notebooks/02_benchmark-parametric-scaling-performance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Internal performance comparison of GAlibrate's core genetic algorithm implementations\n",
    "\n",
    "A few years ago, I tested the performance and scaling of [GAlibrate](https://github.com/blakeaw/GAlibrate)'s different implementations in pure Python, Numba, and Cython: [gao_implementation_scaling_comparison.ipynb](https://github.com/blakeaw/galibrate_performance_comparison/blob/master/gao_implementation_scaling_comparison.ipynb). \n",
    "\n",
    "In this notebook, we will redo this performance and scaling analysis to see how a recent implementation that ports key functions to Julia using the PyJulia package compares to the Python, Numba, and Cython versions. \n",
    "\n",
    "As with the previous analysis, we'll compare how each implementation scales with the number of parameters (or dimensionality), population size, and the number of generations, as well as their relative performance to the pure Python implementation. Note, however, that we are using a different benchmark function this time.\n",
    "\n",
    "To run this notebook we need to have galibrate installed along with Numba, Cython, Julia, and PyJulia.  You also need pandas, matplotlib, and microbench packages.\n",
    "\n",
    "\n",
    "------\n",
    "\n",
    "## Imports and setup\n",
    "\n",
    "First we'll do all our imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Non-galibrate imports\n",
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "# Notebook magic to inline plots\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cython, numba, matplotlib, julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\bwils\\documents\\dev_src\\personal\\galibrate\\galibrate\\gao.py:13: RuntimeWarning: ------Running GAO with numba optimization.------\n",
      "  warnings.warn(\"------Running GAO with numba optimization.------\", RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "# galibrate imports\n",
    "import galibrate\n",
    "from galibrate import gao\n",
    "from galibrate.sampled_parameter import SampledParameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#from allversions import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Manually import each of the run_gao modules -- normally galibrate does this internally\n",
    "# and automatically assigns the version based whether Numba and/or Cython are installed.\n",
    "# Python-only\n",
    "from galibrate import run_gao_py\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Numba accelerated\n",
    "from galibrate import run_gao_numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cython accelerated -- uses pyximport\n",
    "import pyximport; pyximport.install(language_level=3, setup_args={\"include_dirs\":np.get_include()})\n",
    "from galibrate import run_gao_cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "# Julia accelerated\n",
    "from galibrate import run_gao_julia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we'll setup a custom Bench from microbench to capture some key info about the Python version and some of the library versions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Setup a microbench for meta data collection\n",
    "from microbench import MicroBench, MBCondaPackages, MBHostInfo, MBPythonVersion\n",
    "\n",
    "class GaoBench(MicroBench, MBHostInfo, MBPythonVersion):\n",
    "    capture_versions = (np, cython, numba, julia)\n",
    "\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "gaobench = GaoBench()\n",
    "\n",
    "@gaobench\n",
    "def meta():\n",
    "    pass\n",
    "    \n",
    "meta() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "bench_results = pd.read_json(gaobench.outfile.getvalue(), lines=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.10.11'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Python version\n",
    "bench_results['python_version'][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'numpy': '1.23.5', 'cython': '0.29.33', 'numba': '0.56.4', 'julia': '0.6.1'}\n"
     ]
    }
   ],
   "source": [
    "# Here julia is the PyJulia package.\n",
    "for pack in bench_results['package_versions']:\n",
    "    print(pack)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Julia version 1.9.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### OS and hardware\n",
    "\n",
    "  * Windows 11 - 64-bit operating system, x64-based processor\n",
    "  * Processor: 11th Gen Intel(R) Core(TM) i7-11800H @ 2.30GHz   2.30 GHz\n",
    "  * RAM: 16.0 GB (15.6 GB usable)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model problem and fitness function\n",
    "\n",
    "For the purposes of this testing, we'll use the N-dimensional sphere function defined in `galibrate.benchmarks` with a parameter search in \\[-100:100\\].\n",
    "\n",
    "Here is the fitness function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from galibrate.benchmarks import sphere\n",
    "\n",
    "def fitness(chromosome):\n",
    "    return -sphere(chromosome)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling with the number of parameters (dimensionality)\n",
    "\n",
    "We'll start by examining the scaling with the number of parameters while holding the population size and number of generations fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the parameters for the GAO.\n",
    "# Here, we are scaling the number of model parameters or dimensionality.\n",
    "# We'll consider up to 1000 parameters.\n",
    "ndims = list([3, 10, 20, 50, 100, 200, 500, 800, 1000])\n",
    "# We'll fix the population size at 100:\n",
    "popsize = 100\n",
    "# And the number of generations also to 100:\n",
    "generations = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaling_dimensions(ndims, version=None, popsize=1000, generations=100):\n",
    "    if version is not None:\n",
    "        gao.run_gao = version\n",
    "    timings = dict()\n",
    "    timings['n_dim'] = list()\n",
    "    timings['avg_time'] = list()\n",
    "    timings['std_dev'] = list()\n",
    "    # Loop over the dimensionality (number of parameters)\n",
    "    for ndim in ndims:\n",
    "        print(\"Doing ndim: \", ndim)\n",
    "        timings['n_dim'].append(ndim)\n",
    "        sampled_parameters = [SampledParameter(name=i, loc=-100.0, width=200.0) for i in range(ndim)]\n",
    "        go = gao.GAO(sampled_parameters, fitness, popsize, generations=generations)\n",
    "        #print(ndim, popsize, gen)\n",
    "        ti = %timeit -n 10 -r 2 -o -q go.run()\n",
    "        timings['avg_time'].append(ti.average)\n",
    "        timings['std_dev'].append(ti.stdev)\n",
    "        print(ti)\n",
    "    timings = pd.DataFrame(timings)\n",
    "    return timings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing ndim:  3\n",
      "121 ms ± 5.36 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  10\n",
      "141 ms ± 1.14 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  20\n",
      "176 ms ± 3.34 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  50\n",
      "260 ms ± 1.55 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  100\n",
      "439 ms ± 21.2 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  200\n",
      "712 ms ± 3.74 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  500\n",
      "1.63 s ± 22.6 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  800\n",
      "2.5 s ± 20.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  1000\n",
      "3.07 s ± 30.8 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
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       "   n_dim  avg_time   std_dev\n",
       "0      3  0.121270  0.005363\n",
       "1     10  0.140619  0.001135\n",
       "2     20  0.175539  0.003338\n",
       "3     50  0.259961  0.001554\n",
       "4    100  0.438922  0.021184\n",
       "5    200  0.712473  0.003740\n",
       "6    500  1.631512  0.022559\n",
       "7    800  2.503926  0.020377\n",
       "8   1000  3.067354  0.030776"
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     "execution_count": 17,
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   "source": [
    "timings_py = scaling_dimensions(ndims, version=run_gao_py, popsize=popsize, generations=generations)\n",
    "timings_py"
   ]
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  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing ndim:  3\n",
      "49 ms ± 10.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  10\n",
      "43.3 ms ± 1.11 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  20\n",
      "40.7 ms ± 851 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  50\n",
      "46.9 ms ± 203 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  100\n",
      "48.5 ms ± 154 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  200\n",
      "53.6 ms ± 4.5 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  500\n",
      "66.3 ms ± 747 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  800\n",
      "94.2 ms ± 937 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  1000\n",
      "108 ms ± 3.53 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
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       "      <th>2</th>\n",
       "      <td>20</td>\n",
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       "      <td>0.000851</td>\n",
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       "      <td>0.046875</td>\n",
       "      <td>0.000203</td>\n",
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       "      <td>0.004498</td>\n",
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       "      <th>6</th>\n",
       "      <td>500</td>\n",
       "      <td>0.066299</td>\n",
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       "   n_dim  avg_time   std_dev\n",
