Reed_Model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "08d9ca5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import pandas\n",
    "import numpy as np\n",
    "%matplotlib ipympl\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.widgets import Button, Slider\n",
    "import mercury as mc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e59046e3",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "In this paper, I evaluate the single reed model of instruments like the Clarinet or Saxophone as a potential haptic model on the Input Devices and musical interaction Laboratories (IDMIL) 1-DOF haptic devices called the TorqueTuner. First, I design the model in python, creating interactive visualizations to better understand how a user can interact with the reed-model. Then, the model is optimized for implementation as a haptic effect and pre-calculated values are exported from python into arrays in a C++ header file to be used on the TorqueTuner.\n",
    "\n",
    "## Motivation\n",
    "\n",
    "I chose to use the reed model as I was curious to take a concept from the clarinet (a single reed instrument) and model it using haptics. There has been ample literature exploring the acoustics, physical models, and gestures of the clarinet and so as a haptitian, why not explore it using force feedback (FF). What part of the clarinet give feedback to the user? The resulting sound, the pressing of the keys and the pressure felt when blowing into the instrument. The pressure follows the single reed model on the clarinet and is how the musician principally interacts with the instrument, shaping the envelope, attack and exploring extended techniques on the instrument. Without the reed/mouthpiece the clarinet would not become an extension of one body, just like the keys on the piano or the mouthpiece on a trumpet. As such, it seemed a worthwhile concept to explore using haptics as force feedback devices can give back the user that added dimension that is found in playing wind instruments."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a935ffa",
   "metadata": {},
   "source": [
    "## Reed Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dc130f2",
   "metadata": {},
   "source": [
    "Going through the literature of the reed model, I see that it is usually represented using the \n",
    "Bernoulli equation to approximate the flow through the reed's opening."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "cd881ae5",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "    u =  wx \\left(\\frac{2|p\\Delta |}{\\rho}\\right)^{\\frac{1}{2}}sgn(p\\Delta)\n",
    "\\end{equation}\n",
    "\n",
    "Here, x is the delta between the reed's equilibirum position H and its hooks law:\n",
    "\n",
    "\\begin{equation}\n",
    "x = H - \\frac{A_r p\\Delta}{k}\n",
    "\\end{equation}\n",
    "\n",
    "x is determined from viewing the reed as a spring model\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Now, lets plug x into the flow equation:\n",
    "\n",
    "\\begin{equation}\n",
    "u = wH\\left(1 - \\frac{p\\Delta }{p_c}\\right)\\left(\\frac{2p\\Delta }{\\rho}\\right)^{\\frac{1}{2}} sgn(p\\Delta )\n",
    "\\end{equation}\n",
    "\n",
    "Here $\\rho$ is the fluid density, w is the width of the reed channel and $p_c$ is the required pressure to close the reed completely.\n",
    "\n",
    "$$ p_c = \\frac{kH}{A_r} $$\n",
    "\n",
    "Lets were to lump the left sided constants of u together:\n",
    "\n",
    "\\begin{align}\n",
    "    \\beta &= \\sqrt{\\frac{2}{\\rho}}wH \\\\\n",
    "    u &= \\beta \\sqrt{|p\\Delta| } \\left(1 - \\frac{p\\Delta }{p_c}\\right)sgn(p\\Delta)\n",
    "\\end{align}\n",
    "\n",
    "Initially, $\\beta$ and $p_c$ can be set to one the equation is meant for a haptic 1-DOF motor and a physcial model. This leaves the equation:\n",
    "\n",
    "\\begin{equation}\n",
    "    u = \\sqrt{|p\\Delta |} \\left(1 - p\\Delta \\right) sgn(p\\Delta)\n",
    "\\end{equation}"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "114e236e",
   "metadata": {},
   "source": [
    "# Designing the haptic effect\n",
    "When using tuned variables for the initial equation $u = wH\\left(1 - \\frac{p\\Delta }{p_c}\\right)\\left(\\frac{2p\\Delta }{\\rho}\\right)^{\\frac{1}{2}} sgn(p\\Delta )$ I expect:\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a759e78f",
   "metadata": {},
   "source": [
    "Now lets compare with equation:\n",
    "\\begin{equation}\n",
    "    u = \\sqrt{|p\\Delta |} \\left(1 - p\\Delta \\right) sgn(p\\Delta)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4f576607",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 1\n",
    "p_c = 1\n",
    "p_delta = np.arange(-0.1,1.001,0.001)\n",
    "p_delta_diff = 1-p_delta\n",
    "p_delta_sign = np.sign(p_delta)\n",
    "p_delta_sqrt = np.sqrt(np.abs(p_delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "758730e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "u = p_delta_sqrt*p_delta_diff*p_delta_sign"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e52dfd25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2e7e191af10341de8bd21a7179181cc2",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
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       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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AwMkJ+frzStuvWoMaKiopCUlIQPP/ywylneytP0z58/x+nTpzF69GhIJBLFcsnOzkZISAji4+OrXPp9lRY95d6lSxelTnFjx47Fa6+9hpkzZ2Lw4MEQCoWIj49HXl4eLC0tq32Pl6/fODs71zi/F1cKAIoNrPJafEpKCgBU2+PRw8ND6VQil8zNzREcHFzj3yvzcHd3r/K3du3aNbj4Pn/+HIsXL8bu3burLPe8vLwGvWdKSgoCAgKqTK88rZiSkqJUDF71GdZ33kD1n7enpyeOHz9epeNbbetXfbycB1CRy4t5xMfH4/bt2zVernj5M6iOnp5erevKy+qzDfTq1QsbNmzAw4cPkZCQAB6Ph27duikK/ZQpU3D+/Hn06NGj0SMb6vq529nZVem4lJKSAnd39yoxvLiO1Udlezc3typ/c3Nzq3b7asr1trb3rXzvpl6PnJycsHnzZsjlciQkJGDJkiXIzMxU+tIXHx8Pxli1+x0AiksL8fHxAIBJkybVOL+8vDyUlpaiuLi4xv1YdV+4X1RZyCsLe00kEkmV+lLdetQYCQkJAFDrF9uHDx+CMYYFCxZgwYIF1bbJyMio8bJOdVq0oL+Mz+ejT58+WLNmDeLj49G+fXvI5XJYWlpix44d1b7m5ZW0th7tNfXEZDVcC61NZWeIl8lksnq/F5dqujlDdXmMHj0aly5dwty5c+Hr6wt9fX3I5XL079+/xcajNuVn2BBNNWKiLnnI5XL07du3xiPqtm3bNkksDVV5VuXcuXNITExEp06doKenh169emHt2rUoKChAVFRUkwxrquvn3pjPpz7bQn0113rbUuvRy18Me/TogU6dOmH+/PlYu3atYj48Hg///PNPtXFVns2o3FesWLECvr6+1c5PX18fpaWlr4yrNpVf2F7suPmylJQU5OfnVzlzycXIqMrlMmfOnBrPQFT3JbI2nBZ0ACgvLwcAFBQUAABcXV1x8uRJ9OjRo9kXcuWNRuLi4vD6668r/S0uLk7pRiQmJibVni6r77f95lAZZ+U34RfFxcUp/V55pPDyTWBeziMnJwenTp3C4sWL8eWXXyqmVzeP+tzBydHRsUpMABQ3PmnOm7+8+HlXN39zc/MGD0trirtYubq6oqCgoF5H2I1Vn23AwcEBDg4OOH/+PBITExWnfnv37o3Zs2djz549kMlk6N279yvn25x3/XJ0dMTt27chl8uVjtJfXsfqui1Utq9udMWrRlzUl6quRx06dMD48eOxceNGzJkzBw4ODnB1dQVjDM7OzrV+SXB1dQUAGBoa1hqThYUFdHR06rQfq07btm3Rtm1bHDhwAGvWrKn21HvliIDmvu9JZc53796tMWcXFxcAFWcymuqz4nTYmlQqxYkTJyAUChXfrkaPHg2ZTIavv/66Svvy8vImvRuZv78/LC0tsWHDBqVvh//88w/u37+PQYMGKaa5uroiNjYWmZmZimm3bt2qdthFS7OxsYGvry+2b9+udCo8PDy8yjVpR0dHCASCKtfRfvrpJ6XfK79xv3xEUV0P2coiWJfPZuDAgbh27RouX76smFZYWIhNmzbBycmpUdf8X+XF5fRirHfv3sWJEycwcODABr93fZZBTUaPHo3Lly/j+PHjVf6Wm5ur+PLblOqzDQAVp91Pnz6Na9euKQq6r68vDAwMsGzZMujo6MDPz++V89XT02vwZZtXGThwINLS0vDHH38oppWXl2PdunXQ19dXDGms67Zga2sLb29v/O9//1MceADA2bNncefOnSaNXZXXo08++QRSqRSrVq0CAAwfPhwCgQCLFy+usp9gjCmGt/r5+cHV1RUrV65UWn6VKvepAoEAISEhOHDgAB49eqT4+/3796vNpTpffvklcnJyMH369CpnWiIjI/Hdd9/B29sbI0aMqHviDdCpUyc4Oztj9erVVT7LymVlaWmJoKAgbNy4Ec+ePavyHi/Wmrpq0SP0f/75R/EtOSMjAzt37kR8fDw+++wzxTCDwMBATJs2DUuXLkV0dDT69esHbW1txMfHY8+ePVizZg1GjhzZJPFoa2vju+++Q1hYGAIDAzF27FjFkB0nJyd89NFHirb/+c9/sGrVKoSEhGDy5MnIyMjAhg0b0L59+yodLJra06dP8fvvv1eZrq+vj2HDhgEAli5dikGDBqFnz574z3/+g+fPn2PdunVo37690kZkZGSEUaNGYd26deDxeHB1dcXhw4erXFczNDRE7969sXz5ckilUtjZ2eHEiRNISkqqEkflDvzzzz/H22+/DW1tbQwZMqTao93PPvsMu3btwoABAzBr1iyYmppi+/btSEpKwr59+5r9rnIrVqzAgAED0K1bN0yePFkxbM3IyEjp/vv15evrC4FAgO+++w55eXkQiUR4/fXXa+wLUp25c+fi0KFDGDx4sGIoUmFhoWLcbHJysmJYYFOpzzYAVBT0HTt2gMfjKU7BCwQCdO/eHcePH0dQUFCdrkX6+fnhjz/+wOzZs9G5c2fo6+tjyJAhTZLT1KlTsXHjRoSGhiIyMhJOTk7Yu3cvLl68iNWrVyuO3Oq6LQDAt99+i6FDh6JHjx4ICwtDTk4OfvzxR3h7e1dbpBpKldcjLy8vDBw4EL/88gsWLFgAV1dXfPPNN5g3bx6Sk5MxbNgwGBgYICkpCX/99RemTp2KOXPmgM/n45dffsGAAQPQvn17hIWFwc7ODk+fPsWZM2dgaGiIv//+G0DFOPJjx46hV69emDFjhuKLWPv27Ws9lV5p3LhxuH79OtasWYOYmBiMGzcOJiYmuHnzJrZs2QIzMzPs3bu3xqGDTYXP5+Pnn3/GkCFD4Ovri7CwMNjY2CA2Nhb37t1TfEFZv349evbsCR8fH0yZMgUuLi5IT0/H5cuX8eTJE9y6dat+M653v/gGqG7YmlgsZr6+vuznn39W6sZfadOmTczPz4/p6OgwAwMD5uPjwz755BOWmpqqaOPo6Kg0jKJSTUOWqhuOwhhjf/zxB3vttdeYSCRipqambNy4cezJkydV3vf3339nLi4uTCgUMl9fX3b8+HFOh629PN99+/YxT09PJhKJmJeXF9u/f3+18WVmZrIRI0YwXV1dZmJiwqZNm8bu3r1bZdk8efKEvfXWW8zY2JgZGRmxUaNGsdTU1Cr5MVYxVMbOzo7x+XylXF8etsYYYwkJCWzkyJHM2NiYicVi1qVLF3b48GGlNvX9DF9W0+sZY+zkyZOsR48eTEdHhxkaGrIhQ4awmJgYpTaVw9YyMzNrnc+LNm/ezFxcXBRDbCqHsNS0nla3DkgkEjZv3jzm5ubGhEIhMzc3Z927d2crV65kZWVltc4/MDCQtW/fvtY2NQ3Vqus2cO/ePcWwshd98803DABbsGBBrfOvVFBQwN555x1mbGystC7X53OvLd/09HQWFhbGzM3NmVAoZD4+PtWuM3XdFhhjbPfu3czDw4OJRCLm7e3NDh06xEaMGME8PDyqxLlixYoq86puu6mOKq9HlUP1Xsxj3759rGfPnkxPT4/p6ekxDw8P9t5777G4uDil10ZFRbHhw4czMzMzJhKJmKOjIxs9ejQ7deqUUruzZ88yPz8/JhQKmYuLC9uwYYNie6yrAwcOsL59+zITExMmEomYm5sb+/jjj6vdnmvLt6HD1ipduHCB9e3blxkYGDA9PT3WoUMHtm7dOqU2CQkJbOLEicza2pppa2szOzs7NnjwYLZ3794651uJ92+AREOFhoYiIiKC04c9EKKpfH19YWFhgfDwcK5DIYQen0oIIa8ilUqrXHuOiIjArVu3WsVjkIl64LyXOyGEqLqnT58iODgY48ePh62tLWJjY7FhwwZYW1s32c2HCGksKuiEEPIKJiYm8PPzwy+//ILMzEzo6elh0KBBWLZsGczMzLgOjxAAAF1DJ4QQQjQAXUMnhBBCNAAVdEIIIUQDtMpr6Iwx5OfnQyKRwMDAoFlvQ0kIIUR1McYgkUhga2vb7De2am6tsqBLJJIqj7QjhBDSej1+/Bht2rThOoxGUZmCvn79eqxYsQJpaWno2LEj1q1bhy5durzydbt378bYsWMxdOhQHDhwoE7zMjAwwOPHj2Fvb4/Hjx8rbjurbirvhV95e9zWhvKn/Cl/yr+x+efn58Pe3v6Vz1FXBypR0Cvv6bxhwwYEBARg9erVCAkJQVxcXK33ME5OTsacOXMUD4moKx6PpyjihoaGal3QdXV1YWho2Go3aMqf8qf8Kf+myF8TLr2qxAWDVatWYcqUKQgLC4OXlxc2bNgAXV1dbNmypcbXyGQyjBs3DosXL1Y8ho4QQghprTgv6GVlZYiMjFR6Hiyfz0dwcLDSIzZf9tVXX8HS0hKTJ09uiTAJIYQQlcb5KfesrCzIZDJYWVkpTbeyslI8avVlFy5cwK+//oro6Og6z6e0tFTpec+VjzyVSqWQSqX1D1wFVMatrvE3FuVP+b/4b2tD+TdN/pq0/Dgv6PUlkUgwYcIEbN68uV7P9F26dCkWL15cZfqJEyegq6vblCG2uNb+pCfKn/JvLXg8HgQCgeJ3LS0tnDlzhsOIuFWX/GUyGWq7IWpRUVFTh8UZzgu6ubk5BAIB0tPTlaanp6fD2tq6SvuEhAQkJydjyJAhimlyuRxAxYcbFxcHV1fXKq+bN28eZs+erfi9smdjv3791LpTXHh4OPr27dtqO8VQ/pR/a8ifMYaMjAzFmcXKaSUlJRCLxRrRoau+6pO/oaEhLC0tq2334jJVd5wXdKFQCD8/P5w6dQrDhg0DUFGgT506hZkzZ1Zp7+HhgTt37ihN++KLLyCRSLBmzRrY29tXOx+RSASRSFRlura2ttrvDDQhh8ZQlfwZYygtl6O4TIYiqQwl0oojA8YABqDyIIHHA0RafIi1BRBrCSDS5kOkxW/wTllV8udKa8j/2bNnkEgksLKygq6uLng8HuRyOQoKCqCvr6/2N0RpiLrkzxhDUVERMjIyIBAIYGNjU6WNJq07nBd0AJg9ezYmTZoEf39/dOnSBatXr0ZhYSHCwsIAABMnToSdnR2WLl0KsVgMb29vpddX3iTm5emENJZUJkdaXgme5BTjSU4R0vJKkF1YhuzCMjwvLEV2QRlyispQUFKOYqkM8gY+6ojHA3S0BTDS0YaRjjZMdIUw1tX+90cIKwMRrI10YG0kho2RGOb6Vb+cEs0kk8mQm5sLS0tLpSe7yeVylJWVQSwWt9qCXpf8dXR0AAAZGRmwtLRUumShaVSioI8ZMwaZmZn48ssvkZaWBl9fXxw7dkzRUe7Ro0etcoUlLSeroBTx6QV4mCHBg/QCxGdI8Ci7CGn5JQ0q0kIBH2JtPgT8iqNuHo8HHioKt0zOUFYuR0m5HLJ/35wxoKhMhqIyGZ7llbzy/QV8Hiz0hdBlApwtuQtXSwM4munCyUwPTuZ60BepxKZNmkBlpy117+vDpcplJ5VKqaC3hJkzZ1Z7ih0AIiIian3ttm3bmj4gorFyCstw60kubj3Ow60nubj9JBdZBWU1thdq8WFnrIM2JjqwMRLDTF8EMz0hTP/9MdMTwUCsBV2hAGKhALraAmgJ6vYFVCqTo0QqQ4m04lR9bnEZcoukyCkqQ16xFDmFFf9Pzy/Bs7wSpOdX/MjkDGn5pQB4SIxKrfK+FgYitLMygIe1AdpZG8DTxhBulvoQa2vuzkzTtcbr5E2ltSw7lSnohDSXjPwSXE7MxqWH2biSlI2U7Op7tdqb6qCtpQHcrPTR1tIATuZ6sDfRgbm+CHx+8+wQtAV8aAv4MBBX/O6AVx+FyeQMWQWleJQlweEzl2Hi0A6PcoqRnFWIlOwiZBeWIVNSikxJKS48zFK8js8DnMz14GVjCF97Y3S0N4a3rRF0hFTkCdEEVNCJxiktl+FK4nOcvp+OCw+zkJBZWKWNi7keOrQxQkd7Y3RoYwxPGwPoCtVjcxDwebAyFMNUR4BUc4aBQS5KHXvyiqVIzCxAXJoEsWkSxKblIzZNgtwiKRIzC5GYWYjDt58p3qutlQF87Y3QsY0x/BxN4Gap32qOaAjRJOqxByPkFXKLynA6NgMn76fjbFwmCstkir/xeEB7W0N0dzVHNxczdHIwgZGu5vRsfZmRjjZeczDBaw4mimmMMWRISnH/WT7upeYj+nEuoh/nIvPfafef5WPXtccAAFM9Ibo4maKLsykCXEzhYW2o6AtASH2EhoYiNze3yoOzIiIi0KdPH+Tk5NT7yZfnzp3DihUrEBkZiWfPnmHfvn0YPnx40wWtxqigE7VVXCbDzSweDv4ehfMPsyCV/X/vNUsDEd7wtERgW0t0dTGFsa6Qw0i5x+NVHNVbGYoR1K7igUeMMaTllyj6EkQ9ykH041w8LyzDsXtpOHYvDQBgINZCZydTdHc1Q++2FnCnI3jCocLCQnTs2BGhoaEYOXIk1+GoFCroRK0wxnA16Tn+uP4Yx++loahMACATAOBhbYB+XlYI9rKCt61Rs1331hQ8Hg82RjqwMdJBf++KmziVlctx52kuriQ+x7Wk57iR/BySknKcjs3A6dgM4Mh9WBuK0cvdHL3bWqCnmzlM9Fr3lyXSsgYMGIABAwYobihG/h8VdKIWcovKsO/mU+y8mqJ0TdxMxDCmqyuG+7WBm6X6P8+Ya0ItPvwcTeHnaIr3+gDlMjlinuXjSmI2zsdn4VrSc6Tll2BP5BPsiXwCHg/o0MYYQW0t0NfLCu1tDenovQUwxlBUVo7iMhm0yspbdFivjragST/jR48ewcvLq9Y28+fPx/z585tsnpqKCjpRafHpEmw6l4hDt1JRWl7xjVxXKMBQX1u81dEGqXcuYVCwm0bd7UmVaAn46NCmouPg1N6uKJHKcC3pOc49yMS5+Ew8SC/Arce5uPU4F2tOxcPOWAfBnpYI9rJCgLMZhFp0/4jmUCyVwXsRN/ewj/kqpF4dSA8fPgx9fX2laTLZ//dxsbW1feWDtkxNTesVY2tFBZ2oHMYYrifnYOPZBJyKzVBM97QxxLgABwz1tYWBWBtSqRTP7nIYaCsk1hagd1sL9G5rAQBIyyvBuQeZOHk/HefiM/E0txjbL6dg++UUGIi0EORhib5eVnjDwxJ6dLObVqlPnz74+eeflaZdvXoV48ePB1DxDA43NzcuQtM4tIURlcEYw6WEbHx/Ig43H+UCqOihHuJljSm9ndHJwYRO56oYayMxRne2x+jO9iiRynAhPgvhMek4FZuOrIIy/H0rFX/fSoVYm4/XPSwxuIMt+rSzpLHvjaSjLcDdRX0hyZfAwNCgxU+514eenl6Vgv3kyRPF/+mUe9Ohgk5Uwo3k51h5Ig5XEp8DqLiWO6JTG0zp5QwXC/1XvJqoArG2AMH/dkqUyxmiHuciPCYdx+4+Q3J2EY7eScPRO2nQFQrwhqcVBnewQWBbC7p7XQPweDzoCrVQLhRAV6il1rfGplPuTYcKOuFUfLoES47eR0RcRU91oYCPdwIcMCPIFZaGYo6jIw3F5/Pg52gCP0cTfNq/He6l5uPv26k4cvsZnuQUK47cDURa6O9tjRF+bdDFyZRGJrRC9T3lXlBQgIcPHyp6uScnJyM6OhqmpqZwcHBorjDVAhV0wom8Iil+OPkAv11JgUzOIODzMNq/Dd5/3R22xjpch0eaEI/Hg7edEbztjPBZfw9EP87F4dvPcOT2M6Ue821MdDD8NTsM79QGTuZ6XIdNVNSNGzfQp08fxe8ff/wxAGDSpEmt/rkeVNBJi5LJGXZee4RVJ+KQU1TxFKl+XlaYP9CTduKtAI/HU9zF7vOBnrie/Bz7bz7FkTsVR+5rTz/E2tMP4edoghGd2mBQBxsY6dAIBnVVU4ENCgoCYw171nDla+VyOfLz82FoaKjWlxyaEhV00mIepEvwyd7biH6cCwBoa6WPLwe3R093c24DI5zg83kIcDFDgIsZFr3ZHidi0rDv5lNciM9EZEoOIlNysPjvexjkY4OxAQ7wd6ROkYTUhgo6aXZl5XL8FPEQ6888hFTGYCDSwpyQdhgX4FDnx4wSzaYjFGCorx2G+tohPb8EB6KeYt/NJ3iQXoD9UU+xP+op3C31MbaLA0Z0aqPR9+InpKGooJNmFZOaj4/+iEZcugQAEOxphW+GecPaiDq8kepZGYoxLdAVU3u7IPpxLnZde4S/bz1DfEYBvjocg++OxWKQjw1G+9migWdtCdFIVNBJs2CMYevFZCz7JxZlMjnM9IRYPLQ9BvnY0GlTUicvXm//YrAXDkY9xY6rjxCbJlEctdvoCCCxfIKR/g40tp20elTQSZPLlJRizp5bOPugYihasKcVvhvhAzN9EceREXVlKNbGhG5OGN/V8YWj9lQ8K5ZjwaEYrAyPx9ud7TGhmyPamOhyHS4hnKCCTprUtaTnmLHjJrIKSiHS4uOLwV4YH+BAR+WkSbx41P5pP3d8s/MkbuTp43FOMTaeS8Tm84no62WF0O7O6OpiqlHrHT1drOFay7Kjgk6aBGMM2y8l45sj91EuZ2hnZYB177yGtlb0BDTSPAx1tBFkw7A0rCcuJuZg26VknI/PwvF76Th+Lx0e1gYI6+GEYa/ZQaSlvqfjhUIh+Hw+UlNTYWFhAaFQCB6PB7lcjrKyMpSUlLTKYVt1yZ8xhrKyMmRmZoLP50Mo1OxH/VJBJ41WIpVh/l93sP/mUwDAmx1tsWyET72eyERIQwn4PLzhaYU3PK0Qny7B9svJ2Bf5FLFpEny67w5WnniAsB5OGBfgqJZj2vl8PpydnfHs2TOkpqYqpjPGUFxcDB0dHY06E1FX9clfV1cXDg4OGv/Fh/a4pFGyC0rx7v9uIOpRLvg8YP5AT0zu6dwqdzCEe+5WBvhmmA/m9vPAHzceYevFZDzLK8HyY3FYf/ohxnZxwH96Oqvd3QiFQiEcHBxQXl6uePSoVCrFuXPn0Lt371b5+OC65i8QCKClpdUq9klU0EmDJWcVInTrNSRnF8FIRxs/jeuEHm50kxjCPSNdbUzt7YrQ7s44fDsVG88mIi5dgl8uJGHbpWS82dEWUwNd4GFtyHWodcbj8aCtra0oXgKBAOXl5RCLxa2yoLf2/KtDBZ00SNSjHEzefgPPC8tgZ6yD7f/pDDdLul5OVItQi4/hndrgrdfsEPEgE5vOJuJyYrZi2FtQOwvM7OMGfyd6mhdRf1TQSb1diM/ClP/dQLFUBm87Q2wJ7QxLA7pRDFFdPB4PfdpZok87S9x6nItN5xLxz91niIjLRERcJrq5mGHWG+4a1zOetC5U0Em9nInNwLTfI1FWLkfvthb4eVwn6IloNSLqo6O9MdaP64SU7EJsOJuAvZFPcDkxG5cTs9HZyQTvv+6OXu7mVNiJ2tHsLn+kSZ24l4apv91AWbkcfb2ssHmiHxVzorYczfSwdHgHRMztgwldHSEU8HE9OQcTt1zDWz9dwunY9AY/EYwQLlBBJ3USHpOOGTtuQipjGORjg5/GdVLrsb2EVLIz1sHXw7xx/tM++E8PZ4i0+Ih+nIv/bLuBIT9eQHgMFXaiHqigk1e6lJCF93beRLmcYaivLda87Qttekoa0TBWhmJ8OcQLFz59HdN6u0BXKMDdp/mY8r8beOunS7gQn0WFnag02iuTWt16nIsp2ytOs/fzssL3ozrSI0+JRrMwEGHeQE9c+PR1/DfIFTraAkQ/zsX4X6/i7U1XcCP5OdchElIt2jOTGj3MkCB06zUUlsnQ3dUMa8e+RsWctBqmekJ82t8D5z7pg7AeThAK+Lia9BwjN1zGpC3XcOdJHtchEqKE9s6kWlkFpQjdeh05RVJ0tDfGpon+EGvTNXPS+lgYiLBwSHtEzA3C2C4O0OLzcPZBJob8eAHTfruBuDQJ1yESAoAKOqlGiVSGab9F4klOMRzNdLE1tDP0qTc7aeVsjXWwdLgPTn0ciLdeswOPBxy/l47+a85hzp5beJZXzHWIpJWjgk6UMMbw6b7biEzJgaFYC79O6gxTPc1+QhEh9eFopocfxvjixIe9McDbGowBeyOfIGhFBL47Fov8EinXIZJWigo6UbLxXCIORqdCi8/Dz+P94Gapz3VIhKgkdysD/DzeD3/N6I4uTqYoLZfj54gEBC4/g60Xk1BW3jqewU1UBxV0onA1MRsrjscBABa92Z4etEJIHbzmYII/pnXFLxP94Wapj5wiKRb/HYPgVWdx+HYqDXUjLYYKOgEAZEpK8f6uKMjkDMNfs8O4AAeuQyJEbfB4PAR7WeHYB72wdLgPLAxEePS8CDN3RmHY+ou4mpjNdYikFaCCTiCTM3ywOwoZklK0tdLHN295032sCWkALQEfY7s44OzcIMzu2xZ6QgFuPcnDmE1XMGNHJB4/L+I6RKLBqKATbDibgEsJ2dAVCvDTOD/oCqlHOyGNoSvUwqw33BExtw/GBTiAzwOO3knDG6vOYsXxWBSWlnMdItFAVNBbubtP8/BD+AMAwNdDvakTHCFNyMJAhCVv+eDoB73Q3dUMZeVyrD+TgD4rI7Av8gnkcrq+TpoOFfRWrEQqw8d/3kK5nKF/e2sM72THdUiEaCQPa0PseDcAGyf4wcFUFxmSUny85xbe+vkSIlNyuA6PaAiVKejr16+Hk5MTxGIxAgICcO3atRrbbt68Gb169YKJiQlMTEwQHBxca3tSvR/CHyAuXQJzfSGW0HVzQpoVj8dDSHtrhM/ujc8GeFRcX3+cixE/X8KHu6PoxjSk0VSioP/xxx+YPXs2Fi5ciJs3b6Jjx44ICQlBRkZGte0jIiIwduxYnDlzBpcvX4a9vT369euHp0+ftnDk6uvu0zxsPp8IAFg6vAPM9EUcR0RI6yDSEmB6oCvOzA3CaP824PGAA9GpeOP7s9hwNoHGr5MGU4mCvmrVKkyZMgVhYWHw8vLChg0boKuriy1btlTbfseOHZgxYwZ8fX3h4eGBX375BXK5HKdOnWrhyNWTTM7w+V93IGfA4A426OtlxXVIhLQ6lgZiLB/ZEX/P7Al/RxMUlcmw7J9YDFx7HpcSsrgOj6ghzgt6WVkZIiMjERwcrJjG5/MRHByMy5cv1+k9ioqKIJVKYWpq2lxhapSd1x7h1pM8GIi0sGCwF9fhENKqedsZYc/0blg5qiPM9IR4mFGAdzZfxaxdUUjPL+E6PKJGOB+flJWVBZlMBisr5aNEKysrxMbG1uk9Pv30U9ja2ip9KXhZaWkpSktLFb/n5+cDAKRSKaRS9bz3cmXc9Yk/U1KK5ccqlutHwW4w1RG0qvw1CeWvWfkP7WCFPu6m+OHUQ+y89hiHbqXiVGw6PnjdDeMD7KH90qOLNS3/+mqq/DVp+XFe0Btr2bJl2L17NyIiIiAWi2tst3TpUixevLjK9BMnTkBXV7c5Q2x24eHhdW67K4EPSQkf9noMJtl3cfTo3WaMrGXUJ39NRPlrVv6d+YC1N7AnSYCUAhm+/ScOW8/GYpSzDK6GVdtrWv711dj8i4o052Y/PMbxjYbLysqgq6uLvXv3YtiwYYrpkyZNQm5uLg4ePFjja1euXIlvvvkGJ0+ehL+/f63zqe4I3d7eHllZWTA0rGYrUQNSqRTh4eHo27cvtLW1X9n+QboEQ9ZfhpwBf07pgtccjJs/yGZU3/w1DeWv2fnL5Qx7bz7FyvB45BRVHEUO62iDz/q3hZm+SOPzf5Wmyj8/Px/m5ubIy8tT21pQifMjdKFQCD8/P5w6dUpR0Cs7uM2cObPG1y1fvhxLlizB8ePHX1nMAUAkEkEkqtqTW1tbW+03hrrmsCL8IeQMGOhjjS6uFi0QWcvQhM+wMSh/zc1/XDdnDOxgh+XH47D7+iMcuPUMEfFZ+HygJ4Z2qLhMqcn510Vj89ekZcd5pzgAmD17NjZv3ozt27fj/v37+O9//4vCwkKEhYUBACZOnIh58+Yp2n/33XdYsGABtmzZAicnJ6SlpSEtLQ0FBQVcpaDyLj7MQkRcJrT4PMwN8eA6HEJIHZnoCbF0uA/2/7c7PKwNkFskxdy9tzFx6w1k0NB18gLOj9ABYMyYMcjMzMSXX36JtLQ0+Pr64tixY4qOco8ePQKf///fPX7++WeUlZVh5MiRSu+zcOFCLFq0qCVDVwuMMSz/97Go47s6wtlcj+OICCH19ZqDCf5+vyd+vZCE1Scf4EpSDm7wBCgyS8R/+7hDqKUSx2eEQypR0AFg5syZNZ5ij4iIUPo9OTm5+QPSIOfis3DrcS7E2ny818eN63AIIQ2kLeBjeqArBnrbYN7+27iYkI0fTj3EkbtpWDq8A/wcTbgOkXCIvtJpOMYY1p6KBwCMC3CEhQHdEY4QdedgpoutkzphgpsMJrraeJBegJEbLmHBgbvIL9GcYVikfqiga7jLCdmITMmBUIuPab1duA6HENJEeDwe/C0Yjn/QAyP92oAx4LcrKei76ixO3EvjOjzCASroGu7nswkAgLGd7WFpWPM4fUKIejLRFWLlqI7Y+W4AnMx0kZ5fiqm/RWLWrig8LyzjOjzSgqiga7CHGRKcj88Cnwe824uOzgnRZN3dzHHsw96YHugKPg84dCsV/X44i6N3nnEdGmkhVNA12NaLyQCAYE8r2Juq993wCCGvJtYW4LMBHvhrRg+0tdJHVkEZZuy4iRk7IpFVUPrqNyBqjQq6hsorkmL/zYrHyYb1cOY4GkJIS+pob4y/3++J9193g4DPw9E7aei76iwORj8FxzcHJc2ICrqG+vPGYxRLZfCwNkBXF3oKHSGtjUhLgI/7tcPB93rA08YQOUVSfLA7GlN/i0QGPcVNI1FB10CMMfxx4zEAYGI3J/B4PI4jIoRwxdvOCIdm9sDsvm2hLeAhPCYdwavOYl/kEzpa1zBU0DVQ9ONcPMwogFibjyEdbbgOhxDCMW0BH7PecMff7/dEhzZGyC8px8d7bmHqb3RtXZNQQddAeyKfAAAGeNvAQKw5Dx4ghDSOh7Uh9v+3Oz7p305xtB7ywzkcu0vj1jUBFXQNUyKV4e9bqQCAkX5tOI6GEKJqtAR8zAhyw6GZPeFhbYDswjJM/z0SH/95i+4yp+aooGuYsw8yISkph62RGN1czLgOhxCiojxtDHFwZg/8N6hi3Pq+m0/Q/4dzuPQwi+vQSANRQdcwx/89ddbf2wZ8PnWGI4TUTKQlwKf9PfDntG5wNNNFal4J3vnlKhYduofiMhnX4ZF6ooKuQcrK5Qi/nw4A6O9tzXE0hBB14e9kiqOzemFcgAMAYNulZAxadx7Rj3O5DYzUi+LxqUlJSTh//jxSUlJQVFQECwsLvPbaa+jWrRvEYroHuDq4lJAFSUk5zPVF9BhFQki96Im0sOQtH/T1ssIne28jMbMQI36+hJl93PD+627QEtDxn6rT2rFjB9asWYMbN27AysoKtra20NHRwfPnz5GQkACxWIxx48bh008/haOjI9fxkloc//cJSyHtrSCg0+2EkAYIameJEx/1xpcH7+HQrVSsORWPCw+zsHqML91CWsXx165di9DQUKSkpODZs2eIjIzEhQsXEBMTg/z8fBw8eBByuRz+/v7Ys2cP1/GSGjDGEBGXCQDo155OtxNCGs5YV4i1Y1/Dmrd9YSDSQmRKDgauOY8DUU+5Do3UQuvq1as1/lEkEiEoKAhBQUFYsmQJkpOTWy4yUi8JmYV4llcCoRYfAc50q1dCSOMN9bVDJwcTfPRHNG6k5ODDP6JxJi4DXw/zhiHd40Ll1PmiiJmZGfz8/JozFtIIF+Irjs47O5lArC3gOBpCiKawN9XF7qld8VFwWwj4PByMTsXANedxI/k516GRlyg6xT169KjWhg4ODs0eDGm4Cw+zAQA93Mw5joQQomm0BHx8EOyOnu7m+PCPKDx+XozRGy/j/dfdqcOcClEUdCen2h/iIZPRmERVVS6T40piRUHv5WbBcTSEEE3l52iCo7N6YeHBe9gf9ZQ6zKkYRUGPiopS+oNUKkVUVBRWrVqFJUuWtHhgpO7iMwpRUFoOA5EWvGwNuQ6HEKLBDMTaWDXGF4HtLPDFX3cRmZKDAWvOY8lb3hjqa8d1eK2aoqB37Nixyh/9/f1ha2uLFStWYPjw4S0aGKm76Ce5AICO9sY0XI0Q0iIqO8zN/jMa15Nz8MHuaFxOyMbCIe2hI6R+PFx45YWPdu3a4fr16y0RC2mg6Md5AIDXHIy5DYQQ0qrYm+pi15SumPWGO3g8YPf1xxi6/gIepEu4Dq1VUhT0/Px8pZ+8vDzExsbiiy++gLu7O5cxkleovD0jFXRCSEvTEvAxu29b7JgcAAsDER6kF+DNHy/gz+uPwRjjOrxWRXHK3djYuEqnOMYY7O3tsXv37hYPjNRNqQxIzCoCAHRsY8xtMISQVqu7mzmOzuqF2X9G43x8Fj7ZdxsXE7Kw5C0f6Iu0Xv0GpNEUS/nMmTNKf+Dz+bCwsICbmxu0tOjDUFVpxRX/musLYaYv4jYYQkirZmEgwvawLthwLgHfn3iAg9GpuP0kD+vGvgZvOyOuw9N4ikodGBjIZRykgdKLKs6quFsacBwJIYQAfD4PM4Lc0MXJFLN2RSEpqxDDf7qELwZ7YkJXx1qHR5PGqfPdAIqKinDv3r3mjIU0wLPifwu6lT7HkRBCyP/zdzLFkVm9EOxpiTKZHF8evIf//n4TecVSrkPTWPyQkBDs2bMHhYWF1TaIiYnB/Pnz4erqisjIyBYOj7xKWsXlc7hb0RE6IUS1mOgJsXmiPxYM9oK2gIdj99IwaO153HmSx3VoGklr0KBB+OKLL/DOO++gbdu2sLW1hVgsRk5ODmJjY1FQUIC33noLJ06cgI+PD9fxkpekVR6hW9IROiFE9fB4PEzu6YzOTiZ4b+dNPH5ejBE/X8KiN9tjbBd7OgXfhPizZs1CXFwcLl++jClTpsDb2xt2dnYICgrCxo0bkZqail27dlExV0HlMjlySiv+72yux20whBBSiw5tjHF4Zi8Ee1qhTCbH/L/u4OM/b6G4jG4r3lQUneL8/f3h7+/PZSyknjILysDAgxafB3Pq4U4IUXFGutrYNMEPG88lYsXxWOyPeop7qfn4eXwnuFjQWcbGokfkqLG0/BIAFUNF6JavhBB1wOfz8N8gV+x4tyvM9UWIS5fgzR8v4uidZ1yHpvaooKux9PyK8+3WhnR0TghRL91czXB0Vk90cTJFQWk5Zuy4ia8Px0Aqk3Mdmtqigq7GKo/QrQzFHEdCCCH1Z2koxs4pAZjW2wUA8OuFJLy96QrS8ko4jkw9UUFXY5UrPR2hE0LUlZaAj3kDPbFxgh8MRFqITMnBoLXncfFhFtehqR1FQS8poW9E6ia/pBwAYKwr5DgSQghpnJD21jg8qyc8bQyRXViGCb9exYazCfSAl3pQFHRjY2P07t0bCxYswKlTp1BcXMxlXKQOKod76NKzhwkhGsDRTA9/zeiOUX5tIGfAsn9iMXNnFApLy7kOTS0oCvrJkyfRv39/XL16FUOHDoWJiQl69uyJzz//HOHh4VzGSGpQIq0o6GJtunJCCNEMYm0Blo/sgG+GeUNbwMORO8/w1k8XkZRV/d1Myf9TVIKePXti/vz5OHHiBHJzc3HmzBm4ublh+fLl6N+/P5cxkhoUSyt6g+po0xE6IURz8Hg8jO/qiN1Tu8LyhWesn7qfznVoKk3p0O7BgwfYtGkTJk6ciBEjRuDvv//G4MGDsWrVqmYPZP369XBycoJYLEZAQACuXbtWa/s9e/bAw8MDYrEYPj4+OHr0aLPHqGr+/widCjohRPP4OZri8Ps94e9oAklJOSZvv4E1J+Mhl9N19eooCrqdnR26du2KY8eOoWvXrvjnn3+QlZWFv/76Cx988EGzBvHHH39g9uzZWLhwIW7evImOHTsiJCQEGRkZ1ba/dOkSxo4di8mTJyMqKgrDhg3DsGHDcPfu3WaNU9UU/1vQdeiUOyFEQ1UMbeuKid0cAQA/nHyAqb9FQlJCT217maISWFhYoKioCGlpaUhLS0N6enqLdYxbtWoVpkyZgrCwMHh5eWHDhg3Q1dXFli1bqm2/Zs0a9O/fH3PnzoWnpye+/vprdOrUCT/++GOLxKsq6AidENIaCLX4+GqoN1aM7AChFh8n76djxIariqdNkgqKe7lHR0cjNzcX586dw9mzZzF//nzExMTA19cXffr0wZIlS5olgLKyMkRGRmLevHmKaXw+H8HBwbh8+XK1r7l8+TJmz56tNC0kJAQHDhyocT6lpaUoLS1V/J6fnw8AkEqlkErV85te0b+93LV5TG1zaIzKnFtj7gDlT/m3vvyHdbSGq7kO3tt1C0nZRViVI4BV26cY1MGuwe+pSctP68VfjI2N8eabb6JHjx7o3r07Dh48iF27duHq1avNVtCzsrIgk8lgZWWlNN3KygqxsbHVviYtLa3a9mlpaTXOZ+nSpVi8eHGV6SdOnICurm4DIueepEgAgIeoG1eRFsN1NNxp7aMwKH/Kv7WZ6Q5se8BHfD4f56/fBu/JrQa/V1GR5hzmKwr6/v37ERERgYiICMTExMDU1BQ9e/bE999/j8DAQC5jbBLz5s1TOqrPz8+Hvb09+vXrB0NDQw4ja7hPr58EIMfrvXvC2VI9c2gMqVSK8PBw9O3bF9ra2lyH0+Iof8q/Nec/pLQU3/9xGp+8/QaEwobfXKvybK0mUBT06dOno3fv3pg6dSoCAwNb7Pnn5ubmEAgESE9XHo6Qnp4Oa2vral9jbW1dr/YAIBKJIBJVvUWqtra2Wm4McjlDSXnFsDUDXZFa5tBU1PUzbCqUP+XfWvPvZM4gFAoblb8mLTtFp7iMjAzs3bsXM2fObLFiDgBCoRB+fn44deqUYppcLsepU6fQrVu3al/TrVs3pfZAxWmnmtprotLy/38iEY1DJ4QQonQNXSaT4cCBA7h//z4AwMvLC0OHDoVA0LwFY/bs2Zg0aRL8/f3RpUsXrF69GoWFhQgLCwMATJw4EXZ2dli6dCkA4IMPPkBgYCC+//57DBo0CLt378aNGzewadOmZo1TlVQOWQOolzshhJAXCvrDhw8xcOBAPH36FO3atQNQ0ZHM3t4eR44cgaura7MFMWbMGGRmZuLLL79EWloafH19cezYMUXHt0ePHoHP//+x1t27d8fOnTvxxRdfYP78+XB3d8eBAwfg7e3dbDGqmsqCrsVjEPB5HEdDCCGEa4qCPmvWLLi6uuLKlSswNTUFAGRnZ2P8+PGYNWsWjhw50qyBzJw5EzNnzqz2bxEREVWmjRo1CqNGjWrWmFRZ5YNZhHRPGUIIIXihoJ89e1apmAOAmZkZli1bhh49enASHKlZ5U1l6Gw7IYQQ4IVOcSKRCBKJpEqDgoKCRg0JIM0jv7jiZghiKuiEEELwQkEfPHgwpk6diqtXr4IxBsYYrly5gunTp+PNN9/kMkZSjbT8EgCAoTY9pIAQQsgLBX3t2rVwdXVFt27dIBaLIRaL0aNHD7i5uWHNmjVcxkiqUVnQjasOrSeEENIKKa6hGxsb4+DBg4iPj1fcctXT0xNubm6cBUdqlp5XUdCN6GoIIYQQvDQOHQDc3d3h7u7ORSykHp79W9CNhXTKnRBCCKD18lPLarJq1apmDoXUR3rlKXc6QieEEAJAKyoq6pWNeDy6cYmqeZpb8ax6OkInhBACAFpnzpzhOgZST3lFUmQVlAEALHQ4DoYQQohK4CcmJoIxOspTJwlZBQAAK0MRjUMnhBACAOC7u7sjMzNTMWHMmDFVHk1KVEtiZiEAwMVcj+NICCGEqAr+y0fnR48eRWFhIUfhkLqIz6i4ox8VdEIIIZXo0R5q6N7TfACAl40Bx5EQQghRFXwej1elFzv1alddjDHcTc0DAHjZGHIcDSGEEFWhxRhDaGgoRKKKe4iWlJRg+vTp0NNTPp27f/9+LuIjL3maW4zcIim0+Dy4W+njEdcBEUIIUQlakyZNUpowfvx4jkIhdXH339Ptba0MINKiKyaEEEIqaG3dupXrGEg93HqSCwDwtqPT7YQQQv4fHeKpmetJzwEA/k6mHEdCCCFElVBBVyMlUhluP6noENeFCjohhJAXUEFXI9GPc1Emk8PSQARHM12uwyGEEKJCqKCrkcrT7Z2dTWloISGEECVU0NXI1X8LOp1uJ4QQ8jIq6GqiqKwc1/4t6D3czDiOhhBCiKqhgq4mLidko0wmRxsTHbha6HMdDiGEEBVDBV1NRMRVPBEvqJ0FXT8nhBBSBRV0NcAYw5m4DABAUFtLjqMhhBCiiqigq4GEzEI8ySmGUMBHd7p+TgghpBpU0NXAyfvpAIAuzqbQFWpxHA0hhBBVRAVdDRy98wwA0N/bmuNICCGEqCoq6Cru8fMi3H6SBz6PCjohhJCaUUFXcf/crTg6D3A2g7m+iONoCCGEqCoq6CruyJ00AMBAHzo6J4QQUjMq6CrsSU4Rbj3OBY8HhNDpdkIIIbWggq7CDkanAgACnE1haSDmOBpCCCGqjAq6imKMYV/kEwDAiE5tOI6GEEKIqqOCrqJuPspFYlYhdLQFGOBjw3U4hBBCVBwVdBW172bF0fkAH2voi+hmMoQQQmpHBV0FlUhl+PtWxfXzkXS6nRBCSB1QQVdBJ2LSISkph52xDrq60L3bCSGEvBoVdBW082oKAGBEJzvw+fSoVEIIIa/GeUF//vw5xo0bB0NDQxgbG2Py5MkoKCiotf3777+Pdu3aQUdHBw4ODpg1axby8vJaMOrm8yBdgiuJzyHg8zA2wIHrcAghhKgJzgv6uHHjcO/ePYSHh+Pw4cM4d+4cpk6dWmP71NRUpKamYuXKlbh79y62bduGY8eOYfLkyS0YdfP5/UrF0XmwpyVsjHQ4joYQQoi64LT79P3793Hs2DFcv34d/v7+AIB169Zh4MCBWLlyJWxtbau8xtvbG/v27VP87urqiiVLlmD8+PEoLy+Hlpb69ggvKC3H/ptPAQATujpxGwwhhBC1wukR+uXLl2FsbKwo5gAQHBwMPp+Pq1ev1vl98vLyYGhoqNbFHAD+inqKgtJyuJjrobsrdYYjhBBSd5xWwLS0NFhaWipN09LSgqmpKdLS0ur0HllZWfj6669rPU0PAKWlpSgtLVX8np+fDwCQSqWQSqX1jLzpMcbw26VkAMDbndtAJiuHTFb7ayrjVoX4uUD5U/4v/tvaUP5Nk78mLb9mKeifffYZvvvuu1rb3L9/v9Hzyc/Px6BBg+Dl5YVFixbV2nbp0qVYvHhxleknTpyArq5uo2NprLg8Hh5kCKDNZzDIuoejR+/V+bXh4eHNGJnqo/wp/9aM8m9c/kVFRU0UCfd4jDHW1G+amZmJ7OzsWtu4uLjg999/x8cff4ycnBzF9PLycojFYuzZswdvvfVWja+XSCQICQmBrq4uDh8+DLG49oeXVHeEbm9vj6ysLBgaGtYxs+Yz+X+ROBefjfEB9lg42LNOr5FKpQgPD0ffvn2hra3dzBGqHsqf8qf8Kf/G5p+fnw9zc3PFpVt11ixH6BYWFrCwsHhlu27duiE3NxeRkZHw8/MDAJw+fRpyuRwBAQE1vi4/Px8hISEQiUQ4dOjQK4s5AIhEIohEoirTtbW1Od8Y4tIkOBefDT4PmNLbtd7xqEIOXKL8KX/Kn/JvzOs1Baed4jw9PdG/f39MmTIF165dw8WLFzFz5ky8/fbbih7uT58+hYeHB65duwagopj369cPhYWF+PXXX5Gfn4+0tDSkpaVB9qqLzipq8/lEAEB/b2s4mulxHA0hhBB1xHm38B07dmDmzJl44403wOfzMWLECKxdu1bxd6lUiri4OMV1jps3byp6wLu5uSm9V1JSEpycnFos9qaQnl+Cg9EVQ9Wm9HLhOBpCCCHqivOCbmpqip07d9b4dycnJ7x4mT8oKAjNcNmfM9suJUMqY+jsZILXHEy4DocQQoia4vxOca1ZfolUcWc4OjonhBDSGFTQOfS/S8mQlJTDzVIfwZ5WXIdDCCFEjVFB50hBaTl+uZAEAHj/dTd6qhohhJBGoYLOkd+vpCC3SAoXcz0M7lD1nvWEEEJIfVBB50BRWTk2n6sYqvZeHzcI6OicEEJII1FB58DOq4+QXVgGB1NdDPWlo3NCCCGNRwW9hZVIZdj479H5zD5u0BLQR0AIIaTxqJq0sJ1XHyFTUgo7Yx281cmO63AIIYRoCCroLaiwtBzrzzwEUHHtXJuOzgkhhDQRqigtaMuFJGQXlsHJTBej/NtwHQ4hhBANQgW9heQUlmHTv9fOZ/drR0fnhBBCmhRVlRay4WwCJKXl8LQxxGAfG67DIYQQomGooLeAtLwSbLuUDACYG9KW7gpHCCGkyVFBbwFrT8ejtFwOf0cT9GlnyXU4hBBCNBAV9GaWnFWIP68/BgB80t8DPB4dnRNCCGl6VNCb2XfHYlEuZwhqZ4EuzqZch0MIIURDUUFvRteTn+Ofu2ng84B5Azy5DocQQogGo4LeTORyhm8OxwAAxnR2QDtrA44jIoQQosmooDeTv2+n4taTPOgJBZjdty3X4RBCCNFwVNCbQYlUhuXH4gAA/w1yhYWBiOOICCGEaDoq6M1gy8UkPM0tho2RGJN7unAdDiGEkFaACnoTyyooxU9nEgAAc0PaQUco4DgiQgghrQEV9Ca2+uQDFJSWw8fOCMN86fGohBBCWgYV9CYUk5qPnVcfAQC+GORJt3glhBDSYqigNxHGGBYdugc5AwZ1sEGAixnXIRFCCGlFqKA3kUO3UnEt+Tl0tAX4fCDdRIYQQkjLooLeBApLy/Ht0fsAgPf6uMLWWIfjiAghhLQ2VNCbwLrTD5GeXwoHU12824uGqRFCCGl5VNAbKTGzAL9eSAQAfDnYC2JtGqZGCCGk5VFBbwTGGL46HAOpjKFPOwu84UnPOieEEMINKuiNcOp+BiLiMiEU8PHlkPb0rHNCCCGcoYLeQCVSGb7692lqk3s5w9lcj+OICCGEtGZaXAegrgpKy+FuqY+ycjlm9nHjOhxCCCGtHBX0BjLXF+HX0M7IlJRCT0SLkRBCCLfolHsj0aNRCSGEqAIq6IQQQogGoIJOCCGEaAAq6IQQQogGoIJOCCGEaAAq6IQQQogGaJXjrRhjyM/PBwDFv+pIKpWiqKgI+fn50NbW5jqcFkf5U/6UP+Xf2PwrawBjrKlC4wyPaUIW9ZSfnw8jIyOuwyCEEKIiHj9+jDZt2nAdRqO0yoJeeYQukUhgYGCgtvdgz8/Ph729PR4/fgxDQ0Ouw2lxlD/lT/lT/o3NnzEGiUQCW1tb8PnqfRW6VZ5y5/F4MDIy0pijdENDw1a5QVei/Cl/yp/ybwxNqQXq/XWEEEIIIQCooBNCCCEagQq6GhOJRFi4cCFEotZ5P3nKn/Kn/Cn/1pp/dVplpzhCCCFE09AROiGEEKIBqKATQgghGoAKOiGEEKIBqKATQgghGoAKuopbv349nJycIBaLERAQgGvXrtXafs+ePfDw8IBYLIaPjw+OHj3aQpE2j/rkv3nzZvTq1QsmJiYwMTFBcHDwK5eXqqvv519p9+7d4PF4GDZsWPMG2Mzqm39ubi7ee+892NjYQCQSoW3btmq9DdQ3/9WrV6Ndu3bQ0dGBvb09PvroI5SUlLRQtE3r3LlzGDJkCGxtbcHj8XDgwIFXviYiIgKdOnWCSCSCm5sbtm3b1uxxqhRGVNbu3buZUChkW7ZsYffu3WNTpkxhxsbGLD09vdr2Fy9eZAKBgC1fvpzFxMSwL774gmlra7M7d+60cORNo775v/POO2z9+vUsKiqK3b9/n4WGhjIjIyP25MmTFo68adQ3/0pJSUnMzs6O9erViw0dOrRlgm0G9c2/tLSU+fv7s4EDB7ILFy6wpKQkFhERwaKjo1s48qZR3/x37NjBRCIR27FjB0tKSmLHjx9nNjY27KOPPmrhyJvG0aNH2eeff87279/PALC//vqr1vaJiYlMV1eXzZ49m8XExLB169YxgUDAjh071jIBqwAq6CqsS5cu7L333lP8LpPJmK2tLVu6dGm17UePHs0GDRqkNC0gIIBNmzatWeNsLvXN/2Xl5eXMwMCAbd++vblCbFYNyb+8vJx1796d/fLLL2zSpElqXdDrm//PP//MXFxcWFlZWUuF2Kzqm/97773HXn/9daVps2fPZj169GjWOFtCXQr6J598wtq3b680bcyYMSwkJKQZI1MtdMpdRZWVlSEyMhLBwcGKaXw+H8HBwbh8+XK1r7l8+bJSewAICQmpsb0qa0j+LysqKoJUKoWpqWlzhdlsGpr/V199BUtLS0yePLklwmw2Dcn/0KFD6NatG9577z1YWVnB29sb3377LWQyWUuF3WQakn/37t0RGRmpOC2fmJiIo0ePYuDAgS0SM9c0af/XUK3y4SzqICsrCzKZDFZWVkrTraysEBsbW+1r0tLSqm2flpbWbHE2l4bk/7JPP/0Utra2VTZyddCQ/C9cuIBff/0V0dHRLRBh82pI/omJiTh9+jTGjRuHo0eP4uHDh5gxYwakUikWLlzYEmE3mYbk/8477yArKws9e/YEYwzl5eWYPn065s+f3xIhc66m/V9+fj6Ki4uho6PDUWQth47QiUZatmwZdu/ejb/++gtisZjrcJqdRCLBhAkTsHnzZpibm3MdDifkcjksLS2xadMm+Pn5YcyYMfj888+xYcMGrkNrEREREfj222/x008/4ebNm9i/fz+OHDmCr7/+muvQSAuhI3QVZW5uDoFAgPT0dKXp6enpsLa2rvY11tbW9WqvyhqSf6WVK1di2bJlOHnyJDp06NCcYTab+uafkJCA5ORkDBkyRDFNLpcDALS0tBAXFwdXV9fmDboJNeTzt7Gxgba2NgQCgWKap6cn0tLSUFZWBqFQ2KwxN6WG5L9gwQJMmDAB7777LgDAx8cHhYWFmDp1Kj7//HO1f9b3q9S0/zM0NGwVR+cAHaGrLKFQCD8/P5w6dUoxTS6X49SpU+jWrVu1r+nWrZtSewAIDw+vsb0qa0j+ALB8+XJ8/fXXOHbsGPz9/Vsi1GZR3/w9PDxw584dREdHK37efPNN9OnTB9HR0bC3t2/J8ButIZ9/jx498PDhQ8UXGQB48OABbGxs1KqYAw3Lv6ioqErRrvxyw1rBIzs0af/XYFz3yiM12717NxOJRGzbtm0sJiaGTZ06lRkbG7O0tDTGGGMTJkxgn332maL9xYsXmZaWFlu5ciW7f/8+W7hwodoPW6tP/suWLWNCoZDt3buXPXv2TPEjkUi4SqFR6pv/y9S9l3t983/06BEzMDBgM2fOZHFxcezw4cPM0tKSffPNN1yl0Cj1zX/hwoXMwMCA7dq1iyUmJrITJ04wV1dXNnr0aK5SaBSJRMKioqJYVFQUA8BWrVrFoqKiWEpKCmOMsc8++4xNmDBB0b5y2NrcuXPZ/fv32fr162nYGlEt69atYw4ODkwoFLIuXbqwK1euKP4WGBjIJk2apNT+zz//ZG3btmVCoZC1b9+eHTlypIUjblr1yd/R0ZEBqPKzcOHClg+8idT383+Ruhd0xuqf/6VLl1hAQAATiUTMxcWFLVmyhJWXl7dw1E2nPvlLpVK2aNEi5urqysRiMbO3t2czZsxgOTk5LR94Ezhz5ky123NlzpMmTWKBgYFVXuPr68uEQiFzcXFhW7dubfG4uUSPTyWEEEI0AF1DJ4QQQjQAFXRCCCFEA1BBJ4QQQjQAFXRCCCFEA1BBJ4QQQjQAFXRCCCFEA1BBJ4QQQjQAFXRCCCFEA/wfRBFB8u3TuZIAAAAASUVORK5CYII=' width=500.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 2.7))\n",
    "ax.plot(p_delta,u, label='H=1')\n",
    "ax.grid(1)\n",
    "ax.set_xlabel('normalized $p\\Delta$')\n",
    "ax.set_ylabel('Flow (u)')\n",
    "ax.legend()\n",
    "ax.set_title('Bernoulli Equation for the Flow through the Reed Orifice')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a270e3e7",
   "metadata": {},
   "source": [
    "As I can see the resulting Figure 1 follows similarly to that of the desired graphic presented above without the need of determining the required parameters of H, etc. If I are to use this as a haptic effect, further conditioning of the data is required. First, I must consider normalizing the non-negative initial values of the pressure and flow between 0 and 1. But first, let’ see what happens when I wrap the pressure between 0 and 360."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f6e22fbb",
   "metadata": {},
   "outputs": [],
   "source": [
    "p_delta = np.arange(0,360.001,0.001)\n",
    "p_delta_diff = 1-(p_delta/360)\n",
    "p_delta_sign = np.sign(p_delta)\n",
    "p_delta_sqrt = np.sqrt(np.abs(p_delta))\n",
    "u = (p_delta_sqrt*p_delta_diff*p_delta_sign)\n",
    "u = u/np.max(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1939dd38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "375eec79ea5643e5afe489b433c25717",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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jc3FwCgr6//1vn09fWRk5MjM62q46guIiIiEBcXh9mzZ1dq5a1opn/16hXOnz+P4cOHIzc3V/q+vHz5Er169UJMTEylS7/v0qBN7u3bt5fpFDdy5Ei0bt0aM2bMwAcffACBQICYmBhkZ2fDwsKiynW8ef3Gycmp2u29flAAkH7AKq7Fx8fHA0CVPR7d3d1lmhKVyczMDAEBAdW+XpGHm5tbpdeaNWsmd/F99eoVli1bhn379lV637Ozs+VaZ3x8PHx9fStNr2hWjI+PlykG79qHtd02UPX+bt68Oc6ePVup49vbjq/aeDMPoDyX1/OIiYnB3bt3q71c8eY+qIquru5bj5U31eYz0KlTJ2zevBmxsbF48uQJOBwO/Pz8pIV+4sSJuHz5Mjp06FDnOxtqut9tbW0rdVyKj4+Hm5tbpRheP8Zqo2J+V1fXSq+5urpW+flS5HH7tvVWrFvRx5GjoyO2bt0KiUSCJ0+e4LvvvkN6errMj76YmBgwxqr83gEgvbQQExMDABg3bly128vOzkZxcTEKCwur/R6r6gf36yoKeUVhr05ubm6l+lLVcVQXT548AYC3/rCNjY0FYwyLFi3CokWLqpwnLS2t2ss6VWnQgv4mLpeLbt26Yf369YiJiYGHhwckEgksLCywZ8+eKpd58yB9W4/26npismquhb5NRWeIN5WVldV6XcpU3eAMVeUxfPhwXLt2DV988QW8vb2hp6cHiUSC3r17N9j9qIrch/JQ1B0TNclDIpGgR48e1Z5RN23aVCGxyKuiVeXSpUt4+vQp2rRpA11dXXTq1Ak//fQT8vLyEBERoZDbmmq63+uyf2rzWait+jpuG+o4evOHYYcOHdCmTRssXLgQP/30k3Q7HA4Hp0+frjKuitaMiu+KVatWwdvbu8rt6enpobi4+J1xvU3FD7bXO26+KT4+Hjk5OZVaLpVxZ1TF+zJ37txqWyCq+hH5Nkot6ABQWloKAMjLywMAuLi44J9//kGHDh3q/U2uGGgkOjoa77//vsxr0dHRMgORGBsbV9lcVttf+/WhIs6KX8Kvi46Olvl3xZnCm4PAvJlHZmYmQkJCsGzZMixevFg6vapt1GYEJwcHh0oxAZAOfFKfg7+8vr+r2r6ZmZnct6UpYhQrFxcX5OXl1eoMu65q8xmwt7eHvb09Ll++jKdPn0qbfjt37ow5c+bg4MGDKCsrQ+fOnd+53foc9cvBwQF3796FRCKROUt/8xir6WehYv6q7q541x0XtaWqx1HLli0xZswY/Prrr5g7dy7s7e3h4uICxhicnJze+iPBxcUFAGBgYPDWmMzNzaGtrV2j77GqNG3aFE2bNsWxY8ewfv36KpveK+4IqO9xTypyvn//frU5Ozs7AyhvyVDUvlLqbWtisRjnzp2DQCCQ/roaPnw4ysrK8M0331Sav7S0VKGjkbVt2xYWFhbYvHmzzK/D06dP49GjR+jXr590mouLC6KiopCeni6ddufOnSpvu2ho1tbW8Pb2xs6dO2WawoODgytdk3ZwcACPx6t0He2XX36R+XfFL+43zyiq6iFbUQRrsm/69u2LGzduICwsTDotPz8fW7ZsgaOjY52u+b/L6+/T67Hev38f586dQ9++feVed23eg+oMHz4cYWFhOHv2bKXXsrKypD9+Fak2nwGgvNn9/PnzuHHjhrSge3t7Q19fHytWrIC2tjZ8fHzeuV1dXV25L9u8S9++fZGSkoL9+/dLp5WWlmLDhg3Q09OT3tJY08+CjY0NPD098ccff0hPPADg4sWLuHfvnkJjV+XjaN68eRCLxVizZg0AYPDgweDxeFi2bFml7wnGmPT2Vh8fH7i4uGD16tUy71+Fiu9UHo+HXr164dixY0hISJC+/ujRoypzqcrixYuRmZmJKVOmVGppCQ8Px8qVK+Hp6YkhQ4bUPHE5tGnTBk5OTli3bl2lfVnxXllYWKBr16749ddfkZycXGkdr9eammrQM/TTp09LfyWnpaVh7969iImJwfz586W3GXTp0gWTJ09GUFAQIiMj0bNnT/D5fMTExODgwYNYv349hg4dqpB4+Hw+Vq5cicDAQHTp0gUjR46U3rLj6OiIzz77TDrvJ598gjVr1qBXr16YMGEC0tLSsHnzZnh4eFTqYKFoiYmJ2L17d6Xpenp6GDRoEAAgKCgI/fr1Q8eOHfHJJ5/g1atX2LBhAzw8PGQ+RIaGhhg2bBg2bNgADocDFxcXnDhxotJ1NQMDA3Tu3Bk//PADxGIxbG1tce7cOcTFxVWKo+IL/KuvvsJHH30EPp+P/v37V3m2O3/+fPz555/o06cPZs6cCRMTE+zcuRNxcXE4fPhwvY8qt2rVKvTp0wd+fn6YMGGC9LY1Q0NDmfH3a8vb2xs8Hg8rV65EdnY2hEIh3n///Wr7glTliy++wF9//YUPPvhAeitSfn6+9L7ZZ8+eSW8LVJTafAaA8oK+Z88ecDgcaRM8j8eDv78/zp49i65du9boWqSPjw/279+POXPmoF27dtDT00P//v0VktOkSZPw66+/Yvz48QgPD4ejoyMOHTqEq1evYt26ddIzt5p+FgDg+++/x8CBA9GhQwcEBgYiMzMTP//8Mzw9PassUvJS5eOoRYsW6Nu3L7Zt24ZFixbBxcUF3377LRYsWIBnz55h0KBB0NfXR1xcHI4ePYpJkyZh7ty54HK52LZtG/r06QMPDw8EBgbC1tYWiYmJuHDhAgwMDPD3338DKL+P/MyZM+jUqROmTZsm/SHm4eHx1qb0CqNHj8bNmzexfv16PHz4EKNHj4axsTFu376N7du3w9TUFIcOHar21kFF4XK52LRpE/r37w9vb28EBgbC2toaUVFRePDggfQHysaNG9GxY0d4eXlh4sSJcHZ2RmpqKsLCwvDixQvcuXOndhuudb94OVR125pIJGLe3t5s06ZNMt34K2zZsoX5+PgwbW1tpq+vz7y8vNi8efNYUlKSdB4HBweZ2ygqVHfLUlW3ozDG2P79+1nr1q2ZUChkJiYmbPTo0ezFixeV1rt7927m7OzMBAIB8/b2ZmfPnlXqbWtvbvfw4cOsefPmTCgUshYtWrAjR45UGV96ejobMmQI09HRYcbGxmzy5Mns/v37ld6bFy9esA8//JAZGRkxQ0NDNmzYMJaUlFQpP8bKb5WxtbVlXC5XJtc3b1tjjLEnT56woUOHMiMjIyYSiVj79u3ZiRMnZOap7T58U3XLM8bYP//8wzp06MC0tbWZgYEB69+/P3v48KHMPBW3raWnp791O6/bunUrc3Z2lt5iU3ELS3XHaVXHQG5uLluwYAFzdXVlAoGAmZmZMX9/f7Z69WpWUlLy1u136dKFeXh4vHWe6m7Vquln4MGDB9Lbyl737bffMgBs0aJFb91+hby8PDZq1ChmZGQkcyzXZr+/Ld/U1FQWGBjIzMzMmEAgYF5eXlUeMzX9LDDG2L59+5i7uzsTCoXM09OT/fXXX2zIkCHM3d29UpyrVq2qtK2qPjdVUeXjqOJWvdfzOHz4MOvYsSPT1dVlurq6zN3dnU2fPp1FR0fLLBsREcEGDx7MTE1NmVAoZA4ODmz48OEsJCREZr6LFy8yHx8fJhAImLOzM9u8ebP081hTx44dYz169GDGxsZMKBQyV1dX9vnnn1f5eX5bvvLetlbhypUrrEePHkxfX5/p6uqyli1bsg0bNsjM8+TJEzZ27FhmZWXF+Hw+s7W1ZR988AE7dOhQjfOtwPkvQKKhxo8fj9DQUKU+7IEQTeXt7Q1zc3MEBwcrOxRC6PGphBDyLmKxuNK159DQUNy5c6dRPAaZqAel93InhBBVl5iYiICAAIwZMwY2NjaIiorC5s2bYWVlpbDBhwipKyrohBDyDsbGxvDx8cG2bduQnp4OXV1d9OvXDytWrICpqamywyMEAEDX0AkhhBANQNfQCSGEEA1ABZ0QQgjRAI32GrpEIkFSUhL09fXrdRhKQgghqosxhtzcXNjY2NT7wFb1rdEW9KSkJNjZ2Sk7DEIIISrg+fPnaNKkibLDqJNGW9Arhn98/vy5dNjZ2qoYi75ieFp1RDmoBspBNVAOqqEhc8jJyYGdnd07n6OuDhptQa9oZjcwMKhTQdfR0YGBgYFaf3AoB+WjHFQD5aAalJGDJlx6Ve8LBoQQQggBQAWdEEII0QhKL+iXLl1C//79YWNjAw6Hg2PHjr1zmdDQULRp0wZCoRCurq7YsWNHvcdJCCGEqDKlX0PPz89Hq1at8Mknn2Dw4MHvnD8uLg79+vXDlClTsGfPHoSEhODTTz+FtbU1evXq1QARE0KIcpSVlUEsFr91HrFYDC0tLRQVFaGsrKyBIlMsRebA5/PB4/EUFJlqU3pB79OnD/r06VPj+Tdv3gwnJyf8+OOPAIDmzZvjypUrWLt2LRV0QohGYowhJSUFWVlZNZrXysoKz58/V9uOXorOwcjICFZWVmr7ftSU0gt6bYWFhSEgIEBmWq9evTB79mzlBETUVpmEoVBchiLpnwQlpRJwuQCPwwGXywGPw4GQz4W+iA9dAU/jvxCIaqoo5hYWFtDR0XnrcSiRSJCXlwc9PT21HShFUTkwxlBQUIC0tDQAgLW1taJCVElqV9BTUlJgaWkpM83S0hI5OTkoLCyEtrZ2lcsVFxejuLhY+u+cnBwA5U0772rCqk7FcvIurwo0NYfSMgkSs4vw/FUhEl4V4HlmIZKyCvEyvwQv80rwqqAEmQVi1ObRRDwuB3pCHvSFWjDRE8BSXwQrAyEsDUSwNBDC3kQHTmY6MNYRKCQHdUM51I+ysjJkZmbC3NwcxsbG75yfMYaSkhIIhUK1/QGqyByEQiEkEgnS09NhbGxcqfldlfZ1XaldQZdXUFAQli1bVmn6uXPnoKOjU6d1BwcH12l5VaDOOZSUAc/zgUt//IMX+RwkFnCQUgCUspp/EfA5DHwuoMUFJAAYAySs/P/FEkDCOCiTMGQXliK7sBQvsooA5FS5Lh0tBgsRYKHNYKPDYKfLYKsLaNfg06bO+6EC5aBYWlpasLKygkQikZ6I1ERubm49RtUwFJWDRCJBYWEhQkJCUFpaKvNaQUGBQrahCtSuoFtZWSE1NVVmWmpqKgwMDKo9OweABQsWYM6cOdJ/V4wO1LNnzzoNLBMcHIwePXqo9QAO6pZDXnEpbj7LxK34TNyKz8LdF9kolVQ+1RZocWFnrA17E23Ym+jA1kgb5noCmOgKYKpb/l89oRaEWlxwudUXf8YYisQS5BSJkVtUityiUqTnFSMttxipOcVIzSlCcnYR4l8VIjm7CAWlHDzLA57lya7TwUQHHjb68LYzQjsHY7hb6UGLV96cqI774U2UQ/0oKirC8+fPoa+vD5FI9M75K8YmV+fnVCg6h6KiImhra6Nz586V3sPa/EhSdWpX0P38/HDq1CmZacHBwfDz83vrckKhEEKhsNJ0Pp9f5w+uItahbKqew7OMfJyPSsOF6DRcf/oKJWUSmdcN+AztXCzgYWOIFjYGaG5tADtjnbcW6toQCAAD3Xd/mRaUlOJZRgGeZuQhNi0PD5Ny8CApB4lZhYh/VYD4VwU4db/8B6meUAttHIzR3tEY7R2MIGGqvx9qgnJQrLKyMnA4HHC53BpdT5ZIyj8bFcuoI0XnwOVyweFwqtyvqrKfFUHpBT0vLw+xsbHSf8fFxSEyMhImJiawt7fHggULkJiYiD/++AMAMGXKFPz888+YN28ePvnkE5w/fx4HDhzAyZMnlZUCqSfPXxXgrztJ+CsyCdGpsk1vdiba8HM2RTtHE7SxM8C9sFD069da6R9OHYEWWtgYoIWNbKtPZn4JHiTl4M6LLNx69gq34jORW1SKS4/TcelxevmyPB7+ybuLru4W6NLUHBYG7/4BQQghFZRe0G/duoVu3bpJ/13RLD5u3Djs2LEDycnJSEhIkL7u5OSEkydP4rPPPsP69evRpEkTbNu2jW5Z0xA5RWIcj0jEkYhERCRkSadrcTlo52iC990t0M3dAi7mutKmOLFYjPsq3rJorCtARzczdHQzA1Dewz46JRc34l7ixrNXuBKTgZyiUpy8n4KT91MAAB42BujjaYXentZwtdBTZviEyGX8+PHIysqqNGBYaGgounXrhszMTBgZGdVqnZcuXcKqVasQHh6O5ORkHD16FIMGDVJYzOpM6QW9a9euYG/palzVKHBdu3ZFREREPUZFGtr9xGzsuR6P45FJKCgpH0iCywH8XcwwoJUNenlYwVBHc5rGeFyO9Ex+fAcnFBYV49dDZ1Bi2hRXnrzE3RfZePBfc/3qc4/R1FIPvT2t0dfLCs0s1ffaKCF1VdvByBoTpRd00nhJJAzBj1Kx+eITmbNxNws9fNTeHv1bWcNCv3E0O2vxuHDSB/oGuGJen+bIyCtGyKNUnLqXgquxGXicmofHqTH4KSQG7lb6GNzGFoO8balZnjQ6tR2MrDGhgk4aXEmpBMciE/HrxSd4kp4PAODzOOjjaY3RvvZo72TS6M9AzfSEGNHOHiPa2SO7QIx/HqXi9P0UXHqcjqiUXHx/KgorTkehk5s5BrexRc8WVtAWNI7hLUl5L/BCcdVDokokEhSWlEGrpLReOsVp8xU7wFJCQgJatGjx1nkWLlyIhQsXKmybmooKOmkwpWUSHIlIxPp/YpCYVQgA0BdpYayfA8b7O8Fcv/JdCAQw1OFjiE8TDPFpguwCMU7eS8bh2y8QHp+Ji4/TcfFxOvRFWhjSpgnGvGcPVwt9ZYdM6lmhuAwtFp9VyrYfLu8FHUHNS8eJEyegpyfbB+T18dltbGwQGRkp8/qbI8WZmJjUKebGggo6qXeMMZx9kIrV56IRm5YHALDQF2JCRyeM8rWHvkhzro3XN0MdPkb52mOUrz2eZeTjSEQijtx+gReZhdhx7Rl2XHuG95xNMOY9B/RsYQWBlnretkQ0R7du3bBp0yaZadevX8eYMWMAlA+c4+rqKvN6xSA6BgYGanvrnTJQQSf16t6LbCz56z5u/3eN3EiHj+ldXfGxnwNEfGoirgtHM13M6dEUs7u74XJsBnaFxeN8VCr+ffoK/z59BXN9Icb4OuBjPweY6NZ+OFqiurT5PDxcXvWdPRKJBLk5udA30K+3Jvfa0NXVrVSwX7x4If1/anJXHCropF5kFZRg1dlo7L2RAMbKvwQ+7eSEiZ2dYUBn5ArF5XLQpak5ujQ1R2JWIfbdSMC+m8+RnluMtf88xi+hsRjq0wQTOjrB2Zxuf9MEHA6n2mZviUSCUgEPOgIttTi7pSZ3xaGCThSKMYaDt14g6PQjZBaUP/RgoLcNFvZtDkvqkV3vbI208XnPZpjZ3Q2n76dg66WnuJeYjT3XE7D3RgJ6NLfExM7OaOdIX5BENdS2yf1dg5E1ZlTQicIkZhVi/uG7uByTAQBoZqmPZQM98J6zqZIja3z4PC4GtLJB/5bWuB73ClsvPUVIVBrOPUzFuYepaO9kglnd3eDvYtro7ygg6uVdg5E1ZlTQSZ0xxrD/5nN8e/IR8opLIdTi4vOeTRHYwQl8nuo3+WkyDoeD95xN8Z6zKWLTcvHblTgcDk/EjbhXGL3tOto6GGNmdzd0cjOjwk4UrroC+64Bxd6mLstqOiropE5e5Zdg7sE7OB+VBgBoY2+EVcNawYWu1aocVwt9BA1uiVndm2LzxSfYeyMBt+IzMXb7DXjbGWFWdzd0bWZOhZ0QNUWnT0Ru/z59iT7rL+F8VBoEWlx81bc5Dk7xp2Ku4qwMRVg6wANX5nXDhI5OEPG5iHyehcAdNzFscxhuPXul7BAJIXKggk5qrUzCsO6fxxi19V+k5hTDxVwXx6d3wMTOzuAp6HGlpP5ZGIiw6IMWuDzvfUzsVF7Yb8VnYujmMHy68yaiU3LfvRJCiMqggk5qJbtAjE923MS6f2IgYcAwnyb4+/86orm1wbsXJirJXF+Ir/q1wMUvumFke3vwuBz88ygNvddfwucH7uBFZoGyQySE1AAVdFJjsWm5GPTLVVx8nA4Rn4u1I1ph1bBWtRoGkqguSwMRggZ74dxnndHXywqMAYdvv8D7qy9ixeko5BWXKjtEQshbUEEnNRLyKBWDNl5DXEY+bI20cXiqPz5s3UTZYZF64GKuh19G++DY9A7wczZFSZkEmy8+QbfVoThw6zkkEuphrAwSiUTZIaitxvLe0akVeaed155h6d8PwBjQ3skEm0a3gakePUhF03nbGWHvRF+EPErDtycf4tnLAsw7dBe7wuKxpH8LtKXBaRqEQCAAl8tFUlISzM3NIRAI3nongkQiQUlJCYqKitRipLiqKCoHxhhKSkqQnp4OLpcLgUCzh0Cmgk6qxRjDD2ejsSn0CQBgZHt7LB/oQfeWNyIcDgcBLSzRuak5dlyLw4aQWNxLzMbQzWHo38oGC/u6w9pQW9lhajQulwsnJyckJycjKSnpnfMzxlBYWAhtbW21vQVR0Tno6OjA3t5ebX/g1BQVdFIlcZkEXx6+iyO3EwEAc3s2xfRurmr7BUHqRqDFxaTOLviwdRP8eC4a+289x993knD+USo+69EU4/0dlR2iRhMIBLC3t0dpaanMo0erIhaLcenSJXTu3Bl8vno+N0GROfB4PGhpaTWK7y4q6KSSInEZpuwOR2h0OnhcDoIGe2F4Wztlh0VUgLm+ECuGtMSY9xyw5K8HCI/PxLcnH+Hw7UQs6++u7PA0GofDAZ/Pf2eB4/F4KC0thUgkUtuCrgk5KINmtz+QWissKcOnO28hNLq8J/u2sW2pmJNKPG0NcXCyH1YO8YKRDh+PknMwYusN7H/KRXahWNnhEdIoUUEnUgUlpfhkx01cic2AjoCHnYHt0c3dQtlhERXF5XIwop09QuZ0wVCfJmAMuJbKRa/1V3EsIpHG2yakgclV0B89eoQlS5bg/fffh4uLC6ytrdGyZUuMGzcOe/fuRXFxsaLjJPUsv7gU47ffRNjTl9ATauGPT9rDl56SRmrAVE+I1cNaYfcnbWGpzfAyvwSz90diws5bSM4uVHZ4hDQatSrot2/fRkBAAFq3bo0rV67A19cXs2fPxjfffIMxY8aAMYavvvoKNjY2WLlyJRV2NSGWAFP3RuLGs1fQF2lh14T2dEsSqTVfJxPMa1mGz7q7QsDj4nxUGnquuYR9NxLobJ2QBlCrTnFDhgzBF198gUOHDsHIyKja+cLCwrB+/Xr8+OOPWLhwYV1jJPVIXCbBzsdc3Mt8BV0BD7sm+MLbzkjZYRE1pcUFpnV1Rt+WNvji0F1EPs/C/CP3cOJuMoIGe8HOREfZIRKisWpV0B8/flyjHod+fn7w8/ODWEydY1SZRMKw4OgD3MvkQqDFxbZx7aiYE4Vws9TH4an++P1qHFadjcaV2Az