{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2d5ecad8",
   "metadata": {},
   "source": [
    "## Conformer generation for multiple molecules\n",
    "\n",
    "Lets see how two alanine molecules orient themselves using CREST conformer generation.\n",
    "To do this we will constrain the system in a spherical region using the `SphericalWall` constraint.\n",
    "We start by setting up a system of two alanine molecules in a relatively small space."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "756c7d30",
   "metadata": {},
   "source": [
    "## Initial imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6d886366",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scm.plams as plams\n",
    "from scm.base import ChemicalSystem\n",
    "from scm.conformers import ConformersJob\n",
    "from scm.utils.conversions import chemsys_to_plams_molecule, plams_molecule_to_chemsys"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36d711d6",
   "metadata": {},
   "source": [
    "## Alanine dimer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "80a64825",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from scm.plams import preoptimize\n",
    "\n",
    "smiles = \"CC(N)C(=O)O.CC(N)C(=O)O\"\n",
    "dimer = ChemicalSystem.from_smiles(smiles)  # alternatively you may use packmol to build the dimer\n",
    "dimer.translate(-dimer.center_of_mass())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f42a4385-f123-483b-946d-660f2acf121d",
   "metadata": {},
   "source": [
    "Optimize the dimer structure prior to the conformer search."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f20311a1-3927-4627-9816-c8636f378e0d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[09.04|12:12:09] JOB plamsjob STARTED\n",
      "[09.04|12:12:09] JOB plamsjob RUNNING\n",
      "[09.04|12:12:11] JOB plamsjob FINISHED\n",
      "[09.04|12:12:11] JOB plamsjob SUCCESSFUL\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGBA size=300x300>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = plams.Settings()\n",
    "s.input.GFNFF = plams.Settings()\n",
    "s.input.ams.Task = \"GeometryOptimization\"\n",
    "s.input.ams.GeometryOptimization.Convergence.Quality = \"VeryGood\"\n",
    "s.input.ams.GeometryOptimization.Maxiterations = 1300\n",
    "s.input.ams.GeometryOptimization.Method = \"Quasi-Newton\"\n",
    "\n",
    "job = plams.AMSJob(molecule=dimer, settings=s)\n",
    "job.run()\n",
    "dimer = job.results.get_main_system()\n",
    "plams.view(dimer, height=300, width=300, direction=\"along_pca3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1761a2c",
   "metadata": {},
   "source": [
    "## Calculation setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50b4a1e6",
   "metadata": {},
   "source": [
    "To determine the radius of the `SphericalWall` we measure the size of the initial dimer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8f535687-2cdd-4e97-9260-b872e0461920",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Largest distance between atoms: 8.779 ang.\n",
      "Radius: 5.838 ang.\n"
     ]
    }
   ],
   "source": [
    "dists = dimer.distance_matrix()\n",
    "max_dist = np.max(dists)\n",
    "diameter = 1.33 * max_dist\n",
    "radius = diameter / 2\n",
    "print(f\"Largest distance between atoms: {max_dist:.3f} ang.\")\n",
    "print(f\"Radius: {radius:.3f} ang.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f50e15ac",
   "metadata": {},
   "source": [
    "Now we can set up the Crest conformer generation job, with the appropriate spherical wall constraining the molecules close together. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3ca4732b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seed used for stochastic aspects is 3330407.\n"
     ]
    }
   ],
   "source": [
    "# This seed will used for the starting MD velocities in conformers generation\n",
    "# Due to numerical aspects it does not guarantee full reproducibility.\n",
    "seed = random.randint(1, 10000000)\n",
    "print(f\"Seed used for stochastic aspects is {seed}.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a3bfb596-9b95-44e4-b693-ce4823be0eb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "settings = plams.Settings()\n",
    "settings.input.ams.EngineAddons.WallPotential.Enabled = \"Yes\"\n",
    "settings.input.ams.EngineAddons.WallPotential.Radius = radius\n",
    "settings.input.ams.Generator.Method = \"CREST\"\n",
    "settings.input.ams.Output.KeepWorkDir = \"Yes\"\n",
    "settings.input.ams.GeometryOptimization.MaxConvergenceTime = \"High\"\n",
    "settings.input.ams.Generator.CREST.NCycles = 3  # at most 3 CREST cycles for this demo\n",
    "settings.input.ams.Generator.RNGSeed = seed\n",
    "settings.input.ams.Generator.CREST.NMolDynStepsFactor = 3\n",
    "settings.input.GFNFF = plams.Settings()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40603be4",
   "metadata": {},
   "source": [
    "## Run the conformers job"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58b66221",
   "metadata": {},
   "source": [
    "Now we can run the conformer generation job. This job will run somewhere between 30 minutes and 1 hour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "49bb3c31",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[09.04|12:12:13] JOB conformers STARTED\n",
      "[09.04|12:12:13] JOB conformers RUNNING\n",
      "[09.04|12:25:10] JOB conformers FINISHED\n",
      "[09.04|12:25:10] JOB conformers SUCCESSFUL\n"
     ]
    }
   ],
   "source": [
    "job = ConformersJob(molecule=chemsys_to_plams_molecule(dimer), settings=settings)\n",
    "job.run();\n",
    "# ConformersJob.load_external(\"plams_workdir/conformers/conformers.rkf\")  # load from disk instead of running the job"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a580d2b",
   "metadata": {},
   "source": [
    "Now, remove the wall and reoptimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42eb7043-6866-4d49-98bf-39b673570cc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[09.04|12:25:10] JOB conformers STARTED\n",
      "[09.04|12:25:10] Renaming job conformers to conformers.002\n",
      "[09.04|12:25:10] JOB conformers.002 RUNNING\n",
      "[09.04|12:26:43] JOB conformers.002 FINISHED\n",
      "[09.04|12:26:43] JOB conformers.002 SUCCESSFUL\n"
     ]
    }
   ],
   "source": [
    "if \"EngineAddons\" in settings.input.ams:\n",
    "    del settings.input.ams.EngineAddons\n",
    "settings.input.ams.Task = \"Optimize\"\n",
    "settings.input.ams.InputConformersSet = job.results.rkfpath()\n",
    "opt_job = ConformersJob(settings=settings)\n",
    "opt_job.run();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "24f914b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Conformers stored in /Users/ormrodmorley/Documents/code/ams/amshome/userdoc/PythonExamples/conformers-multiple-molecules/plams_workdir/conformers.002/conformers.rkf\n"
     ]
    }
   ],
   "source": [
    "rkf = opt_job.results.rkfpath()\n",
    "print(f\"Conformers stored in {rkf}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c697e7ba-345e-4b81-9e5e-e69f25347fe0",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a412132c-b3c7-4c72-99ec-09c8039abc5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of conformers: 1678\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Conformer Id</th>\n",
       "      <th>Rel. E (kcal/mol)</th>\n",
       "      <th>Population at 298 K</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.079996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.007065</td>\n",
       "      <td>0.079047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.011192</td>\n",
       "      <td>0.078498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.071612</td>\n",
       "      <td>0.070884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.103091</td>\n",
       "      <td>0.067215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>0.205166</td>\n",
       "      <td>0.056572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>0.227356</td>\n",
       "      <td>0.054492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>0.305097</td>\n",
       "      <td>0.047788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>0.314653</td>\n",
       "      <td>0.047023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>0.348506</td>\n",
       "      <td>0.044410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>0.437493</td>\n",
       "      <td>0.038214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12</td>\n",
       "      <td>0.470471</td>\n",
       "      <td>0.036144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>0.494662</td>\n",
       "      <td>0.034697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>14</td>\n",
       "      <td>0.519705</td>\n",
       "      <td>0.033261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>0.934194</td>\n",
       "      <td>0.016518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16</td>\n",
       "      <td>0.948115</td>\n",
       "      <td>0.016134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17</td>\n",
       "      <td>0.967742</td>\n",
       "      <td>0.015608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>18</td>\n",
       "      <td>1.094571</td>\n",
       "      <td>0.012599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19</td>\n",
       "      <td>1.370615</td>\n",
       "      <td>0.007905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>20</td>\n",
       "      <td>1.374833</td>\n",
       "      <td>0.007849</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Conformer Id  Rel. E (kcal/mol)  Population at 298 K\n",
       "0              1           0.000000             0.079996\n",
       "1              2           0.007065             0.079047\n",
       "2              3           0.011192             0.078498\n",
       "3              4           0.071612             0.070884\n",
       "4              5           0.103091             0.067215\n",
       "5              6           0.205166             0.056572\n",
       "6              7           0.227356             0.054492\n",
       "7              8           0.305097             0.047788\n",
       "8              9           0.314653             0.047023\n",
       "9             10           0.348506             0.044410\n",
       "10            11           0.437493             0.038214\n",
       "11            12           0.470471             0.036144\n",
       "12            13           0.494662             0.034697\n",
       "13            14           0.519705             0.033261\n",
       "14            15           0.934194             0.016518\n",
       "15            16           0.948115             0.016134\n",
       "16            17           0.967742             0.015608\n",
       "17            18           1.094571             0.012599\n",
       "18            19           1.370615             0.007905\n",
       "19            20           1.374833             0.007849"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_energies = opt_job.results.get_relative_energies(\"kcal/mol\")\n",
    "print(f\"Total number of conformers: {len(relative_energies)}\")\n",
    "conformer_table = pd.DataFrame(\n",
    "    {\n",
    "        \"Conformer Id\": np.arange(1, len(relative_energies) + 1),\n",
    "        \"Rel. E (kcal/mol)\": relative_energies,\n",
    "        \"Population at 298 K\": opt_job.results.get_boltzmann_distribution(298),\n",
    "    }\n",
    ")\n",
    "\n",
    "conformer_table.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcc163ea-d155-4367-85c8-b75410e9b496",
   "metadata": {},
   "source": [
    "Here we plot the three lowest-energy conformers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "56769936",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7Im4m9o1EIiorK0sNHjxYBYNBY7/33ntPAep3v/udsa0rDLEShy+Jkd+RGCkxcncO+SuLL730EhaLhbPPPhsAr9fLySefzCuvvMKf/vQnzGZzm/2nTJnCtdde2+5x9taLMmzYMD755JN9alNOTs4ebw8Gg9jt9nbbHQ6Hcfv+uH/iv7vbt7m5eY/Pk1BWVsaFF14IwBdffEF+fr5xW01NDV988QW//OUv6d69e5v77Vgq2Ol0Gv+ORqM0NzfTu3dvUlJSWLJkCT/96U93+/yJ4QM33XRTu9vOPfdcvF6v8f+JSmYXXXRRm6G3Rx55JC+//DLbtm2jqKiITz/9lEgkwq9+9as2vWs/+9nP+M1vfsPMmTO59NJL9/raCHEwk/j4/e//fTU1NXHSSSexadMmZs+ezaBBg4zbdF3nf//7H6effnq7ER7wXYzcsb3xeJzGxkY8Hg/9+vXbbZXrHb3//vtthlclnHDCCW2W/UnEx7PPPpukpKR22zdt2kSPHj1YvHgx1dXV3HnnncbrBjB58mT69+/PzJkzueuuu/baLiEOdhIjv//9vy+JkYe+QzpZjMfjvPLKKxx//PFkZGQY28877zzeeecdPvvss3bDFgsKCjjxxBO/93Olpqb+oPvtitPpbDMmPCEUChm374/7J/67u3339jwJP/3pT7FYLKxZs6ZdENu0aRMAgwcP3uNjBINB7r//fv71r3+xbds2lFLGbXsbmpEYPrCrL/rOCWoicezWrdsutzc0NACtcygB+vXr12Y/m81GUVGRcbsQhyqJjz/s/t/Xr371K0KhEEuXLm1zEgStnWnNzc17jY+6rvO3v/2NJ554gs2bNxOPx43b0tPT93jfyspKlixZwt13393utv0dHwH69+/PV199tcc2CXEokBj5w+7/fUmMPPQd0gVuPv/8cyoqKjjvvPPabD/jjDNwOp37dZJyJBKhsrJyn/52/BDvSm5uLpWVlW0SJoCKigqAvY69zs3NNfbd0/1zc3PbbN953709T8JZZ51FY2Mjf/vb3/Zp/135xS9+wb333su0adP473//y8cff8wnn3xCeno6uq7v8b7vv/8+PXr0YODAge1u27nXb2/bd37NheiqJD62ta/3/76mTJmCUooHHnhgr7Fsd+677z5uuOEGxo0bx4svvshHH33EJ598wqBBg/b6mB988AEOh4OJEye2u03ioxC7JzGyLYmRe99+uMbIQ/rK4ksvvYTVauXMM89ss93j8XDqqafy1ltv8dRTT+2XXpJ58+bt8oO2K5s3b25zWXtnw4cP59lnn2XNmjVtEqAFCxYYt+/J8OHD+fLLL9F1vc0QygULFuByuYz1fhKPs3jxYmPiM7ROJi4rK2PGjBn7dDy/+MUv6N27N7/73e/wer3ceuutxm1FRUUArFy5co+P8frrrzN9+nT+9Kc/GdtCodA+VR6dOXNmu0nJP1ZhYSEA69atM44BWgP65s2b91sPoBCdReLjnuPj/jJ16lROOukkLrnkEpKSktqsX5uZmUlycvI+xceJEyfyj3/8o832xsbGNlc8dmXmzJlMnDhxv14N2DE+Hn/88W1uW7dunXG7EIcyiZESI3+owy1GHrJXFoPBIG+++SaTJk0iNTW13e3Tpk2jpaWFd955Z788X2K8+b787W28+ZQpU7BarTzxxBPGNqUUTz31FPn5+RxzzDHG9oqKCtauXUs0GjW2nXPOOVRVVfHmm28a22pra3nttdc4/fTTjbHdgwYNon///jzzzDNteqqefPJJNE3jnHPO2efj/+1vf8uNN97Ibbfd1u6LPm7cOP75z3+ydevWNvfZsQfGbDa365F59NFH99qDVlVVxZIlS3Y5BPXHOPHEE7HZbDzyyCNt2vWPf/yDpqam/f58QhxIEh/3Hh/3p4svvphHHnmEp556iltuucXYbjKZmDp1Ku+++y6LFy9ud79E7NlVfHzttdf2WoI9Go3yySef7Pd4dcQRR5CVlcVTTz3VZrjaBx98wJo1ayQ+ikOexEiJkT/G4RYjD9kri++88w4tLS0APPDAA+1uDwQCQGvP0Y5DDIqLi3nxxRfb7Z+dnc2kSZN2+3z7c7x5QUEBv/rVr3j44YeJRqOMHj2a//3vf3z55ZfGej8Jt912G//+97/b9DSdc845HHXUUVx66aWsXr2ajIwMnnjiCeLxeLsJtQ8//DBnnHEGJ510Eueffz4rV67kscce44orrmhXdnlvHn74YZqamrjmmmtISkrioosuAuCRRx7huOOOY+TIkcyYMYOePXtSUlLCzJkzWbZsGQCnnXYaL7zwAl6vl4EDBzJ//nw+/fTTvY41f//993c7fODHyMzM5LbbbuOuu+7i5JNP5owzzmDdunU88cQTjB492jg2IQ5FEh/3LT5+8cUXfPHFF0Dr3Bm/388999wDwLhx4xg3btw+t/vaa6+lubmZ22+/Ha/Xy29+8xugdfjUxx9/zPjx45kxYwYDBgygoqKC1157ja+++oqUlBROO+007r77bi699FKOOeYYVqxYwUsvvdRm1MOufPXVVzQ3N+/3ExOr1cqDDz7IpZdeyvjx47nggguMsvA9evTg+uuv36/PJ8SBJjFSYuSPcdjFyANcfXW/Of300/epBLHValW1tbVKqT2XPf4+5YD3h3g8ru677z5VWFiobDabGjRokHrxxRfb7Td9+vRdllKur69Xl19+uUpPT1cul0uNHz9+l2WHlVLqrbfeUsOHD1d2u10VFBSoO+64Q0Uikb22ccelM3Zs9wUXXKAsFov63//+Z2xfuXKlOvPMM1VKSopyOByqX79+6re//a1xe0NDg7r00ktVRkaG8ng86ic/+Ylau3atKiwsVNOnTzf223npjHPOOUedeuqp7dqWKI/88MMPt9m+Y6nmvR2LUq1LZfTv319ZrVaVnZ2trrrqKtXQ0NBmH1k6QxxqJD7uW3xMlDTf1d/vf//7PbZxd7Hm5ptvVoB67LHHjG1btmxRF198scrMzFR2u10VFRWpa665RoXDYaVUa1n4X//61yo3N1c5nU517LHHqvnz56vx48fvcsmgRFn4G2+8UQ0cOHCX7QPUNddc02bb942br776qhoxYoSy2+0qLS1NXXjhhaqsrGyXr6EQhxKJkRIjJUbuO02pw3S2pjjoxWIx0tPTuf/++7n66qs7uzlCCHFQGThwIKeddhoPPfRQZzdFCCEOOhIj949Ddhiq6Prq6+u5/vrr200+F0KIw10kEuG8885j2rRpnd0UIYQ46EiM3H/kyqIQQgghhBBCiHYO2WqoQgghhBBCCCE6jiSLQgghhBBCCCHakWRRCCGEEEIIIUQ7kiwKIYQQQgghhGhHkkUBwNVXX73HBWXFD3fUUUdx8803d3YzhBA/gsTIjiMxUohDm8THjnMwxMdOSRafe+45NE0z/hwOB3379uXaa6+lqqqqM5r0vbzzzjuMHDkSh8NB9+7d+f3vf08sFtun++q6zkMPPUTPnj1xOBwMHTqUl19+eZf7/ve//+Woo44iJSWF9PR0xo8fz8yZM3/UY+7K5s2befbZZ/nNb34DwIQJE9q8P7v7u/POO/f5OX6Mzz77jMsuu4y+ffvicrkoKiriiiuuoKKiot2+0WiUu+66i6KiIux2O0VFRdxzzz27fH/Wr1/P+eefT0FBAS6Xi/79+3P33XcTCAT22qZLLrkEj8fTbvu3335LRkYGPXr0oKSkBIBbbrmFxx9/nMrKyu9/8OKwJDFy7/FsT7Fp55OWDRs2cM4555CamorL5eK4445j1qxZ+3w8EiMlRoqDh8TH/RsfKyoqmDFjBj179sTpdNKrVy9uuOEG6urq9qlNEh8Pg/ioOsG//vUvBai7775bvfDCC+rvf/+7mj59ujKZTKpnz57K7/d3RrP2yfvvv680TVMTJ05UzzzzjPrFL36hTCaTuvLKK/fp/rfeeqsC1M9+9jP1zDPPqMmTJytAvfzyy232e+SRRxSgJk+erJ588kn1l7/8RQ0bNkwB6o033vhBj7k7v/zlL1Xfvn2N///444/VCy+8YPxdd911ClC/+c1v2mxfvnz5Pj3+jzVq1CjVs2dPdfPNN6u///3v6rbbblNJSUkqOztbVVRUtNl32rRpStM0dfnll6snn3xSTZ8+3XhtdrR161aVkpKiCgsL1f3336+efvppdckllyhAnXHGGXtt0/Tp05Xb7W6zbcWKFSojI0N1795dbdq0ydgej8dVTk6O+u1vf/sjXgVxOJEYufd4tmMsSvz98pe/VIB66KGHjP22bt2qMjIyVHZ2trr33nvVX//6VzVs2DBlsVjUnDlz9qlNEiMlRoqDh8TH/RcfW1paVGFhocrIyFC/+93v1N///nd17bXXKqvVqoYPH67i8fhe2yTxsevHx05NFhctWtRm+w033KAA9Z///KczmrVPBg4cqIYNG6ai0aix7fbbb1eapqk1a9bs8b5lZWXKarWqa665xtim67oaO3asKigoULFYzNjep08fNXr0aKXrurGtqalJeTyeNh/E7/OYuxKJRFRGRoa64447drvPa6+9pgA1a9asPT5WR5kzZ067gDVnzhwFqNtvv93YtnDhQgW0+0L9+te/VpqmtQlM9957rwLUypUr2+x78cUXK0DV19fvsU07f9FXrlypMjMzVbdu3dTGjRvb7X/ttdeqwsLCNu+nELsjMfKHxbPLL79caZqmSktLjW1XX321slgsau3atcY2v9+vunXrpkaOHLnX45EYKTFSHFwkPu6/+PjSSy8pQL333ntt9v3d736nALVkyZI9PqbEx8MjPh5UcxaPP/54oPWSNkAsFuMPf/gDvXr1wm6306NHD37zm98QDofb3K9Hjx6cdtppfPzxxwwfPhyHw8HAgQN588039+l5KyoqWLt2LdFodI/7rV69mtWrVzNjxgwsFoux/eqrr0Ypxeuvv77H+7/99ttEo1GuvvpqY5umaVx11VWUlZUxf/58Y3tzczNZWVlommZsS05OxuPx4HQ6f9Bj7spXX31FbW0tJ5544h7360zjxo3DZDK125aWlsaaNWuMbV9++SUA559/fpt9zz//fJRSvPrqq8a25uZmALKzs9vsm5ubi8lkwmaz7XP71qxZwwknnIDdbmfWrFkUFRW122fSpEls2bKFZcuW7fPjCrEziZG7j2fhcJg33niD8ePHU1BQYGz/8ssvGTFiBP369TO2uVwuzjjjDJYsWcL69ev32CaJkRIjxaFB4uP3j497+p4Dbc43d0Xi4+ERHw+qZHHjxo0ApKenA3DFFVfwu9/9jpEjR/KXv/yF8ePHc//997d7I6F17PB5553HKaecwv3334/FYuHcc8/lk08+2evz3nbbbQwYMIBt27btcb+lS5cCcMQRR7TZnpeXR0FBgXH7nu7vdrsZMGBAm+1jxoxp8/jQOub7ww8/5NFHH6WkpIS1a9dyzTXX0NTUxC9/+csf9Ji7Mm/ePDRNY8SIEXvc7/sKBALU1tbu9a+hoeEHPb7P58Pn85GRkWFsS/wA7BzcXC4XAN98842xbcKECQBcfvnlLFu2jNLSUl599VWefPJJrrvuOtxu9z61Y926dRx//PFYLBZmzZpFr169drnfqFGjAJg7d+6+HaAQuyAxcvf3f//992lsbOTCCy9ssz0cDu/yhGdXcWFXJEZKjBSHBomP3z8+JhKpX/7yl3z99deUlZXx/vvvc++99zJ16lT69++/xzZJfDxM4mNnXM5MDCH49NNPVU1NjSotLVWvvPKKSk9PV06nU5WVlally5YpQF1xxRVt7nvjjTcqQH3++efGtsLCwnZz+ZqamlRubq4aMWLEXtuTGJO8efPmPe738MMPK0Bt3bq13W2jR49WRx111B7vP3nyZFVUVNRuu9/vV4C69dZbjW1VVVXqhBNOUIDxl5GRoebNm/eDH3NXLrroIpWenr7HfX7IEILf//73bdq+u7/CwsJ9fswd/eEPf1CA+uyzz4xtb7zxhgLUCy+80Gbfp556SgFq8ODB7R7D6XS2ac+OQxL2ZPr06cpqtarc3FyVl5eniouL93ofm82mrrrqqn16fHF4kxjZ1r7Es7PPPlvZ7XbV0NDQZvvpp5+uUlJSVHNzc5vtRx99tALUH//4xz22SWKkxEhxcJH42NaPiY9KKfXss8+qlJSUNt/z6dOntxkquzsSHw+P+PjddfBOsPNl68LCQl566SXy8/N5/vnnAbjhhhva7PPrX/+aP/7xj8ycOZOJEyca2/Py8jjzzDON/09OTubiiy/mwQcfpLKykpycnN2247nnnuO5557ba3uDwSAAdru93W0Oh8O4LL2n++/uvjs+PrT2ZPTr14+CggJOO+00Wlpa+Mtf/sJZZ53Fl19+Se/evb/3Y+5KXV0dqampe9znh7j44os57rjj9rrf3oY47MoXX3zBXXfdxbRp04xhJwCnnnoqhYWF3HjjjbhcLkaNGsWCBQu4/fbbsVgs7V6LHj16MG7cOM4++2zS09OZOXMm9913Hzk5OVx77bV7bUc8Hqe2tpZ+/fq16Z3andTUVGpra7/38YrDl8TI7+674+PvrLm5mZkzZ3LqqaeSkpLS5rarrrqKd999l/POO497770Xt9vNE088weLFi/f4mAkSIyVGioOTxMfv7rvj4+9sT/ERID8/nzFjxhjx4csvv+SRRx4hIyODP/7xj3tsk8THwyM+dmqy+Pjjj9O3b18sFgvZ2dn069fPGFe8ZcsWTCaTkRQl5OTkkJKSwpYtW9ps7927d5v5fQB9+/YFoKSkZI9f9H2V+FDuPN4dIBQK7fVD63Q6d3vfHR8f4Nxzz8VisfDuu+8a26ZMmUKfPn24/fbbjbHT3+cxd0cptdd9vq+ioqJdjrv+sdauXcuZZ57J4MGDefbZZ9vc5nA4mDlzJtOmTePss88GWoPyQw89xL333tumTPErr7zCjBkzKC4uNsbvn3XWWei6zi233MIFF1xgDGXZHafTybPPPsuFF17I5MmT+eSTT/Y49EAp1e4zKsSeSIz87r47Pv7O3njjDUKhULshVgCnnHIKjz76KLfeeisjR44EWl+Le++9l5tvvnmX5ct3JjFSYqQ4+Eh8/O6+Oz7+zvYUH+fOnctpp53G119/bQyPnTp1KsnJydx1111cdtllDBw4cI/tkvjY9eNjp85ZHDNmDCeeeCITJkxgwIAB7SagAgfVD0diwu+u1mapqKggLy9vr/evrKxs98VKPF7i/ps2beLDDz/kjDPOaLNfWloaxx13XJsxy/v6mLuTnp7+g8d874nP56OysnKvfzU1Nfv8mKWlpZx00kl4vV7ef/99kpKS2u0zaNAgVq5cycqVK/nyyy8pLy/nZz/7GbW1tUbgB3jiiScYMWJEm4neAGeccQaBQGCvcwcSzj//fB577DHmz5/PWWedRSQS2e2+jY2N+9R7JESCxMjv7gu7j2cvvfQSXq+X0047bZe3J9ZfmzdvHosXL2bt2rV4vV6ANnFhVyRGSowUByeJj9/dF35YfHz66afJzs5uN4/yjDPOQCnFvHnz9tgmiY+HR3w8qArc7KiwsBBd19tVqquqqqKxsZHCwsI22zds2NDuC1RcXAy0XireH4YPHw5gDF9KKC8vp6yszLh9T/cPBAJtqi8BLFiwoM3jJxaVjcfj7R4jGo22WRx0Xx9zd/r3709DQwNNTU173O/7+uMf/0hubu5e/0aPHr1Pj1dXV8dJJ51EOBzmo48+MoLurmiaxqBBgzjuuONIS0tj1qxZ6LreZshKVVXVbl9fYJ8XyIXWYW733HMPH3/8MRdddBG6rrfbZ9u2bUQikXYT04X4oQ7nGLmjiooKZs2axdlnn73LIVoJbrebo48+mlGjRmE2m/n0009xOp0ce+yxe2yTxMi2JEaKQ4HEx1Z7i48/9nsu8bGtLhsfO2Oi5O7WyNlRYnLyjBkz2my/+eabv9fk5OHDhxvbIpGIWrNmjSovL2/zmOXl5WrNmjUqEonste39+/dXw4YNa7OezR133KE0TVOrV682tjU2Nqo1a9aoxsZGY1tpaelu18jJz883HrO6ulqZTCY1YcKENmuqlJaWKo/Ho04++eTv/Zi789lnn7Wb5LuzHzI5eePGjeqTTz7Z699XX32118fy+XxqzJgxKikpSS1evHif26CUUoFAQI0cOVLl5ua2KXBx2mmnKZvNptatW9dm/6lTpyqTyaS2bdu2x8fd1YKq119//S4n1Cul1Ntvv60A9c0333yv9ovDk8TIfY9nf/7zn/caw3Y2d+5cZTab1bXXXrvXfSVGSowUBxeJj/svPl577bW7jF2/+tWvFKC+/vrrPR6PxMfDIz4etMmiUt9VmJo2bZp6/PHHjf+fOnVqm/0KCwtV3759VUpKirr11lvVX/7yFzVkyBBlMpnUhx9+aOy3efNmo8rTrp5nb5WslFLq3XffVZqmqeOPP14988wz6rrrrlMmk0n97Gc/2+Ux/utf/2qz/aabbjIC2N///nc1efJkBaiXXnqpzX5XXHGFAtTEiRPVo48+qu677z5VUFCgzGazmjNnzg96zF0Jh8MqPT1d3Xbbbbvdp7MXVJ0yZYoC1GWXXaZeeOGFNn9vvfVWm33PPfdc9ctf/lI9/fTT6uGHH1YDBgxQdrtdffrpp232mzNnjjKbzSorK0vdfffd6vHHH1ennHLKbr+oO9vVF13XdXXJJZcoQN18881tbrv22mtV9+7dZcFpsU8kRu57PBs1apTKy8trt+hyQklJiRozZoy655571LPPPquuv/565XQ61YgRI9pVSN0ViZESI8XBReLj/ouPa9euVW63W3k8HnXbbbepp556Sl1wwQUKUJMmTdrr8Uh8PDzi40GdLEajUXXXXXepnj17KqvVqrp166Zuu+02FQqF2uxXWFioJk+erD766CM1dOhQZbfbVf/+/dVrr73WZr/98UVXSqm33npLDR8+XNntdlVQUKDuuOOOdj1Ku/uix+Nxdd9996nCwkJls9nUoEGD1IsvvrjLY3/00UfV8OHDlcfjUR6PR02cOLFNb9j3fczdue6661Tv3r13e3tnf9ETvX67+tu5bPKDDz6o+vfvrxwOh0pNTVVnnHGGWrp06S4fd8GCBeqUU05ROTk5ymq1qr59+6p77713n8pF7+qLrpRSsVhMTZ06VQHq/vvvV0q1vj+5ubnqjjvu+N7HLg5PEiP3LZ6tXbtWAeqGG27YbVvq6+vVlClTVE5OjrLZbKpnz57qlltu2adEMUFipMRIcfCQ+Lj/4mNiv3POOUd169ZNWa1WVVhYqG688Ubl9/v36XgkPnb9+Kgp1QFljA6wHj16MHjwYN57773ObsohadOmTfTv358PPviAE044obOb0+X873//4//+7//YuHHjHsfJC9FRJEb+OBIjO5bESNGZJD7+OBIfO9bBEB8P2gI34sApKiri8ssv54EHHujspnRJDz74INdee62cBAlxiJIY2bEkRgpx6JL42LEOhvgoVxaFEKKLkxgphBC7JvFRiD2TK4tCCCGEEEIIIdrpElcWhRBCCCGEEELsX3JlUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5IsCiGEEEIIIYRoR5JFIYQQQgghhBDtSLIohBBCCCGEEKIdSRaFEEIIIYQQQrQjyaIQQgghhBBCiHYkWRRCCCGEEEII0Y4ki0IIIYQQQggh2pFkUQghhBBCCCFEO5bOboAQB5qu68a/NU1D07RObI0QQgghhBAHJ0kWxWElFovR3NxMQ0MDZrMZr9eL1+vFZJKL7EIIIYQQQuxIzpDFYSMSiTB79myWL19OJBIhJSUFi8VCcXExoVCos5snhBBCCCHEQUWSRXFYiMfj/OMf/2DdunVomkZGRgZerxePx0Pfvn2JRCLE43GUUp3dVCGEEEIIIQ4KkiyKLi8Wi/Hyyy/zzTffYLPZcDgcuFwu43ZN0/B4PBQXF7eZzyiEEEIIIcThTJJF0aXpuk5NTQ0zZ84kEokQCoWIRqPE43HguwI3JpOJwsJC6uvr5eqiEEIASinjTwghBIdlTJRkUXRpSim2bt1KVVUVfr+flpYWGhoaaGhoaHMipJQyit8IIcThbFcnQofjCZIQQiTsLi4eDqQaqujyYrEYkUiEyspKysvLSUlJwePxYDabSU9Px2KxEI1GaWhoQNd1lFKynIYQ4rDV3NxMbW0tsVgMl8uFw+HAZDKRlJSEzWbr7OYJIcQBpes6Pp+PxsZGNE3DarVitVrRNI2UlJQuvwybJIuiS9M0je7du5OVlcWKFSsoKSnB6XRiMpkIh8NkZGTgcDgIhUKEQiH69u3bpb/wQgixO7qus3btWr755hvcbjcDBgwgPT0dh8NBNBrF7/cTj8dxOBwSJ4UQhwWlFGvWrOHbb7/F7XZTVFREt27dsNvtKKWoqakhLS0Nq9Xa2U3tMJIsii7NZDKRk5PDsccey/LlyykpKcFkMhGNRmlpacHr9eJyubBaraSmppKeni4nQUKIw45Sii1btvDyyy+TkZFBfn4+KSkp2O12TCYTdrsdq9VKIBDo7KYKIcQBoZRi8+bNvPjii+Tn55Ofn092djbJycnGPmazmcbGRjIyMrrs+aPMWRRdnsVi4YorrmD8+PEEg0HWrVvH0qVLWbx4MRs2bDCSydzcXEwm+UqIrm/HeRYyF00opQiHw7zxxhts3rwZaI2bNputTUzUNA273U5dXZ1UjhZCdGlKKUKhEE8//TQ1NTXY7XYsFgsOh6PNflarFY/HQ21tbZf9Le3yVxZ3fuO6atYvdk/TNLxeL3/961/517/+xRdffEFNTQ2rVq1C0zTq6uqIRCLY7Xai0Sg2m00+J6JLUkqh6zplZWU0NDQQj8fxer1kZWWRlJQkn/vDWENDA59++inJycmEQiGCwSDhcBhd1zGbzQBG5ejq6mrS0tI6ucVCCNFxdF1n1apVfPvtt+Tm5hIKhQiHw0SjUaBtPmEymYwq+11Rl08WhUhITk7m6quv5qyzzmLr1q18/vnnvPnmmyxfvpzc3FwyMzPZsGED/fv3x2QyyYmz6HJCoRCzZs0yhtK43W5MJhONjY0Eg0GysrLkc38Y0jQNn89HWVkZ+fn5NDU1UV9fT01NDcnJybjdbjRNMzobzGYz8XhcRmIIIbosk8lERUUFdXV1uFwuGhsbqa+vp7a2lqSkpDZzFOPxOEop4vE4ZrO5y/2OdtlkUdd1wuEwW7ZsIRwO43A4cDqdpKenGwVOxOHHarWSn59PTk4OBQUFLF68mOXLl9OjRw9cLheapuH3+0lKSurspgqx3yiliEajvP/++7hcLnJycsjMzDTioNPppLGxEb/fbyQG4vCS6Bmvra2lsrKSjIwM3G43FouF/Px8nE4nuq7T3NxMPB7HYumypw9CCGFUxo/FYtTU1FBdXU1qaqpRFTozMxObzWbcnuhA64q/n10y2sfjcdatW8emTZvo1asXAwcOxGKxoJSisbGRqqoqunXr1qUrF4ndM5lMmEwmCgoKOP/887nvvvtYuXIlqamp5OfnU1paysCBA2UJDdFlKKVYsGABmzdvZsyYMcYVxQSTyURqaiorVqxg8ODBXfYHT+yaUgqv10vfvn1ZuXIlJSUluFwuY85ObW0tHo8HAL/fb1QBlM+IEKIr69WrF1lZWWzatInk5GRjuYxQKERWVhYul4t4PE5zczNer7fLxsQulywmyth++eWX9OnTh7y8PCwWi7EGSmpqKkopysrK6NGjR5d9Y8XemUwmfvKTn/DKK6+wYsUKcnNzSUpKwufzkZubS0pKCrB/57nuOIdWPntif9vxBD7xWUsMjVmxYgUNDQ2Ew+Fdzq3QdR2r1UpNTQ3Z2dkHtN076mrfkUPleJKTk5k8eTLr16+nrKwMi8VCJBLB5/NRXV1tJI9ms5mpU6ce1McihBA/lqZpFBQUMHToUFavXk1JSQnQunZ3S0sLlZWVOJ1OYrEYycnJjBo1qst2onWpZDHxozxv3jwaGxtxuVzY7fY2+2iaRlJSEk1NTUQiEaxWqwxJPUwlOg+uueYafv7zn7NmzRrS09Pp0aMHq1at4phjjmnz2fgxQWB39+2qgUUceOFwmA0bNtDY2IjZbMbtdpOTk0NqaiqAMQ+ttraWmpoanE6nMbpCKYXf7ycUCtHY2NgpcxcT8TsxN85IenUd7RCM0YljSBzPztsPJolFpqdOncqWLVt47bXX2Lx5Mz6fj9raWqOYTVpaGldccQVer7eTWyzE/rNj7En8/8H2He1qlFKQiIsH4YL2Sil8Ph8zZ86ksLCQXr16sWLFCiKRCH6/n7q6OmP5jIyMDKZMmYLL5eqy+USXShYTH7Z58+aRkpKC3+8nHA63SRgTZeIDgQCBQMC4eiQOXxMnTuTYY49lzZo1ZGZmkpSUhMPhYNGiRUZJZLfbTXJysjGX8fsENl3XCQaDVFZWEggEjMcLhUJkZ2dL9VXxoySqmy5dupS+ffsyYsQII+YFAgHKy8tJSkrC5XJRXl5NWVk1bvcawuEwmZmZWCwWgsEgNTU1lJSUMHz48E45hmAgQEtNDeHNm7FFo5idTuIFBSRlZuL2eL73dyQR67VOOBFRShEKBKivria6eTPRLVtwe71QVISzoABvWlqntGtPNE0jIyOD3/3udwwYMICXXnqJqqoqVq1ahcViYeDAgZx++ulGFd1EhVQhDmVKKeMKeiQSQdd13G43SUlJ8hnvAInEPBqNEgmHWzuqbDaj4/JgiImJQl4vvvgimzZt4qijjuKvf/0rb775JjNnzmTr1q2Ul5djsVjo1asXJ5xwAk6nk23btpGfn98lE8ZDNlncuednx56h+vp6QqEQFRXllJaWUlRUhN1uR9M0otEo9fX11NfXk5eXd1B8MEXn0TQNs9nc5upiMBjE5/MZw/JcLhcZGRn06NGDPn36MGLECKMYzt4opdi2bRuffPIJuq4zaNAgCgoKSE5OJhaL4fP5sFqtsmyB+EGUUtTX1/Pxxx8zYMAA8vLycLlcxu2JifgbN26iqKgvJSVOevc+FV0vZenSFXi9HhwOO5FIhIaGBurr6znllFMO6GdRKcXqRYuofvNNLHPmkF5ZSYZSWEwmrDk5NE2YQO0555A/eDCWfexYSQy9DQaDxmLycGBORGKxGBvXrWPd66+jzZxJZmUl3Uwm3JoGLhfa8OEsP/dcBv3kJ9iczg5vz76KxWJs2bKFmpoaTjjhBIYMGUJVVRX/+9//+Pjjj8nLyyMUCqHrOps2baJ3794Ss8QhTSlFRUUFpaWlJCUlkZSUZMzNXbNmDT179sTtdndyK7sOXdepq6lh6/LlaKtX4ygtJdlmw5qXR+3gwfQYNgz3QbIkT3l5Oa+//jqjR49G13VSU1P57W9/y+WXX862bduYN28ef/3rX3E6nUZRsESRsI7qCOzMKQ2HZLKYeMFisZjRw2k2m42e5J49e/Htt2upqvKxatVKwuEwaWlpWCwWAoEANTU1VFVVMXTo0E4dbnCozGU5HAwaNIgTTzyRL774glgshsfjwev1Gj8eJpOJ0tJSqqqqaGhoYOLEibusGrnzAufBYJDHHnsMgFGjRhll6E0mEzabjdTUVKqrq7HZbEaHhhD7Kh6P88knn+D3+3E4HO0WCwaw2WyYzWZKSzX69p2My5WL32+lpGQ58fg6bDYb4XCY5uZmLrzwQhwOxwH7HCqlWPDZZ6x+6CHy166lm9lMns2G02rFpGnQ1IT3zTdpXLyYsl/9iu4/+QnmPVTh3HF+ZqJD0Ol0EgwG6datm3Ei2GHHo+ss/+Yb5jz4IBnLl9M7GqXAYiHDbsdmsaABLFnCgOJi6mpqSL/oIqwH8PXebbuVYt68eaxcuZIePXqQlZVFv379GDp0KKmpqcycOZO1a9eSn5+P1+slGo3SrVu3A/pZEWJ/UkpRXV3N7Nmz6d69OwUFBW06bR0OB1VVVVI9fz9RSrFh1SoWPPIIyUuWkFNbS57JRLKmYdI0krOzqTz6aFwzZpDVt2+nn5cvX76clpYWAoEAPp+P5uZmo4p+Xl4e+fn5zJo1i9WrV9O9e3e8Xi9KKXJycvb7iMVd5Sk7D53uaIdcspgoUbtlyxYsFgsZGRlGaVuv10tKSgoDBgxHqVEMGTKGurqlLFq0kLS0dOOkqKqqitzcXJyd1Kur6zqapqHrOkqpNoFIfngPPE3TjM+Uy+XCZrMZS60kJSWRmppqJIzBYJCVK1fidrsZN26csUg1fDd0IR6Po+s6uq7z+uuvs2TJEo466igALBZLm6EtiaFfGzdupG/fvp1y/OLQpOs6TU1NFBcX43a7iUQixlpPO8cRu92Gw1GApmVRURFi06blLFw4m1Co0igBfskllzB8+PADFoN0XWfpwoV88uCDFK1fT5rJRLrDgdPjQXO7wWqFcBhTSwspJSXod9+Nv29fknr1Ak37br4LwPZ5gU1NTXz00UekpKTQv39/cnJysFqtKKWoq6vD5/ORlZXVISd/Sinq6ut54d57yfr2W9zxOMlWKylOJzaPB83jAZMJQiHsLS2kPvMMzWlppE+ZAp24DIVSivXr1/Pcc88xatQoUlJSyMzMxG63o+s6w4cP58QTT2TWrFn06tWL7OxsunfvzubNm+nfv7/8ZolDklKKTz/9FJ/PR3p6epvRQkop7HY7mZmZRlX9zvycK11vM69P6ToKflAc23F4PhyYc05d1ylevZpXrr+e7uvXkwLkms2kOxxY7HY0sxnl91P4/vs0l5Tg/9OfcHfv3qlz1Wtra43iXlVVVZSWlpKSkkJWVhZms5nc3FzOOussfvvb31JcXEx6ejoOh4Pi4mJGjx4N7J/XNjFMura2lqamJpxOJ263G7vdbpyXHoj38JBKFmOxGMuWLaOkpIQhQ4bQs2fPNgUampub+OqrhSxfbmbw4AkoZQP6s3Llx5hMq7HbHfj9frKzs5k6deoBnyuW+JJWlpVRu3kzjm3bsAcCxL1ewj16kNerF8kpKYdkMYdDlVKKWCzG008/zYYNG0hJSTGuVCeGoKakpJCWlobVasXv91NbW8uCBQtwOp14vV7C4TDhcBiASCQCtI7HN5vNBINBotEogUAAv9+Pz+cjGo3icDiMniGTyUROTk6XXcxVdJxgMEhZWRnZ2dnU1NRQW1tLbm6usQaeUopgMEhTUxOxWJiWljg1NaswmVZz4YWnEQ6HKCgo4IgjjiAjI+OAtVspRUtLCx+8/jrBdeuwKoXDbm+9UuX1oqWmgs0G4TCYzZjicdKrq1n10EP0fuQRzBYLkVAIfYeKr7FYjDffeouW5mZ69OhBRkaGMXdTKUVWVhZ1dXVEIpH9fhU/8V1++cUXqV62jHylsGoaVrMZy/ZjIiWlNQEOBtE0DXttLaH//Ie6MWNIz8/vtLgfjUZ57rnnCG5vF2B0aCVORGbMmMHnn3/O+vXryc3NxeFwGB0UNpttvyffid9KuaIjOkI8Hqeqqori4mJycnLajAbakcViobm5udNGoCXaVV9bS015OYFgEItSuDweMvLySE5NxfQ95lUm1tttbm4Gvpum0JHHppSivLycp++/n6TiYtyAx2wm2enEkpyMlpxsxHqtqQnvqlVU3H03tscf75RRF4mCZAMGDDCG5nu9XqMadF5eHsnJyUSjUXr27MmoUaMoLi4mKysLj8dDPB4nLy+PvLw84/F+6LBUpRQlJSV8+eWXRptyc3NxuVzouk5LSwtOp7NdIc+OcMgki0opGhoaWLBgAb179yY9Pd1Y7wS+q3LqcqWSkdGLeNzG1q0NrFs3h/XrV6FUhLS0NI444gjOPvtsunXrdsATxYDfz5LZs2l+9VXSvv0WR3Mzru3z4kw5OQRHjaLxggvofuSR+9y2Xc3d7IxiDp19ifzHKCkp4YMPPsBkMqHrOrFYDPjuGOx2O06nE6fTidlsNhLGWbNmGVcpTCaTMQzQ4/HgcrlwOByMGjWKd999l+rqaurr66muriY7O5ucnBzjhCwejxONRtF1Xda3E/tMKYXTmYrb7aS0tJTs7GzcbjfRaJS0tDTMZjPhcJj6+gbKysqoqEiipmYLNtsyfvGLsygsLDAeqzM+c+VVVaxbsIAegNI0lMmEslhaTxwcDrDbwWwGvx+sVpSm4VywgE3/+Aem5GQi4TAWmw2T04my2YhoGmuWLSOvqMiYi7zzcXk8HhobGztkaRCfz8eH771HqlLElSKmacQTx2SxtB6P3d56VdTpRLNaMX/7LeG1a6GgoFNit67r1NXVsX79eiKRCM3NzTQ3N+Pz+XA6ncYImF69enH00UfzzTffsG3bNuPKYyIpT/ixx5BI+n0+H9D6fiU6PiQuiv3J5/NRVVWF2+02Rh0k1snTNI14PE5jYyP19fU0NTWRkpJywM8Z/S0tLPr4Y/j4Y1LWrcPb0ECyxYIlNZVI//4UT5pEn9NO2+PQ/MRjRaNRiouLqaurIzc3F6/XS0VFxfapWz077Dji8Thz5syhbOlShmyPDyaTCYvVCm43eL2t8XB7RzuRCGkLF1Ixbx7djz++w9q1NwMHDmTYsGEsXbqUdevW0b17dwC2bNlCNBolHo/TrVs3brvtNs455xw2btxIWloaLpeLuXPnkp+fTyQSIT09nfz8fOM3eV8l5tM++eSTuFwuhg8fTkpKSpuYaLPZqK2tJSsrC+jYGHlIJIuJk/b58+fT0NCA3W7fZSZtMpkpKkpj/foI5eVBSksXMnKkjUsvfQhQOBwOY/jpgf7Sh8NhPvvPf6h6+mn61NeTp2lk2WzYtye8WkMD7vffp3nlStbfdBN9Tjpprz3Nid7XWCxGJBLBYrG0G+bY0XacPxpqaSHq82FzubAnJ+81gHW2HT9XoVAIt9tNZmYmI0eOpHfv3jgcDgKBAOFwmGg0is1mM3q7TSYTzc3NZGdnYzabsVgsxvscjUZpaGgwTpwikQjbtm0jOzvbqEoZi8VITU1F0zSjuuCB/jESh7bWE/kooVAaxcXfkJycjFKKxsZG0tNbh91Ho1GamlpYvXoda9f2x2LZxG23jaewsKBTq3FqmkZldTWV5eXk6Dohk4mAUoR0HWcsBpFIa/yLRmH7cP24UlgjEdJXr8bs9aK7XODxgMeD7nbTYrEQ8vvx+3zGMiCJOXWJ3mKLxWJ02OzP5EwpxabNm6muqcENhJQiCPiVIhSP40gck6ZBLNZ6TJqGJR4ntHo16oQTOu3KRSgUIhQK0dDQQE1NDZWVlZSWluJyuYyheU6nk6OOOoo5c+awdetWsrOzsVqtFBcX09TUhMfjMeoC/NAOr3g8zsKFC9myZQsFBQVkZ2fj9/uNJY4O9O+26NqsViuRSISysjI2b96My+Wie/fueDwe46pNRUUFNTU1xsn5gaKUorGhgY8efxz9jTfo1dhIrsVCmtmMNRZDq6hALy0l6euvKd2yhe5XXolpN1eXEueJie/WjoXQEkMcN2zYQK9evYD9m3Douk4gEODb5csJ+nzElCIGRDWNmMnU2hlosbSOuIDW/1osWPx+QvPmoSZO7JTvvKZpuN1ubrjhBm666Sbq6+tJSkqie/fu1NTU8OGHH5KVlcWxxx5LZmYmxx13HIsXLzaq6ScnJ7N06VJisRhutxun00mvXr34yU9+QlJS0m5HTOxc8+L5559n7dq1HH300ZjNZux2e5vPoslkIi0tjaqqqg5fG/ngPpvfgVKKRYuWo2mtQ/qCwWC7YgWtL7SOrpexbl0J/fpVM2XKVJKSPEYBHDiwPZTG2o+zZjH/oYcYHo3iNZlIc7lwJOaxmM0QCqE1N5OydSvqb39ja3Y23YcOhV388Cbmxm3dupVt27ZhtVrJyMjA4/EYQx8LCgo6/Dh1Xae2upr1s2fT9M47uFevJtXvJ9nlwtG3L/6pU0meOJH0rCxMB2HimDiB3Lx5M5qmMWjQIE444QSGDx9Oz549jZPvLVu2sHLlSmpra4lGo7S0tBCNRmlsbGTVqlVGUY1IJEIsFjMS+MQVw7KyMpRSJCcnG/Nr6+rqSElJwWazEQqFjHHwcjIk9kXiM/b3v3/Ahx+60XU7ur6QpqZGysvLSU1NxW63EYnEqK+vYsGCbjQ2evnDH1Lp168PmtZ5V2oSP4i1lZU0RiI0AQ1KURePkxIO4/T5cGpa64lDPI7y+dAjEfxKUR+PU1ZbiwoE0J1OdJcL3eFAdzoJmkyUV1aC201ZWRnp6emYzWYj4UlUwvb7/R1yXI0NDYRjMZo0jUagUdepi8VIDoex+Xy4oPWqaTSK8vmIRSL4EiMZlEJx4N8Tk8lERkYGmZmZrF27lk2bNhnzYcLhMBkZGVgsFnw+H7m5uYwYMYLNmzeTm5uL2+1m1qxZbNiwgaSkJDIyMhg6dCiDBg2iZ8+e2Gy2fWpDYq7pf//7X+rq6hg6dChZWVkUFBQYw/XD4TANDQ1GB5sQP4bJZDI+Y/Pnz8fpdBIOh6msrDSuLgaDQaqqqojH47ssZtdRErH9g+efZ8uzzzJUKdKtVlJdLqxuN5rDAbqOye/HEQiQ8/e/s9bppM9Pf4rZZmsducB3sUTXdVavXs3bb7/NuHHjyMrKMmKipmk4HA7y8/ONhHF/H2cgEGDTxo2EAT/gA5qVoikWwxMOYwkEWuefb+9QU/E40ViM6MaNhPz+1jnsnfCdN5lMjBkzhnvuuYc//vGPmM1motEosViM3Nxcpk+fTkpKCkopbrzxRs455xw2bdpEWloaoVAIv9+PzWZD13VCoRBr1qyhvLyc448/noEDBxoXGHbMS0KhkFFQp7S0lEWLFhGJRIwOvUQ16p3zmcSFjMP+yiJAaWkFS5euo1s3N5WVVZSVleF0Oo1FMHVdx+/3U1/fQH19GSkpzZx//qkkJ3+XxXfWj4zP5+ONJ54gNxzGajJht1iwORytY7V3mMdi0jSIRnEVF+ObOZNI375Ync5djqffsGEDs2fPplevXvTr188o9NM6d7N1GJGnA79kSik2rF3L53/5C845cygKhSg0mciwWHCEQpi+/ZbY6tX4Pv6YyuuvJ3fo0IN2Lmbih6NPnz6kpqYaVVATn5uePXuiaRqffvopLS0ttLS0GPMPt23bZgw/9Xq9JCcnk5aWRmpqKikpKTgcDoLBIMuWLWPjxo3EYjGCwSC1tbXGOk7dunXj6KOP7uRXQRxqVqzYyEsvLUfXR2KxXEV19Yu0tCwlPb0Er9eL1WolFILGxiFUV5+LyWSlujpIPB7HZOq89cMSJynZ2dlEbDZqw2HqlCI5FsMeCmHSNLKiURxmMyZdJx4M4g+FqI/H2RqP8/7q1YRsNnSLBd1sRjebwWrF4nKxtbycqNlMZkYGNpuNQCBgJDyBQMA4GewIGenpYLFQrxR1QIpSeOJxbMEgAFnRKE6zGS0eJx4M0hyJUK1U6wleJ9E0DY/Hw09+8hO+/PJLo5hHeno64XCYZcuWYTKZCIfDDBkyhKOOOorFixdTXl5uLCmQGHYfj8dZvnw5GzZsYPDgwZx44oltpors/DuW2B6NRnn77bf56quvGDZsGHa7vc1cqsSVzUThMBmqL34sTdNwuVyceuqpLF68mMWLF9PU1ER5eTnJycmYzWZaWloIh8NcccUVB/zztn7dOub8858M03UcJhNumw2b242WltY6dFMpaG5uTfaamsh+5RWKe/TA1a0boUCA6PZ1I2PxODazmU9nzTLOvywWS5tRJYklwtxuN8FgcL9Xf1VKoQMtQCOtHYP1sRhVkQhOn49UwBIIoMXjKL+faChEo67TrOto8fh+a8cPlZ6eblTJjUQieDwefvrTn7apeLpixQpsNhs+n4+amhpjv+TkZLxeL3a7HaUUPp+POXPmYLfb6d27N4FAgPr6eiorK6mtrTUuBEHrvPE+ffowZ84cmpqajJEf2dnZxoUH+K4CeCwWM0Z2dISDPllUSlFZWcOf/vQpa9ZYicU2kJmZg8vlRNd1MjMzcTgcRCIRGhsbqagop6ZmM9dddyH5+TkHxY/K0mXLqNiwgTxNQ1cKZTK1Joh2+3dzc6D131YrlkCA2GefsaJbN5THg8PrxZWS0lpJz2wmpuu88vbbpGdkkJKSYiwUD9/N3ayqqkLX9TYfqv1FKUVVZSXP3X8/SXPmkKMUXrOZVIcDp9uNtv14LKEQyV9/jXb33USefhrb9oT2YGMymfB6vcYSA1ar1bjKl+it6datGykpKaxbt85I+Lp3787ZZ5+N2+3G5XKRnJxsDJFOdGAopejWrRv33XcfS5YsMeYMpKWlkZSUxKRJkzjuuOP2ed1GIaD1O/jeex8QCFjQNDCb++L13k9V1R1UVMzGbnegaS4KCm5AqWmYTKlEoz5mziznzDO9pKQkd3r7szIzSS0ooGrzZtJ0HUc8jikSIa7rtEQieDQNi1LEo1H88TgNSlHl9TLhuuuwp6d/92NJ6wmQx+Ph9TfeYPbs2UbyUl9fbxSnSvxGnHfeecD+7TzUNI3uhYVkpKdTWl9PpabhUQpHPI4GRJXCt/2YzNuvJjZFozSbTKTNn0/k4ouxJ3feezJ58mSWLl3K22+/jcPhMJK1r776ivr6ek488USj0ysjI4N4PE5dXR1JSUmkpKSQnJyMy+XCbDYTCoVYuXIlLpeLcePGGa9PIp4m6LpuFGh65ZVXSEpKMhLCxH12lJgW0NHLn4jDx6hRo5gx4+fcfPPNVFdXkZKSsr3InYWsrCwuueSSA17fAuDDmTNRTU2tz6tpaIk5z05n69B7pUDXIRhENTdjKinB8eKL2IqKcNrtWNxusNkwJyWhuVy8X1tLs9mMf/sSEDvOcUv8tU5ZaNrvqwQklghbBdQCqUrh0nVs4TBmIBSNts7D1HVi4TC+cJgqpYjW1dFUUYEjOdm4WtoZ6uvriUQiRrE4aD1nTJwbLl++nGeffdY4pwOMK7ZJSUmkp6cbHWtNTU1UV1cza9Ys5s2bRzAYxGKxYLVasVqtRs0Lh8OB3W5n8ODBvP/++1RXV5OWlobX68Xj8dCtWzeSkpKMWi6hUKjDR10c9MliLKb44INP+fDDcqLRI9m8eTkOx3Li8RhNTU2kp6fjdLYmjs3NzWzaVMLixaO49tqDY7FjpRRrVq8mEokQBoJKtc5jicWwRaNo26toEo22DrkCIrqOubaWAUuWYPF6UYl5Odv/Wx2JsHnDBjIyM9Fo/6Oa6IltaWkhuQNOQPRYjFfefJOq+fPJAeyahstqxeF2o6WkQFKSUZhCq6sjafVq1v/tb/S5887WoHeQSAx/+uabb4hGowSDQeMvHo8bPXBKKcxmM3l5eVRXVxuB9ZxzzmH48OFG0Ni56lWih2f48OE89dRTfP3118ydO5fa2loGDBjAcccdZ/SkC/F9hMNhVq9eTTSaiskUBIJoWndycq5l06ZyWlrKKSiYQmrqBTQ2tsaAeDzCypVNNDeHSE3tmKtr+0opRX5+PseNHct/t27Fvj1BCMfj+LcP33RrGlal0LfP/2vUNGLHHsu5l1++y95TXdfJzMqiqqqKlStXUl9fT0FBgTGszGQycfbZZ3fYj6rH4+Gss8/mjw8/zLZ4HGvrgRKJxfDF49RHo7gSCbBSNCtFqtNJ3oYNLPvznxlxyy3YOmFeXuIqy3XXXUdZWZlR0S9xEjJlyhT69OnDH/7wB0pKSsjOzjYSw8RVwLS0NFJSUoyK0fX19cydO5eCggKSk5ONoVU+n4/GxkbC4bAxHzFxQlVXV2fs19LS0q6IHUBlZSW9e/c+oK+P6LrMZjM2m43c3EE4nW6CwWYsFifTp5/PMcccQ/oOnVIHSiQSYcny5VjjcUJAyGQiuD1mWOLx1uGa0JosKoXSNPR4HHdzM46WFmLxeOu8wFiMqK5DLIZZ0yivqKCiooKSkhI8Hg+ZmZlGp3ZjYyO1tbX7fd5b4vs9ZMgQPv/8c8oiEdzbO8xUNEpEKRoiEZJMJmzbr5AFdZ0qXad/WRn1jzyCdtttZObnf6+qr/tTOBw2Ch4Fg0HsdrtRF0TXdZ5//nkaGxvbFEcymUxYLBbsdjtut9u4DaClpcVYhiM5ORmr1WpcqEgskRGLxYhGo8ZVyk2bNuFwOLBYLMb75fV6MZlMtLS04HA4KCwsPHyTxdZKbTV89tkaQiE3JlMPotGzWL36NXy+Fiorq7Yniw6i0Qi1tQ2sWTOM8vKhvPLKGq677uhOv1qjaRp1dXWtY7SBRqWoi8WoCYWwtrTgVArNam0dq+3zEQ+H8ek6DfE4EZ8Ps6ZhUqr1D7CYTFT7/dQ1NODz+ajf/t+0tLQ2zxsOhwkEAvt92I6u62wsKWHRxx/jjERa1/8xm8FsRrPZwOVqTRa3T1QmFEILBsn98ksq168nt1+/g2Y4amJYQGLYbkNDA3V1dVRXV5Oenk5qaqoRFBKFbVpaWlBK0atXL8aMGbNPr63JZCI9PZ3JkyczefLkNlcsd1eyW4jdaf3ctuD3NwJmdL2ZeLyRcLiBlJTjGDlyJprWgsXSHZ9PIxxW6HoQaCYa9dHcHO7kI2j9Tng8Hs466yyWLFnChlWriMXj+JWiSSlS43GcgFXTUJqGT9MIduvGJddea3zfdv7emc1mBg0axP3338+LL77It99+S0VFBT6fj8LCQs4880zGjBnTIceT+C6fN20asz7/nEWLFlECxGgtctOoFN54HBdgorXAQ62uUxAKke31kv7VVywtLGTkBRd0Srn4RE95OBzGZrMRj8fRNI0rr7ySgoICPv30U+bMmWMUxUgcc+Jk2+12k5ycbPSIJ+Z2v/rqqyQnJxOLxbBarSQnJxsjMZKSkowTqn79+vHhhx9SU1NDVVWV0UufGEKcmMeV6NkX4sdKfGcXLPgGhyOD/Py+mM0a48b1YsqUKcY+B5qu64SCQUJK0aRpNClFbSyGNxAgxWrFFI+3Xmnz+1GhELF4HF88zrpt22jQdYJmM0GzGb/JhE/XiZhMfFtezrZAgPUbNmC2WIzlHVwuF9FolNraWkKh0H7viNE0DavVytixY3n33XfZtH49m+Nx4kBEKQLRKPWahlvTsG0fruoDGoBcTSP7m2+oevJJ7L/+NclpaQd0KZ3EOVpjYyPRaJRwOIzP5zMSu8SSIKtXryYWixGLxYx1thPDQhO1KxLzDDVNMxK+lpYWdF03al0k5jn6/X5isZhxrLquU11djcViMWJgdXW1ET+TkpKYOHFih78eB3WyaDKZaGioY+3aEmAAEMHhmILZnMemTU9QVvY5SUmJ8cA5+P0n0tw8lWg0yqpVOn5/EI+n84f3Zefk0GIyUQN4lSIpHscZCqGAjEgEp9mMKRYjFgrhC4ep1nWKAwFWrliB2enE7HRicTqxOBzYPB7qo1Gqa2qoqKhg27ZtpKamYjKZjEnYgUDAuAK2v49d0zS2lZVRWlJCTyACrb1ftJ4YWb7bsXX4hNmMMpkwNTVRvnIluf3779f2/BiJoQIOh4PS0lIqKyuNHnKHw0EsFjOGFQQCATZv3kxdXR3dunVj6tSp32tO6O4Sw87+bIpDT+s8syQ8HjtK1aJpdcTjXkIhN01NJpzONCyWXGIxnWBQJxgME4vVo1QtFksDbvfB0VmjaRrDhg3j+uuv58EHH2Tj2rXUAtlApsmES9Mw6TphTcNZVMTZ119PrwED9njCoGkavXv35vbbb2fr1q3U19fjdDopLCzskFEWOz93WloaN998Mw8//DBLlixhUyRCs9lMrVIkKYVFKcyAPS2NKrebTevW4bLbGeVwYH73XTb36UOfY4894HFBKUV9fT0tLS2YTCZCoRDBYBCv14tSinnz5hGJRIy5g4k/XdeNv8RrkBjKbzKZ8Pl8pKSk4Ha7jSp+iQJ1gHHf2tpaGhoaKC8vN8rPJ9qRqE7p8/mMuT8SN8WPlRhWuG7dZjQtiUAgTjweoE+fwk79jGmahslqpZrWpKlW10mORHAGAuhKkRQMYgFUOEw0EKAxFqNO01jS0sKatDSsHg8urxe7y0V6djZeh4OTbDaeefppVq1aRTweJxAIUF5ebnT+NDY2MmDAAGOR9/19PIMGDeLCCy/k/gceoCoQIKZpBJWiRSlSlMKlFFalCGoalWYzFS0tWGw2jsjMJHX+fNb9858Mu+Ya7Adouk5iHeAvvviChQsXYrfb2bJlC83NzQwaNIhwOIzD4aC6uhqfz2ckiYkrgomiNIFAgObtc0stFgt+v59wOIyu68bj+f1+zGYz6enpZGdn07dvX3r16kVWVhapqam88cYbPP/882zbts2Y45ieno7D4WDAgAGMHTu2zZXLjnJQJ4sAgUALjY216LoPTWshHg/j8ZyOxzOUioo/Eg7HSU+fjNl8PNFoBkrFUaqUlpYowWAYt9vVmcOdARg5fDhRu52ycBi3pmHfPjcnpOs0hMMkaRrm7T2n/u1f/NqCAoLDhhGKxTCZza3DTU0mgoEA1XV1NDY1sWHDBiNh8fl8xpWwYDBIZWUl+fn5HZIwNjc3U9/SQqau4wNalKIxHqcpHMYWCKCZTK1XGUOh1kW1dZ1gNIo/MQb/IKFprSXZBwwYwMqVKyktLcXtdhs96zte6m9ububLL78kOzubq6++miOPPPJ7l9Pe8dgPptdBHHrsdjuDBvVnwYIPiMfTicVsgAldjxAON6JpHpSyEIvFiUZD6HojJlMNhYU+kpNdB80Jt6ZpTJw4kQ3ffMO6NWvQnU6+CYdZZTbjsFqx2mwcNXEiF196KUOHDm1dm2sfHtNms1FUVGSsH3ageqTNZjOjRo3ij3/8I6+88gpvvPEGDU1N1MfjuEIhRlgs/CQ5mR55eWT/6ldcdccdzK+owOXz0dtqpfKZZ8jt04ek7OwDdlK0Y3XtxNyZRNW/xMnkihUrjDVodzwpSoxg8fv9RgdbYnssFsPv97N161ZjGFc0GjX+wuGwkZRWV1fT0tJCSUkJbrfbOJGvr6/H7XYbMfjUU089KD634tDWenKv2Lixkbq6ECZTLtGoGafTRo8e+Qf0CtbOEuuXrvn6ayqUwqnr2KJRFOCLRkm1WHAAxGKEYzEaYzGqNI2h06Zx0c9+ht3hMDprbDabcSwul4tHHnmExYsXU1lZaayVqus6xx13HEcddVSHLbtms9k4//zzAfjrX/9KXXMzTbEYNWYzSUphi8exmEz0cLk4/pJLeHfhQj758kt0q5VRTifu2bNZ7vUy9KKLsO/nAjw7i8VifPvtt/z73/+muroas9mM1+s1zq1XrFhBWVkZkyZNMkacJa4QRiIRwuEwwWDQuAqZqKxrsVgIhUI0NzcTiURwOBwMGTKEQYMG0bt3b5KTk431vK1Wq1Hz4tprr+WII47gpZdeYu3atTQ0NOB2u5kwYQKnn356m3VuO9JBnyxarXbs9gCRSC26XkM06sXns+Hx9KGw8Hk0zUQsBi0tinA4gK7XA3WYTA3bk0QFdN6Pi6ZpDBk6lKOPPprZH32EVWtd5DgSi9Gs66RoGm5onccCBIE6h4Oe//d/XHbZZbudz3bHHXfwzjvvAK3VVqurq/F6vcYH0uPxMHbs2A45JrPZTMxkol7TqFcKr67jiUZxba/omhwOt873i0TQ/X58kQh1FgvqAJT3/b5MJhOXX345s2fPpqqqCsBYFLqqqsqoihoIBBg5ciTnnHOOlG8XnU7TNKZMmcJrr71FY+MGNE1tHwbjJxKpRdPcKGVDKR2lwtuHpZZzxhk9SEo6eAqEmEwmotEoaz77jDEOB4OTkpigaZSdfTZF48YxoF8/ioqKgO/fwdJZJ3wWi4XCwkJuueUWpk+fzpo1a1i6bBmv/PnPFEQiZJvNZPn9xD/4gBt/9jN+88ADuBsa0FwuutXX89Wf/8xxt95KUgfHmcQai+vXr2fDhg188cUXuN1uSktL0XWdvLy87ZVzTQSDQXRdN3rNEydFiZ7zxBAph8NBPB6npaWFQCBAS0sLGzduNF4Xi8WC2+0mLy+PjIwMunfvTmFhIevXr+eRRx6hurqaVatWGdMCKioqcDqd2Gw2JkyYYJx8CfFDJEb31Nc3Ul5eyyeffEFzswmv10EwqOjXLx2Xy008rmMytXa067q+26HvHeW8885j5nvvUeLzYdI0lK4TikRojMVI1jQcgKYUUaVo0TRqMzM5ZtIkcnNzW0d07aJj+uKLL6Zv377897//pbS0lNraWvLz8znttNM49dRTO/R4EqO4Lr74YkaPHs3r//0v365cSVNTE1VVVTiqqzkvOZnJKSlYly6l37XXcrffz+crVhCzWBiZn4/to49YmZrKqLPP7rDzyHg8zty5c/nb3/5GS0sLKSkpuFwuPB6PMUIiUSn38ccfNy7MRKNRQqGQ0dm2Y1XSaDRKc3Nz63lzLEYgECAQCDB16lQmT55svD47F/baMck/4YQTOP744wkEAiil2q23eCAc1MmiUgqvN5Xu3b2sXl2JrqcTjboA0PUIgUAamuYkHteIRKJEoz50vQGzuYq8vKYOuaT+Q5jNZq66+mrWrVtHaUkJMU0jrBRNuo4XcAFmTUOZTLSYTDiPPJLhJ5+MdQ+96Ndccw2hUIhPP/2UhoYGSktLjSpxffr04dRTT+2QS9NKqdahmhkZ1JWXU719CIEtHscSChHTddLCYTwmE6ZYjHAkQlMsRp3Nhtlub63idZD92Pfo0YOcnBzKy8upqKgwlrZIDIfKy8tj8uTJjBw5cp/XDhOiow0cOJALL7yAp5/+J7GYjq6H0PVmIAVwA1ZAoWkRzOYahg83cdJJQ7FaLQfNCXeiAFi0pAS3y0WzrlPndnP+ddeRkZPTISMjDoTEsPPc3Fyys7OZMGECUZ+Pd//2N6yNjeB0krluHc6iIs6aPp3XH3sMh8OByekkbdMmFrzyCsf89Ke4OnD5o7q6Ol555RWWLl2Kz+fD5XKRmppKMBhky5YtBINBvvjiC/r27Wv0dIdCIWw2GzabzUj+zGZzm9sS/25pacHr9TJp0iTy8/PJysoyytA7ty8JlTjpGzx4MC6XixdffJFly5axdu1aKisrSU1NZfDgwUyaNInBgwcfkp8FcXBoHVroZ/bs5Xz4YYw1a9KpqGihtdCoRjgcJimpNxaLhWAwyKZNG6mvr8flcmG32+nevTspKSkd/hnUNI2hQ4dy1tln85/nn0dpGjEgoBQN8ThJ0HplUWtd2L7Jbif7zDPpNXgwmsm023Nem83G2LFjOeKII2hoaCAejxurCRyI71Wi8MugQYPo/7vfUV9XR1V1NV999RUvPPQQlX4/xS4XPauqsLz4Ijddey0P/vWvzC0uxupy0cdmI/DmmyxKSWHM9qt6+7PdieG4Tz75JBUVFaSkpGCxWIw52YnzwdWrVzN//nzWrFlDIBAgKSnJWJc2ERMT74FSimg0alzhVUoZlVUHDRrU5hh2977t2FGRqKqaeOwDGQ8P6mQRWtc4GTNmBGvWvAt40HUT0WiEeNyPyVQPOFHKRDweB/xoWjNOZzlHHz0Yu/3gObzBgwdz00038cD997O5tJRaIEfTSDOZWhdrVoqwppEydChX33wzOYWFexwSkJOTw2233dZ6xXL2bMrKyvB6vYwePZpJkyaR3YHDmIqKihg4cCCfl5dTCtgAk65DNEpA16mPRFoTYKWI6ToNuo45EiFv9mzqjjuOtNzcgyKJT/j8889ZuHChMd/G5/MRjUbRdZ2hQ4dy+umn07179w4boiHE95X4rE6f/lNqa2t4552ZBALNmEy1QBrgQSkzuh5F05qw27M5/vjxFBX1Pqi+ewDzP/+cTMDldBIIhzENHkz69qp8h3JysOOPvFKKy668kg2bNvHlzJl4mpoY5XRi+/RTzr36akq2Fw2zuVwMc7mwzJvHmqIihp90Etp+LlKWOCl66KGHWLZsmdFznlj+x+VyGUNKX3nlFdatW8fmzZvRNM0osJA4IUp8lhI95okOzsRQ0549e3LmmWe2WTNxx9cl8W+Xy8Xpp5/OiBEjWLFiBRs3bkTXdfr168ewYcPIycnZY+epEHuilCIQCPLUU7N4+WVFY2MPLJZumEyno2kphMM+otE4b7xRiNu9lj59SklPz2Ho0GE4HHY0TTOqA+fkdPySbGazmRkzZlBfX88HH3yALxKhHshQiiSzGYemEVeKoNlMt+OP57zLLyd5HxLZRKX8HRPEAxljE89lsVjIyMwkPSODnj17onSdf/7+92iNjcQdDnqUl2ObPZsbrr2W2373O+bX1BC32+ntcLDttdf4xm5n5PaRcztWo/+hElecZ8+ezYoVK9qsxZso4uXxePjyyy9566238Pl8xv2CwSAOh8MYqZE4T4zH44TDYWNkRKIojq7rHHvssWRlZf2odh/o38aDJ5vahURJ79NPP41Fixaxdu0GotEoSvmIxeoBL+AEzGhaHAhgMtUzerTGqaeOPWhONBIndoMGDeKYpCQ8VitrgLW6TmNSEi6Hg9SsLMZNnMhlV1xB6j586RMVNs866yymTJlifGESFZc66tgTC9hPmTKF5cuXU1VbC/E4EVqXBWmIxUgGo+pfRNOoU4qj7XbSliyh+rXXSL7qKqwHwXCixEnTo48+SjQaxePx4HQ6GT16NE899ZTxBZckURyMNE0jKyuL3//+dwwfPpx///vfVFVVEQpVoutWdF0jGDRhs52G2TyFpUt91NbGyM42YzJ1fmxMFBEoXriQHjYbusVCdTBI79NPP+gS2h8jEY/T09O54eabuaWigrkrV2Jzuehnt+P/xz+461e/4urKShavW4fF5aKvw0HxW2/RNycHvUcPXC7XfllwOXFC8+9//5svvviCpKQk42QocWUxJSWFsrIy3nvvPaPSn9VqNaY5hMNhzGYzJpMJu91OKBQyqqgmfn90XcfhcDBu3Dhj3dm9vUZWq5UePXrQo0cPY0hW4n6d/VshDl2JRcufeWYmTz7ZCAzCZsvD40nG5UrGZOpJKBQhEtEIBGz8+c/1XHJJMz//eT4pKd8th+BwOKisrKSysrLDE0aTyUR+fj733nMPHouF+W+9hR+o1nVsVivJSUl4MzMZf/LJ/Pyqq9pccdqbg2W0RuK77Xa7mfHzn1NTXc1Hzz5LvK6OqN1Ozpo1ZGZm8sAf/sCNt9yCXlVFxGqlp93OhrfeIgrkdOuGe/sQ0Z2X2dkXidEN0DqP9e233yYWixmfmcS8wUQBmyVLlhiJInx3tTQjIwO/32/MVfR4PAwdOpTMzEzWrFlDTU2NcS5ZWFjIySefjLMTlkn6MQ7qZBFaP1AjR47khhuu5w9/uIeSknUo1YCmZdI63Kr1ymLrvJwmCgvTufnmnxm9QQeTFUuWYN6yhSNdLo6Lx1lbWEjahReS2707ffv1Izsr63slJonjS/xA77y9o2iaxsknn0xpaSlPPPEEFS0thIAWTSNdKTxKtZZB1jT8Fgv1fj9pPh8pLhfWd95h24gR9Ni+WHNnSZRif/vtt1mxYgV2ux2r1YrH4+HSSy81iiwcbJ8hIXaUqIJ84YX/x/jx4/jmm2+orq4iFotRXV3DCy8sJxYrwGbT+fZbE3PmLOGcc47EZOr8DhClFOtWryaybRvJHg9Rkwl/ejo9R48Gul6CYDabGTBgADfceis3X3UVC+rqMLtc9LTbWfTf/3LpxRfz4J//zLf19YS8Xsyaxvr//Ie83r1JS0sjv6CAESNGfO95eztWYdZ1nY0bN/Lhhx9uH43TymQyGfFvy5YtPPPMMzQ0NAAYVxQTQ67i8Tg+n4+MjAxGjhxJVlYWq1atorS0tE2yePTRRzNy5Mjv1dbEVdgdF70W4sdatWotzz23mHh8JFZrEi6Xh9RUSE4Gs9lEMOjAbG5dutDvT+aDD1IZMqSFSZPS8HhsJL5CXq+XZcuWkZmZ2eFzxjRNw+lyYfb7ORPo7fFQHAigTZlC0fjxDB06lO7dux/wuWv7WyLhuv7Xv8bn8/H1q69iqq3lCIeDlnnz6OZ28+A99/C7P/yBpXV1NCcnE9F15r78Msnp6eTm5pKZmcnIkSPp1avXLjumdlzuJ/FvpRR+v5/q6mrKysooLy9n06ZNbYpw7ViIKxAIUFhYyNq1a4nFYng8HgoKChgyZAi//vWveeutt3jnnXeorq7G6XSSl5dH//79MZvNzJw5k3g8ztChQ7n44ovp37//Idchekh8ysxmMyeccAJ2u53HHnucb75ZSjRaha670DQ7rfNyzFitxxAMjsTpTO/sJreRmMOxdsECvJEIOJ3Ux2Kkjx3LlHPOwba95/WH/DB2Ri9RotrgpZdeSnp6Ov/85z/ZsH49LbrONlrH02eYzfRxOBh4+um8+8UXzCspITkpiYEuF2XPPIOze3eye/Q44G1PnIA0NzdTU1PDG2+8QSAQwOPxYLFYGDt2LKNHjzZOWIQ42CW+Q/n5+eTl5Rkn2o2NPrZtu5N33llMPJ6FyZTNG280c9JJLaSmdnyp7b1RSrFy2TLMzc3YU1PxxWK4Bw/Gm5bWpROFcePGceVNN/HnW2/FWVuLxeUiq7aW6KZNDB42jA2bN1PicOCy23EHArQUF2MymUheu5atW7dywgknkJaW1u712bGXHNpeldtx+7p169i0aRMej8e4z44nU5s3bzaW0Ehst1qtnHTSSXTr1o133nmHYDBIcnIymZmZFBYW0tTURHFxMfF4HKvVyoQJE/i///u/1kJn3/N97IzhcaLrUkrx2Wez8PksaJoJs9mE3W7C5QKPR9u+JLQiFAK/HzTNzLZtdl57rQKPx8oJJxSita4ERjwex+Fw0Nzc3OGF7pRS1NTUUF9SQi+bDa/VSp7LxahLLqH3kCFA1/mOmEwmkpKSuP7Xv+Z3DQ18/dFHWOvqGJSXR3TuXJKOOYZhRx5J8fr1bLZa8TgceKxW4vE4lZWVVFVVsXXrVsaOHcuRRx5pxK2dz+FaWlooLy+nuLiYDRs2UFNTY1QvjcViuN1uI0F0OBxGkujz+aivrzc6v5qbm+nZsycejwePx8OgQYPo06cPRxxxBE899RQWiwWXy2XM7c7Ozmb8+PGcdtpp9OnT55B83w6JZBFa3/SxY8cyePBgVq5cydy5X1FcvB5QLFy4mrq64/F4JuPzuXnxxfX89reZmEwHx5fJZDJRX1vL5jlzOMLlAqsVv8tF79GjsTsch2RSkhgiPG3aNCZOnMjixYuZP38+X3z2Ga6NGzknNZXjUlNRPh9H3nkn182YQUpTEzaXi+61tax/4QXSr7sOywFYHyYhHo+zbds2FixYgM1mY9WqVcybNw+bzYbdbic3N5cpU6YYpdqFOJTsPB8sOdnFT396FgsW/IlAoBin08WmTTbefHMVl19+TKcmZLqu09jYyLpvvsFrtaLZ7dRGInQbMQJ3BxZ16WyJ9+j8889n44YNfPz881irqxnmcrF1wQI2BgJ4ts8bTPJ4SElNNSrw6brO6tWrCQQCnHbaaUaxjUSs2nFJi0TVUr/fT2VlJdXV1ca6vBs3biQaje5yKYtgMEh+fj7JycnU19djs9koLCzk2GOPZdq0aYwdO5bx48fz8MMPk56eTmpqKk6n0+h9z8jI4Kc//SmnnXYaSUlJXfZ9FIcGpRQ+n4+VK9cSiTjQtDAQQqno9qH6EI9DPJ74nCo0LU48rlNaWsvcudUcd1wedruFSCRKdXU1jY2NxvDEjv58l2zciKWxEZfLRcRkQu/Zk9ScHKDzqj13FE3TyM3N5Z777uOKigq+XLGCiNXKwIICVnz+OetbWnB7vTicTjweD6mpqSQnJ2O3241leubMmYPFYmHAgAGEw2F8Ph9lZWVs2rSJ4uJitm3bRiwWa9OJlRjNp+u6sRRdKBTCbrdjs9nw+/3G8hiJ4aWJq5KBQIDc3FzMZjNut5vTTz+dNWvWsHz5cpKTk/F4PBQVFXH55Zf/4KGyB4tDJlmE79bFGzduHGPHfjcn8bHH/sXdd39MLLYJl6sPH34Y4Mwzaxg6NKuTW/zd5e9vvv4aa20trvR0WmIx/EVFDBg5spNb9+Mk5khmZ2dz2mmncfLJJ/PuqFH87aab2OD3k+/xkLNiBT369uX3t9/Ow/fei7uhAavHQ/KyZcx5913Gn3celgPwBYrH41RUVPD3v/+d9PR0BgwYwIsvvkg8HjeuKp5yyimMGDHikP0yC7Ejk8nE0UcfycknD+TFF5fi8WThcuXz3/9Wc/zx1fTs2XnxUdM0qquqqF2/nv4eD1FNI56RQbdBg/ZrMZeDkclkwul0ctXVV7N1yxaWz59P1G5no1Lg8WC2WLDabMZcnPT0dGw2G5FIhIaGBkpKSli8eDH9+/fH5/PR3NxMQ0MDgUCApqYmY9REU1MTgUDAqMaXmGdoNpuNuYc7rwtWV1dHfn4+F1xwAatXr6Z79+7GEhpKKcxmMxMmTOC9997D6/WSkpKC0+nk2GOPZeLEiYwYMYLs7OwufWVYHDoSBUh8vhaUiqJUE/F4PeFwHT6fHTBjsWiEQhAIQDSqb1/T2095+VoaGqKUlw9H0zQj8fD7/QesI2Tzhg2Ym5uxJifji8ex9++P0+Xq8OftLJqmkZ2dzeNPPcVlF1/MgpIS4jYb63SdmNWK2WzGarXidDpJTk4mKysLt9tNLBajoaGB6upqPvroI+bPn095eTnV1dXGkhaJOd+JhC0R+xLxLxgMGktThMNh/H5/m0QyGo0SCASMbYmOucGDBxvbNE2jvLzcuOLodrtxu92kpqb+oFEWB5NDKlmEtlcKE4nYBRdM4ZVX3qWkpBi3O51wOIn//GchvXufjMvV+W+QUoov3n6bLLcbi91OcyBA6qhRpKSldYneoR3nmZxw4oksmjaNef/4B2k+Hza3m8jHHzPg8ssZcMIJLPn0U7yNjQx2OuGTT9gybBi9tg+p6AiJL/63337L+++/z5o1a+jWrRtff/01JSUleL1erFYraWlpnHXWWTQ3N7ephCXEoSrRmXP11T/nvfcuJxBYh9vtJhRy8eqri7jhhlOw2Q58YpZIPNauWUO0sRF7Tg6+eBxzt24U9up1QNvSWUwmEwUFBdx4881cO2MGC6ursaSmksJ375vdbjfW93K5XEQiEXRdJxgMMnfuXL744gui0SjBYJBQKGSsiZhICpVSWLefYCVOdqLRKH6/v83Jks1mMyqZmkwmYrEY6enpjB07lkgkQnNzM5qmkZKSgtlsJhKJUFdXR48ePYxkMSsriwEDBkhBGnFQ0TSNpKQkvF4XUA3UEIt5CYU8tLSYiUZTMZlsRCIQCMQIh/3oei1QTW5umOxsO/Pnz8dqtRIMBqmoqOCkk07q8PU+E+ctZZs34wSwWGiKx8no3x/HIVYY5YfIz8/nznvu4c7bbuPLsjIiycmkpqYC382vdjgceDwevF6vUYymubmZyspKNm/ebFRr3rFSaSgUMuJlIBAw1iTPy8tjyJAhFBQU8M4777B+/XqCwWCbCqaJWJuIr/G4To8ehQwaNKjNCI+GhgYyMzNJSkrC7XYby2kc6u/ZIZcsJiReeKUUqampXH31/3H99S8QDueRnNyPZctMfPPNWo47blCnv0mbNmygYvlyCl0uIppGtdnMuZMnd4lEMSExvCopKYnrb7iB5QsXMnflSpwuF0NcLsIffMDFU6ZwV3Exy2trcSUn081u55t//pPce+/F6XQC+3dohVKKiooK/vnPf7J69Wp0XScpKYmGhgY+/fRTnE6nMYThlFNOoVu3bjQ0NEivuOhSunXL56qrzuT++z8iKSkLr7cHixaFWbx4DUcfPYgD9VHfsepcJBJh3scfk+J0YrLb8QUCZPbpQ1p6epeKi3szZMgQfvHrX3PbbbeRtr3Tbed5h4ne9MRc8cTyPoFAwOioS/wler9jsRiRSIRQKNRmqGksFiMUChGJRIjH421OfhKFaRLrJbaeELWWf09LS6N379ZlVxInWWlpaaSkpGAymWhqauryV4TFoSexVES/fr35/PMVRKOVxGIOWlo0wuEQZnMaJpMHk8m8/TviR6kazObN+P2r+PrrMOvXF2Oz2QiHw5x11lkMGzaswz/niUrtVevXk+F0gs1G1OEgpWfPdgUNuxpN07BYLBx55JH88uabueP229Fo/d1IVCVNJIc7DgdOVBs1mUxEo1EjMQwGg8YVxFAoREpKCn369GHgwIEMHTqU3r1743K5jPU0Bw4cyJ133sm2bdvw+/3oum7E00SHWuu5bjKTJrXO495xXUWLxUJycjJutxun09llqukfssliQuuPpc7xx0/kyCPfYfnytXg8aTQ2evj880qGD++Bx9N5c9CUUrz/v/+RbjLhcrvxRyLYBw+mZ//+XfILr2kaGRkZPPi3v3HJ2Wczv6EBm9tNj5oauq1fz69//nPuuPNOnDU1mNxuMmpr+eCf/+SoM88kJSXFKAH9Y18bpRRVVVXccccdbN68Ga/Xa/T0eDwehgwZwvr16zGbzbhcLkaOHEk4HDYC0cFSXlqIHyORTJx11hRmzpzDpk2rSEpKoqnJySefbGLw4L4kJf34JRn2RXV1NcXFxZSXl1NTU8O2qipys7IIWK00Wa0cf9RRHd6Gg01i7rfJZELfYc5hItHz+/34fD6jdzscDhOLxdB1nYaGBvx+v3FiFIlEjB7uxHIYFouFnJwcCgoKyM7OpqioiNTUVJ5//nlmzZpFMBgEMB5/x/USE73q8Xic008/nZSUFCKRCBs2bCA1NZWMjAyjIEReXp50somD1jnnnMNbb71NeXkxPXsmM3p0AQMGmDGbY2zaVM/s2S2UlITR9TAmUzn9+9dxyikTKS3diN/vp3fv3vzkJz9h8ODBB+QzrmkaDfX1NG7ZQqHTSVjTiGdmknkYfc/MZjPdu3fHk5REU1OTERt3HDbf2NhodJS1tLQYIywaGhpobm7G4XCQnp5Ov379GDx4MAMGDKBXr144HA7gu/NMXdeNf59wwgkopXj88cdZvXo1Pp/PiMeJmGixuElLOwabLRX4rnJzU1MTTU1NpKWlGRcjevfuDXDIv2+HfLIIrW94erqXqVNPYOXKN4hECvF6ezF/vo8NG8oZMaJvp7RL13Vqa2tZvWgR6U4nusVCfTDIqFNP7fKlwfv27cuMG27gH/fdR2p9Pc6kJEJLl5Jxyimccv75fPrf/2Lz+0n3eIitWMHWcJjU9HR69OjByJEjSU5O/sGvTWIIxzPPPMOKFSuM4VOJse5paWmce+65bN68mcrKStLS0li8eDFOp5Ps7Gzy8vK67PsiDj+a1roe4/nnn8r99/+XYDCftLTeLF5cx/LlKxk7dkSHPr+u6yxatIgPPviAkpISTCYTHo+H7J49icXjVESjEIlg68JzcXZH0zSjgyoSiRh/iZOhhoYGTCaTkTA2NzcbCWLial56ejrp6emkpaUZZeQzMjLIzs421k1MDMVKXLW02+1s3bqV4uJigsFgm6FWVqvVuJKpaXDEEaM58cQTaWhoYMGCBTQ3N3P++edTVFREcnIy4XDYKAwhxMGosLCQGTN+xmefzWbq1GMYPXo42dlZWK0WotEYU6fW8OyzlXzyicJmW8fllw/mnHPOAFqHzdtstjYVgztS4nlKt24l2tSEJSuLoFKonByycnMPm++ZprWuvQoYcTGRKLa0tBi3JYbVJ7aHQiFGjhzJscceS8+ePcnJyWmzDuXO1aGh7Yg2TdM46aSTKCwsZNasWaxevZry8nJsNhtVVVWsWrWB9PQiGhutzJlTxtChg0lPd7J69WqWL1/O6aefzsCBA8nKysLlctHc3ExjYyMpKSkd/6J1oC6TLFosZk499UzeeedTVq7cQFJSGsGgm1dfXcmwYb0P6BCZHYcFrVi+nEB5OYVJSUQ0jVhGBv266DpiCYlhBOecey6LFy1iyQcf4G1sZIDLRcsnnxBOScFVWEhDaipRhwO3zUZFVRWV1dVs2bKF4uJiTj/9dHJycvZ6xWPnYVuJbcuWLeOzzz5r8xon5gG5XC6ysrIoKioy5t9s27aNdevWkZub2yGviRCdJTFE5+STz+R///uIdevW4/WmYDJ5ePXVpRx99JA2E/T3Z1yKx+MsXLiQf/zjHzQ3N5OUlERycjJJSUnY7Xag9UQgGArx8Sef4HA6jeGOh4vu3bsDEAwGjUXudyyuEIlEjNcqFArR0tKC3+/nyiuvZMiQITi3Vwd0OBxGkrfjie2OFXITt40ePZo777yTO++8k/Xr1+P3+42E9buKfRp5eQOYMuVMmpub+cc//kFqaipDhgyhT58+ZGVlYbVa0XWd6upq6urqSE9P77K/a+LQlPjMtyYBJzB48ECys/O2JxutCcmwYd341a/stLRUsWHDEEaNOgpNM6FptImNB0LinGbV0qW4LBZMNhvBWIykbt1IPoDV4zubpmnk5+eTlpbGtm3bjEI1iWI1ANFoFIfDgaZpxhB8v9/PUUcdxYQJE4whuzu/ZvvyGvbt25fevXvT1NSEz+fDZDKxbNkybrnldvz+RlpaGvnmmwq+/XYT2dkar7zyCt27d2fQoEH06tWLtO01SZKTk6mqqjKmzB2q71+X+UVu7T338NOfTkOpjYTDpVitIRYurOPrr1cdsHYkChBUV1ezefNmFs6bhykcxuJw0KzrZB9xBGkZGe0SnK7GZDKRkpLCTbfcgrl7d76pqWFjUxPrm5tZsmYN3pQUnC4XHo+HtLQ00tPTyc7OxuFwUFFRwVtvvUV9ff0ux6knXrvEfJpED3xVVRVlZWVs3ryZzz77jJqaGuO+uq63aZvFYsFut+N0OnE6nTgcDqOHSoiuRtM0MjPdXHnlJShVgs+3FYslRGlpiJkzvzLmc0Sj0V12wPwQiTnDzzzzDFVVVdhsNqPkeXZ2NgUFBeTn55OVlUWSx0NNTQ2ffvopzc3NXT4+wncnLH379qVnz57GENDE0NOmpibq6uqorKykvLyciooKampqaG5uxmq1Mm7cOKPnPCkpyZhnmBiKursO0kRn3rHHHst//vMfbr75ZkaMGEFmZub2Akghamoa0fUCotE+bNwY4e9/f4aqqmqjyl9KSgr27esDWywW8vLysNlsRvEiIQ4WSilWrFjB2rVrSEtrXW4hUXAk8fUwmTR69PBy5pk68Xga//nPPCKRaKe1OR6Ps3LxYjxuN9hsBKxWCvr377T2dAZN0/B6vZx00knGlcPEmodNTU3U19cbSwJVVlYaFaA9Hg/5+flG9dMfek6XiKMpKSnk5+eTk5PDxIkTmTz5JwQC22hqqqKpKci//72C++67n0AggGv7Oa3H42lTfTo3NxeLxXJIx8cucWUxQdM0TjnlRJ577gWKizeQlOTFZkvmjTcWMWRIL5KSXB2aDMTjcRYvXsy3335LRUUFjY2NNDc04O7Zk4CmEQJGjRhhzFHp6kwmE7179+aW3/6W237xC5ZUV+NrXQkXi8WCzW7H7XaTkpJCamoqDofDKA9fVVXFnDlzmDRpEqFQyOjd8fl8xlCDQCBgBJDEX2JCc2VlJeFwGLvdbqw/tnOZeIvFYswDSlQJbGhokIRRdEmapnHCCRM55pjXmT+/GK83Gbc7hXfe+Yr6+i1Yra3z3NLS0hg0aNA+XdnfWeKHMNGTP2vWLNauXUtmZqbRQZOcnEx6ejperxdd13E4HMRiMcLhMOvWrWPr1q0MGTKkSw/T35HT6WT69Once++9BIPBNusmJirwJU58Eon82LFj8Xg8P/pkKCsri2uuuYaLLrqI0tJSgsEgH3zwAU899W9iMQvhcJx///t96us/YsyYo4yq1zsW2Ui85w6Hg2g02mUKOoiuY+HChcB3RVJ29N3n2ES3bor0dB9ff21l6dJixowZiNl84K4oJtafLSsro6asjCy3m4im4bda6Td06AFpx8Hm3HPP5Z133qG4uLjN/O3EXG2LxWLEHJPJxLhx4ygqKtovz73zVUmTycT06dP54IOPqasrw2rtzrffVmCxrCE7O5tYLGb8bu0cH81mM6FQqM2Q2ENJl0oWAZxOB1de+TOuvPL3BIM5OJ12tm7VWbBgKSeeeKyxn67r+y1hU0oRi8V48cUXmTt3LuFw2KiElJaZCZmZNEcimGIx4mYz8VjssKocN2nSJJZddhnPPfssSVYraduPPTEsNJEwuv+/vfuOs6suEz/+Oef2NrfMvdNLJpl0kkBCeugoEBAUFnStiKwu/izYxdVFXVx1XVdR2V1dsC8qC4oUQQg1kB4CMb1NMjUzd9qd28s55/fHzDkkGVTUzEwyed6vV16pkzm3nO/9Pt/v830en88qD5/JZNi0aRM7duw4rqiDecjZ3GkEXnPyYjayNnuJmQeUzUPRZp8xs2lvJpOhUCicMRNUceYx77kPf/gWNm36CMnkwZF7LsWGDW3WTpHX6+Xll19m+fLlrFy50vraEx076TI/HI9N+QJ48sknrQ9ys0+f3W7H6XQel4ZqVvlUFIXNmzczbwzb6ZxKzNXryy+/nA0bNvC73/3OmhCVSiWreqkZLGqaxrx583jjG994Uhs8l5WVMWfOHAzDIBaLcd999zM42Inb3Ugi0UM+n7JKz2cyGfL5PF6v97hJkcPhoLe3l+rqahlHxSlDURR6enoYGhoikUgwMDBANBq1zrzBq/0YC4U0LtcAPT0hnnyyg7lzp+D3j/3ivmEY9Pb28tvf/paOjg6y2SzhqVPJ2mzENQ08HsorKs64e8pc0Pr0pz/NHXfcQUtLi5UtVsjncXs8VkoqwEUXXcS1115rjU1jcT2zZs3iXe96B3fc8V1crimoai9eb55MJm3tfOZyOSs91mS328lkMif9msbLpAoWzYnKqlVLuOCC2bz00sGRA/gBnn12P/X1UTweLy6X09ouPhlndEqlEj/96U95+OGHcbvdlJWVEQwGKSsrs94w2WyWdDrNc2vXUlNXx9lnn31yHvQpzjykfP0NN/Cr//s/GHmNXqvssTl4m1X88vk8g4ODowLB10pN1V6jkmCpVELTtFG57ooy3GPMO1JQw0xlNd8TJ3MhQYhTiWEY1NXVsXTpTLq6uvF6i4RCYfx+vxUslkolent7eeSRR+jv7+eyyy7D4XBY96qqqtbKrrljXygUSCaT9PX10d7eTnd3N0eOHOHll1/G4/FY9+Kxu/sul8u6F80FIF3XaTl06IyaFA2nCMf43Oc+h01VefzRR8mkhycePq8Xx0gg7fF4WLRoER/60IdoaGg4qWPUsYF+Q0MDf//3b+Ub3/gfUqk4ipIhn88xMNBPf38/8Xicnp4eK33fZAa3QpxKDMOwjrd0dHQQDAZxOp1W6rRZSfPo0aMcPtxGf38XNpuLF17IcumlrSxbNmtMFz9KpRLbtm3jBz/4AZlMxuofWFVfj2qzUdA0DE3j17/+NatXrz6tz739NWw2GxdffDHhQIDbPv95Dh84QDqZJJ3J4B0JysrKynjLW97CTTfdNKbFtszPv5tueh+/+MWvaGs7hMdjYBhZent76e3tpbu7m2g0isvlsub/ZnGy09mkChbh1Sas733vO9i5819Jpzvw+2vZu3c/3/jGC7jdHvx+H7W1tcyfP5/58+f/1TefGbhs3bqV3/3ud1bVLK/XSzAYpKKiAr/fD2BNpBKJBL/5zW9obGw8o276rq4uMum0NXE0AztzpTqZTAJYK+nFYhFd10kmk6P6hJnlk838bzMNwdytsNvtVjNUMy3V/DeKolAqlchms1ZjXXMSW19fT21t7QQ/U0KMHUVReOSRR2htPUIkUo7PN3z+LBKJWB+ymUyGRCJBMplk06ZNhEIhZsyYQTKZJJFIkE6nGRwcpK+vj2QySW9vL319faRSKUqlkrXYY/b9U1XVOhNppnqbu/7m9xsaGrL6YeH1nnE7U6qqUl1dTX1NDWcFAtSWl9OZTJJwuQhVVVFVVcWll17K6tWrrSB7LJj/70033cT//u8vGRzswOsto1DI09XVRSwWs7JADMOgqqoKp9NJsVikt7dXFtnEKen888/nwQcfZN++fdZ4FI/HrZTAZDJJd3c3mzdvo6urj6qqEJpWxv/+7yvMnz8Fn88zJtelaRovvfQSd955J5lMhnA4bG02BAIBbDYbxUKBVDrNzp07URSFG264YVI0ef9LqKrKrBkziHg8VEYiRMNhutJppq1axfS5c1m+fDnTp08ftx6U4XCQj3/8o3ziE3dQLEaBIh0dnZSXl1vF24rFIhUVFTidTnK5HG1tbcycOfO0fd0mXbBoOuusuZxzzjQOHerC4ykQCNjx+UJWgNDR0UF7ezsHDx7kqquuouKELf5jz96YXisPuVAosGHDBqsFw7GplcFgkGAwCAy/2c0moalUihdffJGrrrpqvJ6OCWf2pzF3/o4tgdzf349hGFYD1GQyaW3lt7W1USwWcblcRCIRwuEwwWCQaDRqDarRaBSv10tZWZnVDBXgS1/6EmvWrCGXyx33uplBqtlg1TAMnE4nc+fOJRgMyoRHTEqGYXD48GEeeOABnE4nDocdj8dz3P2kKApDQ0PWWd7BwUEefPBBAoEAhULBSkE0U7jN9Ehd1637CbD6XR0bKJqLQmY6pfnrQqFAOp0mnU6TzWTwRCLW9Z6uH6x/KcMwSCQSvLJpExUOBzMCAaodDpbcfDPTlywhFouN61n3aDTKDTf8Hd/+9r04nZWAj56eHg4fPmxdRzabJR6P4/F40DSN/v5+VqxYAUzeSt/i9DR//nxWrlzJU089RaFQIJVKcfToUXw+n7Vg1dfXRzQaxDC2ks3W4fFM4+BBnWee2cVVVy066eORuaN53333EY/HrRY3gUCAaDRKOBzGbrcPp6H39zMwMMDLL7/MzJkzWbTo5F/PqcwwDHYfPEi2r486t5spPh8NVVW8/eMfp/KYdiLj8XyYccAll1zCihW/4bnnWrDZ3MTjPRw6dAiXy2W9tuXl5TidrpGK1k5rke10fN0mXbBoFgB4+eWXGRrqo6LCQVmZnVBoOMgw02bMEuS7d+8G4LrrrrNWco79f8xUSfNnM8gxK9X19PTw/PPPH9cuA149H2SudBx7CLdUKrF//340TTsu33oy83g8BAIBqziNmRJqPj9mMRrAmlgqisLNN9/MsmXLcLvdIxPc4XRSl8tlPb/mZPXEPki33XYb+/bto62tjVwuBwyfszLPSA0/9zpg55prruGiiy6SQFFMamvXrmVoaMgKDM0debfbbU2cSqWStUNvBo9DQ0PYbLbjqgubKd5mcRrzfPCJ6anHNno3A0XzTIf5+0KhQCabxV8qEWprY+vzz3POqlVnTLEUwzDYs3s3+e5uprnduHWdUlkZc5Yvp7q2dlzPuJvvi6uuupIHHniI3t4kbvdccrlNtLQctgL8/v5+wuEwHo+HfD7PwoULrcVRIU4V5lGYj3zkI6TTadauXUtnZyeVlZXW5L1QKLBy5Uquv/564vEEjz22h0AggM8X4Xe/28o559RRW1t53CbC3zpXMAyDQ4cOsX79eqt6pt1utxa+I5EIDoeDTCZjtYXIZDI88cQTLFy48LQMOP5aqqrScvAgDA0RjESwFYuEm5rw+f0n5bX4a66nsrKSt73tBrZu/TK5XB1wmJaWFjRNJ53OEI/3EgyGcDqH+wpffPGlJ/Wc+XiblJFKT08PP/rRj8jn84TDYXy+4XLtsViMQCBg7V6pqkp/fz8vvfQSjY2N1NTUkM/nrdLlyWTSmigNDg6STCZJJpNWCqQZrLS0tGCz2Y6ruGmmVpmrEOl02kqvLBQKJEeaK/8tzedPF7quU1NTwznnnMPTTz9NOp0+bvKjaRrpdBqn02n9Pp/PEwwGWb16tdW768SSw8fu9L7WYNHc3Mx//ud/8q1vfYtNmzaRSqWsXUq73YHN5iYanUs4PJ+5c9943PkbISajw4cPUygUrPO+J57zNc8Qmqniuq5bizfHNkY2dxbN4lLm+YxYLEZdXR319fVMmTIFVVX5l3/5F3p7e1EUxVqsyWQyVqsHDANN1ylms0yz24nYbOz68Y/xBQLMWLDgzAgYDYOXt27F1t9PpLoaW7FIxbx5BEOhk3Ku/i+lKApz587lyivfwA9+8DAOxyU4nX4ymW3s27ef3t4+YrEooVCYysoKli1bxoIFC6yvFeJUoigKlZWVfPGLX+S2227j+eeft3bFZ82axS233MLSpUsB+OhHP8j69f9IOt2C3+8gHjd44IEnWLp0Nnb78MJ/eXk5NTU1f9EizoktiQqFAps2bSKbzVpB67HXa46t5g/z/2hvb6e3t5dYLHYSn6FTlxnM79+9G08+T0BRMPJ5Io2NeCaws4CiKLzhDW9g5swfsn59HEVZhmG0cvBgG/F430jsEaNQmE9T09u4+GIXhgGn6/A4qYJFc3t348aNtLa2Eo1GUVUVp3N4+9dMW9R13Uo9MCcsv/nNb3C5XCMVsYYnSyfuDsLwG8Tlco3acTQnUeaOpbnzlclkrJSdRCJBZuT/10dSuM4EqqoSjUa5/PLL2bp1K4lEYlRaqLmTYe4Slkol3vSmNxGNRv/qFANFUZg3bx5f+cpXeP7551m/fj3t7e0UCgUGBwc5ciRNMBjGZovwyCObWbSokrKywEl//EKcCszMCHP3z1zUSiQSOJ1OCoUCqqpa6aK5XI5CoUAikaC7u9vqr1dfX08sFqO6uprKykoikQh1dXXEYjHKysqsNBzz+3V0dHDXXXeRTCatYNHMLjB3K0u6TimR4CjQWFdHNJ/nwH33UV5dTbSyclLv+Ou6zmAiwcE//IGYqhK02SgVi0TmzME7sts73hRFwe12c/nll/PAA48wNHSUQOA8HI7lLF8+QF1dAlCprm5g2bLlzJt3lnXEQ4hTlaIMN2+vqamhrq4Ov9/PypUrWbhwoTV/rK2t5frr38hPfrKGXE7DZsuzaZPBrl0v4nA48Hg8VFZWMmXKFC688EJrMdt0bIbTsQGgmbZ9+PBhOjs76e/v59lnn7XG4xNbe7ndbhwOh/VnVtaGppHNZsf9uZsoZkpn1+HDlNvtlKkqhtNJoK5uXM9unrhZoes6zzzzHPG4C7s9jGGcjc32LpzONLo+QDrtQtOaKBbns2FDkG9/O803vlHE6z09dxcnXbRiGAbr1q0b9WKYq7PmpOPYXwPWartZDt48y2aebzu2KMuJxVbMlElzBd4MekqlkpVqZf677EgvwJCi4B5JuzwT2Gw2LrvsMvbv388999wzXEL4NfrlmGlwK1eu5LLLLvubv6+iKFRXV3PDDTdw2WWXkUgkKJVK9PX1cf317yIeb8Xna8Bub+DJJ3dw7bXLTssbWYg/R1EUysrKjgsUk8mk1UzdPItmZleY2RAej4fbbruNGTNm4Pf78fl8+Hw+q9DKsZOjYxd2zIDjhhtuwDAM7rzzTquQjcvlwjZyv3tsNsIeD9ULFnBg7Voqu7uJVFbi2LmTl3/+cy669dYJ2V0bL4qiEO/poXPHDuY4nfiBTCBA5bRpE/64ly5dyooVi3jwwZ04HLPxepfQ3z+LigoDu91HIBChoiJqZYUIcSoz5xtmaqo5Dzx23LLbbVxyyUWsW7cRTTtKWVlwJCXVZ1VPjcfjxONx2tvbufbaa6mpqbEW/83xMJvN0tnZyZ49ezhw4ABHjx4lm81ac0fznLKZqXHs4p3D4aBUKuFwOCgWiwyNZKLl83kK+bz1fSbrmHgsRVGGqzAfPMhMux0foAWDRGtrx/U5KBQK7Nmzh97eXquQ5f/9328YGHDj9y9BUaZht9fi9U4nHPZSVgYuF+Tz0Nur8NxzPp57boArrig/LV+7SRUsmk9+W1vbqPSqVCplla41e+sdu1ozMDBAOp22vubYwNH8GvP/d7vdVvGaiooK+vr6ePHFF0mn01Yhl2Mrbh5baj6by+EvlfC2trJl7VrOPe88bGfADqM5Uf3Upz7Fju3beXnTJvK5HLl8Hrfbjd1ux+12Ew6HWb16NTfeeCPBYPCk3FDmhMtsZ6LrOvX19bz1rW/h3nufwe9vwumsZd26FOee20VDQ/Wk3skQZybDMFi+fDm/+MUvSCaT1kTJMAwymYyVDWGeITQLck2ZMoXly5dbu/zH/oA/veNv3vc33XQTy5Yt42c/+xnbt29ncHCQoe5uFlVWsqK+npCqUnnJJTxRVsYrDz9MVFU5KxRCeewxtjU0sPDaa63gcjIxJ5a7duxA6eqiorwce7GIs6aGKdOnT+i1mVk0t976MR555Bqy2UOoahM7dkxnx44qFCWKzeblv/4ryXvfG+f6672EwxOzEyrEn2O2L0gmk9axoVwuRzgctrLHzA2CTZs2USrlCAT8BINBIpGI1QrN7AOdSqU4fPgwTz31FBdddBGlUonu7m5aW1vZu3cv7e3t5HI5q4csvDoXMeendrsdbWSn0MyuguG6Fslk0vp7q0BYOk1locDGBx4gevPNeAOBM+J+az1yhFx7O+FgEHuxCKEQFVVV4/K9DcOgv7+fn//851RUVLBgwQKmTGli8+ZNvPTSDjStGUUxUBQdVdWw23VcLgW/H3w+yOWgWFRIp1UeeKDAZZcZ2Gyn3/xyUkYpw70V88dV3DRXhFKpFMCraaEjZ3HMM3ORSASXy0U0Gj2uKlU4HKa8vJxIJEIkEsHn81m9x1paWvjCF77Apk2bMFsxnFhxE4bP4hWyWeZ6PJSl07Q8/DD106ZRXVeHcgYEJ4qiUMjnGeroYOnIc9iSTBKbMwd/KERdXR3nnXceS5YsGZODwObrYKa+XX/9dfz+98/R399KIDCDw4d9bNzYSV1d1cjNP/kHYXHmUBSFxYsXM3PmTLZs2YLT6SQcDluBoVlw6tiG8JqmsWDBAqvS819zT5jp/PPnz+drX/sag4ODtLW388XPfpbskSNkkkkqAwEya9Zw3VveQsehQ7yyYwcRYIbXS+anP2V/dTUzV65EmWTnFw3DQNM01j35JDVA1OFA1TRc06YRLi+fsEUrM4gtlUocPNiGw1FONpuiWNRRlAAORwSn04/drpJIhPne9zSOHs3wiU8U8PkkHVWceszqzeavNU07bsHMfM/u3buXBx98EJfLZVW2D4VCRKNRfD4fmqaRSCSA4d2mbdu2sXv3bqutkN1ut7KkzDoIxxYAy2azZDIZa37o9XpJp9PWnMcMWM1gEbA2MUrZLFPcbvRt23jy5z/nje98J55JHDCaR71279hBqFgkYrNhL5UwamoIjcP4aAaK3/zmN3G73cyePZtQKAwYrF+/nmQygc2WxzDyKEoOyABZDCOArivo+vAZRUUxUFU4csTGwECa8vKx6wU5ViZVsGh+wJ177rk8++yzZLNZHA6HtaOYH9nFMvPWzZs2m81SW1vLZz7zGQKBAB6PB6/Xe9xqk+m1VtMbGxv50Ic+xKc//Wk6OjqsYDGfz1sDgG4Y5AsFjMFB+svKKNXW4mlpYft991F5662okzjNymQYBmvXrqXU00N1VRURn49YKMQHv/Y1XGVlVp+38ZggKYrC7Nmzufji5dx33wYGBjqx22t5+uk0l12WJRj0jfk1CDGezFXt6upqysrKrMUwXdc5evQoxWLRChZheIKyYMECLr30b6/iZn6tzWYjEokQCoX45D/9E1/6xCfY29VFVFGoyuVIPvYYN3/kI9zxsY/xh54eohUVNJZKDNx9N/GaGiqmTp1UC2uqqpJIJDi0fj3L7XYCQEpRaDj77An5PDAnzebn3rZtL3HXXT/D4ViBqk5HVeuw2wN4PD78fhsul4FhQDpt4/77fUyd2s873xkd9+sW4k8xx7QjR46QSCSsDApFUfB4PFb2l6qqPPHEE6RHekLb7XZcLpdVoTQQCFiFv8zAsFQqMTg4CGDVszCzMsyfzXmmy+Wirq6Os88+m6amJmbNmsWRI0f413/9V2sjw2xb9GrFdtA1jUKxiH1wkGQgQE0oRPHZZ9kSibDy+uvHtVryeNN1nV2bN1NpsxG02XCoKsFZs8ZlnmgYBhs2bGDXrl0sXrwYAJfLyUMPPcw999yDzaYBSSCJYQyh6wmKxQGy2TJSKTeaplAqQTYLpZJOLpcnk7ETiZx+mxGTKlg0mecnzGqkgLV7aJ6zMYuomCs9l19+OU1NTQCjVtD/XJqVzWZj6dKlfO973+MrX/kKO3futHoFqqqK3WYj4nJxzowZOIJB9q5ZQ63LxexwmPzTT7Nt9mzOufzySX3Dw/CA9+Qjj1BhtxOy21ELBaZfeKGVez6eVQ8VRcHn83HDDdezZs2LDAy04HZP5dChJp544jDXXz/3tMwrF+KP0XWdXbt2kc/nqa+vt7IjBgcHGRwctArc6LqO3W5nyZIlfPKTn6Sqquqk3gfmgtDSpUv5hw9/mP/+ylesc4q+gwdJPvYY//i5z3HP5z9PLB4nGosR27uXI3fdhff22/H5/cMB42m+wKbrOoaus33DBlzd3VRHIriKRbqDQaafc864PzYzTa+/v9/Kmvntbx+ipaUPw2hEUXzYbA4cDic+n51QCAKB4WtMJAzicZWf/9zNxRcPUVMz+at8i9NDsVhk//79PPDAA2zfvp2uri5qamqs7InHH38cl8vFvHnzcDgc/OEPfwCwAkKzmMyJ7dGO/fXQ0JDVG9o82lQsFvH5fEydOpV58+Zxzjnn0NzcbDVtNwtCzZs3jz179vDrX/+aRCIx0pPPZaWvGoZBsVTC53KRKhTY3tZGma4zLRBg4Oc/Z6vHw8LVqydlmj6GQT6dpu2ll7jQZsOvaSRdLmbOmjVO396go6OD3t5e6xx/sVjkgQfup6urk1AojGH0A30YRghN85PP+0kmHWhaJU6nB01TyGQ08vkUZWW9hEKx0/KY06QKFs1c8A0bNjBnzhy2b99OLBYjGo2SyWQYGBiwis/Aqy0aGhsbueiii/7qNCsYXiFesGAB99xzD+vXr2fbtm1s3LCBQ6+8wpKqKpbX1RF0u4lddhn/3dXFjp07KVcUmr1eun/0I1rq6pg6b97ku9lH6LrOrt27ObJ9O9NcLvyGwZCmseDiiye09PGyZct485sv4wc/eAqvdwZOZz333ptg+fIUdXX+CbkuIcZKMpmkpaUFh8NBIBCw0p1g+IPR4/FQUVHBBRdcwM033zxm7WSGC0nYefN117H34EFeuPtuyhWFcyIRYlu3ojc2cvm7381zd99NZW8vi4NBAo8/zr5YjMAVV1AWiRCtrf2bxuyJYk4yM6kUycFBnn7kEaYqCjG7HXuhQMWiRQRPqLA4Hte0bds2tm/fTjgcprm5mWw2y/PPv0ChoKIoGqChKCVsNg2Hw8DlGj6To6qgaZBOQzzuYv36fVx77VxOs5dFTDKGYZDL5XjkkUd4+OGH0TQNp9OJx+OxzmU7nU4SiQT33nsvixYt4sILL6Sjo8M6l2i2CzJ7O5up+WahrmKxeFxaak1NDVOnTmXmzJnMmTOHadOm4fMNZymZ97NZC8PcwQ+Hw3z2s58lGo3y2GOP0dnZ+Wo6q6pS7nZzTijEgpkzmfWGN/DtO+9ke0cH/qoqpno89N19NzvcbuZceCGOSVKR2Ew/zWYybN+2DWdfH9GyMlylEkPBIHXTpo3bvFFRhnsNHz16lK6uLjo6Ojj33HN57rnnRjorDAKdgA9dd1Eo2ND1EoVCEpstiK47KJVyaFqKc87JEAicni3aJlWwCMOppj09PUyfPp1kMmmdNzR7KpqpBuabsaamhne+853U1NSclJssEAjwhje8gUsvvZS9e/fyhU9+kmRrK5lUilCpRPKJJ/inj3yEj956K3t7eqioqqKyWOTgT35C5DOfIRyLTao0K5NhGLy8ZQu2vj7KAwFchkH51KnUTJ06YTt45vd83/tu4pe/fJjBwf14vdOBWTz00F4+8IGF2O2n/8ArzlyvVaRL13XKy8ux2Wz09fWxYMECrr32WlKplNWDtq6ubswrXCqKgsPt5oMf+hAHdu9m64svDhe2CQRQHnmEq268kZ6LLmLvmjVENI1yTcNzzz24n3qKYjTK5nPPpfnaa4lOnTrugdVrVYB9vV/b19PDlscfx9i6lVBvL+e8/DJum41ooUC/rtP0xjda/3Y8HpdhGGzfvp1f/OIXzJw5k5qaGurr69m//wCJxCDgBbJABsPIYBhpNK2IptkoFsFmA11XAINi0eDo0SSqKuOmmFhmZfz7778fwzAIhUIEg0FisZgVKHo8HpxOJ5lMhldeeYU9e/ZYaadmCmg+n+fQoUP4fD78I03gzaqlmUyGfD5PZWUln/70p612HHD82GCOGa91zEZRFAKBAB/96Ee5+OKL2bVrF62trbQeOcL6J55geiDAueEwZb29uHbv5utf+AK33Hor/qNHCVRU0OBwMPg//8ORYJCpixef9hlqhmHQ293N5oceQt21i9yuXfyd3U69YRDI58lNn457pC/lWD9ORVGoqKjAbrdb7fh8Ph/nnnsun/rUp3jmmWfZvv0V4Ci6PpyCrOsahlGgVEqgKH7AjmGU8PsT3HDD8jG93rE06YJFl8uFw+Fg3759uN1uQqEQpVKJ/v5+Ojs7rRQrr9fLqlWr+OAHP8i0adNOas9D8w3c3NzMez/4Qf7j85/nUHc3sepqvIcP0/Pcc7zzox/lF1/+MtXxOLFYjMjmzRz8zW84+6absI9BcZeJpOs6iUSCl9evp7xYJKyqaPk89UuXEigrm+jLo6GhgXe96zq+/e3f098/B4djKuvXB7jkkqPMmFEtEx9x2jGDmeEPL9369QsvvEAwGMTtdluFbRYsWIBhGNaCWiKRsBpUjzVzZf2fvvxlPn3zzWw7coSYYdDsctH7058SUVXKVZVwPk+1qhJTVbytrdDSQsW2bcTXruXgpz7F1BUrUMchjd1cZDR79R7biunP0XWdPdu38/g3vkF02zbqkknCqkqzouC12yGXI6koDO3fj75qFeo4VMk2J74//OEPrYq4Xq8XXdf5j//4Fn19vShKOTAEDGEYCYrFfnK5EMlkDLChqpDJDJeI17Qiul4c8+sW4k8xU6p/8IMfkMlkCAaD+Hw+q1BhIBA4rv81DKeS9vT04Ha7rSJfZiX9TCZDV1cXHo8HwCpgaJ5FPPvss5k+fTqqqr7mjtefGx+OLQI2b948isUiiUSC7wSDrH/gAartdubFYvRt3IhWLPLZz3+ef7v9dgJHjxKqqKCqp4fur36V4He+Q6yh4bQ9QqNpGtu3bOGZr3+dql27qMlkmAZEnE7cmga6TmzbNg6uWcPUSy4Z84JnZvbZvHnzWL9+PS6XC03TGBwcpKGhgUsvvYTOzk56e3ux24cIBILk8ykymX2oahjwYrM5sNtzvP/9s5k9e3wquI6FSRUsmuferrzySr773e/S3NyMy+VicHAQv9/PxRdfzODgILFYjOuuu45Vq1aNWVNPM83qiiuuYP++fTx6551U2GycXV6OsmEDM+rrWXHttbz0619TZ7Nxlt9P7sc/pnvePGpXrDjp1zPROtrb6XzpJc5yOAiqKumyMirnz5/wNDJzwveOd7yb3/zmCbq6duHxzOLQoTk8/XSKKVM0nE7bSEWr02/wFWces4nxvn37sNvtOJ1OnE4nfX19tLW1UTayQDMwMIDb7ebQoUO0trZaFfdWr15NRUXFuL3fVVWlubmZ//eFL/Dtj3+c8r4+fKEQm+JxlGyWWkWhxuGg2uXC7XKh2O2gaai5HLU7d9L/pS9x6GtfY+rChWOammTuMAwNDVmTT/Pzo7Ky8k8+X7qus2vHDn56221U7NxJOVCpqlQ5nZQ5ncOPSdfx5vOUf+c77CmVmHHjjTi83jF7POZ1tba20tLSYh3XMAyDvXv38sAD/0coFMJmSwI9QBhd91EseslkHBiGRi4XQVEc5PMG2WwWm62PSMR+2k5WxanFXJQ5tvDSn2Pu4j3xxBN0d3cTCoVwOp24XC4CgQChUIhQKISiKKTTaTRNI5PJWKmmg4ODVouNZDKJYRj4fL6RgGD4GJOmaZRKJfL5PLquc+GFF56UuaQ5fqmqSjQa5aMf/zgDAwNsfvJJvJrGvEiE4vr1GG43f3fLLfz6zjsJHD3KyvJyao4e5chtt1H68pepbGo6rsrreN+L5ut2rD93DZqmsXHdOu7/53+m8cABIopCpaJQ5XTid7mG8911HW9nJ9kvf5ld+TxzLr8c1eEYs8dh7izefvvt3H777ezYsYOBgQFaWlqoqqqioqKCT3zi4/zoRz8hHp/CwoXvJxIpZ/36H9PRsRlV9VBXV8bb3raUG288f0yq/I+XSRUsmtxuNxUVFZSVlVn55Y2NjdTX1zM4OMiKFStYsWLFmAcqVprjzTfzyubNvLJuHZU2GzP9fpTf/Y5rr7+eb7/8MtsPHqRCUZhmt9PxzW+ihcNUTZtmpYGdrm8ueHWHY+uGDTi7uqiIRLAVi7iampg6c+YEX92ramsreNvbPsK3vvWfJBIt2O3TeeghO4sWHSQWK8PlclJe7sflOv1fEzF5GYZBV1cXGzZsIBgMMnXqVCorK3E6ncRiMd773vfy5JNPsnfvXuvM9osvvkgkEqG6uprrrrvOqvo2nhRF4bzzzmP/Bz7A41/9Kqn+ftK6znzAb7MRdDpx+f0oZWXgdEKphJJKQSJB6OBBUnffjX7nnShjdGanWCzyzDPP0N7eTnNzM01NTQSDQasIRmdnJzU1NdZjOZau6+SyWf7n299G27kTv2HgURQCDgc+rxfV7we3G3QdI5PBnkzS+MtfcnT+fOpWrBjzYwnmxLe/v5+BgQG6urqorKykpqaGgYEBvF4b0A2UYRguNM01souYI5sdBDxomoGmZait7efcc6dJsCj+JmbA19fXZxUmDIfDo85Qn1ip3vw6TdN44YUXrKwKM3PCZrPhcDisoM9sF2QGVmYKp8PhsNLyI5EImqbR398/quaFGSieddZZJ/XxmzuN0WiUf/7Sl/hEby+bt2zBbxicFQzif/ZZ5l59Nan3vpenvvtdArqONxQiuGMH+/7pn2hbtQq9vJzaefOonjEDh8t1Uq/vjzEzFfbt20cymURVVWKxGA0NDVYngtei6zq9vb3c+4MfoBw4gB/wKQplTicenw8CARSXa3iMTCbx9PZS+73vMTBvHpHGxjGfxzc1NfHv//7vPPPMMxw6dIhMJsOMGTNYunQpU6dOpb8/wUMPDVFRESAUCtDUFKGpycusWc1ceOH5LFmyGLfbdVqPiZMuWOzr6+PBBx+kvLwcu91OIpGgv7+fQqGApmlcffXVXHDBBVYlqrFmVt38+G238Zn3vpddvb1U2WzUFgoYzz/PWz/6Uf7jwx+mfmSV37F9O70f+QjtU6YQXLWKpquvxhsOn75vMsPAKBbZ8Mgj1NtsRBwO0HV8c+YQHDlLOtHM5tPXXLOQBx9U2b9/Fw5HDUNDCp/9rA2HI4bd7qemxuCNb/Rw+eV1+P1uSU8VpxRzR/Hxxx/H4/HQ0NBAdXW1VQG6rKyMRYsW4ff7ueuuu1i6dCkrVqwgm80SCASorKwkGp2YtgfmPfiOd72Lln372HD//Sy02XACTlXF4XKh+P0QCoHHA6XS8GG5QgG1UMD17LMM7t9P+dy5J/3azOIvTz/9NOeeey61tbVEIhHs9uEdNJfLRSKRoKenh1gsdtwE1rRx40Z2vPgiCwG7YWBXVVxOJzavF4JBCASGn4dUCjQNT3c3uaefprBwIU63e8wCRkVRCAaDOBwOOjs76ejoIBwO4/P5+Od//mfWrFnDunXrKBaH0PV2FMVFsVjCMPJoWgpV7QXcgIKi5HnjG11Mm1Z9+n5eiQlnGAadnZ288sorVoHCYrHI3r178fv9NDY2HpfuaQaIqVSKo0ePcuTIEQ4fPsyuXbsoFotWURqznVk2m8XpdKKqqlW91GyHYQaHX/3qV3n44Yf58Y9/zODgIPl83jriZFaMNgyDVatW8fd///dW26+TzQy2Pn/HHdz+yU+yZedOgrrOXL8f5de/5rJ3v5vcBz7Alu9/n6CmUaPrlK9fT3DLFnweD1pVFQfOO4/oBz5AbIyb2BuGQXt7O0899RS1tbU0NjYSi8Ww2Wx0dXXh9/uJRqMoMKqStaIobHvlFXavW8dCwGYY2BVl+HXy+VDCYfB6wTDA4YBSicDBg3SvWQPve9+YL06ZO4w33HCDVdTI4/G82gdydws1NYuprg7gcMA118xixYpLiUajuN3uU2Ke+7eaNMGimWP+y1/+knw+TygUolAokMlk+Pd//3erKtVEvHCqqjJn9mxu/NSn+NHnPkd1Tw+x8nLcmzeTV1VWRCJU9PbiLJWoUlWCBw7gPHgQ47nn6HngATo+9jGmrlyJfZxWh04GK30E2LV7N90bN3KO34+vVCIeCHD+SBGHU4WqqsyYMYWrr76E733vBXK5VzCMqRw4MBVVrQAi7Nnj54UX4KGHhvjEJ+LMn1+HzXb6DwJicjAMg61bt9LR0cGSJUuIRCJWoGhSVZWpU6eyevVqZs+ezZQpU6xVdXNlfaKYAe27b7mFjQ89hFIqoSkKJVVFt9nAbgeXa3gXTtMglxueONjtuPN5Dr/wAuVzT37LG13X+elPf0pZWRlutxufz3dcmx9FUfC43bRv3kxbRwdKPo+Sz6Pmcij5PPZCgfU7dpBNp9EBDdBVFc1mw3A6hx+PzzfcvVnXweNBTafR1q4l/YEP4Bw5JzUWVFWltraW5cuX88Mf/pDdu3djs9koFAo0Njby/ve/n0AgwOOP/x6ns5bp02/Ebrexa9dzpNO96LofVXXjdBqsWOHnwx9+O3b76VehVpwaSqUS27dvZ//+/Zx11lk0NDTg9XpRFIW6ujr6+vpoaWnB7XaTSqVIpVL09vYSj8etftpOp5NisWj1KzQDxFQqxeDgoBUk2mw2crkcQ0NDpNNpK3C02+3U19dz66230tzczF133cWBAwew2WzY7Xb8fj/19fX83d/9HTfccMOYbzzYbDZmzJjBp7/0Jb7yqU+x+fBhykolZrjdJL/9baJnnYXL5aKiVKLeZqPKbsdjt6OWSnD4MLGWFjq2biV15534pkwZk2vVdZ3Ozk5++MMfUlNTQ2VlJbW1tXhH0uj9fj8D/f20HjmCe6SqbLFYRMnlyA8N4cjnefZXv6JUKAzP5QHNHPePHSMNA6VQAI8HezpN6oknMG66adx6cysjAeyxvx+uMB5n0aJ6KipcpNNpli5toqamAlUdn77h4+G0DxaP7Xmze/du1q9fT1lZmZWPfvbZZ7NkyZIJ//BSbTYuu/xytm3ezJZf/IIGu52ww8H2Rx5hhqbRoKrUOxxEnE7sZg52qUTdjh303X47+2+/nVkXXzxulVKPrfb3l36dpmm0HjxI5549eAYH2fr888wHKm027MUiZbNnU9/cfErdRIZhcPRoD11d/TidjWhaJYZRgaJEcDiiOJ0BHA4Vw4DNm8u54w4/X/5yN3PmnNwedEL8Ncy+sXv27CGfzwOMqopnpmmpqsq0adPQNO24v5vo97HVs2xwkGypRAbIGAZpwyCt6wRKJez5vHV2hWIRNI2SYZA3DHIjLUBO9jXF43H27NnDwoULrV0Ik/mM2Ww2psZi2HM5jFQKJZXC0DTIZlEKBUKFAhlNI6eqZBWFjGGQ0XVKmoaqaSjF4nCwqGnD2Ri6TrarC1smMy4V/2666SaOHDnC888/T7FYpL+/n7a2Nnw+H3PnzqVYhH37Kpk6dS6RSJRcrptdu+4FPMRiYS66aBYf+chVhELBMb1WMXmZPe02btzI9OnTqa6uHrVjF4vF6O3t5ZVXXrHGL7vdTjgcxuv1WhsEuq7j8/no7OzE5/ORyWQYGhrCZrNRLBaP+7UZSGazWXK5HFVVVdamwtVXX013dzff/va3qaiowOfzsWrVKt7//vcTi8XGbcy02WwsWrSIT335y3zlYx+jrKeHUCRCd6lEy9NPc46uE7XZiLlc+LxeFLd7eDzJ51GyWep27mTvHXdQ97Wv4YtGT+p1m3O+J554gp6eHmbOnEkgELDSTs3Fu2AkQv+uXeTb2yGZxJZOw8AAjlSKQKFARUsLyWKRrM1mjZFpXScyMj4qhcLwNxwpdKMZBlpHB8VsFtdIe5LxcGKF2927d+Nyhaivr6C83Eah0E1NzVTs9vHrGz4eTttg0XyhOjs7OXLkCLlcju7ubhobG0mn09aB5WuuuQaY+DNmZnnkWz7yET62bRvrd+7E6XJRVioRtNkI2e2Ueb3YAoHhVRQYnmioKpH2dtLf/S6FpUtxjlG6w7HMSlw2m41AIPC6z3YahsFAXx/P3n8/6cceI9rSgjOd5vxCAZvDgVIs0lcoUH3FFSjHHL6eaIZhUCgUePjh37JmzW40bS667kJVXTgcPrxeL36/ar0smYzBrl1OvvMdJ9/5jo7TeXqXqhaTwyuvvMILL7xAVVUV6XSaVCpFMBgctShjrrSfqu9Zp8NBRlEYMgwShsGAptGbz+NLpwmqKmouNxwsplLouRwpTWNAUSiO0eJTJpMhmUwyMDDAwMAA8XiciooK6/yUAeQLBdr7+sh1dKCnUhjpNEYqhZZKYctmOZpKkVWU4ZqihsGgrtNfKhHM5ShPpVAMY3hyl81i5HLkdZ2UruM9pvXJWFEUhVgsxhe+8AV+//vf88wzzxCPx3E4HNTW1nPRRReza1c7jY1nUV1dhqJoVFX1UlNTzbRp01i+fDELFpxNeXn5mF+rmJzM+dwrr7xCKpUiEAjg8/lec4yKRCJks1ny+bzVKD2ZTDI0NERfXx+Dg4MMDg6STCbJ5/NkMhlsNpvV4D6Xy+FyubDZbOi6blU2NaubLly40Po78wy43++noqKCUCjE1KlTJyxdf9nKlXzkjjv45j/+I/beXnpsNhoMA6+q4hs536eEQuD3D6fpjwRk6Dq1Gzdy6PnnmfeWtwyPNSeJ+Zy+/PLLVuB44llSAFVRqI5EsPX3o8NwlkWpRMkwUBWFqNdLTlFI8OoY2VcsEsxmCSeTKOYiXTqNns+T0TRSw9/gpD2W1+vYNlQvvrieqVOnUVNTRlmZimHoOJ2OU2Z+e7KclsGirusUCgU2btxIf3+/1RvK5XJx+eWXs3//fu6//36amppobm4+ZV4wVVWpr6/nc//2b9x6ww1My+epVhRcioLH6cTh9w/nZo+cXyGVAsNALZWI7thB2+9/z7TrrhuTN6GZ8//SSy/R29tLdXU10WiUeDyO2+2muroax5+oOmUYBr3xOD/+6lcpPPwwswoFKoFqm42Iy4VjJMWqUdfpe+ABhpYupaymZkJu9Ne69u7ubh555DHSaQPDsAEqqmrD6bTj9doIBg0CAQVVtV4WtmwpY+PGblatqj4VHoY4Q2maxvr16/ne975HR0cHAF1dXbS1teF2u60+s4YxXLHy6NGj9PT0UF1dPcFXfjxzTGuor8cTidDT308UCGoarnweFIXqUgm/3Y5d19HyeVK5HL3FIh2qSnTGjDG5poqKCvx+P+3t7dTU1BAKhXC73dTU1Ay3IMnn6ezq4vH169m9YQN6qYReKAwXYygWMUol2tNp8jYbPYZB2DAIGgb+YhFHJoNuGISy2eEP40KBbDpNv6aRqK+nahz7iVVXV/POd76Ta6+9lmKxiM1mw+PxcPToUQ4dGmDJkmaqqtwMDSX5yEeuoLn5RqvKpBB/C/Ps144dO3A4HFbxmNf6d4Zh0NbWRn9/P319fdaPgYEBhoaGRhY5annTm97E008/zYEDB6zMCXMn0eFwWMGjeVYxk8kQDoe58MILgVfHI7Mno/leDwaDx/39eDG/3yWXXkr8S1/i+1/5ClUjrSVUVcVmt2Nzu4cDxVBoOG1/5HwfuRz2VArnc8+RuvhifK+xiPi3MNujmT8PDAxQWVlppRAbhoGm67T299N/8CD5ZJLMwADZRIJcKkUxk+Hlnh4yikIchsd9XcddKOBIp9F1nUA6jR3QcznS2Sz9uk6yoWFM0/Rfi7m5sHPnTvbu3UtdXS0rVkwhHC6QyQwSjYbH9XrGy2kXLBqGQTqdZu3atbS3t7N06VLq6+utRqhut5vFixcTDoet0vCnSrAIw9c/a9YsZixdirF27fDgpyjDN7bTOVy84djzKy4X2O3Y8nm6Hn+cqW95y0nvJ2Y+p/fddx+apnHOOecwffp0qxdRqVRi3969TJ02zZoYnNhwVtM0fnb33ex/4AHOMQxCDPfGibjdwzezw4Gi66iZDLEtW+j7138l/8//jKuiYtxSa/8YVVXp6Ohg16596HoDUEJRSqhqCUXRraNSXu+rDai9XojHVV58sZ9Vq6p4NSFNiL/ca63Evt6vO3ToED/60Y/I5XL4/X5aW1uprKzE4/GQz+epqqrC6/VSKpVIJBJWX6hzzz33lBobYfjxlJWVseKCC3j2wQcpAzyGAcUieV1nqFAgoKo4R8actKYxoOt01dezZKTl0MlOsfL5fFx55ZX86Ec/oqysDFVVyefzdHZ24vV6KRaLxONxYk1NnLVsmfW1FRUVeL1eDMNg586dfPazn6U7kxl+TLqOo1hEMwwyxSJhux0PYGgaqWKRfsNAXbYMbyAwbivUZrunQCBwXGXJZ59dS3X1TKZMqSYSsZPPtzF37iyrVcCp9h4Spy8zoykej9Pf309VVdVxhWyy2SxDQ0Ns3LiR9vZ2AEKhEDNmzKC5uZlZs2bR2NiIx+NB13UuuOACPvnJT9LV1WWdYczlclYV1GAwyNy5cwkEAuzfv5+rr77aqmoMr57Fc7lcVsBYUVExIc8NvNrq66prrmHT1q20/+Y3FAyDAlBQFDRVxaaqw6n6qjo8YTnmZ6W1lYHeXnwnub+1qqq4XC4OHTpEZ2cnhw8fxuv1Ultba/UmHEom2bhrF1u3bsVQFHTDwGa344nFCIbDeNJp3I89xtFMhhDDY6RSKlHKZEgXiwRtNlyAXiqRKpXoBSJXXAEwbmOkYRgUi0V+9atfsWfPHhYvXszs2bNpbGzE7R4u/jUwMJwK7R3jtkfj7bQJFs0VoJ07d/L444/T3d3NeeedZ+Wqn3g2Z8qUKQBks9lRfz+RzB49R7u6CAO5kR9ZQNN1bJo2vBJkBosjH9h5w0Dp76dYKOA6iSsp5iT1+eefZ/v27axatYpwOGxNiszelVOammg5cMBKv3C6XLjN6zAMdu7ZwxP33cdZhoHTMHDZbHgcDuw+H0owOBxpaRqkUtj6+/G9+CJt69Yx7ZprJjTMMh9/PB6nWMwCOQwji2Fk0fUUDkc3NpudQiFKPu9kpHozuj78cLq7/ZRKGk7nqXP+UpxeTqye+XrPC5spVGvWrLH6JwaDQQYGBnj55ZdRFIWhoSE6OjrwjexQJZNJDhw4gNPppDBSTOBUGRvh1aqo1113HVu3bOFIRwd2TaOo62QMg4Sm4VMUnIaBDmQVhV63m5nveQ+BUGhMrscwDN761reyY8cOtm7dSi6XI5FIUF5ejtvtRtM06urquPLKK61dB/NrYfj1rK+v56GHHuK5p56iDXAYBoquky8WSWoawUIBFyMprYpCsrqauZdeitvjGdez3ccGf7quE4/HeemlPzB9+nlUV/tRFI3Zs92Toq2TOHWYQVB1dTWbN2+murqaYDCIpmmEQiFrgaavr4/29nb8fj8f+MAHqKmpsSo+H9tT0BxD58+fzz/90z9x1113sWvXLqsSqlmUJhqNUl5eTkVFBZFIhIaGBuust7lYkslkrK9xOBzH3eMTSTXPPgMpw2BI00gXCjhyOZR0ejhAzGahUMAYOQOezuVQR860nyyKouB2u1m+fDmbNm3iwIED+Hw+q91IIBBA0zR6e3upnTqVJeedh8fjwefz4fF4cLvd2Gw28okEQ/k8v//d7zhiGDgYHoPyhkFK1/ErCk6Gx8iMYZCbP58FF11kXcN42bBhAw8//DDnnnsuPp/PyjQxW67EYjFrIXEyOW2CRYB169Zxzz330NvbS3NzM3a7/Y82uTSDssHBQXzjePj19VAUhYJhkAJSwKBh0F8sEs7lCI+cX1EUBSObhVyOgqYxNHLYd3RR9r/9WjRN4/777ycSiVgrRCcG306Xi0AuR/+aNZTSafRcDkolitksRibDs/v3k+nrw24YKICiqtgcDlS3ezitNhAYzt202yGTwTMwQNmGDWTf+EY8Xu+EF7sxDB3DKAEpFGWI2tpOlixxMH8+RKMag4MFNm+uoKPDQ6GgkMsZlEoFNC0zodctTl/mAlg8Hqe7u5tisYjb7SYSiRCLxY5L+zYnLnD8hL6/v5/NmzejaRqqquL3+1m8eDHr169n3bp1TJkyhVgsZu0y9vX1YRgG0WiUAwcOUDXG5dT/GqqqsnTpUm655Ra+9a1vsbe3lzSQMAwihoHXMHAoCpqiMORwUH/NNSx+85tHlWM/WRRFoaqqis9//vP85Cc/sRYr/X4/tbW1XHnllVxxxRV/tHy+GQB//OMfp7W1lcMHDmAoCkVdJwUM6Dp+wKUoGIpCzuej8frrmbN8+YSMi7qu09bWxgsvvIDb7Wb16kuJxerwePK0tg4yc2bYelxCnAzme2nZsmX87ne/Y8+ePdZiVzgcxul0Wos0LS0tnHfeeSwb2cU3KxOfOGcxK1deeOGFzJw5k4ceeohHH32U1tZWcrkcpVKJtrY2mpubqayspKyszOqjarfb6e7uZt26dbS1tRGNRq2A0ayaemLPx/FiPi6Pz8cgMAD0GQbBUomybBZ7IoGvUECx2SCfR0+lyBQK9Oo66WCQipM8HzZ7Ql5yySWsXbuWl156CVVVSaVSdHV14fP5KJVK2Gw2rr76asrLy61x7djPMlcwyHvf+15aWlrYu2sXhqqS0XWSDI+RXsClqhQBtamJlR/9KNHq8W3TUyqVeOaZZ0in09b1n3g8S1EUQqEQiUSCYDA4acbJcQsWT1w9/0tTrXbs2ME3v/lNbDYbpVLJqnplVr46MS2yUCiQTqf/5Dm7iaDr+vBO3fTp7D50iB7DIKJpeAsF6/xKWSaDDTAKBQrpNP3FIt1AtqYGx8iK7smUy+Ws803mgXHzOo9dZQ663cQiERSHA9Lp4Z5guRyKotBns/GAplFQFPKKQp7htAjdTIswU2dHSuArNhulnTvJZ7N4JzCYNx9fXV09gYCfZHKIhoY4V17ZzMKF9cyYMZva2lqcTjvXXFPgO98p8LvfqeRyBaCPioo0dvtpteYiTgGGYdDf38/WrVsBmDlzJhUVFaiqSn9/PwcPHrRWvQGrUMOxlfuSySSHDx9m3759OBwOdF1H0zTrvM7dd99Na2srgUCAmpoaAoGAVekvlUoxMDAwkU/Bn+RyuXj7O95BoKyMu/7zP2lrb6czmSQwUszB4/Hgq67m/Ouu4/p3vYuyMf5QttlsNDU1cfvtt/P//t//o7Ozc3gcnzLldfVYU1WVOXPm8G//9m9861vfYttLL7EzmaRHUQgBPsBht+Oprub897yH697znjEZ6/8cTdNYt24dDzzwAIsWLaKxsZGpU6cSCoUAg4oKlWz25FedFQJgwYIFvPnNb+b+++8nlUrR2dlJMBi0MiHMHf2lS5eOqvb8xzgcDhoaGvjgBz/IzTffTE9PD6lUikKhwD333EN7ezvTpk2jqqqKoaEhurq6AFizZg2zZs3iggsusKqq1tTUUFNTQ2dnJ1NG2lBMxNlFt9vNWXPn8lggQGcqhV/XcRWL2LNZ8ppGeSaDV1WhVCKbyzFYLNKpKBSamymvrDzpR39UVaWuro7bb7+d7373u2zcuJGenh7C4TChUIjGxkbe+c53EovF/ugCmM1mY/HixXz961/nW9/6FttfeYU9AwN06ToRRcEN+AIBIjNm8PaPf5xzV64c18U0XddJJpO0tbWRSqWswkrJZJLwSC/0Y+fLPT09p8wu9Mkw5rNcMzUglUrR19cHQFlZGeHwn1+dPDYN4Gc/+xn5fJ5wOEwymSQejxOPx+nq6iIYDBIOh60Dy/l8nt7eXnp7e0c+5E4d5qrQqlWrWP/UU3QWiwQNA0ephJHNkiuVCGezuGE4daBYZFDX6VRVGi+7bExuDrPJrPmcdnR0UF5ebj2n5k1ysKWF3N69qNksaj6PLZdDzWRw5fPsGRgYTodgOCUiaRgkSiVChQKebHZ4lQuGq/2VShQ1jWQigeuY8v0TRdd1qqurOeuseWzbto1p06LEYlWUlUWsXnWgEA7buOWWIu3tcZ55ZgCvt5/zz49KcRvxFzm21LjH42HhwoVUV1dbZ8CqqqoIhUIcPHiQvXv30t/fj6qqFAoFaxEsnU6TzWatys8ej4disWiVha+pqeE973kP+/fvJxgMMnPmTAqFglXV0+w/dqqloZrMD96rr76aefPmsXHTJg7s308ikcDl8TCloYFzzz2Xc845Z1zP9MFw+f5YLGb92YkLoX+MWf7+a1/7Gk8//TRbNm+mp7sbrVgkWF7OtOZmVl1wAYuXLDmuj+N40XWdI0eO8JOf/IRIJILf7ycUCo2cYRz+3CkvD9LXV7KKfpyK7x1xejKDoLe//e34fD4ef/xxtmzZgsvlwuVyUV5ezsKFC3nLW97yRzPKXs//X19fDwyPw5dffjnf//73icfjVFZWEovF2Lt3LwcPHkRVVcrLy/nc5z5He3s7hmFQW1tLOBwmm83S0dFBXV3dWDwVr+uxrFixgpqmJlp37MCtKKi6jl4okB6pHu1RFFRNG66sDPREo5x10UW4PZ4xuW9VVaWhoYE77riDjRs30traimEYTJ06lfnz51tnof/c/7FgwQK+9a1v8eyzz7LjD38Yfu51nYqqKmbPnMmFF11EbV3dhATpdrsdl8tFIpGgp6eH7u5uOjo6CAaD1tEtTdNIpVLWZ8NkGSPHNFg0C6e89NJL5PN56uvr8Xq99Pb2cujQIZqbmyk74aDta63U/OEPf2Dv3r3DFZ9GDiW3t7fT2tpqrerW1tbi8/msakzd3d0MDg7i8XhOqRfMzM1funQpU+fOpW37djwjpYbzxSIpTaNsZBUFIGcYDAHJBQu4fKRK18lkGAYul4vm5ma2b9/OkSNHCAQCOJ1Oampq8Pv9VjGHJ9avZ9eWLRj5PDZdx2YYOHQdJZejZWiIjKIwoCjDabW6Tk+xiDeToVJVh6sZAmSzlLJZErpOtqIC1W4fTk+dwNdHVVWi0ShveMMbOHToEF6vD7vdjtPpsFJNzMuLRh1ccUWJdeuOsHRpjqVLl0zYdYvT186dO2lvb7fOCJuBosnhcOBwOKwzNoVCAZvNhtPptHolqqpKNptF0zSrcIPZ5qG3t5fy8nKqq6utBTeziXU+n7cmTqfKuPjHKIpCU1MTU6ZMoVgsks/nsdvtx137eD6GP5Zm+peora3lXe96F29605tIJBKUSiUCgQCRUAj7BAdgO3fupKWlxTqbbrfbR3Zwhv/eMCAYDNLT03NcIRAhTgZFUQgGg7z97W9n5cqVdHZ2ks1msdvt1NfX09DQ8Fenf77WeHHBBRfw6KOPcuTIEaZMmUI4HCadTrNv3z7mzp2Lw+GgrKyMOXPmHPd/+f1+awdyIuaXiqLQ2NjI+973Pj7zyU9ywDDQgIJhMFQqWXNI1TAoqiqDqkrsyiuZN1IEbCyvy+12c9555x2X6feX7MAqikI4HObNb34zq1evZmhoCF3XKSsrw+Vyve4d5ZNNURR8Ph9Tp07lySefpLW11aqZYp63dblcZLNZq9/kqf75+pcYs2DRMAyGhoZ49tln8Xg8zJkzh8rKSux2u9WXpa2tjUwmQzAYpFgsWumlxWKRTCZjbfO+8MILxONxa5ewrq6Orq4utmzZQqlUYmhoyEoTAEilUrS1tZHP57nwwgtPqWARhoOT6dOn84+33MLXv/519h4+TEbXGTQMes3zK4wUO3A4yNbXc+3nP4/vdazM/KXM/+8f/uEfuPnmm9mxY4dVRrq1tdWq5pdKpbjubW/jHz/2seOaUgMkk0l+8+tfc8/dd9NVKFBmGPh0HWehgAFkSyUidvtwBcNSiWQuR1zTMBYsGP7/mdhaombhj127dpPP5ykWC9bOi3mOzKQoMGOGjXPOOcIXv3gNLpesrou/jGEYrFmzBofDgdPpHBUowvB96fF48Hg8pNNp8vm8lfqSSCRIJpNWPzHA6hOWTCatc8hmr1kYLv9uNp3OZrMEAgHq6upOubHxtRx7/sjcUTjVr/lPMa/dXI02/2wiz20bhkGpVOLw4cMMDg5aRzwymYx1HvbY5zwej0uwKMaEeQ5s6tSpNDc3W2PU693B/0u+j8/n4/3vfz+f/exnmTFjBtXV1dTW1jJnzhyr8qqmaccdNdF1nVwuRzweZ/bs2Sf1mv7S67/66quJx+Pc8z//w+6+PgZ0nRgQZHgOqasqRb+fGW96E2/97GfHbFfxRMeOZX/N9zPHeHNH2fz9RI/7qqpy3XXX8cQTT3Do0CHsdjulUolkMkk0GrUKnpkFmib6ek+mMQkWzZt67dq1xONxVq5cSUVFxXGTIo/HQzQa5Q9/+IPVN7FQKJBKpawVcjMoOXDggHUguVQqYRgGK1eu5IUXXmDDhg10dHRQU1OD1+u1dhYTiQT19fWv2avnVKCqKpdffjkul4u77rqLgzt20JvLEQH8DL8wNp+P+hUruPKmm5i/cOGYTSYURWHevHl8/OMf56c//Slbt24lHo9bh7qDwSArV65k1ty52F7jfJ5hGLzr3e/m4Ycfpre9Ha8yXK1Q0TQK+TzJUongSLl7XdfJGgYDFRXMOP98XG73hLTOMN+jZpGR//mfu3nggUdxOIaLIg0MDNDX10d/fz8+n28kLUxBUQwiEZUPf3gRNTWVk2owEOOjWCzS0dFBJBJhaGiIfD4/apdP0zT6+vrYtm0bfX199Pb2kkgkKBaLVoVil8tFTU0NZWVlrF+/nlQqBbxa3juTyVhjbqlUstJU8/k8c+bMOe1WPk+FycLJNNFFvU5kTtIzmQy9vb309PTQ2dlJJBIhGo1aC73mZ7UQY+nYIijH/nyyzZ8/nwULFrBnzx6amppwu93U1dURj8cZGBigra2NWCxmBQKJRIIjR45MeD0MMy3yve99L7NmzeLBBx9k3549tPb04DIMwqEQNdOmcdGll3LlVVeNW6B4MpnFc04V5o7uF7/4Rf7t3/6NAwcOWOdcg8EglZWVzJ07lyVLlpx2z/WfM2Y7i8lkkrVr17J48WICgcBrrp67XC4CgQDpdBpVVbHb7djtdiv1ylwJNyc/hULBWmH3+XxcfPHF7N+/n7a2Ng4fPozb7cbj8eD3+0+59NMTmROfiy++mPr6ejZs2MArr7xCd0cHDrudqqoqzl62jBVLl1I3DvnZTqeTv/u7v2PBggU899xz7N+/H7vdztSpUznvvPOYN2/en7xpa2pq+MdbbuFfv/IV2jMZ1JHKrRlNY1DXCSgjZY9VlazTif/yy2lauHDc009PLK+tKAoPPvhbfvSj/8PhiFIodNDV1cXRo0eJRCLW4Xrz/ObwDk6a6uqKU/a9JU5t5jh37JkHh8NhldouFov09/cTj8fZuXMnbrebyspKzj77bGpqaqyiAeFwmGAwSH9/P1/4whd44YUXrF1FcyfRZrNZZ5LNPmPhcJjrrrsOz2k4eRBjw5yUNTQ04HQ66ejooLq6mkAggMPhsHp4lkolent7rZoDQpzOzPHvHe94B1/5ylfYuXOndWRq7ty5uN1uisUinZ2d6LpOqVSyCpAdm2o5kddvVnw9++yzaW1tpbe3d7ggYTBIQ0MD0Wj0lAq4TneKorBkyRK+/vWvs379evbt2wcM99VdvHgx55577qQsejhmj6inp4eBgYHjdgNN5kTdvPnMgg3mj2QySSqVYmhoiFQqZZWVNysCOhwObDYboVCIOXPmMGvWLBKJhNU3LJfLkU6nCQaDE1be+PVSFIXp06czbdo0rr32WorForXCa07mxqt4g8fjYf78+cyaNYv8yBlDt9v9Zw+Tm6/nddddRy6X47//+785GI+TASqBMMO7pSqguVxMufpq3vmxj+ErKxvXwdZMtUokEgwNDeF0Ojl06BDf+Ma3sdnCeL0hEonh4kkHDx6yWohks1nKy8utBYxCoTApV47E+FAUhYULF3LvvfcSjUatAmDmh7p55qGtrY0bb7yRWbNm4XK5rHFP1/XjFj2qq6v5/Oc/z6233sqePXvI5/MUCgUcDod15swMIH0+HxdddBEzZsyY6KdBnIIWLVrEkiVLePbZZ9m9e7d13rWnp4dAIABAJpPhqquukvFPTAqGYTBr1izmz5+P3++nqamJ5uZmqz+3YRhks1l2797Ntm3biMfjNDc3U19ff0psSByb1n7WWWf91WcFxetns9msebtZKO7Yz9vJaEzD30QiQX9/Pz09PUSjUXw+n3XzFYtFEokE27Zts5qlmmlSZiCpKIoVEJrBo7lDaa6Su1wua9XE3HnM5/Nomsbs2bOtCkWnMvO8yolNPMf7us1BxTwbZP7Z6xlszGDzxhtvZObMmfzyl79k7969dA4O0qtpRMrKqG5q4rw3vIHr3vpW7BOQwjE0NMSaNWuIx+PU19dTW1vLd7/73wwNGYRCUez2MqLRxSSTuzh06CCaVrJSssydRZfLxQUXXHBaFAcRpyZFUbjqqqt44okn2LJlC6lUing8TjgctnZxzMrRjY2NVhq0+X57rXGhqamJ73//+9x1112sX7+eeDxOOp22dhY1TWPGjBmcf/75KIrC0aNHqa2tHdfHLU5tqqpSUVHBrbfeSiaTYfv27WQyGeLxOBUVFfh8PsrLy3nb29424Sl4QpwsiqKwZ88eisUi9fX1VFZWWnNV8++9Xi8zZsxg/fr11NfXW0eITqU5wIlztVPp2iYjc97+ahHEyR2Yj0mwqCgK5eXlZLNZq2KQ0+mktrbWyvseHByks7OTVCrF9OnTiUQilJWV4ff7rfQqv99PWVkZNpuNu+++mzvvvJNUKmWVnjdXz81gsVQqWZUBZ82axaJFi075QNF0Kr3R/tprMXdEzzvvPM455xwOHDjA0aNHKZVKRKNRpjU3Ez2mIet4MgyD//3f/6WlpYVFixbR0NBAfX0DCxcuobMzj8fjw+NxccMNb6Ci4q389Kc/5Q9/+AP9/f3EYjEqKiqYO3cuK1assPorCfHXMAsrfOYzn+HOO+/kpZde4vDhw5SXl1upzg0NDbz73e+msvL1n4utqqritttuY+/evezbt49EImFlb/ziF7+gsbHRyrZYu3YtV1111evqESjOHIqiMGfOHO644w6efPJJdu7cSX9/Pw6Hg+bmZi688EJisZi8Z8SkYLZnM4slOhyO18xGM6t8LliwgIULFx4XTIoz16k0bx9rY1bgJhQKcf755/Pss8/idDrJ5/N0d3db7S2GhoZob2+nvr6ea665ZqSX3as377HVjwzD4B3veAd79uzh0UcfRdM0SqUS+Xz+uGDRrFLl9/t53/veR21t7RnzQp5KFEXB7/dbB8ePPR84Ea+HYRjs3LmTRx99lHPPPRePx0MoFKKsLMD73/8eAoFyXnzxZd785otYteocKisrmT9/PocOHaK7uxtFUaipqaG5udlqvirE30JRFJqbm/niF7/Ipk2b2LRpE8lkklgsxtlnn83ixYutXn5/CY/Hw4IFCzj77LOt4l66rjM4OMiWLVuor69n6tSpZLNZtm7dau00CmFSFIUpU6Zw0003kUwmrT6ef6z2gBCnK/N41MGDB60e3eYRnBP/XT6fx+l0ksvlrMr7Qpwpxmxn0TAMbrrpJlpaWti0aRNHjx6lurraKjyTSCQIBoOsXr36uOa+r/VBZAYf//Iv/0JVVRWPPPKI1ajaTAUwz/FUV1ezYsUKcrncWDw08TqdWMVqoicYTz31FKlUCl3X0TTNuqZIJMQtt7yDG2+8FkWB1tZWampqqKqqsnrUmf/2VDifICYPm81GLBbjyiuv5IorrrD+/G/ZeT92Qca8/xRF4d3vfjfbtm2z3t/hcJhEIkE8HicWi502GRhifJjjt9new0y5EmIyMqtP9/b20tXVRSAQsGpGmIFib28v8XicadOmTfTlCjHuxuzMoqIMN9a87bbbuO+++9i2bRs7duzA5XIRiUSYPXs2119//etOaVEUhUAgwEc/+lEuvPBC1q1bx4EDB0in0zgcDnbv3k04HOaCCy4gGo2yY8cOmpqaCIfD8iF3hlMUhb6+PlKplFXcZnBwkKqqqpEDyQo+n5dUKkWhUPij70cJFMXJ9scWIU7me01RFKqqqli9ejWPPfYY06ZNs3YtDx8+TCwWk4UQMcqZlGIlzkzm+3vWrFn84he/oKamhkAgYJ3fdbvdlEolBgYG6OrqYmhoaNL1zxPi9RjTAjeKolBXV8cHP/hBOjs7rQbS4XCYmpqa43YUXy+3283SpUtZtGgRiUSCXC6HzWbj8ccf595777Wqpeq6zp49e1i2bNkYPDJxOjF3nHO5HN3d3Rw9epS2tjZCoRCVlZU4HA7rHK357//UTrcQJ9NYT8oVZbgf19VXX83zzz/P4cOHaWxspKKigt7eXoaGhigrK8MwDFlYE0KcMczFuuXLl/PAAw+wd+9eqyJ1LBbD4/GgaRpDQ0McOXKESy+9VIo7iTOSYhzb02KMHHsO0fz9yZiUmKmnuq7T39/Ppz/9aZxOJ8uWLSMSiVAqlTjvvPOoqKiQSdAZzDAM9u3bxzve8Q5UVWXBggXMmTOH6dOnU1NTg9/vp1AoMDQ0xMyZM4lEIhIkiklH13XWrFnDf/7nf7J69Wrmz5+Py+Wiu7ubFStWYLPZcLvdqKoq738hxBmjVCrxxBNPcOedd2K322lqaiIajeLxeKzK/WeddRZve9vb/qpNDiFOd+MSLI6HUqnEgw8+yM9+9jNWrFjBrFmz0HWdmpoalixZAsgu0ZnMMAx+8IMf8F//9V/4fD5mzJhBU1MTsVjMalmyePFiZs+eLe8TMSmZVaQ/8YlPYBgGV1xxBU1NTQwMDOD3+/F6vRQKBUKhEFVVVXIfCCHOGLqus27dOn71q1/R1dWF3W7H7XZTVVXFqlWruPjii61zjEKcaSZNsGgYBgMDA3zqU5/C7XZz/vnnE4vF6O/v5w1veAOBQEDOYJzBDMMgnU7zm9/8hnvvvZeuri5isRjRaJTZs2dz3nnnsXLlSpxO50RfqhBjxjAMdu3axe23384ll1zCkiVLKC8vp7y8HLvdTi6Xo6enB7/fT01NjYyXQogzhll8sbW1lVwuh8PhoKGhQbKNxBlv0gSLMLwy9Nxzz/HNb36TN77xjcydOxeXy0Uul+P8888/ruy33PhnpmKxSG9vL/v37yefz+P3+5k2bRrRaFRSlcWkp+s6yWSS//iP/6CxsZHly5czbdo0HA6HdX5H0zSOHDlCLBazFtmEEOJMYB5tMkklYCHGuMDNeFNVlfPPP58HH3yQvXv3Ul9fT0NDA7lcjh07dlgTn/r6esk7P0PZ7XarLYZJKkGKM4F5Vnznzp2k02mqqqqIRqNWoAivtkwIBAL09PRYhW/k/hBCnAlObPslhIBJt1yiqir/8A//QFtbG21tbWiaRl1dHbFYjLKyMrxeL7t37yaZTDKJNlXF62SmIptFl8w/E+JMYBgGL730khUgvtakSFEUPB4PAwMDMkYKIYQQZ7hJtbMIw5OhxsZGZs2aRbFYxO1209DQgNvttoIEj8dDe3s706ZNkx3GM5S85uJM1dvbSzabJZ1Ok0wmCYfD1u6hmYaaTqfJ5/MTfalCCCGEmGCTbmdRURRaW1txOBzMnTuXqqoqPB6PVQ5eVVVCoRAej4ehoaGJvlwhhBhXVVVVdHR00NHRQUtLC729vRSLRUqlEoVCgd7eXg4fPkyhUJjoSxVCCCHEBJtUO4tmytTatWtRVRW73Y7L5XrNf2ueyYlGo3ImRwgx6Zk7h6tWreL+++9n3759uFwuSqUSlZWVuFwuK1hsaWlhxYoV1tcJIYQQ4sw0qYJFU29vL6VSiVwuNyqVyqx0VSgUiMfjzJ49e4KuUgghxl9zczOrV6/m0UcftaqjRqNR3G63FSzW1tbS3Nw80ZcqhBBCiAk2KYNFgO7ubrq7u2lra8Pn8+HxeIDh0vFDQ0N0dHTgdrsn+CqFEGL8KIqCy+Xife97H06nk9/+9rd0dnZSVlaGx+PBZrNx/vnns3r1ait1XwghhBBnrkkZLC5fvpxnn32WiooK3G43hmEQi8VwOp1ks1l6enrYv38/q1atAiTNSghx5lAUhbKyMj70oQ9x0UUXsXXrVvr6+qiqqmLZsmU0NTVJar4QQgghgEkWLJpnchYuXMjMmTN5+eWXURSFdDpNJBLB5XJRLBbp7u4mEolQX18/0ZcshBDjzgwE58yZw+zZs1FVFV3Xj+u3KIQQQgihGJOwkZau6+zfv59vfvObHDhwgNraWkKhEG63m2KxyMyZM7nhhhuIRCIyKRJCCCGEEEKI1zApg0UYLmSTTqd5+umnWb9+Pclkkrq6Os4//3yWL18OyOq5EEIIIYQQQvwxkzZYhFdbaZiNpu324axbCRKFEEIIIYQQ4k+b1MGiEEIIIYQQQoi/jjrRFyCEEEIIIYQQ4tQjwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKBIsCiGEEEIIIYQYRYJFIYQQQgghhBCjSLAohBBCCCGEEGIUCRaFEEIIIYQQQowiwaIQQgghhBBCiFEkWBRCCCGEEEIIMYoEi0IIIYQQQgghRpFgUQghhBBCCCHEKP8fZCv4iVVjf80AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1200x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scm.conformers.plams.plot import plot_conformers\n",
    "\n",
    "axes = plot_conformers(opt_job, width=300, height=300, direction=\"along_pca3\")\n",
    "axes;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67cb703e",
   "metadata": {},
   "source": [
    "You can also open the conformers in AMSmovie to browse all conformers 500+ conformers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "32e2979b",
   "metadata": {},
   "outputs": [],
   "source": [
    "!amsmovie \"{opt_job.results.rkfpath()}\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "938d9381-cd20-4569-abd0-f73232023cf2",
   "metadata": {},
   "source": [
    "### Filtering out duplicates\n",
    "The `conformerset` attribute holds information about the full set of conformers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cc2d98d2-309a-4b04-ae9b-a2e4951712c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of conforrmers:  1678\n"
     ]
    }
   ],
   "source": [
    "conformerset = opt_job.results.conformerset\n",
    "print(\"Number of conforrmers: \", len(conformerset))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7765e3ce-30aa-4667-9173-e8f055a617bf",
   "metadata": {},
   "source": [
    "This conformerset does not contain any duplicates. However, there is no single definition of the term duplicates when applied to conformers. By default, duplicates are defined based on energy and rotational constants, the latter quantifying the 3D shape of the system. The filtering method uses thresholds for energy and rotational constants, which have been thoroughly tested for (mostly small) single molecules systems. If the user feels that the stored conformers are too similar, these thresholds can of course be changed. Below we refilter the stored conformerset using more lenient thresholds (systems with greater differences will be considered duplicates)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b37e8b20-287d-4d18-89fd-94eb5e2b2a2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[09.04|12:26:52] JOB conformers STARTED\n",
      "[09.04|12:26:52] Renaming job conformers to conformers.003\n",
      "[09.04|12:26:52] JOB conformers.003 RUNNING\n",
      "[09.04|12:27:05] JOB conformers.003 FINISHED\n",
      "[09.04|12:27:05] JOB conformers.003 SUCCESSFUL\n",
      "Number of conformers:  1555\n"
     ]
    }
   ],
   "source": [
    "s = plams.Settings()\n",
    "s.input.ams.Task = \"Filter\"\n",
    "s.input.ams.InputConformersSet = rkf\n",
    "s.input.ams.Equivalence.CREST.EnergyThreshold = 0.2  # default is 0.05\n",
    "s.input.ams.Equivalence.CREST.ScaledRotationalConstantSettings.RotationalConstantThreshold = (\n",
    "    0.01  # default is 0.003\n",
    ")\n",
    "\n",
    "filter_job = ConformersJob(settings=s)\n",
    "filter_job.run()\n",
    "conformerset = filter_job.results.conformerset\n",
    "print(\"Number of conformers: \", len(conformerset))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "337e4874-7f92-4f2a-b3b4-d2cfc5ce25b6",
   "metadata": {},
   "source": [
    "Alternatively, a filtering method can be applied that uses more local comparisons. The native AMS duplicate filter uses the interatomic distance matrix and torsion angles to determine if two structures are duplicates. This approach may be more appropriate for systems with multiple molecules, because the method only takes into account intra-molecular changes. On the other hand, this type of filtering is more time consuming, while in most cases the effect on the conformer set will not be extreme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0f73df25-1bcb-4929-8976-71cdd881a861",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[09.04|12:27:05] JOB conformers STARTED\n",
      "[09.04|12:27:05] Renaming job conformers to conformers.004\n",
      "[09.04|12:27:05] JOB conformers.004 RUNNING\n",
      "[09.04|12:27:36] JOB conformers.004 FINISHED\n",
      "[09.04|12:27:36] JOB conformers.004 SUCCESSFUL\n",
      "Number of AMS conformers:  1674\n"
     ]
    }
   ],
   "source": [
    "s = plams.Settings()\n",
    "s.input.ams.Task = \"Filter\"\n",
    "s.input.ams.InputConformersSet = rkf\n",
    "s.input.ams.Equivalence.Method = \"AMS\"\n",
    "\n",
    "filter_job = ConformersJob(settings=s)\n",
    "filter_job.run()\n",
    "conformerset = filter_job.results.conformerset\n",
    "print(\"Number of AMS conformers: \", len(conformerset))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cab9fc7-b16d-4c47-9064-bec2ca76b121",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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