From d2ede4016016fefa4d90856cb6f0249b9fb00630 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 12 Apr 2025 06:17:08 -0400 Subject: [PATCH 01/19] Update README contents --- README.md | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 84a7f1e..e7b61ed 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,12 @@ -# qec-surface-code -Quantum Error Correction: Surface Code in Q# +# Quantum Error Correction: Surface Code + +The repository implements surface code for quantum error correction and benchmarks the results of noisy simulation of 3 well known quantum algorithms in Q Sharp. + +We also present a surface code generator by specifying the noise levels & thresholds. + +# Plan +- Implement a surface code circuit builder with noise +- Implement a python pipline +- Implement three algorithms and benchmark the results of simulation with and without QEC for: Different code distance, different errors, different +- Explore the relationship between physical noise levels set in the simulator and noise levels of the logical qubits encoded using surface code. +- Develop a UI for interation From abe9e401eaba85a93e2aa8bed91fc53658a50f3d Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Mon, 14 Apr 2025 03:47:07 -0400 Subject: [PATCH 02/19] Project setup --- qsharp.json | 1 + requirements.txt | 3 +++ 2 files changed, 4 insertions(+) create mode 100644 qsharp.json create mode 100644 requirements.txt diff --git a/qsharp.json b/qsharp.json new file mode 100644 index 0000000..9e26dfe --- /dev/null +++ b/qsharp.json @@ -0,0 +1 @@ +{} \ No newline at end of file diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..e4ce35d --- /dev/null +++ b/requirements.txt @@ -0,0 +1,3 @@ +qsharp +pytest +matplotlib From b83588a529a6325d1e229e63c78e38a6efb27c44 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Mon, 14 Apr 2025 03:47:39 -0400 Subject: [PATCH 03/19] Add Rotated Surface Code to build circuit --- src/RotatedSurfaceCode.qs | 147 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 147 insertions(+) create mode 100644 src/RotatedSurfaceCode.qs diff --git a/src/RotatedSurfaceCode.qs b/src/RotatedSurfaceCode.qs new file mode 100644 index 0000000..cbf1cb7 --- /dev/null +++ b/src/RotatedSurfaceCode.qs @@ -0,0 +1,147 @@ +namespace RotatedSurfaceCode { + import Std.Diagnostics.DumpMachine; + import Std.Convert.IntAsDouble; + import Std.Convert.DoubleAsStringWithPrecision; + import Std.Diagnostics.DumpRegister; + import SurfaceCode.MeasureXStabilizers; + function validIndex(d: Int, index:Int): Bool { + if 0 <= index and index < d*d { + return true; + } + return false; + } + operation XStabilizer(d: Int, indexes: Int[], dataQubits: Qubit[]): Result { + use q= Qubit(); + H(q); + for index in indexes { + if (validIndex(d, index)) { + CX(q, dataQubits[index]); + } + } + H(q); + let result = Measure([PauliZ], [q]); + Reset(q); + return result; + } + operation ZStabilizer(d: Int, indexes: Int[], dataQubits: Qubit[]): Result { + use q= Qubit(); + for index in indexes { + if (validIndex(d, index)) { + CX( dataQubits[index], q); + } + } + let result = Measure([PauliZ], [q]); + Reset(q); + return result; + } + +operation GenerateLattice(d: Int, qubits: Qubit[]): (Int[][], Result[], Int[][], Result[]) { + let TOTAL_DATA_QUBITS = d*d; + mutable xMeasures = []; + mutable xMaps = []; + mutable zMaps = []; + mutable zMeasures = []; + mutable isZ = true; + + for i in 0..d-2 { + for j in 0..d-2 { + let id = (i*d)+j; + if (i == 0) and (j % 2 == 0) { + let indexes = [id, id+1]; + xMeasures += [XStabilizer(d, indexes, qubits)]; + xMaps += [indexes]; + } + if (i%2 == 1) and (j == 0) { + let indexes = [id, id+d]; + zMeasures += [ZStabilizer(d, indexes, qubits)]; + zMaps += [indexes]; + } + + let indexes = [id, id+1, id+d, id+d+1]; + if (isZ) { + zMeasures += [ZStabilizer(d, indexes, qubits)]; + zMaps += [indexes]; + } else { + xMeasures += [XStabilizer(d, indexes, qubits)]; + xMaps += [indexes]; + } + + if j != d-2 { + set isZ = not isZ; + } + + + if (j == d-2) and (i % 2 == 0) { + let indexes = [id+1, id+d+1]; + zMeasures += [ZStabilizer(d, indexes , qubits)]; + zMaps += [indexes]; + } + if (i == d-2) and (j % 2 == 1) { + let indexes = [id+d, id+d+1]; + xMeasures += [XStabilizer(d, indexes, qubits)]; + xMaps += [indexes]; + } + } + } + return (xMaps, xMeasures, zMaps, zMeasures); + } + +operation GetSyndroem(initX: Result[], currX:Result[], initZ: Result[], currZ: Result[]): (Bool[], Bool[]) { + mutable xSyndrome = []; + mutable zSyndrome = []; + for i in 0..Length(initX)-1 { + xSyndrome += [initX[i] != currX[i]]; + if xSyndrome[i] { + Message("Found X error at " + DoubleAsStringWithPrecision(IntAsDouble(i), 1)) + } + } + for i in 0..Length(initZ)-1 { + zSyndrome += [initZ[i] != currZ[i]]; + if zSyndrome[i] { + Message("Found Z error at " + DoubleAsStringWithPrecision(IntAsDouble(i), 1)) + } + } + return (xSyndrome, zSyndrome); +} + +operation RotatedSurfaceCode(d: Int, r: Int): Unit { + let TOTAL_DATA_QUBITS = d*d; + use qubits = Qubit[TOTAL_DATA_QUBITS]; + mutable (xMaps, initXMeasures, zMaps, initZMeasures) = GenerateLattice(d, qubits); + + for i in 0..r-1 { + let (x , xMeasures, z, zMeasures) = GenerateLattice(d, qubits); + let (xSyndrome, zSyndrome) = GetSyndroem(initXMeasures, xMeasures, initZMeasures, zMeasures); + set initXMeasures = xMeasures; + set initZMeasures = zMeasures; + } + + ResetAll(qubits); +} +operation RunRotated(): Unit { + RotatedSurfaceCode(5,5); +} + +function printMaps(xMaps: Int[][], zMaps: Int[][]): Unit { + // Utility to print the maps of surface code + Message("Printing X Maps:"); + for i in 0..Length(xMaps)-1 { + mutable str = ""; + for val in xMaps[i] { + str += DoubleAsStringWithPrecision(IntAsDouble(val), 0) + ","; + } + Message(DoubleAsStringWithPrecision(IntAsDouble(i), 0)+"["+str+"]") + } + Message("Printing Z Maps:"); + for i in 0..Length(zMaps)-1 { + mutable str = ""; + for val in zMaps[i] { + str += DoubleAsStringWithPrecision(IntAsDouble(val), 0) + ","; + } + Message(DoubleAsStringWithPrecision(IntAsDouble(i), 0)+"["+str+"]") + } +} +} + + + From b648bc15a4063ad6326be9b36d90d3c0b8f154e8 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Fri, 18 Apr 2025 18:05:31 -0400 Subject: [PATCH 04/19] 1 Round surface code --- src/RotatedSurfaceCode.qs | 123 +++++++++++++++++++++++--------------- 1 file changed, 74 insertions(+), 49 deletions(-) diff --git a/src/RotatedSurfaceCode.qs b/src/RotatedSurfaceCode.qs index cbf1cb7..c3a787f 100644 --- a/src/RotatedSurfaceCode.qs +++ b/src/RotatedSurfaceCode.qs @@ -1,68 +1,76 @@ -namespace RotatedSurfaceCode { - import Std.Diagnostics.DumpMachine; - import Std.Convert.IntAsDouble; - import Std.Convert.DoubleAsStringWithPrecision; - import Std.Diagnostics.DumpRegister; - import SurfaceCode.MeasureXStabilizers; +import Std.ResourceEstimation.MeasurementCount; +import Std.Arrays.ForEach; +import Std.Diagnostics.ConfigurePauliNoise; + +import Std.Diagnostics.DumpMachine; +import Std.Convert.IntAsDouble; +import Std.Convert.DoubleAsStringWithPrecision; +import Std.Diagnostics.DumpRegister; +import SurfaceCode.MeasureXStabilizers; + function validIndex(d: Int, index:Int): Bool { if 0 <= index and index < d*d { return true; } return false; } - operation XStabilizer(d: Int, indexes: Int[], dataQubits: Qubit[]): Result { - use q= Qubit(); + +operation MeasureLogicalZ(d: Int, dataQubits: Qubit[]): Result { + // Logical Z is assumed to be a product of physical Zs on a vertical line + // Choose the first column: index i*d for i in 0..d-1 + let results = MeasureEachZ(dataQubits); + mutable parity = Zero; + + for res in results { + if res == One { + set parity = if (parity == Zero) { One } else { Zero }; + } + } + return parity; +} + + operation XStabilizer(indexes: Int[], dataQubits: Qubit[], q: Qubit): Unit { + Reset(q); H(q); for index in indexes { - if (validIndex(d, index)) { + // if (validIndex(d, index)) { CX(q, dataQubits[index]); - } + // } } H(q); - let result = Measure([PauliZ], [q]); - Reset(q); - return result; } - operation ZStabilizer(d: Int, indexes: Int[], dataQubits: Qubit[]): Result { - use q= Qubit(); + + operation ZStabilizer(indexes: Int[], dataQubits: Qubit[], q:Qubit): Unit { + Reset(q); for index in indexes { - if (validIndex(d, index)) { + // if (validIndex(d, index)) { CX( dataQubits[index], q); - } + // } } - let result = Measure([PauliZ], [q]); - Reset(q); - return result; } -operation GenerateLattice(d: Int, qubits: Qubit[]): (Int[][], Result[], Int[][], Result[]) { - let TOTAL_DATA_QUBITS = d*d; - mutable xMeasures = []; - mutable xMaps = []; - mutable zMaps = []; - mutable zMeasures = []; - mutable isZ = true; - for i in 0..d-2 { + operation GetMaps(d: Int): (Int[][], Int[][]) { + let TOTAL_DATA_QUBITS = d*d; + mutable xMaps = []; + mutable zMaps = []; + mutable isZ = true; + for i in 0..d-2 { for j in 0..d-2 { let id = (i*d)+j; if (i == 0) and (j % 2 == 0) { let indexes = [id, id+1]; - xMeasures += [XStabilizer(d, indexes, qubits)]; xMaps += [indexes]; } if (i%2 == 1) and (j == 0) { let indexes = [id, id+d]; - zMeasures += [ZStabilizer(d, indexes, qubits)]; zMaps += [indexes]; } let indexes = [id, id+1, id+d, id+d+1]; if (isZ) { - zMeasures += [ZStabilizer(d, indexes, qubits)]; zMaps += [indexes]; } else { - xMeasures += [XStabilizer(d, indexes, qubits)]; xMaps += [indexes]; } @@ -73,18 +81,28 @@ operation GenerateLattice(d: Int, qubits: Qubit[]): (Int[][], Result[], Int[][], if (j == d-2) and (i % 2 == 0) { let indexes = [id+1, id+d+1]; - zMeasures += [ZStabilizer(d, indexes , qubits)]; zMaps += [indexes]; } - if (i == d-2) and (j % 2 == 1) { - let indexes = [id+d, id+d+1]; - xMeasures += [XStabilizer(d, indexes, qubits)]; + } + } + for j in 0..d-2 { + if (j % 2 == 1) { + let id = ((d-1)*d)+j; + let indexes = [id, id+1]; xMaps += [indexes]; } - } } - return (xMaps, xMeasures, zMaps, zMeasures); + return (xMaps, zMaps); + } + +operation GenerateLattice(xMaps: Int[][], zMaps: Int[][], qubits: Qubit[], ancillaX: Qubit[], ancillaZ: Qubit[]): Unit { + for i in 0..Length(xMaps)-1 { + XStabilizer(xMaps[i], qubits, ancillaX[i]); + } + for j in 0..Length(xMaps)-1 { + ZStabilizer(zMaps[j], qubits, ancillaZ[j]); } +} operation GetSyndroem(initX: Result[], currX:Result[], initZ: Result[], currZ: Result[]): (Bool[], Bool[]) { mutable xSyndrome = []; @@ -104,24 +122,31 @@ operation GetSyndroem(initX: Result[], currX:Result[], initZ: Result[], currZ: R return (xSyndrome, zSyndrome); } -operation RotatedSurfaceCode(d: Int, r: Int): Unit { +operation RotatedSurfaceCode(d: Int, r: Int): Result[] { let TOTAL_DATA_QUBITS = d*d; use qubits = Qubit[TOTAL_DATA_QUBITS]; - mutable (xMaps, initXMeasures, zMaps, initZMeasures) = GenerateLattice(d, qubits); + use ancillaX = Qubit[(TOTAL_DATA_QUBITS-1)/2]; + use ancillaZ = Qubit[(TOTAL_DATA_QUBITS-1)/2]; - for i in 0..r-1 { - let (x , xMeasures, z, zMeasures) = GenerateLattice(d, qubits); - let (xSyndrome, zSyndrome) = GetSyndroem(initXMeasures, xMeasures, initZMeasures, zMeasures); - set initXMeasures = xMeasures; - set initZMeasures = zMeasures; - } + ResetAll(qubits); + // ApplyToEach(X, qubits); + let (xMaps, zMaps) = GetMaps(d); + GenerateLattice(xMaps, zMaps, qubits, ancillaX, ancillaZ); + let measuresX = MeasureEachZ(ancillaX); + let measuresZ = MeasureEachZ(ancillaZ); + let results = MeasureEachZ(qubits); + // printMaps(xMaps, zMaps); ResetAll(qubits); + ResetAll(ancillaX); + ResetAll(ancillaZ); + return measuresX + measuresZ + results; } -operation RunRotated(): Unit { - RotatedSurfaceCode(5,5); +operation RunRotated(): Result[] { + return RotatedSurfaceCode(3,5); } + function printMaps(xMaps: Int[][], zMaps: Int[][]): Unit { // Utility to print the maps of surface code Message("Printing X Maps:"); @@ -141,7 +166,7 @@ function printMaps(xMaps: Int[][], zMaps: Int[][]): Unit { Message(DoubleAsStringWithPrecision(IntAsDouble(i), 0)+"["+str+"]") } } -} + From 2ede538b7cf9ea53030055bb12938fd77c7ecda2 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Fri, 18 Apr 2025 18:06:35 -0400 Subject: [PATCH 05/19] Playground - Part 1 --- surface-code.ipynb | 726 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 726 insertions(+) create mode 100644 surface-code.ipynb diff --git a/surface-code.ipynb b/surface-code.ipynb new file mode 100644 index 0000000..52103eb --- /dev/null +++ b/surface-code.ipynb @@ -0,0 +1,726 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b2fb789e", + "metadata": {}, + "source": [ + "# Surface Code\n", + "\n", + "Ref: https://www.nature.com/articles/s41586-022-05434-1 - d=3 Implementation\n", + "https://www.nature.com/articles/s41586-022-04566-8 - More on implementation\n", + "https://arxiv.org/html/2307.14989v4/#S5.F7 - Diagrams\n", + "\n", + "\n", + "Core on roateted: https://arxiv.org/pdf/2409.14765\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4a8af2ee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical Error without correction: 0.48\n", + "Logical Error with correction: 0.54\n" + ] + } + ], + "source": [ + "from collections import deque\n", + "import qsharp\n", + "from itertools import combinations\n", + "import pymatching\n", + "\n", + "import numpy as np\n", + "import random\n", + "import networkx as nx\n", + "\n", + "\n", + "def convert_syndrome(syndrome_results):\n", + " return np.array([1 if bit == qsharp.Result.One else 0 for bit in syndrome_results], dtype=np.uint8)\n", + "\n", + "\n", + "def getZCorrections(d, initMeasures, xMaps):\n", + " num_qubits = d*d\n", + " H_x = np.zeros((len(initMeasures), num_qubits), dtype=np.uint8)\n", + " for i, stabilizer in enumerate(xMaps):\n", + " for qubit_idx in stabilizer:\n", + " H_x[i, qubit_idx] = 1\n", + "\n", + "\n", + " z_decoder = pymatching.Matching(H_x) \n", + " z_correction = z_decoder.decode(initMeasures)\n", + " # print(z_correction)\n", + " z_error_qubits = np.where(z_correction == 1)[0] # Qubits needing phase flips\n", + " print(\"Apply phase flips (Z) to qubits:\", z_error_qubits)\n", + " return z_error_qubits\n", + "\n", + "\n", + "def flatten_syndrome_timeline(syndrome_matrix):\n", + " if syndrome_matrix.shape[0] == 1:\n", + " return syndrome_matrix[0]\n", + " return syndrome_matrix.flatten()\n", + "\n", + "def getSyndrome(a,b,c,d):\n", + " return [i!=j for i,j in zip(a,b)], [i!=j for i,j in zip(c,d)]\n", + "\n", + "\n", + "class PauliTracker:\n", + " '''Tracks the Pauli X&Z stabilizers measurements, Record \n", + " the stabilizer measurement outcomes in each round without\n", + " physically correcting the qubits'''\n", + "\n", + " def __init__(self):\n", + " self.XKEY = \"X\"\n", + " self.ZKEY = \"Z\"\n", + " self.tracker = {self.XKEY: [], self.ZKEY: []}\n", + "\n", + " def track(self, xMeasures, zMeasures):\n", + " self.tracker[self.XKEY].append(xMeasures)\n", + " self.tracker[self.ZKEY].append(zMeasures)\n", + " \n", + " def getX(self):\n", + " return self.tracker[self.XKEY]\n", + " def getZ(self):\n", + " return self.tracker[self.ZKEY]\n", + "\n", + "\n", + "def addTimeStep():\n", + " xMaps, initXMeasures, zMaps, initZMeasures = qsharp.eval(f\"RotatedSurfaceCode.GenerateLattice(d, qubits);\")\n", + " PAULI_TRACKER.track(initXMeasures, initZMeasures)\n", + " return xMaps, initXMeasures, zMaps, initZMeasures\n", + "\n", + "def convert_syndrome(syndrome_results):\n", + " return np.array([1 if bit == qsharp.Result.One else 0 for bit in syndrome_results], dtype=np.uint8)\n", + "\n", + "def getCorrections(d, p, syndrome, maps):\n", + " num_qubits = d*d\n", + " H = np.zeros((len(maps), num_qubits), dtype=np.uint8)\n", + " \n", + " for i, stabilizer in enumerate(maps):\n", + " for qubit_idx in stabilizer:\n", + " H[i, qubit_idx] = 1\n", + "\n", + " weights = np.ones(H.shape[1]) * np.log((1 - p) / p)\n", + " decoder = pymatching.Matching(H, weights=weights) \n", + " correction = decoder.decode(syndrome)\n", + " error_qubits = np.where(correction == 1)[0] # Qubits needing flips\n", + " # print(error_qubits)\n", + " # print(\"Apply flips to qubits:\", error_qubits)\n", + " return error_qubits\n", + "\n", + "from collections import defaultdict\n", + "def decode_surface_code(parity_checks, stabilizer_qubit_map):\n", + " \"\"\"\n", + " Args:\n", + " parity_checks (List[int]): List of 0 or 1 values for each stabilizer (1 = error detected)\n", + " stabilizer_qubit_map (List[List[int]]): List of lists, each with qubit indices for the stabilizer\n", + "\n", + " Returns:\n", + " Set[int]: Indices of qubits to apply correction to\n", + " \"\"\"\n", + "\n", + " # Count how many times each qubit appears in stabilizers with parity 1\n", + " qubit_votes = defaultdict(int)\n", + "\n", + " for stab_index, parity in enumerate(parity_checks):\n", + " if parity == 1:\n", + " for q in stabilizer_qubit_map[stab_index]:\n", + " qubit_votes[q] += 1\n", + "\n", + " # Apply correction to qubits that are involved in an odd number of violated stabilizers\n", + " corrections = {q for q, count in qubit_votes.items() if count % 2 == 1}\n", + " return corrections\n", + "\n", + "def applyCorrection(correct, zp, xp, zMeasures, zMaps, xMeasures, xMaps):\n", + " if correct:\n", + " x_correction = getCorrections(d, xp, convert_syndrome(zMeasures), zMaps)\n", + " z_correction = getCorrections(d, zp, convert_syndrome(xMeasures), xMaps)\n", + " print(x_correction)\n", + " for q in x_correction:\n", + " qsharp.eval(f\"X(qubits[{q}]);\")\n", + " for q in z_correction:\n", + " qsharp.eval(f\"Z(qubits[{q}]);\")\n", + "\n", + "\n", + "def runLogicalQubit(d, layers, xnoise, znoise, correct=False):\n", + " TOTAL_DATA_QUBITS = d*d\n", + " PAULI_TRACKER = PauliTracker()\n", + " qsharp.init(project_root=\".\")\n", + " qsharp.eval(f\"import Std.Diagnostics.ConfigurePauliNoise;\")\n", + " qsharp.eval(f\"import Std.Arrays.ForEach;\")\n", + " qsharp.eval(f\"let d = {d};\")\n", + " qsharp.eval(f\"let TOTAL_DATA_QUBITS = {TOTAL_DATA_QUBITS};\")\n", + " qsharp.eval(\"use qubits = Qubit[TOTAL_DATA_QUBITS];\")\n", + " qsharp.eval(\"ApplyToEach(X, qubits);\")\n", + " qsharp.eval(f\"ConfigurePauliNoise({xnoise}, 0.0, {znoise});\")\n", + " qsharp.eval(\"ResetAll(qubits);\")\n", + "\n", + " xMaps, initXMeasures, zMaps, initZMeasures = addTimeStep()\n", + "\n", + "\n", + " # x_correction = getCorrections(d, initZMeasures, zMaps)\n", + " # z_correction = getCorrections(d, initXMeasures, xMaps)\n", + " # # for q in x_correction:\n", + " # # qsharp.eval(f\"X(qubits[{q}]);\")\n", + " # # for q in z_correction:\n", + " # # qsharp.eval(f\"Z(qubits[{q}]);\")\n", + " # applyCorrection(correct, znoise, xnoise, initZMeasures, zMaps, initXMeasures, xMaps)\n", + " corrupt = False\n", + " for i in range(layers):\n", + " x , xMeasures, z, zMeasures = addTimeStep()\n", + " # applyCorrection(correct, znoise, xnoise, zMeasures, zMaps, xMeasures, xMaps)\n", + " xSyndrome, zSyndrome = getSyndrome(initXMeasures, xMeasures, initZMeasures, zMeasures)\n", + " # if any(zSyndrome):\n", + " # corrupt = True\n", + " \n", + " # x , xMeasures, z, zMeasures = addTimeStep()\n", + " \n", + " # print(f\"Visualize If any errors for time({i})\")\n", + " # print(\"X\", xSyndrome)\n", + " # print(\"Z\", zSyndrome)\n", + " \n", + " initXMeasures = xMeasures\n", + " initZMeasures = zMeasures\n", + " # xSyndrome, zSyndrome = getSyndrome(initXMeasures, xMeasures, initZMeasures, zMeasures)\n", + " \n", + " # results = qsharp.eval(\"ForEach(x => Measure([PauliZ], [x]), qubits);\")\n", + " results = []\n", + " re = []\n", + " s = d-1\n", + " for i in range(0, d*d):\n", + " # if ((i//d)*(d+1)) == i:\n", + " # re.append(i)\n", + " # s-=1\n", + " results.append(qsharp.eval(f\"Measure([PauliZ], [qubits[{i}]]);\"))\n", + " # print(re)\n", + " # print(results)\n", + " # for i in range(0, TOTAL_DATA_QUBITS, d):\n", + " # print(results[i:i+d])\n", + " # print(sum(convert_syndrome(results))%2)\n", + " # print(f\"Final Logical State: {sum(convert_syndrome(results))%2}\")\n", + " return int(not sum(convert_syndrome(results))%2)\n", + " \n", + "\n", + "qsharp.eval(\"ResetAll(qubits);\")\n", + "\n", + "d = 3\n", + "layers = 4\n", + "xnoise = 0.01\n", + "znoise = 0.0\n", + "SHOTS = 100\n", + "def failure(r):\n", + " return 1 - (sum(r)/SHOTS)\n", + "\n", + "r = []\n", + "for i in range(SHOTS):\n", + " r.append(runLogicalQubit(d, layers, xnoise, znoise, correct=False))\n", + "print(f\"Logical Error without correction: {failure(r)}\")\n", + "\n", + "r = []\n", + "for i in range(SHOTS):\n", + " r.append(runLogicalQubit(d, layers, xnoise, znoise, correct=True))\n", + "print(f\"Logical Error with correction: {failure(r)}\")\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d9d451f0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running for code distance d=1\n", + "Physical error rate p=0.005\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.050\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Running for code distance d=3\n", + "Physical error rate p=0.005\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.050\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Running for code distance d=5\n", + "Physical error rate p=0.005\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.050\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "{1: [0.008, 0.014, 0.096, 0.179, 0.267, 0.299], 3: [0.073, 0.149, 0.422, 0.468, 0.474, 0.511], 5: [0.133, 0.22, 0.48, 0.505, 0.513, 0.493]}\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import pymatching\n", + "import matplotlib.pyplot as plt\n", + "import qsharp\n", + "import pymatching\n", + "\n", + "import numpy as np\n", + "import networkx as nx\n", + "\n", + "def convert_syndrome(syndrome_results):\n", + " return np.array([1 if bit == qsharp.Result.One else 0 for bit in syndrome_results], dtype=np.uint8)\n", + "\n", + "\n", + "class Decoder:\n", + " def __init__(self, d,p, maps):\n", + " self.d = d\n", + " self.num_qubits = d*d\n", + " \n", + " self.H = np.zeros((len(maps), self.num_qubits), dtype=np.uint8)\n", + " for i, stabilizer in enumerate(maps):\n", + " for qubit_idx in stabilizer:\n", + " self.H[i, qubit_idx] = 1\n", + " \n", + " weights = np.ones(self.H.shape[1]) * np.log((1 - p) / p)\n", + " self.decoder = pymatching.Matching(self.H, weights=weights) \n", + "\n", + " def decode(self, syndrome):\n", + " return self.decoder.decode(syndrome)\n", + " \n", + " def decode_batch(self, syndromes):\n", + " return self.decoder.decode_batch(syndromes)\n", + "\n", + " def getErrorQubits(self, correction):\n", + " return np.where(correction == 1)[0]\n", + "\n", + "def qsharp_runner(d,p, shots):\n", + " qsharp.init(project_root=\".\")\n", + " # qsharp.eval(f\"import Std.Diagnostics.ConfigurePauliNoise;\")\n", + " # qsharp.eval(f\"import Std.Arrays.ForEach;\")\n", + " # qsharp.eval(f\"let d = {d};\")\n", + " # qsharp.eval(f\"let TOTAL_DATA_QUBITS = {TOTAL_DATA_QUBITS};\")\n", + " # qsharp.eval(\"use qubits = Qubit[TOTAL_DATA_QUBITS];\")\n", + " # # qsharp.eval(\"ApplyToEach(X, qubits);\")\n", + " # qsharp.eval(f\"ConfigurePauliNoise({p}, 0.0, 0.0);\")\n", + " # qsharp.eval(\"ResetAll(qubits);\")\n", + " xMaps, zMaps = qsharp.eval(f\"RotatedSurfaceCode.GetMaps({d});\")\n", + " \n", + "\n", + " results = qsharp.run(f\"RotatedSurfaceCode.RotatedSurfaceCode({d}, {d})\", shots=shots, noise=qsharp.BitFlipNoise(p))\n", + " zSyndromes = []\n", + " trueValues = []\n", + " for result in results:\n", + " zSyndromes.append(convert_syndrome(result[len(xMaps):len(xMaps)+len(zMaps)]))\n", + " trueValues.append(convert_syndrome(result[len(xMaps)+len(zMaps):]))\n", + "\n", + " # results = qsharp.eval(\"ForEach(x => Measure([PauliZ], [x]), qubits);\")\n", + " # results = []\n", + " # for i in range(0, d*d):\n", + " # # if (i%(d+1))== 0:\n", + " # results.append(1 if qsharp.eval(f\"Measure([PauliZ], [qubits[{i}]]);\") == qsharp.Result.One else 0)\n", + " # trueLogicalValue = int((sum(convert_syndrome(results))%2))\n", + " return zSyndromes, zMaps, trueValues\n", + "\n", + "\n", + "def is_logical_error(d, correction, true_logical):\n", + " def getParity(d, correction):\n", + " r = []\n", + " correctionParity = 0\n", + " for i in range(d):\n", + " # r.append((i+1)*(d-1))\n", + " # if correction[(d*d)-(i+1)]:\n", + " if correction[(i+1)*(d-1)]:\n", + " correctionParity = 0 if correctionParity else 1\n", + " # print(r)\n", + " return correctionParity\n", + " \n", + " return (int(getParity(d, true_logical))) != (int(getParity(d, true_logical)))\n", + " \n", + " \n", + "\n", + "def run_experiment_for_d(d_values, p_values, num_trials):\n", + " results = {}\n", + " for d in d_values:\n", + " logical_error_rates = []\n", + " print(f\"Running for code distance d={d}\")\n", + "\n", + " for p in p_values:\n", + " logical_errors = 0\n", + " print(f\"Physical error rate p={p:.3f}\")\n", + " syndrome, maps, true_logical = qsharp_runner(d, p, num_trials)\n", + " \n", + " decoder = Decoder(d,p, maps)\n", + " correction = decoder.decode_batch(syndrome)\n", + "\n", + " # Check if correction flips the logical qubit\n", + " logical_errors = sum(is_logical_error(d, c, true_logical[i]) for i,c in enumerate(correction))\n", + " logical_error_rates.append(logical_errors / num_trials)\n", + "\n", + " results[d] = logical_error_rates\n", + "\n", + " return results\n", + "\n", + "print(run_experiment_for_d(d_values=[1, 3, 5], p_values=[0.005, 0.01, 0.05, 0.1, 0.15, 0.2], num_trials=1000))\n", + "# print(run_experiment_for_d(d_values=[1, 3, 5], p_values=[0.005, 0.01, 0.05, 0.1, 0.15, 0.2], num_trials=11000))\n", + "#{1: [0.010181818181818183, 0.01818181818181818, 0.098, 0.1809090909090909, 0.2540909090909091, 0.31836363636363635], 3: [0.07636363636363637, 0.14945454545454545, 0.43618181818181817, 0.48918181818181816, 0.5086363636363637, 0.4979090909090909], 5: [0.15163636363636362, 0.2737272727272727, 0.49772727272727274, 0.5010909090909091, 0.49536363636363634, 0.5014545454545455]}\n", + "\n", + "# print(run_experiment_for_d(d_values=[3], p_values=[0.005, 0.01, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7], num_trials=2000))\n", + "# print(run_experiment_for_d(d_values=[3], p_values=[0.005], num_trials=2))" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "08a20a62", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MPS (Metal) is available!\n", + "mps\n", + "tensor([[1, 1, 1, 1, 1],\n", + " [1, 1, 1, 1, 1],\n", + " [1, 1, 1, 1, 1],\n", + " [1, 1, 1, 1, 1],\n", + " [1, 1, 1, 1, 1]], dtype=torch.uint8)\n" + ] + } + ], + "source": [ + "# !pip install torch torchvision torchaudio\n", + "import torch\n", + "\n", + "if torch.backends.mps.is_available():\n", + " print(\"MPS (Metal) is available!\")\n", + " device = torch.device(\"mps\")\n", + "else:\n", + " print(\"MPS not available, using CPU.\")\n", + " device = torch.device(\"cpu\")\n", + "\n", + "\n", + "import torch\n", + "\n", + "device = torch.device(\"mps\" if torch.backends.mps.is_available() else \"cpu\")\n", + "print(device)\n", + "\n", + "lattice = torch.zeros((5, 5), dtype=torch.uint8, device=device)\n", + "syndrome = torch.ones((5, 5), dtype=torch.uint8, device=device)\n", + "\n", + "lattice ^= syndrome\n", + "print(lattice.cpu())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fdd58514", + "metadata": {}, + "outputs": [], + "source": [ + "!pip install pyobjc\n", + "import numpy as np\n", + "import objc\n", + "from Cocoa import NSObject\n", + "import Metal\n", + "import MetalKit\n", + "\n", + "# 1. Create Metal device\n", + "device = Metal.MTLCreateSystemDefaultDevice()\n", + "\n", + "# 2. Load shader\n", + "source = open(\"my_shader.metal\").read()\n", + "options = {}\n", + "compile_error = None\n", + "library = device.newLibraryWithSource_options_error_(source, options, objc.nil)\n", + "function = library.newFunctionWithName_(\"add_one\")\n", + "\n", + "# 3. Create compute pipeline\n", + "pipeline_state, err = device.newComputePipelineStateWithFunction_error_(function, None)\n", + "\n", + "# 4. Input/output buffers\n", + "array = np.array([1.0, 2.0, 3.0, 4.0], dtype=np.float32)\n", + "buffer_size = array.nbytes\n", + "\n", + "input_buffer = device.newBufferWithBytes_length_options_(array.tobytes(), buffer_size, 0)\n", + "output_buffer = device.newBufferWithLength_options_(buffer_size, 0)\n", + "\n", + "# 5. Create command queue and encoder\n", + "command_queue = device.newCommandQueue()\n", + "command_buffer = command_queue.commandBuffer()\n", + "command_encoder = command_buffer.computeCommandEncoder()\n", + "\n", + "command_encoder.setComputePipelineState_(pipeline_state)\n", + "command_encoder.setBuffer_offset_atIndex_(input_buffer, 0, 0)\n", + "command_encoder.setBuffer_offset_atIndex_(output_buffer, 0, 1)\n", + "\n", + "# 6. Dispatch threads\n", + "thread_count = len(array)\n", + "thread_group_size = pipeline_state.maxTotalThreadsPerThreadgroup()\n", + "thread_groups = ((thread_count + thread_group_size - 1) // thread_group_size)\n", + "command_encoder.dispatchThreadgroups_threadsPerThreadgroup_(\n", + " (thread_groups, 1, 1),\n", + " (thread_group_size, 1, 1)\n", + ")\n", + "\n", + "command_encoder.endEncoding()\n", + "command_buffer.commit()\n", + "command_buffer.waitUntilCompleted()\n", + "\n", + "# 7. Get results\n", + "result_ptr = output_buffer.contents()\n", + "result = np.frombuffer(objc.pythonify(result_ptr), dtype=np.float32, count=len(array))\n", + "print(\"Result:\", result)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5fa4d0a0", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import itertools\n", + "from typing import List, Dict, Tuple\n", + "\n", + "def generate_all_single_pauli_errors(num_qubits: int) -> List[np.ndarray]:\n", + " \"\"\"Generates all single X/Z/Y errors on a code block.\"\"\"\n", + " errors = []\n", + " for q in range(num_qubits):\n", + " e = np.zeros(num_qubits, dtype=int)\n", + " e[q] = 1\n", + " errors.append((q, e)) # single-qubit X (or Z)\n", + " return errors\n", + "\n", + "def compute_syndrome(error: np.ndarray, stab_map: List[List[int]]) -> np.ndarray:\n", + " \"\"\"Compute syndrome based on parity check (mod 2) for each stabilizer.\"\"\"\n", + " syndrome = np.zeros(len(stab_map), dtype=int)\n", + " for i, qubits in enumerate(stab_map):\n", + " parity = sum(error[q] for q in qubits if q < len(error))\n", + " syndrome[i] = parity % 2\n", + " return syndrome\n", + "\n", + "def build_lookup_table(num_qubits: int, stab_map: List[List[int]]) -> Dict[str, np.ndarray]:\n", + " \"\"\"Precompute the syndrome → correction table for all single-qubit errors.\"\"\"\n", + " table = {}\n", + "\n", + " for q, error in generate_all_single_pauli_errors(num_qubits):\n", + " syndrome = compute_syndrome(error, stab_map)\n", + " key = ''.join(map(str, syndrome))\n", + " # Store only if not already stored — minimal weight correction\n", + " if key not in table:\n", + " table[key] = error.copy()\n", + " \n", + " # Add trivial correction for zero syndrome\n", + " table['0' * len(stab_map)] = np.zeros(num_qubits, dtype=int)\n", + " return table\n", + "\n", + "def lookup_decode(syndrome: np.ndarray, lookup_table: Dict[str, np.ndarray]) -> np.ndarray:\n", + " key = ''.join(map(str, syndrome))\n", + " return lookup_table.get(key, np.zeros_like(next(iter(lookup_table.values()))))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f5aef0f2", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "class SurfaceCodeDecoder:\n", + " def __init__(self, d):\n", + " self.d = d # code distance\n", + "\n", + " def _get_syndrome_graph(self, syndrome):\n", + " # Create a graph of syndrome nodes\n", + " G = nx.Graph()\n", + " for i, node1 in enumerate(syndrome):\n", + " for j, node2 in enumerate(syndrome):\n", + " if i >= j:\n", + " continue\n", + " weight = self._manhattan_distance(node1, node2)\n", + " G.add_edge(node1, node2, weight=weight)\n", + " return G\n", + "\n", + " def _manhattan_distance(self, a, b):\n", + " return abs(a[0] - b[0]) + abs(a[1] - b[1])\n", + "\n", + " def decode(self, syndrome):\n", + " G = self._get_syndrome_graph(syndrome)\n", + " matching = nx.algorithms.matching.min_weight_matching(G)\n", + " \n", + " # In real code, we would now apply the correction along the shortest paths\n", + " corrections = []\n", + " for u, v in matching:\n", + " corrections.append((u, v)) # paths to be corrected\n", + " return corrections\n", + " def getSyndrome(self, map, measures):\n", + " syndrome = []\n", + " syndromeMap = []\n", + " for i,measure in enumerate(measures):\n", + " if measure == qsharp.Result.One:\n", + " qubits = []\n", + " for qubit in map[i]:\n", + " qubits.append((qubit//self.d, qubit%self.d))\n", + " syndrome.append((sum(q[0] for q in qubits)/len(qubits),sum(q[1] for q in qubits)/len(qubits) ))\n", + " syndromeMap.append(i)\n", + " print(syndromeMap)\n", + " print(syndrome)\n", + " return syndrome, syndromeMap\n", + " \n", + " def getCoordQubits(self, coord):\n", + " return (coord[0]*self.d)+coord[1]\n", + " \n", + " \n", + "\n", + " def find_shortest_path(self, start, end):\n", + " # Round coordinates to integers\n", + " start_int = (round(start[0]), round(start[1]))\n", + " end_int = (round(end[0]), round(end[1]))\n", + " \n", + " # Calculate horizontal and vertical distances\n", + " x_diff = abs(end_int[0] - start_int[0])\n", + " y_diff = abs(end_int[1] - start_int[1])\n", + " \n", + " # Initialize the path with the starting point\n", + " path = [start_int]\n", + " \n", + " # Current position\n", + " current = start_int\n", + " \n", + " # Determine direction of movement\n", + " x_sign = 1 if end_int[0] > start_int[0] else -1 if end_int[0] < start_int[0] else 0\n", + " y_sign = 1 if end_int[1] > start_int[1] else -1 if end_int[1] < start_int[1] else 0\n", + " \n", + " # Move diagonally as much as possible\n", + " diagonal_steps = min(x_diff, y_diff)\n", + " for _ in range(diagonal_steps):\n", + " current = (current[0] + x_sign, current[1] + y_sign)\n", + " path.append(current)\n", + " \n", + " # Move remaining horizontal steps\n", + " remaining_x = x_diff - diagonal_steps\n", + " for _ in range(remaining_x):\n", + " current = (current[0] + x_sign, current[1])\n", + " path.append(current)\n", + " \n", + " # Move remaining vertical steps\n", + " remaining_y = y_diff - diagonal_steps\n", + " for _ in range(remaining_y):\n", + " current = (current[0], current[1] + y_sign)\n", + " path.append(current)\n", + " \n", + " # Return the path (excluding the starting point if it's already included)\n", + " return path[1:] if end_int != start_int else []\n", + "\n", + "\n", + "def correctErrors(errors):\n", + " for error, emap in errors.items():\n", + " for key, apply in emap.items():\n", + " # print(key, apply)\n", + " if apply:\n", + " # print(\"Applying\")\n", + " if error == \"x\":\n", + " qsharp.eval(f\"X(qubits[{key}]);\")\n", + " else:\n", + " qsharp.eval(f\"Z(qubits[{key}]);\")\n", + "\n", + "\n", + "\n", + "from collections import defaultdict\n", + "\n", + "def decode_surface_code(parity_checks, stabilizer_qubit_map):\n", + " \"\"\"\n", + " Args:\n", + " parity_checks (List[int]): List of 0 or 1 values for each stabilizer (1 = error detected)\n", + " stabilizer_qubit_map (List[List[int]]): List of lists, each with qubit indices for the stabilizer\n", + "\n", + " Returns:\n", + " Set[int]: Indices of qubits to apply correction to\n", + " \"\"\"\n", + "\n", + " # Count how many times each qubit appears in stabilizers with parity 1\n", + " qubit_votes = defaultdict(int)\n", + "\n", + " for stab_index, parity in enumerate(parity_checks):\n", + " if parity == 1:\n", + " for q in stabilizer_qubit_map[stab_index]:\n", + " qubit_votes[q] += 1\n", + "\n", + " # Apply correction to qubits that are involved in an odd number of violated stabilizers\n", + " corrections = {q for q, count in qubit_votes.items() if count % 2 == 1}\n", + " return corrections\n", + "\n", + "\n", + "def correct_surface_code(xcorrections, zcorrections):\n", + " for i in xcorrections:\n", + " qsharp.eval(f\"X(qubits[{i}]);\")\n", + " for i in zcorrections:\n", + " qsharp.eval(f\"Z(qubits[{i}]);\")\n", + "\n", + "\n", + "def getZCorrections(d, initMeasures, xMaps):\n", + " num_qubits = d*d\n", + " H_x = np.zeros((len(initMeasures), num_qubits), dtype=np.uint8)\n", + " for i, stabilizer in enumerate(xMaps):\n", + " for qubit_idx in stabilizer:\n", + " H_x[i, qubit_idx] = 1\n", + "\n", + "\n", + " z_decoder = pymatching.Matching(H_x) \n", + " z_correction = z_decoder.decode(initMeasures)\n", + " print(z_correction)\n", + " z_error_qubits = np.where(z_correction == 1)[0] # Qubits needing phase flips\n", + " print(\"Apply phase flips (Z) to qubits:\", z_error_qubits)\n", + " return z_error_qubits\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "04d0b9ab", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From d1a89e8a1886d3d39f9a244259af75d3f2d09b97 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 18:58:51 -0400 Subject: [PATCH 06/19] Update README.md --- README.md | 28 ++++++++++++++++++++-------- 1 file changed, 20 insertions(+), 8 deletions(-) diff --git a/README.md b/README.md index e7b61ed..351aa93 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,24 @@ # Quantum Error Correction: Surface Code -The repository implements surface code for quantum error correction and benchmarks the results of noisy simulation of 3 well known quantum algorithms in Q Sharp. +The repository implements rotated surface code with MWPM algorithm for decoder. +We build a logical qubit, identify errors using error syndromes at each timestep and finally apply error correction on the data qubits. The logical qubit is measured to finally to know if error correction was successful. + +## Objective +- Implement a d=3 surface code in Q# with separate layouts for data and ancilla qubits. +- Simulate Pauli noise (bit-flip, phase-flip) across multiple rounds of stabilizer cycles. +- Extract syndrome measurements and apply MWPM using a classical decoder. +- Visualize syndrome defects and correction paths for debugging and intuition. +- Assess logical qubit fidelity post-correction by varying physical error rates + +## Workflow +![Workflow](/qec-highlevel.png) + +# Components +- Surface Code Architecture in Q# +- Pauli Tracking Layer for syndrome measurements history +- Error detection at each timestep using Minimum-weight perfect matching decoder with error graphs +- Error correction on logical qubits + + -We also present a surface code generator by specifying the noise levels & thresholds. -# Plan -- Implement a surface code circuit builder with noise -- Implement a python pipline -- Implement three algorithms and benchmark the results of simulation with and without QEC for: Different code distance, different errors, different -- Explore the relationship between physical noise levels set in the simulator and noise levels of the logical qubits encoded using surface code. -- Develop a UI for interation From eebce1852b8a10b42afa414ced566265c2bc08c5 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 18:59:01 -0400 Subject: [PATCH 07/19] Decoder Logic --- decoder.py | 502 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 502 insertions(+) create mode 100644 decoder.py diff --git a/decoder.py b/decoder.py new file mode 100644 index 0000000..208c82c --- /dev/null +++ b/decoder.py @@ -0,0 +1,502 @@ +import math +from itertools import combinations +from collections import defaultdict + +import networkx as nx +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.mplot3d import Axes3D +from qiskit.synthesis import OneQubitEulerDecomposer + + + + +class GraphDecoder: + """ + Class to construct the graph corresponding to the possible syndromes + of a quantum error correction code, and then run suitable decoders. + """ + + def __init__(self, d, T): + + self.d = d + self.T = T + self.virtual = self._specify_virtual() + self.S = {"X": nx.Graph(), "Z": nx.Graph()} + self._make_syndrome_graph() + + def _specify_virtual(self): + """Define coordinates of Z and X virtual nodes. Our convention is that Z + virtual nodes are top/bottom and X virtual nodes are left/right. + """ + virtual = {} + virtual["X"] = [] + virtual["Z"] = [] + for j in range(0, self.d, 2): + # Z virtual nodes + virtual["Z"].append((-1, -0.5, j - 0.5)) # top + virtual["Z"].append((-1, self.d - 0.5, j + 0.5)) # bottom + + # X virtual nodes + virtual["X"].append((-1, j + 0.5, -0.5)) # left + virtual["X"].append((-1, j - 0.5, self.d - 0.5)) # right + return virtual + + def _make_syndrome_graph(self): + start_nodes = {"Z": (0.5, 0.5), "X": (0.5, 1.5)} + for error_key in ["X", "Z"]: + # subgraphs for each time step + for t in range(0, self.T): + start_node = start_nodes[error_key] + self.S[error_key].add_node( + (t,) + start_node, + virtual=0, + pos=(start_node[1], -start_node[0]), + time=t, + pos_3D=( + start_node[1], + -start_node[0], + t, + ), # y-coord is flipped for plot purposes + ) + self.populate_syndrome_graph( + (t,) + start_node, t, [], error_key, edge_weight=1 + ) + + # connect physical qubits in same location across subgraphs of adjacent times + syndrome_nodes_t0 = [ + x for x, y in self.S[error_key].nodes(data=True) if y["time"] == 0 + ] + for node in syndrome_nodes_t0: + space_label = (node[1], node[2]) + for t in range(0, self.T - 1): + self.S[error_key].add_edge( + (t,) + space_label, (t + 1,) + space_label, distance=1 + ) + + + def populate_syndrome_graph( + self, current_node, t, visited_nodes, error_key, edge_weight=1 + ): + """Recursive function to populate syndrome subgraph at time t with error_key X/Z. The current_node + is connected to neighboring nodes without revisiting a node. + """ + visited_nodes.append(current_node) + neighbors = [] + i = current_node[1] # syndrome node x coordinate + j = current_node[2] # syndrome node y coordinate + neighbors.append((i - 1, j - 1)) # up left + neighbors.append((i + 1, j - 1)) # down left + neighbors.append((i - 1, j + 1)) # up right + neighbors.append((i + 1, j + 1)) # down right + + normal_neighbors = [ + n + for n in neighbors + if self.valid_syndrome(n, error_key) + and (t, n[0], n[1]) not in visited_nodes + ] # syndrome node neighbors of current_node not already visited + virtual_neighbors = [ + n + for n in neighbors + if (-1, n[0], n[1]) in self.virtual[error_key] + and (-1, n[0], n[1]) not in visited_nodes + ] # virtual node neighbors of current_node not already visited + + # no neighbors to add edges + if not normal_neighbors and not virtual_neighbors: + return + + # add normal/non-virtual neighbors + for target in normal_neighbors: + target_node = ( + t, + ) + target # target_node has time t with x and y coordinates from target + if not self.S[error_key].has_node(target_node): + self.S[error_key].add_node( + target_node, + virtual=0, + pos=(target[1], -target[0]), + time=t, + pos_3D=(target[1], -target[0], t), + ) # add target_node to syndrome subgraph if it doesn't already exist + self.S[error_key].add_edge( + current_node, target_node, distance=edge_weight + ) # add edge between current_node and target_node + + # add virtual neighbors + for target in virtual_neighbors: + target_node = ( + -1, + ) + target # virtual target_node has time -1 with x and y coordinates from target + if not self.S[error_key].has_node(target_node): + self.S[error_key].add_node( + target_node, + virtual=1, + pos=(target[1], -target[0]), + time=-1, + pos_3D=(target[1], -target[0], (self.T - 1) / 2), + ) # add virtual target_node to syndrome subgraph with z coordinate (T-1)/2 for nice plotting, if it doesn't already exist + self.S[error_key].add_edge( + current_node, target_node, distance=edge_weight + ) # add edge between current_node and virtual target_node + + # recursively traverse normal neighbors + for target in normal_neighbors: + self.populate_syndrome_graph( + (t,) + target, t, visited_nodes, error_key, edge_weight=1 + ) + + # recursively traverse virtual neighbors + for target in virtual_neighbors: + self.populate_syndrome_graph( + (-1,) + target, t, visited_nodes, error_key, edge_weight=1 + ) + + def valid_syndrome(self, node, error_key): + """Checks whether a node is a syndrome node under our error_key, which is either X or Z. + """ + i = node[0] + j = node[1] + if error_key == "Z": + if i > 0 and i < self.d - 1 and j < self.d and j > -1: + return True + else: + return False + elif error_key == "X": + if j > 0 and j < self.d - 1 and i < self.d and i > -1: + return True + else: + return False + + def make_error_graph(self, nodes, error_key, err_prob=None): + """Creates error syndrome subgraph from list of syndrome nodes. The output of + this function is a graph that's ready for minimum weight perfect matching (MWPM). + + If err_prob is specified, we adjust the shortest distance between syndrome + nodes by the degeneracy of the error path. + """ + paths = {} + virtual_dict = nx.get_node_attributes(self.S[error_key], "virtual") + time_dict = nx.get_node_attributes(self.S[error_key], "time") + error_graph = nx.Graph() + nodes += self.virtual[error_key] + + for node in nodes: + if not error_graph.has_node(node): + error_graph.add_node( + node, + virtual=virtual_dict[node], + pos=(node[2], -node[1]), + time=time_dict[node], + pos_3D=(node[2], -node[1], time_dict[node]), + ) + + for source, target in combinations(nodes, 2): + # Distance is proportional to the probability of this error chain, so + # finding the maximum-weight perfect matching of the whole graph gives + # the most likely sequence of errors that led to these syndromes. + distance = int( + nx.shortest_path_length( + self.S[error_key], source, target, weight="distance" + ) + ) + + # If err_prob is specified, we also account for path degeneracies + deg, path = self._path_degeneracy(source, target, error_key) + paths[(source, target)] = path + if err_prob: + distance = distance - math.log(deg)/(math.log1p(-err_prob) - math.log(err_prob)) + distance = -distance + error_graph.add_edge(source, target, weight=distance) + + + + return error_graph, paths + + def analytic_paths(self, matches, error_key): + analytic_decoder = GraphDecoder(self.d,self.T) + paths = {} + for (source,target) in matches: + _, path = analytic_decoder._path_degeneracy(source[:3],target[:3], error_key) + paths[(source[:3], target[:3])] = path + return paths + + def _path_degeneracy(self, a, b, error_key): + """Calculate the number of shortest error paths that link two syndrome nodes + through both space and time. + """ + # Check which subgraph node is on. If x + y is even => X, else Z. + # a_sum, b_sum = a[1] + a[2], b[1] + b[2] + if error_key == "X": + subgraph = self.S["X"] + elif error_key == "Z": + subgraph = self.S["Z"] + else: + raise nx.exception.NodeNotFound("error_key must be X or Z") + + shortest_paths = list(nx.all_shortest_paths(subgraph, a, b, weight="distance")) + one_path = shortest_paths[ + 0 + ] # We can pick any path to return as the error chain + degeneracy = len(shortest_paths) + + # If either node is a virtual node, we also find degeneracies from the other + # node to *any* nearest virtual node + source = None + if a[0] == -1: + target = a + source = b + elif b[0] == -1: + target = b + source = a + + # Compute additional degeneracies to edge boundaries + if source: + virtual_nodes = self.virtual[error_key] + shortest_distance = nx.shortest_path_length( + subgraph, a, b, weight="distance" + ) + for node in virtual_nodes: + distance = nx.shortest_path_length( + subgraph, source, node, weight="distance" + ) + if distance == shortest_distance and node != target: + degeneracy += len( + list( + nx.all_shortest_paths( + subgraph, source, node, weight="distance" + ) + ) + ) + return degeneracy, one_path + + def matching_graph(self, error_graph, error_key): + """Return subgraph of error graph to be matched. + """ + time_dict = nx.get_node_attributes(self.S[error_key], "time") + subgraph = nx.Graph() + syndrome_nodes = [ + x for x, y in error_graph.nodes(data=True) if y["virtual"] == 0 + ] + virtual_nodes = [ + x for x, y in error_graph.nodes(data=True) if y["virtual"] == 1 + ] + + # add and connect each syndrome node to subgraph + for node in syndrome_nodes: + if not subgraph.has_node(node): + subgraph.add_node( + node, + virtual=0, + pos=(node[2], -node[1]), + time=time_dict[node], + pos_3D=(node[2], -node[1], time_dict[node]), + ) + for source, target in combinations(syndrome_nodes, 2): + subgraph.add_edge( + source, target, weight=error_graph[source][target]["weight"] + ) + + # connect each syndrome node to its closest virtual node in subgraph + for source in syndrome_nodes: + potential_virtual = {} + for target in virtual_nodes: + potential_virtual[target] = error_graph[source][target]["weight"] + nearest_virtual = max(potential_virtual, key=potential_virtual.get) + paired_virtual = ( + nearest_virtual + source + ) # paired_virtual (virtual, syndrome) allows for the virtual node to be matched more than once + subgraph.add_node( + paired_virtual, + virtual=1, + pos=(nearest_virtual[2], -nearest_virtual[1]), + time=-1, + pos_3D=(nearest_virtual[2], -nearest_virtual[1], -1), + ) # add paired_virtual to subgraph + subgraph.add_edge( + source, paired_virtual, weight=potential_virtual[nearest_virtual] + ) # add (syndrome, paired_virtual) edge to subgraph + + paired_virtual_nodes = [ + x for x, y in subgraph.nodes(data=True) if y["virtual"] == 1 + ] + + # add 0 weight between paired virtual nodes + for source, target in combinations(paired_virtual_nodes, 2): + subgraph.add_edge(source, target, weight=0) + + return subgraph + + def matching(self, matching_graph, error_key): + """Return matches of minimum weight perfect matching (MWPM) on matching_graph. + """ + matches = nx.max_weight_matching(matching_graph, maxcardinality=True) + filtered_matches = [ + (source, target) + for (source, target) in matches + if not (len(source) > 3 and len(target) > 3) + ] # remove 0 weighted matched edges between virtual syndrome nodes + return filtered_matches + + def calculate_qubit_flips(self, matches, paths, error_key): + physical_qubit_flips = {} + for (source, target) in matches: + # Trim "paired virtual" nodes to nearest virtual node + if len(source) > 3: + source = source[:3] + if len(target) > 3: + target = target[:3] + + # Paths dict is encoded in one direction, check other if not found + if (source, target) not in paths: + source, target = (target, source) + + path = paths[(source, target)] # This is an arbitrary shortest error path + for i in range(0, len(path) - 1): + start = path[i] + end = path[i + 1] + # Check if syndromes are in different physical locations + # If they're in the same location, this is a measurement error + if start[1:] != end[1:]: + time = start[0] + if time == -1: # Grab time from non-virtual syndrome + time = end[0] + physical_qubit = ( + time, + (start[1] + end[1]) / 2, + (start[2] + end[2]) / 2, + ) + + # Paired flips at the same time can be ignored + if physical_qubit in physical_qubit_flips: + physical_qubit_flips[physical_qubit] = ( + physical_qubit_flips[physical_qubit] + 1 + ) % 2 + else: + physical_qubit_flips[physical_qubit] = 1 + + physical_qubit_flips = { + x: error_key for x, y in physical_qubit_flips.items() if y == 1 + } + return physical_qubit_flips + + def net_qubit_flips(self, flips_x, flips_z, decompose=False): + flipsx = {flip: "X" for flip, _ in flips_x.items() if flip not in flips_z} + flipsz = {flip: "Z" for flip, _ in flips_z.items() if flip not in flips_x} + flipsy = {flip: "Y" for flip, _ in flips_x.items() if flip in flips_z} + flips = {**flipsx, **flipsy, **flipsz} + + individual_flips = defaultdict(dict) + + for flip, error_key in flips.items(): + individual_flips[flip[1:]][flip[0]] = error_key + + paulis = { + "X": np.array([[0, 1], [1, 0]]), + "Y": np.array([[0, -1j], [1j, 0]]), + "Z": np.array([[1, 0], [0, -1]]), + "I": np.array([[1, 0], [0, 1]]), + } + + physical_qubit_flips = {} + for qubit_loc, flip_record in individual_flips.items(): + net_error = paulis["I"] + # print("Physical Qubit: " + str(qubit_loc)) + for time, error in sorted(flip_record.items(), key=lambda item: item[0]): + # print("Error: " + error + " at time: " + str(time)) + net_error = net_error.dot(paulis[error]) + physical_qubit_flips[qubit_loc] = net_error + if decompose: + physical_qubit_flips[qubit_loc] = self.decomposeGate(net_error) + + physical_qubit_flips = {x:y for x,y in physical_qubit_flips.items() if not np.array_equal(y,paulis["I"])} + return physical_qubit_flips, paulis + + + def graph_2D(self, G, edge_label): + pos = nx.get_node_attributes(G, "pos") + nx.draw_networkx(G, pos) + labels = nx.get_edge_attributes(G, edge_label) + labels = {x: round(y, 3) for (x, y) in labels.items()} + nx.draw_networkx_edge_labels(G, pos, edge_labels=labels) + plt.show() + + + def decomposeGate(self, unitary): + '''Get decomposed unitary angles''' + return OneQubitEulerDecomposer("ZYZ").angles(unitary) + + def graph_3D(self, G, edge_label, angle=[-116, 22]): + """Plots a graph with edge labels in 3D. + """ + # Get node 3D positions + pos_3D = nx.get_node_attributes(G, "pos_3D") + + # Define color range based on time + colors = { + x: plt.cm.plasma((y["time"] + 1) / self.T) for x, y in G.nodes(data=True) + } + + # 3D network plot + with plt.style.context(("ggplot")): + + fig = plt.figure(figsize=(20, 14)) + ax = Axes3D(fig) + + # Loop on the nodes and look up in pos dictionary to extract the x,y,z coordinates of each node + for node in G.nodes(): + xi, yi, zi = pos_3D[node] + + # Scatter plot + ax.scatter( + xi, + yi, + zi, + color=colors[node], + s=120 * (1 + G.degree(node)), + edgecolors="k", + alpha=0.7, + ) + + # Label node position + ax.text(xi, yi, zi, node, fontsize=20) + + # Loop on the edges to get the x,y,z, coordinates of the connected nodes + # Those two points are the extrema of the line to be plotted + for src, tgt in G.edges(): + x_1, y_1, z_1 = pos_3D[src] + x_2, y_2, z_2 = pos_3D[tgt] + + x_line = np.array((x_1, x_2)) + y_line = np.array((y_1, y_2)) + z_line = np.array((z_1, z_2)) + + # Plot the connecting lines + ax.plot(x_line, y_line, z_line, color="black", alpha=0.5) + + # Label edges at midpoints + x_mid = (x_1 + x_2) / 2 + y_mid = (y_1 + y_2) / 2 + z_mid = (z_1 + z_2) / 2 + label = round(G[src][tgt][edge_label], 2) + ax.text(x_mid, y_mid, z_mid, label, fontsize=14) + + # Set the initial view + ax.view_init(angle[1], angle[0]) + + # Hide the axes + ax.set_axis_off() + + # Get rid of colored axes planes + # First remove fill + ax.xaxis.pane.fill = False + ax.yaxis.pane.fill = False + ax.zaxis.pane.fill = False + + # Now set color to white (or whatever is "invisible") + ax.xaxis.pane.set_edgecolor("w") + ax.yaxis.pane.set_edgecolor("w") + ax.zaxis.pane.set_edgecolor("w") + + plt.show() \ No newline at end of file From 0ea91dc02f3f7fc009c7803572321bfcae088e3c Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 19:27:36 -0400 Subject: [PATCH 08/19] Add Rotated Surface Code --- src/RotatedSurfaceCode.qs | 148 +++++++++++++++++++++++++++++--------- 1 file changed, 114 insertions(+), 34 deletions(-) diff --git a/src/RotatedSurfaceCode.qs b/src/RotatedSurfaceCode.qs index c3a787f..acf54f1 100644 --- a/src/RotatedSurfaceCode.qs +++ b/src/RotatedSurfaceCode.qs @@ -6,14 +6,20 @@ import Std.Diagnostics.DumpMachine; import Std.Convert.IntAsDouble; import Std.Convert.DoubleAsStringWithPrecision; import Std.Diagnostics.DumpRegister; -import SurfaceCode.MeasureXStabilizers; - function validIndex(d: Int, index:Int): Bool { - if 0 <= index and index < d*d { - return true; - } - return false; +function validIndex(d: Int, index:Int): Bool { + if 0 <= index and index < d*d { + return true; } + return false; +} + +operation CorrectDataQubit(qubit: Qubit, theta1: Double, theta2: Double, theta3: Double) : Unit is Adj + Ctl { + // Applies the correction of on data qubit as unitary + Rz(theta1, qubit); + Ry(theta2, qubit); + Rz(theta3, qubit); +} operation MeasureLogicalZ(d: Int, dataQubits: Qubit[]): Result { // Logical Z is assumed to be a product of physical Zs on a vertical line @@ -28,6 +34,52 @@ operation MeasureLogicalZ(d: Int, dataQubits: Qubit[]): Result { } return parity; } +operation MeasureLogicalZTopDown(d: Int, dataQubits: Qubit[]): Result { + // Logical Z is assumed to be a product of physical Zs on a vertical line + // Choose the first column: index i*d for i in 0..d-1 + mutable parity = Zero; + + for i in 0..d-1 { + let index = i * d; + let res = M(dataQubits[index]); + + if res == One { + set parity = if (parity == Zero) { One } else { Zero }; + } + } + return parity; +} + +operation MeasureLogicalZAntiDiagonal(d: Int, dataQubits: Qubit[]): Result { + mutable parity = Zero; + + for i in 0..d-1 { + let index = i * d + (d - 1 - i); // anti-diagonal index + let res = M(dataQubits[index]); + + if res == One { + set parity = if (parity == Zero) { One } else { Zero }; + } + } + + return parity; +} + +operation MeasureLogicalZLastRow(d: Int, dataQubits: Qubit[]): Result { + mutable parity = Zero; + let startIndex = (d - 1) * d; + + for i in 0..d-1 { + let index = startIndex + i; + let res = M(dataQubits[index]); + + if res == One { + set parity = if (parity == Zero) { One } else { Zero }; + } + } + + return parity; +} operation XStabilizer(indexes: Int[], dataQubits: Qubit[], q: Qubit): Unit { Reset(q); @@ -50,27 +102,32 @@ operation MeasureLogicalZ(d: Int, dataQubits: Qubit[]): Result { } - operation GetMaps(d: Int): (Int[][], Int[][]) { + operation GetMaps(d: Int): (Int[][], Int[][], String[]) { let TOTAL_DATA_QUBITS = d*d; mutable xMaps = []; mutable zMaps = []; + mutable order = []; mutable isZ = true; for i in 0..d-2 { for j in 0..d-2 { let id = (i*d)+j; if (i == 0) and (j % 2 == 0) { + order += ["X"]; let indexes = [id, id+1]; xMaps += [indexes]; } if (i%2 == 1) and (j == 0) { + order += ["Z"]; let indexes = [id, id+d]; zMaps += [indexes]; } let indexes = [id, id+1, id+d, id+d+1]; if (isZ) { + order += ["Z"]; zMaps += [indexes]; } else { + order += ["X"]; xMaps += [indexes]; } @@ -80,6 +137,7 @@ operation MeasureLogicalZ(d: Int, dataQubits: Qubit[]): Result { if (j == d-2) and (i % 2 == 0) { + order += ["Z"]; let indexes = [id+1, id+d+1]; zMaps += [indexes]; } @@ -87,60 +145,74 @@ operation MeasureLogicalZ(d: Int, dataQubits: Qubit[]): Result { } for j in 0..d-2 { if (j % 2 == 1) { + order += ["X"]; let id = ((d-1)*d)+j; let indexes = [id, id+1]; xMaps += [indexes]; } } - return (xMaps, zMaps); + return (xMaps, zMaps, order); } -operation GenerateLattice(xMaps: Int[][], zMaps: Int[][], qubits: Qubit[], ancillaX: Qubit[], ancillaZ: Qubit[]): Unit { - for i in 0..Length(xMaps)-1 { - XStabilizer(xMaps[i], qubits, ancillaX[i]); - } - for j in 0..Length(xMaps)-1 { - ZStabilizer(zMaps[j], qubits, ancillaZ[j]); +operation GenerateLattice(xMaps: Int[][], zMaps: Int[][], qubits: Qubit[], ancillaX: Qubit[], ancillaZ: Qubit[], order: String[]): Unit { + mutable xi = 0; + mutable zi = 0; + for o in order { + if o == "X" { + XStabilizer(xMaps[xi], qubits, ancillaX[xi]); + xi += 1; + } else { + ZStabilizer(zMaps[zi], qubits, ancillaZ[zi]); + + zi += 1; + } + } + } -operation GetSyndroem(initX: Result[], currX:Result[], initZ: Result[], currZ: Result[]): (Bool[], Bool[]) { +operation Detector(initX: Result[], currX:Result[], initZ: Result[], currZ: Result[]): (Result[], Result[]) { mutable xSyndrome = []; mutable zSyndrome = []; for i in 0..Length(initX)-1 { - xSyndrome += [initX[i] != currX[i]]; - if xSyndrome[i] { - Message("Found X error at " + DoubleAsStringWithPrecision(IntAsDouble(i), 1)) - } + xSyndrome += [initX[i] != currX[i] ? One | Zero]; } for i in 0..Length(initZ)-1 { - zSyndrome += [initZ[i] != currZ[i]]; - if zSyndrome[i] { - Message("Found Z error at " + DoubleAsStringWithPrecision(IntAsDouble(i), 1)) - } + zSyndrome += [initZ[i] != currZ[i] ? One | Zero]; } return (xSyndrome, zSyndrome); } + +operation Round(TOTAL_DATA_QUBITS: Int, qubits: Qubit[], xMaps:Int[][], zMaps: Int[][], order: String[]): (Result[], Result[]) { + use ancillaX = Qubit[(TOTAL_DATA_QUBITS-1)/2]; + use ancillaZ = Qubit[(TOTAL_DATA_QUBITS-1)/2]; + GenerateLattice(xMaps, zMaps, qubits, ancillaX, ancillaZ, order); + let measuresZ = MeasureEachZ(ancillaZ); + let measuresX = MeasureEachZ(ancillaX); + ResetAll(ancillaX); + ResetAll(ancillaZ); + return (measuresX, measuresZ); +} + + operation RotatedSurfaceCode(d: Int, r: Int): Result[] { let TOTAL_DATA_QUBITS = d*d; use qubits = Qubit[TOTAL_DATA_QUBITS]; - use ancillaX = Qubit[(TOTAL_DATA_QUBITS-1)/2]; - use ancillaZ = Qubit[(TOTAL_DATA_QUBITS-1)/2]; + // ConfigurePauliNoise(0.1, 0.0, 0.0); ResetAll(qubits); - // ApplyToEach(X, qubits); - let (xMaps, zMaps) = GetMaps(d); - GenerateLattice(xMaps, zMaps, qubits, ancillaX, ancillaZ); + + let (xMaps, zMaps, order) = GetMaps(d); - let measuresX = MeasureEachZ(ancillaX); - let measuresZ = MeasureEachZ(ancillaZ); + let (syndromeX1, syndromeZ1) = Round(TOTAL_DATA_QUBITS, qubits, xMaps, zMaps, order); + let (syndromeX2, syndromeZ2) = Round(TOTAL_DATA_QUBITS, qubits, xMaps, zMaps, order); + let (detectionX, detectionZ) = Detector(syndromeX1, syndromeX2, syndromeZ1, syndromeZ2); let results = MeasureEachZ(qubits); - // printMaps(xMaps, zMaps); + + ResetAll(qubits); - ResetAll(ancillaX); - ResetAll(ancillaZ); - return measuresX + measuresZ + results; + return detectionX + detectionZ + results; } operation RunRotated(): Result[] { return RotatedSurfaceCode(3,5); @@ -168,5 +240,13 @@ function printMaps(xMaps: Int[][], zMaps: Int[][]): Unit { } +function printArray(map: Int[]): Unit { + mutable str = ""; + for val in map { + str += DoubleAsStringWithPrecision(IntAsDouble(val), 0) + ","; + } + Message("["+str+"]"); +} + From 8c3f132f98b34073257b63d2780849f2a1281f8c Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 19:28:02 -0400 Subject: [PATCH 09/19] Final Experiments --- final.ipynb | 835 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 835 insertions(+) create mode 100644 final.ipynb diff --git a/final.ipynb b/final.ipynb new file mode 100644 index 0000000..57eb7b5 --- /dev/null +++ b/final.ipynb @@ -0,0 +1,835 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "11d584e1", + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": "// Copyright (c) Microsoft Corporation.\n// Licensed under the MIT License.\n\n// This file provides CodeMirror syntax highlighting for Q# magic cells\n// in classic Jupyter Notebooks. It does nothing in other (Jupyter Notebook 7,\n// VS Code, Azure Notebooks, etc.) environments.\n\n// Detect the prerequisites and do nothing if they don't exist.\nif (window.require && window.CodeMirror && window.Jupyter) {\n // The simple mode plugin for CodeMirror is not loaded by default, so require it.\n window.require([\"codemirror/addon/mode/simple\"], function defineMode() {\n let rules = [\n {\n token: \"comment\",\n regex: /(\\/\\/).*/,\n beginWord: false,\n },\n {\n token: \"string\",\n regex: String.raw`^\\\"(?:[^\\\"\\\\]|\\\\[\\s\\S])*(?:\\\"|$)`,\n beginWord: false,\n },\n {\n token: \"keyword\",\n regex: String.raw`(namespace|open|as|operation|function|body|adjoint|newtype|controlled|internal)\\b`,\n beginWord: true,\n },\n {\n token: \"keyword\",\n regex: String.raw`(if|elif|else|repeat|until|fixup|for|in|return|fail|within|apply)\\b`,\n beginWord: true,\n },\n {\n token: \"keyword\",\n regex: String.raw`(Adjoint|Controlled|Adj|Ctl|is|self|auto|distribute|invert|intrinsic)\\b`,\n beginWord: true,\n },\n {\n token: \"keyword\",\n regex: String.raw`(let|set|use|borrow|mutable)\\b`,\n beginWord: true,\n },\n {\n token: \"operatorKeyword\",\n regex: String.raw`(not|and|or)\\b|(w/)`,\n beginWord: true,\n },\n {\n token: \"operatorKeyword\",\n regex: String.raw`(=)|(!)|(<)|(>)|(\\+)|(-)|(\\*)|(/)|(\\^)|(%)|(\\|)|(&&&)|(~~~)|(\\.\\.\\.)|(\\.\\.)|(\\?)`,\n beginWord: false,\n },\n {\n token: \"meta\",\n regex: String.raw`(Int|BigInt|Double|Bool|Qubit|Pauli|Result|Range|String|Unit)\\b`,\n beginWord: true,\n },\n {\n token: \"atom\",\n regex: String.raw`(true|false|Pauli(I|X|Y|Z)|One|Zero)\\b`,\n beginWord: true,\n },\n ];\n let simpleRules = [];\n for (let rule of rules) {\n simpleRules.push({\n token: rule.token,\n regex: new RegExp(rule.regex, \"g\"),\n sol: rule.beginWord,\n });\n if (rule.beginWord) {\n // Need an additional rule due to the fact that CodeMirror simple mode doesn't work with ^ token\n simpleRules.push({\n token: rule.token,\n regex: new RegExp(String.raw`\\W` + rule.regex, \"g\"),\n sol: false,\n });\n }\n }\n\n // Register the mode defined above with CodeMirror\n window.CodeMirror.defineSimpleMode(\"qsharp\", { start: simpleRules });\n window.CodeMirror.defineMIME(\"text/x-qsharp\", \"qsharp\");\n\n // Tell Jupyter to associate %%qsharp magic cells with the qsharp mode\n window.Jupyter.CodeCell.options_default.highlight_modes[\"qsharp\"] = {\n reg: [/^%%qsharp/],\n };\n\n // Force re-highlighting of all cells the first time this code runs\n for (const cell of window.Jupyter.notebook.get_cells()) {\n cell.auto_highlight();\n }\n });\n}\n", + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# \n", + "# Encoder implementation\n", + "# Decoder from library\n", + "# Results\n", + "# Formatting code\n", + "# Test cases\n", + "# Report\n", + "\n", + "import qsharp\n", + "from collections import deque\n", + "from typing import List\n", + "from decoder import GraphDecoder\n", + "import numpy as np\n", + "\n", + "# StabilizerMap: Holds the information related to the stabilizers present \n", + "# in the logical qubit and defines operations to maintain mapping between\n", + "# measure qubits, its coordinates and relation with data qubits\n", + "\n", + "class StabilizerMap:\n", + " '''\n", + " Position of stabilizer on the lattice matters, this map keeps \n", + " mapping of local qubits to the global order on the surface\n", + " '''\n", + "\n", + " def __init__(self, d, xMaps, zMaps, order):\n", + " self.d = d\n", + " self.zMaps = zMaps\n", + " self.xMaps = xMaps\n", + " self.order = order\n", + " self.orderedMappings = []\n", + " self.ancillaMappings = {X: {}, Z: {}}\n", + " self.__generateStabilizerMap()\n", + " \n", + " def getByAncillaPosition(self, type, ancillaPosition):\n", + " # Position of stabilizer measured ancilla to order on surface code lattice\n", + " orderedPosition = self.ancillaMappings[type][ancillaPosition]\n", + " return self.orderedMappings[orderedPosition]\n", + "\n", + " def __generateStabilizerMap(self):\n", + " # Map: index is position, value is dict - {\"type\": X|Z, \"coordinates\": (x,y)}\n", + " xqueue = deque(self.stabilizerCoordinates(self.xMaps))\n", + " zqueue = deque(self.stabilizerCoordinates(self.zMaps))\n", + " zi = 0\n", + " xi = 0\n", + " for position in range(len(self.order)):\n", + " self.orderedMappings.append({\n", + " \"type\": self.order[position],\n", + " \"coordinates\": (\n", + " zqueue if self.order[position] == Z else xqueue\n", + " ).popleft()\n", + " })\n", + " if self.order[position] == Z:\n", + " self.ancillaMappings[Z][zi] = position\n", + " zi += 1\n", + " else:\n", + " self.ancillaMappings[X][xi] = position\n", + " xi += 1\n", + " \n", + " def _correctCoordinate(self, coordinate):\n", + " # Boundary stabilizers should be corrected to space away from data qubits which lie on 0 or d axis\n", + " if coordinate == 0:\n", + " return coordinate-0.5\n", + " if coordinate == (self.d-1):\n", + " return coordinate + 0.5\n", + " return coordinate\n", + "\n", + " def stabilizerCoordinates(self, stabilizerMap):\n", + " syndromeMap = []\n", + " for i,neighbourQubits in enumerate(stabilizerMap):\n", + " qubits = []\n", + " for qubit in neighbourQubits:\n", + " qubits.append((qubit//self.d, qubit%self.d))\n", + " x = sum(q[0] for q in qubits)/len(qubits)\n", + " y = sum(q[1] for q in qubits)/len(qubits)\n", + "\n", + " syndromeMap.append((self._correctCoordinate(x), self._correctCoordinate(y)))\n", + " return syndromeMap\n", + "\n", + "\n", + "X = \"X\"\n", + "Z = \"Z\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "9ba7561c", + "metadata": {}, + "source": [ + "\n", + "## Pauli Tracker\n", + "Tracks the list of measures and syndrome\n", + "in the logical qubit, effective to identify the errors to perform error correction through detection events that signal possibilities of errors\n", + "\n", + "\n", + "
\n", + "The below class tracks the error in timeline as shown in the above image." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "462d5a71", + "metadata": {}, + "outputs": [], + "source": [ + "# PauliTracker: Tracks the list of measures and syndrome across timesteps in 3D space\n", + "class PauliTracker:\n", + " '''Tracks the Pauli X&Z stabilizers measurements, Record \n", + " the stabilizer measurement outcomes in each round without\n", + " physically correcting the qubits'''\n", + "\n", + " def __init__(self):\n", + " self.tracker = {X: [], Z: []}\n", + " self.order = []\n", + "\n", + " def getChanges(self, type, currentMeasures):\n", + " '''Get parity of previous stabilizer measures v/s current to detect event of error'''\n", + " if not self.tracker[type]:\n", + " return currentMeasures\n", + " return [1 if a==b else 0 for a,b in zip(self.tracker[type][-1], currentMeasures)]\n", + "\n", + "\n", + " def track(self, xMeasures, zMeasures):\n", + " xMeasures = LogicalQubit.convertResultToBinaryArray(xMeasures)\n", + " zMeasures = LogicalQubit.convertResultToBinaryArray(zMeasures)\n", + " \n", + " self.tracker[X].append(self.getChanges(X, xMeasures))\n", + " self.tracker[Z].append(self.getChanges(Z, zMeasures))\n", + " \n", + " def getX(self):\n", + " return self.tracker[X]\n", + " def getZ(self):\n", + " return self.tracker[Z]\n", + " def setOrder(self, order):\n", + " self.order = order\n", + " \n", + " def getTrackedErrors(self, stabilizerMap: StabilizerMap):\n", + " '''Get difference in each timestep errors of X and Z stabilizers'''\n", + " X_ERRORS = []\n", + " Z_ERRORS = []\n", + " for error in self.tracker:\n", + " for timestep in range(len(self.tracker[error])):\n", + " for stabilizerIndex in range(len(self.tracker[error][timestep])):\n", + " if self.tracker[error][timestep][stabilizerIndex]:\n", + " stabilizer = stabilizerMap.getByAncillaPosition(error, stabilizerIndex)\n", + " bucket = X_ERRORS if error == X else Z_ERRORS\n", + " bucket.append((timestep, stabilizer[\"coordinates\"][0], stabilizer[\"coordinates\"][1]))\n", + " return X_ERRORS, Z_ERRORS\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "94e1489d", + "metadata": {}, + "outputs": [], + "source": [ + "# **Logical Qubit**: Complete implementation of the logical qubit\n", + "# Implements rotated surface code through QSharp by first encodes the logical qubit by \n", + "# generating a map of lattice with stabilizers, uses the map to construct the lattice with stabilizers,\n", + "# then decodes the errors using syndromes tracked by PauliTracker & MWPM algorithm to correct \n", + "# errors on data qubits. Finally, measures data qubit to check the true logical state.\n", + "class LogicalQubit:\n", + " def __init__(self, d, T):\n", + " self.d: int = d\n", + " self.timesteps: int = T\n", + " self.PAULI_TRACKER = PauliTracker()\n", + " self.decoder: GraphDecoder = GraphDecoder(d, T)\n", + " self.stabilizerMap: StabilizerMap = None\n", + " self.TOTAL_DATA_QUBITS = self.d**2\n", + " \n", + " @staticmethod\n", + " def convertResultToBinaryArray(result: List[qsharp.Result]):\n", + " return [1 if bit == qsharp.Result.One else 0 for bit in result]\n", + " \n", + " def getDataQubitCoordinates(self, i, j):\n", + " return (i*self.d) + j\n", + "\n", + "\n", + " def runRound(self):\n", + " xSyndrome, zSyndrome = qsharp.eval(f\"RotatedSurfaceCode.Round(TOTAL_DATA_QUBITS, qubits, xMaps, zMaps, order);\")\n", + " self.PAULI_TRACKER.track(xSyndrome, zSyndrome)\n", + "\n", + " \n", + "\n", + " def encode(self, xnoise: float, znoise: float):\n", + " \n", + " qsharp.init(project_root=\".\")\n", + " qsharp.eval(f\"import Std.Diagnostics.ConfigurePauliNoise;\")\n", + " qsharp.eval(f\"import Std.Arrays.ForEach;\")\n", + " qsharp.eval(f\"let d = {self.d};\")\n", + " qsharp.eval(f\"let TOTAL_DATA_QUBITS = {self.TOTAL_DATA_QUBITS};\")\n", + " qsharp.eval(\"use qubits = Qubit[TOTAL_DATA_QUBITS];\")\n", + " qsharp.eval(\"ApplyToEach(X, qubits);\")\n", + " qsharp.eval(f\"ConfigurePauliNoise({xnoise}, 0.0, {znoise});\")\n", + " qsharp.eval(\"ResetAll(qubits);\")\n", + " \n", + " xMaps, zMaps, order = qsharp.eval(f\"RotatedSurfaceCode.GetMaps(d);\")\n", + " self.stabilizerMap = StabilizerMap(self.d, xMaps, zMaps, order)\n", + " qsharp.eval(f\"let (xMaps, zMaps, order) = RotatedSurfaceCode.GetMaps(d);\")\n", + "\n", + " self.runRound()\n", + " for t in range(self.timesteps-1):\n", + " self.runRound()\n", + "\n", + " def __searchOperator(self, operations:dict, query):\n", + " for k,v in operations.items():\n", + " if np.array_equal(v, query):\n", + " return k\n", + "\n", + " def decode(self, xnoise: float, znoise: float):\n", + " flips = {}\n", + " X_ERRORS, Z_ERRORS = self.PAULI_TRACKER.getTrackedErrors(self.stabilizerMap)\n", + "\n", + " for error_key,errors in dict(zip((X,Z), (X_ERRORS,Z_ERRORS))).items():\n", + " if errors:\n", + " error_graph, paths = self.decoder.make_error_graph(errors, error_key, xnoise+znoise)\n", + " matching_graph = self.decoder.matching_graph(error_graph,error_key)\n", + " matches = self.decoder.matching(matching_graph,error_key)\n", + " flips[error_key] = self.decoder.calculate_qubit_flips(matches, paths,error_key)\n", + " else:\n", + " flips[error_key] = {}\n", + " decodedResults, operatorMap = self.decoder.net_qubit_flips(flips[\"X\"], flips[\"Z\"], decompose=True)\n", + "\n", + " for position, operation in decodedResults.items():\n", + " # operator = self.__searchOperator(operatorMap, operation)\n", + " corruptQubit = self.getDataQubitCoordinates(int(position[0]), int(position[1]))\n", + " correction = f\"RotatedSurfaceCode.CorrectDataQubit(qubits[{corruptQubit}], {operation[0]}, {operation[1]}, {operation[2]});\"\n", + " # print(\"Applying:\",correction)\n", + " qsharp.eval(correction)\n", + "\n", + " def getState(self):\n", + " all = qsharp.eval(\"RotatedSurfaceCode.MeasureLogicalZ(d, qubits);\")\n", + " topdown = qsharp.eval(\"RotatedSurfaceCode.MeasureLogicalZTopDown(d, qubits);\")\n", + " antidiagonal = qsharp.eval(\"RotatedSurfaceCode.MeasureLogicalZAntiDiagonal(d, qubits);\")\n", + " lastrow = qsharp.eval(\"RotatedSurfaceCode.MeasureLogicalZLastRow(d, qubits);\")\n", + " qsharp.eval(\"ResetAll(qubits);\")\n", + " return all, topdown, antidiagonal, lastrow\n", + " \n", + " \n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "00a4ebe2", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "553f0940", + "metadata": {}, + "source": [ + "#### Experiment showing that measuring along diagonal is effective\n", + "\n", + "
\n", + "
\n", + "\n", + "- The image shows that the orginal lattice is rotated to save the number of qubits used.\n", + "- This causes the logical qubits positions spacially which also changes the measurement direction.\n", + "- As shown above XL Logical operation of X is defined by applying X operation or measuring it on the anti-diagonal qubits.\n", + "
\n", + "
