examples/analog_hamiltonian_simulation/07_Simulating_Lattice_Gauge_Theory_with_Rydberg_Atoms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "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": "513c4907",
   "metadata": {},
   "source": [
    "# Simulating lattice gauge theory with Rydberg atoms\n",
    "\n",
    "In [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), we introduced a component of analog Hamiltonian simulations (AHS) with Rydberg atom, namely the local detuning that detunes the atoms according to a non-uniform pattern. This is different from the global driving field, which has been the main focus of previous notebooks, that addresses all the atoms simultaneously and uniformly. Here, we illustrate an important use case for the local detuning, which is initial state preparation, in the context of simulating lattice gauge theory (LGT). This notebook is inspired by the paper [F. M. Surace et al. (10.1103/PhysRevX.10.021041)](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.021041).\n",
    "\n",
    "## Background: The propagation of particle-antiparticle pairs in LGT\n",
    "\n",
    "Specifically, we are interested in simulating the propagation of a particle-antiparticle pair in LGT. For that, we will use the so-called quantum link model formulation of the LGT, where the states of an atom are interpreted as left or right pointing electric fields, and the bonds between neighboring atoms are interpreted as particles or antiparticles depending on the configurations. \n",
    "\n",
    "More specifically, the Rydberg states at the odd (even) sites are interpreted as electric fields pointing to the left (right), whereas the ground states at the odd (even) sites are electric field pointing to the right (left). The electric fields correspond to the red and blue arrows in the figure shown below. The bonds between the atoms are interpreted as particles or antiparticles. If the electric fields are diverging at a bond, then it is particle, otherwise if the electric field is converging, the bond is an antiparticle. There is no particle if the left and right electric fields are pointing in the same direction, or we interpret the bond as a vacuum. This is similar to positive charge and negative charge have outward and inward pointing electric fields respectively. The mapping is summarized in the following figure (source: [F. M. Surace et al. (10.1103/PhysRevX.10.021041)](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.021041)).\n",
    "\n",
    "<!-- Further, the bond between an odd and an even indexed atoms corresponds to an antiparticle if both atoms are in the ground states, otherwise it is interpreted as a vacuum state. On the other hand, the bond between an even and an odd indexed atoms corresponds to a particle if both atoms are in the ground states, otherwise it is interpreted as a vacuum. The mapping is summarized in the following figure (source: [F. M. Surace et al. (10.1103/PhysRevX.10.021041)](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.021041)). -->\n",
    "\n",
    "![LGT_mapping.png](LGT_mapping.png)\n",
    "\n",
    "Using the above mapping, we can interpret the 1D $Z_2$ state (see [notebook 02](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb)) as the so-called \"anti-string\" state with all electric fields pointing in the same direction. In order to prepare the particle-antiparticle pair, we will need to prepare a defect in the anti-string state: The domain walls between anti-string and string states will host particles, whereas those between string and anti-string states will host anti-particles. Interestingly, the particle and antiparticle always come in pairs, and their time evolution exhibits light cones, in which the string-antistring oscillation is out-of-phase compared to that outside of the light cone. This is illustrated below (source: [F. M. Surace et al. (10.1103/PhysRevX.10.021041)](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.021041)).\n",
    "<div>\n",
    "<img src=\"LGT_particle_antiparticle_propagation.png\" width=\"800\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "158862c1",
   "metadata": {},
   "source": [
    "In this notebook, we will use the local detuning, together with the driving field, to create a 1D $Z_2$ ordered state with a defect in the center. This is the desired initial state with a particle-antiparticle pair. After that, we turn off the local detuning, and let the atoms continue to evolve under the constant driving field. From the mapping between the Rydberg atoms and LGT described above, we anticipate that the average Rydberg density of the atomic chain will exhibit a pattern that resembles a light cone.\n",
    "\n",
    "To begin, we import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "74b31e7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "tracker = Tracker().start()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "73014d7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from braket.ahs.hamiltonian import Hamiltonian\n",
    "from braket.ahs.atom_arrangement import AtomArrangement\n",
    "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n",
    "from braket.timings import TimeSeries\n",
    "from braket.ahs.driving_field import DrivingField\n",
    "from braket.ahs.local_detuning import LocalDetuning\n",
    "\n",
    "from ahs_utils import (\n",
    "    show_drive_and_local_detuning, \n",
    "    show_final_avg_density, \n",
    ")\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import time\n",
    "\n",
    "from braket.devices import LocalSimulator\n",
    "simulator = LocalSimulator(\"braket_ahs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0cb3a1e",
   "metadata": {},
   "source": [
    "Let's define certain device-specific constraints, such as maximum values for the Rabi frequency and local detuning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6ce1888",
   "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 = 125000000.0 # rad / seconds\n",
    "# local_detuning_slew_rate_max = 2500000000000000.0 # rad / 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": "522c066d",
   "metadata": {},
   "source": [
    "## Define atom arrangement\n",
    "\n",
    "We first prepare a 1D chain of atoms. Since we would like to create a defect that is symmetrically centered at the chain, the length of the chain should be $4n+1$ for integer n. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7206295d",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 9 # 4n+1\n",
    "a = 5.5e-6\n",
    "register = AtomArrangement()\n",
    "for ind in range(N):\n",
    "    register.add([0, ind * a])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4286c0b",
   "metadata": {},
   "source": [
    "# Prepare the state with particle-antiparticle pair\n",
    "\n",
    "There are several approaches to prepare a 1D $Z_2$ state with a defect at the center. Here we will subject the chain of atoms with a $\\pi$-pulse, together with positive local detuning on the odd indexed atoms and the center atoms. Because these atoms are strongly detuned away from resonance, they will remain in the ground states whereas the rest of the atoms are excited to the Rydberg states. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "edcbb3f4-023e-48b7-996b-90efd401e1da",
   "metadata": {},
   "outputs": [
    {
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b1SVpBvdhsTFf7XH5W4rIyEicPXsWr776Kvr27Yu+ffvitddew9mzZxEZGenq8jRHkiTExcXxYw1BMV+x2ZqvVo/IGg16hLasaa45vcAS92GxMV/tcfkRWQBo3rw5Hn/8cVeX4Rb0ej06d+7MjzUExXzFZmu+WRptZIGamjILypFZUI7IiFauLkczuA+LjflqjyYaWQA4deoUMjMzLebKAsC9997rooq0qXZ+DomJ+YrNlnxlRcX5wv9NLdBgIxvGE77qxX1YbMxXe1zeyJ49exYTJ07EiRMnzDdJAGC+RhtviGCp9mONkSNH8mLMAmK+YrMl39ySSlTLCox6HUI0OAe19ihxFhtZC9yHxcZ8tcflx8afeeYZREREIC8vDz4+Pjh58iTi4uIwaNAg7Nmzx9XlaY5er0fv3r35sYagmK/YbMm3tkEMDWgGo0F7Pw+1N2hgI2uJ+7DYmK/2uPztREJCAmJjYxEYGAi9Xg+9Xo9bb70VS5cuxd/+9jckJSW5ukRN0ev1aNu2ravLIAdhvmKzJd9MDd6a9mq8lmz9uA+Ljflqj8vfUsiyDF9fXwBAYGAgLl68CKDm7l+nT592ZWmaZDKZ8MMPP8BkMrm6FHIA5is2W/LV6s0QatU2snmlVaio5hSwWtyHxcZ8tcflR2R79+6NY8eOISIiAkOGDMFbb70FT09PvP/+++jUqZOry9Mcg8GAwYMHw2AwuLoUcgDmKzZb8tXqpbdq+TfzgK+3EaWVEs4XlqNrkK+rS9IE7sNiY77a4/Ijsi+99BIURQEAvPLKK8jIyMCIESMQHR2N1atXu7g67dHr9WjVqhXn5wiK+YrNlny13sjqdDpOL6gH92GxMV/tcXkSUVFRmDRpEgCgS5cuSE1NRX5+PvLy8jBq1CgXV6c9JpMJ33//PT/WEBTzFZst+Wb979JbWm1kgd/m7/KEr99wHxYb89UelzayJpMJRqMRycnJFutbtWplvvwWWTIajRgxYgQv+yEo5is2a/OtqJZxqbQKwG9XB9Ci8Na1R2QrXFyJdnAfFhvz1R6XJuHh4YHw8HBeK9YGOp0Ofn5+ri6DHIT5is3afLMKa45w+nob4d/Mw9FlNRpvilAX92GxMV/tcfnUgn/84x948cUXUVBQ4OpS3ILJZMLXX3/NjzUExXzFZm2+mZd/mx+r5U+neFOEurgPi435ao/Lj42/++67OHPmDNq1a4cOHTqgefPmFl8/cuSIiyrTJqPRiDFjxvBjDUExX7FZm6/WT/SqdfXJXqqqarrpdhbuw2Jjvtrj8iQmTJjg6hLcDncgsTFfsVmTb+3UAq03su1aekOnAypMMi5fqUZgCy9Xl6QJ3IfFxny1xeVpLF682G6vFRcXh2XLluHw4cPIzs7GV199dd1Gec+ePZg7dy5OnjyJsLAwvPTSS/jLX/5it5rsTZIkREdHY9y4cfDw0O7cOWoc5is2a/Ot/ai+vcYbWS+jASF+3rhYXInMgnI2suA+LDrmqz0unyNrT1euXEG/fv2wdu1aq7bPyMjA+PHjcccdd+Do0aOYM2cOHn30Ufzwww8OrrTxjEYjxo0bx3eEgmK+YrM2X3eZWgD8dsIX58nW4D4sNuarPS5JolWrVvjll18QGBho1fbh4eHYt28fOnTocM3txo4di7Fjx1pdx/r16xEREYHly5cDAHr27In9+/dj5cqViIqKsvp1nE2SJO5EAmO+YrtevqqqulUjG97KBwcyCswnqBH3YdExX21xSRJFRUX473//C39/f6u2v3z5skMu0ZWQkIDRo0dbrIuKisKcOXOu+byqqipUVVWZ/15SUgIA5hpr/zQYDBbLkiRBp9OZl/V6PfR6fYPLJpMJBoPBvGw0GiFJEmJiYjB27Fh4eHhY7FCSJMHDwwOqqpqXFUWBLMvmZUVRYDQaG1yWZRmqqpqX6xuHvcek0+nMy7XjaKpjAoCYmBiMGTMGzZo1E2JMIubU2DGZTCbExMQgKioKHh4e9Y4pv6walSYFOh0Q4udlrkWrY2ofUHOd218vX4Esy0LkdCM/e7Ism/dhLy8vIcYkYk6NHVNFRQV27tyJsWPHQqfTCTEmLeZkC5dNLZg+fTomTJhg1aOiwjEX287JyUFQUJDFuqCgIJSUlFzzey5duhT+/v7mR1hYGACYb+yQkpKClJQUAMDx48eRlpYGAEhKSkJGRgYAIDExEVlZWQCA+Ph4ZGdnA6iZ55ufnw8AiI2NRVFREYCa5qa0tNQ8J0eWZfNcHUmSUFlZiejoaABAaWkpYmJiANS8aYiNjQUA5OfnIy4uDgCQnZ2N+Ph4AEBWVhYSExMB1Ey3SEpKAgCkpaXh+PHjDh8TAERHR6OysrLJj8nDwwPDhg1DQkKCMGMSMafGjiklJQX33Xcfzpw50+CYEk+mAwBae+uRm31B82NSSy8BAE5fyBcmpxv52cvPz8d9992HhIQEYcYkYk6NHdPOnTsxbtw4yLIszJi0mpO1dKqqqjY9w03odLrrnuzVrVs3zJgxAy+88IJ5XXR0NMaPH4/y8nI0a1b/HXXqOyIbFhaGgoICBAQEOPSdFAAUFhaiZcuW0Ol0mnwnJeK7Q2eNyWg0ori4GM2bN7/m+NxpTCLm1NgxqaqK8vJy+Pj4mGv//Zi+OZaNuVuPI7JjADY/PlTzYzqSWYj73zuAdi29se/vtwuR04387Ol0Oly5cgXNmjWzGIc7j0nEnBo7JpPJhIqKCvj6+pprd/cxaTGnsrIy+Pv7o7i4+Lo3oGjSkzyCg4ORm5trsS43Nxd+fn4NNrEA4OXlBS+vumfnGgwGiz9/v1z7g2Lt8tVnRNYum0wmJCQkYMyYMfDw8Kh3m9qPOwCYf5itXW6odkeOyZrlpjImk8mEn376CWPGjBFmTNYuN4UxmUwm7Nu3z+I6lL8f0/miSgBAh9bNza+j5TF1DPQFAGQXV0JWdTDUMyZblrUwpustX2scV2dc+/ruPqb6lpvqmHQ6Hfbv32/+P1iEMWk1J2sJddUCWw0bNgy7du2yWLdz504MGzbMRRVdn4eHB8aPH2/xg0fiYL5isyZfdzrRCwACW3iimYcBqgpcKHLMNDB3wn1YbMxXe4RqZMvKynD06FEcPXoUQM08jaNHjyIzMxMA8MILL2DatGnm7f/617/i7NmzWLBgAVJTU7Fu3Tp8/vnnePbZZ11RvlUURUFBQQEURXF1KeQAzFds1uRrbmRbu0cjq9PpLO7w1dRxHxYb89UeoRrZQ4cOYcCAARgwYAAAYO7cuRgwYAAWLVoEoGZicm1TCwARERH4/vvvsXPnTvTr1w/Lly/Hhx9+qOlLb8myjIMHDzrkKg7kesxXbNbke/5/zWCYmxyRBYCwVjVTsXgtWe7DomO+2iPsyV7OVFJSYvWkZCKihlRJMnos3AFVBQ69NNpt7pS15NuT2PDTOTwxshNeGNfT1eUQkZuzpa/SxBHZ9PR0vPTSS5g6dSry8vIAAP/9739x8uRJF1emPYqiIC8vjx9rCIr5iu16+V4orICqAs08DGjd3NPJ1TUepxb8hvuw2Jiv9ri8kd27dy/69OmDAwcOYNu2bSgrKwMAHDt2DIsXL3ZxddqjKAqSk5O5EwmK+YrtevlefaKXTqdzZmk3hI3sb7gPi435ao/LG9nnn38er776Knbu3AlPz9+OQIwaNQo///yzCyvTJqPRiFGjRjXqEhWkfcxXbNfLN8sN58cCbGSvxn1YbMxXe1zeyJ44cQITJ06ss75t27bmO1PQbxRFwYULF/huUFDMV2zXyzersObyVe5y6a1a7QNq6i2tlFBcbnJxNa7FfVhszFd7XN7ItmzZ0nxbtaslJSUhNDTUBRVpm6IoSE9P504kKOYrtuvlm3m5dmpBwzdk0aJmnga08a05Ma2pH5XlPiw25qs9Lm9kH3zwQTz33HPIycmBTqeDoij46aefMH/+fItrvlINo9GIkSNH8mMNQTFfsV0v30w3nVoAcHpBLe7DYmO+2uPyRvb1119Hjx49EBYWhrKyMvTq1QsjR47E8OHD8dJLL7m6PM1RFAW//vor3w0KivmK7Vr5qqpqniPrblMLADaytbgPi435ao/LG1lPT0988MEHSE9Px3fffYf//Oc/SE1Nxf/93/9Z3IuXanB+jtiYr9iulW9RuQmlVRKA3+acupMwNrIAuA+Ljvlqj2aOjYeHhyM8PNzVZWie0WjE8OHDXV0GOQjzFdu18s0qrGkA2/p6oZmn+72JDwuomdd7vrBpN7Lch8XGfLXHJY3s3Llzrd52xYoVDqzE/ciyjIyMDERERPCItYCYr9iulW+mG08rADi1oBb3YbExX+1xSSOblJRk8fcjR45AkiR0794dAPDLL7/AYDBg4MCBrihP01RVRWFhITp27OjqUsgBmK/YrpWvO5/oBQDhrWvqvlBYAUlWYDS4fOaaS3AfFhvz1R6XNLK7d+82L69YsQK+vr74+OOPERAQAAAoLCzEjBkzMGLECFeUp2lGoxGDBw92dRnkIMxXbNfK111vhlAryNcbngY9qmUF2cWVbjuOG8V9WGzMV3tc/pZ5+fLlWLp0qbmJBYCAgAC8+uqrWL58uQsr0yZZlpGamgpZll1dCjkA8xXbtfJ196kFer0O7f93/dusJjy9gPuw2Jiv9ri8kS0pKcGlS5fqrL906RJKS0tdUJH2VVRUuLoEciDmK7aG8s0qcM+7el0t7H9XW8hq4id8cR8WG/PVFpc3shMnTsSMGTOwbds2nD9/HufPn8eXX36JmTNnYtKkSa4uT3MMBgMGDBjASeaCYr5iayhfSVZwocj9G1me8MV9WHTMV3tc3siuX78eY8eOxUMPPYQOHTqgQ4cOeOihh3DXXXdh3bp1ri5Pc2RZRnJyMj/WEBTzFVtD+WYXV0JWVHga9Wj7v1u9uqPfGtmme8SK+7DYmK/2uPw6sj4+Pli3bh2WLVuG9PR0AEDnzp3RvHlzF1dGROQctUcw2wc0g16vc3E1jcebIhCRs7m8ka3VvHlz9O3b19VlaJ7BYEDv3r1dXQY5CPMVW0P5uvuJXrVq62/KJ3txHxYb89Uelzeyd9xxB3S6ho9AxMbGOrEa7ZNlGcePH0ffvn05R0dAzFdsDeWbJUgjG/a/qxYUXKlGWZWEFl4u/y/G6bgPi435ao/Lf8v079/f4u8mkwlHjx5FcnIypk+f7pqiNK5Zs2auLoEciPmKrb58RTki6+vtgQAfDxSWm5BVUI6eIX6uLskluA+Ljflqi8sb2ZUrV9a7/uWXX0ZZWZmTq9E+g8GAHj16uLoMchDmK7aG8nX3myFcLbyVDwrLi5HZRBtZ7sNiY77a4/KrFjTkT3/6Ez766CNXl6E5kiTh4MGDkCTJ1aWQAzBfsTWUr/n2tAHu38iGNfF5styHxcZ8tUezjWxCQgK8vb1dXYbm6HQ6BAQEXHNeMbkv5iu2+vItrTShsNwE4Lc5pu6sqV9Llvuw2Jiv9rh8asHvb3qgqiqys7Nx6NAhLFy40EVVaZfBYECXLl1cXQY5CPMVW3351t7Rq1VzT/h6e7iiLLtq6kdkuQ+Ljflqj8uPyPr5+cHf39/8aNWqFW6//XZER0dj8eLFri5PcyRJQnx8PD/WEBTzFVt9+WYKND8W4BFZ7sNiY77a4/Ijshs3brT7a65duxbLli1DTk4O+vXrhzVr1iAyMrLB7z9jxgyLdV5eXqisrLR7Xfag1+sRGhoKvd7l70HIAZiv2OrLV5RLb9UyX0u2sAKKorr1DR4ag/uw2Jiv9rg8iU6dOuHy5ct11hcVFaFTp042v96WLVswd+5cLF68GEeOHEG/fv0QFRWFvLy8Bp/j5+eH7Oxs8+PXX3+1+fs6i16vR4cOHbgTCYr5iq2+fH870cv958cCQIi/Nwx6HaolBXmlVa4ux+m4D4uN+WqPy5M4d+5cvfcsrqqqwoULF2x+vRUrVuCxxx7DjBkz0KtXL6xfvx4+Pj7XvAKCTqdDcHCw+REUFGTz93UWSZIQFxfHjzUExXzFVl++olxDtpbRoEdoy5qmvClOL+A+LDbmqz0um1rwzTffmJd/+OEH+Pv7m/8uyzJ27dqFjh072vSa1dXVOHz4MF544QXzOr1ej9GjRyMhIaHB55WVlaFDhw5QFAU333wzXn/9ddx00002fW9n0ev16Ny5M98NCor5iq2+fLMKxWpkgZqrL2QWlCOroByREa1cXY5TcR8WG/PVHpc1shMmTABQczT093fw8vDwQMeOHbF8+XKbXjM/Px+yLNc5ohoUFITU1NR6n9O9e3d89NFH6Nu3L4qLi/H2229j+PDhOHnyJNq3b1/vc6qqqlBV9dtHZiUlJQBgPrJc+6fBYLBYliQJOp3OvKzX66HX6xtcNplMMBgM5mWj0Qi9Xo+2bdtCp9NBVVVIkgSjsSZGSZLg4eFhXu/h4QFFUSDLsnlZURQYjcYGl2VZhqqq5uX6xmHvMel0OvNy7Tia8phCQkKgKAr0er0wYxIxp8aOKTQ0FLIsQ5Zl6HR6nL/qZC93HdPvs2l/1RFZUcZky89eaGio+YidKGMSMafGjEmWZbRr1w5AzZ1IRRiTFnOyhcveUtQOOjw8HHl5eea/K4qCqqoqnD59GnfffbfD6xg2bBimTZuG/v3747bbbsO2bdvQpk0bvPfeew0+Z+nSpRZXWggLCwMAJCcnAwBSUlKQkpICADh+/DjS0tIAAElJScjIyAAAJCYmIisrCwAQHx+P7OxsAEBcXBzy8/MBALGxsSgqKgIAxMTEoLS0FJIkITo6GmVlZeZlSZJQWVmJ6OhoAEBpaSliYmIA1Mw1jo2NBVDT6MfFxQEAsrOzER8fDwDIyspCYmIiACAjIwNJSUkAgLS0NBw/ftzhYwKA6OhoVFZWNvkxSZKEH3/8EXv37hVmTCLm1NgxHTt2DLGxsTh58iRSUlKQW1qJalmFQVczt9Qdx1RfTh7VxTXPKygXZkzW/uxduHABsbGx2Lt3rzBjEjGnGxlTbGwsysrKhBqTFnOylk5VVdWmZ2hYdXU1fHx88MUXX5iP+ALA9OnTUVRUhK+//tqq17n//vthNBrx2Wef1fv1+o7IhoWFoaCgAAEBAQ59J6WqKnJychAUFGTeXmvvpER8d+isMRkMBly6dAkBAQHw9PQUYkwi5tTYMSmKgsLCQgQEBECv1+PQr0WY8v7PCG/VDHELRrnlmOrL5puj5/G3zccwqEMANj8WKcSYrP3ZA4CCggK0bNnS/Cmau49JxJwaO6bq6moUFRUhMDAQiqIIMSYt5lRWVgZ/f38UFxfDz+/at7p2SSO7evVqPP744/D29sbq1auvue3f/vY3m157yJAhiIyMxJo1awDAfNR31qxZeP7556/7fFmWcdNNN2HcuHFYsWKFVd+zpKTE6n9wIqJaWw9l4e9fHMetXQLxn0eHuLocuzl+vgj3vvsT2vp6IfEfo11dDhG5GVv6KpfMkV25ciUefvhheHt7Y+XKlQ1up9PpbG5k586di+nTp2PQoEGIjIzEqlWrcOXKFfO1YqdNm4bQ0FAsXboUAPDKK69g6NCh6NKlC4qKirBs2TL8+uuvePTRRxs/QAcymUyIjY3FqFGj4OHh/ncBIkvMV2y/zzersOauXqLcDKFWWEDNePJKq1BpkuHtYXBxRc7DfVhszFd7XNLI1s6F+P2yPUyZMgWXLl3CokWLkJOTg/79+2PHjh3mE8AyMzMtJhIXFhbiscceQ05ODgICAjBw4EDEx8ejV69edq3LXgwGAwYPHgyDoen8x9CUMF+x/T5f0W6GUKuljwd8vYworZJwvrAcXdr6urokp+E+LDbmqz1CzZF1FU4tIKLGmPyveBz+tRBrH7oZ4/uGuLocuxr3zj6cyi7BR38ZhFE9tHttbiLSHs1PLZg7d67V21o7T7WpMJlMiImJwZgxY/ixhoCYr9h+n6/5rl6txLir19XCW/ngVHYJMi83rZsicB8WG/PVHpc0srWXZbgena5p3aPbGkajESNGjDCfYUhiYb5iuzrfimoZl/53C1fRphYAQHjrmjFlFlS4uBLn4j4sNuarPS5JYvfu3a74tkLQ6XScviAw5iu2q/M9/787evl6G+HfTLwjO2EBNUeZa+9c1lRwHxYb89UeTd1jLSsry+YL4TY1JpMJX3/9NUwmk6tLIQdgvmK7Ot/Mq070EvHTp9orMdSe0NZUcB8WG/PVHpc3spIkYeHChfD390fHjh3RsWNH+Pv746WXXuIPSj2MRiPGjBnDjzUExXzFdnW+mYJesaBW7bgyC8rRlM4p5j4sNuarPS5PYvbs2di2bRveeustDBs2DACQkJCAl19+GZcvX8a//vUvF1eoPdyBxMZ8xVabr+iNbGhAM+h0QHm1jMtXqhHYwsvVJTkN92GxMV9tcfkR2U2bNmHjxo144okn0LdvX/Tt2xdPPPEE/v3vf2PTpk2uLk9zrr4vMomH+Yrt6nxrP3JvL2gj62U0IMTPG8BvTXtTwH1YbMxXe1zeyHp5eaFjx4511kdERMDT09P5BWmc0WjEuHHj+I5QUMxXbFfnm/W/s/lFPSIL/NakN6V5styHxcZ8tcfljeysWbPwz3/+E1VVVeZ1VVVVeO211zBr1iwXVqZdfCcoNuYrNkmSoKqq8FMLgN/G1pQaWYD7sOiYr7a4vJFNSkrCd999h/bt22P06NEYPXo02rdvj2+//RbHjh3DpEmTzA+q2YFiYmK4IwmK+YqtNt/c4nJUmGTodEBoS/FuhlDr6hO+mgruw2Jjvtrj8mPjLVu2xOTJky3WhYWFuaga7fPw8MB9993n6jLIQZiv2GrzPfxrIQCgnX8zeBpdfjzBYZpiI8t9WGzMV3tc3shu2LDB1SW4FVVVUVpaCl9fXyGvPdnUMV+x1eabefkKAKB9gLhHY4GrryXbdO7uxX1YbMxXe8Q9FCAoSZKwb98+fqwhKOYrttp8f/1fIyvy/FgACGtV06hnF1egWlJcXI1zcB8WG/PVHpc3spcvX8bTTz+NXr16ITAwEK1atbJ4kCUPDw+MHz8eHh7i3dKSmK/oavO9UFQJQPxGtk0LL3h76KGowMWipnFUlvuw2Jiv9rh8asGf//xnnDlzBjNnzkRQUBAP1V+HoigoKipCy5Ytode7/H0I2RnzFVttvuYrFrQWu5HV6XQIb+WDX3LLkFlQjo6BzV1dksNxHxYb89Uelzey+/btw/79+9GvXz9Xl+IWZFnGwYMHMWrUKO5EAmK+YqvNN7Og5ldvmOBHZAFYNLJNAfdhsTFf7XF5Cj169EBFRdP4yMkePDw8EBUVxY81BMV8xebh4YHb7xyNnJKaqQVhAeI3smFN7Fqy3IfFxny1x+WN7Lp16/CPf/wDe/fuxeXLl1FSUmLxIEuKoiAvLw+K0jROnGhqmK/YFEXBifQLUFWgmYcBgS3Ev3thbbOeVdg0Glnuw2Jjvtrj8ka2ZcuWKCkpwahRo9C2bVsEBAQgICAALVu2REBAgKvL0xxFUZCcnMydSFDMV2yKoiD+2GkANR+5N4VzApratWS5D4uN+WqPy+fIPvzww/Dw8MCmTZt4spcVjEYjRo0a5eoyyEGYr9iMRiMCwrsBR5KbxPxY4LcT2jIvN41Glvuw2Jiv9ri8kU1OTkZSUhK6d+/u6lLcgqIoyM7ORkhICCeaC4j5ik1RFJz6NReA+JfeqlU7taCkUkJxuQn+PmLPLeQ+LDbmqz0uT2HQoEHIyspydRluQ1EUpKen82MNQTFfsSmKgrSLNbenrb1ZgOiaeRrQxtcLQNOYXsB9WGzMV3tcfkR29uzZeOaZZ/D3v/8dffr0qXMmYN++fV1UmTYZjUaMHDnS1WWQgzBfsRmNRlQYfACUNJkjsgAQFtAMl0qrkFVYjj7t/V1djkNxHxYb89UelzeyU6ZMAQA88sgj5nU6nQ6qqkKn00GWZVeVpkmKoiArKwthYWH8WENAzFdssizjXH4ZgKYztQCoGeuRzKImc0SW+7C4mK/2uLyRzcjIcHUJbkVRFFy4cAGhoaHciQTEfMVWeKUKV6prPpJs3wSuIVurKV25gPuw2Jiv9ri8ke3QoYOrS3ArRqMRw4cPd3UZ5CDMV2wXS6oBAG19vdDM0+DiapynKd0Ugfuw2Jiv9mjm7cSpU6ewY8cOfPPNNxaPxli7di06duwIb29vDBkyBImJidfcfuvWrejRowe8vb3Rp08fREdHN+r7OoMsyzhz5gynXAiK+Yrt1/wrAJrOiV61wptQI8t9WGzMV3tcfkT27NmzmDhxIk6cOGGeGwvAfD1ZW39YtmzZgrlz52L9+vUYMmQIVq1ahaioKJw+fRpt27ats318fDymTp2KpUuX4u6778amTZswYcIEHDlyBL17977xAdrZxaIK7DudC6+AYIS1buHqcsjOVFVFYWEhOnbs6OpSyAFOXiwCALT2Ef+OXlcLu2pqwfnCcqGnVXAfFltTzje7uAIZ+VcQEdgcIf7aeTOuU2s7Rxe55557YDAY8OGHHyIiIgKJiYm4fPky5s2bh7fffhsjRoyw6fWGDBmCwYMH49133wVQM58lLCwMs2fPxvPPP19n+ylTpuDKlSv47rvvzOuGDh2K/v37Y/369VZ9z5KSEvj7+6O4uBh+fn421WuLzYmZePGrE1BUQK8DXpvYBw8MCnPY9yMi+/n8UBZe2HYCAKAD8MbkPpgyONy1RTnJZ4mZ5rHzdxeR+/n8UBb+cVX/sXSSY39/2dJXubyRDQwMRGxsLPr27Qt/f38kJiaie/fuiI2Nxbx585CUlGT1a1VXV8PHxwdffPEFJkyYYF4/ffp0FBUV4euvv67znPDwcMydOxdz5swxr1u8eDG2b9+OY8eO1ft9qqqqUFVVZf57SUkJwsLCUFBQgICAAPNRZIPBYLEsSRJ0Op15Wa/XQ6/XN7hsMplgMBig1+uRmV+K296Og0vDIiK70euAn54fhbYtao7O3ujvCJPJBKPRCJ1OZ14GAEmSLJY9PDygqqp5WVEUyLJsXlYUBUajscFlWZahqqp5ubb2hpazLpfhtrf3QuEvLyJhGHQ6xC24DUG+Xjf8O6K+33tlZWVWN7IunyMryzJ8fX0B1DS1Fy9eBFBzEtjp06dteq38/HzIsoygoCCL9UFBQcjJyan3OTk5OTZtDwBLly6Fv7+/+REWVnNkITk5GQCQkpKClJQUAMDx48eRlpYGAEhKSjJfpSExMdF8I4j4+HhkZ2cDAOLi4pCfnw8AiI2NRVFREQDgyx/YxBKJRFGBc/nldvsdERMTg9LSUgBAdHQ0KisrIUkSoqOjIUkSKisrzfP/S0tLERMTAwAoKipCbGwsgJrfoXFxcQCA7OxsxMfHAwCysrLM5xpkZGSYDzCkpaXh+PHjABr+vffjz8fYxBIJRlZVHPklyy6/Ixr6vWctlx+RHTFiBObNm4cJEybgoYceQmFhIV566SW8//77OHz4sLk5tMbFixcRGhqK+Ph4DBs2zLx+wYIF2Lt3Lw4cOFDnOZ6envj4448xdepU87p169ZhyZIlyM3Nrff7uOqI7O3L4yz+Q9DrgG+eGobQVs0BAJIkw8PD+L+jLTXLNUdbFPOyvY+22D4mCQbDb8tGo+F/R5BqlmvHcfUyx8QxufuYLpdLGPvOvjr7b1M9IqvXAd8+PQwhLX00lZOIP3scE8d0o2PKLirH+DU/WezDWjoi6/KTvV566SVcuVJzJu8rr7yCu+++GyNGjEDr1q2xZcsWm14rMDAQBoOhTgOam5uL4ODgep8THBxs0/YA4OXlBS8vrzrrDQaDxZ+/X679z8Ta5avvchYe6Iulk/rghW2Wc1R6h7VqsE7n8HTAsqu5bkyyLCMl5Rf07NnT4mfnxjEnV44p0A/17r+/P2HiRn5H2LKs0+nMy7X/4Vm73NDvt4aWw1q3wNJJffDitmTIqgqDTofXJ/XGTe2v/t2ljZys13CNNftwyu/2YfceU+OXXc3+Y7LMt24f4HjOz6mlj2e9+3BoQHPzNjfyO6Kh32/WcnkjGxUVZV7u0qULUlNTzUc2a69cYC1PT08MHDgQu3btMs+RVRQFu3btwqxZs+p9zrBhw7Br1y6LObI7d+60OKKrFVMGh+OWzq0RdyQFI2/uifatml//SUSkCU15/50yOBwju7XBufxydAz00dQZz0R0fVreh10+tcDetmzZgunTp+O9995DZGQkVq1ahc8//xypqakICgrCtGnTEBoaiqVLlwKomXt222234Y033sD48eOxefNmvP766zZdfstZVy0gIiIiEp0tfZXLj8ja25QpU3Dp0iUsWrQIOTk56N+/P3bs2GE+oSszM9PitnLDhw/Hpk2b8NJLL+HFF19E165dsX37dpuuIVv7XqCkpMS+g6mHLMtITk5G79697fzRM2kB8xUb8xUfMxYb83WO2n7KmmOtwh2RdYXz58+br1xARERERDcuKysL7du3v+Y2bGTtQFEUXLx4Eb6+vjbP67VV7RUSsrKyOI1BQMxXbMxXfMxYbMzXOVRVRWlpKdq1a2fxKXp9hJta4Ap6vf667xjszc/PjzuRwJiv2Jiv+Jix2Jiv4/n7+1u1nctviEBERERE1BhsZImIiIjILbGRdTNeXl5YvHhxvTdkIPfHfMXGfMXHjMXGfLWHJ3sRERERkVviEVkiIiIicktsZImIiIjILbGRJSIiIiK3xEaWiIiIiNwSG1kiIiIicktsZImIiIjILbGRJSIiIiK3xEaWiIiIiNwSG1kiIiIicktsZImIiIjILbGRJSIiIiK3xEaWiIiIiNwSG1kiIiIicktsZImIiIjILbGRJSIiIiK3xEaWiIiIiNwSG1kiIiIicktsZImIiIjILbGRJSIiIiK3xEaWiIiIiNwSG1kiIiIicktsZImIiIjILbGRJSIiIiK3xEaWiIiIiNwSG1kiIiIicktsZImIiIjILbGRJSIiIiK3ZHR1ASJQFAUXL16Er68vdDqdq8shIiIicluqqqK0tBTt2rWDXn/tY65sZO3g4sWLCAsLc3UZRERERMLIyspC+/btr7mN2zWya9euxbJly5CTk4N+/fphzZo1iIyMbHD7rVu3YuHChTh37hy6du2KN998E+PGjTN//S9/+Qs+/vhji+dERUVhx44dVtfk6+sLoOYf3M/Pz8YR2UZRFFy+fBmtW7e+7rsUcj/MV2zMV3zMWGzM1zlKSkoQFhZm7q+uxa0a2S1btmDu3LlYv349hgwZglWrViEqKgqnT59G27Zt62wfHx+PqVOnYunSpbj77ruxadMmTJgwAUeOHEHv3r3N2911113YsGGD+e9eXl421VU7ncDPz8/hjawkSThy5Ag6dOgAo9Gt4iMrMF+xMV/xMWOxMV/nsma6pk5VVdUJtdjFkCFDMHjwYLz77rsAat4ZhYWFYfbs2Xj++efrbD9lyhRcuXIF3333nXnd0KFD0b9/f6xfvx5AzRHZoqIibN++vdF1lZSUwN/fH8XFxQ5vZImIiIhEZktf5TbHxaurq3H48GGMHj3avE6v12P06NFISEio9zkJCQkW2wM10wZ+v/2ePXvQtm1bdO/eHU8++SQuX75s/wHYiaIouHDhAhRFcXUp5ADMV2zMV3zMWGzMV3vcppHNz8+HLMsICgqyWB8UFIScnJx6n5OTk3Pd7e+66y588skn2LVrF958803s3bsXY8eOhSzLDdZSVVWFkpISiwcA83NkWa53WZIki+XaHaGhZZPJZLGsqioURcGZM2cgyzJUVTWvr10GYLGsKIrFsiRJ11yWZdli2Rljunq5qY+pNt/q6mphxiRiTo0dk8lkQnp6OkwmkzBjEjGnGxmTJElIT09HdXW1MGMSMafGjqmqqsr8f7AoY9JqTtZym0bWUR588EHce++96NOnDyZMmIDvvvsOBw8exJ49exp8ztKlS+Hv729+1F6xIDk5GQCQkpKClJQUAMDx48eRlpYGAEhKSkJGRgYAIDExEVlZWQBq5vJmZ2cDAOLi4pCfnw8AiI2NRVFREQAgJiYGpaWlMBqNKCoqMv/CjI6OhiRJqKysRHR0NACgtLQUMTExAICioiLExsYCqHkzEBcXBwDIzs5GfHw8gJqT1BITEwEAGRkZSEpKAgCkpaXh+PHjDh8TAERHR6OysrLJj8loNKJnz57mcYgwJhFzauyYTp06hZEjRyItLU2YMYmY042M6dKlSxg5ciTi4+OFGZOIOTV2TDExMRg+fLh5fCKMSas5WU11E1VVVarBYFC/+uori/XTpk1T77333nqfExYWpq5cudJi3aJFi9S+ffte83sFBgaq69evb/DrlZWVanFxsfmRlZWlAlALCgpUVVVVSZJUSZLqLJtMJotlWZavuVxdXW2xrCiKKsuymp6erkqSpCqKYl5fu6yqqsWyLMsWyyaT6ZrLkiRZLNc3DnuP6erlpj4mWZbVjIwMtaqqSpgxiZhTY8dUXV2tnjt3Tq2urhZmTCLmdCNjMplM6rlz59SqqiphxiRiTo0dU2VlpZqRkWHen0UYkxZzKi4uVgGoxcXF6vVYdbJX7UfntnDESU9DhgxBZGQk1qxZA6DmUHZ4eDhmzZrV4Mle5eXl+Pbbb83rhg8fjr59+5pP9vq98+fPIzw8HNu3b8e9995rVV3OPNlLkiQkJiYiMjKSZ0wKiPmKjfmKjxmLjfk6hy19lVWNrF6vt+mOVTqdDr/88gs6depk9XOssWXLFkyfPh3vvfceIiMjsWrVKnz++edITU1FUFAQpk2bhtDQUCxduhRAzaH22267DW+88QbGjx+PzZs34/XXXzdffqusrAxLlizB5MmTERwcjPT0dCxYsAClpaU4ceKE1Zfh4lULiIiIiOzDlr7K6rcTX3zxBVq1anXd7VRVtbjhgD1NmTIFly5dwqJFi5CTk4P+/ftjx44d5hO6MjMzLS5QPHz4cGzatAkvvfQSXnzxRXTt2hXbt283X0PWYDDg+PHj+Pjjj1FUVIR27dphzJgx+Oc//2nztWSdRZZlZGRkICIiAgaDwdXlkJ0xX7ExX/ExY7ExX+2x6ohsREQEDh06hNatW1v1or1798Z///vfJnPbVmdPLUhKSsKAAQP4sYaAmK/YmK/4mLHYmK9z2H1qAV0bpxYQERER2YfTb4hQe2kHcjxZlpGamnrN69yS+2K+YmO+4mPGYmO+2mNzI/vmm29iy5Yt5r8/8MADaN26NUJDQ3Hs2DG7Fkf1q6iocHUJ5EDMV2zMV3zMWGzMV1tsnloQERGBTz/9FMOHD8fOnTvxwAMPYMuWLfj888+RmZlpvoBuU8KpBURERET24dCpBTk5OeaTuL777js88MADGDNmDBYsWICDBw82rmKymizLSE5O5scagmK+YmO+4mPGYmO+2mNzIxsQEGC+fdiOHTswevRoADWX3WKwREREROQsNl87YtKkSXjooYfQtWtXXL58GWPHjgVQc6/cLl262L1AsmQwGMzXwSXxMF+xMV/xMWOxMV/tsfmI7MqVKzFr1iz06tULO3fuRIsWLQAA2dnZeOqpp+xeIFmSZRlJSUk8+i0o5is25is+Ziw25qs9Vh+RXbRoEe677z4MHDgQ8+fPr/P1Z5991q6FUcOaNWvm6hLIgZiv2Jiv+Jix2Jivtlh91YJHHnkE3333HTw9PXHPPffgvvvuw6hRo+Dp6enoGjWPVy0gIiIisg+HXLXgo48+Qk5ODj777DP4+vrimWeeQWBgICZPnoxPPvkEBQUFN1w4XZ8kSTh48CAkSXJ1KeQAzFdszFd8zFhszFd7bJojq9frMWLECLz11ls4ffo0Dhw4gCFDhuC9995Du3btMHLkSLz99tu4cOGCo+pt8nQ6HQICAqDT6VxdCjkA8xUb8xUfMxYb89Uem2+I0JC8vDx8++23+OabbzBixIh659GKilMLiIiIiOzDoTdEaEjbtm0xc+ZMfP31102qiXU2SZIQHx/PjzUExXzFxnzFx4zFxny1x6qrFkyaNMnqF9y2bVuji6Hr0+v1CA0NhV5vt/cgpCHMV2zMV3zMWGzMV3usamT9/f3Ny6qq4quvvoK/vz8GDRoEADh8+DCKiopsanipcfR6PTp06ODqMshBmK/YmK/4mLHYmK/2WPWWYsOGDeZHUFAQHnjgAWRkZGDbtm3Ytm0bzp49iwcffBCBgYGOrrfJkyQJcXFx/FhDUMxXbMxXfMxYbMxXe2w+2atNmzbYv38/unfvbrH+9OnTGD58OC5fvmzXAt2BM0/2UhQF2dnZCAkJ4UcbAmK+YmO+4mPGYmO+zuHQk70kSUJqamqd9ampqVAUxdaXIxtxfo7YmK/YmK/4mLHYmK/22JzEjBkzMHPmTKxYsQL79+/H/v37sXz5cjz66KOYMWOGI2qkq0iShNjYWH6sISjmKzbmKz5mLDbmqz1Wnex1tbfffhvBwcFYvnw5srOzAQAhISH4+9//jnnz5tm9QLKk1+vRu3dvvhsUFPMVG/MVHzMWG/PVnhu6IUJJSQkANPmbAPCGCERERET24bQbIvj5+bFxczKTyYQffvgBJpPJ1aWQAzBfsTFf8TFjsTFf7bF5agEAfPHFF/j888+RmZmJ6upqi68dOXLELoVR/QwGAwYPHgyDweDqUsgBmK/YmK/4mLHYmK/22HxEdvXq1ZgxYwaCgoKQlJSEyMhItG7dGmfPnsXYsWMdUSNdRa/Xo1WrVpyfIyjmKzbmKz5mLDbmqz02J7Fu3Tq8//77WLNmDTw9PbFgwQLs3LkTf/vb31BcXOyIGukqJpMJ33//PT/WEBTzFRvzFR8zFhvz1R6bT/by8fFBSkoKOnTogLZt22Lnzp3o168f0tLSMHToUN4QwcFzhlVVRWlpKXx9faHT6Rz6vcj5mK/YmK/4mLHYmK9zOPRkr+DgYBQUFAAAwsPD8fPPPwMAMjIycAMXQCAr6XQ6+Pn5cQcSFPMVG/MVHzMWG/PVHpsb2VGjRuGbb74BUHNzhGeffRZ/+MMfMGXKFEycONHuBZIlk8mEr7/+mh9rCIr5io35io8Zi435ao/NUwsURYGiKDAaay54sHnzZsTHx6Nr16544okn4Onp6ZBCtczZUwsqKyvh7e3Nd4QCYr5iY77iY8ZiY77OYUtfZVMjK0kSXn/9dTzyyCNo3779DRcqCmc3spIkwWg0cicSEPMVG/MVHzMWG/N1DofNkTUajXjrrbd4j2EXkiQJ0dHRzEBQzFdszFd8zFhszFd7bJ5acN9992HSpEmYPn26o2pyOzwiS/bCfMXGfMXHjMXGfJ3Dlr7K5jt7jR07Fs8//zxOnDiBgQMHonnz5hZfv/fee219SbJR7U5EYmK+YmO+4mPGYmO+2mLzEdlr3c1Cp9NBluUbLsrdOPOIrMlkQnR0NMaNGwcPDw+Hfi9yPuYrNuYrPmYsNubrHA472Yvq58xGloiIiEhkDr0hArmWqqooKSnhzScExXzFxnzFx4zFxny1x6pGdvXq1aisrLT6RdevX4/S0tJGF0UNkyQJ+/bt4xmTgmK+YmO+4mPGYmO+2mPV1AKDwYCcnBy0adPGqhf18/PD0aNH0alTpxsu0B1wagERERGRfdj9qgWqquLOO++0+iy9iooKq7Yj2ymKgqKiIrRs2fKaJ96Re2K+YmO+4mPGYmO+2mNVZ7p48WKbXvS+++5Dq1atGlUQXZssyzh48CBGjRrFnUhAzFdszFd8zFhszFd7eNUCO+DUAiIiIiL74FULBKYoCvLy8qAoiqtLIQdgvmJjvuJjxmJjvtrDRtbNKIqC5ORk7kSCYr5iY77iY8ZiY77aw6kFdsCpBURERET2wakFAlMUBRcuXOC7QUExX7ExX/ExY7ExX+1hI+tmFEVBeno6dyJBMV+xMV/xMWOxMV/tsXlqwdy5c+t/IZ0O3t7e6NKli0Mvv7V27VosW7YMOTk56NevH9asWYPIyMgGt9+6dSsWLlyIc+fOoWvXrnjzzTcxbtw489dVVcXixYvxwQcfoKioCLfccgv+9a9/oWvXrlbXxKkFRERERPbh0KkFSUlJ+Pe//433338fe/fuxd69e/HBBx/g3//+N3bt2oW5c+eiS5cuOHXqVKMH0JAtW7Zg7ty5WLx4MY4cOYJ+/fohKioKeXl59W4fHx+PqVOnYubMmUhKSsKECRMwYcIEJCcnm7d56623sHr1aqxfvx4HDhxA8+bNERUVZdMteZ3pQuEVfBV/EhcKr7i6FHIARVHw66+/8t2+oG5k/80urkB8ej6yi113w5kbqUEL9TsD92GxNeV8tboP23xEdtWqVdi3bx82bNhg7pKLi4vx6KOP4tZbb8Vjjz2Ghx56CBUVFfjhhx/sWuyQIUMwePBgvPvuuwBqfqDCwsIwe/ZsPP/883W2nzJlCq5cuYLvvvvOvG7o0KHo378/1q9fD1VV0a5dO8ybNw/z5883jyUoKAgbN27Egw8+aFVdzjoiuzkxEy9+dQKKCuh1wJJ7b8Lkge0d9v3I+SRJwqFDhzFo0ECr76RH7uHLw+ex+JuTjdp/b+S59uLu9TsL92GxNdV8f78PL53UB1MGhzvs+9nSV9ncyIaGhmLnzp3o1auXxfqTJ09izJgxuHDhAo4cOYIxY8YgPz/f9uobUF1dDR8fH3zxxReYMGGCef306dNRVFSEr7/+us5zwsPDMXfuXMyZM8e8bvHixdi+fTuOHTuGs2fPonPnzkhKSkL//v3N29x2223o378/3nnnnXprqaqqQlVVlfnvJSUlCAsLQ0FBAQICAiDLMgDAYDBYLEuSBJ1OZ17W6/XQ6/UNLptMJhgMBuj1emTml+L25XFQeI0JIiIiciGDToe4BbchyNcLRqMRiqJAURQYjUbIsgxVVc3LQN1+6Hq9UVlZmeOmFhQXF9f7Uf6lS5dQUlICAGjZsiWqq6ttfelrys/PhyzLCAoKslgfFBSEnJycep+Tk5Nzze1r/7TlNQFg6dKl8Pf3Nz/CwsIAwDxlISUlBSkpKQCA48ePIy0tDUDNtIyMjAwAQGJiIrKysgDUTIHIzs4GAMTFxZnfAMTGxqKoqAgA8OUPbGKJiIjI9WRVxZFfshAfHw8AyMrKQmJiIgAgIyMDSUlJAIC0tDQcP34cgO29kbVsPi5+33334ZFHHsHy5csxePBgAMDBgwcxf/5885HSxMREdOvWzdaXdhsvvPCCxUlvtUdke/fuDQDo2bOn+Wt9+/Y1Lw8YMAA6nQ4AEBkZab5P8/Dhw83LI0eONC+PGjUKBoMBADA5aiTWJFs2s3odsONvwxHaqgWAmo88PDw8oKqqeVlRFMiybF6ufcfU0LI93klZe5TZZDLBaDRCp9OZl2vHcfVyUxqTTqfD0aPH0Lt3b3h7ewkxJhFzsnVM+VckjF6xt87+++Pc29Cmhcc1x5RXWt3gc1v7GJwypouF5Rizal+dGn6YcyuC/byvmdP5gjLc9c5PdX93PXML2rX00VRO9vjZUxQVJ06cwE033QRPTw8hxqS1/cmVY6qsrMLJkyfRr1/N/+0ijOl6OdW3/xt0OtzcLQxBvl0AAGFhYQgNDQUAREREoGPHjgBgceK8Lb1RWVkZrGVzI/vee+/h2WefxYMPPghJkmpexGjE9OnTsXLlSgBAjx498OGHH9r60tcUGBgIg8GA3Nxci/W5ubkIDg6u9znBwcHX3L72z9zcXISEhFhsc/VUg9/z8vKCl5dXnfW1TWftn79fvno+jTXLHh4e5uXwQF8sndQHL25LhqyqMOh0eH1Sb3QLCbiqMI/6l21itG3Z0wHLDY2jiYxp5PAhddbV5V5jso64Y/LzQb37b6c2LSw3r6euFt6ejX6uvcbUJciv3hq6BvnXGevvl7sFt6z/d1dwy+vX7qY/eyOG/e5KOgKMqVHLAo6puZdH/b+j3XhM18upof0/NKC5edPaxhlouAeytTeyVqPv7FVWVoazZ88CADp16oQWLVpc5xk3bsiQIYiMjMSaNWsA1JzsFR4ejlmzZjV4sld5eTm+/fZb87rhw4ejb9++Fid7zZ8/H/PmzQNQc3S1bdu2mjzZCwDOF1zBT8d+wS39uqF9q+bXfwK5FVmWkZaWhq5du1rs6CSGG9l/s4srcC6/HB0DfRDi38xBFTquBi3U7wzch8XWlPN15j5sS19le+v7Py1atLA4NOwMc+fOxfTp0zFo0CBERkZi1apVuHLlCmbMmAEAmDZtGkJDQ7F06VIAwDPPPIPbbrsNy5cvx/jx47F582YcOnQI77//PoCaa9/OmTMHr776Krp27YqIiAgsXLgQ7dq1szihTEtC/L3RrWXNnySmigptXdqE7OdG9t8Q/2YubwBvpAYt1O8s3IfF1lTz1eo+bHMje+XKFbzxxhvYtWsX8vLy6lxLrfYorSNMmTIFly5dwqJFi5CTk4P+/ftjx44d5pO1MjMzzYe2gZqjr5s2bcJLL72EF198EV27dsX27dvNc1kBYMGCBbhy5Qoef/xxFBUV4dZbb8WOHTvg7a3NRtFgMGDAgAGuLoMchPmKjfmKjxmLjflqj81TC6ZOnYq9e/fiz3/+M0JCQswTdGs988wzdi3QHThzaoEsy0hJSUHPnj2b3McaTQHzFRvzFR8zFhvzdQ6HTi3473//i++//x633HJLowskIiIiIrpRNh+RjYiIQHR0tMVlFJo6Zx6RJSIiIhKZLX2VzTdE+Oc//4lFixahvLy80QVS48myjKSkJPN15UgszFdszFd8zFhszFd7bJ5asHz5cqSnpyMoKAgdO3a0uNYpABw5csRuxVH9mjXT3lmDZD/MV2zMV3zMWGzMV1tsbmS1elmqpsJgMKBHjx6uLoMchPmKjfmKjxmLjflqT6NviEC/ceYcWUmSkJSUhAEDBjTqDhikbcxXbMxXfMxYbMzXORw6R5ZcS6fTISAgoM5lz0gMzFdszFd8zFhszFd7rDoi26pVK/zyyy8IDAy8boAFBQV2LdAd8KoFRERERPZh9+vIrly5Er6+vgCAVatW3XCB1HiSJCExMRGRkZH8WENAzFdszFd8zFhszFd7rEph+vTp9S6T8+n1eoSGhlrcipfEwXzFxnzFx4zFxny1p1EneymKgjNnziAvLw+Kolh8beTIkXYrzl1wagERERGRfTj0ZK+ff/4ZXbp0Qc+ePTFy5Ejcfvvt5scdd9zR6KLJOpIkIS4uDpIkuboUcgDmKzbmKz5mLDbmqz02T/D461//ikGDBuH7779HSEgIz9xzMr1ej86dO/NjDUExX7ExX/ExY7ExX+2xeWpB8+bNcezYMXTp0sVRNbkdTi0gIiIisg+HTi0YMmQIzpw50+ji6MZIkoTY2Fh+rCEo5is25is+Ziw25qs9Nk8tmD17NubNm4ecnBz06dMHHh4eFl/v27ev3YqjuvR6PXr37s2PNQTFfMXGfMXHjMXGfLXH5qkF9YWn0+mgqip0Oh1kWbZbce6CUwuIiIiI7MOhUwsyMjLqPM6ePWv+kxzLZDLhhx9+gMlkcnUp5ADMV2zMV3zMWGzMV3sadR1ZsuTMI7KKoqCoqAgtW7bkRxsCYr5iY77iY8ZiY77OYfdb1F7tk08+uebXp02bZutLkg30ej1atWrl6jLIQZiv2Jiv+Jix2Jiv9th8RDYgIMDi7yaTCeXl5fD09ISPjw8KCgrsWqA7cOYRWZPJhJiYGIwZM6bOiXbk/piv2Jiv+Jix2Jivc9jSV9llakFaWhqefPJJ/P3vf0dUVNSNvpzbcWYjq6oqSktL4evry5tRCIj5io35io8Zi435OofTG1kAOHToEP70pz8hNTXVHi/nVnjVAiIiIiL7cOhVCxpiNBpx8eJFe70cNcBkMuHrr7/mGZOCYr5iY77iY8ZiY77aY/MR2W+++cbi76qqIjs7G++++y7CwsLw3//+164FugNnTy2orKyEt7c3P9YQEPMVG/MVHzMWG/N1DodetWDChAkWf9fpdGjTpg1GjRqF5cuX2/py1AhGo82xkRthvmJjvuJjxmJjvtpi89QCRVEsHrIsIycnB5s2bUJISIgjaqSrSJKE6Oho3udZUMxXbMxXfMxYbMxXe2yeWvDKK69g/vz58PHxsVhfUVGBZcuWYdGiRXYt0B04e2qBJEkwGo38WENAzFdszFd8zFhszNc5HHqy15IlS1BWVlZnfXl5OZYsWWLry1Ej8J2g2Jiv2Jiv+Jix2JivttjcyKqqWu+7kGPHjvFuF04gSRJiYmK4IwmK+YqN+YqPGYuN+WqP1VMLAgICoNPpzId5r25mZVlGWVkZ/vrXv2Lt2rUOK1areB1ZIiIiIvtwyFULVq1aBVVV8cgjj2DJkiXw9/c3f83T0xMdO3bEsGHDGl81WYV3FREb8xUb8xUfMxYb89UeqxvZ6dOnAwAiIiJwyy238PITLiJJEvbt28f7PAuK+YqN+YqPGYuN+WpPo25Rm56ejg0bNiA9PR3vvPMO2rZti//+978IDw/HTTfd5Ig6NY1TC4iIiIjsw6FXLdi7dy/69OmDAwcOYNu2beYrGBw7dgyLFy9uXMVkNUVRUFBQAEVRXF0KOQDzFRvzFR8zFhvz1R6bG9nnn38er776Knbu3AlPT0/z+lGjRuHnn3+2a3FUlyzLOHjwIGRZdnUp5ADMV2zMV3zMWGzMV3tsnlrQokULnDhxAhEREfD19cWxY8fQqVMnnDt3Dj169EBlZaWjatUsTi0gIiIisg+HTi1o2bIlsrOz66xPSkpCaGiorS9HNlIUBXl5efxYQ1DMV2zMV3zMWGzMV3tsbmQffPBBPPfcc8jJyYFOp4OiKPjpp58wf/58TJs2zRE10lUURUFycjJ3IkExX7ExX/ExY7ExX+2xeWpBdXU1nn76aWzcuBGyLMNoNEKWZTz00EPYuHEjDAaDo2rVLE4tICIiIrIPW/qqRl1+CwAyMzORnJyMsrIyDBgwAF27dm1UsSJwZiOrKAqys7MREhICvd7mA+qkccxXbMxXfMxYbMzXORxyZ6/fCw8PR3h4eGOfTo2kKArS09MRFBTEnUhAzFdszFd8zFhszFd7rDoiO3fuXKtfcMWKFTdUkDvi1AIiIiIi+7D7EdmkpCSLvx85cgSSJKF79+4AgF9++QUGgwEDBw5sZMlkLUVRkJWVhbCwML4bFBDzFRvzFR8zFhvz1R6rGtndu3ebl1esWAFfX198/PHHCAgIAAAUFhZixowZGDFihGOqJDNFUXDhwgWEhoZyJxIQ8xUb8xUfMxYb89Uem0/2Cg0NRUxMDG666SaL9cnJyRgzZgwuXrxo1wLdAacWEBEREdmHQ2+IUFJSgkuXLtVZf+nSJZSWltr6clYrKCjAww8/DD8/P7Rs2RIzZ85EWVnZNZ9TWVmJp59+Gq1bt0aLFi0wefJk5ObmWmyj0+nqPDZv3uywcdwoWZZx5swZ3h5PUMxXbMxXfMxYbMxXe2xuZCdOnIgZM2Zg27ZtOH/+PM6fP48vv/wSM2fOxKRJkxxRIwDg4YcfxsmTJ7Fz50589913iIuLw+OPP37N5zz77LP49ttvsXXrVuzduxcXL16st8YNGzYgOzvb/JgwYYKDRnHjVFVFYWEhGnnVNNI45is25is+Ziw25qs9Nk8tKC8vx/z58/HRRx/BZDIBAIxGI2bOnIlly5ahefPmdi8yJSUFvXr1wsGDBzFo0CAAwI4dOzBu3DicP38e7dq1q/Oc4uJitGnTBps2bcIf//hHAEBqaip69uyJhIQEDB06FEDNEdmvvvrqhppXTi0gIiIisg+HTi3w8fHBunXrcPnyZSQlJSEpKQkFBQVYt26dQ5pYAEhISEDLli3NTSwAjB49Gnq9HgcOHKj3OYcPH4bJZMLo0aPN63r06IHw8HAkJCRYbPv0008jMDAQkZGR+OijjzT9TkuWZaSmpvJjDUExX7ExX/ExY7ExX+1p9Cl3zZs3R9++fdG3b1+HNbC1cnJy0LZtW4t1RqMRrVq1Qk5OToPP8fT0RMuWLS3WBwUFWTznlVdeweeff46dO3di8uTJeOqpp7BmzZpr1lNVVYWSkhKLBwDzD7Ysy/UuS5JksVx7r+aGlk0mk8VybYN95coVqKoKVVXN62uXAVgsK4pisSxJ0jWXZVm2WHbWmH4/jqY8pvLycuHGJGJOjR1TRUWFcGMSMacbGVNFRYVwYxIxp8aOqby8XLgxaTEna7n02hHPP/98vSdbXf1ITU11aA0LFy7ELbfcggEDBuC5557DggULsGzZsms+Z+nSpfD39zc/wsLCANRcuQGomQqRkpICADh+/DjS0tIA1FyPNyMjAwCQmJiIrKwsAEB8fDyys7MBAHFxccjPzwcAxMbGoqioCAAQExOD0tJSGAwGnD9/HiaTCZIkITo6GpIkobKyEtHR0QCA0tJSxMTEAACKiooQGxsLAMjPz0dcXBwAIDs7G/Hx8QCArKwsJCYmAgAyMjLM1w1OS0vD8ePHHT4mAIiOjkZlZWWTH5PBYED79u3x008/CTMmEXNq7JhOnjyJAQMG4JdffhFmTCLmdCNjysvLw4ABA/DTTz8JMyYRc2rsmH744Qf06dMHJpNJmDFpNSdr2TxH1p4uXbqEy5cvX3ObTp064T//+Q/mzZuHwsJC83pJkuDt7Y2tW7di4sSJdZ4XGxuLO++8E4WFhRZHZTt06IA5c+bg2Wefrff7ff/997j77rtRWVkJLy+verepqqpCVVWV+e8lJSUICwtDQUEBAgICzO8sDAaDxbIkSdDpdOZlvV4PvV7f4LLJZILBYDAvG41GKIqCkydPolevXubXMRqN5n8TDw8PqKpqXlYUBbIsm5cVRTG/Tn3LsixDVVXzcn3jsPeYdDqdebl2HE11THq9HqdOnUK3bt3g5eUlxJhEzKmxY5JlGb/88gu6desGg8EgxJhEzOlGxqSqKk6fPo2uXbvCw8NDiDGJmFNjx1RVVYW0tDT07NkTqqoKMSYt5lRWVmb1HFmXNrLWqj3Z69ChQ+a7h8XExOCuu+667slen332GSZPngwAOH36NHr06GFxstfvvfbaa1i+fDkKCgqsrs+ZJ3vJsoyUlBT07NkTBoPBod+LnI/5io35io8Zi435OoctfZVbNLIAMHbsWOTm5mL9+vUwmUyYMWMGBg0ahE2bNgEALly4gDvvvBOffPIJIiMjAQBPPvkkoqOjsXHjRvj5+WH27NkAYD4U/u233yI3NxdDhw6Ft7c3du7cifnz52P+/PlYsmSJ1bXxqgVERERE9mFLX2XVLWq14NNPP8WsWbNw5513Qq/XY/LkyVi9erX56yaTCadPn0Z5ebl53cqVK83bVlVVISoqCuvWrTN/3cPDA2vXrsWzzz4LVVXRpUsXrFixAo899phNtdW+F6g96cuRZFlGcnIyevfuzXeDAmK+YmO+4mPGYmO+zlHbT1lzrNVtjshq2fnz580nfBERERHRjcvKykL79u2vuQ0bWTtQFAUXL16Er68vdDqdQ79X7YllWVlZnMYgIOYrNuYrPmYsNubrHKqqorS0FO3atYNef+0LbLnN1AIt0+v1133HYG9+fn7ciQTGfMXGfMXHjMXGfB3P39/fqu1ceh1ZIiIiIqLGYiNLRERERG6Jjayb8fLywuLFixu8WQO5N+YrNuYrPmYsNuarPTzZi4iIiIjcEo/IEhEREZFbYiNLRERERG6JjSwRERERuSU2skRERETkltjIEhEREZFbYiNLRERERG6JjSwRERERuSU2skRERETkltjIEhEREZFbYiNLRERERG6JjSwRERERuSU2skRERETkltjIEhEREZFbYiNLRERERG6JjSwRERERuSU2skRERETkltjIEhEREZFbYiNLRERERG6JjSwRERERuSU2skRERETkltjIEhEREZFbYiNLRERERG6JjSwRERERuSU2skRERETkltjIEhEREZFbYiNLRERERG6JjSwRERERuSWjqwsQgaIouHjxInx9faHT6VxdDhEREZHbUlUVpaWlaNeuHfT6ax9zZSNrBxcvXkRYWJiryyAiIiISRlZWFtq3b3/NbdjI2oGvry+Amn9wPz8/F1dDRERE5L5KSkoQFhZm7q+uxe0a2bVr12LZsmXIyclBv379sGbNGkRGRja4/datW7Fw4UKcO3cOXbt2xZtvvolx48aZv/6Xv/wFH3/8scVzoqKisGPHDqtrqp1O4Ofn5/BGVlEU5OfnIzAw8LqH28n9MF+xMV/xMWOxMV/nsma6plulsGXLFsydOxeLFy/GkSNH0K9fP0RFRSEvL6/e7ePj4zF16lTMnDkTSUlJmDBhAiZMmIDk5GSL7e666y5kZ2ebH5999pkzhtMoiqIgOTkZiqK4uhRyAOYrNuYrPmYsNuarPTpVVVVXF2GtIUOGYPDgwXj33XcB1PxAhYWFYfbs2Xj++efrbD9lyhRcuXIF3333nXnd0KFD0b9/f6xfvx5AzRHZoqIibN++vdF1lZSUwN/fH8XFxZxaQERERHQDbOmr3OaIbHV1NQ4fPozRo0eb1+n1eowePRoJCQn1PichIcFie6Bm2sDvt9+zZw/atm2L7t2748knn8Tly5evWUtVVRVKSkosHgAgy7L5z/qWJUmyWK59R9fQsslkslhWVRWKoiAzMxOyLENVVfP62mUAFsuKolgsS5J0zWVZli2WnTGmq5eb+pgURcH58+dRXV0tzJhEzKmxYzKZTLhw4QJMJpMwYxIxpxsZkyRJuHDhAqqrq4UZk4g5NXZMVVVVOH/+vHl/FmFMWs3JWm7TyObn50OWZQQFBVmsDwoKQk5OTr3PycnJue72d911Fz755BPs2rULb775Jvbu3YuxY8ea/1Hrs3TpUvj7+5sftVcsqJ2ykJKSgpSUFADA8ePHkZaWBgBISkpCRkYGACAxMRFZWVkAaqZAZGdnAwDi4uKQn58PAIiNjUVRUREAICYmBqWlpVAUBUlJSSgvL4ckSYiOjoYkSaisrER0dDQAoLS0FDExMQCAoqIixMbGmv8N4+LiAADZ2dmIj48HUHOSWmJiIgAgIyMDSUlJAIC0tDQcP37c4WMCgOjoaFRWVjb5MSmKgtOnT2Pfvn3CjEnEnBo7phMnTiA9PV2oMYmY042OKT09Hfv27RNqTCLm1Jgx7dixA+np6SgvLxdmTFrNyVpuM7Xg4sWLCA0NRXx8PIYNG2Zev2DBAuzduxcHDhyo8xxPT098/PHHmDp1qnndunXrsGTJEuTm5tb7fc6ePYvOnTvjxx9/xJ133lnvNlVVVaiqqjL/vfbsuoKCAgQEBJibYIPBYLEsSRJ0Op15Wa/XQ6/XN7hsMplgMBjMy0ajETqdzrwM1Lx7uXrZw8MDqqqalxVFgSzL5mVFUWA0Ghtcrj3SW7tc3zg4Jo6JY+KYOCaOiWPimBw1prKyMqunFrjNVQsCAwNhMBjqNKC5ubkIDg6u9znBwcE2bQ8AnTp1QmBgIM6cOdNgI+vl5QUvL6866w0Gg8Wfv1+u/UGxdtnDw6POsqIo5uvW6vX6erfR6XTm5dofZmuXG6rdkWOyZrmpjElRFGRlZZmP8oswJmuXm8KYFEXBr7/+at5/RRjT9Zab2pjqy9jdx1TfclMdk8FgQGZmJsLCwoQZk1ZzspbbTC3w9PTEwIEDsWvXLvM6RVGwa9cuiyO0Vxs2bJjF9gCwc+fOBrcHgPPnz+Py5csICQmxT+F2pigKLly4YPMcEnIPzFdszFd8zFhszFd73GZqAVBz+a3p06fjvffeQ2RkJFatWoXPP/8cqampCAoKwrRp0xAaGoqlS5cCqJkzctttt+GNN97A+PHjsXnzZrz++us4cuQIevfujbKyMixZsgSTJ09GcHAw0tPTsWDBApSWluLEiRP1HnWtD69aQERERGQfQl61AKi5nNbbb7+NRYsWoX///jh69Ch27NhhPqErMzPTPNkZAIYPH45Nmzbh/fffR79+/fDFF19g+/bt6N27N4CaQ9vHjx/Hvffei27dumHmzJkYOHAg9u3bZ3UT62yyLOPMmTPXPBmN3BfzFRvzFR8zFhvz1R63OiKrVc48IitJEpKSkjBgwIBGzSUhbWO+YmO+4mPGYmO+zmFLX8VG1g44tYCIiIjIPoSdWkA1H2ukpqbyYw1BMV+xMV/xMWOxMV/tYSPrhioqKlxdAjkQ8xUb8xUfMxYb89UWTi2wA04tICIiIrIPTi0QmCzLSE5O5scagmK+YmO+4mPGYmO+2sNGloiIiIjcEqcW2AGnFhARERHZB6cWCEyWZSQlJfFjDUExX7ExX/ExY7ExX+1hI+uGmjVr5uoSyIGYr9iYr/iYsdiYr7ZwaoEdcGoBERERkX1waoHAJEnCwYMHIUmSq0shB2C+YmO+4mPGYmO+2sNG1s3odDoEBARAp9O5uhRyAOYrNuYrPmYsNuarPVZNLfjmm29sfuE//OEPTWYeCacWEBEREdmHLX2V0ZoXnDBhgk0F6HQ6pKWloVOnTjY9j65PkiQkJiYiMjISRqNV8ZEbYb5iY77iY8ZiY77aY/XUgpycHCiKYtXDx8fHkTU3aXq9HqGhodDrOStERMxXbMxXfMxYbMxXe6x6OzF9+nSbpgn86U9/4kfsDqLX69GhQwdXl0EOwnzFxnzFx4zFxny1x6q3FBs2bICvr6/VL/qvf/0LgYGBjS6KGiZJEuLi4njGpKCYr9iYr/iYsdiYr/bw2Lib0ev16Ny5Mz/WEBTzFRvzFR8zFhvz1R6rrlowadIkq19w27ZtN1SQO+JVC4iIiIjsw+43RPD39zc//Pz8sGvXLhw6dMj89cOHD2PXrl3w9/e/scrpuiRJQmxsLD/WEBTzFRvzFR8zFhvz1R6rTvbasGGDefm5557DAw88gPXr18NgMAAAZFnGU089xaORTqDX69G7d29+rCEo5is25is+Ziw25qs9Vk0tuFqbNm2wf/9+dO/e3WL96dOnMXz4cFy+fNmuBboDTi0gIiIisg+7Ty24miRJSE1NrbM+NTUViqLY+nJkI5PJhB9++AEmk8nVpZADMF+xMV/xMWOxMV/tsfm2FDNmzMDMmTORnp6OyMhIAMCBAwfwxhtvYMaMGXYvkCwZDAYMHjzYPK2DxMJ8xcZ8xceMxcZ8tcfmqQWKouDtt9/GO++8g+zsbABASEgInnnmGcybN69JhsupBURERET24dCpBXq9HgsWLMCFCxdQVFSEoqIiXLhwAQsWLGiSTayzmUwmfP/99/xYQ1DMV2zMV3zMWGzMV3tsPiJLdTnziKyqqigtLYWvry90Op1Dvxc5H/MVG/MVHzMWG/N1Dlv6KpvnyALAF198gc8//xyZmZmorq62+NqRI0ca85JkJZ1Ox+kLAmO+YmO+4mPGYmO+2mPz1ILVq1djxowZCAoKQlJSEiIjI9G6dWucPXsWY8eOdUSNdBWTyYSvv/6aH2sIivmKjfmKjxmLjflqj81TC3r06IHFixdj6tSp8PX1xbFjx9CpUycsWrQIBQUFePfddx1Vq2Y5e2pBZWUlvL29+bGGgJiv2Jiv+Jix2Jivczj0ZK/MzEwMHz4cANCsWTOUlpYCAP785z/js88+a0S5ZCujsVEzQshNMF+xMV/xMWOxMV9tsbmRDQ4ORkFBAQAgPDwcP//8MwAgIyMDPG/M8SRJQnR0NO/zLCjmKzbmKz5mLDbmqz02Ty149NFHERYWhsWLF2Pt2rX4+9//jltuuQWHDh3CpEmT8O9//9tRtWqWs6cWSJIEo9HIjzUExHzFxnzFx4zFxnydw5a+qlE3RFAUxXxoffPmzYiPj0fXrl3xxBNPwNPTs/GVuynOkSV7Yb5iY77iY8ZiY77O4bA5spIk4dVXX0VOTo553YMPPojVq1dj9uzZTbKJdTZJkhATE8OPNQTFfMXGfMXHjMXGfLXH5iOyLVq0QHJyMjp27OigktwPb1FLREREZB8OvWrBnXfeib179za6OLoxqqqipKSEJ9YJivmKjfmKjxmLjflqj82N7NixY/H8889j/vz5+Oyzz/DNN99YPMixJEnCvn37+LGGoJiv2Jiv+Jix2Jiv9tg8tUCvb7j31el0kGX5hotyN5xaQERERGQfDp1aUHvVgvoeTbGJdTZFUVBQUABFUVxdCjkA8xUb8xUfMxYb89UemxtZci1ZlnHw4EG+aRAU8xUb8xUfMxYb89Ueq6YWrF69Go8//ji8vb2tetH169fj4Ycfhq+v7w0X6A44tYCIiIjIPuw+teDZZ59FaWmp1QUsWLAAly5dsnp7sp6iKMjLy+PHGoJivmJjvuJjxmJjvtpjtGYjVVVx5513mu/mdT0VFRU3VBQ1TFEUJCcnY+TIkdc88Y7cE/MVG/MVHzMWG/PVHqumFixZssTmF37mmWfQsmXLxtTkdji1gIiIiMg+bOmrbL78FtXlzEZWURRkZ2cjJCSE7wYFxHzFxnzFx4zFxnydw6GX33K1tWvXomPHjvD29saQIUOQmJh4ze23bt2KHj16wNvbG3369EF0dLTF11VVxaJFixASEoJmzZph9OjRSEtLc+QQboiiKEhPT+f8HEExX7ExX/ExY7ExX+1xq0Z2y5YtmDt3LhYvXowjR46gX79+iIqKQl5eXr3bx8fHY+rUqZg5cyaSkpIwYcIETJgwAcnJyeZt3nrrLaxevRrr16/HgQMH0Lx5c0RFRaGystJZw7KJ0WjEyJEjrZ6vTO6F+YqN+YqPGYuN+WqPW00tGDJkCAYPHox3330XQM07o7CwMMyePRvPP/98ne2nTJmCK1eu4LvvvjOvGzp0KPr374/169dDVVW0a9cO8+bNw/z58wEAxcXFCAoKwsaNG/Hggw9aVZczpxZcKLyCxJRziOzZEaEBzR36vcj5FEVBVlYWwsLC+LGVgG5k/80urkBG/hVEBDZHiH8zB1XouBq0UL8zcB8WW1PO15n7sC19ldu8paiursbhw4fxwgsvmNfp9XqMHj0aCQkJ9T4nISEBc+fOtVgXFRWF7du3AwAyMjKQk5OD0aNHm7/u7++PIUOGICEhwepG1lk2J2bixa9OQFEB/bfnsOTemzB5YHtXl0V2JEkS0n89j4A2QXzHL5gvD5/H4m9ONmr/tXiuDi7Z92+kBi3U7yzch8XWVPP9/T68dFIfTBkc7uqyANxAI1tdXY2MjAx07tzZKWHm5+dDlmUEBQVZrA8KCkJqamq9z8nJyal3+5ycHPPXa9c1tE19qqqqUFVVZf57SUkJAJjv9FH7p8FgsFiWJAk6nc68rNfrodfrG1w2mUwwGAzQ6/XIzC81N7EAoKjAwq9PYuHXJxv+RyP3Fb3L1RWQA93I/quFfd/d63cK7sNia8L5Kirw4rZk3NqlNYJ8vWA0GqEoChRFgdFohCzLUFXVvAzU7Yeu1xvZwubj4uXl5Zg5cyZ8fHxw0003ITMzEwAwe/ZsvPHGG7a+nFtaunQp/P39zY+wsDAAMM+9TUlJQUpKCgDg+PHj5pPHkpKSkJGRAQBITExEVlYWgJq5vNnZ2QCAuLg45OfnAwBiY2NRVFQEAPjyhzhzE0tERETkKrKq4sgvWYiPjwcAZGVlmU++z8jIQFJSEgAgLS0Nx48fB2B7b2Qtmw+lvvDCCzh27Bj27NmDu+66y7x+9OjRePnll+udq2oPgYGBMBgMyM3NtVifm5uL4ODgep8THBx8ze1r/8zNzUVISIjFNv3792+wlhdeeMFiykJJSQnCwsLQu3dvAEDPnj3NX+vbt695ecCAAdDpdACAyMhI87uO4cOHm5evvsjyqFGjYDAYAACTo0ZiTbJlM6vXATv+NhyhrVoAqPnIw8PDA6qqmpcVRYEsy+bl2ndMDS3b452UtUeZTSYTjEYjdDqdebl2HFcvN6Ux6XQ6HD16DL1794a3t5cQYxIxJ1vHlH9FwugVe+vsvz/OvQ1tWnhcc0x5pdUNPre1j8EpY7pYWI4xq/bVqeGHObci2M/7mjmdLyjDXe/8VPd31zO3oF1LH03lZI+fPUVRceLECdx0003w9PQQYkxa259cOabKyiqcPHkS/frV/N8uwpiul1N9+79Bp8PN3cIQ5NsFABAWFobQ0FAAQEREBDp27AgA6Nq1q/k5tvRGZWVlsJbNJ3t16NABW7ZswdChQ+Hr64tjx46hU6dOOHPmDG6++Wbzx+yOMGTIEERGRmLNmjUAaiZdh4eHY9asWQ2e7FVeXo5vv/3WvG748OHo27evxcle8+fPx7x58wDUNKVt27bV5MleWw5m4sVtyZBVFQadDq9P6q2ZOSpEdG03sv9qYd939/qJqPGcvQ/b1FepNmrWrJmanp6uqqqqtmjRwrx89OhR1c/Pz9aXs8nmzZtVLy8vdePGjeqpU6fUxx9/XG3ZsqWak5Ojqqqq/vnPf1aff/558/Y//fSTajQa1bfffltNSUlRFy9erHp4eKgnTpwwb/PGG2+oLVu2VL/++mv1+PHj6n333adGRESoFRUVVtdVXFysAlCLi4vtN9gGZF0uUzfHHlGzLpc5/HuR80mSpKakpKiSJLm6FHKAG9l/LxaVq/Fn8tWLReUOqMzxNWihfmfgPiy2ppyvM/dhW/oqm6cWDBo0CN9//z1mz54NAObDwR9++CGGDRtm68vZZMqUKbh06RIWLVqEnJwc9O/fHzt27DCfrJWZmWkxSXj48OHYtGkTXnrpJbz44ovo2rUrtm/fbp4CAAALFizAlStX8Pjjj6OoqAi33norduzYAW9vb4eOpbFC/L3RrWXNnySmiooKV5dADnIj+2+IfzOXX7bqRmrQQv3Own1YbE01X63uwzZPLdi/fz/Gjh2LP/3pT9i4cSOeeOIJnDp1CvHx8di7dy8GDhzoqFo1y5nXkSUiIiISmUNvUXvrrbfi6NGjkCQJffr0QUxMDNq2bYuEhIQm2cQ6myzLSE5ONk/+JrEwX7ExX/ExY7ExX+1p1AVgO3fujA8++MDetRARERERWc3mqQVHjhyBh4cH+vTpAwD4+uuvsWHDBvTq1Qsvv/wyPD09HVKolnFqAREREZF9OHRqwRNPPIFffvkFAHD27FlMmTIFPj4+2Lp1KxYsWNC4islqsiwjKSmJH2sIivmKjfmKjxmLjflqj82N7C+//GK+WcDWrVtx2223YdOmTdi4cSO+/PJLe9dH9WjWTHtnDZL9MF+xMV/xMWOxMV9tsXmOrKqqUBQFAPDjjz/i7rvvBlBzV4faW6uS4xgMBvTo0cPVZZCDMF+xMV/xMWOxMV/tsfmI7KBBg/Dqq6/i//7v/7B3716MHz8eQM29dWuv50qOI0kSDh48CEmSXF0KOQDzFRvzFR8zFhvz1R6bG9lVq1bhyJEjmDVrFv7xj3+gS5ea++x+8cUXGD58uN0LJEs6nQ4BAQHmG1GQWJiv2Jiv+Jix2Jiv9th81YKGVFZWwmAwwMPDwx4v51Z41QIiIiIi+3DoVQsa4u3t3SSbWGeTJAnx8fH8WENQzFdszFd8zFhszFd7bD7ZS5ZlrFy5Ep9//jkyMzNRXV1t8fWCggK7FUd16fV6hIaGQq+323sQ0hDmKzbmKz5mLDbmqz02J7FkyRKsWLECU6ZMQXFxMebOnYtJkyZBr9fj5ZdfdkCJdDW9Xo8OHTpwJxIU8xUb8xUfMxYb89Uem5P49NNP8cEHH2DevHkwGo2YOnUqPvzwQyxatAg///yzI2qkq0iShLi4OH6sISjmKzbmKz5mLDbmqz02N7I5OTnm29O2aNECxcXFAIC7774b33//vX2rozr0ej06d+7Md4OCYr5iY77iY8ZiY77aY3MS7du3R3Z2NgCgc+fOiImJAQAcPHgQXl5e9q2O6uD8HLExX7ExX/ExY7ExX+2xOYmJEydi165dAIDZs2dj4cKF6Nq1K6ZNm4ZHHnnE7gWSJUmSEBsby481BMV8xcZ8xceMxcZ8teeGryObkJCAhIQEdO3aFffcc4+96nIrzryOrKIoyM/PR2BgIN8RCoj5io35io8Zi435OoctfZXdbojQlPGGCERERET2YUtfZfN1ZAEgLS0Nu3fvRl5eHhRFsfjaokWLGvOSZCWTyYTY2FiMGjWKN6AQEPMVG/MVHzMWG/PVHpuPyH7wwQd48sknERgYiODgYIv7Det0Ohw5csTuRWqds6cWFBUVoWXLlvxYQ0DMV2zMV3zMWGzM1zkcOrWgQ4cOeOqpp/Dcc8/dUJEi4dQCIiIiIvuwpa+y+e1EYWEh7r///kYXRzfGZDLh+++/h8lkcnUp5ADMV2zMV3zMWGzMV3tsbmTvv/9+87VjyfmMRiNGjBgBo7FR05tJ45iv2Jiv+Jix2Jiv9liVxOrVq83LXbp0wcKFC/Hzzz+jT58+dSY7/+1vf7NvhWRBp9Nx+oLAmK/YmK/4mLHYmK/2WDVHNiIiwroX0+lw9uzZGy7K3ThzjqzJZEJ0dDTGjRvHMyYFxHzFxnzFx4zFxnydg9eRdTJnNrKqqqKyshLe3t4WV4wgMTBfsTFf8TFjsTFf53DoyV5XU1UV7IOdj3NzxMZ8xcZ8xceMxcZ8taVRjey///1v9O7dG97e3vD29kbv3r3x4Ycf2rs2qockSYiOjuZ9ngXFfMXGfMXHjMXGfLXH5qkFixYtwooVKzB79mwMGzYMAJCQkIB3330Xzz77LF555RWHFKplzp5aIEkSjEYjP9YQEPMVG/MVHzMWG/N1DofOkW3Tpg1Wr16NqVOnWqz/7LPPMHv2bOTn59tesZvjHFmyF+YrNuYrPmYsNubrHA6dI2symTBo0KA66wcOHMhD7U4gSRJiYmL4by0o5is25is+Ziw25qs9Nh+RnT17Njw8PLBixQqL9fPnz0dFRQXWrl1r1wLdAW9RS0RERGQftvRVjTr17t///jdiYmIwdOhQAMCBAweQmZmJadOmYe7cuebtft/s0o1TVRWlpaXw9fXlxxoCYr5iY77iY8ZiY77aY/PUguTkZNx8881o06YN0tPTkZ6ejsDAQNx8881ITk5GUlISkpKScPToUQeUS5IkYd++ffxYQ1DMV2zMV3zMWGzMV3t4QwQ74NQCIiIiIvtw2g0RyPkURUFBQQEURXF1KeQAzFdszFd8zFhszFd72Mi6GVmWcfDgQciy7OpSyAGYr9iYr/iYsdiYr/ZwaoEdcGoBERERkX1waoHAFEVBXl4eP9YQFPMVG/MVHzMWG/PVHjaybkZRFCQnJ3MnEhTzFRvzFR8zFhvz1R5OLbADTi0gIiIisg9OLRCYoii4cOEC3w0KivmKjfmKjxmLjflqDxtZN6MoCtLT07kTCYr5io35io8Zi435ag+nFtgBpxYQERER2QenFghMURT8+uuvfDcoKOYrNuYrPmYsNuarPWxk3Qzn54iN+YqN+YqPGYuN+WoPpxbYAacWEBEREdmHkFMLCgoK8PDDD8PPzw8tW7bEzJkzUVZWds3nVFZW4umnn0br1q3RokULTJ48Gbm5uRbb6HS6Oo/Nmzc7cig3RJZlnDlzhrfHExTzFRvzFR8zFhvz1R63aWQffvhhnDx5Ejt37sR3332HuLg4PP7449d8zrPPPotvv/0WW7duxd69e3Hx4kVMmjSpznYbNmxAdna2+TFhwgQHjeLGqaqKwsJC8EC6mJiv2Jiv+Jix2Jiv9rjF1IKUlBT06tULBw8exKBBgwAAO3bswLhx43D+/Hm0a9euznOKi4vRpk0bbNq0CX/84x8BAKmpqejZsycSEhIwdOhQADVHZL/66qsbal45tYCIiIjIPoSbWpCQkICWLVuam1gAGD16NPR6PQ4cOFDvcw4fPgyTyYTRo0eb1/Xo0QPh4eFISEiw2Pbpp59GYGAgIiMj8dFHH133nVZVVRVKSkosHgDMHzXIslzvsiRJFsu1k8UbWjaZTBbLqqpClmWcPHkSkiRBVVXz+tplABbLiqJYLEuSdM1lWZYtlp0xpquXm/qYZFlGSkoKqqqqhBmTiDk1dkzV1dVITU1FdXW1MGMSMacbGZPJZEJqaiqqqqqEGZOIOTV2TJWVlUhJSTFnLcKYtJqTtdyikc3JyUHbtm0t1hmNRrRq1Qo5OTkNPsfT0xMtW7a0WB8UFGTxnFdeeQWff/45du7cicmTJ+Opp57CmjVrrlnP0qVL4e/vb36EhYUBAJKTkwHUHEFOSUkBABw/fhxpaWkAgKSkJGRkZAAAEhMTkZWVBQCIj49HdnY2ACAuLg75+fkAgNjYWBQVFQEAYmJiUFpaCgA4c+YMKisrIUkSoqOjIUkSKisrER0dDQAoLS1FTEwMAKCoqAixsbEAgPz8fMTFxQEAsrOzER8fDwDIyspCYmIiACAjIwNJSUkAgLS0NBw/ftwpY4qOjuaY/jemwsJC7N+/X6gxiZhTY8aUnJyMiooKpKamCjMmEXO6kTHl5OSgoqIC+/fvF2ZMIubU2DH98MMPKC8vF2pMWs3JaqoLPffccyqAaz5SUlLU1157Te3WrVud57dp00Zdt25dva/96aefqp6ennXWDx48WF2wYEGDNS1cuFBt3779NeuurKxUi4uLzY+srCwVgFpQUKCqqqpKkqRKklRn2WQyWSzLsnzN5erqaotlRVEslhVFqbOsqqrFsizLFssmk+may5IkWSzXNw6OiWPimDgmjolj4pg4JkeNqbi4WAWgFhcXq9fj0jmyly5dwuXLl6+5TadOnfCf//wH8+bNQ2FhoXm9JEnw9vbG1q1bMXHixDrPi42NxZ133onCwkKLo7IdOnTAnDlz8Oyzz9b7/b7//nvcfffdqKyshJeXl1XjcOYcWfl/Hz337NkTBoPBod+LnI/5io35io8Zi435OoctfZXRSTXVq02bNmjTps11txs2bBiKiopw+PBhDBw4EEBNo6ooCoYMGVLvcwYOHAgPDw/s2rULkydPBgCcPn0amZmZGDZsWIPf6+jRowgICLC6iSUiIiIi13CLqxYAwNixY5Gbm4v169fDZDJhxowZGDRoEDZt2gQAuHDhAu6880588skniIyMBAA8+eSTiI6OxsaNG+Hn54fZs2cDgHlOx7fffovc3FwMHToU3t7e2LlzJ+bPn4/58+djyZIlVtfGqxYQERER2YfbHJG1xaeffopZs2bhzjvvhF6vx+TJk7F69Wrz100mE06fPo3y8nLzupUrV5q3raqqQlRUFNatW2f+uoeHB9auXYtnn30WqqqiS5cuWLFiBR577DGbaqt9L1B79QJHkmUZycnJ6N27Nz/WEBDzFRvzFR8zFhvzdY7afsqaY61uc0RWy86fP2++cgERERER3bisrCy0b9/+mtuwkbUDRVFw8eJF+Pr6QqfTOfR7lZSUICwsDFlZWZzGICDmKzbmKz5mLDbm6xyqqqK0tBTt2rWDXn/tK8W6zdQCLdPr9dd9x2Bvfn5+3IkExnzFxnzFx4zFxnwdz9/f36rt3OKGCEREREREv8dGloiIiIjcEhtZN+Pl5YXFixfzOreCYr5iY77iY8ZiY77aw5O9iIiIiMgt8YgsEREREbklNrJERERE5JbYyBIRERGRW2IjS0RERERuiY0sEREREbklNrJERERE5JbYyBIRERGRW2IjS0RERERuiY0sEREREbklNrJERERE5JbYyBIRERGRW2IjS0RERERuiY0sEREREbklNrJERERE5JbYyNpRXFwc7rnnHrRr1w46nQ7bt2+36fkvv/wydDpdnUfz5s0dUzARERGRG2Mja0dXrlxBv379sHbt2kY9f/78+cjOzrZ49OrVC/fff7+dKyUiIiJyf2xk7Wjs2LF49dVXMXHixHq/XlVVhfnz5yM0NBTNmzfHkCFDsGfPHvPXW7RogeDgYPMjNzcXp06dwsyZM500AiIiIiL3wUbWiWbNmoWEhARs3rwZx48fx/3334+77roLaWlp9W7/4Ycfolu3bhgxYoSTKyUiIiLSPjayTpKZmYkNGzZg69atGDFiBDp37oz58+fj1ltvxYYNG+psX1lZiU8//ZRHY4mIiIgaYHR1AU3FiRMnIMsyunXrZrG+qqoKrVu3rrP9V199hdLSUkyfPt1ZJRIRERG5FTayTlJWVgaDwYDDhw/DYDBYfK1FixZ1tv/www9x9913IygoyFklEhEREbkVNrJOMmDAAMiyjLy8vOvOec3IyMDu3bvxzTffOKk6IiIiIvfDRtaOysrKcObMGfPfMzIycPToUbRq1QrdunXDww8/jGnTpmH58uUYMGAALl26hF27dqFv374YP368+XkfffQRQkJCMHbsWFcMg4iIiMgt6FRVVV1dhCj27NmDO+64o8766dOnY+PGjTCZTHj11VfxySef4MKFCwgMDMTQoUOxZMkS9OnTBwCgKAo6dOiAadOm4bXXXnP2EIiIiIjcBhtZIiIiInJLvPwWEREREbklNrJERERE5JZ4spcdKIqCixcvwtfXFzqdztXlEBEREbktVVVRWlqKdu3aQa+/9jFXNrJ2cPHiRYSFhbm6DCIiIiJhZGVloX379tfcho3s/6xduxbLli1DTk4O+vXrhzVr1iAyMtKq5/r6+gKo+Qf38/NzZJkwmUyIiYnBmDFj4OHh4dDvRc7HfMXGfMXHjMXGfJ2jpKQEYWFh5v7qWtjIAtiyZQvmzp2L9evXY8iQIVi1ahWioqJw+vRptG3b9rrPr51O4Ofn55RG1sfHB35+ftyJBMR8xcZ8xceMxcZ8ncua6Zo82QvAihUr8Nhjj2HGjBno1asX1q9fDx8fH3z00UeuLq2O7OJKpBXrkF1c6epSiIiIqInILq5AfHo+sosrXF2KhSZ/RLa6uhqHDx/GCy+8YF6n1+sxevRoJCQkuLCyujYnZuKFbSegwoB1KXFYOqkPpgwOd3VZREREJLAtB2v6D0UF9Dpoqv9o8o1sfn4+ZFlGUFCQxfqgoCCkpqbW+5yqqipUVVWZ/15SUgKg5iMHk8nkkDqziyvxwlcnUHv3CkUFXth2AsMiAhDi7+2Q70nOV/vz46ifI3It5is+Ziy2ppjv7tN5eO7LE+a/O6P/sOXft8k3so2xdOlSLFmypM76mJgY+Pj4OOR7phXroKoGi3WKCszbuBsTO6pozqk6Qtm5c+cNv4ZOp4PBYLj+huRURqMRu3fvdnUZ5EDulrEsy+BNPm1jj9/RWqaqQHoJsPOCHqnFdWehKirwefRudPV3zM9NeXm51ds2+UY2MDAQBoMBubm5Futzc3MRHBxc73NeeOEFzJ071/z32rPrxowZ47CTvbKLK7EuJQ7K735mDuYbcKrEgKmRYXhkeAe08fVyyPcn5zCZTNi5cyf+8Ic/NPpEAlVVkZeXZ/6kgLRDVVVUVlbC29ub15wWlLtm7Ofnh7Zt27pVza5gj9/RWqaqKuLS8vGvvRk4nFkEoGYqwe97D70OeGDcHQ47ImvL/19NvpH19PTEwIEDsWvXLkyYMAFAzQ0Odu3ahVmzZtX7HC8vL3h51W0YPTw8HPaDHR7ogaWT+ljMUXlwcDiOZBYiNacUH+4/h09+zsSUQWF44rZOaB/gmCPD5Bw38rOUnZ2N0tJSBAUFwcfHh/8xaYiiKCgrK0OLFi2ue5Fvck/ulrGqqigvL0deXh4MBgNCQkJcXZJbcOT/964gKyp+OJmDtbvP4OTFmibS06DH/YPa46+3dUZ8ej5e3JYMWVVh0Onw+qTeCA+8/qWxGsuWf9sm38gCwNy5czF9+nQMGjQIkZGRWLVqFa5cuYIZM2a4ujQLUwaHY1hEAD6P3o0Hxt2B8EBfqKqK2NQ8vLv7DJIyi/B/P/+KzxIzcV//UDx5e2d0advC1WWTE8myjKKiIrRt2xatW7d2dTn0O4qioLq6Gt7e3m7R5JDt3DHjZs2aAQDy8vLQtm1bTklqQkyygq+PXsS6PWdw9tIVAICPpwEPDwnHoyM6Iciv5ojrlFbhGNmtDc7ll6NjoA9C/Ju5smwLbGQBTJkyBZcuXcKiRYuQk5OD/v37Y8eOHXVOANOCEH9vdPVXzYfzdTod7uwZhFE92iLh7GWs252O/Wfy8eWR89iWdB5jewfjqdu7oHeov4srJ2eonSDvqLnaRCSm2t8ZJpOJjWwTUGmSsfVQFtbvPYsLRTWX0/LzNuIvt0RgxvCOCGjuWec5If7NNNXA1mIj+z+zZs1qcCqBO9DpdBjeORDDOwciKbMQ6/akY+epXESfyEH0iRzc3r0NZt3RBYM6tnJ1qeQEnE5ARLbg74ymoaxKwn9+/hUf7stAflnN1ZcCW3jh0REReHhIOHy93W+6BBtZAQ0ID8AH0wYhNacE/9qTjm+PXcSe05ew5/QlREa0wqw7umBE10D+4iIiImoCCq9UY0P8OXwcfw7FFTWf3IW2bIYnbuuEBwaFwdvDfY/Cu8cEHmqUHsF+eOfBAYiddzumRobBw6BDYkYBpn2UiPvW/oQdyTlQfn8qIhE5xcsvvwydTgedTodVq1a5uhwSGH/Wmq68kkq89v0p3PJmLFbvSkNxhQmdAptj2R/7Ys/fb8e0YR3duokF2Mg2CR0Dm2PppL6IW3AHHrklAt4eehw/X4y//ucwolbF4auk85BkxdVlEt2wPXv2QKfToaioyGL97bffjjlz5rikpmu56aabkJ2djccff9y8rrKyEk8//TRat26NFi1aYPLkyXUuD3g92dnZeOihh9CtWzfo9fpGj11VVSxatAghISFo1qwZRo8ejbS0NJteo7KyEn/5y1/Qp08fGI1G89VhbBUXF4d77rkH7dq1g06nw/bt2xv1Oq+99hqGDx8OHx8ftGzZslGvAdT8rN18883w8vJCly5dsHHjRptf4/3338ftt98OPz+/en9urXX8+HGMGDEC3t7eCAsLw1tvvWXx9fnz5yM7Oxvt27dv1OuT+8kqKMc/vjqBW9/ajQ/2ZaC8WkavED+sfehm7Jx7G+4fFAYPgxgtoBijIKuE+DfDont64afnRmHWHV3g62VEWl4Znt1yDHcs34NPD/yKSpPs6jKJNKu6utqur2c0GhEcHGxxct6zzz6Lb7/9Flu3bsXevXtx8eJFTJo0yabXraqqQps2bfDSSy+hX79+ja7vrbfewurVq7F+/XocOHAAzZs3R1RUFCorK61+DVmW0axZM/ztb3/D6NGjG13LlStX0K9fP6xdu7bRrwHUZHj//ffjySefbPRrZGRkYPz48bjjjjtw9OhRzJkzB48++ih++OEHm16nvLwcd911F1588cVG11JSUoIxY8agQ4cOOHz4MJYtW4aXX34Z77//vnmbFi1aIDg4mCdxNQFn8koxd8tR3P72Hnx6IBPVkoKBHQKw4S+D8f3fbsX4viEw6AWbVqjSDSsuLlYBqMXFxQ7/XtXV1er27dvV6urqG36t4opq9d3YNPXmV2LUDs99p3Z47jt18Ks71Q/i0tWySpMdqiVb3Wi+FRUV6qlTp9SKigq71HOxqFz96cwl9WJRuV1e71puu+029emnn1affvpp1c/PT23durX60ksvqYqimLf55JNP1IEDB6otWrRQg4KC1KlTp6q5ubmqqqpqRkaGCsDiMX36dHX69Ol11mdkZKiqqqonTpxQ77rrLrV58+Zq27Zt1T/96U/qpUuX6tT0zDPPqK1bt1Zvv/12dffu3SoA9ccff1QHDhyoNmvWTB02bJiampp63THKsqwWFhaqsiyrixcvVvv162fx9aKiItXDw0PdunWreV1KSooKQE1ISGj0v+szzzxj8/MURVGDg4PVZcuWWdTn5eWlfvbZZ42qZfr06ep9993XqOdeDYD61Vdf3dBrbNiwQfX392/UcxcsWKDedNNNFuumTJmiRkVFWWRsrdqfqcLCQptrWbdunRoQEKBWVVWZ1z333HNq9+7d62zboUMHdeXKlfW+jr1/d4jKnv8H29PxrCL1iU8OqR2f/878//mfPvxZTUjPt/gd6i5s6at4RLYJ8/P2wNN3dMH+50Zh8T29EOLvjbzSKrz6fQpurZ1PU9507ictKlVVUV4t2fz4v4RzuOWNWDz0wQHc8kYs/i/hnM2vodp428uPP/4YRqMRiYmJeOedd7BixQp8+OGH5q+bTCb885//xLFjx7B9+3acO3cOf/nLXwAAYWFh+PLLLwEAp0+fRnZ2Nt555x288847GDZsGB577DFkZ2cjOzsbYWFhKCoqwqhRozBgwAAcOnQIO3bsQG5uLh544IE6NXl6euKnn37C+vXrzev/8Y9/YPny5Th06BCMRiMeeeQR89fOnTsHnU6HPXv22DT+w4cPw2QyWRy57NGjB8LDw5GQkGDTa92ojIwM5OTkWNTi7++PIUOGOL0WrUlISKhzdDkqKsol/y4JCQkYOXIkPD1/u1xSVFQUTp8+jcLCQqfXQ85Ve97LPe/ux46TOVBVIOqmIHz99C34v5lDMLRTa+FP7OZVCwjNPA2YcUsEHh7SAduOnMe/9qbj18vlWLHzF7wfdxZ/GtoBM2+N4O1v3VSFSUavRbZ95Pl7igos/PokFn590qbnnXolCj6e1v+aCQsLw8qVK6HT6dC9e3ecOHECK1euxGOPPQYAFs1ip06dsHr1agwePNh8J6VWrWouL9e2bVuL+Y+enp7w8fGxuO30u+++iwEDBuD11183r/voo48QFhaGX375Bd26dQMAdO3a1WLOYXZ2NoCauZa33XYbAOD555/H+PHjzbcm9fDwQPfu3W2+nm9OTg48PT3rzN0MCgpCTk6OTa91o2q/3++vp+2KWrQmJyen3n+XkpISVFRUOL2WiIiIOrXUfi0gIMCp9ZDjqaqKvb9cwrrd6Ug8VwCg5m6f9/Zrh6fu6IJuQY6745YWsZElM0+jHg9GhuOPA9vj+xPZWLc7HadzS7F+bzo2/JSBBweH4fHbOiO0pfYuiExiGDp0qMXRg2HDhmH58uWQZRkGgwGHDx/Gyy+/jGPHjqGwsBCKUnOSYmZmJnr16mXT9zp27Bh2796NFi3q3v0uPT3d3MgOHDiw3uf37dvXvFx7W8+8vDyEh4cjNDQUqampNtVDRHQtSu1tZPecQfKF324jO3lge/z1tk7o0Lq5iyt0DTayVIfRoMd9/UNxT9922PW/298eyyrCxwm/4tMDmZg4oOb2t53a8Pa37qCZhwGnXomy6Tk5xZUYvWIvrr46m14H/Dj3NgT/765y1n5ve7ly5QqioqIQFRWFTz/9FG3atEFmZiaioqIadRJWWVkZ7rnnHrz55pt1vnb1/eabN6//P4er7wVe23zXNtaNFRwcjOrqahQVFVkclc3NzbU4muwMtd8vNzfX4t8jNzcX/fv3d2otWhMcHFznShK5ubnw8/NDs2bNzHfYc2UttV8j92eSFXxz9CL+tTcdZ/LKANT8bn1oSDgeG9HJpt/JImIjSw3S63X4Q68gjO7ZFvHpl7F29xnEp1/G1sPn8cWR8xjXJwRP394Fvdr5ubpUugadTmfTx/sA0KlNCyyd1AcvbkuGrKow6HR4fVJvh795OXDggMXff/75Z3Tt2hUGgwGpqam4fPky3njjDYSFhQEADh06ZLF97TxBWZbrrP/9uptvvhlffvklOnbsCKNRG78KBw4cCA8PD+zatQuTJ08GUDPfNzMzE8OGDXNqLREREQgODsauXbvMjWtJSQkOHDhwQ2f8i2DYsGGIjo62WLdz506nZ1Rbyz/+8Q+YTCbzm6udO3eie/funFbg5ipNMrYePo/39qbjfGHNlBVfbyP+MrwjZtwSgVb13Ea2KdLGb2/SNJ1Oh1u6BOKWLoE4klmIdbvP4MeUPHx/PBvfH8/GqB5t8fQdXTCwA39pimTK4HCM7NYG5/LL0THQxyn32M7MzMTcuXPxxBNP4MiRI1izZg2WL18OAAgPD4enpyfWrFmDv/71r0hOTsY///lPi+d36NABOp0O3333HcaNG4dmzZqhRYsW6NixIw4cOIBz586Z59I+/fTT+OCDDzB16lQsWLAArVq1wpkzZ7B582Z8+OGHN3SpogsXLuDOO+/EJ598gsjISKuf5+/vj5kzZ2Lu3Llo1aoV/Pz8MHv2bAwbNgxDhw61qYajR48CqDnyfOnSJRw9ehSenp5WT8HQ6XSYM2cOXn31VXTt2hURERFYuHAh2rVrZ/O1YE+dOoXq6moUFBSgtLTUXJstR3bLyspw5swZ898zMjJw9OhRtGrVCuHh4Va/TmZmJgoKCpCZmQlZls21dOnSpd5pJvX561//infffRcLFizAI488gtjYWHz++ef4/vvvra4DqJnDmpOTYx7XiRMn4Ovri/DwcPN87+t56KGHsGTJEsycORPPPfcckpOT8c4772DlypU21ULacaVKwqcHfsUH+zJwqbTmNrKtm3ti5ogI/HloB7e8jaxDOfoSCk2Bu15+60aculisztp0RI246lIfU96LV/f9csktL/WhFVq7/JYz3XbbbepTTz2l/vWvf1X9/PzUgIAA9cUXX7T4edq0aZPasWNH1cvLSx02bJj6zTffqADUpKQk8zavvPKKGhwcrOp0OnX69Omqqqrq6dOn1aFDh6rNmjWzuPzWL7/8ok6cOFFt2bKl2qxZM7VHjx7qnDlzzN+zvktX1XeppKSkJIvXrb0U2O7duy2ee73Lb6lqTYZPPfWUGhAQoPr4+KgTJ05Us7OzLbbp0KGDunjx4mv+e+J3lxwDoHbo0KHOOGprro+iKOrChQvVoKAg1cvLS73z/9u787CoyvYP4N9h2GUT2XeYATdcEDdwYXBJ0yy11FxSMy0FM63esre31Opn2Vv5WqFmKZYtappWLuU2A4o7KO7LDPsuIIuAiHB+f4xS5AbKcGbg+7kuros588w5N/Nw5txzznOee+BA4eLFi3XahIWF1b7P9+Lt7X3XeG671/v1d7fj/efP37e9YMGCOn/j3dxtOrZ/brs+769SqRS6du0qmJqaCn5+fkJ0dLQgCH/18erVq4UHHWIXLFhw11hur0sQ6vf+JiYmCn379hXMzMwEd3d34aOPPrprO06/9eh0eQy+WlYpLN19Ueiy6M/a42rI4j1C9IEkobzyZqNvT581JK9iItsIWmIie1vSlWvCGz8nCvJ/b6/d8Z788oDw55lsobqaCW1DtfRE9mHmOzUk9UlkH6SsrEwwNze/b9JXH2vWrBHkcvkjf5Z4eXnVSbwexr59+wQ7OzuhsLDwkdYzefLkByZ9D/Ko7+/tPn7nnXeEsLCwR4pFEBrn/b2Nieyj08UxOLekQli8/ZzQ4Z2dtcdRxX+VwoajaUJlVf3nI25OGpJXiTq04NSpUw1+TYcOHfRmPBsBvg6tsOSZznhlkD9WxSZh/bE0JKYX4cV18WjrbI2IcBmGd3KFcTMphUfUmE6fPg0rKyt8/PHHiIiIqNdrlEolBgwYAIVC8Ujb3rFjBxYvXlznprWGOnv2LGxtbTF58uRHjuXf//73I43pFAQBKpUKBw4ceKRYGuv9/eOPP/Dll18+0joa6/1dvHgxFi9ejPLy8kdaDzWujKvl+ComCRuOp+PGTe2Nou1crBEZLsewTs2wApeOSAShgTOWNyIjIyNIJJJ6T5puZGSES5cuwc/PT8eRNUxJSQlsbW1RXFwMGxvd3vhUVVWFHTt2YNiwYY90ANKV/GuVWHMgGesOpaK08iYAwLuNJWaGyTC6mzvMjFki8X4etX+vX7+O5ORk+Pr6wtzcsO5kVSgU6Nq1K/73v/+JHYrO1NTUoKSkBDY2NigqKkJhoXYOSEdHR9ja2oocHTWGv/exkZF+fIEvLCx84P+aIX92NKXGOAar865hhUqDX09m4uatqWGCvOwwO1yOAe2cmn0Bg/poSF4l+qnNI0eOwNHR8YHtBEFAYGBgE0REj8LBygxvDG2Hl8JkWHcoBasPJCO1oBxv/XIay/Zcxoz+fhjf07PBd9FT89fQKliGzt7evt439BA9Cv6v6YczmcVYrlJj5xltBS4A6Ct3QES4DCEtoAKXroiaTYSFhUEul99RxeZe+vfvDwsLTsZvCGwtTDB7gD+m9fXFT0fTsSpWg5yS63h/2zlEKdWY1scHz4X4wNZC/84qExERNZbjKYX4UqmG6uKV2mWDOzgjQiFDkBdn+3lUoiaySqWyQe3/OW8f6T9LU2O80NcXk3p74ZeETKxQaZBWWI5Pdl3CVzFJeC7EG9P6+sLBiuVvG5OII4aIyADxM6NxCYKA/ZfzEaVU40jyX2Vkn+jshohwGdq5cP71xqK313erq6tx+vRpeHt7c1LnZsDMWIrxPb0wJtgD205lY7lKjUu517BcpcGauGQ828MLL/b3gxvL3z6S22O2ysvLefWCiOrt9o1g+njvhSGpqRGw61wulqvUOJVRDAAwkUrwdDcPzAyTwcehZZaR1SW9SWTnzp2LTp064YUXXkB1dTXCwsJw8OBBWFpaYtu2bY98BynpB2OpEUYGuePJLm7YfT4XUUrtzr72YAp+OJKK0UEemKXgzv6wpFIp7OzskJeXBwCwtLTkuCs9UlNTgxs3buD69et6cyMQNS5D62NBEFBeXo68vDzY2dk9UiGQluxmdQ1+P5WF5UoNLt8qI2tuYoTxPbUnaZqioExLpTeJ7KZNmzBp0iQAwO+//47k5GRcuHAB69atw9tvv424uDiRI6TGZGQkwZCOLnisgzMOqLWXXw4nFWLD8XT8HJ+O4Z3dEMnLLw/ldn3128ks6Q9BEFBRUQELCwt+wWimDLWP7ezsaj87qP4qb1ZjU3wGVsZokF54q4ysmTEmh3pjWh9ftOGwOZ3Tm0Q2Pz+/difasWMHxowZg4CAAEybNg3Lli0TOTrSFYlEgn7+jujn74j41EJEKTXYdyEPvydm4ffELAxqry1/ywHx9SeRSODq6gonJydUVVWJHQ79TVVVFWJjY9G/f39ewm2mDLGPTUxMeCa2gcpv3MTPh9Px9f4k5JZoy8jatzLFC3198VyIN2xYRrbJ6E0i6+zsjHPnzsHV1RV//PEHVqxYAUA7boc7WMsQ7G2PNVPtcTarGMtVGuw4nY095/Ow53weQmVtMDtcjhAZpyipL6lUyn1Hz0ilUty8eRPm5uYGk+RQw7CPm7fiiir8mSHBwk/342q59kSBi405Xuzvh/E9vWBhys/cpqY3iezzzz+PsWPHwtXVFRKJBIMGDQKgnWe2Xbt2IkdHTamjmy2iJnSD5so1rFRpsOVEJg5qCnBQU4CuntpJowe256TRRETUNK6UVmL1gWSsO5yCskopgCp4t7HErDAZRrHYj6j0JpFduHAhAgMDkZ6ejjFjxsDMTDuuRCqVYv78+SJHR2KQOVrhv2O64JVB/vg6Ngnrj6XjZHoRpn93HO1crBERLsdwlvEjIiIdySyqwKoYDdYfS0flrTKyrhYC/vVEZzzZ1YPl1/WA6Ins5MmT8dRTT2HIkCF45pln7nh+ypQpIkRF+sSjtSUWPRWI2QP8sfpAMr4/nIoLOaWY89MJfLbrImYpZBgV5AFTY36gEBHRo0u6oi0ju+XEX2Vku3jaYVY/H1QkHccTnV2ZxOoJ0XtBLpdj8eLFcHR0xOOPP44VK1YgMzNT7LBIDzlam2H+4+0Q9+YAvDo4AHaWJkgpKMebm08j7L9KRMclo+JGtdhhEhGRgTqXVYLIHxMw8LMY/ByfgZs1AkJlbfDD9F7YGhGKge2dwIuA+kX0RPbdd99FfHw8Ll++jBEjRmDr1q2QyWQIDg7Ge++9h5MnT4odIukZW0sTzBnoj7g3B+A/w9vDydoM2cXXsej3c+i7ZB+ilGqUXOfd+kREVD/xqVcxbe0xDPt8P7afyoYgAIPaO+GXiFD8OKM3+sgdeF+GnhJ9aMFtHh4eiIiIQEREBEpLS7Fz5078+uuvGDBgAKytrTFixAjMmjULHTt2FDtU0hOtzIwxvZ8fJvX2xuaEv+bx+++fF7EyRoMpIT6Y1tcX9q1MxQ6ViIj0jCAIiFMXIEqpxqGkAgDaMrLDO7shQiFDe1fOY24I9CaR/Ttra2uMHTsWY8eORXV1NVQqFX777TccOnSIiSzdwdxEiom9vDGuuyd+P5WFKKUG6rxr+FKpxuoDybWVVVxszcUOlYiIRFZTI2DP+VxEqTRITC8CABgbSTC6mztmKeTwZWVJg6KXiezfSaVSDBw4EAMHDhQ7FNJzxlIjjArywFNd3LHrXA6ilBqczizGmjjtlCnPBGtrXXu34YcUEVFLc7O6BttPZ2O5UoOLuaUAADNjbRnZGf394G7HMrKGSNRENigoqN5jThISEnQcDTUXRkYSDA10xZCOLoi9rC1/ezS5ED8dTceGY+kY0cUNEQo52rpYix0qERHpWOXNavySkImVMRqkFpQDAKzMjPFciDde6OsLB5aRNWiiJrIjR46s/f369etYvnw5OnTogJCQEADA4cOHcfbsWURERIgUIRkyiUSCsABHhAU44lhKIaKUaqguXsGvJ7Pw68ksDO7gjNnhcnTxtBM7VCIiamTlN27ip6Pp+Do2CTkl1wEArS1NMK2PLyaH+sDWgpXXmgNRE9kFCxbU/j59+nTMmTMH77///h1t0tPTmzo0amZ6+Nhj7fM9cSazGMtVauw8k4Pd53Kx+1wu+sodEBkuR28/e96VSkRk4IorqrDuUArWxKWgsOwGAMDZxgwz+vlhQi8vWJrq/ahKagC96c2ff/4Zx48fv2P5pEmT0L17d6xZs0aEqKi5CXS3xfKJwVDnlWKFKglbT2bigDofB9T56OZlh9kD5Ahvy/K3RESGJv9aJdYcSMa6Q6korbwJAPCyt8TMMBmeDmYZ2eZKbxJZCwsLxMXFwd/fv87yuLg4mJvzbnNqXHIna3w6tgvmDvLHqtgkbDiejoS0IkxbexztXW0QGS7D44Esf0tEpO+yiiqwKjYJ64+l4XqVtoxsgLMVIhRyVuBqAfQmkZ07dy5mzZqFhIQE9OzZEwBw5MgRrFmzBu+8847I0VFz5WlvifdHBuLlAfLa8rfns0sw+8cT8HO4hJkKGUZ2dWf5WyIiPZOSX4YVKg1+OZGBqmptGdnOHraIDJdjcHtnGPFERIugN4ns/Pnz4efnh2XLluH7778HALRv3x7R0dEYO3asyNFRc+dkY463hrXHLIUMaw+mIDouBUn5ZXhj0yn8b/clvBQmw7genjA34aUpIiIxXcgpQZRSg+2nslCjzV/R288ekeFy9GUFrhZHbxJZALVFEJpKSkoK3n//fezbtw85OTlwc3PDpEmT8Pbbb8PUlNWgWiI7S1PMHRSA6f388OORVHy9PxlZxdex4Lez+GLfZbzQ1w+TenvB2px3uxIRNaUTaVcRpVRjz/m82mUD2jkhMlyGYG97ESMjMelVItvULly4gJqaGnz11VeQy+U4c+YMZsyYgbKyMnzyySdih0cisjIzxov9ZZgc4oOf4zOwUqVBZlEFlvxxAStUakwN9cHzfXzRmuVviYh0RhAEHNIUIEqlRpxaW0ZWIgGGdXJFhEKGjm62IkdIYtObRLa6uhpLly7Fxo0bkZaWhhs3btR5vrCwsNG3OXToUAwdOrT2sZ+fHy5evIgVK1YwkSUA2vK3z/X2xrM9PPHbySwsV6mhuVKGz/ep8c2BZEy4VRHG2YY3JBIRNRZBELD3fB6iVGqcSCsCoC0jOyrIHTMVMsgcrcQNkPSG3iSyixYtwjfffIPXXnsN//nPf/D2228jJSUFW7duxbvvvttkcRQXF8PenpcoqC4TqRGeDvbAqCB3/Hk2B18q1TibVYJvDiTju0OpeKa7B2b2l8GrjaXYoRIRGazqGuFWGVk1LuRoy8iaGhvh2R6eeLG/Hzxa8zOW6tKbRPaHH37A119/jeHDh2PhwoUYP348ZDIZOnfujMOHD2POnDk6j0GtVuOLL7544NnYyspKVFZW1j4uKSkBAFRVVaGqqkqnMd5ev663Q/c2qJ0DBrZtg/3qAqyIScLx1CL8eCQNG46l44lOLnipvy/8nR7ubAH7t3lj/zZ/7OOHc+NmDX5NzMJXsSlILdSWkW1lKsWEnp54PtQbjtbaMrJiv6/s36bRkPdXIgiCoMNY6q1Vq1Y4f/48vLy84Orqiu3bt6Nbt25ISkpCUFAQiouL672u+fPnY8mSJfdtc/78ebRr1672cWZmJsLCwqBQKPDNN9/c97ULFy7EokWL7lj+448/wtKS3xZbGk0JsCvDCBeK/5qiq7N9DQa718CLV7+IiO7pRjVwKE+CfVlGKLqhnW3A0lhAmEsN+rsKsNSb023UlMrLyzFhwgQUFxfDxsbmvm31JpFt27YtvvvuO/Tq1Qt9+/bFE088gfnz52PDhg14+eWXkZeX9+CV3HLlyhUUFBTct42fn1/tzARZWVlQKBTo3bs31q5dCyOj+88Zerczsp6ensjPz3/gG/6oqqqqsHv3bgwePBgmJrxzXp+cySzBitgk7Dr31/9qX3kbzArzRQ/v1vWaEob927yxf5s/9nH9lF6vwg9H0hF9KBWFZdqzb07WZpjWxxvPdvdAKzP9zGDZv02jpKQEDg4O9Upk9eY/ZdSoUdi7dy969eqFl19+GZMmTcLq1auRlpaGefPmNWhdjo6OcHR0rFfbzMxMhIeHIzg4GNHR0Q9MYgHAzMwMZmZmdyw3MTFpsn/sptwW1U+QTxus8mmDy7mlWKHS4NfELBxQF+CAugDdvVsjcoAcigDHeiW07N/mjf3b/LGP766w7AbWHEjGt4dSUHpdW0bWo7UFZobJ8Eywh8HM1c3+1a2GvLd6k8h+9NFHtb+PGzcO3t7eOHjwIPz9/TFixAidbDMzMxMKhQLe3t745JNPcOXKldrnXFxcdLJNav78na3x2biumDc4ACtjNPj5eAaOp17F89HH0NHNBpHhcgzp6MLyt0TUYuQUX8eq2CT8dDQNFVXVAAC5kxUiFDI82cWNZWTpoelFIltVVYWXXnoJ77zzDnx9fQEAvXv3Ru/evXW63d27d0OtVkOtVsPDw6POc3oy4oIMmKe9Jf5vVCfMGeiPb/Yn4YcjaTibVYKIHxLg59gKEQo5nurqBhN+gBNRM5VaUIaVMRpsiv+rjGwnd1tEhsvwWAcXlpGlR6YXR1ATExNs3ry5ybc7depUCIJw1x+ixuJsY463h3dA3JsDMGegP2zMjZF0pQyv/5wIxX9VWHcoBddvnaEgImoOLuaU4pX1JxD+iQo/HU1HVbWAnr72+HZaT/w2uw+GBroyiaVGoRdnZAFg5MiR2Lp1a4PHwxIZitatTPHq4ADM6OeLH46k4Zv9ycgsqsA7v57Fsr1qzOjni7HBbmKHSUT00BLTi/ClUo3d53JrlynaOiIyXI4ePpyjnRqf3iSy/v7+eO+99xAXF4fg4GC0atWqzvNNMY8sUVOwNjfBzDAZpob6YOPxdHwVk4TMogp8uPMClqvUCGljhJDyG3Cy5Y0ERKT/BEHA4aRCLFepsf9yPgBtGdnHA10QoZAj0J1lZEl39CaRXb16Nezs7BAfH4/4+Pg6z0kkEiay1OyYm0gxOcQH43t6YeuJTKxQaZCUX4Y/MowQ++l+TOrtjel9feHE8rdEpIcEQYDyYh6ilBrEp14FAEiNJBjZ1R2zFH6QO1mLHCG1BHqTyCYnJ4sdApEoTKRGGNPdE6O7eWB7YgaW/J6IzPJqrIpNwtqDKRjb3QMv9ZfB057FNohIfNU1AnaeyUaUUoPz2drKlqbGRhjXXVtGlp9V1JT0JpElaumkRhI8HuiCmtQEtPLvgZWxKYhPvYrvD6fhp6PpeKqrGyIUMp7lICJRVFXXYMuJTKy8dfUI0JaRndTbGy/w6hGJRNRZC1599VWUlZXVu/1bb72FwsJCHUZEJD6JBFAEOGLTzBCsf7E3+vk7oLpGwC8JmRi8NBazvo/Hmcz6l2wmInoU16uq8e3BFCj+q8Ibm04hKb8MthYmeGWgP+LmD8Bbw9oziSXRiHpGdtmyZXjrrbfuuLHrXqKiojBjxgzY2/POR2r+JBIJevu1QW+/NkhML0KUUo1d53Kx80wOdp7JQViA9k7gnr7cH4io8ZVer8L3h9Ow+kAS8q/dAAA4WJlhRj9fTOztDSs9LSNLLYuo/4WCICAgIKBeJTsBNOjsLVFz0sXTDqsmd8el3FIsV6rxW2IWYi5dQcylK+jpY4+IcBnC6ln+lojofq6W3UB0XDLWHkxBya0ysu52FpipkGGMAZWRpZZB1EQ2Ojq6wa9xdnbWQSREhiHA2Rr/ezboVvnbJGyOz8DRlEIcjS5EoLsNIhXa8recaJyIGiq35Dq+jk3Cj0fTUH5DW6RFdqsK4ZOsQkh6StREdsqUKWJunshgebdphQ9Hd8IrA/3x9f4k/HgkDWcySzDrhwTInawwK0zGAw8R1UtaQTlWxmqw6XgGblTXAAA6utlgdrgcj3V0gZRfjEmPcYALkQFzsTXHO090QGS4vPZSoDrvGl77ORFL91zCS2G8FEhEd3c5txTLVRr8lpiF6hptafYePq0RGS7nUCUyGExkiZoB+1ameO2xtnixvx/WHU7F6v3JyLhagXe2nsEXey9jRj8/TOjlhVa8OYOoxTudUYwvlZfx59m/ysj2D3DEbN48SgaIRzWiZsTa3AQRCjmeD/XFhmNpWBWbhKzi6/i/HecRpVLj+VBfTAn1hp2lqdihElETO5JUgCiVBrGXrtQuG9rRBZHhcnTyYBlZMkxMZImaIQtTKab28cWEXt7a8rcxGiTnl2HpnktYFavBpJBbE5hbc+5HouZMEASoLl3BcqUax1L+KiP7VBc3zFLI4O/MAitk2PTmTpBp06ahtLT0juVlZWWYNm2aCBERGT5TYyOM7eGJPa+G4YvxQWjnYo2yG9X4KiYJ/ZYo8e6vZ5BxtVzsMImokVXXCNhxOhtPfHEAz0cfw7GUqzCVGmFiLy+oXlfgs3FdmcRSs6A3iey3336LioqKO5ZXVFTgu+++EyEiouZDaiTBiC5u2PlKP6ye0h1BXnaovFmD7w6lQvFfFV7/ORGaK9fEDpOIHlFVdQ02xWfgsaUxiPghAWezSmBpKsWMfr7Y/2Y4/m9UJ3jaW4odJlGjEX1oQUlJCQRBgCAIKC0thbn5X5c6q6ursWPHDjg5OYkYIVHzIZFIMLC9Mwa0c8KhpAJEKdWIUxdgU3wGNidkYFigK2YpZAh053g5IkNyvaoaPx9Px8qYJGQWaU8K2ZgbY2ofXzwf6oPWrTgunpon0RNZOzs7SCQSSCQSBAQE3PG8RCLBokWLRIiMqPmSSCQIlTkgVOaAE2lXEaXUYM/5XGw/nY3tp7MR3lZb/ra7D+9gJtJn1ypv4ofDqfh6fzLyr1UCABysTDG9nx8m9vKCtbmJyBES6ZboiaxSqYQgCBgwYAA2b94Me/u/Dpympqbw9vaGm5ubiBESNW9BXq3xzZTuuJBTguVKDbadyoLy4hUoL15BL197RIbL0c/fgXNKEumRq2U3sPZgCtYeTEFxRRUAbRnZl8L8MLa7J+eOphZD1ETW3t4ely5dgoODA6ZMmYJBgwbB2pqDz4nE0M7FBp+PD8KrgwOwMkaDzQkZOJJciCPJR9HZwxYRCjke6+DM8rdEIsoruY5vDiTj+8OptWVk/RxaYZZChqe6usPUWG9ufSFqEqImsjdu3EBJSQkcHBzw3Xff4eOPP2YiSyQyH4dW+OjpznhlkD9WxSbhp6NpOJVRjJnfx8PfyQoR4TKM6OwGY5a/JWoy6YXl+CpWg43HM3DjpraMbHtXbRnZoYEsI0stl6iJbEhICEaOHIng4GAIgoA5c+bAwsLirm3XrFnTxNERtWyuthZYMKIjZofLsSYuGd8dTMXlvGuYtyERn+2+hJlhMjwT7AEzY17CJNIVdZ62jOyvJ/8qIxvs3Rqzw+VQtGUZWSJRE9nvv/8eS5cuhUajgUQiQXFxMa5fvy5mSET0D22szPCvIe3wUpgM6w6lYvWBZKQXVuDtLWfw+d/K31qaij7knqjZOJNZjCilGn+czYGgzV/Rz98BkeFy9PK1ZwJLdIuoRx5nZ2d89NFHAABfX1+sW7cObdq0ETMkIroHG3MTRIbLMa2PL346qi1/m1NyHR9sP48opRrT+vhicqgPbC14lzTRwzqWUogv96kR87cyso91cEZkuBxdPO3EC4xIT+nNKZTk5GSxQyCierAwlWJaX19M7O2FLQna8repBeX4dPclfBWbhOdCvDGtjy8crc3EDpXIIAiCgNjL+Yjap8bRlEIAgJEEeLKLGyLC5QhgBS6iexI1kf3888/x4osvwtzcHJ9//vl9286ZM6eJoiKi+jAzluLZnl54JtgD209nY7lSg4u5pVih0mDNgWSM7+mFGf394G5393HvRC1dTY2AXedyEKXU4HRmMQDAVGqEp4M9MDPMD95tWokcIZH+EzWRXbp0KSZOnAhzc3MsXbr0nu0kEgkTWSI9ZSw1wlNd3TGisxv2XsjDl0o1EtOLsPZgCr4/nIrR3dwxM0wGP0crsUMl0gtV1TX4PTELy1UaqPO0paEtTKSY0MsLM/r5wcXW/AFrIKLbRE1k/z6cgEMLiAybkZEEgzs4Y1B7JxzUFODLfWocSirAxuMZ2BSfgWGdXBGhkKODm43YoRKJ4npVNTbFZ2BljAYZV7VlZK3NjTE11AfP9/GFPcvIEjWY3oyRJaLmQSKRoI/cAX3kDohPvYrlSjX2XsjDtlPZ2HYqGwPbOSEiXI5g79Zih0rUJMoqb+LHI2n4en8S8kq1ZWTbtDLFC/18Mam3N2xYRpbooelNIltdXY21a9di7969yMvLQ01NTZ3n9+3bJ1JkRPSwgr1bY/XUHjiXVYLlKjW2n87G3gt52HshDyF+bRAZLkcfeRtOJUTNUlH5DXx7MBXRB5NRVK4tI+tqa46X+vthXA8vWJhyDmaiR6U3iewrr7yCtWvXYvjw4QgMDOSBjagZ6eBmgy8ndMOrV65hZYwGvyRk4lBSAQ4lFaCLpx0iFTIMas/yt9Q8lNwAPv7zEn48mo6yW2VkfR1aYVaYDCODWEaWqDHpTSK7fv16bNy4EcOGDRM7FCLSET9HK3z8TBe8MigAX98qf5uYXoQX18WjrbM1IsJlGN7JleVvySBlXC3HSpUaGxKkqBJSAADtXKwRGS7HsE6uLCNLpAN6k8iamppCLpeLHQYRNQF3OwssfLIjZg+QY/WBZKw7lIqLuaV4Zf3J2vK3o7u5s/wtGQTNlWtYodJg64lM3KwRAEjQ1dMWLw/wx4B2TrzCSKRDenPa47XXXsOyZcsg3K7FR0TNnoOVGd4c2g5x8wfgtcEBaG1pgtSCcrz1y2mEfazC6gPJKL9xU+wwie7qbFYxIn9IwKDPYrApPgM3awSE+tljdodqbJzREwPbOzOJJdIxUc/Ijh49us7jffv2YefOnejYsSNMTOrexfnLL780ZWhE1IRsLUzw8kB/vNDPt/bu7pyS63h/2zlEKdV4oa/27m6WvyV9EJ+qLSOrvPhXGdlB7Z0RGS5DoKsVduzYwQSWqImImsja2trWeTxq1CiRIiEifWBpaozp/fzwXIg3NsdnYmWMBmmF5fjvnxexUqXB5FBt+ds2Vix/S01LEAQcUOfjy31qHEn+q4zsE53dEBEuQzsX7fzIVVVVYoZJ1OKImshGR0eLuXki0lNmxtoqR2O7e2DbqWwsV6lxKfcaopQarL5V/vbF/n5wtWX5W9KtmhoBu8/nYrlSjcQMbRlZE6kET3fzwMwwGXwcWEaWSEx6c7NXRUUFBEGApaUlACA1NRVbtmxBhw4d8Nhjj4kcHRGJwVhqhJFB7niyixt2n89FlFKNUxnFiI7Tlr9lMkG6crO6ps6XKAAwNzHilygiPaM3iexTTz2F0aNHY+bMmSgqKkLPnj1hamqK/Px8fPbZZ5g1a5ZOt19ZWYlevXohMTERJ06cQNeuXXW6PSKqPyMjCYZ0dMFjHZxxQJ2PKKUah5MKsf5YOjYeT7/j8i7Rw6q8WV1nWAsAWJsZc1gLkZ7Sm0Q2ISEBS5cuBQBs2rQJLi4uOHHiBDZv3ox3331X54nsG2+8ATc3NyQmJup0O0T08CQSCfr5O6Kfv2OdG25+S8zCb4lZtTfcBHmx/C01TPmNv8rI5pZoy8jatzLFC3198VwIy8gS6Su9SWTLy8thbW0NANi1axdGjx4NIyMj9O7dG6mpqTrd9s6dO7Fr1y5s3rwZO3fu1Om2iKhxBHvbI/r5njibVYzlSg12nMnGnvO52HM+F33kbRCpkCNExvK3dH/FFVX47mAK1sQl4+qtMrIuNuZ4sb8fnu3pCUtTvTlMEtFd6M0eKpfLsXXrVowaNQp//vkn5s2bBwDIy8uDjY3uLhfm5uZixowZ2Lp1a+34XCIyHB3dbBE1sVudSenj1AWIUxcgyMsOkQo5BrbnpPRU15XSSqyJ0xbjuFapnavYu40lZoXJMIrFOIgMht4ksu+++y4mTJiAefPmYeDAgQgJCQGgPTsbFBSkk20KgoCpU6di5syZ6N69O1JSUur1usrKSlRWVtY+LikpAaCddkXXU6/cXj+neGme2L8Pz8vODB+O7IDZCl98cyAFG+MzcSKtCNO/O452zlZ4qb8vHg90EbVMKPtXfFlFFfgmLhUbj2eg8mYNACDAyQozw3zxeEdnbXlkoQZVVTUPtX72cfPG/m0aDXl/JYIeldLKyclBdnY2unTpAiMjbdGxo0ePwsbGBu3atav3eubPn48lS5bct8358+exa9cubNy4ETExMZBKpUhJSYGvr+8Db/ZauHAhFi1adMfyH3/8kWd1ifREyQ1AlW2EAzkSVNZok1cHcwGD3GrQw1GAsd7UNaSmkFcB7Mk0wrF8CWoE7f+Dt5WAwe416NhagIjfb4joH8rLyzFhwgQUFxc/8Kq8XiWyjeXKlSsoKCi4bxs/Pz+MHTsWv//+e51LjtXV1ZBKpZg4cSK+/fbbu772bmdkPT09kZ+fr9NhEID2W8ru3bsxePDgO6qfkeFj/za+4ooqfHc4Dd8dSkNRxe0xkGaY3tcHY4M9YGHadJeQ2b9N70JOKVbGJGPn2RzU3Dra9fZtjVlhfgjxs2/0ISfs4+aN/ds0SkpK4ODgUK9EVm+GFjQmR0dHODo6PrDd559/jg8++KD2cVZWFoYMGYINGzagV69e93ydmZkZzMzunILFxMSkyf6xm3Jb1PTYv43HwcQErz7WDi+Fyf9W/rYSH+y4iBUxyXihn7b8bVPelc7+1b2EtKuI2qfG3gt5tcsGtnNCRLgcwd66n9WCfdy8sX91qyHvbbNMZOvLy8urzmMrKysAgEwmg4eHhxghEZGOtDIzxoz+2vK3m+IzsDJGg4yrFfj4j4tYodJgaqgPnu/jC/tWpmKHSg9JEAQc1BTgy31qHErSXpWTSIDhnVwRoZCjgxvnGSZqblp0IktELY+5iRSTenvj2R6e+C0xC8tVGqjzruGLfWp8sz8ZE3p5YUY/P7jYmosdKtVTTY2AvRfy8KVSjcT0IgCAsZEEo7u5Y2aYDH6OVuIGSEQ6w0T2b3x8fNAMhwwT0V0YS40wupsHRnZ1x65zOYhSanA6sxirD2inZHo62AMzw/zg3Yblb/XVzeoabD+djeVKDS7mlgIAzIy1ZWRn9PeDux3LyBI1d0xkiahFMzKSYGigK4Z0dEHsZW3526PJhfjpaBo2HEvDk13cMEshR1sXa7FDpVsqb1ZjS0ImVsRokFqgLSNrZWaM50K88UJfXziwjCxRi8FElogI2vK3YQGOCAtwxLGUQkQp1VBdvIKtJ7Ow9WQWHuvgjMhwObp42okdaotVfuMm1h9Nx6rYJOSUXAcAtLY0wbQ+vpgc6gNbC958Q9TSMJElIvqHHj72WPt8T5zJLMZylRo7z+Rg17lc7DqXi37+DohQyNFbB1M30d0VV1Th+8OpWH0gGYVlNwAAzjZmmNHPDxN6ebGMLFELxr2fiOgeAt1tsXxiMNR5pViu0uDXk1nYfzkf+y/nI9i7NSLDZQhvy/K3ulJwTVtG9ruDqSi9VUbWy94SM8NkeDqYZWSJiIksEdEDyZ2s8dnYrpg3KABfxWqw8XgG4lOvYtra42jvaoPIcBkeD3QVtfxtc5JdXIFVsUn46Wgart8qFevvZIXIcDme6OyqLSNLRAQmskRE9eZpb4kPRnbCnAH++OZAMr4/nIrz2SWY/eMJ+DlcwkyFDKOC3GHCROuhpOSXYWWMBpsTMlBVrZ1BprOHLSLD5Rjc3hlG/KJARP/ARJaIqIGcbMzx72HtEaGQITouBWsPpiApvwxvbDqFZXsu48X+fhjXwxPmJrz0XR8XckqwXKnBtlNZtWVke/naY/YAOfrKHTh0g4juiYksEdFDsrM0xbzBAZjR3w8/HE7F1/uTkVlUgQW/ncUX+9SY3s8XE3t5wboJy98akpPpRfhynxp7zufWLgtv64jIcDm6+9iLGBkRGQomskREj8jKzBgvhckwJdQHP8dnYKVKg8yiCny08wKWK9WY2scXz4f6oLSiEpeLJcguvg4vh5aV3GYXVyA5vww+bSyRUlCOKKUaceq/ysgOC3RFRLgMHd1sRY6UiAwJE1kiokZibiLFc7fL357MwnKVGporZfh872WsVKlRVS1AgBTLz8fiP8M7YFSQu9ghN4ktJzLxwfZztcMGbjM2kmBkkDtmKWSQsYwsET0EJrJERI3MRGqEp4M9MDLIHbvO5mDpnku4lHut9vkaAXhv2zm8t+2ciFGK6+lu7pg3OAAerS3FDoWIDBhvrSUi0hGpkQSPd3LFwhEdxQ5F7zwT7MkklogeGc/IEhHpmK9jKxhJUOfSulQCxL4RDldbC/ECawLZxRXo97HyH3+7BD4OTGKJ6NHxjCwRkY652lrgw9GdcHsaVCMJsHh0J7i3toSRkaRZ/7i3tsSHoztBemsKLalEgsWjA5t9Ak9ETYNnZImImsC4Hl4I8W2NjTuUGDssHF4O1mKH1GTG9fBC/wBHpOSXw8fBkkksETUaJrJERE3E1dYc/rYCXG3NxQ6lybnaWjCBJaJGx0S2EQiCdvBXSUmJzrdVVVWF8vJylJSUwMSkZc1D2RKwf5s39m/zxz5u3ti/TeN2PnU7v7ofJrKNoLS0FADg6ekpciREREREzUNpaSlsbe9fJEUi1CfdpfuqqalBVlYWrK2tdV4TvKSkBJ6enkhPT4eNjY1Ot0VNj/3bvLF/mz/2cfPG/m0agiCgtLQUbm5uMDK6/7wEPCPbCIyMjODh4dGk27SxseFO1Iyxf5s39m/zxz5u3ti/uvegM7G3cfotIiIiIjJITGSJiIiIyCAxkTUwZmZmWLBgAczMzMQOhXSA/du8sX+bP/Zx88b+1T+82YuIiIiIDBLPyBIRERGRQWIiS0REREQGiYksERERERkkJrJ6KCoqCj4+PjA3N0evXr1w9OjR+7b/+eef0a5dO5ibm6NTp07YsWNHE0VKD6Mh/bt27VpIJJI6P+bm5k0YLTVEbGwsRowYATc3N0gkEmzduvWBr1GpVOjWrRvMzMwgl8uxdu1ancdJD6eh/atSqe7YfyUSCXJycpomYGqQDz/8ED169IC1tTWcnJwwcuRIXLx48YGv4zFYXExk9cyGDRvw6quvYsGCBUhISECXLl0wZMgQ5OXl3bX9wYMHMX78eLzwwgs4ceIERo4ciZEjR+LMmTNNHDnVR0P7F9BOvJ2dnV37k5qa2oQRU0OUlZWhS5cuiIqKqlf75ORkDB8+HOHh4Th58iTmzp2L6dOn488//9RxpPQwGtq/t128eLHOPuzk5KSjCOlRxMTEIDIyEocPH8bu3btRVVWFxx57DGVlZfd8DY/BekAgvdKzZ08hMjKy9nF1dbXg5uYmfPjhh3dtP3bsWGH48OF1lvXq1Ut46aWXdBonPZyG9m90dLRga2vbRNFRYwIgbNmy5b5t3njjDaFjx451lo0bN04YMmSIDiOjxlCf/lUqlQIA4erVq00SEzWuvLw8AYAQExNzzzY8BouPZ2T1yI0bNxAfH49BgwbVLjMyMsKgQYNw6NChu77m0KFDddoDwJAhQ+7ZnsTzMP0LANeuXYO3tzc8PT3x1FNP4ezZs00RLjUB7r8tQ9euXeHq6orBgwcjLi5O7HConoqLiwEA9vb292zDfVh8TGT1SH5+Pqqrq+Hs7FxnubOz8z3HVOXk5DSoPYnnYfq3bdu2WLNmDX799Vd8//33qKmpQWhoKDIyMpoiZNKxe+2/JSUlqKioECkqaiyurq5YuXIlNm/ejM2bN8PT0xMKhQIJCQlih0YPUFNTg7lz56JPnz4IDAy8Zzseg8VnLHYARHRvISEhCAkJqX0cGhqK9u3b46uvvsL7778vYmRE9CBt27ZF27Ztax+HhoZCo9Fg6dKlWLdunYiR0YNERkbizJkzOHDggNih0APwjKwecXBwgFQqRW5ubp3lubm5cHFxuetrXFxcGtSexPMw/ftPJiYmCAoKglqt1kWI1MTutf/a2NjAwsJCpKhIl3r27Mn9V8/Nnj0b27Ztg1KphIeHx33b8hgsPiayesTU1BTBwcHYu3dv7bKamhrs3bu3zlm5vwsJCanTHgB27959z/Yknofp33+qrq7G6dOn4erqqqswqQlx/215Tp48yf1XTwmCgNmzZ2PLli3Yt28ffH19H/ga7sN6QOy7zaiu9evXC2ZmZsLatWuFc+fOCS+++KJgZ2cn5OTkCIIgCM8995wwf/782vZxcXGCsbGx8Mknnwjnz58XFixYIJiYmAinT58W60+g+2ho/y5atEj4888/BY1GI8THxwvPPvusYG5uLpw9e1asP4Huo7S0VDhx4oRw4sQJAYDw2WefCSdOnBBSU1MFQRCE+fPnC88991xt+6SkJMHS0lL417/+JZw/f16IiooSpFKp8Mcff4j1J9B9NLR/ly5dKmzdulW4fPmycPr0aeGVV14RjIyMhD179oj1J9B9zJo1S7C1tRVUKpWQnZ1d+1NeXl7bhsdg/cNEVg998cUXgpeXl2Bqair07NlTOHz4cO1zYWFhwpQpU+q037hxoxAQECCYmpoKHTt2FLZv397EEVNDNKR/586dW9vW2dlZGDZsmJCQkCBC1FQft6db+ufP7T6dMmWKEBYWdsdrunbtKpiamgp+fn5CdHR0k8dN9dPQ/l2yZIkgk8kEc3Nzwd7eXlAoFMK+ffvECZ4e6G59C6DOPsljsP6RCIIgNPVZYCIiIiKiR8UxskRERERkkJjIEhEREZFBYiJLRERERAaJiSwRERERGSQmskRERERkkJjIEhEREZFBYiJLRERERAaJiSwRERERGSQmskREekqlUkEikaCoqKjJty2RSCCRSGBnZ1ev9rdjlUgkGDlypE5jI6LGFxsbixEjRsDNzQ0SiQRbt27V+TYzMzMxadIktGnTBhYWFujUqROOHz/eoHUwkSUi0gMKhQJz586tsyw0NBTZ2dmwtbUVJabo6GhcunSpXm1vxzp27FgdR0VEulBWVoYuXbogKiqqSbZ39epV9OnTByYmJti5cyfOnTuHTz/9FK1bt27Qeox1FB8RET0iU1NTuLi4iLZ9Ozs7ODk51avt7VgtLCxQWVmp48iIqLE9/vjjePzxx+/5fGVlJd5++2389NNPKCoqQmBgIJYsWQKFQvFQ21uyZAk8PT0RHR1du8zX17fB6+EZWSIikU2dOhUxMTFYtmxZ7eX5lJSUO4YWrF27FnZ2dti2bRvatm0LS0tLPPPMMygvL8e3334LHx8ftG7dGnPmzEF1dXXt+isrK/H666/D3d0drVq1Qq9evaBSqRocZ2JiIsLDw2FtbQ0bGxsEBwc3+DIgERmm2bNn49ChQ1i/fj1OnTqFMWPGYOjQobh8+fJDre+3335D9+7dMWbMGDg5OSEoKAhff/11g9fDM7JERCJbtmwZLl26hMDAQLz33nsAAEdHR6SkpNzRtry8HJ9//jnWr1+P0tJSjB49GqNGjYKdnR127NiBpKQkPP300+jTpw/GjRsHQHsAOnfuHNavXw83Nzds2bIFQ4cOxenTp+Hv71/vOCdOnIigoCCsWLECUqkUJ0+ehImJSaO8B0Skv9LS0hAdHY20tDS4ubkBAF5//XX88ccfiI6OxuLFixu8zqSkJKxYsQKvvvoq/v3vf+PYsWOYM2cOTE1NMWXKlHqvh4ksEZHIbG1tYWpqCktLywcOJaiqqsKKFSsgk8kAAM888wzWrVuH3NxcWFlZoUOHDggPD4dSqcS4ceMa9QCUlpaGf/3rX2jXrh0ANCgJJiLDdfr0aVRXVyMgIKDO8srKSrRp0wYAcOHCBbRv3/6+63nzzTfx0UcfAQBqamrQvXv32s+goKAgnDlzBitXrmQiS0TUXFlaWtYmsQDg7OwMHx8fWFlZ1VmWl5cHoH4HoPp69dVXMX36dKxbtw6DBg3CmDFj6sRCRM3TtWvXIJVKER8fD6lUWue52589fn5+OH/+/H3X8/fPHFdXV3To0KHO8+3bt8fmzZsbFBsTWSIiA/LPS/kSieSuy2pqagDU7wBUXwsXLsSECROwfft27Ny5EwsWLMD69esxatSoh/hLiMhQBAUFobq6Gnl5eejXr99d25iamtZeramPPn364OLFi3WWXbp0Cd7e3g2KjYksEZEeMDU1rXODVmOpzwGoIQICAhAQEIB58+Zh/PjxiI6OZiJL1Axcu3YNarW69nFycjJOnjwJe3t7BAQEYOLEiZg8eTI+/fRTBAUF4cqVK9i7dy86d+6M4cOHN3h78+bNQ2hoKBYvXoyxY8fi6NGjWLVqFVatWtWg9XDWAiIiPeDj44MjR44gJSUF+fn5tWdUH9XfD0C//PILkpOTcfToUXz44YfYvn17vddTUVGB2bNnQ6VSITU1FXFxcTh27NgDx8QRkWE4fvw4goKCEBQUBEA7lCgoKAjvvvsuAO280pMnT8Zrr72Gtm3bYuTIkTh27Bi8vLweans9evTAli1b8NNPPyEwMBDvv/8+/ve//2HixIkNWg/PyBIR6YHXX38dU6ZMQYcOHVBRUYHk5ORGW3d0dDQ++OADvPbaa8jMzISDgwN69+6NJ554ot7rkEqlKCgowOTJk5GbmwsHBweMHj0aixYtarQ4iUg8CoUCgiDc83kTExMsWrSoUff5J554okGfQ3cjEe4XNRERtUgSiQRbtmxpcLnZqVOnoqioqEnKWxIRcWgBERHd1fjx4+Hh4VGvtvv374eVlRV++OEHHUdFRPQXnpElIqI73L7pQyqV1qtsZEVFBTIzMwFoZ0MQs7QuEbUcTGSJiIiIyCBxaAERERERGSQmskRERERkkJjIEhEREZFBYiJLRERERAaJiSwRERERGSQmskRERERkkJjIEhEREZFBYiJLRERERAaJiSwRERERGaT/B9WZK7H+wbnUAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 700x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def prepare_states(\n",
    "    indices, \n",
    "    omega_max=omega_max, \n",
    "    omega_slew_rate_max=omega_slew_rate_max, \n",
    "    local_detuning_max=local_detuning_max,\n",
    "    register=register,    \n",
    "    run_and_show = True\n",
    "):\n",
    "    \"\"\"\n",
    "    Return the driving field and local detuning for preparing the initial state\n",
    "    \n",
    "    Args:\n",
    "        indices: A list of atoms that are in the rydberg states\n",
    "        omega_max: The maximum value of the Rabi frequency\n",
    "        omega_slew_rate: The maximum value of the slew rate for the Rabi frequency\n",
    "        local_detuning_max: The maximum value of the local detuning\n",
    "        register: The register for the anlog Hamiltonian simulation program\n",
    "        run_and_show: If true, run the anlog Hamiltonian simulation program \n",
    "            and show the final average density\n",
    "            \n",
    "    Returns:\n",
    "        drive: The driving field to prepare the initial state\n",
    "        local_detuning: The local detuning to prepare the initial state        \n",
    "        \n",
    "    \"\"\"\n",
    "\n",
    "    amplitude = TimeSeries.trapezoidal_signal(np.pi, omega_max, omega_slew_rate_max)\n",
    "    drive_time_points, amplitude_values = amplitude.times(), amplitude.values()\n",
    "\n",
    "    drive_time_points = np.array(drive_time_points) + t_ramp_local_detuning\n",
    "    drive_time_points = np.insert(drive_time_points, 0, 0.0)\n",
    "    drive_time_points = np.insert(drive_time_points, len(drive_time_points), drive_time_points[-1]+t_ramp_local_detuning)\n",
    "\n",
    "    amplitude_values = np.array(amplitude_values)\n",
    "    amplitude_values = np.insert(amplitude_values, 0, 0.0)\n",
    "    amplitude_values = np.insert(amplitude_values, len(amplitude_values), 0.0)\n",
    "\n",
    "    phase_values = [0 for _ in range(len(drive_time_points))]\n",
    "    detuning_values = [0 for _ in range(len(drive_time_points))]\n",
    "\n",
    "    drive = DrivingField.from_lists(drive_time_points, amplitude_values, detuning_values, phase_values)\n",
    "\n",
    "    pattern = [1 for _ in range(len(register))]\n",
    "    for ind in indices:\n",
    "        pattern[ind] = 0\n",
    "\n",
    "    local_detuning_time_points = [0, t_ramp_local_detuning, drive_time_points[-1] - t_ramp_local_detuning, drive_time_points[-1]]\n",
    "    local_detuning_values = [0, -local_detuning_max, -local_detuning_max, 0]\n",
    "\n",
    "    local_detuning = LocalDetuning.from_lists(local_detuning_time_points, local_detuning_values, pattern)\n",
    "\n",
    "    show_drive_and_local_detuning(drive, local_detuning)    \n",
    "\n",
    "    if run_and_show:\n",
    "        ahs_program = AnalogHamiltonianSimulation(\n",
    "            hamiltonian=drive + local_detuning,\n",
    "            register=register\n",
    "        )\n",
    "\n",
    "        result = simulator.run(ahs_program, shots=1000, steps=30, blockade_radius=6.5e-6).result()\n",
    "        show_final_avg_density(result)\n",
    "        \n",
    "    return drive, local_detuning\n",
    "\n",
    "indices_ryd = [i for i in range(N) if np.mod(i, 2) == 0 and i != N // 2]\n",
    "\n",
    "drive_initial_state, local_detuning_initial_state = prepare_states(indices_ryd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe94958e",
   "metadata": {},
   "source": [
    "# Particle-antiparticle pair propagation\n",
    "\n",
    "From the above figures, we confirmed that it is possible to prepare the $Z_2$ state with a defect at the center with the help of the local detuning. We now turn off the local detuning, and observe how the Rydberg densities evolve under a constant global driving field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "50486082",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trange = np.linspace(0, 1e-6, 10)\n",
    "programs = []\n",
    "trange2 = []\n",
    "\n",
    "\n",
    "for ind_t, t in enumerate(trange):\n",
    "    \n",
    "    time_points = [0, t_ramp_omega, t_ramp_omega + t, 2 * t_ramp_omega + t]\n",
    "    amplitude_values = [0, omega_max, omega_max, 0]\n",
    "    phase_values = [0, 0, 0, 0]\n",
    "    detuning_values = [0, 0, 0, 0]    \n",
    "    local_detuning_values = [0, 0, 0, 0]\n",
    "    \n",
    "    drive_propagation = DrivingField.from_lists(time_points, amplitude_values, detuning_values, phase_values)\n",
    "    drive = drive_initial_state.stitch(drive_propagation)\n",
    "    \n",
    "    local_detuning_propagation = LocalDetuning.from_lists(time_points, local_detuning_values, local_detuning_initial_state.magnitude.pattern.series)\n",
    "    local_detuning = local_detuning_initial_state.stitch(local_detuning_propagation) \n",
    "    \n",
    "    programs.append(\n",
    "        AnalogHamiltonianSimulation(\n",
    "            hamiltonian=drive + local_detuning,\n",
    "            register=register\n",
    "        )\n",
    "    )\n",
    "    trange2.append(drive.amplitude.time_series.times()[-1])   \n",
    "    \n",
    "    # Show an example for the full program\n",
    "    if ind_t == len(trange) // 2:\n",
    "        show_drive_and_local_detuning(drive, local_detuning)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "695bdaed",
   "metadata": {},
   "source": [
    "In the above plots, we have shown a full AHS program as an example, including the preparation of initial state and the evolution of the evolution subject to the constant global driving field. We are now ready to run the programs on the local simulator, and the result is plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a93506b1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The elapsed time = 40.461749792099 seconds\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "densities = []\n",
    "for ind, program in enumerate(programs):\n",
    "    result = simulator.run(program, shots=1000, steps=20, blockade_radius=6.5e-6).result()\n",
    "    densities.append(result.get_avg_density())\n",
    "    \n",
    "print(f\"The elapsed time = {time.time()-start_time} seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "03d66fc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (4,4))\n",
    "shw=plt.imshow(densities[::-1], aspect='auto')\n",
    "plt.xlabel(\"Sites\", fontsize=20)\n",
    "plt.ylabel(\"Times (microseconds)\", fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks([len(trange2)-1, 0], [\"0\", f\"{ ( trange2[-1] - trange2[0] ) * 1e6}\"[:4]])\n",
    "bar = plt.colorbar(shw)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "087cf369",
   "metadata": {},
   "source": [
    "Indeed, we can see that the average Rydberg density exhibit a light cone pattern, as a function of time. The light cone originates from the center of the chain, where the defect is located. The light cone separates two regions where the oscillations of the Rydberg and ground states are out of phase. From the mapping between the Rydberg atoms and LGT, we can interpret the light cone as the result of counter propagation of the particle-antiparticle pair in the two dimensional spacetime. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1eddc11",
   "metadata": {},
   "source": [
    "## Simulating the LGT on a QPU"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "129fa1e4",
   "metadata": {},
   "source": [
    "In previous sections, we have demonstrated how to simulate the LGT with the Rydberg atoms. The results from the local simulator show that the results of the programs meet our expectations. Here we will run the same AHS programs 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": 9,
   "id": "3b40c780",
   "metadata": {},
   "outputs": [],
   "source": [
    "from braket.aws import AwsDevice \n",
    "qpu = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e416a1f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "task_arns = []\n",
    "for ind, program in enumerate(programs):\n",
    "    task = qpu.run(program.discretize(qpu), shots=100)\n",
    "    task_arn = task.metadata()['quantumTaskArn']\n",
    "    task_arns.append(task_arn)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d39c113",
   "metadata": {},
   "source": [
    "We can extract the results based on the task arns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b73a174a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from braket.aws import AwsQuantumTask\n",
    "\n",
    "densities_qpu = []\n",
    "for task_arn in task_arns:\n",
    "    result_qpu = AwsQuantumTask(arn=task_arn).result()\n",
    "    densities_qpu.append(result_qpu.get_avg_density())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f50385e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (4,4))\n",
    "shw=plt.imshow(densities_qpu[::-1], aspect='auto')\n",
    "plt.xlabel(\"Sites\", fontsize=20)\n",
    "plt.ylabel(\"Times (microseconds)\", fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks([len(trange2)-1, 0], [\"0\", f\"{(trange2[-1]-trange2[0])*1e6}\"[:4]])\n",
    "bar = plt.colorbar(shw)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5179794a",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "In this example, we have demonstrated how to prepare a 1D $Z_2$ state with a defect, the key step for simulating the particle-antiparticle propagation in LGT. The local detuning can be used to prepare other states of interest, provided that it respects the Rydberg blockade constraint. This capability opens the door for many applications of AHS with Rydberg atoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fdfcac14",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Task Summary\n",
      "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 2000, 'tasks': {'COMPLETED': 20}}}\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: 26.00 USD\n"
     ]
    }
   ],
   "source": [
    "print(\"Task Summary\")\n",
    "print(tracker.quantum_tasks_statistics())\n",
    "print('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",
    "print(f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3fdb53a",
   "metadata": {},
   "outputs": [],
   "source": []
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