5_notebook/smoothing_vs_mean_smtherr.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What are the numerical effects of `adapt_object_mesh`?\n",
    "\n",
    "## Abstract\n",
    "\n",
    "Additional iterations of `adapt_object_mesh` are positively correlated with improved smoothness by a reciprocal function. However, it also causes a small, linear increase in volume — an undesirable side-effect.\n",
    "\n",
    "## Introduction\n",
    "\n",
    "`adapt_object_mesh` is a function from CIVET which implements Taubin smoothing of polygonal meshes. Its typical usage is\n",
    "\n",
    "```shell\n",
    "adapt_object_mesh surf.obj smoothed.obj 0 {n_iterations} 0 0\n",
    "```\n",
    "\n",
    "Where `n_iterations` is the parameter for \"number of post-adaptation smoothing iterations\".\n",
    "\n",
    "The purpose of this analysis is to numerically quantify the geometric effects of the `n_iterations` parameter of `adapt_object_mesh` on standard (81,920 triangle) polygonal meshes.\n",
    "\n",
    "## Method\n",
    "\n",
    "The containing directory is a [Datalad](https://datalad.org) repository containing the data read by this Jupyter notebook. Full details are given by the command `git log`. A brief description of the data creation:\n",
    "\n",
    "1. A surface of a sphere with a radius of 25 units was created.\n",
    "2. We ran `surface_fit` using a large Laplacian weight to make the smoothness worse.\n",
    "3. We ran `adapt_object_mesh` with varying number of smoothing iterations \\[0, 1000]\n",
    "\n",
    "Surfaces were evaluated using:\n",
    "\n",
    "- [`pl-smoothness-error`](https://github.com/FNNDSC/pl-smoothness-error) \"smoothness error\": average difference in mean curvature between each vertex and its neighbors\n",
    "- [`pl-pyvista-volume`](https://github.com/FNNDSC/pl-pyvista-volume) \"volume\": volume enclosed by the mesh\n",
    "\n",
    "## Results\n",
    "\n",
    "Non-linear regression between `adapt_object_mesh` smoothing iterations ($I$) and mean smoothness error ($\\overline{E}$), $r^2$=0.9996:\n",
    "\n",
    "$$ \\overline{E}(I)=\\frac{10.937}{I+14.531}+0.020$$\n",
    "\n",
    "The slope between iterations of smoothing and volume was +0.60744, $r^2$=1.000.\n",
    "Note that the starting volume was 71784.749.\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "`adapt_object_mesh` improves smoothness, however there are diminishing returns on the improvement.\n",
    "It has a small side effect of increasing volume.\n",
    "\n",
    "The inverse function of $\\overline{E}(I)$ can be used to minimize the parameter value for `adapt_object_mesh` when trying to achieve a specified target mean smoothness error, $E_T$:\n",
    "\n",
    "$$ \\text{predicted } I(E_T)=\\frac{10.937}{E_T-0.020}-14.531 $$\n",
    "\n",
    "The function $\\text{predicted } I(E_T)$'s domain is constrained by the curve's asymptotes:\n",
    "\n",
    "$$ 0.020 < E_T < \\overline{E}(0) $$\n",
    "\n",
    "Given a surface with a mean smoothness error $E_0$: the minimum parameter value for `adapt_object_mesh` ($P$) which is predicted to be able to improve mean smoothness to $E_T$ where $E_T<E_0$ is\n",
    "\n",
    "$$ \\text{predicted } P(E_0,E_T) = I(E_T) - I(E_0) $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from scipy.optimize import curve_fit\n",
    "from sklearn.metrics import r2_score\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "import os\n",
    "from pathlib import Path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dir = Path(os.getcwd()).parent / '4_adapt_object_mesh'\n",