       "0      3  0.048961  0.010367\n",
       "1     10  0.043309  0.001114\n",
       "2     20  0.040693  0.000851\n",
       "3     50  0.046875  0.000203\n",
       "4    100  0.048539  0.000154\n",
       "5    200  0.053567  0.004498\n",
       "6    500  0.066299  0.000747\n",
       "7    800  0.094159  0.000937\n",
       "8   1000  0.107998  0.003527"
      ]
     },
     "execution_count": 18,
     "metadata": {},
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    }
   ],
   "source": [
    "timings_numba = scaling_dimensions(ndims, version=run_gao_numba, popsize=popsize, generations=generations)\n",
    "timings_numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Doing ndim:  3\n",
      "44.7 ms ± 4.47 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  10\n",
      "43.4 ms ± 2.98 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  20\n",
      "42.3 ms ± 1.29 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  50\n",
      "46.6 ms ± 2.09 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  100\n",
      "54.8 ms ± 5.7 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  200\n",
      "64.9 ms ± 2.85 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  500\n",
      "105 ms ± 1.13 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  800\n",
      "129 ms ± 633 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  1000\n",
      "167 ms ± 3.72 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>50</td>\n",
       "      <td>0.046605</td>\n",
       "      <td>0.002093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100</td>\n",
       "      <td>0.054816</td>\n",
       "      <td>0.005696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>200</td>\n",
       "      <td>0.064892</td>\n",
       "      <td>0.002853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>500</td>\n",
       "      <td>0.104800</td>\n",
       "      <td>0.001128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>800</td>\n",
       "      <td>0.128886</td>\n",
       "      <td>0.000633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1000</td>\n",
       "      <td>0.166939</td>\n",
       "      <td>0.003724</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   n_dim  avg_time   std_dev\n",
       "0      3  0.044739  0.004473\n",
       "1     10  0.043425  0.002979\n",
       "2     20  0.042292  0.001292\n",
       "3     50  0.046605  0.002093\n",
       "4    100  0.054816  0.005696\n",
       "5    200  0.064892  0.002853\n",
       "6    500  0.104800  0.001128\n",
       "7    800  0.128886  0.000633\n",
       "8   1000  0.166939  0.003724"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_cython = scaling_dimensions(ndims, version=run_gao_cython, popsize=popsize, generations=generations)\n",
    "timings_cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing ndim:  3\n",
      "352 ms ± 52.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  10\n",
      "327 ms ± 5.54 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  20\n",
      "315 ms ± 6.77 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  50\n",
      "305 ms ± 3.35 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  100\n",
      "338 ms ± 936 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  200\n",
      "422 ms ± 37 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  500\n",
      "462 ms ± 24.6 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  800\n",
      "558 ms ± 1.68 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ndim:  1000\n",
      "599 ms ± 5.96 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n_dim</th>\n",
       "      <th>avg_time</th>\n",
       "      <th>std_dev</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>0.351717</td>\n",
       "      <td>0.052392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10</td>\n",
       "      <td>0.326859</td>\n",
       "      <td>0.005543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20</td>\n",
       "      <td>0.314569</td>\n",
       "      <td>0.006773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>50</td>\n",
       "      <td>0.305353</td>\n",
       "      <td>0.003351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100</td>\n",
       "      <td>0.338454</td>\n",
       "      <td>0.000936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>200</td>\n",
       "      <td>0.422175</td>\n",
       "      <td>0.037019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>500</td>\n",
       "      <td>0.461523</td>\n",
       "      <td>0.024631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>800</td>\n",
       "      <td>0.557848</td>\n",
       "      <td>0.001678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1000</td>\n",
       "      <td>0.599488</td>\n",
       "      <td>0.005965</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   n_dim  avg_time   std_dev\n",
       "0      3  0.351717  0.052392\n",
       "1     10  0.326859  0.005543\n",
       "2     20  0.314569  0.006773\n",
       "3     50  0.305353  0.003351\n",
       "4    100  0.338454  0.000936\n",
       "5    200  0.422175  0.037019\n",
       "6    500  0.461523  0.024631\n",
       "7    800  0.557848  0.001678\n",
       "8   1000  0.599488  0.005965"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_julia = scaling_dimensions(ndims,\n",
    "                                   version=run_gao_julia,\n",
    "                                   popsize=popsize,\n",
    "                                   generations=generations)\n",
    "timings_julia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Timings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZLWVJMrnudm8AQPnb4kq2h863emIDAB07dsSjjz6KJUuWGMr69++PGzdu4L333sOFCxfw6aef4s8//7TYNT/99FOsW7cOZ86cweTJk3Hr1i1MmDABANCqVSscOnQIf/31F/7991+88cYbOHjwoMWuTURE9UPfJRXX0g8KuX2mEfYZVUMWNQIY/S3gFWxc7hWiK7fiPDflvf3220bdUO3bt8dnn32GTz/9FJ07d8aBAwcwbdo0i11v/vz5WLBgATp37oydO3fi119/RdOmuv7YiRMn4oEHHsCYMWNwxx134ObNm0atOERE1DAklCy50Le1fY63AQBBKj8Iw8FlZ2fD29sbWVlZ8PLyMtpXWFiI5ORkREZGwsXFpW4XErW6MTi51wGPQN0Ym3posXEkFv19EBFRneUWaRAzZzM0ooSEV/qjuZ95d/TWRXXf3+VxzI21yORAZB9bR0FERGQxey/chEaU0NzPrV4TG3OxW4qIiIhMssPQJWWfd0npMbkhIiIik5TOb8PkhoiIiBq4yzfzcPlmPpxkAuJa+tk6nGoxuSEiIqIa6bukujVvAg9n+x6yy+SGiIiIapRQsp6UvXdJAUxuiIiIqAbFGhF7L+iSm35MboiIiKihO3LlFvKKtfBzVyIquPo5ZuwBkxsiIiKq1s6Su6R6t24Kmaz88kL2h8kN1Wj79u0QBAG3b9+2dShERGQDO/6171XAy2NyYyVaUYuDaQex8eJGHEw7CK2orZfrpqWl4YUXXkCLFi3g7OyMsLAwDB8+HH///bdJx/fv3x8vvfSSdYMkIqIG42ZuEU6mZgEA+rSx3/WkyrLve7kaqK2Xt2L+gfm4nn/dUBboFogZPWZgUPNBVrvupUuX0KtXL/j4+OC9995Dp06doFar8ddff2Hy5Mk4c+aM1a5NRESOadf5DEgS0D7YCwGeDWOdP7bcWNjWy1sRvz3eKLEBgPT8dMRvj8fWy1utdu1JkyZBEAQcOHAADz30ENq0aYPo6GjEx8dj3759mDBhAu677z6jYzQaDYKCgrB8+XKMHz8eCQkJ+OijjyAIAgRBwKVLlwx1Dx8+jNjYWLi5uaFnz544e/as0bmWLl2Kli1bQqlUom3btvjuu++M9guCgK+++gr3338/3Nzc0Lp1a2zYsMFqPw8iIqo7wyrgDaTVBmByUyNJkpCvzjfpkVOUg3kH5kFCxYXWpZL/zT8wHzlFOSadz5wF2zMzM7Fp0yZMnjwZ7u4VFzPz8fHB008/jU2bNkGlUhnKN27ciNzcXIwePRofffQR4uLi8Mwzz0ClUkGlUiEsLMxQ97XXXsMHH3yAQ4cOwcnJCRMmTDDsW7duHV588UW8/PLLOHnyJP773//iySefxLZt24zimDNnDkaPHo3jx49j2LBhePTRR5GZmWny+yQiovojSRJ2niu5BbyBjLcB2C1VowJNAe74/g6Lne96/nX0/LGnSXX3j90PN4WbSXXPnz8PSZLQrl27Kuv07NnT0KIyffp0AMCKFSvw8MMPw8PDAwCgVCrh5uaGoKCgCse/++676NevHwBgxowZuPfee1FYWAgXFxcsXLgQ48ePx6RJkwDA0Fq0cOFCDBgwwHCO8ePH45FHHgEAzJ07F0uWLMGBAwcwdOhQk94nERHVnyRVDm7kFMFVIUe3iCa2DsdkbLlxEPpWHkGo/ha9p59+GitWrAAApKen448//jBqgalOp06dDK+Dg4MN5wCApKQk9OrVy6h+r169kJSUVOU53N3d4enpaTgHERHZF/1CmXEt/eDsJLdxNKZjy00NXJ1csX/sfpPqHr5+GJP+nlRjvc8GfoZugd1MurapWrduDUEQkJSUhFGjRlVZb9y4cZgxYwb27t2LvXv3IiIiAn369DHpGgqFwvBan0SJolihTE+SpAplZc+hP6bsOYiIyH7o15Pq27rhjLcB2HJTI0EQ4KZwM+nRM6QnAt0CIaDy1hMBAoLcgtAzpKdJ56upFaYsX19fDBkyBJ9++iny8vIq7NfPUePn54dRo0ZhxYoVWLFiBZ588kmjekqlElqt+bett2/fHrt27TIq27NnD9q3b2/2uYiIyPbyizU4dOkWgIaxnlRZTG4sSC6TY0aPGQBQIcHRb7/a41XIZdZp2vvss8+g1WrRo0cPrFmzBufOnUNSUhI+/vhjxMXFGeo9/fTT+Oabb5CUlIQnnnjC6BwRERHYv38/Ll26hIyMDJNbVV555RWsXLkSy5Ytw7lz57Bo0SKsXbsW06ZNs+h7JCKi+rH/YiaKtSJCm7gismnFG1XsGZMbCxvUfBAW9V+EALcAo/JAt0As6r/IqvPcREZG4siRIxgwYABefvlldOjQAXfffTf+/vtvLF26tDTGQYMQHByMIUOGICQkxOgc06ZNg1wuR1RUFPz9/XHlyhWTrj1q1Ch89NFHeP/99xEdHY3PP/8cK1asQP/+/S35FomIqJ7obwHv09rfrJ4EeyBI5txv7ACys7Ph7e2NrKwseHkZL/5VWFiI5ORkREZGwsWlbhMVaUUtjqQfwY38G/B380fXgK5Wa7ExV35+PkJCQrB8+XI88MADtg6nSpb8fRARkXnu+mA7Lt7Iw7LHumJoh2Bbh1Pt93d5HFBsJXKZHN2Duts6DCOiKCItLQ0ffPABvL29MWLECFuHREREdujqrXxcvJEHuUxAz1YNazAxwOSmUbly5QoiIyMRGhqKlStXwsmJv34iIqpIv1BmlzAfeLkoaqhtf/jt1ohERESYNesxERE1ToZbwBvYXVJ6HFBMREREBhqtiN0XdC03TG6IiIiowUtMuY2cQg183BTo2Mzb1uHUCpMbIiIiMthRslBm71ZNIZc1rFvA9ZjcEBERkUFDH28DMLkhIiKiErfzi3H86m0AQN/WTG6IiIioAdOKEpbvToYoAaFNXODv6WzrkGrNpsnNvHnz0L17d3h6eiIgIACjRo3C2bNnqz1m+/btEAShwuPMmTP1FLVjEAQB69evBwBcunQJgiAgMTHRpjEREZFtbDqpQu8F/+Djv88DAK7eKkTvBf9g00mVjSOrHZsmNwkJCZg8eTL27duHLVu2QKPRYPDgwZWual3e2bNnoVKpDI/WrVvXQ8Smk7Ra5O0/gKzf/0De/gOQarHStjnGjx+PUaNG1erYsLAwqFQqdOjQwbJBERGR3dt0UoXnVh2BKqvQqDwtqxDPrTrSIBMcm07it2nTJqPtFStWICAgAIcPH0bfvn2rPTYgIAA+Pj5WjK72sjdvxvW586BJSzOUOQUFIXDWTHgNHmzDyConl8sRFBRk6zCIiKieaUUJc347jcqmd5UACADm/HYad0cFNag7p+xqzE1WVhYAwNfXt8a6Xbp0QXBwMAYOHIht27ZVWa+oqAjZ2dlGD2vK3rwZ1158ySixAQDN9eu49uJLyN682arXB3QzES9evNioLCYmBm+++Wal9ct3S2m1Wjz11FOIjIyEq6sr2rZti48++si6QRMRUb07kJxZocWmLAmAKqsQB5Iz6y8oC7Cb5RckSUJ8fDx69+5dbfdIcHAwvvjiC3Tr1g1FRUX47rvvMHDgQGzfvr3S1p558+Zhzpw5dYpLKigwra5Wi+vvvAtUtsSBJAECcP3duXCPi4Mgr3mFcMHV1SbLzIuiiNDQUKxevRpNmzbFnj178OyzzyI4OBijR4+u93iIiMg60nOqTmxqU89e2E1y8/zzz+P48ePYtWtXtfXatm2Ltm3bGrbj4uKQkpKChQsXVprczJw5E/Hx8Ybt7OxshIWFmRyXVFCAs127mVy/+pPpWnD+7d7DpOptjxyG4OZmmWubQaFQGCWEkZGR2LNnD1avXs3khojIgQR4uli0nr2wi+TmhRdewIYNG7Bjxw6Ehoaaffydd96JVatWVbrP2dkZzs4N93Y2W1m2bBm++uorXL58GQUFBSguLkZMTIytwyIiIgvqEemLYG+XKrumBABB3i7oEVnzcBF7YtPkRpIkvPDCC1i3bh22b9+OyMjIWp3n6NGjCA4OtnB0OoKrK9oeOWxS3fxDh5Dy7H9rrBf2xedwi4016dq1IZPJKqz+rVarTT5+9erVmDp1Kj744APExcXB09MT77//Pvbv31+reIiIyD7JZQJmDWuHF35IrLBPPyhi9vCoBjWYGLBxcjN58mR8//33+PXXX+Hp6Ym0kkG43t7ecC35Yp85cyauXbuGb7/9FgCwePFiREREIDo6GsXFxVi1ahXWrFmDNWvWWCVGQRBM7hpy79ULTkFB0Fy/Xvm4G0GAU2Ag3Hv1MmnMTW35+/tDpSq9dS87OxvJyckmH79z50707NkTkyZNMpRduHDBojESEZF9UMh19xbJBEAs89UV5O2C2cOjMLSDdRoPrMmmyc3SpUsBAP379zcqX7FiBcaPHw8AUKlUuHLlimFfcXExpk2bhmvXrsHV1RXR0dH4448/MGzYsPoKu0qCXI7AWTNx7cWXAEEwTnBKBgYHzppp1cQGAO666y6sXLkSw4cPR5MmTfDGG29AbsY1W7VqhW+//RZ//fUXIiMj8d133+HgwYO1blkjIiL79fOhqwCAZ/q2QP82AUjPKUSAp64rqqG12OjZvFuqJitXrjTanj59OqZPn26liOrOa/Bg4KPFFee5CQy06jw3oijCyUn365w5cyYuXryI++67D97e3nj77bfNarmZOHEiEhMTMWbMGAiCgEceeQSTJk3Cn3/+aZXYiYjINtJzCrG9ZKHM0bFhaOnvYeOILEOQTMkwHEh2dja8vb2RlZUFLy8vo32FhYVITk5GZGQkXFzqNjJc0mqRf+gwNDduwMnfH26x3azaYjN06FC0atUKn3zyidWuUd8s+fsgIqKKvthxAXM3nkHXcB+sndTL1uFUq7rv7/Ls4m4pRyTI5XC/w7Rbvuvi1q1b2LNnD7Zv346JEyda/XpEROQYJEnCL4d1XVIPdTN9ipSGgMlNAzdhwgQcPHgQL7/8MkaOHGnrcIiIqIE4fjUL/17PhbOTDPd1bniDhqvD5KaBW7duna1DICKiBkjfajO0QxC8XBQ2jsay7GptKSIiIrK+QrUWG46lAgAe6mb+5Ln2jskNERFRI7M16TqyCtQI8XZBz5ZNbR2OxTG5qYQoirYOgWDaVAFERGQ+fZfUA11DG+xcNtXhmJsylEolZDIZUlNT4e/vD6VSaZNVuUmX2Ny4cQOCIEChcKy+YCIiW0rLKsSOkrltHLFLCmByY0QmkyEyMhIqlQqpqam2DqfREwQBoaGhZs2uTERE1Vt39BpECege0QQRTd1tHY5VMLkpR6lUIjw8HBqNBlqt1tbhNGoKhYKJDRGRBUmShJ8PpwBw3FYbgMlNpfRdIewOISIiR3I05TYu3siDq0KOezuF2Docq+GAYiIiokZCv0jmPR2C4OHsuO0bTG6IiIgagUK1Fr/r57aJddwuKYDJDRERUaPw16k05BRpENrEFXdG+tk6HKtickNERNQI6Oe2ebBrKGQOOLdNWUxuiIiIHFzq7QLsOp8BQJfcODomN0RERA5u7ZGrkCTgjkhfhPu52Tocq2NyQ0RE5MAkSTJ0ST0cG2bjaOqH2feBFRUV4cCBA7h06RLy8/Ph7++PLl26IDIy0hrxERERUR0cunwLl27mw00pxz0dgmwdTr0wObnZs2cPlixZgvXr16O4uBg+Pj5wdXVFZmYmioqK0KJFCzz77LOYOHEiPD09rRkzERERmeiXkrlt7u0YDHcHntumLJO6pUaOHImHHnoIzZo1w19//YWcnBzcvHkTV69eRX5+Ps6dO4fXX38df//9N9q0aYMtW7ZYO24iIiKqQX6xBn+cUAFw7OUWyjMphRs8eDB+/vlnKJXKSve3aNECLVq0wBNPPIFTp05x0UkiIiI7sOlkGnKLNAj3dUOPSF9bh1NvTEpuJk+ebPIJo6OjER0dXeuAiIiIyDL0A4kf6hYKQXDsuW3KMvtuqZSUFFy9etWwfeDAAbz00kv44osvLBoYERER1V5KZj72XLgJQQAe6NrM1uHUK7OTm7Fjx2Lbtm0AgLS0NNx99904cOAAZs2ahbfeesviARIREZH51h65BgDo2dIPoU0cf26bssxObk6ePIkePXoAAFavXo0OHTpgz549+P7777Fy5UpLx0dERERmEkUJvxxJAdC4BhLrmZ3cqNVqODs7AwC2bt2KESNGAADatWsHlUpl2eiIiIjIbAcuZSIlswAezk4YGh1s63DqndnJTXR0NJYtW4adO3diy5YtGDp0KAAgNTUVfn6OvcooERFRQ/Bzydw293UKhqtSbuNo6p/Zyc2CBQvw+eefo3///njkkUfQuXNnAMCGDRsM3VVERERkG3lFGvx5UteT8nBs4+uSAmqx/EL//v2RkZGB7OxsNGnSxFD+7LPPws2tcQ1YIiIisjcbT6iQX6xFZFN3dA1vUvMBDqhW8zDL5XKjxAYAIiIiLBEPERER1cHPjXRum7JMSm66dOli8g/oyJEjdQqIiIiIaufyzTwcSM5slHPblGVScjNq1CjD68LCQnz22WeIiopCXFwcAGDfvn04deoUJk2aZJUgiYiIqGZrSlpterdqimBvVxtHYzsmJTezZ882vH766acxZcoUvP322xXqpKSkWDY6IiIiMokoSlhTMnHfw7FhNo7Gtsy+W+rnn3/GuHHjKpQ/9thjWLNmjUWCIiIiIvPsvXgT124XwNPFCYOjAm0djk2Zndy4urpi165dFcp37doFFxcXiwRFRERE5tEvkjmicwhcFI1vbpuyzL5b6qWXXsJzzz2Hw4cP48477wSgG3OzfPly/N///Z/FAyQiIqLq5RSqDXPbNMblFsozO7mZMWMGWrRogY8++gjff/89AKB9+/ZYuXIlRo8ebfEAiYiIqHp/HFehUC2ipb87YsJ8bB2OzdVqnpvRo0czkSEiIrIT+i6ph2PDGu3cNmXVKrkBgOLiYqSnp0MURaPy8PDwOgdFREREprl4IxeHLt+CTADu79J457Ypy+zk5ty5c5gwYQL27NljVC5JEgRBgFartVhwREREVL01R3StNv3a+CPQizf2ALVIbsaPHw8nJyf8/vvvCA4OZvMXERGRjWhFCWsO6+a2eahb457bpiyzk5vExEQcPnwY7dq1s0Y8REREZKLd5zOQll0Ib1cFBkUF2Docu2H2PDdRUVHIyMiwRixERERkBv0imSNjQuDs1LjntinL7ORmwYIFmD59OrZv346bN28iOzvb6EFERETWl1Wgxl+n0gBwbpvyzE5uBg0ahH379mHgwIEICAhAkyZN0KRJE/j4+KBJkyZmnWvevHno3r07PD09ERAQgFGjRuHs2bM1HpeQkIBu3brBxcUFLVq0wLJly8x9G0RERA3a78dTUawR0TbQEx2beds6HLti9pibbdu2WeziCQkJmDx5Mrp37w6NRoPXXnsNgwcPxunTp+Hu7l7pMcnJyRg2bBieeeYZrFq1Crt378akSZPg7++PBx980GKxERER2bOfD+m6pB7qFsqbe8oRJEmSbB2E3o0bNxAQEICEhAT07du30jqvvvoqNmzYgKSkJEPZxIkTcezYMezdu7fGa2RnZ8Pb2xtZWVnw8vKyWOxERET15Xx6DgYt2gG5TMC+mQPh7+ls65Cszpzv71pN4nf79m18/fXXSEpKgiAIiIqKwoQJE+DtXbdmsaysLACAr69vlXX27t2LwYMHG5UNGTIEX3/9NdRqNRQKhdG+oqIiFBUVGbY5LoiIiBo6/UDiAW39G0ViYy6zx9wcOnQILVu2xIcffojMzExkZGRg0aJFaNmyJY4cOVLrQCRJQnx8PHr37o0OHTpUWS8tLQ2BgcZLuQcGBkKj0VR6F9e8efPg7e1teISFcR4AIiJquDRaEeuOcG6b6pid3EydOhUjRozApUuXsHbtWqxbtw7Jycm477778NJLL9U6kOeffx7Hjx/HDz/8UGPd8n2L+p61yvocZ86ciaysLMMjJSWl1jESERHZ2s5zGUjPKUITNwXuase5bSpjdrfUoUOH8OWXX8LJqfRQJycnTJ8+HbGxsbUK4oUXXsCGDRuwY8cOhIZWfztbUFAQ0tLSjMrS09Ph5OQEPz+/CvWdnZ3h7MwmOyIicgy/GOa2aQalk9ltFI2C2T8VLy8vXLlypUJ5SkoKPD09zTqXJEl4/vnnsXbtWvzzzz+IjIys8Zi4uDhs2bLFqGzz5s2IjY2tMN6GiIjIkdzOL8aW09cBAA/Hcm6bqpid3IwZMwZPPfUUfvrpJ6SkpODq1av48ccf8fTTT+ORRx4x61yTJ0/GqlWr8P3338PT0xNpaWlIS0tDQUGBoc7MmTMxbtw4w/bEiRNx+fJlxMfHIykpCcuXL8fXX3+NadOmmftWiIiIGpQNx1JRrBXRPtgL0SGc26YqZndLLVy4EIIgYNy4cdBoNAAAhUKB5557DvPnzzfrXEuXLgUA9O/f36h8xYoVGD9+PABApVIZtRRFRkZi48aNmDp1Kj799FOEhITg448/5hw3RETk8PRdUg9zRuJq1Xqem/z8fFy4cAGSJKFVq1Zwc3OzdGxWwXluiIioITqbloMhi3fASSZg/6yB8PNoXONJrTrPTVZWFrRaLXx9fdGxY0dDeWZmJpycnJgwEBERWcEvh3V3+w5sH9DoEhtzmT3m5j//+Q9+/PHHCuWrV6/Gf/7zH4sERURERKXUWhHrjnJuG1OZndzs378fAwYMqFDev39/7N+/3yJBERERUamEszeQkVuMph5K9G/rb+tw7J7ZyU1RUZFhIHFZarXa6C4nIiIisoyfS7qkRsU0g0LOuW1qYvZPqHv37vjiiy8qlC9btgzdunWzSFBERESkczO3CH8npQMAHuLcNiYxe0Dxu+++i0GDBuHYsWMYOHAgAODvv//GwYMHsXnzZosHSERE1JhtOJYKjSihYzNvtAviTTumMLvlplevXti7dy9CQ0OxevVq/Pbbb2jVqhWOHz+OPn36WCNGIiKiRuvnQ7q5bR7i3DYmM7vlBgBiYmLw/fffWzoWIiIiKuNUahZOq7KhlMswonOIrcNpMGo1KunChQt4/fXXMXbsWKSn6/oBN23ahFOnTlk0OCIiosZMPyPxoKgANHFX2jiahsPs5CYhIQEdO3bE/v37sWbNGuTm5gIAjh8/jtmzZ1s8QCIiosaoWCPi18RUAOySMpfZyc2MGTPwzjvvYMuWLVAqS7PIAQMGYO/evRYNjoiIqLH650w6MvOK4e/pjL6tObeNOcxObk6cOIH777+/Qrm/vz9u3rxpkaCIiIgaO32X1ANdmsGJc9uYxeyflo+PD1QqVYXyo0ePolmzZhYJioiIqDG7kVOEbWdL5rZhl5TZzE5uxo4di1dffRVpaWkQBAGiKGL37t2YNm0axo0bZ40YiYiIGpVfE69BK0roHOaD1oGetg6nwTE7uXn33XcRHh6OZs2aITc3F1FRUejbty969uyJ119/3RoxEhERNRqSJBnmtnmYrTa1YvY8NwqFAv/73//w9ttv48iRIxBFEV26dEHr1q2tER8REVGjcvJaNs5ez4HSSYbhnTi3TW3UahI/AGjRogVatGgBrVaLEydO4NatW2jSpIklYyMiImp0filZJHNwVCC83RQ2jqZhMrtb6qWXXsLXX38NANBqtejXrx+6du2KsLAwbN++3dLxERERNRpFGi1+Paab2+bh2DAbR9NwmZ3c/PLLL+jcuTMA4LfffsPFixdx5swZvPTSS3jttdcsHiAREVFj8XdSOm7nqxHk5YLerZraOpwGy+zkJiMjA0FBQQCAjRs3YvTo0WjTpg2eeuopnDhxwuIBEhERNRY/H9J1ST3QtRnkMsHG0TRcZic3gYGBOH36NLRaLTZt2oRBgwYBAPLz8yGXyy0eIBERUWOQnl2IhH9vAODcNnVl9oDiJ598EqNHj0ZwcDAEQcDdd98NANi/fz/atWtn8QCJiIgag3VHr0GUgG7Nm6CFv4etw2nQzE5u3nzzTXTo0AEpKSl4+OGH4ezsDACQy+WYMWOGxQMkIiJydJIk4eeS5RbYalN3tboV/KGHHqpQ9sQTT9Q5GCIiosbo2NUsnE/PhYtChns7Bds6nAbPpDE3P/74o8knTElJwe7du2sdEBERUWOjH0g8NDoIXi6c26auTEpuli5dinbt2mHBggVISkqqsD8rKwsbN27E2LFj0a1bN2RmZlo8UCIiIkdUqNZiQ8ncNg9149w2lmBSt1RCQgJ+//13LFmyBLNmzYK7uzsCAwPh4uKCW7duIS0tDf7+/njyySdx8uRJBAQEWDtuIiIih7D59HXkFGoQ4u2Cni39bB2OQzB5zM19992H++67Dzdv3sSuXbtw6dIlFBQUoGnTpujSpQu6dOkCmczsO8uJiIgatV9KBhI/2C0UMs5tYxFmDyj28/PDyJEjrRELERFRo6LKKsDOc5zbxtJqvXAmERER1Y5WlHAgORP/238ZkgR0b94Ezf3cbR2Ww2ByQ0REVI82nVRhzm+nocoqNJT9m56LTSdVGNqBt4FbAgfJEBER1ZNNJ1V4btURo8QGALIL1Hhu1RFsOqmyUWSOhckNERFRPdCKEub8dhpSJfv0ZXN+Ow2tWFkNMketk5vi4mKcPXsWGo3GkvEQERE5pAPJmRVabMqSAKiyCnEgmXPF1ZXZyU1+fj6eeuopuLm5ITo6GleuXAEATJkyBfPnz7d4gERERI4gPafqxKY29ahqZic3M2fOxLFjx7B9+3a4uLgYygcNGoSffvrJosERERE5igBPl5ormVGPqmb23VLr16/HTz/9hDvvvBOCUDrZUFRUFC5cuGDR4IiIiBxFj0hfNPVQIiO3uNL9AoAgbxf0iPSt38AckNktNzdu3Kh0eYW8vDyjZIeIiIhKqbUiFPLKv3b1356zh0dBzlmK68zs5KZ79+74448/DNv6hObLL79EXFyc5SIjIiJyIAv/OgtVViE8XZwQ4OlstC/I2wVLH+vKeW4sxOxuqXnz5mHo0KE4ffo0NBoNPvroI5w6dQp79+5FQkKCNWIkIiJq0Pacz8BXu5IBAIvHxKB/2wAcSM5Eek4hAjx1XVFssbEcs1tuevbsid27dyM/Px8tW7bE5s2bERgYiL1796Jbt27WiJGIiKjByipQ4+WfjwEAHukRjoHtAyGXCYhr6YeRMc0Q19KPiY2F1Wr5hY4dO+Kbb76xdCxEREQOZ/avJ6HKKkSEnxtev7e9rcNpFGq9tlR6ejrS09MhiqJReadOneocFBERkSP47Vgq1iemQiYAi8bEwN2ZSzrWB7N/yocPH8YTTzyBpKQkSJLxFNGCIECr1VosOCIiooYqLasQr607AQB4fkArdA1vYuOIGg+zx9w8+eSTaNOmDfbs2YOLFy8iOTnZ8Lh48aJZ59qxYweGDx+OkJAQCIKA9evXV1t/+/btEAShwuPMmTPmvg0iIiKrEUUJ034+huxCDTqFeuOFga1tHVKjYnbLTXJyMtauXYtWrVrV+eJ5eXno3LkznnzySTz44IMmH3f27Fl4eXkZtv39/escCxERkaV8s/cSdp3PgItChg/HxFQ5vw1Zh9nJzcCBA3Hs2DGLJDf33HMP7rnnHrOPCwgIgI+PT52vT0REZGnnrudg/p+6HoXXhrVHS38PG0fU+Jid3Hz11Vd44okncPLkSXTo0AEKhcJo/4gRIywWXFW6dOmCwsJCREVF4fXXX8eAAQOqrFtUVISioiLDdnZ2ttXjIyKixqlYI+KlnxJRpBHRr40/Hruzua1DapTMTm727NmDXbt24c8//6ywz9oDioODg/HFF1+gW7duKCoqwnfffYeBAwdi+/bt6Nu3b6XHzJs3D3PmzLFaTERERHqLt/6LU6nZ8HFT4P2HOnFZIhsRpPK3PNUgIiIC9913H9544w0EBgZaLhBBwLp16zBq1Cizjhs+fDgEQcCGDRsq3V9Zy01YWBiysrKMxu0QERHVxcFLmRjz+V6IErD00a64pyOXUrCk7OxseHt7m/T9bfYIp5s3b2Lq1KkWTWzq4s4778S5c+eq3O/s7AwvLy+jBxERkSXlFmkQvzoRogQ82DWUiY2NmZ3cPPDAA9i2bZs1YqmVo0ePIjiYHyIiIrKdt347hZTMAjTzccXsEVG2DqfRM3vMTZs2bTBz5kzs2rULHTt2rDCgeMqUKSafKzc3F+fPnzdsJycnIzExEb6+vggPD8fMmTNx7do1fPvttwCAxYsXIyIiAtHR0SguLsaqVauwZs0arFmzxty3QUREZBF/nUrD6kNXIQjAotGd4eWiqPkgsqpa3S3l4eGBhISECquAC4JgVnJz6NAhozud4uPjAQBPPPEEVq5cCZVKhStXrhj2FxcXY9q0abh27RpcXV0RHR2NP/74A8OGDTP3bRAREdVZek4hZq7VzUL8bN8WuKOFn40jIqAWA4obOnMGJBEREVVFkiQ89c0h/HMmHe2DvbB+ck84O8ltHZbDsuqAYiIiIgK+P3AF/5xJh1Iuw+IxMUxs7IhJ3VLx8fF4++234e7ubug6qsqiRYssEhgREZG9Ss7Iwzu/JwEApg9ti7ZBnjaOiMoyKbk5evQo1Gq14TUREVFjpdGKmPpTIgrUWsS18MOEXpG2DonKMSm5KXvrtz3dBk5ERFTfPt12AYkpt+Hp4oQPRneGTMZZiO2N2WNuJkyYgJycnArleXl5mDBhgkWCIiIiskfHUm7j4390E8e+M6oDQnxcbRwRVcbs5Oabb75BQUFBhfKCggLDfDRERESOJr9Yg6k/JUIrSrivUzBGdA6xdUhUBZPnucnOzoYkSZAkCTk5OXBxcTHs02q12LhxIwICAqwSJBERka3N23gGFzPyEOTlgndGdeCimHbM5OTGx8cHgiBAEAS0adOmwn5BELj6NhEROaRtZ9Px3b7LAICFD3eGj5vSxhFRdUxObrZt2wZJknDXXXdhzZo18PX1NexTKpVo3rw5QkLYREdERI4lM68Y0385DgB4slcEerduauOIqCYmJzf9+vUDoFv/KTw8nM1xRETk8CRJwqy1J3AjpwitAzzw6tB2tg6JTGD22lLNmze3RhxERER2Z82Ra9h0Kg0KuYAPx8TARcFZiBsCLr9ARERUiZTMfLy54RQA4KVBbdChmbeNIyJTMbkhIiIqRytKeHn1MeQWaRDbvAkm9mtp65DIDExuiIiIyvlix0UcuJQJd6Uci0bHQM5ZiBuUWiU3Go0GW7duxeeff26YrTg1NRW5ubkWDY6IiKi+nUrNwqItZwEAs4dHI9zPzcYRkbnMHlB8+fJlDB06FFeuXEFRURHuvvtueHp64r333kNhYSGWLVtmjTiJiIisrlCtxdSfEqHWShgcFYiHY0NtHRLVgtktNy+++CJiY2Nx69YtuLqWrqlx//334++//7ZocERERPXp/b/O4t/ruWjq4Yx5D3TktCcNlNktN7t27cLu3buhVBrPzti8eXNcu3bNYoERERHVp93nM/D1rmQAwHsPdYSfh7ONI6LaMrvlRhRFaLXaCuVXr16Fp6enRYIiIiKqT1n5akz7+RgAYOwd4birXaCNI6K6MDu5ufvuu7F48WLDtiAIyM3NxezZszFs2DBLxkZERFQv/m/DSaiyChHh54bX721v63Cojszulvrwww8xYMAAREVFobCwEGPHjsW5c+fQtGlT/PDDD9aIkYiIyGo2HEvFr4mpkMt0sxC7Kc3+aiQ7Y/ZvMCQkBImJifjhhx9w5MgRiKKIp556Co8++qjRAGMiIiJ7p8oqwOvrTgAAnh/QCl3Cm9g4IrIEQZIkydZB1Kfs7Gx4e3sjKysLXl5etg6HiIhsRBQlPL58P3afv4nOod745bmeUMg5t629Muf72+yWmw0bNlRaLggCXFxc0KpVK0RGRpp7WiIionq1cs8l7D5/Ey4KGT4cE8PExoGYndyMGjUKgiCgfIOPvkwQBPTu3Rvr169HkyZs3iMiIvtz7noO5m86AwB47d4otPD3sHFEZElmp6lbtmxB9+7dsWXLFmRlZSErKwtbtmxBjx498Pvvv2PHjh24efMmpk2bZo14iYiI6qRYI+LFHxNRrBHRv60/Hrsj3NYhkYWZ3XLz4osv4osvvkDPnj0NZQMHDoSLiwueffZZnDp1CosXL8aECRMsGigREZElLN76L06rstHETYH3HuzEWYgdkNktNxcuXKh0II+XlxcuXrwIAGjdujUyMjLqHh0REZEFHbyUiWUJFwAA8x7oiAAvFxtHRNZgdnLTrVs3vPLKK7hx44ah7MaNG5g+fTq6d+8OADh37hxCQ7nYGBER2Y+cQjWm/pQIUQIe6haKoR2CbR0SWYnZ3VJff/01Ro4cidDQUISFhUEQBFy5cgUtWrTAr7/+CgDIzc3FG2+8YfFgiYiIauut307j6q0ChDZxxezhUbYOh6zI7OSmbdu2SEpKwl9//YV///0XkiShXbt2uPvuuyGT6RqCRo0aZek4iYiIam3TyTT8fPgqBAFYNDoGni4KW4dEVlSrOaYFQcDQoUMxdOhQS8dDRERkUek5hZhVMgvxf/u2RI9IXxtHRNZWq+QmLy8PCQkJuHLlCoqLi432TZkyxSKBERER1ZUkSXj1l+PIzCtG+2AvxN/dxtYhUT0wO7k5evQohg0bhvz8fOTl5cHX1xcZGRlwc3NDQEAAkxsiIrIb/9t/BdvO3oDSSYaP/hMDpRNnIW4MzP4tT506FcOHD0dmZiZcXV2xb98+XL58Gd26dcPChQutESMREZHZLt7Ixbt/JAEAXh3aDm0CPW0cEdUXs5ObxMREvPzyy5DL5ZDL5SgqKkJYWBjee+89zJo1yxoxEhERmUWjFTF19TEUqLXo1coPT/aMsHVIVI/MTm4UCoVhNsfAwEBcuXIFAODt7W14TUREZEufbDuPYym34eXihIUPd4ZMxlmIGxOzx9x06dIFhw4dQps2bTBgwAD83//9HzIyMvDdd9+hY8eO1oiRiIjIZIkpt7Hkn/MAgLdHdUCwt6uNI6L6ZnbLzdy5cxEcrJvV8e2334afnx+ee+45pKen44svvrB4gERERKbKL9Zg6k+J0IoSRnQOwciYZrYOiWzArJYbSZLg7++P6OhoAIC/vz82btxolcCIiIjMNXdjEpIz8hDs7YK3R3awdThkI2a13EiShNatW+Pq1avWioeIiKhWtp1Jx6p9urGfCx/uDG83zkLcWJmV3MhkMrRu3Ro3b960VjxERERmy8wrxiu/HAcATOgViV6tmto4IrIls8fcvPfee3jllVdw8uRJa8RDRERkFkmSMHPtcWTkFqF1gAemD21r65DIxsy+W+qxxx5Dfn4+OnfuDKVSCVdX41HomZmZFguOiIioJr8cvoq/Tl2HQi5g8X9i4KKQ2zoksjGzk5vFixdbIQwiIiLzpWTmY85vpwEA8Xe3RXSIt40jIntgdnLzxBNPWOziO3bswPvvv4/Dhw9DpVJh3bp1GDVqVLXHJCQkID4+HqdOnUJISAimT5+OiRMnWiwmIiJqGLSihPjVicgt0qB7RBM827eFrUMiO1GrFcQuXLiA119/HY888gjS09MBAJs2bcKpU6fMOk9eXh46d+6MTz75xKT6ycnJGDZsGPr06YOjR49i1qxZmDJlCtasWWP2eyAioobtix0XcfDSLXg4O2HR6BjIOQsxlTA7uUlISEDHjh2xf/9+rF27Frm5uQCA48ePY/bs2Wad65577sE777yDBx54wKT6y5YtQ3h4OBYvXoz27dvj6aefxoQJE7hgJxFRI3PyWhYWbTkLAJg9PAphvm42jojsidnJzYwZM/DOO+9gy5YtUCqVhvIBAwZg7969Fg2uvL1792Lw4MFGZUOGDMGhQ4egVqsrPaaoqAjZ2dlGDyIiargK1VpM/SkRaq2EIdGBeKhbqK1DIjtjdnJz4sQJ3H///RXK/f39rT7/TVpaGgIDA43KAgMDodFokJGRUekx8+bNg7e3t+ERFhZm1RiJiMi63tt0FufSc9HUwxnzHuhkWMyZSM/s5MbHxwcqlapC+dGjR9GsmfXX8Cj/IZYkqdJyvZkzZyIrK8vwSElJsXqMRERkHbvPZ2D57mQAwPsPdYKvu7KGI6gxMju5GTt2LF599VWkpaVBEASIoojdu3dj2rRpGDdunDViNAgKCkJaWppRWXp6OpycnODn51fpMc7OzvDy8jJ6EBFRw5OVr8bLq48BAB67MxwD2gXYOCKyV2YnN++++y7Cw8PRrFkz5ObmIioqCn379kXPnj3x+uuvWyNGg7i4OGzZssWobPPmzYiNjYVCwTVEiIgc2Ru/nkRadiEim7pj1rD2tg6H7JjZ89woFAr873//w1tvvYWjR49CFEV06dIFrVu3Nvviubm5OH/+vGE7OTkZiYmJ8PX1RXh4OGbOnIlr167h22+/BQBMnDgRn3zyCeLj4/HMM89g7969+Prrr/HDDz+YfW0iImo4fk28hg3HUiGXCfhwTAzclGZ/fVEjYvanIyEhAf369UPLli3RsmXLOl380KFDGDBggGE7Pj4egG6iwJUrV0KlUuHKlSuG/ZGRkdi4cSOmTp2KTz/9FCEhIfj444/x4IMP1ikOIiKyX6m3C/DGet16hi/c1QoxYT62DYjsniDpR+SaSKlUIigoCGPHjsVjjz2GDh06WCs2q8jOzoa3tzeysrI4/oaIyM6JooTHl+/H7vM30TnMB2smxsFJXqv5Z6mBM+f72+xPSGpqKqZPn46dO3eiU6dO6NSpE9577z1cvXq11gETERFVZsWeS9h9/iZcFXIsHhPDxIZMYvanpGnTpnj++eexe/duXLhwAWPGjMG3336LiIgI3HXXXdaIkYiIGqF/r+dgwaYzAIDX72uPyKbuNo6IGoo6pcCRkZGYMWMG5s+fj44dOyIhIcFScRERUSNWrBHx0o+JKNaIuKtdAMb2CLd1SNSA1Dq52b17NyZNmoTg4GCMHTsW0dHR+P333y0ZGxERNVIfbv0Xp1XZ8HVXYv6DHTkLMZnF7LulZs2ahR9++AGpqakYNGgQFi9ejFGjRsHNjYuWERFR3R1IzsSyhAsAgLn3d0SAp4uNI6KGxuzkZvv27Zg2bRrGjBmDpk2bGu1LTExETEyMpWIjIqJGJqdQjfjViZAk4OFuoRjaIcjWIVEDZHZys2fPHqPtrKws/O9//8NXX32FY8eOQavVWiw4IiJqXOb8dhpXbxUgzNcVs0dE2zocaqBqPebmn3/+wWOPPYbg4GAsWbIEw4YNw6FDhywZGxERNSKbTqrwy+GrkAnAotEx8HDmLMRUO2Z9cq5evYqVK1di+fLlyMvLw+jRo6FWq7FmzRpERUVZK0YiInJw6TmFmLn2BABgYr+W6B7ha+OIqCEzueVm2LBhiIqKwunTp7FkyRKkpqZiyZIl1oyNiIgaAUmSMP2X47iVr0Z0iBdeGtTG1iFRA2dyy83mzZsxZcoUPPfcc7VaJJOIiKgy/9t/BdvP3oDSSYbFY2KgdOIsxFQ3Jn+Cdu7ciZycHMTGxuKOO+7AJ598ghs3blgzNiIicnAXb+Ti3T+SAAAzhrZD60BPG0dEjsDk5CYuLg5ffvklVCoV/vvf/+LHH39Es2bNIIoitmzZgpycHGvGSUREDkatFTH1p0QUqLXo3aopxveMsHVI5CDMbvtzc3PDhAkTsGvXLpw4cQIvv/wy5s+fj4CAAIwYMcIaMRIRkQP65J/zOHY1C14uTnj/4U6QyTgLMVlGnTo227Zta1gR/IcffrBUTERE5OCOXrmFT7adBwC8e39HBHu72jgiciQWGbUll8sxatQobNiwwRKnIyIiB5ZfrEH86mPQihJGxoRgeOcQW4dEDoZD0omIqF69+0cSkjPyEOztgrdGdrB1OOSAmNwQEVG92XYmHf/bfwUA8MHDneHtqrBxROSImNwQEVG9uJlbhFd+OQ4AeLp3JHq2alrDEUS1w+SGiIisTpIkzFx7Ahm5RWgb6IlpQ9raOiRyYFyVjIiIrEIrSjiQnIn0nEKcTs3G5tPXoZAL+HBMDFwUcluHRw6MyQ0REVncppMqzPntNFRZhUbl93UKQVSIl42iosaC3VJERGRRm06q8NyqIxUSGwBYf/QaNp1U2SAqakyY3BARkcVoRQlzfjsNqZo6c347Da1YXQ2iumFyQ0REFnMgObPSFhs9CYAqqxAHkjPrLyhqdJjcEBGRxaTcyjepXnpO1QkQUV1xQDEREdWZVpTwy+EUzN14xqT6AZ4uVo6IGjMmN0REVCd7zmfg7T+SkKTKBgDIZUKVY2oEAEHeLugR6VuPEVJjw+SGiIhq5eKNXMzdeAZbk64DALxcnDBlYGsEerlgyg9HAcBoYLFQ8jx7eBTkMgFE1sLkhoiIzHI7vxgf/X0O3+29DI0oQS4T8PidzfHiwNZo4q4EACjkQoV5boK8XTB7eBSGdgi2VejUSDC5ISIikxRrRHy37zI+/vscsgrUAICB7QIwc1h7tArwMKo7tEMw7o4KMsxQHOCp64piiw3VByY3RERULUmSsDUpHXM3JiE5Iw8A0C7IE6/fG4Xerate/FIuExDX0q++wiQyYHJDRERVOpWahXd+T8LeizcBAE09nDFtcBs8HBvGVhiqQNJqkX/oMDQ3bsDJ3x9usd0gyOt/HTEmN0REVEF6diEWbj6Lnw9fhSQBSicZnukTief6t4KHM786qKLszZtxfe48aNLSDGVOQUEInDUTXoMH12ss/IQSEZFBQbEWX+28iKUJF5BfrAUADO8cgleHtkVoEzcbR0f2KnvzZlx78SVAMp4CQHP9uq78o8X1muAwuSEiIoiihA3HUrFg0xnDHU5dwn3w+r1R6Na8iY2jI3smabW4PndehcRGt1MCBAHX586D58CB9dZFxeSGiKiRO3QpE2//kYRjKbcBAM18XPHqPe0wvFMwBIHjaqh6+YcOG3VFVSBJ0KSlIf/QYbjf0aNeYmJyQ0TUSKVk5mP+n2fwxwkVAMBdKcekAa3wVO9IuCjqfxAo2Za5g4HV19ORv28vbq1ebdL5NTduWCrUGjG5ISJqZLIL1fh023ms2HUJxVoRMgEY0z0M8Xe3hb+ns63DIxswZTCwNjcP+QcPIG/vXuTt2YPi8xfMuoaTv79FY672WvV2JSIisimNVsSPB1Pw4ZZ/cTOvGADQu1VTvHZve7QP9rJxdGQr1Q4GnvIisu+5B5r0dBQcOwZoNKUVBAEuUVFwu/NOZK1dC+3t25WPuxEEOAUGwi22m1XfR1lMboiIGoGEf2/g3T9O49/ruQCAFv7ueP3e9hjQNoDjahqxGgcDA8j5809DkSIsDO49e8I9Lg5ud/SAUxPdYHPXzp10CZIgGJ+r5LMVOGtmvc53w+SGiMiBnbueg3c3JmH7Wd14Bx83BaYOaoOxd4RDIZfZODqytbw9e6sfDFyiyZPj4Tt2LJRhYZXu9xo8GPhoccWurcBAznNDRESWcTO3CIu3nsP3B65AK0pQyAU8EReBF+5qDW83ha3DIxtSp6YiNyEBudsTkLtnj0nHuEZ3qDKx0fMaPBieAwdyhmIiIrKsIo0W3+y5hCX/nEdOoW58xJDoQMy4pz0im7rbODqyBUmjQUFioiGhKTp3zuxzmDoYWJDL6+127+rYPLn57LPP8P7770OlUiE6OhqLFy9Gnz59Kq27fft2DBgwoEJ5UlIS2rVrZ+1QiYjsliRJ+PNkGub9mYSUzAIAQHSIF16/N4qLVzZCmlu3kLdzp651ZvduiFlZpTtlMrjGxMCjXz+49+mNq5MmQXM93W4GA1uCTZObn376CS+99BI+++wz9OrVC59//jnuuecenD59GuHh4VUed/bsWXh5lY7s96/H28uIiOzN8au38fbvp3Hw0i0AQICnM14Z0hYPdg2FjItbNgqSJKHozBlD60zB8eOAKBr2y7294d6njy6h6d3LMBAYAAJnzbKrwcCWIEhSZala/bjjjjvQtWtXLF261FDWvn17jBo1CvPmzatQX99yc+vWLfj4+NTqmtnZ2fD29kZWVpZRgkRE1NCosgrw/qazWHv0GgDARSHDs31bYmK/FnBT2rxhnqxMzM9H3t69utaZHTuguX7daL9z27bw6NcPHv37wbVTJwhOVX8m7GnRy6qY8/1ts09/cXExDh8+jBkzZhiVDx48GHtqGODUpUsXFBYWIioqCq+//nqlXVV6RUVFKCoqMmxnZ2fXLXAiIhvLL9ZgWcJFfLHjAgrVur/OH+jSDK8MbYtgb1cbR0fWVJySoktmtm9H/oEDkNRqwz7BxQXucXG6hKZfXyiCg00+rz0NBrYEmyU3GRkZ0Gq1CAwMNCoPDAxEWhW3pQUHB+OLL75At27dUFRUhO+++w4DBw7E9u3b0bdv30qPmTdvHubMmWPx+ImI6psoSlhz5Cre/+ss0nN0f7T1iPDF6/e1R6dQH9sGR2YxdakDSa1G/uEjuu6mhAQUX7xotF/RrBk8+veHR/9+cOvRAzLn2s8wbS+DgS3B5u2W5SePkiSpygml2rZti7Zt2xq24+LikJKSgoULF1aZ3MycORPx8fGG7ezsbITVcDsbEZG92XvhJt754zROpepan8N93TDznnYY2iGIk/A1MDV1AWkyMpC7YydyExKQt3s3xNzc0oPlcrh17QqP/v3g0a8flC1b8vdfCZslN02bNoVcLq/QSpOenl6hNac6d955J1atWlXlfmdnZzjXIZMlIrI2rSjhQHIm0nMKEeDpgh6RvpCXDAS+lJGHuRuTsPm0bjyFp7MTXhjYCk/0jICzU8PsMmjMqlzqIC0N16a8iPTwcKivXDHaJ/f1hUefPvDo3w/uvXpBzvGiNbJZcqNUKtGtWzds2bIF999/v6F8y5YtGDlypMnnOXr0KILN6FckIrInm06qMOe301BlFRrKgr1dMG1wW5xWZePbvZeg1kqQywSM7RGOlwa1hp8H/2BrKCRJglRYCG12DrS3byHtzTmV33JdQp/YuERFGVpnXDp2hCDjbNLmsGm3VHx8PB5//HHExsYiLi4OX3zxBa5cuYKJEycC0HUpXbt2Dd9++y0AYPHixYiIiEB0dDSKi4uxatUqrFmzBmvWrLHl2yAiqpVNJ1V4btURlP+qU2UV4uWfjxm2+7f1x2vD2qN1oGf9BlhHpo4rsWeSKELMy4OYkwNtTg7E7Gzdc06OLmHJyYaYnQNtbo7uOScbYk5uaXlOjvFikyYIWbwY3kOHWOkdNQ42TW7GjBmDmzdv4q233oJKpUKHDh2wceNGNG/eHACgUqlwpUzzXHFxMaZNm4Zr167B1dUV0dHR+OOPPzBs2DBbvQUiolrRihLm/Ha6QmJTlpNMwJfjYjGgXUC9xWUp9nJrsaTRlCYjhqQku0yyUiZpyc0tTV702zk51ba0mEwmg+DsDKmgoOa6ZiZDVJFN57mxBc5zQ0T2YO+Fm3jky3011vvhmTsb3AzDVY0r0U8K1+yjxSYnOGJRkaGVRMzJ1j3nltnOyTWU61tNSrdzIOXnW+Q9CQoFZF5ekHt66p49PMpse+qePT0h9/LSPZfd9vCEzN0N+QcO4soTT9R4rfBvvnGYu5YsqUHMc0NE1FhptCK2nb1ec0UA6TmFNVeyI5JWi+tz51Xe2lFSpvq//4M6PR1Sbl6l3Thlu4Ck4mKLxCW4uUHu6Qm5l6cu2fDyhNzTCzJPD8g9vXTlnl6Qe3ronr08S5MUL6863WKt5xbbDU5BQbrJ9hxoqQN7xOSGiKienE7NxpojV/FrYioycotqPgBAgKeLlaOyDEmrRfGVK8j+Y6NRV1RlxNtZSH/nXdNPLgi6RKNsa0mZxKO0lcS4tcSw7eEBQWH7ldAFuRyBs2Y63FIH9ojJDRGRFaXnFGJDYirWHLmGJFXpDOm+bgoUakTkF2srPU4AEOStuy3cnkiSBE1aGorOndM9/v0XhefOofjCRUhFpiVsAODSsSOc27aBvEwrSvnWEn0yI3N3d5i7hbwGDwY+WlxxPFJgoF0tddDQMbkhIrKwQrUWW5OuY83hq9hxLgNaUfcXulIuw6CoADzQJRT92vrj76TreG7VEQAwGlisn5Jt9vAow3w3tqC5dQtF/54rTWRKHmJOTqX1BRcXOAUFQX3pUo3nDpg2rdGOK3G0pQ7sEZMbIiILkCQJhy/fwpoj1/D78VTkFJbe8dIl3AcPdg3FfZ2C4eOmNJQP7RCMpY91rTDPTZC3C2YPj8LQDvUzh5eYl4ei8+eNEpjCc+egvZFR+QFOTnCOjIBz69aljzZtoGjWDABwfuAgjiupgSMtdWCPmNxYiCPM50BE5kvJzMfaI9ew9uhVXL5ZemdOMx9X3N+lGR7o2gwt/D2qPH5oh2DcHRVU5QzFliQVF6Mo+ZKhO0mfyKivXq3yGEVoKJzbtDFOZCIjICiVVR7DcSVka0xuLMBe5nMgovqRU6jGnyfS8MuRqziQnGkod1PKMaxjMB7o2gx3RvpBZmKCIpNEdMq4YPjjSBbhA6D2X/6SVgv11aulrTAliUzxpctVzqEi928Kl9at4dy6DZzblCQxLVtC5u5u9vU5roRsjfPc1PV8FpzPgYjsl1aUsPt8BtYcuYq/TqWhUC0C0P2n3qtlUzzQtRmGdgiCm9K8vxnr8seRJEnQpKdXHBdz/jykwspvIZd5epbrTtI9OzVpYlbcpmCLNlmSOd/fTG7qQNJqdX3L1dz26OTvj4g1v0Dm6grB2RmCQsEVXC2E/3BSffj3eg7WHLmK9Uev4Xp26d1ALf3d8WC3UIyKaYYQH9danducP460t2+j6Px5QyuM7nEeYlZWpecWnJ3h3LKlUQLj3KYNnAID+W8QNUhMbqphyeQmb/8Bk2abLE9QKnWJjlIJwVkJmaLstjNkzkoICuM6glIJmbK0juCshEz/2lBXAVmZ8wjKysp0x6GBJ1mO3BXIpM32buYWYcOxVKw9cg0nrpUmDz5uCozoHIIHu4aiU6h3nf4bMuWPI8HNDa4xMSg+fx6a9PTKK8nlUDZvbpzEtG4NZXg4PzfkUDhDcT3R3LhRq+Ok4mKLzbpZF7okqTThqZB0KZW6BKmysrJJlyGRKl9WWlfmbJzACQpdGZyczP6CqOqvXc3167ryBtwV6MhJmyVYM/Er0mix7Uw6fjl8DdvPpkNTcvu2k0zAXe0C8EDXUNzVLgBKJ9PnW5EkCWJeHrS3syBmZ0GblQVtVja0WVkoOHWyxsnupPx85O/ZY9hWhIRUaIlRRkZaZPZcIkfC5KYOnPz9TaoX9s1KuHXpAqmoSJfYFBVBLCqCVKyGVFymrLgYUlFxSfKjr2NcJhUXlx5bVKSrV7ZOyTFicZk6+vOo1UZx6fcBQOXTiNUDQSiXPFVsZSq7DaUCuVv/rn5q9zf+D2JeHmQuLrpuQKXSvGcbTRbmyEmbJVgj8ZMkCceuZmHN4av47XgqbueX/jfSKdQbD3YNxfDOIfBxkqDNyoKYfAH52dllkpTbugUWb2dBqy/PzoKo387OBrR1+6/L+6GH4PPgA3Bu3Rpyj6rvuiKiUuyWqgNDs3IN8zm0+nurXTQPS6IISa02TrKKyyVFZRMqdbmkS7+vsoRKXXJshbLySVcxUC7JsjtyeSWJj8JoW6ZQlpSVea5NIlVyLJzkSI1/GdrMzCrDcgoMROSGDZApFbrPk5OTw8zaWhNLDNyXtFrdatBZWUi7dgO7j17E0VNXkH/zFjzUBfAozkcAitDKVUKwrBjOBXklyUp2lYNzTSUolZB7e0Pu4w2Zlzfk3t6QioqQt3t3jcdyEUUiHY65qYbV7pYCKp3PgXdLVSSJYrmEyrhlSteyVVlrVTEKjiYi+/ffa7yGc5s2ui8QtdrQaqV/FtXFQLEaolqta82y92SrOoKgS8ZKHvrXhsTHSQ5Brn/tZFSnsnqQy3T1y9ZzkgOykme5HIJMXnpe/T55SZmhnhMEuazkHGXOW/5chrj1+2QQ9HGW1JMApDzzLLQZVUwoB0Dm7QW/p57SLcCYpW9FuQ0xK9uwXdWsuiaTyXRrFnl7Qe7tA7mXly5h8faCzNsb8pKkRe6tK5d5ldTz9