{ "cells": [ { "cell_type": "markdown", "id": "d432d126-c329-4f02-b1f9-71e27268f775", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Simultaneous Conjugate Interferometer with realistic beamsplitters\n", "\n", "Numerical phase calculations can be integrated into the phase calculation in a relatively straightforward way. These calculations might be somewhat limited and less efficient compared to what code designed for a particular interferometer geometry could achieve--if you want to study a specific interferometer configuration in depth, you probably want to write a dedicated function from scratch. However this approach is good for exploring the performance of different interferometers.\n", "\n", "In this example we will replicate Fig. 3b from the paper [High-Resolution Atom Interferometers with Suppressed Diffraction Phases](http://dx.doi.org/10.1103/PhysRevLett.115.083002)." ] }, { "cell_type": "markdown", "id": "6d360f73-f6d0-4758-b2f6-432be049de69", "metadata": {}, "source": [ "**What you'll learn:**\n", "- How to create custom `Unitary` subclasses that link symbolic interferometers to numerical Bragg pulse calculations\n", "- How to compute diffraction phase shifts as a function of atom velocity\n", "- How to reproduce Fig. 3b from Estey et al. (2015) by averaging over a velocity distribution" ] }, { "cell_type": "markdown", "id": "5613716c-0ee5-49a3-ab5c-da35587d3440", "metadata": { "raw_mimetype": "text/restructuredtext", "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "First we will define the code that links the numerical calculation code to the :py:mod:`mwave.symbolic` module." ] }, { "cell_type": "code", "execution_count": 1, "id": "0157f7d5-e3df-456b-80ce-f94ecc585233", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "from mwave.symbolic import Interferometer, InterferometerNode, Beamsplitter, FreeEv, set_constants, eval_sympy_var\n", "from mwave.integrate import propagate, omega_fnc_gaussian, multi_omega_fnc, phase_fnc_constant, make_kvec, make_phi\n", "import numpy as np\n", "import sympy as sp\n", "\n", "# Define a numeric unitary operator for single frequency Bragg\n", "class SingleFreqBragg(Beamsplitter):\n", " \n", " def gen_numeric(self, node, subs={}):\n", " delta = eval_sympy_var(self.delta, subs)\n", " n_init = eval_sympy_var(node.parent.n, subs)\n", " n_final = eval_sympy_var(node.n, subs)\n", " kvec, n0_idx, nf_idx = make_kvec(n_init, n_final)\n", " def fnc(omega, sigma, v, ratio):\n", " tfinal = 2*2.716*sigma\n", " result = propagate(\n", " kvec, make_phi(kvec, n_init), tfinal, delta + 2*v,\n", " omega_fnc_gaussian, np.array([-2*np.pi*omega, sigma, tfinal/2]),\n", " phase_fnc_constant, np.array([0.0]),\n", " )\n", " return result.phi_final[nf_idx]\n", " return fnc\n", "\n", "# Define a numeric unitary operator for multi frequency Bragg\n", "class MultiFreqBragg(Beamsplitter):\n", "\n", " def __init__(self, n1, n2, delta, k, omega_m):\n", " super().__init__(n1, n2, delta + omega_m, k)\n", " self.delta_numeric = delta\n", " self.omega_m = omega_m\n", " \n", " def gen_numeric(self, node, subs={}):\n", " delta = float(eval_sympy_var(self.delta_numeric, subs))\n", " omega_m = float(eval_sympy_var(self.omega_m, subs))\n", " n_init = eval_sympy_var(node.parent.n, subs)\n", " n_final = eval_sympy_var(node.n, subs)\n", " kvec, n0_idx, nf_idx = make_kvec(n_init, n_final)\n", " def fnc(omega, sigma, v, ratio):\n", " tfinal = 2*2.716*sigma\n", " result = propagate(\n", " kvec, make_phi(kvec, n_init), tfinal, delta + 2*v,\n", " multi_omega_fnc, np.array([-2*np.pi*omega*ratio/4, sigma, tfinal/2, omega_m]),\n", " phase_fnc_constant, np.array([0.0]),\n", " )\n", " return result.phi_final[nf_idx]\n", " return fnc" ] }, { "cell_type": "markdown", "id": "d56b3e00-ba72-496e-8de1-587d3feee4e0", "metadata": { "editable": true, "raw_mimetype": "text/restructuredtext", "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Here we have defined two classes, each of which inherit from the :py:class:`mwave.symbolic.Beamsplitter` class. The first, :code:`SingleFreqBragg`, will act exactly as the :py:class:`mwave.symbolic.Beamsplitter` class does, although it implements the function :code:`gen_numeric`, which we need to override to implement numerical phase calculations.\n", "\n", "The second, :code:`MultiFreqBragg`, modifies the behavior of the :py:class:`mwave.symbolic.Beamsplitter` class slightly as it sets the value of :code:`delta` passed to the super :code:`__init__` function to :code:`delta+omega_m`. This ensures that the analytically calculated phase uses the correct detuning. It then saves the :code:`delta` passed into its own :code:`__init__` function as :code:`delta_numeric`, which is used inside the :code:`gen_numeric` function.\n", "\n", "Both :code:`SingleFreqBragg` and :code:`MultiFreqBragg` return a function titled :code:`fnc`. When called :code:`fnc` computes the wavefunction obtained after applying a Bragg pulse. To do this it uses the :py:meth:`mwave.integrate.gbragg` function. The function calls in :code:`SingleFreqBragg` and :code:`MultiFreqBragg` are very similar--the main difference is that the multifrequency one modifies the intensity by `ratio` and passes in :code:`omega_mod` to compute a multifrequency pulse.\n", "\n", "Next we set up our interferometer as usual by defining our constants, our unitary operators, and writing down the sequence of unitary operators needed to generate the SCI. Finally we determine which nodes are interfering." ] }, { "cell_type": "code", "execution_count": 2, "id": "36bc23b7-9a29-466e-9759-9d26541a3873", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "# Set up symbols for symbolic computation\n", "k, c, hbar, m, n, T, Tp, delta, omega_m, omega_r, t_traj, g, v0, Toffset = sp.symbols('k c hbar m n T T_p delta omega_m omega_r t_traj g v_0 T_offset', real=True)\n", "k_eff = 2*k\n", "set_constants(m=m,hbar=hbar,c=c,t_traj=t_traj)\n", "\n", "# Define the operators needed for an SCI\n", "bs1 = SingleFreqBragg(n, 0, delta, k_eff)\n", "bs2 = MultiFreqBragg(0, -n, delta, k_eff, -omega_m)\n", "bs2u = MultiFreqBragg(n, 2*n, delta, k_eff, +omega_m)\n", "fe1 = FreeEv(T)\n", "fe2 = FreeEv(Tp)\n", "\n", "# Define the interferometer\n", "ii = Interferometer(init_node=InterferometerNode(n=n, v=2*hbar*k*n/m))\n", "ii.apply(bs1)\n", "ii.apply(fe1)\n", "ii.apply(bs1)\n", "ii.apply(fe2)\n", "ii.apply(bs2)\n", "ii.apply(bs2u)\n", "ii.apply(fe1)\n", "ii.apply(bs2)\n", "ii.apply(bs2u)\n", "\n", "# Determine the intefering nodes\n", "inodes = ii.interfere()" ] }, { "cell_type": "markdown", "id": "c6840382-2407-48e3-b66f-97492379cbef", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Lets check that we get the expected SCI phase." ] }, { "cell_type": "code", "execution_count": 3, "id": "0671c492-6bcb-468d-83b3-960a60e51a51", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "16*T*n**2*omega_r - 2*T*n*omega_m - 2*pi\n" ] } ], "source": [ "phi_A, phi_B, phi_C, phi_D = ii.phases()\n", "print(sp.expand(sp.simplify(phi_A - phi_C).subs(k, sp.sqrt(2*m*omega_r/hbar))))" ] }, { "cell_type": "markdown", "id": "d0695989-9ef9-49ea-b9ba-df2bc3ed663d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "That is expected! Next lets plot the trajectories so we can determine which node corresponds to $\\left|\\phi\\right\\rangle_\\text{uuu}$, $\\left|\\phi\\right\\rangle_\\text{uud}$, $\\left|\\phi\\right\\rangle_\\text{udu}$, etc." ] }, { "cell_type": "code", "execution_count": 4, "id": "1dd00544-bee6-4aad-8036-8b9de962fe2b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "# Define our substitutions for the analytic calculation\n", "subs = {hbar:1, k:1, m: 1, n: 5, delta: 4*n, omega_m: 8*n, T:5, Tp: 2}\n", "\n", "tfinal = float(inodes[0][0].t.evalf(subs=subs))\n", "t = np.linspace(0, tfinal, 1000)\n", "\n", "plt.figure()\n", "\n", "def plot_pair(i):\n", " f0 = inodes[i][0].get_trajectory(subs=subs)\n", " plt.plot(t, f0(t), label=f'inodes[{i}][0], $n={sp.latex(inodes[i][0].n)}$')\n", " f1 = inodes[i][1].get_trajectory(subs=subs)\n", " plt.plot(t, f1(t), label=f'inodes[{i}][1], $n={sp.latex(inodes[i][1].n)}$')\n", " \n", "plot_pair(0)\n", "plot_pair(2)\n", "\n", "plt.legend()\n", "plt.ylabel('position')\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", "plt.figure()\n", "plot_pair(1)\n", "plot_pair(3)\n", "plt.legend()\n", "plt.ylabel('position')\n", "plt.xlabel('time')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fe3987c0-4f27-4075-960c-5b027d5b4e67", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Now that we have identified which nodes correspond to which outputs we are ready to perform the numerical calculation. Lets generate functions that can be used to compute the wavefunction at each output.\n", "\n", "Note that we will have these calculations ignore some of the unitary operations: the upper interferometer third and fourth pulses should not be subjected to the unitary operator that describes the multifrequency beamsplitter operation happening on the lower interferometer third and fourth pulses. To do this we define a filter function which only returns true if the node momentum state is equal to one of the states that the beamsplitter is resonant with.\n", "\n", "(Note that you could define the `MultiFreqBragg` operator in a different way where it determines all of the states it is resonant with automatically instead of just those specified by `n1` and `n2`--then we wouldn't need to use the filter function.)" ] }, { "cell_type": "code", "execution_count": 5, "id": "5f129474-f42e-4146-868a-ef2eb5f6b03e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "# Write a filter function that ensures we don't double-count the effect of the multifrequency beamsplitters\n", "def filterfnc(node, unitary):\n", " return node.n == unitary.n1 or node.n == unitary.n2\n", "\n", "# Get the numeric phase calculation for each output\n", "uuu = inodes[1][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "udu = inodes[1][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "uud = inodes[0][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "udd = inodes[0][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "duu = inodes[3][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "ddu = inodes[3][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "dud = inodes[2][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "ddd = inodes[2][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "# Create a function to compute the differential phase\n", "def calc_diff_phase(omega, sigma, v, ratio):\n", " ph = -(np.angle(-uuu(omega, sigma, v, ratio)/udu(omega, sigma, v, ratio)) - np.angle(-duu(omega, sigma, v, ratio)/ddu(omega, sigma, v, ratio)))\n", " phh = -(np.angle(uud(omega, sigma, v, ratio)/udd(omega, sigma, v, ratio)) - np.angle(dud(omega, sigma, v, ratio)/ddd(omega, sigma, v, ratio)))\n", " return (ph+phh)/2" ] }, { "cell_type": "markdown", "id": "cd3563a2-1f06-4468-9223-8068c6502a31", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Now we can determine how the phase changes as a function of the input state velocity." ] }, { "cell_type": "code", "execution_count": 6, "id": "693c9db8-5943-4ab6-bb33-6a3eb4b8521b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 200/200 [01:59<00:00, 1.67it/s]\n" ] } ], "source": [ "from tqdm import tqdm\n", "from scipy.interpolate import interp1d\n", "\n", "# Compute phase value at several velocities\n", "velocities = np.linspace(-3,3,200)\n", "phase_values = np.full_like(velocities, np.nan)\n", "for i in tqdm(range(len(velocities))):\n", " phase_values[i] = calc_diff_phase(5.05, 0.2, velocities[i]/2, 4.1)\n", "\n", "# Interpolate\n", "phase_v_fnc = interp1d(velocities, phase_values)" ] }, { "cell_type": "markdown", "id": "b6c25ee0-0afe-46aa-adf5-633b00abc692", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "We can now plot this against the raw data from Fig. 3b." ] }, { "cell_type": "code", "execution_count": 7, "id": "bf307dd7-6cc3-4b0e-b596-a0a751367582", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set raw data\n", "raw_data_x = np.array([-0.77444,-0.38722,0,0.38722,0.7744,1.16167])\n", "raw_data_y = np.array([0.1785, 0.139,0.108,0.106,0.127,0.1705])\n", "raw_data_err = np.array([0.0054,0.0058,0.00285,0.00155,0.002575,0.0036])\n", "\n", "# Plot\n", "vv = np.linspace(-1.5,1.5)\n", "plt.plot(vv,1000*phase_v_fnc(vv-0.225)/16/25/2/np.pi)\n", "plt.errorbar(raw_data_x, raw_data_y, raw_data_err, marker='.', linestyle='none')\n", "plt.xlim([-1,1.5])\n", "plt.ylim([0,0.2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d3d9fb7a-ee0c-4c74-8db0-c79872478311", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "It doesn't agree because the model in Fig 3b assumes that there is a distribution of velocities entering the interferometer. Lets come up with a form for the velocity distribution based on what we expect after a Raman velocity pulse." ] }, { "cell_type": "code", "execution_count": 8, "id": "95443b00-05fe-462e-8bf9-b97af9e42e3b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import nquad\n", "\n", "# We do double velocity selection, so Brian Estey's equation on p.99 of his thesis is relevant\n", "def vel_dist(w, v):\n", " OmR = np.pi/w\n", " return (OmR**2/(v**2 + OmR**2)*np.sin((v**2 + OmR**2)**0.5*w/2)**2)**2\n", "\n", "# Normalize the velocity distribution\n", "norm_factor = nquad(lambda x: vel_dist(400/77, x), ((-np.inf, np.inf),), opts={'limit':1000})[0]\n", "def vel_dist_norm(v):\n", " return vel_dist(400/77,v)/norm_factor\n", "\n", "# Plot\n", "vv = np.linspace(-2,2,200)\n", "plt.plot(vv, vel_dist_norm(vv))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5bee7ebe-9313-4c95-88d6-a473c4d0f91c", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "\n", "\n", "Now that we have a form for the velocity distribution we can average the phase over it.\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "ebc1e83e-0e78-438c-85ac-b51fa92b9b17", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jack/.pyenvs/lab/lib/python3.12/site-packages/scipy/integrate/_quadpack_py.py:1286: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n", " If increasing the limit yields no improvement it is advised to analyze \n", " the integrand in order to determine the difficulties. If the position of a \n", " local difficulty can be determined (singularity, discontinuity) one will \n", " probably gain from splitting up the interval and calling the integrator \n", " on the subranges. Perhaps a special-purpose integrator should be used.\n", " quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n", "/Users/jack/.pyenvs/lab/lib/python3.12/site-packages/scipy/integrate/_quadpack_py.py:1286: IntegrationWarning: The occurrence of roundoff error is detected, which prevents \n", " the requested tolerance from being achieved. The error may be \n", " underestimated.\n", " quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n" ] }, { "data": { "image/png": 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XQuWibuz3k8XSNaNSaGgoEhIS4OVl3iQj+/7+/pmSobVr1yIsLAx9+vQxO969e3eULFkSxYoVw4kTJzB8+HAEBARg9eokEwT+Z+zYsRgzZgxsjr0jHDrPQcClS9iwOhbxJ27imbKF0b2hr6VzRkREyYiOS8BnS/7BPPtvkZDHDcUr6/v/UNayuikl58yZg5dfflkFOqYGDBhgfFy9enUULVoULVq0QGBgoGouS0pqiKSvkoHUAPn4JD+MPNcpVBYVC5XFJ5GBGPunP8b8cRp1SrqjkjebDImIrM23G8/izbCfUNT+LhLyuUOXz9PSWbIJ6WoCk+YnmY0yJMR8bSrZT6mDc3pcuXIFf//9N95+++0nppXRZ+LChQvJPi/9jaSPkOlma/o3LYPupSPxvW4qhi7aj6hYLpVBRGRNtp4JQeihFehovweazg72HWchSqdD9QXV1RYVl3JXD8rGAMjJyQl169bFtm3bjMcSExPVfuPGjZ8yK8C8efPg6emJV1555Ylpjx8/rn5KTVBu5OroipO9T6pNHmeEnZaAr6O+QVv7A+gaNhuj1nGpDCIia3HtXhTGrdiJbx3nqH3ds0MBn/qWzpbNSPcoMGlWmj17NhYsWICzZ8/ivffeQ2RkpBoVJnr16qWan0w7NUuwIps8vn79unqctOZGAikJgHr37g0HB/OWOWnm+vrrr1UH7MuXL2P9+vXqOs2aNUONGjUy/u5zO3sH2L+mn3epl8NW3D22Hqv8rlk6V0RENi82PhGDF/vh84QZ8NA9QKJ3DaD5cJsvF6vuA9SlSxfcvn0bo0aNQnBwMGrVqoXNmzcbO0YHBQWpkWEGN27cQO3atY37kyZNUpsMcd+5c6fxuDR9yWtl9FdyNU/yvEyiKMGW9OWRyRU///zzjLxn21L2BaDRQODADExwnIUO68qjpk9blPPMZ+mcERHZrPGb/VH95ko87/gvEu1dYNdxFuDg9Fi6kKgQlC5Q2iJ5zO10msy8ZAOkE3SBAgVw//592+sPFBcN7dcXoAs5jR0JNTHe42usHfQsXBztLZ0zIiKbs/lUMN5d5IdiCMXGEgtRsEFXoEF/4/PL/Jfh24PfqseyLuToJqOfuBpAbhaeRd/fXAvMFji6QNdpDjR7Zzxv/y8ahK7C1xvOWDpXREQ2J+hOFD75/V/1uM2z9VHw/b+A+o8G/gRHBmPswbHG/UQkYsz+Meo4ZS4GQLbCszJ0rb5WD1vZ+2HxwSvYeOKmpXNFRGQzYuITMHDJURSLuYjavu4Y/nIlwM7ebMLDoPAgFfSYStQScTXiqgVynLtZ3TxAlIUaDABc3LH/RlVg1xWMWHUC1YsXgG+hjI0yIyKitPtu41kUu7kVvzhPxYNi/eFo1+SxNL5uvqrZyzQIstPZwSe/jcxjl41YA2RL5K+Mml3wUasqqFeyICJi4jFo6VE1GoGIiLLOhhM38Nf+oxjvOFvt58ubN9mlLrzzemNkw5Fmwc/oxqPVccpcDIBskIO9HX7sXBnfuCyG2409ajQCERFljUuhkfhs1b+Y6jQD7rpIoFgd4IWURzG/VvY14+O17dbadAforMQmMBtV7PSv6ImNaOm4Dy/tKYVGZQrhxSrma7wREdHTr/M1cPFR9IpfhYaO/tCc8kHX6Ve1bmNaeLny/+WswhogW9V4IFCoPLx19zDO8Vd8vOI4rt7llOtERJnpqw1n4BJ8BEMcV6l9XZtJar1GsjwGQLbKyRXo9Cs0O0e8ZH8YreO24r3FfuqvFSIienrrjl/HqoMXVNOXg3RqrvY6ULMri9ZKMACyZcVqQfdfO/SXjgsRdcMfo7leGBHRU7tw6wFGrj6JGDjhRMUhgCx10XZysh2fs2ItSHoyBkC2rskHQOlmcEUMZjj+iLVHArHsUJClc0VElGM9jNX3+4mKTUDjMoXwcteBwIBdgEsBS2eNTDAAsnWyblvH2UDeIijjeBcVdNfUqvH/Xg2zdM6IiHKk0etPIfLWRVTMG4UfutWCvZ1O/38tWRXeEQLyewNdFsFp4B4UrdwYsQmJeH/xUdyNjGXpEBGlw+9+17DmyGXMcPwBfzgOh+e94yw/K8UAiPR8G0HnURqT3qiJ0oXz4nrYQ3yw9BgSEm1irVwioqd26vp9/G/NSQx1WImadhfhhASgQAmWrJViAERm3FwcsbB5BBY6T8ChCzcxeWsAS4iI6Amkxvyd3/xQN/EE3nHYoD/42jQGQFaMARCZi3kAnx1D0Ex3HCMdlmDGjkD8dZqrEBMRpSQ+IRGDlx5FTFgwfnT+GXbQgLp9gCqPZnQm68MAiMw55wPa/6Qe9nXYgtZ2hzFsxb9qKnciInrchC0B2H/hNqY7z0Bh7R5QpDLQ+jsWlZVjAESPq9AaaDJYPfzeeTYKxN7Eu7/5ISo2nqVFRGRi/b83MGv3RfS234JGulOAY17gjQWAU16Wk5VjAETJazEaKFEf+bQHmOkyHRdD7mHEqpPQNHaKJiISZ26E49Pf/1WP8zfpB9TsBrw6FShSkQWUAzAAouTJQn2d5qiJu6pp5zHccbn6S2f+vsssMSKyefek0/OiI4iOS0SzCkXw4cu1gA4zgRpv2HzZ5BQMgChlBUsC7fT9gZr5OEKHRHy78SwOX77LUiMimyXTg3yw7Bhu3o1Af7eD+LFLDf1kh5SjMACi1FVuC/TfjvL956NtzRKIT9TUJIm3wqNZckRkkyZuCcA/50Mx0mkl/hf7A9w3D7J0ligDGADRkxWvC51Oh3Edq6OipyvuRkRh0JJjiEtIZOkRkU3ZcOIGZu4KRAs7P/Sz+0N/sFJbS2eLMoABEKVZ3vgwrHH/ASOcV+HQ5bsY88dplh4R2Qz/4HB8svIESuhuY3qe2fqDDd8Fqra3dNYoAxwy8iKyUUH74Rq0A/11wB67ilh0AKjolR9vNi5l6ZwREWWp+1Fxaqbn+LgYLMj/E/LEhavacbz4NUs+h2INEKVd5VeBev3Uw5l5Z8ELd/HlH2ew53woS5GIcnWn5w+XH8OVO1H4Lu9ylI0LAFzcgdfnAQ5Ols4eZRADIEofmd3UqzryxN3D8oI/wS4xDu8v9uNM0USUa03Zeg47A26jrGMoOmlb9Qc7/KIfKUs5FgMgSh9HF6DLQjU/UKmHZ/BjweUIj45HvwWHcf9hHEuTiHKVzaduYvqOC+rxB51awq7fZqDVN0DFlyydNXpKDIAo/TzKAB31HQBffrgRb+Xbj4u3IzF46TG1KCARUW5w+sZ9DF2hn+m537Ol0a5WcX2/n/+WCqKcjQEQZXy9sOYjAPeS6P7aK8jjaI/d527ju03+LFEiyvFkrrO3FxxBVGwCJnn+iZG1Yi2dJcpkDIAo45oPB97ZjXI1GuP7N2qqQ3P3XsKyQ0EsVSLKsR7GJuDthUdw8340Brgfxuvhv8Fh/ktARIils0aZiAEQPcWnxw7I464etqleFN80toMdEvHFulM4ePEOS5aIcpzERA1DVxzHiWv30SDPDYyIn6l/4pkPgfxels4eZSIGQJQ5ji5Ej3/fxPRiWxCXoOG9xUdx9W4US5eIcpRJfwXgz1PBKGL/AAvz/gC7+IdA2ReA5p9aOmuUyRgAUeawd4YuMQ5t7v6Gt4r4425krGo/fxATzxImohzhd79r+GlnIOyRgA1F58PlwVWgYCmg0xzAzt7S2aNMxgCIMkfNLkCDAerh57FTUSffXQSERGDIsmNqEjEiImsmzfYjV59Qj5eW2QKv0H2AoyvQdQng6mHp7FEWYABEmafVt4BPQ9jFhGNx/mko4BCLv8/eUlXKRETW6nJoJN5Z5Kea79tWK4L6rv91dm43A/CqaunskTUFQDNmzECpUqXg4uKChg0b4tChQymmPX36NDp16qTSy4riU6dOfSzNl19+qZ4z3SpVqmSWJjo6GgMHDkShQoWQL18+dc6QEPbItyoyJXznBUA+L+S5F4CNpVYC0PDzzkCsOXbN0rkjIkp2ja+35h9GWFQcapYogIlv1IWu+3Kg5yqgWkeWWC6W7gBo+fLlGDp0KEaPHo2jR4+iZs2aaN26NW7dupVs+qioKJQpUwbjxo2Dt7d3iuetWrUqbt68adz27Nlj9vxHH32EP/74AytXrsSuXbtw48YNdOzID6fVcSsKdJ4P2DmgxLWNmFLzujo8fNVJ+F25a+ncEREZxSUk4r3FfrgYGolSbjrM7lUXeZzs9f19yrVkSeVy6Q6AJk+ejP79+6Nv376oUqUKZs6cCVdXV8ydOzfZ9PXr18fEiRPRtWtXODs7p3heBwcHFSAZtsKFCxufu3//PubMmaOu/cILL6Bu3bqYN28e9u3bhwMHDqT3LVBWK9lEv2ZYi1Fo98bbaFXFC7Hxiei34AgCbz9g+RORxWmahlHrTmFf4B24OQEbisyA546PgbhoS2eNrDEAio2NhZ+fH1q2fBQZ29nZqf39+/c/VUbOnz+PYsWKqdqiHj16ICjo0WR6cs24uDiz60oTma+vb4rXjYmJQXh4uNlG2ajhO0DTYbCzt8fUrrVQ08ddVTH3mXcItyNieCuIyKJ+/ecSlh66Cjsd8Eflv5Hv+h7g1Bog7ArvjI1IVwAUGhqKhIQEeHmZTwYl+8HBwRnOhPQjmj9/PjZv3oyff/4Zly5dQtOmTREREaGel3M7OTnB3d09zdcdO3YsChQoYNx8fHwynD96Oq6IwZIKu1DWwxFX7z5U7e2RHB5PRBby1+lgfPfnWfV4Tt3LKBnwXwtG+xlAkYq8LzbCKkaBvfzyy+jcuTNq1Kih+hNt2rQJYWFhWLFiRYbPOXLkSNV0ZtiuXr2aqXmmNNI0YHFn5N07HmtLr4OHqyNOXr+PgUuOcuFUIsp2p67fx4fLjqv/mj6uEYPn/L/WP/HsR0DVDrwjNiRdAZD0y7G3t39s9JXsp9bBOb2kpqdChQq4cOGC2pdzS/ObBEVpva70N3JzczPbyAJ0Ov0U8tAh/+lFWF//FFwc7bAz4DY+X3tKtcMTEWWHG2EP1QStD+MS8HIZRwwMGQWdzPQsHZ5f+II3wcakKwCSZijpgLxt2zbjscTERLXfuHHjTMvUgwcPEBgYiKJFi6p9uaajo6PZdQMCAlQ/ocy8LmXhyvGt9H9llTj0NZY890C1uy87fBXTtuuDXCKirBQWFYtecw8hODwa5YrkxY9OP0F3X2Z6Lg10+pUzPdugdDeByRD42bNnY8GCBTh79izee+89REZGqlFholevXqr5yUBqbo4fP642eXz9+nX12FC7Iz7++GM1tP3y5ctqZFeHDh1UTVO3bt3U89KHp1+/furaO3bsUJ2i5XoS/DRq1ChzSoKyVuNBQK2egJaIOoeGYmoLV3V48tZzWHGEzZNElLWru8so1Au3HsDbzQUL+jWE47ODgQI++pme8xRk8dsgh/S+oEuXLrh9+zZGjRqlOiDXqlVLdV42dIyWWhkZGWYg8/XUrl3buD9p0iS1NW/eHDt37lTHrl27poKdO3fuoEiRInj22WfV8HZ5bDBlyhR1XpkAUUZ4SV+hn3766WnfP2VnU1jbycDdi0DQPrx2+iNcfuYXTN4bipGrT8LLzQXNKzy630REmSE+IRGDlhyF35V7cHNxwIK3GqC4ex7AvQUw+Kh+AleySTrNRjphyDB4qUmSDtHsD2RBkaHA7BeAuChoPVdh6G4Na45dR14neyx/pzGqFS9gydwRUS4iX2+f/n4CK/2uwdnBDqvb50HVksWAIhUsnTWygu9vqxgFRjYkb2Ggx0qg/w7oitbE+E418Ey5QoiMTUDf+Ydx9W6UpXNIRLnExC0BKviRPoe/tvNC1R39gTktgRvHLJ01sgIMgCj7yTwb7vp5mZwc7PDz62VRyTu/miBRJkqUzopERE9j7p5L+GlnoHo86dVSaHrofSDyFlDAFyhUjoVLDIDIws7+AbefamPJcxEoVsAFgbcj1TDV6LgES+eMiHKo9f/ewFcbzqjHn7Yqi46BXwC3zwL5vAFZ6NQ5v6WzSFaANUBkWef/AmIj4PHnu1jS3h35XRxw5Mo9fLT8OBIT09c9LSouCtUXVFebPCYi2/PP+dsYtuK4etyncUm8F/kLELgNcHQFui8DChS3dBbJSjAAIstq8z1Q8hkgJhyl/noLczuXgZO9Hf48FYzR609zokQiSrOT1+7j3d/8EJeg4ZUaRTGqyE7o/GSZCx3QcTZQ7NGIZCIGQGRZMgT1jd8A95LAvcuof2gIJr9eWY2a/+3AFYzb7M8giIie6FJopOpDKAMqZGDF5NerwS7gT/2TMhFr5bYsRTLDAIgsL28hfbu8U37gyh60DZqE79pXU0/9susipnO2aCJKxa2IaPSaexB3ImNRtZgbZvasC2cnJ+DN1UD7n/UTsRIlwQCIrINnZeD1uYDODjj2G7rlO4bPX6msnvp+6znM2XPJ0jkkIisUHh2H3nNlCo2HKFnIFfN7VkN+F0f9kw7OQK3u+olYiZ52JmiiLFOhFdDqG+D+NaBSW7xt74DImARM+fscvt5wBvmc7dGlvi9vABEpMlp0wMIjOHszHIXzOeG3nlVRZMWrQJnngJZfASarEhAlxQCIrEvjgWa7H7Qoh8jYeMzafREjVp+Ei6M92tXiKA4iWxcTn4D3FvnhwMW7yOfsgPm968J3x3tA8EkgIljf7JXf29LZJCvG8JisV0IcdJtHYGRDJ/Ro6AtZtGXoin+x9UzIE18aEvXkNESUM8Wp9b2OYUfAbbg42mF2r3qodmoCcG4z4OACdF3K4IeeiAEQWa+to4GDM6Fb1BFft/BEx9rFkZCoYeDio9hzPvSx5OsD1xsft1/bHqvPr87mDBNRdixu+uGyY+oPIZlJ/tde9dH4zmrg4M/6BNLp2ac+bwQ9EQMgsl7PDjEOj7db+gYmvFYGL1X1RmxCIvovPIIjl+8akwZHBmPswbHG/UQkYsz+Meo4EeUO8geQ1AJvOhms5gub9WZdPIvjwJ+f6hO88AVQraOls0k5BAMgsl75PIE31wCuhYCbx+Hwex/88EZVNK9QBA/jEtB33mE18ZkICg9SQY+pRC0RVyOuWijzRJTZwc8nK/9Vy1w42OnwU486eM7XCfj9LUBLBGr1AJoOY6FTmjEAIutWqCzQfaV+GvvAbXDe9BFm9qiDBqU9EBETr+b+OBcSAV83X9gl+Tjb6ezgk1+/6CoR5VyyLM5nq09i9bHrsLfTYXr32mhZxQvI4w68OhUo+wLQdiqHu1O6MAAi61eiLtB5PqCzB/5dgjx7x2FO73qoWaIA7kXFoeevBxETnR8jG440C35GNx4N77wcBUKUk2mahi/WncLyI1dhpwOmdqmFl6oVfZRAmrx6rtbPKk+UDgyAKGeo0Fr/l56zG1DqWTXR2YK3GqCSd37ciohB99kH0aBwK2Pyte3WomN59gUgyunBz5g/zmDxwSA1l+H3b9TEqxVcgZV99fOFGXCiQ8oABkCUc9TpBQw+qp/kDIC7qxN+69cQZQrnxfWwh+g995AxqZerlwUzSkSZEfx8t+ks5u+7rPbHd6qBDtUKAUu7AadXAyt6SSIWNGUYAyDKWfIVefT4dgCK3DuORW83hK+HK67ee2jJnBFRJgY/E7cEYPY/+iVwvutQHW/ULqqv+QnaBzgXAF79kTU/9FQYAFHOFHIamNMKWPIGisVewYp3GqN0IVfj0xdvR1o0e0SUcT9sO4+fdgaqx2Neq4ruDXyA9YOBc3/qJzrsvgzw1i+YTJRRDIAoZypYGihcAYgOAxZ1grfuLub3a2B8uve8gwgIjrBoFoko/WbsuICpf59Xj2VB5N5NSgFbv1ADINRACBkQUbIJi5aeGgMgypmcXIHuy4FC5YHwa8DizijiGGN8+s6DOHSdtR+nruvnCSIi62/2mrbtvGr6EsNfqoS3m5YBDv8K7JumT/TaNKDiy5bNKOUaDIAo53L1AHquAvJ5ASGngBW9jU9VL+6mhsh3n30Ax6+GWTSbRPTk4Gfsn/74fus5tT/sxQp477my+icrvgJ4VgFe/Bqo3YNFSZmGARDlbAVLAj1W6ofHXz1oPDynT33UK1kQ4dHxap4g02UziMi6Znj+bM1JzNp90djsNbhF+UcJ3IoC/bcDz3xguUxSrsQAiHK+ojVVTZCrgytOJvrgZNd98MznpuYJalTGAw/UjNGHsC/w8QVUichyYuP1C5suPaSf5HBCpxr6Zq/Le4GTvz9K6JiHt4kyHQMgyh18GgB9NwI9fgec86tDeZ0dMK9PAzQtXxhRsfq1w3adu23pnBIRgOi4BLzz2xFsOHETjvY6TOtWB2/U9wFungCWdgVW9QMC/mRZUZZhAES5R7Ha+s7RBv4bkccBmN2rHlpU8kRMfCL6LziCv8+EWDKXRDYvIjpO1cruCLgNF0c79Tv6So2iwJ1ANaoTMeFAyWeMk54SZQUGQJQ77RwHLOsOrP8ALvY6/NyzLl6u5o3YhES8u8gPf568aekcEtmku5Gx6PHrQRy6dBf5nR3UbO7PVfTUBz/z2wKRtwCv6kC3pWz6oizFAIhypyKVAJ0dcHwRsOljOKkq9tpoV6sY4hM1DFp6DGuPXbd0LolsSvD9aHT5ZT9OXLsPj7xOWDqgEeqX8gDuXgQWvApE3ND/7r65GnApYOnsUi7HAIhyp6rtgQ6/yCqJwJE5wJb/wcFOh8lv1MLrdUuokSdDlh/HL7sC1RBcIspaQXei0PmXfTh/6wG83VzU7O3VihcAIu/oa37CrwOFKwK9/wDyefJ2UJZjAES5V403gNd+1D8+MAPY/jXs7XRqpMlbz5RWh2XukS/Xn1YBERFljXMhEXh95j5cvfsQpQq5YuW7jVHOM9+j+byqd9bP7M7gh7KRTrORP3/Dw8NRoEAB3L9/H25ubpbODmWnQ7NVM5jy/OdA80/Uw1//uYhvN51VC0q3quKFH7vVhoujPe8NUSY6ePkm3t7VSj0uem8yFvVrCs/8LuaJ5JcwJgJw4f/NlH3f36wBotyvQX/9LLIij7vxsMw3Mr1bHTg52OGvMyHoNvuA6qBJRJlj34VQvDXvsHFf5uZSwc+9y8DagUDcQ/0TOh2DH8p2DIDINsgssu/8ow+GTMjQ20X9GqJAHkccCwpDp5/34codriRP9LSWHw5SQ90jYxOMx6K1u8C9K8D8V/UDFDaPYEGTxTAAIttRtMajx1F3gTPr1cMGpT2w6r3GKO6eB5dCI9Hxp334l+uHEWVIYqKs63UWw1edVCMu61S9YHyu/dp2WL2kLXA/CPAoCzRnAESWwwCIbE90uH7I7Yo3gYMyUgwo55kfa95vgqrF3HAnMhZdZx3AtrOcMJEoPR7GJuD9xUfxyy79ul79n/dAYMIi4/OJ0DAmr4bgQqWBPhv063wR5aQAaMaMGShVqhRcXFzQsGFDHDp0KMW0p0+fRqdOnVR6nU6HqVOnPpZm7NixqF+/PvLnzw9PT0+0b98eAQEBZmmee+459XrT7d13381I9snWyVIZpZvrH//5KbB7knro6eaC5e80RrMKRfAwLgH9Fx7B4oNXLJtXohziVng0uszaj82ng+Fkb4epXWrhxRr2SESiWbpEnQ5XX/4OcCtmsbwSZSgAWr58OYYOHYrRo0fj6NGjqFmzJlq3bo1bt24lmz4qKgplypTBuHHj4O3tnWyaXbt2YeDAgThw4AC2bt2KuLg4tGrVCpGR5n0x+vfvj5s3bxq3CRMm8C5S+kmHy9bfPqp+3/41sHW0GomSz9kBc3rXQ+e6JSAj4/+35hQmbvHnXEFEqThzIxztZuw1TnC4pH9DtK9dHL5uvrBL8jVjp7ODT9E6LE/KecPgpcZHamumT5+u9hMTE+Hj44PBgwdjxIjU23OlFmjIkCFqS83t27dVTZAERs2aNTPWANWqVSvZGqTkxMTEqM10GJ3kk8Pgycy+acBfn+sf138beHkiYGenAp6pf5/HD9vOq6c61i6OcZ1qqBFjRPTIdv8QDF5yTHV2LlskL+b2qY+ShfIan1/mvwzfHvzWGPyMbjwaHct3ZBFSzhoGHxsbCz8/P7Rs2fLRCezs1P7+/fszLVPyJoWHh4fZ8cWLF6Nw4cKoVq0aRo4cqWqXUiLNalJghk2CH6LHNBkMtJWgWgcc/hXY/pU6LE2sH71YAeM7VVeTJ64+dh295x7iMHmi/8gfCfP2XsLbC46o4KdJ2UJY/d4zj4KfhDj147WyrxnLbG27tQx+yGqkKwAKDQ1FQkICvLy8zI7LfnBwcKZkSGqUpIbomWeeUYGOQffu3bFo0SLs2LFDBT+//fYbevbsmeJ5JI0EUobt6tWrmZI/yoXq9QU6zgYK+AJ1+5g91aW+r2oSc3Wyx/6Ld/DqtD04dV0foBPZqviERIxadxpj/jijmoq71vdRc/wUcHXUJ7jmB0yrA1z3g6ujK072Pqm20gX0M7ATWQMHWBnpC3Tq1Cns2bPH7PiAAQOMj6tXr46iRYuiRYsWCAwMRNmyZR87j7Ozs9qI0qRGZ6Dyq4CjyQy10jqs06mVqte8/wze+e0ILt+JUnMFfduhulpTjMjWRETHYdCSY9h17rbqTjfy5Uro37SMqjVVArcDy3oCcZHAznFAj5WWzjLR09cASfOTvb09QkLMhwfLfkodnNNj0KBB2LBhg6rlKVGixBP7IokLFx7NMUH0VEyDH/+NwMLX9EPmAVT0zo91g57FC5U8EROfiI9X/otR604hNt58hAtRbnb1bhRe/3m/Cn5cHO3wc4+6GNCs7KPg5+TvwOI39MFPmeeB1+dZOstEmRMAOTk5oW7duti2bZtZk5XsN27cGE/TlizBz5o1a7B9+3aULv3katLjx4+rn1ITRJSpYiOBPz4ELu3WB0EyaSKgZov+tVc9fNiivNpfuP8Kus8+oIb/EtlCZ+dXp+9BQEgEPPM7Y+U7TfBSNZM/fA/OAla9DSTGAVU7At1XAM7/LXhKZIXSPaRFhsDPnj0bCxYswNmzZ/Hee++p4ep9+/ZVz/fq1Uv1vzHtOC3Bimzy+Pr16+qxac2NNHtJ/54lS5aouYCkP5FsDx/q14mRZq6vv/5adcC+fPky1q9fr64jI8Rq1DCZ3ZcoMzjlBXr8DrgWAm4cA+a1ASL0fdzs7PSdo6VfUH5nBxy5cg9tp+2B3xV9kESUG/v7TNjsj7fmH0FYVBxqlCiAtQOfQfUSBR41Fe/4DvhTFhnWgPr9gU6/Ag5Ols46UeavBi9D4CdOnKiCFBma/uOPPxqbpGS4ugx3nz9/vtqXgCW5Gp3mzZtj586d+kwYqk+TmDdvHvr06aM6MEuHZ+kbJMGWjOjq0KEDPv/88zQPieNq8JRut/yB39oDETcBjzJAr3WAu6/xaVk2Y8DCIzh/6wEc7XUY1bYKejYqmeLnmSinCQmPxuClx3Dokj7A7924JD57pTKcHewfJUqIB5Z1B85vAZ77DGj+qX6uLaJMklXf3xkKgHIiBkCUIXcvAQvbAWFXgPzFgO7LzdYUi4yJx6e/n8DGkzfVvnSM/qZ9Nbg4mnxBEOVAey+E4sNlxxD6IFZNEDquU3W0rZHC7M2xUcD5v4Cq7bM7m2QDwq1hHiAim+NRGnhrM1CkEhBxAzi92uzpvM4OmN69thoJY6cDfve7hs4z9+PavZTnqCKy9sVMf9x2Hj3nHFTBTyXv/Fg/6Bnz4CcmQr+OnuHvZydXBj+U47AGiCgtHoYBh2YBTYcBdsnX7uw5H4rBS4/iXlScWg5gWrfaeKZcYZYv5Rh3HsRgyPLj+Od8qNrvUs8HY9pVNa/RjAwFFnUCbh4Hnv+fvsmLKAuxBojIkvK46/+jNwQ/8bHAgZ/1/R/+82z5wvhj8LOoVtxNzRgtf0GP3+zPofKUIxy+fBev/LhHBT8yxH1S55oY/3oN8+Dn3hVgbmt98CODBMo9WhWAKKdhExhRRmz4CNg8Alja1ThXkChR0BW/v9tE/eUsrQM/7wxE+xl7cS4kguVMVkm6gc7aHYiusw4gODxaree1buCzj0/0eWU/MPsF4M4F/azpb/0FFOeippRzMQAiyoiKLwEOeYALW4G5LwFhj5Zakb+Y5S/nmT3roKCrI87cDFdD5efsuaT6VxBZi/tRcei/8Ai+2+SPhEQN7WoVw/pBz6qJP834zQcWvApEhQLe1YF+W4DC5SyVbaJMwT5ARBl1/ai+BuhBCJDXE+i+DChe1yyJTJL46aoT2BlwW+0/U66QalooWiAPy50samfALYxcfRI370fDyd4Oo1+rgu4NfB+fxuHuRWB6A/0Eh1XaA+1/0s+VRZRNOAzeSguQbNz9a8CSLkDIKX2NUMdZQJVHq18bmhgWHwzCNxvPIDouEW4uDvi6fTW0q1XcYtkm23X/YRy+2XAGK/2uqf1ShVwxvXsdVCv+38SGyZEaoMjbQNOPOccPZTsGQFZagERqSPDKvvrmMBd34MN/9Z2mk7h4+wE+Wn4c/17Tryb/Ws1i+LpdtUcraBNlw3IWUusTEh6j5irs26Q0PmldEXmckoxsvHVW/9OzMu8JWRwDICstQCJFRoP99bm+b1CZ51IslLiEREzffgHTd1xQfS6KFnBRTWIcLk9Z3dfnqw1nsOqovtandOG8mPh6DdQr5fF4YlkIePUAIG9hoP8OwDWZNETZiAGQlRYgUYqu+QEFS+q/SJI4FnQPQ1f8q5bTEG89UxqfvlSRM0hTptt6JgT/W3MStyL0tT5vP1saQ19MptZHhi3+MwnY/o1+v1RT4I2FDIDI4hgAWWkBEiXr9jlgTkvA0RV4fS5QssljSaJi4/HtxrOqf5Ao75kP33WsjvrJ/VVOlE73ImMx5o/TWHv8htovU0Rf61O3pEfyS1msG/hopvMGA4DW3wH2bJ4ly2MAZKUFSJTiQqor3gRCzwE6e+CFz4Fnhshy8o8l3eF/C5/8fgKhD2LUfsfaxTGiTSV45ndh4VKGbDkdjP+tOaU+U7JES/9mZfBRywrJ1zDKFA6ymGnwCcDOEXhlElC3D0uerAYDICstQKIUxTwANg4FTizX75dvBbSfCeQtlOxf6xO2+GPZ4auqJSK/swM+erECejUuCQd7TtdFaSMzkH+5/jTW/6uv9SnnmU/V+tT2LZjyi6QDv9T8uBYGuvyWbG0lkSUxALLSAiRKlUQzRxcCf34KxEcDbsWB1+cBvg2TTX78ahhGrTuFE/+NFJOFKL9qVw0NSrNZjJBq5/qlh4IwZes5tRad1Pq827wsPmhR/sn9yqLuAusHAy+NBdx9WcxkdRgAWWkBEqVJ8ClgZW/9MgIN3wVeHp9iUhkdtvzwVVUjFBYVp451qF0cI9ksRknIHFM7Am6pvmSBt/Ud6it65ceE12ugps/jUzEoYUHAyZXAs0M5pw/lCAyArLQAidI1X9DeH4BmnwAOzk9Mrm8WC8Cyw0HGZrEhL1ZAbzaLkYxWDw5XgY9h5XaPvE6q2bRbfZ+Um01PrQb+GALE3Ac6/ALU7MqyJKvHAMhKC5DoqeYOkpE3DfoDJeqlmOzf/5rF/jVpFhvzWlU0LPN4XyLK/W5HxGDy1nNYfjgIsrScLGPR95lSGPhCObi5OKbcH+3P4cDxRfr9EvWBjrMBj9LZmneijGAA9JQYAJHV2TdNP3mijLx58Sug0XspNknIIqrLj1zF+M2PmsXa1yqGj1tXVCvQU+4XHZeAuXsv4acdgXgQE6+OtanujREvVYZvoVQ+A9f9gFVv69f00tnpl7No/imHuFOOwQDISguQKMOi7+s7n55Zp9+v1BZ49YdkJ040bRab+FeA6vAqzWKO9jq8XrcE3n+uHHw80h8IRcVFoeESfYfsg90PwlXmLSKr6+ez4cRNjPvTH9fDHqpjNUoUwBdtqzx5zqjDc/Qd8BPjAbcS+rXqSj2TPRknyiQMgKy0AImeikQxh2YDWz7Tr7btWgh4eQJQrVOqHVRPXAvDhM0B2HNB3//DwU6HzvXSHwgxALJuR4PuqYVLjwaFqX1vNxc1Y3j7WsVhJ0O9niRwB/Bbe6BKO31wnSeV4fBEVooBkJUWIFGmuHEMWDsQuHVavy/NFC2+eOLLDl++ix/+Pm8WCEmN0MDn0xYIMQCyzhqf3edD8cuuQOwLvKOO5XG0x3vPlUX/pmUeX8IiqfCbgFtR8yawYnU44otyrPAs+v7WafLbZgMYAJHVi48F9kzR9w3qvw0oUjHNLz0igdC288YRQRIIdaqjD4RS6x9iGgCtb78epQuwU6ylxCckYuPJm5i56yLO3gw33seOdYpjWKuK8HJ7wszgD+8BW0frR3q9uxvwKJM9GSfKYgyArLQAiTLdwzAgj8kcLn4LgNJN0/SF5nflLqb+/SgQsleBUHEMer58soHQMv9l+Pbgt+qxHewwuslodCzfMTPfDT2BrAm34vBV/LrnEq7d0/fxcXWyR9f6vujXtDSKu+dJ/QTyN6zMNi4d6iNv64+9Mhmo349lT7lCOGuArLMAibJ8RXlZVNXeWd8kJpMo2tmnIRC6p2qEdp+7bQyEZI0x+UKt5K3//AdHBqP1762RiETj6+x0dtjSaQu883pn4Zsiw7IVC/ZdxsL9l9XszaJQXif0aVIKbzYuCXdXp7StObdxGHBlj36/cEWg7WSg1LMsZMo1wrPo+9sh085ERJnP1QMo+Qxw+R99R2lp3mg3HfCsnOrL6pYsiIVvNTALhFb6XVNbbV93dKvvC2/va2bBj0jUEnE14ioDoFRI4BgUHgRfN98MldPVu1H49Z+LalqD6Dh9+ft6uKoFSzvXLfHkpSsMdo4Ddk/Uj/ByyKMf2t54EOCQhsCJiBgAEVk1maiu9x/A0QXAX18A148AM5vqv+xkdfknfNkZAiEZTTRr10X8fTYEx4LC1JbP9QF0JWUkkWZWA+ST3ycb3ljOlNEmQ+nfIx2aJQDddPKmWu5EVC9eAO80L4OXqxVVtXTpoiXqg58KL+uXVilYMmNvishGsRM0UU4RfgPYMBQ496d+v8zzQK+16TrFrYhorPK7rmYRvnwnCo7u++FSVD8PkQ52GF7/c/So0jkrcp/jpbfJUMaXnLoejrXHr6vV2WUGZ4Om5QvjveZl0bhsIehSme7ATNhVIPbBo9q/uIfApX+ACq0y4d0RWS82gRHZOrdiQLelwKlV+sntKrdN9yk887uo4dTvNCuDA5fuYPHBQtgdpw+AIi58hG8u5MexGv+iWwNf1PF1T/uXsw2QZq+0NBlKE9e649ex5th14wKloqCrI9rWKIYu9X1QrXiBtF84IQ7YPwPYNR4oVA4YsFPfD8wxD4MfoqfAPkBEOYkEJNVf19f+uJh0BpS+Qee3As9/Brg/uQlLJtFrUrYwavm6ouES/bEyBYsh8FYcfve7prYKXvnwao1ieL6SJ6oUdUvbxHu5mPT5kWavpDVA0mQoM3RvOHkT645dx5Er94zPOzvY4cUqXuhQuziali8CJ4cUFilNyeW9wMahwG1//b5TPv1w91RmCyeitGETGFFOl5gATKsL3LukHy3W8B2g6dB0z/orTTbSaXrpoavYePKGsYOuKJLfGc9VKKKCoWfLF0550U1b6gOks0P7Eh/i+tUa2HXuFuISNGOM+kzZwmhfuzhaV/VC/oyU1bUjwI7vgMBt+n2ZIfzFr4Fa3TmhIdmccA6Dt84CJLKa4fJbRz0aDu1SAGg6DGjwDuD4hAn0knH/YZzqrLvd/xb2XghFVGyC8TmZnE86V0sw9HxFT1VTZAtNZVImhy7dxfbz53Dw2jlcDs6DxLhHTVlVi7mpmp5XaxZ78qSFqbl6CJjzov6xzh6o0wtoMUo/IpDIBoUzALLOAiSyGjIhnjSD/T0auHVGf0wWwJR5YSq0zvBpY+ITcPjSPewIuKW2iyb9WkSxAi547r9gqEFpDxTIkztqh8Kj43D40l3sD7yj+kudvhGuithU2SJ58VI1b7U2V3mv/Bm/WOQdIG8h/WO5yK8t9TOBN/uYMzqTzQtnAPR0GACRTTWJ/bsM2PEtEH4d6LUOKPNcpp3+yp1I7Ay4rYIhCQ5i4s07BsvMxZWL5lcTLlYu6oZKRfOjVKG86R/mnY0SEzXcDI9GQHA4Dly8iwMX7+DU9fv4b7S6UZnCedGobCE0KiObh+pU/lRuHNfP53P1IPDhv4/6dUnHZ/vcEUgSPS0GQFZagERWS4ZJB2zSryxvsP8n/TIbVTtmqGksqei4BOy/eAc7/W9h57nbuHInKtl0Lo52qOiVXx8Qef/3s6hbttYWSZATEhGNS6GRuBwahct3ItVjCegk30kDOVGqkKsaqq4PeAo9XdOWqZsn9IFPwEb9vs4OeOO3DI3sI8rtwlkDZJ0FSJRjRIcDkyvr55JxLQzU6wvU62e+cngm9JPxvxkO/+AItaCnbAEhEWYdqk3J0PCCrk5wN/50UsdkX//YsO+Egnkd4eJgj+j4BHU+Cb70W6I6FhOXgIeG/f9+hj2MxZX/gh3ZUsqHoW9TyUKuqFfSA43KeqiAp2iBJ6zDlV7BJ/WBj/+G/w7IqL7O+oktC5fP3GsR5RLh1hQAzZgxAxMnTkRwcDBq1qyJadOmoUGDBsmmPX36NEaNGgU/Pz9cuXIFU6ZMwZAhQ9J9zujoaAwbNgzLli1DTEwMWrdujZ9++gleXl5pyjMDILJ5MRHA4V+BQ78C4df0xWHnAFRpp19jrET9LBlhJLMeS/Dhf1MfFPkHS2AUgeth+oU/s5M0w/kUzINShfOqZrnS8lM9dlVNdw726Rymnh5Rd4FJ5fWzN0vgIzVzzYcDRSpk3TWJcoFwa1kLbPny5Rg6dChmzpyJhg0bYurUqSoYCQgIgKen52Ppo6KiUKZMGXTu3BkfffRRhs8pr924cSNWrlypCmLQoEHo2LEj9u7dm5H3TWR7nPMDz34ENB6sb3o5MBMI2qefWFG21mOBxu9nSdBRtkg+tb1So6hZbVHw/Wjci4pFWFSsWhA0TG3y2LD/6Kc8F5+owdFep2qCnB3tVdOai+Gng/w0PWaPfM4Oap0tQ6BTomAeOGZlkGMgf1fePA5c2Qc0Hqg/JqO4Kr4M2DnqAx/PSlmfDyLKvBogCVDq16+P6dOnq/3ExET4+Phg8ODBGDFiRKqvLVWqlKr9SVoD9KRzStRXpEgRLFmyBK+//rpK4+/vj8qVK2P//v1o1KjRY9eSWiLZTCNIOSebwIhM3PwXODgLOL0GGHjw0SSKdwL1k+7lT1sNa3aQ/6qkU7I1d6bGwzDg5Er92m3S3CU+OPZoJFdiosxCadEsEuU0WVUDlK7fxNjYWNWU1bJly0cnsLNT+xKIZERazinPx8XFmaWpVKkSfH19U7zu2LFjVYEZNgl+iCiJojWB9jOAj8+ZzyC9eSQwpSqwtBtwbLF+mLaFyVxDVhn8yN+QMmPz6neA7ysCmz7WBz/2TkC11/VBjwGDHyKrka4msNDQUCQkJDzW70b2pUYmI9JyTukX5OTkBHd398fSyHPJGTlypGpWS1oDRETJcM736HF8LFR/ocQ4/Sgy2WSUUslngEptgUqvpGm5DZshtWe/932071kFqNMbqPEGJy8ksmK5di0wZ2dntRFROjk4AW/9CYScAc7+Afj/oa/RuPyPfpMRTH0Mo5hsiHRivrQLCNwOFK4ANBmsP17hJcCtOFCupT7wKV6Hy1UQ5bYAqHDhwrC3t0dISIjZcdn39n60GnJmn1N+SlNZWFiYWS3Q01yXiJ7Aq4p+e244cO8y4L8ROLtBP2rM4MEtYF4bfefeyq8CxevlnmaehHjg+hHgwjZ90HPjKKD915zlXeNRAOTkCnx4ArDPtX9PEuVK6fqNlWaounXrYtu2bWjfvr2xw7Lsy6isjEjLOeV5R0dHdaxTJ/2kbjJCLCgoCI0bN87QdYkoHQqW0o9mMoxoMpCg6M55YJ9sP+o7TktwUKwWULSWfgZqK+pInS4zGgB3A82PFakElG0BlHvB/DiDH6IcJ91/ski/mt69e6NevXpqnh4Zsh4ZGYm+ffVt4L169ULx4sVVJ2QhNTdnzpwxPr5+/TqOHz+OfPnyoVy5cmk6p3Ri7tevn0rn4eGheoHLCDEJfpIbAUZE2aT66/qZpaVm6PxfQEy4fmi9bKLrUqBSG/1jaVKTUWcSHEkTkp295Wp2pEYr9BwQGgCEntc/DrsKDD37qAareF3g4V2gzPNA2Rf0W4HilskzEVk+AOrSpQtu376tJjeUDsi1atXC5s2bjZ2YpVZGRnEZ3LhxA7Vr1zbuT5o0SW3NmzfHzp0703ROIRMoynmlBsh0IkQisvDcQlU76DcJLCSgkCBH1riSeXAk2DE4sw7YNU7/2NEV8K4OFCqvXwTUtRBQ+81HnYaj7/93frf09aeRddBkCRC1RQFRd4BitR+d48/hwOE5+g7eybkfpK/tEm0m6K9vqUCNiLJUhmaCzok4EzSRhfktAP5dql8HK858RXllyEnA3Vf/eOsoYO8P+qHkEhwZNsc8+uCm8/xHwdL2b/QzXMvx+OjHzyu1Om7F9I+3fQX8870+ACtUTr/iutRGyTIU6mcFLkJKZGWsZiZoIqIMqdtbv0ktzZ0L+pqisCD96KqoUP36ZAaGGqCEWCDipn4zJU1thgBI0jy89/j1HPLoV1ePCH4UADUYANTtqx+1lVs6axNRhrAGiIisU+x/TVhqC9UHStKs5ZgXqNBaH9yIiBB9wCS1Q1KzIz8dXBjgEOUS4awBIiKbIsPLZXvSpIsyyiynjjQjIothHTARERHZHAZAREREZHMYABEREZHNYQBERERENocBEBEREdkcBkBERERkcxgAERERkc1hAEREREQ2hwEQERER2RwGQERERGRzGAARERGRzWEARERERDaHARARERHZHAZAREREZHMYABEREZHNYQBERERENocBEBEREdkcBkBERERkcxgAERERkc1hAEREREQ2hwEQERER2RwGQERERGRzGAARERGRzWEARERERDaHARARERHZHAZAREREZHMYABEREZHNYQBERERENocBEBEREdkcBkBERERkcxgAERERkc1hAEREREQ2J0MB0IwZM1CqVCm4uLigYcOGOHToUKrpV65ciUqVKqn01atXx6ZNm8ye1+l0yW4TJ040ppHrJX1+3LhxGck+ERER2bh0B0DLly/H0KFDMXr0aBw9ehQ1a9ZE69atcevWrWTT79u3D926dUO/fv1w7NgxtG/fXm2nTp0yprl586bZNnfuXBXgdOrUyexcX331lVm6wYMHZ+Q9ExERkY3TaZqmpecFUuNTv359TJ8+Xe0nJibCx8dHBSMjRox4LH2XLl0QGRmJDRs2GI81atQItWrVwsyZM5O9hgRIERER2LZtm1kN0JAhQ9SWEeHh4ShQoADu378PNze3DJ2DiIiIsldWfX+nqwYoNjYWfn5+aNmy5aMT2Nmp/f379yf7Gjluml5IjVFK6UNCQrBx40ZVY5SUNHkVKlQItWvXVs1j8fHxKeY1JiZGFZrpRkRERCQc0lMMoaGhSEhIgJeXl9lx2ff390/2NcHBwcmml+PJWbBgAfLnz4+OHTuaHf/ggw9Qp04deHh4qGa1kSNHqmawyZMnJ3uesWPHYsyYMbzLRERE9HQBUHaQ/j89evRQHaZNSb8jgxo1asDJyQnvvPOOCnScnZ0fO48ESKavkRogaaojIiIiSlcAVLhwYdjb26tmKlOy7+3tnexr5Hha0//zzz8ICAhQHa3T0hdJmsAuX76MihUrPva8BEXJBUZERERE6eoDJLUudevWNeucLJ2gZb9x48bJvkaOm6YXW7duTTb9nDlz1PllZNmTHD9+XPU/8vT05F0kIiKirG0Ck2al3r17o169emjQoAGmTp2qRnn17dtXPd+rVy8UL15cNU2JDz/8EM2bN8f333+PV155BcuWLcORI0cwa9Yss/NKE5XMFyTpkpIO0wcPHsTzzz+v+gfJ/kcffYSePXuiYMGC6X0LREREZOPSHQDJsPbbt29j1KhRqiOzDGffvHmzsaNzUFCQqpkxaNKkCZYsWYLPP/8cn332GcqXL4+1a9eiWrVqZueVwEhG5MucQUlJU5Y8/+WXX6rRXaVLl1YBkGkfHyIiIqIsmwcop+I8QERERDlPuDXMA0RERESUGzAAIiIiIpvDAIiIiIhsDgMgIiIisjkMgIiIiMjmMAAiIiIim8MAiIiIiGwOAyAiIiKyOQyAiIiIyOYwACIiIiKbwwCIiIiIbA4DICIiIrI5DICIiIjI5jAAIiIiIpvDAIiIiIhsDgMgIiIisjkMgIiIiMjmMAAiIiIim8MAiIiIiGwOAyAiIiKyOQyAiIiIyOYwACIiIiKbwwCIiIiIbA4DICIiIrI5DICIiIjI5jAAIiIiIpvDAIiIiIhsDgMgIiIisjkMgIiIiMjmMAAiIiIim8MAiIiIiGwOAyAiIiKyOQyAiIiIyOYwACIiIiKbwwCIiIiIbE6GAqAZM2agVKlScHFxQcOGDXHo0KFU069cuRKVKlVS6atXr45NmzaZPd+nTx/odDqz7aWXXjJLc/fuXfTo0QNubm5wd3dHv3798ODBg4xkn4iIiGxcugOg5cuXY+jQoRg9ejSOHj2KmjVronXr1rh161ay6fft24du3bqpgOXYsWNo37692k6dOmWWTgKemzdvGrelS5eaPS/Bz+nTp7F161Zs2LABu3fvxoABA9KbfSIiIiLoNE3T0lMOUuNTv359TJ8+Xe0nJibCx8cHgwcPxogRIx5L36VLF0RGRqqgxaBRo0aoVasWZs6caawBCgsLw9q1a5O95tmzZ1GlShUcPnwY9erVU8c2b96MNm3a4Nq1ayhWrNgT8x0eHo4CBQrg/v37qhaJiIiIrF9WfX+nqwYoNjYWfn5+aNmy5aMT2Nmp/f379yf7Gjluml5IjVHS9Dt37oSnpycqVqyI9957D3fu3DE7hzR7GYIfIeeUax88eDDZ68bExKhCM92IiIiIVPySnmIIDQ1FQkICvLy8zI7LfnBwcLKvkeNPSi/NXwsXLsS2bdswfvx47Nq1Cy+//LK6luEcEhyZcnBwgIeHR4rXHTt2rIoYDZvUUhERERGpOMIaiqFr167Gx9JJukaNGihbtqyqFWrRokWGzjly5EjVV8lAaoAYBBEREVG6a4AKFy4Me3t7hISEmB2XfW9v72RfI8fTk16UKVNGXevChQvGcyTtZB0fH69GhqV0HmdnZ9VWaLoRERERpTsAcnJyQt26dVVTlYF0gpb9xo0bJ/saOW6aXshIrpTSC+nYLH2AihYtajyHdJKW/kcG27dvV9eWTtlEREREWToMXpqVZs+ejQULFqjRWdJhWUZ59e3bVz3fq1cv1fxk8OGHH6oRW99//z38/f3x5Zdf4siRIxg0aJB6Xuby+eSTT3DgwAFcvnxZBUvt2rVDuXLlVGdpUblyZdVPqH///mrOob1796rXS9NZWkaAERERET1VHyAZ1n779m2MGjVKdUCW4ewS4Bg6OgcFBanRWQZNmjTBkiVL8Pnnn+Ozzz5D+fLl1XD3atWqqeelSe3EiRMqoJJaHgloWrVqha+//lo1YxksXrxYBT3SJ0jO36lTJ/z444/pzT4RERFR+ucByqk4DxAREVHOE24N8wARERER5QYMgIiIiMjmMAAiIiIim8MAiIiIiGwOAyAiIiKyOQyAiIiIyOYwACIiIiKbwwCIiIiIbA4DICIiIrI5DICIiIjI5qR7LbDcLiEhAXFxcZbOBhFlkKOjo1pjkIgoNQyA/iNLosnirrIgKxHlbO7u7vD29oZOp7N0VojISjEA+o8h+PH09ISrqyv/4yTKoX/IREVF4datW2q/aNGils4SEVkpBkD/NXsZgp9ChQpZ+p4Q0VPIkyeP+ilBkPxOszmMiJLDTtCAsc+P1PwQUc5n+F1mfz4iSgkDIBPsL0CUO/B3mYiehAEQERER2RwGQERERGRzGADZkPnz56vhwWlpPli7di2y0+XLl9V1jx8/bpXnS8+1du7cqfazYkoF03uT1e/REp8DIqLswgDIhnTp0gXnzp0z7n/55ZeoVasWciMfHx/cvHkT1apVy/KgJKkmTZqoaxcoUOCJadObLznvyy+/jMyU0ucgK65FRGQtOAzexoYHG4YI53Yy9FkmwrMEJyenTL92bGxslpw3NZYqPyKi7MAaoNQmVIuNt8gm106LDRs2qCYtmcdISFOI1CaMGDHCmObtt99Gz549H2sCk8djxozBv//+q14jmxwzCA0NRYcOHdRw4vLly2P9+vUp5uOzzz5Dw4YNHztes2ZNfPXVV8b9X3/9FZUrV4aLiwsqVaqEn376KdX3t2vXLjRo0ADOzs5qQjt5X/Hx8cbnExMTMWHCBJQrV06l8fX1xbfffvtY85A8fv7559XxggULquN9+vTBwoUL1bxPMTExZtdt37493nzzzRTzdejQIdSuXVu9j3r16uHYsWOp1upcuXIFr776qrp23rx5UbVqVWzatCnFfInnnnsOgwYNwpAhQ1C4cGG0bt06xWYpf39/Vesk+ZEaLym31Jo95fWGUVKpfQ6SXuvkyZN44YUXVBAt5TZgwAA8ePDA+LzkXcpu0qRJ6n5JmoEDB3IoOhFZJdYApeBhXAKqjNoCSzjzVWu4Oj351jRt2hQRERHqC1i+iOWLT74s5QvYQI4NHz482eawU6dOYfPmzfj777/VMdMmG/lSlOBi4sSJmDZtGnr06KG+yD08PB47lzw3duxYBAYGomzZsurY6dOnceLECaxatUrtL168GKNGjcL06dNV8CB57t+/vwoIevfu/dg5r1+/jjZt2hgDFfmSl/TyJS9NNmLkyJGYPXs2pkyZgmeffVY12Ui65JrDJB+dOnVCQEAA3Nzc1Je41Kh88MEHKrjr3LmzcfK8jRs34q+//kq2zOULv23btnjxxRexaNEiXLp0CR9++GGq90mCAKnB2b17t3q/Z86cQb58+VLMl8GCBQvw3nvvYe/evame/5NPPsHUqVNRpUoVTJ48WQVbkq+0TOr5pM+BQWRkpArCGjdujMOHD6tykuBagjTTwHnHjh0q+JGfFy5cUOeX5jW5d0RE1oQ1QDmYfFHJl4sh4JGfH330kQou5Itaggj5EmrevPljr5UvWvkSdnBwUE0dspl++Urg0a1bN1W78t1336nzSc1HcqRGQ2p7lixZYjwmAY/UCsnrxejRo/H999+jY8eOKF26tPopef3ll1+SPafUDkmAIAGT1BZJzYIEZXIOqfmRwO+HH35QQZoEUBJ4SRAkX8rJNYcZAjeZGVjeq5SdvN/u3btj3rx5xrQS1EhNktTAJEfeo1x/zpw56n1LMCQBSGqCgoLwzDPPoHr16ihTpox6TbNmzVLMl4HUvMn7q1ixotpSIkGIBFFSu/bzzz+rc0j+0uJJnwPT9x0dHa2CUallkpoguTe//fYbQkJCjOmkJstwz+R9vvLKK9i2bVua8kJElJ1YA5SCPI72qibGUtdOKwluJPAZNmwY/vnnH1UTs2LFCuzZswd3795FsWLF1BdpetWoUcP4WGotpHbCsL5ScqQWaO7cufjiiy9UE97SpUsxdOhQY+2B1A7169fPrCZAmrNS6ih89uxZVdtgOqGdBBESiF27dk2t3SZNVy1atMDTkPzUr19fBYvFixdXtRkS/KU0kZ7kS8pGaqIMJJ+pkVomqcmRWqWWLVuqYMW0fFNSt27dNL0H0+tLICO1gZLPzCTnkyBXPgum90OCQam98vLyUsckKDRdekJqg6TpjIjI2jAASoF8AaalGcrSpKZCAg/pw+Ho6Kj+8pZjEhTdu3cv2dqftJBzJS0P+bJLidQWSVPb0aNH8fDhQ1y9elU1fwhDPxFprkraVyij6zRlVmduaY6TL3ap2WjVqpVqupMmsMwktVLSfGRoWpMgVWqyBg8enOrrTIONjLKzs3usT1lWLg+R3s8NEZGlsAkshzP0A5J+MIZgxxAAyZZSU46QPjCGDtRPq0SJEur60vQlm/SRkWYdIbUDUhN18eJF1SRmuklzWHKkOWf//v1mX97SFyZ//vzqWlKrJUFQWptX5L2K5N6vBChS8yNNYVJDI01vKZF8Sd8maQ4yOHDgwBOvL+d89913sXr1alVbJ8Hgk/KVVqbXl1o1Pz8/lU9RpEgR9fmQWjiDpPMGpeVzIOeTINv0PHI/JMBKrXmOiMhaMQDK4aTPhTSnSNBhCHakf4nUxMicP6nVAJUqVUp1lpUvRBn1lXQ0VHpJM9iyZcuwcuVK9diU9N+Rmo8ff/xR5UuaRSTgkE67yXn//fdVLZLUkkjH5nXr1ql+RNKsJl+60gQlNU6ffvqpqr2RJjYJBFLq+1KyZElVGyEj527fvm02ekn6AUmzmgQlb731VqrvUdLKeaTpTDozy2guGfWUGhnJtWXLFlXWcl+kg7AhQEktX2k1Y8YMrFmzRpWTdLiWmj/D+5AaNxnJJyP1pIykL49pp+W0fg7kfkqZS38r6TQt70HujYyWMzR/ERHlKJqNuH//vlQlqJ9JPXz4UDtz5oz6mRN9+OGH6r2dPXvWeKxmzZqat7e3Wbp58+ZpBQoUMO5HR0drnTp10tzd3dXr5Xkhj9esWWP2Wnmd4fmU3Lt3T3N2dtZcXV21iIiIx55fvHixVqtWLc3JyUkrWLCg1qxZM2316tXquUuXLqnrHjt2zJh+586dWv369VV6eS/Dhw/X4uLijM8nJCRo33zzjVayZEnN0dFR8/X11b777rsUz/fVV1+p8+h0Oq13795meXvzzTc1Dw8PVSZPsn//flW+ki95P6tWrTK71o4dO9S+lIcYNGiQVrZsWVU2RYoUUdcKDQ1NNV/NmzdX9zUp03tjeI9LlizRGjRooPJTpUoVbfv27WavkfTlypXT8uTJo7Vt21abNWuWel16PwcnTpzQnn/+ec3FxUWVVf/+/c3us+S9Xbt2ZteW9yDvJbvl9N9pIkrb9/fT0Mk/sAHh4eGqw+39+/dVh15T0pwhfwFLc4xp51ayHdKZWjrwSg0V5Xz8nSayje/vp2H9vXyJspA0Fxn6Sz1pYkYiIso9GACRTZNRYBIEjR8/np15iYhsCAMgsmmyHAUREdkejgIjIiIim8MAiIiIiGxOhgIgmXdE5g6REVMyz0hKa0QZyLwwMkOxpJf1kGTuFNNZaWU+FzkuM9/KhHm9evXCjRs3zM4h1zOsVm3Yxo0bl5HsExERkY1LdwC0fPlyNRmdTEonk7rJMgIyzX9K60Tt27dPLZMg60DJIp2yqKVsMpmaiIqKUueRNaTkp8yUK2sLvfbaa4+d66uvvlIrfhu2Jy0lQERERJScdM8DJDU+snikrPgsZJ0fmeZfgpERI0Y8ll7Wg5Lp82WmW4NGjRqpVcxnzpyZ7DUOHz6MBg0a4MqVK2plbkMNkMyoK1tGcB4gItvBeYCIco/wLJoHKF01QLGxsWqdIVkvyXgCOzu1L+s2JUeOm6YXUmOUUnohb1KauNzd3c2OS5NXoUKF1NDliRMnqnWPUiLT+UuhmW5EREREKn5JTzHIOkGyaGLStX9kPzg4ONnXyPH0pJe/3KRPkDSbmUZ6H3zwgVpnStYgeuedd/Ddd9+pdaBSIutOScRo2FJb4NJWyBpQSYPK5EjwuXbtWtja+7bU+dJzrS+//FLVnmY2mQhS7ntYWFiy183KaxERwdZHgUmH6DfeeEOtAP7zzz+bPSf9jmSxT1n4U1bV/v777zFt2rQUF/AcOXKkqkkybLKwpq2T5khZiDSrv0zTKqcGWpYsx48//hjbtm1LU9r05KtJkyaqX538sZCZ5Hc2abN1Vl2LiCjLJkIsXLgw7O3tERISYnZc9r29vZN9jRxPS3pD8CP9frZv3/7Edj7piyRNYDKRXcWKFR973tnZWW30SJ48edRGObcc8+XLp7bMJL97Tk5OKf4OZ7bsvBYRUabUAMl/XHXr1jX7C1Q6Qct+48aNk32NHE/6F+vWrVvN0huCn/Pnz+Pvv/9W/Xye5Pjx46r/kaenJ7JUbGTKW1x0OtI+TFvadJCO5dJMIc2ShjKRWhXTzuhvv/02evbs+VizhjweM2YM/v33X+O0AnLMtLmzQ4cOcHV1Rfny5bF+/Xqza+/atUt1VJcgs2jRouqapn2ypNP61KlTzV4jtRFSK2F4Xsg15NqG/aSktkCaRE3dvn0bjo6O2L17t9qXWkCpGSlevLiaSkGCY2lmSY3UMJYtW1Z9piWA/u2338yel+YZaWqV5lqZvqFatWrGjvxpKce33noLbdu2NTunfM7l8zpnzpwU8yWvlY7/Uu5SNnfu3Em1Vkfep9wHed+Sp2eeeUb9EZHa/ZXH8v5lpKW87ttvv02xWUpq6OT+SxlI3z3TmtQ+ffqoEZ2mpLZHan0Mz8vn5IcffjDmQf5gSe5aq1atUovRyudJPgtSw2tKjkmzt5Rr/vz5VRnNmjUrxXIkInqi9C4fv2zZMs3Z2VmbP3++dubMGW3AgAGau7u7FhwcrJ5/8803tREjRhjT7927V3NwcNAmTZqknT17Vhs9erTm6OionTx5Uj0fGxurvfbaa1qJEiW048ePazdv3jRuMTExKs2+ffu0KVOmqOcDAwO1RYsWaUWKFNF69eqV5nzfv39fRrupn0k9fPhQvRf5+ZjRbilvi143T/uNd8pp57YxTzu+dPLp0iEsLEyzs7PTDh8+rPanTp2qFS5cWGvYsKExTbly5bTZs2erx/PmzdMKFCigHkdFRWnDhg3TqlataixvOSaknOR+LFmyRDt//rz2wQcfaPny5dPu3Lmjnr927Zrm6uqqvf/+++qerlmzRl1X7q1ByZIl1T0zVbNmTWOaW7duqetInuTasp+c6dOna76+vlpiYqLx2LRp08yOvf3221qTJk203bt3axcuXNAmTpyoPqPnzp177H2L1atXq8/gjBkztICAAO3777/X7O3tte3bt6vnExIStEaNGqmy+euvv9Rn7o8//tA2bdqU5nKUz72c88aNG2bXzZs3rxYREZHsez1w4IC6n+PHj1f5+uGHH9TvlmnepfykHEVcXJx67uOPP1bvWz7D8nt55cqVJ95fT09Pbe7cueq9SfodO3ao4/fu3TO+RymjevXqqd+/I0eOaA0aNFDlbNC7d2+tXbt2Zu/hww8/1Jo3b278fDZu3Fjr37+/MQ/x8fGPXUvOLe/7q6++Uu9brp0nTx710/Tz5OHhoe6ZfCbHjh2rXuPv759sWab6O01EOUpq399PI90BkOkXkJOTk/pPUf7jNpD//OQ/RlMrVqzQKlSooNLLf8gbN240Pnfp0iX1xpLb5D9K4efnp77U5T97FxcXrXLlytp3332nRUdH23QAJOrUqaO+8EX79u21b7/9VpWzfMlKoCLvOaVAwPTL1JS85vPPPzfuP3jwQB37888/1f5nn32mVaxY0SwokS8mCZIkeEhLAGS4jgRPqZHASAJoCW4M5Et1+PDh6rF8eUugcf36dbPXtWjRQhs5cmSy71u+xOVL2VTnzp21Nm3092jLli3qy1W+jJOT1nKsUqWKCmYMXn31Va1Pnz4pvtdu3boZ82DQpUuXFK8lAamU4c6dO5M9X2r3d8iQIWbHkguAZN/0d1uCXTl28ODBNAVAQh7LsdSu1b17d+3FF180S/PJJ5+o8jOQz1PPnj2N+/LZkyDu559/Tva9MwAiyj3uZ1EAlKHFUAcNGqS25CTX9NC5c2e1JUeqtp80FVGdOnVw4MABWMRn5jNSm9HZm+9/ciGVtElaG4ecRGZo3ry5KvNhw4bhn3/+UaPfVqxYgT179uDu3btqZm1pwkgv6WxuIM0k0ifLMNnl2bNnVROmNGMYSNPLgwcPcO3aNePcTZmhSJEiaNWqFRYvXoymTZvi0qVLagqFX375RT1/8uRJ1QRYoUIFs9dJs1hKTamS/wEDBpgdk/xLU42hKbFEiRKPnTO9pPlRmmlktKL0e/vzzz9V/7aUSL6k2cuUlPPmzZuTTe/h4aGamaRp6sUXX1TTTUhTsjRJPkm9evWemMbBwUHN+WUgs7lLM5vkU5rdMoucr127do/dD2lClXsr/Q6Tfiblsyf9iFKagJWIKEeNArNKTnlT3hxd0pE2SafZlNKlk/S3kGBH+npIvxj5kpJjEhRJ/wsJkDJCzmVKvnCkv1daSf+spIGt9IHJiB49euD3339Xr1+yZIlaNkU2IUGXfEHK/FQSuBg2+VI1BDTplVkdnGVJl4sXL6qAbdGiRShdurQK4jLTvHnz1Pmlr5TM0i5BW1r+WJCg9mll5j3Ojs8kEZEpBkA5nHyhRkREYMqUKcZgxxAAyWbokJoc6QBs6ECdHpUrV1ZfuqZffnv37lWdU6XmxFBzI0OdDWQiSqm9SfqFlpbrS+2AzA8lNSESAElAZCCTYso5pCagXLlyZltKI40k/5JfU7JfpUoVY02D1GSZDnVPTUrlKDVQ0klYghTpgNy3b99UzyP5OnjwoNmxtAQzUgYy7YMsOyOdtaWMUstXWkmn9iNHjhj3ZYka6bgs+UzuHgsJPk2lJQ8p3Q8J5gy1P0REmY0BUA5XsGBB9YUtTUSGYKdZs2ZqXTX5Ak+tBkiaHyUokS8tGfWV0pxKSb3//vtqNJAsf+Lv749169apteFkriapFRAvvPCCGlklzXLSTNW7d+/Hvszk+jJCUCbFvHfvXqq1FRJIyHpxUrMjk2QayJekBERS2yLryMn7kcV5pSlw48aNyZ7vk08+UQGJjISSkYeTJ09Wr5WRZELKTMqwU6dOasSinFOar1JqikqtHKUZbMGCBSrfUgapkck+5RqTJk1S+ZLlZlK6ppBrSuAjwaiM/Prrr7/U6wwBSkbvr2mAKvdYgjKpYZPmNlnGxtD8JfdYAqSFCxeq68pnwLDGn2nZyOtl9JfkIbkaG2m+lc/B119/rT6zUl7y3g33g4goS2g2IsOdoHMA6WQq7006qRpI51dvb+9UO+9KJ/JOnTqpkUaGEVkpdU6W15mOypGOt/Xr11cdruU60ilZRiUZSDlLB143NzfNx8dHjU5K2gl6/fr1apSadHKWTq6pkRFYkq9mzZo99pyMJBw1apRWqlQpNXKpaNGiWocOHbQTJ04k+77FTz/9pJUpU0allw76CxcuNHteOhj37dtXK1SokOp4X61aNW3Dhg3pKkdDZ115b0k7N6dkzpw5agSejIKSTtMyejKlTtAy8lI6vsv7lfsg15FyMHRET8/9Ta4TtFx31apVqpxkVF3Lli1Vp3NTcj0vLy+V9qOPPtIGDRpk1glaOpLLiDp5P3J+GfSQ9Fri999/V52e5X7IAAtDx36DtHSqz02/00SU9Z2g070Yak7FxVDJEqSPksxPJM1gHTt25E3IJlwMlSj3CM+ixVAzNAqMiFInTT3S5CMT+snIKZl0kIiIrAcDIKIsEBQUpEZ9Sadw6W8kQ8qJiMh68H9loiyQlvmtiIjIcjgKjIiIiGwOAyAiIiKyOQyAiIiIyOYwACIiIiKbwwAok0XFRaH6gupqk8dERERkfRgAERERkc1hAESZRtaKkjW7iIiIrB0DILIYWSBTp9M9toI4ERFRVmMAlIVCokKQ3WJjY7P9mkRERDkNA6BMtj5wvfFx+7Xtsfr8amSl5557DoMGDcKQIUNQuHBhtG7dWh2fPHkyqlevjrx588LHxwfvv/++WphTyAzFRYoUwe+//248T61atVC0aFHj/p49e+Ds7IyoqOQ7cickJGDo0KFqnatChQrh008/fWzm482bN+PZZ581pmnbti0CAwONz8tSEaJ27dqqJkjeizh8+DBefPFF9X5kAbzmzZvj6NGjmVpuRERk2xgAZaLgyGCMPTjWuJ+IRIzZP0Ydz0oLFiyAk5MT9u7di5kzZ6pjdnZ2+PHHH3H69Gn1/Pbt21WQIiTYaNasGXbu3Kn27927h7Nnz+Lhw4fw9/dXx3bt2oX69evD1dU12WvKIp+yxtXcuXNVsHT37l2sWbPGLE1kZKQKko4cOYJt27apPHXo0EEtFCoOHTqkfv7999+4efMmVq/WB4sRERHo3bu3Ou+BAwdQvnx5tGnTRh0nIiLKDFwLLBMFhQepoMdUopaIqxFX4Z3XG1lFAoQJEyaYHZMaIdN1qb755hu8++67+Omnn9QxqW355Zdf1OPdu3erWhhvb28VFFWqVEn9lJqXlEydOhUjR45Ex44d1b4EXlu2bDFL06lTJ7N9CZak5unMmTOoVq2aeiykdkiubfDCCy+YvW7WrFmqFkmCMqlFIiIielqsAcpEvm6+sEtSpHY6O/jk90FWqlu37mPHpFalRYsWKF68OPLnz48333wTd+7cMTZpSXAjgcjt27dVYCEBkWwS+MTFxWHfvn3GJqmk7t+/r2psGjZsaDwmq53Xq1fPLN358+fRrVs3lClTBm5ubioQM6yUnpqQkBD0799fBXbSBCavlea7J72OiIgorRgAZSKp5RnZcOSjwtXZYXTj0Vla+yOkn0/S0VVSU1KjRg2sWrUKfn5+mDFjhlknaekf5OHhoYIf0wBIHksfHAmCmjRp8lT5evXVV1XT2OzZs3Hw4EG1meYhJdL8JSPDfvjhBxWIyWOpJWIHbyIiyiwMgDLZa2VfMz5e224tOpbXNxFlJwl4pJ+N9NNp1KgRKlSogBs3bpilkX5ATZs2xbp161Q/IemsLAFTTEyMahqT2pykgZWB1MpIh2lDQCPi4+PVdQ2ktikgIACff/65qomqXLmy6mtkSvotGTpUm5K+TB988IHq91O1alXVGTs0NDRTyoaIiEgwAMpCXq5eFvmUlStXTtXgTJs2DRcvXsRvv/1m7BxtSmp8li5dqkaA5cuXT3VSls7RixcvTrX/j/jwww8xbtw4rF27VnWcllFmYWFhxucLFiyoam2k/86FCxdUJ2zpEG3K09MTefLkUaPFpNlLmtaENH1JnqVjtgRZPXr0UOmIiIgyCwOgXKhmzZpqGPz48eNVZ2MJaMaOfTQ6zUCCHKl9Me3rI4+THkvOsGHDVL8iaa5q3Lix6mckI7wMJJhatmyZqhWSPHz00UeYOHGi2Tmk35CMVJMap2LFiqFdu3bq+Jw5c1RtUZ06ddQ1pDZIgiUiIqLMotOSTt6SS4WHh6umG6llkE61pqKjo3Hp0iU1L42Li8tTXUcWQG24RN85+GD3g3B1TH4YORFlncz8nSYi6/3+fhocBp/JJOA52ftkZp+WiIiIMhGbwIiIiMjmMAAiIiIim8MAiIiIiGwOAyAThjWqiChn4+8yET0JO0H/NyGfDNuWyQJlfSrZl4kCiShnkUGtMmO4LPEiv9OGyTaJiJJiAPTfnDUyXFbWt0o6YzIR5Tyurq7w9fVVv9tERMlhAPQf+UtR/sOUJR2SLs1ARDmHvb29mmSTtbhElBoGQCbkP0xHR0e1ERERUe7F+mEiIiKyORkKgGbMmIFSpUqpKeYbNmyIQ4cOpZp+5cqVqFSpkkpfvXp1bNq06bGOi6NGjVIrjMuily1btsT58+fN0ty9e1ctiinTYLu7u6Nfv3548OBBRrJPRERENi7dAdDy5cvVqt6jR4/G0aNH1cKbrVu3xq1bt5JNv2/fPnTr1k0FLMeOHUP79u3VdurUKWOaCRMmqEUxZcVyWf07b9686pyyno+BBD+nT5/G1q1bsWHDBuzevRsDBgzI6PsmIiIiG5buxVClxqd+/fqYPn26cb4NHx8fDB48GCNGjHgsfZcuXRAZGamCFoNGjRqhVq1aKuCRy8tK4LK6+Mcff6yelwXPvLy8MH/+fHTt2hVnz55FlSpVcPjwYdSrV0+l2bx5M9q0aYNr166p1ycVExOjNgM5p3Ryvnr1aqYupkZERERZuxiqxBlhYWFqUdRMo6VDTEyMZm9vr61Zs8bseK9evbTXXnst2df4+PhoU6ZMMTs2atQorUaNGupxYGCgBGDasWPHzNI0a9ZM++CDD9TjOXPmaO7u7mbPx8XFqbysXr062euOHj1anZcby4CfAX4G+BngZ4CfgZz/GQgMDNQyU7pGgYWGhqoh4lI7Y0r2/f39k31NcHBwsunluOF5w7HU0nh6epo9L8NcPTw8jGmSGjlypGqqM5DIsWTJkggKCsrcCJIyHM2zNs468H5YD94L68F7YT0MLTjynZ+Zcu0weGdnZ7UlJcEPm8Csg9wH3gvrwfthPXgvrAfvhfXI7IlN03W2woULq0nGQkJCzI7Lvre3d7KvkeOppTf8fFKapJ2sZcJCGRmW0nWJiIiIMiUAktmS69ati23bthmPSSdo2W/cuHGyr5HjpumFjOQypJclKCSIMU0jVY8yGsyQRn5KE5afn58xzfbt29W1pVM2ERERUbqkt9PQsmXLNGdnZ23+/PnamTNntAEDBqgOysHBwer5N998UxsxYoQx/d69ezUHBwdt0qRJ2tmzZ1XnZEdHR+3kyZPGNOPGjVPnWLdunXbixAmtXbt2WunSpbWHDx8a07z00kta7dq1tYMHD2p79uzRypcvr3Xr1i3N+Y6OjlbXlp9kWbwX1oX3w3rwXlgP3ovcfy/SHQCJadOmab6+vpqTk5PWoEED7cCBA8bnmjdvrvXu3dss/YoVK7QKFSqo9FWrVtU2btxo9nxiYqL2xRdfaF5eXiq4atGihRYQEGCW5s6dOyrgyZcvn+bm5qb17dtXi4iIyEj2iYiIyMalex4gIiIiopyOa4ERERGRzWEARERERDaHARARERHZHAZAREREZHNydQD07bffokmTJnB1dYW7u3uaXiN9wkeNGoWiRYsiT548aNmyJc6fP5/lec3tZNLKHj16qFlV5V7069cPDx48SPU1zz33HHQ6ndn27rvvZluec5MZM2agVKlScHFxUXNnHTp0KNX0K1euRKVKlVT66tWrY9OmTdmW19wuPfdCFoRO+jsgr6Ont3v3brz66qtqMW0p17Vr1z7xNTt37kSdOnXUKgPlypVT94ey/17IfUj6eyFbSktj2WQAFBsbi86dO+O9995L82smTJiAH3/8Ua1UL5Mx5s2bF61bt0Z0dHSW5jW3k+Dn9OnTahLMDRs2qA/8gAEDnvi6/v374+bNm8ZN7g+lz/Lly9W6eKNHj8bRo0dRs2ZN9ZlOOru6wb59+9CtWzcVpB47dgzt27dX26lTp1j02XwvhPzRYPo7cOXKFd6HTBAZGanKXwLStLh06RJeeeUVPP/88zh+/DiGDBmCt99+G1u2bOH9eErpvRcGAQEBZr8bSdcMfSLNBsybN08rUKDAE9PJfETe3t7axIkTjcfCwsLU3ERLly7N4lzmXjJhpnzUDh8+bDz2559/ajqdTrt+/XqKr5M5pT788MNsymXuJXN1DRw40LifkJCgFStWTBs7dmyy6d944w3tlVdeMTvWsGFD7Z133snyvOZ26b0Xaf2/i56O/P+0Zs2aVNN8+umnah47U126dNFat27N4s/me7Fjxw6V7t69e091rVxdA5ReEuFLFZo0e5kunirV1Pv377do3nIyKTtp9qpXr57xmJSxLGwntWypWbx4sVqDrlq1ahg5ciSioqKyIce5qxZUlpAx/UxLuct+Sp9pOW6aXkgtBX8Hsv9eCGkqLlmyJHx8fNCuXTtVk0rZj78X1qdWrVqqu8qLL76IvXv3pvv1uXY1+IwwtB96eXmZHZf99LYtknm5Jq2adHBwgIeHR6rl2r17d/Ufv7QLnzhxAsOHD1dVnqtXr2bxplFoaCgSEhKS/Uz7+/sn+xq5J/wdsI57UbFiRcydOxc1atTA/fv3MWnSJNWvUYKgEiVKZEEuKSUp/V7I2pUPHz5UfUYpe0jQI91U5I/qmJgY/Prrr6rPqPxBLX20cm0ANGLECIwfPz7VNGfPnlUdOMk67kVGmfYRko648qFv0aIFAgMDUbZs2QyflyinkIWgTRealuCncuXK+OWXX/D1119bNG9EliJ/GMhm+nsh3wtTpkzBb7/9lnsDoGHDhqFPnz6ppilTpkyGzi2r0ouQkBD1ZWsg+1LVRhm7F1KuSTt5xsfHq5FhhjJPC2mKFBcuXGAAlEbSfGhvb68+w6ZkP6Wyl+PpSU9Zdy+ScnR0RO3atdXvAGWvlH4vpJM6a38sr0GDBtizZ0+6XpPjAqAiRYqoLSuULl1afci3bdtmDHikelOq1dIzksxWpPVeyF+wYWFhqv9D3bp11bHt27cjMTHRGNSkhYy8EKbBKaXOyclJlbl8pmUkl5Byl/1BgwaleL/keRnlYiCj90xrIih77kVS0oR28uRJtGnThrcgm8nnP+l0EPy9sB7y/ZDu7wYtF7ty5Yp27NgxbcyYMWoVeXksm+kq8hUrVtRWr15t3B83bpzm7u6urVu3Tjtx4oTWrl07rXTp0trDhw8t9C5yh5deekmrXbu2dvDgQW3Pnj1a+fLltW7duhmfv3btmroX8ry4cOGC9tVXX2lHjhzRLl26pO5HmTJltGbNmlnwXeRMy5YtUyMZ58+fr0bkDRgwQH3Gg4OD1fNvvvmmNmLECGP6vXv3ag4ODtqkSZO0s2fPaqNHj9YcHR21kydPWvBd2Oa9kP+7tmzZogUGBmp+fn5a165dNRcXF+306dMWfBe5g3wPGL4T5Ktw8uTJ6rF8bwi5D3I/DC5evKi5urpqn3zyifq9mDFjhmZvb69t3rzZgu/CNu/FlClTtLVr12rnz59X/y/JaGE7Ozvt77//Ttd1c3UA1Lt3b1WYSTcZQmcg+zLU1HQo/BdffKF5eXmp/6hatGihBQQEWOgd5B537txRAY8Eom5ublrfvn3NAlEJckzvTVBQkAp2PDw81H0oV66c+o/n/v37FnwXOde0adM0X19fzcnJSQ3FPnDggNl0A/K7YmrFihVahQoVVHoZ+rtx40YL5Dp3Ss+9GDJkiDGt/J/Upk0b7ejRoxbKee5iGEqddDOUv/yU+5H0NbVq1VL3Q/4gM/3uoOy7F+PHj9fKli2r/hiQ74jnnntO2759e7qvq5N/sqpKioiIiMgacR4gIiIisjkMgIiIiMjmMAAiIiIim8MAiIiIiGwOAyAiIiKyOQyAiIiIyOYwACIiIiKbwwCIiIiIbA4DICIiIrI5DICIiIjI5jAAIiIiItia/wOpENNNp11k5gAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define function which computes the phase averaged over the velocity distribution\n", "def weighted_phase_function(v):\n", " return nquad(lambda x: vel_dist_norm(x)*phase_v_fnc(v+x), ((-1, 1),))[0]\n", "\n", "# Compute the phase for a range of different incoming velocities\n", "incoming_velocities = np.linspace(-1.5,1.5)\n", "phases_averaged_over_vdist = np.array([weighted_phase_function(x-0.225) for x in incoming_velocities])\n", "\n", "# Plot\n", "plt.plot(incoming_velocities,1000*phases_averaged_over_vdist/16/25/2/np.pi, label='with velocity distribution')\n", "plt.plot(incoming_velocities,1000*phase_v_fnc(incoming_velocities-0.225)/16/25/2/np.pi, '--', label='without velocity distribution')\n", "plt.errorbar(raw_data_x, raw_data_y, raw_data_err, marker='.', linestyle='none', label='raw data')\n", "plt.legend()\n", "plt.xlim([-1,1.5])\n", "plt.ylim([0,0.2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f6ea5862-5d96-4a35-8193-f619d5ef6178", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "This is the same as Fig. 3b." ] } ], "metadata": { "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": "3.12.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }