{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from helpers import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Try to vary gradient instead of power for spilling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zr=2.952624674426497um\n",
      "3879.36034722613Hz\n",
      "1.29394674177543 uK\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 4.18$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_power = 49 * si.uW \n",
    "initial_grad = 1.5 *si.G/si.cm\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= initial_grad,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer= 1 * si.um,\n",
    "    a=184.4*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "\n",
    "    wvl = 1064 * si.nm,\n",
    ")\n",
    "\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))\n",
    "print(f\"zr={zr*1e6}um\")\n",
    "\n",
    "print(f\"{float(trap.subs(trap.get_omega_ax_tweezer()))}Hz\")\n",
    "print(f\"{trap.subs(trap.a *2*trap.power_tweezer/(np.pi*trap.waist_tweezer**2)/ const.k) /si.uK} uK\")\n",
    "\n",
    "aspect_ratio = trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer()\n",
    "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(Math(f\"{_aspect_ratio_latex} \\\\approx {trap.subs(aspect_ratio).evalf():.2f}\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.09863993e+15 9.18685788e+09 4.97230892e+05 9.24102276e+01\n",
      " 5.97167510e-02] s\n",
      "-2.5424609279680885e-30\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.grad_z] = 0.1*initial_grad\n",
    "plot_solutions(trap,100,-0.5*zr,1.9*zr,n_pot_steps=1000,display_plot=-2,state_mult=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/150 [00:00<?, ?it/s]<lambdifygenerated-1690>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 4.05199317290834e-24\n",
      "<lambdifygenerated-1691>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\scipy\\optimize\\_root_scalar.py:326: RuntimeWarning: Derivative was zero.\n",
      "  r, sol = methodc(f, x0, args=args, fprime=fprime, fprime2=fprime2, **kwargs)\n",
      "  1%|          | 1/150 [00:00<01:07,  2.22it/s]<lambdifygenerated-1695>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "  2%|▏         | 3/150 [00:00<00:38,  3.83it/s]<lambdifygenerated-1704>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1702>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 4.0241804789252e-24\n",
      "<lambdifygenerated-1703>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1703>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1704>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1701>:3: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return 5.61241215754764e-29*x0 - 5.61241215754764e-29*x0/(1132096000000.0*z**2/pi**2 + 1) - 4.0241804789252e-24*z\n",
      "  3%|▎         | 4/150 [00:01<00:34,  4.21it/s]<lambdifygenerated-1707>:2: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1708>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1708>:2: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1706>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 4.01490958093081e-24\n",
      "<lambdifygenerated-1707>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1707>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1708>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "  3%|▎         | 5/150 [00:01<00:34,  4.21it/s]<lambdifygenerated-1710>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 4.00563868293643e-24\n",
      "<lambdifygenerated-1711>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "  4%|▍         | 6/150 [00:01<00:32,  4.45it/s]<lambdifygenerated-1714>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 3.99636778494205e-24\n",
      "<lambdifygenerated-1715>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1716>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1715>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1716>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "  5%|▍         | 7/150 [00:01<00:29,  4.82it/s]<lambdifygenerated-1718>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 3.98709688694767e-24\n",
      "<lambdifygenerated-1719>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "  5%|▌         | 8/150 [00:01<00:27,  5.20it/s]<lambdifygenerated-1722>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 3.97782598895329e-24\n",
      "<lambdifygenerated-1723>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1723>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1724>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1724>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "  6%|▌         | 9/150 [00:02<00:26,  5.29it/s]<lambdifygenerated-1728>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1725>:3: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 5.61241215754764e-29*x0 - 5.61241215754764e-29*x0/(1132096000000.0*z**2/pi**2 + 1) - 3.96855509095891e-24*z\n",
      "  7%|▋         | 10/150 [00:02<00:25,  5.53it/s]<lambdifygenerated-1731>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1732>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1730>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 3.95928419296453e-24\n",
      "<lambdifygenerated-1731>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1732>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.3796196043647e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 1.18980980218235e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "  7%|▋         | 11/150 [00:02<00:24,  5.59it/s]<lambdifygenerated-1734>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 3.95001329497015e-24\n",
      "<lambdifygenerated-1735>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "  8%|▊         | 12/150 [00:02<00:23,  5.84it/s]<lambdifygenerated-1738>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 9.91508168485294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 3.94074239697577e-24\n",
      "<lambdifygenerated-1739>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.96603267394118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 9.91508168485294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1737>:3: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return 5.61241215754764e-29*x0 - 5.61241215754764e-29*x0/(1132096000000.0*z**2/pi**2 + 1) - 3.94074239697577e-24*z\n",
      "100%|██████████| 150/150 [04:20<00:00,  1.74s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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79u0wmUzo06cPRo0aBQD48ccfC+x37dq10Ol0GDRoUKGv+7jvR3GyzunTpwEAYWFh+M9//oPw8HBotVoEBwfjgw8+gMlkKrCPgwcP4tNPP8Xbb7+NmjVrFllHUbUV5zMhhECXLl2wY8cOjBgxwvLzN2DAABw7dszq+fb4TBTwuF3p5j9jtm7d2upPGu+8844AIF5++WXLtoiICCGTycT3339vtQ/zn2HHjBkjhBDi4MGDAoCIioqytFm1apUAIJydncWIESMs2/fs2SMAiE8++UQI8WCsk3lfeccLnTp1Smi1WtGsWbMCr9umTRub/hTdr18/AUAkJiYWeGzdunUCgPjXv/5V5POPHj0qgAeTnwrTqFEjodfrrbaNHTtWuLq6ips3bwoh/vf9LuzPeevWrROurq6WMVYAREREhLh7966lTWZmptDpdKJatWoFhq6Yx7YrlUq2ZdvHaiuEEG3bthUAhIuLixg7dqyYOXOmaNKkiQAgGjRoYLWPmjVrCgBi9uzZlm137twRGo1GABATJkywbE9JSRGurq6ievXqVjV06NBB6PV6y8+9eYjMq6++atmfTCYTo0ePtjxn1qxZAoC4cOGCKK78P4srV64UAESVKlWshnVcvHhRKBQKq/HTu3btEgDE3LlzLdsKG45SWLs6deoIb29vq59rIYR49dVXBQCxePFiy7bHmZj5xhtviMmTJws/Pz/h5+dnNRSlpMwTOoszHKVatWoCgPD29haTJ08WL7zwgggJCREARJcuXSzjui9fviwAiF69epW4viFDhoju3btbvr5w4YJQKpUiPDzc6vt97NgxoVQqLX+CN7/37u7u4saNG5Z25s+XVqsVly5dsmw3TyzLO9nVVt9//70AIFatWmW1PycnJyGXy8Urr7xi2W6eg7Rp06Ziv46Li4sIDw8v9LHp06cLAOLw4cPF2ufDrl+PW4N5bkfeeSlCPDhvAbAapmBu27ZtW5GdnS2EEMJkMlkmmTds2FBkZGRY2nfq1EkAsJpbZavnnntOABDR0dGWbREREcLZ2VkAEFu2bLFsHzt2rFCpVCI5OVlkZGQIZ2dn0aRJE6v93bx5U8hkMjFs2DDLNhRzTLhZUe/H4sWLCx3eJ8SDSZjIM+RrxowZAoDo27evUCqVYvjw4WLatGkiODhYABDjx4+3en5WVpaoV6+eaNGiheVcXZz6S/KZaN++vdX7+dVXXwkAYsqUKZZt9vxM5FVqIdw8PsjMaDQKPz8/UaNGDSGEENevXxcARI8ePQrsw2AwiKCgIKHRaERmZqYwGo2iSpUqokOHDpY2o0ePFnXq1BG9e/cW1apVs2x/7bXXrD7g3bt3FzKZTNy/f7/A65gnGpw6dUoI8b+L3sOCc16dO3cWAKzeCDNzCFmwYEGRz9+7d2+BX0zyatGihVAoFJavzWPQP/74Y8u2on5oLl68KMLCwoRarRZPPfWU1aoVo0ePtvqF5KWXXrKclE6cOCFSUlLE77//Lnx9fYVer7eqgW3ZtqRtu3XrJurXr28VSI1Go5g0aVKBnwNzCM+/wpB5NYv8F9ZWrVoJuVxu9bk2j1U8fvy4EOJ/ASTv2MFGjRoJf39/y9ctW7YsEOZtVVQIf/755wu0DQ0NFWq12vJ1SUO40WgU69atK3Tc+NatWwUA8frrr1u2FTeEF/WvQYMGYtu2bTZ8Vx6uuCE8MzNTNG3aVLRt21YkJCRYbe/bt69VB4y582bkyJEF9hMbG1voyipffPGFpU1ubq7w8PAQixYtsmx7++23iwwjS5YssZybze99/knIP/30U6HHu3nzZgE8ekWswiQkJAi5XC6effZZy7aOHTuKbt26ibCwMNG2bVvL9pEjRwqdTles1UjM5HK5aNmyZaGPmSfBFTbW92GKG8KLU0NJQvh3331n1faFF14QAMSnn35qtX3u3LkCgNi5c6dNdef1yy+/CADiP//5j6UejUYjZs6cKQCI1157zdLW399fdOrUyfK1eTJz3qC3ZMkSAUCsX7/esq20Q/hbb71V5C9v6enpll+AhRBiwoQJAoCQy+VW59rU1FTRsmXLAt+3N954QyiVSnHixIkS1V+Sz8SPP/5o1c48vynvL9z2/EzkVSohXKFQFDrLvH///gKAuHfvnvjtt98EAPH2228Xuh/zklLmN2bEiBFCrVZbAm9AQICYMGGCmD9/vtWHslmzZqJ+/fqW/Xh5eQknJ6dCT7jdunUTAMQ333wjhPjfRe/nn3+26VjNEwiSkpIKPGbuCV+yZEmRz//7778FUHDJQLNGjRoJV1dXIcSDD3qtWrVEmzZthNFotLQp7IcmNzdXhIaGCo1GI/7++2/LdqPRaJmAlHdlgezsbDFs2DCri6xMJhNz584VPXv2FC4uLmzLto/dtiipqalCr9dbLW9Xs2bNAn8FEuJB2AZgWZXDrLCfA/PkZvPJ8plnnhFardaqjbln8vLlyyIjI0OoVCqrMFMcRYXwvCvHmJkvRmaP0xNudu3aNfHbb7+JpUuXigkTJohatWoJAFY9oY8zMdNoNIqEhATx888/i2rVqgmlUvnYQbwkPeFFuXr1qlW4On/+vAAK7wk/fvx4ob9c5L3wm0N83lVyzCut3L59+6G1mN/7/B065rCd9z0R4uHvqy1at25t6eDKyMgQGo1GvP3222Ls2LGW66bJZBLe3t6PnKRaFCcnJ9G4ceNCHzP3OBb3ryPFDeHFqaEkITx/T745WOXtnRbi8SZNp6SkCJVKZVmq748//hAAxP79+0VQUJBl8uOpU6cKfIa2bNkiAIh3333Xsq1Vq1bCw8PD0lsrROmH8A8++EAAhU9cNveE9+/fXwjxv57+wiZpm+s39zj/888/QqVSFfh5KE79JflM5A38Qjz4mQEejBQws+dnIq8Hs20ek4+Pj2XiTl4uLi4AgOTkZMtkEVdX10L3YZ4gY76ZRq9evbBmzRocOHAAQUFBuH79Ojp06IAaNWoAeDAe0dXVFceOHcOcOXMs+0lKSkJubq5lklNh8o5TBwAnJyebjtPDw8NyPPknSCYnJwNAkRMn8z+/MHn3++abb+LGjRv47bffIJc/fOj+n3/+iQsXLuC5556zGuMol8uxaNEirFq1CqtWrcJrr70G4MH487Vr12LmzJnYv38/NBoNunfvjrp166JJkyaoWrWqZR9sy7YlbVsUZ2dn1KlTBydPnoTJZLJ8vvNPVs6rsPF/+eUdFz558mT88ccfaNeunWWuCPDgZldLly7Fvn37EBQUBIPBUKrjwYuqtbiTPh/m5MmTmD59Ovbu3Wt5vYYNG6J58+a4evXq449R/H9yuRyenp4YPHgwnJyc0KtXL0RGRqJbt26lsv/HFRQUBA8PD8vkqBo1akChUBSYgA88mJyY//uS/z3Ztm0bfH190ahRI8s287WiqOtWfkV9hm35/BaH+b24fPkyYmJikJ2djQ4dOsDf3x8rV67EX3/9BVdXV9y9e7dE48GBB9erh12rgIdf70pDWddgj/fLxcUF7du3t4wL37Vrl2XSbocOHbBmzRpkZWVh69atAGD1fnXt2hVVq1bFjz/+iFdffRXR0dE4dOgQnnvuOatJ0qXtYVkl//fd/N9mzZoVaNu4cWMAwNWrV2E0GjF+/HgEBARYzSUpSW3F/Uzkfz/NP/uFnSvt9TNsViohvKi7FJlPYJ6enpZAfvv27Ue2BYCePXtCJpNh586dlskBHTt2RNWqVaHVarF3715oNBoIIdC7d2/LfpydneHt7f3QCZIlFRISAuDBKhEBAQFWj5knAoSGhhb5/MDAQKjV6kInkuTk5OD27duWyVk///wzDAZDkSsC6HQ61KxZE9HR0bhx4waAB5ON8tNqtQgKCir0wtSmTRu0adPG8nVGRgbOnj2Lnj17si3bPlbbtLQ0nDp1Cm5ublaT+cwyMzOhVqsf+QtmcWi1WrRq1QpHjhzB+fPncfv2bbzwwgtWbTp06AClUok///zTsnJQaYfwspSamooePXogNTUVH374Ibp06YK6detCqVRi69athU7iKg3m89LJkyfLZP9FuX//Ps6ePQt/f38EBQVZPSaEQFZWFnx8fAA86Ezp0qULtm3bhtOnT9u0mkpe27ZtK/ALhvmCnJqaCr1eb/VYZmYmtFptqf6CZStzCN+5cydu3LgBrVaLli1bWq5Le/fuhUqlAgCr62NxhISEYP/+/TAYDJZ9mV27dg06na7AdbC0FacG8/uQfyJgYXfJtbdevXph165duHjxInbv3o3WrVtDrVYjIiICX3/9NQ4dOoStW7ciMDDQ6jquUCgwfPhwLFu2DJcvX8a6desAPFhMoizlzTr55c86derUAVD4hH2DwQDgwc/mjRs3LBOZC+v4PHToEGQyGUaPHo1Vq1Y9tDapP5elqVSugElJSbhy5YrVttzcXBw+fBihoaFwdXW1zFbPO3PbTAiBffv2Qa/XW2bK+vj4oGnTpti5cyf279+PwMBABAQEQKPRoFWrVti/fz+2bNkCNzc3tGvXzrKvRo0a4dq1a5aVVvL67rvvEBUVVeLZ1OYlcQpbRnD37t3QaDRo2rRpkc9XKpVo1aoVDh8+bLW8GvDg+2IwGCzBZubMmYiMjCzwz/z9ef311y0zn829j/mXZgIe/BDExMRY3bq6Xbt2VgHKbOPGjcjJyUGPHj3Ylm0fq+3Vq1fRtm1bTJkypUDb2NhYXL16tdCek8cVERGB8+fPY/v27QAe9Hzn5eLighYtWuDUqVP466+/ULt2bctf16RmS5jbuXMn4uPjMXPmTMyYMQMNGjSw/BXy3LlzAArv3Xlc9+/fB2B7j3Bp2b9/P5544okCyx4CwNGjR5GZmWn1OTJ/3l588cWHfh/yP5aSkoK///67wNKE5iUY//777wL7GDVqFFxdXYvslStLzZs3h7e3t+X62Lp1a2g0GtSsWRM1a9a0XB/r169f7NUnzNq3bw+DwWBZmtcsPT0dhw8fRvPmzQv9C3hpKk4N5p7h1NRUq7aFdUDZW69evQAAW7ZsweHDhy2/1JqX+9u2bRv27dtX6F8tzKuk/P777/j5559Ro0YNdOjQoUzrbdasGXQ6XZFZB4DlOmBeSSj/CjAALMt4NmzY0LJiS2H/AMDf37/AinSFKQ+fy1L1WINZxP/GFA0dOtRqXPibb75ZYCyTue3q1aut9mGe/JJ/bOYbb7whFAqF8Pf3t1rRwDwWx83NTTz55JNWz/nyyy8FAPHUU0+JnJwcy/ZLly4Jd3d3odfrLWO6izumJzc3VwQEBAgfHx+rGfDmSZn5ZwEXxnzrefOKDUL8746ZCoWiyJtlmBU2hisrK0v4+fkJnU5X4M5U5okKeSfBPfPMM0Imk4mDBw9atsXExIiAgADh7e1tdcMhtmXbkrQ1mUwiJCREyGQyq8k92dnZYvDgwQKA+Pbbby3bixq7bB4Tnl9RYxnN48Lr168v3NzcCr2F8RtvvCFcXV2Fn5+feO655wo8bquixoTnn8BT2HEUNibYfB7MOw4zfzvzGMv8EwAvXLggqlatKgDru4KW1s16zGMt865SUxLFHROelpYmPDw8hEajsUy4FeLBnVDNq+/knxxovg320KFDrSZzmp09e9YyP6hNmzZCiAdzemQymYiLi7Nqe+bMGSGTyUSzZs2sVsU6efKk0Gg0lkl0Rb335jHh+W/C9rhjwoUQ4umnnxbe3t6WOVBmo0ePFk5OTkKpVIo5c+aUeP/nz58XCoVCdOzY0Wr8sfmaYp5bVRzFHRNenBrMExbzTkw2GAyWVc0KGxOef/y4efxv/oUmSmP8b40aNSwT0PPuv2bNmsLNzU0AEBs3biz0ubVr1xaNGjUSMpms0PcUpTwmXIj//RzlHQud946Zeeeqme+kvHbtWsu25ORkER4eLpRK5SNXnypO/cX5TJRknoA9PxNClOLqKJ6eniI8PFzMmjXLsnRLy5YtrSZUXbhwQXh7e1smz7z44ouiffv2AoAICQkpsOTWgQMHLBNozDOLhfjfCQywXqZJiAeTicyz5sPCwsT06dPFhAkThKurq5DJZFbtH/ZNPH78uIiMjCwwK/73338XCoVC+Pj4iJkzZ4oxY8YIlUol/P39C6zssHTpUhEZGWl18s7NzbVcPHr27Cnmzp1rWQFi/vz5Nn+/8//QbN68WajVaqHT6cSoUaPE7NmzRevWrQUA0aRJE6s7dF69elW4uLgIZ2dnMWnSJDFt2jRRtWpVoVKpCsyGZlu2LWnbPXv2CI1GIxQKhRgxYoSYMWOGCAsLE0DBFSxKK4SbVx4AIAYMGFDgeUJYnz/Md5I1K+rnvjClHcLNy7A2adJEvPLKKyIrK6tAu7S0NBEYGCiAB0uCvfLKK2LEiBFCp9MJHx+fAp0Zj7NEYWRkpHj55Zctd+mtVq2aZanUwuzatUtERkYWuFjl9agQbn7dvH744Qchl8uFTqcTY8eOFVOnTrWEmbydGWZZWVmW22hrtVoxYMAAMWfOHDF9+nTRpk0bIZPJBADRqVMny7KBkydPLnLZM/N1IiAgQDz//PNiwoQJQq/XC2dnZ8sFuzRCeHE+e0II8d1331k+x3lXaDDXAkDs3r3bpn0VxRxAGjRoIObOnWu5DXm3bt2sfsFNTEwUkZGRYunSpQ/d38NC3y+//CIiIyOtftkqTg1xcXGWZRqHDRsm5syZI+rXry+Cg4NFtWrVSj1wFVVvUcx3nVWr1VbHb65Fp9MVuvJa3tdHIZMMhSgYYkvj/YiJiRHe3t5CrVaLMWPGiBkzZghvb2+hVCoL3K3y/PnzwtvbWygUCjFkyBAxY8YMy0Txh60YV1T9Zo/7mahUIfzcuXOia9euQqfTiYCAADF37lyRlpZWoH1MTIwYO3as8PX1FWq1WgQHB4tXXnlFJCcnF2ibm5srqlSpIgDrJXrMF1qZTCbi4+MLPM9gMIjFixeLhg0bCq1WK7y8vETXrl0LfHAe9k00n8jy9sCbbdu2TbRt21bodDpRtWpVMWLECHH16tUC7cwXivy9SykpKWLmzJmiWrVqQqfTiYYNG1otlfUwD/uhOXLkiBg4cKCoUqWKUKlUlu9t3gBudvr0adGnTx/h6ekpPD09Re/eva1WVmFbti2NtseOHRP9+/cX7u7uQqPRiIYNG4ply5ZZ9aIIUXohPO9jy5YtK7SmrKwsodPpCj1/POzn/lE1PG4Iz8zMFMOGDRNOTk7C1dVVnD9/vtB2Fy9eFAMHDhTe3t7C2dlZhIWFiWnTpom7d++KgIAA4evra7kQPe4ShTqdTtSrV0/MnDlTxMbGPnQf5vNp/sCZ16NCuPl189u5c6fo0qWLcHZ2FjqdTrRo0cLqLymFOXTokJg0aZKoV6+ecHZ2Fnq9XoSGhoqJEycW6D2vVavWQ3uNv/32W9GiRQuh0+mEi4uL6NOnj9UqKqURwovz2RPif0sV5l1FTIj/fY/d3NwKXbWsOEwmk1i2bJmoW7eu0Gg0IigoSMydO7fANcX8mnlXPCrMw35uzSFo5cqVJapBiAcrkHXu3Fk4OTkJDw8PMWrUKHH79m0RGhpa6oGrqHqLYl5BLf+t4M3ve+/evYt87sWLFy0di4XJH2JL4/0Q4sEIgsGDBwt3d3fh6uoqOnbsKPbs2VNo25iYGPHss88KHx8fodVqRdOmTR/5M1pU/WaP+5moCCFcJsTjDSCMiIiw3LY07yoEREQV0UcffYSzZ8+W6BbrRI+Dn72KZdCgQRg2bBieeuopqUuhCqr0liYgIqrgcnNz8dNPPz3ytudEpY2fvYolNjYWe/bs4ftFj6UCTSElIipb5vsSTJw4UepSqJIpy89eUlISPvzwQ5vbDxw40LLGMxXum2++wbx58wpdgpXIVhyOQkRE5MCio6MLrLP+MCtXrsSYMWPKriAiAlAKIZyIiIiIiIqHY8KJiIiIiOyMIZyIiIiIyM4YwomIiIiI7IwhnIiIiIjIzhjCiYiIiIjsjCGciIiIiMjOeLMeojJgMpmQlZUFpVIJmUwmdTlERCUihEBubi60Wi3kcvbbEZUmhnCiMpCVlQW9Xi91GUREpSI9PR1OTk5Sl0HkUBjCicqAUvngRys9PR0qlcrm5xkMBuj1+mI/r6Lg8VVsPL6Kq6THZn6e+ZxGRKWHP1VEZcA8BEWlUpXoYl7S51UUPL6KjcdXcZX02Disjqj0cYAXEREREZGdMYQTlSNyuRyRkZEOOwGKx1ex8fgqLkc+NqKKSiaEEFIXQeRoDAYD1Go1cnJyHPbP2kTk+HguIyo7/JWYiIiIiMjOGMKJiIiIiOyMIZyIiIiIyM4Ywols8N1338HZ2dnqn0wmw/fffy91aURERFQBcWImUQksW7YMa9euxe7duwudrMTJTETkCHguIyo7DOFExRQdHY0mTZrg8OHDqF27dqFteOEiIkfAcxlR2eFwFKJieu211zBp0qQiAzgRERHRo/C29UTFcP36dfz++++4cuWK1KUQERFRBcYQTlQMP/zwA3r27AkfHx+b2hsMBsv/y+VyKBSKsiqNiKhUGI1GmEwmANbnMCIqXRyOQlQMmzZtwuDBg21ur9froVaroVarsWDBgjKsjIiodCxYsMBy3tLr9VKXQ+SwODGTyEYmkwmurq44deoUgoKCHtrWPJkpPT3dMpmJPeFEVBHk7wnX6/WcmElUBjgchchGCQkJSE9Ph5+fn83PUalUvHARUYWiUCjYYUBkBwzhRDby8fEB/3BEREREpYFjwomIiIiI7IwhnIiIiIjIzhjCicoZw/1EqUsgIiKiMsYQTlSO3Fi0DEebRyAnLl7qUoiIiKgMMYQTlSP6hvUhsrMR+59vpS6FiIiIyhBDOFE54tGtE7Q1AxD/zRoY09KkLoeIiIjKCEM4UTkik8vh+/QwGFNSEf/9T1KXQ0RERGWEIZyonPHs3R3KKh6I/WIVhNEodTlERERUBhjCicoZuUYD7369kHM7Dsn7/5S6HCIiIioDDOFE5ZBn904AgLs//y5xJURERFQWGMKJyiFtdX/ow+ri/uZtMGZkSF0OERERlTKGcKJyyrN7Z5gyMnF/8w6pSyEiIqJSxhBOVE55dHoCMoUCd39eL3UpREREVMoYwonKKZW7G1xbNUfy/r94K3siIiIHwxBOVI5ViWgPGI24v4VDUoiIiBwJQzhROebWthVkSiXubdgidSlERERUihjCicoxpYszXFs04ZAUIiIiB8MQTlTOeXR8MCQlcdtOqUshIiKiUsIQTlTOubdvDZlCgYTfN0tdChEREZUShnCick7p4gLXls2QvPcgcuLvSF0OERERlQKGcKIKwLNnV8BkQsIvvI09ERGRI2AIJ6oA3Nu2gsLFGXd+/BVCCKnLISIiosfEEE5UAcjVKlTp3BGZFy4h/fRZqcshIiKix8QQTlRBePboAgC48/1PEldCREREj4shnMhGV65cQZcuXeDs7IzQ0FBs3mzf1Ur0YaFwqhuCOz/8F1nR1+362kRERFS6GMKJbGAymTBw4EB07twZKSkpWLZsGYYNG4a0tDS71SCTyVBjyngIQy6uv7fUbq9LREREpY8hnMgGf/75JzIzM/Haa69BLpejR48e2LdvH5RKpV3rcGncEG5tW+He75uR/Offdn1tIiIiKj0M4UQ2OHHiBMLCwjB16lT4+PigadOmSEtLg1artXst1SePg0ytwvmnn0PCrxvs/vpERET0+BjCiWyQmJiITZs2ITw8HDdv3sTLL7+MAQMG4P79+w99nsFgsPwzGo2lUouuZg2Efvg+FM56XJr6Es49Owkph47AlJVdKvsnosrNaDRanbuIqGwwhBPZQK1Wo2bNmpg0aRLUajVGjBgBf39/HDx48KHP0+v1UKvVUKvVWLBgQanV41y/LsL+/RE8ItojaedenBn8NA7VboyjLSJwZuizuPbGAtzfsgNGO45ZJyLHsGDBAst5S6/XS10OkcOSCd75g+iRfv31V0ycOBF37961bKtfvz4WLlyI/v37F2hvMBigVquRnp4OlUoFAJDL5VAoFI98rdzYeIj0dJtry4y+jnvbdyH75i1k345D9q3bMKZnPHhNJx28hw1CtUnjoA2obvM+iajyMhqNMJlMAB6cy/R6PXJyciznMiIqHQzhRDZIT09HcHAwZsyYgblz5+L777/HjBkzEB0dDRcXlwLtzSG8JBeu4obw/IQQyL55C8l/H0PCpm3IvHwVcq0WAa/Phu+YUZDJ+QcwIrLN45zLiOjhGMKJbHTu3DlMmTIFx48fR0BAAD755BM88cQThbaVMoTnJYRAypHjiFm8AjmxcajSpwfqfLwIcl5MicgGDOFEZYchnKgMlJcQbmbMyET0e0uRuGc/PPv1Qp0V/4LMzssrElHFwxBOVHb4d2miSkDhpEOteXPh0bEd7v2+GTHvLpa6JCIiokqNIZyokpApFQiaNxf6+vUQ++9VSD54SOqSiIiIKi2GcKJKRK5UIui12ZBrNLg88xXkpqRKXRIREVGlxBBOVMloq1dD9cnjkHMrFrFfrZa6HCIiokqJIZyoEvLu1wvqqj6I//p7mLJzpC6HiIio0mEIJ6qEZEoFfAb3g+HuPdz7bZPU5RAREVU6DOFElZRXn+6Q67S4/eXX4EqlRERE9sUQTlRJKV1c4NmzKzJOn0PqkeNSl0NERFSpMIQTVWLe/XoBAO7++IvElRAREVUuDOFElZhTcBCc6gTj3u+bYczMkrocIiKiSoMhnKiS8+zZBcbUNCRu3SF1KURERJUGQzhRJVelayfIFArcWcshKURERPbCEE5Uyanc3eDWpgWS9/+J7Nh4qcshIiKqFBjCiQiePboCJhMS1v0mdSlERESVAkM4EcGtTQso3Vxx98dfuGY4ERGRHTCEExHkKhWqdO6IzMtXkX7ytNTlEBEROTyGcCICAHj26goAuMM1w4mIiMocQzgRAQCcQmpDG1QTCb9ugCk7R+pyiIiIHBpDOBEBAGQyGbx6dIExOQWJO3ZJXQ4REZFDYwgnIosq3TsDcjnu/vdXqUshIiJyaAzhRGSh9qwC1+ZNkLhzL3LuJkhdDhERkcNiCCciK169ugJGIxJ+2SB1KURERA6LIZyIrLi3awOFsx531vwEYTJJXQ4REZFDYggnIityjRpevbsj88JlJG7bKXU5REREDokhnMhGL730ErRaLZydneHs7AwvLy+pSyozviOGQKZW48aSj3kHTSIiojLAEE5ko5MnT+KHH35AWloa0tLSkJDguBMXVZ5V4D2gNzLOnGNvOBERURlgCCey0cmTJxEeHi51GXbj+9RQyNRqXHvzbWTHxktdDhERkUNhCCeyQWxsLO7du4dZs2bB29sbrVu3xl9//SV1WWVK7VkFNWe/gJxbsTg3chwM9+5LXRIREZHDUEpdAFFFkJCQgIiICLzyyito1qwZVq9ejb59++LChQvw9PQs8nkGg8Hy/3K5HAqFwh7llhqvnl2Rm5yCm598iWOtusBrYB+4tmoObWAAtLUCoaziAZlMJnWZRFSKjEYjTP+/MlLecxgRlS6Z4KwrohJp2LAh3nnnHfTv37/AYwaDAWq12mpbZGQkoqKiHrnf3Nh4iPT00iqzVNzbsRt3flqP9HMXrLYr3FyhbxAGl6bh8OjeGc6NG0Im5x/YiCqyqKgozJ8/32pbTk4OVCqVRBUROSaGcCIbHDhwAP/88w+mTJli2RYaGorly5eje/fuBdqbQ3h6errlwmVrT3h5DOFmWTduIvPadWTdvIXsW7HIirmOjMtXYcrMAgBoAmrAf9pz8B46APJ8v4QQUcWQvydcr9czhBOVAYZwIhscOXIEERER2LJlC1q3bo1PPvkEixcvxoULF6DVagu0N4fwkly4ynMIL4wwGpF+/hIS9x5AwqZtMKakQlu7FkI+XQp9WKjU5RHRY3iccxkRPRxDOJGNVq9ejbfeeguxsbFo3LgxPvvsMzRs2LDQtpUphOdlzMhA/H9/RezXPwAKBYL/tQDeQwdIXRYRlRBDOFHZYQgnKgOVNYSbpZ27gKuRC5FzNwEhny6BZ9+eUpdERCXAEE5UdjiDiohKnXO9UIR+9B5UHu649MJLSN7v2Ms5EhERFRdDOBGVCY2fL0IWvQ25Wo1L019GbnKK1CURERGVGwzhRFRmdLUCUWPqczDE30H0/PekLoeIiKjcYAgnojLl2bsbXFs2w92165C094DU5RAREZULDOFEVKZkMhlqvjQNMrUK1xcuAeeCExERMYQTkR1oqvrAu28vpP9zBkk7dktdDhERkeQYwonILnxHPQmZWoUbS1awN5yIiCo9hnAisgu1lye8+/1/b/jOvVKXQ0REJCmGcHI48fHxUpdARag6fDAglyPu6++lLoWIiEhSDOHkcJo1a4ajR49KXQYVQlPVB+5tWiJp515kXb8pdTlERESSYQgnh8NbK5