oLMpeL6UA3tjyMiW2NyUw1LJzcAx0nUJ1MHcZvz164kipA0mgpJUG2f9a1TYoX96iqP09y6BW1VA0bJovKdnJGjcIXk4QkPf1/4B/vD2denNBnx8oLcx7skkdEnLN5WWd+IfxwRmY7JTTWskdwAvMOlvjjqX7umJm1hX34J1y5dAK0GkigCGg0krRbQaiFptZA0WkDUv9YAJYmbbr+oO66kLvT1tRpIWhGSVmM4D8qeS1NSZnitAfT1NVpdHFqNbp+o1ZVpy523wj6tcRyV1te9P21+PqS8vBp/Nq7dusIlOhpyL2/ckrvg0E01ElTFuKyWI0fhhlylK/yCmuL+2OYY1aUZwnzdLPGrqzP+cURkGiY31bBWckP1xxH/2nXUpM0STE38fL/4CpuVoVhz+CoSU24byr1cnHBfye3bXcN97HIKBP5xRFQz3gpODs0Rp3YX5HKux1MFt9hu0Pj5Q3bzBirrFBIBZHs0wf2bbqNQvA0AkMsE9G/jjwe6hmJg+wC4KOz758ZFFIksi8kNNUhegwfDc+BAh/pr1xGTNksQBRmWdRyJydu/gggYJTgiAAHAkqgRKBSBqGAvPNgtFCM6h8Dfk3O/EDVW7JYisjPsogDyizVIySzAlcx87Pz3Br7ddxk9U09g4vH18C8snTE43dUHn3cciT0hHbHgwY4Y0z3chlETkTWxW4qoAWsMXRRaUUJadiGu3MxHSmY+Um7l40qm7pGSmY+M3IozeO8J6Yh9wdGIzrgI36IcZDp74lTTFhAFXVuOvXc9EVH9YXJDRFaRVaBGSqZx0qJ/vna7AGpt9Y3G3q4KhPu6wV0px75k3eSGoiDDCf9WldYP8Kw4lwwRNU5MboioVoo1IlJvF5QmL7dKE5grN/ORXaip9niFXEBoEzeE+boh3NcVYU3cEO6r2w7zdYO3qwKArpWn94J/kJZViMrSIQFAkLcLekT6Wv5NElGDxOSGiColSRJu5hWXtrrcLO0+SsksgCqrAGINI/aaejgj3NfVKGkJL3kEerlALqv5tmy5TMDs4VF4btURCIBRgqM/evbwKJPORUSNA5MbIjujFSUcSM5Eek4hAjx1LRLW+uIuKNbiqtF4lwKjLqQCdfWLProoZIZkJczXzdD6Eu7nhtAmrnBTWuafmKEdgrH0sa6Y89tpqLJK13kK8nbB7OFRGNoh2CLXISLHwOSGyI5sOqmq8AUeXIcvcFGUcD1HN3BXn7Sk3CrtSrqRU1Tt8YIABHu5GFpcyj839VDW26R4QzsE4+6ooHpL/IjIfFpRiyPpR3Aj/wb83fzRNaAr5LL6H+zPW8GJ7MSmkyo8t+pIhXEl+q/upY91rTTByS7UDdw1HrxbgJTMfFy9VYBirVjtdT2dnRDu51Zp11GIjwucnXgXEhHVbOvlrZh/YD6u5183lAW6BWJGjxkY1HxQnc/PW8GJGhitKGHOb6crHTCrL5u17iQycotx9VaB0eDd2/nVr2ruJBPQrIlu3Etok9LERZfMuMLbVWGXSxIQUcOx9fJWxG+Ph1TuX7H0/HTEb4/Hov6LLJLgmIrJDTVY9Tk2xZJEUUJOoQa38otxu0CNW/nFOHQp06grqjKZecV4ff3JSvf5uSvLdBm5Go2BCfZ2gZPcsqtZExHpaUUt5h+YXyGxAQAJEgQIWHBgAQaEDai3LiomN9QgWXpsSm1IkoScIg2y8nUJyu2S56wCNW7lqXG7QFd2uySJ0b/OKlDXeJdRVaJCvNC9eZPSriM/XQLj7sz/lInINo6kHzHqiipPgoS0/DQcST+C7kHd6yUm/otoIQ21FaEhqmpsSlpWIZ5bdaTKsSlVkSQJecVaXRKSrzYkKbcL1LidZ5yY6FtasvLVuF2ghra2WQoAN6UcTdyU8HZVQCYAJ1OzazzmjXujENfSr9bXJCKqijmDgdWiGqdvnsbh64ex8eJGk85/I/+GJcOtFpMbC7CHVoTGoqaxKQKA//v1FEJ8XJFbqMGt/HItKPlq3MpXI6ugWLev5HVNs+VWx0UhMyQpTdyU8HFTlDyU8Ckp83Yz3uftqjAaqMuJ6ojIlmoaDFykLcKJGydw+PphHLp+CMduHEOBpsCsa/i7+Vs67Crxbqk6qu0dLg2dVpSg1ooo1opQa0SotWW2tSLUGglqsYp9lew32qeVUKzRvdaUOzY9uwhHU25b5T0pnWRo4qaAj6s+GdG99nHXPTcxJCZKNCkp83FTWGxNI/1nCah8ojpH/SwRNUb2css0UPVgYL0W3i1wNecqikXjNd+8nb3RLaAbugR0wYpTK3Cr8Fal5xAgINAtEJse3FSn98i7peqJKa0Ic347jbujgmrsopIkyZAElH6ZSyVf/rpt4y964336YzVaEcX68xj2S2USB9H4OhrjfcVaCZpKkgzDdslre0+JPZ2dEOTtYtyC4q5rXfHRt6K4luwr2XZRyGx61xAnqiNqHKx9y3RNtKIWOcU5yCrOQmZhJubsnVNlYgMAF7MuAgD8XPwQGxSLboHdEBsYi5Y+LSErWbg21DMU8dunQpAkSGX+HRUkCRCAV3u8Wq/JG5ObOjiQXP0dLhIAVVYhBi1KgLOTrJLEokxSUoexG/bASSZAIZdBIRegdJKVvNZtl39dur9ku2S/k9H+0uOUJXWd5DKkZObj8x0Xa4zni3GxDXJsCieqI3JslrxlWpIkFGgKcLvoNrKKsmp8zirWvc4uyq42manM3F5zcV/L+6r8A3BQXj4WXc/AfD8fXHcqTS0CtVq8evM2BuXlm3W9umJyUwfpOdXfuquXnJFn9rkFAUZf7IYveqfKE4bS/cbbxklCyWsn420nfVKiP8bJeNupmn36a9RXi4dWlLDhWKpDj02Ry4QGmZgRUfVqumUaAN7d9y68nb2RXZxtSEz0CYn+dVZRlmGfWqx+nqvquCvcoZQpcavoVo115TJ51f/Oi1pg06sYlJ+PAfn5OOLijBtyOfy1WnQtLIIcArBpBtDuXoC3gtu/AE8Xk+q9OqQtOob66BINJ1nlSUO5ffxLvXJcRJGI7JEoichT5yGnOMf4odY9Zxdn49ytc9XeMg0AGYUZmPDXBLOurZAp4OPsA29n70qffZx94OXsZXjt7ewNb6U3FHIFDqbuw4Qtz9R4Df+8W8C5rUDeDSAvHchNB/IydK8zk4HsVACAHED3wvLLukhA9jXg8h4gso9Z7622mNzUQY9IXwR7u9TYivBsv5b8srUgjk0hahjsadBsTURJRK46t2JyUuaRXZxdIWnRl+cW55rd1VOVpq5NEeIRoktElN5GSYq3c8VtVydX01vPJQkovA3cugTkZaDrxe0I1GiQLpcbjZXREyQJgVotuq6ZVPc3llt9YmdJTG7qoGwrghwiusvOIAC3kQ4fHBTbQYSMrQhWwrEp5Ei0mmIcOfEdbmRfgb9XOLp2fBxyJ6Wtw6qT+h40qxW1RslJrjrXOBmpLEEp88hVWyY5UcgU8FJ6wVPpaXjWP3KLc/HnpT9rPMd7fd8zfbI7SQKKc0taUTJ0LSv5Jc9lywz7bgJlurLkAGa4uSI+oGnlg4EBvHrzFuTOXoBPOODuD3gE6J71r3PTga2za47VI9C092QBTG7qaGiHYKwdkIHAvXNwzSXX0M/YrNAD1+NmowtbEaxHVMMpez0U2VfgJIUD4uOArGF/IQCO+UVnKY74s9m6ax7m//s/XJeXfqkEHv0QM9o8ikG9Z9owstrTDZqdCkmSdAMIS6TnpSF++1Qs6v9hhQRHn5yUTT5yi8tsq6tPUHLVuRaJ3VnubJSQeCo94aXwqlim9IKH0sNo21PpCWe5c5Xn1mqKceTCRqTLUHUriQh09W4L3E4pSVL0ycmNShKYktca08Z/Gr9RL8DND5A7Y1DGGSxKz8B8vyaVDAa+hUH5BcATP1fdpSRqgQOfA9kqoKp+DK8QoHlP8+OsJc5zU1enN2Dr7/+tOEJco8GMm7cx6L7PgagRdb8OGan0C0ErNegvBMBx35clOOLPZuuueYg//z/d10ElfzEvamWb9yZKIjSiBhpRA7WohlpUG21X97pYW4w5u15Dlibf6D0ZSBKcZQpENe2IXE1pS0ue2vwbLyrjInepkIhU1oriqfSEp6L8tgecBTmgVetaN7Sakmd16XOV+8puawBtcZnXJXUyzmHr2V8QH9BU96Oo7HeenqFLJszl5FrSmtK05FHy2q1paSuLfp9bU0BRMmZU1AKLOwDZKmghVT4Y2CsEeOlE9YOBT28AVo8r2ahkNOTob+v8XWjO9zeTm7oQtdj6WUfEe8iq/scpV8SgSTV8KMgs9vqFUFeO+r4soSH8bERJhFbUQiPpvuyNXkta3baogUbS7SvWFGDKxnHIFFBlEuAlAS/c+RpESMbJhKSBWlvudcm19K/NTUrKvtZK2nr/+em5Cgp4ypXwlDnDU6bQPQQFPAUneEEOT0EGT8jhCQGekv4h6R5aEUpJrDyxqJB8VJKwiJp6eY9b3VwrtJIEaTSlrSQAIFOUJCR+pcmJW9nEpVwio3SvfUCWSkxObwA2vWoYXAwA8GoGDJ1vkT/ymdxUw5LJjfZiAoZsm4jrcnmV/zg11WrxubI15J4BECDT1RNkAHTPgqArEwSh5Bz6ieRK95Wtpz9Od0zZZ905jc4HWemxhuOMjxHKnLP0WLmhXuk5hHKxGJ9XkJWtpy+XG8dX5hjDOWRlriGTVxKnvPQZArSiBiN+uRvpMlT6MxckCQEi8MdjB+DkpGseFgQBQsl/pLacpK86Wk0xhnzbFdereV+BIrBp3BGTumEkSYIoiZAg6V5DNCoz2le2TBQhihpIkhaSqNG9FrWQJC1EUQtRKtkWtRAlbUk9LURRA1ESgZJnwzn0x4kiIOmOEUuOkSSx5LUICWLJ+Uv2lWxLkgStVo15l9cjy/DfSIU3C09JwpP+cZAEQCNpoZFEaCVR9wzds75MK4nQQAuNJFVSR4IW+jpiaR2I0EpSaVkl26IFPgf2zEmSoJAkOEmAAlLJNuBU7nWOIMNlpaLG8z2alY2++YXwEkV4lnnUfGQ9E2S6REOuAGROJc8KQO4EyJWlrw11ym+XHCNX6rqRzm8BAGiBSlpJSjzyI9BmaOWfd2uxVGIianV3ReVe142xad7TYn/cM7mphiWTm4N7FmLCuW8sFBnVN/1f/fp/PoQyr1FJmSFBqqJexfrl/798vdJ9aojIMeHfMVcJkEOAWDL0UQSMniUAon3mb42WPimQA5CXJAdySCiGgNtONf+jH1VYhFCNBk6AIblwgu6cijKvS8t11zR6LUlQQP9al5yUT1RKX5dJZPTHoOJnvlKCDAddnDEhqOY1hJZnadFd6Vf6xW+UOFSSSOjLjepUkUgYbSurP5/RtrLiPpnMlHdumjJdQNWOTampC8harJiYWAKXX6gnN+SmfejdIINCpvtRGz7OUumkTSizR6pkS59+GtdAhS2pkhpSuX0VjpXK1yuz38G/JPX93dbN7qs7u/lXLhBqd5ypZJIEmeE1IINkSNhkAIQyZSXtcxB0bZLlygCZoVwos08o3Vfy+dLV05ULgv51ybGCgEyxCBdkNb/nWFGB5gpvOAkCnCCDXBAghwAnQQYnCJCXPJe+1tVxKqkjF2Rl6pfsKyl3gkz3uuRYhSCHHDLIZWX2Ga6r23YS5Lqp6Q2to2VSW0HAwYyTmFBwqsb3NS2gN7qH3FHaoimTl7SKln0tVFEu0305m1Vecj5BXvJaVu61rOpyQUDXiwkI3Dax5luL71sGtOhX4/t3KDI5MHRBSRdQFTN1DZ1vu4RCJq+3eWiszebJzWeffYb3338fKpUK0dHRWLx4Mfr0qfqHm5CQgPj4eJw6dQohISGYPn06Jk6cWI8Rl/IP6wmcWVFjvU/u/hzdQ+6sh4isT9/QVzZZqrSsfNaEssmXZHRcpWWSVJLVSZAkLSCJgCTh8In/YfKZL2uM8+OWY9Gl7f0lXSNlzyPpriXqzidJYsk+0eg19K9FbUk4+voSJOj2S5JkqKc/l25f2fPqXwPQX7/cdQEJJ1IPYvatAzW+r7lNe6FTs56QyeQQBCddMiBzgiCTQyY4QRBkEOROkAkl2zIZBJlTSX3dMTKZvOQYGQRBodtXcg7jL8ryX36lX2D16eDRrzHh+OIa602KmYzuXZ6yfkAW0lVTjMBvu9Z858zwZUADuiNMHtEbMwoExHug6luLCwTII3rbKkTbihqhG8NSoQsoxGJjU8jGyc1PP/2El156CZ999hl69eqFzz//HPfccw9Onz6N8PDwCvWTk5MxbNgwPPPMM1i1ahV2796NSZMmwd/fHw8++GC9x981qDsCFV5IL86q+h8nZx90NXW+ggZAP2ZF36VSslFvenWbiMBTX9T4hdD3zpcb1C3CLTQT8JkJX3TDhnzcoN6XJXTt+DgCj35YcxLQ8XEbRFd7ciclZrR5FPHn/1d1EtDm0Yb3+5bJMeiu+VhU2V2k+nWG7vvcrro76l3UCN1SBHbcBdTQWbAz0XyLFi3CU089haeffhrt27fH4sWLERYWhqVLl1Zaf9myZQgPD8fixYvRvn17PP3005gwYQIWLlxYz5HryGVyzOg1RzfgtdzQJaFkfodXe75ptzNyNkT6LwQAlf/M0TC/EBz1fVmCI/9sBvWeiUWtHkVAudHIgaJ93AFWa1EjMOi+z/FXFrBcdR0L0jOwXHUdm7IETo+hp+8C6viQ7pnfExZlswHFxcXFcHNzw88//4z777/fUP7iiy8iMTERCQkJFY7p27cvunTpgo8++shQtm7dOowePRr5+flQKCqOsy8qKkJRUek6F9nZ2QgLC7PcPDeofCbOILdAvFpPy9c3RpXNeRKklfBqA57zBHDc92UJjvyzccTJCQHY/QBValgaxIDijIwMaLVaBAYaT8ccGBiItLS0So9JS0urtL5Go0FGRgaCgyvOBjxv3jzMmTPHcoFXYlDzQRgQNqDBrKHiCAb1nokBd77scF8Ijvq+LMGRfzZyJ2WDGi9kMgcaoEoNi80HFJefd0SSpGrnIqmsfmXlejNnzkR8fLxhW99yY2lymdz0tUDIIhz1C8FR35cl8GdDRKawWXLTtGlTyOXyCq006enpFVpn9IKCgiqt7+TkBD8/v0qPcXZ2hrNz1Wt9EBERkWOx2YBipVKJbt26YcuWLUblW7ZsQc+elS+uFRcXV6H+5s2bERsbW+l4GyIiImp8bHq3VHx8PL766issX74cSUlJmDp1Kq5cuWKYt2bmzJkYN26cof7EiRNx+fJlxMfHIykpCcuXL8fXX3+NadOm2eotEBERkZ2x6ZibMWPG4ObNm3jrrbegUqnQoUMHbNy4Ec2bNwcAqFQqXLlyxVA/MjISGzduxNSpU/Hpp58iJCQEH3/8sU3muCEiIiL7xLWliIiIyO6Z8/1t024pIiIiIktjckNEREQOhckNERERORQmN0RERORQbD5DcX3Tj5/Ozs62cSRERERkKv33tin3QTW65CYnJwcArLIEAxEREVlXTk4OvL29q63T6G4FF0URqamp8PT0rHYNq9rq3r07Dh48aLfnre15zD3O1Pqm1Kuujn6tsJSUFIe7td9anyVbX98S57W3z7GpdflZdqxr87Ncv59lSZKQk5ODkJAQyGTVj6ppdC03MpkMoaGhVju/XC63yj9Mljpvbc9j7nGm1jelnil1vLy8HO4LwVqfJVtf3xLntbfPsal1+Vl2rGvzs1z/n+WaWmz0OKDYwiZPnmzX563tecw9ztT6ptSz1s/U3tn6fdvzZ9nePsem1rX179RWbPm+rXltfpbtV6PrliLHwhmnyVHws0yOwh4+y2y5oQbN2dkZs2fPhrOzs61DIaoTfpbJUdjDZ5ktN0RERORQ2HJDREREDoXJDRERETkUJjdERETkUJjcEBERkUNhckNEREQOhckNObT7778fTZo0wUMPPWTrUIhqLSUlBf3790dUVBQ6deqEn3/+2dYhEZktJycH3bt3R0xMDDp27Igvv/zSatfireDk0LZt24bc3Fx88803+OWXX2wdDlGtqFQqXL9+HTExMUhPT0fXrl1x9uxZuLu72zo0IpNptVoUFRXBzc0N+fn56NChAw4ePAg/Pz+LX4stN+TQBgwYAE9PT1uHQVQnwcHBiImJAQAEBATA19cXmZmZtg2KyExyuRxubm4AgMLCQmi1WlirfYXJDdmtHTt2YPjw4QgJCYEgCFi/fn2FOp999hkiIyPh4uKCbt26YefOnfUfKFENLPlZPnToEERRRFhYmJWjJjJmic/x7du30blzZ4SGhmL69Olo2rSpVWJlckN2Ky8vD507d8Ynn3xS6f6ffvoJL730El577TUcPXoUffr0wT333IMrV67Uc6RE1bPUZ/nmzZsYN24cvvjii/oIm8iIJT7HPj4+OHbsGJKTk/H999/j+vXr1glWImoAAEjr1q0zKuvRo4c0ceJEo7J27dpJM2bMMCrbtm2b9OCDD1o7RCKT1PazXFhYKPXp00f69ttv6yNMomrV5d9kvYkTJ0qrV6+2SnxsuaEGqbi4GIcPH8bgwYONygcPHow9e/bYKCoi85nyWZYkCePHj8ddd92Fxx9/3BZhElXLlM/x9evXkZ2dDUC3cviOHTvQtm1bq8TjZJWzEllZRkYGtFotAgMDjcoDAwORlpZm2B4yZAiOHDmCvLw8hIaGYt26dejevXt9h0tUJVM+y7t378ZPP/2ETp06GcY5fPfdd+jYsWN9h0tUKVM+x1evXsVTTz0FSZIgSRKef/55dOrUySrxMLmhBk0QBKNtSZKMyv7666/6DomoVqr7LPfu3RuiKNoiLCKzVPc57tatGxITE+slDnZLUYPUtGlTyOVyo1YaAEhPT6/wlwORPeNnmRyBvX2OmdxQg6RUKtGtWzds2bLFqHzLli3o2bOnjaIiMh8/y+QI7O1zzG4pslu5ubk4f/68YTs5ORmJiYnw9fVFeHg44uPj8fjjjyM2NhZxcXH44osvcOXKFUycONGGURNVxM8yOYIG9Tm2yj1YRBawbds2CUCFxxNPPGGo8+mnn0rNmzeXlEql1LVrVykhIcF2ARNVgZ9lcgQN6XPMtaWIiIjIoXDMDRERETkUJjdERETkUJjcEBERkUNhckNEREQOhckNERERORQmN0RERORQmNwQERGRQ2FyQ0RERA6FyQ0RVerSpUsQBKHeVvE1xZkzZ3DnnXfCxcUFMTExtg6HiOwUkxsiOzV+/HgIgoD58+cbla9fvx6CINgoKtuaPXs23N3dcfbsWfz999+2DqdeRUREYPHixbYOg6hBYHJDZMdcXFywYMEC3Lp1y9ahWExxcXGtj71w4QJ69+6N5s2bw8/Pz4JRVU+SJGg0mnq7njXV5edP1FAwuSGyY4MGDUJQUBDmzZtXZZ0333yzQhfN4sWLERERYdgeP348Ro0ahblz5yIwMBA+Pj6YM2cONBoNXnnlFfj6+iI0NBTLly+vcP4zZ86gZ8+ecHFxQXR0NLZv3260//Tp0xg2bBg8PDwQGBiIxx9/HBkZGYb9/fv3x/PPP4/4+Hg0bdoUd999d6XvQxRFvPXWWwgNDYWzszNiYmKwadMmw35BEHD48GG89dZbEAQBb775ZqXn0V/v+eefh4+PD/z8/PD666+j7DJ6q1atQmxsLDw9PREUFISxY8ciPT3dsH/79u0QBAF//fUXYmNj4ezsjJ07d+LChQsYOXIkAgMD4eHhge7du2Pr1q1G14+IiMA777yDcePGwcPDA82bN8evv/6KGzduYOTIkfDw8EDHjh1x6NAho+P27NmDvn37wtXVFWFhYZgyZQry8vIM7+ny5cuYOnUqBEEwarmr7riy8YwfPx7e3t545plnUFxcjOeffx7BwcFwcXFBREREtZ8xooaGyQ2RHZPL5Zg7dy6WLFmCq1ev1ulc//zzD1JTU7Fjxw4sWrQIb775Ju677z40adIE+/fvx8SJEzFx4kSkpKQYHffKK6/g5ZdfxtGjR9GzZ0+MGDECN2/eBACoVCr069cPMTExOHToEDZt2oTr169j9OjRRuf45ptv4OTkhN27d+Pzzz+vNL6PPvoIH3zwARYuXIjjx49jyJAhGDFiBM6dO2e4VnR0NF5++WWoVCpMmzatyveqv97+/fvx8ccf48MPP8RXX31l2F9cXIy3334bx44dw/r165GcnIzx48dXOM/06dMxb948JCUloVOnTsjNzcWwYcOwdetWHD16FEOGDMHw4cNx5coVo+M+/PBD9OrVC0ePHsW9996Lxx9/HOPGjcNjjz2GI0eOoFWrVhg3bpwh4Tpx4gSGDBmCBx54AMePH8dPP/2EXbt24fnnnwcArF27FqGhoXjrrbegUqmgUqlMOk7v/fffR4cOHXD48GG88cYb+Pjjj7FhwwasXr0aZ8+exapVq4ySYaIGzyZrkRNRjZ544glp5MiRkiRJ0p133ilNmDBBkiRJWrdunVT2P93Zs2dLnTt3Njr2ww8/lJo3b250rubNm0tardZQ1rZtW6lPnz6GbY1GI7m7u0s//PCDJEmSlJycLAGQ5s+fb6ijVqul0NBQacGCBZIkSdIbb7whDR482OjaKSkpEgDp7NmzkiRJUr9+/aSYmJga329ISIj07rvvGpV1795dmjRpkmG7c+fO0uzZs6s9T79+/aT27dtLoigayl599VWpffv2VR5z4MABCYCUk5MjSZIkbdu2TQIgrV+/vsa4o6KipCVLlhi2mzdvLj322GOGbZVKJQGQ3njjDUPZ3r17JQCSSqWSJEmSHn/8cenZZ581Ou/OnTslmUwmFRQUGM774YcfGtUx9bhRo0YZ1XnhhReku+66y+hnRORI2HJD1AAsWLAA33zzDU6fPl3rc0RHR0MmK/1PPjAwEB07djRsy+Vy+Pn5GXXPAEBcXJzhtZOTE2JjY5GUlAQAOHz4MLZt2wYPDw/Do127dgB042P0YmNjq40tOzsbqamp6NWrl1F5r169DNcyx5133mnUdRMXF4dz585Bq9UCAI4ePYqRI0eiefPm8PT0RP/+/QGgQgtM+bjz8vIwffp0REVFwcfHBx4eHjhz5kyF4zp16mR4HRgYCABGP2t9mf5nffjwYaxcudLo5zhkyBCIoojk5OQq36epx5V/H+PHj0diYiLatm2LKVOmYPPmzVVeg6ghcrJ1AERUs759+2LIkCGYNWtWhe4TmUxmNJ4EANRqdYVzKBQKo21BECotE0Wxxnj0iYMoihg+fDgWLFhQoU5wcLDhtbu7e43nLHtePUmSLH5nWF5eHgYPHozBgwdj1apV8Pf3x5UrVzBkyJAKg23Lx/3KK6/gr7/+wsKFC9GqVSu4urrioYceqnBc2Z+rPv7KyvQ/a1EU8d///hdTpkypEG94eHiV78XU48q/j65duyI5ORl//vkntm7ditGjR2PQoEH45ZdfqrwWUUPC5IaogZg/fz5iYmLQpk0bo3J/f3+kpaUZJQKWnJtm37596Nu3LwBAo9Hg8OHDhjEdXbt2xZo1axAREQEnp9r/c+Ll5YWQkBDs2rXLcC1AN1i2R48etYq5/Hbr1q0hl8tx5swZZGRkYP78+QgLCwOACoN7q7Jz506MHz8e999/PwAgNzcXly5dMju+8rp27YpTp06hVatWVdZRKpWGlidzjquKl5cXxowZgzFjxuChhx7C0KFDkZmZCV9fX7PPRWRv2C1F1EB07NgRjz76KJYsWWJU3r9/f9y4cQPvvfceLly4gE8//RR//vmnxa776aefYt26dThz5gwmT56MW7duYcKECQCAyZMnIzMzE4888ggOHDiAixcvYvPmzZgwYUKFL+KavPLKK1iwYAF++uknnD17FjNmzEBiYiJefPFFs2NOSUlBfHw8zp49ix9++AFLliwxnCc8PBxKpRJLlizBxYsXsWHDBrz99tsmnbdVq1ZYu3YtEhMTcezYMYwdO9aklq6avPrqq9i7dy8mT56MxMREnDt3Dhs2bMALL7xgqBMREYEdO3bg2rVrhrvRTDmuMh9++CF+/PFHnDlzBv/++y9+/vlnBAUFwcfHp87vhcgeMLkhakDefvvtCl1Q7du3x2effYZPP/0UnTt3xoEDB6q9k8hc8+fPx4IFC9C5c2fs3LkTv/76K5o2bQoACAkJwe7du6HVajFkyBB06NABL774Iry9vY3G95hiypQpePnll/Hyyy+jY8eO2LRpEzZs2IDWrVubHfO4ceNQUFCAHj16YPLkyXjhhRfw7LPPAtC1dK1cuRI///wzoqKiMH/+fCxcuNCk83744Ydo0qQJevbsieHDh2PIkCHo2rWr2fGV16lTJyQkJODcuXPo06cPunTpgjfeeMOoa++tt97CpUuX0LJlS/j7+5t8XGU8PDywYMECxMbGonv37rh06RI2btxo9u+MyF4JUvl/KYmIGrD+/fsjJiaGs/kSNWJM04mIiMihMLkhIiIih8JuKSIiInIobLkhIiIih8LkhoiIiBwKkxsiIiJyKExuiIiIyKEwuSEiIiKHwuSGiIiIHAqTGyIiInIoTG6IiIjIoTC5ISIiIofy/8mRwctyU1lTAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timings_py['n_dim'].values, timings_py['avg_time'].values, label='Python', marker='o')\n",
    "plt.plot(timings_numba['n_dim'].values, timings_numba['avg_time'].values, label='Numba', marker='o')\n",
    "plt.plot(timings_cython['n_dim'].values, timings_cython['avg_time'].values, label='Cython', marker='o')\n",
    "plt.plot(timings_julia['n_dim'].values, timings_julia['avg_time'].values, label='Julia', marker='o')\n",
    "plt.xlabel(\"Number of parameters\")\n",
    "plt.ylabel(\"Average time (seconds)\")\n",
    "plt.legend(loc=0)\n",
    "plt.xscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative speedup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_o_py = timings_py['avg_time'].values/timings_py['avg_time'].values\n",
    "plt.plot(timings_py['n_dim'].values, py_o_py, label='Python/Python', linestyle='--')\n",
    "py_o_n = timings_py['avg_time'].values/timings_numba['avg_time'].values\n",
    "plt.plot(timings_py['n_dim'].values, py_o_n, label='Numba/Python', marker='o')\n",
    "py_o_c = timings_py['avg_time'].values/timings_cython['avg_time'].values\n",
    "plt.plot(timings_numba['n_dim'].values, py_o_c, label='Cython/Python', marker='o')\n",
    "py_o_j = timings_py['avg_time'].values/timings_julia['avg_time'].values\n",
    "plt.plot(timings_py['n_dim'].values, py_o_j, label='Julia/Python', marker='o')\n",
    "# c_o_n = timings_cython['avg_time'].values/timings_numba['avg_time'].values\n",
    "# plt.plot(timings_cython['n_dim'].values, c_o_n, label='Numba/Cython')\n",
    "plt.xlabel(\"Number of parameters\")\n",
    "plt.ylabel(\"Speedup Factor\")\n",
    "plt.legend(loc=0)\n",
    "plt.ylim((0.1,100))\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary/Discussion\n",
    "\n",
    "The Numba and Cython versions exhibit similar performance, with the Numba version just edging out the Cython one for larger numbers of parameters (>100). Both outperform the the Python-only implementation by roughly 2-30x across the sampled numbers of parameters for this benchmark case, with bigger gains at larger numbers of parameters. These results are consistent with results I collected a few years ago on a different machine and with a different benchmark problem: [gao_implementation_scaling_comparison.ipynb](https://github.com/blakeaw/galibrate_performance_comparison/blob/master/gao_implementation_scaling_comparison.ipynb) \n",
    "\n",
    "The newest version which ports key functions to Julia also outperforms the Python version, but only when the number of parameters is large (roughly >=100). Presumably, the Julia functions incur some added overhead for the type inference and translation of data types between Python and Julia that contributes to loss of performance at smaller numbers of parameters. Regardless, the roughly 4-5x speedup at the largest number of parameters sampled is still a notable improvement over the Python version. However, the Numba and Cython versions still offer the best performance.    \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling with population size\n",
    "\n",
    "Now let's examine the scaling with the population size while holding the number of parameters and number of generations fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the parameters for the GAO.\n",
    "# We'll fix the number of parameters at 100:\n",
    "ndim = 100\n",
    "# And the number of generations also to 100:\n",
    "generations = 100\n",
    "# Here, we are scaling the population size.\n",
    "# We'll consider a population size up to 10000,\n",
    "# which in this case is up 100x the number of parameters.\n",
    "popsizes = list([8, 48, 100, 200, 500, 1000, 10000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaling_population(popsizes, version=None, ndim=100, generations=100):\n",
    "    if version is not None:\n",
    "        gao.run_gao = version\n",
    "    timings = dict()\n",
    "    timings['pop_size'] = list()\n",
    "    timings['avg_time'] = list()\n",
    "    timings['std_dev'] = list()\n",
    "    # Loop over the population sizes\n",
    "    for ps in popsizes:\n",
    "        print(\"Doing popsize: \", ps)\n",
    "        timings['pop_size'].append(ps)\n",
    "        sampled_parameters = [SampledParameter(name=i, loc=-100.0, width=200.0) for i in range(ndim)]\n",
    "        go = gao.GAO(sampled_parameters, fitness, ps, generations=generations)\n",
    "        #print(ndim, popsize, gen)\n",
    "        ti = %timeit -n 10 -r 2 -o -q go.run()\n",
    "        timings['avg_time'].append(ti.average)\n",
    "        timings['std_dev'].append(ti.stdev)\n",
    "        print(ti)\n",
    "    timings = pd.DataFrame(timings)\n",
    "    return timings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing popsize:  8\n",
      "50.4 ms ± 703 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  48\n",
      "196 ms ± 503 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  100\n",
      "438 ms ± 32 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  200\n",
      "830 ms ± 21.1 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  500\n",
      "1.96 s ± 23.6 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  1000\n",
      "3.99 s ± 62.1 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  10000\n",
      "40.9 s ± 70.7 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
    {
     "data": {
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       "      <th>0</th>\n",
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       "      <td>0.000703</td>\n",
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       "      <th>1</th>\n",
       "      <td>48</td>\n",
       "      <td>0.196262</td>\n",
       "      <td>0.000503</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.438162</td>\n",
       "      <td>0.031981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>200</td>\n",
       "      <td>0.830432</td>\n",
       "      <td>0.021143</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>1.963161</td>\n",
       "      <td>0.023637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1000</td>\n",
       "      <td>3.994753</td>\n",
       "      <td>0.062105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10000</td>\n",
       "      <td>40.864540</td>\n",
       "      <td>0.070684</td>\n",
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      "text/plain": [
       "   pop_size   avg_time   std_dev\n",
       "0         8   0.050438  0.000703\n",
       "1        48   0.196262  0.000503\n",
       "2       100   0.438162  0.031981\n",
       "3       200   0.830432  0.021143\n",
       "4       500   1.963161  0.023637\n",
       "5      1000   3.994753  0.062105\n",
       "6     10000  40.864540  0.070684"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_py_pop = scaling_population(popsizes, version=run_gao_py, ndim=ndim, generations=generations)\n",
    "timings_py_pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing popsize:  8\n",
      "13.1 ms ± 98.7 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  48\n",
      "32.3 ms ± 3.63 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  100\n",
      "58 ms ± 900 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  200\n",
      "123 ms ± 4.34 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  500\n",
      "208 ms ± 8.56 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  1000\n",
      "414 ms ± 14.5 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  10000\n",
      "4.27 s ± 43.5 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
    {
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       "      <td>0.000099</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>48</td>\n",
       "      <td>0.032316</td>\n",
       "      <td>0.003629</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.057962</td>\n",
       "      <td>0.000900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>200</td>\n",
       "      <td>0.123138</td>\n",
       "      <td>0.004339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>0.208480</td>\n",
       "      <td>0.008564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1000</td>\n",
       "      <td>0.413525</td>\n",
       "      <td>0.014509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10000</td>\n",
       "      <td>4.272179</td>\n",
       "      <td>0.043517</td>\n",
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       "   pop_size  avg_time   std_dev\n",
       "0         8  0.013127  0.000099\n",
       "1        48  0.032316  0.003629\n",
       "2       100  0.057962  0.000900\n",
       "3       200  0.123138  0.004339\n",
       "4       500  0.208480  0.008564\n",
       "5      1000  0.413525  0.014509\n",
       "6     10000  4.272179  0.043517"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_numba_pop = scaling_population(popsizes, version=run_gao_numba, ndim=ndim, generations=generations)\n",
    "timings_numba_pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing popsize:  8\n",
      "12.7 ms ± 1.54 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  48\n",
      "38.5 ms ± 151 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  100\n",
      "60.7 ms ± 1.42 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  200\n",
      "118 ms ± 775 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  500\n",
      "279 ms ± 993 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  1000\n",
      "579 ms ± 59.2 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  10000\n",
      "5.72 s ± 51 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
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       "      <th>0</th>\n",
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       "      <td>0.001539</td>\n",
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       "      <th>1</th>\n",
       "      <td>48</td>\n",
       "      <td>0.038504</td>\n",
       "      <td>0.000151</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.060670</td>\n",
       "      <td>0.001420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>200</td>\n",
       "      <td>0.118443</td>\n",
       "      <td>0.000775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>0.279283</td>\n",
       "      <td>0.000993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1000</td>\n",
       "      <td>0.579013</td>\n",
       "      <td>0.059193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10000</td>\n",
       "      <td>5.721115</td>\n",
       "      <td>0.050956</td>\n",
       "    </tr>\n",
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       "   pop_size  avg_time   std_dev\n",
       "0         8  0.012695  0.001539\n",
       "1        48  0.038504  0.000151\n",
       "2       100  0.060670  0.001420\n",
       "3       200  0.118443  0.000775\n",
       "4       500  0.279283  0.000993\n",
       "5      1000  0.579013  0.059193\n",
       "6     10000  5.721115  0.050956"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_cython_pop = scaling_population(popsizes, version=run_gao_cython, ndim=ndim, generations=generations)\n",
    "timings_cython_pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing popsize:  8\n",
      "269 ms ± 1.2 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  48\n",
      "288 ms ± 3.2 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  100\n",
      "352 ms ± 21.8 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  200\n",
      "451 ms ± 23.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  500\n",
      "682 ms ± 13.2 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  1000\n",
      "1.15 s ± 66.2 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing popsize:  10000\n",
      "9.44 s ± 192 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
    {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>0.269165</td>\n",
       "      <td>0.001201</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>48</td>\n",
       "      <td>0.288260</td>\n",
       "      <td>0.003200</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.351955</td>\n",
       "      <td>0.021752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>200</td>\n",
       "      <td>0.451238</td>\n",
       "      <td>0.023399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>0.681945</td>\n",
       "      <td>0.013154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1000</td>\n",
       "      <td>1.147224</td>\n",
       "      <td>0.066170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10000</td>\n",
       "      <td>9.438376</td>\n",
       "      <td>0.192466</td>\n",
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      "text/plain": [
       "   pop_size  avg_time   std_dev\n",
       "0         8  0.269165  0.001201\n",
       "1        48  0.288260  0.003200\n",
       "2       100  0.351955  0.021752\n",
       "3       200  0.451238  0.023399\n",
       "4       500  0.681945  0.013154\n",
       "5      1000  1.147224  0.066170\n",
       "6     10000  9.438376  0.192466"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_julia_pop = scaling_population(popsizes, version=run_gao_julia, ndim=ndim, generations=generations)\n",
    "timings_julia_pop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Timings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timings_py_pop['pop_size'].values, timings_py_pop['avg_time'].values, label='Python', marker='o')\n",
    "plt.plot(timings_numba_pop['pop_size'].values, timings_numba_pop['avg_time'].values, label='Numba', marker='o')\n",
    "plt.plot(timings_cython_pop['pop_size'].values, timings_cython_pop['avg_time'].values, label='Cython', marker='o')\n",
    "plt.plot(timings_julia_pop['pop_size'].values, timings_julia_pop['avg_time'].values, label='Julia', marker='o')\n",
    "plt.xlabel(\"Population Size\")\n",
    "plt.ylabel(\"Average time (seconds)\")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative speedup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_o_py = timings_py_pop['avg_time'].values/timings_py_pop['avg_time'].values\n",
    "plt.plot(timings_py_pop['pop_size'].values, py_o_py, label='Python/Python', linestyle='--')\n",
    "py_o_n = timings_py_pop['avg_time'].values/timings_numba_pop['avg_time'].values\n",
    "plt.plot(timings_py_pop['pop_size'].values, py_o_n, label='Numba/Python', marker='o')\n",
    "py_o_c = timings_py_pop['avg_time'].values/timings_cython_pop['avg_time'].values\n",
    "plt.plot(timings_numba_pop['pop_size'].values, py_o_c, label='Cython/Python', marker='o')\n",
    "py_o_j = timings_py_pop['avg_time'].values/timings_julia_pop['avg_time'].values\n",
    "plt.plot(timings_py_pop['pop_size'].values, py_o_j, label='Julia/Python', marker='o')\n",
    "plt.xlabel(\"Population Size\")\n",
    "plt.ylabel(\"Speedup Factor\")\n",
    "plt.ylim((0.1,100))\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary/Discussion\n",
    "\n",
    "As with scaling the number of parameters, the Numba and Cython versions exhibit the best performance in all cases. Here too they have similar performance, with the Numba version just edging out the Cython one for larger population sizes (>=500). In this case, both outperform the Python-only implementation by roughly 3-10x across the sampled population sizes for this benchmark case, with bigger gains at larger population sizes. Again, pretty comparable with results I collected a few years ago on a different machine and with a different benchmark problem: [gao_implementation_scaling_comparison.ipynb](https://github.com/blakeaw/galibrate_performance_comparison/blob/master/gao_implementation_scaling_comparison.ipynb) \n",
    "\n",
    "Here, the Julia version outperforms the Python version when the population size is >=100 and achieves a maximum gain of roughly 3x. Below that range of population size, the added overhead of calling the Julia functions again leads to a relative loss of performance. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling with the number of generations\n",
    "\n",
    "Finally, let's examine the scaling with the number of generations while holding the number of parameters and population size fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the parameters for the GAO.\n",
    "# We'll fix the number of parameters at 100:\n",
    "ndim = 100\n",
    "# And the population size to 1000 (10x ndim):\n",
    "popsize = 1000\n",
    "# Here, we are scaling the number of generations.\n",
    "# We'll consider up to 200 generations.\n",
    "ngenerations = list([10, 50, 100, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaling_generations(ngenerations, version=None, ndim=100, popsize=100):\n",
    "    if version is not None:\n",
    "        gao.run_gao = version\n",
    "    timings = dict()\n",
    "    timings['n_generations'] = list()\n",
    "    timings['avg_time'] = list()\n",
    "    timings['std_dev'] = list()\n",
    "    # Loop over the dimensionality (number of parameters)\n",
    "    for ngen in ngenerations:\n",
    "        print(\"Doing ngenerations: \", ngen)\n",
