examples/analog_hamiltonian_simulation/08_Maximum_Weight_Independent_Set.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7fb27b941602401d91542211134fc71a",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note:</b> This notebook requires you to have enabled Experimental Capabilities through Braket Direct. Follow these <a href='https://docs.aws.amazon.com/braket/latest/developerguide/braket-experimental-capabilities.html'>steps</a> to enable access to local detuning.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21455698",
   "metadata": {},
   "source": [
    "# Maximum weight independent set\n",
    "\n",
    "In [notebook 04](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb), we have illustrated how to solve the maximum independent set problem with Rydberg atoms. Here, we generalize the approach to solve the maximum weight independent set (MWIS) problem. The generalized approach utilizes the local detuning that detunes the atoms depending on the weights of the vertices in the graph, another important use case for local detuning. \n",
    "\n",
    "## Background: MWIS on a weighted unit disk graph\n",
    "\n",
    "In this notebook, we consider the MWIS problem on a weighted unit disk graph. Recall that a unit disk graph is a graph in which any two vertices are connected if and only if they are within a unit disk of certain radius. As an example, let us consider the following 2D square lattice where the vertices are connected to their nearest neighbors.\n",
    "\n",
    "![Blockade_examples_2D.png](Blockade_examples_2D.png)\n",
    "\n",
    "This is an example of a unit disk graph where the radius is slightly larger than the lattice constant. To find the maximum independent set (MIS), one can map each vertex to a Rydberg atom such that neighboring atoms are blockaded by each other, as indicated by the overlapping circles in the above plot (note that the radius of the circles is half of the blockade radius of the Rydberg atoms). This guarantees that the pair of vertices connected by an edge cannot both be in the independent set. For this particular example, one can confirm that the MIS consists of vertices $\\left\\{0, 2, 4, 6, 8\\right\\}$, the black vertices in the plot.\n",
    "\n",
    "A weighted unit disk graph is obtained by assigning weights onto the vertices of the unit disk graph. For instance, let us assign the following set of weights to the vertices\n",
    "\n",
    "$$\n",
    "w = [0.26, 0.13, 0.93, 0.95, 0.23, 0.20, 0.05, 0.96, 0.01].\n",
    "$$\n",
    "\n",
    "\n",
    "An MWIS for the weighted unit disk graph is an independent set with the largest total weights. It is important to note that the MWIS needs not be the same as the MIS for a given graph. For the example at hand, one can check that the MWIS consists of vertices $\\left\\{2, 3, 7\\right\\}$ with total weight $2.84$ which is larger than $1.48$, the weight for the MIS.\n",
    "\n",
    "## Finding the MWIS with Rydberg atoms\n",
    "\n",
    "The approach we will use to solve the MWIS problem is similar to that for the MIS problem, which is based on quantum adiabatic algorithm. In the beginning of the quantum evolution, we prepare the Hamiltonian in such a way that its many-body ground state has all atoms in the ground state $|g\\rangle$. We then slowly turn on the global driving field, together with the local detuning. Particularly, we would like the Hamiltonian at the end of the evolution reads (see [notebook 00](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb) for the full Rydberg Hamiltonian)\n",
    "\n",
    "\\begin{align}\n",
    "H_\\text{final} =  -\\sum_{k=1}^N \\Delta_\\text{local}w_k \\,n_k + \\sum_{j=1}^{N-1}\\sum_{k = j+1}^N V_{j,k} \\,n_j\\, n_k,\n",
    "\\end{align}\n",
    "\n",
    "where $\\Delta_\\text{local}>0$ and $w_k$ are the weights of the vertices. The last term ensures that we will arrive at an independent set, provided the evolution is adiabatic and neighboring atoms are within the blockade regime of each other. Since the first term favor the independent set that has the largest possible weight, we conclude that $H_\\text{final}$ is the desired cost function, where the local detuning plays a fundamental role, for solving MWIS with the quantum adiabatic algorithm. \n",
    "\n",
    "In the implementation below, we will choose to ramp up the local detuning linearly from zero to a positive value, i.e., $\\Delta_\\text{local}(t_\\text{initial})=0$ and $\\Delta_\\text{local}(t_\\text{final})>0$. In order to make sure the initial ground state has all the atoms in $|g\\rangle$, we will turn on a constant global detuning $\\Delta_\\text{global}\\equiv\\Delta_\\text{global}(t_\\text{initial})\\equiv\\Delta_\\text{global}(t_\\text{final})<0$ such that the net detuning for each atom starts from a positive value. The constant global detuning will not change the result of the MWIS because it acts on all the atoms uniformly and hence only changes the energy reference of $H_\\text{final}$.\n",
    "\n",
    "\n",
    "To begin, we import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "56b48c20",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "\n",
    "tracker = Tracker().start()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3820376f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from ahs_utils import show_drive_and_local_detuning, show_final_avg_density, show_register\n",
    "\n",
    "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n",
    "from braket.ahs.atom_arrangement import AtomArrangement\n",
    "from braket.ahs.driving_field import DrivingField\n",
    "from braket.ahs.local_detuning import LocalDetuning\n",
    "from braket.devices import LocalSimulator\n",
    "\n",
    "simulator = LocalSimulator(\"braket_ahs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3ef2d11",
   "metadata": {},
   "source": [
    "Let's define certain constraints, such as maximum values for the Rabi frequency and local detuning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d516f1fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "omega_max = 15800000.0  # rad / seconds\n",
    "omega_slew_rate_max = 250000000000000.0  # rad / seconds / seconds\n",
    "tmin = 5e-08  # seconds\n",
    "\n",
    "local_detuning_max = (2 * np.pi * 7.5) * 1e6  # rad / seconds\n",
    "local_detuning_slew_rate_max = (2 * np.pi * 7.5) * 1e12  # rad / seconds / seconds\n",
    "\n",
    "t_ramp_omega = omega_max / omega_slew_rate_max  # seconds\n",
    "t_ramp_local_detuning = local_detuning_max / local_detuning_slew_rate_max  # seconds\n",
    "\n",
    "detuning_max = 125000000.0  # rad / seconds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34ce27a6",
   "metadata": {},
   "source": [
    "# Define atom arrangement\n",
    "\n",
    "We define the 2D lattice of atoms as described above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f83f5f7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 6.7e-6\n",
    "register = AtomArrangement()\n",
    "\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        register.add([i * a, (3 - j) * a])\n",
    "\n",
    "show_register(register)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1ab0265",
   "metadata": {},
   "source": [
    "## Solving MWIS with the help of local detuning\n",
    "\n",
    "As described above, we now define an AHS program for solving the MWIS problem. The program consists of a local detuning that detunes the atoms according to the weights of the vertices, and a driving field that explores the possible solutions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ca7329ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FfNynS/k/bNgwx/INN9yAl156CVdffbXjsQkTJiAxMREPP/wwFi1apEMLjctisWDUqFEun+NVC7SzIeYjwmzEmI+YUfIJsJgRFmRFfYuEqsY2QwxqGCUbo2I+7tP9qgUHDhxAUlJSl8eTkpLw448/6tAiY5MkCZmZmS5PgLPPixpggF9eehBlQ8xHhNmIMR8xI+XjuJasQU74MlI2RsR83Kd7ITt27FisWbMGbW1n33RtbW1Ys2YNxo4dq2PLjMlsNiMhIQFms/OmU1UVp/v4HFmtbKgd89HGbMSYj5iR8jHatWSNlI0RMR/36T6zeN26dbjuuuswZMgQTJgwAUD7VQ1MJhM+//xznVtnPGaz2Wlqhl2zTUarpADou3NktbKhdsxHG7MRYz5iRsrHfh1xIxWyRsnGiJiP+3T/CDB16lQcOXIETzzxBCZMmIAJEybgySefxJEjRzB16lS9m2c4kiQhIyOjy2EI+y+tQKsZwYF98w4hWtlQO+ajjdmIMR8xI+VjtBFZI2VjRMzHfbqPyAJASEgIbrvtNr2b4RPMZjNGjhzZ5TBE9ZmbIUQHB/bZsx+1sqF2zEcbsxFjPmJGysdo15I1UjZGxHzcZ4hCFgB+/PFHFBcXO82VBYCf/vSnOrXImOzzaTqz38mlr16xANDOhtoxH23MRoz5iBkpH6Pd3ctI2RgR83Gf7h8Bjhw5gokTJ2LcuHG45pprsGjRIixatAiLFy/G4sWL9W6e4UiShPT09C6HIeyfvvvqXb0A7WyoHfPRxmzEmI+YkfKx/w0wyoiskbIxIubjPt0L2T/96U9ISkpCeXk5goOD8cMPPyAjIwMXX3wxtm3bpnfzDMdsNmPcuHFdDkP09bt6AdrZUDvmo43ZiDEfMSPlc3ZE1hg3RDBSNkbEfNyn+9SCrKwspKenIyYmBmazGWazGZdddhnWrFmDP/7xj8jOzta7iYZiNpsRFxfX5XH7NQP76jVkAe1sqB3z0cZsxJiPmJHyGRBqvDmyRsnGiJiP+3T/CCDLMsLCwgAAMTExOHnyJID2u38dPHhQz6YZks1mw6ZNm2CzOX/aPt3H7+oFaGdD7ZiPNmYjxnzEjJSPfUTWKIWskbIxIubjPt1HZMeNG4f9+/cjKSkJ06ZNw9/+9jcEBgbitddew4gRI/RunuFYLBZccsklsFicL7F1do5s3y1ktbKhdsxHG7MRYz5iRsrH/jegvlVCqySjn1XfNhkpGyNiPu7TvZB96KGH0NjYCAB4/PHHce2112LWrFkYMGAANm7cqHPrjMdsNiM6OrrL45wjq50NtWM+2piNGPMRM1I+4UEBMJsARQVqmmyID9e3QDJSNkbEfNyn+9SCBQsWYMmSJQCAUaNGIT8/H5WVlSgvL8e8efN0bp3x2Gw2fPnll10OQ9jnyPblEVmtbKgd89HGbMSYj5iR8jGbTWdP+DLA9AIjZWNEzMd9uhayNpsNVqsVubm5To9HR0f32Yv6n4vVasWsWbNgtToPpleduSFCXx6R1cqG2jEfbcxGjPmIGS2fKAPdFMFo2RgN83GfrskFBARg6NChkGVZz2b4FJPJhPDwcKfHVFXliCxcZ0NnMR9tzEaM+YgZLZ9oA90UwWjZGA3zcZ/uUwv+8pe/4M9//jOqqqr0bopPsNls+PTTT50OQ9S1SJAVFQAQ1YdviOAqGzqL+WhjNmLMR8xo+UQZ6KYIRsvGaJiP+0yqqqp6NmDy5Mk4fPgwbDYbhg0bhpCQEKfn9+7dq1PLuq+urg4RERGora3t9U9WqqqipaUFQUFBjukXRZWNmPv3bQjtZ0XuYwt69ecbmats6Czmo43ZiDEfMaPl8+BHB/CvXcW4+8pk/OnK0bq2xWjZGA3zca0ndZXukzIWLVqkdxN8Ttf5sfZryPbd0Vg7zjMSYz7amI0Y8xEzUj6O29QaYGoBYKxsjIj5uEf3qQWPPPKI8KsnMjIycN1112Hw4MEwmUz45JNPzvmabdu24aKLLkK/fv0watQobNiw4fw64iWSJCE1NdXpvsyOa8j24RO9ANfZ0FnMRxuzEWM+YkbLx37S72kDTC0wWjZGw3zcp3sh60mNjY2YOHEi1q5d2631i4qKcM0112Du3LnYt28f7rrrLvzmN7/Bpk2berml589qteLqq692+gRnn9Dfl+/qBbjOhs5iPtqYjRjzETNaPtEGu2qBkbIxGubjPl2Si46OxqFDhxATE9Ot9YcOHYpvvvkGw4YNE663cOFCLFy4sNvtWLduHZKSkvDcc88BAMaOHYsdO3bghRdewIIFxp1rKkmS007PEdmzOmdDzpiPNmYjxnzEjJSPfVDDCNeRBYyVjRExH/foMiJbU1ODr776Cp999lm3vk6fPt0rl+jKysrClVde6fTYggULkJWVJXxda2sr6urqnL4AONooy7LLZUmSnJYVRREu22w2p2VVVSFJEtLS0hz/t9lsjl9WEf3b3wj2xwFAURSnZfvhC61lWZadlr3Rp47L9rZ3XO5un9ra2pCWlub4ef7QJ09up9bWVqSlpaGlpcVv+uSp7WSz2ZCWlobm5ma/6ZMnt1PH95a/9MmT28mej9Z7y9t9iu50QwQ9t1PH95be28mI+57997K9rf7QJ09tp+7SbWrBsmXLsGjRom592d8AnlZWVob4+Hinx+Lj41FXVyf8mWvWrEFERITjKzExEQAcN3bIy8tDXl4eACAnJwcFBQUAgOzsbBQVFQEAdu3ahZKSEgBAZmYmSktLAbTP862srAQApKeno6amBgCQlpaG+vp6BAS0T+K37yipqak43dAKACgvOQIAqK+vR1paGoD2Dw3p6ekAgMrKSmRkZAAASktLkZmZCQAoKSnBrl27ALRPt8jOzgYAFBQUICcnp9f7BACpqaloaWlxmi/U0tKC1NTUbvepsrISUVFRCAgI8Js+eXI7HT9+HNdffz2ys7P9pk+e2k6yLOPqq6/G5s2b/aZPntxOZWVliI2NRUBAgN/0yZPbqaysDNdffz12795tiD7ZpxacbmiBqqq6bieTyYT58+dj8+bNum8nI+57x48fx+DBgxEQEOA3ffLUduou3S+/1VtMJhM+/vhj4VURkpOTsXz5cjz44IOOx1JTU3HNNdegqakJ/fv3d/m61tZWtLa2Ov5fV1eHxMREVFVVISoqyvHJwmKxOC1LkgSTyeRYNpvNMJvNmss2mw0Wi8WxbD/0UF1djcjISJhMJkiShN+/uw//ySvHX396AX41M8kxchsQEABFUSDLsmNZURRYrVbNZVmWoaqqY9lVPzzdJ5PJ5NS/jodZ7P3oTp9kWUZdXR0iIyOhqqpf9MmT2wmAY7+2t9fX++Sp7WSxWFBfX4/+/fs7Piz6ep88uZ06vrcURfGLPnlyO5lMJjQ2Nmq+t7zdpxYZGPdI+7kePz6+AP0sJt22U8f3VmBgIN9PnZYlSUJ9fb3jveUPffLEdmpoaOj25bf86mSvnho4cCBOnTrl9NipU6cQHh6uWcQCQL9+/RAeHu70BbRvEPu/rpatVqvTstlsFi4HBAQ4LdsL16ysLMiyDJPJhICAAMfho9jw9jbbHwcAs9nstGzfWbWWLRaL07I3+tRx2d72jsvd7ZOiKMjMzHS8EfyhT57cTqqq4ptvvnF8L3/ok6e2kyzL2LFjh6M//tAnT26nju8tf+mTJ7eToijC95a3+xQSaEGgtf3nVTW26bqdOr639N5ORtz3VFV1em/5Q588tZ26q0/PLp4xY4ZjGN1u8+bNmDFjhk4tOreAgABcc801To9VN7XPXenLt6cFXGdDZzEfbcxGjPmIGS0fk8mE6OBAlNW1oLrRhiFR+rXFaNkYDfNxn1+NyDY0NGDfvn3Yt28fgPZ5Gvv27UNxcTEA4MEHH8TSpUsd6//ud7/DkSNHcN999yE/Px+vvvoq3n//fdx99916NL9bFEVBVVWV02Ro+4hsdB+/IYKrbOgs5qON2YgxHzEj5mO/csHpxtZzrNm7jJiNkTAf9/lVIfv9999j8uTJmDx5MgBg5cqVmDx5MlavXg2gfWKyvagFgKSkJHz55ZfYvHkzJk6ciOeeew6vv/66oS+9Jcsydu/effYMP1lBbXP7iGxUH7/8VudsyBnz0cZsxJiPmBHzMcrdvYyYjZEwH/f57cle3tSTewJ7WmVDKy5+4j8wmYCCJxbCavGrzyZERHQeVry7F1/klOLhay/ArZcl6d0coh7pSV1liKqnsLAQDz30EG666SaUl5cDAL766iv88MMPOrfMeBRFQXl5ueMwRLXjGrIBfb6I7ZwNOWM+2piNGPMRM2I+Rrm7lxGzMRLm4z7dK5/t27dj/Pjx2LlzJz766CM0NDQAAPbv349HHnlE59YZj6IoyM3Ndez0Vbyrl0PnbMgZ89HGbMSYj5gR87FPNavSeWqBEbMxEubjPt0L2QceeABPPPEENm/ejMDAs8XYvHnz8N133+nYMmOyWq2YN2+e49IW9vlPUX38igVA12zIGfPRxmzEmI+YEfMxyoisEbMxEubjPt0L2QMHDmDx4sVdHo+Li3PcmYLOUhQFJ06ccHx6O+24YgEL2c7ZkDPmo43ZiDEfMSPmY/+bUGWAqQVGy8ZImI/7dC9kIyMjHbdV6yg7OxsJCQk6tMjYFEVBYWFhlzmynFrQNRtyxny0MRsx5iNmxHwcI7IGmFpgtGyMhPm4T/dC9he/+AXuv/9+lJWVwWQyQVEUfPvtt1i1apXTNV+pndVqxezZsx2HIaoaz1x6iyOyXbIhZ8xHG7MRYz5iRszHMUf2zN8IvRgxGyNhPu7TvZB96qmnMGbMGCQmJqKhoQEXXHABZs+ejZkzZ+Khhx7Su3mGoygKjh07dnZEtok3Q7DrnA05Yz7amI0Y8xEzYj4dR2QVRb+rbBoxGyNhPu7TvZANDAzEP//5TxQWFuKLL77A//3f/yE/Px//+7//67j3Lp3VeT6Nff5TX78ZAsC5RufCfLQxGzHmI2bEfCKD2wc3ZEVFfYukWzuMmI2RMB/38YYIHqDnDRF++soO5ByvxRvLLsYVY+O9+rOJiMi4Llz9NRrbZGxdNQdJMSF6N4eo23pSV+kyKWPlypXdXvf555/vxZb4HlmWUVRUhKSkJFgslrMjspwj2yUbcsZ8tDEbMeYjZtR8okIC0djWjKrGNt0KWaNmYxTMx326FLLZ2dlO/9+7dy8kSUJKSgoA4NChQ7BYLJgyZYoezTM0VVVRXV2N4cOHA+ANETrqnA05Yz7amI0Y8xEzaj7RIYE4Xt2s67VkjZqNUTAf9+lSyG7dutWx/PzzzyMsLAxvvfUWoqKiAADV1dVYvnw5Zs2apUfzDM1qteKSSy4BALTYZDS1yQCA6FAWsh2zoa6YjzZmI8Z8xIyaj+Nasjpegsuo2RgF83Gf7id7Pffcc1izZo2jiAWAqKgoPPHEE3juued0bJkxybKM/Px8yLLsuGKB1WxCWD9euqNjNtQV89HGbMSYj5hR87EfqdNzRNao2RgF83Gf7oVsXV0dKioqujxeUVGB+vp6HVpkfM3NzQDgND/WZDLp2STDsGdDrjEfbcxGjPmIGTGfKAOMyALGzMZImI97dB/GW7x4MZYvX47nnnsOU6dOBQDs3LkT9957L5YsWaJz64zHYrFg8uTJAIDqMxe65vzYdh2zoa6YjzZmI8Z8xIyaj2NqQYN+haxRszEK5uM+3Udk161bh4ULF+Lmm2/GsGHDMGzYMNx888246qqr8Oqrr+rdPMORZRm5ubmQZdnxKTuKN0MA4JwNdcV8tDEbMeYjZtR87NcX1/M2tUbNxiiYj/t0H5ENDg7Gq6++imeffRaFhYUAgJEjRyIkhNe8Oxf7vKdoXnqLiIg6sd/xsUrHObJEvU33QtYuJCQEEyZM0LsZhmexWDBu3DgAvKtXZx2zoa6YjzZmI8Z8xIyaz9kRWZtubTBqNkbBfNyneyE7d+5c4YlK6enpXmyN8cmyjJycHEyYMOHsNWQ5IgvAORteWLor5qON2YgxHzGj5uOYI6vzVQuMmI1RMB/36V7ITpo0yen/NpsN+/btQ25uLpYtW6ZPowyuf//+AM6eicpC9ix7NuQa89HGbMSYj5gR87FftaC22QZJVmC16HNajBGzMRLm4x7dC9kXXnjB5eOPPvooGhoavNwa47NYLBgzZgwAzpHtrGM21BXz0cZsxJiPmFHziewfAJMJUFWgptmGmNB+Xm+DUbMxCubjPt2vWqDll7/8Jd588029m2E4kiRh9+7dkCSJc2Q76ZgNdcV8tDEbMeYjZtR8rBYzIvq3n/Cl100RjJqNUTAf9xm2kM3KykJQUJDezTAck8mEqKgomEwmxyVVOCLbrmM21BXz0cZsxJiPmJHzsV9n/LROhayRszEC5uM+3acWdL7pgaqqKC0txffff4+HH35Yp1YZl8ViwahRo6CqquOGCFEsZAGczYZcYz7amI0Y8xEzcj5RIYFAZaNuI7JGzsYImI/7dB+RDQ8PR0REhOMrOjoac+bMQWpqKh555BG9m2c4kiQhMzMTtU2taJMVALyzl509Gx6icY35aGM2YsxHzMj52Kee6XWbWiNnYwTMx326j8hu2LDB499z7dq1ePbZZ1FWVoaJEyfi5Zdfdtz+1tXPX758udNj/fr1Q0tLi8fb5QlmsxkJCQmobW7f6YMCzOgfyEt2AGezMZt1/3xmSMxHG7MRYz5iRs7HflMEvUZkjZyNETAf9+me3IgRI3D69Okuj9fU1GDEiBE9/n4bN27EypUr8cgjj2Dv3r2YOHEiFixYgPLycs3XhIeHo7S01PF17NixHv9cbzGbzRg2bBiqzxSyHI09y54NfyG4xny0MRsx5iNm5HyiHNeS1eemCEbOxgiYj/t0T+7o0aMu7zHc2tqKEydO9Pj7Pf/88/jtb3+L5cuX44ILLsC6desQHBwsvAKCyWTCwIEDHV/x8fE9/rneIkkSMjIyUFnXDACIDmUha2fPhodoXGM+2piNGPMRM3I+0Y67e+k3tcCo2RgB83GfblMLPvvsM8fypk2bEBER4fi/LMvYsmULhg8f3qPv2dbWhj179uDBBx90PGY2m3HllVciKytL83UNDQ0YNmwYFEXBRRddhKeeegoXXnhhj362t5jNZowcORJZpe07PS+9dZY9G36ydY35aGM2YsxHzMj56H13LyNnYwTMx326FbKLFi0C0D4a2vkOXgEBARg+fDiee+65Hn3PyspKyLLcZUQ1Pj4e+fn5Ll+TkpKCN998ExMmTEBtbS3+/ve/Y+bMmfjhhx8wZMgQl69pbW1Fa2ur4/91dXUA4BhZtv9rsVicliVJgslkciybzWaYzWbNZZvNBovF4li2Wq0wm82Ii4tDdWExACCyvxWqqgJo/2QXEBAAVVUdy4qiQJZlx7KiKLBarZrLsixDVVXHsqt+eLpPJpPJsWzvR8fl7vbJvq3NZrPf9MnT2ykhIcHxyd9f+uSp7TR48GDH9/SXPnlqO3V8b/lLnzy9nUTvLT37dLaQbf+bpcd2sr+3zGaz7tvJaPueqqpO7y1/6JMntlNP6PYRwN7poUOHory83PF/RVHQ2tqKgwcP4tprr+31dsyYMQNLly7FpEmTcPnll+Ojjz5CbGws/vGPf2i+Zs2aNU5XWkhMTAQA5ObmAgDy8vKQl5cHAMjJyUFBQQEAIDs7G0VFRQCAXbt2oaSkBACQmZmJ0tJSAGifNlBZCQBIT09HTU0NACAtLQ319fWQJAmpqak4VdMIAKgtPwlJktDS0oLU1FQAQH19PdLS0gC0zzVOT08H0F7oZ2RkAABKS0uRmZkJACgpKcGuXbsAAEVFRcjOzgYAFBQUICcnp9f7BACpqaloaWlx9O98+nTixAl89dVXkCTJb/rkye1UWFiI9PR07Ny502/65Knt1NDQgPT0dL/qkye309GjR/H1119DkiS/6ZMnt9PRo0eRnp6Ob7/91nB9ss+RLatu1GU7tbS0YMuWLYbYTkbc9woLC7Fp0yZIkuQ3ffLUduouk2ofzvMDbW1tCA4OxocffugY8QWAZcuWoaamBp9++mm3vs8NN9wAq9WKf/3rXy6fdzUim5iYiKqqKkRFRfXqJylVVVFWVob/zqzAxu+P40/zRuKun6QAMM4nKb0+HUqShIqKCseIvD/0yZPbSVVVVFdXIzIy0jG67+t98tR2MpvNqKysRGRkJAIDA/2iT57cTh3fW6qq+kWfPLmdAKCqqkrzvaVnn47XtGLO37chONCCHx+/yuvbqeN7q1+/fnw/dVq22WyorKx0vLf8oU+e2E4NDQ2IiIhAbW0twsPDIaJLIfvSSy/htttuQ1BQEF566SXhun/84x979L2nTZuGqVOn4uWXXwYAx6jvihUr8MADD5zz9bIs48ILL8TVV1+N559/vls/s66urtuBe8rt//s9Nv1wCn9dNA6/mj7MKz+TiIh8S22zDRMfax9Zy//rVQgK4OUayfh6UlfpMkf2hRdewC233IKgoCC88MILmuuZTKYeF7IrV67EsmXLcPHFF2Pq1Kl48cUX0djY6LhW7NKlS5GQkIA1a9YAAB5//HFMnz4do0aNQk1NDZ599lkcO3YMv/nNb86/g73IZrMhPT0dpxtCAfDyWx3Zs5k3bx4CAgL0bo7hMB9tzEaM+YgZOZ/wICssZhNkRUV1UxsGRfT36s83cjZGwHzcp0sha58L0XnZE2688UZUVFRg9erVKCsrw6RJk/D11187DjcXFxc7TSSurq7Gb3/7W5SVlSEqKgpTpkxBZmYmLrjgAo+2y1MsFgsuueQS/C23fc5JVAh3fDt7NhYLRxxcYT7amI0Y8xEzcj4mkwlRwYGobGhFVaP3C1kjZ2MEzMd9fjVHVi96TC246K+bUdXYhk13zUbKwDCv/EwiIvI981/YjkOnGvB/t07DZaNj9G4O0TkZfmrBypUru71ud+ep9hU2mw1fb0pDTVP7/zkie5bNZkNaWhrmz5/PQzQuMB9tzEaM+YgZPR/HJbh0uCmC0bPRG/Nxny6FrP2yDOdiv54jnWW1WjHx4ulQdnwHgDdE6MhqtWLWrFmOsy/JGfPRxmzEmI+Y0fOxF7LVOtwUwejZ6I35uE+X5LZu3arHj/ULJpMJNks/AEBYkBUBFt4NxM5kMnltaocvYj7amI0Y8xEzej72AY/TOhSyRs9Gb8zHfYaqgkpKSnp8Idy+xmaz4bOvtwA4+ymb2tlsNnz66aew2Wx6N8WQmI82ZiPGfMSMno+eI7JGz0ZvzMd9uheykiTh4YcfRkREBIYPH47hw4cjIiICDz30EDesC1arFaPHTQbAaQWdWa1WzJ8/n4doNDAfbcxGjPmIGT0f+98KPebIGj0bvTEf9+me3J133omPPvoIf/vb3zBjxgwAQFZWFh599FGcPn0a//M//6NzC42ntqX9jhgcke2KvwzEmI82ZiPGfMSMnI+eI7KAsbMxAubjHt1HZN99911s2LABt99+OyZMmIAJEybg9ttvxxtvvIF3331X7+YZjiRJyMo+AIAjsp11vGc0dcV8tDEbMeYjZvR8ouxXLdChkDV6NnpjPu7TvZDt168fhg8f3uXxpKQkxz3P6Syr1Yr4xBEAgAGhzKcjq9WKq6++mp9uNTAfbcxGjPmIGT0f+x0gq3WaWmDkbPTGfNyneyG7YsUK/PWvf0Vra6vjsdbWVjz55JNYsWKFji0zrtMN7VlxRLYrfqoVYz7amI0Y8xEzcj7RofapBTbocQ8kI2djBMzHPboXstnZ2fjiiy8wZMgQXHnllbjyyisxZMgQfP7559i/fz+WLFni+KL2Hf7QsZMAgGjeDMGJJElIS0vjLwUNzEcbsxFjPmJGz8c+ItsmK2hsk736s42ejd6Yj/t0v0Xt8uXLu73u+vXre7El58/bt6hdtPZb7CupwWu/moL5Fw7s9Z9HRES+bczDX6HFpiDj3rkYOiBY7+YQCRn+FrUdGbU4NSpVVXG6oQUAr1rQmaqqqK+vR1hYGO8K5wLz0cZsxJiPmC/kEx0ciJO1LahqavNqIesL2eiJ+bhP96kF1DOSJKGyrr2QjWIh60SSJHzzzTc8RKOB+WhjNmLMR8wX8onS6RJcvpCNnpiP+3SfWnD69GmsXr0aW7duRXl5ORRFcXq+qqpKp5Z1nzenFrRJCpIf+goAkP3wT1jMEhHROf3qjZ34pqASz90wET+bMkTv5hAJ+dTUgl/96lc4fPgwbr31VsTHx3No/RyqzkwrMJuAiP482asjRVFQU1ODyMhImM082NAZ89HGbMSYj5gv5BOl0yW4fCEbPTEf9+leyH7zzTfYsWMHJk6cqHdTfEJlfXshGxkcALOZRX9Hsixj9+7dmDdvHn8huMB8tDEbMeYj5gv5ROt0UwRfyEZPzMd9uheyY8aMQXNzs97N8Bl1be1TL6JD+uncEuMJCAjAggUL9G6GYTEfbcxGjPmI+UI+jtvUenlE1hey0RPzcZ/u5f+rr76Kv/zlL9i+fTtOnz6Nuro6py9yVuW4GQKnFXSmKIrLedbUjvloYzZizEfMF/LR6za1vpCNnpiP+3QvZCMjI1FXV4d58+YhLi4OUVFRiIqKQmRkJKKiovRunuGcZiGrSVEU5Obm8heCBuajjdmIMR8xX8jHflMEPQpZo2ejJ+bjPt2nFtxyyy0ICAjAu+++y5O9uqG2pf2uLANCObWgM6vVinnz5undDMNiPtqYjRjzEfOFfKLO3AnS24WsL2SjJ+bjPt0L2dzcXGRnZyMlJUXvpvgE+4hsJK9Y0IWiKCgtLcWgQYM4ad4F5qON2YgxHzFfyOfsHFmbV3+uL2SjJ+bjPt1Tu/jii1FSUqJ3M3xGVeOZQpZTC7pQFAWFhYU8RKOB+WhjNmLMR8wX8rFPLahpaoOseO/y8b6QjZ6Yj/t0H5G988478ac//Qn33nsvxo8fj4AA5wJtwoQJOrXMmGqa2+/+ERMapHNLjMdqtWL27Nl6N8OwmI82ZiPGfMR8IZ/IM4WsogJ1zTav3UzHF7LRE/Nxn+6F7I033ggA+PWvf+14zGQyQVVVmEwmyLKsV9MMyT6/iSd7daUoCkpKSpCYmMhDNC4wH23MRoz5iPlCPoFWM8L6WVHfKqGqqc1rhawvZKMn5uM+3QvZoqIivZvgU+yFbGR/3Ted4SiKghMnTiAhIYG/EFxgPtqYjRjzEfOVfKJDA1HfKqG6sQ2I9c7P9JVs9MJ83Kd7NTRs2DC9m+BT7Bezjg3vr3NLjMdqtWLmzJl6N8OwmI82ZiPGfMR8JZ+o4EAcO93k1SsX+Eo2emE+7jNM+f/jjz/i66+/xmeffeb0dT7Wrl2L4cOHIygoCNOmTcOuXbuE63/wwQcYM2YMgoKCMH78eKSmpp7Xz+1tzW0yWmztE8LDgyw6t8Z4ZFnG4cOHOR1FA/PRxmzEmI+Yr+Sjx929fCUbvTAf9+leyB45cgQTJ07EuHHjcM0112DRokVYtGgRFi9ejMWLF/f4+23cuBErV67EI488gr1792LixIlYsGABysvLXa6fmZmJm266Cbfeeiuys7MdPz83N9fdrnlc1ZlfPmYTUOvl2wz6AlVVUV1dDVX13hm5voT5aGM2YsxHzFfyiTpzwtfe4hqU1nrn1vC+ko1efCmf0tpmZBZWem3f6S6TqnN61113HSwWC15//XUkJSVh165dOH36NO655x78/e9/x6xZs3r0/aZNm4ZLLrkEr7zyCoD2+SeJiYm488478cADD3RZ/8Ybb0RjYyO++OILx2PTp0/HpEmTsG7dum79zLq6OkRERKC2thbh4eE9am9PPJd2EC+nHwbQXsyuWTIeN14ytNd+HhER+Y9fvbET3xRUAmj/G/Lk4vH4+cWJOreKfMH735fgLx8fgKJ6p/7oSV2l+xzZrKwspKenIyYmBmazGWazGZdddhnWrFmDP/7xj8jOzu7292pra8OePXvw4IMPOh4zm8248sorkZWVpfnzV65c6fTYggUL8Mknn2j+nNbWVrS2tjr+X1dXBwCOQwP2fy0Wi9OyJEkwmUyOZXt/tZZtNhssFgvMZjOKK+vxytbDjp+pqMCfPzqAGUlRSBwQCgCQJAkBAQFQVdWxrCgKZFl2LCuKAqvVqrksyzJUVXUsu+qHp/pks9lgtVphMpkcy/Z+dFzubp9sNhsKCgqQkpICk8nkF33y5HZSFAVHjhxBUlISAgIC/KJPntpOJpMJBQUFSEpKQr9+/fyiT57cTh3fWwD8ok+e3E6qqqKwsFDzvWWEPpXWtmDHmSLW/jfkwY8O4MGPDoCoJ9rrj1xcNmoA4sP69crvvZ7QfWqBLMsICwsDAMTExODkyZMA2k8CO3jwYI++V2VlJWRZRnx8vNPj8fHxKCsrc/masrKyHq0PAGvWrEFERITjKzGx/ROtfTpCXl4e8vLyAAA5OTkoKCgAAGRnZzuu0rBr1y7HjSAyMzNRWloKAMjIyEBlZfsvm/T0dNTU1AAA/r0pA53HzmUVeD91KyRJQktLi2Nub319PdLS0gAANTU1SE9Pd+STkZEBACgtLUVmZiYAoKSkxDGPuKioyPHhoaCgADk5Ob3Wp7S0NNTX1wMAUlNT0dLSAkmSkJqael59Kisrw7Fjx/yqT57cTseOHUNzczP27NnjN33y5HZqamrCpk2b/KpPntpOx48fd7TFX/rkye10/PhxNDc347vvvjNsn9J3HYDxD16Tr5BVFXsPlfTq773u0n1qwaxZs3DPPfdg0aJFuPnmm1FdXY2HHnoIr732Gvbs2dOjuaonT55EQkICMjMzMWPGDMfj9913H7Zv346dO3d2eU1gYCDeeust3HTTTY7HXn31VTz22GM4deqUy5/jakQ2MTERVVVViIqK6rUR2TnPZaDjDVksJmDrPbM5Iss+sU/sE/vEPp1zRHb2s9uc/oaYTcAXK2ZicFTIefRJgsVydtlqtZzpU/tyez9kp+WAAOuZPrUvt/dJcSzrv53YJ1d9Kq1pwjUvf9up/jAh477Le21EtqGhwXemFjz00ENobGwEADz++OO49tprMWvWLAwYMAAbN27s0feKiYmBxWLpUoCeOnUKAwcOdPmagQMH9mh9AOjXr5/j8GNHFovF6d/Oy/ZfUt1d7niXs6ExYVizZDwe/OjsHJWnlozH0JiwLuubTCbHsn1n7u6yVtt7o089We5On1RVRX5+PsaOHev4o+HrffLkdpJlGbm5uRg7dqzj+/h6n3qyLGq7LMvIy8vD2LFjYTKZ/KJPouWe9qnze8sf+uTJ7XSu95YR+jQkOgRrlozHnz/KhayqsJhMeGrJOFyQEHVmrY43SPDUMpzeWx3b5B290ydPcs6nOz/H+32KDA50ue8kRIU41umN33vdpXshu2DBAsfyqFGjkJ+f7xjZtP9B6a7AwEBMmTIFW7ZswaJFiwC0n+y1ZcsWrFixwuVrZsyYgS1btuCuu+5yPLZ582anEV2juPGSobh05ABk7M3D7IvGYkh0yLlfREREhPa/IbOTY3G0sgnDY4IxKILXI6fuMfK+o/vUAk/buHEjli1bhn/84x+YOnUqXnzxRbz//vvIz89HfHw8li5dioSEBKxZswZA+zytyy+/HE8//TSuueYavPfee3jqqaewd+9ejBs3rls/01tXLSAiIiLydz511QJPu/HGG1FRUYHVq1ejrKwMkyZNwtdff+04oau4uNgx/A0AM2fOxLvvvouHHnoIf/7znzF69Gh88skn3S5iATiu/2a/ekFvsh/CGjdunA6HaYyN2YgxH23MRoz5iDEfbcxGjPm4Zq+nujPW6ncjsno4fvy448oFREREROS+kpISDBkyRLgOC1kPUBQFJ0+eRFhYWI/n9faU/QoJJSUlnMbQCbMRYz7amI0Y8xFjPtqYjRjzcU1VVdTX12Pw4MFOR9Fd8bupBXowm83n/MTgaeHh4dzpNTAbMeajjdmIMR8x5qON2Ygxn64iIiK6tZ7uN0QgIiIiIjofLGSJiIiIyCexkPUx/fr1wyOPPOLyhgx9HbMRYz7amI0Y8xFjPtqYjRjzcR9P9iIiIiIin8QRWSIiIiLySSxkiYiIiMgnsZAlIiIiIp/EQpaIiIiIfBILWSIiIiLySSxkiYiIiMgnsZAlIiIiIp/EQpaIiIiIfBILWSIiIiLySSxkiYiIiMgnsZAlIiIiIp/EQpaIiIiIfBILWSIiIiLySSxkiYiIiMgnsZD1oIyMDFx33XUYPHgwTCYTPvnkkx69/tFHH4XJZOryFRIS0jsNJiIiIvJhLGQ9qLGxERMnTsTatWvP6/WrVq1CaWmp09cFF1yAG264wcMtJSIiIvJ9LGQ9aOHChXjiiSewePFil8+3trZi1apVSEhIQEhICKZNm4Zt27Y5ng8NDcXAgQMdX6dOncKPP/6IW2+91Us9ICIiIvIdLGS9aMWKFcjKysJ7772HnJwc3HDDDbjqqqtQUFDgcv3XX38dycnJmDVrlpdbSkRERGR8LGS9pLi4GOvXr8cHH3yAWbNmYeTIkVi1ahUuu+wyrF+/vsv6LS0teOeddzgaS0RERKTBqncD+ooDBw5AlmUkJyc7Pd7a2ooBAwZ0Wf/jjz9GfX09li1b5q0mEhEREfkUFrJe0tDQAIvFgj179sBisTg9Fxoa2mX9119/Hddeey3i4+O91UQiIiIin8JC1ksmT54MWZZRXl5+zjmvRUVF2Lp1Kz777DMvtY6IiIjI97CQ9aCGhgYcPnzY8f+ioiLs27cP0dHRSE5Oxi233IKlS5fiueeew+TJk1FRUYEtW7ZgwoQJuOaaaxyve/PNNzFo0CAsXLhQj24QERER+QSTqqqq3o3wF9u2bcPcuXO7PL5s2TJs2LABNpsNTzzxBN5++22cOHECMTExmD59Oh577DGMHz8eAKAoCoYNG4alS5fiySef9HYXiIiIiHwGC1kiIiIi8km8/BYRERER+SQWskRERETkk3iylwcoioKTJ08iLCwMJpNJ7+YQERER+SxVVVFfX4/BgwfDbBaPubKQ9YCTJ08iMTFR72YQERER+Y2SkhIMGTJEuA4LWQ8ICwsD0B54eHh4r/4sRVFw+vRpDBgw4JyfUvoaZiPGfLQxGzHmI8Z8tDEbMebjWl1dHRITEx31lQgLWQ+wTycIDw/v9UJWkiTs3bsXw4YNg9XKzdcRsxFjPtqYjRjzEWM+2piNGPMR6850TV5+ywPq6uoQERGB2traXi9kiYiIzldpbTOKKhuRFBOCQRH99W4O+RBv7js9qatY/vsYRVFQWlqKQYMG8TBEJ8xGjPloYzZizEfMF/JRFBUv/ucQXk4/DBWACcD8C+MxYUhkr/5c+0k7PBnaNV/JJ+d4DdJ+OAUVgNkErFkyHjdeMlTvZgFgIetzFEVBYWEh4uPjDfsLUy/MRoz5aGM2YsxHzCj5dB4xq22y4ZvDFdh2sAJb8spR3dTmWFcFsOmHU9j0wylvtc5LP8dX+U4+igr8+aNczE6ONcSoPqcWeACnFhARkZ427i7Ggx8dgKK2j7YOGxCMkupmyIr4T/zc5FjEhQd5p5Hkk07VtWDboYouj//rt9MxY+SAXvmZnFrgxxRFQUlJCRITEzky0gmzEWM+2piNGPMR0zOfuhYbPt9/En/5ONfxmArg6OkmAMDouFDMSYnFhCER+NN7+9CxrrWYTHjqZ+N7dVSN+46YL+RTWtuMS59O77LvDI8J1q9RHfhUIVtXV9fj1/jbCKmiKDhx4gQSEhIMu9PrhdmIMR9tzEaM+Yh5Mx9VVZFfVo9tByuw9WA59h6rhqQx6vrSLybhp5MSHP9vapPx549yIatqexG7ZFyvHxrmviPmC/kMiuiPNUvGe33f6S6fmlpgNpt7NBnaZDLh0KFDGDFiRC+2ilMLiIio99S32PDt4dPYdrAc2w5WoKyuxen5odH9UVLVjI5/zC0mE3Y8MLdLsVFa24yjlU0YHhNsmEKEfIM39x2/nlrw4YcfIjo6+pzrqaqKq6++2gst8i5ZllFUVISkpCRYLBa9m2MozEaM+WhjNmLMR8zT+aiqioLyBmzNby9cdx+tchp1DQowY8aIAZg7Jg5zkuMwdEAwNu4u7taI2aCI/l4tYLnviPlSPt7ed7rLpwrZYcOGYfbs2RgwoHuTi0eMGIGAgIBebpV3qaqK6upqDB8+XO+mGA6zEWM+2piNGPMR80Q+ja0Svj1ciW2HKrAtvxwna51HXZNiQnB5cizmpMRi+ogBCApwLnpuvGQoZifHGm60lfuOGPNxn09NLTAqTi0gIqKeUFUVhRUNjrmuu4uq0SYrjucDrWdGXVNiMSclDsNjQnRsLZF3+fXUApGamhpERkbq3YxeJcsyCgoKMHr0aMMfhvA2ZiPGfLQxGzHmI9bdfJraJGQVnsbWM3Ndj1c3Oz0/NDoYc1JiMTclDtNHDED/QN/PmvuOGPNxn88Wss888wyGDx+OG2+8EQDw85//HP/+978xcOBApKamYuLEiTq3sPc0Nzefe6U+itmIMR9tzEaM+Yi5ykdVVRRVNmLrwQpsO1iOnUVVaJM6jLpazJg2IhpzUuIwJyUWI2JCDH13p/PFfUeM+bjHZ6cWJCUl4Z133sHMmTOxefNm/PznP8fGjRvx/vvvo7i4GGlpaV5rC6cWEBERADS3yfjuSPsVBrYerEBxVZPT8wmR/TF3TCzmJMdh5qgBCA702fEkol7TJ6YWlJWVITExEQDwxRdf4Oc//znmz5+P4cOHY9q0aTq3rvfIsoy8vDyMHTuWhyE6YTZizEcbsxFjPmKF5XV4PyMXebUW7CyqQmuHUdcAiwlTk6IxJzkOc8fEYmRsqF+OumrhviPGfNzns4VsVFSU424YX3/9NZ544gkA7YdyZFnWuXVEROSvWmwydhZVYWt+ObYfqkBRZaPT84MjgnB5ShzmpsRi5qgYhPbz2T+1RIbns1MLVqxYgS+++AKjR49GdnY2jh49itDQULz33nv429/+hr1793qtLZxaQETk30qqmhzTBTILK9FiOzvqajWbcPHwKMxNicOclDgkx/etUVciT+sTUwteeOEFDB8+HCUlJfjb3/6G0NBQAEBpaSnuuOMOnVvXe2RZRk5ODiZMmMDDEJ0wGzHmo43ZiPXFfFolGbuLqs9cYaAchRXOo67x4f3OFK6xmJ4UjaJDP2LChOF9Jp/u6ov7Tk8wH/f5XCG7evVqXH/99ZgyZQpWrVrV5fm7775bh1Z5V//+xrjQtRExGzHmo43ZiPWFfI5XN2HbmSsMZBaeRlPb2WlqFrMJU4ZFOS6PNWZgmGPUVZblPpHP+WI2YszHPT43teDXv/41vvjiCwQGBuK6667D9ddfj3nz5iEwMFC3NnFqARGR72mTFHx/tArbDlVga345CsobnJ6PDeuHOcmxmDsmDpeOikFEf/+6UySRUfWkrvK5QhYAFEXBt99+i88//xyffvopSktL8ZOf/ATXX389rr32WkRHR3u1Pd4sZCVJQnZ2NiZPngyr1ecG1HsVsxFjPtqYjZg/5VNa29x+N638cnx7uBKNHUZdzSbgoqFRmDsmDpcnx+KCQeEwm88919Wf8vE0ZiPGfFzz+zmyZrMZs2bNwqxZs/C3v/0NeXl5+Pzzz/GPf/wDt912G6ZOnYqf/vSnuOmmm5CQkKB3cz3KZDIhKiqKJxK4wGzEmI82ZiPmy/nYZAV7jrXPdd1+sAL5ZfVOz8eEBuLy5Pa5rrNGxyAyuOdH93w5n97GbMSYj/t8ckRWpLy8HJ9//jk+++wzzJo1y+U8Wk/j1AIiIuM4VdeCbWduA7ujoBL1rZLjOZMJmJwYiTkpcZibEocLB3dv1JWIvMfvpxYYjbenFuzatQtTp07lYYhOmI0Y89HGbMSMno8kK9hbXOO4PFZeaZ3T89Ehgbg8ORZzUmIxe3QsokI8e06F0fPRE7MRYz6u+e3UgiVLlnR73Y8++qgXW6Ifs9mMhIQEmM1mvZtiOMxGjPloYzZiRsynvL4F2w9WYNvBCnxTUIG6FudR1wlDIjE3JRZzUuIwISGiV0ddjZiPUTAbMebjPp8qZCMiIhzLqqri448/RkREBC6++GIAwJ49e1BTU9OjgtfXmM1mDBs2TO9mGBKzEWM+2piNmBHykRUV+0qqsTW/AtsOlSP3hPOoa2RwgNOo64DQfl5rmxHyMSpmI8Z83OdThez69esdy/fffz9+/vOfY926dY6LCMuyjDvuuMOv56lKkoTMzEzMnDmThyE6YTZizEcbsxHTK5/Khtb2UddDFcg4VIHaZpvT8xOGRGBOcizmjInDxCGRsOg015X7jzZmI8Z83Oezqb355pvYsWOH050wLBYLVq5ciZkzZ+LZZ5/VsXW9x2w2Y+TIkTwM4QKzEWM+2piNmLfykRUV+4/XOG5KkHO81un5iP4BmDU6BnNT4jA7ORaxYd4bdRXh/qON2YgxH/f5bCErSRLy8/ORkpLi9Hh+fj4URdF4le+zz6ehrpiNGPPRxmzEejOfqsY2ZByqwNaD5cg4VIHqJudR1wsHhztuBTspMRJWi/H+4HP/0cZsxJiP+3y2kF2+fDluvfVWFBYWYurUqQCAnTt34umnn8by5ct1bl3vkSQJGRkZmD17Ng9DdMJsxJiPNmYj5sl8FEXFgRO12Hrm8lj7j9eg47VzwoKsmD06FpenxGJOciziwoPcbH3v4/6jjdmIMR/3+Wxqf//73zFw4EA899xzKC0tBQAMGjQI9957L+655x6dW9d7zGYzxo0bx8MQLjAbMeajjdmIuZtPdWMbMgoqsP1gBbYfqsDpxjan58cOCseclFjMTYnD5KGRCDDgqKsI9x9tzEaM+bjPL64jW1fXfvaqXid58YYIRERnKYqKH07Wnbmuazn2ldRA6fCXJrSfFZeNisHcMbG4PDkOAyOMP+pKRN7jt9eR1dKXikebzYb09HTMmzcPAQEBejfHUJiNGPPRxmzEupNPbZMN3xyuwNb89lHXyoZWp+dT4sMwZ0ws5iTHYcqwKARa/WcEivuPNmYjxnzc59Mjsh9++CHef/99FBcXo63N+VDV3r17vdYOb47IKoqCmpoaREZG8lBEJ8xGjPloYzZirvJRVRU/ltY5rjCwt7gGcodh15BACy4dFYM5Z07UGhzZX6/m9zruP9qYjRjzca1PjMi+9NJL+Mtf/oL/+q//wqefforly5ejsLAQu3fvxh/+8Ae9m9drzGYzoqOj9W6GITEbMeajjdmI2fOpa7FhR8EpbDtzolZ5vfOo6+i4UMdc14uHR/vVqKsI9x9tzEaM+bjPZwvZV199Fa+99hpuuukmbNiwAffddx9GjBiB1atXo6qqSu/m9RqbzYa0tDTMnz+fhyE6YTZizEcbs3FNVVXkl9Vjy49l+GRnAY42mCB1GHXtH2DBpaMG4PKUOMxJjkVidLCOrdUP9x9tzEaM+bjPZ6cWBAcHIy8vD8OGDUNcXBw2b96MiRMnoqCgANOnT8fp06e91hZvTi1QVRX19fUICwuDyaTPXWyMitmIMR9tzOas+hYbvj182jHqWlbX4vT8iNgQzEmOw9wxsbhkeDSCAiwa36nv4P6jjdmIMR/X+sTUgoEDB6KqqgrDhg3D0KFD8d1332HixIkoKiqCj9bm3WIymfrUyW09wWzEmI+2vpyNqqooKG/A1vz2wnX30SqnUdegADNmjBiAuWPiMCc5DkMH9M1RV5G+vP+cC7MRYz7u89kJTPPmzcNnn30GoP3mCHfffTd+8pOf4MYbb8TixYt1bl3vsdls+PTTT2Gz2c69ch/DbMSYj7a+lk1jq4S0H8rw548P4NKn0zH/hQys+SofWUdOQ1JUJMWE4L9mDseG5Zdg3+r5eO2XkxFRvh+Dwnno05W+tv/0BLMRYz7u89mpBYqiQFEUx50w3nvvPWRmZmL06NG4/fbbERgY6LW2eHtqQUtLC4KCgngYohNmI8Z8tPl7NqqqorCiAdsOtt8KdndRNdrks7fyDrSeGXVNicWclDgMjwnp8np/zsddzEcbsxFjPq71pK7yyUJWkiQ89dRT+PWvf40hQ4a49b3WrFmDjz76CPn5+ejfvz9mzpyJZ555BikpKd3+Ht4uZCVJgtVq5U7fCbMRYz7a/DGbpjYJWYWnHbeCPV7d7PT80OhgxxUGpo8YgP6B2nNd/TEfT2I+2piNGPNxrSd1lU9OLbBarfjb3/4GSZLc/l7bt2/HH/7wB3z33XfYvHkzbDYb5s+fj8bGRg+01PMkSUJqaqpH+u5vmI0Y89HmD9moqoojFQ14Y0cRfvXGTkx6fDNufet7/N93xThe3YxAixmzRsfg4WsvwJZ7Lsf2e+fg8evHYe6YOGERC/hHPr2J+WhjNmLMx30+OSILANdffz2WLFmCZcuWefT7VlRUIC4uDtu3b8fs2bO79RqOyBoDsxFjPtp8NZvmNhnfHTl95lawFSiuanJ6PiGyP+aeuZvWzFEDEBx4fuf3+mo+3sJ8tDEbMebjWp+4asHChQvxwAMP4MCBA5gyZQpCQpzndP30pz89r+9bW1sLAMILFLe2tqK19eyFwOvq6gAAsiw7/WuxWJyWJUmCyWRyLJvNZpjNZs1lm80Gi8XiWLbPB25paXH01/4GsC8HBAQ43hgBAQFQFAWyLDuW7fOKtZZlWYaqqo5lV/3wdJ9MJpNT/9zpU0tLC0JDQ/2qT57aTvafbX/MH/rkqe1ksVhgs9mgqqrjWo5G7dPhU7X4puA0th2qxHdHTqNVOjvXNcBiwtSkaMwaNQBXjB2IkbEhkGXZsZ1sNtt598n+3uL7qWufTCaT8L3li33y1Hbq+N4KDAz0iz55eju1trb6XZ/c3U494ZNTCwDgjjvuwKlTp/D888/jlltuwaJFixxf53vVAkVRcNddd+HSSy/FuHHjNNdbs2YNIiIiHF+JiYkAgNzcXABAXl4e8vLyAAA5OTkoKCgAAGRnZ6OoqAgAsGvXLpSUlAAAMjMzUVpaCgDIyMhAZWUlACA9PR01NTUAgLS0NNTX10OSJKSnp6OhocHpkERLSwtSU1MBAPX19UhLSwMA1NTUID09HQBQWVmJjIwMAEBpaSkyMzMBACUlJdi1axcAoKioCNnZ2QCAgoIC5OTk9HqfACA1NRUtLS1u9enEiRNIT0+HJEl+0ydPbqfCwkKkpaX5VZ88tZ0aGhqwefNmfPXVV4brU4tNxrpPM3D/xt2Y+/dtuPKFHXjsizxsP1SBVknBwLBA3DR1KG67AMi4azre+c10DKr9EUPC2/+IeGI7HTt2zPHe4vupa5+OHTuGtLQ0v+qTp7ZTS0uL473lL33y5HYqLCzEli1bIEmS3/TJU9upu3x2akFv+P3vf4+vvvoKO3bsEJ5E5mpENjExEVVVVYiKiurzn6TYJ/aJfXKvTydrW7ElrwzbD1Ui68hptNjOjrpazSZcPCwKc8fE4bKRURgzKMIx6mXkPvnjdmKf2Cf2qXf61NDQ4N9XLegNK1aswKeffoqMjAwkJSX16LW8s5cxMBsx5qNN72xaJRm7i6rPXGGgHIUVziebxof3w9yUOMxJicWlo2IQFuTd67nqnY/RMR9tzEaM+bjmt1cteOmll9DS0nLuFc9Yt26dYxhdi6qqWLFiBT7++GOkp6f3uIj1NkmS8M033zjmY9FZzEaM+WjTI5vj1U34v++O4Tdv7cbkxzfjl2/sxBs7ilBY0QiLuX2u631XpeCrP83Cdw9egad/NgFXjRvk9SIW4L5zLsxHG7MRYz7u86kRWYvFgrKyMsTGxnZr/fDwcOzbtw8jRozQXOeOO+7Au+++i08//dTp2rERERHo379/t36ON0dkicg3tUkKvj9ahW2HKrA1vxwF5Q1Oz8eG9cOc5FjMHROHS0fFIKI/76JFRH2T3161QFVVXHHFFY65HOfS3Nx8znX+53/+BwAwZ84cp8fXr1+P//qv/+ppE3udoiioqalBZGRkj8/s83fMRoz5aOutbEprm9vvppVfjm8PV6KxTXY8ZzYBFw1tn+t6eXIsLhwcbthDi9x3xJiPNmYjxnzc51OF7COPPNKj9a+//nrhZbSA9uLYl8iyjN27d2PevHnc6TthNmLMR5unsrHJCvYca5/ruv1gBfLLnKc2xYQG4vLk9rmus0bHIDLYe7fSdgf3HTHmo43ZiDEf9/nU1AKj4tQCor7rVF0Ltp25DeyOgkrUt56d62YyAZMTIzEnJQ5zU+Jw4eBwmM3GHHUlIjIKv51aQO2HISorKxETE8NPb50wGzHmo60n2Uiygr3FNWeuMFCBvNI6p+ejQwJxeXIs5qTEYvboWESF+Maoqwj3HTHmo43ZiDEf97GQ9TGKoiA3NxezZ8/mTt8JsxFjPtrOlU15fQu2H6zAtoMVyCioQH2L86jrhCGRmJsSizkpcZiQEOF3o67cd8SYjzZmI8Z83MepBR7AqQVE/kVWVOwrqcbW/ApsO1SO3BPOo66RwQFOo64DQvvp1FIiIv/DqQV+TFEUlJaWYtCgQfz01gmzEWM+2hRFwY+FxcivtWB7QSUyDlWgttnmtM6EIRGYkxyLOWPiMHFIJCx+Nuoqwn1HjPloYzZizMd9LGR9jKIoKCwsRHx8PHf6TpiNGPNxJisq9h+vOXN5rFM40GnUNaJ/AGaNjsHclDjMTo5FbFjfHXXlviPGfLQxGzHm4z6fnVqwcuVKl4+bTCYEBQVh1KhR3br8lidwagGRb6hqbEPGoQpsPViOjEMVqG5yHnW9cHC441awkxIjYbXwDwsRkbf1pK7y2UJ27ty52Lt3L2RZdtyR69ChQ7BYLBgzZgwOHjwIk8mEHTt24IILLujVtnizkFUUBSUlJUhMTOSnt06YjVhfzEdRVBw4Ueu4wsD+4zXo+BsvLMiK2aNjMTs5BqND2jBpzIg+k01P9MV9pyeYjzZmI8Z8XOsTc2Tto63r1693dLK2tha/+c1vcNlll+G3v/0tbr75Ztx9993YtGmTzq31HEVRcOLECSQkJHCn74TZiPWVfKob25BRUIHtByuw/VAFTje2OT0/dlA45qTEYm5KHCYPjUSAxQxJkrBr1y4oynC/zuZ89ZV953wxH23MRoz5uM9nR2QTEhKwefPmLqOtP/zwA+bPn48TJ05g7969mD9/PiorK3u1LZxaQKQfRVHxw8k6bDtYjq0Hy7GvpAZKh99qof2suGxUDOaOicXlyXEYGBGkX2OJiOic+sSIbG1tLcrLy7sUshUVFairaz9pIzIyEm1tba5e7rNkWUZRURGSkpJgsVj0bo6hMBsxf8qntsmGbw5XYGt++6hrZUOr0/Mp8WGYMyYWc5LjMGVYFAKt4pEOf8qmNzAfMeajjdmIMR/3+Wwhe/311+PXv/41nnvuOVxyySUAgN27d2PVqlVYtGgRAGDXrl1ITk7WsZWep6oqqqurMXz4cL2bYjjMRsyX81FVFT+W1mHbwQpsO1iOvcU1kDsMu4YEWnDpqBjMOXOi1uDI/j3+/r6ajTcwHzHmo43ZiDEf9/ns1IKGhgbcfffdePvttyFJ7XfZsVqtWLZsGV544QWEhIRg3759AIBJkyb1als4tYDI8+pabNhRUIltZ07UKq93HnUdHRfqmOt68fDoc466EhGRb+gTVy2wa2howJEjRwAAI0aMQGhoqNfb4M1CVpZlFBQUYPTo0TwM0QmzETN6PqqqIr+svv26rgfLsfdYNaQOo679Ayy4dNQAXJ4ShznJsUiMDvbYzzZ6NnpjPmLMRxuzEWM+rvWJObJ2oaGhmDBhgt7N8Krm5ma9m2BYzEbMaPnUt9jw7eHTjlHXsroWp+dHxIY4rut6yfBoBAX03i96o2VjNMxHjPloYzZizMc9Pjsi29jYiKeffhpbtmxBeXk5FEVxet4+SusNnFpA1D2qqqKgvAFb89sL191Hq5xGXYMCzJg5MgZzUtpP1Bo6wHOjrkRE5Bv6xIjsb37zG2zfvh2/+tWvMGjQIJhMfeO+57IsIy8vD2PHjuVhiE6YjZhe+TS2Svj2cCW2HarAtvxynKx1HnVNignB5cmxmJMSi+kjBvTqqKsW7jtizEeM+WhjNmLMx30+W8h+9dVX+PLLL3HppZfq3RQi6kBVVRRWNDjmuu4uqkabfPaISaDVjBkjBmBuSizmpMRheEyIjq0lIiJf5rNTC5KSkpCamoqxY8fq3RROLaA+r6lNQlbhacetYI9XO8/5Ghod7LjCwPQRA9A/kCMPRETkWp+YWvDXv/4Vq1evxltvvYXg4L4zj06WZeTk5GDChAk8DNEJsxHzZD6qqqKoshFbz1zXdWdRFdqkDqOuFjOmjYh2XNd1REyIoaf/cN8RYz5izEcbsxFjPu7z2UL2ueeeQ2FhIeLj4zF8+HAEBAQ4Pb93716dWtb7+vfv2cXe+xJmI+ZOPs1tMr47cvrMrWArUFzV5PR8QmR/zB3TPuo6Y+QABAf61q8X7jtizEeM+WhjNmLMxz0+O7XgscceEz7/yCOPeKklnFpA/utoZaOjcP3uyGm0dhh1DbCYMDUpGnOS4zB3TCxGxoYaetSViIh8Q5+6IYIReLOQlSQJ2dnZmDx5MqxW3xrx6m3MRqw7+bTYZOwsqsLW/HJsP1SBospGp+cHRwTh8pQ4zE2JxcxRMQjt5x85c98RYz5izEcbsxFjPq71iTmyfZXJZEJUVBRHvlxgNmJa+ZRUNTlO0sosrESL7eyoq9VswsXDo87clCAOyfH+OerKfUeM+YgxH23MRoz5uM+nRmSjo6Nx6NAhxMTEnHPDV1VVea1dnFpAvqRVkrGrqMpxeawjFc6jrvHh/Rx307p0VAzCggI0vhMREZHn+e2I7AsvvICwsDAAwIsvvqhvY3QiSRJ27dqFqVOn8jBEJ8xG2/HqJqTnncInOwuQX62gqU12PGcxmzBlWJTj8lhjBob1udEB7jtizEeM+WhjNmLMx30+ldqyZctcLvclZrMZCQkJMJvNejfFcJjNWW2Sgu+PVmHboQpszS9HQXmD0/OxYf0wJzkWc8fE4dJRMYjo37dHXbnviDEfMeajjdmIMR/3+dTUgs4URcHhw4dRXl4ORVGcnps9e7bX2sGpBWQEpbXN7dMF8svx7eFKNHYYdTWbgIuGRmHumDhcnhyLCweH97lRVyIi8g1+O7Wgo++++w4333wzjh07hs61uMlkgizLGq/0bZIkITMzEzNnzuRhiE76WjY2WcH3R6ux7VA5tuVX4OCpeqfnY0IDcXly+1zXWaNjEBpoRmZmJsbED2cR20lf23d6ivmIMR9tzEaM+bjPZ1P73e9+h4svvhhffvklBg0a1Gf+MJvNZowcOZKHIVzoC9mcqmtpv65rfgW+PVyJ+lbJ8ZzJBExOjMSclDjMTYnDhYPDYTaffV8oiuL3+ZyvvrDvuIP5iDEfbcxGjPm4z2enFoSEhGD//v0YNWqU3k3h1ALqNZKsYG9xjePyWHmldU7PR4cE4vLkWMxJicXs0bGICgnUqaVERESe0SemFkybNg2HDx82RCHrTZIkISMjA7Nnz+ZhiE78JZvy+hZsP1iBbQcrkFFQgfoW51HXCUMiMTclFnNS4jAhIcJp1FXEX/LpDcxGjPmIMR9tzEaM+bjPZ1O78847cc8996CsrAzjx49HQIDzWdcTJkzQqWW9y2w2Y9y4cTwM4YKvZiMrKvaVVGNrfgW2HSpH7gnnUdfI4ACnUdcBof3O6+f4aj7ewGzEmI8Y89HGbMSYj/t8dmqBq41uMpmgqqrXT/bi1ALqqcqGVmw/c0OCbwoqUdtsc3p+wpAIzEmOxZwxcZg4JBKWbo66EhER+bo+MbWgqKhI7ybowmazIT09HfPmzesyCt3XGTkbWVGx/3gNth2swLaD5cg5Xuv0fET/AMwaHYO5KXGYnRyL2LDzG3UVMXI+emM2YsxHjPloYzZizMd9PjsiayTeHJFVFAU1NTWIjIzkoYhOjJZNVWMbMg61j7pmHKpAdZPzqOuFg8Mdt4KdlBgJq6V322y0fIyE2YgxHzHmo43ZiDEf13pSV/lsIfv2228Ln1+6dKmXWsKpBdROUVQcOFHruMLA/uM16PjuCguyYvboWFyeEos5ybGICw/Sr7FEREQG1ScK2aioKKf/22w2NDU1ITAwEMHBwaiqqvJaW7xZyNpsNqSlpWH+/Pk8DNGJHtlUN7Yho6AC2w9WYPuhCpxubHN6fuygcMxJicXclDhMHhqJgF4edRXhvqON2YgxHzHmo43ZiDEf1/pEIetKQUEBfv/73+Pee+/FggULevTatWvX4tlnn0VZWRkmTpyIl19+GVOnTu3Wa71ZyKqqivr6eoSFhfWZm0B0lzeyURQVP5ysa78pwcFy7CupgdLhHRTaz4rLRsVg7phYXJ4ch4ERxhl15b6jjdmIMR8x5qON2YgxH9f6bCELAN9//z1++ctfIj8/v9uv2bhxI5YuXYp169Zh2rRpePHFF/HBBx/g4MGDiIuLO+frObXAv9U22fDN4QpszW8fda1saHV6PiU+DHPGxGJOchymDItCoJXznIiIiM5XT+oqv/uLa7VacfLkyR695vnnn8dvf/tbLF++HBdccAHWrVuH4OBgvPnmm73UyvNns9nw6aefwmaznXvlPsZT2aiqih9O1mLt1sO4YV0mLnpiM1a8m41/7z2OyoZWhARaMP+CeDy1eDwyH5iHTXfPxoMLx2LGyAGGLmK572hjNmLMR4z5aGM2YszHfT47IvvZZ585/V9VVZSWluKVV15BYmIivvrqq259n7a2NgQHB+PDDz/EokWLHI8vW7YMNTU1+PTTT7u8prW1Fa2tZ0fl6urqkJiYiKqqKkRFRTmuYWuxWJyWJUmCyWRyLJvNZpjNZs1lm80Gi8XiWLbf9aOhoQEhISEwmUyQJMnxuCRJCAgIgKqqjmVFUSDLsmNZURRYrVbNZVmWoaqqY9lVPzzdJ5PJ5NS/8+2TLMtoampCaGgoVFXtUZ9qGluw4/BpZBRUYtvBCpTXO4+6jo4LxezRMZg7Jg5TkwbADMUrffLkdgLgaJO9vXpsJyPuexaLBS0tLbBarY55ar7eJ09up47vLUVR/KJPntxOJpMJbW1tmu8tX+yTp7ZTx/dWYGCgX/TJk9tJkiS0tLQgJCQEiqL4RZ88sZ0aGhr8f0R20aJFTl9LlizBo48+igkTJvRoJLWyshKyLCM+Pt7p8fj4eJSVlbl8zZo1axAREeH4SkxMBADk5uYCAPLy8pCXlwcAyMnJQUFBAQAgOzvbcf3bXbt2oaSkBACQmZmJ0tJSAEBGRgYqKysBAOnp6aipqQEApKWlob6+3vF4S0sLJElCamqq442QmpoKAKivr0daWhoAoKamBunp6Y6+ZmRkAABKS0uRmZkJACgpKcGuXbsAtF+fNzs7G0D7nOOcnByv9Ck1NdXtPpWVlWHv3r3d6pOqqkjN3I+/fvgdfv6PLEx5YgtW/Gsf3v/+OMrrWxFkNeHKsXH49YRgbPxlMjavvByXR5xGUnAbAq1mr/XJk9vp6NGjsFqt2L17t67byaj7HgB89dVXftUnT24ne9v9qU+e3E5WqxVZWVl+1SdPbSdJkhyDS/7SJ09tp6NHj+KHH37wqz55ajt1l8+OyHrKyZMnkZCQgMzMTMyYMcPx+H333Yft27dj586dXV6j54isfadbuHAhAgICDPlJSq9Ph62trfj6669x9dVXw2KxdOlTs6Tim0MV2HaoAhmHKlFW1+K0XUfEhGDumDjMGhWNqcOjERwUqHufPLmdJEnCpk2bMH/+fPTr188v+uSpfU9VVXz11Vf4yU9+gv79+/tFnzy5nTq+t8xms1/0yZPbSZZlfP3115rvLV/sk6e2U8f3VnBwsF/0yZPbqaWlBZs2bXK8t/yhT94ekfXZQvbxxx/HqlWrEBwc7PR4c3Mznn32Waxevbpb3+d8phZ05u2rFth3Op7h6KxzNqqqoqC8AVvz26/ruvtoFaQOlxgICjBj5sgYzElpP1Fr6IBgwXf3fdx3tDEbMeYjxny0MRsx5uNan7hqgcViQWlpaZerCpw+fRpxcXGOar87pk2bhqlTp+Lll18G0H6njaFDh2LFihV44IEHzvl6bxeyLS0tCAoK4k7fiaqqOF3XgD3HG7H9UAW25ZfjZK3zqGtSTAguT47FnJRYTB8xAEEBFp1a633cd7QxGzHmI8Z8tDEbMebjWk/qKquX2uRxqqq63Oj79+9HdHR0j77XypUrsWzZMlx88cWYOnUqXnzxRTQ2NmL58uWeaq7HSJKEtLQ0XH311bx4Mtr3g8KKBmw7WIH0vFPYWXQasnp2v+hnNWP6iAGYmxKLOSlxGB4TomNr9cV9RxuzEWM+YsxHG7MRYz7u87kR2aioKJhMJkeV3rGYlWUZDQ0N+N3vfoe1a9f26Pu+8sorjhsiTJo0CS+99BKmTZvWrdfyOrLe1dQmIavwtONWsMerm52eHxod7Chcp48YgP6BfWfUlYiIyNf59dSCt956C6qq4te//jVefPFFREREOJ4LDAzE8OHDnU7a8gbe2at3qaqKospGbD1YgW0Hy7GzqAptkuJ4PtBixrQR0ZiTHIuLhwRj/LA4x6R5Oqsv7jvdxWzEmI8Y89HGbMSYj2t+PbVg2bJlAICkpCRceumljjPt+gpJkvDNN9/4/X2Zm9tkfHfk9JlbwVaguKrJ6fmEyP6YOyYWc1PiMGPkAAQHWh33rL5gyHwWsi70lX3nfDAbMeYjxny0MRsx5uM+nxuR7aiwsBDr169HYWEh/vu//xtxcXH46quvMHToUFx44YVeawenFnjG0cpGR+H63ZHTaO0w6hpgMWFqUjTmJMdh7phYjIwN5adXIiIiP+TXI7J227dvx8KFC3HppZciIyMDTz75JOLi4rB//3688cYb+PDDD/VuYq9QFAU1NTWIjIz0+VHHFpuMnUVV2Jpfju2HKlBU2ej0/OCIIMwZE4c5ybGYOSoGof3Eu6s/ZdMbmI82ZiPGfMSYjzZmI8Z83OezqT3wwAN44oknsHnzZgQGBjoenzdvHr777jsdW9a7ZFnG7t27e3R5MSMpqWrC21lH8esNuzHp8TQse3MXNmQeRVFlI6xmE6aPiMaDC8cg7e7Z+PaBeXhq8XjMv3DgOYtYwPez6W3MRxuzEWM+YsxHG7MRYz7u89mpBaGhoThw4ACSkpIQFhaG/fv3Y8SIETh69CjGjBnjuOWkN3BqgbZWScauoipsO1iBrQfLcaTCedQ1Prwf5qbEYU5KLC4dFYOwIM4RIiIi6sv6xNSCyMhIlJaWIikpyenx7OxsJCQk6NSq3qcoCiorKxETE2PYwxDHq5uw7cwVBjILT6Op7ewnTYvZhCnDojAnpf1ErTEDPXempi9koyfmo43ZiDEfMeajjdmIMR/3+Wxqv/jFL3D//fejrKwMJpMJiqLg22+/xapVq7B06VK9m9drFEVBbm4uFEU598pe0iYpyDxciSe//BE/eX47LntmKx76JBf/yStHU5uM2LB+uGHKELx6y0XY+/BP8P7tM3DHnFEYOyjcoydsGTEbI2E+2piNGPMRYz7amI0Y83Gfz04taGtrwx/+8Ads2LABsizDarVClmXcfPPN2LBhAywW710Evy9OLThZ0+wYdf32cCUaO4y6mk04M+oah8uTY3HhYM8WrEREROS//PqGCJ0VFxcjNzcXDQ0NmDx5MkaPHu31NnizkFUUBaWlpRg0aJBXD0PYZAXfH63GtkPl2JZfgYOn6p2ejwkNxOVnLo01a1QsIoK9P9dVr2x8BfPRxmzEmI8Y89HGbMSYj2t9Yo6s3dChQzF06FC9m+E1iqKgsLAQ8fHxvb7Tn6prab+ua34Fvj1cifpWyfGcyQRMTozEnJQ4zE2Jw4WDw2E26zvq6s1sfBHz0cZsxJiPGPPRxmzEmI/7fGpEduXKld1e9/nnn+/Fljjzl6kFkqxgb3ENth4sx7aDFcgrrXN6PjokEJcnx2JOSixmj45FVEigxnciIiIiOj9+OyKbnZ3t9P+9e/dCkiSkpKQAAA4dOgSLxYIpU6bo0TyvUBQFJSUlSExM9Mint/K6Fmw7VIHtByuQUVCB+hbnUdcJQyIxNyUWc1LiMCEhQvdRVxFPZ+NvmI82ZiPGfMSYjzZmI8Z83OdThezWrVsdy88//zzCwsLw1ltvISoqCgBQXV2N5cuXY9asWXo1sdcpioITJ04gISHhvHZ6WVGxr6QaW/Pbr+v6w0nnUdfI4ACnUdcBof081fRe5242/o75aGM2YsxHjPloYzZizMd9PjW1oKOEhASkpaXhwgsvdHo8NzcX8+fPx8mTJ73WFqNNLSitbUZRZSOSYkIwKKI/Khtasf3MDQm+KahEbbPNaf0JQyIwJzkWc8bEYeKQSFgMPOpKRERE/s1vpxZ0VFdXh4qKii6PV1RUoL6+3sUr/IMsyygqKkJSUpLLS4xt3F2MBz86AEUFTAASovrjeHWz0zoR/QMwa3QM5qbEYXZyLGLDfGfUVeRc2fR1zEcbsxFjPmLMRxuzEWM+7vPZQnbx4sVYvnw5nnvuOUydOhUAsHPnTtx7771YsmSJzq3rPaqqorq6GsOHD3d6vKqxDZ/tO4FHP//x7LqAo4i9cHC441awkxIjYbX43yEMrWyoHfPRxmzEmI8Y89HGbMSYj/t8dmpBU1MTVq1ahTfffBM2W/uhcqvViltvvRXPPvssQkJCvNYWb04tsE8bGBYdjMqGNscVBvYfr4HWlvyfWy7CwvGDerVdRERERJ7Qp26I0NjYiMLCQgDAyJEjvVrA2nmrkF3/bREe//xHaG2wUXGhKCxvcHreYjJhxwNzMSiif6+1yyhkWUZBQQFGjx7NQzQuMB9tzEaM+YgxH23MRoz5uNYn5sjahYSEYMKECXo3o9eV1ja7LGLnJMdi4fiBuDw5DgMjgrBxdzH+/FEuZFWFxWTCU0vG9Yki1q65ufncK/VhzEcbsxFjPmLMRxuzEWM+7vH5EVkj8MaIbGZhJW7+584uj//rt9MxY+QAp8dKa5txtLIJw2OC+1QRS0RERL6vJ3WV/53x46eSYkLQ+apYFpMJw2OCu6w7KKI/Zowc0OeKWFmWkZubC1mW9W6KITEfbcxGjPmIMR9tzEaM+biPhayPGBTRH2uWjHcUs2YT+ty0ASIiIqKOOLXAA7x91QJOGyAiIiJ/1adO9jIC+2eBurq6c6zpviBFhnTyRwRFj0Ndne3cL+hD7Idoxo0bx7M/XWA+2piNGPMRYz7amI0Y83HNXk91Z6yVhawH2O8klpiYqHNLiIiIiPxDfX09IiIihOtwaoEHKIqCkydPIiwsDCaT6dwvcENdXR0SExNRUlLS69MYfA2zEWM+2piNGPMRYz7amI0Y83FNVVXU19dj8ODBMJvFp3NxRNYDzGYzhgwZ4tWfGR4ezp1eA7MRYz7amI0Y8xFjPtqYjRjz6epcI7F2vGoBEREREfkkFrJERERE5JNYyPqYfv364ZFHHkG/fv30borhMBsx5qON2YgxHzHmo43ZiDEf9/FkLyIiIiLySRyRJSIiIiKfxEKWiIiIiHwSC1kiIiIi8kksZImIiIjIJ7GQJSIiIiKfxEKWiIiIiHwSC1kiIiIi8kksZImIiIjIJ7GQJSIiIiKfxEKWiIiIiHwSC1kiIiIi8kksZImIiIjIJ7GQJSIiIiKfxEKWiIiIiHwSC1kiIiIi8kksZImIiIjIJ7GQJSIiIiKfxEKWiIiIiHwSC1kiIiIi8kksZImIiIjIJ7GQJSIiIiKfxEKWiIiIiHwSC1kiIiIi8kksZImIiIjIJ7GQJSIiIiKfxEKWiIiIiHwSC1kiIiIi8klWvRvgDxRFwcmTJxEWFgaTyaR3c4iIiIh8lqqqqK+vx+DBg2E2i8dcWch6wMmTJ5GYmKh3M4iIiIj8RklJCYYMGSJch4WsB4SFhQFoDzw8PFzn1hARERH5rrq6OiQmJjrqKxGfK2TXrl2LZ599FmVlZZg4cSJefvllTJ06VXP9Dz74AA8//DCOHj2K0aNH45lnnsHVV1/teP6//uu/8NZbbzm9ZsGCBfj666+73Sb7dILw8PBeL2QVRUFlZSViYmLOOdze1zAbMeajjdmIMR8x5qON2YgxH7HuTNf0qdQ2btyIlStX4pFHHsHevXsxceJELFiwAOXl5S7Xz8zMxE033YRbb70V2dnZWLRoERYtWoTc3Fyn9a666iqUlpY6vv71r395ozvnRVEU5ObmQlEUvZtiOMxGjPloYzZizEeM+WhjNmLMx30mVVVVvRvRXdOmTcMll1yCV155BUD7DpCYmIg777wTDzzwQJf1b7zxRjQ2NuKLL75wPDZ9+nRMmjQJ69atA9A+IltTU4NPPvnkvNtVV1eHiIgI1NbWcmoBERERkRt6Ulf5zIhsW1sb9uzZgyuvvNLxmNlsxpVXXomsrCyXr8nKynJaH2ifNtB5/W3btiEuLg4pKSn4/e9/j9OnTwvb0trairq6OqcvAJBl2fGvq2VJkpyW7Z/AtJZtNpvTsqqqUBQFxcXFkGUZqqo6HrcvA3BaVhTFaVmSJOGyLMtOy97oU8dld/okSRKKi4uhKIrf9MmT28lms+HEiRNoa2vzmz55ajvJsozjx4+jtbXVb/rkye3U8b3lL33y5HaSJEn43vLFPnlqO3V8b/lLnzy5nWw2m9N7yx/65Knt1F0+U8hWVlZClmXEx8c7PR4fH4+ysjKXrykrKzvn+ldddRXefvttbNmyBc888wy2b9+OhQsXOkJ1Zc2aNYiIiHB82a9YYJ+ykJeXh7y8PABATk4OCgoKAADZ2dkoKioCAOzatQslJSUA2qdAlJaWAgAyMjJQWVkJAEhPT0dNTQ0AIC0tDfX19VAUBdnZ2WhqaoIkSUhNTYUkSWhpaUFqaioAoL6+HmlpaQCAmpoapKenOzLMyMgAAJSWliIzMxNA+0lqu3btAgAUFRUhOzsbAFBQUICcnJxe7xMApKamoqWlxe0+5eTkQFEUv+qTJ7dTYWEhdu/e7Vd98sR2ampqQmFhIb7++mu/6ZMnt1NxcTEOHDgARVH8pk+e3E7FxcUoLCxEVlaW3/TJU9upra0Nhw8fdpx34g998vR2sk8t8Kc+eWI7dZfPTC04efIkEhISkJmZiRkzZjgev++++7B9+3bs3Lmzy2sCAwPx1ltv4aabbnI89uqrr+Kxxx7DqVOnXP6cI0eOYOTIkfjPf/6DK664wuU6ra2tjk+XwNmz66qqqhAVFeUogi0Wi9OyJEkwmUyOZbPZDLPZrLlss9lgsVgcy1arFSaTybEMtH966bgcEBAAVVUdy/ZPefZlRVFgtVo1l+0jvfZlV/1gn9gn9ol9Yp/YJ/aJfeqtPjU0NHR7aoHPXLUgJiYGFoulSwF66tQpDBw40OVrBg4c2KP1AWDEiBGIiYnB4cOHNQvZfv36oV+/fl0et1gsTv92XrbvKN1dDggI6LKsKIrjurVms9nlOiaTybFs35m7u6zV9t7sU3eWu9MnADhx4oQjG3/okye3k6IoOHbsmCMff+hTT5ZFbbeP4icmJjrOkvX1PomWe9on4Ox7y1/65MntdK73li/26VzL3e1Hx/eWv/Sp87I7fTKZTDh+/Hi331u+0CdPbafu8pmpBYGBgZgyZQq2bNnieExRFGzZssVphLajGTNmOK0PAJs3b9ZcHwCOHz+O06dPY9CgQZ5puIcpioITJ070eA5JX8BsxJiPNmYjxnzEmI82ZiPGfNznM1MLgPbLby1btgz/+Mc/MHXqVLz44ot4//33kZ+fj/j4eCxduhQJCQlYs2YNgPY5I5dffjmefvppXHPNNXjvvffw1FNPYe/evRg3bhwaGhrw2GOP4Wc/+xkGDhyIwsJC3Hfffaivr8eBAwdcjrq6wqsWEBEREXmGX161AGi/nNbf//53rF69GpMmTcK+ffvw9ddfO07oKi4udkx2BoCZM2fi3XffxWuvvYaJEyfiww8/xCeffIJx48YBaB/azsnJwU9/+lMkJyfj1ltvxZQpU/DNN990u4j1NlmWcfjwYeHJaH0VsxFjPtqYjRjzEWM+2piNGPNxn8/MkbVbsWIFVqxY4fK5bdu2dXnshhtuwA033OBy/f79+2PTpk2ebF6vU1UV1dXVGD58uN5NMRxmI8Z8tDEbMeYjxny0MRsx5uM+n5paYFScWkBERETkGX47tYDaD0Pk5+fzMIQLzEaM+WhjNmLMR4z5aGM2YszHfSxkfVBzc7PeTTAsZiPGfLQxGzHmI8Z8tDEbMebjHk4t8ABOLSAiIiLyDE4t8GOyLCM3N5eHIVxgNmLMRxuzEWM+YsxHG7MRYz7uYyFLRERERD6JUws8gFMLiIiIiDyDUwv8mCzLyM7O5mEIF5iNGPPRxmzEmI8Y89HGbMSYj/tYyPqg/v37690Ew2I2YsxHG7MRYz5izEcbsxFjPu7h1AIP4NQCIiIiIs/g1AI/JkkSdu/eDUmS9G6K4TAbMeajjdmIMR8x5qON2YgxH/exkPUxJpMJUVFRMJlMejfFcJiNGPPRxmzEmI8Y89HGbMSYj/u6NbXgs88+6/E3/slPftJn5n1wagERERGRZ/SkrrJ25xsuWrSoRw0wmUwoKCjAiBEjevQ6OjdJkrBr1y5MnToVVmu3Nl+fwWzEmI82ZiPGfMSYjzZmI8Z83NftqQVlZWVQFKVbX8HBwb3Z5j7NbDYjISEBZjNnhXTGbMSYjzZmI8Z8xJiPNmYjxnzc163yf9myZT2aJvDLX/6Sh9h7idlsxrBhw/RuhiExGzHmo43ZiDEfMeajjdmIMR/3desjwPr16xEWFtbtb/o///M/iImJOe9GkTZJkpCRkcEzHF1gNmLMRxuzEWM+YsxHG7MRYz7u41i2jzGbzRg5ciQPQ7jAbMSYjzZmI8Z8xJiPNmYjxnzc162rFixZsqTb3/Cjjz5yq0G+iFctICIiIvIMj98QISIiwvEVHh6OLVu24Pvvv3c8v2fPHmzZsgURERHutZzOSZIkpKen8zCEC8xGjPloYzZizEeM+WhjNmLMx33dOtlr/fr1juX7778fP//5z7Fu3TpYLBYAgCzLuOOOOzga6QVmsxnjxo3jYQgXmI0Y89HGbMSYjxjz0cZsxJiP+7o1taCj2NhY7NixAykpKU6PHzx4EDNnzsTp06c92kBfwKkFRERERJ7h8akFHUmShPz8/C6P5+fnQ1GUnn476iGbzYZNmzbBZrPp3RTDYTZizEcbsxFjPmLMRxuzEWM+7uvxbSSWL1+OW2+9FYWFhZg6dSoAYOfOnXj66aexfPlyjzeQnFksFlxyySWOaR10FrMRYz7amI0Y8xFjPtqYjRjzcV+PpxYoioK///3v+O///m+UlpYCAAYNGoQ//elPuOeee/rkxuDUAiIiIiLP6NWpBWazGffddx9OnDiBmpoa1NTU4MSJE7jvvvv6ZBHrbTabDV9++SUPQ7jAbMSYjzZmI8Z8xJiPNmYjxnzc1+MRWerKmyOyqqqivr4eYWFhMJlMvfqzfA2zEWM+2piNGPMRYz7amI0Y83GtJ3XVeRWyH374Id5//30UFxejra3N6bm9e/f29Nv5PE4tICIiIvKMXp1a8NJLL2H58uWIj49HdnY2pk6digEDBuDIkSNYuHDheTeausdms+HTTz/lYQgXmI0Y89HGbMSYjxjz0cZsxJiP+3o8IjtmzBg88sgjuOmmmxAWFob9+/djxIgRWL16NaqqqvDKK6/0VlsNy9tTC1paWhAUFMTDEJ0wGzHmo43ZiDEfMeajjdmIMR/XenVEtri4GDNnzgQA9O/fH/X19QCAX/3qV/jXv/51Hs2lnrJae3zVtD6D2YgxH23MRoz5iDEfbcxGjPm4p8eF7MCBA1FVVQUAGDp0KL777jsAQFFREXjeWO+TJAmpqam8L7MLzEaM+WhjNmLMR4z5aGM2YszHfT2eWvCb3/wGiYmJeOSRR7B27Vrce++9uPTSS/H9999jyZIleOONN3qrrYbl7akFkiTBarXyMEQnzEaM+WhjNmLMR4z5aGM2YszHtZ7UVT0ez37ttdcct6L9wx/+gAEDBiAzMxM//elPcfvtt59fi6lH7Ds9dcVsxJiPNmYjxnzEmI82ZiPGfNzTo6kFkiThiSeeQFlZmeOxX/ziF3jppZdw5513IjAw0OMNJGeSJCEtLY2HIVxgNmLMRxuzEWM+YsxHG7MRYz7u6/HUgtDQUOTm5mL48OG91CTfw+vIEhEREXlGr1614IorrsD27dvPu3HkHlVVUVdXxxPrXGA2YsxHG7MRYz5izEcbsxFjPu7rcSG7cOFCPPDAA1i1ahX+9a9/4bPPPnP6ot4lSRK++eYbHoZwgdmIMR9tzEaM+YgxH23MRoz5uK/HUwvMZu3a12QyQZZltxvlazi1gIiIiMgzenVqgaIoml99sYj1NkVRUFVV5bhyBJ3FbMSYjzZmI8Z8xJiPNmYjxnzc1+NClvQlyzJ2797NDw0uMBsx5qON2YgxHzHmo43ZiDEf93VrasFLL72E2267DUFBQd36puvWrcMtt9yCsLAwtxvoCzi1gIiIiMgzPD614O6770Z9fX23G3DfffehoqKi2+tT9ymKgvLych6GcIHZiDEfbcxGjPmIMR9tzEaM+bivW4Wsqqq44oorcNFFF3Xrq7m5ubfb3WcpioLc3Fzu9C4wGzHmo43ZiDEfMeajjdmIMR/3dWtqwWOPPdbjb/ynP/0JkZGR59Mmn8OpBURERESe0ZO6qseX36KuvFnIKoqC0tJSDBo0SHgptL6I2YgxH23MRoz5iDEfbcxGjPm41quX39Lb2rVrMXz4cAQFBWHatGnYtWuXcP0PPvgAY8aMQVBQEMaPH4/U1FSn51VVxerVqzFo0CD0798fV155JQoKCnqzC25RFAWFhYU8DOECsxFjPtqYjRjzEWM+2piNGPNxn0+NyG7cuBFLly7FunXrMG3aNLz44ov44IMPcPDgQcTFxXVZPzMzE7Nnz8aaNWtw7bXX4t1338UzzzyDvXv3Yty4cQCAZ555BmvWrMFbb72FpKQkPPzwwzhw4AB+/PHHbl+lgVMLiIiIiDzDb6cWTJs2DZdccgleeeUVAO2fZBITE3HnnXfigQce6LL+jTfeiMbGRnzxxReOx6ZPn45JkyZh3bp1UFUVgwcPxj333INVq1YBAGpraxEfH48NGzbgF7/4Rbfa5c1C9kR1I3blHcXUscOREBXicp3S2mYUVTYiKSYEgyL692p7jERRFJSUlCAxMZGHaFxgPtqYjRjzETNKPt353e/tvw9GycaofCkfb+47PamrrL3aEg9qa2vDnj178OCDDzoeM5vNuPLKK5GVleXyNVlZWVi5cqXTYwsWLMAnn3wCACgqKkJZWRmuvPJKx/MRERGYNm0asrKyul3Iest7u4rx548PQFEB8+dH8dhPL8TPpgxxWuffe47jkc9+aF/HBJfr+CtJklB47DiiYuNhtfrMru01zEcbsxFjPmJGyKc7v/v1+PtghGyMzFfy6bzvrFkyHjdeMlTvZgFwY0S2ra0NRUVFGDlypFfCP3nyJBISEpCZmYkZM2Y4Hr/vvvuwfft27Ny5s8trAgMD8dZbb+Gmm25yPPbqq6/isccew6lTp5CZmYlLL70UJ0+exKBBgxzr/PznP4fJZMLGjRtdtqW1tRWtra2O/9fV1SExMRFVVVWIiopy3KHDYrE4LUuSBJPJ5Fg2m80wm82ayzabDRaLBWazGcWV9ZjzXAYUnxk/JyIiIn9kMZmQcd/liA/rB6vVCkVRoCgKrFYrZFmGqqqOZaBrPXSu2qihoaH3TvZqamrCrbfeiuDgYFx44YUoLi4GANx55514+umne/rtfNKaNWsQERHh+EpMTAQA5ObmAgDy8vKQl5cHAMjJyXGcPJadnY2ioiIAwK5du1BSUgKgfS5vaWkpACAjIwOVlZUAgPT0dNTU1AAA/r2JRSwRERHpT1ZV7D1UgszMTABASUmJ4+T7oqIiZGdnAwAKCgqQk5MDoOe1UXf1eCj1wQcfxP79+7Ft2zZcddVVjsevvPJKPProoy7nqnpCTEwMLBYLTp065fT4qVOnMHDgQJevGThwoHB9+7+nTp1yGpE9deoUJk2apNmWBx980GnKgn1E1n4C2dixYx3PTZgwwbE8efJkmEwmAMDUqVMd82FmzpzpWJ49e7Zjed68ebBYLACAny2YjZdznYtZswn4+o8zkRAdCgA4UdWAq17KdLnOkAFhTp+YtJY98Umqu6PMNpsNVqsVJpPJsQy0H2rpuBwQEABVVR3LiqJAlmXHsr3tbW027N+/H5MnT4LZbPaLPnlyO8ly+4W3L7zwQgQGBvhFnzy1nQBg//4cXHjhhQgK6ucXffLkdur43jKZTH7RJ09uJ0VRceDAAc33Vm/36WRNE67672+7/u7/06UYEh0KWZZRVteCBS/u6LLOprsuQ0JUSK9tp47vrf79g/h+6rTc2tqGnJwcx3vLiH06Wd2E+S9+47TvWEwmXJSciPiwUQCAxMREJCQkAACSkpIwfPhwAMDo0aMdr+lJbdTQ0IDu6vHUgmHDhmHjxo2YPn06wsLCsH//fowYMQKHDx/GRRddhLq6up58ux6ZNm0apk6dipdffhlA+yTpoUOHYsWKFZonezU1NeHzzz93PDZz5kxMmDDB6WSvVatW4Z577gHQXpTGxcUZ8mSvjbuL8eePciGrKiwmE55aMq7LHJXurENERP6Ffx+oN3l73+lRXaX2UP/+/dXCwkJVVVU1NDTUsbxv3z41PDy8p9+uR9577z21X79+6oYNG9Qff/xRve2229TIyEi1rKxMVVVV/dWvfqU+8MADjvW//fZb1Wq1qn//+9/VvLw89ZFHHlEDAgLUAwcOONZ5+umn1cjISPXTTz9Vc3Jy1Ouvv15NSkpSm5ubu92u2tpaFYBaW1vruc5qKDndoL6XvlctOd2guc7JmiY183ClerKmqdfbYySSJKl5eXmqJEl6N8WQmI82ZiPGfMSMkk93fvd7+++DUbIxKl/Kx5v7Tk/qqh5PLbj44ovx5Zdf4s477wQAx3Dw66+/7nQSVm+48cYbUVFRgdWrV6OsrAyTJk3C119/jfj4eABAcXGx0+UrZs6ciXfffRcPPfQQ/vznP2P06NH45JNPHFMAgPaTxRobG3HbbbehpqYGl112Gb7++utuX0PW2wZFBCE5sv1f7XX696nLbnXU3NysdxMMjfloYzZizEfMCPl053e/Hn8fjJCNkflKPkatLXo8tWDHjh1YuHAhfvnLX2LDhg24/fbb8eOPPyIzMxPbt2/HlClTequthsUbIhARERF5Rq/eovayyy7Dvn37IEkSxo8fj7S0NMTFxSErK6tPFrHeJssycnNzHZO/6SxmI8Z8tDEbMeYjxny0MRsx5uO+87oA7MiRI/HPf/7T020hIiIiIuq2Hk8t2Lt3LwICAjB+/HgAwKeffor169fjggsuwKOPPorAwMBeaaiRcWoBERERkWf06tSC22+/HYcOHQIAHDlyBDfeeCOCg4PxwQcf4L777ju/FlO3ybKM7OxsHoZwgdmIMR9tzEaM+YgxH23MRoz5uK/HheyhQ4ccNwv44IMPcPnll+Pdd9/Fhg0b8O9//9vT7SMX+vc33lmDRsFsxJiPNmYjxnzEmI82ZiPGfNzT4zmyqqpCURQAwH/+8x9ce+21ANrv6mC/tSr1HovFgjFjxujdDENiNmLMRxuzEWM+YsxHG7MRYz7u6/GI7MUXX4wnnngC//u//4vt27fjmmuuAdB+b1379Vyp90iShN27dztu/UdnMRsx5qON2YgxHzHmo43ZiDEf9/W4kH3xxRexd+9erFixAn/5y18walT7fXY//PBDzJw50+MNJGcmkwlRUVGOG1HQWcxGjPloYzZizEeM+WhjNmLMx309vmqBlpaWFlgsFgQEBHji2/kUXrWAiIiIyDN69aoFWoKCgvpkEettkiQhMzOThyFcYDZizEcbsxFjPmLMRxuzEWM+7uvxyV6yLOOFF17A+++/j+LiYrS1tTk9X1VV5bHGUVdmsxkJCQkwmz32GcRvMBsx5qON2YgxHzHmo43ZiDEf9/U4ucceewzPP/88brzxRtTW1mLlypVYsmQJzGYzHn300V5oInVkNpsxbNgw7vQuMBsx5qON2YgxHzHmo43ZiDEf9/U4uXfeeQf//Oc/cc8998BqteKmm27C66+/jtWrV+O7777rjTZSB5IkISMjg4chXGA2YsxHG7MRYz5izEcbsxFjPu7rcSFbVlbmuD1taGgoamtrAQDXXnstvvzyS8+2jrowm80YOXIkP725wGzEmI82ZiPGfMSYjzZmI8Z83Nfj5IYMGYLS0lIAwMiRI5GWlgYA2L17N/r16+fZ1lEXnE+jjdmIMR9tzEaM+YgxH23MRoz5uK/HyS1evBhbtmwBANx55514+OGHMXr0aCxduhS//vWvPd5AciZJEtLT03kYwgVmI8Z8tDEbMeYjxny0MRsx5uM+t68jm5WVhaysLIwePRrXXXedp9rlU7x5HVlFUVBZWYmYmBh+guuE2YgxH23MRoz5iDEfbcxGjPm41pO6ymM3ROjLeEMEIiIiIs/oSV3V4+vIAkBBQQG2bt2K8vJyKIri9Nzq1avP51tSN9lsNqSnp2PevHm8AUUnzEaM+WhjNmLMR4z5aGM2YszHfT0ekf3nP/+J3//+94iJicHAgQOd7g9sMpmwd+9ejzfS6Lw9taCmpgaRkZE8DNEJsxFjPtqYjRjzEWM+2piNGPNxrVenFgwbNgx33HEH7r//frca6U84tYCIiIjIM3pSV/W4/K+ursYNN9xw3o0j99hsNnz55Zew2Wx6N8VwmI0Y89HGbMSYjxjz0cZsxJiP+3o8Invrrbfikksuwe9+97veapPP8eaIrKqqqK+vR1hYmNO0DmI258J8tDEbMeYjxny0MRsx5uOax6cWvPTSS47lxsZGPP/887jmmmswfvz4LpOT//jHP55ns30XpxYQEREReYbHC9mkpKRu/WCTyYQjR450r5V+xJuFrM1mQ2pqKq6++mqe4dgJsxFjPtqYjRjzEWM+2piNGPNxjdeR9TJvTy1oaWlBUFAQD0N0wmzEmI82ZiPGfMSYjzZmI8Z8XOvVk706UlUVrIO9z2o9r8v/9gnMRoz5aGM2YsxHjPloYzZizMc951XIvvHGGxg3bhyCgoIQFBSEcePG4fXXX/d028gFSZKQmprK+zK7wGzEmI82ZiPGfMSYjzZmI8Z83NfjqQWrV6/G888/jzvvvBMzZswAAGRlZeGVV17B3Xffjccff7xXGmpk3p5aIEkSrFYrD0N0wmzEmI82ZiPGfMSYjzZmI8Z8XOvVObKxsbF46aWXcNNNNzk9/q9//Qt33nknKisre95iH8c5ssbAbMSYjzZmI8Z8xJiPNmYjxnxc69U5sjabDRdffHGXx6dMmcKhcS+QJAlpaWnM2gVmI8Z8tDEbMeYjxny0MRsx5uO+Ho/I3nnnnQgICMDzzz/v9PiqVavQ3NyMtWvXerSBvoDXkSUiIiLyjJ7UVed1qtwbb7yBtLQ0TJ8+HQCwc+dOFBcXY+nSpVi5cqVjvc7FLrmPdwHRxmzEmI82ZiPGfMSYjzZmI8Z83NfjqQW5ubm46KKLEBsbi8LCQhQWFiImJgYXXXQRcnNzkZ2djezsbOzbt68XmkuSJOGbb77hYQgXmI0Y89HGbMSYjxjz0cZsxJiP+3hDBA/g1AIiIiIiz/DaDRHI+xRFQVVVFRRF0bsphsNsxJiPNmYjxnzEmI82ZiPGfNzHQtbHyLKM3bt3Q5ZlvZtiOMxGjPloYzZizEeM+WhjNmLMx32cWuABnFpARERE5BmcWuDHFEVBeXk5D0O4wGzEmI82ZiPGfMSYjzZmI8Z83MdC1scoioLc3Fzu9C4wGzHmo43ZiDEfMeajjdmIMR/3cWqBB3BqAREREZFncGqBH1MUBSdOnOCnNxeYjRjz0cZsxJiPGPPRxmzEmI/7WMj6GEVRUFhYyJ3eBWYjxny0MRsx5iPGfLQxGzHm4z5OLfAATi0gIiIi8gxOLfBjiqLg2LFj/PTmArMRYz7amI0Y8xFjPtqYjRjzcR8LWR/D+TTamI0Y89HGbMSYjxjz0cZsxJiP+zi1wAM4tYCIiIjIM/xyakFVVRVuueUWhIeHIzIyErfeeisaGhqEr2lpacEf/vAHDBgwAKGhofjZz36GU6dOOa1jMpm6fL333nu92RW3yLKMw4cP83Z2LjAbMeajjdmIMR8x5qON2YgxH/f5TCF7yy234IcffsDmzZvxxRdfICMjA7fddpvwNXfffTc+//xzfPDBB9i+fTtOnjyJJUuWdFlv/fr1KC0tdXwtWrSol3rhPlVVUV1dDQ6kd8VsxJiPNmYjxnzEmI82ZiPGfNznE1ML8vLycMEFF2D37t24+OKLAQBff/01rr76ahw/fhyDBw/u8pra2lrExsbi3Xffxf/7f/8PAJCfn4+xY8ciKysL06dPB9A+Ivvxxx+7VbxyagERERGRZ/jd1IKsrCxERkY6ilgAuPLKK2E2m7Fz506Xr9mzZw9sNhuuvPJKx2NjxozB0KFDkZWV5bTuH/7wB8TExGDq1Kl48803z/nJqLW1FXV1dU5fAByHBmRZdrksSZLTsn1yt9ayzWZzWlZVFbIs44cffoAkSVBV1fG4fRmA07KiKE7LkiQJl2VZdlr2Rp86LrvTJ5vNhh9//BGyLPtNnzy5ndra2pCfn4/W1la/6ZOntpMkScjLy0NLS4vf9MmT26nje8tf+uTJ7WSz2YTvLV/sk6e2U8f3lr/0yZPbqa2tzem95Q998tR26i6fKGTLysoQFxfn9JjVakV0dDTKyso0XxMYGIjIyEinx+Pj451e8/jjj+P999/H5s2b8bOf/Qx33HEHXn75ZWF71qxZg4iICMdXYmIiACA3NxdA+whyXl4eACAnJwcFBQUAgOzsbBQVFQEAdu3ahZKSEgBAZmYmSktLAQAZGRmorKwEAKSnp6OmpgYAkJaWhvr6egDA4cOH0dLSAkmSkJqaCkmS0NLSgtTUVABAfX090tLSAAA1NTVIT08HAFRWViIjIwMAUFpaiszMTABASUkJdu3aBQAoKipCdnY2AKCgoAA5OTle6VNqaqrbfSorK8OxY8f8qk+e3E7Hjh1Dc3Mz9uzZ4zd98uR2ampqwqZNm/yqT57aTsePH3e0xV/65MntdPz4cTQ3N+O7777zmz55cjs1NDRg06ZNftUnT22nY8eO4fjx437VJ09tp25TdXT//ferAIRfeXl56pNPPqkmJyd3eX1sbKz66quvuvze77zzjhoYGNjl8UsuuUS97777NNv08MMPq0OGDBG2u6WlRa2trXV8lZSUqADUqqoqVVVVVZIkVZKkLss2m81pWZZl4XJbW5vTsqIoTsuKonRZVlXVaVmWZadlm80mXJYkyWnZVT/YJ/aJfWKf2Cf2iX1in3qrT7W1tSoAtba2Vj0XXefIVlRU4PTp08J1RowYgf/7v//DPffcg+rqasfjkiQhKCgIH3zwARYvXtzldenp6bjiiitQXV3tNCo7bNgw3HXXXbj77rtd/rwvv/wS1157LVpaWtCvX79u9cObc2RlWUZeXh7Gjh0Li8XSqz/L1zAbMeajjdmIMR8x5qON2YgxH9d6UldZvdQml2JjYxEbG3vO9WbMmIGamhrs2bMHU6ZMAdBeqCqKgmnTprl8zZQpUxAQEIAtW7bgZz/7GQDg4MGDKC4uxowZMzR/1r59+xAVFdXtIpaIiIiI9OETVy0AgIULF+LUqVNYt24dbDYbli9fjosvvhjvvvsuAODEiRO44oor8Pbbb2Pq1KkAgN///vdITU3Fhg0bEB4ejjvvvBMAHHM6Pv/8c5w6dQrTp09HUFAQNm/ejFWrVmHVqlV47LHHut02XrWAiIiIyDN8ZkS2J9555x2sWLECV1xxBcxmM372s5/hpZdecjxvs9lw8OBBNDU1OR574YUXHOu2trZiwYIFePXVVx3PBwQEYO3atbj77ruhqipGjRqF559/Hr/97W971Db7ZwH71Qt6kyzLyM3Nxbhx43gYohNmI8Z8tDEbMeYjxny0MRsx5uOavZ7qzlirz4zIGtnx48cdVy4gIiIiIveVlJRgyJAhwnVYyHqAoig4efIkwsLCYDKZevVn1dXVITExESUlJZzG0AmzEWM+2piNGPMRYz7amI0Y83FNVVXU19dj8ODBMJvFV4r1makFRmY2m8/5icHTwsPDudNrYDZizEcbsxFjPmLMRxuzEWM+XUVERHRrPZ+4IQIRERERUWcsZImIiIjIJ7GQ9TH9+vXDI488wuvcusBsxJiPNmYjxnzEmI82ZiPGfNzHk72IiIiIyCdxRJaIiIiIfBILWSIiIiLySSxkiYiIiMgnsZAlIiIiIp/EQpaIiIiIfBILWSIiIiLySSxkiYiIiMgnsZAlIiIiIp/EQpaIiIiIfBILWSIiIiLySSxkiYiIiMgnsZAlIiIiIp/EQpaIiIiIfBILWSIiIiLySSxkPSgjIwPXXXcdBg8eDJPJhE8++aRHr3/00UdhMpm6fIWEhPROg4mIiIh8GAtZD2psbMTEiROxdu3a83r9qlWrUFpa6vR1wQUX4IYbbvBwS4mIiIh8HwtZD1q4cCGeeOIJLF682OXzra2tWLVqFRISEhASEoJp06Zh27ZtjudDQ0MxcOBAx9epU6fw448/4tZbb/VSD4iIiIh8BwtZL1qxYgWysrLw3nvvIScnBzfccAOuuuoqFBQUuFz/9ddfR3JyMmbNmuXllhIREREZHwtZLykuLsb69evxwQcfYNasWRg5ciRWrVqFyy67DOvXr++yfktLC9555x2OxhIRERFpsOrdgL7iwIEDkGUZycnJTo+3trZiwIABXdb/+OOPUV9fj2XLlnmriUREREQ+hYWslzQ0NMBisWDPnj2wWCxOz4WGhnZZ//XXX8e1116L+Ph4bzWRiIiIyKewkPWSyZMnQ5ZllJeXn3POa1FREbZu3YrPPvvMS60jIiIi8j0sZD2ooaEBhw8fdvy/qKgI+/btQ3R0NJKTk3HLLbdg6dKleO655zB58mRUVFRgy5YtmDBhAq655hrH6958800MGjQICxcu1KMbRERERD7BpKqqqncj/MW2bdswd+7cLo8vW7YMGzZsgM1mwxNPPIG3334bJ06cQExMDKZPn47HHnsM48ePBwAoioJhw4Zh6dKlePLJJ73dBSIiIiKfwUKWiIiIiHwSL79FRERERD6JhSwRERER+SSe7OUBiqLg5MmTCAsLg8lk0rs5RERERD5LVVXU19dj8ODBMJvFY64sZD3g5MmTSExM1LsZRERERH6jpKQEQ4YMEa7DQvaMtWvX4tlnn0VZWRkmTpyIl19+GVOnTu3Wa8PCwgC0Bx4eHt6bzYTNZkNaWhrmz5+PgICAXv1ZvobZiDEfbcxGjPmIMR9tzEaM+bhWV1eHxMRER30lwkIWwMaNG7Fy5UqsW7cO06ZNw4svvogFCxbg4MGDiIuLO+fr7dMJwsPDvVLIBgcHIzw8nDt9J8xGjPloYzZizEeM+WhjNmLMR6w70zV5sheA559/Hr/97W+xfPlyXHDBBVi3bh2Cg4Px5ptv6t20LkprW1BQa0JpbYveTSEiIqI+orS2GZn/v707j4uq3P8A/jkzzDAMOwy77KvgAqIimAKmkXkt9ZrmFta9lmWZS/7SFpfqlm3X1MxsUcsstUyzRNMUcNdAQRQB2RGBGfYdhpnn9wc6txEYAYEZ4Pt+vXjVnDnLd76eOfOdZ57zPBnFKKio03Yoavp9i2xjYyPi4+OxatUq1TIej4fx48fj/PnzWoyspd0XcvDmwWtg4OPzG6fw/rTBmDnCSdthEUIIIaQP2/tXLlb+kgTGAB4Hnao/+n0hW1xcDIVCARsbG7XlNjY2SElJaXWbhoYGNDQ0qB5XVlYCaP6JQC6Xd0ucBRX1ePPXa7g7e4WSASv3J8HRTB8jXCy65Zi9zd3cd9e/QW9H+Wkb5UYzyo9mlJ+2UW406w35KSivw8r9SWr1x6pfkhDsag47U1G3HLMj+ej3hWxnvP/++1i3bl2L5ceOHYNYLO6WY96s4MAYX20ZAzD7mzhIRAy+ZgwDzRg8TBiE/Nb30V8cP35c2yGocBwHPl93/kH09PQQHR2t7TB0EuVGM8qPZpSftlFuNNPl/MgVwM9ZPNgbt/wc+/3P03A27tzksAqFApomlq2trW33vvr9FLWNjY0Qi8X4+eefMWXKFNXyyMhIlJeX49dff22xTWstso6OjiguLu62m70KKuoR9skpKO/519LjAU3K/z3W1+NhlJsFQj0lCPWSwMmiewprXSSXy3H8+HFMmDBB653mGWOQSqWq1npdwBhDfX09RCIRjXd8D8qNZpQfzSg/baPcaKbL+VEoGUprGtGoaFkmcgBsTPTB53U+ZhMTE1hbW7f6uisrKyGRSFBRUXHfuqrft8gKhUIEBgbixIkTqkJWqVTixIkTeOmll1rdRl9fH/r6+i2WCwSCbiugnCQCvD9tMFb9kgTl3/qoTBpij7PpxYhJlSImVYaCinrEphUjNq0YOAy4SQwR5m2NMG8rjHS1gEigO62D3aU7/x3aq6CgAFVVVbCxsYFYLNaJC5RSqUR1dTWMjIzuO8B0f0O50Yzyoxnlp22UG810NT81jU0oKK+HmZESfB4HE5EA5bVyMDBw4GBtog8zsbBT+2aMoba2FlKpFHw+H3Z2di3W6chneL8vZAFg2bJliIyMxPDhwzFy5Eh8+umnqKmpwTPPPKPt0NTMHOGEYFdz7IuKxozHwuEkaR5fLcLPFhF+tmCMIbWoCjGpMkSnSBGfU4bM4hpkFmdh+9ksGAj4CHG3RJi3FcK8reHYj1pre5JCoUB5eTmsra1haWmp7XBUlEolGhsbIRKJdOqCqQsoN5pRfjSj/LSNcqOZruWHMYaSmkYUVCrAeHoQ6/PhbCmGUI8P2yYlGpuUEOrxINR7sFgNDAwAAFKpFNbW1g/UBY8KWQAzZ86ETCbD6tWrUVhYCH9/fxw9erTFDWC6wM5UBE9T1moHa47j4GNrAh9bEywMdUdlvRxnbxY3F7apUkirGnAiRYoTKVIA1+FhbYQwLyuE+1hjuIs59PX6fmttT7jbSb27+ksTQgghXU2pZLhdXofS2kYAgJmBEAPMDcC7032gKwrYv7v7GSmXy6mQ7QovvfRSm10JeisTkQATB9th4mA7MMZwo6AK0alSxKbKEJ9bhnRpNdKl1fj6TBbEQj5Ge0hUrbUOZgbaDr/X04XuBIQQQsj9yJuUyCmtRW1jEzgAtqYiSIz0u/VzrKv2TYVsP8FxHHztTeBrb4JF4R6oqJPjzM3i5sI2TQZZVQOOJxfheHIRAMDLxgjh3tYI9bbCcGeLLv0WRgghhBDdUNPQhJzSWjQpmvvDOlmIYSzqPbOMUXXST5kaCDBpiB0+fnIoLq56GL+//BBefcQLgc7m4HFAWlE1tp3KxOyvLmLYO8fx/K447LmUi0KaUYz0IWvXrlUNkbZ161Zth0MIIT2qpLoBmcU1aFIoIRLw4WFt1CVF7M6dO8FxHDiOw5IlSx48UA2okCXg8TgMcjDFS+M8sf+FEFx+awI2zQrAtGEOsDQUorqhCX9cL8LKX5Iw6v0TePTTU1h/JAUXM0sgVyjvfwDSr8TExIDjOJSXl6stDwsL6/YLWmf4+fkhPz8fkZGRqmX19fVYtGgRLC0tYWRkhH/+858oKirSuJ+7F+17/z766KMW6zY0NMDf3x8cxyEhIaHDMf/000/w8fGBSCTC4MGDERUVdd9tdu/ejaFDh0IsFsPOzg7PPvssSkpKVM+HhYW1Gv+kSZM6FFtpaSnmzJkDExMTmJmZ4V//+heqq6s1bnO/fP/9Q/HeP6lU2qH4tmzZAhcXF4hEIgQFBeHSpUv33eZ++X7mmWdgbm4OPp+viuvRRx/tUFwAcPXqVYwZMwYikQiOjo748MMPNa7fnrzMnz+/1ef9/Pw6FFtn3hPV1dV4+eWX4efnB0NDQ9UU8B2Vm5uLSZMmQSwWw9raGitWrEBTU5PGbS5fvowJEybAzMwMlpaWeO6551qch63lZc+ePR2O70HOKbFYjJCQEI3v4YULF4LjOHz66acdjq2tc0rJGG6V1SK/vA6MMZgaCOBuZQR9PT5OnDiBkJAQGBsbw9bWFq+99lqLfO/btw/+/v4Qi8VwdnZucZ2bOXMmCgoKEBwc3OGYO4yRB1ZRUcEAsIqKim4/VmNjIzt48CBrbGzs9mMxxphCoWSJeWXs0+NpbMqWM8xl5e/M+bX//Q1afZS98H0c23splxVW1PVITG3p6dy0pa6ujiUnJ7O6Ou3m414KhYKVlZUxhULRrceJjo5mAFhZWZna8tDQUPbKK6888P4bGhoeeB93rVmzhg0dOrRFbhYuXMgcHR3ZiRMnWFxcHBs1ahQLCQnRuK+CggK1v+3btzOO41hGRkaLdRcvXswmTpzIALArV650KOazZ88yPp/PPvzwQ5acnMzefPNNJhAIWFJSUpvbnDlzhvF4PLZx40aWmZnJTp8+zfz8/NjUqVNV65SUlKjFf+3aNcbn89mOHTs6dO48+uijbOjQoezChQvs9OnTzMPDg82aNUvjNvfLd21tbYv8RkREsNDQ0Psn7G/27NnDhEIh2759O7t+/TpbsGABMzMzY0VFRW1u0558P/300+zhhx9m+fn5qvhKS0s7FFtFRQWzsbFhc+bMYdeuXWM//vgjMzAwYNu2bWtzm/bkpby8XO35vLw8ZmFhwdasWdOh+DrznliwYAFzd3dnv/32G8vIyGDbtm1jfD6f/frrr+0+blNTExs0aBAbP348u3LlCouKimISiYStWrWqzW3y8/OZubk5W7hwIUtJSWGXLl1iISEh7J///KfaegDYjh071PLT0ev2g55T165dY6+++mqb7+FffvmFDR06lNnb27MNGzZ0KLa2zqnPt25lN4uqWGJeGUvMK2NFFXVMqVQyxhhLSEhgQqGQrVu3jt28eZPFxMQwHx8ftnz5ctV+o6KimJ6eHtu6dSvLyMhgv//+O7Ozs2ObN29uEYOm676mz8qO1FVUyHaBvlzI3qukuoEdvHKLvfLjZRbw9jG1otb5td/ZxE9PsQ+P3mCXskqYvKl7C6Z7aTs3d3V1IXu7vJadTZex2+W1D7Sf9hQjoaGhbNGiRWzRokXMxMSEWVpasjfffFN1kWOMse+++44FBgYyIyMjZmNjw2bNmqW6aGdlZTE0Tzqn+ouMjGSRkZEtlmdlZTHGGEtKSmKPPvooMzQ0ZNbW1mzu3LlMJpO1iOmVV15hlpaWLCwsTFUs//nnnywwMJAZGBiw4OBglpKS0qGctFbIlpeXM4FAwH766SfVejdu3GAA2Pnz59u97yeeeIKNGzeuxfKoqCjm4+PDrl+/3qlCdsaMGWzSpElqy4KCgtjzzz/f5jYfffQRc3NzU1u2adMm5uDg0OY2GzZsYMbGxqy6urrdhWxycjIDwP766y/VsiNHjjCO41h+fn6r23Qm31KplAkEAvbdd99pjOdeI0eOZIsWLVI9VigUzN7enr3//vttbtOefD/99NPssccee6AviZ9//jkzNzdX+6L22muvMW9v73bvoz15OXDgAOM4jmVnZ7d7v519T/j5+bF169apnTvDhg1jb7zxRruPHRUVxXg8HissLFQt27p1KzMxMWnzS+22bduYtbW12r/H1atXGQB28+ZN1TIA7MCBA+2OpTUPek7dfW+19h6+desWc3BwYNeuXWPOzs4dLmRbO6eWvbqCubp7ssS8MnYtv5xV1Kl/Xq5atYoNHz5cbdmhQ4eYSCRilZWVjDHGZs2axaZPn662zqZNm9iAAQPUPisY65lClroWkA6xMBTiCX8HfPpUAP56YzwOvBiCVx72xNABpuA4ILmgEluiM/DkF+cx7J3jWPTDZfwcfwuyqob777wPY4yhtrGpw3+7zmdj9PqTmP3VRYxefxK7zmd3eB+sg5P3ffvtt9DT08OlS5ewceNG/Pe//8XXX3+tel4ul+Odd95BYmIiDh48iOzsbMyfPx8A4OjoiP379wMAUlNTUVBQgI0bN2Ljxo0IDg7GggULUFBQgIKCAjg6OqK8vBzjxo1DQEAA4uLicPToURQVFWHGjBktYhIKhTh79qzaT5NvvPEGPvnkE8TFxUFPTw/PPvus6rns7GxwHIeYmJgOvf74+HjI5XKMHz9etczHxwdOTk44f/58u/ZRVFSEw4cP41//+leL5QsWLMCuXbs6PTzb+fPn1WIDgIiICI2xBQcHIy8vD1FRUWCMoaioCD///DMee+yxNrf55ptv8NRTT8HQ0LBDsZmZmWH48OGqZePHjwePx8PFixdb3aYz+f7uu+8gFosxffr0dsfW2NiI+Ph4tePweDyMHz9eY+7am+8zZ87A1tYW3t7eeOGFF9S6bbTH+fPnMXbsWAiF/xtkPiIiAqmpqSgrK2vXPtqTl2+++Qbjx4+Hs7Nzu2Pr7HsiJCQEv/32G27fvg3GGKKjo5GWloZHHnmk3cc+f/48Bg8erDYcZkREBCorK3H9+vVWt2loaIBQKFQbl/XuuKVnzpxRW3fRokWQSCQYOXIktm/f3qHrZVeeU4888ojaNkqlEvPmzcOKFSs63A3k78f5+zlVWtMI3xFjkJVxE/XVlfCwMoLJPf1hGxoaIBKpD+9pYGCA+vp6xMfHa1zn1q1byMnJ6VSsD4JGLSCdxudxCHAyR4CTOZZO8EJxdQNOpckQkypDbJoMFXVyHL5agMNXCwAAgx1MVcN7+TuaPdDUdr1NnVwB39V/PNA+lAx469freOvX1i/ebUl+OwJiYfvf6o6OjtiwYQM4joO3tzeSkpKwYcMGLFiwAADUikU3Nzds2rQJI0aMUM1OY2FhAQCwtraGmZmZal2hUAixWAxbW1vVss8++wwBAQF47733VMu2b98OR0dHpKWlwcvLCwDg6emp1l+woKD5nPrPf/6D0NBQAMDKlSsxadIk1XSPAoEA3t7eHS4YCwsLIRQK1WIHABsbGxQWFrZrH99++y2MjY0xbdo01TLGGObPn4+FCxdi+PDhyM7O7lBcf4/v3jGu7xfb6NGjsXv3bsycORP19fVoamrC5MmTsWXLllbXv3TpEq5du4Zvvvmmw7FZW1urLdPT04OFhUWb8XUm39988w1mz56tKk7ao7i4GAqFotXcpaSktLlde/IdERGBiIgI+Pn5ISsrC6+//jomTpyI8+fPt3t8zMLCQri6urY4zt3nzM3N77uP++Xl9u3bOHLkCH744Yd2xfT32Drznti8eTMWLFgAPz8/6Onpgcfj4auvvsLYsWM7dOzW8n/3udaMGzcOy5Ytw0cffYRXXnkFNTU1WLlyJYD/XTsA4O2338a4ceMgFotx7NgxvPjii6iursbixYvbFVt3nlMffPAB9PT02h1LW8dxdXWFkjEUVNSjpLoBFhIrAIBYUQX9Vmb6jIiIwKeffooff/wRM2bMQGFhId5++20A/8tdREQEli5divnz5yM8PBzp6en45JNPVOu4uLh0OubOoEKWdBmJkT6mDRuAacMGQKFkSMgrV02dm5RfofrbfDIdZmIBxnpaIczbCqFeVrA0ajnlL9GOUaNGqY3vFxwcjE8++QQKhQJ8Ph/x8fFYu3YtEhMTUVZWBqWy+Ya/3Nxc+Pr6duhYiYmJiI6OhpGRUYvnMjIyVIVsYGBgq9sPGTJE9f93pzmUSqVwcnKCg4ODxg+T7rR9+3bMmTNHrdVi8+bNqKqqwqpVq3o8nuTkZLzyyitYvXo1IiIiUFBQgBUrVmDhwoWtFqvffPMNBg8ejJEjR/Z4rPdz/vx53LhxA7t27dJ2KCpPPfUUKisrYWJigqFDh2LIkCFwd3dHTEwMHn744R6JoT15+fbbb2FmZqaajr27bd68GRcvXsQPP/yAgQMH4syZM1i0aBHs7e1btEh2JT8/P3z77bdYtmwZVq1aBT6fj8WLF8PGxkatlfatt95S/X9AQABqamrw0UcfPVDx2BXi4+OxceNGXL58+YHHWlUyhqziGtQ0NN+sdfezlt/GLGKPPPIIPvroIyxcuBDz5s2Dvr4+3nrrLZw+fVqVuwULFiAjIwP/+Mc/IJfLYWJigldeeQVr167VyuxkVMiSbsHncQh0NkegszmWP+INaVU9TqU1j1t7Kk2G8lo5DiXexqHE2+A4YIiDKcK8rRHmbYUhA/pea62BgI/ktyM6tE1hRT3G/zcWyr/90sXjgD+XhcK2lZndNB27q9TU1Khan3bv3g0rKyvk5uYiIiICjY2NHd5fdXU1Jk+ejA8++KDFc3+ff7utn7f/Ph/33Qv+3cK6s2xtbdHY2Ijy8nK1FqiioiK11uS2nD59Gqmpqdi7d6/a8pMnT+L8+fPQ11f/0jZ8+HDMmTMH3377bbvju/du8fvF9v7772P06NFYsWIFgOYvAIaGhhgzZgzeffddtVzX1NRgz549qlaYjrC1tW0xikBTUxNKS0vbjK+j+f7666/h7+/f5pebtkgkEvD5/A7nrjP5dnNzg0QiQXp6ersL2baOc/e5+7lfXhhj2L59O+bNm6fWfaG9sXX0PVFXV4fXX38d+/fvx5gxY2BiYgJ/f38kJCTg448/bncha2tr22IUgPbkZfbs2Zg9ezaKiopgaGgIjuPw3//+F25ubm1uExQUhHfeeQcNDQ0t3qet6a5z6vTp06ov5HcpFAosX74cn376abt/zZFYWyMz9zZqGprA5zg4WogRf7NcFUNbli1bhqVLl6KgoADm5ubIzs7GqlWrVLnjOA4ffPAB3nvvPRQWFsLKygonTpwAAI357S7UR5b0CGtjEaYHDsCW2cNw5a0J+GlhMF4Mc4evnQkYAxJvVWDjiZuY+vk5jPjPn1iy5wp+TchHaU3HiyNdxHEcxEK9Dv25WRnh/WmDwb9ToPE5Du9PGww3K6MO7aej3+jv7ct44cIFeHp6gs/nIyUlBSUlJVi/fj3GjBkDHx+fFoXL3Q9JhULRYvm9y4YNG4br16/DxcUFHh4ean8d6ZvZlQIDAyEQCFQXZqC5v29ubm67hpL55ptvEBgYiKFDh6ot37RpExITE5GQkICEhATVcDt79+7Ff/7zn3bHFxwcrBYbABw/flxjbLW1tS1aSu7+5H1vn8CffvoJDQ0NmDt3brtj+nts5eXlqr50QHMBr1QqERQU1Oo2Hcl3dXU19u3b16LvcXsIhUIEBgaqHUepVOLEiRMac9eZfN+6dQslJSVqXxDuJzg4GKdOnVJNcX33ON7e3vftVtCevMTGxiI9Pb1TuevMe0Iul0Mul7d63nXky2ZwcDCSkpLUrjPHjx+HiYlJu34BsrGxgZGREfbu3QuRSIQJEya0uW5CQgLMzc3bVcQCXXtO/fnnn6pt5s2bh6tXr6quFQkJCbC3t8eKFSvwxx/t66JWVtsId79hiLtwFjymhLu1EUwMBO0+pziOg729PQwMDPDjjz/C0dERw4YNU1uHz+fDwcEBQqEQP/74I4KDg2FlZdWu+LrUfW8HI/fVn0Yt6A6FFXVs76Vc9sL3cWzQ6qNqoyC4rPydTdlyhn16PI0l5pUxhULZ5n50JTfdMWrBufTiHhu1wMjIiC1dupSlpKSwH374gRkaGrIvvviCMdZ8V7RQKGQrVqxgGRkZ7Ndff2VeXl5qd9/funWLcRzHdu7cyaRSKauqqmKMNQ/FM2LECJaVlcVkMhlTKBQsPz+fWVlZsenTp7NLly6x9PR0dvToUTZ//nzW1NSkiuneu15bG+LrypUraqMh3Lp1i3l7e7OLFy+2+Xo1Db/l5OTETp48yeLi4lhwcDALDg5W29bb25v98ssvassqKiqYWCxmW7dubfOYd90d4aEzw2/p6emxjz/+mN24cYOtWbOmxdA9K1euZPPmzVM93rFjB9PT02Off/45y8jIYGfOnGHDhw9nI0eObLH/hx56iM2cOVNtWUeH3woICGAXL15kZ86cYZ6enmrDb7X279KefDPG2Ndff81EIlGLod3aa8+ePUxfX5/t3LmTJScns+eee46ZmZmp3RE/b948tnLlStXj++W7qqqKLV++nB07doxlZGSwP//8kw0bNox5enqy+vr6dsdWXl7ObGxs2Lx589i1a9fYnj17mFgsVht+65dffml1FIP25GXu3LksKCio3fHcqzPvidDQUObn58d+++03lp6eznbs2MFEIhH7/PPP233cu8NvPfLIIywhIYEdPXqUWVlZqQ2/dfHiRebt7c1u3bqlWrZ582YWHx/PUlNT2WeffcYMDAzYxo0bVc8fOnSIffXVVywpKYndvHmTff7550wsFrPVq1d3KC8Pek5dv36dvfbaa/cdQq+9oxYolUqWX1bLEvPK2Jnr2Uxi1TwSTEfOqQ8//JBdvXqVXbt2jb399ttMIBCoje4gk8nY1q1b2Y0bN9iVK1fY4sWLmUgkavVaS8Nv9RJUyHadxiYFu5BRzN6PusEiNsS2GN4r8J1jbOneK+zXhHxWVqM+9Iqu5KY3jyMbGhrKXnzxRbZw4UJmYmLCzM3N2euvv642pMoPP/zAXFxcmL6+PgsODmaHDh1qUZC9/fbbzNbWlnEcxyIjIxljjKWmprJRo0YxAwMDtYIzLS2NTZ06lZmZmTEDAwPm4+PDlixZojpmZwvZu4VidHR0m6+3rUK2rq6Ovfjii8zc3JyJxWI2depUVlBQoLYt7oxB+Xfbtm1jBgYGrLy8vM1j3tVWIdvafu+1b98+5uXlxYRCIfPz82OHDx9Wez4yMrLFGKubNm1ivr6+zMDAgNnZ2bE5c+aoffAzxlhKSgoDwI4dO6a2/G5+Vq9ezZydnTXGVlJSwmbNmsWMjIyYiYkJe+aZZ1RfZv7+uv/+79KefDPGWHBwMJs9e3arx23PvzdjzQWOk5MTEwqFbOTIkezChQtqz4eGhqrO2bs05bu2tpZNmDCBSSQSJhAImLOzM1uwYIFaIdPWfu+VmJjIHnroIaavr88cHBzY+vXr1Z7fsWMHa639SVNeGGsukg0MDNiXX37Z6vNt7ffvOvOeKCgoYJGRkczOzo6JRCLm7e3NPvnkE7XrSWvn6r2ys7PZxIkTmYGBAZNIJGz58uVMLpernr97Pbj73mesuXi0sLBgQqGQDRkypMWQZEeOHGH+/v7MyMiIGRoasqFDh7IvvvhC7frYU+eUj48P++233zQeo7VC9t79ypsULEP6v/FhC8rrWEJCQofPqfDwcGZqaspEIhELCgpiUVFRas/LZDI2atQoZmhoyMRiMXv44YdbvOa/x9jdhSzHWAfH5iEtVFZWwtTUFBUVFTAxMenWY8nlckRFReGxxx5T6x/YVxVU1CEmVYaYVCnOppeguuF/s4vwOCDAyRzhd0ZC8JQY4OjRI1rPTX19PbKysuDq6tpiiBJtUiqVqhtS2uqQHxYWBn9//07NINMbrV27FgcPHsTly5fvm5uekJWVBS8vLyQnJ8PT01Nrcdzr7rmzePFi8Hg87Ny5U9shtRAdHY1p06YhMzOzXXf4d6X2vLecnZ2xbt061VB1umTNmjWIjY3t8FB17XG/3ISGhiI8PBxr167t8mM/qJ44p9pz7rTl7+dUXaMCOSU1aFQoweM4OJobwFTcsb7Q3UHTZ4qmz8qO1FVavdnr6tWrHd7G19cXenp0j1p/YWdqgFkjnTBrpBMam5SIyylFbKoM0alSpBVVIz6nDPE5Zfj4WBqsjIRwNeCBu1aIUB9bmBr0/UKfPLikpCSYmJhg7dq1WLZsmVZjiYqKwnPPPadTRexdjDHExsa2GIdTV0RFReH111/v8SK2Pa5fvw5TU1M8/fTT2g6lVUeOHMFnn33W48etqKhARkYGDh8+3OPHbo/eck6V1zbiVlkdlIxBqMeDi6UhRF14k29n7N69G88//zzq6urg7+/frcfSaossj8cDx3HtHoCYx+MhLS1NK3fFaUItstqRX16HmFQpolNkOJdRjNrG/91IxOdxCHQyR6i3FcK9rTHQzviBhzFpL2qR7T1KS0tRWloKpVIJfX19ODo6arVFVlc9SKtRf0D5aRvlRrMHyQ9jDIWV9aoJh4xFAjiaG0CPr/08V1VVqUZmMDMzg0QiabFOn2iRBZrvkG7PXW6MMQwaNKgHIiK9hYOZAeYEOWNOkDMamhS4kC7Djj/+Ql6TMTJkNbiUXYpL2aX46I9U2JjoI8yreXiv0Z6SFrOZkGbd8dOiLrOwsICFhYXqw4QQQnqDJoUSuaW1qu52Vsb6sDUR9ViDzf0YGxvD2Ni4R46l1UI2NDQUHh4eLWYLacvYsWM7NJML6T/09fgIcbdEuYsSjz02GoVVcsSkyRCTIsXZjGIUVTZgb1we9sblQe/OGLfhPs2FrbdNz7XWEkIIIQ+iXq5AdkkNGpua+8MOMDeAmQ70h9UWrRay0dHRHVr/7riLhNyPo4UY80Y5Y94oZ9TLFbiUVYroVCliU2XILK7BxaxSXMwqxfojKbAzFammzh3tIYGRfte8Leg+SkIIIV2porYReXf7w/J5cLY0hIFQu/1hO6urPiO13rWgLQqFAklJSXB2dtbJjtak9xAJ+BjrZYWxXlbAZCCnpAYxd24YO59RgoKKevx4KQ8/XsqDgM9hhIsFwu70rfWwNupwa+3dvsu1tbX0CwIhhJAHxhhDUWUDpFX1AAAjfT04WYh1oj9sZ9XW1gLAA9/vozOF7JIlSzB48GD861//gkKhQGhoKM6dOwexWIzff/8dYWFh2g6R9BHOloaIDDFEZIgL6uUKnM8sUY2EkFNSi3MZJTiXUYL3olLgYGagKmpDPCwhFt7/LcPn82FmZqaaiUYsFutE1wWlUonGxkbU19fTTRf3oNxoRvnRjPLTNsqNZu3JT5NSiaKKelV/WHOxEFZGfDTJG9Ekb3UTncYYQ21tLaRSKczMzFSzDHaWzhSyP//8s2pKxN9++w1ZWVlISUnBrl278MYbb+Ds2bNajpD0RSIBH+He1gj3tsZa+CGruAbRKVLEpMlwIbME+eV12H0xF7sv5kLI5yHIzQKhXs3dENytDNssUO/OY33v9K3axBhDXV0dDAwMdKKw1iWUG80oP5pRftpGudHsfvmRK5QorWmEXMHAcYC5WICaOj3UlGgh2C5mZmam+qx8EDpTyBYXF6teUFRUFJ588kl4eXnh2WefxcaNG7UcHekvXCWGcH3IFc8+5Iq6RgXOZxYjOqW5tfZWWR1O3yzG6ZvFePfwDThaGCDMyxrhPlYIdpOo9VPiOA52dnawtrZWmztdm+RyOU6dOoWxY8f2+6Hb7kW50Yzyoxnlp22UG8005edsejHWH0lBbWMTrI30se6JQfCy7ZmRALqbQCB44JbYu3SmkLWxsUFycjLs7Oxw9OhRbN26FUBzH4querGEdISBkI9xPjYY52MDxhgyZDWISZUiJlWGS1mlyCutw64LOdh1IQdCPR5GuVmqZhlzlRgCaO5moCvnL5/PR1NTE0QiEX2g3INyoxnlRzPKT9soN5q1lh+lkmHTyZv49M+bAIAgVwtsmTMMEiN9bYaqs3SmkH3mmWcwY8YM2NnZgeM4jB8/HkDzOLM+Pj5ajo70dxzHwcPaCB7WRvj3GDfUNDThXEaJqrDNL6/DqTQZTqXJsO63ZLhYihHmbY1QbysEu1lqfZYVQgghuq+qXo5l+xJxPLl5MoH5IS54Y9JACHrxTV3dTWcK2bVr12LQoEHIy8vDk08+CX395m8efD4fK1eu1HJ0hKgz1NfDBF8bTPBtbq1Nl1Yj+k5R+1d2KbJLarHzXDZ2nsuGvh4PIe6WCLvTF9fJUqzt8AkhhOiYTFk1ntsVj3RpNYR8Ht6dOggzhjtqOyydp/VC9umnn8YTTzyBiIgITJ8+vcXzkZGRWoiKkPbjOA6eNsbwtDHGc2PdUd3QhLPpxarW2oKKekSnyhCdKsMaXIebxBBh3s2TMYx0taDWWkII6edi0mRY9lMSquqbYGsiwhfzAuHvaKbtsHoFrReyHh4eeO+99zB37lyEhYXh8ccfx+OPPw4HBwdth0ZIpxjp6yHCzxYRfrZgjCG1qKp53NoUKeJzypBZXIPM4ixsP5sFAwH/Tmttc99aRwtqrSWEkP6CMYZjtzhEXbgCxoDhzub4fO4wWBuLtB1ar6H1Qnb16tVYvXo1bt26hUOHDuHgwYNYunQp/Pz88MQTT+Dxxx+Hv7+/tsMkpFM4joOPrQl8bE2wMNQdlfVynL1ZrJqQQVrVgBMpUpxIkQK4Dg9rI4R5WSHcxxrDXcyhr0ettYQQ0hfVNDRh+b6rOJrXfJ2fE+SENZP9INSj/rAdofVC9q4BAwbgxRdfxIsvvoiqqiocOXIEv/76K8aNGwdjY2NMnjwZL7zwAvz8/LQdKiGdZiISYOJgO0wcbAfGGG4UVKmmzo3PLUO6tBrp0mp8fSYLYiEfoz0kqtZaBzOaJYwQQvqCnJIaPPddPFKLqsDnGNZO9sO8EFdth9Ur6Uwh+3fGxsaYMWMGZsyYAYVCgZiYGBw6dAjnz5+nQpb0GRzHwdfeBL72JlgU7oGKOjnO3CxuLmzTZJBVNeB4cpHq7lUvGyOE3xkJYbizBX1rJ4SQXuhUmgwv/3gFFXVyWBkJMcelFk+NGKDtsHotnSxk/47P5+Phhx/Gww8/rO1QCOlWpgYCTBpih0lD7KBUMiQXVCImVYroVBmu5JYhragaaUXV2HYqE0b6ehjtYYlwb2uEeVvD1pT6UxFCiC5jjOGr05lYfyQFSgb4O5rhs6eGIP7MSW2H1qtptZANCAho95R1ly9f7uZoCNEdPB6HQQ6mGORgipfGeaK8thGnbjaPhBCbKkNJTSP+uF6EP643t9b62BrfGd7LCsOczWnMQUII0SF1jQq8tv8qDiXeBgDMGD4A70wZBB5Tajmy3k+rheyUKVNU/19fX4/PP/8cvr6+CA4OBgBcuHAB169fx4svvqilCAnRDWZiIR4fao/Hh9pDqWS4drsC0SkyxKRJkZBXjpTCKqQUVuGL2AwY6+thjJcEYV7N3RBsTKi1lhBCtCWvtBbP74pHckEl9Hgc1kz2xdxRzuA4DnI5FbIPSquF7Jo1a1T//+9//xuLFy/GO++802KdvLy8ng6NEJ3F43EYMsAMQwaY4ZXxniitacTpm83De526WYzSmkZEJRUiKqkQAOBrZ4JwHys85G4BBdNy8IQQ0o+cSy/Goh8uo6xWDomREFtmD0OQm6W2w+pTdKaP7E8//YS4uLgWy+fOnYvhw4dj+/btWoiKEN1nYSjEE/4OeMLfAQolw9Vb5YhJlSEmVYqr+RVILqhEckEltkRnwIDPx5/ViRg30BahXlawMqa5uwkhpKsxxrD9bDbei7oBhZJhsIMpts0LhD2NPtPldKaQNTAwwNmzZ+Hp6am2/OzZsxCJ6KdRQtqDz+MQ4GSOACdzLJ3gheLqBpxKkyEmVYbYNCkq6poQda0IUdea+9YOdjBVDe/l72gGPq99fdYJIYS0rl6uwOsHkvDL5XwAwLQAB7w3bTDN4thNdKaQXbJkCV544QVcvnwZI0eOBABcvHgR27dvx1tvvaXl6AjpnSRG+pg2bACmDRuA+oZGfPHTETRaeuF0egmS8itUf5tPpsNMLMBYTyuEeVsh1MsKlkbUWksIIR1xu7wOz++KR1J+Bfg8Dm88NhDPjHZp943tpON0ppBduXIl3NzcsHHjRnz//fcAgIEDB2LHjh2YMWOGlqMjpPfj8zi4GgOPjffA/00cCGlVPU6lNY9bezpNhvJaOQ4l3sahxNvgOGCIgynCvK0R5m2FIQOotZYQQjS5mFmCF3dfRklNI8zFAmyZPQwhHhJth9Xn6UwhC0A1CUJPyc7OxjvvvIOTJ0+isLAQ9vb2mDt3Lt544w0IhcIei4MQbbA2FmF64ABMDxyAJoUSV/LKm8etTZEhuaASibcqkHirAhtP3ISFoRBjPSUI97HGGE8rWBjS+4MQQoDm/rC7LuTg7d+S0aRk8LUzwbZ5gXC0EGs7tH5BpwrZnpaSkgKlUolt27bBw8MD165dw4IFC1BTU4OPP/5Y2+ER0mP0+DyMcLHACBcLrIjwQVFlPWJTm4f3Op3WPBLCwYTbOJjQ3Frr72iGMC9rhPtYYZC9KXjUWksI6YcamhR46+A17Iu7BQB4fKg9PvjnEBgIqT9sT9GZQlahUGDDhg3Yt28fcnNz0djYqPZ8aWlplx/z0UcfxaOPPqp67ObmhtTUVGzdupUKWdKv2ZiIMGOEI2aMcIRcocTlnDJE3xkJIaWwCldyy3Eltxwb/kyDxEiIsV7NN4yN9ZTATEyttYSQvq+woh4Lv49HQl45eBywcqIPFoxxo/6wPUxnCtl169bh66+/xvLly/Hmm2/ijTfeQHZ2Ng4ePIjVq1f3WBwVFRWwsLDoseMRousEfB6C3CwR5GaJlRN9UFBRpxre62x6CYqrG/HL5Xz8cjkfPA4IcDJH+J2REHztTKi1lhDS58TnlGLh95chq2qAqYEAm2cFYKyXlbbD6pd0ppDdvXs3vvrqK0yaNAlr167FrFmz4O7ujiFDhuDChQtYvHhxt8eQnp6OzZs337c1tqGhAQ0NDarHlZWVAAC5XA65XN6tMd7df3cfpzei3GjWVfmRiPUwPcAO0wPs0NikxOXccsTeLEZsmgw3pTWIzylDfE4ZPj6WBisjIcZ4ShDmJcFod0uYGAi64qV0OTp3NKP8aEb5aVtfzM3euFtY9/sNyBUMXtZG+HyOP5wtxJ16jX0xP12hI/ngGGM6MdePoaEhbty4AScnJ9jZ2eHw4cMYNmwYMjMzERAQgIqKinbva+XKlfjggw80rnPjxg34+PioHufn5yM0NBRhYWH4+uuvNW67du1arFu3rsXyH374AWIxde4m/VdpA3CjnMONMg6pFRwalf9rjeWBwdUYGGiuhK8Zg70YoF/gCCG9RZMS2J/Nw7kiHgDA30KJ2R5K6FN32C5XW1uL2bNno6KiAiYmJhrX1ZlC1tvbG9999x2CgoLw0EMP4R//+AdWrlyJvXv34uWXX4ZUKm33vmQyGUpKSjSu4+bmphqZ4Pbt2wgLC8OoUaOwc+dO8Hg8jdu21iLr6OiI4uLi+yb8Qcnlchw/fhwTJkyAQKCbrVvaQrnRrKfz09CkRHxOGWLTihF7sxgZshq1522M9THWS4KxnhKMdreAsUh7/2Z07mhG+dGM8tO2vpIbWVUDXt6TiPjccnAcsOxhDzw/1vWB+8P2lfx0tcrKSkgkknYVsjrTtWDq1Kk4ceIEgoKC8PLLL2Pu3Ln45ptvkJubi6VLl3ZoX1ZWVrCyal9flfz8fISHhyMwMBA7duy4bxELAPr6+tDXbzlYvEAg6LETsSeP1dtQbjTrqfwIBECojy1CfWwBAHmltYhJkyEmRYqzGcUoqmrAT/H5+Ck+H3o8DoHO5gj3aR631tvGWCs3TNC5oxnlRzPKT9t6c24S8sqxcFc8CivrYSzSw6anAhDuY92lx+jN+ekOHcmFzhSy69evV/3/zJkz4ezsjHPnzsHT0xOTJ0/ulmPm5+cjLCwMzs7O+PjjjyGTyVTP2dradssxCemvHC3EmDfKGfNGOaNersClrFJEp0oRmypDZnENLmaV4mJWKdYfSYGdqUg1de5oDwmM9HXmUkUI6Uf2xeXhzQPX0KhQwsPaCF89PRyuEkNth0X+Ric+HeRyOZ5//nm89dZbcHV1BQCMGjUKo0aN6tbjHj9+HOnp6UhPT8eAAQPUntORHheE9EkiAR9jvaya7/KdDOSU1KhGQjiXUYKCinr8eCkPP17Kg4DPYYSLBcK8rRDubQ0PayMa3oYQ0q3kCiXe/T0Z357PAQA84muDT2YM1WoXKNI6nShkBQIB9u/fj7feeqtHjzt//nzMnz+/R49JCGnJ2dIQkSGGiAxxQb1cgQuZJYhJlSE6VYqcklqcyyjBuYwSvBeVAgczA1VrbYi7JQyptZYQ0oWKqxvw4u7LuJTVPH790vFeeHmcBw0lqKN05hNgypQpOHjwYIf7wxJC+haRgI8wb2uEeVtjLfyQVVyD6BQpYtJkuJBZgvzyOuy+mIvdF3Mh5PMw0tVCVdi6WxlSay0hpNOSblXg+V1xuF1RDyN9PWyY6Y8JvjbaDotooDOFrKenJ95++22cPXsWgYGBMDRU74PSE+PIEkJ0j6vEEK4PueLZh1xR16jA+cxiRKc0t9beKqvDmfRinEkvxruHb8DRwkA1dW6wm4SmiSSEtNuBK7ewcn8SGpqUcJMY4sunA+FhbaztsMh96Ewh+80338DMzAzx8fGIj49Xe47jOCpkCSEwEPIxzscG43xswBhDhqwGMalSxKTKcCmrFHmlddh1IQe7LuRAqMfDKDdL1SxjdIMGIaQ1TQol1h9JwddnsgAA43ys8elT/jCh/rC9gs4UsllZWdoOgRDSi3AcBw9rI3hYG+HfY9xQ09CEcxklqsI2v7wOp9JkOJUmw7rfkuFiKUaYtzVCva0Q7GYJkYBaawnp70prGvHyj5dxNr157PmXx3lg6Xgv6g/bi+hMIUsIIQ/CUF8PE3xtMMG3ubU2XVqN6DtF7V/ZpcguqcXOc9nYeS4b+no8hLhbIszbGuHe1rAzoZYXQvqb5NuVeG5XHG6V1UEs5OOTJ4di4mA7bYdFOkirheyyZcvwzjvvtOgP25ZVq1ZhxYoVsLCw6ObICCG9Gcdx8LQxhqeNMZ4b647qhiacTS9WtdYWVNQjOlWG6FQZ1uA6XC3FcBLyYJxejBAPa2qtJaSP+y3xNlb8nIh6uRLOlmJ8OW84vG2pP2xvpNVCduPGjVi1alW7C9ktW7ZgwYIFVMgSQjrESF8PEX62iPCzBWMMqUVVzcN7pUgRn1OGrJJaZIGH2G8vw0DAv9Na29y31tFCrO3wCSFdRKFk+PCPFGyLzQQAjPWywuanAmAqpl9leiutFrKMMXh5ebV7uJyampr7r0QIIRpwHAcfWxP42JpgYag7KuvliE0pwu6TV5BZZwBpVQNOpEhxIkUK4Do8rI0Q5mWFcB9rDHcxh74etdYS0htV1Mrx8p4rOJXWPIvnwlB3rIjwBp/6w/ZqWi1kd+zY0eFtbGxoPDdCSNcxEQnwqJ8NlDlKTJw4FunF9aqpc+Nzy5AurUa6tBpfn8mCWMjHaA+JqrXWwcxA2+ETQtohtbAKz+2KQ05JLUQCHj6aPhSTh9prOyzSBbRayEZGRmrz8IQQoobjOPjam8DX3gSLwj1QUSfHmZvFzYVtmgyyqgYcTy7C8eQiAICXjRHC74yEMNzZAkI9npZfASHkXkevFWDZvkTUNiowwNwAX84bDl97E22HRboIjVpACCFtMDUQYNIQO0waYgelkiG5oBIxqVJEp8pwJbcMaUXVSCuqxrZTmTDS18NoD0uE35mVzNZUpO3wCenXlEqG/x5Pw2fR6QCAEHdLfDZ7GCwMhVqOjHQlKmQJIaQdeDwOgxxMMcjBFC+N80R5bSNO3WweCSE2VYaSmkb8cb0If1xvbq31sTW+M7yXFYY5m0PAp9ZaQnpKZb0cS/Yk4GSKFADw74dcsXKiD/TofdjnUCFLCCGdYCYW4vGh9nh8qD2USoZrtysQnSJDTJoUCXnlSCmsQkphFb6IzYCxvh7GeEkQ5tXcDcHGhFprCeku6dJqPPddHDKLa6Cvx8P6fw7G1IAB2g6LdBMqZAkh5AHxeByGDDDDkAFmeGW8J0prGnH6ZvPwXqduFqO0phFRSYWISioEAPjamSDcp/mGsQBHM2olIqSLHE8uwtK9CahuaIK9qQjb5g3H4AGm2g6LdCOdKWSfffZZbNy4EcbG6gMS19TU4OWXX8b27du1FBkhhHSMhaEQT/g74Al/ByiUDFdvlSMmVYaYVCmu5lcguaASyQWV2BKdARORHsZ4WTXfNOZlBStjfW2HT0ivo1QybD6Zjg1/pgEAglwtsGXOMEiM6P3U1+lMIfvtt99i/fr1LQrZuro6fPfdd1TIEkJ6JT6PQ4CTOQKczLF0gheKqxtwKk2GmFQZTt2UobxWjsNXC3D4agEAYLCDqWp4L39HMxrjkpD7qKqXY/m+RBy7M5rI/BAXvDFpIPVL7ye0XshWVlaCMQbGGKqqqiAS/a/vmEKhQFRUFKytrbUYISGEdB2JkT6mDRuAacMGQKFkSMgrV02dm5RfofrbfDIdZmIBxnpaIczbCmO9rKh1iZB7ZMqq8dyueKRLqyHk8/Du1EGYMdxR22GRHqT1QtbMzAwcx4HjOHh5ebV4nuM4rFu3TguREUJI9+LzOAQ6myPQ2RzLH/GGtKoep9Kax609ndbcWnso8TYOJd4GxwFDHEwR5m2NMG8rDBlArbWkf4tOkWLxniuoqm+CjYk+vpgbiAAnc22HRXqY1gvZ6OhoMMYwbtw47N+/HxYWFqrnhEIhnJ2dYW9Ps28QQvo+a2MRpgcOwPTAAWhSKHHlTmttdIoMyQWVSLxVgcRbFdh44iYsDIUY6ylBuI81xnha0diYpN9gjOHzmAx8fCwVjAGBzubYOncYrI1pNJD+SKuFrIWFBdLS0iCRSBAZGYnx48e36CNLCCH9kR6fhxEuFhjhYoEVET4oqqxHbGrz8F6n05pHQjiYcBsHE5pba/0dzRDmZY1wHysMsjcFj1prSR9U09CEFT8nqkYAmRPkhDWT/WhWvX5Mq4VsY2MjKisrIZFI8N133+HDDz+kQpYQQlphYyLCjBGOmDHCEXKFEpdzyhB9ZySElMIqXMktx5Xccmz4Mw0SIyHGejXfMDbWUwIzMbXWkt4vt6QWz+2KQ0phFQR8DuseH4TZQU7aDotomVYL2eDgYEyZMgWBgYFgjGHx4sUwMDBodV0atYAQQpoJ+DwEuVkiyM0SKyf6oKCiDrGpMkSnSnE2vQTF1Y345XI+frmcDx4HBDiZI/zOSAi+dibUWkt6ndM3ZXjphyuoqJPDylgfX8wdhkBni/tvSPo8rRay33//PTZs2ICMjAxwHIeKigrU19drMyRCCOl17EwN8NRIJzw10gmNTUrE5ZSqCtu0omrE55QhPqcMHx9Lg5WxPkLvjFv7kKcEpgYCbYdPSJsYY/jqdCbWH0mBkjV3odk2L5BmxyMqWi1kbWxssH79egCAq6srdu3aBUtLS22GRAghvZpQj4cQdwlC3CVY9dhA5JfXqYb3OpteDFlVA36Ov4Wf4281j5rgZI5Q7+bCdqCdMTiOWmuJbqhrVOC1/VdxKPE2AGDG8AF4Z8og6OvxtRwZ0SVaH7XgrqysLG2HQAghfY6DmQHmBDljTpAzGpoUiMsuQ3SKFDFpMqRLq3EpuxSXskvx0R+psDHRR5hX8/Beoz0lMBFRay3RjrzSWjy/Kx7JBZXQ43FYPdkX80Y50xct0oJWC9lNmzbhueeeg0gkwqZNmzSuu3jx4h6KihBC+iZ9PT5Ge0gw2kOCN9FcLMSkyRCTIsW5jBIUVTZgb1we9sblQe/OGLfhPtZ4yM0cjGk7etJfnEsvxqIfLqOsVg5LQyE+nzMMQW70ay1pnVYL2Q0bNmDOnDkQiUTYsGFDm+txHEeFLCGEdDFHCzHmjXLGvFHOqJcrcCmrFDF3RkLILK7BxaxSXMwqBQCYCfk433Qd4wbaYrSHBEb6OvODHukjGGPYcTYb/4m6AYWSYbCDKbbNC4S9Wes3gRMCaLmQ/Xt3AupaQAgh2iMS8DHWq3kq3NWTfZFTUqMqas9llKC8UYm9cfnYG5cPAZ/DCBcLhN3pW+thbUQ/+ZIHUi9X4PUDSfjlcj4AYFqAA96bNhgiAfWHJZrRV2pCCCEtOFsaIjLEEJEhLqiqrceWfcdQY+aKUzeLkVNSi3MZJTiXUYL3olLgYGaAsDvDe4W4W8KQWmtJB9wur8PC7+Nx9VYF+DwObzw2EM+MdqEvR6RddOZqo1AosHPnTpw4cQJSqRRKpVLt+ZMnT2opMkII6d9EAj4GmjM89pgPBAIBsoprVDeMXcgsQX55HXZfzMXui7kQ8nkY6WqhKmzdrQypICFtuphZgkU/XEZxdSPMxQJsmT0MIR4SbYdFehGdKWRfeeUV7Ny5E5MmTcKgQYPowkcIITrKVWII14dc8exDrqhrVOB8ZjFi7oxbm1dahzPpxTiTXox3D9+Ao4WBaurcYDcJDIT0UzFp7g/7/YUcrPstGU1KhoF2JvhyXiAcLcTaDo30MjpTyO7Zswf79u3DY489pu1QCCGEtJOBkI9xPjYY52MDxhgy77TWxqbJcDGzFHmlddh1IQe7LuRAqMfDKDdL1SxjrhJDbYdPtKChSYHVB69jb1weAGDyUHt8+M8h9CWHdIrOFLJCoRAeHh7aDoMQQkgncRwHdysjuFsZ4d9j3FDT0IRzGSWqCRnyy+twKk2GU2kyrPstGS6WYoR5WyPU2wrBbpZ0Y08/UFRZj+d3xSMhrxw8Dlg50QcLxrjRr7Ck03SmkF2+fDk2btyIzz77jE5oQgjpAwz19TDB1wYTfJtba9Ol1Yi+U9T+lV2K7JJa7DyXjZ3nsqGvx0OIuyXCvK0R7m0NJ0v6ibmvic8pw8Lv4yGraoCpgQCbZwVgrJeVtsMivZxWC9lp06apPT558iSOHDkCPz8/CATqM8r88ssvPRkaIYSQLsRxHDxtjOFpY4znxrqjuqEJZ9OLVa21BRX1iE6VITpVhjW4DjeJIcK8m2cZG+lqQa21vdzeuFtY9/sNyBUM3jbG+PLpQDhbUtcS8uC0WsiampqqPZ46daqWIiGEENKTjPT1EOFniwg/WzDGkFpUpRq3Ni67DJnFNcgszsL2s1kwEPDvtNY2962lG4J6j8YmJfZl8nD2fDIA4LHBtvho+lAaoo10Ga2eSTt27NDm4QkhhOgAjuPgY2sCH1sTLAx1R2W9HOfSixGd0jwSgrSqASdSpDiRIgVwHR7WRgjzskK4jzWGu5hDX49aa3WRtKoeL+yKR3wRDxwHvPqIN14Mc6fug6RL6cxXorq6OjDGIBY3f9POycnBgQMH4Ovri0ceeUTL0RFCCOkpJiIBHh1kh0cH2YExhhsFVYhOlSI2VYb43DKkS6uRLq3G12eyIBbyMdpDomqtdaDpTHVCQl45Fu6KR2FlPQz4DJtmD8MEP3tth0X6IJ0pZJ944glMmzYNCxcuRHl5OUaOHAmhUIji4mL897//xQsvvNCtx29oaEBQUBASExNx5coV+Pv7d+vxCCGE3B/HcfC1N4GvvQkWhXugok6OMzeLmwvbNBlkVQ04nlyE48lFAAAvGyOE3xkJYbizBYR6PC2/gv7np7g8vHHwGhqblHC3MsRTDhUIo5u6SDfRmUL28uXL2LBhAwDg559/hq2tLa5cuYL9+/dj9erV3V7I/t///R/s7e2RmJjYrcchhBDSeaYGAkwaYodJQ+ygVDIkF1QiJlWK6FQZruSWIa2oGmlF1dh2KhNG+noY7WGJcG9rhHlbw9ZUpO3w+zS5Qon/HL6BneeyAQATfG3wwVQ/nD55TLuBkT5NZwrZ2tpaGBsbAwCOHTuGadOmgcfjYdSoUcjJyenWYx85cgTHjh3D/v37ceTIkW49FiGEkK7B43EY5GCKQQ6meGmcJ8prG3HqZvNICLGpMpTUNOKP60X443pza62PrfGd4b2sMMzZHAI+tdZ2lZLqBry4+zIuZpUCAJaM98TicZ5QKJq0HBnp63SmkPXw8MDBgwcxdepU/PHHH1i6dCkAQCqVwsTEpNuOW1RUhAULFuDgwYOq/rmEEEJ6HzOxEI8PtcfjQ+2hVDJcu12B6BQZYtKkSMgrR0phFVIKq/BFbAaM9fUwxkuCMK/mbgg2JtRa21nX8ivw/K545JfXwUhfDxtm+mOCrw0AQKHQcnCkz9OZQnb16tWYPXs2li5diocffhjBwcEAmltnAwICuuWYjDHMnz8fCxcuxPDhw5Gdnd2u7RoaGtDQ0KB6XFlZCQCQy+WQy+XdEarK3f1393F6I8qNZpSftlFuNOut+RloY4iBNoZ4MdQFpTWNOJNegti0YpxOL0ZZrRxRSYWISipsXtfWGGFeEoz1ksB/gCn0OtBa21vz0xV+TSzAGwevo6FJCVdLMT6f7Q8Pa6MWOemPuWkPyk/rOpIPjjHGujGWDiksLERBQQGGDh0KHq/5InLp0iWYmJjAx8en3ftZuXIlPvjgA43r3LhxA8eOHcO+ffsQGxsLPp+P7OxsuLq63vdmr7Vr12LdunUtlv/www/UqksIITpOyYDcauBGOQ/JZRzyagCG/w0JZcBn8DFj8DVr/q+JUIvB6igFAw7l8BBT0PxZ7WumxNOeShjoTPMY6c1qa2sxe/ZsVFRU3PdXeZ0qZLuKTCZDSUmJxnXc3NwwY8YM/Pbbb2pj2ikUCvD5fMyZMwfffvttq9u21iLr6OiI4uLibu0GATR/Szl+/DgmTJjQYvaz/o5yoxnlp22UG836en5Kqhtw+k5r7Zn0EpTXqbcGDbI3wVhPCcK8JBgywBR8nvo4qH09P/cqq23Ekr1XcS6zuT/sC6GuWDLOAzxey/Fh+1tuOory07rKykpIJJJ2FbJ98ruTlZUVrKzuP9THpk2b8O6776oe3759GxEREdi7dy+CgoLa3E5fXx/6+votlgsEgh47EXvyWL0N5UYzyk/bKDea9dX82JoL8OQIIzw5whkKJUNCXrlq6tyk/Apcu12Ja7cr8XlsJszEAoz1tEKYtxXGellBYvS/z4K+mp+/S75died2xeFWWR3EQj4+eXIoJg62u+92/SE3D4Lyo64jueiThWx7OTk5qT02MjICALi7u2PAgAHaCIkQQogW8XkcAp3NEehsjuWPeENaVY9Tac3j1p5Ok6G8Vo5DibdxKPE2OA4Y4mCKsZ6W0KsCFEqGvlyK/H71Nlb8dBV1cgWcLMT46unh8LY11nZYpJ/r14UsIYQQoom1sQjTAwdgeuAANCmUuHKntTY6RYbkgkok3qpA4q0KAHrYmRmD0DtT547xtIKFYd/oXKtQMnz0Ryq+iM0AAIzxlGDzrACYifvG6yO9GxWyf+Pi4oI+2GWYEEJIF9Dj8zDCxQIjXCywIsIHRZX1iE2V4WRKEWJSClFWK8fBhNs4mNDcWuvvaIYwL2uE+1hhkL1pq31IdV1FrRwv77mCU2kyAMDCUHesiPBu0U+YEG2hQpYQQgjpBBsTEWaMcMRUf1v89ns+bAaNwun0MsSkSpFSWIUrueW4kluODX+mQWIkxFgvK4R5W2Osp6RXtGamFVVhwXdxyCmphUjAw4fTh+LxofbaDosQNVTIEkIIIQ+IzwNGulhgtKcNVk70QUFFHWJTZYhOleJsegmKqxvxy+V8/HI5HzwOCHAyR7h3c2Hra2eic621R68VYNm+RNQ2KjDA3ABfzhsOX/vuHZWHkM6gQpYQQgjpYnamBnhqpBOeGumExiYl4nJKVYVtWlE14nPKEJ9Tho+PpcHKWL+5b623NR7ylMDUQHu3jCmVDBv+TMPmk+kAgBB3S3w2e1if6e9L+h4qZAkhhJBuJNTjIcRdghB3CVY9NhD55XWq4b3OphdDVtWAn+Nv4ef4W82jJjiZI9S7ubAdaGesNtZ5d6qsl2PpngScSJECAP79kCtWTvTp0CxnhPQ0KmQJIYSQHuRgZoA5Qc6YE+SMhiYF4rLLEJ0iRUyaDOnSalzKLsWl7FJ89EcqbEz0EeZljTBvK4z2lMBE1D2ttenSajy3Kw6Zshro6/Gw/p+DMTWAhqEkuo8KWUIIIURL9PX4GO0hwWgPCd4EkFdai5g0GWJSpDiXUYKiygbsjcvD3rg86N0Z4zbcp7mw9bbpmtbaP5OLsGRvAqobmmBvKsK2ecMxeIDpg784QnoAFbKEEEKIjnC0EGPeKGfMG+WMerkCl7JKEZMqQ0yqFJnFNbiYVYqLWaVYfyQFdqYihN25YWy0hwRG+h37SFcqGTafTMeGP9MAACNdLfD5nGFqs5URouuokCWEEEJ0kEjAx1iv5qlwV0/2RU5JjaqoPZdRgoKKevx4KQ8/XsqDgM9hhIsFwu70rfWwNtLYWlvd0IRlexNwLLkIABAZ7Iw3/+ELAfWHJb0MFbKEEEJIL+BsaYjIEENEhrigXq7AhcwSxNwZCSGnpBbnMkpwLqME70WlwMHMQNVaG+JuCcM7rbUFFXU4n1GCTSduIrukFkI+D+9OHYQZwx21/OoI6RwqZAkhhJBeRiTgI8zbGmHe1lgLP2QV1zRPnZsqw4XMEuSX12H3xVzsvpgLIZ+Hka4WMDUQICqpAHfnrzQR6eHbZ0ciwMlcq6+FkAdBhSwhhBDSy7lKDOEqccUzo11R16jA+cxiVWttXmkdzqQXt9imuqEJtqYiLURLSNehQpYQQgjpQwyEfIzzscE4HxswxpBZXIMdZ7Lw/cVctfWUDMguroWdqYGWIiXkwVGvbkIIIaSP4jgO7lZGWDTOA/fOgsvnOLhIxNoJjJAuQoUsIYQQ0sfZmRrg/WmDwb8zkgGf4/DetEHUGkt6PepaQAghhPQDM0c4YayXFbKLa+EiEVMRS/oEKmQJIYSQfsLO1IAKWNKnUCHbBRhrHsyksrKy248ll8tRW1uLyspKCATdM+d2b0W50Yzy0zbKjWaUH80oP22j3GhG+Wnd3Xrqbn2lCRWyXaCqqgoA4OhIA0oTQgghhHSFqqoqmJqaalyHY+0pd4lGSqUSt2/fhrGxscYpAbtCZWUlHB0dkZeXBxMTk249Vm9DudGM8tM2yo1mlB/NKD9to9xoRvlpHWMMVVVVsLe3B4+neVwCapHtAjweDwMGDOjRY5qYmNBJ3wbKjWaUn7ZRbjSj/GhG+Wkb5UYzyk9L92uJvYuG3yKEEEIIIb0SFbKEEEIIIaRXokK2l9HX18eaNWugr6+v7VB0DuVGM8pP2yg3mlF+NKP8tI1yoxnl58HRzV6EEEIIIaRXohZZQgghhBDSK1EhSwghhBBCeiUqZAkhhBBCSK9EhawO2rJlC1xcXCASiRAUFIRLly5pXP+nn36Cj48PRCIRBg8ejKioqB6KtOd1JDc7d+4Ex3FqfyKRqAej7TmnTp3C5MmTYW9vD47jcPDgwftuExMTg2HDhkFfXx8eHh7YuXNnt8epLR3NT0xMTItzh+M4FBYW9kzAPej999/HiBEjYGxsDGtra0yZMgWpqan33a6/XHc6k5/+cu3ZunUrhgwZohoDNTg4GEeOHNG4TX85b4CO56e/nDddjQpZHbN3714sW7YMa9asweXLlzF06FBERERAKpW2uv65c+cwa9Ys/Otf/8KVK1cwZcoUTJkyBdeuXevhyLtfR3MDNA8yXVBQoPrLycnpwYh7Tk1NDYYOHYotW7a0a/2srCxMmjQJ4eHhSEhIwJIlS/Dvf/8bf/zxRzdHqh0dzc9dqampauePtbV1N0WoPbGxsVi0aBEuXLiA48ePQy6X45FHHkFNTU2b2/Sn605n8gP0j2vPgAEDsH79esTHxyMuLg7jxo3DE088gevXr7e6fn86b4CO5wfoH+dNl2NEp4wcOZItWrRI9VihUDB7e3v2/vvvt7r+jBkz2KRJk9SWBQUFseeff75b49SGjuZmx44dzNTUtIei0x0A2IEDBzSu83//93/Mz89PbdnMmTNZREREN0amG9qTn+joaAaAlZWV9UhMukQqlTIALDY2ts11+tN1517tyU9/vfYwxpi5uTn7+uuvW32uP583d2nKT38+bx4EtcjqkMbGRsTHx2P8+PGqZTweD+PHj8f58+db3eb8+fNq6wNAREREm+v3Vp3JDQBUV1fD2dkZjo6O9/0m3J/0l/PmQfn7+8POzg4TJkzA2bNntR1Oj6ioqAAAWFhYtLlOfz5/2pMfoP9dexQKBfbs2YOamhoEBwe3uk5/Pm/akx+g/503XYEKWR1SXFwMhUIBGxsbteU2NjZt9s0rLCzs0Pq9VWdy4+3tje3bt+PXX3/F999/D6VSiZCQENy6dasnQtZpbZ03lZWVqKur01JUusPOzg5ffPEF9u/fj/3798PR0RFhYWG4fPmytkPrVkqlEkuWLMHo0aMxaNCgNtfrL9ede7U3P/3p2pOUlAQjIyPo6+tj4cKFOHDgAHx9fVtdtz+eNx3JT386b7qSnrYDIKS7BAcHq33zDQkJwcCBA7Ft2za88847WoyM6Dpvb294e3urHoeEhCAjIwMbNmzArl27tBhZ91q0aBGuXbuGM2fOaDsUndTe/PSna4+3tzcSEhJQUVGBn3/+GZGRkYiNjW2zWOtvOpKf/nTedCUqZHWIRCIBn89HUVGR2vKioiLY2tq2uo2trW2H1u+tOpObewkEAgQEBCA9Pb07QuxV2jpvTExMYGBgoKWodNvIkSP7dIH30ksv4ffff8epU6cwYMAAjev2l+vO33UkP/fqy9ceoVAIDw8PAEBgYCD++usvbNy4Edu2bWuxbn88bzqSn3v15fOmK1HXAh0iFAoRGBiIEydOqJYplUqcOHGizT41wcHBausDwPHjxzX2wemNOpObeykUCiQlJcHOzq67wuw1+st505USEhL65LnDGMNLL72EAwcO4OTJk3B1db3vNv3p/OlMfu7Vn649SqUSDQ0NrT7Xn86btmjKz73603nzQLR9txlRt2fPHqavr8927tzJkpOT2XPPPcfMzMxYYWEhY4yxefPmsZUrV6rWP3v2LNPT02Mff/wxu3HjBluzZg0TCAQsKSlJWy+h23Q0N+vWrWN//PEHy8jIYPHx8eypp55iIpGIXb9+XVsvodtUVVWxK1eusCtXrjAA7L///S+7cuUKy8nJYYwxtnLlSjZv3jzV+pmZmUwsFrMVK1awGzdusC1btjA+n8+OHj2qrZfQrTqanw0bNrCDBw+ymzdvsqSkJPbKK68wHo/H/vzzT229hG7zwgsvMFNTUxYTE8MKCgpUf7W1tap1+vN1pzP56S/XnpUrV7LY2FiWlZXFrl69ylauXMk4jmPHjh1jjPXv84axjuenv5w3XY0KWR20efNm5uTkxIRCIRs5ciS7cOGC6rnQ0FAWGRmptv6+ffuYl5cXEwqFzM/Pjx0+fLiHI+45HcnNkiVLVOva2Niwxx57jF2+fFkLUXe/u8NF3ft3Nx+RkZEsNDS0xTb+/v5MKBQyNzc3tmPHjh6Pu6d0ND8ffPABc3d3ZyKRiFlYWLCwsDB28uRJ7QTfzVrLCwC186E/X3c6k5/+cu159tlnmbOzMxMKhczKyoo9/PDDqiKNsf593jDW8fz0l/Omq3GMMdZz7b+EEEIIIYR0DeojSwghhBBCeiUqZAkhhBBCSK9EhSwhhBBCCOmVqJAlhBBCCCG9EhWyhBBCCCGkV6JClhBCCCGE9EpUyBJCCCGEkF6JCllCCCGEENIrUSFLCCE6KiYmBhzHoby8vMePzXEcOI6DmZlZu9a/GyvHcZgyZUq3xkYI6XqnTp3C5MmTYW9vD47jcPDgwW4/Zn5+PubOnQtLS0sYGBhg8ODBiIuL69A+qJAlhBAdEBYWhiVLlqgtCwkJQUFBAUxNTbUS044dO5CWltaude/GOmPGjG6OihDSHWpqajB06FBs2bKlR45XVlaG0aNHQyAQ4MiRI0hOTsYnn3wCc3PzDu1Hr5viI4QQ8oCEQiFsbW21dnwzMzNYW1u3a927sRoYGKChoaGbIyOEdLWJEydi4sSJbT7f0NCAN954Az/++CPKy8sxaNAgfPDBBwgLC+vU8T744AM4Ojpix44dqmWurq4d3g+1yBJCiJbNnz8fsbGx2Lhxo+rn+ezs7BZdC3bu3AkzMzP8/vvv8Pb2hlgsxvTp01FbW4tvv/0WLi4uMDc3x+LFi6FQKFT7b2howKuvvgoHBwcYGhoiKCgIMTExHY4zMTER4eHhMDY2homJCQIDAzv8MyAhpHd66aWXcP78eezZswdXr17Fk08+iUcffRQ3b97s1P4OHTqE4cOH48knn4S1tTUCAgLw1VdfdXg/1CJLCCFatnHjRqSlpWHQoEF4++23AQBWVlbIzs5usW5tbS02bdqEPXv2oKqqCtOmTcPUqVNhZmaGqKgoZGZm4p///CdGjx6NmTNnAmj+AEpOTsaePXtgb2+PAwcO4NFHH0VSUhI8PT3bHeecOXMQEBCArVu3gs/nIyEhAQKBoEtyQAjRXbm5udixYwdyc3Nhb28PAHj11Vdx9OhR7NixA++9916H95mZmYmtW7di2bJleP311/HXX39h8eLFEAqFiIyMbPd+qJAlhBAtMzU1hVAohFgsvm9XArlcjq1bt8Ld3R0AMH36dOzatQtFRUUwMjKCr68vwsPDER0djZkzZ3bpB1Bubi5WrFgBHx8fAOhQEUwI6b2SkpKgUCjg5eWltryhoQGWlpYAgJSUFAwcOFDjfl577TWsX78eAKBUKjF8+HDVNSggIADXrl3DF198QYUsIYT0VWKxWFXEAoCNjQ1cXFxgZGSktkwqlQJo3wdQey1btgz//ve/sWvXLowfPx5PPvmkWiyEkL6puroafD4f8fHx4PP5as/dvfa4ubnhxo0bGvfz92uOnZ0dfH191Z4fOHAg9u/f36HYqJAlhJBe5N6f8jmOa3WZUqkE0L4PoPZau3YtZs+ejcOHD+PIkSNYs2YN9uzZg6lTp3bilRBCeouAgAAoFApIpVKMGTOm1XWEQqHq15r2GD16NFJTU9WWpaWlwdnZuUOxUSFLCCE6QCgUqt2g1VXa8wHUEV5eXvDy8sLSpUsxa9Ys7NixgwpZQvqA6upqpKenqx5nZWUhISEBFhYW8PLywpw5c/D000/jk08+QUBAAGQyGU6cOIEhQ4Zg0qRJHT7e0qVLERISgvfeew8zZszApUuX8OWXX+LLL7/s0H5o1AJCCNEBLi4uuHjxIrKzs1FcXKxqUX1Qf/8A+uWXX5CVlYVLly7h/fffx+HDh9u9n7q6Orz00kuIiYlBTk4Ozp49i7/++uu+feIIIb1DXFwcAgICEBAQAKC5K1FAQABWr14NoHlc6aeffhrLly+Ht7c3pkyZgr/++gtOTk6dOt6IESNw4MAB/Pjjjxg0aBDeeecdfPrpp5gzZ06H9kMtsoQQogNeffVVREZGwtfXF3V1dcjKyuqyfe/YsQPvvvsuli9fjvz8fEgkEowaNQr/+Mc/2r0PPp+PkpISPP300ygqKoJEIsG0adOwbt26LouTEKI9YWFhYIy1+bxAIMC6deu69D3/j3/8o0PXodZwTFPUhBBC+iWO43DgwIEOTzc7f/58lJeX98j0loQQQl0LCCGEtGrWrFkYMGBAu9Y9ffo0jIyMsHv37m6OihBC/odaZAkhhLRw96YPPp/frmkj6+rqkJ+fD6B5NARtTq1LCOk/qJAlhBBCCCG9EnUtIIQQQgghvRIVsoQQQgghpFeiQpYQQgghhPRKVMgSQgghhJBeiQpZQgghhBDSK1EhSwghhBBCeiUqZAkhhBBCSK9EhSwhhBBCCOmVqJAlhBBCCCG90v8DIhj0mI7ZKw0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weights = [\n",
    "    0.26,\n",
    "    0.13,\n",
    "    0.93,\n",
    "    0.95,\n",
    "    0.23,\n",
    "    0.20,\n",
    "    0.05,\n",
    "    0.96,\n",
    "    0.01,\n",
    "]  # Weights for the vertices in the graph\n",
    "\n",
    "t_max = 3.8e-6\n",
    "\n",
    "\n",
    "time_points = [\n",
    "    0,\n",
    "    t_ramp_omega,\n",
    "    t_max - t_ramp_local_detuning - t_ramp_omega,\n",
    "    t_max - t_ramp_local_detuning,\n",
    "    t_max,\n",
    "]\n",
    "amplitude_values = [0, omega_max, omega_max, 0, 0]\n",
    "\n",
    "phase_values = [0 for _ in range(len(time_points))]\n",
    "detuning_0 = -detuning_max / 12\n",
    "\n",
    "detuning_slew_rate = local_detuning_max / (t_max - t_ramp_local_detuning)\n",
    "detuning_values = [\n",
    "    detuning_0,\n",
    "    detuning_0 + detuning_slew_rate * t_ramp_omega,\n",
    "    detuning_0 + detuning_slew_rate * (t_max - t_ramp_local_detuning - t_ramp_omega),\n",
    "    detuning_0 + detuning_slew_rate * (t_max - t_ramp_local_detuning),\n",
    "    detuning_0 + detuning_slew_rate * (t_max - t_ramp_local_detuning),\n",
    "]\n",
    "\n",
    "drive = DrivingField.from_lists(time_points, amplitude_values, detuning_values, phase_values)\n",
    "\n",
    "time_local_detuning = [0, t_max - t_ramp_local_detuning, t_max]\n",
    "value_local_detuning = [0, -local_detuning_max, 0]\n",
    "\n",
    "pattern = [np.round(1 - w, 2) for w in weights]\n",
    "local_detuning = LocalDetuning.from_lists(time_local_detuning, value_local_detuning, pattern)\n",
    "\n",
    "\n",
    "program = AnalogHamiltonianSimulation(hamiltonian=drive + local_detuning, register=register)\n",
    "\n",
    "show_drive_and_local_detuning(drive, local_detuning)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6f84eac",
   "metadata": {},
   "source": [
    "We can run the program on the local simulator and inspect the average final Rydberg densities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "52ca355b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = simulator.run(program, shots=1000, steps=30, blockade_radius=7.9e-6).result()\n",
    "show_final_avg_density(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feaf4498",
   "metadata": {},
   "source": [
    "From the above barplot, we see that vertices $\\left\\{2, 3, 7\\right\\}$ have the highest Rydberg densities around 0.5. This is precisely the MWIS for the given weighted unit disk graph. To further confirm that our protocol can yield the result of the correct MWIS, we aggregate over all the results, and find the most likely configuration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b7ffd119",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The configuration with largeset probability reads ggrrgggrg with probability 0.209\n"
     ]
    }
   ],
   "source": [
    "def get_counters_from_result(result):\n",
    "    post_sequences = [list(measurement.post_sequence) for measurement in result.measurements]\n",
    "    post_sequences = [\n",
    "        \"\".join([\"r\" if site == 0 else \"g\" for site in post_sequence])\n",
    "        for post_sequence in post_sequences\n",
    "    ]\n",
    "\n",
    "    counters = {}\n",
    "    for post_sequence in post_sequences:\n",
    "        if post_sequence in counters:\n",
    "            counters[post_sequence] += 1\n",
    "        else:\n",
    "            counters[post_sequence] = 1\n",
    "    return counters\n",
    "\n",
    "\n",
    "counters = get_counters_from_result(result)\n",
    "sorted_counters = sorted(counters.items(), key=lambda x: -x[1])\n",
    "\n",
    "\n",
    "config_largest_prob = sorted_counters[0][0]\n",
    "largest_prob = sorted_counters[0][1] / sum([item[1] for item in sorted_counters])\n",
    "\n",
    "print(\n",
    "    f\"The configuration with largeset probability reads {config_largest_prob} with probability {largest_prob}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52fde076",
   "metadata": {},
   "source": [
    "The most likely configuration has Rydberg states for the vertices $\\left\\{2, 3, 7\\right\\}$, which again confirms that it corresponds to the MWIS of the given weighted unit disk graph. From the above simulation, there are around 22% of the chance we will obtain the correct MWIS. \n",
    "\n",
    "## Solving the MWIS problem on a QPU\n",
    "\n",
    "In previous sections, we have demonstrated how to solve the MWIS problem with the Rydberg atoms. The results from the local simulator show that the results of the program meet our expectations. Here we will run the same AHS program on a quantum device.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note: </b> Since it will take sometime before we can receive the result back from the quantum device, it is suggested to save the task ARN for retrieving the task result in a later time. \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "08a7014b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from braket.aws import AwsDevice\n",
    "\n",
    "qpu = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ea0b844c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARN: arn:aws:braket:us-east-1:545821822555:quantum-task/edaa9952-85dd-45e9-bc92-9d9125077e8a\n"
     ]
    }
   ],
   "source": [
    "task = qpu.run(program.discretize(qpu), shots=1000)\n",
    "metadata = task.metadata()\n",
    "task_arn = metadata[\"quantumTaskArn\"]\n",
    "print(f\"ARN: {task_arn}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca04aa1e",
   "metadata": {},
   "source": [
    "We can extract the result from the QPU and plot the average Rydberg density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "929f8c96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from braket.aws import AwsQuantumTask\n",
    "\n",
    "task = AwsQuantumTask(arn=task_arn)\n",
    "result_qpu = task.result()\n",
    "show_final_avg_density(result_qpu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "afa5aa4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The configuration with largeset probability reads ggrrgggrg with probability 0.125\n"
     ]
    }
   ],
   "source": [
    "counters_qpu = get_counters_from_result(result_qpu)\n",
    "sorted_counters_qpu = sorted(counters_qpu.items(), key=lambda x: -x[1])\n",
    "\n",
    "config_largest_prob_qpu = sorted_counters_qpu[0][0]\n",
    "largest_prob_qpu = sorted_counters_qpu[0][1] / sum([item[1] for item in sorted_counters_qpu])\n",
    "\n",
    "print(\n",
    "    f\"The configuration with largeset probability reads {config_largest_prob_qpu} with probability {largest_prob_qpu}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "745c5c20",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "In this example, we have demonstrated how to solve the MWIS problem for a weighted unit disk graph. The local detuning plays the key role to enable one to define the cost function, which has different weights on different vertices. Given that the MWIS problem has many applications, such as routing, scheduling and network optimization, this example illustrates the potential of Rydberg atoms, together with the capability of local detuning, in different industries (see [Wurtz et. al](https://arxiv.org/abs/2205.08500) for more details)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d467059c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Task Summary\n",
      "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 1000, 'tasks': {'COMPLETED': 1}}}\n",
      "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
      "Estimated cost to run this example: 10.30 USD\n"
     ]
    }
   ],
   "source": [
    "print(\"Task Summary\")\n",
    "print(tracker.quantum_tasks_statistics())\n",
    "print(\n",
    "    \"Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\"\n",
    ")\n",
    "print(\n",
    "    f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e1cc8ac",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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