1363 lines
1.4 MiB
1363 lines
1.4 MiB
{
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"cells": [
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8f563e71-f031-43a7-9e71-1f3bf50cf673",
|
||
"metadata": {
|
||
"tags": [
|
||
"remove-cell"
|
||
]
|
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},
|
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"source": [
|
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"{/* cspell:ignore elist, rarr, qidx, cidx, rbrack, cvar, setminus */}"
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]
|
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},
|
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{
|
||
"cell_type": "markdown",
|
||
"id": "689402c9-cb97-41a8-8587-416c346feb03",
|
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"metadata": {},
|
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"source": [
|
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"# Advanced Techniques for QAOA\n",
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"*Usage estimate: 25 minutes on IBM Sherbrooke (NOTE: This is an estimate only. Your runtime may vary.)*"
|
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]
|
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},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e1fdfd3c-ea42-44f9-8e04-fe013c26c8f9",
|
||
"metadata": {},
|
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"source": [
|
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"## Background\n",
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"\n",
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"This notebook introduces advanced techniques to improve the performance of the **Quantum Approximate Optimization Algorithm (QAOA)** with a large number of qubits.\n",
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"Please see [Solve utility-scale quantum optimization problems](/tutorials/quantum-approximate-optimization-algorithm) for an introduction to QAOA.\n",
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"\n",
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"The advanced techniques in this notebook include:\n",
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"\n",
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"- **SWAP strategy with SAT initial mapping**: This is a specifically designed transpiler pass for QAOA that uses a SWAP strategy and a SAT solver together to improve the selection of which physical qubits on the QPU to use. The SWAP strategy exploits the commutativity of the QAOA operators to reorder gates so that layers of SWAP gates can be simultaneously executed, thus reducing the depth of the circuit [\\[1\\]](#references). The SAT solver is used to find an initial mapping that minimizes the number of SWAP operations needed to map the qubits in the circuit to the physical qubits on the device [\\[2\\]](#references) .\n",
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"- **CVaR cost function**: Typically the expected value of the cost Hamiltonian is used as the cost function for QAOA, but as was shown in [\\[3\\]](#references) , focusing on the tail of the distribution, rather than the expected value, can improve the performance of QAOA for combinatorial optimization problems. The CVaR accomplishes this. For a given set of shots with corresponding objective values of the considered optimization problem, the Conditional Value at Risk (CVaR) with confidence level $\\alpha \\in [0, 1]$ is defined as the average of the $\\alpha$ best shots [\\[3\\]](#references).\n",
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"Thus, $\\alpha = 1$ corresponds to the standard expected value, while $\\alpha=0$ corresponds to the minimum of the given shots, and $\\alpha \\in (0, 1)$ is a tradeoff between focusing on better shots, but still applying some averaging to smoothen the optimization landscape. Additionally, the CVaR can be used as error mitigation technique to improve the quality of the objective value estimation [\\[4\\]](#references)."
|
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]
|
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},
|
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{
|
||
"cell_type": "markdown",
|
||
"id": "637cc0b1-354b-4c91-abd6-ce0d37eea3f2",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Requirements\n",
|
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"\n",
|
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"Before starting this tutorial, be sure you have the following installed:\n",
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"- Qiskit SDK v1.0 or later, with visualization support ( `pip install 'qiskit[visualization]'` )\n",
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"- Qiskit Runtime 0.22 or later (`pip install qiskit-ibm-runtime`)\n",
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"- Rustworkx graph library (`pip install rustworkx`)\n",
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"- Python SAT (`pip install python-sat`)"
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]
|
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},
|
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{
|
||
"cell_type": "markdown",
|
||
"id": "2e64680d-42ef-4d01-bc42-3e4bf08cea4c",
|
||
"metadata": {},
|
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"source": [
|
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"## Setup"
|
||
]
|
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},
|
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{
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||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "90e8ddc0-b27a-4243-a2ea-6465988fec53",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
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"from __future__ import annotations\n",
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"\n",
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"import numpy as np\n",
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"import rustworkx as rx\n",
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"import matplotlib.pyplot as plt\n",
|
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"from dataclasses import dataclass\n",
|
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"from itertools import combinations\n",
|
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"from threading import Timer\n",
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"from collections.abc import Callable, Iterable\n",
|
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"from typing import Sequence\n",
|
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"from pysat.formula import CNF, IDPool\n",
|
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"from pysat.solvers import Solver\n",
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"from scipy.optimize import minimize\n",
|
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"from rustworkx.visualization import mpl_draw as draw_graph\n",
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"\n",
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"from qiskit.quantum_info import SparsePauliOp\n",
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"from qiskit.circuit.library import QAOAAnsatz\n",
|
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"from qiskit.circuit import QuantumCircuit, ParameterVector\n",
|
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"from qiskit.transpiler import CouplingMap, PassManager\n",
|
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"from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
|
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"from qiskit.transpiler.passes.routing.commuting_2q_gate_routing import (\n",
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" SwapStrategy,\n",
|
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" FindCommutingPauliEvolutions,\n",
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" Commuting2qGateRouter,\n",
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")\n",
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"\n",
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"from qiskit_ibm_runtime import QiskitRuntimeService, Session\n",
|
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"from qiskit_ibm_runtime import SamplerV2 as Sampler"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a7b390ce-6a6e-4cce-b586-2980d0e94507",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 1: Map classical inputs to a quantum problem\n",
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"\n",
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"### Max-Cut Problem\n",
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"Let's consider solving the **Max-Cut** problem on a graph with 100 nodes using QAOA.\n",
|
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"The Max-Cut problem is a combinatorial optimization problem that is defined on a graph $G = (V, E)$, where $V$ is the set of vertices and $E$ is the set of edges. The goal is to partition the vertices into two sets, $S$ and $V \\setminus S$, such that the number of edges between the two sets is maximized.\n",
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"In this example, we will use a graph with 100 nodes that is based on a hardware coupling map.\n",
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"\n",
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"\n",
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"### Graph -> Hamiltonian\n",
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"\n",
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"First, convert the graph into a Hamiltonian that is suited for the QAOA. Details on this process can be found in the introductory QAOA tutorial, linked above."
|
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]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "179077e5-50d5-4db2-8b55-591aeca1a35b",
|
||
"metadata": {
|
||
"collapsed": true,
|
||
"jupyter": {
|
||
"outputs_hidden": true
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"<IBMBackend('ibm_kyiv')>\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# QiskitRuntimeService.save_account(channel=\"ibm_quantum\", token=\"<MY_IBM_QUANTUM_TOKEN>\", overwrite=True, set_as_default=True)\n",
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"service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
|
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"backend = service.least_busy(operational=True, simulator=False)\n",
|
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"print(backend)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "056a7cc3-7c8e-41ea-a17b-ef048e8e61d9",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"n = 100 # Number of nodes in graph\n",
|
||
"graph_100 = rx.PyGraph()\n",
|
||
"graph_100.add_nodes_from(np.arange(0, n, 1))\n",
|
||
"elist = []\n",
|
||
"for edge in backend.coupling_map:\n",
|
||
" if edge[0] < n and edge[1] < n:\n",
|
||
" elist.append((edge[0], edge[1], 1.0))\n",
|
||
"graph_100.add_edges_from(elist)\n",
|
||
"draw_graph(graph_100, node_size=200, with_labels=True, width=1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "cdd5c74f-f894-4a80-98bf-27af3f112598",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Cost Function Hamiltonian: SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],\n",
|
||
" coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def build_max_cut_paulis(graph: rx.PyGraph) -> list[tuple[str, float]]:\n",
|
||
" \"\"\"Convert the graph to Pauli list.\n",
|
||
"\n",
|
||
" This function does the inverse of `build_max_cut_graph`\n",
|
||
" \"\"\"\n",
|
||
" pauli_list = []\n",
|
||
" for edge in list(graph.edge_list()):\n",
|
||
" paulis = [\"I\"] * len(graph)\n",
|
||
" paulis[edge[0]], paulis[edge[1]] = \"Z\", \"Z\"\n",
|
||
"\n",
|
||
" weight = graph.get_edge_data(edge[0], edge[1])\n",
|
||
"\n",
|
||
" pauli_list.append((\"\".join(paulis)[::-1], weight))\n",
|
||
"\n",
|
||
" return pauli_list\n",
|
||
"\n",
|
||
"\n",
|
||
"max_cut_paulis = build_max_cut_paulis(graph_100)\n",
|
||
"\n",
|
||
"cost_hamiltonian = SparsePauliOp.from_list(max_cut_paulis)\n",
|
||
"print(\"Cost Function Hamiltonian:\", cost_hamiltonian)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1b61cc7b-37ec-4c1e-ae62-ca59a030a590",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Hamiltonian → quantum circuit"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "99f216ff-e94b-4daf-bc1b-278f9bd1d9f6",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1754.86x1695.63 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"circuit_100 = QAOAAnsatz(cost_operator=cost_hamiltonian, reps=1)\n",
|
||
"circuit_100.measure_all()\n",
|
||
"\n",
|
||
"circuit_100.draw(\"mpl\", fold=False, scale=0.2, idle_wires=False)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4604b82d-2003-4842-bbef-6b9ce5caf782",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 2: Optimize problem for quantum hardware execution\n",
|
||
"### SWAP strategy with the SAT initial mapping\n",
|
||
"We will demonstrate how to build and optimize QAOA circuits using the **SWAP strategy with SAT initial mapping**, a specifically designed transpiler pass for QAOA applied to quadratic problems.\n",
|
||
"\n",
|
||
"In this example, we choose a SWAP insertion strategy for blocks of commuting two-qubit gates which applies layers of SWAP gates simultaneously executable on the coupling map. This strategy is presented in [\\[1\\]](#references) and exposed as a standardized Qiskit transpiler pass (see [here](/api/qiskit/qiskit.transpiler.passes.Commuting2qGateRouter)), where we can choose different qubit configurations. We use a line swap strategy in this example."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "a10620d5-e70b-4d08-badd-ec5103b000e9",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"nodes = rx.longest_simple_path(graph_100)\n",
|
||
"# even edges and odd edges\n",
|
||
"even_edges = [\n",
|
||
" (nodes[i], nodes[i + 1])\n",
|
||
" if nodes[i] < nodes[i + 1]\n",
|
||
" else (nodes[i + 1], nodes[i])\n",
|
||
" for i in range(0, len(nodes) - 1, 2)\n",
|
||
"]\n",
|
||
"odd_edges = [\n",
|
||
" (nodes[i], nodes[i + 1])\n",
|
||
" if nodes[i] < nodes[i + 1]\n",
|
||
" else (nodes[i + 1], nodes[i])\n",
|
||
" for i in range(1, len(nodes) - 1, 2)\n",
|
||
"]\n",
|
||
"edge_list = [\n",
|
||
" (edge[0], edge[1]) if edge[0] < edge[1] else (edge[1], edge[0])\n",
|
||
" for edge in graph_100.edge_list()\n",
|
||
"]\n",
|
||
"\n",
|
||
"swap_strategy = SwapStrategy(CouplingMap(edge_list), (even_edges, odd_edges))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "038dc48a-7dbc-4fcc-9296-440181177d4a",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Remap the graph using a SAT mapper\n",
|
||
"\n",
|
||
"Even when a circuit consists of commuting gates (this is the case for the QAOA circuit, but also for trotterized simulations of Ising Hamiltonians), finding a good initial mapping is a challenging task. The SAT-based approach presented in [\\[2\\]](#references) enables the discovery of effective initial mappings for circuits with commuting gates, resulting in a significant reduction in the number of required SWAP layers. This approach has been demonstrated to scale to up to *500 qubits*, as illustrated in the paper.\n",
|
||
"\n",
|
||
"The following code demonstrates how to use the `SATMapper` from Matsuo et al. to remap the graph. This process allows the problem to be mapped to a more optimal initial state for a specified SWAP strategy, resulting in a significant reduction in the number of SWAP layers required to execute the circuit.\n",
|
||
"\n",
|
||
"In `SATMapper`, the problem of finding a good initial mapping is formulated as a SAT problem. A SAT solver is used to find such an initial mapping for the QAOA circuit. `python-sat` (`pysat` in short) is a Python library for a SAT solver, and we will use it to solve the SAT problem in this example."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "204be7cb-33c0-49dc-bb47-40d93027e940",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"A class to solve the SWAP gate insertion initial mapping problem\n",
|
||
"using the SAT approach from https://arxiv.org/abs/2212.05666.\n",
|
||
"\"\"\"\n",
|
||
"\n",
|
||
"\n",
|
||
"@dataclass\n",
|
||
"class SATResult:\n",
|
||
" \"\"\"A data class to hold the result of a SAT solver.\"\"\"\n",
|
||
"\n",
|
||
" satisfiable: bool # Satisfiable is True if the SAT model could be solved in a given time.\n",
|
||
" solution: dict # The solution to the SAT problem if it is satisfiable.\n",
|
||
" mapping: list # The mapping of nodes in the pattern graph to nodes in the target graph.\n",
|
||
" elapsed_time: float # The time it took to solve the SAT model.\n",
|
||
"\n",
|
||
"\n",
|
||
"class SATMapper:\n",
|
||
" r\"\"\"A class to introduce a SAT-approach to solve\n",
|
||
" the initial mapping problem in SWAP gate insertion for commuting gates.\n",
|
||
"\n",
|
||
" When this pass is run on a DAG it will look for the first instance of\n",
|
||
" :class:`.Commuting2qBlock` and use the program graph :math:`P` of this block of gates to\n",
|
||
" find a layout for a given swap strategy. This layout is found with a\n",
|
||
" binary search over the layers :math:`l` of the swap strategy. At each considered layer\n",
|
||
" a subgraph isomorphism problem formulated as a SAT is solved by a SAT solver. Each instance\n",
|
||
" is whether it is possible to embed the program graph :math:`P` into the effective\n",
|
||
" connectivity graph :math:`C_l` that is achieved by applying :math:`l` layers of the\n",
|
||
" swap strategy to the coupling map :math:`C_0` of the backend. Since solving SAT problems\n",
|
||
" can be hard, a ``time_out`` fixes the maximum time allotted to the SAT solver for each\n",
|
||
" instance. If this time is exceeded the considered problem is deemed unsatisfiable and\n",
|
||
" the binary search proceeds to the next number of swap layers :math:``l``.\n",
|
||
" \"\"\"\n",
|
||
"\n",
|
||
" def __init__(self, timeout: int = 60):\n",
|
||
" \"\"\"Initialize the SATMapping.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" timeout: The allowed time in seconds for each iteration of the SAT solver. This\n",
|
||
" variable defaults to 60 seconds.\n",
|
||
" \"\"\"\n",
|
||
" self.timeout = timeout\n",
|
||
"\n",
|
||
" def find_initial_mappings(\n",
|
||
" self,\n",
|
||
" program_graph: rx.Graph,\n",
|
||
" swap_strategy: SwapStrategy,\n",
|
||
" min_layers: int | None = None,\n",
|
||
" max_layers: int | None = None,\n",
|
||
" ) -> dict[int, SATResult]:\n",
|
||
" r\"\"\"Find an initial mapping for a given swap strategy. Perform a binary search\n",
|
||
" over the number of swap layers, and for each number of swap layers solve a\n",
|
||
" subgraph isomorphism problem formulated as a SAT problem.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" program_graph (rx.Graph): The program graph with commuting gates, where\n",
|
||
" each edge represents a two-qubit gate.\n",
|
||
" swap_strategy (SwapStrategy): The swap strategy to use to find the initial mapping.\n",
|
||
" min_layers (int): The minimum number of swap layers to consider. Defaults to\n",
|
||
" the maximum degree of the program graph - 2.\n",
|
||
" max_layers (int): The maximum number of swap layers to consider. Defaults to\n",
|
||
" the number of qubits in the swap strategy - 2.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" dict[int, SATResult]: A dictionary containing the results of the SAT solver for\n",
|
||
" each number of swap layers.\n",
|
||
" \"\"\"\n",
|
||
" num_nodes_g1 = len(program_graph.nodes())\n",
|
||
" num_nodes_g2 = swap_strategy.distance_matrix.shape[0]\n",
|
||
" if num_nodes_g1 > num_nodes_g2:\n",
|
||
" return SATResult(False, [], [], 0)\n",
|
||
" if min_layers is None:\n",
|
||
" # use the maximum degree of the program graph - 2 as the lower bound.\n",
|
||
" min_layers = max((d for _, d in program_graph.degree)) - 2\n",
|
||
" if max_layers is None:\n",
|
||
" max_layers = num_nodes_g2 - 1\n",
|
||
"\n",
|
||
" variable_pool = IDPool(start_from=1)\n",
|
||
" variables = np.array(\n",
|
||
" [\n",
|
||
" [variable_pool.id(f\"v_{i}_{j}\") for j in range(num_nodes_g2)]\n",
|
||
" for i in range(num_nodes_g1)\n",
|
||
" ],\n",
|
||
" dtype=int,\n",
|
||
" )\n",
|
||
" vid2mapping = {v: idx for idx, v in np.ndenumerate(variables)}\n",
|
||
" binary_search_results = {}\n",
|
||
"\n",
|
||
" def interrupt(solver):\n",
|
||
" # This function is called to interrupt the solver when the timeout is reached.\n",
|
||
" solver.interrupt()\n",
|
||
"\n",
|
||
" # Make a cnf (conjunctive normal form) for the one-to-one mapping constraint\n",
|
||
" cnf1 = []\n",
|
||
" for i in range(num_nodes_g1):\n",
|
||
" clause = variables[i, :].tolist()\n",
|
||
" cnf1.append(clause)\n",
|
||
" for k, m in combinations(clause, 2):\n",
|
||
" cnf1.append([-1 * k, -1 * m])\n",
|
||
" for j in range(num_nodes_g2):\n",
|
||
" clause = variables[:, j].tolist()\n",
|
||
" for k, m in combinations(clause, 2):\n",
|
||
" cnf1.append([-1 * k, -1 * m])\n",
|
||
"\n",
|
||
" # Perform a binary search over the number of swap layers to find the minimum\n",
|
||
" # number of swap layers that satisfies the subgraph isomorphism problem.\n",
|
||
" while min_layers < max_layers:\n",
|
||
" num_layers = (min_layers + max_layers) // 2\n",
|
||
"\n",
|
||
" # Create the connectivity matrix. Note that if the swap strategy cannot reach\n",
|
||
" # full connectivity then its distance matrix will have entries with -1. These\n",
|
||
" # entries must be treated as False.\n",
|
||
" d_matrix = swap_strategy.distance_matrix\n",
|
||
" connectivity_matrix = (\n",
|
||
" (-1 < d_matrix) & (d_matrix <= num_layers)\n",
|
||
" ).astype(int)\n",
|
||
" # Make a cnf for the adjacency constraint\n",
|
||
" cnf2 = []\n",
|
||
" for e_0, e_1 in list(program_graph.edge_list()):\n",
|
||
" clause_matrix = np.multiply(\n",
|
||
" connectivity_matrix, variables[e_1, :]\n",
|
||
" )\n",
|
||
" clause = np.concatenate(\n",
|
||
" (\n",
|
||
" [[-variables[e_0, i]] for i in range(num_nodes_g2)],\n",
|
||
" clause_matrix,\n",
|
||
" ),\n",
|
||
" axis=1,\n",
|
||
" )\n",
|
||
" # Remove 0s from each clause\n",
|
||
" cnf2.extend([c[c != 0].tolist() for c in clause])\n",
|
||
"\n",
|
||
" cnf = CNF(from_clauses=cnf1 + cnf2)\n",
|
||
"\n",
|
||
" with Solver(bootstrap_with=cnf, use_timer=True) as solver:\n",
|
||
" # Solve the SAT problem with a timeout.\n",
|
||
" # Timer is used to interrupt the solver when the timeout is reached.\n",
|
||
" timer = Timer(self.timeout, interrupt, [solver])\n",
|
||
" timer.start()\n",
|
||
" status = solver.solve_limited(expect_interrupt=True)\n",
|
||
" timer.cancel()\n",
|
||
" # Get the solution and the elapsed time.\n",
|
||
" sol = solver.get_model()\n",
|
||
" e_time = solver.time()\n",
|
||
"\n",
|
||
" print(\n",
|
||
" f\"Layers: {num_layers}, Status: {status}, Time: {e_time}\"\n",
|
||
" )\n",
|
||
" if status:\n",
|
||
" # If the SAT problem is satisfiable, convert the solution to a mapping.\n",
|
||
" mapping = [vid2mapping[idx] for idx in sol if idx > 0]\n",
|
||
" binary_search_results[num_layers] = SATResult(\n",
|
||
" status, sol, mapping, e_time\n",
|
||
" )\n",
|
||
" max_layers = num_layers\n",
|
||
" else:\n",
|
||
" # If the SAT problem is unsatisfiable, return the last satisfiable solution.\n",
|
||
" binary_search_results[num_layers] = SATResult(\n",
|
||
" status, sol, [], e_time\n",
|
||
" )\n",
|
||
" min_layers = num_layers + 1\n",
|
||
"\n",
|
||
" return binary_search_results\n",
|
||
"\n",
|
||
" def remap_graph_with_sat(\n",
|
||
" self, graph: rx.Graph, swap_strategy, max_layers\n",
|
||
" ):\n",
|
||
" \"\"\"Applies the SAT mapping.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" graph (nx.Graph): The graph to remap.\n",
|
||
" swap_strategy (SwapStrategy): The swap strategy to use to find the initial mapping.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" tuple: A tuple containing the remapped graph, the edge map, and the number of layers of\n",
|
||
" the swap strategy that was used to find the initial mapping. If no solution is found\n",
|
||
" then the tuple contains None for each element.\n",
|
||
" Note the returned edge map `{k: v}` means that node `k` in the original\n",
|
||
" graph gets mapped to node `v` in the Pauli strings.\n",
|
||
" \"\"\"\n",
|
||
" num_nodes = len(graph.nodes())\n",
|
||
" results = self.find_initial_mappings(\n",
|
||
" graph, swap_strategy, 0, max_layers\n",
|
||
" )\n",
|
||
" solutions = [k for k, v in results.items() if v.satisfiable]\n",
|
||
"\n",
|
||
" if len(solutions):\n",
|
||
" min_k = min(solutions)\n",
|
||
" edge_map = dict(results[min_k].mapping)\n",
|
||
" # Create the remapped graph\n",
|
||
" remapped_graph = rx.PyGraph()\n",
|
||
" remapped_graph.add_nodes_from(range(num_nodes))\n",
|
||
" mapping = dict(results[min_k].mapping)\n",
|
||
" for i, graph_edge in enumerate(list(graph.edge_list())):\n",
|
||
" remapped_edge = tuple(mapping[node] for node in graph_edge)\n",
|
||
" remapped_graph.add_edge(*remapped_edge, graph.edges()[i])\n",
|
||
" return remapped_graph, edge_map, min_k\n",
|
||
" else:\n",
|
||
" return None, None, None"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "0a98c9b9-9b80-47e2-b0e8-33766a109e25",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Layers: 0, Status: True, Time: 0.00903300000000229\n",
|
||
"Map from old to new nodes: {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23, 24: 24, 25: 25, 26: 26, 27: 27, 28: 28, 29: 29, 30: 30, 31: 31, 32: 32, 33: 33, 34: 34, 35: 35, 36: 36, 37: 37, 38: 38, 39: 39, 40: 40, 41: 41, 42: 42, 43: 43, 44: 44, 45: 45, 46: 46, 47: 47, 48: 48, 49: 49, 50: 50, 51: 51, 52: 52, 53: 53, 54: 54, 55: 55, 56: 56, 57: 57, 58: 58, 59: 59, 60: 60, 61: 61, 62: 62, 63: 63, 64: 64, 65: 65, 66: 66, 67: 67, 68: 68, 69: 69, 70: 70, 71: 71, 72: 72, 73: 73, 74: 74, 75: 75, 76: 76, 77: 77, 78: 78, 79: 79, 80: 80, 81: 81, 82: 82, 83: 83, 84: 84, 85: 85, 86: 86, 87: 87, 88: 88, 89: 89, 90: 90, 91: 91, 92: 92, 93: 93, 94: 94, 95: 95, 96: 96, 97: 97, 98: 98, 99: 99}\n",
|
||
"Min SWAP layers: 0\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"sm = SATMapper(timeout=10)\n",
|
||
"remapped_graph, edge_map, min_swap_layers = sm.remap_graph_with_sat(\n",
|
||
" graph=graph_100, swap_strategy=swap_strategy, max_layers=1\n",
|
||
")\n",
|
||
"print(\"Map from old to new nodes: \", edge_map)\n",
|
||
"print(\"Min SWAP layers:\", min_swap_layers)\n",
|
||
"draw_graph(remapped_graph, node_size=200, with_labels=True, width=1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "7b505f06-10c9-4245-8836-4dfefece08de",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],\n",
|
||
" coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
|
||
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"remapped_max_cut_paulis = build_max_cut_paulis(remapped_graph)\n",
|
||
"# define a qiskit SparsePauliOp from the list of paulis\n",
|
||
"remapped_cost_operator = SparsePauliOp.from_list(remapped_max_cut_paulis)\n",
|
||
"print(remapped_cost_operator)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "657c6785-9129-4c66-b144-b34a76d22333",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Build a QAOA circuit with the SWAP strategy and the SAT mapping\n",
|
||
"We only want to apply the SWAP strategies to the cost operator layer, so we will start by creating the isolated block that we will later transform and append to the final QAOA circuit.\n",
|
||
"\n",
|
||
"For this, we can use the [`QAOAAnsatz`](/api/qiskit/qiskit.circuit.library.QAOAAnsatz) class from Qiskit. We will input an empty circuit to the `initial_state` and `mixer_operator` fields to make sure we are building an isolated cost operator layer.\n",
|
||
"We also define the edge_coloring map so that RZZGates are positioned next to SWAP gates. This strategic placement allows us to exploit CX cancellations, optimizing the circuit for better performance.\n",
|
||
"This process is executed within the `create_qaoa_swap_circuit` function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "3bde29ab-1f16-4fc8-81b1-dac467f5ecc1",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def make_meas_map(circuit: QuantumCircuit) -> dict:\n",
|
||
" \"\"\"Return a mapping from qubit index (the key) to classical bit (the value).\n",
|
||
"\n",
|
||
" This allows us to account for the swapping order introduced by the SwapStrategy.\n",
|
||
" \"\"\"\n",
|
||
" creg = circuit.cregs[0]\n",
|
||
" qreg = circuit.qregs[0]\n",
|
||
"\n",
|
||
" meas_map = {}\n",
|
||
" for inst in circuit.data:\n",
|
||
" if inst.operation.name == \"measure\":\n",
|
||
" meas_map[qreg.index(inst.qubits[0])] = creg.index(inst.clbits[0])\n",
|
||
"\n",
|
||
" return meas_map\n",
|
||
"\n",
|
||
"\n",
|
||
"def apply_swap_strategy(\n",
|
||
" circuit: QuantumCircuit,\n",
|
||
" swap_strategy: SwapStrategy,\n",
|
||
" edge_coloring: dict[tuple[int, int], int] | None = None,\n",
|
||
") -> QuantumCircuit:\n",
|
||
" \"\"\"Transpile with a SWAP strategy.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" A quantum circuit transpiled with the given swap strategy.\n",
|
||
" \"\"\"\n",
|
||
"\n",
|
||
" pm_pre = PassManager(\n",
|
||
" [\n",
|
||
" FindCommutingPauliEvolutions(),\n",
|
||
" Commuting2qGateRouter(\n",
|
||
" swap_strategy,\n",
|
||
" edge_coloring,\n",
|
||
" ),\n",
|
||
" ]\n",
|
||
" )\n",
|
||
" return pm_pre.run(circuit)\n",
|
||
"\n",
|
||
"\n",
|
||
"def apply_qaoa_layers(\n",
|
||
" cost_layer: QuantumCircuit,\n",
|
||
" meas_map: dict,\n",
|
||
" num_layers: int,\n",
|
||
" gamma: list[float] | ParameterVector = None,\n",
|
||
" beta: list[float] | ParameterVector = None,\n",
|
||
" initial_state: QuantumCircuit = None,\n",
|
||
" mixer: QuantumCircuit = None,\n",
|
||
"):\n",
|
||
" \"\"\"Applies QAOA layers to construct circuit.\n",
|
||
"\n",
|
||
" First, the initial state is applied. If `initial_state` is None we begin in the\n",
|
||
" initial superposition state. Next, we alternate between layers of the cost operator\n",
|
||
" and the mixer. The cost operator is alternatively applied in order and in reverse\n",
|
||
" instruction order. This allows us to apply the swap strategy on odd `p` layers\n",
|
||
" and undo the swap strategy on even `p` layers.\n",
|
||
" \"\"\"\n",
|
||
"\n",
|
||
" num_qubits = cost_layer.num_qubits\n",
|
||
" new_circuit = QuantumCircuit(num_qubits, num_qubits)\n",
|
||
"\n",
|
||
" if initial_state is not None:\n",
|
||
" new_circuit.append(initial_state, range(num_qubits))\n",
|
||
" else:\n",
|
||
" # all h state by default\n",
|
||
" new_circuit.h(range(num_qubits))\n",
|
||
"\n",
|
||
" if gamma is None or beta is None:\n",
|
||
" gamma = ParameterVector(\"γ'\", num_layers)\n",
|
||
" if mixer is None or mixer.num_parameters == 0:\n",
|
||
" beta = ParameterVector(\"β'\", num_layers)\n",
|
||
" else:\n",
|
||
" beta = ParameterVector(\"β'\", num_layers * mixer.num_parameters)\n",
|
||
"\n",
|
||
" if mixer is not None:\n",
|
||
" mixer_layer = mixer\n",
|
||
" else:\n",
|
||
" mixer_layer = QuantumCircuit(num_qubits)\n",
|
||
" mixer_layer.rx(-2 * beta[0], range(num_qubits))\n",
|
||
"\n",
|
||
" for layer in range(num_layers):\n",
|
||
" bind_dict = {cost_layer.parameters[0]: gamma[layer]}\n",
|
||
" cost_layer_ = cost_layer.assign_parameters(bind_dict)\n",
|
||
" bind_dict = {\n",
|
||
" mixer_layer.parameters[i]: beta[layer + i]\n",
|
||
" for i in range(mixer_layer.num_parameters)\n",
|
||
" }\n",
|
||
" layer_mixer = mixer_layer.assign_parameters(bind_dict)\n",
|
||
"\n",
|
||
" if layer % 2 == 0:\n",
|
||
" new_circuit.append(cost_layer_, range(num_qubits))\n",
|
||
" else:\n",
|
||
" new_circuit.append(cost_layer_.reverse_ops(), range(num_qubits))\n",
|
||
"\n",
|
||
" new_circuit.append(layer_mixer, range(num_qubits))\n",
|
||
"\n",
|
||
" for qidx, cidx in meas_map.items():\n",
|
||
" new_circuit.measure(qidx, cidx)\n",
|
||
"\n",
|
||
" return new_circuit\n",
|
||
"\n",
|
||
"\n",
|
||
"def create_qaoa_swap_circuit(\n",
|
||
" cost_operator: SparsePauliOp,\n",
|
||
" swap_strategy: SwapStrategy,\n",
|
||
" edge_coloring: dict = None,\n",
|
||
" theta: list[float] = None,\n",
|
||
" qaoa_layers: int = 1,\n",
|
||
" initial_state: QuantumCircuit = None,\n",
|
||
" mixer: QuantumCircuit = None,\n",
|
||
"):\n",
|
||
" \"\"\"Create the circuit for QAOA.\n",
|
||
"\n",
|
||
" Notes: This circuit construction for QAOA works for quadratic terms in `Z` and will be\n",
|
||
" extended to first-order terms in `Z`. Higher-orders are not supported.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" cost_operator: the cost operator.\n",
|
||
" swap_strategy: selected swap strategy\n",
|
||
" edge_coloring: A coloring of edges that should correspond to the coupling\n",
|
||
" map of the hardware. It defines the order in which we apply the Rzz\n",
|
||
" gates. This allows us to choose an ordering such that `Rzz` gates will\n",
|
||
" immediately precede SWAP gates to leverage CNOT cancellation.\n",
|
||
" theta: The QAOA angles.\n",
|
||
" qaoa_layers: The number of layers of the cost-operator and the mixer operator.\n",
|
||
" initial_state: The initial state on which we apply layers of cost-operator\n",
|
||
" and mixer.\n",
|
||
" mixer: The QAOA mixer. It will be applied as is onto the QAOA circuit. Therefore,\n",
|
||
" its output must have the same ordering of qubits as its input.\n",
|
||
" \"\"\"\n",
|
||
"\n",
|
||
" num_qubits = cost_operator.num_qubits\n",
|
||
"\n",
|
||
" if theta is not None:\n",
|
||
" gamma = theta[: len(theta) // 2]\n",
|
||
" beta = theta[len(theta) // 2 :]\n",
|
||
" qaoa_layers = len(theta) // 2\n",
|
||
" else:\n",
|
||
" gamma = beta = None\n",
|
||
"\n",
|
||
" # First, create the ansatz of 1 layer of QAOA without mixer\n",
|
||
" cost_layer = QAOAAnsatz(\n",
|
||
" cost_operator,\n",
|
||
" reps=1,\n",
|
||
" initial_state=QuantumCircuit(num_qubits),\n",
|
||
" mixer_operator=QuantumCircuit(num_qubits),\n",
|
||
" ).decompose()\n",
|
||
"\n",
|
||
" # This will allow us to recover the permutation of the measurements that the swap introduce.\n",
|
||
" cost_layer.measure_all()\n",
|
||
"\n",
|
||
" # Now, apply the swap strategy for commuting pauli evolution gates\n",
|
||
" cost_layer = apply_swap_strategy(cost_layer, swap_strategy, edge_coloring)\n",
|
||
"\n",
|
||
" # Compute the measurement map (qubit to classical bit).\n",
|
||
" # we will apply this for qaoa_layers % 2 == 1.\n",
|
||
" if qaoa_layers % 2 == 1:\n",
|
||
" meas_map = make_meas_map(cost_layer)\n",
|
||
" else:\n",
|
||
" meas_map = {idx: idx for idx in range(num_qubits)}\n",
|
||
"\n",
|
||
" cost_layer.remove_final_measurements()\n",
|
||
"\n",
|
||
" # Finally, introduce the mixer circuit and add measurements following measurement map\n",
|
||
" circuit = apply_qaoa_layers(\n",
|
||
" cost_layer, meas_map, qaoa_layers, gamma, beta, initial_state, mixer\n",
|
||
" )\n",
|
||
"\n",
|
||
" return circuit"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "0402a1eb-c450-49ba-b7f0-887e6c28ff04",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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CIwjoPISQ3uOYMneH1/MKUd/JDKUQok61jAos9bhmLwRALbRhCIpAHxCG05pRYpwz95wracbsKh7dKjqoSvdR3VknX2oBugPoshTPKHcH0U5rySLpTmuG53xVA2hRfWO6xrF8Sn8SmrgytfVl/HfQ6xTyj23jzH8fx5mXTUifCYQNfgD/lj1x5qZ7xqV//zbZ6/6HX9MuhA9+EHPjjmSv/YqMnz5AwxW8Hj/fplGI+k5mKIUQdapDmMbBVO99ZJrTgW33KlcnnMgmAFja9SP3t8XkH9uOf7NuADjzssk7vAm/pp1RFB16neJVhqWy6qIW4MV1DIsrnlFuimwKOj1FyYc8Wezgmp0sSj2G5Xy5oaoG0KJmxEcGMO+h3p5e7FuOZ3qysjWnnVh/GNguln/+ewaWFj2IvPnpUhO8Cs8eJG//WkL6TCC0/2QAgrqNRG8JdtVjTRiFPra5T7VWhagPJKAUQtSp7V9P58z+U5gbd0QfFIHTmolt72oc504TdsN9nrZ1Ib3Hkbd/HWnf/Z3gHjehMweQu+NHcDoJ7X8n4NqPVrwMS1W4awGW1V/braq1AH3NKFf8AvCL74ptz2pC+kzwlA6y7v4FrSifgLZ9qx1Ai5rTMS7Ea++sqmo0b96MgRMmYDweQ1FuBpHj70RRdKhFBShGk1dgWXhqDwCW9v29rmtp15+czd9h27cWU3Qzr1qrQtRnElAKIerUA3dPZvfL73Bu+1Kc+bnoTP6YYlsSdv09Xr289QFhxEyeRuaqT8n5bRE4nZjj2hA5+m+YYpqj1ykkNAmrkQ/a8madqlsLcFxCY97886RSM8oVo5mw6+/2jA3tfwfJs54g5eunCew6DEfuOXI3f4dfs274N0+okQBa1A6dTqFVq1YcOnSIfWe3oTNbcFjPkfrta64+9EY/AjoOJHzQAygGk2evrHvvrJtidCWkFSUfBpBSUeKyIQGlEKJOTZgwgWsHj/apDIsxNJboW54t9ZxeUcpNiKmK0madqrtf0Z1Rvm/dUnI2L0QtykNvCcHSug8hfW/HGHahs445tiUxE14ja/UXZP78CYrJn8DOQwgdcBcKGt3LyCgvjyTw1J1WrVqxbt06Tp/LQ1OdpC14lcDOQ/EbcBcFJ3eRu/V71AIbUWOmYgxvBEDh6X0YQ2M913DPXDqt51x/qxpbjpfcVytEfSMBpRCizrkTYh6buwM0DZTKBTy+JMTUhJoKxHzNKAdXx5XYO6ZfdFRDddg58900Tv/hPRo1alTm492zrJuPZXgVz24ZFUjPZuHScaUWtWrVii+++AK7OQTNXkhgtxGED3F1ULK06YPmtGPdsQx7v0n4t+iOPjiazF8+RWc0Y4ptSeGZA2QlzgKdHs1e5LmulIoSlwPJ8hZC1LrS6kSO7tyAyENLQHWUmS17Mb1OwaTXMWN818uqnEr1M8oV/nRNECd2/0aXLl1YvHhxiTHH023cNnMjo95bx1ebTrIvOddTssju1NiXnMtXm04y6r113DZzo2QP14JWrVqRn1/gWcYOaDfA63xA++sBKEzaj2IwET3uRfT+waR993eSPryX9CXvEHLdBHR+QV6tP6tSa1WIuiYzlEKIGufLLNmmZfPZuuAjZi++hYVnAmslIaY+qYmM8geG/s69997LmDFj+POf/8y0adPw8/Nj0Y4kz3WhnOLZ54+7i2f7mqleE670pffdSdmsscbQ/OGPObP0A+zpJ101U4vRB5xvq1hgBcAU1ZQG972PPf0kaoEVY2QTFIOJzJ8/wa/JhW5JUipKXA4koBRC1Jjj6bYys6Xds2QHU618ufEEjjOZjLv3YSaOHsJEqJWEmPqmuhnlERERLFy4kPfff5/HH3+cxMREpn7wDc9+fxANyN4wl6zEWRgjm9Dw/g881yurgPZjdrvnvmra1bL0XuI9H9wAU2wLCo5vx5F7DmPEhe0JjlxXXVW95cLrVhQFU1RTz8/5R7aApnr1C5dSUeJyIAGlEKJGVHaWzNiwLdv17Vm0I4kxXeNqJSGmPqpuRrmiKDz66KP069ePp157mxd/OIQGOHLSyd44D8XoV+Ix6d+/Td7+dQR2HoKpQUsKkw6QvfYrnDlpPGF8jC6NQmts1rcyXyou977VZb3nA9r2I+fX+Vh3Lsc/votnvHXnctDpMTfpVOr1VHshWYlfoQ8MJ6Cdq5yQlIoSlwsJKIUQ1bJnzx4enPIkm7f8htOWhWI0Y4xoTHCvWzxlgDRNxbZrFXkHN1CUchS1IBdDSAyWdv35S2Eh0LPELNmVGEwWV90AukuXLgQN/hPqSVcGcOYvn2Ju2AZNVVHzczzjKiqgnddjNFMXhNZI8ezLYem9pny4aC2PP/0shaf3ouZb0QdHEdB+AMG9bsYU24KAzkOw7VzBmdRjOG2ZrmVuTcPcuINnKTxt4RvoA8MxRjZBLczDtnMF9qxkose96KlDKqWixOVCAkohRLVs2nmAHUeTCeg0CH1gOJq9kLwDG0hb8Crhwx8lqOtwNHsh55bOwNSwDUHdRqCzhFCYtJ/sdV9TcOJ3Hje9UaOzZJejygbQu5Ky2XzctYRacHI3efvX0+Cef5Gx4iOvcRUV0M7dk8jmyPhqFc9evXo1AwcOLPVc7B1vYY5rC0Dy7KcoPLW7xJgJX1/DnG8XXzZB5frfD/DohJEoJgtB14xC5x90/v08m6Lkw0Tf+jwRwx6h6MwB7OknAQWdJQhDSAyFp/aQ8dMHRIz4M6bYllh3rcS6YxmKwYS5UQcib3wCU0xzgBqttSpEbZOAUghRLctyGhA74RWv2aighFGc/WKKq4Vc1+EoegMxk6fj16jdhTFdh2MIiSF73Wysx7YzdUGYtJirhPlbT2HQKdgdDjJWfERgl6GYouNLjPOlgHZ1i2efzc4HIChhNKYGrb3OGcIaeP2sD4okdMBd3scCw3li/s7L5kvFH1/8J2qBlQaT3vTsfwzqOhw0FdvuVTgLrDgyz2BPP+k1Mwy4CvWfb60Ycu2thFx7a5nPUxu1VoWoLVI2SAhRZe5ZsouXNhWdHkNQJGqhK5tV0Ru9gkk3S2tXAFmYdsrTYk74ZvOxDByqhnX7jzhy0gjtf0ep44oX0C6ueAHt6hbPnrnmKADmxh0I7DjQ60/xBBQAndlSYox/fBecmsbUBTurfA91ZVdSNidTXEXHS2RxB4aDokPRGcqdGQYN27615T5PXdVaFaKmSEAphKgy9ywZgFpUgDMvG3vmWXI2LyT/6Fb8mnYp9/FOmyuI0VuCPbNkwjeH06w483PIWjub0D7jSwRubsULaOcd2IAjOxXbvrUlCmhXtXj2rqRs9idf2LOpFrq6xJRHU52oRflex5yqdll8qZi/9RQBTV1JNeeW/ouilKM4ctKw7Uskd/tSghJGozP5+dxa8WKXa61VIWTJWwhRZe5ZMoDMVZ9g3bHMdULRYWndm/Chfyr38TmbFqCYLZ4+1dJizjeqqmF3amQlzkLnH0hQ99FljnUX0E5f9CZp3/3ddVBvJGzgPWRvmOcpoG13avTr35+Y6Giio6OJiYkh+vy/i/8cEhKCUqyz0fytpzyF6c8tfRetKB8UHebGHQgbeC/mBq287seecYaTb48FpwNdQChBXYYRct3tKHrDZdG3evOxDEzNEgjpN5mcjd9w9vAmz7ngPuMJOz9T7GtrRbcrodaquLpJQCmEqLLDaVbPv4N7jMHSti/O3HPk7V+HpqlwfpamNNkb5lFwfAfhQx9G5xcISIs5X+l0Clr2Gaw7fiJs0AM4z9c3BNeeSU114shKQTFb0PsH+VRAW9FUmjZpQmpqKocPHyYlJYW0tDScTu/ZRqPR6BVgnul8F07FgKVNH/ybd0dnCcGefpKczd+RMvtJYidPxxTbAnDtp/Rr2hlTVDyqvYC8/evJ3jAXe8YZom568rL4UuF+zxtCYjA37oClTR/0/sHkHdlCzoZ56ANCCU4YXanWiu0bBF8xtVbF1UsCSiFElbhnydyMEY0xRrjKmwR2GkTKnOdJnf8KsXe+4zWjBWDbl0hW4iwCOw8l6JqRnuPuFnNXesmgmhCjy+OkppK5ciaZK2eWOJ/00X0Edb+R8MEPAhUX0G7XMJSv3vjK6xqqqpKZmUlqaiopKSmkpqZ6/rh/zlEs+DVq571HtlUvLG2v4+ynfyZzzZfEjH8FgMiRj3ldP7DjDZz78d9Yf/+JwqQxmOPa1usvFe73vG3vGjKWvUfDB2diCI4EXL260TSyVn9BQPsB6P2DfZoZBljyaF95z4vLngSUQogq0ekUjHrFK6gsztL2OjKWvYcjI8mrW0j+se2kL3kH/xbdCR/+iNdjpMWc7wZcew0nk59D1bx//1mJs1CL8gkf/CCG0AalPvbiAtplFc/W6XREREQQERFBu3Ylk6pUVaP5s0tLfQ5jWEP8W/Ui7+AGNNWJotOXOi64581Yf/+J/OM7MMe1rbdfKrKzs/nb3/6GFj6K3G1LMcU09wSTbpaWPbHtWklRylH847v6NDMs73lxpZCAUghRZS2jAtmXXPqMkmYvBEAttHmOFZ45QNq3r2OObUXkTU+VCDKkxZzv7hrYmW/25JQ4nrNlEXAhgx4qLqBd1eLZFX2pMARHgtOBZi9EOV+o+2L680GZWuB6H9V2gFWVYHXlypXce++9ZGVl0fb/RnEmL8uzTaM4TzJSsaSkimaG5T0vrhQSUAohqqxns3D2HTsN/t77vjSnA9vuVSgGM8bIJgDY00+R+s3LGEKiiRr3Irrz2a5u0mKucjrGhdAzPpytJzPL7EjjVl4B7eoWzy7vS4UjKxnFYPJa3i1tDFzob90oSI+maSW2SVRVdXqK5+bmMnXqVD766CNuuOEGPvvsMz77PZc94XHkHduGPSMJY/iFTGzb3jWg6DBGxZd6PV9nhoW4HElAKYSosnEJjZn++ANoRXmYG3dEHxSB05qJbe9qHOdOE3bDfehM/qiFeaTMewG1wEpwr1vIP7zF6zrGsFjMce2kxVwlTRvbmaEzEnFyIaCMnfRGiXHlFdCubvFs15eKJPAP9jpelHKUvEOb8W+egKLoUAvzUPRGFIPRM0bTNLI3zAXAr9k1aKqT33/+nvZfTGHSpElMnDiR5s2bV+m+qttT/JdffuHee+8lLS2NDz74gIceegidTsc4QzYze95C3pHfSP7qSYIS/uBKyjm8mYKjWwnsMhRDUARQezPDQtRHiqZp5X+1FUKIclx7/yvs/Pk7CtOOo+bnojP5Y4ptSVDCaE8vb0dWCkkf3VfmNQI7DWLEI69Kp5wqWLQjiSlzd1CV/yNXoNr1DncnZdO9T390RhPmuHbns7xPYf19GegMNLjjLYyRjSk4sZP0xdOxtO+PMayhq0XnoV8pPL2XwK7DiRj+KABPd1NYu/hrFi5ciM1m49prr2XSpEncdtttREdH+3RPxXuKVzR7C67Zcb2iMP3WzgxuFcpTTz3Fe++9x4ABA/jss89KBLW3zdzI+l9/JSNxNvaUozjzczGExhDYcRDB1471bOXI/nU+1l0rcWanemaGQ/tN8poZlve8uFJIQCmEqJbj6TaGzkikyKlW+RomvY7lU/pL7b0qWrj9NFPmbEXR6dGoeKm4eABVE8Wzu43/P/atW4o94yxqUR56Swh+TbsQ0vd2jGENAbBnJZO1+gsKzx5CtWWComCMaExgl2EEdh2OQa/zCrBsNhuLFy/m66+/ZtmyZWiaxpAhQ5g4cSI33XQTQUGl7z1853/LeO6FFyk8vRfNYXcFel2HE9z9RgA0TcW6Yxm523/EkXkWxeiHKbYFIX0m4NeoHbpf/0vypu954403ePTRR9HpSvb/kPe8ECVJQCmEqLZLPUt2tfvuu++47d5HGPjUpxzMUkss8bq5j/dqFl6jxbNrO8A6d+4c33zzDV9//TVr167F39+fG2+8kUmTJjFs2DBMJlc3mv9+s5i7bx+LMaYFAW37oZj8XHs0NZWwgfcCkPHzJ+RuWUhAh4GYG3dALbBi3bEMR04asZOmYW7Qgi9ua8n1CR3KvV95zwvhTQJKIUSNqM4yo3ywVp3T6aRTp040atSI5cuXe5JQthzP5FBqricJpVV0UK0Wz66rAOvEiRPMmTOH2bNns2vXLsLCwhg3bhy33noro2+dgD62DZE3P42ilJxZ1FQnp965Df8W3Ym6+WnPcXtWMmc+up+ghNFEDfujz0vRlX3PozpB03hrXGdu7dGs4vFCXEYkKUcIUSPGdI2jS6PQMhMh3KTFXM2aNWsW+/bt47///S/gyv4uHjDWVU1HdzBY218qmjZtypNPPsmTTz7Jrl27+Prrr/n666/59H/f4szNoOFtd7qSgIoKUIwmr8BSczrQHIXoA0K978MSCooOxWj26ileUeBd2fd8x1gLq998gNV5f+DWHu/59HqFuFzIDKUQosa5Z8lW7z3N8YwCFL2xTmbJrjaFhYW0bt2aHj16MH/+/Et9O0D52dVuNb30rqoqba8dzJGdm4i8+Rkyln+IIyMJxehHQMeBhA96AMXgWhY/+9+/YU87QfjwR/Br1AG10Eb2+jkUnNxF7F3vYAyNRa9TmNyrCS/f2NHne/B1Zvj999/n0UcfZcmSJfzhD3+o1usWoj6RgFIIUWuWLFnC6NGjOZ2URFzDhpf6di57F882vvvuu/z1r39lz549tG3b9hLeWUl1vfQeHNcSa9ppAAI7D8WvSScKTu4id+v3WNr1J2rMVADsmWdIX/gmRSlHPI81hMYSPe4lr45O7RsEs/Qv/ap8P2XNDGuaxujRo9m8eTM7d+4kNja2ys8hRH0iS95CiFqTnp4OQFRkZAUjRWnKK8rdrVEQn344i3vuuafeBZNQ90vv+Xk2NHshgd1GED7kIcDVX1tz2rHuWIa93ySM4XHoTP4YI5tgjmuLX9MuOG1ZZP/6DanfvkbspDc9Bdar21O8rNeqKAqfffYZnTt35p577uGHH34oNZNciMuNvIuFELUmPT2doKAgTxau8M3xdBu3zdzIqPfW8dWmk+xLzvW0N3QX5Z679Qz+N79MWufJHE+3VXDFS6+22ym6l7QD2g3wOhfQ/noACpP2o6lOUuY8h84cQPjQP2Fp04ega0YSM+E1HJnJ5Gz61vM4d0/x2hAdHc0XX3zBsmXLeO+9svdS1tbzC1EbZIZSCFFr0tPTiYqKutS3cVkpnjkMlJnc4m6fvTslj6EzEq/qbHmdTsEQFIE9/WTJhJsA14yjWmCl4ORu7GknCLvhfq8xxvA4jBGNKEzad+FYLfcUHz58OI899hhTp05l4MCBdOrUqVptIoW41CSgFELUmvT0dCIiIi71bVw2ipfeyd4wl6zEWRgjm9Dw/g88Y8oqzP3HExPgb7dftUFlbPP2HDu2HUfuOa+9kI7cDMDVK1zNy3Id1Eqpl6k60VSn58dW0aUXTq9Jb7zxBqtWreKVdz5EufaOKreJFKI+kCVvIUStycrOlhlKHx1Lt/HE/J1ogCMnneyN81CMfiXGZa76jIyfPsAUFU/YoPsJ7nkTjowkkr9+ij+/+81lsfxdGwaPGgOAdedyr+PWnctBp8fcpBOGcFewbdub6DWmMPkw9owkTDGuFot6nUKP+LBav2c/Pz+e/fg7dsSNYuvJTKCcGenzx7eezGTojEQW7Uiq9fsTojJkhlIIUWNKLNm1vBuDAiPeTZQluwo8ueDCMnfmL59ibtgGTVVR83M8YzTViXX7j1jaXEfk6L95jlva9uXMR/eTvfsXpi7odVX2h/7LuKF8/fkQbDtXkKaq+DXpSMHJXeTtX0dw73EYgiIwBEXgF98N2+6fUYvy8G/WDac1k9yt36MYTAR3dwWlTlVjXELjWr3fQ4cOce+jj7Nx43rUfCv64CgC2g8guNfN6M5/kSivTeSUua5Z1qt1RlrUPxJQCiGqrbzagw4NWbKrwK6kbDYfdy3NFpzcTd7+9TS4519krPjIa1xFhbkxmHwuyn2l6RgXwvCHnmfVnGhyfl9B3sGNGEKiCBv0AME9xnjGRY19jpzN35K3by2ZR7eB3oBfo/aE9r8DY0Qj9DqFhCZhtfr7O3XqFN179CQPE0HXjELnH0Rh0n6y182mKPkw0bc+D7hmo91tIoOu+YOnTWTK108RO3kaT8zX0aVRqPxvSdQLElAKIarF5ySSi5bsruYkkovN33oKg07B7nCQseIjArsMxRQdX2KczmjG1LAN1l0/Y4pr61WYW+cXSGDX4eh1Ct9sPXXVBZQAb912DUPPTCL4utvLHKMzmgm97nZCyxijVxSmje1cW7cIuLob5WRn0eiBD9BHNAEgqOtw0FRsu1fhLLCiM/mXOxtt27MaS6O2TF2w86qckRb1jwSUQogq2bNnDw9OeZLNW37DactCMZoxRjQmuNctWFr18owrPHMA666fKTpzgKK046A6afrUEqbM3QHIkh3A5mMZOFQN6/YfceSkEXP762WOjRz9N9IXvsm579/2HDOExhI7eRrG0FicqsaW45l1cdv1TnxkANNv7VytnuLTb6392fMjSWmuf/h7B/36wHBXC0idocbbRApR2yQpRwhRJZt2HmDH0WQCOg0ibPADhPQZD0DaglfJ3bHMMy7/yG9Yf18OioIh9EJXEA1X3+erNYmkuMNpVpz5OWStnU1on/Ge4tqlcRfmDrrmD0Td/AzhQx9GU52kfvsazrxsoPpFuS9nY7rGMWN8V0x6HXofy/7odQomvY4Z47vWyRecgqg2AJxb+i+KUo7iyEnDti+R3O1LCUoYjc7k5zUbbd3zC47sVIpSj3Huh396ZqPd9/7N1lO1fs9CVERmKIUQVbIspwGxE17xWuIOShjF2S+mkLN5oWsJDwi6ZiTB196KzmgmY/mH5GZcyE51atpVv2Snqhp2p0ZW4ix0/oEEdR9d5lh3YW6/xp0IH/pHz3G/+C6c+eQRcjZ9S9jAezxFuWuzjmJ9NqZrHF0ahVbcU1xx1fPs3jSsRnqK+yojrD0h/SaTs/Ebzh7e5Dke3Gc8Yf3v8Pxc0Ww0cFXPSIv6RQJKIUSlFU8iKU7R6TEERVKYfMhzTB9QdvkVWbJzFeXWss9g3fETYYMewJl74feqOe1oqhNHVgqK2UJRylGfCnPXdlHuy0F8ZADzHupdak9xg04h7+wRrm0RxSt3j6jz997hNCuGkBjMjTtgadMHvX8weUe2kLNhHvqAUIITXF8q6qpNpBA1QQJKIUSluZNIHKqGWlSA5ihELcwj/9Am8o9uxdKun8/XupqTSNxidHmc1FQyV84kc+XMEueTPrqPoO43Ym7oWiqtqDB3XRTlvlyU1VO8f//+kBVJx2cn1On9qKpG1q7VZCx7j4YPzsQQ7Opzb2nTBzSNrNVfENB+ADpzgE+z0cBVPyMt6gcJKIUQleZOIgHIXPUJVveeSUWHpXVvwof+yedryZIdDLj2Gk4mP4eqeS/LZiXOQi3KJ3zwgxhCG6CpDsBVmNu/eYJnnLswd2DXYXVWlPty5Q66hgwZwltvvYXD4cBgqLuPQp1Owbp9KaaY5p5g0s3Ssie2XSspSjkKKPWmTaQQvpCAUghRaYfTrJ5/B/cYg6VtX5y558jbvw5NU8Fpr9T1rvYlu7sGduabPTkljudsWQSApfWFPaYVFeaui6LcV4IhQ4bwwgsvsGXLFnr3rts9vLqCHBxGS4njntaPqhO1wOo+WPICl6BNpBAVkSxvIUSluJNI3IwRjfGP70pgp0FEj3sRraiA1PmvoGm+F25xL9ldrTrGhdAzPtynrOSosc8R0m8SjowkMn/+lJzfFmOOa0fs5Gn4RTWmZ3z4Vb19wFfdu3cnJCSEFStW1Plzx8U3pyjlCPYM7/aJtr1rQNFhjIqvd20ihaiIzFAKISpFp1Mw6hWvoLI4S9vryFj2Ho6MJIwRjXy6pizZwbSxnRk6IxFnsQqKsZPeKDGuvMLcdVGU+0phMBi44YYbWLFiBS+88EKdPvczT07lnnGjSf7qSYIS/uBKyjm8mYKjWwnsMrTetYkUwhcyQymEqLSWUYFlntPshQCohb7Xl5QluwtFuasaVtdVUe4ryZAhQ/j111/Jza3bLRd3jx3JoKkfY27QEuu2pWSs/A+OrGRC+99J+LBHPOPKm412t4mUGWlRX8gMpRCi0no2C2ffsdMlOn1oTge23atQDGaMkU18upYs2V3gLqr9xPydOJxOVB/CS71OQa8o0sqyCoYMGYLD4WD16tWMHl12/c/a8MnjExhqaEiRs5Q9kufVhzaRQvhKAkohRKWNS2jM9McfQCvKw9y4I/qgCJzWTGx7V+M4d5qwG+5DZ/IHwJGdinX3KsC1/wsga/0cAAwh0QR2vEGW7IoZ0zWODrGB3PD0p+hi25RdlPv88bouyn0ladGiBfHx8axcubLOA8rLpU2kEL6SgFIIUWkd40Lo3H8EO3/+jtztS1Hzc9GZ/DHFtiTs+nu8enk7spLJXvuV1+PdP/s16cQNo26VJbuLbEv8iVNf/I1vV//GjmyzV1Fuo16hVXQQPeLDGJfQWH531aAoCkOGDLkkiTngPSPt1LRSvziUoDoxGQ1Mv7WLzEiLekXRKpOKKYQQ5x1PtzF0RmK5S3YVMel1LJ/SX2ZZLnL99dejqiqJid4ZvlK8uuZ988033HbbbZw6dYpGjRpdkt/x8XRbxW0izx8vPLWb8c0czHj12Tq9RyEqIgGlEKLKFu1IqtaS3YzxXWWW5SK7d++mU6dOzJkzh/Hjx1/q27ni/XogiT9N/y8R7XpyIrPQMwvcMiqQns3C63QWuLQ2kRfPSP/vg2m8/fbb7NmzhxYtWtTJfQnhCwkohRDVsmhHUqWW7CSJpHyPPPII3377LSdOnMBkMl3q27liVWZWsGd8ONPG1v1+xdJmS202G+3ataNz584sWbKkTu9HiPJIQCmEqDZfPpxRnaDT06tZuCSRlCEnJ4e4uDj+7//+j1deeeVS384V63L/EvTtt98yduxYFi9eXOfJREKURQJKIUSNKW/JLqgghYXvPMX+jSto1qzZpb7Veun999/nscce48SJE8TFXfrA5Uq0aEcSf3p3Plnrvqbw9F40hx1DaAyBXYcT3P1GHFkpJH10X5mPH3Lz7Sz/9us6vOOSNE1j+PDhHDp0iD179uDv739J70cIkIBSCFGLii/Z2Ww2GjRowF//+ldeeumlS3tj9ZCmaXTs2JF27doxf/78S307V6Rj6Tb6/mUGZ+a9hCmmBQFt+6GY/HBkJYOmEjbwXtSiAvIObizx2IJjW7HtWU3sLU+zceazl3yG/eDBg3Ts2JFnn32WF1988ZLeixAgAaUQog498MADLF++nGPHjqHTSaOu4gH36tWrGThwIKtWrWLgwIGX+M6uTDfPWMn3z43DFNeOqJufRlF8fw+m/O9ZCpMP0fSx2fRoHsO8h3rX4p365umnn2bGjBns3bu31Fl/qQog6pIElEKIOrNx40b69OnDypUrGTRo0KW+nTrn3hKw+VgGh9OsXhnF9jP7OL12AfvW/4SiSBBQ03YlZXP9fc+Q8dMHNLz/Q4yRjVGLClCMpgoDS4c1g6T37yag4w1E/mEKAEse7XvJa4DabDbatm3LNddcw6JFi8p9f9V1xrq4+khhcyFEnbn22mtp06YNn3322VUVUJaXtGR3auxLzkVvaIRzwGOM//jXamcUy8xUSfO3nqLw+O8oZgsO6zlSv30NR0YSitGPgI4DCR/0AIqh9Kz6vL2JoKkEdLgecCXpfLP11CUPzgICAnjnnXeY+OBjDJv2Iwcy1TLfXwdTrXy58cQly1gXVz4JKIUQdUZRFO69915efPFFsrKyCA0NBa7sAKh4RjFQZlaxuz781pOZDJ2RWKmMYpmZqtjmYxkUZSSB6iRtwasEdh6K34C7KDi5i9yt36MW2IgaM7XUx9r2rkYfGI5fU1ffbKeqseV4Zl3efpmMLXvT+I8zOZTlegOV/f5yHa/K+0sIX0hAKYSoU3fccQcvzviEez9YRn5Awys6ALq48Hv2hrlkJc7CGNmEhvd/AFBmVvFNr7v+vv/++/nPf/5T6vV9mfmUmSmXw2lWNHsBmr2QwG4jCB/yEACWNn3QnHasO5Zh7zcJY7h3kGXPSKIo+TBBPcZ4LY0fSs2t0/u/2KFDh7j30cfZuHE9ar4VfXAUAe0HENzrZnRGvwqz1ScvGcpXX3wmQaWoMRJQCiHqzPF0G1MXHyfmrn+yI1dDzb3woXylBUDH0m08MX+nJ5h05KSTvXEeitHPa5zOEkLEqL+VeLw7q7jrtf1Lvb7vM58yM6WqGnan5lnSDmg3wOt8QPvrse5YRmHS/hIBpW3PateYDt6JUnandslm1k+dOkX3Hj3Jw0TQNaPQ+QdRmLSf7HWzKUo+TPStz1f4vvJrdg1PzN9Jl0ahl+3/xkT9IgGlEKJOXBwAqZT+QXylBEBPLrjwWgEyf/kUc8M2aKqKmp/jOa4z+RHYsWRWt23XShSzhVX5jXmk2PE9e/bw4JQn2bzlN5y2LBSjGWNEY4J73YKlVS/PuPQl/8S2++cS1731w0bM//nXy/J3WlU6nYJRr6APjMCefhJ9QKjXeX2AazZcLbCWeKxt72oM4Y0wx7b0Om7UK5dsm8asWbPIyc6i0QMfoI9oAkBQ1+Ggqdh2r8JZYEXvF1ju+8rSsidOTWPqgp31ImNdXP4koBRC1CpfAyAAe/opMn7+D4Wn96LoDfi36MGfc++HewZcVgHQrqRsNh/P8PxccHI3efvX0+Cef5Gx4qMKH++wZlBwchcBHW9ga5KN3UnZni0Am3YeYMfRZAI6DUIfGI5mLyTvwAbSFrxK+PBHXYGFm95IxIi/eF1bZ7ZclTNTLaMCSY1tQcHx7Thyz2GMaOQ558h1/bfSW7y3WRSeOYAj8ywh/SaVuF6r6KBau9eKZj6PJKW5/uHvfb/6wHBQdCi60j/ai7+vFIMJp6qx+XiG1/tLiKqSgFIIUat8DYAcOekkz34SnTmA0AF3ohUVkLP5W5LTjvO4ZUadBUA1sYw5f+spDDoFh6qhqU4yVnxEYJehmKLjfXp88aziizOKl+U0IHbCK15L3EEJozj7xRRyNi/0CigVnb7UWaqrcWaqZ7NwdrXvT86v87HuXI5/fBfPOevO5aDTY27SyesxnuXu9td7HdfrFHrEh9XYvVU2qaogqg0A55b+i9B+k84vee8jd/tSghJGozP5lfo8F2eru19LfchYF5c/CSiFELXK1wAoe+M8NHshMXfPwBASDYCpYWtS5zxH1u8rmLogqlYCoNrIkN58LAPH+ddr3f4jjpw0Ym5/3efHF88qLp5RfPHMp5ui02MIiqQw+VCJc5rqRLMXojNbPMeuxpmpcQmN+XJjcwI6D8G2cwVpqopfk44UnNxF3v51BPcehyEowjNeU53Y9q/F1LANxrAGXtdyqhrjEhpX+56qmlSVEdaekH6Tydn4DWcPb/I8JrjPeML631Hm812cre5+LfUlY11c3iSgFELUmsoEQHkHNuDfsocnmATwj++KITwO6961bO4yvEYDoNrMkD6c5tqL58zPIWvtbEL7jC+xnFqW0rKK3RnFxWc+1aICNEchamEe+Yc2kX90K5Z2/byupdkLOfXP21wBpV8glvYDCLv+bnQm/6tuZqpjXAg948P5bcSjZARHYd25kryDGzGERBE26AGCe4zxGl9wfAeqLYuA3uO9jut1CglNwqr9e6tOUtXhNCuGkBjMjTtgadMHvX8weUe2kLNhHvqAUIITRpe4TlnZ6nDpM9bFlUECSiFErfE1AHLkpqPmZWG6KPEBwNygNflHfqvRAKg2M6TdGcUAWYmz0PkHEtS95Ad8WUrLKrY7NZo1b0HUHW/jUI0AZK76BOuOZa4Big5L696ED/2T5zH6wDCCrx2LKaYFaCr5R7dh3fYD9tRjxEz8B070V93M1LSxnRk6I5HQvhMJ7Tux3LH+zRNo+tSSEsf1isK0sZ1LeYRvtm7dygN/+Rs7ftsMgLlhW8IG3oMpprnXuOwN88g7vAlH5lnUonwMwZHn9xSPJ//4DjKWvUfDB2diCI4EXOWP0DSyVn9BQPsB6P2Dva5XVrY6XNqMdXHlkIBSCFFrii/9lhcAOa2uwEYfGF7iGvrAMNSCXBxFRdUKgLZs2cKXX37J4h9XcPrUCXT+wZgbtiG0/x0lSsXkbP2e3G0/4MhKRu8fjKVdP0L73cGUuTsAyg0q3RnFeWmnse74ibBBD+DMvTBLqzntaKoTR1YKitmC3t87uaO0rGIdGrfdNo5v7EbPseAeY7C07Ysz9xx5+9ehaSo47Z7zYdff7XXdgPYDMIbHkZX4X/L2ryOg/YCrbmYqPjKA6bd29qoNWhkKMP3Wqpey2rZtG9f17YtqCSf0utvR0MjdtpTkr5+iwZ3veCUKFSUfxhTdjIB2/VFM/jjOnSL395/IP7IFnX8oppjmnmDSzdKyJ7ZdKylKOYp/fFevc2Vlq8OlzVgXVw4JKIUQtca99AvlB0CaoxAARW8scQ1Fb/KMqU4A9Oabb5K4dh1FTXoR1mYYTmsmuduWcPbzx4i98y1MUfEAZP7yOTmbFmBpcx3B3W/Enn6K3K1LsKefJGb8qz5lSLeMCmT70XOgqWSunEnmypklxiR9dB9B3W8kfPCDnmNlZRW3bRDC3x/9B3OeXeo5ZoxojDHCtY8vsNMgUuY8T+r8V4i9850ye4EH9RhD1tqvKDj+OwHtB1yVM1PuLwPuGeqyZqeL0+sU9IpS7RJWzz//PKrOSMM73wY/1xeJgA4DOfPxQ2St+S9RtzzjGVv8326mhm1JX/gPdEUFXltD3DTV6fqH++/zystWh9rNWBdXDwkohRC1ovjSL1QQABnMgGv27mKaswgAxWCuVgD017/+FQb+he1nrJ4gIqBdP858+ig5v84ncvTjOKwZ5GxZSECHgUSOvlAU2hDekMwVM8k7tAl9m2srzJDu2Sycfcfjibrl2RLnshJnoRblEz74QQyh3skepWUVuzOK3TOfxX+nxVnaXkfGsvdwZCR5zXQVpzOa0fkH4SxwBeZX68zUmK5xdGkUWuYeWjf38e5Nw3jzluoX2V+TuBZjky6eYBLAEBiOX+OO5B3ZjFqUj87kX+bjDaExrvvyD6Yo5Qj2jCSv2XXb3jWg6DCe/3LkOV5GtjrUfMa6uHpJQCmEqBWVCYD0ga4PNKe1ZAKP05qJzi8IxWBEc9pp2bIFLVqU/icwMLDM+wlq2oHfvl/ndcwYHocpsgn29FMAFCXtB9VJQHvv7jQB7fqTuWImtn2JWFr1qjBD2pVRfAJL65JBZ86WRa7Xf9G5srKKi2cUt4wKZF9y6bO0mt01y6sW2sr8HaiFeah5OZ4Eoat5Zio+MoB5D/X2ZPnPT9yBTR8MOj1GvUKr6CB6xIfVaBvQgoIC/I3mEscVoxmcDuxpJzDHtfUc1zTNVQRfVbFnJpG1+ktQdAT3Gsu5pTNI/upJghL+4ErKObyZgqNbCewy1Odsdai5jHUhJKAUQtQaXwMgc0QjdJYQipIPlxhXePYgpphmAMT4aQwYO5YjR46wceNGvvrqK2y2CwFUdHQ0LVq0oGXLliWCzW9+S/UkCHnuQdNw5mVhjHR1G3HPkLpnTN2U80FAUfIRoOLafe6M4q0nM31aUoXSs4ovziju2SycfcdOlyhorTkd2HavQjGYMUY2QXMUoTkdXqWCALI3zAE0/JtdIzNT53WMC6FjXAi/vv83AgMD+eab+bU2a+sf1ZiCpP1oqhNFpwdc77nCMwcAcOSeo/g7T7Vlcfq9C2WA9EGRRN74BAHt+mGMiCNr3ddYty3FmZ+LITSG0P53EnztWK/nLCtbHWouY10IkIBSCFGLfA2AwJWlatu1CkdOGobgKADyj+/AkZFEcI8x6HUKI7q34uUbb75wHU0jLS2NI0eOlPizfPlyUlJSPGM7T/0fDt1FCTB7VuPMPUdoX9feMsP55cOC03u9avUVntoDgNN6zvW3D7X73BnFzovSP2InvVHq+NKyii/OKB6X0Jjpjz+AVpSHuXFH9EEROK2Z2PauxnHuNGE33IfO5I8jK4Wzn/8FS/sBnuXvgmPbyD/yG37NE/Bvfa3MTF0kOTmZvn371uoWAP8uI7Aue59zS//lCvw0lewNcz1JaZqjyGu8zj+Q6AmvoTmKKEo5Qt6BjWhF+QCYG7Yh5raXK37OMrLVofoZ60IUJwGlEKLW+BoAAYT0vo28/etJ+foZgrrfiGbPJ2fTtxij4gnsNKTUAEhRFKKjo4mOjqZ375LLy1arlaNHj3LkyBGe+M0E6oVz9nOnyFjxIea4tgR0GgSAObYlpoZtyNm0AENQBH5NOmM/d4pzP30AOoNnVhUqrt1XGxnFHeNC6Nx/BDt//o7c7UtR83PRmfwxxbYk7Pp7PK0sdX4B+LfsScHx7dh2/4ymqhjDGhA64E6Ce96CQa+XmamLnD17lgYNSi4J1xRV1bB0HUFwdho5m7719Fk3xbYi+Nqx5GyYW6LDjaI3erK1LS174te0KylfPYEuIBRLy57Vup/qZqwLcTEJKIUQtcbXAAjAEBxFzMR/kLnqE7LWfIGiM+DfsgdhN9yHwWSqUgAUGBhI586d6dixE/+3+UKGtNOaSeo3L6MzBxB509Oe5UeAqJufJn3RNM4tfdd1QNER3PMmCk7uxp6R5BnnS4JQbWQUz3njbwyd0YMip1rKo110foFeSUUlnkNmprzY7XbS0tJqNaB07ykOG3Anwb1uwZ52Ap05AFN0PJlrvgQuzJCXxa9RO/SB4dj2rMbSsidGvcJbt3a5JBnrQlxMAkohRK3yJQByM0U1JWb8qyWOVzcAKp4gpBbYSJn3ImqBjZjJb3olMAAYgiKJnTwNe0YSTlsmxrA49IFhnH7vTozhDT3jfM2QvjijWHM6UPQl/6/X14zi+MgApo3tzP/NuzS1FK9EqampAMTGxtbq87j3FOv9AtE37uA5XnB8B/qgyDKz84vTHEWexKtW0UGXLGNdiItJQCmEqFWXupi0W8uoQPaePkfq/FdwZCYRM+E1TOf3b5bGGB7nKclSlH4SpzXDszQOoMtN5d1332XYsGG0adOmzNqPcCGjeOob7/HFmv1cM2wcR9Jtnr7hFWUUl9ZvXK+AqoGGhuu3VD6ZmSrb2bNnAWp1hhJce4oPplq9Aj7bvkSKzh4ibOC9npaIalEBKKAzei+B2/avRy2wYo5t5ZVUdXHG+pbjmew5nYGiN9RaxroQF5OAUghR6y5lMWm37k1CSHx/KoVn9hM99jnMce18epymqWT98jmK0UxQ1xEAKGj45SYxdeorTJkyhaZNmzJs2DCGDRvGoEGDCAkp/UN7+8+LSDAY+HHKAIAKl8zL6zfursakaVq5wazMTFWsrgLKZvaTnJn9DH7NuqHzD6bozH6sO1fi1zyBoGK9xB2ZZ0iZ8xyWdv0whjdCURQKkw9j2/ML+pAYgnrcWOqeYnfGOkCjRo247777efnll2r1NQnhJgGlEKJOXLw0p6ChlTKzVlsB0PEfPiLv0Cb8W/bEmW/FuvsXr/OBHV09jjNWzERz2jFFN0dTHdj2rqHozEEiRv2fpzuJhsLsVx+l2b+nsGbNGn766SeWLVvGxx9/jF6vp3fv3gwbNozhw4dzzTXXoNPpyMvLY+3atbzxxoUs7/KCSV/7jbtntdxX0ikKTs23mU/hkpycjKIoREVF1erz9OvahpAAM2mbvnX15w6NIbT/HQT3vMlrH68+KAJLmz4UnPgd266f0VQHhuBogq4ZRUif2zAFhPi0p7ic7xlC1DgJKIUQdca9NLfzVCbDH3mZmA59sOoDfV76rY5Th/cBkH94M/mHN5c47w4oTTEtyPltkau7iKJgbtCamNtf95QRurh238iRIxk5ciQAx44d46effuKnn35i2rRpPP/880RGRjJkyBAaNGhAYWEhw4YNK/c+t2zZwktvv8+Kn3/BkZ1Sbs9x27615GxZiP3caRRFhzGqKSG9xvLRM/dzc7eK9+MJl7NnzxIdHY3BULsfiS1atODXNasYOiOx3D3FeksIEcMfLfu8JFWJekjRNK0q25qEEKLKdu7cSZcuXVi1ahUDBw6ss37Sx9NtFX6YV8Sk17F8Sv8KZ07tdjsbN270BJhbt24FoEuXLgwfPpxhw4Zx3XXXYTKZvB43YvRNrPglEUvbvhij4z09x7WiAq+e4zm/fU/mypn4t+iBf8seaA471l0rsaceo8HYZ9nw0dOyvO2jP/3pT/z6669s3769Tp5v0Y6kau0pnjG+a4XbQBo1asT999/PSy+9VJVbFKLSdJf6BoQQV59Vq1ZhNps9tSPrqp+0O0Goqs9WmQQho9FI//79ef311/ntt99o3bo1119/PZ07d+bzzz/nhhtuICIightvvJEPPviAI0dcXXgK242kyaOfEz7kIYK6DCP0ugnETnoTTXWS8+t8z/Vzt36PqUErom59gaBuIwnuMYbYSW+imPzJ3rmSqQt2VvFVXn2Sk5Nrff9kcWO6xjFjfFdMeh16H9/7ep2CSa/zKZgU4lKQgFIIUedWrVpFnz598PPzq3hwDbsUH+anTp3i4MGDPPLII/z3v//l7NmzbNu2jWeffZbc3Fwee+wxWrZsScseAzmqj0NVvJdeL+45DqAW5aG3hHol5OjMFldmsMHk6TcuKnbm7NlaLxl0sTFd41g+pT8JTVyZ2mW9F93HuzcNY/mU/pV6/8kCpKhLsodSCFGnHA4Ha9as4Yknnrhk91DXtft++ukndDodgwa5yg7pdDq6detGt27deOqpp8jNzeWXX37hvY0pHFEuZHC7XdxzHMCvSSfy9q8n57fvsbTsieYsImfrEtTCPIK731hhv/GrWYkyTAOfJ12BEe8m0rNZeJ0lMZVW7udQam6N7CkuL/NfiNogAaUQok5t27aNnJwcbrjhhkt6H7X5YX6xn376iV69ehEWFlbq+aCgIG688UY+PJaIM7lkS8eLe44DhA9+CDUvh8yVM8lcORMAnX8wMbe/hjmunU/9xq82FZVh2pecy8FUK19uPEHP+HCmja2bMkvFy/1AxeWkhKiPJKAUQtQZVdVYtWoVAQEB9OjR41LfDlD7H+YOh4OVK1fy2GOPVTj2cJq1xLHSeo4DKEYzhohGBARFupJyivLJ2bKItG//TszkNzGGNayw3/jVxNcyTO7jW09mMnRG4iUpBC/BpLgcSUAphKg1pXV40dGR5o98wms/HqiX9RFr+sN8y5YtZGVlVVguSFU17BetdZfXczxt4Rsoio7ocS96jvm3upYzMx8ka80som560qd+41eDRTuS+NO788la9zWFp/eiOewYQmMI7Dqc4O43esZpTjs5m77DunuVq2STOYDb57Tk3+9/wH3D6scXIF/JkreoaxJQCiFqXHlLiyoKObogvtp0ss6XFi+Fn376idDQ0ApnZIv3GwfK7Tluz0qm4OhWwi+qVaj3D8LcqD2FSXsB3/uNX8mOpdt4eNoXnJ33EqaYFoT0mYBi8sORlYwzN90zTnM6SP3mZQqT9hHYZRimqHjUAiuFZw/yyrdbGZTQ/rJ7j0pOjqhLElAKIWrU5bS0WBeWL1/O4MGDfSqa3TIqkH3JuWiOonJ7jqu283sjtZL1NDXVgaY6AWgVHVT9F3CZ++tXG0lZ/Bb+LXoQdfPTns5CF8vZspCCk7uJnfwm5oZtvM7pdQpTF+xk3kO96+KWq6z4ioDu9n/zX7uB/z23lJZRgXWabCSuThJQCiFqhNVq5f6/Pc+iFYkUnT2IWmAlYuQUAjsP9hp34o1RpT7+ptehS69+7Pg1sS5ut05kZmayadMmPvroI5/G92wWzoHkbJIXvlluz3FDWENQdNj2rSWw6wjP8qYjJ53C03sxN2qPXqfQI770JKCrxa6kbBKXfYfTlkVY/ztRFB1qUQGK0eQVWGqaSu5vi7G07o25YRs01YnmtLtKMOH68uMuw1QfA7JSVwR0ro93u1O7ZMlG4uoiAaUQokZsP3iSuR/PQB8chTG6GYUnd5U6LmLU30ocK0o+RO5vi0kKaMXxdNtl/2Hn3rf4888/o6pqhfsn3cYlNOafrz5L/uHye47rLSEEdh6M9fflpPzvWSxteqMV5ZO7bSmavZCQa8fhVDXGJTSujZd32Zi/9RSFx39HMVtwWM+R+u1rODKSUIx+BHQcSPigB1AMJuzpJ3FaMzBFx3Pux39j3f0zOB0Yo+IJH/wgfk0719syTLIiIOoLCSiFEDVixoY0mvxlFooljMKzh0j+8v9KHefumV3cuZO7AAVL+wGXxdLixUpLPjLqFYI0jda3P0uO3rcgpGNcCH7Zp8il4p7j4cMewRjdDOvvK8ha818ATLGtiBz1VwLiO3n1G79abT6WQVFGEqhO0ha8SmDnofgNuIuCk7vI3fo9aoGNqDFTcWScASBnyyJ0foFEDHPtTc3eOI+UeS/Q4K5/YopuVq/KMB06dIh7H32cjRvXo+Zb0QdHEdB+AMG9bvbMrELpiUbmBi15NPNReGCwBJWixkhAKYSotl1J2WxNsqJYKr/Eqjns5B1Yj7lJR5TAiHq9tHix8pKP7E6NDCzom/Vm1HvrfF5q3LxhrU/9xhWdnuCE0QQnjPY6rmkqmurkzbGdqv7CrhCH06xo9gI0eyGB3UYQPuQhACxt+qA57Vh3LMPebxKqvQBwdR9qcM+7GIKjAPBr2pmkmQ+Ss2kBkaMfrzdlmE6dOkX3Hj3Jw0TQNaPQ+QdRmLSf7HWzKUo+TPStzwPlJxo5C208MX8nXRqFXvYrAqJ+kIBSCFFt87eewqBTcJSx3Fae/CNbUAttBHS4HqDeLi1ezPelRtffvi41uvuNT5m7g6ok6SqKQsqi6byVs4x///vf6HRXZ4dddxkmxWACIKDdAK/zAe2vx7pjGYVJ+1GMZgDMce09wSSAISTalTV/eh9AvSnDNGvWLHKys2j0wAfoI1wJW0Fdh4OmYtu9CmeBFb1fYLmJRgBOTbssVwRE/SQBpRCi2jYfy6hSMAlg27sa9EYC2lwHcFl0eFm0I8kr4MveMJesxFkYI5vQ8P4PvMZevOR4yz8D6HbNNSz835c0atSo1Ou7A053wFpWsFqcXqegVxSm39qZ1OaTeeihh8jNzeWzzz7zKcP8SuMuw6QPjMCefhJ9QKjXeX2A6wuLWmDFFNbw/LFQLqYPCMGecgSoP2WYjiSluf7h7/2lSx8YDooORWeoMNEI6n+ykbi8XH3/LyOEqHGldXjxhVqYR/6R3/Bv0R2dX6DneH1ZWizNsXTXUqE7xHPkpJO9cR5KsQ9qt7KWHA8kH2Tv8bNlBpRQzX7jXR8gKCiIO+64A6vVyv/+9z/MZnNN/QouGy2jAkmNbUHB8e04cs9hjLjw+3bkZgCgt4RgimoKOgPO3HMlruHMzUBncQVb9aUMU0GUa7bx3NJ/Edpv0vkl733kbl9KUMJodCY/itKOV5hoBJfPioCo/ySgFEJUS2kdXnyVd2A9mqOIgPbXex2vL0uLpXlywYVlboDMXz49PwOkoubneI0ta8lRr1P4ZI+DoX3Lf67q9BufMGECgYGB3Hrrrdx44418++23BARcXXvlejYLZ1f7/uT8Oh/rzuX4x3fxnLPuXA46PeYmndCZLfi36E7+4c3Yz53CGOHKjrenn3J9Geg2ol6VYcoIa09Iv8nkbPyGs4c3eY4H9xlPWP87AHxONLocVgTE5UECSiFEtVzc4aUybHtWo5gDsLTs6XW8viwtXmxXUjabj2d4fi44uZu8/etpcM+/yFjhXWuyvCXHyi41VrXf+KhRo/jxxx8ZPXo0w4YN44cffiAk5OqZiRqX0JgvNzYnoPMQbDtXkKaq+DXpSMHJXeTtX0dw73GeDkShA+6k4MTvpPzvWYLOJzrlbv0enX8QIb3rVxmmw2lWDCExmBt3wNKmD3r/YPKObCFnwzz0AaEEJ4z2OdEI6veKgLh8SEAphKg2d4eXynBYMyg4uYuAToNQDEavc/VlafFixZOPNNVJxoqPCOwyFFN0fImxFdU2DGjWpcpLjZUJtgcOHMjKlSsZMWIEN9xwA8uWLSMqKqriB14BOsaF0DM+nN9GPEpGcBTWnSvJO7gRQ0gUYYMeILjHGM9YU2QTYib+g6zVX5C9YS4oCn5NuxA28B4MgeFc0yi4XiwLq6pG1q7VZCx7j4YPzsQQHAm4MtfRNLJWf0FA+wGeZKSKEo2gfq8IiMuHBJRCiGrr2Sycg6lWn5JH3PL2JoKmlljurk9Lixcrnnxk3f4jjpw0Ym5/vdSxviw5bjleN4Hztddey5o1axgyZAgDBgxgxYoVxMX5Vn/wcg803hzbiUFv/0Jo39sJ7Tux3LHm2JbETHitxHHNaWfbR39lU/f36NWrV23dqk90OgXr9qWYYpp7gkk3S8ue2HatpCjlKPpA18xrRYlGUH9XBMTlRQJKIUS1uZYWT5Bzvli00+paFs4/vBlHbjoAwQmj0fld2MNn27safWA4fk296yXWp6XFi7mTj5z5OWStnU1on/HoLaXPWvmy5HioQfO6uXGgc+fOrF27lsGDB9OvXz9WrlxJ8+Yln7+sIu2Xaz/oL997i5RFvxA15okqPV4Bnh/ajE/WGujbty//+Mc/+Otf/3pJyzHpCnJwGC0ljrt7uKM6fU40gvq7IiAuL1dngTIhRI1yLy3mbv6O7LVfYd2+FIC8gxvIXvsV2Wu/Qi24kAluP3eaouTDWNr19+qprNcp9IwPr5cBS/Hko6zEWej8AwnqPrrM8b4sObqXGutK69atWbduHXq9nn79+rF3717PuePpNm6buZFR763jq00n2Zec63m97n7QX206yaj31nHbzI0cT7fV2X1X1T/+8Q9efvllXrhrJO+O74ZJr0Pv40ycXqdg0uuYMb4r9w3uQmJiIn/961954oknGD16NOnp6bV892WLi29OUcoR7BlJXsdte9eAosMYFe9JNCpM2of93CnPGHeikV+zbkD9XhEQlxeZoRRC1IhpYzuz49QXFXZ4ATBGNKLpU0tKHNcrCtPGdq6N26s2d/JRXtpprDt+ImzQAzhzLyToaE47murEkZWCYrb4tOR4KZYamzRpwtq1axk6dCgDBgzgp59+4pQu5orrB/3OO+/wzDPP8NJLL/Hkk08CVL0ME2A0GnnzzTe5/vrrufPOO+natSv/+9//6NevX6Xuqya2EDzz5FTuGTea5K+eJCjhD66knMObKTi6lcAuQ31ONIL6vSIgLi+Kpml19/VYCHFFu7jgd2UowIzxXettgAIw4t1Etm9aT8r/nil3XFD3GwntN5lT707E3LANsZPf9Dqf/NWTOG2ZDHlpDkv/UrmApKasXLmSSZMmkZGbj9NRhM4/GHPDNoT2vwNj+IX/BifeGFXmNfziuzLnuyX17r/Z+++/z6OPPspTTz3F3//+dxTFO4CrShmm4pKSkpg4cSLr1q3jlVde4amnnkKv15c6tra2EAx+6lM2zP+IouQjOPNzMYTGENhxEMHXjkXRXbiXwuTDZK3+gsKk/V6JRsbwOPQ6hYQmYdIpR9QICSiFEDWqeEvCynZ4qW+BycVeXLybL3/ZRd7JPSXOZSXOQi3KJ3zwgxhCG2CKjid1wWvkH95Mw/vf96pteObTRwjuNoIpL77Byzd2rOuXAcCtt97KmsS12Jv2Qh8Vj9OaSe62JWhFBcTe+RamqHgArLt/KfHYouRD5P62mNCB9xDVZxzLp/SvN/2gP/nkEx544AH+7//+j7fffrtEMFmaqswaOhwOXn31VV599VUGDRrErFmziI2N9Zwvr8+7m/u4r33eizuebvOp53t5THpdvfpvJy5vElAKIWpcZT5MezUL91parM92J2Uz6r11pZ5Lnv0Uan6OV+vFovSTJP/3b+hM/l5LjprqpME977Ls6Zsu2X7RDRs28M52B9vPXMjOt2ckcebTRwloe52nRmFpzi39F9adK4h7+HPMoVH1ZpZr1qxZ3HXXXfzxj3/k/fff9ymYrK6ff/6ZSZMmAfDVV18xePDgOvtSdaWvCIjLi+yhFELUuPI6vCiaipaZxOQ/9L3sMobdyUdbT2b6FCiUVdswctC9XNup9SV97UFNO/Db997BsTE8DlNkE+zpp8p4FGgOO3kH1mNu0hFDcGS96Qc9b9487r77bu69917ee++9OgkmAQYNGsTvv//O5MmTGTJkSLlj4x75AkNQJNkb5pF3eBOOzLOoRfkYgiPxb9GDP+eOh3sG+BzkVbfnuwSToiZJQCmEqDWldXhZuPA7xo79E/c/d5LGl1Ew6TZtbGeGzkjEedG8UOykN0odX1ptQ5Ned8mTj4oXaXfTNA1nXhbGyCZlPi7/yBbUQhsBHa73HLvU/aAXLlzIxIkTmThxIjNnzqzzkj4xMTEsW7aMu/70GD+dNaF5FVDRyPjpfQwhMRiCXHUji5IPY4puRkC7/igmfxznTpH7+0/kH9nC38zv06XRUJ9n7C/u+a5DQ6VkMF1WspEQNUUCSiFECbVVzFqnU+jb19XAet26ddx+++01/hy1LT4ygOm3dq7WUuP0Wy/9B3rxIu1utj2rceaeI7TvpDIfZ9u7GvRGAtpc5zl2KftBL126lNtuu41bbrmFzz//vMzkmNqm1+spSphE8EWz1wWn9qDZC70K+EfdUjKpy9SwLekL/0HuwV+ZuiC2UlsI4iMD+HxyZ2Lb9WDgfc/gCGtapWQjIapDAkohRJ0Ws46OjvbUQ7z99tsvy04sV8JSo7tIu5v93CkyVnyIOa4tAZ0GlfoYtTCP/CO/4d+iOzq/QK9zl6If9IoVK7jlllsYOXIks2fPxmC4dB9pF/d5d7PtXQMoBLQfUO7jDaExADgKrFXaQrBixQqsp/bx9sRetGrVCrj8uxyJy4sElEJcxcpLnnEXsz6YauXLjSeqlIlamt1J2USNeIRlDgutnlt62XZiuXipsbJ1DS+l4kXaAZzWTFK/eRmdOYDIm572KjtTXN6B9WiOohLtMqHu+0GvWbOGMWPGcMMNNzB37lyMRmPFD6pFpW4hcDrI278Oc6N2noDRc07TUPNzQFWxZyaRtfpLUHT4NelUpS0Eixcvpl27dp5gEirX812I6pKAUoirVPFMVKj9YtZewaulBU4NnBd1Yqnp4LW2lZZ8tPd0BugN9Xqp0V2k3e7UUAtspMx7EbXARszkNz1FsUtj27MaxRyApWXPEudqqki7L0Hphg0b+MMf/sB1113HggULMJvN1X7e6iptC0H+sW2o+TmlBuCqLYvT793h+VkfFEnkjU9gjGhc6S0ETqeTJUuWcO+991b5/oWoLgkohbgKzdlwkD9OfYnCMwcoOnsQtcBKxMgpBHYe7DUud8cybHtWYz93GrXQij4wgsmLO/H2G6/y4MhrfX6+EsFrGSvEl1MnluKKJx+FhITw/PMv8Pjjf7vEd1W+llGB7D19jtT5r+DITCJmwmuYyknGcVgzKDi5i4BOg1AMJWcDq9oPurLbLbZs2cKIESNISEhg4cKF+Pv7V+l5a9rFWwjg/HK3zoClXd8S53T+gURPeA3NUURRyhHyDmxEK8r3nK/MFoJff/2VtLQ0xowZU7WbF6IGSEApxFXmWLqNp7/eQPb6/6EPjsIY3YzCk7tKHVuUchRDSAyWlj3R+QXiyE4h9/efeHjcMLps2kqvji0rfD5fgldNU7HtWkXewQ0UpRxFLcjFEBLD3Yn9+Xj6S4zr1aLGXn9tcjqd5OTkEBYWeqlvpULdm4SQ+P5UCs/sJ3rsc5jj2pU7Pm9vImhqqbNtVekHXZXtFlmnDzFs2DA6dOjAkiVLCAioHzPYF28hAFCL8sk/9Cv+zbqh9w8u8RhFb8Q/visAlpY98WvalZSvnkAXEIqlZc9KbSFYtGgR0dHR9OxZcuZYiLoiAaUQV5knF+xECQij0aOz0AeGUXj2EMlf/l+pYyOGPVzimH/r3iR/MYUHnn+bnd99WO5z+Rq8avZCzi2dgalhG4K6jUBnCaEwaT9Z677mrvE76b5lPc2iAkt5hvolJycHgLCwygVXl8LxHz4i79Am/Fv2xJlvLdERJ7DjQK+fbXtXow8Mx69ppxLXqmw/6KpstxjyzzXkrvyAFi1a8OOPPxIUVLUZ0dpQfAuBW97BX13Z3cXKK5XHr1E79IHh2PasxtKyZ6W2ECxevJjRo0dfsgx3IUACSiGuKp5MVJ0BfWDVgh5DSDQAJ5LTK8xE9TV4VfQGYiZPx6/RhVmyoK7DMYTEkL1uNne//hlrZvylSvdblzIzXfveQkNDL+2N+ODU4X0A5B/eTP7hzSXOFw8o7edOU5R8mKAeN6Eo3jUe3f2gfd0jumhHEn96dz5Z676m8PReNIfd1Ye663CCu98IuLoOFZ7aXeKxfs2u4e3/fk1ISP3Zj+rWMiqQfckXlqlte1ejmPzxb9XL52tojiLUQhvg+xaCAwcOcODAAaZNm1a5GxaihklAKcRVpLRMVF84z2ejOnLSyF7/PwAszbqWm4lameBV0Ru9gkk3S+veZK+bza49ey95JxZfZGVlAZdHQLl69Wqf+0EbIxrR9KklpZ7TK4rPRdqPpdt4eNoXnJ33EqaYFoT0mYBi8sORlYwzN937ukGRhA64y/tYYDgvLzvKdW0b1buErZ7NwjmY6mpj6czLpuD4DgLa9Udn9PMapxYVgEKJ47b961ELrJhjW1VqC8HixYvx9/dn8ODBFQ8WohZJQCnEVaS0TFRfnH7vLnDaAdD5BxM2+CHMTbuWm4la1eC1OKfNdX1jQPAl7cTiq8tphhLqvkj7X7/aSMrit/Bv0YOom58uMdtZnM5sKbHsDuDUNKYu2FkveocXNy6hMV9uPAGAbV8iqM5Sl7sdmWdImfMclnb9MIY3QlEUCpMPY9vzC/qQGIJ63OjTFgL3/spFixYxZMgQLBZLbbwsIXwmAaUQV5HSMlF9EXPby2iOIuznTmHbsxrNXgCUn4la1eC1uJxNC1DMFszNEi5ZJ5bKcM9QXg57KN2qUqQdTUVTnTwzqInPWfi7krJJXPYdTlsWYf3vRFF0qEUFKEZTmYGlpjrRHEXoTBcyuetL7/CLFe/zbtuzGp0lFL/zSTfF6YMisLTpQ8GJ37Ht+hlNdWAIjibomlGE9LkNkyWYhKbhJV5bWdnwjk53Et86tt79PsTVRwJKIa4SpWWi+sqvqWtJ079Fd/xbXcvZTx9BMfkRnDCa8PAILBZ/AgICCAgIwGKxYLFYOHTNo6BUPUkge8M8Co7vIHzow+j8Ai9JJ5bKyszMRFGUernHrzyVLdKe0DiUnZ88yYwlWYzfuNGn1zt/6ykKj/+OYrbgsJ4j9dvXcGQkoRj9COg4kPBBD6AYTJ7x9owznHx7LDgd6AJCCeoyjJDrbkfRGy557/CyuPu8N7jz7TLH6C0hRAx/tPSTmobTYedPCRf2T1aUDU9oHBvTFUa9t+6yqd8qrkwSUApxlSgtE7UqjGENMMU0x7ZnNaEJo3jqqSex2WzYbDby8vLIy8vDlpeHVo1g0rYvkazEWQR2HkrQNSOBuu/EUhVZWVkEBwej05W9lFtflVakvbx+0AcGf06vXr2YOHEiixcvrjDDePOxDIoykkB1krbgVQI7D8VvwF0UnNxF7tbvUQtsRI2ZCoAhrAF+TTtjiopHtReQt3892RvmYs84Q9RNT17S3uHlqe4WAhQF47a53PKfZcyfPx9rRNs6bT4gRHVIQCnEVeTiTNSqUu1F4LTTtkEIU/8ytdQx7raKlZV/bDvpS97Bv0V3woc/4jleU51YalNmZuZls3+yLMWLtEPZnWvatGnD3LlzGTlyJE8//XSFWcaH06xo9gI0eyGB3UYQPuQhACxt+qA57Vh3LMPebxLG8DgiRz7m9djAjjdw7sd/Y/39JwqTxmCOa1tvZ6yr2+d9wJPXMWrUKG6efB95NitqvhV9cBQB7QcQ3OtmTzJPeZnwU5yveN2LEHXh8vsaLYSosp7NwtH7GJRpqhNnQck9l4VnDmBPO465QatyM1FbVqFuZOGZA6R9+zrm2FZE3vSUV0/pqnZiqUtZWVmX1f5JX5QXxA8bNoy3336b6dOn8+WXX5Y5zr3dwr2kHdBugNd5d7H0wqT9ZV4juOfNAOQf3wFcmLGuj8Z0jWP5lP4kNHG9F8r635z7ePemYSyf0p8xXePIzc1l1+495OfnE3TNKMIGP4A5ri3Z62aTvmi69+ODIokY9TevP8G9xqLhCmiPp9tq9XUKUZzMUApxFSmeiZpzfpnRac0AXPUIHedLtwQnjAY0kt6/G0u7fpgim6AY/bCnHce6ayU6cwDBfcaXm4lavIyKL+zpp0j95mUMIdFEjXsRnfFCf+aqdGK5FK6EGcrKeuyxx9i1axcPPvggrVu3pnfvktnX7u0W+sAI7Okn0QeEep3XB7hmRNVSvsB4xgRHnh/jmpms7zPWld1C4DZr1ixysrNo9MAH6CNcrTCDug4HTcW2exXOAit6P9eXtbIy4aH+ZsOLK5cElEJcRYpnouZs+g5nTqrnXN7BDXBwAwCBHQaiDwonsMtQCk7sJO/AejR7EfrAcALaDSCs7wSu7dy23KSISgWvikLKvBdQC6wE97qF/MNbvK5lDItl3MPX1ejvojZkZWdfdQGloih88MEHHDx4kJtvvpktW7bQuHHJLxotowJJjW1BwfHtOHLPYYxo5DnnyHW9L/SWst9PjqxkrzGXw4w1+L6FwO1IUprrH/7evwt9YDgoOhSd98d2aZnwUH+z4cWVSwJKIa4y7kzURg9/VuHY8MEPlnrcpNdVWMy6MsErgDPH9UGatfqLEteK6jyAdrGlt4e8lEqUcun8MHoFRrybSM9m4SVmn65UZrOZBQsW0KNHD8aMGcPatWtL9Nnu2SycXe37k/PrfKw7l+Mf38VzzrpzOej0mJt0Qi3MQ9EbUQxGz3lN08jeMBdw7RG8XGasS1PRrGpBVBsAzi39F6H9JqHzD6IwaR+525cSlDAanelCQfTyMuGBepsNL65MiqZp9XMTihCi1izakVStYtYzxnf1acO/r51YyqND5fTMP5LQpgmfffYZ7dqV7KhT18or5eLmPl7bpVzqU+b7zp076dOnDyNGjGDu3Lle2e67k7IZ9d460pe+i23nCixt++HXpCMFJ3eRt38dwb3HETbgLgpO7CR98XQs7ftjDGuIZi8k79CvFJ7eS2DX4Z6SO0se7XtFBkoj3k1k44L/kLPxGzRHoed4cJ/xhPW/w/Nz+tJ3MQRHeWXC5x/ehKVtP6JuetIzrn2DYJb+pV+dvgZxdZKAUoir1KIdSVXORK1M9mhNBK+RtuPce++9nDhxgpdeeonHH38cg+HSLLDU1e+tLGUVuG4ZFVgvZkW/++47brnlFl566SVefPFFr3M3vbeGHSczyNo4H+vOlTitGRhCogi6ZhTBPcYAYM9KJmv1FxSePYRqy3SV0oloTGCXYQR2HY5BryOhSdgVuzew1XNLyfx9FbY9v2Bp0we9fzB5R7Zg27mSsCEPnt/fXDp3JnzsHW9hjmsLuPaaHnptZF3dvriKSUApxFWsMjNtvZqF8+YtVZtpq4kgLD8/n5deeom33nqLbt268fnnn9OpU6dK30t1XBwcZ2+YS1biLIyRTWh4/weecWWVdOnWZwDb1q+u0nPXp1nRirz++us899xzzJs3j3HjxgHwyy+/MPGhKZhuehlFb6zgCmUz6XUsn9L/iizeraoaMTc/ybml/6LhgzMxnE9EAkj/YQZ5+9cS9/Dn6P2DS328/dxpzvznj4T0m0zodRM8x4++PrLezGKLK5eUDRLiKubORF3yaF8m92pC+wbBGPWuDx6jXqF9g2Am92rCkkf7MvfB3lX+EK9OGRU3f39/3nzzTTZu3Eh+fj4JCQm88sor2O32Kt1TZUvOHEu38cT8nZ5g0pGTTvbGeShGv1LHl1bSJbXZsCqVclm0I4mhMxLZetJVzNvXAteLdiRV+rlqwjPPPMOECRO46667+O2333jllVcYPHgw7RtH8uofWlPV0KayvcMvNzqdgnX7Ukwxzb2CSQBLy55o9kKKUo6W+fiLM+Gh/mfDiyuHJOUIISqdiVoVVS2jcrGePXuybds2Xn31VV555RW+/fZbPv/8c7p161bu81d3qfjJBRc6lgBk/vIp5oZt0FQVNT+nxPjSSrrodYrPpVxWr17NwIGll4QpvqRZnFpgJenjh1Dzsom86SmmnN+7WtcFrhVF4bPPPqN379707duXoqIiXnzxRZ577jn0ej0hISGXdNtAfaYryMFhtJQ4rqlO1z/cf5fi4kx4uHyy4cXlTwJKIUQJtTmjURPBq9ls5rXXXmPs2LHcc8899OjRg6eeeornn38es9nsNbaiXsj7knM5mGrly40nylwq3pWUzebjGZ6fC07uJm//ehrc8y8yVnxU5n1eXNKlKqVcQnvciD6mldcxQ1iDUsdmrZ2NZr+QyOEucN2lUWidz+pt2rSJs2fPYrfbadeuHU899ZSnPWNle4d3bxpW5e0Wl5u4+OYc2rYee0YSxvALwbNt7xpQdBij4n3KhIfLp36ruDLIkrcQ4pKqTvDarVs3Nm/ezAsvvMC0adNISEhg8+bNnvM1tVQ8f+spDOfvU1OdZKz4iMAuQzFFx5d5b+6SLqfeGcepf08mK3EWmtPhKeXiK1OjDgR2HOj1p7R6jUVpx8ndvpTga8d6v7bzBa7ritPp5LXXXmPQoEF06NCBJUuWcOTIER588EGKb9m3Fjpo1yCI+AgLF2/l1ynQPDKgRrZbXG6eeXIqqCrJXz1J1vr/kbvtB1LmvUj+oV8J7DwYQ1AERcmHSfrwXjJ+/g+5234gZ9O3pMx+krx9awnsOhxzbEvA9b4ur/mAEDVJZiiFEJc1k8nECy+8wM0338w999xD7969+fOf/0ySTWPJz+soOnsQtcBKxMgpBHYe7PXYwjMHsO76maIzByhKOw6qk6ZPLWHK3B3AhaXizccycJwPOq3bf8SRk0bM7a+XeU+GsAb4Ne3sVdIle8Nc7BlniLrpSbYcz6zwdR1Nc3WNUTXNNSNlNHu1orxY5sqPsbTujV+jDmQXO16XBa5TU1OZPHkyK1eu5IUXXuD5559Hr9fz2WefMWnSJDp16sStd/+pwplJRVE4mm4jMtBMoPnq+pi6e+xIvpr6MRvmf4R121Kc+bkYQmMI7X+n58uCPiQac+MO5B381SsTPnzYIwR2He4ao1NIaBJ2RZZWEvXT1fW/VCHEFatTp078+uuvTJ8+nZfffp/Cc0nog6MwRjej8OSuUh+Tf+Q3rL8vxxQdjyE0FkeGa2by4qXiw+eDO2d+DllrZxPaZ3y5XV0iRz7m9XNgxxs8JV0Kk8ZwUNeOwsLCEsvzxa056Cr0fm7pu2hF+aDoMDfuQNjAezE38F4Ct+1fR2HSfhre/yGO7JQS16qLAtdr1qzh9ttvx+l0smLFCgYNGuQ5N3HiRHbv3s1Ln//AzMx2qOfTcnydMb4a9k4W98njExhqaFhm/VZjaCxRNz1V7jX0ilJh8wEhapIElEKIK4bBYODpp59mU0Avth85g2IJo/DsIZK/LL3LTtA1Iwm+9lZ0RjMZyz8kN+PCUrd7qXjOA9did7oCnKzEWej8AwnqXnYtwLIE97wZ6+8/kX98B+a4tvj5+RMSEkxUVBTR0dEl/uxNBkubPvg3747OEoI9/SQ5m78jZfaTxE6ejim2BQCqvZDMVZ8S1GMMhtCYUgNKp6r5NCtaFaqq8ve//50XX3yRAQMGMHv2bBo08N7juWXLFnYcOUNR6hGOTB+Lzj8Yc8M2hPa/w2ufIICmqVi3LyN3x484MpJQDGYmzGrGP6a9xZTxQ2rlNdQ38ZEBTL+1c7Xqt17J2fCifpKAUghxRdmVlM2Os/koloqTEfQBZY9xLxXvPZuDUa+Ql3Ya646fCBv0AM7cCwk6mtOOpjpxZKWgmC3o/UvPqi1e0kWvwBdffE5qaqrnT1paGlu3biU1NZX09HRiH5tH1M3PXLhAq15Y2l7H2U//TOaaL4kZ/woAOb/OB9VJSO/byn2th1Jzyz3vVpkkqeJL3M8//zwvvPCCJ/GmuBdeeZ0VvyRiadsXY3Q8TmsmuduWcPbzx4i98y1MUfGesed+eBfb3tUEdLyBoIRRaEUFFKUcZfqizdw0qM9VEyS5Z2QlG15cLiSgFEJcUdwJNI5K1pksjXupuGVUINuPngNNJXPlTDJXziwxNumj+wjqfmOZ/c+Ll3RpExvMXXf9ocznVVWN5s8uLXHcGNYQ/1a9yDu4AU114sxJJ2fTt4QP/aMnk7wsdqdWarBY1XJKxZe4ly9fzuDBg0uMcStsN5ImHe5BVS585AS068eZTx8l59f5RI5+HADbvrXYdv9M1M3PYGnTx+salSm5dKVwZ8M/9FkiBzI1dAqU9ra+GrPhRf0jAaUQ4opSPIGmutxLxT2bhbPveDxRtzxbYkxW4izUonzCBz+IIbRBhSVdAlokVFjKRadTMOoVz1J7cYbgSHA60OyFZK39Cn1QOOYmnXBkuZa6nTbX0raal4MjKwV9SBSKoitR4Lqq5ZRUVeUf//gHL7zwAv379+frr78uscRd3K6kbI7qS86WGcPjMEU2wZ5+IeM9Z8tCTA1aY2nTB01T0exF6EyuwvF1mVxUn8RHBtD82GL2b9zF5Jc/4rcTVavfKkRtk4BSCHFFcSfQ1JRDqblMG9uZLzeewNK65OxYzpZFAJ5zBSd2kr54Opb2/TGGNUSzF5J36FcKT+919aKObuFTKZeWUYHsSy65TO3ISkYxmFBMfjhy0nBknuXMR/eXGJex3NUKsvGUOSh+gV4Frou3wgTfk2OeHxrPV69PYcWKFeUucRdX1oyxpmk487IwRjYBQC3Mo+jMQYKuGUnmmi/J3boErSgfQ0gModffTUC7fnWSXFTfOBwOFixYwN13380rYzp6jtdG8wEhqkMCSiHEFUNVtVJn9arD7tRo3yCYnvHhbD2ZWeFetvJKuoRcM4LuTcN9Cog6hMPBVO+Zw6KUo+Qd2ox/8wQURUdo/ztKdOkpSjtB9tqvCO41FnNcWxSjH3oFz6zooh1J/Ond+WSt+5rC03vRHHYMoTEEdh1OcPcbS9yHWmDl1PnuO3/d/RSGbDM//fQTQ4b4liBT1oyxbc9qnLnnCO07CQBH5llAw7ZvLeh0hF1/DzqzhZzfFpO+aBo6swX/5gm1llxUX/3yyy+kpaUxfvx4r+MSTIr6RgJKIcQVo7yl4qpyLxVPG9uZoTMScV6Udxs76Q3v8eWUdDHodD6Xcln70XOcTcnHHNfufJb3Kay/L0Mxmgm7/m4A/Bp3KPE4nTmAbMDUoJVn1tSpwf6lX7A+/iEenjaPs/NewhTTgpA+E1wznVnJOHPTS70Pr+47CgQO/iOtuvUpdWxpSpsxtp87RcaKDzHHtSWgk6u8kGrPd/2dn0PsnW9jbtgGAP9WvUj68D6yN8zFv3mCz8lFV4o5c+bQsmVLrrnmmkt9K0KUSzrlCCGuKC2jAmv0eu6lYncpl6rOC1W2lMuk8bfi78wjZ8tCMpZ/SN7+tVha96HB3f/EGOl79xO9Ag30VhIXzeZP//mZlMVv4d+iB7F3TCe4500EdR1O2PV3Ezbw3hKPLa37jqrhc+ed0maMndZMUr95GZ05gMibnvYUa1cMrpqchpAYTzAJoDP549+yJ4VnDqKpTk9y0dWgqKiIb7/9lvHjx6MoMiMp6jeZoRRCXFF6NgvnYKrVpzIrFdGcDrIPb2PTJhM9e/as01Iuf/nLX7hx4n0MnZFYZoHr0vg17UzTp5YUe34d/5syiqwHBjPooRdw2rII638niqJDLSpAMZpQlNLnFkrrvlOZ5JiLZ4zVAhsp815ELbARM/lNDEERF+4zMNz1mIDQEtfRB4SC6kArKsAUEHjVLPcuX76crKwsJkyYcKlvRYgKyQylEOKKMi6hMU5VI2fr92Stn4N15woA8g9vJmv9HLLWz0EtsAHgyE71HCtMPgzg+dm6exWK3kDSuvlce+21dOvWjQ8//JCBzYNYPqU/CU1cexL1ZQQ37uPdm4axfEp/n4PJ4rNvNTkr+t3vZyk8/juK2YLDeo6kjx/i1Du3cuqd2zj30/tojiKvx7q774Rdf0+pr83XfuTuGWPNUUTq/FdwZCYRPe4FTOeTcdwMQRHoA8JwWjNKXMOZe86ViGT290ouutLNnTuX9u3b07Fjx4oHC3GJyQylEOKK0jEuhJ7x4Xz34Xc4slM9x/MOboCDGwAI7DAQnV8Ajqxkstd+5fV4989+TTpxw6hbmfPbGpYvX87MmTP585//zBNPPMHEiRN58qGHMI/qyzdbT7Hl+IVSLprTQYdG4T6XcvGlDuSM8V2rPSu6+VgGRRlJoDpJW/AqgZ2H4jfgLgpO7iJ36/eoBTaixkwFKu6+U5nOOz2bhXMgOZvkhW9SeGY/0WOfwxzXrtSxlnb9yP1tMfnHtuPfrJvrufKyyTu8Cb+mnTHo9RWWXLpS5Ofns3DhQqZOnXqpb0UIn0hAKYS44kwb25kdp76ocKn44uXh4kx6VwKNTqdj+PDhDB8+nKSkJD799FP+85//8J///Ifu3bvz0EMPMfW+2wkICOC/s77irjvvYH9eHv7+5Rcar2wdyM/u6s6/Vh0udbxbeQWuD6dZ0ewFaPZCAruNIHzIQ4CrvaPmtGPdsQx7v0kYw+N86r7ja3LMuITG/PPVZ8k/vAn/lj1x5lux7v7Fa0xgx4EAhPQeR97+daR993eCe9yEzhxA7o4fwekktP+dOFXNp5JLV4Iff/wRq9VaIrtbiPpKlryFEFec2kqgiYuL44UXXuDYsWMsXryY6OhoHnzwQRo2bMgjjzxCns2V0ZyWllbu9RftSGLojES2nnTN8vlSB/LeL39jUq8mLHm0L5N7NaF9g2CMetcrNOoV2jcIZvL583Mf7O117+7kGMVgAiCg3QCv5wlofz0AhUn7cWSlkLPpW0L731Fu9x1fk2M6xoXgl+1aHs8/vJlzS94u8cdNHxBGzORp+MV3Jee3RWQlzsIQFEHMpH/g36A5PeN9K7l0JZgzZw7dunWjdevWl/pWhPCJzFAKIa5ItZlAYzAYGD16NKNHj+bEiRN88sknfPLJJ3zwgauY+GeffcaTTz5ZYpbSarVy/9+eZ9GKRIrOHkQtsBIxcgqBnUu2LbSnnyLj5/9QeHovit6Af4se/Dn3fv59zwBevrFyBa7dyTH6wAjs6SddSS7FX3eAK0hTC6w+d98xGfQ+J8ds3rDW5+QiY2gs0Rd3JNI0nHYHf7ymZjP46yur1cqSJUt48cUXL/WtCOEzmaEUQlyxxnSNq9UEGoCmTZvy6quvcvLkST7++GMAXn75ZRo2bMiUKVPYt2+fZ+z2gyeZ+/EM7OdOYYxuVuY1HTnpJM9+EkfmWUIH3Elwz1vIP7KF5DnP8fjcrRxPt3nG+hrUtYwKxBTbwnX93HPez5frSoTRW0K8uu8kfXQfSR/dR/ri6YCr+07SR/ehFeZVKjmmujPGKArGbXMYc0Mf5s2bV9WrXDaWLFlCfn6+LHeLy4rMUAohrmjxkQHMe6i3J/mleAJNTfZCNhqN3HXXXTz44IO8+eabZGRk8Nlnn/Huu+/Sr18//vjHPzL/XEOa/GUWiiWMwrOHSP7y/0q9VvbGeWj2QmLunoEhJBoAU8PWpM55jqzfVzB1QRTzHirZBrI8PZuFs6t9f3J+nY9153L847t4zll3LgedHnOTTuiDoyrsvmMw+1c6Oaa6M8aDnh3AAw88wPjx41m/fj3Tp0/HZDL5/PyXU6vCOXPm0KtXL+Lj4y/1rQjhMwkohRBXhY5xIV4BY20EGCaTidDQUADeeOMNXn75ZRYuXMhHH33EPX99gQb3vItiqTgQyzuwAf+WPTzBJIB/fFcM4XFY965lc5fhPtWBLG5cQmO+3NicgM5DsO1cQZqq4tekIwUnd5G3fx3BvcdhCIrwqg3pdnH3HfX89SprTNc4ujQKLTMZya2s5KKvv/6afv36MWXKFDZt2sS8efNo0qRJiceDb9nz9Wk/pvv9mJ2dzY8//sibb755qW9JiEqRgFIIcVWqrdmq6OhoUlNd5YrMZjPjx49n/PjxPP6/zXy3O73CmTlHbjpqXham2JYlzpkbtCb/yG+eOpCVCYjc5ZR+G/EoGcFRWHeuJO/gRgwhUYQNeoDgHmN8uo5ep5DQJKzKwVh5M8Y6NApSjnH3qH5M7NWsxHMoisLDDz9M9+7dGTduHNdccw2zZ89m2LBhnjGVzZ6fNtb37kU1qayAt1GwkchhD9Pl+lF1fk9CVIcElEIIUYOKB5TF7Ukt8GmZ12l1JcC4O8cUpw8MQy3IxVFU5HMdyOKmje3M4H+uJvS62wntO9HnxxUvr6RXFJ/7kZentBnjPXt207nzaIbcsYqOcV3LfGzPnj3Ztm0bd9xxByNGjOD555/nhRdeYMmuZM+SOviWPT90RmKluxhVR0UB77HMIvw6DeGeuQfouSntkgW8QlSWBJRCCFGDygooD6dZfXq85igEQNEbS5xT9CbPGF/rQBaXc+YIWcv+TeCQRyv9WKh8P/LK0OkUOnToQGhoKOvWrWPgwIHljo+IiGDJkiX84x//4Pnnn2flb/vYtu9IhdnzmqZi3b6M3B0/4shIQjGYmTCrGf+Y9hZTxg+p8ddV3KIdSfU+4BWiqiSgFEKIGhQdHc2mTZu8jrnrQPpCMZgB0Jz2Euc0Z5FnjLsOpK9L9ydOnGD48OE0bdCAJ25qxwtLDtZ6P/LK0ul0XHfddaxbt87n8c8++ywtu17LhFGD0QdHYYxuRuHJXWU+5twP72Lbu5qAjjcQlDAKraiAopSjTF+0mZsG9am12cAPF63l8aefpfD0XtR8K/rgKALaDyC4183ojH4lxqsFVk59/BBqXjYP7HkKXnxUgkpRr0lAKYQQNai0GUp3HUhfgkp9oCtpp9Se1tZMdH5BKAYjRr3iczB57tw5hg0bhr+/P0uXLiUmJoZrW8ZWOTmmNvXt25fXX38dh8OBweDbR9S8Ywafsudt+9Zi2/0zUTc/g6VNH69zep3C1AU7K50974v1vx/g0QkjUUwWgq4Zhc4/iMKk/WSvm01R8mGib32+xGOy1s5Gs7tmqzVc2fFdGoXK8reotySgFEKIGuQOKDVNQ1EuBHwtowLZl1zxMrUhKBKdJYSi5MMlzhWePYgpppnner7Iy8tj1KhRZGRksH79emJiYoC6K6dUWX379sVqtbJr1y66detW4fhdSdlsTbL6lD2fs2UhpgatXe0mNRXNXoTO5JoddKoam49nVDp73hd/fPGfqAVWGkx6E1NUUwCCug4HTcW2exXOAit6vwv/PYvSjpO7fSkh100ge+1s1/1pWq0FvELUBAkohRCiBkVHR2O328nOzvaUEAJXHciDqVaflpgtbfpg27UKR04ahuAoAPKP78CRkURwjzFoTgc7f/6Ohw/MYfz48fTt2xe9Xl/iOg6Hg/Hjx7Nz505Wr15Nq1atSoypi3JKldG9e3dMJhNr1671KaCcv/UUBp2Co4Lfq1qYR9GZgwRdM5LMNV+Su3UJWlE+hpAYQq+/m4B2/aqUPV+RXUnZnExxFZIv0aEoMBwUHYrO+6M4c+XHWFr3xq9RB7LPH6vNgFeImiCdcoQQogZFR7tqR17cz3tcQmOcqkbO1u/JWj8H684VgKu/ddb6OWStn4Na4OqAE9L7NhSjmZSvnyHnt+/J3jiP9IVvYIyKJ7DTEBS9gZFtw/jhhx+4/vrrady4MY899hgbN25EO5/woWkaf/zjH1m2bBkLFiygR48ePt1/VYJJX3p6+8rPz4+ePXv6vI9y87GMCoNJAEfmWUDDtm8t1p0rCLv+HiJHP47OEkL6omnkH92KU9WqlD1fnvlbTxHQtBMA55b+i6KUozhy0rDtSyR3+1KCEkZ7ZkkBbPvXUZi0n7Dr7ylxLXfAK0R9JDOUQghRg9wBZWpqqteMoLsO5Hcffocj+8Iey7yDG+DgBgACOwxE5xeAITiKmIn/IHPVJ2St+QJFZ8C/ZQ/CbrgPg8lEQpMw/vPQC2hvPs+vv/7K3LlzmTdvHv/6179o0qQJt912G5mZmXz66ad8+eWXDB8+vEZfY20XDe/bty9ffPFFiW0DpfE1e16157v+zs8h9s63MTdsA4B/q14kfXgf2Rvm4t88oUrZ8+XZfCwDU7MEQvpNJmfjN5w9fCFhK7jPeML631HsHgvJXPUpQT3GYAiNwZGd4nWt2gh4hagpElAKIUQNKh5QXmza2M7sOPUFRU61wuuYopoSM/7VEseL14FUFIXevXvTu3dv3n77bdatW8fcuXP56KOPsFqthIeHc+DAAXbu3EmnTp0qDM4qUldFw/v27csbb7zBsWPHaN68eZnjqpI9bwiJ8QSTADqTP/4te2LbsxpNdWJHX6PL/u6A1xASg7lxByxt+qD3DybvyBZyNsxDHxBKcMJoAHJ+nQ+qk5Det5V5vZoOeIWoKbLkLYQQNSgsLAy9Xl9qQBkfGcD0WztT1VClvDqQer2eAQMGMHjwYGw2GzfddBM333wzH374IV26dKF9+/a89NJL7Nu3r0rPvWhHEkNnJLL1pGuGzNcaiot2JFX6ufr0cWVgV7Ts7c6e94W7ULzuon2McH5vo+pAKyqoVPZ8RdwBr23vGjKWvUfEiL8Q1HU4ljZ9iBz5GAGdBpG1+guc+Tk4slLI2fQtof3vQGfyL/Oa7nJRQtQ3ElAKIUQN0ul0REdHk5GRUeoH/5iuccwY3xWTXofex8BFr1Mw6XXMGN+13FqEa9euZeLEiYwbN44FCxbwySefkJyczA8//EDPnj355z//Sfv27encuTN///vfOXLkiE/Pv2hHElPm7qDIqXoCxsLkw6TMfYGT74zj5DvjSJnzPEUpRz2PcaoaRU6VKXN3VDqoDAsLo2PHjj7to/Q1290QFIE+IKz0cky551AMJhSzP62igyp1r+VxB7y525ZiimmOITjS67ylZU80eyFFKUfJWvsV+qBwzE064chKwZGVgtPmCt7VPFfAqWlqjQa8QtQkWfIWQoga4t5b2OKRT/jUCjOfXVrq3sIxXePo0ii0RutA7t69mxtvvJHevXvz3//+F53ONV9gMpkYOXIkI0eOpKCggGXLljF37lz+/ve/8+yzz5KQkMD48eO57bbbaNq0aYnrHku38cT8nRS/u8Lkw6R8NRV9UCSh192OhkbutqUkf/0UDe58B2NEI8/YqtZQ7Nu3L2vWrKlwXKWy59v1I/e3xeQf245/M1cGuTMvm7zDm/Br2hmDXk+P+IrLD1VGy6hAjudlofMrGfhqqtP1D9WJIycNR+ZZznx0f4lxGcs/AKDxlDm0atiwRu9PiJqiaO6UQCGEEFVS3t5CN/fxi/cW1kQdyFOnTtG7d28iIiJITEwkJKTihJi8vDx++OEH5s6dyw8//EBBQQHXXnst48ePZ9y4ccTFuWZCb5u5ka0nM71eU+o3L1GYtJ+GD32M3j8YAIc1gzMfP4R/fDeibnmmxGtPaBJWqRqKs2fPZvLkyaSlpREZGVnmuN1J2Yx6bx05W79HLbDhtGZg3b4US+s+GGNc+y+DE0aj8wvAacvk7OePoRblE9zjJnTmAHJ3/IgzJ53YO6ZjimnOkkf71mhZnhcX7+atv91H3rFtNLzvfYzhF2aYUxe8Rv7hzcQ9/DmOrGTU/ByvxxalnSB77VcE9xqLOa4tga16ckef5rx8Y8cauz8haooElEIIUQ3F+zPXRBvDyiaEZGRk0K9fP2w2Gxs2bKBhFWawcnNzWbx4MXPnzmXZsmU4HA769evH0An385+T4SXGn3xnHP7NE4i66Smv46nfvEz+8e00fux/pe4DrEywduLECeLj41m0aBE33nhjuWNvm7mR7568ySt7vri4P36KIdRV0N2elUzmqk8pOPE7OJ2Y49oQev3dWOLaVDro9cXupGwGT/2IlP89g84/mKCEP7iScg5vpuDoVgK7DCVixF9KfWzBiZ2k/O8ZIm96ioC2fYHK/Q6FqEuy5C2EEFXk3luoAdkb5pKVOAtjZBMa3v9BqeN96c9cmWAyPz+fMWPGkJKSwvr166sUTAIEBQUxadIkJk2aRFZWFgsXLmTu3Ll8uGw75o6DSwTKmtOOYjCVuI5iNIPTgT3tBOa4tl7nKls0vEmTJjRq1Ii1a9dy4403lhtoVyZ73hgaS/Qtz5Y4Xjx7viZ1jAuhf//+rDe9RUbibKzbluLMz8UQGkNo/zsJvnasT9dxz/JKMCnqKwkohRCiCorvLXTkpJO9cR6K0a/cx9Rkf2an08nEiRPZunUrq1atok2bNhU/yAehoaHcfffd3H333Yx4N7HUdpHG8EYUnjmApjpRdK4OPZrTTuGZAwA4cs9hvvh+K1lDcc+ZHBrd9Fe+t4ez8Lml5da6dGfPu4P7yiove74mTBvbmaGnMjHe9tL5Z/ONX9PONH1qCVB7Aa8QNUWyvIUQogqeXOBa5gbI/OVTzA3bYIptWeZ4d3/m4jNS7v7MlaVpGo888gjff/898+bN49prr638C/BBWUXDg64ZiSMjydX5Jf0kRWnHSV/yDk6rK2DUHEWlPs6XGorH023cNnMjo95bR2pwawr8Iz21Jt21Lr/adJJR763jtpkbOZ7u6i5Um9nz1dU0wkKL9A1UdYNZbQe8QtQECSiFEKKSdiVls/l4Bk5Vo+DkbvL2ryds0IPlPqZ4f2a34v2ZK+O1115j5syZfPzxx4waNapKr6Ei5RUND+o2kuDet2Hbu4aznzzM2U8fxZGZ7AmWi7cSLK6iGoola12WPq6sWpdjusaxfEp/Epq4MrXLCizdx7s3DWP5lP61GkwCPP/88yyb+Tq3Ny2olwGvEDVBlryFEKKS5m89hUGnYHc4yFjxEYFdhmKKji9zvLs/c8P7PyzRTu/ivYUVJeV88sknvPDCC7z22mvce++9NfJ6SuOuoVhWUBk24E6Ce92CPe0EOnMApuh4Mtd8CYAhvPTgp6wailu2bOGlt99nxc+/4MhOQecfjLlhG0L73+GVFZ2+5J/Ydv9c4vG3ftiI+T//ypiuccRHBjDvod6lZs/r0ChIOcqdI/oyuU+LOtmPOHPmTF5//XWmT5/O43+6lT9WoiKAL+WihKgvJKAUQohK2nwsA4eqYd3+I46cNGJuf73Msb70Z178+xmf+mIvXryYhx56iIcffphnnnmmtKerUS2jAkvdQ+mm9wtE3/jCjGvB8R3ogyK96lAWF+OnkZeXh8Vi8Tr+wiuvs+KXRCxt+2KMjsdpzSR32xLOfv4YsXe+hSkqvtiTGktkRevMlhL7UTvGhXgFjKr6/+ydd3hT5fuH7+wmTSedFMoehTLLkimCLEWU7QAEt+JWXLgnTlRQ+ao/wYHKUEFEZCiUDRYqlL1bCt0zadMmOef3R0homqRNSwulPfd1cQHnvOfkTdqc8znP+zzPR+T06VO0ajWa/mN/Jzaqe41aLLpj5cqVPPjggzz88MM8+eSTABUK3qq2i5KQqEtIglJCQkKiihzPNGAtLiBv8w8E9p2EQuf5xu+NP3NukZncIrPj/+58sSe3tHD7pEncfPPNfPLJJ5fsy+0NVWkabjwUT+n5YwQNnoFM5ppNJQpWDsavJviNcbaWRMOGMXz4cDp16kRJzCiiO05HkF28JfnGDODc1zMp2LGMkNFPObbL5Ar0sYNdzm/PR/XU9kcul2FUBxN9y5O8uLWIx3dUXOhzqezYsYPJkydz880389FHH7n8vNwJXskBR+JqRhKUEhISElXAnluYF/8dcq0evx6jPY61+zMHD7u/Qn9mT5TNFdx1wkyHkVP54YePUSgU1Z5/VZgQ15RF28+4bDclJ5G/9Ud8WnRDrvWn9NxhDPvW49MyDr+eY9yeSyZXsOjlBzj5bwxr167llVdeYdasWUR27I169Isu41XBUahDojFnpbjsEwUrorkEueZipLNsPmp5UejUeL79YHJFoFyhT1nxXrbxfHU4duwYo0ePpnv37nz//fde/bzsYlISlhJXK5KglJCQkKgCcrkMMf8chsS/CBpyD9bCi97QotWMKFix5KUj0+hc/JkBhz9z/tafyP7zE7BaUAZGoO86Av8etgbe+duWUHR8J5bc8wilxSj9Q9C26onQdxJ/Hc6+bAUasVEB9Goe7OKUo/BrBHI5BTt/sc0vMJzAgVPw73Wzo41QWew9FEf36wL9uvDoo49SUlLC1q1beWvtcY4LVih3nCiKWIvyUIVEO283l5Dy0USboPTRo+swiKBr70Su1rrtdVm28TyAp2Br+UIfT43nKyMjI4ORI0cSEhLCypUr0WorfpCwL317k/IgIVGXkZxyJCQkJKpIr5kfs3v+YxWO8etxE6XpJylJSapwXNCQe2wiUxQIGmwrssn85S3kOn9UjZoiU2uxZKdQ+N9fKHQBNLt7PutnDbtshRqns4wMmxvvVdNwT6gVctY+NtDtnD31ujQk/UP2qg9oNPIR9F2GAZC7caHtfOGtQBQoPrkHY9IGNE06EH7b28jkCjpE+rP6kQGAc+N5O+acVPI2f0/J2YMIxQYU/qH4dhiEf+9bkJfpIyqDKldXG41GBg8eTEpKCtu3b6d58+Yex16KXaeERF1EilBKSEhIVJFBfbqTnDYbodzzeF78dwilxQQPvRdlYCRCidHJn1kwl5CzZh6i2YRfr7H4NIlB26onMoXzpbi8FzaAunF7sn57m8KjO5i1PKLGLQI9UdtNw931ujRnp5Cz7nM0Ue3x7TTEsT3o2judxvl2GIQqOIq8+G8pOrwF3w6DHL0uyzaet2MpyCRt0RPINL74db8RudaPktTD5G/5gdK044SNv7j0XtXG8xaLhYkTJ3Lo0CHi4+MrFJPlo6aeclRrKmoqIXE5kASlhISERBWZNrgzSw8UuGwv2L0CAF1b92KvcO9qRLMJAE3jtvg07wZy79oB272oLSaDx1zB2sIuYmrSsxzc97q0GnLJWPoqco0vITc/53YJvSx+PceQt/l7TKf/w7fDIEevy7KN5+0Yk/5BKDESece7qEOb2Y7vOgJEAWPS31hNBhQ++otzqaTQx44oijz44IOsXbuWP/74g27dunkc+8HiP5k9ezYlqYcA0DRuT9Dg6ajDW178XMwmjPvWU3RsJ+bM0whmE8rASGbsHsGXbz3D2LhoT6eXkLhiSI3NJSQkJKqIPbfQ2wbVdkynE21+19ganad8OJ6UDyeS/dd8F3cZWw5hPlZDLqaUJHLXLQCZHJ/oTo5cwctJbTQNt/e6tCOYjKQveRnBZCRs4qso/RpVOi+5SoNc64fVZItMyhHZsPeoo/F8WYTSItscfQOd56wPBpkcmdw5xuJt4/k33niDL7/8kq+++ophw4Z5HPf7hq08Pe1mLHlpBPa7lYB+kzHnniNt8bOYs886xlny0shZtwAQ8et1M0GDZ6AMDCdn7WfcOX2Gwx1IQqIuIUUoJSQkJKrBu+M6M2xuPNYyi6oRt79T4THmnHMAyFQadO364RPdCVPyfgoTfkcwGQkdM8sxVjDmcXbeFMf/FX4hhNz0NKpGTavsi11T1EYPRXuvS9FSSsay17DkphI++Q3UId5F4YSSIoSiAkfrJlP6SSY9t4rAuBsRyvlm+0R3omDHMrJXf0LggNsvLHkfonDvavziRrt1+HFX6FOWb775hpdeeonXX3+dadOmVTjXex97GplSTcTU91Fo/QHw7TiYc/+7j7xN3zpSHRS+QUTeNc8RRQXw6zaSrD/mUrh/PQ9+vprVL07w6vORkLhcSIJSQkJCohpUJ7dQNJsQzSXou40k+Pr7ANC164toNWNIXIN5wO0OZxi5Vk/Y5DcQLaWUpp+g6Mh2xNJix7m88cWuLWqyh2KvFsEcScsn7bc5lJw7TNi42WiiYlzGiZZSRKvFqVUQQP62nwARbYvuKOQypo7sz+YjrUh1E8TTtowjYMAdFGxfyvnjOx3b/ftOImjgFNcDoELxvmbNGu655x7uvfdeXnjhhQrf5/7UfNKPJqJtGecQkwBKfTA+TWMpOrELobTYVq2uC3Db21TX9hqM+9fz73/7SUodJlV/S9QpJEEpISEhUU2qmlsoU6oB8I0Z5LTdt8O1GBLXUJJ62CEoZQoV2uZdAdC17oVPs66kf/80ct9AdK17OXIF60LPwkuZw4S4pnz0+gsUH9+JtnUvrMUGDEn/OI3Rxw7Gasjl/DePoOswyOHEYzq1h+IT/+LTMg5t2z5YBZE7+rZi+X9p4EHmKwPC0TTtiK5dXxRaf4pO7KZg2xIUvoH4x7nvKXrwfAEjP453auOzZ88exo8fz8iRI5k/f36ljeaXJaQgWs2O34GyyFQasFowZ55BE9Xe4znsLadUvgEVRk0lJK4EkqCUkJCQuATGdI2iS5PASlvAACj0jTBnJbvm8Ple8PE2uVY82/FpEoNCH4zxwEZ0rXt59MW+2oiNCsAnP4VCoPj4LoqP73IZo48djNzHF23rXphO78WYtAFREFAFRRI4aCr+vcaiVCiIiw6iQ6S/R/9x48FN5KyZR+N7F6D0DwFsEWJEkbyNC/HtMMgpeliWss3PO0fo2D3vUTp27MhPP/2EUln5rXTXqRxUwU0oOXcEUbA6io1Eq5mSc0cAsBRmo/FwvGg1U/jvSpQB4Sgj2lyRlAcJiYqQBKWEhITEJeJNbuH5/GJyI1phOr0XS2G2k9+15UJz9IosHMG27CuU2NZy24T51d4buszs2ra50l6Xch89IaOf9LhfIZPx7rjOjkIfd6KycM9q1OEtHWLSjq51L4z711OaftIRFXaH/UFhf5oRzS2vMfPGdvj6etcb8nimAb/uo8j56zOyV3+Cf59xIArkb/sZq8EmDssXZpUlZ+0XmLOSCZvwMjK54oqmPEhIuEMSlBISEhI1REW5hS+vTOLr0wMp2LEMw761aJt3cYwz7FsLcgWa6E4IpSaQ4dRkG8B4eCuCyYAmog0KuYyezYMuz5u6DNR0r0t7oU95rEV5yMu0BbI3OTed2gtA9h9z0XcZ7tTk3JNrUUDfSbz050n8/f0r7Q1pb4/k120UloIsCnb+gjFpAwDqiDb49xlHwbaf3RYFAeTvXI7hv78IGHAH2lY9bXOvQykPEhIgCUoJCQmJWqPszd7mi90S387XY9y3jkxBwCc6FlPyfooOb8H/mgko/RpRmn6S9J9mo4sZgCq4CTKZjJK04xgP/IMiIBy/njdhFUQmxDW9gu+s5qnJXpe9WgRzNMPgcg5VUGOKT+/FnJOKTKl2NDmX+wYhmIxootq7NDkvTTuOOqwFvjEDnVyLik/sJnL6p141P7dYzCjlYBEgaNBU/HuPxZx5BrnGF3VYc3I3LQJAGewqTA371pP3z0L03UYS2G/yxfdST1IeJOoPkqCUkJCQuAzYe1f+O3ImOf6hGPatp+jodpQBoQQNuQf/nmMAm0+2rl1fTGf+w7h/A6JgQekfhl/3GwnoOxG1bwBx0UH1siDD23xU+/YezYKYM9bVhccm3s+4HOffexzFJxNI+/4ZVKHNEEqMqEObUXr2IPouw2g08hGyVn3o1OS8Itei4uM7UcVe69L8PDMzk+3bt7Nt2za2bt3Kv//+S9Ct7zqalyt89CiadnSMN51OROEX4pQGAVB0dAfZf36Crt01BA97wGlffUp5kKgfSIJSQkJC4jJh710Z2P82Avvf5naMQhdAoxEzPZ7DnitYX6koHxXBQoeo4Ep7XdrFe0JyrpMg9YmOJWLKe+RtWezwWLcacggcONWW04jnJudlsbsWCSVGR/Pz1z79hpMJm9i2bRvHjh0DoHHjxvTr14+3336bw74dWHe6xEUgGw/FU3r+GEGDZyCTXfQaMSUnkbXyXTRNYwkZ/bTTvvqW8iBRP5CJolidlBUJCQkJiWqwIjGVR39OBFGESlrNlEcGzJ3UtUH6Ob/44kssXPgNKSneOQSdzjJWWOhTfDKBjCUvo23d26nJefaaeeg7XU/w0HscY0VRtHmyCwLm3FTyNi6i5NwRGt89H1WjpohWC8b/1tAsaxf9+vWjb9++XHPNNURHRzvaCSWl5jN01hfkb/0RnxbdkGv9KT13GMO+9fi06EbY+Jccld+W/AzO/d/DYLUQdN0MZGrn3pvqsOasfW1KvYxSS1y9SBFKCQkJicvIiJgQfPctxdjxZhQqdY35Ytd3QkNDyMrK8np8ZYU+VWlyXpFrEYBMoaTHyEmseexzj/OJjQqge0xLNm5XULDzF1uBT2A4gQOn4N/rZifPckteGuKFav6cta7n7HDDDGKjPEexJSSuBJKglJCQkLiMzJ49m2PrFvPrMw+y6JCVXadzEAWL2yXWynIFGxKNGjXCZDJRVFSETqer/AAqL/Txtsl5Za5FACeyiiqdz2f3j2KYSV9heyQAn2adafbsKrf71Ao5fzw2sNLXkpC43EiCUkJCQuIysW7dOt5//33ee+89bhjYixsG2pZCn//qd/49k4s2oiVWkWr7YtdnGjVqBEBWVhbR0d75fIPnQp+qNDmvzLUIvGvjU9PtkSQk6hKSoJSQkJC4DGRmZjJt2jSGDh3KE0884dgeGxXA8ucn0aNHD9RqNdu2bUelcr00N/SegyEhNtGXnZ1dJUEJ7gt9/v6++k3Oy7sWAajk3rXxqcn2SBISdQlJUEpISEjUMqIoctddd2E2m/n222+Ry+VO+1UqFQsWLKBv374sWPAFM2fOdIifXadyOJ5pcLjutA7VO3lKNxTsEcrs7Oxqn6Ns43nfNwqwqFyXzkXBavuH/W8PlHUtArDmprJt2zb69u1b6Txqqj2ShERdQhKUEhISErXM559/zu+//86KFSuIjIx0O6ZPnz7ce++9zJ7zMRuV3fj3TJ6L0DBbRSdP6V7Ng3l3XMMQGmWXvGuCqOYtObZnK+acVFRlGoobD24CmRxVaHOvXIsAFDJQFaTQr9+93HXXXbzzzjuOiKonvLHrlFIeJK4mpLZBEhISErXIgQMH6NGjBzNmzGD+/PkVjv1x+3FmrzwMcrm0FFoOURTRaDR89NFHPPTQQ5d8vs+/X86DUyci1/rjF3eDrSjn+C5MJxMcTc4rdC3yCyHyzo8ceZYrHryG7X8s4bnnnkMulzNnzhxmzJjhEo2ujIae2iBx9SIJSgkJCYlawmQy0atXL6xWK//++y9ardbj2BWJqY5ijfxtP5MX/x2qkGga3/2ZY4wnX+nAvpP4dPqgei8qIyMjuf/++3n55Zcv6Tzr1q3jrrvuoqTTWAqPbKU07QTW4kKUgeHoY4fg32ccMrkCa1E+efHfYUpJwlqQ5XAtsnl5T0ShC0AhlxEXHeRwysnIyGDWrFksWrSIPn368Nlnn9GtW7dqzVMSlxJXE9KSt4SEhEQt8cwzz3D06FF27dpVoZg8lWXk6WX7EAFLQRb525cgK7fMChX7Sj+pmU+XJsPq9fJ3o0aNLimH0mAw8PTTT/PFF18wZMgQXn37QaYvGe6xjU9lrkXg6lwUFhbGwoULueuuu3jwwQfp0aMHM2fO5LXXXiMgoOKlaylvVuJqRhKUEhISErXA6tWr+eSTT/j444/p3Lliq8RnltsqfgFy//kaTeN2iIJgc2cpQ0W+0oVHdzBreYSTp3R941IE5caNG5k+fToZGRnMnz+f+++/H7lcznuCb6208RkwYAB79uzhk08+4eWXX2bJkiV88MEH3HrrrQ73HDuns4weC3Qact6sxNVF1ZI7JCQkJCQqJT09nenTpzNy5EgefvjhCsfuT81n1+kcrIKIKTmJosNbCRpyr9evZfeVtpgM7DqdQ1Jq/iXNvS4TEhJSZUFZVFTEI488wuDBg4mOjmb//v08+OCDjtzGMV2jmDupK2qFHIWXy8sKuQy1Ql6pDaZKpeLJJ5/k8OHD9O/fn9tvv50hQ4Zw6NAhx5gViakMmxtPQnIugMfcWfv2hORchs2NZ0ViqldzlZC4XEgRSgkJCYkaRBAE7rzzTmQyGQsXLnSJRpVnWUIKSrkMs8VCzrov0HcZhjqsucfx7nylkcnxie6EQi5jaUJKrS6LXsm8vkaNGnHmzBmvx2/dupU777yTs2fPMnfuXB5++GG3RTK13canSZMmLF26lL/++ouZM2fSpUsXnnzySbqPvY9ZvxxwREezVn2EMWmDx/NEPbQQ/EKwIvLYz4mOuUtI1AUkQSkhISFRg3z66aesWbOGP//8k7CwsErH7zqVg0UQMez9E0tBJuG3vlnh+Ip8pa2CyO7TuZf8HspSl/L67EvelYlak8nEiy++yAcffECfPn34448/aNu2bYXnvhxtfIYPH87+/ft59913mfPZN0TK+iFy8X34dRuBj0szdZGcv+ajDAhH6RdSZqutOXqXJoHS8rdEnUASlBISEhI1xH///cesWbN47LHHGDFihFfHHM80YC0uIG/zDwT2nYRCV7FYqcxX+lhG4SW9Bzt1Ka/PLvI2qHsjTuhDyxdWexS1u3btYtq0aZw8eZI5c+bwxBNPoFAovH6tss3PoeYjsj4+Prz00kvsCx3C3rP5UKbRiiYqBk1UjNN4U8oBRHMJvh2udTmXVRSZtXxfvc6blbh6kASlhISERA1QVFTErbfeSkxMDO+8845XxwiCiNkqkhf/HXKtHr8eoys9pjJfaW88pStjRWKqwxoQvM/rq+l+mK6iVgUXtGF5UdujWSCNk/9m/pxX6N69O3v37qVDhw6XPIfaWN7fn5rPv8l5Xo01HtwEyPDtMMhln1UQHXmzUvW3xJVGEpQSEhISVcCTWHvqqac4deoUCQkJaDQar84ll8sQ889hSPyLoCH3YC3McewTrWZEwYolLx2ZRodC6+f2HOV9pZVeekqX58CBA7zyyits3r6LjPR0ZCoNqkZN8e89Fl2b3m6PEa0Wzv/fw5izUwgcPIPHLrTfqQlRWVVR+++pbEQhlqkvfsKXs+9Dqay7tzd73qylkub1otVC0eEtaJrEOIqvynM58mYlJLyh7n7jJCQkJOoA3uQQnvh3I59//jmff/55laNi4fIikkWB3PULyF2/wGV/6hd34dfjJoKHeq78LusrXXT+BD179qRfv36OP40bN650HmfOnCEjOw9zywEEdQpCNJdQdGQbmctfJ3jETPy6ui7hFyb8jqUg8+I8uPS8vt27d/PKB/NZt+EfLPnpyLX+aBq3I3DgFCeLRKf3X0bYrhg8g5uT0ut0sYo9b7Yyik/tQSgucLvcbac28mYlJKqDJCglJCQk3FCVHELL+eOMGD+F++67r8qvM6hPd5LTZiOUMy3Li/8OobSY4KH3ogyM9MpXWiGDPq1C8TW3Z+XKlXz88ccANGvWzElgxsbGuuQVjho1ioUpQZxNznW8V7+4Gzm/8DEKdv3mIiitxjzytv6Ef59x5G/+4eL2S8zre+m1N1n3Tzy69v1RhTXHasilcM8qzn/zKBFT30cd2tzlmLLC9mooVjmeafBqnPHgJpAr0cX0r3BcTeXNSkhcCpKglJCQkChHVZdbVZFtOa6IYeV/56ocGZs2uDNLDxS4bC/YvQIAXVubMKvQVzogHL+eN2EV4bU7RxIbNRmA8+fPs3XrVrZt28bWrVtZsmQJFosFf39/+vTpQ9++fenXrx+9e/fmdIHArtM5TnOQyRUo/UIoSTvmMr/cjQtRBUfh23Gws6C8xLy+kphRRHecjiC7eHvyjRnAua9nUrBjGSGjn3Ia707Y1uViFXvebKXjSospPrYDbYtuDr9wT9RE3qyExKUiCUoJCQmJMnz44xpmv/QyJWcPIlrMNn/nriPw73ETgtmEcd96io7txJx5GsFsQhkYiV/XEei7Dq9Wb8DYqAB6NQ8moUxk0B0Kv0bo2vXFdOY/jPs3OHyl/brfSEDfiah9A4iLDnIScZGRkYwfP57x48cDtsKh3bt3O0Tmxx9/zCuvvIJcLmfMa9+jlAdQaipGtJQglBRRfGwnxScT0MUMcJpLybkjGJP+JuKOOchwFTHVzevbn5rPSYXrZ6cKjkIdEo05K8VlnzthW5eLVeRyGSqFrFJRWXR0h626u+O1lZ5Tpahe3qyERE0iCUoJCQmJC3y7dCVPTRmHKrwVAX0nI1P7YMlLw1qYBYAlL42cdQvwad4Fv143I1frKD61h5y1n1Fy7jAhNz5RreXWd8d1ZtjceKxlDAAjbneuFK/MV7q8p7Q7dDodgwYNYtAgW8WwIAgcPnyYHTt28F1WCBahlNy/v8KQuMZ2gEyOru01BA97wHEOURTJWbcAXcwANFExWPLSXV6nunl9nopVRFHEWpSHKiTaaXtFwrYuF6u0DtVzKK3iZWrjwY3I1Fq0HgqiytImzH3BloTE5UQSlBISEhJAQUEB9949HW2rnoTc8hwymaujisI3iMi75qEObebY5tdtJFl/zMW4fz0B/SajaBRV5eXW5iG+vDe+c614SleEXC6nQ4cOdOjQgbdnrwbAv+cYdO37Yy3MpujwFkRRAKvZcYxx/3rMmWcIveW5Cs99JK2AzZs3o9Pp0Ol0aHU69L6+6HQ6fHx83DrWeCpWMR7YiLUwm8D+tzu2VSZs63KxSq8WwRzNMHhOpSjKx3Q6Ed+YgS45s+VRyGX0bB5UG9OUkKgSkqCUkJCQAN777GtKCnJoPHEqMpkcodSETKV2EpYKXYDbxuO6ttfYhFZWCqqgxtVabrUvk9tzNyta/nbMRy5DIZNdcv/Hsnl9qkZNUTVqCoC+0xDSf3qRjGWvETH1Q8TSYnI3LcK/91iU/qEVntMqwpjXf8CnSUdUIU2RKVSIVjPmrBRMZw9gObIZTVGGQ3DqdDpyh70COAtNc3YKOes+RxPVHt9OQxzbvRG2dbVYZUJcUxZt92whaTwUD4LVq+VuqyAyIa5pDc5OQqJ6SIJSQkJCAli+8k/kGh0WQzYZv7yBJScVmcoH39jBBA+5B5lS7fFYq9EWCVPobMUT1V1utXtKP/bjvySeMyCXgTtdWV1PaU9UlNena9+PnDXzsOSkYjywEawWdDEDHBFBy4V0AMFkwJKXjsIvGJlCBUBQj9GUPaVMoUId3hKf8BYIcaOJUBjozTGUxbkYi4pYU05MWg25ZCx9FbnGl5Cbn0Mmt1WmCyVFXgnbulqsUlnerPHARuS6QDc2jM6IghUx4zjJ/8mIjRpVS7OVkPAOSVBKSEhIAGfPnEQUrGQufx1952H4DJqGKXk/hQm/I5iMhI6Z5fY40Wqm8N+VKAPCUUfa/KIvZbm1eYgvw5UH+WvRRzwy90f2pxXVuKe0Ozzl9YnmEgCEEiOWgkwEk4HzXz3oMq5g+xIKti8hcvonqMNbAuCp7kS4kO+YKfrxpyyO96bYIqxtZq92iFrBZCR9ycsIJiPhd8xB6dfo4mvt/MUrYatWq+ucmLTjLm/WTuTUD7w6h1qlpFnubm644UlmzJjBhx9+SEBA3csZlWgYSIJSQkJCAiguMiKaS9B3G0nw9bZ+krp2fRGtZgyJazAPuN1tY+2ctV9gzkombMLLjggaeLfc6il69uuvv9KvQzRzJsZVOram6BgkcjTDud+maLVgTPobmVKDKiQavx6j0bXt43SctSifnDXz0Lbti1CUR8bSVxBMRhT+ofh2GIR/71uQq3wqrJB/1GwmOzsbWWEG6EIRLaVkLHsNS24q4ZPfQF2uGMdbYduxa9da+axqgprIm31/fBduen0k//d/Q3n88cdZt24d//d//8fQoUNreroSEpUiCUoJCYkGjyCIjiVt3xhnz2TfDtdiSFxDSephF0GZv3M5hv/+ImDAHWhb9XTa52651RvXncZaK//884+jKbmd2o607V38HucOp6BpGovCrxFWQy7GgxuxZJ8l6Lq7kKu1aCJaQ0Rrp+PsEULTyX+R6wLxixuNXOtHSeph8rf8QGnaccLGv1hphfyrwsOI50+gaBlMxm9zKDl3mLBxs9FExbjMtSJh69tpKLo2vdEERdT5YpWaypu96667GDp0KDNmzOD666/ngQce4N1330Wv19fq/CUkyiIJSgkJiQaPXC5D6dcIc1YyCt9Ap30KX9sSomBydjcx7FtP3j8L0XcbSWC/yS7nLNsbsCquO820ZtCHcvPNN9fsm6yEe+68g6RXPyR772qsxYXI1VrUEa0Juna6Ry/vsoiWUsImvOyogPfrOgJEAWPS31hNhkor5AP7TSK27xC2/fARxcd3om3dC2uxAUPSP06vo48dXKGwVYVEo2t7DSJcFcUq9rxZT78fdirLm23WrBnr1q3j888/Z9asWfz111988803DBw4sMpzqot5pxJ1H0lQSkhISAARLTtw6tReLIXZqBo1cWy3FNrcY8pWdxcd3UH2n5+ga+fco7Es9t6AVXXdOVOkIOrez9mdITKmcgvuGmPy5Mn0GTqaYXPjKbUKXh+nDAzHv894CnYscxXj+mCQyZHJlch99BVWyJdmneVwehSqvGQAio/vovj4Lpfx+tjBlc5JIZe5NHmvyzQP8WXJfdc4Iti7T+dWK29WLpfz0EMPMXz4cKZPn861117Lo48+yltvvYVWq/V4nDeR86vls5S4ckiCUkJCQgIYeuMYvtzwA4Z9a9E27+LYbti3FuQKNNGdADAlJ5G18l00TWMJGf20+36VchnnVryP7FHP0aGohxYi99F7yCsczqMXClcupR1QValuXp9PdCcKdiwje/UnBA64/cKS9yEK9662LYGrPfdSLFshr5DLmPrGN/yx/3yVRC3YhG2zZ1fZzuVFk/e6SGxUgJNwq26ksHXr1mzcuJG5c+fywgsvsHr1ahYtWkSfPs5pAlWJnPdqHsy74y69o4BE/UUmimJ18oElJCQk6hVJqfn0GTUB47516NoPwCc6FlPyfooOb8H/mgkEDZqGJT+Dc//3MFgtBF03A5la53QOdVhz1GEtABho3sPaYwXlGnWL5Pw1H2VAOI3v/ozSzNOc//phfJp3wadFN0deYfHR7fjGXkfjMU+x9rGBl/0mXjaq6k1eH0De1p8o2L4U0VLi2ObfdxJBA6d4PEa0mjn/zaOI5hIa3/c/ZHIFHSL9uW9gy+oVq1y4nb02siVTB3Wo6tH1kkOHDjFt2jQSEhKYNWsWr7zyChqNpso/45rqeSpRf5EEpYSEhMQFxn+2mb9/WkDBf+uwGnJQBoTi1/1G/HuOAcB0Zh/pPz7v8fiAfrcSPPB2fIvTMRQWIg9v43SzNqUcIP2HZwgcOJWAvhOxFuVjNeY55RUCjrzCpvd/SZ+uHavkulNTVBS9slN2uyHpH4wH/kHXri8KrT9FJ3Zj3LeeoOvvxT9utNvXyP7zUwz//UXYhJcdRU0qhYxjb4yqluCRA8Ub/0dQwQn++ecfQkJCqv8B1CMsFgvvvvsur7zyCm3btmXWZ0t5+c+TLoK9JO04+VsWu/WxtyMD5k7qKolKCRckQSkhISFxgdNZxirnEJZHrZDz6a3duO/7BJd92X99hmHvn0Td/xXKwHCP5yg6tpPM5a8TOu5FdG16s2pm/yuWw1ZRXl+PZoF8uyMZ48FNZK/+hMb3LkDpf1HEZf0xl6LDm4l68BsUWn+n8+bvXE7eP98QMOAOl6Kmk2+OQi6XVUnU9m4RzJyxnSnOTGbQoEE0adKEv//+m8DAwFr5XK5G9u3bx/Nvz+VIy/GYy32Wxaf2kLHsNdThrfBtP8DhY48oEDR4htNYtUJ+RSLnEnUbKYdSQkJC4gI15am97UQWSrnMablbtFooOrwFTZOYCsUkuOYVVsd1p6aoLK/vx90pFO5ZjTq8pZOYBNC17mUruEk/ibaM60tFFfJlq+OrVawSEsP69esZPHgwI0aMYO3atfj7O4vZhkrnzp3RXXsPQrJz032hpIisVR+ibdWTUA8+9mWximKV/eol6j+SoJSQkJAow5iuUQiiyOM/JSCTyRErubmCa37ZF5tOlMudtEWAhOICfDtcW+G5yjvvXIrrTm1Qvkikdaie00V5yH1cex6KgtX2D/vfVF4hb6+OL0tVi1U6d+7M2rVrGTJkCDfccANr1qzB11eKpu1PzWfX6RyX7caDGxGMeQQN9OxjXxarIFbLr16iflP5lVJCQkKigVFyZAup/3uAtsG2Z26FB/Fi396jWRBrHxvoyCs7nmlwGWs8uAnkSnQx/St8bbvzTvCw+x3OO9647lxuTCYTS5cuJfPgDlRBjSlNP4E5J9VpjPHgJpDJUYU2tx1TSYW8Qi7zqhm5N5XPcXFxrFmzhsTERG666SaKi4u9f3P1lGUJKSjdfHam04nILvjYp/7vPlI+HE/KhxPJ/ms+oqXU7bnskXMJCTtShFJCQkKiDCaTiWeffZYbBvXit1kjq9wbUBBEhx+1Y1tpMcXHdqBt0c0ll7Asnpx33LnuXAlEUeTff/9l4cKF/Pjjj+Tm5hJ3/S349x5H8ckE0r5/Br+4G2xFOcd3YTqZgL7LMJR+jbDkZ5Cx/HVAhm/7fhgPb3E6t71Cviabkffp04fVq1czYsQIxo4dy2+//YZGo6mx819t7DqV4xI5BzDnnIMq+tjXtci5xJVHEpQSEhISZfj0009JTU3lr7/+Aqq+3CqXy1ApZE6isujoDkRzCb4dr/V4nLd5hVeC8+fP8/3337Nw4UIOHjxIVFQU999/P9OmTaNdu3ZMXLCdrer3yYn/AcMem9OOMjCcwIFT8e8zDgBLXhpiiRGAnLWfu7xGYP/b6N8rrsaXUAcMGMDvv//ODTfcwMSJE1m2bBkqlapGX+NqwV3kHEA0m6rlY18XI+cSVw5JUEpISEhcICsrizfffJP777+fdu3auR3jjbBrHarnUNrFm63x4EZkai1aDxaG1ckrrG1KSkr4/fffWbhwIWvWrEGpVHLLLbfw4YcfMnToUBQKhWPsu+M6MywlD9XEVz2ez6dZZ0fjcXeoFfJaa0Z+3XXX8euvvzJmzBhuv/12Fi9ejFLZsG5/7iLndqrjYw91J3IuUTeQciglJCQkLvDaa68hiiIvvfTSJZ2nV4tgR36ltSgf0+lEdG36IFe5OsbUVF5hTWBf0p45cyaRkZFMmDCBrKws5s+fT1paGj/++CPDhw93EpNwsTq+urLCXh1fm21oRowYwZIlS/j111+58847sVqtlR9Uj7BHzt2h0Dey/e2lj72dKx05l6hbNKxHNAkJCQkPHD16lM8//5w333yT0NDQSzrXhLimLNp+BgDjoXgQrG6Xu6uSV1ibkaC0tDR++OEHFi5cSFJSEpGRkdx7771MmzaNmJgYr85hL0iqy+4rY8aMYfHixUyePBmNRsOXX36JXN5w4irlI+d21BGtMJ32zse+LFcici5Rd5EEpYSEhATwzDPPEBUVxSOPPHLJ54qNCqBX82ASknMxHtiIXBeIT5k+jHYqyysM6HcrAVGtueXzrY5ioNahenq1CHYpBqoqJSUlrFq1ioULF/Lnn3+iVCq5+eabee+99xg6dGi1loTHdI2iS5NAr5uR92gWxJyxl9cfesKECZSUlDB16lQ0Gg3z589HJmsYUbZeLYI5mmFw+Zn4th9AwY5llfrYl+VyRs4lrg4kpxwJCYkGz6ZNm7j22mtZvHgxt956a42csyZcdzxhF2S9mgfz7jjvBZkoiuzdu5dvvvmGxYsXk5OTQ69evbjzzjuZNGkSwcHBNTbHqlbHX26+/vpr7r77bh577DE+/PDDSkVlfcgVTErN58Z5W9zuy1r9cYU+9u64kg5OEnUPSVBKSEg0aARBoHfv3shkMnbs2FGjS6ArElOr6bojghcZid4uGaenpzuWtPfv309ERARTp05l2rRpdOjQocqzqw51UZB99tlnPPTQQzz77LO89dZbTqLSLoh3ncrheKahxiPEV4qJC7aTkJzrEqUUrRbyty/BsG+9Wx/7sijkMuKigySnHAknJEEpISHRoPnhhx+44447iI+PZ8CAATV67tNZRmYs2s3JLGOF48w5qeRt/p6SswcRigtR+Ifh22EQ/r1vcRTyFJ/ag/HQZkrPHcGcfRaFXwhNHvw/wCY9507q6iQqS0tL+eOPP/jmm29YvXo1CoWCMWPGcOeddzJs2LAGV+XsiY8++ognnniCV199lZdeeqlK/uFVjRDXBS49ci6iVigkL28JFyRBKSEh0WAoHyUrLi6mffv2xMXF8csvv9Toa61ITPWqQMVSkMn5r2ci0/ji120kcq0fJamHMe5fj7Z1b8LGvwhA1qqPKDq8GXV4KywFmSCTOwQl2Nru/PXYAPJSjrFw4UJ++OEHsrOz6dGjB9OnT2fy5Mk1uqRdn3jnnXd47rnnuPuNBWwqblpni4pqimpHzkUREZjYxMh7MyfVwswkrmakR1QJCYl6S2XLlob96zl37hzr16+v0dcte8PO3/YzefHfoQqJpvHdnwEgmE0Y962n6NhOSlIPIZpNKH2DkGt80Xe+Hr+uI0AUMCb9jdVkQOGjJ3DQVBqNfBiZQknG0lcpzTzj9JoWq5Whzy/k5JcPEx4ezvTp05k2bRqxsbE1+t7qI0OGDKFdz4Es+ugNLAUZyLX+aBq3I3DgFKf+i4WJazAe2Ig5+yxCiQGFvhE+0Z14KPtWuG/4VSMqq1+RL6dNzg4+fPQNeoXLmTBhQm1PVeIqQhKUEhIS9Y6Kli3NVpFDaYUXql3b0Pnx/0MV1LjGXvtUlpGnl+1DBCwFWeRvX4KsXP9JS14aOesW4NO8C+rINpQk70cZFEHO2s8oOXeYkBufQKEPBpkcmdx2mVb6NarwdQVk0KgFn/20invGDZeWtKvAS6+9yfGD+9G1748qrDlWQy6Fe1Zx/ptHiZj6PuoLXuSl6SdRBoSja90LuY8eS346hf/9RfHxXTyunk+XF2+5apaBq1uR3zRoGFPyjnHbbbeh1Wq58cYbr8DsJeoi0hVHQkKiXlF2qRnwGH2xb89TBjNsbnyNLVs+s/zia+f+8zWaxu0QBQGhuMAxRuEbRORd81CHNqP4ZAIZyfuRyRT4tO6NMelv1OGtKNy7Gr+40cjVrs3QPaGQy0jTRktisoqUxIwiuuN0BNnFz803ZgDnvp5JwY5lhIx+CoBGwx90OVbb9hrSFj5G/r71zFre6qoqVGke4suS+66pckX+okWLMJlMjBs3jj/++IOhQ4dW+lp1sShLomaRrjoSEhL1hg9/XMPsl16m5OxBRIsZZWA4+q4j8O9xE+C5sMVqFXjs50SASxKV+1Pz2XXa1gzalJxE0eGtRE7/hJx1XziNU+gCHM2itS3jCBhwBwXblyJaSgDI3fAl/n0nETRwSpVe3yqI7D6dW+35N0T2p+ZzUuH6M1cFR6EOicaclVLh8cqAMAAsJiO7TueQlJp/1VV/V9WvXqVS8eOPP3LLLbcwZswY1qxZ41LQVl+r5CU8IwlKCQmJesG3S1fy1JRxqMJbEdB3MjK1D5a8NKyFWY4xxgObHIUtCr1zgYqILaesS5PAai9bLktIQSmXYbZYyFn3Bfouw1CHNa/0OGVAOJqmHZHrAig68A/aVj0p2LYEhW8g/nGjqzSHYxmuTigSnrH/zCzl2+iIItaiPFQh0S7HWIsLQBCwFGSSv/VHAHyadUEhl7E0IeWqF0reRBI1Gg3Lly/nhhtu4IYbbmD9+vX06tXL63STRdvPXJVV8hKekQSlhITEVU9BQQH33j0dbauehNzynIsftp3KClusosis5fuqvWy561QOFkHEsPdPLAWZhN/6ZqXHGA9uImfNPCLvnkfmstdRBoQTOm422X9+St7Ghfh2GIRC6+/1HMxWUVperAL2n1l5jAc2Yi3MJrD/7S77zs6bBlYzAHKtP0FD70PboluDixBrtVpWrlzJ8OHDGT58OK9/u4ZPduZ4nW6SkJxbo+kmElcWSVBKSEhc9bz32deUFOTQeOJUZDI5QqkJmUrtIiwrK2yxCuIlLVsezzRgLS4gb/MPBPad5NEDuSyFe1ajDm9JwfZlmLOSCZvwMjK5Al3rXhj3r6c0/SRaN7aNnlApZJKYrALHMw0u28zZKeSs+xxNVHt8Ow1x2R8+8VVESynm7BSMBzYimk2OfQ0tQqzX61m9ejXD7n2B97dlYm/Ibzqzj/Qfn3d7TMSU99FEtccqiFgRayTdROLKIwlKCQmJq57lK/9ErtFhMWST8csbWHJSkal88I0dTPCQe5Ap1V6fq7rLloIgYraK5MV/h1yrx6+Hd0vV1qI8REspJamHCBhwB9pWPQEQBeuFE1urNI82YX5VGt+Qsf/MymI15JKx9FXkGl9Cbn4OmVzhcpxPs84AaFv1QNumD+e/fgiZ2gf/uNENMkKcY1aS2+YGcNMs3S9uNOrItk7blEGRTv+viXQTiSuPJCglJCSues6eOYkoWMlc/jr6zsPwGTQNU/J+ChN+RzAZCR0zy+tzVXfZUi6XIeafw5D4F0FD7sFamOPYJ1rNiIIVS146Mo0Ohfai6JMp1VhyUtHFDCSw32THduPBTSCTo7rQssYbFHIZPZsHVXnuDRW5XIZKIXOISsFkJH3JywgmI+F3zKk0og2gCopEHd4S44GN+MeNbpAR4rKdDcqjadoR3/b9Kz3HpaabSFx5JEEpISFx1VNcZEQ0l6DvNpLg6+8DQNeuL6LVjCFxDeYBtzs1qK6M6i5bhsuLSBYFctcvIHf9Apf9qV/chV+Pmwgeei8ARUd3YM44DYDpzH/kbf0RhdafouO7MJ1MQN9lmEPUlGacoujYTgDMuecRS4zkbf0JAHVYC3RtemMVRCbENa3W3BsqrUP1HEorRLSUkrHsNSy5qYRPfgO1m2IcTwjmUkdOZUOLEJftbOAJoaQImUrjNtpr51LTTSSuPJKglJCQuKoRBNGxpO0bM8hpn2+HazEkrqEk9XCVBGV1li2Li4tpHhnC6VueB5nzcXnx3yGUFhM89F6UgbblPlNyElkr30UT3YnAAbeTv30Jhj2rsRYXogwMJ3DgVPz7jHOcozTtBPmbv3c6r/3/vrFD8GvXh7joIOlmXEV6tQjmSFo+ab/NoeTcYcLGzUYTFeMyThSsCKXFKHz0TttLzh3BnHnaVjzVACPEnqrk7WSv/hixtBhkcjRNOxI0eAaayDZux9aXKvmGiiQoJSQkrmrkchlKv0aYs5JR+AY67VP42m5Mgsm18KIivF22zMzMZNWqVaxYsYK1a9di9W9M5PSPXcYV7F4BgK6tbTnPkp9BxvLXARm+7fthyc/At8O10OFaANRhzVGHtXA6h77zUPSdPTeQVshkvDuus3dvUMLBhLimfPT6CxQf34m2dS+sxQYMSf84jdHHDkYsLSZ1/p3oYgagDolGpvLBnHkaw/71yDW+BPSb3CAjxJ6q5FGo0LXri7ZlD+S6AMxZyRTs+pX0H54h4o73UEe0cjmkoVXJ1zckQSkhIXHVYo8iRrTswKlTe7EUZqNq1MSx33Ihj9GbauuyVLRsefToUVasWMGKFSvYtm0bANdccw2vvPIKN910Ey9tyiUhObdCf2RLXhpiiRGAnLWfu+wP6Heri6CsCBnw3nipn191iI0KwCc/hUKg+Pguio/vchmjjx2MTKVB32UYpjP7KDqyFdFcikIfjG/MIAL6TkITHNEgI8TuquQBfJrE4NOkTKS3TW907ftx/uuHyd20iPBJr7k9rqFVydcnJEEpISFx1eDJfUPVti9s+AHDvrVom3dxjDfsWwtyBZroTl6/RvllS6vVys6dOx0i8siRI2i1Wq6//nq++uorbrjhBsLDwx3j3w0xMmxuPFYuCsqI299xeg2fZp1p9uyq6nwELnNVyGRSH79LZNe2zQybG0+pmyplOzKFypH76o6GGCF2VyVfEaqgxmjb9Kbo6DZEweo2p7IhVsnXFyRBKSEhUeepzH2DgGb4dr4e4751ZAoCPtGxmJL3U3R4C/7XTKhyYcvojqGsWLGClStX8vvvv5OZmUloaCijR49mzpw5XH/99eh0OrdzbR7iy3vjO/PYz4l4f6t1plWoLycyjS7v1Y59e49mQcwZK0UmL5VL/Zk11Ahx+Sp5b1D6h4DVgmguQaZx/Q41xCr5+oIkKCUkJOo0KxJTeXrZvkrdNxoNfwilfyiGfespOrodZUAoQUPuwb/nGMeYygpb9G16oTWeZ0Bsc0wmE+3bt2fGjBncdNNN9O7dG4XCc5VqWezRQvu8K1r+tlM+2miPxu4+ncuxjEJHNLZNmB89mwdJXsg1THV+ZghW5DL4aHJcg40Q26vkvcWSl4ZMqUam9nG7v6FVydcnJEF5lSMtDUjUZz5fsZmnnnuBkrMHEYoNKPxD8e0wCP/etyBXXbwhmc4eIm/jN5SmnUCm0eLXbSSBg6YiV2udzldRYYsoClgtZvwOreT111/npptuom3btm7HesOYrlF0aRLoMbLqeF2rBZlC6RJtjI0KcBKM0ne99vH2Z2bf3lRrZsfHD6Me9DU0UEHZq0UwRzMMLp+TtSjfJXe5NP0kRcd2oW0Z59YetSFWydcnZKLooRupRJ3EUw5Z61A9vVoES1ELiXrD1v+OMLBPD2RqHX7dRiLX+lGSehjj/vVoW/cmbPyLgO0mlfbdU6gaNUXfdTiWwmwKdv6CT7POhE981bsXE0WQwRujWnPHgPY1/l4qijae3LmWlrIMVn/v2rdS4srhTYS4Y2N/Ro0aRWJiIklJSTRqVHkj9PpGUmo+N87b4rI9bfHzyFVqNFExF6q8UzD8twbkSiKnvI8qxH01/KqZ/aV72FWKJCivEirKIbNj396reTDvjmt4+TwS9YtON99P0ooFRN41H3VoM8f2rFUfYkz6myaP/YTCR0/6kpcxZ5yi8T1fIL+Qk1X431/k/PkpYZNeQ9uie4Wvo5CDQia/rIUtZaONc+bM4dVXXyUjIwO9Xl/JkRJXCk8R4nPnztGpUyeGDBnCzz//jEzW8KLIExdsd+lsUPDvSowHNmLJPY9QWoRCF4BPsy4E9L8VVVBjl3Mo5DLiooMkp5yrGNeYs0SdY0ViKsPmxpOQbOvP5Sm3x749ITmXYXPjWZGYetnmKCFRk+xPzSc5PRvAtbekPhhkcmRyJUJJEabTifh2vNYhJgH0sdchU2spOuQaOXGc54I46NEsmLWPDbysOXBlhcnEiRMpLi7mjz/+uGyvL1F1PKUbNG7cmM8//5ylS5eyePHiyzyrusG74zqjKCek/XvcROS0D2n62I80m7WCJjO/JWT0k27FJDTMKvn6hiQo6zgfLP6TyWNv4vh74zj1/njSf3qR0vSTbseazh4i7ftZnHp3LCfm3saUux/gp21HL/OMJSQunWUJKfg2s7X6yV79CaXpJ7EUZGI8FE/h3tX4xY1GrvahNPM0CFbUEc7OGzKFCnVYC0rTTyAD/DVyVArbDU+lkNEh0p87ekezamZ/fr73misazW/RogU9e/bk559/vmJzkLg0Jk6cyG233cZDDz1ESkrKlZ7OZcdeJV/d2GxDrZKvb0hFOTVITSfN/75hK09PuxmFXwiB/W5FRKRwz2rSFj9L5NQPnRo4l6afJOOnF1A1akrQkLsceWR3TTlHn52bpC+qxFXFrlM5qFvEETDgDgq2L+X88Z2Off59JxE0cAoAVsOFxuV610R+hT6YkpQDiECTYD2rHxlQZwtbJk2axAsvvEBhYSF+flKV69XIvHnz2LRpE9OnT2ft2rXI5Q0rXlMTnQ0krm4kQXkJ1HaBzL2PPY1MqSZi6vsotP4A+HYczLn/3Ufepm8JHfu8Y2zupkXIffSE3/a2Y+lPGRBGzp+fMvX1L4n/+LFLeq8S9YO6KqjKY3ffUAaEo2naEV27vii0/hSd2E3BtiUofAPxjxuNaCkFbBHJ8sgUKoQL++3uG3X1vY8fP56nnnqKlStXcvvtt1/p6UhUg6CgIBYuXMj111/PvHnzeOSRR9yOu1q+g9XB2yp5OSICMqmPaj1DEpTVoLImy4fSCjmaYWDR9jPVLpDZn5pP+tFEtC3jHGISQKkPxqdpLEUndiGUFiNXax15ZP49x7jkkeVu+Iq9G/8kKXV6jVXO1ecLYn3jauwKUFxswmwVMR7cRM6aeTS+d4GtGTKga9cXRJG8jQvx7TAImVINgGg1u5xHtJqRX9hf1903mjVrRp8+fViyZIkkKK9ihg4dysMPP8wzzzzD9ddfT0xMzFX5HbwUmof4suS+azxWyauKsrGmHWH5e0/Xq/ctIQnKKuNtk+XyBTJVDekvS0hBtJodN8yyyFQasFowZ55BE9W+8jyyjBMsTUip9pe3oV0Q6wOX46GnJjCZTOzbt4+EhATHn6SkJBo/vpTCPatRh7d0iEk7uta9MO5fT2n6SVuBDmA15Lqc22rIcey/Gtw3Jk2axDPPPENeXh6BgYFXejoS1eSdd95h7dq13PvEC0Te/HSd/w7WFp76qC5btowJE95E8+o0QLpv1CcaVpLHJZCQkED3ftdyS+82HH9vHOcWz/ZYHGNHMBk4Pfc2jr05intenVelqutdp3JQBTeh5NwRRMHq2C5azZScOwKApdBWBVtZHpm1MIfdp11vuJVxOsvIxAXbuXHeFr7fmcyhtEKHxZb9gvj9zmRunLeFiQu2czrLWOXXkKh56mpXgOLiYnbs2MH8+fOZMWMGXbp0Qa/X07t3bx555BESEhKIi4vjk08+oUUjHdaiPETR1VvZ8X0QrKhDmoFcQWnaMecxVjOlGadQhbcErg73jfHjx1NaWsrKlSuv9FQkLgGdTsejH37Hua4z6tx38Epif6AbNWoUOp2OpUuXXuEZSdQ0UoTSC/bs2UO//v0RdMGVFseUJW/zD4jmEgBEbMnKXZoEevUUejzTgF/3UeT89RnZqz/Bv884EAXyt/3siMbY88e8ySOz55B5y+WKxErUHHfeeSeLFi3yuD/qoYUo/UIQrRbyty/BuH8DFkM2Sn0jfDtfz6Nm27JxTfz8ioqKSExMJCEhgT179pCQkMDBgwexWq2oVCo6depE7969efDBB4mLiyM2NhYfn4vON2krk9gdHEXRqT2Yc1JRBV+ck/HgJpDJUYU2R+7ji0/zrhgPbCSg72RHyoch6R/E0mJ82/e/atw3mjRpQv/+/fn555+ZOnXqlZ6ORBXZvXs3ixYtYuWf6zibcga51h9N43YEDpzi+P0VRQHj/r8pOrqN0vSTCKZClAHh6GIGEtB7LI/9nAjUzHewrqLT6bjxxhtZunQpzz//fOUHSFw1SILSC1588UUEuYrGUz8AH1ukw1NxjJ3SzNMU7l1NQL/J5G/+AQCrKDJr+b5KG7dmZGZitor4dRuFpSCLgp2/YEzaAIA6og3+fcZRsO1n5Be8UL3JI/M2h8xbUZL2w7OUpCS57J+8uDs//bKyXl8Q6yqjJ01lTW4oFifxL5Lz13yUAeEo/WxLx1m/f0DR4S3oO1+POrI1JalHyN/8PdaCTJ5WPer1Q48dg8FAYmKiQzgmJCRw6NAhBEFArVbTuXNnrrnmGmbOnOkQjxqNpsJzTohryoJeYyk68S9p3z+DX9wNtqKc47swnUxA32UYSj+bK0ngwCmkffc06YufczjlFO76FZ8W3dC2jMMqiEyIc+/KUdeYOHEiTzzxBLm5uQQF1X0RLHGROXPmEL95C6XRvQlqNxyrIZfCPas4/82jREx9H3Voc0RzCdmr56Ju3M7m/qQLoCT1MPlbFmM68x/ht75VpcDD1cqECROYMGECx48fp3Xr1ld6OhI1hCQovWBT/GZU0V0cYhLcF8eUJXf9/9C1vQafJh3Jv7DNKojsOp1DUmo+HRv7c/bsWQ4dOuT4c/DgQQ4dOkRWVhbRT/+KTKEiaNBU/HuPxZx5BrnGF3VYc3I32QSf8sJTrzd5ZHJEUlKSadasmcuYsngrSgBbO6NB05yOV+iDG8QFsS7yc7IW39jBTtFkU8oBRHMJvh2uBaDk/FGKDm8moO9kAgfeAYBft1EodP4U7PqNop6jmbU80ONDj8FgYO/evU45j4cPH0YURTQaDZ07d2bAgAE89thjxMXF0bFjR9Rq1zzgyoiNCmDgwIFsVb9PTvwPGPasxlpciDIwnMCBU20R+wtoIloTPvkN8jYuJHfDV8jUWvSdrydw0DSH+8bVkuM7fvx4Hn30UX777TemT58OSEVwVwtPPPEEDH6Evecu+lr7xgzg3NczKdixjJDRTyFTKAm/4z18msQ4jvPrOgJlQDj5W37AdOY/lC27eRV4uBSu9O9U2WXv55577orNQ6JmkQSlF5hMJrQq14hK+eIYO8bDWyhJPUzjuz/Hkp/ufIwoMP6ZD0hd8REGg601ikajoV27dsTExDB06FBiYmL47JQvp3JtS9kKHz2Kph0vzud0Igq/EMdSe9k8Mt+YAY5x9jwyXfv+mNJP0rz5aKKjoxk4cCCDBg1i4MCBtGnTxskqzBtRYkeu0aGPHezyuXgbiZWoOfan5rPrdI7LduPBTYAM3w6DAChJOQCArsNAp3G6mIEU7PqVwgPx7AppTlJqPtF+MifxuGfPHo4cOYIoivj4+NClSxeuvfZannzySYd4VKlc0y6qy7vjOjMsJQ+VF37cPk07EjHlPZftV5v7RmRkJL1HjufjredZUhAvFcFdRfg168i/vzs7M6mCo1CHRGPOsjU7lylUTmLSjq7tNeRv+QFzVgrW5l0dgYea+jnXtcLKssvekqCsP0iC0gu0oU0xpR5GFKzI5ArAtTjGLjcFcwm5f3+NX88xKAPDXQSlKJOjjGjHSy+9RExMDDExMTRv3hyFQuE0LmllEsk7k11yF42H4ik9f4ygwTOQyWw1VZXlkfnF9GfKiL70HfMbmzZtIj4+nsWLFyMIAuHh4Q6B2Ti2j1eixOn9CFZES6lThLZsJFa68V0eliWkoJTLnCLLotVC0eEtaJrEoAwMv7DNlhZRvnuA7MIDU2nacRAFbnr8bU4tnQOAj48PXbt2ZciQIcyaNYu4uDhiYmJqVDy6w+6+8djPiVTeItmVq819w16Zf77zNGSiQF7axbznhlAVfLXj9jsoiliL8lCFRFd4rNVoW11S6Gwt4hRy2SV15rBTl7s9uFv2vtKRU4lLQxKUXqDtMhLDmvmVFscAFOxYBoKVgGsmejxfiU8QTz9dca+5CXFNWfDzH+Rv/RGfFt2Qa/0pPXcYw771+LSMw6/nGKfxFeWRaVrEMaVfG2KjejBmjO24goICtm7dSnx8PPHx8Tz++OPor51BQNyNiGUMtNyJEjvmnHMkfzAOrBbkvoH4dRlOQL9bkSmUNXZBlPCOXadyyqUpQPGpPQjFBU6RZVWwLapdcvYQqsAIx3Z75NJqyAaZHH3zLnzzzTcO8ahUXplLRUNx3yhfBCfK3DfgkIrg6i7uvoPGAxuxFmYT2L/i633BzuXINDq0LeMA28+5Op05ylLXCytHjRpFcOuuzP5tH/mqc3UicipxaUiCshIEQUTXdST++ZmVFsdY8tIp2PkLwcPud8mpLIs3BTKxUQF0j2nJxu0KCnb+glBafCF/bAr+vW52RErteMojazT4Tno2D3b5Uvr7+zNy5EhGjhwJ2Kpyh8/dREqhc5sWd6IEQBkUiU+zzqhDmyOYTRQd3kr+tp8x55wj9OZnauSCWJeo60/OdmeZshgPbgK5El1Mf8c2baseKPzDyP3na+QqDeqI1pScO0Je/HcgVyCabQ9HxeoA7rxz1GWbf0V4675hX0G42tw3ViSmOkVh87f9TF78d6hComl892eOccWn9mA8tJnSc0cwZ59F4RfCY9b/A+p3VfDVQvnvoDk7hZx1n6OJao9vpyEej8vftgTT6USChz2I3Efv2F7Vzhx2DAYDdz/5IivWxVN6/iiCyUCjUY+h7zzUaVzWqo8c97OyjP+8Ccs27KjV3yl75NRv/BvszpVhFaRofH1AEpSVIJfLUClkXhXH5G3+HoVfMJroTljybEvd9qUMoagAS146ioBQ1EqFV+Lks/tHMcykp9Tq2ovPHe7yyFQKuVc5ZDqdjrQi15u0O1ECEDLqUaf/62OvI/vPTzH89xclqWPQRLWv9gWxLlDXco4qQhBER39Qx7bSYoqP7UDbopuT05JMqSZswstkrZhD5q9v2TYqVAQNnk7+tiXILjwc1TVnmcrcN0LVVg5vWc23rzzAjX27XOnpes2pLCNPL9vnEJOWgizyty9BpvJxGWs8sImiw5tRh7dyFOJVtR2ZRO1Q/jtoNeSSsfRV5BpfQm5+ziUAYMd4KJ68+O/Qdx6GX3fnB7jqfgf3Hk3m5//NReEfiiqsBSXJ+z0PVqhoNNLZIlKu0dXq71Rdj5xKVB9JUHpB61A9h9IKKy2OsRRkYsk9z7kv7nY5R85aW6Sh6WM/0aZxY69e93LmkFVFlHjCv9ctGP77i+LTiWii2tc5UeINdTnnqCyCIHDkyBF2797Nrl27UPiNwFomVaHo6A5bIVXHa12OVYc2I/Ku+ZizkhFMBlQh0ciUanI3fIVPdCxQ951lRNH5d9VgMBARHkHzZs1r/LVq83f4meUXb6wAuf98jaZxO0RBQCgucBobOGgqjUY+jEyhJGPpq5RmngGkIri6gD3wYLaKCCYj6UteRjAZCb9jjqO9VXmKT+0la9WHaFv1IHjEQy77ZaKVTz75mLi4OLp27Yqfn3fN+eduyyT6ke+Q6YIoOX+MtEWPexwrkysua2Fl+Wh8edxF562CiBWxQfTovNqRBOUFKrpp9GoRzNEMg5O4cFccEzhwistNoDTzDPmbv8e/9zg0Ue1RarRVarJ8uXLIyl4Q7VQkSty+7gWLPMFki0zWtiip6Rt9XX1yFkWRlJQUh3jcvXs3//77L4WFts+5bdu2NJo0hAzzxUIb48GNyNRatG16uz2nTCZDHXqxhVTxid0gCvg07wrUPWeZyoS+WeGPomlPbpy35ZKF/uWKTpevzDclJ1F0eCuR0z8hZ90XLuM9CROpCK5u0DpUz8Gz2WQsew1Lbirhk99A7aEYp+TcETJ/eRNNRBtCbn7WbQRTYcjg2WefpaSkBJlMRps2bejevTvdu3cnLi6Obt26ufQq3Z+aT0KqAZnO+3uMKFgRzSWOYk6ond+p8tH48lQUnQcpGn810GAFZVVuGi3MyZz74flKi2N8ykQv7cg1vuQD6sg26NpegwBVbrLsbQ6ZfXt1c8jskVg7lYmS8ljy0mzz0F343II955FWh9q60SckJHDPI0+S+O8uADSN2xM0eDrqC7Z9dtzlsDV58P9q/Mk5Ozub3bt3OwnI9HRbCkVUVBQ9e/bkueeeo2fPnvTo0YPAwEBeXpnE9xe6AliL8jGdTsQ3ZiByDxfnsgjmEvLiv0ehD8Y3ZmCdc5bxWuhf2FxdoX+5o9Nlq4JFwUrOui/QdxmGOqx5lc8lFcFdeXpEBxA/fxYl5w4TNm42mijX9kAA5qwUMpa+ijIgjNAJLyN305JOIZdx+7A+zP6okMOHDztMA/bs2cPvv/+O0WizuW3RooVDZHbv3p1NhjCXSvOKEM0lpHw00SYoffToOgwi6No7kau1Nf47VT4aX56KovN2pGh83abBCcrq3DQGdG2HViUj34vimIq4lCbLleWQtQnzo2fzoEuKnpSNxFYkSoSSImQKFTLlxbYxoiiSv+1nAHxadAfByp6/ljJm01ymTp3KjTfeWKk7iidq80ZfFVtNdzlscGlPzkajkT179jiJx5MnTwEigYGB9OzZk7vvvpuePXvSs2dPGntIlxjfvQmLttuWQI2H4kGweowsZ/72Dgp9MKqQaISSIoz71mHOSyNswsvINbo65Szz4Y9rmP3Sy5ScPYhoMaMMDEffdQT+PW5yjDGdPUTexm8oTTuBTKPFt/0AAgdNrZLQvxLR6bJVwYa9f2IpyCT81jerda76VgR3NXL6jy8oOrYTbeteWIsNGJL+cdqvjx2MUFJE+pKXEEwG/HuPpfj4bqcxqqAINFExju+g3aa0U6dOTJtmM5GwWq0cO3bMSWTOmTOHgoIC2j76DRZtqFfzVeiD8O8zDnV4KxAFik/uwbDnD8wZpwi/7W2sKGrsd8pTn1w7lUXn7UjR+LpNgxKU1b1p9OYohVnpNHvkewQP7Tw84dOsM82eXQXUTJPl2KgApy9STS77Tohr6pUoKU07TtbK99B1GIgqqDGiuYSiYzsoOXsQfdcRaCJsPcUeHNGNNT/+y/jx4wkODmby5MlMmzaNnj17OjVTr4javtFXxVbTUw4bePfkbDab2b9/v5N4PHDgAMrQFgR0G45/62EIE26nmUyOUm5bdvYm8pqWlsZLDz+ASdcH32axGA9sRK4LdCxfl0cd0RrD/vUYEtcgU6rRNOlIyE1Pow5vWaecZb5dupKnpoxDFd6KgL6Tkal9sOSlYS3McowpTT9Jxk8voGrUlKAhd2EpzKZg5y+Yc88RPvHVSoX+xo0bGTzYNYcMIGLK+w7DgvxtSyg6vhNL7nnbQ6V/CNpWPXm4cBJMH1QtUWmvCrYWF5C3+QcC+05yRPerw9VcBFcfSDl+CIDi47soPr7LZb8+djBCcSHWgkwA8jYudBnjGzsEXdMOFX4HFQoF7du3p3379tx2222ALaf61KlTDP+/I+BldDLo2judX7vDIFTBUeTFf0vR4S34dhhUY79T7np02qlqdF6KxtddGoSg9HZJ05M/dUqL7kx5/EXG3NS9zjVZrskcwtioAHo1DyYhObdCUaIICEPTtCNFR3cgGHNBJkPVqCnBwx9C33WEQ5S8dt8NvPb4PRw8eJBvv/2W7777js8++4z27dszdepU7rjjDpo2dR8J89ZTHGzNugt2/ooh6W8s+enINb7c+lNrPp3/GXcN71nhe66KraanHDZwfXIWBIFjx445LV0nJiZiMplQKBTExsbS6ZrrCBj3CikmDYpyF1uLQKWRV1EU+emnn5g5cyZKpZLXPprCBwflRE79oML3HNBnPAF9xrvdV1ecZQoKCrj37uloW/Uk5JbnHHnK5cndtAi5j57w29525IApA8LI+fNTik/tQdEqrkKhfz6/GAC/uNGoI9s67VMGRTr+XZp2HHVYC3xjBiJTa7Fkp1D4318Un9jNk5r5dGkyrErf7bJFcHnx3yHX6vHrMdrr491xNRbB1Sc2btzI6Swjw+bGe+zMoQwMdwQYPFGd76BcLqdFi5ZYhMNVOq48fj3HkLf5e0yn/8O3wyDMVpHOXbriq9Oi1WrR6XQe/65o344TJo/L8FWNzkvR+LpLvReUVVnSBM/+1FtKm/NSk0DmTupar5ssvzuuM8PmxlcoSlSBEYTe/KzH/eUviB06dOCdd97hzTff5O+//2bRokW8/vrrvPDCC1x33XVMmzaNsWPH4ut78Ybsrae4aLWQsfRVSlIPoe8y3NYX02Sg5PxRXvslgSFxHSq80VfVVrMi5Ig8MW8Jwu6f+ffff8nPt7m4t27dmp49ezJp0iR69uxJt27dWHc01/Z7VCoCnn+XPEVe09PTeeCBB/j111+ZNGkS8+bNIyQkhIhKqigroi45y7z32deUFOTQeOJUZDI5QqkJmUrtJCyFkiJMpxPx7znGqaBAH3sduRu+oujQFrQtule4RLZg00kANE074tu+v8t+O2Uj1XbUjduT9dvbFB7dwazlEV7ldeXl5XHgwAGSkpKQ05iSnPMYEv8iaMg9WAsvLgmKVjOiYMWSl45Mo0OhrbxIqq5X5jcErqS7k7vCyiqfQ6VBrvXDeqGwUiYKDBo4gKKiIoqLiykqKqKgoIC0tDTH/8v+bTQaEQRXMd38mZXg5qGwutF5KRpfN6n3grIqS5rgnT/15SiQuVLU5gVRoVBw/fXXc/3111NQUMCyZctYtGgRU6dO5YEHHmD8+PFMmzaNQYMGee0pXrD7N0zJSUTcMQdN43bOryeXVboMXRVbzcoQkHE420I3X1+eeuopevXqRY8ePQgOvphv6W3kVRQFDIlrKNz7J5bc88hUPqgjWnH/mclsu6YZX714PwqFgmXLljFu3DjH8fXFWWb5yj+Ra3RYDNlk/PIGlpxUZCoffGMHEzzkHmRKNaWZp0Gwoo5o43SsTKFCHdaC0vQTgOclsv2p+RxOu5j8L5QUIVNpvM6LtjtHWUwGF9FaVFTEoUOHSEpKcvpz9uxZ25wUCqLv/RxrYTaIArnrF5C7foHLa6R+cRd+PW4ieOi9lc6nrlXmN1Su5HewfGFlVRFKihCKChziLqZxIJ8+8qnXx4uiiNlsdhKZBqORmxYnux1f3ei8FI2vm9R7QVmVJU073vhT13aBzJXkclwQ/f39mTFjBjNmzODUqVN89913fPvttyxatIhWPQdjGfKkyzHlPcVFUaDw35Xo2l5zoTrQimg1O4qIvEngroqtpjdowpqx4n8rPO73NvKa+/f/Ubj7N3w7Dsav+w0IJgOGxDWkLX6WReJb9B9xC1/NfZvQUNcE/MvVFaA2OXvmJKJgJXP56+g7D8Nn0DRMyfspTPgdwWQkdMwsrAZbRE+hd61IV+iDL9pJelgiW5aQguLCDSl79ceIpcUgk6Np2pGgwTPQRDoLVVEUbdWngoA5N5W8jYtAJscnuhMKGTw5fxm6Q6tISkrixIkTjl6ZLVq0IDY2lilTphAbG0tsbCzt2rXjrb+Oseif/YSOfcFlbnnx3yGUFhM89F6UgZEu+13ebx2rzG/oXKnvoLsWd+4QLaWIVotTZB8gf9tPgIi2Rfdq/U7JZDLUajVqtZqAgIvXXJUixSVyas5JrXZ0XorG103qvaCs6pJmVfypa7NA5kpzOS+ILVq04KWXXuLFF19k27ZtvLPuJAfNzq/nzlPcnJWM1ZCDOqy5zaUnaQNYLahCmxM89F58mnWuMIG7Kraa3lLZk7M3kVdRsGLY+ye6dv0IGX1RWOva9+fcF3dTfGQLmrufcysm7VyOrgC1SXGREdFcgr7bSIKvvw8AXbu+iFYzhsQ1mAfc7hD7MoXK5XiZQoVQ5mHg8Pl8fvzxR3x9ffH19UWv17P1mAGrTImuXV+0LXsg1wVgzkqmYNevpP/wDBF3vIc6opXjHIIxj7Pzpjj+r/ALIeSmp1E1aopVhEPZpbQ3Ghk9erRDOHbo0AG9Xo877EVwurauEfSC3baHkrL7SjNOUXRsJwDm3POIJUbytv4EgDqsBRMe7OfdhytxWXD3HTyYmgtyRa19B+2/UwUXHrzsD13Fx3dhuVDM5h83GsFk4Pw3j6DrMMiR9mU6tYfiE//i0zIObds+NdrtwV3k9FKi81I0vm5S7wVlVZY0L9Wfur6ISTuXW5TIZDL69euH5V8r1nIXH3ee4pacc4Dt5iv30dNo+EwA8rcvIX3JS0RO+wh1WAuPP7Oq2Gp6S0VPzp5aZ7hEXq0WREsJCt9Ap3EKXaAtD0mp8bp1xtX40CMIIjKlrUm7b8wgp32+Ha7FkLiGktTDtodCbN/n8ohWM3LlxUbvAjJuu+12KJPIEf30b/g0icGnSZl+gW16o2vfj/NfP0zupkWET3rNsUuu1RM2+Q1ESyml6ScoOrLdFtW8gCasGWv/t9br91m2CM6bVYDStBPkb/7eaZv9/836jKqTDwYSzt/BoUOH0igkhJ9/+qnWXqtX82B+/fxXLPkZju1FR7fB0W0A6DsORu7ji7Z1L0yn92JM2oAoCKiCIgkcNBX/XmNRKhQ12u3BXeRUFdqsWtF5KRpfd6n/grIKS5r13Z+6ulxuUWJvp1IWd57igtlk+7u0iMjpH6P0t0XsfJp1JnXBvRTsXE7I6Kcq/Jl5a6vpLRU9ObtrneEu8ipXaVA3bodh/wbUUe3xadIRocRI/tafkPvoHZX01WmdUdfFJNjmqPRrhDkr2VVU+9rer2AyoL5QhW3/LpfFashx6hWqUsgwGAoxGAwYjUYKDQbG/Jji9vVVQY3RtulN0dFtTg+iMoUK7YWuB7rWvfBp1pX0759G7huIrnWvauV12YvgrOUyliNuf8dlrL7zUPSdh7psVyvkrH1soNevKXHlUCgUCFZrrb7Gu+M6k5iy0GOluZ2yqx/lqeluD2Vb0jleQxfgdXS+LHWpT66EM1VrqniV4VjSvGYixoObOP/Vg5z/eiaW3DSbuIRKlzT9e90CQPHpRODikmZDprbtFL31FLdHsTRRHRxiEmxtYzRNOlBy1tYXrqKfWa8WwY48Ojt2W03/Hjd5bFfjjsqenMs2srbjLvIKtou9KjiK7N8/IPXzGZz/v4cpTT9BxB3vogqMqPetMyJadgBsKwhlsVzItVLoAlCHNAO5gtK0Y05jRKuZ0oxTqMq0BWsT5oevry/h4eG0bNmSLp07o1J4/j1W+oeA1YJoLvE4xqdJDAp9MMYDG4Hq5XXZi+Cq+42qS5X5EpWjUCiw1rKgrIu/U/bIaflrbZURBUzJSTx73+0cO3as8vESl5V6HaGsiSXNy+1P3dCpiqe4Qm/rC1k+imXbFoD5QpWvu59ZXl4e8+bNY8GiJeSb5ZXaakLlOWy6Nr0rfHL2NvIKIFdrUYVEo4lqj0+zLliNeeTvWErGL28QcfscFLqAeh0tH3rjGL7c8AOGfWvRNu/i2G7YtxbkCjTRnZD7+OLTvCvGAxsJ6DvZUWBgSPoHsbTY0QbIk9CvqCLWkpeGTKlGVskDp2gpRSix2eBVN6+rOkVwiAJyRD6aHFdnKvMlKkcul7ttq1PT1MVuD56i8eVxF523o1Yqef7Gtrz9/Bd07NiRJ554ghdeeAE/v+rnVF4NaUBXC/VaUMKlL2mW96eWkoFrH289xdWhzUCutCV3l8NamIPczc8sPT2duXPnMn/+fEpLS5kwYQJrE46Q5YWtZkU5bPpOQ7j2+pEel6CrEnkVBSvpP83Gp2kngofd79ju07wL5756iIKdvxA0eHq9bp3xyIRhLP7meoz71pEpCPhEx2JK3k/R4S34XzPB0WQ+cOAU0r57mvTFz6HvOhxLYTaFu37Fp0U3tC3jAM9LZL1aBHPoVCqU+ezB5r5TdGwX2pZxjh6YyHCxIDUe3opgMqCJaHPJeV1VLYJrprOw7aOHUPT/H0iC8qrhckQo7dS1bg811ZJuTNcoptw8gvfff5+3336bb7/9lnfffZfbb7/dKwc2e03ArlM5HM80OGoCWofqvXImk/BMvReU7pKB7UuaQYNnOJY0vfGnlpKBLw/eeorLNTq0rXpQfHwX5uwUVI1sosGclWJrdN5tpONnlpyczHvvvcdXX32FUqnkwQcf5PHHHyciIqJSdws7nnLYwJbHVlHOUVUir6bkJMyZZwi67m6n7argKFSNmlCSalvKr8/R8tioAEbc9yJ//xRGwX/rKDq6HWVAKEFD7sG/TORYE9Ga8MlvkLdxIbkbvkKm1qLvfL3DnKAiK8kJcU2Z8/DtyFVqNFExF6q8UzD8twaZSuOwprPkniP9p9noYgagCm6CTCajJO04xgP/oAgIx6/nTTWS11WVIriOjf25cedX3HPPPSQlJdGokWcXJ4m6g0KhwGx2LSKrLepat4eaipxqtVpefPFFpk2bxtNPP82UKVP4/PPP+eSTT4iLi3N7ntNZRo/i2mwVK3Umk6icei8oW5iTOffD85UuaXrjTy0lA18evPUUB5u/tunMf6T/+AJ+cbbmuIUJvyPX+hFwzQSsgsiB37+m1bh5+Pv78/zzzzNz5kyCgi4+GFwudwtvI69CUZ7tH6IbgStYEQVbhKO+R8vfn9idYedux7/frRWO82nakYgp77ndV1FxQWxUADF9ruPQltUU7PoNobToQqFAXwL634oqqLHtHH6N0LXri+nMfxj3b0AULCj9w/DrfiMBfSei9g2o0YpYb4vgvvzySzp27MjDDz/M4sWLa+S1JWqXyxmhLEtd6vZQk5HT6Ohofv75Zx544AEeeeQRevbsyV133cWbb75JWFiYY9yKxFSHiAU8CllPzmQS3lHvBeWAru0I8NWQWcmSZmX+1IgCnSP11b5p1NelydrAW09xAHVINOG3vU3exoW2aLJMhk+zLgQNno7CNwhTchIrlsxj6tSpzJ0712OuzeXIOfI28mrP6zUejHcs2wKUpB3HnJOKvuvwBhEtbx7iyxuj2zHr14M21V7FMgNvhP6v899g2NxhFUanFboAGo2Y6Xl/Lfufe7puNG7cmE8//ZQpU6Ywbtw4J8ckibqJXC6/IoLSdR5X9l5U05HTa6+9lj179rBgwQJefPFFli5dyquvvsqDDz7I6gMZTsGC0swz5G9ZTGnacazGPGQqDapGTfHvPRbdhYd7qyBiReSxnxMBJFHpJTLRbudQj/F2SbMiRKuZ3B+e5K3nHufBBx9ELq+4+lfK07g0LvVnJooCMsHKKNlekrb/w+bNm+nbty9vvfUWgwYN8nhcRcsiduzbe7cIrlLOUVJqPjfO2wJAQcLv5K5bQNjEV51Eo530n17EdHov2rbXoG3RDashl8KE3xGtFiLvnIuqURNWzexf73+Hpk+fzorEVBqNegwBz5GFslRV6K+4RP/zuZO6XrEbjiiKjB07li1btnDgwAGnqIxE3eO2227j/Pnz/PPPP1d6KnWSmgi8ZGVlMXv2bP73v/8R02sgpUNnOaUaFZ/YTcG/v6OJao9CH2xbjTyyjZKzBwgeMRO/riOczmdvyyUtf1dOgxCUcOk3jXfGtGfjovf54osvGDhwIF9//TWtW7d2GVsVQSLlaVRMtX9moggy+GhCF27p3hRRFFm3bh3PP/88CQkJDB8+nLfeeovu3bt7PEVt5RxNXLCdhORczi58AkteOk1mLnLrHS2YSyjY9QtFhzZjyUsHhRKfJh0IHDgFbWQr4qKDKvQorw98//33TJkyhYULFzLohvG1JvTBeUmsLlTEVoX09HRiY2MZNGgQS5cu9aowQeLKMGXKFJKTk9m0adOVnkq9Z+/evdz9YxJ5ymCslXylRcHK+YWPIVrMRN37hdM+ex52fb/e1gQNRlBCzdw0/v77b+6++27S0tJ4++23efjhhx3Ryqv5pnS5qOoTaFU/UzkiSoXC7WcqiiLLly9n9uzZHDlyhIkTJ/L666/Ttm3bS563t+9rweJfeCtR7tYu0FsawhPz0aNH6d69O2PHjuXbb791bK/N4oLajE7XNkuXLmXixIksXryYW2+tOOdU4spx9913c/zECTZKEcpaZ39qPqMvrAh5Q8bSVylJO0bTh793u78hrAhdKg1KUELN3DQMBgPPPfcc8+bNo1+/fjzxxBO88cEnJP67CwBN4/YEDZ6OukxjZTui1UzBzl8xJP2NJT8ducYXTWRrPp3/GXcN71lj77Ou5GzWxNK/Nz8zuQwEEa9u9BaLhUWLFvHKK69w/vx5pk+fzssvv0yTJt674lTnfc2dO5cnnniC66bP4kTYgKtyifVyYDKZuOaaaygqKiIhIcGjFzbUzu95XamIrSqTJ09m7dq1HDhwgMhIV8s6iStD2WvFsYxCLAJS+tNl4OWVSfywM9nFTMKOUGpCtJQglBRRfGwnuf/8H7qYAYTe9LTLWIVcxh29o3n1ptjanvZVTYMTlHZq4qYRHx/P7bffztmzqaiCI9F3GYGISOGe1QimQiKnfujU51K0WshY+oqtpU2X4TbPcJOBkvNHCRl4O5venFLtiEddy9msjaX/hFMZvPnj3+xJzkP0j0CmUKGQQbsI/2rd6E0mE59//jlvvfUWhYWFPPTQQzz33HOEhITU6PtqGuTDk08+yccff8ysWbN4++23+X3feSma7YGHH36YL7/8kh07dtC1a9crPZ0683BWGdnZ2XTs2JGePXuycuVKt0vfV8t7qQ9I6U9XlpEfx3s0LgDIXjMPQ+Ia239kcnRtryF45MMofNw/wHaI9Gf1IwNqY6r1hgYrKMtT3QvtiBEj2BC/laj7vgQfWwWxxZDDuf/dh7Z5N0LHPu8Ym79jGXnx3xNxxxw0jds5nae6eRp18aJV00v/BoOBL774gg8++ID09HQmTpzIc889R6dOnWvk5lhYWMiHH37IBx98AMCTTz7JE0884VIRXr33BY1T/mbz9x/x6aef8uCDDzr2X81LrJeKp+/br7/+ytixY5k3bx4PPfTQFZjZ1c2KFSu4+eab+eabb7jzzjvr3INmQ0FKf7rytJm92sVMoizm7BQshdlYC7MpOrwFFEoaDX8Qha/77hkqhYxjb4yqrenWCyRBeYno/fwRm3Qh9OZnnbZnLH2V4tN7afroj8jVWkRRIHX+nWiadCT05mcQBSui1ezSMqYqeRp17aKVkJDAPY88WenSvygKGBLXULj3Tyy555GpfFBHtCKw72S+ePJWx9xycnL49NNP+fjjjzEYDEydOpVZs2Z5lfNYHbKysnj77beZP38+fn5+vPDCC9x///3cf//9LFq0yONxUQ8tBKuV1C/u8jim24Bh7In/y+2+q3WJtSp4I2z8LHl07dqVwYMHs3z5cqm4pJpMnTqV3//ZwXXPfU1CSkGdedBsCOzevZtXPpjPug3/2FKatP5oGrcjcOAUVGVsfkvOHcGwfwOl545QmnkaBCvNnl3VIFJaLgeCINLyhdVVOib9pxcRSgxETP3Q47Xn5JujpAh/BUiC8hJRqtRoYwbS6IbHnbZn/vYORYe3EDHlfTRR7SnNPM35r2cSOHAKlvwMDEkbwGpBFdqc4KH34tOsc5XyND5Y/CezZ892uKa4E2+WvPQKRc7dd9/Nl19+Wc137syePXvo268fgi640qX/nA1fUbj7N3w7DkbTtCOCyYAhcQ2WgkyaTn2fZbPGsPT/PuOLL77AarVyzz338NRTT9G06eVpKp+SksJrr73GN998Q+PGjZk84wG+3ZtTLhdHJOev+SgDwml892cIpSaKjm53OZfpVALGAxuJGPsc2xe84NVNuz4tS1YlChtoziJvzTz2bl7r1Hheomos3naM2b8fRiaX403XLSk6VnOMHH0z6/6JR9e+P6qw5rZ2X3tWIZaaiJj6PurQ5gDkbf6B/O1LUYc1RygtxpKTSrNnVwENo+juclBZhLI8hYlryFkzj8b3fOHWklmKUFZOvW9sXttoQ5tiSj2MKFgd7V9Eq5mSc0cAsBRmowEsOecAKNi9ArmPnkbDbY2S87cvIX3JS0RO+wh1WAt2n86t9DV/37CVp6fdjMIvhMB+tzrEW9riZ53Em1wXQKMbn3Q53i5yuvYZWBMfAQAvvvgiglxF46kfOJb+fTsO5tz/7iNv07eOpX9RsGLY+ye6dv0IGX1xbrr2/Tn3xd3k7f+bm98qxbjyfzzyyCM8+uijl723XtOmTfnyyy956qmneOmll1iV3Qjf2C5OYsiUcsBmm9jhWgDkah/0sYNdzmXcvx6ZRodP617MWr7Pq5SG+iImq+pOUagOQXXzq8SfKWKMJCirxYrEVF74/SgicvK3/Exe/HeoQqJpfPdnTuNMZw+Rt/EbStNOINNo8W0/gEeKpwLXSKLyEiiJGUV0x+kIsou3Vt+YAZz7eiYFO5YRMvopAPy6j8K/z3jkKg05az+nMCfVMd4qil5fKyQ8U96ZrDJEcwkAQonR7f767kxWE0iC8hLRdhmJYc18sld/gn+fcSAK5G/7GavBJgxFSykAgtlk+7u0iMjpH6P0DwXAp1lnUhfcS8HO5YSMfopjGZV/Ae597GlkSjURU99HofUH3Iu3ykTO38VNqakstU3xm1FFd3GISQClPhifprEUndiFUFpsW/q3WhAtJSh8A52OV+gCQSZHptKgbtKR5TsPcE1776uua4N27dox+8P/2VpPlBNDxoObABm+HTw3SbcYcjAl78c39jpEuYpdp3NISs2/6pevK2Pjxo0MHuz6ewc4IvZgK1LL374E4/4NWAzZKPWN8O18PY+aLYDkTlFVTmUZeXrZPkTAUpBF/vYlyMql1ACUpp8k46cXUDVqStCQu7AUZlOw8xfMued4Wvs6XZoEStGxarA/NZ+TCtffWVVwFOqQaMxZKY5tnvL0wPaA1VCuFbVJWWeysliNeS73H9FqwZj0NzKlBlVItMu5GoIzWU0gCcpLQBBEdF1H4p+fScHOXzAmbQBAHdEG/z7jKNj2M3K17YIuU6oB0ER1cIhJAGVAGJomHSg5a1u6NltFjh0/TrPoaNRqtctr7k/NJ/1oItqWcQ4xCe7FmzvKipyEVGONXbRMJhNalcZlu0ylAasFc+YZNFHtkas0qBu3w7B/A+qo9vg06YhQYiR/60/IffTou45AIZex5mjeFReUAMsSUlDKZU7L3aLVQtHhLWiaxKAMDPd4bNHBeBAFhw+5Qi5jaUJKvb9JnM8vBsAvbjTqSOd8V2XQxXY2Wb9/QNHhLeg7X486sjUlqUfI3/w91oJMnlY9KgmbKvLM8ovR4Nx/vkbTuB2iICAUFziNy920CLmPnvDb3kau0QG261DOn59SeCKBWcsDpehYNXB3rQBb/1trUZ5boeKJhnKtqE0mxDVl0fYzLtuz18xDLC1C0zQWhV8jrIZcjAc3Ysk+S9B1d7m9d1oFkQlxlyfl6mpGEpSXgFwuQ6WQETRoKv69x2LOPINc44s6rDm5m2xFHHZfZoW+ke3vck9Gtm0BmNNPALbl8rZt2iCTyYiMjKRZs2ZER0c7/k5UtEG0mh0CtSzlxZs7yoqcmrxoebv0DxAy+kmyfptD9u8fOI5XBkYQcce7qAIjsAqiV0v/l4Ndp8rnTkLxqT0IxQWO5W5PGA9uRKEPxqeZzee5Lr2v2mTBppMAaJp2xLd9f7djSs4fpejwZgL6TiZw4B0A+HUbhULnT8Gu3yjqOVoSNlVgf2o+u07nAGBKTqLo8FYip39Czjpn1w+hpAjT6UT8e45xiEkAfex15G74CsPBzexq3k2KjlUDd9cKAOOBjVgLswnsf7vX52oo14raJDYqgF7Ng0lIznWKUvrGDMCwbx2Fe1cjFBciV2tRR7Qm6NrpDi/vstg7sEjfh8qRBOUlYs/TUPjoUTTt6NhuOp2Iwi/Ekc+oDm0GciXWwmyXc1gLc5DrAhzn+3rdOs6cOcOZM2dITk7mzJkz7N69m5SUFEKnfIgquAkl5454Jd7KU1bkWAWRLUfOc/iwElEUsddn2f/tbpu7f6vVaq+X/gHkai2qkGg0Ue3xadYFqzGP/B1LyfjlDSJun4NCF+DV0v/l4HimwWWb8eAmkCvRxbgXSwDmnFRK047j13MMMtlF3/e68r5qi/2p+RxOuxgRE0qKkKk0LvaSJSkHANB1cM7j1cUMpGDXrxQeiGdXSHNJ2HiJPTpmtljIWfcF+i7DUIc1dxlnryhWR7Rx2i5TqFCHtaA0/YQUHasm7q4V5uwUctZ9jiaqPb6dhlTpfPX9WnE5eHdcZ4bNjcdaxkbCt8OgClOVyqOQyXh3XOfamF69QxKUl4i7PA3joXhKzx8jaPAMh5iQa3RoW/Wg+PguzNkpqBrZwufmrBRbo/NuI1HIZfRvF8HQoe6rvK1WK+1e+gu/7qPI+eszr8RbWdyJnOOZRmJiYi7xU5DR7NnfvVr6FwUr6T/NxqdpJ4KH3e84g0/zLpz76iEKdv5C0ODpmK3iFa92FgTRpUpQKC2m+NgOtC26OaUclMd4YCNgy20tS114X7XJsoQUFBfeW/bqjxFLi0EmR9O0I0GDZ6CJtAkZ0WoGcIm0yy6kTZSmHZeETRWwR8cMe//EUpBJ+K1vuh1nNdiimAq9az6YQh9MScoBKTpWDdxdK6yGXDKWvopc40vIzc+5PFRVRn2/VlwOmof48t74zjz2c2K1ncneG+/cUkv6mXhGEpSXSAtzMud+eB6fFt2Qa/0pPXcYw771+LSMw6/nGKexgYOmYjrzH+k/voBf3GgAChN+R671I+CaCZXmachkciyCiF+3UVgKsioVb+VxJ3JkChWb4uNRXPAjl8lkjj9l/1/RvzUaDTf/eMarpX9TchLmzDMEXXe309xUwVGoGjVxtEFSKWRX/EtrT2koe6MoOrrDVt19IS/SE8aDG1EGN0ET0dppe114X7XJrlM5WGVKdO36om3ZA7kuAHNWMgW7fiX9h2eIuOM91BGtUAXbIvclZw+hCoxwHG+PXFoN2ZKwqQLHMw1YiwvI2/wDgX0nodC5F+H2h013XvIyhQrhwn4pOlY1yl8rBJOR9CUvI5iMhN8xB6Vfoyqfs75fKy4X9uK+qvRsFq1WlEo5H07sRqtQPS+vTJLMAbxAEpSXyICu7Qjw1ZC58xeE0mKUgeEEDpyCf6+bXZ5I1SHRhN/2NnkbF5K/7WeQyfBp1oWgwdPRBIRWmqdR9qLljXgrjzuRo1LIGDjg0u2kWodme7X0LxTl2XaIbhrkCVZEwQrUnRYN5VtPGA9uRKbWonWTa2On5NwRLLnnCRjgmjNVV95XbXE804BPkxh8mpSJerfpja59P85//TC5mxYRPuk1tK16oPAPI/efr22FWhGtKTl3hLz470CuQDRLwsZb7NGxvPjvkGv1+PUY7XGsPSJsjxCXRbSakV/YL0XHqo79WiFaSslY9hqW3FTCJ7+BugrFOGWp79eKy8mYrlF0aRLofU9cSw5nV33Jwqi32Xu20GW82SpyKK2QoxkGFm0/I5kDXEASlJdIq1at2LHpb4bNjafUiy7CmojWhE9+w2W7t3kaZQVOZeKtLJ5ETk1dtLxd+reLXePBeLQt4y7OL+045pxU9F2H16kWDWXfl7UoH9PpRHxjBro4HJXFEQkuV7RTl95XbeBu2c+OKqgx2ja9KTq6zZb7q1QTNuFlslbMIfPXt2yDFCqCBk8nf9sSZBei7JKwqRy5XIaYfw5D4l8EDbkHa2GOY59oNSMKVix56cg0OhT6YABHekxZrIYcx34pOlZ1erUI5khaPmm/zaHk3GHCxs1GE1W9dKL6fq24EjQP8WXJfdd45Uz236k0ZquD2Zdqu9dW1kM3ITmXYXPjG7w5gCQoa4DayNPwhKfeWu7Em9N+NyKnJi9a3i79ayJa49O8G8akDQilRWhbdLO5SST8jkypxr/HmDrVoqFs6wnjoXgQrBUud4uCFePhzagbt0NVpkUO1P/WE+5SBMqi9A8BqwXRXIJMo0Md2ozIu+ZjzkpGMBlQhUQjU6rJ3fAVPtG2PGJJ2HhHuLyIZFEgd/0CctcvcNmf+sVd+PW4yVZpLFdQmnYM35iLKxOi1Uxpxil0F6rypehY1ZkQ15SPXn+B4uM70bbuhbXYgCHpH6cx9r7ANre0vwHbwzRA3tafAFsLJ33sdfX6WnEliY0KcFoJLP/AuiIxldl/HEeUKbCKto4Uxv0bMCXv92inaRVErIg89nMi0HB76EqCsoaoTp5GdSzPJsQ1ZcHPf5C/9Uev8jbBs8ipSYFTlaX/0HGzKdj1C0WHNpN7cg8olPg06UDgwCn4hDatUy0ayraeMB7YiFwXiE/zrh7Hm04nIhjz8L1mktP2htJ6oiJ3CkteGjKl2hF9BFsurjq0meP/xSd2gyg4PmNJ2HjHoD7dSU6bjVDOSTcv/juE0mKCh96LMjASuY8vPs27YjywkYC+kx2tgwxJ/yCWFuPbvr8UHasmsVEB+OSnUAgUH99F8fFdLmMcgjIvjfzN3zvts//fJ7oT1904vt5fK+oKZcVkWXMAOwU7llFy9pCLneb5bx51stMEELFpgIbaQ1fy8q5hquJd3LtFMHPGVj3vYtQbS9n4f+9QknbcId70sUNs4s1Nsn3xyQQylrxM0ND78L+QX2UXODXZ5+90ltHrpX9P1EUf20t9X6IoolbIWPf4tXXqfdUGL69MYtHf+6FcBXxp+knOL3oCbcs4wsa/6PZYwVxC+vezsBpzbX66Wl+vve0bOkmp+dw4b4vL9rQfnkUoLnCyXixJO07ad0+jDolG33U4lsJsCnf9iqZpR8InvQ7Aqpn9JUFTDerrNbChMHHBdpe+laazh9BEtna6t5pzUjn39Ux82/dz2GnaqY1769WCFKGsYaqSp1HdC/Zn949imEnv9UVL2zKOZs+uctpWG721LufS/+WkJt5X3l/zSB0VSPOQfjU9vTrFhLimzHn4duQqNZqomAtV3ikY/luDTKUh6No7HWMzf3sHhT4YVUg0QkkRxn3rMOelETbhZeQaXb1PEahJPDVxdoc9jztv40JyN3yFTK1F3/l6AgdNazCR9Nqivl4DGwJlzQHK4lRgeAF3dpp2GrJ1piQoa4nK8jQuhbp80bIv3T/x8x5Emby8BbZbqrP0f7m5lJSG125owxc7irn++uv55ZdfGDFiRG1P94oRGxVATJ/rOLRlNQW7fkMoLUKhC0DXti8B/W9FFdTYMVYd0RrD/vUYEtcgU6rRNOlIyE1Pow5vKQmbauCuiXPE7e+4HevTtCMRU95z2S41cb50Llf6k0TN4sk60x2V2Wk21B660pL3VcyKxNQrftFyJ5TXrl3LDZPu5NpnvuRYPrW29H8lqG5KQ3FxMRMnTuSvv/7i+++/Z+LEiVdg9pcHadnvyrEiMbVaD5qiKCIDPpzQibFxzSodL1E5lyP9wGjcWQAANJRJREFUSaLmGPlxvMf87/IYkv4he9UHNBr5CPouw9yO6RDpz+pHLr0l39WEJCivci73Rcu+lO+pyevYbo2ZcsO1BAQEEB8fz4FzBbW29H8lqU5Kg9lsZvr06SxevJgFCxZwzz33VPo6V2vLnI9+2czcXfnYet9Xbf4yYO6krlKkpppU50FTJopkrvqQUR3D+OGHH5DLXTtFSFSPpNR8vlj3H7/EJ6KNaIVVpF5cA+sbbWav9tihoizm7BTOf/ukra/07XM8OiCpFDKOvTGqpqdZp5EEZT2hNnM2oWrC1ZScxIIZAxgzpK/LmKtVIFWGt+9LEAQeeeQR5s+fz5w5c5g1a5bT/soE+9Vw80lPTycuLo7g7sMxdR6HVfTcx60s0rJfzVGdB82ETWuYOHEiDz74IJ988onDCUvi0vnll18YN24c6enphISE1str4NWMIIi0fGF1peOshlzSvn8aUbASMeX9Sh2QTr45qkH9rKUcynpCbeZslo14QOVNXnXRHXn6n3xolOoiDOrrl8vb9yWXy/n0008JDg7mmWeeITc3l7feeosz2UUeBcDV5MpQWlrK+PHjsVqt/Pn5a5g13rtT9GgWJC371RDVKQ5sPm4cn3/+Offddx9hYWG8+KL7anyJqnP06FECAgIIDQ2VhHodpLIeulB1O82G2ENXEpT1lJr6Rf5g8Z/Mnj3b4bGtadyeoMHTUYe3dBonWi3kb1+Ccf8GLIZslPpG3Bl/PV9/+AZje0g5WWWRyWS89tprBAUF8cQTT5Dr35q/jY29Fux12ZXh0UcfZefOnWzcuJGoKNvcarvrgYRnqvqgee+995KZmcns2bMJCQnhgQceqPD89XXFoaY5cuQI7dq1k8RkHaaiHrrVsdNsiD10JUEp4ZHfN2zl6Wk3o/ALIbDfrYiIFO5ZTdriZ4mc+qGTxWPW7x9QdHgL+s7Xo45sTUnqEfI2f8/0e7Lovm6ZFHVyw3///QfAgufvdrs/6qGFKP1CKD61B+OhzZSeO4I5+ywKvxCaPPh/dc6V4X//+x9ffPEFX375JX37Oqc71GYEXcJ7vPnMn3/+eTIzM3nooYcICQlhwoQJjn31ISXjSnD06FHatGlzpachUQGeXOhEwUpmFe00G6o5gCQoJTxy72NPI1OqiZj6PooLjap9Ow7m3P/uI2/Tt4SOfR6wWVMVHd5MQN/JBA68AwC/bqNQ6Pwp2PUb9378C2tfn3LF3kddZfSkqazJDS3XpkIk56/5KAPCUfqFAGA8sImiw5tRh7dyeC3bRtYdV4Zt27Yxc+ZMHnjgAe6+271ALoskJusuMpmMDz/8kKysLG6//XaCgoJo3fWaepGScaU4cuRIvW4XVh8oa7Nblty/v/bKTrMsDbWHriQoJdyyPzWf9KOJaFvGOcQkgFIfjE/TWIpO7EIoLUau1lKScgAAXYeBTufQxQykYNev7NywiqT7b5IiF+X4OVmLb+xgZ1eGlAOI5hInz/XAQVNpNPJhZAolGUtfpTTz4kXPKorMWr7viroypKamMm7cOHr37s3cuXOv2Dwkag65XM4333xDTk4Ok2a9R/DIRxAuVOtfzSkZV4Ls7Gyys7Np167dlZ6KRAV4MgcoTT8JVG6naach99CVBKWEW5YlpCBazciUapd9MpUGrBbMmWfQRLVHtJpt28uNlak0AJjTjzfIJq8V4cmVwXhwEyDDt8Mgx7aKkr+vtCuDyWRi7NixKJVKli1bhlrt+vsicXVy9OhRckqg4OR/5L47DplKg6pRU/x7j0XXprfT2IKE3ync8weWvDQUWn90MQN4pHgK0KfWRWVdT584evQoAG3btr3CM5GojKqYA3iiIZsDSIJSwi27TuWgCm5CybkjiILV0WtLtJopOXcEAEthNhpAFWzLpSw5ewhVYITjHPbIpaUwm92ncy/vG6jjuHNlEK0Wig5vQdMkBmVguNfnulKuDKIo8sADD7Bv3z42b95MeLj3c5ao++zcd4T9pzPw7TQEhT4Y0VxC0ZFtZC5/neARM/HralvCzf3nGwp2LkfXrh/+PW7CnJVCYcIqzFnJPK19s8ZTMq62PE67oJRyKOs+ddmF7mpAEpQSbjmeacCv+yhy/vqM7NWf4N9nHIgC+dt+xmqwiUPRUgqAtlUPFP5h5P7zNXKVBnVEa0rOHSEv/juQKxDNpRzL8M6BoKGw61SOi8VX8ak9CMUFTsvd3mAVxFoT7BVFf+bNm8fChQv59ttv6dGjR628vsSVY01BJBGTX3Na/vOLu5HzCx+jYNdv+HUdgcWQQ8Hu3/DtOJiQ0U86ximDG5O7bgEFR3cwa3lgjaRkVNRbsy7ncR45cpQmTZrg63vl5yJROZJ1ZvWRBKWEC4IgYraK+HUbhaUgi4Kdv2BM2gCAOqIN/n3GUbDtZ+RqH8C21B024WWyVswh89e3bCdRqAgaPJ38bUuQqX0wW8U6vzR1OTmeaXDZZjy4CeRKdDH9q3y+mhLs3kZ/Nm7cyOOPP87jjz/OlClSwVV9w1NKhkyuQOkXQknaMQBKUw+DYMW3XP60b8xActctoPDAJna16nXJKRlV7YV7JfM4Xb5DYl9Ud1zDyI/j62QEVcKVMV2j6NJE6qFbVSRBKeFC2SavQYOm4t97LObMM8g1vqjDmpO7aREAyuCLF2p1aDMi75qPOSsZwWRAFRKNTKkmd8NX+ETHNsgmr56wC3anbaXFFB/bgbZFN6ciKG+5VMFelehPl0gd2z+eybXXXsu7775brdeTqNuUTckQSk2IlhKEkiKKj+2k+GQCuhibR/HF/GmN0/H2/OnStBOXlJJx4MAB7n3sGXbt/herMc9jHmdh4hqMBzZizj6LUGJAoW+ET3QnHsq+Fe4bfllEZUXfIQFZnY2gSrinInMAmWhFYcjk9mG9pQeEMkiCUsItZZu8Knz0KJp2dOwznU5E4Rfi1IcSbO1G1KEXm5gXn9gNooBP864NssmrJ9y5MhQd3WGr7u54bbXOqZRXX7BXNfqz/7wR3bi3mH5Te5RK6RJSHymbkpH791cYEtfYdsjk6NpeQ/AwW8Nz+0Ol6exBfJpdLESw509bDdmXlJKxc98REk+mVZrHWZp+EmVAOLrWvZD76LHkp1P4318UH9/F4+r5dHnxlloVb1dTBFWiarjroTtv3qfMmjWLFz4skAoRyyDdDSTc4qnJq/FQPKXnjxE0eAYymdzj8YK5hLz471Hog/HvOKhBNnmtiPKuDMaDG5GptWjLVc96S9H543Tp0oUbb7yRG2+8kV69eqFQKCo8ZuPGjQwe7NpDDSBiyvtootoDIIoChsQ1FO79E0vueWQqH9QRrXjq/GT0er10Q6yHlE3J8O85Bl37/lgLsyk6vAVRFOBCZFIT0Rp143YU7FyO0q8RPtGdMWenkP3XZyBXIppLgOqnZHiTxwnQaPiDLsdq215D2sLHyN+3nlnLW9V4a63du3ezaNEiVv65jrMpZ5Br/dE0bkfgwCmogp2/E+asFHI2fEnJ2YPIFEq0rXoSNOTuOmdOIFE5crmMXr16UVJSwv79+4mLi7vSU6ozSIJSwi0T4pqy4Oc/yN/6Iz4tuiHX+lN67jCGfevxaRmHX88xTuMzf3sHhT4YVUg0QkkRxn3rMOelETbhZUSVtkE2ea2IsoLdWpSP6XQivjEDkat8qnwuhRyu7RiN0tKFBQsW8NZbbxESEsLIkSO58cYbGT58OAEBrksy5/OLAfCLG4060rmliTIo0vHv3L//j8ILhRd+3W9AMBkwJK4hbfGzPKxU0uW9e6Slu3pE+ZQMVaOmqBrZvr/6TkNI/+lFMpa9RsTUD5HJZITe8hxZK94le/XHtgNkcvx73YwpOQlzTipgS5s4euwYTZs0QavVejUPb/M4PaEMCAPAYjLWSmutOXPmEL95C6XRvQlqNxyrIZfCPas4/82jREx9H3Voc9vrF2SR9sMzyDW+BA6ailhqomDXL5RmniZy2od1xpxAwnu6du2KUqlk586dkqAsgyQoJdwSGxVA95iWbNyuoGDnLwilxSgDwwkcOAX/Xjc72gjZUUe0xrB/PYbENciUajRNOhJy09NoI1s12CavFVHWlcF4KN5W2OBhubs04xRFx3YCYM49j1hiJG/rTwCow1qga9Ob5ycPJvbJm7FarezcuZNVq1axatUqvvvuO5RKJQMGDHBEL+398BZssjXs1TTtiG9794VAomDFsPdPdO36OVXx6tr359wXd5Of9A+zlve+oo3VJWoWdykZZdG170fOmnlYclJRNWqC0i+EiDvexZyTitWYiyooCoU+iLPzpqIKbgzYci3bXfi9CwoKonHjxkRFRREVFeX232FhYV7ncZbFWlwAgoClIJP8rT8C4NOsS6201nriiSdg8CPsPXdxJcc3ZgDnvp5JwY5lhIx+CoD87UsQzSWE3znXIXLVjduS8dNsDPs3oOw+8oqbE0hUDR8fHzp37szu3buv9FTqFJKglPDIZ/ePYphJT6lVqHRsQJ/xBPQZ77K9ITd5rYiyrgzGAxuR6wLxad7V7djStBPkb/7eaZv9//pOQ7j2+pGOG6VCoaBv37707duXt956i+TkZP744w9WrVrF888/z5NPPknr1q0ZdPMdHE67mPsjlBQhU2lcHhREqwXRUoLCN9Bpu0IXCDI5KNVXtLG6RO1QPiWjLPZlbKHE6LRdFRzlWOotzUrGasjBt9MQx/m+2bCB1NRUzp07R2pqKqmpqRw8eJD169dz/vx5LBaL41wKhYKOT/2ARaYHKs7jLMvZedMcy/FyrT9BQ+9D26JbrbTW8mvWkX9/3+LyGahDojFnpTi2FR3ZhrZ1T4eYBNA274oyOIqiQ5vx6zpC+g5dhfTq1Yv4+PgrPY06hSQoJTwiNXmtXeyuDJFTP6hwnL7zUPSdh7rdp1bIKxTs0dHRPPDAAzzwwAMYjUb+/vtvVq1axaZzVuw1PNmrP0YsLQaZHE3TjgQNnoEm0taEWa7SoG7cDsP+Daij2uPTpCNCiZH8rT8h99Gj7zriijVWl6g9erUI5tCps6B1/pmKVgvGpL+RKTWoQqLdHiuKAnn/fINMpcGv60gUchn920Vw3XWxHl9PEAQyMjKcBOd7yXrsF56K8jjLEj7xVURLKebsFIwHNiKaTY59h8/n89NPP6HX69Hr9fj5+Tn929fXt9K847K4NScQRaxFeY7PxlKYhVCUhzqitcvxmsi2FJ/4F7hy5gQS1adXr14sWLCAwsJCfH31UhcTQCaKYnW0gkQDomwFo9TktWZZkZh6SYJ97qSu1fqMR34cz95/d1G4+1e0LXsg1wVgzkqmYNeviGYTEXe8hzqiFQDm3HNk/TaH0vQTjuOVgRGETXjFUenfIdKf1Y+4LkFKXJ0kpebTa/AIxNIiNE1jUfg1wmrIxXhwI5bsswRddxf+vW4BIGfdAkSrGXVYS0TBgvHgJkrPHaXRjY+jj70OgFUz+1dJLAmCSMsXVnvcn/7TiwglBkcepzvMuec5//VDBA6ejn/caADOvDMaKvi2abVaJ7FZXnTa/+3v788GdS+OZ5mcjjck/UP2qg9oNPIR9F2GUXL+GGmLHqfRjU84Pgs7uf/8HwU7fyH6qV+RKVXSd+gqIik1n2+3HOPPf49iUgdiFuq2W9PlQopQSlSK1OS19rhSrgzHMw34NInBp0nMxY1teqNr34/zXz9M7qZFhE96DQC5WosqJBpNVHt8mnXBaswjf8dSMn55g4jb56DQBUhOSPWM2KgAOg8cyb4Nv1K4dzVCcSFytRZ1RGuCrp3u1ANSHd6Kgn9XYDywEWQyNJFtCb/1TXyadUYhl1Urh7qqeZzuUAVFog5vifHARvzjRqNSyCgsLMBgMFBYWIjBYKjSv8+fP+/4d1FREb4zvsL2WGfDnJ1CzrrP0US1dyz1ixZbeoBMoXKZn0yhdoyRKVXSd+gqwKXXqDIALlyz67Jb0+VCEpQSXlFRk1eVQkabMD96Ng9qsE9ml8LlFuzuGqvbUQU1RtumN0VHtyEKVgDSf5qNT9NOBA+73zHOp3kXzn31EAU7fyFo8HTJCake8tM7TzJsbs9Kc6grSsm4lBzq6uRxlkcwlzqWxtuEXYwwRkREVGtOjvOWi6BaDblkLH0VucaXkJufc+Qi2xu+i26W50VrqdMY6TtUt5F6jf5/e3caH1V59nH8d2ZNJhsJCQQSIIEAshpMABFkExApCFQoqFAXKta6lNYWrVoXaheXR7EqFR8rKrjgIwqiSAEVQUSWALLKUlQgQCAbk8kks53zvBhmzDiZbJOQhev7+fAiZ5kZ4EzmOvfc1/+unhSUolYqC3mVX4Dhu5AFe3WjP4bYRPC40VwOHKcO4zr7A/EjfxVwjDEhBWPrVBy5B7w/y0pILU5jz6Gu6TxOTfWgOsvQR0QHHOc4eRDX2e+J6jkMvU6p1yzciu8htbyUvHcfQS0vpe2MJzDEtPYfp4/2PqfHFhx/5LEVoYuIQTF4Ry/lPdR0VTY1SXWWYd3yPo6TB3GeOoRabqP1uDn+myuPquFBu6iyRqWgFGGRX4D160IV7FWN/riLT6MYTCimCFR7sXejVskolerxj2LKSkgtk+9D8A//9w0uj8fb2V+N+ppDPTWrA0/94bYq53HqTJGo5TZyX7wZS48rMSV2RDFG4Dr7PbY969CZo4gbPB2PqtV7Fm5GUjT7TxRw5r15uItyaTv9cUw/aVQyxCSis8ThPH0k6HzHqUOY2qb7f5b3UNP0XX4pf3xvd9BNlWq3cm7T2+hjkzC2ScdxbE+l52tw0WSNVv/bQQjRaBqqYB+QngBl1qDtzryj2A9vJSKtH4qi8y+tV7o/MB7DcfoIrsJcTG071/voj2hc6k++ypuYmULagSVw1tuUpQ9xTfq2Z3eKZ82coWGPyPjmcSqKjpKdqyj8zwJKti3HEJNI0nV/9jcFKUYz0ZeOwXnqMMWb3qZw7ULsR7YR1WMY7W6eT0RiKgPSEup9Kk52xzjyVzyB4+S3JE26H3NKj0qPs3S/grIj23Bbz/q3lX2/C3dhLpbz+a/yHmq67lv249fcFemjE0i9azGpv1lE/Ihbq3wMj6Yxd9nuhnqJTYaMUApxEZqa1YEn7r4RndGEOaXH+S7v49i+WY1iNBM//GbAu7ReRFo/Svd+iuq0ezP9bEWU5KxEMZiIzZ7YIKM/4sLxTbPY+l0hR87a/NMsfB2ryWU/sO6Dt1m2bArdBg65oHOoazKPU9EbSRg1O+T+hsrC/f7jl7Af3kJkxgA8ZTZsez8P2B/d27usadygX2D/dhN5bz1ATPa1aC7vV6XGpDSi+4wGkPdQExVqtSYAxWD0T2mojkfVLoqsUSkohbgI9U6Jo8flIznw5SqsW5ejOu3oLXFYul1B3JDrMca39x+bdN1DWLe+j/3ARoqO7gC9gYjUnrQaOpOIpA6yElIzFdSxWmFksmLHqkeF7ne+RL+hY0hPjL6gc6gbex5nVY4f8c4fLjuylbIjW4P2+wpKQ2wSbW/4O0WfvULxF6+h6AxEZvQnfuQsb1FSx0540fAqyxqtq4sha1RyKIW4SH2fX8qY+RtqtBJSKCa9jjVzhrb4uUEtTe2zZUGv6BqtY7WpZuGG/R7SNIwGHWvnDJP3UBN0zXMbQs41r8ifN1qhKacyLT1rVEYohbhIhTP6o2kqCoqshNTM7Nu3j9lz7mPrtu14SotRjGaMrTsQO/DnAdmSAKUHNmLdthxXwQkURYcxqROzD14HD952wYvKppqFG+4IqgZom99Af3sfQN5HTc2Rs7Z6fbyWnjUqTTlCXMQmZqYwf1omJr0uZLPFT+l1CgZF4eyHT/Htf5ZUf4JoMrbsPsiuo6eJ6nMV8aNuI+6KaQCcXfYXSnxrZQPW7SvJX/EE+shY4offRNzg6aiOUs689xh3PP4vvs+vOv+xIfiitT66awgzBnakZ7tYjHrvNWvUK/RsF8uMgR356K4hLJ096ILd6NT1PWTS63hwRHvc//2aIUOGcOjQoQZ+paI2qsrrrStf1mhLJSOUQlzk6jr6s8i0jfvvv5/U1FRuvPHGRnjlorZWW9uRPH1ewP9vTNZ4Tr02B+vW5cRkjgWgJGclpnZdSZrysH9pw+i+oznx4k2c272Ouct+xru3D2qUv0NTzMINZwR13JdfMnr0aK688krWrl1L377130Akaq+6vN66aOlZo1JQCiHqFKz+6KOPcvz4cW655RbatWvHyJEjq3yOpvDBfzEL1bGq6PQYYhJxnD7s36Y67RgTUgLWydaZLeiMEWAwNamO1aZyTdV1cYLU1FQ2bNjA2LFjGTZsGKtWrWLQoMYp1kWgqvJ666KlZ41KQSmE8KvN6I+iKCxcuJCTJ08yefJkNm7cGDC6Ul0cjSzTeWFV7FhVneVobgeqw07Z4S2UHc3B0uPHZoGIjn2wf7sJ6/aVWDIGoHmcWHM+QnXYic2+9qLoWK2ruoygJiUl8dlnnzFhwgRGjRrFihUrGDUqdHNHRXKj1nAGpCecTzqony7vlp41Kl3eQoiwlJSUMGzYMM6cOcPmzZvxRCbU+Ku/AWkJPHmdNPZcCBU7VgtWv4DNN2dS0WHpNoiEa+72L1/oKS0m/8OnKP/hG//5ushY2kz5sz/Au6V3rDYGu93OlClT+PTTT1m6dCmTJk0KOkZu1C6cvbnnGP/ClyH3W3NWopaX4rEVYtu5Cku3KzC27QxAbNYEdBGBv9c+umtIi/6/kYJSCBG2U6dOMWjQINoOHE9R1581uXgXAV0fWuWfD+YqOI67pABPSQH2b78EvYHWV/8GfZR3BEV1llG0/jU0ZzmRGf3RnGVYt61AtZ+j7YwnMMa3x6hXOPz4uMb8K7VITqeTmTNnsmzZMhYtWsTMmTOBqnNDfeRGrf79YuFmco4VVfrvfWLBrXisZyo9L+XX/8bQqi2AP2u0seYdXyhSUAohwrJ+/XpGjBhR6b7kmU9jTrkEd3EeuS/NCvkY0ZeOYclrr0pR2UBUVaPzg6tC7s9758+oDhvJv3wGRVHIe/cRFEVHm6mP+I/xlJVwcuFsItIySZp0HwBH/zpOvm5tAB6Ph1//+te88sorPP/883QYMrlJ5nBeDCSvt+ZkDqUQol606n8t+rZdA7YZ4tsBoLPE0Xr8vUHnlH+XQ+m+9USkX8Yf39vNpamtWvwv3cZQXceq5ZLBFK5+AXdhLugNlB/NIWHsXQHH6CNjMKf2xJG7H2j5HauNSa/X8/LLLxMZGcnvHnsaQ8winKcOoZbbQoZnW3NWUrLjY9zFp9FHxmLpcSX3lM0ELpeiMgyBWaMa3vWXaq4hV2tqaqSgFELUC1NqLyK7D650n84U4V+KrqLSPetQzBYsGQPwaBpzl+1u8V8LNZaqOlY1lwMA1VEK2vmRGC14REZT3WiqB2j5HauNTVEUptx0O88//zya046xTTqOY3sqPbbo80VYtyzD0n0wsdnX4so/TknOR7jyj/HHyL/KjVqYJmamsHfvXl7+xo7OYESrQVF5MY4SS7C5ECIsR8+vJqFqGqrD7i84quO2FVJ+bA+WblegGEx4VM0fRyPq34D0BCgL/rfVPG5K936GYjBjTOyIIb49KDpKD2yk4owotzUfx4n9mNp2uSg6VpuC5zbn0/GexaT+ZhHxI26t9Bi3rRDrtuVE9RpB0uQ/EdNvHAmjbyf+ql9R/t1OrIe+Zu6y3Rf4lbcsJSUl/O9Dt9Nx72Ky0xIAQobY+7Znd4pnzZyhF00xCTJCKYQI0xeHzgJQsOo5NGcZKDrMHXoRP+JWzO26hjzPvn8DaCpRvYb7t0kcTcOZmtWBp/5wG5rTjrlDb/QxrfHYiijdvx53wQniR85CZ4oEUyTRfUdh+2YNeW8/iKX7IDRnGSU7VqG5HMRdPhWPqjE1q0Nj/5VatD2558jJtaFYqi7cnbnfguohqufQgO1RPYZStHYhJfu+YGuXAU0mN7Q5mjt3Lvn5+Xy+4H9IT0+vddboxUIKSiFEWA6eLcPS/QoiO2ejs8Thyj+GdesH5L15H8kznsKU3KXS80r3r0cfnUBEpx+zKz2qxrbviy7US7+o9E6Jo+/Qa9j96QeU7FyFWlaCzhSJKTmD+OG3BKzlnXD1nRjbpGP7Zi3FX7wBgCm5K4njf09UWh+yOsZflB+YF1LF3NCqaB4XAIrBHLBdMXp/dp7+r9yo1VBlmZ6ffvopL730Ei+88ALp6elA01ytqSmQglIIEZaC6DSSJj/w44auA7FcMphT/76boi9ep+20eUHnuApzcZ4+Qkz/iShK4Mybw2fqb2UKEeidf9zLmPn9q+1YVXR6YrMmEJs1IWifXlF48jpZHrChbf2usNpiEsCQ4P1KtfzE/oCbM8fxfQB4bAX1cqPWEoum6jI9x/VIYNasWQwfPpw77rgj5OO0tH+XupKCUghRZ6qqVdo5bIxvT2TXgdgPfYWmelB0+oD9pfvWAxDVK7hRx+XRWuSHV1Pg61j97dJdIB2rTdqR83OTq2NOzsDUvjvWLcswxLQmomNfXAXHKfjPAtAZ/A1Xtb1Ra8kB6lVlero8GgdOl3DojI3XN/+Aa+id/OX316LTSctJdaSgFELUWVVxNIbYRPC40VwOFLMlYF/p/vUYElIxJ2cEnSdxNA3r2kvb88yzz/J92yEYjCbJNWyCQt2ohZI0+U/kr3iSglXPeTcoOmIHTKL82F5chblAzW/UalNsNccA9RW7cv2ZnkDI69+33Zzak1vfO8pTRMu1Xw0pKIUQYQkVR+MuPo1iMKGYIgK2O04exF10irgrb6z08SSOpmEtWbKEDW/8DwvfGsw6a3yNVl7J7hTPEz9vXoVDc1ZdbuhPGWISSZ7xJK7CXDylRRjjU9BHx3PihV9iTGgP1OxGrbbFVs6xIsbM39BsbjRW7Mo9nyfppbldFG9cQum+z1HLbRiT0mg1dCaR6f3856gaOD0qc5buAmgWf8/GIgWlECIsvRLg0JnAgsSZdxT74a1Eds4KmiPp/7q75/Cgx5I4moZ14sQJ7r77bmbMmMHs6yczG6RjtYmqKjc0FGNCCsbzcyqd+cfw2AqJ6nMVUPWNms1m41f3/pkVazdUG6BeemAj1m3LcRWcQFF0GJM6MfvgdfDgbU262Pouv5Q/vrebiiVy/sfPYj+4idjsiRgS2lO6Zx1n/u9R2l7/NyI69Ao4XwNZfKEaUlAKIcKy8aWHOJVXhjmlx/ku7+PYvlmNYjQTP/zmgGM11UPptxsxte+O8fwqOhVJHE3D0TSNWbNmERUVxT//+U//dulYbZoGpCdw6IytRlMSfkrTVIo/X4RiNBOTeQ2a6qHs+F62bYsgOzsbRQn8/9156BhLX56PPjapygB16/aVFK1bSGSX/kQPvwnN7cK2Zx1n3nuMOzQ3l770pyZbbN237MeRV/B+U2I/sIFWI24lbuDPAYjuPZKTr9xJ8fpFJM98OugxZPGFqklBKYQIy43TpvDYswsp3rYc1WFHb4nD0u0K4oZcjzG+fcCx5d/vQi0tJmrQtKDH0esUiaNpQC+//DJr1qzhk08+IT4+9CiwFJNNw9SsDry++QesOStRy0vx2AoBKDuyFXdJPgCxWRPQRURRuHYhmseFqU1nNNVN6f4vcJ48ROvxv8MQ1waAgx+9xoCnf0NGRgY33HADN9xwA927dwdg/ldn6XjPYhRLPI5Thzn9+u8qfU0lOSsxtetK0pSH/UVpdN/RnHjxJs7tXsfcZT9rksXWntxzbP2+MGCb/eAmUHTEZI71b1MMJqIvHU3xF2/gtp7FEJsUcE7FxRfk91QwKSiFEGG55557uPaGWYyZv6HaOJrIzll0uv+joO2apqK6VR4ak9ZAr/LiUdkI49GjR7n33nuZPXs2Y8eODXGmaEp6p8QxIC2BD/71Ae5zZ/zb7Ye+gkNfARDdawS6iChMbbtg3b7CO51EUTC360bb6/9KRKe+/hu1t3d/xeeff86bb77Js88+y7x588jKymLq7feSkxtbbYA6gOq0Y0xICRjh1Jkt6IwRYDA1eLFV19HzyjI9nXlHMSakoPtJw6CpXTf//p8WlCCLL1RFCkohRNh8cTQVJ7zXhqLoKP30X0z54I8sX76cnj171vtrbKmqi3e5rl8Kd99yC0lJSTz9dPDXeKLpevK6vuw6/lq1N2rRfUdVOt8RfswN1ev1jBo1ilGjRrFgwQI+/vhj3nrrLZZu/QFDm741yryM6NgH+7ebsG5fiSVjAJrHiTXnI1SHndjsa+u92Kqv6KLKMj09tkL00cFFtD46wb+/MrL4QmhSUAoh6oVvQr6vS7S2cTS9f/U8kyZNYuDAgSxevJhJkyY18Ctu3moT71KeOo7n5vYnJkY66JuTsG/UqDw3NDIykilTpjBlyhSueW4DhTVs/kkYdTuq3UrRuoUUrVsIgC4ylrbXP445pUe9FVv1HV1UWaan5naC3hi0XTGYftwfgiy+UDlJ6hRC1JuJmSmsmTOUrI7eO399iK+nfNuzO8WzZs5QJmam0KVLFzZv3szYsWOZPHkyDz/8MKpa9cjMxWrFrlzGzN9AzjHvh3d18S6WTr3582YHK3blXrDXKOrHxMwU5k/LxKTXhXw//ZRep2DS65g/LbPazuuaBqiDdzlHQ+tUonpfReKk+2k97rfooxM4+/7fcBWdBMIvtmp7bfuii0Jd26EyPRWDCc4vW1mRr5D0FZaV8WV6ikAyQimEqFdpiVG8e/ugOsXRREdH8+677/LEE0/wwAMPsHPnTpYsWUJcnMxX2rdvH48++igbN2/lTF4eitGMsXUHYgf+PGAd7h/+MT7kY0x/M5N3PvioSce7iGATM1O4NLVVyFE7n9rmhtY2QP3s8n+gKDraTH3Evy2y6+WcXDib4i8WkzTpvjqvdFWb6CIfzePm+P/ejavgOLd8dSuLnpkXdG2HyvTURyfgKSkIekzfV92+r74rI4svVE4KSiFEg6hrHI2iKNx///1kZmZy/fXXM2DAAJYvX06PHj1q/NwtMfrmhx9+4ExBMa7OVxLfJx7N5cB+8CvOLvsLCWPv8nerth5/b9C5ztOHKdn+IRHp/SRLr5kK50YtlNoEqLuKT1N+NIeEsXcFbNdHxmBO7Ykjdz8ARl3diq2aRhdVVJKzErf1LBA6J3Lv3r20idDILQ0819SmM9YfdqM67AGNOc6Th7z723YO+byy+ELlpKAUQlwQtf2QGTt2LNu2bQuYVzlx4sRKj23J6w77jBs3jteOx3PiWJF/dComazynXpuDdetyf0EZ3Tt4ffSCY3sAhagewyRLr5mr79zQmgaoq6Xn50ZqwdNQNNWNpnoAsJ/+L5dffjnZ2dn+Pz169ECv11f5+DWNLvLxlBZTvOkdYi+/jnMb3/RuO39tP/OzDrz99tssWbKE3bt3kz7lPvTdhgaM6louGYx16/uU7Frtz6H05mquxdS+e6Ud3iCLL1RFCkohRJOVkZHB5s2bufnmm5k0aRIPP/wwjzzyCDqdd/p3S193uKLKsvQUnR5DTCKO04dDnqe5XdgPbsLcsTeG2ETJ0mthwh2Jr2mAuiG+PSg6Sg9sJDrzGn90kNuaj+PEfsypPdEp0D8tgRhnV9atW8eLL74IgMVi4bLLLiM7O5v+/fuTnZ1NRkaG/328J/ccObm2GkUX+RStfw1jQgpRvUb8WFCev7a79P8luuITTJgwgXnz5tHx0sFMXrgl4Hxz++5YLhlC8Revo9qLMcS3p3TPp7jPnaHtNb8N+byy+EJoUlAKIZq0mJgY3nvvPf7+97/z0EMPsXPnThYvXsz672wtet3hn/Jl6TnLy9DcDlSHnbLDWyg7moOlx5Uhzyv77zZURylRvYb7t0mWnvCpaYC63hJHdN9R2L5ZQ97bD2LpPgjNWUbJjlVoLgdxl09F1eDxW8fTO+VGAKxWKzt27GD79u1s376dDz/8kPnz53sfMzaWrKws+vfvT17q0KCcyKo4Th6kdO9nJM94AoWfFNSaysQ5f+eVO8YQGxvr3zwgLYGcCqP7AInjf0/xhiWU7v0cT7kNU5s02kx5mIiOvSt9Xll8oWpSUAohmjxFUXjggQfIzMzkF7/4Ba1atar0uOSZT2NOucT/s+ZxYd3yAba9n+E+l4fOHMX172Tw/IsLmHV1/wv06uuHL0uv6LNXsO1a7d2o6LB0G0TCmDtCnle6fz3ojUR1H+zfJll6wqc2AeoJV9+JsU06tm/WUvzFGwCYkruSOP73RKX1CSq2YmNjGT58OMOHD/dvKywsJCcnx19kvvPOO7hHd8SYlFaj16tpGoVrF2LpcSXmlB64i/MCD1B02CLbBhST4M30HDN/A54KAUyKwUT8yFuJH3lrjZ7bl+kpKicFpRCi2Rg3bhx/m7+A3952EzFZE/yrWvgYKqwPrnncnPm/x3DkHiD60qsxJaWhlttwnDrEvPdzuCqrZ7P6+tsX7xLbfyKWS4bgKSnA/u2XaJpaafwJ4B3F/O92Irtko4uIDtgnWXrCp6YB6opOT2zWBGKzJgTtq2mxlZCQwOjRoxk9erR/W9cHV+Gq4ehk6Z51uM7+QNLkP4U8prJru6EyPcWPpKAUQjQr7+/3fliYO/Qi6pIhIY+zbltO+bG9JM94AnP77gH79DqlwRtT6rPTvGK8i7F1B4ytvXO4ovtcRd47f+bMe/NI/uUzAUvigXe9Ys3tJKrn8KDHrGu8i2h5GrPYUlWtxsWk6rBT9MXrxA78ecimGQh9bYe7+EJznCpzIUlBKYRoNvbknuPb01b/z6rDjmI0o+gCO0g1TaVk+4dYug3C3L47mupB87i8aw5DgzSmNGSneVXxLpZLBlO4+gXchbkYW6cG7Cvdtx7FHIUlY0DQeZKlJypqrGKrNtFF1i3vg8eNpceV/q+6ffM81XIb7uI89DEJmEymkNd2Q2V6CikohRDNyHs5x/2rhRSseg7NWQaKDnOHXsSPuBVzu64AuPKP4bEVYmqTRsEnz2Pb+yl43BiT0kgYNZuITn3rrTHlQnSa22w2kiPheCWLmmguBwCqIzBoz20rpPzYHqL6XIViCF5iTrL0xE81VrFV0+git/UsarmNU6/8JmifdfO7WDe/S7tb/kmvzMwqH6chMj2FFJRCiGZk63eFeBQDlu5XENk5G50lDlf+MaxbPyDvzftInvEUpuQuuAu9y8BZt61AFxFN66u9YcznNr9L3rsP0+6mZzG1SQ+7MWXFrtwG6zTXNI1NmzaxaNEili5diqn/FOIHTaXiQI7mcVO69zMUgxljYseA8+37N4CmVvp1t2TpiVAao9iqaXRRTPYELN0uD9jmsZ+jcPULRPUZhaXrQMzxyTW+tus70/NiJwWlEKLZOHLWRkRqDyJSK6ya03UglksGc+rfd1P0xeu0nTYP1VUOgOq00+6W5/zzrSI69SV34WysW5aROOEPdWpMWb9+PSNGBIeHw49d5qqrnNLd67Af3oLr7PeornIMrdoRkzmW6MyrmbN0F0ClReXJkyd54403ePXVVzl8+DDp6enMnTuX/3y+gR1vPYC5Q2/0Ma3x2Ioo3b8ed8EJ4kfOQmeKDHic0v3r0UcnENGpT9BzSJaeqM6FLLZqGl1kTs6A5IyAc31ffRsTO2LpNgjt/OPVhRST4ZGCUgjRLFS17rAxvj2RXQdiP/QVmupBMZgAMKf0DJi8b4hr410m7sQBILzGlFb9r0XftmvANl+Xubv4NIVrFxKRdikxAyahM1ko+24HhWsW4Dj5LYnjfx+wTJzT6WTlypW8+uqrrF69GrPZzHXXXcfChQsZNmwYOp2Obt3e4bePPUPBzlV4ykrQmSIxJWcQP/yWgLW8AVwFJ3CePkJM/0koii5gn2TpibpoyGKrNtFFVZFru3FJQSmEaBaqm7xviE0EjxvN5UAf3RoAfVSroOP0UXG48v7r/UH18OCDD5CVlcVll11Genp6UKd0KKbUXkRWyHYMfI542s16AVNSJ/+2mH7XkP/xfEr3rCNu8HT0rVO4842v6HrsY958803y8/MZOHAgCxYsYPr06cTFBX4oTp8+nctHTWDM/A3VxrsYW6fS6f6PKn9tkqUnmqCaRhf9lKFVW/+1Ltd249JVf4gQQjQNGUnRIfe5i0+jGEwopghvIacz4CkpCDrOU1KIzuIt1iIcRSxevJipU6fSpUsXWrduzahRo5g7dy5Lly7l8OHDqGrgB9zR83mQqqahOuz+NYwr0lviAopJH0s3b0yRK/84HlVj31kn76zZxM0338y+ffv4+uuvuf3224OKSR9fvEtdx4okS080VXJtN38yQimEaDYGpCdw4LtciAxcBcOZdxT74a1Eds5CUXQoZguRXbIpO7IVV8Fxf26jK/+4N+i83zXodQrTRmbx2PwT5OXlsWPHDnbs2EFOTg5Lly7lqaeeAryrffTr188/irnuiLebuqou81A8pd4mIL3F+/p1aNz2t3/zl0k1H1WRLD3RUsm13bwpmqbVJcdUCCEuuL2558i+Yig6owlzSo/zXd7HsX2zGnQG2s18GmOit3h05h/j9Bv3ojNFEnN+ZY+SnJVoqsfbqBOTyEd3DQk53yo/P5+dO3eSk5PjLzSPHj1Kxox5nNy2OqjLXHOV+7vMK6N5XJxa9Fs0l4P2t7/sz87s2S6WVfeEXos7lKriinx82wemJ0iWnmg25NpunqSgFEI0K/2m/Y4DX67CVXgK1WlHb4kjotOlxA25HmN8+4BjHaePULz+NRy534KiENHpUuJH3EJEYipZHeNrvVLOuXPnyH5qU9A8TlfRSU79+27MHXrRdtq8Ss8t+OR5bN/8hzZTHyGyy4/riBv1CocfH1er11GRZOmJlkqu7eZFCkohRLPyfX5pjRpTqmLS61gzZ2itRzVUVaPzg6sq3Xd2xZPYD31Fx3uXBa3cc27LMoo/X0TclTNoNXh60LlH/zquXpdplPgT0RLJtd20SVOOEKJZaczJ+75O88pU7DKvyLZ7HcWfv0Z0v2sqLSbrewlE+cAVLZVc202bFJRCiGZnYmYK86dlYtLr/EsxVkevUzDpdcyflhnW5P1QneYVu8x97Ie+puCTf2LpPoiEMXdUep4sgSiEaAmkoBRCNEsTM1NYM2coWR29y6yFKix927M7xbNmztCwO0F7JQQ/l6/LPCKtnz9IvPzYXvI/fBJzh94kTvhjUMC477XJEohCiJZA5lAKIZq9Czl5f+DgoezJK6uyy9x97gwnX70bPG7iR96KYrIEPIapTRqmNukAVXaaCyFEcyE5lEKIZu9Crjt847QpPPbsQoq3LUd1eLvMLd2uCOgydxefRnN48yoL1/wr6DHiBl9PZHJnWSZOCNFiyAilEELUUmN2mgshRFMkcyiFEKKWZJk4IYQIJF95CyFEHcgycUII8SP5ylsIIcIgy8QJIYQUlEIIUS9kmTghxMVMCkohhGgAskycEOJiIgWlEEIIIYQIi3R5CyGEEEKIsEhBKYQQQgghwiIFpRBCCCGECIsUlEIIIYQQIixSUAohhBBCiLBIQSmEEEIIIcIiBaUQQgghhAiLFJRCCCGEECIsUlAKIYQQQoiwSEEphBBCCCHCIgWlEEIIIYQIixSUQgghhBAiLFJQCiGEEEKIsEhBKYQQQgghwiIFpRBCCCGECIsUlEIIIYQQIixSUAohhBBCiLBIQSmEEEIIIcIiBaUQQgghhAiLFJRCCCGEECIsUlAKIYQQQoiwSEEphBBCCCHCIgWlEEIIIYQIixSUQgghhBAiLFJQCiGEEEKIsEhBKYQQQgghwiIFpRBCCCGECIsUlEIIIYQQIixSUAohhBBCiLBIQSmEEEIIIcIiBaUQQgghhAiLFJRCCCGEECIsUlAKIYQQQoiwSEEphBBCCCHCIgWlEEIIIYQIixSUQgghhBAiLFJQCiGEEEKIsEhBKYQQQgghwiIFpRBCCCGECMv/A2DqO+Kw5x3YAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"draw_graph(remapped_graph, node_size=200, with_labels=True, width=1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "d6e71480-33fe-4843-b27d-04e55259e4d5",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# We can define the edge_coloring map so that RZZGates are positioned next to SWAP gates to exploit CX cancellations\n",
|
||
"# We use greedy edge coloring to color the edges of the graph in the rustworkx. This coloring is used to order the Rzz gates in the circuit.\n",
|
||
"\n",
|
||
"edge_coloring_idx = rx.graph_greedy_edge_color(graph_100)\n",
|
||
"edge_coloring = {\n",
|
||
" edge: edge_coloring_idx[idx]\n",
|
||
" for idx, edge in enumerate(list(graph_100.edge_list()))\n",
|
||
"}\n",
|
||
"edge_coloring = {tuple(sorted(k)): v for k, v in edge_coloring.items()}"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "b3c19d0d-41f6-48e1-8e56-c7e54287a69a",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 8917.87x8478.17 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"qaoa_circ = create_qaoa_swap_circuit(\n",
|
||
" remapped_cost_operator,\n",
|
||
" swap_strategy,\n",
|
||
" edge_coloring=edge_coloring,\n",
|
||
" qaoa_layers=1,\n",
|
||
")\n",
|
||
"qaoa_circ.draw(output=\"mpl\", fold=False)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bfc9c09b-3c1a-4f2b-87e9-085d1c2a937c",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 3: Execute using Qiskit primitives\n",
|
||
"### Define a CVaR cost function\n",
|
||
"This example shows how to use the Conditional Value at Risk (CVaR) cost function introduced in [\\[3\\]](#references) within the variational quantum optimization algorithms.\n",
|
||
"\n",
|
||
"The CVaR of a random variable $X$ for a confidence level $α ∈ (0, 1]$ is defined as\n",
|
||
"$$ CVaR_{\\alpha}(X) = \\mathbb{E} \\lbrack X | X \\leq F_X^{-1}(\\alpha) \\rbrack $$\n",
|
||
"where $F_X^{-1}(p)$ is the inverse cumulative distribution function of $X$. In other words, CVaR is the expected value of the lower $\\alpha$-tail of the distribution of $X$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "ba981a4c-5f1a-48a5-b577-07f0cd3a9d44",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"<IBMBackend('ibm_kyiv')>\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"pass_manager = generate_preset_pass_manager(\n",
|
||
" backend=backend,\n",
|
||
" optimization_level=3,\n",
|
||
")\n",
|
||
"\n",
|
||
"transpiled_qaoa_circ = pass_manager.run(qaoa_circ)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "5d0cede0-cab2-4598-9a9c-9bbd5a03b986",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Utility functions for the evaluation of the expectation value of a measured state\n",
|
||
"# In this code, for optimization, the measured state is converted into a bit string,\n",
|
||
"# and the sign of the value is determined by taking the exclusive OR of the bits\n",
|
||
"# corresponding to Pauli Z.\n",
|
||
"\n",
|
||
"_PARITY = np.array(\n",
|
||
" [-1 if bin(i).count(\"1\") % 2 else 1 for i in range(256)],\n",
|
||
" dtype=np.complex128,\n",
|
||
")\n",
|
||
"\n",
|
||
"\n",
|
||
"def evaluate_sparse_pauli(state: int, observable: SparsePauliOp) -> complex:\n",
|
||
" \"\"\"Utility for the evaluation of the expectation value of a measured state.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" state (int): The measured state.\n",
|
||
" observable (SparsePauliOp): The observable to evaluate the expectation value for.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" complex: The expectation value of the measured state.\n",
|
||
" \"\"\"\n",
|
||
" packed_uint8 = np.packbits(observable.paulis.z, axis=1, bitorder=\"little\")\n",
|
||
" state_bytes = np.frombuffer(\n",
|
||
" state.to_bytes(packed_uint8.shape[1], \"little\"), dtype=np.uint8\n",
|
||
" )\n",
|
||
" reduced = np.bitwise_xor.reduce(packed_uint8 & state_bytes, axis=1)\n",
|
||
" return np.sum(observable.coeffs * _PARITY[reduced])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "cf3d1f9d-fedc-43ce-8957-3d613bb1c476",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def qaoa_sampler_cost_fun(\n",
|
||
" params, ansatz, hamiltonian, sampler, aggregation=None\n",
|
||
"):\n",
|
||
" \"\"\"Standard sampler-based QAOA cost function to be plugged into optimizer routines.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" params (np.ndarray): Parameters for the ansatz.\n",
|
||
" ansatz (QuantumCircuit): Ansatz circuit.\n",
|
||
" hamiltonian (SparsePauliOp): Hamiltonian to be minimized.\n",
|
||
" sampler (QAOASampler): Sampler to be used.\n",
|
||
" aggregation (Callable | float | None): Aggregation function to be applied to\n",
|
||
" the sampled results. If None, the sum of the expectation values is returned.\n",
|
||
" If float, the CVaR with the given alpha is used.\n",
|
||
" \"\"\"\n",
|
||
" # Run the circuit\n",
|
||
" job = sampler.run([(ansatz, params)])\n",
|
||
" sampler_result = job.result()\n",
|
||
" sampled_int_counts = sampler_result[0].data.c.get_int_counts()\n",
|
||
" shots = sum(sampled_int_counts.values())\n",
|
||
" int_count_distribution = {\n",
|
||
" key: val / shots for key, val in sampled_int_counts.items()\n",
|
||
" }\n",
|
||
"\n",
|
||
" # a dictionary containing: {state: (measurement probability, value)}\n",
|
||
" evaluated = {\n",
|
||
" state: (\n",
|
||
" probability,\n",
|
||
" np.real(evaluate_sparse_pauli(state, hamiltonian)),\n",
|
||
" )\n",
|
||
" for state, probability in int_count_distribution.items()\n",
|
||
" }\n",
|
||
"\n",
|
||
" # If aggregation is None, return the sum of the expectation values.\n",
|
||
" # If aggregation is a float, return the CVaR with the given alpha.\n",
|
||
" # Otherwise, use the aggregation function.\n",
|
||
" if aggregation is None:\n",
|
||
" result = sum(\n",
|
||
" probability * value for probability, value in evaluated.values()\n",
|
||
" )\n",
|
||
" elif isinstance(aggregation, float):\n",
|
||
" cvar_aggregation = _get_cvar_aggregation(aggregation)\n",
|
||
" result = cvar_aggregation(evaluated.values())\n",
|
||
" else:\n",
|
||
" result = aggregation(evaluated.values())\n",
|
||
"\n",
|
||
" global iter_counts, result_dict\n",
|
||
" iter_counts += 1\n",
|
||
" temp_dict = {}\n",
|
||
" temp_dict[\"params\"] = params.tolist()\n",
|
||
" temp_dict[\"cvar_fval\"] = result\n",
|
||
" temp_dict[\"fval\"] = sum(\n",
|
||
" probability * value for probability, value in evaluated.values()\n",
|
||
" )\n",
|
||
" temp_dict[\"distribution\"] = sampled_int_counts\n",
|
||
" temp_dict[\"evaluated\"] = evaluated\n",
|
||
" result_dict[iter_counts] = temp_dict\n",
|
||
" print(f\"Iteration {iter_counts}: {result}\")\n",
|
||
"\n",
|
||
" return result\n",
|
||
"\n",
|
||
"\n",
|
||
"def _get_cvar_aggregation(alpha: float | None) -> Callable:\n",
|
||
" \"\"\"Return the CVaR aggregation function with the given alpha.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" alpha (float | None): Alpha value for the CVaR aggregation. If None, 1 is used\n",
|
||
" by default.\n",
|
||
" Raises:\n",
|
||
" ValueError: If alpha is not in [0, 1].\n",
|
||
" \"\"\"\n",
|
||
" if alpha is None:\n",
|
||
" alpha = 1\n",
|
||
" elif not 0 <= alpha <= 1:\n",
|
||
" raise ValueError(f\"alpha must be in [0, 1], but {alpha} was given.\")\n",
|
||
"\n",
|
||
" def cvar_aggregation(\n",
|
||
" objective_dict: Iterable[tuple[float, float]],\n",
|
||
" ) -> float:\n",
|
||
" \"\"\"Return the CVaR of the given measurements.\n",
|
||
" Args:\n",
|
||
" objective_dict (Iterable[tuple[float, float]]): An iterable of tuples containing\n",
|
||
" the measured bit string and the objective value based on the bit string.\n",
|
||
"\n",
|
||
" \"\"\"\n",
|
||
" sorted_measurements = sorted(objective_dict, key=lambda x: x[1])\n",
|
||
" # accumulate the probabilities until alpha is reached\n",
|
||
" accumulated_percent = 0.0\n",
|
||
" cvar = 0.0\n",
|
||
" for probability, value in sorted_measurements:\n",
|
||
" cvar += value * min(probability, alpha - accumulated_percent)\n",
|
||
" accumulated_percent += probability\n",
|
||
" if accumulated_percent >= alpha:\n",
|
||
" break\n",
|
||
" return cvar / alpha\n",
|
||
"\n",
|
||
" return cvar_aggregation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6006dd68-db46-4ed1-ae16-f1ea166067c2",
|
||
"metadata": {},
|
||
"source": [
|
||
"The CVaR can be used as an error mitigation technique as previously discussed [\\[4\\]](#references). In this example, we determine $\\alpha$ and the number of shots according to the circuit's error rate."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "c01f0762-d603-4dc8-bdf5-9694bf751817",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"layer fidelity 0.18178076404510374\n",
|
||
"\n",
|
||
"The corresponding CVaR aggregation value is: 0.06567448516285564\n",
|
||
"To mitigate the twirled noise, increase shots by 15.226613463664926\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"num_2q_ops = transpiled_qaoa_circ.count_ops()[\"ecr\"]\n",
|
||
"\n",
|
||
"for el in backend.properties().general:\n",
|
||
" if el.name[:2] == \"lf\" and el.name[3:] == str(n):\n",
|
||
" lf = el.value # layer fidelity\n",
|
||
" print(\"layer fidelity\", lf)\n",
|
||
" eplg = 1 - lf ** (1 / (n - 1)) # error per layered gate (EPLG)\n",
|
||
" fid_cx = 1 - eplg\n",
|
||
" gamma_cx = 1 / fid_cx**2\n",
|
||
" gamma_circ = gamma_cx * num_2q_ops\n",
|
||
"\n",
|
||
"cvar_aggregation = 1 / np.sqrt(gamma_circ)\n",
|
||
"print(\"\")\n",
|
||
"print(\"The corresponding CVaR aggregation value is: \", cvar_aggregation)\n",
|
||
"print(\n",
|
||
" \"To mitigate the twirled noise, increase shots by \", np.sqrt(gamma_circ)\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "d4cec8e2-f896-46c3-80c4-8cf4a6d063e9",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Iteration 1: -20.770192185845673\n",
|
||
"Iteration 2: -20.662187834467975\n",
|
||
"Iteration 3: -20.530182516117474\n",
|
||
"Iteration 4: -6.094164949444625\n",
|
||
"Iteration 5: -31.42021837469251\n",
|
||
"Iteration 6: -5.8402352967163145\n",
|
||
"Iteration 7: -27.110205884627188\n",
|
||
"Iteration 8: -24.666187995630317\n",
|
||
"Iteration 9: -34.10016519118837\n",
|
||
"Iteration 10: -32.97620048569601\n",
|
||
"Iteration 11: -34.346175102659636\n",
|
||
"Iteration 12: -32.58618477238797\n",
|
||
"Iteration 13: -34.51018171030716\n",
|
||
"Iteration 14: -34.72819049364342\n",
|
||
"Iteration 15: -34.62218622284688\n",
|
||
"Iteration 16: -35.13220677101896\n",
|
||
"Iteration 17: -34.990201049763236\n",
|
||
"Iteration 18: -34.732190654805564\n",
|
||
"Iteration 19: -34.37817639195668\n",
|
||
"Iteration 20: -34.85019540908861\n",
|
||
" message: Optimization terminated successfully.\n",
|
||
" success: True\n",
|
||
" status: 1\n",
|
||
" fun: -34.85019540908861\n",
|
||
" x: [ 2.739e+00 1.124e+00]\n",
|
||
" nfev: 20\n",
|
||
" maxcv: 0.0\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"iter_counts = 0\n",
|
||
"result_dict = {}\n",
|
||
"init_params = [np.pi, np.pi / 2]\n",
|
||
"\n",
|
||
"\n",
|
||
"with Session(backend=backend) as session:\n",
|
||
" sampler = Sampler(mode=session)\n",
|
||
"\n",
|
||
" shots = 1000\n",
|
||
" sampler.options.default_shots = int(shots * np.sqrt(gamma_circ))\n",
|
||
"\n",
|
||
" # Set error mitigation options\n",
|
||
" sampler.options.dynamical_decoupling.enable = True\n",
|
||
" sampler.options.dynamical_decoupling.sequence_type = \"XY4\"\n",
|
||
" sampler.options.twirling.enable_gates = True\n",
|
||
" sampler.options.twirling.num_randomizations = \"auto\"\n",
|
||
" sampler.options.twirling.enable_measure = True\n",
|
||
"\n",
|
||
" # Run optimization loop\n",
|
||
" result = minimize(\n",
|
||
" qaoa_sampler_cost_fun,\n",
|
||
" init_params,\n",
|
||
" args=(\n",
|
||
" transpiled_qaoa_circ,\n",
|
||
" remapped_cost_operator,\n",
|
||
" sampler,\n",
|
||
" cvar_aggregation,\n",
|
||
" ),\n",
|
||
" method=\"COBYLA\",\n",
|
||
" tol=1e-2,\n",
|
||
" )\n",
|
||
"print(result)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1f691aa7-e53a-4d04-80e1-33fa901e7a6b",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 4: Post-process and return result in desired classical format"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "b4f377c5-5501-4568-801d-5599c9315efa",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1200x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"plt.figure(figsize=(12, 6))\n",
|
||
"plt.plot(\n",
|
||
" [result_dict[i][\"cvar_fval\"] for i in range(1, iter_counts + 1)],\n",
|
||
" label=\"CVaR\",\n",
|
||
")\n",
|
||
"plt.plot(\n",
|
||
" [result_dict[i][\"fval\"] for i in range(1, iter_counts + 1)],\n",
|
||
" label=\"Standard\",\n",
|
||
")\n",
|
||
"plt.legend()\n",
|
||
"plt.xlabel(\"Iteration\")\n",
|
||
"plt.ylabel(\"Cost\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "99e70f6e-f794-4dcf-b991-5da71496ba53",
|
||
"metadata": {},
|
||
"source": [
|
||
"The following graph is the results of the standard expectation value."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 36,
|
||
"id": "2e04c7ae-1eb9-4a66-950b-4c9f4b7c0ed1",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"bitstring (int): 426224160272806387142248724306, probability: 6.567713122290818e-05, objective value: -54.0\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# sort the result_dict[iter_counts]['evaluated] by the CVaR value\n",
|
||
"sorted_result_dict = [\n",
|
||
" (k, v)\n",
|
||
" for k, v in sorted(\n",
|
||
" result_dict[iter_counts][\"evaluated\"].items(),\n",
|
||
" key=lambda item: item[1][1],\n",
|
||
" )\n",
|
||
"]\n",
|
||
"print(\n",
|
||
" f\"bitstring (int): {sorted_result_dict[0][0]}, probability: {sorted_result_dict[0][1][0]}, objective value: {sorted_result_dict[0][1][1]}\"\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "f0962c7a-464b-4cd6-ad5b-36df07eb7691",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Result bitstring (binary) : [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]\n",
|
||
"The value of the cut is: 83\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def to_bitstring(integer, num_bits):\n",
|
||
" result = np.binary_repr(integer, width=num_bits)\n",
|
||
" return [int(digit) for digit in result]\n",
|
||
"\n",
|
||
"\n",
|
||
"def evaluate_sample(x: Sequence[int], graph: rx.PyGraph) -> float:\n",
|
||
" assert len(x) == len(\n",
|
||
" list(graph.nodes())\n",
|
||
" ), \"The length of x must coincide with the number of nodes in the graph.\"\n",
|
||
" return sum(\n",
|
||
" x[u] * (1 - x[v]) + x[v] * (1 - x[u])\n",
|
||
" for u, v in list(graph.edge_list())\n",
|
||
" )\n",
|
||
"\n",
|
||
"\n",
|
||
"bitstring = to_bitstring(\n",
|
||
" sorted_result_dict[0][0], len(list(remapped_graph.nodes()))\n",
|
||
")\n",
|
||
"bitstring = bitstring[::-1]\n",
|
||
"print(f\"Result bitstring (binary) : {bitstring}\")\n",
|
||
"\n",
|
||
"cut_value = evaluate_sample(bitstring, remapped_graph)\n",
|
||
"print(f\"The value of the cut is: {cut_value}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5707795-b521-4d33-b361-e75fa924d463",
|
||
"metadata": {},
|
||
"source": [
|
||
"Finally, let's draw a graph based on the CVaR result.\n",
|
||
"We split the graph nodes into two sets based on the CVaR result.\n",
|
||
"The nodes in the first set are colored in grey, and the nodes in the second set are colored in purple.\n",
|
||
"The edges between the two sets are the edges that are cut by the partitioning."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 46,
|
||
"id": "91d3560b-a688-41a4-a4d6-37ab218541f6",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"def plot_result(G, x):\n",
|
||
" colors = [\"tab:grey\" if i == 0 else \"tab:purple\" for i in x]\n",
|
||
" pos, _default_axes = rx.spring_layout(G), plt.axes(frameon=True)\n",
|
||
" rx.visualization.mpl_draw(\n",
|
||
" G, node_color=colors, node_size=100, alpha=0.8, pos=pos\n",
|
||
" )\n",
|
||
"\n",
|
||
"\n",
|
||
"plot_result(graph_100, to_bitstring(sorted_result_dict[0][0], 100))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "213b262e-cb95-47cb-b3b6-e44505e2bcf1",
|
||
"metadata": {},
|
||
"source": [
|
||
"## References\n",
|
||
"\n",
|
||
"[1] Weidenfeller, J., Valor, L. C., Gacon, J., Tornow, C., Bello, L., Woerner, S., & Egger, D. J. (2022). Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware. Quantum, 6, 870.\n",
|
||
"\n",
|
||
"[2] Matsuo, A., Yamashita, S., & Egger, D. J. (2023). A SAT approach to the initial mapping problem in SWAP gate insertion for commuting gates. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 106(11), 1424-1431.\n",
|
||
"\n",
|
||
"[3] Barkoutsos, P. K., Nannicini, G., Robert, A., Tavernelli, I., & Woerner, S. (2020). Improving variational quantum optimization using CVaR. Quantum, 4, 256.\n",
|
||
"\n",
|
||
"[4] Barron, S. V., Egger, D. J., Pelofske, E., Bärtschi, A., Eidenbenz, S., Lehmkuehler, M., & Woerner, S. (2023). Provable bounds for noise-free expectation values computed from noisy samples. arXiv preprint arXiv:2312.00733."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "993f61f9-4fb0-4f69-8734-f108c4287552",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Tutorial survey\n",
|
||
"\n",
|
||
"Please take one minute to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n",
|
||
"\n",
|
||
"[Link to survey](https://your.feedback.ibm.com/jfe/form/SV_cZwpScxyXVDpIeq)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "600bde6b-5d07-475d-8720-0031007f3cf2",
|
||
"metadata": {},
|
||
"source": [
|
||
"© IBM Corp. 2024"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"description": "This notebook introduces advanced techniques to improve the performance of the Quantum Approximate Optimization Algorithm (QAOA) with a large number of qubits.",
|
||
"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"
|
||
},
|
||
"platform": "cloud",
|
||
"title": "Advanced Techniques for QAOA"
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
}
|