{ "cells": [ { "cell_type": "markdown", "id": "7cfb587e-bcac-48d5-93d2-2dbdadada238", "metadata": {}, "source": [ "# Interferometer Geometries" ] }, { "cell_type": "markdown", "id": "f1e6958d-1dd4-4fac-bc6d-621bfc700019", "metadata": {}, "source": [ "**What you'll learn:**\n", "- How to define interferometer geometries using symbolic unitary operators\n", "- How to visualize interferometer tree structures\n", "- How to compute analytic phase expressions for Mach-Zehnder and simultaneous conjugate interferometers (SCI)\n", "- How to plot interferometer arm trajectories" ] }, { "cell_type": "markdown", "id": "3e0f89f2-1011-49b4-9c44-3a1a2346eded", "metadata": {}, "source": [ "## Mach-Zender Interferometer" ] }, { "cell_type": "markdown", "id": "78f062c1-d28e-4684-ba0f-e69bd7f0a64f", "metadata": {}, "source": [ "Define the needed constants, initialize the required unitary operators, and define the interferometer." ] }, { "cell_type": "code", "execution_count": 1, "id": "30e582e2-884e-4543-a08b-d7eb392e7524", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from mwave import symbolic as msym\n", "import numpy as np\n", "import sympy as sp\n", "from matplotlib import pyplot as plt\n", "\n", "# Set up symbols for symbolic computation\n", "m, c, hbar, k, g, gamma, delta, n, T, t_traj = sp.symbols('m c hbar k g gamma delta n T t_traj', real=True)\n", "k_eff = 2*k\n", "\n", "# Register constants\n", "msym.set_constants(m=m, c=c, hbar=hbar, t_traj=t_traj)\n", "\n", "# Define unitary operators needed for an MZ interferometer\n", "bs = msym.Beamsplitter(0, n, delta, k_eff)\n", "mirror = msym.Mirror(0, n, delta, k_eff)\n", "free = msym.FreeEv(T, gravity=g, gravity_grad=gamma)\n", "\n", "# Create interferometer object, perform MZ sequence\n", "ifr = msym.Interferometer()\n", "(bs @ (free @ (mirror @ (free @ (bs @ ifr)))))" ] }, { "cell_type": "markdown", "id": "6cd3e7f2-0285-4d3d-ba1a-ce7cc44b73a7", "metadata": {}, "source": [ "Generate and optionally vizualize the directed tree structure representing the interferometer object." ] }, { "cell_type": "code", "execution_count": 2, "id": "72799857-6871-4f62-9cb9-5df456fb0c32", "metadata": {}, "outputs": [], "source": [ "# Create a graphviz object of the tree\n", "d_test = ifr.generate_graph()\n", "\n", "# Uncomment to display the graph\n", "# d_test.view()" ] }, { "cell_type": "markdown", "id": "d5ed1206-0746-45db-9d86-333c92077d4f", "metadata": {}, "source": [ "Check for interferance, set the gravity gradient to zero as otherwise the interferometer won’t perfectly close and no interferance will be detected." ] }, { "cell_type": "code", "execution_count": 3, "id": "12d3789c-239c-49a7-b5f1-55808cdb9145", "metadata": {}, "outputs": [], "source": [ "inodes = ifr.interfere(subs={gamma: 0})" ] }, { "cell_type": "markdown", "id": "2bdb787d-e2e5-4bd6-a954-d632b0befc38", "metadata": {}, "source": [ "Determine which port each output is in" ] }, { "cell_type": "code", "execution_count": 4, "id": "6c1c6f69-9269-4e42-af50-4a98378fb15f", "metadata": {}, "outputs": [], "source": [ "iports, jports, noport = ifr.get_ports({n:'upper', 0: 'lower'})" ] }, { "cell_type": "markdown", "id": "0c73d40d-16b6-4c77-8a1f-916100c366e8", "metadata": {}, "source": [ "Check that we don’t have any unexpected ports" ] }, { "cell_type": "code", "execution_count": 5, "id": "07d9ce81-3f2d-47d4-964e-ecad4027c73a", "metadata": {}, "outputs": [], "source": [ "if len(jports) != 0 or len(noport) != 0:\n", " print('Unexpected output')" ] }, { "cell_type": "markdown", "id": "565bb9b9-29fb-413c-a567-752ddcb30c36", "metadata": {}, "source": [ "Set interferometer parameters for plotting" ] }, { "cell_type": "code", "execution_count": 6, "id": "be5c0321-466a-42bc-a5b4-69db30cb4231", "metadata": {}, "outputs": [], "source": [ "subs = {m: 1, c: 1, hbar: 1, k: 1, g: 0.3, gamma: 0.001, delta: 4*3, n: 3, T: 5}" ] }, { "cell_type": "markdown", "id": "6f92b369-330f-4644-b347-f974d8df9469", "metadata": {}, "source": [ "Determine the final interferometer time by evaluating the value of t at the end of the interferometer. We can pick a random interferometer port to do this." ] }, { "cell_type": "code", "execution_count": 7, "id": "ad90912a-0d64-415e-a631-13b6f152ab6e", "metadata": {}, "outputs": [], "source": [ "tfinal = float(iports['upper'][0].t.evalf(subs=subs))" ] }, { "cell_type": "markdown", "id": "1713e928-1ed2-43a9-a6c9-224dac97481a", "metadata": {}, "source": [ "Plot the trajectory of the interferometer paths" ] }, { "cell_type": "code", "execution_count": 8, "id": "d8bcc1da-af65-4c77-8940-ac7491e079a2", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, tfinal, 1000)\n", "plt.figure()\n", "for node_pair, ls in zip([iports['upper'], iports['lower']], ['-', '--']):\n", " fnc_traj = node_pair[0].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", " fnc_traj = node_pair[1].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", "plt.xlabel('time')\n", "plt.ylabel('position')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5af1af94-c134-4fd7-9506-e063682014ff", "metadata": {}, "source": [ "Compute the phase of the interferometer" ] }, { "cell_type": "code", "execution_count": 9, "id": "7b2b3b15-f3ec-4d3e-b2f6-4a74a6bcb000", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "phase_1=(-3*T**10*g*gamma**4*k*m*n + 10*T**9*gamma**4*hbar*k**2*n**2 - 34*T**8*g*gamma**3*k*m*n + 56*T**7*gamma**3*hbar*k**2*n**2 - 53*T**6*g*gamma**2*k*m*n + 60*T**5*gamma**2*hbar*k**2*n**2 + 84*T**4*g*gamma*k*m*n - 144*T**3*gamma*hbar*k**2*n**2 + 144*T**2*g*k*m*n - 72*pi*m)/(72*m)\n", "phase_2=T**2*k*n*(-3*T**8*g*gamma**4*m + 10*T**7*gamma**4*hbar*k*n - 34*T**6*g*gamma**3*m + 56*T**5*gamma**3*hbar*k*n - 53*T**4*g*gamma**2*m + 60*T**3*gamma**2*hbar*k*n + 84*T**2*g*gamma*m - 144*T*gamma*hbar*k*n + 144*g*m)/(72*m)\n", "total population sum=1\n" ] } ], "source": [ "# Compute the differential phase\n", "phi1, phi2 = ifr.phases()\n", "print(f'phase_1={sp.simplify(phi1)}')\n", "print(f'phase_2={sp.simplify(phi2)}')\n", "\n", "# Print out the total population, check it is equal to 1\n", "pop = 0\n", "for node in ifr.get_nodes():\n", " pop += (node.get_amp())**2\n", "print(f'total population sum={sp.simplify(pop)}')" ] }, { "cell_type": "markdown", "id": "386c82e5-7776-4547-b16b-f76c30b3c615", "metadata": {}, "source": [ "## Simultaneous Conjugate Interferometer" ] }, { "cell_type": "markdown", "id": "7e251736-0146-4aca-99ae-52bf32762aa2", "metadata": {}, "source": [ "Define the needed constants, initialize the required unitary operators, and define the interferometer." ] }, { "cell_type": "code", "execution_count": 1, "id": "daf88caa-9e0a-4e1d-b1fc-eb73656328b3", "metadata": {}, "outputs": [], "source": [ "from mwave import symbolic as msym\n", "import numpy as np\n", "import sympy as sp\n", "from matplotlib import pyplot as plt\n", "\n", "# Set up symbols for symbolic computation\n", "m, c, hbar, k, omega_r, delta, n, omega_m, T, Tp, t_traj = sp.symbols('m c hbar k omega_r delta n omega_m T Tp t_traj', real=True)\n", "k_eff = 2*k\n", "\n", "# Register constants\n", "msym.set_constants(m=m, c=c, hbar=hbar, t_traj=t_traj)\n", "\n", "# Define unitary operators needed for an SCI interferometer\n", "bs1 = msym.Beamsplitter(n, 0, delta, k_eff)\n", "bs2 = msym.Beamsplitter(0, -n, delta - omega_m, k_eff)\n", "bs2u = msym.Beamsplitter(n, 2*n, delta + omega_m, k_eff)\n", "fe1 = msym.FreeEv(T)\n", "fe2 = msym.FreeEv(Tp)\n", "\n", "# Create interferometer object, perform MZ sequence\n", "ifr = msym.Interferometer()\n", "ifr.apply(bs1)\n", "ifr.apply(fe1)\n", "ifr.apply(bs1)\n", "ifr.apply(fe2)\n", "ifr.apply(bs2)\n", "ifr.apply(bs2u)\n", "ifr.apply(fe1)\n", "ifr.apply(bs2)\n", "ifr.apply(bs2u)" ] }, { "cell_type": "markdown", "id": "54cfd9fe-9821-4bf0-bfcc-87e8e2270f94", "metadata": {}, "source": [ "Generate and optionally vizualize the directed tree structure representing the interferometer object." ] }, { "cell_type": "code", "execution_count": 2, "id": "27190677-68f6-47ea-9887-47f914b38fa1", "metadata": {}, "outputs": [], "source": [ "# Create a graphviz object of the tree\n", "d_test = ifr.generate_graph()\n", "\n", "# Uncomment to display the graph\n", "# d_test.view()" ] }, { "cell_type": "markdown", "id": "27d75a26-7ec9-44b5-9b00-3a6853f81ded", "metadata": {}, "source": [ "Check for interferance, set the gravity gradient to zero as otherwise the interferometer won't perfectly close and no interferance will be detected." ] }, { "cell_type": "code", "execution_count": 3, "id": "4a6191fd-476a-4652-ba6d-4191d702e105", "metadata": {}, "outputs": [], "source": [ "inodes = ifr.interfere()" ] }, { "cell_type": "markdown", "id": "7b944eb1-c5a4-406a-8dfb-62f9c9701636", "metadata": {}, "source": [ "Determine which port each output is in" ] }, { "cell_type": "code", "execution_count": 4, "id": "5cfce863-32e1-4cbb-9d09-7c404494fb95", "metadata": {}, "outputs": [], "source": [ "iports, jports, noport = ifr.get_ports({2*n:'A', n:'B', 0:'C', -n:'D'})" ] }, { "cell_type": "markdown", "id": "0fa5843e-773e-49dc-ac72-f5d3086f4e75", "metadata": {}, "source": [ "Check that we don't have any unexpected ports" ] }, { "cell_type": "code", "execution_count": 5, "id": "b09c0b4b-73d5-447d-b41f-ac9047c5a455", "metadata": {}, "outputs": [], "source": [ "if len(jports) != 4 or len(noport) != 0:\n", " print('Unexpected output')" ] }, { "cell_type": "markdown", "id": "c117b755-0a15-452d-880e-6028c6ffedf9", "metadata": {}, "source": [ "Set interferometer parameters for plotting" ] }, { "cell_type": "code", "execution_count": 6, "id": "032d8eff-04b8-47a4-93e2-bbc0dea12a53", "metadata": {}, "outputs": [], "source": [ "subs = {m: 1, c: 1, hbar: 1, k: 1, delta: 4*3, n: 3, T: 5, Tp: 1}" ] }, { "cell_type": "markdown", "id": "ab52f977-cf93-473b-be05-90c1456f6364", "metadata": {}, "source": [ "Determine the final interferometer time by evaluating the value of t at the end of the interferometer. We can pick a random interferometer port to do this." ] }, { "cell_type": "code", "execution_count": 7, "id": "e11007ae-cd82-4281-92d9-3b7c564b866b", "metadata": {}, "outputs": [], "source": [ "tfinal = float(iports['A'][0].t.evalf(subs=subs))" ] }, { "cell_type": "markdown", "id": "6eda08df-4137-4616-b8a8-c108042cde6e", "metadata": {}, "source": [ "Plot the trajectory of the interferometer paths" ] }, { "cell_type": "code", "execution_count": 8, "id": "c1347b56-1d8f-49db-a58e-740ea2d7107f", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, tfinal, 1000)\n", "plt.figure()\n", "for port, ls in zip(['A', 'B', 'C', 'D'], ['-', '--', '-.', ':']):\n", " fnc_traj = iports[port][0].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", " fnc_traj = iports[port][1].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", "plt.xlabel('time')\n", "plt.ylabel('position')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4929e29b-94f1-4d5d-ac81-6d08e41f3be6", "metadata": {}, "source": [ "Compute the phase of the interferometer" ] }, { "cell_type": "code", "execution_count": 9, "id": "3e4f2efb-3f48-40f8-a4cc-41a5be932bfb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "differential phase=16*T*n**2*omega_r - 2*T*n*omega_m - 2*pi\n", "total population sum=1\n" ] } ], "source": [ "# Compute the differential phase\n", "phiA, phiB, phiC, phiD = ifr.phases()\n", "print(f'differential phase={sp.simplify(phiA - phiC).subs(k, sp.sqrt(2*m*omega_r/hbar))}')\n", "\n", "# Print out the total population, check it is equal to 1\n", "pop = 0\n", "for node in ifr.get_nodes():\n", " pop += (node.get_amp())**2\n", "print(f'total population sum={sp.simplify(pop)}')" ] }, { "cell_type": "markdown", "id": "afe272e8-7804-4875-9b32-e726a5361f95", "metadata": {}, "source": [ "## Simulatenous Conjugate Interferometer with single Bragg pulses" ] }, { "cell_type": "code", "execution_count": 1, "id": "d29d2f87-c8bd-4948-b7df-1831fb28516a", "metadata": {}, "outputs": [], "source": [ "from mwave import symbolic as msym\n", "import numpy as np\n", "import sympy as sp\n", "from matplotlib import pyplot as plt\n", "\n", "# Set up symbols for symbolic computation\n", "k, c, hbar, m, g, T_spacing, T, Tp, delta, t_traj, omega_r, omega_0 = sp.symbols('k c hbar m g T_spacing T Tp delta t_traj omega_r omega_0', real=True)\n", "k_eff = 2*k\n", "\n", "# Register constants\n", "msym.set_constants(m=m, c=c, hbar=hbar, t_traj=t_traj)" ] }, { "cell_type": "markdown", "id": "ce61505f-bc4d-44b9-bf13-c7ea05eb2f91", "metadata": {}, "source": [ "For an n=2 SCI with single Bragg pulses we must run the following pulse sequences for beam splitters\n", "```\n", "Pulse sequence 1: Split initial state into two, mirror one of the outputs to bragg order n\n", "1 2 ... n\n", "pi/2 -> pi -> ... -> pi\n", "\n", "Pulse sequence 2: Mirror state at momentum n down to 1, then pi/2 to bring to correct state and diffract initially undiffracted arm to 1, then mirror initially undiffracted arm up to n\n", "1 n-1 n n+1 n+n-1\n", "pi -> ... -> pi -> pi/2 -> pi -> ... -> pi\n", "\n", "Pulse sequence 3: pi/2 lower interferometer upper arm down (pi/2 necessary to avoid diffracting away the lower arm), pi pulse to -n. Simulaneously do the same for the upper interferometer lower arm\n", "1 2 n\n", "pi/2 -> pi -> ... -> pi\n", "\n", "Pulse sequence 4: pi lower interferometer upper arm up to 0, pi/2 pulse to interfere 0 and -1 states. Simulaneously do the same for the upper interferometer lower arm\n", "1 2 n\n", "pi -> ... -> pi -> pi/2\n", "```\n", "We will next implement the unitary operators needed to perform these sequences" ] }, { "cell_type": "code", "execution_count": 2, "id": "03c4b423-1683-4801-9131-561d493a5130", "metadata": {}, "outputs": [], "source": [ "nbragg = 2\n", "\n", "bsdict = {}\n", "mdict = {}\n", "\n", "# Make function to get/construct a beamsplitter between the two specified states\n", "def get_bs(n0, nf):\n", " tid = (min(n0,nf), max(n0,nf))\n", " if tid in bsdict:\n", " return bsdict[tid]\n", " else:\n", " bsdict[tid] = msym.Beamsplitter(min(n0,nf), max(n0,nf), 4*(n0+nf)*omega_0, k_eff)\n", " return bsdict[tid]\n", "\n", "# Make function to get/construct a mirror between the two specified states\n", "def get_m(n0, nf):\n", " tid = (min(n0,nf), max(n0,nf))\n", " if tid in mdict:\n", " return mdict[tid]\n", " else:\n", " mdict[tid] = msym.Mirror(min(n0,nf), max(n0,nf), 4*(n0+nf)*omega_0, k_eff)\n", " return mdict[tid]\n", "\n", "# Free evolutions\n", "feTs = msym.FreeEv(T_spacing)\n", "feT = msym.FreeEv(T)\n", "feTp = msym.FreeEv(Tp)\n", "\n", "# Beamsplitter sequences\n", "def pulse1(ifr):\n", " ifr.apply(get_bs(0, 1))\n", " for n in range(1, nbragg):\n", " ifr.apply(feTs)\n", " ifr.apply(get_m(n, n+1))\n", "\n", "def pulse2(ifr):\n", " for n in range(nbragg, 1, -1):\n", " ifr.apply(get_m(n, n-1))\n", " ifr.apply(feTs)\n", " ifr.apply(get_bs(1, 0))\n", " for n in range(1, nbragg):\n", " ifr.apply(feTs)\n", " ifr.apply(get_m(n, n+1))\n", " \n", "def pulse3(ifr):\n", " ifr.apply(get_bs(0, -1))\n", " ifr.apply(get_bs(nbragg, nbragg+1))\n", " for n in range(1, nbragg):\n", " ifr.apply(feTs)\n", " ifr.apply(get_m(-n, -n-1))\n", " ifr.apply(get_m(nbragg+n, nbragg+n+1))\n", " \n", "def pulse4(ifr):\n", " for n in range(nbragg, 1, -1):\n", " ifr.apply(get_m(-n, -n+1))\n", " ifr.apply(get_m(nbragg+n, nbragg+n-1))\n", " ifr.apply(feTs)\n", " ifr.apply(get_bs(0, -1))\n", " ifr.apply(get_bs(nbragg, nbragg+1))" ] }, { "cell_type": "markdown", "id": "f783f9e9-3f25-4afe-94e0-1a239e216579", "metadata": {}, "source": [ "Create the interferometer object and apply our sequence of unitary operators" ] }, { "cell_type": "code", "execution_count": 3, "id": "f3e4d22c-4884-4d16-aab9-55933e79ed6d", "metadata": {}, "outputs": [], "source": [ "ifr = msym.Interferometer()\n", "pulse1(ifr)\n", "ifr.apply(feT)\n", "pulse2(ifr)\n", "ifr.apply(feTp)\n", "pulse3(ifr)\n", "ifr.apply(feT)\n", "pulse4(ifr)" ] }, { "cell_type": "markdown", "id": "a784ae21-4a35-48d7-978d-b297f710a336", "metadata": {}, "source": [ "Generate and optionally vizualize the directed tree structure representing the interferometer object." ] }, { "cell_type": "code", "execution_count": 4, "id": "3a436640-ed6a-4ed5-ae96-929f34a02a62", "metadata": {}, "outputs": [], "source": [ "# Create a graphviz object of the tree\n", "d_test = ifr.generate_graph()\n", "\n", "# Uncomment to display the graph\n", "# d_test.view()" ] }, { "cell_type": "markdown", "id": "a5a9c352-262b-4637-9202-d9fc29f67b41", "metadata": {}, "source": [ "Check for interferance, set the gravity gradient to zero as otherwise the interferometer won't perfectly close and no interferance will be detected." ] }, { "cell_type": "code", "execution_count": 5, "id": "9d6e3b5c-3195-40c4-a4f5-1a26f8a51f56", "metadata": {}, "outputs": [], "source": [ "inodes = ifr.interfere()" ] }, { "cell_type": "markdown", "id": "6aaddfa5-1c0c-4cad-a8e6-af13ba15896b", "metadata": {}, "source": [ "Determine which port each output is in" ] }, { "cell_type": "code", "execution_count": 6, "id": "952d59f2-32d3-45d4-86de-cf6566234dd7", "metadata": {}, "outputs": [], "source": [ "iports, jports, noport = ifr.get_ports({nbragg+1:'A', nbragg:'B', 0:'C', -1:'D'})" ] }, { "cell_type": "markdown", "id": "b63de540-a912-43bf-879c-780548ec8634", "metadata": {}, "source": [ "Check that we don't have any unexpected ports" ] }, { "cell_type": "code", "execution_count": 7, "id": "5eef4093-f6a7-47b3-9ef3-a1ad09dbdbb8", "metadata": {}, "outputs": [], "source": [ "if len(jports) != 4 or len(noport) != 0:\n", " print('Unexpected output')" ] }, { "cell_type": "markdown", "id": "83169aa7-381e-4e27-9908-9da7e656779e", "metadata": {}, "source": [ "Set interferometer parameters for plotting" ] }, { "cell_type": "code", "execution_count": 8, "id": "0fb41365-c280-408a-b9af-9c003d9f4377", "metadata": {}, "outputs": [], "source": [ "subs = {k: 2, c: 1, hbar: 1, m: 1, T_spacing: 1, delta: 4*omega_r, omega_r: 1, T:5, Tp: 3, g: 1}" ] }, { "cell_type": "markdown", "id": "078d9cf9-8335-4241-bf30-ad626d7ed742", "metadata": {}, "source": [ "Determine the final interferometer time by evaluating the value of t at the end of the interferometer. We can pick a random interferometer port to do this." ] }, { "cell_type": "code", "execution_count": 9, "id": "b6f7b937-560b-4ec5-ac0e-21fb6827375c", "metadata": {}, "outputs": [], "source": [ "tfinal = float(inodes[0][0].t.evalf(subs=subs))" ] }, { "cell_type": "markdown", "id": "61c52882-40e9-422b-b69d-8d1e53092f80", "metadata": {}, "source": [ "Plot the trajectory of the interferometer paths" ] }, { "cell_type": "code", "execution_count": 10, "id": "69352ff1-59c2-4cdb-9fbd-8ed980611ddf", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjsAAAGwCAYAAABPSaTdAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjgsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvwVt1zgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAeKVJREFUeJzt3Qd0FFUbBuB3tmTTO2kkVOm99470KoggCCiChV5EsFAUQVDpVUSKCEjvIB2UXqX3kJBACOl96/xnJiTCL52Ebe9zzsLu7GT2ztzN7pfbPkEURRFERERENkph7gIQERER5SYGO0RERGTTGOwQERGRTWOwQ0RERDaNwQ4RERHZNAY7REREZNMY7BAREZFNU5m7AJbAZDLhzp07cHNzgyAI5i4OERERPQdpqcDk5GQEBQVBoXhy+w2DHUAOdEJCQp7nuhIREZGFuX37NoKDg5/4PIMdQG7RybpY7u7ur692iIiI6KUlJSXJjRVZ3+NPwmAHyO66kgIdBjtERETW5VlDUDhAmYiIiGwagx0iIiKyaQx2iIiIyKYx2CEiIiKbxmCHiIiIbBqDHSIiIrJpDHaIiIjIpjHYISIiIpvGYIeIiIhsGoMdIiIismkMdoiIiMimMdghIiIim8Zgh4iIiHJNYuw9pFz9C+bEYIeIiIhyReqhbYh5rx6w9G2EXT4Jc1GZ7ZWJiIjIZhkOr8DtPmMgGgTcc3KHYDCYrSxs2SEiIqKcYzIB+yZiy8EhiC+bAX0eFcL7L0Gh0tVgLmzZISIiohxhio+GcXU/nI/ZizGB/jA2AVp5fYnx9avDnBjsEBER0SvTnTuEiI97w2DS4rOevjAIAnyFKhjXuhPMjd1YRERE9EpS187DrW4fQBtrQoJWDVWKEmpDMFZ3nAaFwvyhBlt2iIiI6KWIJhPix/fFvd/3AqKAe/4CRndUIM7FDYubzoKPsxssAYMdIiIiemGmtGRE9WmLxBN3AQgIL+GEkS110KlUGFlhAirmLQRLwWCHiIiIXkxyFO71aonEs2mAIALNK6N/kAc06gNoGdAXXcvVhyVhsENERETPL/IksKIrfPNHI+1WHig+7o2Wt0pDF2NEs0JNMbFpG1ga848aIiIiIquQsWk68GtzIPku1PnfgHrZEnS7XxZpOiNqveGDyW1bwRKxZYeIiIieStRmIHpQJ8TtvYrg2gLcGjZHWpuZeHvVR0h21yJE2Rszu1SESmmZbSgMdoiIiOiJjPfCEPl+B6TeTJUHImu9G8Ct8zK888dQpCmuQuGoweg3C8DLxQGWyjJDMCIiIjI77bGdCG3TXA50BKWIvMO6wHfSCgz5cx5u6XZBFAV8WOwrNH6jHCwZW3aIiIjoP5KXTMKdSb/CZBCgdgOCp/wAx9qtsejkLuy4NxeCAFT36opBNdvB0jHYISIion+JIjKWfYGI8evkbivnfI7I++sqqILfwPGI6/jpny8hKE3wU1THz60/gzVgsENERESZtCnAhk/heG0DvIq4A36l4D9rLQRHZ6RoDfh4+2eAOg0OxnxY02mKRaSCeB4MdoiIiAi6i0eh2D4IqqSLgEIN/1HfQKjyvnxlTCYRQ/44g7iwdnAPXo+FbafA08nVaq4agx0iIiI7l7p+PiJH/wSNhw75WuaB0GUphHzVs5+fuusqdly8BwelHxY2/xVlA7xgTRjsEBER2XMizwn9cG/pHjmRpwkuML6zHKp8pbP3mXhgFX4+GgGgKMa/VQYV81lXoCNhsENERGSviTw/aofE43fkgcju5fIg8JcNULj9G8xsunQcv92YAKcQAxp5jkLHSsGwRtYxsoiIiIhyjCH0IsJb1c4MdAQRfm9XR9DyfY8EOlfu38GXh4ZAUOjhjlKY1Kqt1dYAW3aIiIjsSeQpRH7QFel3pXHIIvJ++SlcOw94ZJdUrRbvbfoUoioBSoMfVnacBY1KDWvFYIeIiMhe/PMHsGkAAsobcMcUgKAps6GpWO+RXUwmEzquHoZ05Q3A6IjpDacj2MMb1ozBDhERkY0T9Tqk/zoQzneXyY81lZuiwPifITh5/mffQdtmIcKwT04F8Ump0ahbsBSsHYMdIiIie0jkGZqC/A0c4PxWP6DhVxAUyv/s+/e1GOy4fgZqT6COz/voW60VbAGDHSIiIhulPb4LEf0GQJcoQlAChor9gcajHrvvrZhU9F12Chnp7VHVrx5mtewGW8Fgh4iIyAYlL/0JdybOh0kvQOUKhEz+Ho51H5+0MzolCb2WnERiuh7lQ7zwc8fmVpMK4nmY9UwOHDiA1q1bIygoCIIgYP369dnP6fV6fP755yhTpgxcXFzkfbp37447d6T1AP4VFxeHrl27wt3dHZ6enujVqxdSUlLMcDZERESWsVBgzIhuiBiXGeg4B2tQcN3GJwY6OoMBb63+FHc0s+DnYcLP71WCo/q/XVzWzKzBTmpqKsqVK4dZs2b957m0tDScOnUKX3/9tfz/2rVrceXKFbRp0+aR/aRA58KFC9i5cyc2b94sB1B9+vR5jWdBRERkIXSpSPm2He6vPykvFOhVMx/ybToIVUiRJ/5I93VjkSj8A6XzDXzR1g9+7o6wNYIoiiIsgNSys27dOrRr9/jIU3L8+HFUrVoVYWFhyJcvHy5duoSSJUvK2ytXrizvs337drRo0QIRERFya9DjaLVa+ZYlKSkJISEhSExMlFuIiIiIrE5COLDiXYh3z+HuMS84NWgLr+HTnvojMw5vwM9Xv5Lvv53vc4xqYF3jdKTvbw8Pj2d+f1tVh5x0MlJQJHVXSQ4fPizfzwp0JI0bN5b7GY8ePfrE40yYMEG+OFk3KdAhIiKyVmlbF8M0qz4QdQ6Ciy+C5i57ZqATm5aM+Rcny/eLaFpYXaDzIqwm2MnIyJDH8HTp0iU7eouKioKfn98j+6lUKnh7e8vPPcnIkSPlwCnrdvv27VwvPxERUY4TRTmRZ9jQCbiz1wQxoCzQZx+Qv+Yzf7TvlkkQVXEQDF6Y3yazdcdWWcVsLGmwcqdOnSD1uM2ZM+eVj6fRaOQbERGRtRLTUxH1STskHJEykgsQvEMgdtsEwfW/CwX+v13X/8H51I0QBOD94oPh4+wGW6awlkBHGqcjDUJ+uE8uICAA0dHRj+xvMBjkGVrSc0RERLbIEHYZYa1qPQh0RPh1qIagFfuheI5ARxRFTNt9HqLOG54oj8G12sPWKawh0Ll27Rp27doFHx+fR56vUaMGEhIScPKkNOo80549e+S8HtWqVTNDiYmIiHJX+r61CH2rPdIjtXIiz5BRH8Hnu0UQnnNdnNUnI3Au1BOmiCGY23SiXVSXWbuxpPVwrl+/nv04NDQUZ86ckcfcBAYGomPHjvK0c2lKudFozB6HIz3v4OCAEiVKoFmzZujduzfmzp0rB0f9+vVD586dnzgTi4iIyFqJZ/5A5LCvYUhVwsFTQPBsKZFng+f++fhUHSZsuyzfH9ioJEoF2Md3pVmnnu/btw8NGvy3knr06IExY8agYMGCj/25vXv3on79+vJ9qctKCnA2bdokz8Lq0KEDpk+fDldX1xyfukZERGQWJiOw+xvg4FSkx6gRe7swAuevgdIv+IUO02bZcFyKUKCAugm2DqgPtdKiO3hy7PvbrC07UsDytFjreeIwqZVn2bLMLK5ERES2xhh9Gxk/94GL4ZD82KldPwQ3/Bp4TCLPp1lx9gBC9dvg6A98WKG11Qc6Njcbi4iIyB5pT+xBRL9+0CcbUaCpKxzfnwaU6fjCx0nTazHx+Hfyt36wqh7eKVsL9sR+wjoiIiIrkvz7ZNx6/1PoEkQoHRVA25kvFehIhm6fBYPqDmB0xqzmX8PesGWHiIjIwhJ5xn7VE/fXHpPXz3EK1iD415VQ5Sv6Usc7c/cW/or5HYICaB3cB4W8/WFvGOwQERFZCFNiLO72aouk87FyoONZPRgBc9ZDcHJ56WMO3DEagkIHJ2NhfNOoJ+wRu7GIiIgsQcJtxH/WNDPQEUQE9GyMwEU7XynQWXbyBGLFMxBFBb6tMxoq5YsNarYVbNkhIiIyt1sHgZXd4R0Qg4zC/vD6eCScW7//SodM0xkwa2cS0tIHoEG5NDQtUgH2isEOERGRGSXN/hyu936BQjBACCqDvEOWAZ75Xvm4M/ZcR2RCOvJ6FsSMVnVhzxjsEBERmTmRp2chFwT0bACh3WzA4eW7rbLsvXEevxw9AiAQY9qUgrODfX/d2/fZExERmYEh/CoiPuiE9AitnMhTXa4e0HEh8Jz5rZ5Gyg85Yv8oaPLfQEnhfbxZsiXsHQcoExERvUYZB9YjtH1bOdCREnkGf9UbvhN+e+5Ens8yas9ipCmvAaISoxq3zpFjWju27BAREb0miXNH4e6MlRCNAhw8BATPnAFNlcY5dvxbcdHYED4PUAI1fbqgUt7COXZsa8Zgh4iIKLeZjDBu+gpRs9ZCNCrgUtgFeReug9IvJEdf5tNt4wBlKlSGQExtPiBHj23NGOwQERHlpoxEYM2HUF7bgbw1NUhT10SeKSshqB1y9GWkRJ+3DXvl+8MqfwFntSZHj2/NGOwQERHlEu2pvTCuGgJnzU1A5QjXvjPhWvbtHH+d/0/02bVc/Rx/DWvGAcpERES5IGX5NNzq8Qlub0mDDkHAB9uBXAh0JL8dCkdKTCVA722XiT6fhS07REREOZzIM+7rDxC9RlrnRoBTXg0UPVcAQSVy5TrfSUjHtN03oNfVwrcN7DPR57Mw2CEiIsohpqQ43P2wLZLOxmQm8qyaFwHzpESerrl2jUdv/AdpOiMq5/dCp8r5c+11rBm7sYiIiHKA/uophLWqlxnoSIk8ezRCwKIduRroTD+8AYe0I+DgehXj2peGQiHk2mtZM7bsEBERvaqww4gb2QMZ0UooHUXkHTsMLm0/zNXrGp+Wgl8uTobCIQ7li8ageIB7rr6eNWOwQ0RE9CpOLgK2DEOeknoYxYLwHTcPDiWr5fo1/WTLJIiqOAgGL8xpNSLXX8+aMdghIiJ6CWJGGhK+7Q5P5U4ICkBRph2Cvs6ZRJ7PsvvGWZxP3QhBAHoWGwQfZ7dcf01rxmCHiIjoBRkiriHy/U5Iu50BfQl3+A0eCNQZCjn6yGVSos8vDoyFoDDCE+UxpPZbuf6a1o4DlImIiF5Axl8bEdqujRzoSIk8nd4aCNQd9loCHcnoPUuQprgK0aTG1MZjXstrWju27BARET2npJ/H4s605XIiT7WHgJAcTuT5LPGpOmy4cgBwZaLPF8Fgh4iI6BlEgwH3h3VG7PYL8vo5LoWkRJ5roPR/vevaTPrzMpJuv4V8wZUx9d1er/W1rRm7sYiIiJ4mIwm62R0Qt/O8/NC7UVGErD/42gOdk2FxWH7sthxs/diyMxN9vgC27BARET1J7A1geRdo4q4gsLobUKE7PPqNf+3XK12vQ/9tEyAoK6Nj+eKoWtD7tZfBmjHYISIieoyUP6ZDeXwynFzjAbcgeHyzFMhbySzXasj2WUh22g7XgicwvPlWs5TBmjHYISIi+v9EnqN7IXr1YagcHVCwZyWoPlgOuJknweaZu7fwV8xSeS2flvneRR5XJ9bXC2KwQ0RE9IApOT4zkec/9zMHIpcOgaL3esCMi/YN3DEGgkIHJ2NhjGv0AevqJXCAMhERkZzI8wzCWtbNDHQEEf7dGiBw8U4ozBjoTD+0AXE4CVFU4Ns6o6FSKllXL4EtO0REZPfStv2GiC++gzFdgFIjJfIcCpd2vc16XeREn5cmy9/UJZ1boWmRCnZfTy+LwQ4REdm3k4sRN3ksjOkaaHyVCJ73CxxKVTd3qdB/65QHiT49MavF5+YujlVjsENERPbJqAe2jwSOz0dgVQHqkPLI89NKKLz8zF0yXLuXjCNnSkDpWx0fVW6OPK7u5i6SVWOwQ0REdscQcQOJ3/WAt985OaWVsskX8K8zDFCYfyirKIr4cv15GAxOqO/VB0NqVzF3kawegx0iIrIrGX9vQsTg4dAnA0Jlb3h/NRMo3hKWYsGRUzgWGgsntQpj2pQyd3FsAoMdIiKyG0m/fIs7U37PTOTpDrj0nwsUbwpLERZ/H9Mu9YVTSCB6l/gKwV7O5i6STWCwQ0RE9pHI87MuiN0m5bcS4FLQGXl/XQNlYAFYkk+3fQsoU+HomIqP65Q2d3FsBoMdIiKyacaYO7jTqz1SriTJj70bFIHf1JUQNI6wJCvOHkC4fq98f2ilkUz0mYPMOhLrwIEDaN26NYKCgiAIAtavX/+fQVqjRo1CYGAgnJyc0LhxY1y7du2RfeLi4tC1a1e4u7vD09MTvXr1QkpKyms+EyIiskixN6Cd0hopVxMhKEQEfdoO/nM2WlygIyX6nHg8M8FoXmVddCvfwNxFsilmDXZSU1NRrlw5zJo167HPT5o0CdOnT8fcuXNx9OhRuLi4oGnTpsjIyMjeRwp0Lly4gJ07d2Lz5s1yANWnT5/XeBZERGSRru8G5jeAs/o6AusA+ad/A48BE2CJpESfBlUkYHTG7BajzF0cmyOIUvOJBZBadtatW4d27drJj6ViSS0+Q4cOxbBhw+RtiYmJ8Pf3x6JFi9C5c2dcunQJJUuWxPHjx1G5cmV5n+3bt6NFixaIiIiQf/55JCUlwcPDQz6+1EJERETWncgz/tuP4JK0Dho3PRBcBXhnKeAWAEskJfrstr2DnP+qZeAAfN/EvCs3W5Pn/f42/4ICTxAaGoqoqCi56yqLdELVqlXD4cOH5cfS/1LXVVagI5H2VygUckvQk2i1WvkCPXwjIiLrZ0pJwN2uDXBv+d+IOOAFU8kuQM8tFhvoSH7ceQomvScTfeYiiw12pEBHIrXkPEx6nPWc9L+f36MrXapUKnh7e2fv8zgTJkyQA6esW0hISK6cAxERvT766//IiTwTT0fLiTy92jaG0HE2oNJYbDXsvnQPf1/UQHtrIKY1msxEn/YW7OSmkSNHyk1eWbfbt2+bu0hERPQK0v5chtC330HGPb2cyDPfd4Pg/dUcCBawIvKTpOuMGL3xgnz/w9pFUCN/IXMXyWZZ7NTzgIDMJsd79+7Js7GySI/Lly+fvU90dPQjP2cwGOQZWlk//zgajUa+ERGR9UuY8hmi5m+CaBKg8VEgeO58OJSpCUvXe+P3iBYSEejRGAMaFTF3cWyaxYa8BQsWlAOW3bt3Z2+TxtZIY3Fq1KghP5b+T0hIwMmTJ7P32bNnD0wmkzy2h4iIbJhRD3HLcCSuXSMHOm4lPFFg816rCHT23DiLMymroPHfhi71tHDRWGzbg00w69WV1sO5fv36I4OSz5w5I4+5yZcvHwYNGoRx48ahSJEicvDz9ddfyzOssmZslShRAs2aNUPv3r3l6el6vR79+vWTZ2o970wsIiKyQmlxwKoeEEIPIG8tBRJVreE95lcIKssPGqQ/yEceGAtBYYQnymNAzdbmLpLNM+u74sSJE2jQ4N+Fk4YMGSL/36NHD3l6+fDhw+W1eKR1c6QWnNq1a8tTyx0d/10M6vfff5cDnEaNGsmzsDp06CCvzUNERLYp49BWpMz7DL4FIwAHV6jemQefEq1gLUbvWYI0xVWIJjWmNhlj7uLYBYtZZ8ecuM4OEZF1SFowDnemLIVoEJD3TSXcv1oJ+JeEtQhPuI+Wa1vL+a+qe3bH/LafmbtIdvH9bfntfUREZPekRJ4xw7siZuvZzESeBZzh8sUawN+yEnk+yydbx8mBjsoQiGktBpi7OHaDwQ4REVk0Y1wU7nzQDimXE+XH3vUKw2/6aovLb/Usu65eRZj2AAQFE32+bhY7G4uIiEh39iDCWjWSAx0pkWfgx63hP2+z1QU6BqMJP26NQlroABRTv8tEn68ZW3aIiMgy3diLjDm9oI3TQOUsIvj7MXBq0hnWaNGhW7gclQxP57z4uW1XcxfH7jDYISIiyyLNmzkyB9jxJdz9TTA1KQGXgfOhLlwG1ujs3TBM3r8HQCBGNi8ObxcHcxfJ7jDYISIii2FKSUT0gA7w8T0JtbMJKPcuPFtNAdTW1W31sAE7xkARfBKF9O/g7UotzF0cu8Rgh4iILIL+xjlE9OqKjCg90n28UWDSEAg1PwUEAdZqxpGNiMUJeYjs5/VbQKGw3nOxZhygTEREZpf+53LcevttOdBROIjwGzwMQq2+Vh3oxKelYP6FyfL9Es4t0bRIBXMXyW6xZYeIiMwqYepwRP28MTORp7eUyPNnOJStZfW18unWSRBVsRAMnpjdYoS5i2PXGOwQEZFZiNoMRPfvgLgDN+WFAl2LeyDo1/VQegdYfY3svXEO51I2yg1TPYoNQh7XJ6/uS7mP3VhERPT6pcVBXNIRqWevyA99W5ZD8Oq/bSLQkRJ9jjgwBoKQmehzcM325i6S3WPLDhERvV73LgIrukARfwvBDVyhLfoB3N7/wmZqYc2pCMTdKwVNnnuY0nS0nKSazIvBDhERvTbJiyZAt3MefIrEA5754NB5ORwCSttMDSSk6TBh2xXoU6thYLV3UTn4DXMXiRjsEBHRa0vkOfI9xGw6A8ARTsUrw7n3SsDFx6YqYMK2i4hL1aGInyv61Clq7uLQA2xbIyKiXGWKj0bk23UeBDqAV93CcBq+2eYCnT/O/oXNcQOhdL2Ice1Kw0HFr1hLwZogIqJcozt3CLdaNUDypYTMRJ59WiLg5y0QNE42ddUz9Dp8f/w7KBzi8EaBUFQrZFuBnLXjmB0iIsoVqWvnInLsVBi1ApROUiLPUXBu+q5NXu0h22fBoIoEjE6Y3WqUuYtD/4fBDhER5Xwiz6PzoFv3LYxadzj6qxG84Deo3yhnk1f6zN1bOBCzFIICaBncG4V9rH/6vK1hsENERDnHoAU2DwHOLIVXYUBRoArcPl8MhauHzV7lQTvGQFDo4GgshHGNPjB3cegxGOwQEVGO0IdeQPTg9+Bf4iZUjgqgyTh4VLfuRJ7PMuPwBsTiJERRgXF1RkOlVJq7SPQYDHaIiOiVpe9aiYjho2BIEyCm50Hw7HlA4YY2fWXTdUYsOr0DcMlK9FnR3EWiJ2CwQ0REryRh+ghEzV0vJ/J08FbAb9KvQOE6Nn9VZ+y5htjwFvDzK4HZfbqbuzj0FAx2iIjo5RN5DnwbcfuuZybyLOaOoAXroPQNsvkreu1eMub/JSUwBb5t2pGJPi0c19khIqIXZoy6hdvtaj0IdADf5mUQvOagXQQ6UqLPjzZNhAFJaFzCD01K+pu7SPQMDHaIiOjFRF+CuLgtdNFJEJQi8g57F3mmrISgso/OgtF7luC+egNcCs3AFy2KQLDhAdi2wj7emURElDMubwHW9oFKl4LgliFAkwlwrN3abq5ueMJ9rA+fByiBGr7tUCiPp7mLRM+BwQ4RET1fIs8vukN1dy+8CqcBBerA8e3FNpff6lk+2ToOUKZAZQjA1GYDzF0cek4MdoiI6JmJPO/0aofki/GAwgMub7aHQ9dpgFJtV1dOSvQZrt8j3x9ScSRcNBpzF4meE8fsEBHRE+kuHMGtVg0fBDoiAj5oAYfus+0u0JESfU48/p18P0hZB+9VsO01hGwNW3aIiOixUtfOQ+TYKf8m8hz/FZybd7PLq/XZn/OglxN9OjPRpxVisENERI8SRcSN74t7S/cAogBHPxWCf1kCddEKdnml7iSkY/fxEBg9a6F9qcpM9GmFGOwQEdGjiTy3DIXpzAZAdId7uTwI/GUDFG5ednuVvtl0EWlaNSo5dsf4xjXMXRx6CQx2iIgoU/I94I9uQMQx+JRSQFOvE1w//QmCwn6Hd649ewHbL9yFUqHAuHaloVBwTR1rxGCHiIiQvnsl7n8/GsHV7kLh4gGh469wK9LYrq9MfFoKxhzvC6d87ugQMhwlAt3NXSR6SQx2iIjsXOLML3B39lo5ked9n3zwn7kW8H0D9q7v1kkQVbFQw4iBDcqauzj0ChjsEBHZKVGvQ/TAjojbcy0zkWdRN/jOXA/YQX6rZ9l78xzOpmyElAmiR7FBTPRp5RjsEBHZIeO9MES+3wGpN1Plxz7NSiHPjyvsJr/VsxJ9jtg3BoLSCE+xHAbXbG/uItErst9RZ0REdkp7YjdC2zSXAx05keeQzvCbupqBzgNj9vyGNOVViCY1pjQeA4UdD9C2FQzhiYjsyZVtUKzrA5PWCWpXJYKnTIJjnTbmLpXFuJ0Qg3Xhc+VEn9W930HlYI5dsgUMdoiI7IEoAn/9COz5Dmq1iHydi0HVbQ5UwUXMXTKLMmnnCRj1rtCIrpjWbJC5i0M5xKLb5oxGI77++msULFgQTk5OKFy4ML799luI0i/tA9L9UaNGITAwUN6ncePGuHZNGmxHREQSU0IMIt6ujaTFP0qfmkCVD+H42TYGOv/nZFg8Np00Ii20P76rMZWJPm2IRQc7EydOxJw5czBz5kxcunRJfjxp0iTMmDEjex/p8fTp0zF37lwcPXoULi4uaNq0KTIyMsxadiIiS6C7eBS3WtVH8vk43D3uCWPDiUDLn+wukeezGIwmfLX+vHy/Y6X8aFGylLmLRPbSjXXo0CG0bdsWLVu2lB8XKFAAy5cvx7Fjx7JbdaZOnYqvvvpK3k+yZMkS+Pv7Y/369ejcubNZy09EZE6pGxYgctQPmYk8HaVEnl9CWbc7K+UxBm+bhRu6ULg7NcbI5sV5jWyMRbfs1KxZE7t378bVq1flx//88w/+/vtvNG/eXH4cGhqKqKgouesqi4eHB6pVq4bDhw8/8bharRZJSUmP3IiIbIVoMsmJPMNHZAY6UiLPgiuXwbkFA53H+efuLey9vwgav51oU/M+fFw1r73OyI5bdkaMGCEHIsWLF4dSqZTH8Hz33Xfo2rWr/LwU6EiklpyHSY+znnucCRMmYOzYsblceiKi10/UZSDqw1ZIOBYpLxToXs4XgfM3QOHuzep4goE7xkBQ6OBoLIQxDbvxOtkgi27ZWblyJX7//XcsW7YMp06dwuLFi/Hjjz/K/7+KkSNHIjExMft2+/btHCszEZHZpERD+K0tFIlX5IHIfm9XR9Dy/Qx0nmLm4Y2IxUmIogLf1h4NlVL5+uqLXhuLbtn57LPP5NadrLE3ZcqUQVhYmNwy06NHDwQEBMjb7927J8/GyiI9Ll++/BOPq9Fo5BsRka0QI05CWPkekBQJv6oecOs1GM5tPjJ3sSw+0ef8S9JgbaC4cws0K1rR3EUie2zZSUtL+8/KlVJ3lrSUt0Saki4FPNK4nixSt5c0K6tGjRqvvbxEROaQOOsr3H7vHYjxkYBPEQgf7WGg85yJPk3KOAhGT8xpMTL3K4rMxqJbdlq3bi2P0cmXLx9KlSqF06dPY/Lkyfjggw/k5wVBwKBBgzBu3DgUKVJEDn6kdXmCgoLQrl07cxefiCj3E3kOehtxu6VJHGrEp1SG95drAUcPXvln+CfyDs4mbYWgBLoXHchEnzbOooMdaT0dKXj59NNPER0dLQcxH330kbyIYJbhw4cjNTUVffr0QUJCAmrXro3t27fD0dHRrGUnIspNxnvhiPzgLaTeeJDIs0kJeE1aAagdeOGfQVq2ZPzmMKRG9EexwtcwpOZbvGY2ThAfXo7YTkldX9KUdWmwsru7u7mLQ0T0VNrjuxHRrz90iaKcyDOo/ztw/5gzTJ/XmpMRGLrqHziqFdg5uB5CvJ35jrPx72+LbtkhIqJHpf4xDRHj5sCkF6ByBUJ+mgDHeu15mV4g0ee4XdsBBGJAoyIMdOwEgx0iImsgNcL/PRmqo+MB+MIp2BHBv66EKl9Rc5fMqny8dRz0/nsQ6NYKH9bOXKCWbB+DHSIiCydmJEPYNAC4sBYadyB//9rQvDcdgpOLuYtmVf44+zfC9bshCMCnNRrDQWXRE5IpBzHYISKyYPrLJxDxUU/4lbwHl0AV0HwSHKv0MnexrE6GXoeJJ76T19QJUtbBexUamrtI9BoxrCUislBpmxYitHM3ZNwzIuq0D8RuGwAGOi9lyPZZ0CsjAKMTZjf/d0Yv2Qe27BARWaD4Cf0QtWQXIEqJPJUI/nkxhEKVzF0sq3Q26hYOxPwOQQG0yNsbhX0yV98n+/FSwY60rs33338vr1wsrX+TtaJxlps3b+ZU+YiI7IqYnoqoT9oh4UhEZiLPsj6ZiTw9fMxdNKs14M+xEBRaOdHnd40zF6Ul+/JSwc6HH36I/fv347333pNzUkkrGRMR0asx3Q9DeJe2SI/QZiby7FAN3t8uhPB/aXPo+e25dA8Rd/LD0e8yvq3DRJ/26qWCnW3btmHLli2oVatWzpeIiMge3TkDYfm7cFClQqt2Qt6RH8H13cHmLpVVS9cZMXrTBRgSq6BTmXZoVvTJCaLJtr1UsOPl5QVvb++cLw0RkR0Sz6yEsHkABEM6ApoWhm+9yXCoWN/cxbJ60/dcxu24dAR6OGLom6XNXRwyo5dqG/3222/l/FRSVnIiInqFRJ7930LE0OEQ9enAG29C8fEeBjo5YO/Nc1hy+1Oo3M5jVKuScNFwPo49e6na/+mnn3Djxg34+/ujQIECUKvVjzx/6tSpnCofEZFNMt6PROT77ZB6PQWAE1J9msL13dmAQmnuolk9adLMiP1joHCIQ2Dec2hayt/cRSJrDHbatWuX8yUhIrIT2lN7EfFpX+gSMhN5BvbrBNdPvjF3sWzG2L2/IU1xFaJJjSlvjoGCA7zt3ksFO6NHj7b7C0dE9DJSlk1B5IR5mYk8XYDgn76DU/0OvJg5mOhzbdhceaXk6t7voHLwG7y29GqLCp48eRKXLl2S75cqVQoVKlTgJSUiehxRRPx3fRC19C95/RynYA2CF6yAKn9xXq8c9MnWcYAyBSpDAKY1G8RrSy8f7EgLCXbu3Bn79u2Dp6envC0hIQENGjTAihUrkCdPnpc5LBGRbdKlARv7wTF6IwSlLzwqByNg7nom8sxhK8/9jVu6PXKizyEVR8JFo8nplyB7mo3Vv39/JCcn48KFC4iLi5Nv58+fR1JSEgYMGJDzpSQislJiTCjwa1Pg/Bo4+Yoo9P2HCFy8k4FODjMYTZh6aCMEQWSiT8qZlp3t27dj165dKFGiRPa2kiVLYtasWWjSpMnLHJKIyOakbV6EO2O+R96aMXAK9gE6LYFDgdrmLpZNWnToFu6E1oO7Vwhmf/i2uYtDthDsSNP6/n+6uUTa9v95soiI7FH8pIGIWvQnYBIQcy0IId9sBjzzmbtYNuluYjqm7Lwq3x/ZoC0TfVLOdGM1bNgQAwcOxJ07d7K3RUZGYvDgwWjUqNHLHJKIyGYSed59vymift0hBzpupb2Rd/keBjq56KMNU5BmikPFfJ54p3JIbr4U2VOwM3PmTHl8jrSgYOHCheVbwYIF5W0zZszI+VISEVkBQ/hVhLepjYTD4XIizzztKyPvyr+g8PQ1d9Fs1qwjmxAqLodLoan4slVBKBRMTE051I0VEhIir5Isjdu5fPmyvE0av9O4ceOXORwRkdXT/7Mbt3r1gyEFUKhFBH3eG27dhpq7WDYtPi0VP1/4Sf4mK+7aCJXyBZm7SGRr6+wIgoA333xTvhER2bXza6Da0BeO7k7QKZ0QPHMGNFX4x19u67v1B5hUsRCMnpjTYmSuvx7ZQbAzffp09OnTB46OjvL9p+H0cyKyl0Se2D0OwpFpkDpPgrpUA9pMh9I/v7mLZheJPs+mrJfX1HmvyEDkcXU3d5HIggmiKIrPs6M0JufEiRPw8fGR7z/xgIKAmzdvwppIY408PDyQmJgId3f+whDR8yXyvPNBeygN9xBYNQFCrQFA4zFM5PkaSLN+ayx+W85/5SGWxYHuvzH/lZ1Kes7v7+du2QkNDX3sfSIie6M9tR8RfT+BLl6EoHCCz4Dh0DTpa+5i2Y1v9y17KNHnWAY6lDuzsb755hukpaX9Z3t6err8HBGRrUpZMR23enwkBzpSIs/8M8dB05yBzuuSmKbHhkOe0MXWRQ3vLqjCRJ+Uk91YD1Mqlbh79y78/Pwe2R4bGytvMxqNsCbsxiKiZxFNJsSN7oXo1YcBUYBTkAOCFyyHqmBJXrzX6It157DsaDje8HPF1gF14KB6qb/ZyUbkeDfWw6T4SBqb8//++ecfeHt7v8whiYgslz4d9z5sgfijUXLGco8qQQiYtx4KZzdzl8yu7L1+A8uO3pI7Jb5rV5qBDj23Fwp2vLy85CBHuhUtWvSRgEdqzUlJScHHH3/8IockIrJsiRHAiq5wc7qIBIUP/Lo1gteIGRAUbFF4nTL0Ogw90A/O+RWo5zUQ1Qr5vNbXJzsKdqZOnSq36nzwwQcYO3as3HSUxcHBQV5RuUaNGrlRTiKi1850ZR8UGz8EUu/DpaA3Cvf+AepKrVkTZjD0z9nQKyOg1DhhaOMyrAPKvWCnR48e8v/S1POaNWs+NhkoEZEtiP9xMO4v3Yr8DeOgKVIa6LwMai+un2MOZ6NuYf/9pRAUQPO8H+IN30CzlIPsINiRBgFlDf6pUKGCPPNKuj0O16ohImslZqThXt+3EH8wTB4bkpBYDv69NgMOLuYumt0a8OdYCAotHI2FML5xL3MXh2w52JHG62TNwPL09HzsAOWsgcvWNhuLiEhiiLiGyA86IS08Q36cp21F+Ez4DeD4HLMm+ozFCYiiAt/UHgWVUsk3K+VesLNnz57smVZ79+598VciIrJgGX9tRMTgz6HPSuT52Qdw6z7c3MWya48k+nRugeZFK5m7SGTrwU69evUee5+IyNqlb5iBsC9mQTQKUHsICJkxHZqqTHJsbtP2noLeoIFKYKJPejUvNXdy+/bt+Pvvv7Mfz5o1C+XLl8e7776L+Pj4VywSEdFrYjIBu7+F44mv4Oilg0tBZxTcsJWBjgW4Hp2M3w8lIy20L4aXncpEn/T6g53PPvtMHrAsOXfuHIYMGYIWLVrIObOk+0REls4Yexfisi7AXz9CUAIhQzsgZP1BKAMKmLtodk8a//nV+vPQG0U0LB6IrpUq2v01oVfzUisoS0FNyZKZS6SvWbMGrVu3xvjx43Hq1Ck56CEismS6Mwdw+5NP4OqfBP9KGqDNdCjLdTZ3seiBb/b+jlNJJ+Do0BBj25R67IQYolxv2ZEWEMxKBLpr1y40adJEvi8NYM5q8SEiskQpf8xAaPc+0MWbkHTbBca3VwMMdCzG7YRYrL41C5o8u1G/cihCvJ3NXSSy12Cndu3acnfVt99+i2PHjqFly5by9qtXryI4ODhHCxgZGYlu3brBx8cHTk5OKFOmDE6cOPFIc+eoUaMQGBgoP9+4cWNcu3YtR8tARLaRyDN2VC/cHjMLJl1mIs8Cq9dAWbyuuYtGD/lk67eAMgVKQwB+asr0Q2TGYGfmzJlQqVRYvXo15syZg7x588rbt23bhmbNmuVQ0SAPdq5Vq5a8UrN07IsXL+Knn36S1/zJMmnSJEyfPh1z587F0aNH4eLigqZNmyIjI3OdDCIiU3I87rzbANErD8kZyz0qByLf5r+hLliKF8eCrDp3ELd0e+T7gyuMgItGY+4ikY0QRKlpxEKNGDECBw8exF9//fXY56WiBwUFYejQoRg2bJi8TUrz7u/vj0WLFqFz5845miKeiKyPmBCB8I4tkBahlz7x4N+1Iby+mMlEnhaY6LPmkrbQqyIQpKyDP7vNNneRyAo87/f3S6ftlVZJlgYnjxs3Tr6tW7cux1dO3rhxIypXroy3335bXrlZSlMxf/78RwZKR0VFyV1XWaSTrlatGg4fPvzE42q1WvkCPXwjIhsUfhTC/AbwyncPSo2IfN8NhvdXsxnoWGqiT1UEYHTC7OajzF0csjEvFexcv34dJUqUQPfu3bF27Vr5Jo2rKVWqFG7cuJFjhbt586bcTVakSBH8+eef+OSTTzBgwAAsXrxYfl4KdCRSS87DpMdZzz3OhAkT5KAo6xYSEpJjZSYiy2DYNxdY1BJIjYZ75cIovHkNXN76yNzFoscIi0vA/nt/yPelRJ+FfQJ4ncj8wY4UcBQuXBi3b9+Wp5tLt/DwcDkbuvRcTjGZTKhYsaI8rV1q1enTpw969+4tj895FSNHjpSbvLJu0nkQke0k8oz6sDluDpoMfYoRKNEa6LUDyhCOz7FUE7fdQOqtT+Gla8JEn2Q56+zs378fR44cyc6VJZFmS33//ffygOKcIs2wylrPJ4vUoiR1n0kCAjKj/3v37sn7ZpEeSys6P4lGo5FvRGRbDBE3EPlBxweJPJVI9ewIz7fnMZGnBdt7JRpbz0VBqfDB3JajmeiTLKdlRwoUkpOT/7M9JSVFXoMnp0iB05UrVx7ZJk1vz58/v3xfakmSAp7du3dnPy+Nv5FmZdWoUSPHykFEli/j4Bbcat9KDnQUKhHBI3rA84v5DHQsWEJ6Kr7Yukm+/37NAigZxAkiZEHBTqtWreQuJSmokGZESTeppefjjz9GmzZtcqxwgwcPlo8rdWNJ44SWLVuGn3/+GX379pWfl1bVHDRokDxAWhrMLKWukMYRSTO02rVrl2PlICLLlrRgHG71GQp9MqB2B/LPnwq3niPMXSx6hr5bfkCK91R4B+/CoDeL8nqRZXVjSeva9OjRQ249kdbAkej1erRt2xbTpk3LscJVqVJFnuUljbH55ptv5JacqVOnomvXrtn7DB8+HKmpqXLwlZCQIC94KCUqdXR0zLFyEJGFMpmQ9NPHiFwgLU8hwKWAM/IuXANlIPNbWbp9N8/jn5T1kDJBdClXE66al/o6Inour7TOjtTaIi30J5HG1rzxxhuwRlxnh8gKZSQB6z6C6fw23NrlC5fyxeE3fTUEDf/QsXTS5JOaizshVXEFHmJZHOj+GxSKl14JhexY0nOus/PSofSCBQswZcqU7NQM0vRwqUvpww8/fNlDEhE9F/3lY1Dt6gch5goUjhoUmPYVFNV78upZiW/2LZUDHdGkxpQ3xzLQoVz3UsGOlItq8uTJ6N+/f/ZAYGkRP2mMjTQFXepyIiLKDSkrZyJy3Ez4lkiGT5UAoPPvUARX5sW2okSfa27NkSbLoZrXO6gSbJ09AmQH3Vh58uSRx+106dLlke3Lly+XA6CYmBhYE3ZjEVlHIs+4bz5C9B9/yfmtnILUyL96KwTvnE0+TLmr9bLBuKXfJSf6PNhtM/NfkeV2Y0mDkaU0Dv+vUqVKMBgML3NIIqInMqUkIqp3WySevicPRPaoFICAeeshuHrwqlmR0+HxuBzmAwc/Vwxjok96jV5qRNh7770np3H4f9K08IdnShERvSr99X8Q1qpOZqAjJ/Ksi8DfdkPBQMeqGIwmfLnuPPSJFdDYdRp6VGxk7iKRHXmlAco7duxA9erV5cfSmjvSeB1pnZshQ4Zk7yeN7SEiehmm6wdxq3MvGFIEOZFn3lED4dLhE15MK7ToUCgu3k2Ch5MaX7csZ+7ikJ15qWDn/Pnzcs4qSVbiT19fX/kmPZdFWvSPiOilnF4KxebB8C2uQnyoN4Ln/gyHMjmXjoZen/NR4Zh6uTdU7o0xvGFX+LoyXQ9ZQbCzd+/enC8JEZE0EFmbAcPaz6G+ski+Hl6tmsCjxTQo3H15faxU/x2jITjch2fAEbxT5XNzF4fsEJesJCKLYbgTisj3O0Afm4yCbwpQNh0B1B3OdVis2KwjmxAjnoAoKvBNLSb6JPPgkpVEZBEyDm3FrbYtkBaWDkOGEtpKY4H6I5jI08oTff584Sf5fjGn5mhRrJK5i0R2ii07RGR2Sb+Ox53JSyAaBKjdgOBpk+FYs4W5i0U5kOjTpIqFYPTA7JYjeT3JbBjsEJHZiAYDYj7vipgtZ+X1c5wLOCHvr2ugCirIWrGhRJ/digyAP5cKIDNiNxYRmUfUOcT0bfwg0AG86xZCvg2HGOjYAGlh/nF710AQjHKiz2G1Opq7SGTn2LJDRK+NKTkehoO/wyFiPRBxHF7eCiS5+8Ln3XbwHPQDa8JGrD8TievXKsPJ3RtTujfnAHMyOwY7RJTrtCf3IOHnyUg4fB0OLnoUbBoDKFRQVWyNQp/0g5CPiTxtRWKaHuM2X5Lv96vRnIk+ySIw2CGiXCGmpyL5tx8Qv3oD0sIzHmwVYHRwgKHqZ1DV7QO4+oFLj9qWvptmI07rizf8gtG7TiFzF4dIxmCHiHJW/C0kzhmDeyuPwJjxIJQRRLgW9YBX53fh0vETCGoHXnUbtPrcQZxJXwCXwmoMq7EcDioOCyXLwGCHiHJk1WPx0jYozi8Fru+GItIBxgwfqJxFeNYvB8+PP4e6aGaKGbJNGXodxh8bB0ElIlBVFc2KFzV3kYiyMdgholfKSJ4w73sk7DkDzwLJyFMmWd7uWrsmgmtVh2vnARAcnXmF7cCwP+dAr4oAjE6Y3Wq0uYtD9AgGO0T0wmvjpK6di4RlS5F8JQEQM7uqku+6wLdPTwiV34fgUxhuvK52lehz3/3fICiA5nk/xBs+AeYuEtEjGOwQ0fNJjUHcTyMQt/kg9ElZGwU4B2vg+VZruPUcDsGZIY496r9jDASFFo7GQhjfuJe5i0P0Hwx2iOiJRJMJCDsE4eRC4NJGaI86QZ/kAoVahEf1QvDqPQiaqk14Be3YnKNbESMelxN9jq01Ciql0txFIvoPBjtE9B/G6NvYMWU87t2JQ2nXa6ic50bmB0a1kjhTrhwcChZHweBg3InNALZtxP3EZCSnZ8Db1QWeri5yigCD0YTw+zHyzzVv3wHOHp7y/dOHDyH06hXkK1AAles1kLfptFps+WOZfD+/vx8U0gGkiV0pKUhMSYO7ixN83KVWI0FenffWvfvy83XffBPeAUHy/ctnz+DK2X/gHxCI6o3/DcA2L18Ko8mEkDy+2V/ESWlpiEtKgauTI/J4ekiHlYXfuw+TaEKVmrURkD8zZcWta1dx/sRxeHp7oXbTf/N17Vq/BtoMLQJ9vKFxUMvbUtLTEZuYBEcHB/h7e8nbBEFA5P1YGIwGlC5fESFFi8nboyIjcPrQ33BxcUXdFq2yj3vwz21ITk6Gn5cnnBw18rZ0rRb34xPg6uqGqg0aQe1gGbPZMvRGLNuvhFZZH+WCPZjokywWgx0iym7Fydi7GvEL5yLp9B2ca9IUaQVLwBQJVK5YG6j8PtJSXXDl92XA7bu4tWtr9pXLCMwPvWceOERHQBMbJW8zKVVILVpeyh2AWjH3s4OdM6dOIOx+HGKjox4KdjLwz80w+f6NrWshiKJ8X5snL3S+gVDHRsExOiKznFJQUSJzEcJiRW5lBztnT53ExVu34R0a+kiwc+LSVTlz+tWt66Ew6DJfz9sfWv8QqBJj4XQnNHvflCLlIKrU8PXwzA52Lp09ixNXrsHFpH8k2Dl88jSMShWcQy9CmZEmb9O7eyMjbyEoUxLhfPta9r6phUrBpHGCYNBnBzs3Ll/G0QuX4aDXPhLsHDh4EFqFCk7hV6FKzewvNLi4Iz1fUfnnz65dhjINmqBso6Zwz+Nn1nfvrL3XcTvOgAD3dljYrp5Zy0L0NAx2iOycLu4edv70LS6mArUOHIRXmrQAoIDS4Vdw5Y0SyN+wBdCmh7yvU2QEvNVKCIISBWvWzTyAKOK+1oAkgwneBQrBs2gRebPBJCI8XS/fd3RxzX69wMBAJMYnIDAob/Y2hVIJT1Vm80qBKtUzW3ZEIFZvRILBBM+8eeGdP+TBy4kIzTDK9109MwMoiZ9fACJuR8DfP88j5+fpoIRJFBFSthxU8nFFJBpFxBkAFx8f+AX4Zu8bphNhFAF3H5/sbd6+PnBTAD6e3o8c18vZERk6PYKKloBGWk5GFJFiAu4bRTi5uyOgXEW5rJJIgwA9RHj5/hucuHt4wEUwwdXN9dHjurkhOTUVfgUKwVnI/Pl0UcA9kwlCWiLSEuJxdN0fOLp+JRxLV0LpipVQq0kzqFSZrUuvy6mISMzdLwV0Asa0KQlXDb9OyHIJYtZvox1LSkqCh4cHEhMT4e7ubu7iEL0WiRf/wrm183Hu0j1EF6gIUa1B8JXzaC7eh1eP3nBq+i4EBReFsyRGgwE3ThzBPzu3IfTaVaQVKiU1yaFjszdRukad11YOk8mEmos7IUmbirKaj7C8Z1u5u47IUr+/GYoT2RFd3H3smT4el2JSYbwfCUEerKKGS+xdeLq5otHA/shbnd0RlkqpUqFo9dryLezqFezcshmJsfdRslrN7H02/7EcPr6+qFa/odxilhu+2bcUqYorUGhUGPpmaQY6ZPEY7BDZgZh9m3Bq4TxcSRMRW6IS4OsB5+REFHTXolzj5ijc/H0oLWTQKz2f/EWL4cOixeSusqxWlZTkZJy4eAnygjcmA2q82TzHL+fthFisuTUHUALVvN5hok+yCgx2iGyUPjkRe6eNw9Xb0dDGx0jTggCFAMe4e/DWKNGkVy8UqMtp49bu4e6jjLQ0BLq5IC4hAVXqN8revm/LRri5e6JCrdpQvGLX5KdbxwHKFCgNAZjefPArHYvodWGwQ2Rr4sOAU4txcdufOOT6JhCQHy7JifDXpaFs1Qoo1W8U1M4u5i4l5QJff398NOxzmIzG7C4sg0GPv44ck2eOHd28DjUaNkLJOg2geYn3wOrzBxGq2y3HzYPKfw4XTebUeCJLx2CHyAYYM9Kxb/o4xN8ORUcfaUq4iHKuwI6kinCFEc0/+AAFGrcxdzHpNXl4rE5qcjK8XZ0Rk5yKtLDr2PPrNRz4fSFCqtRC0eq1ULpKtedP9Hn0u8xEn8ra6FmpcS6eAVHO4mwszsYiK6YPvYDEOeNx+EosTlaoDkGvw2D9fLiXrglU/gAo1gJQvt4pyWSZUpMSceXgAZzdtQ2xEeFIy1cURhd35DGko26jRiheoy7Ujo5P/PkZ+05hzuUvoXSIxdo2G1DEN/C1lp/oVWZjMdhhsENWOP3471njEX/yFIodvywn4jQoFNjYuiW8dMno+O7b8KvS0NzFJAslDWi+ffEc1m/YgLgMPVxunJcXW5S6tQrVrIsi0q1UmUd+JioxA41+2odUnR5DWnhhQN3aZis/0cM49ZzIBhnSU7BwxEBEeoVAGVAYhYWrcAtygFf7lvi8+zCo3DNTFBA9bUBzvlJlMaBUWcTH3Mf1Q1Jrz3Yk3LuL0+cv4FhENCq8cQpt38tcSFLy7eaLSNUZUSGfN/rV/neaO5G14JgdIiuRGnEVG74ZhIQUBwgufvDUpyFg6ljkafK2uYtGVsrLNw+qtOmAyq3aI+z8P1i3fj0SpcWpdenZ+8w5ugU7o7ZDqWyE79qVgULBxQPJ+jDYIbICNzYuwq6VK5CiV8FJmYG2VfKhaPsJ5i4W2QhppewCZStgYOlyOLJjG2o0yVyfJyE9FXPP/QCNbyxKhviiZFA7cxeV6KUw2CGycOtHDcYZ0RVOKk/4qRLQ7vPR8CpRw9zFIhskrcFTs1nL7McD1k1Eq9Dy+MfrGqZ/PMisZSN6FUx8Q2ShjNp0bOnRCueTDYBSCbWHF96dsoiBDr0W+26eh++lKKjVnqgaVwbeDk688mS1GOwQWaDU0EtY/m4bXM4AHO+GoUD8bQycNBUarwBzF43sgJToc8T+Mfg75AT02ni0at4MaqYTISvGbiwiC3NxzRJs+3MPoNJAaTKhXtnCqPD1NHMXi+xIVqJPUa1C20/7oWJIkeznzhw+iAJFi8HTx9esZSSy2Zad77//Xp42OWjQv33HGRkZ6Nu3L3x8fODq6ooOHTrg3r17Zi0n0cu6s+0XrDxzFclBBSA4u6FDl44MdOi1ikvNwJrQX+X7UqLPqg8FOjcuXsCGbdsxc+pU3LpyiTVDVsNqgp3jx49j3rx5KFu27CPbBw8ejE2bNmHVqlXYv38/7ty5g7feests5SR6KaIIHPgRQUeHIW9sKBxTEvHuwIEIeesDXlB6rX7acQ0pob3hlF7vP4k+ddoMKEQRJm0GNk4YjRsnj7F2yCpYRbCTkpKCrl27Yv78+fDy+nfRNGl56AULFmDy5Mlo2LAhKlWqhIULF+LQoUM4cuSIWctM9LySI24hZva7wJ5v5ZxWHzT1x+CvRyGgfHVeRHqtTofHY9mxcIgGT0x7c+x/En2WqFAJH3/6KQo5KaFPT8P6H77F0XUr5TE+RJbMKoIdqZuqZcuWaNz40cRzJ0+ehF6vf2R78eLFkS9fPhw+fPiJx9NqtfIS0w/fiMzh5u4NmD5jFhZc84HW6AC0ngZl28nQeHAlZHq94tNSMGjTUrmR8a2KeVGjsM9j98sTGIQuX49DuTdbyC2Se7Zvw4wJ3yGVn6NkwSw+2FmxYgVOnTqFCRP+u4BaVFQUHBwc4Onp+ch2f39/+bknkY4lJQ7LuoWEhORK2YmeJnXjAoR+/xP0GidkuLgjrMw4oFJPXjR67aSWmQ6rByLO9Wd4Bu7HFy1KPHV/pUqNxh9+ijo9+kDrH4x4vRELv/8WSfejX1uZiWwm2Ll9+zYGDhyI33//HY5Pycb7okaOHCl3gWXdpNchel1Ekwlx4/si/PMfEHT7PipfPomeTeugaKePWAlkFh9unIj74jGIogLD6jWHr+uj3VdPUrVFG7Rq3AhOKQnIuHEJS0cOkpOMElkaiw52pG6q6OhoVKxYESqVSr5Jg5CnT58u35dacHQ6HRISEh75OWk2VkDAk9cj0Wg0cir4h29Er0N6XAzmDPoYJ7eelrOVu5fzRYsFS5G/buby/ESv2+S/1+J44jL5fovAvuhWvsEL/XzluvXxyYgv4F+wMNKTk7Bq3FfYuvx3juMhi2LRwU6jRo1w7tw5nDlzJvtWuXJlebBy1n21Wo3du3dn/8yVK1cQHh6OGjW4nD5ZltTIa5g19mtEewfhaI0a8HirKoKW74fCjeNzyDx2XDuDX6+Nl+8XcmiCSU37vNRx3H390HnsRBSvVQ/pPoE4duUa5v80CSaTlFWUyPwselFBNzc3lC5d+pFtLi4u8po6Wdt79eqFIUOGwNvbW26h6d+/vxzoVK/OmSxkOaKObMaGWTMhis5QuHighp8zgj5bbO5ikR0LjYvGZwcGQVBp4WIqjuUdM4Oel6XWOKJF/2FI/mUeLkfchbuDGoJg0X9Pkx2x6GDneUyZMkVOXictJijNsmratClmz55t7mIRZTsy7UscPXwaBlEFH6c0tO7UHHnK1+MVIrPRG034ZO1SmNSxUBh8sKL9LDirn2+cztNIi7527v0xLhw7jOIVK8uPswZAS5/TROYiiKI00dC+SVPPpVlZ0mBljt+hnKJPT8WvXwzFXbc8cL51GUU8tWgxZh403oG8yGRWX68/j9+OhMHF6zymdWiGxm+Uy7XXykhPx/QfJqJMieJo/nbnXHsdsk9Jz/n9zVCbKBek3rqMP7q1Q7TSCVAo4efjibaTVzPQIbP77fAtOdCRGl2mte6Zq4GOZPPKFUgzAcf+OYe4e09eEoQoNzHYIcphd7evxG9DBuCeSgOX29dRVUhGzynzoVA58FqTWS05vQcT/ukHQZWIYU2KoXFJ/1x/zXZdu6GAjyca16oBb/8nz5Ilyk3sxmI3FuWgHRO/xOkbd6BKvA8nvR6tu3VCyFu9eI3J7E5EXMf7O7oBylQEKRphe7cp2WNqXrezRw7DycUVRcqUMcvrk/11Y1n9AGUiiyCKOD19GA6luQKB+RCYloQuo7+Be8mK5i4ZEe6nJKH3n/0AVSocjCFY8fY4swU6d8JvYf2WLRAFAU3vRaJ642asIcp17MYielW6VGD1Bygb+wt84iLgmxiNnjPnM9Ahi2AwGtFxTX8YVJGA0Q0Lms+Gl7Or2crj4KCBo1IBQafF3wvmyIlEOU+Gchu7sdiNRa8gbN8WeB2fAPfUc4BCBX3j8VDXZNoHshzvrfkGZ1JWQTQp8XWlGXinbB1zFwk6rRa7Fs/Hpd3b5cdFq9dGk48GQOPsbO6ikZXhbCyiXHZo9vdYtOsQfgkrCYODL9BjEwMdsigTD6yUAx1Jm+D+FhHoSBw0GrTo0w9v9ukHhVKFCxcu4KfvxyP8+jVzF41sFLuxiF5C/Pf9EbthN0SlCunO7khsuQTIX5PXkizGhTuJWLTXAGOGP4o4tsD4Ny1voHzZRs3Q8atx0Afkg06hworZ05lIlHIFu7HYjUUvwJSWgnuftkfCkQj5cViNEqg9bipc8+bjdSSLEZOiRduZBxGZkI6aRVzxa/cacFRb7tIHkaE3sXLBzzBeOw+lUon6PXqjfJOWZhtETdaD3VhEOezuyUOYPGI4rl5KkKZfIU+Hqmi6YDUDHbIoqVoteixbLgc6BX1dMKdLTYsOdCR5CxZCv1FjUaJWPZiMRuz+dS6WTv1BXn2ZKCewZYctO/Qc7h3dil9W74LexR2OCTH4tEohuHcdwmtHFkXKQdVq+UCE6/dDiG2Dde+NwBt+5pt59aKkWVknNq3Fzu3boPMLhpNoxMDhI+Do4mLuopGF4jo7RDnk0vJJ2LFhH9QOLhAD86Ndg5pwb/sury9ZnMHbZ+O2YZ/0dyw+rlXNqgIdidRtVaVNB2g1zth98BB8nR2gcXIyd7HIBnBRQaKnJPL885u+uHIzRh7L/4aHFs2GDYRznhBeM7I4C078id3R8+WcV7V9eqBv9dawVrWbNkeBIkXgF5QXwoNs6TqdVl6jh+hlMNgheoz46xcxf/ZcpDkHw0WdhOolvVFr+GzmtyKLdCT8Cqae/RqC0oRARS3MbjkY1i640BvZ9/V6PaZPnAgvNxf06DcAKpXarGUj68Op50T/J2rnGvzx+WBkSIM6FQqUKloQdb74hYEOWaSo5Hh8srMfoEyHxlgAq96eDMWD1hBbcWz/XqQYTbgdG4/QSxfNXRyyQmzZIXrIxSlfYufBUzCo1PAMvYJarZqiUvd+vEZkkYwmEb3XLIBBFQUYPbC45Wx4ONreKsS1GjdBWnIyRIMeRcqUM3dxyAox2CGSvjQMBiwd0R93k9KgVirho9ei/Tfj4VG6Cq8PWayfdlzBucsl4OjTHuNbNEcpf9sdT/Zm+w6PPL5y9gzuhIejQas2ZisTWQ8GO0S6NPz59ccIdS0EuJhQSJuIt375HSo3D14bslgbzkRi9r4b8v0Jjfugfalg2IuEmBisWrUaBqUK8VF30b5XHy5ASE9lWx27RC8q4TawsBmaajbAPT4KJbRx6LhwLQMdsmgbLh7FFwcHA4o0fFSvENpXsJ9AR+Ls5oY8Hu5y5vQbe7Zh85TvocvgAoT0ZFxUkIsK2q1TCyaj5N05cDREA84+MHZYBGXhuuYuFtFTXb4fgU6bOkNUJiKPWB87u0+HUmGfaRVObN+Cv5bMh8loQJ58BdBi0OfwzWu7XXn0X0wXQfQUa77oj43hCfglsiZMfqWBPvsY6JDFS9amo9umT+VAR2nwx9K3xtptoCOp3KwlOo0aD2cPT9yNicWsufNwdM9ucxeLLBC7sciuiOmpuPt+U4jnbwGCAjpHN+g7rwU8mciTLD8VRMdVQ6FVhgJGJ8xqPANB7t6wd3mLl0TX8VOAkEIQlSrs2rgOp7ZtklNPEGVhsEN2Q3/rMsLb1EbC4XCUunoNDVJvY+APU6Hx9jd30YieGej02vA97hj/gigK6F9mLGrlL8Gr9oC7bx70/3wk8krpJaLCsHfRPOyYNx0GvZ7XiGQcs8MxO3bh9NLZ+PPkJdTb/ze89ekI+rw33LoNNXexiJ4pQ29El5Xf4bphlfy4rk8vzGo1iFfuMaTWnJOb1+HA74sgiiY4FiuDjn0+hX8wx/HYKo7ZIXrg4u/fY9PF28jw8MGRqhVR4NeZDHTIKkQnZaDzz0dw5lJhmPRuqOP9AWa0GGDuYll0ItHKrd/CWyNGQ/QLwn2FBvPmzUN0eJi5i0ZmxnV2yGZJq63+/cOnOHbmLjROrlB4+6H74AHQFOMKrGT59l2/gc9XhuJekhYeTnnwY+0VeLM4x5Y9jwLlK+GtvoOw/Pdl8FQBPkF5c72+yLKxG4vdWDabyHPLT1/jXpxWfly5jB/qjJjL/FZkFb7etQjrbk9DRmQXFHSuhvndK6OAr4u5i2V1khMSoFQq4OzmLj9OT0uDWq2GSs1EovbWjcWWHbI5VzevwB9/n4LJuxjcEi+gWcsaKNl1hLmLRfRMGXoduq4dhasZW6TJgggOuYa17wyGmyO/nF+Gm6fnI4O850+fBp02A7369oOXbx6+I+0IZ2ORTbk4bRS2LlkKURCkZks0aPomAx2yCrcTYtFw6XtyoCMp59oRu7rNZaCTQ0KvXEZcWjpSjCJunDubU4clK8GWHbIJJqMRfw14Fyfup0ijFBEYehEth3yGoKpcEZks354bZzF43yCYVPchmtToWuhzjKz3jrmLZVMKlyiJTu3a4NblS6jcoJG5i0OvGYMdsnqp9yLx8/fjoc1QQy0IKKwwoMXcZXDw4IJrZPlWnzmPMac/gKDSQjB44/vaP6FlscrmLpZNKlmxsnzLEnHjBv7avQPv9OoDhVJp1rJR7mI3Flm3xAisHfc5Ej3yICOoACrn9UGbpVsY6JBVrAkzc881fPZHGPQJleBsKop17f5goPOaSGN3lixeiCt37mHexO+YSNTGMdgh6xV+BPi5Pjp5boV7QjQa+Tmh3uTF/AuNLF5sWjI++v0v/LjjKqSsBh0LfIq93ZahsE+AuYtmNxw0jihdrBgEvQ4pF85g+defITE6ytzFolzCqeecem6Vdn8zGHWNS6EWdIB/aaDzMsArv7mLRfRMJyNvoPef/ZCe4QBD5IcY26Yc3q3G9XPMJezCOWydNhFpiQlwdHXDm58ORtFKVc1WHnoxXEGZbJKYkYa5gz7GXyYPLL7bECjZFui1g4EOWYXfTu9Bzz+7Qq+MgMoxGj91DWGgY2b5S5VBtwlT4V+oCFINRizbsAmrFy6Qp6qT7WA3FlkNQ8Q1hLeuBdc7MdKAB6hcvWDqsBBw4GJrZPmGbJuDif8MBpSpcDCGYEmzZWhTsry5i0XSejw+vnhn7PdwL1kOUChx6fw5JhK1MQx2yCqk7F2HW+3aIO12BipfOo92PgJ6Tp7L8Tlk8VK1WrRaNgg7o2dDEEzwU1THrs4rUSGooLmLRg9RO2jQ57ORKFsgBM53b+HCvl1YOXYEUuLjeJ1sAMfscMyOxdvyzWf4J0GHJrv2wtPJgJAZ06Cp+qa5i0X0TDEpWrT9oz+SVIchigJqeL2Hea2HQqHg35mW7NbZ09gydSIyUlMg5C2ARp3eRbnqNc1dLHoMjtkhqycaDNj9TW8c1ztC5+6Ff6qWQcGN2xjokFU4H5mINjP+xt2wGoDBEx8VH4f5bT9joGMFCpStgHfHT4ZT/jeQ5O6LdVu348Kxw+YuFr0CLipIFkkbH4WtYz7CzSgjnFzT4OHuhu5T50Lp6mbuohE906JjJ/H9pmhk6E0o5FsQs1psQIlALnJpTbwCgvDeF6Mxf8Z0CAYdipavaO4i0Suw6LbUCRMmoEqVKnBzc4Ofnx/atWuHK1euPLJPRkYG+vbtCx8fH7i6uqJDhw64d++e2cpMr+7qlj+waEhmoKMUTGjdsBQ+njIXagY6ZOF0BgM6rxqFHy/2gl59HfWK5sG6vrUY6FgpN08vDPriK/QZPlIe0yPR63RIiI0xd9HIloKd/fv3y4HMkSNHsHPnTuj1ejRp0gSpqanZ+wwePBibNm3CqlWr5P3v3LmDt956y6zlppf310+jsfzIOUQFlICTg4jOAz9Gya5f8JKSxbuTFIeGS3vgQto6CIIR1Usk4deeVeDhxIzl1kxKI+Hi7pG96vWvs2Zg5tSpuHL2jLmLRrbSjbV9+/ZHHi9atEhu4Tl58iTq1q2LxMRELFiwAMuWLUPDhg3lfRYuXIgSJUrIAVL16tXNVHJ6qUSeA7viWGw6UKgkHAw6tO0/HAFV6/FiksX7+9Yl9NvdH0bVPYgmFd7OPwSjG75n7mJRDkuMi0N0XDyMCiUiblxHsbJcOsBaWHSw8/+k4Ebi7Z3Z9y0FPVJrT+PGjbP3KV68OPLly4fDhw8/MdjRarXy7eHR3GQ+2pgobOrbA2FQy02NxcIvos3U+XD28WO1kMWbc3QLZl8YC6jSIRg88W2NH9CuJP/QskWePj74pF8/HNu7C43adzR3cchWurEeJq1mOWjQINSqVQulS5eWt0VFRcHBwQGenp6P7Ovv7y8/97SxQB4eHtm3kJCQXC8/PV7YgT/x08RJuOHsJa2DgGqBXui0aC0DHbJ4UpfGtzu3Y9alkYAyHY7GwljZZjkDHRvn6x+AFp27ZT+OibqLeT9OREpS5h/jZJmsJtiRxu6cP38eK1aseOVjjRw5Um4lyrrdvn07R8pILyj8KDavWgmdizu0/vnRon4N1J76GxcKJIuXoTdiyMp/sGC3AYakcghW1ceerstRPE+wuYtGr9mieXNxNyUdsyd9j4R7TCRqqawi2OnXrx82b96MvXv3Ijj43w+TgIAA6KSR8QkJj+wvzcaSnnsSjUYDd3f3R270mp1aAixqiR5um+AZH4Wujaqj+KdfsRrI4p2PCkfHeXux7nQklAoFhlcajS1dpsFN42TuopEZNGzUGEqDDgi7ht+/GIywcxy4bIkUlt5MLAU669atw549e1Cw4KPLq1eqVAlqtRq7d+/O3iZNTQ8PD0eNGjXMUGJ6Fm1iPDYM7QnT+v6ASQ/Xck0xaNKPKPxme148sngrzh5Al62dcV38BZ7OSvz2QVV8UOsNLhRoxyrWroMBAwchKDgEGSnJWDN+FP5ev4qJRC2MRaeL+PTTT+WZVhs2bECxYsWyt0vjbJycMv+K+uSTT7B161Z5ppbUQtO/f395+6FDh3J8uWl6Ndqwq5g6fTbS3TxRJOI0ur5XC6gzDODS+WQFvtixABsjZ0BQGKEyBOG3FgtROjDI3MUiC6HXabHr55k4f/QQUguUQB4XZ/QaOBiOD76rKHc87/e3RQc7giA8drs0vbxnz57ZiwoOHToUy5cvl2dYNW3aFLNnz35qN9b/Y7CT+zIObkHEoGHYV7wiIgoUQg0nA5p+MeE1vDLRq0nTa/Humq9wQ5u5FIYPKmFVh+nI48o/jOhR0tfphiULceZmGJTpKSjkALQd+iVcvbh6dm6xiWDndWGwk7vuzx2D2BkrIBoFqNwB1ehRKNiySy6/KtGruxUXjc4b+iJVcVl+XNGtMxa0HQGVUsnLS090aNcOnFyxGLrkRDnQaTPsSwS+8W/vBOUcBju5cLHoxRi1WiwcMRD3RTWa7dwDn3yOyPvrGigDC/BSksW7dDcRXTZ3h9HhJkSTA3oWGYlhtbm2Cj2f+Kg72PDDOMRGhMPg44/SdRuhZed3eflyGLOek9kTef4xtBsi3Pyg9fRBWN1yCFl/kIEOWYXt56PQYc5hJEU2g8Lgj8m1FzDQoRdOJPruuB8RVKEa0vPkxfHLV7F7zSpeRTOx6NlYZJ3iLx3B8iE9cfd+OpyjQlHOmIB2c5ZB0Diau2hET2UwGjFq2y58vPQk0nRG1AiugN3vbEKTIkwLQC/OwckZ73z2BQrl8YWzLh01mzTjZTQTq0oXQZZv3+Qx+OfUaRj0KrioDWjbswMCa7Yzd7GInul+ShI6rhmAWNNZKDSfoEflmviyRQmolPybkF4tkWj3fgOgy0iHg2PmzCyj0YjIsFDkK/QGL+1rwmCHciyR5+rhn+KiawAUeYuiYOwFtB81Ba75SvAKk8U7Gn4NH+/sB4PqDgAl3qvrhNGNSpm7WGRDsgIdybJffsaNyDuoW7kSGrbhH4OvA4MdemW6+PvY9HE3hKldAKc88NCmosOEX+Gc5/mn/xOZy68ndmDK2a8BVRpgdMPXlSfinbJ1WCGUKwx6fWbuRoUSKQnxvMqvCaeeczbWK4k9vg8bJnyHeLVGTuRZNq8vGvywAEoV42iyguTC22Zhz/1fIAgmaIz5sbDFLJQJyG/uopGN02m1+GvLJjRs3+GJ68nR8+FsLMp1R+f/hFlrtyPG1RNqoxEtG9RA4ymLGeiQxdMajOi5cgH2xvwsBzoBilrY1eUPBjr0WjhoNGj0VsfsQCc5IR7TvvsWYdeusgZyCUfe0cs5vRR/XbwJk8YRRt8gdBnQF8U+YSJPsnzRyRno8vMRHDgTAENKcdT27ok/u86Gp5OLuYtGduq3eXMRrzdiycKFuHX2tLmLY5PYjcVurBdjNAA7vgKOzkFsugv+yGiFrkOGwyM/ZxWQ5dt8+SS+XRuDe0kGuDuqMK1LeTQo5m/uYpGduxN+C7/98guEsGtQ6dJR/71eqNC8Dbu4ngNXUH4BXEH5+USfP4n9c39AB+9tmbk7648E6g5nIk+yCmP2LMHqsCnQJ5VHsLEHfuleBQV92ZpDlkGv1WLXL7Nw8cAe+XGhWg3Q/MNP4OjsbO6iWTQGO7lwsezZ/d1rMXfXMRgdNCh/9xjaDf4UKNHa3MUieiadwYCua0fhcvom+bGnWA7r354HHxcGOmRZpFSVp7ZuxN7lS5BaoDg0CgXe79MH/sEh5i6axeIAZcq5N9Ov4xE78At434+GUqdF4cYdGeiQVYhIjEODpe9lBzplXNpj73uLGeiQRZIGLFdq2RZ1e30KCArodFqs+e4r3LmamYiWXh7H7LBl56mJPCM+fw9p28/Jjx0KOsNj8i/wLVHhFd5yRK/HvpvnMXDvAJhU9yGa1OhScBi+rM9EjGQdbl25jJ3zZyLp9i15hmvj3v1Qun5jcxfL4rAbKxculj1JuHUNv0yfDqPOgOZ79sO/TiH4TV/N/FZkFXZejMSQQ10AdTwEgxfG15qMVsUrm7tYRC9El56GbbMm4/rxI9C7ecGnRFm8P2AQVGo1r+QD7Mail5Zw5RiWffcFUty8ke6dB6mdGsF/3mYGOmQVYx5m77uOPr+dQdrd9nA2FsWatn8w0CGrTSTaZsgXqNjubWQEFUBkcipWzptl7mJZJS5zS48I27EYmxctR4ZRBTdlKOpUKo+qvb/hVSKLF5+WgsHrdmLfOQf5cefSjTGq1QBo1EpzF43opQkKBRp06QFxwzqcOHoErbr049V8CRyzw24smdFgwKov+iPydqS0jj4C3I1o+/VPcM1X8mXeV0Sv1ek7oei1vS90iIE2rB9GN6+HbtWZ9oFsL+GylEU9qxXz4umTKFXRvrtnk55zGApbdgi6hBj88tUIRPsGQxnshErCbTQZvQAqF45fIsu39MxeTDz1BaBMgWB0wdj2BfBueQY6ZHuyAh3J2t9/w7nrN3H6yGF0/aQfFyB8BgY7di7+zCGs/2Y0Ulw9Aa8AFEIGmo5fzvxWZBU++3Mett2dA0FphNoQjPnNZqJS3sLmLhZRrkuMjZH/V0JkoPMcGOzYsetLZ2D7ui3QqjVwTEtBUz8VyvWfbe5iET1Tml6LzqtHIFS3C1IuxTxCVazqMhU+zm68emQXPhg4BEf37ESV+g3NXRSrwGDHTq37ehDOmpzh7OQCj7RktB/QH3nqc0VksnyxKVp0WjEB0epdEEUB1Tzfxfw2w6GQc5gQ2Y9qDd/Mvp+Rno5ZP0xEjRo1UPPNpmYtlyVisGNvjAbot36JSxkKiC4OcPD0xnuTfoJTUAFzl4zomS7cSUSfJScRmVgBrvnO48Ny3TCoZjteObJ7axcvRLIJ2Ln/AJTpKaja+i12bz2Es7HsaTZWWhywqicQuh+RKV7YLTZD1/HToNRozF0yomeafnA75mw3IV0vooCPM+Z3r4Qi/jb8+0r0AjLS0rBg+hSkXL0AVWoSStZtiDd794PKIXMpBlvFFZRz4WJZs/OrF+LSro14O2APoHYB2s8BSrY1d7GInslgNKLH+m9xNmUNtDH1Uc2zG2Z2qQgPZ64iS/QwaTr66W0bse+3BRBNJni/URxNP+qHoHy223LPFZQp26WZY7D6n5u44F8Ge+5XBXrtYKBDViEqOR4NlvaUAx1JuRBX/NqjMgMdoickEq3Yoi06fPENHNw9EC6q8cv8X3Du6GG7v14c0WfDRIMB9z/rAnHmH/CIvQ/H1CSU7vMdEFDa3EUjeqZDYZfRfGUnJOAMRJMK7YOHYlWnCVCruCIy0dPkL1MebT8fA5VSCdFoxM6ZP+L83p12fdE4ZsdGu7GSwm8gatB7MF6Mlx+71CkM/x9/g8bDy9xFI3qmece2Yub5MYAyHYLRA2OqTcJbpWryyhG9gOTEBGydNxMRJ4/Ijys2b4O63T6wqXXUOGYnFy6WtbixYx2W7z4Ep4Q4NPv7IPL2agnPIT+Zu1hEzzXmYNb+s5h78wMISh00xoL4rdVslPAL5tUjegnS2J0ja//AoVW/w+DiDkW+N9Dr077w9vO3ievJMTt2KnznEqxftQoGJxek+PrD8cv+DHTIKmTojRi66h/8uD0CGVEdkFdZF3u6rmCgQ/SKiURrdOyClkNGQhtUAKlQYPnPc+zumtpOW5adk6L30z9/gX17z0lvb/iob6Ltu92Qr3YTcxeN6Jku3LuNoWsP4XKYK5QKAV/W64KeNQtwnRCiHFK8Wi284+iMTatXoVPvT+zuujLYsQFpsdFYMuYLpNyPhgABJfM74c3RM6By8TB30YieafW5gxh7fDhMasDddTDmdK6PWm/48soR5bBi5SqgaNnyj/wRcWjPblSvV/+RJKO2iMGOlYvc+BuW7j2GdJ9gqFROaFbIAZX6/iA3XRJZ+vo5o3YvwsbIGXIiTwcxEHN7lEO1EAY6RLlFeCjQ+XP9Whw+cxZHD/6N/iNGQqW23QUIGexYaUvOuWljcOn8NcSqNYCTKwQXd9QK9kHl/mPMXTyip7oRG4WJB3/D0ftbYFLFQlAAXqiIVe9Mh78rWyOJXheTXgeYTHB3dYZSZduLdDLYsSZxofhj/ARcdswDh1gtHNQaae0AFEiNQ+36nZG3MXMEkeXOsjoWGoffjtzAvox+EJTpmZ8+RkdU9e6Aea0/k9cEIaLXp/nbnVGo6GkUKlEqu8Xn0M4/8dfff6NC2TJo2LqdzaSbYLBj4fTpqTBe+hOOF38Hru+GIqU2RNcgmFw8UM6YgEqfDoVXea4/QpbpdmIsZhzeiFMXC+F6dIq8TRNYCm5u99EkuD2G1u4EH2c3cxeTyK7H8Tzs2NEjSBeUOL5/L65tW4/S9RujbKOm8ArMC2vGRQUtdJ0dQ+hFrJ45DVc13igTfQrtgzMXhUr2b4iD8cXQaMCXULvyS4Isj8lkwrpLRzD/9O+I0B+GoNAjNbQfNMb8aFchCG9XDkTFfHnMXUwieoyo8DDs3rIJCRfPIiP6jrzNJI3lKVIaFcuXR/2WbSxqUUIuKpgLFyu3GQ0GpG1cgMTflyD5YiwOVKuKuwUKwSXhPj5r4Q1Ufh/wLmS28hE9zf2UJPxwcDl2R26ATnk7e7vKEIQOBfpiQK3mcHe07XEBRLbCZDIi9PRJnN21DZci7kLnEwBlSiLyJMegTMMmKNOoKdx9/cxdTAY7uXGxcktGTCTWTvoONxSuKHPyBIrdvpu5vZAXwipXQ5P+w+GcJ/C1l4voeVy6m4Q5h/7CnqTREBRaeZuUyypIVQ0flHsXnUrXhoKzA4ms1u0b17F762YkXL0I44PWHihUUJQsj0qVK6NWk2ZQKlUW/f1tOW1RdijqyGb8s2EpLocmIjlvURidnXHjjcKoFqyCV6/+cKzdGo/2phJZhsSMNPx+8iR2n1XiZJiUf80Ilzc0UJrcUcuvNYbX6ooC3ub/q4+IXl1I4TfQs/8gGA163DhxFP/s3IYbtyOQYQT2/nUQ5atUg7uvZXdN20ywM2vWLPzwww+IiopCuXLlMGPGDFStWhWWJj0qAltnTMJVrRLqyJsQTEYASvgkRsJbbUCTz4bCq1BxcxeT6LH+Cr2IqceW4GrqXphMKqSGfQ6VQoUmpfKiWbl5aFmiJJRKrvFEZIuUKjWKVq8t325evoQ927ZCLTpnBzrSrMtFs2ageIkSqFa/oUUtVGgTwc4ff/yBIUOGYO7cuahWrRqmTp2Kpk2b4sqVK/Dzs4y/LqP+XI0TSxfiRroJiW+UhcnVCYK7N8q4J6Ncq07IW6cjFwIki5Sq1WL6kfXYcHM1UhWXMzcqAaXohd4NPNC7RjX4uTuau5hE9BoVKl5Cvj3s4j9nEBYTh7D9B1C4aFH4heS3mDqxidlYUoBTpUoVzJw5M3s2SEhICPr3748RI0aYbcxORGQUDs6ehPAUHYSoW8hat1Jw8YSbhzuKNnkT+So0zt4/Pvk+9CY9BEcBwoO/jkW9CaJOlBdeC/QJydwmAvdjo6AzaiFK4WrWipgmETCKEAUgwOPfLNEJyTHIMKYDagGC+sFxDSaI2qzj5oNCUEB6I8TE3UOGIQ2iFJArBPm1pOMKBlFKuYU8HnmhFDKj9cTUWKTpUiE6AIqs4xpNQIacngsBviHyX/3SMeISopGqTck+blZ5BeOD47oFQqXMXM8hMTUOqdokiGpAcPjvcf19gqFRauTyJiTFIjEt/tHjilJ5M+/6uAXCUZX5RZycnoiEjFj5ixqaf/cV0zN/Bfy8A+GsdpXLm5QSj7jU+4ACEJX/Pa63sz+cHVzl+ykZSYjPuAdRKqrmQauGdJCMzOP6ePjDTeMpb0pJS8L95DtyHWUfVyq6dH0BeDrngbvGU76fpk3F/bQIed/s40rSTZllcPODp7MvRIhIS09BVFL4Y48rva6How88nTJXJtbqM3A3JTTzuI7/HlfIMGXu6+IDX9dAGE0mLD65GcfuL4GoTIFOoYcoCvBEabxdqD16lH8TDo4OEB5cd1GqS6meBMDB9d+1OfRpOohGQKFRQuWQ+d4xGkwwpmdeTOHBtsz3uxFyxSoVEB6chyi9rw2Z56x2VWevB2JIM8BkNEHhoIBKk/l3m8lgguGxxzVl1onyod+th4/ros4+D0OGASa9CQqVAiqnB8c1mWBIfcxxpZ+XjqMQIKgeHFd6Hen1pNNwVmW3dBm0Bph0JggqAWqnfwdq65J1mXfUiuxze9xx5e06qSUYUDoqoVQ/uJY6A4xak1x+6Tz+c1yV4qE6MsmfEdJnRtZnwcPHVTgqoco6rt4EY4ZB/h1wcPm3PnUpusw6euS4/9a9oP5vfSoclFBplI/W0f+/T1J1EE1PrvvH1af0uaNyfFBHRpP8npA4uD38/tNnlu8Jdf+4+ny4jqR99an6/77/0g3yuTyp7h9Xn9J5qZ0fHFcUoU/JPK7KWQVF1vvkwfvvSXX/yHXPep8oBTg8OO7DdaR0UkH54BgGnQEmremJdf+k94mD67/H1afoMn+NHnn/GWHUGuX6jIgIxY6N62DU69F74OfZ75P1vy9EhRrVUaRUGeQ0uxmzo9PpcPLkSYwcOTJ7mzQYsnHjxjh8+PBjf0ar1cq3hy9WzhcsDYbZ9XBD9R50Xga4p6RC0LpBqSmH4q6FUFKjwq0dJmzdcDz7R1p6qKASBHztswwn/P6Wt/W63Q0dU2riqikRdRTXs/fdZXKFo0KBPUl6JD/43crvIKC8swp39SZsT43K3vdNdxX8FQKmuW3H9uCN8rb2d1uhT0ILRJrS0VB5DXJkAWCTyRmBChX+TjEg9sEXcIBaQDUXFWINJuxJuZ993LquSgSqFPjN8QiWFVwib6sTWxNfRHdDvNGAZpqzEA2ZX9x/mDQootDgeKoBd/SZx/VWCqjjpkKKUcTu5Njs41ZzUaKoWoFNqouYXSQzgC2eUgRTbg9GuklEU+c1MGVkBnMLTCqUUDjjbJoRobrMC+GiABq7q6EXRWxNlMaTZKrgrEQpBwUOCOGYUPx7eZuP3gNLr0+ASRTRwmkVUjLekLdPMQmoonDD5QwjrmRkHlclSHWUeZ02JlyTf48lJR0VKOuoxBkxBiNLjpK3KUUFNl/OLPt7mrUI1RaV748xmdBY4YlQrRFnHwQtktYeKigEAX8m3sqKkfCGRoGKTkpcM6ZgQOnh2fuuvzgTGkGBYZpNOKItIm8baDLibYUXInUmnEh78OEFoIm7Ck4KAXuTI3HJGClvC3EQUNVZhTsGPXqVGZi97/KLU+ApaDDRYTc26QrK27rCFasxGjEGEw6m/Hvc+pdVSPjzJA6lGHD/wfvEXyWguqsK8QYTyvxYL3vfmxNPwEVrREoFPxR/p5i87e7fkcD2W0gyitib/CCCBFDDRQk/tQInUw2IePA+8VQKqOemQppJRMjX1eH04IvsxtSTcEnSIaGwJ0r3zvwQjb0UC+3vl6E1idie9O9xKzorEeKgwLl0I25KH/gAnBTS9VHDIIpwG1gRPkGZweuNOf/A5V4aYgNcUG5QRXlbenQ64qeeku9vSMj8gpKUdlKgsEaJqxlGXHrwPpG+Alp5PviC6FYSwaV95Luhiy/C6WYiYtwdUP6LatnHiP7uqPz/tkQ9dA/qvqhGgRJOStzSmvBPuvE/nxHaFoVQuG7muifha65D/c99xGqUKDf23zW3IsYdhYOAJ35GHEs1PvIZ4awQkFQjCCXbFs6so51hwIEIxCsElBlfO3vf0O+OwUUUn/gZ8fdD7xPpM8JLpUBsCR+U61FS3hZzIgq69TeQJAIlJ9bJ3vfa98fhrjc95TPC8MhnRIBagegQN1TsW17elnozEYkLzsufEUUm1c3e9+pPJ+GRqn/KZ4Thkc+IfA4KRHk7ovLwKvI2U7IO0ROOyZ8Reb769/13ZeYZeMSmP+UzQv/IZ0QRRyXuOqlRZXT1zI0mMbvuHT8qA9+CmZ+V1xach9vt5Kd8Rugf+Ywo5aRElFKByt/Vyt73zrijmV/ubxVBcNUAedvN5VfhfCn2KZ8ReiQ92Cx9RlR0VuG+Cagw6d86CptwDI5GEdoGISjctEDmtq234HDkzkOfEZnDR66NPQIPpYB9KTG47hOB4mVTYU5WH+zExMTAaDTC39//ke3S48uXHzS5/58JEyZg7NixuVswB2dEOedDmbR8MAom3HUoBZM680NPStb5NNJMFtGU+Qslys0FmT/l/NBfIHIrxwuSjguT4/9VvQA36a9iuYlI+lR/8ePKP2t0yrwvZXN8wM1RDcH44PHLvM+l5hqjS+b9rONDaqXQQHjQCiQkiy953AdrFBkzv+Ak7o5OcFRp5PuKZP1LHFcBGN3l2hXkpqZMrhoN/DWZx1UlPfhr+4UIEIyZH4QPc1Y5Isgxsz41yVrA9BJHNnjLf5FlvY7EUalBsFfm9Q7SewApVt/4S0RmI0KToEDZqg+CPDOx+m6sO3fuIG/evDh06BBq1KiRvX348OHYv38/jh7NjJyf1bIjdXvl+NTz5HvQSV+mSjWbqNlEbfVN1I/rnnhSVwa7sdiN9fD7hN1Y9tGNJTzlM0L9oBszp9nNooJSN5azszNWr16Ndu3+zQ3Vo0cPJCQkYMOGDRa/zg4RERG9uOf9/rb6OaIODg6oVKkSdu/enb1NGkwoPX64pYeIiIjsk9WP2ZFI086llpzKlSvLa+tIU89TU1Px/vvvm7toREREZGY2Eey88847uH//PkaNGiUvKli+fHls3779P4OWiYiIyP5Y/ZidnMAxO0RERNbHbsbsEBERET0Ngx0iIiKyaQx2iIiIyKYx2CEiIiKbxmCHiIiIbBqDHSIiIrJpDHaIiIjIpjHYISIiIpvGYIeIiIhsmk2ki3hVWYtISysxEhERkXXI+t5+VjIIBjsAkpOT5YsREhLyOuqGiIiIcvh7XEob8STMjQXAZDLhzp07cHNzgyAIORpxSgHU7du3n5qzwxbx3O2v3lnn9lfn9lzv9nrelnbuUouOFOgEBQVBoXjyyBy27EgDlxQKBAcH51plSG8Gc78hzIXnbn/1zjq3vzq353q31/O2pHN/WotOFg5QJiIiIpvGYIeIiIhsGoOdXKTRaDB69Gj5f3vDc7e/emed21+d23O92+t5W+u5c4AyERER2TS27BAREZFNY7BDRERENo3BDhEREdk0BjtERERk0xjsvKJZs2ahQIECcHR0RLVq1XDs2LGn7r9q1SoUL15c3r9MmTLYunUrrM2ECRNQpUoVecVpPz8/tGvXDleuXHnqzyxatEhenfrhm3QNrM2YMWP+cx5Sfdp6nUvv8f8/b+nWt29fm6vvAwcOoHXr1vKKrFK5169f/58VW0eNGoXAwEA4OTmhcePGuHbtWo5/Vljauev1enz++efye9jFxUXep3v37vLq8zn9O2OJ9d6zZ8//nEezZs2svt4PPOO8H/d7L91++OEHq6pzBjuv4I8//sCQIUPkKXinTp1CuXLl0LRpU0RHRz92/0OHDqFLly7o1asXTp8+LQcJ0u38+fOwJvv375e/5I4cOYKdO3fKH4JNmjRBamrqU39OWmnz7t272bewsDBYo1KlSj1yHn///fcT97WVOj9+/Pgj5yzVu+Ttt9+2ufqW3sfS77L0JfU4kyZNwvTp0zF37lwcPXpU/uKXfu8zMjJy7LPCEs89LS1NLvvXX38t/7927Vr5j5w2bdrk6O+Mpda7RApuHj6P5cuXP/WY1lDvqc8474fPV7r9+uuvcvDSoUMH66pzkV5a1apVxb59+2Y/NhqNYlBQkDhhwoTH7t+pUyexZcuWj2yrVq2a+NFHH1l1LURHR0vpZsX9+/c/cZ+FCxeKHh4eorUbPXq0WK5cuefe31brfODAgWLhwoVFk8lk0/Utva/XrVuX/Vg634CAAPGHH37I3paQkCBqNBpx+fLlOfZZYYnn/jjHjh2T9wsLC8ux3xlLPfcePXqIbdu2faHjWFu94znqXLoGDRs2fOo+lljnbNl5STqdDidPnpSbsB/OsSU9Pnz48GN/Rtr+8P4SKcp/0v7WIjExUf7f29v7qfulpKQgf/78cgK5tm3b4sKFC7BGUpeF1ORbqFAhdO3aFeHh4U/c1xbrXHrvL126FB988MFTE+faSn0/LDQ0FFFRUY/UqZSXR+qeeFKdvsxnhTX97kvvAU9Pzxz7nbFk+/btk7vuixUrhk8++QSxsbFP3NcW6/3evXvYsmWL3FL9LJZW5wx2XlJMTAyMRiP8/f0f2S49lj4MH0fa/iL7W0vG+EGDBqFWrVooXbr0E/eTPhyk5s8NGzbIX5TSz9WsWRMRERGwJtKXmjQeZfv27ZgzZ4785VenTh0566691LnUp5+QkCCPYbD1+v5/WfX2InX6Mp8V1kDqtpPG8EjdtE9LBvmivzOWSurCWrJkCXbv3o2JEyfK3fnNmzeX69Ze6n3x4sXyWM233nrrqftZYp0z6zm9EmnsjjT+5Fn9sTVq1JBvWaQvvhIlSmDevHn49ttvraYWpA+3LGXLlpV/qaXWi5UrVz7XXzu2YMGCBfJ1kP5qs/X6pseTxul16tRJHqwtfZnZw+9M586ds+9Lg7SlcylcuLDc2tOoUSPYg19//VVupXnWZANLrHO27LwkX19fKJVKuVnvYdLjgICAx/6MtP1F9rd0/fr1w+bNm7F3714EBwe/0M+q1WpUqFAB169fhzWTmu+LFi36xPOwtTqXBhnv2rULH374oV3Wd1a9vUidvsxnhTUEOtJ7QRqo/rRWnZf5nbEWUveMVLdPOg9bq/e//vpLHpD+or/7llLnDHZekoODAypVqiQ3aWaRmuqlxw//RfswafvD+0ukD4sn7W+ppL/mpEBn3bp12LNnDwoWLPjCx5Cad8+dOydP37Vm0riUGzduPPE8bKXOsyxcuFAes9CyZUu7rG/pvS59UT1cp0lJSfKsrCfV6ct8Vlh6oCONx5CCXh8fnxz/nbEWUpesNGbnSedhS/We1aIrnY80c8sq69zcI6St2YoVK+RZGIsWLRIvXrwo9unTR/T09BSjoqLk59977z1xxIgR2fsfPHhQVKlU4o8//iheunRJHrGuVqvFc+fOidbkk08+kWfa7Nu3T7x79272LS0tLXuf/z/3sWPHin/++ad448YN8eTJk2Lnzp1FR0dH8cKFC6I1GTp0qHzeoaGhcn02btxY9PX1lWek2XKdZ80kyZcvn/j555//5zlbqu/k5GTx9OnT8k36iJw8ebJ8P2vG0ffffy//nm/YsEE8e/asPDulYMGCYnp6evYxpNkqM2bMeO7PCms4d51OJ7Zp00YMDg4Wz5w588jvvlarfeK5P+t3xhrOXXpu2LBh4uHDh+Xz2LVrl1ixYkWxSJEiYkZGhlXXe/Iz3u+SxMRE0dnZWZwzZ85jj2ENdc5g5xVJFSx9ATg4OMjTDI8cOZL9XL169eTpig9buXKlWLRoUXn/UqVKiVu2bBGtjfQL8bibNN34Sec+aNCg7Ovk7+8vtmjRQjx16pRobd555x0xMDBQPo+8efPKj69fv27zdS6Rghepnq9cufKf52ypvvfu3fvY93fW+UnTz7/++mv5vKQvskaNGv3nmuTPn18ObJ/3s8Iazl364nrS7770c08692f9zljDuUt/yDVp0kTMkyeP/MeKdI69e/f+T9BijfW+9xnvd8m8efNEJycneZmFx7GGOhekf8zXrkRERESUuzhmh4iIiGwagx0iIiKyaQx2iIiIyKYx2CEiIiKbxmCHiIiIbBqDHSIiIrJpDHaIiIjIpjHYISIiIpvGYIeIrJKUbVoQBCQkJJi7KERk4biCMhFZhfr166N8+fKYOnWq/Fin0yEuLg7+/v5y0ENE9CSqJz5DRGTBpKzSUgZyIqJnYTcWEVm8nj17Yv/+/Zg2bZrciiPdFi1a9Eg3lvTY09MTmzdvRrFixeDs7IyOHTsiLS0NixcvRoECBeDl5YUBAwbAaDRmH1ur1WLYsGHImzcvXFxcUK1aNbmLjIhsB1t2iMjiSUHO1atXUbp0aXzzzTfytgsXLvxnPymwmT59OlasWIHk5GS89dZbaN++vRwEbd26FTdv3kSHDh1Qq1YtvPPOO/LP9OvXDxcvXpR/JigoCOvWrUOzZs1w7tw5FClS5LWfKxHlPAY7RGTxPDw85G4rqbUmq+vq8uXL/9lPr9djzpw5KFy4sPxYatn57bffcO/ePbi6uqJkyZJo0KAB9u7dKwc74eHhWLhwofy/FOhIpFae7du3y9vHjx//ms+UiHIDgx0ishlSMJQV6EikwctS95UU6Dy8LTo6Wr4vtd5IXVpFixZ95DhS15aPj89rLDkR5SYGO0RkM9Rq9SOPpTE9j9tmMpnk+ykpKVAqlTh58qT8/8MeDpCIyLox2CEiqyB1Yz08sDgnVKhQQT6m1NJTp06dHD02EVkOzsYiIqsgdUcdPXoUt27dQkxMTHbrzKuQuq+6du2K7t27Y+3atQgNDcWxY8cwYcIEbNmyJUfKTUTmx2CHiKyCNHBY6mqSBhnnyZNHHlScE6SByFKwM3ToUHnKert27XD8+HHky5cvR45PRObHFZSJiIjIprFlh4iIiGwagx0iIiKyaQx2iIiIyKYx2CEiIiKbxmCHiIiIbBqDHSIiIrJpDHaIiIjIpjHYISIiIpvGYIeIiIhsGoMdIiIismkMdoiIiAi27H8pbM1tRdcJSQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, tfinal, 1000)\n", "plt.figure()\n", "for port, ls in zip(['A', 'B', 'C', 'D'], ['-', '--', '-.', ':']):\n", " fnc_traj = iports[port][0].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", " fnc_traj = iports[port][1].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", "plt.xlabel('time')\n", "plt.ylabel('position')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2993b56d-fb03-46ac-b372-789f10fdd5ff", "metadata": {}, "source": [ "Compute the phase of the interferometer" ] }, { "cell_type": "code", "execution_count": 11, "id": "857b5077-4a1f-4d93-a920-80f7d4515190", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "differential phase=-64*T*omega_0 + 64*T*omega_r - 48*T_spacing*omega_0 + 48*T_spacing*omega_r - 2*pi\n", "total population sum=1\n" ] } ], "source": [ "# Compute the differential phase\n", "phiA, phiB, phiC, phiD = ifr.phases()\n", "print(f'differential phase={sp.simplify(phiA - phiC).subs(k, sp.sqrt(2*m*omega_r/hbar))}')\n", "\n", "# Print out the total population, check it is equal to 1\n", "pop = 0\n", "for node in ifr.get_nodes():\n", " pop += (node.get_amp())**2\n", "print(f'total population sum={sp.simplify(pop)}')" ] } ], "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 }