    "        timings['n_generations'].append(ngen)\n",
    "        sampled_parameters = [SampledParameter(name=i, loc=-100.0, width=200.0) for i in range(ndim)]\n",
    "        go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngen)\n",
    "        #print(ndim, popsize, gen)\n",
    "        ti = %timeit -n 10 -r 2 -o -q go.run()\n",
    "        timings['avg_time'].append(ti.average)\n",
    "        timings['std_dev'].append(ti.stdev)\n",
    "        print(ti)\n",
    "    timings = pd.DataFrame(timings)\n",
    "    return timings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing ngenerations:  10\n",
      "330 ms ± 476 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  50\n",
      "1.45 s ± 14.5 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  100\n",
      "2.83 s ± 14.6 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  200\n",
      "5.6 s ± 11.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
    },
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       "   n_generations  avg_time   std_dev\n",
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       "2            100  2.832689  0.014581\n",
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      ]
     },
     "execution_count": 46,
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   ],
   "source": [
    "timings_py_gen = scaling_generations(ngenerations, version=run_gao_py, ndim=ndim, popsize=popsize)\n",
    "timings_py_gen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Doing ngenerations:  10\n",
      "32.2 ms ± 503 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  50\n",
      "134 ms ± 1.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  100\n",
      "265 ms ± 4.88 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  200\n",
      "528 ms ± 1.73 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
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       "      <td>100</td>\n",
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       "      <td>0.004878</td>\n",
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       "   n_generations  avg_time   std_dev\n",
       "0             10  0.032223  0.000503\n",
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       "2            100  0.265397  0.004878\n",
       "3            200  0.527726  0.001735"
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     "execution_count": 47,
     "metadata": {},
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   ],
   "source": [
    "timings_numba_gen = scaling_generations(ngenerations, version=run_gao_numba, ndim=ndim, popsize=popsize)\n",
    "timings_numba_gen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing ngenerations:  10\n",
      "43.2 ms ± 244 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  50\n",
      "181 ms ± 730 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  100\n",
      "360 ms ± 10.4 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  200\n",
      "695 ms ± 5.93 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
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       "      <td>0.043196</td>\n",
       "      <td>0.000244</td>\n",
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       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>0.181007</td>\n",
       "      <td>0.000730</td>\n",
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       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.360353</td>\n",
       "      <td>0.010384</td>\n",
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       "      <td>200</td>\n",
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       "   n_generations  avg_time   std_dev\n",
       "0             10  0.043196  0.000244\n",
       "1             50  0.181007  0.000730\n",
       "2            100  0.360353  0.010384\n",
       "3            200  0.695183  0.005932"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_cython_gen = scaling_generations(ngenerations, version=run_gao_cython, ndim=ndim, popsize=popsize)\n",
    "timings_cython_gen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing ngenerations:  10\n",
      "91.7 ms ± 11.7 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  50\n",
      "369 ms ± 4.97 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  100\n",
      "692 ms ± 931 µs per loop (mean ± std. dev. of 2 runs, 10 loops each)\n",
      "Doing ngenerations:  200\n",
      "1.45 s ± 32.7 ms per loop (mean ± std. dev. of 2 runs, 10 loops each)\n"
     ]
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       "      <th>0</th>\n",
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       "      <td>0.091718</td>\n",
       "      <td>0.011711</td>\n",
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       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>0.368789</td>\n",
       "      <td>0.004966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.692280</td>\n",
       "      <td>0.000931</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>200</td>\n",
       "      <td>1.450889</td>\n",
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       "   n_generations  avg_time   std_dev\n",
       "0             10  0.091718  0.011711\n",
       "1             50  0.368789  0.004966\n",
       "2            100  0.692280  0.000931\n",
       "3            200  1.450889  0.032674"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timings_julia_gen = scaling_generations(ngenerations, version=run_gao_julia, ndim=ndim, popsize=popsize)\n",
    "timings_julia_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Timings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timings_py_gen['n_generations'].values, timings_py_gen['avg_time'].values, label='Python', marker='o')\n",
    "plt.plot(timings_numba_gen['n_generations'].values, timings_numba_gen['avg_time'].values, label='Numba', marker='o')\n",
    "plt.plot(timings_cython_gen['n_generations'].values, timings_cython_gen['avg_time'].values, label='Cython', marker='o')\n",
    "plt.plot(timings_julia_gen['n_generations'].values, timings_julia_gen['avg_time'].values, label='Julia', marker='o')\n",
    "plt.xlabel(\"Number of Generations\")\n",
    "plt.ylabel(\"Average time (seconds)\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative speedup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_o_py = timings_py_gen['avg_time'].values/timings_py_gen['avg_time'].values\n",
    "plt.plot(timings_py_gen['n_generations'].values, py_o_py, label='Python/Python', linestyle='--')\n",
    "py_o_n = timings_py_gen['avg_time'].values/timings_numba_gen['avg_time'].values\n",
    "plt.plot(timings_py_gen['n_generations'].values, py_o_n, label='Numba/Python', marker='o')\n",
    "py_o_c = timings_py_gen['avg_time'].values/timings_cython_gen['avg_time'].values\n",
    "plt.plot(timings_numba_gen['n_generations'].values, py_o_c, label='Cython/Python', marker='o')\n",
    "py_o_j = timings_py_gen['avg_time'].values/timings_julia_gen['avg_time'].values\n",
    "plt.plot(timings_py_gen['n_generations'].values, py_o_j, label='Julia/Python', marker='o')\n",
    "plt.xlabel(\"Number of Generations\")\n",
    "plt.ylabel(\"Speedup Factor\")\n",
    "plt.ylim((0.1,100))\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.legend(loc=0)\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### Summary/Discussion\n",
    "\n",
    "Alhtough the total time increases with number of generations, the relative performance isn't really affected by the number of generations. In this case, the relative performance increases are consistently around 10x, 8x, and 3x for the Numba, Cython, and Julia implementations, respectively. As in the other scaling cases, we can see that the Numba and Cython versions perform the best, but the Julia version still has a notable performance increase over the Python version.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary and Closing Thoughts\n",
    "\n",
    "The analysis here shows that the Numba, Cython, and Julia versions of the GAO can have significantly greater performance than the Python-only version, particularly for large problems (large numbers of parameters and/or population sizes). The Numba and Cython version have comparable performance with the Numba version just mildly outperforming the Cython one for large problems. The Julia version only sees improvement for large problem sizes, with the added overhead of converting data between Pyton and Julia slowing things down some when the numbers of parameters and/or population sizes are small.  \n",
    "\n",
    "In all, the accelearated vesions using Numba, Cython, or Julia can yield relative performance enhancements of anywhere from about 2-30 fold speed increase over the Python-only version depending on the number of model parameters (dimensionality) and choice of GA population size.  \n",
    "\n",
    "In our previous analysis with a different test case (different model and fitness function) we got pretty comparable results in comparing the Python, Numba, and Cython versions: [gao_implementation_scaling_comparison.ipynb](https://github.com/blakeaw/galibrate_performance_comparison/blob/master/gao_implementation_scaling_comparison.ipynb). \n",
    "\n",
    "Based on profiling data, evaluating the fitness function tends to be the major bottleneck. When using the Numba version, it may be possible to JIT the fitness function as well to further improve performance. I may test this further in the future. Also, as of GAlibrate version 0.5.0, the GAO can use multiprocessing-based parallelism when evaluating the fitness function. It would be interesting to more rigorously benchmark the parallel performnace and identify when it may be most helpful. I'm also considering if it may be worth implementing GPU offloading with Numba and its ability to compile CUDA kernels.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}