{ "cells": [ { "cell_type": "markdown", "id": "6ca82943", "metadata": {}, "source": [ "# Robust Phase Estimation\n", "\n", "This example introduces the Robust Phase Estimation algorithm; this QPE version requires only a single ancilla/phase qubit. The way the algorithm is implemented is inspired from J.Gunther et al., *Phase estimation with partially randomized time evolution* [arxiv:2503.05647](https://arxiv.org/abs/2503.05647).\n", "\n", "In this notebook we explain the idea of the algorithm and apply it to simple models: the Heisenberg model with $4$ spins, the H$_2$ molecule in the minimal basis.\n", "\n", "We study the Trotter and statistical errors, and check that the RPE algorithm verifies Heisenberg scaling, i.e. the possibility to measure the energy with precision $\\varepsilon$ in time $\\mathcal{O}(1/\\varepsilon)$." ] }, { "cell_type": "code", "execution_count": 1, "id": "251c23be", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:11.076107Z", "iopub.status.busy": "2026-04-03T03:59:11.075953Z", "iopub.status.idle": "2026-04-03T03:59:13.071548Z", "shell.execute_reply": "2026-04-03T03:59:13.070699Z" } }, "outputs": [], "source": [ "import time\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import quimb.tensor as qtn\n", "from pyscf import gto\n", "from tqdm import notebook as tqdm\n", "\n", "import qpe_toolbox.estimation as qpe\n", "from qpe_toolbox import EXACT\n", "from qpe_toolbox.hamiltonian import (\n", " chemistry_hamiltonian,\n", " do_dmrg,\n", " heisenberg_hamiltonian,\n", ")" ] }, { "cell_type": "code", "execution_count": 2, "id": "8b6bc5b2", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:13.073163Z", "iopub.status.busy": "2026-04-03T03:59:13.072855Z", "iopub.status.idle": "2026-04-03T03:59:13.075753Z", "shell.execute_reply": "2026-04-03T03:59:13.075052Z" } }, "outputs": [], "source": [ "plt.rcParams.update({\"font.size\": 12})" ] }, { "cell_type": "markdown", "id": "73d1bac1", "metadata": {}, "source": [ "## Hadamard test\n", "The Robust Phase Estimation algorithm relies on the Hadamard test procedure, which we introduce below. Our presentation takes inspiration from [Lin Lin's lecture notes](https://math.berkeley.edu/~linlin/qasc/) and the [\"Hadamard test\" Wikipedia page](https://en.wikipedia.org/wiki/Hadamard_test).\n", "\n", "The goal of the Hadamard test is to compute $\\bra{\\psi} U \\ket{\\psi}$ where $U$ is a unitary operator. Since $U$ is generally not Hermitian, it is not an observable, therefore the real and imaginary part of $\\bra{\\psi} U \\ket{\\psi}$ must be measured separately.\n", "\n", "The idea is to build a random variable whose expectation value gives the real (resp. imaginary) part of $\\bra{\\psi} U \\ket{\\psi}$.\n", "Consider the following circuit:\n", "\n", "\n", "\n", "*Taken from Günther et al. arXiv:2503.05647*.\n", "\n", "The Hadamard test uses a single auxiliary qubit initially in state $\\ket{0}$ and a data register with $n$ qubits initialized in state $\\ket{\\psi}$.\n", "We start by applying the the Hadamard gate $H$ to the auxiliary qubit to put it in a superposition state. Then we apply a controlled-$U$ gate to the data register conditioned on the auxiliary qubit, followed by a a rotation (PHASE) gate $R(\\theta)$ and finally another Hadamard gate on the control qubit.\n", "\n", "At the end of the circuit we measure the control qubit and define a random variable $\\textbf{Z}_\\theta$: if the result of the measure is $\\ket{0}$, we output $1$, if the result is $\\ket{1}$ we output $-1$. The expectation value of $\\textbf{Z}_\\theta$ satisfies:\n", "\n", "$$ \\mathbb{E}\\textbf{Z}_\\theta = P(0) - P(1) = \\mathrm{Re} \\left(e^{i\\theta} \\bra{\\psi}U\\ket{\\psi}\\right). $$\n", "\n", "We use two special choices of $\\theta$:\n", "\n", "$$ \\theta = 0 \\qquad \\implies \\qquad \\mathbb{E}\\textbf{Z}_\\theta = \\mathrm{Re} \\left(\\bra{\\psi}U\\ket{\\psi}\\right). $$\n", "$$ \\theta = -\\frac{\\pi}{2} \\qquad \\implies \\qquad \\mathbb{E}\\textbf{Z}_\\theta = \\mathrm{Im} \\left(\\bra{\\psi}U\\ket{\\psi}\\right). $$\n", "\n", "\n", "Let $\\textbf{X}$ and $\\textbf{Y}$ be the random variables corresponding to $\\theta=0, -\\pi/2$ respectively.\n", "Define $\\textbf{Z} = \\textbf{X} + i \\textbf{Y}.$ Then we get\n", "\n", "$$ \\mathbb{E}\\textbf{Z} = \\bra{\\psi}U\\ket{\\psi} $$\n", "\n", "Let us first illustrate a simple instance of the Hadamard test with $U = |0\\rangle \\langle 0| + e^{i\\alpha} |1\\rangle \\langle 1|$ and $|\\psi\\rangle = |1\\rangle$." ] }, { "cell_type": "code", "execution_count": 3, "id": "90c862dc", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:13.077420Z", "iopub.status.busy": "2026-04-03T03:59:13.077275Z", "iopub.status.idle": "2026-04-03T03:59:15.000911Z", "shell.execute_reply": "2026-04-03T03:59:15.000166Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cos(alpha) = 0.866 and sin(alpha) = 0.5\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Re() = 0.866\n", "Im() = 0.5\n" ] } ], "source": [ "alpha = np.pi / 6\n", "print(f\"cos(alpha) = {np.cos(alpha):.4g} and sin(alpha) = {np.sin(alpha):.4g}\")\n", "\n", "# Hadamard test with theta=0\n", "circ = qtn.Circuit(2)\n", "circ.apply_gate(\"X\", 1)\n", "circ.apply_gate(\"H\", 0)\n", "circ.apply_gate(\"CPHASE\", alpha, 0, 1)\n", "circ.apply_gate(\"H\", 0)\n", "\n", "probs = circ.compute_marginal(where=[0])\n", "print(f\"Re() = {probs[0] - probs[1]:.4g}\")\n", "\n", "# Hadamard test with theta=-pi/2\n", "circ = qtn.Circuit(2)\n", "circ.apply_gate(\"X\", 1)\n", "circ.apply_gate(\"H\", 0)\n", "circ.apply_gate(\"CPHASE\", alpha, 0, 1)\n", "circ.apply_gate(\"PHASE\", -np.pi / 2, 0)\n", "circ.apply_gate(\"H\", 0)\n", "\n", "probs = circ.compute_marginal(where=[0])\n", "print(f\"Im() = {probs[0] - probs[1]:.4g}\")" ] }, { "cell_type": "markdown", "id": "6056e467", "metadata": {}, "source": [ "Now take the Heisenberg Hamiltonian with $4$ spins" ] }, { "cell_type": "code", "execution_count": 4, "id": "4b93c09d", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:15.002775Z", "iopub.status.busy": "2026-04-03T03:59:15.002606Z", "iopub.status.idle": "2026-04-03T03:59:15.045772Z", "shell.execute_reply": "2026-04-03T03:59:15.045046Z" } }, "outputs": [], "source": [ "n_qubits = 4\n", "H = heisenberg_hamiltonian(n_qubits)\n", "E0, psi0 = do_dmrg(H)" ] }, { "cell_type": "markdown", "id": "9029beee", "metadata": {}, "source": [ "We run the Hadamard test on the time evolution operator $U = e^{-iHt}$ with the physical register in state $\\ket{\\psi} = \\ket{\\psi_0}$. Then\n", "\n", "$$ \\mathbb{E}\\textbf{Z} = e^{-i E_0 t}. $$\n", "\n", "The function `run_hadamard_test` runs the Hadamard test and returns $\\mathrm{Re}~e^{i\\theta} \\bra{\\psi}U\\ket{\\psi}$.\n", "\n", "Below we estimate $E_0$ by running the Hadamard test for a time evolution during a random time $t$.\n", "\n", "We first consider exact time evolution." ] }, { "cell_type": "code", "execution_count": 5, "id": "0020c8e1", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:15.047246Z", "iopub.status.busy": "2026-04-03T03:59:15.047058Z", "iopub.status.idle": "2026-04-03T03:59:15.089641Z", "shell.execute_reply": "2026-04-03T03:59:15.089281Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "error = 4.4e-08\n" ] } ], "source": [ "rng = np.random.default_rng(seed=42)\n", "t = rng.random()\n", "data_reg = list(range(1, n_qubits + 1))\n", "U = H.get_U_exact(t, data_reg, controls=(0,))\n", "\n", "n_shots = EXACT # exact computation (no sampling)\n", "\n", "X = qpe.run_hadamard_test(psi0, U, 0, n_shots)\n", "Y = qpe.run_hadamard_test(psi0, U, -np.pi / 2, n_shots)\n", "Z = X + 1j * Y\n", "\n", "print(f\"error = {abs(np.angle(Z) / t + E0):.2g}\")" ] }, { "cell_type": "markdown", "id": "62098fa5", "metadata": {}, "source": [ "The previous relation defines a function $g: t \\to \\mathbb{E}\\textbf{Z}(t) $.\n", "\n", "\n", "At this stage let us emphasize two points:\n", " * In general:\n", "\n", "$$ \\mathbb{E}\\textbf{Z}(t) = \\sum_k c_k e^{i E_k t}, \\qquad \\text{where} \\qquad H\\ket{\\psi_k} = E_k \\ket{\\psi_k},~c_k = |\\langle \\psi | \\psi_k \\rangle|^2. $$\n", "In the following, we consider the simplest case $c_0=1$ ($\\psi$ is the ground state).\n", "\n", " * With a QPU emulator like $\\texttt{quimb}$, the probabilities $P(0)$, $P(1)$ can be computed exactly. On a real quantum device, these probabilities are estimated from repeated measurements (shots).\n", "With a finite number of shots $N_{\\rm shots}$, we can estimate $g(t)$ by taking the statistical mean over $N_{\\rm shots}$ samples:\n", "\n", "$$ \\bar{\\bf Z}(t) = \\frac{1}{N_{\\rm shots}} \\sum_{n=1}^{N_{\\rm shots}} {\\bf Z}^{(n)} (t). $$\n", "If $N_{\\rm shots}$ shots are used, the statistical error scales as\n", "\n", " $$\\mathcal{O}\\left(\\frac{1}{\\sqrt{N_{\\rm shots}}}\\right).$$\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "7482565d", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:15.092073Z", "iopub.status.busy": "2026-04-03T03:59:15.091913Z", "iopub.status.idle": "2026-04-03T03:59:22.981644Z", "shell.execute_reply": "2026-04-03T03:59:22.980888Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "535226ab9f3641f19d5be784ea6d000b", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/5 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax_e, ax_t) = plt.subplots(nrows=2)\n", "fig.subplots_adjust(hspace=0.4)\n", "ax_e.loglog(shots_list, errors, \"-o\")\n", "ax_e.loglog(\n", " shots_list,\n", " errors[0] * np.sqrt(10 / shots_list),\n", " \"--\",\n", " label=\"$\\\\propto 1/\\\\sqrt{N_{\\\\rm shots}}$\",\n", " zorder=0,\n", ")\n", "ax_t.plot(shots_list, durations, \"-o\")\n", "ax_e.legend()\n", "ax_e.set_xlabel(\"number of shots\")\n", "ax_t.set_xlabel(\"number of shots\")\n", "ax_e.set_ylabel(\"error (units of J)\")\n", "ax_t.set_ylabel(\"duration (seconds)\");" ] }, { "cell_type": "markdown", "id": "7cf0f287", "metadata": {}, "source": [ "## Robust phase estimation algorithm\n", "\n", "### Introduction\n", "\n", "Quote from Günther et al. [arxiv:2503.05647](https://arxiv.org/abs/2503.05647):\n", "> \"If we think of g(t) as a time signal, then the phase estimation routine will constitute a signal processing transformation to compute the lowest frequency of $g(t)$ (corresponding to the energy $E_0$), provided that we have some guarantee on the overlap of $\\ket{\\psi}$ with the ground state; we assume a lower bound\n", " $c_0 \\geq \\eta$. With appropriate signal processing methods, one can find the value of $E_0$ with accuracy $\\varepsilon$ using $M$ circuits with time evolution for\n", " times $t_1, . . . , t_M$. This can be done such that the maximal time evolution $t_{\\rm max} = \\mathrm{max}\\{t_1, . . . , t_M\\}$ and the total time over all circuit runs $t_{\\rm tot} = t_1 + t_2 + · · · + t_M$ both scale as $\\varepsilon^{-1}$. This Heisenberg scaling is known to be optimal.\"\n", "\n", "### Algorithm\n", "To get precision $\\varepsilon$, the idea of the robust phase estimation algorithm is to consider $M$ different circuits where $M = \\lceil \\log_2 \\varepsilon^{-1} \\rceil$ and estimate\n", "\n", "$$ g(2^m) = \\mathbb{E}[Z(2^{m})] = \\exp(-i 2^{m} E_0) $$\n", "\n", "for $m=0,1,..,M-1$. Each iteration gives a supplementary bit of precision on $E_0$.\n", "\n", "**Algorithm 1 (p.24)**\n", "\n", "1. The algorithm is initialized with $\\theta_{-1}=0$ so that $\\theta_0 = \\phi_0$.\n", "\n", "2. For each $m$:\n", "\n", " - Take $N_{\\rm shots}$ samples to compute the average:\n", "\n", " $$ \\bar{\\bf Z}(2^{m}) = \\frac{1}{N_{\\rm shots}} \\sum_{n=1}^{N_{\\rm shots}} {\\bf Z}^{(n)} (2^m) $$\n", "\n", "\n", " - From the outcome we compute $\\phi_m = - \\arg(\\bar{Z}(2^m))$ using `numpy.angle`\n", "\n", " - By definition $\\phi_m \\in ]-\\pi, \\pi]:~\\phi_m~$ is an approximation of $2^mE_0$ modulo $2\\pi$\n", "\n", " - Given a previous guess $\\theta_{m-1}$ for the ground state energy $E_0$, the new energy estimate $\\theta_m$ is given by\n", "\n", " $$ \\theta_m = 2^{-m} (2\\pi k + \\phi_m), $$\n", " where $k$ is an integer between $0$ and $2^m - 1$ which minimizes the distance\n", "\n", " $$ d(\\theta_m, \\theta_{m-1}) = \\min_{q\\in\\mathbb{Z}} | \\theta_m - \\theta_{m-1} + 2q\\pi|, $$\n", " under the condition $-\\pi < \\theta \\leq \\pi$.\n", "\n", "The algorithm ensures that at each step, $\\theta_m$ is the best $m$-bit approximation of $E_0$.\n", "The following lemma guarantees convergence:\n", "\n", "**Lemma B.1. (p.25)**:\n", "if $d(\\phi_k,2^{k}E)<\\frac{\\pi}3$ for $k=0,1,...,m$ then $\\theta_m$ is such that $d(\\theta_m,E) \\leq 2^{-m}\\frac{\\pi}3$" ] }, { "cell_type": "markdown", "id": "35d7ab34", "metadata": {}, "source": [ "#### Illustration of the distance $d(\\theta,\\phi)$\n", "\n", "To build an intuition, let us plot the distance $d(\\theta, \\phi)$ as a function of $\\theta$ for a given $\\phi$ ($ 3\\pi/2$ in the example) and vice-versa (the distance is symmetric by definition)." ] }, { "cell_type": "code", "execution_count": 8, "id": "368d9654", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.301947Z", "iopub.status.busy": "2026-04-03T03:59:23.301804Z", "iopub.status.idle": "2026-04-03T03:59:23.403490Z", "shell.execute_reply": "2026-04-03T03:59:23.402720Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thetas = np.linspace(-2 * np.pi, 2 * np.pi, 600)\n", "plt.xticks(\n", " [i * np.pi for i in range(-2, 3)],\n", " [r\"$-2\\pi$\", r\"$-\\pi$\", \"$0$\", r\"$\\pi$\", r\"$2\\pi$\"],\n", ")\n", "plt.yticks([0, np.pi / 2, np.pi], [\"0\", \"$\\\\pi/2$\", \"$\\\\pi$\"])\n", "\n", "plt.xlabel(r\"$\\theta$\")\n", "\n", "plt.plot(\n", " thetas,\n", " [qpe.rpe_distance(t, 3 * np.pi / 2) for t in thetas],\n", " label=r\"$d(3\\pi/2, \\theta)$\",\n", ")\n", "plt.plot(\n", " thetas,\n", " [qpe.rpe_distance(3 * np.pi / 2, t) for t in thetas],\n", " \"--\",\n", " label=r\"$d(\\theta, 3\\pi/2)$\",\n", ")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "8024006e", "metadata": {}, "source": [ "Let us now illustrate the first two steps of the algorithm for concreteness. We start with $N_{\\rm shots}=2$ and $\\epsilon = 0.2$. We also consider exact time evolution." ] }, { "cell_type": "code", "execution_count": 9, "id": "10813558", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.405021Z", "iopub.status.busy": "2026-04-03T03:59:23.404858Z", "iopub.status.idle": "2026-04-03T03:59:23.454642Z", "shell.execute_reply": "2026-04-03T03:59:23.453062Z" } }, "outputs": [], "source": [ "sign_E0 = np.sign(E0)\n", "\n", "epsilon = 0.02\n", "M = int(np.ceil(np.log2(1 / epsilon)))\n", "\n", "n_shots = 2\n", "\n", "# m = 0\n", "phi_0 = qpe.rpe_get_hadamard_output(H, psi0, 0, EXACT, n_shots)\n", "theta_0 = phi_0\n", "\n", "m = 1\n", "phi_1 = qpe.rpe_get_hadamard_output(H, psi0, m, EXACT, n_shots)\n", "S_1 = [(phi_1 + sign_E0 * 2 * np.pi * k) / 2**m for k in range(2**m)]" ] }, { "cell_type": "markdown", "id": "ed7bb097", "metadata": {}, "source": [ "Let's visualize how the different elements of $S_1$ compare to $\\theta_0$" ] }, { "cell_type": "code", "execution_count": 10, "id": "003b363d", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.457686Z", "iopub.status.busy": "2026-04-03T03:59:23.457515Z", "iopub.status.idle": "2026-04-03T03:59:23.530586Z", "shell.execute_reply": "2026-04-03T03:59:23.528698Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hlines(1, -np.pi, np.pi, \"k\")\n", "plt.plot([-np.pi, np.pi], [1, 1], \"|\", markersize=10, color=\"k\")\n", "plt.plot(theta_0, 1, \"*\", markersize=20, color=\"r\", label=r\"$\\theta_0$\")\n", "y = np.ones(np.shape(S_1))\n", "plt.plot(S_1, y, \"o\", markersize=15, label=r\"$S_1$\")\n", "\n", "plt.text(-1.1 * np.pi, 0.99, r\"$-\\pi$\", fontsize=16)\n", "plt.text(np.pi, 0.99, r\"$\\pi$\", fontsize=16)\n", "plt.text(1.05 * theta_0, 0.99, r\"$\\theta_0$\", fontsize=16, color=\"r\")\n", "\n", "plt.axis(\"off\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "ecbe70e2", "metadata": {}, "source": [ "We compute $\\theta_1$ as the element from $S_1$ closest to $\\theta_0$ and check that the error decreases between the first and second iteration:" ] }, { "cell_type": "code", "execution_count": 11, "id": "0f9c724f", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.532668Z", "iopub.status.busy": "2026-04-03T03:59:23.532498Z", "iopub.status.idle": "2026-04-03T03:59:23.535536Z", "shell.execute_reply": "2026-04-03T03:59:23.534923Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact energy E = -1.6160\n", "theta_0 = -2.3562\n", "theta_1 = -1.1781\n" ] } ], "source": [ "theta_1, d_min = qpe.rpe_update_theta(S_1, theta_0)\n", "print(f\"Exact energy E = {E0:.4f}\")\n", "print(f\"theta_0 = {theta_0:.4f}\")\n", "print(f\"theta_1 = {theta_1:.4f}\")" ] }, { "cell_type": "markdown", "id": "ad401cdc", "metadata": {}, "source": [ "### Run RPE. Statistical precision\n", "\n", "We will now run the algorithm and see the influence of statistical noise. The `robust_phase_estimation` function returns the full list of $\\theta_m$, $m=0,...,M-1$.\n", "\n", "We start with $N_{\\rm shots}=1$." ] }, { "cell_type": "code", "execution_count": 12, "id": "6029d4c1", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.537634Z", "iopub.status.busy": "2026-04-03T03:59:23.537477Z", "iopub.status.idle": "2026-04-03T03:59:23.679274Z", "shell.execute_reply": "2026-04-03T03:59:23.678361Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Target precision epsilon=0.02: requires M=6 iterations\n", "\n", "m \t phi_m \t theta_m \t time (s)\n", "0 \t -0.7854 \t -0.7854 \t 0.0 \n", "1 \t -2.3562 \t -1.1781 \t 0.0 \n", "2 \t -0.7854 \t -1.7671 \t 0.1 \n", "3 \t 0.7854 \t -1.4726 \t 0.1 \n", "4 \t -0.7854 \t -1.6199 \t 0.1 \n", "5 \t -2.3562 \t -1.6444 \t 0.1 \n", "6 \t -2.3562 \t -1.6076 \t 0.1 \n" ] } ], "source": [ "epsilon = 0.02\n", "M = int(np.ceil(np.log2(1 / epsilon)))\n", "print(f\"Target precision epsilon={epsilon}: requires M={M} iterations\\n\")\n", "\n", "n_shots = 1\n", "\n", "theta_list = qpe.robust_phase_estimation(\n", " H, psi0, epsilon, sign_E0, EXACT, n_shots, verbosity=1\n", ")" ] }, { "cell_type": "code", "execution_count": 13, "id": "dbf4bbe7", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.681282Z", "iopub.status.busy": "2026-04-03T03:59:23.680666Z", "iopub.status.idle": "2026-04-03T03:59:23.883715Z", "shell.execute_reply": "2026-04-03T03:59:23.883075Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(\n", " [qpe.rpe_distance(theta, E0) for theta in theta_list[1:]],\n", " \"-o\",\n", " label=f\"$N_{{\\\\rm shots}}={n_shots}$\",\n", ")\n", "plt.semilogy([np.pi / 3 / 2**i for i in range(M + 1)], \"k--\", label=\"$2^{-m}~\\\\pi/3$\")\n", "plt.legend()\n", "plt.xlabel(\"iteration $m$\")\n", "plt.ylabel(\"$d(\\\\theta_m, E)$\");" ] }, { "cell_type": "markdown", "id": "224a3d00", "metadata": {}, "source": [ "We see that for such small systems, with exact time evolution, a single shot gives an estimate that converges. We now increase the number of shots to improve the precision" ] }, { "cell_type": "code", "execution_count": 14, "id": "9c383a0e", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:23.885463Z", "iopub.status.busy": "2026-04-03T03:59:23.885297Z", "iopub.status.idle": "2026-04-03T03:59:24.809654Z", "shell.execute_reply": "2026-04-03T03:59:24.808848Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAHRCAYAAABzQ13AAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjgsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvwVt1zgAAAAlwSFlzAAAPYQAAD2EBqD+naQAA829JREFUeJzs3Xd8jdcfwPHPvTc3OxKRyCDEJsQIsVftrbVXf1pbjVpFldKqqlJFqV3UHrVCa1ObWAliRiIhIiJ73/H8/rikTSWRxL03wXm/Xvfl5hnnfJ8g95vznOd7ZJIkSQiCIAiCIAg5Is/vAARBEARBEN4mInkSBEEQBEHIBZE8CYIgCIIg5IJIngRBEARBEHJBJE+CIAiCIAi5IJInQRAEQRCEXBDJkyAIgiAIQi6I5EkQBEEQBCEXRPIkCIIgCIKQCyJ5EgRBEARByAWRPAmCIAiCIOSCSJ4EQSjQHj16xIABA3B1dcXMzAx3d3fGjBlDdHS0Qdt6/vw5q1at4qOPPqJs2bJYWFhga2tLw4YNWb16NVqtVh+X94pWrVohk8mQyWQsWrQoy+MGDhyYftyAAQMMEsvrHD16lI8++ghnZ2fMzMxwdXWldevW/Pnnn/kSjyAYi0l+ByAIgpCVwMBA6tevT0REBJ07d6ZixYpcvHiRhQsXcuDAAc6cOUORIkUM0tb27dsZPnw4Li4ufPDBB5QoUYKnT5+yc+dOBg0axF9//cX27duRyWR6vebLly9jYmKCWq3G398/02POnz/PmjVrUCgUaDQaatWqpdcYcmLixInMnTuX4sWL06lTJxwcHHj27BmXL1/mxIkTtGvXzugxCYLRSIIgCAVUq1atJEBatGhRhu1jx46VAGno0KEGa+vo0aPS3r17JY1Gk2H7kydPJDc3NwmQduzYkcsryl5gYKAESPXr15ecnJwkb2/vV47RaDSSl5eXVLRoUalOnToSIF24cEGvcbzOihUrJEDq37+/lJqa+sr+tLQ0o8YjCMYmkidBEF5x69Ytafjw4VLZsmUlS0tLycbGRqpQoYLUo0cPKSUlxSgx3L9/XwIkd3f3VxKYuLg4ycrKSrK0tJQSEhKM2pYkSdKsWbMkQBo5cmTOLygHtm7dKgHSqFGjpDZt2kiWlpavxPvrr79KgLR27VrJwcFBUiqVRvs7kSRJSklJkRwdHaUSJUpkmjgJwvtAzHkSBCGDEydOUKNGDX777TeqVavG6NGj+eSTTyhVqhR+fn6YmZkZJY7jx48DujlAcnnGH1U2NjY0aNCApKQkzp8/b9S2AJRKJQAmJvqd+XDp0iUAatasiZeXF0lJSQQGBqbvj4yM5KuvvqJ+/fo0adKEyMhIqlSpYrS/E4DDhw/z7NkzunTpglwuZ//+/cyZM4eFCxdy7tw5o8UhCPlJzHkSBCGDr776CpVKxcWLF/Hy8srxeQsWLCAmJibHx1evXp0PP/wwy/137twBoHz58pnuL1euHIcOHeLu3bs0b94827702ZZareb3338HoE2bNtkem1svk6datWphZWUFgL+/P+XKlQNg8uTJxMbGsnjxYi5fvpx+bHb0/ffi6+sLgLm5OTVq1ODGjRsZ9jdu3JgdO3bg6OiY4z4F4W0jkidBEDKIjIzE1tYWDw+PXJ23YMECHj58mOPj+/fvn+2HdGxsLAC2traZ7n+5PSeJgT7bmjx5Mjdu3KBdu3a0bt36tcfnlCRJXLlyBUtLSypWrIiFhQWgS566du3KhQsX+O233xg2bBg1atRg+/btQM6SJ33+vURERAAwd+5cPDw8OHXqFNWrVycoKIgJEyZw6NAhunfvzokTJ3LcpyC8bUTyJAhCBvPnz2fAgAF4eXnRtm1bbGxsaNasGY0bN872vODgYOMEmI8WLVrETz/9RMWKFVm/fr1e27537x6xsbHUr18fhUJBqVKlsLW1xd/fH61Wy4gRIyhSpAizZs0CMo5SZUfffy8vSzSYmJiwd+9e3N3dAfD09GTXrl1UqFCBv//+m3PnzlGvXj299i0IBYVIngRBSCdJEk+fPqVkyZL4+vpy69YtACpWrGj0WF6OBr0cNfqvl9vt7OyM0tbixYv5/PPP8fDw4OjRo9jb27+239z4bzIkk8moUaMG169fZ8WKFVy+fJmVK1dSuHBhQFfSwMzMDE9PT73G8Tovv0c1atRIT5xesrS0pHXr1qxevZqLFy+K5El4Z4nkSRCEdKNHj2bx4sUMHz6cNWvWULZs2RxPRtb33JoKFSoAcPfu3Uz337t3D8h6HpM+21qwYAFjx46lSpUqHD16lKJFi762z9z692Txl2rUqMHff//NlClT8Pb2ZuDAgQAEBQURFRWFt7d3+uT1rBjq7yWrRPNlcpecnJzjPgXhrZPfj/sJglAwPH36VJLL5VLr1q3zdH7JkiUlIMev/v37Z9teQSlV8MMPP0iAVL16denZs2ev/0bkUaNGjSRAunHjRvq29evXS4Akl8ulixcvpm/fvn27BEjDhw9/bbv6/nsJDg6WZDKZVKJEiVe+l5IkSW3atJEAacuWLTm/eEF4y4jkSRAESZIk6fr16xIg1atXT1Kr1a/sT0pKMnpMeSmSef/+fenWrVuvFGrMS1vffvutBEg1a9aUnj9//tp4+/fvLwHSmjVrcnB1/9BoNJK1tbVkZWWVISF5/vy5tGvXLun48eMZjp80aZIESKtXr85VP/rSqVMnCZDmz5+fYfvBgwclmUwm2dnZSTExMfkSmyAYg0ySJMmQI1uCILwdVCoVVapU4e7du5QvX56WLVtia2tLZGQkN2/epHz58vz2229Gjem/S6pUqlSJCxcucPz4ccqXL8/Zs2dfWZ7F3d2dhw8fEhQUlGFOTm7bWrduHZ988gkKhYJRo0Zl+qSeu7s7n3zySfrX//vf/1i/fj3r16+nX79+Ob7OgIAAKleuTIMGDTh9+vRrj2/ZsiVHjhzBz8+PqlWr5rgffXn06BH169cnNDSU5s2bU6NGDYKCgti9ezcymYwtW7bQtWtXo8clCEaT39mbIAgFR2hoqDR48GDJ3d1dUiqVkqWlpVS6dGmpW7du0smTJ/MlppCQEOmTTz6RnJ2dJaVSKZUoUUL6/PPPpaioqEyPf3mbKigo6I3amj59+mtvcTVp0iTDOdWrV5dsbGyyjC0r69atkwBp9OjROTre3t5esrCwyHSE0FgiIiKkkSNHSiVKlJCUSqVUpEgR6cMPPzT6UjGCkB/EyJMgCIIexMTEUKRIEcaPH8+PP/6Y3+EIgmBAYnkWQRAEPTh16hRKpZJx48bldyiCIBiYGHkSBEEQBEHIBTHyJAiCIAiCkAsieRIEQRAEQcgFkTwJgiAIgiDkgkieBEEQBEEQckGsbWcAWq2WsLAwbGxskMlk+R2OIAiCIAg5IEkS8fHxuLq6IpdnPb4kkicDCAsLw83NLb/DEARBEAQhD0JDQylevHiW+0XyZAA2NjaA7ptfqFChfI5GEARBEISciIuLw83NLf1zPCsieTKAl7fqChUqJJInQRAEQXjLvG7KjZgwLgiCIAiCkAsieRIEQRAEQcgFkTwJgiAIgiDkgkieBEEQBEEQckFMGBcEQRDeSSqVCo1Gk99hCAWAUqlEoVDorT2RPAmCIAjvlLi4OCIjI0lNTc3vUIQCQiaTYWtri7Ozs16KV4vkSRAEQXhnxMXF8fjxY6ytrXFwcECpVIqVHt5zkiSRmJjIs2fPsLCwwM7O7o3bFMmTIAiC8M6IjIzE2tqa4sWLi6RJSGdhYUFqaioRERHY2tq+8b8NMWE8E8+ePaN9+/ZYWVlRoUIFjh49mt8hCYIgCK+hUqlITU3Vy4ej8O4pVKgQGo1GL/PgxMhTJkaMGIGzszPPnj3jyJEj9OjRg3v37mFvb5/foQmCIAhZePmhqFQq8zkSoSAyMdGlPGq1Ov19XomRp/9ISEhg9+7dfPPNN1haWtKpUyc8PT3Zs2dPfocmCIIg5IAYdRIyo89/F2998pSQkMD06dNp06YN9vb2yGQy1q5dm+mxqampTJo0CVdXVywsLKhTpw6HDx/OcMy9e/fS75e/5Onpyc2bNw15GYIgCIIgvCXe+uQpMjKSb7/9llu3blGtWrVsj/3kk0+YP38+ffv2ZeHChSgUCtq1a8fp06fTj0lISHhlMd9ChQqRkJBgkPgFQRAEQXi7vPXJk4uLC0+ePOHhw4fMnTs3y+MuXrzIli1bmD17NnPnzmXIkCEcO3aMkiVLMnHixPTjrK2tiYuLy3BuXFwc1tbWBruG3Pj+++8ZNmwYT58+ze9QBEEQBOG99NYnT2ZmZjg7O7/2uB07dqBQKBgyZEj6NnNzcwYOHMi5c+cIDQ0FoFy5ciQkJPD48eP0427cuEHlypX1H3wuxcTE8P3337N8+XLKli3LzJkzSUxMzO+wBEEQBCM6ePAgMpkMmUxGQEDAK/s7duyYYerJuyQ3U3UM6a1PnnLq6tWrlC9f/pVbcrVr1wbg2rVrgG7kqXPnzkyfPp3k5GT27duHv78/nTt3NnbIr7Czs+Ovv/6idu3aJCQk8PXXX1O+fHnWrFkjliAQBEF4T/j5+QEgl8vZt29fpvurVq1q7LCMIjdTdQzpvUmenjx5gouLyyvbX24LCwtL3/brr78SFhZGkSJFGDduHFu3bs22TEFqaipxcXEZXobSqFEjzp8/z5YtW3B3dycsLIwBAwZQo0YNrly5YrB+BUEQ3mcarcS5wOfsufaYc4HP0WilfIvF39+fQoUK0bp1a3x8fDLsi46OJjQ0NF8TC0PK6VQdQ3tv6jwlJydjZmb2ynZzc/P0/S85Ojry559/5rjt2bNn880337x5kDkkk8no2bMnH374IUuWLGHmzJncvn1bLyXnBUEQhIwO3HjCNz4BPIlNSd/mYmvO9I4etKny6i/lhubn54enpycdOnRg9OjRPH/+nCJFiqTvA97ZkaecTtUxtPdm5Ollafb/SklJSd+fV19++SWxsbHpr5fzpwzNzMyMcePGERgYyI4dOyhdunT6vlWrVmWYtyUIgiDk3oEbTxi+4UqGxAkgPDaF4RuucODGE6PGk5aWxp07d6hWrRodOnRAo9Fk+GXf398foECOPKlUKiIjI3P00mq1+R1utt6bkScXF5dMk4knT3T/8F1dXfPctpmZWaajWsZib29Pp06d0r++fPkygwcPxsLCgvHjxzNx4kRsbGzyLT5BEIT8JEkSyarczwvVaCWm771JZjfoJEAGzNgbQIOyDijkOS/AaKFU5LlgY0BAACqViqpVq1KiRAk8PT3x8fHh448/BnQjT2ZmZlSoUCFP7RvSmTNn+OCDD3J0bFBQEO7u7oYN6A28N8lT9erVOX78OHFxcRkmjV+4cCF9/7tCqVTSsGFDTp8+zXfffceKFSv45ptvGDRo0BuXpBcEQXjbJKs0eHx9UO/tSkB4XAqeMw7l6ryAb1tjaZq3n8UvR5Ze3pbr0KEDS5YsQaVSoVQq8fPzo3LlyigUimzbkclkhIaGGvWpvGrVqr1SmDorBeHWXHbem9t23bp1Q6PRsGLFivRtqamprFmzhjp16uDm5paP0elX1apVOXnyJDt37qRcuXJEREQwfPhwqlatyr59+5Ck/JvoKAiCIOSdn58fMpkMT09PQJc8xcXFcfLkSTQaDTdv3jTofCd3d/cMhaVzo3DhwrRo0SJHr5fzkQuqd2IYYvHixcTExKQ/Mefj48OjR48AGDVqFLa2ttSpU4fu3bvz5ZdfEhERQdmyZVm3bh3BwcGsXr06P8M3CJlMxkcffUSHDh1Yvnw5M2bM4NatWwwcOJAHDx5gZWWV3yEKgiAYhYVSQcC3rXN93sWgKD5Z4/va49Z+6k3tUjlfON5Cmf2oUHb8/f0pXbp0euHmunXr4uDggI+PD66urqSkpBTI+U6gm68VFRWVo2MdHR1fO3qWn96Jkad58+Yxbdo0li5dCsDOnTuZNm0a06ZNIzo6Ov2433//nTFjxrB+/XpGjx6NSqVi3759NG7cWC9xLFmyBA8PD7y9vfXS3r/l9TFZpVLJyJEjCQwMZPLkyXz//ffpiZMkSWJSuSAI7zyZTIalqUmuX43KOeJia05Ws5Nk6J66a1TOMVftvskCtf7+/hlGluRyOW3btsXHx+eVJ+20Wi2jR4/GwcEBOzs7vL29iYyMTD/Xx8eHUqVK4eDgwOzZs9O337x5k0aNGmFnZ0fNmjU5c+YMAIMGDSIkJIRWrVphbW3Nxo0bX9vHv509exYXF5ccvYz14FVevRMjT8HBwTk6ztzcnLlz5xqsNsSIESMYMWIEcXFx2Nra6q1dfTwma2trm+E/B8D27dv53//+x5gxY/jyyy/1GrMgCMLbTiGXMb2jB8M3XEEGGSaOv0x/pnf0yNVk8TcRHh5ORETEKyNLHTp0YP369WzevBn450m7Q4cOcfbs2fS7DX5+fhluhx07dozr168THBxMrVq16NGjB25ubnTs2JExY8Zw7Ngxdu7cSceOHQkMDGTVqlUcOXKEDRs20LBhQwAOHDiQbR//9i7NeXonkqd32cvHZP87zvTyMdml/bzyXGfkwIEDpKamMmfOHFatWsX06dMZOnQopqambx64IAjCO6BNFReW9vN65RdY53yo85RVDafWrVujVCrTb929rPmkVCqJj4/n9u3beHt74+XlleG8yZMnY21tTZUqVahatSrXr18nLCwsfTQJoGfPnixYsIADBw7Qu3fvV2J6XR//9nLO05vKyVQdQxPJUwGm0Up84xOQ7WOy3/gE0NLDOU+/+axevZquXbvyxRdfcOvWLUaPHs2iRYuYM2cOH3300RsNLQuCILwr2lRxoaWHMxeDooiIT6GojTm1S9kbbcTppf8+afeSra0tDRs25Pjx4xn2NW/enGHDhjFkyBDCw8Pp168fs2fPRqlUAuDk5JR+rKWlJQkJCaSmpr7yAFXJkiUzrMLxb6/rwxDmzZvHw4cP07/euXMnO3fuBKBfv35GSZ7eiTlP76qLQVGvFGb7Nwl4EpvCxaCcTcD7L5lMRvv27fH392fZsmU4OTlx//59unbtyrBhw/IYtSAIwrtHIZdRr0wROlcvRr0yRYyeOAF88cUXSJJEmTJlXtl37NgxJEnir7/+yrB97NixXLt2DV9fXw4ePMjGjRuz7cPV1fWV+UYhISHptRAz+6U6t328qeDgYCRJyvRlrNpQInkqwCLis06c8nJcVkxMTBg6dCj37t1j2rRpWFpa0rNnzzdqUxAEQchfly5dwtfXF7VajY2NDUql8rVPsNWpUwfQ3RpTq9Vs376dW7du0aZNGwCKFi2aYZ5xXvp4F4jkqQArapOzOhf2lvqZo2RjY8O3335LSEgIzZo1S9/+448/Mm7cuBw/YioIgiDkv9jYWAYMGICdnR0VKlSgQYMG9OnTJ9tzTE1N2bt3L5s3b6ZIkSLMnj2bvXv3UrhwYQAmTZrE5MmTsbOzY9OmTXnq410gk0TFRL1ZsmQJS5YsQaPRcPfuXWJjYzNUM88tjVai4ZxjhMemIENNZauTWJpEkqR24GZiY7Qvpqx5uNiwsFcNyjnpfwmWqKgoSpYsSUJCAnZ2dkydOpWRI0fm63I0giAImUlJSSEoKIhSpUoV+CKLgvHl5N/Hy6flX/f5LZInA8jpNz8nDtx4wuq904h0OkekyT8DhQ5qLUWe1uNWSjcS0zSYmsiZ1KYin9Z3R67ne/GHDh3iiy++SJ+sWKpUKb7//nt69uwpJpULglBgiORJyI4+kydx266AM4lZyx3X80QqMiYpzxUy7rqeZ3ZTX5pWcCRNrWXmvgD6rb5AWEyyXmNo1aoVV65cYc2aNbi6uhIUFETv3r2pW7cu169f12tfgiAIglDQieSpANOo0/jh7kZdqYL/jPBIL77+JXgrq/pVY+aHVTBXyjkb+JzWC06y55p+K4crFAo++eQT7t27x8yZM7G2tubq1atYWlrqtR9BEARBKOhE8lSAXbm+nqcK2SuJ00uSTEa4QsbVGxv4uG5J/hzdiGrFbYlPUfP5lmuM2nyVmKQ0vcZkaWnJ1KlTuX//Pps2bcrwyOz69et59uyZXvsTBEEQhIJGJE8F2LO4kFwdV9rRmh3D6zOmRTkUchk+fmG0WXCKU/f0n9A4OTnRrVu39K+vXLlC//79KVOmDLNnzyY5Wb+3DgVBEAShoBDJUwHmWKhEro9TKuSMaVGeP4bXp5SDFeFxKXy8+iIz9t4kRaUxVKhIkoSXlxfx8fFMmTKFChUq8Pvvv6PVag3WpyAIgiDkB5E8FWBenh/jpJGQZfNApI1Wwsvz41e2V3ezY//ohnxctyQAa88G037RKa4/ijVIrDVr1uTixYts3LiREiVKEBoaSv/+/alVqxZHjx41SJ+CIAiCkB9E8qRHS5YswcPDA29vb720pzAxZXL5vgCvJlAvvo6Xy9h4Z0um51uamjDzwyqs/dQbRxszAp8l8tGvZ1h87B5qjf5HhORyOX369OHOnTvMmTMHW1tbrl69Su/evUlKStJ7f4IgCIKQH0SdJwPQZ50ngCOnZ/PD3Y26yeMvOKvVeJoU5jDxAHxZ+0v6VMq6qmt0YhpTdl3nrxvhAHiVsGN+j+q4O1i9cXxZiYyMZObMmVSpUoXBgwcDutt7z549o2jRogbrVxCE95Oo8yRkRxTJLOD0nTyBrmzBlevreRYXgmNaCl5nliE3tWZh81Gsvq1bhHFa3Wn0qNAjyzYkSWLX1cdM33OT+FQ1lqYKpnXwoJe3m9GKXW7bto0BAwYwceJExo8fj5WV4ZI3QRDeLyJ5ErIjimS+hxQmpnjXGEi7Jt/g3eIHFEU9kKUl8LnKnP4e/QGYeX4mu+7tyrINmUxGF6/i/DWmEXVK2ZOUpuHLndcZtO4Sz+JTjXIdu3btIjExkenTp1OuXDlWr16NRmO4ieyCIAiCoG8ieXobyWRQb4Tu7cUVjK8xmn6V+gEw/ex09gbuzfb04oUt2Ty4Ll+1q4SpQs7R2xG0XnCSgzfDDR76pk2b2LZtG6VLl+bJkycMGjSI6tWrc+DAAcQgqCAIgvA2EMnT28qzO1gVhbjHyAJ2M9F7Ij0r9ERCYtqZaex/sD/b0+VyGYMbl2bvqAZUdLYhKjGNoesvM3GHHwmpaoOFLZPJ6N69OwEBAcyfP5/ChQtz48YN2rZty5gxYwzWryAIwrvi4MGDyGQyZDIZAQEBr+zv2LEjxYsXz4fIDM/X15eRI0dSuXJlrKysKFGiBD169ODu3btGjUMkT28rEzOoPUT3/uwvyIApdabQtVxXtJKWKaencDD44GubqehciD0jGzC0SWlkMth26RFtF57ENzjKoOGbmZkxduxYAgMDGT9+PKampnTq1MmgfQqCILwL/Pz8AN0Tzvv27ct0f9WqVY0dllHMmTOHP/74g+bNm7Nw4UKGDBnCyZMn8fLy4saNG0aLQyRPbzPvgWBiAeH+EHwauUzO1/W+5sOyH6KVtEw6OYmjD19fY8nMRMGXbSuxZXBditlZEBqVTI/l55hz4DZpasMWuSxcuDDz5s3j4cOHNG/ePH37Tz/9xNSpU4mLizNo/4IgCDmi1UDQKbi+Q/enNv/mavr7+1OoUCFat26Nj49Phn3R0dGEhoZSrVq1fIrOsMaNG8fDhw9ZtGgRgwYNYurUqZw6dQq1Ws0PP/xgtDhE8vQ2s7SH6i/KE5xbDIBcJmdGvRl0LN0RjaRhwskJnAg9kaPm6pQuwoExjehWsziSBEtPBPLhkjPcCY83TPz/4uzsnP7++fPnzJgxg1mzZlG2bFmWLl2KSqUyeAyCIAiZCtgLC6rAug7wx0Ddnwuq6LbnAz8/Pzw9PenQoQPnzp3j+fPnGfYB7+zIU/369TE1Nc2wrVy5clSuXJlbt24ZLQ6RPOmRvotk5kjdzwAZ3D0Az3T3fBVyBTMbzKSte1vUWjXjTozj1KNTOWrOxlzJvO7VWNbPi8KWSgKexNFx8WlWnXqAVmucCd329vZs2LCB8uXL8+zZMz777DM8PT3Zu3evmFQuCIJxBeyFbf+DuLCM2+Oe6LYbOYFKS0vjzp07VKtWjQ4dOqDRaPjzzz/T9/v7+wMUyJEnlUpFZGRkjl65WdpLkiSePn2Kg4ODAaPPSCRPejRixAgCAgLw9fU1XqcOZaFCW93780vSNyvkCr5v9D0tS7ZEpVUx5vgYzj4+m+Nm21Rx4eDYxnxQwZE0tZbv9t+i76oLPI4x/IK/MpmMzp07c+PGDZYsWYKDgwN37tyhc+fONG3a1Ki/XQiC8A6QJEhLzP0rJQ7+mghk9kvbi20HJumOy027b/BLYEBAACqViqpVq1KiRAk8PT0z3Lrz8/PDzMyMChUq5LkPQzlz5gyOjo45eoWEhOS43Y0bN/L48WN69uxpwOgzEkUyDcAQRTKzFXwG1rYDE3MYexOs/sm+VVoVE05M4FjoMcwUZixpvoQ6LnVy3LQkSWy6GMJ3+26RrNJgY27CzM5V6Fzd1WiFNWNjY5kzZw4///wzarWaW7duUbZsWaP0LQjC2yPLIohpifC9a/4F9l9TwsA0bwWCf//9d/r378/Zs2epV68eU6ZMYcmSJURGRqJUKqlVqxaSJHH58uVs25HJZISGhhr1qbzo6OjXxvVSw4YNc1To9Pbt29SpU4fKlStz6tQpFApFlseKIplCRiXrg2sNUKeA7+oMu5RyJfOazKNJ8SakalIZdWwUl8Iv5bhpmUxG3zol+fPzRlR3syM+Rc2YrdcYufkqMUlp+r6STNna2vL9999z9+5d1q1blyFx2rp1K9HR0UaJQxAEIb/5+fkhk8nw9PQEoEOHDsTFxXHy5Ek0Gg03b9406Hwnd3d3Tp8+nadzCxcuTIsWLXL0ykniFB4eTvv27bG1tWXHjh3ZJk76ZmK0ngTDkcmg3kjdREbfldDgc1D+8w9PqVAyv+l8Rh8fzZnHZ/js6Gcsb7mcGkVr5LiLUg5W7BhWj19PBLLw6D32+z/hUnAUc7tVo3F5R0Nc1Svc3Nzo0+ef9fteLjpcuHBhvv76a4YPH/7KREJBEASUlrrRntx6eBY2dnv9cX136H6JzU08eeTv70/p0qWxtrYGoG7dujg4OODj44OrqyspKSkFcr4T6OZrRUXlrAyOo6NjtslQbGwsbdu2JSYmhlOnTuHqatyRRTHy9K7w6AyFikPiM/Df+spuU4UpC5ouoK5LXZLVyQw/Mhy/Z3656sJEIWd083LsHF6f0o5WPI1L5X+/XWT6nhskpxn/sd2UlBQqVapEVFQUY8aMwcPDgx07dohJ5YIgZCST6W6T5fZVphkUcgWymqIgg0LFdMflpt03mPLg7++fYWRJLpfTtm1bfHx8XnnSTqvVMnr0aBwcHLCzs8Pb25vIyMj0c318fChVqhQODg7Mnj07ffvNmzdp1KgRdnZ21KxZkzNnzgAwaNAgQkJCaNWqFdbW1mzcuPG1ffzb2bNncXFxydErNDQ0y+9BSkoKHTt25O7du+zbtw8PD488fz/zSiRP7wqFEuoO070/twQyeVLB3MScRc0WUdu5NomqRIYdHsbNyJu57qqamx37RzWif72SAKw795D2v5zC/1HMm1xBrtWrVw8/Pz9WrFiBs7MzgYGBdO/enQYNGnDu3DmjxiIIwjtIroA2c1588d+E58XXbX7QHWcE4eHhREREvDKy1KFDBx48eMDmzZuBf560O3ToEGfPnuXBgwc8f/6c5cuXZ7gdduzYMa5fv86JEyf45ptvCAwMJC0tjY4dO9K9e3eePXvGxIkT6dixI9HR0axatYoSJUpw6NAhEhIS6Nu372v7+Ldq1apx+PDhHL3+Xb7m3zQaDT179uTcuXNs376devXq6eNbm3uSoHexsbESIMXGxhq34+QYSZpVTJKmF5Kku4eyPCwxLVH635//k6qsrSLV21RPCogMyHOXJ+5ESN7fHZZKTtonlflyv7TwyF1Jpdbkub28io+Pl6ZPny5ZWlpKgOTo6CglJSUZPQ5BEPJPcnKyFBAQICUnJ+u34Zt7JOmnirqfrS9fP1XSbTeiAwcOSIC0c+fODNtjYmIkpVIpyWQyydXVNX37kSNHpPLly0sXLlyQtFpthnMA6dKlS+lfe3t7S7t27ZJOnjwplSxZMsOxdevWlTZt2iRJkiSVLFlSOnXqVI76MITPP/9cAqSOHTtK69evf+WVnZz8+8jp57cYeXqXmNtCzf6692d/yfIwS6Ulv7b4leqO1YlPi2fw4cHcibqTpy6blHfk4JjGtPd0Qa2VmH/4Lt2WnSMoMjFP7eWVtbU1M2bM4N69ewwaNIhvv/0WCwsLQPfEoJhULghCnnl0gjE3oP8+6Lpa9+eY67rtRvSyhtN/J4Tb2trSsGFDJEnKsK958+YMGzaMIUOG4OLiwoQJEzIUHHZyckp/b2lpSUJCAmFhYbi5uWVov2TJkoSFZT5n7HV96Nu1a9cA3S3Hjz/++JWXsYjk6V1TZyjIFBD0Nzzxz/IwK6UVS1ssxdPBk9jUWAYfGsz96Pt56rKwlSmL+9RgQc/q2JibcC00hnYLT7HxwkOjzz9ydXVl5cqVDBs2LH3bH3/8QalSpZg7dy4pKSlGjUcQhHeEXAGlGoFnN92fRrpV929ffPEFkiRRpkyZV/YdO3YMSZL466+/MmwfO3Ys165dw9fXl4MHD7Jx48Zs+3B1dX1lvlFISEj6hOzMStTkto83ceLECSRJyvJlLCJ5etfYldBNHgfd3KdsWJtas6zlMirZVyI6NZpBhwbxIPZBnrqVyWR8WKMYB8Y0pl7pIiSrNHy16wYD1voSEZ+/CcvmzZuJjY1l4sSJVKxYkU2bNuWqeq0gCMLb6NKlS/j6+qJWq7GxsUGpVL72cf46dXR1ABcvXoxarWb79u3cunWLNm3aAFC0aFGCg4PfqI93gUie9ChflmfJTP2Ruj9v7Hh1SYH/KGRaiJWtVlKhcAWepzxn0MFBPIx7mOeui9lZsHFQHaa2r4SpiZzjd57R+ueTHLgRnuc239S2bdtYu3YtxYoV4+HDh/Tt25c6derw999/51tMgiAIhhYbG8uAAQOws7OjQoUKNGjQIEO5l8yYmpqyd+9eNm/eTJEiRZg9ezZ79+6lcOHCAEyaNInJkydjZ2fHpk2b8tTHu0BUGDcAo1cYz8xvbSHkLDQcCy1mvPbw6JRoBhwcwP2Y+xS1LMra1mtxK+T22vOycyc8njFbr3HrSRwA3WsW5+uOHtiYK9+o3bxKSkpiwYIF/PDDD8TH6xY7njBhAnPnzs2XeARB0K+cVJAW3l+iwrjwei9Hny79BqkJrz28sHlhVrVaRWnb0kQkRTDw0EAeJzx+oxAqONuwe0R9hjctg0wG2y8/ou3CU1wMylmRNH2ztLRkypQp3L9/n88++wyFQkGrVq3yJRZBEATh7SWSp3dV+bZgXxpSYuFazibvFbEowqpWq3Av5M6TxCcMPDiQJwlP3igMMxMFk9pUZOuQehQvbMGj6GR6rjjH7L9ukao2fmFN0N2zX7JkCQ8ePKBly5bp2xcuXMisWbNISkrKl7gEQRCEt4NInt5VcjnU/Uz3/vyvoM1ZouJo6ciqVqtws3HjccJjBh4ayNPEp28cTu1S9vz1eSN61CqOJMHyvx/QefEZbofHvXHbeVWiRIn095GRkUybNo2pU6dSvnx51q5di0aTP8mdIAiCULCJ5OldVr0vWBSG6GC4vS/HpzlZOfFb698oZl2M0PhQBh4ayLOkZ28cjo25kh+7VWNZv5rYW5lyOzyeTr+cYeXJB2i1+Tv1zt7enuXLl1OyZEkeP37Mp59+Ss2aNTl8+HC+xiUIgiAUPCJ5epeZWkKtgbr3rylb8F/OVs6sbr0aFysXHsY9ZOChgUQmZ75eUW61qeLMgTGNaF6xKGkaLbP+vEWfVed5HJOsl/bzQi6X07t3b27fvs3cuXOxtbXFz8+PVq1a0bZtW+7fz1sNLEEQBOHdI5Knd13tIaAwhdALEOqbq1OLWRdjdevVOFk6ERQbxOBDg4lK0c9k76I25qzqX4vZXTyxNFVw/kEUbX4+ya6rj/J1YV9zc3MmTJhAYGAgY8aMQalUcuTIEbHYsCAIgpBOJE/vOhsn8Oyue38u6yVbsuJm48bq1qtxtHDkfsx9hhwaQmxqrF5Ck8lk9K5dgj9HN6JGCTviU9WM3erHyE1XiU5M00sfeVWkSBF+/vlnAgICWLVqFeXKlUvft2vXLhISXv8EoyAIgvBuEsnT+6DeCN2ft3x0859yqWShkqxuvZoi5kW4E32HwYcG6y2BAnB3sGL70HpMaFUeE7mM/def0HrBSf6+++bzrN5U2bJl6d+/f/rX165do2vXrpQrV46VK1eiVqvzMTpBEAQhP4jk6X3gVBnKNANJC+eX5qmJUralWN16Nfbm9tyKusWww8OIT4vXW4gmCjkjm5Vj12cNKONoRUR8Kv1/u8jXe26QnFZwnnqLi4ujdOnShIeHM2TIEKpXr86ff/4pbusJgiC8R0Ty9L6o96Jo5pX1kByTpybK2JVhZauV2JnZceP5DYYfGU6iKlF/MQKexW3ZN6oRn9R3B+D3cw9pv+gU10Jj9NpPXjVu3JiAgAAWLlyIvb09N2/epH379rRs2ZKrV6/md3iCIAiCEYjk6X1RphkU9QBVIlxem+dmyhcuz8pWKylkWgi/Z358duQzklT6LSppYapgRqfK/D6gNk6FzHgQmUjXpWdZeOQeak3+L+hramrK6NGjCQwMZOLEiZiZmXH06FHatGlDSkr+LoIsCIIgGJ5Int4XMtk/c58uLAd13idkV7SvyIpWK7BR2nAl4gojj40kWa3/MgONyztycExjOlR1QaOV+PnIXbouO8eDZwVjsradnR1z5szhzp079O3bl+nTp6evlyRJUvr6eYIgCPp08OBBZDIZMpmMgICAV/Z37NiR4sWL50Nkhnfz5k26d+9O6dKlsbS0xMHBgcaNG+Pj42PUOETypEdLlizBw8MDb2/v/A4lc57dwdoJ4sPg5q43aqpykcosa7kMK6UVvuG+jDo2ihS1/kdd7CxNWdzHi4W9qmNjboJfaAztF51mw/mHBWaeUcmSJdmwYQOfffZZ+radO3dSpkwZlixZgkqlysfoBEF41/j5+QG6+nT79r1aANnPz4+qVasaOyyjePjwIfHx8fTv35+FCxcybdo0ADp16sSKFSuMFodMKiifQO+QnK7KnC9OzoVj34FzVRh6Ujci9QauRVxj6OGhJKmTaODagIXNFmKmMNNTsBmFxSQzYbsfZwOfA9C0giM/dq1K0UIFb/X0Dh06sH//fgDKly/PnDlz6Ny5M7I3/H4LgpC1lJQUgoKCKFWqVPoosL5otBquRFzhWdIzHC0d8SrqhUKu0GsfOdWvXz98fHxo0KAB8fHxnDp1Kn1fdHQ09vb2TJ48mdmzZ+dLfMam0WioWbMmKSkp3L59O8vjcvLvI6ef32Lk6X1TayCYWEC4PwSfev3xr1G9aHV+bfErFiYWnAk7w7gT40jTGKZGk6udBRsG1mFaBw9MTeScuPOM1gtOcuDGmy1ebAi7d+9m6dKlODo6cvfuXT766COaNGnCxYsX8zs0QRBy6cjDI7T+ozUDDg5g0qlJDDg4gNZ/tObIwyP5Eo+fnx+enp506NCBc+fO8fz58wz7gHd25CkzCoUCNzc3YmJijNanSJ7eN5b2UKOv7v3ZxXppsqZTTRY3W4y5wpyTj04y4e8JqLSGuVUll8sY2LAU+0Y1xMOlENFJKoZtuML4bX7Epej61GglzgU+Z8+1x5wLfI4mH9bNMzExYdiwYdy/f5+vvvoKCwsLTp06RZ06ddKHmQVBKPiOPDzCuBPjeJqUcYH0iKQIxp0YZ/QEKi0tjTt37lCtWjU6dOiARqPhzz//TN/v7+8PQLVq1YwaV06oVCoiIyNz9NJqs384KDExkcjISAIDA/n555/566+/aN68uZGuRNy2M4gCfdsO4Hkg/FITkGDERXCsoJdmz4WdY+TRkaRp02hZsiVzGs9BKVfqpe3MpKm1LDhyl2V/B6KVoJidBT293dh8MYQnsf/Mv3KxNWd6Rw/aVHExWCyv8+jRI6ZNm8a6des4cOAArVq1yrdYBOFdldVtGUmS8vRQi0ar4cO9HxKRFJHlMU6WTuzqtCtXt/AsTCzyfAv/2rVr1KhRg2XLljF06FCqVq1KxYoV2bZtGwADBw5k48aNJCYmolDkz23FrJw4cYIPPvggR8cGBQXh7u6e5f5hw4axfPlyQDf3q0uXLqxYsYLChQtneY4+b9uJ5MkACnzyBLC5D9zZD179odMivTV7+vFpRh8bjUqroo17G2Y3mo2J3ERv7WfmUnAU47b5ERKVecmElz+ilvbzytcECuD+/fuULVs2/eslS5aQlpbGZ599hpmZYeaKCcL7IqsPxyRVEnU21cnHyDK60OcClkrLPJ37+++/079/f86ePUu9evWYMmUKS5YsITIyEqVSSa1atZAkicuXL2fbjkwmIzQ01KhP5UVHR782rpcaNmyY7by127dv8+jRI8LCwti2bRumpqYsXboUJyenLM8RyVMB91YkTw/Pwpq2oDCDcQFg5aC3pv8O/ZsxJ8ag1qppX7o9sxrMMvjEythkFXW/P0qyKvNq5DLA2dac05OaoZAXjEnbz549o0yZMsTHx1O6dGlmz55N9+7dxaRyQcij9yF5Gj9+PD///DNxcXFYW1tz9uxZGjRowJEjR2jatCnW1tb06tWLNWvWZNtOXpMnd3d3NmzYQMOGDfMUv6G0atWKmJgYLly4kOXPUH0mT4YdEhAKrhL1wNULwq6A7ypoOllvTTdxa8K8JvOYcGIC+x/sx0RmwrcNvkUuM9wUu4CwuCwTJwAJeBKbwsWgKOqVKWKwOHLD3t6en3/+mWnTpvHgwQN69uzJzz//zLx582jQoEF+hycI7wwLEwsu9LmQ6/MuP73MZ0c/e+1xvzb/lZpONXMVT175+/tTunRprK2tAahbty4ODg74+Pjg6upKSkpKgZzvBLr5WlFRUTk61tHRMVe3Hbt168bQoUO5e/cuFSroZypKdsSE8feVTAb1XyzZcnElqPRb5LJ5iebMaTwHhUzBnsA9fHvuW7SS4aqDR8TnrMZUTo8zBoVCwcCBA7l37x7ffPMNVlZWnD9/noYNG9K1a1eCg4PzO0RBeCfIZDIslZa5ftV3rY+TpRMyMh/JkCHD2dKZ+q71c9Xum4wu+/v7Z3iSTi6X07ZtW3x8fF550k6r1TJ69GgcHByws7PD29ubyMjI9HN9fHwoVaoUDg4OGcoa3Lx5k0aNGmFnZ0fNmjU5c+YMAIMGDSIkJIRWrVphbW3Nxo0bX9vHv509exYXF5ccvUJDQ3P1fUlO1n2Gxcbqb9H67IiRp/dZpc5g6waxoeC/FWp+otfmW7m3QiNpmHxqMn/c+wMTuQlf1fnKILelitrkrKZLEStTvff9pqysrPj6668ZPHgwM2bMYNWqVezdu/e9qdEiCAWVQq5gcu3JjDsxDhkyJP6Z5fIyoZpUe5LR6j2Fh4cTERHxyshShw4dWL9+PZs3bwb+edLu0KFDnD17lgcPHmBlZYWfn1+G21XHjh3j+vXrBAcHU6tWLXr06IGbmxsdO3ZkzJgxHDt2jJ07d9KxY0cCAwNZtWoVR44cyXDb7sCBA9n28W/VqlXj8OHDObpWZ2fnTLdHRERQtGjRDNtUKhW///47FhYWeHh45Kj9NyWSp/eZwgTqDINDX8G5JVDjfyDX72Bk21JtUWvVfHX6K7be2YpCpvthpO8EqnYpe1xszQmPTSG7SXw//HWbeTZmVHQueHPRXFxcWL58OaNHj+bs2bOUL18+fd/+/ftp3ry53gv/CYKQvRYlWzC/6Xx+uPhDhnIFTpZOTKo9iRYlWxgtlqxqOLVu3RqlUpl+665IEd3UBKVSSXx8PLdv38bb2xsvL68M502ePBlra2uqVKlC1apVuX79OmFhYemjSQA9e/ZkwYIFHDhwgN69e78S0+v6+LfChQvTosWbfb+GDh1KXFwcjRs3plixYoSHh7Nx40Zu377NTz/9lH4709DEbbv3ndf/wKwQRN6F+4apV9KxTEe+qf8NAJtub2LepXl6X1pFIZcxvaPuN47/pmUvv7ZQyrkRFkfHX07zy9F7qArAIsOZqVy5MoMHD07/2s/Pj44dO1KhQoX0YXJBEIynRckWHOx6kN9a/8acRnP4rfVvHOh6wKiJE/xTw+m/yZOtrS0NGzZEkqQM+5o3b86wYcMYMmQILi4uTJgwIcNyUf9+Ms3S0pKEhATCwsJwc3PL0H7JkiUJCwvLNKbX9aFvPXv2RC6Xs3TpUoYPH878+fMpXrw4e/bsYdy4cQbr979E8vS+My+kS6AAzv1isG4+KvcR0+tNB+D3gN9ZcGWB3hOoNlVcWNrPC2fbjKMzzrbmLOvnxd9ffECLSk6oNBI/Hb7Lh0vOcOtJnF5jMIRnz55RrFgxQkJC6NevH97e3hw/fjy/wxKE94pCrsDb2Zt2pdvh7eydL0uzfPHFF0iSRJkyZV7Zd+zYMSRJ4q+//sqwfezYsVy7dg1fX18OHjzIxo0bs+3D1dX1lflGISEhuLq6AmR61yC3fbyJXr16cfjwYcLDw1GpVERFRXH48GE6depksD4zI5InQXfrTqaAoJPwxN9g3XQr342v6nwFwG83fmPxNf1UOP+3NlVcOD2pGZsH12Vhr+psHlyX05Oa0aaKC0ULmbPyfzVZ0LM6thZKbobF0WnxaRYeKbijUAAtWrTg7t27zJ49GxsbG65cuUKzZs3o2LEjt27dyu/wBEEooC5duoSvry9qtRobGxuUSuVrn2CrU0dX0mHx4sWo1Wq2b9/OrVu3aNOmDQBFixbN8DBLXvp4F4jkSQA7N6j8oe79Of0nNP/Wq2IvJtfWlUVY4b+CpX5L9d6HQi6jXpkidK5ejHplimSo6ySTyfiwRjEOj2tMSw/dKNTPR+7SefEZAsIK7iiUhYUFkydPJjAwkJEjR2JiYsK+ffv44IMPSEszzFqCgiC83WJjYxkwYAB2dnZUqFCBBg0a0KdPn2zPMTU1Ze/evWzevJkiRYowe/Zs9u7dm165e9KkSUyePBk7Ozs2bdqUpz7eBaJIpgG8FUUy/+vxFVj5AchNYMx1KORq0O7W3VzHvEvzAPjc63MGeQ4yaH+ZkSSJvX5hTN97k5gkFSZyGSObleWzpmUxNSnYv1fcvXuXyZMn88EHHzBq1ChAdz0pKSlYWOS9howgvM1yUgRReH/ps0hmwf6EEIynmBeUbABaNVxYbvDu+lfuz+denwOw8MpC1t5Ya/A+/0smk9G5ejEOj21C68pOqLUSC47co/OSM9wMM06tkLwqX748O3fuZOTIkenbdu/eTdmyZVmzZg0aTdYFQwVBEIQ3I5InPVqyZAkeHh54e3vndyh5U+/FB/HlNZCaYPDuBnkOYkT1EQD8dPkn1gesN3ifmXG0MWNZv5r80rsGhS2V3HoSR+fFZ5h/+C5p6oI7FwoyTt5ctmwZYWFhDBgwgBo1anDo0KF8jEwQBOHdJZInPRoxYgQBAQH4+vrmdyh5U74N2JeBlFi4usEoXQ6rNoyhVYcC8KPvj2y+vdko/f6XTCajYzVXDo1tQtsqzqi1EouO3qPT4tPceFywR6Fe2rt3Lz/99BN2dnZcv36d1q1b07p16/THmwVBEAT9EMmT8A+5HOq9WMfp/K+gNc6tnxHVRzCwykAAvr/wPdvvbjdKv5lxtDFjab+aLOnjhb2VKbfD4+m85Aw/HbpDqrpg3wozMzNj3LhxBAYGMm7cOJRKJYcOHaJ69ep89913+R2eIAjCO0MkT0JG1fqAhT3EPITb+4zSpUwm43Ovz+nv0R+Ab899y657u4zSd1baV3Xh0NjGtPd0QaOV+OXYfTr9cgb/RzH5GldO2Nvb89NPP3Hr1i169OiBJElv761kQRCEAkgkT0JGppbgrRsF4qxhyxb8m0wmY3yt8fSr1A+A6Wen4xPoY7T+M+NgbcaSvl4s6eNFEStT7jyN56NfzzL34O0CPwoFUKZMGbZu3cqNGzdo3bp1+vZly5axfPly1Gp1PkYnCILw9hLJk/Aq78GgMIVHFyH0otG6lclkTPSeSM8KPZGQmHpmKn8++NNo/Wfl5ShUh6q6UaglxwPp+Mtp/EJj8ju0HKlcuXL6+2fPnjFp0iSGDRtG1apV2bdvn94rvQuCILzrRPIkvMrGCTx76N6fNdySLZmRyWRMqTOFruW6opW0TDk9hYPBB40aQ2aKWJuxuI8XS/t64WBtyt2nCXz06xnmHLhNiqrgj0K9ZGtry3fffUeRIkW4desWHTt2pHnz5ly5ciW/QxMEQXhriORJyFw9XQkBbu+DqCCjdi2Xyfm63td0LtMZjaRh8snJHA05atQYstLW04VDY5vQqZorWgmWntCNQl17S0ahTE1NGTVqFIGBgUyaNAkzMzOOHz9OzZo1+fjjj3n8+HF+hygIglDgieRJyJyTB5RpDpIWLiwzevdymZxv6n9Dh9IdUEtqJvw9gb9D/zZ6HJmxtzJlUe8aLOtXEwdrM+5FJNDl1zPM/uvWWzMKZWtryw8//MCdO3fo17cvAFu2bCbx9t9Ge8pSEAThbSWSJyFr9V8UzbyyHpKjjd69Qq5gZoOZtHVvi1qrZuyJsZx+fNrocWSlTRVnDo9tzIfVdaNQy/9+QPtFp7gSYvzvVV6VTPRjvddlLg22YmErJeVPDYcFVSBgL0eOHBHr5gmCIGRCJE9C1kp/AEUrgyoRLq/NlxBM5CZ83+h7WpZsiUqr4vNjn3M27Gy+xJKZwlamLOhVgxUf18TRxozAZ4l0W3qW7/98C0ahAvbCtv9BXBg1XRV85m2q2x73BP9f+tKqVSuqVKnCrl27xKRyQShADh48iEwmQyaTERAQ8Mr+jh07Urx48XyIzPhmzZqFTCajSpUqRu1XJE9C1mSyf+Y+XVgO6vwZhTCRmzCn8Rw+cPuANG0ao4+N5uIT4z0FmBOtKutGoT6qUQytBCtOPqDdolNcflhAR6G0GjgwCcgsKZJ4HKelqLWce/fu0aVLFxo1asSFCxeMHaUgCJnw8/MDQC6Xs2/fq/X4/Pz8qFq1qrHDMrpHjx7x/fffY2VlZfS+RfIkZM+zG1g7QfwTuLkz38JQypXMazKPxsUbk6pJZeSxkVwKv5Rv8WTGztKUn3tWZ9X/alHUxowHzxLptuwss/YHFLxRqIdnIS4sy91ty5lwb4Ql00b1x8LCgjNnzlC3bl169uzJgwcPjBioIBQMkkZD4oWLxO7bT+KFi0j5uPi2v78/hQoVonXr1vj4ZKyHFx0dTWhoKNWqVcun6IxnwoQJ1K1bl1q1ahm9b5E8CdkzMYPaQ3Tvzy2GfLx9Y6owZX7T+TRwbUCyOpnPjn7GtYhr+RZPVlp4OHF4bBO6eBVDkmDlqSDaLTzFpeCo/A7tHwlPX3uIjZmMbwd34N69ewwYMACZTMa2bdto2LChmAslvFfiDh3ifvMWhPTvT9iECYT078/95i2Iy6fFt/38/PD09KRDhw6cO3eO58+fZ9gHvPMjTydPnmTHjh0sWLAgX/oXyZPwerUGgNISwq9D0Ml8DcVMYcaCDxZQ16Uuyepkhh0Zhv+zgrfwra2lkvk9qrO6fy2cCpnxIDKR7svPMXNfAMlpBWAUytopx8cVK1aM1atXc+3aNVq3bs3kyZMxNdXNj5IkSSRSwjst7tAhHn8+BnV4eIbt6qdPefz5GKMnUGlpady5c4dq1arRoUMHNBoNf/75TzHhlwuBF8SRJ5VKRWRkZI5eWq02y3Y0Gg2jRo1i0KBBeHp6GvEK/iGSJ+H1LO2huu5xds4Zb8mWrJibmLOo2SK8nb1JVCUy7PAwbkbezO+wMtW8khOHxjShW83iSBKsPh1E24UnuRiUz6NQJeqBiXn2xxQqBiXrp39ZtWpVDhw4wMiRI9O37d69m4oVK7J161YxqVwosCRJQpuUlOuXJj6ep9/NynzEXZIAiaezvkcTH5+rdt/k/0pAQAAqlYqqVatSokQJPD09M9y68/Pzw8zMjAoVKuS5D0M5c+YMjo6OOXqFhIRk2c6yZct4+PAhM2fONGL0GZnkW8/C26XucPBdBfcOwbM74Ji//zEtTCxY3Gwxw48M50rEFYYcHsKqVquoVKRSvsaVGVtLJfO6V6O9pwtf7rxO8PMkeq44xyf13fmidQUsTfPhv+HF5aBOyf6YZlNBrnhls1z+z+9cixYtIigoiF69evHzzz8zb948GjZsqO9oBeGNSMnJ3PGqaYCGdSNQd71r5+q0ClcuI7O0zFOXL0eWXt6W69ChA0uWLEGlUqFUKvHz86Ny5cooFK/+3/03mUxGaGioUZ/Kq1atGocPH87Rsc7Ozpluf/78OV9//TXTpk3D0dFRn+Hlihh5EnKmSBmo2F73/tyS/I3lBUulJb+2+JVqjtWIS4tjyOEh3I2+i0arwTfclz8f/IlvuC+aAlL08YOKRTk4tjE9aulGodacCabtwlNcePD89Sfr06NLcPhr3Xuv/lDINeN+2Ysfutc2gUaVbVP79u1j5syZWFtbc+HCBRo1akSXLl24e/euAQIXBMHPzw+ZTJZ+u6pDhw7ExcVx8uRJNBoNN2/eNOh8J3d3d06fzlu9vcKFC9OiRYscvczNMx8Znzp1Kvb29owaNepNLuONiZEnIefqjdQt1+K3BZpNA+v8y/pfslJasbTFUoYeHsr1yOv0/6s/Zgoznqf8k5A4WToxufZkWpRskY+R6thaKPmxWzXavRiFevg8iZ4rzvNJfXcmtjHCKFRyNGz/FLRq8PgQOi7UVZF/eFY3idzaCcztYE0bCD4Ff02CDvOzbM7KyoqpU6cyePBgZsyYwYoVK9i1axc+Pj7Mnj2bCRMmGPZ6BCEHZBYWVLhyOdfnJV26ROiQoa89zm3Fcixz8cSXzMIi17G85O/vT+nSpbG2tgagbt26ODg44OPjg6urKykpKQVyvhPo5mtFReVsyoKjo+Mro2f37t1jxYoVLFiwgLCwf54WTklJQaVSERwcTKFChbC3t9dr3JkRI09CzpWoC8VqgiZVdwuvgLAxtWFZy2UUsy5GgiohQ+IEEJEUwbgT4zjy8Eg+RfiqphV0o1C9vN0AWHs2mDYLTnEu0ICjUJIEu0dAbAgUdodOi3S1vOQKKNVIV5aiVCNw8YQuKwEZXFoNF1e+tmknJyeWLl3K9evX6dChA2q12uhF6wQhKzKZDLmlZa5fVg0aYOLsrPt/knnDmDg7Y9WgQa7alWXVXg74+/tnGFmSy+W0bdsWHx+fV56002q1jB49GgcHB+zs7PD29iYyMjL9XB8fH0qVKoWDgwOzZ89O337z5k0aNWqEnZ0dNWvW5MyZMwAMGjSIkJAQWrVqhbW1NRs3bnxtH/929uxZXFxccvQKDQ195fzHjx+n91eqVKn014ULF7h79y6lSpXi22+/zfP3NjfEyJOQcy+LZu4YAL4roeEYUOb9Nyh9sjKxIk2T+VNfEhIyZMy5qCu0qchkHk9+KGSu5IeuVWnr6cKXf/gTEpVE75Xn+V+9kkxqUxErMz3/97ywDO7sB4UpdF8L5rZZH1uxHTT/Go5+oxt9cigPpZu8tgsPDw98fHy4cuUKNWrUSN++atUqzMzM6Nu3b4Y5U4JQkMkUCpymfMnjz8fofv79e6L3iwTIacqXyF4zv0hfwsPDiYiIeGVkqUOHDqxfv57NmzcD/zxpd+jQIc6ePcuDBw+wsrLCz88vw+2wY8eOcf36dYKDg6lVqxY9evTAzc2Njh07MmbMGI4dO8bOnTvp2LEjgYGBrFq1iiNHjrBhw4b0uY0HDhzIto9/e9M5Ty9XPPivqVOnEh8fz8KFCylTpkyO2n9TInkScqdSZ7AtoRu98NsCtT7N74gAuBJxhWfJz7LcLyERnhTOlYgreDt7GzGy12tS3pGDYxvz/Z+32XwxhN/PPeTY7Qh+7FaV+mUc9NPJ48twaJrufatZ4Foj++MBGo6FiFtwfRts7w+Dj4F96Rx15+Xllf4+MjKS8ePHExcXlz6pvFmzZnm5CkEwukKtWsHCBTz9fnaGcgUmTk44TflSt99Isqrh1Lp1a5RKZfqtuyJFigCgVCqJj4/n9u3beHt7Z/h/CTB58mSsra2pUqUKVatW5fr164SFhaWP7gD07NmTBQsWcODAAXr37v1KTK/r499eznnKKwcHBz788MNXtr+s9ZTZPkMRvwIKuaMwgbrDdO/P/wrZ1OIwpmdJWSdO/7b7/m7uRN1BKxWMuF+yMVcyu4sn6wfWppidBY+ik+mz8gJTd18nMVX9Zo0nx8D2T0CrgkodofbgnJ0nk+lu7bl66eZKbeoFKXG57t7a2pqvvvqKQoUKcfXqVZo3b06HDh0yXZNLEAqiQq1aUfboEUqsW4frvHmUWLeOskePGDVxgleftHvJ1taWhg0bIklShn3Nmzdn2LBhDBkyBBcXFyZMmIBK9c9DIE5O/9R7s7S0JCEhgbCwMNzc3DK0X7JkyQxzjP7tdX28q0TyJORejY/BrBBE3oX7ORuCNTRHy38mr8u0Eh4PtTS4qcXjoRaZ9p+h9r2Be+nm041GWxox+thofr/5OwHPAwrME3mNyjlyYEwj+tYpAcCG8yG0XnCSM/czn0PwWpIEe0ZATAjYlYROi7Oev5EZpQX02gQ2LhB5B/4YqFsXLxfMzc2ZOHEigYGBjBo1ChMTE/bv34+npydDhgzh6dPXVzsXhPwmUyiwqlMb2w7tsapT22i36v7tiy++QJKkTG9NHTt2DEmS+OuvvzJsHzt2LNeuXcPX15eDBw+ycePGbPtwdXV9Zb5RSEgIrq66p3Izm6+V2z707cSJE9y4ccOofYrkSY+WLFmCh4cH3t4F67aQ3pkXgpr9de/P/pK/sbzgVdQLJ0sn6tyRWPKrhhmbtHy+V8uMTVqW/Kqh9h0t1kpr6rvWx9LEkri0OI6HHmfupbn03NeTRlsaMfLoSNbdXMfNyJuotW842vMGbMyVzPrIk42D6qSPQvVddYEpu66TkNtRqIsrdE9IypW6eU4WdrkPqJCLLoEyMdfV+ToyI/dtoBtyX7RoEQEBAXTp0gWtVstvv/1GdHQBXTxZEN5yly5dwtfXF7VajY2NDUql8rX1n+rUqQPA4sWLUavVbN++nVu3btGmTRsAihYtSnBw8Bv18S6QSaIssN7FxcVha2tLbGwshQoVyu9wDCMmFBZWA0kDQ0+CS/4/Gnt64zzsZ64G4N+/G2lffB01bSAN+05ArVVz6/ktLj29hG+4L1cjrpKgSsjQlpXSCq+iXtRyrkUtp1p4FPHARG78KYIJqWp++OsWG87rqu0Ws7NgTteqNCyXg7lQj6/A6la623Vt5vxzuzWvru/QjTwBfLgMqr86/yE3zpw5g6+vL2PGjEnfdurUKerXr/9e/PAV9C8lJYWgoCBKlSqV5aTl98nRo0cZM2YMQUFBWFlZ0aNHDxYsWIBCoXilSGbTpk0ZNGgQ/fr1w9/fn+HDh3Pjxg3KlCnDwoULadSoEQA7d+5k9OjRJCQk8Ouvv+Lk5JRlHwVNTv595PTzWyRPBvBeJE8AOwbCjR3g2QO6vv5xdkOSNBruN2+BKjyczG5KSYDS2ZmyR4+8Mtyu1qq5E3WHS08vcSn8EpefXiZeFZ/hGEsTS2oUrZGeTFV2qIxSrjTcBf3H2fuRTPzDn0fRyQD0ru3GlHaVsDHPIobkGFjeGGIeQsUO0HND7m7XZeXoTDg1T/fE3if7wS13lZWzc/36dapXr46Hhwdz586ldevWb/RIt/D+EcmTkB2RPBVw703yFHYVVjQFuQl87g+2xfItlMQLFwnp3/+1x5VYtw6rOtl/4Gu0Gu5G300fmbr89DJxaRknSluYWFDdsTq1nGvh7exNlSJVUCoMm0wlpqqZc+A2v597CICrrTk/dK1K4/L/KVYqSbDtf3BrL9iV0I0MWhTWTxBaLWz7WHcr0KooDDkOtvpZ3mHPnj18+umn6bfxWrZsydy5cwtswT+h4BHJk5AdkTwVcO9N8gSwpj08PA0NPoeWxilOlpnYffsJy0E1a9d587Dt0D5XbWslLfei76WPTF16eomY1JgMx5grzKnmWC19ZKqqY1VMFaa56ienzgU+Z+IffoRG6Uahenm7MaV9JQq9HIW6uBL+nKCb5zTgIBTX85peqQnwW2t4egOcq8KAA2BqpZemo6OjmTVrFr/88gtpaWnIZDL69+/PzJkzjboGl/B2EsmTkB2RPBVw71XydOcv2NwLzGxh3E0ws8mXMPQ58vQ6WklLYEwgvuG+XHqqu80XlZJxyQFTuSnVilajlpNuZMrTwRNzE/39ME9KU/PjgTusPRsMgIutObO7eNLUJgxWtwRNGrSeDfU+01ufGUQ/hJUfQNJz3TIv3dfq57bgC0FBQUyZMoUtW7YAULx4cYKCgjAxEaXphKyJ5EnIjkieCrj3KnnSamGJNzy/D21+gLrD8yUMSaPh/gfNUEdEZHmMSRZznt64b0niQewDLoVfwvepL5fCL72yRIxSrsTTwRNvZ29qOdeimmM1LEzevDr7+QfPmbhDV53chiSOF5qOQ9pjqNAeem3Ua0LziodnYV0n3YT0plOg6SS9d3Hx4kUmTJhA165d+fzzzwHd91uj0YhESniFSJ6E7IjkqYB7r5InAN/VsH+cbn7NqKu6QppGJqWlEdS9O6l37mZ5jGW9epT4bbXBJyFLkkRwXHD6yNSl8EuvVD83kZvg6eBJLada1HKuRXXH6lgqLfPUX1KamrkHblPLdxztFRd4giP3P/qTRtXK6+Nysnfld9j7YnXzHr+DR2e9dyFJElqtNv3pnd27d/Pll18yZ84cOnbsKCaVC+lE8iRkRyRPBdx7lzylJcHPlSE5Crqvg8ofGrV7SZJ4MnkysXv2gqkpChsbNM//GflRFC6MJiYGJAmH0aNw/MxAt7KyiS8kPiTDyNTTpIyFIU1kJng4eODtpBuZqlG0BlbKXMwj8l0F+8ejRkG31Olck8rSrWZxprX3wNbSwE8F/jUZLiwFpaVu/pOBy1Y0atSI06dPA9CkSRPmzZtHrVysaC+8u0TyJGRHJE8F3HuXPAEcmwUnf4Ti3jDoiFG7jvh5Ac+XLweFArelv2LVoAFJly6jfvYME0dHLGvVJGbbNsK/0U1od5k1C7uuXYwa479JksSjhEfpk899w315kvgkwzEKmQKPIh7pI1NeRb2wNrXOvMEnfrCqBWjSUDWfyeyYFqw5G4QkgVMhM2Z38aRZRafMz9UHjRo2dYfAY1CouO4JPOuiBusuNjaWOXPm8PPPP5OSkgJAnz59mDVrFu7u7gbrVyj4RPIkZEckTwXce5k8JUToRp80aTDgEJSoY5Ruo7dsIXzGNwC4zPoOu65dszw2Yv7PPF+xQpdkLVuGdaOGRokxJx4nPNaNTL241fc44XGG/XKZnIr2FdNHprycvChkWki31tyKJhD1AMq3hd6bQSbjUnAUX+zwJygyEYAuXsWY3qGy4UahkmNgVXPd3LfiteGTfWBiZpi+XggNDWXq1KmsX78eSZIwMzNj7ty5jBo1yqD9CgWXSJ6E7IjkqYB7L5Mn0K2hdnWDbvHZnhsM3l38sWM8GjkKtFocRo7EceSIbI+XJImwSZOI2+uDzNKSkut/x6JyZYPHmRdPEp7o5ku9GJkKjc+41pQMGRXtK1AzLgrvxzepaeqA7ZCTYGmffkxymoafDt1h9RndKFRRGzO+/8iTFh4GGoWKvAcrm0NqLFTvC52XGHbC+gtXr15lwoQJHDt2jP3799OuXTuD9ykUTCJ5ErIjkqcC7r1NniJuwa91ARmMvgL2pQ3WVbKfHw/7f4KUkoJtt664zJyZo4nDUloaIUOHknTuPAoHB9y3bMG0eP4V98ypp4lPMxTtDI4LzrBfhoxyhcvpnuZzqkVNp5oUNtcVxrz8MIovtvvz4MUo1Ec1ijG9owd2lro6VGlqNZv8ThASF06JQs70qdYU07w+yXb/KGzsBpIWWn0H9Y0zCiRJEufOnaNevXrp/w7Wrl2LtbU1Xbt2FZPK3xMieRKyI5KnAu69TZ4ANnSF+0eg9lBo96NBukh7+JDgXr3RREdj1bgRbkuWIFPm/HaUJj6eh/0+JvXOHUxLlcJ98yYUdnYGidVQIoL+5vLOfviaKrhUxI0gVcwrx5S1K5teZ6pKkRqsPRXJqlMP0ErgaGPGrA+r4Bd1ivX3FiEp/jlfprHj43Kj+aJR97wFd34pHJgMMjn02QblWuatnTfw/PlzypQpQ2xsLPXq1eOnn36iXr16Ro9DMC6RPAnZEclTAfdeJ0+Bx2H9h6C00hXN1NeyIC+onz8nuHcfVCEhmFeuTMnf1yG3yn11a9XTpwT36o36yRMsvLwo8dtq5G/LD9vUeFjeBKICoVxr6L2FyNSoDGvz3Y+5/8ppZWzLUNLKE9/bdjwJL4bC8iHmxXS3V/89MPPyJ0L/Ml/nLYGSJF35gqvrwayQ7gECxwp5udI8S0xMZO7cucydO5ekpCQAunXrxuzZsylbtqxRYxGMRyRPubdw4UJOnjyJqakp+/btw9PTk507dzJz5kw2bdqEm5sbBw4cwNXVNb9DfWP6TJ7khgpSeE+VbgpOVUCVCJfW6LVpbVISocOGowoJQVm8OG7Ll+UpcQJQOjlRYsVy5DY2JF+5QtgXE5E0Gr3GaxCSBD5jdIlToWLw0TKQy3GwcKCNexum1p3Krs67+Lvn38xvOp/eFXtTrnA5AAJjAzkWtpv4QmuxLj8L82KbgFenJb38ev3dRaSp1bmPUSaD9vOhRH1IjYNNPSEp6vXn6ZGVlRUzZszg3r17DBo0CLlczo4dO/Dw8GDMmDE8f/789Y0IQgHk6+vLyJEjqVy5MlZWVpQoUYIePXpw927WNe6y4+/vz8WLFxk/fjwREREkJSXRvHlzunTpwrNnz3BxcWH9+vV6vQatVoujoyM//qi7O3Hz5k26d+9O6dKlsbS0xMHBgcaNG+Pj46PXfvVJJE+CfslkUO/FxO2LK0CdppdmJbWax+PGk3L9Ogo7O9xWrMDEweGN2jQrV47iixcjUyqJP3yYpz/MocAPxF5ZBzd2gEwB3dZkmCD+b/bm9rQs2ZIpdaaws9NOTvY8yYKmC+hXqR8VCutGgWQybZbzuWUykExi2OR3Im9xmphCz/VgWwKig2D7J6BR5a2tN+Dq6srKlSvx8/Ojbdu2qFQqFi9eTEQ2legFoSCbM2cOf/zxB82bN2fhwoUMGTKEkydP4uXlxY0bN3Ldnr+/P99++y21atXCwsKCUqVK0atXL5o3b46JiQkVKlRAo+dfLC9evEhkZCTt2+vWGX348CHx8fH079+fhQsXMm3aNAA6derEihUr9Nq3vojbdgbwXt+2A13CtMATEsLho+VQrdcbNSdJEuHTZxCzbRsyMzNKrFmDpVcNPQULsfv3EzZet6hw0YkTKTLgU721rVfhN3TlANQp0OIbaDgmz01NO7qK3Y8Wvva47iUm8fUH/fLcD+E3YHUr3Uik92BoPy/vbenBkSNHuHr1Kl988UX6tosXL1KrVi3kcvG75Nvufbhtd/bsWWrVqoWp6T8Lj9+7dw9PT0+6devGhg26W/ENGzbkzJkzmbbx1Vdf8d1336HVarGxsSEwMBBnZ2cAKlasyIYNG9ILz7Zp04bBgwfTNZsyMLn19ddf8/vvvxMcHJzlMRqNhpo1a5KSksLt27f10q+4bScUbCamUGeI7v3Zxf9Mosmj58tXELNtG8hkuM6bq9fECcC2fXuKTpwIQMSPPxK7f79e29eL1HjY3l+XOJVtCfVHv1FzZezcc3Tc09QA4tPi896RcxXo8uI3R9+VcOm3vLelBy1atMiQOF2/fp169epRp04d/v7773yMTBBypn79+hkSJ4By5cpRuXJlbt26lb7t9OnTSJKU6eu7774D4P79+1hbW6cnTsnJyQQFBVGlSpX0dvz9/alatWq2MX322WfIZLJsX/9OlPbv358+6pQVhUKBm5sbMTExOfm2GJ1IngTDqPmpbrmOp9chKO8fSjG7d/NswQIAnL76ikItDfPklv2nn1D4448BeDL5SxIvXDRIP3kiSbBvnK4ApY2rbjTvDUdJ+lRrikxjl2Ve+3L7yac+tNzRknm+8whPDM9bZ5U6QLOpuvd/fgFBp/LWjgHcunULS0tLLl26RNOmTencubPefssVBGORJImnT5/ikMupDP7+/lSr9s9ySjdv3qRMmTLpozKRkZHExsZSpkyZbNvp2rUrtWvXxtnZmfXr16e/SpcujYeHB5s2bUqv/h8eHs7Vq1czrceWmJhIZGQkgYGB/Pzzz/z11180b948V9dkLCJ5EgzD0l5XKBF0o095kHDmDE+m6u59Fxk0EPt+ffUV3StkMhlOkydh06oVkkrFo5EjSb13z2D95crV9XB924t5Tr+BVZE3btLUxISPy+lGr/6bQL38WhVdjyKmJUhUJbIuYB1t/2jLl6e+5HZUHpKLRhOgSlfQqmHbxxAV9IZXoB89evTg/v37DB8+HIVCwd69e6lSpQojRowQ86LeQYmJiVm+Xi71k5Njk5OT83ysIWzcuJHHjx/Ts2fPXJ13/fr1DMlTZl9Xrlz5tbe0mzdvTlpaGjVq1KBfv37pr6ioKBo2bEjv3r3Tj/3zzz8xNzenWbNmr7Qzfvx4HB0dKVu2LBMmTOCjjz5i8eK8fX4YmpjzZADv/Zynl54Hwi81AQk+uwBFK+b41JRbt3jY72O0iYkUat8e17k/IjPCnBRtSgohAwaSfOUKJs7OuG/dgtLJgOvCvc7Tm7Cyme52XfPp0GicXpufe2r7q3We1HYU0/biVqA7ING6VjQq6+P4PvVNP6auS10+rfwp9Vzr5bwApSoZ1rSFsKvgWAkGHgLzgvP/4/bt20yaNIm9e/cC4O7uzr179zDJa8FQweheN6clu3+r7dq1Y/+/btlbWVmll7n4ryZNmnDixIn0rx0dHYmMjMz02Fq1auHr65vpPn24ffs2derUoXLlypw6dQqFQmGwvrKi0WiwtrZm1KhR6U/QhYaGUqJECRYtWpRhyaRu3bqRnJyc4Xv90u3bt3n06BFhYWFs27YNU1NTli5dipOefgaLOU/C26FIGaj44r72+SU5Pk31+DGhQ4aiTUzEsk4dXGZ/b5TECUBubk7xJYsxLVUKdXg4oUOGool/gzk/byI1QfeUmjoFyraABmP03sUXjbpz6X/HGV/lZ7qXmMT4Kj9zqf9x/hz0GRPbVABkHLxkj+rxUFa12EBb97YoZArOPznP0CND6ebTDZ9AH1Q5eZJOaQG9NoG1Mzy7BTsHg7bglIeoWLEie/bs4cSJE9SqVYvPP/88PXGSJAmtVpvPEQpCRuHh4bRv3x5bW1t27NiRL4kT6OZOpaSkUPlfy11dv34dIMP8KZVKxeHDh7Oc71SxYkVatGjB//73P/bt20dCQgIdO3YskE9Bi5EnAxAjT/8Sch5+aw0KMxh7A6yLZnu4JjaW4D59SQsMxKxcOUpu3IAiH76HaY8eE9y7F5pnkVjWq0uJ5cuR/WeSpkFJEuwaBv5bwMYFhp0GqzcrzZAXB26EM3brNZJVGso4WrG6vzdK8xg2BGzgj3t/kKzW3ZIoalmUjyt9TNfyXbExtcm+0UeXdSNQmlRdQtjyG8NfSC5ptVq0Wm168rR3716+/vpr5s2bR4sWLfI5OiErrxtZSExMzPJchUKR4ZzsjpXL5VhYWOTpWH2JjY2ladOmhISEcOrUKTw8PPTeR0798ccfdOvWjUuXLlGzZk0AfvjhB7788ksiIiJwdHQE4Pjx4zRr1oygoKD0OVDZWbFiBUOHDuX27dtUqPDmhXbFyJPw9nCrA8Vq6T4ofVdle6g2NZXQESNICwzExMkJtxXL8yVxAjAtXgy3ZcuQW1qSdO48YVOnGve3n2sbdYmTTA5dV+dL4gTQpooz24fVw8XWnMBniXz46xlCnpozqfYkDnc7zOden+Ng4UBEUgQ/Xf6Jljta8tOln7KfXF68pm7RYIAzC8Bvq1GuJTfkcnmG23WzZ8/Gz8+Pli1b0rZt2zzV0xHyn5WVVZav/36YZnfsf5Oh3ByrDykpKXTs2JG7d++yb9++fE2cAG7cuIFcLqdSpUrp265fv07RokXTEyfQPWXn4eGRo8QJSJ8vFhsbq9d49UEkT4Jh/btopu8q3byXTEhaLWGTJpN86TJya2vcVqxA6eJixEBfZVG5MsUWLgSFgri9Pjz7eYFxOo64Bft1daf44Ctwb2CcfrNQpZgte0Y0oJqbHTFJKj5efYEtF0OwNbNlkOcgDnY9yLf1v6WMbRkSVYmsvbk2fXL5nag7mTdatTs0fDF/a+8oeHTJeBeUB/v27ePzzz9HqVRy4MABqlWrxqBBgwgLC8vv0IT3jEajoWfPnpw7d47t27cXiDUbb9y4QalSpbC0tEzfdvv27Qy38UA3WTyzW3aZPZyhUqn4/fffsbCwyPfkMDMieRIMr1InXaXppOfgtyXTQyJ+nEv8gQOgVFJ88WLMK5Q3cpCZs27UEJdvvwXg+YoVRG/ebNgO0xJhW39QJ0OZZv8kGPmsaCFztg6pS4eqLqi1EpN3XmfmvgA0WglThSkflfuInZ13sqT5ErydvVFLavY92Ec3n24MOTSEs2FnXx25azYNKrTTjUpu6QOxj/Pn4nKgSJEiLFiwgICAALp164ZWq2X16tWUK1euwFZAFt5N48ePZ+/evbRt25aoqCg2bNiQ4ZUfbty48UqiFB4ejkqlSq/TFBQUxK1btzJNnoYOHUrz5s355ptvWLVqFd999x1Vq1blypUrfPfdd1hbWxvjMnJHEvQuNjZWAqTY2Nj8DqXgOLtEkqYXkqRFNSVJo8mw6/natVJAhYpSQIWKUsxen3wKMHsRixfrYqzkIcUdOWK4jnYO032f5paXpPgIw/WTR1qtVlpw+K5UctI+qeSkfdInv12Q4pLTXjnuxrMb0oQTE6Sq66pKVdZWkaqsrSJ13dNV2nt/r5Sm+dfxKXGStKSu7pqXNZak1EQjXk3enTlzRqpXr54ESPv27cvvcIQXkpOTpYCAACk5OTm/QzGYJk2aSECWL2NLTU2VTExMpClTpmTYPnDgQMnMzEzq0qWLJEmStHjxYsnW1lZSqVSvtLF582apRYsWkpOTk2RiYiIVLlxYatGihbRnzx69xpqTfx85/fwWE8YNQEwYz0RqPMyvDKmx0HsrVGgDQNyBAzweOw4kiaITxlNk0KB8DjRzkiQR/vXXxGzfgczcnJJr12BRvbp+O7m6EfZ8ppvn1N8H3Bvqt3092ucfxvhtfqSqtZR3smZ1f2/c7C1fOe5R/CM23NrAzns70yeXO1k68bHHx3Qt1xVrU2uIDoYVH0ByFFTuoqtlldPyB/lIkiSOHTtGs2bN0h+B37BhA/b29rRt2zbnJRwEvXkflmd5W7Vr1w5ra2u2bduWbzGICePC28fMBmr2170/pyt6lnTpEmETJ4EkUbhPH+wHDszHALMnk8lwnj4dqyaNkVJSCB3+GWnZrMuUaxG34c8X85yaTinQiRNAh6qubBtaj6I2Ztx9mkDnJWfwDY565bjiNsWZXHsyh7sdZnSN0RQxL8LTpKfMuzSPljtaMv/SfMJNzXWLCMtN4OZOOJm/69/llEwmS69+LEkSkZGRjBw5kvbt29OyZUuuXr2azxEKQsHRtGlTxo4dm99h6I0YeTIAMfKUhdhHsLAaaNWkttpI8JiZaOPisG7RnOILFyLLpxoluaFNTORh/09IuXEDpZsb7ls2Y1LkDSt+pyXqCmE+uw2lm0K/nSAv+N8LgPDYFAb97suNx3EoFTK+/8iT7rXcsjw+TZPGvgf7WHtzLUGxuirjJjIT2pZqS3+ZHRWOzNId2HMDVOpojEvQm9jYWL777jsWLVpEWloaMpmMjz/+mO+++w43t6y/J4L+iJEnITti5El4O9kWh8ofoUqWEzJuKtq4OCyqV6fYvHlvReIEILeywm3ZUpTFi6MKDSV02HC0WVQhzrE/J+oSJ2sn6LLyrUmcAJxtzdk2tB5tqzij0kh8scOf2X/dQqvN/HcyU4UpXcp1YXfn3SxutphaTrVQS2p8HvjQLXA9w8p7cc7cDGnnEAi/buSreTO2trbMnTuXO3fu0Lt3byRJ4vfff6d8+fJMmTKFuLi4/A5REAQ9EcmTYFSaqgMI/bsI6phUTEsUp/jSX5G/Zb8hmjg44LZyBQo7O1KuX+fx2HFIanXeGru2Ga5teFHPadVri4gWRJamJizp48WoZmUBWP73A4ZuuExiatbfE7lMThO3Jqxps4bN7TfT2r01cpmcM6pIhrg40cOxEPv+6I0q7omxLkNv3N3d2bRpExcvXqRx48akpKTw448/8vhxwX2aUBCE3BHJUxaWLl2Kl5cXSqWSGTNm5Hc47wRJpeLx7NWkxihRmGlw+6QKJoUL53dYeWJWqhTFl/6KzMyMhL//Jvybb3NfRPPZHdj/ohRBk8lQqrH+AzUSuVzG+FYVWNirOqYmcg4HPKXbsnM8jnn9oqhVHKowr8k89n+0nz4V+2ChMOe2mSlfWstot7Mt666vJiEtwQhXoV/e3t6cOHGCPXv28O2332YoIOjn51cgl5wQBCFnRPKUBRcXF2bMmEHXrl3zO5R3giRJPJk6jcSzZ5GZm+LWJArTh3/onsJ7S1nWqEGxn+aBXE7M9u08X7Ys5yenJenWrVMl6ZKmxhMMFqcxda5ejC1D6uJgbcatJ3F0XnyGKyHROTq3uE1xvqzzJYe7H2FU+d4U0WgJl2mYd2WBbnL55fk8TXxq4CvQL5lMRqdOnZgyZUr6tps3b+Ll5UWTJk24ePFiPkYnCEJeieQpCx9++CGdOnXCzs4uv0N5JzxbtIjYPXtAoaD4zwuxKOeuK1twZX1+h/ZGbFq0wOkr3Qfjs4WLiNm5K2cn/jURIgLAqih0WfVWzXN6Ha8ShdkzsgGVXAoRmZBKrxXn2XMt57esbM1sGVJvCgcbzGNGZBSl0lQkqBJYc2MNbXa24avTX3E3+q4Br8Cwrl27hqmpKadOnaJOnTr07t2boKCg/A7rnSJG9YTM6PPfRYFOnhISEpg+fTpt2rTB3t4emUzG2rVrMz02NTWVSZMm4erqioWFBXXq1OHw4cPGDVjIVPTWbTxfqhuVcflmBtYfNIV6n+l2XlgKmjzOFyog7Pv2pchgXX2qJ19/TcLpM9mf4LcVrq4HZNB1Jdg4GT5IIytmZ8GOYfVoUcmJNLWWz7dc46dDd7KcSJ4Zswpt6Vp/CrsfP+GXp5HULFQGtVbN3sC9dN3blWFHhnH+yfm37oOyb9++3Lt3j/79+yOTydiyZQsVK1ZkwoQJREfnbJTubaDRSpwLfM6ea485F/gcTS7+7vNKqVQik8myXahXeH8lvXi4R6lUvnFbBbpUQXBwMKVKlaJEiRKULl2aEydOsGbNGj755JNXju3duzc7duxgzJgxlCtXjrVr1+Lr68vx48dp2DDvNXOGDRuGs7NzruY9iVIF/4g/fpxHI0aCVovDiBE4jhqp26FKhp8r65Zs6b4WKn+Ur3G+qZdr88X5+CC3tKTkhvWYZ7Ye07O7sKIpqBJ185w++NLosRqTVivx48E7LPs7EIC2VZz5qUc1LE1NXnPmC5IEe0bqJtWb2XK9+zLWPjrKkZAjaCUtAJXsK9G/cn9aubdCKX/zH4rGdO3aNb744guOHDkCQNmyZbl9+zaKt+Tp06wcuPGEb3wCeBKbkr7Nxdac6R09aFPFsGtWPnnyhJiYGAoVKkShQoUwMTERBUvfc5IkkZSUREREBHZ2drhks25qTj+/9ZY8paSkIJPJMDMz00dzgG40KTo6GmdnZy5duoS3t3emydPFixepU6cOc+fOZcKECenxVKlShaJFi3L27Nn0Yxs2bMiZM5mPDHz11Vd89913GbaJ5Cnvkv39edj/E6TkZGy7dsHlu+8y/hA7/j38PQeK1YJBR96KqtLZkdLSCBkylKTz51E4OlBqyxaUxYr9c4AqGVY2h4ib4N4I/rfnnbpdl50dlx/x5U5/VBqJKsUKsep/3jjb5vApS3UqrOsIoRfAvgwMPkqoOoH1AevZfX93euVyFysX+lXqR9fyXbFSWhnwavRLkiQOHjzIF198waeffsq4cePStwNv3Qf/gRtPGL7hCv/9YHl5FUv7eRk0gZIkidjYWCIiItBoNAbrR3j72NnZ4ezsnO3/KYMnTy+fIjlz5gwBAQEkJ+t+gFlaWlKpUiXq16/Phx9+SNOmTfPS/CuyS54mTpzI/PnziYqKynCxs2fPZsqUKYSEhOS5SJ1InvIm7eFDgnv3QRMVhVWjRrj9ugTZf4dKEyLg5yq6hWEHHIQSdfMnWD3SxMfzsG8/Uu/exbR0adw3bUTxct7c3tFwZR1YOcKw02DjnK+xGptvcBRD118mKjGNojZmrOpfi6rF7XJ2ckKErpBobKiukGjfP0BhQkxKDFvvbGXT7U1EpegqnNsobeheoTt9K/WlqOXbU/pBo9Gg1WrTbyn4+Pjw/fffM2/ePBo0aJDP0eWMRivRcM6xDCNO/yZDVxvs9KRmKOSGTQolSUKj0aDOaxkR4Z2iVCpzNKJrkORJpVKxfPly5s+fT3BwMPb29nh5eVG6dGkKFy6MJElER0cTFBTElStXiIqKomTJkowfP56hQ4e+0X3G7JKnli1b8vjxYwICAjJsP3r0KC1atGDv3r107Ji7asVqtRq1Ws2oUaNwcnJi6tSpev/mv6vUUVEE9+6N6mEI5h4elFz/O3KrLEYC9ozUzf+p2AF6bTRuoAaiCg8nuFdv1OHhWNSsSYnfViO/sxd2DgJk8PEuKPNBfoeZL0Kjkhi4zpe7TxMwM5HzU49qdKjqmrOTn/jDb611TyjWGQZt56TvStWk4hPow7qb6wiOCwbARG5C+1Lt6V+5P+UKlzPA1RhW7dq18fX1BaBLly788MMPlCtXsK/jXOBzeq88/9rjNg+uS70yb1iZXxAMwCAVxsuWLcusWbPo0aMHly5dIjIykkOHDrFs2TJmz57NDz/8wPLlyzl06BCRkZH4+vrSs2dPvv/+e4P+p3/y5Emm9zBfbgsLC8t1m9999x0WFhasWrWKWbNmYWFhwfr1mT8ZlpqaSlxcXIbX+0qbnEzo8OGoHoagLFYMt+XLsk6cAOq9mAN1ez9EPTBOkAamdHbGbcVy5DY2JF++TNjnI5B8xuh2Nv7ivU2cANzsLfljeH0+qOBIqlrLyE1XWXjkXs4mfbtUhY+W695fWAaX16bvMlOY0a18N/Z8uIdfmv2CV1Ev1Fo1ewL30GVvF4YdGcaFJxfeeHK5pNGQeOEisfv2k3jhIpIBbwvt2bOHIUOGIJfL2blzJx4eHowePZrIyEiD9fkmtFqJAzdyVtQ0Ij7zkSlBeFvkKnmaMmUKwcHB/PDDD3h5eb32+Jo1a/LDDz8QHBzMl18abmJscnJypnOtXq5d8/KWYm7MmDEDSZIyvDKbqA6624O2trbpr/d1HStJrebx+Amk+PmjsLXFbeVKTBwdsz+paEUo2xKQ4PxSo8RpDObly1P8l1+QKZXEnzhDxAU5lGwITSfnd2j5zsZcyar+3gxqWAqAn4/cZfSWa6SocpCIeHSCD77Svd8/HoIzzl+Uy+Q0dWvKurbr2NhuIy1LttRVLn98hkGHBtFzX0/+fPAnam3ub+XEHTrE/eYtCOnfn7AJEwjp35/7zVsQd+hQrtvKCRcXF5YvX46/vz/t2rVDrVbzyy+/UKZMGdatW2eQPvNCkiSO3X5K+19Os+7cwxydU9Tm7VpVQBD+K1fJ09ChQ/M0IdzU1JShQ4fm+rycsrCwIDU19ZXtKSkp6fsN6csvvyQ2Njb9FRoaatD+CiJJkgifNYuEY8eQmZlRfOmvmJUulbOT678Yfbq6AZKiDBekkVnVrYNLd11V6ai71jxPbf3eTBB/HYVcxtQOHvzQxRMTuQwfvzB6rjhPRFwORiQaf6F7OlOrhm0fQ3RwpodVdazK/Kbz2ffhPnpV6IW5wpxbUbeYdGoS7Xa2Y33AehJVOXukPe7QIR5/PgZ1eHiG7eqnT3n8+RiDJVAAlStXZv/+/Rw5coTq1asTFxdHkTddjFpPzj94Trdl5xiw9hK3nsRhZarA2syE7GYz2VuZUruUvdFiFARDyHWdpw0bNvD8+XNDxJJnLi4uPHny6nDxy22urjmcU5FHZmZm6Y/Fvny9b56vWEnM5i0gk+E690csczAyma5UE3CqopvLcnmN4YI0tus7sNUeoGg13W3ciAVLifvrr3wOqmDpVbsE6wfWwc5SiV9oDJ2XnOHG49jsT5LJoPOv4FJNV+pic+9sK9W7FXLjq7pfcbjbYUZUH4G9uT1PEp/wo++PtNzRkgWXFxCRFJHl+ZJGw9PvZ+vKJryyU7ft6fezDXoLD6B58+ZcvnyZ/fv30759+/TtW7Zs4cSJEwbt+7/8H8Xw8eoL9FpxnssPozEzkTO0cWlOT2rGvO5VAbJMoOKSVVx4ULA+QwQht3KdPPXv35+DBw+mf61Wq7l//75eg8qt6tWrc/fu3VfmGl24cCF9v2A4sXv28OznnwFwmjKFQq1a5a4BmeyfuU8XVoA6Tc8R5oPngeDzOQD2g4dSuG9fAMImTiLpxSRgQademSLs/qwBZRyteBKbQvdl5zh4Mzz7k0wtoddmsHbSVWrfORS02mxPsTO3Y1i1YRzsepCv632NeyF34tPiWX1jNa3/aM20M9O4H/3qz7KkS5dfGXHKQJJQh4eTdOlyTi73jcjlctq1a5f+qHVUVBTDhw/ngw8+oFOnTty6dcug/d97Gs+w9ZfptPgMp+5FYiKX0a9uCU5O/IAv21WisJUpbaq4sLSf1yulKFxszfEsVgi1VmLguksigRLearlOnv474TI2NpYKFSpw7NixV469ceMGGzca/gmqbt26odFoWLFiRfq21NRU1qxZQ506dd7bOUjGkHj2LGFfTQXAfsAA7D/ul7eGqnQFGxdICIcbf+gxwnygSoHt/SEtAUrUR/bBFJymfIlNyxZIKhWhI0aSms+/cBQ07g5W7PysAY3KOZCs0jB0/WV+PXE/+wnetsWg1yZQmMGd/XD8u6yP/RdzE3O6l+/Ong/3sOiDRemTy3ff381Hez9i+JHhXHxyMb1v9bOsR6X+Tf3sWY6O07e+ffuiUCjw8fHB09OT4cOH8/SpftcADI1KYty2a7RecJIDN8ORyaBLjWIcG9+U7z70xKlQxkSpTRUXTk9qxubBdVnYqzqbB9fl9KRm7BhenyblHUlWafh0rS+Xgt+d2/TC+yXXdZ7kcjkbNmygT58+ADx//hxHR0eOHDlCs2bNMhy7ceNG/ve//71RobLFixcTExNDWFgYS5cupUuXLtSoUQOAUaNGYWtrC0CPHj3YtWsXY8eOpWzZsqxbt46LFy9y9OhRGjc27mr170upgpTbt3nYtx/axEQKtWuH67y5yORvsOLPqflw9BvdLbxhp9/eopn7xsGl1WBZRHcdhXS3jbUpKYR8OoDkq1cxcXXBffMWlE5vTx0iY1BrtMzcF5A+8bhLjWLM7uqJmUk2c8X8tsKuIbr3XVZB1e657tfvmR/rbq7jyMMjSC/KO3oU8WCIaXNK/rIP1b17r22jxLp1WNWpneu+9eHOnTtMnjyZ3bt3A2Btbc2kSZMYN24clpaWeW43Ii6FX47dZ4tvCCqN7vvSurIT41tVoLyTTZ7aTFFpGLTuEqfvR2JtZsLvA2vjVaJwnmMUBH0yWJFMYydP7u7uPHyY+RMcQUFBuLu7A7rJ4dOmTWPDhg1ER0dTtWpVZs6cSevWrfPcd24tWbKEJUuWoNFouHv37judPKnCwnS1jCIisKxdG7dVK5Gbmr5Zo8nRMN9DN/fp491v5yP9N3bCjk917/v+AeVaZNitjo7mYe8+pAUHY1axIiU3rEdhbZ0PgRZs688FM8MnAI1WombJwiz/uCYO1tk8rHL4azizUDcK9elfULxmnvoNjQtlXcA6jl/bxUfHk/nAT0IO6dWyM0vntYDW0Y4qJ04jy+dlVU6dOsX48ePx9fVFLpdz/fp1PDJbJug1ohPTWHYykHVng0lR6W6HNirnwIRWFajmZvfGcSanaRiw1pdzD55jY2bCxsF1cl4wVRAMyCB1nvJDcHDwKyUDXr5eJk6gK0swd+5cnjx5QkpKChcvXjRq4gQwYsQIAgIC0gvbvas0sbGEDBmCOiICs3JlKb74lzdPnAAsCkONF7f9zi1+8/aM7Xmgroo4QMNxryROACaFC+O2aiWKIkVIvX2bx6NHI6W9A3O89Ozjeu6s+7Q2hcxNuPwwms6Lz3A7PJv6ac2nQ/k2umr1W/pAXO5ruwEUM3di+E0XlqyE5i8Sp5OVZSxvo/tRmdmsKhmwtrkCbQEYKG3UqBHnz59n8+bNfP311xkSp9u3b7/2/IRUNYuO3qPxj8dZ/vcDUlRavErYsWlwHdYPrKOXxAnAwlTB6k9qUdvdnvhUNf1WXXj9gwKCUIDkKXmKiYnRcxjC20KblsajESNJux+ISdGiuK1YgUKfo2t1hwMyuH8EIgw7+VWvVCmw/RNIi4cS9f6pRZQJ0+LFcVu+HJmlJYlnz/Fk2rQ3Lt74LmpYzoFdIxpQysGKxzHJdP31LEdvZTGXR66ALivBsZJu3tyWPrq1BHNIkiTijx3jQYeORMydh5SYhLmnJy4b1hI3+VOO1ZDzUxc5UZncqZKAx/JorkRcyduF6plcLqdXr15Mnz49fVtAQACVK1emTZs2+Pv7v3JOikrDqlMPaPzjceYfvkt8qpqKzjas7l+LP4bXp34ZB73HaWlqwm+felOzZGHiUtR8vPpC9gmyIBQgeUqeRo0ahb29Pc2bN+frr79GJpMRFhYm1hB6x0laLU8mTybp0iXk1ta4rVyBMpvVqfPEvjRU6qB7f26Jfts2pENTIdwfLOyh62pQmGR7uEWVyhRf8DMoFMTu2cuzhQuNFOjbpYyjNbs+q0+90kVITNMw6PdLrDz5IPNk07wQ9N6sG8EMu6pb+icHSWnK3buEDhzIo89GoAoJwcTREZcfZuO+dQt2tepQuUhlAC5WkDPiMwUz+shZ2EnOjD5yjlTT/RAd6aPleXiwfi9ejy5cuIBCoeDgwYNUr16dgQMH8vjxY1QaLZsvhvDBvBN8t/8WUYlplHKw4pfeNfhzdCOaV3Iy6MLE1mYmrP3Um2pudkQnqei78gL3nmZddkIQCopcz3k6dOgQfn5++Pv74+fnx507d1CpVMhkMkxMTChVqhSVKlWiYsWKPHv2jDVr1rx3K1u/qxPGn875kag1a0CppMTKFVjVNdBCviEX4LdWoDCFsTfBuoBPqr65W/d0HUDfHVCuZY5PjfnjD568eFrRecYMCvfqaYAA334qjZav99xk88UQAHrUKs53H3piapLJ739BJ2H9iyKazaZB4wmZtqmOjibyl8VEb90KGg0yU1PsP/0UhyGDMywp5Bvuy4CDAzJtwyxN4oc1GopFgbpRTaqsWG/QZONNBAYGMmXKFLZt2waAqbk5zg26I3l2RG5miYutOZ83L0e3msUxURh3Rkdssoq+q85z43EcDtZmbBlSl7JFxVxAwfgMNmH8v1QqFQEBAenJlL+/P/7+/kRE6B7vlclkInl6B0T9/ruuUCDgOvdHbHO50HKurWoBj3yh8URolvUtsHwX9QCWN4HUOGgwBlp+k+smni1eQuTixSCXU3zxYmyavYUT5Y1AkiTWng1m5r4AtBLULmXPsn41sbfKZL6d72rYP073vtcmqPhPUUlJpSJ6y1aeLV6MNlY3z8amZUuKTvwC00zKmmi0Glr/0ZqIpIj0J/H+rVQ4zPpdjYkGnL/5hsI9e+jngg1AkiR+2fIX07+aTEzQdQDMHNz45Y/jfFzPHXNl/k14j0lKo/fKC9x6EkdRGzO2Dq1HKYds1sUUBAMwWvKUladPn6YnUxMmZP6b37vqXUue4g4e4vGYMSBJOI4fh8PgwYbv9OYu3RwiC3vd6JNp3h+3Nhh1KqxuBU+ugVsd+GQ/KJS5bkaSJJ5MnUrsHzuRmZtTct1aLKpV03+874gTdyIYtekq8alqSthbsrp/Lcpl9tj8/gnguxKUVjDwEDhXIeHMGZ7Onk3a/UAAzCpUwOnLL7GqWyfbPo88PMK4E7pk7L8JlAwZKyLbY7tyNzJzc0rt/AOz0qX1c7F6dDYwkrkH73A1JEb30E3QBVLOrmfMqBFMmfQF8E8dv/waPYtKTKP3ivPceRqPi605W4fUo0SRAvh/X3hn5Xvy9D56F0sVJF2+TMinA5DS0ijcpzdO06YZ5werRg2/1ICYEOjwM9TK/LZJvvpzIlxcrptjM+w02BbPc1OSSkXoZyNIPHUKReHCuG/ZjGnJknoM9t1y72k8A9ddIiQqCRszE37pU4OmFf5ze1ejgg1dIOgkabjxNKwuCSd1Cwkr7OxwHDMGu+7dclxe4MjDI/xw8QeeJv0zad3CxILvG35Pc7dmhA4aTOLZs5hVqoT71i36eQJVD66FxjDv4B1O348EwFwp55P6pRjWpDSWL6bmmb6Idd++fcyfP5958+blaPF3Q4hMSKXXivPcj0igmJ0FW4bUxc1eJFCCcYjkKR+9KyNPqQ8eENy7D9rYWKybN6f4ooXGrWNzfikcmAxFysIIX3iTApz6FrBXtygtQJ9tUP7Ny2JoExN5+PH/SAkIQFmiBO5bNmNiLxZQzUpUYhrD1l/mYnAUchlM6+DBJ/XdMyT3mohQIke3JcpfDVoZmJhg37cPDp99huJFgd3c0Gg1XIm4woUnF1juvxxzhTnHexzH2tQaVUQEQZ0/RBMdjf0nn+A0eZI+LzfX7oTH89OhOxwK0CV7SoWM3rVLMPKDshT9T0Vw0I061axZk6tXrwLQr18/Zs2aRYkSJYwaN+iKc/ZacZ4HkYm42VuwdUg9XO0Mu8C7IMA7VOdJyB+qiAhCBw1GGxuLRbVqFJs31/gFAGv0AzNbeH4f7h18/fHGEhWke5ILoP5ovSROAHIrK9yWL0NZrBiqkBBChw1Hm5Skl7bfRfZWpmwYVIfuNYujleAbnwCm7r6BSqNF0miI2bGDwI96E3VNA1oZVi4plB7jjdPkyXlKnAAUcgXezt6MqD6C0ralSdGksP/BfgCURYvi8v0sAKLWriXh9Bm9XWtuPHyeyNit12iz8CSHAp4il0FXr+IcG9+UbztXyTRxAt2tul27dtGvn67W2oYNGyhfvjyTJ08mNta4NZiKFjJn0+C6lCxiSWhUMr1Xnic8NsWoMQhCdsTIkwG87SNPmoREHv7vY1IDbmFasiQlt2zGpHA+LZ9waBqcXQQlG8Kn+/Mnhn9Tp8FvrSHsChSvDZ/+mad5TtlJfRDEw9690cTGYt20KcUX/4LMJPvSB+8zSZJYdSqI7/+6hSRBT7PnDPLbhfpFUUjTUqVw+rgl1ne/ASRoMwfqDnvjfjcEbGCO7xzKFS7HHx3/SB/xCv92JtGbNqFwcKD0nt2YFCnyxn3lRHhsCr8cu8dW31DUWt2P9bZVnBnXsnzmc8KycfnyZSZMmMCJEycAcHBw4JdffqFXr176DjtbYTHJ9FxxjtCoZEo7WLFlaF2K2mSe/AmCPhSIkadmzZrRr18/AgICDNmNoEeSSsXjMWNIDbiFokgR3FatzL/ECaDOMJCbwMPTuto9+e3w17rEydwOuv2m98QJwKx0KYovXYrMzIyEEycIn/mdKKKZDZlMxuDGpVnT1o2plzfyydbZusTJ2pqikydRes9urPuMhZbf6k44+CXcP/rG/XYs0xEzhRn3ou/h98wvfXvRiV9gVq4smshInkz5yuB/d1GJaXz/5y2azD3OxgshqLUSTco74jOyIUv71cx14gRQs2ZNjh07ho+PDxUrViQyMhIrK+M/+eZqZ8GmQXUpZmfBg8hE+qy8QGRCqtHjEIT/MmjydOLECTZt2kTVqlX5+OOPDdmVoAeSJPHk6+kknj6NzMICt2VLM31026hsi0HlLrr3+V0089Y+uLBU9/6jZWBnuO+NpVcNXOfNBZmMmK1beb58hcH6ettpk5J4tugXnEf9jwahV9HKZOx3r8ugFpO53bADspcTt+uPgmp9QNLq1h+MvP9G/dqa2dLaXXfLdvvd7enb5ebmuM77CZmpKQl//030xk1v1E9W4lNULDhyl8Y/HmfFyQekqrXUKlmYrUPqsm5AbTyL5+3W5EsymYwOHTpw/fp1/vjjDzp06JC+b8eOHVy4cOFNLyFH3Owt2Ty4Li625tyPSKDfqgtEJYoljYT8ZdDkSavVEh8fz969e3HRdyVqQe8if1lM7K5doFBQ7Of5WHh65ndIOvVfzC+6sRNiH+VPDNEPYc9nuvf1RkKFtgbvslDLljh9patx9WzBAmJ27zZ4n28TSZKI9dlHYNt2RP76K1JqKpa1a1Nk4xbOdR7MY8z5328X2XD+xcLiMhl0XKC73ZoSC5t76hajfgM9KuhqOh0MPkhs6j/zgswrlKfoF7rH/yN+/JGUO3ffqJ9/S1FpWHlSt5TKgiP3SEhV4+FSiDWferN9WD3qlNbvbUITExO6dOmSflsyKiqKIUOGULduXXr16sWDBw/02l9mShSxZNPguhS1MeN2eDz9Vl0gJkkkUEL+MfiEcSsrK9q1a8ePP/5o6K6ENxC9bRuRv/4KgPP0r7Fp2jR/A/o3l2rg3ggkDVxYZvz+1Wm6kYqUWChWC1rMMFrX9v36Yj9QV6bhydRpJJzJn0nIBU3y9es87NOXsC++QP30KcpixSi2cCEl1q3F2asqGwfV4aMaxdBoJabuvsGMvTdRa7RgYgY9N0Ch4roHEXYM0JXFyKOqDlUpX7g8qZpUfAJ9Muwr3K8vVk0aI6WlETZhAtqUN5vwrNJo2XjhIU3mHmfWn7eITlJR2tGKJX282DeqIR9UKGqUMiIajYaPPvoImUzG1q1bqVixIuPHjycqKsqg/ZZysGLT4Lo4WJsR8CSOj1dfJDZZZdA+BSEr4mk7PVqyZAkeHh54e3vndyi5En/iBOHf/L+9+w5vqvwCOP5N0j2hu2UWyt57yFDZMmQv+bERQUQEZIngYomIIKhsAQFlKnsUAVE2yJDVAi2jdNHSvZP7+yNQqayWpklazud5+khvbt73JBZy+t5zz6uvB3EbPozC3c2wQ3KDB6tPp1dCipE3D/X/BEJOg40zdFuRJ3VOz+IxZgxObdtCRgYhI98n5XI+2jDZwNIjIrg7cRLB3bqT/PffqOzscB81ilI7d+DUqmVm8mBjqeHr7tX4sFU5AH48EsyAH0/qP2wdPaHXWrC0g+u/w76PXzgelUpF97L6vy/rA9ZnqW9SqVT4TJ+Oxs2N1MBAImZ/9UJzaHUKv/4dQvOvD/HRln8Ij0ulSCFbvuxalb2jmtC2qjdqtfGaWrq7u7Ns2TLOnj1Ly5YtSU9P5+uvv8bPz4+vv/6a1NS8q0ny83Bg7ZB6uNpbcSEklr7LTxCXIgmUML48udsuLCyM1atXo9VqKVeuHFWrVqV06dKGnsZs5ae77ZIv/MPNvn1RkpNx7tQJ7+nTzHNvLp0OFtaFqEBoNQMaDDfOvFd2wM+99X/+zzYfxqRLS+P24CEknTiBhbs7JX/5GUsfH5PEYgq61FSiV64i6ocfMts3OL/5Ju6jR2Pp+ey9D3f/E8oHv5wjOV1LaXd7lvWrQ0k3+6x7Enb4Fmr2faHYEtISeH3D6yRnJLOi1Qpqe9XO+vjhP7n9oCt/0e+/w/G17G2/oygK+y6FM2dvAFcfbJbr5mDFiNf86FWvONYWpttK5VF79uzhww8/5MKFC6jVas6fP0+lSpXydM7LoXH0WnKMmKR0ahYvxKpB9XCwljtSRe6ZtElm9erV8fLyoly5cgQEBHD+/Hni4uKoVKkSx44dM/R0Zie/JE9pt28T3LMX2qgo7F95hWI/fI/K0rirKjlyagVsHwXOxWHk36DJ438sY27BD430l+vqvwutp+ftfM+hjYvj5lt9SA0MxKp0aUquXfPC/YryC0VRiPf3J+LL2aTfvg2ATbWqeE2alKMtbP4JiWXIqlOExqZQyM6SH/rUon4pVzg4Ew7OALUl9NsGJRq8UJyfHPmETYGbaOPbhi+bPF6iED5jJtErV6IpXBjf337F0uPZCd+Ra/f4cs9Vzt6OAcDJxoKhTUvTv2FJ7M0wSdBqtaxcuZIbN27wxRdfZB6/ceMGpfJoq5p/QmLpveQYcSkZ1C3pwo8D62BnZX7vjchfTJo8ubi4cO/ePdSPdISOioriwoULvGpOtTR5JD8kTxn373OzZy/Sbt7EumIFSqxajcbBzDfhTE+GuZUh6R50XQGVO+fdXBlpsKINhJyCIrVgwG6wMP12G+mhoQT37EVGeDh2tWtTbNlS1NbWpg4rT6RcDSB8xgySHvzCZeHhgcfYMTi1a4fqBbrNR8SlMGT1ac7djsFCrWJap8r0qFUUNvaHS7+BnRu8fQAK5byj9sWoi/Tc3hMLtQX7u+3HxSZrZ3hdWhrB3XuQeuWK/heVJYuf+Br+vnWfr/Ze5a9rUQDYWmoY8EpJhjYpjbOdGf9i8wSXL1+mSpUqtG/fnlmzZlG2bFmDz3H+TgxvLT1OfEoG9Uu5sKJ/XWytzGNFTuRPJu3z1Lt3b/74448sx1xdXV+KxCk/0CUnc+edYaTdvImljw/FfvjB/BMnAEtbqDNY/+ejCyAv++fs/1SfONk46/s5mUHiBGDp7U2xxYtROziQdOoUdydMQNHpTB2WQWXcv0/op58S1KkTSceOobKywnXYO5TetRPnDh1eKHECfdfqX96uT7uq3mToFMZvusAXO6+g7fAdeFXRJ+XrekFqQo7HruRaiUqulcjQZfDbtd8ee1xtZUWROV+hsrEh8a+/iF65KsvjV8LiGLzyFJ2+O8Jf16Kw0qjp37Akh8a9yrjW5fNd4gTwxx9/oCgKv/76K5UqVWLEiBFERkYadI6qRQuxamBdHKwtOHYjmiGrTpGSrjXoHEI8SZ6sPIWHh9O8eXN69uxJmzZtqFy5cubGky8Dc155UrRa7ox8n4T9+1E7O1Ny7Rqs81M9WkIkzK0E2lT9atALXmZ5pqu7YN2DTso91kCFds8+3wQSjx3j1pC3IT3dLPZRMwQlPZ3769YRuWAhujj9TQGOrVvjMXYsVkWLGG4eRWH+/mvM9de3D3i9vAfz27jhsKolJEZA+XbQfXWO91LcHLiZqUemUsyxGNs7bUetevz5939ZT9jUqWBpie8vPxPmUYK5/gFsPXcXRQG1CrrWKsrIZmUoWjj/b4Z76dIlxo8fz/bt2wFwdHRk0qRJvP/++9jaGm6vulPB0fRdfoKkNC1Ny7qzuG8ts6kJE/mLSS/bNWrUiMTERHx9fbl8+TLBwcGULl2aatWqsWbNGkNPZ3bMNXlSFIXwzz/n/tp1qKysKL5iOXa1apk6rJzb+h6cWaX/kOtp4J+nmNsP6pxioN4waDPTsOMbUOy27dx90EvIc+IEXPr1M3FELy7h8GHCZ8wk7UHPIOvy5fGcNBH7unXzbM7t5+8yZv05UjN0lPN0ZFVL8NzcBbRp0ORDeH1yjsZLSk+i2YZmJKQnsLjFYhr4PJ7YK4pCyMiRxO/zJ9bNh4ENR5Ck1v9i2baqNx80L4ufh4NBXp85+f333xk7dmzmpsNVqlTh7NmzWUo7cuv4jSj6rzhJcrqWZuU9+L5PLaws5IZykTMmvWx3/vx5jh07xubNm7l8+TL3799n5cqVtGjRIi+mE9kUtXQp99euA5UKn9mz82fiBP+2LbiyA6KuG25cbbq+709KDPjU+Hc7DzPl3L4d7mNGAxA+cxZxu81o8+RsSr0RxK2hQ7k95G3SbtxA4+KC12ef4rtpY54mTgDtqvqwfmgDPBytuRoezxubUwlq8OCmgD9mw4WNORrPztKOdqX0q5SPdhx/VHRiGmsb9SHKxgnne3cZdH4rr5VzZ/t7jVjYu2aBTJxAv1XXqVOnWL16NcWKFaNv374GTZwA6pVyZVm/2lhbqNl/JYL31p0hXVuwLmkL85EnyVO7du2y7GdnY2NDrVq16N+/f15MJ7Ihdts2Iud8DehXKZxatTRxRLngXg7KtAQUOPa94cbd/xncOQHWzvqCdDOpc3oW18GDKdy7NygKd8eNI+nUKVOHlC3auDjCZ87iRocOJB76AywscBkwgNJ7dlO4e3dUGuNccqlWrBBbRzSichEnohLTaHWgKAGlB+gf/O1dCDmTo/G6lesGwO+3ficy6d/6nriUdL7ep99K5bu/7zG7Vi90qHgj+BjzisRQuUjBvmsSQK1W06dPH65evcp7772XeXzHjh2PfWa8qIZ+bizpWxsrCzV7LoYz6uez+uaoQhhYniRPaWlpdOzYkVWrVhEREZEXU5glc22SmXj0KHcn6bf5cBkwAJe+L9bPxqw8XH06uwaSDNDZOGAPHJmv//ObC8DFN/djGoFKpcLzo0k4NGuGkpbG7XdHkHrdgKtxBqZotdz/ZT3XW7Um+scfISMDh6ZNKbV1K57jx6FxzPkmtrnl5WzD+qENaFPZizStjtYXm3G9UEPISNH3+IoLzfZYZQuXpbp7dbSKli3XtpCcpmXRoes0+fIA8/cHkpimpXIRJ0aPfwu3IYMACP14CulhYXn18syOra0t1g/uEFUUhY8++ogdO3ZQpUoVhg4dSlgu34smZd1Z1KcWVho1Oy6EMnr9ObQ62VhbGFae1DzNnz+f8+fPc/78eS5duoSjoyPVqlWjWrVqzJo1y9DTmR1zqnlKuXqVm2/1QZeQgNMbbfD56qsXvlvJrCgK/NAYwi/A6x9Dk7EvPlbsHX2dU/J9qDsU3sh/WwnpkpO51X8AyefOYeHjTcl1Pz+3eaSxJR4/QfiMGaReuQKAValSeE6cgEPjxiaOTE+nU5jrH8C3v1/DkST2OH6GT/otfauK/jv0d3tmw7br25j05yScLNxJC55AZLy+A3Zpd3vGtixH68peqFQqlLQ0gnu/Rco//2BXty7FVyw32oqbOQkICGDixIls3rwZ0G/pNW7cOMaMGYO9/YvfBex/KZx3fjpNhk6hc40izO5WDY0RO7GL/MmkBeOPUhSFa9eucf78eS5cuMAnn3ySl9OZBXNJnrL0BKpTR98TqCDd9XjuZ9gyFBw8YdQF/b5lOaVNhx/bwu3j4F0dBu19sXHMQJbeXRUqUGK1efTuSrsTQsTs2cTv0ddkqZ2ccB8xgsK9epplU9bfzobw4cbzeGvvst1mCo5KAlTpDp0X6zcXfgatTmHjmRtMu9AbRZ1E0q3+eFnW4IMWZelY3QcLTdZfXNKCg7nRuQtKUhLuo0fj9vaQvHxpZu3PP/9k7NixHD9+HABvb28WLlxIp06dXnjM3f+E8u7av9HqFLrVKsqsLlWNupWNyH/yLHnS6XQcPHiQc+fOER8fj729Pb6+vlStWhU/P79cB14QmEPypO9G/Rapgdew8itNyTUFsBt1RhrMqwrxodDxe6jeO+dj7JsKf30D1k4w9BC45E03ZGMxp67xusRE7i1ZQvTyFShpaaBWU6hHd9xHjsSicGGTxJRdZ27d5+1VpymTdIbVVjOwQAfNP0Fb/z2uHN9D8v0QbAsXoXy9VmgsLFAUhT0Xw5mz9yqBEQlYe2zHyvVPStvX5ZeOi59523zM5i2ETpoEFhaUXLsG26pVjfhKzYuiKGzYsIEJEyYQFBTEb7/9RocOHXI15vbzdxm57m90CvSqW5xpHStLAiWeKk+Sp8DAQDp06EBAQMBjG2ACeHp60rlzZ9555x0qV66ci/DzN1MnT1n2QfPwoOTP6wruPmh/ztVv3OtRCYb99dyVgSwC98Garvo/d1sJlTrmRYRGl2W/wo4d8Z4x3aj7FSo6HXHbthEx52syHtQ82tWvj+fEidiUM3yX6bwSEpPM4JWnqBWxiS8sV6AAsThSiPjMc8Jx5Xj5cSy7V5lzd2IBcLa1pEdDa9bdHYFapWZPlz142Xs9dR5FUbg7ZgxxO3dhWbw4vps3m8WKoSmlpqayefNmevbsmfmz++uvv+Lr60u1HGzL89BvZ0P44Jez6BTo26AEn3aoZJ57eAqTy5NWBUOGDCEqKoqffvqJoKAg7ty5w5EjR1AUhZ49e1KpUiWWLl1KtWrVGDhwIAkJOe/UK3JH0ekInTCRpBMnUNvbU2zxooKbOAHU6g+W9hBxEW4cyP7zYkNg89v6P9cZUmASJwDbKpUp+s1c0GiI/fVXIufPN9rcyefOEdyrF3fHTyAjIgLLYsUouuBbiq9Ynq8SJ4AihWzZ+E4Dwsr24ZC2CirAWYnPco67EkW7y+PxursPOysN773uxx/jXmNSi6bU8aqDTtGxKXDTM+dRqVR4ffIJFj7epN+6Rfgje8O9rKytrenVq1dmgnP//n0GDhxIjRo1GDBgAHfu3MnReG9WL8LsrtVQqWDV0Zt8vv0yeVyxIgq4HCVPJ0+e5KOPPqJXr16UKFECHx8fypQpA8CgQYPYt28fERERzJ07l+3bt9O0aVMSExPzJHDxZBFz5hC3cydYWFD02/nYlC9v6pDylm1hqNFH/+ejC7P3HG0GbBoEydHgVRVaFrwPK4emTfH6ZCoAUd//wP1f1ufpfOnh4dwdP57gHj1JOXcetZ0d7qNHU2r7NhybN8+3v+XbW1vwfa9qlFOHoCiPL2w+vPrzieVqDoxuzJiW5XC21V8m7V62OwCbAzaToct45jwaJyeKfPklqNXE/vorsTt2GPy15Gepqam0atUKRVH48ccfKVu2LJMnTyY+Pv75T36gS62izOqsvyS6/K8gZu66IgmUeGE5Sp48PT1JTk5+5jlOTk6MHDmSM2fOcO/ePSZPzlmXXvHiolf/RPSy5QD4TPsC+4YNTRyRkdQfBio1XPOHiMvPP//ANLh1FKwcoduPYGmT5yGaQuFu3XAbPhyAsE8/Jf5ADlbmskmXksK9H37geus2xP62FQDnTp0otXsXbm8PKRCbFgec3IuXKvqpV4TVKvBWRaHs/BAubYW7ZyEpmmbFXsfFxoWI5AgO3Tn03HnsatfG7Z13AAj75FPS7oQY8FXkb15eXqxbt47jx4/TuHFjkpOTmTZtGn5+fnz//fdkZDw7OX2oe51iTOukLylZ9McNvtp7VRIo8UJylDwNGjSIr7/+misPbjV+lqJFi/L+++/zyy+/vHBwIvvi9u4lfLq+O7L7Bx/g/OabJo7IiFx89Vu1gH7D4Ge55g9/6puF0mE+uOajff1egNt7I3Du3Bl0OkJGjyH5wgWDjKsoCnG793CjbTsiv5mHkpyMbfXqlNywHp8Z07H0MK82CbmRfD97SYxXwBpY/z9Y3BS+9MXyy1J0jNeXLmz46wv9yujlbRB6DpJjnjiG2/Bh2Favji4+nrvjxqFkMyl4WdStW5dDhw6xZcsWypYtS0REBCNGjODq1avZHuOtevqaJ4CFB67zjX9gXoUrCjCLnJw8YcIEjh8/Tp06dfjggw94++23n7m5Y1xcnNQ9GUHSmTPc/XAcKAqFevbA9WW83bnhe3B5K5xfD69PAUfPx8+Ju/tvnVPtQVC5s3FjNAGVSoX3p5+QERFB4p9/cnvoO5T8eR1WxYu/8Jgply8TPn0GSSdPAmDh5YXHmDE4tWubby/PPYtt4extShzrWR9niwyIuaXfYDgtnq5hySwv5sOR1Ehu7/+YYhnaf59g7QyFimf5UhUugc/4wQQNGU/ymTPcW7QI93ffzaNXlj+pVCo6duxI27ZtWbx4Mbdu3aJSpUqZj9++fZtixYo9c4x+DUuSrtXxxY7LzNsfiKVGxYjXy+R16KIAeaFWBbNnz2bGjBkkJCRQsWJFLl68yPjx42natCn29vYkJCRw4MAB5s2bR/v27dmw4cn7PBVUxrzbLvVGEDd79UIbG4vD669T9Nv5L2WjPQCWNoc7J5+8qas2A1Z1gJt/gVcVGORfYC/XPYk2IZGbff9H6qXLWJYoTsl167BwccnRGBnR0UR+M4+YDRtAUVBZW+M6aBCugwehtrPLo8hNT5uRwb0vyuKuRPGkO9x1CkSoXHGfHIDG4sHvo2lJ+uarMbcYem4uRxJvMcjCi1FJ2gfJVeTjAz0iNtiWu8cKgwpKDCiLXdVKjyVa2JjPpuPm4vLly1StWpXu3bszbdo0SpYs+czzfzh0nZm79FdSJrQpzztNC/ZKtHi+PG+SGRcXx08//cSWLVs4duwYiYmJmb91KoqCWq2mY8eOLF26lEKFCr3Qi8hvFi5cyMKFC9FqtQQEBOR58pQRGUlwz16kh4RgU60qJX78EfUzVgILvIu/woZ+YOsCH1wEq0c+0Pd/Doe/AisHGPpHgb9c9yTpERHc7NmL9Lt3c/TzoqSlEb1mLfe++w7dgwJdpzfa4DFmDJZFsrcqk9/9vWcl1Y6MBMiSQD3c9eNcw/nUaNXvic/1v+nPBwc/wMXGBf+u/lhqLCEtEWJu6xOpmJsP/vvIn5OiuHusELHBdljaZeDbOhKN1X/+qbYt/EgyVeI//y0G1sbf6sbU5s+fz/vvvw/o79h7//33mThx4jM/gxb8HshXewMAmNy2AoMb5+9ebyJ3jNphXKfTcf36dYKDg0lMTMTR0ZGqVavi7u6e26HzpbxYeVK0WpJOnSYjMhILd3dsKpTnVv8BpFy69MIrCQWOTgvza+g/gOoP12+r4eAJ6cmwtjugQJdlUKWrqSM1mdQbNwju1RvdIyuVQJafLbvatTJXLxMOHSJ8xkzSgoMBsK5YAa9Jk7CrXdtUL8Fk/t6zEp+jn+JJVOaxMFwJbTD1qYkTQLounVYbWxGZHMnsprNpXbL18ydLTUB79ypBA94nPSwKp5pF8engiSr2QcKVnI39HG1d/k2uCpd4JLEqDs7FwNohOy/7xem0cPMIJITr/x6WaAjqvF8VP3PmDB9++CG///47AK6urkyZMoV33nkHq6fssDB3XwDz9utrnz7tUIl+DUvmeZzCPJnN9iwvI0MnT/pi8BlkPLJhpsrKCiUtDY2LS65rWAqUX0fA2dVZj6nUoOj0PaHazzNJWOYk6cwZbvUfgJKWhl2jV0i7do2MsPDMxy28vHAdOJCEw4dJPHwYAI2rKx4fjMK5U6eX97Iw+kt4T+ow/jwL/l7AovOLqOtVl2WtlmV7vuRz5wju/RZotfjMmvnvjSCp8Q9Wrp6wahVzS79P4/PYuWZNqB6uXBUuoU+urHJxKfbSVtg9Xl9n+JCTD7SeBRVz1zE8OxRFYdeuXXz44YdcunQJgNq1a3PixIkn1uUpisJXe6+y8IB+U+1pnSrzVr0SeR6nMD+SPJmQIZOnuL17CXl/lH4j3CdwHzMatyEvYYH4k1zaCuv7Ak/5kX7JV50eFbdnLyEPLm88k6UlLn3/h9uwYWgc8nilogALTQil9ebW6BQdWztuxdfZN9vPvffDD0R+Mw+1nR2+v27J3i9KKbGPXBZ8NLl6kGClxD5/DHv3xxOrRy8LPm2j5Kf+PXyQtHRfZZQECiAjI4MVK1bw8ccfM2bMGD788MOnnqsoCjN3XWHRHzcAmNWlCj3qyC+lL5s8SZ4qVqzIhAkT6Nmz51OXP/8rNTWVtWvXMnv27MzfAAo6QyVPilbLtWbNs6w4/ZeFlxd++/1f6tUAQH+J4JvKWX/T/S+nIvoNhI1w6cDcKVotAfUbZNYwPYnK2hrfzZuwLv3y1YflhRH7R3DoziH6VuzLh3We/iH+X4pWy61+/Uk6dQqbqlUpuean3O9XmBwDsbfh/s3/JFgPkqzUuOePYe/xyCXBBwmWUxHYOgISIp7yJJV+BcrIfw8TEhKwtLTE+kHfsV27drF8+XJmzJiRZU9WRVH4fPtllv8VhEoFs7tWo2utokaLU5hedj+/c9SqoH///owePZr333+fDh060Lx5c2rWrImvry92D+62SUxMJCgoiFOnTuHv78+2bduwsrJ6ZsYvnizp1OlnJk4AGWFhJJ06jX29ukaKykzdPPLsxAkgLkR/nm9j48RkxpJOnX5m4gSgpKaScS9KkicD6Va2G4fuHOK3678xsuZIrDXZayCq0mjwmf0lN97sSMr580QuWIjHB6NyF4xtIf2XV5UnP558/wlJ1a0HydZNSEvQt2NIjICQUzmYWDHJ30OHR1ZNFUVhwoQJnD9/nt9++43hw4fz8ccf4+rqikql4uN2FcjQ6Vh19CYfbjyHpUbFm9VfjhsjRPblKHkaN24cw4YNY9myZfz444+sXr068/qxxYPr/g87vSqKQuXKlfn0008ZOHCgSTbIze8yIp99O3NOzyvQEsKff05Ozivg5GfL+BoVaYSXvRdhiWHsDd5L+9Lts/1cS29vvD/7jJBRo4havBj7VxpiXzcPf2GyLaz/8n7CJryK8p/k6pHVq7AL+uToeUz491ClUvHTTz8xbtw4du/ezbx58/jxxx+ZPHkyI0aMwMbGhk/aVyJdq7DuxC0++OUsGrWKdlUL8B6hIsdylDwBODo6MmrUKEaNGkVQUBBHjhzh6tWrREXp70BxdXWlfPnyNGjQAF/f7F/XF4+zyObditk9r0BzeEJTzNycV8DJz5bxadQaupbpyoKzC9gQsCFHyROAU+tWJHTtQuzGTdwdN55Sv25BY4o2MCoV2Lnov3yqZ30s6DCsbPf8MUz897BKlSrs2rWLffv28eGHH3Lu3Dk+/PBDFixYwMKFC2nbti3TOlZGq9Ox/tQd3v/5LBZqFa0re5s0bmE+cpQ8TZw4kSpVqlClShUqVKiAr6+vJEh5yK52LSy8vMgID39ywbhKhYWnJ3a1axk/OHNToqG+liIulCcXjD+otSjxkuz39xzys2Uancp04vtz3/N3xN8E3g+kTOGcdbX2mjiR5FOnSQsOJvTjKRSZP8+8uro/9+8hgAqiAqHEK6DO0Q5hBteiRQtOnz7NTz/9xEcffcTNmzdJT08HQK1WMaNzVTK0Cpv/DmHE2r/5vo+aFhXlFzCRw73tvv32W/r06UP16tWxt7enSpUq9O7dm+nTp7Nt2zaCH/SCEYah0mjwnDTxwTf/+QfywfeekyZKsTjoi09bz3rwzX8/TB5833qmFIs/ID9bpuFh58FrxV4DYENAzndeUNvb4/PVV2BpSfy+fcRs3GjoEHPnmX8PH1Jg+wewog2Em/4mIo1GQ79+/QgICGD58uW8+ci+oLt27mBQFWs6VPMhQ6cwfM1pDlx5WjG8eJnkuFVBcHAwFy9ezPw6duwYgYGBmb/9ODg4UKlSpcwVqsqVK/Pqq6/mRexmyxh9niy8vPCcNBGnli1zPX6B8sT+MkX0iZORbo/OT+Rny/iOhBxhqP9QHC0d8e/mj51lzvspRS1bRsTsr1DZ2uK7aRPWpczsCsDT/h62nAYJYfD7F/qic7UFNByp31IpN32l8kBMTAylS5cmNjaWwUOGkFqlCwdupWJloWZp39o0KSuXtAsio/R5OnnyJO3ataNr1640bdqUjIwMTp48yerVq4mOjs5MqLRa7XNGKliM0WH80S7Q4j9M1Nk4v5KfLePSKTrabm7LnYQ7fNbwMzqV6ZTjMRSdjluDBpF09BjWFStQ8uefUWezfYzRPOvvYewd2DUermzXf1+4JLSdA37NTRbuf4WEhDB8+HC2bt0K6Ot9y7f6H2HFX8fW1o4V/evQ0M/NxFEKQzNK8lSnTh0aNGjA/PnzsxxPSkri888/Z/ny5cybN4+ePXu+6BT5kjE3BhZC5D/LLizjmzPfUNm1MuvarXuhMdLDIwh68020MTG4DByI57h82A7m8nbYNe7fO/Qqd4FWM8DRfOqKDh06xNixYzl1St+Swa6wB7YN3sKtejNWDqpPvVKuJo5QGFJ2P79zVa33zz//ULVq1ceO29nZMWPGDBo1asS2bdtyM4UQQhQ4Hf06YqG24J+of7gU9WJ1P5aeHnhPnwZA9PLlJPz1lyFDNI4K7eDd4/q9KFVq+GcTLKgDp5aDTmfq6ABo2rQpx48fZ82aNZQoUYKk+xFE75pHfPhtBvx4klPB2dhnUBQ4uUqeypcvz+7du5/6eOvWrdm3b19upshXFi5cSMWKFalTp46pQxFCmDFXW1daFG8BvFjh+EOOr79OoV76lf3QCRPJiM6HH+TWjtB6Bgw5AN7VITVWX1C+vBWEXzR1dACo1Wp69+7NlStX+PLLL3nv/ZG83qAGSWla+q84yb7TV00dojCyXCVPEyZMYPPmzUyZMoWUlJTHHv/7779JS0vLzRT5yrvvvsulS5c4efKkqUMRQpi5buW6AbDzxk4S0xNfeBzPceOw8itNRmQkoR9NJt9uV+pTHYb8rr9bz8oB7pyARU1g31RISzJ1dADY2Njw4YcfMm/uXBb/rzYNSrly/24QrepVoXOvvty9+5xdDkSBkavkqUePHsyZM4eZM2dSvHhxxo4dy9q1a1m7di2DBw9m8eLFvPbaa4aKVQghCozanrUp6VSSpIwkdtzY8cLjqG1tKTJnDiorKxIOHOD+uheroTILag3UfwfePQHl24EuA/76Br6rB4HmdRXD1krDsv61cYu+iKJNZ8vPq/HzK8Mnn3xCQkKCqcMTeSxXBeMPnT17lmnTprFr1y6Skv79DaFly5asWrUKDw+P3E6Rr0jBuBAiO1ZdXMXsU7MpV7gcG9pvyFXDy+hVqwmfPl2/ofPGDViXyVkDTrN0ZSfs/BDi7ui/r9RJ33bE0cu0cT0iITWDdh8t4+i6uaTd1V++8/Ly4rPPPmPAgAGZW5eJ/MEod9v9V1paGtevXycpKYkSJUrg5vZy3sYpyZMQIjtiU2N5ff3rpOnSWPPGGqq6P34DTnYpisLtoUNJ/OMw1mXLUnLDetTW2dt82KylJsDBGXDsO1B0YO0EzadCrYEm71D+UHxKOm8tPc5R/x3E/bGStPuhADRs2JA///zTvLrAi2cyyt12/2VlZUWFChWoVavWS5s4CSFEdjlbO9OqZCsA1l9dn6uxVCoVPtOno3F1JTUggIiv5hgiRNOzdoBW0+Dtg+BTE1LjYMcYWN4Swv4xdXQAONpYsnpQPeo3a4vXoO8o+sYwChUuzJtvvimJUwFlHmm7EEK8pLqX6w7AnuA9xKbG5mosCzc3fGbOAOD+6tXEHzyY2/DMh3c1GOwPbWaDlSPcOfmgoHwKpL14wb2hONtasnpQXSoVdUVTpS2+w5fRofegzMd3795N3759uX37tgmjFIYiyZMQQphQNfdqlClchhRtCttvbM/1eA6NG+PSry8AoZM+IiMyMtdjmg21Buq9DSNOQIUOoGjhr3nwXX0I2Gvq6ChkZ8VPg+tR3suR6AwrBqw+y62oJBRFYdy4caxevZqyZcsyceJEYmNzlygL05LkSQghTEilUtGtrL5twYarGwzSasB99Gisy5VDGx3N3UkfoZhJw0mDcfKBHquh18/gXAxibsHabrC+H8SFmjQ0F3t9AlXGw4HQ2BR6LTnGnfvJLFu2jCZNmpCSksLMmTPx8/Nj4cKFpKenmzRe8WIkeRJCCBNrV6odtha2XI+9zpmIM7keT21tTZE5X6Gytibx8GHur15tgCjNULk2MPwYNHwPVBq49CssrAsnluj31jMRNwdr1gypRyl3e0Jikum99BhFylTm4MGD/Pbbb5QrV4579+4xYsQIKleu/FI1ky4oJHkSQggTc7RypI1vGyB3HccfZe3nh+fECQBEfDWHlMuXDTKu2bF2gJZf6AvKi9TSF5TvHAvLWkDoeZOF5eFow7oh9Snpasft6GR6LTlGeFwqHTp04MKFC3z33Xe4u7sTEBAgfaHyIUmehBDCDHQvqy8c3xu8l/sp9w0yZqEePXBo1gwlPZ2QMWPRJScbZFyz5F0VBu2DN77StzMIOQ2LX4W9k01WUO7pZMPaIfUp5mLLzagkei85RkRcCpaWlgwbNoxr167x/fff07Fjx8zn7N69m6CgIJPEK7JPkichhDADldwqUdG1Ium6dH679ptBxlSpVHh/8TkW7u6k3bhB+KxZBhnXbKk1UHeIvkN5xY76gvIj38LCenD16fuw5iWfQrasHVyfIoVsuXEvkd5LjxMZnwqAk5MT77zzTmY7g5iYGN566y3Kly/P2LFjuX/fMEm0MDxJnoQQwkw8LBzfGLgRnWKYIm+LwoXx+XIWqFTE/PwL8f7+BhnXrDl5Q/eV0Hs9OBeH2Nuwrgf88j+IM/7+c8Vc7Fg3pD7ezjZci0igz9LjRCc+vu9rbGwsNWrUIC0tjTlz5lC6dGnmzp1Lamqq0WMWzybJkxBCmIk3fN/A3tKem3E3ORF2wmDj2jdogOuggQCEfjSZ9PBwg41t1sq2gnePQcOR+oLyy1thQV04vtjoBeXFXe1YO6Q+Ho7WXA2P562lx4lJyppAlShRgn379rFz504qVarE/fv3GT16NBUrVmT9+vX5d9PnAkiSJyGEMBN2lna0K9UO0LctMCT3kSOxqVQJbWwsd8dPKHjtC57Gyh5afg5DD0GR2pAWD7s+hKXNIfScUUPxdbNn3dv1cXOw5nJoHP9bdoLY5HS0OoWj16P47WwIx25E07JVa86ePcuSJUvw8vLixo0b9OzZk6tXrxo1XvF0Bt3bTujJ3nZCiBd1NfoqXbd1xUJlwb5u+3CzNdxWV6lBQQR17oKSnIzH2DG4Dh5ssLHzBZ0WTq8A/0/1d+Wp1FB/OLw6UX/XnpEEhsfTc/ExohLTKOFqR0q6lvC4fy/NeTvbMLV9RVpX9iYhIYE5c+YQFRXF/PnzM8+Jjo7GxcXFaDG/LEyyt93LbuHChVSsWJE6deqYOhQhRD5VzqUcVd2rkqFksCVwi0HHtvb1xWvyRwBEfDOP5AvmsTec0ag1UGcwjDgJlTrpNxo+uuBBQfkuo4VRxtORNUPqYW+l4WZUUpbECSAsNoVhP51h9z+hODg4MHXq1CyJ09WrVylatCgjR47k3r17Rotb/EuSJwN69913uXTpEidPnjR1KEKIfOxh24JNgZvQGrg2x7lzZxxbt4aMDELGjkGXaPp94YzO0Qu6/QhvbYRCxSHuDqzrCT+/BbEhRgmhjIcjtlaaJz728HLQp9suodU9fnFo06ZNJCcn8+2331K6dGlmzZpFckFuQ2GGJHkSQggz06pkKxytHAlJCOHI3SMGHVulUuH96SdYeHuTfvMWYdOmG3T8fKVMCxh+HF4ZpS8ov7Jd36H82A95XlB+IiiaewmP33H3kAKExqZwIij6sccmTZqEv78/1atXJy4ujgkTJlC+fHnWrFmD7mWpZTMxSZ6EEMLM2FjY8GbpNwHDdRx/lMbZmSIP2hfEbt5M3C7jXbIyO1Z20OJTGPoHFK0DaQmwezwsbQZ3z+bZtBHxKbk6r1mzZpw+fZqVK1dStGhRbt26RZ8+fWjRooXclWcEkjwJIYQZetjz6dCdQ4Qlhhl8fLs6dXB9ZygAoVOmkh5inMtVZsurMgzcC+3mgrUz3P0blrwGuydCarzBp/NwtMn1eWq1mr59+xIQEMD06dNxdHSkRYsWmU03Rd6R5EkIIcxQqUKlqOVZC52iM3jh+EPuw4djW60auvh4QsaPR9GabjNds6BWQ+2B+oLyyl30BeXHvtMXlF/ZYdCp6vq64O1sw7PSHE8na+r6Pv+OOltbWyZOnMi1a9d4//33M4/v3buXd955h/CXpa+XEUnyJIQQZuph4fjGwI1k6DIMPr7K0hKfr2ajtrcn+dRpohYvNvgc+ZKjJ3RdDm9tgkIlIC4Efu79oKD8jkGm0KhVTG1fEeCpCZSFWsX9pKfXRf2Xh4cHtra2AOh0OsaOHcuiRYvw8/Pj888/J/FlvDkgj0jyJIQQZqp5ieYUti5MRFIEf9z5I0/msCpWDK+pUwCIXLCQpL//zpN58qUyzWH4MWg0GtQWDwrK68HR70Cb+2S2dWVvvu9TEy/nrJfm3B2tcbKxICQmhZ6L9ZsJ55RarWbBggXUqVOHhIQEpkyZQtmyZVmxYgXal32F0QCkSWYekCaZQghD+frU16y4uIJGRRrxffPv82yekA/HEbdtG5ZFiuD76xY0jo55Nle+FH4Jto+C28f133tXg/bzwKdGrofW6hROBEUTEZ+Ch6MNdX1duBWdRO8lxwiNTaHkg61dfArZ5nhsnU7H+vXrmThxIsHBwQBUqVKFBQsW0KRJk1zHXtBIk0whhCgAupbtCsBfIX8RkpB3Rd1eUz7GsmhR0kNCCPvs8zybJ9/yrAgDdkO7b8DGWb+1y5LXYdeEXBeUa9QqGpR25c3qRWhQ2hWNWoWvmz3rhzagaGFbgqOS6L7oKLejk3I8tlqtpmfPnly5coWvvvqKQoUKceHCBaKionIV88tOkichhDBjxZ2KU9+7PgoKmwI25dk8GkdHfGZ/CRoNcdu2Ebt1a57NlW+p1VB7ALx7Eip31ReUH/9ev9nw5e0Gn66Yix2/DG1ASVc77txPpseiowTfe7G6JWtra8aMGcO1a9eYO3cuHTt2zHxs//79hLzsd1vmkCRPQghh5rqX0xeObw7cTLo2Pc/msatRA7d3hwMQ9ulnpN2+nWdz5WuOntB1GfTZDIVLQvxd+OUtWNcLYgz7nhUpZMsvQxtQ2t2eu7EpdF90lGsRCS88nqurK6NGjcpsZxATE0OPHj0oU6YMU6ZMIT7e8G0ZCiJJnoQQwsy9WuxV3GzdiEqJ4vfbv+fpXG5Dh2Jbuxa6xERCxo5FSc+7ZC3f82umLyhvPEZfUH51p76g/MgCgxSUP+TpZMPPbzegnKcjEfGp9Fx8lCthcQYZOzo6mvLly5OcnMznn39OmTJlWLRoERkZhr+7syCR5EkIIcycpdqSTn6dgLzpOP4olUZDkS+/RO3oSMq580R+912ezpfvWdpCsynwzp9QrD6kJ8Lej2DJqxBy2mDTuDtas+7t+lTyceJeQho9Fx/jn5DYXI9bqlQpDh8+zKZNm/Dz8yM8PJx33nmHqlWrsn37dulW/hSSPAkhRD7QtWxXVKg4Hnqcm3E383QuSx8fvD/7FICoRYtJks3On8+jAgzYBe3n6wvKwy7AkmawcxykGGaVyMXeirWD61OtWCFiktLpveQYZ2/H5HpclUpF586duXjxIvPnz8fV1ZXLly/ToUMHAgMDcx94ASTJkxBC5AM+Dj40KtIIgI0BG/N8Pqc2bXDu3Bl0OkLGjUcbm/tVjgJPrYZa/WDEKajSHVDgxCL9ZsOXtoIBVnGc7Sz5aVBdapcoTFxKBn2WHudU8OObB78IKysr3nvvPa5du8b48eMZOnQoZcuWzXw8Ls4wSWBBIMmTEELkEw8Lx3+99iup2tQ8n8/ro0lYlShBRmgooVOmyiWc7HLwgC5L4H9boLAvxIfC+v/Bup4QcyvXwzvaWLJyYF0alHIlITWDvstPcOT6PQMErleoUCFmzpzJ99//21csICCAIkWKMGHCBGIlkZbkSQgh8otGRRrhaedJTGoM/jf983w+tb09Pl99BRYWxO/ZQ+zmzXk+Z4FS+nUYfhSafAhqSwjY/aCg/NusBeU6LQQdhgsb9f/VPb8DuL21Bcv716FxGTeS0rQMWHGSQwGRefZS1qxZQ0JCArNmzaJ06dJ8++23pKVlf+uYgkaSJyGEyCcs1BZ0KdsFgPVX1xtlTtsqlXF/fyQAYdOmkxoUZJR5CwxLW3h9sr6gvHgDSE+CvZNh8atw55T+ct43lWFlO9g0SP/fbyrrjz+HrZWGJX1r06y8B6kZOoasPMX+y3mzCfAnn3zC1q1bKV++PFFRUYwcOZJKlSqxefPml3JFUrZnyQOyPYsQIq+EJ4bTalMrtIqWLR224FfYL8/nVHQ6bg0cRNKxY9hUqkTJdWtRWVnl+bwFjk4HZ3+CvR9DSswzTnywVXD3VVCxw3OHTcvQMXLd3+y+GIalRsW3vWrQurK3QUL+r4yMDJYuXcrUqVOJiIgAoE2bNuzYsSOzd1R+JtuzCCFEAeRp70nTok0B2BiY94XjACq1Gp9ZM9E4O5Ny8SKR8+cbZd4CR62Gmn0fKSh/mgdrGrsnZOsSnpWFmgW9a9C+mg/pWoV31/7N1nN3DRPzf1hYWPDOO+9w7do1Jk+ejK2tLU2aNCkQiVNOSPIkhBD5zMPC8a3XtpKckWyUOS09PfGe9gUAUUuXkXj0qFHmLZAc3PVJ1DMpEBcCN49ka0gLjZpvelSnS82iaHUKo37+m42n7+Q+1qdwdHTk888/JyAggPfffz/z+L59+xg9ejTR0Ya5A9BcSfIkhBD5TAOfBhRxKEJ8ejx7gvcYbV7H5s0p1KMHAHfHTyDj/n2jzV3gJGSzNmnHGNjzkb6Y/F6g/tLfU2jUKmZ3rUqvusXQKfDhxnOsO5H7u/uepWjRotja2gKg0+kYM2YMc+fOpXTp0syZM4fU1Ly/K9QUJHkSQoh8Rq1S07VsVwA2XM3bjuP/5TlhPFalSpEREUHo5I9fymJhg3DwzN55967C0QX6YvIFtWFmcVjxBuyeBOfXQ2RAlkt7arWK6Z2q0K9BCRQFJm6+wMojwXnzGv5DrVYze/ZsKleuTExMDGPHjqVChQr8/PPPBe7nRArGDWjhwoUsXLgQrVZLQECAFIwLIfLMveR7tNjQggwlgw3tN1DepbzR5k65fJng7j1Q0tPx+mQqhXv2NNrcBYZOq7+rLi6UzBqnLFRg766/Uy/sPNw9C+H/QEbK46daOYBXFfCuDj7Vwbs6iqsf03cHsOSw/u7Ij96owJAmpfLu9TxCq9WycuVKJk+eTGhoKAB169Zl/vz51KtXzygxvKjsFoxL8pQH5G47IYQxjD00lj3Be+hetjsfN/jYqHNHr1xJ+IyZqKyt8d20EWu/vL/rr8C5tBXWP6x9evSj+Cl322kz9CtRd89C6Fn9f8MuwJPq3iztULyq8Hd6CdbccuGC4subzZvybrMKefJSniQxMZGvv/6aWbNmkZiYyMaNG+nSpYvR5n8RkjyZkCRPQghjOBF6gkF7B2FnYcfv3X/H3tLeaHMrOh233x5K4p9/Yl2+PCV/+Rm1tbXR5i8wLm2F3eMh7pG745yKQOuZ2WpTgE4L9wIeT6jSEx87NVmx4r5jWbwrNED1YIUK93KgsTTMa3mKsLAwVq5cybhx4zLvyjt06BAVK1bE3d09T+fOKUmeTEiSJyGEMSiKQodfOxAcF8yUBlPoVrabUefPiIzkxpsd0UZH49KvL54TJxp1/gJDp9XfVZcQrq+FKtEQ1JrcjRd1LUtClRZyFitt0uPnWtiAZ6Usl/zwqJCnCVVsbCylS5cmLS2NiRMnMmrUqMyic1OT5MmEJHkSQhjLyosr+erUV1RwqcAv7X4xer+dhEOHuD30HQCKLV6EQ5MmRp1fZJNOxyb/Qxw6uI8q6iBaFAqlRNo1VGnxj5+rsXpCQlURLAzTGDUgIIBevXpx5swZAIoVK8YXX3xBnz59UKtNex+bJE8mJMmTEMJYYlJiaLahGWm6NNa1XUdlt8pGjyFs2nTur16NxtWVUr/9ioWbm9FjENmz5vhNPtryDwBv1S3K543tUYed/feSX+h5SH3Cxr9qS/CsmDWh8qwEFi92qVan07F27VomTZrE7du3AahRowazZ8+mWbNmLzSmIUjyZEKSPAkhjGni4Ylsv7GdTn6d+OyVz4w+vy41leBu3UkNCMC+SWOKLVr00nWczk82nLrNuE3nURToVqsoM7tURaN+8P9LUeB+UNYaqtBzT95ORm2pv8TnXe1BQlVDn1BZ2mQ7luTkZObPn8/06dOJi4tDpVIRGBhI6dKlc/9CX4AkTyYkyZMQwpjOhJ+h3+5+2Ghs2N99P05Wxv93JyUggOBu3VFSU/GcNAmXvv8zegwi+347G8Lo9efQ6hTerO7DnG7VsNA85ZKZokDMzf8kVGch+QlNUtUW4P5oQlUdvCrrN0h+hsjISD7//HOSk5NZsmRJ5vGkpCTs7Oxe7EW+AEmeTEiSJyGEMSmKQuetnbkWc42JdSfSu0Jvk8QRvXYt4Z99jsrSkhK//IwuPoGMyEgs3N2xq10LlSYXRdDC4HZeCGXkur/J0Cm0qezFvJ41sLLIZs2RokDs7ccTqqSox89VacC9/H8Sqipg9XhSpChK5qplYGAgdevW5YMPPmDMmDHY29sbvrj+PyR5MiFJnoQQxrb28lpmnJiBXyE/NnfYbJLLZoqicGf4uyQcOAAaDWj/7Xxt4eWF56SJOLVsafS4xNP5Xwpn+JozpGl1NK/gwcK3amJt8YLJiPJgP77/JlSJkY+fq1KDW7nHEyprh8xTJk6cyMyZMwHw9vbm82Fd6G+7D01C6L/jOPlA61nZa+uQDZI8mZAkT0IIY4tLi6PZ+makaFNY1WYVNTxqmCSOmM2bCZ300eMPPEjmisz7RhIoM3PwagRDV58mNUNH07LuLPpfLWwsDbSaoygQH/p4QvXEvf1U4FY2M6FSvKqx/q9rTJzyGUFB+k7pVTzUzG5hQys/i3+fA483FH1BkjyZkCRPQghTmPLXFLZc20K7Uu2Y0XiG0edXtFquNWtORljYk09QqbDw9MRvv79cwjMzR67dY9DKUySna2lY2pWl/WpjZ2Xx/Ce+qPiwxxOq+NAnnKgi1cmXhf7X+OJAAvcf7E4zu4U1YxtaZ56Dkw+MupDrS3iSPJmQJE9CCFO4EHmB3jt7Y6W2Yn+3/RSyKWTU+ROPn+BWv37PPa/4ypXY16trhIhETpwIimbAihMkpmmpU7Iwy/vXwdEmb7uPZxEfrr+z79GEKi4k8+HoZIVpf6Sy7O80/hnuQFGn/9Rn9dsOvo1zFUJ2P79N241KCCGEwVR2q0wFlwqk6dL47fpvRp8/I/IJtS1PcH/NGlJv3MjjaERO1fV1YfXgejjaWHAy+D7/W3aC2OR04wXg6AllW0LTcdBrLYy+BGOvwSujAHCxVTGnlQ23P3B8PHGCp1wKzBuSPAkhRAGhUqnoWrYrABsDNmLsCwsW2dynLH7vXm680ZYbHd7k3g8/kBYcnLeBiWyrWbwwawfXp5CdJWdvx/DW0mPcT0wzXUAO7uDXPMshR+un3Azh4GmEgPQkeRJCiAKkbam22FnYERwXzMmwk0ad2652LSy8vDKLw59E7eyMfZMmYGlJakAAkd/M43rrNtzo3Jl7S5aQdueOESMWT1KlqDPrhtTH1d6Kf0Li6LXkGPcSUk0XUImG+pomnvZzpdJvplyiodFCkuRJCCEKEHtLe9qVagfA+oD1Rp1bpdHgOenB5sD/TaBUKlCp8P78M4ovXkTZPw/jPW0a9o0agUZD6qXLRM75muvNWxDUrTtRy1eQfveuUeMX/6rg7cTPb9fH3dGaK2Hx9Fx8jIi4FNMEo9bo2xEAjydQD75vPdOg/Z6eRwrG84AUjAshTOlK9BW6beuGhdqCfV334WZr3L3m4vbuJXz6jCx33T2rz1PG/fvE79tH3K5dJB0/ATpd5mO21avj9EYbHFu1wtLTeJdljEmr03Im4gyRSZG427lT06MmGiMmAs8SdC+R3kuOERqbgq+bPWuH1MPb+dndwvPMpa2wezzEPZJUOxXRJ07S5yn/k+RJCGFqb+14i/P3zvN+zfcZXGWw0edXtFqSTp3OcYfxjHv39InUzl0knTql7xMEoFJhW6smTm3a4NSqVYHZfNj/pj8zT8wkPOnfYmdPO08m1J1A8xLNn/FM47kdnUTPxccIiUmmmIstawfXp5iL8bZMyUI6jBdckjwJIUxtS+AWphyZQhGHIuzsvBO1Kv9VaaSHRxC/Zw9xu3eTfObMvw+o1djVqYNTmzY4tmyBhYuL6YLMBf+b/ow+OBqFrB/DqgeXor5+9WuzSaBCYpLpveQYN6OS8HG2Ye2Q+pR0szd1WAYnyZMJSfIkhDC15Ixkmq1vRnx6PD80/4FXirxi6pByJT00lLjde4jbvYuUc+f/fUCjwb5ePf2lvebN0RQqZLIYc0Kr09JqU6ssK06PUqHC086T3V12m80lvPC4FHovOcb1yEQ8HK1ZO6Q+fh4Oz39iPiJ9noQQ4iVma2FLBz99Hcj6q8YtHM8Llt7euA7oj+8vv1Da3x+PsWOwqVQJtFoSjxwhdPLHBDRqzK233yZmy69o4+NNHfIznYk489TECUBBISwpjDMRZ556jrF5Otnw89sNKOfpSER8Kj0XH+VqmHm/z3lFkichhCigupXtBsChO4cITzReA8G8ZlW0CK6DB+O7aSOl9+zGfdQorMuXh4wMEv84TOjEiQQ2fIXbw4YTu20b2oREU4f8mMik7DUUvRx1OY8jyRl3R2vWvV2fit5O3EtIo+fio/wTEmvqsIxOLtvlAblsJ4QwF/129eNMxBmGVx/OsGrDTB1Onkq9cYO4XbuI27WLtGvXM4+rrKxwaNoEpzZtcHj1VdR2Jip2fsTJsJMM3DMwW+dWdatK21Jtae3bGhcb86jvik1Kp+/y45y7E4uTjQWrBtWjerFCpg4r16TmyYQkeRJCmIvtN7Yz8fDEzPoZC3UebvZqRlIDA/WJ1M5dWTqYq2xtcXi1KU6t2+DQtAlqGxuTxBeTEsNrG14jQ5fx1HOs1Fak69IzC8o1Kg0NfRrSrlQ7Xiv+GrYWJmoZ8EB8SjoDVpzk1M37OFhb8OOAOtQuaR7J3YuS5MmEJHkSQpiLVG0qzTc0JyY1hm9f/5ZXi71q6pCMSlEUUq9eJW6nfkUq/fbtzMfUdnY4vP46Tm1aY9+4MWorK6PElJieyNv73uZ85PknPv7o3XbVPaqzO2g3229s52LUxcxzbC1saV68Oe1KtaOud12TJcWJqRkMWnmSYzeisbPSsKxfHRqUdjVJLIYgyZMJSfIkhDAnX538ipWXVtK4SGO+a/6dqcMxGUVRSLl4ibhdO4nftTtLB3O1gwOOzZrh2KY1Dg0bosqjRCopPYlh/sM4E3EGJysn3q76Nqsvrc5SPO5l58X4uuMfa1MQFBvEjhs72H5jOyEJIZnHXW1caePbhnal2lHRtSKqZ2yPkxeS07S8vfoUhwPvYW2hZknf2jQpm719Ds2NJE8mJMmTEMKcBMcG0/7X9qhQsbvLbnwcfEwdkskpikLK+fP6Fandu8kI/zd5UTs749i8GU6t22Bfvx4qS0uDzJmckcyI/SM4EXYCR0tHlrRaQiXXSjnuMK4oCuciz7H9xnb2BO8hJjUm87GSTiVpW6otbUu1pZhjMYPEnR0p6VqGrznD71cisNKo+b5PTZpVyH8d4SV5MiFJnoQQ5mbw3sEcDz3OkCpDGFlzpKnDMSuKTkfy2bP6RGrPbrSR9zIf0xQqhGPLlji1aY1d3brZ6pL+JKnaVN7b/x5HQ49ib2nP4haLqepeNdexp+vSORJyhO03tnPg9gFStf9u4FvdvTptS7WlVclWFLYpnOu5nictQ8d7686w52I4lhoV3/aqSevKXnk+ryFJ8mRCkjwJIczNnuA9jD00FjdbN/Z23Yul2jCrKQXNw21l4nbvIn7PXrTR0ZmPaVxdcWrVEqc2bbCtWTPbiVSaNo33D7zPnyF/Ymthy6IWi6jhUcPgsSekJbD/1n523NjB8bDj6BT9HoEWKgteKfIK7Uq1o2mxpnlaaJ6u1TF6/Tm2nbuLRq3imx7VaV8t/6x0SvJkQpI8CSHMTbo2nRYbWxCVEsXXr35NixItTB2S2VMyMkg6cYK4XbuJ37sXbey//Yws3N1xbN1an0hVr4ZK/eS2ienadEYfHM3BOwex0djwXfPvqONVJ89jj0yKZFfQLrbf2M7l6H97Rdlb2tOseDN9oblX3TzpXq7VKXy48Rybz4SgVsHsrtXoUquowefJC5I8mZAkT0IIczTvzDyWXlhKA+8GLG652NTh5CtKejqJx47pEyl/f3RxcZmPWXh749SqFU5vtMGmSpXMgu10XTrjDo3D/5Y/1hprFjRbQH3v+kaP/UbMDbbf2M7OoJ1ZCs3dbd0zC83Lu5Q3aKG5TqcwacsFfj55G5UKpneqQq+6xQ02fl6R5MmEJHkSQpijO/F3eGPzGygo7Oi0g+JO5v9hZo6UtDQS/vqL+N27ifffjy7x3w7mlkWK6OujWrfks3ur2XVzN5ZqS759/VuT7y+oKApnI8+y/fp29tzcQ2zqvytppZxL0a5UO94o9QZFHIoYZD6dTuHTbRdZefQmAJ+9WYm+DUoaZOy8IslTLqSmpjJs2DD8/f2JiYmhYsWKzJ07lwYNGmTr+ZI8CSHM1Tv+7/BXyF8MqDSA0bVHmzqcfE+Xmkri4cP6FakDB1CSkjIfCy0MxytoaNxvIq806f3UlZ2HdVYZkZFYuLtjV7vWCxemZ1e6Np0/Q/5k+43tHLx9kDRdWuZjNT1qZhaaO1s752oeRVGYvvMySw4HATC5bQUGNy6VqzHzkiRPuZCYmMicOXPo378/RYsWZf369YwYMYLg4GAcHJ6/g7QkT0IIc/X7rd95/8D7FLYujH83f6w0xmkM+TLQJScTf+ggx1bPwfNcCNaPNA+3KlUKp9atcXqjDdZ+fpnH4/buJXz6DDLCwjKPWXh54TlpIk4tWxol7vi0ePxv+rPjxg5OhJ3I7GhuobagcZHGtC3VlqZFm2Jj8WLd2BVFYc7eABYcuAbAh63K8e5rfs95lmlI8mRgPj4+bNu2jVq1aj33XEmehBDmKkOXQatNrYhIimBW41m8UeoNU4dUYCiKwmfHPmNjwEZs01XMsehFyVMhJP5xGCXt35Ud6zJlcGzTGo2TE+HTpsN/P4YfrFAVmfeN0RKoh8ITw9kVtIsdQTu4En0l87iDpQMtSrSgbam21Pas/UKF5vP3B/L1vgAARr7uxwctyhq9oefzFIjkKSEhgdmzZ3P8+HFOnDjB/fv3WbFiBf3793/s3NTUVKZMmcLq1au5f/8+VatW5YsvvqBFi9zfURIYGEiVKlUIDw/H2fn5S5iSPAkhzNl3Z7/j+3PfU9uzNitarzB1OAWCoijMODGDdVfWoULFjMYzaFuqLQDahAQSfv+duJ27SPjrL0hPf/6AKhUWnp747ffP80t4TxN4P5AdN3awM2gnoYmhmcc97Dx4w/cN2pVqR9nCOUuAfjh0nZm79EnZ0KalmNDasIXquVUgkqfg4GB8fX0pXrw4pUqV4uDBg09Nnnr16sXGjRsZNWoUZcqU4ccff+TkyZMcOHCARo0avXAMycnJvPrqq7zxxhtMnTo1W8+R5EkIYc7CEsNotakVOkXHb2/+RqlC5luDkh8oisLsU7NZfWk1KlR8/srnvOn35hPP1cbFEe+/n/vr1pFy4cJzxy6+ciX29eoaOuQc0Sk6zoSfYUfQDvYE7yE+LT7zMb9CfvqO5r5t8XbwztZ4y/8M4rPtlwAY8EpJprQz/pYyT5Pdz+8nN6YwE97e3oSGhnLz5k1mz5791PNOnDjBzz//zIwZM5g9ezZvv/02v//+OyVKlGDcuHFZzm3UqBEqleqJX5MnT85ybnp6Ot26dcPPz48pU6bkyWsUQghj87L3oknRJgBsCNhg4mjyN0VR+ObMN6y+tBqAqQ2mPjVxAtA4OVGocydc+vXL1vgZkZEGiTM31Co1tb1qM7XBVA52P8g3r35DixItsFRbci3mGvPOzKPlppb0392fjQEbs9zF9yQDG/nyRcfKAKz4K5jJv/6DTme26zhPZNbJk7W1NV5ez2/tvnHjRjQaDW+//XbmMRsbGwYNGsTRo0e5/cgu2n/++SeKojzx64svvsg8T6fT8b///Q+VSsXKlSvNJisWQghD6F62OwC/Xf+NlIwUE0eTf3137juW/7McgMn1JtOlbJdsPc/CPXsb52b3PGOx0ljRrEQzvn71aw72OMinDT/NbPp5Ovw0nx79lNfWv8aoA6PYd3Nflu1iHtWnfgm+7FoVlQrWHL/F+E3n0eajBMrC1AEYwt9//03ZsmUfW2KrW1e/1Hn27FmKFcvZBolDhw4lNDSUPXv2YGFRIN4mIYTI1NCnIUUcihCSEMKe4D3PXC0RT7bo3CJ+OPcDAOPrjKdH+R7Zfq5d7VpYeHnpNyR+SvWMys4O22q53/8urzhZOdG5TGc6l+lMWGIYO4N2sv3GdgLvB7L/1n7239qPo6UjLUu2pG2pttTyrIVa9e+aTffaxbC2UDN6/Tk2nL5DulbHV92qYaEx63UdwMxXnrIrNDQUb+/Hr7U+PHb37t0cjXfz5k2WLl3KiRMncHNzw8HBAQcHBw4fPvzE81NTU4mLi8vyJYQQ5kyj1tCljH6VRC7d5dyyC8tYcHYBAGNqjaFPxT45er5Ko8Fz0sQH3zyl/1NSErcHDyEjKipXsRqDl70XAysPZHOHzWxsv5EBlQfgaedJfHo8mwI3MXDPQFptasXXp78m4H5A5vPerF6Eb3vVwEKt4tezdxn589+ka3UmfCXZUyCSp+TkZKytrR87bmNjk/l4TpQoUQJFUUhOTiYhISHzq3Hjxk88f8aMGTg7O2d+5XSVSwghTKFTmU5YqCw4F3mOq9FXTR1OvrHq4iq+OfMNACNrjKR/5f4vNI5Ty5YUmfcNFp6eWY5beHnhOmQIant7kk6dIqhrN5IvXsxl1MZTzqUco2uNZm/XvSxvtZzOZTrjaOlIWGIYK/5ZQZetXeiytQvL/1lOWGIYb1Tx5vs+tbDSqNl5IYxhP50hNUNr6pfxTAUiebK1tSU19fHrqikpKZmP56WJEycSGxub+fVojZUQQpgrN1s3Xiv+GiCrT9m17so6Zp/S38A0rNowhlQdkqvxnFq2xG+/P8VXrsTnq68ovnIlfvv98RgzmpLrf8GqRAkyQkO5+VYfYrfvMMRLMBq1Sk0drzp82vBTDvQ4wNevfk2z4s2wVFsScD+Auafn0nJjSwbuGUi85V9807sc1hZq/C+H8/aq06Skm28CVSCKeby9vQkJCXnseGiovi+Fj49Pns5vbW39xJUvIYQwd93LdWffzX1sv7Gd0bVGY2dpZ+qQzNaGgA1MPz4dgCFVhjCs2jCDjKvSaJ7YjsC6dGlKblhPyNixJP5xmLtjx5Jy+RIeo0ebrPfTi7LWWNOiRAtalGhBbGps5s/c6fDTnAw7ycmwk1iprahXvz6n/vHlUGAGg1aeZEnf2thZ/ZuqaHVazkScITIpEnc7d2p61Hyhhp25VSBWnqpXr05AQMBjtUbHjx/PfFwIIcTj6nrVpbhjcRLTE9kZtNPU4ZitLYFb+OzoZwD0r9Sf92q8Z5S7sDVOThT7/ntch+hXuKKXLef20HfQxj67HYA5c7Z2pmvZrvzY+kf2dNnD+zXfx6+QH2m6NP6O+gON90ocykzjVMISuv+4hrgUfXd2/5v+tNrUioF7BjL+8PjMOir/m/5Gfw0FInnq2rUrWq2WxYsXZx5LTU1lxYoV1KtXT2qQhBDiKdQqNd3KdgPk0t3TbLu+jalH9E2S36rwFqNrjTZq+xqVRoPHmNEU+XoOKhsbEv/8k6Du3UkNDDRaDHnFx8GHwVUGZxaa96/UHw9bD1SaZKwKn+Cm9Vc0XdeCEf4j+eDgB4QnhWd5fkRSBKMPjjZ6AmXWHcYBFixYQExMDHfv3uX777+nc+fO1KhRA4D33nsvc7uU7t27s2XLFj744AP8/PxYuXIlJ06cYP/+/TRp0sSoMUuHcSFEfnI/5T7NNjQjXZfOz21/ppJbJVOHZDZ2B+1m/OHx6BQdPcr14KN6H5m071/K5cvceXcE6Xfvorazw2f2lzg2a2ayePKCVqflVPgpVl/YzKGQ30H97D5kKlR42nmyu8vuXF/CKxDbswCULFmSmzdvPvGxoKAgSpYsCeiLwz/++GN++umnzL3tPv/8c1q1amW0WBcuXMjChQvRarUEBARI8iSEyDfG/zGenUE76VKmC580/MTU4ZgF/5v+jD00Fq2ipXOZzkxtMDVLnyJTyYiOJmTUBySdOAGA24gRuA0fhkpt+tgM7eztSPptnomu0N7nnru81fLMhp0vqsAkT/mRrDwJIfKb0+Gn6b+7P7YWtuzvth9HK0dTh2RSB28f5IMDH5ChZNChdAc+f+Vzs0icHlLS0wmf9SX3f/oJAIfmzfCZOQuNg72JIzO85X9vYu75T5573qzGs3ij1Bu5mqtA7G0nhBDCOGp61KSUcymSM5LZfmO7qcMxqcN3DjP64GgylAze8H2Dzxp+ZlaJE4DK0hKvyR/hPW0aKktLEvz3c7NXT9KecqUmP6vomb26ZRcbtzyO5F/m9dMghBDCJFQqFd3L6fe72xCwgZf1osTRu0cZdWAU6bp0WpRowbRG00xyK3x2FerSmRKrV2Hh7k5q4DWCunUn4c+/TB2WQWmTSqJLd37aLjYoCujSndEmlTRaTJI8CSGEAKBdqXZYa6wJvB/Iuchzpg7H6E6GnWTk7yNJ06XxWrHXmNVkFhZq82+HaFu9OiU3bsS2WjV0cXHcfvttopYtLzAJ8L2EdFLD2wOPbwP48PvU8PbcS0g3WkySPAkhhAD0/Xdal2wNvHxtC06Hn+bd/e+Sok2hSdEmfNX0KyzVlqYOK9ssPT0ovnoVzl06g05HxOzZ3B03Hl3Ks+9Uyw88HG3IiK9MSkgflAznLI8pGc6khPQhI74yHo42RotJCsbzgBSMCyHyq/OR53lr51tYqa34vfvvOFs7P/9J+dzZiLMM3TeUpIwkGvo0ZP7r87HW5M9dIxRF4f6atYTPmAFaLTYVK1J0wbdY5vFOG3lJq1NoNOt3wmJTUNChsQtCZRGPkuGINskXFWq8nG34c/zraNS5ayMhBeMmsHDhQipWrEidOrm7VVIIIUylilsVyhUuR5ouja3Xt5o6nDx38d5FhvkPIykjiXpe9Zj32rx8mziBvnbNpc9bFF++HE3hwqRcukRQ124knTpl6tBemEatYmr7igCoUKNNKk1GXHW0SaVRPUhjpravmOvEKSckeTKgd999l0uXLnHy5ElThyKEEC/k0cLx9VfXF5i6mSe5HHWZIfuGkJCeQC3PWsx/fT42Fsa79JOX7OvVxXfjBqwrVEAbHc3N/gO4//PPpg7rhbWu7M33fWri5Zz1/4+Xsw3f96lJ68reRo1HLtvlAblsJ4TIzxLSEnh9w+skZyQbpPGgOQq4H8CgPYOISY2hunt1fmjxA/aWBa9Hki45mdCPPiJu5y4ACnXvjtfkj1BZWZk4shej1SmcCIomIj4FD0cb6vq6GHTFSS7bCSGEeCEOVg60LdUWgA1XC17h+PWY6wzZO4SY1BiquFXhu+bfFcjECUBta4vPnDm4jxkNKhUx69dzs19/MiIjTR3aC9GoVTQo7cqb1YvQoLSrUS/VPUqSJyGEEI/pXlZ/6W7frX1EJUeZOBrDCYoNYtCeQUSnRFPBpQLfN/++wHdTV6lUuA0ZQrFFP6B2dCT5778J6tqN5AsXTB1aviXJkxBCiMdUcK1AZdfKZOgy+O36b6YOxyBuxd1i8J7BRKVEUa5wORa3WPxS3E34kEOTJpRc/wtWpUuTER7Ozbf6EPPrr6YOK1+S5EkIIcQTZXYcv7oBnaIzcTS5E5IQwqC9g4hIjsCvkB+LWy6mkE0hU4dldNa+vpT85WccXnsNJS2N0AkTCZ8xAyUjw9Sh5SuSPAkhhHiiViVb4WDpwJ2EOxy7e8zU4bywsMQwBu0ZRFhiGL7OvixpuQQXGxdTh2UyGgcHii5cgNvwYQBEr1zFrSFDyLh/38SR5R+SPBmQ9HkSQhQkdpZ2tC+t3xYjv3YcD08MZ+CegYQkhFDcsThLWy7FzdZ4G8iaK5VajfvIkRSZPw+VnR1JR48R3K07KVcDTB1aviCtCvKAtCoQQhQUgfcD6by1MxqVhr1d9+Jh52HqkLLtXvI9BuweQHBcMEUcivBj6x/xsvcydVhmJ+VqAHdGjCD99m1Udnb4zJiBU6uWpg7LJKRVgRBCiFwrU7gMNTxqoFW0bAncYupwsi0qOYrBewYTHBeMt703y1otk8TpKWzKlcV3w3rsGzZASUoi5P33ifjmGxRd/q5zy0uSPAkhhHimbmW7AbAxcCNandbE0TxfTEoMQ/YN4XrsdTzsPFjWchlFHIqYOiyzpilUiGKLF+PSvz8AUT8s4s7wd9HGx5s2MDMlyZMQQohnalmyJc7WzoQlhvHX3b9MHc4zxabG8va+twm8H4i7rTvLWy2nmFMxU4eVL6gsLPCcMB6fWTNRWVmRcPAgwT16knojyNShmR1JnoQQQjyTtcaaN0u/Cej3uzNX8WnxvLPvHS5HX8bFxoWlLZdSwqmEqcPKd5zffJMSa9Zg4eVF2o0bBHfvTsKhQ6YOy6xI8iSEEOK5upbtCsDhkMOEJoSaOJrHJaYnMsx/GP9E/UMh60IsbbmUUoVKmTqsfMu2SmV8N27AtmZNdAkJ3H5nGPcWLynQG0XnhCRPQgghnsvX2Ze6XnXRKTo2BW4ydThZJKUnMdx/OOciz+Fk5cSSlksoU7iMqcPK9yzc3Cjx4woK9egBikLk118TMno0uqQkU4dmcpI8CSGEyJaHheObAzeTrks3cTR6yRnJvPf7e5yJOIOjpSOLWy6mvEt5U4dVYKisrPD+9BO8PvkELCyI37Wb4N5vkXYnxNShmZQkTwYkTTKFEAVZs+LNcLFxITI5kj9u/2HqcEjVpvL+7+9zIuwE9pb2/NDiByq5VjJ1WAVS4Z49KLHyRzSurqReuUJw164kHjtu6rBMRpInA3r33Xe5dOkSJ0+eNHUoQghhcJYaSzr5dQJgfYBpC8fTtGl8cOADjoYexdbClu+bf09V96omjamgs6tVC9+NG7CpVAltTAy3Bg0ievVPL2UdlCRPQgghsq1L2S4AHLl7hNvxt00SQ7o2nTGHxnA45DA2GhsWNltIDY8aJonlZWPp7U2JNT/h1KE9aLWET5tG6EeT0aWmmjo0o5LkSQghRLYVcyzGKz6vALAxYKPR58/QZTD+8HgO3j6Itcaab5t9Sx0vKZUwJrWNDT6zZuExfjyo1cRu3szNvn1JD48wdWhGI8mTEEKIHHlYOP7rtV9J1xqvcFyr0zLp8CT23dyHpdqSb177hvre9Y02v/iXSqXCdUB/ii1ZjNrZmZRz5wnu2pXks2dNHZpRSPIkhBAiR5oUa4KHrQfRKdHsv7XfKHNqdVo+/utjdgXvwkJtwdxX59KoSCOjzC2ezuGVV/DdsB7rMn5kREZy8399idlo/BVJY5PkSQghRI5Yqi3pXLYzYJzCcZ2i49Ojn7LtxjYsVBZ81fQrmhZrmufziuyxKl6cEut+xrFFc5T0dEInf0zY51+gpJtHO4u8IMmTEEKIHOtSpgtqlZqTYSe5EXsjz+ZRFIUvjn3BlmtbUKvUzGwyk2bFm+XZfOLFaBzsKTJvHm4j3wPg/po13Bo4iIzoaBNHljckeRJCCJFjXvZeNCnSBMi7wnFFUZh5YiYbAjagQsX0RtNpVbJVnswlck+lVuM+fDhFFy5AbWdH0smTBHXtSsrly6YOzeAkeRJCCPFCupXTF47/du03UjJSDDq2oih8deor1l5ZiwoVn7/yOW1LtTXoHCJvODZrRsn1v2BVogQZd0MJ7tWb2B07TB2WQUnyJIQQ4oW84vMK3vbexKXFse/mPoONqygK887MY9WlVQBMaTCFN/3eNNj4Iu9Z+/lRcsN67Bs3RklJ4e6YsUTMmYOi1Zo6NIOQ5MmAZHsWIcTLRKPW0KWMvmnm+quGKxz/7tx3LPtnGQAf1fuIrmW7GmxsYTwaJyeK/fA9rkMGAxC1ZCm3hw1DGxdn4shyT6W8jH3V81hcXBzOzs7Exsbi5ORk6nCEECLPRCZF0mJjC7SKlk0dNlG2cNlcjbfo3CIWnF0AwPg64+lTsY8hwhQmFrt9B6GTJ6OkpGBVogRFFy7A2s/P1GE9Jruf37LyJIQQ4oW527nzevHXAdhwdUOuxlr+z/LMxGlMrTGSOBUgzu3aUnLtGix8vEm7eZPgHj2J//13U4f1wiR5EkIIkSsPL6ttv7GdpPSkFxpj9aXVzD09F4CRNUbSv3J/Q4UnzIRNxYr4btyIXZ066BITuTP8XSK/+w5FpzN1aDkmyZMQQohcqe9dn2KOxUhIT2B38O4cP3/dlXV8efJLAIZVG8aQqkMMHaIwExYuLhRfvozCb70FwL353xLy/ih0iYkmjixnJHkSQgiRK2qVOnP1KaeF4xsDNjL9+HQABlcZzLBqwwwenzAvKktLvD6ejPcXn6OytCR+3z6Ce/Yi7dYtU4eWbZI8CSGEyLWOfh2xUFtwMeoiF6MuZus5v177lc+OfgZA/0r9GVljJCqVKi/DFGakUNeuFF+1Eo27G6mBgQR1607CX3+ZOqxskeRJCCFErrnYuNCieAsge4Xj265vY8pfU1BQeKvCW4yuNVoSp5eQXY0a+G7ciE3VquhiY7k95G2iVvyIuTcCkORJCCGEQTzsOL4zaCcJaQlPPW938G4m/zUZBYUe5Xowvs54SZxeYpaenpRYvQrnTp1ApyNi1izujh+PLsWwXesNSZInIYQQBlHbsza+zr4kZySz48aTt+PYf3M/E/6YgE7R0blMZybVmySJk0BtbY339Gl4TpoEGg1xW7dx860+pIeGmjq0J5LkSQghhEGoVCq6ldWvPq0PWP/YpZeDtw8y9o+xaBUtHUp3YGqDqahV8jEk9FQqFS59/0fxZcvQFCpEysWLBHXtRtLp06YO7THSYTwPSIdxIcTLKjY1lmYbmpGqTWVSvUk4WznjbudOckYyow6MIl2XThvfNsxoNAONWmPqcIWZSrsTwp133yX16lWwtMTro48o3LMHilZL0qnTZERGYuHujl3tWqg0hvs5yu7ntyRPeUCSJyHEy2zA7gGcCj/1xMdalGjBl02+xEJtYeSoRH6jS0ri7kcfEb9L3zvM7pVXSLt2jYzw8MxzLLy88Jw0EaeWLQ0yp2zPIoQQwuj8b/o/NXECaFmypSROIlvUdnYU+fpr3D/4AICkv/7KkjgBZISHE/L+KOL27jVubEadrYBbuHAhFStWpE6dOqYORQghjE6r0zLzxMxnnjPn5By0Oq2RIhL5nUqlwnXwIDSFCj35hAcXz8Knz0DRGu/nSpInA3r33Xe5dOkSJ0+eNHUoQghhdGcizhCeFP7Mc8KSwjgTccZIEYmCIOnUabQxMU8/QVHICAsj6ZTxCssleRJCCGEQkUmRBj1PCICMyOz9vGT3PEOQ5EkIIYRBuNu5G/Q8IQAs3LP385Ld8wxBkichhBAGUdOjJp52nqh4ctNLFSq87Lyo6VHTyJGJ/Myudi0svLzgac1UVSosvLywq13LaDFJ8iSEEMIgNGoNE+pOAHgsgXr4/fi646W/k8gRlUaD56SJD775TwL14HvPSRMN2u/peSR5EkIIYTDNSzTn61e/xsPOI8txTztPvn71a5qXaG6iyER+5tSyJUXmfYOFp2eW4xaenhSZ943B+jxllzTJzAPSJFMI8bLT6rSciThDZFIk7nbu1PSoKStOItfMpcO4dCoTQghhcBq1hjpe0vNOGJZKo8G+Xl1ThyGX7YQQQgghckKSJyGEEEKIHJDkSQghhBAiByR5EkIIIYTIAUmehBBCCCFyQJInIYQQQogckORJCCGEECIHJHkSQgghhMgBSZ4MaOHChVSsWJE6daQxnBBCCFFQyfYseSA2NpZChQpx+/Zt2Z5FCCGEyCfi4uIoVqwYMTExODs7P/U82Z4lD8THxwNQrFgxE0cihBBCiJyKj49/ZvIkK095QKfTcffuXRwdHVGpVAYb92FGLCtazyfvVc7I+5V98l5ln7xX2SfvVfbl5XulKArx8fH4+PigVj+9sklWnvKAWq2maNGieTa+k5OT/OXKJnmvckber+yT9yr75L3KPnmvsi+v3qtnrTg9JAXjQgghhBA5IMmTEEIIIUQOSPKUj1hbWzN16lSsra1NHYrZk/cqZ+T9yj55r7JP3qvsk/cq+8zhvZKCcSGEEEKIHJCVJyGEEEKIHJDkSQghhBAiByR5EkIIIYTIAUmehBBCCCFyQJKnfCA1NZXx48fj4+ODra0t9erVY9++faYOyywlJCQwdepUWrdujYuLCyqVih9//NHUYZmlkydPMmLECCpVqoS9vT3Fixene/fuBAQEmDo0s3Px4kW6detGqVKlsLOzw83NjSZNmrBt2zZTh2b2pk2bhkqlonLlyqYOxewcPHgQlUr1xK9jx46ZOjyzdObMGTp06ICLiwt2dnZUrlyZ+fPnGz0O6TCeD/Tv35+NGzcyatQoypQpw48//sgbb7zBgQMHaNSokanDMyv37t3js88+o3jx4lSrVo2DBw+aOiSzNWvWLP766y+6detG1apVCQsLY8GCBdSsWZNjx47Jh90jbt68SXx8PP369cPHx4ekpCQ2bdpEhw4dWLRoEW+//bapQzRLd+7cYfr06djb25s6FLM2cuRI6tSpk+WYn5+fiaIxX3v37qV9+/bUqFGDjz/+GAcHB65fv86dO3eMHou0KjBzJ06coF69esyePZuxY8cCkJKSQuXKlfHw8ODIkSMmjtC8pKamcv/+fby8vDh16hR16tRhxYoV9O/f39ShmZ0jR45Qu3ZtrKysMo8FBgZSpUoVunbtyk8//WTC6MyfVqulVq1apKSkcOXKFVOHY5Z69uxJZGQkWq2We/fu8c8//5g6JLNy8OBBXnvtNTZs2EDXrl1NHY5Zi4uLo2zZsjRs2JCNGzc+c985Y5DLdmZu48aNaDSaLL/Z2tjYMGjQII4ePcrt27dNGJ35sba2xsvLy9Rh5AsNGzbMkjgBlClThkqVKnH58mUTRZV/aDQaihUrRkxMjKlDMUt//PEHGzdu5JtvvjF1KPlCfHw8GRkZpg7DbK1du5bw8HCmTZuGWq0mMTERnU5nsngkeTJzf//9N2XLln1s88O6desCcPbsWRNEJQoqRVEIDw/Hzc3N1KGYpcTERO7du8f169eZO3cuu3btolmzZqYOy+xotVree+89Bg8eTJUqVUwdjtkbMGAATk5O2NjY8Nprr3Hq1ClTh2R2/P39cXJyIiQkhHLlyuHg4ICTkxPDhg0jJSXF6PFIzZOZCw0Nxdvb+7HjD4/dvXvX2CGJAmzNmjWEhITw2WefmToUszRmzBgWLVoEgFqtpnPnzixYsMDEUZmfH374gZs3b+Lv72/qUMyalZUVXbp04Y033sDNzY1Lly7x1Vdf0bhxY44cOUKNGjVMHaLZCAwMJCMjgzfffJNBgwYxY8YMDh48yLfffktMTAzr1q0zajySPJm55OTkJ+7fY2Njk/m4EIZw5coV3n33XRo0aEC/fv1MHY5ZGjVqFF27duXu3busX78erVZLWlqaqcMyK1FRUUyZMoWPP/4Yd3d3U4dj1ho2bEjDhg0zv+/QoQNdu3alatWqTJw4kd27d5swOvOSkJBAUlIS77zzTubddZ07dyYtLY1Fixbx2WefUaZMGaPFI5ftzJytrS2pqamPHX+4TGlra2vskEQBFBYWRtu2bXF2ds6ssxOPK1++PM2bN6dv375s376dhIQE2rdvj9x386/Jkyfj4uLCe++9Z+pQ8iU/Pz/efPNNDhw4gFarNXU4ZuPhZ12vXr2yHO/duzcAR48eNWo8kjyZOW9vb0JDQx87/vCYj4+PsUMSBUxsbCxt2rQhJiaG3bt3y89UDnTt2pWTJ09Kb6wHAgMDWbx4MSNHjuTu3bsEBwcTHBxMSkoK6enpBAcHEx0dbeowzV6xYsVIS0sjMTHR1KGYjYf/Lnl6emY57uHhAcD9+/eNGo8kT2auevXqBAQEEBcXl+X48ePHMx8X4kWlpKTQvn17AgIC2L59OxUrVjR1SPnKw8vmsbGxJo7EPISEhKDT6Rg5ciS+vr6ZX8ePHycgIABfX1+pp8uGGzduYGNjg4ODg6lDMRu1atUC9D9jj3pY92vsS8SSPJm5rl27otVqWbx4ceax1NRUVqxYQb169ShWrJgJoxP5mVarpUePHhw9epQNGzbQoEEDU4dktiIiIh47lp6ezqpVq7C1tZWk84HKlSuzZcuWx74qVapE8eLF2bJlC4MGDTJ1mGYjMjLysWPnzp1j69attGzZ0uS9jMxJ9+7dAVi2bFmW40uXLsXCwoJXX33VqPFIwbiZq1evHt26dWPixIlERETg5+fHypUrCQ4OfuyHSOgtWLCAmJiYzN9Itm3bltmB9r333sPZ2dmU4ZmNMWPGsHXrVtq3b090dPRjTTH79OljosjMz9ChQ4mLi6NJkyYUKVKEsLAw1qxZw5UrV5gzZ46sEDzg5uZGx44dHzv+sNfTkx57mfXo0QNbW1saNmyIh4cHly5dYvHixdjZ2TFz5kxTh2dWatSowcCBA1m+fDkZGRk0bdqUgwcPsmHDBiZOnGj8cgNFmL3k5GRl7NixipeXl2Jtba3UqVNH2b17t6nDMlslSpRQgCd+BQUFmTo8s9G0adOnvk/yT0NW69atU5o3b654enoqFhYWSuHChZXmzZsrv/32m6lDyxeaNm2qVKpUydRhmJ158+YpdevWVVxcXBQLCwvF29tb6dOnjxIYGGjq0MxSWlqa8sknnyglSpRQLC0tFT8/P2Xu3LkmiUW2ZxFCCCGEyAG5oCqEEEIIkQOSPAkhhBBC5IAkT0IIIYQQOSDJkxBCCCFEDkjyJIQQQgiRA5I8CSGEEELkgCRPQgghhBA5IMmTEEIIIUQOSPIkhDCpH3/8EZVKRXBwsKlDyZb8Fq8QwvAkeRJCmJUjR47wySefEBMTI3EIIcySbM8ihDAprVZLeno61tbWqFQqvvrqKz788EOCgoIoWbKkyeJ6Whz/jVcI8fKxMHUAQoiXm0ajQaPR5Pk8iYmJ2Nvb53ocY8UrhDBfctlOCGFSj9YQffLJJ3z44YcA+Pr6olKpHqsvCgkJYeDAgXh6emJtbU2lSpVYvnx5ljE/+eQTVCoVly5donfv3hQuXJhGjRoBcPPmTYYPH065cuWwtbXF1dWVbt26ZZnjWXE8rebp77//pk2bNjg5OeHg4ECzZs04duzYE+O6du0a/fv3p1ChQjg7OzNgwACSkpKy9X61aNGCBg0acPToUV599VXs7e3x8/Nj586dAOzcuZP69etjb29P9erVOX36dLbGFUJkn6w8CSHMRufOnQkICGDdunXMnTsXNzc3ANzd3QEIDw+nfv36qFQqRowYgbu7O7t27WLQoEHExcUxatSoLON169aNMmXKMH36dB5WKJw8eZIjR47Qs2dPihYtSnBwMN9//z2vvvoqly5dws7O7rlx/NfFixdp3LgxTk5OjBs3DktLSxYtWsSrr77KoUOHqFevXpbzu3fvjq+vLzNmzODMmTMsXboUDw8PZs2a9dz36Pz587i6utKjRw8GDRpEp06dmD59Or1792bWrFnMnj2bIUOG8OabbzJ9+nQGDhzIuXPncvT/QQjxHIoQQpjQihUrFEAJCgpSFEVRZs+eneX7Rw0aNEjx9vZW7t27l+V4z549FWdnZyUpKUlRFEWZOnWqAii9evV6bIyH5zzq6NGjCqCsWrUq89jT4vhvvIqiKB07dlSsrKyU69evZx67e/eu4ujoqDRp0iTz2MO4Bg4cmGXMTp06Ka6uro/F9V/h4eEKoHh6eip3797NPD5//nwFUMqXL6/ExsZmHh89erSiUqmUlJSU544thMg+uWwnhMgXFEVh06ZNtG/fHkVRuHfvXuZXq1atiI2N5cyZM1me88477zw2jq2tbeaf09PTiYqKws/Pj0KFCj32/OzQarXs3buXjh07UqpUqczj3t7e9O7dmz///JO4uLhnxtW4cWOioqIeO++/zp8/D+gv/3l7e2ced3BwAGD27Nk4OTllHnd2dkatVqNWyz/1QhiS/I0SQuQLkZGRxMTEsHjxYtzd3bN8DRgwAICIiIgsz/H19X1snOTkZKZMmUKxYsWwtrbGzc0Nd3d3YmJiiI2NfaG4kpKSKFeu3GOPVahQAZ1Ox+3bt7McL168eJbvCxcuDMD9+/efOdeFCxcA6NChQ5bjV69exdbWlhYtWmQ5HhAQQOnSpbG0tMzeixFCZIvUPAkh8gWdTgdAnz596Nev3xPPqVq1apbvH11leui9995jxYoVjBo1igYNGuDs7IxKpaJnz56Zc+S1p92tpzync8z58+fx9vbGx8cny/Fz585RuXJlrK2tHzv+3/dECJF7kjwJIczK03onubu74+joiFarpXnz5i88/saNG+nXrx9z5szJPJaSkvJYM8zs9nByd3fHzs6Oq1evPvbYlStXUKvVFCtW7IXjfdT58+epVq3aY8fPnTtH27ZtsxxLT0/n6tWrdO/e3SBzCyH+JZfthBBm5WEvpv8mMxqNhi5durBp0yb++eefx54XGRmZrfE1Gs1jKzzffvstWq02W3E8abyWLVvy22+/ZWlfEB4eztq1a2nUqFGWOqQXpdVquXTp0mPJ07179wgNDX3s+OXLl0lPT5eVJyHygKw8CSHMSq1atQD46KOP6NmzJ5aWlrRv3x57e3tmzpzJgQMHqFevHkOGDKFixYpER0dz5swZ/P39iY6Ofu747dq1Y/Xq1Tg7O1OxYkWOHj2Kv78/rq6u2YrjSb744gv27dtHo0aNGD58OBYWFixatIjU1FS+/PLLXL4jeoGBgaSkpDyWJD1sQ/Df4w+LyyV5EsLwJHkSQpiVOnXq8Pnnn/PDDz+we/dudDodQUFB2Nvb4+npyYkTJ/jss8/YvHkz3333Ha6urlSqVClbPZIA5s2bh0ajYc2aNaSkpPDKK6/g7+9Pq1atshXHk1SqVInDhw8zceJEZsyYgU6no169evz000+P9Xh6UQ+Lxf+bDD0tSbpw4QJOTk4m3eJGiIJK9rYTQgghhMgBqXkSQgghhMgBSZ6EEEIIIXJAkichhBBCiByQ5EkIIYQQIgckeRJCCCGEyAFJnoQQQgghckCSJyGEEEKIHJDkSQghhBAiByR5EkIIIYTIAUmehBBCCCFyQJInIYQQQogckORJCCGEECIHJHkSQgghhMiB/wMn7Eh/ccC2rAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_shot_list = [1, 2, 3, 4]\n", "\n", "for n_shots in n_shot_list:\n", " theta_list = qpe.robust_phase_estimation(H, psi0, epsilon, sign_E0, EXACT, n_shots)\n", " plt.semilogy(\n", " [qpe.rpe_distance(theta, E0) for theta in theta_list[1:]],\n", " \"-o\",\n", " label=f\"$N_{{\\\\rm shots}}={n_shots}$\",\n", " )\n", "\n", "plt.semilogy([np.pi / 3 / 2**i for i in range(M + 1)], \"k--\", label=\"$2^{-m}~\\\\pi/3$\")\n", "plt.legend()\n", "plt.xlabel(\"iteration $m$\")\n", "plt.ylabel(\"$d(\\\\theta_m, E)$\")\n", "plt.title(rf\"$\\epsilon={epsilon},\\; M={M}$\");" ] }, { "cell_type": "markdown", "id": "d6bf3e86", "metadata": {}, "source": [ "### Trotter approximation of the time evolution operator\n", "\n", "We now apply the same algorithm but replace the exact time evolution operator by a second order Trotter approximation.\n", "\n", "The `n_steps` argument in the `robust_phase_estimation` function sets the number of Trotter steps for $m=0$. The number of steps is multiplied by $2$ at each iteration to keep the Trotter timestep constant.\n", "\n", "The computation will now take longer since the number of gates for the time evolution now grows like $2^m$." ] }, { "cell_type": "code", "execution_count": 15, "id": "11c462f6", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T03:59:24.811096Z", "iopub.status.busy": "2026-04-03T03:59:24.810938Z", "iopub.status.idle": "2026-04-03T04:00:19.481212Z", "shell.execute_reply": "2026-04-03T04:00:19.480507Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "epsilon=0.02, M=6\n", "m \t phi_m \t theta_m \t time (s)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "0 \t -1.5708 \t -1.5708 \t 0.5 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "1 \t -3.1416 \t -1.5708 \t 1.3 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2 \t -0.4636 \t -1.6867 \t 3.1 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "3 \t -0.7854 \t -1.669 \t 6.6 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "4 \t -0.7854 \t -1.6199 \t 13.5 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "5 \t -0.7854 \t -1.5953 \t 27.3 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "6 \t -2.0344 \t -1.6026 \t 54.7 \n", "CPU times: user 55 s, sys: 520 ms, total: 55.5 s\n", "Wall time: 54.7 s\n" ] } ], "source": [ "%%time\n", "print(f\"epsilon={epsilon}, M={M}\")\n", "\n", "n_steps = 1\n", "n_shots = 4\n", "thetas_ttr_list = []\n", "\n", "thetas_ttr = qpe.robust_phase_estimation(\n", " H, psi0, epsilon, sign_E0, n_steps, n_shots, verbosity=1\n", ")\n", "\n", "thetas_ttr_list.append(thetas_ttr)" ] }, { "cell_type": "code", "execution_count": 16, "id": "355e3207", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:00:19.482622Z", "iopub.status.busy": "2026-04-03T04:00:19.482481Z", "iopub.status.idle": "2026-04-03T04:00:19.696763Z", "shell.execute_reply": "2026-04-03T04:00:19.695918Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(\n", " [qpe.rpe_distance(theta, E0) for theta in thetas_ttr_list[0][1:]],\n", " \"-o\",\n", " label=f\"$n_{{\\\\rm steps}}={n_steps}$\",\n", ")\n", "plt.semilogy([np.pi / 3 / 2**i for i in range(M + 1)], \"k--\", label=\"$2^{-m}~\\\\pi/3$\")\n", "plt.legend()\n", "plt.title(r\"$N_{\\rm shots}=4$\")\n", "plt.xlabel(\"iteration $m$\")\n", "plt.ylabel(\"error\");" ] }, { "cell_type": "markdown", "id": "bce2473d", "metadata": {}, "source": [ "Let us increase the number of Trotter steps. This will take a few minutes" ] }, { "cell_type": "code", "execution_count": 17, "id": "c6f3e89f", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:00:19.698201Z", "iopub.status.busy": "2026-04-03T04:00:19.698029Z", "iopub.status.idle": "2026-04-03T04:02:07.693728Z", "shell.execute_reply": "2026-04-03T04:02:07.693028Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "m \t phi_m \t theta_m \t time (s)\n", "0 \t -1.1071 \t -1.1071 \t 0.9 \n", "1 \t -3.1416 \t -1.5708 \t 2.7 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2 \t -0.7854 \t -1.7671 \t 6.1 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "3 \t -0.4636 \t -1.6288 \t 13.1 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "4 \t -0.7854 \t -1.6199 \t 26.8 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "5 \t -1.5708 \t -1.6199 \t 53.9 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "6 \t -2.6779 \t -1.6126 \t 108.0 \n", "CPU times: user 1min 48s, sys: 796 ms, total: 1min 49s\n", "Wall time: 1min 47s\n" ] } ], "source": [ "%%time\n", "\n", "n_steps = 2\n", "thetas_ttr = qpe.robust_phase_estimation(\n", " H, psi0, epsilon, sign_E0, n_steps, n_shots, verbosity=1\n", ")\n", "thetas_ttr_list.append(thetas_ttr)" ] }, { "cell_type": "code", "execution_count": 18, "id": "f78c201f", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:02:07.695127Z", "iopub.status.busy": "2026-04-03T04:02:07.694986Z", "iopub.status.idle": "2026-04-03T04:02:07.894076Z", "shell.execute_reply": "2026-04-03T04:02:07.893434Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i, n_steps in enumerate([1, 2]):\n", " plt.semilogy(\n", " [qpe.rpe_distance(theta, E0) for theta in thetas_ttr_list[i][1:]],\n", " \"-o\",\n", " label=f\"$n_{{\\\\rm steps}}={n_steps}$\",\n", " )\n", "\n", "plt.semilogy([np.pi / 3 / 2**i for i in range(M + 1)], \"k--\", label=\"$2^{-m}~\\\\pi/3$\")\n", "plt.legend()\n", "plt.text(4.5, 0.3, \"$N_{\\\\rm shots}=4$\")\n", "plt.xlabel(\"iteration $m$\")\n", "plt.ylabel(\"error\");" ] }, { "cell_type": "markdown", "id": "21ef48bf", "metadata": {}, "source": [ "## Heisenberg scaling\n", "\n", "The experimental time is proportional to $N_{\\rm shots} \\sum_{m=0}^M 2^m$, i.e. it scales like $2^M$. The RPE algorithm reaches a precision $\\varepsilon$ in $M = \\lceil \\log_2 \\varepsilon^{-1} \\rceil$ iterations.\n", "Hence it achieves Heisenberg scaling: reaching a precision $\\varepsilon$ in time $\\mathcal{O}(2^M) = \\mathcal{O}(1/\\varepsilon)$.\n", "\n", "Let us illustrate that below: we run the RPE algorithm for various $\\varepsilon$ and plot experimental time versus energy error. (We take exact time evolution for simplicity: in this case we consider that the experimental time is exactly $N_{\\rm shots} \\sum_{m=0}^M 2^m$.)" ] }, { "cell_type": "code", "execution_count": 19, "id": "a479cd67", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:02:07.895751Z", "iopub.status.busy": "2026-04-03T04:02:07.895590Z", "iopub.status.idle": "2026-04-03T04:02:11.234738Z", "shell.execute_reply": "2026-04-03T04:02:11.234107Z" } }, "outputs": [], "source": [ "epsilon_list = [0.1 / 2**m for m in range(11)]\n", "n_shots = 5\n", "\n", "cost_list = []\n", "res_list = []\n", "for epsilon in epsilon_list:\n", " M = int(np.ceil(np.log2(1 / epsilon)))\n", " cost_list.append(sum([n_shots * 2**m for m in range(M + 1)]))\n", " theta_list = qpe.robust_phase_estimation(H, psi0, epsilon, sign_E0, EXACT, n_shots)\n", " res_list.append(theta_list[-1])" ] }, { "cell_type": "code", "execution_count": 20, "id": "c5afbedf", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:02:11.236717Z", "iopub.status.busy": "2026-04-03T04:02:11.236543Z", "iopub.status.idle": "2026-04-03T04:02:11.708286Z", "shell.execute_reply": "2026-04-03T04:02:11.707677Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(cost_list, [abs(en - E0) for en in res_list], \"-o\", label=\"RPE\")\n", "plt.loglog(cost_list, epsilon_list, \"rd\", label=r\"target $\\epsilon$\")\n", "plt.loglog(\n", " [1 / eps**2 for eps in epsilon_list],\n", " epsilon_list,\n", " \"k:\",\n", " label=r\"$t_{tot}=1/\\epsilon^2$\",\n", ")\n", "plt.loglog(\n", " [1 / eps for eps in epsilon_list], epsilon_list, \"b:\", label=r\"$t_{tot}=1/\\epsilon$\"\n", ")\n", "\n", "plt.xlabel(\"Experimental time $t_{tot}$ (number of shots x repetitions)\")\n", "plt.ylabel(r\"Energy error $\\epsilon$\")\n", "plt.title(\"Heisenberg scaling of RPE with exact time evolution\")\n", "plt.text(10, 5e-5, \"Heisenberg Hamiltonian \\n4 spins, $S=1/2$, $J=1$\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "3f25621d", "metadata": {}, "source": [ "## Quantum chemistry example: diatomic Hydrogen" ] }, { "cell_type": "markdown", "id": "4e04e0f8", "metadata": {}, "source": [ "Let us now consider a molecule: we take $H_2$ in the minimal atomic orbital basis STO-3G. The Hamiltonian in qubit form is obtained via a Jordan-Wigner transformation.\n", "Contrary to the previous spin Hamiltonian, the molecular Hamiltonian is non-local: it couples qubits at long distance." ] }, { "cell_type": "code", "execution_count": 21, "id": "540b3708", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:02:11.710024Z", "iopub.status.busy": "2026-04-03T04:02:11.709866Z", "iopub.status.idle": "2026-04-03T04:02:11.828468Z", "shell.execute_reply": "2026-04-03T04:02:11.827631Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "converged SCF energy = -1.116998996754\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "nOrb : 2\n", "nElec : 2\n", "E_HF : -1.1169989968\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "E_CI : -1.1373060358\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "E_DMRG : -1.1373060358\n" ] } ], "source": [ "mol = gto.M(\n", " atom=[(\"H\", (0.0, 0.0, 0.0)), (\"H\", (0.0, 0.0, 0.735))],\n", " basis=\"STO-3G\",\n", ")\n", "\n", "H_H2 = chemistry_hamiltonian(\n", " mol, hf_mode=\"rhf\", encoding=\"original\", do_fci=True, do_ccsd=False\n", ")\n", "E0_H2, psi0_H2 = do_dmrg(H_H2)\n", "print(f\"E_DMRG : {E0_H2 + H_H2.e_const:.10f}\")" ] }, { "cell_type": "markdown", "id": "a2c740ae", "metadata": {}, "source": [ "### Exact time evolution" ] }, { "cell_type": "markdown", "id": "9fc18740", "metadata": {}, "source": [ "The system is small enough for exact exponentiation of the Hamiltonian matrix, and exact time evolution" ] }, { "cell_type": "code", "execution_count": 22, "id": "3d1d152f", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:02:11.829927Z", "iopub.status.busy": "2026-04-03T04:02:11.829785Z", "iopub.status.idle": "2026-04-03T04:02:12.755898Z", "shell.execute_reply": "2026-04-03T04:02:12.755214Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "epsilon = 0.02\n", "M = int(np.ceil(np.log2(1 / epsilon)))\n", "sign_E0 = np.sign(E0_H2)\n", "n_shot_list = [2, 3, 4]\n", "\n", "for n_shots in n_shot_list:\n", " theta_list = qpe.robust_phase_estimation(\n", " H_H2, psi0_H2, epsilon, sign_E0, EXACT, n_shots\n", " )\n", " plt.semilogy(\n", " [qpe.rpe_distance(theta, E0_H2) for theta in theta_list[1:]],\n", " \"-o\",\n", " label=f\"$N_{{\\\\rm shots}}={n_shots}$\",\n", " )\n", "\n", "plt.semilogy([np.pi / 3 / 2**i for i in range(M + 1)], \"k--\", label=\"$2^{-m}~\\\\pi/3$\")\n", "plt.legend()\n", "plt.xlabel(\"iteration $m$\")\n", "plt.ylabel(\"$d(\\\\theta_m, E)$\");" ] }, { "cell_type": "markdown", "id": "30433c86", "metadata": {}, "source": [ "### Trotter" ] }, { "cell_type": "markdown", "id": "4a35039b", "metadata": {}, "source": [ "The Trotter decomposition of the molecular Hamiltonian is longer, and simulations become harder. The following run will take a minute..." ] }, { "cell_type": "code", "execution_count": 23, "id": "dcb17939", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:02:12.757632Z", "iopub.status.busy": "2026-04-03T04:02:12.757481Z", "iopub.status.idle": "2026-04-03T04:03:42.299791Z", "shell.execute_reply": "2026-04-03T04:03:42.299071Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "m \t phi_m \t theta_m \t time (s)\n", "0 \t -0.7854 \t -0.7854 \t 0.7 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "1 \t -1.5708 \t -0.7854 \t 2.2 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2 \t 1.5708 \t -1.1781 \t 5.1 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "3 \t -1.5708 \t -0.9817 \t 11.0 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "4 \t 2.3562 \t -1.0308 \t 22.2 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "5 \t -1.5708 \t -1.0308 \t 44.8 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "6 \t 1.5708 \t -1.0554 \t 89.5 \n", "CPU times: user 1min 30s, sys: 625 ms, total: 1min 30s\n", "Wall time: 1min 29s\n" ] } ], "source": [ "%%time\n", "n_shots = 2\n", "n_steps = 1\n", "\n", "thetas_ttr = qpe.robust_phase_estimation(\n", " H_H2, psi0_H2, epsilon, sign_E0, n_steps, n_shots, verbosity=1\n", ")" ] }, { "cell_type": "markdown", "id": "8b132d7b", "metadata": {}, "source": [ "... and fails to get the desired precision" ] }, { "cell_type": "code", "execution_count": 24, "id": "f11a95fc", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:03:42.301355Z", "iopub.status.busy": "2026-04-03T04:03:42.301209Z", "iopub.status.idle": "2026-04-03T04:03:42.492037Z", "shell.execute_reply": "2026-04-03T04:03:42.491332Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(\n", " [qpe.rpe_distance(theta, E0_H2) for theta in thetas_ttr_list[i][1:]],\n", " \"-o\",\n", " label=f\"$n_{{\\\\rm steps}}={n_steps}$\",\n", ")\n", "\n", "plt.semilogy([np.pi / 3 / 2**i for i in range(M + 1)], \"k--\", label=\"$2^{-m}~\\\\pi/3$\")\n", "plt.legend()\n", "plt.title(f\"$N_{{\\\\rm shots}}={n_shots}$\")\n", "plt.xlabel(\"iteration $m$\")\n", "plt.ylabel(\"error\");" ] }, { "cell_type": "markdown", "id": "c97916a0", "metadata": {}, "source": [ "If you want to reach the expected precision, what would you try to increase first? $N_{\\rm shots}$ or $n_{\\rm steps}$?" ] }, { "cell_type": "markdown", "id": "4914786b", "metadata": {}, "source": [ "### Chemical accuracy?\n", "\n", "The standard for chemical accuracy is $\\varepsilon = 10^{-3}$ Ha. Hartrees are the default unit in `pyscf`. We can compute directly the number of iterations required for chemical accuracy:" ] }, { "cell_type": "code", "execution_count": 25, "id": "d71159be", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:03:42.493657Z", "iopub.status.busy": "2026-04-03T04:03:42.493514Z", "iopub.status.idle": "2026-04-03T04:03:42.496424Z", "shell.execute_reply": "2026-04-03T04:03:42.495706Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chemical accuracy eps=0.001 requires M=10 iterations\n" ] } ], "source": [ "epsilon = 0.001\n", "M = int(np.ceil(np.log2(1 / epsilon)))\n", "print(f\"Chemical accuracy eps={epsilon} requires M={M} iterations\")" ] }, { "cell_type": "markdown", "id": "6fecddd5", "metadata": {}, "source": [ "Reaching chemical accuracy requires at least ten iterations, and a sufficient number of shots and Trotter steps.\n", "If you want to go further, you can first make an estimation of the runtime for $M=10$ and a given number of shots and Trotter steps,\n", "then with some patience try to run the simulation." ] }, { "cell_type": "code", "execution_count": null, "id": "b50adfe3", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b994dde2", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.13.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "2b9cc094238c4c65a259e4e5c5c3ddf6": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "HTMLModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "HTMLModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "2.0.0", "_view_name": "HTMLView", "description": "", "description_allow_html": false, "layout": "IPY_MODEL_78c1d38ecc76463a9d5b92e30be78a7f", "placeholder": "​", "style": "IPY_MODEL_ea614ff4e39a4a2aa77357ba5f972888", "tabbable": null, "tooltip": null, "value": "100%" } }, "535226ab9f3641f19d5be784ea6d000b": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "HBoxModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "HBoxModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "2.0.0", "_view_name": "HBoxView", "box_style": "", "children": [ "IPY_MODEL_2b9cc094238c4c65a259e4e5c5c3ddf6", "IPY_MODEL_793134aad33f4ed0b459050f172bf4f5", "IPY_MODEL_fbfe758c36454591ad2a9d45bd2c1acf" ], "layout": "IPY_MODEL_5869a3e57975420bb857f54e8ec65c0a", "tabbable": null, "tooltip": null } }, "5869a3e57975420bb857f54e8ec65c0a": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "69fef768fea64faeba0bd4c3cbc83b16": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "HTMLStyleModel", "state": { "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "HTMLStyleModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "StyleView", "background": null, "description_width": "", "font_size": null, "text_color": null } }, "78c1d38ecc76463a9d5b92e30be78a7f": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "793134aad33f4ed0b459050f172bf4f5": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "FloatProgressModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "FloatProgressModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "2.0.0", "_view_name": "ProgressView", "bar_style": "success", "description": "", "description_allow_html": false, "layout": "IPY_MODEL_9f0cbd0f249a49cb96808571eb22b788", "max": 5.0, "min": 0.0, "orientation": "horizontal", "style": "IPY_MODEL_e66111cbd92745d19c60d8aa6e36221e", "tabbable": null, "tooltip": null, "value": 5.0 } }, "9f0cbd0f249a49cb96808571eb22b788": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "d1427963026f4e17804a3097e661012e": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "e66111cbd92745d19c60d8aa6e36221e": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "ProgressStyleModel", "state": { "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "ProgressStyleModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "StyleView", "bar_color": null, "description_width": "" } }, "ea614ff4e39a4a2aa77357ba5f972888": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "HTMLStyleModel", "state": { "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "HTMLStyleModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "StyleView", "background": null, "description_width": "", "font_size": null, "text_color": null } }, "fbfe758c36454591ad2a9d45bd2c1acf": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "HTMLModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "HTMLModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "2.0.0", "_view_name": "HTMLView", "description": "", "description_allow_html": false, "layout": "IPY_MODEL_d1427963026f4e17804a3097e661012e", "placeholder": "​", "style": "IPY_MODEL_69fef768fea64faeba0bd4c3cbc83b16", "tabbable": null, "tooltip": null, "value": " 5/5 [00:07<00:00,  2.26s/it]" } } }, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }