{ "cells": [ { "cell_type": "markdown", "id": "trotter-page-00", "metadata": {}, "source": [ "# Hamiltonian simulation: build, evolve, measure\n", "\n", "**Download Notebook** - {nb-download}`ham_sim_trotter_demo.ipynb`\n", "\n", "- **Build an evolution circuit** from a Hamiltonian written as Pauli terms.\n", "- **Measure observables directly**, with expectation values and uncertainties calculated by the library.\n", "- **Swap circuit components**: replace the underlying rotation implementation while keeping the evolution and measurement interfaces.\n", "\n", "This demo follows one two-qubit system from preparation to measured dynamics. The same components can be reused for other Hamiltonians and input states.\n", "\n", "| What you want to do | Library component |\n", "| :-- | :-- |\n", "| Build a Trotter step | `trotter_first_order` |\n", "| Evolve for several steps | `ham_sim_trotter` |\n", "| Measure a Pauli observable | `make_direct_measure_pauli_simple` |\n", "| Calculate a mean and uncertainty | `estimate_pauli_observable_expectation_from_bitstrings` |\n", "| Replace the rotation implementation | The step factory's `rz_method` argument |\n", "\n", "- Each section introduces one part of the workflow, with runnable code and saved results.\n", "- Run from a source checkout with development dependencies installed. The repository default is little endian.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "trotter-page-01", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "from math import ceil, log2\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import zixy.qubit.pauli as zqp\n", "from scipy.linalg import expm\n", "from matplotlib import pyplot as plt\n", "from selene_sim import QuantumReplay, Quest\n", "from guppylang import guppy\n", "from guppylang.std.builtins import array\n", "from guppylang.std.quantum import qubit, h\n", "from guppyalgos.utils import qarray, transversal\n", "from guppyalgos.algorithms.time_evolution.trotter import ham_sim_trotter, trotter_first_order\n", "from guppyalgos.primitives.measurement import (\n", " make_direct_measure_pauli_simple,\n", " estimate_pauli_observable_expectation_from_bitstrings,\n", ")" ] }, { "cell_type": "markdown", "id": "trotter-page-02", "metadata": {}, "source": [ "## 1. Build an evolution circuit\n", "\n", "### Choose a Hamiltonian\n", "\n", "- Describe the system as a weighted sum of Pauli strings, $H=\\sum_j a_jP_j$.\n", "- This example uses two qubits and four terms:\n", "\n", "$$\n", "H=-0.5Z_0X_1-0.1X_0Z_1-0.2Y_0Y_1-0.3X_0X_1.\n", "$$\n", "\n", "- Change the coefficients and Pauli strings to describe a different system." ] }, { "cell_type": "code", "execution_count": 2, "id": "trotter-page-03", "metadata": {}, "outputs": [], "source": [ "hamiltonian = zqp.RealTermSum.from_str(\n", " \"(-0.5, Z0 X1), (-0.1, X0 Z1), (-0.2, Y0 Y1), (-0.3, X0 X1)\", 2,\n", ")\n", "n_qubits = 2\n", "time_step = 0.2\n", "n_shots = 1024" ] }, { "cell_type": "markdown", "id": "trotter-page-04", "metadata": {}, "source": [ "### Compose the simulation\n", "\n", "- `trotter_first_order` builds one step from the Hamiltonian.\n", "- `ham_sim_trotter` repeats it. Five steps of size $0.2$ give total time $t=1$.\n", "\n", "$$\n", "U_r(t)=\\left[\\prod_j e^{-i\\pi\\Delta t\\,a_jP_j/2}\\right]^r,\n", "\\qquad t=r\\Delta t.\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "trotter-page-05", "metadata": {}, "outputs": [], "source": [ "trotter_step = trotter_first_order(hamiltonian, n_qubits)\n", "simulation = ham_sim_trotter(trotter_step, n_steps=5, time_step=time_step, n_state_qubits=n_qubits)" ] }, { "cell_type": "markdown", "id": "trotter-page-06", "metadata": {}, "source": [ "### Choose the input state\n", "\n", "- `qreg` holds the two system qubits.\n", "- `transversal(h, qreg)` prepares $|+\\rangle^{\\otimes2}$; `simulation(qreg)` evolves it.\n", "- Replace the preparation gates to study a different initial state." ] }, { "cell_type": "code", "execution_count": 4, "id": "trotter-page-07", "metadata": {}, "outputs": [], "source": [ "@guppy\n", "def prepare(qreg: array[qubit, 2]) -> None:\n", " transversal(h, qreg)\n", " simulation(qreg)" ] }, { "cell_type": "markdown", "id": "trotter-page-08", "metadata": {}, "source": [ "## 2. Measure an observable\n", "\n", "### Choose the measurement basis\n", "\n", "- `make_direct_measure_pauli_simple` builds the basis changes and measurements for a Pauli string.\n", "- Use the same interface for $X$, $Y$, $Z$, or products such as $Z_0X_1$.\n", "- The small runner below prepares a fresh state for each shot and collects the library's measurement output." ] }, { "cell_type": "code", "execution_count": 5, "id": "trotter-page-09", "metadata": {}, "outputs": [], "source": [ "def sample_direct(\n", " preparation, pauli, seed=7, extra_qubits=0, shots=n_shots, simulator=None,\n", "):\n", " measurement = make_direct_measure_pauli_simple(pauli, n_qubits)\n", "\n", " @guppy\n", " def experiment() -> None:\n", " qreg = qarray(n_qubits)\n", " preparation(qreg)\n", " measurement(qreg)\n", "\n", " emulator = experiment.emulator(n_qubits + extra_qubits).with_seed(seed)\n", " if simulator is not None:\n", " emulator = emulator.with_simulator(simulator)\n", " result = emulator.with_shots(shots).run()\n", " return [shot[\"bitstring\"][0] for shot in result.collated_shots()]" ] }, { "cell_type": "markdown", "id": "trotter-page-10", "metadata": {}, "source": [ "### Turn shots into an expectation value\n", "\n", "- Ask for $\\langle Z_0\\rangle$ and collect 1,024 shots.\n", "- The built-in estimator handles parity, averaging, and standard error:\n", "\n", "$$\n", "\\widehat{\\langle P\\rangle}=\\frac{N_+-N_-}{N},\n", "\\qquad \\mathrm{SE}=\\sqrt{\\frac{1-\\widehat{\\langle P\\rangle}^2}{N}}.\n", "$$\n", "\n", "- A Pauli expectation lies in $[-1,1]$. For $Z_0$, the corresponding probability is $\\Pr(q_0=1)=(1-\\langle Z_0\\rangle)/2$." ] }, { "cell_type": "code", "execution_count": 6, "id": "trotter-page-11", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Observable Expectation Standard error Shots\n", " Z0 0.3633 0.0291 1024\n" ] } ], "source": [ "observable = zqp.RealTermSum.from_str(\"Z0\", n_qubits)\n", "pauli = zqp.String.from_str(\"Z0\", n_qubits)\n", "samples = sample_direct(prepare, pauli)\n", "estimate = estimate_pauli_observable_expectation_from_bitstrings(observable, {str(pauli): samples})\n", "print(pd.DataFrame([{\n", " \"Observable\": \"Z0\", \"Expectation\": estimate.expectation,\n", " \"Standard error\": estimate.standard_error, \"Shots\": n_shots,\n", "}]).to_string(index=False, float_format=lambda value: f\"{value:.4f}\"))\n" ] }, { "cell_type": "markdown", "id": "trotter-page-12", "metadata": {}, "source": [ "## 3. See the dynamics\n", "\n", "- Increase the number of steps to follow the state over time.\n", "- Measure $\\langle Z_0\\rangle$ and $\\langle Z_1\\rangle$ using the same measurement runner.\n", "- Here $\\Delta t=0.2$ stays fixed, so more steps mean a longer evolution. To improve the Trotter approximation at a **fixed** time, increase the step count while reducing $\\Delta t=t/r$.\n", "\n", "### Set up a reference\n", "\n", "- Exact evolution uses $e^{-i\\pi tH/2}$.\n", "- The Trotter reference multiplies the same Pauli rotations as the circuit, with later gates on the left.\n", "- Keeping both references lets us distinguish approximation error from measurement noise." ] }, { "cell_type": "code", "execution_count": 7, "id": "trotter-page-13", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "initial_state = np.ones(2**n_qubits) / np.sqrt(2**n_qubits)\n", "h_matrix = np.asarray(hamiltonian.to_sparse_matrix(True).todense())\n", "step_matrix = np.eye(2**n_qubits, dtype=complex)\n", "for term in hamiltonian.to_terms():\n", " matrix = float(term.coeff) * np.asarray(term.string.to_sparse_matrix(True).todense())\n", " step_matrix = expm(-0.5j * np.pi * time_step * matrix) @ step_matrix\n", "\n", "\n", "def reference_mean(state, operator):\n", " matrix = np.asarray(operator.to_sparse_matrix(True).todense())\n", " return float(np.vdot(state, matrix @ state).real)" ] }, { "cell_type": "markdown", "id": "trotter-page-14", "metadata": {}, "source": [ "### Reuse the circuit and measurement builders\n", "\n", "- Build an evolution for each time point.\n", "- Pass each observable to the same `sample_direct` runner.\n", "- Check the measured values against the Trotter reference, allowing for finite-shot noise." ] }, { "cell_type": "code", "execution_count": 8, "id": "trotter-page-15", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "step_counts = [0, 2, 4, 6, 8, 10]\n", "rows = []\n", "for steps in step_counts:\n", " evolve = ham_sim_trotter(trotter_step, steps, time_step, n_qubits)\n", "\n", " @guppy\n", " def prepare_at_time(qreg: array[qubit, 2]) -> None:\n", " transversal(h, qreg)\n", " evolve(qreg)\n", "\n", " time = steps * time_step\n", " exact_state = expm(-0.5j * np.pi * time * h_matrix) @ initial_state\n", " trotter_state = np.linalg.matrix_power(step_matrix, steps) @ initial_state\n", " for index in range(n_qubits):\n", " label = f\"Z{index}\"\n", " operator = zqp.RealTermSum.from_str(label, n_qubits)\n", " pauli = zqp.String.from_str(label, n_qubits)\n", " samples = sample_direct(prepare_at_time, pauli, seed=100 + 2 * steps + index)\n", " stats = estimate_pauli_observable_expectation_from_bitstrings(operator, {str(pauli): samples})\n", " reference = reference_mean(trotter_state, operator)\n", " assert abs(stats.expectation - reference) < 5 / np.sqrt(n_shots)\n", " rows.append({\"Time\": time, \"Observable\": label, \"Sampled\": stats.expectation,\n", " \"SE\": stats.standard_error, \"Trotter\": reference,\n", " \"Exact\": reference_mean(exact_state, operator)})\n", "dynamics = pd.DataFrame(rows)" ] }, { "cell_type": "markdown", "id": "trotter-page-16", "metadata": {}, "source": [ "### Read the result\n", "\n", "- **Dots and error bars:** sampled expectations with one standard error.\n", "- **Dashed curves:** the implemented Trotter product.\n", "- **Solid curves:** exact Hamiltonian evolution.\n", "- The gap between the curves is Trotter error; fluctuations around the dashed curve are sampling noise." ] }, { "cell_type": "code", "execution_count": 9, "id": "trotter-page-17", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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fZ5fmy/NbmQRrdjk7GiDtF3f53Dtz5gyqVq2qbkvaqaSi6i56ycU1nbS3pXeuU6dOKvXUkscyRcYb6sjz0AWAafcvXbq0ungn6bMlS5ZEQkICzp8/r3od5T4Zeyk9n3KRLioqSgWbOnJhT+7T9TbKeE7d3y6f37du3dIXFMroby3M1q1bh5deekmdMxnvKb9PnToVdnZ2JrefNGmSvndYRwJFGe+qO+8y/lTGwOrGlepIyrHuvUZERGRVweP333+Pn376CRs2bFDVA7/99ltVVOHkyZOoXr26yX10V9h11q5dq4pODB061Gh9nz59sGTJklx9/kRUgDl75M62OezNN99UKaqHDx/G1atXVeGYWbNmqfskHVU+FyWzolWrVuluT5kyBU8++aRK+5QUUiFprNK7aSlJoZUCP35+fpg5cyYWLzZI5zUgF+NkjKMEJAMGDFBjJOvVq6cWIZ/Bcl+/fv3UfRL86UiA++KLL6J///7qIp6u4qz0so0fP14FyxIAS0EdKZgjt+VvlbGR8nthLpgjPc9yXuS1lHMhY06lOq9McSIXQk2RC66y6EhALsF32nZQSLBPRERUKArmSOM3evRolbIlXzRk7Is0gL/88ovFx5DxPfLlxTD1SkfSV23lyjURFUwjR47U9+ZJgCfBlaEhQ4Zg2bJlqpepfv36OHbsmD71cNiwYXjllVdUz5z03KW9LcGa9CRJ6qoEnnJxTXr9RLt27SxKW5UCPhLcSS+jVIbVVVA1tb9khrz77rsqU0SK6cjUIToSeEqPmQSGMsejZJXo5nj8/PPP1XmQVMovvvhCHUN6L4WMo5Tjyn26gjlCAkdpG+TvKswFc3799VfVYzhx4kQ4OTmptkzaRRkHa6l///1XnTfZLy05r4X5/BER0aOx05gaEFgAhYaGqnEx0ujJVVcdqdYnV2J37dpl0THkS5lciX/55Zf166UK4Jw5c/QpVy1btlS9nFm5Gh8ZGanG4kgqkK68PBEVTPLlWKa7kHF20itHlvd6SuAiPwvTa29Nn9/SsyrBvxRJ0pGgvG/fvqrarG7qlcxI4SSZqkV6kXWk+q5cXJCpXeQ+SXH+3//+p4J+S1nTeSQioux9hltNz6MEfkJ3ZVpHbuvuM2f+/Pmqx1JXpVCnQYMGaryH9DxKQQa5wi2pXJkdV9J+5CQbLkREhZmlvZOUe6RdMtUO6u4zR3prZZ5Pw7lFdWnGkpkjaatSJ0AuEDz77LOZDudgO0hEZHusJnjUFQLQjX3RkSuk5irN6UjvooyFSVtFVXoepbdRjiONsBTPkUAyo7E8QooTSHSuW+RKMBFRYSa9W7o0Vcq/ttBUOygsaQulHZQ2UMahGpLKuTJGVcaVSnVfGXMqNQVkXs2MsB0kIrI9VhM86irrSYU+Q3JbKveZI0UlpDJg2qutpnh4eKjHu3TpUobbSPU66dbVLYaVAomIiHKDtE2m2kFhri2UMf3z5s1TxYYsSdeWIkRsB4mIyCqDR+ndk0I3Mi5DR66+SvpN27Zt9esk3UZX4t2QpOPUqFHDaNuMyITVkr6a2aTVUh5d8oENFyIiotxOHd66datR76NUIK9Vq5bRnI2Sfpq2h1K2kwudpi6imip/IFV52Q4SEZFVBo/ivffeUymlv//+O4KCglS6qaTrjB07Vr+NzN/Ypk0bo/0kBXXhwoUmG0wZsyEFCNasWaOq9ElZeCnII2Xo046NJCIiyk+STio9iPLz3Llzaiy/tIvSPurI1CcyBEPm1Ux7EVUq0tapUyfdcaU9lcrlMo9nYGAg3njjDRWkSlVXIiIiq5zncfDgwapS3rRp01TpdqmGKj2PhtXlZNB/8eLFjfaTcvKSimqqapz0IH755ZeqHLzMlyX7Su/k8uXL042NJCLbFBoTitDYjIuR+Lj5wMfduIgJUW6QquO6oE6mTJHbEvQ99dRT+m1kzKK3t7fR3JkyvGLPnj1qnKIpH3/8sbpPpsRKSEhA7dq11XAPU9NaERGR7bKaqToKOpYoJyq8U3X8fOxnzDg+I8P7x9Yfi3ENxuXws7Ruhw8fVpWsdVMgFRTWPlVHQcbzSERU+D/DrarnkYgoPwyqPggd/DsgJjEGI9ePVOveafoO6vvWh72dvep5fFQS0EjhkyZNmhj1GEkQJnPvyZg2a9KtWzdcuHCBGRxERESFiFWNeSQiyg+SknrrwS1M3Jk6/uvzg5/j9a2vq/U5kbIqqfOSMr9ixQr9utOnT6tphMaNY68mERER5T8Gj0REZmy6ugnjt41HSEyI0Xq5Levl/pwgxbpk/JqO/N6vXz+jbaSCphQMk8neDcntffv24ciRI7h37166Y0uVzQMHDqhtpIiYkMIokqaiI8fVVauWYivh4eGIiopSQaxh2uepU6dMTkgvFT4zm9qBiIiIrBuDRyKiTCSnJOPzA59Dg/TDw3XrvjjwhdruUclE7boALDY2FmvXrsXAgQP190vQJpUyBw0ahA4dOqBz584qmBNLly5V1aZfeOEFVK1aFdOnT9fvJ5U5pfDJK6+8orbRzUsrtyXY1Hn77bexa9cu/Vy2zz33nJoiSYqpiEWLFqFKlSqq+JgUVHnnnXf0+0ohMxlH2LdvX/To0UNNF0FERESFC8c8EhFl4kjIEQTHGE/KnjaAvBNzR23XtFTTRz6XEvz9+uuval5a6XWUitA6Mt2QBH/169dXt2V6hj///FMFeRMmTMDo0aPV2Mnbt2+rqYZefvllNX+fbCPjKaXqdFY4OTnh4sWLsLe3V72Qb775JubMmaMG1EvQOnToUPWcihQpgo8++gjHjh1TweV///2HdevWPfK5ICIiooKFwSMRkZlpOnJyO3OGDRuGhg0bqkIzf/31lz5lVHryDh06lG4yd91E8N9++60K4CpUqKAK7Eg6qixSMU2mOQoICFBz2g4YMEClx1pCglcJHMXx48dVBbbJkyfr75fHkhRZCVgloJXAUcjx5TkQERFR4cLgkYgoE5YWw8mpeR6lF0/SQq9evYpq1arpg0fpBXR3d8cff/yh1qc1ZcoUldbq7++vxjRK8CmTyQvpLZQxkTI/oMyRK/dLkCq9mvHx8fpjSO+iIcNeTwlCpcdx9+7d6abfkLGUhmMgJWg1PC4REREVDgweiYgy0ci3Efzc/VRxHFPjHu1gp+6X7XLK//73vwxTWp988km8//77KF26tFonPYoS1BUvXhz//POP6rX86aef9D2USUlJqsdSSGBZokQJxMTEqNsyD6OMVZTAVArpSBCYEdm2TJkyKuiUNNmiRYvqx2k2atRI9YzKGMguXbpg5syZsLOzy7HzQURERAUDg0ciokw42DvgnWbvqKqqpgJHMbHZRLXdo6hcubIKztKSYE83x6NM5yHjIefOnat6+iRAlOCvRYsWWLhwIT799FPVMygBnhTckfkipZdRxknqeg979+6tgj/1vCdOVD2RctxevXrh1VdfVUGoqF69Ory9vVPPg4MD1q9fj6+++gpffvmlqsIqduzYAWdnZ3WfBL3ff/+9Ggf54MEDo/kqiYiIyPrZadIOoKFskTQtufovY4LkCxoRFVxS7EXG6Ul1UFdXV4vGM666tApzT83FvfjUaTC8Xb0xovYI9K7cO8fSVinvX3t+fucMnkciosL/Gc6pOoiIzFgctBjfHv7WKHAUYXFhar3cT0RERFTYMaeIiMiMQdUHoYN/hwzv93FjryMREREVfgweiYjMkJRUpqUSERGRrWPaKhEREREREZnF4JGIbBbrhdkevuZERETZx7RVIrI5Mq+hzEMo0134+PhwTkIbChzlNZfXXt4DRERElDUMHonI5sicheXKlcONGzdw5cqV/H46lIckcJTXXt4DRERElDUMHonIJhUpUgTVqlVDYmJifj8VykPS48jAkYiIrF1oTChCY0ORoklBYFggIuIj4OXihQDvANjb2atK8LlR7I/BIxHZLAkiGEgQERGRtVkctBgzjs/I8P6x9cdiXINxOf64LJhDRERERERkRfzc/R7pfpvqeYyKikJYWBjKli1rtuhBcHAw7t27Z7TOxcUFlSpVeqTjEhER5ZekpCQ1ZrdEiRIoVqxYptvGxMTg2rVr6dZXrlwZzs7O2T4uERHlj+SU5Ex7He1gh5nHZ6J/1f5wsHew3Z5HadRefPFFlCxZEs2aNYOfnx/+/PPPTPeZPHmy2rZ///765bXXXnvk4xIREeWHf/75R7VT0l5JteDRo0erdiwje/bsQUBAgFE7KMvNmzcf6bhERJQ/joQcQXBMcIb3a6DBnZg7ajub7nn8/PPP8e+//+LkyZOoXr065syZgxEjRqBu3bqoV69ehvt17doVS5YsyfHjEhER5aXTp09j+PDhmDlzpgruLly4gFatWsHf319dLM3M2bNnc+W4RESU98VycnK7Qtvz+Msvv6hGTQI8MWrUKFStWhWzZs0yO7eXpOzcv38/R49LRESUl3777TeVbiptlpC26vnnn1ftmDl3797FrVu3cvy4RESUtyytopob1VatJni8c+eOGofRokULo/UtW7bE4cOHM9132bJlaj9Jx5GexN27d+fIcYmIiPLSwYMH07VX0kN4+/btDANDHQkI69Spg+LFi+Pbb7/NseMSEVHeauTbSE3FkRm5X7az2eBRCtkIGZdoSG7L1dSMtG7dGkFBQarxi4iIUI1jr169VMD4KMeNj49HZGSk0UJERJSbpM0y1V6JjNosKX6zfPlyhIeHq0V6Gd9++23MnTv3kY7LdpCIKH9IERxzgaHcn9PFcqwqeNTNxZaQkJCu8XJ0zHjo5tNPP60mAheurq6YPn06kpOTVW/koxx36tSp8PT01C8yLoSIiCg3SZtlqr0SGbVZjRo1Qt++fWFvr23yBwwYgCFDhhgFj9k5LttBIqL8M7HZRIxv9AZKOLobrfd29cb4xuPV/bnBagrmyPQZdnZ2KoXGkKSdlitXzuLjSFnyUqVK6cuWZ/e4kyZNwvjx4/W3peeRASQREeUmaWdMtVe69sxS5cuXNxrCkZ3jsh0kIspjGg1wYhFQZ4Aazziy7ig8U3uEqqoqxXFkXW71OFpdz2PRokXRuHFjrFu3Tr9OrpJu2rQJHTp0MGrsLl++rC+Uk7bM+PXr13HlyhV9cRxLj5uWzBUpc2AZLkRERLlJ2qWtW7ca9RKuXr0aDRs2VFkwIjo6WlVW1W2TmJiY7jg7d+7Ut4OWHjcttoNERHkoJQVY+zbw7wvA8nHaQPJhCmvTUk3Rs3JP9TM3A0er6nkUU6ZMUak3UvRGCtrIgH9JRR0zZox+m/fffx/79u3DqVOnVIMpYxxff/111K5dW/U2fvDBB6hSpQqGDRuWpeMSERHlN5mT+Mcff8TQoUNV9sv+/fvVvMQy3ZRhYNijRw8EBgaiZs2aeOGFF1SxnPbt26uLqlJJXArkyEXSrByXiIjySXISsPJV4JjMQ28H+DcH7Ozy5alYTc+j6NmzJ/777z+sX78eY8eOVQHerl27VDEAndKlS6ty47oU1b///lttI4HgjBkzMHjwYFVF1cPDI0vHJSIiym9eXl4qOJQ2bNy4cVi7dq0aw9+nTx/9NkWKFEGNGjVUz6CQoFB3cXXixIlqvcxr3LZt2ywdl4iI8kFSArB0lDZwtHMAHv8FaPoc8oudRi5D0iOTMY+S2iNzSTKFlYjIevDzm+eRiKhASogBFj0NXNgEODgDA+cAAX3ytS20qp5HIiIiIiKiQk+jARaP0AaOjm7A0H8yDBwXHbyOPRcynmIwJzF4JCIiIiIiKkjs7IDmYwD3ksDT/wJVO5vcbN7uy3h76QmMnn8IV+5G5/rTsqqCOURERERERIW6x9HuYTEcCRhfPwE4p9ZqMTRz+0V8vvas+v2pZuVRwdt4zsfcwJ5HIiIiIiKi/BZxHZjbA7h7PnWdicBRStZ8tzFIHzi+2qkq3usVoOauz20MHomIiIiIiPJT2EVt4HhtL7DiFf08jqYCx6lrz+L7zdoA8+3uNTC+a408CRwF01aJiIiIiIjyS/BpYH5/IDoE8K4GDJhtch7HlBQNJq84jT/2XVW3J/ephZGtK+XpU2XwSERERERElB9uHgYWDABi7wF+dbXFcYr4pNssOUWDd5aewOLDN1Rc+dnjdTG0Wfk8f7oMHomIiIiIiPLald3AX0OAhCigbBNg+BLArXi6zRKTUzB+0XGsPH4LDvZ2+HpQPTzesFy+vF4MHomIiIiIiPKSRgNs/0IbOFZsCwz9G3Apmm6z+KRkvPzXUWw8EwwnBzv88GRD9KhbOt9eKwaPREREREREecnODhg8H9jxFdDpfcDJLd0msQnJeHHBYewICoWzoz1mDm+ETjX98vV1YrVVIiIiIiKivCqOo+PmBXT71GTg+CA+CSPnHVCBo5uTA+Y+2zTfA0fB4JGIiIiIiCi3HZgFzGgF7P05083uxybi6dn7se9SOIq4OGL+c83QumrJAvH6MG2ViAqO0HPA/RtATDgQE2a8JCcCQ//K72dIRERElHW7vgM2faj9/f71DDcLj05QgePpW5HwdHPC/FHNUN/fCwUFg0ciyllJCYCjc+rtC5uB8Evpg0FZUlKAcXtSt13zFnB5u+nj2tlrt7d/mDCx5RPtz9pPAH61+CoSERFRwSyMs+VjYOc32tvt3gI6vmdy05CoOAz/bT+Cgh/A28MZC0Y3R0DpYihIGDwSUeaBYGw4EB8FlKyWuv7wPCAkME0wKL2F4drAceKV1G33/ABc2pbBA9gBKcmAvYP2pjyGHMO9BODubbA8vK1J0WbbJ8YB+38B4iO1A819agJ1BmgDyZJV+YoSERFR/ktJAdZPAvbP1N7uMgVo87rJTW9FxGLYb/tx+W40/Iq54M/RLVDVtwgKGgaPRLZC0j5lAlpdsJcUB1Ttknr/lk+BW0cMUkbDteWjhasX8M7V1G1P/5txQJgYYxwQVmgNuHqmCQYfBoRuJbQBpE6vh1flLKlQ1utb4PQy4MImIPQssPVT7VKqLtB8LNBwWNbPEREREVFO9TiufAU4uiD1O07T0SY3vRYWg6d+24cb92JR1ssNfz3fHBW8PQrk68DgkaiACY0JRWhsKFI0KQgMC0REfAS8XLwQ4B0Aezt7+Lj5wMe1xMNAMM3YwJQkoOlzqQf7dwxwbZ92u/j7xg+UNiC8cRC4tDX9E7JzABycjVNGaz8OlGlkOiCUn5JiqtP+7dw5F2Vrw6dqB/jYOQFnV2sDSQlo75w0HksgvZRybjzLZvt5EBEREWWJXOguWUP7Par/z0D9J01udiHkgUpVvRMZh4re7vjz+RYqgCyoGDwSFTCLgxZjxvEZGd4/VuOJcVdOySWt9HdKD59h8Bh1B7h32WADO8CtuDbA8yhpHBA2HwPUHZg+GHTxTN1Gp/GzKBDnov5YjGswTtvLKIsEyYErgErtUzc6vx5Y9Azg30Kb2lqrH1A0/0tdExERUSHX+lWgejfAp4bJuwNvR6riOHcfJKCabxH8Obo5fIu5oiBj8EhUkMRHwS/8emq6g1y1SsPPzjk1cJTeQ6PxgSWN9+v8AdDhHW16qNwv8wnp0knTqtEdBY2fu1/W7pdzkTawVfMp2QHX92mXdRO1qbR1ngAC+gEe3rnwzImIiMjmxEcBmz8COr2vvaAvMggcT9yIwNOzD6hpOWqVLqaK45TwMCg4WEDZaTTyTZMeVWRkJDw9PXH//n0UK1awqiKRFTi/CTg0B8kXNqFbGW8EOziYDBztYAc/t5JY1+MvOEig6FA4rv+kpGgQFp2A2/djcSsiTv28GRGD/+6OQ7wm3GhYZNrgcf2A9XDIKCDWibwFnP5Pm9oq6bk6kkryxmmgWOmc/YPIqvDzm+eRiOiRxYQDfw4Cbh4CqnUFhi3OcNNDV8Ixcu5BRMUnoYG/F34f2Qye7k5W0RZa5TfP69evIzg4GNWrV7coUEtOTkZQUBAcHR1RqVIl9dPQxYsXcfv2baN1Hh4eaNiwYY4/dyIl7j7g4AI4PUxNuHUUOLcaR1xdEJzm/WlIAw3uxIbiSPR1NC1ayipOplyfkjmLbt+XoDBOHyDekZ8Pbwffj0dCslRSTeXgfhHuFTIOHEVwTDD6z16AXtXboF01HwSULgo7E0E3ipUBWo7TLveuagv+SCCp7jMIHHd+CxQrC9ToAbjyIhAVXNLIS7vm6+uL8uXLW7TPrVu3EBoaisqVK6No0aJG98mXhZMnT6bbp3HjxnBzK7hjb4iICoQHIcAfjwPBp7TDgyTrKwN7LtzFc78fQmxiMppXKoHZzzZFERfrCckcrer7dlwchg0bhrVr16JChQq4evUqvvjiC7zyyisZ7vPpp5/ixx9/RIkSJRAbG4vExETMnDkTvXv31m/z1VdfYcmSJahZs6Z+nTSu8+fPz/W/iWwsYDy3VtsDdnEz8Pgv2tRJIT+T4xFa3Bc48aNFhWQKSmAo6RaGQaH8VLcNfo9PMg4MTZGYz7eoC0p5uqGMpysSXW9hf7T55xAYegMnL57F52vPwqeoiwoi21UvibbVfEynfxSvoC2TLUv8g9T1cZHAts/V66AC+2qPaV+X6t0B54JZ8Yxs088//4w333xTtYPXrl3DY489hr///jvDIG/Dhg145513cOfOHfj4+ODChQt46aWX8OWXX+q3OXjwoDpO69atjfb966+/LA5OiYhs0v0bwPx+QNgFoIgf8PR/Gc4/vfVsCF5ccBgJSSloW60kfn26CdyczWRPFTBWFTxOmTIFBw4cUD2FpUuXxn///YfHH38czZo1Q/PmzU32OErAeObMGRU8ig8//BBDhgxRxyhVKrXnpkOHDiqAJMpRsRHagPGMBIxbgOSE1PukCqouePSuovLjfe4cBE6YP6yPu0+evFCRcYm4cz9OzT2kDQgf/pR1EhhGxKkrZ5YoWcQFpT1d1VLGy037u+6npyv8irnCySG1MM/BOynYv978cUc0rYvLN32x92IYQqPisfTIDbVIMFq3rCfaV5dg0gcN/b3gaHB8xcVg/iSpVCsB5allQNh54Owq7eLkrg0gpRBRxTaWnzyiXHDo0CG8/PLLWLp0qWr/JCBs2rQpJk+ebBQMGpL2bs6cOWjQoIE+UGzXrp26YDpq1CijbXft2sXXjYjIUmEXtYGjVHn39AeeWa79TmfCulO38crfR5GYrMFjtfww/amGcHG0rsDR6sY8SrA3duxY1Ujq1K1bV10pld5ES0i6qxxn9erV6Nmzp1o3ZswY3LhxAx999JHK9ZXUVvu01SXN4JgZSif6LvBtgHHAKJPZ1+oP1O4P+Aak2yU5JRmPLXlMTU+REZmqY+PAjebH+ZkRHZ+k7zGUIFAXDN6OTA0SH8QnWXQs6eHTBYGlPd1Q2ssVZTzdUEoCRU83+Hm6ZPkDUs5Ft6XdEBITotJ1TY7/dPfDugHr1LmIT0rGoSv3sCMoFNuDQnH2zsM5Kh8q6uKI1lVLqkBSeibLFXc3/cDykSjTfUhaqwSSEQ+nM+n6KdDqZe3vSfHaIjyOBX9gOxWuz2/pMdyxY4dRiqlcWJ0+fTpCQkJMp22b0LZtW1SrVk0FlWLTpk2q5/Hs2bOIj49X92U1XdWaziMR0SPTaIBfOwC3jwHeVbWBo2c5k5suP3YT4xcdR3KKBr3rlcZ3QxoYXTAvCArdmEcZqyGBn4y/MCS9jkePHrX4OHLFVVSpYnxVYP369Sr9R67iuri44JdfftEHl6ZI4yqL4QknGyZzLp5do01d6DBRu06mwvCrAyTGZBowGpIgqJFvI6y/mnGXm9xvLnCMS0xWvYWq1/Bhj6H8lHGGqtcwIhaRcZYFhp5uTvreQm0wmBogqp+ernB1yvkrZ/I3ylQcH+790OT9ElCOqT9Gfy4kOJXgUJZJPQMQHBmnDyR3XbiLiJhErDt9Ry2iio+HCiSlZ7J5Je/UtBH58l26nnbpPBm4dUQbRMrcljonFwPr3wMCegO1n9BODVJIihdRwSbtnal28O7du+oiqL+/v9ljREdHIzAwED169Eh3n6yTugDSHo4fP14N/cgoIGU7SEQ2zc5OOwRp7VvAgNlAEV+Tm/1z4Bom/XtSxZoDG5fDFwPqwcHesgt9BZHVfNsJDw9XP729jcvqy23dfeZI4yrjIwcPHowaNVLL5nbr1k31OkrhAUl1nTRpEgYNGoQTJ06kCzJ1pk6dqq72kq0HjDI5/X/ayelTEgF7J6D5i9opMcQz/6WWarbQxGYTUbtkbcw7PQ/hcanvbW9Xb4yoPQJdK/TA1bDodOMMteml2t/vxSRa9FjSG2cYBKbrNfRyhbtz/n1MSEGc7N4vabCDmvirRa70nbx5Xx9MHr12DxdDo9Uyd/cVODvaq0HruhRXmWtJfWGWpWxj7WJIUpDjIoCjC7SLTIMS0FebhizTgDxirzBRRqS9M9UO6u6zJHiU3ksJEF944QX9Oj8/P+zevRutWrVSt7dt24bu3burISIZ1RVgO0hENikuMrWonm9NYMTKDDedt/syPlx5Rv0+vEV5fNS3DuytOHC0qrTVc+fOqfEZW7ZsQceOHfXrpVGTdadPy1xuGZMu2M6dO8PJyUkVD0hbac6QBJDSGEt67BtvvGHxFVdptJmuYwPObwT2z3wYMBr03vnW0vYwNnteO9/gI4qIicOCY9tw9NY1PIh2R3Rkedy5H68mkrWEu7OD0fhCXSEaGWcoPyU4LOqav2WhLSkMJCm8KZoUBIYFIiI+Al4uXgjwDoC9nb1K4c3O+E8p8iPVziSQlIBSemUNyfmSgeztq/uiTdWS6ctnpyQDV/doU1vPLAdiwlLvK1oGeOUw4JxBWiwVONaUbilDNWS84k8//aRft337djVuX8b3BwRknt0gF0el4M7GjRtVj2Vmnn32WZw/f14FlaawHSQim3NhE7DkOWDwfKBy+0w3nbHtIr5Yd1b9/nzbSni3Z4DFQwvyQ6FLW5XATMYh3rx502i93DZXCU5ORteuXeHg4IB169ZlGjgK2U6Cx7SPZUhSW2UhG5m3x8E5tbiKDI6WDw/hW1ubjipBo0/1R36oK3ejsflsiKrGtf9ymBpUDZR9eG/qGD4XR/vUojO6XsOHPYaqJ7GYG4q5ORboDylLSGCoCw7rlKyTY8eVVNwedUurRa6fXQx9gG3nQrHj/F3svxSmenUXHbqhFrlAWN/fS98rWb+clzZVtlJb7dLjK+DKDuDUUiBwpXagvGHgePA3oHRDoGwjk3N3EmWFVFg11Q7K/3VzvY7vv/++CjplmIa5wFHXGyk9kBlhO0hENuXMCmDJKG2m2aE5GQaP8r3iu03n8cPm8+r2q52r4Y0u1az+O5nVBY/u7u4qnWbFihUYPny4ftyGDPKXCqo6UoI8KipKP0ejLnAU0uMoEXXaF1imADEsDCBXWmUakDp1cu7LKllhwCiBgFRJvbwD6PUN0PhZ7X21+gHxUdqgsWS1R3qYxOQUHLwSroJFCRovhRrPTVG5pHZcnozPM0wp9XJ3KjQfQvlNzmNV36JqGd22shovuv9yuOqRlOV8yAMcvRahlmmbzqvAs430SqopQXxUDy6qdNIuvb4DokOM531a8xagSQG8KmjTWmWMZKm62Qokc6snlqyHFLX53//+p9o/mY9YLF++HC1atECRItoLXBERETh16pTRHI0ffPABfvjhB3UBtWXLlumOa3g8kZKSgs2bN7MdJCISx/8B/hsHaJK13wOfmGXyvEhcMXXtWfy645K6/Xb3GhjXoWqhOodWk7aqS82RhnPChAmq8ZP5Gy9fvoxjx47pG83Ro0dj3759quGUOR0llUcCSqkoZxg4SiU5uaqakJCgypfLfrVr11ZFAj777DM1F9bOnTst7l20prQnykB0GHB2pXYMowSM8gGh02QU0Pu7HDl14dEJ2HZOGyxKcBJlULjG0d4OzSqVQKeavmqp7GMwlQTlCykupALJ86HYdf5uukJDNfyKquqtEkg2rVjCuHhQ+CVg88dA0Dpt4SQdqcomQWT9JzMs6W3Kz8d+xozjMzK8XwoMjWswLot/IVnT57cEeXJxVDJuZNjG/v371VzFcnFUN6RDAkQpfCNFcWS4h0zhIfM8fv755/oxjaJ48eKq3RMjR46El5cX2rdvr778zJ49W7W50vOYtkBPYTiPREQWkwyi1RO0vzcYBvT5wWSRvJQUDSavOI0/9mmrtE/uUwsjW1eymhNd6NJWhTRqW7duVWk3Mt+jjP34448/9IGjLiiUgFDExMSoXgVZJwP7DUlD2rt3bzg7O6urqxKITps2TTWmb7/9tgomZXwk2dDgZzWtRuo4VtU7JOmospTM/lUj+SIm00Zskd7FwGAcvR6hKm7peHs4o0MNX3QO8FU9WsUK+DhEWyPpwU82K6+WpOQUHL8Rge1Bd1VAKb+fC45Sy6ydl+HqZI8Wlb3R7mGvZBWfSrAbNBdIiAaC1mvHSAZt0E4kvONLwMs/NXhMSQHMTBEkU5M8yv1k/aR3UOZilEBQehKl0JuM+5epN3SkHZMprCRjR1y/fl2fuSOLjvRWfv311+r3X3/9VV1kXbBggWpDpX2dNWuWKphDRGSzdn8PbPxA+3uzF4DuX5hsq6Uw38SlJ7DksHae6amP11XfGwojq+p5LMh4xdXK5l+UlFT5At/t09T1v/cBYiNSxzBmoUcordiEZOy9dBebA0NU0Chj6AzVKl1MBYvSuyhj6Ky98patuhedoKYB0VVxDYkyuPggo1W93B5OB1ISrao+vDAgKc/n1gKn/wX6/ZRaXGnfDODYX6mprcUrmJz3MqMKs2nnvSTL8fM7Z/A8ElGhIiHS0tHAqSVAm/FA5w9MDjmRIUhvLDyGVSduqyk4vhlUH/0b6upVFL7PcAaPeXzCKZ88CE1NSb2y62FKqh0w4SxQtJR2m8RYwClrk2KnTW+UQFGW3RfuIj4pRX+f9EhJ1c5ONf3QsaaPGr9IhYtch5MeSF0gefDyPSQkp74HpEFpVN5L9Uq2r+GDOmU8jS8azOkOXNubertsk4eB5ONAsTI4eOcgRq0fZfZ5zOk2B01LNc3xv68w4+c3zyMRkUnJicDZVcZzPRuIT0rGy38dxcYzwXBysMMPTzZUxfisUaFMWyXKsvObgD3fPwwYU7/Io3R9be+iVFHVyWLgKCkKx65HYMvZYNXDKKmpaXuddGMXW1bxNh4LR4WOpMjXLFVMLS+0q4KYhCTsvxSunw7k0t1oHLxyTy3fbAxCCQ9ndUFBqri2rV4SvkP+BAJXaKu2Xt0N3DykXda/pyq6hbZOnZPPXFEdIiIiygaZiuvYn0CD4dr0VAenDAPH2IRkvLjgsGrjZb7oX4Y3RseavoX+tDN4pMJFqlvKf3S34g9vB2uL34jSDVJTUktkbwCzzA+483wotgSGYFtQqCp+oyOdSI3KF0enh+moUkiFFVFtl7uzo2pEdA3J9fAYVXRn+7lQ7LkYpt47K47fUosIKF0M7aq3QPu2fdCkfyKcz0lP+TJtb6STO3w8LGuQWG2ViIgoG5ISgH9f0A4ruX0C6KUdE27Kg/gkPDfvoKrO7ubkgN9GNEHrqiVt4rQzeCTrFxWs7bGRydqlx+axj4BWr2jvq9kTiJ6iLaucjYBRUhGlx0iCxc1ng3Hoyj0kpaQOEy7q6qiK3XSqKePafFVvEpEp/iXcMax5BbXI+AiZ+mN7kFTcvYuTN+8j8HakWn7Zfgnuzg5oWbkh2gd0RcdOifD30KCRdxU1pjEkJhiaTMY8NvJtxBeAiIgoK2To0qIRwPn1gL0TULFNph0Jz849oNrxIi6OmDeyKZpUfFi/wAYweKQCIcvz1+kCRhnDKAGj4dfp0HOpv0sPZJvXs/RcEpJScOByuAoWZf7FK2EGUywAqOpbRJ+O2rhCcTg5ZF4hkygtec/IlCyyvNUNuPsgXk0Dop0S5K66LVO5yCLKl3BH++oJaO8zDIuufqt9u6cZs6+BBmPqj2GxHCIioqyIfwD8/SRwZSfg6AoMWQBUe8zkpuHRCXh69n6cvhWp5n2eP6oZ6vt72dT5ZvBIBcLioMWWz1+XGAf80BBIjE7doGzjh9Nq9EtXpdISoVHx2HouRAWLO8/fVekIOjIAWqZf0AWMFbxTJ9Imygkli7ioymyyyDxRZ25HqhRXCSalt/taeIyaN8q55HG4yDWUDIrzBoecBKoP4ItCRERkidh7wJ+DgBsHAeeiwFP/ZNjrGBIZh+Gz9yMo+AFKFnHGH881V0NObA2DRyoQzM5fF7QZ0AWPTq5A1U5A5O2HYxj7AV7ls5yOKleN1FQa50Jw/HpEui/zkooq1VFl7kVJSyDKC1KBtU5ZT7WM61BVXcjYezFMBZJbL3TArcu1ZEQ/7F1vwd05BsO876Bn8DY4JMXBJ/QPoPnER6oaTEREZBNkfuUFA4CbhwFXL+DpZdrOiAwq6g/7bT8u342GXzEX/Dm6hcpEs0X8Rkz5Tuavy6zX0U6jwcyoM+h/NwgOJatrVw6cqy2MkwVS/XL3hTBVHVWm0wiONJ6Tr25ZT9WzKPMvpptGgSifyIWLx2r5qQWogyt3o1Wv5KJD13HqZiRmhAAHvfpius8SlKz/mHHgKHNUmZiTioiIyOZJNdW2E4A1bwHDFgN+tU2ekmthMRg6ax9uRsSqSvp/Pd/cprPQGDxSvjsSciTDic+Fxs4OdxwdceTBdTTVBY8WBo5S4VLSUaWHce+lMDWeUUeKkshUCRIsdqzhC99iro/+xxDlsoolPdQyvHkFLD1yA1+tP4dDEUCLiBFonlwc/yt7X/Va4txaYO9PQM+vAd+afF2IiIjSXlit2Quo0inDjJ0LIQ8w7Ld9qsOhUkkP/Dm6Ocp42XZ2D4NHyvv/sGEXtIOSZe7F5mMQmnjXol1DU4x7Ck1JkiqW1yO06ahng1VeuqFyxd3QJcBPTZ/QvFIJzr1IVkt6xgc18UfPuqUxc/tF/LrjEvZfuYc+03dhUKOy+OzOZDiGnQNmtgZajAPaTwRcbDPFhoiISAk5CywfBwycAxSvqF2XQeAoFdCH/7YfYdEJqO5XBAtGN4dvUXY0MHik3A8W755PDRZlidZWkFS8q8EnoMsjzV8XEZOgJmKXVNRt50JVCWUdB3s7VRFVpaPW9FX56Zx7kQoTDxdHTOhaA082K48v1p5V80YuOnwTR51fxi8+S1A5bDuw5wfg1FKg22faMcJMZSUiIltz6yjwxxNAbDiwbhIw9O8MNz1xIwJPzz6gvlPWLlNMFcfhdGxaDB4p54PFxBjA+WEu+O3jwK/tjbdxcAH8mwEVWqt5GBv51nk4f12Imm7A3Px1UuxG0ghkGgOZf/HQ1XAYTL2oSid3rOGjehfbV/eBlzvnXqTCT8Zh/DC0IUa0qoiPV53BsetAp5svYmDRNpji9Ds8Im8Ai0do03N6fAWUrJrfT5mIiChvXN0L/DUYiI8EyjQC+v2U4aaHroRj5NyDiIpPQsPyXpg3spn6bklaDB4pB3oWgwx6FncD1boC/R/+pyxVF/DwBXxqaEsfy1K2ibZi6kMOD6fi+HDvh6YfAhqMrvMCdl0Ix5bAYBU03rgXa7SNpBNIZVQZv9jQ3wuOnHuRbJT0tC8b20r1QH6x7iyW3K+NlfgEH3tvxMC4JbC/uAUIv8jgkYiIbIO0e38/BSTFajsuhv4DuJqeYmP3hbsY/fshxCYmo0XlEvhtRFNW3M+J4DEhIQFbtmzB8uXLERwcjL59+6J3794oWbJkdg5H1hgwHpoNXN4JXN0NRIca3y9z5ejYOwATzmp/ZiKzgjnio3V7ER3srr/t7GiPlpW99cVu/Euk3kdk62Q8pMwZ2a12KTUWUsZEvh3WC9PtmmBiudNo7NcepXQbR1wDPP2ZypoNJ0+exH///Yc9e/agbdu26NevH2rXNl2tj4iI8kHgSmDJKCA5Aaj6GDB4PuBs+jujzPX94oLDqrhiu+o++GV4Y7g5Z/791RbZaSQH0AL379/HmjVrVMC4du1aeHp6qqDRz88PK1euxNGjR9GqVSvVePbv3x+VK1eGLYmMjFTnRM5TsWKFaMJQeXuEntMWuQnonbr+p+ZA6Fnt746u2jTUim0f9iw2BhxdLH6IxOQUHLt1Dafu3MD1ew9wNjwQ1+7fxZ17DkiJKyNfhaFJKgpfd5l30Vf1MLau6g13Z3acE1nizv04fLn+LJYdualuuzk5YEz7KnihURG4/dIcKN8c6PEFUMK2Prez+vmdnJyMXbt2qXZQgsaQkBB07dpVtX2yfuPGjShTpoy+HZT19lIK3kYU2naQiKxTSjLwW2ftWMeAvsCA2YCj6aFMa0/exqv/HEViskZNjTX9qYZwcbStwDHSws9wi4LHe/fuoVSpUggICFCNoiyNGmnHn+ncunULK1asUI3q1q1bMXv2bAwbNgy2otA0mipYPPswBVVSUXcDMXcBRzfgnaupQeH+X4G4+w+DxUZmg0V5m4VGxePS3WhcCo3G5bsP1E+5fS08BsmGgxYN1Pf3UoVuJGiUAcssdkOUfcevR+CjVWdw+Oo9dXtokaP4NPk72GuStGOR27wBtHk9w8pztv753aNHDxw7dgx9+vRRF0+7dOkCV9fUFPzY2FgVQEo7uGrVKhU8/vvvv7AVhaYdJKLCI/ousH8m0P4dwMF0p8N/R29iwuLj6rton/pl8O3g+nCyweFPkTkZPCYmJuL27dsoX768RQ8eFRWFmJgY1StpKwpFo7nja2Dfz0BMmPF6CRylZ6L/DKCY9ARmLDo+CZclQFRB4gPt7ypYjMaD+KQM95OeEJk/p5KPB6qU9EAV3yJoVaUkfIpa3oNJRObJR/7qk7cxdc1ZNeFxJbvb+K7IAjRIPKrdQEqX9/gSqN7NZk6npZ/fly5dQqVKlSy6iJWSkoIrV67YVBZOoWgHicj6SU9jmYYWbfrPgWuY9O9J1XcysHE5fDGgnqrUb4siLfwMtyjvz8nJyeLAURQtWlQtVAClpBj3LEqqmi4glHGJEjjqgkVV4KattiqVQTe/zKUoXzolKLyYJkC8ExmX4UPL/8Vyxd1R2cdDBYqVfYqgsvrpAb+irmqcFhHlLgl8etcro+Y7nb3rMn7e6oD+UW+ip/1+fOb+F7zuXdFWpAvoAwyaLwMo+ZI8lJVAUNJVbSlwJCLKdxIBbv0M2PEl0OcHoPGITDefu/sypqw8o35/ukUFTOlbm99FLfDIg8ZCQ0Px22+/qcIBUkhHrsqOGjVKpbhSQQkWA43TUGV+Gx3JAa83SPt73UFA+ZYqWNQ4OKlJUVVgePSOQbppNK6GRauc8IzIPDgSFOoCRPlZxccD5b3dbS5/nKigcnVywEsdq2JQ43L4esM5LD5sh20PGmC8878Y6bAGKR6l4cTAMdtkfOSPP/6I119/PSdfNiIiyihwXP+uNoNOpM2iS+PnbRfw5bpz6vcX2lXGpB41OTQqpwvmmBIREaHGPso4kM6dO6seSgkiv//+ezXeo2nTprAV2UnXCY0JRWhsKFI0KQgMC0REfAS8XLwQ4B0Aezt7+Lj5wMfdJ+vBYnJ86pilU8uAJSONt3FyB8q3UD2LcdX64LKmVLpxiJJyGhmXcZqpi6O9Ns30Yc9hpZJF1E8JGjmvIpH1OXXzvpofcv/lcFS1u4Fkj1IY170RBjQqB/uwIOD+daBqFxRGuZFuGRcXBy8vL/XTVjBtlYjyrTDOqteBI/O1t2XoRfMXTW4qYc93G4Pww5YL6varnavhjS7VGDgih9NWM7Jjxw7Vw/jTT6kTbUohAQki//nnn1wLHqWyq0wRIiXR/f39c2yf7Bz3USwOWowZx2dkeL/MfTiuwTjzwWLI6Yc9i7u0U2e0egVoO0F7f4VW0Dh5IK50U9wu3gSBznVxMLEiLtyNx+Xd0bi5+jwAWdKTYT1lPN30QaFhT6JMSM40U6LCo05ZT/zzQgusPx2Mz9a4q0JWby05gd/3XMZfTp+gWPB+baZC96mAZ7n8froFhmTc1KtXL936R7gua5EbN27g1KlT8PX1RcOGDS364mPJPtk5LhFRvklOBP59ETi1FLCzB/r+CDQcbnJT+Vz+bE0gZu28rG5P7F4TYztUyeMnbP0eKXiUeR0vXryIBw8eoEiRIvr1x48fz5W5rqQQj8wnGRgYiBo1auDw4cN4++238eGHHz7SPtk5bk7wc/fL3v0JMcCR31ODxVht5USdW6e2Y0F0L32a6bXYXxEbZPgFQFuuX6eYq6N2/OHDIFH3e0VvD5XaRkS2QQKF7nVKoWNNH/y+5wp+3HwB527dwyLHEhjpaA+HwBXAhU1A+7eBFi9lWPLclkhhnMuXL+PcOW36k058fDzq16+fK4/58ccfY+rUqWjcuDGCgoJQvXp1rF69OtMrxZbsk53jEhHla4/jomeAc2sAe0dgwG9A7cdNb5qiwQcrTmHBvmvq9od9auHZ1pXy+AkXDo+UtipefvllLFq0SF2hlB7HM2fOqF47SVvN6aI5r732mmrIDh48iOLFi2PLli0qXVamBunQoUO298nOcR81XSc5JRndlnZDcEywyfvtYKeCx3WPr4GDjFmUcYqVOyAuMRnXQiNQeXZtOCbHqm1j7dxwRFMDOxNrYn9KAE5qKiEpzXUBJwc7VPB+2IOoKppqA0TpRZQxiry6TERp3X0Qj283BqlqdNVxDZ84zUUT+4dBUskaQM+vgMrtbTrdUoJEuVh64YI2BcqwR1IuSm7YsCFHn+vOnTvRrl07bN68GZ06dVJTaUmWjwwfkTGW2d0nO8fNqfOYK0M4iMg2bJ0K7J4GDP4DqN7V5CYyBcfEpSew5PANlVU39fG6eLKZ5YVAbUVkTk7VoStRLtXjKlasmO4+meNReu10BXNq1qyJnCZPU3o633zzTUyaNEm/vkmTJurqrswrmZ19snPcnGg0D945iFHrR5ndbmbIA7SODsctR38Mcf4BN+/FQqZEnOC4CNEaV+xLqYVTmor6YLFUMVdtD2KacYiSZupog3PWENGjO3snEp+sCsSuC6F4wn4n3nP+G964r71z6EKgRnerPs2Wfn7LFFQyrr958+bILy+88ILKjpFF5/PPP8cXX3yBsLAw1U5nZ5/sHDengsefj/386EM4iMh2ehsjbwJeD4M/CWPCLwHeptNPE5NT8MbCY1h14raaguObQfXRv2HZvH3OtjrmcdmyZfjggw/U5MePPfaY0X1lypRRS26ScRjh4eHp0oAaNGig0mSzu092jqu72iyL4QnPCrnSaon7iMMDjSvOxZdA8INIpMAJRVwcsdHneRUUdixZBM897EGUxcPlkQvoEhEZqVmqGP54rhm2nA3Bp6uLoOPdxhjvuBhtnc8jxK4+WtrI+QoJCUGLFi1UBdXvvvsuX56DtEum2ispYHf9+nVUqFAhW/tk57iP2g4+8hAOIrItt44idOWrCE18gJSBsxF4/2JqpoImNl2mQnxSMl7+6yg2nglWGXg/Dm2I7nVK5/dfYfWyFGnIlce+ffuqALJr1/Rdw//++6/qyXviiSeQ0yQKFpJWasjb21s1btndJzvHFTIuZMqUKcguS1Nw1nm9jGMBfVDJ1wvzH1Y29SniwjRTIspTktreOcAPbav54I99V/HtJk98FhOLhDlH8FgtP7zbrTIqbX0FaDEOqNi60L46Li4uKo1TxjpKZfG0pOjaV199ha+//jpXHl/aLFPtlZA2y1SQZ8k+2Tnuo7aDuiEcmfU6Sq/Cj7s/RsCx4ygT0Ape1VoCrp6P9JhEZGXiIoGtnwIHfsViz6KYUdwTWD8i00yF2IRkvPDHIew8f1fNEDBzeGN0rOmb50+9MMpSHuPzzz+PAQMGoF+/fli/fn26+6V4zp49e5AbnJ2d9WlDhqRYjzTm2d0nO8cVkuIqja1ukSuzWdHIt5G6mipjG02R9aXcS+G7597Bu73rYWiz8mhR2Ru+RV0ZOBJRvnF2tMdzbSph+1sdMbRlVZUGJFd1F01/Dzi7CpjXE1j2IvAgpFC+SqVKlcKff/6pqoy/+uqr6e6PjY3FkiVLcu3xpc0y1V6JzNpCc/tk57iP2g6KIyFHMhz7r9jZIcw+GdGXZsJr6RB89O13GL/wGP7cfxUXzwci5eI2IDbjC71EZMUkJfXMCuCn5sD+mYAmBX5+mRcik+/WD+KT8OzcAypwdHNywNxnmzJwzK+eRwcHB8yfP1/1QEoAKT2NMpg+L5QvX149ftrGSW7LOMvs7pOd4+oa08yCS3Mc7B3U1ZEP95qu6KqBBmPqj1HbEREVNMU9nDGlXx0Mb1EBn64JxF/nOqCcJhhDHbfA/sQ/0JxbDbtO/wOaPAc4FK50+iFDhqiLeMOGDVM9kNOnT8+zx65cubLJ9kraZWnPsrtPdo77qO1gVoZwbHeujZIxN7E1qhwuH72JZUdv4nmHVXjP6S91/z238kjyqw/PKs3g7N8YKF0PcMnZon1ElIdkZgGZpzxonfZ28UpI7vkVZhz7AkhAhh0vPx+bgT82+eLYtUgUdXHE3JFN0aRiCb50OSjLFVSkIZk3b55qPB9//HGsXbsWecHV1RUdO3bE0qVL9eukGpxUhjMMYI8dO6aqpVq6j6XHzQ2ZXm214H4iovxWza8o5o1shu9HdsTcEq+hf/xHOJ5SGXbxUcDat4FZHYDrB1DYDB48GH///Td++eUXvPTSS7k+r6OOtEtSCVzaKZ3Fixejffv2cHd314/N/O+///Q9h5bsY8k2ucHSIRztn/oS3u+exocj+6lJvVtX9Ya9gyOupWj3Lx57DT5XVsJ58/9U77dmqj927NiK4Mg47QEehAIJ0bn2dxBRDnNy0xbHsXcC2r0FjNuLI0W9Mv1uLB0vIbHBOHn3KLzcnfDn880ZOOaCbF0OlgBy7ty56sqrBJASePXq1Qu5TcZXtG3bVqXPtmzZUjXaVapUwahRqVVL5Qrwvn371CTHlu5jyTa5YVD1Qejg3yHT8uRERNagQw1ftKlaEn8dqIBRG6qhe8IGvOW4EF53TiJ6w6fweG45CpuBAweqdvDJJ59UwaOksua2Z599FjNnzkS3bt3w4osvYv/+/di4cSO2b9+u3+bIkSOqbZYq6FL93JJ9LNkmN+iGcITEhKgvfhlNWyXbSSZO++o+ahFJyc1w9s4n+DvoEsIuHIDjnWOokHAede0vww/38PyaCMSv2ayqjX/hOhetIlYhoXhVOJdvDPsyjYAyDYFSdbRfUoko/10/qK2a6l5Cpayj97dAYizgUyNLmQrFisTir6EtEFCac9TmhmznEkkAOWfOHPVTCuQY9tzlFpk+49ChQyq4kzGXffr0UWNOpPdQR+ab9PDwyNI+lmyTW1dcdVdd65Ssk6uPRUSU22Q6oGdaVkS/+mXxw5YK6LqnOV63/wezL/ZB2xWn8VrnaijulAQ4ugCFJCVf6gAsXLhQBZCSwjpx4sRcfTxJE92xY4cq2iNzSPr6+qo5iuvWravfxs/PTw0t0c21bMk+lmyTGx5lCIe83+qU9USdsg2Bjg3VupsRsTh89R5OX7iCqjeTEXg7Uq1LcroKe4cUuN4LAmQ5/rf2+HYOSPEJgMPzm1KDSOlFli+uRJQ3ZNzy5inAoblAw+FAv4dDAXTTcWQxU2Fyj5YMHHORxfM8SnB4+fJlNR+iIWkspcduwYIFKr2lXr16uVZlrrBOMk1EVBhdCn2Az9acxaZAbZqRp5sTFpX5B9VSLsG+9zdA2cawps9vSQcdPXo0VqxYke4+SROVVFapRC6ZL1euXIGtKYjzPErhjGPXInDoajguXrqAlJtHUT35AuraXUJd+0vwsYvEdY0PxnjPRZMKxdG4Ygl0PfoyXOPDtD2TamkA+NYCHJyy9RyIKAMSgpxaCqybBEQ/LLLWYBjQ90eTFxilOnO3pd0yzFSQVSXd/LBp0HrWDMnFz3CLg8fMyCEkgJw9ezYmTJjA4JHBIxGR3u4Ld/HxqjO4fec2dri8Dk+7GGik0nTjZ2HX+QNtilIhuPinCyBl3mMGj5afR0lFC40NzXQIh6U9DuYkp2hw9k4kjly9h0NXwnH1ygVoIm/juKbqwy00OObyArzsjMdHahxcYCcprpXaAV1M95ISURaEXwJWTwAuauuUwLsa0Ps7oFLbTHdbGrTUdKaCRDN2wIctP8SA6gP4UuRiW5gjJfBkzMesWbNUgyllzImIiHRaVy2J1a+2xcKD1zFo/fcYk/g7nnDYBRyei6TT/8Gx60dAg+EyHsKqT1r//v1VFfJ//vknv5+KVcnLIRwytUztMp5qebplRRl1iTv341TP5KEr93D4Sjj63pmK2riIevaXVA9lPfvLKJYcA9w8jKsPHHC1fCgalvdCUVcnYOFwoGiZ1F7KktUKTUo2Ua45v1H7fycpDnBwAdq9CbR+TTukwYwMC+Y8zDRnscncZ1HPY1xcnBr70KpVKzWthTkXLlxQAaUUnbEVTFslIrLgszIuET9tvYCTu9disv1s1LC/odYnlm4Mp0G/ASUqF9jPb5nHuE6dOhb1TkZERODs2bNo0aIFbEVhaQej45Nw/EYEDl+5h0NX7+HItXCUiL+JenaXEAU3bEtpCHs7oKmvBgvvDzPe2ckDKF1fG0hW7axdiMhYTDgwvSngV1vb2yhFciy07cIFfL7hAIJCImHveguliydjdKs6aFy6bo5nKtiayJxMW5WDVK2qTemQYjIyEF/Gdbi5aQeXyyEkuFy+fLlK27l48aIqYS7V3mxFYWk0iYjywtWwaHyx+hTKnPsdrzsuRZKdI1a0XYkn2zeAs6N9gfz8fuqpp9T4f5neSdpBWSTjxnBeRBkPKe2gVCkdPny4KixnKwprO5iSokFQSJS2Z/KqdrkWHgN3xOEx+0OqZ7KO/WXUtb+i1ukkNx4Jhz7TtDcS44Ctn6T2UBavxKI8ZFvBohSpajEu9X0fcQ3w9Lf4/0FoVDy+XHcWiw9rLzgWcXFURdhGtKqY521GYZXjYx6lMM7u3btVgCiN482bN1UAKRXZVq1ahdjYWPTs2VM1pt27d9dXebMVhbXRJCLKTfsuheHnFTuQFBKEPSl1UNHbHZN61ERXl9Owk16bPKh6mZXPb7k4Ku2gLNITKRW+W7dujZ07d+LEiRNo06aNPrCsWFHSIm2HLbWDIZFxKog89HA5ffM+UlKSUdnuluqhlOlCDtjVR4R/ZzSpWBwdilxD4w0DUw/g6mlQkKch4N8CKOqXn38SUc6TEEOCxg3vAzFhwMA5QJ2sjUdMTE7B73uu4PtN5xEVn6TWDWhUDhO714BvsdydFcHWROZ2wRyZP0oaz+DgYNUb2a5dOzg65sgQSqtkS40mEVFOkiImS4/cwFfrz6mry93sD+AX52mIKdUU7o9/r01tKoCf32FhYVi9erUKIiVolPmOixcvDltly+1gbEKyNtX1Yc+kLPdjE/X3V7G7iWcd16OZ81VUSbkCR03qfcpjHwOtX9X+/iAEuH5AG1QWK8MeSrJOd88Dq94AruzU3paKxX2+B/ybWXyIXefv4sOVp3Eh5IG6XbesJz7sWxuNK9ju52yhqbZKtt1oEhHlBJlWYea2i4jYNQvv2s+Hu108kuGA+Eaj4d71fcA1dz5b+fnN85gbqa4XQx9oeyZVums4roTFqPuckITqdtdV72Qzl6to4nQFJ2pPRNkGXVQhH+fAZcDS51K/cDd4Cqg3BCjim+PPkyjHSYr2rm+BXd8ByQmAoxvQYSLQ8mWLp7u5Hh6DT1cHYt3pO+p2CQ9nvN2tBgY38Ye9DDimXMHgMY/xywcRUc64cS8Gv6zYjpYXvkVPhwNqXbSzN5x6TIVzg8GqJyYnp3fg53fO4HnMnPSqa3slw9XPkzfvIzHZ+Pq9q+sDDPA+jG6JG3BHcxf37QGv5BQEJCbDvnwL+NQZDJ/agwBH5xx61Yhy2F9DgKB12t+rPgb0+hooXtHiHvyZ2y+qJT4pRVVHfrpFBbzRpTo83TnPam5j8JjH2GgSEeUsmYdv1bL5GBHxMyrZa8uzX6s4CP4jZqlJ5XNqYnl+fucMnsesiUtMVgGkrmdSAspo9zVw8dmc4T5j793HuBE7LP4yTpTnLu8Alr0AdJ8K1OpvUdq1JEGuO3UHn6wOxM2IWLWuZWVvlaJao5Rt1VCxmXkeiYiIclqTiiXQ6PXXsPJIH2xY+xVGJC3Be0FVEPfLXrRtmHkKq587i49Qwebq5ICmFUuoBaiivkDPPHIXP58yETw+7KB0K1YLKZ4VoK8tuf49bcXKuoMAD++8fPpEkp8NHP0D0CQDTUZpz0ildsCrxwAny4rZBAVHYcrK09h9IUzdLuPpivd61ULPuqXUtH9U8HDMYw7hFVciotwTk5CE+RsPYdq+e4hLTIJH1S9g73hfPzG0ITvYqeBx3YB1cLBgwnZ+fucMnsdHk5ySjG5Lu2U4yblUqNAkeaJE+BQ806ISBtd0gueM+tov7vZOQI3uQIPhQNUugAP7BiiXhQQCK18Hru8DnNyBlw8CnuUs3l0KSkkF1d/3XlFF02S6jTHtq2Bs+ypwczb/uU05jz2PRERUaLg7O2JMrxbo1yYW76z+D0cS72e4rQYa3Im5gyMhR9C0VNM8fZ5E2SXv14wCRyGdMHZO93Er7jQ+XROHmRvj8UG5V9A1cTPc7p4EAldqFw9foP4QoNGzQEntHN1EOSYhBtjxJbDnRyAlCXDyADq+CxQpZXExqcWHr+PLdecQFp2g1nWt5Yf/9a4F/xLufKGsAC9NERGR1Sjt6YYhLTxx5GH198xIUR0ia2Hp+/WpVl44dLoYAm9H4rXLMu1BMwwoG4FxXvtR+fZq2EWHaL/Ye1Vg8Eg56/wmYPV4IOKq9naNXkCPLwAvf4t2P3rtHj5ccRrHb2gv/lXx8cDkPrXRrrplxc2oYGDwSEREVsXSKqqWbkdUEFj6fu1bJwAfdW6iCuz8vvcq1p68jaU3vbD0ZjeULtITkwKuo2viVrjWHZi609EFwIXNQINhQJWOgAXp3ERG7t8E/n4SSEkEipUFen4F1OxlcaXhL9adxZLDN9TtIi6OeL1LNTzTsqJKVyXrwuCRiIisSiPfRmpMY0hMiEpRzWjMo2xHVBjf11JIRApKyRLSKwB/7r+Gvw5cw+2oeLx6tAwc7Yejh8MVjGipUROq2x2aC9w8BJxeBhQtA9R/UhtIMq2VMiMDbXVFazzLAm3eABKigY6TABfzVVATk1Pw+54ramxjVHySWjewcTm83b0GfItaVlCHCh4WzMkhLBRARJR3lgYtxYd7P8zw/g9bfogB1QdYdCx+fucMnsf8fV8nJKWoSdXn77mCQ1fv6dfXKl0Mr9eORqe4zXA8vRiITb0P/s2BRs8ADYfnwLOnQuX2CWDNm9oextL1s7z7zvOhmLLyDC6EPFC365XzVFNvNCpfPBeeLOUEFswhIqJCK7PCIpbcT1TY3teS/te3fhm1nLp5H3/svYr/jt3EmduReOE24On2GJ5qPByjfM7B58IS4MJG4Pp+wNXLOHg07G0i2xP/ANg2Fdg3Q1vJd8P7wIiVFu9+PTwGn6w+g/Wnte9Vbw9n1dM4qLE/7O35vioM2POYQ3jFlYgob4uLhMaGIkWTgsCwQETER8DLxQsB3gGwt7OHj5uPxWPI+PmdM3geC9b7WkTEJGDxoRuYv+8KrodrJ1+XuLBTDV+MbuiO5lGbYF+6LlCl08MdrgHzegH1JK31KaBEpRz4q8hqnFsLrH4TiNSOTUSt/kD3z4Fipc3uGpuQjBnbL+KX7RcRn5QCB3s7PNOyAl7vUh2ebk65/9wpzz7DGTzmEDaaRETWiZ/fPI+Fncyjtz0oBL/vuYrtQalVXSuV9MDTLSpgQONy2i/4O74CtnySumOF1tqxkbX6AS5F8ufJU94Uw1n7NnB2lfa2V3mg5zdA9a5md9VoNFh76g4+XR2ImxHaCxQtK3urFNUapcyPi6SCg8FjAT3hRERUsPDzm+fRllwKfYAF+65h8aHr+iIm7s4O6N+wLEY09UWNezuBY38CF7eqWVMVmcuvdn+g8wdAUcvm8yMrcmCWdnyjvSPQ6hWg3duAs/k5F4OCo9TUG3suhqnbZb3c8F6vAPSoU0oVdSLrUmiDx8TERGzbtg3BwcGoW7cu6tc3P4j35s2bOHDgABwdHdGkSROULm3c/b57924EBgYarStRogSeeOIJi58Xv3wQEVkna/z8PnHihFp8fX3RsWNHODllnhYWExODffv2ITQ0FAEBAahXr57R/bdu3cKaNWvS7Tdo0CB1bgrrebRl0fFJakzk/D1XcS44Sr++eaUSGNGqIh4rlwSnkwuBY38B4Re1AeSbQak9kIlxgBMrZlqthJjUADElGVjzFtB0NOBXy+yu92MTMW1TEObvvap6tWW87Zj2VTC2fRW4OXMaGGtVKAvmhIWFoXPnznjw4IEKHF966SU8/fTTmD59usntJS5+5plnsHPnTjRq1Eg1nvL7559/jldeeUW/3R9//IH169erY+uULVs2S8EjERFRXnj99dcxd+5cdOrUCadOnYKrqyu2bNkCHx/TY+Fk2ylTpqBy5cpqm02bNqF169ZYsmQJnJ2d1TZnzpzB888/j+eee85o3969e1scPJJ18XBxxLDmFfBUs/LYfzkc8/deUUVO5HdZShVzxbDm/fDksy/DJ+I4EHYhNXCUfoffugAe3tq01pq9LeqpogIgLlKbmnx+AzB2j/Z1k3k/e39rdteUFA0WH76OL9edQ1h0glrXrbYf3u9VC/4l+PrbCqsKHidNmqR6Ho8fPw4PDw8cPHgQzZs3R69evdCjRw+TwWO3bt0wb948ODhor4TI79I4yj7SkOo0btwYv/32W57+PURERFmxYcMG/PDDD6oXsVmzZoiOjlY/33nnHcyePdvkPiVLlsThw4fh7e2tbt+4cQN16tTBjz/+iAkTJhhty3bQ9kh6YYvK3mq5fT8Wf+2/hr8PXMOdyDh8szEIP2w5j151S+OZVj3RUKPRpiOGXQSCT2oPcGkb4FIMqP24NpD0b8ZqrQWRBPxnlgPr3gGibmvXBa0F6lg2pdGRa/dUiuqJG/fV7aq+RTC5Ty20rWZ5AScqHKwmbTUlJQXFixfHBx98YNTYtWrVClWrVsX8+fMtOk5ISAj8/PywevVq9OzZU60bM2aMSlt98cUX1RVWSW2VbbKC6TpERNbJmj6/R44cibNnz2Lv3r36dd9++y0mT56MiIgI/YVSc9q1a6fazjlz5qjb0hv52GOP4b///kN8fDxq166tlsJ6Hilz8UnJWHvyDn7fewVHr0Xo19ct66kqaPapXwauD24Ax//Wjo+UKq063lWBLlOAgN48zQWlCu+9q9oxjdLbKEpUBnp9C1TpaPaxQ6Li8MXac1h6RFuBtaiLI17rUk2lNjs52PM1LkQKXdrq9evX1R9Vq5ZxLrY0bnJF1VIypsPe3l6lvRq6ePGiajRlfOTRo0fx9ddfY9y4cRkeRxpXWXTkuREREeUmSVNNO15R2kEZznH16lWjjJqMSM2AI0eOYODAgUbr3d3d8csvv6j6AJIG27VrV/z9999wcXExeRy2g4WXi6O2gI4sJ25EqLFtK47fwsmb9/HWkhP4bE0ghjQtj+EtXkU5Ka5ydbd2bOSZ/7TprQ7adGglNgJwdOX4yEewOGgxZhyfkeH9Y+uPxbgGJr6zpqQAe38Etk4FkmIBeyegzRtA2wlmX4/E5BT8vucKpm06jwcPCysNbFxOzdnoW5RjXW1ZvgaPO3bsQFBQUKbbDB48WEW/uuBMeh/TFraxNHCTxxo/frwaL+Lv769fP2LECJW+oys4MGvWLIwdOxYtWrRQYyVNmTp1qhpDQkRE9CgXRmXMfWYkLVUXMEp7Z6od1N1njgz9GDZsGMqXL4/Ro0fr10vQee7cOZQrV07dvnTpkhrO8cknn+Djjz82eSy2g7ahXjkvfD3IC+/2DMDCg9exYN9VNSXDzO0X8euOi+gc4IcRLQPQuv/PsOv5JRC4KnXeSLF7GnBoDlBnINBwGFCmEdNas8jP3S9799vbA9f2awNHmXal93eATw2zj7fzfKhKUb0YGq1u1y/nqabeaFje+LOHbFO+Bo/S2yfjNjLTr18/9dPNzU39jIpKrQimu627LzNXrlxBly5d1PLll18a3deyZUuj21I04L333lNjSzIKHmX8pQSiOtJoGwakRERE5ty7d89sOygF3HTBo7R3ptpB3X2ZSU5OVoHj+fPnsX37dtXTqJO2x1JuDx06FGvXrs0weGQ7aFtKeDhjbIcqeKFdZWwODFa9kbsu3MXGM8FqqeLjgWdaVsQTjQaiqIPB18sru4G4+8Ch2drFJwBo8BRQbwhQNGtDhGxRckpypr2OdrDDzOMz0b9qfzhI4ZvYe9rxje7ai0qQgL5mL+05NzN9xvXwGHy86gw2nAlWt709nDGxe03V42hvz6k3qAAEjzJ2QxZLyFVS6RmUINDQ5cuX1biNzEgqT4cOHdTV27/++suiMSHSCIeHh2d4v6TxZJTKQ0REZAkJCrNSpEbaO1PtoKSaVqhQwWzgKIGqTHdVsWJFs4/FdpBMcbC3Q9fapdRyISQKf+y9iiWHb6heqskrTuPLdWcxoHE5NTayqm9RYNQ64PIO7djIwJVAaCCw8X/Apg+BeoOBx2fyRGfiSMgRBMdogzlTNNDgTswdHAk+jKahV4H1k7Q9v0/8qt3As5y2xzcTsQnJmLHtAmbuuISEpBT1Go9oWVGNbfR0y3waILI9VjPSVcqJS+XUf/75R1VRFbdv38bWrVvRp08f/Xa7du3CsmXL9LevXbumAkcpgiP7SgObtkGVtCFDUohA1qXtkSQiIspP0t5Jr6G0fzoyLlGK3ciUHbpqqhKQStEDXTs3fPhw7NmzR7WZpsZFpg1IY2NjsWLFCraDlCkJDqf0q4N973bGR/1qq97H6IRk1SvZ5dsdGPbbPqwPDEVSxfbAgN+080T2ngaUawpokgHnh1N/CPlud+cUz7iJYjmWCN0wCVg2GogOBW4dA+KNMxRMke/Tq0/cRudvtuGHLRdU4NiqijfWvtYWH/SpxcCRrLvaqm4eKqmuKnNbyXjE33//HV5eXuoqqm68oozhkCurUlQgLi5OlSOXlB4Zn2gYOLZt2xY1atRAUlISGjRooI4rRQck2Pz111/VVB7SSynFdSzBKnNERNbJmj6/pc2SNvDu3btqvP6BAwdUpVS5cKorBLdu3To1fZVUEa9ZsyZee+01Na5fpvMwDBxlqIVclBVSC0DGPLZv3159oZT5j6UgzubNmy3qpbS280i5Q947ey6GqUIrmwKDkfLwG2ZZLzcMa1EeQ5r4w7vIw6yt0CDA0QUo/rDH/OpeYG53wK+u6ikLrdoJoXbJ2a8wWkgcvHMQo9aPMrvdnNvBaJoopZTfAlq/qj23mTh3J0qNa9x7KUz/Gr3fKwDd65TSTsdCNieysFVbFVJp9cSJE2quRklFfeWVV1Taqy5w1AWFMj5E18hKr6M4dOiQ0bGkQZXgUQJKqda6cOFCVWVVChHI1daOHc2XLyYiIspL0mZJsCjtoMx5LGmvMlWHYcqqBIUyn7FcXBVSBGfUqFFqqipZdKRCqy54nDZtmurR3LhxIxISEjBx4kQ8+eSTHJ5BWSJBR+uqJdVy414M/tx/Df8cuKYK7MjE8lK5s0+9MhjRqgLqlatuvHPIGW2VVpk/ct07WFy8OGZ4Fc16hdFCppFvI1UQJyQmRKWopmWn0cAvORmNSrfQFsTxrpLp8e7HJuK7jUH4Y99VJKdo4OJojzHtq6jFzdmyqX7ItllVz2NBxiuuRETWiZ/fPI+Ue+ISk7HqxG3VGylTfeg08PdSQWTPuqXV1CBKTDhwaqkaH7k08hw+LOmtXW+iJ+xD+9IY4FhSW1HUzgGQYjHy08EJ6P9z6oaH5gLBp1PvT7t9+4mArsDPuXXA3XPG9+u2t7MH6j+Z2qN387B2/kT9dg6p28k+5VulToch20k6qbrPcLuHv3uVBxwfTm8SFwkkyrQaqdssvbQKHx78PP3JffgV/sPyfTCg42eZFsSRQHHxoev4cv05hEcnqHXda5fCe70C4F8itXgW2a7IwtjzSERERETWw9XJQVXrHNCoLI5d184ZKePs5PdjCyPwyapAPNnMH8OaV0AZrxJAs+eR3GQUZizqBMSbLlwoIdLMhOvof3E/0vWV2TsaB4/nNwDn1mT8BNu/nfr7ycXAqSUZb1urX2rweHgecGR+xtuODwScymh/3zcD2J9xxVS8fBgo+bD4467vgF3fGt0d7OUJFPdMv9/DYDG4hH+mgeORa/cweflpffBe1bcIPuxTG22qlcz4ORFlgMEjEREREeV6SqvMEyiLds7Ia1iw7xruRMbhp60XMXP7JTwW4IdnWlWAo/slBGcQOArpb7vj6IgjHcejqVsZbQ+cFOBJSU6/ce0nAL/a2vtkG00KkJKS+rv07ulUaKkNPvXbPdxHbZ+iTavV8a6qnTtRbfPwePrH0Bhv6+YFeJZPf1zdc5FeRqO/ztigqCh0iIlBCoDAx/6HCBf3dOM/TQmJisMXa89h6ZEb6nZRF0dVQXVEq4pwcrCamplUwDBtNYcw7YmIyDrx85vnkfJHUnKKmiPy971XsO9SarBYrtxZ3C86z+z+X7T9Aj0r90ShJAGoPng1CFClQq1RsJmeVE2VNOHvN5/Hg/gktW5Q43J4u3tN+BTlNHNkGtNWiYiIiKjAcnSwR4+6pdUi1T/n772Cf4/exO1wJ7hnXCtHr1BXW5U0VDUWM2tJgjuCQvHhytO4FBqtbtcv56mmU5ExpkQ5gWmrRERERJSvapQqik8fr4uJPWpi8aGq+D5oIVLsIzMcyucCL6za74qd7kFqPkJZirk6an/qbrs5wcPZwSamnrgWFoOPV59RPbnC28MZE7vXVONN7e0L/99PeYfBIxEREREVCMVcnfBcm6o4k9QCG65uyHC7B/f98XvgNbPHc7S3U0GkYWCpDy5ddUGmo9Ft/Xaujqp3tCCLTUjGjG0XMHPHJZWu6mBvh2dbVcSrnaupv4MopzF4JCIiIqIC5Z1m76BOyTqYd3oewuNSx0MWcSyOZsUfR4VybZBUvSgi4xJxPzYJkbHyM1Hd1v2emKxBUopGTU2hm54iq6Tn0uKg0934Pjen3Ov1lJn2Vp+8jc9WB+LW/Ti1rnVVb1VFtZqfBTm/RNnE4JGIiIiIChQZzziyzkg8U+sZHAk5gtCYULWukW8jOJgpGKMLruISU/QBpfr5MKjU/p5k8j75GRmXpC80E52QrBZdgJYVTg52+uDSOPjUBp2emQSkRV2dVC+iKTI+9MMVp7H3Upi6XdbLDf/rHYButUvZRIou5S8Gj0RERERUIEmg2LRU0yzvJ0GUm7ODWkp5umarEmxUnHGAaSro1AecD4NO3brkFI3q+bz7IEEt2SFTa6QGnY4qwLS3s8PGwGB1fBdHe4ztUAUvtqui/k6ivMDgkYiIiIjI8Auygz2KezirJauk1zMmITk1yIxJDSyNej8fptimDUhlXxEVn6SWmxGx6R6jR51Sar5M/xLufN0oTzF4JCIiIiLKIdLr6eHiqJYycMvy/lL4JkqXTpsm6JTe0EblvdC8sjdfL8oXDB6JiIiIiAoIZ0d7eBdxUQtRQVOw6w8TERERERFRgcDgkYiIiIiIiMxi8EhERERERERmMXgkIiIiIiIisxg8EhERERERkVkMHomIiIiIiMgsBo9ERERERERkFoNHIiIiIiIiMssRViYmJgarV69GcHAw6tati/bt22e6/aZNm3Ds2DGjdSVLlsSzzz77SMclIiLKLzt27MCJEyfg6+uLXr16wcPDI8Ntr127hkWLFqVbP2rUKJQoUSLbxyUiIttjVT2Pt2/fRv369fHpp5/i8OHDGDRoEIYPH57pPkuWLMGsWbNw584d/RIWFvbIxyUiIsoPcvFzwIABqr2aOnUq6tWrh5s3b2a4fVBQEN566y2jdlCW5OTkRzouERHZHqvqeZw4cSKKFi2KvXv3wsXFBadOnVJB38CBA9G/f/8M95OexK+//jrHj0tERJSXVqxYgT/++APHjx9HnTp1EB8fj5YtW6p2bMGCBZnum1k7+CjHJSIi22E1PY9yhXTZsmUYMWKECvCENHBt2rQxmY5j6NatW/j555/x559/4uLFizl2XCIiory0ePFitGrVSrVTQtqtkSNHqnYsKSkp031///13/Prrr9i9e3eOHpeIiGyH1QSP169fR3R0NGrUqGG0vmbNmggMDMx033v37qlxj3/99Rdq1aql0nEe9bhyVTYyMtJoISIiyk3SLplqr2JjY3H16tUM9ytevDjWr1+PXbt2oU+fPujcubNq+x7luGwHiYhsT76mra5bt06liGZm9OjR8PLyQlRUlLotvxsyvM+UsWPHYsaMGbCzs1O3Fy5ciKFDh6Jjx45o0aJFto8rAeiUKVMs+CuJiIhMu3Tpkurdy0y7du3QrFkz9bu0S6baK919plSvXh3nz5+Ht7e3fpx/gwYN8OGHH+Krr77K9nHZDhIR2Z58DR7v37+vBu1nRjeg393dXf1M28Mnx8isGpyMXTQ0ZMgQvP7669i8ebMKHrN73EmTJmH8+PH627K/v79/pn8LERFR2t47c+2gYQ+htFmm2iuRUZtVvnx5o9ulS5fG4MGDVTXyRzku20EiItuTr8GjBHKyWKJChQpqDEbaMYtyu1q1all6XEdHR30jmd3jyj66MZJERETZERAQkGkhm7QktdRUe+Xs7Kzas+y0g9k9LttBIiLbYzVjHqWhkzmnpOhNSkqKWnflyhVs374djz/+uH67DRs2YN68efpey7NnzxodR6603rhxQ6UBZeW4RERE+a1fv37YuXOnaqeEtFtSJbVnz54q0BNynwSk4eHh6vbp06eNjiFBo6TK6tpBS49LRERkp9FoNNZyGuQqqFSDk6k3ZPzHP//8o3oH16xZAwcHB/0YyX379qmxlFIhTrarWrUqateurSZKlqI5Ull15syZWTquOdIYe3p6qjSfYsWK5do5ICKinGVNn98S1PXu3VsVuHnyySdx6NAhVRBuz549+mwZqSfQo0cPtY0UvXnvvfewbds2tG3bFtLky9h/+XvXrl2LMmXKWHzcwnQeiYgoe5/hVhU8itDQUPz9998IDg5Wwd6gQYOMAjwpNy5B4oQJE/QN4qpVq3D06FFVbU6m4GjUqFGWj2sOG00iIutkbZ/fklWzdOlSNSejr6+vKgInP3XOnTuHWbNmqTkafXx81DoJBCXzJiEhQV1MlUAxbRtn7riF7TwSEZENBI8FFRtNIiLrxM9vnkciIlsXaWHwaDVjHomIiIiIiCj/MHgkIiIiIiIisxg8EhERERERkVkMHomIiIiIiMgsBo9ERERERERkFoNHIiIiIiIiMovBIxEREREREZnF4JGIiIiIiIjMYvBIREREREREZjF4JCIiIiIiIrMYPBIREREREZFZDB6JiIiIiIjILAaPREREREREZBaDRyIiIiIiIjKLwSMRERERERGZxeCRiIiIiIiIzGLwSERERERERGYxeCQiIiIiIiKzGDwSERERERGRWQweiYiIiIiIyCxHWJmwsDAsWrQIwcHBqFu3Lh5//HHY22ccA0+ePBnx8fHp1jdr1gxPPPGE+v2///7Dvn37jO4vVaoUXn/99Vz4C4iIiLIvJSVFtVsnTpyAr68vBg8ejJIlS2a4/eLFi3H48OF0693c3FQbKS5cuIDffvst3TYTJkyAj48PXy4iIrK+nsfLly+rgHHhwoWIjo5WjVqfPn1UQ5oRT09PeHl56ZeEhAR88cUXuHnzpn6bdevWYfXq1UbbFS1aNI/+KiIiIstoNBr0798fb7zxhmoHJTCsU6cOLl68mOE+7u7uRu2bLHPnzsWWLVv021y5ckW1jWm3c3Bw4EtDRER6dhppiayEXF29ceMGdu7cqRq0S5cuoUaNGpg/fz6GDh1q0TG+/PJLdaX11q1bKF68uFo3ZswY3L17F0uWLMn2c4uMjFSB6v3791GsWLFsH4eIiPKWNX1+S+bNsGHDcO7cOVSuXBnJyclo27YtSpcujaVLl1p0DAk0q1WrptrO4cOHq3WbNm3CY489poJTWziPRESUvc9wq+l5TEpKwsqVK1VDp7sSKg1n+/btsWzZMouPM2fOHAwcOFAfOBpedf3oo4/w/fffm0zvISIiym/S3kmwKO2fkPbwmWeewapVq1RmjaXtoHxBkLYwrW+++QafffYZli9frgJTIiIiqwwer127hri4OFStWtVovdwOCgqy6Bi7du1SV2uff/75dPe5uLio4x85cgStWrXCm2++memxZBylROiGCxERUW6S9s5UOyiB49WrV83uLwHhvHnz8PTTT8PV1dXoPn9/f3UMycR5+eWX0bRpU0RERGR4LLaDRES2J18L5mQ0iN/QW2+9BW9vbzW2Q6TtRpWrp7r7zJFiANWrV0e7du2M1kugaNgYP/XUU+jevTt69+6NDh06mDzW1KlTMWXKFIsel4iIyJSzZ8+qYC4zPXr0UFk2Qto7U+2g7j5z1q5dq4ZtpL2IKuMmAwMD4eHhoW5/8MEHqFevHt5//31Mnz7d5LHYDhIR2Z587Xk0NYg/o8H6RYoUUT8lD9eQXBXV3ZeZqKgoFaya6nVMexW3W7duKFu2LHbs2JHh8SZNmqSei265fv26xX83ERGRcHJyMtsOSmaMjrR3ptpB3X3mzJ49G82bN1fF59JWGNcFjkIeVyqSsx0kIqIC0/PYq1cvtViifPnyqmGTtFMJ7nTkdkBAgNn9//77byQmJmLEiBEWPZ6k9kgaa0akMTds0ImIiLKqSpUqeOeddyzeXto7afcMyW2ZdqNixYqZ7hsSEqIqi8+YMcOix2I7SEREVjvmUXogZU5HqQ6nKwpw5swZNY5x0KBBRsUEpk2bZvJqq5Q3TztflRTiSTvHo1Ssu3PnDjp37pxrfw8REVFWSXu3Z88e1f4JaQ8l7VXaN0dHR/24SAlIQ0NDjfb9/fff1TjHIUOGpDuuHNNw2iuZS1myddgOEhGR1U7VIXMzSpU5qZTauHFjrFixQo1JlF5FOzs7tc3o0aNVMHjq1Cn9fvK7pOhs2LBBlSJPe2VVGkd7e3vUrl1bFeZZv369Ggf5ySefWPzcWKKciMg6Wdvnt0zVIVNr9O3bF0ePHlUFbmQKKyl4o5u7WMZJyhjGmjVrGvVaypj/X375Jd0xZY7HBQsWqJRW+Vog1VZlHKRckC1RokShPI9ERJT1z3CrCh7FgwcPVNAoV0UlIOzSpYvJYgDPPfecft2BAwfUuI0JEybog0xTV12lEZbAtEWLFvoy6JZio0lEZJ2s8fN7y5YtOH78OHx9fdGvXz+j8Y6XL1/GwoUL8cILL+gDP/nbJF11wIABao5HU2TKqm3btqneTLmY2rp160J/HomIqJAHjwUVG00iIuvEz2+eRyIiWxdpYfBoNWMeiYiIiIiIKP8weCQiIiIiIiKzGDwSERERERGRWQweiYiIiIiIyCwGj0RERERERGQWg0ciIiIiIiIyi8EjERERERERmcXgkYiIiIiIiMxi8EhERERERERmMXgkIiIiIiIisxg8EhERERERkVkMHomIiIiIiMgsBo9ERERERERkFoNHIiIiIiIiMovBIxEREREREZnF4JGIiIiIiIjMYvBIREREREREZjF4JCIiIiIiIrMYPBIREREREZFZDB6JiIiIiIjILEdYmbt372LevHk4e/Ys3nrrLdSoUcPsPteuXcPvv/+O4OBg1K1bF88++yxcXFyyvA0REVF+S0pKwvLly7F+/Xp06NABTz31lNl9EhISVNt54sQJ+Pr6YsSIEahQoUKWtyEiIttmVT2PP/30E+rXr48zZ85g9uzZuH37ttl9ZFvZ58iRI/D398cPP/yATp06ITExMUvbEBER5Tdpr6pUqYIFCxZgw4YN2LNnj0XBZpcuXTBt2jTVxh0/fhz16tXDqVOnsrQNERGRnUaj0VjLaZDexkqVKiE0NFQ1blu3blVXXTPTp08fxMTEYNOmTbCzs1MBpxzj559/xqhRoyzexpzIyEh4enri/v37KFasWI78vURElPus6fNb2j+5sFmmTBm0aNECTZo0wfTp0zPdR7JqXnjhBVy5cgWlS5dW6yRQdHZ2xpo1ayzepjCdRyIiyt5nuFX1PNasWTNLqaSSgiNpPU8++aQKCoU0ih07dsTKlSst3oaIiKgg8PHxUYFjVkhbJhdadUGhGDp0KDZu3Ii4uDiLtyEiIrKq4DGrZByjXKGtWLGi0XrpVbxw4YLF25gSHx+vInTDhYiIqKCRtsxUGyepqlevXrV4m7TYDhIR2Z58LZgzd+5c7N69O9Ntpk6dqq60ZkdsbKz6WbRoUaP1clt3nyXbZPS8pkyZkq3nRUREJKQ4jYyzz8yAAQPQo0ePbJ8wactMtXG6+yzdJi22g0REtidfg0cZ9J+cnJzpNo9S8VSXr3vv3j2j9eHh4fr7LNnGlEmTJmH8+PH629LzKOMwiYiILFW8eHE1djEzZcuWfaQTKm2ZqTZOd5+l26TFdpCIyPbka/DYrl07teQWCeak0ZPqdIZXbU+fPo06depYvE1GQS2n8iAiokdtp0aPHp2rJ1HaMmnjDEkbV6RIEf1UHJZskxbbQSIi21PoxjxKxbjJkyer3+3t7TFkyBDMmTMH0dHRat3Bgwexb98+VQjA0m2IiIishQR9EpDeuXNH3Za2bP/+/aptE1JdXNq8wYMHw8HBweJtiIiIrGqqDpnPShozadT+/vtv9OzZU1WG69u3r1qENJgS+Onmprp79y46d+6sAkOZs2rz5s0YPny4mjNSx5JtzGGJciIi62RNn99SpOall15Sv69YsULVBGjZsqVKbdWNw1+3bp3KpAkMDFRVysVrr72GefPmqTmMpX10dXXFli1bjGoKWLJNYTmPRESUvc9wqwoez58/j+3bt6db36hRI7WIXbt2ISQkBE888YT+fqmmKnNCBgcHo27dumjQoEG6Y1iyTWbkRHt5eeH69etsNImIrIhuzHpERIRqOAsyqX4qAV5aJUqU0Ld7N27cUAHkoEGDjP4eKc5z/Phx+Pr6qgDRyckp3XEs2SYjbAeJiAp/W2hVwWNBJo01C+YQEVkvufhXrly5/H4aVovtIBFR4W8LGTzmkJSUFNy6dUuVNrezs8t2tM+ey5zB85mzeD55Pgvz+1OuoUZFRaFMmTJqHDzlTzso+FmTs3g+eS4LKr43C975tLQtzNdqq4WJnOScuGItLzjHiuQcns+cxfPJ81lY358FPV3VltpBwc+anMXzyXNZUPG9WbDOpyVtIS+xEhERERERkVkMHomIiIiIiMgsBo8FhEy2LPNTyk/i+Sxo+P7k+SzI+P4sPPha8nwWVHxv8nwWZC55GEewYA4RERERERGZxZ5HIiIiIiIiMovBIxEREREREZnF4JGIiIiIiIjM4jyPeSguLg5nzpxBkSJFUL169Vzbx1ZERETgwoULKFWqlNm5xcLDw9V5TKtZs2ZwdnbOxWdpPe7evYuzZ88iICAA3t7eFu1z+/Zt3LhxA1WqVEGJEiVy/Tlak8uXL+PmzZto2rSp2QHsp0+fxr1794zWyfmsVatWLj9L6xAdHY3z58/D19dXTV5s6YT18n8+OTkZderUgYODQ64/T7LMuXPn1Gtau3Zti4s7ZGcfW5CUlKQ+PxwdHdXnhZ2dXabb7969W00Ebqhy5coW/7+yhfN5+PBhNdddzZo1LdonJiYGgYGB8PLyUm0hpXrw4AGOHz+OChUqmP2eFhISgqCgoHTrW7VqlemE9bYiOTlZtYNyLuT/rPyft4R8R7tz5w6qVauWc/MZayhPrFy5UlOiRAlNlSpVNF5eXppmzZpp7ty5k+P72IqvvvpK4+rqqgkICNC4ublphgwZoomPj89w+3///Vdjb2+vad26tdESEhKisXWnTp3SDBs2TFOqVCn5RqFZvHix2X2SkpI0zz77rHoNatWqpXFxcdFMmTIlT55vQbdp0yZN165d1f9dOZ+XL182u0+3bt00ZcuWNXpvvv322xpbd/PmTc3TTz+t8fT01DRo0EB9DrZt21Zz9erVTPc7ffq0pmrVquo9Lee1fPnymoMHD+bZ8ybTbt26pWncuLGmePHimsqVK2u8vb01a9asyfF9bMX+/fs15cqV0/j7+2v8/Pw01atX1wQGBma6j4ODg6Z27dpGnzWLFi3S2Lro6GjN5MmT1WdF0aJFNQMGDLBov3/++UdTrFgxTbVq1dR+7du314SHh2ts3fXr1zXjxo1Tn8FOTk6aqVOnmt1n7ty5Gmdn53Tf02JiYjS27tNPP1XnsmbNmppKlSppypQpo/nvv/8y3ScuLk4zcOBA9R1ZvivL97XvvvsuR54Pg8c8IAFfkSJFNJ999pm6Lf8RmjZtqunTp0+O7mMrtm3bprGzs9OsX79e3ZYvkr6+vpkGLxI8enh45OGztB7yxWH+/PmaiIgIi4PHr7/+WgVHFy5c0L8m8qVk9erVGlsnH85r167V7NixI0vB44QJE/Lk+VmTPXv2aP744w91sUJERkaqLxMdO3bMcJ/k5GT15VgazZSUFLVuxIgRmgoVKmR6gYlyX/fu3TWtWrXSxMbGqtvyZV2+eIeGhuboPrZAvhhK4PjCCy/o3/d9+/bV1KtXL9P95HNaPp/I2LVr19R7S4Kefv36WRQ8Xrp0SQU7P//8s7p9//59dTFVLnjZOvlOMH36dHVO5AKepcGjbEvpvfvuu0afeR9//LEKBm/cuKHJyPvvv6+CTN020iEl30l2796teVQMHvPADz/8oAJBXeOnu1olPWHBwcE5to+teOaZZzQtWrQwWvfmm2+qL4fmgsczZ85oTpw4YXReSUvOiaXBozSQL7/8stG6Dh06WHy11hbs3LkzS8Hjiy++qHrH5GKILuih9GbOnKl6ujM6RxJwynk/duyYfp1c5JB1/NKcv73IctHP8Gr5gwcP1FXxGTNm5Ng+tmLFihXqPS3Bjs6+ffvUusx62SV4nDNnjtrm7t27efRsrYulweNHH32kLlxL4J7280nep6SVleCxdOnSmpMnT6qMKF7sy5j835X/68uXL89wGwkcJYA0JBk8zz33nOZRMYk4Dxw9elSN03B1dTUaaydjciQXPKf2sRVybho3bmy0Ts7N1atX040bMyTjZfr06YPHH38cxYsXx8cff5wHz7bwkXG4Mr7D1Gsgrw1lz7x58zB69GjUr19f/d/fv38/T6UJBw8eVOM9MhrbJe9BGQtSr149/TrdmFy+P/PPsWPH1Fg7w88NDw8PNcY6o9clO/vYCvn7/fz8jMaRNWnSRP2/MHdu3nzzTTz33HMoW7Ys+vbtq8aaUfZeg4YNGxqNx5N2MD4+3mSNBbKsjsKAAQPQu3dv9Zn93Xff8bRl0A6KjMbYyv/pW7du5dr3NAaPeUCKtaQtQKK7Lffl1D62Ijvnxt/fH4cOHVIFdmRZtmwZPvroI8ydOzdPnnNhK1QkX+hMvQa2/t7MrhEjRiA0NFR9WZbGs1GjRujfv3+mF0Ns0fr169X/2f/9738ZbiPvQfnSkTa45Pszf+k+G7LyuZGdfWy5HZSiUFK0JbNzM2PGDPVZIxehpS28ePEiRo4cmQfPuPDh97ScJQVdTp06pYpjScG5OXPmYMKECfj3339z+JGsW1hYGF566SU88cQT6kJzfnx2MnjMA05OTqq3xlBsbKz6mVGlz+zsYyuyc27k6ovhFZgePXqgX79++Oeff3L52RbO8y9MvQa2/t7MrqFDh6Jo0aLqd8k2mDZtmqqOtm3btvx+agXGvn37MGjQIEyaNEmdr6x8Pgi+P63vc4OfNcjy+1zWZfY5/Pzzz+t7yqTXUi7ErFmzBpGRkRa+kpTZa8DvadnXunVro2Bo8ODB6NSpE7+nGZD/pz179lRBYGadH7n92cngMQ9IiWIp2W9Id7t8+fI5to+tyOjcyH8WmbbDUpLyk/Y4ZJ706kigY+o1sPX3Zk6eY3k/8/2pJSm83bp1w7hx4/DJJ5+Y/XyQBjYqKkq/LiEhQfW28P2Zf+R1EVn53MjOPrZCzk1wcLAq368jPQry5TAr50baQSEpbpT114Df03IXv6elkjate/fu6v/8hg0bUKxYMWREUtIlEyG3PjsZPOaBxx57THXDG85fs3z5cvj4+KjxTUJy5Hft2qXvTrZkH1sl50b+48g5Mzw3HTp00F9tkW59OZ/ypVE33jHtXE7SqyPzv5F5Mp70wIED6ndJB+zcuTNWrFihvz8xMVFdvZbXhsyT1BzdmBh5H8v70dDWrVvVOeX7Uzu2QwLHMWPG4PPPP88wuLx27Zr6vWPHjmrM48qVK43SXeWzoEuXLnx75hPJ/JCLIoafGydPnlTpaYafG5JOqWv3LN3HFsl7Wdq1zZs3G7WD0ga2b99ev07aQV1gmLYdFNKWyjjSihUr5tEzt15y/uR83r9/X92W96AMh5GhBoavQaVKlTjfowXk4oecT6nloTu/huRCiNzPdhD6wFHasY0bN6r09LQkBf3IkSP6DKa2bdsafXbK+ZR9c+Sz85FL7pBZUhWwU6dOmrp166pKllLKX8o7//LLL/ptpCKjvBxSFdTSfWyVzKEkczH17NlTVZwbP368Ojd79+7VbyPnzLAS3eDBgzVvvfWWqky1ZMkSTZcuXdSccVLRy9bJ+ZTKoJs3b1bnTEpAy+2LFy/qt5k4caKaR0zn6NGjquLhSy+9pF6D/v37qzmIbL0SsJBqqXL+pHy7rnqt3DY8N507d9b06tVL/3+/YcOGmp9++klNPzNt2jRNyZIlVdl9Wyf/P+X/qfx/lXNouCQmJuq3k7n/3nvvPf1t+b8u66SqpEz1IRX8dFMaUP6R97iUl//+++/VFEEy95jMiWpI5nSUeWezso+tGjlypJquY8GCBZrffvtN/V+Rkv6G5DNIN7fbvHnzVCVRmZpJKg/L9EAyB5985pC2UrN8tshcslI9XH6XCraG7Z6cz61bt6rbMoWQTKEmy7Jly1RFUUdHR83ChQtt/nTK9HK6z2ofHx/NmDFj1O+G37lmzZqlzmdUVJS6Ld/p5HNcppSQcyjTMkk1W5kSxZYlJiaq96R8L5BzY9gO3r59W7+dVGyvUaOG/vauXbvU/2/dd1/53KxYsaKaPuVR2ck/jx6CkjlyReWbb77Bzp07UaRIETz99NNqsKuOjG8aOHAgpk6dqq4WWLKPLZOu9y+++AKnT59G6dKl8corr6B58+b6+6VX8f3331cDraW3Vnp3Zs2ahS1btqirXHIl67XXXlP32bo9e/bg7bffTrdeKp698cYb6veZM2di7dq16qqqjlTskrF5N27cQI0aNTBx4kR9mpktk0H+sqT13nvvqbG2Qs6rjDuQ97A4f/48fv75Z9UbKWk6coVRxvVlVFHUVqxatSrD3sbVq1fD09NT/S6V+WQMs4znEvJ//LffflPvV/ldxoiMHTtW9UhS/lq8eDH+/PNPxMTEoF27dhg/fjzc3d3190vFYfkcMSyKZG4fWyUZC9OnT8e6devUe1uKbEkVVcPPjTZt2qi2TsYLi02bNqlzKb1l0kP27LPPGrWdtqxr167qPWZIenjkc0hIgSE5Xz/++KOqsiqkF/LLL79U2Q+yrZx/3ee8LZNMkKeeeird+hYtWuDrr782+nyX3jA3Nzd17uW7xvbt21XKpWTZvfrqq6o6vi178OCB+k5gyltvvaXaPiHnVb6Xyf9vnb1796rPCIkx5HvvO++8o74zPyoGj0RERERERGQWxzwSERERERGRWQweiYiIiIiIyCwGj0RERERERGQWg0ciIiIiIiIyi8EjERERERERmcXgkYiIiIiIiMxi8EhERERERERmMXgkKiRkYt1jx44VmONY22MTEZF1u3z5MlasWFFgjmNtj01kCUeLtiKibNu7dy+uXr2abn2JEiXQtWvXHDuzU6dORZ06ddCgQQOL99m2bZt6HvXq1Xuk42RHfj42ERHlnZs3b2Lnzp0m7+vduzeKFCmSYxcg33//ffTt29fifS5duoTTp0+jT58+j3Sc7MjPxybKLgaPRLns+++/V41B+/btjdZXqVIlR4PH7Pjkk0/QpEkTowCuQ4cO8Pf3L9SPTUREeefgwYMYOnQonnjiCTg5ORnd17FjxxwLHrNjy5Ytqj0yDOAqVaqEfv36FerHJsouBo9EeaB+/fr4559/TN4naZp3795Fly5djNYfPXoUYWFh+vXx8fHYs2cP7t+/rwKuypUrZ/qYa9asQbVq1dSis2vXLri7u6NRo0aqRzQ4OBiBgYH65yYNWMuWLeHp6Wl0LHOPvXnzZvj5+aFcuXLqeYsWLVrAzc3N5HOz9LF1xy1Tpow6T8nJyWjXrh1cXFwQGhqKffv2oXjx4mo/BwcHo8dISUnBoUOHcOvWLRWo161bN9PzRUREuWv27Nnw8vJKtz48PBwbNmxQvW3SRulIG7hx40bVPnh4eKh1J06cwIULF1C6dGk0b94c9vYZj8A6deqUams6d+6sX3ft2jUcPnwYjz/+uOoRlcA2Ojpa3xZJe12+fHl069Yt3fEye+zz58+rRS4Ky3a3b99WWTRly5Y1+dwsfWzdcR977DF1XNlPLrxKu5iYmKjaZjmGtLmSzZOWZD5J++nt7a3afsPzS5QdDB6J8pl8sMsVWWngihYtql8/evRo1eBJ8ChBVvfu3eHq6ooKFSpg9+7dGDduHL766qsMjzt+/Hi8/PLLRsHj119/rQI8aUCk0ZIATAKy//77T90vj5c2ddSSx548ebJqRCVQq1mzJs6dO6fW79+/32RjZuljy3GlcZRGWILW48ePqyvUb7zxBj777DO1rXwJkO3Xrl2rP740rvIl5MGDB+r5SEBbu3ZtLFu2LMOAloiI8ocEhmPHjkVSUhKGDx+uXz9nzhz89NNPGDJkiLpv8ODBasiDBEoSSJUqVUp99vv4+Jg87pIlS7Bp0yaj4FGCLWkbJXiUtkXah5iYGH1bJMGVBLOGqaOWPPb69evx6aefomLFiuoCp64NXLhwockUVEsfW44rvZMlS5ZUF1OlXZPHnz59Or799lsVRN67d08FxdI+69p8jUaD119/HQsWLFDPWS5Sy2MuXboUTZs2zbHXjmyQhohy1ZAhQzT169fX/P3330bL4cOH1f3x8fGaEiVKaObNm6ffJzAwUCP/PY8fP65ut2nTRtOvXz9NUlKSur1nzx6Nvb29ZvPmzfp9unXrppkwYYL+do0aNTQ//vij0XORY7z00kv62507d9ZMnDjRaJu0x7HksVu3bq0pU6aMJjg4WP83ValSRfPZZ59leF4seWw5btmyZTV3795Vt0NCQjRubm6aihUrau7du6fWXb9+XePo6KjZvn27fr9OnTppxo4dq0lJSVG3Y2NjNU2aNNFMnjw5w+dDRES5499//1Vt2uzZs43awWXLlum3ee655zTdu3c32k/azkmTJqnfp0+frtrKq1evqtuRkZGaevXqaZ5//nn99nPnzlVtho585ks7Ykge19vbW3971qxZmgoVKhhtk/Y4ljy2tLfyNy5ZskS/7s0331TbZcSSx9YdV86hTu/evdW6tWvX6td16NBBtXs6v/76q2qHde2n+OSTTzQ1a9bM8PkQWYLVVonygPQqypVFw0V60YSzszMGDRqEP//8U7+9/C5pltLbJr1okm46ceJEfWqmpGl26tQpw1TYnJKVxx4wYAB8fX31f5Nsp+uBfBRyXEm3EXKFV1JQ5QqwLvVJelJlCQoKUrfl6quMI5Ht5Arr4sWLVeU6SbXdunXrIz8fIiLKntWrVxu1g4YZI9LjKCmqISEh6rYUkpF2UtcTKW2O/C5pnUIydV599VXVs5fbLH1saaOkzTIcx58T7aC0rf3799fflp5EeS6SFWS4TtcOirlz56rvENLuSTu4aNEilblz9uxZ1QNJlF1MWyXK5zGPYtiwYapowJ07d1QqzF9//YUXX3xR3aer1Jp2nKEER1LSOzdl5bHTpqdK2o6k1zwqGdOY9rim1sXFxanfr1y5on5K+o6kx+rY2dmpcSJERFSwxjwKKSonKZgSkL3yyivqImrDhg1Rq1YtfXs0cODAdG1RZGSkSttM2y7kJEsf21Q7KDUD8rod1LWFCQkJKnXXkKQAy3qi7GLwSFQAtGnTRvWeSYApg/DlQ/+pp55S98k4ByHjIGS8g47c1t1nioxBlKIxhgwbFktk97HzU7FixdRPGTMiYzuJiKjgkwt8Mv5fgkYZkygXUaV3T0faHGl7DMltqd6q+9zPjXYwu4+d3+R5SZbQl19+md9PhQoZpq0SFZBGU4JFaTRlkSuwEkzqev3kaqwUe9GRqqeS3iNBZ0akwptUhdOJiopSxWUMSQpLZg1pdh/bEuYeO7sk3Vf+9pkzZ6a7Twr6EBFRwSSpoVJk5vfff8eNGzdUMKkjbY6kuhoGg5KOaarato60BZIlI8XZdNIOX7CkLcrOY+dnOygkpVW+T0jbn3Y4CtGjYM8jUR6QdNS0aauSYiLV3gwbTak2KuMRZG5I/X9SR0dVUe3pp59GRESECuhmzZqlKrpJRdaMPPPMMyr1VcZKyJjBefPmpbsCK2mcv/32mwq4pNqd4VxTj/LYljD32NklDbmkRsm5lTLvUvJcrhCvWrVKpR1J9TkiIsp7ciEy7VQRMmRDl9ki7YEskrYqvWYyJYaOZJNIwNazZ081X6RM+bR8+XJVATUjUrF0woQJ6uKstAUynGHdunVG20iGilT/loqmVatWVcNM0srOY1vCksfOrg8++EBNdyWVVZ9//nl13iUwv3TpEnbs2JFjj0O2h8EjUS5r1aqV+qkrxW2YUmIYPMq4DmkwpSFJO7ZCxij4+/ursSAyt6EEc9IYGE62LAPzZRsd2UYG9UtDKeMypk2bpkqUG47JePPNN9U20qBKuXApZ572OJY8tkwnItNmGGrWrFmmV1QteWxTx5UvALoxMDq9evVC9erVjbaRYgvz589Xx5de3G+++UalBBMRUd6Sz2BpS2Qux7TkM95wWMS7776r2stnn33WaDu5ECrzFf7yyy+qkJvUBzhy5IiajkmnUqVK6Nevn1EBGxn7/uuvv+LAgQOqB3HkyJGqbdCRtkPmRZbCatJuSJCV9jiWPLYcR9oiQ7Kd/N0ZseSxTR1XHtewWI7uPBqStl7+ZpmqQ4JGmW5L2tQnn3wyw+dDZAk7Kblq0ZZERERERERkszjmkYiIiIiIiMxi8EhERERERERmMXgkIiIiIiIisxg8EhERERERkVkMHomIiIiIiMgsBo9ERERERERkFoNHIiIiIiIiMovBIxEREREREZnF4JGIiIiIiIjMYvBIREREREREZjF4JCIiIiIiIrMYPBIRERERERHM+T9v5AYWV/7qWAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(9, 3.2), layout=\"constrained\")\n", "for index, axis in enumerate(axes):\n", " values = dynamics[dynamics[\"Observable\"] == f\"Z{index}\"]\n", " axis.plot(values[\"Time\"], values[\"Exact\"], label=\"Exact evolution\")\n", " axis.plot(values[\"Time\"], values[\"Trotter\"], \"--\", label=\"Trotter product\")\n", " axis.errorbar(values[\"Time\"], values[\"Sampled\"], yerr=values[\"SE\"], fmt=\"o\", capsize=3, label=\"Measured\")\n", " axis.set(xlabel=\"Evolution time\", ylabel=rf\"$\\langle Z_{index}\\rangle$\", ylim=(-1.05, 1.05))\n", "axes[0].legend(fontsize=8)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "trotter-page-26", "metadata": {}, "source": [ "## 4. Swap the rotation implementation\n", "\n", "- Pass a different `rz_method` to `trotter_first_order` to change the rotations inside each Pauli exponential.\n", "- `ham_sim_trotter` and the measurement runner keep the same interfaces.\n", "- Here we use `comparator_based_rz_cascade`, which implements approximate rotations with measurement feedback.\n", "- `epsilon` controls individual rotations; it is not a bound on the full simulation error." ] }, { "cell_type": "code", "execution_count": 10, "id": "rus-overlay-0", "metadata": {}, "outputs": [], "source": [ "from guppyalgos.primitives.rotations import comparator_based_rz_cascade, n_comparator_based_rz_cascade_ancillas\n", "\n", "epsilon = 0.1\n", "rus_step = trotter_first_order(\n", " hamiltonian, n_qubits, rz_method=comparator_based_rz_cascade(epsilon),\n", ")\n", "rus_ancillas = n_comparator_based_rz_cascade_ancillas(epsilon)" ] }, { "cell_type": "markdown", "id": "rus-overlay-1", "metadata": {}, "source": [ "### Build the RUS evolution circuit\n", "\n", "- Use the same Hamiltonian, initial state and time step as above; sample the comparator implementation at step 4.\n", "- Only the rotation implementation changes. The builder returns the preparation circuit for a chosen number of steps." ] }, { "cell_type": "code", "execution_count": 11, "id": "rus-overlay-2", "metadata": {}, "outputs": [], "source": [ "def make_rus_preparation(steps):\n", " evolve_rus = ham_sim_trotter(rus_step, steps, time_step, n_qubits)\n", "\n", " @guppy\n", " def prepare_rus_at_time(qreg: array[qubit, 2]) -> None:\n", " transversal(h, qreg)\n", " evolve_rus(qreg)\n", "\n", " return prepare_rus_at_time" ] }, { "cell_type": "markdown", "id": "rus-overlay-3", "metadata": {}, "source": [ "### Sample the comparator dynamics\n", "\n", "- Use **256 shots** at step **4** ($t=0.8$).\n", "- Measure only $Z_0$ for this comparison point.\n", "- `QuantumReplay` fixes each RUS attempt to immediate success, avoiding repeated probabilistic retries. The underlying Quest simulator still samples the final observables." ] }, { "cell_type": "code", "execution_count": 12, "id": "rus-overlay-4", "metadata": {}, "outputs": [], "source": [ "rus_steps = 4\n", "rus_shots = 256\n", "n_rus_bits = 1 + ceil(log2(1 / epsilon))\n", "n_rus_rotations = rus_steps * len(hamiltonian)\n", "immediate_success = [False] * (n_rus_rotations * (2 * n_rus_bits - 2))\n", "replay_simulator = QuantumReplay(\n", " simulator=Quest(random_seed=900 + rus_steps),\n", " measurements=[immediate_success.copy() for _ in range(rus_shots)],\n", ")\n", "\n", "label = \"Z0\"\n", "samples = sample_direct(\n", " make_rus_preparation(rus_steps), zqp.String.from_str(label, n_qubits),\n", " seed=900 + rus_steps, shots=rus_shots, extra_qubits=rus_ancillas,\n", " simulator=replay_simulator,\n", ")\n", "operator = zqp.RealTermSum.from_str(label, n_qubits)\n", "stats = estimate_pauli_observable_expectation_from_bitstrings(\n", " operator, {label: samples},\n", ")\n", "rus_dynamics = pd.DataFrame([{\n", " \"Time\": rus_steps * time_step, \"Observable\": label,\n", " \"Sampled\": stats.expectation, \"SE\": stats.standard_error,\n", "}])" ] }, { "cell_type": "markdown", "id": "rus-overlay-5", "metadata": {}, "source": [ "### Compare $Z_0$\n", "\n", "- Circles show standard-Rz samples; the square shows the comparator-Rz $Z_0$ sample.\n", "- Compare the step-4 point with the standard-Rz sample and Trotter reference; exact evolution is also shown.\n", "- Comparator results also include rotation-approximation error; error bars describe sampling uncertainty only." ] }, { "cell_type": "code", "execution_count": 13, "id": "rus-overlay-6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "standard_z0 = dynamics[dynamics[\"Observable\"] == \"Z0\"]\n", "fig, axis = plt.subplots(figsize=(6, 3.5), layout=\"constrained\")\n", "axis.plot(standard_z0[\"Time\"], standard_z0[\"Exact\"], label=\"Exact evolution\")\n", "axis.plot(standard_z0[\"Time\"], standard_z0[\"Trotter\"], \"--\", label=\"Trotter product\")\n", "axis.errorbar(standard_z0[\"Time\"], standard_z0[\"Sampled\"],\n", " yerr=standard_z0[\"SE\"], fmt=\"o\", capsize=3, label=\"Standard Rz\")\n", "axis.errorbar(rus_dynamics[\"Time\"], rus_dynamics[\"Sampled\"],\n", " yerr=rus_dynamics[\"SE\"], fmt=\"s\", capsize=3,\n", " label=\"Comparator Rz (replay)\")\n", "axis.set(xlabel=\"Evolution time\", ylabel=r\"$\\langle Z_0\\rangle$\", ylim=(-1.05, 1.05))\n", "axis.legend(fontsize=8)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "trotter-page-30", "metadata": {}, "source": [ "## Explore further\n", "\n", "- Use the {doc}`QPE demo ` to estimate energy eigenvalues with controlled evolution.\n", "- Explore {doc}`Pauli exponentials ` to see how the rotation and CX-ladder implementations fit together." ] } ], "metadata": { "kernelspec": { "display_name": "guppyalgos (3.14.x)", "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": "3.14.7" } }, "nbformat": 4, "nbformat_minor": 5 }