{ "cells": [ { "cell_type": "markdown", "id": "46596b1c", "metadata": {}, "source": [ "# Example : Spin-Boson model\n", "\n", "### Introduction\n", "\n", "The HEOM method solves the dynamics and steady state of a system and its environment, the latter of which is encoded in a set of auxiliary density matrices.\n", "\n", "In this example we show the evolution of a single two-level system in contact with a single Bosonic environment. The properties of the system are encoded in Hamiltonian, and a coupling operator which describes how it is coupled to the environment.\n", "\n", "The Bosonic environment is implicitly assumed to obey a particular Hamiltonian , the parameters of which are encoded in the spectral density, and subsequently the free-bath correlation functions.\n", "\n", "\n", "### Bosonic Enviorement\n", "\n", "$$\n", "H=H_{\\mathrm{S}}(t)+\\sum_k \\omega_k a_k^{\\dagger} a_k+Q \\sum_k g_k\\left(a_k+a_k^{\\dagger}\\right)\n", "$$\n", "\n", "\n", "$$\n", "H_{\\mathrm{S}}=\\frac{\\epsilon}{2} \\sigma_z+\\frac{\\Delta}{2} \\sigma_x\n", "$$\n", "\n", "$$\n", "Q=\\sigma_z\n", "$$\n", "\n", "where we can define the spectral density as:\n", "\n", "$$\n", "J(\\omega)=\\pi \\sum_k\\left|g_k\\right|^2 \\delta\\left(\\omega-\\omega_k\\right)\n", "$$\n", "\n", "and the Correlation function:\n", "\n", "$$\n", "C(\\tau)=\\langle\\bar{X}(t+\\tau) \\bar{X}(t)\\rangle\n", "$$\n", "\n", "where: $$ X=\\sum_h g_k\\left(a_k+a_k^{\\dagger}\\right) $$\n", "\n", "\n", "\n", "Note that in the above, and the following, we set $\\hbar = k_\\mathrm{B} = 1$.\n", "\n" ] }, { "cell_type": "markdown", "id": "2d2e8320", "metadata": {}, "source": [ "### HEOM\n", "\n", "The correlation function:\n", "$$\n", "C(t)=C_R(t)+i C_I(t)\n", "$$\n", "\n", "The evolution of the system is given by the influence of the bath operators in term of the real and imaginaty part of the correlation function:\n", "\n", "$$\n", "\\bar{\\rho}_{\\mathrm{S}}(t)=\\mathcal{T} \\exp \\left\\{-\\int_0^t d t_2 \\int_0^{t_2} d t_1 \\bar{Q}\\left(t_2\\right)^{\\times}\\left[C_R\\left(t_2-t_1\\right) \\bar{Q}\\left(t_1\\right)^{\\times}+i C_I\\left(t_2-t_1\\right) \\bar{Q}\\left(t_1\\right)^{\\circ}\\right]\\right\\} \\bar{\\rho}_{\\mathrm{S}}(0)\n", "$$\n", "\n", "$$\n", "\\bar{Q}(t)^{\\times}=[\\bar{Q}(t), .], \\quad \\text { and } \\quad \\bar{Q}(t)^{\\circ}=\\{\\bar{Q}(t), .\\}\n", "$$\n", "\n", "HEOM is based in the expansion of the Correlation funtions in exponencial functions in time. \n", "\n", "\n", "$$\n", "\\begin{aligned}\n", "C_R(t) & =\\sum_{k=1}^{N_R} c_k^R e^{-\\gamma_k^R t} \\\\\n", "C_I(t) & =\\sum_{k=1}^{N_I} c_k^I e^{-\\gamma_k^I t}\n", "\\end{aligned}\n", "$$\n", "where $c_k^j$ and $\\gamma_k^j$ themselves can be real or complex. formally taking repeated time derivatives of the system evolution equation, one can arrive at an infinite set of coupled first-order differential\n", "equations\n", "\n", "$$\n", "\\begin{aligned}\n", "\\dot{\\rho}^n(t) & =\\left(\\mathcal{L}-\\sum_{j=R, I} \\sum_{k=1}^{N_j} n_{j k} \\gamma_k^j\\right) \\rho^n(t) \\\\\n", "& -i \\sum_{k=1}^{N_R} c_k^R n_{R k} Q^{\\times} \\rho^{n_{R k}^{-}}(t)+\\sum_{k=1}^{N_I} c_k^I n_{I k} Q^{\\circ} \\rho^{n_{I k}^{-}}(t) \\\\\n", "& -i \\sum_{j=R, I} \\sum_{k=1}^{N_j} Q^{\\times} \\rho^{n_{j k}^{+}}(t)\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "### Drude-Lorentz spectral density\n", "The Drude-Lorentz spectral density is:\n", "\n", "$$J_D(\\omega)= 2 \\lambda \\frac{\\omega\\gamma}{{\\gamma}^2 + \\omega^2}$$\n", "\n", "where $\\lambda$ scales the coupling strength, and $\\gamma$ is the cut-off frequency. We use the convention,\n", "\\begin{equation*}\n", "C(\\tau) = \\int_0^{\\infty} d\\omega \\frac{J_D(\\omega)}{\\pi}[\\coth(\\beta\\omega) \\cos(\\omega \\tau) - i \\sin(\\omega \\tau)]\n", "\\end{equation*}\n", "\n", "With the HEOM we must use an exponential decomposition:\n", "\n", "$$\n", "\\begin{aligned}\n", "C(t) & =C_{\\text {real }}(t)+i C_{\\text {imag }}(t) \\\\\n", "C_{\\text {real }}(t) & =\\sum_{k=0}^{\\infty} c_{k, \\text { real }} e^{-\\nu_{k, \\text { real }} t} \\\\\n", "C_{\\text {imag }}(t) & =\\sum_{k=0}^{\\infty} c_{k, \\text { imag }} e^{-\\nu_{k, \\text { imag }} t}\n", "\\end{aligned}\n", "$$\n", "\n", "As an example, the Matsubara decomposition of the Drude-Lorentz spectral density is given by:\n", "\n", "$$\n", "\\begin{array}{r}\n", "\\nu_{k, \\text { real }}= \\begin{cases}\\gamma & k=0 \\\\\n", "2 \\pi k / \\beta & k \\geq 1\\end{cases} \\\\\n", "c_{k, \\text { real }}= \\begin{cases}\\lambda \\gamma[\\cot (\\beta \\gamma / 2)-i] & k=0 \\\\\n", "\\frac{4 \\lambda \\gamma \\nu_k}{\\left(\\nu_k^2-\\gamma^2\\right) \\beta} & k \\geq 1\\end{cases}\n", "\\end{array}\n", "$$\n", "\n", "$$\n", "\\begin{gathered}\n", "\\nu_{k, \\text { imag }}= \\begin{cases}\\gamma & k=0 \\\\\n", "0 & k \\geq 1\\end{cases} \\\\\n", "c_{k, \\text { imag }}= \\begin{cases}-\\lambda \\gamma & k=0 \\\\\n", "0 & k \\geq 1\\end{cases}\n", "\\end{gathered}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "4b239d8a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n", "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/luis/anaconda3/lib/python3.8/site-packages/IPython/core/magics/pylab.py:159: UserWarning: pylab import has clobbered these variables: ['identity', 'axes', 'squeeze', 'shape']\n", "`%matplotlib` prevents importing * from pylab and numpy\n", " warn(\"pylab import has clobbered these variables: %s\" % clobbered +\n" ] } ], "source": [ "from qutip import basis, sigmax, sigmaz\n", "import numpy as np\n", "from qutip import *\n", "%pylab inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "\n", "mpl.rcParams['figure.dpi'] = 100\n", "mpl.rcParams['text.usetex'] = True\n", "#mpl.rcParams['font.family'] = 'Avenir'\n", "mpl.rcParams['font.family'] = 'Latin Modern Roman'\n", "plt.rcParams['font.size'] = 18\n", "plt.rcParams['axes.linewidth'] = 2\n", "colors = cm.get_cmap('tab10', 2)\n", "\n" ] }, { "cell_type": "code", "execution_count": 40, "id": "ebb8af09", "metadata": {}, "outputs": [], "source": [ "\n", "# The system Hamiltonian:\n", "eps = 0.5 # energy of the 2-level system\n", "Del = 1.0 # tunnelling term\n", "H_sys = 0.5 * eps * sigmaz() + 0.5 * Del * sigmax()\n", "\n", "# Initial state of the system:\n", "rho0 = basis(2,0) * basis(2,0).dag()" ] }, { "cell_type": "code", "execution_count": 41, "id": "6b9a27be", "metadata": {}, "outputs": [], "source": [ "# Bath properties:\n", "gamma = 0.5 # cut off frequency\n", "lam = 0.1 # coupling strength\n", "T = 0.5 # temperature\n", "\n", "# System-bath coupling operator:\n", "Q = sigmaz()" ] }, { "cell_type": "code", "execution_count": 42, "id": "3be5f141", "metadata": {}, "outputs": [], "source": [ "from qutip.nonmarkov.heom import DrudeLorentzBath\n", "from qutip.nonmarkov.heom import DrudeLorentzPadeBath\n", "\n", "# Number of expansion terms to retain:\n", "Nk = 2\n", "\n", "# Matsubara expansion:\n", "bath = DrudeLorentzBath(Q, lam, gamma, T, Nk)\n", "\n", "# Padé expansion:\n", "#bath = DrudeLorentzPadeBath(Q, lam, gamma, T, Nk)" ] }, { "cell_type": "code", "execution_count": 43, "id": "bbdda1f5", "metadata": {}, "outputs": [], "source": [ "from qutip.nonmarkov.heom import HEOMSolver\n", "from qutip import Options\n", "\n", "max_depth = 5 # maximum hierarchy depth to retain\n", "options = Options(nsteps=15_000, store_states=True)\n", "\n", "solver = HEOMSolver(H_sys, bath, max_depth=max_depth, options=options)" ] }, { "cell_type": "code", "execution_count": 47, "id": "36fb5a48", "metadata": {}, "outputs": [], "source": [ "# Define the operators that measure the populations of the two\n", "# system states:\n", "P11p = basis(2,0) * basis(2,0).dag()\n", "P22p = basis(2,1) * basis(2,1).dag()\n", "\n", "# Define the operator that measures the 0, 1 element of density matrix\n", "# (corresonding to coherence):\n", "P12p = basis(2,0) * basis(2,1).dag()\n", "\n", "tlist = np.linspace(0, 20, 1001)\n", "#result = solver.run(rho0, tlist, e_ops={\"11\": P11p, \"22\": P22p, \"12\": P12p})\n", "result = solver.run(rho0, tlist)" ] }, { "cell_type": "code", "execution_count": 48, "id": "5fd16bb6", "metadata": {}, "outputs": [], "source": [ "# Calculate expectation values in the bases\n", "P11exp = expect(result.states, P11p)\n", "P22exp = expect(result.states, P22p)\n", "P12exp = expect(result.states, P12p)\n" ] }, { "cell_type": "code", "execution_count": 49, "id": "6fbb60bf", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/luis/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the results:\n", "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", "#axes.plot(result.times, result.expect[\"11\"], 'b', linewidth=2, label=\"P11\")\n", "#axes.plot(result.times, result.expect[\"12\"], 'r', linewidth=2, label=\"P12\")\n", "axes.plot(tlist, P11exp, 'b', linewidth=2, label=\"P11\")\n", "axes.plot(tlist, P12exp, 'r', linewidth=2, label=\"P12\")\n", "axes.plot(tlist, P22exp, 'y', linewidth=2, label=\"P22\")\n", "axes.set_xlabel(r't', fontsize=28)\n", "axes.legend(loc=0, fontsize=12)" ] }, { "cell_type": "code", "execution_count": 50, "id": "9adcd2ea", "metadata": {}, "outputs": [], "source": [ "steady_state, steady_ados = solver.steady_state()" ] }, { "cell_type": "code", "execution_count": 51, "id": "5d7fbd83", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", "Qobj data =\n", "[[ 0.29945549 -0.36355841]\n", " [-0.36355841 0.70054451]]\n" ] } ], "source": [ "print(steady_state)" ] }, { "cell_type": "code", "execution_count": 52, "id": "4e4a9b70", "metadata": {}, "outputs": [], "source": [ "# Matsubara expansion:\n", "bath = DrudeLorentzBath(Q, lam, gamma, T, Nk)\n", "\n", "# Padé expansion:\n", "#bath = DrudeLorentzPadeBath(Q, lam, gamma, T, Nk)\n", "\n", "# Add terminator to the system Liouvillian:\n", "delta, terminator = bath.terminator()\n", "HL = liouvillian(H_sys) + terminator\n", "\n", "# Construct solver:\n", "solver = HEOMSolver(HL, bath, max_depth=max_depth, options=options)" ] }, { "cell_type": "code", "execution_count": 55, "id": "050fc17a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True\n", "Qobj data =\n", "[[ 0. 0. 0. 0. ]\n", " [ 0. -0.01602647 0. 0. ]\n", " [ 0. 0. -0.01602647 0. ]\n", " [ 0. 0. 0. 0. ]]\n" ] } ], "source": [ "print(terminator)" ] }, { "cell_type": "code", "execution_count": 59, "id": "c7629a78", "metadata": {}, "outputs": [], "source": [ "result = solver.run(rho0, tlist)" ] }, { "cell_type": "code", "execution_count": 60, "id": "358c3db0", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/luis/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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qqioKCgpIT0/H5YMNAZTohplDDjEbRlRUwLJlTkcjIiISvvr16wfgSXbFN9LT0z3/tj2lRDfMREXBxInwv//Btm2wZw9kZTkdlYiISPixLIv+/fvTp08f6uvrnQ4nLMTExPhkJtdNiW4YmjzZJLpgZnVPPdXZeERERMKZy+XyaXImvqPFaGFo8mTvWOULIiIiEqmU6IYhJboiIiIiSnTD0ogRZvMIUKIrIiIikUuJbhhyucyCNICtW2HvXmfjEREREXGCEt0w1bJ8Yfly5+IQERERcYoS3TClOl0RERGJdEp0w5QSXREREYl0SnTD1MiRWpAmIiIikU2JbphyuWDCBDPevBmKihwNR0RERCTglOiGMS1IExERkUimRDeMqU5XREREIpkS3TA2aZJ3/PXXjoUhIiIi4gglumFs5EiIjTXjlSudjUVEREQk0JTohrGYGBg92oy//Raqq52NR0RERCSQlOiGOXfnhaYmWL3a0VBEREREAkqJbpgbP947VvmCiIiIRBIlumHOPaMLWpAmIiIikUWJbpgbN8471oyuiIiIRJJopwOwLGsqcDKwCUgHsG17XjeuM635Oi3Ntm27pIchhrSMDBg8GLZtM4luUxNE6e2NiIiIRABHE93m5HS6bdvntTg31bKsxbZtt01a93educBi27ZntjiXA7xnWdZJkZ7sTphgEt3yctiyBXJynI5IRERExP8cm9uzLCsdeAK4quV527aXAJmWZc3o5HUmtXhey+vkNl/7CV/EG8q0IE1EREQikZMfYp8P5HYw2/oCMLOd8+2ZCnzV3h22bS8HJrV3XyRRoisiIiKRyMlE9zygqIP7coFJzbO+ndFuUtxcvpDb9dDCizoviIiISCRyMtGdQsdJqPt8Z6pJFwFTLcta2E5iPBuY273wwsfQoZCcbMaa0RUREZFI4WSimw6UHOAxB0x0m2txZwPTgM3NXRxorvFd3LZ2ty3LsuIsy0p13wCrE7GHlKgob5uxLVugpMTJaEREREQCI1gbTZU0f83szIOb25Gdh0meF1uWtQlYYtv2ok48/U6gtMVtQFeDDQUtyxdWrXIsDBEREZGACdZEtztKgHnAEsxM8GJ3R4YDmAOktbjt8FeATtKCNBEREYk0wZropjd/7WixWivNfXTTbdue3dx/dyYm2V3mLmXoiG3btbZtl7lvgN2DuIOWEl0RERGJNMGa6Haau99uyzIF27YXAMMwi9raW6QWccaO9e6Ips4LIiIiEgmcTHRz6XixWWaLxxzIbNu2Z7c92bxIbXLz4X5ndSNBYiIcfLAZr1kDjY3OxiMiIiLib04musvxlii0lQOeDR861DxTW9LR/c2bUcyhc23Kwt7YseZrTQ1s2uRsLCIiIiL+5mSiu5iOE9BhmEVl+9WcyKZ34rUiftMIgDFjvONvvnEuDhEREZFAcDLRfRHIbN69rK1pwPyWJyzLSu9gYVnuARacnUwnkuZI4J7RBSW6IiIiEv4cS3SbZ2Ovos3OZZZlTQNy2+mBuxDTMmxGm/PnAXPbJrvNifF8YG7za0W8ljO6q1c7F4eIiIhIIEQ7+eK2bS+yLKukuT3YJprLEJpbhLW1GLNt8NI21ygBJluWNdeyrPPaPGe2klyvYcMgIQGqqzWjKyIiIuHPsu2wbBvbbZZl5QEDBw4cSF5entPh+NyUKbBsmWk1VlFhEl8RERGRUJKdnU1+fj5Avm3b2R09LuT76ErXuMsXmppg3TpnYxERERHxJyW6EUYL0kRERCRSKNGNMEp0RUREJFIo0Y0w6rwgIiIikUKJboTp3x8ymzdY1oyuiIiIhDMluhHGsryzujt2QFGRs/GIiIiI+IsS3QjUsk5X5QsiIiISrpToRiAtSBMREZFIoEQ3ArVckKZEV0RERMKVEt0IpM4LIiIiEgmU6EagtDQYPNiMV68G7QItIiIi4UiJboRyz+qWlsL27c7GIiIiIuIPSnQjlDoviIiISLhTohuhtCBNREREwp0S3QilFmMiIiIS7pToRqhDDgGXy4xVuiAiIiLhSIluhIqLg4MPNuP166Gx0dl4RERERHxNiW4EGz3afK2thU2bnI1FRERExNeU6EYwd6ILsGaNc3GIiIiI+IMS3QimRFdERETCmRLdCKZEV0RERMKZEt0IdvDBEB1txkp0RUREJNwo0Y1gsbEwYoQZf/stNDQ4G4+IiIiIL0U7HYA4a/RoWLsW6upg40bTXzcUNDXVUlT0H4qL36e2dhuWFUtS0ih69TqDlJTJTocnIiIiQUCJboQbPRoWLjTjNWuCP9G1bZvdu58jN/cO6uryW91XWAhbttxLauoxDB/+MKmpUxyKUkRERIKBShciXCgtSGtsrGbduotYv/6SfZLclsrKPmH58iPYunUOtt0UwAhFREQkmGhGN8K1THTXrnUujgNpbKzkm2/OpKTkA8+5zMzTGTDgapKTx9PUVE1JyQfk5T1MVdV6oInNm39BTc1mRoz4C5al93QiIiKRRoluhBs+HGJioL4+eGd0bbuJdesu8SS5LlcyI0c+TZ8+01o9LjFxBP36/ZStW3/H1q33ATY7dz6BbTcycuRfsSzLgehFRETEKZrminAxMa07L9TXOxtPe7Zs+TV79rwMgMuVyvjx7+2T5LpFRcUwdOi9jBr1L8AFwK5dT7F16+8CFa6IiIgECSW64ilfqK83nReCSXHx+82zswBRjB79Iqmphx/weX36TG9Ods0s7pYtd7Nnz6v+C1RERESCjhJdCdoFaY2NlXz77ZWe45ycP5CZeWqnn9+nz3kMHeqdyV2//nJqavJ8GqOIiIgELyW6ErSJ7ubNd1NTsxmAtLTjGDTo1i5fY/DgO+jd+zwAGhpK+Pbbn2Lbtk/jFBERkeCkRFeCMtGtqvqOvLxHAIiKim9eTNb1H1fLshgxYj6xsQMAKC5ezI4d830aq4iIiAQnJbrC8OFmO2AInkR38+a7gEYABg2aTWLiiG5fKyYmg0MOebrFte+krq6wpyGKiIhIkFOiK0RHw8iRZvzdd2Y7YCeVlX1JYaHZri0mpg+DBt3W42tmZp5C376XAKaEITf3zh5fU0RERIKbEl0BvOULDQ2wYYOzsWzZcp9nPGTIPURHJ/vkujk583C5UgHYtetJysqW+uS6IiIiEpyU6AoQPHW6FRWrKSp6E4C4uMH073+Vz64dF9ePoUO9SfTmzb/w2bVFREQk+CjRFSB4Et3t2//oGQ8adAtRUTE+vf6AAdcQHz8UMAvTios/OMAzREREJFQp0RWgdaK7dq0zMdTU5FFQ8E8AoqMz6NfvZz5/jaioWIYM+bXnePPmX6jdmLSrsbGahoZSGhurnQ5FRES6KdrpACQ45OSYzgt1dc7N6O7cuQDbbgBgwIBrfVab21bfvheybdtcqqrWUFb2OXv3vk5W1ll+eS0JDU1NdRQVvUNx8RLKyj6junoDDQ0lnvtdrmTi44eRkjKRjIypZGb+kJiYDOcCFhGRTlGiK4DpvHDIIbBqlVmMVlfnbTkWCE1NDezc+WTzkYuBA6/x22tZloucnN+xevU5AGzd+jt69ToTy7L89poSnGpqtrF9+4Ps3v13GhqKO3xcY2MFlZUrqaxcya5dfwNcZGaeysCB15OZeWq3ejyLiHSGbdvU1xdSU7OV2tpt1NUVUl+/h/r6PTQ07KWhoZSmphqammqbv9Zg2w1YVnSLWwxRUbG4XKlER6cTHZ3mucXEZBEb24/Y2P7ExvYnJqZXWP1OU6IrHqNHm0S3ocG0GRszJnCvvXfvG9TV7QAgK+tM4uIG+vX1evU6i6SkcVRWrqK8/EtKSj4iI+MEv76mBI+GhjK2bLmX/PxHPZ8ieFnExx9EXNwgoqISaGqqoa5uF9XVm3D3doZGioreoqjoLRITD2Ho0N+SlXWu3ixJK01NDdTUbKK6Opeamlxqa3fQ0FBCQ0MJTU21WJYLy4rC5UomJqa3J+FISDiYxMQRREenOf0tSAA1NtZQVbWeysrVVFWtobJyDdXVG6ip2UpTU+BKqCwrhtjYvsTFZRMfP4T4+KGeW0LCUOLiBvt8/Yw/KdEVj7YL0gKZ6O7c6d2trH//mX5/PcuyGDz4DtatuxCAbdv+oEQ3QhQWvsKGDddSV7fTcy4qKoGsrHPp0+d80tK+R0xM+j7Pa2yspqzsC/bufZ3CwkXU1m4DoKpqPWvWTCMl5QhGjHiMlJTJgfpWJMg0NlZSUvIhxcXvUVb2JRUVK2hqqur29WJi+pKSMpGUlMNJTT2C1NQjiYnJ9GHE4hTbbqKq6lvKyj6nrOwLysu/oKLiG7xvprvLIioqHstyYduN2HZ9O2/mDxRbPbW1edTW5lFW9nk7j4giLi6bhIQcEhKGk5BwcPNtOAkJw3G5Enr4PfiWpYU4rVmWlQcMHDhwIHl5eU6HE1CvvAI/+pEZ33033Hfffh/uM7W1O/jss2zAJj5+CEccsSkgH5s0NTXw5ZcjqKnZDMDkyctJSZno99cVZzQ11ZGbO5u8vIc956Ki4snOvpXs7JuIjc3q9LVsu5E9e15n+/b7KSv7pMU9UQwadCtDhvw66H7Zi380NJRSWPgSBQXPU1LyEbbtzx13LFJSppCRcQqZmaeSmnpkSM2sRTLbtqmsXE1x8XuUlLxPScl/aWwsPeDzoqISmj9hOqh5dvUgYmP7ERPTi5iYLGJisoiOTicqKr45wY3Z55Mlk+c10dRUQ0NDqefW2Gi+1tUVUFe303OrrTVf6+sLuvGdWhx3XAUuV2I3nts12dnZ5OfnA+Tbtp3d0eM0oyseTrUYKyh4ATBvuPr2vTRgtUFRUdEMGnQ7GzZcC8D27fMYNepfAXltCay6uj2sXn02ZWWfes716nUGw4c/QkLC0C5fz7Jc9O59DllZZ1NU9BabNs2mqmoN0MT27X9k7963GD36RZKSRvnwu5BgYds2paX/Iz//MfbseRXbrm33cfHxQ0lJmUxCwkjPR77R0RmexASasO1GGhvLqK/fQ11dIbW1eVRXf0dV1bdUVa2lvn5Py1emvPwrysu/Ytu23+FypZGVdTa9e08jI+NkXK74gHz/0jl1dXuaS5zeprj4/QMkjlEkJY0mOXkCSUmjSUoaQ2LiaOLjB/f4b6JJfF24XEm4XEnExQ3o1PMaG2uord1KdfVmamq8N/dxQ0PRPs+Jje0fkCS3KzSj20Ykz+g2NkJyMtTUmC2B168PzOsuW3YY5eVml7LDD19PYuLIwLww5uPozz8fQn19AZYVzZFHbu30LwEJDTU121m16hSqqswPtGXFMnz4wwwYcLXPamqbmurZvv2PbNnya8+MXlRUIiNG/IV+/S7xyWuI85qaGigo+Cd5eQ9RUfH1PvfHxQ0mM/MHZGaeSlrascTG9u7R69m2TU3NFsrLv6Ss7HOKi9+jsvKbdh/rcqXQq9eZ9O17ERkZpxAVpXmsQLNtm6qq9ezd+xp79rxOWdlnQFO7j42J6U1a2jGkpBxBauoRpKRMITo6JbAB91B9fTHV1Rubbxuort6Ay5XCiBGPB+T1Ozujq0S3jUhOdAEmToSvvwaXCyorIS7Ov69XVfUdX35pEtvk5MlMmRL4bXk3b76brVt/C8BBB/2KoUN/fYBnSKioqtrIypUnUlu7HTCzDWPGvEZq6hS/vF5l5TrWrp3eKhkZMOA6hg9/WIlHCLPtRnbv/hdbt/6a6uqNre6LielNnz4/oW/fi0hJOczvCxJra3dSXLyYoqL/sHfvmzQ2lu3zmNjYfvTtezH9+l1OUtLodq4ivmLbNuXlyygsfIHCwpepqdnU7uNcrhTS048nPf0kMjJOIilpjBav9pAS3W6K9ET34ovhuefMeOVKGDfOv6+3Zcuv2bLlXgCGDXuAQYNu8e8LtqO2Np/PPjsIaCQmpi9HHbWNqKgA9lYTv6itzWf58mOord0KQELCcMaNW0xCwhC/vm5jYxUbNvycXbue9JzLzPwBo0Y9T3R0ql9fW3xv79432bTpNs8nAm4pKYeTnX0jvXtPc+z3RVNTLcXFSygoWMjeva+26v3slpIyhb59L6Nv3wu1kM1H3PW2BQUvUFDwfIfJbWLiIfTqdRa9ep3ZXE+tN7u+pBpd6Za2dbr+THRt22b37n82H1n06TPdfy+2H3FxA+nd+1wKCxdSX7+bwsJF9O17oSOxiG/U1e1h5cqTPUluUtIYxo9fQmxsX7+/tsuVyCGH/JW0tGP47ruZ2HY9RUVvs2LFMYwd+zbx8R3+PpYgUlW1kY0bb6Ko6M1W59PTv8+QIb8mPf04hyLzioqKo1ev0+nV6/TmTU/+w65dz7B37+vYdj0A5eVLKS9fyqZNt9G794/o1++nZGScFFZ9UgOlquo7Cgqep6DgBaqq2ttC1EV6+vfo1etMevU6k8TE4QGPUfalRFdaCeSCtIqKFVRXfwdAevoJfu+duz8DB15PYeFCAPLzH1WiG8KamupYs+ZHVFWtAyA+fhjjxr0bkCS3pf79ryAhIYfVq39EQ0MxlZWrWbHiWCZMeI+EhGEBjUU6r6mplq1bf8e2bXNbdVBITT2aoUN/S0bG9x2MrmNRUbFkZZ1FVtZZ1NXtoaDgX+za9QwVFcsAsO3a5iTteeLiDqJ//yvo1+9y4uMPcjjy4FZdvYXCQjNz215dNkSRnv59+vSZTu/e5xIT0yvQIcoBKNGVVlomumvbe8PqQ3v2vOIZ9+59vn9f7ADS0o4jKWkslZXfNPc1XOq3Ok7xH9u22bDhOkpLPwZMTe748YuJi+vvSDzp6cczadLnrFr1Q2pqNlFbu5UVK45j3Lh3SU4OYKNq6ZTy8mWsX385lZWrPediYwcwbNj99OlzQcjUVMbGZpGdfQPZ2TdQUfENu3Y9ze7dz3o6ONTWbmXLlnvZsuXXZGRMpV+/n5KVdY66NjSrrc2noGAhBQXPU17+RbuPSUs7lt69p9O79zTi4voFOELpCtXothHpNbotOy+MGAHffuu/1/rqq/FUVq4C4Kij8h3vdrBjxxN8990MAPr1u4JDDnnK0Xik6/Ly/sTGjTcApkfuhAn/C4o3LLW1O1m16hRPAhUdncm4ce8ERWxiumZs3XofW7fOwd2w37Kiyc6+lYMOuovo6GRnA/SBpqY69u59nZ07n6So6B3adgOIjs6gb9+L6NfvZ6SkTHAkRifV1u5iz56XKCh4ofmN8r65UUrKYfTpcwG9e59HfPygwAcprWgxWjdFeqILMGkSrFgBUVGm80K8H97kV1dv4YsvTP/SlJTDmTy5/XfNgdTYWMmnnw6gsbGMqKgkjj56Z8i1e4lkZWVfsWLF0Z5dgA499LmgKkGpry9i1arTKC//CgCXK40JE97TTmoOq67ewtq1F7SauUtKGs8hh/wtbBO+mpo8du9+hp07n6KmJnef+5OTJ9K//8/o0+dCYmIyHIgwMOrq9niS25KSj2ivFVhS0nj69JlOnz7TSUjICXyQ0qHOJrqqRpd9uMsXmpr8N6O7d+9rnnFW1ln+eZEucrmS6NPnJwA0NVU2b2QhoaChoYy1ay/wJLmDBt0WVEkuQExMJuPHv0da2vEANDaWsnLlyZSXf+1sYBGssPAlli6d4ElyLSuaIUPuZfLkr8I2yQWIj8/moIN+yRFHbGD8+A/o2/cSoqK8O/lVVKxgw4br+fTT/qxdeyFFRUuw7fb7wYaa2tqd7NixgJUrT+XTT/vx3XdXU1LyAS2T3MTEQzjooHs47LC1HHbY1xx00J1KckOYanRlH20XpI0f7/vX2LPnVc+4V6+zff8C3dS//5Xs3DkfgF27nmTAgCsdjkgOxLZtvvvuGs/MVErKEQwd+nuHo2pfdHQK48a9yapVP6S09L80NBSzcuVUJkz4UDW7AdTUVMvGjTezY8efPefi43MYNep5UlMPczCywLKsKDIyTiAj4wQOPvhRCgqeZ+fOJz2fOpgFbP+ioOBfxMUNIivrR2Rl/Yi0tGNDplWWaQW2hr17X2XPntcoL/+y3cclJAynd28zc6set+ElNH5SJaD83Xmhvr64+WMi88clmBqap6RMJilpHJWVqygr+5zKyjVBFZ/sq7BwIQUFpk2dy5XKqFH/IioqxuGoOuZyJTF27BusWnUaZWWf0tCwl5UrT2TChA+1ZXAA1NbuYM2aH1NW9rnnXO/e0xk5cj7R0WkORuas6Og0BgyYyYABM5sXsD3Frl3P0tCwF4Da2u3k5z9Cfv4jREf3au7wcDbp6ScE3b9bXV0hJSXvU1z8HsXFi6mp2dLu4+LiDvKUJSQnT1RyG6aU6Mo+/J3oFhW9hXvBR1bW2UH1y8WyLPr3v5KNG38OwM6dTzJ8+IMORyUdqavbw4YN13uOR4z4CwkJQx2MqHPMzO7brFx5CuXlX1BfX8jKlSczceLHIRF/qCot/Zw1a86lrm4nYBYsDh/+CP37XxlUv4eclpw8luHDHyIn5w/s2fM6u3Y9TXHxYk9v3oaGveza9TS7dj0NuEhJmUJGxolkZJxESsoRAV28t+82ye97Fjm3JylpPFlZZ9Gr11mkpEzWf/cIoMVobWgxmqnNTUmBqioYPhw2bPDt9deuvZiCArP92vjxH5CRcYJvX6CH6uuL+PTTAdh2LTExWRx1VB5RUX7eC1m6Ze3aizyzuVlZ5zJ69KKQ+sNVX1/CypVTPb1O4+OHMXHix2pX5Ac7dz7Jd99d6+mNGxc3iDFjXtZiwE5qaChl79432bPnZfbufZumpsoOHmmRmHgoKSlTSEmZTGLioSQkHEx8/CAsy9XDGMqoqvqWqqr1VFWtp6Lia8rLv/S0TWs3GiuWtLTjyMo6m169zvT7zogSOOq60E1KdI0pU2DZMrAs03khIeHAz+kM227i00/7U19fgMuVzDHH7A3K7XbXrr2QgoJ/ATBq1EL69JnmcETS1p49r7F6tanvjo7O4LDD1oZkglhXt4evvz7Os8VsUtI4Jkz4iJiYdGcDCxO23cjGjbeQn/+I51xa2vGMHv0isbF9HIwsdDU2VjeXBbxLcfF7HewS1pplxRIfP5TY2H7ExvYmJqY3MTG9sKw4oqJisKxYLCuKxsYqGhsraWqqpKGhhNrandTV7aC2doenjOIAr0RKymTS008iI+Mk0tKOweVK7Pk3LUFHWwBLj4webRJd24b162HiRN9ct6JiFfX1BYDZSjMYk1yA/v1/5kl0d+/+uxLdINPQUM53313jOR4+/OGQTHLBNPcfN24xK1YcQ23tNiorV/HNN2cwfvy7+gPdQ42Nlaxde2GrLi8DB97AsGEPBHUdd7BzuRLIyjqDrKwzANPJoKTkA0pKPqK8fCmVlas8HVDcbLuO6upvqa72bSuf6OhepKYeTkrK4aSmHk5q6pHExGT69DUktCnRlXa1rdP1VaJbXPyOZ5yZeapvLuoH6eknEBs7kLq6fIqK3qaurpDY2N5OhyXNtm79DXV1OwDIzDyNvn0vcTiinomPz2b8+MWsWHEs9fWFlJV9wpo10xgz5pWgfTMY7Gprd7F69ZmUly8FTOuwESP+Qv/+P3M4svATF9efvn0v9LT0a2ysobLyGyoqvqa6egPV1RuoqtpATc1mmpqqunx9y4ojLm4AcXHZJCaOJDHxkObbKOLjh4RUuZIEnhJdadeYFp2OVq/u+HFdVVT0rmeckXGK7y7sY5blom/fi9i+fR623UBBwQtkZ19/4CeK31VWricv7yHA/AE8+ODHwuIPXWLiCMaN+w9ff/19GhvLKCp6m/XrL+PQQ//R49rGSFNZuY5vvvmhZ7W9y5XK6NEvkZk51dnAIoTLFU9q6mHttmprbKykrq6Q+vpCGhqKaGqqw7brm29NuFyJREUl4XIl4XKlEBc3gOjojLD4f1ycoURX2tUy0fVV54XGxsrmrRUhPn4oCQnDfXNhP+nb9xK2b58HwO7dzyrRDQK2bbNx4w2ej0UHD54dVo3cU1ImMXbs66xadSpNTTUUFDxPdHRG2CTzgVBS8hGrV59DQ0MJYBadjR37JsnJY50NTADTXi8hIUmLwiRgtDOatGvQINN5AXw3o1tS8pFnxXNGxilB/4c7OXkMyckTACgv/5KqKj9tEyedtmfPyxQXLwFMD8zBg2c7HJHvpad/j1GjXgTMLO6OHX9m8+a7nA0qROze/RwrV57sSXKTkycyadLnSnJFIpgSXWmXZXnrdLdsgYqKnl+zZdlCZmbwli201LfvpZ7xrl3POhiJNDXVsmnTrZ7j4cMfCtvFWllZZ3LIIX/zHG/b9nu2bfujcwEFOdu22br1d6xbd7Gn12tm5g+ZMOG/xMUNcDg6EXGSEl3pUMsFaWsP3D3mgEpK3mseRZGefmLPLxgAffr8BPf/Jrt3/yNs9nsPRfn5f/bUXGZkTCUr6xxH4/G3fv0uZvjwRz3Hubmz2LFjgYMRBaempnq++25Gq1nv/v1nMmbMqwHduEBEgpPjNbqWZU0FTgY2AekAtm3P6+a1coC5zYdFQIlt2+H32WaAtF2Qdvjh3b9WXV0hlZWmBiIlZXLI9AiNi+tHZuYpFBX9h9rarZSWfkx6+vecDiviNDSUsnXrbz3HOTnzgr70xReys6+nsbHUk8R9993VuFwp9O37E4cjCw4NDWWsWXMexcXeT4tycuYyaNDtEfHzISIH5miia1nWNGC6bdvntTg31bKsxbZtn9yNa90JnGfbdm7zuXTLsuYq2e0eXy5IKy39r2ecnn5Czy4WYH37XkJR0X8AsyhNiW7gbds2z9Msvk+fi0hJ8VG/uxAwePAvaGgoZfv2PwI269dfisuV4ulhGqlqavL45pvTPdu9WlYchx76DH36THc4MhEJJo6VLliWlQ48AVzV8rxt20uATMuyZnThWpOar3WSO8lt9gSgTv/d1LJ0oacL0kpKPvSMQy3Rzco6B5fLfARaWLiIpqZahyOKLLW1+S3aicUydOhvD/CM8GJZFjk5c+nf3/xKtO0G1q49j+LiD50NzEEVFStZvvxIT5IbHZ3J+PFLlOSKyD6crNE9H8i1bbuknfteAGZ24VpzgTntXGsxML9b0Qn9+kFm8wYzPZ3R9Sa6UaSlHduziwWYy5XoqQdtaCihqOid/T9BfGrLll/T1FQNwMCB10ZkWyLLshgx4nH69LkAgKamGlavPpOysi8djizwioreYcWKY6mrywcgPj6HSZM+Iz09tH6viEhgOJnonoepo21PLjCpedZ3v5pnc6cC+6zSsG17QXfrfaV154X8fCgp6d516ur2tKjPnUR0dKpvAgwgsyjNcG8NLP5XVfUtO3c+CZim/4MH/9LhiJxjWS4OOeTvZGaeDkBjYwUrV55CWdlXDkcWODt2/JVVq06nsdG0gUlNPZJJkz4nMXGEw5GJSLByMtGdgklo2+M+35lO8DPpeGZYesgXdbqhXJ/rlpExlehoM729Z89rNDZWOhxRZNiy5TeA6XQxePAsYmOznA3IYVFRMYwevdDz/1FjYykrV54c9jO7tt1Ebu4v+e67q4BGALKyzmX8+Pe1NbeI7JeTiW46UHKAx3Qm0Z1Kc2JsWdas5tsMy7LmdmZGWPbPF3W6oVyf6xYVFUvv3qbcu6mpij17Xnc4ovBXVfWtZ/Y8OroXAwfe6HBEwcHlSmDs2DdISzseaJnsfuFwZP7R2FjNunUXs23b7z3nsrNvZvToF3G5EhyMTERCQbD20S1p/prZicfmACWWZc2ybXte820BpjZ32YGSXcuy4izLSnXfAPWkaaFti7HuCOX63JZUvhBYpp2Ymc0dNOg29URtweVKYty4N1vM7JaxcuUplJZ+5mxgPlZbm8/XX3+vxf9vFsOHP8Lw4Q9iWS5HYxOR0BCsiW5XTQIWtTzR3H1hCabzwv7cCZS2uGkbnRZazuh2p3Shvr6YyspvALMdZ3R0mo8iC7z09OOIjTU/HkVFb1NfX+xwROGrquo7du/+J+Cezb3O4YiCj8uVxNixb5Ke/n3AnexODZvFkqWln7Ns2RTKy5cCEBWVyJgxL5OdfYPDkYlIKAnWRDe9+WtHi9X20aatmNsyYNoBZnXnAGktbjs6+5qRICsL+vY14+7M6JaVfe4Zh/JsLpjFQH36nA+AbdezZ8/LDkcUvvadzU1xNqAg5XIlMnbsG2RkTAVMWc0335zheZMQqnbteoavvz6eurpdAMTFHcSkSZ+SlXW2w5GJSKgJ1kS3qw60qG1KR0+0bbvWtu0y9w2wfR5diHOXLxQWQkFB155bWvqJZ5yWdrQPo3JGMJcvlJfDokUwcyacfDJMnAjHHw8XXwx/+Qts2+Z0hJ1jZnOfA0x/VM3m7p872XXXkNt2A+vWXcT27Q9j26H166ypqZYNG25g/frLse06ANLSjmfy5K9ITh7vcHQiEoqc3Bktl44Xm2W2eExnrlNygMd0ZlGbdGD0aHjvPTNeswb69On8c8vKPvWMU1NDP9FNSTmM+Phh1NRsorj4fWprdxEX18/RmHbvhvvvhz//GSo7aAbx3HMQFQVnngl33QVTOnzr5zzN5nZdVFQco0Y9z3ffXcfOnaZ1+KZNN1NVtZ6DD36EqKhYhyM8sKqqjaxdO52KiuWecwMGXMvw4Q8TFRXjYGQiEsqcnNFdjrdEoa0cANu2l3dwf9vrHCiRXdr5sKSt7rYYa2pq8KwEj4sbRHx8to8jCzzLsjxN+6GJwsKFjsVi2/Dss3DIISbRbZvkutqs1WlqgldfhcMPhxkzoLQ0cLF2VnX1pjazudc7HFHosCwXI0b8mYMO+pXn3M6d81m5cip1dYUORnZgBQUvsmzZJE+Sa1lxjBixgBEjHlOSKyI94mSiu5iOE9RhmIVknfECZjFae9zX78zMsHSgu50XKitX0dRUBYTHbK6bN9GFgoLnHYmhthYuuwwuvdS7kUdcnElg33kHioqgvh6qquCLL+Dee2HgQPM424YnnoDJk+Hrrx0Jv0Pbtz+Edzb3Fs3mdpFlWQwd+msOOeRZLCsOgNLS/7Fs2WFB2Wu3vr6EdesuZ+3a6TQ2lgOQkDCCyZO/YMCAqw7wbBGRA3My0X0RyLQsq71kdxpttu61LCvdsqypbR9o2/YiTHuxae1c5zxggTaT6JlRo7zjrszolpZ6yxbCoT7XLTl5DElJJvsvK/uUmpqtAX39khJTg/vss95zF10EmzfD/PlwyimQkWF2tktIMDO499xj7n/wQUhpzh03bYKjj4Y33wxo+B2qr9/Lrl1PARAVlcSAAdc6HFHo6tfvYiZO/C+xsf0BqK3dyooVx7B16x+w7UaHozP27n2Lr74aze7dz3jO9elzEZMnL1U9roj4jGOJbnPyeRUwt+X55oQ1tzmBbWkhsNiyrBntXO48oNUGEc2PywFm+zDsiJSWBoMGmfHq1WZGsDNa1uempR3jh8ic03pRWuBmdcvL4Qc/gP/9zxwnJMALL8A//gH9++//uTExcPPNsGqVt0a3uhrOPtvU8Dptx46/0NRUDUD//j8jJibD4YhCW2rq4UyevJTU1KMAs0ht8+Y7WblyKlVVGx2Lq7Z2B+vWXcI335xOXZ1pcuNypTJy5FMceuizmsUXEZ9ytOtCczI7v3kXsxmWZc0CcmzbPrmdhy/GLDrbp97Wtu0lmK2An7Asa75lWQuBYbZtD9Nsrm+4++mWlMCOTjZgc8/oRkUlkpQ0zj+BOaRPn+me8e7dgem+UFcHZ50Fnzd3bOvdGz76CM4/v2vXGTIEPv4Ypjd/C42NpgTiZQe7pTU21pCX92jzURTZ2Tc5F0wYiYsbwIQJHzF48C9x74VTUvIhX301hi1bfktTU23AYmlsrGHr1j/wxRcj2L37H57zmZmncdhhq+nf/wosS/v1iIhvOdl1AfAkqQesx7Vtex4wr6fXke4ZMwb+8x8zXrPGW+/ZkdrafGprzUf6qamHh92CkoSEYaSkHE55+ZdUVq6ksnIdSUmH+u31bBuuvRY+/NAcZ2TA4sUwvpuf8MbFmVncjAzTeqypCS64wNT3nnCCr6LuvIKC56iv3w1A794/JiFhaOCDCFNRUTHk5PyWzMyTWbfuUmprt2HbtWzZcje7dz/DkCG/pk+f6X7baaypqZadO59k69bfU1eX7zkfHZ3BsGH306+fElwR8Z9w6aMrftZyh7TOLEhruRVpOC1EaymQ5QuPPQZPPmnG8fHw9tvdT3LdXC5z3UsvNcd1dTBtGmzZ0rPrdpVtN7F9+wOe40GDbg1sABEiPf14DjtsDdnZtwImqa2u3si6dRfx1Vfj2b37OZ/O8NbW7mLr1t/z+efD2LDhuhZJbhQDBlzLEUdsoH//nyrJFRG/UqIrndLVFmOt63PDNdE9H/fHwQUF//Jbc/5Vq+DWFrnfU0/BEUf45tpRUSaBPu00c7x3L5xzjunWEChFRf+hqmodAGlpx5Ga6qNvTvYRHZ3M8OH3M2XKMtLTT/Ccr6paw7p1F/PZZ4PYuPFWSks/w7abunz9hoYydu9+ntWrp/H554PYvPmXrWZxe/U6iylTVjBixGPExPTyxbckIrJfjpcuSGg49FCzit+2Ozuj23KjiCP9GJlz4uIGkJ5+PCUlH1JdvYGKihWkpHTU6a57ampMR4U6s0kUt9wCP/nJ/p/TVdHR8K9/me4MGzbAypVmd7WWXR38afv2+z3jQYNuC8yLRrjk5PFMmPABxcXvs3nzXZSVmU9g6usLyct7kLy8B4mJ6Uta2rGkph5JYuJIEhJyiI7OICoqEdtuoLGxjLq6nVRVbaCy8hvKyj6lvHwZtl3f5tUsevU6iyFDfuXz/z9ERA5Eia50SlISDB0Kubmwdq2p6Yzq4POApqY6KipWAKYnZjjP3PTp8xNKSj4EzKyur/+Q//KX3jcW48bB73/v08t7pKfDK6+YmeKKCtPF4Qc/gAsv9M/ruZWXL6ek5APA/Kz06nWGf19QWsnIOJH09E8oLf2YHTv+TGHhIk+iWl+/mz17XmLPnpe6de2YmD707/8z+vefQULCEB9GLSLSeSpdkE5zly9UVMC2bR0/rqJilWef+pSUwwIQmXN69/4xlmXeLxYUPN+tj3s78uWX8NBDZhwXZ5LPuDifXX4fo0aZjSTcrr12//+dfaF1be4tWJZ+JQWaZVmkpx/HqFH/5OijdzJy5NP06nUmLldql6+VkDCSgQOvZ/z49zjqqHxycn6vJFdEHKUZXem00aPhtdfMePVq06aqPeXlX3nGqamH+z8wB8XE9CIj4xSKit6itjaP0tJPSE8/rsfXbWyEa67x9iz+zW9g7NgeX/aALrgA3njDdGQoLTUL1d5/v+PZ+56oqdlGQcELAMTEZNG376W+fxHpkpiYXvTvfzn9+1+ObTdSWbmWiorlVFfnUlOzhcbGchobK7GsaKKjU4mJySIhYTgJCQeTknI4sbFZTn8LIiKtKNGVTmu7IO2MDj5lbpnohvuMLpjyhaKitwAzq+uLRHf+fFi+3IzHjoWbburxJTvtT38yG1Js22b69D7xhKnZ9bW8vP8DzC5dAwZch8uV4PsXkW6zLBfJyWNJTg7AOywRET/R54TSaS0T3f0tSHMnupYVTXLyBP8GFQSyss4mKioegMLChTQ1NfToeoWFpjbX7fHHza5mgZKeDk8/7T2ePRt27vTtazQ0lLJzp6mTiIqKZ+BAbfcrIiK+p0RXOm3kSNN7FTpOdBsaKqisXAtAUtKYiJili45O8Syiqq8vpKTkvR5d7ze/MTvQAVx+ORx7bM/i644TTzSvDaaE4cYbfXv9HTueoLGxHIC+fS8jNraPb19AREQEJbrSBXFxMGKEGa9dCw3tTFxWVCwHzIKslJTwrs9tyVebR+Tmmp3KwHS6mDOnp5F13/33Q1ZzyeXChd6d8XqqqamOvLyHPceDBt3smwuLiIi0oURXumTcOPO1rg6+/Xbf+yOtPtctM/OHuFwpABQW/pvGxppuXefuu6G+uQ3pLbdAv36+irDrevWCBx/0Ht98sze2nigoeNGziUCvXmeRmDiy5xcVERFphxJd6ZKW286uWrXv/WVlLTsuRE6i63LFk5X1IwAaG8soKnq7y9dYsQL++U8zzsqC24Jg74SLL4ajjjLj9eu9s83dZds2eXktW4oFwTcpIiJhS4mudIl7RhfaT3TLy78EICoqgcTE0QGKKji0Ll/4V5eff8893vFdd0Fq19uY+pxlwcMPe4/vuQeKirp/vZKS96mo+BowM/5paQ4UIIuISMRQoitdsr9Et65uDzU1mwFITp5IVFRkda/LyDiJmBhT1Lp37xs0NJR3+rkrV8Lrr5txdjZcfbU/Iuyeww+HSy4x4+JiuPfe7l+r7Xa/lmX1LDgREZH9UKIrXZKdbdpPwb6Jbnn5Us843DeKaE9UVAy9e08DoKmpmr17X+v0c1tu7Ttrln93QOuOOXMgMdGMH38cvvuu69eoqFhNUZFZ0RYfP4SsrHN9GKGIiMi+lOhKl1iWd1Y3L6/1x9jusgWIrIVoLbUsX9i9u3PlC+vXm64G5vlw5ZX+iKxnBg40/XTB7Nr2q191/Rp5ed6VbdnZN0XcjL+IiASeEl3pspblC9984x2Xly/zjCM10U1LO5bY2IEAFBe/Q339gQta58zxbvV7222QEKSth2++GXr3NuMXXoCvv+78c2trd7J79z8AiI5Op1+/n/o+QBERkTaU6EqXdVSna3rogsuVQkLCsABHFRwsK4o+faYDYNsNFBa+tN/H5+d7Oy1kZARXbW5bKSnwi194j++6q/PPzc9/FNs2vckGDLia6OgUH0cnIiKyLyW60mXtJbp1dXuorc0DIDl5ApYVuT9aXem+8Pjj3o03rrnGJJPB7OqrYdAgM37zTfjkkwM/p6Ghgh07TF8yy4ph4MAb/BihiIiIV+RmI9Jto0ebWl3wJroVFSs89ycnT3IgquCRkjKZhIThAJSUfEht7Y52H1dV5e1LGxMD110XqAi7Lz6+dRu0X/zCW3bRkV27nqahoRiAPn0uJC5ugB8jFBER8VKiK12WnAzDmisTVq82i5NaJropKRMdiiw4WJbVYlbXprBwYbuP+8c/vIv5pk+HASGS/112mXcr6P/+Fz76qOPH2nYjeXkPeY4HDbrVz9GJiIh4KdGVbnGXL1RVQW4ulJcv99yXnBzZiS5Anz4XeMa7dz+3z/223Xojhptu8n9MvhIdbbYqdvvtbzt+bGHhy57eyhkZp5KcPNbP0YmIiHgp0ZVuaVmnu3Kld0bXsuJITDzUoaiCR1LSKJKTJwBQXv4VlZXrWt3/7ruwrvnUccfB5MkBDrCHLrjAO6v/3nvw2Wf7Psa2bbZv/6PnWLO5IiISaEp0pVtaJrpr1pRTXb0BgOTksURFxTgUVXDp2/cyz3j37r+3uu+RR7zjm28OVES+Ex3dugPDb36z72NKSz/x9FZOShpHRsbUAEUnIiJiKNGVbmmZ6O7evRIwK5JUtuDVt+9PABcAu3Y9i203ArB1K7z9tnnM4MFw1lkOBdhDl1wCBx1kxm+/DUuXtr5f2/2KiIjTlOhKtwwdCklJZlxfr44L7YmN7UuvXj8AoK4un+Li9wF48klvp4KrrgKXy6kIeyYmBu64w3vcsla3quo7zxbIsbEDPL2FRUREAkmJrnRLVBSMbV5XlJmpjgsdaVm+sGvXMzQ0mEQXTIL70xDfIOyKK8z2wACvvuptN2c6LZhsPjv7RqKiYp0JUEREIpoSXem28ePN1+HD3YluFElJWlXfUlbWmURHZwCwZ8+/eeONcnY0t9U988zQaSnWkbg4mDXLezxvHtTVFbBr198AcLmS6d9/hjPBiYhIxFOiK902bhzExNQydOhqABITD8XlSnQ4quASFRXnaTXW1FTNp58u8tw3c6ZTUfnWlVdCr15m/PzzsHbtn2hqqgGgf/+riIlJdy44ERGJaEp0pdvGjYMhQ9YQHW32sFXZQvv69r3UMx4w4BnALOI6+WSnIvKtxES4oXlX35iYSgoKHgPAsqLJzg7BlhIiIhI2lOhKt40dCwcf3HIhmhLd9qSmHkFCgtlKbMKEj+jXb3NIL0Jrz3XXQUIC/OAHTxEba7Z769PnJ8THD3I4MhERiWRKdKXb0tJg0iRvopuYqI4L7TFbAnsXpZ166rMhvwitraws+NnPGjj//Ac85wYNut3BiERERJToSg+NGuXd+nf37gnOBRLk1q27hKYm00f23HOfol+/Jocj8r0ZMxbSr99WAFas+AEulxYmioiIs5ToSrfZdiN9+qwEYMeOoaxcme5sQEHsb38bxFdfnQpAaupWioredTgi37Jtm9raeZ7jZ56Zxd//vp8niIiIBIASXem26upcXK4qADZunMCKFQd4QoQqLjY9Zt94w9tma+fO+Q5G5HvFxe9RUfE1AOvWHcbKlcdz//3Q2OhsXCIiEtmU6Eq3VVau8ow3bRrP8uX7eXAEe/FFqKuDzz47g+rq/gDs2fM6tbU7HI7Md7Zv987mrlkzC7DYuBFeecWxkERERJToSvdVVHgT3dzccaxY4d3aVryeMR3FaGyMIS3tZ81nG9m58ynHYvKl8vIVFBcvBiA+fhhnnvkjz33z5ulnQkREnKNEV7qtomKlZ5ybO46iIti+3cGAgtB338Fnn5nxmDEwceKVgFmUtnPnX7Ht0P9sf+vW33nGgwbdwimnuDy75n35JXzyiUOBiYhIxFOiK93mLl1oaEhi586hACpfaKPlgqzLLoOEhIPIzDwNgNra0F+UVlm5hj17XgIgNrYf/fpdgWXBrbd6H3P//Q4FJyIiEU+JrnRLQ0MZNTWbAbDtsdi2+VHSgjSvpiZ49lkzjoqCiy4y4wEDvHv/7tgR2ovSWs/m3o7LlQDA9OkwcKA5/9prZmZbREQk0JToSrdUVq72jNPTx3nGSnS9PvoItm0z41NPhf5mHRqZmacTG2uywL1736CmZptDEfZMVdW3FBQ8D0BMTFarBD42Fm680YxtGx56yIkIRUQk0inRlW5puRCtf/9xpKaasUoXvNyL0MCULbhFRUUzYMBVzUeN5Oc/FtC4fGXr1t8DZqVZdvatuFxJre6/6ipITjbjv/0NCgsDG5+IiIgSXemWlq3FkpPHM3GiGefnK6EBqKqCRYvMOC0Nzjqr9f0DBlyNZcUCsHPnAhoaKgIcYc9UV+eye/dzAERHZzBw4HX7PCY93SS7ADU18PjjAQxQREQEJbrSTS1ndJOTx3oSXVD5AsAbb0BlpRlPmwYJCa3vj43tS9++pmi3oaGE3bufIZRs2zYHMB0jsrNvIjo6pd3H3XgjuFxm/NhjUF0doABFRERQoivdYNu2Z0Y3Lu4goqPTWiW6Kl+Af/3LO/7JT9p/THb2jZ5xXt7/YdtNfo7KN6qqNrBz59MAuFypDBz48w4fe9BBcP75ZlxY6F2cJyIiEghKdKXLamq20thYDkByslmINmmS9/5In9EtKYG33jLjfv3ghBPaf1xy8njS008EoLp6A3v3vhWQ+Hpqy5Z7cM/mDhp0GzEx6ft9fMtWYw88YLpRiIiIBIISXemylvW5SUkm0T3kEIiPN+ciPdF9+WWz5S+Y2Uz3R/ftyc6+yTPOy3vQv4H5QEXFSgoKzHR1TExWq/g7MnmyN9n/7jt4803/xSciItKSEl3pstb1uSbRjY6GsWPNuQ0boKzMiciCw/PPe8cXXLD/x/bqdToJCQcDUFLyAaWln/sxsp7bvPkuz3jw4F90WJvb1m23ecfaQEJERAJFia50WXszutC6fCFS63QLCuC998x4yBA48sj9P96yohg8eLbneNu23+3n0c4qLf2UvXvfACAuLpsBA67p9HN/8AMz6w/w3/+arYFFRET8TYmudJl7RjcqKp6EhOGe84cd5n3MV18FOqrgsHAhNJryVS64ACzrwM/p2/cS4uIGAWYDifLy4Kv9sG2bTZu807IHHXQPLld8p58fFbVvra6IiIi/KdGVLmlsrKK6egMAiYmjiYqK9tynRLd12UJH3RbaioqKbTOr+3sfR9VzBQXPU1b2GQCJiYfSr99lB3jGvi6+GPr0MeNFi2DLFh8GKCIi0g4lutIllZVrAbNs3l2f6zZqFCQmmnEkJrrbtsHHH5vxoYd6a5Y7o1+/nxIb2w+AwsKXWtVBO62xsYrcXG8iPmzYg0RFxXT5OvHxcMMNZtzUBA8/7KMARUREOqBEV7qksnKlZ9yyPhfMgjR3ne6WLZG3Q9oLL3jHP/lJ58oW3FyuBAYNur35yCY39xc+ja0ntm9/gNra7QBkZv6QXr1O6/a1rrnGu3nGX/8KxcW+iFBERKR9SnSlS9rruNBSJJcvdKXbQnsGDLjWU6tbVPQmJSX/9VFk3VdTk8e2bX9oPnIxbFjPimt79YIrrjDjykpYsKBn8YmIiOyPEl3pko46LrhFaqL73XfeThOTJ8PBB3f9Gi5XPEOG/NpznJs7G9u2fRRh92zceCNNTVUADBx4HUlJh/T4mjff7J3t/r//8/YcFhER8TUlutJptm17ZnRjYwcQG5u1z2MOP9w7jqREtzNb/nZGv36Xkpg4GoCyss8pLHyph5F1X2HhK+zZ828AYmL6MGTIvT657vDhcM45ZrxzZ+t/OxEREV9SoiudVle3i4aGIgCSksa0+5icHMjMNOOvvgKHJyQDwrZbly1Mn979a1mWi5ycOZ7jTZtupqGhogfRdU9DQxkbNlzvOR4+/GFiYjJ8dv2WG0g88EBk/JyIiEjgKdGVTqusXOMZd5ToWhZMmWLGBQWmE0G4W7kS1q834+OOg+zsnl2vV68zyMw0C75qa/PYuvU3PYyw63JzZ1NXlw9AZuZp9OnTjaLj/Tj6aDjqKDP+5htYvNinlxcREQGU6EoXVFau9ow7SnQh8soXfFW24GZZFsOHP4plxQGQl/dgc1u3wNi790127PgLAFFRiRx88ONYXWkh0UnaFjh01NVBbq55U/fZZ2Znu/XrTWcVzcaLSDBToiud1jrRHd3h4yJpQVrLsgWXC6ZN8811ExOHezaRsO0G1q//KU1NDb65+H7U1RWwfv1PPcfDhz9IQsJQv7zW2WfDsGFmvHixSaLEebYNy5aZNx8/+pHZyjohwfy3mjDBzMYfcYTpFd2nD6Snmze3119v3vQVFDj8DYiItKBEVzqtqspbupCYOKrDx0VSovvZZ97yjJNPht69fXftwYPv8GyxXF7+hd93TLPtJtavv5z6epOp9Op1Bv37z/Db67lcpgOD24MP+u2lpBPWrYNbbjGJ7ZQpcPvt8MorsHWr2eCjI2Vl5v/zxx6DCy+E/v3he9+DRx9Vn2QRcZ7ldPuiYGNZVh4wcODAgeTl5TkdTtCwbZuPP06jsbGc+PghHHnk5v0+Pjsb8vMhORlKSkxSE45uuAH+9Ccz/tvf4LKu74y7X6Wln7NixbFAI+Bi0qRPSE09wrcv0iw39y62bfsdYLosHHbYN8TG9vHLa7lVVsLgwVBUZDYc2by55zXO0nm2De+8A3Pnwocftv+Y1FQYMQKGDoWMDLP7YUODSXB37YING8wGMe39KYmPNz2lb7jBu5mMiIgvZGdnk5+fD5Bv23aHfzk0oyudUlu7ncbGcmD/9blu7oVGFRWwZs3+HxuqGhrgxRfNOC7OfMzra2lpR3LQQXc1HzWydu1PqK/f6/PXKShY5ElyIYpDD33O70kuQFKS2S0NzL/no4/6/SWl2YcfmsWTP/hB6yQ3OhpOPRUefxxWrzazsl99ZX7W58+Hhx4y/52eecYkybm55s3sO+/AHXfAIS1aLdfUmDeAkyfDWWeZkggRkUBSoiud0rI+193ndX+OPto7/vRTf0TkvA8/9NYjnn66mfnyh4MO+iUpKWYWt6ZmM2vWnEdTU73Prl9a+jnr13unoocN+yOZmVN9dv0Duf56iI014/nzobw8YC8dkfLzTS35978Pn3ziPT9ihElid++G//zHvAEZPRqiOvFXIjUVTjkF5swxJRDffAM//zmkpXkf8/rrpiRi2jQzAywiEghKdKVTOtNarKVISHRbdlvozpa/nRUVFcPo0QuJiTEzrCUlH/Dtt1di2/spnOykiopv+OabH3p2P+vT5yKys28+wLN8q18/uOQSMy4thSefDOjLR4ymJnjkEbOI7KUW+5AccoiZrV23Dm66ydsHuyfGjDG73u3YYWp3W5ajvPSSieGee6C6uuevJSKyP0p0pVM621rMbeJE83E+hGeiW1sL/zabhpGcDGec4d/Xi48fxJgxL2NZZupz9+6/s2HDdT1KdsvKvuDrr0+gocGsGEpPP5GRI//ql1ZiB3LLLd7xQw+ZMgbxnR07zIzrjTd6Z8x794annjLlCeed17mZ265KTIRrr4WNG00pRN++5nxNDdx3H4wf33pWWUTE15ToSqd4E90oEhMP2e9jwXwU7e6+sGmT+Tg0nLzzjqlLBLOdbUKC/18zLe1oRo36J2BW9u3Y8RfWrr2AxsauT4sVFv6br78+ybPTXUrK4YwZ8wouV7wvQ+60UaPghz80423bYNEiR8IIS2+8AePGwXvvec9ddZXpg3vFFYFZKBoXZ0ohvvvO9E+OjjbnN2wwdcK33AJVVf6PQ0Qij+OJrmVZUy3LmmtZ1gzLsmZZljXLR9edZVlW4AoNw5htN1JVtQ6AhIThnU6GWpYvfPaZPyJzjq83ieis3r1/zKGHPoP7f93CwoWsWHEMFRWr9//EZg0N5WzY8HPWrPkxTU2VAKSnf5/x4xcTHZ3ir7A7pe0GEmoI0zNNTXDvvXDmmbC3ef3igAEm4V2wwDclCl2Vmgp//COsWgVHHmnO2baZxZ80yZwXEfElRxNdy7KmATNt255t2/YC27bnAcsty+rRhqCWZaUDc4H0nkcp1dWbaWoys4b72yiirZaJbjh9PFlZCa+9ZsaZmTA1wG+n+va9iLFjX8PlSgagomIFy5ZNYsOGG6mp2d7ucxoaysnPf4wvvxxJfr63tUGfPj9h7Ni3iI7200q6LjjhBG8LqmXL4KOPHA0npFVUmHKEX//ae+7ss00ieeKJzsXlduih8PHH5g1NfPP75m+/NRtRLFigNzki4juOJbrNyegTwFUtz9u2vQTItCyrJ53q/dflPgK13CiiM/W5bu4WYxBedbqvv+79mHXaNG/HgEDq1et0Jk78xLNxh23Xk5//CJ9/fhDLlh3Jhg03sGXLb9m0aRYrV57Gp5/2Z8OG66mr2wmAZcVx8MF/5tBDn3OsXKEty4Jbb/Ue/96/+2OErW3b4JhjvDXklgXz5sHLL0OvXs7G1pLLZf57f/21qekHU7s7c6bZeKKszNHwRCRMODmjez6Qa9t2STv3vQDM7M5Fm8sVlvQgLmmjqwvR3Pr0geFmYy+WLjULuMKBU2ULbSUnj2Py5GUMHvxLoqISm8/alJd/QX7+n9iy5W62b/8jxcXveMoUAHr1OovDD1/LwIFXO7LwbH/OPx9ycsx48eLweoMUCGvWmE9S3CUAqammRvf2203CG4xGjjT/na+7znvu+efNtsLffutcXCISHpxMdM8Dijq4LxeY1Dzr21WTbNte3u2oZB+tE93Oly6AmVkCqKuD5WHwX6W4GN5+24z79zcLaZzkcsWTk/NbjjxyCwcddE+Hb0RiY/vRv/9VTJnyNWPHvkpCQk6AI+2c6Gi46y7vccuP3mX/PvvM/DyajYLMm8wvvvAu8gtm8fFmh8GFC739qN2lDO7/30REusPJRHcKJqFtj/t8l/4aW5Y1o7nOV3zI3UPXsmJISDi4S88Nt366L78M9c17NUyfHjxbG8fG9mbo0Hs57LBvOOqonUyc+AljxrzK+PEfcMQRGznqqB2MHLmA5OTxTod6QBdfbLabBXj33fD4ufG3t9+Gk04yb8TAbMzw6aetdykLBdOmwYoVMHasOS4tNa37tDhRRLrLyUQ3HSg5wGM6nehalpVDxzPE0k1NTfVUVa0HICFhBFFRXStIDbcFacFStrA/cXH9SEs7mqyss8jIOIGEhGFBV6KwPzExmtXtitdeMwvN3JsvTJ0K779v+uSGopwck6S7t9RuajKlF5deamp4RUS6wvH2Yh0oaf7alQY402zb7nL3Tcuy4izLSnXfgNDJCAKgunojtm2mMLtSn+s2ahSkp5vx//4X2rMyu3aZBALMH2N3n2DxvUsuaT2rG27t6Xzl1VfNLKj7U4bzzjM1uSnOdorrseRk00v5nnu85/7xDzNrvWePc3GJSOgJ1kS3S5rblHW3xfydQGmL2wBfxRUOelKfC2a3JXcd6549sHatryILvIULzewSmC1/Q2iSNOTExMAvf+k91qzuvl55pXWSe9FF5hMH946EoS4qyvQBXrTI7LAGZqb36KPNTmsiIp0RrIluevPXA5YiNC9Yy7Rtu6N63wOZA6S1uO3o5nXCkrs+F7o3owumP6rbhx/2LB4nPf+8dxysZQvh5NJLYcgQM37nHc3qtvTyy2b21r1V8iWXwDPPBE/NuC/9+Mfm06B+/czxhg2mdaF+HkSkM4I10e2KGbZtL+juk23brrVtu8x9A0L4w3Xf625rsZbCIdHdutW7KGrMGHMT/2pbq3vnnaFd+uIr77xjFkK6k9xLL4Wnnw7PJNdt0iTTQWJ084dKe/aYjS9eesnZuEQk+DmZ6ObS8WKzzBaP6ZBlWZOAMGhaFbzciW5UVHy3W1KNHw9paWb80Uehmay0nM294ALn4og0l14KBzc3+vjoI7Wa+vhjs0jLXa5w6aXw1FPhneS6DR5sFrSedJI5rqkxs9oPPBCav1NEJDCcTHSX0/EWvTkAneiHmwPMtCxrYZubewvhO5uP5/sm5MjS2FhDdbUphktMPBTL6t5fU5fLW6dbWAjr1vkqwsBp2W1BiW7gxMS03iHtjjugsdG5eJy0fDmcfrq3u8K0aZGT5LqlpcFbb8Fll5lj24bbboMbbojcnwsR2T8nE93FdDyjO4xO7G5m2/Yi27bPa3vDbEYBMKf5XLd2WYt01dXfAuavR3cWorUUyuULq1fDypVmfPjhMGyYs/FEmh//2Py7A3zzjVl9H2nWr4dTT/Vui3vqqebfIZKSXLfYWFOqce+93nOPPWZmuisrO3yaiEQoJxPdF4HM5v63bU0DWs3CWpaV3ry9rwSILxaiuYVyovvss97xxRc7F0eksiyY12IbmLvvjqx+qlu2mN647rZaxx4L//53+HRX6A7LMq3HnnnG7KYH8PrrcPzxpg2giIibY4mubdslwFXA3Jbnm1uF5bbTE3chsNiyrBmduLw7ee5KH15po+VCtMTEns3oTpjg3drzww9Dp6ausRGee86Mo6NVtuCU44/3bmW7fbvZLjYS7Nxpklz3tr4TJ5o+ue52W5Hu0kvN4jz3GoBly+DII0O7jaGI+JajXReak9n5lmXNtSxrhmVZs4Ac27ZPbufhizEbSSzt6HqWZU2yLGsh8ETzqbnNNbqdSY6lDV/O6Lpc8L3vmXFhIaxa1aPLBcyHH3qTjB/8IHR3mwoHf/iDt3fxb38LBQXOxuNvRUWmRGHTJnN8yCGtkzoxTjzRLFIbPNgcb91qeu1+8IGzcYlIcHC8vZht20ts255t2/YC27bn2bY9r4PHzbNtO2N/C9Rs217eXJM72bZtq/nx5/Wk/Vgkc8/oulzJxMcP7vH1TjnFO3733R5fLiBali1ccolzcQiMHQtXXGHGpaWm3Vi4qqyEM84wNckABx0EixfrjVZHRo+Gzz83bcjA/Hy465hFJLI5nuhKcGpsrKSmxnR3S0wchWX1/Ecl1BLdqipvn860NDjzTGfjEZgzxzuj+dRTprdquKmthXPP9W6I0LcvLFkC2dnOxhXs+vc3LejcJS719ebN6W9+EzqlUiLie0p0pV2Vld4eYD0tW3AbMcLMTIHZ6aiqyieX9ZtXXoGKCjM+7zyIj3c0HAH69IH77vMeX3ddeLWVamw0yZn7jWBamilXGD7c2bhCRXIyvPoqXH2199yvfgVXXuntPSwikSXa6QAkOLXeEa1nC9HcLMvM6j7xhJm1+u9/4bTTfHJpv1DZQnC69lrzM7R6tVl89OSTMCMMqvBt23xvCxea44QEs/Bs/Hhn4wo10dHw+OOQkwOzZplzTz1lFjEuWuRdFCuBUV4OGzearZs3bzZrNNy3oiKoqzNvQurrzf8DCQmQlGQWXKammpn6AQPMLTsbRo40X931+iIHokRX2lVV5buFaC2deqpJUsDMVAVrortrl3dWbcgQ09JJgkN0tOm64G5ZN2uW2Uhh4EBHw+qxX/wCFjSvJoiONmUz+rnrHsuC2283nyBdeql5Y714MRx1lJnx1Qy5f+zYAUuXem9ff206h/haUpJZnDlqFBx2mLlNmKBP3aR9SnSlXf6Y0QWzQjoqCpqagrtO9x//MDGC6Z0bpSKfoHL88WZ3rGeeMQuPrrnGJDChOsvzxz+arhJgvoe//910+ZCeOf988wbo7LNh717Tduyww8xOh8H6JjuUFBaa7hbvvQfvv29mbrsqJsZ7syyz819t7f6fU1lpPs1Ztsz7yVt0tPn045hjTEu+44/X7L0Ylq0q/VYsy8oDBg4cOJC8vDynw3HMZ58NprZ2Oy5XGsceW4zlwwziqKPMCmmAbdtg0CCfXdonbBsOPRS+/dYcb9igGaBgVFRkZnR27zbH//wn/OQnzsbUHX/9K1x1lff48cdN4i6+s3GjSXbd/XUty2wtPXt26L45coJtw5o18PLLZg3D8g57IBm9epnfpQcfbH6HDh8O/fqZ7iG9e0NmZvuTCA0NZg1HSYmZEd6xw9w2bza/l9evh9xc72REe1wu86bmpJPMJ4lHHx2ZOwmGs+zsbPJN/89827Y7XK6rRLcNJbrQ0FDGxx+bpe2pqUczadInPr3+vffCr39txn/5C8wMsg2aP/nE+5HxCSeoH2cwe/ll06EAzB/VtWvNgrVQ8eyzZmba/Wv4N7+Bu+5yNqZwVV5uyhheecV77vzzzRuNlBTHwgp6tm3KEBYtMjvydTRrGxNjNus45hiYMsXcBg/23xuJmhqTdH/5pfe2bl3HHTZ69TIt+846y6wVSU72T1wSOEp0u0mJLpSVfcHy5UcC0L//VYwc6ds2xMuWmV+CYD6efestn16+x664Av72NzN+9llt+xvspk+HF1804zPOgNdeC41Zun/9y/xsuWelbr4ZHnggNGIPVU1N8LvfmU4MbgcfDC+8YHadE6+CAlPC9eSTHe80N3GiKRM46SQzOZCUFNgY2youNi3m3nvP3Nata/9xcXEm5mnT4JxzICMjoGGKjyjR7SYlurBz51N8++3PABg+/GGys2/06fVt25Qr5OdDbKypnQuWd9dlZWaVb1WVae20c6dZBSzBq6AAxowx9YIADz8MN/r2R9bnFi0y20m7W6Nddx08+qiS3EB57TXzJqO83BzHxsL998P110f2f4OGBrNI+Mkn4fXXzXFLUVFmh8sf/cgkiIN7vo+QX+3YYXpQv/46/Oc/3naRLcXEmNKG6dPNbK/qekNHZxNdLbGRfbTc+jcx0XcL0dwsy/xCAdNa5p13fP4S3fb8897+vhddpCQ3FPTpYxZvuc2adeDaQSe98oqpJXYnuTNmwCOPRHaCFWhnnWV+RiZPNsd1dfDzn5sELty3lm7Phg2m68dBB5lPRV5+uXWSe+yxpsRj925TyvXznwd/kgumJdmll5qWfYWF8PbbpsfygAHex9TXmzZ+l1xifpece675O1BZ6Vzc4ltKdGUfLRPdpKRRfnmNs8/2jl991S8v0S1PPukd/+xnzsUhXXPaaXDrrWZcVwc//jHs2eNsTO157jnzcak7ibjiCvjzn9XVwwnDh8Onn5qSEbdXXzXbCbt7GYezykrTteT4481mPnPmmBlQt/794Y47zOKv//3P/D7MynIu3p6Kjze/J/78Z8jLMzsP3nRT67aEtbUmyf/JT8xiuenTzXFNjWNhiw+odKENlS7AZ58NorY2j+jodI45psinHRfcamvNL5LycrPydvdu0x7GSV9/7a3TmzABVqxwMhrpqro6M/P01Vfm+IQTTAu7mBhHw/KYP990U3D/yr3kEnj6aa0EDwZvvAGXX27KqNymTTP9mvv2dSwsn7Nts232U0+ZWUt36YZbdLSZ0f3Zz0xS6PTv5EBoajILkF94wZQUubu4tJSSYiZnLrgATj7ZlLqI81S6IN3S0FBKba1J8BMTR/slyQWzGMDdJ7SoCD7+2C8v0yV/+pN3HA47bUWa2FizKtydmHz4oanVdfq9vG3DvHnmI1N3LFdfbRY8KskNDmecYVbwuzt4gEl6RoyAhx4K/e2DCwrMQscxY0x7xyeeaJ3kHnKI6eWcl2dmMM84IzKSXDCfphx3nPn9n59v+gHPnGm6NLiVl5uFeWecYdqjXXml2YCkbQ2zBCclutJKZaV3ea0vN4poT8vyhX//268vdUBFReZjZTCLEbTlb2jKzjZ/qN0zLn/+M9x3n3PxNDTADTeYfq1us2aZXrkqVwguffua5Pb5571JTlkZ3HKL+YTn3Xedf9PUFfX1ZtHdueeaj+dvu61194TkZJOwffqpOX/bbeE1e90dLhd8//um7eXOnWYB2xVXmIXJbsXFpsTtlFNMre+115rt7PfX01ecpV+10krr+lz/Jrqnn25mdsG0h3Ly3fFTT3nrsK64Ini6QEjXuWes3O691yz2CrSyMrPo6bHHvOd++1uzA5oWngUnyzJ1mevWmSTQ/d9p7VqzMv+EE0z7qmC2cqWpO3bvCNfewrKnnzaJ3BNPmP9f9PO4L3c3hqeeMuUMr74KF17YuoVaYaF5M3388aaT0E03mU+SNNMbXFSj20ak1+hu3HgzeXkPAzB+/BIyMk7y6+tNmwYvvWTG775r6p8CrbHRLEzZssUcf/ut+chSQttDD5nZOLcHHmh97E/r1pmfbfcMWkyMSSouuywwry++8dVXpuXYl1+2Pn/iiWbx42mnBcfMfG6u+T36z3+atQZt9etnfvZ++lP9buupqirT+/355+HNN9tfqJaeDj/8IZx5pvkZSU8PdJSRQTW60i3+bi3W1oUXesfu0oFAe+stb5J72mn6QxAubr659S5jt94Kd97p/4+fn33WbIjiTnIzMkw9n5Lc0HPYYWZ1/j//CSNHes+//775ROqQQ0zf5vYWMPmTbZs35HPmmBZpw4aZkpiWSW5srNn57a23YPt280mCfrf1XGKieRO7aJF3U40zzmi96LWkxLslee/eZnOKuXPNDnPutoISOJrRbSPSZ3Q//XQgdXU7iI7O5Jhj9vhtMZpbTY2pCysrMytbd+8OfO/aU04xiQiY1dennx7Y1xf/sW2zre4993jP/fjHpsauZd2dL+zdaz66/Mc/vOfGjDEzbUowQl9jo0le7rtv321wXS6zQ9h555k3yy1bVvlKUZHpYfvuu+bmfnPe1hFHmA4S06drx69AKi42bypef9306y0ra/9xGRmmBObEE00ZyZgx4bHwr6EBtm4133egdhnUzmjdFMmJbn19CZ98Yn4zpqUdx8SJ/w3I6/70p6ZmDEz/ymnTAvKyAKxaBePHm3FODnz3nVbCh6PHHzcfQbt/3Q0fbj5BOPzwnl+7qcl8jHnTTd7d2cC0aHrkETMDJOGjsdG8IX7kETOz255x40wSc9hhZnZ/+HDTx7UzbNus/v/uO/OpwJdfmpZg333X8XOmTDG/N3/8Y/Na4qy6OtN7+PXXzYLAzZs7fmxiopmVP/JI8yZlwgQYOjQ4SmLaqqw034v7tmmT2Wxk40Zz3NBgEvdvvglMPEp0uymSE93S0k9ZseIYAAYMuJoRI/4ckNddssRbm3v22WbnqEC56CIzSwNmC9brrw/ca0tguXc/Kikxx5Zl2sj97netWwl1lm3De++ZpvrLlnnPp6WZnyV17gh/a9eaGfx//tPMZu3PwIFmN7GMDPMzkpBg3iQ1NppZsD17zBul/PwD78oVG2taYp12mkluhw713fckvmXb5k3K+++b3xcffGBm5/cnIQEOPdRsXnLooTBkiPfWt69/kuDaWrNAcdcu83XnTlPy0jKxbflGfn+xV1QEJlFXottNkZzo7tjxBN99ZxrIDh/+KNnZgcn6GhvNitWdO81s6rZtrbdo9JfcXDj4YPPHJivL/KHS7Ft427zZ1C0uXeo9l5xs+tpedVXnSgyKikw5wp/+ZD4RaOlHPzLnA/HzK8GjqcnMvL79tmlJ9dVXvq0Fj401M31HH21Krb73vdar/yV0NDWZzhgffmhm6r/4ouMylPbExZmtinv1Mn+3srLMYrf4eHOLizNfo6PNDGvLW00NlJZ6byUl5mtBgSm96K6kJPNJwsEHm6/33NP5TzB6orOJbhhUhoivBGLr3/a4XOZj3t/+1iS9Tz3VehGRvzzwgLf34Y03KsmNBEOHmr6hjz5qfhlXVJjb/feb2/jxpn5u/Hgz+5aQYP447NoFq1ebHZQ++WTfBSXjx5vFJqee6si3JQ6LijIfPR95JPz61yZ5WLbMJLwrV5o31bm5B54RS001M3YjRpjbyJGm3nH8eG8rRgltUVHmv2nLOtbdu03C+9VXZuOS1atNWUB7vXlra81M6/btgYvZsswnEkOH7ns7+GDT1SOYW9RpRreNSJ7RXbnyZIqLlwBw9NG7iI0NXPfwrVvN/zS2bRKM3Fz/1sru2mVer6bGzOht26aFG5EmP9+8uXr6afPHozuOPNK8STr//OCsqZPgUl/vnUmrrTW/4yzLLMTNytLWsuJVXQ3r15v6161bzazvli1mvGePufmiX29qqpkd7t9/35s7uR08ODjfaGlGV7rMPaMbHd2LmJg+AX3tgw4yWwK/9ZZJOt9+27Rs8Zff/c7b/3DGDCW5kWjgQNPs/Z57zMK0f/2rda1tRw4+2GwEMX26WWwk0lkxMd6Pm0X2JyFh35nflmzb1Hbv3et941Rba/6u1daaN1UxMaaEwX2LjTX14e5bSkpkLL7WjG4bkTqjW19fzCefZAKQlvY9Jk4M/PY/r79uEggw2zB2tKK5pzZvNh8J1teb2qJNm7T1pRhFReYjxI0bYccOs3o6OtrUxA0fbv7oDB7sdJQiIqIZXemSQG7925Ef/tDMlm3YYFamfvWVf2bM7r3XJLlgWkIpyRW3zEzzyYKIiIQHVZUJAFVVzie6Lhfcfrv3+I9/9P1rrFljdq4CU65w222+fw0REREJDkp0BQj81r8dueQS7wzrSy/BunW+u7Ztm4VD7mqdO+7QHuQiIiLhTImuAMFRugCm997NN5txUxP84he+u/aiRaZhN5jFbzfc4Ltri4iISPBRoiuAN9GNielNbGxvR2O5/nrT2gTMLmmffNLza5aVeRNogP/7P7OqVURERMKXEl2hvn4v9fW7AWdnc92SkkzTdbdbbtm3QX9X3Xyz6ZsKZrGRu7uDiIiIhC8lukJl5VrP2Mn63JauuMLs8Q1ma81HH+3+tV57zey2BmZziMceC+5dXERERMQ3lOhK0NTnthQdDfPne49/+UvT77arNm2Cyy/3Hv/f/5mdXkRERCT8KdGVNq3FRjkYSWvHHQfXXWfGVVVw7rlQUdH555eXw9lnQ3GxOT7nHDNTLCIiIpFBia4ETWux9syZYzaRAFi1Ci67rHP1umVlphZ3TfO3duih8MwzKlkQERGJJEp0pUXHhT7ExgbXJuwpKabGNjXVHP/733DxxWY/747s3AmnnOLt1pCRAa++6r2GiIiIRAYluhGurm4P9fUFQPDU57Z1yCHwwgumbhfg+efhmGPMFsEtNTTAP/4BEyfCF1+Yc5mZpneue1ZYREREIke00wGIs4Jh69/OOO0001N32jQzm7t8ORx+OEyaBBMmmBre//4XduzwPmfgQHjzTRg/3qmoRURExElKdCNcMNfntnX66Wamdvp0WL/enFu+3NzaOvtseOIJ6O3s3hciIiLiIJUuRLhgbC22P+PGmUVpjz9uShRaio+HM8+ExYvN7K+SXBERkcimGd0IF2qJLkBMDFxzjbkVF8O2bRAXZ/rjxsU5HZ2IiIgECyW6Ec5doxsb24+YmEyHo+m6jAxzExEREWlLpQsRrK6ugPr6PUDw1+eKiIiIdJUS3QhWWbnWMw6VsgURERGRzlKiG8FCpbWYiIiISHco0Y1grVuLjXIwEhERERHfU6IbwUKx44KIiIhIZynRjVC2bXsS3djY/sTEqHWBiIiIhBcluhGqrm4XDQ17AUhKGuNwNCIiIiK+p0Q3QlVWrvaMk5LGOhiJiIiIiH8o0Y1QlZXfeMZKdEVERCQcKdGNUK0TXZUuiIiISPhRohuhvKULFklJai0mIiIi4UeJbgSy7UZPx4WEhOG4XIkORyQiIiLie0p0I1B19WaamqoBlS2IiIhI+FKiG4G0EE1EREQigRLdCKREV0RERCKBEt0I1LqHrkoXREREJDwp0Y1A7hldy4ojIWG4w9GIiIiI+IcS3QjT2FhDVdUGAJKSRhEVFe1wRCIiIiL+oUQ3wlRVrQcaAZUtiIiISHhTohthtBBNREREIoUS3QijhWgiIiISKZToRhjN6IqIiEikUKIbYdyJbnR0OnFxAx2ORkRERMR/lOhGkPr6Empr8wBTtmBZlsMRiYiIiPiPEt0I0ro+V2ULIiIiEt4cb6JqWdZU4GRgE5AOYNv2vG5cZwYwDJgEZAJLbNue7btIQ58SXREREYkkjia6lmVNA6bbtn1ei3NTLctabNv2yV24zlxgvm3bC5qP04GFlmUVA0Nt2y7xbeShqfVCNHVcEBERkfDmWOlCczL6BHBVy/O2bS8BMptnaDtznWnAC7Zt57a4RglwHmaGeKFvIg59SnRFREQkkjhZo3s+kNvBbOsLwMxOXucw27aXtz3ZfN0FwNTmpDqi2bbtSXTj4rKJiclwOCIRERER/3Iy0T0PKOrgvlxgUicT1BmWZS3u4L5lzV+ndDG2sFNbu42GhhIAkpLGOxuMiIiISAA4mehOwSS07XGfz+nEdZbu57705q8dJdQRo6JipWecnKxEV0RERMKfk4vR0oGSAzwmB9inLKGlAyxaG9b8mA6vYVlWHBDX8tQBYgpJFRVfe8bJyRMci0NEREQkUIK1j25J89fMHl5nBqZOd3/uBEpb3Ab08DWDkmZ0RUREJNIEa6LbY80tx3KBA/XSnQOktbjt8HNojnAnulFRiSQkDHM4GhERERH/c3zDiA6kN3/tVm2tZVmTMLO5kw/UQ9e27VqgtsVz7e68ZjBraCijpmYTAMnJ47Asl8MRiYiIiPhfuM7oLgROatlbN5K17p+rsgURERGJDE4murl03FUhs8VjuqS51djM/S1AizSqzxUREZFI5GSiuxxviUJbObD/bgntsSxrPjC3eXc1aaaOCyIiIhKJnEx0F9PxjO4woEvJqmVZs4CFbZNcy7JyLMua2r0Qw4N3RtciKWmso7GIiIiIBIqTie6LQKZlWe0lu9OA+S1PWJaV3lHCalnWNGB5BzO5k+hGCUS4sO1GT41uQsIwoqOTHY5IREREJDAc67pg23aJZVlXAXMx2wEDnqQ117btRW2eshCYalnWTNu2F7R4/CRgJrDQsqwZLR6f3vx1um3bk/3xPYSCqqoNNDVVAypbEBERkcjiaHsx27YXWZZV0tzzdhPNyWkHu50txmwb3HbL3/ean9dReULEzuYCVFZ6F6IFvOPC6tXwv//B119DcTE0NMCAATByJJx8svlqheVGdCIiIhIEHO+j21xucMB6XNu25wHz2jmf4Y+4wkXrhWgBSHTr6uDpp+FPfzKJ7v6MGgU33QSXXALx8f6PTURERCJKuPbRlWatW4tN8O+LvfUWHHIIXH31gZNcgLVrYcYMk/C+8YZ/YxMREZGIo0Q3zLkT3ejoDOLisv3zIlVV8LOfwemnw+bN3vNHHQUPPgiffALbtsH27WZ8//1w9NHex23eDGeeCT/9qbmWiIiIiA84Xrog/lNXV0hd3Q7AlC1Y/qiH3b4dzjkHlrdoeXziiTBnDhx++L6Pz842Se6tt8JXX8Hs2fDBB+a+p5+GpUvN7O7gwb6PVURERCKKZnTDWMv6XL8sRNu40SSt7iQ3ORn++ldYsqT9JLetww6D994zCW5iojn3zTdwzDGmrEFERESkB5TohrHy8mWecUrKJN9efMMGOOEEyMszxzk58PnnpoShKzPHlgWXX25md4cPN+fy8uD445XsioiISI8o0Q1jFRUtE10fthLets0kufn55njsWPjsMxg9uvvXHDXK1O9Obo5zzx6YOhVyI7o7nIiIiPSAEt0w5p7RjYpKJDHxEF9dFM44A3aY2l/GjjXlB3369PzaffqYa01qnn3eudMscCst7fm1RUREJOIo0Q1T9fVF1NSYDgjJyROwLFfPL9rYCD/5iamjBRg2zCSmvXv3/NpuaWnwzjtw6KHmeP1685qNjb57DREREYkISnTDVHm5twuCz8oWfvUrePNNM05PN2NfJrluWVmm80Jmpjl++224807fv46IiIiENSW6Ycrn9bmLF5uWYQAuF7z0ktnC119ycmDRIohu7oD3xz+aDSlEREREOkmJbphq2XEhObmHie6uXXDxxWDb5vj3vze9cv3t+9+HBx7wHl9+uanbFREREekEJbphyrsQLaFnC9FsG664AgoKzPFpp8Ftt/kgwk664Qaz+A2gsBAuuwyamgL3+iIiIhKylOiGofr6YmpqTFuu5OQJREX1YAO8p5+G//zHjPv3h7//HaIC+GNjWfDUU+a1wZRQPPFE4F5fREREQpYS3TBUUeGjhWh5eXDLLd7jJ57wz+KzA+ndG/72N+/x7bd7N6oQERER6YAS3TDkk/pc24arr/b2sL30UtPT1imnnGJKKMD08r32Wm/NsIiIiEg7lOiGodZb/3Yz0X3lFW8rsf794eGHexxXjz3wAPTrZ8avv266MoiIiIh0QIluGGq9EO3Qrl+gshJuusl7/OijkJHhm+B6IiMD/vQn7/Gtt5pYRURERNqhRDfM1NeXUFOzCYDk5PHdW4j2u9/Btm1mfOqpcO65Poywh84913R+ANi+HebOdTYeERERCVpKdMNMefmXnnFKymFdv8C338L995txbKyZzbUsH0XnA5ZlyijcG0nMmwebNzsakoiIiAQnJbphpqzsC884NfWIrl/gxhuhvt6Mb78dDj7YR5H50MiR3tKK2trA9vUVERGRkKFEN8y0THRTUrqY6L77LrzzjhkPHgy/+IUPI/Oxu++Gvn3N+N//hg8/dDQcERERCT5KdMOIbduUl5tENzq6FwkJwzr/5MZGM4Pr9oc/QGKijyP0odRUmDPHezx7ttqNiYiISCtKdMNITU0u9fV7AEhNPRyrK7W1f/87rFplxlOmwPTpfojQxy69FMaMMeMvv4SXX3Y2HhEREQkqSnTDSOv63CM7/8SqKrjrLu/x/fcHdpvf7nK54Pe/9x7/8pfQ0OBcPCIiIhJUQiCbkc7q9kK0hx6CHTvM+Mwz4fjjfRyZH51xBhxzjBmvXw/PPONsPCIiIhI0lOiGkdYL0Q7v3JMKC729aF2u0OtLa1mtY77nHqipcS4eERERCRpKdMNEU1MtFRUrAEhIGEFMTCd3Mps3D8rLzfjKK+HQbuyk5rRjjjEz0QD5+fDXvzobj4iIiAQFJbphoqJiJbZdB3ShbGHXLnjsMTOOi4Nf/cpP0QXAffd5x3/4g+mvKyIiIhFNiW6YKC391DPudKL7hz9AdbUZX3MNDBjgh8gCZMIEOPtsM87PhyefdDQcERERcZ4S3TBRWvqxZ5yWduyBn5CXB3/5ixknJMAdd/gpsgC6+27veM4czeqKiIhEOCW6YcC2bU+i63KlkZQ05sBPapkIXn+9d5exUDZ5sunCACaR/9vfHA1HREREnKVENwxUV2+ivn43AGlpR2NZrv0/YetWeOIJM05Ohlmz/BxhAN1zj3f8+99DXZ1zsYiIiIijlOiGgS6XLfzud1Bfb8Y//zlkZfkpMgdMmQI//KEZb9tmdnwTERGRiKRENwx0KdHNzYWnnzbj1FS49VY/RuaQlt0j5s2DxkbnYhERERHHKNENA+5E17JiSEk5bP8P/s1vvNvk3nwzZGb6OToHHHEEfP/7ZrxhA7zyiqPhiIiIiDOU6Ia4uroCqqu/BSAlZQouV0LHD/7uO+9H+enpJtENV7Nne8dz54JtOxeLiIiIOEKJbogrLf3EMz5g2cJ990FTkxnfdhukpfkxMoedcgqMH2/GX30FH37oaDgiIiISeEp0Q1xp6f884/0muuvWwT//aca9eplFaOHMslp3k5g717lYRERExBFKdENccfH7zSNr/4nuvfd6P76fNQtSUvwdmvPOPx+GDDHjd96Br792MhoREREJMCW6IayurpDKypUAJCdPJCamg4Vl33wDL75oxn36wHXXBShCh0VHt+4qMW+ec7GIiIhIwCnRDWElJR94xhkZJ3X8wJabKNxxByQl+TGqIPPTn3r7BL/wAmze7Gw8IiIiEjBKdENYcfF7nnGHie7y5fDyy2bcvz9cfXUAIgsiiYlwww1m3NQEDz/saDgiIiISOEp0Q5g70bWsmI7rc1tunvCLX0DCftqPhavrrvN+3089BaWlzsYjIiIiAaFEN0TV1GylpmYTAKmpR+FytVOO8Pnn8OabZjxoEFx1VQAjDCK9esFll5lxRQX89a/OxiMiIiIBoUQ3RHm7LUBGxontP+juu1uP4+L8HFUQu+km7/iRR7y7w4mIiEjYUqIbolrW56ant1Of+9FHsGSJGefkwOWXByawYDVyJPzwh2a8bZu3bllERETClhLdEGTbTRQXLwYgKiqJ1NTD2z6g9WzuPfdATEwAIwxSLbc8fvBB5+IQERGRgFCiG4LKy5dRX18AmG4LUVGxrR+wZAn8r3nHtJEj4aKLAhxhkDrpJBg71ow//9zcREREJGwp0Q1Be/e+6Rn36nV66zvbzubeey+4XIEJLNhZVuta3YceciwUERER8T8luiGoqMib6GZm/rD1nW++CV98YcZjxphtcMXrwgvN7nAAL71k6nVFREQkLCnRDTG1tbsoL18KQFLSeOLjs713NjbCnXd6j++7D6L0n7iV+Hi49lozbmyERx91Nh4RERHxG2VBIaao6G3PuFevNrO5zzwDq1eb8WGHwTnnBC6wUHLNNd5WawsWQHm5s/GIiIiIXyjRDTF79njbYrWqz62qal2be//9piZV9tWnj3eBXlkZPP20s/GIiIiIXyjRDSENDWUUFb0LQGxsf1JTj/Le+dBDsGOHGZ91Fnzvew5EGEJaLkr7v/8zZQwiIiISVpTohpC9e9/EtmsByMo6F8tq/s9XUABz55qxywV/+INDEYaQsWPh5JPNODcXXn/d2XhERETE55TohpDCwkWece/e07x33Heft870yivh0EMDHFmIarmBxMMPOxaGiIiI+IcS3RDR2FjpWYgWE9Ob9PTjzB3ffAN/+YsZJyWZvrnSOaeeajbUALNl8ooVzsYjIiIiPqVEN0Ts2fMKTU3VAGRl/QjLcpnNIa67zltfescd0K+fg1GGmKgobSAhIiISxpTohohdu/7mGffte4kZPPusd6vf4cPhttsCH1iou+QSyMgw4+efh507nY1HREREfEaJbgioqdlGcfF7AMTHDyMt7RgoKYHbb/c+6E9/MpshSNckJcHMmWZcXw+PP+5sPCIiIuIzSnRDwK5dfwdsAPr1uxzLsuCXvzTdFgB+/GNTbyrdc911EB1txn/5C1RXOxuPiIiI+IQS3SBn243s2uXe0MCiX79L4YMPvDOPiYmqLe2p7Gw47zwz3rMHnnvO2XhERETEJ5ToBrk9e16npiYXgIyMk4mvz4Cf/tT7gN//HgYNcii6MNK21ZhtOxaKiIiI+IYS3SCXl+edrc3OvsksONuyxZw4/ni44QZH4go7hx0GxxxjxmvWwJIlzsYjIiIiPaZEN4iVly+jtPS/ACQmHkLmu0WwYIG5MykJnnrKtMgS31CrMRERkbCiLCmIbd06xzPOjpqOdeUM750PPQQ5OQ5EFcbOOQcOOsiM334b1q93NBwRERHpmWinA7AsaypwMrAJSAewbXueU9cJFmVlS9mz5yUAYqL70PeKf0JVlbnzssvMVr/iW9HRphTE3Y/4//4P/vxnZ2MSERGRbnN0RteyrGnATNu2Z9u2vaA5MV1uWdZiJ64TLGzbZtMm7+YPQ15NxbV6gzkYP950XLAsh6ILc1deCcnJZvzMM7B3r7PxiIiISLc5luhalpUOPAFc1fK8bdtLgEzLsma09zx/XSeY7N79D0pLPwIgviSR/g9vNHdkZcFLL5mWYuIfaWnerhbV1fDEE87GIyIiIt3m5Izu+UCubdsl7dz3AjAzwNcJCtXVW9i48eee44PnVBHVgFl89uabMGyYc8FFip//3Dtj/qc/mR3TREREJOQ4meieBxR1cF8uMKl5tjZQ13FcQ0MZa9b8mIaGEgD6vAe9vgQSEuDll+Hwwx2NL2IMGwZnnWXG+fmwaJGz8YiIiEi3OJnoTsEkou1xn+9MWwFfXcdRNTV5rFx2IhUVywGIz4cRDwHp6aan68knOxpfxGnbakwbSIiIiIQcJxPddKDkAI/pTILqq+sEXNn/FrD9mTNY/+w4vvpoCOXVywCILoWxd0H08PHwxRdw9NEORxqBjj8eJkww46++gk8/dTQcERER6bpg7aNb0vw109/XsSwrzrKsVPcNCFg7g925C9h00JvsGvQNjXGNAMTthvF3xpA0fTZ8/jmMGBGocKQly9p3W2AREREJKcGa6AbSnUBpi9uAQL1wAtmecVQtDFicyJTl15Dyzib4wx8gPj5QoUh7pk+Hvn3N+N//9m69LCIiIiEhWBPd9OavHS0y8+V15gBpLW47evianZY55WoOKb+eiTzG0cNWMuK3FcTMfRwGDQpUCLI/cXFw3XVm3NRkOjCIiIhIyAjWRDdgbNuutW27zH0DArbqKHH0afQ781HSTriW6OHjtAlEMLr6apPwgumpW17ubDwiIiLSaU4murl0vEgss8VjAnUdkX317g0XX2zGZWXaQEJERCSEOJnoLsdbWtBWDoBt28sDeB2R9t16q3f8wANQW+tcLCIiItJpTia6i+l4JnYYsCTA1xFp36GHwtlnm/GOHfDcc87GIyIiIp3iZKL7IpBpWVZ7Seo0YH7LE5ZlpVuWNbWn1xHpljvu8I7nzTOL00RERCSoOZbo2rZdAlwFzG153rKsaUCubdtt911dCCy2LGtGD68j0nVHHgnf+54Zf/stvPqqs/GIiIjIAUU7+eK2bS+yLKvEsqy5wCaaa21t225vv9vFmO1+l/bwOiLdc8cd8N//mvEf/gDnnKNOGSIiIkHMsu2AddMKCZZl5QEDBw4cSF5entPhSDCxbbMt8KpV5viDD+CEE5yMSEREJCJlZ2eTn58PkG/bdnZHj4v4ProinWZZMHu293ju3I4fKyIiIo5ToivSFeefD0OGmPF//gNff+1kNCIiIrIfSnRFuiI6Gm67zXs8Z45zsYiIiMh+KdEV6aorroA+fcx44UJYu9bZeERERKRdSnRFuioxEW6/3YxtG37zG2fjERERkXYp0RXpjmuugd69zfiFF2DNGmfjERERkX0o0RXpjqQkmDXLjDWrKyIiEpSU6Ip01zXXeGt1X3xRs7oiIiJBRomuSHdpVldERCSoKdEV6Ymrr9asroiISJBSoivSE21nde+5x9l4RERExEOJrkhPXXMN9O1rxi+9BF984Ww8IiIiAijRFem5xMTWM7mzZpnZXREREXGUEl0RX7jySjj4YDP+73/hrbecjUdERESU6Ir4REwM/P733uM77oDGRufiERERESW6Ij7z4x/DEUeY8erV8Pe/OxuPiIhIhFOiK+IrlgVz53qP774bKiudi0dERCTCKdEV8aXjj4fTTzfj/PzWia+IiIgElBJdEV974AFTswswbx7k5jobj4iISIRSoiviayNHwk03mXFtLdxyi6PhiIiIRColuiL+cNdd0K+fGb/6KrzzjrPxiIiIRCAluiL+kJpqyhbcbrgBamqci0dERCQCKdEV8ZeLL4ZjjjHjDRvgvvucjUdERCTCKNEV8RfLggULWi9MW7nS2ZhEREQiiBJdEX8aNQp++UszbmyEn/0MGhqcjUlERCRCKNEV8bc774TRo8142TJ48EFn4xEREYkQSnRF/C02Fv76V1PKAKYjw4oVzsYkIiISAaKdDkAkIhx5JNx+u6nTra+HCy80s7uJiU5HFpxqamDzZigshNJSKC+HqCiIi4P4eOjfHwYNgsxM7xsIERGRNpToigTKb34DS5bA8uWwfj3ceiv8+c9OR+W84mL45BP44gv48ktYu9Zsn2zbB35ucjJMmABTpsDhh8PJJ0NWlt9DFhGR0GDZnfljEkEsy8oDBg4cOJC8vDynw5Fw8+23MHEiVFeb40WL4Mc/djYmJ6xZA6+/Dm++CZ9+Ck1NvrmuZcERR8BZZ8FFF8Hgwb65roiIBJXs7Gzy8/MB8m3bzu7ocUp021CiK363YAHMnGnGycnw+efexWrhbMcO+Oc/4dlnYdWqjh/XqxcMHw7DhsGAAWbzjdRUM8NbWwuVlWbGd/t288Zh27b2r2NZcOKJcOWVMG0aROsDLBGRcKFEt5uU6Irf2baZbfzXv8zx8OHmI/uMDGfj8gfbhvfeg0cfhTfeaH/mduRIOO00s7nGEUeY2tuu1N0WFpp65/ffh7feMrPFbR10ENx8s0l6k5K6//2IiEhQUKLbTUp0JSCqqkxi9/XX5vi000wi6HI5GpbPVFXB3/9uEty1a/e9/8gj4YIL4IwzzMytL23eDP/4BzzzDGza1Pq+vn3h7rvhqqtMNwwREQlJSnS7SYmuBMzWrWYR1Z495njGDPjLX0K7i0BZGTz+uOkVXFjY+r7sbLjiCrjkEjj4YP/HYtvwwQdw//3w9tut78vJgT/+EX70o9D+9xYRiVCdTXTVR1fEKQcdBAsXemtHFyyAe+91NKRuKy6GX/8ahgwxG2S0THKPO858n5s3w333BSbJBW+N7ltvwTffwPnne+/LzTWLAM84w4xFRCQsKdEVcdIJJ5iP2N3uuw8eeMCxcLqssBB+8QuTtN97r0l4wfS8/clPTCu1//7X+cVgY8bACy/AV1/BSSd5z7/1llkIOGeOtmYWEQlDSnRFnHbhhfDww97j226D3//esXA6paDAbIAxZIhJEsvLzXmXCy6/HNatMx0WJk50Msp9TZkCixebtm4DBphzNTUmWT/uONi40dn4RETEp5ToigSDG280G0q4/fKXcMcdvusv6yu7d5tEfOhQU/taVWXOx8SYlmkbNsDTT8OIEc7GuT+WZcoW1q83nRiimn8Nfv45jB8P8+d3brMKEREJekp0RYLFXXeZBVJuc+fCeeeZvrFO27XL7OQ2dKgprXAnuHFxcMMNps71L38x94eKlBSzaO7jj02LNzDf19VXm3resjJn4xMRkR5ToisSTG67zXQtcM8y/vvfcPTR7bfoCoTt2+GWW0yXggcf9O7oFh9vZqFzc+GRR0xHhVB11FGwYoV3Ew8wpQ1TpphFbCIiErKU6IoEm2uuMVvjpqaa41WrYPJk+NOfAlfKsGIFXHyxmaF96KHWCe5NN5kE9+GHvXWuoS452cxIv/oqpKWZcxs2mA0sWi4WFBGRkKJEVyQYnXYafPYZjBpljmtqTInAEUeY8/5QU2N2azvxRJg0CZ57DhobzX3x8aaeNTfXJL79+/snBqeddZbpFDFpkjmurjaL6268UV0ZRERCkBJdkWA1ahQsXWoSXLelS00pww9/CB991PNFU01N8Mkn5jUGDDAdID74wHt/r17wq1+ZzS0efDB8E9yWcnLMv8mMGd5zjzwCZ54JpaXOxSUiIl2mndHa0M5oEpQ++AB+/nNYvbr1+ZEjzVa6Z55pOgZ0plft1q1mAdZHH8Frr5lOCm2NGGFmcC+9FBITffM9hKKnnjKL0+rrzfGhh8Lrr/t+22IREekSbQHcTUp0JWg1NMBf/wp/+INJVttKSoIJE0xd7YABptzA5TLdA4qKYNMm+Pbb9hNbMI8/7zy48krTU1Zb4xoffWTake3da4579TKLBL/3PWfjEhGJYEp0u0mJrgS9hgZ48UXT7/V//+tZ+UJ8PJx6Kpx7rqlPTU/3WZhhZdMmM2u+bp05jo2FZ59tva2wiIgEjBLdblKiKyElPx9eecUkvJ9+atqB7U+/fmY73GOPNbcjjzQzwXJgpaUwfTq88445tiyzMO/GG52NS0QkAinR7SYluhLSKitNWcPu3VBXZ2pL09IgIwMGDfK2zpLuaWgw/Xafesp77vbbTTlJlNb2iogESmcT3U6sXBGRkJGUZLo1uNuSiW9FR5s66QED4Le/Nef++EfYscMkv7GxzsYnIiKtaApCRKQrLAt+8xv485+9s7jPPQdnnAHl5c7GJiIirSjRFRHpjquvhpdeMgv6ABYvhhNOgIICR8MSEREvJboiIt11zjmwZImpgQazq9oxx8DmzY6GJSIihhJdEZGeOOYY0/Vi4EBzvHGj2b1u1Spn4xIRESW6IiI9Nnq0ae92yCHmeNcus6HEf//rbFwiIhFOia6IiC8MHmy2Vj7iCHNcWgqnnAKvvupsXCIiEUyJroiIr/TqBe+9B6edZo5ra82uc08+6WxcIiIRSomuiIgvJSXBa6/BRReZ46YmuPJKmDOnZ9s1i4hIlynRFRHxtZgY+Pvf4eabved+8Qu46SaT+IqISEAo0RUR8YeoKHjgAbM9sNsjj8DFF5vtmUVExO+U6IqI+ItlwezZZntgl8uc+9e/4MwzoaLC2dhERCKAEl0REX+74gp4+WXvLmrvvgsnnQR79jgbl4hImFOiKyISCGeeabYJTk83x19+CcceC1u3OhqWiEg4U6IrIhIoxx5rNpEYMMAcf/ut2VltzRpn4xIRCVNKdEVEAmnsWPjkExgxwhzn58Nxx5md1URExKeU6IqIBNqQIWYXtSlTzHFxMUydCm+84WhYIiLhRomuiIgTeveGDz6Ak082x9XVcM458Le/ORmViEhYUaIrIuKU5GQzi3vBBea4sdF0aPjNb7SLmoiID0Q79cKWZU0FTgY2AekAtm3P68Z1ZgDDgElAJrDEtu3ZvotURMSPYmPhuefMDO+jj5pzv/oVfPMNPP202VJYRES6xZFE17KsacB027bPa3FuqmVZi23bPrkL15kLzLdte0HzcTqw0LKsYmCobdslvo1cRMQPoqLg//4PsrPhjjvMbO7ChbBhA7z6Kgwe7HSEIiIhKeClC83J6BPAVS3P27a9BMhsnqHtzHWmAS/Ytp3b4holwHmYGeKFvolYRCQALAtmzYLXXoOUFHPu66/NgrWPP3Y0NBGRUOVEje75QG4Hs60vADM7eZ3DbNte3vZk83UXAFObk2oRkdBxxhnw+ecwbJg5LiyE738fHnxQdbsiIl3kRKJ7HlDUwX25wKROJqgzLMta3MF9y5q/TulibCIizhs1yuycdtJJ5rihAW69FX70I9OKTEREOsWJRHcKJqFtj/t8Tieus3Q/96U3f+0ooRYRCW6ZmfCf/8DsFmtrX30VJk2Cr75yLi4RkRDiRKKbDpQc4DEHTHRt2z55PwvXhjU/Zp/SBhGRkBEdDX/4g2lBlplpzm3ZAkcfDffdB/X1joYnIhLsgq2Pbknz18weXmcGpk73gCzLirMsK9V9A6wevraIiG+dfjqsWAFHHWWOGxrgnntMwrtunbOxiYgEsWBLdHusueVYLtDZXrp3AqUtbgP8FJqISPcNHgwffQR33w2u/2/vXmOkvOo4jv/OwC5drtMtUGChyC5tAdMqtzYmmEBZYo01pspCYzQ2USEx8fIKYmJMGk0q7QuTNsZAo402JlKaeveFS20btZrCrjWKpTQspSxQLl0WClv3wh5f/J9hLszs7kx353k48/0kJ8/yPM8yZ+DJ2d+cPZdJdu7gQWnlSunxx+ndBYAikhZ009GxorG1zrlVst7cTWWsofuopFk55VQlrw0AE66uzoYsvPKKtGyZnevvt2XJVq+W/va3eOsHAAkz5qDrnGt3zvkKS3oC30OufZI25q6tOxrvfb/3/lKmSGL9HgDJds89Umen9K1v2fq7ku2ktm6d9OUvS6dPx1o9AEiKMQfdaPKXq7D05vxVXSo92awx556yREuNbWcCGoCa0NAg/fCH0t//bsMXMn76U2npUhvicOlSfPUDgASIY+hCp7JDFAo1S+WvluCc2y1pV7S7GgDUjnvvteXGnnhCmjnTzvX1Sd//vgXexx8n8AKoWXEE3XaV7tFtkVRWWHXO7ZC0rzDkOueanXOtlVURAG4gkyZJX/+69Oabdqyrs/Pnztn43cWLpe98RzpzJt56AkCVOV/lLSWj8brHJK0uHEvrnDsqaaf3/rmC+9cU6611zm2W1DvCtc5yxutG39ctqampqUnd3d3lfCsAJMPRoxZs9+7N3za4rs52V9u2zbYVTiVtPvIHcPWqdP68hfkzZ6TeXunyZenKlWwZGLB7nbOSSknTpkkzZliZOVO6+WZpwQKpqcmuAUikhQsX6uTJk5J00nu/sNR9VQ+60rUQutV731ZwbnvhJhDR2NvW6NqenPOrJO2STUDLlY6OW733qyuoG0EXQBgOH7ahC888c/3yY0uWSFu2SJ/7nLRmTXZSW1JduiQdOyZ1ddkxU44ft2B7/nx+qB8Ps2ZZ4F261Fa5yJTly6V0enxfC0BZEh10JSkaVrBJ0lFF4dR7/1iR+3bI1rrdmDt21zl3QaXH+kpSl/e+pYJ6EXQBhKW7W3rySenpp204Q6HbbpPuv996eTdskG69tfp17O+X3n47G2BzA21Xl9STsB3dly6V1q61smaNlYaGuGsF1IzEB92kIugCCNbAgPSb30hPPSW98II0PFz8vttvlz76USt33y21tNg436lTK3td76ULF6R33rGlz7q783tljx2TTp6srEe2vl6aN8/C+a23SnPn2rGxUZo+3YYfZI719dn6eG/v/8oV6y1+7z0r589bXXLL//43ej2mTLGd6zZskO67z5aAy7wegHFH0K0QQRdATTh71kLv889b6B3Lzmpz5liQnDXLfnU/a1Z24ltm6ENfnwXGy5ft2NNjAbfSndtSKWnhQhtq0dxsx0xpbrZQO5FjjYeHpRMnbBjI4cO25fK//mVbMvf3l/6+qVOl9eulT39aeuABew8Axg1Bt0IEXQA158oV21XtxRell16SXnttbL2Y42X27OsDbOa4aFEye0YHB6X//Me2Yf7HP+zfrWuEuc8rV1roffBB6SMfSf6YaCDhCLoVIugCqHlDQ9KRIxZ4Dx2yCV9vvWVjaHt6LBiPxZQp1us7f74NL8iU+fPzg+306RP5bqrn+HH7sPDnP0v795feoe6OO6SHHpK2bpVWrKhuHYFAEHQrRNAFgFEMDkoXL1oZGrJzmZ8lU6dacJ0xIzusoRZ5b9s0/+53VjpL7IN0110Weh96yHqwAYwJQbdCBF0AwLjr7pZ++1tb2/gvfyk+8e7jH5ceflhqa7MPCgBKIuhWiKALAJhQJ09Kzz0n/fKXNr630NSptr7xww/bhLaQNvYAxglBt0IEXQBA1Rw/boH3Zz+zFR0K3Xab9KUvWWkpe2l4IFhjDbp8TAQAIC6LF0s7d9qkv1dflb72tfxd195+W/re92yDivXrLRCPdTIgAIIuAACxc852WfvRj2y1hr17pU9+Mn/Ywssv23CGefOkr3zFloTjt7LAiAi6AAAkyU03SVu2SH/8o21WsWuXtGxZ9vrly9JPfiKtW2fnf/AD6dSp+OoLJBhBFwCApFqwQNqxQ/rvf6VXXpG++tX8FRmOHJG+/W3bWONTn7JJbiPt2AbUGIIuAABJ55z0sY9Je/bY0Iaf/1zasCF7fXjYeoDb2iwcf+MbtuEHUOMIugAA3EimTZO++EXbge3oUem737XVGTJ6eqQnn7Rth1eulJ54Qnr33fjqC8SIoAsAwI2quVl65BHp2DGpvV36/OdtjG/Ga69J3/ym9fK2tUm/+pX0/vuxVReoNoIuAAA3ulRKam2VfvELG9rw4x9L99yTvT4wYON3P/tZae5c6QtfsJ3aGM+LwLFhRAE2jAAABOPQIenpp6VnnpHOnr3++syZ0mc+Y729ra1SQ0P16whUgJ3RKkTQBQAEZ3BQeuEF6dlnbfhCb+/19zQ0SPfdJz3wgK3gsGhR1asJjBVBt0IEXQBA0AYGpP37bVOKX/9aunSp+H133y194hO2usO6dfnLmgExI+hWiKALAKgZ/f3Sn/5k43X/8Acb31vMpEnSmjUWetevl+69N3+rYqDKCLoVIugCAGqS99I//2mB9/e/l159deT7b7/dJrytXWvlrrvo9UXVEHQrRNAFAEDSuXPSyy9LL74ovfSS7c42mkWLpA9/WFqxwkpLi7R4sbRwoVRXN+FVRu0g6FaIoAsAQBFnzljg/etfpQMHbI3esS5PlkpZ2F28WJo3z5Y4mzMne5w9W5o+3TbDmDYt+3V9ve0KN1bDwzbxbmjIjpkyMJBfip0rdb7w3OCg1WnSpPwyeXL22NCQfS+FJZ2WGhtZ4eIDIuhWiKALAMAYDAxI//63hd6ODuvxPXRIunhx/F4jlbLgmEpZiMw9OpcNtZlgeyNlmoYG6ZZb8sucOba5R1NT9tjUJM2aVV7grwFjDbqTq1clAAAQjPp6afVqKxneS++8Y6H39delt97KL+VuRTw8bIE6RO+/L3V3WxnN1KkWeD/0IdsNr7AwMbAkgi4AABgfzknz51vZuPH661eu2MYV587lH3t67NqVK9Lly9ljX5909aoF3qtX87/23sb91tVZr2+p45Qp9nV9fX6p9NzkyfbamfoUlqEhq3fm/RSWCxcs8OeWoaGR/137+qQ337RSzM03W+BdulS6805p2TIrd9xhwyVqGEEXAABUx7Rp0pIlVmC8t1D/7rs2DvrUKenkyWzJ/PnECQvKxVy4YMNHOjquv7ZoUTb45obgBQtqYjgEQRcAACAuztmybDNm2NCEUry3MNzVVbycOGG93YVOnLDS3p5/fsYMC7wrVkjLl2dLc7ONgw4EQRcAACDpnLPVKWbPtvWLCw0MWOB94w3p8GErb7xhY6WLbfn83ns2kfDAgfzz9fXW85sbfpcvt2EQN900IW9tIrHqQgFWXQAAAMHw3sZC5wbgw4ezkwXHmgNTKevtzQ2/K1ZYr/DMmRP6FophebEKEXQBAEBN6OuTjhyx0JtZKeP1123S2+Dg2P+epqZs+H300apMgCPoVoigCwAAatrgoA2DyA2/mdLXV/r7GhpsYl0qNeFVZB1dAAAAlK+uzsbp3nmn9OCD2fPDwzaxLTf4ZsJwT4/dX4WQWw6CLgAAAEaXStk2zosXS/ffnz2fGQdc7oYgVUDQBQAAQOWck+bOtZIwyepfBgAAAMYJQRcAAABBIugCAAAgSARdAAAABImgCwAAgCARdAEAABAkgi4AAACCRNAFAABAkAi6AAAACBJBFwAAAEEi6AIAACBIBF0AAAAEiaALAACAIBF0AQAAECSCLgAAAIJE0AUAAECQCLoAAAAIEkEXAAAAQSLoAgAAIEgEXQAAAASJoAsAAIAgEXQBAAAQJIIuAAAAguS893HXIVGccwOS6lKplObPnx93dQAAAFDg9OnTGh4elqRB7319qfsIugWcc0OSJsVdDwAAAIzqqvd+cqmLJS/UsH5JUyQNSzpbhddzkhZIOiWJTx0YC54ZlItnBuXimUG5qv3MzJUNwe0fsVL06MbLOTdT0kVJs7z3l+KuD5KPZwbl4plBuXhmUK6kPjNMRgMAAECQCLoAAAAIEkE3fv2SHtEoY0yAHDwzKBfPDMrFM4NyJfKZYYwuAAAAgkSPLgAAAIJE0AUAAECQCLoAAAAIEkEXAAAAQWJntJg451olbZJ0VFJakrz3j8VZJySTc26fpB5Ju733nc65tKQ1krZLetR73xln/RCv6HnYJanXe79zhPtocyBpbM8M7Q5yOee2SWqRtEpSo6T9Izw7iWprCLoxcM5tlrTVe9+Wc67VOdfuvd8UY9WQTGlJmyVtc85lzvVKauOHTe1yzu2S1CzpgKRWSftHuJc2B2U9M6LdQSR6bnZ77/dEf05L2uecuyBpife+N+fexLU1LC9WZdEDckwFD0d0rUM5DxMgXWtk2mWfpCWpy3v/XIxVQsJEbcdB7/32ItfSos1BgZGemeg67Q4ywbWr8MNN1K5ckPXsbso5l7i2hh7d6tsie2h6i1zbK/u1ED90kMd7v18j974ApdDmoCK0O5C0ttgHHO99r3Nuj6zHPx21L4lsa5iMVn1tsnFPxXRJWhV9KgKA8UCbA6BS25xz7SWudUTHNdExkW0NQbf61sj+w4vJnG+uUl0AhI82B0ClDo5wLR0dM+E2kW0NQxeqLy0b0D+SZkkM9sc1zrlm2eSRjBbZzOfeeGqEG0hatDmoAO0ORplA1hLdk2k70kpgW0PQTZbe6NgYZyWQOM2SVuUO4nfOrZLU4ZxbzQ8dfAC90ZE2B4VodzCabRr7mNve6Fj1toahC0DCee/bCicDRJ+gOyU9FU+tAISMdgcjiVbl6JJUcu3upCDoJks6OpYazA3kapetcwlUKh0daXMwVrQ7NS7q2d8maVMZPfvp6Fj1toagC9y4eqRrjQ4AVAPtDvZJ2ui9LzXxLFEIutXXpdKzDhtz7gHknNsd/YqomN7oyPhKjIQ2B2Wh3UEp0VJj20vsjpfItoagW32dynbhF2qW8mYwAltUuuHInB9p+ReANgflot3BdZxzuyXtijYSKSaRbQ1Bt/raVboBaRG70CDfntw9wwtsUuldaIAM2hyUi3YHeZxzOyTtKwy5zrlm51xmCbpEtjUE3ep7VlJjtD5hoc2Sdle5Pki2A8XGwkW7y2zWDTDjFbGjzUG5aHdwjXNus6TOEj25q5QdjpDItsZ57+N43ZoWPTRbcz8xR+e2j7I4M2pQ9Oui3bm/8nHOdUg66L3fHl/NkBTOuaOyH0RFe+Foc1BoDM8M7Q4ykw53ySag5UpHx63e+9U59yeurSHoxiTq6t8k6aiiB8Z7/1icdUJyRb82ukX2rDRK2lu4xiVqS/RMrFW0sH90er9sstB1zwdtDip4Zmh3apxz7oJKj7uVbBhLS8H3JKqtIegCAAAgSIzRBQAAQJAIugAAAAgSQRcAAABBIugCAAAgSARdAAAABImgCwAAgCARdAEAABAkgi4AAACCRNAFAABAkAi6AAAACBJBFwAAAEEi6AIAACBIBF0ACJhzrj3uOgBAXAi6ABC25rgrAABxIegCQKCcc4RcADWNoAsA4WqNuwIAECeCLgCEa3vcFQCAOBF0ASBAzrnNklbFXQ8AiBNBFwAC45xrlbQv7noAQNwIugAQCOfcNudch6TcJcWanXO+SKG3F0DwnPc+7joAAMZZFGQ7JHV571virg8AxIEeXQAAAASJoAsAAIAgEXQBAAAQJIIuAAAAgkTQBQAAQJAIugAAAAgSQRcAAABBIugCQA1iwwgAtYCgCwC1aVfcFQCAiUbQBQAAQJAIugAQtsa4KwAAcSHoAkCAvPed0ZfpErf0VqcmABAfgi4AhGu/JDnnWnNPOuc2S9obS40AoIqc9z7uOgAAJkC0skKHpE5JG733vc65tKR93vtNsVYOAKqAoAsAAXPONctWWFglC7w9knZ673vjrBcAVANBFwAAAEFijC4AAACCRNAFAABAkAi6AAAACBJBFwAAAEEi6AIAACBIBF0AAAAEiaALAACAIBF0AQAAECSCLgAAAIJE0AUAAECQCLoAAAAIEkEXAAAAQSLoAgAAIEgEXQAAAASJoAsAAIAgEXQBAAAQpP8DNtZV+I8LEXIAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "P11exp = expect(result.states, P11p)\n", "P22exp = expect(result.states, P22p)\n", "P12exp = expect(result.states, P12p)\n", "\n", "# Plot the results:\n", "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", "#axes.plot(result.times, result.expect[\"11\"], 'b', linewidth=2, label=\"P11\")\n", "#axes.plot(result.times, result.expect[\"12\"], 'r', linewidth=2, label=\"P12\")\n", "axes.plot(tlist, P11exp, 'b', linewidth=2, label=\"P11\")\n", "axes.plot(tlist, P12exp, 'r', linewidth=2, label=\"P12\")\n", "axes.plot(tlist, P22exp, 'y', linewidth=2, label=\"P22\")\n", "axes.set_xlabel(r't', fontsize=28)\n", "axes.legend(loc=0, fontsize=12)" ] }, { "cell_type": "code", "execution_count": 56, "id": "70577d59", "metadata": {}, "outputs": [], "source": [ "# Convenience functions and parameters:\n", "\n", "def cot(x):\n", " return 1. / np.tan(x)\n", "\n", "beta = 1. / T\n", "\n", "# Number of expansion terms to calculate:\n", "Nk = 2\n", "\n", "# C_real expansion terms:\n", "ck_real = [lam * gamma / np.tan(gamma / (2 * T))]\n", "ck_real.extend([\n", " (8 * lam * gamma * T * np.pi * k * T /\n", " ((2 * np.pi * k * T)**2 - gamma**2))\n", " for k in range(1, Nk + 1)\n", "])\n", "vk_real = [gamma]\n", "vk_real.extend([2 * np.pi * k * T for k in range(1, Nk + 1)])\n", "\n", "# C_imag expansion terms (this is the full expansion):\n", "ck_imag = [lam * gamma * (-1.0)]\n", "vk_imag = [gamma]" ] }, { "cell_type": "code", "execution_count": 58, "id": "57ceeffe", "metadata": {}, "outputs": [], "source": [ "from qutip.nonmarkov.heom import BosonicBath\n", "\n", "bath = BosonicBath(Q, ck_real, vk_real, ck_imag, vk_imag)" ] }, { "cell_type": "code", "execution_count": 62, "id": "43f44111", "metadata": {}, "outputs": [], "source": [ "solver = HEOMSolver(HL, bath, max_depth=max_depth, options=options)\n", "result = solver.run(rho0, tlist)" ] }, { "cell_type": "code", "execution_count": 63, "id": "27e892a6", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/luis/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "P11exp = expect(result.states, P11p)\n", "P22exp = expect(result.states, P22p)\n", "P12exp = expect(result.states, P12p)\n", "\n", "# Plot the results:\n", "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", "#axes.plot(result.times, result.expect[\"11\"], 'b', linewidth=2, label=\"P11\")\n", "#axes.plot(result.times, result.expect[\"12\"], 'r', linewidth=2, label=\"P12\")\n", "axes.plot(tlist, P11exp, 'b', linewidth=2, label=\"P11\")\n", "axes.plot(tlist, P12exp, 'r', linewidth=2, label=\"P12\")\n", "axes.plot(tlist, P22exp, 'y', linewidth=2, label=\"P22\")\n", "axes.set_xlabel(r't', fontsize=28)\n", "axes.legend(loc=0, fontsize=12)" ] }, { "cell_type": "code", "execution_count": null, "id": "16511ea2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }