{ "cells": [ { "cell_type": "markdown", "id": "8a068471", "metadata": {}, "source": [ "# Example 3: Quantum Heat Transport\n", "\n", "### Setup\n", "\n", "In this notebook, we apply the QuTiP HEOM solver to a quantum system coupled to two bosonic baths and demonstrate how to extract information about the system-bath heat currents from the auxiliary density operators (ADOs).\n", "We consider the setup described in Ref. \\[1\\], which consists of two coupled qubits, each connected to its own heat bath.\n", "The Hamiltonian of the qubits is given by\n", "$$ \\begin{aligned} H_{\\text{S}} &= H_1 + H_2 + H_{12} , \\quad\\text{ where }\\\\\n", "H_K &= \\frac{\\epsilon}{2} \\bigl(\\sigma_z^K + 1\\bigr) \\quad (K=1,2) \\quad\\text{ and }\\quad H_{12} = J_{12} \\bigl( \\sigma_+^1 \\sigma_-^2 + \\sigma_-^1 \\sigma_+^2 \\bigr) . \\end{aligned} $$\n", "Here, $\\sigma^K_{x,y,z,\\pm}$ denotes the usual Pauli matrices for the K-th qubit, $\\epsilon$ is the eigenfrequency of the qubits and $J_{12}$ the coupling constant.\n", "\n", "Each qubit is coupled to its own bath; therefore, the total Hamiltonian is\n", "$$ H_{\\text{tot}} = H_{\\text{S}} + \\sum_{K=1,2} \\bigl( H_{\\text{B}}^K + Q_K \\otimes X_{\\text{B}}^K \\bigr) , $$\n", "where $H_{\\text{B}}^K$ is the free Hamiltonian of the K-th bath and $X_{\\text{B}}^K$ its coupling operator, and $Q_K = \\sigma_x^K$ are the system coupling operators.\n", "We assume that the bath spectral densities are given by Drude distributions\n", "$$ J_K(\\omega) = \\frac{2 \\lambda_K \\gamma_K \\omega}{\\omega^2 + \\gamma_K^2} , $$\n", "where $\\lambda_K$ is the free coupling strength and $\\gamma_K$ the cutoff frequency.\n", "\n", "We begin by defining the system and bath parameters.\n", "We use the parameter values from Fig. 3(a) of Ref. \\[1\\].\n", "Note that we set $\\hbar$ and $k_B$ to one and we will measure all frequencies and energies in units of $\\epsilon$.\n", "\n", "      \\[1\\] Kato and Tanimura, [J. Chem. Phys. **143**, 064107](https://doi.org/10.1063/1.4928192) (2015)." ] }, { "cell_type": "code", "execution_count": 1, "id": "39e5d111", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import qutip as qt\n", "from qutip.nonmarkov.heom import HEOMSolver, DrudeLorentzPadeBath, BathExponent\n", "\n", "from ipywidgets import IntProgress\n", "from IPython.display import display" ] }, { "cell_type": "code", "execution_count": 2, "id": "956a042b", "metadata": {}, "outputs": [], "source": [ "# Qubit parameters\n", "epsilon = 1\n", "\n", "# System operators\n", "H1 = epsilon / 2 * qt.tensor(qt.sigmaz() + qt.identity(2), qt.identity(2))\n", "H2 = epsilon / 2 * qt.tensor(qt.identity(2), qt.sigmaz() + qt.identity(2))\n", "H12 = lambda J12 : J12 * (qt.tensor(qt.sigmap(), qt.sigmam()) + qt.tensor(qt.sigmam(), qt.sigmap()))\n", "Hsys = lambda J12 : H1 + H2 + H12(J12)\n", "\n", "# Cutoff frequencies\n", "gamma1 = 2\n", "gamma2 = 2\n", "\n", "# Temperatures\n", "Tbar = 2\n", "Delta_T = 0.01 * Tbar\n", "T1 = Tbar + Delta_T\n", "T2 = Tbar - Delta_T\n", "\n", "# Coupling operators\n", "Q1 = qt.tensor(qt.sigmax(), qt.identity(2))\n", "Q2 = qt.tensor(qt.identity(2), qt.sigmax())" ] }, { "cell_type": "markdown", "id": "7e5afb82", "metadata": {}, "source": [ "### Heat currents\n", "\n", "Following Ref. \\[2\\], we consider two possible definitions of the heat currents from the qubits into the baths.\n", "The so-called bath heat currents are $j_{\\text{B}}^K = \\partial_t \\langle H_{\\text{B}}^K \\rangle$ and the system heat currents are $j_{\\text{S}}^K = \\mathrm i\\, \\langle [H_{\\text{S}}, Q_K] X_{\\text{B}}^K \\rangle$.\n", "As shown in Ref. \\[2\\], they can be expressed in terms of the HEOM ADOs as follows:\n", "$$ \\begin{aligned} \\mbox{} \\\\\n", " j_{\\text{B}}^K &= \\!\\!\\sum_{\\substack{\\mathbf n\\\\ \\text{Level 1}\\\\ \\text{Bath $K$}}}\\!\\! \\nu[\\mathbf n] \\operatorname{tr}\\bigl[ Q_K \\rho_{\\mathbf n} \\bigr] - 2 C_I^K(0) \\operatorname{tr}\\bigl[ Q_k^2 \\rho \\bigr] + \\Gamma_{\\text{T}}^K \\operatorname{tr}\\bigl[ [[H_{\\text{S}}, Q_K], Q_K]\\, \\rho \\bigr] , \\\\[.5em]\n", " j_{\\text{S}}^K &= \\mathrm i\\!\\! \\sum_{\\substack{\\mathbf n\\\\ \\text{Level 1}\\\\ \\text{Bath $k$}}}\\!\\! \\operatorname{tr}\\bigl[ [H_{\\text{S}}, Q_K]\\, \\rho_{\\mathbf n} \\bigr] + \\Gamma_{\\text{T}}^K \\operatorname{tr}\\bigl[ [[H_{\\text{S}}, Q_K], Q_K]\\, \\rho \\bigr] . \\\\ \\mbox{}\n", "\\end{aligned} $$\n", "The sums run over all level-$1$ multi-indices $\\mathbf n$ with one excitation corresponding to the K-th bath, $\\nu[\\mathbf n]$ is the corresponding (negative) exponent of the bath auto-correlation function $C^K(t)$, and $\\Gamma_{\\text{T}}^K$ is the Ishizaki-Tanimura terminator (i.e., a correction term accounting for the error introduced by approximating the correlation function with a finite sum of exponential terms).\n", "In the expression for the bath heat currents, we left out terms involving $[Q_1, Q_2]$, which is zero in this example.\n", "\n", "      \\[2\\] Kato and Tanimura, [J. Chem. Phys. **145**, 224105](https://doi.org/10.1063/1.4971370) (2016)." ] }, { "cell_type": "markdown", "id": "0f74639e", "metadata": {}, "source": [ "In QuTiP, these currents can be conveniently calculated as follows:" ] }, { "cell_type": "code", "execution_count": 3, "id": "e242685a", "metadata": {}, "outputs": [], "source": [ "def bath_heat_current(bath_tag, ado_state, hamiltonian, coupling_op, delta=0):\n", " \"\"\"\n", " Bath heat current from the system into the heat bath with the given tag.\n", " \n", " Parameters\n", " ----------\n", " bath_tag : str, tuple or any other object\n", " Tag of the heat bath corresponding to the current of interest.\n", " \n", " ado_state : HierarchyADOsState\n", " Current state of the system and the environment (encoded in the ADOs).\n", " \n", " hamiltonian : Qobj\n", " System Hamiltonian at the current time.\n", " \n", " coupling_op : Qobj\n", " System coupling operator at the current time.\n", " \n", " delta : float\n", " The prefactor of the \\delta(t) term in the correlation function (the Ishizaki-Tanimura terminator).\n", " \"\"\"\n", " l1_labels = ado_state.filter(level=1, tags=[bath_tag])\n", " a_op = 1j * (hamiltonian * coupling_op - coupling_op * hamiltonian)\n", "\n", " result = 0\n", " cI0 = 0 # imaginary part of bath auto-correlation function (t=0)\n", " for label in l1_labels:\n", " [exp] = ado_state.exps(label)\n", " result += exp.vk * (coupling_op * ado_state.extract(label)).tr()\n", "\n", " if exp.type == BathExponent.types['I']:\n", " cI0 += exp.ck\n", " elif exp.type == BathExponent.types['RI']:\n", " cI0 += exp.ck2\n", "\n", " result -= 2 * cI0 * (coupling_op * coupling_op * ado_state.rho).tr()\n", " if delta != 0:\n", " result -= 1j * delta * ((a_op * coupling_op - coupling_op * a_op) * ado_state.rho).tr()\n", " return result\n", "\n", "def system_heat_current(bath_tag, ado_state, hamiltonian, coupling_op, delta=0):\n", " \"\"\"\n", " System heat current from the system into the heat bath with the given tag.\n", " \n", " Parameters\n", " ----------\n", " bath_tag : str, tuple or any other object\n", " Tag of the heat bath corresponding to the current of interest.\n", " \n", " ado_state : HierarchyADOsState\n", " Current state of the system and the environment (encoded in the ADOs).\n", " \n", " hamiltonian : Qobj\n", " System Hamiltonian at the current time.\n", " \n", " coupling_op : Qobj\n", " System coupling operator at the current time.\n", " \n", " delta : float\n", " The prefactor of the \\delta(t) term in the correlation function (the Ishizaki-Tanimura terminator).\n", " \"\"\"\n", " l1_labels = ado_state.filter(level=1, tags=[bath_tag])\n", " a_op = 1j * (hamiltonian * coupling_op - coupling_op * hamiltonian)\n", "\n", " result = 0\n", " for label in l1_labels:\n", " result += (a_op * ado_state.extract(label)).tr()\n", "\n", " if delta != 0:\n", " result -= 1j * delta * ((a_op * coupling_op - coupling_op * a_op) * ado_state.rho).tr()\n", " return result" ] }, { "cell_type": "markdown", "id": "70a84d8c", "metadata": {}, "source": [ "Note that at long times, we expect $j_{\\text{B}}^1 = -j_{\\text{B}}^2$ and $j_{\\text{S}}^1 = -j_{\\text{S}}^2$ due to energy conservation. At long times, we also expect $j_{\\text{B}}^1 = j_{\\text{S}}^1$ and $j_{\\text{B}}^2 = j_{\\text{S}}^2$ since the coupling operators commute, $[Q_1, Q_2] = 0$. Hence, all four currents should agree in the long-time limit (up to a sign). This long-time value is what was analyzed in Ref. \\[2\\]." ] }, { "cell_type": "markdown", "id": "87cab4c3", "metadata": {}, "source": [ "### Simulations" ] }, { "cell_type": "markdown", "id": "b1e8feb7", "metadata": {}, "source": [ "For our simulations, we will represent the bath spectral densities using the first term of their Padé decompositions, and we will use $7$ levels of the HEOM hierarchy." ] }, { "cell_type": "code", "execution_count": 4, "id": "3ce6dddd", "metadata": {}, "outputs": [], "source": [ "Nk = 1\n", "NC = 7\n", "options = qt.Options(nsteps=1500, store_states=False, atol=1e-12, rtol=1e-12)" ] }, { "cell_type": "markdown", "id": "d1994815", "metadata": {}, "source": [ "##### Time Evolution\n", "\n", "We fix $J_{12} = 0.1 \\epsilon$ (as in Fig. 3(a-ii) of Ref. \\[2\\]) and choose the fixed coupling strength $\\lambda_1 = \\lambda_2 = J_{12}\\, /\\, (2\\epsilon)$ (corresponding to $\\bar\\zeta = 1$ in Ref. \\[2\\]).\n", "Using these values, we will study the time evolution of the system state and the heat currents." ] }, { "cell_type": "code", "execution_count": 5, "id": "902d119f", "metadata": {}, "outputs": [], "source": [ "# fix qubit-qubit and qubit-bath coupling strengths\n", "J12 = 0.1\n", "lambda1 = J12 / 2\n", "lambda2 = J12 / 2\n", "# choose arbitrary initial state\n", "rho0 = qt.tensor(qt.identity(2), qt.identity(2)) / 4\n", "# simulation time span\n", "tlist = np.linspace(0, 50, 250)" ] }, { "cell_type": "code", "execution_count": 6, "id": "5bbaaf5a", "metadata": {}, "outputs": [], "source": [ "bath1 = DrudeLorentzPadeBath(Q1, lambda1, gamma1, T1, Nk, tag='bath 1')\n", "bath2 = DrudeLorentzPadeBath(Q2, lambda2, gamma2, T2, Nk, tag='bath 2')\n", "\n", "b1delta, b1term = bath1.terminator()\n", "b2delta, b2term = bath2.terminator()\n", "solver = HEOMSolver(qt.liouvillian(Hsys(J12)) + b1term + b2term,\n", " [bath1, bath2], max_depth=NC, options=options)\n", "\n", "result = solver.run(rho0, tlist, e_ops=[qt.tensor(qt.sigmaz(), qt.identity(2)),\n", " lambda t, ado: bath_heat_current('bath 1', ado, Hsys(J12), Q1, b1delta),\n", " lambda t, ado: bath_heat_current('bath 2', ado, Hsys(J12), Q2, b2delta),\n", " lambda t, ado: system_heat_current('bath 1', ado, Hsys(J12), Q1, b1delta),\n", " lambda t, ado: system_heat_current('bath 2', ado, Hsys(J12), Q2, b2delta)])" ] }, { "cell_type": "markdown", "id": "b64eb930", "metadata": {}, "source": [ "We first plot $\\langle \\sigma_z^1 \\rangle$ to see the time evolution of the system state:" ] }, { "cell_type": "code", "execution_count": 7, "id": "f840b0f7", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(figsize=(8,8))\n", "axes.plot(tlist, result.expect[0], 'r', linewidth=2)\n", "axes.set_xlabel('t', fontsize=28)\n", "axes.set_ylabel(r\"$\\langle \\sigma_z^1 \\rangle$\", fontsize=28)\n", "pass" ] }, { "cell_type": "markdown", "id": "887ddf73", "metadata": {}, "source": [ "We find a rather quick thermalization of the system state. For the heat currents, however, it takes a somewhat longer time until they converge to their long-time values:" ] }, { "cell_type": "code", "execution_count": 8, "id": "785d481c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(16, 8))\n", "\n", "ax1.plot(tlist, -np.real(result.expect[1]), color='darkorange', label='BHC (bath 1 -> system)')\n", "ax1.plot(tlist, np.real(result.expect[2]), '--', color='darkorange', label='BHC (system -> bath 2)')\n", "ax1.plot(tlist, -np.real(result.expect[3]), color='dodgerblue', label='SHC (bath 1 -> system)')\n", "ax1.plot(tlist, np.real(result.expect[4]), '--', color='dodgerblue', label='SHC (system -> bath 2)')\n", "\n", "ax1.set_xlabel('t', fontsize=28)\n", "ax1.set_ylabel('j', fontsize=28)\n", "ax1.set_ylim((-0.05, 0.05))\n", "ax1.legend(loc=0, fontsize=12)\n", "\n", "ax2.plot(tlist, -np.real(result.expect[1]), color='darkorange', label='BHC (bath 1 -> system)')\n", "ax2.plot(tlist, np.real(result.expect[2]), '--', color='darkorange', label='BHC (system -> bath 2)')\n", "ax2.plot(tlist, -np.real(result.expect[3]), color='dodgerblue', label='SHC (bath 1 -> system)')\n", "ax2.plot(tlist, np.real(result.expect[4]), '--', color='dodgerblue', label='SHC (system -> bath 2)')\n", "\n", "ax2.set_xlabel('t', fontsize=28)\n", "ax2.set_xlim((20, 50))\n", "ax2.set_ylim((0, 0.0002))\n", "ax2.legend(loc=0, fontsize=12)\n", "\n", "pass" ] }, { "cell_type": "markdown", "id": "d1ebad7a", "metadata": {}, "source": [ "##### Steady-state currents\n", "\n", "Here, we try to reproduce the HEOM curves in Fig. 3(a) of Ref. \\[1\\] by varying the coupling strength and finding the steady state for each coupling strength." ] }, { "cell_type": "code", "execution_count": 9, "id": "1bf706b9", "metadata": {}, "outputs": [], "source": [ "def heat_currents(J12, zeta_bar):\n", " bath1 = DrudeLorentzPadeBath(Q1, zeta_bar * J12 / 2, gamma1, T1, Nk, tag='bath 1')\n", " bath2 = DrudeLorentzPadeBath(Q2, zeta_bar * J12 / 2, gamma2, T2, Nk, tag='bath 2')\n", " b1delta, b1term = bath1.terminator()\n", " b2delta, b2term = bath2.terminator()\n", " \n", " solver = HEOMSolver(qt.liouvillian(Hsys(J12)) + b1term + b2term,\n", " [bath1, bath2], max_depth=NC, options=options)\n", " \n", " _, steady_ados = solver.steady_state()\n", " return bath_heat_current('bath 1', steady_ados, Hsys(J12), Q1, b1delta), \\\n", " bath_heat_current('bath 2', steady_ados, Hsys(J12), Q2, b2delta), \\\n", " system_heat_current('bath 1', steady_ados, Hsys(J12), Q1, b1delta), \\\n", " system_heat_current('bath 2', steady_ados, Hsys(J12), Q2, b2delta)" ] }, { "cell_type": "code", "execution_count": 10, "id": "27bf89a5", "metadata": {}, "outputs": [], "source": [ "# Define number of points to use for final plot\n", "plot_points = 100" ] }, { "cell_type": "code", "execution_count": 11, "id": "929c2e2d", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "", "version_major": 2, "version_minor": 0 }, "text/plain": [ "IntProgress(value=0, max=300)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "progress = IntProgress(min=0, max=(3*plot_points))\n", "display(progress)\n", "\n", "zeta_bars = []\n", "j1s = [] # J12 = 0.01\n", "j2s = [] # J12 = 0.1\n", "j3s = [] # J12 = 0.5\n", "\n", "# --- J12 = 0.01 ---\n", "NC = 7\n", "# xrange chosen so that 20 is maximum, centered around 1 on a log scale\n", "for zb in np.logspace(-np.log(20), np.log(20), plot_points, base=np.e):\n", " j1, _, _, _ = heat_currents(0.01, zb) # the four currents are identical in the steady state\n", " zeta_bars.append(zb)\n", " j1s.append(j1)\n", " \n", " progress.value += 1\n", "\n", "# --- J12 = 0.1 ---\n", "for zb in zeta_bars:\n", " # higher HEOM cut-off is necessary for large coupling strength\n", " if zb < 10:\n", " NC = 7\n", " else:\n", " NC = 12\n", "\n", " j2, _, _, _ = heat_currents(0.1, zb)\n", " j2s.append(j2)\n", " progress.value += 1\n", "\n", "# --- J12 = 0.5 ---\n", "for zb in zeta_bars:\n", " if zb < 5:\n", " NC = 7\n", " elif zb < 10:\n", " NC = 15\n", " else:\n", " NC = 20\n", "\n", " j3, _, _, _ = heat_currents(0.5, zb)\n", " j3s.append(j3)\n", " progress.value += 1\n", "\n", "progress.close()" ] }, { "cell_type": "code", "execution_count": 12, "id": "5fe9f1bf", "metadata": {}, "outputs": [], "source": [ "np.save('data/qhb_zb.npy', zeta_bars)\n", "np.save('data/qhb_j1.npy', j1s)\n", "np.save('data/qhb_j2.npy', j2s)\n", "np.save('data/qhb_j3.npy', j3s)" ] }, { "cell_type": "markdown", "id": "ce5ded7e", "metadata": {}, "source": [ "### Create Plot" ] }, { "cell_type": "code", "execution_count": 13, "id": "de447398", "metadata": {}, "outputs": [], "source": [ "zeta_bars = np.load('data/qhb_zb.npy')\n", "j1s = np.load('data/qhb_j1.npy')\n", "j2s = np.load('data/qhb_j2.npy')\n", "j3s = np.load('data/qhb_j3.npy')" ] }, { "cell_type": "code", "execution_count": 14, "id": "7b42a6b7", "metadata": {}, "outputs": [], "source": [ "matplotlib.rcParams['figure.figsize'] = (7, 5)\n", "matplotlib.rcParams['axes.titlesize'] = 25\n", "matplotlib.rcParams['axes.labelsize'] = 30\n", "matplotlib.rcParams['xtick.labelsize'] = 28\n", "matplotlib.rcParams['ytick.labelsize'] = 28\n", "matplotlib.rcParams['legend.fontsize'] = 28\n", "matplotlib.rcParams['axes.grid'] = False\n", "matplotlib.rcParams['savefig.bbox'] = 'tight'\n", "matplotlib.rcParams['lines.markersize'] = 5\n", "matplotlib.rcParams['font.family'] = 'STIXgeneral' \n", "matplotlib.rcParams['mathtext.fontset'] = 'stix'\n", "matplotlib.rcParams[\"font.serif\"] = \"STIX\"\n", "matplotlib.rcParams['text.usetex'] = False" ] }, { "cell_type": "code", "execution_count": 15, "id": "3265efb6", "metadata": {}, "outputs": [ { "data": { "image/png": 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48GGaN2+Or6/vM6P7ADNmzEjqkIVIVrTW3PK7xeX7lymdvTSODo4AHLpyiFt+t6icuzJZ0poJ4Hf87xASGkJmt8wR+wkhhHhMSnoSmZT0CJG8ye9i4gkJDeHkrZMcvHKQM7fPcOn+JS7fv8yl+5e4cv8KASEBANz/5D4eLh4A1JlTh50XdvLbG79Rt2BdAD7d+inf7fkOhSKTWyY803qSPV12SmQtQSnPUpTKVopSnqXI5p4tVnNzhBAiOZKSHiGEEHZh89nNbDm7hYNXD3L46mF8g3yj3TeTayZyp8/9xHuVc1fGzdmNTG6ZIt5zdHAks1tm7vjfiXicvn2a3y/8/sSxWdyyUCpbKcpmL8sH1T6gQMYCNv1sQghhr2SEP5HJCL8QyZv8LsZfSGgIey/tpXzO8rincQeg+8ru/PzXzxH7FMhYgMq5K/NStpfImz4vedLnIU/6POROn5t0adLF6XrBocHc9b/LTb+bXL5/mRM3T3D8xnGO3zSP+wH3I/b9t8+/FM5cGIAVJ1fg6OBI3QJ1I+4kCCFEciMj/EIIIZLcq4teZeO/G1nefjltSrQB4LWSr1EgYwEq5apEpdyVyOaezWbXc3JwwtPdE093T0p6lqRR4UYR27TWXHlwhWM3jvH39b8plKlQxLYvdnzB0RtH2dFtB7ULmPU3gkKCcHZ0tllsQghhJUn4hRBCJNiRa0eYfGgyg2sOjkima+evzZnbZwgMCYzYr9kLzWj2QrMkj08pFXH34JUir0S8r7WmTYk2eLp7UiVPlYj3X1/2Ov89/I/XSr5Gu5LtyJshb5LHLIQQtiIlPYlMSnqESN7kdzF6j4IfseT4EiYfmsyBKwcAGFh9ICMbjgTMKLmTg1OymygbGBJIzjE5ueP/eDXpKrmr0L1sdzq/1FnKfoQQdklKeoQQQtjMubvnmOI1hVl/zOK2v1kdOaNrRt4s+yZvlX8rYr/kWhKTxjENF/tfZP2Z9Sw5sYR1/6zjwJUDHLhygAFbBtDlpS68W/FdyuQoY3WoQggRKzLCn8hkhF+I5E1+Fx87d/ccX+/8mnl/zyNUhwJQPmd53q/0Ph1e7EBa57QWR5g4fAN9WXV6FVO8prDr4q6I96vmqcq7Fd6lfan2uDm7WRihEELEPMIvCX8ik4RfiORNfhfhyv0rfPP7N8z4YwbBocE4OTjR8cWOvF/pfSrnrpzsSnYS4viN40w9PJWf//o5outPJtdMzG09l1dfeNXi6IQQqZmU9AghhIiX6Yen02dDHwJCAnBQDrxR5g2+qP3FE11uUpNS2UoxockERtQfweLji/nJ6yf+uPYHpTxLRewTEhoiK/4KIeyKJPxCCCGi9WK2FwkICeC1kq/xVZ2vKOGZuu92hHNP406Pcj3oUa4H/9z+h4KZCgKm60+1mdUon7M8I+qPeGKBMCGEsIqD1QEIIYSwHxv/3cigLYMiXlfLW41/+/zLkteWSLIfjReyvBDx3OuqF15XvVj7z9oUO6dBCJH8