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</svg>" ] } }, "cell_type": "markdown", "metadata": {}, "source": [ "# Design error-robust digital SFQ controls for superconducting qubits\n", "**Generating single flux quantum gates robust to leakage and frequency drift**\n", "\n", "Boulder Opal enables you to [optimize](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-error-robust-quantum-logic-gates/learn-to-design-robust-single-qubit-gates-using-computational-graphs) and simulate quantum systems subjected to a wide range of pulsed controls. Single Flux Quantum (SFQ) logic provides a means to use digital control sequences consisting of trains of ultrafast flux pulses applied at rates comparable to the qubit frequency to manipulate qubits. This approach helps by circumventing issues that can arise from the room-temperature electronics used to generate microwave control pulses. However, the digitized nature of such controls opens up new challenges, such as susceptibility to leakage to other levels and frequency drifts. \n", "\n", "In this application note, we address these issues by designing the spacing between individual pulses, constructing sequences that are robust to leakage and frequency detuning. We will cover:\n", "\n", "- Simulating SFQ digital logic for qubit manipulation\n", "- Optimizing SFQ digital logic sequences to generate noise-robust quantum logic\n", "- Validating performance by calculating quasi-static noise susceptibility\n", "\n", "\n", "![designing-error-robust-digital-sfq-controls-for-superconducting-qubits.svg](attachment:7d398ff8-a0ce-44a9-923e-78f75dd9770c.svg)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports and initialization" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import qctrlvisualizer as qv\n", "import boulderopal as bo\n", "\n", "plt.style.use(qv.get_qctrl_style())\n", "\n", "\n", "def sequence_times_to_control_format(pulse_times, gate_duration):\n", " \"\"\"\n", " Create control sequences describing a qubit's frequency omega,\n", " anharmonicity alpha, and SFQ Rabi rate for each PWC segment.\n", "\n", " The `pulse_times` define the start of each SFQ pulse,\n", " represented as square piecewise-constant segments.\n", " \"\"\"\n", " segment_durations = pulse_times[1:] - pulse_times[0:-1]\n", " segment_durations = np.append(segment_durations, [gate_duration - pulse_times[-1]])\n", "\n", " control_durations = np.array([])\n", " # Binary switch to mark the segments where the square SFQ pulses are turned on.\n", " control_switch = np.array([])\n", " for segment_duration in segment_durations:\n", " # Encoding for pulse controls (1 during pulse duration, 0 otherwise).\n", " control_durations = np.append(\n", " control_durations, [pulse_duration, segment_duration - pulse_duration]\n", " )\n", " control_switch = np.append(control_switch, [1.0, 0.0])\n", "\n", " return {\n", " \"omega\": {\"durations\": np.array([gate_duration]), \"values\": np.array([omega])},\n", " \"alpha\": {\"durations\": np.array([gate_duration]), \"values\": np.array([alpha])},\n", " \"pulse\": {\"durations\": control_durations, \"values\": Omega_eff * control_switch},\n", " }\n", "\n", "\n", "def evolve_states(initial_state, controls, sample_times):\n", " \"\"\"\n", " Simulate the qubit state evolution for a given set of controls\n", " (as defined by sequence_times_to_control_format).\n", " \"\"\"\n", "\n", " graph = bo.Graph()\n", "\n", " a = graph.annihilation_operator(3)\n", " adag = graph.creation_operator(3)\n", " n = graph.number_operator(3)\n", "\n", " # Hamiltonian terms.\n", " omega_signal = graph.pwc(**controls[\"omega\"])\n", " alpha_signal = graph.pwc(**controls[\"alpha\"])\n", " pulse_signal = graph.pwc(**controls[\"pulse\"])\n", " hamiltonian = (\n", " omega_signal * n\n", " + alpha_signal / 2 * (n @ n - n)\n", " + pulse_signal * (a + adag) / 2\n", " )\n", "\n", " # Calculate the evolution unitaries.\n", " unitaries = graph.time_evolution_operators_pwc(\n", " hamiltonian=hamiltonian, sample_times=sample_times\n", " )\n", "\n", " evolved_states = unitaries @ initial_state[:, None]\n", " evolved_states.name = \"evolved_states\"\n", "\n", " graph_result = bo.execute_graph(graph, \"evolved_states\")\n", "\n", " return graph_result[\"output\"][\"evolved_states\"][\"value\"]\n", "\n", "\n", "# Data holders for SQF pulse sequences.\n", "gate_durations = {}\n", "pulse_times = {}\n", "controls = {}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard SFQ gate\n", "\n", "In this section, we set up the standard $X$ gate based on a train of uniformly spaced SFQ pulses set apart by one Larmor period of the qubit ground state, described by the following Hamiltonian:\n", "\n", "$$\n", "H = (\\omega + \\Delta) a^\\dagger a + \\frac{\\alpha}{2} (a^\\dagger)^2 a^2 + \\frac{\\Omega (t)}{2}\\left(a + a^\\dagger\\right), \n", "$$\n", "\n", "where $a$ is the lowering operator, $\\omega$ is the transmon frequency, $\\Delta$ the frequency drift, $\\alpha$ the anharmonicity, and $\\Omega (t)$ the train of SFQ pulses. \n", "\n", "We'll now construct an $X$ gate of duration $d_{\\text{gate}} = 10$ ns composed of $n=50$ SFQ pulses at times $t_k =k \\frac{2\\pi}{\\omega}$, $k\\in [0,1,... n-1]$, where each pulse perform a rotation of $\\theta = \\pi/50$.\n", "\n", "As the SFQ pulse duration $d_{\\text{pulse}}=10$ ps is short relative to the precession of the qubit, $d_{\\text{pulse}}\\ll\\frac{2\\pi}{\\omega}$, one can conveniently model $\\Omega (t)$ as a sequence of square pulses of equal amplitude $\\Omega_\\textrm{eff}=\\theta/d_{\\text{pulse}}$, as follows:\n", "$$\n", "\\Omega (t) = \\begin{cases}\n", "\\Omega_\\textrm{eff} & \\quad t \\in (t_k, t_k + d_{\\text{pulse}}) \\\\\n", "0 & \\quad \\text{otherwise}\n", "\\end{cases}. \n", "$$\n", "\n", "In the code below, we configure the \"standard\" $X$ gate and evaluate its state evolution using a three-level representation of the transmon." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Standard gate duration: 10.00 ns\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# System parameters.\n", "alpha = -2 * np.pi * 400e6 # rad.Hz, transmon anharmonicity\n", "omega = 2 * np.pi * 5e9 # rad.Hz, transmon frequency\n", "\n", "# SFQ pulse parameters.\n", "pulse_duration = 10e-12 # s\n", "theta = np.pi / 50\n", "Omega_eff = theta / pulse_duration\n", "\n", "# Define the standard sequence of pulses (pulse rate is equal to transmon frequency).\n", "pulse_count = 50\n", "gate_durations[\"Standard\"] = 10e-9 # s\n", "pulse_times[\"Standard\"] = np.arange(0, pulse_count) * 2 * np.pi / omega\n", "\n", "controls[\"Standard\"] = sequence_times_to_control_format(\n", " pulse_times[\"Standard\"], gate_durations[\"Standard\"]\n", ")\n", "\n", "# Plot the controls.\n", "print(f\"Standard gate duration: {gate_durations['Standard'] * 1e9:.2f} ns\")\n", "fig = plt.figure()\n", "qv.plot_controls({\"$\\Omega(t)$\": controls[\"Standard\"][\"pulse\"]}, figure=fig)\n", "fig.suptitle(\"Standard SFQ pulse sequence\")\n", "fig.set_size_inches(15, 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotted is the sequence of square SFQ pulses representing the standard $X$ gate. Here the spacing between the single flux pulses is set equal to the transmon frequency. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Your task (action_id=\"1827924\") is queued.\n", "Your task (action_id=\"1827924\") has completed.\n" ] } ], "source": [ "initial_state = np.array([1.0, 0.0, 0.0])\n", "sample_times = np.linspace(0, gate_durations[\"Standard\"], 100)\n", "\n", "state_evolution = evolve_states(initial_state, controls[\"Standard\"], sample_times)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax1 = plt.subplots(figsize=(10, 5))\n", "plt.xlabel(\"Time (ns)\")\n", "plt.suptitle(\"State evolution\")\n", "\n", "probabilities = np.abs(state_evolution) ** 2\n", "\n", "p0 = ax1.plot(sample_times * 1e9, probabilities[:, 0], label=\"$P_0$\")\n", "p1 = ax1.plot(sample_times * 1e9, probabilities[:, 1], label=\"$P_1$\")\n", "ax1.set_ylabel(\"Probabilities $P_0$, $P_1$\")\n", "\n", "ax2 = ax1.twinx()\n", "p2 = ax2.semilogy(\n", " sample_times * 1e9,\n", " probabilities[:, 2],\n", " label=\"$P_2$\",\n", " color=qv.QCTRL_STYLE_COLORS[2],\n", ")\n", "\n", "ax2.set_ylim([1e-8, 10])\n", "ax2.set_ylabel(\"Probability $P_2$\")\n", "\n", "lgns = p0 + p1 + p2\n", "lbs = [l.get_label() for l in lgns]\n", "plt.legend(lgns, lbs, loc=\"center left\", bbox_to_anchor=(0, 0.75))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evolution of the populations of the three transmon levels during the application of the standard SFQ $X$ gate for the system initialized in the ground state. The populations for the qubit states $0$ and $1$ are shown in a linear scale (left axis) while the smaller population of state $2$ is shown in the log scale (right axis). Note that the leakage to the third state induces a significant operational infidelity ($I \\sim 10^{-2}$)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimized SFQ gate\n", "\n", "In this section, we use Boulder Opal to generate an SFQ gate robust to both leakage and the drift in the qubit frequency. We will do this by allowing the application time of each pulse to vary. In experiments, the pulse time $t_k$ commonly changes discretely, in increments defined by a clock rate $\\omega_c$. However, in the present example we'll make a simplifying assumption that the clock rate is significantly greater than the qubit frequency $\\omega_c\\gg\\omega$. This allows the free precession periods between the pulses $\\delta_t = t_{k+1}-t_k$ to vary continuously $\\delta_t\\in (0,1)\\frac{2\\pi}{\\omega}$.\n", "\n", "Leakage suppression is achieved by including the third energy level into the Hamiltonian and by providing the ideal $X$ gate qubit unitary as the target operation to the optimizer. Robustness to drift is achieved by including a Hamiltonian noise term corresponding to the energy variation between the first two transmon levels.\n", "\n", "In the cells below, we optimize an SFQ gate, plot its evolution and finally compare its performance against the standard gate from the previous section." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Your task (action_id=\"1827928\") has started.\n", "Your task (action_id=\"1827928\") has completed.\n", "Optimization cost: 3.173e-05\n", "Operational infidelity: 3.086e-08\n" ] } ], "source": [ "# Ideal X gate target unitary.\n", "target = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])\n", "projector = np.diag([1, 1, 0])\n", "\n", "optimization_pulse_count = 160\n", "optimization_count = 4\n", "\n", "graph = bo.Graph()\n", "\n", "a = graph.annihilation_operator(3)\n", "adag = graph.creation_operator(3)\n", "n = graph.number_operator(3)\n", "\n", "# Binary switch to mark the segments where Omega_eff is turned on.\n", "control_switch = np.tile([1.0, 0.0], optimization_pulse_count)\n", "\n", "# For convenience, encode signal pwc values in units of phase by setting the\n", "# effective duration of all pwc segments to 1; use number of segments as the effective gate duration.\n", "segment_count = len(control_switch) # SFQ + free precession segments.\n", "\n", "# omega component during the SFQ pulse.\n", "pulse_omega_signal = graph.pwc_signal(\n", " values=omega * pulse_duration * control_switch, duration=segment_count\n", ")\n", "# alpha component during the SFQ pulse.\n", "pulse_alpha_signal = graph.pwc_signal(\n", " values=alpha * pulse_duration * control_switch, duration=segment_count\n", ")\n", "# SFQ pulse.\n", "Omega_eff_signal = graph.pwc_signal(\n", " values=Omega_eff * pulse_duration * control_switch, duration=segment_count\n", ")\n", "# Total pulse controls.\n", "pulse_terms = (\n", " pulse_omega_signal * n\n", " + pulse_alpha_signal / 2 * (n @ n - n)\n", " + Omega_eff_signal * (a + adag) / 2\n", ")\n", "\n", "# Define free precession durations to be optimization variable.\n", "free_durations = graph.optimization_variable(\n", " count=optimization_pulse_count,\n", " lower_bound=0.0, # Min free precession duration.\n", " upper_bound=2 * np.pi / omega, # Max free precession duration.\n", " name=\"free_durations\",\n", ")\n", "# Repeat elements to match the total number of segments, then switch off during the SFQ pulse segments.\n", "free_durations = graph.repeat(free_durations, repeats=2, axis=0) * (\n", " 1.0 - control_switch\n", ")\n", "# omega free precession terms.\n", "free_omega_signal = graph.pwc_signal(\n", " values=omega * free_durations, duration=segment_count\n", ")\n", "# alpha free precession terms.\n", "free_alpha_signal = graph.pwc_signal(\n", " values=alpha * free_durations, duration=segment_count\n", ")\n", "free_precession_terms = free_omega_signal * n + free_alpha_signal / 2 * (n @ n - n)\n", "\n", "# Total hamiltonian term.\n", "hamiltonian = pulse_terms + free_precession_terms\n", "\n", "# Physical duration of the gate: pulse durations + free precession durations.\n", "gate_duration = graph.sum(free_durations) + optimization_pulse_count * pulse_duration\n", "gate_duration.name = \"gate_duration\"\n", "\n", "detuning_noise_signal = graph.pwc_signal(\n", " values=free_omega_signal.values\n", " * 1.0\n", " / graph.sum(\n", " graph.abs(free_omega_signal.values)\n", " ), # Normalized free precession phase values.\n", " duration=segment_count,\n", ")\n", "detuning_noise_term = detuning_noise_signal * np.array(\n", " [[-1.0, 0.0, 0.0], [0.0, 1.0, 0], [0.0, 0, 0.0]], dtype=\"complex128\"\n", ")\n", "\n", "# Cost.\n", "cost = graph.infidelity_pwc(\n", " hamiltonian=hamiltonian,\n", " target=graph.target(target @ projector),\n", " noise_operators=[detuning_noise_term],\n", " name=\"cost\",\n", ")\n", "# Gate infidelity.\n", "gate_infidelity = graph.infidelity_pwc(\n", " hamiltonian=hamiltonian, target=graph.target(target), name=\"gate_infidelity\"\n", ")\n", "\n", "result = bo.run_optimization(\n", " graph=graph,\n", " cost_node_name=\"cost\",\n", " output_node_names=[\"free_durations\", \"gate_duration\", \"gate_infidelity\"],\n", " optimization_count=optimization_count,\n", ")\n", "\n", "print(f\"Optimization cost: {result['cost']:.3e}\")\n", "print(f\"Operational infidelity: {result['output']['gate_infidelity']['value']:.3e}\")\n", "\n", "optimized_free_durations = result[\"output\"][\"free_durations\"][\"value\"]\n", "\n", "pulse_times[\"Q-CTRL\"] = np.arange(\n", " 0, optimization_pulse_count\n", ") * pulse_duration + np.concatenate([[0], np.cumsum(optimized_free_durations[:-1])])\n", "\n", "gate_durations[\"Q-CTRL\"] = result[\"output\"][\"gate_duration\"][\"value\"]\n", "\n", "controls[\"Q-CTRL\"] = sequence_times_to_control_format(\n", " pulse_times[\"Q-CTRL\"], gate_durations[\"Q-CTRL\"]\n", ")" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Q-CTRL gate duration: 27.09 ns\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the controls.\n", "print(f\"Q-CTRL gate duration: {gate_durations['Q-CTRL'] * 1e9:.2f} ns\")\n", "fig = plt.figure()\n", "fig.suptitle(\"Q-CTRL SFQ pulse sequence\")\n", "qv.plot_controls({\"$\\Omega(t)$\": controls[\"Q-CTRL\"][\"pulse\"]}, figure=fig)\n", "fig.set_size_inches(15, 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pulse sequence for the optimized SFQ $X$ gate. Note that using variable pulse spacing allows the optimizer to exploit more degrees of freedom in order to mitigate the effects of leakage and drift, as indicated by a more complex state evolution below. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Your task (action_id=\"1827942\") is queued.\n", "Your task (action_id=\"1827942\") has started.\n", "Your task (action_id=\"1827942\") has completed.\n" ] } ], "source": [ "initial_state = np.array([1.0, 0.0, 0.0])\n", "sample_times = np.linspace(0, gate_durations[\"Q-CTRL\"], 100)\n", "\n", "optimized_state_evolution = evolve_states(\n", " initial_state, controls[\"Q-CTRL\"], sample_times\n", ")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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l/1bYdsmVExl60RBeeXI+z7z+BL7+PgCsW7GBNf+sw2qx0mdQb2bdMqNWdXZjEjPpHBnYKOOvj9gdVr6YXUBBugMA30g5Q6/VMvQ6LQHtW8VnFUEQBEFoMSS7nfx/lpP91dc4SkoAUEdFoR83Bs8xY1CHhTbzCGunpcYtLVGrCHabQkt+0RRmOtjwuYEdv5jITXKUb+84XMUlj7nTfXzz5iQLgiAIQmtgOnmKjHffx3T8OAC6wYPwv+1/aDp0aHXpCS05bmlpRLBbqjW8aBwOiZP/Wdm2wMS+P01YDM7t3caquGqeB+G9ROUGQRAEQTibJElY4uLJX7ac/D//AocDpb8/gffeg8eoka0uyC3TmHGL0WDko/mfkZ6SwSMvPEBoROteiCeC3VKtIdg9m6nYwaavjKx8y4CxQEImgyHXapn6vA6fMJFfJAiCIFy4HEYjhr37KN65k5IdO7FlZjkfkMvxuepK/G++Ebm7e/MOsp4aM26x2+wYDEaW/vI346aMbvXBrkj6bKW0HnImPqhj+A1urHizhI1fGNn+s4k9f5gYer0bF93mRnhP8eMVBEEQLhzm+ATyfl9E4Zq1SNYzTZwUPj7ohgzG56or0Hbs2IwjbB0USgWeeo/mHkaDEdFQK+fhJ2fG656MvsONpS+WsHeJmc1fG9n8tZH2Q1RcdJsb/a/QoNK2zts0giAIglAdSZIwHjxI7sLfKdm+w7lRJkPbtSu6oYPxGDoETceOyOQXXlfSjas3s2PzLtKS0ug/tD833Hlt+WMlxSX8/NVCjh+KQeepY+rMKQwcPqAZR9t4RLDbRgS0V3L7D16kHrOx+Wsj238xEbvDSuwOK78/IWPaCx6M+p9oTiEIgiC0DZIkUbJjJznf/4jpxAkAZGo1+kkT8Z0xHXV4eDOPsPl5eXsxaeoEjh86gcVirfDYb9//gUKp5NWP55KckMJnb39FWGQYIeHBzTTaxiOC3TYmtJuSWW95Mu1FHbt/N7PpayNJB2z8/EAR2fF2pr2oE3V6BUEQhFbNHBtH5qefYdizFwCFXo/3FVPxnjYVpY9PM4+u5eg7qDcASXFJWHILyrebTWYO7DrI0689hkaroUOX9vTq34OdW3YzbdZlzTXcRiOC3TZK6yFn5C1ujLhZy7YFJn66v4h/3zWQn2rnhk/0KNUi4BUEQRBcI9nt2AsKUPr6Nsv1bbm5ZH/7PQUrVoLDgVynw2/29XhPuxy5VtssY2ouxmIDbzz/TvnXI0YPY8TYYbU6NjM9C7lCTmDImQVuYRGhnDp+uvzrT9/8guTEVDLTMxkxZhhDLxrccINvYiLYbeNkMhnDb3DDO0TOF7ML2bnQTEFGPncu8MLN68LLXxIEQRBqR5IkzKdOY4qJwXzqFKaTpzCfjkUym/GZOYOAO29vkrJdZeMoXLOG/H+WO9v5KhR4X3kFfjfORunl1ehjaIncPNx5/KWH63Ss2WxB61bxw4HWXYvJZC7/+u7H7qjX+FoSEexeILqP1/DwSm8+nl7AiQ1W3p6cz71/eOEdIsqUCYIgCBVJkkT6G29SuGp15QdlMvJ++x2ZSkXArbc02hgsqWkUrV1H4dq1WBKTyrd7DB9GwB23o46MaLRrt3UajRqT0VRhm8loRqttm02qRLB7AYnsq+KxtT58dFU+KYdtvDEmjzmLvQnrIV4GgiAIwhk5Py6gcNVqZFotHsOHoe3UCU2nDmg7dsSw/wCpL80j96efkavV+N1wfYNe215cTPobb1H835bybQovLzxHX4x+4gTcunVt0OtdiAKDA3DYHWSmZxEYHABASmIqwW1wcRqIYPeC4x+t4NHVPnw6q4DYHVbempDH7T/q6T6ubX6aEwRBEFxTuHYdOd/9AHI5oc89g8ewoRUe97xoFCFPPUHaq6+T/e13yNRqfGfNaJBrm+PiSXn+Bawpqc5Ae+QI9OPGohvQH5lShCyustvtOOwOHA4HkuTAarEiV8jRaDX0GdiLZYtXct2tM0lJTOXQ3sM8/Pz9zT3kRiE6qJVqbR3U6stqkvj+rkL2LDYjV8C173oy8paKpckcdomEvTY0HjJCu4k3GUEQhLbOePgISY88hmS1EjjnbnymX3XefQtWriL9jbcACLxvDj5XXlGvaxdt2kza/DeRjEY0HTsQ9tKLqILb5kxjQ6hN3LL8j5WsWPJvhW2XXDmRKVdNpqS4hJ++XMiJwzHoPN2ZOvPSNltnVwS7pS60YBfA4ZD4a24Jq94xADDpYXcmPeLOsfUWDi23cPhfM8XZzpfHRbe7MX2eB2p3UcVBEAShLbKkpZE4537s+fl4T72cwAfuq3EBWv5ff5Px3gcABD/+KF6TJ7l8XcnhIOe7H8hZ8BMAnmPHEPzowxdcdQVXXYhxS12JYLdUdS8am91BVl4xFquNtvhkmYslSnIdVT4mV4CxAA4tlkjbJeemT72IHqhq4hEKgiAIjcleXELifQ9gSUjAfeAAwl97BZmidguYcxf9QdYnn4JSScTbb+Leq2etr+uwWEh7aR7FW7eBXE7AHbfhM+PqJqny0NqJYLf2xL3pWsjKK8ZdqyLYz7PN/gIaCx1kx9lx2EGjk+HmJcPNS45SI2EqseMbaOB4dzNvjs9jypM6Jj/qjkLZNp8LQRCEC4k1K5vUF+diSUhAHRVF6PPP1TrQBfC9+ips6enk/bGE1BfmEvXJR6iCg2o8TrLbSXv5VYq3bkOu9yT0uWfRDehfn29FEKokCq3WgsVqQ6/TttlAF8BNLye0h5Lw3kqCuyjxClagdpMhl8tx91TRobsnncbIcdjhn1dKePeSfCzGtjjPLQiCcOEwHDhIwl13Yzp2HGVgAGGvvozCQ+fyeQLuvhP3Af2x5+eT8uzzOIzGaveXHA7S579J8ZYtyD08iHj7TRHoCo1GBLu1IEGbDnTLKJSy887WKhVy3H3lPPCPN17Bck5vt3JgmbnKfRtKfqodc4kIqAVBEBqaJEnkLf6DpEcew56Xj3u/vkR99gnqkJA6nU+mUBD6/LOowsMxx8aS9up8JEfV6XGSJJHx/ocUrlmLTKsl/PVX0HboUJ9vRxCqJYJdwSVdL1Yz4UF3APb/1fDBriRJHFtv4cMr83mqSw4fTM3D4RABryAIQkNxmEykvfo6mR9/Cg4HPrNmEv7G6yi9vet1XoWnJ+HzXkKu01G8ZYuzfNk5JEki6/MvKfj7H2RqNeGvvIxb9+71uq4g1ETk7Aou63u5hkVPFnPkXwsWo4Tarf6z3narxJ4/zKz+wEDyQVv59tidNnYvMjN4pliVKwiCUF+WlBRSX3gJc2wsMq2WkMcfxXP0xQ12fnVkBKHPP0vyU8+Qs+AnLKmpKPR65FotMjcttoxMCpavAIWC0Befx71f3wa7tiCcjwh2BZf5RSqI6q8kYa+NY+ss9Lm0fg0pchLtvHdZHtlxzlte+kA5o+9yQ6WRsfiZYv56qZh+0zSoNG0/lUQQBKGxFG3ZSvrr83GUGFCFhxE290U07aIb/Dq6QQMJvPtOMj/+lKJ16yvvIJcT+sxTeAwd0uDXFoSqiGC3jfvwtU+JOXoSALlcjq+/D+MuHcPIscPrdd6+l2tI2Gtj/1/mege7fzxbTHacg8AOCiY86M6Qa7SotDLsNoktPxhJP2Fn01dGxs1xr9d1BEEQLkSS3U7219+S++tCADxGjST48UdR6FxfiFZbPtOvQtO5M5akJCSTCYfJhMNoQrKY0Q0ZjK6/WIwmNB0R7LZxSfHJXHLlJEaOHYbFYmXdig389t1iotpHEhEdXufz9p2q4c+5JRxcYcZulVCoKs+6phyx8e97JVz6pI7ADlW/1E5vt7J3iRmVGzy03Bvv0DPlbhRKGVfM9eCzawpY8UYJw2drcfMSaeaCIAi1ZcvNI23eqxj272/yOrbuvXq6VHNXEBqLiBzasKyMbIwGI+07t0Pvrcc/0I/JV0xEkiSS45Prde7gzkpCuiow5EnEbLZWelySJH6cU8jOX818MbuwyjJlkiSx6KkiACbc714h0C3Te4qaDsNUlORK/PueoV5jFgRBuJDYi4tJvO9+DPv3o/DxIeLtN/CdOeOCqC4kCGcTwW4bllQa0IZFhpZvy8/NB8DTy7Pe5+871Zm+sK+KqgwHl1lI2ONcaJZy2MbiZ4or7bN7sZn43Tb0QfLyCg/nkslkXPWyBwBrPzaQn2qv97gFQRAuBBnvf4g1LR1Nxw5Ef/Ep7n36NPeQBKFZiDSGOrjbM7NZrvtpkWttAZPikvDy0eOpdwaLWRnZLF6wFP9AP7r06MzhfUdY8vNfSJLE+MvGMnz0UJfO32+qhhVvGDjwt5lr3vZArnDOFjgcEn/Pcwa3I27Ssv1nE5u+NNJttLo8QLaaJJa+4Nzn8md1aD3O/7mr/RAVfadq2P+XmX9eLWH2R3qXxtkW5SbZST5kQ+crxy9Sjj5YjlwuZmsEQXAqXLuOorXrkGm1hD7/LEo/v+YekiA0GxHstmFJ8SkU5hfxyG1PIjkcSEDvAb24+Z7ZyBVy/vj5L+5/6m7c3N1447l36DOgFzrP2i9YCO+txC9KTk6Cg7idVjoMUwOw5w8zKUfs+ITLmfW2J6Hdlfz+RDE/zCkksp8vvhEK1n9qIDfRQVgPBcNvqLms2LQXdBxcZmbrjybG3etOSNfW/9K1WyUsRgk3ffU3WCRJIuWwjVNbrZzebuX0Nit5KRWLtStU4BMuxy9KQb+pGobf6CaqVwjCBcqankHGex8AEDjnbtThdV+fIQhtQeuPGJqBqzOszSUpIZmxl1zMiLHDUKlU6L31yOXOwCo2Jo6QsCC8fb0B6N6nK8cOn2DgsNqvkJXJZPS9XMPaj4zs+8tMh2Fq7DaJf14pAWDK4zpUGhlj7nbj+HoLh1Za+OZ/hdz+o54Vbznzb6965cyMcHWCOysZcbMbm782suipYuYs8qrVcS1RcbaDTd8Y2fiFEUO+gylP6Jj4oHuVi/yy4uz8/EAhx9dXzIt285YR2VeJqUgiN9FOUZZEdpyD7DgHJzZY+fddA1Oe0DH0Om2V5xUEoW2S7HbS5r+Bo6QEjxHD8ZpySXMPSRCanQh226jszBwMxQa69OhMQFBApccL8gvx8vEq/9rLx4uC3AKXr9NvqjPY3f+3memverDjFxOZp+wEtFcwbLZzxlYmk3Hjp3rmDc/l9HYr88fkYSqU6D5BTfdxtS9bdulT7uz6zcTRNRa+va2Qm7/Qt6pALu24jXWfGNjxiwmr6cz2v14qYe8SM7M/8iSqvwoAh11i/adG/nq5GIsB3H1k9JqsocNQFR2GqQjuoqiQtmAxSOQm2Uncb2PlWyWkHbez4N4iVr1j4NKndAyaoWm1Hw4EQai93N9+x3jgIAofH4IeeUgsRhMERLDbZpUtTotsF9Go12k3RIU+yJnKEL/bxrLXnbO6lz6lqxCIevjL+d83et67NJ+8ZAcyOUx/xcOla3kFKZizyIuPry5g9yIzNksht36rR6luuW/mxkIH+/8ys2OhiRMbzszO9pyoZuy9zkV5Pz9QSPIhG/PH5DHuXncGXKVh4aNFxO92LvAbOEPDzPmeeAacP91B7S4juIuS4C5KBl6tYfdiM8teLSHztJ3vbi9k5ZsKLnlcx8CrRdArCG2VKeYk2d9+D0Dw44/Wu/2vILQVIthto5LikvAL8D1vDq6Xt56CvDMzuQV5BUS1j3T5OnK5M5Vh01dGvr29kNxEByFdFQyaUXnGtvNINVOe1LHs1RJG3epGaDfXX34dh6u5/09vPrwqn/1/mfn8ugLuWOCFSttyAjibReLIagu7fjNxcLm5fBZX5QZDr9Uy9h53gruc+d6f3ebHP68Us/ZjI2s+MLDmA2eKh3eonOve86TXJa417ZArZAyeqWXAVRp2/GJi+fwS0mPsfHtbIcteVzDlcXcGztCiULac50wQWgpLcjIlu/cgWW0oPHTIdTrkHjoUOh2q8PBGbcRQH5aUVFLnvQo2G97TpuIxZHBzD0kQWgyZJEmVC6BegGISM+kcWXUubnxaLtEhvk08osZlt9t55Yn53P/0PeUL1B5+/v5qF6id73k4tt7CB1Pzy7++fYGe/tOqXnQmSRLJB22E9lDWK9hK3G/lg2n5lORKdBur4q5fvFG7N2/wZix0sOkrI+s+NlKYeWYBWacRKgbN1NL/Cg063/PPzsbvsbLg3iJSDtsYdasbV76kq3HxWm3YrRI7fjGx4q2S8pbMAR0UDL1Oi3+0Ar9IBX5RcvRBoqKDcOGR7HaMR45SvG07Jdu2YUlMOv/OSiXu/friOXIEHsOHtYgKB5IkUbBsBZmffIpkMqGOiiLq04+Qa2te+Cu0btXFLUJFItgtdaEFuwCH9h5myS9/IzkcjL90LCPGDqt2//M9D3arxOMdsjHkSUT0UfLUZp8myRNLOWLj/cvzKMqS6DxKxZxFzRPwFmU5WP+ZgQ2fGzEWOH+dQropGDJLy8AZWvwiKzfLOB+HXaI4V0JfTcpCXdmtEjsXmljxpoGs2Mr1ipVqiBqgYurzOjqPVDf49QWhJXFYLOQv+ZPchb9hz88v3y738EA3aCAKH28cJSU4ikuwl5TgKCzCHB8PjtIPsjIZ2m7d8LxoJPqxY1D6+zf592DLzSX9rXcp2b4dAM8xowl64D4UelGe8UIggt3aE8FuqQsx2HVVdc/D708WseEzI/cu8abbmKYLlNJP2Hjv8nwK0hx0HaPint+8myylwW6V+HNuCRu/NGApbe7WaYSKyY+6022cusUuDLHbJPb9aSZhr43cJDs5iXZyEuwUZ595K+g1Wc0VL3nUKdVEEFoyyeGgcM1asr/5Dlums2a6KjQUj+HD8Bg+DLeePZApq37d2/LzKdm2naLNWzDs2YNkLc3Dl8lw798P/fhxeI4aidy96iY5DfY9SBLFm/8j4933sRcUIPfwIOiB+9CPG9uo1xVaFhHs1p4IdkuJYLdm1T0PdpuEIU+qdhFVY0mPsfHuJfkUZjroOVHNnb94NfqiNYdD4rvbC9n1m7N7XM9JaiY/4l5ea7g1MhY4WP+5kX/fNWAulpDJYfgNWi57WldlK2dBaE0kScKwezdZX3yF+XQsAOr27Qi4/TZ0gwe5/OHUYTRSsmMnhevWU7x9B9icC0plGg2eY0YTePedKDzr36mywvfgcFCybTs5P/2C6fhxANz79yP4icdQBVSuuiO0bSLYrT0R7JYSwW7NWvLzkHLUxruX5FGSK9H3cg23fd94ZckkSWLho8Vs/MKIxkPGnEVedBrReoPccxVmOVj2Wgn/fWPEYQeZDEJ7KGk/ROUsfTZUhV+UvMXOXAvCuUwxMWR9/iWGffsBUAYG4H/LzejHj0OmqP8HOXthIUWbNlO4ei3GQ4cAUAUHE/L8s7h17VLv80t2O0UbNpLzy69YYuMAUHh54XfjbLynTUUmb/pJBqH5iWC39kSwW0oEuzVr6c9D0gEr716WjzFfYuDVGm75Sl9tma2sWBs7fjWRetTO8Bu19JxYu6oHf88rZvl8A0o1zPnDm64Xt51A92zpMTb+eqmEg8vN2Cv2tMA3Us7U5zwYPEsjgl6hxbKkpJL9zbcUrd8AOPNx/a67Fu8rpyHXuFblpNbXTEom7dXXMJ2IAaWSwLvvxPuKaXX6PZHsdgrXrSfnhx+xpqQCoPT3x2fmDLwvvQS5m1tDD19oRUSwW3si2C0lgt2atYbnIX63lfen5mMqkug7VUPfy9T4RijwjVTgHSrHUiKx5w8z238xcXpbxQhuyLVaZrzuUW3FhLUfGVj0VDFyBdz+oxd9L2+cP5gticUokbDXSux2Z7vi2B1WSvKcbxudRqq49l3PNtG+WWg7bLm55Pz0C/l//wM2GzKVCu+rrsTv2llNsnjLYbGQ9dkX5C/9EwDP0RcT9MhDtS5bJkkSxf9tIfvb77HExwOgCgnB99pr0E8cj1zdNj9gC64RwW7tiWC3lAh2a9ZanodTWy18eGV++aKxMnIFyOSUz1Kq3aHfNC1+UXJWv2fAagJ9kJxr3/WsFMRKksS2H038OKcIgBs/82TY9RfmrIrDIbHjZxN/PFtMcY6EXAnj73NnyhM6NDoxyys0H0tqGrkLf6Nw5Srn4jGZDP3ECfjffBOqoKYPCgo3bCTjrXdwGAwoAwJw69UTdWQE6shI1BHhqIKDQQLJbgOrFclmx5yQQM53P2A6cQIAZVAQ/jfdgH7C+AZJuRDaDhHs1p4IdkuJYLdmrel5SD5kZdfvZme1gQQ7uUkOCtKdJYM6X6Ri6HVa+k3VoPV0zuJmnLTx45yi8tneftM0+EXKyY53kBVnJzvejrnY+asyY74HY+9p3NXWrUFJroM/5xbz37cmJAl8I+Tc+4e3mOUVmpzpdCy5v/xK0YaN5aXBPEaOwP/mm9C0b9esY7MkJZM692XMsbEuHafw8cFv9nV4XTpFzOQKVRLBbu2JYLeUCHZr1tqfB6tZwmaScPOqOk3B4ZDY+IWRpS8UV5oVBnDzlnHJozomPCAC3bPF7bLyy0NFJB2wEd5byZMbfBptcaAgnE1yOMj8+FPylyx1blAo0I8fi+81s9BERTXr2M4m2e2Yjp/AkpSEJTGp/L/WrCxkCjkyhRJUSmQKJXI3N/QTx+NzxTSRkytUSwS7tdcqgt2S4hJ+/mohxw/FoPPUMXXmFAYOH1BpP6vVxuIFSzi4+xB2u532ndox65ar8fb1rvEaItit2YXyPGTF2dn6gxGthwz/dgr8o53/3H1kYjHWeZiKHcwblktOvINLn9Zx2VMts6Wq0HZIkkTm+x+S/9ffyFQqvC6/FN8ZM5olXUEQmoMIdmuvVdxv/O37P1Aolbz68VySE1L47O2vCIsMIyQ8uMJ+G1dtIu5kPE+++hhublp++eZ3fv9xCbc/cEszjVxojQLaKZj2gkdzD6NV0XrIufETPe9OyWfFGyX0maImoo+quYcltFGSJJH54cflgW7YKy+jG1h5AkQQBAGgxRfnM5vMHNh1kMumT0aj1dChS3t69e/Bzi27K+2bk5VLt15d0Xt5olKr6D+0L+nJ6c0wakG48HQepWb0XW44bPD9XUXYLC3+ppHQCkmSRNbHn5K/9E9noPvyXBHoCoJQrRYf7GamZyFXyAkMOTNVHxYRWmUQO+ziIcSejKMgrwCL2cLurXvo3qdrUw5XEC5oV7zoQUB7BSmHbax4o6S5hyO0MZIkkfXZF+T9sQSUSkLnvoBu8KDmHpYgCC1ci09jMJstaN20FbZp3bWYTOZK+wYE++Pj682z989FLpcTGhHCjBuvOu+5t6zbxpYN2wC4/JbrGnbgLcSHr31KzNGTAMjlcnz9fRh36RhGjh3ezCMT2iKNTsYNn3jy7iX5rHzLQO9LNUT1E+kMQv1JdjtZn35eHuiGvfg8HkOHNPewBEFoBVp8sKvRqDEZTRW2mYxmtNrKxfx/+34xNpuN1z99GbVGw9pl6/j0zS95dO6DVZ57xNhhjBg7DHAmerdFSfHJXHLlJEaOHYbFYmXdig389t1iotpHEhEd3tzDE9qgTiPUjLnHjXUfG/n+zkKe2uyLSiMW9gl1Z83MJG3eqxgPHwGFgtDnnsFj+LDmHpYgCK1Ei09jCAwOwGF3kJmeVb4tJTGV4HMWpwGkJKQyZNRgdB46VColF00YRUJsIsVFxU055BYjKyMbo8FI+87t0Hvr8Q/0Y/IVE5EkieT45OYentCGTXveg8AOCtKO2Xn/snwS9llrPkgQqlC8fQfxd9yF8fARlP7+RLz9Jp6jRjb3sARBaEVafLCr0WroM7AXyxavxGwyExsTx6G9hxk8YmClfSPbR7Dzv10YDUbsNjub127By0ePh+eFubI+qTSgDYsMLd+Wn5sPgKeXZ3MMSbhAqN1l3PK1Hg9/Gae3W5l/cR4/3F1IQbq9uYcmtBKSzUbmZ1+Q8vSzOAqL0A0eRNQXn+Leu1dzD00QhFamxacxAMy8eTo/fbmQp+e8gM7TnVk3TyckPJhTJ2L59M0vePur1wG48tqpLPpxCS89+hp2u42Q8BBua4SyYyfGTmjwc9ZGl3WrXdo/KS4JLx89nnpnsJ+Vkc3iBUvxD/SjS4/OfPneN5w8dpouPTpx6/03N8KIhQtZ9AAVL+33Y/kbBtZ/amDbAhN7l5qZ/Ig74+51R6UVqQ1C1cyJiaTPfxPTseMgl+N/6y34zpqJTN7i52cEQWiBWkVTiabgSlOJ1hLsfvT6Z8QcPYlKrUJyOJCA3gN6ccU1l+Hj58PJY6cwGc3s/G9XrYLdC6WphNDwMk/ZWPxMMQeXWwDoOkbFnEXeKNUi4BXOkOx28hb9QfY33yJZrSgDAgh57mnce/Zs7qEJQosjmkrUXquY2W1pXA06m0tSQjJjL7mYEWOHoVKp0HvrkZ81M9KpW0dOHjvVjCMULhSBHZXcvdCbY+stfHdbIcfXW1lwbxE3fe4putIJAFgSk0h74y1MR48CoJ88icB77kLhcWGmoQlCS2U0GPlo/mekp2TwyAsPEBoR0txDqpEIdtuo7MwcDMUGuvToTEBQQHMPRxAA6DZGzT2LvHhnch47fjHhFynn8mdFMHMhkySJvMVLyP7qaySLBaWfH0GPPCTKiglCC6VWq7nrkdtZ+svfzT2UWhMJUG1U2eK0yHYRzTwSQagoqp+K2773QiaH5fMN/PedsbmHJDSTsm5oWZ98imSxoJ80gehvvhSBriC0YAqlonwtUGshZnbbqKS4JPwCfNF56pp7KIJQSa/JGq5915OfHyjilweL8A6V03Ni5drZQtsl2e1kvPseBctXglJJyNNPoh99cXMPSxDalI2rN7Nj8y7SktLoP7Q/N9x5bfljJcUl/PzVQo4fikHnqWPqzCkMHN42W2+LYLeNmjrrMqbOuqy5hyEI5zXqf27kJNpZ9baBr24s5MFl3kQPEN3WLgSSzUbaa/MpWr8BmUZD2EsvoBsk2v4KQkPz8vZi0tQJHD90AoulYr3z377/A4VSyasfzyU5IYXP3v6KsMgwQsKDKcwv5NuPf6x0vlvm3IDeW99Uw28wIti9gH34+qekJqZiNlt47v65/O++m2jXKbq5hyVcQKa9oCM3yc6u38y8OS6Pkf9z49KndOgDRIZVW+WwWEid+zIl27Yjd3cn7JWXce/Tu7mHJQhtUt9Bzt+tpLgkLLkF5dvNJjMHdh3k6dceQ6PV0KFLe3r178HOLbuZNusy9N56HnhmTnMNu8GJYPcCdt+Tdzf3EIQLnEwm44ZP9Gg9i/nvWyObvjSy81cTEx9yZ9wcd9TuolJDWyFJEqYjR8n65luM+w8g13sS/vpruHXt0txDE4RWyVhs4I3n3yn/esToYYwYW7s22pnpWcgVcgJDzpQuC4sI5dTx07U6/tM3vyA5MZXM9ExGjBnG0IsGuzb4JtbgwW78qQSiO0Y19GkFQWijVBoZ173nyeg73VjyXDGHV1n466USNn1l5LKndQy9XotCKYLe1sqalU3h6tUUrPwXa7Jz4azCx4eIN+ejad+umUcnCK2Xm4c7j7/0cJ2ONZstaN20FbZp3bWYTOZaHX/3Y3fU6brNpcHvFX7z0fcNfUpBEC4Aod2UzFnkzYPLvInoqyQ/1cGCe4uYOzCXHb+acNhF/5vWxHDgAMlPPk3stdeT/dU3WJOTUfj64nvNTKI+/UgEuoLQjDQaNSajqcI2k9GMVts2FwrXaWb3mw+rDmglCUqKDfUakCAIF7YuF6l5cqMPexab+eeVEjJP2/nu9kJWvqXgsmd09JumQS4XM70tleHAAXK+X4Bh/37nBqUSj5Ej8Jo8Cd2ggcgUimYdnyAIEBgcgMPuIDM9i8BgZy3+lMRUgsODm3lkjaNOwe6JIzHccNf1aDTqSo+dPlG7fA9BEITzkctlDJqhpf+VGnb8YmL5/BLST9j56sZCOgxT8cBf3qi0IuBtSQwHDpLz/Y/lQa5cp8NnxnS8p01F6eXVvIMThAuU3W7HYXfgcDiQJAdWixW5Qo5Gq6HPwF4sW7yS626dSUpiKof2Hubh5+9v7iE3ijoFux27dUSr1dCxa4dKj4VGhNZ7UIIgCAAKpYzhN7gxeJaWbQtM/PNKCae3WVn5VonovNaC5Cz4iexvvgPOBLk+V10pWv0KQjNb9edqViz5t/zrXVv2cMmVE5ly1WRm3jydn75cyNNzXkDn6c6sm6cT0kZndmWSJNUqES45IYXkhBQ89R506dkZpbJtFXKIScykc2RglY/Fp+USHeLbxCNqecTzIDS3k1ssvDM5H4UKnvrPl7Dubet9qDXKX76CjLfeAbkcv9nX43P1VSLIFYQmUF3cIlRUq78UW9ZtY+F3i8q/Dgjy576n7sbb17uxxiUIglBJpxFqRv1Py+ZvTCyYU8hja3yQK0Q6Q3Mp3r6DjHfeAyDo/nvxnnp58w5IEAShCrWqxrBm2TpGjR/BKx++yKNzH8RD78GfC/9p7LEJgiBUcuVLHngFy4nfbWPjl8bmHs4Fy3jsOKkvzQOHA7/Z14tAVxCEFqtWwW5uTh7jpozG08uTyHYRzL7jWg7sPtTYYxMEQajEzUvONe94AvDn3BJyk+zNPKILjyU5mZSnn0UymdBPmojfLTc195AEQRDOq1bBruSQUKnO9KwPCPIHoCC/sHFGJQiCUI2+l2voN02DuVjilweLqOXSA6EB2LKzSX7iaewFBegGDyL4kYeQyUQqiSAILVetV3dsWb+ddp2iCY8KReehQy6XY7VYG3NsQgP48LVPiTl6EgC5XI6vvw/jLh3DyLHDm3lkglA/s97y4PgGC4f/tbB7sZlBV2trPkioM8nhoGDZcrK+/BpHcTHaLp0JfeE5ZG1ssbIgCG1Prd6lOnXryPqVG1j+h7PbhpePF1arlS3rt9Gleyci20fgrnNv1IEKdZMUn8wlV05i5NhhWCxW1q3YwG/fLSaqfSQR0eHNPTxBqDOvYAVXvezBT/cX8dtjRUT0VhLcWQRejcF08hQZ772P6dhxANwHDSTkyceRu7k188gEQRBqVqu/DPc9dTcA2Zk5JMUlkRifTHJ8Mts27GDtsvUA+Af68fxbTzfeSAWXZWVkYzQYad+5HXpvPQCTr5jI5jVbSI5PFsGu0OoNv0nLniUmjq+38tb4PO761YuOwys3uxHqxl5SQs6335O39E9wOFD6+RE45248Lr5IpC40ApvDQWxBAVaHAxnO51cGKOQy2un1qET3OUGoE5emQfwD/fAP9KPfkL7l23KyckmMSyIpPrmhxybUU9nPJCzyTKOP/Nx8ADy9PJtjSILQoORyGXf94s3XNxdwaKWF96fmc/OXegZcKVIa6kNyOChcs5asL77CnpsLcjk+06/C7+YbUeh0zT28NsXmcLA3M4s1CUmsS0omz2yucj9vjYbJ0ZFc3r4dXXy8xYcNQXBBve/5+QX44hfgS7/BfRpiPK3CgJ8WNst191w/y6X9k+KS8PLR46l3FnjPyshm8YKl+Af6ERYZyvuvfExxYTFyhZzJ0yZU+BAjCK2FRifjzl+8+O2xYjZ9ZeSrGwvJe8XBuPvcREBQB6aYGDI++BjT0aMAaLt3I+iB+9F26tjMI2tbYvLyWHTyNOsSKwa4oTod3ho1ElC27LLIYiGluIRfT5zk1xMn6ejtxWXto7m8fTu8NZpmGb8gtCYiwa0NS4pPoTC/iEduexLJ4UACeg/oxc33zEauUDB99hWER4VRmF/IG8+/Q/c+3dBoxRun0PoolDKueccDv0g5S54vYfEzxeQk2Zkx3wO5XAS8tWErKCD7q28oWL4CJAmFjw8Bd96Ofvw4ZPJaFe4RauFYTi5fHj7KxuSU8m2Rnh5MiIxkfFQ4nbwrz9pKksTxvDz+jo1nZVwCp/ILeG/vAb4+fJQ7e/Xk6s4dUYmfkSCclwh268DVGdbmkpSQzNhLLmbE2GGoVCr03nrkZ70hepXm8eq99eg8dBhKDCLYFVotmUzGxId0+IQr+OGuQjZ8ZkTtJuPKl0Tr2po4zGaSHnwYS0IiKBTOlIUbrhcpCw3ocHYOXx46wn+paQBoFAqu7NieaR3aVRngnk0mk9HN15duvr481K8Pm1PTWHjiJLszMnlrzz4WnzzNIwP7MSwkuKm+HUFoVUSw20ZlZ+ZgKDbQpUdnAoICqt03MS4JySHh4+fTRKMThMYzaIYWna+Mj6cX8O+7BoI7Kxg2W1QNqE72dz9gSUhEFR5O2Ly5aCIjm3tIbcoH+w7w/VFnJQutQsGMzh2Z3a0L/nWoZqFSKBgbEc6Y8DA2paTyzp79xBUWcu+6jVwUFsojA/oR7ik+4Alth8ViwVBswNvXu8L2tOR0QsJr9wFPBLttVNnitMh2EdXuV1Jcwo+f/8y1/5vZFMMShCbRfZyGa97x5OcHivjp/iL8oxV0GimqNFTFePQoeb8vArmckKceF4FuA9uRls73R4+jlMu5vmtnbujWBR9t/RdQymQyLg4PY1hIML+eOMlXh46wKSWVE3l5LL58Cm6i/rHQBuzbeYA/FixF56lDkiSu/d9MojtGAfDDZz/xxLxHanWeBkvyyc3Ow+FwNNTphHpKikvCL8AXnef5b0NarTa+fO9bJlw2jvad2zXh6ASh8Y36nxvj5rhht8Ln1xWQFWtr7iG1OA6zmfT5b4HDge/Mq3Hr1q25h9SmlFitvLR9FwB39OrB/f36NEigeza1QsGN3bvyx9QpdPHxJsNg5Lsjxxr0GoLQXFb9uZrHXn6YJ195lOtvv4afv1rI7q17XD5PgwW7Lz48j9efeYtTJ2Ib6pRCPUyddRkvvvPseR+XJIkFX/xC5+4dGTxyYBOOTBCazlWveNBzkpqSPIlPZhRgyBcfyM+W/d0PWJKSUEdG4HfzTc09nDbn/b0HSDcY6Orrw43duzbqtfzd3HhsYH8Afjx2grTikka9niA0Bbvdjr60VGpkuwgeeHYOW9ZtY8WSVS6dp8GC3etum0Wfgb1Z+vNfDXVKoRHFxsSxb8d+Du45zOvPvMXrz7xFalJqcw9LEBqUXCHj1m/1hPVQkB5j56ubCrDbpJoPvACcnb4Q/MRjyNUizaMh7UhLZ/Gp0yjlcl4cOrhJqiX0CwxgYlQEZrudD/YfaPTr1ZZDktifmcUbu/YwZcnfPLtlO5Ikfg+FmnnqPUhJPBOb6Dx0zHnyLtJTM0lNSqv1eWSSeMUBEJOYSefIwCofi0/LJTrEt4lH1PKI50ForXIS7cwfnUtRlsSMNzwYe/eF3d7cYbGQcMddWBKT8L1mJgF33F6v8xltNtYmJmG229EoFGgUSjQKBe4qJT39fNFeYPmjJVYrs5atJK3EwD19enFrz+5Ndu20khKm/70Cs93O1xPG0jew+gXKjelkXj7L4uL5NyGJDIOhwmNvXjSCsRFN28WzwGwmobCI1JISUotLSCkuIcto5LJ20UyMbn256tXFLa1ZckIKyQkpeOo9CIsMRS6Xl3eBPVtsTFytUzAvrHcgQRAuSH6RCq5515MvZxey4XMjo+90u6Dr72Z/8x2WxIZJXyiyWLhv/SYOZedU+bifVsttvbpzZYf2F0y72/f3HSCtpGnSF84VotNxQ7cufHX4KG/t2ccPkycgb4bmKqfy87l2+aryxhhB7u5MiopELpPx3dFjvLtnP8NDgpvsg9DG5BSe+m8bZru90mO70jPo4O1FB2+vJhmLcH5b1m1j4XeLyr8OCPLnvqfurnJfV9Ya1flVZigxcOzQCQryCgDw8vaiW+8uuOsu7BkTQRBapj6XavCNkJN12s7RNRZ6TrzwakpLkkTuz7+Q99vvDZK+UGSxcO+6jRzOySXI3Z1hIcGY7fbyf6nFJcQVFjJ/115+PHqCO3r3YEp0FIpGvqWfaTBwODuXdl56ovWeTdpJb2d6BotPNm36wrlu7tGNP0/HcSw3j39i45naoekXIO/NyEICevn78WC/PvQO8Ecuk2FzONiSmsrJ/AJ+PHaC23v1aPSxZBmNzN2+E7PdTkdvL6I8PQn10BGq07EnM4s1iUk8t3U7308af8F8IGup1ixbx6jxI5g8bQJ5ufksXrCUPxf+w013z67XeesU7G7bsJ01yzfQo0+38sYE8acTWLF0FeMuGc2w0UPrNShBEISGplDKuOg2N5a+UMKGz40tLth1SBIbklPYlJyCXCZDo1CgViic6QBKJT38fOkT4I+6jn+MJUki+8uvyP31N5DJCHr4wXpVXyiyWJizbiNHcnIJ0bnzxfixhHpUrP4iSRLrkpL59MBh4goLeXHbTr47coynBw9kQFDD3n6VJIkDWdn8euIk65KSsZdm6Hmp1fT096O3vx/9AgPoHxjQaMFvkcXC3G07AWf1hU4+3o1ynZq4KZXc17c3z2/bwUf7DzIuMhydStWkYziamwvAlOioCqkUSrmcxwb254416/n2yDEuaxdNiEfjNS+RJImXt++iwGxhWEgwH465qMLP/9L20RzLzeVEXj6fHjzM/f36NNpYhJrl5uQxbspoPL088fTyZPYd1/La02/W+7x1CnbXLFvP4y8/XKnbltlkZv5z74hgVxCEFmnETW4se62EI/9ayDxlI7Bj82dy2R0O1iQm8/Xho5wuKKh2X41CQf/AAAYHBzE0JKjGzltlJIeDjPc/pODvf0ChIOTpJ9GPGV3nMReaLcxZt4GjuXmE6nR8MX5MlQGLTCZjXGQEo8PDWBmfyOeHDhNfWMRDG//j1ymTKgXHdWGx21kZn8ivJ2I4kZcPgEImo39gAIlFRWQbTWxJTWNLaeeyKdFRvDhscKPMLr+1Zx/pBgPdmyF94VyXtItiYcxJjuTk8u2RY9zbt3eTXv9oTh4A3fwqr/MYEBTIxKgI/k1I4r19B5g/anijjWPxydNsSU1Dr1bzwtDBlX5fdCoVLw8fym2r1/HD0eOMDA2hfwN/EBNqT3JIqM76YBYQ5A9AQX5h+eRqXdTtnV4mw2wyVwp2TSYzbTELTobz02FT3gpraSRJapM/W+HC4uEnZ9AMLVt/NLHhSyMz53s221isDgcr4xP49vAxEoqKAAhyd2NW507oNWpnKoDNjtnhIN9kYk9mFqfyC9iWls62tHTe3wdhHjqmtItmSnQUkfqqvxfJZiNt/psUrV2HTK0m9MXn8Rg6pM7jLjRbuGfdBo7l5hHmoePz8WMIqaGtsEIu59L2zkVAT2zeysbkFJ7dso0vJoxFWY+g02y3c++6jezNzALAS6NmescOTO/UkWCdO5IkkV5i4GB2Dgeys/nrdBzL4xNQKeQ8O2RQg+ayrktK5p/YeDQKBS8NH9os6Qtnk8tkPDawHzevWsuPx04wIjSEfk20WM1osxFXWIhCJqPTefJgH+jXl03JqaxJTGJXegaDgoMafByJhUW8u3c/AE8NHkCAe9Ud6/oE+HNL9258feQoz2/bwS9TJuEpqpM0my3rt9OuUzThUaHoPHTI5XKsFmu9zlmnagyH9x1hyc9/ERIejLeP84Wcl1dAenI6V143lZ79Gj8Hp6FVt6oxKSOPYD89KuWFm8tjstjIyS8mLNC7uYciCPWSdNDKqyPy0OplvHbCD61H0wclJ3LzeHH7TmJKZyJDdTpu6dGNy9pHV5umkG00sjM9g53pGWxNTSfHZCp/rKefL5e2i+bS9tHlt6wlh4PUF1+i+L8tyNzcCH/lZdz71v02bZHFwt1rnYFuuIcHn48fQ7CL6zTyzWauWbaKLKORO3r14M7ePes0FrvDwVP/bWNtUjIBbm7c06cXk6Ij0VTz/O3JyOS+9Zsw2+3M6NSRJwb1b5BJjGyjkVnLVpFvNvPYwH5c06Vzvc/ZUN7Zs4+fjsfgo9Hw4yUTavxgcra4gkL+TUhkZudO+Ghrn/azPzOLW1evo4uPNz9PmXTe/b4+fJRPDhyig5cXP0+ZWK8PPueyORzc+u9aDufkckl0FPNGVH/H2epwcMuqNRzLzePSdtG8NLzuHwibSlusxvDha5+SnJCM0eB8b/Py8aKwoJCxl4ymS/dORLaPqNPasFoHu2eXgujSszNyuZyE04kU5J9ZoBbVIRJ5M3+aravqXjR5RQasVjv+Ph7Nsqq1OUmShNlqJyuvGF+9Gzq3lpXnKAh18dbEPE5vs3LNOx5cfHvTLaq12u18c+QYXx8+il2SCNXpuKN3DyZHR7k8E2h3ONiTmcWyuHjWJSZjsDk7xPXw8+WbieNQyuUUb9lKynMvIPfwIHz+a7h1q/ut9WKrlTlrN3A4J5cwDx1fThhLkHvdnrud6Rncs3YDMpmML8ePcbk8liRJvLVnH7+eOIlOpeLrCWNrnR+7Iy2dBzdsxuJwcH3XzjzUv2+9Al5Jknho439sTkllSHAQH429uEX9nbA5HNy/fhM70jPo4uPN1xPH1aqVcLHVyjWl5dO6+vrw+fgxeNQy7/fn4zG8vWcfV3Roz3NDB513P7Pdzox/VpBSXNLgHxK+PHSEzw4eJsjdjYWXTq7VTG1cQSHXr/gXs93OHb16EK3X46ZU4q5S4q5UEqn3rPVz0BTaYrBbJjszh6S4JBLjk0mOTyYpPgVDibN8nX+gH8+/9bRL56tVsFtVKYj7n74HL5+2U6ajuheNJElk5hVjMlu50IoSywClQo63pwh0hbZj92ITX99cSHAXBc/v8m2SFKVzZ3Nnde7Iff361CrwqInRZmNjcgof7DtAhsHIA/36cEO3LiTOuR/T8eMEzrkbn+lX1fn8BquVe9dv4kBWtjNHd0LNqQs1+XDfQb47eowQnbvLt41/OHqc9/cdQCWX8+GYi1y+Bf5fSiqPbNqCzeHg5u7duLdvrzq/Bv44dZpXduzGU61i4aWT6/wBoDEVmi3cuGo1SUXFjIsMZ/7I4TV+v3O37eSv2LjyrwcEBvDBmItqVSrs2S3bWRGfwNODBzC9U8dq992QlMIjm/7DS61m1VVTG6QawtGcXG5etQa7JPHpuNEMduH18duJk8zfvbfKx4Ld3flj6pRq7x40pbYc7FYlJyuXxLgkkuKTmTrzUpeOrdW7bFWlIJb++ne9S0G0FjKZjCDf5svtEwShYfWbqsErRE76CTvHN1jpNqZx8/MWxZzijd17sUsSYR46Xhg6uEGrEbgplUyOjkKvVnPf+k18dvAwQwrz4fhxFF5eeE25pM7nNtpsPLBhMweysglyd+ez8aPrHegC3NWnJ7syMjiSk8urO3fz6ohhtQo4V8Yn8P4+Z3ewucOG1CnXc2RYKK+PHMYTm7fy3dFj+Ltpubar67OKSUXFvLNnPwBPDBzQIgNdAL1GzbsXj+KmlatZm5jMV4ePVlvya31SMn/FxqFRKHhj1HDm7djNnswsnvpvG29cNKLGuxBllRi6+9bchOji8FCi9Z7EFxZxMDun3r8XBquVZ7Zswy5JXNe1s0uBLsCMzh1RyGUcycnFYLVhsNkw2mycLigg3WBgZXwC0zq0r9cYhbrxC/DFL8CXfoNdT8Wq1X2zs0tBRLaLYPYd13Jg9yGXLyYIgtASKFQyLrrVuVhlw2eGGvaun2KrlXf37scuSczq0omFl05u8LJbZYaHhnBpuyjMdjuv7j+EBPhcfRVyt6oX5tTEZLPx0IbN7M3MIsDNjc/HjybMw6NBxqqSy3llxFDclEr+TUjiw/0HWZuYxN6MTOIKCskzmSkwm0ksLOJQdjabklP59UQML5SW9nqwfx8m1aPr1ZiIcOYOc+ZlfnrwMPlms0vHS5LE3G07MdpsTIiMYHIL78DVzkvPKyOHIQM+O3iYdUnJVe6XYzQxb8duAO7r25uRYaF8PPZivNRqNqWk8tK2nTiquSFcbLWSUFiESi6vVZMGmUzG8NAQALalpbv+jZ3jrT37SCwqpqO3V50qUMhkMqZ36sjzQwfz+qjhfDDmIr6cMJZH+vcD4KdjJ0Sr41aoVsFudaUgBEEQWqORt7ihUEvs3JtPZnz9VvpW59/4REx2OwMCA3h8YP8GSVuozsMD+uGtVHDYU8+GXr3wnja1TuexORw8sXkruzIy8dNq+Wz8aCI8G/YOV4SnJ48P7A/A90eP8/jmrdy+Zj1X/7OC8YuXMnbRUq78ezk3r1rLQxs38+bufdgcDq7t0onZXbvU+/qXtItiSHAQJVYr3x055tKx29LS2ZeVhY9Gw5ODB7SKaj2jwkK5rzQAfOa/bXyy/xAG65nXviRJvLxjF/lmM4ODg5jVpRMAHby9eH/MRbgplSyPT+CtPfvOG/Adz3WWHOvk7VXrmtDDQoKB+ge7qxOS+PO0c0b61RHDGjTdYGJUBP5uWk4XFLI9PaPBzis0jVq/6zZGKYjaKiku4eevFnL8UAw6Tx1TZ05h4PABVe6bFJ/M4gVLSYpPRqNRM3HqeEZPuqhJxikIQuth9bSQ+sIREvyymLXCnYfG9GJK58gGXREOsPR0LABXdGyaW5/eGg23xsfzdngEPw8azHS5AlcLTkmSxKs7d/NfahpeGjWfjR9NtL7uNS6rc3n7aJRyGXszs8gzmckzmcgzm8kzm5EkZzkxb40GL7UaL42G7n4+XNOlc4MFl/f17c2OlatZeOIk13TpXOvqEt8cdgbHs7t1wVvTetYz3Ni9KxkGAwtjTvH1kaP8GRvLnD69uKx9O/48HcvmlFQ81SpeHDa4wkK7Xv5+vH3RCB7YsJmFJ07S1cebqVXczj+a40xhqKq+7vn0DwxAo1BwPDePHKMJPzety99XWkkJr+zcBThn/Ru69a9KoWBW5058fOAQPx07UR6gC61DrYLdTt06sn7lBpb/caYUhNVqZcv6bfUqBVFbv33/Bwqlklc/nktyQgqfvf0VYZFhhIRXfLEVFxXzyRtfcNX10+g7uA92m4383OqLtAuCcOHZnJLK3G07yfNz3rou1BuYu2cH3xw/wh19ejAxqmGC3pi8PI7k5OKhUjE2Irze56sN0+lY+q9aRf9Jk9kbHs5ru/bw9kUjXAoOvzx0pHyG7P3Ro2jv1XiLkWUymbNWcLvoRrtGdbr5+TIhMoLViUl8cegwzw8dXOMx+zKz2JeVhadaxdWdq1+A1dLIZDIeHzSASdFRvL1nH0dycpm7fRe/njhJYlExAE8Oqjr/eEhIMI8N7MerO/ew6OTpKoPdYy7k65bRKpX0Cwxge1o6O9LTXX4t2B0OntuygyKLlYvCQplRw6K4upreqQNfHz7KtrR0TuXn09Hbu1GuIzS8Wr2b3/fU3cz/7BWef+tpbplzAwOH96dzt45s27CDT978gifvfo6XHn21UQZoNpk5sOsgl02fjEaroUOX9vTq34OdW3ZX2nfdio10692FQSMGoFIp0bppCQ5r+ELVgiC0Tiabjfm79vDghs3kmc0MCgrkm16T6bG0G5osLUklxTy3dQcz/1nJkZycel9v6WnnavYp7aJqtYq9IeT+/Asy4EEPd3RKJRuTU1iTWHV+ZlWWnDrN54eOIJfJeG3kMHr5+zfeYFuIe/r0QiGT8XdsPHEFNafnfXP4KACzOndqUaWoXNEnwJ/vJo3n5eFDCHRz40RePkabjYlREUyOjjrvcVPaRaNTKjmSk0t8YeXnqqxzWnc/H5fGM7wslSHV9VSG744eZ19WFn5aLc8PHdRoKSVeGg2Xt28HOMurCY3ni3e/4fC+IzgcjgY5n0vvvv6BfvgH+tFvSN/ybWeXgmgMmelZyBVyAkPOLOgIiwjl1PHTlfaNP5VAaEQI78z9gKyMbKI7RDLjpun4+lf9S7dl3Ta2bNgGwOW3XNco4xcEoWU4mZfPU/9tI66wEKVczpw+vZjdrQtymYy353fnnanBnAxNI/OKBBIoYt6O3fx8ycQ6/+E02Wwsj4sH4IomWr1tSU6maOMmUCrpPGM69+cX8tquPczbsYtQD3d6+PlVe/zmlFRe27kHgCcH9efi8LCmGHazi9R7ckWH9iw+dZpPDhzizYtGnHffY7m5bE1LR6tQtKjmEXUhL51VHxMRzk/HTpBQWMSjA/tVe4ybUsnYyHD+jo1neVwC9/TpVf5YodlCcnExGoWCdi7eDRgWGgx7nXm7Dkmqda3iQ9k5fH7wMAAvDR+Cj9b1FAhXXNu1M4tOnmJFXAJz+vSuU8qFUDONRs23H/2I1l3LkFGDGHrRYAKD694BsN736crKQLha86y2zGYL2nNeTFp3LSZT5ZWz+XkF7PxvF9NvuIKX3nsOvwBfvvvkx/Oee8TYYTz+0sM8/tLDKBStsxmGIAg1WxYbz02r1hBXWEi03pPvJ43nxu5dy/+gBrRX8uhyP7pnhNPtmUGoDSpi8vI5lF332d31SSkUWax09/Whi69rs1x1lfvrQnA48Jo4HlVgIFd16sC4yHCKrVbuXrux2u/nUHYOT27eil2SuLVn9xrro7Y1t/fqgUahYF1ScrXP07elC9mmd+rgUlexlsxNqeS2Xj14ecRQvGqRf1yWZrAiLqFCZYayFIbOPt4uN0lpp9cT5O5GntnMiby8Wh/3y/GY8jJjQ5sgjzZK78lF4aFYHA4WnTzV6Ne7UN10z2zmffQik6dN4MSRGOY9/jrvzfuIHf/twmKxuHy+Fh/haTRqTEZThW0moxltFW8yKpWS3gN6EdU+EpVaxSVXTiLuZDxGg7GphisIQgtisdt5bedunt+2A7PdzmXto1lwyUS6VhF8+kUqeHiFN6Ht1fhtcpZC+i2m7n/MljTxwjTT6dMU/LsG5HJ8r5kFOGfuXhkxjPGREZSUdkA7mJVd4TijzcZH+w9y2+p1mOx2Lm8fzd11bOHbmgW4u3Ft6Uzth/sPVlltIK6gkHWJyajkcmZ3q381iNZqYFAgQe5upJaUcOCs19PR0koM3evw4U4mkzEspLQEmQupDLEFznU5k6KarvTb9aWVQH6POYWptHOh0PDc3LSMGj+Cx+Y+xFOvPkZEdDgLv/mdZ+97kV+/+Y30lNpXxWjxwW5gcAAOu4PM9KzybSmJqQSHV/4EFxYZWvGWY8uvBNNmbE1N4+GN/7lcq1IQwNldbG9GJrEFBeSaTNgaIE8rraSE21avY9HJ06jkcp4ZMpAXhw6utvSXd6iCB5d70+5IGDjg37gk8kym8+5/PomFRezJyESrUDCpmvzHhmJJTib58afAZsNr8kTU4WcWw5XVs50YFUGJzca96zZyICsbSZLYkJTCjH9W8O2RY9gcDq7q2J5nhjRezmNLd3OPrujVavZkZLIlNa3S498dPYaEs4JEYAttINEU5DJZeV7vstJUHYBjdajEcLZhoa6VILM7HOWL6qL0Tdf4qX9gAF19fcgzm1kRn9Bk171QFeQVcHDvYY7sP4pcoaDPwN7k5eTz2jNvsnbZ+lqdo2lWTNSDRquhz8BeLFu8kutunUlKYiqH9h7m4efvr7TvkFGD+fqD77h44ihCwoJZuXQ17Tu3w829bgXVhdr7+XgM29LS+S8ljMtKE/gF15ntdtJKShqtzNP5SJLEuqRkHBJMiIposusmFxXzzt59bExOrfSYXq2mo7cX4yLDGRcRQUAtfo+LLBaO5TorIPx47DgFZgshOnfeGDWC7rX8A+wVpOCW5wM5ss2Pgt45/LLnNPeMOH+3qar8WbowbUJURKMvYLJmZZH02JPY8/JwH9CfwPvvq7SPUi7n5eFDkSFjVUIi967bSC9/P3aU1gvt4uPNk4MG0Dug7S9Gq46nWs3N3bvywf6DPLTxP0aFhXJNl04MCgokrcTAirgE5DIZN3Xv1txDbXaXtovm+6PHWZ2QxGMD+6NRKFzqnFaVIcFBKGQyDmRlU2y11vi7k1ZiwGy34++mdanddH3JZDKu79qZ57bu4KdjMVzRof0F+wGxsdhtdg7uPcz2jTs4fiSG8Kgwxl06hoHD+qMpvbN/aO9hfvz8Z8ZdOqbG87X4YBdg5s3T+enLhTw95wV0nu7Munk6IeHBnDoRy6dvfsHbX70OQJcenbh8xhQ+e/tLLGYrHTq34+Z7LoyWxs0ttaQEgIw2kDJistnYkZ6Bj0ZDF1+fJuuDLkkST2zeyuaUVN69eCQXNdHioKSiYl7duZudpYGPQjaCsZGNWybLaLPx3ZFj/HD0OBaHA3elkk7eXuRbLBSYLRSYzRRaLOzNzGJvZhZv7d5H34AAxkeF09XHh0KLlUKL2bmvxUJKcTFHc3LLZ3nKDAsJZt6IoS7XQe1/hZbhG6NZQQ4LD5/mjqFdUdbydWB1OPg71hnsNvbCNFtBAcmPP4ktIwNt926EvfQi8vP80VfK5bw0fAhymYwV8QnsSM9Ap1JxT5+eXN2pY4PXF26tru3amcSiYv6Ji2djcgobk1No76XHR6vFLklcEh1FuGfDdJFrzTp4e9HFx5sTefn8l5JK/8AA0koMaBUKous4y+qpVtPTz5cD2TnsTs9kdET174Fl1SDaNfHkAMCEqEje3L2PuMJCMgzGWtdnFmrnmfteREJi4LD+PD7rMsIiQyvt06FLB9xqeYfFpWA3LSUduVxOUGllhOOHTrDjv12EhAUz/rKxyBvpzVLnoeOOh/5XaXvHLu3LA90yo8aPYNT486+kFRqeJEmklzhbrmaUNG7r1caWXFTM45u3cCIvH3AGCJ29vejh50cvfz9GR4Sha6SZuvVJKWxOcc5wvr/vAMNDQxo1ALE5HPx8PIbPDh7GbLejUSgw2+28vGMXPfx9q6yzWV9lM8jv7NlPusH5WpkSHcX9/fpUmLm1OxwUWCzsSMtgdWIS21LT2JflrG1aHZVcTmcfb7r7+tIvMIDxkeEo6vgcPvxENOt/P0Kxr5Fvf07i9huia3XclpQ0ckwm2un19GnEmVJ7SQkpTz6NJSERdbtowl+dV2NbYKVcztxhgwnWuVNksXB7rx7417GVcFulVih4bugg7u7Tkz9OxbL45CliCwqhtCTZzT26NvMIW45L20VzIm8/y+ISytODuvr61Pl3DmBoaAgHsnPYmpZWi2C3CKDJ74SB873GR6uh0GLBYGuaBlsXkquun0a/wX1Qqc//99Zd58bcd5+t1flcCnZ//vJXRk+6mKCQQPJy8vjivW/o1LUDm9dswWQ0MXXWZa6cTmgjck1mzHY7ABmG1hvsbkpO5flt2ymyWAl2d0enUhJbUMjR3DyO5ubx+8lTTE6L5JURwxr82kabjbf27ANALZcTX1jE37FxXNmxQ4NfC5wtPV/avrM8qJ8SHcVDA/ry4radbElN47mtO/h07MX1+qN1rkyDgdd27mFTaUDfxcebxwf2p29g5XIyCrkcX62WS9pFcUm7KIqtVjYnp7I2KYksgxGv0o5aeo0aL7Uaf3c3uvn60NHLC1UDzcT7BiuZ7NeepdJRfjtxihlpEXiH1HzuJaecZRGv6Nh4tzYdZjMpz72A6UQMqpAQIt54HUUt/+Ar5HLuLW0ZK5yfv5sbd/TqwS3du7IuKYW/Y+Po5e8nGgmcZVJ0JO/tO8CW1DTCPHQAtU4XOp/hIcF8fvAw29PSkSSp2t+hsprI7byaPtgFygN84wW2SK2woIiv3vsWhUKOTC7npntm4+XdsD+Djl07oFRVDlElSSIvJ/+8JWXPx6VgNyMtk4ho5yetfTsPEt0hkrsfu4OYoyf56ctfRbB7gSpLYYDWGezaHQ4+P3SEr0sLxV8UFspLw4fgqVZTYrVyNCeXfVnZfH7wMFtS07A5HA0+4/rVoaNkGAx08fFmdrcuPLd1B58fPMLk6KhqF1TVRWxBAf/7dy1mu50QnTtPDx7I8FDnKugXhw3mmmWr2JORyfdHj/O/nt3rfT1JkvjzdBzv7t1PsdWKTqXi3r69mN6xQ62DaQ+VqjzwbUpzruzIX78fI7dLDp8/mcnj3wVX+8f3QFY2/6WmoZLLubSRxmovKSHl2ecxHjiIws+X8Lfmo6yhfq5QdyqFgknRkUyKbrrV/q2Fv5sbQ4OD2JqWzu+llUu61bPMXjdfH7zUalKKS0gqKiaympSIsjSGuqZN1JeboizYtTfL9ZuLh6eOB5+7F7lczvZNO9m2YQeTr5jQoNd48eF5vPLhi3h6VfzZGooNvPjwPD744W2XzufSX2yHQ0JR+oc35uhJuvdxJun7B/pTVFDk0oWFtiOt+Oxgt3Xl7BaaLdy3fhNfHz6KXCZjTp9evH3xyPLFDjqVikHBQdzRqwcRnh4UWazltSQbSlxBIQuOnwDgqcEDmBwdRVdfH7KMRn49cbJBr2Wx23lmy3bMdjvjIyP47dLJ5YEugK9Wy4vDnO1SPzt4uF51ZgFSiouZs24jL+/YRbHVyqiwUBZdNpmZnTs16KxxY/F1c2NsaATIYbMjnv++NVVZkgqcaSGv7XR2dryxe9dGKW5vLygk+dEnMB44iNLPj4i33kAdElLzgYLQSMpq7lpLK6jUd2ZXIZczJMTZ+XRrWuWKGGcrT2Notpld552eC21mVy6Xl6etmk1mQsIbqVNtFRMLZrMZVR1SCV2aMgoJD+a/tVvo0a8HMUdimDpzCuAsC6ETCfsXrLNndgstFow2W4PPRjaWzw4eKl+M9urIYQwOPv8v7dDgYJKKTrEtLaPBWqhKksT8XXuwORxc0aF9+Xnv79ube9Zt5Lsjx7iqY/taFXqvjU8OHCImL59wDw9eGDoI9yreNIaHhnB91878dDyGZ7Zs4+cpk+pUUeBwdg53rd2A0WbDS6PmsQH9mRwd2epWLV/fpxNr/k0ka0QaCx5px+7FJq562YOo/hWfk4UnTnIyv4AwDx3/69Hwq/VtOTkkPf4klrh4VCHBhL/5BupQEegKzWt0RBjuSiUGmw2dUkmkZ/1nWYeFhPBvQhLbUtPP26Uuz2Qm32zGXakksJnyzltDGsPG1ZvZsXkXaUlp9B/anxvuvLb8sZLiEn7+aiHHD8Wg89QxdeYUBg4fUKvzJiek8Os3v2M0GJnzxJ0NNt5FP/xR/v9//7YM9Vk5uw6HREJsImFRlRer1cSliGTarMv48r1vWLt8A0NGDSI0wnnBQ3sPE9W+6coVCS3L2cEuQHqJoUlzqPJMJiwOh8sLquwOB2sSnW2u3xs9ip7+1d8KHhoSzO8nT7E9LZ07erlWiup8VicksSsjEy+1ukIe5ZCQYIYEB7EjPYNvjxzjwf59632tnekZLDh2AoVMxrwRQ6oMdMvc27c3uzMyOZGXz/yde3h5xFCXr/fNkaMYbTYuCgvluaGD8G3kNp6NpZe/H519vIkhn5JRWcSsD+L1i/MYMF3DtOd1BLRXkmkw8Flpy9JHB/RH28Af9qzpGSQ99jjWlFTUUZGEvzEf1QVeJkxoGcraB/8TG09XP99at/mtzrDSTmi7MzKx2O2oq8jDPzuFobk+QJf9nptacBqDl7cXk6ZO4PihE1gsFRfS/fb9HyiUSl79eC7JCSl89vZXhEWGERIeTGF+Id9+XLkD7S1zbkDvrSc8KoxH5z7I3h37+ffvtVxzy4wGGW9q8pnZ/PTUDJTKMz97hVJJRHQYY6fUXGrsXC69I3fs2oHXPnkZk9GE+1llNkaMHV4h+hYuLGVpDDJAwpm321TBbp7JzDXLV2G221lx5VSXZpQPZGWTYzIR5qGjRy1uvQ0MDkQhk3E4O4cii6XedR1LrFbe2bsfgHv79a7UevS+fr3ZsWI1C0+cZFaXToTodHW+VqHZwgtbdyABt/XsXuPMtFqh4JURw7h+xb8sj09gYnQko8Jq/2k602Dgv5Q0FDIZzw5pvYEuOGtqzujUkVd27ib7pjiGDPYh5j01exab2f+XmTF3ubF94kEMNhujw8O4KNz1WYfqWFLTSHroEWxZWWg6dSL8jddQenk16DUEoT6u79qZXekZXN4+ukHOF+DuRgcvPacLCjmak1vlItYzwW7zpDDAmTSGltxFre8g5yRKUlwSltyC8u1mk5kDuw7y9GuPodFq6NClPb3692Dnlt1Mm3UZem89Dzwzp8pz2mw2lKV/a93ctKgbsMbx/U87r7ngi1+YfsOVuLk1zN8Ol5Pmjh06wQ+f/cwrT8wnL8fZGvDEkZgK0bhwYSmb2e3s4w007SK113ftIdtooshiJbHQtbzxNUnOWd3xkRG1mhnwUKno5e+HXZLYnZFZp/Ge7YtDR8gyGunp51tlPdZuvr5MiorE4nDweemsYV1IksSrO3eTaTTSy9+v1ovO2nnpuadPLwDe2bMPi732sxd/nY7DLkmMjgjDr4HerJrTlHZR9AnwJ8tk5KcO2xi8vIAh12lw2GDR2mTWpSSjkSl4dGC/Br2u5HCQ/vp8bFlZuPXsQcTbb4pAV2hxOvv4sPzKqVzegA2FygLcfee0ty7T3JUY4MzMbnOlMRiLDbzx/Dvl/7as21brYzPTs5Ar5ASWlpIFCIsIJT255u51yQkpvDfvIz549WPWr9pUq6YOrpp9x7UNFuiCizO7u7bsYeF3ixh28RBijsRgtzsT0h0OB2uWradLj6pza4S2S5Ik0kpr6/YN8OdEXn6T1dr9NyGRNYlJ5V8nFxfTpZYrgR2SxLrSFIZxLjRQGBoSzP6sbLanpTMmou6NFzIMBhaeOIkMeHLQgPPe+runTy/WJiXzT2w8s7t1qVPZo2Vx8axOTMJdqeTl4UNdqiQxq3NHlpw6TXxhEb8cj+GmWuSiOiSJpadjARqtdFpT0yqVfD5uNO/s3c9vMad47+Rept7cjjm39uDundsBCPojij3xEpc8JqFQNcxt1fylf2I8fASFry9h815C4VH32X1BaE36BQSw+ORp9mdmQRXvO81ZY7dMec6uCxMBDXp9D3cef+nhOh1rNlvQnhNMat21mEzmGo+N7hDFg8/eW6frVufzd77mxruvx81Ny+fvfF3tvnc+fKtL53ZpZnfNsnVc+7+ZTJ99BfKzcmiiO0SRkpDi0oWFtqGsxq6XWk270hmn9CaY2c0xmnh91x4AgktzdZPP6Z5VnYNZ2WQZjYTo3F1qbTm0NJdse1qGC6Ot7NvDx7A6HIyPjKi2j3y4pwdXdWyPBPxw9LjL18kzmXhj114AHhvYjwgXF5KqFAoeHdgfgK8OHyXLWHO1je1p6aSVGAjV6RhSzYK/1kalUPDEoAG8NGwIGoWCv2LjuDfhX0p8jPibPAhcE8Gy1wy8MS6PtOP1n+mxpKaR9dU3AAQ99ECt6+gKQlvQN9CZanUgOxtHFRVQytMYvJqn7BiAm6L1VmPQaNSYjKYK20xGM1ptwyyGrgudhztl0wTuOnd0Huf/5yqXZnazMrJp16ly7UiNVlPpSRMuDGUpDCEeuvIFYo1dfkySJF7ZuZsCs4WhIcGMDA3hrT37SC6ufbC7NqlsVrd2KQxluvv64KlWkVxcTFJRscvBI0BaSQlLTsciA+7oXfNCt9ndurDo5GlWJSRxf78+LnW8+i81jRKbjQFBgXW+xTgsJJiLw0PZmJzKh/sO8tLwIdXuv/SUc1b3io7tG2SxSktzaftoOvl48eimLaSU5qu/etkgPDp588NdhSTus/HGuDye2uRDYIe6LVSTHA4y3noHyWTCc8xoPEcMb8DvQBBavhCd829KhsFAbEFBhbtaJpuN1OISFDIZER7NVwmqNVRjOJ/A4AAcdgeZ6VkEBjtTRlISUwkOD262Mc2+40yliLOrRjQEl96Jvbz1ZKZl4etfcSbq9IlY/APFyuALUVppsBuq0xGscwZh1aUxmO12Fp88xaSoqDrnci6PS2Bjcgo6lYrnhgziVH4+AMnFJdUfWMohSawtTX8Y70IKAzhrQA4ODmJtYjI70tKJ8Ozo0vHgnNW1ORxMioqkfS3yL8M8PLg4PJT1SSksOnmau3r3rPW1dpTOQI8OD63XiuWH+vdja2o6y+LimdG5w3kXuOUYTWxITkEhkzG1AfP3WprOPj4smDyRzw4eItzTgwFBgRAEz2735Zv/FXJ4lYWvbi7ksTU+qDSuP+8Fy5Zj2L8fhbc3gfc3/O1CQWgN+gb4syohkf2Z2RWC3aSiYiQg3MOjwTom1sWZagwtN9i12+047A4cDgeS5MBqsSJXyNFoNfQZ2Itli1dy3a0zSUlM5dDewzz8/P3NNtaaUhfKyGRwx0ONmMYwYswwFi1YQmxMHAB5OXns2LyLP3/9m5HjxMxDa2S12zmRm8dfp+N4e88+/jh5+rxF86tSVokhROd+1syu4bznWHLqNG/v2c/XR47WabyZBgNv7nHeln90QF+Cde6El86u1jaN4UhOLhkGI0HubvSoQ+ep8lSG9JoT+c+VWlzC0tOxyGUybnehfNm1pbUmF8WcKm/NXBNJktiZ7gx2hwTX79N6hKcHs7t1AeCNXXurvK0I8Hesc2HayLBQAtybp/ZlU9Fr1Dw+aADXde1Svs1NL+d/X+vxi5aTtN/GH8/W/m5DGWtGJlmffwlA4P33igVpwgWrLJVhX1ZWhe1li9OaM4UBzp7Zbbmlx1b9uZqHb32C1f+sY9eWPTx86xOs+nM1ADNvno7VYuXpOS/w3Sc/Muvm6YQ048xudWkLZ/87uxpYbbk0szv+srEYjSY+mv8ZNquND1/7FKVSwdgpY7howkiXLy40D7vDwYf7D7IzPYPTBYXYSjvflEktKWFOn161mgksS2MI9dChV6vRKhQYbDaKrdYqS3PF5OUDcDq/oNJjNTFYrby4bSdFFisjQ0PKb8uH6nTIcOYKW+32Gj/pl83qjo0Ir9Nt9qGlgePO9EyXWwd/dfgIdkliSnSUS6uI+wcG0MXHmxN5+ayKT2Rqh5pnTU/lF5BjMhHg5kb7Blix/L8e3fgnNp6juXn8HRvHtHMqSDgkiSWnyhamVa4ucaFw85Jz+/devDk+jw2fGek8UkW/abW7iyFJEunvvIvDYMBj1Eg8L76okUcrCC1XvwDn7fX9mRUrMrSEsmPQOkqPTblqMlOumlzlYzoPHXc89L8mHtH5nZ3G0NBcTii7fMYUJk0dT3pKBg7JQUhYMJpmTGgWXLcrI5Mfj50o/zrS04MuPj4Eurvx64mTfHvkGBa7nYf6960x4C2rxBCi0yGTyQjSuZNQWER6iaHKYDe29BN5UpFrZcL2ZmTy4vadpBSXoFereXbIoPKxqRUKgtzdSTcYSCsxVNtLXZIk1iaeydeti1APHVGeniQUFXEkJ5c+tSzun1RUzD+x8ShcnNUFZ63Xa7t25sVtO/nlRAyXt4+u8WdTNvM8ODioQYquu6tUPNCvD89u3c5H+w/Sw8+3wq3F3RmZJBcXE+TuxvCQ5psdaAmi+qu4ap4Hvz9RzI9ziojoo8I/uvoPYZIkkbvgZwy7diPXexL0wH2trtucIDSkDt5eeKhUpe/tJeW1xltCJQZoHTO7glOdVk+oNWoiRce0VmtDkrNyxszOHbm3b290Z3XS6hsQwFNbtvHT8RhsDgePDuxf7exnavGZnF1wVkZIKCwi02CkU2nd3TKSJJUHuxkGY63aCptsNj45cIifj8cgAV18vHlp+JBKt8jDPD1INxhILi6uNtg9nptHakkJ/m7aWgepVRkaEkRCURHb09JrfZ6vS2d1L2sfXe0Yz2dSVCQf7DtATF4+ezOznHmi1SjL1x0a0nAVESZHR7L45Gn2ZWVxzbJVTI6O4s7ePYjw9CxfmDatQ3sULsx2t1Vj7nYjZpOFA8ssfH1LAY+s8kGprvp3yV5QSNr8NynZXlrG7L57UbpQJUQQ2iK5TEafAH+2pKZxICu7PNiNKyyrsdu8aQza0pldo73lzuy2Jo1ZeqzGYLcxLy40PYcksTHZGexObd+uQqALMDYynDflI3h88xYWxpzC4nDw9OCBVQa8kiSVpzEEl+bQnJ23e64so5ES65l2hclFxZUC4rMdycnh+a07iC8sQiGTcUuPbtzWs3uVaQrhHjr2ZNSct7u6nikMZYaGBLMwxtk6+M5aLBhLLCxieVwCCpmM23rWrdWwWqHg6k4d+eLQEX4+HlNtsGu229mb6cxzG9yA5b9kMhlvXTyCLw4eZvGpWFbEJ/BvQiKXtY9mXVIycpmsVikWFwKZTMYNn+hJGplL/G4bS58v5urXK/9xNhw+TNrLr2LLykLu4UHwE4+J6guCUKpvabC7PzObydFROCSJhBY3syuC3YZwdumxupQXq06NwW5jXlxoesdyc8k0OhdndT1PA4aLwkN55+KRPLppC0tOxSJJ8NzQQZX2yzM7a+zq1erylIWg0qC3qlq7ZbO6ZRKLis4b7GYZjdyxej0mu512ej1zhw+udjFZeGn5merKj52dwjC+jikMZQYElbYOzsmtVevgslzdaR3a1alcWZnpnTrwzZFjbExOIbmouHxx3rkOZGVjttvp6O3lUqmy2vDWaHh80ABmd+vKl4eO8E9cPH+edi5aHREaUq+2xm2NzlfOrd958fakPNZ+bKQg08E1b3mi85UjORzk/rqQ7G++A4cDbfduhD77DKo2VJtYEOqrX2kntf2li9TSSwyY7Xb8tNp6t2yvLzdFy6/G0JqcnbPb0Pm7NQa7jXlxoemVpTCMDg+rNh9weGgI740exYMbNrP0dCw39+hKhGfFWanUsyoxlAkqTS+oamY3tqDiorSEatr7HsrOwWS308PPly/Gjykv8XI+5RUZqgl2Y/LySS4uxleroW89UhgAdCoVfQL82ZuZxa70TMZWU8Isw2BgZXwiCpmMW2vZqvd8/N3cmBQVybK4eH6LOcnDA6puT1uWwtCYTR1CPXS8MGwwN3bvyucHD7MnM5P/1aLD2oWm/WAVN32m56f7C9n9u5mTm63Mfj4L/e4vMB5ytoH2vWYm/v+7BVkNr3NBuNB09/NFJZdzKr+AIoulRbQJLqMVObtNwlza1a0+68NcemfNzc7Dx8+7yiApNzsPX//atWoVms+G0hSG0bVodTs4OIgRoSGsS0pmT0ZW5WD3rEoMZcrTGKqotVs2s9tOryeusJCkalIOyqo19A8MqDHQBcoLi1eXxlA2qzsmIrxBckqHhgSzNzOL7Wnp1Qa7i0+exi5JTIiMIKwBCqBf27UTy+LiWXoqljt698TjnFQUgB2li9OGNsFCsXZeel4fJW67V2fwLC3RA5X8clcawam/ovhmNUaZhNzLi5AnHsNjaPWNOgThQqVRKOju68OB7BwOZGWflcLQvPm6cKYag0hjaBzrV25k/cqN5Oc64wEvHy/GTL6YMZMvcnnxrkt/8V98eB7FhZWDiZKiEl58eJ5LFxaaXkJhEbEFhXiqVeW3hmrSv3S/svzPs6WdszgNqs/ZLQt2R0eEAc40hvMpC3Y7eNeuxuiZmd2S89b43ZnhnO28OCysVuesybDSQHJNUlKFXOSzWex2lpw6DcCsLp0a5LrdfH3pFxBAic3GHydPV3o832zmeG4eKrm81j9noXFJDgfq4/9yqcdD9A36F4B9GZP46eTb5Gr7N/PoBKFl61ueypDdYsqOgTMQlwFWh6NSCU+hfpb+8jcrlqxixJhhzHniLuY8cRcjxw5j5dJ/+fPXf1w+n+vTW1VE02azGVUVs0tCy1K2MG1UaCiqWs5sngl2Mys9dnbZsTJlObsZBmOFoFOSpPLbT6PDaxHslqY8dKxlQX1PtRovtRqz3U62qXLr6rLmGQC9A1xvJFGVbr4+9Pb3o8BsYeGJk1XusyYxiVyTmU7eXvVOnTjbzT26AvDloSPlXezK7EzPQAL6BPjXWO1CaHySzUbKM8+R8fa72AsKcOvdC49nPibO739kJLjx1sQ89iwR7dYF4Xz6nlVvN67A+XejJaQxyGSy8vdYUy2b/Qi1s23jdq69dRaTpk2gS49OdOnRiUnTJnDtrTPZtmmHy+er1V/CRT/8Uf7/f/+2DLX6TGDrcEgkxCYSFhXq8sWFprUhyXkbv2xmtTY6envhqVaRVmIgrbiEkLNSFsrSGM4Odj1UKnQqFSVWK/lmCz6lOTY5JhOFFgt6tZrufr5oFApyTWaKrdZKt+EtdjsJhUXIgGgX3tDCPT0oyMkluaiYgHMWZZ3ML8DicBCl92ywRQ0ymYy7+/Ti7rUb+PHYCWZ07ljp3L/FnAJgZpdODVozdWRYKOMiwlmblMxrO/fw/uhR5ec/U3Lswq512xJIkkTGhx9RsmMnCr2ewPvm4Dl2DDKZjEdHSfzyYBHbFpj46sZC0p6yMeVJHXK5qK0rCGfrUzpBcSQnpzytrSXM7IKzIoPBZsNos1WZUibUXVhESJXbJEftu7yWqdX0XmpyGqnJaQCkp2aUf52anEZWZjYR0WFi8VoLl200cjA7B7VcXn77vTYUcnn5p+pzUxnSynN2K1bpCK5ikVrsWYsK5DJZefWEpCoWqSUUFmGXJMI9PVyamayuIsPhnBwAevo1bO3SQUGB9A8MoNBi4ZdzZneP5uRyKDsHT7WKS6KjGvS6AI8N6o+HSsWW1DT+TXCWVJMk6Uy+rljV3+zyFi2m4O9lyNRqwl59Gf24seUfSlQaGTd84snVr3kgk8Oy1wx8fVMh5hLX38gFoS3z0mjo4KXH4nBQaLHgplSWL4ZubtpW0EWtNRo8ciCb1myptH3z2q0MHjHA5fPVKpK4/+k5ACz44hem33Albm61a30ptBybUlKRgCEhwbi7+Omzf2AAm1NS2ZuZxaXto4HSGrvFlWd2wZm3e7qgkAyDoby8WVkKQ1nb2ki9B6cLCkgoKqLbOQHoqbJ83VqmMJQJr2aR2uHsXAB6VlO+rC5kMhl39e7JHWvW89OxE1zTuRN6jXN297cYZ/A7tX27RkknCHBz48H+fZi3Yzdv7t7LkJAgCs0W0koMeGnUdDlPaTmhaRRt2UrWZ18AEPzk47h1r1yJQyaTMe5ed4I6K/j6lkL2LjWTFZfHvUu80QeIxhyCUKZvQACnC8rydT1bTHdBrULU2m0oZ2cR2B0Odm/Zw7FDJ4ju4JwsSohNoCCvkIHDXV/n4NK76ew7rhWBbit1dskxV1WVt5tvNmOy2/FUqyrdui/P2z2rIkNZDm55sFta2SGxisC0bN/aLk4rE+7pDLqrndn1b9hgF5w1dwcHB1FstbLguLMNc57JzKr4RGTAjM4dG/yaZa7o0J4BQYHkmc28u3f/mRbBQUH1apoh1I8p5iRpr7wGkoT/rbegH31xtfv3nKjh8bU+BLRXkHTAxk/3Fp53oaUgXIj6Bp5Z89BSUhjg7IoMIme3vs7OGshIzSCiXThe3p7k5eSSl5OL3suTiOgwMlIrryGqieig1goczMrmn9h4bunRrULObG2VWK3sTM9AhrNhhKu6+vrgplSSWFRMltFIgJvbmbJjVTQQKKvIcHZjiTO1EZ0BbHmwW0UaQ1klho6uBrvnmdktslhIKCxCLZfTycVz1tZdvXuyMz2DX47HcF3Xzvx5OhaLw8GI0JBKJdsakkwm49nBA5m1bCX/xMazrzTVZEgDtggWXGPNyiLlmeeQTCb0kybge13tUrxCuip5cJk3Lw/J5eByC7t+NzN4pphcEASAfgFnKsu0hLJjZUQXtYZTlkXQGGqc2T27g5q7zh2dx/n/CY3ju6PHWXzqNDeuWs3BrGyXj9+amo7V4aBPgD++Wtf/eCrlcvqUVhLYl+EMplKLK1diKFNV+bHYc9IYovRlM7tVBLsFdQx2zyo/drYjOc4Uhi6+PlW2Gm4IfQL8GR4SjMFm47sjx/i9bGFaI87qlonUe3JHacvilNLvfWiwWJzWHIzHjpP86BPYcnJw69Ob4Icfcul2q2+4gumvOF/Hvz1aRGGmKGckCOBsSV+Wp9sSKjGUEcFu6+BSB7Ub7hSL0JpDeuksaq7JzJ1r1vPc0EFMaRdd6+M3JLteheFcAwID2J6Wzt7MLCZGR561OK1ysBtcmsaQaTACkGcykW82o1MqCSytklDWMjexqAhJksoDAoPVSkpxCUq53OUZUX83NzQKBfnmilUeyoLdHg28OO1cd/buyda0dH485kxlCPPQMTy08mrSxjC7WxdWJyRyIi+fSE+POt0BEOrOYTSS/d335C1eAg4H6uhowl58AVkdVmePuEnL3iUmjq2z8uvDRdyxoHHuRghCayKTybixe1f+jU9kcAtafCuC3cZjt9tJOJ1IXk4+NnvF53fIyEEunatWaQy1IZPBHQ+JNIbGUJYOMCkqklUJiTy3dQfxBUXc1adnjXmZRpuN/1KclTTqkq9bpt85ebvnW5wGlWd2z67EUBbU+mm1uCuVFFkqliiLPWsBQm1rAZeRy2SEeeiILSgkuai4fHHc4eyySgwNn697tp7+fowKC2VzSioAMzt3arK8WZVczgtDB/PIpv+Y0blhmlcItVOydx8Zb7+LNS0N5HJ8r5mJ3003ItfUrbWlTCbj+g/1vDwkl31/mtmzxMSAK0U6gyBc06Uz13Tp3NzDqKC8GoOos9ug0lMz+OKdr8nJykWSJORyOQ6HA4VCjlKpbPhgV6QnNC+TzUaB2YJSLmfeiKH0CfDnrT37+PrIUWILC5gUFYWPVoOPRoO3RoObUsGRnFz2ZGaxNyOTQ9k5WBwOOnh51St3tEdpbdzTBYXkmcxn1dit/PoILC89ZsQhSeUB7NkLzmQyGZF6T47n5pFUVFQe7JYvTnOxEkOZcA8PZ7Bb7Ax2JUkqn9nt6d+4M7vgzN3dnJKKVqFgavt2jX69s3Xx9eGfKy5v0mteyGy5uWR//S0FK1YCoGnfnuDHHkbbpUu9z+0XqeDKl3X8+lAxvz5cROeRajxFdQZBaHHKm0qImd0G9ceCpUREh/PEvEd45r4XeWLeI5iMJhZ+u4jLrr7E5fO5lMYgNL2yVIAgdzfkMhmzunQiUu/Jk5u3sj4phfWlVRaq08nbi3v79q7XONQKBT39/diTkcm+rKzy1IqqFqi5KZV4adQUmC3kmkzElQaw5+ZZRXp6cDw3j4SiInqX5gTXdXFamfK83dJFauklBnJMJrzU6vIFbI2pq68P748ehYdKVV6CTGhbHCYTeb8vJufXhUhGIzKVCr8brsf3mlnIGrDE3Kj/ubH3DzMxm6389ngRt34r0hkEoaU5k8YgZnYbUkJcEg88PQeNVoNMJsPhcBARHc60ay5j0Y9LeKrXYy6dT/QSbeHKUhgC3c7MoA4LCeb7yeNZeOIkWUYjeSYz+WYzeWYzxRYrHb29GBAUyIDAQPoF+uNVx9up5xoQGMCejEz2ZmSSWlpWrKqcXYBgd3cKzBYyDIby2ojt9RX/WJdVZEgqPFM94VR9g91zGkscPitft6nqMo4ME90E2yLJ4aBw9Rqyv/4WW7Zzoahu2FAC77wDdWREg19PLpcx+2M984bmsHuRme7jjAyb3TIK6QuC4CRydhuJJKEunTDy8NSRn1tAUEgg3r7eZGW4vlBflB5r4cryXoN0Ff/IRev1PDGocheRsxd7NbSyvN0NySnlrRHP13o30N2dE3n5ZJQYKzWUKHOm1u6ZigzlDSXqG+wWlQW7jVdfV7hw2IuLSX78KUzHjwOg6diRwLvvxL1f30a9bkA7BVfN8+DXh4v54e4iSnIlxt8vUssEoaXQKsrq7IpgtyGFhIeQkpiCf6AfUR0iWbNsHXK5jK0bthMQ5F/zCc5Rq5xd2Vn/LzStssYMZYu+atKYs5e9/P1QyuWk1TCrC5SXiInJzyfHZHK2dzwnvzfynPJjeSZz+b5VLXyrjTPlx5zB7pHspqnEILRt2V99g+n4cZR+fvjffiv68eOQubiAsq4uvt0dqxEWP1PM4meKyU+zc9UrHsjlommIIDQ3MbPbOCZNHY/ZbAHgsqun8NnbX/Lha5+i89Dxv/tudPl8LuXsivzdplc2sxtcy2C3MbkplfTw9eFAaXWD6gLSsuB8W6qzEkQ7vWelygSR5eXHipEkidizuqzVtYpBqM4duUxGhsGI0WbjWG5ZsCtmdoW6MR47Tv7f/4BCQfgbr6Fp17QLDwHG3++OPljOD3cVsvYjIwUZDm76TI9SLQJeQWhO5dUYRM5ug+rWu2v5//sH+vHs/CcpKS7BXedep0m9Ok9NmE1mzCZzXQ8XaimjbIFaFVUPmkO/wMDy/w+tZkxltXaP5uYBZzqnnc1Lo8FLrcZos5FtMtV7cRqASqEgyN0NhyTxX0oaJrudMA9debUHQXCFZLeT8e77IEn4zpjeLIFumcEztcxZ7I3GQ8bu3818ND0fY6FoOiEIzUnM7Da+snhT56Gr891rlxeorV+5kfUrN5Kf6wxMvHy8GDP5YsZMvqjJFgBdSMpzdlvAzC7AgKAAvjt6DKgpjcE5XockAdDhPB1vIvWeHMrOIbGwiFP1LDtWJtzDg7QSA6sSEoDGr68rtF35f/6F+dQplIGB+N0wu7mHQ7cxah5Z6c1HVxVwYoOVD6blc/+f3rjpRVkyQWgO5aXHRJ3dBteQ8aZLwe7SX/5m64ZtjJsyhuiO0QDEn4pn5dJ/Kcwv5IprRY3PhnYm2G0Zq7B7B/gjl8lwSBLBtUhjKFPVzC44UxkOZeeQWFRUPrNb18VpZcI9PdiVkVneTKMp6usKbY8tO5vsb74DIOi+OcjdWsbvYEQfFY+u8eH9y/OI323jo6sKuG+JF1pPEfAKQlMTM7uNo6HjTZeC3W0bt3PtrbPoN7hP+bYuPToRGBLIr9/+LoLdBmawWimyWNEoFHg3UPmw+vJQqegfGMC+zCw6eXufd7/Ac4LzcysxlCmvyFBYXN5Qoj5pDHCmIoPV4bzFK2Z2hbrI/OQzHAYDHsOH4TFieHMPp4KAdgoeWubDO5fkEbvDykfTC7j3Dy+0HiLgFYSm5KYU1RgaQ0PHmy6/M4ZFhFS5TXJIrp5KqEFZvm6gu1uLShF5feQwFlwygQjP8zdpUCsU+GmdLU41CkWVndbgTLC7JzOTIosVL426/Li6Cj9rXAqZjC6lbYMFobZKdu2iaMNGZFotgffOae7hVMkvSsGD/3jjHSrn9DYrn8wowFwi3ocFoSmJmd3G05DxpkvB7uCRA9m0Zkul7ZvXbmXwiMo1XxtSSXEJX773DY/c+iTPP/gyu7fuqXZ/m83GvCde57n75zbquBpTegvL1y3jo9XS2afmALIs9SJa74niPGWaIvTOwLSspW9HL696B/Znd0rr7OONprQOoiDUhsNsJuP9jwDwu3E2quCgZh7R+QW0V/LQMm+8guWc/M/Kp7PysRhEwCsITUWrKGsXLHJ2G1JDx5s1pjEs+uGP8v+3Oxzs3rKHY4dOEN0hCoCE2AQK8goZOLy/yxd3xW/f/4FCqeTVj+eSnJDCZ29/RVhkGCHhwVXuv3bZejw8PTAbW2/FCFdr7LY0QTp3jubm0b6aBWdlM7tl6puvCxVndkUKg+AKh8VC6gtzsaamoo6Oxvfq6c09pBoFdlTy4DJv3r0knxMbrfw4p1C0FhaEJqIVaQwNpjHjzRpndlOT08r/ZaRmENEuHC9vT/JycsnLyUXv5UlEdBgZqZkuX7y2zCYzB3Yd5LLpk9FoNXTo0p5e/Xuwc8vuKvfPzsxh19Y9TLh8XKONqSm0pBq7dRFWOsNaXQ6uTqWqkLZQ30oM4MwrLstx7iEWpwm1VBboluzchcLLi9DnnkambB0d1YM7OwNelRvsXmQmYZ+1uYckCBeEs9MYJEncVamPxow3a3wnv//p5s9Xy0zPQq6QExhypsZrWEQop46frnL/RT8u4fIZU1CrVdWed8u6bWzZsA2Ay2+5ruEG3EDO1yq4tbi+a2f0ajVXdexQ7X5Rek9yTCagYWZ2wVkibWtqOoOCWu4taKHlcFgspL74EiU7dqLQ6wl/641mralbFyFdlVx8uztrPjDw18sl3PeHd3MPSRDaPKVcjkoux+pwYLbb0baSD8gtUWPGm63ip2I2W9C6VVy0pHXXYqqiqcWB3QdxOBz0Gdibk8dOVXveEWOHMWLsMABiEhtvZrquzixQa50zu4Hu7tzas3uN+0V4erA3MwtomJldgJeGDcFgs+Fbz8VuQtsnWa2kzn2Zku07nIHu22+g7dC+uYdVJ5MecmfzN0aOrrZwaquFjsPVzT0kQWjz3JRKrBYLJhHsNqjCgiI2r/mP9JQMQEZIeBCjxo3A08uzxmPP5fJPxW63k3A6kbycfGz2ijkqQ0YOcnkAtaHRqDEZTRW2mYxmtOd0xTKbzPz56z/c9ejtjTKOplaWs9ta0xhqK6o0bzfI3Q29pmH+OGuVSvGmI9RIslpJfWkeJdu2I9d7Ev7WfLQdqr8T0ZJ5+MsZN8eN5fOds7sPLVe1qEougtAWuSkVFFqcqQwtpUxoaxcbE8cnb36Bp96Ddp2iAdi1ZQ/rV2zknsfvLN9WWy5FA+mpGXzxztfkZOUiSRJyuRyHw4FCIUepVDZasBsYHIDD7iAzPYvA4AAAUhJTCT5ncVpWRjY52bm8N8+5ktpus2E0mHj63hd45IUH8AtoPfmbkiS1uO5pjaVjab3erqJEmNDEcn9fTPGWrcg9PYl48w20HTs295Dqbdy97qz/3MjJ/6yc2Gil62gxuysIjalsYkVUZGg4S375iwFD+zHrlquRl1ZzcjgcLPx2EUt+/ouHX7jfpfO5VHrsjwVLiYgO543PX0GtUfPM/Cd47KWHCIsM49b7b3bpwq7QaDX0GdiLZYtXYjaZiY2J49DewwweMbDCfiHhwbz83vM8Oe8Rnpz3CNfeOgtPL0+enPcIPn7ejTa+xlBstWKw2XBTKvGsIfe4tRseGswLQwfz6IDGreghCGeTbDbylywFIOTpJ9F2av2BLoC7t5wJ9zs/IP85t1gsmhGERiZq7Ta8lIQUxk4ZXR7oAsjlcsZccjHJCckun8+lYDchLolJ0yag0WqQyWT8v737jm+q7h44/slOmibdpZO9EVAoIEsBcTAVQYaKMhRUnPj4UxHBPR/0ER+cqAyZsgRBBFERQWQpQ5bMQqF7p9nJ749ieSqrhbZJ0/N+vXhJb27uPbmm5fSbc8/xeDwk1k3g1qF9WTpveblPXh6DRwzE6XAyYdxkZnwwmyEjBhKbEMOhA0d48r5nAFCpVJhDzSV/jMFBKBUKzKHmUhesOki1nB0THOgfQyoUCvo3qEdc8IXHDwtR0QrW/4wrKwttnToY21fOp1K+0v1BA8GRCo5tc7FntcPX4QgR0AwqSXYrmj7IQFZG1jnbszKyMQSV/6b98hU1er1oz9RUBpuM5GbnUSs2mtDwUDLSMst98vIwBhsZ88Soc7Y3bFKfKdPfOO9zGjVryMtTJ1dqXJWlppQwCOELXq+XnEXFPR3DBg4IuF8o9cFKbnnSyKJnC1n+ioUWN2tRKgPrNQrhL6TXbsVre+3VzJ2+gFuH9Cupzz3611G+XvANbTuW/1PgciW7sQmxpCSnEBkdQZ0Gtfl+5Q8olQo2/bSZqFqR5T65uDBJdoWoPLa9+7AdOIDSbMLcs3r3476QrqMNrJ1axMldLn7/2k7bAdKZRIjKcLaMoWbU7GZlZPPvye8SE19839SoR+7FZA6+xLPK59ah/fB6Ye70+bjdHgBUahVdenSi/5A+5T5euZLdm/v3xG4v/kis76DefDTlU95//UOMwUZGPXJPuU8uLuzvtmO1jJLsClHRcpYsBSC0Tx+UAdqeTmtQ0Ov/gpj/RCGLJxSScJWaWo2kQ4kQFc1QA1d2GzZtUKn3aqnVagYNH0D/wX3ITC+uHIiMjiypLij38cqzc7NWTUv+HhkdwcQ3n8FSaCHIGBRwHwP62tmV3eo5UEIIf+VMT6dg/c+gVBJ6W39fh1OpOt9jYPMcG8e2uXi7Zw4PfRVK/faBfcOrEFWtpBuDu+Yku0cOHuXdl9+nQZP69Lujd4XmgG6Xm3dffp/hD9xJrdho4hLjrviYl/1rvv3MQAej3FRUKdIsUsYgRGXI/XoFeDyYundDExXl63AqlVqr4LEVoUy/N58/1zj4T98c7psRQqve0gtUiIpi8OPWY+vXbuC3DVs5feI0ba5tw/Cxw0oesxRamDt9Aft3H8RoMtJ/cG+SOrW95DHNoWYm/XsCWp2WeZ8tZOe2XVzdrnWFxaxSq8jKyKYil1DLnez+uHo9P65eT252HgAhYSF0v+V6ut9ynazuVqC/V3ZjpIxBiArjsdnI/WYlAGG3D/BxNFVDH6zkwfkhzH2sgE2zbXw0LI9h75roOko+NRKiIvhz67GQ0BBu7n8j+3cfwOFwlnps4cwlqNRqXpv2IiePp/DRlOnE144nNiGG/Nx8vpg2+5zjjRw3HHOoGTTFr7l1UkuOHT5eockuQIeuSWz6aTO3DauYT9/Klewum7eCTT/9yg29u1O3YV0Ajh06xupla8jPzee2Yf0qJKiarnigxJmaXVnZFaLC5H+/Dk9BAfqmTdE3b+brcKqMSqPg7mkmQuOVrHqjiLmPFZCf7qHPM/LJnBBXyqDy35rdq9u1AuDE0RM4zixSQvGn8zu37mLC60+h0+to0KQ+Ldu0YMvGbdw6pC/mUDOPPTfuvMe0WW3oDcX3Ohw+cIRa8bUqPG673cG2TTvYv+cgiXUT0P2jVnfQPbeX63jlSnZ/Xb+ZYaOHcE37sxl8kxaNiI6NZv4XX0myW0Fy7Q7sbjfBGg1GjdTXCVERvF4vOYuLb0wLxHZjl6JQKOj3XDChsSrmPVHAN69aqNNGzVU3SUmDEFfCVyu71sIi3pr0TsnXnbt1pHOPjmV6bnpqBkqVkujY6JJt8YlxHNp/+JLPPXzwKCsXfYtGqyEiKoI+g3qVP/hLSDuVRmLdeIDz9Nst/8/ucpcxxCfGnneb1yNTeiqK3JwmRMUr2rYdx/HjqCMiMF3X1dfh+EzXUQaseR6WTrIw97ECnv9Ng8FcvYbuCOFPzvbZrdqaXUNwEP/30vjLeq7d7ihZnf2bPkiP7cz9WBfTonUzWrSu3E/GHp1w/lXly1Wun3DtuyTx8/cbz9m+Yd0m2ne+dFGzKBvpsStExXJlZZE65V0AQm/rj6KGf2JywyNB1L5GTc5JD8smW3wdjhDVWkk3Bj8sY7gQnU6LzWortc1mtaPX+/aTHofdwcIZi5n46As8+9AkZnwwm8KCwis+7iVXdhfNWlLyd7fHw7aN29m3+wB1G9QB4PiR4+Tl5JPUqfwTLcT5lSS7cnOaEFfMY7VycsLzuNLT0TdvRtiggb4OyedUagX3fGjm9a7Z/DzdStuBOhp3ubz+lULUdP58g9qFRMdE4XF7SE/NIDqmuCtNSvIpYhJifBrXqiWr+W3DVpI6tUGjUbN98+8s+GIxox+994qOe8mV3VMnT5f8STuVRmK9BEJCTeRkZZOTlY05xERi3XjSTqVfUSDirDSL3JwmREXwut2cevlV7H/9hSYujvhXXkKpkxpVgPgWam75V/HPmC8fLsBRJKVoQlyOktZjbv9rPeZ2u3E6nHg8HrxeD06HE7fbjU6vo3VSS1YuXo3dZufIwaPs3rGH9p2TfBrvzm27ufO+IQwbPZhB99zO2CfvY9eO3Xg8nis67iVXdiu6bkJcmpQxCHHlvF4vaVP/i2XzbyjNJhJefxV1aKivw/Irt/zLyO9f2zm1182KVy0MfLViR34KURP48wS1775ey7dL15R8vXXjdnoNuInet9/C4BEDmfPpAiaMm4zRFMSQEQOJ9fHKbk5WLg2a1Cv5um6DOqiUSvJy8giLCLvs45b7BrX8vAI2fP8LqSlpgILYhFp0vaEzphDTZQchSpMeu0JcuewFC8lb8Q0KjYb4V15Cm5jg65D8jlqrYPgHZt7qkcO6/xbRdoCOukk1u55ZiPLy5zKG3rffQu/bbznvY8ZgI2OeGFXFEV2cx+NBpS6dmipVKtzuSl7Z/V9HDh7lg7c/wWQOpl6jukDxbwk/frueh/5vbMk2cWX+TnajpRuDEJclb+33ZH4yHYDYZ58m6KqrfByR/6rbVsMNDwfx/dQiZj6Qz2PLQwmNU/k6LCGqDYPq72TX/8oYqqNZH81B/T8Jr9PpZN7nC9Fqz95XMHb86HIds1zJ7tJ5y2l77TUMGTkIpbK43Nfj8bDgi0Usnbuc8ZMfLdfJxbk8MlBCiMvm9XrJnr+AzE8/AyBq7BhM3a73cVT+r99EI7tW2Uk94Oal9tkMfiuYDsP0Na4XsRCXozp2Y/BX7bucWzPcrgwjjC+lXMluyvEU7h4zrCTRBVAqlXTvdT1vTZxyxcHUNF8fPkJyfiEPtL4KzZlrmm2z4fJ4CNFqSz4aEUJcmtftJm3q++StKB4HHDV2DGGDB/k4qupBa1Aw/ttQ5jxSwO7VDmaOLWDHMjt3TTUREiOrvEJcjD/X7FY3d48ZVinHLVefXX2Q4TyTLCArIxuDfORebtP+2M2MvfuYvOk33GfuNEz/e1VX6nWFKDNPUREpzz1P3oqVKLRa4iY/T/iQO2RlshxCYlQ8uDCEez4yYQhRsPtbBy+1z2bLQtulnyxEDaZTqVAADo+n5N9y4V/Kley2vfZq5k5fwNaN28lMzyIzPYutG7cx77MFtO0ofXbLy+0tbvXz3fFk3ty6A6/XS6p0YhCiXJwZmSQ/Ph7Llq2oQkJInPI2puuv83VY1ZJCoaDjXQae/y2c5j21FOV4+WJ0PjPG5GMrlH/EhTgfhUJRUspg9cP2Y6KcZQy3Du2H1wtzp88vuTNOpVbRpUcn+g/pUykB1gQqhYLFhw5j0mqJPDO+T0YFC3FpHoeDk08/i+PYMTQJ8SS8/ira+Hhfh1XthcWreHhJCBtn2PjqmQJ+m2fj6FYn988yk9BSujUI8U8GtQqry4XN5SK4hk9o9EflSnbVajWDhg+g/+A+ZKZnAhAZHYlWJ5N3rsTEDkm88ts2ZuzdR+yZ8gVZ2RXi0rLnLShJdGu//x7qkBBfhxQwFAoFXUYaaNBRw/R78zi1182b3XMY9EYw1402SImIEP+j+B4bu3Rk8FNlLmNwu9z8e/J/SDudjlanJS4xjrjEOEl0K0DX+Dhe7NgBBXDaImUMQpSF/dhxsubMBSDmySck0a0ksU3VPP1TOF1G6nHZYf4ThUy/R8oahPhfepV0ZPBnZU52VWoVWRnZyO/ylaNXvTo83e5sew0ZKCHEhXk9HlL//Q64XIT07UNQ69a+DimgaQ0K7ppqZtQXZvQmBTuW2fny4QK8XhkxLARIRwZ/V64b1Dp0TWLTT5srK5Ya747GDZnYIYm+9evSKirS1+EI4bdyl6/Atncvqohwosbc5+twaox2g/Q8tS4MXbCC7Yvt/Dzd6uuQhPAL/jxFTZSzZtdud7Bt0w727zlIYt0EdP8oYRh0z+0VGlxNNKBhAwY0bODrMITwW870dDLODI2o9egjqIKDfRxRzRLXTM3d/zXx2Yh8Fj1TSN22Guq0kRtyRM12NtmVml1/VK5kN+1UGol1i+90PrffrhQ4CCEql9frJe0/7+O1Wgnu2gVT1y6+DqlGShqo56+NTn7+1Mqn9+Tx7IZwjGHl+qBQiICilzIGv1auZPfRCeMqKw4hhLikgp/WY9m8GaXRSK1H5OeRLw16PZhj25wk/+5i9oP5jJ0XIh0aRI1VsrLrlmTXH5Up2XXYHSybt4JdO3bjdnloclUjBg0fQLBJPj4UQlQ+V04OWXPmlhoFrI6UunZf0ugU3D8rhNe6ZLNzpYN171vp+ajcWCtqpr+HStikjMEvlelzp1VLVvPbhq20aN2cttdezYE9B1nwxeLKjk0IUcO5Cy1kfj6DI3fdQ+6SZXhdLkL69SGk9y2+Dk0AkXVV3PuRGYClkwrZ8LkVt1M6NIiaxyCtx/xamVZ2d27bzZ33DaFtx2sASOrclndffh+Px4NSKXVaQoiK5XE4yF36NVnz5uHJLwDA2PFaIkeNRN+gvo+jE/+rdV8dPR8N4vupRcx9rIDv3rFw83gjHe/Wo9ZKWYOoGaT1mH8rU7Kbk5VLgyb1Sr6u26AOKqWSvJw8wiLCKi04IUTN4vV4KPjxJzKmf44rLQ0AQ6uWRN03GsNVLXwcnbiQAS8bSWyl5tu3LKQedDP3sQK+fdvCzeODaD9Ej8EsiyIisEnrMf9WpmTX4/GgUpfeValS4XbLBB0hRMUo2rmTjI8+wXbgIADaenWJGnM/xvbt5MYnP6dUKmg/RE/SIB07ltlZ9aaF0/vczB9fyMKnCqnbVk3T7lqadtNSr71GVnxFwJHWY/6tzN0YZn00B/X/JLxOp5N5ny9Eqz3ba3fs+NEVG50QIuB5rFZOv/EWhRt+ASgeFDFqJOabbkShUvk4OlEeSpWCpIF62gzQ8ccKOz9Ms3J0i5MjW1wc2eJi1ZtFaIOg60gDt74YjEYnSa8IDNJ6zL+VKdlt3yXpnG3tOrU9z55CCFF2XpeLlBdeomjrNhR6PeFDBxN+xyCUBoOvQxNXQKlU0OZWPW1u1WPN93Boo5N9PznY/6OD0/vcrJtm5dCvTkbPCCGqnvxCI6q/v1d2bdJ6zC+VKdm9e8ywyo5DCFHDeL1eUv/9DkVbt6EKCaH21P+gTUzwdViighnMSlr20tGylw6AY9udTL83j+M7XLzeNZt7PjBzdX+dj6MU4spI6zH/JncNCCF8InP65+SvWYtCryf+9Vcl0a0h6rbV8OyGcFr30WLN8/LxXXl89UwBLoe0LBPVl0ElZQz+TJJdIUSVy1myjOx580GpJG7y8xiaNvF1SKIKGcOUjJ0XwqDXg1Gq4YdpVt7umUPKXkkURPUk3Rj8myS7QogqVfDTetKnfQBAzFNPEtyhvY8jEr6gUCi44eEgnvwujPBEJcm/u3i9Szar3rLIYApR7Ug3Bv8mya4Qokp4rFYyZ3/J6dffBK+XyPtGEXLzTb4OS/hY/fYaJm4Op+soPW4nrHjZwpvdczi52+nr0IQoM1nZ9W+S7PqQF1m9EIHP63aT9+1qjt4zkqwvZuJ1OgkbNJDwYUN9HZrwEwazkjvfM/PYilAi6ig5sdPF69flsPINCx63/JwU/u/v1mMyLtg/lbnPrhBClJdl6zbSP/4Ex5GjAOgaNyL6gbEEXd3ax5EJf9S0m5aJm8NZNtnC+k+sfPOqhYMbHIz63ExILWlRJvxXycqu243X65VBOH6mWiS7lkILc6cvYP/ugxhNRvoP7k3Sefr8fr/yB7Zs2EZ2Vg7GYCNde3aiZ58ePohYCJHz9XLS33sfAHV0NFH3j8bUvRsKpXygJC5MH6xk6BQTV/fX8cWofA7+7OS1TjmM/NxM0+u1lz6AED6gVirRKJU4PR4cHg86GYjjV6pFsrtw5hJUajWvTXuRk8dT+GjKdOJrxxObEFN6Ry8Mf+BO4hJjyUzPYtqbHxMWHkbbjtf4JvAyk98ARWCxJyeT8eHHAESMvJfwIYNRaiVREWXX9HotEzaF8fmZhHdqv1z6TDDS66kglCr5mSn8j16twunwYHO5JNn1M36/xGK32dm5dRd9B96CTq+jQZP6tGzTgi0bt52zb8++PUism4BKpaJWbDSt2rTgyF9HfRC1EDWX1+Ui9fU38TocmG++kcjhd0uiKy5LSC0Vjy0PpfczQQB886qF/w7Mw1EkdbzC/xhU0pHBX/l9spuemoFSpSQ6NrpkW3xiHKknUy/6PK/Xy+GDR4mNj7nofkKIipU1Zx62AwdRR0cTPW6cr8MR1ZxSpaDfc8E8siyU4EgF+9Y5mDEmH49HEl7hX6Qjg//y+2TXbnegN+hLbdMH6bHZ7Bd93qol3+HxeOhw3YV7eG784VfemvQOb016B7fbUyHxClGT2Q4cIGv2lwDEPv0UqmCjjyMSgaJZDy3jvw3DEKLg96/tLJtk8XVIQpQiHRn8l9/X7Op0WmxWW6ltNqsdvf7Cs9TXr93All+28fjzD6PRXPgldu7Rkc49OgJwMDm9YgIWooby2O3FPXQ9HsIG3k7QNVf7OiQRYGKbqhnzZQjvD8hl7XtFRNVX0XWUwddhCQHIyq4/8/uV3eiYKDxuD+mpGSXbUpJPEfPPm9PO+HX9b3y/4gceefZBwsJDqyhKIUTmp5/hSD6Btk5tIu8b5etwRIBq2k3LXVNNAMwfX8Cfay/+KZ8QVUWmqPkvv092dXodrZNasnLxauw2O0cOHmX3jj2075x0zr5bN25nxVerGPf0A0RGR/ggWhEILNt3kPL8ZE69+joZn31O7jersGzbjiPlFF6v1An+k9frJf/7deQsWQoqFbHPPo1Sd+FPXoS4Up2GG7jlqSA8bph+bz4n98hKmvC9s7125f3ob/y+jAFg8IiBzPl0ARPGTcZoCmLIiIHEJsRw6MARPnz7E6ZMfwOAbxZ9i6XQwtuT3y15brvObRk68g5fhS58xOv14kpLx5mZgSsjE1dG8X+9LhemHt0xXNXinKbfrtxcMj78mPy131/wuMHXdSXuuWdRaDSV/RKqBcep06RPfR/Llq0ARNxzN/rGjX0clagJ+k00knnUzbZFdj4YlMvwD8006y5dP4TvGM7U7EoZg/+pFsmuMdjImCfO/Vi0YZP6JYkuwIvvTqzKsISf8tjtpEx6gaKt57anA8j9ejna+vUI698P8409Uej15K/9nowPPsKdn49CqyX8rmFooqNxpqbhTE3FmZaG7cBBCn/ewCmPh7hJE1Goq8W3T6XwOBzkLPiKrDlz8TocKI1GIu8bTWj/vr4OTdQQSqWCez40k5OSy+FfnUztn0uLm7QMeDmY+OY193tT+I7+zL8JNilj8DvyE0EEFK/bzemXX6Vo6zYUBgO6unVQR0WhiYxEHRWFOz+fvG9X4zhylLT/TCXjk+loEuKxH/wLgKA211DricfQxsefc2zbwb848a//o/CXjZx65TXiJk6oUQmv1+vFmZJC0e9/kLNoCY4TJwAw97yBqAfGog4P83GEoqbR6BU8+nUoP0wr4rt3ivhzjYO932fT8W49/SYaCY2Vxv6i6uhVNWNl9+hfx1i+cCUAebn5tGjdjIF33+bboC5B4ZUiRKC4G0Pj2tGX3rEC9Vi0lDy7g+8H3kbYRbpLiLLxejykvvVv8tesRWkyUfs/U9DVq3fOfh6Hg8INv5C7fAXW3XsAUJnNRD30QPFK70VmmtsOHODEv57GY7Fguv46YidOQBHAk3LcefkU/vorRb//QdHvf+DKzCx5TJuYSPRjj2Bs4+8TCkVNUJDhYdWbFn7+zIrHBRoDXH9/EDc+HoQ5yu9vTxEB4MOdu5m+Zy9jW7ZgTKurKv18vshb/mn2x/O49rp2NGrW0KdxXErNWZYSAc3r9RbX265Zi0KvJ+H1V86b6AIotVrMN/TAfEMPbIePYN25C1OPbqhDQy95Hn2TJiS8/SYnn/o/Ctb/DEolsROeCbiE1+t2k/v1cjK/mInHcrafqSokhKCrWxOU1BbzjT1lMprwG6YoJUP+baLbWAPLXrDwx3I7308tYv2nRVx/n4EbHzdijvZN0puf4SHtoIugUCXGMAXGcCUavYw8DjQ1rRuDy+Ui+Ugyd90/xNehXJIkuyIgZH85l5zFS0CtJv6lFzA0b16m5+kb1EffoH65zmVo2oSEt97g5FPPUPDjT7hycoi8dziGVq0uuipcXRTt3Ena+9NwHCketW1o3QpTl84EXXMN2rp1UChllUz4r1qN1IydE8Lx352sesPCrlUOvn/fyvrpVq4bZaD7g0FE1Kn8X04zjrrZ+Y2dnd/YObzZifcfc4u0QcUJemIrDXXbqqmTpKHO1WoMIfL9VV35Y5/d9Ws38NuGrZw+cZo217Zh+NhhJY9ZCi3Mnb6A/bsPYjQZ6T+4N0md2pb52Af2HKRxi0Yoq8G/CZLsigrhcThwZWahjYut8nPnfL2czC9mgEJB3IRnMCaV/Zv1chmaNSPhzdc5+cwErH/s5MQfO9E3b0b40CEEd+pYrRJCr9eLp6AAZ3o62fMXUvDDjwBoYmOIfuhBjJ06BkQSL2qWOtdoeHBBKMl/FCe9O1c6WDfNyg8fWGnaQ0vne/W06q1Do7uy97bb5SU72U364TN/Drn5a6OTlP9ph6bWQnxLNQ6LF0u2F0uOB0cRZB33kHXczh8rzvYKjmmi4rr7DHQZabji2ETVKunG4Eetx0JCQ7i5/43s330Ah8NZ6rGFM5egUqt5bdqLnDyewkdTphNfO57YhBjyc/P5Ytrsc443ctxwzKFmAH7fspNrLzKl1p9IsisqRPq0D8hbsZK4l1/E1LlTlZ03e9ESMj74EIBaTzyOqdv1VXZuQ4vm1P9yFjnLviZ36TJse/dxatILaGsnEjbwdkzdu6EKDq6yeMrKnpxM7pJl2A4fxp2VjSsrC6/z7A9BhVZL+J1DCR8yWPrlimqv9tUaHpgfyomdTr5/v4gdy+zsW+dg3zoHwREKOgzV0/g6LTFNVETWVaFUnT/B9Hq9ZCd7OLnHxam9LlL+dJGyx0XGETdu57n7600KrrpZS+u+OlrcqMVgVpY6lr3QS06Kh+M7nBzb7uL4Dicnd7lIPeBm4VOFfD+1iN5PG7n2Lj0qtSS91YHeD1d2r27XCoATR0/gyM4r2W632dm5dRcTXn8KnV5Hgyb1admmBVs2buPWIX0xh5p57LlxFzyu2+Um+cgJ7rzP/0sYQJJdUQE8DgcF64pXAzM++pjgDu0rvUuB1+sla/aXZM2YBUD0w+MI7du7Us95PqoQM5H3Did88CDyvl1N9sKvcCSfIO3d90j/7wcEd+6E+aYbMSa1LdM1cRdacJxIRt+0aYWvplr3/En2goUUbtx0zmNKYxDq8Aj0TRoTOWoEmpjzTygUorpKbK1h5PQQBr/tYetCG7/MsJGyx8W6aVbWTbMCoNZBrYYqajUu/l4tzPJgyfJQmOXFku3B5Tj/scPilUQ1UBHdQEV0AzXxV6lo1EV7wZVZhUKB3qQgtqmS2KZqrr2zeLvT7uXP7xyseLWQU3vdfPlwAWveLaLvRCNtbtNJ0uvnDFXcesxaWMRbk94p+bpzt4507tGxTM9NT81AqVISHXv2Brf4xDgO7T9cpufv//MgjZs3rBYlDCDJrqgAlq3b8BQVAeBMOUXuNysJu+3W8+7rOHWazC9mEH7HwMsePuD1esn46BNyvloESiUx/xpPyC03X3b8FUFpMBB2+wBC+/ej4Kf15H27mqI/dlLw03oKflqPKiwU8403EjZwAJqoqHOe7/V4yFv9HZmffoY7Lw9Dq5ZEP/JwueuJzzmu14vl181kz1+Adc+fACg0Gsy33IS5e3fUUZGow8NRGgxXdB4hqgtjmJJuY4O4foyB4ztcbPvKRsre4hXV3FMeUv50k/Ln+ZMVc7SSuBYq4purib9KTVwLNTGN1eiMFZOEanQKru6vo1UfLdsW2/nmNQvph918PjKfeY8raHKdlmY3aGnWXUNUffnn29+cTXarZmXXEBzE/700/rKea7c70Bv0pbbpg/TYbGUbv92idTNatG52Wef2BfluEVesYP3PABhatsS6ezdZs77EfGNPVEZjqf08djunJr2A/cgR7IcOUffTj8u9Aux1u0n7z1TyVq4CtZq4557FdP11FfZarpRCrcbc8wbMPW/AmZZO/rp15H+3FseJE+Qs/IqcJUsx97yB8KGD0dWuDYB1/wHS33sf24EDxcfQaLDu2s3xsQ8Selt/IkfcW+5yCK/bTcGGX8j+ci72I0cAUAYHE3prf8IG3CY9cUWNp1AoqNtWQ922Z6chWvM9pB10k3bIjUoDxnAlwREKgiOUGMOVaA1Vs7KqVCloP1hP2wE6fp1jY+17RaQfcvPHirP1vRF1lSTdruf6MQbC4gOrG0x1VZ367Op0WmxWW6ltNqsdfYC2QZVkV1wRj8OBZdOvAMT835OcfuMtbH/uJWfBV0SOGlFq3/QPPixJvBzHk8ld8Q1hA24r87m8Xi+pb75N/vfrUGi1xL04meAO/lscr6kVTcSdwwgfNhTb/v3kLFpCwfqfyV/9HfnfrSG4cydUJhN5q78Drxd1RARRD4zB2L4dmTNmkfv1cnKXLKPgh5+IHD0S03VdUZlMFz2n1+Uif90PZM+dXzL0QR0ZSdgdgwjt0wtlUFBVvHQhqiWDWUndJCV1k/xjHLhKo6DLCANdRhjIOu5m3w8O9v3gYP96B1nHPHz3ThFr3yuizQAd3R8Mon57/4i7pqpOrceiY6LwuD2kp2YQHVP8aWNK8iliEgKzhE2SXXFFis6UMOgaNkQbH0/02DEkP/o42V8tIrR/X9SRkQDk//AjeStWotBoCL9zGFkzZ5E5cxbmnjdcMoH7m2XTr8WJrsFAwmuvENS6VWW+tAqjUCgwNGuG4fnncIwaQfbCr8hfvYbCXzYW76BSEX7HQCLuvqskGa31yDhCevci/f3/Yt21m7Qp75I25V008XHomzRB36QJugb18OQX4EhNxXk6FWdqKvYjR3BnZQOgiYkh/M6hmG+6UfrhClHNRdRR0WVkcZcGj9vLkd+c/PSJld+X2dm2qPhP3SQ1/SYaaX5DYK7O+Tt/bD3mdrvxuD14PB68Xg9OhxOlSolOr6N1UktWLl7NnaMHk5J8it079jB+0qO+DrlSSLLrSwEwu+7vEgZTt+JSAsNVLQju2oXCDb+QOWMWMf8aj+PkSVKnvAtA1EMPEtq/L0U7d2L9YydZs74ketyDlzyP1+0m49PpxccYPbLaJLr/pI2PJ+aJx4m8Zzg5S5bhTE8nYvhdJSUN/0vfoD6J706h4IcfyVn6Nfa//sKZcgpnyqmS9mDnPUdiIuF3DcPco3uNGmcsRE2hVClo2ElLw05ask+6+flTKxu+sHJsm4v/3p7HPR+auPZOqcOvav7Yeuy7r9fy7dI1JV9v3bidXgNuovfttzB4xEDmfLqACeMmYzQFMWTEQGIDdGVXxgWf4ZNxwV8tJc9RfccFexwODg+8A4+liHqzZ6CNjwfAceIkR0eOBqDOB++T+u93sB86XDxed9JEFAoFtkOHOD72IVAqqff5dLSJCRc9V+43q0h75100sbHUm/EZCk3N+7jO63JhP3oM24ED2PYfwH78OOrQUDQxMWhiY0r+q61dO+AmugkhLs5u8fLtWxa+e6f4ZuFh/zFx3WhJeKuS1eWiy4LF6FQqNg0dVOnn84dxwdWFLPv4gerar79o23Y8liJ0DRuUJLoA2sQEQvv1IffrFSQ/8S+8ViuauDhqPTm+pJ2WvmFDQnrdTN6q1aR/9DEJr758wfN4rFYyZ84EIHL0yBqZ6ELxzW/6Rg3RN2oIffv4OhwhhB/RGRXc9mIwQaEKlk6yMO/xAhxFXno+InX6VUWvUqEA7G43bo8HVTVpy1UTyP8JcdlKShjO0w0h4p7hKAwGvFYrCo2GuEkTUQWX7s4QOWokCoMBy6+bsWzfccHz5CxagjsrG32TxlU6NEIIIaqbm54wMmRKcfeWxRMKWfWmBfkAt2ooFIqSwRI2t//fpFaTSLIrLovH4aBwU/FwAtN15ya76rAwIkfcCwoF0Q8/hL5xo3P3CQ8n4s6hAKR/+BHe8/xwcOXkkL1gIQBRY+6vVmN4hRDCF7qNCWL4ByYUSljxioXFzxbitEvCWxX+rtutqsESomwkcxCXpWj7juIShvr1L1hvG37HQBqtWEZov74XPE7YoIGoa9XCceQomZ99jsdqLfV41uw5eIqKMLZvR9A1V1fkSxBCiIDVabiBkZ+ZUapg3TQrr1ybzf6fLjACTlQYf+zIICTZFZfpYiUM/+tSfV2VOh3RD4wBIHv+Qg4Pu4vMmbNx5+fjSEkhd8U3oFAQNeb+iglcCCFqiHaD9Dz+TSgxjVWkH3LzXr9cPh+dR16arDpWluo0WKImkWRXlJvH4aBw45kShgqYXma6/jriX3sFffNmePILyJo5i8ND7yJl4iRwuzHfdCO6+vWu+DxCCFHTNOqi5blfw+k/yYhGD1sX2nmxbTbrpxdJLW8lOFuzK8muP5FuDKLcinb8jsdiQVu/HtraiRVyzOBrO2Ds0B7rrl1kzZ1P0dZtOI4no9BqiRx5b4WcQwghaiK1VkGvp4wkDdKz4F8F/LnGwfwnCvlzjYN7PjQTHFE5614ndjmx5HjRByvQGRXoTQr0wQr0ZkVJZ55AE6HXE2nQ45HfI/yKJLuiXLxOJ7nLvwEqZlX3fykUCoJatyaodWtsB/8id+Uqgq5ujSZa+ggKIcSViqqnYtyiEHYstTPnsQJ2f+vgtc7ZjP7CTIOOFTdl0W7xsvCpAjbNtp338bpJakZ8YqZWo8BLQd7t1tXXIYjzkDIGUWaO5BMcf/gxLJs3o9BoMPfoUWnn0jduRMwTj2Hu3q3SziGEEDWNQqGg7e16nvslnLpJanJSPLzTK5fV/7bgqYDlyFP7XLzZLZtNs21o9NCoi4ba16ip1UhFSKwSjR6ObXPxWpdsNs60SimFqBKB92uVuCxet5vsefPxFFkxdmiHoUWLklGzXq+XvG9Wkv7BR3jtdjQxMcROeAZtfJyPoxZCCHE5Iuqo+NeaMJa/ZGHNf4r4+kULB39xMnZOCDpj+UsMvF4vm2bZWPBUAU4rxDRWcd+sEOJblE4zrHke5o0vYOtCO18+XMDe7x3cOdWEMUzW3kTlkXHBZ/hyXPC6QbcRqvPduGBPURGnXnoFy5atJduURiPGpLYY27ejcOMmCjf9CoD5xp5EP/owKqPxQocTQghRjexZY2fmmHwKs7x0GKbn3o9N5aqpdRR5mfNoPlsW2AG49k49Q98xXTRp/m2+jfnjC7AVeAlLUDLiEzONu1ZcKUVNIOOCy06S3TNqarLrzMgg5dmJ2I8cQRUSgqlHd4p27MBxPLnUfkqjkVpPPIa5R3efxCmEEKLy/F1+4CiC4R+Y6DTcUKbneTxePh2ezx/L7WiDYOg7JjreVbbnZhx18/moPI5tK+5ckDRIx4CXgglPVF3266hJJNktOyljqMFshw6R8uxEXFlZaBISSHj91ZLSBMfp01h+24Jly1aUQUFE3X8fmlryTSWEEIEorpmaoe+YmPVAAfOfLKBOWw3xzS+dIiybZOGP5XYMIQrGrw4j4aqypxVR9YpLKVZPKeK7KRa2LbKzc6Wdmx4P4qbHjWiDArNjg6h6srJ7Rk1b2S3c/BunXnoFr82GoWVL4l9+AZXZXKUxCCGE8C+zHsjn1zk2YhqreHp9GPrgC9fS/vKFlTmPFqBUwyNLQ2na7fLLELKS3Sx9vpDtS4pLIcLilfR9zsg1/XUYQqSe93xkZbfs5B1UA+V8vYKUiZPw2myYet5AwttvSKIrhBCCoe+YiG2mIvWgm3lPFFywW8K+Hx3Me6IAgGHvmq4o0QWIqK3ivpkhjF8dSmLr4i4Rsx8q4Kl6mbw/IJf104vIPSWT38TlkWS3BvF6PKR/9Anp700Fj4eI4XcR++zTKLVyU4AQQgjQBim4f1YI2iDYMt/Oplnn9so9vd/Fp8Pz8LjhpseD6DKibDW6ZdGos5Zn1odxz4cmGnXW4HHD3u+Lh2A82ySLf9+Yw4mdzgo7n6gZpIzhjEAvY/DY7Zx+/U0Kf94AKhUxTz5ByC03V+o5hRBCVE+b51qZObYAtRYSW6sxhikJCldgDFOyc6Wd7GQP19yq475ZZpTKyqutLcjwsHu1nV0r7exd58BpA5UG+jxr5KYnglCpa25dr5QxlJ3coFYDuHJzSZk4GdvevSiNQcS9OBljmza+DksIIYSfuvZOA8e2u1j/iZWjW13nPF6nbfEUtMpMdAFMUUo6DTfQabgBW6GHZZMtrP/EyvKXLOxZbefeT8xEN5BURlycvEMCmMdmo+DHn8j6cg7O06moo6NJeP0VdPXq+To0IYQQfm7oFBM9HjJQkO7BkuPFkuOhKMeLQgkdhuqrvFuCPljJ0CkmWvXWMuvBAo5scfFqp2wGvmai6yh9uXoDi5pFkt0AZD9+nLwVK8lbsxZPYSEAukaNSHjtZdQRET6OTgghRHUR3UBNdANfR1Fa8xt0PL9Zw/wnC9i2yM68xwv4ba6VwW+bqNNG4+vwhB+SZDeAFO3cRdbM2RT98UfJNn3TpoT274upR3e5EU0IIURAMIYrGf1FCK362Fj0dCFHtrh4s1sOHe/Wc+sLwZij5f57cZYkuz5UUXcG2pOTyfxkeslIX4Vej/mGHoT264u+caMKOosQQgjhX9oN0nPVTVpWvVnEjx8WsWm2jR1f2+nztJFuDxhQa6W0QUiy6xcu91vRlZ1D1qzZ5H6zEjweFHo94UMGEzbwdlTBxgqNUQghhPBHBrOSga8G02WEnkXPFLJnjYPFzxWyfnoR/ScF0/Z2XaXfSCf8myS71YzX68V+8CB5q9eQt2YtXqsVlEpC+vYhcsQ9qMPDfR2iEEIIUeVqNVIzbnEoe76zs3hCIakH3Xw+Mp/vp6oZ8HIwTa+XUr6aSpLdasKVnU3+2nXkfbcGx7FjJduN115L1Jj70NWt47vghBBCCD9x1c06mt2g5dfZNr55zULy7y7e65tLi5u0DHotmJgmkvrUNPJ/3M95XS4yPplOzpKl4PEAoAoJwdzzBsw334i+YUMfRyiEEEL4F5VaQZeRBtoN1vPDB0WsebeIP9c4OPBTNr2fMXLT40GoNFLaUFNIsuvHXNk5nHrpZay7doNSSXDnzphvuYng9u1QaKS9ihBCCHExOqOCXk8Z6TLCwLLJhWyabWP5Sxa2L7Ez/AMTda6Rf0trAkl2/ZR1335OTX4RV2Ymqohw4l+YjKFFc1+HJYQQQlQ7piglwz8wk3SHnjmP5pOyp7hVWc9Hgug62oApUoEuWCGDKQJUtUl2LYUW5k5fwP7dBzGajPQf3JukTm3P2c/r9bJ8wTdsWv8bAJ2u70D/IX2r1Rs4d9W3pL/3Pl6nE32L5sS/MEmGQQghhBBXqFl3Lc9vjmDFy4X88KGVte8Vsfa9IgDUuuKkODhSSWxTFY27aGl8nZbIuspqlUOIc1WbZHfhzCWo1Gpem/YiJ4+n8NGU6cTXjic2IabUfht//JVd2/fwzKv/QgFMe/NjIqIi6HJDJ98E/g9uiwXHiZM4kpPx2O2gUHD6jbfILyzEYynCXViA82QKAKG39iP6oQelZEEIIYSoIDqjgkFvmGg7UM/XLxWScdhNQaYHpxVyTnrIOenhxB8utsy3AxCeqKRRFy2JrdWYopSYIpUERyowRSkxhilR65Bk2M9Vi2TXbrOzc+suJrz+FDq9jgZN6tOyTQu2bNzGrUP6ltp3y4Zt9OjVjbDwUAB69LqeTT9t9mmy68rJ4fTLr+E4cQJXVlbJdu/dd4NOj+XX31A47CXbFVottR57hJBet/giXCGEECLg1Wun4fEVYSVf2y1eCjM95KV5OLbdyV8bnPz1i4PsEx5+m2fjt3nnP45SDbpgBXqjAp1Rgc6kYNg7MrrYn1SLZDc9NQOlSkl0bHTJtvjEOA7tP3zOvqdTUomvHXd2v9rxnE5JO+9xN/7wKxt/Kp461m/knRUc9Vmq4GCKdu0qHvyg1aJNSEBbOxGFVgdAzNP/IjQ4GKUxCGWQEXVkpAyFEEIIIaqQzqhAZ1QRUUdF/fYaejwIHo+XlD0uDm5wknnUTUGGh4JMD4WZHgozvVhyPLidYM31Ys09OxfV7fThCxHnqBbJrt3uQG/Ql9qmD9Jjs9nP3ddmRx+kL7Wf3WbH6/We8zFD5x4d6dyjIwAHk9MrIfJiCo2GxClvoalVC3V0NApl8cxu5VdLweEguFNHjDpdpZ1fCCGEEOWnVCpIbKUhsdWFV2ldDi/2Qi92y5k/hV5imqqqMEpxKdUi2dXptNistlLbbFY7ev25CaJOryu1r81qQ6fX+byeJqh1a5+eXwghhBAVT61VoA5XYJQBpn5L6esAyiI6JgqP20N6akbJtpTkU8T84+Y0gNj4GFKST5XaLza+VpXEKYQQQggh/Eu1SHZ1eh2tk1qycvFq7DY7Rw4eZfeOPbTvnHTOvu27JPHj6vXkZueSl5PHD9/+RIeu7X0QtRBCCCGE8LVqUcYAMHjEQOZ8uoAJ4yZjNAUxZMRAYhNiOHTgCB++/QlTpr8BFNfhZqZn8fqEtwHoeP21JXW5QgghhBCiZlF4vV7vpXcLfAeT02lcO/rSO1ag7l8tJd/h4IdBtxEiN6gJIYQQoox8kbdUV9VmZVcIIYQQQviWx+Nh9sdzycvJIyIqgqGj7kCl8u/uE9WiZlcIIYQQQvjezm27iYiK4NEJ46gVG83Obbt9HdIlSbIrhBBCCCHKJDM9k4Q6xcO7EuomnHfAl7+RMgYhhBBCiAC0fu0GftuwldMnTtPm2jYMHzus5DFLoYW50xewf/dBjCYj/Qf3JqlT20seMyYuhn279nN1u9Yc+PMgVou1Ml9ChZBkVwghhBAiAIWEhnBz/xvZv/sADkfpGcYLZy5BpVbz2rQXOXk8hY+mTCe+djyxCTHk5+bzxbTZ5xxv5LjhXHVNc/7af4ipr31AbEIMplBTVb2cyybJrhBCCCFEALq6XSsAThw9gSM7r2S73WZn59ZdTHj9KXR6HQ2a1KdlmxZs2biNW4f0xRxq5rHnxl3wuLffeSsAq5aspnHzRpX7IiqAJLtneL3FbTwqk9vtQaU6Wyb9cYfOAKSl5ZFWqWeu2f553UXlk2vuG3Ldq55cc9+Q6w5Oh4u3Jr1T8nXnbh3LPFcgPTUDpUpJdOzZ1mXxiXFlqr/Nz81nxgezUSiUNG7RiIZNG5Q/+Comye4ZTepUfq+6tya9w/+9NL7SzyNKk+te9eSa+4Zc96on19w35LoXa3GZ18Bud6A36Ett0wfpsdnsl3yuOdTMoxMuvOrrj2r2r0VCCCGEEDWMTqfFZrWV2maz2tHrA3PAlSS7QgghhBA1SHRMFB63h/TUjJJtKcmniEmI8WFUlUeS3SrUuVvZamlExZLrXvXkmvuGXPeqJ9fcN+S6l43b7cbpcOLxePB6PTgdTtxuNzq9jtZJLVm5eDV2m50jB4+ye8ce2ndO8nXIlULh9Xq9vg5CCCGEEEJUrFVLVvPt0jWltvUacBO9b78FS6GFOZ8u4MCegxhNQfQf3KdMfXarI0l2hRBCCCFEwJIyBiGEEEIIEbCk9VgVuNyRfOLKvPfqNI4dPo5SWfw7XWhYCM+//ayPowosFxtFeeDPgyycuYScrBzqNqjN3WOGER4Z7sNoA8eFrntWRjYvjH8FrU5bsu+NfXtwy203+SrUgOF0ulg4YxEH/vyLIksRkdER9BvchxatmwHyfq8MF7vm8l4X5SHJbhW42Eg+UbnuuOd2OnW71tdhBKwLjaIsLChk+nszuHP0YK66pgUrF3/LF/+dxZMvPO67YAPIxUaAArz18auoVCofRBa4PG43YRGhPPbcOMIiQtm7cx9f/HcWz772FDq9Vt7vleBi1/xv8l4XZSFlDJXs75F8fQfecs5IPiGqu6vbtaJ1UkuMwUGltu/cupvY+Biu6XA1Gq2GXgNuJiX5FKmnZFZgRbjQdReVR6fX0fv2W4iICkepVHLVNS2IiArnxLET8n6vJBe75kKUh6zsVrIrGcknrtyKhStZvmAl0bFR9LujN42aNfR1SDXC6ZRU4mvHlXyt0+uIjI4kNSWVmLhaPoysZpj8xMsoUNDkqsbcNqwfwaZgX4cUcPLzCkhPzSAmPoZf1m2S93sV+N9r/jd5r4uykGS3kl3JSD5xZW4d0peY+Fqo1Gp2bP6dj9/5jKdfeZKoWpG+Di3g2W12gs2l/9HRB+mxWeV9X5mCTUaeevEJ4uvEYSks4quZi5n54RzG/d9YX4cWUNwuNzM//JIOXZKIiasl7/cqcL5rLu91UVZSxlDJatpIPn9St2Ed9AY9Go2aDl3bUb9RXfbu3OfrsGoEnV53nve9Db1B3veVSafXUbt+IiqVCnOIiTvuuZ39uw+c8/9CXD6Px8Osj+agVqm4456BgLzfK9uFrrm810VZSbJbyWraSD6/plAgbaWrRmx8DCnJp0q+ttvsZKZnlfr4UVQBhQJA3vcVxOv1Mnf6AgryCxj92AhU6uIbo+T9XnkudM3PIe91cRGS7FaymjaSz18UWazs27W/ZDTi1o3bObz/CM1bNfV1aAHlQqMoWyW15PTJVP7YuhOnw8nqZWuIT4yV+sUKcqHrfuzQcdJOp+PxeLAUWFg0eymNmjXAEGTwdcgBYcGMRaSdSmPs+PvQas+2vJL3e+W50DWX97ooD5mgVgVq0kg+f1GQX8hH//6UtNPpKJUKasVG02dgL5q2bOLr0ALKxUZR7t9zkK9mLSEnM5s6Depw95hhRERJ39GKcKHrHh0bzYqFqyjML0Rv0NHkqibcNrQv5lCzjyINHNmZ2Ux+4hXUGnVJ726AoSPvoF3ntvJ+rwQXu+YKpULe66LMJNkVQgghhBABS8oYhBBCCCFEwJJkVwghhBBCBCxJdoUQQgghRMCSZFcIIYQQQgQsSXaFEEIIIUTAkmRXCCGEEEIELEl2hRBCCCFEwJJkVwghhBBCBCxJdoUQQgghRMCSZFcIIYQQQgQsSXaFEEIIIUTAkmRXCCGEEEIELEl2hRBCCCFEwJJkVwghhBBCBCxJdoUQQgghRMCSZFcIIYQQQgQsSXaFEEIIIUTAkmRXCCGEEEIELEl2hRA12uaft/Dkfc/47PxFliImjJtERlpmhRzP6XQx6fGXSD5yokKOJ4QQ1Z3C6/V6fR2EEEJUhkeGj7/o4+27tGPIyIHYrXZMIaYqiqq0ZfOWU1hg4e4xwyrsmOvXbGDX9j088uyDFXZMIYSortS+DkAIISrLq++/UPL3PX/sZd5nC0tt02g1aLVatFpt1QcHOOwONv30G2PHj67Q4yZ1asOyecs5fTKV2ISYCj22EEJUN5LsCiECljnUXPJ3Q5DhnG1QXMbw1awlTJn+BgCrlqzmjy27uKFPd1YtWU1hvoVrOrRm6Kg72PTTb6xdsQ6Hw0GHLu24bVg/lMriajCXy8XKRd+ybdMOLJYiYuNj6DuoF81aNb1gfH/u3IdCAfUb1yvZ9te+Q0x97QMefuYBVixcxamTp4mJr8WwUYNJrJsAgLXIylezlrBv1wFsNhshoWauv6kr3W+5HgBjsJF6jeqx/dcd9L2jdwVcSSGEqL4k2RVCiH/Iysxm1449jB1/H3k5eUyfOoP83HzMoWbG/d9Y0k6n8fl/Z1G/cV2ubtcagDmfzCczPZN7H7qb0PBQ/ty5l4/f+Yx/vfg4CXXiz3uewweOkFg3EYVCcc5jyxeu5NYhfTGHmln85TJmfvglz73xNAqFgm8WfcupE6cZ++RozCEmsjKyKcwvLPX8Og1q89f+wxV/cYQQopqRG9SEEOIfvB4Pd98/lLjEWJq1akrzVk05cewkQ0fdQUx8LVontaJ+o3oc3HsIgIy0TLZv/p2RD99Lw6YNiIyO4Pobu9K8dTM2/vjrBc+TnZlDSJj5vI/1HdiLxs0bERNXi1633UTaqXRyc/JKnpdYN4G6DeoQHhlOo2YNuabD1aWeHxJqJjszp2IuiBBCVGOysiuEEP8QFhFWUvYAYDKbiIqJQq0++yPTFGIqWU09eewkXq+XV595s9RxXC4XjZs3uuB5nE4nZk3weR+Lqx1X8ve/Sy8K8wsJCw+lyw2d+HzqTJKPnqDpVU246prmNGrWsNTzNVoNToezjK9YCCEClyS7QgjxDyqVqvQGxbnbFIDnTDMbj9eLQqHgqRefQKUu/YGZRqO54HmCg40UWawXiOHscf4uc/B6is/XonUzXvzPRPbu3M+BP//ioynTuaZ961IdHYosRQSbjRd/oUIIUQNIGYMQQlyhxDrxeL1e8vPyiaoVVepPaHjoBZ+XUCee1JS0yzpnsCmY9l2SGD52GHfeN4Qtv2zD6XSVPH76ZCqJdRIu69hCCBFIJNkVQogrFB0bTVKnNnz5yXx+37KTzPQsko+cYN3KH/lj664LPq9ZqyaknkrDUmAp1/lWLv6Wndt2k56aQWpKGju37SYiKhyN5uyHdYcPHLloJwghhKgppIxBCCEqwN33D+O75Wv5ev4KcrPzCAoOok792jRq3vCCz4lLjKNOg9ps3/w7193YpcznUqvVfLNoFVkZ2Wg0auo2qMPY8feVPH70r2NYi2xc3b7VFb0mIYQIBDJBTQghfGjvrn0snr2M5958uqRn75X6bOpMEurGc3P/nhVyPCGEqM5kZVcIIXyoeatmpPfMIDc7l/DI8Cs+ntPpIr52LN1vua4CohNCiOpPVnaFEEIIIUTAkhvUhBBCCCFEwJJkVwghhBBCBCxJdoUQQgghRMCSZFcIIYQQQgQsSXaFEEIIIUTAkmRXCCGEEEIErP8Hz5R+FxH/5kgAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax1 = plt.subplots(figsize=(10, 5))\n", "plt.xlabel(\"Time (ns)\")\n", "plt.suptitle(\"State evolution\")\n", "\n", "probabilities = np.abs(optimized_state_evolution) ** 2\n", "\n", "p0 = ax1.plot(sample_times * 1e9, probabilities[:, 0], label=\"$P_0$\")\n", "p1 = ax1.plot(sample_times * 1e9, probabilities[:, 1], label=\"$P_1$\")\n", "ax1.set_ylabel(\"Probabilities $P_0$, $P_1$\")\n", "\n", "ax2 = ax1.twinx()\n", "p2 = ax2.semilogy(\n", " sample_times * 1e9,\n", " probabilities[:, 2],\n", " label=\"$P_2$\",\n", " color=qv.QCTRL_STYLE_COLORS[2],\n", ")\n", "\n", "ax2.set_ylim([1e-9, 100])\n", "ax2.set_ylabel(\"Probability $P_2$\")\n", "\n", "lgns = p0 + p1 + p2\n", "lbs = [l.get_label() for l in lgns]\n", "plt.legend(lgns, lbs, loc=\"center left\", bbox_to_anchor=(0, 0.75))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is the evolution of the optimized SFQ X gate for the qubit initialized in the ground state. As in the plot for the standard gate, the population of the third level is shown in a log scale (right axis). Note that by the end of the gate, this population is minimized, allowing the operational infidelity ($I<10^{-7}$) to improve by 6 orders of magnitude as compared to the standard gate.\n", "\n", "To demonstrate the gate robustness, in the cell below we calculate quasi-static noise susceptibility of the two controls as a function of qubit frequency detuning." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Your task (action_id=\"1827956\") has started.\n", "Your task (action_id=\"1827956\") has completed.\n", "Your task (action_id=\"1827970\") is queued.\n", "Your task (action_id=\"1827970\") has started.\n", "Your task (action_id=\"1827970\") has completed.\n" ] } ], "source": [ "detunings = 2 * np.pi * np.linspace(-20, 20, 200) * 1e6\n", "drift_infidelities = {}\n", "for scheme in [\"Standard\", \"Q-CTRL\"]:\n", " scan_controls = controls[scheme]\n", "\n", " # Set up the graph for the quasi-static scan simulation.\n", " graph = bo.Graph()\n", "\n", " a = graph.annihilation_operator(3)\n", " adag = graph.creation_operator(3)\n", " n = graph.number_operator(3)\n", "\n", " omega_signal = graph.pwc(**scan_controls[\"omega\"])\n", " alpha_signal = graph.pwc(**scan_controls[\"alpha\"])\n", " pulse_signal = graph.pwc(**scan_controls[\"pulse\"])\n", " detuning_signal = graph.pwc_signal(\n", " values=detunings[:, None], duration=gate_durations[scheme]\n", " )\n", " hamiltonian = (\n", " omega_signal * n\n", " + alpha_signal / 2 * (n @ n - n)\n", " + pulse_signal * (a + adag) / 2\n", " + detuning_signal * n\n", " )\n", "\n", " # Infidelities for detuning rates.\n", " infidelities = graph.infidelity_pwc(\n", " hamiltonian=hamiltonian, target=graph.target(target), name=\"infidelities\"\n", " )\n", "\n", " # Calculate the graph and extract infidelities.\n", " graph_result = bo.execute_graph(graph, \"infidelities\")\n", "\n", " drift_infidelities[scheme] = graph_result[\"output\"][\"infidelities\"][\"value\"]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colors = {\"Standard\": qv.QCTRL_STYLE_COLORS[1], \"Q-CTRL\": qv.QCTRL_STYLE_COLORS[0]}\n", "\n", "fig = plt.figure(figsize=(10, 5))\n", "for scheme in [\"Standard\", \"Q-CTRL\"]:\n", " plt.plot(\n", " detunings / (2 * np.pi * 1e6),\n", " drift_infidelities[scheme],\n", " color=colors[scheme],\n", " label=scheme,\n", " )\n", "fig.suptitle(\"Quasi-static scan\")\n", "plt.xlabel(\"Frequency drift (MHz)\")\n", "plt.ylabel(\"Infidelity\")\n", "plt.legend()\n", "plt.ylim([0, 0.25])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Operational infidelity as a function of the drift in the qubit's frequency, allowing a comparison between the performances of the standard and the Boulder Opal gates. You can see the detrimental impact of leakage on the standard gate by its higher infidelity levels. In contrast, by minimizing leakage, the robust gate produces a much lower infidelity. Furthermore, due to the gate's robustness to frequency drift, this low infidelity level extends over a large range of detunings." ] } ], "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": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 4 }