0WncJ8/u4Y4yvA7j0EB9CFK5WTe61vX2AbjdQXYwxLD/xEMfvJIPLYdjwUSv4udA1c6I4PC4Hn3ZyxpnZndHe0QQFJWVYfPwBxvx2HUlZdG2dEEWT+z705cuXv/X1xYsXy7tq0gB+uxKHHdeegcMBRrtI8H4zc2WHRDSUk5ku9k16D7v+jceK01G49uQleq+7hG8GeWKgt62ywyNEY8h929rRo0dl/g4cOICVK1fixx9/xLFjx2q9vo0bN8LR0REikQi+vr64cePGW+dft24dmjVrBm1tbdjZ2eGzzz5DUVGRnNk0LmcfpOC7U48AAPN7NUVbc+qwROoXl8vBOH9HnJzZEa3sjJBTVIpZ+yIx888IZBfQpTlCFEHuM/SIiIhK03JycjB+/Hh8+OGHtVrX/v37MWfOHGzevBm+vr5Yt24devXqhejoaFhYVL4Peu/evZg/fz62b98Of39/PH78GOPHjweHw8GaNWvkTalRuPsiC7P3RYIxYLSvPQL9HXD69ENlh0UaCWdzPRya4oeNF2Kx4Xws/rqThJvPXmH1sFbo4Gqm7PAIUWsKHVjGwMAAy5Ytw6JFi2q13Jo1azBx4kQEBgaiRYsW2Lx5M3R0dLB9+/Yq57927Ro6dOiAUaNGwdHRET179sTIkSPfeVbf2CVlFWLCzlsoFJehS1NzLBvg0SjGNyaqhc/jYnZAUxya4gcnM10kZxdh9Lbr+ObEQxSXvn2cckJI9RQ+Ulx2djays7NrPH9JSQnCw8MREBDwv6C4XAQEBCAsLKzKZfz9/REeHi4t4E+fPsWpU6fQt2/fugWvwYrEZZi6OxzpucVwt9LHz6NaQ4uemkaUqLW9MU7O7IjRvvYAyvt1DNl0DXEZ+UqOjBD1JHeT+08//STzb8YYkpOTsWvXLvTp06fG68nIyEBZWRksLS1lpltaWiIqKqrKZUaNGoWMjAx07NgRjDGUlpZiypQpb73nvbi4WGagm5ycHADlT/WR9/a6iuXU4fa8Jccf4M6LbBhqa+GXUa0g4snmrg45VIdyUA3y5MDnAEs/cEdnN1PMP3If9xNz8MFPl7F8QAsMaGVdX6FWq7HuB1XTkDmo8/v0Jg6TcwgnJycnmX9zuVyYm5vj/fffx4IFC6Cvr1+j9SQlJcHW1hbXrl2Dn5+fdPq8efNw8eJFXL9+vdIyoaGh+Oijj/Dtt9/C19cXsbGxmDVrFiZOnFhtc//SpUuxbNmyStP37t0LHR3NHuwiLJWDfU954IBhcnMJmhtRJziierKKgT9ieHiSW34ZyNdcgiFOEgh5Sg6MaLSCggKMGjUK2dnZMDAwUHY4dSJ3QVeUkpIS6Ojo4NChQxg0aJB0+rhx45CVlYXjx49XWqZTp0547733sGrVKum03bt3Y9KkScjLy6vyIfZVnaHb2dkhIyND7p0oFosRHByMHj16qOw993dfZOOjbTcgLmOYE+CKqV2cZV5XhxzehXJQDYrIobRMgo2hT7Hx4lMwBriY6+KnES3R1LJmJwh1RftBNTRkDjk5OTAzM9OIgq7056ELBAL4+PggJCREWtAlEglCQkIwY8aMKpcpKCioVLR5vPKf8dX9PhEKhRAKhZWm1+T5wu+iiHXUh+xCMWbuvwtxGUPPFpaY8X7TakfoUtUcaoNyUA11yYHPB+b2bg5/N3PM3heJJ+n5GLz5OpYO8MBH7ewarBNnY98PqqIhclD39+h1teoVNWXKFLx48aJG8+7fvx979uyp0bxz5szB1q1bsXPnTjx69AhTp05Ffn4+AgMDAQBjx47FggULpPP3798fmzZtwr59+xAXF4fg4GAsWrQI/fv3lxb2xo4xhq+O3kNiViHsTLSxengrGm6TqA1/FzOcmtUJXZqao7hUggVH7uGLQ3dRJKZe8IRUp1Zn6Obm5vDw8ECHDh3Qv39/tG3bFjY2NhCJRMjMzMTDhw9x5coV7Nu3DzY2NtiyZUuN1jtixAikp6dj8eLFSElJgbe3N86cOSPtKJeQkCBzRv7111+Dw+Hg66+/RmJiIszNzdG/f3989913tUlHox0Mf4ETd5OhxeXgp49aw0CkOb9CSeNgpifE7+Pb4ddLT7HqbBQOhb/Aw6QcbB7jA3tTze73Qog8alXQv/nmG8yYMQPbtm3DL7/8gocPZQck0dfXR0BAALZs2YLevXvXKpAZM2ZU28QeGhoqG7SWFpYsWYIlS5bUahuNxZP0PCw5/gAAMKdnU7S2N1ZyRITIh8vlYGpXF7RqYoj/+zMCD5Nz8MGGy1g7whvdm1u+ewWENCK1voZuaWmJr776Cl999RUyMzORkJCAwsJCmJmZwcXFhQYqUbKSUglm/hmBQnEZ/F1MMaWzi7JDIqTO/F3NcGJmR0zbcxsRCVmYsPMW/u99V8wOaAoeXUoiBEAdO8UZGxvD2JjO/lTJL6GxeJCUAyMdPtaO8Kbr5kRjWBtqY/8kP3x38iF2hsVjw/lYRD7PwvqPWsNEV6Ds8AhROhoqTIM8SMrGz+djAQDLB3rC0kCk5IgIUSyBFhfLBnpi3QhvaPN5uByTgf4bruBBUs1HpyREU1FB1xAlpRLMPXgXpRKG3h5W6N+y4UfZIqShDGpti6PT/eFoqoPErEIM3RSGU/eSlR0WIUpFBV1D/BIai0fJOTDW4eObQZ7Ul4FoPHcrAxyf3hGd3MxQKC7DtD23sSb4MSQSGgmRNE5U0DVAVEqOtKl92UBPmOtXHkCHEE1kqMPH7+Pb4dOO5UNR/xQSg6l7wpFfXKrkyAhpeHIX9O3btyMuLk6RsRA5SCQMXx+9j1IJQ48WltTUThodLR4XX3/QAquHtYKAx8XZB6kYsukanr8qUHZohDQouQt6UFAQXF1dYW9vj48//hjbtm1DbGysImMjNXAo/AVuxWdCR8Cj55uTRm2oTxPsm/wezPWFiErJxYCfr+Dakwxlh0VIg5G7oMfExCAhIQFBQUHQ0dHB6tWr0axZMzRp0gRjxoxRZIykGpn5JQg6/QgAMDvADTZG2kqOiBDlamNvjL9ndETLJobILBBj7G83sP9mgrLDIqRB1Okauq2tLUaPHo21a9di/fr1+Pjjj5Gamop9+/YpKj7yFivPRCGzQIxmlvoI7OD07gUIaQSsDEU4MNkPA1rZoFTC8OXhe1h5Joo6yxGNJ3dBP3fuHBYuXAh/f3+YmppiwYIFMDY2xqFDh5Cenq7IGEkVbidkYt/N5wCAbz/0BJ9H/RsJqSDi87D+I2/M7O4GANgU+gT/92cEPdyFaDS5R4rr3bs3zM3N8fnnn+PUqVMwMjJSYFjkbRhjWP53+Tj6Q32aoJ2jiZIjIkT1cDgczOnRFA4mOph/5C5O3ktGUnYhto5tCzM9uhOEaB65T+vWrFmDDh064IcffoCHhwdGjRqFLVu24PHjx4qMj1Th77vJiHyeBR0BD/N6NVN2OISotCE+TbBrgi8MtfmISMjCoI1XEZOaq+ywCFE4uQv67NmzceTIEWRkZODMmTPw9/fHmTNn4OnpiSZNmigyRvKaInEZVp6OAgBM7eICCxrelZB3es/ZFEem+cPBVAcvMgsxeNM1XImhHvBEs9TpwitjDLdv30ZwcDDOnj2LCxcuQCKRwNzcXFHxkTdsvxqHxKxCWBuK8GknZ2WHQ4jacDHXw9FpHdDWwRi5RaUY//sNHA5/oeywCFEYuQt6//79YWpqivbt22PPnj1o2rQpdu7ciYyMDERERCgyRvKf9Nxi/HLhCQBgXu9m0BbwlBwRIerFRFeA3Z/6SnvAf37wDn4JjQVj1AOeqD+5O8W5u7tj8uTJ6NSpEwwNDRUZE6nGxguxyCsuRasmhhjYylbZ4RCilkR8HtaN8IaVoQhbLj3FD2eikZZTjEUftFB2aITUidwFfdWqVYqMg7xDYlYh9l4vHyDjy97u9JxzQuqAy+VgYd/msNAX4tuTj7Dj2jOk5Rbhhw89lB0aIXKr0zX0ixcvon///nB1dYWrqysGDBiAy5cvKyo28pqfz8egpEwCP2dT+LuaKTscQjTCp52c8dPI1uDzODh1LwWf/HEbBfRcF6Km5C7ou3fvRkBAAHR0dDBz5kzMnDkT2tra6N69O/bu3avIGBu9Zxn5OHCrvPPO5z2bKjkaQjTLgFY22BHYHnpCLdx4lomfHvCQklOk7LAIqTW5C/p3332HH374Afv375cW9P3792PFihX45ptvFBljo/dTSAzKJAxdm5mjLQ0iQ4jCdXA1w/7J78FcT4DkAg5GbLmB2DS6V52oF7kL+tOnT9G/f/9K0wcMGECPVVWg2LRcHI1MBAB83oMGkSGkvnjYGOLAJF9YiBiSsoswbHMY7r7IUnZYhNSY3AXdzs4OISEhlab/888/sLOzq1NQ5H9+CX0CxoCeLSzh1YTuJiCkPjUx1sYszzK0tDVAZoEYo7Zex79PXyo7LEJqRO5e7p9//jlmzpyJyMhI+Pv7AwCuXr2KHTt2YP369QoLsDF7/qoAxyOTAAAz3ndVcjSENA56fGBnYFtM23sHYU9fYtz2G9g0pg3ed7dUdmiEvJXcZ+hTp07Fvn37cO/ePcyePRuzZ8/G/fv3sX//fkyePFmRMTZaWy8/RZmEoaOrGVo2MVJ2OIQ0GnpCLfwe2A4BzS1QXCrBpD/Ccfy/S1+EqCq5z9AB4MMPP8SHH36oqFjIa9Jzi7H/v8ejTuvqouRoCGl8RHweNo3xwRcH7+BYZBJm749EXnEpRvs6KDs0QqpED9FWUb9fjUNxqQTedkbwczFVdjiENEp8HhdrhntjrJ8DGAO+Onofm0KfKDssQqpUq4JubGwMExOTGv3V1saNG+Ho6AiRSARfX1/cuHHjrfNnZWVh+vTpsLa2hlAoRNOmTXHq1Klab1cV5RaJsSssHkD52TmHQ6PCEaIsXC4HywZ4YEa38n4sK89EYeWZKBr/naicWjW5r1u3rl6C2L9/P+bMmYPNmzfD19cX69atQ69evRAdHQ0LC4tK85eUlKBHjx6wsLDAoUOHYGtri/j4eBgZGdVLfA3twK0XyC0uhYu5LgKaU0ccQpSNw+Fgbq9mMNDWwvenorAp9AkKikuxdIAH/eAmKqNWBX3cuHH1EsSaNWswceJEBAYGAgA2b96MkydPYvv27Zg/f36l+bdv345Xr17h2rVr4PP5AABHR8d6ia2hlUkYdl57BgAI7OBEY7YTokImdXaBvoiPhUfvYWdYPMQShm8HetLnlKiEWneKW7x4MebPnw8dHR0AQGZmJoyNjeUOoKSkBOHh4ViwYIF0GpfLRUBAAMLCwqpc5q+//oKfnx+mT5+O48ePw9zcHKNGjcKXX34JHq/qR4oWFxejuLhY+u+cnBwAgFgshlgsliv2iuXkXb4qIVFpSHhVAAORFvp7WSh03VWpjxwaGuWgGhpLDkNbW4MHhvlH72Pv9QQUi0vx3UAP8FSkqDeW/aDobWkCDqvlhSAej4fk5GRpU7iBgQEiIyPh7OwsVwBJSUmwtbXFtWvX4OfnJ50+b948XLx4EdevX6+0jLu7O549e4bRo0dj2rRpiI2NxbRp0zBz5kwsWbKkyu0sXboUy5YtqzR979690h8nqmDjQy4eZ3Pxvo0EAx0kyg6HEFKNW+kc7InlQgIOfMwkGO0qAU81ajqphYKCAowaNQrZ2dkwMDBQdjh1Uusz9DfrvzI6hkgkElhYWGDLli3g8Xjw8fFBYmIiVq1aVW1BX7BgAebMmSP9d05ODuzs7NCzZ0+5d6JYLEZwcDB69Oghbfqvi8epuXgcFgYuB1g8sgtsjbTrvM53UXQOykA5qIbGlkNfAO3up2DOwXsIz+DC0soaq4d6gc9T7s1DjW0/1FVFa60mqNN96IpgZmYGHo+H1NRUmempqamwsrKqchlra2vw+XyZ5vXmzZsjJSUFJSUlEAgElZYRCoUQCoWVpvP5/DofMIpYBwDsvlH+RLVeHlZwNG/YX4qKykGZKAfV0JhyGNDaDiIBH9P33sap+6koY8CGkW0g0FL+HcGNaT/UdRuaotZHHYfDQW5uLnJycpCdnQ0Oh4O8vDzk5OTI/NWUQCCAj4+PzLjwEokEISEhMk3wr+vQoQNiY2MhkfyvSfrx48ewtrauspirg9wiMY5FlA/zOt7fUbnBEEJqrKeHFbZ83BYCLS7OPkjF1N3hKBKXKTss0gjVuqAzxtC0aVPpPel5eXlo3bo1jI2NYWxsDCMjo1p3kpszZw62bt2KnTt34tGjR5g6dSry8/Olvd7Hjh0r02lu6tSpePXqFWbNmoXHjx/j5MmT+P777zF9+vTapqMyjkcmoVBcBlcLPbR3okekEqJOurlbYNvYthBqcRESlYZJu6iok4ZX6yb3CxcuKDyIESNGID09HYsXL0ZKSgq8vb1x5swZWFqW34OdkJAALvd/vz3s7Oxw9uxZfPbZZ2jZsiVsbW0xa9YsfPnllwqPraHsu5kAAPionR3d10qIGurc1By/B7bDhB23cOlxOibvCseWsT4QalV95w0hilbrgt6lS5f6iAMzZszAjBkzqnwtNDS00jQ/Pz/8+++/9RJLQ7ufmI37iTkQ8LgY3KaJssMhhMjJ38UMOwLbYfzvN3HxcTqm7r6NTWPaUFEnDUL5PTcI/rxRfnbe08MSJrrq2QeAEFLO19kUv41vCxGfi/NRaZi+JwIlpXQLKql/VNCVrKCkVPrM85Ht7ZUcDSFEEfxdzLBtbDsItbj451Eq/u/P2xCXUVEn9YsKupKdupeCvOJS2JvowM+ZnqpGiKbo6GaGrWP/1/t91r4IKuqkXlFBV7JjEYkAgKE+TWg8aEI0TOem5vh1jA8EPC5O3UvBZ/sjUUpFndQTKuhKlJpThKtPMgAAg7xtlRwNIaQ+dHO3wKYxbcDncXDibjI+P3gHZRJ69CpRvFr1ch88eHCN5z1y5Eitg2ls/r6TBMYAHwdj2JuqznjyhBDF6t7cEhtHtcG0PbdxPDIJPA4Hq4e1olY5olC1OkM3NDSU/hkYGCAkJAS3bt2Svh4eHo6QkBAYGhoqPFBNdPS/5vZBrensnBBN19PDCj+Pag0el4MjEYn4+vh9pTwLg2iuWp2h//7779L///LLLzF8+HBs3rxZOqZ6WVkZpk2bpvZPrGkIMam5eJCUAy0uBx94WSs7HEJIA+jtaY11Ixhm7ovA3usJ0BXwsLBvcxpMiiiE3NfQt2/fjrlz58o8IIXH42HOnDnYvn27QoLTZMciy8/OuzazgDHde05Io9G/lQ1WDPYCAGy9HIf1ITFKjohoCrkLemlpKaKioipNj4qKknloCqmMMYa/7pTfez6otY2SoyGENLQR7eyx+IMWAIB1/8Rg2+WnSo6IaAK5H58aGBiICRMm4MmTJ2jfvj0A4Pr161ixYoX0oSqkag+ScvD8VSFEfC7ed7dQdjiEECX4pKMT8otL8WPwY3x78hF0BFoY5UuDSxH5yV3QV69eDSsrK/z4449ITk4GUP6c8i+++AKff/65wgLURGfupwAAuja1gI5A6Y+kJ4QoyYz3XZFXUopfLz7FV8fuQVfIw0C6hZXISe5qwuVyMW/ePMybN0/6/HPqDFczp++X/wDq42Wl5EgIIcrE4XAwv7c7CorLsOvfeMw5cAfafB56etB3A6m9Og0sU1pain/++Qd//vmntJdmUlIS8vLyFBKcJopJzcWT9HwIeNTcTggpL+rLBnhgcBtblEkYZuyNwOWYdGWHRdSQ3AU9Pj4eXl5eGDhwIKZPn4709PIDcOXKlZg7d67CAtQ0p/9rbu/oZgZ9EV/J0RBCVAGXy8EPQ1qij6cVSsokmPRHOMLjM5UdFlEzchf0WbNmoW3btsjMzIS2trZ0+ocffoiQkBCFBKeJKgp6b09qUiOE/I8Wj4v1H7VGl6bmKBSX4ZMdN/E4NVfZYRE1IndBv3z5Mr7++msIBLL3UDs6OiIxMbHOgWmi568K8Cg5BzwuBz2aWyo7HEKIihFocbFpTBu0sTdCdqEYY3+7gReZBcoOi6gJuQu6RCJBWVlZpekvXryAvr5+nYLSVBei0wAAbR2MaTAZQkiVdARa2D6+Hdws9JCSU4Sxv93Ay7xiZYdF1IDcBb1nz55Yt26d9N8cDgd5eXlYsmQJ+vbtq4jYNM75qPKC3o06wxFC3sJIR4A/JrSHrZE2nmbkI3DHTeQVlyo7LKLi5C7oP/74I65evYoWLVqgqKgIo0aNkja3r1y5UpExaoTCkjKEPXkJANS7nRDyTtaG2vhjQnuY6Apw90U2Ju+6heLSyq2ihFSQu6A3adIEd+7cwVdffYXPPvsMrVu3xooVKxAREQELCypYbwp7moHiUglsjbThZqGn7HAIIWrAxVwPv49vBx0BD1djX2LOfnqWOqlenYYp09LSwujRozF69GhFxaOx/tfcbk5PViKE1FgrOyNs+bgtAnfcwMl7yTDRFWD5QA/6HiGVyH2GzuPx0K1bN7x69UpmempqqswT2Ej5w1guRJXfp0/N7YSQ2uroZoa1I7zB4QC7/o2nJ7SRKsld0BljKC4uRtu2bfHgwYNKr5H/iU3LQ2JWIYRaXPg5myk7HEKIGvqgpQ2WD/QEUP6Etl3/xis5IqJq5C7oHA4Hhw8fRv/+/eHn54fjx4/LvEb+50psBgCgvZMJtAXUekEIkc/H7zlgdoAbAGDJ8fs49yBFyRERVVKnM3Qej4f169dj9erVGDFiBL799ls6O6/Ctf96t/u70Nk5IaRuZnV3w8j2dpAwYOa+CNxOoCFiSTmFPLtz0qRJcHNzw7Bhw3Dp0iVFrFJjlJZJ8O/TioJuquRoCCHqjsPh4JuBnkjJLsKF6HR8uvMWDk/1h5OZrrJDI0om9xm6g4ODTOe3bt264d9//8Xz58/lWt/GjRvh6OgIkUgEX19f3Lhxo0bL7du3DxwOB4MGDZJru/XtQVIOcotKoS/SgqetobLDIYRoAC0eFz+PaoOWTQzxKr8E43+/gQwaTa7Rk7ugx8XFwdRU9ozT1dUVERERePr0aa3WtX//fsyZMwdLlizB7du30apVK/Tq1QtpaWlvXe7Zs2eYO3cuOnXqVOv4G8rVJ+XXz99zNgWPS30LCCGKoSvUwm/j2sHORBvxLwswYcdNFJTQaHKNWZ2eh14VkUgEBweHWi2zZs0aTJw4EYGBgWjRogU2b94MHR0dbN++vdplysrKMHr0aCxbtgzOzs51DbveXIstb27vQM3thBAFM9cXYmdgexjr8HHnRTb+b28ESsskyg6LKEmtrqGbmJjg8ePHMDMzg7Gx8Vt7s795f3p1SkpKEB4ejgULFkincblcBAQEICwsrNrlli9fDgsLC0yYMAGXL19+53aKi4tRXPy/JqmcnBwAgFgshlgsrlGsb6pYrrrli0sluPms/H1o72gk93bq07tyUAeUg2qgHJTDzkiIzaNbY+zvtxASlYYlfz+EP1+9cnhTQ+4HdX6f3lSrgr527Vrpk9RefzBLXWRkZKCsrAyWlrKPE7W0tERUVFSVy1y5cgW//fYbIiMja7ydoKAgLFu2rNL0c+fOQUdHp1Yxvyk4OLjK6U9ygOJSLejxGR7fvIQYFW5xry4HdUI5qAbKQTlGO3Pw+2MuDoQnId+OA44a5vCmhtgPBQWa83jaWhX0cePGVfn/DSk3Nxcff/wxtm7dCjOzmt8GtmDBAsyZM0f675ycHNjZ2aFnz54wMDCQKxaxWIzg4GD06NEDfD6/0uu/XooDHsTA380S/fp5y7WN+vauHNQB5aAaKAfl6gugyb8JWH4yCief89CxTXMMbWun7LDk0pD7oaK1VhPUqqDXJvGaFkkzMzPweDykpqbKTE9NTYWVlVWl+Z88eYJnz56hf//+0mkSSfk1Iy0tLURHR8PFxaXSckKhEEKhsNJ0Pp9f5wOmunVEvsgGALR3MlX5LwdFvA/KRjmoBspBeT7p5ILk7CJsvfIMi/6OgoOFgVqPf9EQ+0Ed93N1atUpzsjICMbGxm/9q5inpgQCAXx8fBASEiKdJpFIEBISAj8/v0rzu7u74969e4iMjJT+DRgwAN26dUNkZCTs7FTjFyljDOHx5QM++DjU/P0ghJC6mNvDDa1NJSiVMEzZFY4n6XnKDok0kFqdoV+4cKFegpgzZw7GjRuHtm3bon379li3bh3y8/MRGBgIABg7dixsbW0RFBQEkUgET09PmeWNjIwAoNJ0ZXqakY/MAjGEWlx42ND954SQhsHlcjDaVQLoGCPieTY+2XETR6d1gImuQNmhkXpWq4LepUuXeglixIgRSE9Px+LFi5GSkgJvb2+cOXNG2lEuISEBXK7C77CrV+HPys/OWzUxgkBLvWInhKg3PhfYNLo1hm25jviXBZj0xy3s/tQXIj49S0KT1Xno14KCAiQkJKCkpERmesuWLWu1nhkzZmDGjBlVvhYaGvrWZXfs2FGrbTWEW/Hlt6v5OFJzOyGk4ZnqCvD7+Hb48JdruBWfiS8P38W6Ed708CwNJndBT09PR2BgIE6fPl3l62VlZXIHpQkqrp+3pevnhBAlcbXQx+YxPhi3/QaORybB0VQXn/VoquywSD2Ruy149uzZyMrKwvXr16GtrY0zZ85g586dcHNzw19//aXIGNVOTpEYT9LzAQCt7amgE0KUp4OrGb4dVN6/aH1IDI5GvFByRKS+yH2Gfv78eRw/fhxt27YFl8uFg4MDevToAQMDAwQFBaFfv36KjFOtPEgsv73P1kibOqIQQpTuo/b2iHuZj18vPsWXh+7B1kgH7Z1MlB0WUTC5z9Dz8/NhYWEBADA2NkZ6ejoAwMvLC7dv31ZMdGrqXmIWAKBlE+rdTghRDV/2ckdvDyuUlEkwedctPMvIV3ZIRMHkLujNmjVDdHQ0AKBVq1b49ddfkZiYiM2bN8Pa2lphAaqje/+dodPjUgkhqoLL5WDtCG+0amKIzAIxPtlxE1kFJe9ekKgNuQv6rFmzkJycDABYsmQJTp8+DXt7e/z000/4/vvvFRagOrqfWD5CnBcVdEKICtEW8LB1XFvYGmnjaUY+puwOh5iezqYx5L6GPmbMGOn/+/j4ID4+HlFRUbC3t6/VGOuaJqdIjLj/mrKooBNCVI2Fvgi/jW+LIb9cw79PX2HpXw/w3Ydeyg6LKIDCRjzR0dFBmzZtGnUxB/53dt7EWBvG1CGOEKKC3K0MsP6j1uBwgD3XE7Ar7JmyQyIKIPcZOmMMhw4dwoULF5CWliZ9QEqFI0eO1Dk4dUTN7YQQdRDQwhLzerlj5ZkoLP37IZzN9dDBtXGfkKm7Ot2H/vHHHyMuLg56enowNDSU+WusopJzAQAtrOV7JCshhDSUKV2c8WFrW5RJGKbtuU0939Wc3Gfou3btwpEjR9C3b19FxqP2olPLC3ozK30lR0IIIW/H4XAQNNgLcRn5iHyehQk7b+Lo9A4wEGnOI0UbE7nP0A0NDeHs7KzIWNReaZkEMWnljyp0t6IzdEKI6hPxedjysQ+sDER4kp6PmX9GoEzClB0WkYPcBX3p0qVYtmwZCgsLFRmPWot/VYCSUgm0+Tw0MdZWdjiEEFIjFgYibB3bFiI+F6HR6Vhx+pGyQyJykLugDx8+HJmZmbCwsICXlxfatGkj89cYPU4pb25vaqkHLpeeaEQIUR9eTQyxelgrAMDWy3E4eOu5kiMitSX3NfRx48YhPDwcY8aMgaWlJT2SD/+7ft7Ukq6fE0LUzwctbfA4NQ8/hcTgq6P34WSmi7aONOa7upC7oJ88eRJnz55Fx44dFRmPWntMHeIIIWpudnc3xKTm4vT9FEzZHY5j0zugibGOssMiNSB3k7udnR0MDKjj1+uiU+gMnRCi3rhcDn4c3grNrQ2QkVeCybvCUVhSpuywSA3IXdB//PFHzJs3D8+ePVNgOOpLXCbBs5cFAABXCz0lR0MIIfLTEWhh27i2MNUV4EFSDhYcuQvGqOe7qpO7oI8ZMwYXLlyAi4sL9PX1YWJiIvPX2LzILESZhEHE58LKQKTscAghpE5sjbTx86g24HE5OBaZhN+uxCk7JPIOcl9DX7dunQLDUH8VIyw5mupSD3dCiEbwczHF1/2aY9nfDxF0OgotrA3gT8PDqiy5CrpYLMbFixexaNEiODk5KTomtRT3WkEnhBBNMd7fEfcSs3HkdiKm772Nv2Z0hJ0JdZJTRXI1ufP5fBw+fFjRsai1+Jf/FXQzKuiEEM3B4XDw/Yde8LI1RGaBmDrJqTC5r6EPGjQIx44dU2Ao6i3uvw5xTmb0y5UQollEfB5+/dgHproCPEzOwXzqJKeS5L6G7ubmhuXLl+Pq1avw8fGBrq7smenMmTPrHJw6eUZN7oQQDWZjpI2No9tgzLbrOB6ZBC9bQ3zaiZ7noUrkLui//fYbjIyMEB4ejvDwcJnXOBxOoyroJaUSvMisOEOngk4I0UzvOZd3klv690N8f+oRmlsb0DPUVYjcBT0ujm5hqJCUXQgJA3QEPJjrC5UdDiGE1Jtx/o64l5iDw7dfYAZ1klMpcl9Dfx1jrFFfT0nKKgJQft8mjWlPCNFkHA4H333oSZ3kVFCdCvoff/wBLy8vaGtrQ1tbGy1btsSuXbvkWtfGjRvh6OgIkUgEX19f3Lhxo9p5t27dik6dOsHY2BjGxsYICAh46/z1LSm7vKDbGNEjUwkhmo86yakmuQv6mjVrMHXqVPTt2xcHDhzAgQMH0Lt3b0yZMgVr166t1br279+POXPmYMmSJbh9+zZatWqFXr16IS0trcr5Q0NDMXLkSFy4cAFhYWGws7NDz549kZiYKG86dZKUVf5MeCrohJDGoqKTHI/LwfHIJPwRFq/skBo9uQv6hg0bsGnTJqxcuRIDBgzAgAED8MMPP+CXX37BTz/9VKt1rVmzBhMnTkRgYCBatGiBzZs3Q0dHB9u3b69y/j179mDatGnw9vaGu7s7tm3bBolEgpCQEHnTqZOKM3RbIxrylRDSeLznbIoFfdwBAN+efIjw+EwlR9S4yd0pLjk5Gf7+/pWm+/v7Izk5ucbrKSkpQXh4OBYsWCCdxuVyERAQgLCwsBqto6CgAGKx+K1jyBcXF6O4uFj675ycHADlo96JxeIax/u6iuUSM8vP0C31BXKvS1kq4lW3uF9HOagGykE1NHQOY32b4NazVzjzIBXT9oTj+NT3YKpXt87BDZmDOu/rN8ld0F1dXXHgwAEsXLhQZvr+/fvh5uZW4/VkZGSgrKwMlpaWMtMtLS0RFRVVo3V8+eWXsLGxQUBAQLXzBAUFYdmyZZWmnzt3Djo6deuh+ST5FQAOEqIicSopsk7rUpbg4GBlh1BnlINqoBxUQ0Pm0E0XiNDmITWnGB9vuoCpLSTgKaB/cEPkUFBQUO/baChyF/Rly5ZhxIgRuHTpEjp06AAAuHr1KkJCQnDgwAGFBfguK1aswL59+xAaGgqRqPom7wULFmDOnDnSf+fk5Eivvcv7XHexWIxz54KRLeYBkGBwr25oYqxe19HFYjGCg4PRo0cP8Pl8ZYcjF8pBNVAOqkFZObT0zcOQX68jJgeI5rtgbs+an9i9qSFzqGit1QRyF/QhQ4bg+vXrWLt2rXQI2ObNm+PGjRto3bp1jddjZmYGHo+H1NRUmempqamwsrJ667KrV6/GihUr8M8//6Bly5ZvnVcoFEIorNwMxOfz63TA5JUCJWUScDhAE1M98HkKuROwwdX1fVAFlINqoBxUQ0Pn0NzWGD8MbYkZeyPw6+U4+DiaoKfH27/D36UhclD3/fw6uQs6APj4+GD37t11CkAgEMDHxwchISEYNGgQAEg7uM2YMaPa5X744Qd89913OHv2LNq2bVunGOoiu6T8v6a6QrUt5oQQoggftLTB7fgsbL8ah88P3MFf/6dPo2c2IJWoQHPmzMHWrVuxc+dOPHr0CFOnTkV+fj4CAwMBAGPHjpXpNLdy5UosWrQI27dvh6OjI1JSUpCSkoK8vLwGjz1XXH6hyExP0ODbJoQQVbOgrzvaOhgjt7gUU3eHo6CkVNkhNRq1LuhcLhc8Hu+tf1patTvxHzFiBFavXo3FixfD29sbkZGROHPmjLSjXEJCgkzP+U2bNqGkpARDhw6FtbW19G/16tW1TafOcv/rIElDvhJCCMDncbFxdBuY6QkRlZKLr47ep0FnGkitm9yPHj1a7WthYWH46aefIJFIah3IjBkzqm1iDw0Nlfn3s2fPar3++pL7X5O7eR1v0yCEEE1haSDCz6NaY/S26zgakYg2Dsb4+D0HZYel8Wpd0AcOHFhpWnR0NObPn4+///4bo0ePxvLlyxUSnDrIqWhypzN0QgiRes/ZFF/2bobvT0Vh+d8P4GljgNb2xsoOS6PV6Rp6UlISJk6cCC8vL5SWliIyMhI7d+6Eg0Pj+SUmbXKnM3RCCJExsZMz+nhaQVzGMG3PbWTmlyg7JI0mV0HPzs7Gl19+CVdXVzx48AAhISH4+++/4enpqej4VF5FQTfTp05xhBDyOg6Hgx+GtoSzmS6Ss4sw50AkJBK6nl5fal3Qf/jhBzg7O+PEiRP4888/ce3aNXTq1Kk+YlMLOSUVvdzpDJ0QQt6kL+Jj4+g2EGpxcSE6Hb9eeqrskDRWra+hz58/H9ra2nB1dcXOnTuxc+fOKuc7cuRInYNTB3n/3ZFhqksFnRBCqtLc2gDLBnhg/pF7WH0uGm0djdHOsfpnbxD51Lqgjx07FhyOAgbp1QCMMRT+V9CNdDRntCFCCFG0Ee3scD3uFY5GJGLG3ts4NbNTnR/iQmTVuqDv2LGjHsJQT4XiMpSx8h83htpU0AkhpDocDgffDvLE3RdZeJKej88O3MGO8e3A5dIJoqKoxEhx6ir7v9NzLS4HOgKekqMhhBDVpivUwi+jfSDic3HpcTp+CY1VdkgahQp6HeQWlXdx1xdp0WUIQgipgWZW+vhmYPkdUWuCH+PakwwlR6Q5qKDXQcUZOjW3E0JIzQ1ra4ehPk0gYcCsfZFIzy1WdkgagQp6HeQUlp+hG2jX6aF1hBDS6Hwz0BNNLfWQnluMWfsiUEb3p9cZFfQ6yCn67wxdRGfohBBSG9oCHjaOagNtPg/XnrzETyExyg5J7VFBr4Ps/66hG1BBJ4SQWnOz1Md3H5ZfT//pfAyuxND19Lqggl4H+cVlAAA9EfVwJ4QQeQxu0wQj2tqBMWD2/gik5RQpOyS1RQW9DorE5QVdm08FnRBC5LVsoAfcrfSRkVeC2fsj6Xq6nKig10EhFXRCCKkzEZ+Hn1+7nr7lcpyyQ1JLVNDroOIMXUQFnRBC6sTVQg/LBnoAANaff4K4XCUHpIaooNdBYYkEQHlvTUIIIXUzzKcJBrSyQZmEYedjHrL/uzWY1AwV9DoolJ6h09tICCF1xeFw8N2HnrAz1kZmCQdfHXsAxuh6ek1RJaoD6hRHCCGKpS/iY/2IluBxGM4+TMOe6wnKDkltUEGvg0K6hk4IIQrnZWuID+zLL2l+c+IholJylByReqCCXgdF4vIDjprcCSFEsbpaM3RxM0NxqQQz9kagoKRU2SGpPKpEdVBaVl7Q+Tx6GwkhRJG4HGDlYA+Y6wsRm5aH5X8/VHZIKo8qUR2U/jf4AY8enUoIIQpnqifEuhHe4HCAfTef4+87ScoOSaVRQa8DyX+9L3lcKuiEEFIfOriaYVpXFwDAwiP38PxVgZIjUl1U0OtAeoZOBZ0QQurN7ICm8HEwRm5xKWb8GQHxf5c7iSyVKegbN26Eo6MjRCIRfH19cePGjbfOf/DgQbi7u0MkEsHLywunTp1qoEj/R0IFnRBC6h2fx8X6j7xhINLCnedZWH0uWtkhqSSVKOj79+/HnDlzsGTJEty+fRutWrVCr169kJaWVuX8165dw8iRIzFhwgRERERg0KBBGDRoEO7fv9+gcdM1dEIIaRhNjHWwckhLAMCvF5/So1aroBIFfc2aNZg4cSICAwPRokULbN68GTo6Oti+fXuV869fvx69e/fGF198gebNm+Obb75BmzZt8PPPPzdo3BUPBOKqxLtICCGarY+XNUb52gMA5hyIxMu8YiVHpFqUXopKSkoQHh6OgIAA6TQul4uAgACEhYVVuUxYWJjM/ADQq1evauevL6WS8us4WtTkTgghDWJRvxZwtdBDWm4xvjx8l4aGfY2WsgPIyMhAWVkZLC0tZaZbWloiKiqqymVSUlKqnD8lJaXa7RQXF6O4+H+/5nJyykceEovFEIvlewBAxTN7JWVlcq9D2SriVtf4AcpBVVAOqkHTc9DiAGuGemHIr//in0dp2HH1Kcb8d9Zel21pAqUX9IYSFBSEZcuWVZp+7tw56OjoyLVObfDA+MCNf6/hqaiuESpXcHCwskOoM8pBNVAOqkHTc/jAjoMzz7lIePwAp17K33+qoEBzboNTekE3MzMDj8dDamqqzPTU1FRYWVlVuYyVlVWt5geABQsWYM6cOdJ/5+TkwM7ODj179oSBgYFcsffoIUZwcDB69OgBPp8v1zqUTSymHFQB5aAaKAfVUJMc+jCGuXklsNAX1mlbFa21mkDpBV0gEMDHxwchISEYNGgQAEAikSAkJAQzZsyochk/Pz+EhIRg9uzZ0mnBwcHw8/OrdjtCoRBCYeUdz+fz63zQK2IdykY5qAbKQTVQDqrhXTnYmggUsg1NofSCDgBz5szBuHHj0LZtW7Rv3x7r1q1Dfn4+AgMDAQBjx46Fra0tgoKCAACzZs1Cly5d8OOPP6Jfv37Yt28fbt26hS1btigzDUIIIURpVKKgjxgxAunp6Vi8eDFSUlLg7e2NM2fOSDu+JSQkgPvavWH+/v7Yu3cvvv76ayxcuBBubm44duwYPD09lZUCIYQQolQqUdABYMaMGdU2sYeGhlaaNmzYMAwbNqyeoyKEEELUg9LvQyeEEEJI3VFBJ4QQQjSAyjS5N7SK0YXqcsuCWCxGQUEBcnJy1LanJOWgGigH1UA5qIaGzKGiBmjCiHONtqDn5uYCAOzs7JQcCSGEEGXLzc2FoaGhssOoEw7ThJ8lcpBIJEhKSoK+vj44cj4trWJwmufPn8s9OI2yUQ6qgXJQDZSDamjIHBhjyM3NhY2NjczdVOqo0Z6hc7lcNGnSRCHrMjAwUNsPTgXKQTVQDqqBclANDZWDup+ZV1DvnyOEEEIIAUAFnRBCCNEIVNDrQCgUYsmSJVWOEa8uKAfVQDmoBspBNWhCDsrQaDvFEUIIIZqEztAJIYQQDUAFnRBCCNEAVNAJIYQQDUAFnRBCCNEAVNDrYOPGjXB0dIRIJIKvry9u3Lih7JCqtHTpUnA4HJk/d3d36etFRUWYPn06TE1NoaenhyFDhiA1NVWJEQOXLl1C//79YWNjAw6Hg2PHjsm8zhjD4sWLYW1tDW1tbQQEBCAmJkZmnlevXmH06NEwMDCAkZERJkyYgLy8PJXJYfz48ZX2S+/evVUqh6CgILRr1w76+vqwsLDAoEGDEB0dLTNPTY6fhIQE9OvXDzo6OrCwsMAXX3yB0tJSlcmha9eulfbFlClTVCaHTZs2oWXLltKBVvz8/HD69Gnp66q+D2qSg6rvA7XAiFz27dvHBAIB2759O3vw4AGbOHEiMzIyYqmpqcoOrZIlS5YwDw8PlpycLP1LT0+Xvj5lyhRmZ2fHQkJC2K1bt9h7773H/P39lRgxY6dOnWJfffUVO3LkCAPAjh49KvP6ihUrmKGhITt27Bi7c+cOGzBgAHNycmKFhYXSeXr37s1atWrF/v33X3b58mXm6urKRo4cqTI5jBs3jvXu3Vtmv7x69UpmHmXn0KtXL/b777+z+/fvs8jISNa3b19mb2/P8vLypPO86/gpLS1lnp6eLCAggEVERLBTp04xMzMztmDBApXJoUuXLmzixIky+yI7O1tlcvjrr7/YyZMn2ePHj1l0dDRbuHAh4/P57P79+4wx1d8HNclB1feBOqCCLqf27duz6dOnS/9dVlbGbGxsWFBQkBKjqtqSJUtYq1atqnwtKyuL8fl8dvDgQem0R48eMQAsLCysgSJ8uzeLoUQiYVZWVmzVqlXSaVlZWUwoFLI///yTMcbYw4cPGQB28+ZN6TynT59mHA6HJSYmNljsFaor6AMHDqx2GVXLgTHG0tLSGAB28eJFxljNjp9Tp04xLpfLUlJSpPNs2rSJGRgYsOLi4oZNgFXOgbHyYjJr1qxql1G1HBhjzNjYmG3btk0t90GFihwYU899oGqoyV0OJSUlCA8PR0BAgHQal8tFQEAAwsLClBhZ9WJiYmBjYwNnZ2eMHj0aCQkJAIDw8HCIxWKZXNzd3WFvb6+yucTFxSElJUUmZkNDQ/j6+kpjDgsLg5GREdq2bSudJyAgAFwuF9evX2/wmKsTGhoKCwsLNGvWDFOnTsXLly+lr6liDtnZ2QAAExMTADU7fsLCwuDl5QVLS0vpPL169UJOTg4ePHjQgNGXezOHCnv27IGZmRk8PT2xYMECFBQUSF9TpRzKysqwb98+5Ofnw8/PTy33wZs5VFCXfaCqGu3DWeoiIyMDZWVlMgcWAFhaWiIqKkpJUVXP19cXO3bsQLNmzZCcnIxly5ahU6dOuH//PlJSUiAQCGBkZCSzjKWlJVJSUpQT8DtUxFXV+1/xWkpKCiwsLGRe19LSgomJicrk1bt3bwwePBhOTk548uQJFi5ciD59+iAsLAw8Hk/lcpBIJJg9ezY6dOgAT09PAKjR8ZOSklLlvqp4rSFVlQMAjBo1Cg4ODrCxscHdu3fx5ZdfIjo6GkeOHJHGqewc7t27Bz8/PxQVFUFPTw9Hjx5FixYtEBkZqTb7oLocAPXYB6qOCnoj0KdPH+n/t2zZEr6+vnBwcMCBAwegra2txMgat48++kj6/15eXmjZsiVcXFwQGhqK7t27KzGyqk2fPh3379/HlStXlB2K3KrLYdKkSdL/9/LygrW1Nbp3744nT57AxcWlocOsUrNmzRAZGYns7GwcOnQI48aNw8WLF5UdVq1Ul0OLFi3UYh+oOmpyl4OZmRl4PF6lXqSpqamwsrJSUlQ1Z2RkhKZNmyI2NhZWVlYoKSlBVlaWzDyqnEtFXG97/62srJCWlibzemlpKV69eqWyeTk7O8PMzAyxsbEAVCuHGTNm4MSJE7hw4YLMY4drcvxYWVlVua8qXmso1eVQFV9fXwCQ2RfKzkEgEMDV1RU+Pj4ICgpCq1atsH79erXaB9XlUBVV3Aeqjgq6HAQCAXx8fBASEiKdJpFIEBISInM9SFXl5eXhyZMnsLa2ho+PD/h8vkwu0dHRSEhIUNlcnJycYGVlJRNzTk4Orl+/Lo3Zz88PWVlZCA8Pl85z/vx5SCQS6ReFqnnx4gVevnwJa2trAKqRA2MMM2bMwNGjR3H+/Hk4OTnJvF6T48fPzw/37t2T+XESHBwMAwMDaXOrMnOoSmRkJADI7Atl5lAViUSC4uJitdgH1anIoSrqsA9UjrJ75amrffv2MaFQyHbs2MEePnzIJk2axIyMjGR6YKqKzz//nIWGhrK4uDh29epVFhAQwMzMzFhaWhpjrPyWF3t7e3b+/Hl269Yt5ufnx/z8/JQac25uLouIiGAREREMAFuzZg2LiIhg8fHxjLHy29aMjIzY8ePH2d27d9nAgQOrvG2tdevW7Pr16+zKlSvMzc2tQW/5elsOubm5bO7cuSwsLIzFxcWxf/75h7Vp04a5ubmxoqIilclh6tSpzNDQkIWGhsrcTlRQUCCd513HT8XtRj179mSRkZHszJkzzNzcvMFuN3pXDrGxsWz58uXs1q1bLC4ujh0/fpw5Ozuzzp07q0wO8+fPZxcvXmRxcXHs7t27bP78+YzD4bBz584xxlR/H7wrB3XYB+qACnodbNiwgdnb2zOBQMDat2/P/v33X2WHVKURI0Ywa2trJhAImK2tLRsxYgSLjY2Vvl5YWMimTZvGjI2NmY6ODvvwww9ZcnKyEiNm7MKFCwxApb9x48YxxspvXVu0aBGztLRkQqGQde/enUVHR8us4+XLl2zkyJFMT0+PGRgYsMDAQJabm6sSORQUFLCePXsyc3NzxufzmYODA5s4cWKlH4TKzqGq+AGw33//XTpPTY6fZ8+esT59+jBtbW1mZmbGPv/8cyYWi1Uih4SEBNa5c2dmYmLChEIhc3V1ZV988YXMPdDKzuGTTz5hDg4OTCAQMHNzc9a9e3dpMWdM9ffBu3JQh32gDujxqYQQQogGoGvohBBCiAaggk4IIYRoACrohBBCiAaggk4IIYRoACrohBBCiAaggk4IIYRoACrohBBCiAaggk4IIYRogP8Hdoy0aSeL6TMAAAAASUVORK5CYII=' width=500.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 2.7))\n",
    "ax.plot(p_delta,u, label='H=1')\n",
    "ax.grid(1)\n",
    "ax.set_xlabel('Angle $Deg$')\n",
    "ax.set_ylabel('Normalized Flow (u)')\n",
    "ax.legend()\n",
    "ax.set_title('Bernoulli Equation for the Flow through the Reed Orifice')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0389d20f",
   "metadata": {},
   "source": [
    "The problem with this approach is that it requires the flow to be precomputed, locking in H and k into the array. This requires a recalculation of the array every time one of the variables changes making it inefficient for haptics. A better way can be achieved parametrically. Let's look at the equations from earlier.\n",
    "\n",
    "\\begin{align}\n",
    " \\beta &= \\sqrt{\\frac{2}{\\rho}}wH \\\\\n",
    " p_c &= \\frac{kH}{A_r} \\\\\n",
    " u &= \\beta \\sqrt{|p\\Delta| } \\left(1 - \\frac{p\\Delta }{p_c}\\right)sgn(p\\Delta)\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c3385c6",
   "metadata": {},
   "source": [
    "The equilibrium position H appears in both the reed closure pressure and the scaling variable $\\beta$. This would be a perfect variable to expose and map to the model. K, the spring constant is also a good parameter to expose as it works in conjunction with H in $p_c$. $A_r$ affects the weight of $\\frac{p\\Delta }{p_c}$ and $\\sqrt{\\frac{2}{\\rho}}w$ is technically the amplitude value that I shall visit later on in this paper. Both set of variables can be exposed in future iterations of the haptic model if greater fine tuning of the curve is desired. For now, I shall analyze how H and k interacts with the model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "416eea16",
   "metadata": {},
   "source": [
    "I am left with:\n",
    "    $$\n",
    "     u = H \\sqrt{|p\\Delta| } \\left(1 - \\frac{p\\Delta }{kH}\\right)sgn(p\\Delta)\n",
    "    $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a8dff0f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_mult(x,y):\n",
    "    return x*y\n",
    "def u(x,H,k,func):\n",
    "    arr = H * np.sqrt(np.abs(x))*(1-x/func(H,k))*np.sign(x)\n",
    "    return arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c29eac7f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "adf598592fdf48b5b48bacaac15f6693",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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NC9jdMdzxeUaZGSUYjk9AKcuV6A09cLkJxegEItsCclG3tSsgFUjlD2bOuMvv6tcW8nVwS3cYbSxJ+FiKg+DIBE1Cwu5xRjW9J1/HQ8DZeyi6s9F+jpgP4dXNG/Q2uE+bvA0dr8r61ztFahj58L+vj9fSvIopIyfPnjr7D17Yrj1wpw8PIN5BSV48ClXBy4lIvlu8/DwVqJ/h1aY2Bndwzu4g4PR2sRPwURUSUGQCIymoIyLbYeS8MPiddw/Fq+YbuVQo7+HVsjoosHBndxh5eTjYhVGo9apUB7B+Ch/u2gUqkgCAIu5RTj4KVc7LuYg30XcpBXosWvpzPx6+lMYAvQ3ccJEV08MLSrBwI9HZrldDYRUX0YAInorgiCgBPX8rHh4F/43/F0lGorJ3Ao5DLc09EVI3p6Y0iQJ+zVlv91I5PJ0MHNHh3c7PF0eFtU6AWcSsvH7+eysSclC0lX83AyLR8n0/Lxwe5z8He1w4PdPfFgNy909XZkGCQik7H8b2QiahYVegG7Tmfg898vVZsx29nDHqPD2uLhYG+42t9572cpUchlCL51XeMLgzshu1CDvWezEJucid/OZeNSTjFW7L2IFXsvwt/VDo+E+GBET2+0a20ndulEZOEYAImoUcq0Ffgu8RpW/3HJMIPXSinH8O5eGBPeFr3bteJIVi3cHNR4so8vnuzjiyKNDnvOZuGXk+nYm5KFSznF+GD3OXyw+xx6tnXG473b4OFg7xZxfSQRtTwMgETUIOU6PTYfuYoVey4go6AMAOBsq8LYvu0wrp8f3BykPdrXWPZqJf4d7I1/B3ujSKPDrtMZ2HIsDfsu5OBYah6Opebhrf+dwUPdvfBEaBv082/NYE1ERsMASER1qtAL+CHxGj6MO4+0vFIAgLeTNabe548n+/jC1opfI3fLXq3EY73a4LFebZBVWIafjl3Ht0eu4nxWEbYcS8OWY2nwd7XD0+Ft8XjvNnC2tRK7ZCJq4fjNTUS1Srh0A+/8cg5nMwoBAO4Oakwf1BFPhflyseNm4u5gjSn3+WPyve1x/Fo+Nh++iv8dv45LOcVYuD0Z7/+agoeDvTGhvx+6+dy5XiERUUMwABLRHf66UYIvz8pxMiERAOBko0LUoI4Y268drFUMfqYgk8kQ4uuMEF9nvD68C35KSsPXB1KRnF6A7xOv4fvEawjzc8HEAX4YEuTBxaaJqFEYAInIoFynx8rfLuLjPeehrZBDIZfhmfC2mBnRGa3seNpRLPZqJcaEt8PTYW1xNDUPMfuv4JeT6Th0JReHruSiTSsbTL6nPU/JE1GD8ZuCiAAAR67kYvaPJ3E+qwgAEOikx7Jx9yDIp5XIlVEVmUyG3u1aoXe7Vsh4qAvWH7iCbw6m4trNUsz73xksjzuPcX3bYXx/P7SW+BI8RFQ3BkAiiSsp12HRjrNYf+AvAICrvRVefzAAsqvH0MndXuTqqDaeTtZ4NTIQUYM64fuj17Dq90tIzS3BR3su4Is/LmFMeDtMvc+ft54johoxABJJWNLVPLy0OQmXcyrv1Tsq1BezHwqEnUqGHdeOiVwdNYSNlQJj+1aeHt55KgMrf7uIk2n5WP3nZaxP+AtPhLbBtPs7oE0rW7FLJSIzwgBIJEG6Cj1W7L2Ij/acR4VegKejNZY8EYx7OrkCALRarcgVUmMp5DIM7+GFh7p74vfzOfhkz3kcvnITGw6m4tsjVzGqjy+mD+poMfdhJqK7wwBIJDGZBWWI+uYoDl+5CQD4Vw8vLBzRjWvLWQiZTIaBnd0wsLMbDl66gQ/jzmP/xRv4+kAqvj18DU+Ht8XzgzrA3YGnhomkjAGQSEISLt7ACxuPIqeoHPZqJRaO6IZHQrx5hwkLFe7fGt/4t8aBSzewLPYcDl3ORcz+K9h8+CqevccPU+/rACcb3mqOSIq4cBSRBOj1Aj6Nv4AxXx5ATlE5Aj0d8L8X7sGInj4MfxLQ1781Nk/tiw2TwxHi64xSbQVW7L2I+97bi89/u4gybYXYJRKRiXEEkMjClZZX4OXvkrDjZAYAYGSvNlg4ohtsrLigs5TIZDIM6OiK/h1aY9eZTLz/awouZBVh0S9n8VXCX/jvsAA83MMbcjn/QUAkBRwBJLJgWQVlGPVFAnaczIBKIcOix7pjyRM9GP4kTCaTIbKrJ36deR/ee7wHPB2tkZZXihmbkjDi0304eOmG2CUSkQkwABJZqNPX8/HIin04cS0frWxV2DC5L0aHteUpXwJQOWv4yVBf7H3lfrwytDPsrBQ4cS0fo744gOkbjuJqbonYJRJRM2IAJLJAv53LxhMrE5CeX4YObnbYOn0Awtq7iF0WmSEbKwWiHuiE+FcH4enwtpDLgO0n0zF42W9YuisFxRqd2CUSUTNgACSyMP87fh2T1x1GSXkFBnRsjR+fH4B2re3ELovMnJuDGu882h3bX7wX/fxbo1ynx8d7LiBi2W/YfiIdgiCIXSIRGREDIJEF2XDwL7y46Ri0FQL+1cMLayeEcZkPapQuXo74Zko4Vj7TC21a2SA9vwzTvzmKZ1YfxIVb94kmopaPAZDIQqzYewGvbzkFQQDGhLfFh0/1hJWSf8Wp8WQyGYZ188Lu6IGYMbgTrJRy7LtwA8OW/47Fv5xFaTmXjSFq6fjbgcgCfLj7PN7/NQUA8MIDHbFwRDcouJwH3SVrlQIvDemM2Jfuw+BAd+j0Alb+dhFDPvgNe89miV0eEd0FBkCiFm7F3gv4YPc5AMDsBwPx8tAAzvQlo2rX2g6rJ/TBqnGh8HayxrWbpZgYcxjPb0hEVkGZ2OURURMwABK1YCt/u2gY+XttWCD+M7CDyBWRJRsS5IHY6IGYcm97KOQy7DiZgcHLfsOmQ6mcJELUwjAAErVQX/5xCYt/OQsAeGVoZ0y7n+GPmp+dWonXhwdhW9QA9GjjhMIyHWb9eBJPrzqIKznFYpdHRA3EAEjUAn135CoWbk8GAMyM6ISoBzqJXBFJTVdvJ/w4rT/eGN4F1io5Ei7dQOTy37Hq90uo0HM0kMjcMQAStTB7U7Iw68eTAID/3OePGYMZ/kgcSoUck+/1x66ZAzGgY2todHq8vSMZT6zcj4vZXDKGyJwxABK1IElX8/D810dRoRfwWE8fvDYskBM+SHRtW9vi60nhWPxYd9irlTiamoeHPvwDX/x+kaOBRGaKAZCohbiUXYRnYw6jVFuB+zq74d3He0DOpV7ITMhkMjwV1ha/vnQf7uvsBo1Oj3d2nMUzaw4jhxOFicwOAyBRC3CzuBwTYw4jt7gcPdo44bMxvaBS8K8vmR8fZxusm9gH747sDjsrBY78lYd3jyuw8fBVzhQmMiP8DUIGK1asgJ+fH6ytrREeHo5Dhw7Vuu+PP/6I0NBQODs7w87ODiEhIVi/fr0Jq5UObYUe0785ir9ulKBNKxusmdAHdmql2GUR1Uomk2FUn7bYOfM+hPm1QrlehjnbkjEx5jCyCjkcSGQOGAAJALB582ZER0dj7ty5OHr0KIKDgxEZGYmsrJpX+3dxccHrr7+OhIQEnDhxAhMnTsTEiRPx66+/mrhyy/f29mTsv3gDtlYKfDk+FK72arFLImoQXxdbrJ8YihHtKmCllCM+JRvDlv+B2DOZYpdGJHkMgAQAWLZsGaZMmYKJEyciKCgIK1euhK2tLdasWVPj/vfffz8effRRdOnSBR06dMCMGTPQo0cP/Pnnnyau3LJtPJSKmP1XAAAfjApBoKejuAURNZJcLsMgbwFbp/VFFy9H5BaXY8pXRzD7x5MoKdeJXR6RZDEAEsrLy5GYmIiIiAjDNrlcjoiICCQkJNT7ekEQEBcXh5SUFNx3333NWaqkHL6Sizk/nQIAvDykMyK7eopcEVHTdXK3x9bp/fGf+/whk1X+4+ZfH/2JU2n5YpdGJEm8kIiQk5ODiooKeHh4VNvu4eGBs2fP1vq6/Px8+Pj4QKPRQKFQ4NNPP8WQIUNq3V+j0UCj0RgeFxQUAAC0Wi20Wu1dfoqGqzqWKY/ZWDeKNJi+4Si0FQIe7OqB/9zbjj0yQ+xT/W7vkUqlwitDOuKeDi549YeTuJRTjEc/3YdXh3bGhH5tJb2kEX+W6mfMHrHPDIB0FxwcHJCUlISioiLExcUhOjoa/v7+uP/++2vcf9GiRZg/f/4d23ft2gVbW9tmrvZOsbGxJj9mQ+gF4PNkObIK5fCwETDILg2//JImSi3m2iNzwz7V7589erEzsPGiHCdvyvHOLynYmpCMMR31sFeJVKCZ4M9S/YzRo5KSEiNU0rIxABJcXV2hUCiQmVn9wuzMzEx4etZ+2lEul6Njx44AgJCQECQnJ2PRokW1BsDZs2cjOjra8LigoAC+vr4YOnQoHB1Nd22bVqtFbGwshgwZApXK/H7brPztEs7mX4C1So41k8LR2cPB5DWYe4/MBftUv7p69Lgg4JvD17DolxScyQM+TLHBsie6I7y9izjFiog/S/UzZo+qzkBJGQMgwcrKCr1790ZcXBxGjBgBANDr9YiLi0NUVFSD30ev11c7xftParUaavWdM1hVKpUoX3hiHbcuhy7n4oO4CwCAt/7dDV3biPuL0Bx7ZI7Yp/rV1qMJA/zRr4Mbor45ivNZRRi39ghmRnTG9EEdoZDgQuf8WaqfMXrEHnMSCN0SHR2NVatWYd26dUhOTsa0adNQXFyMiRMnAgDGjRuH2bNnG/ZftGgRYmNjcenSJSQnJ2Pp0qVYv349nnnmGbE+QouXW1yOFzceg14AHu3pgydC24hdEpFJBHg64KeoAXi8dxvoBWBZ7DmMW3MQ2YW1/4OSiO4ORwAJADBq1ChkZ2djzpw5yMjIQEhICHbu3GmYGJKamgq5/O9/LxQXF+P555/HtWvXYGNjg8DAQHz99dcYNWqUWB+hRRMEAf/340lkFJTB380OC0d0k/QF8SQ9tlZKLHkiGP38W+ONraew78INDP/oD3zydC+ESfCUMFFzYwAkg6ioqFpP+cbHx1d7vHDhQixcuNAEVUnDT0nXsfN0BpRyGT4e3ZN3+iDJGtm7DYJ9nTDt68pTwqNXHcBrwwIw5V5//qOIyIh4CphIZBn5ZYb1/mYM7oSu3k4iV0Qkro7uDtg6fQAeCfFGhV7AOzvO4j/rE1FQxqU7iIyFAZBIRIIg4LUfTqCgTIfgNk6Ydn8HsUsiMgt2aiWWjwrBghHdYKWQY9eZTDzyyT6cyywUuzQii8AASCSiTYev4rdz2bBSyrH0yWAoFfwrSVRFJpNhbN92+O65fvB2ssblnGKMWLEPP5+4LnZpRC0ef9sQieTazRIs/PkMAOC/kQHo6G769f6IWoJgX2f874V7MKBja5SUVyDqm2N4e/sZ6Cr0YpdG1GIxABKJQBAEzP3pNIrLK9DHrxUmDmgvdklEZq21vRrrJobhuYGVl0ms+uMyxq89hJvF5SJXRtQyMQASiWDXmUzEnc2CSiHDose6S3LBW6LGUirkmPVgID4b0wu2Vgrsu3ADD3/yJ85c510diBqLAZDIxIo1OszfdhoAMPU+f576JWqkB7t74cfn+6Otiy2u3SzFyM/287pAokZiACQysQ/jzuN6fhnatLJB1KBOYpdD1CIFejpiW9QA3NvJFaXayusCl+1KgV4viF0aUYvAAEhkQsnpBVj952UAwIJHusHGSiFyRUQtl7OtFdZO6IPJ91ReQ/vRnguYtiERxRqdyJURmT8GQCIT0esFvLH1FCr0Ah7s5olBge5il0TU4ikVcrzxryC8/3gPWCnk+PV0JkZ+th/XbpaIXRqRWWMAJDKR/524jsS/bsLOSoE5DweJXQ6RRXki1Bcbp4bD1V6NsxmFGLFiHxL/uil2WURmiwGQyATKtBV4b2cKAOD5QR3h5WQjckVElqd3OxdsixqAIC9H5BSVY/SqA/gpKU3ssojMEgMgkQnE7L+CtLxSeDlZ41mu+UfUbLydbfDdc/0wJMgD5To9ZmxK4uQQohowABI1s9zicqzYcwEA8MrQAE78IGpmdmolPn+mN/4z0B9A5eSQGZuTUKatELkyIvPBAEjUzD6KO49CjQ5BXo54tKeP2OUQSYJcLsPsB7vgvZE9oJTL8L/j1/HMlweRyzuHEAFgACRqVpeyi/D1gb8AAG8M7wI57/hBZFJP9vHFV8+GwcFaiSN/3cRjn+7D5ZxiscsiEh0DIFEzenfnWej0Ah4IdEf/jq5il0MkSf07uuLHaf3RppUNrtwowaOf7sPhK7lil0UkKgZAomZyKi0fv57OhFwGzH4wUOxyiCStk4cDtjw/AMG+zsgr0WLMlwex42S62GURiYYBkKiZLN99HgDw72BvdPLg/X6JxObmoMamKX0R0aVyhvD0b47iyz8uiV0WkSgYAImawam0fOxOrhz9i3qA9/slMhc2Vgp8PrY3xvZtB0EAFm5Pxvz/neYyMSQ5DIBEzeCjuMrRv4eDvdHR3V7kaojodgq5DG890hWzbl2asXbfFbyw6Rg0Oi4TQ9LBAEhkZGeuF2DXmUzIZMALD3QUuxwiqoFMJsNzAzvgw6dCoFLIsP1EOiasOYyCMq3YpRGZBAMgkZFVjf79q4c3Orrz2j8ic/ZIiA/WTgiDnZUCCZduYNTnB5BVUCZ2WUTNjgGQyIiS0wuw83QGZDLgRY7+EbUI93Ryxeb/9IOrvRrJ6QV47LP9XCuQLB4DIJERfXLrlm/Du3tx5i9RC9LNxwk/TusPv9a2uHazFI9/th+n0vLFLouo2TAAEhnJ1dwS/HKqcl2xKI7+EbU4bVvb4vtp/dHNxxE3isvx1BcHsP9CjthlETULBkAiI1m3/wr0AnBvJ1cEejqKXQ4RNYGrvRobp/RFP//WKNLoMGHtYfzCBaPJAjEAEhlBkUaHzYevAgCeHdBe5GqI6G44WKuwdmIfDOvqifKKygWjv73195vIUjAAEhnBd0euolCjg7+bHQZ2dhO7HCK6S9YqBVaM6YVRob7QC8B/fzjBu4aQRWEAJLpLFXoBa/ddAVA5+ieXy8QtiIiMQiGXYfHI7ph6nz+AyruGLN2VAkHgXUOo5WMAJLpLu5MzkZpbAicbFUb2aiN2OURkRDKZDLMfDMSrkQEAgI/3XMD8/53hreOoxWMAJLpLq/+8DAB4OrwtbKwUIldDRMYmk8kwfVBHLBjRDTIZELP/Cl774QQqGAKpBWMAJLoLp9LycehyLpRyGcb38xO7HCJqRmP7tsPSJ4IhlwHfJV7Di5uOoVynF7ssoiZhACS6C18lXAEADO/hBU8na3GLIaJm91ivNvh0TC/D/YOf+zoRZdoKscsiajQGQKImKtLo8POJyvXBnunbTuRqiMhUhnXzwhfjQqFWyrHnbBYmrzuCknKd2GURNQoDIFETbT9xHSXlFfB3tUNou1Zil0NEJjQowB0xE8Nga6XAnxdyMGHtYRRpGAKp5WAAJGqib49cAwA8EeoLmYxLvxBJTb8OrbF+Uhgc1EocupyLsasPIr9UK3ZZRA3CAEjUBBeyipD4100o5DKM7OUjdjlEJJLe7VywYUo4nGxUOJaah2e+PIi8knKxyyKqFwMgGaxYsQJ+fn6wtrZGeHg4Dh06VOu+q1atwr333otWrVqhVatWiIiIqHN/S/PdkcrbQg0KcIO7Iyd/EElZjzbO2DilL1rbWeFkWj6eXnUQucUMgWTeGAAJALB582ZER0dj7ty5OHr0KIKDgxEZGYmsrKwa94+Pj8fo0aOxd+9eJCQkwNfXF0OHDkVaWpqJKzc9bYUePxyt/JxPhvqKXA0RmYMgb0dsmtoXrvZqnEkvwNOrDuBGkUbssohqxQBIAIBly5ZhypQpmDhxIoKCgrBy5UrY2tpizZo1Ne6/YcMGPP/88wgJCUFgYCC+/PJL6PV6xMXFmbhy09t7Ngs5RRq42qsxKNBd7HKIyEx08nDApql94e6gxtmMQoxedQDZhQyBZJ4YAAnl5eVITExERESEYZtcLkdERAQSEhIa9B4lJSXQarVwcXFprjLNRtXkj5G9fKBS8K8QEf2to7s9Nk3tCw9HNc5lFjEEktlSil0AiS8nJwcVFRXw8PCott3DwwNnz55t0Hu89tpr8Pb2rhYi/0mj0UCj+fuLsKCgAACg1Wqh1Zpu5lzVsZpyzKxCDfamVJ4WfzTEy6R1m9Ld9EhK2Kf6SbFHvs5qbHi2D55ZcxgXsorw1BcJ+PrZULjaq2t9jRT71FjG7BH7zABIRrB48WJs2rQJ8fHxsLaufULEokWLMH/+/Du279q1C7a2ts1ZYo1iY2Mb/Zq912Wo0CvgZy8g5fBvSGmGusxJU3okRexT/aTYo8n+wCdnFLiYXYxHP4rH9KAKOFrV/Rop9qmxjNGjkpISI1TSsjEAElxdXaFQKJCZmVlte2ZmJjw9Pet87ZIlS7B48WLs3r0bPXr0qHPf2bNnIzo62vC4oKDAMHnE0dGx6R+gkbRaLWJjYzFkyBCoVKpGvXbdqkMA8jD+/i54KLxt8xRoBu6mR1LCPtVP6j26//4SjFlzGBkFGqxLdcLXz4aidQ0jgVLvU0MYs0dVZ6CkjAGQYGVlhd69eyMuLg4jRowAAMOEjqioqFpf99577+Htt9/Gr7/+itDQ0HqPo1aroVbf+cWnUqlE+cJr7HEz8stwNDUPMhnwUA8fSXxJi/X/pqVhn+on1R519HTC5qn98NQXB3AhuxjjYhIrl4yp5XSwVPvUGMboEXvMSSB0S3R0NFatWoV169YhOTkZ06ZNQ3FxMSZOnAgAGDduHGbPnm3Y/91338Wbb76JNWvWwM/PDxkZGcjIyEBRUZFYH6HZ7TxVed/f0Hat4MG1/4iogfxc7bDxtokhY748iJtcJ5BExgBIAIBRo0ZhyZIlmDNnDkJCQpCUlISdO3caJoakpqYiPT3dsP9nn32G8vJyPP744/Dy8jL8WbJkiVgfodntOJUBoPJG8EREjdHe1Q4bp/SF260lYsbwjiEkMp4CJoOoqKhaT/nGx8dXe3zlypXmL8iMZBWW4fCVXADAsG51XxdJRFQTfzd7bJwSjqe+OIAz6QUYu/oQvp5ceRs5IlPjCCBRA/x6OhOCAIT4OsPH2Ubscoiohero7oBvpvSFy63bxo1fcwhFGp3YZZEEMQASNcAvJytPfz/UnaN/RHR3Ons4YMPkcDjbqpB0NQ/Prj2MknKGQDItBkCietwo0uDApRsAgAd5/R8RGUEXL0esfzYcDmolDl3JxbRvkqDVi10VSQkDIFE9dp3JhF4Auvs4wdfF9AtWE5Fl6t7GCTHPhsHWSoH9F3OxJkWOch1TIJkGAyBRPXbcOv37IE//EpGR9W7XCmsm9IG1So4zeXK89N0J6CoYAqn5MQAS1SGvpBwJF3n6l4iaT1//1vj06RAoZAJ2ncnCf78/Ab1eELsssnAMgER1+P18DnR6AQEeDmjvaid2OURkoe7t6IqJnfVQyGX48Vga5mw7BUFgCKTmwwBIVIc/z2cDAO7r7CpyJURk6bq7CHh/ZDfIZMDXB1Kx+JezDIHUbBgAiWohCAL+PJ8DALink5vI1RCRFDzcwwuLHu0OAPj890tYsfeCyBWRpWIAJKrF5ZxiXM8vg5VCjjA/F7HLISKJeCqsLd78VxAAYMmuc/gq4Yq4BZFFYgAkqsWfFypH/3q3awUbK4XI1RCRlEy6pz1mDO4EAJjz02lsOXZN5IrI0jAAEtXiD8PpX17/R0SmNzOiEyb09wMAvPLdCew6nSFuQWRRGACJaqCr0OPAreVf7mUAJCIRyGQyzPlXEEb2aoMKvYCojcew/2KO2GWRhWAAJKrB8Wt5KNTo4GyrQldvJ7HLISKJkstleHdkdwwN8kC5To+pXyXi5LV8scsiC8AASFSDqtO/Azq4QiGXiVwNEUmZUiHHR6N7oq+/C4o0OoxfewgXs4vELotaOAZAohrsu8Dr/4jIfFirFFg1LhTdfZyQW1yOcasPIT2/VOyyqAVjACT6hyKNDsdS8wAA93RkACQi8+BgrULMxD7wd7VDWl4pxq4+hJvF5WKXRS0UAyDRPxy4eAM6vYB2rW3h62IrdjlERAat7dVYPzkcXk7WuJBVhGfXHUZJuU7ssqgFYgAk+oeq9f84+kdE5sjH2QZfPRsGJxsVjqXmYfqGo9BW6MUui1oYBkCif/jj1v1/ufwLEZmrTh4OWDOhD6xVcuxNycZrP5yAXs/7BlPDMQAS3SanSIOL2cWQyYB+/gyARGS+erdrhU/H9IJCLsOPR9OweOdZsUuiFoQBkOg2J9Mq19fyd7WDk61K5GqIiOr2QKAH3h3ZAwDwxe+XsPrPyyJXRC0FAyDRbaoWWO3RxlncQoiIGujx3m3w2rBAAMCCn89g2/HrIldELQEDINFtTtwKgN19ePcPImo5nhvob7hv8MvfJmH/Bd4yjurGAEh0m5NpeQCAHm0YAImo5ZDJZHjzX0EY3t0L2goBU9cn4vR13jKOascASHRLZkEZMgs0kMuAIG9HscshImoUhVyGpU8GI7x95S3jJq49jGs3S8Qui8wUAyDRLVXX/3Vyd4CtlVLkaoiIGs9apcAX40IR4OGArEINJqw9jPwSrdhlkRliACS65cStGcDdefqXiFowJxsV1k7sA0/HyruFTFl/BGXaCrHLIjPDAEh0y8lreQB4/R8RtXzezjaIebYPHNRKHLqci5e/O86FoqkaBkAiAIIg4GRaAQDOACYiyxDo6YjPx/aGSiHD9hPpWPRLstglkRlhACQCkFFQhpwiDRRyGbp4cQIIEVmG/h1d8f7jwQCAVX9cxlcJV8QtiMwGAyAR/l7/r7OHA6xVCpGrISIynhE9ffDK0M4AgHnbTmP3mUyRKyJzwABIhNvuAMLTv0RkgaYP6oin+vhCLwAvbDyGE7eueSbpYgAkAmcAE5Flk8lkWDCiG+7r7IZSbQWejTmMq7lcI1DKGABJ8gRB4AxgIrJ4KoUcn47phS5ejsgpKsezMYeRX8o1AqWKAZAk79rNUtws0UKlkCHA00HscoiImo29Wom1EyrXCDyfVYTnNyRCW6EXuywSAQMgSd7JW6d/Az0doVZyAggRWTZPJ2usnhAKWysF9l24gde3nIQgcI1AqWEAJMmrmgHM6/+ISCq6ejvhk6d7Qi4Dvj1yDZ/GXxS7JDIxBkAyWLFiBfz8/GBtbY3w8HAcOnSo1n1Pnz6NkSNHws/PDzKZDMuXLzddoUZ2Mi0PAGcAE5G0PBDogXn/7goAeP/XFPx84rrIFZEpMQASAGDz5s2Ijo7G3LlzcfToUQQHByMyMhJZWVk17l9SUgJ/f38sXrwYnp6eJq7WuC5kFQEAArkANBFJzLh+fnh2QHsAwMvfHsex1JsiV0SmwgBIAIBly5ZhypQpmDhxIoKCgrBy5UrY2tpizZo1Ne7fp08fvP/++3jqqaegVqtNXK3xaCv0yCrUAAC8na1FroaIyPReH94FgwPdodHpMeWrRFy7yeVhpEApdgEkvvLyciQmJmL27NmGbXK5HBEREUhISDDacTQaDTQajeFxQUHlvXe1Wi20WtMtRVB1LK1Wi5ySMggCoJTL4GQlN2kd5uz2HlHt2Kf6sUcNI3afljzeDaNXHcLZzCI8u/YwNk0Jg4O1eUUEY/aIP48MgAQgJycHFRUV8PDwqLbdw8MDZ8+eNdpxFi1ahPnz59+xfdeuXbC1tTXacRoqNjYWlwsBQAlHlR47d/5i8hrMXWxsrNgltAjsU/3Yo4YRs09P+QDLchU4l1WEMSt2Y0qgHgqZaOXUyhg9KinhKCcDIJnM7NmzER0dbXhcUFAAX19fDB06FI6Oprv+TqvVIjY2FkOGDMHulBvAqRNo79EKDz0UZrIazN3tPVKpVGKXY7bYp/qxRw1jLn3qEZaPp1cfRnIecFzmhzceChStln8yZo+qzkBJGQMgwdXVFQqFApmZ1W8QnpmZadQJHmq1usbrBVUqlShfeCqVCllFlacBvJxt+MupBmL9v2lp2Kf6sUcNI3afevm5YtmTIXh+w1GsS0hFZ09HjAlvJ1o9NTFGj/izyEkgBMDKygq9e/dGXFycYZter0dcXBz69esnYmXNLyO/DADg5cQJIEREAPBQdy+8PKQzAGDOT6ex/0KOyBVRc2AAJABAdHQ0Vq1ahXXr1iE5ORnTpk1DcXExJk6cCAAYN25ctUki5eXlSEpKQlJSEsrLy5GWloakpCRcuHBBrI/QJBkFlQHQ08lG5EqIiMxH1AMd8UiINyr0Ap77OhGXsovELomMjKeACQAwatQoZGdnY86cOcjIyEBISAh27txpmBiSmpoKufzvfy9cv34dPXv2NDxesmQJlixZgoEDByI+Pt7U5TcZRwCJiO4kk8nw7sgeSM0twbHUPExadwRbnx8AJ1ueOrUUDIBkEBUVhaioqBqf+2eo8/Pzs4h7R6bnV40AMgASEd3OWqXAF2ND8cgnf+JyTjGiNh7F2gl9oFTw5KEl4P9Fkiy9XkBmAUcAiYhq4+agxqrxobBRKfDH+Rws3J4sdklkJAyAJFk3isuh0wuQywA3+5Z7NxMioubU1dsJH4wKBgDE7L+Cbw6milwRGQMDIElW1QQQdwdrntIgIqrDsG63zww+hQOXbohcEd0t/tYjycrIr7wtnQdP/xIR1SvqgY54ONgbOr2AaV8n4mou76bRkjEAkmRVjQB6OTIAEhHVRyaT4f3He6C7jxNulmgx5asjKNboxC6LmogBkCTr7zUAGQCJiBrCWqXAF+N6w9VejbMZhYj+Ngl6fctfEUKKGABJsqpOAXMGMBFRw3k52eDzsb1hpZDj19OZ+DDuvNglURMwAJJkZRZyBJCIqCl6t2uFhY92AwB8GHceO0+li1wRNRYDIEnW3yOAvA0cEVFjPRnqi2cHtAcARH97HGczCkSuiBqDAZAkSRBumwTCEUAioib5v4cCMaBja5SUV2DqV4nIKykXuyRqIAZAkqQSHaDR6QEA7o5cBJqIqCmUCjk+Gd0Lvi42SM0twQsbj0FXoRe7LGoABkCSpLxb/0h1tbeCWqkQtxgiohaslZ0Vvhj79+3i3t15VuySqAEYAEmS8splADgBhIjIGLp4OWLpk5W3i1v1x2VsPZYmckVUHwZAkqSqEUBPR04AISIyhoe6e2H6oA4AgFk/nsCptHyRK6K6MACSJOVpKkcAOQGEiMh4oocE4P4AN5Rp9fjP+kTkFnNSiLliACRJMowAMgASERmNQi7Dh6N6ol1rW6TlleKFjUc5KcRMMQCSJFUFQI4AEhEZl5OtCl+MDYWtlQL7LtzgpBAzxQBIkpRfNQnEkQGQiMjYAjwdsPSJvyeF/O/4dZEron9iACRJ4ilgIqLm9WB3Lzx/f+WkkP9+f4J3CjEzDIAkOYVlOmgquAwMEVFze3loAO7t5IpSbQX+sz4R+aVasUuiWxgASXKqbgHnZKOErZVS5GqIiCyXQi7DR0/1hI+zDf66UYKXNidBrxfELovAAEgSVBUAef0fEVHza2Vnhc/H9oZaKcees1n4MO682CURGABJgjLyNQAYAImITKWbjxPeebQ7AODDuPPYczZT5IqIAZAkxzAC6KQWuRIiIukY2bsNxvVrBwCYuSkJqTdKRK5I2hgASXIybwVAD44AEhGZ1BvDg9CzrTMKynT4z9eJKC2vELskyWIAJMnJKapcA8bNniOARESmZKWU49MxvdDazgrJ6QV4fetJCAInhYiBAZAkp6BMBwBwtOYMYCIiU/NyssHHT/eEXAb8eDQNGw6mil2SJDEAkuQU3gqADjYMgEREYujfwRWvDQsEALz1vzNIuponbkESxABIklNUVrkQqYOaAZCISCxT7/PHsK6eKK/QY/qGo8gtLhe7JElhACTJKdTcGgG0VolcCRGRdMlkMrz3RA+0d7VDWl4pZmw6hgouEm0yDIAkKYIg/H0KmNcAEhGJytFahc+e6QVrlRx/nM/BR1wk2mQYAElSissrUPUPTJ4CJiISX6Cno2GR6I/2nMfelCyRK5IGBkCSlMJb1/8pZAKsVfzxJyIyB4/1aoMx4W0hCMBLm5OQllcqdkkWj78BSVKqTv9aKyqvPyEiIvMw5+EgdPdxQl6JFtM3HEW5Ti92SRaNAZAkpaC0cgTQRiFyIUREVI1aqcCnY3rB0VqJpKt5eGdHstglWTQGQJIUwwggL/8jIjI7vi62WPZkCAAgZv8VbD+RLm5BFowBkCSloKxqBJBLDRARmaOIIA88N7ADAOC/3x/HpewikSuyTAyAJClVI4C8CQgRkfl6ZWhnhLV3QXF5BZ7fcBRl2gqxS7I4DIBksGLFCvj5+cHa2hrh4eE4dOhQnft/9913CAwMhLW1Nbp3744dO3aYqNKmqxoBtOY1gEREZkupkOPj0T3ham+FsxmFmLfttNglWRwGQAIAbN68GdHR0Zg7dy6OHj2K4OBgREZGIiur5vWY9u/fj9GjR2PSpEk4duwYRowYgREjRuDUqVMmrrxxDCOADIBERGbNw9EaHz7VEzIZsOnwVWw5dl3skiwKAyABAJYtW4YpU6Zg4sSJCAoKwsqVK2Fra4s1a9bUuP+HH36IYcOG4dVXX0WXLl2wYMEC9OrVC5988omJK2+cqnUAOQmEiMj8DejoihmDOwEA5v7vDDJKRC7IgvDXIKG8vByJiYmYPXu2YZtcLkdERAQSEhJqfE1CQgKio6OrbYuMjMTWrVtrPY5Go4FGozE8LigoAABotVpotdq7+AQNl19SebNxG4VgsmO2RFW9YY/qxj7Vjz1qGPapds/d64dDl29g/8VcrDmnwMjiMjjZ3d17ss8MgAQgJycHFRUV8PDwqLbdw8MDZ8+erfE1GRkZNe6fkZFR63EWLVqE+fPn37F9165dsLW1bULljXcxVQ5ADhslEBsba5JjtmTsUcOwT/VjjxqGfarZg87AKZUCOWXA6p/2ItD57lZyKCnhUCIDIJnM7Nmzq40aFhQUwNfXF0OHDoWjo6NJavgq7RCQlwdrBTBkyBCoVCqTHLel0Wq1iI2NZY/qwT7Vjz1qGPapfu27Z+PokcOY/Njd96jqDJSUMQASXF1doVAokJmZWW17ZmYmPD09a3yNp6dno/YHALVaDbVafcd2lUplsi+8Ik3lUgI2CtMet6VijxqGfaofe9Qw7FPtwju44UaKcXrEHnMSCAGwsrJC7969ERcXZ9im1+sRFxeHfv361fiafv36VdsfqDx1Udv+5qJqEoiNkgtBExGRdHEEkAAA0dHRGD9+PEJDQxEWFobly5ejuLgYEydOBACMGzcOPj4+WLRoEQBgxowZGDhwIJYuXYrhw4dj06ZNOHLkCL744gsxP0a9CqpuBcdlYIiISMIYAAkAMGrUKGRnZ2POnDnIyMhASEgIdu7caZjokZqaCrn87wHj/v3745tvvsEbb7yB//u//0OnTp2wdetWdOvWTayPUK8KvYAiDe8EQkRExF+DZBAVFYWoqKgan4uPj79j2xNPPIEnnniimasynqrwB3AhaCIikjZeA0iSUXX9n1oph5I/+UREJGH8NUiSUVBaOQLowNuAEBGRxDEAkmRUjQA6qBkAiYhI2hgASTIKyzgCSEREBDAAkoQUaipHAO0ZAImISOIYAEkyqq4BdLTmCvBERCRtDIAkGYZrADkCSEREEscASJJhuAaQk0CIiEjiGABJMqpuA8drAImISOoYAEkyCm6dAnZkACQiIoljACTJ4DIwRERElRgASTL+Xgias4CJiEjaGABJMjgCSEREVIkBkCSjoJTLwBAREQEMgCQhHAEkIiKqxABIkqCt0KNUWwGAAZCIiIgBkCSh6NboHwDYcyFoIiKSOAZAkoSq0782KgVUCv7YExGRtPE3IUmCYRFoG47+ERERMQCSJFQFQAdrrgFIRETEAEiSwBnAREREf2MAJEn4OwByBJCIiIgBkCSBi0ATERH9jQGQJKFqBNCRI4BEREQMgCQNhVWzgDkCSERExABI0sBJIERERH9jACRJ4DIwREREf2MAJEkwXAPIhaCJiIgYAEkaqq4BdFBzBJCIiIgBkCSB1wASERH9jQGQJIHXABIREf2NAZAkoYAjgERERAYMgGTxNLoKlOv0AABHG44AEhERMQCSxau6/g8A7NUcASQiImIAJItXdR9ge7USCrlM5GqIiIjExwBIFo8zgImIiKpjACSLZ1gEmjOAiYiIADAAEoDc3FyMGTMGjo6OcHZ2xqRJk1BUVFTna7744gvcf//9cHR0hEwmQ15enmmKbQLDItAcASQiIgLAAEgAxowZg9OnTyM2NhY///wzfv/9d0ydOrXO15SUlGDYsGH4v//7PxNV2XQFDIBERETV8DeixCUnJ2Pnzp04fPgwQkNDAQAff/wxHnroISxZsgTe3t41vm7mzJkAgPj4eBNV2nR/XwPIU8BEREQARwAlLyEhAc7OzobwBwARERGQy+U4ePCgiJUZT05ROQCglS0DIBEREcARQMnLyMiAu7t7tW1KpRIuLi7IyMgw6rE0Gg00Go3hcUFBAQBAq9VCq9Ua9Vi3O5dReRy/1jbVjtWcx2zp2KOGYZ/qxx41DPtUP2P2iH1mALRYs2bNwrvvvlvnPsnJySaqptKiRYswf/78O7bv2rULtra2zXbc41cUAGTIvXQKO26cMmyPjY1ttmNaCvaoYdin+rFHDcM+1c8YPSopKTFCJS0bA6CFevnllzFhwoQ69/H394enpyeysrKqbdfpdMjNzYWnp6dRa5o9ezaio6MNjwsKCuDr64uhQ4fC0dHRqMeqUqzR4UbCHgDAM/+OgIudFbRaLWJjYzFkyBCoVDwtXBP2qGHYp/qxRw3DPtXPmD2qOgMlZQyAFsrNzQ1ubm717tevXz/k5eUhMTERvXv3BgDs2bMHer0e4eHhRq1JrVZDrVbfsV2lUjXbF95fGcUAAFd7NTyc7Ux2XEvBHjUM+1Q/9qhh2Kf6GaNH7DEngUhely5dMGzYMEyZMgWHDh3Cvn37EBUVhaeeesowAzgtLQ2BgYE4dOiQ4XUZGRlISkrChQsXAAAnT55EUlIScnNzRfkctUnJLAQABHjai1wJERGR+WAAJGzYsAGBgYEYPHgwHnroIdxzzz344osvDM9rtVqkpKRUu2Zi5cqV6NmzJ6ZMmQIAuO+++9CzZ09s27bN5PXX5fytANjJ3UHkSoiIiMwHTwETXFxc8M0339T6vJ+fHwRBqLZt3rx5mDdvXjNXdvdSMivvaBLgyQBIRERUhSOAZNGqRgA7e/AUMBERURUGQLJY+aVapOeXAQA6eXAEkIiIqAoDIFmsqtE/bydrOPI2cERERAYMgGSxzt26/o+jf0RERNUxAJLFOmdYAoYBkIiI6HYMgGSxzhmWgOEEECIiotsxAJLF4gggERFRzRgAySLdKNIgp6gcMhnQkSOARERE1TAAkkWqmgDi28oWtlZc75yIiOh2DIBkkc4ZFoDm6V8iIqJ/YgAki3SOdwAhIiKqFQMgWSROACEiIqodAyBZHEEQ/l4E2p0BkIiI6J8YAMniZBVqkF+qhUIug7+bndjlEBERmR0GQLI4KRmVp3/9WtvCWqUQuRoiIiLzwwBIFuf41TwAQJC3k7iFEBERmSkGQLI4x24FwF5tnUWtg4iIyFwxAJJFEQQBx1JvAgB6tm0lcjVERETmiQGQLMpfN0pws0QLK6UcQV6OYpdDRERklhgAyaIcu1o5+tfdxwlWSv54ExER1YS/IcmiHP0rDwDQ09dZ1DqIiIjMGQMgWZSqEUBe/0dERFQ7BkCyGKXlFUhOr1wDsCdnABMREdWKAZAsxsm0fFToBXg4quHlZC12OURERGaLAZAshmH5F99WkMlkIldDRERkvhgAyWIcvRUAe7VzFrcQIiIiM8cASBZBEAQcTc0DwAkgRERE9WEAJItwPb8M2YUaKOUydOM9gImIiOrEAEgWoer6vy5ejrCxUohcDRERkXljACSLcMxw+tdZ1DqIiIhaAgZAsgiGGcAMgERERPViAKQWT6OrwKm0AgCVS8AQERFR3RgAqcU7c70A5RV6uNhZoV1rW7HLISIiMntKsQsgultB3o74/rl+yCnScAFoIiKiBmAApBZPrVQg1M9F7DKIiIhaDJ4CJiIiIpIYBkAiIiIiiWEAJCIiIpIYBkBCbm4uxowZA0dHRzg7O2PSpEkoKiqqc/8XXngBAQEBsLGxQdu2bfHiiy8iPz/fhFUTERFRUzEAEsaMGYPTp08jNjYWP//8M37//XdMnTq11v2vX7+O69evY8mSJTh16hRiYmKwc+dOTJo0yYRVExERUVNxFrDEJScnY+fOnTh8+DBCQ0MBAB9//DEeeughLFmyBN7e3ne8plu3bvjhhx8Mjzt06IC3334bzzzzDHQ6HZRK/lgRERGZM44ASlxCQgKcnZ0N4Q8AIiIiIJfLcfDgwQa/T35+PhwdHRn+iIiIWgD+tpa4jIwMuLu7V9umVCrh4uKCjIyMBr1HTk4OFixYUOdpYwDQaDTQaDSGxwUFlbdv02q10Gq1jay86aqOZcpjtjTsUcOwT/VjjxqGfaqfMXvEPjMAWqxZs2bh3XffrXOf5OTkuz5OQUEBhg8fjqCgIMybN6/OfRctWoT58+ffsX3Xrl2wtTX9LdxiY2NNfsyWhj1qGPapfuxRw7BP9TNGj0pKSoxQScvGAGihXn75ZUyYMKHOffz9/eHp6YmsrKxq23U6HXJzc+Hp6Vnn6wsLCzFs2DA4ODhgy5YtUKlUde4/e/ZsREdHGx4XFBTA19cXQ4cOhaOjY90fyIi0Wi1iY2MxZMiQemuWKvaoYdin+rFHDcM+1c+YPao6AyVlDIAWys3NDW5ubvXu169fP+Tl5SExMRG9e/cGAOzZswd6vR7h4eG1vq6goACRkZFQq9XYtm0brK2t6z2WWq2GWq02PBYEAQBQWlpq0i88rVaLkpISlJaWQqfTmey4LQl71DDsU/3Yo4Zhn+pnzB6VlpYC+Pv3kBTJBCl/egIAPPjgg8jMzMTKlSuh1WoxceJEhIaG4ptvvgEApKWlYfDgwfjqq68QFhaGgoICDB06FCUlJdiyZQvs7OwM7+Xm5gaFQtGg4167dg2+vr7N8pmIiIjqc/XqVbRp00bsMkTBEUDChg0bEBUVhcGDB0Mul2PkyJH46KOPDM9rtVqkpKQYrpk4evSoYYZwx44dq73X5cuX4efn16Djent74+rVq3BwcIBMJjPOh2mAqlPPV69eNemp55aEPWoY9ql+7FHDsE/1M2aPBEFAYWFhjUudSQVHAElyCgoK4OTkZFi6hu7EHjUM+1Q/9qhh2Kf6sUfGxXUAiYiIiCSGAZCIiIhIYhgASXLUajXmzp1bbUYyVcceNQz7VD/2qGHYp/qxR8bFawCJiIiIJEayI4C///47Hn74YXh7e0Mmk2Hr1q0Net2KFSvg5+cHa2trhIeH49ChQ81bKBEREZGRSTYAFhcXIzg4GCtWrGjwazZv3ozo6GjMnTsXR48eRXBwMCIjI++4kwYRERGROeMpYAAymQxbtmzBiBEj6twvPDwcffr0wSeffAIA0Ov18PX1xQsvvIBZs2aZoFIiIiKiuyfZEcDGKi8vR2JiIiIiIgzb5HI5IiIikJCQIGJlRERERI3DANhAOTk5qKiogIeHR7XtHh4eyMjIEKkqqk1jr9X87rvvEBgYCGtra3Tv3h07duwwUaXiaUyPVq1ahXvvvRetWrVCq1atEBERIZnrX5t63e+mTZsgk8nqPbNgCRrbo7y8PEyfPh1eXl5Qq9Xo3Lkz/87VYPny5QgICICNjQ18fX3x0ksvoayszETVml5Trs2Pj49Hr169oFar0bFjR8TExDR7nZaCAZAsTmOv1dy/fz9Gjx6NSZMm4dixYxgxYgRGjBiBU6dOmbhy02lsj+Lj4zF69Gjs3bsXCQkJ8PX1xdChQ5GWlmbiyk2rqdf9XrlyBa+88gruvfdeE1Uqnsb2qLy8HEOGDMGVK1fw/fffIyUlBatWrYKPj4+JKzetxvbpm2++waxZszB37lwkJydj9erV2Lx5M/7v//7PxJWbTmOvzb98+TKGDx+OQYMGISkpCTNnzsTkyZPx66+/NnOlFkIgAYCwZcuWOvfRaDSCQqG4Y79x48YJ//73v5uvOGq0sLAwYfr06YbHFRUVgre3t7Bo0aIa93/yySeF4cOHV9sWHh4u/Oc//2nWOsXU2B79k06nExwcHIR169Y1V4lmoSl90ul0Qv/+/YUvv/xSGD9+vPDII4+YoFLxNLZHn332meDv7y+Ul5ebqkSz0Ng+TZ8+XXjggQeqbYuOjhYGDBjQrHWai4b8Xv7vf/8rdO3atdq2UaNGCZGRkc1YmeXgCGADWVlZoXfv3oiLizNs0+v1iIuLQ79+/USsjG7XlGs1ExISqu0PAJGRkRZ7bacxrmctKSmBVquFi4tLc5Upuqb26a233oK7uzsmTZpkijJF1ZQebdu2Df369cP06dPh4eGBbt264Z133kFFRYWpyja5pvSpf//+SExMNJwmvnTpEnbs2IGHHnrIJDW3BFL77jY2pdgFiKWoqAgXLlwwPL58+TKSkpLg4uKCtm3b4pNPPsGWLVuqBb7o6GiMHz8eoaGhCAsLw/Lly1FcXIyJEyeK8RGoBnVdq3n27NkaX5ORkSGpazub0qN/eu211+Dt7X3Hl68laUqf/vzzT6xevRpJSUkmqFB8TenRpUuXsGfPHowZMwY7duzAhQsX8Pzzz0Or1WLu3LmmKNvkmtKnp59+Gjk5ObjnnnsgCAJ0Oh2ee+45iz4F3Fi1fXcXFBSgtLQUNjY2IlXWMkg2AB45cgSDBg0yPI6OjgYAjB8/HjExMcjJycHFixervWbUqFHIzs7GnDlzkJGRgZCQEOzcufOOH0AiS7Z48WJs2rQJ8fHxsLa2Frscs1FYWIixY8di1apVcHV1Fbscs6XX6+Hu7o4vvvgCCoUCvXv3RlpaGt5//32LDYBNER8fj3feeQeffvopwsPDceHCBcyYMQMLFizAm2++KXZ5ZAEkGwDvv/9+CHUsgThv3jzMmzfvju1RUVGIiopqxsrobri6ukKhUCAzM7Pa9szMTHh6etb4Gk9Pz0bt39I1pUdVlixZgsWLF2P37t3o0aNHc5Ypusb26eLFi7hy5Qoefvhhwza9Xg8AUCqVSElJQYcOHZq3aBNrys+Sl5cXVCoVFAqFYVuXLl2QkZGB8vJyWFlZNWvNYmhKn958802MHTsWkydPBgB0794dxcXFmDp1Kl5//XXI5byCq7bvbkdHR47+NQB/gsiiNOVazX79+lXbHwBiY2Mt9trOpl7P+t5772HBggXYuXMnQkNDTVGqqBrbp8DAQJw8eRJJSUmGP//+978NMxR9fX1NWb5JNOVnacCAAbhw4YIhHAPAuXPn4OXlZZHhD2han0pKSu4IeVWhua7BCymR2ne30Yk8CYXI6DZt2iSo1WohJiZGOHPmjDB16lTB2dlZyMjIEARBEMaOHSvMmjXLsP++ffsEpVIpLFmyREhOThbmzp0rqFQq4eTJk2J9hGbX2B4tXrxYsLKyEr7//nshPT3d8KewsFCsj2ASje3TP0lhFnBje5Samio4ODgIUVFRQkpKivDzzz8L7u7uwsKFC8X6CCbR2D7NnTtXcHBwEDZu3ChcunRJ2LVrl9ChQwfhySefFOsjNLvCwkLh2LFjwrFjxwQAwrJly4Rjx44Jf/31lyAIgjBr1ixh7Nixhv0vXbok2NraCq+++qqQnJwsrFixQlAoFMLOnTvF+ggtCgMgWaSPP/5YaNu2rWBlZSWEhYUJBw4cMDw3cOBAYfz48dX2//bbb4XOnTsLVlZWQteuXYXt27ebuGLTa0yP2rVrJwC448/cuXNNX7iJNfZn6XZSCICC0Pge7d+/XwgPDxfUarXg7+8vvP3224JOpzNx1abXmD5ptVph3rx5QocOHQRra2vB19dXeP7554WbN2+avnAT2bt3b43fM1V9GT9+vDBw4MA7XhMSEiJYWVkJ/v7+wtq1a01ed0vFewETERERSQyvASQiIiKSGAZAIiIiIolhACQiIiKSGAZAIiIiIolhACQiIiKSGAZAIiIiIolhACQiIiKSGAZAIiIzMGHCBIwYMeKu3sPPzw8ymQwymQx5eXm17hcTEwNnZ+e7OlZNqo7dHO9NRMbFAEhEVI+EhAQoFAoMHz5c7FLq9dZbbyE9PR1OTk4mP3Z6ejqWL19u8uMSUeMxABIR1WP16tV44YUX8Pvvv+P69etil1MnBwcHeHp6QiaTmfzYnp6eogRPImo8BkAiojoUFRVh8+bNmDZtGoYPH46YmJhqz8fHx0MmkyEuLg6hoaGwtbVF//79kZKSUm2/hQsXwt3dHQ4ODpg8eTJmzZqFkJCQWo+r1+uxaNEitG/fHjY2NggODsb333/fpM8QExODtm3bwtbWFo8++ihu3Lhxxz4//fQTevXqBWtra/j7+2P+/PnQ6XSG58+ePYt77rkH1tbWCAoKwu7duyGTybB169Ym1URE4mIAJCKqw7fffovAwEAEBATgmWeewZo1a1DTLdRff/11LF26FEeOHIFSqcSzzz5reG7Dhg14++238e677yIxMRFt27bFZ599VudxFy1ahK+++gorV67E6dOn8dJLL+GZZ57Bb7/91qj6Dx48iEmTJiEqKgpJSUkYNGgQFi5cWG2fP/74A+PGjcOMGTNw5swZfP7554iJicHbb78NAKioqMCIESNga2uLgwcP4osvvsDrr7/eqDqIyMwIRERUq/79+wvLly8XBEEQtFqt4OrqKuzdu9fw/N69ewUAwu7duw3btm/fLgAQSktLBUEQhPDwcGH69OnV3nfAgAFCcHCw4fH48eOFRx55RBAEQSgrKxNsbW2F/fv3V3vNpEmThNGjR9daa7t27YQPPvig2rbRo0cLDz30ULVto0aNEpycnAyPBw8eLLzzzjvV9lm/fr3g5eUlCIIg/PLLL4JSqRTS09MNz8fGxgoAhC1btlR73dq1a6u9NxGZJ44AEhHVIiUlBYcOHcLo0aMBAEqlEqNGjcLq1avv2LdHjx6G//by8gIAZGVlGd4nLCys2v7/fHy7CxcuoKSkBEOGDIG9vb3hz1dffYWLFy826jMkJycjPDy82rZ+/fpVe3z8+HG89dZb1Y41ZcoUpKeno6SkBCkpKfD19YWnp2eD6ici86cUuwAiInO1evVq6HQ6eHt7G7YJggC1Wo1PPvmk2oQHlUpl+O+qCRh6vb5Jxy0qKgIAbN++HT4+PtWeU6vVTXrP+o43f/58PPbYY3c8Z21tbfTjEZH4GACJiGqg0+nw1VdfYenSpRg6dGi150aMGIGNGzfiueeea9B7BQQE4PDhwxg3bpxh2+HDh2vdPygoCGq1GqmpqRg4cGDTPsAtXbp0wcGDB6ttO3DgQLXHvXr1QkpKCjp27FjjewQEBODq1avIzMyEh4dHvfUTkfljACQiqsHPP/+MmzdvYtKkSXcsbTJy5EisXr26wQHwhRdewJQpUxAaGor+/ftj8+bNOHHiBPz9/Wvc38HBAa+88gpeeukl6PV63HPPPcjPz8e+ffvg6OiI8ePHN/hzvPjiixgwYACWLFmCRx55BL/++it27txZbZ85c+bgX//6F9q2bYvHH38ccrkcx48fx6lTp7Bw4UIMGTIEHTp0wPjx4/Hee++hsLAQb7zxBgCIstwMEd09XgNIRFSD1atXIyIiosZ17UaOHIkjR47gxIkTDXqvMWPGYPbs2XjllVfQq1cvXL58GRMmTKjz9OqCBQvw5ptvYtGiRejSpQuGDRuG7du3o3379o36HH379sWqVavw4YcfIjg4GLt27TKEtyqRkZH4+eefsWvXLvTp0wd9+/bFBx98gHbt2gEAFAoFtm7diqKiIvTp0weTJ082zALmKWKilkkmCDWsZ0BERM1qyJAh8PT0xPr16432nn5+fpg5cyZmzpxptPeszb59+3DPPffgwoUL6NChg2F7TEwMZs6cWeet6IhIfAyARETNrKSkBCtXrkRkZCQUCgU2btyIt956C7GxsYiIiDDacfz8/JCeng6VSoW0tDSj3pVjy5YtsLe3R6dOnXDhwgXMmDEDrVq1wp9//mnYx97eHjqdDtbW1gyARGaO1wASETUzmUyGHTt24O2330ZZWRkCAgLwww8/GDX8AcBvv/0GrVYLoPI6QmMqLCzEa6+9htTUVLi6uiIiIgJLly6ttk9SUhKAylPGRGTeOAJIREREJDGcBEJEREQkMQyARERERBLDAEhEREQkMQyARERERBLDAEhEREQkMQyARERERBLDAEhEREQkMQyARERERBLDAEhEREQkMQyARERERBLDAEhEREQkMQyARERERBLDAEhEREQkMUqxCyAiIiIyFUEQoNVqUVFRAYVCAZVKBZlMJnZZJif5ABgTE4OZM2ciLy9P7FKIiIiomWi1WmRmZiItLQ2lpaWG7TY2NvDx8YGHhwdUKpWIFZpWizgFnJ2djWnTpqFt27ZQq9Xw9PREZGQk9u3bd9fvPWrUKJw7d84IVdavvLwc7733HoKDg2FrawtXV1cMGDAAa9euhVarNUkNMTExcHZ2bpb3njdvHkJCQprlvYmIiJoqNzcXBw4cwMWLF2Fvb4+goCD06NEDQUFBsLe3x8WLF3HgwAHk5ube8drff/8dDz/8MLy9vSGTybB169YGHXPFihXw8/ODtbU1wsPDcejQISN/qrvTIkYAR44cifLycqxbtw7+/v7IzMxEXFwcbty4cVfvq9VqYWNjAxsbGyNVWrvy8nJERkbi+PHjWLBgAQYMGABHR0ccOHAAS5YsQc+ePRmeiIiIjCw3NxcnT55Eq1atEBAQALVaXe15d3d3aDQapKSk4OTJk+jevTtcXFwMzxcXFyM4OBjPPvssHnvssQYdc/PmzYiOjsbKlSsRHh6O5cuXIzIyEikpKXB3dzfq52sqmSAIgthF1CUvLw+tWrVCfHw8Bg4cWOt+MpkMn376KbZt24b4+Hh4eXnhvffew+OPPw4AuHLlCtq3b49Nmzbh008/xcGDB7Fy5UoAqHYKeN68edi6dStefvllvPnmm7h58yYefPBBrFq1Cg4ODgCAwsJCPPfcc9i6dSscHR3x3//+Fz/99BNCQkKwfPnyGut77733MHv2bBw5cgQ9e/as9pxWq0V5eTns7Oyg0Wjw6quvYtOmTSgoKEBoaCg++OAD9OnTBwAQHx+PQYMGYffu3Xjttddw5swZhISEYO3atQgICAAAHD9+HDNnzsSRI0cgk8nQqVMnfP755ygqKsKgQYOqHXvu3LmYN28e1q9fjw8//BApKSmws7PDAw88gOXLlxt+UOs7bkxMDCZOnFjtvdeuXYsJEybU+f/Xb9b2Op8nIiJqKlsl8MEgO3i4uqBH926Qy2s/8anX63Hq1Cnk5+ejb9++NZ4Olslk2LJlC0aMGFHnccPDw9GnTx988sknhvf29fXFCy+8gFmzZt3VZzIWsz8FbG9vD3t7e2zduhUajabOfd98802MHDkSx48fx5gxY/DUU08hOTm52j6zZs3CjBkzkJycjMjIyBrf5+LFi9i6dSt+/vln/Pzzz/jtt9+wePFiw/PR0dHYt28ftm3bhtjYWPzxxx84evRonbVt2LABERERd4Q/AFCpVLCzswMA/Pe//8UPP/yAdevW4ejRo+jYsSMiIyPvGJZ+/fXXsXTpUhw5cgRKpRLPPvus4bkxY8agTZs2OHz4MBITEzFr1iyoVCr0798fy5cvh6OjI9LT05Geno5XXnkFQGUIXbBgAY4fP46tW7fiypUrNYa32o47atQovPzyy+jatavhvUeNGlVnT4iIiJrTAB8lrBRAl8CAOsMfAMjlcgQEBECv1yMzM7PJxywvL0diYiIiIiKqvXdERAQSEhKa/L7GZvangJVKJWJiYjBlyhSsXLkSvXr1wsCBA/HUU0+hR48e1fZ94oknMHnyZADAggULEBsbi48//hiffvqpYZ+ZM2fWO4Sr1+sRExNjGPEbO3Ys4uLi8Pbbb6OwsBDr1q3DN998g8GDBwOoHOny9vau8z3Pnz+P+++/v859iouL8dlnnyEmJgYPPvggAGDVqlWIjY3F6tWr8eqrrxr2ffvttw0jorNmzcLw4cNRVlYGa2trpKam4tVXX0VgYCAAoFOnTobXOTk5QSaTwdPTs9qxbw+Q/v7++Oijj9CnTx8UFRXB3t6+3uPa2NjA3t4eSqXyjvcmIiISw5B2VnBzdbvjtG9t1Go1XF1dkZaWBh8fnybNDs7JyUFFRQU8PDyqbffw8MDZs2cb/X7NxexHAIHKawCvX7+Obdu2YdiwYYiPj0evXr0QExNTbb9+/frd8fifI4ChoaH1Hs/Pz88Q/gDAy8sLWVlZAIBLly5Bq9UiLCzM8LyTk5Ph9GttGnKm/eLFi9BqtRgwYIBhm0qlQlhY2B2f4/bw6+XlBQCGGqOjozF58mRERERg8eLFuHjxYr3HTkxMxMMPP4y2bdvCwcHBEPJSU1MbfFwiIiJzYa8C3G1lcHd3a9Tr3NzcUFpaCp1O10yVmYcWEQABwNraGkOGDMGbb76J/fv3Y8KECZg7d26j36fqVGtd/nneXyaTQa/XN/pYt+vcubNRk//tNVb9C6Wqxnnz5uH06dMYPnw49uzZg6CgIGzZsqXW9youLkZkZCQcHR2xYcMGHD582LB/eXl5g49LRERkLqyVlb+jlMrGneys2r+pAdDV1RUKheKO08iZmZlmdYasxQTAfwoKCkJxcXG1bQcOHLjjcZcuXYx6XH9/f6hUKhw+fNiwLT8/v96lZJ5++mns3r0bx44du+M5rVaL4uJidOjQAVZWVtWWt9FqtTh8+DCCgoIaVWfnzp3x0ksvYdeuXXjsscewdu1aAICVlRUqKiqq7Xv27FncuHEDixcvxr333ovAwMAmjerV9N5ERERiKNNVnnlrbJCr2r+xwbGKlZUVevfujbi4OMM2vV6PuLi4O85UisnsA+CNGzfwwAMP4Ouvv8aJEydw+fJlfPfdd3jvvffwyCOPVNv3u+++w5o1a3Du3DnMnTsXhw4dQlRUlFHrcXBwwPjx4/Hqq69i7969OH36NCZNmgS5XF7ntQIzZ87EgAEDMHjwYKxYsQLHjx/HpUuX8O2336Jv3744f/487OzsMG3aNLz66qvYuXMnzpw5gylTpqCkpASTJk1qUH2lpaWIiopCfHw8/vrrL+zbtw+HDx82BGE/Pz8UFRUhLi4OOTk5KCkpQdu2bWFlZYWPP/4Yly5dwrZt27BgwYJG98bPzw+XL19GUlIScnJy6p20Q0RE1FyKtEBWiYCsrOxGvS47Oxs2NjaGAFhUVISkpCQkJSUBgOH3XNUlUp988olhTkCV6OhorFq1CuvWrUNycjKmTZuG4uLiO1bLEJVg5srKyoRZs2YJvXr1EpycnARbW1shICBAeOONN4SSkhLDfgCEFStWCEOGDBHUarXg5+cnbN682fD85cuXBQDCsWPHqr3/2rVrBScnJ8PjuXPnCsHBwdX2+eCDD4R27doZHhcUFAhPP/20YGtrK3h6egrLli0TwsLChFmzZtX7WRYtWiR0795dsLa2FlxcXIQBAwYIMTExglarFQRBEEpLS4UXXnhBcHV1FdRqtTBgwADh0KFDhvfYu3evAEC4efOmYduxY8cEAMLly5cFjUYjPPXUU4Kvr69gZWUleHt7C1FRUUJpaalh/+eee05o3bq1AECYO3euIAiC8M033wh+fn6CWq0W+vXrJ2zbtq1av+o7btXnGzlypODs7CwAENauXVtnP4iIiJrT1atXhfj4eKGsrKxB+5eVlQnx8fHC1atXDduqfv/988/48eMFQajMDbdnhCoff/yx0LZtW8HKykoICwsTDhw4YIyPZDRmvw5gQzV0bZ7mUFxcDB8fHyxdurTBI3VERETUvLRaLQ4cOAAnJyd063b36wBaErM/BWyOjh07ho0bN+LixYs4evQoxowZAwB3nJImIiIi8ahUKnTt2hU3b97EqVOnar00SaPR4NSpU7h58ya6du1q8eEPaAHrAJqrJUuWICUlxXCx5x9//AFXV1exyyIiIqLbuLi4oHv37jh9+jQOHDgAV1dXuLm5QalUQqfTITs7Gzk5OZDL5XfcBs6SWcwpYCIiIqLaaLVaZGZmIi0tDaWlpYbtNjY28PHxgaenZ5Nn/rZEDIBEREQkGYIgQKfTQafTQalUQqlUNumOHy0dAyARERGRxHASCBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHEMAASERERSQwDIBEREZHE/D9910xHvgHWEAAAAABJRU5ErkJggg==' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_k = 1\n",
    "init_H = 1\n",
    "\n",
    "p_delta = np.linspace(-0.03,1,100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.grid(1)\n",
    "line, = ax.plot(p_delta, u(p_delta, init_H, init_k,simple_mult))\n",
    "ax.set_xlabel('Angle [deg]')\n",
    "fig.subplots_adjust(left = 0.25, bottom = 0.25)\n",
    "\n",
    "axH = fig.add_axes([0.1, 0.25, 0.0225, 0.63])\n",
    "H_slider = Slider(\n",
    "    ax=axH,\n",
    "    label = \"Tip Rquilibrium\",\n",
    "    valmin = 0.1,\n",
    "    valmax = 1,\n",
    "    valinit = init_H,\n",
    "    orientation = \"vertical\"\n",
    ")\n",
    "axK = fig.add_axes([0.25, 0.1, 0.65, 0.03])\n",
    "K_slider = Slider(\n",
    "    ax=axK,\n",
    "    label = \"Spring Constant\",\n",
    "    valmin = 0.1,\n",
    "    valmax = 1,\n",
    "    valinit = init_k\n",
    ")\n",
    "\n",
    "def update(val):\n",
    "    line.set_ydata(u(p_delta, H_slider.val, K_slider.val,simple_mult))\n",
    "    fig.canvas.draw_idle()\n",
    "    \n",
    "H_slider.on_changed(update)\n",
    "K_slider.on_changed(update)\n",
    "\n",
    "# resetax = fig.add_axes([0.8, 0.025, 0.1, 0.04])\n",
    "# button = Button(resetax, 'Reset', hovercolor='0.975')\n",
    "\n",
    "plt.grid(1)\n",
    "# def reset(event):\n",
    "#     H_slider.reset()\n",
    "#     K_slider.reset()\n",
    "# button.on_clicked(reset)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "318b7422",
   "metadata": {},
   "source": [
    "Now, both variables affect the amplitude and zero crossing point of the effect showing that on a clarinet, the stiffness of the reed (spring constant) and the reed tip equilibrium, both affect the maximum flow. Mathematically, this is visible when taking the derivative of the flow equation and finding the zero point of the equation.\n",
    "\n",
    "In this case, lets assume that the pressure (p) is positive."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a78a2de9",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "    \\frac{du}{dp\\Delta } &= \\frac{d}{dp\\Delta }\\left[\\sqrt{p\\Delta } \\left(H - \\frac{p\\Delta }{k}\\right) \\right] \\\\\n",
    "    u^{'}&= \\frac{p\\Delta ^{-\\frac{1}{2}}}{2}\\left( H-\\frac{3}{k}p\\Delta \\right)\n",
    "\\end{align}\n",
    "\n",
    "When $u^{'} = 0$, it marks the critical point in which the flow value goes from increasing to decreasing in value, in other words the maximum value of the curve:\n",
    "\\begin{align}\n",
    "    0 &= \\frac{p\\Delta ^{-\\frac{1}{2}}}{2}\\left( H-\\frac{3}{k}p\\Delta \\right)\\\\\n",
    "    0 &= \\left( H-\\frac{3}{k}p\\Delta \\right)\\\\\n",
    "    H &= \\frac{3}{k}p\\Delta\\\\\n",
    "    p\\Delta &= \\frac{Hk}{3} \n",
    "\\end{align}\n",
    "    \n",
    "Inputting this value for the pressure difference back into the curve gives:\n",
    "\n",
    "\\begin{align}\n",
    "    u &= \\sqrt{p\\Delta } \\left(H - \\frac{p\\Delta }{k}\\right)  \\\\\n",
    "    &= \\sqrt{\\frac{Hk}{3} } \\left(H - \\frac{H}{3}\\right)\\\\\n",
    "    &= \\sqrt{\\frac{Hk}{3}} \\left(H - \\frac{H}{3}\\right)\\\\\n",
    "    &= \\sqrt{\\frac{H^3k}{3}} \\left(1 - \\frac{1}{3}\\right)\\\\\n",
    "    &= \\sqrt{\\frac{H^3k}{3}} \\frac{2}{3}\\\\\n",
    "    &= \\sqrt{\\frac{4H^3k}{27}}\\\\\n",
    "\\end{align}\n",
    "\n",
    "Now, lets set $u = 1$, the desired max value, the relation between H and K can now be determined to keep the max flow to one.\n",
    "\n",
    "\\begin{align}\n",
    "    u &= \\sqrt{\\frac{4H^3k}{27}}\\\\\n",
    "    1 &= \\sqrt{\\frac{4H^3k}{27}}\\\\\n",
    "    1 &= \\frac{4H^3k}{27} \\text{ for x > 0}\\\\\n",
    "    k &= \\frac{27}{4H^3}\n",
    "\\end{align}\n",
    "\n",
    "Now, the spring constant (k) is dependent on the tip equilibrium (H), (something that is not true within the real-world model).\n",
    "\n",
    "To find the optimal value of H, the equation must be solved for $u = 0$ and $x = 1$.\n",
    "\n",
    "\\begin{align}\n",
    "u &= \\left(H \\sqrt{|p\\Delta| } - \\frac{\\sqrt{|p\\Delta| }p\\Delta }{k}\\right)sgn(p\\Delta)\\\\\n",
    "0 &= H - \\frac{1}{k}\\\\\n",
    "H &= \\frac{1}{k}\\\\\n",
    "H &= \\frac{4H^3}{27}\\\\\n",
    "H^2 &= \\frac{27}{4}\\\\\n",
    "H &= \\sqrt{\\frac{27}{2}}\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cae6f21b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def u_N(x,H):\n",
    "    k = 27/(H**3*4)\n",
    "    arr = np.sqrt(np.abs(x))*(H-x/k)*np.sign(x)\n",
    "    return arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4aac43ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7b1772c680784f39b52cb75066cfcb44",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_H = np.sqrt(27)/2\n",
    "\n",
    "p_delta = np.linspace(-0.03,1,100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.grid(1)\n",
    "line, = ax.plot(p_delta, u_N(p_delta, init_H))\n",
    "ax.set_xlabel('Normalized Pressure')\n",
    "fig.subplots_adjust(left = 0.25, bottom = 0.25)\n",
    "\n",
    "axH = fig.add_axes([0.1, 0.25, 0.0225, 0.63])\n",
    "H_slider = Slider(\n",
    "    ax=axH,\n",
    "    label = \"Tip Rquilibrium\",\n",
    "    valmin = 0.1,\n",
    "    valmax = 3,\n",
    "    valinit = init_H,\n",
    "    orientation = \"vertical\"\n",
    ")\n",
    "def update(val):\n",
    "    line.set_ydata(u_N(p_delta, H_slider.val))\n",
    "    fig.canvas.draw_idle()\n",
    "    \n",
    "H_slider.on_changed(update)\n",
    "\n",
    "\n",
    "# resetax = fig.add_axes([0.8, 0.025, 0.1, 0.04])\n",
    "# button = Button(resetax, 'Reset', hovercolor='0.975')\n",
    "\n",
    "plt.grid(1)\n",
    "# def reset(event):\n",
    "#     H_slider.reset()\n",
    "#     K_slider.reset()\n",
    "# button.on_clicked(reset)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f48d42b",
   "metadata": {},
   "source": [
    "The variable 'A' can be added to represent $\\sqrt{\\frac{2}{\\rho}}w$ as previously mentioned that can control the amplitude of the flow independently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dcc17f97",
   "metadata": {},
   "outputs": [],
   "source": [
    "p_delta = np.linspace(-0.03,1,100)\n",
    "p_sqrt_delta = np.sqrt(np.abs(p_delta))\n",
    "p32 = p_delta*p_sqrt_delta\n",
    "p_sign_delta = np.sign(p_delta)\n",
    "\n",
    "def u_N_Amp(H,A):\n",
    "    k = 27/(H**3*4)\n",
    "    arr = A * (p_sqrt_delta*H-p32/k)*p_sign_delta\n",
    "    return arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "05e1fc0c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "159acee3dd1b4af781ce160cac11872a",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_H = np.sqrt(27)/2\n",
    "init_A = 1\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.grid(1)\n",
    "line, = ax.plot(p_delta, u_N_Amp(init_H, init_A))\n",
    "ax.set_xlabel('Normalized Pressure')\n",
    "fig.subplots_adjust(left = 0.25, bottom = 0.25)\n",
    "\n",
    "axA = fig.add_axes([0.1, 0.25, 0.0225, 0.63])\n",
    "A_slider = Slider(\n",
    "    ax=axA,\n",
    "    label = \"Amplitude\",\n",
    "    valmin = 0.1,\n",
    "    valmax = 1,\n",
    "    valinit = init_A,\n",
    "    orientation = \"vertical\"\n",
    ")\n",
    "axH = fig.add_axes([0.25, 0.1, 0.65, 0.03])\n",
    "H_slider = Slider(\n",
    "    ax=axH,\n",
    "    label = \"Tip Equilibrium\",\n",
    "    valmin = 0.1,\n",
    "    valmax = 3,\n",
    "    valinit = init_H\n",
    ")\n",
    "\n",
    "def update(val):\n",
    "    line.set_ydata(u_N_Amp(H_slider.val, A_slider.val))\n",
    "    fig.canvas.draw_idle()\n",
    "    \n",
    "H_slider.on_changed(update)\n",
    "A_slider.on_changed(update)\n",
    "\n",
    "# resetax = fig.add_axes([0.8, 0.025, 0.1, 0.04])\n",
    "# button = Button(resetax, 'Reset', hovercolor='0.975')\n",
    "# def reset(event):\n",
    "#     H_slider.reset()\n",
    "#     K_slider.reset()\n",
    "# button.on_clicked(reset)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51315dea",
   "metadata": {},
   "source": [
    "# Discussion\n",
    "Why would this be a useful design parameter? It has been discussed in mapping literature that cross-coupled mappings lead to interesting interactions with DMIs. For example, in ... To have the parameters decoupled, the user would have a more transparent mapping of parameters, but the depth and interaction would be lacking. This is of course a perfect thing to test with some participants. To have two models, with the spring constant and tip equilibrium coupled and decoupled. Like that I can study how the users interact with each model.\n",
    "\n",
    "So far, the mathematical analysis of the Reed Model has been done. It is no wonder why the clarinet is so popular. Its timbre and mappings of acoustical parameters to controls render the clarinet an optimal wind instrument. From what I have analyzed above, the user has a very fine control over most of the mouthpiece’s variables. They can change the mouthpiece in different lays, inner widths for easier or harder control affecting the timbre but also the tip equilibrium. They can change the reed hardness, affecting the spring constant. The lip position affects the damping coefficient of the clarinets sound synthesis model. The closing of the tone holes affects the pressure difference felt in the mouthpiece. This creates an interactive model where the note played helps determine how much pressure the user needs to achieve an optimal flow.\n",
    "\n",
    "That last part is of particular interest to us and will be modeled as part of the DMI. Technically, the lower the note, the more holes are covered. This results in higher pressure in the clarinet column and less pressure for the user to input into the system. Inversely, the higher the note is less the pressure. But this aspect will be explored later once the basic model has been implemented.\n",
    "\n",
    "Finally, before I continue to condition the model for the TorqueTuner, I shall discuss the reed model in terms of a convergent modal system. Depending on how much pressure is put on the mouthpiece, different sounds can be generated. A negative pressure, sucking on the mouthpiece will induce a percussive sound on the clarinet called tongue slapping. At pressures above the optimal flow point, beating will occur up until the reed shuts. As such, at each edge cases of the model, different effects can be played. This falls in line with ... view on mappings and DMIs, one can even say that what I am modeling is the metaphor of a clarinet. How well it is integrated into the DMI will therefor determine its transparency for the user and the crowd. This also means that the choice of synthesis model will be crucial for transparency."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5a36fbc",
   "metadata": {},
   "source": [
    "$$\n",
    "u = H \\sqrt{|p\\Delta| } \\left(1 - \\frac{p\\Delta }{kH}\\right)sgn(p\\Delta)\n",
    "$$\n",
    "Now in terms of implementing the model on the TT, calculation efficiency is crucial. Right now, the models is of $O(x^{\\frac{3}{2}})$ on account of the pressure values being square rooted and multiplied to each other at every cycle. So there is room for improvements algorithmically. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a81409b",
   "metadata": {},
   "source": [
    "For starters, the pressure values can be precomputed and stored in either a simple array or a hash table. Reducing the big O notation to approximately 0(n). I can also reduce the amount of operations needed:\n",
    "\n",
    "$$\n",
    "u = \\left(H \\sqrt{|p\\Delta| } - \\frac{\\sqrt{|p\\Delta| }p\\Delta }{k}\\right)sgn(p\\Delta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bd35a12",
   "metadata": {},
   "source": [
    "Here, the pressure values can be precomputed leading to an abstracted equation:\n",
    "    \n",
    "$$\n",
    "u[n] = \\left(H x_A[n] - \\frac{x_B[n]}{k} \\right)sgn(p\\Delta)\n",
    "$$\n",
    "\n",
    "Where $x_A[n]$ and $x_B[n]$ are precomputed values of pressure that are accessed with a indexed value in the TT. This results in approximately $O(Hn+1) + O(k^{-1}n+1) \\leq O(x^{\\frac{3}{2}})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de13ea84",
   "metadata": {},
   "source": [
    "Now, from figure 1 at the beginning of this notebook, the maximum flow only reaches 0.4 and not 1. To resolve this issue, I have determined the relation between H and k to keep the max flow at 1 and, as a result, affecting the stretching factor. This is not optimal as it removed a degree of manipulation from the equation. It did however give us the optimal curve for us to do an initial implementation. \n",
    "\n",
    "Re-evaluation of the variables H and k must be done when designing in more depth the mapping between the reed model and another controller that can control those parameters. Like the z and y axis (height and pressure) on the Linnstrument."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63bb18f2",
   "metadata": {},
   "source": [
    "Now, let’s generate the values for the effect starting with the pressure values. The TT angle has a range from 0 to 3600 integer steps and a max torque of 180."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "feddbde3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.598076211353316 0.3849001794597505\n",
      "(3601, 4)\n",
      "[[0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [2.77777778e-04 1.66666667e-02 4.62962963e-06 1.00000000e+00]\n",
      " [5.55555556e-04 2.35702260e-02 1.30945700e-05 1.00000000e+00]\n",
      " ...\n",
      " [9.99444444e-01 9.99722184e-01 9.99166782e-01 1.00000000e+00]\n",
      " [9.99722222e-01 9.99861101e-01 9.99583362e-01 1.00000000e+00]\n",
      " [1.00000000e+00 1.00000000e+00 1.00000000e+00 1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(0, 1,3601)\n",
    "x_A = np.sqrt(np.abs(x))\n",
    "x_B = x*x_A\n",
    "x_sgn = np.sign(x)\n",
    "\n",
    "H = np.sqrt(27)/2\n",
    "k = 27/(H**3*4)\n",
    "\n",
    "\n",
    "pressure = np.stack((x,x_A,x_B,x_sgn),axis=1)\n",
    "print(H,k)\n",
    "print(pressure.shape)\n",
    "np.set_printoptions(threshold=10)\n",
    "print(pressure)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e77e4a67",
   "metadata": {},
   "source": [
    "Now that I have the values, I can write them to the headfile to be stored and used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a7ee984a",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('TorqueTuner/software/include/pressure_table_values.h', 'w') as f:\n",
    "    f.write('const float rp_table[] = {')\n",
    "    for var in x_A[:(len(x)-1)]:\n",
    "        f.write(str(var) +', ') \n",
    "    f.write(str(x_A[len(x)-1]))\n",
    "    f.write('};\\n')\n",
    "    f.write('const float rp_B_table[] = {')\n",
    "    for var in x_B[:(len(x)-1)]:\n",
    "        f.write(str(var) +', ') \n",
    "    f.write(str(x_B[len(x)-1]))\n",
    "    f.write('};\\n')\n",
    "    f.write('const int rp_sgn_table[] = {')\n",
    "    for var in x_sgn[:(len(x)-1)]:\n",
    "        f.write(str(int(var)) +', ') \n",
    "    f.write(str(int(x_sgn[len(x)-1])))\n",
    "    f.write('};\\n')\n",
    "    \n",
    "    f.write(\"const float H_init = \" + str(H) + ';\\n')\n",
    "    f.write(\"const float k_init = \" + str(k) + ';\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "080591d5",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  }
 ],
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