From b094081e6c3351b7cece5ba8f7d824f38a6d35d1 Mon Sep 17 00:00:00 2001 From: Arif Cem Gundogan Date: Thu, 27 Jun 2024 14:54:32 +0100 Subject: [PATCH] From Colab --- Build Repetition Codes.ipynb | 510 +++++++++++++++++++++++++++++++++++ 1 file changed, 510 insertions(+) create mode 100644 Build Repetition Codes.ipynb diff --git a/Build Repetition Codes.ipynb b/Build Repetition Codes.ipynb new file mode 100644 index 0000000..600963a --- /dev/null +++ b/Build Repetition Codes.ipynb @@ -0,0 +1,510 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f5d21946", + "metadata": { + "id": "f5d21946" + }, + "source": [ + "# Build repetition codes\n", + "\n", + "*Usage estimate: 2 seconds on ibm\\_algiers. (NOTE: This is an estimate only. Your runtime may vary.)*\n", + "\n", + "## Background\n", + "\n", + "To enable real-time quantum error correction (QEC), you need to be able to dynamically control quantum program flow during execution so that quantum gates can be conditioned on measurement results. This tutorial runs the bit-flip code, which is a very simple form of QEC. It demonstrates a dynamic quantum circuit that can protect an encoded qubit from a single bit-flip error, and then evaluates the bit-flip code performance.\n", + "\n", + "You can exploit additional ancilla qubits and entanglement to measure *stabilizers* that do not transform encoded quantum information, while still informing you of some classes of errors that might have occurred. A quantum stabilizer code encodes $k$ logical qubits into $n$ physical qubits. Stabilizer codes critically focus on correcting a discrete error set with support from the Pauli group $\\Pi^n$.\n", + "\n", + "For more information about QEC, refer to [Quantum Error Correction for Beginners.](https://arxiv.org/abs/0905.2794)\n" + ] + }, + { + "cell_type": "markdown", + "id": "88672bd6", + "metadata": { + "id": "88672bd6" + }, + "source": [ + "## Requirements\n", + "\n", + "Before starting this tutorial, ensure that you have the following installed:\n", + "\n", + "* Qiskit SDK 1.0 or later with visualization support (`pip install qiskit[visualization]`)\n", + "* Qiskit Runtime (`pip install qiskit-ibm-runtime`) 0.22 or later\n" + ] + }, + { + "cell_type": "markdown", + "id": "14c29e8b", + "metadata": { + "id": "14c29e8b" + }, + "source": [ + "## Setup\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1b9fd8ad", + "metadata": { + "id": "1b9fd8ad", + "outputId": "b93dc780-3a31-4a4a-f635-569c2bb6f245" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> Connected to ibm_algiers.\n" + ] + } + ], + "source": [ + "# Qiskit imports\n", + "from qiskit import transpile, QuantumCircuit, QuantumRegister, ClassicalRegister\n", + "from qiskit.result import marginal_counts\n", + "\n", + "# Qiskit Runtime\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler\n", + "\n", + "service = QiskitRuntimeService()" + ] + }, + { + "cell_type": "markdown", + "id": "4d01e8d3", + "metadata": { + "id": "4d01e8d3" + }, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n" + ] + }, + { + "cell_type": "markdown", + "id": "cdee0b18", + "metadata": { + "id": "cdee0b18" + }, + "source": [ + "### Build a bit-flip stabilizer circuit\n", + "\n", + "The bit-flip code is among the simplest examples of a stabilizer code. It protects the state against a single bit-flip (X) error on any of the encoding qubits. Consider the action of bit-flip error $X$, which maps $|0\\rangle \\rightarrow |1\\rangle$ and $|1\\rangle \\rightarrow |0\\rangle$ on any of our qubits, then we have $\\epsilon = \\{E_0, E_1, E_2 \\} = \\{IIX, IXI, XII\\}$. The code requires five qubits: three are used to encode the protected state, and the remaining two are used as stabilizer measurement ancillas.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b588703a", + "metadata": { + "id": "b588703a" + }, + "outputs": [], + "source": [ + "num_qubits = 5\n", + "backend = service.least_busy(operational=True, simulator=False, min_num_qubits=num_qubits)\n", + "backend" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "606dff18", + "metadata": { + "id": "606dff18" + }, + "outputs": [], + "source": [ + "qreg_data = QuantumRegister(3)\n", + "qreg_measure = QuantumRegister(2)\n", + "creg_data = ClassicalRegister(3, name=\"data\")\n", + "creg_syndrome = ClassicalRegister(2, name=\"syndrome\")\n", + "state_data = qreg_data[0]\n", + "ancillas_data = qreg_data[1:]\n", + "\n", + "def build_qc():\n", + " \"\"\"Build a typical error correction circuit\"\"\"\n", + " return QuantumCircuit(qreg_data, qreg_measure, creg_data, creg_syndrome)\n", + "\n", + "def initialize_qubits(circuit: QuantumCircuit):\n", + " \"\"\"Initialize qubit to |1>\"\"\"\n", + " circuit.x(qreg_data[0])\n", + " circuit.barrier(qreg_data)\n", + " return circuit\n", + "\n", + "def encode_bit_flip(circuit, state, ancillas) -> QuantumCircuit:\n", + " \"\"\"Encode bit-flip. This is done by simply adding a cx\"\"\"\n", + " for ancilla in ancillas:\n", + " circuit.cx(state, ancilla)\n", + " circuit.barrier(state, *ancillas)\n", + " return circuit\n", + "\n", + "def measure_syndrome_bit(circuit, qreg_data, qreg_measure, creg_measure):\n", + " \"\"\"\n", + " Measure the syndrome by measuring the parity.\n", + " We reset our ancilla qubits after measuring the stabilizer\n", + " so we can reuse them for repeated stabilizer measurements.\n", + " Because we have already observed the state of the qubit,\n", + " we can write the conditional reset protocol directly to\n", + " avoid another round of qubit measurement if we used\n", + " the `reset` instruction.\n", + " \"\"\"\n", + " circuit.cx(qreg_data[0], qreg_measure[0])\n", + " circuit.cx(qreg_data[1], qreg_measure[0])\n", + " circuit.cx(qreg_data[0], qreg_measure[1])\n", + " circuit.cx(qreg_data[2], qreg_measure[1])\n", + " circuit.barrier(*qreg_data, *qreg_measure)\n", + " circuit.measure(qreg_measure, creg_measure)\n", + " with circuit.if_test((creg_syndrome[0], 1)):\n", + " circuit.x(qreg_measure[0])\n", + " with circuit.if_test((creg_syndrome[1], 1)):\n", + " circuit.x(qreg_measure[1])\n", + " circuit.barrier(*qreg_data, *qreg_measure)\n", + " return circuit\n", + "\n", + "def apply_correction_bit(circuit, qreg_data, creg_syndrome):\n", + " \"\"\"We can detect where an error occurred and correct our state\"\"\"\n", + " with circuit.if_test((creg_syndrome, 3)):\n", + " circuit.x(qreg_data[0])\n", + " with circuit.if_test((creg_syndrome, 1)):\n", + " circuit.x(qreg_data[1])\n", + " with circuit.if_test((creg_syndrome, 2)):\n", + " circuit.x(qreg_data[2])\n", + " circuit.barrier(qreg_data)\n", + " return circuit\n", + "\n", + "def apply_final_readout(circuit, qreg_data, creg_data):\n", + " \"\"\"Read out the final measurements\"\"\"\n", + " circuit.barrier(qreg_data)\n", + " circuit.measure(qreg_data, creg_data)\n", + " return circuit" + ] + }, + { + "cell_type": "code", + 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def build_error_correction_sequence(apply_correction: bool) -> QuantumCircuit:\n", + "\n", + " circuit = build_qc()\n", + " circuit = initialize_qubits(circuit)\n", + " circuit = encode_bit_flip(circuit, state_data, ancillas_data)\n", + " circuit = measure_syndrome_bit(circuit, qreg_data, qreg_measure, creg_syndrome)\n", + "\n", + " if apply_correction:\n", + " circuit = apply_correction_bit(circuit, qreg_data, creg_syndrome)\n", + "\n", + " circuit = apply_final_readout(circuit, qreg_data, creg_data)\n", + " return circuit\n", + "\n", + "circuit = build_error_correction_sequence(apply_correction=True)\n", + "circuit.draw(output=\"mpl\", style='iqp')" + ] + }, + { + "cell_type": "markdown", + "id": "609c0c47", + "metadata": { + "id": "609c0c47" + }, + "source": [ + "## Step 2. Optimize the problem for quantum execution\n", + "\n", + "To reduce the total job execution time, Qiskit primitives only accept circuits and observables that conforms to the instructions and connectivity supported by the target system (referred to as instruction set architecture (ISA) circuits and observables). [Learn more about transpilation.](https://docs.quantum.ibm.com/transpile)\n" + ] + }, + { + "cell_type": "markdown", + "id": "c8ea2716", + "metadata": { + "id": "c8ea2716" + }, + "source": [ + "### Generate ISA circuits\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "67b55eef", + "metadata": { + "id": "67b55eef", + "outputId": "1e98cbef-3c16-44d1-847e-3481f763ca96" + }, + "outputs": [ + { + "data": { + "image/png": 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NZGRma+DibIvmjavBwb7yfqXa9ftt7D56R+/1DD0G3lp0CgO61kVVV3u91yXT+OibCNy+n6H3eoYcAzm5Wvx74Un8sXGA3vszlQtRifhys/5j7Rp6Dnzyfxcwum8DiyuaEj3r9u3bWLt2LWJiYvRaLyoqClFRUahWrRomT56MNm3aAChcLASAunXr4oUXXjB63EREREREZJjKe3XLBNq1a4eoqCjY2toWmq5UKjFz5kxERUVh7dq1WLduXYkFQ2s3b968Qo9Pnz4tUSREVB4HT8bjWkyKWff59Y9X8e74ANjasldsS/Dttijk5JbdWsCYVmy5XCkLhtdjU/BN6DV8v+cm0jLyC6Z7VHPA5KGN8cbIpniutouEERpmuQGFkopITsvDD79G4+2xzcy6XypeWkYe1v98w6z7/POsCuevqdHKz8Os+y3JV1uv6H3jTEVoNCK+Cb2Grz/oaL6dEulBq9Xil19+wc8//1yoRaGbmxvat28PX19f1K9fH1WrVgUAZGVl4fbt24iJicHZs2dx7949AI+76lu6dCk6d+6M/v37Y9myZYWKhR9++CFcXV3N/vyI9PHHH38UmTZx4kSrvVH807cDMfe1lpj00TFs+uVmkflHN/RHxxY1ETh6N65Es5tOIiKiykb2V2vVajVmz56Nhg0bwsHBAXXr1sWMGTOQmZmJyZMnQxAErFq1CgDg6upapFj4tD59+gAArl+/bpbYzYXjRhBZr9Wh18y+z/sPs/Drn/q3ZiLjy83TYv3P5s9pu47cxv2HmWbfb0VsOxiD5iN2YeWPVwsVCwFAnZyDxRsvIWD4Lvx26p5EERrm0o0knDj/wOz7XR16jd8/LMSWvdHIyMove0EjW7PNMsb2TkzJwU8H9Gs9ZQzf77kpyetOVJa8vDysWLEC27dvLygWent746233sKqVaswadIkdOvWDfXq1YOrqytcXV3h6emJ9u3b45VXXsHSpUvx4YcfokWLf3qTOHnyJD788EMWC4lkYP7q84i8mYQv/9MedWoVHnZn5rhm6N7WCx+vjmCxkIiIqJKSdcHwwoULCAgIwJIlS6BSqeDv74/8/Hx8/fXXGDVqFK5de3yhvGXLluXaXk5ODoDSxyLcsWMHhgwZgh49emDkyJH48ssv8ejRowo/F310794dgiAgLi6uzGUvXbqEVq1aITo62vSBkaw4OTmhffv2VjE2p1w9SspG2PG7kuz7u91F70atbORwDuw/cRePknPMvl+tVsTWsFtm36+hwo7dwSvv/4G8fF2py6Vn5uOlt3/DqYvmL8AZ6vs90pyL1+NSceaSeb8fUfG+k+gY2Bp2C3n55m3dXJxtB2PN3soaANIy8vHLkdtm368xySEPUmEajQZfffUVwsPDAQCCIGDw4MFYtGgROnfuXOrNtU8IgoBmzZrhgw8+wLRp0+Do6AgA0Oke59DatWuzWEhUieVrdJgw7xicHW2xYX7XgumNfdzw6VttcPrSQyz5LlLCCM2LuZCIiORGtgVDtVqNQYMGQaVSYdasWUhISEBERARUKhUWL16MsLAwhIeHQxAENG/evFzbDA0NBQB07dq1xGXCwsKwe/duHD16FNu3b8esWbNQv359bNmyxSjPy9g2bdqEixcvIigoSO+xKci61atXDytXrkS9evWkDoUMFH5FbdYu2J52JvJhpW9dJIdz4EykdAWbvy9XjmJRfr4OU4JPQqcr3/Gak6vFvxecrDTHN48B65abp8WFqCRJ9p2Vo7GI1gdSngNS7tsY5JAHqbCQkBCcO/d4XGN7e3vMmTMHr7zySrkKhc8SBAGNGzeGnZ1doen29vaoUqWKUeIlImmcv5aIRRsuok9nb0wZ3gQKhYAfPn0BggBMmHes3N+b5YC5kIiI5Ea2BcO3334b8fHxePPNN7F06VK4uPwzptDs2bPRokULaDQa+Pj4lOvuxn379mH37t0F6z+rcePGWL58OS5cuICUlBRkZmbi2LFj6N27NzIzM/Hqq68iLCzMeE/QSJYtW4bx48cjPj4eQUFB5WqVSAQ8HtskIyOj0LgmVLmcu6qWbN8Pk3Jw70GWZPs3BjmcA1IeA+euJkq2b338cvQ2Eh7pd6xG3kzGSQm6+dSXVqvD+WvSvQ9SHn/0WOTNJORrSm85a0qW8Dkg7edg5T4H5JAH6R/Xr1/Hvn37AAA2NjZ47733yn1jbXFUKhUWLFiA1NRUAIBSqQQAxMbGFuyHiCqvhevO40JUIpbOaoeVczqifUBN/HflOdyIS5U6NLNiLiQiIrmRZcHw2rVrCA0NhYeHBxYtWlTsMoGBgQBQaGyFkty6dQvjx48H8LgQ2alTpyLLzJ07FzNnzkSLFi3g5uYGJycndO3aFQcOHMDgwYMhiiJmzpxZpMXBjh07MHz4cDz33HNwcnJC06ZN8d///hcZGRn6Pu0i4uPjERcXV+rfnTt3MH/+fPTo0QN37txBUFAQ7tzh2GJUtps3b6JHjx64ebPydy1prS5L3LIj8qY0rVqMRQ7nwOXoFMn2HXsvHZmVYPyujbtuGLbeL4atZ05x9zOQlaORbP+RN6VvXWbtrD0PaLU6XI1JkWz/lf0ckEMepMfy8vKwZs2agt+qo0aNwvPPP2/w9p4UC58es3DWrFkQBAHA4557EhISKh44EUlGoxExYd4xONgrMW2UH45HqLBiy2WpwzI75kIiIrIUoigiMzMTmZmZFer1ysaIMVmMkJAQ6HQ6jB07tsTuTp6MpVBWwVClUqFv375ISkpC7969sXTpUr1iEQQBixcvxu7duxEdHY3IyMhCd2ouXboU9erVw2effQZvb29cuHABwcHB+PPPP3Hs2DEoFIbXdEvrOrUkcXFxGDduHI4dO2bwfk2lTZs2UKlUUochWyNGjNBr+YcPHwIA9u/fX9B1UVmGDh2qd1xkOuoqYwG7xsXOCw95CZ4eJY/D4OnhWPDv3d9Gl7oflToLbV/ZU2T6uFcnwzH/qh4Rm5Y1ngOqanMAwaHYecY6Bkp6/wGgYZPnoRQz9YjY/B64TQeUNfVe78ftB3Fo4xgTRGQ8eUpPwO2NYueV9f4DFT8GLl25Dm9vbz0iJmPLsG8POPcvdp45joH1m7Zg56qX9YjYuHSwhc59XonzTf05mJGZizre3hD0iNnU9MmFhuRBwPJyoTWws7Mr8UZaADh9+nTB76xGjRphwIABBu+ruGLhkzEL+/Xrh3379iE/Px9hYWF47bXXStxO48aNkZeXZ3AcRAAwuFoNrKj/z++dK1cuY6CVfvfQwRYoJecZIjUjD7l5WtjZKrHv+F2jD3fRqHFjKFD8DYYdqrghpPE/Nzao1Wq0NcJ7a47fhABzIRERGZ9Opyu4Ka9ly5Y4f/68QduRZcHwyJEjAICgoKASl4mPjwdQesHwSZEwOjoanTt3xq5duwwav6FJkyZwd3dHUlISbt68Wahg+Ouvv6JGjRoFj7t164YaNWpg7NixOHHiBF544QW99/dEQEBAkTEjSpKYmFjQHamfn5/B+zQllUqFe/fuSR2GbGVm6nfRPjs7u+Df8q7L98/C+OQCJXxEeHo4wbuWc5mbsFEqyrVccZKSk4FUyzkmrPIccAOgLH6WOY4BlUoFaNIMWtdsnLQlvkalyc3Ntbz3+1kOisfHQDHK+/4Dhh8DWo3W8l8juaueCpTw1pnjGMjKzEKWlMeAwh5wL3m2yT8HBQXuW9g5oE8uNCQPAhaYC62Avb19qfMPHTpU8P9x48YZfNNqacVCAHj55Zdx5MgR5OTk4Pjx4xgzZgycnIovyt+/fx+5ubkGxUH0RDKUQP1/Hufn51vvZ5BgV2rOM8SmBV1hZ6vE1VvJmDe1JbYdjEVMfLrRtp9w/z4gFn/jgLp6HvDUva86nc4o7605fhMCzIVERGRaDx4YPkyOLAuGt2/fBgA899xzxc7XaDQ4efIkgJILhmlpaejbty8iIyPRunVrhIWFlfhjpjyeFBo1msJdfz1dLHyiTZs2ACr+BWLPnj3w8fEpc7n4+Hh069YNwOPuZ1avXl2h/ZqKp6en1CHImrOzfhe6nnwZdnR0LPe6derU0TsuMp1EewVySpinUpc+ZpunhyNslApotDqo1NmlLlvStqpXqwKHKpZzTFjjOZAgaFDS6GXGOgZK245XrepQwKXE+ZZArcyCIZcrHW3z4G5h7/ez8hXV8LCEeWW9/0DFjwFbpQ41Lfw1krtMOyeklDDPHMeAs5Mtqkp4DIhQ4L6oA4TiiyOm/hwUxDzUtrBzQJ9caEgeBCwvF1qD0m4ivX37NqKjowE8/v3cuHHxvU+UpaxiIfD4WHnhhRdw6NAh5Obm4sSJE+jdu3ex26tduzZbGFKFVatWuEJma2trtZ9BOtjCmB0BvzXGH0HtamPu12ex++htRIQOwcYFXdF9kvHGKPWqXbvEFoYeVQrf9aZQKIzy3prjNyHAXEhERMb3dAvDWrVqGbwdWRYMnyTsJ3f6PCs0NBRqtRouLi6oX79+kflZWVkYOHAgwsPD4efnh4MHD8LNrYRb8Mvh0aNHBd0UlKfrraNHjwIwT0u/e/fuISgoCDExMRgxYgS2bNlSMCC9pTl79qzUIchaeHi4XstHRUUhJCQE/fr1Q9OmTcu1zooVKwyIjEzlo2/OYeHaC8XOK6kLySfu/jYa3rWcoVJno26vnwzaf/jxPajvbTnFIms8B4Im78Mf4cVfOjD1MeBdyxl3L8XovZ65/bDnJibM07+b7t3fvY9eHb82QUTGk5+vg0vHH5Cbpy0yr6z3H6j4MTBiUGf8uNi4XWORfk5dfIBO4/cWO88cx8CShe/gjVHr9F7PmJq+tAPX41KLnWfqz8HA52sjPCRe7/VMSZ9caEgeBCwvF1oDjUaDnTt3Fjvv2rVrBf/v1q1bwTiD+ihPsfDpfTxp0Xj16tUSC4Y3btyAjY0sL1eQGen+OA7tl6sKHjdr9jziD4dJGJF0MrPyUaXDD0bZVsN6rlg0ow3+jnyExRsvQacTMX9NBBbNaIu3xvhj5Y/GGXbi5o0bcHYqvpcv3aXL0M5bWPDYw8OjoCexijDHb0KAuZCIiIwvMzOzYHi+EydOGLwdwwfIs2BPWqJFREQUmZeQkID33nsPANC8efMiP4jy8vIwdOhQHD9+HL6+vjh8+DA8PDwqFM+yZcsgiiLc3NzQtm3bUpe9d+8ePvzwQ/Tt2xctW7as0H7LIzg4GNHR0Rg6dChCQkL4o4zKrWHDhjh48CAaNmwodShkoDb+Fftsqwh3N3v41Cl+jNnKQg7ngJTHQKB/dcn2rY+RferD3a30rtye1bCeK15sX9tEERmPra0CLZsYuW8qPQRKePzRYy0aV4dSKd0Iem2aSX8MSBmDlJ/BxiCHPEhATMw/N+80adJE7/X1KRYCgI+PT0HvO7GxsQZETERSEgTgu4UvQKkQMGHen9DpHg9c+MWmSIRffoRFM9qggQXdFGpqzIVERCQ3siwY9uzZEwCwePFi3Lhxo2B6eHg4goKCoFarAaBIQU6r1WLMmDE4dOgQvL29cfjwYdSuXfYFv99++w0ffPABbt26VWh6VlYWFixYgC+++AIAMGfOnFK7g8nIyMDgwYNhZ2eHjRs3luu5Fqdbt24YPnx4ubpD+OqrrxAcHIzQ0FAWC0kvNjY2qFatGo+bSkzKi6Rtm3kYdAe7JZHDOdAuoGi32ObStpl0+9aHg70Nvv6gQ7mXVyoFrJrTEQpF5Ti+pT0GKnexRA6cHG0Q0KiaJPu2s1VItu+ntXtewnNAwn0bgxzyIKFgHHulUom6devqta6+xcIn+3kybMaDBw+QlVV298dEZDlmTQhA51a18NHqCETF/tNCX6cTMfHDY7BRKrBxQVcJIzQv5kIiIpIbWRYMZ8+ejerVq+Pu3bto1qwZAgIC0KhRI7Rr1w4NGjRAjx49ABQdv3Dbtm0FXbXY2dlh3Lhx6NKlS7F/KpWqYL3MzEwsXrwYDRs2RO3atdG2bVsEBgbCw8MDH3/8MURRxNSpUzF79uwSY87OzsagQYMQGxuLQ4cOwcvLy+DnHxwcjB07dhQ7PuKzHB0d8dFHHxXc5VlRJ0+ehIeHR8Hfl19+CQD46aefCk1/MoYkVV7x8fGYNWuWUbr9IGnUruksWSuo8YMq/x2YcjgHBnStCzeXkm9kMRVBAMb09zX7fg01dkBDrP5vpzKLgHa2Cvz4eXf06Vx29+OWYqxE74NP7Sro3MrwPvXJeMb2l+bz+OXe9eFgL/3FtZF96sPGxvwFfkcHJYa9WPx465WFHPIgAenp6QAANze3Um9ufZYhxcInnu7BJyMjQ8+IiUgqTeu7YeH01jh18SGWfX+5yPyrt1Iwf00EurXxwltj/CWI0PyYC4mISG6k/5VuAt7e3jh+/Djee+89/Pnnn4iLi4O/vz/Wrl2LKVOmwNf38cWxZwuGubm5Bf+PiYkp1D3Ls3Jycgr+HxgYiHnz5uHUqVOIjo7G1atXodVqUatWLXTs2BFTpkzBiy++WOK28vPzMWLECJw9exa///47/P0r7xer/Px8JCYmFpmem5tb6PXNzy9+4GqqPDIyMnD8+HFMmTJF6lCoAqaN8sPvZ+6bdZ8e1RwwolfR8WMrGzmcA06ONvjX4EZYseWKWffbv2tdixq/sjzeGOWHlk3d8dXWK9j5Wxw0WrFgnoO9Eq/0a4CZ455H88bSdfFpiHYBNdDarzoirhXN3ab0+simUCpled9apfOvIY0wb9W5YseyNKVpo0w/Vnd5eHo4YXhPH4QeMG/XiGP7+6Kqq37dHVsaOeRBAqZNm4bs7GwoFPp9Jh84cMCgYiEA9O3bF+3bt4ednV251yEi6UXFpsKx7felLvP5hkv4fMMlM0UkPeZCIiKSG1kWDAHAz88Pe/fuLTI9IyMDcXFxUCgUeP755wvNmzhxIiZOnKj3vurWrYuFCxeWvWAxdDodxo4di99//x379u1Du3btDNqOpejevTtEUSx7QSKyCC91rwef2lUQd998d3e//nJT2NspzbY/Kt20UX5Y9dNVaDTm++x+u5LecdyxRS10bFELKnUWmg3diaTUPFR3s8eNvS/rPc6hpRAEATPGNsOEecfMtk9nRxtMGtLYbPuj0lWv6oDxA32x/ucbZS9sJIH+HujYoqbZ9leWt8c0M2vBUBCAN1+pnJ+DJD8BAQEGrTd+/HikpqYiPj5er2IhYNhYiUREREREZHpWd2v3lStXIIoiGjVqBCcnJ6nDwfTp07F9+3a88847cHJywunTpwv+Hj16JHV4RCRzNjYKrP2os9n21+g5V8yZ3KLsBclsGj3nZtb3ZHTfBujdqfJ02VkcTw8nOP6vK0UHe2WlLRY+MW5gQ3Rva3hX6Pr64p22qOHuaLb9UdkWzWiLmu4OZtmXUilg3UedLWoc204ta+G1YeYrYs8c1wwtmlQ32/6ITEGpVOLNN9/Exx9/zFaCREREREQyYXUFw8jISABFuyOVyv79+wEAn3/+OTp27FjoLywsTOLoiMga9O7kjSnD9bvTW6XOQvyDTKjUWeVeRxCAjcFd4eQo28btlda8qS0R0KiaXusYcgzUdHfAyjkd9Q2PTEyhELAxuCuc9Tw3DTkGgtp64fWRltEVJf3Do5oD1szT/+YRQ46Bua+1QGt/j7IXNLNl/2mPup7Oeq1jyPNv9JwrPnmzjb7hEVkkpVKJKlWqSB0GEREREREZidVdtbW0gmFcXJzUIRAZpEaNGpgxYwZq1KghdShkBMv+0w7nrqrLPY5Z21f26L2PT99qgy6tPfVez1LJ6Ryws1Xipy+C0HViGJJSc8teAfofA3a2Cmz9vDs8qpmnFRPpp763CzYu6IrRs4+ivD2L63sM1PV0xvefvgCFwnJaltE/hvX0wdtj/PH1j1fLvY6+x8CL7Wtj3tSWekZmHq5V7PDTF0HoOXU/snPKN56jvs/fxdkWPy0Oks2NM3LKg0RERIZgLiQiIrlhC0MiMkj16tUxduxYVK/OLrXkwMXZDgfW9EGLJu4m2f5/p7TAB5Obm2TbUpHbOeDvWw0H1vRBNVc7o2/bzlaBbUt7oGeHOkbfNhnPyD4NsH5+V5iip8g6NZ3w29q+qOvJliiWbPnsDibrmvOFQE/88lVP2Nla7hi2nVrWwu6vesHRwfgxujjbImxVb4tsXWkoueVBIiIifTEXEhGR3FhdwfDIkSMQRREDBgyQOhSiSi0tLQ2HDx9GWlqa1KGQkdRwd8QfG/qjb2fjjS9nZ6vAV+93wCdvtbGo8aqMQY7nQNvna+DPjQPQ+Dk3o22zVnVH7F/dB4ODnjPaNsl0Jg1tjO1Le8DNxXiF49Z+1XHi+4FoUr+q0bZJpqFQCFj3cRd89O9WRm0J+kq/Bjiwpg+qONkabZum0qtjHRxe1w/etfTrnrQ09eu44OiG/ugaKJ9W9oA88yAREZE+mAuJiEhurK5gSETGcf/+fcydOxf379+XOhQyoqqu9ti3ujfWz+8C1yoVu7Db9nkPnN82BG+PbWak6CyLXM+BgMbuuLB9CGa9+nyFW5qNHeCLq78MR4/2tY0THJnF8F71ceXnYejftWI3D9jaKPDJm4E4veUl+NRxMVJ0ZGqCICB4emv89cNA+DWoWqFt1ajmgB3LeuDHxUFwdKg83XB2alkLl38ehslDK97acvpoP1zaORSBMmpZ+IRc8yAREVF5MRcSEZHcsGBIRESFCIKAycOa4Oqu4fhgcnO9x5xr93wNbFrYFX/9MAj+vtVMFCWZkqODDZb+pz3OhgzGq4Mawt6u/N3zKRQCBgfVw+F1/bBlUXe4u9mbMFIylTq1nLF3VW/s/qonenXUr+BbxckWr7/cFJd2DsV/p7aErS2/blZG7ZvXREToYHwztyOa+VbVa906NZ2wYHprXP1lOIb3qm+aAE3MzcUO64O74timARjRywdKZfnvoLC1UeCVfg1wessgrJrbqVK0rCQiIiIiIiKqPLf6EhGRWdWp5YxFM9pi/hutsev3OBw7p8K5q4m4eCMJuXnaguVqujsg0N8Dgf4eGBxUD22accB3uWjt74HvP+2GL99rj58OxODMpUc4e1WNqNgUiOI/yzXwdkGgvwfaNvPAqL4NUM+L49TJgSAIeCnoObwU9BxuxKVi+6FYnL2qxrmratxVZRZatnljdwT6V0enFrUwsk99uFYx/liYZH4O9jaYNtofb4zyw4mIBwg7fhfn/ncMJKflFSwnAOjYsiba+HsgqJ0XBr5QDzY28igUdw30RNdAT9x/mImfDsQg/LIaZ6+qEX2ncNdjTXzcEOjvgXbPe2B0P1/Uqu4oUcREREREREREhmHBkIiISmVvp8Tofr4Y3c8XAKDV6lC3109IUGfDq4Yj7h1+RXbjE1Jh1as6YPpof0wf/fhxXr4WPn1CkaDORu0ajri1b6S0AZLJNfZxw3+ntix4nJ2jgW//bQXHwMUdQ6ULjkxOEISCwhkAiKKIrGwNGg7cDtX/csHJHwZJHKVp1a7pjHdfDSh4nJunRf2+/3wORu0ZIWF0RERERERERBUnj1t/icjs7O3t0aRJE9jbs7tBa6NUKqBQPC4QKgTBaouF1nwO2NkqC44Ba33/rZ2jgw2PASsmCAKcnWyhtOJjwN6On4PWnAeJiIgA5kIiIpIftjAkIoPUr18fmzdvljoMIsnwHCAiImvGPEhERNaOuZCIiOSGLQyJiIiIiIiIiIiIiIiIrBgLhkRkkOvXr6Nz5864fv261KEQSYLnABERWTPmQSKqfESpAyBjsZC3krmQiIjkhgVDIjKIKIrIz8+HKFrIN3UiM+M5QERE1ox5kIgsnq1t4cd5edLEQcaXl1v48bPvtZkwFxIRkdxwDEMiIiIiIiIimVIqlRg+fLjRtrdkbSjSMzPh4uyM9/49qshjY1AqlUbZDlm5Ks6FHz94BDEzC4KzkzTxSMjJ0QYZp1+VOgy9ODmWfMlSjL1TeMKz7zUREREZhAVDIiIiIiIiIpkSBAE2Nsb76S8C0ImP/7WxsSnymMhSCA19ARsbQKN5PEGjgfjXGQi9gqQNTAKCIMDZSZpWeMYmanXQHf+r0DSFf1OJoiEiIpIXdklKRERERERERESyIjg7QWjdotA07f9tgu6vMxCfFBGpUhETk6D9ajVwu3ALQ6FzB4kiIiIikhfe/kdEBvHx8UFISAjq1KkjdShEkuA5QERE1ox5kIgqA0XnDtD+fe6fCTm50H7+JVDFGYJvA8DRARAE6QKk8tFqgaRkiLdigWfHC6zqBsHfT5KwmAuJiEhuWDAkIoM4ODjA19dX6jCIJMNzgIiIrBnzIBFVBkKXThBO/Q3xdHjhGRmZEC9GShMUGY+NDZRvvQ5BKU0HasyFREQkN+ySlIgMkpCQgE8++QQJCQlSh0IkCZ4DRERkzZgHiagyEGxtoHxvJoQObaUOhYzNxgbKObOgaNtashCYC4mISG5YMCQig6SmpmLPnj1ITU2VOhQiSfAcICIia8Y8SESVxZOioWLSeAiNG0odDlWUkyOEoK5QfvqRpMVCgLmQiIjkh12SEhERERERERGRbAm2NlAOGQgMGYiV67chPS0DVRQCpnu64puEFGRoRVRRCpjuVVXqUKk4CgFwdoZQswaElgEQbG2ljoiIiEiWWDAkIiIiIiIiIiKrkJ6bj7R8DVDFGcrRw5HxzVakZWQCjo8fExEREVkrdklKREREREREREREREREZMXYwpCIAABt2+o3CLy3tzc+/vhj9OzZE15eXiaKish8eA4QERGVn0KhQKtWraBQ8B5UIiKyTsyFREQkNywYEpFBvLy8MH/+fKnDIJIMzwEiIrJmOp0O58+fh06nkzoUIiIiSTAXEhGR3LBgSEREREREREREREREZEVEnQ7gTQ+Vg0IBwQwt2lkwJCIiIiIiIiIiIiIikjExMQm6v85APHkaYtxtICtb6pCovAQBcHKC0NgXis4dIHRoB8HVxei7YcGQiIiIiIiIiIiIiIhIhkRRhG7jZuj27ANEUepwyBCiCGRmQjx/Cdrzl4DV66F49RUoh71k1N2wYEhERERERER6cXFxQd++feHiYvy7WomIiCoD5kIiqgxEUYTu/76Dbu8BqUMhY9LpoPtuKyCKUA4fbLTNsmBIREREREREeqlTpw4WLFggdRhERESSYS4kospAt+MXFgtlTPf9jxDc3YF2rY2yPRYMiYiIiIiISC+5ubl4+PAhatasCXt7e6nDISIiMjvmQiKydKIoQnfw98ITFQoI3TpD0bE9BK9agK2tNMGRfnLzIMbfg+74XxBPhxeapTt4mAVDIiIiIiIikkZsbCxeffVV/PDDD2jatKnU4RAREZkdcyERWTrx5i3g4aNC05TvTIeiWxeJIqKKEOo/B0XXTtDu3A3d9z8WTBevXQeSko2yD4VRtkJEREREREREREREREQWQTxztvCE2l4QXugsTTBkNIqX+gNOjv9MEEUoIi4aZdtsYUhERERERERERERERCQjolpd6LEisCUEQZAoGumIooisbI3UYejFydGmxPdKsLWF0Pz5Ql2TColJRtkvC4ZERERERERERERERERykpVd+LGri9E2ffToUcyZMwdXrlxBRkYGNm3ahIkTJxpt+8aUla1BlQ4/SB2GXjJOvwpnp1LGl3R1Lfz42ffaQCwYEhERERERERERERERyYn4zGOF/iPUde/eHWfPnkVGRkbBtOTkZAwbNgze3t5YtmwZnJyc0KlTpwoGS/oQFIpn3t5n32zDsGBIREREREREemnatCn+/vtvqcMgIiKSDHMhEVmr8PBwpKSkYMOGDRg2bJjU4ZAR6V9SJiIiIiIiIiIiIiIiIqujUqkAAO7u7hJHQsbGgiERERERERHp5fbt25g0aRJu374tdShERESSYC4kImvk4+ODCRMmAACCgoIgCAIEQZA4KjIWdklKREREVA4qdRbOXVXj3NVEpKTnAQBS0vPw2f9dQJtmHgj090D1qg4SR0lEZB7Z2dm4fPkysrOzpQ6FiIhIEsyFRGSNVqxYgf3792PdunWYO3cu/Pz8pA6JjIgFQyIiIqISpGXkYfPeaKwJvYYrt1KKzM/M1uC/K88VPG7TzAPTRvlhVJ8GcHLk1ywiIiIiIiIiko8hQ4YgJSUF69atQ69evdC9e3epQyIjYpekRERERM/Iz9dh4drzqP1iCN787FSxxcLinL2ixqSPjqNOzxB8teUydDrRtIESEREREREREREZAQuGRERERE+5dCMJ7cfuwUffRCAzW2PQNlLS8zDzizPoPikM0XfSjBwhERERERERERGRcbFgSERERPQ/v/5xB+3G7MH5qESjbO94xAO0eWU3Tp5/YJTtERFZCi8vLwQHB8PLy0vqUIiIiCTBXEhERHLDgiERERERHhcLh717GLl5WqNuNzU9D73/fQB/XWDRkIjkw83NDf369YObm5vUoRAREUmCuZCIiOSGBcOniKKIkydP4v3330enTp3g7u4OW1tb1KpVCwMHDsSePXvKtZ1ffvkFgwYNgpeXF+zt7eHl5YWgoCAsWbLExM9AWsZ6/YiIiMwt8kYSXv7PEWg0phlzMCtHgwHTD+GuKsMk2yciMrfk5GRs374dycnJUodCREQkCeZCIiKSGxYMn3LkyBF06dIFX3zxBU6fPo3q1aujRYsWyM3NRVhYGAYPHozJkydDFIu/mJiXl4eXX34ZQ4cOxd69e+Hk5IQWLVrAzs4Ox48fx+LFi838jMyroq8fERGRFPLzdZj44TG9WhaGh7yEu7+NRnjIS+VeJyU9D1Pmn2AeJCJZePDgAZYsWYIHD9h6moiIrBNzIRERyQ0Lhk8RRRENGjTAypUr8fDhQ9y8eRNnz55FYmIili9fDkEQsHHjRqxZs6bY9V977TXs2LEDffv2RXR0NG7duoW///4bt2/fhlqtxsaNG838jMyroq8fERGRFL7YdAkR1/Qbs9DTwwnetZzh6eGk13oH/7qHjbtu6LUOERERERERERGRqbFg+JR27dohKioKb775Jjw8PAqmK5VKzJw5E1OnTgUArFu3rsi6hw4dwubNm9G+fXv8+uuv8PX1LTS/atWqeOml8rdCqIwq8voREZHly83TImTfLfScsh8qdTYA4FFyDr7ddg3pmXkSR2eYjKx8fPHdJbPuM/jb89BqdWbdp7Ekpebiyx8i0W7M7oJjQJ2Sg91Hb0OjqZzPiUgfWdkabPj5Ol6YuLfQ5+APe24iJ1cjcXRERERERETG9ccffyAjo/DwKhMnToQoiujevbs0QUno07cDIV6ajH8NaVTs/KMb+iPn7EQ0a1jNzJEZh+wLhmq1GrNnz0bDhg3h4OCAunXrYsaMGcjMzMTkyZMhCAJWrVoFAHB1dYWtrW2J2+rTpw8A4Pr160XmLV++HAAwb9482NjYmOCZmI6xukaryOtHRESW7dc/7qBe758w5oM/8PuZ+9DqHueOvHwd3vjkL9Tp+RO+3XZN4ij1tzXsFtIy8s26z7uqTIQdu2vWfVaUKIr4dN0F1OkZgllL/0b4ZXXBMZCbp8OQGYfRoP82nIhQSRwpken8sOcmavcMwWvzT+B4xINCn4MT5h2Dd6+fsP1QrMRREhERERERkanMX30ekTeT8OV/2qNOrcK9Ts0c1wzd23rh49URuBJdOce3lXXB8MKFCwgICMCSJUugUqng7++P/Px8fP311xg1ahSuXXt8YbNly5bl2l5OTg4AwMmp8IGQnZ2Nw4cPQ6FQICgoCGfOnMHrr7+Onj17YsiQIfj888+hVquN+txK0717dwiCgLi4uDKXvXTpElq1aoXo6GiTx1XS60dERJZt+6FYDJl5GA+TckpcJj0zH2988hcWb7xoxsgq7tvt0hQ512yLkmS/hhBFEe98cQbzVp1DTm7J4zzeVWWi59T9OHLmvhmjIzKPb366ignzjiE1veTW1IkpuRj5nyP4brd1dDvs5OSE9u3b87s9ERFZLeZCIiLrk695fMOos6MtNszvWjC9sY8bPn2rDU5feogl30VKGGHFyLZgqFarMWjQIKhUKsyaNQsJCQmIiIiASqXC4sWLERYWhvDwcAiCgObNm5drm6GhoQCArl27Fpp+8eJFaDQaVK9eHatWrULHjh2xdu1a/P7779i9ezfmzJmDRo0a4ejRo0Z/nhW1adMmXLx4EUFBQYiJiTHpvkp6/YiIyHJF30nD+Ll/QKcrX2v0D1acrTQFo8SUHFyISpJk33+eS6g0XXj+tD8GX229Uq5lc/N0GPbO71Anl1xcJqpszlx6iLcWnSr38lPmn0DkDWk+W8ypXr16WLlyJerVqyd1KERERJJgLiQisk7nryVi0YaL6NPZG1OGN4FCIeCHT1+AIAAT5h0r9zU0SyTbguHbb7+N+Ph4vPnmm1i6dClcXFwK5s2ePRstWrSARqOBj48PXF1dy9zevn37sHv37oL1n5aQkAAASE5OxgcffID+/fvjypUryM3NxaVLl9CjRw+kpKRg2LBhiI+PN+KzrLhly5Zh/PjxiI+PR1BQULlaJRqitNePiIgs15pt15Cbp19ha8WW8hWXpBZxLVGyfWfnaHEtJkWy/evjy82X9Vo+NSMPm36xjhZWZB2+2noF+vTgr9GKWPXTVdMFZCG0Wi0yMjKg1Zbc8piIiEjOmAuJiKzXwnXncSEqEUtntcPKOR3RPqAm/rvyHG7EpUodWoXIsmB47do1hIaGwsPDA4sWLSp2mcDAQABAixYtytzerVu3MH78eACPC5GdOnUqND8zMxMAoNFo4Ovri127dsHf3x92dnYICAjAr7/+Ck9PT6SkpGDFihWF1n1S1GzXrh3s7e0hCIK+T7dE8fHxiIuLK/Xvzp07mD9/Pnr06IE7d+4gKCgId+7cMVoMQNmvHxERWabsHI1BhZ+9x+4g7l66CSIyrohr5usuvDjnJN5/eYRffoSzV/SPc822qEp9Rx3REw8Ss7Hjtzi919uy9xZS0nKNH5AFuXnzJnr06IGbN29KHQoREZEkmAuJiKyXRiNiwrxjcLBXYtooPxyPUGHFFv1uuLZENlIHYAohISHQ6XQYO3YsqlSpUuwyjo6OAMouGKpUKvTt2xdJSUno3bs3li5dWmQZBweHgv+/+eabsLW1LTTfyckJb7zxBj7++GMcOHCg0Daio6Oxc+dOtG3bFnZ2djh58mS5n2dZDOn6My4uDuPGjcOxY8eMEkN5Xr/yatOmDVQqlVHiIqKKSaj6LqBwQ4IqAd7e3lKHQyaSp/REstsbeq8nikBgl+FwzLfsFjYpTn0Ah+JvYgkPeQmeHiWPReLp4Vjw793fRpe6H5U6C21f2VNk+oxZH2LedOPlfVPIsG8POPfXe73Ye+mo85wflGKGCaIiS2ENuSDHtiHyXcbrvV5WjgaNmgfBXmPcG/FMbcSIEeVe9uHDhwCA/fv349y5c+Veb+jQoXrHRZZl6L9mwrmKa8G5/+xjIkvHY5hKok8eBJgLicjyrWvQFL2qVi94/Pnnn2PNO29JGJE0dLAF3OcZfbupGXnIzdPCzlaJfcfv6tUzTVkaNW4MBfJLnL+wbgOMq+FV8HjLli0F/+/SpQvOnz9v0H5lWTA8cuQIACAoKKjEZZ50DVpawfBJkSs6OhqdO3fGrl27ihQDAaBatWoF//fz8yt2W0+mx8bGFpr+wgsvFHRpOn/+fKMWDAMCAmBnZ1euZRMTEwu6Iy3pOeirvK9fealUKty7d88osRFRBbloAQWg02p5XsqZkyPgZtiqSalZQLKFHxu1cwCH4md5ejjBu5ZzmZuwUSrKtVxx0tIykfbIwl+jGtmAYU8PqofJQN5D48ZDlsUacoGrJ+BS9mLFUSemARmV63V50nNKeWRnZxf8q896sj1WrIjuf13vPTn3n31MZOl4DFNJ9MlnAHMhEVm+nNo+hR6npaVZ52eQYAe4G3+zmxZ0hZ2tEldvJWPe1JbYdjAWMfHG6XEr4f59QMwrcX6mey2gxlOPn8pDDx48MHi/siwY3r59GwDw3HPPFTtfo9EUFOZKKhimpaWhb9++iIyMROvWrREWFgYnp+JbGjRt2rTg/yUV6J60Qny2X3OFwnS9wu7Zswc+Pj5lLhcfH49u3boBAEaNGoXVq1dXeN/6vH7l5enpWeG4iMg4EpRK6AAolEp41akjdThkIvlKFxha7nF3c4Sjk2UfG6mODiip/ZtKnVXqup4ejrBRKqDR6qBSZ5e6bEnbcnV1houdZb9GGfb2MLT3fc+aVaEUDb9RiCyfNeSCHBtnGDraqUd1F9i7Va7Xxdm5/HcIPPlB6ujoqNd6dWR6rFgThVJZ8G+dOnWKPCaydDyGqST65DOAuZCILN/TPSMCgKurq1V+BulgiwQjb/OtMf4Ialcbc78+i91HbyMidAg2LuiK7pP2GWX7XrVrl9rC8Nm88/TjWrVqGbxfWRYMnyTsJ3f6PCs0NBRqtRouLi6oX79+kflZWVkYOHAgwsPD4efnh4MHD8LNreQmFnXq1EG9evVw584dxMTEFNuy8datWwBgcd1b3Lt3D0FBQYiJicGIESOwZcsWKP/3ZdlQ+r5+5XX27NkKb4OIjMO7ZwjuPcyCl6cX4i/HSx0OmYhGo4NP31Dce1h68exZdrYKRJ3bgxrujiaKzDhWbL6Md5acKXZecV2IPu3ub6PhXcsZKnU26vb6yaD9r135GUb38zVoXXO5HpuCpoN36r1eiybuOL8tyqhjM5PlsYZckJaRhzo9Q5CRpdFrvepV7XE3/Dgc7CvXz63w8PByLxsVFYWQkBD069ev0A2UZXl2THeqfD77ZivSMjIfn/vx8UUeE1k6HsNUEn3yIMBcSESWT/PJEoh//3NN/YMPPsB/X7a+bpEzs/JRpcMPRttew3quWDSjDf6OfITFGy9BpxMxf00EFs1oi7fG+GPljxUfoufmjRtwdir5Jmzt6vXQHfit4PG4ceMw5cwJAMCJEycM3q/pmrdJ6ElLtIiIiCLzEhIS8N577wEAmjdvXuRCVl5eHoYOHYrjx4/D19cXhw8fhoeHR5n7HDlyJADg+++/LzJPFEV89913AIAePXro9VxMLTg4GNHR0Rg6dChCQkJgY1OxixqGvn5ERGR5bGwU+PfL5f/h+8SoPg0svlgIAIH+0uYnqfdfHk3qV0XPDrX1Xm/6KD8WC0kWXKvYYfzAhnqvN3lo40pXLNRXw4YNcfDgQTRsqP/rQ0REJAfMhURE1kcQgO8WvgClQsCEeX9Cp3s8cOEXmyIRfvkRFs1ogwbeBo5rYQFkWTDs2bMnAGDx4sW4ceNGwfTw8HAEBQVBrVYDAFq2bFloPa1WizFjxuDQoUPw9vbG4cOHUbt2+S6Svffee3B1dcXx48excOHCgq5HNRoN3n//fVy8eBH29vZ45513jPAMS9etWzcMHz68XN0hfPXVVwgODkZoaGiFi4UVef2IiMgyTRneBNWr2pd7eTtbBd599XkTRmQ8rfyqQ6qalmsVW/jWdZVm53p6f1JzvV6nel7OGNPfsltOEuljxthmcHIo//dk1yq2mDbKOGOCWzIbGxtUq1atwr8hiIiIKivmQiIi6zNrQgA6t6qFj1ZHICr2n0FcdDoREz88BhulAhsXdJUwwoqRZcFw9uzZqF69Ou7evYtmzZohICAAjRo1Qrt27dCgQYOCVn7Pjl+4bds27Nz5uNstOzs7jBs3Dl26dCn2T6VSFVq3Zs2a+Omnn2Bvb4+PPvoIXl5eaN++PTw9PbFkyRLY2Nhg/fr18PMz/cWD4OBg7NixAzVq1ChzWUdHR3z00Uewta34GEMVef2IiMgyeXo4Yc/XveDiXHaeUCoFbP6sG1o2rW6GyCquipMturaWZnzcfl28oVBUjhZ4PTvUwco5Hcu1bI1qDtj3TZ9Su80gqmya1K+K0CVBsLMt+6eTo70SP3/ZE8/Vrrx3lJZXfHw8Zs2axe77iIjIajEXEhFZl6b13bBwemucuvgQy76/XGT+1VspmL8mAt3aeOGtMf4SRFhxsrwFxtvbG8ePH8d7772HP//8E3FxcfD398fatWsxZcoU+Po+vuv92YJhbm5uwf9jYmIQExNT4j5ycnKKTOvXrx/Onz+Pzz77DL///jvOnz8Pd3d3jBw5Eu+//z5at25tpGdomSr6+hERkWXq1LIWjm0agNcXnsSZyEfFLtO0vhu+er8DeneyrLF6yzJtlB+OnTP/TSzTRlau1kfTR/ujRjUHvL88HHH3M4pdpkc7L6z7uEulaTlJpI+B3erht7V98eaiU4i8mVzsMq39qmP1fzuhffOaZo5OGhkZGTh+/DimTJkidShERESSYC4kIrIuUbGpcGxbdEi6p32+4RI+33DJTBEZnywLhgDg5+eHvXv3FpmekZGBuLg4KBQKPP984S7TJk6ciIkTJ1Z4v5s3b67QNiorY7x+RERkmVo2rY7TW1/CuatqbNx1A3H306HViqhd0wnjBzZE97ZelXLMuqEvPgdPD0eo1Nlm22cz36roGihNy8aKGNmnAYb39MGBk/H46UAMHiblwNZGgcbPuWLK8Kbwa1BV6hCJTOqFNl64uGMoTp5/gO/33ET8gywIAlDPqwr+NbgR2gXUqJSfg0RERERERESAjAuGJbly5QpEUUTjxo3h5OQkdTgAgB07dgAArl69Wuixj48P2rRpI1lcREREzwr090Cgv4fUYRiNna0Sn77VBpM/Pm62fX7xbrtKW1RQKhUY8EI9DHihntShEElCEAR0ae2JLhJ1Z0xERERERERkKlZXMIyMjARQtDtSKb388svFPp4wYQK+++47CSIiIiKyHv8a0gg7fovF/hOmH3tk4uBG6N+1rsn3Q0REREREREREpA8WDC2AKIpSh0BERGS1BEHAuo+6oNWoX6BOLt8Yuyp1VqF/y8OndhUsf6+9QTESEVmaGjVqYMaMGahRo4bUoRAREUmCuZCIiOSGBUMiIiKyet6ezji4pg96TNmP1PS8Mpdv+8oevbbv6eGI39b1Q1VXe0NDJCKyKNWrV8fYsWOlDoOIiEgyzIVERCQ3CqkDMLcjR45AFEUMGDBA6lCIiIjIgrT298DR9f1Q093BqNutX8cFJ74fiIb1XI26XSIiKaWlpeHw4cNIS0uTOhQiIiJJMBcSEZHcWF3BkIiIiKgkrfw8ELlzGIb39DHK9iYPbYzz24bAty6LhUQkL/fv38fcuXNx//59qUMhIiKSBHMhERHJDQuGRERERE+pWd0R25f1QOiSIDR+zs2gbbRo4o79q/tgfXBXuLnYGTlCIiIiIiIiIiIi47K6MQyJiIiIyiIIAkb2aYCXe9fH72fuY01oFH7/+36p4xtWr2qPvp29MW2UHzq2qAlBEMwYMRERERERERERkeFYMCQiIiIqgSAI6NmhDnp2qANRFHHrbjoirqmhUmcjL18HezsF6tR0RqB/ddTzqsIiIRERERERERERVUosGBIRERGVgyAIaFjPFQ3rcTxCIiJ7e3s0adIE9vb2UodCREQkCeZCIiKSGxYMiYiIiIiISC/169fH5s2bpQ6DiIhIMsyFREQkNwqpAyAiIiIiIiIiIiIiIiIi6bBgSERERERERHq5fv06OnfujOvXr0sdChERkSSYC4mISG5YMCQiIiIiIiK9iKKI/Px8iKIodShERESSYC4kIounEAo/1mqliYOMTtRqCk9QGKfUxzEMiYiIiIiIiIiIiIiI5MTJqfDjpGRp4pCYk6MNMk6/KnUYenFyLKN0l/jMe/nse20gFgyJiIiIiIiIiIiIiIhkRPCqhafbQOv+PgfF65MhGKk1WmUhCAKcnWylDsNoxKwsiJFXCk+rVcMo27auI4OIiIiIiIiIiIiIiEjmFJ3aF56QlAzdjl8kiYWMQxRF6L77EcjP/2eijRK61i2Nsn22MCQiIiIiIiK9+Pj4ICQkBHXq1JE6FCIiIkkwFxKRpRPqegP1vIE78QXTdFtCIZ45C6FTewietQA7+bS8ky0RQF4exLvx0J08Xej9BAChZXOgirNRdsWCIREREREREenFwcEBvr6+UodBREQkGeZCIqoMlEMHQfvVmkLTxJu3IN68JVFEZFQKBRSD+hlvc0bbEhEREREREVmFhIQEfPLJJ0hISJA6FCIiIkkwFxJRZaB4sTsUUydKHQaZgkIB5XszoGjVwnibNNqWiIiIiIiIyCqkpqZiz549SE1NlToUIiIiSTAXElFloRzYD4rXJwMuVaQOhYzFvRqUs2dC0bmDUTfLLkmJiIiIiIiIiIiIiIhkStm/NxS9e0CMvIJVh08jI1+LKpp8vHHnJtbUbYgMpQ2qaDV442601KFScWxtIVRxhtDIF0KXjhCaNoagMH57QBYMiYiIiIiIiIiIiIiIZEywsYHQqgUy/rqMtIxMwM0Nth/NQMY3Wx8/rlYNth/PlDpMkhC7JCUiIiIiIiIiIiIiIiKyYiwYEhERERERkV7c3d0xYcIEuLu7Sx0KERGRJJgLiYhIbtglKREBAMLDw/VaXq1W4+eff8awYcPg4eFRrnXatm1rSGhEZsFzgIiIqPwUCgVsbW2hMMG4GURERJUBcyEREckNMxoRGUStVmP9+vVQq9VSh0IkCZ4DRERkzZgHiYjI2jEXEhGR3LCFIREREREREREREZHMiTodxBvRECMuACmpELNzpA6JykMQIDg5AtXdoWjfBkK9ulJHREQyxYIhERERERERERERkUyJ+RrotoZCd+wkoE6UOhwygPi/f3WbfwLq1oGiVw8oBg+AIAiSxkVE8sKCIREREREREREREZEMifkaaBd/CfHvc1KHQsZy9x50GzcDiUlQTBrPoiERGQ3HMCQig7i4uKBv375wcXGROhQiSfAcICIia8Y8SERE1q4y5EJRq2WxUMZ0u8Og27RF6jCISEbYwpCIDFKnTh0sWLBA6jCIJMNzgIiIrBnzIBERWbvKkAvFS5eLLxZ614bieX/AyQlg6zTLp9NBTM+AeOFSkS5ldb/shWJQPwg1PCQKjojkhAVDIjJIbm4uHj58iJo1a8Le3l7qcIjMjucAERFZM+ZBIiKydpUhF+pOni48wdEByrnvQWjejN1YVkKiTgfx6DFoV34L6MSC6bq/zkA5eICEkRGRXLBLUiIySGxsLIYPH47Y2FipQyGSBM8BIiKyZsyDRERk7Sw9F4oaDcRTfxeaphg5DIoWz7NYWEkJCgUUL3aHEPRCoeniiVMSRUREcsMWhiRroigiK1sjdRh6cXK04Rc3IiIiIiIiIiIynDoRSM8oNEnRuYNEwUhLbtcHFZ07Qvv7nwWPxZg4M0VFRHLHgiHJWla2BlU6/CB1GHrJOP0qnJ1spQ6DiIiIiIiIiIgqq8zMwo8VCqBWTaNs+ujRo5gzZw6uXLmCjIwMbNq0CRMnTjTKtk1BbtcHhdqehSfk50PMzYNgb2eGyIhIzlgwJCIiIiIiIiIiIpIRUaMtPMHOVu8erbp3746zZ88iI+OflorJyckYNmwYvL29sWzZMjg5OaFTp07GCJnKy66YwqBWA4AFQyKqGBYMiYiIiIiIiIiIiKhM4eHhSElJwYYNGzBs2DCpwyEiIiNiwZCIDNK0aVP8/fffZS9IJFM8B4iIyJoxDxIRkbWz1lyoUqkAAO7u7hJHQkRExsaCIRERERERERERERGVysfHB7dv3wYABAUFFUwXRVGqkIiIyIgUUgdARJXT7du3MWnSpIIvikTWhucAERFZM+ZBIiKydtaYC1esWIGpU6cCAObOnYvNmzdj8+bNEkdFRETGwhaGRGSQ7OxsXL58GdnZ2VKHQiQJngNERGTNmAeJiMjaWWMuHDJkCFJSUrBu3Tr06tUL3bt3lzokIiIyIrYwJCIiIiIiIiIiIiIiIrJiLBgSERERERERERERERERWTEWDImIiIiIiIiIiIiIiIisGAuGRGQQLy8vBAcHw8vLS+pQiCTBc4CIiKwZ8yAREVk75kIiIpIbFgz/RxRFnDx5Eu+//z46deoEd3d32NraolatWhg4cCD27NlT4roTJ06EIAil/kVFRZnx2ViO//u//yt4DTgQsry4ubmhX79+cHNzkzoUIknwHCAiImvGPEhERNaOuZCIiOTGRuoALMWRI0fQs2dPAIAgCPD19UWDBg0QHR2NsLAwhIWFYdKkSVi/fj0EQSh2G40aNULNmjWLnefk5GSy2C2VSqXC7NmzpQ6DTCQ5ORmHDx9Gz549Ua1aNanDITI7ngNERGTNmAeJiMjaMRcSEZHcsIXh/4iiiAYNGmDlypV4+PAhbt68ibNnzyIxMRHLly+HIAjYuHEj1qxZU+I25s6dixMnThT7V69ePTM+G8vw1ltvIS0tDQMHDpQ6FDKBBw8eYMmSJXjw4IHUoRBJgucAERFZM+ZBIiKydsyFREQkNywY/k+7du0QFRWFN998Ex4eHgXTlUolZs6cialTpwIA1q1bJ1WIlcqePXuwY8cOTJ8+HYGBgVKHYxSfvh0I8dJk/GtIo2LnH93QHzlnJ6JZQ95VJmfJablYv/M6Fq49j0/XXcDWsGhkZWukDstsdDoRB0/GIz0zHwCQkZWPmPg0iaMiIjKf/HwdfjkSh0XrLyJ4TQS++ekq7j3IlDoss7oSnYzlmy8jLSMPAJCbp4UoihJHRURERETG9scffyAjI6PQtIkTJ0IURasceojXBolI7mRdMFSr1Zg9ezYaNmwIBwcH1K1bFzNmzEBmZiYmT54MQRCwatUqAICrqytsbW1L3FafPn0AANevXzdL7OZiios76enpmD59OmrXro1PPvnE6NuXyvzV5xF5Mwlf/qc96tQq3MXszHHN0L2tFz5eHYEr0ckSRUimdPt+OiZ/fBx1eoZgSvAJfPRNBOatOodxc/5EnZ4heHfJaSSl5kodpslotTqs2HwZjQZuR983DiLtfwXD1Ix8NBywHf2nHcTJ87yrkojkKzdPi4Vrz8OnXyiGzvwdc78+i/lrzuPNz07hub6hGPHu77h4PVHqME3q4Ml4dJ8UhueH/Yx3l5xBetbjG2bUKbkIGPYzNvx8nYVDIiIiIpItXhskIrmTbcHwwoULCAgIwJIlS6BSqeDv74/8/Hx8/fXXGDVqFK5duwYAaNmyZbm2l5OTA6D0sQh37NiBIUOGoEePHhg5ciS+/PJLPHr0qMLPRR/du3eHIAiIi4src9lLly6hVatWiI6ONmoMc+bMQXx8PFasWAFXV1ejbltK+RodJsw7BmdHW2yY37VgemMfN3z6VhucvvQQS76LlDBCMpVLN5LQfuyv2LjrBrJztEXmp6TnYfnmK+j86q+IV8mvlUlevhYv/+cI3llyBjHx6UXmiyKw/0Q8gibvQ8i+WxJESERkWumZeejz+gF89E0E7j/MKjJfqxWx83AcOo3fi0N/xUsQoel9vfUK+k07iD/Pqoqdf+VWCl6bfwL/XnASOh2LhkREREQkP7w2SERyJ8uCoVqtxqBBg6BSqTBr1iwkJCQgIiICKpUKixcvRlhYGMLDwyEIApo3b16ubYaGhgIAunbtWuIyYWFh2L17N44ePYrt27dj1qxZqF+/PrZs2WKU52VsmzZtwsWLFxEUFISYmBijbPPUqVNYs2YN+vXrh5dfftko27Qk568lYtGGi+jT2RtThjeBQiHgh09fgCAAE+Yds6oLZE5OTmjfvn2pRXQ5uP8wE33fOIgHidllLhsVm4r+0w8iMyvfDJGZzxuf/IVdv98uc7l8jQ6v/vdPHDlz3wxRSc9azgEiayeKIkbPPlpioexpWTkaDJ0pv5aG2w7GYMbi0yhP48H/23kd81aeM31QJDnmQSIisnbMhdaJ1waJSM5kWTB8++23ER8fjzfffBNLly6Fi4tLwbzZs2ejRYsW0Gg08PHxKVcLuH379mH37t0F6z+rcePGWL58OS5cuICUlBRkZmbi2LFj6N27NzIzM/Hqq68iLCzMeE/QSJYtW4bx48cjPj4eQUFB5WqVWJr8/HxMmTIF9vb2BV29ytHCdedxISoRS2e1w8o5HdE+oCb+u/IcbsSlSh2aWdWrVw8rV65EvXr1pA7FpL7aegUJj4q2JilJ5M1kbJVRK7trMSnYuOtGuZfXaEX8d+VZE0ZkOazlHCCydn+EJ2Df8fK3GszK0SD42/MmjMi8dDoRH6zQ73N96feReFiOG22ocmMeJCIia8dcaL14bZCI5Ep2BcNr164hNDQUHh4eWLRoUbHLBAYGAgBatGhR5vZu3bqF8ePHA3hciOzUqVORZebOnYuZM2eiRYsWcHNzg5OTE7p27YoDBw5g8ODBEEURM2fOLHZMl9jYWLz00ktwcXFBtWrV8OqrryIxseJ3pcfHxyMuLq7Uvzt37mD+/Pno0aMH7ty5g6CgINy5c8fgfX7++ee4cuUK5s2bhwYNGlT4OVgqjUbEhHnH4GCvxLRRfjgeocKKLZelDsvstFotMjIyoNUW7aJTLnJyNdigR7HsiW9+uiabMZzWbLum9zqnLz1CxFW1CaKxLNZwDhARsDpU/8/B3UfvyKaL6oMn4xF7r2h31KXJ1+gMyp9UuTAPEhGRtWMutF68NkhEciW7gmFISAh0Oh3Gjh2LKlWqFLuMo6MjgLILhiqVCn379kVSUhJ69+6NpUuX6hWLIAhYvHgxACA6OhqRkYX7sE5PT0dQUBDi4+MREhKCdevW4fjx4xg4cCB0Op1e+3pW165dUb9+/TL/fH19ceTIEQBAXFwcxo0bZ9D+rl+/jk8//RR+fn547733KhR7ZZCakYfcvMdfCPcdv1uuLrrk5ubNm+jRowdu3rwpdSgmc/TvBCSm5Oq93qUbSbK5q2zbwVjD1jtk2HqViTWcA0TWLi9fi11Hyu6S+Vk6nYidh+XxOWjo53noQeN0d0+Wi3mQiIisHXOhdeO1QSKSIxupAzC2J8WvoKCgEpeJj3/crVRpBcMnRcLo6Gh07twZu3btgq2trd7xNGnSBO7u7khKSsLNmzcLjZm4bt063Lt3D8eOHSvovsDb2xudOnXCnj17MGTIEL3390RAQADs7OzKtWxiYmJBd6R+fn4G7e+NN95Abm4uvv32W4Nep/Jo06YNVKqyxw96mg62gPs8o8eyaUFX2NkqcfVWMuZNbYltB2MRE6/f3fcladS4MRQw/xh4I0aM0Gv5hw8fAgD279+Pc+fKN1bR0KFD9Y5LSpl2LYAqwwxat0tQP9hr7ho5IvMSATyo9jEg6H9vycrVm7BlaeV6v3kOENGztIIztNWKdkdfHh8Gf4ElHxwxckTmp64yFrBrrPd6kdfi4O3tbYKIyJT0yYWG5EGAuVAOhv5rJpyruCJBlQBvb+8ij4ksHY9hKok5fhMC5suFLZ2qYFfTf659ZmZm4XkrPcZNcX3QlNcGgdKvD3ra2uFUQNtC0/ya+iFDx9auVD7MhfLzdAO0Ll264Px5w4ZKkV3B8Pbtx3eBP/fcc8XO12g0OHnyJICSC4ZpaWno27cvIiMj0bp1a4SFhVVoAOMnBTSNRlNo+t69e9GlS5dCfZ137NgRDRo0wK+//lqhguGePXvg4+NT5nLx8fHo1q0bAGDUqFFYvXq1QfuLiIiAQqHAyJEji8zLyMgAAPz111/w9PQEANy4caNc40c+TaVS4d69e/oFJtgB7vqtUpa3xvgjqF1tzP36LHYfvY2I0CHYuKAruk/aZ5TtJ9y/D4h5RtmWPjIz9es6LTs7u+Df8q6r9/snNbc6QPENlcukfqgCsivZ8y1OVc3j80hPWZlpyLpfuZ4/zwEiKkLhCFQzbNX0tGSkP5TBOV8vA9A/DUCnyeVnXiWkTy40JA8CzIVyoPtf13s6rRb37t0r8pjI0vEYppKY4zchYL5cWLuqO9D0n8eiqLPeY9zI1wdNfW0QKOP6oIMjEFB40v2E+0h/5tozUUmYC+XtwYMHBq8ru4LhkwT9JGk/KzQ0FGq1Gi4uLqhfv36R+VlZWRg4cCDCw8Ph5+eHgwcPws3NzeB4Hj16VHDH0bPV+atXr+Lll18usk6zZs1w9epVg/dZXvfu3UNQUBBiYmIwYsQIbNmyBUql0uDt6XS6Ug/G/Pz8gvmGdLn6pNioV0ywRYLea5WsYT1XLJrRBn9HPsLijZeg04mYvyYCi2a0xVtj/LHyx4q/b161a0vSwtDZ2Vmv5Z+ca46OjuVet06dOnrHJaU8pRaPAEAUAUEo/4qiFp7VbaEUK9fzLc5DXSLyFV56r+fmkIMqlez95jlARM8SIUClS4dO4aL3utWc8+Akg3M+1S4TGQasZ48UeMjg+VsbfXKhIXkQYC6UA8X/fjMqlErUqVOnyGMiS8djmEpijt+EgPlyYU2nwndAC4LCao9xY14fNMe1QaD064OetkXv6KvtVZstDKncmAvlR6fTISHh8SddrVq1DN6O7AqGnp6eSE5ORkREBDp27FhoXkJCQsH4es2bN4fwTAEgLy8PQ4cOxfHjx+Hr64vDhw/Dw8OjQvEsW7YMoijCzc0NbdsWbiqenJyMqlWrFlnH3d0d169fr9B+yyM4OBjR0dEYOnQoQkJCYGNj+OGQkpJS4rz58+cjODgY3bp1wx9//GHwPs6ePav3OplZ+ajS4QeD9/k0QQC+W/gClAoBE+b9CZ3ucefkX2yKxLAXfbBoRhuEHbtb4e4Hbt64AWcn03TrWprw8HC9lo+KikJISAj69euHpk2blr0CgBUrVhgQmbTajdmN8MtqvdYZ3a8RQr64YaKIzGtN6DVM+/QvvdZxsFci5vhWuLvZmygq0+A5QETF+eibc1i49oJe69R0d8Cds/tgb2f4jViW4tbdNDQauF3vMVl+Wv06hvT43DRBkcnokwsNyYMAc6EcfPbNVqRlZMLL0wvx8fFFHhNZOh7DVBJz/CYEzJcLdddvQvveP91wOjs7We0xbqzrg+a6NgiUfn1QVCdCM2laoWnXoq5BqEAPeWRdmAvlJzMzE1WqPL5R5MSJEwZvR/+BqSxcz549AQCLFy/GjRv/XLAPDw9HUFAQ1OrHF/5btmxZaD2tVosxY8bg0KFD8Pb2xuHDh1G7du0y9/fbb7/hgw8+wK1btwpNz8rKwoIFC/DFF18AAObMmVPuMQUrolu3bhg+fHi57mz66quvEBwcjNDQ0AoVC63FrAkB6NyqFj5aHYGo2NSC6TqdiIkfHoONUoGNC7pKGKF5NWzYEAcPHkTDhg2lDsWkpo/y13+d0YaNBWqJxg30hWsV/QrYY/r7VrpioSGs5RwgsnZThzeFjVKPVuYApgxvIotiIQD41nVFvy76jWFR19MZA1+oV/aCVKkxDxIRkbVjLrQ+vDZIRHInu4Lh7NmzUb16ddy9exfNmjVDQEAAGjVqhHbt2qFBgwbo0aMHgKLjF27btg07d+4EANjZ2WHcuHHo0qVLsX8qlapgvczMTCxevBgNGzZE7dq10bZtWwQGBsLDwwMff/wxRFHE1KlTMXv27CKxVqtWrdiWeUlJSXB3N6xj7eDgYOzYsQM1atQoc1lHR0d89NFHBWMsUsma1nfDwumtceriQyz7/nKR+VdvpWD+mgh0a+OFt8boX2CqjGxsbFCtWjXZF5vHD2qIl3sX7b64JO9Pao4urfXvPtdSuTjbYctn3aFQlO9ieRMfNyx5t52Jo7IM1nIOEFk7b09nfPth53Iv36F5Dcx9raXpApLAtx92Ru2a5btb2d5OgZDFQbCxkd3PDHoG8yAREVk75kLrwmuDRGQNZPdL3tvbG8ePH8eAAQPg4OCAuLg4uLu7Y+3atQgLCytodfhswTA3N7fg/zExMTh58mSJfzk5OQXLBgYGYt68eXjxxRdhZ2eHq1ev4sqVK6hRowZGjRqFw4cPY+3atUW6PwUAPz+/YscqvHr1Kvz85NNCSQ6iYlPh2PZ7dBr/a0F3A8/6fMMlCM03GK2vcksXHx+PWbNmyb6ZukIhYMuibnh1UNl3DM6b2hKLZrQxQ1TmNah7Pez8sgcc7UtvLdParzqObuhvFa0LAes5B4gImDysCdbP71JmS8Me7bywf3UfODnK66JRXc8q+HPjADR6zrXU5aq62OHgt33RuZXh4yVQ5cE8SERE1o650Lrw2iARWQPZFQyBx4W4vXv3Ij09Henp6Thz5gymTp2KzMxMxMXFQaFQ4Pnnny+0zsSJEyGKYrn+fHx8CtarW7cuFi5ciMOHDyMuLg6ZmZnIycnB7du38dNPP+HFF18sMc6BAwfixIkThb5YnDlzBrdu3cKgQYOM/rpIZf78+RBFsULjF5LlycjIwPHjx5GRkSF1KCZnZ6vEd5+8gNNbBuHVQQ0LdTMnCMCbr/jjyq5hWPhmYLE3B8jBkB4+iDswCp+93Qb1vAp3edyzQ238vPxFnNn6ErxqWE9/+dZ0DhDR46JhzP6R+O+UFqjp7lBo3kvd6+HAmj74bV0/VHWV500TDeu5InLnMGxZ1A2dWtYsNK/xc25YMbs9YvePRLc2XhJFSObGPEhERNaOuZCIiORGXrc/l+HKlSsQRRGNGzeGkwUMAjt16lSsXLkSgwcPRnBwMHJycjB79my0a9cOgwcPljo8InqKIAho37wm2jeviXUfd4FPn1CoErPh5eGIlXM6Sh2eWdSs7og5r7XA+5OaIyU9D9k5GlR1sStxEG4iIrmp61kFn7zVBsHTWsO7109QqbNRu4Yjdn/dS+rQzMLeTomxAxpi7ICGSM/MQ2p6PpydbFDVxU62N8wQERERERERWQurKhhGRkYCKNodqVRcXV1x5MgRzJgxA6NHj4aNjQ0GDhyI5cuXQ6GQZeNPIlmwt1NC+b9u6azxAqlCITzudtRKuh4lInqWUqmAUmG9eQB4PMati7Od1GEQERERERERkZGwYCgxX19f7N27V+owiIiIiIiIiIiIiIiIyEpZVTM2SywYElVWNWrUwIwZM1CjRg2pQyGSBM8BIiKyZsyDRERk7ZgLiYhIbqyqheGRI0ekDoFINqpXr46xY8dKHQaRZHgOEBGRNWMeJCIia8dcSEREcmNVLQyJyHjS0tJw+PBhpKWlSR0KkSR4DhARkTVjHiQiImvHXEhERHLDgiERGeT+/fuYO3cu7t+/L3UoRJLgOUBERNaMeZCIiKwdcyEREckNC4ZEREREREREREREREREVowFQyIiIiIiIiIiIiIiIiIrxoIhERERERERERERERERkRVjwZCIDGJvb48mTZrA3t5e6lCIJMFzgIiIrBnzIBERWTvmQiIikhsbqQMgosqpfv362Lx5s9RhEEmG5wAREVkz5kEiIrJ2zIVERCQ3bGFIREREREREREREREREZMVYMCQig1y/fh2dO3fG9evXpQ6FSBI8B4iIyJoxDxIRkbWrdLlQlDoAMhqRbyYRmQYLhkRkEFEUkZ+fD5FfUshK8RwgIiJrxjxIRETWztJzoeDwzNiKubkQNRppgiHjysoqOs3ewfxxEJHscAxDkjUnRxtknH5V6jD04uTI05KIiIiIiIiIiCrA1bXIJPFqFITmz0sQjLTkdn1Qd+Va4QkuVSAo2S6IiCqOlQmSNUEQ4OxkK3UYREREREREREREZiNUqwrUfw6IvV0wTXfgMISAZhAEQbrAJCCn64Nifj7Ew38Umia0aiFNMEQkOywYEhEREREREREREcmMonNH6J4qGIonTkGrUEDRvzeEpo0hKNgqrbIQ8zUQL0VCt2svxOiYQvMUXTpKFBURyQ0LhkRkEB8fH4SEhKBOnTpSh0IkCZ4DRERkzZgHiYjI2lWGXKjo0hG6H0MB3T/jLIrHTkJ77CSgVAJOjoCVtTaslHS6x+MW6ooZL9PZmS0MichoWDAkIoM4ODjA19dX6jCIJMNzgIiIrBnzIBERWbvKkAuF2p5Qznob2mVfFy02abVAeoY0gZFxODpC+fEHEOztpI6EiGSC7c6JyCAJCQn45JNPkJCQIHUoRJLgOUBERNaMeZCIiKxdZcmFiq6doJz1NqBgS0JZcXSEMnguFE0bSx0JEckIC4ZEZJDU1FTs2bMHqampUodCJAmeA0REZM2YB4mIyNpVplyo6NoJNquWQfHKCKCut9ThUAUITRpBMflV2HyzjMVCIjI6dklKREREREREREREJGOCdx0oX3kZq/OUSG+aARc7W0zv1BzfnLiA9Lz8x4+7tJQ6TCqOIEBwdATcq0GoVlXqaIhIxlgwJCIiIiIiIiIiIrIC6RnZSMvKARRKKAKaIf3YBaTl5AE2tlAENJM6PCIikhC7JCUiIiIiIiIiIiIiIiKyYiwYEpFBFAoFWrVqBYWCHyNknXgOEBGRNWMeJCIia8dcSEREcsOMRkQG0el0OH/+PHQ6ndShEEmC5wAREVkz5kEiIrJ2zIVERCQ3HMOQiIiIiIiIiKyGqE6EmJwMZOVIHQqVl5MDhKpVIdTwkDoSIiIiItliwZCIiIiIiIiIZE1UPYDu2F/QnTwNxMZJHQ4Z6rl6UHTuAMULnSDU9pI6GiIiIiJZYcGQiIiIiIiIiGRLd/4itJ8uAfLypQ6FKur2Hehu34Fu204o58yCom2g1BERERERyQbHMCQig7i4uKBv375wcXGROhQiSfAcICIia8Y8SJUFi4UypdFCu2gZdOHnpI6ErBhzIRERyQ1bGBKRQerUqYMFCxZIHQaRZHgOEBGRNWMepMpATM8ouVhoYwM4OwGCYP7ASD+iCGRmARpN4en/KxoKG1ZDqFZVktDIujEXEhGR3LBgSEQGyc3NxcOHD1GzZk3Y29tLHQ6R2fEcICIia8Y8SJWBeDq8SLFQaNsaiiEDIfj7QVCy06XKQtTqIF6Lgu7X/RBP/f3PDI0WulNnoOzfR7rgyGoxFxIRkdzw2zERGSQ2NhbDhw9HbGys1KEQSYLnABERWTPmQaoMdCdPF3osBDSDcu5/oAhoxmJhJSMoFVA87w/l++9ACGxZaJ74zPtMZC7MhUREJDdsYUhERERERESyJYoitFqt1GHoRalUQmBXmRUianUQL0YWmqbo/SIEpVKiiKQjiiKysjVlL2hBnBxtij0HBIUCit4vQnvuQsE08fI1iLl5EOztzBghERERkfywYEhERERERESypdVqsXPnTqnD0Mvw4cNhY8Of6xWSmQk8UygWmjWVKBhpZWVrUKXDD1KHoZeM06/C2cm22HlF3kdRBDIyAHt3M0RGREREJF/sg4OIiIiIiIiI5CU3t+g0JyejbPro0aPo0KEDXFxcIAgCvvvuO6Nsl8qpuPcxO8f8cRARERHJDG9ZJCIiIiIiIiL507Ob1+7du+Ps2bPIyMgomJacnIxhw4bB29sby5Ytg5OTEzp16mTsSKk07K6XiIiIyCRYMCQigzRt2hR///231GEQSYbnABERWTPmQbJW4eHhSElJwYYNGzBs2DCpwyEiCTEXEhGR3LBLUiIiIiIiIiKiclCpVAAAd3eOl0dERERE8sKCIREZ5Pbt25g0aRJu374tdShEkuA5QERE1ox5kKyRj48PJkyYAAAICgqCIAgQ2D0mkdViLiQiIrlhl6REZJDs7GxcvnwZ2dnZUodicjqdiNOXHuLvyEc4d02NazGpeJD4+Hk/TMrBax8fR6C/Bzo0r4GWTavzooGVsKZzQBRFXLyehNOXHuLsFTUibyYjPSsfoijC2dEWfg3cEOjngbbP10DHFjWhUPAckJv8fB1OnFfh7BU1zl1T40ZcGrJzNVAoBLhVsUOLxu4I9PdAp5Y14e9bTepwTeJGXCpOXniAc1fVuHA96ak8kI2R/zmCQP/qaONfA10Da8HOVilxtMaXmp6HP88m4NzVRJy7psZdVSZy87SwtVGgprsDWvt5oE0zD7wQ6AmvGk5Sh0tmYE15kOiJFStWYP/+/Vi3bh3mzp0LPz8/qUMiIgkxFxIRkdywYEhEVAJ1cg427rqBb7dHIfZeerHL5Gt02LDrBjbsugEAaN7YHdNG+WHsAF9UcbI1Z7hERpeRlY+tYbewZts1XLyeVOJy566qsWXvLQBA/ToueP3lppg0tDE8qjmYK1QykXsPMvF/O69j3c7rSHiUVeJypy4+LPh/xxY1MW2UH0b08oGDfeX+qpmXr8Wu329jdeg1HDunKnaZfI2I7Ydisf1QLACgprsDXhvWBP9+uSnqeVUxZ7gmcSEqEWu2XcOWvbeQlaMpcbkjfycAAJRKAYO7P4dpo/zQo70Xb6IhIlkZMmQIUlJSsG7dOvTq1Qvdu3eXOiQiIiIiIqNhl6RERM/Q6USs/ukqfPqG4v0V4SUWC4tz6UYSXl94Er79t+Hnw3GmC5LIxH4+HAff/tvw+sKTpRYLnxV7Lx3vrwiHT99QrP7pKnQ60YRRkqloNDp89n8X0KD/NgR/e77UYuGzTl18iPFz/0TTwTtx5Mx9E0ZpWifPP8Dzw37G6NlHSywWFudhUg4+W38RDfpvw4erziEvX2vCKE0nKTUX4+f+gVYjf8G6HddLLRY+TasV8fPvceg5dT+6/SsM0XfSTBwpERERERERERkDC4ZERE+5q8pAzyn7Mf2zU8jMLt/F0eI8TMrB8Hd/xyuzjyIlLdeIERKZVkpaLl6ZfRTD3/0dD5NyDN5OZrYG0z87hZ5T9uOuKsOIEZKpRcWmoMO4X/HfleeQl68zeDu372fgxSn7Me2Tk8guZ7HJEuTla/HuktPoOnEvbt42vNil1Yr4ZN0FtBm9G5dulL/obgn2Hb+LZkN3FrQcNtTxiAdoMWIXVoVchSjy5gEiIiIiIiIiS8aCIREZxMvLC8HBwfDy8pI6FKO5HpuCTuP34mh4gtG2+dOBGHSfvK9grCuSDzmeAw8Ts9F98j78dCDGaNs8Gp6ATuP3Iio2xWjbJNP5O/IROo3/Feeuqo22zTXbotBv2kGkZeQZbZumkpWtweC3D2P55iswVn0r8mYyukzYi2NnjZdbTGnDz9cx6K3foFIbJ29l5Wjw1qJTeHfJGRYNZUaOeZCIiEgfzIVERCQ3LBgSkUHc3NzQr18/uLm5SR2KUcTGp6PHlP2If5Bp9G1fvJ6E3v8+gGS2NJQVuZ0DyWm56PXvA3p1P1pe8Q8y0eO1/YiJZ9eEluzi9UT0fv0AktOMX9j786wKg976zaJbGublazHsncM4cDLe6NtOz8xH/+mHcObSw7IXltAPe27itfknTNKV8IotV/Desr9ZNJQRueVBc9NoLPfzkIiIyoe5kIiI5IYFw6eIooiTJ0/i/fffR6dOneDu7g5bW1vUqlULAwcOxJ49e0pcd+LEiRAEodS/qKgoMz4b84uLiyvzNXjyFxwcLHW4VEHJycnYvn07kpOTpQ6lwvLzdRj27mHcf1j+Mbr0delGEib89xgvlMqInM4BURTxrw+PmbTbxIRHWRj2zu+Vdjw3uUvPzMPgGYeRmm66VoDHzqnwzpIzJtt+Rc396iwO/nXPZNvPzNZg8IzDSEq1zJtHLkQlYvL84ybdx7IfLuPHfRXr5pQsh5zyYHlpNBrExMTg8OHD2Lp1K7777jts3rwZu3btQkREBFJSUsq1nXPnzuHdd99FQkLlaHlMRETFs8ZcSERE8mYjdQCW5MiRI+jZsycAQBAE+Pr6okGDBoiOjkZYWBjCwsIwadIkrF+/HoIgFLuNRo0aoWbNmsXOc3JyMlnslsDBwQGdO3cucX56ejouXboEAOjUqZO5wiITefDgAZYsWYKAgABUq1ZN6nAq5LP1F3AhSr9CSXjIS/D0cIJKnYW2r5R8M8HTfv3zDraG3cK4gQ0NCZMsjJzOgR/33cLuo3f0WseQc+Di9SR89n8XMX9aa0PCJBN678tw3L6v31iThhwDa7dHYUQvH/TsUMeQME3mrwsP8OXmy3qtY8jzf5CYjbc/P4Uti7obEKXp5OVrMfHDY9Bo9LupxZDX4K1Fp9CjXW141ZD392JrIKc8WBpRFHH58mX89ttviIiIKLNloKenJ1588UV069YNrq6uReafO3cOy5cvh0ajwcKFC7Fw4UJUr17dVOETEZEJWUsuJCIi68GC4VNEUUSDBg3wzjvvYPTo0fDw8AAAaLVarFy5Eu+++y42btyIwMBATJs2rdhtzJ07FxMnTjRj1JbD09MTJ06cKHH+F198gUuXLsHb2xsvvviiGSMjKtmV6GR88n8X9F7P08MJ3rWc9V7v7c9PoW9nb3hUc9B7XSJTUCfn4K1Fp/Rez9Bz4NP1FzCilw+eb+Su97qWQhRFJKXmIiMrH65V7FDVxa7EG4kqgz/PJmDtdv17QTD0GJj88XFE7R4BRwfL+Bqan6/Dvz48rveYhYY+/61htzCmvy/6d62r97qmsmRTpEHdERvyGiSn5eGtRaew40t+FyTLd+nSJXz33Xe4f/9+uddRqVTYunUrtm3bhhdffBGjR4+Gg8Pj731PFwsBoGnTpqhataopQiciIiIiItKbZVypsRDt2rVDVFQUbG1tC01XKpWYOXMmoqKisHbtWqxbt67EgiGV7IcffgAAjB8/HgoFe8Mly7B882W9W1RURHJaHtb/fB0fTG5htn0SlWbDrusmGbOuJBqNiBVbrmB9cFez7dNYUtJy8cOv0Viz7RqiYlMLprf2q443RvrhlX4N4OxkW8oWLNMXmy6ZdX93EjKx7WAsJgxuZNb9lmTPH7dx43Zq2Qsa0RebLllMwTA3T4sVW6+YdZ87D8ch+k4aGtYr2vqKyBJkZWVh69at+P333wtNr1q1Kp5//nk0aNAAdevWhYODA3Q6HRITExETE4ObN2/i+vXrAID8/HwcOHAAERER+Pe//42cnJxCxcJOnTph+vTpUCqVZn9+VH5//PFHkWkTJ0602puEP307EHNfa4lJHx3Dpl9uFpl/dEN/dGxRE4Gjd+NKNLtoJCIiIqpsZF+1UavVmD17Nho2bAgHBwfUrVsXM2bMQGZmJiZPngxBELBq1SoAgKura5Fi4dP69OkDAAU/AuXCHGOqnTt3DleuPL4YNWHCBJPvj6g8UtJy8eN+84+l9O32KGi1OrPvl+hZWq0O324z//i6P+6/heQ0yxzHrSR/XXiAhgO3Y8bi04WKhQAQcS0RU4JPwG/ITly+abpxIE0hNj4d+0/Em32/q0OvmX2fJZEilj/PqizmQuqO32KhTs4x+34NadVKZA5JSUn48MMPCxULGzVqhJkzZ2LVqlV488030b9/fwQEBKBRo0Zo0qQJOnXqhHHjxiE4OBjLly9H//79YWdnBwB4+PAhFi5ciGXLlrFYSJXe/NXnEXkzCV/+pz3q1CrctfTMcc3Qva0XPl4dYTE5joiIiIj0I+uC4YULFxAQEIAlS5ZApVLB398f+fn5+PrrrzFq1Chcu/b4AlHLli3Ltb2cnMcXU0obi3DHjh0YMmQIevTogZEjR+LLL7/Eo0ePKvxc9NG9e3cIgoC4uLgyl7106RJatWqF6Ohok8b0/fffAwDat2+PJk2amHRfZB5OTk5o3759pR6bM2R/DLJztGbf7+37Gfj9TPm7tiLLJIdz4MjfCYjTc9w6Y8jO0SJkn/mL9YY6e+URek09gMSU0oucd1WZ6D55H26aubVaRWzafUPvrjiN4e/LjxB5Q/riakx8Go78nSDJvtf/bBk3oK3/+YYk+934yw3ePFPJySEPPis5ORnBwcG4d+8eAMDe3h6TJk1CcHAwOnToABubsjvo8fLywquvvoovvvgCTZs2LZiu0z0+3lkspMosX6PDhHnH4Oxoiw3z/+ktorGPGz59qw1OX3qIJd9FShghkXnJMRcSEZF1k23BUK1WY9CgQVCpVJg1axYSEhIQEREBlUqFxYsXIywsDOHh4RAEAc2bNy/XNkNDQwEAXbuW3I1aWFgYdu/ejaNHj2L79u2YNWsW6tevjy1bthjleRnbpk2bcPHiRQQFBSEmJsYk+8jPz0dISAgAWG3XLXJUr149rFy5EvXq1ZM6FIOdvPBAsn3/deGhZPsm45DFOXBewnPgYuU4B3Q6EWM/+BNZOZpyLZ+YkotJHx03cVTGY+3HwCkJY7CEPKDR6HAmUpo4klJzcT2u8hTXqSg55MGnaTQaLF68GA8ePP5crFmzJhYvXozevXsbNJyCp6cnBg4cWGTdDh06sFhIldr5a4lYtOEi+nT2xpThTaBQCPjh0xcgCMCEeceg00lwJxKRROSWC4mIiGRbMHz77bcRHx+PN998E0uXLoWLi0vBvNmzZ6NFixbQaDTw8fGBq2vZ46fs27cPu3fvLlj/WY0bN8by5ctx4cIFpKSkIDMzE8eOHUPv3r2RmZmJV199FWFhYcZ7gkaybNkyjB8/HvHx8QgKCipXq0R9hYWFQa1Ww97eHqNGjTL69kkaWq0WGRkZ0GrN30LPWM5dVVvlvsk4eA5U3n3r4/cz9/Ue3+7E+Qe4ZAGt58oiiiIiriVKtn9LOAakjOHijSTk50vbwu5aTIokLe2fsIRjgAwnhzz4tF27dhX8FqpRowY+/vhjeHp6Gry9c+fOYcWKFQUtC5/YsGED0tPTKxIqkeQWrjuPC1GJWDqrHVbO6Yj2ATXx35XncIM3gpCVkVsuJCIikmXB8Nq1awgNDYWHhwcWLVpU7DKBgYEAgBYtWpS5vVu3bmH8+PEAHhciO3XqVGSZuXPnYubMmWjRogXc3Nzg5OSErl274sCBAxg8eDBEUcTMmTOLjBf4pKjZrl072NvbQxAEfZ9uieLj4xEXF1fq3507dzB//nz06NEDd+7cQVBQEO7cuWO0GADghx9+AAC89NJLqFatmlG3TdK5efMmevTogZs3iw52Xxlk52gkbdlw4brlFxOodJX9HAAeFyykcj0uFdnlbLUnJUPHWVu3w/LHZ7uTkIGU9DzJ9n/hunTFyicuSvhZnJunxfW4FMn2D0j7GQAwF1Z2csiDT8TGxuKXX34BACiVSsyaNQvVq1c3eHvnzp3D8uXLC8Ys7NixI1q1agUASE1NxXfffVfRkIkkpdGImDDvGBzslZg2yg/HI1RYseWy1GERmZ2cciEREREAlD0IQyUUEhICnU6HsWPHokqVKsUu4+joCKDsgqFKpULfvn2RlJSE3r17Y+nSpXrFIggCFi9ejN27dyM6OhqRkZGFukCNjo7Gzp070bZtW9jZ2eHkyZN6bb80pXWdWpK4uDiMGzcOx44dM0oMiYmJBS0rK9odaZs2baBSqYwQFRVnxIgRei3/8OHjLsz279+Pc+fOlWudoUOH6h2XqWgFZ4jVirYWfiI85CV4epQ8DoGnh2PBv3d/G13icip1Ftq+sqfI9HuqRHh7e+sRMZmatZ0DAHC/6hxA4VDsPFOfA6IINGjUDEoxU8+ozeuB6zTAppbe663f/Ct+WT3SBBEZT76yFuA2rdh5Zb3/QMWPgfMXo+DtPV2PiI3voeu/AZvaxc4z1jkAlPwaBPUaAHvNXT0iNq4M+3aA84Bi55njGPh23fcIXTFcj4jJ1PTJhYbkQUCaXGhnZ1fijaQA8PPPPxe0DhkyZAh8fHwM3tezxcInYxampqbivffeQ2ZmJk6ePIlhw4ahTp06JW6ncePGyMuT7qaO0gz910w4V3FFgioB3t7eRR5bitq2djgZ0LbQtCZNGiNLZ33jp+pgC7jPM+o2UzPykJunhZ2tEvuO3zX6mMiNGjeGAvnFzlMCiG7dudC0bt26ISY3u1zbrizHMJmfOX4TAtL/LuQ5QET8HJCfp3s26dKlC86fP2/QdmRZMDxy5AgAICgoqMRl4uPjAZReMHxSJIyOjkbnzp2xa9cu2Nra6h1PkyZN4O7ujqSkJNy8ebNQwfCFF15AQkICAGD+/PlGLRgGBATAzs6uXMsmJiYWdMHj5+dntBhCQkKQl5cHT09P9OnTp0LbUqlUuHfvnpEio2dlZup30T47O7vg3/Kua1Hvn40bUEqDV08PJ3jXci57M0pFuZZ7ligKlvV6kPWdAwDgVvIsU58DAKBSPQA0Ft51lbNo0Lel3Fyt5b3fz3JQlngMlPf9Bww/BjQanfSvkaOmxPfXHOeA+lEikCXha1A9DSghdHMcA1lZOciS+higQvTJhYbkQUCaXGhvb1/iPLVajbNnzwIAqlWrVqGLuCUVC5VKJdzd3TFs2DBs3rwZAHDo0CH861//KnFb9+/fR25ursGxmJLuf8VVnfZxrnv2saVQODoBAYWn3b+fgEyt5fdwYHSCHeBu3E1uWtAVdrZKXL2VjHlTW2LbwVjExBuvu92E+/cBsfiiuVIQgNaFpz148AD3Msu3/8pyDJP5meM3ISD970KeA0TEzwF5ezIuuyFkWTC8ffs2AOC5554rdr5GoykozJVUMExLS0Pfvn0RGRmJ1q1bIywsDE5Opd9lXZonhcYnPx6fUChM1yvsnj17ynV3bHx8PLp16wYAGDVqFFavXm20GL7//nsAwNixY6FUKiu0rYqMIUJlc3bW70Lfky/Djo6O5V63tLuozU0n2COhlPkqdVap63t6OMJGqYBGq4NKXfKdrCVtRwENvCzo9SDrOwcAIEHQoqR77E19DgCAl6cHFGLxPQFYikeKXBjSvsPBToPqFvZ+PytfUQ0PS5hX1vsPVPwYsFGKqCXxa/TIBiW+v8Y6B0rbVg2PqrDTSvcaZNo7I6WEeeY4BpydbFHVws8Ta6NPLjQkDwLS5MLSbqL8/fffC4aN6NmzJ2xsDPuJXFqx8Inu3bsjNDQUeXl5OHbsGF555RU4OBTf0r927doW28JQ8b/npFAqUadOnSKPLYWnbdH3vXZtL6ttYVjabx99vTXGH0HtamPu12ex++htRIQOwcYFXdF90j6j7cOrdu1SWxg+q1atWsjMdS3XtivLMUzmZ47fhID0vwt5DhARPwfkR6fTFTRMq1VL/56ynpBlwfBJwn5yp8+zQkNDoVar4eLigvr16xeZn5WVhYEDByI8PBx+fn44ePAg3NxKaYZRhkePHhV0U2BpTXrv3buHoKAgxMTEYMSIEdiyZUuFC3tPXL16teBu3Yp2RwqgYFtkGuHh4XotHxUVhZCQEPTr1w9NmzYt1zorVqwwIDLTEEURtbr/iEfJOcXOL67rtKfd/W00vGs5Q6XORt1eP+m9//at6uOvzfF6r0emY23nAAB0Gv8rTl0svmRk6nOgRjUH3Lt406hj95rCyh+v4O3PT+u93uav38KI3l+aICLjycnVwKXjD9BoivYhVtb7D1T8GHipT3vsXD5X7/WMacJ//8QPv0YXO8/U5wAA3Ig8jqquJbd8MrU/whMQNLn4i7vmOAY++fAtzBy/Vu/1yHT0yYWG5EFAmlyo0Wiwc+fOYuddvvzPuGul9VBTmvIUC4HHF6I7dOiAY8eOITs7G7du3UKzZs2K3eaNGzcMLl6a2mffbEVaRia8PL0QHx9f5LGlEB+poZlcuOvr69dvQHAsvkgrZ5lZ+ajS4QejbKthPVcsmtEGf0c+wuKNl6DTiZi/JgKLZrTFW2P8sfLHq0bZz80bN+DsVHwPT6JWC83QMYWm/fnnnxC8i+9m/FmV5Rgm8zPHb0JA+t+FPAeIiJ8D8pOZmVkwPN+JEycM3o7pmrdJ6ElLtIiIiCLzEhIS8N577wEAmjdvXuRCZV5eHoYOHYrjx4/D19cXhw8fhoeHR4XiWbZsGURRhJubG9q2bVv2CmYUHByM6OhoDB06FCEhIUb9UfrDD49/kLRu3RrPP/+80bZLlqFhw4Y4ePAgGjZsKHUoBhEEAYH+FTu3K0LKfZNxVPZzAJD2OAz097D4YiEAvDqoEZwc9MuNXjWcMDio+F4OLImDvQ2a+ZbSN7OJBfpXl2zf/8Qg3TngW9dF0mIhALRqKu17wFxYuckhD2q12oJhGWrVqgV3d/37bCxvsfCJpy8ox8bG6h80kYQEAfhu4QtQKgRMmPcndLrHNx19sSkS4ZcfYdGMNmjg7SJxlETmI4dcSERE9DRZFgx79uwJAFi8eDFu3LhRMD08PBxBQUFQq9UAgJYtWxZaT6vVYsyYMTh06BC8vb1x+PBh1K5d9h1qv/32Gz744APcunWr0PSsrCwsWLAAX3zxBQBgzpw55R5TsCK6deuG4cOHl6s7hK+++grBwcEIDQ01arFQp9Nhy5YtAIAJEyYYbbtkOWxsbFCtWjWLvfO5PNo0k7JYIv2FcqoYWZwDkhYMK8c54OZih49eb6nXOp+9HQhb28rxFUvaY0D6YpGUeUDKfT/h5mKHxs8Z3otGRSgUAlr5VY7PASqeHPLgvXv3kJ//uMvDBg0a6L2+vsVCAPD19S34f0xMjN77JJLSrAkB6NyqFj5aHYGo2H/GodbpREz88BhslApsXNBVwgiJzEsOuZCIiOhpleNqlp5mz56N6tWr4+7du2jWrBkCAgLQqFEjtGvXDg0aNECPHj0AFB2/cNu2bQVd1djZ2WHcuHHo0qVLsX8qlapgvczMTCxevBgNGzZE7dq10bZtWwQGBsLDwwMff/wxRFHE1KlTMXv2bLM8/+DgYOzYsQM1atQoc1lHR0d89NFHBWMsGsvhw4dx79492NraYsyYMWWvQJVOfHw8Zs2aVambqb/cu2iXxObgYK/EoG71JNk3GY8czoFB3evBwd443VDra2Qf/S/MSmX2v5rj3VfL11L+85ltMHFwYxNHZDwj+0jzOVijmgO6t/WSZN9Pa/d8DdT11G+sGmMZ2dsyzgGpjoH+XbxRpYSu5qhykEMeTElJKfi/vuOlG1IsBAqPJ5KamlrKkkSWpWl9Nyyc3hqnLj7Esu8vF5l/9VYK5q+JQLc2XnhrjL8EERKZnxxyIRER0dNkWTD09vbG8ePHMWDAADg4OCAuLg7u7u5Yu3YtwsLCClodPlswzM3NLfh/TEwMTp48WeJfTs4/454FBgZi3rx5ePHFF2FnZ4erV6/iypUrqFGjBkaNGoXDhw9j7dq1laLrNWP5/vvvAQADBgyocJeuZJkyMjJw/PhxZGRkSB2KwZo3dkeXVoYPAmuo0X0boHpV6xs7RW7kcA64u9njlX7mL1p0aVULzRvr3+2bVARBwLL/tMfWRd3RuoQWUV1b18KvK3vh/Uktip1vqXp2qIOG9VzNvt/XhjWBvZ00xeqn2dgo8PrL5R9vxljq1HTCS90t48aRqSOaQKEw/3fUaaP8zL5PMi455EFPT0+MHz8eo0aNQkBAQLnXy8rKwpo1a/QuFgKPb0x9+eWXMXbsWPTq1cvg2InMLSo2FY5tv0en8b8WdEX6rM83XILQfIPRxjEksnRyyIVERERPk22beT8/P+zdu7fI9IyMDMTFxUGhUBQZV2/ixImYOHGi3vuqW7cuFi5caGiosrR161Zs3bpV6jCIyvTmK/44cf6BWfc5fTQvkpLlmD7aH5t+uWnmfVbOc2DMAF+80r8Bwi+r0fvf+5GakQ+3KrY48f3/s3ffcVmV/x/H3zcbBAcuUFQUF+5tbjBNNMuVWY4iM1t+KyvNbGlZZlra15ZWjqzUtEzLmZkjM/deiYoKgooLQfZ9//7wJ18JUG7Wgft+PR8PH3qfc65zPudwbo7wvq/r6qkGtYpPAHorBweTnh0QqJGTtxbaMR0dTRr+QJ1CO96dPN63jt6esUdJyWmFdsynHqwrJ6ei8bm9Kj6e6h1cTT/9Hl5oxwyo4qVu7fwK7XhAdipUqKB7773X6nYeHh566aWX9P7776t58+Y5DgslycHBQf369bP6mAAAAABQ0IrGbyoK0cGDB2WxWFSrVi15eHgYXY4kafHixVq8eLEOHTqU4fWOHTsMrgywff3vqa7gQhwWb1jf2mpR/87DBQOFpXm9cnqiX+GFN8EtfYvVcKT/ZjKZ1Kph+fShFD09nIttWHjTMw8FqmGtMoV2vLHDGsu/slehHe9OKpZ119vPNCu049WqVlIvDsl5T6bCMOWlVirhXnifI/zstbaG9GoE8lNgYKAmTJhgVVgIAAAAAEWZ3QWG+/fvl5R5OFIj9e/fX/3799eiRYsyvP7kk08MrgywfQ4OJn09vkOh/KK0ik8Jffhy6wI/DmCtKS+1KpR53Eq4O+nr8R0ICooYF2dHzXmnoxwdC/7r0rBWGb0+vEmBH8daLz3aQK0bFvyHOUwmafbbHeVRiOFcTlT389IHI1sWyrGe6FdH97SldyFsQ5UqVQgLAQAAANgMAsMiwGKxZPlnzpw5RpcGZKt8+fJ6/vnnVb588e8tV93PSzPebGdVm+iY64o4F6/omOs52t7F2UHz3uukkp4uuSkRRZAtvQdKerro2/c6WTWnnLXvAUn6/PW2qu5XdHqW4X+a1SunSS9YFxhZew+U9HTWtxOD5OJc9H657ujooG/e7aSypV1z3CY374E3n2yqdgbMnZsTTz0YqN6dq1nVxtpr0KBmGU15qVVuykMRZEvPQQAAcoNnIQDA1hStjzcXgqIYGALFUdmyZTVo0CCjy8g3g+6tqcuxyfrPxC052r7lw8tyvG8XZwctmtJZnVoU3tCnKHi29h7o2MJXi6Z01gMv/a7kFPMdt7fmPSBJ/x1zl4bcVyu35aEQvPRoQ125lqwJM/fkaHtr7gFPD2ct/+QeNapddIdvre1fSqs+76auw1fpyrXkO25v7Xvg+UH19dbTTXNbXoFzcDBp/qQg9Xp+rdb8FZmjNtZcg9rVSmnNjBA+OGNDbO05CACAtXgWAgBsjd31MFy3bp0sFkuuJrcH8D+xsbFau3atYmNjjS4l34x4uJ7mvNNRbq751/ulTEkX/frJPbo/2LpeGyj6bPE9cF9QVf36yT0qUzL/fqHv5uqo2e900H8G1s+3faLgvDOiuSa/2CpfhyetVMFD677qrvbNfPJtnwWlRf3y2jD7XlWr5Jlv+zSZpPHPNNPU0a1lMhXt4XjdXJ207L9d9XD3/J1n9K5G5bVpzr3yLV805g9H/rDF5yAAANbgWQgAsDV2FxgCyB9nz57V2LFjdfbsWaNLyVeP9qqlPT/0VpvGFfK8r17BVXXo537q2qZyPlSGosZW3wNd21TWoZ/7qVdw1Tzvq03jCtrzQ2+F9qqdD5WhsLwc2lBbv7tfDWqWyfO+QnvV0oGf+qplg+IzTFOj2t7a/2MfPdW/bp73VbtaKW3+pqfefKppkQ8Lb3J1cdR37wdpwQfBVg3RmhUXZwe9/0ILbZrTUxXKuudThSgqbPU5CABATvEsBADYGgJDAPiXOtVLa9OcezXjzXaqH1Da6vZtm1TQ4g87a8m0LvIpR28KFD8+5Ty0ZFoXLf6ws9o2sT48rx9QWjPebKdNc+5Vneql879AFLjm9cppx4Je+vDlVqqRi3knu9xVSau/6KbZ73RUmZJ5C52M4FXCRZ+/0U5/fN1DPTr4ydqsr6pvCU18voX2LOqtNo2L5pyFt2MymTQgpIYOLemnkUPqq7SXdb2OXV0c9ch9NbVnUR+9MrSxnJz4kQMAAAAAgKLO7uYwBICccHR00PAH6uqJfnW0aWe0vltxXNsPxOhA2GWlpGac383N1VFN6nirdcMKCu1VS03qljWoaiD/mEwm9etaXf26Vtfeoxc1Z+kxbd1/QbuPXFRiUlqGbZ2cTGpY01stG5TToB4B6tDcp9j0pkL2XF0c9eIjDfXC4AZa81ekFq4+oR0HY3ToxBWZzZYM23p6OKtpXW+1bVJRQ3vXVm3/UgZVnb+CWvoqqKWvTkTEataSf7R5z3ntOhyj2LiUDNs5OJhUt3opNQ8sp/73VFePDn5ydCz+IVmFsu76aNRdmjCihRauPqHlG89o56EYhZ+Ny7ytt5ta1C+n4JaVFNqrlsqVcTOgYgAAAAAAkFsEhgBwGyaTSR1b+KpjC19JUlJymo6fiVV8QqpMJsnLw1kBVUrSewI2rXGdspo6+kYQnppq1vEzseoQ+qsuXE5SBW83nV7zkFxd8m/uTxQtDg4mhbT3U0h7P0nS9YRUnYiIVedhK3ThcpIqervp7LqBcnCw3ZC4hl9JTfhPC0mS2WzRychrunItWampZrm7OamGn5c8PZwNrrLgeLg76bHetfVY7xvDC1+8kqiIc/HqOnylLlxOkk/ZG/cAHxQAAAAAAKD4IjAEkCuurq6qU6eOXF2L31BzeeHq4qh6AXmf1wvFn72+B5ycHFSnemm5ON8ICJ2dHAgL7YyHu5Ma1PJOvwecnBxsOiz8NwcHkwKqlDS6DEOVLe2msqXd0u8BR0cHwkI7ZK/PQQAAbuJZCACwNQSGAHKlevXqmjdvntFlAIbhPQAAsGc8BwEA9o5nIQDA1jCGHgAAAAAAAAAAAGDHCAwB5MrRo0fVrl07HT161OhSAEPwHgAA2DOegwAAe8ezEABgawgMAeSKxWJRSkqKLBaL0aUAhuA9AACwZzwHUeQ5ZjHHcnJy4deB/JeUxdfRiTm1Ufh4FgIAbA1zGAIAAAAAbJajo6P69euXb/ubPGOhrsXHy6tECY16ckCm1/nBMauwC9YpUSLTIkvkWZlKlTSgGGN5uDsp7u9HjC7DKh7ut/l1VVRU5mWemb/eAAAAsA6BIQAAAADAZplMJjk55d+PvhZJZsuNv52cnDK9RtFgcnWR/CpJEWfTl1n+2irVq2tgVcYwmUwq4eFsdBn5xvzn3xkXVCifZUAMAAAA6zAkKQAAAAAAsDkO7dtkeG1evlrmTX8xfGAxZbFYZP57u8zLVmRY7tC+jUwmk0FVAQAA2A4+/gggV/z9/TV//nxVrlzZ6FIAQ/AeAADYM56DKA4c2t0l84If/7cgLU1pkz+W5nwnU6MGMnl5Sg58jrrIs1hkiYuTZe8B6fyFTKtN7e4yoCiAZyEAwPYQGALIFTc3NwUEBBhdBmAY3gMAAHvGcxDFQtUqcuh2t8yrf8+4/EKMLL+vF/0Miz9TcAeZatYwugzYKZ6FAABbw0fpAORKVFSUJkyYoKisJpwH7ADvAQCAPeM5iOLAZDLJ4elhMt1zt9GloACYgjvI8blnGI4UhuFZCACwNQSGAHLl6tWrWrZsma5evWp0KYAheA8AAOwZz0EUFyYHBzk+M0wOjzwsVa5kdDnID74+chj44I2w0JFfa8E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" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "pm = generate_preset_pass_manager(backend=backend, optimization_level=1)\n", + "isa_circuit = pm.run(circuit)\n", + "\n", + "isa_circuit.draw('mpl', style='iqp', idle_wires=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "67acea4f", + "metadata": { + "id": "67acea4f" + }, + "outputs": [], + "source": [ + "no_correction_circuit = build_error_correction_sequence(apply_correction=False)\n", + "\n", + "isa_no_correction_circuit = pm.run(no_correction_circuit)" + ] + }, + { + "cell_type": "markdown", + "id": "bcd61a1f", + "metadata": { + "id": "bcd61a1f" + }, + "source": [ + "## Step 3: Execute using Qiskit primitives\n" + ] + }, + { + "cell_type": "markdown", + "id": "e68d10d2", + "metadata": { + "id": "e68d10d2" + }, + "source": [ + "Run the version with correction applied and one without correction.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d53319ba", + "metadata": { + "id": "d53319ba" + }, + "outputs": [], + "source": [ + "sampler_no_correction = Sampler(backend)\n", + "job_no_correction = sampler_no_correction.run([isa_no_correction_circuit], shots=1000)\n", + "result_no_correction = job_no_correction.result()[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "df7421d0", + "metadata": { + "id": "df7421d0" + }, + "outputs": [], + "source": [ + "sampler_with_correction = Sampler(backend)\n", + "job_with_correction = sampler_with_correction.run([isa_circuit], shots=1000)\n", + "result_with_correction = job_with_correction.result()[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1cba37f5", + "metadata": { + "id": "1cba37f5", + "outputId": "ba8bc050-c675-4d91-8ef7-ee77e9e5205c" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Data (no correction):\n", + "{'101': 146, '111': 516, '011': 180, '000': 25, '110': 23, '100': 16, '001': 46, '010': 48}\n", + "Syndrome (no correction):\n", + "{'01': 206, '00': 736, '11': 20, '10': 38}\n" + ] + } + ], + "source": [ + "print(f\"Data (no correction):\\n{result_no_correction.data.data.get_counts()}\")\n", + "print(f\"Syndrome (no correction):\\n{result_no_correction.data.syndrome.get_counts()}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7b7697f2", + "metadata": { + "id": "7b7697f2", + "outputId": "677b27de-252a-4cb4-be2d-7b17b45a6186" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Data (corrected):\n", + "{'010': 18, '101': 139, '111': 540, '100': 18, '001': 47, '011': 169, '000': 18, '110': 51}\n", + "Syndrome (corrected):\n", + "{'11': 19, '00': 809, '10': 90, '01': 82}\n" + ] + } + ], + "source": [ + "print(f\"Data (corrected):\\n{result_with_correction.data.data.get_counts()}\")\n", + "print(f\"Syndrome (corrected):\\n{result_with_correction.data.syndrome.get_counts()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "1b652319", + "metadata": { + "id": "1b652319" + }, + "source": [ + "## Step 4: Post-process, return result in classical format\n", + "\n", + "You can see that the bit flip code detected and corrected many errors; resulting in fewer errors overall.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fa59fb42", + "metadata": { + "id": "fa59fb42" + }, + "outputs": [], + "source": [ + "def decode_result(data_counts, syndrome_counts):\n", + " shots = sum(data_counts.values())\n", + " success_trials = data_counts.get('000', 0) + data_counts.get('111', 0)\n", + " failed_trials = shots - success_trials\n", + " error_correction_events = shots - syndrome_counts.get('00', 0)\n", + " print(f\"Bit flip errors were detected/corrected on {error_correction_events}/{shots} trials.\")\n", + " print(f\"A final parity error was detected on {failed_trials}/{shots} trials.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5b1ff3a3", + "metadata": { + "id": "5b1ff3a3", + "outputId": "bcf011e0-d32d-44b1-b3d0-57df8e306b53" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Completed bit code experiment data measurement counts (without correction): {'101': 146, '111': 516, '011': 180, '000': 25, '110': 23, '100': 16, '001': 46, '010': 48}\n", + "Completed bit code experiment syndrome measurement counts (without correction): {'01': 206, '00': 736, '11': 20, '10': 38}\n", + "Bit flip errors were detected/corrected on 264/1000 trials.\n", + "A final parity error was detected on 459/1000 trials.\n" + ] + } + ], + "source": [ + "# non-corrected marginalized results\n", + "data_result = result_no_correction.data.data.get_counts()\n", + "marginalized_syndrome_result = result_no_correction.data.syndrome.get_counts()\n", + "\n", + "print(f'Completed bit code experiment data measurement counts (no correction): {data_result}')\n", + "print(f'Completed bit code experiment syndrome measurement counts (no correction): {marginalized_syndrome_result}')\n", + "decode_result(data_result, marginalized_syndrome_result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f1c2d48", + "metadata": { + "id": "7f1c2d48", + "outputId": "7fd731ff-b947-4972-f4a9-c086f14be59e" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Completed bit code experiment data measurement counts (corrected): {'010': 18, '101': 139, '111': 540, '100': 18, '001': 47, '011': 169, '000': 18, '110': 51}\n", + "Completed bit code experiment syndrome measurement counts (corrected): {'11': 19, '00': 809, '10': 90, '01': 82}\n", + "Bit flip errors were detected/corrected on 191/1000 trials.\n", + "A final parity error was detected on 442/1000 trials.\n" + ] + } + ], + "source": [ + "# corrected marginalized results\n", + "corrected_data_result = result_with_correction.data.data.get_counts()\n", + "corrected_syndrome_result = result_with_correction.data.syndrome.get_counts()\n", + "\n", + "print(f'Completed bit code experiment data measurement counts (corrected): {corrected_data_result}')\n", + "print(f'Completed bit code experiment syndrome measurement counts (corrected): {corrected_syndrome_result}')\n", + "decode_result(corrected_data_result, corrected_syndrome_result)" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "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" + }, + "vscode": { + "interpreter": { + "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6" + } + }, + "colab": { + "provenance": [] + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file