docs/source/tutorials/classical_shadows.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Classical Shadows in Pauli Basis"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Overview"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "[Classical shadows](https://www.nature.com/articles/s41567-020-0932-7) formalism is an efficient method to estimate multiple observables. In this tutorial, we will show how to use the `shadows` module in `TensorCircuit` to implement classic shadows in Pauli basis."
   ],
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   "cell_type": "markdown",
   "source": [
    "Let's first briefly review the classical shadows in Pauli basis. For an $n$-qubit quantum state $\\rho$, we randomly perform Pauli projection measurement on each qubit and obtain a snapshot like $\\{1,-1,-1,1,\\cdots,1,-1\\}$. This process is equivalent to apply a random unitary $U$ to $\\rho$ and measure in computational basis to obtain $|b\\rangle=|s_1\\cdots s_n\\rangle,\\ s_j\\in\\{0,1\\}$:\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\rho\\rightarrow U\\rho U^{\\dagger}\\xrightarrow{measure}|b\\rangle\\langle b|,\n",
    "\\end{equation}\n",
    "$$\n",
    "where $U=\\bigotimes_{j=1}^{n}u_j$, $u_i\\in\\{H, HS^{\\dagger}, \\mathbb{I}\\}$ correspond to the projection measurements of Pauli $X$, $Y$, $Z$ respectively. Then we reverse the operation to get the equivalent measurement result on $\\rho$:\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\rho\\xrightarrow{measure}U^{\\dagger}|b\\rangle\\langle b| U.\n",
    "\\end{equation}\n",
    "$$\n",
    "Moreover, we perform $N$ random measurements and view their average as a quantum channel:\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\mathbb{E}\\left[U^{\\dagger}|b\\rangle\\langle b|U\\right]=\\mathcal{M}(\\rho),\n",
    "\\end{equation}\n",
    "$$\n",
    "we can invert the channel to get the approximation of $\\rho$:\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\rho=\\mathbb{E}\\left[\\mathcal{M}^{-1}(U^{\\dagger}|b\\rangle\\langle b|U)\\right].\n",
    "\\end{equation}\n",
    "$$\n",
    "We call each $\\rho_i=\\mathcal{M}^{-1}(U_i^{\\dagger}|b_i\\rangle\\langle b_i|U_i)$ a shadow snapshot state and their ensemble $S(\\rho;N)=\\{\\rho_i|i=1,\\cdots,N\\}$ classical shadows."
   ],
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   "source": [
    "In Pauli basis, we have a simple expression of $\\mathcal{M}^{-1}$:\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "    \\rho_i&=&\\mathcal{M}^{-1}(U_i^{\\dagger}|b_i\\rangle\\langle b_i|U_i)=\\bigotimes_{j=1}^{n}3u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}|u_{ij}-\\mathbb{I},\\\\\n",
    "    \\rho&=&\\frac{1}{N}\\sum_{i=1}^{N}\\rho_i\\ .\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "For an observable Pauli string $O=\\bigotimes_{j=1}^{n}P_j,\\ P_j\\in\\{\\mathbb{I}, X, Y, Z\\}$, we can directly use $\\rho$ to calculate $\\langle O\\rangle=\\text{Tr}(O\\rho)$. In practice, we will divide the classical shadows into $K$ parts to calculate the expectation values independently and take the median to avoid the influence of outliers:\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\langle O\\rangle=\\text{median}\\{\\langle O_{(1)}\\rangle\\cdots\\langle O_{(K)}\\rangle\\},\n",
    "\\end{equation}\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\begin{split}\n",
    "        \\langle O_{(k)}\\rangle&=\\frac{1}{\\lceil N/K\\rceil}\\sum_{i=(k-1)\\lceil N/K\\rceil+1}^{k\\lceil N/K\\rceil}\\text{Tr}\\left[\\bigotimes_{j=1}^{n}P_j(3u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}|u_{ij}-\\mathbb{I})\\right]\\\\\n",
    "        &=\\frac{1}{\\lceil N/K\\rceil}\\sum_{i=(k-1)\\lceil N/K\\rceil+1}^{k\\lceil N/K\\rceil}\\prod_{j=1}^n\\text{Tr}\\left[3P_j u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}|u_{ij}\\right].\n",
    "    \\end{split}\n",
    "\\end{equation}\n",
    "$$"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:51:21.649753Z",
     "start_time": "2023-08-09T04:51:21.598273400Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "('complex128', 'float64')"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tensorcircuit as tc\n",
    "from tensorcircuit import shadows\n",
    "import numpy as np\n",
    "from functools import partial\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "tc.set_backend(\"jax\")\n",
    "tc.set_dtype(\"complex128\")"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Construct the Classical Shadow Snapshots"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We first set the number of qubits $n$ and the number of repeated measurements $r$ on each Pauli string. Then from the target observable Pauli strings $\\{O_i|i=1,\\cdots,M\\}$ (0, 1, 2, and 3 correspond to $\\mathbb{I}$, $X$, $Y$, and $Z$, respectively), the error $\\epsilon$ and the rate of failure $\\delta$, we can use `shadow_bound` function to get the total number of snapshots $N$ and the number of equal parts $K$ to split the shadow snapshot states to compute the median of means:\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "    K&=&2\\log(2M/\\delta),\\\\\n",
    "    N&=&K\\frac{34}{\\epsilon^2}\\max_{1\\le i\\le M}\\left\\|O_i-\\frac{\\text{Tr}(O_i)}{2^n}\\mathbb{I}\\right\\|^2_{\\text{shadow}}=K\\frac{34}{\\epsilon^2}3^{\\max_{1\\le i\\le M}k_i},\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "where $k_i$ is the number of nontrivial Pauli matrices in $O_i$. Please refer to the Theorem S1 and Lemma S3 in [Huang, Kueng and Preskill (2020)](https://www.nature.com/articles/s41567-020-0932-7) for the details of proof. It should be noted that `shadow_bound` has a certain degree of overestimation of $N$, and so many measurements are not really needed in practice. And `shadow_bound` is not jitable and no need to jit."
   ],
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  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N: 489600\tK: 16\tnumber of Pauli strings: 97920\n"
     ]
    }
   ],
   "source": [
    "n, r = 8, 5\n",
    "ps = [\n",
    "    [1, 0, 0, 0, 0, 0, 0, 2],\n",
    "    [0, 3, 0, 0, 0, 0, 1, 0],\n",
    "    [0, 0, 2, 0, 0, 3, 0, 0],\n",
    "    [0, 0, 0, 1, 2, 0, 0, 0],\n",
    "    [0, 0, 0, 3, 1, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 3, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 2, 0],\n",
    "    [3, 0, 0, 0, 0, 0, 0, 1],\n",
    "    [0, 2, 0, 0, 0, 0, 3, 0],\n",
    "    [0, 0, 1, 0, 0, 2, 0, 0],\n",
    "]\n",
    "\n",
    "epsilon, delta = 0.1, 0.01\n",
    "N, K = shadows.shadow_bound(ps, epsilon, delta)\n",
    "nps = N // r  # number of random selected Pauli strings\n",
    "print(f\"N: {N}\\tK: {K}\\tnumber of Pauli strings: {nps}\")"
   ],
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    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:51:21.707924900Z",
     "start_time": "2023-08-09T04:51:21.604342400Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Then we use random quantum circuit to generate an entangled state."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [],
   "source": [
    "nlayers = 10\n",
    "thetas = 2 * np.random.rand(nlayers, n) - 1\n",
    "\n",
    "c = tc.Circuit(n)\n",
    "for i in range(n):\n",
    "    c.H(i)\n",
    "for i in range(nlayers):\n",
    "    for j in range(n):\n",
    "        c.cnot(j, (j + 1) % n)\n",
    "    for j in range(n):\n",
    "        c.rz(j, theta=thetas[i, j] * np.pi)\n",
    "\n",
    "psi = c.state()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:51:21.814604700Z",
     "start_time": "2023-08-09T04:51:21.615066400Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We randomly generate Pauli strings. Since the function after just-in-time (jit) compilation does not support random sampling, we need to generate all random states in advance, that is, variable `status`."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [],
   "source": [
    "pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(nps, n)))\n",
    "status = tc.backend.convert_to_tensor(np.random.rand(nps, r))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:51:21.815119500Z",
     "start_time": "2023-08-09T04:51:21.813574500Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "If `measurement_only`=True, the outputs of `shadow_snapshots` are snapshot bit strings $b=s_1\\cdots s_n,\\ s_j\\in\\{0,1\\}$, otherwise the outputs are snapshot states $\\{u_{j}^{\\dagger}|s_j\\rangle\\langle s_j| u_j\\ |j=1,\\cdots,n\\}$. If you only need to generate one batch of snapshots or generate multiple batches of snapshots with different `nps` or `r`, jit cannot provide speedup. JIT will only accelerate when the same shape of snapshots are generated multiple times."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of snapshot states: (97920, 5, 8, 2, 2)\n"
     ]
    }
   ],
   "source": [
    "@partial(tc.backend.jit, static_argnums=(3,))\n",
    "def shadow_ss(psi, pauli_strings, status, measurement_only=False):\n",
    "    return shadows.shadow_snapshots(\n",
    "        psi, pauli_strings, status, measurement_only=measurement_only\n",
    "    )\n",
    "\n",
    "\n",
    "ss_states = shadow_ss(psi, pauli_strings, status)  # jit is not necessary here\n",
    "print(\"shape of snapshot states:\", ss_states.shape)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:51:24.715816800Z",
     "start_time": "2023-08-09T04:51:21.883673400Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Estimate the Expectation Values of Observables"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Since the operation of taking the median is not jitable, the outputs of `expectation_ps_shadows` have $K$ values, and we need to take the median of them."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "outputs": [],
   "source": [
    "def shadow_expec(snapshots_states, ob):\n",
    "    return shadows.expectation_ps_shadow(snapshots_states, ps=ob, k=K)\n",
    "\n",
    "\n",
    "sejit = tc.backend.jit(shadow_expec)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:51:25.082792700Z",
     "start_time": "2023-08-09T04:51:24.750909500Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "It can be seen from the running time that every time the number of Pauli strings changes, `shadow_expec` will be recompiled, but for the same number of Pauli strings but different observables, `shadow_expec` will only be compiled once. In the end, the absolute errors given by classical shadows are much smaller than the $\\epsilon=0.1$ we set, so `shadow_bound` gives a very loose upper bound."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observable: No.0\tnumber of Pauli strings: 1000\ttime: 0.9454922676086426\n",
      "observable: No.1\tnumber of Pauli strings: 1000\ttime: 0.001840353012084961\n",
      "observable: No.2\tnumber of Pauli strings: 1000\ttime: 0.0014374256134033203\n",
      "observable: No.3\tnumber of Pauli strings: 1000\ttime: 0.0013763904571533203\n",
      "observable: No.4\tnumber of Pauli strings: 1000\ttime: 0.0013554096221923828\n",
      "observable: No.5\tnumber of Pauli strings: 1000\ttime: 0.0013613700866699219\n",
      "observable: No.6\tnumber of Pauli strings: 1000\ttime: 0.0013325214385986328\n",
      "observable: No.7\tnumber of Pauli strings: 1000\ttime: 0.0013136863708496094\n",
      "observable: No.8\tnumber of Pauli strings: 1000\ttime: 0.0013325214385986328\n",
      "observable: No.9\tnumber of Pauli strings: 1000\ttime: 0.0013117790222167969\n",
      "observable: No.0\tnumber of Pauli strings: 10000\ttime: 0.9969091415405273\n",
      "observable: No.1\tnumber of Pauli strings: 10000\ttime: 0.012966394424438477\n",
      "observable: No.2\tnumber of Pauli strings: 10000\ttime: 0.012765884399414062\n",
      "observable: No.3\tnumber of Pauli strings: 10000\ttime: 0.012974739074707031\n",
      "observable: No.4\tnumber of Pauli strings: 10000\ttime: 0.012665033340454102\n",
      "observable: No.5\tnumber of Pauli strings: 10000\ttime: 0.012889623641967773\n",
      "observable: No.6\tnumber of Pauli strings: 10000\ttime: 0.013180255889892578\n",
      "observable: No.7\tnumber of Pauli strings: 10000\ttime: 0.012682914733886719\n",
      "observable: No.8\tnumber of Pauli strings: 10000\ttime: 0.012678146362304688\n",
      "observable: No.9\tnumber of Pauli strings: 10000\ttime: 0.012636423110961914\n",
      "observable: No.0\tnumber of Pauli strings: 20000\ttime: 1.015674352645874\n",
      "observable: No.1\tnumber of Pauli strings: 20000\ttime: 0.025749921798706055\n",
      "observable: No.2\tnumber of Pauli strings: 20000\ttime: 0.02578139305114746\n",
      "observable: No.3\tnumber of Pauli strings: 20000\ttime: 0.02524733543395996\n",
      "observable: No.4\tnumber of Pauli strings: 20000\ttime: 0.025956153869628906\n",
      "observable: No.5\tnumber of Pauli strings: 20000\ttime: 0.02669525146484375\n",
      "observable: No.6\tnumber of Pauli strings: 20000\ttime: 0.026634931564331055\n",
      "observable: No.7\tnumber of Pauli strings: 20000\ttime: 0.026463985443115234\n",
      "observable: No.8\tnumber of Pauli strings: 20000\ttime: 0.0273745059967041\n",
      "observable: No.9\tnumber of Pauli strings: 20000\ttime: 0.026821374893188477\n",
      "observable: No.0\tnumber of Pauli strings: 30000\ttime: 1.0086262226104736\n",
      "observable: No.1\tnumber of Pauli strings: 30000\ttime: 0.03922295570373535\n",
      "observable: No.2\tnumber of Pauli strings: 30000\ttime: 0.038678884506225586\n",
      "observable: No.3\tnumber of Pauli strings: 30000\ttime: 0.03868269920349121\n",
      "observable: No.4\tnumber of Pauli strings: 30000\ttime: 0.04024958610534668\n",
      "observable: No.5\tnumber of Pauli strings: 30000\ttime: 0.03927755355834961\n",
      "observable: No.6\tnumber of Pauli strings: 30000\ttime: 0.039815664291381836\n",
      "observable: No.7\tnumber of Pauli strings: 30000\ttime: 0.04002213478088379\n",
      "observable: No.8\tnumber of Pauli strings: 30000\ttime: 0.03934764862060547\n",
      "observable: No.9\tnumber of Pauli strings: 30000\ttime: 0.04060721397399902\n",
      "observable: No.0\tnumber of Pauli strings: 40000\ttime: 1.2912404537200928\n",
      "observable: No.1\tnumber of Pauli strings: 40000\ttime: 0.05326724052429199\n",
      "observable: No.2\tnumber of Pauli strings: 40000\ttime: 0.05272030830383301\n",
      "observable: No.3\tnumber of Pauli strings: 40000\ttime: 0.054486989974975586\n",
      "observable: No.4\tnumber of Pauli strings: 40000\ttime: 0.0538792610168457\n",
      "observable: No.5\tnumber of Pauli strings: 40000\ttime: 0.05555129051208496\n",
      "observable: No.6\tnumber of Pauli strings: 40000\ttime: 0.05361533164978027\n",
      "observable: No.7\tnumber of Pauli strings: 40000\ttime: 0.05325675010681152\n",
      "observable: No.8\tnumber of Pauli strings: 40000\ttime: 0.05487465858459473\n",
      "observable: No.9\tnumber of Pauli strings: 40000\ttime: 0.05441641807556152\n",
      "observable: No.0\tnumber of Pauli strings: 50000\ttime: 0.999931812286377\n",
      "observable: No.1\tnumber of Pauli strings: 50000\ttime: 0.06137228012084961\n",
      "observable: No.2\tnumber of Pauli strings: 50000\ttime: 0.06159329414367676\n",
      "observable: No.3\tnumber of Pauli strings: 50000\ttime: 0.06138134002685547\n",
      "observable: No.4\tnumber of Pauli strings: 50000\ttime: 0.060491085052490234\n",
      "observable: No.5\tnumber of Pauli strings: 50000\ttime: 0.06045842170715332\n",
      "observable: No.6\tnumber of Pauli strings: 50000\ttime: 0.0629739761352539\n",
      "observable: No.7\tnumber of Pauli strings: 50000\ttime: 0.06146860122680664\n",
      "observable: No.8\tnumber of Pauli strings: 50000\ttime: 0.061437129974365234\n",
      "observable: No.9\tnumber of Pauli strings: 50000\ttime: 0.061475515365600586\n",
      "observable: No.0\tnumber of Pauli strings: 60000\ttime: 1.03033447265625\n",
      "observable: No.1\tnumber of Pauli strings: 60000\ttime: 0.06811189651489258\n",
      "observable: No.2\tnumber of Pauli strings: 60000\ttime: 0.06913161277770996\n",
      "observable: No.3\tnumber of Pauli strings: 60000\ttime: 0.06945395469665527\n",
      "observable: No.4\tnumber of Pauli strings: 60000\ttime: 0.06843304634094238\n",
      "observable: No.5\tnumber of Pauli strings: 60000\ttime: 0.06950116157531738\n",
      "observable: No.6\tnumber of Pauli strings: 60000\ttime: 0.07009696960449219\n",
      "observable: No.7\tnumber of Pauli strings: 60000\ttime: 0.06856656074523926\n",
      "observable: No.8\tnumber of Pauli strings: 60000\ttime: 0.06969141960144043\n",
      "observable: No.9\tnumber of Pauli strings: 60000\ttime: 0.0678703784942627\n",
      "observable: No.0\tnumber of Pauli strings: 70000\ttime: 1.0191996097564697\n",
      "observable: No.1\tnumber of Pauli strings: 70000\ttime: 0.07705307006835938\n",
      "observable: No.2\tnumber of Pauli strings: 70000\ttime: 0.07620859146118164\n",
      "observable: No.3\tnumber of Pauli strings: 70000\ttime: 0.07670450210571289\n",
      "observable: No.4\tnumber of Pauli strings: 70000\ttime: 0.0766746997833252\n",
      "observable: No.5\tnumber of Pauli strings: 70000\ttime: 0.07552027702331543\n",
      "observable: No.6\tnumber of Pauli strings: 70000\ttime: 0.07716488838195801\n",
      "observable: No.7\tnumber of Pauli strings: 70000\ttime: 0.07647228240966797\n",
      "observable: No.8\tnumber of Pauli strings: 70000\ttime: 0.07623863220214844\n",
      "observable: No.9\tnumber of Pauli strings: 70000\ttime: 0.07545590400695801\n",
      "observable: No.0\tnumber of Pauli strings: 80000\ttime: 1.0341267585754395\n",
      "observable: No.1\tnumber of Pauli strings: 80000\ttime: 0.08658909797668457\n",
      "observable: No.2\tnumber of Pauli strings: 80000\ttime: 0.08614206314086914\n",
      "observable: No.3\tnumber of Pauli strings: 80000\ttime: 0.0857245922088623\n",
      "observable: No.4\tnumber of Pauli strings: 80000\ttime: 0.08441877365112305\n",
      "observable: No.5\tnumber of Pauli strings: 80000\ttime: 0.08495783805847168\n",
      "observable: No.6\tnumber of Pauli strings: 80000\ttime: 0.08582544326782227\n",
      "observable: No.7\tnumber of Pauli strings: 80000\ttime: 0.0861966609954834\n",
      "observable: No.8\tnumber of Pauli strings: 80000\ttime: 0.08437252044677734\n",
      "observable: No.9\tnumber of Pauli strings: 80000\ttime: 0.0852508544921875\n",
      "observable: No.0\tnumber of Pauli strings: 90000\ttime: 1.031904697418213\n",
      "observable: No.1\tnumber of Pauli strings: 90000\ttime: 0.09243512153625488\n",
      "observable: No.2\tnumber of Pauli strings: 90000\ttime: 0.09180665016174316\n",
      "observable: No.3\tnumber of Pauli strings: 90000\ttime: 0.09398865699768066\n",
      "observable: No.4\tnumber of Pauli strings: 90000\ttime: 0.09126615524291992\n",
      "observable: No.5\tnumber of Pauli strings: 90000\ttime: 0.09299516677856445\n",
      "observable: No.6\tnumber of Pauli strings: 90000\ttime: 0.09152960777282715\n",
      "observable: No.7\tnumber of Pauli strings: 90000\ttime: 0.09381914138793945\n",
      "observable: No.8\tnumber of Pauli strings: 90000\ttime: 0.09076142311096191\n",
      "observable: No.9\tnumber of Pauli strings: 90000\ttime: 0.08988714218139648\n",
      "observable: No.0\tnumber of Pauli strings: 97920\ttime: 1.050750494003296\n",
      "observable: No.1\tnumber of Pauli strings: 97920\ttime: 0.09993815422058105\n",
      "observable: No.2\tnumber of Pauli strings: 97920\ttime: 0.10038924217224121\n",
      "observable: No.3\tnumber of Pauli strings: 97920\ttime: 0.09895133972167969\n",
      "observable: No.4\tnumber of Pauli strings: 97920\ttime: 0.09973955154418945\n",
      "observable: No.5\tnumber of Pauli strings: 97920\ttime: 0.10170507431030273\n",
      "observable: No.6\tnumber of Pauli strings: 97920\ttime: 0.09864187240600586\n",
      "observable: No.7\tnumber of Pauli strings: 97920\ttime: 0.09945058822631836\n",
      "observable: No.8\tnumber of Pauli strings: 97920\ttime: 0.09991574287414551\n",
      "observable: No.9\tnumber of Pauli strings: 97920\ttime: 0.09802794456481934\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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//e9j9+7deOeddyBJEm677Tb4fL4eu0dPkjbRVF9fD0VRMGDAAMvxAQMGoLq6Ou451dXVHY6vra1FW1sbVq5cidtvvx1//vOfMWPGDHz729/Ge++9l3AuCxYsQEtLi/l15syZi3y6xPAc+5H7gtaSWtcyTdYNEkk0EQRBEL3NtGnTkJ+fjxUrViQcs3nzZowZMwYOhwNFRUVYvXp1h9fcunUrysvLMWbMGFx33XXYsGEDTp8+jcrKyp6efo9gS/cEehJVVQEAd911F/71X/8VAFBSUoKdO3di/fr1uOWWW+Ke53A44HA4UjJHI9PkC/ktx7vUp6m900SZJoIgiMsSTdMQkAOdD+wFXDZXl0prgiBg+fLluPfeezFv3jwMGjTI8n5lZSVmzZqFJUuWYPbs2di5cyceeeQR5OXloby8PKl7tLS0AAD69OmT9LxSSdpEU9++fSEIAmpqaizHa2pqkJ+fH/ec/Pz8Dsf37dsXNpsNo0ePtowZNWoUPvjggx6cfffhdXMvEL4I0dRu9Rx1BScIgrg8CcgBTHp5Ulru/eG9H8Iturt0zowZM1BSUoLFixfjhRdesLy3Zs0alJaWYuHChQCA4uJiHDx4EKtWrUpKNKmqih/+8IeYMmUKxo4d26V5pYq0lefsdjsmTJiAbdu2mcdUVcW2bdswefLkuOdMnjzZMh4A3nnnHXO83W7HxIkTY0JkR44cwdChQ3v4CboHr6v6QLidW9SlIDgrz9lsmexcKs8RBEEQKaKiogIbN25EVVWV5XhVVRWmTJliOTZlyhQcPXoUitJ5E+bvf//7OHDgADZt2tSj8+1J0lqemz9/Pu6//37ccMMNuPHGG7F27Vr4fD488MADAID77rsPAwcONOunjz76KG655RasXr0ad955JzZt2oS9e/fi+eefN6/5xBNPYPbs2Zg6dSr+/u//Hlu3bsUf//hHbN++PR2PGIORaQpK7VbAdcNpstv7QZZbqTxHEARxmeKyufDhvR+m7d7dYerUqSgrK8OCBQuSLrt1xty5c/HGG2/g/fffjyn7XUqkVTTNnj0bdXV1WLRoEaqrq1FSUoKtW7eaYe/Tp09bumjffPPNePnll/GTn/wETz31FIYPH44tW7ZYbLwZM2Zg/fr1WLFiBebNm4cRI0Zg8+bN+MpXvpLy54uHYIimMBNNIi9CUqUu9WkyWg7Y7f3g958gp4kgCOIyheO4LpfILgVWrlyJkpISjBgxwjw2atQo7NixwzJux44dKC4utuy9Go2mafjBD36A119/Hdu3b8dVV13Vq/O+WNIeBJ87dy7mzp0b97147tDdd9+Nu+++u8NrPvjgg3jwwQd7Yno9jhEED0msxJbrzEWtv7ZrLQcUQzT1Za8p00QQBEGkkHHjxmHOnDl45plnzGOPPfYYJk6ciGXLlmH27NnYtWsX1q1bh5///OfmmNLSUsyYMcP83P/+97+Pl19+Gb///e+RmZlprobPzs6Gy9U9J6w3Sfs2Kl82jPKcJIUBAHnOPABdzTSx8pzD3o+dS+U5giAIIsUsXbrUXLUOAOPHj8err76KTZs2YezYsVi0aBGWLl1qKeEdP34c9fX15uvnnnsOLS0t+OpXv4qCggLz65VXXknloyRN2p2mLxtGeS4shwEB6ONkyyq7lmmKlOcACoITBEEQvcuGDRtijhUVFSEUsvYNnDlzJmbOnJnwOidPnrS81jStJ6aXMshpSjG8KZpYhinXmQuge9uo2B2sPEcb9hIEQRBE70OiKcUYwXZZYaKpq06TpmmmaHKQ00QQBEEQKYNEU4ox+jTJMhNJXXWaNE2Cpu9ZZ5TnFMo0EQRBEESvQ6IpxRjlOVlhIqmrQXAjzwRERJOqhqCq4Z6cJkEQBEEQ7SDRlGIM0WR0RzXLc0m2HDBKcwAPUcw1j1OuiSAIgiB6FxJNKUbQM03GigFWntOSbm5pdAMXBCd43gZBcOvHSTQRBEEQRG9CoinFGE4Tr3HgwEGuew2LCoJwILnymuE08bwTACAIGQAoDE4QBEEQvQ2JphRjrJ7jNB4Z9gz4W3aij03DIFuokzMZii6aBIF1SrXZDNFEThNBEARB9CYkmlKMKZrAIcueBU0PgDu5JDNNennOcJpstkwA1BWcIAiCIHobEk0pxugIzmk8E00ayzJ5eA2KqnR6fsRp0kUTlecIgiAIIiWQaEoxPM92euaAGNGUzAo6VWmXadKdJtq0lyAIgugtysvLwXEcVq5caTm+ZcsWcHr/we7w3HPP4dprr0VWVhaysrIwefJk/OlPf7rY6fYaJJpSTHSmKdOeCU0XSh5BS6pXk+k08e0zTeQ0EQRBEL2H0+lERUUFmpqaeuyagwYNwsqVK1FZWYm9e/fi1ltvxV133YXPP/+8x+7Rk5BoSjGWTJMjC5relDKDT040mZmm9uU5yjQRBEEQvci0adOQn5+PFStWJByzefNmjBkzBg6HA0VFRVi9enWH1/zmN7+Jr3/96xg+fDiKi4vx05/+FBkZGdi9e3dPT79HsKV7Al82hCjRlClmQA0y0eThkVSvpojT1C4ITuU5giCIyw5N06AFAmm5N+dydam0JggCli9fjnvvvRfz5s3DoEGDLO9XVlZi1qxZWLJkCWbPno2dO3fikUceQV5eHsrLyzu9vqIoeO211+Dz+TB58uSuPk5KINGUSk7tAu89CwDgNA5Z9gwAKgA905SU06RnmvSWA4JenlOoPEcQBHHZoQUCODx+QlruPWJfJTi3u0vnzJgxAyUlJVi8eDFeeOEFy3tr1qxBaWkpFi5cCAAoLi7GwYMHsWrVqg5F02effYbJkycjGAwiIyMDr7/+OkaPHt3l50kFVJ5LJad3Qmg6wb7XgCwx8seakXSmSe8ITi0HCIIgiDRQUVGBjRs3oqqqynK8qqoKU6ZMsRybMmUKjh49am4dFo8RI0Zg//79+PDDD/Hwww/j/vvvx8GDB3tl7hcLOU2pRHSD150lVp5zmW+5eECK2ow3ERGnqX3LARJNBEEQlxucy4UR+yrTdu/uMHXqVJSVlWHBggVJld06w26345prrgEATJgwAXv27MHTTz+N//mf/7noa/c0JJpSSZRoAoBM0YXoFFMo3ADgmg4vQavnCIIgrhw4jutyiexSYOXKlSgpKcGIESPMY6NGjcKOHTss43bs2IHi4mIIgpD0tVVVRSiU3C4ZqYZEUyoR3RBM0cTBY3OgOertcLix00vErJ6jPk0EQRBEihk3bhzmzJmDZ555xjz22GOPYeLEiVi2bBlmz56NXbt2Yd26dfj5z39ujiktLcWMGTMwd+5cAMCCBQtwxx13YMiQIWhtbcXLL7+M7du34+233075MyUDZZpSieiKlOc0Dhmi0/K2JHXe+6L96jlzw16FnCaCIAgidSxduhSqGqmejB8/Hq+++io2bdqEsWPHYtGiRVi6dKmlhHf8+HHU19ebr2tra3HfffdhxIgRKC0txZ49e/D222/ja1/7WiofJWnIaUoldmt5zmNzWN6W5c5FU0ymKarlgKZpF9WZlSAIgiDisWHDhphjRUVFMWW0mTNnYubMmQmvc/LkScvr9ivwLnXIaUolohsqF1lB4BbslrdlqbnTSyTKNGmaBFVvlEkQBEEQRM9DoimViC7InKa/4CCY3zNkuaXTSxiZJmPDXkHwgO1kRyU6giAIguhNSDSlEtEDmYu0HGjvDKlJiCbDaTI27OU4XhdO1OCSIAiCIHoTEk2pRHRBinKXVM26bYoqezu9hKpaO4ID1HaAIAiCIFIBiaZUIrogmZkmztys10BLorymGOU5PhIip/3nCIIgCKL3IdGUSkQ3wtFOU7sNepMRTarKVipYnCa97YBCW6kQBEEQRK9BoimV2BwI8SzTpEEzBZCk6Z1SkxA9EacpIpoEKs8RBEEQRK9DoimVcBxCAlvppmmAqrHyXBB6qFv1dXi6pmlRmaZIY0wqzxEEQRBE70OiKcUEDdEEDZpengtyzDXiNAmK4k94ruFMAZGO4ED0pr3kNBEEQRBEb0GiKcUE9EocK88xp0nmHJD1qFM4nLgruKoGzO95Po7TRJkmgiAIgug1SDSlGD/P1JEKzWw5oEFAm8IcKElKvGmvom+hwnEi9niD+N+zddA0DQJt2ksQBEH0IuXl5eA4DitXrrQc37JlS49t37Vy5UpwHIcf/vCHPXK93oBEU4rxRwXBzZYDnA0+fUu6jjbtNfJMguDEj46cxU+OnsPHrX7q00QQBEH0Ok6nExUVFWhq6nyf1K6yZ88e/M///A+uvfbaHr92T0KiKcW06X2a1KjyHDgb2lTDaUr8x2g4TTzvhFdm1zkdCMMmUHmOIAiC6F2mTZuG/Px8rFixIuGYzZs3Y8yYMXA4HCgqKsLq1as7vW5bWxvmzJmDX/ziF8jNze3JKfc4JJpSjI+XAeiZJqMjOGeDTxdN4Q7Kc0amSeBdCKuszHc+JJHTRBAEcZmiaRqkkJKWL03TOp9gFIIgYPny5fjZz36Gs2fPxrxfWVmJWbNm4Tvf+Q4+++wzLFmyBAsXLsSGDRs6vO73v/993HnnnZg2bVqX5pMObOmewJcJTdPQyhmiCVAUthqO40T4jExTuKNMExNNvOCApLA/9guhMGwZlGkiCIK4HJHDKp5/9L203Pv/PX0LRIfQpXNmzJiBkpISLF68GC+88ILlvTVr1qC0tBQLFy4EABQXF+PgwYNYtWoVysvL415v06ZN2LdvH/bs2dOtZ0g1l4TT9Oyzz6KoqAhOpxOTJk3CRx991OH41157DSNHjoTT6cS4cePw1ltvWd43AmvRX7fffntvPkJSBJUggrpoAmCW5zhOTKo8Z7QcEHgXJC3iNJnNLak8RxAEQfQyFRUV2LhxI6qqqizHq6qqMGXKFMuxKVOm4OjRo1AUBe05c+YMHn30Ufz617+G0+mMef9SJO1O0yuvvIL58+dj/fr1mDRpEtauXYuysjIcPnwY/fv3jxm/c+dO3HPPPVixYgW+8Y1v4OWXX8b06dOxb98+jB071hx3++2346WXXjJfOxyOmGulmtZwKxQu8oejGk4TL5pB8HCHmSbDaXJBUg2nSaI+TQRBEJcpNjuP//f0LWm7d3eYOnUqysrKsGDBgoQOUjJUVlaitrYW48ePN48pioL3338f69atQygUgiB0zQnrbdIumtasWYOHHnoIDzzwAABg/fr1ePPNN/Hiiy/iySefjBn/9NNP4/bbb8cTTzwBAFi2bBneeecdrFu3DuvXrzfHORwO5Ofnp+YhksQb8kKOcpoi5TlbpDyXxOo5nnOYTtOFkASbLQcA6wiuaVqPLf8kCIIgeheO47pcIrsUWLlyJUpKSjBixAjz2KhRo7Bjxw7LuB07dqC4uDiu+CktLcVnn31mOfbAAw9g5MiR+NGPfnTJCSYgzeW5cDiMyspKS/iL53lMmzYNu3btinvOrl27YsJiZWVlMeO3b9+O/v37Y8SIEXj44YfR0NCQcB6hUAher9fy1Rt4w16r06R3BOc4e1R5rvM+TargMY/VhCTAfK122FGcIAiCIHqCcePGYc6cOXjmmWfMY4899hi2bduGZcuW4ciRI9i4cSPWrVuHxx9/3BxTWlqKdevWAQAyMzMxduxYy5fH40FeXp6lcnQpkVbRVF9fD0VRMGDAAMvxAQMGoLq6Ou451dXVnY6//fbb8ctf/hLbtm1DRUUF3nvvPdxxxx1xa6oAsGLFCmRnZ5tfgwcPvsgniw8rz6ngNCaQFD2jxPNiZPVcR0FwffWcxrnNYyqAeskGjmOKXKFcE0EQBJECli5dClVVzdfjx4/Hq6++ik2bNmHs2LFYtGgRli5dainhHT9+HPX19WmYbc+Q9vJcb/Cd73zH/H7cuHG49tprMWzYMGzfvh2lpaUx4xcsWID58+ebr71eb68IJ2/YC5VTwYODEtWniePtZqZJlpuhaSo4LlbPqrrTpAhuy/HqsAxByIAst0CW2+BwDIg5lyAIgiC6S7y2AUVFRQiFQpZjM2fOxMyZMxNe5+TJkx3eZ/v27d2YXepIq9PUt29fCIKAmpoay/GampqEeaT8/PwujQeAq6++Gn379sWxY8fivu9wOJCVlWX56g1YeY6JJiCyeo7n7eY2KpqmJAx0K3qmSeWsouliejWpmoafn67FnhZfl84jCIIgiC8baRVNdrsdEyZMwLZt28xjqqpi27ZtmDx5ctxzJk+ebBkPAO+8807C8QBw9uxZNDQ0oKCgoGcm3k28YS8UKDGiSeDtUMBB0o2/RLkmIwiu8C7L8QuhcLc37d3n9WPp8fP48ZHYRmUEQRAEQURIe5+m+fPn4xe/+IXZ8+Hhhx+Gz+czV9Pdd999WLBggTn+0UcfxdatW7F69WocOnQIS5Yswd69ezF37lwArB37E088gd27d+PkyZPYtm0b7rrrLlxzzTUoKytLyzMa3DXsLqwafi84XTRpptPE2iGENRFA4hV0RssBlbP2szgfkiB0s+1AfZit5muS4+e9CIIgCIJgpD3TNHv2bNTV1WHRokWorq5GSUkJtm7daoa9T58+DZ6PaLubb74ZL7/8Mn7yk5/gqaeewvDhw7FlyxYzaS8IAj799FNs3LgRzc3NKCwsxG233YZly5alvVdTYUYh8vuNwwfYDSCyek7g7QCAEER4EEjYq8nMNPFW0cTaDnSvK3irHo4PRoX5CIIgCIKIJe2iCQDmzp1rOkXtiRcKu/vuu3H33XfHHe9yufD222/35PR6FM7pNstzmr73HM8xMRfUbACXeCsVI9Okce3LcxJsju51BW/VHaagQqKJIAiCIDoi7eW5Lx12F3itXaZJYKIpoHWWaWLlOYWzOmbnQ+FudwVv08VSUO3axo0EQRAE8WWDRFOqccQ6TYKeaQqorNdSovKc0dzSEE0unl2nOiSBF7pZntOdJknToHRxx2uCIAiC+DJBoinFcPZY0WTTnSaf1vFWKubqOV00FTrs4AHIGuDlcgF03WnyRgXAqURHEARBEIkh0ZRqxDhOky6a/Cr7dXS2ek6B7jQJPAY42Iq7euiiqYuZprYooeSnMDhBEARBJIREU6oR3eYPXQMTTaLed6mzrVQMp0nmmFASOQ4FumhqUPU+TVFOk893DOfPvwa5g5Jda7TTRLkmgiAIgkgIiaZUI4h6nyYNAOuRZBNYC4E2Xb8kCoK3zzTZ+YhoqlPZpr3hcB3OnP0V9uyZgd0flqHq0JM4e/aXCafTqlB5jiAIguiY8vJycByHlStXWo5v2bIFHMd1+7pLliwBx3GWr5EjR17sdHsNEk2phuPAgwPHaWDCCRAF5jS1mqKp40yTjIjTVGiIJkUXXm2HcOTIEnhbPzXPCycQYQDQJkeEEvVqIgiCIBLhdDpRUVGBpqb4n1HdZcyYMbhw4YL59cEHH/To9XsSEk1pQADAcRGHx2aKJiaiZNlrNr6MxnSa9PZaIs+hwMEaY9YpHnNcZsYYDB/+EwwadB8AQFVDSITFaaLyHEEQRErRNA1SMJiWL62LK6anTZuG/Px8rFixIuGYzZs3Y8yYMXA4HCgqKsLq1as7va7NZkN+fr751bdv3y7NK5VcEs0tv2zw4MDzEVdHNMtzKqCX7iS5BQ575A9H0xRoGuvrpMRxmmplETdM2AxBcCEjYwQA4NSp/wEQ6SQej9Zop4nKcwRBEClFDoXwzP3/kJZ7z9v4W4hOZ+cDdQRBwPLly3Hvvfdi3rx5GDRokOX9yspKzJo1C0uWLMHs2bOxc+dOPPLII8jLy0N5eXnC6x49ehSFhYVwOp2YPHkyVqxYgSFDhnT3sXoVcprSAA+A4wyBwsGm92mSVAWimMO+bxcGV6KEj8xFO01MNF0IScjOLjEFEwDw+nYrSgdOU1uU0xSg8hxBEATRATNmzEBJSQkWL14c896aNWtQWlqKhQsXori4GOXl5Zg7dy5WrVqV8HqTJk3Chg0bsHXrVjz33HP44osv8Hd/93dobe1a+5xUQU5TGmBOExMrPG+HKDDhI2syRDEXktQUEwY3uoGzcawJpp2ziiZN0yyBPGMj4ETluZCqIhRVkqPyHEEQRGqxORyYt/G3abt3d6ioqMCtt96Kxx9/3HK8qqoKd911l+XYlClTsHbtWiiKAkEQYq51xx13mN9fe+21mDRpEoYOHYpXX30V3/ve97o1v96ERFMaYEFw5upwnAgbr2+fokoQxT4ATsR0BVcUJnx43gFJ1zYizyFfF01hTUODpKCvPfIr5fWyXyLRFB0CBygIThAEkWo4jutSiexSYOrUqSgrK8OCBQs6LLt1h5ycHBQXF+PYsWM9et2egspzaYDnrE6TIZpklTlNQOwKOsNp4nkXJD28Z+d42Hke/XShdCEUtt7HcJoSZJqiS3MAEKBME0EQBJEEK1euxB//+Efs2rXLPDZq1Cjs2LHDMm7Hjh0oLi6O6zLFo62tDcePH0dBQUGPzrenINGUBphoYgKF5+0QedF8z5Yw08REkyA4EdbLaKK+91xhVIkuGoHv2GmKbmwJkNNEEARBJMe4ceMwZ84cPPPMM+axxx57DNu2bcOyZctw5MgRbNy4EevWrbOU8UpLS7Fu3Trz9eOPP4733nsPJ0+exM6dOzFjxgwIgoB77rknpc+TLCSa0kB0eY7nIk4TAAi2bADxnCajPOeMcpoM0cTaDpxvJ5p4nh1X1PhOU2s7ZymoUKaJIAiCSI6lS5dCjfrH9vjx4/Hqq69i06ZNGDt2LBYtWoSlS5daSnjHjx9HfX29+frs2bO45557MGLECMyaNQt5eXnYvXs3+vXrl8pHSRrKNKWB6PIcx7cTTUIWgNiGlNFOk9TOaSpI4DR1lmkip4kgCIJIhg0bNsQcKyoqQihk/XyZOXMmZs6cmfA6J0+etLzetGlTT0wvZZDTlAYEjgNnludE2Lio8HZCpymoj3chrDtNImcVTecTZZqSFE3UcoAgCIIgEkOiKQ3wHA+eiwTBBV7Q96MDOBvbeLd9y4Fop0nWEmSagl3MNMWU50g0EQRBEEQiSDSlAZ7jzSA4xzHBY5boBCaawuH2fZoMpykqCG46TSy7FFOe66LTFGz3miAIgiCICCSa0gDPRwXB9bC2KZpsOQCAcLgWqhoptxlhbkGIajlgOE1OozwnWfYSMjuCK/H3GGrTnSVeL8sFZPniH44gCIIgrlBINKUBnhcsfZqAaKcpB4LggaYpCAROm+eoitGnyYGwLnIMpynfzkRTQFXREuUWGU4ToELTYgWR4TRlt7F29UGFnCaCIAiCSASJpjQgcHwkCK6X54xeTYqmwO2+GgDg8x83zzH2j7M6TezX5xR49BFZ47DoEl1ENEXKe9G06iIp19sCAPDLlGkiCIIgiESQaEoDPC+YQXDOcJq4SFdwj3sYAMDvO2GeYzhNAu+KyTQBkV5N5yyiyR45P06uydhGJbeViaagSk4TQRAEQSSCRFMa4HnB0nIAgGUrFY+HiSar0xQpzxl9moxMExDdqymSg+I4znSbjL3rojHKc328zQCouSVBEARBdASJpjTACzz4qI7gQJRo0mS4TacpIppUJbY8F+00mb2agu1X0CVuO9C+PEfNLQmCIAgiMSSa0gDP26KC4MwJinaa3B4j03TCXPUWcZoiLQeinaZE+89F2g7EZpradKcpUp4jp4kgCIIgEkGiKQ0INpvZcoBrV56TVAlu1xBwnABFaUM4XAsAUBW9T5PgTOA0xe/V1FGDy1apndNEmokgCIKIQ3l5OTiOw8qVKy3Ht2zZAi7qs6g7nDt3Dt/97neRl5cHl8uFcePGYe/evRd1zd6CRFMKebOuGd878AXe7pMdcZq42EwTzzvgdA4GAPj0Ep3Zp4mPKs/FcZpitlIRHJbzo/G2L8/F6eVEEARBEADgdDpRUVGBpqamzgcnSVNTE6ZMmQJRFPGnP/0JBw8exOrVq5Gbm9tj9+hJSDSlkBP+EN6sa8FxlzMSBNd/BdFOEwAzDO73sxV0xjYqfPSGvVHqfoAummrD1n5MibqCS6pmOkt99PJc/L7hBEEQRG+haRrUsJKWr3hNjzti2rRpyM/Px4oVKxKO2bx5M8aMGQOHw4GioiKsXr26w2tWVFRg8ODBeOmll3DjjTfiqquuwm233YZhw4Z1aW6pwtb5EKKncAtMIIWig+AaEz7RLQcAwOMehnpsM1fQqabT5ERY05tbRjlNffU+TS2ygpCqwqH3cDJFU7vVc21RjSwNpykMDoqmQbhIq5UgCIJIDk1ScX7RzrTcu3DpzeDsQtLjBUHA8uXLce+992LevHkYNGiQ5f3KykrMmjULS5YswezZs7Fz50488sgjyMvLQ3l5edxr/uEPf0BZWRnuvvtuvPfeexg4cCAeeeQRPPTQQxfzaL0GOU0pxBRNPA9OL89xumgymlsaosndrleTEp1pMoLgUeLGeeQwbPo2KHVRblOiTJPRbsAeDsMdDJjHadNegiAIIhEzZsxASUkJFi9eHPPemjVrUFpaioULF6K4uBjl5eWYO3cuVq1alfB6J06cwHPPPYfhw4fj7bffxsMPP4x58+Zh48aNvfkY3YacphQSEU1cxGnSBVB0pgkAPOYKumMAop2m6ExTRPOqTc3I9YZQ1ycPdWEZg5wsGJ5o9Zyx75wn4IdDiuSgAqoGT488LUEQBNEZnMijcOnNabt3d6ioqMCtt96Kxx9/3HK8qqoKd911l+XYlClTsHbtWiiKAkGIdbVUVcUNN9yA5cuXAwCuv/56HDhwAOvXr8f999/frfn1JuQ0pRCP/gcT4DnTaUokmoytVEKhashym5lpEoRIR/Bop0ltazVbB9T4/OZxXtA37U3gNHmCAfCaBlEXTtSriSAIInVwHAfeLqTlq7ur3qZOnYqysjIsWLDgop+/oKAAo0ePthwbNWoUTp8+neCM9EJOUwpx685QiOPA60FwThcp7UWTKOZAFPMgSQ3w+78wy2s874CkMdcoOtOktLaij7cNAFDrbQUK+urjmeMUU57TnSajNOeQwpBEO4kmgiAIolNWrlyJkpISjBgxwjw2atQo7NixwzJux44dKC4ujusyAcyJOnz4sOXYkSNHMHTo0J6fdA9ATlMKMcpzQS66PMccHzPTpEXySNHbqajxmltGO02trWagu6YtymkyMk1Ku/JclNMEAI4wW7VHmSaCIAiiM8aNG4c5c+bgmWeeMY899thj2LZtG5YtW4YjR45g48aNWLdunaWMV1painXr1pmv//Vf/xW7d+/G8uXLcezYMbz88st4/vnn8f3vfz+lz5MsJJpSSEQ0IVKeU+KX5wCYG/f62g5D09h4jXfCWCQa6zQ1AwDqAhFXKVHLAWMLFXeACSyHWZ6jXk0EQRBE5yxduhRqVHVi/PjxePXVV7Fp0yaMHTsWixYtwtKlSy0r544fP476+nrz9cSJE/H666/jN7/5DcaOHYtly5Zh7dq1mDNnTiofJWmoPJdCPLpoCkQ7Tbp4ad+nCQDcutPU2nrQPKZyDvN7q9PUZmaaasORawiJRJNsLc/ZKdNEEARBJGDDhg0xx4qKihAKWT9bZs6ciZkzZya8zsmTJ2OOfeMb38A3vvGNi51iSiCnKYUYTpPEAar+k+dkJnDiO00sDN7a9rl+hIcM0XzfZnGavOjTwkRTvRwRPkZ5rqMgOAA4wkw0Bag8RxAEQRBxuSRE07PPPouioiI4nU5MmjQJH330UYfjX3vtNYwcORJOpxPjxo3DW2+9lXDsv/zLv4DjOKxdu7aHZ911DNEEAJIukkyniYsVTUavJkliLesFwQkpqnomJnCa6rTI8cQtB/TyXDAAiKJZngtQeY4gCIIg4pJ20fTKK69g/vz5WLx4Mfbt24frrrsOZWVlqK2tjTt+586duOeee/C9730PH3/8MaZPn47p06fjwIEDMWNff/117N69G4WFhb39GElh5zgIup6R9OA334HT5HQWmqIHYK6RpHcDt3EA3y4IbmSaGoRI1dXYe659ec4rG32aAhBysqk8RxAEQRCdkHbRtGbNGjz00EN44IEHMHr0aKxfvx5utxsvvvhi3PFPP/00br/9djzxxBMYNWoUli1bhvHjx1vS+ADbNfkHP/gBfv3rX0MUxbjXSjUcx5m5prAhmhQmmtp3BGfjebNfE6BvoWLuO2f91Sltbeijr55rE2xmmS2yjUpip8mWk2OW52j1HEEQBEHEJ62iKRwOo7KyEtOmTTOP8TyPadOmYdeuXXHP2bVrl2U8AJSVlVnGq6qKf/zHf8QTTzyBMWPGdDqPUCgEr9dr+eot3DzrVSFxupCT2jlNmnXD3WjRxAuRbuB23tqUTPV64Qn4zSaVdXoYvLNtVDzBAIScXDj0eZDTRBAEQRDxSatoqq+vh6IoGDBggOX4gAEDUF1dHfec6urqTsdXVFTAZrNh3rx5Sc1jxYoVyM7ONr8GDx7cxSdJHrfpNLGmkwgzMROvPAcAHs815vdC1L5zYrtOrkpbGzjAdJuM/ecMpyk2CB5ZPSfk5sKhz4NaDhAEQRBEfNJenutpKisr8fTTT2PDhg1Jt4hfsGABWlpazK8zZ8702vxM0aQ7TZruDCUUTdFOE+9EOI7TpGka1DbWDTy3vWgS4jtNRnnOE/BDyMmJBMGpPEcQBEEQcUmraOrbty8EQUBNTY3leE1NDfLz8+Oek5+f3+H4v/3tb6itrcWQIUNgs9lgs9lw6tQpPPbYYygqKop7TYfDgaysLMtXbxHJNOkB77BVNEX3aQIiK+gAfbPeOE6T6vMDelmtT7teTYlWzxnlOXcwYBFNVJ4jCIIgiPikVTTZ7XZMmDAB27ZtM4+pqopt27Zh8uTJcc+ZPHmyZTwAvPPOO+b4f/zHf8Snn36K/fv3m1+FhYV44okn8Pbbb/fewySJ4TSF0E40xWk5AABudxEAJpB4IWoLFT565Vwkg5Xb0gwg4jR1mmnSnSZ7mDqCEwRBEERHpL0j+Pz583H//ffjhhtuwI033oi1a9fC5/PhgQceAADcd999GDhwIFasWAEAePTRR3HLLbdg9erVuPPOO7Fp0ybs3bsXzz//PAAgLy8PeXl5lnuIooj8/HzLxoLpIiKadDHTSXlOEFxwOgciGDwLgXdC1mKdJqW1lX1js0WcpqCxwS/LTilRq+cUTYNPF0eeUBBCdpYZBKfyHEEQBEHEJ+2ZptmzZ+O//uu/sGjRIpSUlGD//v3YunWrGfY+ffo0Lly4YI6/+eabzQ39rrvuOvz2t7/Fli1bMHbs2HQ9Qpdw8e2dpo6D4EAk18QLLjPTFN0N3Mgzifn5yNV7NdX6mUji4zhNvihhlMFx4OwOKs8RBEEQCSkvLwfHcVi5cqXl+JYtW5LOD8ejqKgIHMfFfF2qG/am3WkCgLlz52Lu3Llx39u+fXvMsbvvvht333130tePt9dNujAyTUE4oWkcpFAYrY31kT5NWhzR5BmOhsb3YRM8kHRRE73vnKK3SBCys5GnN8usDTERFG/DXqM0J0oSnC4nOFGMKs9dGqLpjPcMNGgYkjUk3VMhCIIgADidTlRUVOCf//mfkZub2yPX3LNnDxR9YRIAHDhwAF/72te69BmfStLuNH3ZiC7PqSqPvxzz4PlHHoDa5AMQ32kaOHAOCvK/jcLC2abTJPLWLVQAgM/MRF+V/fHVS8bquTiiKaqxJe/xgLNHtlEJKunPNMmqjHveugez35iNtnBbuqdDEATRa2iahnA4nJYvTeva/99PmzYN+fn5ZlwmHps3b8aYMWPgcDhQVFSE1atXd3jNfv36IT8/3/x64403MGzYMNxyyy1dmluquCScpi8T0UFwVRXQHBQATYXSwHJJ8UST2z0Uo0evAgBIbY0AAHtUR3C1jZ0rZGain16Wq9OFuxEE1zQZqiqD521oM7ZQMUSTaL+kynNt4Ta0hFg268PqD1E6pDTNMyIIgugdJEnC8uXL03Lvp556Cna7PenxgiBg+fLluPfeezFv3jwMGjTI8n5lZSVmzZqFJUuWYPbs2di5cyceeeQR5OXloby8vNPrh8Nh/N///R/mz59/USW/3oScphTjFlhH8BAc0DQeisZ+BZzMFH880RRNPKdJiXKa+olMB/s5Dj5ZsexdZ7hN0e0GmGgSzW1UApeAaPLJPvP7Hed2pHEmBEEQRDQzZsxASUkJFi9eHPPemjVrUFpaioULF6K4uBjl5eWYO3cuVq1aldS1t2zZgubm5qQEVrogpynFuM1MkwuqykPRmPjhJCZWOhNNRp8mOxfbckDIzEBmKARHOISQ3YE6ScZQZ3vR5IHXKM8F4pTnLoGWAz4pIpp2nt8JTdMu2X91EARBXAyiKOKpp55K2727Q0VFBW699VY8/vjjluNVVVW46667LMemTJmCtWvXQlEUCLppkIgXXngBd9xxBwoLC7s1r1RAoinFeKLKc5omQDHMPr1k1r65ZXukuE4TK8/xGZmwSTL6eJtxoe8A1IVlFLkc4Dg7NC1sNriMlOf84D1ui9N0KWzY65f85vfn2s7hpPckrsq+Ko0zIgiC6B04jutSiexSYOrUqSgrK8OCBQt6zBU6deoU3n33Xfzud7/rkev1FiSaUoybj8408VA0XXlLzP2Jt3oumnC8juB6eU7IygQ0FbneFlzoO8DsCi4IDshyOHF5zn5pZZqinSaAuU0kmgiCIC4dVq5ciZKSEkv/w1GjRmHHDmukYseOHSguLu7UZXrppZfQv39/3Hnnnb0y356CMk0pJnr1nKYKUE2nSRdNccpzJ06cwJo1a3D48GGzuaXd4jSx8hyfkQkhO7vTTXuN1XOeYABCRgZrOSBdQpmmdqLpg3MfpGkmBEEQRDzGjRuHOXPm4JlnnjGPPfbYY9i2bRuWLVuGI0eOYOPGjVi3bp2ljFdaWop169ZZrqWqKl566SXcf//9sNkubS+HRFOKcUf1aVI1HqqxCq6DTNOnn34Kr9eLQ4cOdeg08ZkZ4LOzzU17I/vPWRtcGuU5M9NkKc8ll2mSVQ3/e7YOn7X6Ox/cRQzRlO9h+wnurd6LkBLq6BSCIAgixSxduhRq1D+0x48fj1dffRWbNm3C2LFjsWjRIixdutRSwjt+/Djq6+st13n33Xdx+vRpPPjgg6maere5tCXdFYgl06TygC5+NEkGxPiZpvPnzwMAfD5f3ExTdMsBThTRR+8KXt/OaVL1rVSinSbebS3PhTUNiqZB6CR4/cK5Oiw+dh43ZLnxxoTiLv4UOsYvMyE2ru84qKqK2kAtKmsqcXPhzT16H4IgCCI5NmzYEHOsqKgIoZD1H7QzZ87EzJkzE14nXrPp2267rcs9o9JFl50mSZJgs9lw4MCB3pjPFY+luaXGQzNFU/zynCRJqKurAwD4/X6EdVVv3XvOcJqyIGTnILfV6jS137S31QiCB/wRp0kXTUDnuSafouBnp2oBAF8Ewh2O7Q5GEDxDzMDNA5lQ2nluZ4/fhyAIgiC6QpdFkyiKGDJkiKXtOZE80c0tFVUAwMSPqguc9qKppqbGVODRTpOdj2pu6Y20HBBystGnpRlAdKaJrcwwV8+17wgetY0K0HmJbuO5BrPjeIMk9/iKO6M85xE9mDJwCgBgx3nq10QQBEGkl25lmn784x/jqaeeQmNjY0/P54rHWD2ncDbIqt0sz6m6wGkvmozSHGA4TdZMk6YoUP3MmeEzWRDccJrqjEyTwJwmpd3qOU+UaBI0DTaZ3bsjp8knK1h3usZy7EKo4zYJXcUQTW7RjckFk8FzPI41H0O1r7pH70MQBEEQXaFbmaZ169bh2LFjKCwsxNChQ+HxeCzv79u3r0cmdyXijlp2GYAzIpqk+E7ThQsXzO9DoRBCuktkrJ5T2yJ7swkZGQDHmavnakMyNE2LyjQZq+f0IHiUaAIARzgE2WbrUDS9eK4ejZKCq1x2qBpwKhjG+VAYV7kdCc/pKkamySN6kO3Ixti+Y/Fp3afYeX4nvj382z12H4IgCILoCt0STdOnT+/haXx5EHkOIlRI4BHSnGamKVF5Llo0AUBAL4sZTpORZ+KcTnB6g7Q8RXeMNA0+RY2zek53mgIB8BkecIIACAIcUhg+eBJ2BW+VFfz8NMsyPVaUj00XGnXR1DtOk8fGxPhXCr+CT+s+xQfnPiDRRBAEQaSNbommeHvOEMnj5BRIGo8QF3GaFMNp0mRz2xBZllFby0QKz/NQVRVBfZyxes7YQoXPzDCvn+F2wRUMIOB0oTYsQzCcJtW6es4d9EPQXcLoMHggQUbpf8/WoUlWcI3bgRkDcvF+E1u1dz7Ye+U5ALh54M34+Sc/x+4LuyGrMmw8LfokCIIgUs9FffpUVlaiqqoKADBmzBhcf/31PTKpKx0Xp6BVExHUXODABIoSFcSWNRkiJ6KmpgaqqsLlciEjIwN1dXUI6i6R3XSa9HYDGZnm+YLeqyngdKEuLCHLFE0hqJoWWT2nl+cA6GFwJn7iledaJBnrz7BVfI8X5UPgOAx0MGfrXKhnV9AZq+c8Ipvb2LyxyLJnwRv24kD9AZT0L+nR+xEEQRBEMnQrCF5bW4tbb70VEydOxLx58zBv3jxMmDABpaWl5vJ4IjFOnpXPQnCCM4Lh0aJJL9EZpbnCwkIzNxbSw9piu0wTnxUlmnKyzV5NtWEZvGB0BA/Cr6gwim/uQACc24ljxyoQHKN26DQ9f7YOLbKCYrcT3+yfAwAocLAsVK+V53TRJPACJhdOBkCr6AiCIIj00S3R9IMf/ACtra34/PPP0djYiMbGRhw4cABerxfz5s3r6Tlecbg4PXMEBzj9VyCHEoumgoICuN2sVBVU2jlNRruBKKeJb7eCjo9ymozSHK8ocHJAi/8znDr9PFrK2qL2n4vNNP3yfAMA4LGrBpiNLwudzGm60MNOk0+2iiYAmFQwCQDwad2nPXovgiAIgkiWbpXntm7dinfffRejRo0yj40ePRrPPvssbrvtth6b3JWKE8yZCcMB8EwgyOFIV1VDNBntBgoKCsyuq2FFBTgBNjPTZDS2tJbnovefiw6CR5fmBI8HUpi1jVCdGhyN8TftlVTN7Pn0d7mR+ww0nKZezjQBQIGnAADQEGjo0XsRBEEQRLJ0y2lSVRWivkw9GlEULfvQEPFxcHp2iHPAaG4ph8PgDddJlS0h8MLCQtNpMjqCG05TZAuVSBBcyM4x95+riw6CKyFz5ZzRbkCW2fmaXTM37W0vmpr0FXscgGxbpGVCoS6ammQF/h5qcKlpWiTTZIs4TXnOPABAQ5BEE0EQRKopLy8Hx3FYuXKl5fiWLVvAdbLtVkcoioKFCxfiqquugsvlwrBhw7Bs2bJLdluVbommW2+9FY8++qil8eK5c+fwr//6rygtLe2xyV2puDh9nzfOAXCRX4FDY8afrMqoq6uDoihwOp3IyckxM03mNipGFipqCxUD5jQ1A2BbqVicJsXYQiUAPiMDsqKLJjGSaWrfEbxBF025omDZky7LJph76Z3voRJdSAlB0fSWCFHluTwXE01NwSaoGglzgiCIVON0OlFRUYGmpqYeu2ZFRQWee+45rFu3DlVVVaioqMB//ud/4mc/+1mP3aMn6ZZoWrduHbxeL4qKijBs2DAMGzYMV111Fbxe7yX7oJcSDjCBEYLDotAdKnNuZFW2lOY4jjOdJknXM6bT1BrZQsXAWD0HGOW5SBC8VY60G7A4TTYNDomVAGOdJnZOH9FazeU4znSbLvRQic4ozQHW8lyuM5c9g6agOdTcI/ciCIJIN5qmQVH8afnqqpszbdo05OfnY8WKFQnHbN68GWPGjIHD4UBRURFWr17d4TV37tyJu+66C3feeSeKiorwD//wD7jtttvw0UcfdWluqaJbmabBgwdj3759ePfdd3Ho0CEAwKhRozBt2rQendyVigN6Pomzx3WaJE2yhMABmE6TsfecsXrOdJoyEq2ek8zVc9FBcE8gAN7jhiRHOorbFX31XDvR1Gg4TbbYP5dChx1H/aEeaztglOZcNhf4qJ+NyIvIdmSjJdSChkAD+jj79Mj9CIIg0omqBrD9vXFpufdXb/kMguDufKCOIAhYvnw57r33XsybNw+DBg2yvF9ZWYlZs2ZhyZIlmD17Nnbu3IlHHnkEeXl5KC8vj3vNm2++Gc8//zyOHDmC4uJifPLJJ/jggw+wZs2ai3m0XqPLokmSJLhcLuzfvx9f+9rX8LWvfa035nVFY4imEBfZew6wOk3R7QYAdOA0MacourmlkJNjBsHrJRkcZ2Sagmhr16PJcJrY/Zlb1BBqw/pP1uO7o76LDHuGKZr62CN5JoNCZ8+2HYi3cs4gz5nHRFOwAcMxvEfuRxAEQSTPjBkzUFJSgsWLF+OFF16wvLdmzRqUlpZi4cKFAIDi4mIcPHgQq1atSiiannzySXi9XowcORKCIEBRFPz0pz/FnDlzevtRukWXRZMoihgyZAgU3bEguo4DrDO3xFudJrvGRElYCqO6mm1O295pUnSxFHGa9CB4ljXTZLQcCKka/HABsDpNkfJcc+T+KnOLdld/jLdOPYuwEsa88fMSlueASBi8p1bQte/RFE2eKw8nWk6gMUAbRRMEcWXA8y589ZbP0nbv7lBRUYFbb70Vjz/+uOV4VVUV7rrrLsuxKVOmYO3atVAUBYIQ+w/vV199Fb/+9a/x8ssvY8yYMdi/fz9++MMforCwEPfff3+35tebdKs89+Mf/xhPPfUUfvWrX6FPHyqTdBUnAgCM8ly008R+HY0NjVAUBQ6HA7m5LMvjcunCxxBN7Z2mDGumySFJ8AT88LncaFJYEFxRQ2amyRMMQMj0QJbPmOfZNeaAnffXwwngw+oP2Xw6Kc8BPdcV3Gw3YIu1jGkFHUEQVxocx3WpRHYpMHXqVJSVlWHBggUJHaRkeeKJJ/Dkk0/iO9/5DgBg3LhxOHXqFFasWHHliKZ169bh2LFjKCwsxNChQ00XxGDfvn09MrkrFcNpCnF2GC0HAMBuiKZa5qQUFBSA11fJCYIAl8sFRXem7IbTZLYcsDa3BIA+3mb4XG40qA7YwJymNn31nDsQAJ+fb66eAwBRD6iHVcAJ4PP6z+GX/GjUu5D3EeOU54wgeA+V59pvoRKNsYKOejURBEGkl5UrV6KkpAQjRowwj40aNQo7dlh3bdixYweKi4vjukwA4Pf7zc85A0EQLtn2Rd0STdOnT+/haXy5cGjMaZJ40VKeExX2fVMtW85plOYMPB4PVP2PK+I0xTa35O12cG43cr0tODOgEI2KiP5gG/Z6E/RpAgC7xkSTxjH3SNEU7K/dj8ZwPgCgjz2O06R3Be+plgMdlufIaSIIgrgkGDduHObMmYNnnnnGPPbYY49h4sSJWLZsGWbPno1du3Zh3bp1+PnPf26OKS0txYwZMzB37lwAwDe/+U389Kc/xZAhQzBmzBh8/PHHWLNmDR588MGUP1MydFk0ybIMjuPw4IMPxiTnieSwg7kpYU60lOdElSnx5rpmALGiye12Q9VFlshz0MJhaEHmWkU7TYC17UCDbIgma3mO92RYRRMXEU0e0QOf5MOemj1oVO8AAPSJU54zuoJ7ZRVtsoIMW/x/TSRLvG7gBuQ0EQRBXDosXboUr7zyivl6/PjxePXVV7Fo0SIsW7YMBQUFWLp0qaWEd/z4cdTX15uvf/azn2HhwoV45JFHUFtbi8LCQvzzP/8zFi1alMpHSZouiyabzYZVq1bhvvvu6435fClwaEwYSLwILUo02VQenMahtYEJGWPlnIHL4jTxUNq85nvRmSaAiaa+LcyxWntewu2YiW/I2yPluXhOk16eA2fH/WPux8/3/xx7q/eiqQ9bIRmvPJdhE5Bl4+GVVZwLSRhxsaKpg9VzRpsBcpoIgiBSy4YNG2KOFRUVmVt8GcycORMzZ85MeJ2TJ09aXmdmZmLt2rVYu3ZtD8yy9+l2R/D33nuvp+fypcGu6k4T385pUnh4ZA9UhW1T0z5k73BH3Bc7z0VC4G43uHb1YiE7G996/x2MUsJoU4DfcvdinrYKR3zMmfIEAoDHAVUNRu7PM9Fkt2XiG1d/AwBwoP4AGsJGy4H4GrvA0XMb9xqZpg6D4OQ0EQRBEGmgW5mmO+64A08++SQ+++wzTJgwISYI/q1vfatHJnelImoshyS1E002lYNdYQLE4/HEhOMcUT9nkeOitlCxluYAJpqG1FzAazVHsf2rU7Hs8AHUcAVAVEdwzc1BrxSy63PsXwwuexYGZQxCvicfF3x15tYr8VbPASwMftgX7JG2A8kEwRuDjdA07aL2OyIIgiCIrtIt0fTII48AQNyOnRzHUQ+nTjDLc4INGjiIvAxJtcGmcLDpK+gcDkfMeaLLDX3hHew8h6CxhUpWfNEEAFpLC6YP6IPMwz/Edq0Ub9gfhr+1DYNqq6E5YRFNhtMkCB5wHIcbBtyAP5x8HwBb45cTpzwHAAN7sO1Ah80tddEkqRK8YS+yHdkXfT+CIAiCSJZuledUVU34RYKpc+waK6tJvA0aBzh5Vv4SFA6ixoLV8USTXS/PcZoGgePMxpbRW6gYCDlMUKgtLeB5B2yQMQ1v48OJA/Hb/3gCWX4fVKd1SacoMKfJWD03MX8iVIFdu/1mvdH0ZFfwjoLgDsGBDJFltxqD1OCSIAiCSC1dEk1f//rX0dLSYr5euXIlmpubzdcNDQ0YPXp0j03uSkTTNNj18hw4DrJgg1PQRZPMQdS3UnE6nTHnik7W4FLQmNiJtBvIiBkr5OQAAJTmFvC8DRzHHCxeC8Gp71Ct2q0CVxT0jYRVtlfLDQNugMoz0ZRtS/ynUtCDXcHN8pwt1mkCaAUdQRAEkT66JJrefvttS1J++fLlaGyM/ItflmUcPny452Z3BaJpYTgQKWOFbVGiSUEn5Tkmmni96ZdilOcys2LGGuU5RRe5PM9EmOxvAfTzVbtsvb4umoL6+4MzByPLNZDNB9YVEtEY5bme6NXUUZ8mgHo1EQRBEOmjS6JJ07QOXxOdo6ph8FAh6luWWJ0mmE5TPNFkczDhwxvl0A6cJj5GNOkNK33N+gAeCm8VOXabvpGwqkHVg9aDsplzqEpNCZ8pujwX/TchSRL27t3bpQ7xHZXnAHKaCIIgiPTRrSA40X1UlZWwnAhCggNhmw0OPdPEK1qHoknQj/GaimAwCDXOFirm2HaiSeCdkABIumji3W4oSpvlHFGMiKigqsEtcOibOQzwAr5QdcJnMvaf8ykqvLICl6aisrISO3bsQFsbu8eIESNiVlnGo6PVcwD1aiIIgiDSR5dEE8dxMcu8adl311D1rUocCKEVQDjKaeLljstzit6CgNc0+Hy+SMuBeEHw7Bx2juE0Cex6ip+V9KIbW8qww4YwRFu0aFLhFnhkOAsBbwjN/tMIykE4bbFZK7fAI9cmoElW8NaHe3B21wfw+XyWMX6/PynR1NHqOeDS6tUkqzIe2/4YRvYZiYdLHk73dAiCIIhepsvlufLycnz729/Gt7/9bQSDQfzLv/yL+bq7e8U8++yzKCoqgtPpxKRJk/DRRx91OP61117DyJEj4XQ6MW7cOLz11luW95csWYKRI0fC4/EgNzcX06ZNw4cfftitufU0mu40GbkmKSrTxMlah0FwSQ9oC6oKv98PtaOWAzkRp0nTtEimKRglmvTNepsVJnx5hwpBZeHwoN6bSeb0Mpncgs/qP0v4XEYY/J19H8Pn8yEnJwff/OY3kZXF8lbBYDDhuQaapnXqNJnluUvAaTrSdAR/OfMXvPT5S+meCkEQBJECuiSa7r//fvTv3x/Z2dnIzs7Gd7/7XRQWFpqv+/fv3+XtVV555RXMnz8fixcvxr59+3DdddehrKwMtbW1ccfv3LkT99xzD773ve/h448/xvTp0zF9+nQcOHDAHFNcXIx169bhs88+wwcffICioiLcdtttqKur69LcegNVjThNAOvV5DBFk9phywFJzwvxmpqE06T3MJJlqD4feF53moJ6m4Iop6leYkJOs2twyGwuAT0M3igxEcWpbdhTvSfhcxkb97Y5XJg4cSJ+8IMfYMKECXDp4fX2rfbjEZAD0MCeMV5HcCDiNDUG0t9yoD7A9k8KyAEE5c5FIUEQxOVKeXk5OI7DypUrLce3bNlyURWn1tZW/PCHP8TQoUPhcrlw8803Y8+exJ816aZL5bmXXur5f1GvWbMGDz30EB544AEAwPr16/Hmm2/ixRdfxJNPPhkz/umnn8btt9+OJ554AgCwbNkyvPPOO1i3bh3Wr18PALj33ntj7vHCCy/g008/RWlpacw1Q6GQ5UPd6/XGjOkpDNHk1MIAB0iCYPZp4mStw/JcOMpp8vl8cBl9muIFwZ1OcA4HtFBIbztgiCZdaEWJJq/uNKkOwClL8NsdCOr3atJFFK+2Ym/N3oTPVag7TW0ONwoKCiDo27oYjlkyTpMRAuc5Hi6bK+6YS8lpii4RNoeakW/LT+NsCIIgehen04mKigr88z//M3Jzc3vkmv/0T/+EAwcO4Fe/+hUKCwvxf//3f5g2bRoOHjyIgQMH9sg9epJuNbfsKcLhMCorKzFt2jTzGM/zmDZtGnbt2hX3nF27dlnGA0BZWVnC8eFwGM8//zyys7Nx3XXXxR2zYsUK0y3Lzs7G4MGDu/lEnaNpRhCc/S8rz7HvOUntMAge7TT5/X4oHQTBgegweDMEQzSFDXcqIppadNGkOQCH7joZ5blGyQipt+KT2k9Q7YsfCDfaDrQ5XBBF0TxuiKZknCZz5ZzNnfBfLqbTdAk0t6wLRJzL5lBz+iZCEMRli6Zp8ClKWr66ugJ+2rRpyM/Px4oVKxKO2bx5M8aMGQOHw4GioiKsXr064dhAIIDNmzfjP//zPzF16lRcc801WLJkCa655ho899xzXZpbqkjr6rn6+nooioIBAwZYjg8YMACHDh2Ke051dXXc8dXV1g/zN954A9/5znfg9/tRUFCAd955B3379o17zQULFmD+/Pnma6/X22vCySzP6YHwsGCDU9T/cGWlC05TEKrXcJoSiya5tpZ1Bc8wRBMTJoLHA1lmPzNTNNkBh96gMlKeY6JpkDsbNc1hfOeN72D1V1djwoAJlnsZbQd87UST8RxJOU1yx+0GgIjTFJAD8Ev+Dsf2NkZ5DgCagolbMhAEQSTCr6oY9n7ivGhvcnzqOHiE+NtjxUMQBCxfvhz33nsv5s2bh0GDBlner6ysxKxZs7BkyRLMnj0bO3fuxCOPPIK8vDyUl5fHXE+WZSiKEpPhdblc+OCDD7r1TL1NWp2m3uTv//7vsX//fuzcuRO33347Zs2alTAn5XA4kJWVZfnqLczyHJgYkQQbHJk57E1J6TAILsc4Tcw16txpagEvsOspRgnME+s0wQbYJaPBpQZJ1eCVmXj6779bguLcYjQEG/BPb/8TfnPoN5Z/pRSY5TlnXKcpGdHUWQgcYILKKN2lewVdtGgip4kgiC8DM2bMQElJCRYvXhzz3po1a1BaWoqFCxeiuLgY5eXlmDt3LlatWhX3WpmZmZg8eTKWLVuG8+fPQ1EU/N///R927dqFCxcu9PajdIu0Ok19+/aFIAioqamxHK+pqUF+fvx8SH5+flLjPR4PrrnmGlxzzTW46aabMHz4cLzwwgtYsGBBzz5EFzFaDjj1Mp0kCHBmM/dE09BhENxwmnhVha+1FdBLaQmdptwcALpo0stzqhSAACaalHaZJgBwGKJJUdGs55k4AKNzh+BXd/wKS3YuwZ9O/gnLP1yOz+s/x8LJC+EQHGZ5zudwmXkmoHvluURbqBj0cfbBubZzaAg2YHBW75VSOyNatJHTRBBEd3DzPI5PHZe2e3eHiooK3HrrrXj88cctx6uqqnDXXXdZjk2ZMgVr166FoiiWzwaDX/3qV3jwwQcxcOBACIKA8ePH45577kFlZWW35tbbpNVpstvtmDBhArZt22YeU1UV27Ztw+TJk+OeM3nyZMt4AHjnnXcSjo++bjIf3L2NpjtNriinyZatCz4+8gfVUaZJ0DT42iL71/Hu+CUqoyu4XN9gthxQlAB7L6rlQJvCwfhTsCvsZxRUVTTopbkcG9us1y26UTG1Ao/f8Dh4jsfvj/8e/7H7PwBEnCZZsMEvRLR4l8pznWyhYnCp9GqiTBNBEBcLx3HwCEJavrq76m3q1KkoKyvrERNi2LBheO+999DW1oYzZ87go48+giRJuPrqqy/62r1B2stz8+fPxy9+8Qts3LgRVVVVePjhh+Hz+czVdPfdd5/lF/Poo49i69atWL16NQ4dOoQlS5Zg7969mDt3LgDA5/Phqaeewu7du3Hq1ClUVlbiwQcfxLlz53D33Xen5RmjMTuCa2wpvywIQGY+OGjQdNGk8RpstlgTMKznjHi9TxPAXCYuwb8WHFexP7rGl16C2sQEkqow8cK5nVAUdo2gxoHnmKiyy4Zo0tCktxvoI0bmwnEc7h9zPyr+rgIAsPP8TvY8Ag+XxM5t0CL/IXZn9VxnOaU+rkujKzhlmgiC+LKycuVK/PGPf7Qswho1ahR27NhhGbdjxw4UFxfHdZmi8Xg8KCgoQFNTE95+++0Yx+pSIe3bqMyePRt1dXVYtGgRqqurUVJSgq1bt5ph79OnT4OPEgU333wzXn75ZfzkJz/BU089heHDh2PLli0YO3YsABZUO3ToEDZu3Ij6+nrk5eVh4sSJ+Nvf/oYxY8ak5RmjibQcMESTDWpGPkS+CrLAnlMT4q9osKyeCwahARAyYtsNGOR+dw7a3nsP/o8+gu+td4GvAorKxIuWEfnVi0ImbIKGsOy3OE1GCDxaNBlMLmTOXq2/Fj7JB4/ogScUREB0oE6NjDOcpmRcvmQyTcCl4TT5JT8CcsB8TU4TQRBfJsaNG4c5c+bgmWeeMY899thjmDhxIpYtW4bZs2dj165dWLduHX7+85+bY0pLSzFjxgzT6Hj77behaRpGjBiBY8eO4YknnsDIkSNN4+RSI+2iCQDmzp1r/gDbs3379phjd999d0LXyOl04ne/+11PTq9HibQc0MtzvADF0x8ip8LPs19HItFkrp7TVKiaBkkU4UyQZwIA3uHAoJ8/i9P33Y9WL1udoQSY46R5eP2aQP+MQgg8W8Iv6k0aA0pENOWKsf9CyHZko4+zDxqDjTjpPYlRuaOQEfSjPiMbtVGiqUtOUydbqBhcCr2aol0mAGgKkdNEEMSXi6VLl+KVV14xX48fPx6vvvoqFi1ahGXLlqGgoABLly61rJw7fvw46usj///Z0tKCBQsW4OzZs+jTpw9mzpyJn/70p5YFRZcSl4Ro+jJhOE0u3WmSBBtUdz/YeAXQHTVVUOOeazhNxi8t5HAgpwPRBDAnavAvnkfT2q8DqNc7gtugugDIQFADCj2FEATmmjh0pymgqtD1XVynCQCuyr4KjcFGfNHyBYZnDkdGkDlFF/SyHtDNPk2dlOd6uleToip4+uOnMcA9AHNGzUnqnOg8EwA0B5t7ZC4EQRCXIhs2bIg5VlRUFPP/7TNnzsTMmTMTXufkyZOW17NmzcKsWbN6YoopIe2Zpi8bkfKcvrebIEB194PIq2amKaFo0p0mh42NCzkcCVfORWPLy0Pe7O8CADS9J5TqZPcIqhwKMgogCEyo2DVj9ZxmBsETiaairCIAwMmWk5AkCVm6aDobls0xXQmCm+W5TlbPmU5TD5Xnfnfsd3jpwEuo+KgCNb6azk9AxGky2h+Q00QQBHHlQ6IpxahGeU4XTZJgg+LqCxunQNODcoqgxD03rDtNTn11WsjpiLuFSjzEPvoKPbcICAK4PuzDPqByzGnShYodsZmmeOU5gDlNAPBFyxeQZRlZQeYUndEbZAJWp6mz7rNddZp6ojzXEmrBz/b9DACgQcPWk1uTOs8QTcOyhwFgTlNXu+sSBEEQlxckmlKM6TSpehCcF6DasyDymtlyIJFoMpwmp+40BR1OCHE2642H0afJOeFaXPXb16Bl6NfQwJwmfYNcO4zmlqq5ei6vg/IcAJz0MqcpU3eaTgfD5hjDadI0DeFwGKqmYXN1I85EjTHwy8kFwc3Vcz3gND33yXNoCjXBxrFnfOuLt5I6z7j3NbnXAADCatgSDCcIgiCuPEg0pRizT1O006RpsNlFszyn8AlEk+5kuPSAXMjhAJ+VpGgSdPFi0+AcNcrsBh7jNHGRjuAdrZ4DgKuymGg65T2FsBRGVoA5Rc2ygmb9XFEUzdWPwWAQ7zZ48f2q03jy8NmY63XVaWqT2hBSut9762jTUWw6tAkAsPzvlkPgBBxsOIhT3lOdnmtkmgZnDoZD/9lSiY4gCOLKhkRTijE6gjvUqEyTqkK0283ynMRLcc81nCaXLmJCDkfCLVTaY3YE11sOhMPNAICgCkumSeQiHcE7K88VZhRC5EWElBCqvdUQVQVuvaO44TZxHGcp0X3WytyYw/5YVybZTFOWPQsiz4Rjd90mTdNQsacCiqagdEgp7rjqDtxUeBOA5NwmozzXz9UPOY4cABQGJwgiOaiUf3Gk8+dHoinFRMpzhmiyQVYU2Bwu02lKJJrCujvlsrMtS0JOB/gky3OC3hHcuH9LkAWeJdiQ58yDILCMkyGaAlHluUROk8ALGJo1FABwtoU5R7l6g8vTgdgSXTAYxIkAe/98UDKbdRok2xGc4zj0cV5ciW7b6W348MKHsPN2PH7D47hwYTO+mc+cs7dOvNXpf5TGffNcech15gIgp4kgiI4xltEbzYmJ7mH8/NLRloBaDqQYTe8I7lAiH8o+WYHocgM+XTRxHTtNbnukPCckGQQ3nCZF7wjeFmSbF9tsWeA4DgKvZ5p4JnbaZBUtcseiCWAr6I41H8MFL9tcsY8SxjkAp6IyS9G9mo759dV7AM4FJVzljmwXk6xoAphYqfHXdCsMHpSD+K+9/wUAeGDsA+jncOKDPf8GN++CS3DgpPckDjUewqi8UQmvEc9poq7gBEF0hCAIyMnJMTePd7vd3d7K5MuIpmnw+/2ora1FTk5Op13GewMSTSnGcHrsqsp26OU4+GQFNlcGtGBnTpMhmuwIwGg5kJXUfSPlOeb0+MMNEAE4xRwAiDhNApvfhbBeXgOQk6A8B0TC4NWt1QCAPIXN/XQgkjWKdpqOR/0D61QwZBFNRhC8s0wTcHFdwX958Jc413YOA9wD8ODYByGFmEumqgGUDZyMLad3409f/CmhaFJUxewR1dfVF7kO5jRRV3CCIDrD2FzeEE5E18nJyTF/jqmGRFOKMVoOcCoHUVEg2WxokxWI7ixoLWxMmItdWQZEnCaPwxERTRmduzIAzA17zUyT1AIRgMfRFwAgCHoQnGdipzrE5mls1puIouwiAEB9Wz3ykIc+DXVATr5lBZ3hNF0IhNCmROzUU1ElPEVVzNVnyTpNQPcaXL576l0AwPdLvg+36EZLlFV+S//h2HJ6N9764i38cMIPwXOxFeymUBMUTQEHDrnOXOQ4c9hxcpoIgugEjuNQUFCA/v37Q5Li/wOZSIwoimlxmAxINKUYw2nSVAGiqkCCDX5FQa4nBxrPVrQlFE260+RxOlAPJpo4lyup+7Z3mozVc5lOtsef4TTZBf19vXrYUWkOiDS4bPQ1Ig95yD5xDBg2ziKIDNF0MiQBiC+aDJcJSFI0XUSvpvO+8wCAsX3ZfoWK4jPfG+pyIEPMQI2/Bh/XfowJAybEnG+4W7nOXNh4GzlNBEF0GUEQ0vrhT3QPCoKnGKPlAFQOdoUFof2KCjGzD6Bv2Bvi4i+jN/aey3Dq+SSbDYotOd0rCBHRpGkaNJWJlFx3gf6+vnrOZhVsiVbOGRhOUyDMXKK+LcxtORsMQ9FFnlGeOyVZWymcCkae08gz2Tgb7Ly90+fpbhDcL/nREmKWXoGHPbuiRARbyH8CpUNKAQB/+uJPca8RnWcCYDpNJJoIgiCubEg0pRijPKepHOwKExE+RYUtq5+5ei6RaDL7NNlECHpIO5DkykvDaQKY28XrrQ/yPIMAxGaaDDpzmrLsWchz5iEjwP6U+rQ2w6aqCGuaWeIznKYzuma6ysVEUfQKO6PdgFtMLhjZ3U17L/hYYD1TzESGnYXoo0WTz3cUX7/q6wCAt0++DUmNtc8N0dTXxUqbhtNE5TmCIIgrGxJNKcYoz6lyRDT5VRWCJ9fsCB5E/M7SRqZJ1FQ4QiybFNDi71PXHiPTBACy4ocdrAdTfgYLcvO602SzWwVbZ6IJYGHwvq1s7nZZRn67zuCG03RBY39ut/Zh4fV4TlMypTmg+/vPGaKpIKPAPCZHled8/i8wccB49HH2QXOoGbvP7465htHY0pgDOU0EQRBfDkg0pRijPKe2K89pUWW2IOJvbms4TaIUhqgHCJONEXKcDcavu67tLJz6b75/JuuzZDPKc2LXynMAK9Hl6u0SBFlBYSsrf53SV9AZTlM1z57xq31YbymvrJqdw31yF0VTNzNN59tYnskozQFWp0nTwgiHzuO2obcBYP2c2mMINXKaCIIgvlyQaEoxRkdwVYbpNAVUDZq+SktTFUiQ4zZXNDJNNkkyRVNIlpO6L8dxEARdvLQeNY87RPaBLyQQTUk5TVlXIdvP5i8oCgqb2Yo2I+jtdDqhcBwaBVaWG5vpQn87u67RzynZLVQMDJenJdQSt4SWiGofa42QSDQBrER3UwHrDv55w+cx14jJNBkdwUO0aS9BEMSVDImmFGOunlMQcZpUFaqxtN3YyFeNFUOSXoqzhSNOUyiU/N5rRq6pvvU4AEDRODMgzhuZJodVNCXarDeaIs9geELMabIpMvIbWP+RM1HlOa/TA5Xj4BF45NtFDNXD7IawSnYLFYMcRw4Ejt2zMZB824F45bno1XMA4PMdMXs0HWs6FrO/XftMk1GeUzQFrVJr0nMhCIIgLi9INKUYVXdFFBlw6KIpoGpQwcLPnC6a4rknptMUDsGml7W6I5qaA2fYHLjIKjWjI7hNUCBEuSXJlOeG1GnQ9NKboCgoqGHC5GQghIf+/BB+uvenaHaz0PUwlwMcx2GoHgY3SnhdzTTxHG9uX9KVEl1H5TlBYHP0+Y6hwFOAHEcOZE3GsaZjlmsYoslwuxyCA24b+/nR/nMEQRBXLiSaUoyZaZI1i2gylucboknW4jlNbIwQCkOUu+80tR1hwkHjIz2ejNVzAOCICpcnU57LPHIBit5vRFAUFJxjouxIWyt2X9iNqtYqUzRdrXcAH2KsoOtmeQ6I5Jq60uAybnlO7xGVlcn6Nvl8R8FxHEb1YW7TwcaDlmu0d5oA0P5zBEEQXwJINKUYo+WAIqtwqHFEk9JBec5wmkLBbpXnjE17RX3/OaMLOADwvAio7M/BGXXvZERT6NNPodgiQfD+Z04BALyqAI2zQ+IltLh00aSLpUh5rntOEwD0d/cHAJz2nk5qvKzKqPGzjYqjRZOstAEAsrJL2Fz8X0BVZbNEd7AhIpoCcgBtEhtvZJqASBi8sXEH/vbBTaitfTvp5yAIgiAuD0g0pRiz5YAU2bQ3qAGyLqB4RQWnxRdNxt5zQjh0UZkmu521NLCL2db3FSaQHFqkCWVuEqIp8MmnFqcpy9sCJ8euoQh9IXGS6TQN1QPgkfKcnmnS3Z6uiKZr+10LAKisqUxqfH2gHoqmwMbb0M8dETxGec7jGQ6ed0HTwggETmF03mgAQFVDFQCgpeVjHD3xLDhocApOy1yNXFOweSfC4TrU1L6R9HMQBEEQlwckmlKMIZpkWYFD1p0mALJeqoOqQFC4jp2mYDDpTFP0ai7OEE0ic5pc9j6WsbzKtjhx6PfmwPae6wi5qQnhkychCzb9Ggo4AEKQlcEcrqFQeRXNLtZmYBDP5mOIprOhMGRV65bTdMOAGwAAe2v2JrVqzQiBD3APsOwpZ4gmm5ABj2cYAJZrGt2HiaYjTUcQVkL47MBc1J19DiOcKvJceZYmnIbTpIYv6OdHVigSBEEQVwYkmlKMZpTnwiqculAKaoCktw7gVAWyYyyqWn3tztNMp8kWTK489+7BGkz86bvYftjYTZuJIlF3mozNeg14jb1vVyOb9dr4jrtzBz/7DAAgO5gIUgV9jgGWmyopvAMq50bQzgRbvu5iDbCLcPAcFA04FwpHMk225DNN4/qNg523ozHYiC+8X3Q6Pl4IHIisnhNsHng8wwGwFXSDMgchU8yEpEqoOv8mQiEmBPNF1VKaAyJOEy+zvJPffxJqHOFLEARBXL6QaEohmqZC0wPesqyaQfCQFhE/Ndl5qBv4b/i349al60qUkSL4/UmJpveO1KG+LYz3j9TrR5gbZLczp8kh5ljGG06TXRd2SZXm9n8CAFD1jFKIZ+d6fEyoKbZ+UEQmUtyhAGx6gJ3nOAxxRrZTMVsOdMFpcggOs0S3t3pvp+MNp6kwo9ByPOI0eZChi6Y2Iwyu55rOXfiDOb6/TbWEwAHmNImcBlFjeSdNkxAIJJe16grUB4ogCCJ9kGhKIWpUGwElpJiZpkCUaDpQxD6kL0gc1KgPyHDU90IwkNTqOX+YuTreoL7fne4kiSI7R7BlWMYLYCLGoZcQ+yTRbiDw6afs2Wzs2iFB354lxIRIGzKgiPkAgBx/G4LBSLfzwbpoOhUMd2v1HADckB8p0XXGhTYmmvI9+ZbjkZYDbtNp8vtYm4FRfUaBgwb4Irmp/jbNbDdgkOPMQZ5NQ7Qv5/P3bIkuHG7Ezp1TceToT3v0ugRBEERykGhKIZoWaRwphWW4dNEUAodQKISwYMORIcUAABUc2pTI0n9JjXxv8weSyjQF9DHegCGarM6RzZZpec1rzC0STdHUsdOkqaopmhQ93xOysXve6h4IAKiXbVBszGnKCbRZ5jvUxe53OhCKBMGTbG5pYOSaKqsrO3VhTKfJ095p0stzUaIpegXdULsKhxbpGt5fjO809bNZ9wH0+az9nS4Wr3c/gqHzqKv7c49elyAIgkgOEk0pRFUjgkEOy2amKQQmfo72HwRZd2wAoEkXPVI4hCP7Ik4KHwwkVZ4znKbWILuOpnYimjg9KK6xa3ZWngufPAnV6wWcTsh6q4SgLhymCqwdwPmwClVkIiW7ndM0tAecpmv7XQuRF1EbqMWZ1jMdjjW7gUdlmlRVMsP5guCB0zkwZgXd9W72bHl5twIAsgSgn8Pq0uU4ctDPZhVtPS2aQiFW8pTllh69LkEQBJEcJJpSiFGe4zgRsiTBaThNHHOaqgqKLOObJPZh/cnbb+LN/3kGAGDnOKCdaErksLQvz6mq9dfdXjQJ0EVTkuU5I88kjhtrHgvZmWgapG/a61NUyM4RAJjTZBFNUW0HupNpAgCXzYVxfccB6LhEp2maGQTPz4iU5xQlYH4vCC5wHA+P5xo2d99RDMkcjBK33g4i+xb49RJnnmDt2J7rjDhNmRlj9POZaPrfz/4XD/35IbSELk7shMJ1AABZboUW1RaCIAiCSA0kmlKI4WjwvB2KIsGlf+6FwOMLzob6zBwIigx7iG0L0qyvqKs/exoKr+/txnNQA5HVc6qqQk6waW8gRjS1c5qEdk6T3vxycIg5MmMyXOiIwKe6aBo7zjz2jdEz2LW9rShwMIEh81kAgBx/a/zyXDDUrZYDBhMGTADQcRi8VWo1S4DWLVTYfTnODp5nIi5aNLV69yNbUBFQgZOyG3Uy+z1kwLq6Mdpp6tOXOVJ+/3FISgjPf/o8dl/YjZcPvdzlZ4smHK41v5dl70VdiyAIgug6JJpSiNFugONsUDXVzDTJHIc9OQMAAMNPHoIjyFa7GU6Tt77ObB5p5ziogQBsUUIpUYnOHzYyTex/FaUTp4ljounbje9g16RRmDkgt8PnCXzC8ky2USy8zvM8nLms95Pa2mqujgNYK4XMoN/iNBnvN0oKghp7PkM0VR16CgcP/ltSq8WSCYMbIfBcRy5ctogYjA6BG0SvoKut/RMA4EBAwOcNh3E+xH4nomLduiXbkY1+IpurI/N68LwdqhrCoZodCMjMzfpN1W/M77uDUZ4DAEmiEh1BEESqIdGUQkynibNDg2aW5wDgUB5zP66tqoRdd12MTNP5c9Wm0yTyHLRAABwAO89+fYlEU8DMNEnQNA1yZ6LJ2IuOD+Mqt8PSvFFRgpCkyL5qqt+P0OHD7LwRLLwuiiL4DHZNpbXV3F8OAJzhRvCARTRl2ATk6bkp1cb6HrlFN2S5DefPv4IL1Zshy80AgBZJxo8On8GeFqvDAwAl/Upg42y44LuAc23n4v4szDxTRvweTbYo0eTxsOfx+Y6gtm4rAGC/X8DuC7tRY1TlpGrrDdQQsvUeVUEuF243a5J5pPY9c0hTqAl/OPYHdJdwiJwmgiCIdEKiKYUYoonjRGiaCocKcLqTovACsv2tGHz+BOxh5n40SQoTO61NUHWnidcAVRcedv1YQqdJd6pUDfCFFYTC1hxMjGjShYPKx5b7KitnYcfOr0KWWf+o1m1/AVQVtvx8IDtbv54NfCYLSLd3mhx6Hqf9XI1ck2LrDztvh8iLFkEgSez7N+tbsPF8A54+VRMzN7foxui+rHt3ohJdosaWclRjS4Po8lwoVA2Od+NQUMCJlhOoldl/MkH/Sct1AgH2uk0BvIpkXqO2eT8AYGAGW0248eBGKGr38kihcLTT1NytaxAEQRDdh0RTCjE26+VggwYVAnjYlIhAGXXhFDhVgV0PRTfLMkI+Hzg5bDpN/qAMNWjsHaf3RkpYnot8OHsDEoLJiqZ2IWdFCaG17XMoShsCwXMInfgC1UuWAACyv/UtSHq+ShRFCJm609TWamaWAEAMM7ET7TQBkRV0iq2/WZozhBn7nomm2hC7R0M4fn4rekuVeFT7mDMU2w08tjxnrKAz6N/vaxAF9rpWZu6bP3ASmhZpMeDXRVStzKM52AyPm4mmcIBtXvxvE/8N2Y5snGk9g22nt8WdY0domopwuN58LdEKOoIgiJRDoimFaLrTBD3TxIGDqC/V51UVo2vPsLJbyHCaZLQ2MIdG1UWTLyAh3Mbed3QgmhRVQ1iOfKh7gxKCUuS1qnIxwXBeFw6aYBVXxvYhABBurcXZH/wAqs8H9w03oN8P5lpEE6+LJtXbagoiABD1clas08SElWLrZ7YbiCeaGvRSZYsc36UxRNOe6j1x34/XbgAAFDnSo8kgegUdAAwYcCeK+7CSXaPMQdE4qGoIweB5c4xfd5rqZQ5NoSaz31MW5wPP8bgx/0Z8Z8R3AAAvHXipy529JanJ7CYPALJE5TmCIIhUQ6IphZjlOd1p4jXOdJquqj+PTP17pyGaQiG0NjB3wQiCQ1XR0sxEhcPOREk80eRv58h4AzJC4YhoUhQ7wuGwZYxN3/dNtbUXTRfM7+te+jnCx4/D1r8/Bv73GnCiaK7ea+80RWeaeJldIxC0BqGHdOo0sW1J6vXnaU6wUvD6/teD53icaztnukrRnPfp5bmYTJPhNFlX7RlhcEHIQF6fr2BUHxZ2V8EhyLFn9PtPmOP9frb3XZ3EoznUbIquATYVw3OuQYY9A/eMvAcOwYEDDQeS6mAejdFuwIB6NREEQaQeEk0pRNWiRJOmgQeHnEAbOE3DmPNfwGZjwsgZYsKiWZIiokl3mnhVheTTnSaHvt9bHNEUaFeKaw1KFtEky2JMqczI9bQXTcEop8l3aB8gihj49FrY+rHwtuE02Ww2MwiutrZhgF1Ef7sNLp5HNtfMrtXunoawUm394LIl5zTFc2ky7BmmsInnNlW3dVyes7UTTVnZ1wMABvT/OnjegdF5oyNzsrEtVKJFU0Avz9XJHJqCTXC5hkAFDwcP3NiXCbA8Vx7uGnYXAGDD5xti5tgR0SFwgDJNBEEQ6YBEUwoxnCZoutMEHrceqsQ/VP4VhS0NEG2sXOYKspJRs6TEiKYMAXDo+845nKxFQHynySp8vEEJUpSxpMj2mPMEMUOfnnU7kFAwIpo0J5D/1AK4r7/ePGbJNGXpoqmNicE3xg/H2zcUo3+G7iJJMhQlMrdIea4vWnzsGWWlzXy/vWhSNFi2l4nG3FKlptJyXFIk1AWYUxMrmmLLcwBQWDAL1477HxQXLwQAi2ji7OwaPt1dAgC/nl2qk5nTxPMiWlT2bGOyIq0b7htzHzhweP/s+zjWlHzH8OgQOABItHqOIAgi5ZBoSiGauWEvDw3MaXLKEvJ87APQLhqiibkxTbIayTTp5bkBbhscClM/qq2j8lw70RSQLaJJVsSEokkVraIkGFWes98wGjnf+Y7l/XiZJmgaVJ8PQ1wOFHuc6JfZzxwffd9waxhQVYAT4ZVz2NyinCZDHDREPU9zolxTgn5N1f5qaNDgEBzo4+xjeS9eEBwAeN6Gfv2mmceHZQ+DyLMMmct1FYCI0yRJLZAk1rfJcJqCchCn9aaigx2R7NjQrKEoHVIKAHjp85fiPkc8wiEqzxEEQaSbS0I0PfvssygqKoLT6cSkSZPw0UcfdTj+tddew8iRI+F0OjFu3Di89dZb5nuSJOFHP/oRxo0bB4/Hg8LCQtx33304f/58B1dMDdFOUzzsIhNB7qC+ek4FWkyniZ2TKWiw6au2DtWz68Utz0ntM00SZIvTFFues9l1p8luLX+FghHR5LjpWkv/JgBmpslms4F3OMDpAXW1NSJ+CrMKIXOxmwy/8ckF8GHmLHmVHP161vKcpmmm0wSwnk3xGD9gPGy8Dae8p/BJ3Sfm8eiVczFzT5Bpao8oiLi+P3PXCvqUAIiIJiMEDiEbYY1Dc6gZBxsO4oKukW2yVfA8MPYBAMBbJ95K2FeqPYbT5HQOBkDNLQmCINJB2kXTK6+8gvnz52Px4sXYt28frrvuOpSVlaG2tjbu+J07d+Kee+7B9773PXz88ceYPn06pk+fjgMHDgAA/H4/9u3bh4ULF2Lfvn343e9+h8OHD+Nb3/pWKh8rLkbLAU1jP3au3ft2PdjtCjAxo4JDg5c5LQEbK8XxUqQdwL5qln1KtjynSBGxJiux5Tmbg213otk1S24o6D8beQabNTwOWJ0mAKbbpLRGymwFngJIPBtniDVN0/D7/efAhdkzetUcqKpm6dMky154ZQVS1HwSOU1Z9ix84+pvAAA2HNhgHjf3nPPkx5xjludsnW8UvOqWVfj113+N0fl/D4CtKlQUv5lnsjkGAQCagk3YX7cf1RL7Pfvbbdx7bb9rcVPBTZA1GS989kKn9wUiTpMRMO9Kc8vW1la8+OKL2L17d9LnEARBELGkXTStWbMGDz30EB544AGMHj0a69evh9vtxosvvhh3/NNPP43bb78dTzzxBEaNGoVly5Zh/PjxWLduHQAgOzsb77zzDmbNmoURI0bgpptuwrp161BZWYnTp0/HvWYoFILX67V89QZmywF941y+nWyqPspExgBvX4gKExh1PiaMvHYmaLgwEzoKx6NNbxmQjGhqDUjQlMgGvPGcJsGul9b4KFcMQCgUaSgpq7EduduLJmMFndoa+TnGE02fnm3BiXofBN1ZkoVMnG70x6yea5Csz5Ko7QAAlI8pBwBsO70Np7wsZ5So3QCQePVcPPo4++DaftdCFHMhiiyn5Pd/Ya6cc7mHAgCaQ83YX7sfNXojTJ//WEx4/V+u+xcAwOvHXo+72q89htNkiKauBMF37dqF06dPY9euXUmfQxAEQcSSVtEUDodRWVmJadOmmcd4nse0adMS/h/8rl27LOMBoKysrMMPhJaWFnAch5ycnLjvr1ixAtnZ2ebX4MGDu/4wSRApzzHxwrVbBKbqzoSo8HCFmKBqE5gwahWZEOH0YJJks0NC4o7gMavn/AGoSrTTFJtpsjkizS4ViQkXRQlBUpujrtOM9iR2miLiJ1o0Gffdsp+VprJtTBiqQiYOVXtjynMN7cpxzVJi0TQsZximDpoKDRp++fkvASTeQoU9X/xMU2e43SzX5POfMMtzWbqgaZPasK92H2olDgAPWW61bLYLsE2Gb8y/EbIq438/+99O79ddpykcDmPfvn0A2H8Hfr8/qfMIgiCIWNIqmurr66EoCgYMGGA5PmDAAFRXx//Xd3V1dZfGB4NB/OhHP8I999yDrKysuGMWLFiAlpYW8+vMmTPdeJrO8WQUIz9/BgSlCABi8jUjJ7LyjgYZLl3PBB0u+HkXQiIrz3F6byVZtCPcgWhq7zS1BUJQ1YjTJMv2WKfJ4Qb06p8c8urXtv5cQ+HYD+voTBOAyFYqbVHluYwCyLwMQQijtn4Famq34Y+fMDGTJTKRpIkeVF1ojRFN9WFrh/JE5TkDw236/fHfoyHQYG7WG9dp0vtA2bosmq4GwDqBG93AczNHgufYf1ItoRbwvB0u1xAAgM8Xu1LOcJt+d/R3qPHFbg9joGma6TRl6PviKYoPqiolPMfgk08+sfyea2oS3ycZWkIt+NvZv3W5OSdBEMSVQNrLc72JJEmYNWsWNE3Dc889l3Ccw+FAVlaW5as36Ne3FGNG/xdEaSIAgG8nmvr01++rSXCF2YdSwOlGqy0Dso25ONDLc7LdAUnrSDQxIZOhr9zyB/wW0aTIsU4TJ4rg9ENyML5okpVWtCe2PMeeI9pp6uPsA4VXUFBwFFL4A3x+5FnUt4WQ49HQ7D8IAFCFLByuboUSLZokb2x5LkEQ3OCGATdgXN9xCCkh/ObQb0ynqdBTGDO2K+W5aCKi6YRZnvO4r0KOI8ccMyZvjNkk0+c7Gnee4/uPh6RKHa6kU5Q2qGrQcl+gc7dJ0zR8+OGHAABBX315saJpTeUaPLLtEbx+7PWLug5BEMTlSFpFU9++fSEIQsz/kdfU1CA/Pza0CwD5+flJjTcE06lTp/DOO+/0mhDqDops7EFnxenWP7ijRFPQ4UKbLQOqqO/jposmVXQkVZ4bkMXO84daoGk8DINAVmKdJogieL2CKIeZcDHaDXC6aaQlIZpMp8kbGctzPGwOG/rksVC5198AAJgwsg6KxEpPmujCoWovpHYtB9rvN9eZ08RxnOk2bTq8qcNMk9zN8pxHL881N++BorQB4OByDbWIpuv7Xx+1+W+s08RxnOk2/fbIb1Hnr4sZAwAhvbGlIGTAZsuAILCfb2cr6E6cOIH6+nrY7XZMnMiEeiJHNh6apqGt7TAUJfL3dbCBCdw3T7yZ9HUIgiCuFNIqmux2OyZMmIBt2yIbmKqqim3btmHy5Mlxz5k8ebJlPAC88847lvGGYDp69Cjeffdd5OXl9c4DdBNFFxmcZpVNbg8TTRpkOEOsrUDQ6UabLQPQ2xEYQXDV0bFo8uvuTH42K+sxIcKZblNcp4njwIXZnBRdNBmNLcULnD7n2CB4+/KcYHQFb7MKrGw3j6wsXSCp7APflnkAvNLMjjkEnGz0Wxo3Kkob6vUcl4tnc+goCG5QOqQUgzMHoyXUgpD+oT/AMyBmXKLmlp1hOD7GFjNORwEEwWERTdf1v87cgy6eaAKAmwpuQkm/EoSUUEK3ySjNORz9AQCiyO7RWa8mw2UqKSnBkCGsTJiM06SqEqqrf4+P9nwLH370dVQd+hEAJqJOe9liir01e9EQaOj0WgRBEFcSaS/PzZ8/H7/4xS+wceNGVFVV4eGHH4bP58MDD7BeNvfddx8WLFhgjn/00UexdetWrF69GocOHcKSJUuwd+9ezJ07FwATTP/wD/+AvXv34te//jUURUF1dTWqq6tj9lpLF4mcJrcnwzzu0p2igNOFNsED2JljpElMAGgOF8J6eU6WrV22gWiniYkmo8u2orc7iJdpAgBOD6MrEhtvOE02XTTxXMiysg6I4zRlxbYcAIBBuc3g9PS72+bDoD42fNa0yxRNEDhA0KAqVmFWF2LzvErvHt5RENxA4AXcP/p+83U/Vz/YBSY8jx49ij/84Q8Ih8NR5bmMTq8Zjcs1BBwXKXcawfBcZ6T793X9rjOdpjbf0bg5oGi36bXDr6E+UB8zxgiB2+2sQahoywYASB2IpoaGBhw5cgQAcOONN5pObG1tbczfiqapkOVWBAJncer0/2Lnrq/i84Pz0dbGXKXWVva/jcFG+GX281I1FX8585eE9ycIgrgSid9lMYXMnj0bdXV1WLRoEaqrq1FSUoKtW7eaYe/Tp0+D5yPa7uabb8bLL7+Mn/zkJ3jqqacwfPhwbNmyBWPHjgUAnDt3Dn/4wx8AsH9hR/PXv/4VX/3qV1PyXB0hh4096Kya1XCaAMAVYu5N0OGGZAsDYiTTpAGA0wkp6vxQKAS3O+KWGJkmQzQJYCvUfAE3HJ4WBIOZcDhiHSpe4gEokPWGk0amSTwfkXiy3Aq7PeLeJdNyAAAGeCIuh41XMXlUDbY2tqKvMw+SjUeLrEJ0KwB7QmgaB47TUK//vK52O3DQF0y4aW977rrmLjy7/1k0hZospbm//OUvuHDhAq6+usjMCtmS6NMUDc/b4XQOQkDfPsXlLgIA02kanDkYfV19oSgeABxkuRmS1AC7vW/MtW4uvBnj+o7DZ/Wf4VtbvoWZw2fiOyO/g4EZAwHEOk02kZWaZSlxpmnPHrb/3jXXXIO+fftCVVXY7WyT5oaGBoD7GMeOrkRYatTdNqugs9v7on//r+Ps2V8iGDwPTdNwptW6QOLPJ/+Mu4vvTv6HRhAEcZmTdqcJAObOnYtTp04hFArhww8/xKRJk8z3tm/fjg0bNljG33333Th8+DBCoRAOHDiAr3/96+Z7RUVF0DQt7telIJiAiNPUHrfHA+gC0aWvGDMyTZze+JJXVcgCD87phAYeGhe/RGesnuub4QDPAaIeVtp3aCyu+QiQJGd8p0nvLaTIPv26zGkSGjlIYaaxo1e3AXGcpoxYp0lRQsgWrR+6ds9+AMCtQ25Ffzs7V3SxsqSq8pDCTPAZmaZr3Ox1MuU5AHDanLh31L0AWCsCgJWYGhvZlidebyRD1NXyHGANZbtdRQCAvi4mikr6lejXdcHpZKsifb7jca/DcRwWTV6EwZmD0RpuxYbPN+Drv/s6fvjXH2J/7X5zs16HXRdNnThNoVAIH3/8MQCY/y3xPG/+Q+TChXM4enQ5AsHTeh5L0+dhR0bGKIwauQI3T34fw695EgCgqgHIcrMpmgwxt6d6D5qCTcn+uAiCIC570u40fRlJlGlyOBzg7AK0oApniI0JON2QBQ0OGxNHgqIgLPDgXUxAqJwAQVNiRJNRnvPYBWS5RNi5MAA7bKqKjLC1X1I0vGxknphoCupbqAhNQEhyQLTLMau2ErYciFo919y8GzwnIRRyQeNUOO0hHG9iHaqnDZmGT2tFHPWHYHNr+v1FyLIddkcAjbIKgMMwNyvPtSRRnjP4p3H/hMGZgzGpgImHQCBgPndbWwMEG8BxNnCcvdNrhcNh+Hw+5OayEpzHfTUaGv4KIFKemzl8JppDzZgzao55nts1FMHgGQQCp5GbOyn2wgBG9hmJP07/Iz449wF+XfVr7LqwC9tOb8NfTv8F/3sdy+vZHUZ5znCamuNea//+/QiFQsjLy8OwYcPM4/n5+Thz5gxqa98GL5yFKPbB+PEvQxRzYRMyIQiOmGvZ7X0RDtcjGDyPs60sxH9TwU042HAQVY1V+OuZv+Lbw7/d6c+OIAjiSuCScJq+bCjGkvl2okkURfD6pr3OABMmQYcLPpsbvKBnilQZkiDA5nIBAGQufldww2ly2QVkOUWIHBNKdoThBBsrSVJMvoXXu4Yrko81ttQ3ohWaOQRkPR/VidNkthyICoLX1bP8S2PDIEgyEyhhqRmZ9kxMzJ+IAQ52LsduAVmxQ5bt0AA06j+uYXqmqUVWoCbZJ8jG23Dn1XeaDlBTU8QZ8fn0ZxPcMT2z4vHb3/4WTz/9tLnFjyGU2PdFAFg/qp/c9BNclR15z+gUbpTyEiHwAm4ZfAuev+15bLlrC4qyiqBBQ7OfnWc4TUYQXErQcmDvXrZh8Y033mgpbRtOk6z8CQAwaOAcZHiGw2HvG1cwAYDTwdo0BIPncbqVhcAHZQ7C14Z+DQDw51N/7vCZCIIgriRINKWBeEFwh8MBnufNzW6dQfaBHnS6oXICeH3lmKAokGw8BLcumhKsoDNWz7ntNmQ6bRA5XUQhDAeit0hpt4JO7xp+9vQheBv1FV9hgPMBfomVsILtGlx21nJA0zTU178LAGhoHARZYh/Qbl7DVwd9FaIgor+d3ZdzGOF2EbIiIgA3JF1cXq07TSqA1iRLdO2JFk1+P/s+mdKcqqr44gvWj+ncOdbJ3CjPcZxgluDiYTS49Afib+MTj2E5w3BTwU0AAClsDYIb5Tk5TssBSZJQV8fGjxkzxvJefn4+MjPrYLefBc/bMXDQdzudh8MZEU1GeW5w5mBTNH14/kO0hGjz4HQjy204ePAJ1Nf/Nd1TIYgrGhJNacAIgkONHHM4mCDg7YbTxD74gg4nNACc7jQJqoKwIED0sA/6cIIGlwE9B+Q2nCb9Zi4tBAEqRMhxz+N10VRdcxIHd7JAvdAEBFxuBFVmA3n91hyLUZ5rHwRX9I7gbW0HEQpVg+edaGnON0WTh9dQOrQUADDAyDR5mAulKKw85wVzrdwCjxzRBqcuHjvr1ZSIaNEUDDaz+SbR2LKhocEUh8Y1srKuhcczHAP6fxM8LyY8162Lps6cpvaMzhsNAOD13ljtg+DxMk3Nzc0AWDsPj8f6XP3798egQWwlXF7enXDECaW3x2mIppBVNBVlF2F47nDImoy/nqEP6nRz/sJruFD9O3zxxTPpngpBXNGQaEoDhtOkRpXnnE59lZsuPBx+VgLSOB6wceD4iGiSbDzsumgK6S0E2rdTsJTnXDbYdNGUqbFxDr1E1z4Mzqt64Nymoq2VfcgLzRz+UnorcjQ272jRpGmaKSYimSYmmjS/H5oso66e9dXKzr4ZqmqDopf5smwibi68GQDM8pzmZIJKlu1QZDtaddGUp5ctc/R7JBsGb48RAmfPzkRHMk5TdFNIQzQJgguTbvwTxoxZbb7n8/mwdetWtLREBI3LZZTnkneaAGBU3iiInAa77hI6HKy8JnbgNBlzy83NjSk5Kko18voy4WMTbk9qDoZoavOfQaPufg7OZHsz3jb0NgDAO6feSf6hiF6hsfFvAIBA8GyaZ0IQVzYkmtKAEQTX1MimvYbTJDh00SLVQzR6Mok8oIsmXlEgCYIpmgIK+xUmCoJHnCZGpi6WjFxTjNOk6iU2UTXbDWitNvgyMqAobG6+QOTDWo5a/m86TRmRnkdKayvqddHUvx/baNlwmoZnFcJlY2VGozwX0nspsSC4aDpNhmjKFpmz1pUweDTRTpMGJhi7K5qA2P0Dd+3ahd27d2P79u3mMZeLiQxZ9kJKEN6Ox7DsYcjVFwBwvMPsJRXJNHUsmtpz+swGcJyGxsZCNDW5kpqDkWlq03NVuY5cZNqZKDZE087zO9Eaju0UT3TOp59+ivfff/+i9vJTlBCamlgjU0lqNHuPEQTR85BoSgMRpwng9V+BKZr0zt/Q2uAKst5KsPNmZlxQFUgCD0cGK70E1fiiyXCa3KINWS4Ron6BbJWNS+Q0Cbq8EmwqFJV1fA6H3Pq82XuBcOTD2nCZgIho4kQRnB5UDzSdQGvrAQAc+vUvhcxpZhB8aEakPGQ4TW2c7jTpQXAvmKsScZqYiOiJ8pwg6A5ZEuW5CxcumN9Hu1XtMfJE58+fj7qPG3Y9xJ3IbTpV14Ant/4Vh05H2jKIgojR2Wx5v8pnmgLNZqyeixMETySaJKkFFy68BgA4d3YU9hzdg69s+gr2VO9J+CwA4HSy/lZG6wnDZQKAq3OuxrDsYZBVGdvPbO/wOkQs4XAYv//97/GXv/zlojYJb2nZa/YbA4BA8FxPTI8giDiQaEoDptOkAbweB2/vNAGAM8T+xaiJPLSoIHjYJsCVyYRMvK1UVFVDQIqU5zwODja9jJejduw0cZrudIkaNBtzD3yy8SGtr3qLCoIbThPHceamsEDEbapv3A4AyM4qgcPeFzLHQZbZs/azM2F1dM8u7Fj9HwCAAESEYGdOkxLJNOXZ2bWzTdGUXIPLaGRZhtfL5u5yuSDw7BqdOU2aplmcJr/fH7ddAwDU17OO3nV1dRYXLhIGj59r+vHOSmxw5OLf/rIDe/fuNZ2H4iwmtvxaJDMlinqfpk7Kc9GcP78JiuKHaCtCc3MBqmuq0RJqwXOfJN7IGoiU56C0QICGQZnWwPvXilggnEp0XefMmTPm6tVjx+Jvs5MMDY3vW14HA1SiI4jegkRTGpAN0QQuRjTZ7FGiyXCaRN7s12w4TfYMD0SBgxQnCB6McmHcdgF2ewg2lTk1uYIAiB5zBV2s06QH0m0qRLeeYUIfNm+9PBfdcqD9yjkDXt8gudG3EwDQty8LfEsQzfKcprJeUPu3/hF1B/bDobHcVTNyIcvMaWrVnaa++vWN8lwyW6kArHRx/sJvEQrVoqWlBZqmQRRF5OfnQxB00WTr2GlqbW2F3+8Hx3Hm7ynasYrcSzGPq6pqtiYAosPgsU5TfX09vgiy30eT04M33ngDf/jDHyBJEga72PM3yZFVA8bqOVUNQFWt4s24/5+PtZnCS1UlnDn7SwDAwIHlADjYA3bwGo891XtwuPFwwmcXxTzwvB0cgGxBszhNQKREt+PcDgTkQMLrXOl88MEHeO2112JaeHTEyZMnze8vRjQ1NrA8E8+zv80gOU0E0WuQaEoDptMEgOtANLminCZVL8/xKss0cU4nPA4bwnGcJqM0BwAuUYBNDEDUnQqPwwHYPWZ5LibTZDpNKsQMfbWYjZXRjPKcqnYumoSMDEgFKlrkzwBERFNYdZiOlZHvaa6pBgcgV2XXakYu5Har5/L0zFNuF4PgtbVvoKrqRzh+YrXFhcnMzDTLc52tnjNKc/369UPfvuxnEa9E19zcDFWNiJtod8rVgWj68MMP4XMw182RXwCO4/Dxxx/jxRdfRK7+93E+GNmPz2bLhNGwQoraSkXTNPMZX/2sCcdq26BpKg4d+jFCoWrY7X1RVHQ3bA4bePDIDLNs0m8O/SbhszOhyNymXFusaLom5xrkOfMQVsM40nQk4XWuZHw+H7Zt24bPP/8cp08nH/Y3WlgArJzr88Vuht0ZoVAN2nyHAXDo34+F+0k0EUTvQaIpDRiZJuY0sV+BsXpOdESaDEY7TYZoYuU5HrzLBY/dBkmLzTQZIXCnyIPnOWhcm+k0OZwuwO6BM4HTpIEJGsGhQHSx63g53WmSjbxV5P/c27cbMOCyPGi+T4HGKejbtxQZGcVQVA0BRYCkO02y1AJFltCql7SywuwZmpELRWYlukimyVqeS1Y0BfUwe8B/yhQ6EdGUXHnOED/5+flm2Sue09TQ0GB5HZ2DMlfQ+a3luUAggP3798NnZ79/v9OD7373u3C73bhw4QJqTjAhUhsKoc7P8lIcx0flmiIlOp/PB0mSoGlAm2bHuWY/Dh3+CS5UbwbHCRg54j8gCE5oGXrpz1YMAHjzxJsd9loySnS5goYhWUMs73Ech1F5owAAVQ1VCa9xJXPo0CHT1Wv/N5CIUCiEc+fOweFoQ79+7L/BEydOdPneDfqquczMscjMZPtv0go6gug9SDSlAcNpUhGbabLZo0ST3mtJE3mzpZPhNPFOJzIctriZJjMErrszGlpNcWZ3eQB7RkKnSdbYOfYM/d4Kb2aQZIUJIxsie8q1bzdg0Hx9DaShGgTViZEjlgEA2oIywhAiTpPcjJbaWmh6WS5Ld9aakAtZFhFWXDEtB7panjPC0qFwrcVpysrKAq+LJlsPiSYjz2Rku5Jxmj7++GOEJQk+J3OaLoQkXH311fh//+//ISMjAxzPXD2vwqGqMSJKjLYDYakZp72nLS6TD3ao4NBW+584f/4VADxGj16Nfv1Y/qjexuY5wT0BxbnFCCpBvH709YTPb7ezVgc5ccpzQKSfVPT8vkwcPHjQ/N74G+iMU6eOYciQj3HDxN9jxMjNsNv93SrRGaW5vD5/B6eLLRogp4kgeg8STWlAic40aVbRJFZH/k/XFWL/etVEHrIeahIUlmmC3QGPQ0ggmpgYcOkCI3q7DbsrA3BkJHSaVNW6B5sUcALgoKkaFF3s2LhIdiVeea6t7TDqi1lOpvDCV83+Qi0BCZImmCJMVUNorD5pnufxM4HAynN2eOVMszzXV3+WnC4GwWW9fBUO15miok+fPt0qzxUUFKBPH+a6deQ0FRczB6e6utos17n1rVRC4RooSlB/fhUfffQRgqIdKsf+UwyoKryygpycHBQUFMBhZ0LSq3IWJ8docPnHI5tw5+t34o0Tb5hzatPsmFW8BS5pCwAOo0dVIH/ANwEAPsmHL1RWFhJ9Iu4dyTY03nR4ExQ1vhAN8yzU30/kkefMi3l/dB9dNF0BTtORo/+BXbunIZBkmNrn81kcomREU1PThzh95p8wZOhn4HkVHKciK6sOx48f71LrAU1T0Ni0AwDQJ28qXHpX+mTnzsYGsGXLFmzZsgV//etf8fHHH+PEiRPmggmCIKyQaEoDslGe07iYTJP98ElznMvoVynykPUouKAqAMdBgsYyTXGC4NE9mgAgLOnbmUAC78ruMNOkqILldSjIHJBgiDcdIqfgR2tjAzY89gj2vf0mm6Jo5J0kHKz6N4BX4fiUQ9a5iDPREpAQhgBFsUHTy4rNNZEPHHdrMzuGXIQkO+pCbtNpyhHYD8MszyXtNLFnVxQ/mptrAHStPBcIBMwu29FOU7xMU7RoEkURkiSZ42y2HD2LFHGbjhw5gubmZshZOZbrXNA3VM7NzYXdzgRqSwKn6aPz2wEAfzn9F1M0XT1kP8qKWJfukSN/ioKCyIa6H9d+jEaRzamxrhF3XHUHsuxZONd2Du+fta7CMvDqpd18hz3uHn1Gee5o81GElXDM+wBQ56/DtlPbLqofUW+jaRouXNgMv/8LHDm6NKlzjNKc4bR2VJ6TZR+qqhZg38f3guNqEQq5YNNLpNnZTWhra0NNTU3S821t/RyS1ARByEB2Vom5lY8kNZjCvDMqKyuxf/9+7N+/H++99x5+//vf45e//CX++7//u0v5LIL4skCiKQ0o4YjT5NT7ImVlZUGuq4N29Lg5ziUxgcCcJvZhI+rOTliVkensrDynvyezDBLPSZAdWXqmKX6fJlm1ltkCEnMZmkJ2yHoQXOBVHK7cgYazp3Hy04/1Y+xP6fTpX6C19QAExYmcl21Q2yKlvJaApIs8DprGhIq3MfJ/zM5m9oHTjFwEZRfaOA8kjgm1bN3dytXLdMn2aYruZeT3s95J7UUT34FoMkps2dnZcLlcpmhqaWmJWSlluAz9+vUzN8c1XCqO42JKdLt37wYA9B9l3SOuOsR+xzk5mRDt7PfkVTgcajxkjrHpbQc0hf18P679WBdNKq4dynovfdRwPwYWzrZce2/1XrTaW6FxGoLBICS/hJnDZwIAXj70ctyfQb3E3LJcW9y3UeApQLYjG7Iq42jz0bhjluxagh9u/2HCe6SC8+d/i8bGHQnfl6RG8++lvn4b6urYfolerzdhiwmjNDdhwgQAbDFAdO+yaE6eeg7nL7wKALhwoRiVe7+FQQPZ7yevL/tvtCsluoYGJnL75E4Gz4uw2bLMBqjJluiM+40cORITJkzAsGHD4PF4oGlap3MJhxugql1v/UEQlzMkmlKMqihmhkcDh7+TRuGOEbdg4MCBaH59C4TodgFh3fUReUi6aHJI7F/yIVnWg+AR0WSUgvxRPZoAIBhiH6wCF0ZYyNAzTWHzvGjCivWTMSgxd6QZ2VBVm7n1S/VpFlDWdLFUc+wwas59iBP63leDWu+E4OWgtrYTTWDXV1XmYLW1REoJTm+tfq9chFQ3WkUWjrZrIYgac4y6GgSPbo/AcSzsnJOTg4yMDLM8J0tC3HOBiGgqKGBNHpnYEqCqqqWEEQqF0KYLxLy8POTn51vOB6zbqVRXV+PkyZPgOA7ZRVdb7nlBF03nPmUiT9N4+FXgXNs5M7BtOE0u/b/ghmADztVegMPpgyjIkFQB752dGvM8e2r2QOVUuLJd5vxmj5wNnuOx+8JuHG8+HnPOWX1BggfBuE4Rx3EY1SdxGDz0/9l77zA7zvL8/zPl9La972rVi1UtybLcuzEumAA2zWBTQvgCKQS+JHxDSUgjgYQaejVgOsbYxrg3yVaxei/bez29zJny++OdmXPO7kqWwRYmPz/XpWu1e+ZMn3nv937u536MAtuGhWP1N/d/k7wugHr3RIa+yZJ79djYGJ/73OfYvXv3rHX8oZFI7OHwkY+w/8AHTsl2ZXM9Fb8fO/5PTE2P8IUvfIFvfvObs8BQeWruvPPOw+fzYVnWKc1PE4ldAMSi7+HE8U1UVTXT0HAeAD7fCPD8QKU8HBF4Ta24zpIkEfA7uqbnT9Hl83mXTbrmmmu48cYbue2227j00kuBSoPWmTE1tYWnnj6Pnp4vnfH+vhIvn+jt7eXBBx+s8JI7k8hkMgwMDLysGeOXOl4BTWc5jLIXr4VElRViWd0CsCziP/85SlnJeqBo64u8JdAUsL+fz+cIlQnBoaQvKjXrFQAlY5ereyiSs0HTKZkmy8LUSykYrRAkmE6TCVYDkms7MD0mBouWZaJiR8uk2frA32BZRerqrqROvRAAM1UCFo6mCcAwRDoymy6lI0L5EtNkSH6yqt2jjoSrTaqytU1J3cA4gwe3Qs/lzRGNRlFV1f4ngNcpSASgUgQOIMvynCk6Jy0TDAYJBAIuyKqsoCsxTdu2CRCxfPly4nIlUB0pFLEsi/iI7ciuBWgNiTSnk6LL2enNoGzRGhYD5cTUJMGAON6xbD1DiRku8cUshyYEM9LWIlI5fX19tIZbubRNDJRz2Q90Z+IAKBQrQGh5nK6Cbt/4PgqG2JeJ3AQ/P/ZzxlMFbvjCU9zwxadIZMV9u2/fPuLxuMvAiWOfYnDwLk6c+A/2H/gA23fczJNPbTwt+JkrxieE+aauJ1x384mJCX7605+61zibFVqvWHQdPl8z+fwgRw7/F7quMz4+zpNPVqYvndRcU1MTtbW11NYKvdepUnSZzHF7u1UAzJ8/n1BoMbLsBbL4/Sn6+vpOyWqVh66nSCYFuKytudj9uz9g65rOgGnq7u7GNE1qampcrR5AS4uolhwaGjrlOR4bfwCAqemtz7udV+LlFel0mrvuuoutW7eyf//+F/TdX/ziF3zzm9+c9Sz8/yleAU1nORw9EwjQBIBpkd2+g2JfX0X1XNAxgVQlDKdHXcFmiDJpwj4VAwnL1pk4L9vyZr0A2byYzXvRyMjh02qaNNPALJZui0IhSCSZwAxXIUmSq2vKJ8QstHbefLFfgQCSVwyoIc8FKGGhRTJmME0Fm2kq2oCwkCsNMDFdaHJSUhRD9ZGzz0WUpJs2cZgmCwGcni/0GaCpfHBQVQEuczlz1veccECPA5qAOSvonIHS8XEqZ5qcgccBTal0l/uyOv/8811myW+7vg8XiuRSRTyyALtawc/ymAAlRyZFiu5IXDAEHaFarp53NbIlY+aLBGzQNJJpIJnXyRRKM8k9Y3vQLZ2WUAtrV6wF4PDhw1iWxZuXC0H4PSfvIVnm+A7QkxoibZ/qfGFu9sEVg89RQeewTDGfYMe+feDb/Oy5k2Q0g2Re52fPiRYizrkeHR11PYsOH/k7jhz9B3r7vsbY2P2kUvspFqcYG7ufdPrMhedO/0OATFYA/vvvv59Dhw7x1FOCsclmewAIR1awZMnHxN9ydxMICHZvy5YtFczhwYMHATjnHJFeda79XGJwTZugWJwCJHp6xERl/vz5yLKHcFicu6amPKZpVpheniqmp5/BsgwCgU63tyGA33/mFXTHjwsQt3jx4oq/NzY2Issy2Wz2lILwREIAtlfcx//04sEHH3Qny729c3comCuKxaJ7bz722GNs3fr/T8D8Cmg6y1FimiQXNFmmRfxnoi9YdPNmd9mgbmttysS3fodNSqcJ+VSxHlmwPzNBU9BTqXfyo5EiVOHTpGlahSGjZhoVTFOhEMKXTqOGw/j9freCztLjAHhDovJs6XkXEKgW3xs82IcSFWk9M1ViJhK5Ijnb0qBQED9lj4asKARjVYRJo1ji+IqBEDmPAE0Rki7D4ZVlAnZK8PlSdJZlVTAjXm+uor2IbLdRyWbnBk3FYtEdAB3mCOYGTc5yDtvQ0NCAJEkVA0/QTs8lkyfQdZ3m5mba29tdDdNquzXOSKFIejqPJyD2XdMCLPQsBODQ1CEM02DnuGCM5oXqWVu/lqAeRELCZ39numCDtmSJSdw5uhOADU0bWLx4MYqiMDU1xdjYGJuaNrGoahE5Pccvj/3S/Y5pmQykBpg2bGCenxs0OUzT0amjFM3KNJYDmj6w9gM0h5oZz41z58Gfup/f+WwvhmFWsHLOyzmTFgN7Y8MNLF70/1i96qvU1gpWbGTk7jn3ZWZksz0uywOQzZygr6/PTa319QnLhpwNmoLB+dTXXUNt7aVIksHCRdsJh0OYpslvfvMbTNMkk8m45pQrVgjQ44CmuZimdFqks32+NkZGBEPZ2dkJQDSyCoDmZvFMnkmKzknN1dZeXPF3FzQ9D5gp1ywtWrSo4jOPx0N9fT0wd4pO19Ok06I6VlSDPj8z9kq8PKK7u5t9+/a5v78Q0DQ0NIRpmm4xyIMPPsiOHafvXfm/MV4BTWc5jKJTXaQgKeL0m9kcqQcfBKD6WuHqiwWKFUSdkXP220xTPp0k7BOgyJQcICJeXjOr55y/By2NlBWs8Gkq/xygaBiYeiXTRL5AyK8SDAZdrybFaxCuqXWBnz8YQLXL/aZ6p5EjAjQZM0BT3gFNebFvis8gWt9AMFaF4jWpIg6AFghSsN3RoyQqGKPqM/RqMs0CllUawMtBk2WZyLLY30xm7rz++Pg4pmkSCASI2m1hgDltB5yB0gFN5QOPAwYcpsk0xwGTDRs2IEkSQ/Y1XWeDpuFCkdRkHtUvGA5NC9AoC2H5kakjbB3aykhenNcqj5c1DWsIFQV49dqgqYAYPIfjJdDkNOfd0LgBn8/HwoUCiB0+fBhJknjr8rcCQhCu2wLfsewYmqkRN2x93ClAU3uknZAnhGZqdCdKTteZYoYDEwcAuKjtIt69+t0AJH0P4vcaRPwqvZNZHtrXQzZb0jd1d3djWZZrTrpw4Yfo6HgH9fVX09ryJgBGRn+DZc19Dxw7dowHHniAQqHAxMSjFZ9lsicr0gupVIpEIkE2J/Y7GOhEkiTmd34U05Sprh7h1dc34vP5GBwcZMeOHbNSc1C69nMxTSXQJsB3Q0MDIXvCEYmKFHcwJMxLnw80FbQJJsYFc1ZbU6lbc20HnodpGhsbI5lMoqqqC97KozxFNzOSyb1AaaLxii/Un0bous69994LwKpVAqhPT0+TSs2dcp8Zjv5t2bJlXHTRRQDcd9997N279yXY25dvvAKaznI4feeQFBSvOP3ayS6sYhHfiuU0XnQRAdVDLK8gSTJ+rXJQcDVNLtMEhlQJjkrpORXd1DFscBGyNOJWAHxhVExUyaz4HgiBuWGn5wxDeCoZxQJhn0ogEHDTc4rXpK59Xpm5ZREk8f+RYyPI9oBQzjQl80UKdrWgZqfnFL9BVWMzgUgUxWsQc0BTMIhm2xhEytJzcOZi8PLvQCVoMoyS11Q6PXe1U3lqrrzU/nSaJmfghBI75aR0fL4mJDxIkkkkUmTlSjFYOkzTumgZaJqqBE1hXVRF9SR6+MHhH5CzLeINI0VdoI42RQyWoaDt7K0KVms4IY4zW8xyYFKAlw1NGwChp4JSBdj1C66n2lfNcGaYR/rEoNyfEqmzoixA8KlAkyzJrhj80GTJ7PG50efQLZ3WcCut4VZuXngzfqkW2ZNi5bLD3LJBpJZ+vfVgxfq6u7spFqewLM0+dw3uZ7W1l6KqVWjaGNPTzzIzTNPknnvu4dlnn+W+++5jfEJUwTmO2VNThzhx4gSSJFFVVQVAb2+Pm54LBjsBiMc99PeJ70xOfoUrr7wAgEceeYSdOwVr56TmoDI9N1ML5ICmTFpsb/78+e5n0chqAAy9C1kWA9mpdVFd7Nz5egraKF5vA9XV51d87j9DIbgDzDo7O2e5+cPpQZOTmnMin++fcxu6rvP973+fH//4x6fVaZmmeUY6rlfiD4stW7YwOTlJOBzm1a9+tVvhe6bWEv394jp3dHRw5ZVXsmnTJgDuvvvuCoPX/+3xCmg6y1FKz6koDhNk2wxUvf71eP0B/mz9xSwftYGPVnr5Klj4bOYpn065oGmm7UCu6AjBFRKFhNtCJUKBKd0PXgFofJK9rjIxuKZrrqZJ04JIxSKaBCGfYJocIbjiNaht63CrL1RVgCM9r5CNp8g6XlSahqmJgS+ZK2IgI6ulpr2qzyDmgCafSRWCvSkGAui2vUCUREWPNQc0jR05yvAnPolRZmtQHqcHTXZfP0simZy70ezMyjknytNzlmVhWdYsTROUdE0l2wEZXa8CYPnyOnw+H2ndIGUI8OqApomiztRUDjVQAk2FVIGGQAMWFluHtpI1nd5zYpkmqRVZLhLyCy1QINApjiEhru3e8b3opk5TqIm2sABYS5cuRZZlxsbGmJycxK/6uWXpLQDceehOoASaFI84rlNpmmBuMfj24e0AnN8sBndNl8iOXib2Tfott25sQpJgaGjY3SdJkpicnGRySjwXommw7Uqv6/z853dTyNuAc+TXs/ajv7/frWQ8dGgH8bhg2ObNew8AaTvlt2bNGpYtWya+M3AA08wjSarrdzQwMEB//0p0vRZNGyMafZT29nY0TXOvqZOagxIDWSgUZvWRS9ugaXRU3Lvl7E4otBBZDmCYWRYsEM/mXGxTIrGL53bdQj7fTyDQwfpzfzTLYyxgC8E1bfy0abNT6ZmccEDT8PDwLACYSO6q+P1UZppHjx6lq6uLI0eOcOedd5LLzX7O4vE43/rWt/j0pz/NPffc43qivRIvbkxOTrrs6rXXXksgEGDePDGxOpMUnWmaLmhqb29HkiSuvfZa1q1bh2VZ3HPPPS+oWfWfcrwCms5yOH3nkBQ8dnrNSKaQ/H5iNwrXZk91DV67Y3yoUHpheSzw2N3uc+kUYRs0zTS4LPdpihfiqHZKzI/GyKP38Y0v/AzNUPDbzFD5LE8rFt30XKEQRM5n0TyyC5p0w+lNV8k0yYoAKJZmD/xjI64Wy2GbEjmxrNdfxlj5DKoamwhEIihewwVNms+H7nVAU5JCoZQKcyroBh59nPhPfkLqgQfmPNcl0CT2w1MBmjL2T5VUam7QNbNyzglnHYVCgVwuRyqVQtM0JEmq0EzNZJrS6TSJpBj8O+eLwdERgUcUmQ6/F699zgaTBZQypml6eprO6BJ33R1Vy+xjjAPgK0QI2Kk5Va2iNmr7RNmaJlfP1LjBZc2CwaA7eB8+LIDOG5e9EY/sYe/4XvaN73NBU6mU/TSgybEdmDpMsVjEMAy2jwjQdF6TKK2/b/8wmcl1yEY1CW2SHVO/5bIl9dTKAsTOnz/fPW/9/UJ74feXzv+xY8c4dOgQBw6I8zc2/rsK1rD8WAKBANU1g4CJ37+Q2hqhhVKUDB6PxsUXX0xHh0iZTkwctL/TjmxrBAcHB7EshYD/XeL3oR9y5ZULkG1NXXlqDkRK1mGuylN0lmWRyQhN0+io+G45aJIkhUhEMFbt7eL5Pnmy0vphfPxBdu1+K8XiNNHIajas/xnB4HxmhqpWuUCqcAqAW241MFPP5ERDQ4MrBk8kSn0JLcskkdgDQCwmvKlyp2Cayq0jBgYG+N73vlcBJru6uvj617/O4OAgpmmya9cuvvCFL3DvvfdWbPPlHCdPnnzZu6dblsV9992HYRgsWLDAZbide/9MmKbJyUlyuRyqqrrPpyzL3HDDDfj9fvL5fIUm8X9zvAKaznI4TJOEgmKDJiSZ6KtehWLrgJSqKlRdDCLBQiktpFoGXhvNlzNNBbOyaW959Vy8EMdjikHA0C2sviMk40nGCyHXq6mcaSpoBVcIXiiEUPJZTAXCXmVGes6gtr2jBJpk8eJQZDHbHuvtclN0hv1ScUBTIBCkqJeYplJ6rsQ0FbxeLJuJi5CkoMXdfYzZ7svTWTFYFk7O3ejUsRvwesRD7vFo+HxO6jFr/1TnzOmbpnlK0OTxeIjY1+pff7WDu54UA25VVVVFDz7ne4lEgmw2y549e8hlw/Y6xHE6qbkmnwdJkmj02QN2VkMNiGPWtCBTU1N4jDZ33esbrrP3UxPuz1nFrZwLBjtpjgm7Bodp2jkiQNPGpo0VxzIzRVcXqOO6+WLddx660wVNVSHhJZXJ9PPwww/PmU5xetANDw3zb//2b/zzP/8zHXs7uGj4IjL7MuzYsYOfbu8FVC6qE6aO397/bd66uZ1au1Kwuq7BTV2Njzni6RLTt2uXYDmSyXosqxbDSFdUxlmW5YKmG2+8kfZ2kUIdGqoHfBiGqOBbubKO2tpa2ttFejCfF7Nth6EDMdADtLdfTVPTawGL0bHPcNllQny9YcOGWedgLjG4po3ZAF4mm43R3NxMIBCo+F40KjQm4cikvb8lwDM6dj/79r8P0yxQV3sF5577Q7zeOuYKSZLcFN2pGKByq4Fy0FceHo+HhoaGWfuSzXaj6wlk2e/2MpxLdJ5IJFy27NZbbyUUCjEyMsJ3v/tdUqkUTz/9NHfeeSfZbJbm5mZuvfVW5s+fj2ma7Ny5ky984Qs88sgjFUUqL7fo7e3lzjvv5Pvf//7Lej8PHz5MV1cXiqJw/fXXu5MmBzSNjo7Osp6ZGQ6wam1tdXtrguiz6UwAnMKI/+3xCmg6y1GuafL4xc0nyQrRG29wl1FiMVSbaXJbqQCWXsBjp3Ly6ZQrBM/NAE3lQvB4Pu6m58ZzJSo/q3tcr6YKpknTMLVKpgnJIkixIj0ne01q20qgSZLiAPgDgtYf7T7pisEdV3AHNIVCIfTiTKZJaJqqbU1TzqNi2ZqvKEmKWmnm6TBNCZuE007xsOp6iiFa+bDxUZ4xhW9UsSjEtiXQ5CGTycyilqempigWi6iq6g6ExcFB0k88gWVZLqO05WAv9+4QqY7y1ByA3+93lxseHua5554jn69spTJkg6YWnzgfzTZoGtVzeOz0XD4fEq7UKQHCLNPDxPg6JFvLVizGsXIFAkG7z55SQ5MNmoYTefJ6nv0TwuJgQ2PlQO+kp4aGhtzUyNtWvA2Ah3ofYu+4EHk22JYHxeI4Tz/9JM8888ys890Z7cSv+GmdbsU0TSzLIqyHacw3cnDPQe677z7igyeRJfj7S95GzBdjLDeG39dNyGY9t4+YLmhKJAWQ8flK4LOUtpIYHe0EKlN0w8PDJBIJPB4PCxZ0EImI89zXW8XPf/5zksmgfdwCPEUiEaqrq8sAp9h2MpkkmUwiSRItLS0sXvRRPJ5q0ukjzJt3nA9/+MOuC3h5zCUGd1JzhlGLZSlzCq+dCjrDEAxTOp0mk8lgWQYnTnwaMGlufgOrVn3ltG1/ADe9eCpd0/Ol5pyYS9fkGHRGI6sIBsS5motp2rNnDyAYteXLl3P77bcTiUQYHx/nC1/4Ag8//DCWZbF27Vre8Y53sHz5ct7+9rdz++23M2/ePAzD4KmnnuJXv/oVhmFQKIxy+PDfu15ac4Wu6/zud7+rqA57KcNhAycmJlyg/nIL0zR57DHRUunCCy+sAMnRaJTq6mosy3JTb6eK8tTczHCe11dA0yvxkkRJ06SgektMk6+MJleqYihGAck08Jdpmiy9gEd3mKaSEDznlIO7TJPTsFdlujDtpufGsn53XRnDi88UwMyZZeiahmHoTB6rZnqqmbHRBfjTgoUJFOIVTJPlk1C9flfTZFmCOYlWiQdorPuky5yZqRSmaZG0QVMkHHab9ip+g5gNmuQypimjKGCfnygJimXWAU7T3nRQMFmnA03PsYEeq5lHucY+R8J13EnPmYZqp08qNSgOy+R41gAMfPCD9L/nL8gfOOCCobBUwG+va65Zu8M2bdmyhenpaXRdMHEOaCpnmsp/xv0CaBpFP7pmu6ePNKNNbyQ/cjO/2R1HUURFXyo1imzp7sA/rstlTFOOx/sfp2gWaQg20B6pfOlFIhF3xnnkiPCAWlqzlPOazsOwDEYydhsZsx3TlJEkC68vx759+2ZpXRRZYVnVMlozgumQ18k80fQE6irVbWLcIU9z+dIG2qoiXNwqGJstR54GIGH6+MGOIdrb28U5twRL5LdBkzMQt7e3EwgEGOgX25mcehJNE8s6g9fixYvJZHZjmhlkuZpUqo4jR46QzQqwJMslU9WOjo5ZoGlwUFSE1dfX4/P58HprWLTo7wDo6v48sjw9Zx++ubyaHBF4Mhl2921mRGzQlMkcpqpKXNfx8XHGxh8knx/A46lm6ZJPIM8wQnXCsRBIp9NuBd1cVW2nsxqYGacDTbHYOtcfaiajZZqmm5pbt24dIM7jHXfcQSwWo1gsIssy119/Pa95zWsqhOidnZ3cfvvt3HzzzciyzP79+/nxj39Md883GBr+Kd2ncSDftm0bzzzzDL/97W/PimN1eVrr6aefflm6ZB86dIjx8XF8Ph+by+xsnDjTFF25CHxmOKCpr6/vBTuM/ynGK6DpLEdJ06Si2OkxFBXVLk8HkZ6TAFXPEizTNCmmjtdhmjJpgh4bLJlza5pCPlvTZDNN2UKJVs3qHnxWtuJ7+YwYqFPTNRw4cBVWOkIoKwCBL5+osBzALxHPFV2mybIHuOqGJSBJpKcm0cJOei5FWtMx7UOpioZLaT6PheKR8M9Iz41ZgCKOL0oSwyiBJkcInnJA08AAlja7UaxeTJJAgJtRxMBb0ATTpNtAB0mAi5kpOucl4QwcRjJJfp9ga7S+Pqps0BSRCkQlATrnAk1O/t/xBJo/X6THcjnhDeTYDTgMk/MzExbn1cg1ohiCWRibTFAYeR1yZiMjyTw64vhHJ8QLz28zTcczSZqjAmhN51N8esd/APDaRa+du+GunaIrny3ftuI29//BYpDHf/2EsJ8AQsE8U1NTc1ZWLTGW4LE8SH6JHcYOJgITXLDxAi6+ROiJmuUkr1snzsll7ZcBcKxXpOEShDk6muK/Hu3CCtbg9Yn787vbssQzmjsQb9y4kZUrV5LLxTD0VixLZ2zsfizLctOMy5cvd9N2TU3XcN55otLHAU2OwSU4IExcf8dLy0nNtbWVUqLNTa+jqmoTppnn6LGPzzlIzuUKnrE9mlJJ4XXmCHDLIxjsRFHCmGYB+5ZjbGyM/r5vAdDa+mYUJTDre04cOXKEH/zgB/zoRz/C5xcrmMt24PmsBsqj3NXeOdaE7UIei53rMlq6Hq/wQ+vt7SUej+Pz+dx7C4RQ/h3veAcXXngh73znO9m4ceOc96MkSaxdu5Y3vvGNqKrK8ePHOXFC2EakUgdnLQ+ivYcjdM7lchX2FS9FGIbhAmtJkhgeHp6lQ/tjh2maPP744wBs3rx5VkoYzgw0ZTIZ934ufx6cqK+vF9kDXXefm//N8QpoOstRoWkqigdbDoaQ5NKlUGLixe7RswS0Uq7ca5h4nDSSZeHRxYBbZEZ6rlhKz03np11NE2V596zundVKpeCwLV7xcNXksgRt1krJJggEAq65peS1mEwXXNBkmgI0BcPt1DQLBiDpF9s10ym3VYZXlYlGBGhyxpxiMemm51ymyf5MNg185DHNkli7yq6qS4XC9kk10Oagl3U9SZwqAKbkGoqoaA7TZGvGZEkc60zQVAI5YhaV3bULZ4eNqWmSpu0hJReInQY0zdRDrV17FSBhGFm04iQjdvNmFzR5Pfax2SdAb0IxBLALmDkifpVb7TL96Zz4e99IH2ARtAf+56YGiPgVAh4FX8NvmciNMy86z/VImhnOwNbb2+tWnV3SdgnzovPw634uG72MdCqNZYpz2Tlf3J9zpUEiU4JdHI4M05PqQZZkNjRt4HBCIWN58Egm833iPruw5UJUWQX71Le0ikH6a090sTvuxWeDpmd6ZH72+HMVA/GaNWsA6B8Q99rIyN2Mj48zOTmJoigsWrTItRqor7uKq6++mnPPPZcVK64AIJspDXDt7S34/WInfD4BaJwBsXyQkCSJZUv/GUnyMjn5BOPjD846fodpEqyieHac9FwmU8WSJUsqNCGldcuuGLy2VuzL+PizJJK7kSQvba23zfpOeTjXYmhoiPi046k1ewB7PquB8nBY1lwuZzciTrqsWSy2DlUN4fE4zGlpW47ubOXKlXhtrzUnYrEYV199Na2trafdNsCSJUt429veht/vQ1UF45nJdAkN34x44oknKmQGp7JseLFiZGSEYrGI3+/nvPNEkYPjLP9yiYMHDzIxMYHf7+f888+fcxkHwA8MDMzJEllWqWquvr6eYLAyNVwojLJ33ztZueoJaut6Odl17EU+ipdfvAKaznKUp+ekvGAGZJsxcUKxjRRVPVuRnovIHmQLLNtYrpBNE/QqsywHXCG4R62onpNMg+mAEHdmDc+sVioO02T5xf5UJ5IEbNBEekowTTZoUr0GE2nNfdAMQ6Qj/L5mGuYL08S4aouuU2lXzxQLeGxTP8nVNRX1uCsEjxF3wQmAV9NE7ZuVdWe7M5kmgELXbDG4bqRI2KDJkmTGaHSZJic9J9v6kHLQlEwmGR8Xyzmz8ZztywNgTE9zYEKc45iUIyyJ8zdT0wSVdgXt7e00N7fjt4XNuVyvWz3XPCM9l/TbjulWC4ohgF1EKnBOS5Q3bBAD+VBSLDsxPYLHk8ejapgWHE1NM5odpa52EG+1cOP+xOZP4FNKLXrKo6qqymXUnBSdVtB4Teg1XDxyMYFigOrqato71gLQ0iLA2oEDByq0YJqmkRoU5/GgRzACK2pWEPVG+fXeIfqNKgBOHBcv1rA3zMbGjVQVxN9fs/kcXnVOE9evbmbdisUuaJouxOg7Jta3evVqPB4Pra2t1NbWMjLSDsgkkrs5dOgJABYsWICud1MoDCPLfqqrL8Dj8bD5qs2sXHeVOPf5fnfwDYUKyLKFYShMT1uYpumCppmDeyi0gI6Od4jzP/yzWecyEong9XqxLMu1pHCARjZb5WrI5gpHDB4I2MDeFFWhTU2vweerP+X3CoWCq1MC2LdP7Hs+N5tpOnHiAIqinVbPVCwmmJ7ejqIorpfP0NAQyeQesX/+DleIXkoFioE1l8u5jKWTmvtDoqOjg7e85Xo8HgcQGUxMVpopjo+Pu87U4bCYSL3UoMlhZtrb27nggguQZZne3t7n1QadrTBNkyeeEM/D5s2b8fv9cy5XW1srtKqGMYs5nph4jCeeXEP/wCdQFG2WnimTOcnO597A5OQTeL2HWbHiSQzjgxw79ilSqZenxuvFiFdA01kO3UkjSQpyWgh9ZX8lepc8HuRwGLWYJVgGmvx2k1ZLEgNVKjElmvbOsBzIzbAc8BgOaNI5FBUVThnDPwfTJEBTMShePDWjo66ZppGcsjVNYqD2ejQmM4JpkiQDwxDH4vM10uiAJttV2kylSOZngiZc0KQXEwQiEWSfiYJJUC/NJBXH9VsyXfF2dRlokuyZrNbdM/tcF0tME8AwLSWmyV6Xqop9KS8bdgSNLS0t7swqu6MEmvTpaZ7otYX6ko4sgaSobkVdeUQiEfdF7lRbBYJidpfL9s0CTc7PhM32edU2FF288CJSgVWtMVa1xljaGCFta53yuQlXk5OxvOhIbBvZRq7qxwCcW33trKq5meGwTdu2beMHP/gB//mf/8ng1kGixSjBcJC3ve1tRMKCyg+HCwQCgYpWIiB8eQzdIKNmiHvjAJzXLGbhx0dT9NtM1bFjx1wAfHHjxa5x54qFHXz1tvV8+c3n8pE/W4OiiPvHU1CREgIAnHvuuYBgfdasWUNRC5LPdwJQ0D7FqlUP0THvCU52fRaAmpqLUBQ/hycP8+pfvpp3PvLXqGoMsFxRcb7Qa5/HCP39A4yNjVEsFvF6va6re3k0Nb4GgOnpLeh6pRZOkqQKMXihMIxhpDFNCU2rcl3Y5wrH5BKpF78/RTAowGVH+x2n/I5zPnVdd5tR9/fbaXdtDNMssS+Dg93U1f8P567/DQsWzE6zOHHk6MfYtftN9PV9o0LX5JhaxmLnusu6DYJtpunAgQPouk5DQ8MZsUlnEoFAJQB6/LHvo5Wl4x966CEsy2Lp0qXuffxSg6ZyjU8sFmP1anHtXi5sUznL5JhQzhWSJM2ZojOMPEePfhzDyCLLOzl3/b00N5fu9Xh8Jzufu4V8fpBAoJPGhrdRKARQlBz9A99l+44bGBj4wUt3gH/EeAU0neUo5JyXmIKUEGyG5J+da3Yq6PyFUkrNY9iia5vd//WBnxP2qWhlTJNlWa4QPOhViOfiKHaTXI8PRmSRWskaXtdywAFbhUwaS5bRAwIoVA8MuExTMTEJRQ3D9mnyezSm0jmKxaLLCMiyD1WN0TBfCEynNAEsjFTKFYHHAh4XiDi2A8ViHI8/gOoVxxouA01ywcC0jRzdpr2ekhA8aFPjc4nBdT3pMk0AozRT0CqF4F6PGLDLmSZHm7BggSizN7NZcgdLWorEyBjHJjWKVllKNRCdU58BcNNNN3HppZe6/ihOO5Vkto8J+/zOEoIrESzA729303MRqcDK1hiSJPH69W1k7d6ElhF3K+dMj2ASP7PzMxSkEUw9zJrQW2bt06Sm88vRafK2Rs4ZbMbHxzlx4gSGYVBbW8tFF13Ee979Hqqrq/HbWhmtMOIeS3mKzmlgm6vPOdZYbGreJKpzpnKMmFFUj4dUKuV6uiz3iu1m1SxFpeTMruvi2SgWvWxQhpGxaGxsqmDunIHq5IkOQEZVM1RVj6BpjzA5+TggUnMFo8BHn/4oeSPPifhJ8IqUaSYrUlUOeMrlovT397ssU0tLi1sEUB6h0GICgQ5MU2NqavYg6TCOfSN9xJOH3HXPn78Yn29utg9KTFM+f4K29kNIkkU0uplweOkpvwMCqIAw61y/fj3Fog/TVAGLfF6cZ03TeOyxf8fvT+P3Z1HVuRkRyzKYmhLaoK7u/6axUdwfoiqxJAJ3IuC3xeA201QuAD/V8/BCI5WudJsuFk/yk5/8BF3X6erq4tixY8iyzNVXXz2npuzFDsuyXIDhAA6nrcixY8cYHR095XdfSKRSqd/L7HMmy2QYA2x95gr6+r8z5/JzmVz29X2TfGEIr7eRXC6C358hmfo4XV2fZ2zsAXbveRu6HicaXcuG9T9j5cpPcOzoOziw/wr8PgGqR0ZnG8/+b4hXQNNZjnxaAAJF9WBOOaBpNnWqxGJ49EqmyelDVx0WOoJHjz2Izx+vYJoKuukKrgNehWSuxKBYQR9ZOx2V1dVZTFM+k8bwh0CSCGYyBLJZFzTlpyeZHhpAL5Ruman0tD0jF6DJ52tEkiQa5tuePoU8miJjplJzpOdwK+iKehywkD2CVQoXS7NIVTNdHZUjNo1a4kWeCQQJXHYZANoc6blsMUtGKrE/IzSjuUJwsc9en1OBJtZtWZarZ3JAU27vXijL908NjQMSpreUHjS8lSnW8li4cBHnb7zQ1bIEbLHxYGYCC/BIErW2TssBTbrkIU2YULizIj3X1hAib5i8Zl0LORs0qVKaoM00RUICsCYKgvkrjNxIPD1bu/Lv3cP8n0O9/NhuHltXV8emTZtob2/niiuu4H3vex8f+MAHuOqqq4jZGjsHNOULQ27vqiNHjqBpGvl83k0R1c0XoMEje1jXsI6JtEauaGBJMgsWCKbl2DHBohTj4r6Y9k7z1GAJgBTsnnOFQohqWYDvhvmVqa2qqio6OzuZmmrn4IE72LvnWqYmX0Nn5/tpbLyJ5uY30Nh4I1/c9UVOxEsO20N2cUU2I66z0z4lm4vS19c3pwi8PCRJor5OeBSNTzw063Nn4P7xcz/mR/s+Y2/r9Kk5EABZVWNYVpGmJsej6obTfiefz7s6pXPOOYcLL7wQRVHJ50L25wIAPvjg74hEn3O/Nx2fu9FqOn3Mfc5MU6OofwMwGRoaJGGn5+ZimvK5AUZGRhgaGkKWZRfQvhiRTouUsVNhGIlMc/LkSX71q1/xu9/9DhAsbl1d3VkBTdPT06TTaWRZdpm4uro61x3+6aef/oO3kc1m+cpXvsLnPvc57rnnHldrODMsy6JQKFSkyQ8cOFDBMo2PP0Qu18vx4/88pw7PAX79/f12S5tRenq/CkBN9Z+ze9f1TE4uAUy6e77A/gNlnmHrfoDXK8aj+fMXMj3dSibzWgCSyX3o+tz7/accc9evvhIvWRSyAqgoXg/GyDhqI8jeOUBTVRXqcKWmyWNX3tVG60nGU3g0SPsPUkTMRAuFgpuaAwh6VawJu4rEMilGq8gWxQCsGTKqWQS5nGnKYATEy7bWfulItp2BlkkxfPwo6EL7oSgGqYwYcB2myTEh9IfCVDU2Ex8dJhnwUZOuBE1eO73mgKap3/yY9N1fQfqQ2NWwVmIcVM1EN7x4KLhMU8C2AwDQba+cQk8PlmXxwIERgj6VS5fUMz6joe8IzWWWA2Kf/b4qoOiCpvHxcdLpNKqqujn87E4x2Cj1dRjjExQmxLmpqakmMyq+l5dP7Z3z26/sp//IFLd9ajPhar/LNA3kxHebfB5ke1buk2VCRYOMR2GaeiKxNmRjGsuCdDDA64/3csVUlG+tnE9TlWCVAmoO1WZp2mrWA8KFe2FoI3tSqxlOzBbO7k2J49+fKlUZXXfddac8BsCtysrnhS1AVVUV8XicAwfuxTRNDMOgvr6elvkt/GL4F5zbcC4BNcChKSHub44FWL6shWNHj3D06FEuu+wyl3GKe+M83v84Ny4UrvhOo17NrtjTLYm4v4mZsWbNGnp6epia0oAG2jquZeGCUmn1jpEdfP/Q9wF407I3cdeRu9ibGOXqcIlpytmgqZCPkk6nXV3XqUATQF3dVfT1f4uJiccxTb3CCmDQEkAlXAxjZPohIvRMju3CqUKSJKKRVUxNP40kiT51Pu+p9wHslKhhUFdXR2OjmLSsW7eOXP5BgqEEufwAR44c4djx+1mzpuSqnzgFaIonxN8jkXPI5frI5w/T0RFgYqIFw0ijKEFCodJxOExTKtXN3r1iQF66dKk7MXoxIpUSTFNz8+tIpfYTiSaR5RKz6fP5uPRSUZ1Zbi5qmuacTOEfGuWVteVi+osuush2qz/A5Zdf7rbV+X1iy5YtbgXgrl27OHDgAJdccgmbNm1ClmX6+vo4evQoR48edRuHy7KMx+NxdaYXXHABfr/ftTcBOHjoQ2zY8AvCoZKmrampCY/HQz6ft4spPoNp5ohF1zE1tRDD6ME03s45K4IcOfoxDCNNS8utLF3yTxX3/fz589m9ezfd3SlWrmonn+8nHt9BXd3lv/d5eDnGK0zTWYxHDo+y45igbj0eD6btgSR5vLOWVaoE06RY4Ldbp6i2vshvC6B9mkxOPVTBNGVsZsirypjo1A2JzxRTp+ivRpO8yKp40C2jsmFvPpPGdECTDQyyaoC8LPave/dOJEN3mZ9MVoAmr6/ENDnhiMGTAR/mDCF4emIcDJ2is57je9GmxUBjmjLhYgk0+fKWKz53ZsBWfx+BvGAfMk0tIEmYiQR3PbiX9/5wF3/+vR1s2badgVRlI94RmikWp2wXbadHWxVQYpoclmnevHnuCzFri8AjV14pjjctwNuittIgHrfmFloCDJ+IY+oWE/1i1hW0XaeH8mIfHB2TOH6LaEGAnJS6mHBVEAkZ2fTRW9tMzrR4ajqFZVmsbhcDqkfV3PRcY9Ua1jeupy5Qx1sX/TUgua7g7jYsi+MZcc2PZc68UaojYNf1JIaRZtWqTpYs3cJ0/MPE4/+AomisXLmSGxbewIc3fJiPbf4YAP1T4v5orwm4AuTh4WGSyWQJNPnibBnagmbYKeO8AE1FW+/Ua1ZzcGw2+FuxYgWWXJpYfHnwywykBFOU1tL8w9P/gIXF6xa/jg9v/DDVvmq6c2I9TgVdNifSc6GQuGedHmmn0+TEYufi8VSj63ESiZLe7cGeB/naia8BAjS12LYZ/sCCOTVvMyNip+gABgZXuAUJRWPuptIOcDjnnHPcdNhFF11EoSC2NdC/l3vuuYeWliP2fgtdXTyxC9OcvU6nT1993TUsWfxxADrm7aGpWbCI0chqd6AsFAqcOBEHIJvro6vrJJIkudVkL0boeoZcTqSNGupfhaKEsCyNm24qbePSSy91QVosFkNRFAzDeMlascxMzTnR0tLCwoULsSyLH/7wh7/39lOpFNu2iQKOK664gpaWFjRN4+GHH+aLX/win/nMZ/je977Hs88+6wImKDU+NgyDcDjsXoecXUWpKGEMI8O+fe9xe1aKvyvuBKGr61GGR34JwOIlHytzxW+nqekmzj//d6xb9wOWLf2XWZ5hTqXx8PAw0ajY9vT0bBPcP/V4BTSdxTg6mmJiSgycqiKDnWZCmn0Z5FgM1bYkCNmGli5oskvtvUWZlHQETRLrMU2TtD0gOM162ybFsj40DF8UJAk1LFJSpusuniN/YppcOoUREMs7TFPaGyStihfw0LEjSIbuejUVNPHA+nw5++ds0JQIeDFSSRc0Rf0qE4cOIum6yzSZYQnTb5fz6x7CZaXD/jyu+Nxhmop9/URt0XpSUfDYFPmPfv4U9VKaq5UDPPTb+0nZqcj6hKjsm5LqKOBF0yZcpikUckqmhT5rZmrO0jRytqli5GqRkolqGda0xWhrKomEJ4qzgS9AIVtEy4vrl0kU7G0uRJI8TNj+S+WgKZvQiNngMONdQDBm+1npfoZiIvWQ1E2mdYOVHTZo8uTx22aYweB8vnPtd3jgdQ+wvEGkAYcTlb3ZBgtFcrb9xLFs/oxN+VQ1jKqKe6e375so6j/R2CjOlyQXCYenWLlyJR7Zw9vOeRvzomL7fTZo6qgJEg6H3Re0I1YFkKMymWLGbffipOeqqxYgyQqH9Eb2DcwehMa1cfoDYuYf98fZm9rLLb+5hUf6HuHTOz7NUGaI1nArH974YTyyh2s6r2G0KMBFNteNYWTdfnoNDSvd9cZisdOCHFlWqasV9gWOtcEjvY/wkSc/QlIV96nP9FLnEyCwre3MgEQsusZefxXjY52Mjo7y38/9Nxt/uJGHex+uWDaXy1Wk5pyoqqqipkakabu6dqAb49TViXO0dOk/oqoxTDM3y/PIsizi8Z32OjbS1PRa6uquRJJMWluP2uflXEZHR7n33nv57Gc/ywMPbMeyQFEMVq9ewB133OEOni9GZDJHAQuvtwGfr55wWKQ4m5qK3HrrrVx88cUVIE2WZZfhealSdOWVczPjhhtuIBaLMTk5yXe+850KUHOm8dRTT6HrOm1tbVx88cW8613v4uabbyYSiZBMJsnlcgQCAdasWcMtt9zCRz7yET7ykY/wwQ9+kA984AO85z3v4X3ve59bMZfLiWu/YsV/4Pe3ksv1cvDgX2NZJSZe6JoskslvAtDUdDPRyOpZppZ+XxM11Zvn1KtFIhGX6dM08f6cmt76go//5R6vgKazGO3VQTz2japKFpYp/m+ZswctKRIt9Z+zvZpUu2IkYL/MY2YQEw0rUBLwJdNigAx6FAZ6jxPJiwcnJOexvGLAk21gZOhiuwVdY/qek6TSGSzVg2SaVNsPe9IbIm9/DywBmhwQo4nBwe8XQM1xbgbcCroS06SDZbFo56N0/cenkY2iWz3nXbMY09bC64aXUL40yIfykss05fOC2dL6+gjbppuJokG+qQ3N42FFcJzrfYepk7NIqkzKFr0vHOglnBPLj9JEQRsvpef8MbdfXCKRoKenByjTMx04iFUooFRXE7RTgapl8ur54YrmvEO5uTPdqakSO5JNiusny15CocVMIV7uTWWgKTWVp8Z2V0+obQQiXixANgIMV5UsDXpyBYI+sf1gKI4sm8iyH5+vCUmS8Ck+mmPipE6kNVLJFJYDlDKlfUroBmOOrcQZhKNr6un5EoaRoFCoJ5UUYK6lpTinV1U5aAKRvgHYunUrlmURCoXY3ClSao/1i5YP+YJgoFatvoR3ve8vmbTCnBxPky5U7usvj/+Sw1WHKcQKvPWmt7Kmfg2pYoq/fuyvufvE3UhI/MtF/0LII5iI6+Zfx5QhUbSwhdxbAQtVjdDevsJd75lUftXXC/uC8fGHebT3UT70xIfQLZ1XLXoVsVgMnz+NqhiYpsyypRefwdmFurorWbTwIyxa+N9YlsLo2Cjf3v9tDMvgU89+ytWqgUjNmaZJfX292yfOiaVLLgDA50/T2nICSbKoqtpEJLyMqipRSemk4pzI5frQtDEkyUM0uqbMl6qUatu+fYKvfOUr7Ny5E03TqKlpQJbEfXzllWvmdIz+QyLl6JlssBQJi2uUSh1k+fLlXHnllRX9HmFug9EXK3K5nMv+zXWs1dXV3HHHHdTU1BCPx/n2t79d4Q7/fBGPx9lpM9tXXHEFkiQhyzJr167lAx/4AK973eu4/fbb+dCHPsRrX/taVqxYQSAQIBAIEI1Gqa2trehtaJq627g5Gl3D6lVfQZb9TE49yYkTnyaXG6RYTNDe3kpdfS+qpwfT9DA4sIlt27aRzWZRFKWiAON04QDm0ZEqANLpw65b//+WeAU0ncVorwnitdkl1dRLTNMcE30zItJzAP4ZoMkfFWCg0W6Oq4aPgWKbImbFgBjwKnTtfBbLzun7JQ0pIL5HQICuYtHesAT5ZI6E3QA3nEyg2ANs0hvE8la5+yWZJWG26doMOOm5EmhymKaM30sukyU/Hefvdv6Qxd//AhnJQtJ1t3rODFlYtiRI1z2uCzlApAw05VzQ1EvEXubYVIb7lBgPXPcqgtXiWI/rdZyoXePaDdROx2kbFYPwKM1ohTE3PaeqIZdRcETNgUDA9adxUnPBDRvISio5Vezz5U1eYf6nKEybfsayxpyMTWqyBFAy8RKDFgkvZwrxcncMLQHSU3lqJPFSjlOHBWRli6lQNZpaWq43p9ml82KWD4JlkspYy+qgB68qEyvG+eZ7b+N3X/28OD+ZyjTXsczstNepwtGwyLKPhQs+TCz6H0xOir81NM69nj43PScusqPtcVKizc3NXN4hdA+PDzxui1sF0xQItNBaG6O1KoBlwYHBEmjQTZ27T9xN2pvmstdexoYVG/jOq77D21e83V3m9pW3s76x1CNuXcM6GoJNjNlsk8MSBQPz8deVUqwH9AMYZqUmbmbU1FyELPvI5/v5zNa/Qbd0ruu8jn++8J+pra0lFBT7ms5FqK+frceaKyRJZt68P6e19SIUVcEyRf++gBpgKj/F53d93l22PDU3M+rqltnnL0l7Rw8A7W2ip6ALmmbompzfo9HVKIo4Fz5fAy3NQmxoWXDypNBerVixgre//e28//3vJxaz05pz9KD7QyNt65nCEQGWIvbPmRV15fFSgiaHeamtrT2lbquqqoo77riD+vp6UqkU3/nOd864ou6JJ57ANEX/RWfi5oTX62XVqlV0dnbOaZA6VxQKw1iWgSx78XkbiETOYfmyfwOgr/9bbH3mEp586lx6el/FsmWiEKOvbwVbtx7igQeET1hra+ssYHqqcEBTV9eEq32bjj87a7lsNsvJkydflq1nni9eAU1nMdqrA6g206Ro+RJoMmbfOMVQuNS01x6LVE0MuoFYFQARm55Rwsew7PxyxgY+Qa/KVG8fyOLh8lICTYZPME0FQ8V59Ar5PGk7DVhVlotPe4J47MEZwOf1o9u2Awp22X5Z9ZwTwWiMcJUAdVsWvom3fe+fuHRwD5aioC9ZJBirogAghkcrpecMD6FMqeKiOm+h28dZyAsGptjX74KmXz2+hdyCanLBIFFd57rX3soWfT4nJ6Zdu4GaRJy2UTEID9NSwTQpSgk07d0rTPMWLFjgCkizO8VAEty4gd8dGeVEo0gttUkFIpEI73zXn/M7bRlFwyKZn83YpKZKQCmTKFUFRiIrmHaYJtki8Zt7Gf33TxPvm6BWFQBvwooKdkWyGCxjtUAwTcUZKUGnb5oTkiTRHPPTnB/B1HX6Dgp7gGPZSnBzNHvmoGn+/L+io/2dbDrvfjo7/4JVq9aSTtvVcp7ZZooAAzOYpoaGBqqqqtzPm5ub2dS8Cb/iZyQzwrHpYy5octjLVa22C/lA3P3ekwNPMp4bp8ZfwxXtIlXmkT18aOOH+NrVX+NDGz7EB9Z+oGJfZEnmuvnXMaqL6+u0WgkEO/nX3f/q+ks9mn6Uj235GLp5ahZOUYIoIZHSW+4vcFXHVfzrxf+KKosmz8GgWNeYptCfemGAYjQ7yrQq7veLYxfz5Su/DMDPjv2MPWN73EEH5gZNTlWb15vHspL4fE3U1QlmrASadmI57yBKzJPzuROLFr2ZiYlr6O+7kgsvvIa/+Zu/4ZZbbmH+/PlIklRRQfdih8M0OWk5BzylUodOOeD+PqDpTAfv06XmyiMSiXD77bfT1NREJpPhe9/73ikr4JyYmJhw+yteccUVZ7Q/zxdOas7vb3MnVE1NN7F40UfxehuQ5ZIFhiSB19PG2jUfZuPGjbS1tREOh11/uTMJxwx4YmKCcFh8b3pqdopu+/bt3Hnnndx9992/55H98eKPDpq+/OUv09nZ6ZZHbt++/bTL/+xnP2PZsmX4/X5WrVrF/fffX/H5L3/5S6655hpqa2uRJMm9CV8OURPy4rVBk5TNuKBprvScFgy76TlvXnyu2lqfgD3geAogIaP4xtHtFHMmV2KasqMTLtPkQ0MNioG3aJfHZ3UPXvtB0iSdvA2haspAU9IbxKdE3d/93pCbngt6coCFx2P3pysDTQB17WIQLyg5fLrCcLCG7H/+D1mPimQUSwJvOYflpOd0L8FUAlW3UAyL+qxFwS65L2hxLF1HGxx003MeRcOyYPnBQ7z6uec4b/UyWmJ+vEq2BJqSCdrGxSA8YjNNjimhogRd0OTQ7q6eyTDI7RK+M8ENG/jXoTH++u//kROtHRi2f0prcyOKXf04lZnd/64iPZcoAahQaJnLNOl/+ZcMffjDTH33u0w+s496r0i3Thh+9g8kSEsW/bUC6AZsO4aenMazz1a2MZkJmgCaon5ithYsPTmJoesuszTPL86/yzyNHoSBnbPWUR6RyHIWL/4owWAnIDqlX3fdXwBQKPRTLCYrli/oBsNJsX6HaZIkyU3RgQBNftXP+S2i1cO39/2PK/p32MvV7QI07S3TNf3i+C8AeM3C1+BRKm0VLmi5gLef8/ZZfweRohstivu+WBTs5bF0gm0j29jVsovGSxtJ+9P8pus3fPSpj1KcQzANcGjyED8dENYA50f9fPqST4u2MIgqrmBI7GufobN3fO+c65grssUsf/nYXzKlin27uuZqNjZt5DULhanmp579FAcPH8Q0TRobG+c04PR6aisGxLbWt7jC3Uh4BYoSRNcTrls5lJimqljlIKmqKrfe8hXuuOPrXH755USj0YrPZ3o1vVhhWUbJbsBOy4VDi5EkFV1PuFq0mfFCQdPExASf+cxn+MUvfvG8y55KBD5XhEIh3v72t9PQ0EA2m+Whh2bbU5TH448LlnXJkiXPC8rONJxr4ji3O9HR8U4uvugZLr/sEJdfdpiLL9rBBZsf44ILHmD9+s1cf/31vOtd7+JDH/rQC7KPCAaDbiovlxWaxqkZYnBN01yh++mc6V+u8UcFTT/5yU/44Ac/yCc+8Ql27drFmjVruPbaaxkbG5tz+a1bt/KmN72Jd77znezevZubb76Zm2++2TV3A9Fc8KKLLuLTn/702TqMMw5JkvDYLVDkVBwcId4coCkfiOCxheARuyo8khIv4UCNeClomQxtAWEOWLBbeWQdIbhHpjiZxLKZJh8a3lCVWLcqBq+M7sVr3wI5SaOgiJdqfbyUg056QwQoY5p8MTc9F1RzeDx5JMkEZLzeypd3xBYim8Yoezo28f7L/4bgmlUkJ8YqhOC6lS5pmnQvci7Dm55K8canUlTrEvmiACXFYpLiyAgUi0TsCjNN9bBq/SWs3r8fq68fq1hk04Jaaoi76bkGVaZ1TLA3I7bBZYlpCs4S/DqgqXD0KGY6LdzZlyxhyAOmorB19XqMMoFnbVgcx2R6diVaRXrOZpr0iQkm3/1PLtNUkxxEtqn+dDZBrcdOJRYl9g8mSMkW/XbqaPGIeGmfSGXYuXOfa/wJEAxW0vkAzTE/0aLjQWWSmpzguG17cX29OD/HsnmRe/nejfCd6yA9Pms9p4slS9a5zVtTqQMVnw1O57AsUZhQG/KWfadUtu68ZG9aeBMAOwdFykzHw/GEeOmvaRP7ut8GTSOZEZ4eFH44f7b4z17Q/i6vWe6agDpxb7+YrP3lBX/Jey9/L5+99LOosspve37L/33i/86qXjsZP8l7HnoPz6V1LAtqpBRmsTRINzQ0ELKZpi4rz56xPWe0b5Zl8bEtH+PI1BH0oGC5pifFvfa3G/6WmC/GseljPLJdMGRzsUwg3jV+v9BlybKXlpZb3c9k2UMsKryWpuPiuAuFcbtKTSIWWz9rfaeLwEvENOVyfZhmDln2uyBdln2E7HL5dHru5r0OaBL98uYGvE6Ypsk999xDJpNh//79czahdkLXdffzM9VuBQIBbrpJ3Nd79+49ZWPckZERdxy7/PIXr0Q/7zBNgVPvryx78XprCAQ6TtsU+kzDSdEdOqQDMrlcTwXAfe6558jlclRXV7veVn9K8UcFTf/1X//Fu9/9bu644w5WrFjBV7/6VYLBIN/+9rfnXP7zn/88r3rVq/jwhz/M8uXL+dSnPsW5557Ll770JXeZ2267jY9//ONcddVVZ+swXlDINlDyJiddYe5cTFPOH0IxCmCZrD9R4BONNbz+0d8CJdCUz2ZYHhWzwrwkqN+8zUZFjTToBqbNNHlli3BQPBBZW6+QMzx4bXZpSJ4GSULSNWKZsvScN0DACLu/ez1VbvVcQM27eiavtw5ZrpzVe4NCNGzpozzecT551YuajWMaBgqWm14yjDRWTOyHoXuwtDydYzoLRnWCluR6S+l6kqL90vE6x6L6WL5+HXIwCIZBsa+PTfNrWFTod5mmxtpq2sYE0zRqezU5mqby9BwIIacj8Hb0TIFz13E8V8Syy8f3LD0HY7oELGvD4jgm0rOZpvR0pRDcNEyGP/FJJnon0CVxvhZ96t10fP97AGj+JDWIdU/rJvuHE4xWKRS8Mh69yMJxkQI7kcxgmhaWIwbjFExTLEBUL2sRMzpKQjeQgevqBRg+lilAbhqyk2BoMLRr1nqeLyIRkaaaCZrKReDlFTfz5s2jvb2dhQsXuqm6q+ddzecv/zwba0Xl13hR55Z7b+Gdv3sn0WjcXd90RuNXx3+FaZlsbNpIZ6zzBe2rJEmsaLqy4m/DmsVl7ZfxusWvA+DKeVfyucs+h0f28HDfw1z186t43T2v412/excfeuJDvPvBdxMvxJlXvZJIdC1QSvUBdHS0EY4IsDqiy2fMNO0Y2cGDvQ+iyipvPe+tAO4kstpfzd+u/1vCxTC5UZGGPxVoAlzQ1NhwA15vpUC/qsq2HrDZJSc1Fw4vw+OpZJKeL/wO05R7cZmmVPqwvU9LkaSShqckBp9b1xQKhdzKsamp04uQn3vuuQogs2XLllMuOzw8jK7rBIPBOQseThVtbW1u+5/77ruvwogShEHpr38t3LPPOeecMxZdn0k418QBtmcjNm7ciKqqdHePoCpC7+ZU0em6zjPPCObpwgsvfEl8tF7q+KPtsaZpPPfccxXgRpZlrrrqKvekzoxnnnlmFhi69tprT7n8mUahUCCZTFb8eynCMi0kWyPhK2TcVhNzMU1ZXxAJC1XPEihavF5SqLJ9nQLOA2tZrAqLEuW8HBc/8wI06Vkx4Gs+Oz2nykQDtlgcATgyuhev3cx3UBazZCWXwUfpofZ4LbyaHyTxElKVejetFlBzc+qZnJCUBvu4p1g/8jXe1/N1fvMPQmMSjkTd9QCYTXZFnuHF0rMVGgMHNBlGGs15wdmgKaMEaK0O4XXYoe5uzptfw7zikAuaGgIBFzTFpWqmsqM46ntFCVakG8rFl06/ueCGjWwZL90TB+cvJhMvAcvakM00ZUQbmyOZHLp9TcuZJsu0GPvlfaQfeYTxenG+olYcq7WIb/FiUBSsqgIh0ngRM+QDkxlG68W5aUsmieUEOE4oKoaiEAiUXt6hUzFNeqlFzIHJOACdAR8rwuKaThZ1JqbLZthDewDhGfXdLd0cHy1rZjyZ48gzwxh6SQsDELXdmpOp/RV/758hAndCVVXe+c53ctttt1WAqSs6ruAv19wGgMfbgCqpbB/ZzrseegstrWIQ3TMwxS9PCC+Z1y9+/axjPpO4fOEbKx47Q63lHy/4x4p9ubT9Ur50xZcIqkGm8lMcmz7GtpFt/K7nd4znxllUtYivXvVVmhquBWB8/EFSqcMMDt7F4SMfAYpIkpdJXeJ4/DiZYobni30TIuV6ZceVXLj0QkCkmRzG5OZFN3NB/gIkJArVBYKxU5uqdrTfQW3NJcyf/1ezPquqEmX68fgO22rA0TOduX7FCZdpKgxVlLED5HKDFAovjLl0whWBhyud1Eti8Lmbwpb3/ztdii6RSLgps/V2ZeyhQ4dOCbTK9UwvtEXMlVdeid/vZ3R01K2OAzEO/uhHP2J4eJhgMPiiT/Ydj6aA/8WtajxdVFdXc5ndqaG/XzDojl/T/v37SSaThMNh1q5de9b26cWMPxpompiYwDAMt0rJicbGRkbKHJ/LY2Rk5AUtf6bxb//2b8RiMfffi5VPnhmFrO6m5Dx6HrXWdoydAzSlfSF7OTGjzMXF4CMFAqgeL167pHSetxlTD1OUBVjStAJIRZKJRwHwBsTA6PWoRPx2aT3ib1nDg8cUA/KEJAZGj1ZAkUovvnP9EyKtGLoBT/BVSEaVm57zlzFNc4GmXMqD7Jk9kAN0LF0KyC5wMuxqekP3IBkaoKP6xOwyn7d7rJlptF7x4tJUcetG1QCeo3G8NiWsdXUzvy5Eo5SgYAO9xmiIcC5LVVGcy54ywbaiBCqYJqehqmVZFZVzO6dLIk7N62WvWXp06mymaTKt8d2hSS7bfpSvDYyjFw3XZkDxiOUHvvQtsY43vRmAGiZJpw4je73IC5ciRxNIQJ3dOiQnQ7xerH9eIoNfL+K1dU0ta9fj94vBweutQ1Vn+wo1hBTCRmmwPpoW12txyEdIUWh3dE3TZWXRw3sAuHf/MJ/8zSH+392CPereO85P/nkHj3zvMEe3VT5zTt+00zFN5WEYJvd9eS8PfuvgLBGuY2y5qukS7v+z+9nQuIGsniUV/R6+pl/ym+MPMpIZIeaLceW8SsboTGNh9VJSlgC7SQP+4YJ/psY/28H5gtYLePgND/OTG37C1676Gv928b/xkY0f4W/Xf5hvX/ttqvxV1NcL/66p6S1s33EDR47+AyMjdwNQXbWRplALpmWyf2L/rPXPjCNTQsOzvGY54XCYQCCAZVlu2fr09DTRSQHyt/i3cOOvbuQ3J3+DaZmz1lVbeylr135nTpZBWAp40bQxcrm+Mj3T6Rs7zxWifZIHy9LJ50v3RS43wLbtr2Lb9uvRtBdeyZaaoWdyIhwR7NpMn6nyeD7QZFkW9913H5qm0dbWxvXXX8+iRYuwLIutW+f2FprpWfRCIhQKcaVtjvvoo4+STqfRdZ2f/vSn9PX14fP5uO222ypsTF6McNzAzybTBKLnXUNDAxMT4sU+PfUMhmG4LWY2b958xhV5L7f40+PGXoL4+7//exKJhPvPeThe7MilNbBZHMU0UG1zxLnSc1kdcqrXNbgs2GJa2aad/bZBpUfLYqSXoMt2Y12tgLfmKfwpsXzMthfweT1E/QIgTduDRd7w4LH/77BeAclCogQqlnlso75QJ4pvBcVMyWwyoOZdN3DHLbo84qM5vOGb8VX9NYXq9/Oz5X/Be7/+A/7ia3dy6a2CTXBSdMWYrfcxPEiGAVaO2paQvYz4aZFF6+/DAvK2xqTg8ZL8bTeeeTZo6u6GYhHJJrF8lkbUBqdt6TgAw5Z4kBUlhCTJFUyTU/2hdXVhTE8j+XwEVp7DYVssrdrU+o5ACaDUuqCpwF1D4iX9+FSS9LQAsqpHprpRgIZ8UcG/ciWZy8ULtIYpUrY2w1i4Gm9YzMobPHbqNqCQqRXXqH3Cvqa2k3jTmnVuKiUYmNtQsMpIVfzeZdtXLAn6K34eT5faqThM03M9YsZ9aCDB1l+d4P6v7EfLiXtj5GSJadNyWTyKOG+5XF+F23D/lAB/7dWVWonefZP07J/k+I5RcjOc20uVc800h5v5xjXf4D2r3wNIeKu389Ck6Od208Kb8CmnboD7fBGwmTnJ08QlbZeccrmIN8KK2hVc0HoBNyy4gVjxCv71rnq2HLMrVYPziUVFE1tFCVNdfQGd897L6lVfZfXqr7KmXrDBe8eeP0VXDpokSXL9l5wU3dNPP41lWdS01hCoDTCaHeWjT3+Ut9z3FnaNnnlaVVH8LtCdmHjEFVzPrJw7k5AkpdSXsEwM3t3zJQwjS7E4yfHj//qC15t203MzmCb790JhmGJxbvPI5wNNBw4ccBv93nTTTTwZTzN/k/AK27Nnz6xKt9HRUbda8fedVK9fv57m5mYKhQIPPvggv/rVrzhx4gSqqvLmN7/5RU3LgXBTdwodAqfRNL0UoSgKN954I8lkPaYpU9BGOXjwYSYnJ/H7/S6z96cYfzTQVFdXh6Ios/wrRkdHaWqa29OkqanpBS1/puHz+YhGoxX/XorIpTSXaZItC0+jLUadAzRlNJ2M1+9W0OVtECTZzFFNi9AraOOD6JklFGUx8OQKSbx1jxHLCBTv+Hn4vF6iAQ/n51VWDKhIsoRH9uG1ynRIFkQ8MlIZ0yTJYubTvKjK3g8T0xQDlV/N4ztFes6yLBLjNjsmyUTwEA6FCMaqCFVVEwzaPcUczyev2H9D94Jp4A0UidSKYzW1kL2ePFpvL4lYDMVmW7KqipHUkFQhLNa6u8kfPkw8LEBNwMyj2C61HWMCkIzQbJ8bsQ81NTVceumlXH/99e5+ZXeImXdg7VrweOi1+/6tHhMv4R01JSGxk57rzWvss81FD6ZzJCfF/yO1fry2XYIWqKHl3/+NEbsvXg2TZLNdGEYevWURHhs0NfvE9TPq/OiqhLdo0TgmAEvUNuockxTXq2kuPROAv8wMEaDPrqBaHLJBk73vx8rtElJDkB5jz0CCoAmvnlbY/TsxY21eJLY31mc3dTUM7vzIX3HX3/8Dft9sMbjLNNVWMk0Hny6lA+OjJSYsa5hu3zmf3WtOlVXev+79/O2q/8TUQzip1d83NefEogZhOLmk8dSAaa544tg4mmHy6JFSwcq6dXdywebHuPSS3Zy77k4WLvwQ9fVXoyhB1jasBWDP+J7TrjdTzNCXFOd5aY2oLiwHTfF43K0Gvvma1/Dr19zNX537V4Q8IQ5MHuDtD7yd7xyYu5O9E1sHt/Jon2ChnRRdX/+3AItAoAOfr+E03z51uBV0thg8m+1hxG7HARIjo3czOfnUKb49OzRtygXPM0GTqkZcEHAqXdPpQFM2m+W3vxX60EsuuYSxQJg37u3inxI6ra2t6LruVncBJJNJfvjDH1IsFuno6DhtT8LThSzLXH/99QDs27ePgwcPIssyb3zjG21H7hc38nZqTlVjc7LQL3W0t7ezfv1mkglxTx089CtAaJ78czSp/1OJPxpo8nq9rF+/nkceKYknTdPkkUceYfPmzXN+Z/PmzRXLAzz00EOnXP7lFmJGLQYn2bQw607DNGkGKW/QNbjMpwRrIfvFjL1xgRDLpgd70TOLKUpivVPaQSS5SE3WHqRsBsnrDxDxKWzKq7TnJbz+EH4lhLesZ3PU8BLweSq6usQt8YJoXVIFgF4w3VYaPrUwZ985gExcQ9dMJFlCUiVkJBqU0rYURSEQCLgVdE7oumCaPL4ioSrxmWX30ZIkA22kn/GGevy2xiPlEQdYGPAh+aIUurvJ7nyO6YjYX4+WReoXndBbh4SIeiZoAlGxsnFjaZadekw4U4c2n89AoUheAkyLS21H6gMNLeTsNjQO03S8DGxOFQ26Jp1WLRIcFtYF6qXX4lu0iOGC2P86JYdlGWQyx9CqW/CGBGhq8QugaDaIl0vHeBHVbl5bq5dsB5xZtzMAAkwXdYYLtig9IQaNnCzWM+IXon6HYXLA0zG9UsRfHNhN70CS21I+5ukKkkfmmnedw9XvEKmR6aEMumaQHB8jPjpManIcqSjOa9IGTZZluZqm8vRccjJH36HSYBa3Rc1bp9Msfmofd6YEYCh3mAe4ZeWV5Lv/imJ8Pbcvfw8LquZO/Z5ptLfdRmvrm5nX8a4X9L2BaXFMPRMlsKcoAQKBjgpzUSccpmnf+L4502hOHJs+hoVFQ6CBWlurVg6ann76adv4sJOOh96J/6sX865lb+Xe197r2hF8/9D3T+k5lCgkeN+j7+OvHvsrtg5updpmlRxwUn4PvdBwvJqcEvfuni9iWQa1tZfS3ibMRkWz19wp11EeDssUCHSgquFZn0fCp0/RnQ40Pfjgg2SzWerr67nooovYlxL7dDidZ/OFQke2Y8cOCoUC+XyeH/7whySTSWpra3njG9/4B4mXy0XhkiTxute9jkWLFs257I+39/H1J39/A8iSCPylkZucSVx55ZVkswLgytJRVFXl/PPP/6Ptz4sRf9T03Ac/+EG+8Y1v8L3vfY/Dhw/z3ve+l0wmwx133AHA2972Nv7+7//eXf6v/uqveOCBB/jsZz/LkSNH+OQnP8nOnTt5//vf7y4zNTXFnj17OHRIzECOHj3Knj17/mDd04sRuZTmCiUVyyQZO7WmKVPQSXpCrsGllq5MzzmO29N9XWCEKBoCWFhmDqWo4M/ZZpH2+nz+ID5TwmujKFkRoMljlYBMnRHG55WQ7Aaoms/HlCEeuOZ2L7Iqvqvavk1etYDPO7vvHEB8TAws0Vo/clQMyHWulaaIUCjktlJxwiiqQgDvKRK2QZOihbAssW1DyjPe0IBPd5gmiVxUB93Cu/w1mMkkqYcfZipYJbapTeI7JKoxW3pFn7QSaJrb0ddIp8luFcLFyFVXcdB+qUoZnXMaqqmNT1NUVZ5LikHTYZqGA5Xi0ANJ29ag6yDejNCkmAtFlZkDmlp8AkykUgfJ+SKoQcFINXrsgcLWbi1MWHiKUa65/HquWy9SQT25Ah0df84Fmx+nqelmQACVm3ef4OJtRxjKayQnBBsy6G8h5wuQtsHY4qDY56U2eDqGvT170J88vo2FOYmoJROXTcwrGli8oZFwtQ9/2INpWkwMppkeKWOM+m3xuw2a4tkiKRtktlWXQNPhLcMVLvjTo+I8PR1PYViwvSjAkG8GaAp6VRbVtpIffgOrw2/gDw2/v4VlSz/lNuo90xiMi/uhe+L5hd0gWCO/4iepJelJ9pxyOSc157BMIEBTb00j/x5r5+EjwlPp0sYMDOyAyeMwso+6QB0f3/xx/IqfidwEJ+In5lz/s8PPumadH9/6cZTAEsqHgN9Hz+SEwzTlcwNkMicZGbkHgAXz/5oFC/4Gn6+ZfL6f7u4vnNH60q6p5fI5P38+Z3AHNGWzWbLZUup5cnKC0bGfMK9zNzfe+GpUVeWEbcGhWRbheQuora0ln8+zfft2fvrTnzI6OkooFOKtb32ry0T/IXH11Vdz3nnnceutt56y+jFT0Pnor/bzr/cf4T9+d/T32o7r0XSWU3PlIfwUxbMaqxrh3HPXntJJ/U8l/qig6dZbb+Uzn/kMH//4x1m7di179uzhgQcecMXefX19bhd0gAsuuIAf/ehHfP3rX2fNmjX8/Oc/5+6772blylKjzXvuuYd169a5NOgb3/hG1q1bx1e/+tWze3BzRC5dxIExsgUTtkP3XJPPrGYQ95YMLvN2N3rJrhqr6xADy2R/L9dmJdYOixRDbbaZ4IgYVAORKEWbDfEGQpApaUd0PTCLaWq0qvCrlgua4sE6Uoa4FjWJRwnYjIoqC4CmKAY+u1Gsb4amKWGDplhDECsktlFlVoKKYDDotlJxwtSctGKeUEx8FjC8ro7KCMJ4YyNevXQsR8M9AHjmXYgcbSW3ezfTgSoAGopTqH5xDloHBV09F9OUiU+Tt3UMmaeewioW8XZ24l24kP223kdKajS2N7H2mJjdbpkQqa/asBfLK5MNCVB4UZUAIIcdtmfgKF67T58jDHdAU3tYAOdU+jBZcwJJsrA0hVxXZb+q5Xlx7trqF7CqUaQbe3MakiQRCJSqeXpyGkczedKGyd1jcRJ21eCwv4nJGgFCWjwKIVXsq8M0jSgREkoY2jcBoPXvos0Qy+z1Ghy2/b9y+ye4KCATlGG8N8X4YMmbZ3CvmNUnk0Lw7KTmGqM+/B6xLtMwObxVPNMti8U1itugqS8nzk2/1YzF7HsKYE1TlDenvBz+Zdesz85G6IbJcFyci+lskXh2ts3EzPDIHlbUrmDe1Dk8+M9djHTNbjwMJdC0rKaUjmpoaOBI0zzGQ1EONM1jXkcbnfs/V/rSiDjXXsXrtot5ZugU1cdlfx/NjvJfu79CJFICJb9P5ZwTgTKmqbvni4BJXd1VRKOrUdUwS5f+IyBSgadKqZWHA4YipwBN5c7gc4XX63VlFg7bVCzGeW7XO1i0aDsdHQeQFXE+TpQ54vcUNC602aZHHnmErq4uPB4Pb37zm180kXYgEODVr341y5YtO+UyA9M5dy79lcdP8v1nekinj7L1mcvp7//uGW3HFYH7z64IfGasWnUjluXH49FYsyb2/F94mccfXQj+/ve/n97eXgqFAtu2bWPTpk3uZ48//jjf/e53K5Z/wxvewNGjRykUChw4cIBXv/rVFZ/ffvvtWJY1698nP/nJs3A0p4+lm5pw2ofJpsWA176BTsU0eUOuwaWWtdN6dnruyR8Pg+TDMg1WZhPUFGxtSzFEaFS8aKpb2nD6m/qCEfLxEtAwjAB+JehaDgC0UI9PKuJYokxFxOwxIE/jP/x9AhGx84oUxWGMnb5ns5kmMRuvagyg+cVtFp7hMxcKhSpsBwDMgti4JBXc9FzI8LrLpeuC5L1eVEsiZPfOO5boJrCyFkmS8Z0jdC5xu5lta3EMWbWQPSattit4SoqRIYhqg6ZsIs53P/hefvyJ/4tlWaQeEuaKkauuRJIk9ttMk5ws0trewNrjYnDbMiWAUG3Yi9EYAEliXSTI1XXiZX3STsWGksP4NDFQ9gwkMU2LEbuP4LyI0KalUodcEa005SOz/1jpPCkyS21n62xCozMgzkt/XsOYQd1vT5TYj7vHpkmMCQ1g3BNjqknMODulEkqPqgrNdsPg46F5sORV4lpNHqTNbjUyoJocHUlhmRaJ+7oJFU3me2XG+1J0nehx15UZFevJ5/spFuNzVs71HpwiEy/gD3lYd43YHxc05cU5yUtB4nL7nDqMJWloNRSUgZxdWHF2YzRVcO0k4MzZpjUNa1g5cglGSubos3Oz3nOBpkAgQC4oQPhwrJZLa8YhU2b+O1rSj21uETKFZ4dn9/qyLIutQ6Iq7N2r3o2ExK9O/IqMIu4/r7eeQOD319X47RRQOn2Y0dF7AVhQZnVQX3clDQ2vxrIMDh/56CxrgpnxvEyTnZ4TesDsnMuUp+iSyX08u+1GFKWUzuvp+R9MU3OZJoCT2QKrV692K2olSeL1r3/9GTVwfjHDSWt7bG+4T9xzkGf2/Cu5XB/9A987o3U4ZqP+P2J6DkBRPDQ3CVuOZPL+51n65R9/dND0/6eI1gWw7JYMBcVDr24DFtOalbfOagYpT9BlmgoF20k84Cc5kWPwaBxZEUBlwDPKMz7xfUs2aCiI71Q3t6DZ7I43FHWFyQCSFMQnl5gmn6VSRYigVWKaUrY5ZY06AP3bCPoFCFAkH4ZR0sDoph9VraRcnYGwqiFI1iv2wZ+vpNREem4G01Sw12vlXdAUNjwuaBqYLzQeDVaMqC72c2Rqmsg18wATtfEclIZziPuqAFhQsMWQfpNgIU+1JfZrhGZOTppsPTnBoWeeJp9JMznQR3pinPQTTwAiNQew106zeTI6TbEg60fEOndlCnz5L9/D1q/9N2ajYGwuj4VZGRbAtte+Jr78NNgePYmpPLd+axtJ2+doYbUQsKfTRygaAjQpExLK/tLL/bxYiIjNumUSBZp9HrySRNGyGMxXAocdZaBpXypHt83eJNUI47XierYUK3UlS+xU3bHgPFh8jfhjwUvQkkCRGFFMuicypI9MYtitYBo8MmO9KUYGxD6nlDCGpmDmxWCTTB0oNeotS80dsgXgyzY3UdsqwEByPIdhmPTmSoPXiGflLC+comZgHin5ZY33VVYGno0YnK48d2cMmmrX0pQSYv2p4dnfKZpFjk+L9NvymkqgkLUnSlOhKLVHbOPfpYJJZ6QEms5vFlqRnaM7ZzmYdye7Gc4M45E9vHv1u3nrCmGc+d2efYBMY8P1L9h7qDwcNkMAGIv6+le5KTQnliz+GKoaIZXaz8DgD0+5LtMskMmIFOPMdTjh89Xj9TYAFv0Dd865jABNFpOTv2Tnc7eiaUPkcmEG+t+C19tAoTBMz+Av6M2X7rvuXAFVVbniiivweDzceOONFS1/zlb027q5K5c18pZNHbSEhpA1Ua6fy/WdsoVMeZRaqPxxQRNAa6uwWBkZ/Y3bIulPNV4BTWcxLMvC0AXwGPdV0Z8sa5Q6g2zKanqFENwmJpD8AU7sEjPNaL2YqefVcfYqXrBkTKVAoyxuyqrmVixbw+QLV7lGixoWkhzErwRpNGO0hetYZXQgIREwS6Ap4xcAJVItfg/kuwGQx7vcdBlAujC72rCUnguQVG0jyVwlaJqZnjNNGez1mmaWUJUASh5kTEOAu6kWwag1m1X47fL5jKKSKk6h1ts98M55HXFFLNdpi1xVv5jZBlKCqh+hmQNDRd78jW388Mf3uvsw/MjDmJkMan09/tWrmSrqjBZtXY6sIMsSjZZOLDmNLkkcUf0c2LcLs1ocx3qfn3Ns0DQdkMl7JPz5KXK2HixkSWwbFqyTX5JoiMxHlgOYZg5PTJSke8ZM5vcex6HzLqgKE4qJc5FNaCiSREdA/N6bqwRNDtMUUcSjvbdF6HVSapTxqC0uTleWaS+2yb5jwXlQuwijZiFDmhisGuZHiQQ9GKbFxNbSizqqSGRHMuQnBJO1q2otAMkhsd1U8oArmHaMLdPTeXr3i7TjiotaCFf5UL0ypmkxNpZlVCtV8A3Js3tSHXxykGKmtMyxI6d3e34pwjkmJ84UNLUXFuOxq04nBlOzJkndiW6KZpGQJ0RrpMRqFE2LlM0yWpLEzuB8aF4LV/yDWGD0INidBRZXL6bGX0NOz81yIHdSc+c2nktADfCBdR+gM9rJrlSSpzw3sWjR353ZCThFeDw1ZeluiQXz/3LWMj5fAwsXfAiA3t6vYZpzM4WTk09gWToeT82cKVon5nW8G4CTJ/+DgYHZIKymJsySpVtB+iGWpRGf7mT3rus599w30DlP9Evc1vuLin7pXTbrtG7dOj760Y+6ou2zHQM2OG+vCfBPr1nJO9ZUVh467W9OFZZluUJwr6+N3+wd4rMPHuXDP9vLbd/axlX/9QTXff4pHjs6d8uyFztisfWEQosxzRzDtofZn2q8AprOYjiACWAiWE1/vAw0zUjRZezqOYdp0uwGo7Lfz8nnxI3esVLQ+NW5MTRUQrJgEiJhsWyo3kmZWXhD1S5oOuw1kCRbCI7KG1dvYqkpKvl8hqsFRvOJQTaySAy8gUlRhisl467BJUAyG6jQdpimRWLCTs81BJly0kFpHbPsOJUBrUIIbugeZNsCwShmUT0KeMXOWEUBmqSgSN81mdUoNtOUDYSZ6OshtFGk5OSqZrfvXFPOdjq3dU3ViTggQFNLdQ3tQZOW3KC7D8NbxGwufOUVSLLMAUcEntWZFwty9JmneTQs0Toimur2ty7hROdykCWkVJGAZlLlUWn1iuMYqZIJeLwEmsW1UpCY1ykAnZ7QSBdMt6Q61CAqhryjRRbGBwnaGYxLaiIEow7TZKf1/OL3nrJZ8nRRF33kgL/pFPqlI4tWIwcjFGUPExGx3erJStuOJbK4x45FFoPqZSq6wgVN85bVsLQpQhUSiu3NJEfFNauXLdSsOJ8ngwuY8lSRGbMNI1P7Z6XnDm8dxrKElqm6KYQkS1TZ/lWHhytnn4NU6jB0zWD3g0KjkfHb+q0Tc3v0vJihFw3u+5997Ly/BygNZg4pc6agKdtfuu+1bMn01AlXBF69FLmsAm9MK1bMp7bFVsPV/wh1S0DxCQZz2p7MSDKbmoW84ZnhSl2Tk5q7oOUCAAJqgE9d+ClkSeYXXQ/y5OCp24ecSYhed+KaNTZcTzg8NzvT0vIGm+UZYXT0NwB8+bET3PSlpxlPCUf9nt6v2sveelr2q6PjHcyb914Ajh77OMPDpYa7uVwfuvEvNDZ2YVkSft9b2L//IsLhelasWEFLyxvxeRvp1WydpnM9y9jO34d5y+eH6en5yilThgBDeY3znz3EF3tLz6FhZEkk9rhg2knPtVUHKeR76QzZjtoT4l0xPT07BVsemjaBaeYBic8+EucDd+3mi4+e4GfPDfDU8QlOjKU5PJzkju/s4B9/c5B88fTp0j80JEmiteVNAAwN3vV7VwS+HOIV0HQWwyhrHjkSqKGvbNY603bAYZocc0vNFuXmvDHGelNIEqy8TAi+Q5kxZMsgErLN+kJBTNVLyO5R50VDClSRtIHMMY+BoQbx29VjilejYIrPvDrItrEi3ioAqtdugGgrAdkWsAbnoRslsOMtSGzrLs3601N5TN1CViXCNX7GDR0DC0yLTFy8lNLPDiEdSVdYDuiGFyyxXr1g94azReSmDZpUVUNCosGMEcyJB32stonx3h4Cyxdh5qbRlRxJu8lwc16AJjUglt1gNzYepZnLl8/jyxd6kcuGpYkTQksUuUq4PO+3fZekZJGlQ1u493P/jobFkh6xXH/bSo7PFwBDGc0xmRGD4RKbHZisgdDFH2LBoptosDVhncvEdbHGc/xkR78rxpVsfZgyIVFTSPE+JL5xTidrIkGCDtOUFPvfaTNNPWVMk5OaWxjw8daWWrxYTNY0kF2wFEuRyNku8pGhHspjiSGu3bFQp/gpL2JIE5qRlkUxljVFeBUeZAs87RHC5wlA1qAaSFgUJZW1S9s5HlpEblykKVNl6bmO2iCmaXFoi2CqVlzU4m67qkGApmNTleCj16xs/nxoyxDZpEa4xoe0RoDj9MiZla//ITFwZJqefRM899seTNNymabVreL+OlPQNHQ8XvH71FDl9+bSM0GpYMCJbY0Xw4LLQFGhwV62XNfUPFvXpBkaO0aE79iFLRe6f1/bsJbblguT2R8ePnW67EyjtfXNRCLnsHDh355yGVn20dF+OwC9fd8gpxX58mMn2DeQ4Fe7B5iefoZkcm/FcqeLhQv+ljbb0uDQ4b9jdPQ+JiYeY/uO11AsdqFpPg4dvJbnnqsDJDZv3oyiKCiKj3mdf8EQgtU7325H05fXKM6hMT3TOHH8XznZ9RkG+udOGQI8OJmkJ6fxzYFxFzwcO/4v7HzudRw99klh1VHGNPX2fg0wicQu5alB0cx3eGxu13InHH2kKTfw3WfEc3frhnY+fO1SPvuGNfzwXZu4/YJOAL6zpYfX/s9WToy9tGmzpqbXIst+0pmjJJIvvL/lyyVeAU1nMYyyiq/RcC1ZoyxdNRM0FYSmyU3P2QzMoCbYo5bFVTQtaMcbCCKbBo3aGPPyB/AUwiBJFGsb8dqu4T6KWL6oyzTFZYsxXwCfTafLao68PTPyGlCzNIPv1ltdoXRLZy2880ECl/252NXggor0XJ2m8mxXme+Ok5qrCyDLEom8TsJO+SXGc2T3jxP/9Un8eCmWaZrEOsXArtk91rw20CjaVXWqolFHGA8KYZu4G61vYbyvG7W+Hk9jhOlAHkMSyzdo02ieqFtBtzwhNDHDtKAoQY5vFy+fgr8KgAwGciRC6DxRfn0gJY5FTmoEu0VbleU1jdywTVQtDddF6WkXPitVAyNMpgWomW+IRytb40X2ievQEFAxJXjWLoFWxgt8Z0sPwWClhmUyIyrqbiXOjQ1iv0KxSqbJEYOfSOTYeX83+UzRBU0bYyGiqsJ6+945sXg1fjt9GMqkMIZLzBrAErv1xYCnloxusC0xn4xZh4RB44IYSxvDXI+4DqENjfiXiv1r8HiQkMkHa3jVqhZOhBaSnRCgKZ8fIJER90RHTZD+Q1Okpwr4gioLzy0BIodp6rbNW+cpAsD1FMOY9oCiFw12PSCYvfWv6mTVKvF9T9ZAKzflfAlioj9l74NJYizr2g1cvFjsQ/dE5nlnzZZpMXxCTDjSXsGOTQxWDlCnBE22Zq3ebkOy2z+PvPPeaBSO3nPpmg5MHCBpV2zuHd9LTs9R669lcXVl2vOaTqFh64r/4dWI7W23cd7Ge563xL219c0oSphM5jhbD/2GrCYmCw8dGqXXYZmab8HrrXvebUqSxJLFH6Ol+RbA5OChv2Hvvnej60kiAgiWbQAAoxpJREFUkTXs3XMjU1P1TE1N4ff7WbdunfvdluZbGVHEs7ta6SYgyxgW9JWxt+VhmkVM89T3m2VZTI8Jf7fk4AOnXM6p1hvVdPryGpZlMTn5OACDgz+gq/tzDNgTjuZwkuERYQq5ZNH72LTsCkxLAmOQXG5wzvVDyaPp5JR49/yfyxby6dev5n2XL+J169u4cFEdn7zpHL5z+0ZqQ14ODye54YtP8+Ptfadc5x8aHk+UxsYb7eP80Uu2nZc6XgFNZzEcpkkyLYr1zVQofGal5/SK9JyBB1OSGciIWfbCcxuQZJlG26/pzfrvWJT6Hb6kAB3FqnqyGTGIetHI6WH0ogkSpGSL47IXvw2KJDlN1n7BKgTxhg1SrxGGfxnZIhTxQqyNwDxBues5qSI9F8vXsO9kqfTcMSt0BsRETidug6Z0V4KpHx8FC2pWNVdUzxm6F0Wy241kxKASjPmwLItiXjBtqqrRrItBO+IVwGisrpmxvh4AfItamAiK8xyxkngsA+/y61xNU1ufoMRHaMYsqvTt34MhKwxceBNTsVoyPg/hSy9F8or9OmAzTf5EGrJJkCTWLFqOR2ojljEwZQlDUamOj7N85JDLNLVlxPEOVpeOr0qBgVqVlGVRpSrU6cLzZ/9YyYXZsmS6TTH7DfR3u393maaESGHMs5mmQyNJtt3TzRM/OuqCpvOqBIO4YUq8VHfWttLcKgTatfFxkhPjWGbp7qvJDFCnCbByPFvgwLAABI2e43j0BKskD/NRyGMRXFOPpzWM5VPwyAp1/hZ8NY1ctqSeKW8N41Y9+bjYt/ZwLz5Vpj7s4+izwmZg6flNIu3qnBP7Hum3GZU18lE8lkbekum3AcPhLcNkEhrhah/LNzezaXk9KUmc3+7jL22Kbryv1E5jYiDtpuc2L6xFlkTBxnhq7kHWiemRLPlMEcUj09sowPbRkz3u55Zlldqn1NoAeuwwPPrPDD/8bwCcH99HnZlFs2CvDeRpsq1Wypim5nAzndFOTMt02SUnNbe5ZXNF6g+gM9YpNpcbI61Vtg4pj6JZnCUunysM03heEKmqEVpb3wjA1Oh33b9PTu9hanoLkqTQ8QIMRyVJYtmyf6ax8Sa7Ks+itfUtbFh/F+FwSQS9YcMGfL7SJE1RfEx4BPAMJn7NfLuheVd29vW0LINdu9/Mlq0XVbQJKo98fgBNEvdHJtc95zIAxzOl9T8bz5DPD9gGo3bauedLnNcoTJyt1I+wrCJVVZuoiq3n3ZespD8lQOmTBx8+5TaSaQF+RjM1bJpfwwevXlLx+XMP9PCDjz3DhoYov/3ri7l4cR35osnf/XI//3LfoQoZxYsZbbYgfGzs/lO2wHm5xyug6SxGUbNdvS0LpbWN8izyrPRcwdE0lXRP6XAbU9kASLBgnRjYHJPL5dpJouoIaiaPpOWxZJkd2wVF70MjlbaZgpiPltoA/V4fqiwGt0xmiqzdbkOWIhCoYWJEDFiJMqPooK1l0bMyeln1nJxbQtPY066uqcKjybJI5oouaLKOTIJh4VtcRdMNyytAk2548EsC9BlFjWIhT7jah2WMohfEraqqGs1mFQOYzIv48csSmtdPn2ZSyGZQa/yM26m4aisuVrz01S7T1NIlZtRZKcwvB1TuveRm/ueOj/LLxUu488/ey2h1LcHLBQWeMQy3HLnOFjxXNTYRqKtnvH4d88ZKs84lXYdYkjnJhD2ANk2Jz7pCMrmM+G7IsjjRLM7b5TURbjtflHh/a5uCZYnjyxfq6A4L0FQ4WjK1c5imYkFHy+ku0zSqihqCo7vH2G1X+Z0XE6BpYe9RPMUC46qPdL1YvmZ6HNPQScfLRNSpERZnBZOzczKFJy3AaIv3EAztpqlHANhHKJIwhMu7d6FITzUFFlDf3EJ7TZCF9SGOhxa6Kbp50X7aqgXbODEgBuR559RSHg5oGrafhgaji2YE2DuayWMUTXb9TuzbudfOQ/HIVIe8pINigNl3YJyXMsor9Mb7UwzZTFNnXcgVuHc9T4pu6EQcgKYFUeYtEEzxUH+JmR3KDJHSUqiyykI88LVL4X/Ohyf/kyGbsWyJVLHJLqHf5lRINtqgqYxpghLb5Ii/Z+qZyiPqjVIXEIxOd2Lugb5oFHntr1/LLffe4ppjzhVf3P1F1t25jtXfX83q761m3Z3r2HjnuXzogdkAqL3tdiRJpcZzkPmxHoJehVd1PiQOq/HGF9xgVpIUViz/TxZV38Kqjn9g2dJ/QpZ9ru2AoigVdjYgwGqfLio464sHaZaEVrRc1+TEyMivSSR2oWnjTE3N3Q4mPllKmWWlFKY5N5gu94XankgTt0Xd0ehaFsz/GwDevOwX3Lj2P+gbEmm+znn/B4DqkBd/WPhpHep57JTg5plj+8R+GI188U3rUJXSUJ/PFNl5Xw+J8Rxde8ZpiPj53h3n8aFrBLD6xlPdvP+uXS+JzikSWUUkcg6mqTE8/Mvn/8LLMF4BTWcxilNioFIsi/A8MQNy/R7Lbn7LsgTT5AkId2ybbRpqFnqElkVV7iDaaHfcHiuEmQ7EwJzGOyUe/uNdPQD4JINk3O5bVutnaWMExXaa1k2NkyeS5HQxqElEIdLMtF0W7YhuAQIRAXC0FBVgRym08hppgO22rsn1aGoIUNBNNMNkWjGRgcC43Y/t4jaCoSCWpaDb1gu67iVo+XBuy1wqSVWtH6PYhW4zTV5vjkazimMYtMQCbqXaSH0L4309qLUBJu3JZLWt1WH+Jaj2vqtDg9RKcQA+y3oOLl1H3uNDxkLz+Xn0wuvRFglt2OF0XqidCgZNKZHCqu+YjxasJRFbQOdYaea9pPsINcVpUsOCFm/vShLTLAxZ4ki/qM7zFQxO2qDpitoot22eh1eV2dWXpZgRVUKj6Rq6Y+L/+WMlryaPT0FVUxQSX+W3X/4v2n0eJMtC80joUZXhaoWCZVHjUVhoA6rcyBCLegSDMaCI+yuaEoxicqysaiY9wpKMACbPjiZcf6ZmzyHMvn0UD4gB/l6KHBkRIMK3XLB9zYEFNNeJ/b18aUNFim5RtJuOmmBlYUBjpaOy08h4wr5mtUYXbYhzeCST58izw6SnCwRjXpZf2IxlWkz97Bg3BL20eiRGTsZ5McPxdQPIp4ukpkoD3HBvkqJhocoSjREfnbUCnD6frmnYBk3Ni6q4ZJUYuKVpv8vsOCzTouh8PHe9BYb3gOKFpa9mZKGwFmheeT2bagXLvC1ub89hmhJ9kIu72zu/RYCmbcPbmMpPcXhSFBg4Pk4zY35MWCF0JwVoskyLfLp0b5+In6A32cuJ+AkOTByYcx2GafDjIz/GsvWBFha6qZM3i/xudBsnh3dWLO/3N6OGhHfPjQse470XKqxvFAP9vI73zLmN5wu5fzvzfv0/NPz2S+7fnL6k5d5LToxqOmnDRMGikREiGSGG75pRkWqaGl3dn3d/n5qeW0+UGCm1+LIkyGRng9CMbjBYplPbnsgQj4tzU121kc7O92EEhIP2zQ0DeCSL3oLMB579ckmXtlykVBv9h7n/wDAz46c7+klnBdN0w7oNNEQr+7wd3jossg7ApD2ZkWWJ91+xmM+/cS1eReb+/SO8+RvPunKDFyuEIFywTQODP/qTFIS/AprOYhQGxQxaliRabK2KkyQpdwUv6CamBaasIPk9rhh8tFHobBatL6VzGsbFgzqWD/PvVR/CMibxJCZQypJ/XsVy9UyRWj9LmyLU2Jc+b2Tp7c1SsDVNFjGINJG2gU8hWLpFAmHb3FJXKtJz3kI16wiz/aQYiB1NU1VDkEROvCCSCjR6JFTTQo568S2qQpZlgsGgKwY3dA8hSUWW7EE/maS21odZ7CYftz2bQnE8KBzFoCnqZ3VEDLqj9S1M9Pag1Phd0FRjTkOoAYI1KC2C1THicTYExP5FsgnO3b+V77dFuOvkXmTT4NjClfxkQJTFOyJwOVmkXhcArE6dZiAZBklmbf8QYUWmPQ/NdkpK7dtHcSxLY1JjSUrM1I7WBJD8CpMeiZFqARAvq4lQF/bxZ+taUS3ITYqZ9WC2lnRLJwDaiRNYZcUDprEfrDxdu7YytH+YiG3hsPJdyxlsEttfbqhIkiQYvrFRlp3YR3ksysdYFttE4YlxJu86wvg39jFy8LU0Ji8V1643zvkeBa9k0ew9TPZwFqtoMu6V2I/B0REBunqiKpZlUe1rJIaYzV+2tIFpbzUjU0LovbT6OB01vlJhgCIKA8rDG1AJRL3EwwIUNzBKuySEq0czeQ48KZ6Zc6+Zh+pRKA5nyD43SlvRYkNI5YaUztTPjlHoiv/BL2DTtHj/XbvZ/G+PMpEuuCyTU0Q1OSjASnOVH1WRmV8nQFPP8zFNtgi8ZVEVG5euwZQMvIaf3+4X6RW3ci4+DOOHIdIMH9gFb7qL4YAY9Jv9HjbZTvM7kmlhahqohqjNyIyW+Xo1nYcsyfQke7jr0C+wsFhavdRllGbGgpiYJDhM05ZfnOA7//dptz/g8fhxd1mHtZoZhyYPkdSShD1hHrvlMR675TEeDqzhwqx4hh589jOzvrNz4joAVtftYW3sWwDsHV+N6nthbW3cePZ/xM/JEy6IvOCCC7j55pu57rrrZi3uMD7zAj6qQvNpMAUL3VXGBAEMDf2UfH4AyXb9nZqa+xzEU3vEf+yZ8NZfP8S9X9rLrz+3m6d/fhzLtDhhs1hhm/k5ni3QMy2uXVXVeUiSRI/2Tp4dK2nPnsiE2D9xgHf87h38xcN/gRLuxLJkGoMTfOuJbRj2hDunGfzLfYf4u1/uoz4grt2qzkqNnGVa7jMFuAywE69Z28r333keUb/Krr44r/vKVvomT10J+PtEY+ONKEqYXK6H6em53etfzvEKaDqLURgSg4GiqLTX2Gko58MypskRRgKoYX9J16T4AMtNzTHwHNUHv45HMjAsmfHJLIYZRzJN2vMl12GfIs0ATVFq7Px53sgwNpEjb4gXv0kVRJrJ28vr4ZJjuOpV8PgVQrIENtAxTRlPIYZpriV3/AkMw3S3FSsDTUZApt22DwiurUeSbd+iMldw3fASkTwotkt5Lp0iWOjBMkYpDhWxTAnFo6H7pgVoivlZHRHncbS+VYjBa/1MesXLrU6PQ73QYamti8Gu4PvS/I18T57mPd//DG/o2c81ixfScf9vuGybEHH+j+EhoxulnnPJIk26yL/X9/6Cvm4xmC4a2s3WTcv5rBRD9Qhqu3rkENO/PI4MtMXFdTw2byHe1jDP1In96shY1NuWBO+8aD61hkSi+0LyiRaeHlnP6g3LkEMhrGIRradHnD+9SN5uT2KZBk//5HGq0wI0JaIKqRVC8Bk9lER74FNkfvQu9KLGgoEuomUNRm9lBWtqLsPbLZPbO07hZAJda2B+WlzP3pDK8oDKNVEPWeMOMsOChRhoFwDh6Kg49ueGp5nSbA8sm1naOL+aoFdhR3YVel7G79VYVNVPwgbgUbswYGYorUGKqoSERS3jzPeIF/nhZJaJ/jRIsOQ8kdYqDorPzJBKxrDwSBLZ50YZ//p+Uo/3z1r3C4nvPdPDffuGGUnmefr4BOO2CLx9hQCFxVQRvwmtVeKeW1Avzsnp0nPJyRzp6QKyLNG0IIbqUVCqxX3x9AHBHByZtPVMk33gDcObfwpVgol2queavR7OCQUIKTJJ3eRIxh7YXV1TCTRFvBFW1om/f2XP1wEws4t57OjYnCkXl2myQVP/4SlM0+LZu7uwLItjUyXG0wFNJ8fTXPf5p7hnr3inbRkSLM2m5k3UBeqoyyZoPHwfr8qId9fDk/sgXzImtSyLXx/0s298BZJkoWXFufhN11U8fbyyhdAZRbwfjtxX+n1MsGs+n4+1a9fi9XpnfeW4nXpfFPSzfNm/0oS4n0+kS/tpGDm6ewRztXDB3yJJKvl8v9uixIliMUnGFEAlNSTE5on4EXoPTDJwZJq9D/cz0pXghH3dVoYDbtPsffkQIBGLiTY4A/ECdw4s5amUyoC8kM+8+kHeuPSNqJLKlsEt/MuOzxKOiOpWr7GXe/cNsfXEBNd+7km+8VQ3Ejo1fiG3CPgrRfl9h6ZIjufcPqJTwxlMo0Jdy/kLavnl/7mAtuoAPZNZ/u8vKj2//tBQ1RBNTaLB9ODQXS/qus9GvAKazmIURoW2RfF4XO8apw1GuaYpY/c+8XtklHAQj14qrW5skEVqrpiHu9+LjEnMFgl7JnqQTPGi7ywWcBwzvapC0gYy0doAy5oiVNugqWBkyedTbvWcaVVR8LVipMU+SLHKl00g4iWoSMhFsf+aFsCDStFawsrpnQz1i3YbqlcmVOV1QVMkqNJoP6jKshp3feWu4IbuISKpKPZMLZdKMnlM6Adkow7PmLhdC5EBjtlM0xqHaaprZrSvBznkYdInQFdNMSX8bACpYRGKT7wcPFOT5HdsQcJiyfkXUhwbI3/oEDc/ei+x5DRxj4//7Blxe84pyQKxvHiRR7wwMmH3/+t/lnqvysIFVcjehVgorFCb0HqS6JaFOi6O/XjnQjwtYbbWif1aPFrShSxujHBxfYzs2HIef+TjHIsv4qpzmvAtEfudPyoGrJM7t2HqpcF5eugwNVlxPD05jWP2sTUOFNj90CCJvb8DIFZdxbWSuIaRosVYZpzu1H4mYqPErp9PzS1LqPN9kobpfwdgIADDegJFksgY11HU20EGdbUADk567sCRLkayYmaezJgM5DV8qsIFC2s5HFpOalCwInXGU2XMY4C5It8sBo9as4AHnUX2sRzPFTAlaOiIlFLDQwI0Rc5t5N50kadSOqk2AV5Sjw9gFn6/aroTYyn+/bdH3N8PDCZcpql1SRXROrtRtiG7zYfPJD3nVM3VdUTw+ARobmm323sMphlMD3JkWGhalmo6vP470LwaANOyGHFAk9+LKktsiIptbovbDIGjaxrdX7HdTU0iRScp4rnfe6yRO76zgzX/+CCf+PWBClZuflSApq5El2iVY6fQx/tS9B2cqmCa9k/sJ6kl+e3+YQ4PJ7lrmwAPs3RTT/83WCaXN25CteCYR6Fn63+56zk6mqJ3Mssj/Ve7f4vrq+hOdPLQoUofsTOKHd+spOvHDrmsyi//8zkG5jBCdQDMoqCfWOxczrXlD8NFyBTF+R0Y+D6aNo7f30b7UJGoLiYnM9mmRHIXSKCnasiMCnanedEQl9+2jLZlIq16cve4q5FcHPKzyS7YOMoywuFleDxi3f1TWfCN8ou4F+rfQn2wgf93/v/ju9d9F4CdIzuprhJZh2U1J/h/vzrAm7+5jb6pLC0xP994SxuSZCLL/lkViPufEAU7Ky9pRfUpGEXTlVOUx6KGCHe9+3w8isSzXVM8c3Jy1jJ/SLS1vpWFC/6WJYs//qKu92zEK6DpLIbcKtIWnnDYFZG61nVzME0hr4oSCblME8D8hTaIefI/YOKoSD8tFC/IzqQ9I5T8yFY9Szkp1uOTSdktVCK1fubXhaiTnPRcBsuYpmAzTRZ+pjS7j5Rk4Q+VKcERKbqQLGFmxcOYTtcQsLW9FwM7D4gUXawhiCRJJLLipX+Z5EGWJOK6SYYS2xAMBslmhag4m40Rkz147MlwLpmk/4iYQcue+Shpkaoohg8jk6Ip5mdJ0I9PAs3r5/h0EiyLuFeAsNpi3mWaqF2EGhAv1ezgIN17ngNgyaYLye8TKayIN8hVT4nu7F/vH+dQ2mbMpqaQTANVMpg01mAhE071EUiPYGYyNMyLIiteFM98WoOCVj9ZMKmeFi/InqZWpJYQz9qgaV5vrmLQ2hAVAGNMMfF7ZC5YWIdvqQBNjhh8/6MPikuriNSsWexheaPQaDw2lWSyaOAFmqd1dmdew2ih3r4Ojbw2KSNbFsvy8F/5LrZP3M8Jc6/QlS1V8Us7mZ4YIZhLY8kyP9KfIHtJK36fGIhDSwwWdYoX/9GRFKZp0d/Tx3Cum/6gxHvPD3LF9iNMFXUuXdpAWg1zckykQ6XM0+4gHGuYu0N8usZmBiVxvy6KtRGQJYrAdEimY2VJPF60QZOvLUwxqjJlWDwekFDrA1gFg8yOFz7gFg2Tv/nJXgq6SdQvrtH+wQRjNmiq74hQ1ybOdb0h0VYtwJ+TnuubzLopkpnhiMBbFpUalbZ2iGenJtfED576BCP2hGXpZR+HJde4y00WdTRLePo32pWizkDrisGb5haDh8ySjYUqeXn9yotpifkp6Cbfe6aXJ46VBPQO09Sf7Cc+lcEolsDHzvu7XabJK3sxLZPtw9vpGhfb75pIk9JS7BsXz9CFrRdCYgD2/hiA2GV/z3kRsf6HD/8Y7BY+Dx4U16mp/nyqqs4DZOqbhVHlI0dGT3k+54xiDnaJfmxHTZGuHD/Rxa8/v5snfnSU4ZMJHvjGgQp9GuACmEUh281/0QcIksNCZsvxb6HrKXp6vwbAgo73IT/0SWr6BZs5Nb2FpG5w656TfHdwgsS4mNxlJpZQSIhCDtnXy4oLW1h1mdink7vGOGYDtcVBH5tiDmhaXtEsuX86h+IXWqVyC4rVdaup8deQN/LEZcG8Lq89QdqeKLxt8zwe/OClrGkR57i8kTcIu5deW5+46tI2alvE9idnpOicaK8JcutGMRb898PHXlT9UTi8hM7O/4PPV//8C7/M4hXQdBbDa/cw8tbVUR/24VXlOdNzGbudRNCnoMQirqYJy6RzaRgMHWvbt0SXjes/Q7RTvCDb7H5EklxNIrCWG3iES3iWDQ26mzKL1vnxKLJbsp43sljmNLpVxLDEdrt7xQM5oZiEfKX0HNhMkwxSupmdO27i6JELCa6yG/uayxk9Il6wDqvgME0X5MTD26eVZrIgmKaurvU8t/MGpqdbiEge/KYYRDPTk/QO2OJ5zwJkTXiqFCPHWRpI4PcoqLLkisEHY3UkxkaZUgQrUFfQXaaJ2kWu7UDPgT0YxSLVzS3UdXSS2y8GnGjnQhb0H2fxyYOYQNGy8JjQEBcvsHpfhq6CmI02TAtAYUxP4/Ep1LaGUbxLqbddkceKJtXTSTxFjZzXy30hk5RHIqqZNI/rFLIlRsSTEudoTLG4aFEdfo+C375X8seOkhwfo2ffbrFs8FpAxjITrGkTgHanXTW3Rk7RoRzEwMehtJiJxuqbWDVS4GdPZ/i/Uoik3QQ3OW4LwdMjmBb0ZmpoHRZi8MHGejytOepWbqfF93qqFuxifl0IryKT1Qx29U1jJMYZL47y96v8ZDwSScPkx8NTXLZEvAQfT10EgBoYYWq4r+KeKI98fogB9X4AGhlh6mgVU/taWWynLsZjiltxZxkWRbtAwdMSJtosXvpjfWnCF4qBKr11aFYl6vPFFx85zv7BBLGAhy+8SaRWjg8kSdr3aX17hNo2AWzLmaaWqgBeVUYzTLeqbmYM23qm5kVV7t9q7MGqOtvMj0dFhWubEiRy/vsqvuuwTHVeFa+dYnUG2qdGEtz9ud1s2dXGsdxFTA/Gsco6DhzqqsYyxTO+qXkjn/6z9Wz5yOX8qOMePq5+n288edJdtjHUSEANoFs6J3rFtQpEvSgemZGuJL5RwQxfv0CI0rcObeWkza6NJgs80bcVwzLojHbSGm6FrV8EswidF0P7eVx9zlsAeMhjwu4fAPDgIZEKu2ZFM2tWf4PN5z/I5hVXE/GrTKQ1nuuarABvp439P4PcNP1WPd/Qr2df5tX84smLGTwaR/XKROsDFDI6D337YEUqytE0OfeaxxN2bQd2j2zj0KEPo+sJgsFFNMmLwSxSYzc9n55+hgfG4zwxneJLfaPEJ0V6MjuxBD0t3p95M4Gup+hYUYPqU/4/9v463K7yWv+HP1OW217b3ZKdHfeEKBIkOCkOpQVKcdpS6KFKaUspdaNIkSIFCsUhQLAQIe6eHdvuvtzmnO8fz9xGAuWc3zmUvt91XxcXO0vmmvo893OPMe5BqDfO/n7xrI522gerXOuoxOYVBQKGYdDU341sFeNetX/IWV2SJGbli+da2E7I5Dg6WTJJ5Z/Xz+Vn503EbVMHQ4cDDu0D2L2qGQwoHZ9JRp6TbPOe/nhe03DcfNJorIrMxtr/XbUpmtD48wcHSaQ+4zX+AiFNmj5HDJhbKhYLsixWrAOkyRjWACkSH6Y0+byDBpcZ/YdxZ7ugeTM9oRtoTTyDVnwaWeWmE7j5fVnJpJ9SPFKcRaxDsWYNejS5/WKAKLIIMiRymXTzb1MZqTHdrGUDj30kaXJ6hNJkx0I06kNRnDgnCgUopk/D0i6I24DTc380SQUyxXFRV9Oc1I8iTYahEIn4kQwZFRmvLAaTg5vWk0yBjA1JyUONm0TC3cY451DewRQzZNFmmlz2ymJyzkpIQ0pTZiWqXccADuwXhKfquPlIkkRstyBNZcfNwgBOWfMGbjP3xhHTyE+KVbnflqApKUInBRGhgGlmRWRBpQ+3rRKH6kEzUvTE21Fi/VQ2i5XpA719AMzt1vBKovEuiLBsl5lg7My1c93xIgnWVi1WmPH9Nez68D0wDLJKxiKrOciqUCztbSMNCY9reo8F3r8BBl0JoQz5cnNJdkQoixiMHZNFcBhpMnQdgq20RT3ENJWiDpEg2lRQRv3O9VAwFVmKITVvRlVkRueKQfYfGxvJSPazetYi9meoSOYK9MnmLor8DkbnutlnjCXc50CSIRh61dyXkUpTZ9cHbNh4Ni2mZ5S1TqFhRQE73n2PEs3MucixkFsuwhapLpGULlkV1CwHo8aIY9R7Ejim5SA7VbSeGLG9n21wT8SivP7MP3j0A3Et7/nSRBaMzsamyrjM0Kcn047dbRmcYHJ0eTCnSZElyj7FdiAaTNDbJp7dwmGkKatQbCszmk9v5tfpy/0heZlzjvr+YD6TbUjtneZ1oQI9ssHuxn62rwnyXv/tPNv+Ox65fTW7VzYRT2m8u7eLVFgsMhYWLwRAOvgO8zqe42vqMvqObGF384DNiEy5txyAhkazSrTEM+jcPqPpNEo8JZxSJhpYr2lZw5HOISuG92qFyjK3cC6EOmGLUH1YeBsAi8pPRUZir81G07o/09wdYHdzAFmCk8floqpunM4KLIrMSdW52HXYcN9uXv3Dtn+tbhgGxgZhiPlU8nR8gYWsDl6LZlgpGpPBpXfO5txvTsFiV2g91M/GpSJvK6wNVbGNcg55N1V5hArYRj6dXcICYVTlt5Ha97IycB2r6+9A0SCZ7GVbr/m8xJJ0xMXf0a7RNKo9pBKmL12oBtWqUD4pC12C+oT4zdFOG/lKDL/RjSap1MrCL6orlCApizE0z5lHhmm6O4BZZjHQxs6deMy8pu+dHGN2hSC2hm5Qs0XkICkM9e1LJTT2mb0jJ5rK12chTQU+B5fN/hS1KdIDDy2Elz97xWMipXPjM1v4/XsHuO2f2z/z974oSJOmzxED5paKKgbBEr9zSGkyjqE0WRXkDD+5HVtwBxupqHsTye4gvmkjUX0BuuEjfiRIbnEpSWmI3EiKn2Cfhj7tqwAEVREycmfYBq0GhofnBvfPEANhbraFpEthjzWFy3ospUnCZjqUWywWLIVuJFsKAycFCTEA+YaRptNNN+l4loOEweAKHgRpGoAFFQkJryoe5t4WEX93GhlIkoQrJAhFzBVilG0oR2F4MnhrfR0B0yAzM+YUlUgAzkxUj5Vmv4fmni5kRWH8wkUYhjFImrJmzCBq9eKOhLgoGUMC1M4YlQkz6dNWim6oZKoN+DRBhlK9IkE8r9JHjkWs7HvibcTDb6LGDzC6sQ4YCgXM60zhUyQifaanVWeUVFxDsci88F/HDw5+tjHimiXb29n9gXAXrp4hVqMWqxj0krtGtiKY3bOJnEIb2cUuDF2QSp9FQjf7nGWV+sjIyUZHQksliQT6IdhObUj8Zo7pLdWcX8r+9WswKkRFHTVvQetOxuYLwvXmrhai2S42ThVq0s92xfAkDepjCZb3BIXaJEk0BwXxU32bMQwd3zClKRptZNeum0il+ulWxHW1HhZ5Y5H+PlwNYvIOFQ4ljyfMJHBLoehbN3WyCFX6k1DXF8U1W1zr4Eef7JQ8HGteep6Drz/Dcd3rOG9qIWdPLkRVZMYVeMkz/ZFyysQxD6hDWZpEoXdokv20CrqBfKbMQhd29xDx8eY4UFQZTbYS85xI0j6WMOOP+n6LOakXDiNNTkWmIiHOR2CCl0knFJHnakIhTjJusPr5g7y/vplgLIUndBE/Ou5OLq6+WDT1/eDuwe2cpmzh0dVDpHsgRNfZ1gcIVXDaqaUgGxQGqpicmsPMvJmoskpLqIWQ1m6OWQZbO4VaNr9wvqhgS0WhcDpUCr+zTHsmM/NE49v3tV4OLxekamZ5JlnuoXMJcOr4PMpSCnJcp+1IP33tgnRGAv18+MTD9Hd8LPxavwapfQ8Rw0Zr+EwyUy5UKcrx3r9y3jWF+HKc+HKcnHSFuBe3LKuncV/PoIFllkUl0zI0xlWaBKpDLgfA45lATs5imnY1sTtyBg3xWdh7xGd2mH0sAZrJh4SFRDCfXmcrh822V6GwUN5HTcul1yWTksAuSxTbrQQCW6lGJKxvi4h9aOyNIB8jNDeAAaVpe8d2vD7x9/A+dM0HegmYvQj3rNDY/n4Dum5wcHM78XAKT6adMjPcnWWGnLubPr19yk0njcaqymyq62XNoY8tSFb+Ctp2Yux8HuKfTL4GoOkG3/7ndlbUdGK3yIOtXP6TkCZNnyNSySGlCURfoSHLgeE5TQOkSUX1Z+INNTJ7yy/x9x1EdjoI7hlasSeaQ3idNrqsw0wDlUx0zSA052644iUCuSJPwpM1VO7tMX84rg/lSykIRWXO6eXUzvLSrhq4bEPuzSBympwyI0iTJEs4xokVWoYswjMDfjyBSILTTNIkVwtloL9z6DeHkybVrJpzK+4Rv+mO2VEBbzQXOWXHkKHEOVQpNTwZ/EirmGwVI4UvkT1ULw6EM3LYUyT2c95FXyaruIRkYyNafz9q/nhkdyH4xERcdPAgO+aOJ1LThz8hiFHQKnxuKu0bUBSzorFHvJdf6SPTLCPuSrRj6H1EpZ1YYiNdb+d2a/gUibDZQ26gQiuryI08zIBOcbuxjRtHp8dJqK8Xu9PFzNFx5nse58TMtwHo2b6BDHXo+szs3w2n/4LsYi+GLiZsb0hsX/ZYkR0qk0qzCJs9B/s72iHYyhHTZT6rz401qRO3Oag1ZNoiTphwPmDAsu9TnSeuSxTYuGARSDJnxJOc0Zri3GZxbz/e1MWls0sp9jvILFsCgKeoF/RaPP6h+6+h8TEMI0VGxnH0WIQi4gsODcjqPqEGdniHji9p9muzmkpNTqGblAwWJDbsbMc9rwAUiURdgMSnTASGYfD2rlY+eF8oJBXxZn527sTB9ycWeckzla6cEjGxxG0ScQxUJOzRoZBCRc4nJ4O3HCM0B8ITx5/vGLSfAOhMFPJxDITn8m1DxRixcJLcOrHoCE70cvxl1Vx44hauy7uc8oJu0eNvaR0YcNb4cVwy9mIssgX2vAwdQxV2p8pbWLqzdTCsOECaQl3iN325TjyZdiKjxARecmAqTouT6bmC/EwJreXlpT/k/Nq36Eu2o8oqs3xVIiEbYOHtI569U8tPB+A9l5PKmoeR0DltfB4fx4nVOZQOi9g07BGLoy1LX2Hr26+z5p9Pj/i8vl7kHP0zeinj4nZqCi34il9nknMZfQ1DVV9VM/MYv7AQDHjv8b3s7hITfJVzJGmrND3OAs55eL1TqK4WRHPjriHVRu8sFIp1fOi6NFOM1l0ASPQ422gyG6yHQiInsWxiFn3m9S5XzfzOvo2DpGmj6b3V2BNBtgtFqDrz6KbHFb4KsuxZxLU4fbIYq3r7Ngy+v29dKxaXWHzE+7NZ8+IhXvrVZra9J8bLiScUDS5CsorEvRvuTxANjfSmGo48r53LZ4sqvOFqU6JtL/qGRwCQMKBz/yduA8Rz98NXdvHmzlacssSvZo5iRpn/U7/zRUSaNH2O0JLixlRNpak00yka2cLInCYzPOe0Ksj+kdUPWnsvscjQw5RsDuGyqXQOq5LQXeLvQE8SRp9CsF9sbzhpssYHQnLDB3sx0eoRnZDZ08v9sZwmp0VCkSRsJhFSVfG+Y6IYVDJVQWBSpr9TRmeMHGQSFgn3JLFfw8NzTucQAZTMXCandciETkbHHzXwKRISEpaQmFx81iFTtzFOOzZEMvhWc7+99CPH8wcfcC2VYnUiC02RydY0Zp13AQDRXbuQfaU45txK91P78eaK7Xc2NRIJJbFoCYyU2EZHUORHjRkdHqzE00ylyZttJ8siBqM+ZQKKbRaSAc7QEBGYJKlkJgwyFGmwcfGANJ5d4kZPjGxBUfS739FUKEhoYWcf+p51THW9zoSMQziVBMlEioKgUFWqwnVkVs6DUYvwFzowzCpKR18fABZT5ZlanEHQVPICne2EO5roiJlqilRBcbe4V5ryy6hZ/xGc+jNQ7VD/EQtS6zCA1AQfEZeHzN4OfjKulJ6UzoWN4t5e3hPA4rHw0XcXccGCL2HoMjZvEtWxbtBmIpHooaXlBXGMpbfQaiayZgR68BeYqmijUNGaSA02UB1SmsT+y7IEGaYK88xLJFvrcE4W5+uT1Ka9LQEue2Q93/r7OnwRkdflSgRg+HUq8g0pTaXi3DT1xehUxDXvax1WmJH1ybYDx0oCH0CmN0JL5tCz1RY/evJoiYtzOlxp2r+uleJ2QWx26qaHV95EZElnQdHbKKqEsy/FmKTMOVPMiV5LwvKfi7/n3AySwni5nnyjgyfW1gFDXk1Gn9nj8cAWjFSK3SUr0dGgyU17bWDQIPOyXVtwaAkWN4sJe7rqx/nydRAPQM44qD5zxLGcXHoyEhI77TZUo5nT5C2cNj7/qGP22C1USkO5WbW7xDXqqBfqSeuBYRNzXyPsX0pcd9IdOptWv8I/F3r42czL0ZFoqtkyYtsLL6ois9BFNJDg/fXi/hjtHOkbNkCaGpMOZs18GZ93Ck37emgNDuUHBdom00UOIWPouy0UE+wW40PA1Um7qQa2dIvzY7EpJKvMYoKwuI96+zYNkqZNgTAp3aCpN4pi+2SlaXhe085gBAyZaLSeut2PUV/3LF29/8TqFudsyokzsdoVOuqD9LaGUVSZcfOHyJ/VruLNEePCp4XoQPSus6kyW+p7WX2wi7WHu9j2yC0My8olUC/yLuPRFHtWNxMNDhExwzC45819PLepEVmCH5QV0fR2E+8/vvdTf/eLiDRp+hyhfVxp8jsZGB6G5zRFB6rnbCpK5sjqgtCKQwCoFqGoJFpCOC0yHWYVgo4EXqE6DZCT4XYDAEZSB5OYDSdNskmatFBisCLj44ngdmPgs0NKE4CtKgMkA7ciU21LseKJD+j7qJkZLeK3u0rc+PLFBBMNJgcbrQ5XmiRTabLbhiaQPCmEMx4g07Qr0CNidapYh6kSssQ4swJmV4Z430cfUsKNbjobr3/5eTpjBqqmMb2rC1kWBC22azfW6rPMbacYlS8mj1hXG029UaoTYrC2yBYk2UHl1Bz8U+agDpCmPkGa9GAStyxMJXuSChbnQmY0Jpl45PBgKXR1h1jtifCcSZpMpanI0Gn58VpafrqOjgd30PvKQUK1GjGfIHFFTW3U/2kF0W4L0lm/pWyUSHz2d9YBMDuwB04TE6PDNWA3IaOYvdJUM1w6udhHQBU5QoGuTmqPiMnDsHpQZBcVEXGBmwrKObD+IwxfMcz/FgBjd/4KudiGludE0VKcv+YNCjPsdMSilEQM5gZEztiTzeLaqKoL1azismftp7tJhDmbmp9B12N4PBMJO6ZjAJZkAmc0TNH4JVgdHrzBdqwpjaQBR6JxDN0YrJyzFA0pkQMhBndnP213/QT3AnFeoju7SPUPuRkbhsFvX9vD9X/+iKYjfcxJ9uCz+HGpgtA07BkyAR2b7SbTtL3ILhG/1dQbocN0VR8+wQyE5xydEdZ/WDuoGCdiqcFr+3GlCSBT30erf0hF61ct9IZHrvY/ntNk6Aa7VjZT3CWencPROO3x5KDtgK9/Hd5p4tk/NW5lYo65+Nj2NPTWgjMbTvoBlAric6q8mWc3NBCIJYXSZEjYwuJ4Yw/+hs5HHmFvYjsHcoRj9ea3aplXOI+SToPJTabRZ18YSTeY13YA6sz2Isd/B+SRU0uOM4dpuSLJ/n2XkytcGyjNOrqaMhpM4I0Ovd5yqJ9kQqPL7C3Z195KxAyLJdY/jIzOy/23Y9dVWirF93qsPva6RhFtGmnDoFoVFl87EdUqU5sQ53r0x5SmCvPfbYkkYU0sYja8IohajkUkz3f0zqQpVT7ie80U0d8uji+7yMO0oFmpGzlMzGyFFTatNZxNUVKpCMHgLkpoxKNIhDWdveEoDT1BZJsIQQ5PAh+OAdLUva8be0BUqR7u+AWHjtxJ7tSnUaxRQGbivOlcdtccKqaIxer4hYU43CMtZAbymj6pgm4AuV47Xz5O/NY3n9vGw4/9leO0LSRRWSGJ/emr3YGuG7z90C5WPFPDG/ftGEzmf+3FPSgftWAFfr6omuAOoSCOnnm02vhFR5o0fY7QzOoWxcx9KckcRpqGVYoMz2lScoZWY3JGAdF68eD5pzSAImHENKT+BN3uIjRk2mx5KKZtfsBsXTHcbgBAMwfnFAYSw0iTZBKAUHJwHz6uNFnNagd3MoPMzEzGjxe5GLJNRc8VE8hYh4OT+rMILT1CuTkJh6t82BzqYG7HwL4NJ03o4rcsw5yLC6IhrPF+ck0Vpz0qJOmUdeRDPjVDTBB1xSLUk0EfSspJqidGc80+Nrz8PAATm7qw9g4dc6ymBUvhUOfzURli0rWGuzjYEWRGykz4lsXrM84og+rTB5WmVIcgr/E6QTj7NQavaUaoh+OauxknG0i6jnvFqxgYWGWJhElkuxpDyIDzsPi+EdNI1AcIb2gj+l4rpxVcxaSKE8ipGoMW1an/MItATYyyk0VF0sSaHUwKHuDqbAtkC5VGUc2WOLKPRFicF4tJmiYW+QhaxGvtzS3UmoOlrgqyeHKhIKzNheUEujppO3RAkCZPIXKgEVuluH4LNr7HOJtK8PU3CHUKH58LD4lj+kdrN9GBKqWYGFC9xWG2LVuKpkVpanoKgLLSa2kwm/L6Aj3ISjaJmA931gRRZh8WeVk14RhaTwwjroEqDapmAGPKxN9BdwnR7dvReuuxVnhBNwivbUHrjxNa20LtX7Zx0bpu/oGH53DzC1s1ZxZfy9klN3Bq4Vfp+Kh2UOXzJ4SqGZQMusxntrkvOqg0Dc8BqchxobhVPpzq5QK9jz17zf5lO7owDPHMeT7mgo6uk9n/Ia3DwnOGW2Vb48hQbtvHSNOAMWGGojDVrBh9u6sf8kRCMMEWdihd9Mk6Tk0SPfuSUVj5a/H+8d8BmxvGChXoXPt2QvEUz29spMxbhjeRiWJYkPQUtngv3Y8/jhSJsqd0JUhQt6ubYqmcMzcPkT1LSiKvD+aOOgtO+Slc9hxMvIBj4dQy4cn0nsvBRLnumJ9ZvUWoQ732doK2bowU1G5vItQztEhqPVQDukZyy9PUxmbRE58OEgQmegc/syJzFu7+g0dtP7PARdWsPLrMsO9o18hr47eoZJoNpeuiCRr29NDeGEclzqmjhHlmUMunNV4OQI4snp8Wion1VhBVQ4zKL+NKLR/dAIes8/edfwag3fwpV2ucptp1GEYKhy2XmT5BXDb2hzncW4skp7DKDoo9x+6/NzN/Jm7NwZl7Z5F98CJcnZNxdU0m1TuDYNN0LPqJjB37c1TVjdtv44wbJnHlvfNZeFHVUdv6LMngA7jhxErsFplQJMqPVBEm1WddR0uBSP+QOvaw+c1ammvEfdzZEGTda4dJtIaYsqWHr2Dj4cpCnLsC6LpB+eRsKiYf26X+i4w0afocMWrmcZxxy+1MPEkMHiV+J40MeAcNDcSREUrT0E1lHX0qIGOTt2KbPhOLWXKdaA6he7J5tuhi3sw7HdU0pBxQmoa7gYNQRQDiFnCpQ6tb1ezJpoUSgyHCjytNSlS8nkyq3HLzLRx//PGD7/WVeGlO6AT0ThzyGupoYCUpHiSG1Xw4faYcPOASbbfbB71ENDM8pzj8KIi/s3qj2LUomYr4zLqAWJlE7CnQhmT8gWTwqEOcEx99yCkn4YYu3rrvtxiGzripkyjsC6HHDfR4HEPT0HVBFgZKDzN1sZ/eZIDle1opTZg2DkoOpROyyC3zQmYlSrYgb1qzUP7itYL09JhkQTN0LMkQSl4ez86dxK9DjeR0N9OXEJOq3Bsj3B8nEkhQapMhmkLxWcn95jQyL63GOttPd7IVSZIYJx1H3re/jzMvjpGSaf7p79F/eo84zsONvFbqYOIptw+ei5gZapJkHwmjXFzbHOfg9XSa91RLYxN1XeLAbYpQhM6Yko9Fkgg5PfR5M6lZtxqsLjj1p2zwTabP4UNJJpm6ZyMZ+YX0Pvss9p4D9KR0FnRqFCHTm9J4vUPcS+EOMaG7iyLsXf0BjfXPkkz2YLeXkJNzOvUmacoI9KJYqulpDROPiX3O7BDK1P5wdNDU0pLvQhqW+5V5WDhJh9wlGEDvs8/iWSAmm+DqZlrv3Ujf64exNodRkIjLYFhkEnqchBZDN3QybQVUh8fT8edtRHd30WuSonZFZ3ezIG5NvVE6TNI0fIIJypCcmU3AKqPJEm8d6cTQjcEmwwMVaCPQvBmbXkPPQL6WYYBVYU1j34iPtXyMNO1aIQojxs0r4GyzDdObnX1g90KGUAHaD29luUN8b/v7jfS+/3cItoh2KzOuFhs2Q2dT9L34CPG3NbVIqIySxD3giHUhGzoEgpy+2SCvwE9BpVDkatc3sWC3eO5iVkEyS9psOOb9FhbcCtVnjMhlGo5Tyk7BmjQo2m4hHugQlVcfw6ZtYpHS6j1CQ4ZQeA5u3DfiM60Ha4gcXoMcT7I8IBrZTj6lhO3JIWVxpX8mZXoDDV1Hk4GyKdn0mG17RtuPdgqvMEN0R8IxNr4hkuUnOt/GX140mKt5WBehs+M00QqnjQJSWOh1tDE2eywefyVSTNwvyw89TUN/A4fMez07oLF+h1jEZWTMYo5Jmjb0hWmKiPGk1D0KWTr29FzhreDWzq+SlcrA3pBFwQdLKN56G8rqm2hZfxMzZj1AUeElg5+XJAm33zYYHh+OrKLPTppyPXZ+8aVJ/Lx4I6PlFnBmYVv0XTxloqI42mVl01t1AIw3w4A732+k6Yk9WMwBdlRtiODhPhSLzMKLjyZx/wlIk6bPEdklZYxfeBJF1WJw8jktHFHFwBM0lQoYcgR3WhWUjAwAJKsHtUBUT3lsS6F0zmBCbLJF5DX1Wf3EFAe2DDEQBLpiogfZYHjOVJrMpD/doeJUhnqbWWQxiOmh5LDw3MhEcMlUqSI6xMIj3Ze7Iik2RzRCo2WyrPcyw3Yrf5VqeYYEPqfYp0HSZBK6gf5z4ofVQZVmSp/MiTmHsXYZuLwFyJJESDP4sLscgLhdIdV/aPC3B5LBB5Bh9CPrVjb/40UCne34cvNYdONtSLKZ49R4mMjWA6j5UwFwH19kHkQKTbEiY3DgwCEs5sQlq9nMPLN8cPtKpUiI1dpFeCtRJybX7pQglTajFwlwFBVSYLNyxbnnMmbOAnrjpit8MER3UwgJGONQzH0oxlroJlUMry3/Ax80/Z12vQHJkOh9K0jewgyyZrtR/H7U1ja8Zh+rrX95CS04NOgFOs3fUPwYhgjXWIaV+xeYJquh2v0kNBmLDIqST2ahi4JCD1PNc9lcUMaB9WuENcGki3i+8goApjftwppK4kppJGpr8QbqaE4aKMCFnWKieLxZJKP2NuSRirtQrDpWfw+HDoiWFKWl1yDLKof7zCq/YA+ytZpQb5xUKh9JduHvFOe2JhwbDM0N3PMAhq6jv/E0kp4iZXESs2cRePNN1HwJNdsxmCdoLfPydo7ChQRZvjCPtwMhXqn/I680/Anp0hL29m0gqcdJtoZ58+0D/LO+jZRVol3R2dXcT2jVKqIHD9FthueiwSTh/jiNsQQX7zhMwqZgM8PrH2px6rZ10NMSxmJXmHRCEUdh3+vU+kxLiLBGtiGG4fWdQzYawZRG2CTg+TYLfR0R6vcIMjzxhKJB0rS2L0R3IkmzZRzL2yqpCu0jmScqpHTNYPU7cVHkduJ3wWJKHZkVkDse2dA417mb1v4Y33tpF66gSPZ1RDvRnGLxcc5GnXH28sHWTTXLD2JL6dTlwrqxYr9LmjOo7frX/cmy7Lmct9rDVz40qN3mh7aRfRHbw+0km0w3/7JcGjNEvkvTfqEYSSaJaDmwn9rVz7E6cA0xPQN/gQvnSfmENB2LSdg2+iYjKbBj98jfAJAq3KRUCUUzsLTHjnp/gDRtru2loz6IKieZ7n6FJ6wp2l11ABy0isXWVLZgNyLokkKPW6bH2cpY/1jwl5NnLk5z1ARXvn8r/SlNWIcENSyaIGMZvlnMNg1LN/aH6NME2R6XNY5PQnRXF/N7p6AbGrHNj5E4LPqPlltlysb7B5u5fxqW1S3jx2t+jCNPnNPe1jDaZ/BMOn+sk0tDZjL+oh+BI4PS6mn0p7L4qO8GMMRC4aSvjGPSScVU2WSs/QmChkGNHSQDpjlUJp1eij3zX+/nFxFp0vRvRtgvbpyBnlrwMUdwr5CcLaMWISkWLFINttGZoNoGczsSzaER1gAO82bs74wSCSTQkjrSMI+mgTwf1WvHoQ6RJptJmrRQcpC4fTw8p5ku12HdGJHoB9B2xGwZMXseRsUJOKQE96qPAgY+0zRuIPFwoOs9DIXoJF0lYfaNK47bGKd3YegSlgKRs9GR0lGSHlRznAt1bhzcxhinHYs+9ND7UkItcEoeCqqqWXLHj7Fn5KA4xaCaOrKD4IomJEnGiNbhNsvVk61hFDMvakpiLz1xQSDyKispGDWU0KuOE+X4Wn8/eig6aLooIXKgslJCobIUiPCqJEmcfuOtJEwVwB5rp622myKLhAOQXSquWfmEerp54Wc/JNDZTkZBAWP+azG2UT6MlExP6qf4zzmd0StXUPjb31LgEvvTVF9L1wMPDu7bQFm2x5qLJMlIcgzZM5RMPM50tB7ItbKbnxtoBD3gOt1SNIpgdyethw4Q1nVe980GYG7NKnEO9golICtHGcy/OXtXCKsksT0YYWtfiGBXgki7COEWz+tAsgaQcFFYcCEAe9vEvhZbVRymR44kyfgLJ5PdI1S5A+HYUBL4sHym8OrVaI31uKJiG3WF0zDicQKvvkL21RPwX1JNwQ9mk3X9ZP4cCNJhGNg29RAL1gGQWVRCybRKaqVGljY+xAZnH7dPc/BYhZWHTvdxqMBC7+atNF53PZc9+wvUVAybX5D/mvp+Lt5+iOZ4kpKwzl83CdKw0yuz+x1xD0w6oQibc6SjPoYBe19nl1ckDef3alQinrGacAzdJHoDKpNPVXApypAx4YQsMnKd1DcGyEdCM+Anf/0rz60Ks623CE9bC48nvs/C2HdQpCSNsQnUWc+BKZeP3A9TbboyUyg7L21tItkhrCeckU6eLZ1PZ44DdwzmremlcqogTZ1BGwmLi7dnytTniGeptEPhcMenNy0GONQeZN6+FEr2WFwtLhpqPhjx/ot7XiYrLFTCS09eRLPvIJqUItovEqMrponebG2HDiAf3svB2AmAwSlXjWOj2Vz7xEwPRTYLcdnKBt9kWg9uO2o/ak2vpMygRv32o/vcDdgObKsXYabJGSvot4T5fec6NusfEbFKdNvFuFxGLYUIct/lVeh1tTHaPxr85bhNA9siK7QkxbimprqQieP1i+80puxM9TixSBLtiRS6SwxuU/OOTZq0QIK+V8Visa3lbfS+OhKt24lrOnZZYnyp55jfG4BhGDyw/QH+a+V/8cqhV3ineylWu4KuGYOeYp+Klb+GWB/kTgDT0mZMQRZL+79LVPeRkaUNKkiz5uZTbS4I18STHLBZSOgGGarEDnuKiat38Ye6tk/6pS8s0qTp34zJM8Rk7YhopEwFaFBpsilIqorstGM1PU+86otIVcJkzmpOIMnmEG7rkCLkNhWlRDQ12D/LNcyjSTNJkzvLgUUZIhp2WaxkjWiKhEncPk6aUj1icIp8jDRFQ8ON/PxI5/wJQ3UwX9nDt7M2UOAT+5RhkqbhiYeDpMlQ0Z3i9yR3LqFWMXipZquIjqSBW5eQImLiCvUPlRRbZImC0JDy5U2azVbLJnLZ3b8lu0SEL1SP2GbiUB2pbnP7uQGUTDuyUwXNoDBHPPTjorVohg7IzP3SjBHnQakWZoSpGMSXvya2IzXjVMWA5oiLwdiSP1StYrHbmXLJOeI8WDLY9MrvGW0V59C9oIhoJMALd/+QvvZWfLl5XHTnL/DkZJP11fFY7G3oZNC17ySMmIHv7LOY/EPRt6nT4yC4ShAZwzDobxcDkddiqkzUI+kpjGSSrkceYcpvfjDiWOKKyOkaNc0kTaZTcVuZOA97Vy3nrc5+woZEmdaPv0kM+Mo2cf5LfvIjlGAz3Skdf9LgTMT1eay2A103iHSK6+fIFhNC2zYXXfViG/VhcT9NLisbYX45Zs4CsnsFGToSiRNuHWk3ANDz7LPiXOaIe2ZfwQKSqoPeZ/+BkmHFNS0XxWtjX2uAUCzF6QkrwZYIEiLMVTpxsvlbM4jrMX5bIRNXJGTDoNch03BcJtt8ELHZ8cRCnHtkDfYSN0fyVG7sbKM2mqBEVXloU4TKfo2CmI4mSxy06iiqRIVWM9g7cBBtu6Cvnq1uMSkW9KSoSJq9Fu0ytd3iOFvNyrkCm4VkQmP/WkEcJp1YxIH2IPfe9wylm1cAsMWTgyHJuNU4SV1h62EVb3AjU5yiJdDmxJUY8kjFeCCvaVRgA7cvKuOrc8soU8RiwRHtYFdWJS/OE89H4dLNuGwpMjMMkGRa86bROjpFvbhdKO8OcbjzX4d3Dq7bRnnmdJwLbsM99gL+tmIpEbPbQVJLsmrzZmRkVJ/OuPevR5WTtHqOoGviWaqeuxCrw0EyHmNvr/AIq5wmQubrzF58czPcHJ8piMNK/0ySrbuPMmRc3yEUveygzpFtnUe9P1BB1yrpWGwy09S/87rbhYFBp6uBNjOBvzDVgpMoReb91OVVsGeDQ3WAvwJ3WIyhszOLOK3qGgAW5pVTOaMbWU0QS1p5qW4tDkVmirkS1M1q6fHHUJoMw6D35YPokRR6Jng2v4kuQW/uBOqS4hjszf18Y/k3uO7d6/io+aMRx5bUkvxozY94cMeD5CT9nNQ/m+WH3x90u/9Xfk0E22Hz38Tfi+8BRTx329+upy9ZhUWKMHbMVlSrgpHSCbx8CBlhaByPSej1EXab6R3LegMEdAPdbBP1n4Q0afo345zZJYN5Tfu3i8luQGlymkTIWr4AyeLEiLRgl9fDqEUAWPJcIEvokRSFyjDS5LTgMvOamsykvOF2A7pJzpwZdob5umFX+gZzezLMP4bnNOkJbTAfKqyLMMUABoz8/AWmkV9mBdKiHwLwTe1JVLPZbFF1JkjQXhsY7AVVWVmJhIwl6cEwG7PKrhxCrXZkdz6yxUvKMOhKCdKkxcUqLxQZagXR3Rwip32o/NVjVirqfdIIDyw1U6gz0eYsQCLVvhvn1HIkSRpUMcr95QBIIaGqWWx+SsaPrGJUsrLNcyITXy+ad1rtDfzRMo5Gay/lXWIVbXGO7CqfNbkcwzBwqh4KpSx8FicJPc7SN37J87d9lZ6WJjzZOYIwmb8hWxWybXejSi1oEQudj+1GCycpGjsOi81GwqKyNRnihTvv4MHrrhCJsoDXIo5VpZ7IBy9Se/4FdP7u96ixOIppo4ABklqJv8A1aOA42+dCAtptLkIONzvee4vH9ojJ/8L8XCIpMam4Ygmcc+bgnDkTv95Fi+mCfG6dOG/v94fQJVC1IcJpaAodO328/vt76ayvpcMqiNLcyZPw5w2RpimnzCbfasEWj6IBRyQNZJHTBJBobCS8SlRrjTtdkJ8MSw7r5vyMQ/I4+j5YCUAslGTNG0e4uU9lQlQ8IzaHIGOlE6YAMOa4mewfPZna4iJUzeC+VSEurRfPyM5J47nmR7/iF1fdxPuXnMp3xsEzJ3qpl3XyZY3HIw7y4gYbSOENimu9K1+l0t1N74++Q8OVVw4aoAKwTxCZjR5BJAt6NbJ6zHvVbWHH/mZavvtdjmwUCdEFNgsHNrQRj6TwZtspHZ/Jz17eyqKO5Uw8tB2A2uIqHq64ko0FczEkmYZIBtur72bKjV9HUSU62hVaDvSNuA8pmAaeQqREiG9UtPKz8yZSpAmyYYt1ciAzjxVjgzRlgRQM0/P3v5PTIX6vtXgGx6ViNOSKMaIw3EtT8792YU++9w5qvjjnatEMyvYn+Mm6n2AYBu/Vv4e7W7CwykINuWkT42MRGjP2YOhi2znlleSPEgpdUzQb0JlzXhWaYbC+X5CmeRluTvAPkKZZFCfrONgxROj2tgR4ZKvIlcsOafR3RulpGamSlZt5Tj0ehcnTDWxykNd8GQB0uZoGSdPYUB0AZQlRFdvlVcgvMZuR+8txDaQvxFvwme7dY5x23JV/ByDSMoVNB3bSHeliSf1L4rWM0zGwMTpj9Ih9MpIavS8eJLa/B1QJq7IPDI0dFRLNo06iLq5jYKDVh6k9WMO61nXc+P6NXLL0Et6rf4/+eD83vn8jrx9+HQWFv3TfyR0tV3Hz5iVkusR9O9CZ4BOx/n7Q4lByHFSeSCKW4oOn9rF1mQgpnuS9H1tAVFoGPmgg2RYGp8of9aGognViNpE82GKewwW7j1YCv+hIk6Z/MzKcVkKm5L93qyBN4WHmlgBKrhhgjY4PkTLLIUs4KEsWGYs50VRoQ0l+DsuQ/0bTftNHKGuo4mhAaZLdVmxWcQtY5RSKbCA7xc2ciYQqS9jUoVtE6xUkJyVLpAyIDFOaWk1PmoLhnjRzbgJ/BVKsHw6KlgRuv22wpcShzSL8snDhQqbnnIMl6UU2Q4iyK5d4nwUlV4R2GnUdDfAYEilNqDchMwQGsOejFgp6hwhKiVsQUYtusOLJfYPESc3OQXJkkkoJFSVR8yaOSaKFgdUsX88zPa80XVyHgsryEY0vARSfbzDhNa6L62M75UvU2vJ4zmkn1SsGarV52YjvyTaFqJmQOTVTKIaHA9tobW6gN2zgtktcfOcv8OUOK8Xtb0SJ15Nt+wmyx0KqPULXY7uQkhIlEwRhaMzy0nBgL9FAP5IsUzpxKl7VJBjRPupvvZv4wYMofj8Fv7yXHr8Ig1jxIckORk0fIoU+i8o4s6rIcc4l9Lsz2C6Lf59qJiVbUhoWTcd/0RIAsrMlWswK0PE1QXyKTL+h05yp4s0oxuUS57ug8EI8vhICne08+cufkbCJ7Y4tKBhMss0uceP2O6ies4C8LqGw/KXKhpTrRLKYORj/eA4MA9eCBYw5bQLx4/x0yTop1cnhUV/i5ZcivPvYHp74/hpS23txSBYsiSCVB58m2NUCkkTxeHHd7GWVLJ8vlJd5u7uJdab4zv44D20Mk9/TQ1t2Lu8dt5DmPHHfZYQ0pjf08PK2b5Bj5hl9RAqtWagm63JUCvaIXmRaXx8dv/r10LXc9wZBxUmbUxCEgt4U7ibxXBlulcRzT9P/2uscXvURADmSzLpXxeJg0onFvLWnjaZ9u1HQKVVlqhxWDEVmyblTKD/xUqrPE3lnq95eyQbJz5ozsolaJLa+Wz/iPkSWRdI2wP6l6LpB3Eyr7HZ1oHnbMWSJd04Sz3P3I4+SsX0pAFF7Jef3pajMKiRhVq0mDh9dqTYchmGQt20dSpa4D2Sbl1ndZSyveYu/7/07z9U8R0FAjGvFNkH6xyUSdDr2gxEHZLzZ+aj55WJ7qVYqRsfx57vYG4oSSOm4FZlKI8FclwUJg33uUWTZgqw5JJSqlr4oVz+xkbhdjHEec7g4sn2oeTGAvqcPgLBdZlTZQbbbrDQoYFfspJQkDVlmK5TOAGMOhZhcJ9Ia2n0wpkAcA94iHAkZRTPQjQQ1IbFNf3QdKeMQqYSb7u2XsnjP13ll3aN89dBj5MVa0FU/Kd/F2NWhRW6qJ0bHgzuIbGkHCTLOHUVo2YsArBnvostSQcyA7rjIk1oSOJmLx1yMQ3Wwr2cft624jUX/XMSGtg04VSePTLgPb6/ZTiuZy+j6OJMdMr0NQzl1A9BCYZHTGO2DTabKtOA22moDPH/PJlMBNYiO2s8ox1q8/QeI1wcIrhREsnFmNuusGkcyJLJL3MyclGLZwaVossSooMaEeRd96n3zRUSaNH0BUDRWhFH01jCBWHLIp8mqYqR0JK9YdUih3TD65BHfHVBHSoelFzmtymDC9UAYbITSZJIdxWPBZjd9luQUSAqK2SLCj4TLpo4gCykzoVwzk8OHh+daTKVpeI8tZAUmLBF/73tj8OWqWYIQHNw81BIhHhLHbM0W+y27xKSimh40ByVBety6hKaI8xGmD8MwSCY0ata3jSBNRRlWDHOCbdrczopna9A0HTW/CGvVaSCppDr3g9aFpUT0VhoId9rCIytqyqZP5uOQFEUQJ9lCErH6tY0tJtMlvpuKit+29GyAhvUjvhsz1TuLrKIZMPeHV3B6ST3T/M1cXLabjKyMEZ+nVYTB1Pwscq6djOyykGwJ0/X4buaccwnFWXmUdvUzw+nn8nt+xzeefIGL7vw5GebvdHdJoBs458yh8q03yViyhOxiccyGXYQBRk/PHfGTx2WIc9E/aRa951wGQGnTYepfE93rXfEkqkPDIwvzvoKxOWLgTumoBizQxX11sNCCL8dBieVG/NrxjCr+Jufc9n1Ui5V2RXwm09BwKjLVc/LJK7Yxc7EgdNXzFnLC+mVYUxprc1R+OcaKYRjo0Sh9L4mVuf9ykauz8KQynvDE2WLvxxbrISY5ObipHS2p4wo2Mm7fk8w98EesYeHdk11cisMjFMt76zuJONxk9XQwZ+cO+jSDSJadmb06zyw7yOmrVlO59QC//Msv+ec9P+Ybb/Zz9jqNwp4+kh1xkGAtSabWJnAmDfqsMvXjZuJZvBgkif5XXyW8fj10HoDO/ezwiMore1LHFTew1EdEragq490jzme7XTwHkT19xMMpcko9VM7N554391EcFaHNnPZOFqfEKr7TrXDn2eM5+5ILKZ04hX5F5dpDbbzn1Fg/1k7Dnp5B9/lBmCE6at4m1BVBNyQkPcnh/D5y8kW+2pGp1VhHj8KIRnFG2lCS/RioaOEpPD3/XrzjxbOR1d5IX+STXaXDu3aTq7iRLEPjkCNnMlOPGPxuy+/Y1bqb3JBIRC+MvgPAuEQSOSnGFUn203I4xJFWM4yVamH+ZSLHbiA0N82u8sQ3vs47P/0eE01i1JhZxIZD7QRiSa5+fBNtiRSGqcI3m27ow0mTltTZvbQel+n63hxo5DWPeBZOrzid0RmjB5WmrKifdeuqSB0y+yR6VMb4TUNKRUXylQyqTQNtlKzdIon673svoFez4ovn0Losj1jSwoJD4p4Oek6k08y7itb00H7fNpItYWSXSvY1E5HVNtHJwG6lpfBU1ox1YQ83Ejj4KgCnBebxw2nf550L3uH6ydfjsXpI6AlyHbk8ecaTjDosnvWeijhvZpiu+DaFsW1hYgeGVNHgihUcmDmTI2efQ89vbkMPh9BzJrLxwBhe/u1WAp1RrD6J1ybcx5O5D3JLXg72ZIrup/aADo4pOXxICiRYUvIPlug30fPtG1g9WhDLkzpSaIGhaMV/CtKk6QuAykniJq4yZF7b3jKkNNkUEg0BJNmKHutHSjbC6FNGfHdgos+PDeUmDSdNAxhOmrSwqTS5LGT7bcjo5NrD4M5DNs3P/MjHyGcyByyXmOwGwnPJuEZXw4CR38fcj8eJHB4OvgtJ8f1R03OQZYnOhuBgb6kBAmbLF/stOTNBdaBkC0JyyCy0KEvJyPYJSLpBStaIx1s5vKWDRDTFaElienQ7042NeJzZWM0cGZcisfejFt68fyda7lgspSIfIlHzFvaJEweJocVsmWH0JFGG9fLLLS3nWFD8fpTMCkBB9lpRMu1ku604kjGcZvmz6tTgg5+N6C2YHNaHrMdtwZ06yAR3A4vyj+CXe+DwhyN/yCRNFEzBkusk++uTkJ0qiYYgyuo45954OxObu8jfvoe8knIsVhuGbuAw3ebbA6aCc+3XUf2iauvqb97AuPJKZMdsnJE2XLGRPb0G8po29IfZmCdabEys2cahTYIAuuJJ/KPDSJv+Cp0HyJlRjZoMD4boFjSJ4z9UaCG/KYDxz0xyP/ga4bf6yC2v5JRrb6bPK0IZFW6xf8k3X2TC01/H+N6VBJd/SMHoaqr0JN/ZVIdkGLzg0PjtnkME3noLvb8fS2Eh7hOOh3iQ6XWPUuXoY7ndymzjXcYc/CfliT1M3/knZm/5JS1SkDFvvkZfgXjWss28wQ19IZ5uFWrRaateQzL7DCqz8zH0FL6s8RQ3WWjtcFDV2UN200EseggDhd7UYgCsuSlyrFbGJmQq28R9vL5qNPnf/Dr+U0WVZeu3r0d/7GwAlmeJ8HqRrOLwWpE1g7yoOG9t2ULl7MowG7A2RlAtMqd+bTwPrT5Ca3+MsVGhGmU0tTLlpz8C4MOeAOGUhiTLnHbDt3hv0QWErOKZPzha3Anb3m0YeV+VLwSrB0Lt9JltaxzRLg4XWahKdiEZEnqygJybbwZE5L7NKkI4h+NzIXcCznHCgLG8v4XDnZ8c3ml85Q2UHEEoJHPRpeZP5oJDLnRDJzdUhmKouLwq3j6hso3Nn4E/JJ4VSclm+Yf1WNvFfWnovVjNPMl1ZguSosZDJOMxOhvqqGwXeUZrMmfQWruHG5/eQk17EGV8BigSjkCS+mAUJOGVNuAbt3t1M8GeGDnm9dgf6GeZS9yf5406j5kF8wmalYVSUx+NkQy6m7pRNANNUfA4Rw0ddKbIa4phozUpxpNCo54D/TP4qGM6LziTxJUomcEynmo8lYqP2vEE6tBkK7+rayewopHuJ/ZgRFNYSjzkfmM69tF++l8XOZShxaexc+z5LJ/iZHt5jMzDNSQydOQkRLZ14Lf7uWXaLbx1/jucN/0+7l/8LFW2UUR2CpJYfOoEHip6ge8X30dIM7BL0PX47sH3e//xDwASR47Q8OJe3t3yVZ7afQeb3qzD0A2qZuXRd842Wr1CCd1uzaZB/wl6OIWl0IX//NFsquvBR4jZDa/Q8Eo/4UiMjRNFDuUFJ43Gt7j8E++ZLyrSpOkLAGuRBwPIQ2bp2oYhjySrSswMe2md+1FUSQx0wzDQUiI7PKSyOKzKYHjOY15h7zFymhSPlfwcL9dVbeSc4n0ELFkog6RJOspuQDNJk+QVnxkgOu21/ei6gdtvGxEGBETjTm8RJEJwZIXYP7eV4nFiUjiwqd3cliBgjuZXQI8iSTKW0rlIihXFa+VIjoWgZODXZToOlOOMiOMNhWrYs1qsvCeW1vOnrh9wO7/CYvOjmqaCMxcUolplGvf2cKB+LJJqRetvROvaj33iUM8xxWtFdlvAgAxb+eDr2WUVHAtKZuZguMFW7kWSJLLcNnKifQDIbheK3Qr1a+DQsEoh8xzphkFyjB8OvGO+Yap6+5eO/KFB0jQVAGuBi+yvTUSyKSRqA4Q2aKi5BRjRKJHNmwevlWyAZhj0yH5Uh4Zz7JBnkCczG8kyFUlSye3YRuCNN0b85BxTadodilIfS+BWZC4YVTL4viulkXHaHNBTsOy7OCZOwBusoyUpXMFn1QSRDIP2DJWe3ogYaSSI7ugkuruLCSecTP7icwFBmuKHD9Pxm98AkGxqoummm2i68SZOWnIxZ/Q5uW2/IGG/6wxz98aN9Ljs+C+/DElRYOWvUFbcw5+cInywfcYiiptXUrn2ATJ6DvBR4WTevex2bD4vvTnivnNt3kb/4SP8V42YXL/kUihuq0dKHaHYspWcvvdJ1oq8qEWZ1SDJ1J59ORLgDoj7rdcQJKi+pYlzA8IQc0qNCJF8lKMSffxX5HiWojo0kr0JujZGQFJ43zkTgMluB4u+MhZFlfF3iGfpSFEZyfkn0p4p1FhvRGf+RVX0KgaPrD6CXYvhMNWXXLuLUY11FHa0EdMNlu0WYa2lSYWDJWNQtBRKKkW7Fdr8Coc2t49oYYRqY+fYyxgzfyl/rhG5Jc5oJxdZb+UXDd/k5rZL6OrKxLN4MRkXX4zz8ivocYvntT4xkxQW7NWCNFUEWtm/t4ut79QfVbpuGAaJ998bJE2e44sBA8VXQmW9lSmecRQFxXNUmBcWUe+8SVScci+ZAUGaXJYiquqC+IxyJFkszNoO1qAbButNpcm25v3B37SvFP0ZV2bM5puxDFoO9WLNthPJsSMBl7o8xGToc4kB8tDaBuLBKFvergNgnNke51VrHmFZptiZz4y8GRRkzgVJxhXV0VqEJYJs6PhNl/JOfdj4Z+Y1tSGeO4/Rj09ReXDbl5AkiR5ZZW3Re6T0DuIxYVFy6kfvAvD35i52rqoHA1xzCsi9fjKq0Yrx8KkE3ngNA7hn4cWEHYKMLZ8+GkNSyKgQY15obctgl4nHW8M82pXBXbUhIpvbQTOwFLnJrCxgfuF8tnv28aESpjGhgwE9z9UQ3tRIaO16urImsv+U77J27t0cLl9C2PCgpiKceGYWp35tPMvbRdrFLRNu5p7GG8hP5tOh9rBqfg1xCXY393NhZAWNH2SQiqhsmzWZuMVCsU2louhjxQn/IUiTpi8AZJuCYpIcpSNCj+mF5LQqxE3SlOrch5pXKBx9h8FS4AIJHAmdLHPSdVpVvNkOxtplFnktVNlkPAMtVDQD3SyFld0WXG4fLjWJIhls67WTtA3lNH3c2HJAaVLMvKMB0jQQmjtWuwgkCcaKyWV4iG7MLLHiP7ipnWRCIznQb2/TvciayO2yVpwIgG2MH5fXxuuuBBoG/fUGyYAo5e9o3ELbkQCyLDE28RRJs92KRfWimkTRa1c4/zszcPssFJimmf1NYpJwTBoiTcOTwbPs5eJ9jxdXxrGbSir+jCHSVCEG8iyXleyYOB+WgkKYfa348Ac/EZ3mAbXEw5G4xo6ohn9UxmC+F7NEhQ01b40w7qTV9JopmDL4krXYI4iTVSZ+qA/H/K8ADCZHJzuEghfSIeQuwlsWRWrePPj9RCxFfbfwEMrp3EbgjaUid8FEvs1C2TDjv3NzMzjzquuo9mVjSWlUTJ6Gev6vQbHC4eUoTSvJVPqJGRBRdDKSMKVPXNM1FQ5yb5qK50RBunpfOYQWShDLF/8utaq0fPd7GIkErvnzybr2WrBYCK1cifaDn+OQ3Vxan2DhVpEn9NwpF/LyvDkoJy8SfdV2iJDhuMhmKqRWXpYKsVYIortvykJ+OfPLzBqdS39XJwdUOxunzOe3X76ZqYe7ORCJkW1R+bmvC5ucQjMMjnP+gejrfydR8xYpLcEYSeXaUCPq8SdiywJPoB6LBG4zBLk7XIQSDqAlDjB951sA7Pcp1CunoIyeT96lotKyuyaD4Hnvcsgm1KQT8zMon5TNWbdMJt9MIt8y4RQ2nHcD7VmCNFX5YPyCAn76xl6SmsGZXhE+cUcTVP7615Q8cD8n7Bf3x4vvr2Lny69y5yFB6s5trmFUvQizNU7zYRiw/f2RatOf8r9EQPXwfOVsQnaJIreNMQmhlpzVdzznto2hO5yg4Gc/pevKG6m07sYtd5EwbPxtezPh0UIJ9kteet9oZN0rh9n5YdOI34jt2oW1pwfFL7yNHJOzseaKe03JnMifXVdzuu18AAqtppFlxfFY8ieSFxIS8xRfNZVWhYkOBb/N7Ot2sIb94Ri9KQ27oZPVWkfcr9I/1kVhWwOWZIJOWwayO58bsJM3R4wZ891RphQcQpIMNmtiTNv73GpWXP1LosEkvhwHV00URGdV1mloSibnjbkASZLQrOK+yu0No6e6kZUBE15xzAfDw3yf/OW4IxrNiOeskGZqotcRSHg5bXweC0ZnMzd1mCbri4NfGdXQwIzWrWjA/WNsOGfm4V8yGkmVYfk9hDbuRA/HeOm8S9nksqBoBmoqRndGFh9NnYke2o9kV0h1RgmubCSc0ni4Vuzbyt4gO3eIHEH3HJGfd3qFaKTcbK9ja0QjlucE3aDnpVpqZ/2AnZNupCVViiEp5Lp7mdT3LvPX/pDsPW9zsO8gTaEm7LKdJXvnUxUbRUwKc2fpX/jZ7l/wm/UPM7btIOevWEkypGJxpthyksgfHaW0s+iFRfxp65/4T0OaNH1BYDdDQ2MZYt9OGOzWnl25k8zrbznqe7JVGewrVs1Aw1sFj11htE1c3tE2GadLECA9nBRtySSQnZYRJKwh6ePDRpHU6Ef6xPCc1SR4EVMdav2UxqTAUIiu5s1BMlAxNQfFItPXHqFxr/hNRUph1XpRHKbxpUcMcvYxfnxOCy2qzoemz1FzlwixtTUJFaZirBVX70ZSqin9q14UU2nSemLklHo455wKHLJETDdYm38yvb7R2M0k8AH0m7wh2+zll116dBL4AJSMLJRMMREMkKYcj43siDgfan6+6PZu84pS8wMiKdyZYWNXVKchYZDjC0BXDUgKnPRDcGZBtFeoUwDBNgi1gSQPtcswYSvz4r9gjLkzo0CxEVotSFOqU5CmoGYQcebhLktA41A39Prd3WiGBZ/cgtfoJtncTHTr1hHbH/BrArgkPxMjGqVq8y5O2VNH5VevEgUJ874hPvD2d8nNESvbxqgg0/M7xLXeOCUDS5Ebz/EFqHlO9HCSvtcPU2+ac2auX0Ns925kr5eCX9xD7u23Ufnaa7jmzUN2iHvACLVz16P3M/fAbjTVwquLL2PDyg8E4QwP5aRcobzPjpYg7j/8mcI//oG7p19MosTDKpfG7G2HeOqim1k59ww2T5hC1GIhC537fD1kvXApxU5BdhvCPgLbmmhyGewNCC+wSxyVlO7ZSM74bsoa3mdS/w5kSSIW7Se/5ln0vsdJhpfS5uylsEMUKKzIrmajeiXWWx7AfcrJoGnsv/ePg+HtRQUZABRX+5nXICwjWrN9BN/rJmIXz9784HqW7Wln5YFOrIrMgqAgFTmSgnPWLDyLFnH51SL5e/2EKdzamySi6czNcPGj+bMYe1iE3XbmShjAvrWtRALmYieWYJnpQ5ZUFLaMsVOSJ5Sjja7dAFyuZVH3hgi/HO4MM0Gup9K+ng1j7Pw41MM1YWjNm87B8V9DMp+d7e81kEoOa+T69jKUzFFIioW4Q0HNdmCfKEihmj+Z8LJ36a0XY0th1CycqDwBLZXCEbbgUjNoLMxg8YkuVlVYmVgiyHzrwf2sNVWm/LZaFF1nc3E7b5TuI2KPUdoqwpjrsxUC+TYOJpOgx9hbcwf3bP4+Y6v2EkqIe6ffU05thjAPHuc4xPF+FzPlPnTZQsR7HueUnUXNmx/w0V6xzcwe4cWVWzEN2TKGrF6xnQORj5GmcIpWRI5epV3i0c1ivLhgejHfP300l8R3kdstnlXFKp7vszc3IxsGH+ZZODDPzDXsrYPdL9Ff5+BASTkPnSbG1HMPJbm2TJzLl046nfjeXWScK0hv4P0GnljzEb0MjePPew0ku4JjihjfTio5CZtio8EiEvn3INHvtiAhMTGngAKLxlTnq1xe8mMuuvcspl17KoqeIPD226w8uJzxkUp+2ncLyb19GJJOseVuZsZEQnng9Sf5xdqHkRMGjqwERTdM4f080fewv/ttknqS7GEts/5TkCZNXxAM5CZVD7skanMYdFCz7Pgf3Ihy3OXH/q4ZohuDjCSBTZVJrG9FMSd7qywR2yJk9QE3cNllEbb61iHS1IGflc19gMhpGm6YaRjGIGlyFIjvRIMJNE2nrVY8JMdUmkA0CP0YGbDaVconiQT4nctFpYVD6kWyubFUTxzxdfvojEFzzJ12narZecT6xUAUNx10J2SLEu2UR2xTVb2omYLcpXqEM3pymxjY2npb0RQruydeSzg1pKbomk6NadCZa5LJimkzj31MgOwqQ1LtQHKQuF40s4QFPjFhWPLzwZkJM832FRuEAeWAY69qU/B1fzjsHGUOVTQNqHIDKlP2GNHO5GNwTMoWilpKwlKxkMSRIySamkmabWrCyTiGpBB158PeVyEkzsHe1WJiH+VYi/ck0Qqn//WRIbq5Zoiu3GFlts9F8P330SMRrCUlOKaLXB0W3Ab+cuhvpCD4MgA1EYXYtFxspvXAR/0h6n7zO2pmzkDvWSHCdDu7qOs3eyK+IFpK5N95J5Y8MQHYKisoeexR/FeKhYK1IpPqD97n6a9fRq5sEHZ5eaGumdB6Ub49ELq8xLIKuxHjwYDMYm8JrbOzSU30szoao191YEnEmd6yne+sf55Hfv5dXr3nNk58+UJIxSgpF6vvw6FitmTls6M0jwP9G+mMt2FTHBQfyEPLOQ1Prk6+6SwvNayh39dASjZwyElcSoLyekFs1uQodH90iEdu/hp10yeR8rg5FBETpD2pk2NWIoY/WsPYdSKc1OlVCJmLHWsiifzWK9z2D0Fmv76wgq4G4QNWNmPWIJmfWVJAoc1C1O5gb2UVzliU36gJikaPYb5VwpKM02oYRCd40ZI6Oz8Uz9vfW7rRYLDX2ubRdqKqhUO2Bn5a8hAvZZnXZWcPwY+aOdIZZoJcS4ljIxvGiAXJtlCMp86+EUNWCcj9uDNtRAIJ9q0Rioah6wTefnswNKeYYWzHFJH0reSMpXVbE6mkjt0l4w9vEAuI0rn0tjYj6VCZMZM/jrXTbZP51Xg7NWNEb7u2Qwd4x3TkL2k4QsyiMWb+Qm6YeTOH51uZaloNrMpRud/cX2dgKaUJodYFUs/yXxsfxBOoA0lGU+24gw04nrqXhiuvYkbDCwAkXMdT8+Vb0G+/hfoW8Xt57SIUqmlVqI75ZJqkaU/XMHsJfwXWpEFnUihNmZZJdIUSZLqsnFidy4TYNpr63ci6TJc3Tn1JFoqSycnyDM5rEovD7zW1sayzn9jaB9DiOh3dGfzs67eiyTLVTQlum1nG9WXFqBjsHj2WbZ09OKfl4piYRcIweMhsfvylPrFgWlpkwZjoQDbtbFwWF8cXH0+3SxxXU00fK5sitCQ0FElitkuh2l6C7v4vel6qI9FVhGPezdgmf4MzXp7A7+q/w+RmQQTl+RJ2eTfXdLVz1WoL1ywNoBo63tIopZfksunUu+m3ePAnemnqfJfcfgdnVJzBfxrSpOkLAotZ7j5RFkRFlkA3+5nZRmd8Yj8nGKqgq0bBaVHQemKEzVyh+rhY/gVXN2Ok9EE3cGUgGXnYRDy6sopeM3nYj4TbPsyjKZiElA4SOAvN1WlMo/1IgFRcw+ZUySw4elIXP6YOOhAfq4qu2fSQccj9cOrPsIwqHTq2Qgey0zJImnK9Nk66YizOuPgti7sNb45KcYfIZ0m5xHlUVc9gTlOqJ0b8SL9wXVdlsvY8jDdQR9Li5s37NhMzE+MPb+uktUdM9DYlg5v+/Bizzjn/E8+7njAbamp1g32dKrJdnGI6JaumGzizrhUTQe0qaNtNXrmXsklZzDqzHOnQu+bJEP0IGSfyfNj/pgjnDeQz5R9dwQcgyRLu48V+2MaeAZJMePWqwfBcKizKrbsdc4Ui8/o3aK7poammF5kkExzv4jtfuHMHli1DTwxVQF2Q5+fbZXk8ML4MSZLof1UkoPrOO29IfbO54eq3IW8iPlcjzrAIre5pi+Ds08hOQlw3WL5lB2ga/S88SuLwu8RkaDZVx4K2VjyLF+M9+6yRB2cAZhsY16xqLIWFuBSFa8oEudk0bhYbN5jmeEseEIaCRpjF9s08GuynLp4EwyAjmuS2puf4+ht/4RtP3MP923/Ot4MPUt1VS6qpnfbNdoyqMyn98i8BaIlaac70IhkGtjmL+YpF4VC4BlmSCenX4z7z+6hFUwFIXDiPZosVWTK4sGwXRmUuAa94b2OWSpl/GqlojI3vvMGH1cWsmSDUhCmH9hIzjf26H32U/O5O7FoKTZE44BULgJz+HtS+XqraD3H6hHyuKkgQNEQrjjGXfWXoHpAkzsoZUnm/+dzjGDffRLKtjTmnn8XouoEQnXg2dq9sJhBO8PcWkQB/T0UBeYEUEYvEKyUW/lr0Erqk0+x8i055OQD9S4+QU9NCodTD1sJcgk4ZybTxWD7FhT24jUDbaqacKp7dre/Wk0pqHFr6Gl39vcimdUjWBKEsqLlOFGs/kmIhkSN8vApzzHymohlg99LVUIdVttNWMZ1DHjHJG5LEDwsLaS8eRSwSZm2PUOKLW2spO34uvzzp11w/5Xr+fs3rnIUYX7ZlqrQ5ZHLjKVbte5K3Gho5KRjhllcSlAR7cfbtHzx3s07MQnE6iGzezKX3LOe43dvQZZXHF5xMXFE5UiSOr6CjCSQHgd5cZMWP22x7dzAS5x8b6ogkUuAXhrpdCTEO1DeIcebcKYVYVZnU9hfZ3iPCgHvKYnw4+jnG5JyGU/XwlZou3DLsD8e4anctE63ncX35j/n5Vd+gOTcPb0Tj6pYUo2fkkm+zcLZfzAEvjJ2C3t9PxvEqS4uTdNos5Cfi/Hb+pZSFNCKqxNvJ90RY28QZFWcQVppJhF4hGX6HXOUI0qp70Dq3ARZi+hyirZlEtncS3daJmjsF2S3ObZfai1zlJvPysRSeKhK8XQcSnPmRWBCtnKVQOLcXecqXeDMh9rEkuJEph7ycuSaX+hVr+E9DmjR9QWApcIEMPl0iBwmXVSV+aBhp+hQMqFRjUHBYVQLv1YNuEHSo7IhqJFUZPZAgsrVjSGkyE76Hk6bFc6diNZO8Mz8WnkuZHk1Khg2b24psNtA9Yqo3BaN8x2wIOYhBMrB0MLenbEIWFvtQONLhVmDG1Vjzh7qVO0xTyQyTNOV57VisCqdOrkVL2JFkjTFTmpD6asHiJGX6SqmqByXDJtinZtD/tpDTXdNzsfpsTNr9V5xaF319Csse3o2W0tmyrJ64AZoRBmTk8Cf3RorX9aNHHRhaEr13ZFgr1SqIgyXPJE0ZJTDePP4ND6JYZM6+eQrTT8qBOhFOY4yoxKLiBKH+BVugZSu0bhevD8tn+jhc03OR3RYk1YNaOIPQqtWk2kxDv37TeK/0SlCsGDVvs/4ZUQE33vk+Xq+Bc8481Lw89ECA0IoVg9u1yjLfrSxgutdFsq2N8Lp1APiWnDdyB7yFcPVb2KbNwRsU57l5Xw8SMNvM+1k3YQqOKVOwjx9PfNcr/KEiiSZJ5Ibj5Dpc5P/krhFhUD2h0f33vcQP94MEtqqMwfeuKMzGikF7bhFvW2cRzpohQpdmTphS5iAlS2QkDWzLW/nLrgeo+HA1/uY2VKDojuUoZ/yY3Hli33oPuqh/S8bn9A7aENiSKc5y7uekRdMJyTYed4XZ3vMhhmEQ78pHkixILpXlHzwDwJwlF2K5ZQW/0S7jYF2MTEUhrErsz/Rx3pI7yC4tJ5lMsqdS2GWMPbSXuosupv3eXxLZsAFZURhlKrsNhWJCUswy9SsTh/nL5dOoe1HkbmUoFhy5pUT3dRNvCJDqjXFZjh+7LHFRloezu1tIdXTQeMONVIybzNQOocYuT4bw5TuJR1L89aNaupIpCmwWZh5u4qt1YhL9R5WDeL44L1WJJOPU+3gRUZ12aptKXB/FX8u+DMCCvTEKu1MkLBLvTnNR2t+KY4wPh8dCf/s+7rn7bs7RvXzzOz9FzxD5a44qkR8oSRKOfLFdS54IkRfaRGI1FUL57Gqsp9IzjSdGizHqqsZ/sqAzTlyWePm0L3O4bCya6kFNJijsbmPJhTcP3T+hJJN6POQMqyr+Zk2S3FguctEMvvNekqm1BjELPDOtBU2VqJiSzbivn03FKy+Tqha5S5ctE2rTe8ct5NKv3kvCasWaiOPv70GxViNJYvxKeCQkXSdqsfLnFz/gxqe3krJ4aPBVc8gpiNaOfWKsPH96ESRj1GxYS1izIjuc1KhzyUj6GWd+trHlA27+4COuL86hyIgQUl0srVrE2skzkHSDL60Lc+qo3YPPzHUVgnwtnzmPpk1rMV6+mL9XCFJ7xRGDyNJGLm4U1/gpTzXGqt8MnpfRdb2cstGDnqxFS+zBaH4CV6gJpf+P1GU9hX1yAxnnjsJ3VgXe08txTJCIrPkDbR/cxp/nvEjhNdNwTs5BsnloMwrY3lXFL666iR997UTuP1mm1aKgjzuPZV1iPnPXHmb6AfE8x0L/2kn+i4Y0afqCQLYqWHLF4HBapoeLx+WT6oiICaMy41O/azGdnPOQOcvnIrJDPJzJCdkYQMLsUB5c2Yhm5jMMKU1D4Tm7v4hbzhK+PRlIuKxDt8dAaE7NtIsBz3TuPrxdGFR+YmhuAJUniPLmYCs0i5W0apGpzBxy9XZWTgJZRs0eqvSzjRGD7MQicQwzysS//QWZeEwPlLj/HhoL7ejVi0lppqmk6kWSJdSB3n6mX5V7QRG26mpsiQCnWn+FRYrSXNPLq7/fSndTCIscxyGLfI7Ep3T+Dpod55ON60h1t4x4L9lmkqYBpQmE0SfAzhfAVH+oXSX6sPhKwQxfYLFD1Wni731vHDMJ/OOQLAruuWLQtFYtJrJtH0bSwNA1nBkiVNjd54CTf0xDYjptHXYURWem6wXw5CMpyqDK8/EqugH0v/EGGAbOmTOxFhcf/QG7D/nKl8mSzLCMWZSwYLsoW14/aTq5+asoPyPIvpsv5KXRoortx/s0PCfcSaIxNdjyQQsl6HxkF7F9PaDKZF4+bkT7lCyryvn54vubJsxnU9TMS5v6ZbrtObxaLGw53NsOcnnjP9mxtZOGsB9Zlllw6Vex5pTCwtvIuH8nRXd/F9nlIrplK3UXXsScUeMp6+xj4ZFmqoq7qG59nXu+NJEfn+JC199iVfsLpDCrRlP1xMIhcitGMfvCr+AvHsPM8kwkoFwXz87qHBX7YZUrfvZ7Tv/mHbTmiFCNriSI6ho9Tz4JgHLaqVgOiT5w9cUiJ0VJmC1mjmxF0TUadghyPnb0Qtp/u5nuJ/fS+cAO2n61Ce8vt7JiRYS7WyRKHnwIJSuL+P79tH33Di4YV401HqMLBdtiodL9MyQUmq8UZhFb3cKX2lJkx3Q6ZIPs/Itxqk6Ot2Zjl5McllbTX+pGRuJD5w/Z4RqFVZI4oUPnO1YvCgYrZ8yhv9DPzg1rSUX+QU3mXh5dcAZ9viwaC8t4fLSdQLKH5c8/TLBH3P9ShbiGWU4PspagLCzCu1SKvo5d9fX0V85hr09B0ZPMT27iT4ko4/o1QlYrr50m/MMK2xsZP3su7syswXskurMTyYA5veI4x3QHWdyaYl/iWprD5xKuEWPmQ2erHBqzg4dKP2D+lWPZ37OfH9Xfz1VLmvjuVQo1i2uYY7cJv62p4hnL6W5DwsCwD7l22wutZJk2I1XU0rhtI7/82W+5MeNGUrJKWUstZW37qMp1M6nIh3HgHba0i+Ofefb5eFKncUXtD7AYElGli6ZIDcbBtcxb3sbTH/yJh5b9niUrPqCgO8hp28IsCGygqPWvg1Ym030uJvR2kbRYeHr3Rl61jqbRkUWmDksak8QP9HJWcxKXoXPQVcZHOz+AA++w8w/X8OoDT+BIKPS7khgSHHZm8/A557Hk5n9y4cybOadyGnvGe/EsLMZ7YgmZl88lEDuEKxhiSU/5iGGgpbWE7339u7x33ELWzLqe7sLf8OPRV7DRWkR7IoVNS3LcVhEFWXj6AuZeeBn/aUiTpi8QLGYPoDumlHBbtRjcLIVuFJfl076GbFNFV3fg+oAMhsh1mfClUVz4vZmMurQa2amS6o4R2SQm9CGlaVg1nqeAWRNMU0kkpmQPNX/UusUAPpAn5DAbwIbMcFbhMCXgmFBtQ2qK2UqC9Q9SFX1q8COOLDGIyB4rjknZ2MdlDrp0zyzPZPOPTuGHZ5o9mXzFTKjtxJGykJRiHBjtZl3OHpJmObZqEYrBQDI4gL3ajyXXSeEv7qHi9dconpHLab7fAwZtR0Re1gT729gVIdcnPqEXU7ItLNoZAImD75JsaUHr6xt8P2WSJnVY3zmKZwn7BS0Omx8Xrx0cFpobHn4dZ1Yb7nwe+s1qp/yRCesfh3tuAZJFRskoRS2cB4AR7qRggcgP624KYRx3ExsS1wEwybEUl9ILZrK971yhHgVXrCRRP9I92jCModDcx1Wm4VCt5I0tHfHS5E2bscdidGVkcrikkPbOQ/xozIkAfHX3SuZ2tGDEJXqe3U/3PU8Te+IndPxxLcnGILJTJefaSTgnHZ0seo1NnP8DlRP46FAP4b5ecGbyyJQfElad5HW3cOnWp8iOdaFIOlPKZL72p0eYfd6FQxuRFbwXXUX5iy9gGzMGrasLx5PPMKGlm+yZE5FVkHY+z5dnFjKqdw2L8g7Tk2rgncYnaLYeYd3BV5EVlTNu+jaKKlSixRPE+YyaDYafL7Nwb4lM05pmAsUT6fOJid3b0cDGmROIOB1EHXZWRrrIaBXXOm4Tz1hOqIO4PwOtu5uuBx+iUzbId1RQqs3GSOoofptQU03VV42mCK1oJrw2TPH99yPZbIRXriLrmecYY1bRrZL6CI120ZipohpwQUTGFnBiNeD0OrHPe43xfHTpGqrHfgmAM9SNPGxPkSTE02Xi+l6Q7+eWu+dz+blj+HqmGEOeuOBCDr30Vz7KyeXl068gabFR1CEI0uMVVjZZO9n1wTv87VvXs3XZ+7yx2k7KMLDLEscdfp7Y+mYMxQ7FwrTS1qrydJVYLNlCy2mddRE5J8/iD1uj5Ec1dLNyraSllswnnuHAvPkcOeccGq69jr43RXXsTY07ueTwm9yy4gVhF6FV8vqqd+l22cmeEGR+mZgC5dylXP7mVVy89GLern2bhGxQ4ItxizUfZ30EDAPDXETmdrfiiiWQ9aGk79wiH7LZlFfz2DirYxmBroNsKRchqxPWvsUZne9xVvcHxMIhGj98js64G1WVmXn6WTy0qJrTzZ6NReeXYpMNDD3A/nUf8l7rCdS1FFBVs5ErXvgVU7f9g9kZL0H3oRHGuV/VRUj+H6OO50/lVwJwfXkergyzithh4aJCodw/VrCED37/fd5b346OjL9I4bUFfaxYMJuHv3w7z515KU1mAnltNMGSbYe461AzUU2nPxlkVbVQ8MZtGWqfo0Wj/HrchTTmFeKLBHAmA+iWPJbmfY2LtotcvIoj+1D0FNqoJmY7dvGfiDRp+gLBapKmRHNo0GrgX4XmBjCQ16QHEyCB97QyFEUmr9yL6rTgnidWSQOu3ornYzlNsgWcmUiqjGTmMp1UMlRqP2g3kCmUG6dnKIFascjk/Ivu2sBQFd2+N+Dwcnj3hxRbd2K3CcVoQL2SJImsL48j+8oJI0J+2W4b8sC/fUV4QxpzNnRSfTCENWEQ03rA7ONnUQVpUof5RrkXiFW+7HRiHzMGpl5OuX0z8/OEuiLLBlNdr2M1e2p9ktIUXClUJvt4P4rTQO/vp/7qr5Hq7UULBtHDZtghf1grFEkaUps2PQKp+BBpGiCTA6g6TZTyB4Vqg78CHBmfdmaRnRZcs8SEbR0t8qP0SAfF554IEkQCCfasaaMznIdFijLdaZY5u80KxeoxOOfOgWSS5jvuwEgNWR7Edu8hcfgwks2G5/TTP3U/cqdWIGvxwX+rhwPM3C8Gx3fOeJJvLHyKHksGk6IN3N1zN4XOG/AozwJJYqFyuvafjBZSUJQucubVYCs4tpfLpH3PcFzfDnRFYUvVdDa9/hId4Qh/tQpyOXfThxiSxDR/M9eM3sIpt987sjXNMNgqKih//jl8S5YMvua54CvgyoFwh6h6PPQBbkuChecsJpTq5aOaF4hpIeZddDnZw8xPF08Qv1G3p4uzMr3oksQLpVZO1fv4zZFWkCTsCY1Cn49EXEM+8Tu4TrkbdzyTcmOkO7In1Ef9BGFp0fjYo/gyqlmQdz6SDvZxmeTfPpOC782m6OfzKbxrLv4Lq0AWxoaRHSpFf/gTss8He/czf5tIBH6nP8q+4zIAmNcSQ3mqBllSaIs2cnw0hFeVORSJ835PaDCkPtfYjfbRU6yKf8jyPDE2fEVTMQyDuu1bKHvhEbzBPvp8mTy75HrePWEJhiwzpTbOTW+2M781iiZLPHrSdPKqx5NKxPnwiQfo7eykxyz593lz6D3kom1vBYZiJR4J0589ma2ZKophYA++yb7ufUi5VkKWFu7bEsNp5t9NPriXjEgcraeH+MFDRLbsBd2HYeg4nn2GG377NJPef59UrA+b4iDTN46No4voGeXnK211TFSrkCSNhsguFEnhzIozecG/gL+2d+LInMiGne3IbUP+VoXd3RT1BilrE6FvHR2bL5vuTnHf92TmImUW8OYCkbB+dstyKvQOdCS0Q1t58vYbWWkuXiccNwslGKPwfeHv5ZiShXP6dI4rEYu/VHQFyfBbaIk9YIhxRU/VszlWKkSmbU8P7td5xkEy+3vp8mRy0FGCV5W5uiyXzEurUXMc+BaXc3WJIE3vZM1nVVIsQGefupDUrX+lq+wPbJ5wLhGnB2+wj5NXv8FLlgCXFWRiAH9t7OSUTTX87fA6PhIpamir16NHxbl54O0PWTH1OBQtxa/2/IYN6y4lp/tp5FQfZj9hRtftYdXULs51N0HN26I6+D8MadL0BcKAqpJsChI/JKow7KMyPtt3i4YUI+eMPCw5zhHvu+cVIg0Lt8muj+U0eQoG1Y4BQjXQow5GhudgiOAA5JV7UdTPcCuNPgVUO/TWwnNfBkNHmXYp084cg2qVKRl/bD+kY8InQkSylqK4Nca82GmMGnUHqurF7R6PLAuyNECaLPnOownohCVgcTKFxznlXBtnj38Tl9KLdYIYEbSeGHpk5ESW6okR2SFCkt5FZZT+7TERCtm3j4arv0Zsn6ickn0+ZOfIa8D488R5DrXDintFvpFqP8qwFJsHKk8a+venhOaGQ5BCA8nsaK9m27FneQfd4de8KMqKp8yUccimiuYZCiEW3nMPssdDbMdOuh58aPD1/ldfFR895RQU90ifsI/DNWUS3qBQqlQphTXWywlRoeLd15VidcqNQ5Z58MTTsN1xCOmmVfiuvYK8JTFsuWLwtShHyFVvxfLRt+APE2D5PRAe1hA2FYddL3BNswjn7Jgwiy0fvMs3n3qGqKyS09XKqZ1ruKpiC4vyj+CZddFRdg0fh+xwUHDvLyj87W/JuuF6PKcthsmXiDeX/QDi/eDMYsoF11IwRoRS80ePYda5F4zYTrHfycQiL4YOpyVUXpoyijExCFgk1iLupWLVwsX/dQ+nll5FjrUEl+JjYd4FXFZ8zohtecIBjoT7iFoU4iXTmZ93Poqk4piQRdaXxwnvHsQiQ3aouGbmk/WV8aDKxPb1ED3op+Ll1/CccTqnbdqAPRYhYLWzzGy9clWjCN0eCmxlTfuLNO9/gctN1egvDR0Y+ZPpd5TxRkM1FeFaXiwtQZckZnencPxtM09860Zeuvcueg/u5dTVYuHRmS3up2sP7OZLazsxXAX8qEbDnTQ4aJHZNOFyZEsxGAlIvUdZkbB0cFSOBwz6tvXTdtdP6Fx3kH+OEQT0ZK+GovWyr2cfz+5/liPdy6kI6zy8qo3z33qKS792FVUfrabitVcpeexRMq/+gTgvRje2sWVYiorwnnk6zlFiwTep9AQM4K3GcmpDfv6STCKHp5Pons8M5Vf8Mu8kRm1+nuaIh2WhsUzWZX7baKCYie+XWU6katr3qMoupdgi4XUGiW7xMSMk3rdNmM+4639Cd34+sq7x44a/Mj67h0PHXY0/20+4r4+OmBh3c97dQPP3nkOPyOjRXsIfPoShaUw5fgEe1SSUqTgVHX2cVDyGM7/5A2RFYX99hJUdFbDnFYgHoWMf3r2/5dxV7w3eP18rysGrKthKveTfPhPXrHyqXXYmxAIYsszOCceR983v84NJ5/Ljw21ospOStma+98QD/HDHa0zfs4GND/yeKw5v4/GqAvKtFg5H4/y6PZ8tk66nYXQZRiRC6MMP2dLVx688IkrxnU2PsSSyihwjzFUdy7no9V9y8uo3mL9lOU0ZK7BMKGZs3nQwNNj+zKc+l19EpEnTFwiWfBcoEnokhdafAEXCWu79119kSGlCkfCeUnrU+7LTgmv2ULhIHlCaSmZDyRyY/fWh98xwYLIpRGh9K93P7CNh9q36eHgOPkNobgA2N4wye+clI1A0E876PdMXl3Pdn04gu/gzqFUD8BaN+Kcy8SLKy65n4YJNzJr58mCCpGtmHq45Bfgvrj7ab8nmgfHnIUlQHX2ckl6xapMnLh40xkw0j1SbgqubQBcKoLXYg62qirInn0DJzia+fz9NtwjfIkt+PkdBtcIs8zx/9Efx//KFYHUe/dlxwybQz0ia1Ew79glDxNM5TeRcZJv3RiqhY3OqTL3sFJhh2iCUHDf4eUthIfl33QVA10MPEdm2DSORIPDmmwAjlJhPgm3UKHxhsQK3B1qRgHNOE21D4uak8/OqIkY77UI9yxsP5fOxzDmT7G+fSt6t08n90YUoZ/1IWBlEe2HVr+GPEwV5CbQI889YH2fED1NoVYk43GyumsLaSqEy3aq2cX7JHnJsYTTFAYt+9JnOnyRJ+M4+i9xbbxVO41NFwvNgiHT0qUiqhbO/9V1mnXsB53z7+4PmhsOxeLy49st2tzE/08PThfl8b08MX0KooEuyfYSeqcMt+UhIMRr1AyBB5v4QnoElOTAtaxzjvHOR591E0YQrUSSFkC9E5uVjBwnTx+EYl0XOoFt8Pz3PN+GYdR2jLvsDJ7UNKYDVAY3Szg4+bHuHfSEbKclOpL+TrKfvxypJbAlEuGXHQR5qm01n3I1kk9k7XthMnF8bxGPxU5asRrVYmXHWEq6V7Zy9+n0siQS/tiS4/A/3UNK8kmxVIiducP0+QQBeyjQI5pyFJFtJRBp51yZx10QbVy2YxD++dQ9NJ91AeHeCHWtbWZujIhsG/1VVDkBzqJn337iPacs3YqQSjNX8fGvBOYyZuxA1Oxt7dTXu+fMxNEG2/BfOo+L55xn9wfsU/f73+C8V3m7epJ8Jx52Mrhu80TSOyJ4dPD31Ziq6lpDa1Ubt337JSw2nsarzQip3FnAfLo7v1fnJ7ihf39fDmKCG25GJL388M1wqJ1uz+Wqrn5vC4l44GE/w8wahoFzYGMcVvJyKYCl37LmfE7avo7yzD4CiniBuZSyWgqkYeorY9scIr3qPtp/+FMvEc7iycitfy9/E/D1NjGvrYcLN32Dc/HksvvFWALb0FLO5LUOoTf/8KoYeZf6RzVgTMRzJBJd5RvrsAWx/9y1GrxAEd+O0hXwn4eJgJE6mReFnyQCP330HU2tW87fRWyifNRtdS7HiqUeo+d4N/GDbu5xh1UGSiLsXcu237+GR8y5l74eruHb7AVKqygl7d3BjVPTQi2kqmftGU9qhMmn/OhyuD2jOi3DeqPNg+pXChkaxHrWPX3QcfVb/Dbj//vv5zW9+Q1tbG1OmTOG+++5j9uzZn/j5F154gTvvvJO6ujqqqqr41a9+xZlnnjn4vmEY3HXXXTzyyCP09fUxf/58HnzwQaqqqj6Pw/kfQ1JlLPkuURqPMC8c8NP4V7BV+PAsKsFS4ELNsB/zM56FRYTWtYBmDDbmxeaBa94Z8TnFVJEGKs4GX8+yo5qd6IcrTUf1m/s0TPiSMLn0FMClz4jEZ/hEA8lPhGoDV64InzizRdUZIMsjb2nZoeJfMvpYWxCY+mXY8Q/YJapkyCiD3HFYimtIdccIfdSMHtOwlXtFmMtsMuw5cSgZ2jZ6NGVPPkH9lVehdYkcDjX/2KEgZlwNq34jEsDh6NDcAKqFfQCG/plJE4D35Apie0Q+h2v+VACyit0cNqscp51Wis1pgbP/IMw03Tkjvu87+yxCK1YQWLqUlju+S84tN6P19aHm5OCaN/df/r5ksVDsDdCga2T17MY1by6lM6cxZXMNO4JRzsrxcXlB5rG/K0li4QDCSX3m10Qo96PfC+uF9ffDxofBJXKcLFMu4qriHH5xpJUV887AkGTGO21cPf9S9AM/Q4n2oCy8dYSa9t9C3ngonAYt4nwOXCtvdg7Hf/nqT/za4on5/O69A6w51M3hzhDXvLuPm7sNXmlLsnOMmzlrWtFCSdRsB/lfm0Vlpp1ES4jelw9SGdLY4Rf38HGhMWT7h8as+tAeii87Dkn59LWurdJHznWT6frbblIdEVFQgsxZhoW3y8VnFuzby9ruWhL2k5AkCauWi0V+lfCRGo4/uJX3R0/jpb4onHMTE2t3Ml05QtjqojTRzUXnTKX3ib2M8c1k6leX4J9TTtc/X+D2u+7i5PdWMMOpoQETZmfQFBb7Or0pyfgqJ3sdsPHC0Zwa+xZPdPTTmj+0wNvpH8XDY0dRHtJQTe44r6OZCZZqitxFhNuauPGFMGoCJKkVKCMnWTRi7Ei2h0m2RUR/uYlDieEAlhwn1jIvifoAc6dfQDwZJnUgRHfyCrJfj/MoLqASpLtZMOyW0fQUR0I7SDVuxJ8K0H/1N3hxj5t5NZsZiw9dVmi2eTDM1jfdNpluG3iTBjcc0ojqi5Dti1Ajh4mlnmF8dxMT7F488y/FiAkFNPPiceinf4umW75B3wsvYikoILt4Ej3v9AJJ3IsWYasUFX3jF55EuLeHVc88zsqOSqRn7yOUtLInMIeoTeWrLz6AZBgsfT7FKV+/ieq5Qsmu3b6F5Y8/xGgDsvUkXbIFVYJrinO4rSyP0HfvIKDr1EzJpCfRy5ppvVwx4Xp2L3+HzoY6Gld/wMTVH2AryWPFCWfR567k2dPP4x+6jiHLFHa08Wu/lVB8NFrPAV5qmEhPPIJmlXhnZjtdzgSqpHJW5Vlg8cCkC8U4/h+Gf7vS9Pzzz3Pbbbdx1113sXXrVqZMmcLixYvp6Og45ufXrl3LZZddxjXXXMO2bdtYsmQJS5YsYffu3YOf+fWvf82f//xnHnroITZs2IDL5WLx4sXEYrFjbvOLhIG8Jvjs+Uwg/Hp8p5XjnJTziZ9RfDayLhuLd3E5lvxjqBsmhqtW1gof3lPLyLlpCvm3zRwkcQNKkyRBfuV/gzRNvACWPARfW/Y/n8wGYIbomLBEeEH9T1A2HzKGKXPVZ4IkYasQCl+sppeeZ/bRes8G2n63BSOpYyl2Y/tY2NQ2ahRlTz2JkiMmdGvRMSrMAFxZMPnioX8P+DMd9blsWPgdGHO62MfPCGuhG8+iEpzTc7GWiGPIMd3mHR4Lk08y+8dJ0lGEaQD5P74TtbCAZGMjrT+6EwDvuecI9eUzIH98Acd/dDuVtW+SbTZ7/eWYEr5Zmsvvq0s+O0GWFXFtr1sJV7wEpfNATw7lek39Ml8uyMImSxiSGMpuryxAtjpQLnhUGG/O/9Zn+61PwoDaJCkwatFn+kpVrpuKbBcJTefc+z6irjvCKx7wpmDB3hBqKImlyE3ODZMHw93WQje5N01lXJZ49hTdIC/fTbvcwPaeD1nR+hybepdROG78Z9oHa5Gb3G9MxXdmBb5zKvFfWMVpp42iLBwmLxzkuovnseibNwxeC6s9k4vuvAenL4Np77/EZa8+wqi6/SDJ7K6cylNlwq/scq0J19gsXMeJZzfyWhNdj+zClivI3dTOw2j1daR8GXiuuAafadSpHZ/H304ai0OW2JyIc6/sozW/FFlLMfPQVn6+71UWBdqwGFDnVgZ9mc7+xyMcmL+AW16K8V8vavjDoFcUk/U18dxEd3YSWt8ymD4Q2S4WB/YxftHx4GNwzhAhpPCqZmZGTuK4nLPItpdiGDoxLUQ0FSKmhYnocXolnX/qYd4p7yIxWULJsJFTWs6Y4xcy/eRybvUUsenA48RW/IKsd75P5c6HyB+mAH5t/1bUVX8mfuBtjFQMJXMUrpPuJO8nz1P58PNgTAEkXHMKcM3Mx7NoEXk/FKHFzj/fR7d6Jf2HxPXJuuZrI45j5jnnM/0UcQ5WtFeyuaeYaErFaXcy4+BhyoMBYqEgS//4K16/58cceXcZS//wSwxdZ9LxJ/HYjHHcUJLDytlj+aGaJP7nPxH8QHhyLfzKd1Ellfea3qelWuIrv76PC352L5nHTUSzQFVjO19/+m9cX7OOku4ODFnGkkzw8xefJP/sM+mxVvN8/WQ6425cGX6qb76MrgyRf7agaAFZjiyhuv8HEiYAyRio8/034bjjjmPWrFn85S9/AUDXdUpKSvjGN77B9773vaM+f8kllxAOh1m6dKip6Zw5c5g6dSoPPfQQhmFQWFjI7bffzne+8x0A+vv7ycvL44knnuDSSy/9l/sUCATw+Xz09/fj9X628Nj/FsIb2+h9WeSe5Nw0BVvp5/v7IPrTpTojKJn2T1S6mg/08urvt5FX4eXC736ya/b/KdY9AOsfEBNqTvX/fDsrfilyjAC++jpUnoChGUT3dBE/0k+iLkCyPYzp+0nWFeNwTDy2/X+ivp7efzyH//LLsJYeHSYFoGM/PHwiFEyGa979n+/3Z4ShG2z/oJHCqgzyPmO4N7xxIw1XXjVY0lzx+msief4zILj8Q5puugnX/PmUPvbo/3S3j436tbDpUWHRcMIdANy6r4Hn2noY77Lz/qxq5P+uavlpiAXg+SuE4eIpd33mr/3y7f08tFLYaRRlOHjuujm4PmgisqUdW6WPrK+OR7YfTfQfa+rkhwebKbRZ2DpvAvW7tvPiz0V4sXj8RC6565f/nw7HMAx0QJEkDN3g+Xs20t0cJqvIxaV3HkdXQx3P/+wHxIIBCqvHM+6W7/LAtpW8aSklL97DO0UJciafjZHU6X+nblC5Bki2bidZvwYls5K+8oXkmZW5SQwiN0xkQnkmjzZ18qODzeRaVS7PdCHf/wuUzlZmZDYxfclXCE75MsuDMR5fvZbc1jq+s2oFrvrGwf1P2FXGvvI61vJyOv68jWRrePA9NdeBHk6ih1NkXlqNc2ruUcevx1K0/HyDMOoFZL+Vw03vsKt7L1EtRKYtyqHqc3jGbCBsVWXWfW8RWe6RE3w8pTHv3uX0hGKce2QNX9//NmoywXe+fSdbxownr6eLp+66Dauhk3n28fhPPY5g2yyiu7tHbMda7iXn65NGhFvbf/Mbeh772+C/HVOmUPbcP45abBi6zrLvXcS++hgVFblMuvAGCp1e6s8/Hx04lOfncJ4fY9j3snWJk6un4JoyBUlR6X/55cEm3wDOWbMofepJHtr5EA9sfwCP1cPMvJmsbVlLXIujpiQmHfYxtT4TI6WBrNDrL6G4s4OsggxaertJJUQY2Ot1cuHdf8Sdk8OpL55Kd6ybP5z4B04pO+UT7s7/Hfxfz9//VtKUSCRwOp28+OKLLBmWL3HllVfS19fHa6+9dtR3SktLue2227j11lsHX7vrrrt49dVX2bFjB0eOHGHUqFFs27aNqVOnDn7mhBNOYOrUqfzpT0c3CIzH48TjQ/H+QCBASUnJv4U0JdvDtP9hK7JTpeCHc5CU/8UJ4H8RhmFwaEsHuWUefDmfrFr9R6C3Hu6fDQ4/3LoLlKNXqHo0RaIhgGGAY+yxw0v/LQRaRY6X7b+Rx/U5o+N3v6f7kUewT5xIxYsvfObvGYZBdPNm7OPHI7s+wSX+fxEd8SS/rm3ja8XZjHc7/vUXPgfsbQlw9n2ryfPaef66uZRmOTE0g0R9AGup5xNzkvaGoizaVMPp2V6emFSJYRg8d9d3aanZy/yLr2DOBf960fffQd2uLt56cBeTTyxmwcWCKPS2tdC4ZyfjFpyIxWaH+rV0PX0pqqGR8Y2N4BvKJ0z1xQi830BkS/vgomIAGga70Xhb1fjDTxdhMcOKddE4hTYLVlnm4Ma1vP67Xxxz3yRJ5pYn/4l24BB9b79F58bVlH7zdjKOP1FsP5QgvKmNWE0viYbAQOEskkWm4M45n7jgi+zoIF4bwDEpG1uFj/hHD7Di6cfxW6PMuO5u+ivP4ty/rKG5L8oF04v53cXHDo//atl+HlxxGEWWeO+iCuRf381zniweuOAr/PixP3OKRai29uqhBV2spofe1w+jdceQvVbyvjFtMB1iAIau0/Kd/yLwlmj+XPTnP+E97bRj7gOJMFrHAZRiYW1gaBoNV11NZOtWJFWlz+Vge76PsEXFFUsw91AzVk0fuQ1Zxr1wIRkXXYj7hBOQLBaSepKvvPUV9nTvGfxYsbuYU8pO4fSK0ylMZPDhEw9Tu33LUbvkzcmjatYcZp57AW6/GCt3d+1mf89+Lqi64L+fivHfxP9fk6aWlhaKiopYu3Ytc+cO5UvccccdrFy5kg0bNhz1HavVypNPPslllw2ZYj3wwAP89Kc/pb29nbVr1zJ//nxaWlooKBhKfL744ouRJInnn3/+qG3+5Cc/4ac//elRr/87SBNAZFcniteGrezz/+3/Z9FZAxbHyFDd/+MwUin6ly7FOX36J6tmaXwiatqC5Pvsgy2APiuOROLk2yw4TZIR7O5i30crmLb4bCz2Y+cr/n9BJJDA7lKRPylXStfglRvE83HOn47Z0inZEaHr0dWkupPYxxfgmlFCd46dNc19VOW5mVH2yQuND598hJ3vLxtUNQcwdsGJLL7hm5/pGPRIktihPuJH+rGNyjimt9cnIhmFZd8TauL0rwJQ2xXmHxsbuHZhJTmeY4eROgIxrnlyM6eMy+Nbp1RhaBo9f/87vcveIfvSS0a2GxoGI6kR3d2Ntcw7GJ496ngSCVp/8EPQdQp/8+vPHBo/5uHFYxzavIHCnHykunpiu3YR3bkLrb8f7+LT8H3pS8csXGkMNvLHLX9kVMYoTi49mTH+MSOOxzAMjmzdyJqnn8CQYPScBVTNnktOWcX/OTH6NKRJ08fwf0GavkhKUxpppJFGGmmk8T/D/zVp+rcmgmdnZ6MoCu3t7SNeb29vJ/9YJdtAfn7+p35+4P//nW3abDa8Xu+I/9JII4000kgjjTSG499KmqxWKzNmzOCDDz4YfE3XdT744IMRytNwzJ07d8TnAd57773Bz1dUVJCfnz/iM4FAgA0bNnziNtNII4000kgjjTT+Ff7tPk233XYbV155JTNnzmT27Nn88Y9/JBwOc/XVwgflq1/9KkVFRdx7r6hu+ta3vsUJJ5zA7373O8466yyee+45Nm/ezMMPPwwIr5dbb72Vn//851RVVVFRUcGdd95JYWHhiGTzNNJII4000kgjjf8O/u2k6ZJLLqGzs5Mf//jHtLW1MXXqVJYtW0ZenjAKa2hoQJaHBLF58+bx7LPP8qMf/Ygf/OAHVFVV8eqrrzJx4sTBz9xxxx2Ew2Guu+46+vr6WLBgAcuWLcP+f5BEmUYaaaSRRhpp/L+Bf7tP0xcR/06fpjTSSCONNNJI43+G/79OBE8jjTTSSCONNNL4T0GaNKWRRhpppJFGGml8BqRJUxpppJFGGmmkkcZnQJo0pZFGGmmkkUYaaXwGpElTGmmkkUYaaaSRxmdAmjSlkUYaaaSRRhppfAakSVMaaaSRRhpppJHGZ0CaNKWRRhpppJFGGml8BqRJUxpppJFGGmmkkcZnwL+9jcoXEQMm6YFA4N+8J2mkkUYaaaSRxmfFwLz9f9XsJE2ajoFgMAhASUnJv3lP0kgjjTTSSCON/y6CwSA+n+9/fbvp3nPHgK7rtLS04PF4kCTpf7ydQCBASUkJjY2N6R52nxPS5/zzR/qcf/5In/PPH+lz/vnjf3LODcMgGAxSWFiILP/vZyCllaZjQJZliouL/9e25/V60w/Z54z0Of/8kT7nnz/S5/zzR/qcf/74757z/wuFaQDpRPA00kgjjTTSSCONz4A0aUojjTTSSCONNNL4DEiTpv9D2Gw27rrrLmw22797V/6fQfqcf/5In/PPH+lz/vkjfc4/f3wRz3k6ETyNNNJII4000kjjMyCtNKWRRhpppJFGGml8BqRJUxpppJFGGmmkkcZnQJo0pZFGGmmkkUYaaXwGpElTGmmkkUYaaaSRxmdAmjT9H+H++++nvLwcu93O/6+de41pqw7DAP4WSksJljIZLcwxWdggY1wcc7Xq5gca6yReFhPJ0ph5iYqyZIvLdPOG8YPtpjFxRImJcfhpzWYEjWNEwm1uYcwhDDoIboqiZoC6cVPcgD5+WDjZGTjODFgKzy9pQs//Tc/TN/0nb0rPsdvtcvLkyWBHmhOOHj0qDzzwgCQmJopOp5Py8nLVOgB5/fXXJSEhQUwmkzidTjl79qyq5sKFC+J2u8VsNovFYpGnnnpKhoeHVTWtra2yfv16iYyMlKVLl8revXsnZTl06JCkpaVJZGSkZGRkSEVFxQ1nCQUej0duv/12uemmmyQ+Pl4efvhh6ezsVNX8/fffUlhYKDfffLNER0fLI488Ir29vaqa7u5uycvLk6ioKImPj5edO3fK2NiYqqaurk7WrFkjRqNRUlJSpLS0dFKe6faGlixzXUlJiWRmZio35XM4HHLkyBFlnf2efV6vV3Q6nWzfvl05xr7PrDfeeEN0Op3qkZaWpqzPy36DZpzP54PBYMDHH3+MM2fO4Omnn4bFYkFvb2+wowVdRUUFXnnlFXz22WcQEZSVlanWvV4vYmJiUF5ejtOnT+PBBx9EcnIyRkZGlJr77rsPWVlZOHHiBL7++mukpKRg8+bNyvrAwACsVivcbjf8fj8OHDgAk8mEDz/8UKk5fvw4wsPDsXfvXrS3t+PVV19FREQE2trabihLKHC5XNi/fz/8fj9aWlpw//33IykpCcPDw0pNQUEBli5diurqapw6dQp33HEH7rzzTmV9bGwMq1evhtPpRHNzMyoqKhAXF4fdu3crNT/88AOioqLwwgsvoL29HcXFxQgPD0dlZaVSo2VvTJclFHzxxRc4fPgwvvvuO3R2duLll19GREQE/H4/APZ7tp08eRK33norMjMzsW3bNuU4+z6zioqKkJ6ejvPnzyuP3377TVmfj/3m0DQL1q1bh8LCQuX5+Pg4EhMT4fF4gphq7rl2aAoEArDZbHj77beVY/39/TAajThw4AAAoL29HSKCb775Rqk5cuQIdDodfv31VwDABx98gNjYWFy6dEmpeemll5Camqo8f/TRR5GXl6fKY7fb8eyzz2rOEqr6+vogIqivrwdw5X1FRETg0KFDSk1HRwdEBA0NDQCuDLthYWHo6elRakpKSmA2m5U+v/jii0hPT1edKz8/Hy6XS3k+3d7QkiVUxcbG4qOPPmK/Z9nQ0BBWrFiBqqoq3HPPPcrQxL7PvKKiImRlZU25Nl/7zX/PzbDLly9LU1OTOJ1O5VhYWJg4nU5paGgIYrK5r6urS3p6elS9i4mJEbvdrvSuoaFBLBaLrF27VqlxOp0SFhYmjY2NSs2GDRvEYDAoNS6XSzo7O+XixYtKzdXnmaiZOI+WLKFqYGBAREQWLVokIiJNTU0yOjqqeq9paWmSlJSk6ntGRoZYrValxuVyyeDgoJw5c0apuV5PtewNLVlCzfj4uPh8Pvnzzz/F4XCw37OssLBQ8vLyJvWGfZ8dZ8+elcTERFm+fLm43W7p7u4Wkfnbbw5NM+z333+X8fFx1YdARMRqtUpPT0+QUoWGif5cr3c9PT0SHx+vWtfr9bJo0SJVzVSvcfU5/q3m6vXpsoSiQCAg27dvl7vuuktWr14tIlfeq8FgEIvFoqq9th//taeDg4MyMjKiaW9oyRIq2traJDo6WoxGoxQUFEhZWZmsWrWK/Z5FPp9Pvv32W/F4PJPW2PeZZ7fbpbS0VCorK6WkpES6urpk/fr1MjQ0NG/7rb+haiIKaYWFheL3++XYsWPBjjLvpaamSktLiwwMDMinn34qW7Zskfr6+mDHmrd+/vln2bZtm1RVVUlkZGSw4ywIGzduVP7OzMwUu90uy5Ytk4MHD4rJZApistnDb5pmWFxcnISHh0/6VX5vb6/YbLYgpQoNE/25Xu9sNpv09fWp1sfGxuTChQuqmqle4+pz/FvN1evTZQk1W7dulS+//FJqa2vllltuUY7bbDa5fPmy9Pf3q+qv7cd/7anZbBaTyaRpb2jJEioMBoOkpKRITk6OeDweycrKkvfee4/9niVNTU3S19cna9asEb1eL3q9Xurr62Xfvn2i1+vFarWy77PMYrHIypUr5dy5c/P2c86haYYZDAbJycmR6upq5VggEJDq6mpxOBxBTDb3JScni81mU/VucHBQGhsbld45HA7p7++XpqYmpaampkYCgYDY7Xal5ujRozI6OqrUVFVVSWpqqsTGxio1V59nombiPFqyhAoAsnXrVikrK5OamhpJTk5Wrefk5EhERITqvXZ2dkp3d7eq721tbaqBtaqqSsxms6xatUqpuV5PtewNLVlCVSAQkEuXLrHfsyQ3N1fa2tqkpaVFeaxdu1bcbrfyN/s+u4aHh+X777+XhISE+fs5v6GfjZMmPp8PRqMRpaWlaG9vxzPPPAOLxaK6QmChGhoaQnNzM5qbmyEiePfdd9Hc3IyffvoJwJXL/C0WCz7//HO0trbioYcemvKWA7fddhsaGxtx7NgxrFixQnXLgf7+flitVjz22GPw+/3w+XyIioqadMsBvV6Pd955Bx0dHSgqKprylgPTZQkFzz33HGJiYlBXV6e6NPivv/5SagoKCpCUlISamhqcOnUKDocDDodDWZ+4NPjee+9FS0sLKisrsXjx4ikvDd65cyc6Ojrw/vvvT3lp8HR7Y7osoWDXrl2or69HV1cXWltbsWvXLuh0Onz11VcA2O//y9VXzwHs+0zbsWMH6urq0NXVhePHj8PpdCIuLg59fX0A5me/OTTNkuLiYiQlJcFgMGDdunU4ceJEsCPNCbW1tRCRSY8tW7YAuHKp/2uvvQar1Qqj0Yjc3Fx0dnaqXuOPP/7A5s2bER0dDbPZjCeeeAJDQ0OqmtOnT+Puu++G0WjEkiVL4PV6J2U5ePAgVq5cCYPBgPT0dBw+fFi1riVLKJiq3yKC/fv3KzUjIyN4/vnnERsbi6ioKGzatAnnz59Xvc6PP/6IjRs3wmQyIS4uDjt27MDo6Kiqpra2FtnZ2TAYDFi+fLnqHBOm2xtassx1Tz75JJYtWwaDwYDFixcjNzdXGZgA9vv/cu3QxL7PrPz8fCQkJMBgMGDJkiXIz8/HuXPnlPX52G8dANzYd1NERERECw9/00RERESkAYcmIiIiIg04NBERERFpwKGJiIiISAMOTUREREQacGgiIiIi0oBDExEREZEGHJqIiIiINODQRERERKQBhyYimvcef/xx0el04vV6VcfLy8tFp9MFKRURhRoOTUS0IERGRsqePXvk4sWLwY5CRCGKQxMRLQhOp1NsNpt4PJ5gRyGiEMWhiYgWhPDwcHnrrbekuLhYfvnll2DHIaIQxKGJiBaMTZs2SXZ2thQVFQU7ChGFIA5NRLSg7NmzRz755BPp6OgIdhQiCjEcmohoQdmwYYO4XC7ZvXt3sKMQUYjRBzsAEdH/zev1SnZ2tqSmpgY7ChGFEH7TREQLTkZGhrjdbtm3b1+woxBRCOHQREQL0ptvvimBQCDYMYgohOgAINghiIiIiOY6ftNEREREpAGHJiIiIiINODQRERERacChiYiIiEgDDk1EREREGnBoIiIiItKAQxMRERGRBhyaiIiIiDTg0ERERESkAYcmIiIiIg04NBERERFp8A9Cp2nB7y2sSwAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bz = 1000\n",
    "\n",
    "exact = []\n",
    "for ob in ps:\n",
    "    exact.append(tc.backend.real(c.expectation_ps(ps=ob)))\n",
    "exact = np.asarray(exact)[:, None]\n",
    "\n",
    "bzs, res = [], []\n",
    "for i in range(bz, nps + bz, bz):\n",
    "    res.append([])\n",
    "    ss_states_batch = ss_states[:i]\n",
    "    bzs.append(ss_states_batch.shape[0])\n",
    "    t0 = time.time()\n",
    "    for j, ob in enumerate(ps):\n",
    "        expcs = sejit(ss_states_batch, ob)\n",
    "        res[-1].append(np.median(expcs))\n",
    "        t = time.time()\n",
    "        if i == bz or i % (bz * 10) == 0 or i >= nps:\n",
    "            print(\n",
    "                f\"observable: No.{j}\\tnumber of Pauli strings: {bzs[-1]}\\ttime: {t - t0}\"\n",
    "            )\n",
    "        t0 = t\n",
    "res = np.asarray(res).T\n",
    "bzs = np.asarray(bzs) * r\n",
    "\n",
    "error = np.abs(res - exact)\n",
    "plt.figure()\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"Error\")\n",
    "for i, y in enumerate(error):\n",
    "    plt.plot(bzs, y, label=f\"No.{i}\")\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:53:57.091936Z",
     "start_time": "2023-08-09T04:51:25.071809100Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Estimate the Entanglement Entropy"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can also use classical shadows to calculate entanglement entropy. `entropy_shadow` first reconstructs the reduced density matrix, then solves the eigenvalues and finally calculates the entanglement entropy from non-negative eigenvalues. Since the time and space complexity of reconstructing the density matrix is exponential with respect to the system size, this method is only efficient when the reduced system size is constant. `entropy_shadow` is jitable, but it will only accelerate when the reduced sub systems have the same shape."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sub: [1, 4]\ttime: 0.1788625717163086\texact: 1.3222456063743848\tshadow entropy: 1.323659494989336\n",
      "sub: [2, 7]\ttime: 0.03922629356384277\texact: 1.313932933107046\tshadow entropy: 1.315937416629094\n",
      "sub: [3, 6]\ttime: 0.03881263732910156\texact: 1.342032043092265\tshadow entropy: 1.3427963599754822\n",
      "sub: [0, 5]\ttime: 0.03893852233886719\texact: 1.3458706554536102\tshadow entropy: 1.346507278883028\n",
      "sub: [7, 0]\ttime: 0.039243221282958984\texact: 1.3496695271830874\tshadow entropy: 1.3504498597279848\n",
      "sub: [1, 4, 7]\ttime: 0.2567908763885498\texact: 1.8741003653918944\tshadow entropy: 1.8777698830270055\n",
      "sub: [0, 3, 6]\ttime: 0.11173439025878906\texact: 1.8633273061204374\tshadow entropy: 1.8638162138941512\n",
      "sub: [5, 4, 2]\ttime: 0.11144137382507324\texact: 1.908653965480665\tshadow entropy: 1.9084333256925539\n",
      "sub: [7, 2, 5]\ttime: 0.1119997501373291\texact: 1.8916979397866593\tshadow entropy: 1.88828077605345\n",
      "sub: [0, 1, 2]\ttime: 0.11184382438659668\texact: 1.8717789129825904\tshadow entropy: 1.8724197548909916\n"
     ]
    }
   ],
   "source": [
    "subs = [\n",
    "    [1, 4],\n",
    "    [2, 7],\n",
    "    [3, 6],\n",
    "    [0, 5],\n",
    "    [7, 0],\n",
    "    [1, 4, 7],\n",
    "    [0, 3, 6],\n",
    "    [5, 4, 2],\n",
    "    [7, 2, 5],\n",
    "    [0, 1, 2],\n",
    "]\n",
    "\n",
    "\n",
    "@tc.backend.jit\n",
    "def shadow_ent(snapshots_states, sub, alpha=2):\n",
    "    return shadows.entropy_shadow(snapshots_states, sub=sub, alpha=alpha)\n",
    "\n",
    "\n",
    "for sub in subs:\n",
    "    exact_rdm = tc.quantum.reduced_density_matrix(\n",
    "        psi, cut=[i for i in range(n) if i not in sub]\n",
    "    )\n",
    "    exact_ent = tc.quantum.renyi_entropy(exact_rdm, k=2)\n",
    "\n",
    "    t0 = time.time()\n",
    "    ent = shadow_ent(ss_states, sub)\n",
    "    t = time.time()\n",
    "    print(f\"sub: {sub}\\ttime: {t - t0}\\texact: {exact_ent}\\tshadow entropy: {ent}\")"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:53:58.139584Z",
     "start_time": "2023-08-09T04:53:57.091936Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "On the other hand, for the second order Renyi entropy, we have another method to calculate it in polynomial time by random measurements:\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "    S_2&=&-\\log\\left(\\text{Tr}(\\rho_A^2)\\right),\\\\\n",
    "    \\text{Tr}(\\rho_A^2)&=&2^k\\sum_{b,b'\\in\\{0,1\\}^k}(-2)^{-H(b,b')}\\overline{P(b)P(b')},\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "where $A$ is the $k$-d reduced system, $H(b,b')$ is the Hamming distance between $b$ and $b'$, $P(b)$ is the probability for measuring $\\rho_A$ and obtaining the outcomes $b$ thus we need a larger $r$ to obtain a good enough priori probability, and the overline means the average on all random selected Pauli strings. Please refer to [Brydges, et al. (2019)](https://www.science.org/doi/full/10.1126/science.aau4963) for more details. We can use `renyi_entropy_2` to implement this method, but it is not jitable because we need to build the dictionary based on the bit strings obtained by measurements, which is a dynamical process. Compared with `entropy_shadow`, it cannot filter out non-negative eigenvalues, so the accuracy is slightly worse."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sub: [1, 4]\ttime: 3.794407606124878\tshadow entropy 2: 1.2866729353788704\n",
      "sub: [2, 7]\ttime: 3.796651840209961\tshadow entropy 2: 1.2875279355654872\n",
      "sub: [3, 6]\ttime: 3.760688066482544\tshadow entropy 2: 1.314993963087972\n",
      "sub: [0, 5]\ttime: 3.765700101852417\tshadow entropy 2: 1.317198599992926\n",
      "sub: [7, 0]\ttime: 3.784120559692383\tshadow entropy 2: 1.3218300427352758\n",
      "sub: [1, 4, 7]\ttime: 3.859661817550659\tshadow entropy 2: 1.7701671972428563\n",
      "sub: [0, 3, 6]\ttime: 3.874009132385254\tshadow entropy 2: 1.7684695179560657\n",
      "sub: [5, 4, 2]\ttime: 3.831859827041626\tshadow entropy 2: 1.8037352454314826\n",
      "sub: [7, 2, 5]\ttime: 3.824885368347168\tshadow entropy 2: 1.8006117836020135\n",
      "sub: [0, 1, 2]\ttime: 3.8377578258514404\tshadow entropy 2: 1.782393800345501\n"
     ]
    }
   ],
   "source": [
    "nps, r = 1000, 500\n",
    "\n",
    "pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(nps, n)))\n",
    "status = tc.backend.convert_to_tensor(np.random.rand(nps, r))\n",
    "\n",
    "snapshots = shadows.shadow_snapshots(psi, pauli_strings, status, measurement_only=True)\n",
    "\n",
    "t0 = time.time()\n",
    "for sub in subs:\n",
    "    ent2 = shadows.renyi_entropy_2(snapshots, sub)\n",
    "\n",
    "    t = time.time()\n",
    "    print(f\"sub: {sub}\\ttime: {t - t0}\\tshadow entropy 2: {ent2}\")\n",
    "    t0 = t"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:54:36.511330700Z",
     "start_time": "2023-08-09T04:53:58.139683500Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Reconstruct the Density Matrix"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can use `global_shadow_state`, `global_shadow_state1` or `global_shadow_state2` to reconstruct the density matrix. These three functions use different methods, but the results are exactly the same. All functions are jitable, but since we only use each of them once here, they are not wrapped. In terms of implementation details, `global_shadow_state` uses `kron` and is recommended, the other two use `einsum`."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exact:\n",
      " [[0.5+0.j 0. +0.j 0. +0.j 0.5+0.j]\n",
      " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]\n",
      " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]\n",
      " [0.5+0.j 0. +0.j 0. +0.j 0.5+0.j]]\n",
      "\n",
      "shadow state: error: 0.02441655995426051\n",
      " [[ 0.49141+0.j       0.00159+0.00219j  0.00378+0.00306j  0.5004 +0.0081j ]\n",
      " [ 0.00159-0.00219j  0.0019 +0.j      -0.00855+0.00297j -0.00567-0.00126j]\n",
      " [ 0.00378-0.00306j -0.00855-0.00297j  0.00805+0.j      -0.00273-0.00249j]\n",
      " [ 0.5004 -0.0081j  -0.00567+0.00126j -0.00273+0.00249j  0.49864+0.j     ]]\n",
      "\n",
      "shadow state 1: error: 0.02441655995426051\n",
      " [[ 0.49141+0.j       0.00159+0.00219j  0.00378+0.00306j  0.5004 +0.0081j ]\n",
      " [ 0.00159-0.00219j  0.0019 +0.j      -0.00855+0.00297j -0.00567-0.00126j]\n",
      " [ 0.00378-0.00306j -0.00855-0.00297j  0.00805+0.j      -0.00273-0.00249j]\n",
      " [ 0.5004 -0.0081j  -0.00567+0.00126j -0.00273+0.00249j  0.49864+0.j     ]]\n",
      "\n",
      "shadow state 2: error: 0.02441655995426051\n",
      " [[ 0.49141+0.j       0.00159+0.00219j  0.00378+0.00306j  0.5004 +0.0081j ]\n",
      " [ 0.00159-0.00219j  0.0019 +0.j      -0.00855+0.00297j -0.00567-0.00126j]\n",
      " [ 0.00378-0.00306j -0.00855-0.00297j  0.00805+0.j      -0.00273-0.00249j]\n",
      " [ 0.5004 -0.0081j  -0.00567+0.00126j -0.00273+0.00249j  0.49864+0.j     ]]\n"
     ]
    }
   ],
   "source": [
    "n, nps, r = 2, 10000, 5\n",
    "\n",
    "c = tc.Circuit(n)\n",
    "c.H(0)\n",
    "c.cnot(0, 1)\n",
    "\n",
    "psi = c.state()\n",
    "bell_state = psi[:, None] @ psi[None, :]\n",
    "\n",
    "pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(nps, n)))\n",
    "status = tc.backend.convert_to_tensor(np.random.rand(nps, r))\n",
    "lss_states = shadows.shadow_snapshots(psi, pauli_strings, status)\n",
    "sdw_state = shadows.global_shadow_state(lss_states)\n",
    "sdw_state1 = shadows.global_shadow_state1(lss_states)\n",
    "sdw_state2 = shadows.global_shadow_state2(lss_states)\n",
    "\n",
    "print(\"exact:\\n\", bell_state)\n",
    "print(f\"\\nshadow state: error: {np.linalg.norm(bell_state - sdw_state)}\\n\", sdw_state)\n",
    "print(\n",
    "    f\"\\nshadow state 1: error: {np.linalg.norm(bell_state - sdw_state)}\\n\", sdw_state1\n",
    ")\n",
    "print(\n",
    "    f\"\\nshadow state 2: error: {np.linalg.norm(bell_state - sdw_state)}\\n\", sdw_state2\n",
    ")"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:54:36.634162200Z",
     "start_time": "2023-08-09T04:54:36.517005400Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n",
      "Python version: 3.10.11\n",
      "Numpy version: 1.23.5\n",
      "Scipy version: 1.11.0\n",
      "Pandas version: 2.0.2\n",
      "TensorNetwork version: 0.4.6\n",
      "Cotengra version: 0.2.1.dev15+g120379e\n",
      "TensorFlow version: 2.12.0\n",
      "TensorFlow GPU: []\n",
      "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n",
      "Jax version: 0.4.13\n",
      "Jax installation doesn't support GPU\n",
      "JaxLib version: 0.4.13\n",
      "PyTorch version: 2.0.1\n",
      "PyTorch GPU support: False\n",
      "PyTorch GPUs: []\n",
      "Cupy is not installed\n",
      "Qiskit version: 0.24.1\n",
      "Cirq version: 1.1.0\n",
      "TensorCircuit version 0.10.0\n"
     ]
    }
   ],
   "source": [
    "tc.about()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-08-09T04:54:36.638744200Z",
     "start_time": "2023-08-09T04:54:36.634714500Z"
    }
   }
  }
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