dv3gN6A0Ig/ru1UpdCREQkGaXUBRCVtieffBLdunXDk08+iVq1akGn01k9Pn36dIkqIwBwbdEUmmq+uPPDz6jx4jTINWqpSyIiIrI7meAyBeRggoKCinxMJpPh6tWrZV6DwWCAWq1GTk5OsXvmc2PjIdLTy6iy8iHuh59w87P/IOSzD+HZr6fU5RBRER7nXEZED8eecHI4165dk7oEegTP7p1x84tVuPPjOoZwIiKqlDgmnBxSTk4OfvjhB0RFReH+/fvYvXs37ty5I3VZ9P9UnlXg1qoFknbvR3YsV7MhIqLKhyGcHE5MTAzq1auHF198Ee+88w6SkpKwbNky1K9fHydPnpS6PPp/Xr27ASYTEn76VepSiIiI7I4hnBzOjBkz0KFDB9y8eRNarRYAsGbNGvTo0QMvvviixNWRmVubllC6u+HO2nW8gyYREVU6DOHkcPbt24eXX34ZCoXCsk2tVmPevHk4fPiwhJVRXnKlEp7dOyPrWgxS/vxb6nKIiIjsiiGcHI5cLkdGRkaB7bGxsZaecSofvAf0BgDErfxO4kqIiIjsiyGcHM7QoUMxe/ZsxMTEQCaTQQiBI0eOYOrUqRg0aJDU5VEe2ur+cG3RFPe3/oHs23FSl0NERGQ3DOHkcBYvXgx/f3/UqlULaWlpqFevHlq1aoXQ0FAsWrRI6vIoH59BfQGjEfHf/Sh1KURERHbDm/WQw4qOjsaZM2eQm5uLsLAw1KlTx26vzZv12E4YjTg1cjxMOQY03rUBKi9PqUsiov/Hm/UQlR32hJNDys3NxbFjx3D06FGcO3cO58+f5woc5ZRMoYD/xDHIvZ+Iyy++xveJiIgqBd4xkxzOtWvX0LlzZyQkJCAkJAQmkwkXL15EcHAwfvvtNwQGBkpdIuXj2TUCKX8fxb2tfyDuP9/Ab/yzUpdERERUptgTTg5n3LhxaNasGW7duoWjR4/i+PHjuH79OqpXr44pU6Y81r7Pnj0LrVaL6Ojo0imWLAJmToHazxc3Fi2HsRINxyEiosqJIZwczl9//YW3334brq6ulm2enp744IMPsGfPnhLvNzc3F2PHjkV2dnZplEn5KJyc4DdyKIwpqbizdp3U5RAREZUphnByOKGhoTh9+nSB7ZcvX36soSgLFy5E+/btH6MyepQq3TtD4eqC2C9XQxiNUpdDRERUZjgmnBzCb7/9Zvn//v37Y+LEibh48SJatWoFhUKBkydPYsGCBXjjjTdKtP+TJ09i7dq1OHz4MJYsWVJaZVM+Cq0WPgN6I/abtbi/aTs8+/WUuiQiIqIywSUKySHI5bb9UUcmk8FYzB7WnJwctG7dGsuXL0e7du0gk8lw7dq1h/aqm5f1Sk9PtyzrJZfLoVAoHvl6lW2Jwvxy7t3HqeFjIQwG6BuGwblJOLQ1q0NTozq0NWtAU6M6lG6uj94REZWI0WiEyWQC8OBcptfruUQhURlgTzg5BPMFoyy89dZbiIiIQLt27Yr9XL1eb/n/yMhIREVFlWJljkntWQWhH76Hu79tQtKBQ0g/dbZAG6WHO5ybhMO1bUt49u0BbY3qElRK5JgWLFiA+fPnS10GkcNjTzjRI9StWxexsbGQyWQAgOTkZLi4uOCzzz7DyJEjC30Oe8JLhxAChvuJyL4di5zYeGTHxiE7Nh5ZMdeRcfEKRG4uAMC1TUtUn/U83Nq1lrhiooqPPeFE9sEQTg7n0KFDeOGFF3D69Gnk5OQUeLy4w1HyK85wFN4xs+yYsrORcvQE7u/YjcTd+yGMRnh0jUDtj96H0t1N6vKIHALvmElUdhjCyeE0aNAAfn5+mDBhArRabYHHBwwY8Fj7Zwgvf7Jj43Dr31/j/s490AbVRN1Vn0JXu5bUZRFVeAzhRGWHIZwcjl6vx9GjR1G3bl3JamAItz8hBO7+sgHXV3wOlYcH6v/8DYM40WNiCCcqO1wnnBxO9+7dcejQIanLIDuTyWTwGdwPwW+9jtzEJJx5cjQyr8VIXRYREVGh2BNODufWrVto0qQJ2rRpg6CgoALLF9pjnW/2hEvr/u79uDr/PTjVC0XDDWshV6ulLomoQmJPOFHZ4RKF5HDmzJmD5ORkxMXFISUlxeox8won5NiqRLRH5pXhiF39A24sXo6ar86WuiQiIiIr7Aknh6PX67F+/Xp07dpVshrYEy49U24uzj8/GxkXL6PBL9/BpUVTqUsiqnDYE05UdjgmnByOj48PfH19pS6DJCZXKhH0+kuQyeWIfut9sL+BiIjKE4ZwcjhLly7FCy+8gMOHD+PevXtISUmx+keVh65mDXj174W0Yydxf8sOqcshIiKy4HAUcjgeHh5IS0srcCt7IQRkMtlj36zHFhyOUn4YEpNw6qnxUFfzReOdv0Om5FQYIltxOApR2eHViBzOr7/+KnUJVI6oPNxRdfggxK76Hgm/bYb34H5Sl0RERMSecKKywJ7w8iU3JRUnhzwDfYN6aPj7WqnLIaow2BNOVHbYE04Op3Pnzg99fOfOnXaqhMoLpasLPLtFIGHjNqSdPAXn8IZSl0RERJUcJ2aSwwkPD7f6FxYWBrVajb///lvSZQtJWj4DHwxDiVv5ncSVEBERsSecHNDSpUsL3f7RRx/hr7/+snM1VF44hQTDuWEYEtZvQs03X4bKs4rUJRERUSXGnnCqNAYOHIgNGzZIXQZJyGdwP4icHNz54SepSyEiokqOIZwqBZPJhM8++wzu7u5Sl0IScn+iLVSeVRC3+geI3FypyyEiokqMw1HI4Xh4eEAmk1lty8jIgMFgwPLlyyWqisoDuUoF7/69cHvld7i/fRc8e3WTuiQiIqqkGMLJ4Xz44YcFtqnVarRq1Qq1atWyf0FUrnj164XY1WsQt/I7hnAiIpIMQzg5nNGjR0tdApVjas8q8Ihoj/t/7EHGxctwCqktdUlERFQJMYSTw8nKysKnn36KQ4cOwWAwIP/9qNatWydRZVRe+Azuh/t/7EHcqu9R6915UpdDRESVECdmksOZPHkyXn/9deTk5MDV1RVubm5W/4j09evBqU4w7v73F+SmpEpdDhERVULsCSeHs27dOvzwww8YMGCA1KVQOSWTyeAzqB+iP/gQd//7C/zGPyt1SUREVMmwJ5wcjlarRb169aQug8q5Kl07QuHqgrj/fMvlComIyO4YwsnhTJgwAe+88w5ycnKkLoXKMblGA5+BfZEVfR0Jv26UuhwiIqpkZCL/rDWiCm7gwIHYvHkzNBoNatSoAY1GY/X4sWPHyrwGg8EAtVqNnJwcqFSqYj03NzYeIj29jCqjvHJTU3FqxDiovDzReM8myJQcoUeU1+Ocy4jo4XjFIYfTpEkTNGnSpNT3+/PPP+P111/HzZs3Ua9ePSxbtgxt2rQp9dch+1G6uMBn6ADErvoed9f9Dp9hg6QuiYiIKgn2hBPZIDo6Gg0aNMAff/yBVq1aYeXKlZg3bx5u3LhRaHv2hFccualpODViHOROOoRv/xUqL0+pSyIqN9gTTlR2OCacyAaBgYGIi4tDq1atkJycjISEBHh6Mqw5AqWLMwJmToHhzl1cmjYHwmSSuiQiIqoEOByFyEbOzs44deoUGjduDKVSiQ0bNkhdEpUSz26dkHr8HyRs3Iprb7yNwMhXINeopS6LiIgcGHvCiYqhbt26yMrKwmeffYYhQ4bg7t27UpdEpSRgxmQ4NwxD/Nff41S/4bi/ZQeMHBZERERlhGPCiUqoYcOGiIqKwpAhQwo8Zh5HmZ6ebhlHKZfLoVAoHrlfjgmXjik3F7Gr1yD2mzWAyQSZSgltUCC0tQKhCw6CrlYgtMFB0NWuBZWHu9TlEpUJo9EI0/8PyzIYDNDr9RwTTlQGOByFHNLGjRtx+vRpZGdnF3hs3rx5xd7fjh078P7772P79u2WbTk5OXB3d3/o8/R6veX/IyMjERUVVezXJvuRK5XwH/c0vHp1Q9LBQ0g5chxZ128gcftOJG6xHiuuqeEPl+ZN4N6lIzy6REDp6iJR1USla8GCBZg/f77UZRA5PPaEk8OZMmUKvvjiC9SpUwdardbqMZlMVqJ1whMSEhASEoJPPvkEQ4cOxWeffYalS5fi9OnT0Ol0BdqzJ9yxmAwGZN+OQ/bNW8i6cQuZV64h/cIlZMU8WB1HrtPBe0h/VJsyHtrAAImrJXo87Aknsg+GcHI47u7u+OyzzzBixIhS3e/+/fsxbdo0XLt2DU2bNsWnn36K0NDQQttyicLKISfhHpIP/o27G7Yg48IlyNQqVJs8Hv7TJ0Oh0z56B0TlHJcoJCo7DOHkcAIDA7Fx40bUr19fshoYwisXIQRST5zCjWWfIfNqNPQNwxD61cfQ+PtJXRrRY2EIJyo7XB2FHM7bb7+NadOm4cSJE0hKSkJKSorVP6LSJpPJ4NqkEcK+WA6/Z59C+qmzONVnKNJPn5W6NCIiKqcYwsnheHl54fjx42jWrBk8PT3h4eEBDw8PuLu7w8PDQ+ryyIHJlAr4j38GwW+9htzkFJx9ajwyLl2RuiwiIiqHOByFHE5wcDCaNGmC8ePHw8nJqcDjHTt2LPMaOByFkg4cwpU334bSyxONtq6D2ttL6pKIio3DUYjKDkM4ORy9Xo/Tp08jKChIshoYwgkAEjZtQ/T7H8JvwmgEzn9V6nKIio0hnKjscDgKOZw+ffrgjz/+kLoMInj26ganOsGI+2YNcuLvSF0OERGVI7xZDzmc8PBwzJgxA+vWrUNwcHCB3pslS5ZIVBlVNjKZDNXGjsLl197CrY+/RNBbr0ldEhERlRMcjkIOp1OnTkU+JpPJsHPnzjKvgcNRyEwIgXPPzUBm9HU03r0R2po1pC6JyGYcjkJUdhjCicoAQzjllXLsJC7OehWubVsh7MdVkMlkUpdEZBOGcKKyw+Eo5JBSU1PxxRdf4MyZMzAajahXrx5Gjx4NX19fqUujSsi1aTi8+vVCwu+bcefbtaj6TOnezZWIiCoe9oSTwzl9+jS6du0KlUqFFi1awGg04ujRo8jMzMS+ffsQFhZW5jWwJ5zyM6Zn4PSYyTBlZqHpX39A6e4mdUlEj8SecKKyw9VRyOHMmjULnTt3xpUrV7Bu3TqsX78eV65cQffu3TF79mypy6NKSqF3gv/40TCmpiFu9Q9Sl0NERBJjTzg5HL1ejyNHjqBevXpW28+cOYM2bdrY5db17Amnwphyc3H6qfEQJiOa/LUTCp1W6pKIHoo94URlhz3h5HA8PT1x9+7dAtsTEhKgVqslqIjoAblSiarDB8GQcB93f/xF6nKIiEhCDOHkcIYOHYrJkyfj0KFDEEJACIFDhw5h6tSpGDRokNTlUSXn1acnFK4uuP3ZfyByc6Uuh4iIJMIQTg5nwYIFCAwMRJs2baDVaqHVatG2bVuEhIRg0aJFUpdHlZxCp4XP4H7Ivn4D9zZuk7ocIiKSCMeEk8M6c+YMzp49C41Gg3r16qFOnTp2e22OCaeHMSQl49SwMdDWroVGW9dx3XAqtzgmnKjssCecHE6tWrVw//591K9fH08++ST69++POnXq4Pbt2/Dx8ZG6PCKo3N3g1acHMs6cQ/LeA1KXQ0REEuDNesgh/Pe//8XmzZsBANHR0Zg6dSp0Op1Vm+joaMjl/L2TyoeqwwfhzvoNuPXxl3Dv2F7qcoiIyM6YSMghtG/fHklJSUhMTAQAJCcnIzEx0fIvKSkJ1atXx9q1ayWulOgBjW9VVOncESkH/kLaiVNSl0NERHbGMeHkcMaOHYuPPvoIrq6uktXAMeFki4wr13B23FRU6d0doV8sk7ocogI4Jpyo7LAnnBzOypUr4erqivT0dKSkpCAlJQXJycm4c+eOZcgKUXngFBwEtzYtcH/zdmReuSZ1OUREZEcM4eRw9uzZg1q1asHV1RUeHh7w8PBAlSpV4OfnhyFDhkhdHpEV35HDACFwa/nnUpdCRER2xBBODufFF19E/fr1sWXLFuj1eqxbtw7Lly+Hu7s7Vq9eLXV5RFZcGtWHS7PGuPvTeqSfOS91OUREZCcM4eRwzpw5g/feew/dunVDs2bNoNPp8Pzzz2P58uW8WQ+VSzWmjAcAxLz9gcSVEBGRvTCEk8PRaDTQ6/UAgNDQUPzzzz8AHqygcu7cuRLtc/369ahfvz5cXV3RvHlzHDjAtZ2p9DjVCYZnjy5I3nsQidt3SV0OERHZAUM4OZy2bdvi448/htFoRMOGDS2TMU+ePAmNRlPs/V27dg3PPvssPvnkEyQlJWHWrFno378/UlNTS7t0qsT8xz8Lhd4Jl198Ddm3YqUuh4iIyhhDODmcd999F6tXr8bSpUsxatQoXLx4EQEBARg2bBiefvrpYu/v+vXrmDhxIjp27Ai5XI5Ro0YBAC5evFjapVMlpvbxQuBrs5F7PxEXJ82AKTtH6pKIiKgMcZ1wckgZGRlIT0+Ht7c34uPjsW7dOnh6euLJJ5+ETCZ7rH3/9ddf6NSpE+Lj44tci5zrhFNJ3fx8JeK+/y/0jRsh5LMl0NaoLnVJVIlxnXCissMQTlQMly9fRseOHTFr1iy89NJLRbZjCKeSEkYjbn31DeK++xEKVxd4Dx0Azz49oA2qCZW3F2Ry/gGT7IchnKjsMIQT2ejvv/9G37598fzzzyMqKuqhbc0XrvT0dMuFSy6XQ6FQPPJ1GMIJAJL+OoybH3+BrOs3LdtkKiXUfr7Q+PtBXa0aNDX8oQ2oDm3NGtAE1IDar+pj/6WHyGg0wmQyAXhwLtPr9QzhRGWAIZzIBlu3bsWwYcOwePFiTJgw4ZHtzSE8r8jIyEeGd4AhnP5HCIH08xeRevwf5MTfQU78XeTcTUBO/F0YC5kYrPSsApdmjeHeqQM8unWCxq+qBFVTRRcVFYX58+dbbWMIJyp9DOFEj3Dp0iU0bdoUq1atsvmOm+wJp7JmzMhAdmw8smPjkH07Dtk3byP9/EVkXr4KYTQCMhncO3eA3/hn4NahHXvIyWbsCSeyD4Zwokd46aWXsGTJEjg5OVlt37x5M5544olCn8Mx4SSV3LR0pPx9FPd37EbSn38DJhPc2rdBzchXoA8Llbo8qmA4Jpyo7DCEE5UBhnAqD7Lj4nF71fe4t2UHZEoFAl6dDb/nxrBXnGzGEE5UdhjCicoAQziVJ+nnL+Lq2/9C9o1b8OjZFXVWLIJCp5W6LKoAGMKJyg7XuiIicnD6uiEI+/cyVOncEYlbduDcyPHITUqWuiwiokqNIZyIqBJQOOkQ9OYcVB0+GKl/H8XpwU8jOzZe6rKIiCothnAiokpCJpejxvMTUH3yOGReuITTA59CVvR1qcsiIqqUGMKJiCoZ36eGIvDVF5FzKxbRb70vdTlERJUSQzgRUSXk1bMr3Fq3QOL2Xci+dVvqcoiIKh2GcCKiSspnYB/AZEL86jVSl0JEVOkwhBMRVVKuLZtB4++H+B9+gik7R+pyiIgqFYZwIqJKSiaXw3tAH+Teu4+7P6+XuhwiokqFIZyIqBLz6t0dSg93XH93MQz37ktdDhFRpcEQTkRUiSldnBEwfTJyE5MQHbVQ6nKIiCoNhnAiokrOo9MTcGvTEgnrfkfyvj+lLoeIqFJgCCciquRkMhkCZk6BTKVCzLuLIISQuiQiIofHEE5ERND4VoX3wD5I/+cM7m/YKnU5REQOjyGciIgAAH5PD4fcyQnX318Kk8EgdTlERA6NIZyIiAAAKnc3+A4fjKxrMbj74y9Sl0NE5NAYwomIyKLqsIFQurvhxuIVMGZmSl0OEZHDYggnIiILhZMT/J59Cob4O4hb+Z3U5RAROSyGcCIisuLdrxfUvlVxa/m/YUhMkrocIiKHxBBORERW5GoV/Cc8C2NKCm4u/VjqcoiIHBJDOBERFVClS0fo64Ui/usfkHn5qtTlEBE5HIZwIiIqQCaXo8YLEyFycxH91vu8gQ8RUSljCCciokI5NwhDla4RSPpjDxJ+2SB1OUREDoUhnIiIilRj2iQoPdxx7fUFyImLl7ocIiKHwRBOVAxLlizBmDFjpC6DyG5U7m4InDMdxpQUXJr2MkzZOVKXRETkEBjCiWyQnZ2NN998E3PmzJG6FCK7c2/XGt4D+yDl4CFcnjEXwmiUuiQiogpPKXUBRBXBmDFjkJqaiokTJyIrK0vqcojsLmD6ZOQmJuHe75sBALXenw+lm6vEVRERVVzsCSeywZIlS7Bhwwb4+vpKXQqRJGQKBYLeeBnuT7TFvd8342TX/rjz4y8wZmRIXRoRUYXEnnAiG/j5+UldApHk5GoVghe8joSNW3Fjxb9xZdariH7zbTg3CYdT3TpQeXtB5eUJff160IUEQ65WS10yEVG5xRBOVIYMBoPl/+VyORQKhYTVED0+mUwG77494dGhHe7v2I17f+xG6uGjSN53sGBjhQIKvRMUri5QurpC4eoMpasrlK4uUPv5QhNQHdoa1aEJrAFNdX/IZDL7HxAVYDQaYTKZAFifw4iodDGEE5UhvV5v+f/IyEhERUVJVwxRKVK6usBncD/4DO4HYTQi585d5CanIOdOAjIuXkL2rTiYcnJgzMyEMS0dxuQU5NyKhTEtrdCJnUoPdzg3aQTnxg3h3CQczo0bQlXFQ4IjowULFmD+/PlSl0Hk8GSCt0EjsllUVBSio6OxatWqh7YzGAxQq9VIT0+HSqUCYHtPeG5sPER6emmUS1TuCCFgysxEzp0EZMfGISc2HlnXbyL9wkVkXLoKkafn1aVVM9T+8H1oA6pLWHHlk78nXK/XIycnx3IuI6LSwZ5wojKkUql44SLKQyaTQeHkBF1gAHSBAVaPmQwGZF65hvRzF5D6zxkk7tyLf3oMQs15c+E9dADk/FmyC4VCwaFzRHbAnnCiMmDuCS9J7xF7wokeSP77KK69swi5SclQ+/uhxkvT4f3kQI4dt6PHOZcR0cMxhBOVAYZwotKRm5qGu79uRPxPvyI3KRlu7dsgePHb0FT3l7q0SoEhnKjsMIQTlQGGcKLSlZuaipuf/gcJG7dC6e6G2isWwaPTE1KX5fAYwonKDm/WQ0RE5Z7SxQWBL89A7YWREEYjzj/zHGK/XC11WUREJcYQTkREFYZ721YI+/dH0AZUR3Tku4hZuBj8gy4RVUQM4UREVKFoqvmh7vJ/QR9WF7dXfIHrC5dIXRIRUbExhBMRUYWjdHNFyJJ3oW8Qhtsff4FbK/4tdUlERMXCEE5ERBWSQqdFnfeioKtdC9cXLkHc1z9IXRIRkc0YwomIqMJSujgj5F8LoKnuj2uvv4W7v/wudUlERDZhCCciogpNVcUDIYvfhsrLE5dnvIL723ZKXRIR0SMxhBMRUYWn8a2KkMXvQOnsjIuTZiL54CGpSyIieiiGcCIicgi6mjVQZ9ECyFVKnB89Gcl//i11SURERWIIJyIih6EPqY06HywAIMP5p59D0u59UpdERFQohnAiInIozg3qIWTJO5ApFTg3aiKuzXsHGRcuIefOXalLIyKykAneaoyo1BkMBqjVauTk5EClUhXrubmx8RDp6WVUGVHlkXUrFtELFyPt1FnLttofvQ/voQMkrKpieZxzGRE9HHvCiYjIIWn9/RD60fsIev0l+D41FACQduIfiasiInpAKXUBREREZUWmUMCze2cIkwnxP61H9o1bUpdERASAPeFERFQJyORyqH28kcUQTkTlBEM4ERFVCmpfH2TfvAVOhSKi8oAhnIiIKgWNb1WY0jOQm5QsdSlERAzhRERUOaj9qgIAsm9ySAoRSY8hnIiIKgVNVR8A4ORMIioXGMKJiKhSUPv+f084QzgRlQMM4UREVClofDkchYjKD4ZwIiKqFFSeHpAplewJJ6JygSGcyEaHDh1CkyZNoNfr8cQTT+DKlStSl0RExSBTKKCu6o3sm7elLoWIiCGcyBZZWVkYNGgQ5syZg8TERHTr1g1jxoyRuiwiKia1b1WuFU5E5QJDOJENdu3ahSpVqmDkyJFQq9V4/fXXcfr0aZw/f17q0oioGDRVfWBMTYMxOUXqUoiokmMIJ7LB+fPnUbduXcvXCoUCwcHBOHv2rIRVEVFxqX0fLFOYvO9PpJ08xR5xIpKMUuoCiCqC9PR0ODk5WW1zcnJCRkaGRBURUUmYV0i5OHkmAMCpQT34jXsaCmdnCauyH/eI9lDo9VKXQURgCCeyiZOTEzIzM622ZWRkwPkRF26DwWD5f7lcDoVC8cjXkjvrIdSqkhVKRA/l0acHMq7fhMJJh9yUVNz9ZQOuvPi61GXZTZOD2x8Zwo1GI0wmEwDrcxgRlS6GcCIb1K1bF19//bXla6PRiMuXLyM0NPShz9PnudhFRkYiKirqka8ld6kcPXJEUlB4VkGt9+dbvq7x8gykHDoKCJOEVdmPyqvKI9ssWLAA8+fPf2Q7Ino8MsEBcUSPlJmZiaCgIHzwwQcYMWIE3nvvPaxfvx5Hjx4ttL3BYIBarUZ6ejpUqge92rb2hBMRSSl/T7her0dOTo7lXEZEpYMTM4lsoNPpsHHjRixfvhyenp7Yvn07fvzxx0c+T6VSWf4xgBNRRaBQKKzOXURUNtgTTlQGzD3h7D0iooqM5zKissOecCIiIiIiO2MIJyIiIiKyM4ZwIiIiIiI7YwgnIiIiIrIzhnAiIiIiIjtjCCciIiIisjOGcCIiIiIiO2MIJyIiIiKyM4ZwIiIiIiI7YwgnIiIiIrIzhnAiIiIiIjtjCCciIiIisjOGcCIiIiIiO2MIJyIiIiKyM4ZwonLEaDQiKioKRqNR6lLKBI+vYuPxVVyOfGxEFZVMCCGkLoLI0RgMBqjVauTk5EClUpX58yoKHl/FxuOruHhOIip/2BNORERERGRnSqkLIHJE5j8wGQyGYj3P3L64z6soeHwVG4+v4irpsZnb84/mRKWPw1GIykBGRgb0er3UZRARlYr09HQ4OTlJXQaRQ2EIJyoDJpMJWVlZUCqVkMlkUpdDRFQiQgjk5uZCq9VCLucIVqLSxBBORERERGRn/LWWiIiIiMjOGMKJiIiIiOyMIZyIiIiIyM4YwomIiIiI7IwhnIiIiIjIzhjCiSRw6NAhNGnSBHq9Hk888QSuXLlSoI3JZMLMmTPh6ekJHx8fvP/++xJUWjK2HF9ycjKeeeYZeHt7w9fXF9OnT0dOTo4E1RafLceX1zPPPIMxY8bYp7jHZOuxLVq0CNWqVYOHhwdGjRqFzMxMO1daMrYcn8FgwHPPPQdvb2/4+PjgxRdfhMlkkqDakluyZEmRn7mKfG4hciQM4UR2lpWVhUGDBmHOnDlITExEt27dCr1YLl++HH/99RcuXbqEgwcP4rPPPsMff/xh/4KLydbjmzNnDrKysnDt2jWcOnUKhw8fxqJFi+xfcDHZenxm69evx/fff2+/Ah+Drcf2448/4tNPP8WBAwdw48YN3L17t0IEOVuP7+OPP0ZMTAyio6Nx5swZbN26FatXr7Z/wSWQnZ2NN998E3PmzCmyTUU9txA5HEFEdrVp0yZRv359y9e5ubnC3d1dnDt3zqpdy5YtxX//+1/L14sWLRLDhw+3W50lZevxTZgwQZw4ccLy9bJly0Tfvn3tVmdJ2Xp8Qghx9+5dERISIsaPHy9Gjx5txypLxtZj69q1q/j6668tX8fFxYlr167Zq8wSs/X4pk6dKrp06SKSk5PFnTt3RIMGDcSaNWvsXW6JjBgxQvTp00dMmjSpyM9cRT23EDka9oQT2dn58+dRt25dy9cKhQLBwcE4e/bsQ9uFhoYWaFMe2Xp8X3zxBcLDwy1fb9q0CQ0bNrRbnSVl6/EBwPPPP4+XX34Z1atXt2eJJWbrsZ04cQKpqalo3LgxfH19sWDBAvj5+dm73GKz9fgmTJiAf/75Bx4eHvDx8UG9evUwfPhwe5dbIkuWLMGGDRvg6+tbZJuKem4hcjQM4UR2lp6eDicnJ6ttTk5OyMjIeGi7wtqUR7YeX15z587FuXPnMHv27LIu77HZenxr165FSkoKxo8fb8/yHoutx5aYmIhVq1Zhw4YNOHXqFI4fP46FCxfas9QSsfX4srOzMWrUKCQkJODatWs4e/YsPv74Y3uWWmK2/DJUUc8tRI6GIZzIzpycnApMYsvIyICzs/ND2xXWpjyy9fgAIDc3FxMmTMBPP/2EP/74A56envYqs8RsOb74+Hi89tpr+OKLL+xd3mOx9b1Tq9WYPn06qlevDm9vb8yePRsbNmywZ6klYuvxjR07FiNHjoSHhwcCAwPx+uuv46uvvrJnqWWqop5biBwNQziRndWtWxcXL160fG00GnH58mWEhoY+tN2FCxcKtCmPbD2+7Oxs9O/fH6dOncKff/6J4OBge5daIrYc3/bt2xEXF4eGDRvC3d0d7733Hr7//ns0atRIipJtZut7FxISguTkZKt2FWH1EFuP7+bNm1Yr9ahUKqhUKrvVWdYq6rmFyNEwhBPZWadOnRAfH4/Vq1cjJycH77zzDoKDg1GvXj2rdiNGjMB7772HO3fu4MqVK1ixYgVGjRolUdW2s/X4pk2bhsTEROzatQs+Pj4SVVt8thzf008/jfT0dCQlJSEpKQmvvPIKRo4ciX/++UfCyh/N1vfumWeewZIlS3Djxg0kJCRg0aJFGDJkiERV287W4+vZsyfefPNNJCcnIy4uDu+//z6GDh0qUdWlr6KeW4gcjtQzQ4kqoyNHjojmzZsLZ2dn0b59e3H58mUhhBBhYWHi22+/FUIIYTAYxOzZs0XVqlWFj4+PeO+996QsuVgedXxJSUlCLpcLjUYj9Hq95V/Pnj0lrtw2trx/eUVGRlaI1VGEsO3YjEajWLBggQgICBDu7u7i+eefF9nZ2VKWbTNbju/evXti1KhRwsvLS/j5+YlXXnlFGAwGKcsutvyfOUc5txA5EpkQQkj9iwARERERUWXC4ShERERERHbGEE5EREREZGcM4UREREREdsYQTkRERERkZwzhRERERER2xhBORERERGRnDOFERERERHbGEE5EREREZGcM4UREREREdsYQTkRERERkZwzhRERERER2xhBORPT/oqOjIZPJcOLECalLsRIVFYXGjRsDKP0as7Ky8Nlnnz2y3csvv4wVK1aUyms+yoEDB9C9e3e7vBYRkVQYwomIKpAaNWogNjYWDRo0KJX9ff7553jvvfce2ubkyZNYv349Jk2aVCqv+Sjt2rWDVqvFt99+a5fXIyKSAkM4EVEFolAo4OvrC6VSWSr7E0I8sk1UVBSee+45qFSqUnlNW8yYMQNRUVEwmUx2e00iIntiCCcihyWTyTBv3jz4+voiNDQU2dnZuHPnDp566im4ubmhatWqePbZZ5GQkFCi/Qsh8Pbbb6NatWpwdnbG6NGjMXLkSIwZMwYAsGrVKjRq1AhjxoyBm5sbXnvtNQDAxx9/jLCwMGg0Gnh4eGD48OFISkqy7Hfbtm0IDw+HTqdDjx49cO/ePctj+YejpKenY8qUKfDy8kKVKlUwYMAAREdHW9oHBgbiww8/RLdu3aDT6RAYGIivv/7aUt+sWbMQExMDmUxm9by8r/f7779jyJAhlm0JCQkYM2YMqlatCpVKhaCgICxfvrzI79OYMWMwcOBAq22NGzdGVFRUkc/p2LEjEhMTsXHjxiLbEBFVZAzhROTQvvnmG+zYsQNr1qyBRqPB4MGDkZOTg3379mHLli24e/cu+vfvb1OPcH6LFy/G4sWLsWzZMhw+fBhCCKxZs8aqzalTp6DVanHs2DFMnDgRP/74I1599VV88MEHuHjxIr777jvs3LkTS5cuBQBcunQJ/fr1Q//+/XHy5En06tULn376aZE1PPfcczhz5gw2bdqEffv2wd3dHZ07d0ZWVpalzZtvvolnnnkGJ06cQO/evTFx4kTExsZi+PDheOutt1C9enXExsaiRo0aBfa/adMmhISEIDAw0LLt2Wefxc2bN7F9+3acO3cOo0aNwowZM3DlypVifw+LolQq0a1bN2zYsKHU9klEVJ6Uzt8ziYjKqQkTJljGT+/evRtHjhxBYmIidDodAOCHH36Al5cXDh48CH9//2Lte9myZXj11VcxdOhQAMCXX36JnTt3Fmj35ptvWvZ9/fp1rFy5En379gUA1KxZE927d8fp06ct+wgLC8OCBQsAACEhIdi3b1+hAffatWv44YcfcOXKFQQFBQEA/vOf/8Df3x8///wzRo0aBQB48skn8eyzzwIAFi5ciE8//RTHjx9H79694eLiYhniUpjDhw+jfv36Vtt69eqFXr16oXbt2gCAyMhIvPPOOzh79iyCg4OL8R18uAYNGmDdunWltj8iovKEIZyIHFqtWrUs/3/69Gnk5OTA29vbqo3JZML58+eLFcLv3buHGzduoE2bNpZtarUazZs3t2qn0WhQrVo1y9cdO3bE8ePHERkZiYsXL+L06dM4e/Ys+vXrZ6mxadOmVvto1apVoSH8zJkzEEKgYcOGVtszMzNx/vx5y9ehoaGW/3dzcwMAGAwGm44zPj4eNWvWtNo2ZcoU/Pzzz1ixYgUuXryIY8eOAQCMRqNN+7SVt7c34uPjS3WfRETlBUM4ETk0c483AOTm5sLf3x+7du0q0M7b2xuJiYk279c8MTL/xEGZTGb1tVartdr2zTffYOLEiRg7diw6d+6Ml156CUuWLEF6erqlTf6hMWq1utAacnNzoVAocOzYMcjl1qML3d3dLf+v0WgKPNfW4TdyudzqGIUQ6NWrF2JiYvDUU09h3Lhx+PzzzxEQEGDT/sxs+SXAaDQWOC4iIkfBEE5ElUZYWBji4uKg0+ksvd7x8fEYP348Fi5cCBcXF5v35ebmhho1auDw4cPo2LEjgAeh+Pjx44iIiCjyecuXL8eLL76Id99917Lt0qVL8PPzAwA0atQIv/32G4QQlvB+5MiRIo/HaDQiKSkJLVu2BABkZ2djxIgRmDZtGjp37vzI48j/S0N+fn5+uHv3ruXrc+fOYceOHbhw4QJCQkIAAGfPngVQdLBXq9VITk62fJ2Tk4Pr168/sraEhIQih8kQEVV07GIgokqja9euCA8Px/Dhw3H48GGcOnUKTz/9NM6dO4c6deoUaJ+ZmYm4uLgih1nMnj0bCxcuxC+//ILz58/j+eeft6w0UhRPT0/s3r0bp0+fxrlz5/DCCy/g8OHDyM7OBgBMmjQJMTExmDVrFi5cuIDPP/8c//3vfwvdV0hICAYNGoQxY8Zg9+7duHjxIsaPH4+9e/ciLCzMpu+Js7MzEhMTcfHiReTm5hZ4vHnz5jh58qTlazc3NygUCqxZswYxMTHYtWsXnnrqKQCwHENOTg7i4uKQk5MDAGjdujX27t2Ln3/+GZcuXcKkSZOsXstoNCIuLg6ZmZlWr33ixAm0aNHCpuMgIqpoGMKJqNKQy+VYv349qlWrhq5du6J9+/bQarXYtm0btFptgfZr166Fn58fbty4Uej+pk2bhsmTJ2PSpElo3rw5TCYT2rRpU+TwEeDBZE6VSoVWrVqhc+fOSEhIwFtvvYUTJ07AaDQiMDAQW7duxYEDBxAeHo5vvvkGM2bMKHJ/K1euRLt27TB06FA0bdoUt27dwvbt223uQe7Tpw8CAgLQqFEjy9ju/I9fu3bN8j3w9/fHl19+iZUrV6Ju3bqYPHkynnnmGbRt2xZHjx4FABw8eBB+fn44ePAgAODpp5/GxIkTMW7cOLRp0wY1atRA7969La9x48YN+Pn5Ye3atZZtRqMRBw4csExgJSJyNDJRknW5iIgIW7ZsQXh4uGUoCQDUrVsXI0eOxLx58ySsrHQNHDgQLVu2tKxzbg+bN2/GtGnTcOHCBSgUCru9LhGRvbAnnIiohFauXInhw4fjxIkTuHr1KqKionD16lWrG9s4gjfffBNfffWVZXiJPaxYsQKvv/46AzgROSyGcCKiElq+fDn8/f3RtWtXNGjQAFu2bMHGjRsLrKtd0TVr1gwDBw586E2DStP+/fuRmZlpufMoEZEj4nAUIiIiIiI7Y084EREREZGdMYQTEREREdkZQzgRERERkZ0xhBMRERER2RlDOBERERGRnTGEExERERHZGUM4EREREZGdMYQTEREREdkZQzgRERERkZ0xhBMRERER2RlDOBERERGRnTGEExERERHZGUM4EREREZGd/R+g0WP9oz4higAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "trap[trap.grad_z] = initial_grad\n",
    "plot_occupation_grad(trap,100,-0.15*zr,1.9*zr,grad_fac_down=0,grad_fac_up=1,n_spill_steps=150,n_pot_steps=int(1e3),t_spill=25*si.ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/50 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 94%|█████████▍| 47/50 [01:54<00:01,  2.48it/s]<lambdifygenerated-1074>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 6.681550963956e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 2.67062937174555e-24\n",
      "<lambdifygenerated-1075>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.6726203855824e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 6.681550963956e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\scipy\\optimize\\_root_scalar.py:326: RuntimeWarning: Derivative was zero.\n",
      "  r, sol = methodc(f, x0, args=args, fprime=fprime, fprime2=fprime2, **kwargs)\n",
      " 96%|█████████▌| 48/50 [01:54<00:00,  2.79it/s]<lambdifygenerated-1078>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 6.61275243797947e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 2.67062937174555e-24\n",
      "<lambdifygenerated-1079>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.64510097519179e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 6.61275243797947e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 98%|█████████▊| 49/50 [01:54<00:00,  2.93it/s]<lambdifygenerated-1084>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.57054893888071e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 7.85274469440353e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1082>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 6.54395391200294e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 2.67062937174555e-24\n",
      "<lambdifygenerated-1083>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.61758156480118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 6.54395391200294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1083>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.61758156480118e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 6.54395391200294e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1084>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.57054893888071e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 7.85274469440353e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "100%|██████████| 50/50 [01:54<00:00,  2.30s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "trap[trap.grad_z] = 0*initial_grad\n",
    "plot_occupation(trap,100,-0.15*zr,1.9*zr,power_fac_down=0.66,power_fac_up=1,n_spill_steps=50,n_pot_steps=int(1e3),t_spill=25*si.ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}