{ "cells": [ { "cell_type": "markdown", "id": "d295a8ae-fdbb-4151-bf34-92f2b74e34d8", "metadata": { "tags": [] }, "source": [ "# Environment Dynamics\n", "\n", "An example on how to compute the dynamics of a gaussian bosonic environment using the OQuPy package.\n", "\n", "- [launch binder](https://mybinder.org/v2/gh/tempoCollaboration/OQuPy/HEAD?labpath=tutorials%2Fbath_dynamics.ipynb) (runs in browser),\n", "- [download the jupyter file](https://raw.githubusercontent.com/tempoCollaboration/OQuPy/main/tutorials/bath_dynamics.ipynb), or\n", "- read through the text below and code along." ] }, { "cell_type": "markdown", "id": "12128a31", "metadata": {}, "source": [ "First let's import the necessary packages" ] }, { "cell_type": "code", "execution_count": 1, "id": "557f8f8b-10c1-4797-9092-6062dfdccf73", "metadata": { "tags": [] }, "outputs": [], "source": [ "import sys\n", "sys.path.insert(0,'..')\n", "import oqupy\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "edf53a96-c6c8-482e-aea6-ed126754652a", "metadata": { "tags": [] }, "source": [ "and define the necessary spin matrices for convenience" ] }, { "cell_type": "code", "execution_count": 2, "id": "aad71653-f73f-4c3b-8910-4e10b57bbf2e", "metadata": { "tags": [] }, "outputs": [], "source": [ "spin_down = oqupy.operators.spin_dm(\"down\")\n", "s_z = 0.5*oqupy.operators.sigma(\"z\")\n", "s_x = 0.5*oqupy.operators.sigma(\"x\")" ] }, { "cell_type": "markdown", "id": "acdfcb0f-004e-43ab-ab6a-7b3e8c3e5e3f", "metadata": {}, "source": [ "## Example - Heat transfer in a biased spin-boson model\n", "Let's try and recreate a line cut of Figure 2 from [Gribben2022b]([Quantum, 6, 847 (2022)](https://doi.org/10.22331/q-2022-10-25-847) / [arXiv:2106.04212](https://arxiv.org/abs/2106.04212)). This tells us how much heat has been emitted into or absorbed from the bath by the system and how this transfer is distributed over the bath modes." ] }, { "cell_type": "markdown", "id": "90641216-6ff9-434f-b21d-6870ccb3254f", "metadata": {}, "source": [ "### 1. Hamiltonian - Biased spin-boson model\n", "The system Hamiltonian we consider is:\n", "$$H_S = \\epsilon s_z + \\Omega s_x$$\n", "describing a spin-$\\frac{1}{2}$ particle with energy splitting $\\epsilon$ and transition frequency $\\Omega$. Here $s_i = \\sigma_i/2$ where $\\sigma_i$ are the Pauli matrices.\n", "\n", "The interaction Hamiltonian is given by:\n", "$$H_I = {s_z} \\sum_k g_k \\left(a_k+a_k^\\dagger\\right),$$\n", "and the bath Hamiltonian by:\n", "$$H_B = \\sum_k \\omega_k a_k^\\dagger a_k.$$\n", "This describes a linear coupling to bosons of frequency $\\omega_k$ with strength $g_k$. These bosons are described by the ladder operators $a_k$ and $a^\\dagger_k$ which satisfy the canonical commutation relations:\n", "$$ \\left[a_k,a_{k'}^\\dagger\\right]=\\delta_{kk'},$$\n", "$$ \\left[a_k,a_{k'}\\right]=\\left[a_k^\\dagger,a_{k'}^\\dagger\\right] = 0.$$\n", "We can characterise the bath entirely by its spectral density:\n", "$$ J(\\omega) = \\sum_k |g_k|^2 \\delta(\\omega - \\omega_k) = 2 \\, \\alpha \\, \\omega \\, \\exp\\left(-\\frac{\\omega}{\\omega_\\mathrm{cutoff}}\\right) \\mathrm{,} $$\n", "where we have decided on an Ohmic spectral density with dimensionless coupling strength $\\alpha$ and high-frequency cutoff $\\omega_c$.\n", "\n", "Also, let's assume the initial density matrix of the spin is the down state\n", "$$ \\rho_S(0) = \\begin{pmatrix} 0 & 0 \\\\ 0 & 1 \\end{pmatrix} $$ and the bath is initially in thermal equilibrium at $T=\\Omega$.\n", "\n", "For the rest of the parameters we choose to set:\n", "\n", "* $\\epsilon = 2.0 \\Omega$\n", "* $\\omega_c = 10.0 \\Omega$\n", "* $\\alpha = 0.05$" ] }, { "cell_type": "markdown", "id": "9af12897-6c75-434f-ad92-57472749e29f", "metadata": {}, "source": [ "### 2. Building the process tensor\n", "\n", "The setting up of the system and general running of TEMPO/PT-TEMPO has been covered in detail in the previous tutorials so for now let us go right ahead and build a process tensor for this spectral density. Here we'll use much rougher convergence parameters than in the paper, the qualitative result is not really changed though." ] }, { "cell_type": "code", "execution_count": 3, "id": "46477052-8b66-4441-8529-6e8d9e2a191c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--> PT-TEMPO computation:\n", "100.0% 100 of 100 [########################################] 00:00:00\n", "Elapsed time: 0.5s\n" ] } ], "source": [ "Omega = 1\n", "alpha = 0.05\n", "w_cutoff = 10 * Omega\n", "epsilon = 2 * Omega\n", "tcut = 2.0\n", "epsrel = 1e-5\n", "final_t = 20\n", "delta_t = 0.2\n", "initial_state = spin_down\n", "corr = oqupy.PowerLawSD(alpha, 1, w_cutoff, temperature = 1)\n", "pars = oqupy.TempoParameters(dt=delta_t, epsrel=epsrel, tcut=tcut)\n", "system = oqupy.System(Omega*s_x + epsilon*s_z)\n", "bath = oqupy.Bath(s_z, corr)\n", "pt = oqupy.PtTempo(bath, 0.0, final_t, pars)\n", "pt = pt.get_process_tensor(progress_type='bar')" ] }, { "cell_type": "markdown", "id": "4b1b995d-57ae-4c33-b73e-ef74c9a187c7", "metadata": {}, "source": [ "Now as we saw previously the process tensor can readily be used to calculate system dynamics, for example let's look at how the density matrix elements evolve." ] }, { "cell_type": "code", "execution_count": 4, "id": "b9b0eab6-f1e0-4a8d-b10d-cf05f63a94fb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--> Compute dynamics:\n", "100.0% 100 of 100 [########################################] 00:00:00\n", "Elapsed time: 0.1s\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dyns = oqupy.compute_dynamics(\n", " system=system,\n", " initial_state=initial_state,\n", " process_tensor=pt)\n", "times, states = dyns.times, dyns.states\n", "plt.plot(times, states[:,0,0].real, label=r'$\\rho_{00}$')\n", "plt.plot(times, states[:,0,1].real, label=r'$\\Re[\\rho_{01}]$')\n", "plt.plot(times, states[:,0,1].imag, label=r'$\\Im[\\rho_{01}]$')\n", "plt.xlabel(r\"$\\Omega t$\")\n", "plt.ylabel(r\"Amplitude\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "095087e0-859f-45fa-a95a-3c741398ba1b", "metadata": {}, "source": [ "Already the process tensor tells us everything we could want to know about the system but actually we can infer a lot about how the bath behaves as well.\n", "\n", "### 3. Bath dynamics\n", "\n", "In [Gribben2022b] we can see that for linearly coupled Gaussian environments the bath dynamics can be calculated through relatively simple transformations of system correlation functions. For example the change in energy of mode $k$ can be expressed as\n", "\n", "$$ \\omega_k\\left\\langle a_k^\\dagger (t) a_k (t)-a_k^\\dagger (0) a_k (0) \\right\\rangle = \\omega_k g_k^2 \\int_0^t dt' \\int_0^t dt'' \\left\\langle s_z(t')s_z(t'')\\right\\rangle F(\\omega_k, t', t'', T), $$\n", "with\n", "$$ F(\\omega, t', t'', T) := \\cos[\\omega (t'-t'')]-i \\sin[\\omega(t'-t'')]\\coth(\\omega /2T). $$\n", "\n", "However we typically take the continuum limit in which case the coupling to any single mode becomes infinitesimal and it makes more sense to talk about how heat is exchanged within a band of modes $(\\omega-\\delta/2,\\omega+\\delta/2)$. This gives us the expression:\n", "\n", "$$ \\Delta Q (\\omega,t) = \\int_{\\omega-\\delta/2}^{\\omega+\\delta/2}d\\omega' \\omega' J(\\omega') \\int_0^t dt' \\int_0^t dt'' \\left\\langle s_z(t')s_z(t'')\\right\\rangle F(\\omega', t', t'', T),$$\n", "$$ \\Delta Q (\\omega,t) \\approx \\omega J(\\omega)\\delta \\int_0^t dt' \\int_0^t dt'' \\left\\langle s_z(t')s_z(t'')\\right\\rangle F(\\omega', t', t'', T),$$\n", "where $\\left\\langle s_z(t')s_z(t'')\\right\\rangle = \\mathrm{Tr} [s_z(t')s_z(t'')\\rho]$ and we have approximated the integrand as constant over the bandwidth. The validity of this is reliant on the system relaxing much faster than the timescale set by $\\delta^{-1}$.\n", "\n", "To be compatible with PT-TEMPO we must now discretise this expression according into timesteps, a rough discretisation can be expressed as:\n", "$$\\Delta Q (\\omega,t_N) \\approx \\omega J(\\omega)\\delta \\sum_{k=0}^{N-1} \\sum_{k'=0}^{N-1} \\left\\langle s_z(t_k)s_z(t_{k'})\\right\\rangle F(\\omega,t_k,t_{k'},T) \\, dt^2.$$\n", "Here $dt$ is the same timestep set as the convergence parameter in PT-TEMPO and we have defined timesteps $t_k = k dt$. In practice this discretisation breaks down at large $\\omega$, the actual implementation does something slightly more sophisticated which will be detailed elsewhere.\n", "\n", "To calculate this in OQuPy we begin by initialising a `TwoTimeBathCorrelations` object from the `bath_dynamics` module:" ] }, { "cell_type": "code", "execution_count": 5, "id": "51429960-28a3-47b8-8eb2-f92611294daa", "metadata": {}, "outputs": [], "source": [ "bath_corr = oqupy.bath_dynamics.TwoTimeBathCorrelations(system, bath, pt, initial_state)" ] }, { "cell_type": "markdown", "id": "a6111f16-bd3f-4645-875e-197f8af44394", "metadata": {}, "source": [ "As inputs this requires everything necessary to calculate the system correlation functions:\n", "* `system`: the system Hamiltonian.\n", "* `bath`: characterises bath containing information about its spectral density and temperature.\n", "* `process_tensor`: the process tensor which when combined with the system Hamiltonian can be used to calculate any system correlation function.\n", "* `initial_state`: the initial system density matrix which must be either built into the process tensor or input here.\n", "\n", "We can now use the method `occupation` to calculate the energy dynamics of a particular mode by multiplying the output by its frequency, in this case let's look at `w = Omega` and a bandwidth of `delta = 0.1 * Omega`:" ] }, { "cell_type": "code", "execution_count": 6, "id": "58c0cbf3-b214-4070-99e4-b3b18b844a8e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--> Compute correlations:\n", "100.0% 100 of 100 [########################################] 00:00:04\n", "Elapsed time: 5.0s\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Delta Q ( \\\\Omega, t)$')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = Omega\n", "delta = 0.1 * Omega\n", "tlist, occ = bath_corr.occupation(w, delta, change_only = True)\n", "energy = w * occ\n", "plt.plot(tlist,energy)\n", "plt.xlabel(r'$\\Omega t$')\n", "plt.ylabel(r'$\\Delta Q ( \\Omega, t)$')" ] }, { "cell_type": "markdown", "id": "3d876074-7492-4f05-b2fb-70372946ba2b", "metadata": {}, "source": [ "...that took quite a while. From the expression for $\\Delta Q$ is would seem that to calculate the change in energy of the bath up to time $t_N$ requires the $N^2$ two-time system correlation functions. In fact we only need the $N(N+1)/2$ time-ordered correlation functions due to $\\left\\langle s_z(t_{k'})s_z(t_{k})\\right\\rangle = \\left\\langle s_z(t_{k})s_z(t_{k'})\\right\\rangle^*$. However, this can still be quite time-consuming to calculate, but let's see what happens if we want the energy of another mode now, let's say `w = 2 * Omega`" ] }, { "cell_type": "code", "execution_count": 7, "id": "c86048d1-2212-4fc6-8ef0-632ea2639670", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Delta Q (2 \\\\Omega, t)$')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = 2 * Omega\n", "delta = 0.1 * Omega\n", "tlist, occ = bath_corr.occupation(w, delta, change_only = True)\n", "energy = w * occ\n", "plt.plot(tlist, energy)\n", "plt.xlabel(r'$\\Omega t$')\n", "plt.ylabel(r'$\\Delta Q (2 \\Omega, t)$')" ] }, { "cell_type": "markdown", "id": "9325b043-269f-4a6b-a1f6-b74037aa6d1c", "metadata": {}, "source": [ "Much quicker! This is because the same set of system correlation functions can be used to compute any bath correlation function $\\langle \\alpha_2(t_2)\\alpha_1(t_1)\\rangle$ where $\\alpha_2, \\alpha_1 \\in \\{a_k^\\dagger,a_k\\} $ and $t_1,t_2 < t_N$. So now we see the logic of having a bath_dynamics object, it allows us to conveniently store the calculated system correlation functions and re-use them as we like :)\n", "\n", "### 4. Recreating Figure 2\n", "\n", "Now we have all the tools necessary to recreate the study of total heat exchanged as a function of $\\epsilon$. However, this would take a while as we would need a new set of correlation functions for each $\\epsilon$. Here we will just look at the case where $\\epsilon = 2\\Omega$. We are only interested in the total heat exchanged over the process so simply look at the final value of $\\Delta Q$." ] }, { "cell_type": "code", "execution_count": 8, "id": "96b8d7aa-c279-4107-85c5-8ebfb01476ce", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Heat Exchanged$/\\\\Omega$')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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A0+lEU1NT0u1NTU2orq7WXVNdXW16PPuv2THDhg0DAEyYMIF/3+v14ogjjsDu3bt179fr9aK4uDjpi8huWPUqz+3kFSTFRyVSwYpXjIoTg57tmtyZwb3A64LTIXFxJzoup1sVUipJ7JzE24Tq82zupAoWQRCEXXJWYHk8HkyZMgVr1qzht8ViMaxZswb19fW6a+rr65OOB4DVq1fz42tra1FdXZ10jN/vx/r16/kxU6ZMgdfrxfbt2/kx4XAYX375JUaPHp2xx0cMLrw9WOTht9mpYKlT3AEoSe6iHqygUsEC4q1CQFxg9XCB5kRRQiDaaRN2J7UIqYJFEARhF9dgn0BfWLhwIebMmYOpU6fipJNOwoMPPohAIIC5c+cCAGbPno3hw4dj6dKlAIAFCxbg9NNPx3333YeZM2fi2Wefxfvvv4/HH38cACBJEq6//nrcfffdGDt2LGpra3H77bejpqaG51wVFxfj2muvxR133IGRI0di9OjR+PWvfw0AuOiiiwb+SSD6BR7RkGgPAvZM7uoMLADweRT/lizLkFhZyQBewfKoKmABpXVoRTdvMbpQ5HPD3xuxFdWgTo0nDxZBEIR9clpgXXzxxWhpacHixYvR2NiIyZMnY9WqVdykvnv3bjgcSpHulFNOwcqVK7Fo0SLcdtttGDt2LF588UVMnDiRH3PzzTcjEAjgmmuuQXt7O6ZNm4ZVq1bB5/PxY37961/D5XLhyiuvRE9PD+rq6vDaa6+hrKxs4B480a9oDe6AEtMg1CJkFaxE9Yh5sGIyEIrGuFgzglewvJoKluDAZ7YLMM/jRHGeG/vae+C30SJMqmB1UgWLIAjCLjktsABg/vz5mD9/vu733njjjZTbLrroItNKkyRJWLJkCZYsWWJ4jNvtxr333ot7773X9vkSuYE2ogFQ2nxiFazEHEKfO2ktEN8JaCWwdCtYsG9yL/A4uQ/MVgVL7cGiChZBEIRtctaDRRD9iVkFSyRotKs3uYLldkpwOuJtQZEKmHoXIRD3UgHiHiw2xzDP40JxXlzk2TK5h9Qm9yBiMUpzJwiCsAMJLILQoVXHg2WvghUXM6x6JEkSz8ISEVg8Bysh0PLtmtzDikArTlTR7Jjc1TEN0ZiMA4GQ8FqCIAiCBBZB6HIg0McKlmYXIQBVmrtAErymgpVvs0XIhFi+x4niPPstQm2cBBndCYIg7EECiyB0aO1iFSzFg8WT3NPwYMXXi2dhGVWwAqIm95Bici9Ko4KlrZRRFhZBEIQ9SGARhA6tnSwHS9Ui5Gns4qNymAcrvl68RWhYwQrbM7nnJ5nc7e8i9CREJWVhEQRB2IMEFkFo6A1HecxCRYE6B4sJJPs5WIC9NHftLsICJrCEK1hsFqHa5G6nghVfP7o8HwC1CAmCIOxCAosgNLAdhB6ng/uXAFUFKyLuwVILLG6SFxJYyTlY+V57JvckDxZvEdqvYNVWFACgChZBEIRdSGARhAbmvxpS6ElKXGcVrHRysAB7Jne1QFL/167JvcCbpsldI7DsZmFFYzKih0C0Q284ijv/thVrd7QO9qkQBJFjkMAiCA3cf6XaQQiID3uWZVnZRajyYNkxuSuzCNOLaeAmd7fLdkyDLMtcyI1hAstmmvulv/sPTlv2elLcQy7y1mctWPHul7hv9WeDfSoEQeQYJLAIQoMS0eBJut0rOOw5GIkhHI1Xb5JahDZM7loPlt0KVk9IJwdL0OQejMTAik9jhrAWoXgFKxaTsWFXG/a19+DdLKj8tHYFcf/qz7Cvvcf2WiYs27vTywFb+0UrPt7bkdZagiByGxJYBKFBiWhIr4LFDO6SpAgkAMhzp1HB8ia3CEViGmRZ5qNu1DlYPeEowlHx9iSgtAhbu4KICKxl98N447MWoTX9ydPrvsJDaz7HE+/ssr22LRGw2pVGJa69O4TZf9iAOSs2QJZzv11KEIQ9SGARhIYWnYgGQKlAWVWwmP+q0OOCw6F4uJhJ3sqDFW/RaStYikiyIhiJgV3P8zzOpDalyLgcViXzuByoLPLC6ZAQkyGc5q5uC765vWXQxcWu1gAA4GAaafRcYNnYIMBo7gwiEpPRFggJ+e4Igji0IIFFEBrYLsIhBZoWoeCoHL0Ud0AxuVvtIgxFY4gkenSpFSwRgaT8/HyPCy6ng4ssEaO72mDvcEioTAhN0TZhQHX/+9p78EVLl9C6/mJPWzeA9KpQ7LUQCEVtm/Y7VM+1nZBXgiAODUhgEYQGdlEdqqlgeQU9VHoZWAD4LEKrKpQ66yrfzYY9JypYAiZ3dQWKDZjmYaMCF3pt9UwRWGJGd60IfGP74LYJ9x6MC6yAoH9NTZuq6mV3fUe3SmDZ2MFJEMShAQksgtBg5MESHfasCCx30u1et5iHi13IvS4HXM74nyivYIUili23Hk3Eg/pcRIzuPKQ0sb6y2AdAvIKl3en45iD6sLpDEf777BIMaVWjFlh224TqClYHCSyCOOwggUUQGlgFK8XkLlzBSniwvJoWITe5mws0JcNKWc/EUky2FngBTQUKgJKFJVDB0gq0quL48yCahcUqWKxqtn5nm/DuRyOCkSi2Nfptr9t7UNk5mE5khNp3ZrfF2NcWYTQmC1UsCYLITkhgEYSKSDSG9kRrZ4gmpkFJchfzYKW0CEUrWEElYoGRrxJLVllY2goUAB7VIDIuJ8AztBICq4hVsARbhIn7HzesGCPK8hCKxvCfnQeE1hpx8/99hLMefBvrvrD3c5j/CrAvsGIxOckYL7JBQE2SwLIxB5Ix98n3cPLSNVT9IogchQQWQajoVokfrUBiSe6hSMy0TWfowRKsgGk9UADgdEj8/q2Egl6LkM0jFLnQswwtVkGrYi3CTsEWYaIVV+h14fSjhgLomw9rf0cP/vZhAwDgs6ZOW2vVFSy7FSh/b5hvNkhnfV9bhBu/bENHTxg7mu09ZoIgsgMSWAShIqhq33mcyX8eTOAA5lUspYKV7MHKs1vB8jqTbudGd0GBxu4PSM/krniw7Jncu1QVuDOOrgQQF1jpxjU8994eHnxqV+RoK1h2zkEbS2HXg+XvSd/kHo3JvJLIPGQEQeQWJLAIQgUb5Ox1OZLmEAJKiw9IFmJajDxYojlYehUsQBFMfatg2YhpYC3CRAVL1IPFWpQFHhfqvzYEbqeE3W3d+PJAt8XKVCLRGJ7dsIf/226bb89B5T5jstgcSEabVmAF7YmkvlSw1GJOex4EQeQGJLAIQgWrTKmrVQyXQwLLDe2NGFeRjFuEYknugVCqBwuID24GxD1Yat9WEa9gie8iVEzucYF1IBBCSGDQdUBl0i/0unDimHIAwBvbmy3Xanl9ewsaVcLOtsBqSx6PY6cCdkBTOeqTB8umyV19/IEue3MgCYLIDkhgEYQK1r7zup0p35MkSTG6m1awUgc9AzY8WMHUXYQAkCc48Jn5yPRM7rYqWIn7L8t3w+2MK8tWgYs9E0FMEJ5xdNyHlU5cwzPrv4r/rMRjsRu1oK5gqc9NBDaTktGnXYQ2Te5JAosqWASRk5DAIggVrILFxJAWVtkKmlSwjDxYoi1CwwqW4MBnLtB0WoQiVZgeTYtQkiRUFolnYbF5iayCdvpRcR/Wui8OCA26Zuxp6+ai7OITRyV+trhQ6egOp1QT7Yiktq6+ebD60iJU/560lTSCIHIDElgEoYJVpthYHC3KwGdrD5a2RShqctfLwQIUwWLdImQVLFUOFqtgpWFyB5QsLBGjO/dgJSpYR1UVYliJD8FIDOt3tVmuZzz33h7IMnDqkUMwcXgxAHtp6qx6VVHowdBEppm9ClZc2LC28EDmYKkrjeTBIojchAQWQahQm9z1UAY+m1SwLDxY6eRgqf9taXIPp67nQaNCLcLkmAZAZXQXiGrQBp1KkqSKaxDzYYWjMTz3ftzcftlJo/m52BE5bAfhiLJ8vt6OQGPCpqY0DwDQaeO+e8PRpJ2mdgWWuoIl0pYlCCL7IIFFECrMTO7x20UqWPoeLFbBisRkhKPG6412EYqb3HV2EfIKlviw6PykCpadFmFyBQtQ+bAE87D+/UkTWjqDqCj04lsTqvhzaacCxSpYI8vz+bnY8XAxD9boIfnxtTZahFohq55LKII6EDadClZvOIqtDR1pR2MQBNF3SGARhApucjdoEVpVsGIxGV0ho1mEyp+bWRXLKAcrz223RaieRahUgKIx84uuXo7WUBsDn5UKnCIQTzmyAi6HhJ2tAexr7zFaylm5YTcA4HtTR8DjcigVKBsCie0gHFmWl5ZAY96n0UMKANirnrH2IEv66AxGELN43tX4NTENdoXSnX/bipkPvYO3P2+1tY4giMxBAosgVFib3M3H5cSHMcf/Xy8Jnl1wzSpg1hUs+zlYarFnVYlR1qe2CEUqWHoesmKfG8NKxX7Gl60BvP15KyQJuPSkuLm9kFeg0q1g2RdYrHI0utx+BYsJrOrE8ybL4MJbBHUFKxKTbe9C/KI5AAD4aG+7rXUEQWQOElgEoUJpERqY3C2iFpgAcDullDajJEnwuax9WEa7CMVN7olZhG5F4HhcDl6RsvID8fv3pprcm21UsAo0FbhCb1zkWQmVP70Xr16dNnYoRibEjVogiVZz2JickSoPlqhAk2UZB7vjAmsUE1hpVLCGFnn568BOm1C721MbGWEF+x3vbrMf7koQRGYggUUQKoI8Byu9Cpbaf6VNggfEsrCMcrDyRWMadCpYgGJ0t4oM0KuA2ZlHGFAluaspSjweq6iI/+yM7zS84ITh/Db2XERisuWwbSAukPbyCpb9FqG/N4JwNC7kRg1JX2CV5LmVFH0bRvdUgWXPh8XWk8AiiMGDBBZBqLA0uVsIJCV3ya37/TyBNHfjChbbRSga86ARWIJRDcqoHFWLMJGD1d4dNhWH0ZjM259agVjIfWDm98/aY0zUAcliTUQktXQF0RuOwSEBw0ry+HMnanJn6ekFHicqEhEPXTaqZ0xgFee5UZIQWHaysLS/I7tZWOw51CbZEwQxcJDAIggVVi1Cn2UFS38OIV8vEDZqlYPVI2pydyevV+YRGguUWEzm4i9PE/PARGdLp3G7Sl1d0wpE5kmzqmDpjRpyOiTVLEZrkcSERXWxDx6Xw3YFi/mvhhR6+Vq1eLQiqYLFxhTZ8FExk7srEcJlp0UYi8m82tbQ0SM03oggiMxDAosgVLAWoaHJne0iNLjQKinu+gLLK5CFZZiDlahIWWU59RhUwJR5hMaVFHVlTV0BkyRJyOjOxI/TkepBKxT0QTGRWqypAtrxUbH24AgdD5cIrCVXXuBBvsep2g0oVoXqe4swfizzoGlT5c0IhCJgGxZlGWgQ2LVJEETmIYFFECosTe4J0WA07Nlo0DMjLyHQjFqEkWiMn0O+dhehQAVLlmU+izDFg+WzHpejNtD7NM+BSJq74r9ypnjQeIvQ5P7D0RivEmmrgIWCAhNQQkZHlmkEluBOPl7BKvBAkiRFHAruJFQLrJI88TmQDFbtGpPwf9nxYGl/v+TDIojBgQQWQaiwTnI3H/bcZeHBskpz71bdbujBMhEJwUiMx0TkGZjczS70PaoMLIcjWSBVClSwjAz6gJjJXS1gCjUi1U4Fi2dglcdT2Lk4s+nBKi/wJJ27qNHdn9QitC+wWAVrTEU8g4sEFkHkHiSwCEIFn0VoMezZuIJl7sGymkfYbdJi47sITUSCugKlrYCJmNyNDPaAYnRvNvFgdRm0NwGxFiH7Xp7bCbcz+fHbafPxDCxWwfKk1yIckjC4i1Tf1HCTu8+tCFvBtaGIUsWsZQLLxricTs3vdw8JLIIYFEhgHQY8995u/PE/Xw32aeQEliZ3iwpWp4UHy8rkrhY42hYbz8EKRw13szGTucflgFNTgRIxufMdhF4dgcWzsEwqWDpzDBmsqmc204+JP231CoAto7o6ZFR9PqIVKHWLUH3fovMI9VqEorsI1QKJe7D6UMFiz8XhyOvbmvGrVdsspxcQRH9AAusQpzccxW1/3YLbX9piK8fncKXXyuTuMh+Vw3OwDE3u5jEPPQYp7oAieqImWVBKCnyqQBKpYPXoRDQwRLKwtIOe1ShVIOP7N/OwKSLJvM0XicbQ0B4/R6VFmN4uQtYiLPSJhaQyOvrQIvSrstQqEyOKWm2Y3LW/38O5RXjn37bif974Apt2H7S9dkdzJ361ahvau+3PgiQI4BAQWI888gjGjBkDn8+Huro6bNiwwfT4559/HuPGjYPP58Oxxx6LV199Nen7sixj8eLFGDZsGPLy8jB9+nR8/vnnuj8rGAxi8uTJkCQJH3zwQaYeUkZp7w4jGpMhy/Y8IIcr1iZ38wqUlQfLKgfLaA4hAOSrZgMaGd27dcbcMJSYBOPXAU+B1xFolSImd4MUd8CeB6tIpwKm+KjMRc7+jl5EYzI8Tgdvayom96jQTEAmaMoL0/NgZaKCVeRzYUhB/Dk/2B0SnmXInl/WXtx9wJ7AavL34vYXt2RNa7EtEEpr4HUsJnOhbafFynjk9S/wP298gRc377O9liCAHBdYzz33HBYuXIg77rgDmzZtwnHHHYcZM2agublZ9/i1a9fi0ksvxbx587B582bMmjULs2bNwpYtW/gxy5Ytw0MPPYTly5dj/fr1KCgowIwZM9Dbm/qp/eabb0ZNTU2/Pb5MoH5TpwqWNdYmd4sKVmIbv55AiK83F2hGcwgBwOV0wJM4LyOju5lAstMi1BNIlQmx0tRhFtOQOuiZUeizFin8+dMRqKI+KtYSG16Wx436ak9ct0lEBqMtkTtVkRA4ohETQPy1wX6/6cQ0qKt4rIIWjcm2108YVpy434itMT3PrN+N//3PV1jyyifCa/qLYCSKbz/wFmY8+BYiUXt5Xm3dIYQSa9ptPH5GY+J13mTiOSQIM3JaYN1///24+uqrMXfuXEyYMAHLly9Hfn4+nnjiCd3jf/Ob3+Css87CTTfdhPHjx+Ouu+7CCSecgN/+9rcA4tWrBx98EIsWLcL555+PSZMm4emnn0ZDQwNefPHFpJ/1j3/8A//6179w7733Wp5nMBiE3+9P+hooSGDZg1ewrEblWFaw0jO5m5nMAaX1ZzSPUG/MDaNYIAfLKKQUACoS1ZzOYARhg4udUUgqoIgmszabWIvQ/HXMZhCOKMvjt/ncDjBLmpVAk2VZaREWshahWEgqoPzNSVL8cSgtQns7EIt8bnhcDv5ciLYJWQVsaJGXp9DbaRMycfnm9hZb2V39wRfNAbR2BdHSGcRBmyKpUfVBoD2N6j0Ld7WTQUYQanJWYIVCIWzcuBHTp0/ntzkcDkyfPh3r1q3TXbNu3bqk4wFgxowZ/Phdu3ahsbEx6ZiSkhLU1dUl/cympiZcffXV+N///V/k5+dbnuvSpUtRUlLCv0aOHGnrsfYFtcAS9Z8czvBdhIYmd/MKlt8ypsHcg2UWcwBYD3zuVsUsaCkWyGPqNhF4RT43D9w0anepc7C08CpQKGLY7lLPcjRab/U63psQEyPKlL9NSZKEBVpcQMbPT2tytxrzA6gEktcFh0NKo0UYPz8miJlIEm2TqdePSnjQ7BjdmRAMRWNYvbVJeF1/sL1J+TBqZ9QQEG8Vp7sWUMYT2Z0DCcRF+qf7/ZSif5iTswKrtbUV0WgUVVVVSbdXVVWhsbFRd01jY6Pp8ey/ZsfIsoyrrroK1157LaZOnSp0rrfeeis6Ojr41549e4TWZQISWPbotWgRWg17Zs93aX56OVhWFSwlqkH/d2lewVJ28RkJHLP1TofEW59GLRfFQ2bsAZNl4zad2SxHUZP7noPJGVgMUYHGKhb5Hif/fRXZiGng/qvEa4DFNPSEo0IXXH9vcpuUtQlFfUSdqvWjErsQ7VSw1FWrVz5qEF7XH2xv7OL/b7ea1tihJNjbbRFGYzLaEub2g2mY3P/+8X6c/Zu3cf/qz2yvJQ4dclZgDRYPP/wwOjs7ceuttwqv8Xq9KC4uTvoaKNQCS6S9cbjDKlg+nQoQYL4LMBaT+Y4jVrXQ4rMwuZt5sACVwDKsYBl7oNQCp8vAwxUwMckDQGl+/GJvVBFgFbhCHQ+X1+Xgs/WMjPZd3IOl1yIUM7lrU9yV9WIVLNYaYsIGsOfBYhUg9hpQi0WzDQbKMcltUlZFE62kqNenI7DUv9u3P28d1F102xszVcGy9xjaAiEe2JuOwf6zxk4AwCf7B84OQmQfOSuwKioq4HQ60dSUXMJuampCdXW17prq6mrT49l/zY557bXXsG7dOni9XrhcLhx55JEAgKlTp2LOnDl9f2AZhipY9rA0uZtUsLpUM+CsBJZhDpbJLkJAET6GJnedQc3q+2YmeSOxbTTHkKG0u/QvOgETgSdJkmVgp5kHi1egLMbdaDOwGEpQqXkFjLWGWMgokJ4Hiz1X6sqfiEhglRrW0h1SyCpYYhd6dQWMzWK0syOQtThdDgmRmIx/btXvCIgiyzJWbdmPHc2dttdub1TW2N0FneTBslnBUg/XTmcHIvOLmW0IIQ59clZgeTweTJkyBWvWrOG3xWIxrFmzBvX19bpr6uvrk44HgNWrV/Pja2trUV1dnXSM3+/H+vXr+TEPPfQQPvzwQ3zwwQf44IMPeMzDc889h1/84hcZfYyZQP2mFDCZYUfEsYxpMKlgsZ1aPrfDsAJmFdNgVcFiVRzDChbzcBkIJKtMJu7hshRYRi1C412IgCoqwkDs99Xk3huO8hiJkWXaFqFYBUwbMhpfK17B0gosQOV/ExBoqRUs5sESbRH2rYLFznHGMfEPla98tF94rR7PvbcH1/5xE37y/Ee21vl7w2jog49qf18ElkrM+nuNN3UYwdqLjSahvMShj/67eI6wcOFCzJkzB1OnTsVJJ52EBx98EIFAAHPnzgUAzJ49G8OHD8fSpUsBAAsWLMDpp5+O++67DzNnzsSzzz6L999/H48//jiA+Cfs66+/HnfffTfGjh2L2tpa3H777aipqcGsWbMAAKNGjUo6h8LCQgDA1772NYwYMWKAHrk4tIvQHla7CM0qWNx/ledJ+R5fz0zyaeRgAUCeqMndQKAV57nQ2hW0FFiGFayEr8ho279ZBQsACr1uAD2GFawubnJPrQCKeKj2tfck7t+Z1OIDFNFq3SJMDhlV33e6AouJJZEqTKeBB6s1jRYhC4fdd7AH0Zicku6vBzvHy+pG4e8f78faLw7gQFcwqaInSmtXEEv/sY2fgx0+a0yueNmuYPnTF2etmqrVwe4QjykR4WDid9XRE0ZvOGr4gYs4tMlpgXXxxRejpaUFixcvRmNjIyZPnoxVq1Zxk/ru3bvhcCgXylNOOQUrV67EokWLcNttt2Hs2LF48cUXMXHiRH7MzTffjEAggGuuuQbt7e2YNm0aVq1aBZ9P/I8rm0gSWOTBMiUSjfGRGoYmd76LMFVgsU/JRu1BoG85WPHbLUzuYfMWn5Lmbp6jZXT/7LEZbXtXPFj6663CRv2qkE0tIi0+tf9KO2pI1OTOW4RqgZWGyb1Y9Tqws5OQebjYLkLWIhSNC1C3GKuKffA4HQhFY9jf0ZO0s1KP3nCUv7YnDi/BscNL8PG+DvxjSyOuOHm00P2ruefvn/LH7O8JQ5bllN+LEdubkgWWHZEkyzL2J5nc7fmotO3YtoBNgaX6ANLY0cuHdhOHFzktsABg/vz5mD9/vu733njjjZTbLrroIlx00UWGP0+SJCxZsgRLliwRuv8xY8YYzoXLBsiDJU6vSjQZmtwTwisakxGOxpIGErcnfEklBjsI1T/XMMndwgPFWndGu/CsKlBWUQ1WLcJSC6FgNuwZUIeN6q83bxEmWnyhiOGF2mgHYXy94C7CRCuOCRvA3ixC8xahQAUrqAyKBpQW4QGBFmEsJvPfQZHPBadDwoiyPOxsDWB3W7elwGLPvyTFxfC5k4bh430deOWjBtsCa+0XrXhBlYIeisbQG44Zvra0MP8V84LZEVjxypHy9xwIRVP+Xs3QPtd2s7AOqqqNTX77AsuOECWyl5z1YBFiUItQHHXbzmPwRqwWXtoqltIiNBNYfcvBYpUlowqWlUAq5mZt/YsVE36WJneDFqHZsGdAPa7HoEVoMiybiRxZNm6R7j2YmoHFEI15UFqESkusKNGyDEVihhloDD2BZaeCpRWZrEUospstLj7j/88Emh2jO68gJjK8Zk4aBgBYv6vNdMi3lmAkikV/jU/IuOLkUbw1aUckbUsIrEkjSmyvZf4r9e/AzvqUCpaNCpgsy0nH2/VhtQVCOOWXr+HnL2+1tY7IPkhgHeIkVbAsdl8d7jDB5HE6+IgVLWrhpRVJdlqE6Vaw8i1M7mY5VoDi6zFqEbLqjmEFK9/C5G6S5A6Ye5lkWV19SX0O89xOyzT21s74hY15j5LvO32Tu9q0b7ULUbeCZSPNXZsFxhL02wLW8wjZWrdT4tVWHjbaZu2B0rY3R5Tl4/hRpZDleLaTKI+9uRM7WwMYWuTFTTPG2Q5blWUZnyVahCfWlttaCyg7CIeX5vEPFXaM7trUfDtRDdq8syabAuvDPe3Y39GLv27el9XdEcIaEliHOOTBEkfZQWj8Z+FwSDzqwLCCZdIiZLsIjUbtmI2aAZSBz1Y5WHqjbgAl9NKoRdhj4QEz82CFozF+YTHaxWjmZeoJR7kHTs/DJUmSpVGdhUKW6fwOeAXL4oMGq16oTe4up4P/7qz+jvy6LULrMUVAXFj4uciJrylLnEdMth75ohZnrMVkZychv2+VwD13Unzequhuwl2tAfz29R0AgNvPnZA08FrUC9XcGUR7dxhOh4QTRpUlzk38/YtVsIaV+FTZbeIiibUIWYq+aEQGkCrGGjvsxTyw13BHT1h4PBKRnZDAOoTp1XySohahOTwDy2AHIYMJMO1OQNY2Y2/oerAKVkhlqFcTsPAw5VtkQZkNawbUJneDFp9Fi7DYpBLRrarsGO0iNDO5s9ucDsl4FqOF0Z0LrILU34HIsOikOYSan8GzsCzG5fSlRdgbjiGSeF2wCpbb6eDrraIaOnU2CdgSWGzMTp6yfuaxwyBJwMavDqKh3bwKJssybn9xC0KRGL4+tgLnJVqMZq8bPZj/asyQfAwt8tpaCygp7tUlPv6Bx04Fiwmqo6riu8TtpLkfDCTfT1OnvQqW2iC/o7nL5Egi2yGBdQijfUOyam0c7vRazCFksO9rdwIyk3uxSYtQPSNQz4fV9yR3UZN7eh4uFkGhd7Fios/jdPAqnxazFiETB4Vel6HBlwlHwwpWgFWwdASWgMm9KxhBKJF5pDa5A4o47FuL0KoCFf++Q0quArJ2pVVFQ2+TwEg7HiydClZ1iQ8njo636f5uUcV6/6uDeGdHKzwuB+46fyL/PdptETKBdXR1EV9rJ6ZBXcFSqmd2BFZcyI6tjAssO/MItWLMbtiousq3o4UEVi5DAusQJlVgUQXLDFaRsqpgGQ18Zm/gZiZ3dftRK7BkWVY8WAYVKG5yt6hgGbYIfcatqkhSi8+gRZivXOy0/pBui3MHlKqM3m48s0HPDKuoBfbpv7xAr0XIxJmxQGLVqzy3M6UKZ7UDEoi3SdnvIJ2gUXUKu1pkDikUM7orJnXlvpnAOhAIWb4HaFPkGWeOrwQAfLCn3XT9VwfiIq6utjxp55xdgcUM7kdXFfO1ncGIbtVXD2Ysry7J4xVlq/YqoycU5V7CsVVFAOztImQCi32YsmtyVwu0HZqoCiK3IIF1CMPezNgn4a7E9nZCH6sUdwYTSdoKlogHS+3h6tV4uHrDMb4DLN0KltWoG3ax0btQq6MfrGIa2JZ7NV1B8+oboPZgpV7szCIaGAUmLdJINKb6HaRWsERysPRCRrXrzcblqAWE2qgvWoXxGzwHogOf9Z7DYp+bvybZGCHD++cZXMmvYbZpwKpV1t6tX0EssfD+aWEG96Ori5LORWSWI6DxYNkUd8x/5XE5eHvVjsmdHXtUdVycNfuDtt531S1GqmDlNiSwDmGYJ6imNL6LyGx7OyFmcgcUH5W2giWS5A6oxuVofhdq0ZBnkMOVz2MaUn+PsixbeqiqiuN+lpbO1As1Ox+HZPwc5HucfGBzu8Y03G3hHwPEPFjai7sas3E56guoXhVRpEWozCE0FlhmXkZ2DiyDimG1uYCh3UHIYCnqVq0qvyYFnsF9WAcsBFav/k5YJtAOWrTZWBVXu8nATgUrGpOTBJbHpWwwEBVJbBdhtapF2CHoo2KvgYoCjxKRYceDlXgOxicEVigasyXQkipY5MHKaTIusGKxGHbv3p3pH0ukAXszqir2WW5vJ6wHPTO8BrsIRWIaAOMsLCaa8j1Ow5iIfFXYZur5KxUwowpUVSKN+kAglLQBAlD7t4w9UJIkGUY1WEU0AOo2W+r5s9ZboUkFy6wKxS5MxT4XXDo5ZiLDonnIqF4FSyDNXc9/FT8n5Tkzq2b4VQJNzRBewbLvwQKUNqGV0V2JaUhezypSVrsA2e9AW0G0I7C+OhBAMBKDz61UkOzliIX566u6WGVyt1nBGlLo5UL7YCAkXIViPsDKIi//vbH5mELrVSK2yR8UCqc9FOkNR/H4W19gZxpVvGgimHawOzZpC6wVK1bgrLPOwvjx41FXV4cbb7wR+/btQ0tLC2prazN5jkSa8Df7fDe/6IkkUR9qNPt7cf/qz1C/dA0WPLvZ8DjW8rKaG6aY3BWBFIxEebaVWZI7oFSntALLao5f/HtK9SvVA2W9i680382zvFo07SarHYyMYgPTsBIyau3B0hMpYi1CYx8VuzDp7SCMr43/3N5wDBGD4b16IaP83G1UsLQCi/07EpMNM9AA4yreEMGw0U4DD9UoQaO7nskdUASWdYuw7xUsVr0aW1nEq4B21rPqVbHPhQKvy7bJvVVVxWQVrEhMFo6JaFPtZGWtVTtZWFoRa7eKtWn3QWzefdDWmmzkbx824J5Xt+HX/9xue+2+gz047s5/Yerd/x5UkWVbYEWjUZx//vm49tprkZ+fj+985zs47rjj8Pzzz2P8+PFYtWpVf5wnkQbqcr/oHLZDiQ/3tOP6Zzfj1F+9hofWfI79Hb147dNmw+NFK1g+nXmE7I3fISkXYuP1+rsQRQQKE06RmMx3u2nXe1wOw6G+kiShMtEm1L7pW6W4M4wudsqYHOsKVFcokhKaKWJyN2vzme0gjK9VhYUatMrbzFqEFin0gH4GFhB/TtnvxOxCzQWS1oOVaBFqhxCnrk+eY8gYmUi232MxcFmJadC0CBObBnrDMcMpBIBZBYtlUVmLnG2qHYTKenGBpfiv8pLORbiCxWdReuF1OfnrUbRNyARSeYGHt+TtGN2ZiGai2I7A6g1HccXv1+Pix/5jK3m/v+gNR7HuiwOGH2jM+DzxuK2iQfRgcyiL89yDOnLI9izCBx54AO+99x4++ugjHH300fz2WCyG+++/H9dcc01GT5BIH/WnaTPvyqFGdyiCeU++j3U7D/DbJgwrxif7/egORw3nfLHwT69gBUudg8X8bsV5bsP2Hl9vVMEKsh2AZgJL+V5PKJpkyFciHszPv6rYh70He1LegJWIBvO3BW4a1lawLAY9A0p1Spbjpnr1sUb+IzWFJllWZiGjQPz35nZKCEdlBIIR3Vauuck9UX0TqGBpK0CSJKHY58LB7jA6esKoLtEfHGxUxROvYOmvF83C6uzRF3hFXhefCXiwO8TFi5aDPAuu7xWscSqBpXjYrN+/1P4r9bmIe7BYyGj8OS8rcKMrGEFbIIhagZmCbQFlowU7h0bBqIaekDJs+8Qx5djd1o0vbAisls4g/zv+v0178d9nHCm8tj94+LXP8cjrX+Cu84/BlfVjbK39sjUAwDqaRA8msqt1JjoMJLYrWE8++SSWLVuWJK4AwOFw4MYbb8Tdd9896H1PIo6ewLKbhfX+l2147M0vLEd0ZBNbG/xYt/MAXA4JF5wwHH+bPw1/uuZkAPHevLbywxA3uadWsNinY7OIBkZeYr22VWQ1xw+Ih06yFp+2CqP2UJlRxStYydUQqx2IDKOLpdWYHyD+3DKTvHZHmF5IphazDwpWLUL1eqNK7gGdMTkMIQ+WiQ+P7yQ08dQYxSSIxjR0Wpjc97R1m/4tG92/2nunDdJUY7yLkL1mrAUSq2AdVaUWWOlUsBICy2T6gB78NZB4zlm7WDTNnVVSy/OVFmGzYNgo+5DgdkqYPDI+g9FOBUv9+nj+/b2Dfi1+67NWAMAXLQHba1nkR2uXvV2YQOprYLCwLbC++OIL1NXVGX7/pptuQixmvxxIZB51u0Lxj9gzTN7x8lYs/cc2bMqhnj4zbx9ZWYj7vzcZx44oSan86CFucme7CFUCi11YTVLcGT6LCpaVwOHzCDUigY/JsVhfWaTvCxG9f2X0iH7OmplAlCTJUKiYDXpmmJrcLVqEACxH7XCTu06L0JYHS6eKpoS8Gv8NGlWg1LvZzLKgjNYPK/XB6ZAQjMRSvHeM+Jge/RYhoGq1mVSCDhoJLJP8NDW94SivXIxLs0XY6FdS3LX3LfJBkbVhhySElWj1EIg/h8o0ATevoIhWsNQt1q8lQk4/tyOwVL+bXa0BbNjVJrw20wSCEXyy3w/AXlArAMRiMr48EH8dBCMx250XdZL/YGJbYBUUFKClpcXw+x988AG+//3v9+mkiMyQXMGyDlnUg23nt/J+ZBOsQuVyKq06deXHKKqCCSZLk7vOLsAOWxUsfYHFK1gWFSijeYRWg54ZivE2+XdqFfHA4CZ3TUxDwCKFnlHER84kv2naysHSNbkbt/cYhRaV3DY+hzDV5F4osFHEyOSuvs1MJBhVoMoTgkWWzQWOUZvV7XSgpjT+ezdqEwYjMf63o3f+ZRZRDb3hKPcVlhbotwj18tPU7GjuQkyOt/XYiBz1+nQqWGxtTBbb5KON6rAT1dATVlp8ZfkeVLEWoeAuQlYdLMt348iEwNpzsNvU95a8Pvkcn3t/j9C6/uCDPe38w4DViCctTZ29SR9g7cyCBFSvgVL9VvZAYVtgnX766Vi+fLnu9xobG3HJJZfgqaee6vOJEX1Hv0Vo75MA+xlWCdTZRCQa/6N2a7bq51mEdLI3MfEcLHUFK/4GYBXRoF6vvdAwgWKWhB7/vn7cgJLibiWw4hcubduiR2AXI6DyYGnaPd28gmV+/9zL1KsVWKkp5FrMRuUo3pf01suyjFahFqHxRV6JOdCpYAmMy2EVJK3IdDkd/HGZVQP8Jm1WbnQ3EFh+1UYNPR9fqcVOQlbFdTmklI0eBSqTv1aYq+EjcqqKknySIu1VhuLBil9cvS6nkqMlsJNQO+iZCyyBizyrcnlcDuR7nDwWRXQXoboCOLTQi5I8N2QZ2CnYYmP3P2ZI/Hf96sf7+xzz8HlTJ/783h7bNpH3vlSqZ3YF0petya9Rux/wucDKNQ/WHXfcgb/85S+YM2cOtmzZgt7eXjQ0NOCxxx7DiSeeiIqKiv44TyIN1AIrnV2EvapPY2Y7p7KNcOJTuFZgKSno+o/FfpK7TgXLIqIBMMvBEqtgFaiiGtTYr2DptwitWozKtvfkN82uoJgHzChslFUXhHKwdH6HfPeWWYvQ5O8gEFKGo5sluacT0wCojNpmuxD5LsLU9VZZWLGYbNpmHZ74NG+0K0stDvU2gZTl6//eGUp7K3W9JElCVSg9gzsgPssR0PffKFlY5hf6WEw2rmAJtLmYyCzP90CSJN6iaguEUoKJ9dcrAkuSJF7FEk10Z+d4xtGVGFtZiN5wDC9/0CC0Vo+NXx3ErEfexc1/+Qj/UW0aEl3LsNsiZO1Bhl2j+37NRofBwrbAmjRpEv7xj3/gnXfewaRJk1BQUICRI0fixz/+MS699FL86U9/GnRjHRFHT2DZEUrqTz6iIyqyASawPDYrWMouQsEKVjg1pkGkRcjWa03uohUs9jhSTe5iFShDk3tYbBei0dgXkZgJwHimn70WoU4FyyAiIOm+TQQaq1D43A5dkcoFVhpBo4CYUdvsOWCeoAMG7ZZAKMKDZvUEGovnMLpYmYk7QJ2FpX/+By2quEqiuvHj5wZ3jcASbRF2hyL8GPXFVTQLy98bRiRRqWHCyk6LkAkcJujK8t18NFazQJtQ2agRX3/k0ITAEpxJ2KbaBXvxiSMBAH9Os034wZ52XPXEBv4+s9ci4kNNJBrDJpXAshPUCugJLPEKVigS48fnnMl98eLFKCgowI4dO7B27Vr88Y9/xMsvv4z9+/dj2bJlKC8vxx133NEf50rYIBhR/BDFabYI1RfQXKpgsSqE2oMFJId06mE/yV35Oe3dxq0hLZY5WJYVLDYuJ/l3EhCsYFUmKlgdPeGkKppikrdoERokY9v2YGlN7kxcmLQIzapIvHogsItQbz1P8C7w6lZwmDAMhKKGRnOjHCxArApj5MECrHcSssqY2ynpvoZZy0tvTFL8vJjB3SikVqxFaLTJQERgshahtoJVYjA9QAtrDxZ4nEltStE0dyY+i30uXskuN5nfqUXrA5QkSfWBxrpNqM0RS7eCVVbgwQUnjIDbKeGjvR34pMEvtJ7x8d4OXPmH9UmetVYbPqptjZ0IhKL8w5qdoFYA+CrRImRtZTstRvY8e1wO0/eCgcC2wNq7dy/OPvtsjBw5Ek899RRKS0vxrW99C+Xl5QDiJngSWIMPeyOSEsGXImNCjH4GkFsVLPYJNKVF6E4Ik76a3HWGPfOYBoFdhHkGFSxW1jbKceLrDSpxoi3CIq+Ln4P6U3W34HqjagKfRWjpwUoVOeFojD8fIhUsbRp7LCar2ivWAk23AmaSgaVeCxj/HfWlghWLyfyCpidy2HkZVaDU4kxPIDLTuKHAsqxgmVeBjEJGGVZVqI6eMA/kHFuVXgVLnYGlfg7YfFCrLCwlA0sx2JcXio0pAlQ7WVWvIb6TUERgBZJfw0dWJQSW4E5C9jsYkpij+K0JVQDsVbG27OvAFX9Yj87eCE4cU4YrTx4NwJ7IeT/hv5o6ppz/3RhVXvVgFazxw+KvAzsVLPY8D9O8BgYD2wLriSeeQGNjI/70pz+hqKgI119/PSoqKnDhhRfi6aefRlvb4G0LJRTUIy8cDkn1yV18F6H6E0cuVbCMWoQ83sDg4ihqcvfqDHtmb9xiLcJEBUwlsGIxmXsWJo8sM13PK1hGJneLClLSp2qV0Z0FhVq2CFXVBLXxNSDoIdNLRFe33cw8WEZp7P7eMNipmIlctl5vFyETHnoRDUD8deFOVEX12oThaIyfUzo5WFYtPjbw2WhHllWLdSirYBlcrIzG5DDEK1gWLUIDkcS8YeUFnpRzUFf/zFpN2hR35dzFBJo2AwuwF9PQpvMcVNqIajioqQKyFuGu1oBQGvoBTVTJxSeOAgD8dfM+oZ2In+7344o/rEdHTxhTRpdhxdyTeIbaARsi5/3Ee9nU0WX8uRT1YcmyzDOwpo4uT6wVv2/2OhrskFEgzVmEDocDX//617Fs2TJs374d69evR11dHR577DHU1NTgtNNOw7333ot9+/Zl+nwJQbSfpBX/iHglquMQbRFaVbDETe6pHiyrOYSAqkWoEmifNXeiszeCfI+Tf2ozwrCCFRYLCgWUN31124LFNFgJNPaakjXb3kWGPQOqPCm1wEr8HJ/bkVJ5VMPS2IHkKhS7+BV6XdzzoodZi5C9MdcYbO2WJMm0Ralu/WmT0NW3GbVKOi1afFYm906LCpR1BSt+/0YeKqsKFq8gGlQAS3gau/56dl6VRakRGeqoBbNNBqx6oTU3l1icO+OAJgMLUCqHPeGoob2AoQ4ZZVTzsFFrkaANah1emoc8txPhqIyvLFL41ffPRM20IytQU+JDR08Y//qkyXL9z/76Mdq7w5g8shRPzj0RhV4Xf/x2BNL7XyYE1phyZb1gBay5M4iecBROh4TjEmGrdkzujVkSMgr0YdizmvHjx+Pmm2/Gu+++i927d2POnDl4++238ac//SkTP55IAyOBZSfJPXdN7gYxDYItQvGYBpUHKx2Tu+o83ku8IZ0wqgwuE4EBKFUYbSVEtMUH6GdhiSa5q7e9qy+WoiZ3PvBZdaH0m3iPtOj5CbXmYCPMWoTMxDuizDg7x2weIfubK/S6dH+HVi1CdYtOr7VhdaGzrGAlhEtXMKIrFHgFy8CDxYSTUQXLaEwOw6qCxQTIUB2B5XMrOXZmVSg2g057cWUtQlEPlrqCVeh1cVFvZXQ/qCMy7YSNal/HDoeEI4bGx/NYtQmjMZk/PibQnA4J/zU1YXZ/z7pNyBLXf3XhJP63OMRGixQA9rX3oNHfC5dDwuSRpbYqgIAyImd4aR6qi+N/i3ZahPs1MR2DSUYElprKykrMmzcPL730Em688cZM/3hCEK3AMsv/MfwZ3blZwYpYxDT0GMU0sBahxS5CxeQev59YTE6vgqWqgCmeBfP2IKCMEGGfEhlKi1BAYCUuYup5hHbWa3dlBSNRLmytdjHqBXaK7CBk6KWxi6S4G61lMIE13CSc0GweoZn/Sn27UYvQ6jlQLnTmFSij9YVeF3/t6l2wjOYoMtRtNj2Tfztvk6fnwWK5bHoCS5IkIZO8dg6h9r4tK1g8yV85B0mShLOw9JLslbBRcQ+Wus09lhndLQRWe3eIt5jVIveiKSMAAO/saE0JIlUTjET5c8ssBIDiRxNt07H3pWOGlyDP41TFXIitZ/6r0UPyMbTInrgDlNcAC9YdTGwNe164cKHwsffff7/tkyEyh3YmWhHfAZWeyT2XgkYVD5a9FmFI2OSenMTeGVS8MyJBo3omd/amdOKYcsv1Xx87FJIU36nT5O/l1ShRkzugn4XVLbgLEIg/zkZ/L3+NdKsqo1YeLr3ATmUHofV961VjjUa0aDHbTbuvnVWw8g3X67U3GWYho4AiXLqCEcRicspQcLMdhIDStjKqBFitlyQJQ4u88UHfnUGMLE9+nEZzCBlMOMlyvNqlbQUe7KMHS2kR6l8YS/JcaO0Kmu5GM5pBp4hDK5N7/PsVGh9eeYEXTf6gpchgYbd6FSyrXYThaIx/6FC3GI8UFFjqmAz1h8uR5fmoKPSitSuIho4ewxYue+xup5T0PqauYMmybGkcf/+rxIfF0WWJ9ebxIFq+TPivaisK+Gu+oyeMUCRm2v5nsCpmNniwbAmszZs3J/1706ZNiEQifPDzZ599BqfTiSlTpmTuDIm06NDMFCtQXRhE/kiA3G0RhhKVFG2bhnuXDMye4knuyRUsJmbz3E5L/5Z6Pbu/fe092NfeA6dDwvGjSi3Xlxd4MGlEKT7c0443P2vB9xItAB6z4Lb+s67UycLqFmwRAipPS+KCxYS71+WwbHHqBY12Bu20CFOrsQcFdhCq12pb5eFojL8xjxRoEerN9FQqWPrPP2u9yXL8sWurnaIVrPaeMCLRWMrzLFIFZAJLz4dlFdPgcTlQ6HWhKxjBwe6QjsCy2kWoP8OSYdYijJ+XjQpWscbkLlrBYi1Czaik8gI2JsiigqXjwWLVoMaOXtP3XnZukpQsckUF1gE+5in1+a8sigssI/8doAjcisLkmBL281jUglWVXvmwmBBYNluEX/EKVgFK8txwOSREYjLaAiGh4FCjjQ6Dga0W4euvv86/zjvvPJx++unYu3cvNm3ahE2bNmHPnj34xje+gZkzZ/bX+RKCpLYI42+akZicNOJF5GcAiTllgusGG6MWIavMGOdgiZrck1t8TGSIpLgDqaN2WHtwYk2xZXuNcfpRQwEAb37Wwm/jFSgLDxSgGvjc2bcWIa9gCRrcAbVISd1FWCiw3syDZRWTYWRyb+zoRUyO7zxVb9FPOXeTwF4rk7jX5eTiWq9NaLWLL57uHRdoemGfVhUswHwnoVVMA6C8xvXuv93CBydewdJ//o0Cbhm94Sj3p2krWCWiOVgGw77ZbEqzVpV60LP6vYBVi4ORmGn1TT1uy6mqbjKB9UVLl+m4GrNZnEy0mhntWdtYK3C9LiVTzCoLq6MnjO2JUNQpiR2AdpLwAWBXIgNrzJB8OBySKp7EusUYjirDzAc7xR3ogwfrvvvuw9KlS1FWpnhGysrKcPfdd+O+++7LyMkR6ZMisFQXbtGwUe0bYa5UsYxahDwB3eDxi5vck4NGrbw3WvI0Jnf1jhtRmMB65/NWLijtmdyZByv+ZiTLsq0Wo7YiwASLiLjjJneVSLHyD6nRy3RrN7m4WK0FVP6rsryU1l3Seh1xyDALGWUw8aInMqyeA6dD4i1QvYsVE316OxgZFYmLZ6tuBcs6LJfdv3ZcTnIOmZUHS//vT1RgGVbAEq9lr8uR8mGHCe8Oi5gHoxahSBVGPehZ/Tr0uZ38fMx8WG0GPsLRQwrgckjoDkWx32S9NqJBTaXFDlL19/Q+YFiF3DI27T4IWY6LIybU7OxCjEc0KBWs+H2zFqO1wGruDEKW421OvXmiA03aAsvv96OlpSXl9paWFnR2isX6E/2H9qLvdEj8wilqdNd+2soVo7tRi5Cb3A1ahDzJ3crkrqlAtXfbE1i8RZi4PzYU9UQBgztj8shSlOS50dETxod72wGohz2LtAjjn+66ghF0BSMIRWM8oFWkiqatJigZWuICqSsU4Z/IlfaW+C7CLp2YBusWob4Hi/mvzAzugJgHy+x1YFaFEXkO2IVfz88j1CI0rWCZV+AA4wpWZzCiyiEzqGDlm2dZsQ0XRi1CK4Gl3kGobcOxDwShSCxlggIjFInxn53aIjTfQQmoBj07U0ctiYSNGu3CdDsdGFMRFxufm4zM4e1JnQqiVUSH+ntDdQUWq+CZi5yNiQ+LrHoFqEzyAgKppSuI7lAUDgkYWZ6XWG8esKtmP8vAKvGZflAaKNIWWN/97ncxd+5cvPDCC9i7dy/27t2Lv/zlL5g3bx4uuOCCTJ4jkQZ6n6bNMoD0SK1g5YbAsh72nCqwojGZ74ITzcEKRWLxT+42Bj2rf35PKKpbUhfB6ZDw9bHxwepvbm9J/DxxD1WhKt2/2d+b1DYVqmBpghsDNu6bCQBZVtYxT5NZyKj63AGjmAaLClZCAIajclLMxt6D8baEWURD0n3rbBbRbizRg1WHdFuE3GRu/ByMKo9faL/SzGoDBFuEBhdaWZYtW5SAcQWL/TvfY+xDZM9LSJXazwgEIzxHrdLAnMzDRg0q6UYZWOy8WNSC0cBnJp6cDinld1gmkOWkbpFqBR7PnTOJajAbVs5nEpr4sJjBvrwgVSCJCCyjFiGgVPCsRA4zuKs/LKrFqdU8wi8T7cGa0jz+OrIj0Lj/qnjw/VdAHwTW8uXLcfbZZ+Oyyy7D6NGjMXr0aFx22WU466yz8Oijj2byHIk00Ps0bTcLi72RsTemXGkRKh4sbYvQOAdL7S/zCQ57BuIXiw6L7elaWKsyGIkPRJXl+I4Zo0/uRqh9WLIsc/O+iMgBko3u7DlxOyXToE+Gdts7T3EX8FB5XQ64Ep8umdgXaW8x9IzqwjEN6iT4oFpgWWdgAWI5WOYtQlfSsWpEKli1FfGdf8ynooZVnK1M7kDqhbY7FOUVTDOBV8YrWMkXWl59MXnsBR4n9xZpHz87n3yP09CHZ13BMjY3S5KU8prVwgRGeYEnpfoh0iI0avEBQLXAPEIzH6Hah2V8/+z8U38HzHPZ3Gl8/y18TFDq/YtkYYWjMXywpx1ActwME1jhqGy5G51FNIxJtAfV5yPSIjSK6Rgs0hZY+fn5ePTRR3HgwAFs3rwZmzdvRltbGx599FEUFBRY/wCiX9F7s1cuTNaVqGhM5m/4LNk6V6IaWCVKu6W3wCQHSz1GQjtiR4vao9UbVrJjRDKwgGSB9s6OVgDKlmY7MIH10b4O7O/o5VERIiZ1AKhSvekq7UWxtdodXaKDnoH4xa7Il9xq60zD5N6lV8GyEFgup4P//tR/B/tUHiwzzJLcrWIaAHWLMHW9UoEyfg6YL+XLPlawtBcr9mHK5ZBMXwPKuJxkkWK1gxBIFjlakWS1gxCwFlhWF1crgaXsIEx9DCJGbbOoEJEWodkszbECMwnZmJ60K1idocSxqc8fa5maxVRsbfCjNxxDab4bR1QU8tt9bid/77XycLHK7JgKJUJEaU8KtAizKMUdyEDQaEFBASZNmoRJkyaRsMoizCpYnQICS12tYr6UXKlghRIVLJdDP6YhoFPBYn4ql0OyjBlwOx38k3gwErPvwVIJtLc/j7f3RPKvtFQW+zB+WDFkGfjn1kZ+u+hOxCrVp2olhV1sLbuQtnMPltigZwavBCXWddnwYGlbhLKsMlhbJLmr16tF0t521iI0zsCKn1/fPFimLULeojP+HdRWmAks6yog92B1BpPaNX5VrItZhIsyLke/RWj1/HOR1K1fwTIyuLNzA8Q8WHooRnf9CzUTD7ombyawTDxYigcqVWCxsFGzChavgOms/9pQVsFK/b0r680qWNa7CIUqWCYCiYcljy5LrQAKtvm+5DsI1RWsxIcCAZN8o1/xYGUDfRJYb7/9Nq644grU19fzuYP/+7//i3feeScjJ0ekRyiieBz0W4TWAou94eZ7nPwPPlc8WEYtwnyTmAZucBcIslMfFwzHbHuwXE5laPBnTfFPpCIJ7nqwKtY/Po4LLI/LkbTF2wz1uBw7EQ1AqllbdNAzgyeiJ15TfoHqDUObxt4ZjPD2llUFC1BEJBOV0ZiM/e3xC5+Vyb0vSe6A+S5CRSAZr2dm5z1t3UnDf2MxGV0hEZN8/GIVjMSSPmgpEQ3mzz8flxPQVLACYjEZRiKJta6MQkYB65gGJQPLQGCJVrB0BAZ73O3dYcOhy20mMRV2TO56r+GRCeHfFggZDqtnvwO99ayC1R2KGr7/t5hUEUUE0od7OwAAx49KfS8T3Un4pWYHYfy+Ey1CgVmODe3Zk4EF9EFg/eUvf8GMGTOQl5eHzZs3IxiMP/iOjg7cc889GTtBwj7szUuSki9YZinWRj+j2Ofmb7q5IrCMWoSKyT2SYrbkEQ2CLTI+8Fk1XkLUgwUAPpUReEiBh1cm7HLG0XGB9V7CXGqVoq5GPfDZTkQDoL5YsaBR8RwsIDVslAkWEZO79nXMKgd5bqdlCr96fVfCg9Xk70UkJsPlkLjoNMLMgyUS09DXXYTDin3wuBwIR2V+MQHiOzLZS9pMpOZ5lEwjdbtIJKIBULcINRUsPgNPsIKVRouQecOMYh4arFqE+eYVsFaDkFFAySAD9DPAAHMfYBWfR2gsEsxahMV5yqYUNpRcC6uA6Z1/gdfF3xv0qlg9oSj/G9T7HVQImPzZRpEjdN7LRDxs8YgGluKuVJKH2hjVk02DnoE+CKy7774by5cvx+9+9zu43coL4tRTT8WmTZsycnJEerA3kCKvK6lUa2cXofrTOHvDz7UWYcqw58QbTExGSthqMLF12ydYweJhoeGY0O6xlPUqITN1TJlQsr4eJ4wqQ6HXxS+uou1BIDkLS9kFKLaePdZAKIpwNKa0GAUFmjYR3Y7JXbtZ4yD3nogJ3EKNF5FFNNSU5llW/4w8WNGYzCtC5i3C+Ho9P6OIB8vhkDA6MeJml6pNyJ4/j9NhKTL1/DisgmX1GlZahMnvBVYZWAwjgWVWPdGu1Yt56ApG+M9QVz/UWA18ZtUZvQqW0yHxDxXGw66tBdaBQJDvcjZar1cFlCSJV1fZhgw1PaEo71oYtWnNfFjMk+dNpPVrKRdoETLhp+djFPGwtXaF0BWMQJKSW/Vqg71Z0GokGuOV0JwXWNu3b8dpp52WcntJSQna29v7ck5EHzEyXZtl+GhRv+HqjTbJZsJRxU+lJl914dG2CXt5Bpb9CpbdJHcgeadiOv4rhsflwClfG8L/LdriA1QtQpXJXbSCpa50+HvCXOzki1awVJUgWZa5YElnVI4yIFfs+dd+0GCfvK3ag+rz7gpGNB4m5aJtVgUyahFGojFeBbSqIrE24VdJAku8xVqhY3TnHiyL57/MoIIlmqTPxghpK3h2TO6haGqW1a6EN6mi0GMoEksNxCGDiQc9DxJgHdVglqQ+pMADt1OCLBsbzQ9aJOEz4bJPp4LFvGEep75AAsx3EraoIhr0PuyxqtjB7pDuoO9QJMZ/hzU6f0ciYaHs9VxTkpf0ISFpVI/Jh/yWriBicvx9f4jJNIaBJG2BVV1djR07dqTc/s477+CII47o00nZ4ZFHHsGYMWPg8/lQV1eHDRs2mB7//PPPY9y4cfD5fDj22GPx6quvJn1flmUsXrwYw4YNQ15eHqZPn47PP/+cf//LL7/EvHnzUFtbi7y8PHzta1/DHXfcgVBIfNp3f2PUquCtFYGBz8qOKJdyMdSZv5aNRBItQremGuVyOnjbUDuPkFWwRD1Y6gqWXZM7kLxbz06Cux6nJ9qEgLhAApRdhOm0CJ0OZSdge0+YV4MKRU3uKpHTE47yN22RXYTaLCqzC5se2hbj3jaxiAb12mhMTrrIs6pIPG/J+DVk1CJUV8SsRBJrJ+9qTa1giQgstdGdof57N4OJlGAklvQhpZ1HlaTXIhQxuRd6XWCfmbTrd7bGvYxmrXargc+8gqXTYovfbl6FaeM+tNTnwOGQuMDR82Gpk/D1crAA5QPAPp0KVluXssnAqBpuVsEyS3EH4pVLZUxT6uNvTOxi9rocurswRVqEbMizegchEM8NZJVtM4HGWuZVxT5hH2p/k7bAuvrqq7FgwQKsX78ekiShoaEBzzzzDG688Ub88Ic/zOQ5GvLcc89h4cKFuOOOO7Bp0yYcd9xxmDFjBpqbm3WPX7t2LS699FLMmzcPmzdvxqxZszBr1ixs2bKFH7Ns2TI89NBDWL58OdavX4+CggLMmDEDvb3xX962bdsQi8Xw2GOPYevWrXjggQewfPly3HbbbQPymEUwMttqvSdmqD0ZSoswtypYenEL3IelafGka3Lv6AnzdqNoTAOgCDSf24FjaoqF1+nBjO6AeMwCoORg9YZj/E1fJAWeob5Y2m0xqr1M7HXlkMQEnlYgtQWMWyu69+1JXr/PpLWhJd/t5F4c9QeOdV8cAGB+gQeMTd7sOfC5HZY5ZKOHxC9AX7bqVbCsX4O6LUKBkFEgLnJYZVh9oT1odxdhisCyNrlLkmS4C5PtrlPHAxjdt3EOlrHJHVC3ufQv8lbjmviuXZ2w0c5edRK+gcASqGCZtWjN5hGahYwC8Q+n7GfrVfDYLtzhpXm6Ak+kRagdkaOG7yQ08YBlm/8K6IPAuuWWW3DZZZfhzDPPRFdXF0477TT84Ac/wP/7f/8PP/rRjzJ5jobcf//9uPrqqzF37lxMmDABy5cvR35+Pp544gnd43/zm9/grLPOwk033YTx48fjrrvuwgknnIDf/va3AOLVqwcffBCLFi3C+eefj0mTJuHpp59GQ0MDXnzxRQDAWWedhRUrVuDb3/42jjjiCHznO9/BjTfeiBdeeGFAHrMIRgJL6z0R+RnFPjf/VJwrOVghgxYhoLQJtWGjooOeGew4tu3a6ZB4K1UEZnI/fmSZULCnGSPK8nkQoZ0Kls/t5K8R1mIRmSXI4BWB7rCtQdNAcruaiYNCr0vIi8YEFktjZxfMctstwvg5KyGj5hENQLwSwQSautX+4gfxXdTnHVdjur7EQCB0CAocAKjlWVhK2KitCpaJB8uqPSlJkq7RXXQXoZ7AikRjvD1nFbZrJNBYNe+IocYC10xgybLMRYZRFYflS7UF9NebBY0C6l27qQKLPZcFHmfK5hwGq7DqVbBYm9xIHAJ9q2ABShVKbychqx4ZfUgpFwgqZb/DMUNS/w4rBFqMLKYjWyIagD4ILEmS8LOf/QxtbW3YsmUL/vOf/6ClpQV33XVXJs/PkFAohI0bN2L69On8NofDgenTp2PdunW6a9atW5d0PADMmDGDH79r1y40NjYmHVNSUoK6ujrDnwnEd06Wlxu3eYLBIPx+f9JXf2L0Zq3dGi/yM3LR5G7UIgQUj1KqwBKbQ8hgxzUlPnmXWOQHaWEmdzvzB81gVSxRDxSDfapm26PteLjUF7sumzENfOBzMCK0e06N2kgfCEb5p3fhCpaByV2kRQikDnze196DDbvaIEnAdywEFvub7A3HkkSWHYGkF9VgZ1i23jxCxYNlvV7P6C5ucleGLjMOBEKQ5fiHFKsBvUY5WjsTCedHDDWuYKkHPmsJhJRBzcYVrPh961Ww1IOejcY18Z2E/tT1Iq9h3iLUqWCZDXpmiAgsM4HLqlB6eVRM9NUYxCNUCASVsh2EY3QqWCJJ8tlYwbL3bqxi4cKFurdLkgSfz4cjjzwS559/vqnw6Autra2IRqOoqqpKur2qqgrbtm3TXdPY2Kh7fGNjI/8+u83oGC07duzAww8/jHvvvdfwXJcuXYo777zT/AFlEOMWofiwZ/Xg16Kci2kwaxEmsrDCyY+lN5xeBas58WZp5T3RctYx1djZ0oXvTB5ua50Rs+tHY1ujH5ecONLWuqpiHz5r6uICK99Gi5DvyuoOKcOeBQWeOvTWjrgA4u0Kn9uB3nAMgWDEsjWjRd1ijMVkJcVdwOSuPnf2QeXlDxoAACeNKdc1+KopznPha0ML8EVLAH/dtA9zThkDwF6Lr7rYB6/LgWAkhn3tPRg9pMDW+oqi1NEjohUsINXoHoooBv10YhrY31BFYeqIGpH1siwLVbBKDapfgFKVyXM7Ddvc5VwkpF7kmUHd43QY7qStNgkbFQlqZdWhJn8vwtFYUuWbV7BM/gbMwkatWoSA+UxAsx2EgFLBagvE5xFqP4zKsqyMydFps4tVsFhMR3ZkYAF9EFibN2/Gpk2bEI1GcfTRRwMAPvvsMzidTowbNw6PPvoofvKTn+Cdd97BhAkTMnbC2cS+fftw1lln4aKLLsLVV19teNytt96aJEj9fj9GjrR3IbSD0cgOs0G1Zj+jOMcqWEbDngGTClbYXgWL7QJkb5YiFyY1l9WNwmV1o2ytMWP0kAI884OTba9jnhcmMO20GBU/UcTWsGdAVQXqDat2EIq/HRV6XegNx7d1HzQxF+uh3kXY2hVEKBqD0yEJf/LVptC/lGgPzjreWixLkoQ5p4zB4pe24qm1X+LKk0fD4ZBsiUyHQ8LoIfn4rKkLu1oDGD2kQGgOIWNoYfxxptMiBJTnmYkKtotWkqxbnLoCK1EFFpnFqefBavTHd8G6HBJGlRu3edl5dwUjKQLFyn8FKOJFz+TNM7BMTOasQqrenKCsNw4JZVQUeOFxORCKxNDY0YuRqsd6wCQFniFUwTJ7/IXGPqqGDiXqRHetah5hZzCS8jppC4T434De75CHjZpUsFiLsCaLKlhptwjPP/98TJ8+HQ0NDdi4cSM2btyIvXv34lvf+hYuvfRS7Nu3D6eddhpuuOGGTJ4vp6KiAk6nE01NTUm3NzU1obq6WndNdXW16fHsvyI/s6GhAd/4xjdwyimn4PHHHzc9V6/Xi+Li4qSv/sTK5G7Hg1WS5+Y7i3rDMcMMl2yCDW52OVPf6Aq4yd3IgyVqck/2YNmJaMgmWIuQITrqBlBte+8J2Rr2DCQHjdqpvjDUr2W7uwjVHzT2JKpX1cU+yxFJ2vVdvRFsa/RjW2MnPE4Hzpk4TGj9BSeMQKHXhZ2tAbydmEVpR+AAShuFGd07eRK7uMm9VZUrJBrTACgioD1xoVXvorWsQKnCPlnMhbKD0PrCqBdzsTPhHxxVnm/qZyzyufkGBW0VS8nAMhZ5ZjENVv4rABg/LP6+v63RnxJ1YJahxXA4jLOwzMb0MNjzeyAQTEmjZ8LFTOSy3ZV6Ioe3CEv1f4c+t5N/+GrTWc/8hDUlPt0cN7PqGSPbBj0DfRBYv/71r3HXXXcliYWSkhL8/Oc/x7Jly5Cfn4/Fixdj48aNGTlRLR6PB1OmTMGaNWv4bbFYDGvWrEF9fb3umvr6+qTjAWD16tX8+NraWlRXVycd4/f7sX79+qSfuW/fPpxxxhmYMmUKVqxYAYejbyblTGNschdv9XWq5qKpt87nQpuQjU0xaxFqx03YNrknKljptgizBW1yuZ0KFnt9NfuDfAeUcItQ5WOy2yIEFK9Xp0pgiYzJUZ9jVzCqZGAJ+q/U59kVjODFzfH24DfGDRXeRVrodeG/powAADy19ksA9oJWAfVMwu6k9SLPIasGRGMyf+6U3Dvr9aUFyRUsswRzLew1E47KPBizWSCiQbs+WWBZRzQAcY8XE2haozvPwDIRKGZRAyKvwdohBSjwONEbjvFzZrTzMTnmryFFYHUn3d4m8CGjvMADRyJqQf0YZFkWMrkrRvVkkSPLsuJjLDWuICrzDFNFktkOwvh5pba11URjMpoSjyFbxuQAfRBYHR0dunEILS0t3MRdWlrar/lQCxcuxO9+9zs89dRT+PTTT/HDH/4QgUAAc+fOBQDMnj0bt956Kz9+wYIFWLVqFe677z5s27YNP//5z/H+++9j/vz5AOLl++uvvx533303Xn75ZXz88ceYPXs2ampqMGvWLACKuBo1ahTuvfdetLS0oLGx0dCjNRgY5WAxoRSMxAznaTHUYaUup4NfeHOhTSjUItTmYCVM7j7RFmFCiImkd2cz2gpWOjENrD0QXy+4i5CZ3FUxDSIZWAz1XE37LULF5G7X4K6+b39PGC+z9qBNLx3zXr2+vRlftgZsV/HGaIY+26lguZ0OfiFu6QoiFpOFYxoAVQUrcVFXQkYFQmI9Tp5RxN5jRAzWDF2BJeC/YhhlYZmluDPKVS1CbZK8SAXJ4ZB4FWtrQ/JGJ9GNGkZGdyaYjDK0gLjAZAJK7cMKqFLgzQQWH5ejEZgHAiEEIzFIknn1iHvYdCpYnzcnRLLB75DPQjSIeWjtCiIak+F0SEKvo4EibQ/W+eefj+9///u47777cOKJJwIA3nvvPdx4441cjGzYsAFHHXVURk5Uj4svvhgtLS1YvHgxGhsbMXnyZKxatYqb1Hfv3p1UXTrllFOwcuVKLFq0CLfddhvGjh2LF198ERMnTuTH3HzzzQgEArjmmmvQ3t6OadOmYdWqVfD54i+c1atXY8eOHdixYwdGjBiRdD7aP7rBwqpFCMR3X5Xk64sJWZZTRmcU+VzoDkWzvoIlyzKfRajXImRCUZvkHrRrctcIsRLB6km2UampYNmKaWACK/Fmn+d2Cgf88TZbKKIa9GynRahsMmCxHLZbhMGIEtEgaHCPr4+f52vbm9HQ0YsinwvfGFcpvB6IV1vOOHoo3tjegqfXfcVbrKIVLG0Wlt0qYEWhB22BEFo7QxheqmQwiZncWQWLtQjFK1iSJKEkz422QAgdPWEMK8lTDXoWF1h+nRah2Q5C7XptBYu1vUwrOCY+ojZBkXlMTTHe/+ogtuzrSPLsiW7UGG4Q1cAFnolABOIitrkzmOTDYkOUCzxO0wq00cBn9vdfWeQ1jJgAzCuAn+6PC87x1UW6a7nJ3SAFX30O2RIyCvRBYD322GO44YYbcMkllyASif9xu1wuzJkzBw888AAAYNy4cfj973+fmTM1YP78+bwCpeWNN95Iue2iiy7CRRddZPjzJEnCkiVLsGTJEt3vX3XVVbjqqqvSOdUBw0hgeVwOeJwOhKIxdIUihi2NnnCUixT2JlLkc6PJHzQdVZANRFTeBjsm916bQaM+jRA7rFuE7A3aRgWKCQFZVnxstlqEiftiAsnjcghXz1ibuCsY4RcqkQwsBmtvbt7dDgA4e2K10JBpLXNOGYM3trfg+ff34ITR8bgOUZHJ2mF7D/YgHI3ZjroYWuTFZ01daOnqhb83/rM8TofQ61/JwQon/Ve0gsgFVmKdyJgcBp/lqBr4zFLc9YYM6903oOPB4jlSxufAfETdoSjaukJJAktUIB1TUwIgtYIlWoXVq2DFVK1eswoWEBcgW5E8LofFdVRYPP9DDOYRKv4r8w8p5QYVMEAlsIbp+5PZfQdCUfSEoilxMtkY0QD0QWAVFhbid7/7HR544AHs3LkTAHDEEUegsFD5FDF58uQ+nyBhj/jg3bhY0GtbFfpcaAuETLOw2JuPyyHxC26uRDWoTfi6Hiw382AZVLBs5mAxcrVFOLSwDy3CxMVA5v4rcZHhdTngckiIxGQeUmh3FyEA7El4UcrzPcI5ZMkVrDQ8WBohabc9yDh97FDUVhRgV2sAb33eEv/Zgs9BVZGPR1XsO9hjaxYhkDwuRz21QeQ51LYI2S5CUQ+cNs1eaRFaXxy1Aqk3HOUiW6SCVcrPXRFY0ZiMTV8dBGAd1VFe4EF3qAcHAqGkOAERkzsAHDOctQg7kuIKRH2EemnuHT1hXoE020UI6O8kbOU7CM0FFsuy6uyNIBiJ8mo/n4Rg8dwZZVm1BUJoSnhZxxkIrCKvi++gbO0KJu2gBJSIhmzyXwF98GAxCgsLMWnSJEyaNClJXBGDg9XQWZEsLPbpUB2emSvjcsIRdQVLZxehl1Ww+mhy13zSz9VdhB7N7LB0KljKWnGBJEnKLEO2vbovFSw7zz97DcRkJdzQlgdLdZ5VxV7UHTHE5GhjHA4Js+tHA1BEqmgFyuGQ+E7CXQcCtluE6gutIrDE1pZpYxp4xIB4BQtQdhL2xeT+1YFuyHL8cRsNaVbDKs3tqvfJtz5vwb72HpTkuXGGaq6nHkZtLtFRQWMri+B2SvD3RpJ2AgoLrISI2d/ey3eAMv9Wkc9lORVCb1xOi0WCPaM4TxmTpH78wgLLYNQQq16NKs839GFKkmToAQOU+Y7ZtIMQ6EMFCwDWrFmDNWvWoLm5GbFYsmnaaFwN0b+wN54ir0u3F12gmcNm9jPUAk2pYGV3izCkqmDpPX6rJHdhk7umJZSrAguI+7DYm5a9mIbki4HooGd+vM+Fg91h/mbPvE0icIHVlqhgCfqvgOS0+UhMhiTZ++SrvgicP3l4nzwf/zVlBO7953Ye1CnqwQLiPqxtjZ3Y2RJAV8h+ixBICCy+g1FsLfu9+3vDSTsRRX2IapHk74nwWJV0TO48wb2iQKj6pox3Ui7Sf1q/GwBw4QkjLFu93OiuFVgCOVZA/APNUVVF2Nrgx9aGDowsz4csy8Jt1mEl8UHGoWgMLV1BVBX7FIO7wN8Ai2rQrWBZPP+SJKG8wIPmziAOdIX434xVyCjDKKiVCawJBtUrRkWRFw0dvbo+LHYO2dYiTLuCdeedd+Lb3/421qxZg9bWVhw8eDDpixgcjEJGGYWqkEU7P6M4R1qEkZiS4q73hmtocu9jBYuNAMlF1DsJ7VSh1DvC7K4FFEGlVG/stAiTd3GKtqeAePVHXamrKvKZmnNT7tunFljmo3GsKPK5ceGUEUn/FoW1qOLtJrZe1OSuZBr5Ld4ztJSqWsMdPWHhiAFGCfdRhdHSlQjq9bmEfGxMYPWEowhFYqodhGLdkxJNBavJ34s12+K74S89yTr8mbXg9msGNtvJYpuo8WGxxyKy3uV0oDrhm2QVMDsCqy8VLEDxqKnjElgFy2hMDl9rkCP2iYX/KmW9TsxDY5a2CNOuYC1fvhxPPvkkrrzyykyeD9FHjAzuDO0cNT2ULdvKyyNX5hGyFqFeexBQPEbaFmFv2KbJXXMxyFUPFhAXGAxRoziQvCMMsOfBAlK9TOm0CBlWrRm99ayKaac9CMSrJU6HhIk1xZafukWYXT8GT6/7CoC9x8GGPm/Z1wEg/qFC1GyvrmB16Py9m+F2OlDkdfEMMrs5ZOoqFMuR0+5mNUItQP29YWUHoYDBHUj1YD3//h5EYzJOHFOGsVX6O9jUHDeiFC9s2ocVa3fhsrpR/HkU9WABCR/W+4rAUo/ZEWnRDy/Nw772Huxr78GU0WVCEQ2MSh0Plp2YjAqdNHerQc8MoyT4T/d3AgDGDzN//tUfCrTsz8KQUaAPFaxQKIRTTjklk+dCZAArgSWS5q73M4pshJQOJqxFqDfoGVAqWKktQrtJ7oeGyR1QKlhel8N2u0u9e9JuBUsrqIpstAi1Xg07FSztejsGdyAehrhqwdfx5NyTbA34NuLIykLcdf4xuPHbR9n6BM5CGXckMoTsCFQusLqCtlPkASVstL07lNYuQiAhsAQN1gynQ+LvRR09YWUHoWAFS+3BisVk/GnDHgDApSeJja26rG4UjqkpRnt3GItf2gIgXg23GvSs5piauChnwpi1G0vzxTYZaKMa0qtg9SpJ+gIp7gxtFao7FOH3L7qLkM0jBOJTN3Y0M4FlUcEymEcYi8l8J/Ih0yL8wQ9+gJUrV2byXIgMYBQyyigU8GBpM7CA3NtF6DJI1+ctQm3QKN9FaG/YMxBvldlpMWUbrHpgJ2aBob4o2wkKBZJbbUB6Se4MuwJLXW2zW8ECgLFVRUIXU1GurB+D+d8ca2sNi2qIpdFiZYKmLRDiF0hRDxagGvgcCNvKwQKSBRYfk1MsJrCA5F2ISgaWWAWL7Xz194Tx9o5W7GvvQbHPhXOOFRtz5HY6sOy/JsHlkPCPLY149eP93GRuNuhZzfhhxZAk8DwquxVAJaoh7j8UCTllMBHVG47xLkYrT3G3Xs98VK2JNh3fAex1WX7IZKN2QlHlvr9o6UI4KqPI57L8O6ww2IXY2hVEJCbDIYmJxIEk7RZhb28vHn/8cfz73//GpEmT4HYnP7n3339/n0+OsI9oBavTtsk98cZko0UYjsbweVMXxg8rysgnfREiUTYmR//+8rnANDC5C7cIleNyuXoFKFlYdtqDDHXVws4ORCBVkGkFlxl9bhGqBNpwk/Ee2UxVsRd5bif/sGCnAlWW74HTISEak/nwYTuvY9Zq23uwm2fPiQusRJuuJ2wrZFRZ78a+9h582RpAR08YkmQ9Joefd55SeWPm9gsEzO1qjqkpwX+f8TU89NoOLH5pCx64eHL8ZwtWoPI9LhxRUYAvWgLY2tDBNxmIvoaNKlgigj/fEx991hWMoKUziEKvi3uwhCpYGpHDzOVW1SsgvsGIvV4PdIVQ5HOrAkaLLZ+7CoMKFpsnOrTIa7mLcqBJ+2w++ugjTJ48GQ6HA1u2bMHmzZv51wcffJDBUyTsoB5xowe7iNluEaZRwXrw35/hnIfext8+2i+8pq+Itgh7jGIa0qhg5WqKO2PSiBLke5yYPKrU9lr1a8RuBUwtqHxuh603x0y2CNOpYGUDkiTxRHfAXgXL4ZB4u4dVgURjGgDF0M5mIXpdjpTwRyP0Klh2Kg/sPFnQa01JnrBAKslXWoT//rQJgHh7UM113zwSR1UVorUrhEUvxluFdnayqgNH7VYAtWGjInMI1VSqjO7+XmUXp4jJvUIzj3Cf4A5ChjasVAkYtfa/GeVo/XXzXgDApBGlQucwkKRdwXr99dczeR5EhrA0ufM5bFHd7wPJOViMdEzunzXF/RHawab9idIiNKpgKbMI1UF/vWF7Hix1BStXU9wZVcU+vL9oeko6vQjqxy7SHlGjNrnb2T0HpBrq7bcIc19gAcCYIQXY1hj3sNjxsAHK2BR2kUynRch28dmJKVGPu1EysMS9M2z9B3vaAYi3B9VrZRmIyDKmjC7D0QbjWczwupz49X8dh+8++i7PUrPzGpw4vBgvf9iArQ0dOLoq7j2ymkPIUFewZFm2ZXIH4nEHO1sDaOkMoqIw/vwXCe7iZG0+dp9KBUvs9zekwIO9B3v4esXgbr1ZRK+CdTAQwv9tjAusuaeOETqHgSS76mlEn7GKaSgQiGnQG/yaTgWLfTIzS43PNKxFaFQNYZ+yZVmpWgFKi1Dc5K6qYOW4wALirQNHGnlO6seeb7OCpRZV2h2FVmgrWHaqB0CywBJpb2Qr6jRxOxUsILVqZMvknhBUuxImczvioiRfqWDZGZPD1yfOk1U/RHcQAvG/W3UrO53qFeO4kaW4+rQj+L/ttKnVFSzFgyXYIky8XgOhKDp6worAEvBQAckVLCZWRDcZsPtgO/lYm1K0zV6uChuVZdlyRI4avguxO4Rooi39x/98hd5wDMfUFKM+zcDf/qRPQaMA8Mknn2D37t0IhZLLdt/5znf6+qOJNLCuYCUElsCoHPXPKE4jyZ3tLjITc5mGVbCMTOfqnW7doSj/1Ga7RaiuYOVwyGhfKU6qYKUvkuyKA2070u7vgFVyhxZ505ojmC3UVqhbhDYrWJqLqp2QUyao9qWRpM/eV8JRGXsSQbF2PViAMndUdAchozTPje5QFEU+F2YKmtuNuGH6UVj9SRN2tgRstgjjguKrA938ORAVqT63ExWFHrR2hZKqQaIVLHVEB2vRWs0hZFTwsNC4QNpns4LFTfJdIbR0BnEgEIJDglAVMT4OK/7huC0QQpHPhacS8SZXf/2IAfP52iFtgbVz505897vfxccffwxJkvi2S/Ygo1HjFhTRf3TotPfU8DlsIetdhGpPBrsAxgdBx4T8MqyCZWaozzTcg2Vwfk6HBK/LgWAkhkAwgvICD2RZ5j4EYZN7kgfr8BVY6raG3RwstQfLjsEdiLd62Zut2ynZ3sHIBJrVeI9sh43LAeyLVO1FNZ0KFp+BZ6OCxQJqozGZf7BJp0XIsNMiBOKeyYaOXlxw/HBh35gRPrcTj15+Ah5c/TkuO2m08LrSfA/Ps1q/qw2AmEmdMbw0D61dIexsDfDIGdH16qiGqi5v0m1WsCpSbzg+85YJLNE2uzpHiwWM1lYUCH3IcTkdKMv3oC0QwoFAEK9vb0ZrVxDDSnyYOalvQrm/SLtFuGDBAtTW1qK5uRn5+fnYunUr3nrrLUydOhVvvPFGBk+RsINVTINIi1CvgqW+AIq0/GRZ5mF+AxntYOXBAlKjGtStwrQqWDmc4t5X+mJyT/Jg2fQPSZLEK2alNgY9M1imjujus2ylTy3ClAqWfQ8WQ9Q/BCgBtQyPy2HLYK8VgnYrWDOPrcbI8jx8f1qtrXVGjKsuxvIrp2BCjb3QWVbF6uLTCMSf/xFl8coly9JyOSThCqR6XE6LzRyyfI+T+09bOoM8QV20za7OwrLjv2IwgdbSGcQf3t4FALjqlDFZt3uQkXYFa926dXjttddQUVEBh8MBh8OBadOmYenSpfjxj3+MzZs3Z/I8CUFEW4RGuwjD0Rj/RKT+GW6ng2+x7eyNWH5a6gxGeAm/awDT33lMg0klKt8Tn4HHHmeSwEojaPRQ8GClS19iGop0PH52KPA60RWM2LowMc6fXAN/TxjnZuknX1Eqi7zI9zjRHYraEkiAngfLfotQ+be9+1ZPABha6LUlkNV/bz63A8MEU+AZ87851nbmWH9wTE0J/vVJE/+3HZHKjO4f740LrLIC8Q8Z6hZhq42IBiAujocUeLGvvQef7vcjEpPhckjCFchy1cBmO/4rRtxk34W/bt6H7U2dKPA4cUkffHT9TdqyLxqNoqgo3jetqKhAQ0MDAGD06NHYvn17Zs6OsEVEFeBmWcEyqCqxChiQ6ulgF0GRLKz2gHLMQHqwrFqEgHrgc/y8golKlkMyr3ypkSSJi7jD2YOVVOXsQ0yD3RYhoLyW7e4gBOLVmuu+cSRPQ89VJEnibUK7rWr1RdXndgjP4QRSX/N2fwfqKpSdkFHt2tqKwrQ2Z2QDE4cnCws7IpW1tlkFa4iN9mKlngdL0CAPKG3CjxL3XZ0YQG1n7YGuoPCQZzWsrf3XzfsAAN87cWRWf8BNu4I1ceJEfPjhh6itrUVdXR2WLVsGj8eDxx9/HEcccYT1DyAyjl8lmozKxYoHK4pYTE55c2IVsCKvK+WPpsjnQnNnUKjld1A1rX4gdxHaahFqKlhel9PWJ2mvy4FQJJbzMQ19oS+jcgr7ENOgXp+OwDqUuGnG0Vi1pRFfH1tha50698hu9UtbwbYr7tQXRdH2lN5aOzsIsw22k5BhxyTPBFY6w86ZsD4QCPEZfnZ2cTIx99He9qRzEVsbv5/Gjl4+cNteBSt+37Ic/0D8/VMz0+btL9IWWIsWLUIgEM9AWbJkCc4991x8/etfx5AhQ/Dcc89l7AQJcYKRKMZWFsbLtgYVHPVFrTscTak6MJGmZ3i1k4WlFlgDaXLnMQ0mrT6WWK60CBMRDW57Bd3SfDc6eyO2P4EfSpTme1DgcUKGvRYTkNwWtLODjcE8WJkcWZOLfGNcJb4xrtL2OvVF1Y7BHYgb1d1OCeGovRR3RklfKlgqMWjX4J5NVBV7MaTAw3fS2RG52mBPO+KsXJXi/0Uio3BooXiblfkXWXvSjsBStwiBeNWuysbvX11pO3viMIwsz+4pDGkLrBkzZvD/P/LII7Ft2za0tbWhrKwsK7dLHg4MK8nD6oWnmx7jczvgkOK7fwLBSIrAMsvRspOFxQzuQLxFqA717E94TINJi5C1lliLkIWM2g3a/NWFk/BFSwBHVtoPKjxU8LgcWHn1yYjJsq0WExCvALocEiIx2XZ7EVC3CA/fCmJfKPa54ElUYe0KXEmSUJrv4S0m+x4s5f7s7CCMrz00BJYkSThmeAne+qwFJXluW63Ovggsh0NCRaEHTf4gF8gVRfZbhOzDuJ1h6UM0rcj4XEbxx62uuv7g69ldvQIyHDRaXl5O4irLkSRJmUeoI5QUk3zqG25xmhUsWY63JAcCxYNl/DpUPFiaFqHNCtYpX6vAlSeLb80+VDluZCmOH1Vme50kSVy0p9MirC6Jv9naeYMnFCRJ4u05uxUsIFlU2TFoA5oWoc0BvcktQns7CLMNtpPQtofN506qANut4mpFLWvdiVChOdZOUG++x5U0BcNOe1B9/KlHDknrPWeg6VPQ6Jo1a7BmzRo0NzcjFoslfe+JJ57o04kR/UeR14XO3ojuTkK9FHe+zkYF62B3sgjr6k2tlvUH4Uj8E5lRixQA8rUtwrC9FHcicxT64js60zG5LzjzKEwaXorzjqvphzM7PBhaFN8RZteDBSSLqnR2ETLshIwC8arppBElaPYHcVRVblePj0vMz6susVfFA+KtOTYmyY7JHUgWtaX5btNd11q01TK7kxDYLkTAvsA6bmQp/rHg6xiV5a1BRtpXvDvvvBNLlizB1KlTMWzYMKpc5RAFJlENZjEPXGAJeKrau5OT/buCYQD230TsEolZtwjNTO7EwHLWMdV49eNGTBpeYn2whqFFXnzvxJH9cFaHD6zlks5OLLWosru+LxUsAPjLD09BNCbndAo/AHxrQhVuP3cCTj3S/piXEWWKwLJfwVKec7ubDLRtPrthvUMKPSqBZV8g2xVlg0naAmv58uV48sknceWVV2byfIgBwCxslEUw6AssOy3C5GMGKmxUrEXIPFgakztVsAacn82cgNvOGU8f0AYJ1mZNx8fG2lpFPpdpxViPElU4r10PFhCPYclxbQUgPlliXpqBp2phIzomh6EWtRU2BZb2eNExOQxWAXM5JBxZmdstXivSFlihUAinnHJKJs+FGCBYJUpXYAmY3P1CJndtBWtgBJZQi1Cbg8XG5BwK79g5CImrwWNO/RiEIzIummq/EshahOnEZLAPcJKUWhEhxFB7D+0OO1cLLLsVRPXvq7zAYzuehZ3rkZWFh3zXIO2P7D/4wQ+wcuXKTJ4LMUCw7e32W4TiA58PagTWQFWwWIvQLGg0X2tyD7MWIVWwiMOLsVVF+NV/TUpruzureqVT/WJb84cV+7J2zEm2w8blAPYFVmUfBJb6vuxWrwClJZlLrb50sSU9Fy5cyP8/Fovh8ccfx7///W9MmjQJbnfyH9n999+fmTMkMo7SIkzd2efvYTlYqS8NxeQu0CJMJLmX5btxsDs8YGGjSkyDWdBocouwN80cLII4nGHG7Cqbo2qA+PzAX114bNKwasIe6hZhWUH6Kf52W4RelzO+USoYSWtY+ndPGI5tjZ2Yc8oY22tzDVsCSztfcPLkyQCALVu2ZOyEiP6n0Buv4MSN58kImdxttAhHlefjYHfHgIWNhhItQpEKVk+YjcohkztB2GXGMdX46Vnj8K0J9kNOAeDiE7N3hlwu8LXKQhT5XKgs8tp+71L73tLZZDCk0IPOYMT2DkIgPhz7qe+fZHtdLmJLYL3++uv9dR7EAMK2xAd0KlhmAks0BysUifHcqxHl+fhwb8eAV7DMPFipOVhkcicIu/jcTvzwjK8N9mkcthR6XXj9xjPSet9KrmDZ98ANKfTiywPdaVWwDifSvqIsXbpUN+vqiSeewK9+9as+nRTRv4jsIuxLDharXjkkoCbRRtCrlvUHSkyD/VmEZHInCCKXqCj0phXS63M7+cDudFq8dbXlcDsl1NXaj5c4nEhbYD322GMYN25cyu3HHHMMli9f3qeTIvqXQoMcrFhM5rsIzUzu3aEoItFYyvcZLKKhNN/DhdpA7SK00yIMaHYRUgWLIIjDhUUzJ+Ca047AuGr7WVQ3nzUOH90xA8eOsJ9fdziRdkxDY2Mjhg0blnL70KFDsX///j6dFNG/sF2EWtHTFYogFtcnpjENbK3ReAy2g7A0383bkSLRDpkgHBXZRRg/px5KcicI4jDlv6aM6NN6ZrUgjEn7ijJy5Ei8++67Kbe/++67qKmh0RXZTKFBDharXnlcDt12mdvp4HOkzNqErEVYmufm1bKB8mCxFqFLoEXIdxEykzu1CAmCIIgMkXYF6+qrr8b111+PcDiMb37zmwDiswlvvvlm/OQnP8nYCRKZx6hFaGZwZxT53OgNB7lXSw/WIizL95iGmvYHLGjUbFROHt9FGIUsy2RyJwiCIDJO2gLrpptuwoEDB/Df//3fCIXiFQufz4ef/vSnuOWWWzJ2gkTmUWYRJu8i5BlYJoN3i3wutHQGTStYSovQw31bA1XBCtloEcpyvHrFPVhUwSIIgiAyRNoCS5Ik/OpXv8Ltt9+OTz/9FHl5eRg7diy8XvuZGsTAwnKwtHELohWs+FqzFqESMlposmOxP1BiGkxmEaqEVCAUIZM7QRAEkXHSvqKwTKzCwkKceOKJmDhxIhdXjz32WGbOjugXCr1xkRQIxVtkDLMdhIxigTT3g4F4BauswMP9XiLp75kgErVuETodEveS9YSi1CIkCIIgMk7aV5SzzjoLN910E8Jh5cLZ2tqK8847j1qEWU5BooIVjcm8egOoMrBMK1jWWVhKTIMbRaoKllrM9Rd8F6GFWFKPy+mlJHeCIAgiw/SpgvXXv/4VJ554Ij755BP8/e9/x8SJE+H3+/HBBx9k8BSJTFOgmn7eFlCGMgu1CL3Wae5sF2FZvlLBisnKrr3+RMSDBShtwu5QRKlg0SxCgiAIIkOkfUU55ZRT8MEHH2DixIk44YQT8N3vfhc33HAD3njjDYwePTqT52jKI488gjFjxsDn86Gurg4bNmwwPf7555/HuHHj4PP5cOyxx+LVV19N+r4sy1i8eDGGDRuGvLw8TJ8+HZ9//nnSMW1tbbj88stRXFyM0tJSzJs3D11dXRl/bP2FwyHhiKHxIas/+tNmvptQzIMlUsFScrDy3E44HXE/1ED4sLgHy2HswQKS09zZLEIfVbAIgiCIDNGnj+yfffYZ3n//fYwYMQIulwvbt29Hd3d3ps7Nkueeew4LFy7EHXfcgU2bNuG4447DjBkz0NzcrHv82rVrcemll2LevHnYvHkzZs2ahVmzZiUNq162bBkeeughLF++HOvXr0dBQQFmzJiB3t5efszll1+OrVu3YvXq1XjllVfw1ltv4Zprrun3x5tJHr70eBT7XNj41UH84Kn30RuOcg+W3pgcBjO5mwWHtqtiGiRJ4kZ3kSHRfYV7sCxbhEoWlrKLkCpYBEEQRGZI+4ryy1/+EvX19fjWt76FLVu2YMOGDdi8eTMmTZqEdevWZfIcDbn//vtx9dVXY+7cuZgwYQKWL1+O/Px83RmJAPCb3/yGe8fGjx+Pu+66CyeccAJ++9vfAohXrx588EEsWrQI559/PiZNmoSnn34aDQ0NePHFFwEAn376KVatWoXf//73qKurw7Rp0/Dwww/j2WefRUNDw4A87kxwTE0Jnp5Xh0KvC+t2HsD/+9+NaO2KV57EKlj6LUJZltHeowgsAAO6k1C4Ragal0Mmd4IgCCLTpH1F+c1vfoMXX3wRDz/8MHw+HyZOnIgNGzbgggsuwBlnnJHBU9QnFAph48aNmD59Or/N4XBg+vTphgJv3bp1SccDwIwZM/jxu3btQmNjY9IxJSUlqKur48esW7cOpaWlmDp1Kj9m+vTpcDgcWL9+ve79BoNB+P3+pK9sYPLIUqyYeyLy3E68+VkL3tnRCgAozjPPwQKMq1H+3giiiXk7bJgoDxsdgAqWaIuwQDUuh0zuBEEQRKZJW2B9/PHHOPvss5Nuc7vd+PWvf41//etffT4xK1pbWxGNRlFVVZV0e1VVFRobG3XXNDY2mh7P/mt1TGVlZdL3XS4XysvLDe936dKlKCkp4V8jR44UfJT9z4ljyvH7OVOTWmrmuwjNTe4difZgntvJx+0oLcL+j2oQbRHmJbUIqYJFEARBZJa0rygVFRWG3zv99NPT/bGHJLfeeis6Ojr41549ewb7lJI49cgKPHbFFLgT4ZzDSvIMjy22qGAd5DsIFZHGs7D6uUUYi8mIJKpnVi3CfNW4HObB0pu/SBAEQRDpYFtgnXPOOejo6OD//uUvf4n29nb+7wMHDmDChAkZOTkzKioq4HQ60dTUlHR7U1MTqqurdddUV1ebHs/+a3WM1kQfiUTQ1tZmeL9erxfFxcVJX9nGN8ZV4s//rx4PXXo8aisKDI+zSnJXj8nRrunvFmE4pmR6uU2S3AElB6ujJwwWz0Umd4IgCCJT2L6i/POf/0QwGOT/vueee9DW1sb/HYlEsH379sycnQkejwdTpkzBmjVr+G2xWAxr1qxBfX297pr6+vqk4wFg9erV/Pja2lpUV1cnHeP3+7F+/Xp+TH19Pdrb27Fx40Z+zGuvvYZYLIa6urqMPb7B4PhRZfjOcTWmx1iZ3PkOwgJVBWuATO7hqBJkKmpyP6jKAaMWIUEQBJEpbM8i1KZxD0Q6txELFy7EnDlzMHXqVJx00kl48MEHEQgEMHfuXADA7NmzMXz4cCxduhQAsGDBApx++um47777MHPmTDz77LN4//338fjjjwOIz1e8/vrrcffdd2Ps2LGora3F7bffjpqaGsyaNQsAMH78eJx11lm4+uqrsXz5coTDYcyfPx+XXHIJamrMxcmhABNYgVAU0ZjMM64Y+hWsgRFYkai6gmXRIky0A9n5AubjdQiCIAjCDmkPe84GLr74YrS0tGDx4sVobGzE5MmTsWrVKm5S3717NxwO5aJ5yimnYOXKlVi0aBFuu+02jB07Fi+++CImTpzIj7n55psRCARwzTXXoL29HdOmTcOqVavg8/n4Mc888wzmz5+PM888Ew6HAxdeeCEeeuihgXvgg0iRKiOrqzeCkvxkQ/xB1aBnxkCZ3FlEg0NCivDTkp84J3a+XpcDkmS+hiAIgiBEsS2wJElKuRAN5oVp/vz5mD9/vu733njjjZTbLrroIlx00UWGP0+SJCxZsgRLliwxPKa8vBwrV660fa6HAh6XA16XA8FIDP7ecIrAUo/JYQxU0ChrEboEKlH5mhYhGdwJgiCITJJWi/Cqq66C1+sFAPT29uLaa69FQUHcGK32ZxGHJkU+N4JdQV3BpAx6HrwWoUirjwushCAk/xVBEASRSWwLrDlz5iT9+4orrkg5Zvbs2emfEZH1FPtcaO0K6rb82nViGgYqaDTMU9ytK6ps2DObv0g7CAmCIIhMYltgrVixoj/Og8ghmGDSm0d4ULdFmIhp6OcKVigiloEFKDENMRbRQCnuBEEQRAahj+2EbUaU5QMAdjR3pXzvYIC1CHWCRgesgmX9smYxDQxqERIEQRCZhK4qhG0mDi8BAGzZ15HyPXOTe//uIozExFuEBV4SWARBEET/QVcVwjbHJgTWR/vak24PRWIIhOJz/coMTO79mZtmq0XoTu6O0y5CgiAIIpOQwCJswwTWnrYeXrEClOqVQ1JEFaD8f0yOz/7rL6hFSBAEQWQLaV9Vdu/erVuNkGUZu3fv7tNJEdlNSb4bo8rjPqwt+/z8dhbRUJLnhkMV9JnndoL9sz93EtppEeanCCyqYBEEQRCZI22BVVtbi5aWlpTb29raUFtb26eTIrKfY0ektgn1dhAC8fBW7sPqx52EdlqEeZqWIMU0EARBEJkk7auKLMu6Ce5dXV1JY2WIQ5NjdYzu7XwOoTvleDZipz8rWHZahA6HlCSyqEVIEARBZBLbOVgLFy4EEK9K3H777cjPz+ffi0ajWL9+PSZPnpyxEySyE25036sILGUOoSfl+IEYl8MElkugRQjE24TME0Ymd4IgCCKT2BZYmzdvBhCvYH388cfweJSLqcfjwXHHHYcbb7wxc2dIZCUTa+ICa+/BHhwMhFBW4OEtwlIdgaXsJOy/qIZIYhahyKgcIGF0D8T/nypYBEEQRCaxLbBef/11AMDcuXPxm9/8BsXFxRk/KSL7Kcl3Y/SQfHx1oBtbGjrw9bFD0c4rWKktwoEIGw3ZaBECyUZ3MrkTBEEQmSTtj+0rVqwgcXWYo20THgwkTO4Fxi1C0XE5B7qCWPTix7phpkZwD5ZgNSrPo3y+oAoWQRAEkUlsV7C0fPLJJ9i9ezdCoVDS7d/5znf6+qOJLOfY4SV45aP9XAQxD5a+yd3ewOe/fdiAP/5nNzp7I/jNJccLrWEtQrdD0IOlNrnTLkKCIAgig6QtsHbu3Invfve7+PjjjyFJEs/EYjsLo9H+C5QksgNtBUtvTA7DbkzDgUQ1zN8j7tmy2yJUj8shkztBEASRSdL+2L5gwQLU1taiubkZ+fn52Lp1K9566y1MnToVb7zxRgZPkchWjkkIrH3tcaP7QZOYhkJv/DZRDxbzc7HROyIoLUKxCha1CAmCIIj+Iu2ryrp167BkyRJUVFTA4XDA4XBg2rRpWLp0KX784x9n8hyJLKUkz40xQ+IxHR/v61CZ3M12EYoJrI5E5ao7JG6K5zENDkGTu5tM7gRBEET/kLbAikajKCoqAgBUVFSgoaEBADB69Ghs3749M2dHZD3HjigFAHy0tx3tPSY5WNyDJdbyYz8rEBSvYPGYBmGTOwWNEgRBEP1D2leViRMn4sMPPwQA1NXVYdmyZXj33XexZMkSHHHEERk7QSK7OXZ4fCfp2i8OIBqLCxxdk7vNXYQdXGCJV7AUD5Z40CiDTO4EQRBEJknb5L5o0SIEAvGUxjvvvBPnnXcevv71r2PIkCF47rnnMnaCRHYzMeHDev/LgwDiM/70DON2c7A6En6u7nQ8WGnkYPmoRUgQBEFkkLQF1owZM/j/jx07Ftu2bUNbWxvKysp0ZxQShyZMYLHqkV7IKGB/VA6vYIUihnMvtYRtDHsGgHy1yZ0qWARBEEQG6dNV5e2338YVV1yB+vp67Nu3D+Xl5fjjH/+Id955J1PnR2Q5xT43aisK+L/1xuQAqmHPAi2/WEzmAkuWgd5wTOhcwrE+tAipgkUQBEFkkLQF1l/+8hfMmDEDeXl52Lx5M4LBIACgo6MD99xzT8ZOkMh+WB4WAJQV6Few1LsIWWaaEV2hCGKqQwKCOwnDUXsVLDK5EwRBEP1F2leVu+++G8uXL8fvfvc7uN3KRfXUU0/Fpk2bMnJyRG6gFlhGFSzWIozGZMuKVEd38k7DbsGdhOGIXQ+WOgeLKlgEQRBE5khbYG3fvh2nnXZayu0lJSVob2/vyzkROcZEdQXLwIOV73GC2ag6g+ZRDR2a9HbRnYeRPrQIfeTBIgiCIDJI2leV6upq7NixI+X2d955h2IaDjMmDleGfutlYAHxEUp84LOF0b1dW8ESbBGG+tQipAoWQRAEkTnSFlhXX301FixYgPXr10OSJDQ0NOCZZ57BjTfeiB/+8IeZPEciyynyuXFEwuhu1CIElCwsq52E2gqW6Lgcuy3CAtpFSBAEQfQTacc03HLLLYjFYjjzzDPR3d2N0047DV6vFzfeeCN+9KMfZfIciRzgm+MqsevdXUl+LC1FPjfQ0WvZ8mvvCSX9u1uwRRjuQ9CoR1CUEQRBEIQIaQssSZLws5/9DDfddBN27NiBrq4uTJgwAYWFhZk8PyJH+NnM8fjvbxyJ8gLjCpZo2GjaFayYvRZhZbEX1cU+VBR54HBQdhtBEASROWwLLL/fn3LbiBEjAACxWIx/v7i4OOU44tBFkiRTcQUoOwmtKlgpuwhFYxpstgi9LifeuOkMOElcEQRBEBnGtsAqLS01TdVmqdvRqPiIE+LwQHTgs9bkLrqL0O6oHAC6Y30IgiAIoq/YFlivv/46/39ZlnHOOefg97//PYYPH57REyMOPeya3N1OCeGoLJyDFeEtQqpIEQRBEIOLbYF1+umnJ/3b6XTi5JNPpmgGwhJ1mrsZzOReXeLDnrYe4ST3kM0WIUEQBEH0F3QlIgaMQm88hLTTyoPVE/9+TUkeABtJ7mm0CAmCIAiiP6ArETFgKB4sK5N7vIJVUxoXWOKzCO3FNBAEQRBEf5ERgWVmeicIRpHoLsKEB6um1AcA6BaMaYjYTHInCIIgiP7CtgfrggsuSPp3b28vrr32WhQUFCTd/sILL/TtzIhDDpEKVjga47lXwxItQtFdhCFWwXKRwCIIgiAGF9tXopKSkqSvK664AjU1NSm39zdtbW24/PLLUVxcjNLSUsybNw9dXV2ma3p7e3HddddhyJAhKCwsxIUXXoimpqakY3bv3o2ZM2ciPz8flZWVuOmmmxCJKBf4F154Ad/61rcwdOhQFBcXo76+Hv/85z/75TEearAcLL9JTAOrXkkSUF3MKljUIiQIgiByC9sVrBUrVvTHedjm8ssvx/79+7F69WqEw2HMnTsX11xzDVauXGm45oYbbsDf//53PP/88ygpKcH8+fNxwQUX4N133wUARKNRzJw5E9XV1Vi7di3279+P2bNnw+1245577gEAvPXWW/jWt76Fe+65B6WlpVixYgXOO+88rF+/Hscff/yAPPZcRWQXIcvAKvK6+PEiJvdoTEYipQFuB1WwCIIgiMEl7VE5g8mnn36KVatW4b333sPUqVMBAA8//DDOOecc3HvvvaipqUlZ09HRgT/84Q9YuXIlvvnNbwKIi8Xx48fjP//5D04++WT861//wieffIJ///vfqKqqwuTJk3HXXXfhpz/9KX7+85/D4/HgwQcfTPq599xzD1566SX87W9/MxRYwWAQwWCQ/1svDf9wQERgsQpWab4HBYmKl4jJnVWvAGoREgRBEINPTl6J1q1bh9LSUi6uAGD69OlwOBxYv3697pqNGzciHA5j+vTp/LZx48Zh1KhRWLduHf+5xx57LKqqqvgxM2bMgN/vx9atW3V/biwWQ2dnJ8rLyw3Pd+nSpUnt05EjR9p6vIcKLKahqzcCWZZ1j+lIZGCV5ru5wBKpYCUJLGoREgRBEINMTgqsxsZGVFZWJt3mcrlQXl6OxsZGwzUejwelpaVJt1dVVfE1jY2NSeKKfZ99T497770XXV1d+N73vmd4vrfeeis6Ojr41549e0wf36EKM7lHYjKCkZjuMayCVZLnRoEnPsYmEDIWZIxwVPk+tQgJgiCIwSarrkS33HILJEky/dq2bdtgnyZn5cqVuPPOO/HnP/85RfCp8Xq9KC4uTvo6HMl3O8ESPYzG5TAPVkmeG/mJClZMhqEgY0QSFSynQ4KDhjcTBEEQg0xWebB+8pOf4KqrrjI95ogjjkB1dTWam5uTbo9EImhra0N1dbXuuurqaoRCIbS3tydVsZqamvia6upqbNiwIWkd22Wo/bnPPvssfvCDH+D5559PajsSxjgcEgq9LnT2RtDZG8bQIm/KMeoKVp5qEHNXMGI6mDlEOwgJgiCILCKrBNbQoUMxdOhQy+Pq6+vR3t6OjRs3YsqUKQCA1157DbFYDHV1dbprpkyZArfbjTVr1uDCCy8EAGzfvh27d+9GfX09/7m/+MUv0NzczCtSq1evRnFxMSZMmMB/1p/+9Cd8//vfx7PPPouZM2f26TEfbhQlBJaR0Z1VsErz3XA6JOS5negJR+M+rELjnxumkFGCIAgii8jJq9H48eNx1lln4eqrr8aGDRvw7rvvYv78+bjkkkv4DsJ9+/Zh3LhxvCJVUlKCefPmYeHChXj99dexceNGzJ07F/X19Tj55JMBAN/+9rcxYcIEXHnllfjwww/xz3/+E4sWLcJ1110HrzdebVm5ciVmz56N++67D3V1dWhsbERjYyM6OjoG58nIMazCRv2qChYAFHgVH5YZEZpDSBAEQWQROXs1euaZZzBu3DiceeaZOOecczBt2jQ8/vjj/PvhcBjbt29Hd3c3v+2BBx7AueeeiwsvvBCnnXYaqqurkxLnnU4nXnnlFTidTtTX1+OKK67A7NmzsWTJEn7M448/jkgkguuuuw7Dhg3jXwsWLBiYB57jsLBRo4HP7SymIc8DAMpOQguBRS1CgiAIIpvIqhahHcrLy01DRceMGZOy88zn8+GRRx7BI488Yrhu9OjRePXVVw2//8Ybb9g+V0Kh0KdENejRnhj0XJyoYOV7EllYFlEN1CIkCIIgsgm6GhEDitXAZyVoNNEiTEQ1WFWwWA6WhwQWQRAEkQXQ1YgYUFiae6fBPMIOjQcrnwsyqwpWXGC5qEVIEARBZAEksIgBpSRRmWrtCqV8T5blPlSwqEVIEARBZA90NSIGlFHl+QCA3W3dKd/rDkW5UCqx68GK0C5CgiAIInugqxExoIwuLwAAfHUgkPI9Vr3yOB08ZJTFNIh6sGgXIUEQBJENkMAiBpTRQ+IVrD0HexCLJe/yZCGjxXluSImZOiymwbKCFaMWIUEQBJE90NWIGFCGlfjgckgIRWJo9PcmfU/rvwJseLCoRUgQBEFkEXQ1IgYUl9OBEWV5AICvDiT7sDp64sZ35r8CVB6skNguQhJYBEEQRDZAVyNiwBk1JO7D2t2W7MPiFSyVwOKjcgxysxhKi5A8WARBEMTgQwKLGHBGJ3YSaitYzIOlW8GyEljUIiQIgiCyCLoaEQMOM7p/1aZtESYEVn5qBaubWoQEQRBEDkFXI2LA4VlY2gpWT2oFq4B7sCimgSAIgsgdSGARA87oIfpZWPoerLjA6qZhzwRBEEQOQVcjYsBhFSx/bwTt3crInI7u1BZhfiKmQbyCRS9pgiAIYvChqxEx4OR5nKgs8gJINrorFSwPv00JGo1AlpODSdVwgeWiFiFBEAQx+JDAIgYFPaN7eyIHqzgvtYIVk4FgYqegHrxF6KCXNEEQBDH40NWIGBRGJWYS7lb5sFhMQ2l+akwDYB7VQC1CgiAIIpugqxExKPAKVqJFGI3J6OyNCyj1LkKnQ4LPHX+ZmkU1UIuQIAiCyCZIYBGDgrZF6E/4r4BkgQUAhV7rqAZqERIEQRDZBF2NiEFhpCYLixncC72ulDafkuYuUMGiHCyCIAgiCyCBRQwKbFxOo78XveGobsgogxndu00rWKxFSC9pgiAIYvChqxExKJQXeHjrb09btzImR0dgqaMajKCgUYIgCCKboKsRMShIksQDR7860M0DR80qWNQiJAiCIHIFEljEoKE2ujOTuzqigcHmEQq1CKmCRRAEQWQBdDUiBo1RCYG1p62bZ2CZtghNYxqoRUgQBEFkDy7rQwiifxhdrgx9djnirb0SvQqWN2FyFwga9ZDAIgiCILIAuhoRg4a6RWi+i1C8guUiDxZBEASRBZDAIgYNZnLf29aDg4G4yV096JlRwE3u5MEiCIIgcgO6GhGDRk1pHtxOCaFoDNubOgEYVLCEPFgksAiCIIjsga5GxKDhdEgYUZaoYh3sAWC0i9DagxXhJndqERIEQRCDDwksYlBhbUKGeQXLWGCFqIJFEARBZBF0NSIGFWZ0Z+gJrEK2i5BahARBEESOQFcjYlBJqWDptAiVYc8mJvcIxTQQBEEQ2QNdjYhBZfSQAv7/ToeEIm9qNJuS5G5SwYpRTANBEASRPZDAIgYVdYuw2OeCJKUKpPxEi7DLoIIlyzK1CAmCIIisgq5GxKCibhGW5qdmYAHJFSxZllO+H43JYDdTi5AgCILIBuhqRAwqPrcTVcVeAECxjsEdUCpY0ZiMYMJrpYaluAPUIiQIgiCyg5wVWG1tbbj88stRXFyM0tJSzJs3D11dXaZrent7cd1112HIkCEoLCzEhRdeiKampqRjdu/ejZkzZyI/Px+VlZW46aabEInot6beffdduFwuTJ48OVMP67CEzSQsNRBYrIIF6PuwwjFFdFGLkCAIgsgGcvZqdPnll2Pr1q1YvXo1XnnlFbz11lu45pprTNfccMMN+Nvf/obnn38eb775JhoaGnDBBRfw70ejUcycOROhUAhr167FU089hSeffBKLFy9O+Vnt7e2YPXs2zjzzzIw/tsONUQkfll5EAxA3v/vc8Zeq3k7CcEQtsKiCRRAEQQw+OSmwPv30U6xatQq///3vUVdXh2nTpuHhhx/Gs88+i4aGBt01HR0d+MMf/oD7778f3/zmNzFlyhSsWLECa9euxX/+8x8AwL/+9S988skn+OMf/4jJkyfj7LPPxl133YVHHnkEoVAo6edde+21uOyyy1BfX9/vj/dQZ2JNMYDUTCw1ZjsJw6oUdz2TPEEQBEEMNDkpsNatW4fS0lJMnTqV3zZ9+nQ4HA6sX79ed83GjRsRDocxffp0ftu4ceMwatQorFu3jv/cY489FlVVVfyYGTNmwO/3Y+vWrfy2FStWYOfOnbjjjjuEzjcYDMLv9yd9EQqX1o3Cirkn4odnfM3wGLOdhGwHocuRky9ngiAI4hAkJ69IjY2NqKysTLrN5XKhvLwcjY2Nhms8Hg9KS0uTbq+qquJrGhsbk8QV+z77HgB8/vnnuOWWW/DHP/4RLldqZpMeS5cuRUlJCf8aOXKk0LrDBa/LiW8cXckDRfVQKljGAovagwRBEES2kFUC65ZbboEkSaZf27ZtG7Tzi0ajuOyyy3DnnXfiqKOOEl536623oqOjg3/t2bOnH8/y0CQ/MfA5EDRuEXpcWfVyJgiCIA5jxEowA8RPfvITXHXVVabHHHHEEaiurkZzc3PS7ZFIBG1tbaiurtZdV11djVAohPb29qQqVlNTE19TXV2NDRs2JK1juwyrq6vR2dmJ999/H5s3b8b8+fMBALFYDLIsw+Vy4V//+he++c1vpty31+uF1+s1fVyEOQVekQoWCSyCIAgiO8gqgTV06FAMHTrU8rj6+nq0t7dj48aNmDJlCgDgtddeQywWQ11dne6aKVOmwO12Y82aNbjwwgsBANu3b8fu3bu5Ub2+vh6/+MUv0NzczFuQq1evRnFxMSZMmAC3242PP/446ec++uijeO211/B///d/qK2tTfuxE+awFmFA1+Se8GBRi5AgCILIErJKYIkyfvx4nHXWWbj66quxfPlyhMNhzJ8/H5dccglqamoAAPv27cOZZ56Jp59+GieddBJKSkowb948LFy4EOXl5SguLsaPfvQj1NfX4+STTwYAfPvb38aECRNw5ZVXYtmyZWhsbMSiRYtw3XXX8QrUxIkTk86lsrISPp8v5XYiszCTe7euyZ3tIqQKFkEQBJEd5KTAAoBnnnkG8+fPx5lnngmHw4ELL7wQDz30EP9+OBzG9u3b0d3dzW974IEH+LHBYBAzZszAo48+yr/vdDrxyiuv4Ic//CHq6+tRUFCAOXPmYMmSJQP62IhURCpYNCaHIAiCyBYkWW+4G9Gv+P1+lJSUoKOjA8XFxYN9OjnB0n98isfe3Il502px+7kTkr73xvZmXLXiPUwcXoxXfvT1QTpDgiAI4lDHzvWbPvITOYF5TAO1CAmCIIjsgq5IRE5gHtNAuwgJgiCI7IKuSEROUCgQ00AeLIIgCCJboCsSkRPkJwSWWdAoxTQQBEEQ2QIJLCInKEi0CClolCAIgsgF6IpE5ARsTqHZsGdqERIEQRDZAl2RiJyggAWN6uZgUYuQIAiCyC5IYBE5AatgBUwqWNQiJAiCILIFuiIROYG6gqXNxg1HSGARBEEQ2QVdkYicoCCxizASkxFKVKwYigeLWoQEQRBEdkACi8gJ8t1O/v/dmqiGcIx5sOjlTBAEQWQHdEUicgKX0wGvK/5yDWiiGqhFSBAEQWQbdEUicoYCg7BRahESBEEQ2QYJLCJn4PMItRUsahESBEEQWQZdkYicoSAR1ZDiwaIWIUEQBJFl0BWJyBlYVENKBYvnYFGLkCAIgsgOSGAROQPzYGnnEbIkd4+LXs4EQRBEdkBXJCJn4B4sA5O7y0EvZ4IgCCI7oCsSkTMUGIzLoRYhQRAEkW2QwCJyhnzuwdJWsKhFSBAEQWQXdEUicgZlF2FyBStEw54JgiCILIOuSETOkM9ahJoKVoR7sKhFSBAEQWQHJLCInIHFNBjtInRTi5AgCILIEuiKROQMyqgcfZO7h1qEBEEQRJZAVyQiZ6gu9gEAvmgJJN0ephYhQRAEkWWQwCJyhhNGl0GSgF2tATT7e/nt1CIkCIIgsg26IhE5Q0meGxOGFQMANnzZxm+nFiFBEASRbdAVicgpTqotBwCs35kqsCimgSAIgsgW6IpE5BR1CYG1YZdaYMVbhC5KcicIgiCyBBJYRE5x4pi4wNre1ImDgRAAahESBEEQ2QddkYicYkihF0dWFgJQfFjUIiQIgiCyDboiETmHuk0oyzK1CAmCIIisgwQWkXOcpBJYkZjMb6cKFkEQBJEt0BWJyDmYwNra0MF9WAB5sAiCIIjsga5IRM4xrCQPo8rzEZOBdTsP8Nvd1CIkCIIgsgQSWEROwnxY7+5o5bc5aVQOQRAEkSWQwCJykpO4wIpXsDxOBySJBBZBEASRHZDAInKSutohAIB97T0AqD1IEARBZBc5K7Da2tpw+eWXo7i4GKWlpZg3bx66urpM1/T29uK6667DkCFDUFhYiAsvvBBNTU1Jx+zevRszZ85Efn4+KisrcdNNNyESiSQdEwwG8bOf/QyjR4+G1+vFmDFj8MQTT2T8MRLGjCzPQ3Wxj//bRQZ3giAIIotwDfYJpMvll1+O/fv3Y/Xq1QiHw5g7dy6uueYarFy50nDNDTfcgL///e94/vnnUVJSgvnz5+OCCy7Au+++CwCIRqOYOXMmqqursXbtWuzfvx+zZ8+G2+3GPffcw3/O9773PTQ1NeEPf/gDjjzySOzfvx+xWKzfHzOhIEkS6o4ox0sfNACgiAaCIAgiu5BkWZatD8suPv30U0yYMAHvvfcepk6dCgBYtWoVzjnnHOzduxc1NTUpazo6OjB06FCsXLkS//Vf/wUA2LZtG8aPH49169bh5JNPxj/+8Q+ce+65aGhoQFVVFQBg+fLl+OlPf4qWlhZ4PB6sWrUKl1xyCXbu3Iny8vK0zt/v96OkpAQdHR0oLi5O81kgnln/FX721y0AgJoSH9beeuYgnxFBEARxKGPn+p2TH/vXrVuH0tJSLq4AYPr06XA4HFi/fr3umo0bNyIcDmP69On8tnHjxmHUqFFYt24d/7nHHnssF1cAMGPGDPj9fmzduhUA8PLLL2Pq1KlYtmwZhg8fjqOOOgo33ngjenp6DM83GAzC7/cnfRF9h+0kBAC3KydfygRBEMQhSk62CBsbG1FZWZl0m8vlQnl5ORobGw3XeDwelJaWJt1eVVXF1zQ2NiaJK/Z99j0A2LlzJ9555x34fD789a9/RWtrK/77v/8bBw4cwIoVK3Tve+nSpbjzzjttP07CnK8NLcSQAg8OBEJwUUQDQRAEkUVk1cf+W265BZIkmX5t27ZtUM8xFotBkiQ888wzOOmkk3DOOefg/vvvx1NPPWVYxbr11lvR0dHBv/bs2TPAZ31oIkkSj2sgDxZBEASRTWRVBesnP/kJrrrqKtNjjjjiCFRXV6O5uTnp9kgkgra2NlRXV+uuq66uRigUQnt7e1IVq6mpia+prq7Ghg0bktaxXYbsmGHDhmH48OEoKSnhx4wfPx6yLGPv3r0YO3Zsyn17vV54vV7Tx0Wkx0m15fjHlkYSWARBEERWkVVXpaFDh2LcuHGmXx6PB/X19Whvb8fGjRv52tdeew2xWAx1dXW6P3vKlClwu91Ys2YNv2379u3YvXs36uvrAQD19fX4+OOPk8Tb6tWrUVxcjAkTJgAATj31VDQ0NCRFQnz22WdwOBwYMWJERp8Pwppzjh2GIyoKcM6xwwb7VAiCIAiCk5O7CAHg7LPPRlNTE5YvX85jGqZOncpjGvbt24czzzwTTz/9NE466SQAwA9/+EO8+uqrePLJJ1FcXIwf/ehHAIC1a9cCiMc0TJ48GTU1NVi2bBkaGxtx5ZVX4gc/+AGPaejq6sL48eNx8skn484770Rrayt+8IMf4PTTT8fvfvc7oXOnXYQEQRAEkXsc8rsIAeCZZ57BuHHjcOaZZ+Kcc87BtGnT8Pjjj/Pvh8NhbN++Hd3d3fy2Bx54AOeeey4uvPBCnHbaaaiursYLL7zAv+90OvHKK6/A6XSivr4eV1xxBWbPno0lS5bwYwoLC7F69Wq0t7dj6tSpuPzyy3HeeefhoYceGpgHThAEQRBE1pOzFaxchipYBEEQBJF7HBYVLIIgCIIgiGyFBBZBEARBEESGIYFFEARBEASRYUhgEQRBEARBZBgSWARBEARBEBmGBBZBEARBEESGIYFFEARBEASRYUhgEQRBEARBZBgSWARBEARBEBmGBBZBEARBEESGIYFFEARBEASRYUhgEQRBEARBZBjXYJ/A4Qibr+33+wf5TAiCIAiCEIVdt9l13AwSWINAZ2cnAGDkyJGDfCYEQRAEQdils7MTJSUlpsdIsogMIzJKLBZDQ0MDioqKIEnSYJ9O1uL3+zFy5Ejs2bMHxcXFg306BOh3ko3Q7yQ7od9L9pGJ34ksy+js7ERNTQ0cDnOXFVWwBgGHw4ERI0YM9mnkDMXFxfQGlWXQ7yT7oN9JdkK/l+yjr78Tq8oVg0zuBEEQBEEQGYYEFkEQBEEQRIYhgUVkLV6vF3fccQe8Xu9gnwqRgH4n2Qf9TrIT+r1kHwP9OyGTO0EQBEEQRIahChZBEARBEESGIYFFEARBEASRYUhgEQRBEARBZBgSWARBEARBEBmGBBaRVSxduhQnnngiioqKUFlZiVmzZmH79u2DfVqEil/+8peQJAnXX3/9YJ/KYc++fftwxRVXYMiQIcjLy8Oxxx6L999/f7BP67AlGo3i9ttvR21tLfLy8vC1r30Nd911l9DcOiJzvPXWWzjvvPNQU1MDSZLw4osvJn1flmUsXrwYw4YNQ15eHqZPn47PP/884+dBAovIKt58801cd911+M9//oPVq1cjHA7j29/+NgKBwGCfGgHgvffew2OPPYZJkyYN9qkc9hw8eBCnnnoq3G43/vGPf+CTTz7Bfffdh7KyssE+tcOWX/3qV/if//kf/Pa3v8Wnn36KX/3qV1i2bBkefvjhwT61w4pAIIDjjjsOjzzyiO73ly1bhoceegjLly/H+vXrUVBQgBkzZqC3tzej50ExDURW09LSgsrKSrz55ps47bTTBvt0Dmu6urpwwgkn4NFHH8Xdd9+NyZMn48EHHxzs0zpsueWWW/Duu+/i7bffHuxTIRKce+65qKqqwh/+8Ad+24UXXoi8vDz88Y9/HMQzO3yRJAl//etfMWvWLADx6lVNTQ1+8pOf4MYbbwQAdHR0oKqqCk8++SQuueSSjN03VbCIrKajowMAUF5ePshnQlx33XWYOXMmpk+fPtinQgB4+eWXMXXqVFx00UWorKzE8ccfj9/97neDfVqHNaeccgrWrFmDzz77DADw4Ycf4p133sHZZ589yGdGMHbt2oXGxsak97GSkhLU1dVh3bp1Gb0vGvZMZC2xWAzXX389Tj31VEycOHGwT+ew5tlnn8WmTZvw3nvvDfapEAl27tyJ//mf/8HChQtx22234b333sOPf/xjeDwezJkzZ7BP77Dklltugd/vx7hx4+B0OhGNRvGLX/wCl19++WCfGpGgsbERAFBVVZV0e1VVFf9epiCBRWQt1113HbZs2YJ33nlnsE/lsGbPnj1YsGABVq9eDZ/PN9inQySIxWKYOnUq7rnnHgDA8ccfjy1btmD58uUksAaJP//5z3jmmWewcuVKHHPMMfjggw9w/fXXo6amhn4nhyHUIiSykvnz5+OVV17B66+/jhEjRgz26RzWbNy4Ec3NzTjhhBPgcrngcrnw5ptv4qGHHoLL5UI0Gh3sUzwsGTZsGCZMmJB02/jx47F79+5BOiPipptuwi233IJLLrkExx57LK688krccMMNWLp06WCfGpGguroaANDU1JR0e1NTE/9epiCBRWQVsixj/vz5+Otf/4rXXnsNtbW1g31Khz1nnnkmPv74Y3zwwQf8a+rUqbj88svxwQcfwOl0DvYpHpaceuqpKREmn332GUaPHj1IZ0R0d3fD4Ui+rDqdTsRisUE6I0JLbW0tqqursWbNGn6b3+/H+vXrUV9fn9H7ohYhkVVcd911WLlyJV566SUUFRXxnnhJSQny8vIG+ewOT4qKilI8cAUFBRgyZAh54waRG264AaeccgruuecefO9738OGDRvw+OOP4/HHHx/sUztsOe+88/CLX/wCo0aNwjHHHIPNmzfj/vvvx/e///3BPrXDiq6uLuzYsYP/e9euXfjggw9QXl6OUaNG4frrr8fdd9+NsWPHora2Frfffjtqamr4TsOMIRNEFgFA92vFihWDfWqEitNPP11esGDBYJ/GYc/f/vY3eeLEibLX65XHjRsnP/7444N9Soc1fr9fXrBggTxq1CjZ5/PJRxxxhPyzn/1MDgaDg31qhxWvv/667nVkzpw5sizLciwWk2+//Xa5qqpK9nq98plnnilv37494+dBOVgEQRAEQRAZhjxYBEEQBEEQGYYEFkEQBEEQRIYhgUUQBEEQBJFhSGARBEEQBEFkGBJYBEEQBEEQGYYEFkEQBEEQRIYhgUUQBEEQBJFhSGARBEEQBEFkGBJYBEEQBEEQGYYEFkEQBEEQRIYhgUUQRE5yxhln4Prrrx/s0yAIgtCFBBZBEBnnqquugiRJuPbaa1O+d91110GSJFx11VUDf2Ia2Hlqv3bs2DHYp5Z1zJ07F4sWLQIAfPTRR7jgggswZMgQ+Hw+HHPMMfj1r3+NSCQyyGdJENkDCSyCIPqFkSNH4tlnn0VPTw+/rbe3FytXrsSoUaMG8cySOeuss7B///6kr9raWt1jQ6HQAJ9ddhCNRvHKK6/gO9/5Dt566y2cfPLJyMvLw0svvYQPP/wQP/3pT3H//ffjggsuQCwWG+zTJYisgAQWQRD9wgknnICRI0fihRde4Le98MILGDVqFI4//nh+WzAYxI9//GNUVlbC5/Nh2rRpeO+995J+ViAQwOzZs1FYWIhhw4bhvvvuS7m/WCyGpUuXora2Fnl5eTjuuOPwf//3f5bn6fV6UV1dnfTldDoBxNuQ8+fPx/XXX4+KigrMmDFD6H70zlfb0hwzZgwefPDBpHWTJ0/Gz3/+c+HHdMYZZ+DHP/4xbr75ZpSXl6O6ujppPfsZy5Ytw5FHHgmv14tRo0bhF7/4BZ5++mkMGTIEwWAw6fhZs2bhyiuvTLpt7dq1cLvdmDJlCubOnYsLLrgAzzzzDKZNm4ajjz4as2fPxuuvv45Vq1ZhxYoVls85QRwOkMAiCKLf+P73v590wX3iiScwd+7cpGNuvvlm/OUvf8FTTz2FTZs24cgjj8SMGTPQ1tbGj7npppvw5ptv4qWXXsK//vUvvPHGG9i0aVPSz1m6dCmefvppLF++HFu3bsUNN9yAK664Am+++WafHsNTTz0Fj8eDd999F8uXLxe6H5HzFUHkvp566ikUFBRg/fr1WLZsGZYsWYLVq1fz799666345S9/idtvvx2ffPIJVq5ciaqqKlx00UWIRqN4+eWX+bHNzc34+9//ju9///tJ5/Hyyy/jvPPOw4YNG7Bz507cdNNNKec6btw4zJw5E88995ztx0kQhyQyQRBEhpkzZ458/vnny83NzbLX65W//PJL+csvv5R9Pp/c0tIin3/++fKcOXPkrq4u2e12y8888wxfGwqF5JqaGnnZsmWyLMtyZ2en7PF45D//+c/8mAMHDsh5eXnyggULZFmW5d7eXjk/P19eu3Zt0nnMmzdPvvTSS03P0+n8/+3cW0hUWxgH8L+XcbTxPhqIdKG0QCEdr4QDZqNpmBXYS0EEXh4GYkB0FBWNUKi8IAgW4UMbQXwunQchwZeIyFcZkGpAcAIDh5lGwRmc1cPBddjpke1hS+fo/wfzsPa39vrWGl8+116zY4TJZJKfe/fuyXhlZaWwWCyyrSWPlvkKIcS5c+fE2NiYapyCggLx5MkTzbkqKyuF1WpVxUtLS0VXV5cQQohAICCMRqOYnJzcd/12u13cvHlTtkdHR8WFCxdEJBJR9cvNzRVzc3NienpaABCbm5v7jud0OsWlS5f2jRGdNLF/usAjouMrMzMT9fX1UBQFQgjU19cjIyNDxr9+/YpwOIyKigp5zWAwoKysDG63W/YJhUIoLy+XfdLT03H58mXZ/vLlC7a2tlBTU6PKHwqFVI8j91NVVYVXr17JtslkUsWLi4sPlUfLfLXQuqYrV66o4llZWVhfXwcAuN1ubG9vw2az7ZujtbUVpaWlWFtbQ3Z2NhRFkQf/d7ndbni9XthsNrx//x4AsLGxgVOnTu0Zz+fzITk5+VDrJDquWGAR0ZFqamrC48ePAQATExNHkiMYDAIAXC4XsrOzVTGj0XjgvSaTCTk5OQfG9cjzu+joaAghVNfC4fChcxkMBlUsKipKHjRPSEg4cA4WiwUFBQWYmprCjRs3sLy8DJfLperz7t071NTUID4+HlevXoXBYMDs7Czsdruq387ODubn59HY2HhgTqKTgmewiOhI1dXVIRQKIRwOo7a2VhW7ePGiPN+0KxwO4/Pnz8jLy5N9DAYDPn36JPv4fD6srKzIdl5eHoxGI1ZXV5GTk6P6nDlzRre1aMmjZb7AX7t7379/l+1AIACPx6PrmnJzc5GQkICFhYV/7NPS0gJFUfDmzRtUV1fvGfvt27e4c+cOAMBsNsPhcGBwcBBer1fVb2xsDBsbG2hra9M0N6LjjjtYRHSkYmJi5OO+3V/n7TKZTLDb7XA6nUhPT8fZs2cxNDSEra0tNDc3AwASExPR3NwMp9MJs9mM06dPo7e3F9HRf/9/mJSUhI6ODrS1tSESicBqtcLv9+PDhw9ITk7Go0ePdFmLljxa5gsA169fh6IoaGhoQGpqKvr7+1Xfjx5rio+PR1dXFzo7OxEXF4eKigr8+PEDy8vL8vt98OABOjo6MDk5iampKdX96+vrWFpakgfhg8EgHA4HPn78iKqqKszMzKCoqAjDw8Po7e3F69evERcXh52dnT1/a6KThgUWER25g87lPH/+HJFIBA8fPsTPnz9RUlKC+fl5pKWlyT7Dw8MIBoNoaGhAUlIS2tvb4ff7VeMMDAwgMzMTz549w7dv35CamoqioiL09PTouhYtebTMt7u7Gx6PB7du3UJKSgoGBgZUO1h6ramvrw+xsbHo7++H1+tFVlaW6gWwKSkpaGxshMvlwt27d1X3zs7OoqysTJ6bGxkZwdOnT2V8fHwciqKgs7MTAOSvDz0eD86fP695jkTHUZT4/RAAERHp7tq1aygsLNzz7qv/ApvNhvz8fIyPj6uu3759G1arVRZQRKQdd7CIiE4on8+HxcVFLC4u4uXLl3viVqsV9+/f/wMzI/r/Y4FFRHRCWSwW+Hw+vHjxYt/XSHDniujf4yNCIiIiIp3xNQ1EREREOmOBRURERKQzFlhEREREOmOBRURERKQzFlhEREREOmOBRURERKQzFlhEREREOmOBRURERKQzFlhEREREOmOBRURERKSzXwxGvUqefiw3AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heat_list = []\n", "freq_list = np.arange(1, 10, 0.1)\n", "for w in freq_list:\n", " tlist, occ = bath_corr.occupation(w, 0.1, True)\n", " heat_list.append(w * occ[-1])\n", "plt.plot(freq_list, heat_list)\n", "plt.xlabel(r\"Mode Frequency$/\\Omega$\")\n", "plt.ylabel(r\"Heat Exchanged$/\\Omega$\")" ] }, { "cell_type": "markdown", "id": "ca545275-50dd-4c67-912c-b746cba6779a", "metadata": {}, "source": [ "This is highly oscillatory, perhaps unsurprising from the dynamics we generated but still it would be nice to smooth this out. We expect the result to eventually equilibrate but with such a small bandwidth this will take a while, instead we simply period-average the result. The period at which each mode oscillates is $T(\\omega)=2\\pi/\\omega$ so we average over the last $n$ timesteps where $(n+1) dt \\geq T(\\omega) > n dt$." ] }, { "cell_type": "code", "execution_count": 9, "id": "3ce24ca0-866a-45b6-89d0-8ed8e4994c56", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Heat Exchanged$/\\\\Omega$')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "heat_list = []\n", "freq_list = np.arange(0.05, 10, 0.1)\n", "for w in freq_list:\n", " tlist, occ = bath_corr.occupation(w, 0.1, True)\n", " sel = tlist > (tlist[-1] - 2 * np.pi/w)\n", " energy = occ * w\n", " period_averaged_energy = np.mean(energy[sel])\n", " heat_list.append(period_averaged_energy)\n", "plt.plot(freq_list, heat_list)\n", "plt.xlabel(r\"Mode Frequency$/\\Omega$\")\n", "plt.ylabel(r\"Heat Exchanged$/\\Omega$\")" ] }, { "cell_type": "markdown", "id": "37980eff-caf4-4bd2-bed7-cca871611f81", "metadata": {}, "source": [ "Here, as in the paper, we see heat is absorbed by the system from the band of the modes in the vicinity of $\\tilde{\\Omega}=\\sqrt{\\Omega^2+\\epsilon^2}$. This seems sensible as in a Markovian theory the system would sample the environment purely at its eigensplitting $\\tilde{\\Omega}$." ] }, { "cell_type": "markdown", "id": "8793c039-6a4c-4d4d-9289-1e0ffeff96a7", "metadata": {}, "source": [ "-------------------------------------------------" ] } ], "metadata": { "interpreter": { "hash": "56674a1249193ed385a20db9ba6c6497b0cb98d98f01f014399e91d8567384eb" }, "kernelspec": { "display_name": "oqupyPR", "language": "python", "name": "oqupypr" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.14" } }, "nbformat": 4, "nbformat_minor": 5 }