    "assert data_dir.is_dir()\n",
    "data_files = list(data_dir.glob('*.smtherr.txt'))\n",
    "assert len(data_files) > 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sibling(p: Path, measure: str) -> Path:\n",
    "    glob = p.parent.glob(f'{p.name.split(\".\")[0]}.{measure}.txt')\n",
    "    return next(glob)\n",
    "\n",
    "\n",
    "def read_volume_for(p: Path) -> float:\n",
    "    fname = sibling(p, 'volume')\n",
    "    data = fname.read_text()\n",
    "    return float(data)\n",
    "\n",
    "\n",
    "def parse_iter_smooth(p: Path) -> int:\n",
    "    return int(p.name.split('_')[2])\n",
    "\n",
    "\n",
    "def load_file(t: tuple[int, Path]) -> pd.DataFrame:\n",
    "    i, p = t\n",
    "    data = np.loadtxt(p, dtype=np.float32)\n",
    "\n",
    "    if len(data) != 40962:\n",
    "        raise ValueError(f'{p} contains wrong amount of data, {len(data)} != 40962')\n",
    "\n",
    "    return pd.DataFrame({\n",
    "        'iter_smooth': parse_iter_smooth(p),\n",
    "        'mean_smtherr': data.mean(),\n",
    "        'volume': read_volume_for(p)\n",
    "    }, index=[i])\n",
    "\n",
    "\n",
    "with tqdm(data_files) as pbar:\n",
    "    df = pd.concat(map(load_file, enumerate(pbar)))\n",
    "\n",
    "df.sort_values(by='iter_smooth', inplace=True)\n",
    "df.reset_index(drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression(df: pd.DataFrame):\n",
    "    x = np.array(df['iter_smooth'], dtype=np.float32)\n",
    "    y = np.array(df['volume'], dtype=np.float32)\n",
    "    A = np.vstack([x, np.ones(len(x))]).T\n",
    "\n",
    "    m, c = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "    pred = x * m + c\n",
    "    r2 = r2_score(y, pred)\n",
    "    print(f'y = {m:.4E}*x + {c:.4f}, r^2={r2:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Increase in\n",
    "\n",
    "Ordinary least-squares regression analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(71784.7492231343, 72395.273776247)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.volume.min(), df.volume.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 6.0744E-01*x + 71787.2927, r^2=1.0000\n"
     ]
    }
   ],
   "source": [
    "linear_regression(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x7f136243e440>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(df, x='iter_smooth', y='volume')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-linear Decrease in Smoothness Error\n",
    "\n",
    "Non-linear least-squares regression analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='iter_smooth', ylabel='mean_smtherr'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(df, x='iter_smooth', y='mean_smtherr')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reciprocal_func(x, a, h, k):\n",
    "    return a / (x - h) + k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Workaround: for model fitting we only consider the data points for less than 300 iterations. We include fewer data points to convince `curve_fit` that the steep part of the curve are not outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_left = df[df.iter_smooth < 300]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9996121100213473"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt, pconv = curve_fit(reciprocal_func, df_left.iter_smooth, df_left.mean_smtherr)\n",
    "\n",
    "\n",
    "def predicted_func(x):\n",
    "    return reciprocal_func(x, *popt)\n",
    "\n",
    "prediction = df.iter_smooth.map(predicted_func)\n",
    "r2 = r2_score(df.mean_smtherr, prediction)\n",
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 10.93738233, -14.53134114,   0.01999569])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='iter_smooth', ylabel='mean_smtherr'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w9IhA1zZsnR2ZiYiIPIahRwS/9ulpFLkSIiIi38HQIwJ2ZCYiIvI8hh4RhGn8AQCmphbUm1tEroaIiMg3MPSIIEgpR5BSDoATFBIREXkKQ49IOGydiIjIsxh6RMJ+PURERJ7F0COStqUo+HiLiIjIMxh6RNLW0qPnsHUiIiKPYOgRya99eswiV0JEROQbGHpEYu/TY2JLDxERkScw9IhEx/W3iIiIPIqhRyThv0xQaKizwNxiFbkaIiKiSx9Dj0gGBPhBIW+9/ZUm9ushIiLqaww9IpFIJBf06+EjLiIior7G0COitn49evbrISIi6nMMPSL6dVZmjuAiIiLqaww9IuJcPURERJ7D0COiMDXn6iEiIvIUhh4R/boUBfv0EBER9TWGHhGF/TJXz1mGHiIioj7H0COitpaes7VmWG2CyNUQERFd2hh6RKQNUkImlcBqE2CoY2dmIiKivsTQIyKZVILBwUoA7NdDRETU13ocelpaWiCXy/Hjjz/2RT0+59dh6ww9REREfanHoUculyM6OhpWKxfJdAdOUEhEROQZLj3eevLJJ7Fy5UpUV1e7pYjMzEzExMRApVIhISEBu3fv7vTcnTt3QiKRtNt+/vlnt9TiafalKLj+FhERUZ+Su3LRa6+9hhMnTiAiIgLR0dEIDAx0OP7DDz84/VpZWVlYtmwZMjMzMX36dGzYsAFz587FkSNHMHTo0E6vO3bsGNRqtf330NDQnn8QLxDOx1tEREQe4VLomTdvntsKWLNmDRYvXoz7778fALBu3Tps374d69evR0ZGRqfXDR48GCEhIW6rQyxtc/Uw9BAREfWtHoeelpYWAMCiRYsQFRXVqze3WCzIz8/HihUrHPanpKQgLy+vy2snT56MpqYmjBs3Dk8++SSuvPLKTs81m80wm38dEm4ymXpVtzv9uhQFQw8REVFfcqkj88svv+yWjswGgwFWqxU6nc5hv06nQ0VFRYfXhIeHY+PGjdiyZQu2bt2K0aNHY86cOcjNze30fTIyMqDRaOxbb8OaO124FIUgcIJCIiKivuLS4605c+Zg586dWLhwoVuKkEgkDr8LgtBuX5vRo0dj9OjR9t+TkpJQVlaGl19+GTNnzuzwmpUrVyI9Pd3+u8lk8prgM1jdOk+PpcWG8w3NGBCoELkiIiKiS5NLoWfu3LlYuXIlfvzxRyQkJLTryHzzzTc79TparRYymaxdq05lZWW71p+uTJs2De+//36nx5VKJZRKpdOv50lKuQzaIAUMdRbojU0MPURERH3EpdDz+9//HkBrJ+SLSSQSpx99KRQKJCQkICcnB7feeqt9f05ODm655Ran6ykoKEB4eLjT53sbnVoFQ50FFaZGjItQd38BERER9ZhLocdms7mtgPT0dCxYsACJiYlISkrCxo0bUVpairS0NACtj6bKy8uxefNmAK2ju4YNG4bx48fDYrHg/fffx5YtW7Blyxa31eRp4RoVfjpj4lIUREREfcil0HOhpqYmqFQql69PTU1FVVUVVq1aBb1ej7i4OGRnZyM6OhoAoNfrUVpaaj/fYrHgj3/8I8rLy+Hv74/x48fj3//+N66//vrefhTRtC1FcZahh4iIqM9IBBeGDFmtVjz//PN46623cPbsWRw/fhzDhw/Hn//8ZwwbNgyLFy/ui1rdxmQyQaPRwGg0OkxwKJY3d5zAS9uP4Y6ESLx0x0SxyyEiIvJKvf377dIyFP/3f/+HTZs24cUXX4RC8WvH2wkTJuDtt9925SV9mo5z9RAREfU5l0LP5s2bsXHjRtxzzz2QyWT2/fHx8f12DSwxXThXDxEREfUNl0JPeXk5RowY0W6/zWZDc3Nzr4vyNezTQ0RE1PdcCj3jx4/vcCX0Tz75BJMnT+51Ub6mbSmKWnMLvj1xDifP1cHYYBG5KiIiokuLS6O3nn76aSxYsADl5eWw2WzYunUrjh07hs2bN+OLL75wd42XPGNjM2RSCaw2Afe8/R0AYOZILVbPj0dEiL/I1REREV0aXGrpuemmm5CVlYXs7GxIJBI89dRTOHr0KP71r3/hmmuucXeNlzRjgwWPbzkEq81xEF1uoQErthxiiw8REZGbuDxPz7XXXotrr73WnbX4JEOdBbsLDR0eyy00wFBngSaAS1MQERH1Vq8mJ7RYLKisrGw3Q/PQoUN7VZQvMTV13fG7tpvjRERE5ByXQk9hYSEWLVqEvLw8h/1tq6M7u/YWAWqVX5fHg7s5TkRERM5xKfQsXLgQcrkcX3zxBcLDwyGRSNxdl8/QBikwc6QWuR084po5UgttEB9tERERuYNLoefAgQPIz8/HmDFj3F2Pz9EEKLB6fjz+8FEBvi+pse+fOVKLF+bHsz8PERGRm7g0emvcuHEwGDrufEs9FxHij7/em4DBwUoAwAvzJ+D1uyYjnMPViYiI3Mbp0GMymezbCy+8gD/96U/YuXMnqqqqHI6ZTKa+rPeSFRKoxIyRoQCAkqoGtvAQERG5mdOPt0JCQhz67giCgDlz5jicw47MvZMcOwhbfjiNvJNVYpdCRER0yXE69OzYsaMv6yAASbGDAACHTp+Hqam525FdRERE5DynQ8+sWbPsP5eWliIqKqrdqC1BEFBWVua+6nxMRIg/YrSBKDbU4/viaswZqxO7JCIiokuGSx2ZY2JicO7cuXb7q6urERMT0+uifNm04a2tPXzERURE5F4uhZ62vjsXq6urg0ql6nVRviw5lqGHiIioL/Ronp709HQAgEQiwZ///GcEBATYj1mtVvz3v//FpEmT3Fqgr2lr6TmqN6G63oKBgRzFRURE5A49Cj0FBQUAWlt6Dh8+DIXi1z/ICoUCEydOxB//+Ef3VuhjQoOVGK0LxrGztdhXVIXrJ4SLXRIREdEloUehp20E129/+1u8+uqrUKvVfVKUr0uKHYRjZ2uRd9LA0ENEROQmLvXpee+99xh4+hD79RAREbmfS2tvNTU14fXXX8eOHTtQWVkJm83mcPyHH35wS3G+aurwQZBKgKJz9ThraoJOzc7hREREveVS6Fm0aBFycnJw++234/LLL+cq626m8fdD3BANDp02Yu/JKsybPETskoiIiPo9l0LPv//9b2RnZ2P69Onurod+kRQ7CIdOG5F30sDQQ0RE5AYu9ekZMmQIgoOD3V0LXSCJkxQSERG5lUuh55VXXsHjjz+OkpISd9dDv7hs2EDIpRKcrmlEWXWD2OUQERH1ey6FnsTERDQ1NWH48OEIDg7GwIEDHTbqvUClHJOiQgAAeScN4hZDRER0CXCpT89dd92F8vJyPP/889DpdOzI3EeSYwdhf0kN8k5WIfWyoWKXQ0RE1K+5FHry8vKwd+9eTJw40d310AWSYrV47ZsTyDtZ1el6Z0REROQclx5vjRkzBo2Nje6uhS4yeWgIlHIpztWacfJcndjlEBER9WsuhZ7Vq1dj+fLl2LlzJ6qqqmAymRw2cg+VnwyJwwYA4CguIiKi3nLp8dZ1110HAJgzZ47D/rZHMFartfeVEQAgOVaLb09UYe/JKtybNEzscoiIiPotl0JP28Kj1Pem/TJfz96iKthsAqRS9ushIiJyhUuhZ9asWe6ugzoRH6lBoEKG8w3NOFphwvgIjdglERER9Usu9enZtm0b9uzZY//9zTffxKRJk3D33XejpqbGbcUR4CeT4vKY1rmP9rJfDxERkctcCj2PPfaYvcPy4cOHkZ6ejuuvvx5FRUVIT0/v8etlZmYiJiYGKpUKCQkJ2L17t1PXffvtt5DL5Zg0aVKP37M/SY7VAmBnZiIiot5wKfQUFxdj3LhxAIAtW7bgpptuwvPPP4/MzEx8+eWXPXqtrKwsLFu2DE888QQKCgowY8YMzJ07F6WlpV1eZzQace+997brTH0pSopt7dfz36IqNFttIldDRETUP7kUehQKBRoaWteD+vrrr5GSkgIAGDhwYI+HrK9ZswaLFy/G/fffj7Fjx2LdunWIiorC+vXru7zuwQcfxN13342kpCRXPkK/Mi5cDY2/H+otVhwuN4pdDhERUb/kUui54oorkJ6ejr/85S/47rvvcMMNNwAAjh8/jsjISKdfx2KxID8/3x6a2qSkpCAvL6/T69577z2cPHkSTz/9tFPvYzab+/VcQlKpxL7qOvv1EBERucal0PPGG29ALpfj008/xfr16zFkyBAAwJdffmmfw8cZBoMBVqsVOp3OYb9Op0NFRUWH1xQWFmLFihX44IMPIJc7N/gsIyMDGo3GvkVFRTldo7dIHtEaerj4KBERkWtcGrI+dOhQfPHFF+32r1271uH31atXIy0tDSEhIV2+3sVrSnW2zpTVasXdd9+NZ599FqNGjXK63pUrVzp0sDaZTP0u+CT/0q9n/6kamFusUMplIldERETUv7jU0uOs559/HtXV1Z0e12q1kMlk7Vp1Kisr27X+AEBtbS3279+PJUuWQC6XQy6XY9WqVTh48CDkcjm++eabDt9HqVRCrVY7bP1NbGgQQoOVMLfYUFB6XuxyiIiI+p0+DT2CIHR5XKFQICEhATk5OQ77c3JykJyc3O58tVqNw4cP48CBA/YtLS0No0ePxoEDBzB16lS31u9NJJJf+/Vw6DoREVHPufR4y53S09OxYMECJCYmIikpCRs3bkRpaSnS0tIAtD6aKi8vx+bNmyGVShEXF+dw/eDBg6FSqdrtvxQlxw7C5wfPYO9JA3CN84/3iIiIyAtCT2pqKqqqqrBq1Sro9XrExcUhOzsb0dHRAAC9Xt/tnD2+om2SwoLS82iwtCBAIfp/fERERP2GROjuGVQvBAcH4+DBgxg+fHhfvYVLTCYTNBoNjEZjv+rfIwgCrnhhB8rPN+Jviy7HrFGhYpdERETkMb39+92nfXrIvSQSiX0UF4euExER9Uyfhp4ZM2bA39+/L9/C57TN18NJComIiHrG5U4hNpsNJ06cQGVlJWw2x/WgZs6cCQDIzs7uXXXUTtLw1n49P5YbYWxohibAT+SKiIiI+geXQs++fftw9913o6SkpN2wdIlEAqvV6pbiqL0wjQrDtYEoMtTjv8VVSBkfJnZJRERE/YJLj7fS0tKQmJiIH3/8EdXV1aipqbFvXU1GSO6RFMv5eoiIiHrKpZaewsJCfPrppxgxYoS76yEnJMdq8cF/S7GviKGHiIjIWS619EydOhUnTpxwdy3kpGnDBwIAfq6ohaHOLHI1RERE/YNLLT2PPPIIli9fjoqKCkyYMAF+fo6daePj491SHHVsUJASY8KC8XNFLfYVVeHG+AixSyIiIvJ6LoWe+fPnAwAWLVpk3yeRSOyro7Mjc99LjtXi54pa5J1k6CEiInKGS6GnuLjY3XVQDyXHDsK73xZzvh4iIiInuRR62tbFIvFcPnwgpBKg2FCPM+cbERHCSSCJiIi60qsVK48cOYLS0lJYLBaH/TfffHOviqLuqVV+mBAZgoNl57H3ZBXmJ0SKXRIREZFXcyn0FBUV4dZbb8Xhw4ftfXmA1n49ANinx0OShg/CwbLzyGPoISIi6pZLQ9b/8Ic/ICYmBmfPnkVAQAB++ukn5ObmIjExETt37nRzidSZtsVH9540tJsZm4iIiBy5FHr27t2LVatWITQ0FFKpFFKpFFdccQUyMjKwdOlSd9dInUgcNgB+MgnOGJtQUtUgdjlERERezaXQY7VaERQUBADQarU4c+YMgNYOzseOHXNfddSlAIUck6MGAAD2cnZmIiKiLrkUeuLi4nDo0CEArbMzv/jii/j222+xatUqDB8+3K0FUte4DhcREZFzXAo9Tz75JGw2GwDgueeeQ0lJCWbMmIHs7Gy89tprbi2QusZ+PURERM5xafTWtddea/95+PDhOHLkCKqrqzFgwAD7CC7yjElDQ6Dyk8JQZ0FhZR1G6YLFLomIiMgrudTS0+bEiRPYvn07GhsbMXDgQHfVRD2glMtw2bDWe593wiByNURERN7LpdBTVVWFOXPmYNSoUbj++uuh1+sBAPfffz+WL1/u1gKpe9OGs18PERFRd1wKPY8++ij8/PxQWlqKgIAA+/7U1FRs27bNbcWRc+KHaAAA35404PjZWhgbLN1cQURE5Htc6tPz1VdfYfv27YiMdJwFeOTIkSgpKXFLYeScM+cbsSH3JACg3mxFytpczBypxer58VyPi4iI6AIutfTU19c7tPC0MRgMUCqVvS6KnGNssODxLYew54TjY63cQgNWbDnEFh8iIqILuBR6Zs6cic2bN9t/l0gksNlseOmll3DllVe6rTjqmqHOgt2FHXdezi00wFDH0ENERNTGpcdbL730EmbPno39+/fDYrHgT3/6E3766SdUV1fj22+/dXeN1AlTU3OXx2u7OU5ERORLXGrpGTduHA4ePIjLL78c11xzDerr63HbbbehoKAAsbGx7q6ROqFW+XV5PLib40RERL7EpZYeABgwYABuuOEGXHbZZfbZmb///nsAwM033+ye6qhL2iAFZo7UIreDR1xDQlTQBilEqIqIiMg7uRR6tm3bhnvvvRdVVVXtlj6QSCSwWq1uKY66pglQYPX8eKzYcqhd8Kmub4aNq1IQERHZufR4a8mSJbjjjjtw5swZ2Gw2h42Bx7MiQvzx+l2T8Z/0WfjnQ8n4+tGZGB0WjMZmKzbv5fQBREREbVwKPZWVlUhPT4dOp3N3PeQCTYACsYODMGnoAIzQBePhK0cAADblFaPB0iJydURERN7BpdBz++23Y+fOnW4uhdzl+rgwRA30R01DM/7xfZnY5RAREXkFiXBxpxwnNDQ04I477kBoaCgmTJgAPz/HUUJLly51W4F9wWQyQaPRwGg0Qq1Wi11On/j7vhL8+Z8/YkiIP3Y+Nht+sl6tLUtERCS63v79dqkj84cffojt27fD398fO3fuhEQisR+TSCReH3p8wR0JkXj16+MoP9+ILw6dwa2TI7u/iIiI6BLm0v/9f/LJJ7Fq1SoYjUacOnUKxcXF9q2oqMjdNZILVH4y/HZ6DADgrZ1F7UbZERER+RqXQo/FYkFqaiqkUj4y8Wb/My0aQUo5jp2txY5jlWKXQ0REJCqXUst9992HrKwstxWRmZmJmJgYqFQqJCQkYPfu3Z2eu2fPHkyfPh2DBg2Cv78/xowZg7Vr17qtlkuJxt8Pd08dCgBYv/OkyNUQERGJy6U+PVarFS+++CK2b9+O+Pj4dh2Z16xZ4/RrZWVlYdmyZcjMzMT06dOxYcMGzJ07F0eOHMHQoUPbnR8YGIglS5YgPj4egYGB2LNnDx588EEEBgbid7/7nSsf55K2+IoYbPr2FL4/VYP9p6qROGyg2CURERGJwqXRW12tpC6RSPDNN984/VpTp07FlClTsH79evu+sWPHYt68ecjIyHDqNW677TYEBgbi73//u1Pn+8LorQut2HIIH39fhqvHDsbb910mdjlEREQuEWX01o4dO1y5rB2LxYL8/HysWLHCYX9KSgry8vKceo2CggLk5eXhueee6/Qcs9kMs9ls/91kMrlWcD/1u5nDkbW/DF8frcSxilqMDgsWuyQiIiKPE7UnssFggNVqbTezs06nQ0VFRZfXRkZGQqlUIjExEQ8//DDuv//+Ts/NyMiARqOxb1FRUW6pv78YHhqE68aHAQA25LJvDxER+SavGH514Tw/ACAIQrt9F9u9ezf279+Pt956C+vWrcNHH33U6bkrV66E0Wi0b2VlvjdLcdqsWADA5wfOoPx8o8jVEBEReZ5Lj7fcRavVQiaTtWvVqays7HZdr5iY1jloJkyYgLNnz+KZZ57BXXfd1eG5SqUSSqXSPUX3UxOjQpAcOwh5J6vw9u4iPH3TeLFLIiIi8ihRW3oUCgUSEhKQk5PjsD8nJwfJyclOv44gCA59dqhjv5/d2trz8XdlqK63iFwNERGRZ4na0gMA6enpWLBgARITE5GUlISNGzeitLQUaWlpAFofTZWXl2Pz5s0AgDfffBNDhw7FmDFjALTO2/Pyyy/jkUceEe0z9BdXjNBifIQaP50x4W95p/DoNaPELomIiMhjRA89qampqKqqwqpVq6DX6xEXF4fs7GxER0cDAPR6PUpLS+3n22w2rFy5EsXFxZDL5YiNjcXq1avx4IMPivUR+g2JRILfz47Fkg8L8Le9p/DgrOEIUIj+FSAiIvIIl+bp6e98bZ6eC1ltAq56ZSdKqhrw1I3jsOiKGLFLIiIickpv/357xegt8hyZVILfzRwOAHh7dxGarTaRKyIiIvIMhh4fNH9KJLRBSpwxNuHzA2fELoeIiMgjGHp8kMpPhkVXDAMAvLXrJGw2n3vCSUREPoihx0f9z7RoBCvlKKyswzc/V4pdDhERUZ9j6PFRapUf7pnWOkJu/S4uTUFERJc+hh4ftmj6MChkUuSX1OD7U9Vil0NERNSnGHp82GC1CvMTIgEA63eytYeIiC5tDD0+7nczh0MC4JufK/HPgtM4ea4OxgYuUUFERJceTsfr45RyKQYFKWCos2BZ1kEAwMyRWqyeH4+IEH+RqyMiInIftvT4MGODBY9vOQRDnWPLTm6hASu2HGKLDxERXVIYenyYoc6C3YWGDo/lFhrahSEiIqL+jKHHh5mamrs8XtvNcSIiov6EoceHqVV+XR4P7uY4ERFRf8LQ48O0QQrMHKnt9PgPpTUerIaIiKhvMfT4ME2AAqvnx7cLPlEDWkdtrfrXEZRWNYhRGhERkdtJBEHwudUmTSYTNBoNjEYj1Gq12OWIzthggaHOgtqmZgSr/BASIMfv/v4D8ktqMDFSg0/SkqGQMx8TEZG4evv3m3/JCJoABWIHB2HS0AGIHRyEQUEqvHbXZGj8/XDwtBEvf3VM7BKJiIh6jaGHOjQkxB8v3h4PANiYW4Qdx7gSOxER9W8MPdSpa8eHYWHyMADA8n8cRIWxSdyCiIiIeoGhh7q08voxGB+hRnW9BcuyCmC1+VwXMCIiukQw9FCXlHIZXr9rMgIUMuwrqsbr3xSKXRIREZFLGHqoW8NDg/B/t8YBAF77TyH2FVWJXBEREVHPMfSQU26dHInbEyJhE4A/fFyAqjqz2CURERH1CEMPOW3VLeMRGxqIsyYz/vjJQdjYv4eIiPoRhh5yWoBCjjfungKFXIodx87hnT3FYpdERETkNIYe6pGx4Wo8deM4AMAL237GgbLz4hZERETkJIYe6rF7pg7F9RPC0GIT8MhHP8DU1Cx2SURERN1i6KEek0gkyLgtHpED/FFW3YhHPizADyXVOHmuDsYGi9jlERERdYgLjnLBUZd9feQsHti8Hxd+gWaO1GL1/HhEhPiLVhcREV2auOAoicLYYMHf9p7CxYk5t9CAFVsOscWHiIi8DkMPucRQZ8HuQkOHx3ILDTDUMfQQEZF3Yeghl3TXebmWnZuJiMjLMPSQS9Qqvy6P53bSCkRERCQWhh5yiTZIgZkjtZ0eX5NzHBtzT3qwIiIioq4x9JBLNAEKrJ4f3y74zBgxCAumDQUAPJ/9M17efgw+OECQiIi8kFzsAqj/igjxx+t3TYahzoLapmYEq/ygDVJAE6BAeIg/Xtx2DG/sOAFTUzOeuWk8pFKJ2CUTEZEP84qWnszMTMTExEClUiEhIQG7d+/u9NytW7fimmuuQWhoKNRqNZKSkrB9+3YPVksX0gQoEDs4CJOGDkDs4CBoAhQAgIdmj8Bz8+IgkQCb95Zg+ScH0Wy1iVwtERH5MtFDT1ZWFpYtW4YnnngCBQUFmDFjBubOnYvS0tIOz8/NzcU111yD7Oxs5Ofn48orr8RNN92EgoICD1dO3fmfadFYlzoJcqkEnxWU4/fv56Op2Sp2WURE5KNEn5F56tSpmDJlCtavX2/fN3bsWMybNw8ZGRlOvcb48eORmpqKp556yqnzOSOzZ33z81n8/v0fYG6xIWn4IPz1vkQEKflklYiIeqZfz8hssViQn5+PlJQUh/0pKSnIy8tz6jVsNhtqa2sxcODATs8xm80wmUwOG3nOVWN0+NuiyxGklGNvURXu+es+1NRz8kIiIvIsUUOPwWCA1WqFTqdz2K/T6VBRUeHUa7zyyiuor6/HnXfe2ek5GRkZ0Gg09i0qKqpXdVPPTRs+CB89MA0DAvxw8LQRd27Yiwpjk9hlERGRDxG9Tw/Qumr3hQRBaLevIx999BGeeeYZZGVlYfDgwZ2et3LlShiNRvtWVlbW65qp5yZEavCPB5MQplahsLIOd2zIw0/l53Gysg4FpTVcpZ2IiPqUqB0rtFotZDJZu1adysrKdq0/F8vKysLixYvxySef4Oqrr+7yXKVSCaVS2et6qfdG6oLxSVoS/ued/6KkqgG3Zu6F5YJRXVylnYiI+oqoLT0KhQIJCQnIyclx2J+Tk4Pk5OROr/voo4+wcOFCfPjhh7jhhhv6ukxys6iBAXj3vkQEKGQOgQfgKu1ERNR3RB9Ck56ejgULFiAxMRFJSUnYuHEjSktLkZaWBqD10VR5eTk2b94MoDXw3HvvvXj11Vcxbdo0eyuRv78/NBqNaJ+DekqCBkvHw9fbVmlvm/OHiIjIHUQPPampqaiqqsKqVaug1+sRFxeH7OxsREdHAwD0er3DnD0bNmxAS0sLHn74YTz88MP2/ffddx82bdrk6fLJRVylnYiIPE30eXrEwHl6xHeysg5z1uzq9PjDs2OxPGU0l64gIiK7fj1PD/mu7lZpf3PnSdzz9n9xuqbBg1UREdGljKGHRNHVKu2PpYyCv58Me4uqcN263fjH/jKu1E5ERL3Gx1t8vCUqY4Olw1XaTxnqsfyTg8gvqQEAXD1Wh4zbJiA0mFMPEBH5qt7+/WboYejxWlabgL/uLsKar47DYrVhYKAC/zcvDnMnhItdGhERiYChxwUMPf3LzxUmPJp1EEf1rWumzZsUgWdvjgMgwFBngampGWp/P2gDFRzmTkR0CWPocQFDT/9jabHhtf8UInPnCdgEIDRYCV2wEj+e+XXxWM7mTER0aePoLfIJCrkUf7x2NLb8PhnRgwJwrtbsEHgAzuZMRERdY+ihfmXy0AHIvHtKp8fbZnMmIiK6GEMP9TsXr9d1MVMjQw8REbXH0EP9jlrl1+XxZ/51BPkl1R6qhoiI+guGHup3uprNWSIBDp42Yv76vVi06Xv8dMbo4eqIiMhbMfRQv9PZbM4zR2qxNS0Zv7ksCjKpBN/8XIkbXtuDJR/+gJPn6kSqloiIvAWHrHPIer/V2WzOAFB0rg5rvy7Evw6eAQBIJcDtCZFYOmckIgcEOFzPeX6IiPoHztPjAoYe33HkjAlrco7h66OVAACFTIq7pw7F7QmReGHbz9hdaLCfy3l+iIi8G0OPCxh6fE9+SQ1e2v4z9hW1dnCWSgBbB9/8mSO1eP2uyWzxISLyQpyckMgJCdED8NED0/D+4qkYExbcYeABOM8PEdGljKGHfIZEIsEVI7V4/ta4Ls/jPD9ERJcmhh7yORr/rh9d/SHrIN7dUwxjY7OHKiIiIk9g6CGf09U8PzKJBKXVDVj1xRFMff5rPP7pIRw+3X6uH2ODBScr61BQWoOT5+q43hcRUT/AjszsyOyTzpxvxIoth5B70eitp24ch73F1fhgXwl+rqi1H5sYFYL/mToUN02MQHW9BY9vOcSRX0REHsbRWy5g6CGg63l+BEHA/pIavL+vBNmH9Wi2tv7XRK2SI1glR/n5pnavx5FfRER9i6HHBQw91BOGOjP+sb8MH+wrRfn5xi7P/U/6LMQODvJQZUREvoVD1on6mDZIiYdmj0Dun67EE9eP6fLc6nqzh6oiIqKeYughcpJMKsFVY3RdnvPbTfux/B8HsePnSlhabJ2ex47QRESeJxe7AKL+pG3k14UdoNsoZBLUmVuw5YfT2PLDaahVclwzLgw3xIfhihGhUMhb/z/GmfON7AhNRCQC9ulhnx7qoc5Gfj1/6wSUn29E9mE9sn+swLnaXx91BavkSBkXhtmjtPh4fxm+PVHV7nXZEZqIqGvsyOwChh7qra5GfgGA1SZg/6nqDgNQV9gRmoioc739+83HW0Qu0AQoumyRkUklmDp8EKYOH4SnbhpvD0CfHzyDmobOZ3p2dgmMttBlamqG2t8P2sCu6yEiIrb0sKWHPOp4RS1S1uV2ejxMrcJVYwdj5kgtkmK10Pj7tTuHfYKIyFfx8ZYLGHpILMYGCx75qKDDjtASABf+l1EmlWBSVAhmjNRixshQTIzUoN7cgiUfFTgEnjbsE0RElzqGHhcw9JCYOusI/fRN41BS3YDc4wbkFp5D0bl6h+vUKjkmRoV0GHjasE8QEV3K2KeHqJ+JCPHH63dN7rAjdOzgYPtcQKdrGrC70IDdheewp9AAU1NLl4EHAGqbul8Znv2BiMhXsaWHLT3UD1htAg6ePo//V1COv+0t6fS8K0ZoMWtUKBKHDcD4CI19bqA27A9ERP0ZH2+5gKGH+quu+gRdTCmXYmJUCBKjByBx2ACMDA3C//7zR/YHIqJ+i4+3iHyIJkCB1fPj2/UJuiJ2EP5nWjSKqxqQX1KN/JIa1DQ047vianxXXN3t6+YWGmCoszgVevh4jIj6K4Yeon6mqz5BrWIhCAJOnqtHfkk19p+qQX5JDYoM9V2+7r8OnsGNE8MRow2CTCrp8Bw+HiOi/swrHm9lZmbipZdegl6vx/jx47Fu3TrMmDGjw3P1ej2WL1+O/Px8FBYWYunSpVi3bl2P3o+Pt8gX5Z+qxvy39nZ7nr+fDOMi1JgwRIPxEWrEDdFgxOAgNHC4PBGJrN8/3srKysKyZcuQmZmJ6dOnY8OGDZg7dy6OHDmCoUOHtjvfbDYjNDQUTzzxBNauXStCxUT904jBQZ0ulhqhUWGwWoXjZ2vRYLEiv6S1daiNQi7FcG0gfq6o7fC1nX08xkdjRCQm0Vt6pk6diilTpmD9+vX2fWPHjsW8efOQkZHR5bWzZ8/GpEmT2NJD5KTO5gh6YX48wkP8YbUJKDbU4cdyE34sN+JwuRFHzphQa27p9rWXXzMKKePDEKMNbDdqrO29+WiMiHqjX7f0WCwW5OfnY8WKFQ77U1JSkJeX57b3MZvNMJt/XfDRZDK57bWJ+pPu+gPJpBKMGByMEYODMW/yEACAzSagtLoBXx89i+f+fbTT134l5zheyTkOuVSCGG0gRumCMVIXhNG6YIRrVHj5q2PYc9Hq8rmFBqzYcsjpR2NsKSKi3hA19BgMBlitVuh0Oof9Op0OFRUVbnufjIwMPPvss257PaL+rLvFUi8mlUowTBuIOxIikXv8XIePx8LUSujUKpw8V486cwsKK+tQWFkHHO7+9Z19NMaWIiLqLdH79ACAROI4UkQQhHb7emPlypVIT0+3/24ymRAVFeW21yfyBZ0Nl7/w8ZggCNAbm3D8bO0vWx0Kz9bi54pamFtsnb72nRv2YpQuGMO0gRiuDUSMNhAxoYGIGhAAhVwKY4OlXeABetZSxFYiIhI19Gi1WshksnatOpWVle1af3pDqVRCqVS67fWIfFV3j8ckEgkiQvwREeKP2aMH268rPFuLa9Z2vrp8Vb0Fe4uqsLfI8fGXTCpB5AB/6IJV+O5Ux/MNOdNSxFYiIgJEDj0KhQIJCQnIycnBrbfeat+fk5ODW265RcTKiKgzPX08BgCDg5WdjhxLGj4QD80egXN1ZhQb6h22BosVJVUNKKlq6PL1n88+iolRIYga6I+oAQGIGhiA0CAlpFKJW1qJALYUEV0KRH+8lZ6ejgULFiAxMRFJSUnYuHEjSktLkZaWBqD10VR5eTk2b95sv+bAgQMAgLq6Opw7dw4HDhyAQqHAuHHjxPgIRNQNZx6NXUwQBJyrNaPIUI/viqqx5uvjnb7+f36uxH9+rnTYp5RLMWSAP7SByl61EgFsKSK6VIg+ZB1onZzwxRdfhF6vR1xcHNauXYuZM2cCABYuXIhTp05h586d9vM76u8THR2NU6dOOfV+HLJOJI621pKOZ5Lu+rrO1hwbrQvCnLE6nKs1o6ymAWXVjdAbG2Fz8n/ZJgzRYHRYMCI0KoT/8miu7ecgpRzGBkuvJ2VkKxGRe3DBURcw9BD1P93NMXShZqsN+vNNKKtpQP6pmi5bibqiVskxKEiJ4i6W8Pj60ZkYoQvusm62EhG5B0OPCxh6iPonV1qKumolih+ixp2XRcHY2ILy843Qn2+E3tiE8vONqG3qfkJGoPUxWvgvM1rr1CrogluH7w9WKxGslCNz50nsv2B26zY9WbqDLUVErRh6XMDQQ+RbetJK1KbO3AL9+UbsP1WDlZ85MeGQC+6/IgajwoIRGqxEaJASocFKDAxUwE/264zW7mgpYmiiSwVDjwsYeoh8T1/0J5oeOwgr545BQ7MNZ01NOGtqQmWtGRXG1p9LqxugNzb1uNaBgQpogxQYEKBAkaEe52rN7c65fNgAvPqbyZ2Gtja9DU0MTORNGHpcwNBDRD3hSksRAJysrMOcNbs6PZ4yToemFhsMtWYY6syoqrfA6mwP7F+o/KQYFKjEoCAFBga2boMCFRgYqESAQoqs70/jiL790jvOPF5jKxN5G4YeFzD0EFFPubs/UUehw2YTUNNgwbk6Mwy1Fnx/qhqv/qfQ7Z+lTfwQDcJDVBgQoEBIgAIDAvwwILC1hclPKsHrOwqRX3Leqdo7wlYmcjeGHhcw9BCRp7jaSgR031L0ryXTofFXwFBvRnWdBdX1FlTVW1Bdb0ZVnQXFVfUoKD3vro/iYPaoUAwZ4A+Nvx9CAvyg8feDxl/xy79+kEmAZ784gryTVe2uZSsTuYqhxwUMPUTkSX3Rn8iZ4NBdaPrzDWOhkEtR09CMmgYLzjc0o7regvMNFlSYmnDW1L4vkbvcGB+OyAEBUPvLoVb5Qe3vB7VKDrW/H6QAMr78Gf8tbj+pJFuZfBtDjwsYeoiov+hNS1FvQlN3gemh2bHwk0lhbGyGsbEZ5xssrf82NsPU2IyahuYe909y1hUjtAjTqBCskiNYKUewyq/1Z5UfglRySCFg3X9cfzTHVibvxdDjAoYeIupPXG0pAlwPTb1tZTpxthZXd7HI7H1J0ZBJpTA1tYak1n9bYGpqbXWqN1ud+nyuGBsWDG2wEoEKOYJUcgQpW7dApRxyKfBp/mkcO1vX7rrk4QPx5j1TMCCw6wWs2crUdxh6XMDQQ0S+xNXQ5K2tTH+YMxJKPylqm1pQ19SC2qZm1Da1oNbcgtqmFlTVmVHZwTB/d/H3kyFQKUegUoZAReu/AYrW4CSXSfD9qWqcOd9+qoK4CDXSrxmFwWoVAhSt1wQoZQjwk0H+y9xMYrcyeXvgYuhxAUMPEZFz+mMrU3ehadXN4xHsL0ddUwvqzFbUmZtRb7aitqkF5ecbsK+o4wVq+5JCLkWAnwyNzVaYW2ztjuvUSlw5ejBCAhQIUMjg7yeDv0L2S3iSQeXXGqLqzS1446JRdzNGDMILt0/sNjSJHbicwdDjAoYeIiLPuNRambakJSE0WIV6SwvqzS2ot1hb//1lO1FZh/f/W9rp9REhKlhtAhosVjRYrH3W7+liUgmg8fdDoFJuD0wqv1/Ck58MMqkE+SU1qDC1b6EarQvC/TOGY2CgAv5+Mih/uUblJ7W/hspPhqp6M1ZuPdyn68wx9LiAoYeIyPtdiq1M/0mfhdjBQQAAQRBgsdrQYLai3tKCH0pqsPTjA51ee0dCJIJVfmhstqLR0oIGi/WXn1sDlLGxGeXnGzu9Xiw9WWeuO739+y3vdQVERER9QBPg+qORiBB/vH7X5B6HJk2AAqvnx3camLq7XhukwMyR2k5Dkzbo1+slEgmUchmUchkGBCpgbm7/WOtCabNi7YGpIwWlNbg1M6/T46+mTsTQQYFobLaiqdmKRoutNTQ1W3Gyshab8ko6vXZ8hBoyqQRNzVY0Ndvsr9HUbEWzteu2k9xCAwx1Fq/oG8TQQ0RElyRXQ5OrgantPV0NTT0JTB1Rq/y6PB43JKTT0HSysq7L0PPabyZ3em2L1Ybviqtx99v/7fT62qbmLmvzFIYeIiKii1zqrUzuvFYuk0KnVnVZW3A3gcxT2KeHfXqIiMiLiNGXqbfX9rYvlLPYkdkFDD1ERHSp6k1oEitwOYuhxwUMPURERO7Xm9DkDI7eIiIiIq/Qm75QniAVuwAiIiIiT2DoISIiIp/A0ENEREQ+gaGHiIiIfAJDDxEREfkEhh4iIiLyCQw9RERE5BMYeoiIiMgnMPQQERGRT2DoISIiIp/gk8tQtC03ZjKZRK6EiIiInNX2d9vVZUN9MvTU1tYCAKKiokSuhIiIiHqqtrYWGo2mx9f55CrrNpsNZ86cQXBwMCQSidte12QyISoqCmVlZVy9vQd431zD+9ZzvGeu4X1zDe+ba7q6b4IgoLa2FhEREZBKe95DxydbeqRSKSIjI/vs9dVqNb/gLuB9cw3vW8/xnrmG9801vG+u6ey+udLC04YdmYmIiMgnMPQQERGRT2DocSOlUomnn34aSqVS7FL6Fd431/C+9RzvmWt431zD++aavrxvPtmRmYiIiHwPW3qIiIjIJzD0EBERkU9g6CEiIiKfwNBDREREPoGhx40yMzMRExMDlUqFhIQE7N69W+ySvMYzzzwDiUTisIWFhdmPC4KAZ555BhEREfD398fs2bPx008/iVixOHJzc3HTTTchIiICEokE//znPx2OO3OfzGYzHnnkEWi1WgQGBuLmm2/G6dOnPfgpPK+7+7Zw4cJ2379p06Y5nONr9y0jIwOXXXYZgoODMXjwYMybNw/Hjh1zOIffN0fO3DN+19pbv3494uPj7ZMNJiUl4csvv7Qf9+T3jKHHTbKysrBs2TI88cQTKCgowIwZMzB37lyUlpaKXZrXGD9+PPR6vX07fPiw/diLL76INWvW4I033sD333+PsLAwXHPNNfZ10nxFfX09Jk6ciDfeeKPD487cp2XLluGzzz7Dxx9/jD179qCurg433ngjrFarpz6Gx3V33wDguuuuc/j+ZWdnOxz3tfu2a9cuPPzww9i3bx9ycnLQ0tKClJQU1NfX28/h982RM/cM4HftYpGRkVi9ejX279+P/fv346qrrsItt9xiDzYe/Z4J5BaXX365kJaW5rBvzJgxwooVK0SqyLs8/fTTwsSJEzs8ZrPZhLCwMGH16tX2fU1NTYJGoxHeeustD1XofQAIn332mf13Z+7T+fPnBT8/P+Hjjz+2n1NeXi5IpVJh27ZtHqtdTBffN0EQhPvuu0+45ZZbOr2G900QKisrBQDCrl27BEHg980ZF98zQeB3zVkDBgwQ3n77bY9/z9jS4wYWiwX5+flISUlx2J+SkoK8vDyRqvI+hYWFiIiIQExMDH7zm9+gqKgIAFBcXIyKigqH+6dUKjFr1izevws4c5/y8/PR3NzscE5ERATi4uJ8/l7u3LkTgwcPxqhRo/DAAw+gsrLSfoz3DTAajQCAgQMHAuD3zRkX37M2/K51zmq14uOPP0Z9fT2SkpI8/j1j6HEDg8EAq9UKnU7nsF+n06GiokKkqrzL1KlTsXnzZmzfvh1//etfUVFRgeTkZFRVVdnvEe9f15y5TxUVFVAoFBgwYECn5/iiuXPn4oMPPsA333yDV155Bd9//z2uuuoqmM1mALxvgiAgPT0dV1xxBeLi4gDw+9adju4ZwO9aZw4fPoygoCAolUqkpaXhs88+w7hx4zz+PfPJVdb7ikQicfhdEIR2+3zV3Llz7T9PmDABSUlJiI2Nxd/+9jd7Jz/eP+e4cp98/V6mpqbaf46Li0NiYiKio6Px73//G7fddlun1/nKfVuyZAkOHTqEPXv2tDvG71vHOrtn/K51bPTo0Thw4ADOnz+PLVu24L777sOuXbvsxz31PWNLjxtotVrIZLJ2ibOysrJdeqVWgYGBmDBhAgoLC+2juHj/uubMfQoLC4PFYkFNTU2n5xAQHh6O6OhoFBYWAvDt+/bII4/g888/x44dOxAZGWnfz+9b5zq7Zx3hd62VQqHAiBEjkJiYiIyMDEycOBGvvvqqx79nDD1uoFAokJCQgJycHIf9OTk5SE5OFqkq72Y2m3H06FGEh4cjJiYGYWFhDvfPYrFg165dvH8XcOY+JSQkwM/Pz+EcvV6PH3/8kffyAlVVVSgrK0N4eDgA37xvgiBgyZIl2Lp1K7755hvExMQ4HOf3rb3u7llH+F3rmCAIMJvNnv+eudjxmi7y8ccfC35+fsI777wjHDlyRFi2bJkQGBgonDp1SuzSvMLy5cuFnTt3CkVFRcK+ffuEG2+8UQgODrbfn9WrVwsajUbYunWrcPjwYeGuu+4SwsPDBZPJJHLlnlVbWysUFBQIBQUFAgBhzZo1QkFBgVBSUiIIgnP3KS0tTYiMjBS+/vpr4YcffhCuuuoqYeLEiUJLS4tYH6vPdXXfamtrheXLlwt5eXlCcXGxsGPHDiEpKUkYMmSIT9+33//+94JGoxF27twp6PV6+9bQ0GA/h983R93dM37XOrZy5UohNzdXKC4uFg4dOiT87//+ryCVSoWvvvpKEATPfs8YetzozTffFKKjowWFQiFMmTLFYRijr0tNTRXCw8MFPz8/ISIiQrjtttuEn376yX7cZrMJTz/9tBAWFiYolUph5syZwuHDh0WsWBw7duwQALTb7rvvPkEQnLtPjY2NwpIlS4SBAwcK/v7+wo033iiUlpaK8Gk8p6v71tDQIKSkpAihoaGCn5+fMHToUOG+++5rd0987b51dL8ACO+99579HH7fHHV3z/hd69iiRYvsfxtDQ0OFOXPm2AOPIHj2eyYRBEHoWdsQERERUf/DPj1ERETkExh6iIiIyCcw9BAREZFPYOghIiIin8DQQ0RERD6BoYeIiIh8AkMPERER+QSGHiIiIvIJDD1E1GOzZ8/GsmXLxC7Dq0kkEvzzn/8UuwwiugBDDxH12NatW/GXv/wFADBs2DCsW7dO3IJE9Mwzz2DSpElil0FETpCLXQAR9T8DBw50+2taLBYoFAq3vy4RURu29BBRj7U93po9ezZKSkrw6KOPQiKRQCKR2M/Jy8vDzJkz4e/vj6ioKCxduhT19fX248OGDcNzzz2HhQsXQqPR4IEHHujyPS0WC5YsWYLw8HCoVCoMGzYMGRkZ9uMSiQQbNmzAjTfeiICAAIwdOxZ79+7FiRMnMHv2bAQGBiIpKQknT550eN3169cjNjYWCoUCo0ePxt///neH46WlpbjlllsQFBQEtVqNO++8E2fPngUAbNq0Cc8++ywOHjxo//ybNm2yX2swGHDrrbciICAAI0eOxOeff97je01EbtTLxVOJyAfNmjVL+MMf/iBUVVUJkZGRwqpVqwS9Xi/o9XpBEATh0KFDQlBQkLB27Vrh+PHjwrfffitMnjxZWLhwof01oqOjBbVaLbz00ktCYWGhUFhY2OV7vvTSS0JUVJSQm5srnDp1Sti9e7fw4Ycf2o8DEIYMGSJkZWUJx44dE+bNmycMGzZMuOqqq4Rt27YJR44cEaZNmyZcd9119mu2bt0q+Pn5CW+++aZw7Ngx4ZVXXhFkMpnwzTffCILQuvrz5MmThSuuuELYv3+/sG/fPmHKlCnCrFmzBEFoXVV7+fLlwvjx4+2fv6GhwV5PZGSk8OGHHwqFhYXC0qVLhaCgIKGqqsot/xkQUc8x9BBRj7WFHkFoDS9r1651OL5gwQLhd7/7ncO+3bt3C1KpVGhsbLRfN2/ePKff85FHHhGuuuoqwWazdXgcgPDkk0/af9+7d68AQHjnnXfs+z766CNBpVLZf09OThYeeOABh9e54447hOuvv14QBEH46quvBJlMJpSWltqP//TTTwIA4bvvvhMEQRCefvppYeLEid3WU1dXJ0gkEuHLL790+jMTkXvx8RYRuV1+fj42bdqEoKAg+3bttdfCZrOhuLjYfl5iYqLTr7lw4UIcOHAAo0ePxtKlS/HVV1+1Oyc+Pt7+s06nAwBMmDDBYV9TUxNMJhMA4OjRo5g+fbrDa0yfPh1Hjx61H4+KikJUVJT9+Lhx4xASEmI/pysX1hMYGIjg4GBUVlY683GJqA+wIzMRuZ3NZsODDz6IpUuXtjs2dOhQ+8+BgYFOv+aUKVNQXFyML7/8El9//TXuvPNOXH311fj000/t5/j5+dl/butf1NE+m83Wbl8bQRDs+y78ubNzunLhe7e914XvTUSexdBDRL2iUChgtVod9k2ZMgU//fQTRowY4db3UqvVSE1NRWpqKm6//XZcd911qK6udnk02dixY7Fnzx7ce++99n15eXkYO3YsgNZWndLSUpSVldlbe44cOQKj0Wg/p6PPT0TeiaGHiHpl2LBhyM3NxW9+8xsolUpotVo8/vjjmDZtGh5++GE88MADCAwMxNGjR5GTk4PXX3/dpfdZu3YtwsPDMWnSJEilUnzyyScICwtDSEiIy7U/9thjuPPOOzFlyhTMmTMH//rXv7B161Z8/fXXAICrr74a8fHxuOeee7Bu3Tq0tLTgoYcewqxZs+yP5oYNG4bi4mIcOHAAkZGRCA4OhlKpdLkmIuo77NNDRL2yatUqnDp1CrGxsQgNDQXQ2pdl165dKCwsxIwZMzB58mT8+c9/Rnh4uMvvExQUhBdeeAGJiYm47LLLcOrUKWRnZ0Mqdf1/xubNm4dXX30VL730EsaPH48NGzbgvffew+zZswH8OqvygAEDMHPmTFx99dUYPnw4srKy7K8xf/58XHfddbjyyisRGhqKjz76yOV6iKhvSQRBEMQugoiIiKivsaWHiIiIfAJDDxF5heeff95hiPuF29y5c8Uuj4guAXy8RUReobq6GtXV1R0e8/f3x5AhQzxcERFdahh6iIiIyCfw8RYRERH5BIYeIiIi8gkMPUREROQTGHqIiIjIJzD0EBERkU9g6CEiIiKfwNBDREREPuH/A63D6kD/MOprAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(df_left, x='iter_smooth', y='mean_smtherr')\n",
    "sns.lineplot(x=df_left.iter_smooth, y=prediction, ax=ax)"
   ]
  }
 ],
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