yAi/EEIIAG763qTN4jb4B/vTtGjTiEWowlekFc9XKXclTrx/gos+F3FxcgHA55EPI/eM5KNqH5ElbRaLIxRCpEYywi+EEKlYSGhIRMcdT3dPRtQfwagGo6iet7rFkSVfxbMWf2KV31F7RjFi9wgKTyjMyN0j8Q/ytzA6IURqJAm/EEKkUn/99xfVZlZj1h+zIt7rV7UfA14ekGx76NujdiXb0bBQQ3wCfPhk2ye8MOkFZv8xm5DQEKtDE0KkEpLwCyFEKhOqQxm7byyVplfi0NVDTDo4KWKUX9heuZzl2Nx1M5u6bKJM9jJcvn+ZHqt7UGFaBfZe2mt1eEKIVEASfiGESEX+e/gfTRY04aPNHxEUGkSvir3Y9eYuHJT8c5DYGhVuxJF3jjCv9TzyZcjHX9f/4uVZL/PWqre46XvT6vCEECmY/A0vhBCpxPoz6yn9U2k2n91MFrcsrOqwisnNJuPh4mF1aKmGg3KgS+kunHz/JINrDMbZwZlZf86i2KRiTPWaKndahBCJQhJ+IYRI4R4FP6Lfhn40W9iMm343qVewHn+9+xctirWwOrRUK61zWr6t/y1Hex2lQaEG3H10l3fXvUvVGVW54XvD6vCEECmMJPxCiERz+/ZtLl26ZHUYqdrpW6epMqMKEw5OwMnBiZENRrKl6xZyp89tdWgCKJa1GJu7bGZxu8Xk8siFo4MjWdNmtTosIUQKIwm/EKmU1ppZs2ZRvXp1SpcuTbFixahTpw6rVq1K8Lnv3bvH559/TsGCBdm2bZsNohXxsf7MeirPqMzf1/+mSOYi7O2xl4EvD5R6fTujlKJ9qfacev8Ui9ouivjvc+X+FX6/8LvF0QkhUgL5W1+IKJw6dYqBAwdSpEgRlFIRj5o1azJnzhyrw0uwkJAQ2rZtS8+ePenbty9///03J0+epGHDhrRq1YpBgwY9/yRRePDgAd9++y0FCxZk2LBhPHjwwMaRi9g6fPUwry58lfsB92lboi1Heh6hUu5KVoclYuDh4kGBjAUA84X8nbXvUHtObWYcmWFtYEKIZE9W2hUiCsWLF2fUqFE0bdqUunXrAlCuXDl27tyJg0Py/5780UcfsWLFCnr37k2HDh0AcHBwYMiQIezatYtRo0ZRrFgxevToEafzrlq1ivbt29OgQQOqVq2aGKGLWCqfszw9yvUgf4b8DKk1REb1k5lQHUqFnBU4eOUgTYs2tTocIUQyJ/8CCBGDyPXn3bt3TxHJ/vHjx5kwYQIAvXv3fmZ73759ARg0aFCcR+i7dOlC0aJFqVy5csIDFXF2+f5lzt45C5gykenNpzO09lBJ9pMhRwdHvqr7FWf7niWXRy7ArIr8/d7v8Q30tTg6IURyI/8KCBGDyPXnzZs3tzAS2xk7dixaawoXLkyxYsWe2V6/fn1cXFy4desWc+fOjdc1lFIJDVPE0dHrR6k4rSLNFzXnfsB9QP47pASRW6aO3TeWAVsGUGFaBf649oeFUQkhkhtJ+IWIhtaaDRs2AFCiRAkKFixocUS2Ef6ZypcvH+V2FxcXSpUqBcCyZcuSLC6RMAUyFiBr2qzk9MhJcGiw1eGIRNCwcENKepbk9O3TVJ1ZlR/2/SB9+4UQsSIJvxDR8PLy4sYN0w+7WbNmFkdjGxcvXuTatWsAMX6BKVSoEACHDh1Ca50ksYn4Cf/v4+HiwZauW9jYeSOZ3TJbHJVIDGVzlMXrbS/eq/gegSGBfLj5Q5ouaMp/D/+zOjQhhJ2TSbtCRGPdunURz1NKwn/27NmI5zly5Ih2v/Btvr6+XLx4kfz58yd6bE/z9fVl1qxZrF69mnTp0pEjRw78/PwICQlh7NixZMuWLcljsidaaz777TOu+15nevPpKKXI6ZHT6rBEInNzduPHZj/SuEhjeqzqwaazmyj9U2nmtJojk3uFENGShD8liKlOd+pU6NnTPJ82Dd55J/p9I4/kVqgAR45Evd/bb5tzARw+DBUrRn9OLy9zLjBxTJ8e9X7ly5tzhYv8mSwaYV6/fj0AGTJkoEaNGtHu9+jRI1xdXW167UGDBrF8+fJ4H58nTx527NjxzPt3796NeJ42bdpoj4+87c6dO0me8B86dIg2bdqQMWNGFixYQOnSpQHYvn079erV4969e6xduzZJY7InwaHBvLPmHWb9OQtH5ch7ld6jfM6oS7REytSiWAv+7vU3b6x4g23nt9FsYTP6Vu7LqIajcHFysTo8IYSdkYRfiCjcuHEDLy8vABo1aoST07O/KtevX2f48OGcPn2ajRs3RnmeKVOmMG7cOLy9vcmbNy+dO3fm008/xcUl5n+Qr1+//sRofFwFB0ddw+3n5xfxPE2aNNEeHzk+X9+k7Qji4+ND06ZNuXXrFps2baJkyZIR2w4dOgTArVu3kjQme+IX5EeHZR1Y888a3JzcWPraUkn2U6lcHrnY3HUzY/aOYfBvg5lwcAL7r+xn6WtLyZchn9XhCSHsiNTwpwRaR/8IH90H8zymfSM7fDj6/cJH98GM3sd0zvDRfTDHRbdf5NH9pz+TBTZs2BBRGx1VOc+6dev4/vvvmTBhAo8ePYryHD/99BNTp06lU6dO9OvXj+DgYL766it69er13OvPmTMHrXW8H97e3lGe183NLeJ5UFBQtNePvC3yMUlh8+bN3Lp1iwwZMjyR7AO8//77LF26NNWO7t/1v0ujeY1Y888aMrlmYtsb22j2QsooNxPx46AcGPDyAPb22Ev+DPk5eOUg5aeWZ8vZLVaHJoSwI5LwCxGF8Pp9BwcHmjRp8sz2Zs2aMXr0aHLlyhXl8X5+fqxcuZKDBw/y+eefM3LkSI4dO0bRokWZPXs2N2/eTNT4o+Pp6Rnx3N/fP9r9Im/LkiVLosb0tMKFC6OUwsfHh8WLFxMaGorWmoCAANzd3WnXrh1Zs2ZN0pjswfWH16k1pxZ7Lu0hT/o87O6xm2p5q1kdlrATlXJX4nDPw7xS5BXu+N9BI5PthRCPScIvxFOCg4PZssWMjlWqVCnGyaHOzs5Rvr9//36GDRv2xHZ3d3e6desGEO0IfGIrUqRIxPPr169Hu1/4Njc3N/LlS9rSgLJly/LJJ58A0KFDBzw8PHBxccHd3T2ipWhq89/D/6j7c12O3ThGiawl2NtjLyU9Sz7/QJGqZEmbhXWd1rGj+w4aFW4U8X5QSPR384QQqYMk/EI8Zc+ePdy7dw+I/2Jb9erVi3K12YwZM+Lo6EjhwoUTEmK85cqVKyKBj+lLx4ULFwCoXLlykq4ufPPmTerUqcOIESNo2bIlBw8exMfHh0uXLrFv3z4aN26cZLHYi2sPrlH357qcvHWSF7O9yI7uO8ibIa/VYQk75aAcqJW/VsTr7ee3U/zH4hy6csjCqIQQVpNJu0I8Jbw7D0C7du1seu5jx47RqlUrMmeOuU/6xx9/nKBFr/LkycPu3buj3Pbqq68yefJk/vzzzyi3BwcH89dffwFJv7rwW2+9xa5du+jYsSMLFy6MeD979uxkz549SWOxB1cfXKXuz3X55/Y/vJTtJba9sQ1Pd8/nHyhEmHEHxnHu7jmWn1xOpdyVrA5HCGGRFJnwK6WyAGm11pcS4dwKeBm4rbU+aevzi6TVrVs3zp49y5w5cyLKXcLr9+vUqUOxYsVsdq2HDx+yfv36KNtlPu3WrVsRo+y21rNnTyZPnszJkyfx9vamQIECT2zfuXMnfn5+uLq60r1790SJISo+Pj4Rk3E7d+6cZNe1Vw8CHkQk+6Wzl2Zr162S7Is4W/raUmYcmcE7FWJoySyESPFSVEmPUiqjUupr4DxQP4Hn6qCU0k8/gFBgAfCPDUIWFvL29mbu3Lns2bOHpUuXAnDu3DmOHz8OwJdffmnT6w0ePJhx48bFuMJtuMTq0gNQpkwZ3nzzTQAmTZr0zPYJEyYAMGTIkGcm7A4bNoz06dPz7rvvxhh/eEkUxNwNKDJfX9+IzkjhKxw/beLEiezbty9W50vuPFw86PRiJ8pkLyMj+yLe0jim4b1K7+Ho4AjADd8bvLXqLXwe+VgcmRAiKaWIhF8p5aGUGoJJ9IcCHjY47YAYtk3QWofY4BrCQnny5IkoEwlfkOqbb74BoH///tSuXdtm15o1axYvvPACrVu3ttk5E2L8+PHUr1+f8ePHR3zZ0VozZswYVq9eTadOnfj000+fOW7UqFE8ePCAqVOncufOnSjPHRoayuTJkyNer1ixIsaOQOFy5coVscDZF198wfbt2wkMDMTHx4d169bRunVrsmTJQrVqqaczzRd1vmDvW3vJmjb1dSUSiaPnmp7M+nMWVWZU4Z/bMm4lRGqRIhJ+oCWwBHjFFidTSjUAcgGlgBJPPYoAY21xHWEtJycntmzZQtOmTZk1axb58+fnyJEj/Pjjj4wda7v/xCtXruTu3bv07t3bZudMKA8PDzZs2MDEiRMZPXo0ZcuWpXTp0qxatYqFCxeyYMECHB0dnzmuT58+Ed2GopqH8OGHH5ItWzaGDBkS8d6GDRvw9PSkVKlSBAYGxhjXqlWr6NOnD05OTjRu3BhPT09q1qzJ3r17+fHHH+nUqVPCP7wdu/7wOo3nN+aiz8WI99I6R78ishBx9UPjH3gx24ucvn2aKjOqsPnsZqtDEkIkARV+Cz0lCKuvDw17+abWek48z7MZ2Ka1HpnQmCpWrKjDV2yNi5MnT1KiRImEXl4ksgIFClCgQIFo6/I3bNiAl5cXQ4cOfeL9ffv2UahQoVQ5ETW5Scrfxa4rujL/7/m0KdGG5e2XJ8k1RerzIOABXVd0ZdXpVTgoB35o/AN9q/S1OiwhRAIppQ5rrStGtS1FTdrVWmuT88efUqos0BBYpJTKpbW+aovYRMr08OHDaGvUt2/fTt++fenWrVtEqRCYyanHjx9/ohuQEAATm0zEUTkyquEoq0MRKZiHiwe/vv4rX2z/gm92fUO/jf04d/ccYxqNiaj1F0KkLCkq4beRgWE/ZwEopU4DvwI/JUbXH5E87dixg6VLl3L79m0OHTrEd999R4MGDahY0XyxPnz4MM2bN8fX1/eZ0X2AGTNmJHXIwk4FhQTh5OCEUoqMrhmZ02qO1SGJVMBBOTCs3jCKZS1Gj1U9GH9gPBd8LrCgzQIpIxMiBUpRJT0AYZ10IB4lPWHtPK8BUS2f6gt8oLWeHpdzSkmPEMlbYv4uhoSG0HF5R9KlSce05tNwcpAxGJH0dnjvoPXi1tx7dI9KuSqxpuMasqeTckMhkpuYSnpSyqRdm9Ba3wbcgGyYsp6RwK2wze7ANKVUzP0IhRAiFrTWvLP2HZaeWMryk8s5f/e81SGJVKpOgTrs7bGXAhkLcOjqIarOrMrJm7LMjBApiST8T9Fah2itb2qtt2qtPwHyAaOB8Dack5RSpayLUAiR3GmtGbBlADP/mImbkxvrOq2jaJaiVoclUrESniXY/9Z+KuWqhPc9b1r+0pLg0GCrwxJC2Igk/M+htfbXWg8E3gh7y5GYe/SjlOqplPJSSnndvHkz0WMUQiQvI/eMZMy+MTg5OLG8/XJq5KthdUhCkD1ddnZ030GHFzswp9UcKTETIgWRhD+WtNYLMSvsAlR9zr7TtNYVtdYVPT1ldUwhxGML/l7Ap9s+RaGY33o+TYo2sTokISKkdU7LoraLqJ63esR7x28ctzAiIYQtSMIfN+ETdvNZGoUQIlnafn47b656E4Cxjcfy+ouvWxyREDFbdmIZL/30Ep9v/9zqUIQQCSAJf9z8FfbzkaVRCCGSneM3jtN6cWuCQoPoV6Uf/av2tzokIZ7rYeBDlFK4OLpYHYoQIgGeW6CnlHIASgL3tNaXw97zAL4GWgJZgNPABK31/ESM1R74h/28YmkUQohk5eqDqzRZ0ASfAB/alGjDmEZjrA5JiFjpXrY7FXJW4MVsL1odihAiAWIc4VdK5QeOYka2vZVSE5VZynY10BfzhWEesAf4SCmV0lcTKh72c6OlUQghko0HAQ94deGrXLp/iWp5qjG/9XxZzVQkKy9lf4nwVewv3LtAl1+78CDggcVRCSHi4nkj/N8DLwCTgRNANWAdUBs4BNTRWvsDhH0RGKWUaqC13pp4IVvqTUw5z1SrAxFCJA8rT63kj//+oEjmIqzuuBo3ZzerQxIi3rqt7MbOCzs5eeskGztvxNNdGlMIkRw8r4a/DjBJa91Ha/2T1voNYC2ggS/Dk30AbZbsHQS0SqRYn0splTHSy6hWyw3fb6hS6r5Sakqk95yUUkuUUtuVUm+r8OGMx9tfBt4D+mut/7V17EKIlKlrma7MajGLDZ03kDVtVqvDESJBZrWcRZHMRThy7Qh1fq7DtQfXrA5JCBELsZm0uz/yC631ZODI0++HbQsFCtkmtLgJm2vwXqS3WiulohtKGwh4AO8opTKHveeKmZNQB5gG7FRKVVdKZVdK9QSWAG9rrWV0XwjxXAHBARHP3yz3JkUyF7EwGiFso1CmQux6cxcvZnuREzdPUHN2TS7cu2B1WEKI53hewr8XKBDF++OAe0+/qZQqAdRKaFBxpZQaC9wAvo30dhPgplLquFIqzVOHTAR8gZ+11ncAtNYPgabAVuA2j8uXVgI5gUpa658T83MIIVKGVadWUeLHEhy9ftTqUISwuRzpcrCj2w7K5yzP2btnqTm7Jv/ekRvfQtiz5yX8g4E3lFJP3IfWWi8IK+F52hggxFbBxZbW+kOtdVattXrqkU5rXUprHfjU/oPDtnV/6v1tWuuGYedy1lpn0lpX01p/pbW+mqQfSgiRLGmtmXhwIufvnWfDvxusDkeIRJElbRa2vbGNanmqcen+JWrNrsWJmyesDksIEY0YE36t9XGgHfClUqpoLM5XAdhsi8CEECI5UkqxpuMafmr2EwOqD7A6HCESTUbXjGzuupm6Bepy7eE1as+pzR/X/rA6LCFEFJ5bw6+1Pqm17g2cjcX5SgCdExyVEEIkM4EhgYTqUADcnN14t+K7PDX3X4gUJ12adKzrtI6mRZtyy+8WdX+uy/7Lz0zxE0JYLNYr7YZNyH3ePneeLp8RQoiUTmtNzzU9abukLQ8DH1odjhBJys3ZjRWvr6BNiTb4BPjQcF5D9lzcY3VYQohIYp3wx4ZSykMpVVwpVVkpVUUpVVIplc6W1xBCCHvz/d7v+fmvn9l8djPn7p6zOhwhklwaxzQsbreYTi91Io1jGtI6p7U6JCFEJM9beOu5lFL1gY5APSB/NPtcArYBv2qt1yX0mkKI5EdrzZ49e8iSJQslSpSwOhybWXN6DYO2DgJgXut5lM5e2uKIhLCGk4MTc1vNxfueN4UzF7Y6HCFEJPEe4VdKlVZK7cZM0n0T075TRfPIB3QHViulTiml6iUsbCFEQmmtmTVrFtWrV6d06dIUK1aMOnXqsGrVqgSd95dffkEp9czDwcGBzp0788ILL9joE1jvxM0TdPq1ExrNsLrDaFOijdUhCWEpRwfHJ5L9eX/NY++lvRZGJISAeCb8SqnmmB791TEJfTBwGtgOLAcWAvOBZcAm4BgQELbvC8BmpdTbCQ1eiMRy6tQpBg4cSJEiRZ5IWmvWrMmcOXOsDi/BQkJCaNu2LT179qRv3778/fffnDx5koYNG9KqVSsGDRoU73OPHj062m19+/bF0dEx3ue2Jz6PfGj1SyseBj6kw4sdGFJziNUhCWFXdnrvpNvKbjSe35gr969YHY4QqVqcS3qUUsWARZh++2OAX4HDz5usq5RyBMpg2ny+C0xSSh3UWv8V56iFSGTFixdn1KhRNG3alLp16wJQrlw5du7ciYODTae+WOKjjz5ixYoV9O7dmw4dOgDg4ODAkCFD2LVrF6NGjaJYsWL06NEjTufdunUrV69e5fjx48/8OTk7O1OokCULcdtcqA6ly4ounLlzhjLZyzCzxUzpyCPEU17O9zIdX+rIi54vkjt9bqvDESJVi08N/yDMiH1zrfXN2B6ktQ4BjgBHlFLfA6uAD4Fu8YhBiCRx6dKliOfdu3dPEcn+8ePHmTBhAgC9e/d+Znvfvn3ZtGkTgwYN4rXXXsPDwyPW5x41ahT9+/enZMmSNovXHn2982vW/rOWzG6ZWfH6CpmgKEQUnBycmN96/hNfhkN1KA4q+f89KkRyE5/furpA+7gk+0/TWt/BTPStHt9zCJEUtm3bFvG8efPmFkZiO2PHjkVrTeHChSlWrNgz2+vXr4+Liwu3bt1i7ty5sT7vn3/+yZYtW8iWLRtXr6bchalXn17NVzu/wkE58EvbXyiYqaDVIQlhtyIn+2fvnKX81PJ4XfWyMCIhUqf4JPxaa30xoRfWWl/G1PQLYZe01mzYsAGAEiVKULBgykjswj9T+fLlo9zu4uJCqVKlAFi2bFmszztq1CgAevToQe7cuSlevDiDBw9+4i5Jcnfq1im6/NoFgBH1R9CwcEOLIxIi+fhh/w/8df0vGs9vzNHrR60OR4hUJb6TdrMn9MJKqZzAcxfzEsIqXl5e3LhxA4BmzZpZHI1tXLx4kWvXrgHE+AUmvNb+0KFDaK2fe97bt28/8+Xg9OnTjBgxghIlSjB9+vQERG0fgkKCaLO4DQ8CH/BaydcYUH2A1SEJkayMbTyW5i80547/HRrMa8DpW6etDkmIVCM+Cf924BelVMb4XlQp5YHp4iPrbwu7tW7d4yUjUkrCf/bs2YjnOXLkiHa/8G2+vr5cvPj8G3pZsmTB39+fGzdusGXLFgYNGkTWrFkjztGzZ0+mTJkSp1h9fX2ZOHEiDRs2pHXr1vTq1Ytu3brRpUuXiC9iScnZ0Zlv631L9bzVmdVylkzSFSKO0jimYclrS2hYqCE3fG9Qf259zt89b3VYQqQK8Zm0Owr4AzinlJoCrAD+0FoHx3SQMv86vgS0Bt4DMgGV4nF98RT1VdwSj/I5y3O45+FnjtdfPB7JrTCtAkeuHYnTeaM63uttLyrkqgBAzzU9mX4kbiO9kY9PauvXrwcgQ4YM1KhRI9r9Hj16hKurq02vPWjQIJYvXx7v4/PkycOOHTueef/u3bsRz9OmjX6iaeRtd+7cIX/+KNfUe4KjoyOenp40aNCABg0a8MUXX/DFF18wduxYQkJC6N27NzVr1owoF4rJoUOHaNOmDRkzZmTBggWULm0Ws9q+fTv16tXj3r17rF279rnnsbXWJVrTqngrSfaFiCdXJ1dWvL6CVxa8wu6Lu6k3tx673txFnvR5rA5NiBQtzgm/1vq0UqobMBfTsWcQEKiUOgtcAe5ieu5rwBVID+QCigBuYadRwHvSklPYqxs3buDlZSaWNWrUCCenZ39Vrl+/zvDhwzl9+jQbN26M8jxTpkxh3LhxeHt7kzdvXjp37synn36Ki4tLjNe/fv36E6PxcRUcHPX3bz8/v4jnadKkifb4yPH5+vrGKwY3NzdGjRpF2bJl6dy5MyEhIYwePfq56xj4+PjQtGlTbt26xaZNm57o+HPo0CEAbt26Fa+Y4uNR8CMOXD5AlTxVACTZFyKB3NO4s67TOhrMbcChq4eoP7c+v3f/nezpElwtLISIjtY6Xg9Mh50zmDr8UExf/pge4fudAxrH97rJ7VGhQgUdHydOnIjXccI25syZozFfWvWcOXOe2b527Vr98ccfa0DXrl07ynNMnjxZly1bVn/11Vd64MCBukCBAhrQb775ZiJHH71ly5ZFfK6pU6dGu98nn3wSsZ+Xl1eCr9u5c2cN6GLFij133yVLlmhAZ8iQ4ZltDx8+1EuXLtU3b95McEyxERAcoDft26Sdv3bWBy4fSJJrCpFa3Pa7rUv/VFrzJfrFyS/qW763rA5JiGQN8NLR5KPxboartd6LWTW3PWbxrf8wI/dRPa4A84BWQBGt9ab4XleIpBBev+/g4ECTJk2e2d6sWTNGjx5Nrly5ojzez8+PlStXcvDgQT7//HNGjhzJsWPHKFq0KLNnz+bmzXh3tU0QT0/PiOf+/v7R7hd5W5YsWRJ83bffNgtrx2Y+QOHChVFK4ePjw+LFiwkNDUVrTUBAAO7u7rRr1y5ifkBic3Jwwj2NO/UL1adiropJck0hUovMbpnZ0nULxbMW59iNYzRd2JSHgQ+tDkuIFClBq1+EfaFYprVup7XODWQHSgIvY+4AvAik11rn01p301qv1lpLZx5h14KDg9myZQsAlSpVIlu2bNHu6+zsHOX7+/fvZ9iwYU9sd3d3p1s3s86ct7e37QKOgyJFikQ8v379erT7hW9zc3MjX758Cb5umTJlAGI116Fs2bJ88sknAHTo0AEPDw9cXFxwd3ePaCmaVByUA5ndMrO6w2pZLEiIRJDNPRtbu24lf4b8HLxykDaL2xAQHGB1WEKkODb9F0xrfVNrfUprvU9rvV9rfUJrLV/XRbKyZ88e7t27B8R/sa169epRuXLlZ97PmDEjjo6OFC5cOCEhxluuXLkiEviYvnRcuHABgMqVK9tkdWE3NzN9J3fu3DHud/PmTerUqcOIESNo2bIlBw8exMfHh0uXLrFv3z4aN26c4Fhi437AfYJDH8+DcHaM+oudECLhcqfPzZauW/BM68kf//2B9z1vq0MSIsWJT5ceIVK08O48AO3atbPpuY8dO0arVq3InDlzjPt9/PHHcVr06ml58uRh9+7dUW579dVXmTx5Mn/++WeU24ODg/nrLzOf3larC586dQqAV155Jcb93nrrLXbt2kXHjh1ZuHBhxPvZs2cne/akmdDnH+TPv3f+xcnBiRJZSyTJNYVI7YpmKcrmrptxdXKlWNZnVwAXQiSMJPwiVevWrRtnz55lzpw5EeUu4fX7derUoVgx2/3D8/DhQ9avXx9lu8yn3bp1K2KU3dZ69uzJ5MmTOXnyJN7e3hQoUOCJ7Tt37sTPzw9XV1e6d+9uk2vOnj0bV1dX3nnnnWj38fHxiWi12blzZ5tcN65CQkM4e/csoTqUdGnS4eQgf0UKkVTK5ij7xOuj14/yUvaXrAlGiBTG0qJUpdRmK68vUjdvb2/mzp3Lnj17WLp0KQDnzp3j+PHjAHz55Zc2vd7gwYMZN25cjCvchpszZ06CukPFVK5TpkwZ3nzzTQAmTZr0zPYJEyYAMGTIkGcm7A4bNoz06dPz7rvvRrwXHBxM+/btqVu3LtOnT39mZd49e/YwefJkxo0b98Qcgqf5+vpGHBvdwloTJ05k37590Z4jIbTWeN/z5lHwI9yc3MifIb+04BTCIj8e/JEyU8owfv94q0MRIkWwLOFXSjkA1ay6vhB58uSJKBMJX5Dqm2++AaB///7Url3bZteaNWsWL7zwAq1bt7bZORNi/Pjx1K9fn/Hjx0d82dFaM2bMGFavXk2nTp349NNPnzlu1KhRPHjwgKlTp3Lnzh3ALDy2atUqduzYQc+ePalduzZ79+7l+vXrTJs2jfbt2zN9+vQYR/fBzC8IX+Dsiy++YPv27QQGBuLj48O6deto3bo1WbJkoVq1xPlr44bvDe4+uouDcqBw5sI4OjgmynWEEM/nnsYdgKDQIIsjESJlsCThV0q5Ah8D0S/1KUQic3JyYsuWLTRt2pRZs2aRP39+jhw5wo8//sjYsWNtdp2VK1dy9+5devfubbNzJpSHhwcbNmxg4sSJjB49mrJly1K6dGlWrVrFwoULWbBgAY6Ozya8ffr0ieg2FD4PIV26dKxfv54GDRqQJUsW9u3bR7NmzWjVqhXXrl3j0KFDEd2JnmfVqlX06dMHJycnGjdujKenJzVr1mTv3r38+OOPdOrUyaZ/DuF8A325fP8yAAUyFsDVybYrJwsh4qZ72e4c7XWUj6t/bHUoQqQI6unb7zHurFR3YKYtA9Bap+hhtIoVK+rwFVvj4uTJk5QoIRMG7V2BAgUoUKBAtHX5GzZswMvLi6FDhz7x/r59+yhUqFCSTUQV0QsODebEzRMEhgSSzT0b+TI82YZUfheFsN75u+e59+ge5XKWszoUIeyWUuqw1jrKRWPiOiNtAfAlkPDG3Ebsv20IYYcePnxIUFDUt5y3b99O37596datW0SpEJjJqcePH3+iG5CwRnjdfmBIIO7O7uRJn8fqkIQQT/n3zr/UmGXK/fa9tY+CmZ4/D0oI8aQ4Jfxa6yCl1DBgOnAM+AOIz0JaOYB6cb2+EPZix44dLF26lNu3b3Po0CG+++47GjRoQMWK5ov14cOHad68Ob6+vs+M7gPMmDEjqUMWUbjue517j+7hqBwplKmQLK4lhB3KlyEfL2V/ia3ntvLKglfY02MPWdMmzWrbQqQUcSrpAVBKOQKngPJa6wfxvrBS9YAtUtITNSkjECJxPQx8yOlbp9FoCmcqTCa3TFHuJ7+LQljvfsB9as+pzZ///Um1PNXY+sZW0jrLNEAhIouppCfOw1la6xDga6BkQoLSWv8G3E3IOYQQIj601ly4dwGNJrt79miTfSGEfUjvkp51ndaRL0M+9l3eR+dfOxMSGmJ1WEIkG/G9f70AyGaD6w+xwTmEECJOlFIUyVwEz7Se5E6f2+pwhBCxkMsjFxs6byCja0ZWnlpJ3w19n1n3QwgRtXjV0GutQ4E1Cb241npqQs8hhBDx4eLkQv6M+a0OI/GEhMA//8CVK3DzJigFDg7g6Gh+lisH4assP3pkfrpKO1Jh30p6lmR1h9U0nNeQyV6TyZshL5/U+MTqsISwezJpVgiRajwMfIhvoC/Z3LOljFV0AwPhr79g/37w8oLMmeGHH8y2gAAoGUPl5bRp8Pbb5vkvv8Cbb0L27JA/P+TLZ34WLw7Vq5ufDjKhWdiHmvlrMr/NfNovbc+n2z6lYMaCvP7i61aHJYRdk4RfCJEqhIaGcu7uOQJDAnF0cEy+XT5274bly+HAAThyxCT24YoWfZzwp00LFSpAunSQLZtJ2ENCIDTU/Awf3Qe4dw+cnOD6dfM4ePDxtjRp4P59cHExr48cgSJFIH36xP6kQkSrXcl2jGk0hg83f0i3ld3IlyEf1fImzircQqQEkvALIVIFBwcH8qbPy02/m2R2y2x1OLF3/jy4u5ukHUzCP27c4+3Fi0OVKubxdDeh2HYI698f+vSBa9fgwgW4eBG8veHPP82Xg/BkPzQU6taFhw+hWjVo2xbatDF3A4RIYv2r9uef2/8w5fAUWv7Skv3/20+hTIWsDksIuyQJvxAi1cjklomMrhntv5znzBkzir9sGRw+DN9+C4MHm21NmkBQkEnwK1eGjBltc01HR8iTxzxefjnqfW7dMl8wjhyBPXvM48MPoWJFk/x37w45ctgmHiGeQynFxKYTOXfvHCdvnsQvyM/qkISwW5LwCyFSNL8gP7TWuKdxB7DfZD8oyCT448ebcp1w6dKBv//j12XKmIcVsmUzsT14AOvXmy8l69aZOwleXtC48eOEX2szUViIROTk4MSSdkvwD/YnRzr5silEdCTht2Naa/tNToRIBkJCQzh75yyBIYEUzVKU9C5xqztP0pZ/PXrA/Pnmefr00KIFtGsHjRqBm1vSxREbHh7w+uvm4ecHmzbBjh1QtuzjfVq2hJw54f33oXRpqyIVqUAG1wxkIEPE610XdlEjXw3591OISKTtgp1ydHQkJEQWFREivrTWXPC5QEBIAK5OrqRzThfnc4SEhODomEiLgR8/DqdOPX7dtaspl5kyxdTSz5tnkmZ7S/afljYttG5t7kyEJ1gXLsCaNaYTUJkyULOm6QQUGGhtrCLF+2L7F9SaU4sx+8ZYHYoQdiXBCb9SqpxSaqpSKk7nUkqVUErNUUq5JDSGlCht2rQ8fPjQ6jCESLZu+9/mjv8dHJQDhTIVwiEebSUfPnxI2rRpbRvYqVNmouuLL8Jnnz1+v2FD8yXgnXdMEp2c5c8PJ05A797mbsDu3dCxo+kMNG7ckyVKQtjQS9lfwtnBOc5384RI6RKU8Icl+QuA/wGLlVKxKhFSSr0I7AC6Ap8mJIaUKn369Ny5c0dG+YWIB/8gfy76XAQgX4Z8uDnHfZQ8JCSEO3fukN5W7SevXoWePaFUKVixwozc58plat3h8cJYKUWJEjBxoln4a/Jk87mvXTOTj318rI5OpFDtSrbjTJ8z9KzQ0+pQhLArCfrXJWzF3bbADaANsFwp5RzTMUqp0sBvgCewDvg2ITGkVB4eHri7u3PhwgXu3btHcHCwLCEuRCyE99sP1aFkccsSp377WmuCg4O5d+8eFy5cwN3dHQ8Pj4QF5OMDQ4aY3vXTp5vE/t134exZmDAh5U9s9fCAXr3g6FFYvRpGjXo8sTc4GGbMkBF/YVORV9A+desUN3xvWBiNEPZB2SKJVEoVB7YD2YCNQButdUAU+5UHNgOZgVVAe611UIIDsGMVK1bUXrHthf0UrTUPHjzg/v37+Pn5yWi/ELFw2/82DwMe4uToRM50OXGIW7Uhjo6OpE2blvTp0+Ph4ZHwiX/nzpna/KAg07ry22+hWLGEnTOl+Pln08ozZ07zpahnT3COccxIiFj7/cLvNF/UnNLZS7PtjW2kcUxjdUhCJCql1GGtdcWottmkS4/W+pRSqg5m5P4VYI1SqoXW+lGkICoCm4BMwArgda11sC2un1IppUifPr3tSgqESOGWn1hOuzXtSOOYhgP/O0CpHKWsCeT4cShZ0ozeFypkJrSWKwdVq1oTj73Kndt09vnzT1PvP3myWSm4USOrIxMpQNHMRfFI48Hui7t5b917TG8+XTr3iFTLZgWjWuvTQB3gGlAfWK+USguglKqCGdnPBCxHkn0hhI1duHeB/635HwDfN/yesjnKJn0QDx6YFWtfegkWL378fq9ekuxHpUEDs4jX8uVQuLCZ6Nu4sWlJeuaM1dGJZC6nR05WdliJq5MrM/+YyaSDk6wOSQjL2HSGmNb6DCbpvwrUBjYqpV7BJPsZgWVAB0n2hRC2FBQSRMflHbn36B4tirWgd+XeSR/EmjVmVH/SJDP59uLFpI8hOVLKdC06fhxGjjQLja1ZAxs3Wh2ZSAEq5qrI7JazAfhg0wdsPbfV4oiEsIbNW0Jorf/FJP2XgZcxE3M9gCVAR621FKILIWxqitcU9l3eR26P3MxqMStpb9v/9x+0b29GpS9fhkqVzKj1wIFJF0NK4OJi/szOnDGdfHr1erztzJnH3YyEiKMOL3ZgcI3BhOgQ2i9tz793/rU6JCGSXKL0gNNanwU+A1TY4z7wniT7QojE0LNCTz6o+gEL2y4kS9osSXfhQ4fMqP7SpeDubnrM79snK8smRI4cZmKzU9gUs6tXzZeoRo3MBGgh4mFYvWG0KNaCu4/u0mJRC3weSWtYkbokSsKvlKoLTA576Y8Z4d+olMoQ/VFCCBE/Lk4ujG08llr5ayXthUuWhOzZ4ZVXTElKv36QWCvzplb//GOS/61bzWJlY8aYdp5CxIGDcmB+6/mU8izFyVsn6bqiK6E61OqwhEgyNmnL+cQJlaqPabmZFpgFfA1sAwoDh4FGWuu7Nr2oHUtIW04hRPRCdSij9ozinQrvkMktU9Jd+OhRKFjQ1JoD3LgBnp6J0k8/JMQMcJ87Zx7nz8P9++b9px9aQ5YskCfPk48cOVJAp8sbN6B/f1i0yLyuWBFmzpQ7KSLOzt09R8VpFbn76C5f1fmKz2t/bnVIQthMTG05bZrwK6UaYVpuugHTtNbvhr2fC9Oy8wXgD6Ch1vqOzS5sxyThFyJxjN8/nv6b+lMuRzkO9zyc+HX7WpsJuQMGQMeOMHu2TU9//z7s2QM7dsBff5kE/8IFCAxM2HmVMgv6VqwI1aubR4UKZqHfZGfdOlPbf+mSGfWfONEsYiZEHGz8dyNNFzQFYE3HNTR7oZnFEQlhG4nehz/sIk0wLTddgR+11n3Ct2mtr4b16d8GlAO2KaUaaK1v2+r6QojUpXmx5iw8tpDBNQYnfrJ/8yb06AFr15rXadKYYfUElO9ETvB37IDDh80pn5Y9u2nlX7CgeWTJYi779CM8zMuX4coV8/PyZTOn+MoV81i1yuzn7GyWBaheHWrVMp0w06aN90dJOs2amdKpwYNhyhTzLUaIOHqlyCsMqzuMz7Z/xte/f03Tok2lP79I8Wy10u6rwFLABRintf4wmv08MUn/i8BRoL7W+laCA7BjMsIvROIJ1aFxXkk3zg4dMm0jL1+GjBlhxgyzYm48PHwIK1bAvHnw229PJviOjmZuau3aUK0aFCkCBQqYucAJERQE3t6wfz/s3WseR48+2fTG3R2aN4fXXzfTEVxdE3bNJHHpEuTN+/j1xo3QsKHMoRCxEqpDGbN3DD0r9CSDq0wvFClDopb0KKVaAb8AaYDRWutBz9k/C7AVKAMcwyT9NxMUhB2ThF8I29p8djMNCzVMmhG5n3+Gd96BgAAzHL5oEeTLF6dThISY+abz58Ovv4Kfn3nfyckk+HXqmCT/5ZcfTwtIbPfvw8GD5g7D+vXmeTgPD2jZ0iT/jRqZmxl2b+VKaN3a/EH+/DPkz291RCIZ0lrLSL9I1mJK+BM0NKaUcgCGYpL94c9L9gHCynjqAkcwI/3/S0gMQojUY95f82g8vzGdf+2c+BfTGrZsMcn+u+/C9u1xSva9veHjj83E2VdeMQm/n5/53vDTT3D9uhltHz7clNQkVbIPkD69WeT2iy/gwAEzGXjkSChf3iwWPH++GfHPmxe+/tqUCtk1NzfIlg127jQTeefPl779ItYCggPouaYnP+z/wepQhEg0thjhzwq8prX+KY7HpQfe1FqPT1AAdk5G+IWwjTO3z1Buajl8g3yZ2WImPcr1SPyL+vubVV/bt4/1IceOmeR50aLHJTuFC0PXrtCli3luz86cgSVLTPzHj5v3XF3hjTdMo5wSJSwNL3o3b8Lbbz+eqNC+PUydasqwhIjBlrNbaDS/Ee7O7pzvdx5Pd0+rQxIiXpKsS494liT8QiRcYEgg1WZW48i1I3R4sQML2yxMnFvvR46YYe9ffolz8fzevTBixON5vY6OppnPe+9B1aqJ0rUzUWltJhOPHfv4MwE0bQoffgj16tnhZ9IaZs0y6yH4+ppJEOvWmfUShIjB2H1jqZ2/NhVyVbA6FCHiLdFKeoQQIil8uvVTjlw7QsGMBZnSbEriJPuLF5tC+rVrzRB9LGht5orWqvX4UFdXeP99+PdfMzm3WjU7TIxjQSmoW9fc4Dh1ylQ1ubmZmv8GDczn+v13q6N8ilLw1lumr2mFCo97kgrxHB9W+1CSfZGiScIvhLBrG85sYOz+sTg5OLGo7SLbd9TQGr77Djp0gEePTMI4ZMhzDzt2zNTeN2kCu3aZypEhQ0zv/EmTzOBySlGsmJl3cPEifPONKZc/cMDMkW3ZEk6etDrCpxQubGYkb9nyuKQnIADupIrlX0QC/XLsF4b+NtTqMISwKUn4hRB269qDa3Rb2Q2AYXWHUSVPFdteIDjYDF1/+qkZDR4zBqZPBxeXaA+5edOU6ZQp8zifHDnSJPrhyXBKlTWr+VJz9ix8+aWpelq9Gl58EXr2NKsC2w0XlycnTHz8MZQtC/v2WRaSsH/n756n64qufLPrG1acXGF1OELYjCT8Qgi7FKpD6bqiKzf9btKgUAMGvjzQthd49MgMT0+bZupwli41xenR1N8EBprvA0WLmtFupaB3b1O6M3Cg6XyTWqRLZ6Y6nD1rFr5VynxPKlIEhg416w3YlUePzHoKly5BzZowerR08RFRKpipIKMajALgzVVvcvbOWYsjEsI2JOEXQtilkbtHsu38NjzTejK31VzbL7Dl4gI5cphh699+i3ExrbVroVQpM0js42PabP79N0ycaFa+Ta2yZ4fJk003nzZtTFOjb74xf1br11sdXSSurmbCwUcfmdZJAwea/97371sdmbBD/av2p3Xx1vgE+PDa0td4FPzI6pCESDCbd+kJW1irClAa8AQ8gIfAbeA4cEhrfcWmF7Vj0qVHiLjbd2kfNWfXJESHsKHzBl4p8ortTq7141H8oCBThxLNQk23b0PfvrBwoXldooQZ5W/SxHbhpCR790KfPqbZEZhpEePGmS8GdmP1atNj1McHXnjBrIZWqpTVUQk7c+/RPSpMq8C5u+d4t8K7/PRqnDqPC2GJRO/So5RyUEp1VkptA/4D1gDfAv2Bt4B+wNfAcuCiUuqAUqqXUio5rOEohEhCj4If0enXToToED6q9pFtk/2dO01LHR8f89rZOdpkf/ly081x4ULTnWbsWNP8RZL96FWvbibzfv89pE1rupuWKAGzZ9tRBU2LFuDlBS+9BP/8A99+a3VEwg5ldM3IsteW4eLowpTDU1h4dKHVIQmRIAlO+JVSrYF/gLmYFXQdAfWcRyVgEnBOKRX9fXQhRKrj6uTK2EZjaVS4EcPrD7fdideuNbU4u3ebNjrRuHEDXnsN2rUzz2vXhqNH4YMPzPcDETMnJ1M5E97F6O5d6NED6tc3i3rZhSJFzOTdAQPMhAwholAuZzkmNJkAQM81PTl5097aUQkRe/Eu6VFKuQOzgXbAdWATcAg4BlwDbgCPgAAgDeAKZAVyAS8CVYGmQOaw87yjtQ5JwGexS1LSI0T8aK1t129/wQLo1s3Ub7/zDvz4o1kZ64nrmVb8vXubUh53dxg1yjTxcZDZTvGitblD0r8/3LplSulHjzbrFNjd2gQBAWaSxpAhZm6HEJi/h7qu6MqCowso6VmSQ28fIq1zWqvDEiJKNi/pUUrlBPYCxYC2QC6tdXet9Y9a651a63+01ve01o+0EaC19tFan9Va79Ja/6S17gbkBHoCrwBrpcRHiNTrxM0THLxyMOK1zZL9H3+ELl1Msv/JJ2ZE96lk38fH1Jt37GiS/fr1zQj1e+9Jsp8QSkHnzqZPf9eupllOnz6mqubGDauje8oXX5g7PxUqwMGDz99fpApKKaa8OoUSWUtw4uYJ+m/sb3VIQsRLnP8pU0plBDYD64AKWusVOp63CbTWwVrrmZgJvoHAvPicRwiRvPkH+dN+aXtenvUyG85ssM1JtTYtY3r3Nq9HjoQRI54ZWj50CMqVgyVLTLvJqVNNf/2UtHCW1bJmhblzTefTjBlNdVXp0rBpk9WRRdK/v2nZefWqmefx889WRyTsRLo06VjcbjEuji5MPzKdpceXWh2SEHEWn7Gr+cAPWuvBWutgWwShtb4DtALuKKUG2eKcQojkw0E50KBQAwpnKkzN/DVtd+KrV02CP22aacUYidbwww/w8stw/rxJ+o8cMQtI2V25SQrRrp1pZ1q7Nly/bqZUfPCBqaaxXI4csHWrWVggIAC6dzfBBdvknzmRzL2U/SXGNh4LwKaz9vRNVYjYiVMNv1KqPZBTaz0+0QJSajowUmv9b2JdIylJDb8Qsfcw8CHp0qSz3QlDQ2H/ftM+JpLbt00+t3ated2nj6ktj2GBXWFDISHmhssXX5h8ukwZU+tfsqTVkYWZNs3cGQoKMvVdK1ea2z8iVdNas+nsJhoXbmy7kkMhbMiWNfxLEzPZD9MzpST7QoiYXb5/mbv+dyNeJzjZDw6Gzz4zGT2YAvynkv3du6FsWZPsZ8wIK1bAhAmS7CclR0cYPBj27IHChU2700qVYNEiqyML07OnWYwtWzbIkMH0GBWpnlKKV4q8EpHsh+pQiyMSIvbilPDHt1bf3q4hhLBeUEgQry19jXJTy3HsxjEbnDDIzLz99ltTO/LUXyVam0Wz6tSBy5ehalX4809o1SrhlxbxU7ky/PGHmVPt5wedOplS+qAgqyMDatQw/fp//vnxzG27CEzYg39u/0Pl6ZX57fxvVociRKxI/wkhhCU+++0z9l/eT6gOJZdHroSdLCDANM9fvtyMyD41Odff3yyu+vHHppxk4ED4/fdo19wSScjDw0zo/fFHs87B+PGmiua//6yODMib93Epj7+/+RIwfLgdrSImrLLk+BIOXzvMFzu+QMYpRXLgZHUAAEqpgcARrfVWq2MRQiS+jf9uZNTeUTgqRxa1XURmt8zxP9mjR2ZEf906yJQJNm+Gio9LGC9fNqP4hw+b3vo//wxtZbk/u6KUaYFarpz5T7lrF5Qvb7r6vPyy1dGF2brVtHQ6eBCOH4cZM8wSzCJV+qTGJwD0rdJX6vlFspCoI/xKqbxKqbFKqfVKqRlKqWbR7DoRmKqUOpuY8QghrHftwTXeWPEGAF/X/ZqX8yUgo/P3h5YtTbKfJYupu46U7O/ZY14ePgwFC5rFVSXZt1/VqplOSbVrw7Vrpvxq4kQ7GVBv3vzx5N2FC01w165ZHZWwiJODE5/V+oz0LumtDkWIWEm0hF8pVRz4A+iHWVirB7BGKbU/bFsErbU/cBgokFjxCCGsFxIaQpcVXbjpd5P6Besz6OUEduGdNcuM6Ht6wvbtZjZumOnToW5d0/6xXj0zOPvSSwm7nEh82bObdRA+/NDMwe7b13RUsovWnS1awN69ZpGGgwfNJIQjR6yOSljML8iP/hv7c/T6UatDESJaiTnCPxLIjFmkqwyQFpPQzwbmKqVeeWr/EFtdWCmVRSmV11bnE0LYxojdI/jt/G9kc8/G/DbzcXRwfP5BMenVy6yeu2NHRDYfFATvv28arQQFmUmgmzaZGwAieXB2NhOsf/nFNMiZOxcaNIBbt6yODPP/2cGDpp7/8mXz8+RJq6MSFvpu93eMPzCeLiu6EBBsD99MhXhWYib8tYGrQBut9VGt9SOt9UWt9VSgBlBXKdXZlhdUSmVUSn0NnAfqJ+A8SinVQym1Vyn1t1LqtFJqh1Kqpe2iFSJ12XVhF1/s+AKAea3nkSNdjvidyM8P7twxzx0czATdsAbu9++byovJk02bzTlzzOJaTnYxW0nE1euvmzaquXObn1Wq2Elu7elpavrffBNat4bixZ9/jEixBr48kMKZCvP39b8Zun2o1eEIEaXETPjTAHvDynWeoLUO1FoPAtIppd5O6IWUUh5KqSGYRH8o4JGAczkCy4FpwAStdWmgBLAFWKmUGpnQeIVIbW773abTr50I1aF88vInNCrcKH4nCq/Zr1//meHey5ehZk0zmu/paQb9u3VLeOzCWuXKmQH1ihXh3DlT5795s9VRYb5RzpxpvlWGT9r87z8ziVykKunSpGNe63k4KAe+3/s9O713Wh2SEM9IzIT/D0zSH62w0f6HSqkPEnitlsASzFyBhBoDtAZ+0lr/AqC1DtVafwtsAgYqpXrY4DpCpApaa7qv6s7l+5eplqcaX9f9On4nevQI2rQxI6vXrj1eXAuzcFPVqvD33/DCC2ZybtWqNvoAwnK5csHOnaaDj48PNG0KP/1kdVSYRN/Z2Tx/+BBeecVMGLlxw9q4RJKrlrcaQ2oOQaN5Y+Ub+DzysTokIZ6QmAn/MKCBUqpwTDtprRdhRubrxfdCWuv5WuszwMH4ngNAKVUK6Bv2clIUu0wI+zlSKRXvuwhCpCYTDkxg7T9ryeSaiV/a/YKzo3PcTxIQYLK9jRvN8P22bVCsGGBG9GvWhCtXTDn13r1m9VaRsqRNC4sXw5AhZi2F996Dfv3MxF67cPWqKTXbt89M5j1mg8XkRLIytNZQKuaqyEWfi/Td2Pf5BwiRhBIt4ddabwRaAYuUUv8LK5WJbt+VQDcgQfdCbbBK74eAAs5qrU9HsX0bEABkBd5I4LWESBVaFGtB5dyVmdNqDvky5Iv7CQIDoX37x603t26FUqUAU1HRrBk8eGAW2d2yRSbnpmQODvDNN2YtBWdnmDDB3PTx87M6MsytpfDOPRcuQPXqsGGD1VGJJOTs6Mz81vNxc3Jj7l9zWXZimdUhCREhUfvwa623aq0rA0eBjM/ZdyNQNzHjiYUmYT+j7LOmtQ4Ajoe9bJckEQmRzBXMVJB9b+2jRbEWcT84OBg6doTVq82iWlu3QunSaA2ffQb/+58Z7f30U1iwAFxdbR+/sD9vvGGWXMicGdasMVU0dtHBJ0cOM3mkfXvzLfTVV83SwXaxkIBICsWyFmN0w9EAvLP2Ha4+uGpxREIYiZrwh9NaH9Ba347FfgkqyUkIpVQ+IGfYy/Mx7Hou7GclJcvrCRElrTUrT62MWHLeQcXzrxpHR8iZEzJmNMl+2bIEB5uWm99+azZPnQrDh5vRX5F61KhhFlbLnx8OHDAD6ufOPf+4ROfmBosWweefQ2io6Qu7VRaRT03eq/QejQs35o7/HXqs6kHCiw+ESDj5J/KxyFW//8WwX/g2dyAe9QlCpHzjD4yn9eLWdF/VPWEnUsostfrHH1C+PI8emcHTGTNMXrVqlUn+RepUvLgpmS9bFs6cMUm/XayD5eAAX31lbju9/75ZRECkGkopZrWcRWa3zGw6u4kRu0dYHZIQ9pXwK6WyWnj5TJGex1QRGnlb5kSKRYhkrUDGAmR0zUirYq3ifrDWMGrU4xoNpaBAAe7fhyZNYMUKM+C/ZYup3xepW86cpoNPgwZmVeXate2kbSdAp04wadLjtp3nzoG3t6UhiaSRyyMX05tPB2D03tH89zCmcUQhEp9dJfxAWwuvnTbS88AY9ou8jJ57VDsopXoqpbyUUl43b960SXBCJCetirfiXN9ztC7ROm4Hag0DBsCgQSa7Dw0FTCJXp44pj86ZE37/HV5+2eZhi2QqfXozp7tzZ9Mds1kzszqvXbl3zwRWpYq5LSFSvDYl2jCv9TzWdFwT/4UGhbCRRFl/UilVFkgfx8PSAu8AU20eUOxEXiAspr6Bkbc9s6gYgNZ6GmbhLipWrCjFeyJV0Frzz+1/KJbVtMvM5JbpOUdE4csvYcwY04Llq6/AwYHz56FRI/j3XyhSxIzeFixo29hF8pcmjUnyc+c2N4i6dTPt8D/+2OrIwigFefPCqVNQt65ZsKtDB6ujEomsS+kuT7ze+O9GauWvRVrntNEcIUTiSKwR/tbA9jg+1gFlEime2Ig8FO8Ww36Rtz13IrIQqcWEAxN48acX+elQPFdEGjkSvv7a1D8vWgRNm3L0qBnJ//dfs+Lqnj2S7IvoOTiY/43GjzevBwyAwYPtpElOhgzmNsS775p1JTp2NP+/20VwIimsPr2aZgub0XBeQwJDYiokEML2EmWEH7NabS9MEu8dy2OyA12eu1fi+TfS8+wx7Be+zR+4mHjhCJF87L+8n4+3fExwaDDZ08X06xONiRPhk0/MKOjPP0Pbthw6BI0bw927ppxn1SpTuiHE8/Tta1p2du8OI0aY9bB+/NF0dbKUszNMnmwWjfvwQ/jiC/jnHzMLXXrKpngvZHmB3B65aVSoEWkc01gdjkhlEiXh11rfV0p9CyzQWse6O7JSyrJZLVrrq0qpi5jOOwVi2DV/2M+DWuvQRA9MCDt32+827Ze2Jzg0mP5V+tOmRJu4nWDXLpOhAUyZAl268PvvpoX5gwfQooVZYVXyIREXXbqYQfX27U3r1rt3Yd48U/pjKaVMq84iRUxJz4IF0LIlvPaaxYGJxFY8a3H+fPdPMrnGo9xRiARKzEm7k4G8cTxmZSLEERdrw36WjWqjUsqJx2VHa5IiICHsWagOpeuKrly6f4mqeaoysuHIuJ+kRg0z2vnDD9CzJ5s3wyuvPF49d9kySfZF/DRvDps2mTtDS5aYL4++vlZHFebVV02N2tdfS7KfimR2y0z4Ej7e97x5e/XbBAQHPOcoIRIuXgm/Uup/z9tHax2ktf4jLufVWv8dn3hsaFrYzxJKqQJRbK+NmVz8CJiTRDEJYbe+2/0dG/7dQGa3zCxutzhut6nDa5eVMhN1+/dn1SqTpPn7Q48eMH++qYIQIr5q1YLt28HT0yT/DRua0X67UKYMDB36+PXp06bfrEjxtNa0WdyGGX/MYNDWQVaHI1KB+I7wd7NpFDailMoY6WW0aYJSaqhS6r5Sakrk97XWfwGzw172juLQsLoDvo3NysFCpGTbz29n6HaTrMxvPZ98GeKwDt3OnWaVpOvXI95atAjatoXAQFPhM326HdRcixShfHnYvds0ydm3z/Tqj/S/nn0Ib9vZpIkpbRMpmlKKKa9OwcnBifEHxrPy1EqrQxIpXHwT/peVUmuVUs2VUnZxs10p5QC8F+mt1kqp6LrtDAQ8gHeUUk8vntUP2Ab0U0q9FnZupZT6CGgBLARk2TyRql17cI2OyzsSqkMZUnMITYo2if3BXl5mGH//fjOBEZg50/RQDwmBTz+FceNMxxUhbOWFF0wFTfHicPSoGfm/fNnqqCJJn96U9oSEQK9e8MEH5rlIsSrnrszIBqYM8s1Vb3Lh3gWLIxIpmdLxaAmmlAoFwg98BOwE1gPrtdbnbBderOMZC7wBZHlqky9wASintQ6MtP9wzGj9Mq119yjO5wy8BfQA0gCOwF3gJ631orjEVrFiRe3l5RWXQ4Swa8GhwTSY24CdF3ZSt0BdtnTdgqNDLIfijx83mdadO/D667BgAZN+cqRPH7P5229NG0UhEsuNG2Zdh7/+ggIFYNs2KFTI6qgimT0b3nkHgoLMiP+iReDhYXVUIpForWnxSwvW/rOWqnmq8nv333F2lDpGET9KqcNa64pRbktAwh9Z5JOcwST/G4AdWuugOF8gBZGEX6Q0g7cNZsTuEeRIl4M/3vkj9itInjtnJuheu2YmLP76Kz9McubDD83mceOgX79EC1uICHfvmsqZAwcgVy6T9BcvbnVUkezcCW3amC/GL70Ea9ZA/vzPP04kS7f9blN2alku37/MgOoDGNVwlNUhiWQqpoQ/vjfNQzGlLWswi0+pSI+imLKYjcAdpdQqpdQ7Sqk88byWEMJObD+/nRG7R+CgHFjUdlHsk/0rV6BBA5Ps160LS5Yw6ofHyf5PP0myL5JOpkxmbmytWnD1qvn5559WRxVJ7drm20ixYqb+aNcuqyMSiShL2iz80vYXHJUjo/eOZv2Z9VaHJFKg+Cb8a7TWXbTWLYFsQBXgS+AAZrQ/PPl3B17FtOi8oJTaq5TqoZSyuhOyECIeXs73Mn0r92VE/RHUKVAn9gfOnQvnz0OlSrBqFd+OdWPQINOgZ/p0s/ioEEnJwwM2bDDlPTdvmu+hBw5YHVUkRYqYGcYzZ5pFBUSK9nK+l/mm3jcAvLHiDS7ft6cJJiIliG9Jz0CtdZT3nJRSWYDGQJOwn1kjbQ6/2CWgn9Z6VZwvnsxISY9IibTWEb2kY3kATJyI7tyFryZm5quvTLI/ezZ0s8ueXyK1CAgw00lWrYJ06WDtWjPAbpf+/htWr4YhQ8wvkEhRQnUoTRY0YfPZzdTMV5Pfuv2Gk0OirI8qUiibl/REl+yHbbuttV6ote4KZAeqAl8BB3k8+p8P+FUp9V505xFC2AetNeP3j+eO/52I92KV7Pv7w+3b4Qeg+/Tls7Em2XdwMKueSrIvrObiAkuXQseO8PChqe3futXqqKIQEACtWpm+/R06gJ+f1REJG3NQDsxrPY+c6XKy6+Iuvt75tdUhiRQkURvfaeOg1vorrXVVzBeALsAC4AEwWimVLTFjEEIkzIwjM+i/qT+159QmJDSWbQKDgsywaa1acOUKWsMnn8Dw4aa3/qJFpg2nEPbA2dl8Ae3Rw3xPffVVWG9vZdQuLvDjj6YWackScxviyhWroxI2ls09GwvaLEChmPf3PHwD7WVpaJHcJWmn66dG//NgOvk0TsoYhBBx06hwIyrmqsjgGoNj134zNBTefNN0FvnvP/TdewwYAKNGgZMTLF4M7dsnftxCxIWjo5lP0qvX48H0VfZWdNqkiVm/olAhs55FpUrmp0hR6hasy6K2izjc8zDuadytDkekEPGq4bfZxZVqDpTUWo+0LIhEJjX8IiUIDg2OXS2p1tC7t1lQK1069NZtfLykMmPHmlHUpUuhZcvEj1eI+NLarHk1frz5grpwoVkPy67cugXt2pn2na6u8PPP8i1aCJEobTkTEoyHUuonpdRcYDxmQSshhB0JCQ1h0dFFhA8IxHri2NChJtl3cUGvWi3Jvkh2lIIffoCBAyE42JTLL1xodVRPyZoVNm+G//0PHj0y31JEihQYEsiHmz7kh30/WB2KSOasWLy+F9AT6IyZvLvTghiEEDEYun0onX7txLtr49Av8/vvzVK5jo7oxUv4aG3diGR/2TJJ9kXyoRR89x18/rmpUOvSxXSUsitp0sC0aaZ15+uvP35fkv8UZdeFXfyw/wc+2/4ZN31vWh2OSMasSPiPYRbuUsC3WuvTFsQghIjGshPLGLF7BI7KkY4vdYz9gf/9B4CePYcPd7Tghx8eJ/stWiRSsEIkEqXgq6/gm29MDt2jh8mv7YpSULXq49eHDkH16nDhgnUxCZuqX6g+w+sN57c3fsPT3dPqcEQyZtMafqWUI/A5UAR4X2t9L5r9PIFQrfVtm13cTkkNv0hOjt04RtUZVfEN8uWHxj/Qv2r/2B+sNfqQFx8uqsS4cSbZX74cmjdPrGiFSBrffw8DBpjnkybB++9bG0+06taFHTvA09P88tWsaXVEQogklJQ1/F8AQ4EOQEwdth+lhmRfiOTkrv9dWv3SCt8gX7qU7kK/Kv2ef9DOnXD9OgAaJcm+SJE+/hjGjTPPe/c2E3rt0q+/QsOGZung+vVN2yGRoqw6tYp5f82zOgyRDNk64X8VGAF4AXsBlFJPXEMplRYYr5TKbONrCyHiKSQ0hM6/dubs3bOUy1GOqa9Off7iWnv2mDaBNWqgb97iww+RZF+kWP36mTb4AP37m1F/u5Mpk1lA4IMPzFoYPXuabyhBQVZHJmzA66oXrRa34p2173Di5gmrwxHJjK0Tfh+t9RCtdRWt9aGw904ppTKF76C19gM+Bobb+NpCiHj6fPvnbPh3A1ncsrDi9RWkdU4b8wF//gnNmoG/P7pmLT4ankWSfZHivfceTJ1qng8YACNGWBtPlJycYOxYmDXLTOz98UfTwlMkexVzVaRbmW74B/vTYVkH/IP8rQ5JJCO2TvgzRfFedsAt8hta6zvAVqVUUxtfXwgRR8tPLGf47uE4KAeWvLaE/Bnzx3zAmTPQuDH4+KDbtGFQxqn8ME5FTNCVZF+kZD17mlxaKRg8GIYNszqiaLz5pqnnz5nTzDgWKcKkppMomrkoR28c5ePNH1sdjkhGbJ3wOyilns4WvLXWV6PYdyUgqYEQFjp+4zjdVprpNqMbjqZewXoxH3DpEjRoADduoBs25NN8Cxn9g1NEn33pxiNSgzffNGtdOTiY1p1ffGGn3TCrVTNf0CP3xD1/3rp4RIKlS5OOX9r9grODM5O9JrPi5AqrQxLJhK0Tfi/gw/AXSikXoJBSyvXpHbXWwUAWG19fCBFL9x7do9ViM0m300ud+KDqBzEfcP++mRB48SK6alU+L/UrI8e54OQES5ZIn32RunTtCvPng6MjfP01DBlip0m/u/vj53v3QvHiZlWxkBDrYhIJUj5neUY1HAXAW6vf4qLPRYsjEsmBrRP+X4A+SqkflVKvAD8AaYm+Y09xG19fCBFL6/5Zx793/qVM9jJMbz79+ZN0PTygbVt0mTJ8XWU934xLF5Hst2qVJCELYVc6doRFi0zZ/IgRJo+2y6Q/3OnTJtEfPdpMuL9zx+qIRDz1q9KPZkWbcffRXbr82oXg0GCrQxJ2zqZ9+AGUUluBupHe8gUeATUjL7KllHoVWKi1Tm/TAOyM9OEX9mz5ieVUyFWBAhkLxGp/reHLgX58/X1anJxg8WJo0yZxYxTC3q1YAe3bQ3Cw6eAzdqyp8bdLO3fCa6+Z1p2FCpngS5e2OioRDzd9b1JmShmuPbzGF7W/4Ms6X1odkrBYUvbhB9ODfy9mJV0foBOmdOewUmqOUuprpdQi4FfgZCJcXwgRg8CQwIjnbUu2jTnZDwgwqwxduYLW8Nln8PX3aXF0hF9+kWRfCIDWrU13Kmdn05q2b187HumvXRu8vKBCBTh3ztT5L15sdVQiHjzdPZnfZj4KxbDfh7HTe6fVIQk7ZvOEX2t9S2tdEygKFNBarwW+xZT2dAWGAO0BJ2COra8vhIjenot7KDapGAevHHz+zsHB0KkTTJ6MbtuWz4dqhg8nItlv2zbx4xUiuWjRAlauBBcXsxpvr14QGmp1VNHIlw927YI33gA/P3j3XSnvSabqFazHpzU+JVSH0vnXztz2kzVNRdQSY4QfAK31Wa31/bDnnwPvA1cxI/9+wCit9U+JdX0hxLMmHJyA9z1vFh97zoheaCi8/bZZuTNDBqaUmcI33yocHU3NsrT1FuJZTZvCqlUm6Z861bTwtNuk380N5syBiRPN7OPMshZmcvVlnS+plqcaVx5cYerhqVaHI+yUzWv4n3tBpdIDvlrrVNEiQGr4hT0JDAlkitcU3qv0Hk4OTlHvpLVZVnTiREiblpkdtvC/WdVxcICFC+H115M2ZiGSm61bzYi/vz906wYzZ5o7Y8nCzJlQrBjUqGF1JCIOvO95s+b0GnpX7v38BgwixYqphj9OCb9SykNr/cBmkUV9DVcgQCf1N5FEIgm/sFqoDiVUh0af4D9tyBAYPhzSpGF+h7V0ndsQBwczCNixY+LGKkRKsX07vPqqqZjp1Mn07XeK5a+gZQ4fhqpVzfMxY6BPHzuefSyEeJotJ+1WVUpNtEFMUVJKpQGWYer/hRA2MGznMJotbMZd/7vP33n7dsIL9Re3XRKR7M+bJ8m+EHFRty5s3Ajp0pk7Y507Q1CQ1VE9R+nSZsZxcLC5y9e5M/j6Wh2ViKPzd8/TbWU3/IL8rA5F2JE4Jfxa6y2Ak1JqorLxPSOllAewGtirtf7HlucWIrVafGwxX+78ki1nt3D42uHnH1CnDgwbxso2c+mwqCUODmZkslOnRA9ViBSnZk3YtAnSpzfrVbz+OgQGPv84yzg7m5H9xYvNgl2LFkHlynDihNWRiVjSWtPp107M/WsuX+34yupwhB2Jz6TdfkAZYK1SytMWQSilygH7gDta6+G2OKcQqd2+S/vottKsefd9o+9pUKhB9DuHZyFK8a36jNZLO6GUmdPXpUvixypESlW9uqnpz5jRtLxv0wYePbI6qudo3x4OHoQSJUyyX6kSrF9vdVQiFpRSTGk2hddLvc6gGoOsDkfYkTgn/FrrQKAlkA04oZT6QCmVLj4XV0qVVEpNBw4Ax4h+RV4hRBycv3uelr+0JCAkgHcqvMMHVT+IfufFi82t/AsX+PZb02tfKTOy37Vr0sUsREpVqRL89ptphLNunVmZ2t/f6qieo2RJk/R37mzaDpUqZXVEIpbK5CjDL+1+IbObdF4Sj8W7S49Syh1YALTArKS7AziIWUzrKnAbCABCABfAHcgJ5MfcIagFvBC2/Rut9dcJ+Bx2SybtiqTm88iH6rOqc+LmCRoWasi6TutwdnSOeuc1a8yQY3Awm5uOo/H6fpLsC5FIjh6F+vXNIrf16sHq1aZyxq5pDZcumd794a+vXIE8eayNS8RKYEggU72m0qtSr9g3bhDJVkyTduP9X19r7Qu0Ukp1B0YArwCNYxtT2M/fgA+01kfjG4cQ4rGgkCBeW/oaJ26eoKRnSZa8tiT6ZH/rVnjtNQgOZm/NgTRe31eSfSES0UsvwY4dJun/7TfTt3/tWvDwsDqyGCj1ONkHU+M/bBjMmiWr7yUDry19jdWnV3Pb/zZf1vnS6nCEhRK88JbWeg5QAHgP2A1oTEIf3eMmMB2oorVuIMm+ELahtabvhr5sObcFz7SerO24loyuGaPe+fffTaPwgAC8qrzHy7u+Qyklyb4QiaxkSdi5E3LnNr+GjRrBvXtWRxVLWoOXF9y/b1bf69MnGUxISN36VemHQjHs92H8fuF3q8MRFrL5wltKqQyYkp0XgIxAGuAB8B/wF3AmpfTYjw0p6RFJZdz+cXyw6QNcHF3Y3m071fJWi3rH/fuhYUN4+JA/y/eg/JHpoBwk2RciCZ07Z8p6LlyA8uVh82bIksXqqGJBa5gwAQYMMH1Gy5Y184BeeMHqyEQ0hmwbwvDdw8mTPg9/vfuX1PanYLbsw/9cWmsfrfXvWusZWuvvtdbDtdYTtdZLtdb/pKZkX4iksub0Gj7c9CEAP7f6OfpkH8zw4sOHHCvdiQpHpkmyL4QFChUyI/xFisCRI6Yj7vXrVkcVC0qZHv1790LhwvDnn+Yby7x5VkcmovFlnS+pmqcql+9f5n+r/4ekYamTzRN+IUTSuvfoHl1XdEWjGVZ3GK+/+HqM++uBg/il/a+U/ftncHCUZF8Ii+TLZ5L+EiXg2DGoXdvMh00WKlY031Q6dDCLc02eDCEhVkclouDs6MzCNgtJ75KeFadWMPXwVKtDEhaQhF+IZC6ja0YWt1vM+5XeZ0jNIVHvdOoUXLqE1vD559BxSWu0gxPz5kmyL4SVcuY0E3lLl4bTp6FWLfD2tjqqWEqf3iwjPGuWWaTL0dG8LyPIdqdgpoJMe3UaAB9s+oBjN45ZHJFIajav4RdPkhp+kVi01sRqwet//4VatdAuLoxq9juf/JgXR0dYsMCs/CmEsN6dO9C4sZkTmzcvbNsGRYtaHVU8aG1a/daqZUp/HGRc0Z68teotZv05i1KepTj09iHcnN2sDknYUJLW8AshEp9fkB9NFjRh67mtMe94/ryZGXjtGudCCvDVj1lwdDSDcZLsC2E/Mmc2nXKrVzdt72vVMmU+yc727bByJXz4ITRpAteuWR2RiGRCkwkUy1KM4zeP89Hmj6wORyQhSfiFSIamHZ7GprOb6LWuF0EhQVHv5O0NdevCpUucz1WdMpfWEOSUliVLTPt9IYR9yZABNm0y39H/+8/U9Ce7G8T16pmEP0sW03qodGmzwpiwC+5p3FnUdhFpHNPwk9dPrDi5wuqQRBKRhF+IZKhvlb58VvMzVnVYFfXCWhcumGT/wgXO56xGmasbCHROx7Jl5m67EMI+pUsH69ZB8+amzKdePdi1y+qo4qhlS/j7b9P+99Yt87pXL/DzszoyAZTLWY5RDUYB8O66d/EP8rc4IpEU4pTwK6X6KaXyJlYwQoiYhYSaLhgOyoFh9YZR0rPkszvdv2+yBG9vzmerTNlrGwhIk57ly82/u0II++bqCsuXm7K7Bw9Mbf+mTVZHFUe5csHGjTB2LKRJA1OmmE4+wi70rdKXXhV7sbrDaqnjTyXiOsL/A+CtlNqvlPpYKVUoMYISQjxr4dGFVJ9VnesPn9OsO316Qrv34HzWipS7sYkAlwysWGFGDIUQyYOzs5lY/9Zb4O9vfn9//dXqqOLIwQE++AAOHIAuXaBvX6sjEmGUUkxuNpkqeapYHYpIInFN+CcBV4HKwEjgjFLqiFJqsFKqmM2jE0IAsPHfjXRb2Y2DVw6y8tTKGPcNDoZu/wyh+K3dBLplZO1aaNo0aeIUQtiOoyNMm2aa3QQFQfv2MH++1VHFQ9myZmGuNGnM65s3ze3GM2csDUs8turUKnZdSG61YyIu4pTwa637aq3zAtWBccAFoCwwDDihlDqmlPpSKfWSrQMVIrXad2kfbZe0JTg0mI+rfcw7Fd95dqdr1+CVVwg6402nTiYpSJPOhY0boUGDpI9ZCGEbDg7www/w2WdmXas33kgBlTFDh5qJvGXLmg8j7cEtteb0GlotbkXH5R259+ie1eGIRJLgPvxKqQrAa0AboEjY2xo4CywFftVaH07QRZIx6cMvEuL4jePUnF2Tu4/u0r1sd2a1mPVs7/2rV03N/unTHMjRgqr/rSJ9elM+W62aNXELIWxv1CgYNMg8HzYMhgyB2CzFYXfu3jXlPeG3Kxo1Mot35c5tbVypVFBIEI3mN6JlsZb0q9Ivduu7CLsUUx9+my68pZQqjUn+2wLFw97WwEVgGSb532ezCyYDkvCL+Lpw7wIvz3qZKw+u0KJYC5a3X46Tg9OTO12+bJL9M2c451Gayg+2EZopK5s3Q8Uof+WFEMnZ9OnwzjtmULx/fxgzJhmvbbVsGbz7Lty+DRkzwsSJ0LlzMv0Wk7yF6lAcVHL9H0mES7KE/6mLFgfaY5L/8BIfDVwDloc9dukUvtSvJPwiPm763qTG7Br8c/sfauWvxcbOG5/tpHDxomm9ee4cZzzKUfXBFhyyZmHrVihTxpq4hRCJb+lSkxcHBUG3bjBjBjg5Pf84u/Tff/D227B2rXn911+md7+wjPc9b/yC/KLuAifsmiUJ/1MBFMaM/LcDyoe9rYEbWuuciR6AhSThF3F1P+A+9X6ux+FrhymTvQw7u+8kg2uGJ3cKX1TL25uT7hWp7rsZ1xyZ2LYNSsrf0UKkeJs3Q+vWprV9ixaweLFp55ksaQ0//wz//gvffGN1NKnaoSuHaDivITk9cuL1thfuadytDknEQUwJf5Lcv9Fan9VafxcWREFgAHAQyJYU1xciuXgU/IhWv7Ti8LXDFM5UmI1dNj6b7ANs2ADe3hxNW5lqvltIny8Tu3ZJsi9EatGoEWzbBpkymfmvTZqYJTiSJaWge/cnk/1t26BZM1O2KJJMqWylyJ0+N6dunaLfxn5WhyNsKMkLtrTWF7TWY7TW1QBZxEuIMEEhQbRf2p7t3tvJkS4Hm7tuJke6HFHue6VFLz7JOYcafpvJ/kJGdu+GIkWi3FUIkUJVrQq//w45c8KOHWY6z40bVkdlA1rDgAGwfj2UKgUzZ0onnySS1jktv7T9BVcnV2b+MZPFxxZbHZKwEUtnaGitr1p5fSHsybEbx9h6biuZXDOxqcsmCmV6al27f/6Bc+c4dw5q1oSR17qR/6UM/P475JWvzkKkSi++CHv2QOHCcPgwvPwynDtndVQJpBSsW2dWG7t/H/73P2jYEM6etTqyVOGl7C8xttFYAHqu7cm5u8n9fygBFif8QojHyuUsx6Yum9jUZROlsz81ae3YMahVi6AadXm92kXOn4fKlc2oXvbsloQrhLATBQuapL9cOVMGX706/PGH1VElUM6csGqVad2ZJYsp8XnpJdObNDjY6uhSvHcrvkvr4q25H3Cfjss7EhgSaHVIIoEk4RfCQlprjt84HvG6Zv6aVMpd6cmdDh+G2rXh+nX23HqBEzeyUKcObN0KmTMnbbxCCPuUPbsZAKhfH65fN39l/Pab1VElkFKmHdHJk+anv79ZhezhQ6sjS/GUUsxsMZN8GfJx8MpBhmwbYnVIIoEk4RfCIlprBm0dRLmp5Vh5amXUO+3ebQpz79xhg+OrvBK0htpN3Fm/Hjw8kjRcIYSdS5/eVMK8/jo8eGAm8i5ZYnVUNuDpaUb6N2409fwZM5r3Hz0CX19LQ0vJMrllYlHbRTgqR77f9z0bzmywOiSRAJLwC2GhoJAgNPrZBbXADOE3bgz377PUoT0tQn6l1euurFwJbm7P7i6EEC4usHAh9OsHgYHQoYNZzypFaNwYmjZ9/HrYMDOJYd0662JK4arnrc439Uz3pDdWvsHVBzL1MrmShF8IiyilGNt4LEd6HuHVF159cuOFC/Dqq+DnxxzVnQ6hC/nfu84sWABp0lgTrxAieXBwMJUv331nmtv07QuDB6ewRjfBwWYxAm9v83dlmzZw6ZLVUaVIA18eSMNCDbnld4suv3YhJDTE6pBEPFie8CulKiqlWiqlpBpZpAo///kz1x9eB0zS/1L2l57dKX9+djX4ih95jx56JkOGOjJ5Mjg6JnGwQohkSSkYNAhmzzZ/b4wYAV27mlH/FMHJCfbtg7FjIV06WLECSpSA7783SxALm3FQDsxrPY/s7tnZ7r2d8QfGWx2SiIckS/iVUrOUUjOVUm9Feu874ACwAjiplCqTVPEIYYXx+8fTfVV36s+tT0BwwLM7+PigNQwZArXWDaI3k/hhnANff23+ARdCiLjo3h3WrAF3d1iwAF55Be7dszoqG3Fygg8+MJN627Y19fwDBkD58nDnjtXRpSjZ02Vnfpv5tCnRhu5lu1sdjoiHpBzhbwPM0FrPBFBKNQQGAv8ALwPdgM+TMB4hktT4/ePpv6k/AL0r98bFyeXJHUaPRpcsyWedzzN8uBmVmztX0U8WOxRCJECTJmaBrhw5YPt206v/4kWro7KhPHlg2TKzUFehQmZhkkyZrI4qxWlQqAHL2y8ns5sUZCRHSZnwz9Na7wNQSrkAPwKhQGet9T6t9UbgZBLGI0SSiZzs/9TsJ96t+O7jjVqbe+8DB6KuXuXSol24upo71F27WhOvECJlKV8e9u+HkiXhxAmzSm+y79X/tCZNzJols2c/viX6998wbpyU+dhYYEgg0w9PR6eoiSEpW1Im/P9Fev4ZUAQz4n8k0vueSRiPEEkixmQ/JAR69oRRowhWTnRiAaszvMGmTWaRSSGEsJX8+U2n3zp14No1qFULNqS0Totubo9XI9Qa+vQxZT9ly5rFu4RNtFjUgp5re/LD/h+sDkXEUlIm/DmUUoOUUhOAIcApYED4RqVUPaBLEsYjRKKLMdkPCID27WHGDPyVGy30Kn7P3Yndu80/xEIIYWuZMpl29p06mfWrmjeH6dOtjiqRKGVq+gsXNrc1GjSAdu1MFzSRIL0q9qJAxgK8nPdlq0MRsaSS6naMUio9MBqoBvwJDNRa/6eUKgF8BNQKi6dokgSURCpWrKi9vLysDkNYYNz+cXyw6QMgmpH9Jk1gyxZ8VAaa6bXcLVmDjRtN+akQQiSm0FD47DPTvQfgo49g5MgU2gksIMB08/nmG/DzA1dXGDjQPNzdrY4u2XoU/AhXJ1erwxCRKKUOa60rRrUtyUb4tdb3tdbvaK1La63f0Fr/F/b+Sa31/7TWL6S0ZF+kXiN2jYg+2QdwdOTfF5ryn8pBTf07DjVrsHu3JPtCiKTh4ADDh8OMGabZzZgxppX9w4dWR5YIXFzg00/h9Gno2NGs0Pv99+DjY3VkyVrkZH/PxT1Sz2/n7KkPv0ypF8me1poh24Yw+LfBKBTTm09/MtkPDQVMQ4lS0/tTUh+naJvSbN4sTSWEEEnvrbdg0ybImBFWr4aaNeHyZaujSiR58phliHftgh9/hFy5zPvBwaanv4iXz377jBqzazDhwASrQxExsKc+/KekD79I7i76XGTCwQk4KkcWtFnA/8r/7/FGLy906dLM+vQf2rc3C+B0fC8zS5aYO8xCCGGFevXgwAEoUgT+/BOqVIHDh62OKhHVqGEWKAg3cyZUr256+f/7r2VhJVflc5YHYMCWARy6csjiaER0pA+/EDaUP2N+1nVax7L2y+j4UsfHGzZsQNepgzp+nJDvRqO1uZ0+aVIKrZkVQiQrL7xg2nbWrg1Xr5qR/l9/tTqqJBIQAGnTmg9csiT07w+3blkdVbLRpkQb+lTuQ1BoEO2Xtefeo3tWhySiIH34hUigoJAg9lzcE/G6Vv5atCre6vEOs2ejmzdH+fryM2/wgfOPLFpkSkpl9VwhhL3IkgU2bzaD3/7+ZsB7+HDT3TJF69sXzpwxHzw4GMaPN519hg83k3zFc41uOJoKOSvgfc+bt1a/JfX8dkj68AuRAMGhwbRf1p7ac2qz+vTqJzdqbbpC9OiBCgnhWwbzYaY5bPwtDR06WBOvEELEJE0amDULvvvODEgMGWLmuab4vDdXLrNg1x9/wCuvwP375sMvXmx1ZMmCi5MLi9stJr1Len49+SuTDk6yOiTxFOnDL0QCOCpHimcpjoeLB9ndsz+5sU8fGDqUUBTv8SOzC3/Lvv2KGjWsiVUIIWJDKbP496pV4OFhct4aNeDiRasjSwJlypjVyLZtgw4dnlzu/PTpVHC7I/4KZy7MzBYzAfho80ccvHLQ4ohEZEmZ8A8BCgF1gPlAPa31A6VUCaXUDGAKcDUJ4xEiwZRSDK8/nL/f/Zsqeao8se24Uxn8caUty/mr+nvs22fqZIUQIjlo3tzU9RcubAa+K1UyK/WmCvXqwaJFpmcpmKWJy5eHqlVhyxZJ/KPRrmS7x/X8S9tzx/+O1SGJMNKHX4g48r7nTeP5jbn6wHw/VUqRN0NYA/2QEMB0fCsz6W2KcZo07VuzbRt4SsGaECKZKVkSDh40i9TeuGHy4BS7Mm9MTp82tzsOHoRGjaBuXdiz5/nHpULfN/qeyrkrc8HnAm+seINQHWp1SIJ4JvxKqbRKqVbSO1+kNkevH6X6zOpsPruZAVsGPLnx4EF0iZIMe/0YvXub3L/Lp/lYtEjabgohkq/MmU2VS//+EBQEPXtC797meapRpw6cPWuWJs6UCXbuNHVOTZvCkSPPPTw1SeOYhiXtlpDJNRPrzqxj9J7RVockiP8I/0ZgObA5/A2lVDGlVEGbRCWEHdp9cTe15tTi2sNr1ClQh8lNJz/euHy5abt55h/yLBmDiwvMm2eaPDhYvrydEEIkjJMT/PCDmdeaJo25i1mvnql0STXc3eGTT+DcORg6FNKlM9+EBg2yOjK7kz9jfua1ngfAkN+GcPT6UYsjEvFNRYoBCsgf6b1awL9KKW+l1BylVDelVP6oDxcieVl9ejUN5zXk3qN7tCnRhg2dN5DBNYOp4xw1Ctq1Q/n7M4O3GJptGjt2QBeZgi6ESGG6dzeD27lzm3r+ChVSYWVLxozw9dcm8f/oI/j228fbTp6Ev/6yLDR70uyFZgytNZTRDUfzYrYXrQ4n1VPx6ZWqlGoC9AJmaq1Xhb33MrArbJfIJ70A7AC2Azu01pcSErDVlFIKs1DYba31c9cNqFixovby8kr8wESimX54Or3W9SJEh9CzfE8mN5uMo4OjWazl/ffNKo3AIL5jU+mBrF6jyJfP4qCFECIRXb8Or79ukn8nJxg71pT5pPq1RV59FdatgzZt4PPPTdcfIZKIUuqw1rpiVNviNcKvtd6gtW4RnuyHORP2cw2wFriOuQtQAOgOzAG8lVL/KqVmKKU6K6We6mMYP8rooZTaq5T6Wyl1Wim1QynVMgHn7KCU0k8/MIuFLcCsECxSsFAdyidbP6Hn2p6E6BCG1hrKlFenmGRfa3SzZjBzJv640o6l/NNqELv3SLIvhEj5smeHrVvhww/NWlV9+5oOlim+X39MQkKgSBFwcTGr9pYtaxL/P/6wOjK7cP7ueaYfTo0zvu2DzaqLtdY3gCta65Zhj1xAUeBtTIJ8BfMFoBDQA5gLXFFKHVBK9VZKZYjPdZVSjpj5BNOACVrr0kAJYAuwUik1Mp4faUAM2yZorUPieV6RDDwKfkTH5R0ZuWckjsqR6c2n83Xdr1Fhw1ePAhTTArpziTzUYDfFBrdj+XJT0imEEKmBkxOMGQO//GLK2xcsgGrVzNzWVMnREcaNM6U+/fqZbg0rVph2nk2bmtV8U6l7j+5RaXoleq7tyZazW6wOJ1WKV0lPtCdTapbWukcM28P78NcOe4SPhWrgPjAc+F7HISil1DigHzBJa93nqW0bgcbAW1rrWXE4ZwNgHlAfM6IfWRBwLrYxSklP8nPL7xYtf2nJ3kt78UjjwbL2y2hUuJHZeO0al4Jz0qYNeHmBp9tDJs5Ox+uvWxuzEEJY6fhxaN3a5LQZMpjJva1bWx2Vxa5dg++/hylTzG0Qb2/ImdPqqCzz7e/fcvDqQX5u9TMZXTNaHU6KFFNJj00T/rhSShXAJNUNMYl5BmA90Fpr/dyGX0qpUsBRzJ2D4lrr009tbwqsA24BhbTWD2IZ12Zgm9Y6vncHIkjCn7xoranzcx1+v/A7edLnYX2n9byU/SUIDYWvviJk9Bgaue7it7vlKFAAVq6UEk0hhADw8YE33zSD2mAGuUeNMl19UrVbt2DvXmjRwrwOCYGOHc2jZctU08otvB+/g0odn9cKNq/htxWttbfWeqbWugOQDXgNyAkMjuUpPsQk+2efTvbDbAMCgKzAG7E5oVKqLOYLyA2lVK5YxiFSCKUUYxuNpUa+Ghz43wGT7D98iH7tNdOVwd+fgncP06CBGeGXZF8IIYwMGWD5ctO+08kJxo+HmjXNwHaqljXr42QfzB/S0qWmvr9kSZgxAx49si6+JOKgHCKS/YDgAOb9NQ8rB51TG7v5mqW1DtJaLweqAZVjeViTsJ9RrnqhtQ4Ajoe9bBfLcw4M+zkLM8fglFJquFIqbyyPF8nQn//9GfG8Qq4K/N79d3J55ILTpwmtXAX166/cIwPNWEemj//Hhg2QJYt18QohhD1SyizQtXs35MtnFqYtVw5WrXruoanHq6/ChAnmD+j0aXj7bShQwCzqdfeu1dElOq01ryx4hTdWvsGMIzOsDifVsJuEH0Ap9Q3wCZA+Fvvmw9wNADgfw67nwn5WUirmhmFKqSw8+8WgGPApcFIp9fbz4hLJz+Btgyk3tRyLji6KeE8pBStXElqxEg4nT3CCEtR2OcAbC15h9GgzeiWEECJqVaqY5jTNm8O9e9CqlenoExhodWR2IG1a6NMH/v3XzHQuW9b0OR082NwSSeGj3kop3iz7JgC9N/TG66qUPScFu0n4w5LtwcAXPDtRNiqFIz3/L4b9wre583iScJS01rcBN0x5UUNgJKb+P/z4aUqpd2MRm0hGcqbLiZODEw8CI03xuHWL4E5dcXj4gKW04/X8B5izrxidOlkXpxBCJCeZM5uR/e+/f7xSb82aqbiLz9OcnaFTJzhyBDZvhoYNzWh/+NjkzZtw4IC1MSaSN8q8Qa+KvQgMCaTdknbc9rttdUgpnt0k/GHJ9ieYFp5vxuKQTJGex9T5N/K2zLGII0RrfVNrvVVr/QnmS8JoILwN56SwycIiGQsODY543rtyb472OkrPCj3NtmD4dExWOvnP5GNGM7/5Enb96UG5clZFK4QQyZNSZjHa339/ssRn/nyrI7MjSplkf/Nms6BBuEmToGpVqF7d1PwHB0d/jmToh8Y/UDl3ZS74XKDzr50JCZVu54nJbhJ+AK31KK31G1rrc8/fm7SRnsd0kzAg0nP3eMTkr7UeyONJv47E3KMfpVRPpZSXUsrr5s2bcb2kSGS/nf+N4pOKc+a26YmslKJ41uJw5Aj3pi6mUSP47jtY7tCebCM/ZuUqRcaM1sYshBDJWbVq8Oef8Npr8OCBWaSrSxe4f9/qyOxM5MrjtGkhY0bYtw/at4fChc3tknv3rIrOplycXFj22jKyps3KprOb+GrnV1aHlKLZVcIfR/6RnjvHsF/kbf7R7vUcWuuFmLsPAFWfs+80rXVFrXVFT0/P+F5S2JjWmkkHJ9FoXiPO3j3LpIOTwjfAtGmEVquO67vduLX9b7Jnh99+g4EDZal4IYSwhUyZYPFimDnT5LLh5ev791sdmZ0aNAguX4Yff4SiReHiRRgwAPLkgWnTrI7OJvJmyMsvbX/BQTkw7PdhrDi5wuqQUqzknPBHHjp3i2G/yNsSWiQWviZ0jHMBhP3xC/Kj28pu9NnQhxAdwicvf8LYxmPhwQNCO3WGd97BITCAOXQnW41i/PEH1K5tddRCCJGyKAU9/t/encfZWP5/HH9ds1gnyS5liyxZi0opshRl3xLSRt+INi1f2n6l0qJVlrRIvmVJIcqWlESWxBj7rsjaEGP2uX5/XDNmaIxl5px7zvF+Ph7ncZZ7OZ/Iud/nPtf9ue51w9avvBK2bYOGDeHll117ejlJwYLQty+sXw/Tp0OTJhATAxUrpq+zf39AD/dpWrEprzZ9FYA7p9zJ6r2rPa4oOAVy4N+c4XHJLNZLWxYL7Mzme65KvQ/+hrlBZMvfW2jwcQPGRY6jQHgBxnccz5BmQwhdHUVSnasImTCeI0TQjc/Z/tQoZs3Pez5Phigi4nNVqri5qB5/3AX9Z56Bxo1h65kM6D0fhYS4dp7z5sG6ddC0afqy3r3dcJ9XX3XhPwA9ft3jdK/ZnZjEGNpOaMuBYwdOv5GclYAN/Nba3aQH+PJZrFou9X6ptfZMuv9kJW1I0K5s7kf8ZMbGGVw1+ioi90ZSuUhllvRaQtcaXeGrr0iufw1hWzexilrcfNFy7prVjVdfVctNERF/yJsX3ngDZs+G0qVd7/7atd08VEHemTJ7qlZNH2saF+fO/u/cCQMHuuE+3bu7P8wA+kM0xvBh6w+pd3E9th3aRpcvu5CYnOh1WUElYAN/qhmp93UyW2iMCQPS5kKdngPvVzX1flYO7Et8KDklmefmP0fr8a05HH+YdlXbsaz3MmqUqEFiIrwxswbHEsP5gPsZ2PhXvl5ThVtu8bpqEZHzz803w+rV7rrUo0fdCevWrWFPVg23xcmXD9auhZkz4bbbIDERvvjC9T+tWROWLfO6wjOWPzw/U26fQsmCJfnlj1/Unz+HmUCe1tgYUxtYmfq0grV2+0nLmwLf44bgXJLa+jM77/cO8B+gprV282lWB6BevXp2+XL9T+tPB48dpPvX3Zm9ZTYhJoSXm7zMk9c/ScimzWwLq8wd3QxLlkD5kJ30HlyWp56C0FCvqxYRkQkToE8f14imaFEYNQo6nTwdppzajh3ugt6PP4YDB+CPPzg+RnXfPihePNd3ovj1z1+x1tLg0gZelxJwjDG/WWvrZbYsoM/wW2tXAWNSn/bLZJW0hrYvZwz7xphnjTH/GGNGZXgtzBgzyRgz3xjT++RZeY0x1wN9gUfONOyL/63Zt4a6H9Rl9pbZrtVXj9n897onMa+9QUr1K3in+miWLHH9oP+3oCyDBinsi4jkFl27QlSUO+t/8KBr49mjB/z9t9eVBYhy5dwV0Dt3wk8/pYf9lBQ3/XHduq6/fy5u7XntJdeeEPY1tCdnBHTgT/UwMA942BjTGcA4A4A2wBfAkJO2eRK4APiPMSZtMq58QFugMTAa+MkYc50xpqQx5n5gEtDbWvuBr/+D5NxdeuGl5A3LyzVlruG3+3+jWZ6qJDZqhhn4X0KSkygdv40OHdyU79df73W1IiJysjJlYNYsGDEivX1n9eowRR0bz1yePCce5LZscRMgrFoF/fu7LwI9e8LPP+fqsf5T1k2h2vBq/HH4D69LCXgBH/ittUeAlkB/4AljzEogEhfeu1lru1trT272NQyIAcZaa/9O3c9R4FbcEKCDQAPgW2AqUBqob60d6/P/IDlr+2L2EZvorqculLcQ39/5PT/f8zNl5y0nsXotwhfOZy8l6JDvO0p+8iqTJ7sp30VEJHcyxg3tWbnSDUffuxc6dIDbb3cjU+QsVa4Mu3a5MVPNmrmLfceNgxtvhGrVYPt2ryv8F2stI5ePZEv0Fj5d+anX5QS8gB7DHwg0ht+3Fu5cSOcvO9OuSjtGthrpXjx2jKT+jxD2iZs24TtaMqLeGN6bWPKE1sUiIpL7paS4s/3//a9rQV+sGAwb5sJ/Lh+Onntt3QqffOJuISFu7H/a+NZFi+Cqq1wbJY/9Hfs3E6Im0KdeH4z+sk8raMfwi0TkiSA6Npp1B9YRl+SmR4hcE8rmL5YSR14eCXmP3wd/y9TFCvsiIoEoJAT69XOdfJo2ddei3nEHtG8Pf/3ldXUBqmJFeOklN9b/hx/Sw/6+fW7WyYsvhocecuNfPTwxXCR/EfrW73s87CckJ3hWS6BT4JeAs/fo3uOP65Sqw4J7FvD97d8SeiieF1+Eq67LS7u4CXQut4zuv/bn6WeMeuuLiAS4ChVg7lz48EMoVAimTXOjUT74wP0KIOcgLAwuvzz9+a5d7oKJv/92P6NceSXUquUmTNi927s6ge2HtlNvdD0+W/WZp3UEKgV+CRjWWj75/RMqDavE+NXjj79+9b5wkmpdy/zKvXn+eUtSEjR7sCoT1tSkfn0PCxYRkRxlDPTqBWvWuLbzhw/DAw9Aw4buFwDJprp13YUTK1a4i3uLFnVtk558EsqX97Rd0twtc1m9bzW9p/dm4c6FntURqBT4JSAcOHaAjpM6ct8393E04Sjzt8+HpCSS/28wyfWuJt/mKCoc+p06l/7NDz+4rmMFC3pdtYiI+MIll8D06TBpEpQqBYsXu5PRAwfCsWNeVxfgjHHB/7333Fn9adPcFdO33JLe8SIlBR55BObMgaQkv5TV+6rePFj/QRKSE2g/sT3borf55X2DhS7a9TFdtJt9szbP4p5p97Dn6B4uyHMBw28dTo+wK4nteg8FotwsgsPox5Zer/LS2wWJiPC4YBER8ZvDh2HQIBg50g03r1DBXeTbooXXlQWZlBR3QQXAwoWufRJAyZJuAoXu3aFePZ9eSZ2UksRtX9zGnC1zuKL4FSy6bxGF8hby2fsFGl20KwEpJiGG/t/1p+XnLdlzdA83lL2ByD6R3DFtJym161Igahk7uZTuJeZyxbxhvPOhwr6IyPnmwgth+HDXXKZWLdi2DVq2hC5d3ESzkkNCMkTGChXg//7PtfvcuxfefReuvhqqVoUXXvDZzyxhIWFM7DSRqsWqsmb/GrpO7kpyysmd1yUzCvySKy3YsYDao2rz/rL3CQ8JZ0jTIcy/az6715Zn/Lv7CU1OZDS9eevu1Yza3IwmTbyuWEREvHTttbB8Obz+OuTPD19+6fLnq69CfLzX1QWZMmXg+edhwwZYuhQeftid6d+40V1FnbGl54EDOfrWhfMVZsYdMyiavygzN8/kkVmPoNEqp6chPT6mIT1nJyYhhoHzBjJs6TAAapaoyactRnL5/ot4amx1Ro6E/DaGdmWW0/t/jWjc2Nt6RUQk99mxAwYMgK++cs8vv9wNSb/lFm/rCmpJSa7F54ED0K2be+3gQTer79VXu2E/nTu7LwY5YMGOBTQf15yE5ASGNh/KgOsG5Mh+A1lWQ3oU+H1Mgf/MLdixgHum3cPW6K2EhYQxqOEgnk65noQefTm0P5GqyWuID4vgySfh2WchXz6vKxYRkdxs7lzXbGbDBve8XTt4+23XcEb8YO5caNsWYmPd85AQaNzYjbfq0AGKF8/W7idETeCOr+4AYFKnSXS+onM2Cw5sGsMvAWFb9Da2Rm+ldsnaLO04mydH7iBPs1uI2LOFv5Mv5OZae/ntN3j5ZYV9ERE5vebNITLSDfMpWBCmTnW9+59/Ho4e9bq680Dz5m4yr88/h1at3ARfP/zgeqmWKQPR0dnafdcaXXmt2WsA3DnlTrXrzILO8PuYzvBnbWv0Vipe5KbAtdbyReT/aL84BvPYIPLHRhNHXt4If5rCQ56i7yN5jk8GKCIicjZ27XLt5L/4wj0vXRpeeQV69jzxelTxoUOHXJvPSZMgMdG19QTXXunOO+HGG90Uymdx5t9aS7/v+jFi+QjKFy7Pxn4bCQ8N9039uZyG9HhIgT9zySnJdPu6G1PXTyXygUiqFKsCwL6md1DihwkAzKE5U5sN56mPKlOunJfViohIsFi4EB591F3gC67l/NtvQ6NG3tZ13snY5nPJEnfVNbhfARo3hk6d3LCfEiVOu6vklGQe/O5B+tbvS62StXxXcy6nIT2S64SGhBIRHkFYSBir961m7153lqX3D135i1I8XGI8STNmM2Kuwr6IiOSchg1dvhw3zk3g9fvvLl926ACbN3td3Xkk488qVarAxx+7yROMgXnzoE8f9zNMkyawZ0+WuwoNCWVUq1EnhH2d0D6RzvD7mM7wp4vaF0VcUhz1LnZfPv8+dpBDk75g3+TDtFj4DIcPu05ezz4Ww2PPFiR/fo8LFhGRoHbsGLz5pmvdeewYhIe74eXPPHNGJ5bFF6Kj3bCfyZPdkJ+LLnIz/qaN6Z00yU3wVbHiKXfx8YqPmb5xOpO7TCYsJMxPhXtPQ3o8pMAPRxOO8tKCl3hz8ZtUKlKJlf9ZSd6odUTf+RAXRf1MEqHUIIqKLasybBhcdpnXFYuIyPlk9254+mkYO9YNJ4+IgMcfh8cegwsu8Lq689ihQ7B+ffpwn+ho900sKQlq13Y/y7RvDzVqHJ/hNzo2msrDKnMw9iDTuk6jTZU23tXvZwr8HjqfA7+1lglRE3h87uPsPrIbg+GBGnfz9NchlPpiDKGksI/ivFVsCNd+cA9t24f4ckZuERGRLEVGwqBB8O237nnx4vDcc3D//ZAnj7e1CW6ChYEDYcYMOHIk/fXLLnPB/9FH4eKL+fXPX/n9r9/pU7+Pd7V6QIHfQ+dr4I/cG0n/mf1ZsGMBAPUursfQvxtR//mPKRB/iETC+CC8P4kDn6PPwMJqsykiIrnGzz/DU0/B4sXuecWKMHgw3H476haXG8THu3H+X38N33wD+/e7M/y7drlx/+AmXyhfHvLm5WjCUSLyRHhasj/ool3xm0Nxh3ho5kPU/aAuC3YsoFiBYoy69UPuS1nC4ed3UCD+EHNozgvtV9Fxx1s8+oLCvoiI5C433AC//AJTpri+/Vu3QvfubhTJ5MmuwYx4KG9euPVW+Ogj+OsvWLAA3norPexb66ZVLlaM9T1aUP2N8nyw4G1va/aYzvD72Plyhj8pJYlPfv+EZ354hv3H9hNiQuhTrjMtDj7AEx82Zv16KMsO7qi6kk6ftaFefY3dERGR3C8pCT77DF580Y0oAahVC154wU0iq6GoudD+/W7Sr1Wr+KQu3NcWjIXx62tw+/X3u5l+S5b0usocpyE9HjofAv/3W7/nkVmPsGb/GgAalqzPi9+X4KavvmUp9bmWX6lQMYRXXnH/xvThKCIigSYhAcaMgZdegj//dK9deaUL/rfdpmNbrrR9O3zzDa+seIenK2wjPBmmfwG3fPgD3HSTWyc6GgoXDoq/QA3pEZ9a8dcK1uxfQ/lCZfnoUFu+fzCSm776lnjysCzfjQwbmsC6dW7sYxD8exIRkfNQnjzwn//Apk0wbJgbPbJiBbRuDVdfDVOnaqhPrlO+PDz0EAPHbOGxOn1JDIUO3UNZVD7DhRg9esCll0LfvjBrlrs+IAjpDL+PBeMZ/j1H97Bm3xqaVmwKQNyRaIa9fg/3vvUTRY8dAmBSSFd2PvAKvV+pwIUXelisiIiID8TGwqhRrof/vn3utRo1XJefLl10cW9uY63l3m/u5dOVn1I4X2Hm9ZzHlSVqu0m/tmxJXzEiAm6+2X2Ta9UKihXzruizpCE9Hgq2wL/90HZqjqxJeEg4mx/aTNKRIrz3QjQDRlTkIg7xI41Y2Oo17h55DZdc4nW1IiIivnXsmLt29PXXXZMYgEqVXPfIHj3UzjM3SUpJosuXXZiyfgpF8hfhh54/ULtkLfdTzTffuAm/Vq1K32DYMOjXzz2Oj3d/mbl4qIICv4eCIfAnpSQdn6nOWkuTsTeRf+8RqkRP5MP3KxETAz0YR5UbStJhZHOqX5F7/zGIiIj4Qny8u7j31VddVx9wI0UGDID77nMnjsV7CckJdJzUkRkbZ1CsQDHm3zWfGiVqpK+wY4fr8z99OnzwAZQr515/4gnXBjTtzP+NN+a6b3MK/B4K5MCflJLEpys/ZfCCwcy4YwY1i1/Bsc8ms3/Q85T7az2P8hbv8CitWrnuBXXrel2xiIiIt5KSYMIEeOUVWLfOvXbRRdCnD/TvD6VKeVufQHxSPO0ntmfm5pmUKFiCH+/6kWrFq2W90fXXw6JF6c8LFXKtP1u3hpYtc8XQHwV+DwVi4E+xKUxeO5ln5z/LxoMbAehbsAXPv76TEvvXArCdcnxW4w2aj+5MgwZeVisiIpL7pKS4ESJvvJE+gVeePNCzpzvrX7Wqt/Wd7+KS4mgzvg1zt86lVEQpfrzrR6oUq3LqDZKTYckSd+Z/xgyIikpf1qcPjBiRvl5IiCdDf9SlR85IckoyE6MmUmtkLW6ffDsbD26kYvjFjJp1McOenEWJ/WvZQVmGVhrF9lkbeG61wr6IiEhmQkKgfXt3UviXX6BdO0hMdOP9q1WDNm1g/nw3R5T4X76wfEzrOo0mFZpgrSXZJme9QWgoXHcdDBkCq1e7cVvvvecu8G3XLn29ceOgQgU39n/WLIiL8+l/x5nSGX4fC4Qz/MkpyXy59ksGLxjM2tQz+JdElOWKv5+m+NsFGRfbg22UZ0rVQdQbdhc3NstdY9ZEREQCwYYN8Pbb8Omn6d0fa9aEhx5yM/nmz+9peeelmIQY9hzdw2VFLsuZHd59N4wdm/68YEE3CVirVm524LTZgH1AQ3o8lJsDf3JKMpPWTGLwgsGsO+AGGl5KEdpGNuCj2V8TF5OHEJJ5udYkGg3rRIMbwz2uWEREJPDt2wcjR7rb3r3utaJF4f77XTt4dbnzzoe/fUij8o24vOjl57aDlBRYtiz9wt+MXX8aNYIff3SPrXW3kJwbbKPA76HcGvh/3vEzvab3Oj5G/5LkwjwxO4kHfjuKTc5DebZTv3Vpnn0W6tf3uFgREZEglJAAkybBu+9CWlQIDYUOHdyw8MaNc3UXyKAzdf1U2k9sT6mIUmzot4FCeQtlf6d//AHffee+ANxyS3qbz2XLoG1bd9a/VSto1izbrZwU+D2UmwK/tRaT+smx8eBGqr5flTIJFzBwdjy9VsaTJxmWU49FjQbS5N221KitWUNERER8zVr49VcX/CdPdtd9gruw94EH3IW+F13kbY3ng5iEGNpPbE+bKm3od3U/377Zq6+6yRrS5MkDN93kwn+rVm6W4LOkwO+h3BD4j8Qf4Y1Fb7D4z8XM6TGHxETDtNF7KTL0Ehr9kURYCvwQ0oz17QfS6s2bKFtOpxNERES88Oef7sLeDz+E3bvda/nzQ9euLvzXr6+z/r6UnJJMaEj6Cc/4pHjyhuXN+TeyFiIj3Zn/GTNcB6C0TF6iBPz1V/pwn5SUMxr6o8DvodwQ+GMTYyn/bnn2xeyjF78wY9R17NkDU2mLyZOH/fc+RfuX61GkiKdlioiISKrERDcEfNQomDs3/fU6ddxEXt2766y/r60/sJ5b/ncLH7T6gBaVWvj2zfbtg5kz4dtv3YW9777rXj90CKpUcUN+WrWCFi1O+RevwO8hfwd+ay3zt89nxLIRfNTmIwonhbF7yFi+m/0SVffvYeDOBSzkBmrUgEcfSqbbnaHky+e38kREROQsbdoEo0fDmDFw8KB7LW9eN9b/vvvcSJAcvPZTUg2aN4ghC4cQHhLOhE4T6FCtg/+LmDbtxLafoaFuErC0oT9Vqx7/yUeB30P+CvzxSfGMjxrP27++TeTeSACe2nE9z3y2mojkfwDYRnnG1X+P64e0pkkT/SQoIiISSOLiXP77+GP4/vv0ESAVKsA997ix/uXKeVtjMLHW8tjsx3hnyTuEmlA+avMRd9e52/+FbNzozvzPmAELFrjpnNPs2QMlSwIK/J7ydeD/858/Gf3baEb/Npq9Ma63V9G4fDy8KI4HlkPxY/BLSEPWNX+YG99qx+XVw3xWi4iIiPjHjh2un/+YMe5xmkaNXPDv1AkK5UCTmfOdtZbnf3yewQsGA/Bi4xd55sZnjjdB8bvDh2HOHBf+9+93HYBcoZiQEAV+r/gi8KcN2xm+bDjT1k87PjvchbG1+GfOo7wYGcWjySP59sLuJD/wILcOrM2FF+ZoCSIiIpILpKTAvHnwyScwdWr6xK758rmRIHfe6SaDDdP5vmwZvnQ4/Wf2x2LpVbcXI1uNJCwkF/2hbtmCqVRJgd8rORn4D8cd5rNVnzFi+QjWH1gPQFiKod1aSF7Wjyk73iU01HDnrQe5t3coDVsV1rAdERGR88Q//7i2nuPGpc/vBK7pS5curtNPgwYa73+upq6fyh1f3UFcUhy3Vr6ViZ0mEpEne73zc5KG9HgoJwN/y89bMmvzLABKHQnlgeXJ9F4BJY6E8lHEI+wZMJTevaFMmRx5OxEREQlQO3bA55+78L9+ffrrZcvC7be78F+3rq7nO1uL/1hM6/GtORh7kKtKX8WMbjMoFVHK67IABX5PnWvgP3DsAP+L/B+NyzemTqk6bN4Mnw7qyMICX9NvGbRdD3+kVGBRtV6U+u/dNO52sX6uExERkRNYCytWwMSJMGGCm/g1TeXKLvx36gS1ain8n6lNBzfR8vOWbIneQvnC5ZnVfRZVilXxuiwFfi+da+B/Ys7jDF38Jk3oTPzcSfzyC3Tlc8ZyD98XbMc/t/em0YtNKV1Gv8uJiIjI6aWkwOLFLvhPmuRav6epVAk6dnS3evUU/k9nX8w+Wo9vzdJdS7mmzDUsvm+xdxfyplLg99CZBP51+9fx2arPqF68Ondc1JTNL37Onu8/4LWGW6i0rDnvb5xDgQLQtV0c93T8h+valdD4OxERETlnSUlunP+XX8KUKa7hS5qyZV2P/w4d4LrrXOt3+beYhBj6zezH0zc8TaUilbwuR4HfS6cK/AePHWRC1ATGrhrLst3LALhi/wVEDj9KCO7vZB/FmV3uP6S8MJiOHSEi91wXIiIiIkEiORl+/hm++gq+/hp2705fVqyYm9+pTRvX7adgQe/qzO2stYyLHMftV9xO3rC8fn9/BX4PZQz8MQkxTN84nfFR45m5aSaJKYkA5IvPQ4+oBO5aBfV35uGngrcR3fZurn2hJeUqhXtZvoiIiJxHUlLg119d+J86FbZuTV+WLx80a+bCf6tWULq0Z2XmSsOXDqffzH40q9iMOT3m+H2IT1aBX5d5+pjFMn2DC/nTNkzjWOIxAEyKgS0tYNVdXLa+IneFDGRXo24U/LQjzRurnaaIiIj4X0iIG8Zz3XUwdCisXetm9/3mG1iyxM33NGOGW7duXbjtNrj1Vrj6ag39ufaSa7m00KXcV/c+z8fzn0xn+H0s7JIwm9w7+fjza/+AO6LgsjV1uTN8BZ06QbducMMN+ociIiIiuddff7mw/803brKv2Nj0ZUWKQIsWLvzffDMUL+5dnV46lniMAuEFjj/fcWgH5QqX88t7a0iPh8zFxtZq60L+7VFw5J86bKzdmaIPdOb6uyuTJ4/XFYqIiIicndhY+Okn+O47+PbbE4f+AFx5pQv+N9/sfi3I6/8h7Z77bfdvNBzTkJ61evJOi3fIH57fp++nwO+hK8KNHW/rsKlOZ4o90JkGPRXyRUREJHhYC5s2ufD/3XfuAuC4uPTlBQpAo0bQvDk0bQo1apwfs/1+sfoL7p12L/HJ8dQsUZOJnSZSrXg1n72fAr+HqpavaVdvWk24rr0VERGR80BsLCxcCHPmuFtk5InLixWDm26CJk3crXLl4O37v2rPKrpM7sLGgxspEF6AEbeO4K46d/nkvRT4PXSuE2+JiIiIBIO//oLvv4e5c+GHH2DXrhOXlynjvgDceKP7JSDYvgAciT9Cn2/78PnqzwG4q/ZdvH/r+0Tkydl+6wr8HlLgFxEREXGshc2bXfBPux04cOI6pUq58J92u+KKwB8CZK3l05Wf8uB3DxKbFEvVYlWZ2GkitUrWyrH3UOD3kAK/iIiISOZSUiAqyl0AvGCBu+3bd+I6hQtDgwZw/fXuVr9+4E4AtmbfGrpM7sLa/WvJE5qHwTcNZkCDAYSGZL9VowK/hxT4RURERM6MtbBhQ3r4/+kn+PPPE9cJC4M6dVz4v/ZadytXLnCGAR1LPMajsx5l9IrRADS4pAFj242lctHK2dqvAr+HFPhFREREzt3OnbBoEfzyi7utWuV+GcioRAm45hoX/q+5xv0KUKiQN/WeqZmbZtJrei92H9nNgAYDGHrz0GztT4HfQwr8IiIiIjnnyBFYutSF/yVL3O3gwRPXMQaqVIF69Vz4r1fP/SpQoECmu/RMdGw0QxYO4YXGLxzv059iUwgxZ3/RggK/hxT4RURERHzHWjfx16+/pn8B+P13SEw8cb3QUKhe3YX/unXdrXZtuOACb+rOzOG4w9ww5gb6Xd2PXlf2Oqvgr8DvIQV+EREREf+Kj4fVq2H58vRbVBQkJ5+4njFQqZIL/1de6X4FqFXLdQry4pqA4UuH029mP64pcw2/3PvLWV3Mq8DvIQV+EREREe8dOwYrV8KKFe4XgN9/d18CTv4lAKB4cRf8a9dOv69aFfLl822N1lomrZlEteLVjrfsPHDsAAXDCx4f8nMqCvweUuAXERERyZ0SEmDNGhf+V6xwswJHRsLhw/9eNyTETQpWo4abG6BGDXerVAnCw31Tn7WWthPasu7AOkbdNoqmFZuecl0Ffg8p8IuIiIgEDmtdZ6DISNcRKO1LwKZN/+4OBC7sX345VKvmbtWru/vLL4f8WZ+UP63o2GgajmnI2v1rAehZuydDmw+leMHi/1pXgd9DCvwiIiIigS8uzs0REBWVfluzBrZty3x9Y6BCBdct6ORb6dJnfo1AQnICQxcN5cWfXiQ+OZ4i+YvwerPXuafuPSdc1KvA7yEFfhEREZHgdfSo+yKwbh2sXevu162DzZv/fZFwmogINzwo461SJXdfvHjmXwY2/72Zvt/2Ze7WuQA0LNuQkbeNpEaJGoACv6cU+EVERETOP/HxsGWL+zKwcaO7T7udPG9ARoUKwWWXuVvFiic+vuQSy+T1E3h09qPsjdlLWEgYAxoM4NkbnyUib4QCv1cU+EVEREQko4MH3TUBabfNm9MfZ3bBcJqwMChbFspcdogDtZ5m/QUjsVhK5SvHnv/uUOD3igK/iIiIiJwJa+HAATeR2JYt/77fteukDcosgVYPQOmV8H+cMvCH+b50ERERERE5HWPcGP7ixeGaa/69PC4OduxwFwpv3w7btl3Dlm3LWLnrG7bQ8ZT7VeAXEREREQkA+fKld/pJFwZ0yLLrT8ipF4mIiIiISKBT4BcRERERCWIK/CIiIiIiQUyBX0REREQkiCnwi4iIiIgEMQV+EREREZEgpsAvIiIiIhLEFPhFRERERIJYUAR+49xrjFlkjIk0xmwwxvxojGmbG/YnIiIiIuKVgA/8xphQ4CtgNPCetbYWUA2YC0w1xrzm5f5ERERERLwU8IEfeBNoD4y01k4AsNamWGtfBmYDTxpj7vVwfyIiIiIingnowG+MuQJ4KPXp+5ms8l7q/WvGmAv8vT8REREREa8FdOAHHgMMsMVauyGT5fOAeKAY0NOD/YmIiIiIeCrQA3/L1PsVmS201sYDa1KfdvJgfyIiIiIingrYwG+MKQuUTn26LYtVt6be1zfGGH/tT0REREQkNwjYwA9cluHxnizWS1tWECjrx/2JiIiIiHgukAP/RRkeH8tivYzLivhxfyIiIiIingvzuoBsKJDhcUIW68VneFzQH/szxtwP3J/6NM4Ysyaz9c7RhcBhD/dxLtue7TbFgANn+R6SM/9v+JvXNfvj/XP6PXJqf+e6H39sp8+Ac+P1v6dz4XXNgfgZkFP7VBYIPpVPtSCQA39shsfhWayXcVnsKdfKwf1Za0fjJu7CGDPaWnt/Zuudi5zYX3b2cS7bnu02xpjl1tp6Z1/d+S2n/1/zB69r9sf758bPgOzsxx/b6TPg3Hj97+lceF1zIH4G5NQ+lQWCjzFm9KmWBfKQnv0ZHufPYr2Myw76cX9ppp/BOmcjJ/aXnX2cy7Y5/WcgmQvEP2eva/bH++fGz4Ds7Mff28mZC8Q/Y69rDsTPgJzap7JA8Dnln7Gx1vqzkBxjjLkY2JX6dIi1dtAp1hsPdMWdjY+w1qb4Y39y7vStXuT8ps8AEdHnQM4K2DP81trdwM7Up+WzWLVc6v3SrMJ5Tu9PsuWUP0mdK2NMvpzep4j4TI5/BohIwDnnzwEd8/8tYAN/qhmp93UyW2iMCQNqpz49k5+Scnp/cg5Sr4HIEcaYksaYd4GpObVPEfGts/kMMMZUNMZ8Zox50RgzIvVxcV/WJyK+dy5ZQMf8Uwv0wJ/2P0M1Y0z5TJY3wnXfiQM+9WB/4iFjzG3A48BDgL7tiwQZY0xF4FdglrX2OWttX2Az8JMx5gJvqxMRf9IxP2sBHfittauAMalP+2WyykOp9y9ba49fYGuMedYY848xZlRO7E9yJ2vtt9baJ4DdXtciIj7xLu56qvEZXnsbqABkeh2WiAQnHfOzFtCBP9XDwDzgYWNMZwDjDADaAF8AQ07a5kngAuA/xpiTJ886l/1J7pbodQEi5zNjTFFjzKU5vM+LgduAH22G7hPW2iPAcqBX6jBMETm/6JifiYAP/Kkf7i2B/sATxpiVQCTQFuhmre1urU0+abNhQAww1lr7dw7sT/DNQV1EApcxprAx5kVgG9D0NOsaY8y9xphFxphIY8wGY8yPxpi2p9ikAWCAjZks24ibtKd6duoXkZylnOCdgA/8ANbaRGvtKGvt1dbaOtbamtbaG62140+x/iBrbYS19u6c2N/5zscHdREJMMaYC4wxT+M+E57F/aKa1fqhwFe466jes9bWAqoBc4GpxpjXMtmsbOp9ZjNxpr1W8RzKF5EcppzgvaAI/OINPx3URSTwtAUmAS3OcP03gfbASGvtBABrbYq19mVgNvCkMebek7ZJmwQxIZP9xafeR5xV1SKSo5QTcg+Nb5TsSDuof4/rlHE6aQf19zMe1IGXjTE34A7qG6y1n2TcyBhTFtcd6UxstdZmFgBExE+stf8Dd6budOsaY64gvSHC+5ms8h5wC/CaMebL1GGXkH4WPzyTbdJeiznjokXEF/ySE+T0FPjlnPnpoA7wGa4l6pmoCUSd4boi4kPWWnsGHw+P4cbib7HWbshk+TzcGftiQE9geOrraZ04imayTdprm8+qYBHJUX7MCXIaGtIj2ZaxQ0YWzvagnnH/ja215gxvCvsigaVl6v2KzBZaa+OBNalPO2VY9DPuM6NSJptVBv7IsJ2IeMjXOUFOT4Ff/OVcD+oiEqRSh+uVTn26LYtVt6be1087U2itPQx8BzQ+aZ8FgauBz1OHAohIYFBO8CEFfvG57BzUc0gEmY/zFRFvXZbh8Z4s1ktbVpD07jwATwMljDFdMrz2CBCNGwssIgEgh3OCjvmZUOAXf8juQf2cGGMaG2OG48bz1jfG/NcYUy+7+xWRHHNRhsfHslgv47LjkyVaa9cB1wNdjTFvGmPex/Xev9Zam1m7ThHJnbKdE3TMz5ou2hV/ONeD+o7svKm19kfgR+DB7OxHRHwmY/etrLprxWd4XDDjAmttJNAhJ4sSEb/Ldk7QMT9rOsMv/pDtg7qIBKXYDI+z+gk+47LYU64lIoFKOcHHFPjFH3RQF5HM7M/wOP8p1zpx2UEf1SIi3lFO8DEFfvEHHdRFJDMZ++SXzGK9tGWxwE7flSMiHlFO8DEFfvEHHdRF5F+stbtJ/7dePotVy6XeL1WrTZGgpJzgYwr84nM6qItIFmak3tfJbKExJgyonfp0uj8KEhH/Uk7wPQV+8Rcd1EUkM6NT76sZY8pnsrwR7oK+OOBTP9UkIv6nnOBDCvziLzqoi5xnjDGFMzzN9EI8a+0qYEzq036ZrPJQ6v3L1lqN2RUJXsoJPqTAL9mmg7qInMwYEwL0zfBSe2PMqS7GexiYBzxsjOmcur0xxgwA2gBfAEN8Wa+I+I5ygvcU+CVbdFAXkZMZY94C9gEvZ3i5JbDfGLPGGJMn4/rW2iOpy/sDTxhjVgKRQFugm7W2u7U22S/Fi0iOUk7IHYy11usaJEClHtR74qaxzigGN/tdXWttwknbhAP3AfcCeYBQIBoYaa0d7/OiRURExC+UE3IPBX4RERERkSCmIT0iIiIiIkFMgV9EREREJIgp8IuIiIiIBDEFfhERERGRIKbALyIiIiISxBT4RURERESCmAK/iIiIiEgQU+AXEREREQliCvwiIiIiIkFMgV9EREREJIiFeV2AiIicv4wx/YB+p1ltl7W2qT/qEREJRgr8IiLipWJAldOsk88fhYiIBCtjrfW6BhERERER8RGN4RcRERERCWIK/CIiIiIiQUyBX0REREQkiCnwi4hIrmGMCTXGdDXG9PW6FhGRYKHALyIiuYIxphSwBCgOjEx9La8xZoAxZqMxJtoYU9HTIkVEApC69IiISK5gjPkSuMha2yz1eQ1gIlA9dZWNwJXW2hiPShQRCUg6wy8iIrlFOaCSMaaYMaY57mx/dSAZ+By4XmFfROTs6Qy/iIjkCsaYK4GhwFVAIhAFLAI+tNZu87I2EZFAppl2RUQkV7DWrjDGjMGF/R7W2v1e1yQiEgwU+EVEJFcwxnQDOgKtrbUJXtcjIhIsFPhFRMRzxpibgP5AU4V9EZGcpTH8IiLiKWPMxcBCXNjXWH0RkRymLj0iIuK1scDrCvsiIr6hwC8iIp4xxnQFSgCjva5FRCRYKfCLiIgnjDEhwP8BL1lrUzwuR0QkaCnwi4iIV1oARYEpXhciIhLMFPhFRMQrXYB51tokrwsREQlmCvwiIuKVG4D1XhchIhLsFPhFRMTvjDHhQEVAZ/dFRHxMgV9ERLxwQep9I0+rEBE5D2jiLRER8TtjjAGOAgWAz4APgZ1APHDIWhvvYXkiIkFFgV9ERDxhjPkIuO8Ui/8APgZesdYm+q8qEZHgo8AvIiKeMMYUBJ4DOgGXAuGZrPaStfZZvxYmIhJkFPhFRCRXSb2gtzLwCfCPtfZmj0sSEQloYV4XICIiklHqEJ61xpiZQBGv6xERCXTq0iMiIp4zxjxvjJlsjKltnKa48f3veFyaiEjA05AeERHxVOpY/qMZXooHkoFu1tpp3lQlIhI8dIZfREQ8Za2NAd4EjgD7gAlAbYV9EZGcoTP8IiIiIiJBTGf4RURERESCmAK/iIiIiEgQU+AXEREREQliCvwiIiIiIkFMgV9EREREJIgp8IuIiIiIBDEFfhERERGRIKbALyIiIiISxBT4RURERESC2P8DzFoqBdqF9CYAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(figsize=(12,7))\n", "axes.plot(zeta_bars, -1000 * 100 * np.real(j1s), 'b', linewidth=2, label=r\"$J_{12} = 0.01\\, \\epsilon$\")\n", "axes.plot(zeta_bars, -1000 * 10 * np.real(j2s), 'r--', linewidth=2, label=r\"$J_{12} = 0.1\\, \\epsilon$\")\n", "axes.plot(zeta_bars, -1000 * 2 * np.real(j3s), 'g-.', linewidth=2, label=r\"$J_{12} = 0.5\\, \\epsilon$\")\n", "\n", "axes.set_xscale('log')\n", "axes.set_xlabel(r\"$\\bar\\zeta$\", fontsize=30)\n", "axes.set_xlim((zeta_bars[0], zeta_bars[-1]))\n", "\n", "axes.set_ylabel(r\"$j_{\\mathrm{ss}}\\; /\\; (\\epsilon J_{12}) \\times 10^3$\", fontsize=30)\n", "axes.set_ylim((0, 2))\n", "\n", "axes.legend(loc=0)\n", "#fig.savefig(\"figures/figHeat.pdf\")\n", "pass" ] }, { "cell_type": "code", "execution_count": 16, "id": "1f6c6438", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.7.0.dev0+b71625e
Numpy1.21.2
SciPy1.7.1
matplotlib3.5.0
Cython0.29.25
Number of CPUs6
BLAS InfoINTEL MKL
IPython7.29.0
Python3.9.7 (default, Sep 16 2021, 13:09:58) \n", "[GCC 7.5.0]
OSposix [linux]
Thu Dec 30 17:02:38 2021 CET
" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] }, { "cell_type": "code", "execution_count": null, "id": "5a88460e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,md:myst" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 5 }