1444 lines
378 KiB
Plaintext
1444 lines
378 KiB
Plaintext
{
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"cells": [
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{
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||
"cell_type": "markdown",
|
||
"id": "3d6f69f5-07dd-4053-82a2-56d224c73c8d",
|
||
"metadata": {
|
||
"tags": []
|
||
},
|
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"source": [
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"{/* cspell:ignore mapsto multigraph inds extrap sharex sharey pidx */}\n",
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"\n",
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"# Utility-scale error mitigation with probabilistic error amplification\n",
|
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"*Usage estimate: 60 minutes on IBM Kyiv (NOTE: This is an estimate only. Your runtime may vary.)*"
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]
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},
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{
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"attachments": {},
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||
"cell_type": "markdown",
|
||
"id": "b06bc36a-212e-4f9a-a81e-e1870fc0e629",
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||
"metadata": {},
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"source": [
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"## Background\n",
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"\n",
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"The tutorial demonstrates how to run a utility-scale error mitigation experiment with Qiskit Runtime using an experimental version of *zero noise extrapolation* (ZNE) with *probabilistic error amplification* (PEA).\n",
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"\n",
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"\n",
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"__Reference__: Y. Kim et al. *Evidence for the utility of quantum computing before fault tolerance.* [Nature 618.7965 (2023)](https://www.nature.com/articles/s41586-023-06096-3)"
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]
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||
},
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{
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||
"cell_type": "markdown",
|
||
"id": "8ea69d52-514c-4141-9317-3cb26a8685b8",
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"metadata": {
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||
"tags": []
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||
},
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"source": [
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"### Zero-Noise Extrapolation (ZNE)"
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]
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},
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{
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"cell_type": "markdown",
|
||
"id": "c6c0d2e9-25c7-4d80-8863-7fc4b86e75c1",
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||
"metadata": {},
|
||
"source": [
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"Zero-noise extrapolation (ZNE) is an error mitigation technique that removes the effects of an *unknown* noise during circuit execution that can be scaled in a *known* way.\n",
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"\n",
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"It assumes expectation values scale with noise by a known function\n",
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"\n",
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"$$\n",
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"\\langle A(\\lambda) \\rangle = \\langle A(0) \\rangle =+ \\sum_{k=0}^{m} a_k \\lambda^k + R\n",
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"$$\n",
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"where $\\lambda$ parameterizes the noise strength and can be amplified."
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]
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},
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||
{
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||
"attachments": {},
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||
"cell_type": "markdown",
|
||
"id": "fa804cd1-080e-4b2b-9024-0dffc08a427c",
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||
"metadata": {
|
||
"tags": []
|
||
},
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||
"source": [
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"We can implement ZNE with the following steps:\n",
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"\n",
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"1. Amplify circuit noise for several noise factors $\\lambda_1, \\lambda_2, ... $\n",
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"2. Run every noise-amplified circuit to measure $\\langle A(\\lambda_1)\\rangle, ...$\n",
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"3. Extrapolate back to the zero-noise limit $\\langle A(0)\\rangle$\n",
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"\n",
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"\n",
|
||
""
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||
]
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||
},
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{
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||
"cell_type": "markdown",
|
||
"id": "4bb6a1a4-7dc4-47ac-9e81-02929901feb7",
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||
"metadata": {},
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"source": [
|
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"#### Amplify noise for ZNE"
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||
]
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||
},
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||
{
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||
"attachments": {},
|
||
"cell_type": "markdown",
|
||
"id": "b6bb245c-6dc1-49ae-b511-92e66619d7b3",
|
||
"metadata": {},
|
||
"source": [
|
||
"The main challenge in successfully implementing ZNE is to have an accurate model for noise in the expectation value and to amplify the noise in a known way.\n",
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"\n",
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"There are three common ways error amplification is implemented for ZNE.\n",
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"\n",
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"| **Pulse stretching** | **Gate folding** | **Probabilistic error amplification** |\n",
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"|-----------|-----------|-----------|\n",
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"| Scale pulse duration via calibration | Repeat gates in identity cycles $U\\mapsto U(U^{-1}U)^{\\lambda-1}/2$ | Add noise via sampling Pauli channels |\n",
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"|  |  |  |\n",
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"| Kandala et al. Nature (2019) | Shultz et al. PRA (2022) | Li & Benjamin PRX (2017) |"
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||
]
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||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "94188baa-79de-4258-912b-9f75d3bcbd30",
|
||
"metadata": {},
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||
"source": [
|
||
"For utility-scale experiments, *probabilistic error amplification* (PEA) is the most attractive.\n",
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"- Pulse stretching assumes gate noise is proportional to duration, which is typically not true. Calibration is also costly.\n",
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"- Gate folding requires large stretch factors that greatly limit the depth of circuits that can be run.\n",
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"- PEA can be applied to any circuit that can be run with native noise factor ($\\lambda=1$) but requires learning the noise model."
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||
]
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||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87b0337b-cf2b-4d72-b22a-ad72b736f374",
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||
"metadata": {
|
||
"tags": []
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||
},
|
||
"source": [
|
||
"### Learn the noise model for PEA"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
|
||
"id": "22c21618-fb61-457b-86e6-0029a2272633",
|
||
"metadata": {
|
||
"tags": []
|
||
},
|
||
"source": [
|
||
"PEA assumes the same layer-based noise model as *probabilistic error cancellation* (PEC); however, it avoids the sampling overhead that scales exponentially with the circuit noise."
|
||
]
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||
},
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||
{
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||
"attachments": {},
|
||
"cell_type": "markdown",
|
||
"id": "8f885d1c-a54a-47c3-b567-c6bc7389b3e7",
|
||
"metadata": {
|
||
"tags": []
|
||
},
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||
"source": [
|
||
"| **Step 1** | **Step 2** | **Step 3** |\n",
|
||
"|-----------|-----------|-----------|\n",
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||
"| Pauli twirl layers of two-qubit gates | Repeat identity pairs of layers and learn the noise | Derive a fidelity (error for each noise channel) |\n",
|
||
"|  |  |  |\n",
|
||
"\n",
|
||
"__Reference__: E. van den Berg, Z. Minev, A. Kandala, and K. Temme, _Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors_ [arXiv:2201.09866](https://arxiv.org/abs/2201.09866)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a6fc9357",
|
||
"metadata": {},
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||
"source": [
|
||
"## Requirements\n",
|
||
"\n",
|
||
"Before starting this tutorial, ensure that you have the following installed:\n",
|
||
"\n",
|
||
"- Qiskit SDK 1.0 or later with Visualization support (`pip install 'qiskit[visualization]'`)\n",
|
||
"- Qiskit Runtime 0.22 or later (`pip install qiskit-ibm-runtime`)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eb1e2b8a",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Setup"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
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||
"id": "af76d0bc",
|
||
"metadata": {},
|
||
"outputs": [],
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||
"source": [
|
||
"from __future__ import annotations\n",
|
||
"from collections.abc import Sequence\n",
|
||
"from collections import defaultdict\n",
|
||
"import numpy as np\n",
|
||
"import rustworkx\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"from qiskit.circuit import QuantumCircuit, Parameter\n",
|
||
"from qiskit.circuit.library import CXGate, CZGate, ECRGate\n",
|
||
"from qiskit.providers import Backend\n",
|
||
"from qiskit.visualization import plot_error_map\n",
|
||
"from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
|
||
"from qiskit.quantum_info import SparsePauliOp\n",
|
||
"from qiskit.primitives import PubResult\n",
|
||
"\n",
|
||
"from qiskit_ibm_runtime import QiskitRuntimeService\n",
|
||
"from qiskit_ibm_runtime import EstimatorV2 as Estimator"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "aef7ca65-a2cd-4440-ac2e-953d218df219",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 1: Map classical inputs to a quantum problem"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "20ef0ab5-dc96-4e52-9836-f5339190899d",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Create a parameterized Ising model circuit"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4729e2ed-64f1-44ce-ad02-8efe792ad90f",
|
||
"metadata": {},
|
||
"source": [
|
||
"First, choose a backend to run on. This demonstration runs on a 127-qubit backend, but you can modify this to any backend available to you."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "50c0b07c-b43a-4d48-8d06-d141469fd0e6",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
|
||
"backend = service.least_busy(\n",
|
||
" operational=True, simulator=False, min_num_qubits=127\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e589eef0-755e-4a98-bea4-3ee5e5fdbe85",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Helper functions for circuit construction"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d63c2c20-7694-427a-b0f1-68bfe4c720d1",
|
||
"metadata": {},
|
||
"source": [
|
||
"Next, create some helper functions to construct the circuits for the Trotterized time evolution of a two-dimensional transverse-field Ising model that adheres to the topology of the backend."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "795e151a-a4d9-44ea-b349-b10256663611",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"Trotter circuit generation\"\"\"\n",
|
||
"\n",
|
||
"\n",
|
||
"def remove_qubit_couplings(\n",
|
||
" couplings: Sequence[tuple[int, int]], qubits: Sequence[int] | None = None\n",
|
||
") -> list[tuple[int, int]]:\n",
|
||
" \"\"\"Remove qubits from a coupling list.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" couplings: A sequence of qubit couplings.\n",
|
||
" qubits: Optional, the qubits to remove.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" The input couplings with the specified qubits removed.\n",
|
||
" \"\"\"\n",
|
||
" if qubits is None:\n",
|
||
" return couplings\n",
|
||
" qubits = set(qubits)\n",
|
||
" return [edge for edge in couplings if not qubits.intersection(edge)]\n",
|
||
"\n",
|
||
"\n",
|
||
"def coupling_qubits(\n",
|
||
" *couplings: Sequence[tuple[int, int]],\n",
|
||
" allowed_qubits: Sequence[int] | None = None,\n",
|
||
") -> list[int]:\n",
|
||
" \"\"\"Return a sorted list of all qubits involved in 1 or more couplings lists.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" couplings: 1 or more coupling lists.\n",
|
||
" allowed_qubits: Optional, the allowed qubits to include. If None all\n",
|
||
" qubits are allowed.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" The intersection of all qubits in the couplings and the allowed qubits.\n",
|
||
" \"\"\"\n",
|
||
" qubits = set()\n",
|
||
" for edges in couplings:\n",
|
||
" for edge in edges:\n",
|
||
" qubits.update(edge)\n",
|
||
" if allowed_qubits is not None:\n",
|
||
" qubits = qubits.intersection(allowed_qubits)\n",
|
||
" return list(qubits)\n",
|
||
"\n",
|
||
"\n",
|
||
"def construct_layer_couplings(\n",
|
||
" backend: Backend,\n",
|
||
") -> list[list[tuple[int, int]]]:\n",
|
||
" \"\"\"Separate a coupling map into disjoint 2-qubit gate layers.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" backend: A backend to construct layer couplings for.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" A list of disjoint layers of directed couplings for the input coupling map.\n",
|
||
" \"\"\"\n",
|
||
" coupling_graph = backend.coupling_map.graph.to_undirected(\n",
|
||
" multigraph=False\n",
|
||
" )\n",
|
||
" edge_coloring = rustworkx.graph_bipartite_edge_color(coupling_graph)\n",
|
||
"\n",
|
||
" layers = defaultdict(list)\n",
|
||
" for edge_idx, color in edge_coloring.items():\n",
|
||
" layers[color].append(\n",
|
||
" coupling_graph.get_edge_endpoints_by_index(edge_idx)\n",
|
||
" )\n",
|
||
" layers = [sorted(layers[i]) for i in sorted(layers.keys())]\n",
|
||
"\n",
|
||
" return layers\n",
|
||
"\n",
|
||
"\n",
|
||
"def entangling_layer(\n",
|
||
" gate_2q: str,\n",
|
||
" couplings: Sequence[tuple[int, int]],\n",
|
||
" qubits: Sequence[int] | None = None,\n",
|
||
") -> QuantumCircuit:\n",
|
||
" \"\"\"Generating a entangling layer for the specified couplings.\n",
|
||
"\n",
|
||
" This corresponds to a Trotter layer for a ZZ Ising term with angle Pi/2.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" gate_2q: The 2-qubit basis gate for the layer, should be \"cx\", \"cz\", or \"ecr\".\n",
|
||
" couplings: A sequence of qubit couplings to add CX gates to.\n",
|
||
" qubits: Optional, the physical qubits for the layer. Any couplings involving\n",
|
||
" qubits not in this list will be removed. If None the range up to the largest\n",
|
||
" qubit in the couplings will be used.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" The QuantumCircuit for the entangling layer.\n",
|
||
" \"\"\"\n",
|
||
" # Get qubits and convert to set to order\n",
|
||
" if qubits is None:\n",
|
||
" qubits = range(1 + max(coupling_qubits(couplings)))\n",
|
||
" qubits = set(qubits)\n",
|
||
"\n",
|
||
" # Mapping of physical qubit to virtual qubit\n",
|
||
" qubit_mapping = {q: i for i, q in enumerate(qubits)}\n",
|
||
"\n",
|
||
" # Convert couplings to indices for virtual qubits\n",
|
||
" indices = [\n",
|
||
" [qubit_mapping[i] for i in edge]\n",
|
||
" for edge in couplings\n",
|
||
" if qubits.issuperset(edge)\n",
|
||
" ]\n",
|
||
"\n",
|
||
" # Layer circuit on virtual qubits\n",
|
||
" circuit = QuantumCircuit(len(qubits))\n",
|
||
"\n",
|
||
" # Get 2-qubit basis gate and pre and post rotation circuits\n",
|
||
" gate2q = None\n",
|
||
" pre = QuantumCircuit(2)\n",
|
||
" post = QuantumCircuit(2)\n",
|
||
"\n",
|
||
" if gate_2q == \"cx\":\n",
|
||
" gate2q = CXGate()\n",
|
||
" # Pre-rotation\n",
|
||
" pre.sdg(0)\n",
|
||
" pre.z(1)\n",
|
||
" pre.sx(1)\n",
|
||
" pre.s(1)\n",
|
||
" # Post-rotation\n",
|
||
" post.sdg(1)\n",
|
||
" post.sxdg(1)\n",
|
||
" post.s(1)\n",
|
||
" elif gate_2q == \"ecr\":\n",
|
||
" gate2q = ECRGate()\n",
|
||
" # Pre-rotation\n",
|
||
" pre.z(0)\n",
|
||
" pre.s(1)\n",
|
||
" pre.sx(1)\n",
|
||
" pre.s(1)\n",
|
||
" # Post-rotation\n",
|
||
" post.x(0)\n",
|
||
" post.sdg(1)\n",
|
||
" post.sxdg(1)\n",
|
||
" post.s(1)\n",
|
||
" elif gate_2q == \"cz\":\n",
|
||
" gate2q = CZGate()\n",
|
||
" # Identity pre-rotation\n",
|
||
" # Post-rotation\n",
|
||
" post.sdg([0, 1])\n",
|
||
" else:\n",
|
||
" raise ValueError(\n",
|
||
" f\"Invalid 2-qubit basis gate {gate_2q}, should be 'cx', 'cz', or 'ecr'\"\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Add 1Q pre-rotations\n",
|
||
" for inds in indices:\n",
|
||
" circuit.compose(pre, qubits=inds, inplace=True)\n",
|
||
"\n",
|
||
" # Use barriers around 2-qubit basis gate to specify a layer for PEA noise learning\n",
|
||
" circuit.barrier()\n",
|
||
" for inds in indices:\n",
|
||
" circuit.append(gate2q, (inds[0], inds[1]))\n",
|
||
" circuit.barrier()\n",
|
||
"\n",
|
||
" # Add 1Q post-rotations after barrier\n",
|
||
" for inds in indices:\n",
|
||
" circuit.compose(post, qubits=inds, inplace=True)\n",
|
||
"\n",
|
||
" # Add physical qubits as metadata\n",
|
||
" circuit.metadata[\"physical_qubits\"] = tuple(qubits)\n",
|
||
"\n",
|
||
" return circuit\n",
|
||
"\n",
|
||
"\n",
|
||
"def trotter_circuit(\n",
|
||
" theta: Parameter | float,\n",
|
||
" layer_couplings: Sequence[Sequence[tuple[int, int]]],\n",
|
||
" num_steps: int,\n",
|
||
" gate_2q: str | None = \"cx\",\n",
|
||
" backend: Backend | None = None,\n",
|
||
" qubits: Sequence[int] | None = None,\n",
|
||
") -> QuantumCircuit:\n",
|
||
" \"\"\"Generate a Trotter circuit for the 2D Ising\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" theta: The angle parameter for X.\n",
|
||
" layer_couplings: A list of couplings for each entangling layer.\n",
|
||
" num_steps: the number of Trotter steps.\n",
|
||
" gate_2q: The 2-qubit basis gate to use in entangling layers.\n",
|
||
" Can be \"cx\", \"cz\", \"ecr\", or None if a backend is provided.\n",
|
||
" backend: A backend to get the 2-qubit basis gate from, if provided\n",
|
||
" will override the basis_gate field.\n",
|
||
" qubits: Optional, the allowed physical qubits to truncate the\n",
|
||
" couplings to. If None the range up to the largest\n",
|
||
" qubit in the couplings will be used.\n",
|
||
"\n",
|
||
" Returns:\n",
|
||
" The Trotter circuit.\n",
|
||
" \"\"\"\n",
|
||
" if backend is not None:\n",
|
||
" try:\n",
|
||
" basis_gates = backend.configuration().basis_gates\n",
|
||
" except AttributeError:\n",
|
||
" basis_gates = backend.basis_gates\n",
|
||
" for gate in [\"cx\", \"cz\", \"ecr\"]:\n",
|
||
" if gate in basis_gates:\n",
|
||
" gate_2q = gate\n",
|
||
" break\n",
|
||
"\n",
|
||
" # If no qubits, get the largest qubit from all layers and\n",
|
||
" # specify the range so the same one is used for all layers.\n",
|
||
" if qubits is None:\n",
|
||
" qubits = range(1 + max(coupling_qubits(layer_couplings)))\n",
|
||
"\n",
|
||
" # Generate the entangling layers\n",
|
||
" layers = [\n",
|
||
" entangling_layer(gate_2q, couplings, qubits=qubits)\n",
|
||
" for couplings in layer_couplings\n",
|
||
" ]\n",
|
||
"\n",
|
||
" # Construct the circuit for a single Trotter step\n",
|
||
" num_qubits = len(qubits)\n",
|
||
" trotter_step = QuantumCircuit(num_qubits)\n",
|
||
" trotter_step.rx(theta, range(num_qubits))\n",
|
||
" for layer in layers:\n",
|
||
" trotter_step.compose(layer, range(num_qubits), inplace=True)\n",
|
||
"\n",
|
||
" # Construct the circuit for the specified number of Trotter steps\n",
|
||
" circuit = QuantumCircuit(num_qubits)\n",
|
||
" for _ in range(num_steps):\n",
|
||
" circuit.rx(theta, range(num_qubits))\n",
|
||
" for layer in layers:\n",
|
||
" circuit.compose(layer, range(num_qubits), inplace=True)\n",
|
||
"\n",
|
||
" circuit.metadata[\"physical_qubits\"] = tuple(qubits)\n",
|
||
" return circuit"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c8ce28f6-91fe-4776-a127-84002a14f40d",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Define entangling layer couplings"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ee25eb37-9519-48ff-b307-c4f66846e3fd",
|
||
"metadata": {},
|
||
"source": [
|
||
"To implement the Trotterized Ising simulation, define three layers of two-qubit gate couplings for the device, to be repeated at each of the Trotter steps. These define the three twirled layers you need to learn the noise for to implement mitigation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "6587f181-487a-41f5-977d-a8abb1079c07",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Layer 0:\n",
|
||
"[(4, 15), (6, 7), (8, 9), (13, 12), (20, 19), (22, 23), (24, 34), (26, 25), (28, 27), (30, 31), (32, 36), (35, 47), (37, 38), (40, 39), (42, 41), (43, 44), (50, 49), (54, 45), (56, 57), (58, 71), (60, 61), (62, 72), (65, 64), (67, 66), (69, 68), (77, 78), (81, 82), (83, 92), (85, 73), (87, 88), (91, 79), (93, 106), (94, 90), (97, 98), (100, 99), (102, 103), (105, 104), (108, 107), (109, 96), (114, 115), (117, 118), (121, 120), (122, 111), (125, 126)]\n",
|
||
"\n",
|
||
"Layer 1:\n",
|
||
"[(1, 0), (3, 2), (4, 5), (10, 9), (11, 12), (14, 18), (16, 8), (17, 30), (20, 33), (21, 22), (24, 23), (27, 26), (28, 29), (36, 51), (39, 38), (41, 53), (42, 43), (46, 45), (48, 47), (52, 56), (54, 64), (55, 49), (57, 58), (59, 60), (62, 63), (67, 68), (73, 66), (74, 70), (76, 75), (77, 71), (79, 80), (81, 72), (84, 83), (85, 86), (88, 89), (93, 87), (94, 95), (97, 96), (99, 98), (100, 110), (101, 102), (104, 103), (107, 106), (108, 112), (113, 114), (116, 117), (118, 119), (122, 121), (124, 123)]\n",
|
||
"\n",
|
||
"Layer 2:\n",
|
||
"[(2, 1), (4, 3), (6, 5), (7, 8), (10, 11), (12, 17), (14, 0), (15, 22), (16, 26), (18, 19), (21, 20), (25, 24), (28, 35), (30, 29), (31, 32), (33, 39), (34, 43), (40, 41), (44, 45), (46, 47), (48, 49), (50, 51), (52, 37), (53, 60), (55, 68), (58, 59), (62, 61), (63, 64), (65, 66), (69, 70), (74, 89), (75, 90), (77, 76), (79, 78), (80, 81), (82, 83), (85, 84), (86, 87), (92, 102), (95, 96), (98, 91), (101, 100), (105, 106), (110, 118), (111, 104), (112, 126), (114, 109), (116, 115), (120, 119), (122, 123), (125, 124)]\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"layer_couplings = construct_layer_couplings(backend)\n",
|
||
"for i, layer in enumerate(layer_couplings):\n",
|
||
" print(f\"Layer {i}:\\n{layer}\\n\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bed79488-f197-4f4d-af6e-4b0c0c91f95b",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Remove bad qubits"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "846ee187-85b3-47f1-87c2-9c2e52e61d89",
|
||
"metadata": {},
|
||
"source": [
|
||
"Look at the coupling map for the backend and see if any qubits connect to couplings with high error. Remove these \"bad\" qubits from your experiment."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "401e2d48-1b39-40c8-bf32-7b439ae0980d",
|
||
"metadata": {
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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mcXlizlsXLPN5f02fmYziTEJHk3ZaEkaGjn5zvsaGx9NnwE9CI8IZfnCtZSWOB/ZDQoMJDo8yu37564FRVGottSQV+j8YB8ZHUGb9Fa0bZ/GojkrnC4n7XhtOEbViLUJ90VeC1XVVVS5uKKampZM154dMZvNLJqzwuV+HR0ZSaA50CtHzgwGA0WlxVRWOZ+S16FzOh27pFNba2HVknUuZ3W2apWMYvHOIgqgvLzCZeEbmxBNUmoCB3Y1fG9nWloKWrV3Hpd0dC7m52Cx1V84qAaVMZOGYzCo5OUUsGfbAafbUhSF9NZpWCu9M1vtmp2zORew2us/lphMRgYN7UtCUhw7t+zj3Nksp9uqy1a7lx6XMChcznF+lTGtbSpJyfFERIYTHhnKkYMnOLDnSL2vDQjwJzIqgkonjzi43mw2m8sVNXv27UZlRSWnT2Yy8+7JzP1ksdPXhoQGYfI3NWqFzuvBarW6LPJHjR9KzuU8Rk8YyqWsbDas3up0KnZwcBBms9krzyNUVcVitVBR4byQmjZrAof2H6NTt/aEh4eyeN4qyssq6n1t+05tefeLFwkJDW6pJnurNVeuSJUUlTpCzfEQ7u8wGFSCggJZ/9VWevTp4nKruq5TWlLepJtqrwWjydhgMJvNJgIC/RvclqZplBaXodm978QMwGhy/YDD0pIyVi5eS7uObRr8vGw2u6P48L5jgkMDz3KsKK/k+JEMJs0Y2+DzZywWK2Ul5V47R9+Gzem+ChAZFU67jm0AvcER/cryKnQNr52CYNNcfy8DAv0pL6sgJTWxwW1VVVZjr/bOfqqq6ihmXXyuXXt0pLbWQlBwYIO3xpUUlWLSvO/KGzgywq67LnyK8ovp1L09AYH+DS68UVJYisHunSv36bre4D2bAQF+hIaHNHjDt67rFBWUoNq8s0C2a5rje+nkO6waVAKDAgkIDCCtbYrLQkrTNEpLytG98CQUHIOUTimO4igg0B8/fzMb12ynU9f2Tl9usVgozC/26B66Fld3vPnW56ooCoFB/tTU1DTqvKm6qoaKykqvHbgDQAGlni+wqqoEBQdSWlLGqqXrSW/f2uV5U01NLTVVtV45cKcoCoqLr7DBoBIYHEh5eQXHj2QwecY4VBezGwryixq19P+N6Bv3SLmiaRqartG9T+dGrmjmfV+cxlIUhc7d2jf60rM397Sh/TcoOJB2Hdtg9vMjJi762jTqOgkNC6F1eivH/H0vPLA1p9MnM6msqMRoMjZ4cHP8Knz396EoColJ8ezYus/lccwnethAIy+cv4Sfv5ncRix37+tf8ei4KDRNY/CIfg0u+e2NJyrusFis5OcWYjA2MBqEb/fVaDQSHBLE5awcypyMbH+Tb/bVbDbRq1+3r09WVbr16oTF4nxWgH7V//c1AYGOB7SajEY6d+9AWFiIy9fr+O6xKSwilC7dOhAaFkzb9mkEBPkTFR1Z72sdseqjHQXiEmJp2y6NiIgw0tqkfr2KZv2vdXymvttXT125IhURFY7RaHA6Emq3a2zbuJv2ndqyf/dhlxtVFIXouGgMXjo3XzWoZDp58jg4vhDHj5xq9IP14uJjUF2V9teRjk7mOeeXbstKK8g8c4GgkCCXo4PguJIXl+C9fa2x1FJW5XxENz+vkOSyCg7nF1FW6jrE/fzMxCXE1Dsqdb0pikJpRZnLvgJsWL2NxJT4Bq80hYQFERIS4pXTDwCKiospLXU+DfPi+cu0ap3c4MCHAgSHBBEdEYkni5G0FFVVuZyTjaXM+UDV4f3HMJlMZJ271OD2omIiCDIHeu35WW5Ovsvp31ExEZhMJooKSlAUxWVQx8RHYVK887lZuqZTcs75lXzNrrF3x0HS2qZw7KDrlcIUVSEuMQaD5p3HYKvNRu7pfKe7V1VlNTu37CU+MY5jh0663JZqUImNj0H10udmabpG6dn6j0uWWitrV27CaDSiaRrp7Vuzz8XKfGazmaTkBKxeuvpkdVUNRU4WEKmuqmH5wjWUl1VQWVlNba3rBUICAwMIiwzFavXOq28VFZWO2Sj1KC0uY/4Xy7iUlY3BYMA/0J+sC/Uv0KYAAUEBRIR7571giqpSVlpGcXH9t/Pk5uQz//NlXDh/mYioCA7sOUKlk2mAChATG+2oIW5CV+6RslisPHz7Mxw73PQlH+sYjQZ++cdnGpwCeL1UlFfyq2f+xOVLuR5vKzg4iD/+65e0bpvaDC1rftmXcvndz551eu+bO+ITYvm/f/yCuPiYZmhZ8zt+9BT//L//urx5srHadWzDL//wA699MO+2zXt4+d9vN3jDdmP0H9KLp3/2CAEBDU9lvR4Wz1vFx+/OaZZ788bdNoJHnroHk8k7p7y9/8bnLFuwullG9+5+eCYz7rjNSx/gqvPqP95jz7ZmeKSCAo//+D4Gj+jv+bZagM1q4y+/eo5TJzxboRAc2fqLP/2ALt07NEPLml95WQW//OGfyW6ObA0J5A///AVprVOaoWXNL/tSDr9tpmxNSIrjD3//OdEx9V/duN6OHc7gP39+tVmytUOXdH72u6cIbeDK1fWyZeNOXnv+vWbJ1n6DevHMzx9r1G0i15qiKCyet5KP35nbLKsoTp45jt/99Sc344N5/3ePlNFoYNiYwRw/kuHx1cjo2ChuHTWQWC+dKmaptTBk+ADmuLghsrGSWyVyy/D+BAR654pncYkx9OjTlQ2rt3q8rfQOrek3uJfXjjqERYTQOj2Vw/uPe7QdRVHo2rMT3ft2wdDAvVTXiznAzBcfLuDiBc+WfTYaDfQZ0JMu3Tt8vRqR95k4dRQLvljWpAcGXs3P34/Bw/vTvnNbLy0uYMLUkaxass7j+weCQ4IYPKwfrdunemVfdV1n5G23snf7IY+LxrDwUPoP7U1q2ySv7KumaQwdO4jTJzM97mt0bBT9b+1NdKx3nnBbai0MHtaPeZ8u9XhbyalJDB7Wz2sHeGITo+neuysb1zRHtrah3yDvzdaIqHDmf7qUwweaIVt7dKJn325em60BgQHM/WQJF51caWoso9FI/0G96Nqzoxdn62jmf7Gc8mbI1n4De2G+CVfsg6vukVIUhZHjbqFVG89Gf4xGA1NuH0dkZLinbWsxJrOJSdPHEh0b5dF2/PzMzLp7sldX4MHBQUy9fYLHy28GBAYw696pXnvwA8dKdZNmjG3UfQauhIaFMH32RK/ua0JSHOMmj/R4aeu4hBgmTh3ltQd6gDbt0hg+ZojHJ8ntOrRm6MiBXnmyXadrz070H9Lb4+307t+dbj07eXVf+wzqQcdu6R5tQ1EVbh09kKTUBK/tq6IoDBsziJS0hhdDccVoNDBhxijCI73zKjk4snXitNFEeXhlxc/PzMy7J+Hn593ZOm3WeI8fGxEQGMAd90zx6ryJio5g0sxmyNbwEKbPnuDVfU1MjmPc5BEeZ2t8YiwTp432+mwd0SzZ2oZbvTxbW9I3CqnW6a2YOmtCk0dFFMUxsjJt9gSMJu+crw6Ovnbv3Zlxtw1v8pdcURT6DOjBqAlDvXpHURSFIcP6MWRY/yZ/yVWDyqhxt9J3YA+v3lEURWH0hKEeTSk1moxMmTWedh2989kldRRFYcqscbTr0KbJ2/D392P2/dNISI5rxpY1P5PJyOz7p5GY3PTnlwUGBXDvI7OI8OIBHnBcSbrroRketTMsPJR7H73dq5ehVRSFmLgopt09Ef+App8sxybEMOO+2zzaRktTFIW09FQmzhzj0Ylomw5pTJo5FqPR+7N1zMRhHmfryHG3uFwl7HpTFIXBw/oz2MNsHT3+VvoM8IFsnTiMHr2bnq0mk5FpsyaQ3rHpmXUtKIrCtFkTPc7WO++f7lFmXQsmk5HZ93mWrUFBAdz36CyvfS7YtfCNI52qqsy8exKTZ45rUjEVlxDLT377Pa99qNzVVFXlkafuYfiYIW7fzKoo0LptKj/9zVNef2IGYPYz88NfPkbvft3cfq+iKHTr2Ykf/PxRgrzwoXLfFhYRys9+9zRt26e5/V5FUbhleH8eevJOr3xg69UURSE5JZGf/f4pYptwz5qqKkyaOZbpd3rrPTT/oygKnbu254e/fLzBFaHqYzKbuP+x2Ywce0sLtK55KYrCgCG9efT79xDYhOnCgUEBPPXTh+jZxzsf2Ho1RVUYPmEIM+6bhNnP/f0tLDKU7/38AVq1TW6B1jUvVVWZducEJkwb1aRiKi4xhh/86lFiE7xzuvzVVFXl4afuYuioQe4fWxRIa5vCj379BOE+cGLm52fmR794nF593d/fFEWhe6/OfP/nj3rtw9CvFh4Rys//8DRt26W5/V5FURgyYgAPPnnXlYe7eitFUUhJTeTnv/t+k+4HV1WVKbePZ4avZGu39vzwF4816Z41k9nE/Y/fyYgxQ1qgdb7jymITdXRdp7iolNeff59l81dTXd3wQ9NUVaVVm2R+9runvfoemm/TdZ3LF3N4/tk32LBmK5ZGrJhjMBjo3K09v/q/Z+jSw3vnvn6bruucPnmW//z1NXZvP9CoZ3yZTEb6D+7NT37zJG3bpXn9QaGOrusc2HOEF//+JkcPnmzU85H8/M2MGDuEp376MInJ8T7TV82usXn9Tl7+19ucPXW+UfdgBAUHMnHaaB7/4f1ERUdcg1Y2D6vFyqql63n5P++QczmvUX0Njwjljvum8cBjswkOCboGrfScruvUVNey4IvlvPPyJxQXlTTqfdGxkTz05N3MuHOiV083vpqu61SWV/Hl+4uY99EyqioafiCpoijEJkTz2E/uY+iYgV4/6FFH13VKikp556VPWLloPTWNzNbU1kk88+vH6DOwh8dTq64VXdfJvpjLC39/k01rt7uVrT//w9N09uJ7Nr9N13VOnTjLc399jd073MvWn/7mSdr4WLbu332YF599k6OH3MnWW3j6Z4+QmBznM3212zU2r9vOS/96y61snTxjLE888wCRPpatK5eu45X/vOtGtoYx+76p3O9D2dpC1nynkIK6IK9h9fJNfPruPM6eOlfvUuCqqhIQ6M/4ySO566EZtE73zhubXdF1nfKyChbPW8XnHyzgUlZ2vSuYGAwqIaEhTL9jomM6VJLvHBDq6LpOUWEJcz5exPwvllOQV4C9niWvDQYD0bGR3H7XZG6/ZwoRkWE+1de6r3T2pVw+/2AhyxaspqykvN6DvsFgIDk1gdvvmczUOyYQGBTgk309k3GOz96fz1dLN1BdVY1Wz0N4jUYDbTu05q4HpjNuykjMZpNP9vXQ/mN8+t481q92DH58+xCmKApGo5GuPTtx3yOzGDZqEAajwef6qmkau7bu57P357Fzyz5sNtt3FgJSFAWz2UTfQT25/7E76D2gO6qq+lxfbVYb2zfsYc4HSzhx6FS9J6OqqmD282PQ8L7c8dAU2ndp6zMn23XqiuT1Kzfz5QeLOXf6Qv3ZalAJCPBn9G1DmXX/FFq1TfGpzxT+l61L533FFx8t5HJWjpO8UQkJDWbqHRO4496pxCfF+mRfiwqL+fKjxSz4chkFeYUus3XW3VOYefdkn83Wyxdz+Pz9BSxbuIaykrJ688ZgMJDcKpFZ90xh6h3jfTZbT2dk8ul781i1dD3VVTX1nkcYjQbadWzLXQ9MZ8KUUZh8NFsP7jvKp+/PZ8NXW7FYnGdrt16ObB060veytQXUX0jV0TSN4qISdm3dz5K5q9iz49CVZ81ERYcz5Y7xjJpwK63bpvrMCKgzdrudgrwitqzfwa7t+8nLLaC21oLJaCQ8MowevbswfPRgUlol+cwIaH10Xcdus5OTnceGNVvZv/swRYUlWGotmM1mIqMj6DuwB7cMH0hCUqxXz8dviK7rWK02ss5fYtOa7Rzef5zSkjKsVht+/mZiY6PoP6QPA2/tQ3RsJAaDb4z21kfXdSy1Fs6cOsf6VVtZv3gT5SUVoOuO6ZkDuzBq0jD6D+lNeESoz52AXk3Xdaqrazh59DTrV2/h9MlMyssq0HWdwKAAUlolccvwAfQZ0IOQkGCPbxq+nnRdp6K8kqOHTrJh9VYuZF6ksrwKFMfoZ+u2qQwdNYiuPTv53InKt+m6TllJBYf3HWfHht1kX8yjuqoaRVUJDgmiTftUhowaQNsOafgH+Pl0XzVNo6SolD3bD7J8/lr27zh05QQtMjqCSbPGMGzsYFq1ScHP37dXwqrL1q0bdrJ7x0HycwuorbFgMtVla2duHTWIlNTEGyJbsy/nsXFtPdkaE0G/AT0ZMnzADZWtG1dv4/CB45QWO7LV399MTFw0A4b0ZuDQvkTH3BjZejrjHGtXbmLR3JUUF5bgeECfwpDh/Zk4dTQDhvQmPCLM97O1qoaTx06xfvXW+rN1xED69O/u89najFwXUldbu3wzf/rFf65cou/VvxvPvf1H/L10aVJPaHaNysoqamssGE0GgkOCfPqg54yu69jtGpUVVVgtFkxmE8EhQT590HNG13VsNjuVFVXYbDb8/MwEBQf69EHPmerKGt7/w/ucPnAGcIwiPfrXh+nQr4NPn3zWpy7kKiur0DWdgEB/AgJ9u6BwRtd1ampqqaqsvvKwR39/3y4onKkL9JrqWlRVISAowOeuoDbW+hVbePb/vYil1vGA0p79u/L313/n1QtoNNWVbK21YDRKtt4IbqZsLS+r4CdP/p49Ow6A7sjW/777LIOH9rvhjk3fzdYAAgL9b7h+NoM1N94RrBmoX081CPHeVWabheMyrYGwcO98MF5zUhTFMQLqpQ/YbV46mqajfz3dQkf3+Nlw3kpRFPz8/Xz+inhjKIpCQIC/1z5XpzkpikJgUIBP3ITvsZvoxORKtl7vhrQwydYbl2bXrszMAr4z/e1GcTNlq6duvCEDIYQQQgghhGhhUkgJIYQQQgghhJukkBJCCCGEEEIIN0khJYQQQgghhBBukkJKCCGEEEIIIdwkhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG6SQkoIIYQQQggh3CSFlBBCCCGEEEK4SQopIYQQQgghhHCTFFJCCCGEEEII4SYppIQQQgghhBDCTVJICSGEEEIIIYSbpJASQgghhBBCCDdJISWEEEIIIYQQbpJCSgghhBBCCCHcJIWUEEIIIYQQQrhJCikhhBBCCCGEcJMUUkIIIYQQQgjhJimkhBBCCCGEEMJNUkgJIYQQQgghhJukkBJCCCGEEEIIN0khJYQQQgghhBBukkJKCCGEEEIIIdwkhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG5qVCGl2TVsNhuqqoACiqKgKGC12NB1vaXbKIRoJF3XsVlt2O12NF1H0zV0dCwWi+yrQngZza5hs9pQ1K+jWHH8sVqtsr8K4UV0XcdqtaFrmmM/xXEubLXIvnqzU3Qn3wBd19F1nQvnLrFu1WZ2bdvPyWOnqaqsxmBQiU+IpfeA7gwZ1p9Bt/bFz98PRVGudfuFEDj219qaWrZu3MX2TXs4sv0oFSUVaLqOyWQktVMqvQf3YOS4W0hNSwaQ/VWI6+DqbF3/1RZ2bdtPxrEzVFVWYzQYiE2MoXf/bgwZ1p+Bt/SRbBXiOqrL1i0bdrF14062bNhJUUExmq5jNpno0bsLg4b2ZeS4oaSmJQGSrTeZNfUWUrquU1RYwoIvljH/s6XkZOdjt9vr3UJQcCC9+nbj4SfvpmffbhgMMltQiGvJZrNzYM9h3nn1Ew7tP0ZFeWW9rzMYVBKS4pl2xwRm3T2FsIhQOeALcQ39L1uXM//zZeS6yNbg4EB69u3GQ0/eRc8+XSVbhbjGbDY7+3cf4t3XPuXgvqMuszUxOcGRrfdMISxcsvUm8t1CStd1ci7n8a8/v8KmtduwWm2N2lJ8YizP/Pwxxk4agdFokC+RENeAzWZj2cI1vPqfd8jJzm/Ue4wmIyPHDOGnv32KuIRY2VeFuAbqsvXff36Vjeu2Y3MrWx9lzG3DJVuFuEZsVhtLF6zmlefeIdedbB17Kz/77VPEJcTIvnpzWGP89t+UFJXyt989z5YNO9G0xs/7zLmcx7/+8jIms5ExE4c3ZyOFEPXQNI31X23lX3/6L+Vl9Y+U1cdmtbFm1WZsmsbv//pTIqLCW66RQgigLltfZOvGpmTrK5jMJkZPGNqCLRRCgCNb1321mX/+6b9Or0LVx2a1sWblRux2O7//m2TrzeIbcwVsNhsfvzuHbZv2uHWgr1NcWMprz79P5pkLcvOdEC1I13XOZJzj5X+/7VYRVUeza2xet4PPPpjvdGqREKJ52Gw2Pn5nLts3e5CtL7zPOclWIVqUruuczsjkv/96x60iqo5m19i0brtk603kSiGl6zonj51h6YLV2GyNm3JQn3Nns5j36ZJGTwkUQrhP13XmfLKYc2ezmrwNq8XKvM+WebQNIYRrddm6bKGH2Xomi3mfL5NsFaIF6brOlx8v4nymp9m6lHNnJFtvBlcKKU3TWb18Q6PngjqjaRrLF62lIK/Q48YJIep37swFNq/f4fF2igqLWTr/Kxk5E6KFOLJ1I7k5BR5uR2OFZKsQLSrz9AU2r/M8WwsLilm6QLL1ZnClkLLZbGzduMvltIGg4EAAjEYjZj+z09eVlZZxaP+xZmymEKKOruscPnDc5QlVQIA/RpORsPBQwiNCUdX6V/zSNI0jB09QVlrRUs0V4qZms9nYuqHhbDUaDURGhRMQ6O/0daUl5Rw5eKIlminETU/XdQ7tP0ZhfpHT1wQE+KMaVAKDAlwuJqFpGocPHKe8TLL1Rnfl7Kq4sIS8HOdXo0xmE1NmjqNzt/ZMnTWB26aNwWAw1Ptau13j2JGM5m+tEAK7XeN85kUsFqvT1wwbPZi0Nin06tuVUeOHkZAU6/S1585mycFeiBZSVFhCXq7zq1Fms4nJM8bStWcnBgzpw5iJw5yeoNntdo4dlmwVoiU4sjXLdbaOGUJMbBS9+3cnNj7a5fbOS7beFK4UUqUlZdjtmtMXBgcHYjAYCAwMICDAj8L8Iuxa/ZcsdV2nqKC4+VsrhECz2yktKXP6c6PRQGBQICaTiYCgAGw2Gzab8+kF5aXlWCyWlmiqEDc9R7bawckFqaDgIAwGAx06tcU/wIzNZnd69UqyVYiW03C2GgkKCgAUDu49So9eXTAa67+gAFBaWo6l1nlRJm4MVwopZ1N/6n7WoUs7/Pz9OHLwBAGBAWi65jQYGtqeEMIDiuJy/woOCSa9fRqaphEWFkJBXqHTcNABRVXleRdCtBCDi/1LVVU6dknHz9+PjBNnMZvNVFdVu9yeKg/mFaJlKK7PXUNCg0hv35qgoADadWhDaptkUtKSnb5eVVUkWm98V54jFRUTicn0ncdKAY65nru37+fi+cvU1NQy//OlLk+8VFUlMTm++VsrhMBoMBAdG+n05yXFpXz49peUlZSjqirBIUFO91cFiI6JxN/fr4VaK8TNLSomEqPJ6NjZvqUuW7POXyY3Jx+bzc6lC5edbks1qCQkxbVga4W4eRkMRpfZWlxUyodvfUlNTS2R0RGcOHKKMhdXsKJjIvEPcH7Po7gxXKmcQkKDaN02laLCknpfaLfZufj1Ab6wgakFqkGlW89OzddKIcQViqrQJj2NwKAAqirrH73OuZwHwPFG3KvYOj2V0PDQZm2jEMIhJMSRrcVOstV2VbYebmCRJlWVbBWipaiqQtt2aQQG+lNVVVPva7Iv5wKwZ8eBBrfXOj2V0LCQ5myi8EJXrmEaDAZGjLu1WabkpaQm0alLO4+3I4T4LkVR6Nm3K3EJzheQaCyT2US/Qb0I/npFTiFE8zIYDYwYM6RZsjW1VRIdJVuFaBGKotCrbzfiEjy/6msym+g/qPeV1a7FjevKkV1RFEaMvYX2ndp6tEGzn5mZd00iLEJGuIVoKdExkcyYfZvH90u0SktmwpRRco+UEC2kLlvbdWzj0XbMfmZm3HUbYeEywi1ES4mOjWLGnbd5PPCR1jqZCVMlW28G3yikkpLiuevBGS6fY+GKoij07NOVSdOdL40uhGge4yaPoO+Ank0+UIeEBvPA47OJjApv3oYJIa5QFIWk5HjuemA6AU28X6IuW2+bNlqyVYgWNn7ySPoO7NHkhSJCQ4N54Ik7JVtvEt8ouRVVYcLkkdz9wAz8XDxwtz6KotAmvRU//e1ThEeGNWsjhRDfpCgKsXHR/Ox3T9GqtfNVg5wxGo3c9eAMxk8eKSNmQrQwRVWYMGUkdz0wvYnZmspPf/M9wiMkW4VoSYqiEBsfzc9++zSt0lLcfr/RZODuh2YyfpJk681C0b/1wApd16mpruGT9+bx0TtzKCkqbXAjRqOBnn268os//IB2HdvI0udCXCO6rnPs8Ele+Psb7NlxEE1z/iy4OlHREdz36B3cce9Umb8txDXiyNZaPnlvHh+/M5eS4sZla48+XfnlH75PeofWkq1CXCOapnPs8Amef/YN9u5sfLbe/9hsydaby5rvFFJ1LLUW9uw6yEdvzeHwgWNUVlR954vk5+9HVHQEM+68jSkzxxEbHyMVuBDXQfalXJbMX8X8z5dRVFBMbe03H7CrGlSCggLp0acr9zw0g/6DejuWZBZCXFOWWgt7dh7i43fmcPjAcdfZOvs2Js8cS2x8tGSrENfB5Us5LJn3FfM/X+oyW3v17crdD91O/0G9JFtvLs4LKXCMoFlqLRw+cJyFXy5nzYrN2Gw2FCAhOZ4HHruDW0YMJCYuSkbKhLiOdF1H13Vyc/LZsn4HH741h+xLjmVaFRQm3z6W26aNoWvPTpjNJjkpE+I6+ma2rmDt19mKAonJ8dz/2B3cMmIAMbGSrUJcT1eyNTufzeu289Hbc8i+lAfoKIrCpJnjmDRdsvUmtsblEVpRFPz8/eg7sCfDRw9BVVR0u45m10lIiOW26WOIS4iRA70Q15miKKiqSkJiHBOmjCYxMR7drn+9v2qMGj+U3v274+dnlgO9ENfZ1dk6bNRgFAU0u4Zm04hPiOW2aaOJi5dsFeJ6u5KtSXFMmDqaxKR4dE1H10Cz64yeINl6s2v09UddB13TqLuApWk6Ti9lCSGuq7pRtP/9xfVrixDCBV135OnX+6veiHsxhBDXx9X7KiDZKpDhLiGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG6SQkoIIYQQQggh3CSFlBBCCCGEEEK4SQopIYQQQgghhHCTFFJCCCGEEEII4SYppIQQQgghhBDCTVJICSGEEEIIIYSbpJASQgghhBBCCDdJISWEEEIIIYQQbpJCSgghhBBCCCHcJIWUEEIIIYQQQrhJCikhhBBCCCGEcJMUUkIIIYQQQgjhJimkhBBCCCGEEMJNUkgJIYQQQgghhJukkBJCCCGEEEIIN0khJYQQQgghhBBukkJKCCGEEEIIIdwkhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG6SQkoIIYQQQggh3CSFlBBCCCGEEEK4SQopIYQQQgghhHCTFFJCCCGEEEII4SYppIQQQgghhBDCTVJICSGEEEIIIYSbjI15kdVqo7KyClVVURQFFNA0jcqKKvz9/Rx/dwPQdR2LxUpRQTFlZeVYLTYMBgMhoUFERoUTEBhwQ/W1tqaWwoJiyssrsdlsGI1GQkKDiYqKwD/A73o3sdnouk51VQ2FBcVUVlRit2uYTCZCw4KJjI7AbDZd7yY2G13Xqayswm63X/muqqpCRUUldpsdo6lRu7xP0DWd0tJySopKqKqqRtfBz99MREQY4RFhGIyG693EZqNpGqXFZZQWl1FdXYuigL+/H+GRYYSGh6CqN86YmN1up7iwhJKSMmprLKiKQkBQABGRYYSGhdwwx2Bwlq06FRVV+N1E2RoYFHi9m9hsrs7WivJKbDY7RqOBkNBgIm/AbK2qqqaooJiKckfumM0mQsNCiIwOx2w2X+8mNhtd16mqrEazayiqAjqoqnpjZquuU1ZSTvHX2Qrg5+dHeEQo4ZFhGAw3VraWFJdSUlRGdXWNI1sD/ImIDCMsPLRR2arouq7X9wNd17FarBw9dJKlC77i4L6jXMi8hM1qQ1EUwsJD6NStPUOGD2D8pBGER4b5bJjruk5NTS37dh1i+cI1nM44y+WLudTU1GAymYiNj6F121SGjRrEqPFDCQ4J8tmAqzsYbNu0m6+WbSDzzHlyLudhqbXg5+9HXEIMbdunMWrcUG4dMRD/AN8Nc13XKS+rYP2qLWxcu53zZ7LIzy3EarMSEOBPQlIc6R3aMG7yCPoM6IHZz+Szfa07GCxfuIZtm3Zz7NBJysoq0HUdo9FI67YpdOvVmckzxtG5ewdMJqNP9lXXdTRNJz+3gCXzVrFn50Gyzl2iqLAYHQgJCSK5VSJdunVg6qwJtElv5bMB5+irxsXz2SxfsIbD+45z6UI2pSXlKIpCaHgwKa0S6da7MxOnjyIxJd5nA07Xdew2O6dPZrJkwVccPXiCi1nZlJdVYlBVIqLCSU1Lot+gXkycOorYuGhUg+/mjdVi5cihEyyd78jWrMxLWG112RpK5xstW3ceYvmi72ZrXHwMaTdUtlaxbdMeVi/fSObp8+Rk538zW9ulMWr8rdwyfIDPZ2tZWQXrVm5mw5qtnDtzgfy8QqxWKwEBASQmxZHesQ0Tp46mT//umP3MPtvXK9m6aC3bN+3h2KEMysvKr2RrWnoq3Xp2YvLMsXTq2v4Gydav2LvrIBfOXaK4sAQdnZCQ4CvZOuX2cb6frXaNrPOXWDxvFQf2HuHShWxKikuvHINT0pLo2bcrk2eMIzk1wVW2rqm3kNJ1nUtZ2bz/xuesWLyWyooqnNRbGI1G2rZL45Gn7mbUhKEYjb71i9V1nVMnz/L2yx+zce02qqtqnL7WbDbRuXtHnvjBfQwe2t8xKuFDNE3j8IHjvPHiB+zdeZCamlqnr/X396N3/+48+aMH6dars88dGGw2Ozu37uWtlz7ixNFTWGqtTl8bFBTA4OH9eeKHD9A6PdXn+mq1WFmzchNvv/Ix585mYbXU31dFUQgJCWbspOE89v37iE+M9bm+1tTUsujL5Xz87lwuX8zBZrPX+zpFUQiPCGPGnbdx78O3ExEV7nN9rSivZO5HS1jw2XIK84uw27Wvf6ID/+uLqqpExUQw+8FpTJ09nqDgQJ/ra0F+ER+/PYdFc1dSWlKOpmn1vs5gMJCUEs8Dj9/JbdNH4+/vW6P7uq5z8UI277/+GSuWNCJb26fx6FP3+G62njjL2680Llu7dO/I48/cz+Bb+/lmtu4/zhsvfci+XYcazNY+A3rwxA/vp1vPTj63r9psdnZs2cMbL77P8aOnsdRanL42KCiQW0YM4MkfPUjr9FY+11erxcqaFZt49/XPOHfmAlarrd7XKYpCSGgQY28bwSNP3e2z2brwyxV8+t48l9mqqo5CY8adt3HPQzN9MlvLyyr4/IMFzPlkMQX5hVdl6zepqkp0bBT3PjyTGXdOcjbQ891CStd1Mk6c4W+/e5HD+486/Qe+LTwilAcfv5M7H5zhM9P9NE1j/+7D/PV3z3P21Hmn4f1tcQkxPPmjB5k8YxwmH5kWZrfb2bBmG//+8ytkX8p1Gt7fltYmhWd+8RgjxtziMyPANquNRXNW8saLH1KQV9io9yiKQscu6fz4N9+jz4AePvH9BaipruXDt7/g43fmUFJc1qj3qAaVnn268us//Yh2Hdv4TF/LSst546UPWPD5Miorqxv1HpPJyOCh/fjVH39IQlKcT/RV13UK8op4/T8fsGb5RpeDAFfz8zczeuJQnv7lI4RHhPpMX7POX+bff3mVbZt2Y3NyovJtQUEB3H7PZB59+l6fuYqh6zoZx8/wt9+9wKH9x7Db6z9R+bbwiDAeesL3snXfrkP87XcvcPa0u9n6EJNnjsVk8p1sXb96K8/99fUmZOujDB8zxGeuONqsNhZ8uZzXX3iffLeytR0/+93T9PWpbK3hw7fn8Ml78yhtZLYavs7WX/3xGdI7tPaZvjqy9UMWfLGcKneydVg/fvmHH/hUtubnFfLSP9/iq6XrqXUxCHA1f38/xk0awY//3/cIjwz7dl/XfGfvzc3O5y+/eY4Dew83uogCKCku482XP2LJvFWNfs/1pOs6pzMy+ctv/sPpk5mNPtCD43f03LOvs3n9jkYfNK8nXdfZv/sw//zjf7l8McetNp87m8U//vRfDh045hN91TSNjWu3899/vd3oIgocv6PjR07xz/97mcwzF3yirzabnSXzVvLWyx81uogC0Owa+3cf4h9/fImcy3k+0VerxcrH787h0/fnN7qIAsc9KJvX7+Q/f3uNkuIyn+irpdbC2y99zIqFaxtdRAHU1lhYtWQDb734ETXVzkfEvUl5WQX//vMrbF63o9FFFEBlZTWff7iQT96d2+iC5HrLyc7jz7/+D/v3HnarzSXFpbzx3w9ZOt+HsvVkJn/57XOcznA/W59/9jW2rN/pE/tqXbb++0+vNClb//mnVzi8/7hP9FXTNDas2cqL/3yz0UUU1GVrBn//w4s+la2L533FO6980ugiCsBu19i3+xD//NPL5GT7ULa+M5fP3l/Q6CIK/petzz/7OqU+kq21tRZefe5dls7/qtFFFDiu1i1btIZXn3+v3mz9RiFVW2vhzf9+yJEDJxyzR9xUVVnNO69+wpGDJ7z+l1pTXcNL/3ybs6cvNOn9ZSXlvPLcu5w7m+X1fS0pLuP5Z18nNzu/Se/PvZzPi/94i4K8Qq/v66UL2bz09zcpKylv0vvPZJzj1X+/69YB5XrQdZ2jB0/w+ksfUlvT+APC/94Pe3cd4p1XP8Hu5BK+t9B1nc3rd/D5BwvR3BjcqaNpGuu/2sKcTxa3QOual2bXWL5gLauXbmzSvmaz2lg2bzVrl2/y+n3VZrXxyXvz2L55b5PaWltj4dP357Ojie+/lmprLbz50occOdj0bH37ZV/K1rfIbGK2lpaU88p/3uW8z2TrG+TmFDTp/TmX83jpn29RmF/k9X29eOEyzz/7RpOz9fTJTF7+19s+k61v/fcjt062//d+R7a+99pnPpKtO/nio0VuDXjU0ewa67/aytxPl7RA65qX3a6xeO5KVi1Z3+RsXThnBV8t++77rxRSuq5zeP8x1q/e2qRfaJ3c7Hzmfrq4SV/Aa6XuxGzvzoMeHbzOnDrH0vlfoWneewDUNI0Vi9dw8vgZj/p6cN8R1q/e2owta352u50FXyzn4oXsJm9D13W2btzFnu0Hmq9hLcBut/PZh/PJz21agIPjIPjVsg0cO5LRjC1rfjXVNXz6/nxKSxo/MvhtdpudJXNXcj4zqxlb1vyKikqY98kyl/eTNMRSa2Xh5yvIz238qPG1pus65zMvsmTeV1itjb/q9m3lZRV8+fEiykormrF1zUvXdQ7tP8oGD7M1JzuPuZ94f7ZuWreDvbs8zdZMli5Yje7t2bpoLRknPM3Wo2xYs60ZW9b87HY78z5bysULl5u8DV3X2bJhJ7t3HGi+hrUAu93O5x8ucOuq27dpdo3Vyzdy3Muztbq6hs88zFbH1btVnM+82Iwta35FhcV88dGiK6sQNoWl1sLcT5eQ963zriuFlKY5PviiguKmtxTHzrJmxSZyv76s6Y1/aqprWLF4HZUVlR71VbNrLFu4mrLS8uveJ2d/iotKWb18o9MFCBrLbrOzaM5Kaqprr3ufnP25fDGHzes8n25ZW2Nh8bxVWGot171Pzv6cOnG2WYq90pIyli9ag81mu+59cvbnwN6jHDt00uO+XrqYzYbV29Ds2nXvk7M/u7fu51wTR/KvdvLoGQ7uOXrd++PsD8CGNdvIvpTjUT91HXZu3ceZU5nXvU/O/miaY8CisDmydeUmcrPzr3ufnP2prq5h5deLaHjCbtdYuuArysq8PFtXbMRqafyU1PrYbHYWzV1JTY33ZuulrGw2rduOrnuWrTU1tSyeu5JaL87WjONn2bPzoEf9BMfVyuWL13l9th493AzZmpXNprXb0TTvzdYdm/eQefq8x309fiSD/bsPf2NfuLIMkNViY/uWPU7frCgKMXFRVFfVEBsfQ2lJKQV5RfW+trqqhmUL15Devo3HjW4JlRWV7HExKmI0GgmPCEXTNCKjI7h8Mcfp5ejiolLmf7GMlNSkFmqtZwryCjh+5FS9PwsNCyEmNgq73U5trZWw8BAunLvotK/Zl3JZMvcrYmKjWrLJTXbm1Dmyztc/YhYZHUF4RChWi5VLWdnExEW7nOqYeeo8q5dsJCQkuKWa65Gd2/dRVFhS78/i4mMIDglC0zVUVUXTdLIv5VJT/d2rHLruuBK9cvE6r10BbfWKjVRX1/+dTEpJwM/fD0ttLUaj0bFceFZ2vVMA7XaN7Zv2kJSYgMkLl21VFIWVi9bXf/+MAimtkjAYVUqLyygvqyQ4ONDpvXE2u41Nq7fjZ/LOZYdVVWHN8k3Ud15mMKiktk4GHFPagoIDKS+rcHqFzWKxsnLRekoLmzblqKXpmsbmdTvq/ZnZz0xKaiKarlNaUkZ4eCilJWVOi66qymoWzVlBxy7tW7LJTVZdXc2eHfWfhAYGBZCQGIemaxQVlKBpGuVlzq8klhSVsujLlaS28s5szcst4MTRhrO1pqaWwKAA8nIKqCivf/A2+1Iey+avJiIyvAVb3HQZx89w0Um2RkVHEB4Zhs1qw2azYTKZuJSV4/RKc8bxMyyZt5LQsNCWbHKTKArs3XWYYifZGhIaTGxcNBUVlQQE+KMaVC6cu1Tv/Z26rnPkwHFWL93otdn61bIN9Z4XAEREhRMZGU5RYTGVFVUEhwQ5Peew2zV2bt1HfHys1z6/cen8r5zemxoTF01ISBBWqw2z2YTNZiPr/OV6ZxBYrTb27jzImInDriyJfmXVvktZ2dw1+Qmnl/jMZhO33z2ZgoJiLLUW4uJj+OKjhfW+VgHCo8IpKWr65cKW5KhQnU+xiIgKZ+jIQZzJyCS1dTKaXWPlknX1vlZRFQL8A1wud3o9mc0mamvrb1tqWhK3TR/L0YMniE2IoazE8UAyZ6FvMhoJDQzD5uEIXEtRjArllfWfTHXoks7w0YPZs+MAB/Ye5c4HpvPJO3OdbisoKIBQvxCstd7Z1xprDaU1ZfXebtFvUC969unK8SMZdOnRkdMnzrJr+36nJy0hocHYLHa3bva/ljTdjuZkJHT0hKEkJMVzIfMiVquV9A6tWTx3FSXFpfW+Piw4BFUzNOk+lZamGlRsdhtW23c/B0VVmHz7WFSDgcL8IqKiI4lPjOHDN750OvARERoGnl2IbjEGo4Hc8nwstu820OxnZvZ9UykuLLkyhaJNuzS++HCh0xHxiNBw7LXeeT+C0WSkqLwIrZ7MCQkN5s4HpnPuzAUMBgO1tRYiIsNY8MVyp30NCgqk2ksXEzGbTdTU1H9iFhMXxcy7JnP8SAYXMi+SmBzPts27nU7fU1WViJBwrG4suHItGUwGSp3kTWqrJG6bPoajh0+SnBJPfn4xtdU1bHJWUJvNBAcGUV3hnfcP2TU7Nbb6P9dOXdszbPRgDu49ivL1gM+h/cecTmszmUyg4J15o4DZZMJqrf9Y0rNvV4xGx0qwF89fRjUo7Niy1+ntBKGhISh2sDvZ3vVmsVux2OvfvwYM6Y2CQkJyHDu27KFH7y6sXLLe6bYiIsKxVNZ67a0uFrsFm/bd75yqqgwe2g/VYKBTl3RUg4F9uw6xZ+cBp/e49ejTlXe/eKHukRT/W7WvvKzC6fxtRVGIiArHYDRQUVZBp67tMbhYClsHqr38hkJnVFUhKioCVVVJTXMUUalpzkfEdE33aI5/S3N1Kb64qJSvlq2nTXoqAf5+HD+SQWBggNPXa5runQe/r+m67vjy1dPlvOwCNqzeRpv0NCIiwhpcWtdqsXn15+rKuTMX2LFlD4nJ8axYvJaIyHCCQ4Kcvr62ptZnVj77tiMHT3D8SAYRkWHkXM4jPCLM5X0oFqvNK4soAHTn+6uu6ezeeoC87HwiIsMwmgxknr5ArYsBHE+n87YoF/uq3WZj3aotWC1W2rZLIyYumvycApfHMm/uq6t219bUsnLxWoKDg+jWqzORUeGUFJW6fI/FR/taWV7FisVrSUiMo6y0HH9/P6KiI11uy5uPwa7ypri4lK+WbyC1VRIGg4E2bVNdnmDabDaX+7I3y8nOY8PqrXTq2o7ElATMfiaioiOcvt5ut3tv3uiOQ5OzjLh4/jIKEBEVRkF+ETnZ+Zj9zE43V1NT6/ULTjjra+aZC/gFmDEYDERENvysqOrqaq8tolzRdI3TGZmEhAZRkF/EmhUbad02BdVFf0uLS78xm+JKNWQym5z+ohRFIaVVEqBQVVlNQX4hFQ3MgTb42MMD6yiKY1qJpmnU1NRiMhk5dTLTxevx8mdAOP8yBAcH0W9gL4wmE5WVVQwdNZiiQtfz+FUvflCiq5aFR4bSo08XgoIDSEyOdzkQAKCoKopXf67OxSXG0qFzOpFR4Qy8pQ9+/maXD/NUDQavnP7VGK3bppLSKon4pDh69+9Ofl6h00JKx7u/v4DjgFLvXyt07NaOqJhIykoruJyVQ2hYSL1T4+p493EJpzusqhroM6A7waHB2Gx2IqPCyc93feO3V/fVxVfOZDYx8Ja++AX4cfxwBv4B/qgG11NjvLqvLvgH+F05HvXo05WwiDCGjR7ssj++2tfg4ED6DeyJn7+ZstIKCvOLnM4MAcdxydDA5+6tIiLD6NG7C/4Bfmh2OxXlVeTmOJ82ryiKy5NUb5aSlkRyaiJnMs6RlBpP67apLlchNBhU789WJ81r37EN4RFhVFZUkZqW3ODjkAw+eh6hKgrde3XGZDKhGlT69O9BgIsLCjp8p3i+MrWvtKSMGWMepCC//vueFEUhMjqC0pIyUtOSybmU63T1C1VV6TuwJ35+3jkv1GKxsGfHfqdPbjYYDYSGhlBZUUlSSgJZFy47vRJjMpno3rsLQUGBLdnkJqutrWX39v1ORwpT0pKoqa6lqqKK2PhoLpy76HSHCQoKpG+fnvj7+7dkk5uspKSUvXvqXy1KURTS2qZSXFRCSVEp0TGRTr/rANExkfTu1R2D6p3hdv5CFoeP1v/8EYPBQJt2rci+lEtgYAB+/mYuZmU7nUKTlJJAevs2LgvR6+ns6XNkOVktys/PTGrrZLLOXSImLhqLxUpuTp7TUbZWrVLo2D4dxQsLKlVVOX70lNN79wKDAohPjOXCuUuoikJwaBBFBSVOt9eufRvSWiXjeojh+jAYVDZu3U5RcUm9Pw8LDyUyKpyc7DzS2qZSWV7JhXOX6n2tokDXrp1IiI9rwRY3naIqbNiwhWon9yJEx0QSGBRI9uVcklMTyMspcLpYg6qqdOvZmbBw77u/BByjuzs273aarQmJcSiqgslkJCQ0mNKSMi5eyK73OGY2m+jbrxfBQc6vpl9PNTU1bN2622m2pqYlUV1dQ3VVDTGxUVw4f8np1YmQ0CD69O2Bqnhn4ViQX8jBg0edZmvrtqkUFZZgt9sJjwjjYtZlp3kTFh5Kp67tMZm9b7BdQSEvt4CM42fr/bnRZKRNeisuZWXj5+9HQIAfly86fwhzUkqCI2+8ssDQOX0qk3Pn619tzz/Aj9S0ZM5nZqHZNQKDAl2u7te2XRqtUpNbqrGe0eHIkePk5tafrSGhwcTFx3A+M4vElAQqyispdHF+OGrcrfzrlf+rux9szZVCyma18cxjv2Hrhp0et9lkMvLqB/+kW8/OHm+rJZSXV/DMI/+PY4c9X5oyLDyUtz9/ntRW3vkFunwphx8+9huynJyEuCM1LZnXPvwX0THOL9tfT8ePnOJX3/+zR8uW1unZtyv/ePn3hIR642ITOts27eZ3P3uW8jLPVp4EGDNxOL/964+9tkBeMn8V//rTK1gsni/7fPeDM3n6Jw9jNHlngfzhG3P44LXPm2WKxNM/f4iZ90720hCHZ//wIovmrPR4O4oCf33+14wce0sztKr52Wx2fv70H9i6cbfH2zKZTLz2oZdn68O/4piTBY7cERYRyrufv0hyq8RmaFnzy76Y68hWJ4swuKNVm2Reff8fRLqYEnc9HTt0kl98/4/Nkq29+3XnHy//ntDQkGZoWfPbtmk3f/jFP50uDOKO0ROH8ts//xi/AO+8qLBk7ir+/ZdXm2W68N0PzeCpHz/knYtN6PDOqx/zzqufeJ6tCvz0109y7yOz6q6Yr7kyJGAwGhg1/lZ2bd3n8bzkDp3b0b5TOgGB3nliZjIbGTZqCCePnfF4rm6P3l1o3bYVZrPre26ul+SUBPoP6sXF85ddzl9viKIo9BvYk8TkOK+dbtG+U1s6dm1H/jrPDvaqqjLw1r5Ex0Z67Ulo7/7dSU5N8vg5FX7+ftwyrD/hEWFe29dbRwzknVc/JedyrkfbCQ0LYdDQfgSFBHptX4eNGcScDxd7HOKx8dH0GtAd/wA/r+yrruuMnjCUlUvWNemB0ldr1TqFbj074x/gnXmjazqjxg9j17YDHmdrxy7pdOjs3dk6dPQQTh4/2yzZmtYmBZOXZmtSSjz9BvV0ekWtsRzZ2ouEJO/N1o5d0unUtT3567Z7tB2DwXFjf2xctFcelwD6DOhOcmqi0xUZG8vP348hw/oTFhHqtX29ZeQA3nntU5crGDdGaFgIg27tR1Cw92bryPFD+eyDBR5na1x8DL37d/9GP7+x1w4bOYjO3Tt49I8EBPpz+z2TCQ3zxpF8B4PBwOSZY0lOTfBoO2Hhodxx31SvXEq5jtnPzKx7phIW4dlUkOjYSGbe7b2j2+CY+jT7gWn4ubj5szGSWyUwacYYr+5rWHgod94/3ePRnw6d2jJqwlCv7mtsfAwzZk9EbeC+tob0GdCDAUN6eXVf09JTGT3Js89DURVuHTWQ9p3bem1fFUWhZ5+uDL61n0fbMZmMTJoxlsQk75zWB4ACw0cPbpZsnXXPFC+9Su5gMBiYMnMcSSmeZ+vs+6Zh9IVs9XCaZXRsJDPvus1r91WAwKBA7npghufZmprI5JnjvLqvju/eVI/vWevQqS2jx3t3tsbFxzJj9m0eF/B9B/Sg/2Dvzta26a0YP3mkR21UVYURY26hQ+f0+gspRVGIionkkSfvJjwirEn/iKIq3DpiIGMnDvfakRVw9DUpJYEHn7iryfc2GQwGJs0YS//Bvb36y6MoCu06tubuB2fi18RnGZj9zNz94Ezad2rj9X3t1bcbU++Y4HJxBVeCQ4J4+Ml7iEuIaebWNb8RY4cwZsKwJi+gEB0TyeM/uN+rT8zAcfCaMms8fQf2bPI2klITeOSpuzGbPTsRaGlms4nZD0wjvWPrJm+jbbtW3PnQNK8e4AHHvvbQ9+4ioYlFkKIo9OjdhRl33uad00m+diVbn7qb8CYOaKmqwrCRgxhzm69k650eZevkGWPpN8i7T8zqsvWuB6c3ucBwZOsM0ju09vq+9u7fnWmzJzY5W0NCg3n0+/cSGx/dzK1rfiPGDGHU+Fs9ytbHvn+vy9VyvcGVbB3Qo8nbSEpN4OEn7/LaWVl1zH5m7nn4dtp1bOLzbRVI79CGex++/TurPn/jiKwoCoOH9ePRp+8hNMy9+auqQaV3v+58/2ePEhjkfMULb6EoChOnjubOB6YT4OaUEKPRwNCRA3nkqXu89kFrVzMajdz14HQmThnl9smV2WzitmmjmX3ftAaXDPcGAYH+PPbMfQwe2s/tESV/fz/uuH8q46eO9PoVlBRFITwijB/8/FG69ezs9slVUHAgj/3A8Xvy5gAHR18TEuP40S+foG27Vu61V3E8F+5Hv3yCzt06+ERfW7VJ5smfPUhCsnsFhqIoJCbH88PfPEFiSnwLtbD5KIpC154defonDxMd43wZbGfvbd+xDT/5zZNERDZt4O9aUhSFIcP68+jT9xHq5sDFlWz9+aMuH0/hLRRF4bZpo7nz/iZm66hBvpWtD8xgwuSmZ+sd9071mWz93jMPMGRYE7I1wI8775/OhCmjfSNbIx3Z2rVHpyZl66Pfv5dBQ/v6RN4kJMbyw189Tpv0pmbrY3Tq1t4n+tq6bSo//OXjJCW7l4+KopCcksDPf/c0SfXMZLuy2EQdXdfR7BpLF67m1efeJTc7z+USu+A4IAwfPYSf/vZJ4hJivf4XWkfXdSwWK59/uIB3X/vU6dOsrxYQ4M/kmeP4/k8f8eq5r9+m6zqVFZW8/8bnfPr+fKerQl0tODiIux+eyQOPzfbqua/fpus6RQXFvPnSRyyasxJLbcP3YERGhfPoD+5l6h0T8Pf3zvtK6qPrOpeysnnpn2+xesXGRj2zIik5nu//7FHG3jbca+8/qI+u65zJOMe//vwyu7fvb3A5VoD0Dq350a+eaFJhfb04HhgOR/Yf5/m/vEHGsTMun40FjgN9l54d+cGvHqFbr04+9f3VdZ3N63by3LOvcyHzYoP3mxgMBvoP7sXPfveU++F/HdVl65IFX7mVrSPG3MJPf/sUcQkxPtVXi8XC5x8s5N3Xb/xsrSiv5IM3v+DT9xdQVdmIbA0J4u6HZnD/o3f4XLYWFhTz+gvvs3DOikZn6xPPPMC02RN9MFtzeOmfb7F21eZGZWticjzf/9kjjJkw1Oey9XTGOf7951fYveMAWmOz9ZePM2hoXx/LVp2D+47yzz++zImjpxqVrd17deanv3mS7r271Pf9XfOdQqqOzWbj3JksPvtgPju27CU3Ow/rVUuAK4pCaFgIaW1TmH3fNIaOHERwSJDP7CRXs1qsHD96ik/em8eB3YfIzyv8xvKtiqIQGRVOeofW3PvwLPoN6kVAoL9P9rW2ppYDe4/w6fvzOXrwBIUFxd/4IqmqSnRMJJ27d+Deh2+ne68u+Pl793QoZyorq9i9bT+fv7+AUyczv/OgS4PRQGxsFD37d+OuB2bQsUu6V8/Jd6W0pIzN63fw+YcLOX/2AqUl5d/4uclsIi4+hiHD+nPHvVNp0y6twWdpeaO6IF+7chPzP1/GxQuXv3PzqL+/H/GJsYwcdyszZt9GUmqCV0+HckbXdfJyCli5cB2rlmwg+2IONdXffBZNQGAAiSlxjLltGBOnjyI6Nsorl3ZviGbXuHQxm7mfLmXDmq1kX8r7zklacEgQqWlJTJ01gbG3DSfch062r2az2cg8c4FP35/PTmfZGh5C6zapzL7/BsnWd+eyf89h8vMKv3FC+o1sfWQW/Qb6drbu33OEzz5YwNFDJygqKPlOtkbFRNKlW3vufWQW3Xp18vieo+ulsqKKndv28tn7Czh14gzF9WVrXDR9+nfnrgdn0qlLO5/O1i0bdvLFh4s4fzaL0tL6sjWaIcP6c/s9U2iT3spns7WooJg1Kzcz//NlXLpw+TvPi72SrWNvYfqdE0lK8d1szc3OZ8n8r1ixaA2XL+Z85/EUgUEBJKUkMGHKKCbPGEtMbLSzbHVeSNWx2+1knr7AiWOnuHj+MqUl5ZjMRuISYmmTnkqX7h0JCQ32yQPft1mtVk6dOEvG8TNczMqmoqwSf38/EpLjaNs+jU5d2xMYGHBD9LWmppYTR0+x+rPVnNqbAbrumC7TvyOjZ4+mQ+d0/PzMN0RfKyuqOH4kgzMZ58jNzqemppaQkCASUxLo0Lktbdun+cTUiobouk5pSTnHDp/k7Olz5OUUYLVYCQsPJblVIp26tCOtbarPjB65UldQHT10gnNns8jPdTyINyIyjNS0ZDp1bUdKq6Qb4vuraRr5OYVsXbeLee8toay4AhQd/0B/Hv7J3fQe0J3YBO9dBcsdml3jYlY2xw6fJOv8ZYqLSjAYDMTERZHWJpUu3TsQGRV+Q/TVbrOTeeY8J46eIutCNqUlZZhNJuISb9BsPX6WjBP1ZWtrOnVtd4Nl62k+eONzdmzei/51tt46ciD3PDLzBsvWSo4dzuB0RqYjW6trCQkNdjw/qUv6DZitGWSePk9ebj5Wi43Q8FBSWiXSsUs6aW1SfbKA+rb/ZetJzp/NuvKQ+/CIMFq1TqZjl3aktEq8Ib6/mqaRm5PPhq+28u7rn1FcVIqCo4j66W+fpP+g3o2ZCdBwIVVH13U0TXM8ZE1xPH2+qTfiebtv9lXxjadTN4Gu66x//yt2Ltx25e8G3X4rQ+8e6fEKad6m7muu2TVHsKkKqnrjfq667jhIcFP0Vb8y8qsqKoqq3JB9PX8qi3/85CXyLhcAEBwaxHNf/oXImPDr27AWoOs6uqaj6V9/rl9/f2/Ez/U7eaOqPnlVsTFupmx98dm3+PTdeVf+7qGn7uLxH953QwxkXa0uW+32myVvvs5WdBRFRb1B8+ZmytaM42f40eO/4/LFHMCxcuPcVe8QExvVmLevafS1VkVRHAeAG+sYUK+bqa/f4flzQL1S3c7vzat7NRfHCadjsONGV3dy7YvTC5pCd/LfbzSKoqAYFFRu/M/1Zsqbm6mvN/Ye+j912WqUbL2h3GzZevUNq7qb++5N8hsSQgghhBBCiOYjhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG6SQkoIIYQQQggh3CSFlBBCCCGEEEK4SQopIYQQQgghhHCTFFJCCCGEEEII4SYppIQQQgghhBDCTVJICSGEEEIIIYSbpJASQgghhBBCCDdJISWEEEIIIYQQbpJCSgghhBBCCCHcJIWUEEIIIYQQQrhJCikhhBBCCCGEcJMUUkIIIYQQQgjhJimkhBBCCCGEEMJNUkgJIYQQQgghhJukkBJCCCGEEEIIN0khJYQQQgghhBBukkJKCCGEEEIIIdwkhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG6SQkoIIYQQQggh3CSFlBBCCCGEEEK4SQopIYQQQgghhHCTFFJCCCGEEEII4SYppG5Suq5TUV5JcWkptZqNapuFWs1GcWkpFRWV17t5Qoir2O12CvKLsGt2tK//D1UnLycfu81+vZsnhPhaXbZWVlRhMBhQFAWD0UBFeSUV5VXXu3lCiKvY7XYKC4pBAVVVUVUVo8FAXk4BdnvjslXRdV1v4XYKL6JpGnk5BaxevoGvlm0g/1I+NRXVaLqOqqj4hwQQlxzLqPG3Mn7yKKJjI1FVqbeFuNZ0XaemppajB08w55PFHD9yisLcIqwWKygKJqORmMQoOnVrz+13TaZL9w74B/hf72YLcVPSNI3cnHxWL9vIV8s3cOn8ZUpLy9G/ztaw8BBS0pIYNf5WJkwZRVSMZKsQ18O3s/XYkQxys/Ox1FpAUTCbjCQkx9OlWwdm3jWpoWxdI4XUTcRms7Fl/U5ef/EDTh47jaZpTl+rqirtO7blqZ8+xK3DB6KoCoqiXMPWCnHz0nWdooJiXnvhfVYsXktFueurxEHBgUy7YyIPP3k3UdERsq8KcQ3ZbDY2r9/B6y98QMbxMw1na6e2PP2Th7hlxEAURbJViGtF13UKC4p5/YX3WbFoDRUVrq8SBwUHMv3rbI2sP1ulkLpZWK1W5n++jFf+8w6lJeWNfl90TASPfv8+Zt0zFaPR0IItFEKA40B/PvMif/v9C+zdcQBbI6fuGY0G+g/uxW/+8hOSUhLk5EyIa8BqtTLv06W88vy7lLmVrZE8/oP7uP3uKRgkW4VocVey9XcvsHenu9nam9/+9SckJsd/O1vXyHXlm4Cm6Wxas53XX3jfrSIKoCC/mDde+pAtG3a6HGUTQjSP8rIKXvzHG+zauq/RB3oAm83Ozq37eOEfb1JW6t5+LoRwn6ZpbFyzjddf/MCtIgqgIL+I11/6gC0bJVuFuBbKyyp48e9vsGtbU7J1Ly/8/Y16s1UKqRucrusU5BXy0r/eoqiwpEnbKC4s4ZX/vEPO5TzkAqYQLcduszP30yVsWb+zSfua3a6xduUmFs1ZKfuqEC1I13Xy8wr577/epriopEnbKCoo4eV/v0Nudr7sr0K0IJvNzpxPFrNlgyfZupnFc7+brVJI3eA0u8b8L5Zx8UK2R9s5fTKTZQtXN1OrhBD1ycnOY+6nS7BYrE3ehmbXWDR3BVnnLjVjy4QQV9PsGgs+X0ZWM2TrcslWIVpUbjNkq91uZ9GclWSd/2a2SiF1gyssLGbzuu3YbDaPtqNpGquXb2zwpnchRNNt3biLnMt5Hm8n8/QF9u05LKPcQrSQwsJiNq3bgb0ZsvUryVYhWtSWDTvJzc73eDtnT59n/+5vZqsUUje4vJwCTh4/U+/PgoID6d2vO916dqJ9p7b0GdCDqOgIp9sqyCvidMa5FmqpEDc3u93Orm37nD67ok16K/oM6EFMbBR+/uavb3p1vq29Ow/KvRdCtJC8nAIyTrjI1v7d6dqzE+06tKFXv26ER4Y53VZBXiFnTp1roZYKcXNzZOv+BrM1MTmeHr270LFLO6eLNdntdvbuOvSNbJVC6gaXfSnH8dyZekRGRWC1Whl4S1/i4mMIDAqkR+8uTrdVUV5B9qWclmqqEDe1yooqCvKL6v2ZoipERIbj52fmnodv5457pzLrnikEBgU63d6ZjHNomlyREqIlNJitFiuDbulDTFwU/v5+LrO1vLyS7Eu5LdVUIW5qFeVVFDrJVrUuW/39mH3fNGLjY+jdrztms8np9s5kZKJrckXqpuFqukB5WQXV1TX4+ZvJyc4jOCQQu4sRbJvNTnVVTUs0U4ibnqXWgqXWyfxtHfJy8wkKDiT7Ui52u8bpk5ku98eK8grHG4UQza6hbK2priUgMIDE5HhCQoPJPHPB6ettVptkqxAtxGKxYLFY6v2ZXpetQQGEhAYTGxdNQX4hVqvzKbvl5ZXfSFYppG5wAYFOn8ZMQKA//Qb1Ii+3kI6d0wkOCaKooNjp6w0GFT8/c0s0U4ibntFkxGQyOv15+07pRESGk3HiDMePZLjct3UgIDAAkGdJCdESGsrWvoN6knM5j4rySsLCQ7G7WG7ZYDBglmwVokWYTEaMDWRreGQ4G9dsAwWCQ4KcTu1zZKv/N5LV+ZbFDSEhMQ6D0VDvQTz7Ui5rlm+kprYWu9VOSFgw+XmFTrcVFBJEXEJMSzZXiJtWcEgQEU7uo9B1na0bdxEWHkpBXiGKAqdOnHV6D5QCpLVJQZWH8grRIhrM1hUbqa2xoOs6YeEhLpdID5ZsFaLFBAc3PltDw4Kx2+1O76dSgNZtUlHU/2WrXJG6wcXEx5DWJtXpz/PzCikvraCqqprc7Hw0u/OpfeERYaS3b90SzRTipmcwGOjRpyuqWv9huaa6htzsPOx2Ozab3eXUIkVR6NWvG6pBDvFCtARHtqY4/Xl+biFlpeWUl1Vw8UI2VZXVTl8bHhlGevu0FmilEMJgNNCjd+OytbiolLLSCqfbupKtV21LUvYGFxMbyZBh/T0+oVIUheGjBrtceUgI0XSKojB8zBAiIsM93lZKq0T69O/heaOEEPVq1mwdPZjwCMlWIVqCoiiMGDvE6VUpd6S0SvpOtkohdYMzmUzMvGsSMbHRHm0nJS2JSTPHNlOrhBD1SU5JYMrt41ANhiZvw2BQGTtpBK3TWzmd5y2E8ExdtkbHRnm0ndS0JCbNkGwVoiUlpyQy+fbxHmargXGTRpDWNvUb2SqF1E0gtVUSj33/XoKCnS+V7Ip/gD+PPHk3rb/15RFCNC+jychdD86gV9+uTXq/oij06NOVO++fjtHY9MAQQjQstVUyjz3d9GwNCPTn4SfvIa1NimSrEC3IaDJy94Mz6NXH+WMIXFEUhZ59u3Ln/dO+k61SSN0EVIPK5BljuefBmQS5eO5MfYJDgnjgsTuYMGUUBg8qeSFEwxRFITYump/8+nt06dbBrZMrVVXp3K09v/y/Z4iOiWzBVgohwJGtU2aO464HZjQtWx+fzYQpIyVbhWhhddn6418/2cRs7cAv//ADourJVkXXdXnQyE2itqaWhXNW8NbLH1GYX+x0xS8ARVWJiYnk8WfuZ8rt4/Dz87uGLRXi5qbrOpmnL/Cfv73K7m37qa2t/xkYdcxmM0OG9eeZXz4mV46FuMZqa2pZ+OXX2VrgTraOl0eKCHEN6brO2dPnee6vr7F7e+Oy9Zbh/fnBL5xm6xoppG4ydpudc5lZzPl4MTu27CHr/CVsVy3fajAaSGudQv/BvZh9/3RS05JktEyI60DXdSorq9iweiuL567i+JEMykrLv/Ga8IhQOnVtz+SZ4xg+ZgiBgQFSRAlxHdhtds6dvcCXnyxhZwPZeucD00lpJdkqxPVwJVu/2sriec6yNYxO3dozecbYhrJVCqmbldVqJftiLu+9+hlrlm9C10FRYNyUEdz3+B0kJsdhNBrlpEyI60zXdUpLytm9fR8vPPsmBXlFKDie6/bX5/8fnbq2JzQ8RPZVIbxAXba+/fLHrFnxdbYCE6eP5r7HJFuF8BaObC1j17b9vPjsG+TnF6HoEBwazF9f+DWdurYjNKzBbF0jD+S9SZlMJlLSkoiKjsRu/d80hOjoKJJTE2SkTAgvoSgK4RGhpLVJRVUUbFYbAJpdo2371oRFhF7nFgoh6tRla2RUBDbL/65IRUVHSrYK4UUc2RrmWOwFBZvFka12u5227dMIC29ctspiE0IIIYQQQgjhJimkhBBCCCGEEMJNUkgJIYQQQgghhJukkBJCCCGEEEIIN0khJYQQQgghhBBukkJKCCGEEEIIIdwkhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG6SQkoIIYQQQggh3CSFlBBCCCGEEEK4SQopIYQQQgghhHCTFFJCCCGEEEII4SYppIQQQgghhBDCTVJICSGEEEIIIYSbpJASQgghhBBCCDdJISWEEEIIIYQQbpJCSgghhBBCCCHcJIWUEEIIIYQQQrhJCikhhBBCCCGEcJMUUkIIIYQQQgjhJimkhBBCCCGEEMJNUkgJIYQQQgghhJukkBJCCCGEEEIIN0khJYQQQgghhBBukkJKCCGEEEIIIdwkhZQQQgghhBBCuEkKKSGEEEIIIYRwkxRSQgghhBBCCOEmKaSEEEIIIYQQwk1SSAkhhBBCCCGEm6SQEkIIIYQQQgg3SSElhBBCCCGEEG4yuvqhrusAVFRUcfLoKTLPXKC8rAKj0UhCUhztO7UlOTUBVVVRFOWaNLil6LqOruuUlpRz4mgG5zMvUllRhdnPTHJKAh27tCMuIQZFUW6cvhaVUVlaRYC/P5pdQzWoVJRWUlpURnhU2A3TV03TyMsp4PiRDC5fysVSayU4OJDU1sl06tqOkNDgG6avdrtGzqVcTh07S35OITabnZDQIFLbJpPesTWBQQEAN0RfbTY7585mcer4GfJyC9B1nbCIUNq1b016h9b4B/gDN0ZfrRYrWecvoQOqwTH+ZTQZOXf2AqHhIZjNJsC3+1qXNzXVtWQcP8PZ0+cpLi7FaDAQExdF+45tadU6GYPRANwYfa2sqCLj2BnOnc2ivLQCo8lIfGIs7Tq1ISkl/obK1rLSco4fOcWFzItUVlbj52cmKSWeDp3Tb7hsLSwoprioFKPJiN1ux2AwUFRQTFFBMVExkTdMX+uy9diRDLIv5lJrsRAcHEir1ik3YLbauXwxl5NHT5ObnY/dbickNJjW6am079SGwKBAwLePS/C/bD1/NovTJzLJzyt0ZGt4KG07pNG2fRr+/n7AjdFXi8XKxQuXATAYVEDBZDJy7swFwsJCMDUiWxW97oj+7X9A08m+nMvKJetYMv8rCvOLqKqqxm6zoygKfv5mAoMC6dGrM3fcN42efbte+eX6Gk3TOH82i6ULVrNyyVpKS8qoqqpBs2soqkKAvz9BIYH0H9yb2fdOpVPX9ld+ub5Gs2ucO5XFxiVb2LVhP+Wl5dTUWEDXHZ9rgB9h4aH0ubUHo6YPJblNIgaD4Xo3u0msVitHD55k3mdL2bF1L1WV1dTU1KJrOgaDin9AAOERIYybNIJJM8aSmpaEqvrmRdramloO7zvBwk+Xc+xgBtVV1VhqLeg6GIwqAQEBRESHMWH6KIaPH0JcYoxPHgR1Xaeysord2/bz2QcLOHXyLNWV1dRaLKA7iovAwADiE2O5/e7JjBgzhOjYqOvd7CapG9jZvH4HX368iPNnL1BRXoXdbgfAYDAQHBJE6/RUZt0zlVtHDCAsPPQ6t7pp6k4+167YxIIvV5BzOZeqqhpsVhuKAmazmYCgADp2TmfWPZMZMKTPlUEBX+PI1jxWL93A8oVrKMwvprq65lvZGkC3Xp24/Z7JdO/dGT+fz9Y1rFq6nrKSMqqq/5et/v7+BIcE0n9QL2bdO4VOXdr5bLba7XZOHjvD4rkrWb96C6Ul5dRU1wCgoOAf4Ed4ZBhDRw1i5p2TaNs+zaez9cjBE8z7tC5bq76RrQEBAYRFhDJ+8kifz9aa6loO7j3KnI8Xc+TAcaora6itrUXXwWg04B/oT1R0BFNuH8eoiUOJT4z16Wzds+0AX360mDMnM6mqqsHyjWz1Jz4xlul33caw0YOIiom83s1ukrps3VKXrZlZjmy12UEBg6oS/HWRPOvuKdw6YiCh4SHONrem3kLKbrOzc9s+Xnv+PY4cPIGmaS4bFR4RxtTbx/PIU/cQGh7iU18ii8XKupWbePuVjzl1MhMndeUVsXHR3PnAdO5+cCYBgf4+1dfa6lo2LtvG0o9XkXspD1ddVRSFmMRopj0wkaG3DcZkNvpMX3Vdp6K8ki8+XMiXHy8iP6/I5eeqqiqt01N56scPMXTkQIwm3+praXEZn7w1j1UL11NWUu7y9QaDSoeu7XjkR/fQs18XnwpyXdfJyyng5X+/zbpVm6moqHL5epPJSL9Bvfj+Tx+hU7f2PhXkmqZxIfMizz/7Ots376Gmptbl6/38/Rg2ajBP/+Qh0tqm+sz3FxyDO8eOnOSlf77Nvt2HsVltLl8fFBzI2NuG870fPkBsfLRP9dVus7N7+37efPEjjh3KaDhbI8OYNGMMD3xvNqFhPpitqzbzzqufcrqR2Tr7/mnc9eB0AgJ8K1urq6pZMm8VH779JRcvZLvsq6IoJKUk8PCTdzNp+hjMfmaf6Wtdtn7+wQK++HghBY3I1jbprXjqJw8xdOQgn8vW4qJSPnjtc5YtXENpSRm4+AobjAY6d2vPUz99iF79u/lktr72n/fYsHoblY3I1r6DevK9nzxIxy7pPpet5zMv8sKzr7Njy95GZevw0YN58scPkdYmpb7v73cLKbvdztqVm3j2Dy9RXFjs8mT7akajgRFjb+H//fGHREZH+MTOYrVamf/ZUl74x5sNfnGuZvYzM+X28fz0108SFBzYgi1sHnVTgxa8t4zFH67EarE2+r3+gf5MvHM0tz82BaPJ5UxQr6DrOtVV1fz7L6+xeN6qBk/KrhYWHsL3fvQAd943HUX1/u9vXRH1z9++ws7Nex2jKY0UER3OM795jOHjBvvEvqrrOpeysvnNT57l0P6jaHbXJ6BXS2mVyP/94+f0GdDTZ/p6/EgGv//ZPzidcRZNa9xBWFEUOnZJ50//+hXtO7X1mb7u3LqPP//6OS5fzGnwZLuOqir0G9SL3/3tJySlJPhEX+12O+tWbuHff3qVkqKSRmerwWBg+Ngh/PwPTxERFe4TfXVk6zJe/NfbVLmRrX5+ZibPHMeP/98TPpOtlloLb73yMR+8+TmW2sZna2BQAPc+fDuPP/MAJh/J1qqqav7951ealK1P/vghn8rWkqJS/vz/nmPbxt1uZWtUTAQ/+8PTjBp/q0/sq7quc+lCNv/3839xeP/xBgd3rlAgOSWR3/79x/Tu391n+nr8SAa///k/OJOR2aRsbdexzbf7uuY7ZeShfcf4959fpaig8UUUgM1mZ/1XW3jjvx9iqbU0/o3Xia7rbFyznVeef8+tIgrAUmth8dwVfPLeXLeKkutF13XWL97K8s/WuN3emqoaVnyxlo3Ltrl1MLlerFYbH7z5JcsWrnbrQA9QWlLOO698ysa12xp/MLmOqqtqeO/lz9wuogCKC0p4+/mPObzveKNPXq+nkuJSnv/b6xzce8StIgog68Jl/vXnVzlz6pxP9DUvp4B//vFlMk6eafSBHhz7+Yljp/nnH/9LXk5BC7aw+WSevsA///gyl7Jcj+J/m6bp7NlxgBf+/iYV5ZUt2MLmc3jfcV7825sUFza+iAJHAbZx9VbeeflTn8rW1174wK0iCqC21sLieSv57P35PpOtC79cwafvzXOriAKoqqzm0/fns2T+Kh/JVisfvPE5yxY0LVvffvljNq7zjWytqqzm9Rc+cLuIAijML+bVf7/Hwb1HfSJvSorLeOnvb3Fo3zH3PhsdLmZd5oW/vkHm6Qs+0de8nHz++ceXOXWi8QOUcFW2/um/5OV+N1vVq19YVlrOWy9/VO8LG8Nms7NswWq2bNjp1b9Ux3z8It7874eUFJU2aRuWWiuff7iQwwe8+0RU13VyL+az6INlVFdWN2kb1ZXVLHx/OdlZeV7f1+NHMvj0/fnU1jTthKMgv4g3XvyQ4sKS5m1cM9N1nT1bD7Bq4fomh/ClC9l89NqXTf5dXSuaprFi8To2rdvetO+fDieOnuLDN79wuwi71qxWK59/uIBD+4+6nEbijK7p7Nl5kDmfLPbqvtZdOX7/jc85dzarSduw2zU2rd3OysXrvPrkrC5b3331M/Lzmp6tKxatZfumPV5/DC7ML+btlz+mpNiDbP1oEUcOnvD6vmadv8S7r3/q9mBsnYrySt599VPHQjJe3tdjh7/O1iYW8wX5Rbz+wgdNPue6VnRdZ+eWvSxfsKbJ2Zp17hLvvvIptQ1MG7veNE1j1ZL1bN2wy4NsPc3Hb8/x6mMwgNVSd85+rEnv1zWdPTsOMveTJd/J1m9ckdq6cRd7dx3yaIeumz/b1APLtaBpGssWruHMqXMebacgr5AvPlp45eZvb2S32Vk9bz1F+SUebSf3Uh7rFm1qnka1kNpaC5++N5+K8gqPtpNx4gwrl6xrpla1jOqqGuZ8uISaas8O1If3HWf7xj3N1KqWUVxUwucfLsDi4Qj15vU72L/ncDO1qmVcPH+ZBV8ux+bBCLWu6yxftIbTpzKbsWXN7+ihDNat2uxRAFssVuZ9tpT83MJmbFnz275pDwf2HHbrStS3VZRX8uVHi6iq9OZsdXz3miNbv/x4EXYvHgyw2Wx8+fHiJg8817l4wbHPezNHts6j3MOrvxnHvT9bqyqr+fS9+R5n64E9R9iyflcztaplFBeVMuejRR5n69b1uzi492gztaplZF24zMJmyNYVi797fLsyMbfu3qi6VWbqpdCoUdKD+45x9vR5OnVp18TmtqzKiirWf7WlUVMHFEVxWVju3LaPy1k5JCTHN2cTm01hbhEHdzbynhJXn68OB7YdZtI9YwkJD27OJjYThbOnznH4wLFGnay4+lztdo2Na7dz2/QxBAV55zz9o/tPcOFM00byr1ZTXcu29bvof0tPzGZzM7SsmSmOk9Dcy3keb6q4qJStG3fRtUdHr70ReP3qrZQ2cST/apcv5rB350HS2qTirTPX167cREUzFAWnTp7l2OGTREaHe96oFmC3Oe6N8vTEDODw/uNkns6iQ5f0ZmhZ86usqGT96q1Y3Zz6VZ9d2/aTfSmH+ITYZmhZ88vJzmfHlj0eX/nVdZ0t63dy7yOzCPfGVTcVOHMyk8MHjtOYcHWdrXY2rt3GxGmjvfYeuEP7jnHutOfZWl1Vw6a12xk0tC9mPy/MVmDH5r3kZjduIEBRnH/8xUWlbN+4h87dOmAweufCExtWb6WkuMzj7VzKymHf7kOkd2h95V6pK4tNVJRXMmPMg+Tm5H/njX5+Znr374HZz8Sp42cIDg0m4/gZp/+QQVUZOX4oYaFOlwu8rmpqalm1bL1jWcdvCQoOpE//7qAolBSVEhsfzbkzWZzOqH9018/PjwnjRxIREd7CrW4aS7WF/RsP1XuwDwkLpkPPdtisNqorqwmPCuP4/gzKiutf+c0/yJ92/dpi9vfO5Wnz8gtZv2ZrvSPciqIQGhZCfGIMkVERhIWHsHPrPoqdTDOIS4hh4JA+GL30hPvSuWxOHDpdb+GrKAqR0eEEBgeSczGX9l3acvTASafbikmMomPP9CvP5/EmiqJw4uhpjh2uv/2qqhKXEENSSgJx8TFYai1s27SbSicn6J27tqdDl3QULy0vdu84wIVzF+v9maqqJKcmEhgUQGJyPFWV1ezattfpXO9+A3uS1joVL+0qG9dupyC/qN6fqapKWtsUx/6pQ0RUGGdPna9/Q4rC0BEDiY/3zhNuza6xbuVmKirqH803Gg20Tm+FqiokpSaQde4yp06crfe1qkFl5MhbvLavVquVL+Yudnovl5+fmdbpraitraV1m1Qyz1wg88yF+l/r78fo8bfi7+edS7+XlpSxbvWWemekKIpCYFAAyamJ1FTXUllR6fS7DhASEsyQEQMIDPTOJf0L84vYvH6Hy2xNSIojJDSY4OBADh04TqGT/sYnxHLL0AEYjN65wMa50xc4sPdIvcWgoipERUUQGR1BRFQ4qqqwb9dhp1P4UlITGTioDybT/86ZdLzjkKwoCocOHuPwoeP1/rx1eippbVPJvpRLWptkKiuq2bF5j9NBkk7d2tOxc7qj4vJCO7bu4fy5egpkBbp07UBsQgwnj53GbrNj9jORdf6y021NmDqKvz7367oB2f+t2pd55gL3z3iastLvnkQHBQeS0iqRrj06kXH8DFExkezYsofqKudXr0JDQ6gs984pCLquY9frv7wXGRVOdGwUg4f2x+xnIvP0BYKCAlg4Z0W9r1cVlfiwGJxs7rrz9/PDrBjrPXGMjo8iKCSAfsN7c+ZYJqERodisNrau2lnvtjR0Sixl1NR657xfxahQXlX/yUq/gT3p3qcLUdERZBw7w6WLOWh2O3t3Har39WY/Myq4fQPxtWJUjQSY6l8ieMjI/qR3bE11VTUrFqxj5IRbWPT5Sqfb0lWdsqoy7F44x1lRFAxGg9O56pOmj6FVmxRKisuoLK/kYlY2B/cecXqwDwoOpKqqGt2NG02vJWcjuapBZeadk0hMjqcwv4jdOw4wdNQgPnjzC6cnrSGhIdRUuphhcB3pOB5cWl9vAwL8mT57InEJMdTU1GKz2dA0nQ/f+tLpLILwsDBqK73zuKTrOhr171uRUeGMnzrSEeJHTpN55gI9enfmy48WOR39jQmLQvH8gk+LUIwKWUXZ9f4spVUSI8YOIS4hhpLiMo4eOkF0TCRL5q2qt6+qqhAYGOj2ghXXiqvPtVPX9gy8pQ/hEWEsmrOCxJQEtqzf4XRbqqpiMBrdXsThWjGZjU6PM/0H96J7ry5ERIaRfSmXysoqzp46z8F99U/18vPzw89gxmb1zpMmTdfQ9Po/12FjBtO+Uxt0HY4fOUWHzm1Zv2oLmafrHwwI8PMnwODvlfe/KYpCrVZLZU3998537tYeRVGYOnsCq5dtJDE5nk1rtjkdfA4ODqK22uKVfQWw2C3YtO/uX4qi0L1XZ4wmIzGxUVw4d4mg4AB2bz/gdFsdu7Tjk4Wv1a1k/b9V+2prap3+AjRNQ7PrGIwGrFYbFeWVdOzsetqep3Mur5e6OdkGg0p1ZTVRMRENzGbUvfIEtDEcD4BUMRgNJKTGU1lW6XKJc13XvfwGdhzDPfV8YKdOnsVmtXEh8yKK+vXUAxcDJ3a73avn57ty6ngmdrvGxfPZJKXEN/iAS03TPLp3o8W5aNuJo6ex1FrJvZzHiWOnaN+xDcEhzqeeWi3WJi3icL1pdo2ME2eoKK/kwrlLKIqCqigu7y/yhVXP6vssamstnDubRVFRCds27sZms3PuTJbL/tQ3u8AXlJVVkJudT252PooKbdJT2bvzkMv9UfPmFd70b/3nVfJyCygtLuPi+cvY7XbCI0I5e+q8077quuMKly86n5lFTXUN5zOzyM3JJzDQn5RWiU5f7xPZ6kTG8bPYbDbOZJwDRSEoOAjNxRt8OVsdVyw0SopKCQsLobqq2uUzlBzZ6r2B46pp0XFRJKclcXDvUUcfG+iHxWql/qEx7+Z4rls8kVHhHD96itbpqSiK6+mJ1dU13+jplVcHBgWgOlvfX4fO3Ttgs9pITUuiXYfW9OzTxeWzD/y9+Ensrta713Wdnn27UlRYwqmMTHRN50Jm/VNtvt4YRi+cElVHUXA6jUlHp1Pv9uRezCMnK4/w6DDOHHV+g7qiKqhe3Vfnn2tJcRkH9x6hpLiM8rIKOnZOJ/tSrtPXG41GjF469aAh+TkFnD15DqvFiqbpDa5AaDAYvPbZHoqiuJwpcPb0eS5fzKG8vJKefbths9updXLFVMcxXcibn3fhasrhkYMnKC0po7amlr4De5J1IdtlIeXv7+etsyxc9lPTNHZvP4Cl1kJOdh5HD5zAZnM9Uu+reWOz2ti+aS/okHM5n5i4aIJDg1xuz5uf5+eqr7U1tWzbtBtFVdi9fT9hYaH4ufjcFEXBz0vvLQFcDsRVVVazc9s+DAYDQ0cOJDklgU5d2zv9/Siqt59HuMrWUg7sPUJ1dQ2XsrKpqa6hqKC43tfqfJ2tXvwddiX3cj6nTp4lP68Qm81GZUUVBXnOp2x6f7Y6b1thfjGxcVHkZueRmpaEwWhwOQvNz8+M2kAB4o10XaO4qIzYuGj8/MxfT8V1fhVcB4JDgr6x+1+Z2ldVVc3t4x7iUlZOvW/28/fDYFDRdR2z2XzlS1Qfg8HAjDsnkeSlCzBUVVbz8btfUulkOfCAQH/HaJjFQkBgAFWV1U5PWAIC/LnznhkkJsS1ZJObrKK0knVzNzqd6hQQ5I/NZsdus+PnZ3a5owSFBjJwQj8Cw7zvJlEFx6os875Y5vSkS1VVjEYDuq5jMpuocrEcfFJKPJOmj/XaE7RTx86yY91ep99Lg9GAoijYrDbMZpPLK8TJrRO5ZUx/TH7ed++boijs2raPHVv2Oh3ZM5qMoDumn+i67vKm/l79unPLsP6oBu884K9etoGjTu4HAzCZTWh2Df8AP6xWm8vnCg0bNZje/bzzQYm6rrPgi+VcOH/J6WvMfiZsVjuKAqrB4PSKlKIoTJw6mg4d27ZUcz1it9n54sOFFLkY0DD7mdE1jYCgACy1FqffYYNBZdrtE2nTtlULtdYzNTU1vP7qB06zFQX8vj5/8A/wp7qqxnm2Bvoz654pRESEtWCLm64g37GyoLNjq6IqmM0mTCYTBoOB2tpap59reEQYU2dNINxL+3rxwiUWzVnpPFsNKkbDVdlaVe30yn9yaiJTZ4zHP8C/BVvcdEcPnmTD6vrvtQZHtqqK4hhENxiodrFAW9v0VkycMho/b7zPT4FtW3azfXP9j1QwGo0EBgdQW2O5sg6Zq+Xce/XrxuBh/VxeobueVi5dx9HDJ+r9mdlsIiDQcTyy2+2OcycXV/6nzZrA7//+syv3SF0ZFvAzOxaUcFZIXf0LdHWyXdeoO+6bSvuObVy+7nqprKji8MFjbNu0u96fX92/hh72GBwSxD2PzSQ2PrpZ29hcivKKOXXgDGePn6v359VX3UPR0OcaHRfFvd+bRVCI9xVSAGdOnWP71j1cOFf/yZmmaVgsjoNjQ6tKpbVN5cEnZhPgpTf/Ht53nOP7Tzm92nT1PUUNTbPt0acLjzx9T4NTAK+XVq2THSOeTr6fdfcVNHTVQlEVBt7Sh4eevMtrV+0LDAzgxLFTTqe+1BUTDT1eQjWojBx3K9PumOC1hVR5eSXvvv6p0xOuq+9PdDUVyGBQmTRjDANv6eOVfbXZ7JzPzGL5wrVOX1NXEFtL6l/op47ZbGbm/ZNI79C6WdvYXCorqti2Yw/bNzt5pILOlecQNfQdDg4J4r5HZxETG9XczWwWeTn57Nt92OlCOLqmU1tjadRz+uITY3ns+/cSEuqNK+LC6YxMdm/f7zxb7RoWe+OytXXbVO57fJbXZuv+3Uc4sOew04EPu81OXbpacZGtCnTt05k7H5uB2UuzNSY5mv27D9dbDNpsNsoaOB7VUVSF/kN6cd/js7w2W03+Jk4cy6g3SywWa6NvR1INKr36d/9Gwahe/cOxtw1vlh158LD+JKckeLydlhIQ6M/Y20Z4frVBgVHjhxIVHdE8DWsBYVFh9B3a0+MV2RRFYfDY/gQGe+fBDyA1LZl+g3p5fDJlNBqYMHmk146YAXTokk6HLp6PwAcGBTJiwi1ePdWi/+DepLVJ9Xg7MbHRDBs1yGtHzACGjhpEfKLnV7fbpLeiz4AezdCiljNq/K1ERoZ7vJ3uvbvQvlNbryyiwFHojZ44jOAQ11P2GmPQsL4kpXjnTA9wZOuYicNcTtlrrFHjbiUyKtzzRrWQqJhIho0e3CzZOm7SiGb5frSUVq1TmilbjYyfMsqrs7VL9/Z06ub5o3uCggIZc9swl7fAXG/9BvWkVZtkj7cTExvFrSMHenW2Dhs1iLhmeJRCm/Q0x8reV7nSa0VR6DugJ4OH9ffoH4mOieSO+6YSEOi9O4qqqoyeMJQuPTp6tJ1WaclMv2Oi104TAkeIj5h6K/HJnn2BWndsxeCxnn03WprJZOTO+6d5VNgqikLfgT25ZcQArz0xA8c0ttsfmOLRwIeqKgwe0ZdufTp5dV+Dg4O45+HbPRrBNBhUJkwZ6dUn3ACx8THMunfqN5bLdZfJZGT6HbeRnJrgtX1VFIX0Dq2ZMGWUR+EbFBzIHfdOIaIZCrKWoigKvQd0Z+CtfT3aTlRMJDPvnuTVJ6FXsrV7B4+206p1MlNnTfDqEzODwcD0OyaSkpbk0XY6dW3PuEkjmqlVLcORrdOJjPEsW/sN6smtw709W03c+dAMD7NVZeiogfTs08Wr+xoUHMSdD04nwINjisGgMm7yCNI7tvbqvjqydYpHM29MZiPTZ08kKeWb2fqNo1RAoD+Pff9e2rRr2vxro8nI7XdPpt/Anl79CwUICQ3mqR8/REJS00Z//fz9eODx2Y5n0nh5XyOjw7nje9MIjWjac72CQgKZ+ehkYhOivb6vrdNTeewH9zX5QbpxCTF874cPEOaND0a8iqIodOvTiZn3TcJkbtqIV1p6Kvc8PtNrpx3UUVSFkWNvYdL0MU06sVIUhR59unLXgzO8+sQMHFdDZ955W5MLeVVVuXXkIKbcPs7r++rnZ+a+R2fRrVenJj1XxWAwMH7ySEaMGeJ8oSQvERDoz8NP30Xr9KZdWTWajMy4ayK9B3jnPW9XCwkN5skfPUhCE6+s+vmbuf+xO+jQ2bsHPQBi4qJ4+scPNfnKamh4CE88cz8JSXFe39c27Vrx+Pc9zNYfPUhouHc+X7SOoij06tuV2Q9Ma/KAVpv2rXjge3d67YN466iqwvCxQxg/rWkDWoqi0L1PF+64f6rX543RaGDG7EncMqx/07N1xCCmzPxutn7jfymKQtt2afy/P/6Qdm7Owfbz9+PuB2dwzyOzvP4XCl+PEvbvzs9++zSJSe5NlQgJCeJ7zzzApOljfaOvqkL/4b254wn3i6mwyFDu+cEseg/p7rWrz1zNaHSMGNz/6B3uTZVQFBKT4/j575+me+/OXh9q4DgRveOhqdx2+xj8Axo/lUZRFFq1SeZHv3uctPRUn+hrUHAgT/7oQcZNGuHWNERVVenWsxO/+fOPiU+I9Ym+hoaF8NPfPMktwwe4VSAYDAZuGd6fX/z++4SGeffJSp24hBh+9Ycf0KNPV7feZzQauW3aaJ768YNef7ICjn2uTbtW/PwPT9O2fZpb7/Xz92P2A9O488HpvpE3X2frT37zPbcHKoNDgnjimfu5bVrTBk2uNVV13Iv4vR896HYxFRUdyY9/9QS3jBjgE301Go3MuHMS9z06y61sVRSFxOR4fvmHH9C9l49kq78f9z56O1PvGO/WLSCKotA6PZVf/t/3adOulU/0NSg4kCd+eD+jJw51a6ViVVXp2rMjv/zjD4hLiPGJvoaFh/CTXz/JkGH93TqfrcvWn//+6XqvVF5Zte9quq5z9NBJXn3+PfbvPuRydTNVVUlIjOPOB6Yx8+7JTR6tuF4cS+3u59Xn3+PY4QyXq5IYDAZS05J56Ht3MWHqKO9emrUeNquNfVsPMefNRVzKzHb58D+jyUhym0RmPT6VXoO7efU9NN+m646bfFctXc87r37CpYs5Th/oCo4R0E5d2vPMLx6lR+8uHs95v5Z0Xaeqspqlc1Yz76MlFOQWorl42GxAoD/d+3bhsR/dS5sOrXwiwOvouk5pSRkfvPkFS+atoiC/yOUzOoJDghg6chDf+9GDpKYl+cSBvo6u6+Tm5PPGSx+ybuUmpw9BBEd4h4WHMn7ySB5+6m7i4n0j1Orous65s1m89vz7bN+8h/KyCqevVVSF6OhIpt0xgXsemkl4pHeucuaMruscO5zBmy98xME9RxyrmzmhqirxibHMum8K0++cSGCQ996fWh/NrrF7xwFee/59jh/NcLnogsFoILVVEg8+cSfjp4z0uWy1Wq1sXreD1154n8wzF1w+88xkNtE2vRVP/vghhgwf4NX30HybI1trWblkXSOz1Y/OXdvzzC8fc2Srly5EUB9d16msqGbB58v48sNF5OUUuHzcREBQAL37dePpnz1E2w6tfTBby/n4rTksW7Cawvwil4+NCg4J4paRA3jsmftIaZXoc3lTl63rV21ufLY+eTex8fXOylpTbyFV94/VVNeybtVmVi1dz95dB7+xgp3BoJLWNpVbRwxk6u3jaZ3e6so/7Gt0Xae8rIKVS9azevl6jhw47njglg4ojpGY9h3bMHTUIKbOmkhCouN+I1/ta0lhGVtW7mDnur2cO/nNg77JbKJt5zT6DuvF0ImDCI0I8cl+gqOv2ZdyWTR3JZvWbud0xjnHym664/laAQEBdOvdmdHjhzJu0nDHswF8tK+appGVeYnlc9ewc8s+zp+9+I2DfmhYCN16d2LUbUMZPKIf/gHe/TwlZ3RdR9M0Thw5xcI5K9i2eTfZF3OuFI+KohARFU7fAT24bfoYBt3SF5PZ5LN9tds19u46yNJ5q9ixZQ/5+UXodX1VFWLjohl4Sx8mzxhH737dUQ2qz/bVZrWxZcNOVixex+7tBygtKbtSKKsGlcSkeIYM68ekGWPp3O3/s3fXcVJddxvAn3vHZd2NhcVtcXcJhGBJCDHi7mkj7ds3bdq+bZO0adzdSEgCSZAEXdwdFneWdfcdv+f9Y9gNhJllZwVmluf7+eTThpm5OYeZe5/7O/fcczu7n5EXoH21WmxYs3wjVixei707DqC68tcV7FQqGUkpCRg2aiCmzJiAtu2TAARuXysrqrDs59VYsXgtDuw9fF62atRqdOySghFj3ecRsQGerUWFJVi8IA0rl67DkQPHYbPb3atSSu4VF7undsboq4Zh6vUTERYeEpD9BNx9zcnKw8IflmFt2sYLs9VoQGqfbrjqmlGYMHlMwGdrxsksLPh+KTav247TJzLPy9agkCD06d8DE6eNwYixgwM/Ww8cx6K5y7Blw07kZedfkK19B/bENdeOx8DhfaHRqAO2ry6Xgp1b9+LnH5dhy8ad7oFZD9k65foJ7myVvWar90Lq3P9gdXUNlixYif/8/a26JQJT+3TDf97+KyKjI6A++8yaQKcoCqoqq1FRXom8nAJUVFRBr9chLiEGoWEhCAo2QxWgJyq/pbgU1FTVoLK8CsX5paiptsBg1CMqLgLmEDOMJgMkuf4HtgUKp9OJyopqlJaUoSCvEJYaG4JCzIiNi0ZIaBBMZmNAjR55I4SA0+lCQW4h/vqH/2Df7oMA3AfAv7/8R4wYMwgGk6FVfKdCCDjsDlSUV6KoqLRutDA8IhQxsVEICjHDYNC3mr7arHZUlFegsKAEhQXFkCUJEVHhiI6JQFBwEHR6bavpq8ViRUV5JQryilBSXAaVSoXomAhERIUjONgcsIXxb9VeTV6zeCM+eXl23YBWl14d8cxLjyI8Krx1ZWtVDSrKKpGXm4/K8mroDTrExkcjLDwE5qDWk60ulwtVldUoKy1HXm4hqitrYDIbEZcQg5DQYJiDjPWdlAUUd7ZWobSkHPm5hbBYrAgONiM2PqYVZqsT+TmF+OvTL+PAnl+fR/S3V57FiHGD3edMreA7/TVbq1BcVIrC/CIoikBYRAiiYyIRHGKG/krJ1pAg6HQXzda0i15TliQJZrMJIaHB521Mq9MiNDwkoC5LX4wsywgOCUJwSBAS28Rf7ua0KFklwxxihjnEjLg2/rucbnNQq9UICw9BWHgIUjr454Msm4MkSdBo1AgJCwYgYLX9Ok3VFGRsNUUU4O6rVqdFZHQEIqMj0KVbh8vdpBYjSRL0Bh30hihEx0Zd7ua0KEmSYDQaYDQaENsMS9X6M0mSYDIbERoaDJWsgiK7R7l1Ol3rzNZgM4KDzUhs47+PRmkOKpUKIaHBCAkNRnK7pMvdnBblztZQhIWHXgHZqkFIWMgFJ9YhocGtpogCzs3WcERGh6NzN/980HlzaK5sDfyhAiIiIiIiokuMhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBG1QuJyN4CIiIiolWMhRdQKSZe7AUREREStHAspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvIRCykiIiIiIiIfsZAiIiIiIiLyEQspolaIz5EiIiIialkspIhaIT5HioiIiKhlsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8lG9hZQQAna7HdmZuTh1IgNBIUHQ6XUwmoyQJAkH9h5GVWU1FEW5VO0lIi8URUFFeSUOpB9BdVUNNBo1VGoVDAY9Du07itzsfNjtDgjBpSiILqdzs/XosZOAHrDCDofahRqHBfuZrUR+ozZbD+0/CqfLCa1BA5VWheAwM44ePsFsvcJJwss3rygKjh05hbmzF2DFkrWoqqyGy+mq+6GoZBkqjRqdurTHTbdPx7irR9QVWER06QghUF1Vg5VL1+H7rxbg6OETcDpd552EqdVqmIOMmDhlLGbcMgWdurYHAO6vRJdYbbbOm70QK5asQ1XVb7JVpYJKrULnrimYedt0jJs4AkaTgfsq0SX2a7aux/ezF+DY4ZNwuRS4XC4A7vxUqVUwm424eupYXHfzZHTqklL3Gl0R0jwWUjabHYsXpOGTd2Yj60zuRatsg9GAkWMG4Yk/PoCEpDj+gIguESEEzpzOwlsvf4wNa7bCUmOt9/2yLCMhKQ4PPnE7JkwZC51Oe4laSkS12frpu980MFv1GDFmMJ74w/1ISIplthJdIr9m6yfYuHZbA7JVQkKbeDz4+O24avJoZuuV48JCyuFw4IdvfsabL3+E6qqaBm9JkiT0H9wLf3vpD0how2KKqKUJIZCbnY//efIfSN99EEJp+LQCc5AJjz97H2bOmgaVStWCrSQi4Ndsfeu/n/iWrbKEAYN74fkXn+FAJdElIIRATlYe/vS7f2HfnkM+ZWtQsAmPP3MfZtw6hdl6ZUi74B6pjWu24Z1XfDvQA+4f3o6te/H6fz5EdbVvnyUi35WXVeKVf72Lfbt9O9ADQFVlNT586yusX72V87qJLoGNa7bh3Vc/8z1bFYEdW/bizf98jBpmK1GLKy+rwKv/eh/79xz2OVsrK9zZumHNNmbrFaKukBJCoDC/GJ9/+C0qKqoatTGhCGxYtQVpi9fyJlmiFiSEwOrl67F25eZG72vFhSX45J3ZqGzk/k5EF/drtn7X6GxVFIH1q7cgbcl6ZitRCxJCYNWyDVi3akuj97WiwhJ8+u7XzNYrxHlXpNav3oL9ew43aYMWixXfz16AyorqJm2HiLyrKK/Ed18tgMPuaNJ2Dh88jpXL1nPkjKgFrV+9BQf2NjFba9zZWlXJbCVqKRXllfh+9kI4HE3M1gPHsGrZBmbrFaCukHI5XUhbsrbeH09D52YfPXwSx4+cbHrriMijvTsPIOtMjtfXz91X69tv7TY7Nq65+I20RNQ47mxdB4fD6fU9vmTrsSOnmqtpRPQbe3bsb5ZstdkcDVqkggKfuvb/VFfX4MihEx7fpNNrMWR4f+j0OhiMBhiNepw+mYktG3Z6vPSpOF3Yu/sg+g3q1XItJ7pCKYqC40dPobLS87SB5HaJ6NmnG6ora6BWq6DRabBp3XaUlZR7fP/JY6dRXl4Bo8nQks0muiJVV9fgaAOydf+eQ9Ab9dDptDi476jH97tcLuzbfRD9Bqa2ZJOJrki1jyaoqvJ81Te5XSJ69u6KiooqqFUqaLRqbNmwE+VllR7ff+JYBirKK5mtrVzdFamigmLYbTaPb1Kr1aisrIZao0ZZSRnKyyqRl1vgdf6oS1GQeTqrZVpMdIVzOV3Izy0AvMwY0Ov1OHk8A116dMTxo6cQFR2BkJAgr9vLzyuEpZqjZkQtobCgGDab3eP+qlarUVlRBbVGjetvmYJxV49E156dvK72pbgUnDmd3cItJroyOZ0uFOQVAl5ujdIb9Dh5/AxSe3d1Dz4ajQgLD/W6vYK8Ql6RugLUFVIOhxPepnKqVDJS2rdBcWEJqqstyDiViaEjB9Q/ZaiJ924QkWdCiHqnCQWFmNGpcwo2rduGkNBgWK02KPXM03Y6nVAEb2AnaglOh9PrfRIqlQrtOrRBUUEJFs5bCpVKRk5Wft0DPz1p6n2RROTFxbI12IyOndth47rtaNc+GVmZucjLKfD6fqfTycVhrgB1hZQ52AxZvmA1dACApcaGiooqxMXHwG6zo2efbjh84Lj3m+gkCSGhwS3SYKIrnaySERRs9vp6bnY+gkOCEBISjLiEGFSWV3md1icAmMwmaDRqj68TUdOYg0xQqWTAw7ijpcaCyopqxCVEo7KiCju37kWFl2lCgPueDGYrUcuQVTKCgkwe91XgbLaGBsFkMsBSY0FcQjS0Oo3X7ZlMRmbrFaDuG46MCkdoeDDKyyoueJPD4UDakrWQJBkulwsH0g/D5fJeZatVMjp3bd8yLSa6wqlUKiS2iYdarYLTeeHIdXZWLr754kcIRYGAOxO87a8SgDbJCTAHeS/MiKjxIqMiEBoW4vE+CofDeU62OrF98556t6VSyejUNaWFWkp0ZVOpVEhMTqg3W+d88VPds6UkSYLT6f0KVlLbBJiCTC3WXvIPdZegNBo1Bg/v7/WNLpcCp9M9RcHpdNW7pKPBZESvfj2at6VEBMB98O7RqwvCI8I8v0G4pxO5XAoUl1LvoIckS+jas1O991ARUeNptGoMGt7P6+u/Zqt72m592WpkthK1mNpsDYsI9fyGumx1weVy1VtESbKEbj07ISSU2dra1RVSsizjqmtGIzzSy8lZA0mShDFXDUNsfHSTG0dEnnXskoK+g3p5nYLQUEFBZkyaNg4qteeb24moaWRZxlWTRiLc28lZA0kS3NkaF9U8DSOiC3TqmoK+zbAqZnCwGVdPHet14RhqPeoKKUmS0Ktvd4y7eqT7iN1IcQnRuPmO66DTaZulgUR0IZVKhdvuuQGR0RFN2saU665C1x6dGvwcGyLyjSRJ6NWvB8ZNHNGkcY+4hFjcdMe10DJbiVpMXbZGhTdpG5OvZbZeKc5bXUKr1eCuB25Gn/49GvXlG0wG3PXgLejaoyN/PEQtSJIkdOneAQ88djtMjXlGhQT0GdATt907E2pejSJqUVqtBnc+eDN6NzJbjUYD7nrwJnTp3oHZStSCarP1vsdug9HY2GztgdvuvYHZeoW4YJm+hKRY/O///Q59+vs2D9tkNuKR392F6TdM4oGe6BLQaDS4/qbJuPuhW+pdxe+3ZFlG77498Kf/exLxibHcX4kugYSkWPzp/36H3v26+/Q5k9mIh39/F6bdcDX3VaJLQKPR4PqbJ+Puh26G2YfFImTV2Wz9+5OIS4jh/nqFkISHO1uFEMjOzMVn78/BqmUbUFJc6nUDarUaXXt0xB3334TR44dy2gHRJSSEgMPuwOoVG/H5h9/i6MHjHlcbqhUeGYZxE4bjvsduR0xcFA/0RJfQr9n6LVYv34CS4jKv71WrVejaoxPuuO9GjLpqCLRaZivRpVKXrcs34ouPvseRQ8fhqidbIyLDMHbCcNz72CzExDJbryBpHgupWna7A3t27MOKxWuxbtVm5OcW1j2dXavXolffbhg/aRRGjR+K2DguLkF0uQghUJBXiFXLNmDlsvVI33XgvIdixyXEYMSYwZgweTRS+3TjgAfRZXRutq5fvRUFeUV1q/XpdFqk9u2GcVePxOjxQxHDxSWILht3thZh1fL1WLl0A9J3H4TdZgfgXuspLjEWw8cMOputXTngceWpv5AC3D8ixaUgbek6vPDc67BabZAA9BmYiv+88zxMZiMkSWL1TXSZ1S6dXFFeieeefAG7t+8H4J7z/e+3/4IhI/tDVsncV4n8QG22rly6Hv95/m3YrO6Tsz4De+CFN5+D0WxgthL5gdpsLS+rwJ8e/+fZbBWQJAkvv/c3DB05gNl65Uq76COXJUmCSq2CLMuw2x1wOtzr5rucLqg1asjyBbdZEdFlUHvSpVarobiUun0VcM/d5oGeyH/UZqtKVsFhd56TrQrUGhWzlchPnJutLpcCh+PX2R6yzGy90vFITURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPlI35E1CiJZuh9+or6+SJF3ClrQ89tWtNfWV++qvrpTvtTX1E2BfWyt+r27sa2DivvqrK+V7bWg/6y2khBCorKjCiaOnsWXDTqjVKjidMiRZQllZOdIWr0WfAT0RGx8DtVrlW+v9jBACZaXlOHLoBHZtS8fRQydQWVEFvV6Hdh2S0ad/D3RL7YyY2CjIcmBfyFMUBcWFpTh04Ch2bt2Lk8cyUF1dA5PZiA6d2qHfwFR07tYRkdHhAb/DuFwK8nMLcHD/Uezalo6Mk5mwWm0IDglCpy4p6DeoFzp2SUFoWEjA99XpdCE3Kw97dx1EaUk5NBoNFEWBVqvBprXbYTIbkdIxGeYgU8D31WF3IDszF/t2HcKBPUeQk5UPIRSER4ahW2onpPbrhuT2STAY9AHfV6EocNmscFZXwVlTDeG0Q0CCrNFAbTRBbTRDpTvbzwDuqxACNdUWnDpxBju37cWhfUdRVFgClVqFhMRYpPbpjl79uiMhKQ4ajTqgv9fabD1+9DQ2b9gOSQUIWUCWZZSUlGJFa8vWkrPZut1Dtg7oiW49O7WqbD188Bh2bU3HqWMZqKmxwGgyon2ntug7MBWdurVHZFTgZ6viUpCfV4jD+49h9/b9OHMqG7az2dqhSzv0GdATHTq3RUhYcMD31eV0IScrH+k7D6CirBJ6nQ5CEdBoNdiybgeCgsxo17FNq8hWu92BrDM5SN95APv2HEJOVj4gBMIjw9A9tTN69++Btu3bwGAM/Gy1WqzIOJWNXdvTcTD9MHJzCyFLEmLiotCzd1f07t8DbdomQqfT1ttXSXgox4QQcDqd2LktHd98+gO2btoFm9V2QeUmSRIS28Rj2oyJuP6WKYiIDAu4v1ghBOx2B9av2oLvvpqP3dvT4XS6zuurBECSZbTv2BbX3zIFk68dj+CQoIDsq9Viw9JFK/Hjt79g355DEEKc31dJgqyS0b1nZ8ycNR1XXTMqIHeY2hOVhfOWYsHcpTh25GTdn9eSJAlqtQp9B/bCjbdNx8hxQwLyBE0IgeLCUsz/bjEWz1+J7DM5AKQL+qrVaTF4RF/MvG0a+g3uBVmWA7KvOZn5+GnOL1jxyzoU5RfB3c3avkqQJMBkNmLYmIGYefs0dOnZEZIkBWRfXTYrbEUFsJeXQricHt8nqdTQhoRCFxnjLqiAgCuoXE4XDu4/iq8/nYf1q7eguqrGY97ExEZh4pQxuPnO6xCXEBOQ36nT6cTOren45rP6szUpOR5TZ1yN62+eHODZuhnffTkfu3bsg6uebJ1xyxRcc+1VCA4xB2RfrRYbli1ahZ++W4wDe494zdZuPTvhhlnTMG7SiIAc6KnN1p9/WIFfflyBE0dOAxA49ydcm619BvbEjFunYOiYgQGdrQu+W4qlC1Yi+0yuO2mEgPvX6z7UanU6DB7RFzNum4K+g1IDNluzM3Mx7+tFWLZwNQoLivDb6kCSJJjMRowYOxg333UduvXsFJDZqigKThw7jTmf/4SVS9ehvKzC45Wp8IhQjJ04ArPuuQFtU5K89TXNYyFVXVWDrz6Zizmf/4Cy0oqLNkqtVqNnn6549i+PoWuPTpDlwPlLLS0pwwdvfIFFPy5HVWX1Rd+v0WowdOQAPPW/DyO5XWJA/YBys/Pxxr8/xOrlG2CxWC/6fq1Oi0lTx+LRp+9FTFxUwPRVCIGTxzLw6ovvYdvGXbDbHRf9jNFkwMxbp+Luh25FaHjgXJ0SisCB9MN448UPcWDvUTidnk+260gSQkKDcOvd1+OmO6fDaDJemoY2A5fLhZ1b0vHmCx8h42QmXC6l3vdLkoSomAjc8dCNmHLDBGi1mkvU0qYTigJHRRlqcrOgOOwN+oys1cEYmwBNSGCddFstNiyYtwQfvPEFSorLLjqtRKVSoX2ntnj6uYcxcGjfgLqK4c7W7zHnsx9RVtawbE09m61dAjBb33/jC/zsQ7YOO5utbQItW7Py8dbLn2Dtio0NyladTouJU8fi4afuQnRsZMD0VQiBU8fP4K2XPsaOzXsanK3X3TIZdzwwM6CuTimKwMH0I3jzxY9wKP0onE5X/R84m6233H0dZt4xDUaT4dI0tBm4XC5s37QHr/zzvbPZWn9fJUlCdEwk7nn0VkybeXVAZavd7sDq5Rvw+ovvIy+3AIpSf97Isoyk5Hg8+vS9GD9pJFSqC2YIXFhIWSxWfPzObHz18VzYrLYGN06SJHTu1h5/e+kP6NKjo9/vLLWjKq+/9AEWzF1y8Z3kHLIso3f/7vjHf/+ExDbxLdjK5iGEQFFhCf7159ewZsVGKEr9J6DnUqtVGDFmMP72nz8gLDy05RrZTGpHVf789IvYs2O/T/OatVoNplw/Ac8+/xiMRv8/CAohcOzwSfz5dy8h42SmT33V63WYdd8M3PXwLdDptC3YyuYhFIGdW/fiH398DYV5RT59NijYjAd+dzum33Q11JoG3RZ6WQkhYC8rQU1OpterUN5Iag1M8UkBU0w5HU58+9VPeO+1zxt0sn2uNu0S8Nw/fo9Bw/oFRF8tFis+fvsrfPXJvMZl67//gC7dr4Rs7YF/vvInJCTFtWArm0dttr745zewbuVmn7N1+NjBeP7FpxEaHtKCrWwe7tkAefjbsy9j365DPmfrNdeNw++eewgGo74FW9k8hBA4dugk/vrUf5BxMsu3bDXocOu91+OOh24KmGzdtnk3/vbsf1DgY7YGh5jx8FN34/qbJwdEtiqKgqWLVuE/f38LpSXlPn02OiYCz/7lMYybNAoq1XmDd2nn/ZsQAit+WY3ZPhZRtZ89fOA4XnvpfZSVer5M5m++/2oBFs5b6tOBHnB/Gbu378c7r36Kqspqv++ry+nCR299hbUrN/l0oAfc992sW70Fn777Daw+/iYuh5pqC1578X3s3XnA5+/Fbnfgl/lpmDt7IZwO305gL4fiwhK89s8PfC6iAMBqteG7LxZg5eJ1Pv8mLjUhBDIzsvHWix/7XEQBQGVFFT59+xvs2pru9/uqEAIuSw0sedk+F1EAIJwO1ORmwWW14IJ5GX5GCIEtG3fiwze/9LmIAoAzp7Lxyr/eQ252fkB8r8t/Xo3ZPhZRtZ91Z+sHAZOt3301vwnZui+gsvWTt2Zj/eotjcrWDau24LP35wRMtr7174+xf/fhRmXrkgWr8OM3v1x81sRl5p7OV4I3XvjQ5yIKcF9h//6LhVi1ZENAZGvGqSy8/q/3fS6iAKCivAofvfkVdmzZ6/f7qhACB/cdwZv/+cjnIgoACvKL8dpLH+DYkZMX9LWukBJCIOtMLmZ/+kOTdurd2/dh0Q9L/foHJITA0UMnMG/OIjgaecIshMCa5RuxftXmZm5d8xJCYOf2dPwyfwVcPoZaLZfThZ++X4x9uw769c4ihMDalZuw1seRwXPZrDZ89fFcZJzOaubWNS8hBJYsWIndO/Y1+jupqqzGlx9+h5LisuZtXDNzuRT88PUvOHH0dKO3UVpSji8/mIua6prma1hLEAqshXkNns7nieKww1qYByH8+xhcUlyGzz/4FuVllY3ezvGjp/HtFz81+jh+KbizNQezP53XtGzdtg8//7jM77P1yMHjmPdN07J19bINWL96SzO3rnkJIbBrWzqWLFzZ6Gx1Ol1Y8P0SHNjje3FyKQkhsH7VFmxYtbUJ2WrHnM9+RFZGTjO3rvktmb8ae3b4Phhbq6qyGl99+D1KAyBb585egONHT+HX+4x9U1Jchs/en4PqKv/OVkuNFV98+B3ycgoavY2crHx88cG3FxzHzyuk1q3cdPYvtPHsdgd++m5xk8KxpTmdTixekIb83MImbaemxoK5Xy9q0Dzhy8VisWL+d4sbNeJ7rorySsz9ZqFfH+wryisx//vFcDTx+ygqLMaCuUv8+oSluLAUv/yUBuUi9wldzJnTOUhbvM6vv9eczFysWrL+onOZL+bw/mPYun63X/fVabHAXun7aNlvOSor4Ky5cMEGf7Jr217s2bGvSdtQXC4s+3k1sjNzm6lVzU8IgbVpm3Di2Okmbcdut+On7xajIgCytTGj2+dyZ+vCJh/LW5LFYsWCuUtRVdm0E8iK8ir8MOdnv95XK8orsWju8iYPWBQVlODnH1Y0+VjekooLS7Bk/somZ2vW6RysXLzer7/XrDM5WLF47dnvo/FThg+mH8GWDTv9uq9HDh7H+tVbmthGgc3rd+DQvqPnbaduUqPLpSBt6TqvIyvu1SrcN+DJslzvSeaZ09lI330A/Qb2akKDW05lRRXWpnmf5lY7B70hf+FHD5/A4f1HkdKxbXM2sdlkZuRgx9Y9Xvsiy3Ld6kIqlaremwz37TmEk8dOIyYuuqWa2yQH0o/gyMETXl+v/d1KkgRJlrweKIUQ2Lk1HdmZeQgL88+569s37UZetveRFVmWoCjCvVKULHv9Xp0OJ7Zt3IWxE4f77X1h69O21HvyeLHjUa2aagu2bdiFfoNSodH643xuCa7SYqAZCnjhcsJWUQZnwx4VeFks/3lNvSdmskqG4lLc369QvA6Y5ucVYte2vYiMCm+hljaN0+lE2hLv2Qo0/DeccSoLe3cdQL9Bfpqt5VUXvVeotq8X6/Oxwydx+MAxtOuQ3BJNbbKsMznYudX7lKZzzyMu1tf9ew7h5LEMxPppth5KP4rjh096fb2h50zuq3j7kJuVh1B/zdaNexqUrZAAlSx7XfTIcTZbR08c5p/ZKgFrV2xqULbKsgwBAeGlAK6ptmDL+p3oP6gXNBr/XHhi+S9rGjStWqVynxN7K/ZLS8qwY8se9O7fo+53X7fYRElxKWZMvAclRaUXfFBv0GP46IEwmY0ozC9GTFwUSorLsDZtk8f/kCxJ6NK9E+xW/xxNcrlcyDiT6fFEOjjEjKEjB0Jv0OHQ/mPQ6bRI333Q67Y0GjXad2qHmmpLSza50Rx2B3JzPN9DEBkVjkHD+0Gn1cJmt0Oj0eDU8Qzs3XXA47aMJgOSkhMatCrR5WC1WFGYX+zxtfjEWPQb1AuyJKGivBIRUeHYuGYbcnPyPb4/LCwECfHxfnuvVGVFFYqKSjy+1qZdAnr37wGXS4Hx7NL1aUvWoaSozOP7Y2KjEBkaftFV8C6XkuJSlJSVeXytc/f26NA1BYV5xThx5BQ6dW2Pzet2eN1Wu4QEtI1JgNSE0beWolLJmD6zP9qmRHp8XW0yQ9bqIKlUkFVquGw22MtLvN4LlZFRhiU/7ITw0yur6/ftRG7phVcuVCoVhozsj4jIcNhtdmi0GiguBT//tNzrtjp3aQ+nwz/7CSFwJjMbDseFeajTaTF8zGAEBZtw7PApGIx6aDQabNmww+MxW5IkJLdNguynC07IKhVOnjjtsWgwmY0YOXYI9AYdSopKERIajJzsfOzYssfjtjQaNTp2ToGl2j/zxmF3IC+30OP3FBoWjOFjBkOtVqGosAThEWE4fuQkDu476nFber0OyclJXk9ULydJAhxOJzK9TMmLjo3EoOF9Ybc7UJBXhOwzufVekQwLD0VyQiJcjsZNh2xpZeXlyMnL8zhu06ZdAnr17w5AgqIoUKtV2Lh6O4oKPJ93hIYFIzw8zC9vV5VlCcWlJSgo8Pxdde3RER27tofNaoNKpYJao8KyRd6LkbZtkxAVFNHYGYIt7kTmaRR4yBsAaNehDTRqNcrLK3HN9PEoKy3HwnlLvZ4TjRg7GK9/+K/aZ/yl1Q1XFheWer2MrlarUFNjhdFkxMhxQ7FrWzri4t3P8PB0EFGEQObpbL8tpIQQXq9GaDRalJdVICy8Daqra9CmXSK0B4/DbvN8z4LT6ULGyUy/LS4gAOHll63T61BUUIwevbvC5XRBcSn1rh5ktdpw6sQZr38XfkGCx5Nkg0GPvJx89B3YCzU1FgSHBKF9p7ZeC6nqqhqcOZUFl9M/T86Ueu5/Se3bHRaLFb3798CmNdsBAKFhIV4LqYqySljKrH4Z4gDgqGfRhV79u6MwvwSx8VHIPJ0Nc7Cpni0JVJVXo8BR6LeFlM3ifcRMbTRDsdsgADhtZ99XT0JbqywozCr0y+9VCAGn3fP3qjfo0D21C7IyciDLEk4ez8DQEf295g0AZGfm+XXeOBXPfQ0ND0FKh2QUF5Vg+OhBcDgcKMgv8tpXIQTysgv89oZ9jUbt9cpLfGIsomIi4XI6YTXZkJ9XhISkWOzwciuU0+nC6ZOZsFn8OG9+fXzdedp3ageDUY/g0CAkto3HsUMnERkTAXiZyWq3O5B9JrfJ08laikrj/aHQ3VI7QxECkdHh2LZhF3r174HC/GKv+2p1VQ2yTudAuPzvuAQAdqfday2Q2q87LDVWdOyagoqySmh1GugN3lfmq66sQU2l1S+nvEmSBKfwfszsPaAnCvOK0LZDG2SezkbPPl2xcc12r4VUSVEZ7CV2v8xWALBYvF/syMsuwIixg+FyurBy6XoMGdEfGo0GLpfnvuZmnX9xou4eqfouO0uShMSkWOTlFGDXtnQYTQacOpFR74/Dn+8vqY+sktCmbSIOHTgKl9MJp92BIWdD3JtA7atKpULblDbYvmk3qiqrUV5e6WmN/F+Jhk139EcajbquryGhwcjOzK23+K3v0q6/K8wvhtFowJEDJxAdG4nI6PB6r6wpihKw32tRQQn0Bi1yMvOQ2rcb1Or6p7IJIfx2xOxiFKfTPTwsBCAEVAZj/Q/eDdDv1Ol0oaKsEg6HA4oioNfrYLc7WmXeWK02WCxWVFZUYeXSdTCZjCgrKa+3P/68r9bXsqrKaiguBQX5RdBqNYiIDMOGNdvq3V6gHoNLS8qgUquQeTobRWdnSeRk5tX7GX/+Xuv7YosKS6DX65B9JhcGox4hoUFo37mt900JAcWf+1qPwvxi9/nvsTNwOJyoqbKgvnuLRD0D2f6uqKAYOoMOlRVVcLlcyMnMg6ueAZxAPQYDQFCIGRKA9p3boWvPTjAY9fXe5uL8zWt1Zx0hocFeT6ItNRbkZhcgMioc+/ceQreenVFWWs8N0ZKE8Mgwvx1JUhQFxSUlHg9c5WWVKCkuRUxsFEJDgxEWEYrSknLIsgSXhxEUWZYRERXut1P7XE4nKiqqPL5WWFCE6uoaRMVEIH33QSS3S7roNMbwyDBYavzx6puAw+FEtZdV2XKy89G1ZyeYzEYcSD+CmNgoHDl43OvWdHodwkND4fTH6QdCwGqzee3r/j2HEBRiRm5WPnR6LYKCTPVOtTCajDAbTFD89OpbVXU1nBbPB/A92/aj7+BUFBeWIjc7H+ag+q5ISdAb9TCHmv1yzExWyVDXM/LrrKqA2miC02qBWm+As6bKe7EkAI1OC1OwyS+vSAECUrHnB+narDZs27QLKR2TcfTwSXTr2QnbNu+ud2thEWGwW/0zbyAEiktLPX4PFWWV2L19H2LiopCfV4i0petgt9fTD0lCcGiQ307XVKnVsBXYPGZrfm4hDh84ClOQCTlZeejcrQPCI0JRXOh5irKskhEZFQ6Ln2ar0+nyuohTxslMxCXEQFHcKwR37JKCinLv96Ko1CqEhAX751UayV38WG2eR+ePHjiOyKgwWC02dOnZCRqNut4BLZ1eh7DwECh+ORVXoKq6GtUOz7+5/bsPISioP3JzCqDJVsEUZEJRgeffLwDo9FoYDQa/LJIlWUZVTRWsds/f686t6RgwuBf2bN+P4NAgVJRVorKeRcuCgs0I0QX7ZV8BoMJZCXjoqiRJ6NSlPYKCzTh68Dh0eh327TlU76MbIqPCzxvDrLtHymaz49ZpD+L4kaat2ge4pwL+7k8PoXvPzk3eVkuoqqzG3//nZRR5OYD7wmQ24g9/fRxJfvpg3pzsPLz01zdQWdG0VfsA91zoZ//ymN/e1H3owFG8/fInzTLNsn2ndnjyD/cjOCSoGVrW/LZu2IWvPvy+WZZ97jOgB+55ZBYMBv97UKIQAssWrcbCucuaZdrLqHGDcds9M6Hxw4cHShIQorFB7WyeE0eXLhgVNpV/jocK4MV/vokd2/c2eVOSJOHeR2Zh2KiBzdCw5ud0uPDPv7yKjJOZTd6WWq3C48/ej9Q+3ZqhZc2vqqoaf/vjy16LI1+YzCb88a+P++1D73Oz8/Cfv73d5BVxAffDPn//3COIifV8f+TlduTgCbz7389gbZZsbYtHn7nHP7NVAFvW78RXHzVPtvbs0xX3PHoLDH662MQv89Pw07e/NMvVpLETh2PWXTdcdFbI5fLZh98gbdm6ZtnW7ffOxFP/+zBk94N5f71HSq1WY+TYITh+9HSTp4SEhIVg3MQRiE+MbVprW4jVasOQkQOw6IdlTd5WTGwUxl898iIj4ZdPh7J2WPxTGjauq38KRUO0bZeEMROGQ6v1z1VZEtrE4ecfV+DQfs839DaUJEno2r0jho0a6LdP6w4LD8WS+SuRm+35Hq+GUqlk9OrfA/2H9qp/WudlJKtkpP2yrsknLBqtBgNG9EXXfp0hy/54TQqwl5ei6szJJh+DJVlGSGw0IoND6p2WfLkIITB+ymjs3NH0hySbzEaMmTAc3VM7+2VfXS4FYyeOwGfvz2ny9xoaFoKJU8YgLiGmmVrXvKxWG4aM6I+ff/S+MEhDxcRFYdzVI/w2W8vL2mLJ/JXYvN774jYN1bZ9G4yZOMxvszU2IRq//LgCRw54n8XREJIkoXP3Dhg0sq/fnnAHhZqweH5ak543BLizte+gVAwY3hcqleer75edBCxbtKpZsnXQ8H5IHdDdb7P1muvGY83KTU2+v9Rg0KP/4N6Qzuln3bcryxLGXT0CcfFNW35TlmVcPWUMIqP986oF4F4p6eqpYxESFtyk7ajVKky74WoYTX442nBWcHAQrp4+Dnq9rknb0Wg1uO6myX45kl8rOiYS4yeNqh0laDSDQY/pM6/22yIKAJLaJmDY6IFNPnEMCw/FxKlj/LaIAoBO3dqj76DUpjzmAgCQmByPYaMH+u2BHgDUpiCoDcYmb0dlMEFtMvllYVFr2KiBSOnYtKWtJUnCsFGD0K59G7/tqyxLGDexebJ14tSxiPDTGQFAbbaOa5ZsnX7DRL/P1onTxkDXDNl67Y3X+He2xkZi7MThTc9Wox5TbrjKb4soAEhql4Cho+u/L74hwiJCcdXUUf5bRAHo0r0D+g3u1eRsbdM2AcPHDPLrbO07MBXde3Vp8nZ69O6K1L7dz/t91H3DkiSha49OuOba8U36AbVpm4Abb7/Wb9eSB9x9HTy8H0aOHdKEjQA9enXFNdOb9vfV0iRZwlXXjEKfAT0bvQ1ZljB81EAMHzPIr/sqyzKunXk1OnZJafQ2VCoZk6aPQ2qf7s3YsuYnyxJuuG0qEpLiGr0NtUaNa2+ehLbtk5qxZc1Pq9PgprumIzwirPHb0Gpw4+1TER3nn1NnakkqFfSRsZDkxoevJMvQR8VAUvnvyYokSUhsE4eZs6ZD04RR+PDIUNx+30y/PuGWJAndenZqclYkt0vEjbdN9+sTbkmSMGR4P4wYM7gJGwF69u6KSdP8P1vHTxqF3v16NHobsixh2KiBGDp6gF/3VZZlTLnhKnTo1LbR21CpZEycOgY9muFktiXJsowZs6Y2aUaVWqPG9JsCIVu1mHX3DERENiVbtbj5zusQExfVjC1rfqFhIbjt3htgMjd+oNJoMuCO+25E2G9Wtz4vrVUqFWbdfQPGThgOVSOCPCwiFI8/ez+S2yb69UEBcPf1wSfuwIDBvRvV1pi4aDz5xwcQHRvp9301GPT43f88iC7dOvj+YQlI6dAWT/zhAf+c0/wb4ZFhePbPjyKxEQWGJEno3b8nHnj8Duj03pc09QeSJCE5JRGP/eGeRj3YUJIkjBo/BDNvmwa5CSftl4IkSejZtyvufvRmGIy+38elUqkwdeZEjJ88qgVa17wkSYImOAS6yJj6V+TzvgHoo2KhMQf7/XFJlmVMmzER02ZMbFRxYA4y4aEn70K3Hp38vq8qlQqz7pmBMU3I1seevS8wslWtwoNP3NnobI2Ni8YTgZKtRj2e+J/70alr+0Z9PqVjMh579l4EBZubuWXNLzwyDE/+74ONKzAk99Lhdz96C7S6AMjW9ol45Nm7EdqIK6uSJGHk+CGYcduUgMjWXv27477HbmtUtqrVKlx70yRMmDK6+RvXzCRJwujxQ3Hr3TOga8RvUKfX4a4Hbsag4f0uOC5d8C2HR4Timb88gjEThjf48qskSYiKicQfnn8Mo8YNOW/uoL9yj4jG449/ewL9BzX8/hBZlpHcLhHPv/A0evXr7vcHesDd1y7dO+KPf3sCXbt3bPDOLatkdOvRGc+/+DRSOiQHRF9lWUb/wb3x9F8eRXJKUoPbrFarMXBoH/zp708iJi4qIPqqUqkwavxQPPbsPYj24SZlrVaD0ROG4on/uR9hEaEB0Ve1Wo0pM67CPY/PQnBowwt6vUGHyTOuwr2P3wpTkDEg+lp7RUkfGQP4EMTnfq4pV7QuJaPJgEeeugfTb7japytTIaHBeOSpuzHthquhUvvvtNRzhUeE4Zk/P4LRjc3WsYGTrUnJ8fjj3x5HP5+zNcmdrX0DKVs74Nm/PobO3Tv4lq09O+G5fz2Fdh38d1rquWRZRr/BqXjyfx9Am3YJDR7nUavVGDCkN57966MBURwDZ7P1qiF4+Jm7fctWnTtbH//jvQgL98/7U39LrVZj2syr8cATdyDEh2w1GPSYdsPVeODJO2AO8u9p5LU0Gg3uuP9G3HbvTJ8KR7PZhDvum4nb7pvpsQirW7XvXEIIlJdVYN43i/Djt78gJyvP6w3BWp0Ww0YOwJ0P3IzUvt38+l4LT4QQKCwoxtefzsPPP61AcaHnZdEBwGA0YOzE4bjrgZvRoXOKX88H9UQIgawzOfjs/TlYsXgtKsoqvK7oFRIajImTx+Cuh25BQlJsQOwktYQQEELg2JGT+PS9b7Bu5eZ6l6ePionE5GvH4477b0J4gBQWtWr7unfnQcz+aC62btgJu5cHa0sSkJAUh6k3TMTM26fBZA6MwqKW+9leCjav2YHvv1iA3dv3eX3yuCRLaNc+CdfPmoJJ17nvEQykvgKAUBTYy0thLSqAy1L/zcAqgwn6qBhog0MBSQqovgohUFNjwaIfluH72Qtx8thpr8dgtUaNvgNScecDN2HwsH5+fR+jJ75n60Dc9eBN6Nmnu1/fa+GJEAKF+cX4+rN5+PnH5SguKq03W8dNHIE7H7gpgLM1F1+8/y1WLl2H8jLvS50HhwZh4uQxuOPBGxGfGJjZevzIaXz5/nfYuHobamrqy9YIXD1tLG69b0bAFBa1fs3WA/jmox+wdeNuOLxkKyQJCUmxmHrDBMy4bUpgZqtLwYY1WzHnsx+xa1t6vdma0iEZN94+HZOvuwp6Q2BlqxACDrsDy35Zg2+//AkH9h72elxSqVTo2qMTbr9vZt1Cax76muaxkKrldLpw5nQW1q3chA1rtqKooAR2uwOyLMNkNqBLt44Yf80o9OrbPSCmfdXHbnfg1PEMrFy6Dts270ZpcRkcDidUKhnmIBN69e2OcVePRPfUzjCamn4z+OUihIDNasPRQyewYvFapC1Zi9xzVqeJS4jBhMmjMXbiCHTp1qHJN9JeTrUnaAf2HkbaknVI330Q1VU1cLlc0GjUCIsIxZDh/TH6qmFI6ZDcpHs1LjchBCorqrF35wGsWb4Bhw8ch6XGCqEo0Gg0iIqJwJBR/TFi7GAktImHOkBG8T0RQqCspBy7t+3DmuWbcOrYGVit7mfXaLUaxCXGYOjogRg6qj9i4qP8fnpFfYQQEA4HHFUVsBYXoTKvCMrZ51tIsoyQxBjowiKgCQqCpPZ4kA8YiqIgOzMXm9Ztx5oVG5GXUwC73Q5JkqA36NG+U1tcNWkU+g5MRVh4YA14/FZttq5N24SNa3+brUZ06d4BV00ahdRWkq0nj53GqmXrsW3TbpSWnJut5rPZOgLdU7v49b1uF1OXrYdPYuWSdVj+yxrk5xTWvR6XGIOJU8Zg9IRh6Ny1favI1kPpR7Fq6Qbs33MYNdU1cLkUqNVqhEWEYNCwvhgxfgjatU8K+GytqsvWTThy4DisFisURUCjUbuzdWR/DBs3CAlJcQGfraXFZdi5NR2rlq3HyWMZsFpsEHBna0JiLIaPHYxhowciNi66yYuPXE5CEcjPL8TWjbuwZEEadm1LrxuEVqvVGDKyPyZcMxqDhvdDVHREfXlTfyEF/Pq0bfdIWiWqq6qhVqsRGh5Sd4krkAPtXLV9VRQFZaUVsNRYoNFqEBYeWjeHv7X19a1/f4zZn8yDgIAECXc9fDMefPIOyLLc6vrqsDtQVloBu80Og8mA0LDgupPs1tZXm9WO8rIKOJ1OmExGBIcG1fWxtfXVYrGiorQSihAwB5kQFPzrcsmtqa8VOcXY8tEvqC6uAABoTXqM+9Ot0AcH1ujnxQghAAFUVFShsqIKKpWMkNDguqkYraWv52drBaqrapitrUBtX1/91/v4+pN5dX9+76Oz8NDv72zV2eqwO2AwGhASFtR6s9VmR3lpBVxOF4xmI4JDzK03W2usKC+rgFAEzMGm8+7la019PXb4JJ558G/IycoD4J6R9e3SD+uemXqRvqZddF7EuT+QsPCQC1araE1q+6pSqc6uYtL4lUz8nSRJEELApSjnrauvuFx1r7cWtX3R6rQ+zXcORLV91Rt00Bv8exWdpqrtq9FogNEfH3jYjGr76nIpdQ8mdjlb374KnO2PBISEBvk0Zz/QnJ+toQgLD728DWpBV2K2etsrW9P+ekVmq14HvZ+vUNdUddlqMgT0VeKGkCQJEjwXwg3dVwP3uhwREREREdFlwkKKiIiIiIjIRyykiIiIiIiIfMRCioiIiIiIyEcspIiIiIiIiHzEQoqIiIiIiMhHLKSIiIiIiIh8xEKKiIiIiIjIRyykiIiIiIiIfMRCioiIiIiIyEcspIiIiIiIiHzEQoqIiIiIiMhHLKSIiIiIiIh8xEKKiIiIiIjIRyykiIiIiIiIfMRCioiIiIiIyEcspIiIiIiIiHzEQoqIiIiIiMhHLKSIiIiIiIh8xEKKiIiIiIjIRyykiIiIiIiIfMRCioiIiIiIyEcspIiIiIiIiHzEQoqIiIiIiMhHLKSIiIiIiIh8xEKKiIiIiIjIRyykiIiIiIiIfMRCioiIiIiIyEcspIiIiIiIiHzEQoqIiIiIiMhHLKSIiIiIiIh8xEKKiIiIiIjIRyykiIiIiIiIfMRCioiIiIiIyEcspIiIiIiIiHzEQoqIiIiIiMhHLKSuUEKIun88/TkR+Q8hBBRFcf/v2X8AQHEp3F+J/Ehdtv72z8FsJfI37kxVAOnXP5MkCUJpeLaqW6ht5MdcLhdOn8jEtk27sHtHOtRaNVxOF9RqFXZu3Yt53yzCgMG90a5DW8iydPENElGLqayowp4d+7Fz/S7kHDwJW40FEgCdUY/T732DfkN7o3f/7jCZTZAk7q9El4s7W89g26bdOHTgKIxBBthtduj0Ouzfc6guW1M6tIXEbCW6rCrKq7Bnxz5sWLsNilCg0qogSRJ0Ri2+/HguBg3riz79e1w0WyXBIZIrhhACJUWl+H72AixeuBJnTmV5rLhlWUZScgImXzseN9w6FRFR4TxBI7rEHA4ndm3di9mfzsOe7ftRXVXj8X1mswm9+3fHHQ/ehF79ekCtVnF/JbqEhBAoLirF91/Nx5JFqy6arVOuuwozbp2KiMgw7qtEl5jD4cDOrXvx1cdzsXvHvnqztc+AnrjrwZvry9Y0FlJXCCEETh7LwIt/fQM7t+6Fy+W66GckScLQUQPxzJ8fQUqHZB7wiS4BIQRsVjt++m4xPnj9C1SUVzboc2ERobjv0Vm44bZpLKaILhEhBE4cPY2X/voGdm5Lb3C2Dhs1EM/8+VG069CG+yrRJeDOVht++PYXvP/6Z6gor2rQ58IjQnH/Y7dj5m3TPWUrC6krgRACZ05n4S9Pv4S9uw74NE9blmX07N0VL735FyQkxbVgK4kIAFxOF+Z8/iPee+1zWGqsPn02KMSMB5+8EzfeNg1qDWduE7UkIQTOnMrCn59+Eem7D/qcral9uuGlN/6MeGYrUYtzOV34+rN5ePe1z3zO1uAQMx763d246bbpv83WNC42cQWw2+x499XPkL7HtwM9ACiKgn17DuGDN75AVWU1b5YlakFCCGzfvAdffPi9zwd6AKgsr8Kn73zt84AJEfnOZrPjnVc/xb49hxqVrem7D+L9N79EdRWzlaglCSGwbdMufP7hd43K1oryKnz8zmyP2cpCqpUTQmDDmq1Yk7YRiktp1DYURcHSn1djx5Y9zds4IjpPdVUNvvzoOxQXljR6GyXFZfjyg+9QXel53jcRNV1ttq5N2wRFaUK2LlqFHVvTm7l1RHSuqspqfP5hE7O1qBSff/Atqquqz/tzFlKtXFVlNRb+sKxRFfi5rBYr5n69sEHzv4mocdJ3HcSubfuavJ3dO/b5PNWIiBquqrIai+Ytg8XSHNm6gNlK1ILSdx3Aru1NH7DYtS0d6bvPvwLNQqqVK8wvwt6d+72+rlarzvn/9d9TceLoaWRmZDdb24joV0IIrFu5GQ67w+PrsixBkiXIKhlarQYarcbrtqoqa7Br214WUkQtpDC/CHt2XTxb1Ro1DAY9ZNn76dbxI6eQmZHT7G0kIne2rqk3W+XzHkegUnnfV6uqqrFz614WUleS3Ox8lBSXeX19zIThMJoMAIAbZk2td1vl5RU4dSKzOZtHRGdZLVacPpnptfhp274NuvfsjK7dO+Lhp+/GuKtH1FtM7d97pNFTjoiofrnZ+Si9SLYGBZsx5qphuGryaPQf3NvreyvKK3H6xJnmbyQRwWKx4vSJM16ztd3ZbI2KjsCQEf1x4+3XQqfXet3e/r2HzstWFlKtXNFF5oOePJaBzt06QKPVwGA01Ptem9WGstLy5mweEZ1VU2NFTXUN4OUiUmZGDuKT4pCdlYcNq7ZCUUS99z0W5heBF6SIWsZFs/V4Bjp1ScGB9CNQqVTQG3Re32u12FBWVtHcTSQiAJZqiztbvcjMyEZCm3jExkcjpUMyFJcCRfEengW/yVauj9vK1XceFRRsRlCIGf0G9YYsy4iNjWraBomo8QTq3b/iE2KgUsm47qZrkJ2Zi+R2CVCrVV7vrXAf6LnDErWEi2ZrsBn9h/RBbnY+KiuqIOEiz4rirkp06UlAXEIM1LKMqOgIWK02GAx6uJxechW4YICShVQrFxUT4fU1g0GP8IgwZJ/Jwcljp7Hwh6X1bktv0CMsIrSZW0hEAGA0G2AyG+HpfEuSJERGR8DlcmHPzv3Q6/VYv2oL7Ha71+3FxkXxQZ9ELeRi2RoRGYYzp7OQcSoLYeGh9d6rrDfoEBYe0hLNJLriGU1Gd7Z6IEFCVEwknC4XigpLsHvHPkTFRHqdBigBiI2LxrnRykKqlYuLi0Z4RKjH+6QK8ouwatn6un8vLal/2l5wSBCS2yU2dxOJCIBer0Ny+yRs27T7goO4EAI7t+71aXtdUzvVe4M7ETXexbJ15dL1F37Ii5CQYGYrUQvRG3Rom+I9W3/7aJ+LnQt3S+18XrYyZVu56Ngo9O7Xo1m21aFTOyS35cGeqCVIkoTRVw09byXNxjIHmdB/cG9ekSJqIdGxUejVt5mytXM7tGG2ErUISZIwZsJwqJolW80Y8JtsZSHVypnMRlx74zUwmTxf1mwoo8mAG2+bDrmeZSGJqGm6p3bB4BH9m7yd/oN7oWfvriykiFqIyWzEtTddA2NzZOvtzFailtSjV1cMGd7f49R5XwwY0vuCbOWe28pJkoQhI/pjxLjBjT6pUqlUuGrSKPQb1IsnZkQtyBxkwi13X4/wyLBGbyMsPAS33TcT5iBTM7aMiM4lSRKGjuiPkWOblq0TrhmNvgNSma1ELcgcZMKse25AeETTsvWO+268IFtZSF0BtDotnnj2fvQf1Mvnz0qShNS+3fDYs/fVPW+KiFqGJEkYOKQP7n/8tkbtb0aTEY88cw9S+3ZrgdYR0bm0Oi2e+MP96Dcw1efPSpKEXv2647Fn7mW2ErUwSZIwaGhfPPD47TA1Yn8zmY14/Nn7PWarJLwtTUGtihACJ49l4NUX3sPmDTvgdDgv+hmNRoMhI/rjqeceRrv2bThiRnQJCCFgs9qxcN5SfPTmVyguLm3Q0sjRsZG499FZmDbzauh03h8mSETNRwiBE0dP49UX3sOWjTsblq1aDYaOGICn/vchtGW2El0S7my1YcHcJfjgzS9RUlzaoGctRsdG4f7HbsP0mZM8ZWsaC6kriBACpSXlmPfNIvwwZxEK84vg9LBWvlqtQlRMJG6cNR3X3zIZoWEhPNATXUJCCCiKwM4te/DNZz9iy4YdcNidEEKct+yqJEnQ6rQYOLQvbr9/Jnr37wGVquk31BJRw7mztexstv588Wy9bTquv3kKQsOCma1El1Bttm7fshvffPoDNm/YAYfdccFqfrIsQ6vTYNCwfrjz/pvqy1YWUlcaIQRcLhcK8oqwbuUm/DDnZxw7fKru9U7d2mPGLVMwYsxgxMRGNcsqJ0TUOEII1FRbcHDfEWxYuRnVRYWQai9PSRJMkdEYPnYIuqV2hsGo50kZ0WXy22yd+/UiHDtysu71Lt074IZbp2H46EHMVqLLTAiB6uoaHEw/gl/mr8CqpRtgqbECALQ6DabOmIDxk0ahe2qXi2VrGp8jdYWRJAlqtRrxibG46Y7rkJtdgJNHz9S9PnLMENxw61SOahP5AUmSYDIbMWBIH/Tp3RlVp49DcbgfwiupVAjp1B2yhtP4iC6332Zr1plcHD/66yDlyLFDMOOWKcxWIj8gSRLMZhMGDu2LsPBQpO84hNysfABAkNmM+x+7A5HR4Q3aFgupK5zU1LUgiYiI6HyMVqKAobgUKIoCAHA5lYbcllyHq/YRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGPWEgRERERERH5iIUUERERERGRj1hIERERERER+YiFFBERERERkY9YSBEREREREfmIhRQREREREZGP1A15k8vlgqXGCqvVBpfLBUmSoNVqYDAaoNVqIElSS7fzkhBCwOVSYKmxwGazQ3EpkGQJOq0WBqMeGq3mcjex2Qgh4HS64FIUyLIMIQQkSYKiKHA6XVCpVJe7ic1GCAGHwwlLjQV2mwOKUKBSqaDTaWE0GqBSt66+2u0OWGoscNgdEAJQqWToDTroDQaoVK1n7EQIAZvVBovFCofdCUBApVbDYNBBb9BDlltbX+2osdjhtFoBCVBrNNBb7dCrW88xGAAURanLG6fTCUmSoNGoYTAYoNNrW1Vfa7PVZrXB6XJBliRozuZNq81Wq82dO5IErU5bdx7RWtRmq6KIX7NVluBytfZstUMRolVnq8PugKXG6s5WnO2rXgeDQQ+5VWarDQ6HAxCAWq2C3qCH3qBrddlqt9nP+zNJkmCz2urOiy/GayElhIAQAqdPZCJt6Vrs3XkAJ49loKKiEmqNGvEJsejSrQOGjhqI4aMHQm/QB+xBXwgBRVFw9NBJrF62AQf2HkHGyUxUV1mg02mQ0CYOXXp0xLDRAzBgSB+oNeqA7qvT6UL6rgNYtXwDdm1Lh9aggd3ugE6rwZaNO+FwOjFq/FD06d8DsiwHdF8ddge2btyF9au34OC+o8jOzIXdbofJbELblCSk9umGsROGo0uPjpAkKaD7arXYsH7VFmzZsAOH9x9DXk4hXC4ngoKDkNIxGal9u2HcpJFo2y4JkBCQfRVCAAAqK6qwevkGbN20C0cPnUB+biGEEAgND0HHzino078HrrpmNGLjowOyn8CvfS0tLsemtG04sPMQSgqKUFNZA0mSYAwyICxmK3r264Yh4wYgNDw44Puak5WHtKXrsGtbOk4cPY3SknKoVDJiYqPQqVt7DB7eH6PGDUFQsDmg+/prtq5zZ+vxDFRWVEGjUSMuIRadu7XHsFEDMWzUgFaRrYcPHMfKpeuwb89BnD6RierqGmh1WiS1iUe3np0xfMwgDB7Wr9Vlq8FocGerToOtG3fC5XRhZCvL1nWrt+DQviPIzsyry9Z27ZPQs3c3jJ04Al26dwj8bLXasGn1dmzfuBtHD7rzxuV0ISjYjLYdktCjTxeMmTgcSe0SAAR+tq5ZvhHbNu/GsUMnUZBXdDZbg9GhUwp69++O8deMQkxcVED2E/i1r8WFJUhbuh6b1m1DWXk5FCjuIsphw2svvofBw/tj7MQRCI8Irbevkqjd4m/+I8VFpfhhzs/46dtfUJBfBJfL5XEDRpMBvfr2wL2P3Iq+A1MDbrRFCIG87AJ89+V8LPt5DUqKSiGUC/5KAAkICjJhwNC+uOOBmejas1PA/YgURUHGyUx89sG3WLdyM0pLyjy+T5IkhIaFYOS4Ibj7wZvRtn2bgOury6Xg8IGj+Pidr7Fjyx5UlFd6fJ8kSYiKjsBVk0fjjvtuDMiDg9Ppwq5t6fjs3W+wf+9hVFfVeHyfSiUjJi4a02ZOxMxZ0xAaHhJwfXXYHVi3ajO++PA7HDl0AlaL1eP71GoVEpLicctd12Hq9RNgMpsCrq9Wiw3rl23B/K8XI+tULhx2BwBAADi3JxqtBolt4zDj7qkYOnZAQF61qSivxKIfluG7r+YjOysPTofT4/v0eh06d+uAex+ZhaEjBwTcLIFzs3X+d4tRkF/sNVtNJgNS+3bHPQ/fir4DewZktuZk5+ObT+dhyaKVKK43W80YPLw/7nnoFnRL7Rxwv19FUXD6ZCY+e38O1q/actFsHTV+KO564KaAzdZD+4/ik3dmY8fWvRfN1gmTR+P2AM7WPdv3YfaH83Bw71HUVHvJVllGdHwUrrl+PK679RqEhAbeoJY7W7dg9sdzcfTQCVgtNo/vU6tVSGgTh5vuuBaTr7sKJrMx4PpqqbFi2c+r8fVn83D6RCbsdrvH92m1GrRt3wZ3PXgzxk4cAb1e56mvaRcUUrUHv5f/722sX7UFTqfnQPutmLgoPPb0vZg0fRzU6sAYVRJC4MTR03j5b28jfdchr4H2W21TkvD4H+/D0NEDAibcFEXBnh378eJf38DxIyeheAo0D3r06oKnn3sYvfunQpb9/zsF3H1dk7YJr73wHjIzcuBhrOACkixh0NC+ePq5R9CxS0pA/H4BwOFw4ucfl+OD179EQV5hgz6jVqsxctxgPPXnhxGXEBMwfbXUWPHtVz/hs/fmoLysokGf0et1mDR9HJ7844MIDQuMcBNCoLqyBnM/XYhF3y6HtcZzsfhbRpMB19w0Hrc8cD30Bo8HfL8jhEBxYQnefuUT/PLTCtjPFosXExoWjHsfmYWbbr8WWl1gFI5CCORk5eHlf7yLDWu2ei0Wf8udrffg6mljAypbjx85hX/9+TXs3bUfLpfSoM+169AGT/3pYQwfMyigsnX39n146W9v+pStPXt3wVPPPYI+/XpCCqRsXbERr734PjIzstGAaIUsSxgYoNm6dP5KfPLWNyjKL27QZ9RqNYaNHYjH/+c+xMQHTuFoqbHi+68W4PMPvkVFmefC+Ld0eh0mTRuLx/94X8AUjkIIVFZU4ZP3vsF3X/4ESwOz1Ww24sbbpuP+x++AwXjBDIELC6mS4lL85ekXsXHdds+jR/UIDQvGn/7vd5g4ZYzf/6UKIZB9JhfPP/1vHNh7pEEn2+eKionA31/5I/oNSg2Ivh4+cAx/evKfOHXijE+flSQgOSUJ/33n7+jYJaWFWth8hCKwbfMuPPfUCyhs4MGvliRJSO3TDf9+63nEJcS0UAubj+JSkLZkHf7xp1e8XoXyRpZljBw3GH9+4SmER4a1UAubj8vpwrdf/YTXXvyg7spMQ6k1KkybcTWefu4RmINMLdTC5uN0OPHl29/jpy8XN3hwp5ZWp8V1t0/CLQ/NCIj7TmpqLHjhz6/hlwVpUBp4sl3LHGTEI0/dg5vvuD4g7v0rKSrFX575Nzat2+5z3riz9UlMmDw6IPImMyMHf/rdP7B/z6EGnWyfKzo2Ei++/mf0H9w7IPp6aP9R/OnJf+L0yUyfPitJQNv2bfDyO39Dx84BlK2/fwGFBY3I1r7d8O83AyRbFQWrlmzAy8+/3YhslTBszCD84R+PISwitGUa2IxcThe++3I+3vzPx43IVjWmzpiA3//vgzCZ/T9bHQ4H3v7vJ/jqk7lwOX3LVr1eh9vum4kHH78DWp323JfSzksfp8OJLz/6Hls27PS5iAKAstIKvPf65zh5LMPnoLjUHA4nPnprNg6mH21UWwvzi/H+q58jL6fA7/taXVWD11/6wOcDPQAIAWSczMJb//0YpSXlft/XgvwivPrC+ygqKPH5s0II7N97CB+8+WWDRyouFyEEjh89hXdf+dTnAz3gDoqNa7Zhzuc/+XxAudSEENixdQ8+f/9bnw/0AOB0uPDL/BX4+acVfv/7VRQFG9O2YekPq3wuogDAbrNj0Zzl2LF+t9/31eVy4advf8GKxWt9LqIAoKqyBp++Nwfpuw/4fV+dDie+/Hgutm7c2ai2lpVW4P3Xv8DJ44GQrQ689/pnZwcoff98QV4R3v7vx8jNzvf7vlZX1eCNlz5Exqksnz8rBHD6RCbe/u8nKCv1/2zNzy/Eq/96D0WFjczWPYfw4VtfwuJlOra/EELg5NHT+PiN2Y3MVoHN63Zg3leLGnUMv5SEENi5dS++/Oj7RmarE4vnp2Hx/JV+//tVFPfA84/f/tKocx6r1YY5n/+IDWu2XtDXukJKCIHDB49h8YKVcDbhxOrMqSz8MGeRe6UPPyWEwI7Ne7Bx9VYoiu8BXutA+hGs+GWtX/+AhBBYuXQddm3f1+h2CiGwae12bFq3rZlb17wURWDhD8tw5NDxRvfV5VKwdNEq7NtzsJlb17yEEJj39SKcOZ3d6G04HE4s+H6xz1cpLzW73YGvP/sBBflFjd6GzWrH91/NR35uQTO2rPlVVVRjwddLUVVR3eht1FRbsOCbZSgvbdgUjcuhdprb3K8Xwmr1PBe/IYoLSzDn8x9RU21pxtY1L3e2HseShU3L1oxTWfhxzs9wNHBK4OUghHAv7rNqS5Oydd+eQ1j282q/z9a0peuwa0fTsnXjmm3YvG57M7eueSmKwKIfluHI4RNNy9aFq3Bg76Fmbl3zEkLgpzmLkZWR0+htOB1O/DxvOTJO+F5gX0p2uwNzPv/x7Oydxn2vNqsdc79agPzcht1acLlUlFfi689+8HpPX0NUV9Xgm89/RFlJ+Xl/XldIKYrAisVrG3yfhTeKomDxgpU+T6u6lGw2O5YuXIWK8qombcfldGHh3GWNGrW4VMrLKrBk4coLlnf0lcPhwA/f/NyoUYtLJT+3ACuXrm3U1dRzWWos+PHbX/z6hOXU8TPYuKbphW1JcRkW/5Tm1yNnB9IPY9e29CZvJ+NUFlav2NikE7yWlr79II4fPNnk7RxJP4aDu32fsnwprVu5GadP+X6V/FxCCKxfvdWvr9QoioIVi9egIK/xAwG121mycBWKfJxWdSnZrDb8Mn9Fk05WAPdN/j99t9j/s3VBWrNk67w5/p2teTn5SFuyrsnZWlNjwY/fLvbrbD19IhNb1u1s8nZKi8uwbGHjZhZcKgf2HsaubfvO/lvjp9FmnM7GurTNfp2t2zbtxqH9R5u8nfTdB7H7N4MndcufO51ObFy7zWsYGU1GWCwW6LRaBAWbUV1d43UUsKK8EquWbUDvfj2a3OiWUFNdg+2b9nh93WQ2orrKvTxrULAZ1VXVXlcwKS4swe51u9GxY7sWam3TnMnKwf69h72+bg4yoaqyGjq9FopLqfcAl3kmGxvWbEVUdGRLNLXJDu4/itMnvY8AmcxG1FRbEBRshlanRXlpudf+Hj10AlvX70JYeEhLNbdJNq/fjmIvUyxkWYLeoIfVYkXw2ZtAy0rLPYagogik7z6AnVvTYTDoW7rZjbJ04SqvqyXpDXoEBZthqbHAaDTA5XKhpLjM43HM6XRix+a9SO3ZDRqNf94/tG7JJq/BazAZYDTqUVlRDaEokGTZ60mc3ebA9o27YQ4zwV9vM1mx2PugR1CwGXq9Dk6nE7JKBafD6XWBEUuNBetXbYHsp8+XdzqdWJe2xeNvUpIkBIcEQaNRw2q1wWDUo6ba4rWAKC+vxMql69Grb/eWbnajVFdVY9umXR5fk2UZIaHBkGUJpSXlUGvUwNnn3nlSWFCE1cs3ol37Ni3Z5EbLzcnHgfQjHl9TqVQIDQt2L4nucEKj06KyvNJrXzMzsrF+9VZERUe0ZJMb7eC+I8jwMuih1qgRGhYCh90Bp9MJvUGH8tJKrwuVHT10Als37ERIaFBLNrnRtq7fhZKiUo+vaXUaBIcGw1pjrXvenbdzZkUROLDnMNK3H/TbbE37eR0sNZ7P493ZaoKlxgqNVgMJ8Hp7h9PhxPbNe9Clawf3fu2Hli1a7XVKn8lshNFkgKXaCoNRD6vVhsoKzxdabFYbdm1Lx+jxwyCp3OFat9hEbk4Bbp58H8pKPYfV4OH9kHUmB+YgM2LjoxESGowFc5d4fK8EIDQkDHZL00ZqWopGp653nu6IcYNxMP0IOnVtj6BgM1wuBSuXrPP4Xq1ag0k9+sEo+eeJWZm9BvP3bvL6+vhJo7Bt007ExEVDr9dh3x7vl911Oi1CzMGorvTPaTQuxQWr0/P3qlKpMO7qEdizYz/GTBgOm82OE0dPee2vQa+HWWuCy+l/IyySBLgkBZXVnnd0o8mAISP6Y+fWvejVvwcS28QhbfE6r5feQ0KDoDjE2Yfa+h+7yw6Hy/MJyDXTx8PpdKF9x2SUlVVAq9Hgx+9+8XoQjI+JRQjMTR5ZbSk2pwN2D32VZRlXXTsKVosNdpsdhbnFMJoNSN/ufQqqMcyArNycRt2ncinYnXYo4sL9y2DUY+qMibDWWBGXGAu9Xodtm3Zj68adXkc8E+LiYCn3z3svBAQqbdVwKReGeHhkGMZfPQKKIqBWq5CbXYComAjM+2aR1+2ZzSZY/HQqo1arQbXFcxHYpm0CBgzpA4PRgIK8IsTERiI/rxBpS9Z6XOlOlmWEBoXCbvXP8wiVVoWKKs/nS117dELHLimIiAzDqeNnoNVpUVFegS0bPF/p0Om0MBqMXo9bl5siFI/7KgAMGNIHUTGRSEiKRW5WHmRZxrGjp3Bon+fRf5PJCI1aA2tN46f0tiQJElSS52d8DR83CFqtFqFhwcjNzseJo6dRkOv9SnNoaDA0igYuP70CV2mrRoXN829u0vRxcDqd6NqjEzJOZ8FsNmHRD8u8ruoXFRUBV43it9laaavyeH4oq2RcO3MSLDVWhIQFo6y0ApGRYZjzpff7x/sN6oUPv34FarUaANLqSseKsop6lyjdu+sARo0biopy90MD67sZX8A9b9JfE/xiNzbv33MYvfp1R0rHZBTmF6HcS3EJ1D4V2QGjzj8LqYstxXr00HF07dEJO7elY/ykkTh+9LTXEQqnw1nvCMzlVl+7XC4XsjNzkdQ2AQajHhGRYTh+9JTX9zudLjhlV2OnDbcoIQAhiQsfKHSWpcY9ot22fRuEhgYjPCIUIWHBXgspS40NMmS//V7r+w7sdgc6dklBfEIMNq7dhjZtE367os55aqqqYTYYITdhGkNLEl46W/vniW3jkHE8C6Yg40W3VVNpafBSzJeaEMJrXxWXAp1Wi4jIMBw5eAKlJWWIT4z1eiIHAFWVVZCFfy6XLYQ4u9Pigv3V6XAgKMQMvU6H7Vv2QK1WQ3uRLLFZbX67r7rqmdpjtdoQHRMJrU6L6qpqKEKgqLDE62/Una12v+1rfecRNdU1SGoTD41Og6AQM+w2e733AjocTlhg8du+1ncMrq6qwcChbRAUZILRaMCZU1lw1jMoZ7PboTiF//YV8DrLzVpjRZceHVFVUYV9uw5hwLA+KCnc7PXeR4vF5l7a3o+76o3d7kCHzm3hsDsQGxcNzdkryN5UV1mgFf55Hlyvs11KTkmCLEuoqqxGuw7JUKtUXgupkqLS8/4q6uZCyPUsH6vT69Cle0fExccguV0CIiLDcezwiXrb5t/LlnpvmznIiJSOyejYpR3KSyugVqthu8gcaL/uaj3CwkOR2CYeAwb3Qb+BqTAZjRgyor/3706SAuZ5F78VExuFyKhwDBs1EDab3b18q5eDQt2fBmZXkZAUD6PZgDETh0Oj0SA3uwDVld7vNZBkKVC7CpvNhrycAmRn5iK1TzdExkTC4eXhegKAJPtrCXURwv2A3qL8EqjUKrTv0vaix1hZ9s+pbhcjhEB1dQ0K84sRlxCDxKR4xMZHw9uvVCAQ+uq57YoiUFVejeKiUqR0TEZQsMnrNPK6LQVo4CiKQFlpBUpLyrFnx36Eh4de9Cp4oPbV5VJQXFyKyvIqqNUqqFQqZNazMJAkSQHbV6fTicKCIhQXlyInKx8uRYHDy7Q+91hC4PbV4XCgIK8IKo0aHbq0Q1LbeCQmx3t9vyxJAXseYbfZkJ9TCIfDibKScpSXVdZ7bUSWA7WvApYaK/JzC6FSqSAUgdMnM71OsRcA5N88467uilRkVLi74vRAgvvHf+TQceTlFiAmNqrevzBJltGmbTyMRoPPXbokJAkH9x3xMk1EghAC+3YfwqnjZxAVE4FTx72vaqZSyQhPjEJkUHDLtbcJ5MpyYJ/n1yTJfRDctT0dTqcLOdl5yMspgLfhE51eh07d2kO4/HN4pby8AidOnPY80i25r5JuXrcdOVl5CA4NwrEjnq9ISXBPL+rQoR3U/vhQSElCcUkJqk54XtlNkiXUVFuwaul6FBWUQG/QITc73+vmQsOCER8X67cjhFlZucgv8Lza3s6te9GhUzusWLwGkdERgBCo9LLinQQgIioc7RPbej0pv5wEgIzTWSjzcC+QEAI7N+5FQnIsTh/LhEaruWjxEJMQhcg24f46MQBHj5xATc2FBb7d7sDalZsQExuNU8cz0Klbe2ypZ9lwCUBicgLM+otfpbscFEVB+v6DcNkvDOaqymqsXbUZwSFByM3OQ6euHbDZy/QvwH2y0qZdAvR6/7znQpKAfXsPeczWosJibFy3DRq1GhmnsvDdV/PrHaRUq1Vo2yEJOq33K8yXk8PpQHq656m12Zm52LFlD2xW9xW1hKTYegchdXodOnVu77cLE1SUVyDjtOf7j48fPQWVSoXiolI4HA7EJ8QgOzPX43sluO/Lbteujd9eLS8rLkdRvuf7jw+mH4PT4UJJURmi46NweP9xlNfzANvgsCAkJyT67RWpk2cyUJHjeWrfzq3paN+pLdKWrENktDtHqiq9ryYbER2O2MhoP+2rwJHjJ2AtuXAmnaIIbFy3DcltE7Fk4UokJMWhuqra61VGCUBCYux5gwF190g5HA48dPuz2LFlT5ObrFar8fI7f0Ovfn56Q2xlNZ59+O/1FkgNFRxsxhsf/xNtU5KaoWXNLyszF088+NzZAqlpEtvE49X3/4HI6PBmaFnzO7jvCP7y9EsoLSlr8rZ69OqKf77yJ4SE+meBvGnddrz0/BvNsuzzyHFD8Ozzj0Jv9M+Ts4XzluKdVz5plpWeZtwyFY88eZff3hD7/ScLsODrpc1S1N7y0PWYNHOcf47+CoEX//YmVvyypsmbkiQJf/7XUxg7YUTT29UCnE4n/ueJf2LX9qavPKnWqPGft59Hrz7dmqFlza+yshq/f+A5nDiW0eRtBYcE4a1PXkSbdonN0LLml5OVh2ce+WuzZGtScjxeee//EBnln9l6IP0Inn/2JZT+Ztnnxkjt0w3/99//QXCIfy42sWXdDrz+jw+93uLgi2FjB+J3zz0IvV8uNiGwcO4yvPfaZ82SrdffMhn3P3577X1Dfufjd77CN5//2CzZ+tgz9+LeR2bVDmb+eo+USqXC2AnDsWt7eqMejniuNu0S0bt/d4RHhDWxuS0jOCQIw0YPxOkTmU3+S23fpR06dG8PXT33ZVxObbSJ6DsgFYsXpDV5Wz16dUHHLu38dhpNat/u6NglxeuqUQ0lyzL6DUxFckqi3/Z18PC+iI2PxskmnrBotBoMHNYX8Umx/nnCDWDsxOH48uPvva6k1FAmsxGDh/dDREy43/Z1+IRBWDJvpfse0yYICQ9Gn0E9EBEZ5pd9FUJg4uQxWLVsfZMfCB0TF41+g3ohLCLEL/uqKArGXj0ce3btb3K2JrdNRO9+PRAeEdo8jWtmwaFBGD5mME4eP9PkbO3UpT26pXb222w1GvXoMyAVS5olW7uiY5cUv82bXv26o0PnFGzfvLtJ25FlGX0H9kJyO3/O1n6IiYvE6RNNezSDRqtB/8G9EZsQ7ZfHJQAYPWEoZn8yFyXFZU3ajslsxKDh/RAVE+G3fb1q8mjMm/MzbE14biEAhEeEot/AXuf1s+6XLEkSxkwYjs5dOzTpP6LTaXHDrVP9diQfcE8ZmHz9VYiNj27SdkwmI2beNhVarf/eYKc36DFz1jQENXH0JzQsGDfePt1vdxLAfXXwxtumQdPE7yMqJgLX3TzZbw/0gHuKWnO0sW1KIq6eOsavv9eEpHhMvX5Ck+/P69m7K4aNGujXfU3pnIwh4wY06b5LSZLQf1gvdOze3q/72n9wLwwY0qdJ21CpVLhm+jgktonz275KkoSxE4ajU5f2TdqOTqfFjFun+O2y0YB7Nsq0G65GbHxMk7ZjMhtx853X+n+23joVQcHmJm0nNCwYN91+rd/+fgH34PONt01vcrZGx0Tiupuu8etsDY8Kw9QbJza5jW3aJWD8lJF+/b0mtInHNddd1eRs7dG7K4aOrOf+ej/QpVsHjJ04okmLGkiShGGjB6FbamfvhVRcQgxuvXsGjKbG3dskSRL6DOiJydPHQ+WP95acJUkS2nVog+tvmVzvCl/1kWUZI8cPweD6FmfwA5IkoWfvrph6/YRGT2dSa9SYPnMSuqd28fu+DhkxAGMnjmj0QVBv0OO2e25AUj03kPqLqyaPwsChfRr9nQSHmHHHAzch1E+flVVLpZJx3U2T0bV7p0ZvIyIqHHc9eEujj22Xik6vw7WzJiE2sfEnotHxUbju9snQ6f1zJB9w76uhYSG4476ZCGvs1RUJ6NilnfsEz0+fCwack613Xd/o+4YlSULfAT1xzfRxfp+t7Tu2xczbpjUpW8dOGI6hI/170EOSJKT26YYp109o9HQmjUaNa2deg249O/l9X4eOHICxE4Y3OlsNRj1m3XMDEtvENXPrmt/YSSPQd3Bqo7+ToBAzZt03AyFhgZCtk9ClW+MvoEREhuPOB26EwV/XRDjLfW43A4lJjf/9xSfG4vZ7Z0Kv15335+ftEZIkYeKUMZh194wL3ngxkiShfae2ePq5RxAS5r9Xo2rJsowZs6Zg8rXjoVb7FkyyLKFHn654+Om7YDL75w3O51Jr1Lj/0dswcsxg98oqPpBVMoaPHoR7H5nlt1MszmUyG/G7Pz6AXn27+3wQVKlUmHzdVbjxtmv9+mQFcO9vUdER+P1zDzXq/jy1Ro1b7p6BqyaP9usAB9x9bZuShKf+9yH3Qjc+MhgNePj3d2PAkN4B0deO3VNwx+M3IjjM9ysPIWHBuP+ZWWjbyT/v2TyXJEkYPLw/7n/0NpjNJp8/G58Yi2f/8liTZxZcCpIkYeLUMbj1rusbla0dOrXF7597yK9netSSZRk33T7dPXjXiGzt1bc7HnvmvsDJ1sdux4gxgxqXrWMG455HZzW66LyUTGYjfvc/D6JXn26+Z6tahcnXXoUbb5seENkaGR2Ox/54L9q0S/D582qNGjfeOR1jrh7u9ys6S5KE5JQkPPmnBxEdE+nz5w1GAx76/R3oNzgwsrV7ahc8/sy9CGtEgRsWEYqn//wIOnZJuXDb4jcTmYUQsFltmPPFT/jio+9Q2oC5k2q1Gn0HpuIPf30M7Tu29evLtucSQqCqshqfv/ctfvp2cb0rktTSajUYPmYQnvjT/YhLiPH7H08tIQSKCorx7mufY/GCFRddYhcADAY9Jl93FR763V2IjPLf+0p+SwiBM6ez8dbLH2H1io1wNuBGyqBgM26+41rcft+NCA4JCqi+HjlwHG/8+yNs37Tb6wNLzxURFY47HrgRM26Z4vdXaM7lcinYs2Mf/vuvd3F4/7EG9TUhKQ4PPnEHJk0fB62frv71W0IIuFwKdqzfjU9e/QY5Z/Iuer+JJElISknAXU/ejAEjevv9yUotIQQcDgcWz0/Du69+hoL8oov2VZZldO3RCc/+5VGk9u0OVT2P7vAn7my1Y84XP+HLj75r0I377mztiT88/xhSOiYHVLZWVlTh43dmY943ixqYrVqMGjcETz/3MOIS/feezd8SQqCwoBjvvfYZFs9Pq/d5UbUMBj2mXDcBD/3uTkQEXLZm4a2XP/YxW6/D7ffNDLhsPXrwJN57+VPs2rqvgdkahlvunYHpN030+ys056rN1tde+ABHDhxr0IqKCUmxuP+J2zFx6li/noJ7LiEEXE4X1q/egtdefB9nTmc3KFtTOrbFk3+4H8NHD4LqwsGhtAsKqVp2ux27d+zHVx/PRfquA6isrLrgRlm9QY/I6HDMuHkKplw3wa9vNKuP1WLF1g27MOezn3D00AnUVNdc8EMyGg2IiY/CTXdci7GThiMkNDgg+1pVWY3VKzZgzuc/4fTJM6ipPv8hgJIkwWQyIjklEbfdMxOjxg+BycfRYn9RWlyGZb+sxvdfLUBOdv4Fq/DIsgST2YQu3Tti1t0zMHTkQL+eDlWf/NxCLJ6fhh+//QXFBSUXhLlKJcMcZELv/j1wy13Xo+/AVL9dua4+tUG+YO5SLPpxOcpKy2H/zRLKarUaQSFmDBnRH7feeT26pXYOmMLiXIqiION4JhZ/vxKbVm5DZUUVnI7zF2bQaNQICg3CkDH9MeXmq5CUkhAwJ9vncjpdOLjvCL757Ads2bATFRWVFyxCodNpER4ZhknTx2HGzVOQkOS/90XVx25zZ+vsT+YiffdBVFZUX3CSpjfoEBkVgRm3TMHk68YjKjows9VisWLzuu346pO5OHrohPtBvL/NVpMBcfHu2wrGTxqF0LDAzdZVyzfg2y8akK33zsSocUMD4qqbJyXFZVj+82p8P9tbtsowmY3o0uOcbA2Aq26e5OcWYvmiNVj0/TIUF5ZesFiBSiXDFGRCar9uuOH2qeg9oIffrlxXn9oB6EXzluGXH1e4s9XuOO89tdk6eHg/3Hzntejas1PAZuuxI6cw7+uFWLl0HcrLKy8YFNBoNQgNC8aYCcNx0+3XIqWD14Es74UUcHa00O7AgfTDmP/9Eiz/eQ0cTqd7HfWkONz10M0YNmogIqLCAzK8z1V7JW7vzgNI33UIudn5qKmugVarRXRsJLr27IR+g1MDtoCqVft1V1dVY/uWPdi/9zDycwphsVhgMOgREx+NXn27o8+AnjCbTa2ir2Ul5di2eTcO7juCwvxi2Gw2mMwmxCfEoM+Ankjt0x16gy7g+1o7MrppzXZ8+f73yM/+dVneqTdNxKRrx6FbamdoNOqA76uiCORm52HLhp04cfQUiotKIYRAcEgQklOS0H9Qb3Tq2h4qlRz4fXUpyM7IxZ6t+5F5KgcVpZWAJCEk1IyklAT0GtQdicnx7gcrB3hfnU4njh0+iW2bdyPzdDbKyyqgUqkQHhmGDp3aYfDwfnUzAQK9rw67A/vTj2Dh3KVIW7zOHeSSe6T39gduxLCRAxERFdYqstVqsWH3jn3Yu2s/crLyUVNVA61Oi+i4KPRI7YwBg/sgJEALqFq1eVNVVY0dW/Zg/57DyM/9NVtj42OQ2rdbK8zWXTi47+jZbLXDZDYiPjEGffr3RGrf7tDrW0e2FhWUYMu6nZjz4Y8oyCmse33SDeMx8drR6NKjI9StKFu3btyFk0czUFJcCkURCA4xo21KEvoO6oVOXVIgt4JsdblcyDiVha0bduL0yUyUlpTV3b+b0iEZA4f1RXK7JMj1Z2v9hdR571y8Fs8/8++6ZXn7D+6F1z/5Fwx+uT5+0whFwO5wwOV0QZZlaHUXf/hlIKo9QNjtDiguBbJKhrYBD/oMRLUHCIfdAUVRoFKroNVqAvpA4E1VZTX+/NiL2LNtf92f/fuD5zFwROMXpvBXtQdDh90BAUCjVgd8mHlTOy3B4XBCktyjgyq1qtX21elwnu2rBI1WDZWqdfZ15eL1+McfX627stp3cCr++8HfoDf4di9VIFAU91ROd7ZK0Oq0rTZvmK2tb1+tqqzG/z3xX+zbcajuz/7x7v+g3/Bera6/tVPM3dkqWn22Op0uOBwOSADUGg3UDc/WtAZffxTCXWDU1l3++lTq5iDJkvsydOvLsfPUjur6evNzIJIkCSqVBFUrPDn5rdZ3mPNOkiSo1eqAnErhK0mSoNaoA3JKpq/cxZOmycstB4raE2/AnbNA68xXmdna6lxJ2QqgSctnBxJ3tqp8XjAmEEmSBI1GDU0js7X1DY8QERERERG1MBZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+YiFFRERERETkIxZSREREREREPmIhRURERERE5CMWUkRERERERD5iIUVEREREROQjFlJEREREREQ+alAh5XA4UF1VDVklQ5IkyLIERVFQVVkNIURLt5GIGkgIgepqCyDBvb/KEjQ6Daqra+B0ui5384joHA6HA1WV1ZBlCZAAidlK5JeEEKipskBAQFJJgAyotWpUMVuveJLwcrQWQsBus2PfnkNY9ONy7NtzCFkZ2XA6nJAkCcEhQejcvSOGjRqISdPGIjwyDLLMC1xEl4OiKCgpLsPSBauwbcMunDyegfLSSghFgVavRUKbOHTu1h6Tr78K3VM7Q6PVQJKky91soivOr9l6GD//tBz7dx9C1plcOJ2us9lqRqdu7TFs1EBcPXUswiNDma1El0ltti6ZvwrbNu7E6eOZKC87m606LeLbxKJzt/aYMmMCuvXsxGy98qR5LKSEEMjMyMFn732DpT+vgqXG6nV0TKVSoV2HNrj34VmYMGU01Gp1i7eaiH7lsDuQtmQdPn/vO2SeHezwSALMZiPGXj0S9zx6C+ISYnjAJ7qE6rL1/TlY9vPqerNVrVahbfs2uOfhWzFh8ihmK9El5rA7sGLxWnzx/vcNyFYTxk0agXsevRWx8dHM1ivHhYWUUAQOHzyOF/7yGg6kH4bLpTRoSyGhQbjjvhsx654boDfo+SMiugSsFiu++mguvvtiASrKKxv0GVmW0aN3Fzz7t0fRqWt77qtEl4A7W4/hheffxMFGZOutd1/PbCW6RCwWK776cC6+/9K3bO3Zuyue+duj6NQ1hfvqlSHtgvkCebkF+NefX0X67oMNPtADQHlZJT5+72ssmLcUnNpN1PKcTicW/bACX3zwfYMP9IB7qkL67kN49Z/vIy+7gPdiEF0C7mx9Hfsaka2fvPc1Fv6wnNlKdAk4nU4smrscXzYiW/fuPojX/vke8nKYrVeK8wopm82OD978AgfSjzRqY5ZqKz599xvs33OQPyCiFiSEwIG9R/DpO9/AbrM3ZgPYu+MAPn//W7hcvFGWqCXZrHZ88OaXOLjvaKM+X1NtxafvfYMDew8xW4laUG22fvbuN7DbG5ete5itV5S6QkoIgfRdB7A2bTMUpeGjZb9VkF+Eud8sgq0xJ3dE1CAulwtzv1qI4sKSRm9DURSsWrYeB9Mbd3JHRBcnhMDeXQewbmUTszWP2UrU0lxOF77/agGKi0obvQ1FUbB66QZm6xWirpBSFAUrFq9BSXHjfzyAOzRWLV2PvJyCJjeOiDw7fvgUdm/f1+TtVJRVYfnPq+F0ermJloiaRFEUrFiyFiXFZU3ajhACq5ZtQH5uYfM0jIgucOzwSeze1vRsLS+rZLZeIeqWAXLYHdi8YafHN6lUMhKS4qBSqVBWVoE2yQnIzsxFkZfRcIvFij079qFtSlLLtJroCiaEwIH0I15PzIKCzYhLjEFBXhEqyioRGR2BgjzPJ19CCBzefxzlZZWIiAxrwVYTXZnsdge2NiBblbPLKVdX1SAnOw/wMIPPna37kdwusYVbTXTlqZ3WV1pS7vH12mwtKSqD0WSASpaRlZkLh93hcVuH9x9HRVklwpmtrVrdFaniolKUl1Z4fJNGq0Vim3gMGTkA186chLCIUIyZMNzrRhVFwdHDJ5u/tUQEl8uF7MxcuLw8BDAiKgyJbeJx1eRR0Ol1GDFuUL3byz6Ti+rK6pZoKtEVr7ioFGVl3rM1oU0chozsj2GjBmLY6IEIDjFDgufVvhSXgmPMVqIWcfFsDUdim3hcf8s1iE+MRd9BqYiNj/a6vewzuaiuqmmp5pKfqCukKiuqvM7fNhr1iI2PhsGgR0qHZOzalg61Rg1J9nywF0Kg3EtwEFHTKC4FVRXeC5/E5Hi4XC4kJccjIioMKllV7/aqq2rg8PZ8DCJqksryKiguxeMVJqNRj9g4d7YWFRRj19Z0dOjUDsLTm8FsJWpJiktBZT2DiklnszUsIhTZZ3IQFhFS732PzNYrQ10hVd/TmJ1OJ4QiUFZaga2bduG6myajsqIKQvG+epBWq23+1hIRJEmCRqvx+np1VQ3MQSYcO3wK8YmxUET9N7irNWrI8gVPQiCiZqDV1ZetLgjhzladXodOXVOgN+o9Fl2/bo/ZStQSJEmCtgHZmnk6G/0G90JZSYX3h/SiNlv5LKnWru4eqcjocGh1nn9AFeVVWLlsPcxBJhTmFyGxTTxyc/K9blSlUiEpOb75W0tEUKlViI6N9Pr63h0HUFRQgqKCYtisNhw7dKLe7UXHRsJg1Dd3M4kIQGRUOHQ6LSo9nE9VlFdi1bINMAcZUVRQgjZtE5Cdled1WyqVjMQ2cS3YWqIrl0qtQlRMhNfX9+zYj6KCYhQWFCMoJAgqlYyCvCKv74+OjYTewGxt7eqGoU1GI7p07+T1jRXllcjJyoPD4cSpE2dgtdi8b1SW0Lt/j+ZtKREBcI+adejcDkHBJo+vK4qCzNPZsNRYoSjC642ztVI6JiMkNKglmkp0xTOajOjSvaPX193Zmg+73YHjR0/DUmP1+l5ZlpmtRC1EkiR07JwCc5D3bD1zNlsLcguRm5Vf73Pd3Nka3FLNJT9RV0ip1CqMv3pkvVOGGqpL905o37Ftk7dDRBeSJAk9endFYnJCk7el0+swZNQAjpoRtRC1WoVxVw9vlmzt2qMTUjq0bXqjiOgCkiShZ99uzTKj6tds1TVDy8ifnXdjxMixg9G9V5cmbdBoNGDmrGkICjY3aTtE5F1wiBkzb5sKlVp98TfXo3O39hg9YajXeziIqOlGjh2C7j07N2kbRpMBN8ya6vVKNBE1XXCIGTcwW8kHdYWUJEkIjwzDfY/MQlh4SKM2JskSRo0fgquuGcWb14la2IhxgzF+0ohG38waGR2Oex69FWYzT8yIWkpttt77yK1Ny9ZxQzB+0khmK1ELGzluCMZdPbxJ2Xovs/WKcd4RWZIkDB7eHw88fofP8zpVKhUGDO6NR5++lzeuE7UwSZIQEhqMh5+6Cz37dPP55MoUZMK9j83CwGF9OGJG1MIkScLgEf1x/2O3+3w/oqySMWBwbzzy1N0wcAouUYuSJAkhYcF4+Om70LO379lqPputA5itVwxJ/OZOOSEEFEXBkoUr8c4rnyI3u/6b6QD3UudjJ47AU889hOiYSP54iC4RIQTycgrw3iufI23xOjidF39mRUJSLB5++m6MmTgcGk3Tpi8QUcO4s1VgyYKVeOfVT5GXU9DAbB2O3//vg8xWoktICIG87AK8+8pnWLlkfQOzNQ6PPHM3Rk8Yxmy9cqRdUEjVcjpdOHM6C99+8RM2r9+B3Jx8OOyOutclSUJoWDDadUjGTbdfi+GjB8FkNvJAT3QZVFZUYfO6HZg3exFOHz+D8rLK8x7qqdVqEBMfjaGj+uP6WyYjuV0SZBWnCBFdanXZ+uV8bFm/A7nZ+ec9tLN2RDylQzJuun06ho0ayGwlukzOzdZTx89c8EDs2mwdNmoArrtlMpLbJTJbryzeC6laLpcLGaeysGjecsz7clHdw8fadkjCY/9zL1L7dIM5CUkZnQAAXbdJREFUyMSDPNFlJoRAZUUV9u06hPde/hwZJ7LqXrvzkRsxfsooJLVNgIoHeaLLrjZbf/lxBX74+ue6YqpdhzZ45Jm70bN3V2YrkR8QQqCyvAr7dh/EB699iYwTWRAQkCQJtz94I8ZfM5LZeuVKu+i3rlKpkNIhGam9u0Kn0UGj0kCj0iAqKhL9BqYiKNjMAz2RH5AkCcEhQejdvzuioiKgllV1//Ts0w3JKYk80BP5idps7dajMyRFgnAKCKdAaEgI+g7oyWwl8hOSJCE4NAi9+vdASGgwXE4XFKcCl8OFHr06M1uvcPzmiYiILqNzp+EC9d83RUSXiQB3T7oACykiIiIiIiIfsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvIRCykiIiIiIiIfsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvIRCykiIiIiIiIfsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvIRCykiIiIiIiIfsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvIRCykiIiIiIiIfsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvIRCykiIiIiIiIfsZAiIiIiIiLyEQspIiIiIiIiH7GQIiIiIiIi8hELKSIiIiIiIh+xkCIiIiIiIvKRuiFvslptKC+rgE6vgcPpgEolQ5IllBSVIS4xBpIktXQ7LwkhBGqqLcg4lYW83AJYLVZoNBpExUQguW0iQsNDWlVfKyuqcPpkJgrzi2Cz2aHTaREdG4W2KUkICjZf7iY2GyEEykrLcfpEJooKS+B0OKE36hEbF4XkdkkwmgyXu4nNRlEUlJaUQ0gCKq0KiiKg02lRWloGu80OnV53uZvYbBRFQV5OATIzst19FgLmIBMS28QjMSkOGq3mcjex2bhcLmSfyUVWZi7KyyohSxKCQ8xITE5AfEIMVGrV5W5is3HYHTiTkY2crDxUVlRDpZIRGh6CNskJiImLgiy3jvE/IQRsNjtKikuhUqkgyU5IkgSn04XiolLEJ8a2qrzxmq3tEhEa1vqyNeNkJgrzi8/L1uSUxNaXrSXlOH3y12w1GPWIiYtGcrvEVpetJcWlsNvtkGQJQgio1SoUFpS02mzNyshBaUk5AAGT2YTENnFIaG3Z6nQhKzMX2Zm5KC+rgCRJCA4JQlJyPOITYhuUrZIQQnh6QQiB8rIKbFq7HQvnLUPmaffJitPhhCxJMJqNiIqJQL/BvXDdTdegbfs20GgaVJf5HSEEigpKsHrFBvzy0wrk5RaivLQcDocTKpWMoJAgREaFY9iogbj2xklISIwL2BOX2h1k2c+rsXzxGhQVlKCirAJOpwtqtQrBocGIiY3E2IkjcM308YiOjQzYExeXy4WsjBws/GE5NqzZguLCUlRWVMHlckGj1SIkNAhx8dG4Zvp4jJk4HBGRYQEb5g6HE6dPnMFP3y7Grq3pKMwvRk21BUIIaDRqhEWEIjE5DtNmXo0hI/ojODQoIPsqhIDdZsfRQyfw3ewF2L/3MEqLy1BdVQMBAb1eh7DwULRtn4SZt05Dv0G9YA4yXe5mN4oQAlaLFem7D2Hu1wtx7PBJlJaUo6bGAgkSDEY9wsJD0aV7e8y4ZSp69u4Kg1F/uZvdKEIIVFfVYNum3fjxu19w6kQGykrKYbXYIMkSTCYjwiNCkdq3O2bcMgVdunWAVqe93M1ulNps3bhmGxbOW4aMk5koLS6Dy6VAkgCDwYDYhGj0H9K7lWRrMVYv34hf5l+YrcEhQYiMDsewUYMwfeYkJCQ27MTFHymKgrzsAiz/ZQ3SFq91Z2t5JZxOJ9QaNUJCghAVG4WxE4dh0vTxiIqJCOhszczIwaIflmPD6i0oLqrNVgUarQYhocGIi4/CNddehbEThiE8oLPVgVMnzmDe14uwY+te5OcUwGKxAgKQVTIiIsPQpl0irr9pMoaM7I+Q0OCA7Ou52Tp39kIcSD9Sl60AoDsnW2fcOgV9B6YGdLZaLFbs23UQ33+9EMcOn7gwWyNC0aVbB9xw67SLZWuax0JKCIHD+4/hvde/wJZ1O+ByueptVHRsJG69ewZm3j4NOp02oH5ELpeCnVv34L3XP8eeHfugKB7rSgCABAlJbRNwz8O3YuqMCe5RxADqq8PhxLqVm/DBm1/i6KET8FJDAwBkWUaHTu3wyFN3Y+S4IZBlOWD6KoSA3e7A4vlp+PS9Ocg6k1NvX1UqFXr27oIn/nA/evfvAUmSAqqvFosV82Yvwref/4SigpJ6+6rRqDFwWF888szd6NglJWD6CZwd6a2sxifvzMb875egvKyi3r7qdFqMnzQSD//ubiQmxwdcX4sLS/Dua59j2c+r68LMG6PJgGkzJuLeR2YhMjo84Pp65nQ23nnlE6xZsRE2m73e94eGhWDmrGm44/4bERRsDri+Htp/DO+/9jk2NyBbY2KjcMs91+PG26cHZLbu2LIb77/+BfbsbFi23vvIrZhyfaBm62Z89OZXOHb45EWyVUKHzil46Hd3YsS4wYGXrTY7fpmfhs/en4OsM7kNyNaueOIP9wVmttZY8d2XP+Gbz39EYUHxRbJVg8HD++GJP9yPjp1TIMmB0U/A3deqimp88u43WDB3CSrKKlBPV6HTaTFu0kg8+OSdSEyOC5jvFDg7uFNYgndf/RTLFq1GdfXFstWI6TdMxL2P3OYtWy8spBRFwbaNu/Hi828g+yI7ybn0eh2mzJiAR5++B0EhgRFuTqcLaYvX4D//eAclRaUN7qs5yIRb7rwO9z16G/SGwBgBdtgdmPv1Qrz72meorKhq8OfCI0Jx7yOzcPOd10GtDoxRUavVho/e+gpzvvgJNdWWBn8uNi4KT/zxfkyaNi4gfr8AUFlRhddf+BDLFq2GzWpr0GckSUJicjz++PfHMHBY34Dpa0FeIV54/g1sWL0FDoezQZ+RZRmdu7XHX196Fl26dwyIvgohcPpkJv7159ewe8d+uJz1n2zXUqlU6DcoFX954SkktgmMwlEIgf17D+Gfz72Go4dOQFGUBn1Oo1FjzIThePb5xxAVHREQfVUUBVs37sKLf3kD2Zm5EPUUFufS63WYesPEAMtWJ1YsXouX//E2SorKfMrWW++6Hvc+MitgstVud2De7IX44I0vfc7Wex6dhRtvnw51gFyFs1pt+PDNr/Dtlz5ma3wUnvjDA5g0bWxA/H4BoKK8Eq/8610sWbgSNmv9gzu1JElCm7YJ+N9//A6DhvULmL4W5BXixeffxKa12+GwOxr0mdps/cuLT6Nz9w4B0VchBE6dOOPO1u37LjqQVUulUqH/4F74ywtPe8rWtAuuK588loGX/+9tZGXUP4r/W1arDQvnLcOcL35scOMuJyEEdm9Px2svfYDiwvpH8X+rqrIasz+dh0U/Lg+IviqKgtUrNuDDt3w70ANASXEZPnpnNtat3Nzgk5zLyel0YsH3S3wuogAgL7cQ77zyKXbv2O/T7+FysVnt+ObTH7FkflqDiyjA/dvPPJ2Nt/79MY4fORUQfa2uqsEHb3yBNWkbG1xEAe7f/uEDx/HKv95FbnZ+QPS1orwSb7z0IXZuTW9wEQW4p9vs3LoXr7/0IcrLKlqwhc0nP7cQ//m/t3H44DGfji8OhxOrlm/AB29+6dNv/3I6efQ0Xv77O+5sbWARBbizdcHcpZjzeSBl6z68/uIHKC5s+AAl8Gu2/vzTioDoq6IoWLN8Iz5+++tGZesn78zGhlVbAiZb53+3xOciCgDyctzZuidgstWG2Z/MxS8/rWhwEQW4f/sZp7Lw2osfBFS2fvjGV1i3ckuDiyjg12x97YX3AypbX3/pA+zcuten44vL5cKOLXvw+ksfeMzWukKq9mbQD9/4EhknMxvVSLvNju++WIAdm/f69V9q7c2gb//3E+TlFDRqG5YaKz559xscOVj/FLnLTQiBwvxivP3yJ2dvGvRdWUk53nn1M7/fWYQQOHksAx+8+aXPB/pa2Zl5ePu/n6CivLKZW9e8agcCvv38J58Ki3MdOXgCH781G85Gfv5SURSBtCVr8cv8NJ9OQGsJIbB981589fFcwH9/vgDcV8nnfb0IG9dtb9S+5nIpWL18IxZ8v8Sv91UAsNns+Oz9OTiw90ijvhenw4lFPyzDymXr/bqvtdn6fhOz9dsv52PnlsDI1rde/hh5uY3L1ppqCz555+uLTj+/3Gqz9d1XPkVZaeOytbS4HO+++hnycgr8vq8njmXgw7eakq25ePu/n/hccF5qQgjs2LoXX3/2Q6Oz9fCBY/jgzS8a/flLxZ2t67B4QRpEI4p5IQS2b9mDbz79ISCy9fvZC7CpCdm6atkGzPeQreddkdq+eQ+2btzVpB26orwCc2cvgKXG2uhttDQhBJb/sub/27vv8Ciue3/875nZpi3SqveGOghRRAdRRO/VYANu2DiuuN3cOMnN/abd5Jd7024SJ459XeKCMTY2zRTTewchhAoSqKDe20pbZ35/LJIBzQpWu4JZ+LyeR8/jaFeTc9idec/nzJkzyLtc6NJ2qitr8PXn28DbpDuaZLPx+HrDdpSXV7u0nWuFJfj2mz1ualX/sFqs2PCvb/pcMHa5dCEXB/Ycc1Or+ofZZMbnH36D9jaDS9s5ffQ8zpzIck+j+kl7WzvWf/S1/QbfPhOwb9dh5F4qcFu7+kNNVS02fb7dqZHB2/E8j61ff4eykgo3tsy9BEHAlbyr2P3tAZeuPJiMJnz56VY01De5sXXud/r4BZx2NVubW7HxE0/I1gPIzy1yaTtVlTXY9Pl2SV+psWfrt6hwQ7bu3LzPTa3qHxY3ZWv2hVwclHi2mkxmfPbBVy5n64kjZ3Hm+Hk3tap/tLW2Y8NH38DY6cJVfQHYt/Mw8nKuuK9h/aD6xjHF1Wzdtml3j2ztvumFt/HYv+vwjS9P3+c6CgJw6th5lJdVIj4xts/b6U8GQwf27Trs8pQQQRBwcO9xrH3lCQQE+bupde5VX9uAIwdOwmZ1bWSE53ns2XkIK55YBK1Omsu3lhaX4+wp10dsLRYr9nx7CNNnT5LsPP28S1eQn+PayQpg3xf27zqK4aPTIJdLb0lTBsCZExdQWty3kfyb1dXU48iBk0gcGA+Ok+ZqWUcOnEJ1dZ3L2ym5Wobzp7MRERUKxoXjeX868N1RNLt4YgYAl7LycCWvCL5+I9zQKvez2WzY152tfScIwMmj51BeVok4iWZrh6EDe3cecWO2Po6AQIlma10Djh045dT0WzFdVwWWrZ4v3Wy9dt1t2frdjkOYOmuiZLP1cnY+8nJcG2QHAEObAXt3HUb6mKGSzdazJy6grLjc5W3V1Tbg6IFTSEgZAI6V5v1+Rw+cQm11vcvbKb5ahgtnshEVE959r1R3IWUymXHuVLboH8rkMiSlxEEmlyE/pxAqLyUUSgXqahpE3282WbDp0+0ICw+F/Xofg/657ie23Zt/d/vr9v/d2WFE1tkc0S0qVUqkpCbAarHB0G5AYLA/SovLUVMlfnLT3mbAx+99Ab3ex6We9JeG+iZcybsq+ppGo0bK4ES0tbbD0N6BkLBAFBeVORzdramqw3t/+QQ+eu/+bHKfVVZUOxwd9NHrkDIoAdVVdbDZbKirbYSxlyscxVfL8NE7GyT7bIj8nEI0NzWLvuYf6IeE5FhUllfD20cHuVyO/MuFoiPZggBcPJeDj/6+AQoJPhuCYRicOnHO4YhZeGQIomIjcb2kAkHBATAajcjPLRK9SswLAs4cvoAgjZ8kF05hGAa7Nu8TbTvDMohPjEVDXSOGj0pD8dUy+PnrAQDZ53N7rHRns/HYs/0Q2hsNkrwJmGNZ7NlxSPTETKFUICIyFEajCSmDEnD5UgHaWtvh56/H9dLKHu+32WzY+tVu5Ga7fvLTH3ibDccPnhZ9TavTwEfvDaVKgYioMDQ3tUCj1cBkNOHi+cs9TtLNJgu+/GQrQsOC70XTndbRYUTWuUuir9kHGwUEhwRB7+uNyvJqBIUEorGhCYX513q8v62lDe//7TMESnSQsqWlDYX5xaKvRUSFobWlDfFJsZDJZMi+kAuVSgG5XI662p7nTTWVtXj/b+vho9f1d7P7pOJ6FSodZGtcQgyqKmowJH0QTCYzWppb4eevR2lxueiJa3FRGT78x+dQSvTxBZcvFTicqpmYEoeyknKMHp+OpoZmNDe1ICg4AFeLStHU0HzLewUAF87k4IO3P4NCIb2+MiyDM8ezYHQw6JE4MA4VZVUYPT4d18sqYeo0oqa6TvSeMZ4XcPTAKbAMC46TXiHFsAx27xCf/cDeyNb6+iakj0xDSfF1eKlVkMlkyL1U0OPcw2az4dzpbMxfOrO7r92r9pWVlOPJxa+I3hui8lIibfggxCfFwstLBYZl0N7ajq8+2warg9GYQH9/GNuleRMwL/BoM7WBFwlxbx8dUockI3VICooKrqGxsRlRMRHY+tUu0W2xLAudVuvyaGN/EQQBPMSnRwQE+iF5UAKGj0pDXU09KstrwDDAwb3HRd/PsSzkcjksZmnO+5Ur5DCZxW8MDY0IQUJiDFJSE7Fv12FotBpcPH/Z4bZUKiVkLAezqe+XgftTbyODMXGRiIqJwJiJ6SjMuwaWY3Hm2AWHU70UCgXAQ5LTaBiWgU2wwmgWP5YkD0pAeGQo4hNjkHMxH4OHpmDDx9+guUl8sYUw3yCEePlL8ioNyzK42lSBpo6ebZfJZFj++ALUVNWjpqoWM+dNQU5WPuRKObLOXkJ5WVWPv/HT6SHjpRdqAMDJONS3N8Bs7bl/+ei9kTkzA2aTGWWlFYhPjMHp4xcwcHAi9uw4JLo9X189Otr6du9GfxMEATZePCejYiOQkDwAGo0Xyq9XYdDgJNh4HjlZecjJyhfdJ/189TBIuK9GqxGCyMDp8JFpUKrsD6ZtrG9CVGwEss5ewogxQ/Hxext7HNMYhoGXSiXZY7BcIYfZwVL90+ZMQn1tI0LCAiEIAsIjQyGTydDU2IyvN3zbo0DmOA4KuUKy96tycg4dRvHv3LKV81CYXww/fz38A31RV9uItpY2hEaEiN4OoFQpwQJOLeJwL/ECL/r9BYDVzzyC3EsFUCoVSBoYj85OI2qq6mC1WHH04Kke71cqlWB49Lr0//3CsPal6C0W8f3r8bWP4OqVEnQYOjEoLQmnj1+AykuJSxfyRN+v9vICbxMkea8Uy7EwWY0wi/RVJpdhxeqFqKmuQ3VlLWbNn4riq6WQy+U4cuAkKq73zNZBacn4eNPfILM/3+/7Vfs6DJ3gBfETKY1Wg9CwoO6H61nMFlwrLHVYRAFwWOVKnZ+/Hno/H8hkHCKiwhAaFoz8Xu6lsj+d3jP7GhoeDJWXEmqNF4JDg6DRqXud780LAmxW6Z1sdxGEGzuxyI4cHRMOAND5aFFWWonwyNBer6xZrdZev99SFhsfBZPJDKVSCR+9N/S+Pr0WSTabzeG+f9/d4bgclxgDY6cRCckDoPPWQqFUgOvlapPVau31+Rj3kwDYLxHe1j6GYRAaEQyFQg5vHy2qK2uh8lLBaDLB0N4B1sEIoNVqdXhCcN8JEP0cWJZFeGQIOI6FRqtGTVUdlEoFwqNCe314qUes3HdbfzkZ191XhVKBhtpGgAFOHT2H1KEpDqefemK2yhVyhEYEQyaXgWEYNDU2o721HSxrH8EWGxgSBAFWi4SPwQ7yRuWlQnBIAJQqe2HU3mZAZXk1TCYziq+Wik4F5Hle2qsUOuir1lsD/wA/qDVeaG/vQGenCWERwQgKCUCBg/vkPDVbff318PbRQeetRWNDM2w2G4JDAqFWe6Gqokb0b2xWm+iAvSQIEM0bAAgMCYCX2gvePjrU1TSAv/Gsv8jocHj7iF81tVptkiyiADjMG4ZhEBYeDLlCDp23DtWVtTAajfD108PH19vheVN7u+GWrnYfqVVeKrCM+IG7s6MTFosVxk4TzpzIQkN90x3/vaQ4TehutDS3Qi6Xo7amHuXXq+AX4Nv7vGAGkEvwsu3dqKtpgLePDlfyruH86WzodFqoepnKxjAMWIneWwKg1ylM1ZW1CAwOQHFRKSZNG4ewyBAkD4p3+H6O4yR5ifpuVFXUIjwyBOdPZ6O+tgEtTa29nnxJ/YGQvbWspqoOoeHBOLT3BFReKlRcr3K4qpQA3HjQZ78002UMAEeN0+k06Ogw4lJWHhavmINLWbkIDglAeGSIw1WwOI6T5JU3APbOOmia1luLDkMnCguuYf6SGai4Xg2NRu1wkQUB9umAnkijUaO9zYCaqjpMnjEeVRW1GDtxpH1ww0GIS3Ga0J0wDAOVSoXmxhaYTWYMHzUEJrMFacMGodLBSSjDMOCk/HwlB/sqx7GQyWWorqyFt16HmLgoXDyXg5amFvuIveimGMnetwnAYV+77v0pLipFQnIs9L7eqK2uh6+/r8NV4GQemq0qlRJWixWXswswNmMkLGYrss/nQqvTQKnquU8KsF8JkWy2MnD4uWo06u7pxbMWZMJmtWHS1LEIjwpFfJL4/ZnS/v46fknnrUVHhxE5F/OweMVclJdVoq62Hk2NzaJXTQUAarXXLZvsntrX3mbA8lnPOrwXyEutglKlRHNTC5QKBRiWcXjfAsdxmDFnMgIDpDm3ubOzE998vcPhyaVWpwHLsrBYLPD106O1pc3h1D2VSokZc6dAo1H3Z5P7rLmpBXt2HnQ4AuSj18Fm5WEym+Gj90ZTQxNsDlYh1Om0mDx9PLRaTX82uW8Ye2F4YO8xh6so+vrpYTabodGqIZPJ0NLcCkO7+FOtg8MCMXHyWMjl0ruXBrA/7+38qWzRIp9hGPgF6NHW0g65Qg65Qo6WphaHV2LCI0MxevxwyCU4+MEwDC5eyMHFC+LTMDmOg6+fD5oaW6DWeAFAr8vrDkkdiKkTJ0gyyBmGwbd79iE3X/wKuFanQYehA/4BfmhuboVSoYBMzolPY2SA9OGDMXToYEkGOcsy2LptN6oqe55EsywDlZcXzCYTfP31aKxvBmAfnBNbuZFhGEzMHIeIyND+bnaf8DYeO7fuE/1eymQcZHIZeBsPb70OjfXN8PXXw9hpFD02cRyL6XMmw8/f91403WnGDiO2bt4tOktDoVQAggCWY6HRqNHc1IqAID+HAz1KpQKZMzLg66e/By13XnubAbu27Re9wuTlpYLZbIFSpYRCKUdzYwuUKiUYBqLnTTpvCWcrgJqaOuzfc1Q0WzVaNToMndB5awAwsFqt0Pv6ODxvCgkLwvhJoyCX4H2qAFB05ZrDhTW0Og3a2wzQ+/nAYrbAYrbY99uGZtF/m4ioMIybMFKai02wDC5l5SEnS3yqXldf/QN8YTSaoNFqIJNxaGlqhcHQ89iUkDwA6aOGgOtl5sD9wrAsjh4+iauFJaKv27O1E/4BvvZsVSogk8nQ3NwiepVtzsJp+PUff9x1HrG3+5us8lIidWiKw0Kqs8PYPSJ4+43Nt+M4FiufWYKUwYl31cl7rb3NgIKiqzh/WnxxjZt3/s6O3pc29VJ74fnXnkRYRIhb2+guVZU1KLxyDUUF4jfFtjR/f09cvchNsDcLDPbHm//xAvS+0lxYoyDvKvIuX0FlufgIZ1NjMwA4LJ5uFh0TgVffWguNVpoF8pnjWSgqKEaLyEm0IAhoqLMvGGK+i6U+09IH4vWfPS/Zm393bNmLgrwi0ZMtm82G+rpGAL0XUF3SJw7DqteXS3ak26oVkP+7q6JXI7qOS103q/e2jCsDBjMWZuKRVfMlWUgBQJvZgPUfburxe54X0HEjqG9e0Kiz08F0IAZY8thcTJo6tl/a6Sqr1YaGhkbs23lE9LWuQa76Wvv3uOHG91kMJ+Oweu0jSElN6J/Guqi9zYCiayW4cKZntt58P1FXMeHofAOwn6Cv+9FahIZLc2GN6spaFFwuRNGVkh6vdRX8HYYOdNw4neht+mlgiD9e+8kPoPeV5kJO+blFuHypQHQKW1eetrZ8f/zt7VlT0bEReP3HP5Bstp48dg5X8q+JPni16xh882qjXfutmKHpqXjzZy+KXrGSgp1b9uFX+VdFr7x09bVr8bE7nTdlZI7B8689Kdls9X3XB3/53XuuZyvDYNjIwbdMNe/+L47jMH3OJHipXV+ScvjoIYiKjQDDMJL8UWvUmDZroltG4MdPHoXgkMD73idHP4FBAZgwebTLU/IYhsHk6ROg9/W5731y9BM7IBJD01NdWb0fgH1fmDozAxqt+r73ydFP6rBkxCfGuNZR2AcCpswcD6VScd/75OhnbMZIhLphoMI/wA8ZU8aAk3H3vU+OfiZNGwe/AL3LfY2MDkf66LT73h9HPwAwffYk6LxdX+55YGoiUgYl3Pc+OfqRyThMnzvZLdmaPnpI97K7UvxRa9SYNttN2TppNIJCAu57nxz9BAT5Y9zkUW7IVmDKtPHQ+3rf9z45+hkQF4WhI9yUrbOkna1Dhg1CfNIA1zoK+/SvzJkZUKqkm61jMtLdchHAP9AXE6aMlnS2Tpk+vnulW1dExUQgfVTaLb/rPgIwDIPRE4Zj2Mi0Hn/oDG8fHZaunCfZ0QbAfsVs5vxMxLl4IhocEoglj86TbAUOAHK5DEsenYegkECXthMdG4F5S6a7qVX9Q6lS4tEnFkPn4rM4UlLjMXVWBhhGmiP5gH3qyPInF/V6T9udMAyD4aMGY/SEdEn3Ve/rjRWPL3Tp5IxlGUzMHIPBQ1Mk3dfwyBAsWDbLpamHHMdh1vwpiB0QJdm+MgyDlNQETJkxwaU2qlRKLFo+B4HB0pxGDtj7OmZCOoaNHOzSdnz0OixbOV/y2TprXibiEmJc2k5waCCWPDpXklNwu9izdS6CggJc2k50bCTmLPaEbF0EnYtTD1NSE5A5U+LZqlZh5VNLoPJyLVvTRw/B2IwRku6r3tcHy1YtcGnqIcsyyMgcg9QhyZLua3hkKBY84oZsXZCJmNuy9ZahFJ23FmvXrUZIWFCf/k9YlsXshVORMWW0pP9BAcA/wBfPv/pUn+dfczIOK55YhCHDB0q+r5HRYXju5dXQ6vp2EPRSq7DmxVU9vjxSlJyagCeefaTP09R8/Xzw/KtPwS/Az80tc78xE9KxcMXsPt/kGRYRjGdeXgUviT4YsQvDMJi9YBoyZ0zo84BoQnIcnnr+UcgkPOgB2Jc5f+yJRX0+6WYYYOiIVCx/fKGkB3gA+wJHz7y4ss8DWsyNAJ+3eHqvK/pJgT1bH3cxW6dhgidka6Avnn/1SZey9dEnFiNt+CDJ9zUiKgzPvLyqz8Wtl1qFp194rHsGj5SlpCbi8bXL+56t/no8/9qTkr2/72ZjJ47A4uVz+pyt4ZGheG7dE265Ct2fGIbB7IVTMXnGuD5vIyF5AJ58boXk80Ymk+GxJ5dg2Ii+Zqt9St+K1T2zlb39jYPSkvDaj3/g9LxkuVyOWQumYM2LK7vWVpc0hmEwYfIovPj6U05f7vPyUmHF44uwfPVCST7Y83Ysy2Le4hl4/JlHnL6ZVeetxZrnV2LW/Expr8pyg0Ihx8o1y7DwkdlOjyj5+uvx0ptrMDZjBFhW2qHGMAzUGi888/IqTJ4x3qmrNQwDBIUE4LWf/ACD0pIkH+AMw0Dv641XfrgWo8enO/U9ZBgGsXFReOsX6xAVI/2TFYaxTxl64yfPO331jGVZpA5NwVs/fwX+AdI/WWEYBtGxkfjhz15yepoqx3GYMGkUXnvrB/BSe/VPA92IYRikDknuY7bKMGthJta85EHZOmU0Xuhjtj76+CI8snqh5Ac9APuqbPOWTMeqNcucLqZ03ho8/cJjmDF/isdk66o1S7Fw2SynZ0L4+uvx0htPY+wEz8hWjUaN59Y9gcwZGU5drWEYBiGhQXjzP15Eapq0r9AA32fryz98FqPGDXc6W2PiovDvP38FkTemG0sZwzAIDLLf59+XbB08NAVv/WId/ESytXvVvpsJgoCTR8/hb//zPooKint9SBzDADpvHRY8MhNrXlzZ67N5pMhms2HvzsN4+48foLy0stdnOTAMAz9/PVatWYaVTy3xiAC/mclkxrZNu/HuXz+2Pxugl2cLsSyLoOAA/GDdE5i7ZIZkFyIQIwgCDIZObPxkMz5+70u0NLf2uoQ9x7GIiArHqz9ai4zMMZJdqU+MIAhobmrFx//8Apu/2AlDu6HX5yTJZBwSUuKw7q1nMWxkmkcEeBdBEFBbXY+//eF97N15qNcbmgH74M7wUWl49UfPYeDgRMkf6G8mCAJKrl3Hn3/7T5w6dv6Ozw5SKhXImDIGL//bGkQPiPS4vuZczMcff/MP5FzM6/0BrAygVqsxc+5kvPD60wgOdW3K8r0mCAJOHDmLv/33+yi6cqdsZaDz1mLh8lmema1WG/bsPIS//+nDu8xWX6xas9Qzs9Voxravd+P//voZ6mvvIltDArD2lccxZ/E0z8vW9g588ckWfPJ/G9HS3HaHbOUQGR2GdT9ai4wpnpitLfjgH+vx9YZv0d5u6PU5STKZDEkD4/D6j1/A8FGDJT0t9XZd2fr2Hz7A/p1H0NFxN9k6GK/8aC1SUhM8Lm9Krl3HH3/zDk4fP+dw9fEuSqUSGZlj8MoPn0F0rGi27hUtpAD7ykktTS3Ytuk7HPjuKK7kXYPxpqVnGdZeeQ8dkYplq+Zj0JBkyG7caOZpeJ5HbXU9Nm3YjsP7TuBaUektKwyxLIvI6HCMGDMEK55YjLiEGHBSfj5AL2w2G66XVuKr9dtw/NBplBaXw2r9PsxlMhli46IwJiMdy1cvQnhkqEedbN/MarWiqKAEGz/dgrMns1BeVnVLwCmUcsQlxmJi5lgsXjEHQcH+kp8i5IjZbEFudgG++nQbss/norqy9paA81KrkJA8AJmzMjB70VT4+vl45PfX/gBsM86ezMJX67fh0oXc7lX7uui8tUgelIA5C6di+pzJ0Oo0HtvXzg4jDu8/ga1f7cbl7IIeK0np/XyQOiQZ85fMwMTMsVB5KT22r13LSe/efgC5lwpuWSWKYRgEBPphSPogLF4xF6PGDoNcIffIvvK8/QRt21e7b2Tr1VvCnGEZhIYFYciIVDyyaoHHZ2tNdR2+/vxbHN5/AteKSm4plFmORVR0ONJHD8GjTyzGAE/P1pIKbPp8O04cPovS4vJblkaXyTjExkVh1IR0LH98AcIiPD1bi7Hx0604cyILFddvz1YF4hJjMGnqWCy+cQ+jJ2fr5Yv5+OKTzcg6lyOSrV5ISonDtDmTMHfRNPj66T3y+9uVredOZmHT+u3Iycp3kK3xmLVwKqbNnujx2Xpo3/Eb2ZrfI1t9/XyQOiQF85fOvFO2Oi6kuvA8j4b6JlRX1qKqvAbNTS32p5SHBSE4NAih4UE3no/gef+Yt7PZbKitrkd1VS0qy2vQ1tIGlZcSYREhCAkLQkhokMeG9+0sFitqqmrx7p8/we6tB7p/P3fJNDz90kqEhAV5bHjfzmQyo7qytvuns9MIbx8dwsKDERIehMAgf48aPXJEEAQYO03d/aypqoPFbIHe1xuhESEICQuEX4CvxwbazexXHTtQVV6Dqsoa1FbXg7fx8AvQ39hfgz22WLydIAhoa23H2ZMX8Zffvte93K5Wp8av/vwWkgbGQ+etfSD6yvM8mptaUVVRjcqKGjTWN4HjOASHBCI0PBih4cFQa7wemL421NmztbK8Gs3NrVAo5N1Z8+BmazXaWtof8Gytw9//8AF2bd3f/fuFj8zCMy+tQvADm6016Ow02bM1IhghYQ9athpRVVmLqoqaW7I1LDIUIWFB8H8As7W6staerTwPP3999/6qf4CytbWlHWdPZuHPv3mnO1t13hr81//+9G6zde8dr7OyLIvAIH8EBPohdUjyLa89CP+QN+M4DqHh9gPA0PTUW1570Poql8sQHhmKwCB/sMz3O39gcADCIoIfiINfF6VSgaiYcETFhPd47UH6XBmGgZdahZi4SMTERYq+/qBgGAZarQbxSbGiT1p/0Prq7aNDVHQ4WLCwWeyj3LxNQOyAKHj76O5zC92HZVn4+evh6+eDgYOTbnntQfpMgRvZGuyPgCA/pA6lbH1Q2LM1BAGBty5YFBDkj1DKVo9kz1YvxMZFITYuSvT1B8XDlq0+enu2MmBhvZGtNquAmLi7z9a7nrD6IP3j3cnD1NeHxcP0mVJfiad7mD5X6ivxZA/TZ0p9JWI8/zokIYQQQgghhNxjVEgRQgghhBBCiJOokCKEEEIIIYQQJ1EhRQghhBBCCCFOokKKEEIIIYQQQpxEhRQhhBBCCCGEOIkKKUIIIYQQQghxEhVShBBCCCGEEOIkKqQIIYQQQgghxElUSBFCCCGEEEKIk6iQIoQQQgghhBAnUSFFCCGEEEIIIU6iQooQQgghhBBCnESFFCGEEEIIIYQ4iQopQgghhBBCCHESFVKEEEIIIYQQ4iQqpAghhBBCCCHESVRIEUIIIYQQQoiTqJAihBBCCCGEECdRIUUIIYQQQgghTqJCihBCCCGEEEKcRIUUIYQQQgghhDiJCilCCCGEEEIIcRIVUoQQQgghhBDiJCqkCCGEEEIIIcRJVEgRQgghhBBCiJOokCKEEEIIIYQQJ1EhRQghhBBCCCFOokKKEEIIIYQQQpxEhRQhhBBCCCGEOIkKKUIIIYQQQghxEhVShBBCCCGEEOIkKqQIIYQQQgghxElUSBFCCCGEEEKIk6iQIoQQQgghhBAnUSFFCCGEEEIIIU6iQuohJAgCbDYbamvq0dZugEqjBCtn4aVRoq21HfW1DbDZeAiCcL+bSshDTxAEmIwmXC+pBABwHAdOxkEul6O4qAxGowmCIND+Ssh9dnO2Ggwd0OjUkCvk0OjUaGtrR31tI2UrIRIhCAKMRhOul1aAYQBOxkEm46BQyFFcWHrX2coItEc/VGw2G/JzCrH5y504sOcYDG2G7i8LyzJQKpXQ+WgxMXMslj42D4nJceBk3P1uNiEPHUEQ0NLchqP7T+Gb9d/iekklOgydsNlsAACOY6HRqhEVG4FFj83GhMzR8NF73+dWE/JwstlsyMspxBaRbGUYBiqVEjofHSZmjsGylfORkDSAspWQ+0AQBLQ0teLw/pP4ev23uF5SIZKtGkQPiMDix+Yio/ds3UuF1EOkw9CJzV/uwKfvf4XK8upeq2yGYRASFoSnn38MC5fNglKlBMMw97C1hDy8eJ5H6bVy/O137+PcyYswGc29vl+hVGDspBF47rXHERsfRfsqIfdQh6EDmzfuxKcffInK8po7ZmtoeDCe/sGjWEDZSsg9xfM8Sq5ex19/9x7OnrgIk6n3bFUqFRg3eSR+8NqTjrKVCqmHgSAIMJnMeO+vn+Bf730Bi9ly13/rpVbhsSeX4MXXn4ZcIe/HVhJCAPv+mp9TiF//6E8oLiq762lADAPEJw/Af/x/ryMhZQCdnBHSz7qy9d2/fIyP/2+jU9mqVqvw2NNL8cKrT1G2EnIPCIKAvEtX8Msf/cHpbE1IjsPPfvcmEntm6166R+ohIAgCvtnwLT7/6GunDvQA0NlhxIZPNmPzVzthtVr7qYWEkC41VfX406//iWtFpU7dSyEIQFF+Mf7063+itrq+H1tICAEAgRfw9Ybt+PxfzmdrR4cRG/71DbZ8tQtWq62fWkgI6VJTVYc//OodXCt0PlsL86/hj7/6h2i2UiH1gBMEAWUl5fjonxtgMHT0aRsd7R346J0NKCsup5tkCelHFrMFmz7dhtzsK0AfdjVBEHDx7GV8s35H93xvQoj7CYKA0hvZ2mHo7NM2DO0d+PCdz3G9hLKVkP5kMVvw5SdbkZtd0Ke/FwQBWWdz8PXn23tkKxVSDzirxYovP92K2lrXRqgrrlfh6w3fuqlVhBAx5WXV2L5pD2wujFALgoA92w+iuLDMjS0jhNzMnq1bUFfb4NJ2Kq5X4esvKFsJ6U/lZZXYtuk7lwYYBUHAd9sO4lph6S2/p0LqAVdX14gTR8+Bt/G9vq9rzqej+yoEQcCxw2fQ1NDs7iYSQm44uv8kWlva7vr9jvbX6spaZJ3JgcDTKDch/aGurhEnj905W+9EEAQcP0TZSkh/OrzvJFqb7z5bHamsqEHW2ZxbriBTIfWAq62uQ8lV8ZHppIHxCAjyQ+bMDMyYOwmpQ5Ixa0EmomMjRd/f1NCMq4Ul/dhaQh5eVqsVl87niZ6YsSyLYaNSAQDJgxPg6+eDzNkTMHnmeHipVT3ez/MCLp6/DJ537SSPECLOnq3XRV9LGhgPH70OMpkMw0YOBgCkDRsIlVfPfRUAGhuacLWoVPQ1QohrrFYrss/niuahPVvt+2jK4ERExoRj7uJpmD5vEvS+Pj3eL/D26fM3b4sKqQdcVUWNw0uZUTHhiB0QBZZlYDJaEB0bCWOnCTPmThJ9v6HdgOqq2v5sLiEPrfa2DjQ3tYi+xrIsElLiAAAxAyIREx8Fs8kClmEQEOgn+jelV+m+C0L6y52yVaPVQCbjkHRjv41PjIVSqRB9f3ubATWVlK2E9If2NgOaGx1kK8cisStb4yIh8ALMZgtam9vQ2WkU/ZvSa9dvme1BhdQDzujgi6DRqhEdGwmGZSFXyMEwQFxiDFqbW8Gy4l8Lm42H2eTcykSEkLtjs1pFV+9iWAYxcZFQqRTQ6jSIiA4FyzL2JZMZx2tSGDtNfVmvghByF+6UrTIZhwEJ0VAoFPDReyMsMhSOnkhgs/EwO7nqHyHk7lgttl6yNQoqlRJabw0iosOgUMpRXlqF0PBgh4OUnbdlKxVSDzitTiP6e5uNR1NjCyrLq8AyLELCgnH6+HnEJcbi7KmLon8jk3Gi04gIIa6TKxRQiD1PRgCsNhvqa5vA8zwaG1pwvbQSarUX9L4+aGluFd2eVqcBPUmKkP5xp2w1Gc2wWm2or2uEzWZDQ32jw2XOZXIZZSsh/UShlDvMVpvVivraRvA2Hk0NzejsMCJpUBxkMs7hStdaneaWQRFZP7WbSERYRAgUSgXMtz292dhpxJYvd8Jms6Gmqh6cjIXJaEb2+VwYjSbRbem8tQiPCLkXzSbkoaPRqhEQ1HMETBAElBSVoaKsChazBVs37oLNasN32w+CZVmYHOyvcUkxYFgqpQjpD3eVrdV1KL5aBovZgq8+2warVfyqk7e3FmGUrYT0C41Wg4Ag/x6/FwQBxUVlKL+RrZu/2Amb1YYdm/eBZRkYO8WzNT4p5paFnuiK1AMuMDgACUkDRF+zWq0QBAEWi8U+DUgQ0NHR6fAGdf9APwxIiOnH1hLy8OI4FsNHpYHjxA/LXQ/8tFpu7Ldmi8MiiuNYDEkf6HCaLiHENYHBAYhPihV9rStbge/3W4vFAke3LNqzNbpf2knIw47jWKSPvvtsNZvMDosojmMxdETqLdlKKfuA8w/wxeTp4yGTuXbxkWEYzJ4/1eF0BkKI68ZNGYngsCCXtxMTH9W9EhEhxP38A3wxZfp4yGScS9thGAazF0yFVkvZSkh/GT9lNELckK2xCdE9spUKqQccx3FYtHw2ogZE9H0jDDAoLQkz5k12W7sIIT0FBvljyaq59oUk+kiukGHB8pkIjQh2+JwpQohrOI7DokfmIMrB40LuSle2zp3stnYRQnoKCvbH0pXzXcxWORYun43Q8GCa2vewCQj0w0uvr4F/gG+f/t7bxxvPrXuix5eHEOJenIzD/GUzMH7yyD7tayzLYsKU0Zi9cCpN6yOknwUE+eHFN57uc7b66L3xg3VPIiSMspWQ/sTJOCx4ZCbGTx7V52zNyByNOSLZSkn7EGBZFlOmj8dLbzpfTAUE+uGNnzyP8ZNG0YkZIfeAzluLl3/0LMZPHgXWicUiOI7DuCkj8epPnoPWm6YJEdLfWJZF5vQJePH1p+HnbLYG+eONn7yAcZOc288JIX2j89Fi3Vtr7cWUk9k6YcpovP7T50WzlRHoiY0PDYvFiuOHTuMff/4IV68U9/rcCrlCjoSkAXjh9acwLmMkZHJa4JGQe0UQBNTXNuJf/9iAA7uOobGh2eF7GYaB3tcbMxZMxqpnlyEgyI9Gtwm5hywWK44dOo1//PlDXLtScsdsTUwagBdefxpjM0ZQthJyDwmCgLraBnz49uc4sPsYGhuaHL6XYRjo/Xwwa/4UrF77iKNs3UuF1ENGEAQ0NjRj17b92LvjEC5fKoD5ppW/FCol0oamYMrMCZizcBr0vj50UkbIfSAIAnieR/a5XOzcvB+njp5DXXVD92pgDMMgOCwQoycMx6yFmRg8PAUsy9L+Ssh9IAgCGuub7Nm68/CNbP1+aXSFSoG0YSmYMmMC5iycDr2vN+2rhNwHXdl68exl7Ni8D6eOnEVtza3ZGhIWhNEZwzF74TSk9Z6tVEg9rHgbj/Z2A97+/Qf4Zv2O7t8vf3Ih1q5bDZ1OC4Zl6EBPyH0mCALMZgtyLxbgNz/5M2qq6gEI0Pno8JeP/sv+NHaFnPZVQiSgO1v/50Ns2bCz+/crnlyINa+spGwlRCK6svVyVj5++dbvUVNVBwDw9tHh75/8991m6166pvyQYjkWOm8tNGr1LV8StdoLWp0GrIP19gkh9xbDMFAqFdB5a2Gz8t8/l8ZsgY+PDkql4j63kBDSpStb1WqvW7NVo6ZsJURCurJV662B1WrrnpJrNlvgrb/7bKU9mhBCCCGEEEKcRIUUIYQQQgghhDiJCilCCCGEEEIIcRIVUoQQQgghhBDiJCqkCCGEEEIIIcRJVEgRQgghhBBCiJOokCKEEEIIIYQQJ1EhRQghhBBCCCFOokKKEEIIIYQQQpxEhRQhhBBCCCGEOIkKKUIIIYQQQghxEhVShBBCCCGEEOIkKqQIIYQQQgghxElUSBFCCCGEEEKIk6iQIoQQQgghhBAnUSFFCCGEEEIIIU6iQooQQgghhBBCnESFFCGEEEIIIYQ4iQopQgghhBBCCHESFVKEEEIIIYQQ4iQqpAghhBBCCCHESVRIEUIIIYQQQoiTqJAihBBCCCGEECdRIUUIIYQQQgghTqJCihBCCCGEEEKcRIUUIYQQQgghhDiJCilCCCGEEEIIcRIVUoQQQgghhBDiJCqkCCGEEEIIIcRJVEgRQgghhBBCiJOokCKEEEIIIYQQJ1EhRQghhBBCCCFOokKKEEIIIYQQQpxEhRQhhBBCCCGEOIkKKUIIIYQQQghxEhVShBBCCCGEEOIkKqQIIYQQQgghxEmy+90AqRAEAUajCZXl1cg6m4OigmK0tRmgUikRMyASacMHYkB8NDRaNRiGud/NdYkgCOgwdKKstAJ1dQ1Q67xgMpmhVCpQW1uPK3nXEBUbDrXay/P7ygtobzeg+GoZLp7NQVlJBUxGE3TeOsQlxWDoiFSEhgdDpVJ6fF95nkdrSxuKCkqQfe4yKq5XwWq1wsfXB0kD45A2fBCCQgKgUMg9vq82mw0tzW0oyCnE5ewCVFXUQuAF+AXokTw4AYPSkhAQ5AeZTObxfbVarGhqbEbWuRxYbBaAZcAwACtjcfrEBYwcOxS+/npwHOfRfRUEARaLFQ11jcg+fxkFl4tQX98EGcchNDwYqUOTkTwoAd56HViW9fi+mk1m1FTX4+K5HFzJu4aWplbIFTJERocjdWgKElMGQKvTgGU9e7xTEASYjGZUV9Qi53w+SgrL0N5ugFKpRGRsGAYNTULUgAiotQ9A3tzI1uulFWiob4Baq4LJZIFKpUBNTR0K868hKiYcXg9QtpZevY6sc5dRXloJk9EMnbcWcYkxSEsfiNDwICgfoGwtLCjGxXM5KC+rgtVqg97XG8kD4zEkfRCCQgIfnGxtakVeTiEuX8xHZUUNIAjwC/BFyuBEpA5JRkCgH2TyByNbGxubcfH8Zdh4G1iOBRgGMjmHMycuYOSYYfD197ljtjKCIAj3sN2SIwgCeJ5H1rnL+PLTLTi8/yTMJjOsNhtw41+G4zjIZBxShyTj0ScWIyNztEceHARBgM1qw/HDZ/Dl+q04dfQcrFYbbDZb93s4joNcIcfIscPw2BOLMGrccI/cYQRBgMlkxsE9x7Dps23IvpAL3sbDZuMBAAzDgONYKJRKTJw6BstWzcfQ9FQwLOORfTW0d+C7bw9i02fbUFRQDJ7v2Ve1Ro3pcydh6WPzkDQovvs1TyIIApoamrFr6wF8s2EHKq5Xgbfx4Plb++rj643ZC6di4YrZiIoJ737NkwiCgOrKWmzeuAObv9yJupp62Gw8ug7ZXX0NDg3CwmWzsHjFXASFBHhcPwH7SVlZSTm+Wr8Nu7YeQEtTyy19ZVkWLMciKiYci5bPwbyl0+Gj9/a4vgqCAEEQcCXvKjZ+sgX7dx9FR3vHLX3lOBYsxyEhKRbLVi3AtDkTPXIArytbcy7kY+vnu3Hq0DmYzRZ73tzIVpZjIZPJkDw4HotWzcboSelQKhUe2deubN20fjtOHzsPq9XafQwGbs7WoVjxxCKMHDfUIwd6urL18J4T+Obzb3HpQl6PvGE5FkqlAhlTR2PJynlIGz4QDOOZ2dreZsCeHQex8dOtKCq45jBbZ86bgqWPzUeyh2frji178fX6b1HuIFv1vj6Ys2gaFj821+Oz9ZuNO7DF9Wzd+9AXUu3tBnzx8WZ88fEW1NbU3/H9Gq0aM+dOwQuvP4mAIH+P+gI1NjTjw3fWY9um3WhqbLnj+719dFi2cj6efG6FR520dO0k7/7vx9i36wja2wy9vp9hGPgF+OKJtcux5LE5UGs856RFEASUXruOv/7P+zhx+CyMncZe38+yDELDQ/DMy6swe0EmlCrlPWqp63iex5W8q/jf37yLSxfyYDZben0/y7GIjYvCc68+joypYyCTec4FeKvVhgtnsvH7X7+NwvxiWK3WXt8vk3EYODgJ6364FiPGDvWoqxgWswWH95/E279/H2XFFd3B7YhCIcewkYPx6lvPIXFgPFjWM/ZVADAZTdj+9R589M7nqCyvwZ3i18tLhXGTRmLdj9YiIjrMY45LAGBo78CW9TuxZf0u1Nc23vH9aq0XpswejydfWgG/QF+P6mtjQzP+9c4GbNv0HZqb7iJb9TosfWweHl+7HD56ncf0VRAE1FTW4b2/fooDu47C0N7R6/vt2arH6meXYeGK2VBrPOdKnCAIKLlahv/97/dw4sgZGDtNvb6fZVmEhQdj7SuPY/aCqR6XrQW5Rfjjr9/BpQu5d5WtA+Kj8fxrT2HiNE/LVivOn76EP/z6bRQWXIPVauv1/TIZh4FpyVj3w2cxYoxotj68hZQgCDB2mvD+3z/Dv97bCMsdvjg34zgOGZmj8bPfvAn/AN9+bKV72EdV2vHH37yDzV/uBG/r/UTlZgqFHHMWTcOP/t86qDVe/dhK9+gaVfnlW3/A0QOn7nhSdjOVlxKPPbUEz7/+FORy6R8YBEFA5fVq/PjV/8Ll7HwI/N3vyhqdGi++8TSWr14ITsb1YyvdQxAEFFwuws/e+B3KisvveAJ6Mz9/X7z5ny9g6uwMjygwBEHAiSNn8PMf/Q9qquqc6mtEdBj+8zf/htHjhoPxgALDZuOxe9t+/OFXf7+rwZ2bJQ2Kx89++yZSUhM84uTMYrbgy0+34u9//Agdht5PQG/GMAyGj07Df/72TY8oprqydf27m/DlR1thMfc+CHAzjmMxelI63vjF8/D11/dfI91EEAS0tRnwp/96B9s27XY+WxdPw7/97CWPytb/+vGfcfzQGaezdcWTi7D21cc9JlsrrlfhrXW/Qs7FfKeOwVqdBi+/uQbLVy/ymGzNyynET1/7jdPZ6h/gix/+v5cxbfZE+7Q4iRMEAScOn8HP33I+WyOjw/Cfv/03jBrbI1v3Sr/n/Wjbpt347INNThVRgH0O6ZH9J/HuXz5G5x2uAEgBz/P4+L2N2P71d04d6AHAbLZgx5a9+PSDr+44SiEFJqMJb//+Axw7dNqpAz0AGDtN2PjJFmzftPuW6Y5S1dLcij/+1z+Qm13gVBEFAIa2Drz/9noc2X/SqYPJ/VJTVYc//OofKL3m3IEeABobmvC3/34fl7KcC8T75VpRKf77F39DdWWt0+0tL63E737xF5QWX++n1rnXpQu5+N/fvut0EQUAV3Kv4g+/+jsa6pv6oWXud+TAKbzz5385VUQB9vA/fyobf/nde3e8AiAV3205gK8/+dapIgqwF9YnD57Dp//46o5XAKSA53l8+u5G7Ny8t2/Zunkf1n+4yWOy9R9/+Agnj5ztU7Z+9ek27Phmr2dka1Mrfv+rt+0DlE4eg9vbDHjvb5/i8AHPyNbqylr8/pdvo9TJIgoAGuqb8JffvYdLWXke0ddrhaX471/2LVuvl1bidz//K0pLynu89lAWUoIg4HpJBT77cFOfCyGbjcfOrftx5vgFSX+BukYbvlq/rc8Ha7PJgi8+3owreUWS7+uZE1nYuXUfbHe4XOuIob0DH72zAdWVtW5unXsJgoD9u444fdXtZo31Tfjg7+vR1tLu5ta5l81mw9YvdyEnKx/dN1c4qaqiBp/88wuYTGb3Ns7NjEYTPn3/K5Rc63shdK2wVPIDH4IgoLWlDf969wvU19152pejbVy6kIvNG3bccXrG/SQIAmqr6/HxuxvvOM24t20cO3Qae3cc6vP+fi8IgoCKsip8/cm3Nwoh5/dXnuex79vDyDp9SfJ5k59TiE0bvnUhW83Y+MkWFOVfk3xfz568iO+2H+zzvmZo78An/9yI2qo730JxPwmCgL27DuPowVPgnRyg7NJQ34T33/7UI7J188aduHQhD+jj96+yvBr/+ucGz8jWD750KVuvFpbgs/d7ZutDWUjZbDy+3bIX5WWVLm2ntaUNX3yy5Y73L9xPZpMZmz7fhqa7mLfdm/q6Bny1fpubWtU/Ogyd+PLTrS6PZFZcr8L2Td9JOthamtvw1WfbYLG49t27kn8V+3YdkXRf66obsO0r168Snj9zCWdPZEm6r8VFpdi9bb9LJ8uCIODAnmMoyJX2wMfF87k4cfisS220Wm3Y/vV3qK6scWPL3EwAjhw4idxLBS5txthpwlefbetzMXYv2Gw89m47gsrrXQNRfZuG2NZiwJb1u/o8IHYv2LN1+13dE9Wb+tpGbPp8u5ta1T86DJ3Y9Nl2t2Trjm/2Svq41NLcii8/2+JythbkXsXeXYcl3dea6nps+XKXy9l67tRFnD0u7Wy9VliC3dsOuJyt+/ccxZXbslX6k1X7QYehAwf3HL9lRZ3eMCzjcOpUzsV8XL1SiujYCHc20W0qrlfh9PELTk/9EnPuVDbKSysREOTvhpa5X/7lQuTnFN71+xmGEd3xeV7AyaPnsHD5bPjovd3ZRLc5dzIL5WVVd/1+R301myw4fug0pswYDy8vlTub6DZH9p9EU4NrJysA0N5qwInDZzEkfZBkb4797tuD6OjovOv3sywjOmpaX9uA08fPIy4hRrL31OzZdgDmuxzF7OqD2Hf4emklss7mwD/Az63tcxer1Yq9Ow7BepcnZizLQBDE+1pYUIzcS1cwZPggdzfTLQxtBhzffxq8G6Zv5V8qQknRdYRHh7qhZe5XWV5tH5hxQ7aeP5WN8rIqBARK8zucn1OEgstFd/1+R8clnhdw6uh5zFs2Hd4+Onc20W3OnLjgVLY6YjabcfTgKUyeNg5eamlm6+G9x9Hc0HzX73d0HtHWasDxw6cxZMQgyCR6X9ieHYecylZHfa2vbcCZk1kYmJbUnUsP5WITZSUVeGT2MzAZe4Z4XEI0bDYeJdeuI3PmBBRfLcOgtGS0tbbj0N7jPd6vUCowatRQMII0T1YMhg5kZV2CTaQKHzZyMMpKKtDa3IZxE0fgzMksRESFQS6X43J2fo/363QaDB2eBsEmza9Mc3ML8nMLRb/84yaNwvnT2VAo5UgaGA9TpwkR0WEoLipFnkjxpdd7IzklARwnwYMCA9TXN6IgTzzYJs8Yj0N7jyM0LBg+vt5QKBQIjwhBXs4VFF8t6/H+2JhIjEkdCo6RYF8BXC68gpzCK6KThCbPGI+D3x1D0qB4tLW0wz/QD2Ul5WhpahXdVmx8NAID/fo6i6HfXSkoQk1tXY/f2xe4GYODe45h1LjhqLhehcFDUyCTy3D0wEk0i/Q3dXAyfPXSXQznck4+WlvaevxerVEjbfhAnDxyFhmZY5CXcwXpo4fAarXi8N4TPUaKGQApgxLh66u/Nw13EsuxOHs6S3QaeWBwAMIjQxAbHw2ZnENlWTViE6JRXVmLfTt7jmazLIshQwZBo9Xcq+Y7hWEY5F24InolKSY+EnKFHKnDk2ExW5F1Ogc6Hy1qq+rRILKqn0wuQ0pqAuQKaQ56GE0mnDglfr/Q0BGpaG8zYPSEdHQYOsDJOCjkclwrLMWp4+d7FF86bw2GDUuDINFZmy1NLSjILwIvmq0jUVNVh9EZw9HWakBLUys0WjWuF1cg52LP8whvvQ4DEqIludomwzD2bC0oEp2VmjljAiorajBq7DA0NjTj5NGziIqNQG1VHcqv9yy+AoP8ERMbJcnBLJZlUFVR63BmVubMDDQ1NmPQkCQ01DWhs6MTKi8Vzp/ORm11z+mZAxKiERgYgL5Ov+9vVwquoa6uZ7u7spW38YiKjUBVRTUEAVCqlDh28JRoRk2dNRG/f/vnXYuJ7JXmEaqf1VTX2ef5Cugx88Bb7w2rxQqGAcIjQ5F/uQhXC4oxbtJIHN53okewWcwW5FwsgNUozfsReIF3eCkzINAftdX1MHAGhIaHYNLUcYiKiUBtTR3yL1/pccWus8OI7HO5sDp5A/G9wgs3ngMg8rmGhAdBJuOgVCgQFBKA8tJKVFXUIDElTrSQam/vwKULeW4ZbewXLET7CQBhESFgGAYarRpBIQGIGRCJ8rJKRMaGixZSTfXNuHKxCDJIs5Bqam92eGgOj7SPVut9fWCz2VBZXo3UIck4dvC06PtrKmtRXlwp2SkIJqv41BmGZbr7GhQSAGOnEf4BflCqFNBoNaKFVFlJBUrMPW+MlQJBEGDhLaLfYblChpDQQABAaEQIrhWWwGwyY+TYYTh3KhvNty1MIQAoLS5HSaE0F9iQyTkYjSbRvqrVKuh9fXA5Ox/RsREIjQjG4b3HMXbSSMgVMphNt+YKz/O4WlACXqKDWXKFHLCKt03nowVv43El5yp8A/RobW5D1IBwtDX3PFEBAJvVisLcq7BapDm9j+Hw/QITt32uAUH+aGxoRmHeVShVSlSWVyMxJQ411XWimdLZYUTO+TzJ9pXnedEiCgBCwgKRf7kIpdfKYbPxqK9pQGCIP6LjIkQLKUObAdnnc51enONeYTg4rAXCI0Nx+sQFRESGorPTiNkLp8JH743Txy+IFlLNjS24UC/Ne/0YlgHHsg7PI8KjQnH2VBaCQgLQWN8EQbBfOAgODRQtpKora1FeXCXJvgKA2SY++4G9ka17dhyE1lsDgEFYeBBMJjN89DrRQqqspBy8IHSfMT2U90hZzBbRHUXlpcTAwYmQyWRISI6Dj48OGq0acqUcVqvN4RfEE1ahuZ3OW4ukgXGQyWUYODgJKi8Vzp26CJmMQ1VFjei0R0EQJHvw601AkB9iB9hHQwcNSYZcLkNgsD8Cg/1x/PAZ0b/penCmVAkOjvThUaEIDQuGUqnAoCFJYBkGZpMZLMuirFj8pJrneUn3VQzD2EfA9H4+8FJ7ITk1HjKZDALPwy9Aj4joMNG/s9lsDv/tpIplWQxMTYRa4wW9rzcSkgbAarWCYZlejz02q+ftq5yMw6C0JMgVcgSFBiIyOgxBoYEAGNTVNTgcFOrrTeH3gqNdSy6X2Y9HChl8fHRoaWpF8qAEhEeFQi6XOSyWpNxXR2egSpUSiYPioFAqoPJSQhAEpI0YiPiUWIfL9AuCtPvq6HPVeWuRmBIHjcYLYBjofb0xeNhAXC+txNiMEaJXJwQBorNGpM4/0A9RAyLh7aNDZ4cR0bHhiIwJg62X8yVe4tnqSERUKILDguAf6IeGhiYkpsSh4HIReBuP2uqeswgAOCw+JUEQ/w4zDIO4xBjofb0RFByAqvIajBo3HDFxkWhrace1wlLRzdlsvEdma0pqItRqLwQGB6CspALpo9PAchwaG5rR4mCQ5/bVSB/KK1LdD8C77XhmMVtRVFCMxsZmGNoMKMi7irbWdgwfORiXRUZWAHs1q9NpYDRIc6lWG28FRApxk9GEvJxCGNoMsFqsKC4qRV1tPc6czEJbq/iXh5PJoNVpJLssrdVmhdlq7vG5Gto7cTm7ACajCRXXq9De1o7OThMGD02Br68P6moaemxLJuOg8lJJsnBkGMAm8Og09pwq1NbShtxLBbCYrSgpKkNnp+nGlbd4hzduK1VKqLxUYHnpTT8AIPp8CkEAmhpbcCW3CBazGYV512A2mTFqwnD4+unh6+eD8tKeUxbUai9YzFbJnqBZeAtw28fE8zzqaupxtaAYnZ1GXM7OR21NA8qKy6HRqh3e7K7RqWEz2SQ7jdHWacXtXznexncP5BjaDMjNLkBxYSmGj0pDcWEZOgzic9xVXkoIDq6E3G9yuQwGYwcE5tb22Ww2++AGw4DjWMQlxuCbDd8iaVD8jdF98f1VpVaBl2iRrFDIYLL2DByrxYriwjI01DUhOCwAOh8tLp3NA8/z6GgX/0wZloHKS3nX95bdc2zPcwjAnq35OVfQ2NCMsIgQCAJw7UoJBqYlIvfSFdEiQsZx0GrVMEl0ZovVaoVJZES/w9CB3OwCNDc2I2VwAlqa2tDW2o6I6HBknckR3ZZMJoNcLpPkSpsMw4CHDRA5xWltaUdudgEa65uQPioN18sqceFcDvR+PqL33giwX6GVMZwkV9pkWRa8wPc4znQ9L6wgtwgN9U0YNnswLmcXgGUZBIcFwitfJfoYBrXaC1azTZJ9BQCb0Qobf2tf7dnagKtXitHc2IKMzDE4tPcE5HIZfHy9HfZF7+uNm8dDHsp7pOprG/HI7GfEn13CoHtQrWuRCY7jHI7aqzVeeOn1pxEWHtK/je6jqspa/PX374nu6DffTNf1373d1B0Q6I8XXnsKfv7SvO+iMP8qPnpHfBnO2/sK2E/QeZv45xoZE46nn38MPpK8IZbBudMXsfGTzaJhJPa5chzrcHGVIcMH4plnV0EtwcUmBAA7t+/D9q17RIuf27+3LMsCDBx+rmMnjsC8JTMk+qBEAV98shknjp4VffXmvgqCAIZlwIBxeLCfu2g6ps2aJMn5+YCA//vrp8jPFb/P7/a+siwDARCdFsUwwLKVCzBmQno/t7lveF7An377D1SWi68saP98BLCsfR9lWdbhFXFOxuHpHzyGgYOT+rnVfdPZ0Yl//s/HaGsWWfb5RrYyDAOGZcDbeIc3dAP2gvHx5x9BeFRw/za6j2qq6/Gn372Dzo6eA1pi+yjHcQ6L48Bgfzy/7knJZuuVvKv4+L0vRReH+X4ftQ94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],
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||
"text/plain": [
|
||
"<Figure size 1500x1200 with 5 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Plot gate error map\n",
|
||
"# NOTE: These can change over time, so your results may look different\n",
|
||
"plot_error_map(backend)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "2744f347-84c5-4acf-8eb8-873125b99c3a",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Physical qubits:\n",
|
||
" [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"bad_qubits = {\n",
|
||
" 56,\n",
|
||
" 63,\n",
|
||
" 67,\n",
|
||
"} # qubits removed based on high coupling error (1.00)\n",
|
||
"good_qubits = list(set(range(backend.num_qubits)).difference(bad_qubits))\n",
|
||
"print(\"Physical qubits:\\n\", good_qubits)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "27d0b3eb-233c-4ea9-bea1-4c8a56fa038a",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Main Trotter circuit generation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "40777c29-b2db-48e6-8255-eb00cd69b0b5",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"num_steps = 6\n",
|
||
"theta = Parameter(\"theta\")\n",
|
||
"circuit = trotter_circuit(\n",
|
||
" theta, layer_couplings, num_steps, qubits=good_qubits, backend=backend\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "698446a5-febd-4c1b-bfbc-746a833e3520",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Create a list of parameter values to be assigned later"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "d3e78bc6-7ced-431a-a744-f42af3f835d6",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"num_params = 12\n",
|
||
"\n",
|
||
"# 12 parameter values for Rx between [0, pi/2].\n",
|
||
"# Reshape to outer product broadcast with observables\n",
|
||
"parameter_values = np.linspace(0, np.pi / 2, num_params).reshape(\n",
|
||
" (num_params, 1)\n",
|
||
")\n",
|
||
"num_params = parameter_values.size"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "59bc09ba-3a3c-400d-b25d-59e271465511",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 2: Optimize problem for quantum hardware execution"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9772c2b1-96a0-45cd-acfb-df563e11d216",
|
||
"metadata": {},
|
||
"source": [
|
||
"### ISA circuit"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ae9c228a-9402-4478-a68d-7d468fac3ecf",
|
||
"metadata": {},
|
||
"source": [
|
||
"Before running the circuit on hardware, optimize it for hardware execution. This process involves a few steps:\n",
|
||
"\n",
|
||
"- Pick a qubit layout that maps the virtual qubits of your circuit to physical qubits on the hardware.\n",
|
||
"- Insert swap gates as needed to route interactions between qubits that are not connected.\n",
|
||
"- Translate the gates in our circuit to [Instruction Set Architecture (ISA)](https://docs.quantum.ibm.com/transpile#instruction-set-architecture) instructions that can directly be executed on the hardware.\n",
|
||
"- Perform circuit optimizations to minimize the circuit depth and gate count.\n",
|
||
"\n",
|
||
"Although the transpiler built into Qiskit can perform all of these steps, this notebook demonstrates building the utility-scale Trotter circuit in a ground-up fashion. Select the good physical qubits and define entangling layers on connected qubit pairs from those selected qubits. Nonetheless, you still need to translate non-ISA gates in the circuit and avail any circuit optimization offered by the transpiler.\n",
|
||
"\n",
|
||
"Transpile your circuit for the chosen backend by creating a pass manager and then running the pass manager on the circuit. Also, fix the initial layout of the circuit to the already selected `good_qubits`. An easy way to create a pass manager is to use the [`generate_preset_pass_manager`](https://docs.quantum.ibm.com/api/qiskit/transpiler_preset#qiskit.transpiler.preset_passmanagers.generate_preset_pass_manager) function. See [Transpile with pass managers](https://docs.quantum.ibm.com/transpile/transpile-with-pass-managers) for a more detailed explanation of transpiling with pass managers."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "45be8872-20c2-4ef5-a3de-443f1b8fd2b6",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"pm = generate_preset_pass_manager(\n",
|
||
" backend=backend,\n",
|
||
" initial_layout=good_qubits,\n",
|
||
" layout_method=\"trivial\",\n",
|
||
" optimization_level=1,\n",
|
||
")\n",
|
||
"\n",
|
||
"isa_circuit = pm.run(circuit)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "56b4f3ae-a06e-4e0a-89ce-c8f71f2de97e",
|
||
"metadata": {},
|
||
"source": [
|
||
"### ISA observables"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "76667b2a-06ad-468c-a808-36d850c8d8ea",
|
||
"metadata": {},
|
||
"source": [
|
||
"Next, create all weight-1 $\\langle Z \\rangle$ observables for each virtual qubit by padding the necessary number of $\\langle I \\rangle$ terms."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "4a0439fb-599f-4974-9fd6-f7e7821cd687",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"observables = []\n",
|
||
"num_qubits = len(good_qubits)\n",
|
||
"for q in range(num_qubits):\n",
|
||
" observables.append(\n",
|
||
" SparsePauliOp(\"I\" * (num_qubits - q - 1) + \"Z\" + \"I\" * q)\n",
|
||
" )"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd05ea8e-7cd2-42ea-ae25-ac7824d7580b",
|
||
"metadata": {},
|
||
"source": [
|
||
"The transpilation process has mapped the virtual qubits of your circuit to physical qubits on the hardware. The information about the qubit layout is stored in the `layout` attribute of the transpiled circuit. Your observable is also defined in terms of the virtual qubits, so you need to apply this layout to the observable. This is done using the `apply_layout` method of `SparsePauliOp`.\n",
|
||
"\n",
|
||
"Notice that each observable is wrapped in a list in the following code block. It is done to _broadcast_ with parameter values so that each qubit observable is measured for each theta value. The broadcasting rules for primitives can be found [here](https://docs.quantum.ibm.com/run/primitives)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "3eaac647-f3ae-4533-a494-6cbeff2e6121",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"isa_observables = [\n",
|
||
" [obs.apply_layout(layout=isa_circuit.layout)] for obs in observables\n",
|
||
"]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a0906ff6-4fed-4e03-b4d2-9e08dc7eb40d",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 3: Execute using Qiskit primitives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "4d94b8c5-28e0-4ea7-9ec7-750f5803353a",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"pub = (isa_circuit, isa_observables, parameter_values)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9ebd1b29-6558-40bd-8c3b-0419392c5588",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Configure Estimator options"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fbaca21d-0ebb-4b06-8b72-9d66792c487c",
|
||
"metadata": {},
|
||
"source": [
|
||
"Next configure the `Estimator` options needed to run the mitigation experiment. This includes options for the noise learning of the entangling layers, and for ZNE extrapolation.\n",
|
||
"\n",
|
||
"We use the following configuration:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "a68c1ced-e098-44e3-9d68-5781b4c2c057",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Experiment options\n",
|
||
"num_randomizations = 700\n",
|
||
"num_randomizations_learning = 40\n",
|
||
"max_batch_circuits = 3 * num_params\n",
|
||
"shots_per_randomization = 64\n",
|
||
"learning_pair_depths = [0, 1, 2, 4, 6, 12, 24]\n",
|
||
"noise_factors = [1, 1.3, 1.6]\n",
|
||
"extrapolated_noise_factors = np.linspace(0, max(noise_factors), 20)\n",
|
||
"\n",
|
||
"# Base option formatting\n",
|
||
"options = {\n",
|
||
" # Builtin resilience settings for ZNE\n",
|
||
" \"resilience\": {\n",
|
||
" \"measure_mitigation\": True,\n",
|
||
" \"zne_mitigation\": True,\n",
|
||
" # TREX noise learning configuration\n",
|
||
" \"measure_noise_learning\": {\n",
|
||
" \"num_randomizations\": num_randomizations_learning,\n",
|
||
" \"shots_per_randomization\": 1024,\n",
|
||
" },\n",
|
||
" # PEA noise model configuration\n",
|
||
" \"layer_noise_learning\": {\n",
|
||
" \"max_layers_to_learn\": 3,\n",
|
||
" \"layer_pair_depths\": learning_pair_depths,\n",
|
||
" \"shots_per_randomization\": shots_per_randomization,\n",
|
||
" \"num_randomizations\": num_randomizations_learning,\n",
|
||
" },\n",
|
||
" },\n",
|
||
" # Randomization configuration\n",
|
||
" \"twirling\": {\n",
|
||
" \"num_randomizations\": num_randomizations,\n",
|
||
" \"shots_per_randomization\": shots_per_randomization,\n",
|
||
" \"strategy\": \"active-circuit\",\n",
|
||
" },\n",
|
||
" # Optional Dynamical Decoupling (DD)\n",
|
||
" \"dynamical_decoupling\": {\"enable\": True, \"sequence_type\": \"XY4\"},\n",
|
||
" # Experimental settings for PEA method\n",
|
||
" \"experimental\": {\n",
|
||
" # Error Mitigation configuration\n",
|
||
" \"resilience\": {\n",
|
||
" # ZNE Configuration\n",
|
||
" \"zne\": {\n",
|
||
" \"amplifier\": \"pea\",\n",
|
||
" \"noise_factors\": noise_factors,\n",
|
||
" \"extrapolator\": [\"exponential\", \"linear\"],\n",
|
||
" \"extrapolated_noise_factors\": extrapolated_noise_factors,\n",
|
||
" }\n",
|
||
" },\n",
|
||
" },\n",
|
||
" # Just in case, disable any further qiskit transpilation not related to twirling / DD\n",
|
||
" \"optimization_level\": 0,\n",
|
||
"}"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b1e67f48-ad36-4a70-a066-f8d9dbbb49c3",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Explanation of experimental ZNE options"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "246cea82-7665-481d-84c0-89a8a50619ac",
|
||
"metadata": {},
|
||
"source": [
|
||
"The following gives details on the additional options in the experimental branch. Note that these options and names are not finalized, and everything here is subject to change before an official release.\n",
|
||
"\n",
|
||
"* __amplifier__: The method to use when amplifying noise to the intended noise factors.\n",
|
||
" Allowed values are `\"gate_folding\"`, which amplifies by repeating two-qubit basis gates,\n",
|
||
" and `\"pea\"`, which amplifies by probabilistic sampling after learning the Pauli-twirled\n",
|
||
" noise model for layers of twirled two-qubit basis gates.\n",
|
||
"* __extrapolated_noise_factors__: Specify one or more noise factor values at which to evaluate the\n",
|
||
" extrapolated models. If a sequence of values, the returned results will be array-valued with specified noise factor evaluated for the extrapolation model. A value\n",
|
||
" of 0 corresponds to zero-noise extrapolation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "58afd2a7-844b-4c41-ae96-6ebf78b704d8",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Run the experiment"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "ebf57c70-d167-44f7-be3b-9abb10d46fd0",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"estimator = Estimator(backend=backend, options=options)\n",
|
||
"job = estimator.run([pub])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "386026be-d410-48c7-a1fd-5b48f7991427",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Job ID csne1ne0c2pg008c11hg\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(f\"Job ID {job.job_id()}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "15b1431a-5bea-4674-84c8-fc1439a863af",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 4: Post-process and return result in desired classical format"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "84ef5b13-4cea-4c73-9fdc-c3662413786c",
|
||
"metadata": {},
|
||
"source": [
|
||
"Once the experiment is finished, you can view our results. You fetch the raw and mitigated expectation values and compare them with exact results. Then, plot the expectation values, both mitigated (extrapolated) and raw, averaged over all qubits for each parameter. Finally, plot expectation values for your choice of individual qubits."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "f9029431-620b-4191-a248-a56ea2c70eff",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"primitive_result = job.result()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a359efa8-b6fe-4535-9e6e-6258d4cb065b",
|
||
"metadata": {},
|
||
"source": [
|
||
"### General result shapes and metadata"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5c454847-f488-4459-aac7-9f6014f508c7",
|
||
"metadata": {},
|
||
"source": [
|
||
"The `PrimitiveResult` object contains a list-like structure named `PubResult`. As we submit only one PUB to the estimator, the `PrimitiveResult` contains a single `PubResult` object.\n",
|
||
"\n",
|
||
"The PUB (primitive unified bloc) result expectation values and standard errors are array-valued. For estimator jobs with ZNE, there are several data fields of expectation values and standard errors available in the `PubResult`'s `DataBin` container. We will breifly discuss the data fields for expectation values here (similar data fields are available for standard errors (`stds`) as well).\n",
|
||
"\n",
|
||
"1. `pub_result.data.evs`: Expectation values corresponding to the zero noise (based on heuristically best extrapolation).\n",
|
||
" - The first axis is the virtual qubit index for observable $\\langle Z_i\\rangle$ ($124$ virtual-qubits/observables)\n",
|
||
" - The second axis indexes the parameter value for $\\theta$ ($12$ parameter values)\n",
|
||
"2. `pub_result.data.evs_extrapolated`: Expectation values for extrapolated noise factors for every extrapolator. This array has two additional axes.\n",
|
||
" - The third axis indexes the extrapolation methods ($2$ extrapolators, `exponential` and `linear`)\n",
|
||
" - The last axis indexes the `extrapolated_noise_factors` ($20$ extrapolation points specifed in the option)\n",
|
||
"3. `pub_result.data.evs_noise_factors`: Raw expectation values for each noise factor.\n",
|
||
" - The third axis indexes the raw `noise_factors` ($3$ factors)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "d136d707-3f3b-42fe-b1e6-55e8f841d598",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"pub_result.data.evs.shape=(124, 12)\n",
|
||
"pub_result.data.evs_extrapolated.shape=(124, 12, 2, 20)\n",
|
||
"pub_result.data.evs_noise_factors.shape=(124, 12, 3)\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"pub_result = primitive_result[0]\n",
|
||
"\n",
|
||
"print(\n",
|
||
" f\"{pub_result.data.evs.shape=}\\n\"\n",
|
||
" f\"{pub_result.data.evs_extrapolated.shape=}\\n\"\n",
|
||
" f\"{pub_result.data.evs_noise_factors.shape=}\\n\"\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5b3a54d3-c651-4fcc-b221-53a22ce029c1",
|
||
"metadata": {},
|
||
"source": [
|
||
"Several metadata fields are also available in the `PrimitiveResult`. The metadata includes\n",
|
||
"- `resilience/zne/noise_factors`: The raw noise factors\n",
|
||
"- `resilience/zne/extrapolator`: The extrapolators used for each result"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"id": "6cbd9f65-e125-48fe-82d5-688e189954b0",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"{'dynamical_decoupling': {'enable': True,\n",
|
||
" 'sequence_type': 'XY4',\n",
|
||
" 'extra_slack_distribution': 'middle',\n",
|
||
" 'scheduling_method': 'alap'},\n",
|
||
" 'twirling': {'enable_gates': True,\n",
|
||
" 'enable_measure': True,\n",
|
||
" 'num_randomizations': 700,\n",
|
||
" 'shots_per_randomization': 64,\n",
|
||
" 'interleave_randomizations': True,\n",
|
||
" 'strategy': 'active-circuit'},\n",
|
||
" 'resilience': {'measure_mitigation': True,\n",
|
||
" 'zne_mitigation': True,\n",
|
||
" 'pec_mitigation': False,\n",
|
||
" 'zne': {'noise_factors': [1.0, 1.3, 1.6],\n",
|
||
" 'extrapolator': ['exponential', 'linear'],\n",
|
||
" 'extrapolated_noise_factors': [0.0,\n",
|
||
" 0.08421052631578947,\n",
|
||
" 0.16842105263157894,\n",
|
||
" 0.25263157894736843,\n",
|
||
" 0.3368421052631579,\n",
|
||
" 0.42105263157894735,\n",
|
||
" 0.5052631578947369,\n",
|
||
" 0.5894736842105263,\n",
|
||
" 0.6736842105263158,\n",
|
||
" 0.7578947368421053,\n",
|
||
" 0.8421052631578947,\n",
|
||
" 0.9263157894736842,\n",
|
||
" 1.0105263157894737,\n",
|
||
" 1.0947368421052632,\n",
|
||
" 1.1789473684210525,\n",
|
||
" 1.263157894736842,\n",
|
||
" 1.3473684210526315,\n",
|
||
" 1.431578947368421,\n",
|
||
" 1.5157894736842106,\n",
|
||
" 1.6]}},\n",
|
||
" 'version': 2}"
|
||
]
|
||
},
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"primitive_result.metadata"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1f8c5fee-7b20-46ef-b991-a313871bccd7",
|
||
"metadata": {},
|
||
"source": [
|
||
"The `PubResult` object has additional resilience metadata about the learned noise models used in mitigation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "df429d8a-9a8e-4d2c-8960-1745875f2252",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"noise_overhead: 7.027950761897537e+52\n",
|
||
"total_mitigated_layers: 18\n",
|
||
"unique_mitigated_layers: 3\n",
|
||
"unique_mitigated_layers_noise_overhead: [1278.1896246163867, 208.48769026509322, 2410.6217963719228]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Print learned layer noise metadata\n",
|
||
"for field, value in pub_result.metadata[\"resilience\"][\"layer_noise\"].items():\n",
|
||
" print(f\"{field}: {value}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "b309df58-8d84-4222-9fd4-7ede91bfdc37",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Exact data computed using the methods described in the original reference\n",
|
||
"# Y. Kim et al. \"Evidence for the utility of quantum computing before fault tolerance\" (Nature 618, 500–505 (2023))\n",
|
||
"# Directly used here for brevity\n",
|
||
"exact_data = np.array(\n",
|
||
" [\n",
|
||
" 1,\n",
|
||
" 0.9899,\n",
|
||
" 0.9531,\n",
|
||
" 0.8809,\n",
|
||
" 0.7536,\n",
|
||
" 0.5677,\n",
|
||
" 0.3545,\n",
|
||
" 0.1607,\n",
|
||
" 0.0539,\n",
|
||
" 0.0103,\n",
|
||
" 0.0012,\n",
|
||
" 0.0,\n",
|
||
" ]\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "28be7131-af2d-43e4-a61f-12f328e90b4f",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Plot Trotter simulation results\n",
|
||
"\n",
|
||
"The following code creates a plot to compare the raw and mitigated experiment results against the exact solution."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "0338f87d-9b37-46a7-91a1-de206a794843",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"Result visualization functions\"\"\"\n",
|
||
"\n",
|
||
"\n",
|
||
"def plot_trotter_results(\n",
|
||
" pub_result: PubResult,\n",
|
||
" angles: Sequence[float],\n",
|
||
" plot_noise_factors: Sequence[float] | None = None,\n",
|
||
" plot_extrapolator: Sequence[str] | None = None,\n",
|
||
" exact: np.ndarray = None,\n",
|
||
" close: bool = True,\n",
|
||
"):\n",
|
||
" \"\"\"Plot average magnetization from ZNE result data.\n",
|
||
" Args:\n",
|
||
" pub_result: The Estimator PubResult for the PEA experiment.\n",
|
||
" angles: The Rx angle values for the experiment.\n",
|
||
" plot_raw: If provided plot the unextrapolated data for the noise factors.\n",
|
||
" plot_extrapolator: If provided plot all extrapolators, if False only plot\n",
|
||
" the Automatic method.\n",
|
||
" exact: Optional, the exact values to include in the plot. Should be a 1D\n",
|
||
" array-like where the values represent exact magnetization.\n",
|
||
" close: Close the Matplotlib figure before returning.\n",
|
||
" Returns:\n",
|
||
" The figure.\n",
|
||
" \"\"\"\n",
|
||
" data = pub_result.data\n",
|
||
"\n",
|
||
" evs = data.evs\n",
|
||
" num_qubits = evs.shape[0]\n",
|
||
" num_params = evs.shape[1]\n",
|
||
" angles = np.asarray(angles).ravel()\n",
|
||
" if angles.shape != (num_params,):\n",
|
||
" raise ValueError(\n",
|
||
" f\"Incorrect number of angles for input data {angles.size} != {num_params}\"\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Take average magnetization of qubits and its standard error\n",
|
||
" x_vals = angles / np.pi\n",
|
||
" y_vals = np.mean(evs, axis=0)\n",
|
||
" y_errs = np.std(evs, axis=0) / np.sqrt(num_qubits)\n",
|
||
"\n",
|
||
" fig, _ = plt.subplots(1, 1)\n",
|
||
"\n",
|
||
" # Plot auto method\n",
|
||
" plt.errorbar(x_vals, y_vals, y_errs, fmt=\"o-\", label=\"ZNE (automatic)\")\n",
|
||
"\n",
|
||
" # Plot individual extrapolator results\n",
|
||
" if plot_extrapolator:\n",
|
||
" y_vals_extrap = np.mean(data.evs_extrapolated, axis=0)\n",
|
||
" y_errs_extrap = np.std(data.evs_extrapolated, axis=0) / np.sqrt(\n",
|
||
" num_qubits\n",
|
||
" )\n",
|
||
" for i, extrap in enumerate(plot_extrapolator):\n",
|
||
" plt.errorbar(\n",
|
||
" x_vals,\n",
|
||
" y_vals_extrap[:, i, 0],\n",
|
||
" y_errs_extrap[:, i, 0],\n",
|
||
" fmt=\"s-.\",\n",
|
||
" alpha=0.5,\n",
|
||
" label=f\"ZNE ({extrap})\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Plot raw results\n",
|
||
" if plot_noise_factors:\n",
|
||
" y_vals_raw = np.mean(data.evs_noise_factors, axis=0)\n",
|
||
" y_errs_raw = np.std(data.evs_noise_factors, axis=0) / np.sqrt(\n",
|
||
" num_qubits\n",
|
||
" )\n",
|
||
" for i, nf in enumerate(plot_noise_factors):\n",
|
||
" plt.errorbar(\n",
|
||
" x_vals,\n",
|
||
" y_vals_raw[:, i],\n",
|
||
" y_errs_raw[:, i],\n",
|
||
" fmt=\"d:\",\n",
|
||
" alpha=0.5,\n",
|
||
" label=f\"Raw (nf={nf:.1f})\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Plot exact data\n",
|
||
" if exact is not None:\n",
|
||
" plt.plot(x_vals, exact, \"--\", color=\"black\", alpha=0.5, label=\"Exact\")\n",
|
||
"\n",
|
||
" plt.ylim(-0.1, 1.2)\n",
|
||
" plt.xlabel(\"θ/π\")\n",
|
||
" plt.ylabel(r\"$\\overline{\\langle Z \\rangle}$\")\n",
|
||
" plt.legend()\n",
|
||
" plt.title(\n",
|
||
" f\"Error Mitigated Average Magnetization for Rx(θ) [{num_qubits}-qubit]\"\n",
|
||
" )\n",
|
||
" if close:\n",
|
||
" plt.close(fig)\n",
|
||
" return fig"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "2e0f0e84-32ba-4655-91c1-8445016bbeb2",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
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],
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||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
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||
]
|
||
},
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||
"metadata": {},
|
||
"output_type": "display_data"
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||
}
|
||
],
|
||
"source": [
|
||
"zne_metadata = primitive_result.metadata[\"resilience\"][\"zne\"]\n",
|
||
"# Plot Trotter simulation results\n",
|
||
"fig = plot_trotter_results(\n",
|
||
" pub_result,\n",
|
||
" parameter_values,\n",
|
||
" plot_extrapolator=zne_metadata[\"extrapolator\"],\n",
|
||
" plot_noise_factors=zne_metadata[\"noise_factors\"],\n",
|
||
" exact=exact_data,\n",
|
||
")\n",
|
||
"display(fig)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a5414c0f-4b6f-47b4-ae5a-17b7f8d1859c",
|
||
"metadata": {},
|
||
"source": [
|
||
"While the noisy (noise factor `nf=1.0`) values show high deviation from exact values, the mitigated values are close to exact values, demonstrating the utility of the PEA-based mitigation technique."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3a04fdb0-287d-44ec-b263-25aa8d0eb674",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Plot extrapolation results for individual qubits\n",
|
||
"\n",
|
||
"Finally, the following code creates a plot to show the extrapolation curves for different values of theta on a specific qubit."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"id": "f7971ece-944e-4dfd-ba4c-066d2c4b7ddc",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def plot_qubit_zne_data(\n",
|
||
" pub_result: PubResult,\n",
|
||
" angles: Sequence[float],\n",
|
||
" qubit: int,\n",
|
||
" noise_factors: Sequence[float],\n",
|
||
" extrapolator: Sequence[str] | None = None,\n",
|
||
" extrapolated_noise_factors: Sequence[float] | None = None,\n",
|
||
" num_cols: int | None = None,\n",
|
||
" close: bool = True,\n",
|
||
"):\n",
|
||
" \"\"\"Plot ZNE extrapolation data for specific virtual qubit\n",
|
||
" Args:\n",
|
||
" pub_result: The Estimator PubResult for the PEA experiment.\n",
|
||
" angles: The Rx theta angles used for the experiment.\n",
|
||
" qubit: The virtual qubit index to plot.\n",
|
||
" noise_factors: the raw noise factors.\n",
|
||
" extrapolator: The extrapolator metadata for multiple extrapolators.\n",
|
||
" extrapolated_noise_factors: The noise factors used for extrapolation.\n",
|
||
" num_cols: The number of columns for the generated subplots.\n",
|
||
" close: Close the Matplotlib figure before returning.\n",
|
||
" Returns:\n",
|
||
" The Matplotlib figure.\n",
|
||
" \"\"\"\n",
|
||
" data = pub_result.data\n",
|
||
"\n",
|
||
" evs_auto = data.evs[qubit]\n",
|
||
" stds_auto = data.stds[qubit]\n",
|
||
" evs_extrap = data.evs_extrapolated[qubit]\n",
|
||
" stds_extrap = data.stds_extrapolated[qubit]\n",
|
||
" evs_raw = data.evs_noise_factors[qubit]\n",
|
||
" stds_raw = data.stds_noise_factors[qubit]\n",
|
||
"\n",
|
||
" num_params = evs_auto.shape[0]\n",
|
||
" angles = np.asarray(angles).ravel()\n",
|
||
" if angles.shape != (num_params,):\n",
|
||
" raise ValueError(\n",
|
||
" f\"Incorrect number of angles for input data {angles.size} != {num_params}\"\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Make a square subplot\n",
|
||
" num_cols = num_cols or int(np.ceil(np.sqrt(num_params)))\n",
|
||
" num_rows = int(np.ceil(num_params / num_cols))\n",
|
||
" fig, axes = plt.subplots(\n",
|
||
" num_rows, num_cols, sharex=True, sharey=True, figsize=(12, 5)\n",
|
||
" )\n",
|
||
" fig.suptitle(f\"ZNE data for virtual qubit {qubit}\")\n",
|
||
"\n",
|
||
" for pidx, ax in zip(range(num_params), axes.flat):\n",
|
||
" # Plot auto extrapolated\n",
|
||
" ax.errorbar(\n",
|
||
" 0,\n",
|
||
" evs_auto[pidx],\n",
|
||
" stds_auto[pidx],\n",
|
||
" fmt=\"o\",\n",
|
||
" label=\"PEA (automatic)\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Plot extrapolators\n",
|
||
" if (\n",
|
||
" extrapolator is not None\n",
|
||
" and extrapolated_noise_factors is not None\n",
|
||
" ):\n",
|
||
" for i, method in enumerate(extrapolator):\n",
|
||
" ax.errorbar(\n",
|
||
" extrapolated_noise_factors,\n",
|
||
" evs_extrap[pidx, i],\n",
|
||
" stds_extrap[pidx, i],\n",
|
||
" fmt=\"-\",\n",
|
||
" alpha=0.5,\n",
|
||
" label=f\"PEA ({method})\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Plot raw\n",
|
||
" ax.errorbar(\n",
|
||
" noise_factors, evs_raw[pidx], stds_raw[pidx], fmt=\"d\", label=\"Raw\"\n",
|
||
" )\n",
|
||
"\n",
|
||
" ax.set_yticks([0, 0.5, 1, 1.5, 2])\n",
|
||
" ax.set_ylim(0, max(1, 1.1 * max(evs_auto)))\n",
|
||
"\n",
|
||
" ax.set_xticks([0, *noise_factors])\n",
|
||
" ax.set_title(f\"θ/π = {angles[pidx]/np.pi:.2f}\")\n",
|
||
" if pidx == 0:\n",
|
||
" ax.set_ylabel(r\"$\\langle Z_{\" + str(qubit) + r\"} \\rangle$\")\n",
|
||
" if pidx == num_params - 1:\n",
|
||
" ax.set_xlabel(\"Noise Factor\")\n",
|
||
" ax.legend()\n",
|
||
" if close:\n",
|
||
" plt.close(fig)\n",
|
||
" return fig"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "6948475c-bc15-493f-8af9-f8e66d0e467c",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
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],
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"text/plain": [
|
||
"<Figure size 1200x500 with 12 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"virtual_qubit = 1\n",
|
||
"plot_qubit_zne_data(\n",
|
||
" pub_result=pub_result,\n",
|
||
" angles=parameter_values,\n",
|
||
" qubit=virtual_qubit,\n",
|
||
" noise_factors=zne_metadata[\"noise_factors\"],\n",
|
||
" extrapolator=zne_metadata[\"extrapolator\"],\n",
|
||
" extrapolated_noise_factors=zne_metadata[\"extrapolated_noise_factors\"],\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2fc07ea9",
|
||
"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_9z7nltLeb5cX9Cm)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cf8eff5f",
|
||
"metadata": {},
|
||
"source": [
|
||
"© IBM Corp. 2024"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"description": "Run a utility-scale error mitigation experiment with zero noise extrapolation and probabilistic error amplification.",
|
||
"kernelspec": {
|
||
"display_name": "Python 3",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
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||
},
|
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"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3"
|
||
},
|
||
"platform": "cloud",
|
||
"title": "Utility-scale error mitigation with probabilistic error amplification"
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|