94oY6Qbpt7oOkqz0NvSUCx9rY/uFr9i7C0AAPAXBj9Q8ioqKnglEr5BX+FH9BYAALjGnh8AAAAAAKCoMfhxEpuKK/PGKu46AF+iv/AT+goAAIBCYfDjJPbtdcrselH27XWuowBnjf7CT+grAAAACoU9P+qxqYTMZYOzdx1of6XrOMBZob/wC5uKy36wR6b9lfQVAAAABcHMj3rsO+uUXv+I1OoymVCZ6zjAWaG/8Av7znplNs+Q/WCPAp2vpq8AAADIO2Z+6NirkK/LtBuSfRXy3ItdRwIajf7CT7IzlAZlu9qmh+s4AAAAKBHM/JBk39kgu/Up2Q9eV6DTVbwKCV+hv/AT+856Zdb/XmrJDCUAAAAUDjM/JJl2g7Pv21zuOAlw9ugv/OR4X89t6zgJAAAASgmDH5JMqEym00jXMYAmob/wE/r6/7N35+FRlXn+9z93UpVUEtxNY7sgLoACCkhEZZFVQNkEUXFBu9seepn+Pb+Z38z1PL1NL/Y6M90/nV7UtlttZUdkEdl3BBQFV0RRXFptbQQVJaklS93PH1lMQvZU1Tn3qffruuo6oVKp883J53uf4q5zTgEAAMALnPYCAAAAAAACLesnP2xlQsm3d8hWJrwuBWgzcgvXkFkAAAB4icmP93bLvrZS9r3dXpcCtBm5hWvILAAAALyU9df8MGeVNFgCLiC3cA2ZBQAAgJeY/Ajly5wzxOsygHYht3ANmQUAAICXsv60FwAAAAAAEGy+m/wwxvzMGPOSMeYFY8w6Y8zpNfcbY8zvjDEHar5/ide1AgAAAAAA//Pd5Iek/7bWXmyt7S/pCUk/qrn/akk9am6zJN3b2RXZyoTsOzv59AE4g8zCNWQWAAAAfuC7yQ9r7ef1/lkkydZ8PUXSI7ba05JONMZ8uVMre3+P7P7V0vt7OvU0QMaQWbiGzAIAAMAHfHnBU2PMLyTdJukzSSNr7j5D0nv1HvZ+zX0fdnhFZw6UqVkCTiCzcA2ZBQAAgA94cuSHMWaDMWZvE7cpkmSt/YG19ixJcyV9p/bHmngq2/gOY8wsY8xuY8zuQ4cOtVxHKF+m+2CZUH7nfiGgk9qaWzILvyCzcFF7XiMAfkBm4RoyCz/zZPLDWjvGWtu3idvyRg+dJ+m6mq/fl3RWve+dKemDJp77fmttibW2pLi4OD2/AJBi5BauIbNwEbmFa8gsXENm4We+u+aHMaZHvX9OlvRazdePS7qt5lNfLpf0mbW246e8AAAAAACArODHa3782hjTS1JS0t8kfbPm/lWSrpF0QFJU0le9KQ8AAAAAALjEd5Mf1trrmrnfSvrnDJcDAAAAAAAc57vTXgAAAAAAAFKJyQ8AAAAAABBopvpskmAyxhxS9XVDWnKqpMMZKMcFbIsvNN4Wh6214zOx4jbm1iXkqpoX2yEjue1gZv2aCz/W5ceapPTUlW1jrV//tp2VTb9XEDPr4t+PmtsnU68Pjkran+71tJMfs+K3mvxWjyRFrLV9O/skgZ78aAtjzG5rbYnXdfgB2+ILbIvUYVtWYzs05Nft4ce6/FiT5N+6XBLUbcjv5TYXf09q9ic//o7U1Dq/1SOlriZOewEAAAAAAIHG5AcAAAAAAAg0Jj+k+70uwEfYFl9gW6QO27Ia26Ehv24PP9blx5ok/9blkqBuQ34vt7n4e1KzP/nxd6Sm1vmtHilFNWX9NT8AAAAAAECwceQHAAAAAAAINCY/AAAAAABAoDH5AQAAAAAAAo3JDwAAAAAAEGhMfgAAAAAAgEBj8gMAAAAAAAQakx8AAAAAACDQmPwAAAAAAACBxuQHAAAAAAAINCY/AAAAAABAoDH5AQAAAAAAAo3JDwAAAAAAEGhMfgAAAAAAgEBj8gMAAAAAAAQakx8AAAAAACDQAj35MX78eCuJG7dU3DKG3HJL4S0jyCy3FN4yhtxyS9EtY8gstxTeMoLMckvhLSUCPflx+PBhr0sA2o3cwjVkFi4it3ANmYVryCz8JtCTHwAAAAAAAEx+AAAAAACAQGPyAwAAAAAABBqTHwAAAAAAINB8OflhjHnQGPORMWZvvft+Yoz5uzHmhZrbNV7WCAAAAAAA3ODLyQ9Jf5U0von777LW9q+5rersSmxlQvadnbKVic4+FZARZBauIbNwEbkFACB4fDn5Ya3dJumTtK/o/T2y+1dL7+9J+6qAlCCzcA2ZhYvILQAAgRPyuoB2+o4x5jZJuyX9m7X2004925kDZWqWgBPILFxDZuEicgsAQOD48siPZtwr6TxJ/SV9KOm3TT3IGDPLGLPbGLP70KFDLT6hCeXLdB8sE8pPda1Au7Q1t2QWfkFm4SJyC9e053Ut4AdkFn7mzOSHtfagtbbKWpuU9GdJg5p53P3W2hJrbUlxcXFmiwQ6iNzCNWQWLiK3cA2ZhWvILPzMmckPY8yX6/1zqqS9zT22PWxlQsm3d3BRMziF3MI1ZBZBQI4BAHCXL6/5YYyZL2mEpFONMe9L+rGkEcaY/pKspHckfSMV67Lv7ZZ9bWX1es8ZkoqnBNKO3MI1ZBZBQI4BAHCXLyc/rLU3NXH3A+lYlzmrpMEScAG5hWvILIKAHAMA4C5fTn5kkgnl8+4NnENu4RoyiyAgxwAAuMuZa34AAAAAAAB0BJMfAAAAAAAg0Jj8AAAAAAAAgcbkBwAAAAAACDQmPyTZyoSSb22XrUx4XQrQbuQXLiGvCBLyDACAO5j8kGTffVb21Sdk333W61KAdiO/cAl5RZCQZwAA3JH1H3UrSabbpQ2WgEvIL1xCXhEk5BkAAHcw+SHJhPJlzh3qdRlAh5BfuIS8IkjIMwAA7uC0FwAAAAAAEGhMfqBJyXipPn9qiZIVXMQNSMZL9enqe5WMl3pdCtAkxmygfZKJqGL7n1YyEfW6FABAhjD50YitTCj55rasv3J76fPrVNh7mD5Z94Cq+A+fM8hveny2ebYOzfm+Pts8W5JUFS/Vx6vvpTc6ibymDmO2f5BrN9jKcpW98axsZbnXpQAAMoTJj3psVaXs355W8pXHZf+2y+tyPNWlZIKObH9UB+f+UEc2z/G6HLQB+U2fE0bOVPGtv9QJI2dKko5snq1/zP4BvdFBtjKh5Cdvy/5tF3lNEcZsb1V/5O2TNeMwuXbBka3zdXDej3Vk23yvSwEAZAgXPK3H/mOvzJkDlSPJnH2Z1+V4JhkvVezAbp006jaZnBydOPJWr0tCG5Df9EjGS1X2wjqdMOZrygnnS5JOHDlTkqE3Osi++4ySH7yo3EF3kNdOSsZL9fmW2Tp+1Fd10mjGbK/Yd59R8pUVysk/Tubsy8i1A04cNVMyRieOuFVHn16iov5jlRPp4nVZAIA04siPekzXC2UPH5DpPkQmlO91OZ75fMtsffjrqYq+uE6nXP1N5fJiwAnkNz0+3zJbB/9whz7f+GDdfbmRLvRGJ5hug5Rzej8pJ1c5511JXjvh8y2zdXjO9/X5pofIpYdMt0HK6TNJpuuFMqF8cu2A2n6JvriueozfMtvrkgAAaebLIz+MMQ9KmijpI2tt35r7Tpa0UFJ3Se9IusFa+2lK1xvKlzmjfyqf0knHj6g+tL+o/1iPK0F7kN/0qO2H2iU6r/rjQYd5XUYgkE9/INPuKuo/Vqfe+kt6CACygF+P/PirpPGN7vuupI3W2h6SNtb8GymUjJfqszX3SCZHJ47/Fod/ImvV9kIyXqqcSBf6Ab6UjJcq+sJaHT/6a+QT6CiTo8i5AyTj15fEAIBU8eVIb63dJumTRndPkfRwzdcPS7o2o0VlgaNbHtGRud9X6eaHW38wEGB1vcBh0PCxo1se0cd/vEOl9U7JAtA+Rzf/VQd/Np7XPgCQBXx52kszulprP5Qka+2HxpgvNfUgY8wsSbMkqVu3bhksz33HjbhNRkZdOPQz48itv9ALrSOz3iOn7Udu0Zjf+4jMwjVkFn7myyM/OsNae7+1tsRaW1JcXOx1OU7JiXTR8c0c3l8VL9UnO5cqWZHwoLLgI7f+0lIv1KqKl+rgqvtUFS/NYGX+QWa919qYfXDVfapKRD2ozL/IbXZqabxuy3jvJTIL15BZ+JlLkx8HjTFflqSa5UfpWpGtTCh5YKtsZfb8Rz8ZL9XRtdXXODjmexUJfbZ7nY7rM1Sf7lqpqlipPlh5n6piXzy2Mlaqd564X5Wx7PyPoB9kY25TraU+qFUVL1Xp/l06vHGO/v7ID/XZc+tVFS/VP2r+o1nXH4kofdFGZLd9WstpsiKhwxtm68hTy2Qry/XxzqVNjtsSY3emkPHUaGteq2Kl+uCJe+vyfnhT9Xh9eNOc6u/HS3Wo0WRIW8Z/AIDbXDrt5XFJt0v6dc1yebpWZN95Wsm9y5QjyZw/PF2r8ZWyrY/o87nfkyQdN+7bDb732bOrdELJWB3aMFuVRw8rceSg/jb7R5KMTp/wDUnS+xvnaf9DP5IkdZ84K6O1o1o25jbVWuqDWp9smqPPnl6q7v/fQslIJ156jT5a/5Dee+SHKjpvgI4eeF5/e+Q/1OW8AfrkwIv0RRuQ3fZpLaefPbtKJw+brsLzB+jwlgWq/PyQEp/845hxW2LszhQynhptzevBjbNr8i6dPvFbOnXUrZJUt/xk0xx9OPsHkqTia74pqW3jPwDAbb6c/DDGzJc0QtKpxpj3Jf1Y1ZMei4wxd0h6V9L1aVt/98urX6B0vzxdq/CdouG3NVjWd/wlV6ns9T0qHj1TR55frxMHXCWZHHUdU31+bGUiqjNG3ChJOnP0zZkrGg1kY25TraU+qHVyzYtnE8pT15oXzcU19xV2v0iF3foofOJp6nL+JSo8u49kk/RFK8hu+7SW0+MvuUqfP7deJwyaoMLufXXkuXrj9qhbJFW/g354z4a6bJLR9CLjqVE/r5WJqD5YP0enj75ZoYKGp6x0HT2zwTI30qVuvJa+GMdrl1Lbxn8AgNuMtdbrGtLgp3DAAAAgAElEQVSmpKTE7t692+syAqsyVqrSd17RZ2++oI92Pq4LZv23juve2+uy0sVkakXk1n21vRH7+ENVlR3RCb0u1XHd+3hRSkZyS2bdUlWR0PtrHtIbD/9Eff/lPp021FcfnsZYixZVVZYr+v4b+mTvdr3x1x+r51fuVDdvj1ois3ARrw/gmpRk1qVrfiANkvFSla39Y7vPcU1WJPThhjl6a86dOn3EDJ11zT+poGs3vbXiflXGytJULZA+He2Fpny4ca7emnOnii8Zo65DpurQyzvoC3RaZzNaFSvVZ6/t0uFdq/XlK6erx+0/0akDx0iSKmNljN/wtdqMJuMxfbDmQZ0+YoZ6fuVOnT76Zn20Y9kx17Npj1SO/wAA/2LyI8vFtj6so3O/p9jWR9r1c4efWa2uV16n4ismyYTDOm3otXp3wzzte+jHOrhngySpIlam/Y//RRW8mIYDOtoLTTlt5AwVXzZBJhzWRy9sVuKzw/r09T1136c30BGdzeiHm+bq7dk/1ckDRurTl7frzPFfrTtd4N0NcxuM3xI5hTeay93BPeu176Ef673NC9V1+I0y4bC6TZylT57boP3/M0v/2DS3w+tM5fgPAPAvX17zA5lTMPx2SUYF7TzH9ZRLxuiT5zbojHFfVU44X5LUbcwtyj+pq7peepUqE3G9tW6uXnjoThkj9Zz09TRUD6ROR3uhKTmhsI7vOVCS1HXgGFkrndjzEr2x4s86d/ztemv9fL3w4E/oDbRLZzP65VG3yKg6n10bnepSN34PHK33ty/Xly8bzxgOT9SOj5J0So+LdUL33jq4Z6NOGzhGA/7Pfeo6cIxCBUV1jz/lkjE69/af6bSa69l0RCrHfwCAfzH5keVyIl1U1IGrmucWdFHxkIYvnkMFRTpj6BR9/OozKvvo7zp7+DRJ0jljbkpJrUA6dbQXmpKbX6gTLrhMknRgzSNKHDmk6KcH9fJDdypyUlede9VNMobeQPt0NqO5BV10Rr1Peqmvdvw+sOLPShw5pKS1jOHwRO342H3k9drx85k6Y/BEVXx2WPFPP9L5k/7pmMe3lOu2SuX4DwDwL057aYGtTKjqjc2ylQmvS3HKCedepNMGjtKhvTt0/jVfUbjeOzTIHPLrD93H3KwTzumjc666RRd/7af68sDRChcUqeekr9Mb9ZBXf6jN65dLxujQ3p2M4WlE5ptWOz7mhPN05pDJOueq6kx2H8MnEgEAOofJjxYk396p5EtLlXz7Ka9LcUoov0B5XU7QWUOnKDecJ6n6HN59yzl3PJPIrz+ECop05tApChd0UY9JX29wuHYt+oO8+kX9vJ41dHLdGC6R01Qj89Way1Uov0A9Jn1d4YIuOnPolCbHTgAA2oPTXlqQc85gSUY551zhdSnOe2PdfO1+4KeSkXpP5tzxTCC/7qA/yKsLyGlqkflq5AoAkClMfrTAhPKV22OE12UEQo+xN0lG6nEV545nCvl1B/1BXl1ATlOLzFcjVwCATGHyAxkRLijiHR2gGfQHXEBOkQ7kCgCQKVzzoxW2Iq6q1zfLVsS9LsVZFbEyvfb4X1SZiHldSlYhu/5V2xNcO+FY5NZ/yGtmZWsPkDMAQLox+dGK5NtPKfnSkqy/IFlnvLl+vt7d/riqKsr1ChfLyxiy619vrp+v5x74id5cP7/B/RWxsqzvEXLrP43zSk7TK1t6oHGOmhsXAQBIFU57aUXthciy/YJknXHeVTfp5PP76Y2Nj+qZv9wpSeozhUNc043s+td5Nee2n9foHPf3nt2o2JGP9d6zG3XulZO9KM1z5NZ/Guf19XXztYuxPG2ypQca56i5cREAgFRh8qMVJhxRbs+RXpfhtHBBkb7U+1KddE5vGUm9rp6p8liZXl27QBeOm6E8Pr4uLciuf4ULinRBE+e4n3npKH3+8Uc689LRHlTlD+TWfxrntefY6v+cMpanRxB6oC25qM1R7bK5cREAgFThtJcsloyXKrr2HiXjpRlZX7igSH2mfF3GGO1bM087/nynXl27ICPrBpqT6T5oyatrF2rnX36mfWvmq6qi3Oty4CN+yiljOVrz6toFTeaiIlaml5c9oIpYWV2Owj6eNPNT3wEAOs+5Iz+MMe9IOiqpSlKltbbE24rcFd/6iErnf0+SVDju2xlb7zs716rXyKkqPLmrzh08PmPrBZriVR80pc+EmSo4qVhn9Rusd55aq/OunORpPfAPP+W0Vu1YLhn1vvpmr8uBj9Tm4cJxMxrc/9raBXr6L3dKRrpoyh1elNYufuw7AEDHOTf5UWOktfaw10W4LJmIKjK0+sVJZPhtGV13t0GjdPC159V90GjtXTlbvTlcGh5IxktV/uK6uvxnug8aK4+Vad/aBeo9boY+eu15dbt0lKf1wB/8ltP6ug0apXef3aSLJt2uqopyvbDsAcbzLFd/HOt37bGTGxeMmyEZ6YKxM5r4aX/x8nUSACA9OO0lS8W3PqzP7r5BoXMvUU6kS0bXHS4o0pkDhmrf2gXa/uef6Z1nNmV0/YAkxbfN1tE/3aHyF9epcNy3M94Hje1bu0AHnlypw2/t05kDhvr6UHBkjt9yWl+4oEjnXTlJuaGw3nlmk2JHPmY8z3K1+/V9zZwGFS4o0kVT7nBifPPydRIAID1cPPLDSlpnjLGS/mStvb/+N40xsyTNkqRu3bp5UJ4bIlfOlCSFzurrWQ29x81Q4UlfUvdBo/Tc0gfUd3z2vmNIbjOvtgfy+o31uJJqfa6+WReMma596xfr1HN7+74XyGxm+C2nzek+aJSOfnJQ3Qf5+4glcps65bEy7V2zoMG+u3fNaS69x/n/yI7W+OF1kkRm4R4yCz9z8ciPIdbaSyRdLemfjTFX1v+mtfZ+a22JtbakuLjYmwodkBPposKx3/L03Yy8giL1HD5Je9cs0NY//1x71y70rBavkdvM80MP1BfOL9C+9Yud6QUymxl+y2lz9q5ZoG1//oXvs0tuU6epfXdeQZH6X3uH7ydv28IvvUdm4RoyCz9z7sgPa+0HNcuPjDFLJQ2StM3bqtAZfcfPkIxR33E3el0K4Cl6Aa4iu9mHvzkAwDVOTX4YY4ok5Vhrj9Z8PVbSnR6XhU7KKyjSJdd+zesyAM/RC3AV2c0+/M0BAK5x7bSXrpK2G2NelPSMpJXW2jXpXqmtiKvq9Y2yFfF0rwpIOfIL15BZZDt6AACA1HNq8sNa+5a1tl/NrY+19heZWG/y7R2qeuExJd/emYnVZa3yWJn2bV2hRLRMu5Y8qPJYmdclBQL5dVNFIqZ46WdZ2Qtk1l3ZnNtU8rIHymNN74PLY2V6dil/VwCAu5ya/PBKzjlDlNt/unLOGex1KZ2SjJcquuFPSsZLvS6lSS+uWaiP3npNz69eoH3bVungW696XVIgBCW/neX3/Dd28MAreuOZLSo78rHeeGaz1+VkVDZn1rWcNnbwwCt6fs0ixvBO8rIHnl+9UOv/9As9v2ZRg/tfXLNQG//0c724xt8XtU0F1/sQANA0p6754RUTjii3p78/vq8t4tvnKrF7uULd+yvv/Mu8LucY/cbfqAPPbNL5l41Rv3HT9cK6JfrSuRcqPwBXjfdSUPLbWfHtc1W26D8kSYVjvuFxNa07rcdFKj7nApV+eljnXzrS63IyKpsz6/dxujVdz++j4nMuUP/xNzCGd0KmeyARK9Nzqxfpkqtv0CUTbpKM0YDxNzR4TL/xNzZYBpnrfQgAaBpHfmSRyLCZOuF/zVPl28/77t2M8liZ3npmk3oOHqe8SIFeWLdE6+77hZ5fvaj1HwbaIDL0FhXd8DNFhs2sfldv/X2+64Na5bEyffL+W3puzaNa96dfHfMOLILLz+N0a8pjZXrz6Q0K5TOGu+a51Yvq/l7h/AJdNvWrx3xcbV5BkS6d+jXlFRSpPFamPQE+BcblPgQANI8jP7JITn6hotseUdnCH0qSCq/6pscVfeHlNQu15f6fa8SsH2rg1K/pkqtvkJE04OobWv1ZoC1yIl3qjviIrr/Pl31Q6+U1C7V/20pN+9mD9EGW8fM43ZracXzCd8UY7pj2/r1q/9aSNHBq8D7xxeU+BAA0j8mPLBMZdmuDpV9cVHMYbe0yv6BIl0/7qpclIcD82ge1avsgN5xHH2Qhv+ezObW5PXfQKOUxhjulvfvcxvvsIHK1DwEAzeO0l4BLxssU3fhnJePVh6bmRLqo8KpvKifSxePKGsorKNLAmsNpgVRonP36/NoHtWr7IZxf4HUpSLOmcur3fDaHcTx7BPlvXduTMrlO9iEAoHlMfrSDrYirav9G2Yq416W0WXzHPEUX/0TxHfO9LqXdErEy7XzsISUCek5xJrmY3c5yOfv1ZXMfZENug5LTxrI5t+mUyp7gb9S0up7cPtfrUgAAKcZpL+2QfGuHqp5/VIocr9yzL/W6nDaJDLlZklFk6C1el9Jue1Yt0ur7fqkup3xJF4+Y4HU5TqvLrqTcXqM9riYzXM5+fXtWLdLerat0Rq+LdXbfgV6Xk1HZkNug5LSxbM5tOqWyJ/7x5qvau3WVZIwGT/tKCqoLhsjQWyUZRYbc5HUpAIAU6/CRH8aY04wxp9V8XWyMmWaM6ZO60vwn59whyr3iDuWcfpEqX13nxLuROZEiFY7+umSrFN1wv1NXLR94zQ26/gd3q9egEXpp8xOqrCj3uiRn5Zw7RLkDrlfOeUNlK+LO5LczXM5+fSUTZ2jmL/+iI4c+zLoeqMvtuUMkKZDZDUpOG8vm3KZT455oSlv6JBEr03v7X9bMX/5FJROCe92O9kjGSxXdcL9kq1Q4+uvKiQTvlB4AyHYdmvwwxnxD0lOSnjbGfEvSE5ImSlpijLkjhfX5iglHlHv2pao6sE1Vexaq6sCTXpfUIhsvU2zTX2QryhXfPk/RR3+k+I55XpfVZvkFRbp4xATt37VZ5/a/QjuXz+Hw3A4y4Yhye42WCeU7k9/OcD379eXlF+iNZ5/UeVnYA3W5DUckKVDZrctozbU+XM9pY9mc23Rq3BNNaa5PErEyPfnYX5WIlWn/05u16r5f6rl1S5XHtYUk1evB7XNkmbADgEDq6Gkv35HUR1KBpL9JOt9a+w9jzEmSNkt6IEX1+VLu+VdKMso9f5jXpbQovnO+oo/9VDnHf0mRoTdLpvYQa7f0HjpWO5fP0RP3/VrG5GjYdV/xuiSnuZLfzghK9mvRA9WClN3ajEpSwaivByKnjZFbbzTXJ8+selQr7v2lJOmKyTdrwrd+oJKrr/egQn+KDL1ZUlKRQdNV/uIa5ZdM9rokAECKdXTyo8JaG5UUNca8aa39hyRZaz81xtjUledPJhxR6MKrvC6jVZHB1eer5vUdLRMpUuHoWR5X1DGhcJ4um3CjjMnRZRM5PLezXMlvZwQl+7VC4TxdPukmnXVBP53Ro7fX5XgmSNmtzWjtMifSxfmcNhYK52nwlFt1/ClddeHlI7wuJ2s01yeDrrm+bhkK52kI1/loICfSRQXDv6byF9cor28wrzEEANmuo9f8SBpjwjVf112J0hgT6cRzOsFWxFX12gYnzjk3kSIVjPq6TADOW80vKNKw674im0xq6+K/cgh1B7mU384IUvZr2WRS7772smwy6XUpGRfE3AYxo40lYmXasXyeLrx8hPID+JGoXmtLXyRiZXX7zNr9KH+L5plwnvJLJge6LwEgm3V0omKaJCtJ1tr3691/iqR/62xRfpZ8c7uqnluk5JvbvS4lKz298lEtu/dXenrVYq9LcRL5dVc2Z5/cuimbM5sJbekL/gYAAHyho6e95Em6TNKORvefJ+ntTlXUCmPMeEn/IylX0l+stb9O5/oayzlvaIMlMuvyCddLxujya6Z7XYqTyK+7sjn75NZN2ZzZTGhLX/A3AADgCx098uNuSUebuD9a8720MMbkSvqjpKsl9ZZ0kzEmoyfAm3BEuReMafFK60if/IIiDb/udg7b7SDy665szj65dVM2ZzYT2tIX/A0AAPhCRyc/ultrX2p8p7V2t6TunaqoZYMkHbDWvmWtLZe0QNKUNK6vRbYirsp9awN1HjqyA9mFy8gv0H70DQAg23V08qOlt9/S+YHxZ0h6r96/36+5r44xZpYxZrcxZvehQ4fSWIpU9cZWVe1ZoKq/v5jW9SD4MplbqV52D2xL+7oQTJnObH3kFx3lZW69Rt+4KZszCzeRWfhZRyc/njXG/FPjO40xd0ja07mSWmSauK/BR+taa++31pZYa0uKi4vTWIqU22O4cod9U7lnXKzKV9b46t0UGy9TbPMDsvHgfSpKIlamLYsfDtQnvmQyt1JNdktuUu75V1avvyLuuwx3BLnPnExntr66/PYY7mR2g5zT+vyWWcnb3KZba9u78bhfn4t9lAl+6NUgZxbBRGbhZx294Om/SFpqjLlFX0x2lKj6QqhTU1FYM96XdFa9f58p6YM0rq9FJhxRqPtlqnxljSqfmStJCvUZ71U5DcSfWqDokjslSQUj7/C4mtR6auViLb3nV5KkEdNv97gaN5lwRKELx9b9u+r1Lb7LcEeQ++xQP79+HH9bE+Sc1kdmM6u17d143K8vKPuAVMuWXgWAbNGhyQ9r7UFJg40xIyX1rbl7pbV2U8oqa9qzknoYY86R9HdJMyTdnOZ1tshWJpR7/jBJUm7PEV6W0kDkihkNlkFyxYTpOv7kYl08bIzXpTjPVsRV9d4Lyu05XJK/MtwR5D67+HX8bU2Qc1rf4Ek3qFuvvjqzZ0avS561rpgwvcGyKbYirqrXtyq35/AGF0qt7R+X+igTsqVXASBbdOi0F2NMxBjzL5Kuk1Qu6d4MTHzIWlsp6TuS1kp6VdIia+0r6V5vS6r2b1H5xt/KnHqurz6JwESKVDDyDplI8K7wnl9QpN6XD9fWZfMVj/rncGoXVb2+VZVP3quq919UqM94X2W4I8h9dvHr+NuaIOe0vmRVUm+/tlfJqqTXpQRWPFqmjY8+rHi0TPkFRRoxveVPdql6fasqd89T1RtbG9xvwpFA7ANSLVt6FQCyRUdPe3lYUoWkJ1X9sbMXqvpUmLSz1q6StCoT62qL3J7DJSPlnHJ29Tsq+zcrt9dIXkCk2Y6Vi/XYPb+WMdIoDqfusNr85p7ZX5LIsM+R+4YYf/2NvKZfe7dx3ZjfY3izj6GXAABB1dHJj97W2oskyRjzgKRnUleSW0w4olDvcZKkyr2rVblrtiQp1PdqL8sKvCETpssYafA1zR/ei9bVz68kVe3fTIZ9jNw3xPjrb+Q1/dq7jRuP+U1hPwAACKqOTn5U1H5hra00pqkPYck+ub1GNlgifSKFRbyTmAZk2N/IffPIrv+Q1/RLxzamlwAAQdXRyY9+xpjPa742kgpq/m0kWWvt8SmpzjEmHOFdEjiNDMNVZBdIDXoJABBUHf20l9xUFwIAAAAAAJAOHfq0F/iXTZQptvkB2QSfBoHsQObhCrIKuIN+BYDgYfIjYOI7Fyi69OeKP7XQ61KAjCDzcAVZBdxBvwJA8HT0mh9ohq2Iq3L/JoV6jfLkI+Iig2dIxihyxY0ZXzeCwesMtxeZR31+zi9ZhUv83EuZQL8CQPBw5EeKVe7fpMqnH1Hl/k0ZX7dNlKl832ZFht4qk1+U8fUjGLzMcHuReTTmx/zaRJliWx+STI4KRnyNrMIJfuylTGHfAgDBxORHioV6jVLo8tsU6jUq4+uOP71IZY/8i+I75mZ83QgOLzPcXmQejfkxv/GnFym27BeKP7XA61KANvNjL2UK+xYACCZOe0kxE44o3PcaT9YdufyGBkugI7zMcHuReTTmx/ySU7jIj72UKfQsAAQTR34EiMkvUsHwr2bVIZrxaJk2PPqw4lGuxp6Nsi3z5N1N2ZbTxsht6rAtMyPbexYAgorJjzSwFTFVvLRStiLmdSmBt33lYj36x19rx8rFXpcSKGTYn8h725BffyG3qePFtqSfAABBwWkvaVD56iZVPvWwJCl88QSPqwm2oROmy0gaMmG616UEChn2J/LeNuTXX8ht6nixLeknAEBQMPmRBqELRzVYIn0ihUUaff3tXpcROGTYn8h725BffyG3qePFtqSfAABB4cxpL8aYnxhj/m6MeaHm5turcJlwgcIXT5AJF2RsnTZRpti2v8omOA8YnedFhtuDvKMlfsovWYXr/NRPmULfAkAwuXbkx13W2t94XYSf2ESZKj94TZXvvazY8l9Kkgqu/Iq3RQFpYBNlSuxarPzBNym+61HyDl9jbAbcVbePsVaRIbfIhPK8LgkAkAKuTX6gkcSuxSp/cbW63HG/JCly2fUeVwSkR2LXYsUe/5XMccV1OSfv8CvGZsBdkcuul6xV/iWTVf7yBuUP8O3BxgCAdnBt8uM7xpjbJO2W9G/W2k+9Lshr+ZdVX/TMhMK8q4hAq816Xu/h1R9DSN7hY4zNgLtMfpEiQ25R+csblNd7uNflAABSxFfX/DDGbDDG7G3iNkXSvZLOk9Rf0oeSftvMc8wyxuw2xuw+dOhQBqv3hskvUuTK22Xysudc3CDKttx2RF3W84u8LgUis61hbPYncou2MqE85Q+4xvN9DpmFa8gs/MxXkx/W2jHW2r5N3JZbaw9aa6ustUlJf5Y0qJnnuN9aW2KtLSkuLs7sLwBPJOIxlR39XGsXPaJ41M2Lk5FbtEc8WqY1Cx/2NO9kFm3lh7zWcim38WhZ3X4tEY9p3aP+2IbILJcyC0hkFv7mzGkvxpgvW2s/rPnnVEl7vawH/vHuG/t04JWXtPCe6mvhjrvhNo8rAtJry4rFWvDH/5KRNO5GPkIU/kZeO2brE49p/h/+U5J07oV9tPAP/ykjo6uuZx8HAEBHODP5Iem/jDH9JVlJ70j6hrflwC+69eit07v3UE5OroZPvM7rcoC0GzFpuoyk4ZOme10K0Cry2jG1+7PhE6+TycnRjO98V8MmsI8DAKCjfHXaS0ustTOttRdZay+21k6udxSIb9mKmCpefEK2IuZ1KYGWHylQ0XHHa9wNtylSyPUg0oEs+0uksEjjbrydvLeC3PoDee2YSGFR3X4tP1Kgq6733z6OHgMAuMSZyQ8XVe7bqIqdD6ly38a0PL9NlCn+5COyCc4BrhWPlmmNw9f+8Kt0Z7k1ZL0a+W4fL3JLVo9FbjvGhe3m9b4hnehlAAgel057cU6o9+gGy1RLPPOYYiuqzweODOMcYEna8sRjmvP7/5JkNP6GmV6XExjpznJryHo18t0+XuSWrB6L3HaMC9vN631DOtHLABA8TH6kkQkXKNxvYtqeP3/QdQ2WkEZMvE6S0YiJ07wuJVDSneXWkPVq5Lt9vMgtWT0Wue0YF7ab1/uGdKKXASB4mPxwmMkv4t2IRiKFRb59hwwdR9arkW//I6vHIrcdw3bzFr0MAMHDNT/SzJbHVPHiCtny1F4MzCbKFN/OuaidFY1GtXD+PEWjUa9LcUK68tzs+sh5A+S1YzKRW7LaMrKbHdsg0/uIdKGfASCYOPIjzSpf3aCKHQ9KksL9JqXseRPPPqbYE9XnAkeG8s5Qe0WjUR1443W9+so+/e7u30qSbrzpZo+r8r905bk55LyhFcuWkdcOyERuyWrLyK60Yvky/e6u6m1wYe/eOr9HTxUWFnpcVWpleh+RLvQzAAQTkx9pFrpwTINlquRfWn0ucP6l/j0X2M+eWL5Umzes13/d9TudcuqpunLECK9LckK68twcct7QNRMn6qSTT9TwEaO8LsUpmcgtWW3ZxClT1OvCC9SjZy+vS/HM1Oum65RTTtVll1+u//df/x+NHDNWNwRsIijT+4h0oZ8BIJg47SXNTF6Bwv0myeQVpPZ584sUGTpTJr8opc8bBIl4TGVHP9f2DauViMcULStT6dHPtXTBHMVqDjeeOGWqRo4Zq7z8fA0eOlSPLV4c6EORUyVdeW52feS8geq8XqklS5aotLRUibjbh5ZnSiZyS1ZbZoy079VXZYxUWVHhdTkZF41G9djixRo8dKjy8vM1csxVmjh5irauX6NYtEzbN6yuW5Yd/dzZ3s70PiJd6GcACCaO/EDgvPP6a9r/yos6+tkRnVzcVdZavbZvr/7y+7t08inFGjRkmJ7e/qSmXjdd4bw8zZ83T3ff9VsZI80I2LtwCJZEPKqVK1fr7ppD5y+7tETn9ujpcVVA65YvW67/uev/yshoypTJCoXDXpeUUcuXLavr20GXlujaadP18gt79OsffVez/ve/q/TIx/rk8CEdPfKJPjl0UL369FOviwd4XDUAAMHC5EeG2PKYKvetV6j3Vc6/I+J33XteoDPPOU/PP7ND5/W6UFVVSZ19Xg/l5ORq8PCRWv7Yo7rn7t/o2//675o+4xZNufZaGSNNnnKt16U7gSx7p7DoOE2cOFHJZKUmTpyoggK2f1uRW2/Vz21efsTrcjKudj8zYcJEfe9f/5dGjBmrSdOu06z//e8aP3mq9ux8UgMHD9Oep7ZpwKAhgZocovcAAH7B5EeGVO5br4rtD0iSwv0ne1xNsOVHCpQfKdDQ0Vc3uH/qjFslSROmTJWMNGHyVElSYWEhR3y0A1n2TigUUl5eni6+6GLl5eUF6j9I6UZuvdUgt6Hse+lRu59JxOMacdVYTZg8Vfn5kbr90tAx46uXjfZbQUDvAQD8IvtegXgk1PuqBkt4IxaN6ukd2zRl2vUK5+V5XY6TyLL3jKzXJTiH3HqP3Er5kYimz7ilwX2xaFSrHl+iayZPU0HAPv1FovcAAP7BBU8zxOQVKNx/Mod8emzV40v0y//4rlYsedTrUpxFlr31xLLF+tdvfFUrlz3mdSlOIbfeIrfNW/X4Et1392+0+vGlXpeSFvQeAMAvOPIDWeWaydNkZHR1zSkvgGvIMFxEbpvHtgEAIDOY/EBWKSgs1LRGhxwDLiHDcBG5bR7bBgCAzAP1BJgAACAASURBVPDdaS/GmOuNMa8YY5LGmJJG3/ueMeaAMWa/MWacVzV6ySaiiu+YI5uIel0KkFZkHa4gq0Bw0M8AEFy+m/yQtFfSNEnb6t9pjOktaYakPpLGS7rHGJOb+fI6zpbHVPH8ctnyWIefI7F7ieIr/1uJ3UtSWBnQPqnIcmvIOtIhHdklq0DzMrG/SCX6GQCCy3envVhrX5UkY0zjb02RtMBam5D0tjHmgKRBkp7KbIUdV/nKOpU/+RdJUnjAlA49R37JtAZLwAupyHJryDrSIR3ZJatA8zKxv0gl+hkAgst3kx8tOEPS0/X+/X7NfQ0YY2ZJmiVJ3bp1y0xlbRTqM7bBsiNMfqEiQ25NVUnwCT/ntimpyHJryLq/uZbZWunILll1h6u5dVkm9hep5Ld+JrNwDZmFn3ly2osxZoMxZm8Tt5beEjjmUBBJ9pg7rL3fWltirS0pLi5OXdEpYPIKFB4whY97wzH8nNumkGW4ltlaZDe7uZpbl9FznUNm4RoyCz/z5MgPa+2YDvzY+5LOqvfvMyV9kJqKAAAAAABAUPnxgqfNeVzSDGNMvjHmHEk9JD3jcU0ZZRNRxXfO5QrkCCwyDteQWcBd9C8AZBffTX4YY6YaY96XdIWklcaYtZJkrX1F0iJJ+yStkfTP1toq7yrNvMSepYqv+q0Se5Z5XQqQFmQcriGzgLvoXwDILr674Km1dqmkpc187xeSfpHZivwjf+BUSUb5A6/1uhQgLcg4XENmAXfRvwCQXXx35EfQ2fKYKp5b2uzn3dvyqBK7FsmWH3sIpskvVGTwzTL5hekuE2iT1vLc8LHNZ7sWGUcmpDK3ZBZov/b0YPuet/X9TH30LwBkFyY/Mqxy7xqVb/uzKveuPeZ7trJc5c+vUGLD71X591dky+NKxo4q8dQ8zkeFL7WU51q2PKrK915W+fNPKLHh96o48FTN/eQb3mhvbitf3aSqTz+QTURV/vJ62URUiafmk1ugg9rSg21ly6Mqf+bRmtdQjfYz9CwAoB7fnfYSdKG+4yUZhfqOa3C/raxQ5etPKtx3rEyXUxQ6q5+q/r5PVX/fq/i638l0OVV5F431pmigGc3muTymihdXKjxgiipeWKmK1zar8Ib/lDnuFIXPu0KV774kWauqv79MvpFxzeVWqs5u1UcHlPzgVVW8tkWFN/638i6+WlWH3lL5c8tlo5+qvPSQKl7ZqNzTeyt0dr/M/wKA41rqwZbU7Vv6Taj76NyKF1YqsfEPMl1OVt6AiQ32M1V/f4WeBQDUYfIjw0xegcKXHHtuaeXrTyr37EtU9bfnFL5ghCpe3aLQeYOU86VzZY77ksI9hyixc57yBl7L4ZnwjebyXPHiSiU23SPT5WSF+0+QjKTcsPJ6j1bi6YWq3LdRBbfcRb7hieZyK1Vnt+K1LSq8/leSMVIoT+XPLqnO7E2/VeWbTyvcc5jC/Seq4vknlHtaDzILtFNLPdiS2n2LjJRXMl2S6vYxofOvkMkrbLifoWcBAPUw+eERWx5TxctrFL5ovExegULnX6HKN59SqOeVMrkhhXsOVsUbOxXuNVx5F41VYuc8xVf/VpKUP/hmj6sHvtA4y5IU7lfzYvS8K2TyCpR36fV1j8+7ZJJkJJOTK5NfRL7hmZayq9y8utzWZTYUVl7fqyRJ5TuXkFkgBZrqw+bU9mf44gl195m8wgb7GImeBQA0jckPj1S8vEblW/8kScobOLX6XZALR9V93+QVKq/PmLp/59VciTyPK5LDZxpnWap+V6/2XbnGTF6h8i+7scF95BteaGt2ySyQPk31YXNa2rc0fBw9CwA4FpMfHglfNL56efE1bXq8yS/knQr4Ul2Wa5YdQb7hhc5kl8wCqZGKfUhb0LMAAD7txSMmr6D6HQ6bVPnuxSn/uDcgU2qzXHu4si2PkWk4oX52yS3gjcb7kMboTQBAqjD54bGKl1YqseleVby0yutSgJQg03ARuQX8id4EAKQKp714rPqiXabNp78Afkem4SJyC/gTvQkASBUmPzxWffGu67wuA0gZMg0XkVvAn+hNAECqcNqLh6rPY13CeawIBPIMV5FdwF/oSQBAOjD54aGKl1arfMt9qnh5tdelAJ1GnuEqsgv4Cz0JAEgHTnvxUPjiqyUjhS+62utSgE4jz3AV2QX8hZ4EAKSDr478MMZcb4x5xRiTNMaU1Lu/uzEmZox5oeZ2n5d1pkr1x7tNa/bj3QCXkGe4iuwC/kJPAgDSwW9HfuyVNE3Sn5r43pvW2v4ZrgcAAAAAADjOV5Mf1tpXJckY43UpAAAAAAAgIHx12ksrzjHGPG+M2WqMGdbcg4wxs4wxu40xuw8dOpTJ+oAOI7dwDZmFi8gtXENm4RoyCz/L+OSHMWaDMWZvE7cpLfzYh5K6WWsHSPo/kuYZY45v6oHW2vuttSXW2pLi4uJ0/ApAypFbuIbMwkXkFq4hs3ANmYWfZfy0F2vtmA78TEJSoubrPcaYNyX1lLQ7xeUBAAAAAICAceK0F2NMsTEmt+brcyX1kPSWt1UBAAAAAAAXGGut1zXUMcZMlfR7ScWSjkh6wVo7zhhznaQ7JVVKqpL0Y2vtijY83yFJf2vlYadKOtypwoODbfGFxtvisLV2fCZW3MbcuoRcVfNiO2Qktx3MrF9z4ce6/FiTlJ66sm2s9evftrOy6fcKYmZd/PtRc/tk6vXBUUn7072edvJjVvxWk9/qkaSItbZvZ5/EV5MfXjDG7LbWlnhdhx+wLb7AtkgdtmU1tkNDft0efqzLjzVJ/q3LJUHdhvxebnPx96Rmf/Lj70hNrfNbPVLqanLitBcAAAAAAICOYvIDAAAAAAAEGpMf0v1eF+AjbIsvsC1Sh21Zje3QkF+3hx/r8mNNkn/rcklQtyG/l9tc/D2p2Z/8+DtSU+v8Vo+Uopqy/pofAAAAAAAg2DjyAwAAAAAABBqTHwAAAAAAINCY/AAAAAAAAIHG5AcAAAAAAAg0Jj8AAAAAAECgMfkBAAAAAAACjckPAAAAAAAQaEx+AAAAAACAQGPyAwAAAAAABBqTHwAAAAAAINCY/AAAAAAAAIHG5AcAAAAAAAg0Jj8AAAAAAECgMfkBAAAAAAACjckPAAAAAAAQaIGe/Bg/fryVxI1bKm4ZQ265pfCWEWSWWwpvGUNuuaXoljFkllsKbxlBZrml8JYSgZ78OHz4sNclAO1GbuEaMgsXkVu4hszCNWQWfuPLyQ9jzIPGmI+MMXvr3XeyMWa9MeaNmuVJXtYIAAAAAADc4MvJD0l/lTS+0X3flbTRWttD0saafwMAAAAAALTIl5Mf1tptkj5pdPcUSQ/XfP2wpGszWhQAAAAAAHCSLyc/mtHVWvuhJNUsv9TUg4wxs4wxu40xuw8dOpTRAoGOIrdwDZmFi8gtXENm4RoyCz9zafKjTay191trS6y1JcXFxV6XA7QJuYVryCxcRG7hGjIL15BZ+JlLkx8HjTFflqSa5Uce14OAiEajmj9vnqLRqNelAK0ir3BRtuc2239/BA+ZBuAilyY/Hpd0e83Xt0ta7mEtCJDly5bp7rt+q8eXL/O6FKBV5BUuyvbcZvvvj+Ah0wBcFPK6gKYYY+ZLGiHpVGPM+5J+LOnXkhYZY+6Q9K6k672rEEEy5dprZYw0eQrX0IX/kVe4KNtzm+2/P4KHTANwkS+P/LDW3mSt/bK1NmytPdNa+4C19mNr7WhrbY+aZeNPgwHaJBaNavH8uYrVHKpZWFioGTfdrMLCQo8rA1qXFw7r0pIS5eb4cvgGmhTKzdWIESMUys31uhRP1O5n8sJhbVq3tm7/A7im9jVUbk4Or50AOIdXz1kkGS9VdMOflIyXel2Kp1YuX6p77v6NntrxpKLRqBbO55zVbBCE/EejUS1+dKFOPuVU7Xhyq9flIA2CkNOmJBIJbdq4QYnyhNeleKa2fweUXKqndjzpdTloQVD7MBVqX0OtWPZY3X2uv5bi7w1kD1+e9oL0iG+fq7JF/yFJKhzzDY+r8c6EKVMlIw0bPlJLHlus3931W0nSjTfd7HFlSKcg5H/F8mX6/d13SZKum36Dx9UgHYKQ06aseuIJ/fF3/6Pc3FDWjrX0rzuC2oepUPsaasLkqXX3rVi+zOnXUvy9gezB5EcWiQy9pcEyWxUUFmr6jOptMKnmXNVJnLMaeEHIf/28hvPyPK4G6RCEnDZl0rXXSia7x1r61x1B7cNUqP8aqpbrr6X4ewPZw1hrva4hbUpKSuzu3bu9LgPBYDK1InKLFMpIbsksUoixFq4hs3ARrw/gmpRklmt+IKvEolE9tmCOEvG416UAHVJRXq7N69dwwUQ4JRGPa++LzzP2NqF2v0RPw6/IKICgyOrJD1uZkH1np2xl9l6ALdusenyJtm5Yp/KKci2aP9e5i3OR2ewWjUa1ZPEi9R84SLscuWAimYUklVeUa+/LL6u8otzrUtoknbmNRqMN9j+rHl+i++7+jVY/vjTl6wJSobmMNs4y/IN9L9C07L7mx/t7ZPevrj6Gpvtgr6tJq2S8VPHt8xQZerNyIl28Lscz10yepl4X9tXqFSv0h7t/K8noBpcuzpVFmU2VIGX/ieVL9ce7/68kaZorF0wks20SpJw2ZfWKFbrnd3crJzdXN9zkwHn1acztE8uX6g93fbH/uWbyNBkZXV3vApLIvKD3YGc0l9HGWfarrPzbsu8FmpTdkx9nDqweFM4c6HUlaRffPk/RR38kGalw9Cyvy/FMQWGh+vbrr3N79JSM0UTXLs6VRZlNlSBlf+KUqZKqc+vMBRPJbJsEKadNmXjtVLfG3DTmtn4fS9X7pWkzHJgQCrig92BnNJfRxln2q6z827LvBZqU1ZMfJpSfNbOhkaE3S0aKDPHvzHwmFRYW+vpdiuZkU2ZTJUjZdzG3ZLZtgpTTpriW3XTm1rVtkS2C3oPp4EqWs/Fvy74XaFpWX/Mjm+REuqhw9KwGh/sl46WKrr1HyXiph5UB6dVU9uujD+AH5BTwFq+Tgqu18bUtyAIQDEx+ZLH41kdUOv97im99xOtSAM/QB3ABOQUyj75DLbIABAOTHwFl42VK7FlRPVO98c9Kxssk1Vz06ZmlSiaiigy9WV1u+pUiw2/zuFogNWy8TLHND8gmYkrGyxpkv75kIqpk2RHFdy1RZPht9AEyqrWcJuOliq6/rzqn8VJyCmRQMl6mxL5tvE5yQN1Y2sR+vjl1Y24i9sVY28LRHIzBQLBk9TU/giz+1AIljx5W1acfKvrYTyUZFY7+uuJPzlHy80NKfvqBEruXq+iGO7PnytcIvPhTCxRdcqdC3S5WxTsvKLr4J6rNfn2V776syjefUdmiH+m4bzygwnHf9qReZKfWchp/co7KFv5Qoe4DVPn2cypb8H1yCmRIfMc8hU7rofiWh6pfJ13/U9lEVOK1ku/UjqWSVDDyjrb9zI55ii7+iUJn91fl23tUtvCHkqTCq77Z9OO3zWYMBgKEyY+AilwxQxXvPK9Q9/6SyVFkyE3V9w+7VeUvrVfexVdJJkehs/p6XCmQOpErZkiSQmddrNwzeksyddmvL9TtIoVO7yXlhJTXb2yGq0S2i1wxQznHf0mhs/s3mdPIsFsl1eT0rD6SRE6BDIkMuVkVbz2nyPDbJVX3ockJe1wVmlK7z69dtulnhtwsySh0Vl+Fzryw+r6aMbfJx185UxJjMBAUxlrrdQ1pU1JSYnfv3u11GZ6x8TKV792ovH7jZcKOfCymf5lMrSjbc5sKZL9ORnJLZtvPxssU3zlfkSG3yOQXeF2OnzDWwjO2olwVB3YpfP5l7dl3kFkfqxtrB98kEynyuhw/4fUBXJOSzHLNjwCL75yv0of+WfEnW784UzJeqqMBvop1LBrV0gVzFItGvS4FGdCe7NfnSh+QZ/fFd85X9LGfKr5jbrt/1pWc1kdmj8U28ZdkvFSlG+5X7hkXqPzFNV6X42suZbdurN053+tSnBy7gaDhtJcAiwy+qcGyJWVbH9Hnc78nSTougOc0rnl8ie7/n99IMpo64xavy0GatSf79bnSB+TZfR3NqOROTusjs8dim/hL2dZH9Pn8H0hG6jJ6ltfl+JpL2e3MWJtqLo7dQNAw+REwNlGm+M4FigyeIRMpUsGor7f+Q5KKaq5eXRTAq1gn4nFdNWGyJGn85KkeV4NUa5D5/OpDWtuT/fpc6APy7K6Ojs+NuZDTxsZNniprrcZNvtbrUnyBPvaf+n1lwnlN7ltQLRP9nKrt35mxNtVcHLuBoOG0l4CJ71yg6NKfK/7UwjY9PhkvVdnaP0omR8eN+3YgP/llzfLF+um//bN69e6jgsJCr8tBirU3881JxkuVeGGNikbd4es+IM/u6mxWXR6vd+98UqVHPtGenU96XYov0Mf+0tT4n6p9SxBlop+DsP1rx+za01xyIl2cG7uBoMn6Iz9sZUL2vd0yZ5XIhPK9LqfTIoNnSMYocsWNbXp8bOvDOjr3e5KMigJ6CN7YSdNkJJ1zfi+vS0mZoOW2M9qb+ebU9sJxt/za173gap7JbOez6vJ4fengK3Xk48MqGXyl16V0Sqpy7GofB1VT43+q9i1BlIl+DsL2z9SYzf4VaDsmP97bLfvaSkmSOWeIx9V0jk2UqXzfZkWG3ioTattVyguG3y7JqCDAh+AVFBZq8o3Nf4yZi4KU287oSOab40ovuJrnbM6sTZQp/vQiRa6YoYIRX+vw87iS0aa4mtvGUpXjoGyPoGjcW6nctwRROvObqvHSDzI1Zmfz/hVor6yf/DBnlTRYuiz+9CLFlv1CyWt/oILhX23Tz+REujj3DiKCldvO6Ejmm0MvpFc2Z7Y2p5I6lVMy6r1sznGQNe6tVO5b0D6pGi/9IFNjNuMS0HZMfoTyAzNLGrn8hgZLVH8c24YVj2nMpOsCdV51kHLbGdmaeRdznc2ZzdacNuZibhtLR46DsF2Chp5tWTozy7Zvv2zevwLtxQVPA8TkF6lg+Fe5Knk9G1Y8pgd/99/asGKJ16UgDbI18+TaLdma08bIbdPYLv5Dz7YsnZll2wNIp6w/8gPBNmbSdZKMxkya5nUpQMqQa7iI3DaN7QLXkFkArmLyA4FWUFioSVxUDgFDruEicts0tgtcQ2YBuIrTXlAnGS/VZ2vuqfs8ciBb0QtwATkFOo8+ghfIHeANJj9Q5+iWR3Rk7vdVumW216UAnqIX4AJyCnQefQQvkDvAG5z2gjrHjbhNRkZdRsz0uhTAU/QCXEBOgc6jj+AFcgd4g8kP1MmJdNHx47/ldRmA5+gFuICcAp1HH8EL5A7whnOTH8aYdyQdlVQlqdJaW+JtRQAAAAAAwM9cvebHSGttfyY+vmATZYpt+6tsoszrUoC0I+9wBVkF3EPfphfbF4BXXJ38QCPxXY8qtvyXiu96tNPPlYyX6siae7kCNXwrlXlvDf2Azkh3Vskn0DlN9VAm9zHZiO17LMZyIDNcnPywktYZY/YYY2Y1/qYxZpYxZrcxZvehQ4c8KC9zbKJM8ScfkS2PKXLZ9SqY8n1FLru+08/7+ZbZOjzn+/rc4StQx6JlemLRbMWibryrkE257Yi6rNe8S5TKvLfGj/3gh3yT2aZlOqt+zGdT/JBZyd+59cs2yjZN9VBt3+aXTJMtj3lYnT8z21JWG4+BTcnkPtwVrozlbeHHzAK1nLvmh6Qh1toPjDFfkrTeGPOatXZb7TettfdLul+SSkpKrFdFZkLimccUW/GfkqTIsNtUcOVXUvK8x4+YqdwTu6po4ISUPJ8XNj6xRA//7r8kSRNv8P+VtLMptx3ROOsmvyhleW+NH/vBD/kms03LdFaPr/mkgONH3p62daSCHzIr+Tu3ftlG2aa2d46v96kbJr9IobMuVumD31Rev/GKDLvNq/J8mdmWstp4DGxKJvfhrqgbywPw6S9+zCxQy7nJD2vtBzXLj4wxSyUNkrSt5Z8KpvxB1zVYpkpOpIuK+o/VZxse1AkjZyon0iWlz58JoydOa7CE29KV9bbwYz+Qb//KdFZzIl104vhvKRkv1aer7/VNRhsjs61jG2VWMl6qzzbP1gkjZ+rEJj51I3R6L+X1G+/JfsfvWsqql/trl9WO5VLDbPpxPAdc5tTkhzGmSFKOtfZozddjJd3pcVmeMflFaXs34rPNs3VozvclSSdd7d5HcRUUFvHOWYCkM+tt4bd+IN/+5VVW/ZbRxshs69hGmdVaz3i93/GzlrLKdus8v4/ngMucmvyQ1FXSUmOMVF37PGvtGm9L8pZNlCmxa7HyL5suk1+Usuc9YeTMBkvAa+nKelvQD2ivTOeVjALt01rPeLnPCTK2a+sYz4H0ceqCp9bat6y1/Wpufay1v0jJ81YmlHxru2xlIhVPl1GJXYsVe/xXSuxanNLnzYl00UlXf4vD7Rzgcn7bI11Zbwv6IXXIa3qQUW9kS56DqLWe8XKfE2Rs19Y1zibjDJA6Tk1+pIt991nZV5+QffdZr0tplU1EFd8xR7Y8Lv3/7d15fJvlne/9z8+WZDtOmUKhEKCQhQQSQgJJCAEKgSSQhSVQwg6lU7owc3qemdc8c57pnM7MaeneTk+fmWmHHYY1UHZIQnYIWyAkELKShbAFKKXlQIlXyb7OH5ITxci2JN+37kXf9+vll2xZ1v3Tpe913bcv3QtQd8IcGs79R+pOmBNwZeHR2tzEgt/dSWuVnDE/SvkthWtrpm3dQlymHVDWIR7ZjmNeu2cVlNfu4pDdQrzOc1zbKUpcWzPt21+o6j68e1uzrbnHx5Sb1Wpu13LFcb0pEpSoHfbiCzvs+L1uw6xt9UOk1y0iNe5c2p79HXUTL6T+1HCf5b/Sls97iDtyZyGfVQXHT0cpv6Vo3/I0yaHH07ZyLnUTs7vHVnvW45DtOOa1UFaV173FIbuFeJ3nuLZTlHT15/bNK6g76VIskQq6pIprW/0QrfN/CUD9yVcUfEx+Vs+YeDSJQUcWdRiLxsbSxXG9KRIUTX4AlqjDhn456DKKUjfhK9QecjTtax6hZd4vAKP+y9pAyjcld/bxKVVyxvwo5bcUqVFTaFs5l5b5vwSrUc6JR7bjmFdltW9xyG4hXuc5ru0UJfn92Z39D1XZn+smfGWv20K6Mnr6rNm03PFXpMbMqMq2qoQ4rjdFgqLDXvJkj6l7JtTH1FndAJKDj6Pu+AtoOPsfqDvevw2kjtZd/OmJ6+ho3eXbMvxQP6CRWRddSf2A6jqRVhTyWwpLpKibOMf3nJcjqL4Rl2wrq/4I85gdl+z2xKtMx72dwqSn/hKW/hwkqxtA/clXYHUDenzM7qymkqTGzKjatvKKy7TT0fzn0I7hInGhyY887u1VdG58HPf2qqBL6ZPVNVL/5St9PVP2x0/eye/v/B4fP3mXb8sQ70Qpv8WqRM7Lob7RP8qqP5TL4MQx03HXW38JQ3+OCks1qK084P78rsZwkQrQYS957LCJ1AB22AlBlxIKnz/9SsD4/OmFj/eUcLHDTqDm84di+xwSdCmxp77RP3vG2olBlxIrymVwlOnoUX+RMLF9DslmsqZWmRTxkfb8yGOJOmqGngI4OreviM0u2eWqrR/IF2ZeQ60unRgRDj56O3srvlLf6J+usdYSdUDukAGNuf2mXAane6a7U8bDR/1FKq23ccASKWoH7KNMivhMkx8FuDdfoHPDI7g3Xwi6FJGiKbcSVcquxJ0yLiIaB0SCp8NeCrDBk7K7rw4+MeBKRIq3J7eTAq5EpDQ2eBI19ftgg44JuhQRX2h8FhGNAyLB054fBViijpojJgOOjm1PajdViYSu3OYfSqD8ShRYog47aFSsrgAjkq/7+Awao0Xipq8+XWgcEJHK0uRHLzrfeJ7OdQ/T+cbKoEsRKZnyK1GivEq1UeZF4kV9WiT8dNhLL2qGnAQYNUPCcfiLa2umbc3D1I0/v9drr4tA+PJbDGW8ekUxr6DMSvmimvk4Uf9VG3hJfVok/LTnRy8sUUft8NNCs3ta25qHaV3wK9rWPBJ0KaHV2tzEwt/dQWtzU9ClBC5s+S2GMt67OOc7inkFZbYYcc5tf/SVebWb/9R/vW+Das5tVNdjItVEe35ESN348wGjbvx5QZcSOq3NTby9fQuvv7aBu//jF4Ax46Irgy5LSqSM9+6peQ9yVy7fQ486msOOOJL6AY1Bl1XVlNm+PTnvQY3LZVC7+U/91/s2yF9PzbjoSlqbm1gx70Emn32B1lciEjhNfkSI1Q2g/qTLgi4jlFbMe5BVTy7k735xPYZx2tlfCbokKYMy3rvTzr4AME6ZOZv//f9dw8TTZzD9oq8GXVZVU2b7durM8+js6OCUmbODLiVS1G7+U//1vg261lNd22Er5j3I3N/8HEDrKxEJnCY/unGZNtxbL2KHn6Dd1iJk8tkXAJBIJqv6EzLlN97qBzQy46IraWttYeLpM3bnPqqU1+qQSCYZfvRYEslk0KVUhFe5rrZ2k3joWk916VpPRX19VQlaJ4r4T+f86Ma99SKdGx/DvfVi0KWESkfrLj5YcD0drbuCLqWg+gGNTL/oq9TVNwRdSqCU38oJsk/U1Tcw/aKvRn4XYuXVP2Eas+vqGxgxZlzVjM9e5bra2s1PYeoP1aZr+yzq6yuv9JZFrRNF/Kc9P7qxw0+gJncrWZ3pNv649E7eveufAThw1jUBVyQ9UX7919G6i5a3NtK0/RXevfOfAPWJcimv/tCYHSzlOnz+uPwu3r1jz3jd0bqLj5bfxX5TrqC2fmDA1Um16Gts1tgh4j9NfnRjiTps2KlBl/EZrq2Z9jWPkBp/XsUvRfbJSwvY75Q5YLD/lCsqumwpTVjz25cg812qj5bfxScvPMzgf7hPfaKfoppXCHdmNWYHK8q5jquufrD/5EtxmTQfLb+L9+/8HgAHVMnkYJjHrGrR19ishw+S7wAAIABJREFUsUPEf5r8iIj2NY/Q+sSvAKir8Mm59hl3Bn9+eQkHTL+amkSqosuW6hBkvku1X26DxRIpfaJexcKc2d1j9plfpyap48ZFausH8oWjJ9Fy99+QmnTZ7nF8vyqaHAzzmFUt9hk/nfbfv6HtaZEAVeScH2b2k0osxy8u3UrH1mW4dGtgNaTGn0f9zP+XVACXY6utH8i+J52Py7Tzex0zGzlhyG9fgsx3qWrrB3LArGuozfvkrKN1l/qGh5TZ/ukas2uSdcpmREWhD4RZodzXHjSC5OgzSR755T3jeBUd8hLmMSsMKtLnXCefbHwGl2n3bxki0ivP9/wws3/vfhdwpZkNBHDO/T9eL9NvnW88R8faBwGjdsSUQGqwugGBz9R/uPwu3skdM3uQPvGOjDDkty9hyHd/qG94S5n1jrIZTVHoA2FWKPdR6bN+qfbX35dK9DmNxyLB8+Owl68ATwGLyU58AFwCrPFhWRVRM+RkwKgZclLQpQTqgNzuoQdU0W6icaD8+k99w1vKrHeUzWhSH+gf5V5KVYk+p1yKBM+Pw15GAn8EZgBLnXO3A586527PfR8pLt1K5/sbqRl2CpasD7qcQNXWD+SgEO4m2trcxOL7b6e1uSnoUkIluwvnk2DZTzGqPb9+qnTfiHPmNeZ6Kwzjdpzz6odCfUBtWJow5F6yopJdS9aXtK3UtY1VymEyyqVI8Dyf/HDOfeqc+1vgV8BdZvb3fiynUjrfWEnnqv+i8/Vngy5FevD0/Ae47zc/55n5DwZdSqh0vrGSznUP0bnj+aBLEY/FOfMac+Mnznn1Q6E+oDaUqIprdndvY72xMuhSRKQEvl3txTm3xsymAH8NRHYrtmbIiXvdCnS07OKD5Xdx4JQrqG0Ifvb61LPmYBinnHVB0KWEirIbjEr0jzhnXrn1R5Djdpzz6odCfUBtWJqwbadUs7hmt5x1lXIpEjw/Tnh6BHCgc+4555wDfgv81sxOAd5zzr3u9TL9lN0N7vSgywiVD5bfxVt3/DNgHHzWt4Muh/oBjZxx4VeDLiN0lN1gVKJ/xDnzyq0/ghy345xXPxTqA2rD0oRtO6WaxTW75ayrlEuR4Pmx58f/D/zPAve35H53jg/LjC3X1kz7y4+SGjcby7u0ZpAOnHIFYBw45fKgS5GIC2O++0v9I/6imFvlUqpJ97xHsc/6RW0RHI3DIsHzY/JjsHNuXfc7nXOrzWywD8uLtfaXH6V10a8BqDvx0oCryaptGKgZa/FEGPPdX+of8RfF3CqXUk265z2KfdYvaovgaBwWCZ4fkx+9nSa5wYflxVpq3Oy9bkXiRPmWKFJuRaJFfXYPtYWIVDM/rsLykpl9s/udZnY1sKa/T25mM8xsi5ltN7Pv9vf5ws7qBlB34qXaNbEHrc1NLI3AJdSkMOW7NMp7OCi3pVFuvaO2LI/67B5hbAvlWkQqxY89P/4WeNjMLmfPZMcEIAWc358nNrNasidQPQPYSXai5THn3Kb+PK9E17PzH+D+3/4MA6ZeeFXQ5Yj4SnmXKFJuvaO2lDhSrkWkUjyf/HDOfQCcZGanA6Nzd893zi334OknAtudczsAzOxeYDagyY8q9eWz5mDAyWfNCboUEd8p7xJFyq131JYSR8q1iFSK54e9mFm9mf0tcAHQDlzn0cQHwCHAO3k/78zdVxEu3UrHlmW4dGulFil9qB/QyNQLr6J+QGPQpYSashsP1ZZ35TYeqi23fqpLJTj9tJOpS/mx465IMCo1RmidIiJ+nPPjdrKHuawHZgL/6uFzW4H73F4PMPuWma02s9Uffvihh4uGzh3P0fHK/XTueM7T5y3EpVvpbPmUtpVzcW3Nvi9PguVnbqGy2e2La2+mfcNSXFszbSvvVb4jyu/MQnhyq8zGRyVy66fO158ls+xf6Xz92aBLCbU49VkvM1vt25ZhWafEXdTHWYk3Pz46GOWcOwbAzG4BVnn43DuBL+X9fCjwXv4DnHM3AjcCTJgwYa+Jkf6qGXryXrd+6nh/Kx0719O65D/AjLpJl/i+TAmOn7mFyma3L+0vP45r/oj2T/9A6+J/B0P5jiC/Mwvhya0yGx+VyK2fwtInwi5OfdbLzFb7tqX6T2VEfZyVePNj8iPd9Y1zLmNWaGeNsr0EDDezIcC7wCXAZV4uoDeWrKf2yKkVWVbtoBHUHDAEampJHXduRZYp8VXJ7PYlNe4c0tueJ3nESWA1yrf0KCy5VWYlLMLSJ8JOfbawat+2VP8RET8mP8aa2Z9z3xvQkPvZAOec26fcJ85NpnwHWATUArc65zb2u+IQsmQ9lqyvull5iT9LDSB19DQgup/ESXVRZkWiRX22MG1biki18/ycH865WufcPrmvzznnEnnflz3xkff8C5xzI5xzw5xzP/aiZildR8suds6/gY6WXUGXIhI66h8SRsqlxJFyLWGlbIqEjx8nPJUq8P7yu3nj9n/m98vvDmT5rc1NLLv/dlqbmwJZvkhvuvrHRy8v9fR5lXvpj0qP28qr/9TG8KeXlwa6PSKVF5Xc+7UtICLl07XSpCyDplyOAQdNu5JMyy7eW3YPB0+9jETDwIos/7n5D/Dgf/4MM5gy56qKLFOkWIOmXE7d5w9k33HTeHvejZ71DeVe+qPS47by6r9qbuP8DB/1Nzey37hpQZckFRKV3Pu1LSAi5dPkh5SltmEgh5z1bQDenncjW//rXwA47OxvVWT5J581BzM4adaciixPpBS1DQM54OTzPO8byr30R6XHbeXVf9Xcxu8tu6fi2x4SDlHJvV/bAiJSPk1+SL8dPPWyvW791tbSxKYXVnDq7EtJJFMVWaZIObzsG8q9eKkS43ZNbQ2DjxxNTa2OsPVL/YDG3Z98t7U0sXL+A5x41hzqGhoDrsx/ld72kPCIWu6VVZHw0BaJ9FuiYSCHnf2tiu3Kt3L+A9z+o7/j2UfnVmR5IuXysm8o9+KlSozbzz/+O/7tby7n+cd/59syZI+V8x/g4f/8KSvnPxB0KRVR6W0PCaco5F5ZFQkP7fkhkXPiWXP2uhWpBsq9RI0yW1lqb6lGyr2IlEJ7foSMa2+m7cXf4dqbgy6lT5mWXbwz7wYybc1kWnbx5rwbyVTgcl51DY2cNueq0O7eKIVFKdv9lWnZxQfPPuJpv1DugxHH3FZq7FZmK6sa2jub1xtI7/qETNtn+2Qc+6sf4tROYc99UNvKIlKYJj9K5NKtdLy2FJdu9eX521+ZR9vS/6B97Txfnt9L7y+7m9dv/xd27djAzmX3sOW2f2HnsnuCLkt64Xd+exOlbPfX+8vupumtjexcepf6hQeUW29p7I6HIPtFULJ5/V/sXHY3u3Zs+Mzv49hf/RD3dgpT39B4KxIuOuylRJ2vP0vHy9njl2uP8v6yaqnjzgaD1LFne/7cXhs09XLAGDh0NAMHjwLg0H6czKm9pYlXF97H2BkXkwrpDH7U+Z3f3kQp2/01aOrl/GnNUr4wfhpYTVn9Qv1hD+XWW16P3fmU28qpdL8Iw3vbldNDTrsYSyY/8/s49lc/xL2dyukbfuXbz/FWREqnyY8S1Qz78l63XnLtzWS2ryQ17jwsEf6rOSQaBvKlvEt2De7n5bteXXgfy274EY37HcCoyef0tzwpwM/89sS1N5NeO5/kcedQN/Giii03SImGgRz45fOA8vvFqwvvY/PT8xk0YgyHHj3By/IiR7n1ltdjdz7ltnIq3S+61tEAx5//9Yoss7tEw8DP5HV3Xz32LCw1IHb91WtR29YsRzl9Y/uq5TR9/Ce2r1ru6Taon+OtiJROh72UyJL11B41DUvWe/q8LpMmvXYerY9eS/qVRz197qgYO+Nizv3Hf2PY8VN48aFbaW9pCrqk2PErv9259hbaX3ogl+v5tC37Dem1j/u6zLg5dtalXPTDW3l3y7qq7wuVyi1ks5vZuZ702nnKbRnyc5tuawm6nFjzq1+0tzQVXAePnXExU7/9T4ydcbGnyyvF7nVL+55s7V7HvDo/sLqiolq2NcvpG8OOn0L9Pvsx7PgpPlYmIkHT5EdIZLY+Q+LoM6ib+t9Ijj0r6HICkWpoZNTkc1i78D6W3PBjXlm45/KIbS1NrH1yPq3NTax44L9oq/J/BsMu/ep82pb/J5ltz5A89izqpn2nanNdrmRdA68ufpAlN/yYna+9QmtzE0/dfxutzcq+n9KvzqftyRtIjpmp3JahK7ebnl5AJp1mxQP/RfOnf6ZdEyGBaGvZs85sb2vhmQf7Xn++8sRn18GQXUcff/7XAz2cqWvdkl63Z6JD65jiVcu2Zjm5X7vwPpbe+BPWLtKluUXiTIe9hETiiBPJvL6S5LjzscRnj2OtJsfNvBjMOG7Gnl1XVy24n10f/4mP//gHHr3+Z2DG5AuuCrBK6U1y7FlgkBh2IpZqIHX8hUGXFEldfeHwMZN45qE7s9kHTrvwLwOuLL66skttSrkt03EzL+bgI8ewauFDPHLdT+ns7GDwqGMZMnp80KVVnRfm388j1/0UzDjsyNE8ft1PADjlgq/1+DeF1sFh0dU/k2P2/ONuqQHqq0Wqlm3NuOVeRLyjyY+QsFQDyZHa1Q6yny6dcP7e/9xNnHUhm194iqNOOA2rqWHSLF3PPcws1UBqgt6j/srvC5POumivW/GHstt/qYZGvnT0BL44dCSYcfyZ55NIxfcfrTCbdNaFYMakWXOwmhrO+av/ycRZvU8UFFoHh4X6Z/9Uy7Zm3HIvIt4x51zQNfhmwoQJbvXq1UGXIfFglVqQciseqkhulVnxkMZaiRplVqJI2wcSNZ5kVuf8kNBqa2li3ZPzaGtu4rkHb9N5PqQqtbe10PLpJzyrPiARotyGW1tLE88+eBstn36i87FI7LW15LYjm3PblRqTRKqWJj8C5tpbaF+995nLBTLpdlbPv48PdrzGSwvuY/71P2H1E/cHXZYUQZn2TibdzntbN7J64f0sUB/wlXLrrfe3KbdhtnrB77LvzcL7eX/bJjLpdlY+FM6JKvXN8qjd9li94HfMv/4nvLQgu125Jm9MamtpCm32RcR7OudHwNLr5tO2/DrASE24IOhyAtPe0sT6hfdxzIyLSTU0svm5xYydOpsdrzzPkZOmYDU1TJipE5pFgTLdf+0tTXy4YzMfffh7ho07hQMHD6emNqE+4CPltv+6xvGx51zJQUOP4ouHK7dhNWHWRWDGuDPPpzaZYvNzi1l8/Y8xYNJX+j7vQfd1tp/UN8ujdtujK+8TZlzIllVPceQJpwHZDxheXnAvi2/4adHZF5Fo0+RHwLJnLDeSY2YFXUqg1i+8j6du/BEA48//OiNOOJ1tLz7JqFOmk0imOPkrXwu2QCmaMt1/6xfex5an5/OVH97K9tXPcNSXp6sP+Ey57b+ucbxxvwMYOmkan7z/DiecezmJGF9VIqrqGhr3GlNGnHA606/5HsfNLO6Eyt3X2X5S3yyP2m2P/LyPOW3PlYK2P7+IMVPPA6zo7ItItGnyI2DZM5dX94w8wDEzLt7rtq6hkdGnnR1kSVImZbr/uvpBbTKlflAhym3/deV26MQppOoaOGjYyIArkmLVNTSW9Kl393W2n9Q3y6N269vQiVPYsWo5x597BYlkKuhyRKQCNPkhoZBqaPT90yORqFB/kChSbquH3muJg1RDI0dNPifoMkSkgnTCUxERERERERGJNU1+iGcyLU3sePxGMjpjtshu6hcSBcqphJ0yKlGjzIqEjyY/xDNvL72bTbf9L95edk/QpYiEhvqFRIFyKmGnjErUKLMi4aNzfohnDpt2OZhx2NTLSvq79pYmNiy8l9EzLvH9knkilVZKv1BfkKCUO353UXarT6Xf8/5mVKQUXuRbmRUJH+35ERDX3kL6tRW4TDroUjyTaGhk6NnfJNFtJZFuaeK1x24m3cNufxsW3suKm37EhkX3VaJM8Zhrb6F9zcO4dFvQpYRSoX7RU59QX6gsZXePnsZv6HsMB2W3Gnn1nndtD6VbdvWas94yKr3bPda1twRdSmT0le9ixkVlViR8tOdHQDI7VlF72FjSax8jOWYWlmoIuiTfvL5kLi/f8n0Ajjr3G5/5/egZl4AZo6f7f8k88V56/UIyW58mefQZtL86n+SYmbHOsxd66hPqC5Wl7BanrzEclN1q5NV7nl6/ENf8MW9s2cLLt14LwJGzriKz7TkSw0/GEkkvyo09195Cet0TBcex9PqFtK+4AYDU+PODKC9y+sp3MeOiiISPJj8CkjjiJNJrH6P9qRvAjNT4rwRdkqcyLU28sfQehpx5BcPOuBRg9213qYZGxp2nS+ZFVfKYGdQcNIL0hsW0P3U9GLHLsxeK6RPqC5Wl7PaslDEclN1q5NV7njxmBpkdqxg2YTxYDcPOuJSOnevh0DFsX3AbQ864XJ+cFyG97okex7HkMTP2upW+9ZXv3sbF3ePntMuUXZGQ0eRHGVy6lY7tT1N7xKlYsr6s57BEkuSYWWBG8piZHlcYrI50OzuW3MX6264FjOHnfEOz4iHiRX7zWaqBxCFH4w4YCkbs8txfmZYmPnlzIx9tf5V1t34f9YnyKbv+U16jz+t+4jdLNZA8ajKw5xN0d+gxbF9wG+tu+wGYsd8RY/mLwUfrH8leJMfM7HEcs1RDVe/x4UefSDY09jguvrH0ntz4CcPP+aYnyxMRb2jyowwd25+mY819gJEYeUbZz5NdGcXvU8b3X3yCwyZfQP2+B3LIpFlBlyPdeJXf7uKa5/56c+k9vPvcY5z4T3cBxpBpPX96Lr1Tdv2Xn9f6fQ/k4BP0SXHU+NVPKskSSYZMvxKshsNPv5CVP7qCQ04+lyP0j2SPNI71rNJ94vDTL6Jun/05eJIm1EXCRpMfZag94lTAqD3ilKBLCaWDxk/jo61rGDRhGtufuIOhZ1xKUp/WhIbyW1mDp2XP8l6TTDH8nOynROmWJnYsmau+USJl13+785qq56DxUzWGR1DU+0n++Dj8nG+QaWvhkJPP3Z1NkVJVuk/UpOoZdPw0Xl90J0PPuEzjp0iIROZqL2b2fTN718zW5r4C26XAkvUkRp4Rid1Jg5BoaOSLY09lx5J7WXvr93lj6dygS5I8ym9lJRoaOeKcb5Ko23MCuh1L5qpvlEHZ9d/uvKbqlNOIino/6Z67RF1DNpP6B1LKVOk+kUjVsWPpfay99QcaP0VCJmp7fvzaOfevQRfRH669hcyGhSRGz4j9VQWGnnEpZmg3/xirpjx7SX0jWMptcZRT8UtvfVC585/GQP8pxyLhFLXJj8jLbFhI+9M3AUZy3HlBl+OrZEMjI87RSfLirJry7CX1jWApt8VRTsUvvfVB5c5/GgP9pxyLhFNkDnvJ+Y6ZrTOzW81s30IPMLNvmdlqM1v94YcfVrq+PiVGzyB16rdIjJ4edCmBa29pYu0jt9De0hR0KYELe257ojx7J2r9IaqZBeXWD1HJb5RzGwXF5kB9sHh+ZFbtX7yojG1honFWwixUkx9mttTMNhT4mg1cBwwDjgXeB35V6Dmcczc65yY45yYccMABFay+OJZqIDnuPO1mCGxadC/P3vRDNi26N+hSAhf23PZEefZO1PpDVDMLyq0fopLfKOc2CorNgfpg8fzIrNq/eFEZ28JE46yEWagOe3HOTSvmcWZ2EzDP53L65NKtdGxbQe3wyZE9sVilpFua2LZ4LsPP3HPVgFHTL9nrVipH2Q2XTFsLI6fNAdQfiqH8BqPQON5F43n4VaLflJOD3nIlUgw/s11sppVjkWgI1Z4fvTGzQXk/ng9sCKqWLh3bVtCx5l46tj8ddCmht23xXN589nE+emPT7vtSDY0ce97VpLSSqDhlN1y2LrybZT/4KkMnTlF/KILyG4xti+ey+pYfsHP1ss/8TuN5+FWi35STg50vLWP1LT9g2xJdFUPK42e2i8101/ioHIuEW6j2/OjDL8zsWMABbwLfDrYcqB0+Gcxy1w+X3oyYcTnDpl7ItmX384Vho+ns7GTzonsZOf0SbSwHQNkNl+FnXsrnDz+S+n0PYO3DNzFqxqWkGgYGXVZoKb/BGH7mpTTs90UOnTCFjY/ezJEzLtdYHiGV7DftLU195iLd0sTWxXMZceYlnPI/fsuhE6b6XpfEU+WzPZejpl1IbTK1+zL2w8+8FAyGn6Gru4iEWWQmP5xzVwZdQ3fZ64afGXQZkZCoa2DLwrtZdfO1HDB8LL/fuo7nbroWgLHnXR1wddVH2Q2XZEMjBx97Cmsfvonnb/4RYBx7vs4S3xPlNxjJhkaGnHIuGx+9mRdvvpb9NZZHSiX7zeZF9/aZi62L5/LizdnHHD1b452Ur/LZ/iGus4NBR43jwFHHA9nxcdS5yrFI2EVm8iNKXLqFzOblJEZOwZI6mVSXEWdmZ8O/cMQY9h0yCoCROj48lJThYIyacSlguVspl/LrL43l1aWc/tSVh95y0ZWjrlupTlEbr7syfdS0OdQmUwFXIyKlisw5P6Iks3k5mZW3k9m8POhSQiXZ0MjRs7+B68jwzqrljD7rSu0mHVLKcDBSDQM55uyv8s6q5aR1Wb2yKb/+0lheXcrpT6mGRsYWOE9CuqWJ9Y/cQrqlaXeOdHLI6haV8boruzU1NYw972rqBv7F7kNeRCQ6NPnhg8TIKSROvIrEyCm773PpNlzrLtKvPIprbwmwuuC9tuhelv/yO2xacGfQpUgPCmW4i7Lsr03z72T5L7/Da4t1Wb1yFRyD21vIbH0G196i7HpEY3l16G19UAzX3kL65UdwmTSvLbqXF26+VuNbyPU0Trr2FtJrH/N0/OxvviqlK7ubF94TdCki0g867MUHlmwgOeasve7r/PB1On+/hfZnbwUgedzsIEoLhaOmXwIGR52p3aTDqlCGuyjL/lL/6L9C+c1sWoJr+Ri360+0P3sLoOz2l7JaHXpbHxQjs2ER7c/egjXuq8xERGbjYtqfuRnYe5zMbFpCumv8PPZcT5bV33xVirIrEg+a/PCZa2+h46011A4+npr9DgOrIXF0dZ+oL9nQyDGzdWK8KHLpNmr2H6ws+0j9w3su3UZi5BQ63nqF2sETwEzZ9YCyKt259hYym5eSGDkNS2UPCUiMng4GtUMmYqkGZSYCusbH7uNkYtQZe91C4fc8jjTeicSDDnvxWWbzUtqX/IqON1/C6geSPG52rFcOEm+ZTYtpe/xaOnf9UVmWyMhsWkzbvB9hn9sfSzUouyI+yWxeSvq5W8lsXrr7vmyfO099LkJ6Gict1UDy2HP3ur/Qey4iElba88NHLtNG4qjTAag9fHzA1YiUz6Vb6HhzDYmR0wCo2efAgCsS6dtncvuFwcEWJBIzLt1CZtMyEqOmYsmG3X2t61bir9B73j0XIiJhoT0/POTSrWQ2PIFLtwKQ2biEtvk/puaLR+gTD4mE7hnuktm0jPalv6bjrTUkx56jPEvoFMqucitSup7WA4VkNi0j/fxtZDYtA3J7BqivVZVC73n3XHiplHyKiHSnPT881LHlSTIvZs96nxg9k8SoqQDU7D84wKpEitc9w126slw7WHswSTgVyq5yK1K6ntYDhXT1sa5bEfA3F6XkU0SkO01+eKj2yNP3urVkA8mxZwdZkkhJume4i7IsYVcou8qtSOl6Wg8Uoj4mhfiZi1LyKSLSnQ578YBLt5LZuDB7BYHRM7FkfdAliZREGZaoUnZF+q+rH7l0K5asV1+S0MrPZ35uRUSKockPD3RsfYrMqrvp2PJk0KWIlEUZlqhSdkX6b3c/2vpU0KWIFE25FZFS6bCXfnKZNmqPOAWA2hGnBVuMSIlcupWOd9ZSO2IyoAxLtGj8FSmNS7fSsXUFtSMm77VnR1f/UT+SqND4LyLl0J4f/dSx5Snal/0K23+odhGVyOnYuoLMM9fRsfNVEkfPUIYlUjT+ipSmY+sKMqvvoWPbir3ut2S91gESKRr/RaQc2vOjn2pHTAaDmv0OA3LHzW5ZTuLIKRqMJfS68lt76LG771OGJSq6j7+g/Ir0ZveYP3xyn49VX5IgFJu7QuO/iEhftOdHP1mynsSo6bsH6MyW5WReuIPMluUBVybSt+75BWVYokP5FSlNoT7TE/UlCUKxuSslyyIiXbTnh8cSR07Z61YkapRhiTLlV8Qb6ksSBOVORPykyQ+PWbKe5OhZQZchUjZlWKJM+RXxhvqSBEG5ExE/6bAXEREREREREYk1TX6IiIiIiIiISKxp8kNEREREREREYk2THyIiIiIiIiISa5r8EBEREREREZFY0+SHiIiIiIiIiMSaOeeCrsE3ZvYh8FYfD9sf+GMFyokCtcUe3dvij865GZVYcJG5jRLlKiuIdqhIbsvMbFhzEca6wlgT+FNXtY21YX1v+6uaXlccMxvF9081l6ZS2wefAlv8Xk6JwpiVsNUUtnoA6p1zo/v7JLGe/CiGma12zk0Iuo4wUFvsobbwjtoyS+2wt7C2RxjrCmNNEN66oiSubajXFW1RfJ2qOZzC+BpVU9/CVg94V5MOexERERERERGRWNPkh4iIiIiIiIjEmiY/4MagCwgRtcUeagvvqC2z1A57C2t7hLGuMNYE4a0rSuLahnpd0RbF16mawymMr1E19S1s9YBHNVX9OT9EREREREREJN6054eIiIiIiIiIxJomP0REREREREQk1qp28sPMZpjZFjPbbmbfDbqeSjOzN81svZmtNbPVufv2M7MlZrYtd7tv0HX6xcxuNbM/mNmGvPsKvn7L+vdcVtaZ2bjgKg+fUrIU57bsoR2+b2bv5u5ba2az8h7/j7l22GJm04Or3F9mdqGZbTSzTjOb0O13Bdug0uNzmN+nMK2rqn294SUz+6WZvZYbBx82s8/n/S7SY0OYMlsuM/uSmT1pZptz49ff5O6Pdd7LGa+DFpW8lbLdGRV9tb2Z1Zm7EAdbAAALFklEQVTZfbnfv2hmg/N+53meiqjn78xsU27cXWZmh+f9riNvG+AxL+opsqavmdmHecv+Rt7vrsplY5uZXVXBmn6dV89WM/s473eet1OhvtHt92Y9/O9QVhs556ruC6gFXgeGAingVWBU0HVVuA3eBPbvdt8vgO/mvv8u8POg6/Tx9Z8KjAM29PX6gVnAE4ABk4AXg64/TF+lZCnObdlDO3wf+PsCjx2VG3fqgCG58ag26NfgU7uMBI4EngIm9NUGQYzPYX2fwrauqvb1hsdteSaQyH3/87wxMtJjQ9gy24/XMQgYl/v+c8DW3HsT67yXOl6HoN7I5I0Stjuj8FVM2wN/DVyf+/4S4D6/8lRkPacDA3Lf/1VXPbmfdwXURl8DflPgb/cDduRu9819v28laur2+P8O3OpzO32mb3T7fcH/Hcpto2rd82MisN05t8M51w7cC8wOuKYwmA3cnvv+duC8AGvxlXPuaeCjbnf39PpnA3e4rBeAz5vZoMpUGllqy97NBu51zrU5594AtpMdl2LHObfZObelwK96aoMwjc9Bv09haoueVM16w0vOucXOuUzuxxeAQ3PfB525/opCZvvknHvfOfdy7vtPgc3AIcQ872WM10GLTN5K3O6MgmLaPv/1PQBMNTPDnzz1WY9z7knnXHPux/xx1y/9yed0YIlz7iPn3P8BlgAzAqjpUmCuB8vtUQ99I19P/zuU1UbVOvlxCPBO3s87c/dVEwcsNrM1Zvat3H0HOufeh+yKH/hiYNUFo6fXr7z0rpQsxbktC7UDwHdyu+ndmrdLa5zboVg9tUFQbRPG9yno5Xen9YY/vk72Uy0I33teqqjX/xm5XfWPA16kevMe1vc1rHUVK8p5Kqbtdz8mN9n7CfCFIv/Wj3ryXc2ecReg3sxWm9kLZubVJFSxNV2Q2/54wMy+VOLf+lUTucOChgDL8+72o5364un2YsLT0qLDCtxXbdf8Pdk5956ZfRFYYmavBV1QiCkvvSslS3Fuy0LtcB3wQ7Kv8YfAr8j+oxOrdjCzpcBBBX71Pefcoz39WYH7HIUn5fvdNr3VSHjfp6CX353WGyUopl+Y2feADHB3158VeHyUxoao178XMxsIPAj8rXPuz9kPraPN4/E6aGGtqxoU0/Y9PcaP963o5zSzK4AJwOS8uw/Lrd+GAsvNbL1z7vUK1PQ4MNc512Zm15DdU2ZKkX/rV01dLgEecM515N3nRzv1xdMcVevkx07gS3k/Hwq8F1AtgXDOvZe7/YOZPUx2N6gPzGyQc+793O5Efwi0yMrr6fVXfV56U2KWYtuWhdohtysfAGZ2EzAv92Os2sE5N62MP+utDTxvm2JrDNn7FPTy96L1Rmn6ylzu5GxnA1Nd7gBmQvaelyHq9e9mZkmyEx93O+ceyt0d+bz7MF4HKax1FSvKeSqm7bses9PMEsBfkD28wY/3rajnNLNpZD/0mOyca+u6P2/9tsPMniK7t1d//6nvsybn3J/yfryJ7Dmguv72tG5/+1Q/6ymqpjyXAP8t/w6f2qkvPdVcVhtV62EvLwHDzWyImaXIvrmendk37Mys0cw+1/U92ROvbSDbBl1nyr0K6OkTgLjq6fU/Bnw1d7bhScAnXbspVrsyshTLtuypHbqdz+R8sm0D2Xa4xLJnQh8CDAdWVbLmEOipDSo+Pof4fQrNukrrDW+Z2QzgH4Bz845Bh+Az11+hyWx/5M5LcAuw2Tn3v/N+Va15D2suo563KOepmLbPf31zgOW5iV4/8tRnPWZ2HHAD2XH3D3n372tmdbnv9wdOBjb1s55ia8rf/jiX7PmFABYBZ+Zq25fsOndRJWrK1XUk2ZOIrsy7z6926ktP/zuU10bO4zO2RuWL7Jljt5Kdrfpe0PVU+LUPJXt231eBjV2vn+xxeMuAbbnb/YKu1cc2mAu8D6TJzhxe3dPrJ7tb1W9zWVlP3hnQq/2r1CzFtS17aYc7c69zXW7wHpT3N9/LtcMWYGbQr8HHtjk/18fagA+ARX21QaXH5zC/T2FZV2m94Xl7bid7rPLa3Nf1eb+L9NgQlsz28zV8mezu0+vy3qNZcc97OeN10F9RyRslbHdG5atQ2wPXkp1cAKgH7s+Nd6uAoX7mqYh6luZy3dWnH8vdf1JuG+DV3O3VFWyjn+bWqa8CTwJH5f3t13Nttx34y0rVlPv5+8DPuv2dL+3UQ9+4Brgm9/se/3cop40s94ciIiIiIiIiIrFUrYe9iIiIiIiIiEiV0OSHiIiIiIiIiMSaJj9EREREREREJNY0+SEiIiIiIiIisabJDxERERERERGJNU1+xJSZfd7M/jr3/cFm9kDQNYkUy8w6zGytmW0ws/vNbEDu/oPM7F4ze93MNpnZAjMbkfvdVWa2Lfd1Ve9LEPFWmZldaGYfm9m8YKuXalRqZs3sWDNbaWYbzWydmV0c9GuQ6lNGbg83szW5v9loZtcE/RqkupSzfZD7/T5m9q6Z/Sa46uNHl7qNKTMbDMxzzo0OuBSRkpnZLufcwNz3dwNrgF8DzwO3O+euz/3uWOBzZK+RvhqYALjc48c75/5PAOVLFSo1s865Z8xsKjAA+LZz7uyASpcqVcY4+wHgnHPbzOzg3ONHOuc+DuQFSFUqI7cvkv1/p83MBgIbgJOcc+8F8gKk6pSzfZD7+d+AA4CPnHPfCaT4GEoEXYD45mfAMDNbC2wju4Ey2sy+BpwH1AKjgV8BKeBKoA2Y5Zz7yMyGAb8l2+magW86516r/MsQ4RlgDHA6kO5aSQA459YCmNmlwBLn3Ee5n5cAM4C5lS9XpO/M5r5fZmanVb48kc8oKrN5971nZn8gu42gyQ8JSkm5BerQXu8SrKIya2bjgQOBhWQ/2BOPaACIr+8CrzvnjgX+R7ffjQYuAyYCPwaanXPHASuBr+YecyPw351z44G/B/6zIlWL5DGzBDATWE82t2t6eOghwDt5P+/M3SdSUSVkViQUysmsmU0k+8HJ6/5WJ1JYKbk1sy+Z2Tqy2wk/114fEoRiM2tmNWQ/nO7+/5t4QJMf1elJ59ynzrkPgU+Ax3P3rwcG53YLPAm4P7fnyA3AoGBKlSrVkMveauBt4JY+Hm8F7tMxfVJJpWZWJGhlZdbMBgF3An/pnOv0sT6RQkrOrXPuHefcGOAI4CozO9DnGkXylZrZvwYWOOfe6eNxUgYd9lKd2vK+78z7uZNsJmqAj3N7jYgEoaV7/sxsIzCnh8fvBE7L+/lQ4ClfKhMprNTMigSt5Mya2T7AfOCfnHMv+FyfSCFlj7W5w7U2AqcAuhCAVEqpmT0ROMWyF64YCKRy5w35rs91VgXt+RFfn5I90VPJnHN/Bt4wswsBLGusl8WJlGE5UGdm3+y6w8yON7PJwCLgTDPb18z2Bc7M3ScSpN4yKxJGPWbWzFLAw8Adzrn7A6tQ5LN6y+2hZtaQu29f4GRgS0B1inTpMbPOucudc4c55waTPfXAHZr48I4mP2LKOfcn4Dkz2wD8soynuBy42sxeJXsljdle1idSKpe9NNX5wBm5y4JtBL4PvJc70ekPgZdyX9d2nfxUJCi9ZRbAzJ4B7gemmtlOM5seWLEi9JnZi4BTga/lLtu4Nnd1ApFA9ZHbkcCLue3ZFcC/OufWB1asCH1vH4h/dKlbEREREREREYk17fkhIiIiIiIiIrGmyQ8RERERERERiTVNfoiIiIiIiIhIrGnyQ0RERERERERiTZMfIiIiIiIiIhJrmvwQERERERERkVjT5IeIiIiIiIiIxNr/BUiXQMOiBxELAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b897e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = sns.PairGrid(df, hue='time', \n",
    "                 palette=reversed(sns.color_palette('Oranges_d', n_colors=len(df))))\n",
    "g.map_lower(plt.scatter, edgecolor=\"white\", marker='.')\n",
    "g.savefig(os.path.join(datapath,'images', 'PCs.pdf'))\n",
    "g.savefig(os.path.join(datapath,'images', 'PCs.png'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also look at plots of the cumulative variance to visualize our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "cvars = np.load(os.path.join(datapath, 'cumulative_variances', 'cumulativevars.npy'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to create an axes object and set some labels, and then we can graph the cumulative variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12cd0c6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(4,3))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_title('AdK PCA '+selection)\n",
    "ax.set_xlabel('component number')\n",
    "ax.set_ylabel('cumulated variance')\n",
    "ax.set_xlim(None, 20)\n",
    "ax.plot(cvars)\n",
    "ax.axhline(y=1, color='r', linestyle='--')\n",
    "ax.xaxis.set_major_locator(ticker.MaxNLocator(integer=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can save this plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax.figure.savefig(os.path.join(datapath, 'images', 'cumulative_variances.pdf'))\n",
    "ax.figure.savefig(os.path.join(datapath, 'images', 'cumulative_variances.png'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing Projections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to project the original trajectory on the principal components, i.e., we want to see the motions of the protein that are contained in the PC. The first few PCs contain most of the motion so large conformational changes should be obvious in the first few projections. Smaller scale motions should be filtered out."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But first we need to finish the rest of the projection from where pca.transform leaves off."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's load the data we saved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/oliver/anaconda3/envs/mda3/lib/python3.6/site-packages/MDAnalysis/topology/PDBParser.py:301: UserWarning: PDB file contained CONECT record to TER entry. These are not included in bonds.\n",
      "  \"PDB file contained CONECT record to TER entry. \"\n"
     ]
    }
   ],
   "source": [
    "pc_components = np.load(os.path.join(datapath, 'pcs' ,'pcomponents.npy'))\n",
    "u_mean = mda.Universe(os.path.join(datapath, 'mean_atoms', 'meanatoms.pdb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need to set the size of the projected trajectory and get some other data about our initial conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "start, stop, step = u.trajectory.check_slice_indices(None, None, 1)\n",
    "n_frames = len(range(start, stop, step))\n",
    "n_components = pc_components.shape[1]\n",
    "n_atoms = int(pc_components.shape[0]/3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need the principal component space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "space = np.load(os.path.join(datapath, 'transforms', str(npc)+'components.npy'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need to iterate over each component and for each component calculate the position of the atoms along that axis for each timestep. Then we write the new positions to a trajectory (here in DCD format). There will be one trajectory for each of the `npc` PCs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "components = pc_components[:, :npc]\n",
    "for component in range(components.shape[1]):\n",
    "    yc = np.zeros((n_frames, components.shape[0]))\n",
    "    for time, weights in enumerate(space):\n",
    "        for atom in range(components.shape[0]):\n",
    "            yc[time, atom] = weights[component] * components[atom, component]\n",
    "    yc = yc.reshape(n_frames, n_atoms, 3)\n",
    "\n",
    "    with mda.Writer(os.path.join(datapath, 'trajectories', 'PC', \n",
    "                                 str(component+1)+'.dcd'), \n",
    "                    n_atoms=n_atoms) as f:\n",
    "        ts = Timestep(n_atoms=n_atoms, dt=1)\n",
    "        for pos in yc:\n",
    "            ts.positions = u_mean.atoms.positions + pos\n",
    "            f.write(ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting trajectories show the original data filtered on the first to fifth PC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "View the trajectory, e.g., component 2\n",
    "```\n",
    "vmd PCA_tutorial/AdK/mean_atoms/meanatoms.pdb PCA_tutorial/AdK/trajectories/PC/2.dcd\n",
    "```\n",
    "(or using nglviewer TODO)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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