\n", + "The following snippet experimentally proves that we should that measuring along the anti-diagonal data qubits is effective." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "20a80f0c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Round 0:\n", + "Success Rate 0: 0.58\n", + "Success Rate 1: 0.39\n", + "Success Rate 2: 0.63\n", + "Success Rate 3: 0.55\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 1:\n", + "Success Rate 0: 0.53\n", + "Success Rate 1: 0.43\n", + "Success Rate 2: 0.69\n", + "Success Rate 3: 0.51\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 2:\n", + "Success Rate 0: 0.54\n", + "Success Rate 1: 0.48\n", + "Success Rate 2: 0.7\n", + "Success Rate 3: 0.52\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 3:\n", + "Success Rate 0: 0.54\n", + "Success Rate 1: 0.59\n", + "Success Rate 2: 0.54\n", + "Success Rate 3: 0.55\n", + "Best in Round: Parity of top to down\n", + "Round 4:\n", + "Success Rate 0: 0.56\n", + "Success Rate 1: 0.45\n", + "Success Rate 2: 0.59\n", + "Success Rate 3: 0.51\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 5:\n", + "Success Rate 0: 0.5\n", + "Success Rate 1: 0.63\n", + "Success Rate 2: 0.65\n", + "Success Rate 3: 0.56\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 6:\n", + "Success Rate 0: 0.58\n", + "Success Rate 1: 0.54\n", + "Success Rate 2: 0.63\n", + "Success Rate 3: 0.45\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 7:\n", + "Success Rate 0: 0.55\n", + "Success Rate 1: 0.43\n", + "Success Rate 2: 0.61\n", + "Success Rate 3: 0.46\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 8:\n", + "Success Rate 0: 0.54\n", + "Success Rate 1: 0.49\n", + "Success Rate 2: 0.64\n", + "Success Rate 3: 0.47\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Round 9:\n", + "Success Rate 0: 0.59\n", + "Success Rate 1: 0.56\n", + "Success Rate 2: 0.67\n", + "Success Rate 3: 0.48\n", + "Best in Round: Parity of qubits in anti-diagonal\n", + "Best data qubits for logical measurement in Z basis is Parity of qubits in anti-diagonal\n" + ] + } + ], + "source": [ + "d = 3\n", + "noise = 0.1\n", + "T = 1\n", + "import networkx as nx\n", + "\n", + "true_state = qsharp.Result.Zero\n", + "\n", + "# Warm up for experiment\n", + "for i in range(10):\n", + " qubit = LogicalQubit(d, T)\n", + " qubit.encode(noise//2, noise//2)\n", + " qubit.decode(noise//2, noise//2)\n", + " state = qubit.getState()\n", + "\n", + "maps = [\"Parity of all data qubits\", \"Parity of top to down\", \"Parity of qubits in anti-diagonal\", \"Parity of qubits along the last row of lattice\"]\n", + "votes = {}\n", + "for round in range(10):\n", + " successResults = [[], [], [], []]\n", + " print(f\"Round {round}:\")\n", + " for i in range(100):\n", + " qubit = LogicalQubit(d, T)\n", + " qubit.encode(noise//2, noise//2)\n", + " qubit.decode(noise//2, noise//2)\n", + " state = qubit.getState()\n", + " for i,s in enumerate(state):\n", + " successResults[i].append(1 if s == qsharp.Result.Zero else 0)\n", + " winner = 0\n", + " winpos = 0\n", + " for i,r in enumerate(successResults):\n", + " successRate = sum(r)/100\n", + " print(f\"Success Rate {i}: {successRate}\")\n", + " if max(successRate, winner) == successRate:\n", + " winner = successRate\n", + " winpos = i\n", + " votes[winpos] = votes.get(winpos, 0) + 1\n", + " print(\"Best in Round:\", maps[winpos])\n", + "print(\"Best data qubits for logical measurement in Z basis is \", maps[max(votes, key=votes.get)])\n", + "\n", + " \n", + "\n", + " \n", + " \n", + "# qubit.decoder.graph_2D(qubit.decoder.S[X],'distance')\n", + "# qubit.decoder.graph_2D(qubit.decoder.S[Z],'distance')\n" + ] + }, + { + "cell_type": "markdown", + "id": "595dfaf8", + "metadata": {}, + "source": [ + "### Setup for Noisy simulation experiment" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8d13b78", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running for code distance d=3\n", + "Physical error rate p=0.005\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.015\n", + "Physical error rate p=0.020\n", + "Physical error rate p=0.025\n", + "Physical error rate p=0.030\n", + "Physical error rate p=0.035\n", + "Physical error rate p=0.040\n", + "Physical error rate p=0.045\n", + "Physical error rate p=0.050\n", + "Physical error rate p=0.075\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Physical error rate p=0.300\n", + "Physical error rate p=0.400\n" + ] + } + ], + "source": [ + "def isLogicalState(state):\n", + " # Anti-Diagonal Measurement\n", + " return qsharp.Result.Zero == state[2]\n", + "\n", + "\n", + "def run_experiment_for_d(d_values, p_values, num_trials):\n", + " results = {}\n", + " for d in d_values:\n", + " logical_error_rates = []\n", + " print(f\"Running for code distance d={d}\")\n", + " \n", + " for p in p_values:\n", + " logical_errors = 0\n", + " print(f\"Physical error rate p={p:.3f}\")\n", + " true_state = qsharp.Result.Zero\n", + "\n", + " for i in range(num_trials):\n", + " qubit = LogicalQubit(d, d)\n", + " qubit.encode(p//2, p//2)\n", + " qubit.decode(p//2, p//2)\n", + " state = qubit.getState()\n", + " logical_errors += int(not isLogicalState(state))\n", + " logical_error_rates.append(logical_errors / num_trials)\n", + "\n", + " results[d] = logical_error_rates\n", + "\n", + " return results\n", + "physical_error_values = [0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04, 0.045, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4]\n", + "\n", + "TRAILS = 100\n", + "logical_errors = run_experiment_for_d(d_values=[3], p_values=physical_error_values, num_trials=TRAILS)" + ] + }, + { + "cell_type": "markdown", + "id": "2312303d", + "metadata": {}, + "source": [ + "### Physical v/s Logical Noise" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3a80a1b7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{3: [0.03, 0.09, 0.1, 0.1, 0.03, 0.06, 0.1, 0.05, 0.06, 0.06, 0.03, 0.04, 0.05, 0.09, 0.04, 0.04]}\n" + ] + }, + { + "data": { + "image/png": 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Z+nw8e/as2J6nmmpOwWY85ZKnGmsvEeDpnIynX+p6PvD0Tu2/z1KVv3kaL9M1ZZ3vs0WLFmIdaHZ2tmhHxFNBmeb0eglPDa5pyrFE3+eDhKe4c394nq7K6+0118aaOg2Xp37zUgZ+LfHSAOm1zOtyebovL6HQxNNkedmC5vKJ9u3bi+JVfDvXrl0TS1X4MeWpuPw8MPa9k58LPG2ZpynzulsejzZuEaWN18gzXncs4fHxFGae2v3f//5XvTSHpxvzc53fTyQ8DZiX6fASCH6O8nR5XirDzwdL7F+e9vzVV1+JqeRcG4AfX0Pfr2vCy0AMKaTG0+urwq91XfuiutcTL0Hh3+P3Dm38HDP2ecz7TxtPZde1BIeTZt99952YNs71KbgOgebaf0Mea+l9jF+Tumor8Psiv1b5xHUreJkO72d+DvLzmZcT8HuoPRZZBDAnBN0AUC1eWyi1K+F1W1yojNuY8Po3/kImtW7hL7esqjW3UlVcabuacBEzDiJ5XTIHPLy+mL9curi4iC87XHFY3/6l/OWPv6RwQKl9AEETr3XUHKPm2j9NNa0r1oUD6l69eokT4/Hw38BraXkd6vjx48V6SVMYMy5eg8hfSvlv5kCUv6TzGl8OMDhA4vWBmo8zf7njv6WmKseGPubV4S/YHLzybfF6YX0Y+nzkv8vQfc7PUSatt5WTPn8vB928HQfd1T3Hed/r+wVaetz0aTPFa855TTG/Z/D7Ctdb4CBRKvhnapEyDgz57+f12xyo8HsFB6Z8sI4Dcm28ZprX62oeBOSDDXzwiddS81p1DnoY1zrgYltcdZxv19D3Tn3w606bdPBDM3hlXN+Ai6NxmzweFwdMfJCLi71prpvmx5iDKv57eL3+r7/+Ki7nYm281v++++6rdkz6vt4Zr+fmyuL8WPG+4AMGvA6c8YEWc/SbNvf7Ij//dR3srO71xNvz5fx+ZMh91YQPynIgy2v4+aAYF6Djx5QPBEnFSzULA/J6a157zZ/FvH+kehb8fmvIYy29jy1evLja7fi9mt8X+DnDrx1e875kyRLxe/yY8OcHj1dzrTgA3IagGwD0xl+m+EsVfxF7//33RYVm/jKl+YUxOTlZ5+8mJSVV2E6fo/4ccM+dO1fcjybOfku9dfUh3SdnkrjIlb7bV1Vxt6q/0RD8JYWzaFygiL/88hd9KeiWMmraFXI1g5yqbtNQ3IaLA2TODko9hSVcuV27JRwf+OBgmrNN1QVahj7m1eGDLnwAgDN1nInWh6HPRylQMWSfS78rBbJyMvTvre45zhkzzmrpE0hLWVYOQGrqkcyBH2cIeaYHF9bTxIGyqTgY5kJj/J60fft2EfTy85pfT5yR087ecZE5rsCtndXn4oecQeZijXywh1+b/DMXoeKMNWeO5cYHL/i9g6uZc9DN/2sWUNMUFhYmDj7w7BJ+7HnmEP9tfBs8E6W6fuH6vt75vYrfqzn444Oimgdz+PerqrZuDdW9L1Z1nebrSbtwHv89fLmuzzJTZysxzpTzAWc+SMIHGTnA5hkK0uPPr1kOdHnGAwfqmjN5+HVe3UFOXaS/gw/a8HNFHzw7hE88c4Y7JkiF3Xic/JqR3hcA4Da0DAMAg3F1YP6yxtVvpXYonDnhL9TcCkdXeyKpzZDmUXApY6SdxWHSNDftytmMp7Zrq+62OCDibAFXT9acplndlxBur8NZYClYqen+jSXNFNAkVYnVlUmRpj2aS1WPM3+x5C9TVU3V5IClOoY+5tXhKsC8f7kdDc+2qI6U4TH0+cjtdnh7PkDAAZl2EMqV4XVNw9acniknXsLAdLXz4qr7vJ95SrF0cECaaq1rH/MMFl0HfHTR9/nAeAz8nNAOuDmg4yUO5iBltDkDzH83HzTiDJx2wMhBOWfudL2/aAZQPF6emi21GuMqz0rAGWSeJcMZUV6ysmrVKjHW6gJoPmDAmVQOyjjo5tc4L28xx/7lgzR8QJCnXmvPnuDXlPbSIKWr7vXEswr4PcLSGV0+yC21+9MMpPm1wvuOZ39pL52p6rOpus9H6X2MA3hD8fsJB9r83szv03wwgh8fAKgMQTcAGPWFj6eYc+aEsxvS0XnOMvGXL14frImnWPK6V14DrvmlkKd2Mv5yrE3KLmj3feb2QpwB0BWo8pdkXbfFOFvAX144E6RrSjOv4dbsp8pf3nmaH7c40sRfPg1Zz80BzA8//FApkGMcQEoZKs21tdLabM1+sYyzVdqZZ1NV9TjzbAJdvaw5+81f4Hj2gfZ0YP4iqLmW0NDHvCr8vOH2SPzc4t6w/Hva+PHl6Y6cTTXm+chTM7llDmeReIqkJt5HPDVbG0//5CwptyTiWRna+GCD9kES3o4zQebu4c3BI2freZ3nqVOnKuwTfq1yEK3Zl5e35wM+nJ3SXMfJ282YMUPv++XpzHw7/JjpWuOqeeCIn2t8IEszG8/7bfLkyeo1/qbitdxci2HdunVibTH//bqmlvNMGd7nnA3XxM9HXc9Jacza6/3lJPXi5hkqnHHUleXmzLauJT36/j36vt450ObPBV7Lrfnc5lk0UmtHW8IzI/i1ze8pmu9p/JnAryem3efaUvuYD3Dz61p635Pes/lAoOY6bq5BUNUsjOo+a3mZAgfPvHRC871DwvtT88AityPTFbxLs2aU9BoBUBJMLwcAo3AvTi6QxQElZ75btmyp7hHKU8/5CwEfQecvsLyWk4/I8xcHzWJEPFWY117ybfGaZu6Dyl8o+Esyn/j2+AsbZ3L4cs7qcMDLU0J5Opsm/uLPwSp/IeDf5Wwa35fUV5e/vPAXB16Tztk9zhLwlxn+8slBEB+d54BemiLLQR7fB/e95S8i/fr1E19YeE0k93vlIkz64C9sHJjwFFC+Dc7A8pc5/gLLWSbuD8u3p7m2kgMifjw56Ob75KwLZ4x5muuIESN0HnQwFn+p5v3Cjz8HnTy1lh8n/vKs6+/kokM8fZcD6g4dOogp8vz48owAfuz5d6QlB4Y+5tXh5xQHaDwdnqdc8nOHp0Jy9o6/jHLmknvi8nYSQ5+PfKCBn18cYPBBCOlx58eb16hqZ/v4/nm2BweNPCbeN7zfOADibBTfN38x53WPEs5OGtOnm8dcVdE53gd84ucqH2jgv5OnDnOmjB8XDrw4Y8l9oCU8/ZMDCn7t8RIALo4k9enmYJT3kz6FwzjY4vcA/n2+D15fyo8FH+zg/cv7VuqFza9lPvHjeu+994oAnzPIHLxx5l0q7mYqfs1z8MFTmnk/83NbEwcqXFyNC0BpzzThAwf8/sJ/i1RIUepbz48HT+lWCh4fr0fn7CbvM35uaePp9Xzwgd97+LnJs3i4/zLvZw7EOOCqjr6vd35spDXIvC+5NgQH+zyVnbfn55O58GeGrhlCjLOunM03lfR5xmv6eRo3vzfy5xM/b7joIr9Hay/HsQQOYLnwHj/+vAyJ37N4Cj8/p7nmQLdu3cTzmN9T+fOEz+sqhsbvl3zQln+PD1zy7Ur7id8nuHAgfwbxZfwY8ucUzxri90t+v+JaJFJ9Ah4Lf67xgWJ+ffPBbn6/5APM/NjrKs4IAOjTDQBG9JqV/Pe//xXbPPLIIxV6y3KLE27H4ubmJlqN3HvvvWUnT57UeRsfffSRaMfE2/JtcWsTCbf4GTJkSFmdOnVEr1q+jns1V9VKiFuYjBgxQvS2dXJy0tmOZtWqVWWDBg0St8n3yb1JuZUNtyHjsWu3X3nmmWdE6ydu88Ptn7jFl6H9g7lnKj9G3DaMx8btm/g2ufXYt99+W1ZcXKzz8edewfx3c9st3vbw4cPVtgzj66pSXcsY/v3evXuL++Lx8WPIbZeqa+nDl3HLs4CAANFajXvhjh8/XrTT0WbIY14TfgyefPJJ0WOb+zJzX2JuNTVx4sSybdu2Vdre0Ocjt9fivtb8OHh7e4s2T7t27ar2seAeug8++KDoqSvdB7fZmTZtmmgPZo4+3dWdNPc7ty8bPny4GD/vlzZt2pTNmDGj7NatWzpvf/Xq1WWdO3cWjyO3S+NWRfy85x7e3H9cU3WPwbFjx0RrLm4lyI9B/fr1xTj++OOPCq2jlixZIl4H/Hri9krcJiklJUXn89PQlmES7qvMvaWrav0ltXziPvK6+orzfrvjjjvE48GPYZMmTUSbJO0+yqa8d5rSIlDTN998I67n558uBw4cKHv22WfLwsLCxHOCXzP8fst9l7V7V1c3Dn1e74WFhWUffPCBuH1+PvHjxi0BuXc3v/70aUFnSsswPn366ad6/T1M15i0bdiwQdwvvzfy38St7fh9i/vZa6qpZaUxfbo1e4Pzeya3t5PadPFjyo8tv/fxuPgxnzt3rtgH2p+jjMf75ptvin3Cnz+6xsotGfn1yI8J72N+v+a/l98/NfuEr1y5UrzWuSUev0dyqzZ+r+D2avr0sQdwVE78j9yBPwAAACgDTwHnmSKc3eO1wvaGpwf/5z//Edk6Q1pPKRHPoOGiWoYUGQQAAOvDmm4AAAAHxOtttVsLccEraQo1TyW2R7yem6fg23rALbVw5On8XCwOAACUC2u6AQAAHBCv1eT+v7xevUmTJmIdNtcN4HWcnDXldeH2qKq18baC6yxwzQVeo8s1Ibh4oDlaVQEAgOVgejkAAIADOn/+vKhUzkXmpFZsXNGdg+3XX38dVYgViovzcYabi5Px9HIl9A0HAIDqIegGAAAAAAAAsBCs6QYAAAAAAACwEATdAAAAAAAAABaCQmp6KC0tFa1FfH19UawEAAAAAAAAiFdqZ2dnizobzs5V57MRdOuBA+7GjRvLPQwAAAAAAABQmKtXr1KjRo2qvB5Btx44wy09mH5+fla976KiItq6dato6eLm5mbV+4aaYf8oG/aP8mEfKRv2j7Jh/ygb9o/yYR8pW5EN7J+srCyRnJXixaog6NaDNKWcA245gm5vb29xv0p9sjky7B9lw/5RPuwjZcP+UTbsH2XD/lE+7CNlK7Kh/VPTEmQUUgMAAAAAAACwEATdAAAAAAAAABaCoBsAAAAAAADAQrCmGwAAAAAAzNJmt7CwkGxpzbCrqyvl5+dTSUmJ3MMBBe4fXkvu4uJi8u0g6AYAAAAAAJNwsB0XFycCb1vqsRwSEiI6FNVUCAscd//Url1bjMOUMSDoBgAAAAAAk4KjxMREkRHk9knOzraxgpUPENy6dYtq1aplM2N2JKUy7x9+Xufm5lJKSor4uX79+kbfFoJuAAAAAAAwWnFxsQhOGjRoIFo82dp0eE9PTwTdClSqgP3j5eUl/ufAu169ekZPNcezCwAAAAAAjCatt3V3d5d7KABmJx1I4jXmxkLQDQAAAAAAJsO6aLBHTmZ4XiPoBgAAAAAAALAQBN0AAAAAAAAmmj17NnXq1MmqGdj169db7f7AeAi6AQAAAADAYSQlJdGLL75IrVq1ouDgYGratCmNGjWKduzYIffQ6PHHHxfBNJ+4RzSPb/DgwbRs2bJK7di4Yvzw4cP1ul0E6PJC9XIAAAAAAHAIly9fpt69e4veywsWLKDmzZuTh4cHbdu2jV544QU6c+aM3EOkYcOG0XfffScK1CUnJ9OWLVvo5Zdfpt9++41+//13cnUtD+G4dzTYBmS6AQAAAADAITz//PMi63vo0CEaP368yHZ36NCBXn31VTpw4IB6u/j4eBo9erToEe3n50f333+/CIA1zZ8/X2SifX196amnnqL8/PxK9/fNN99Q+/btRdurdu3a0f/+978ax8gHATigbtiwIXXp0oXefvtt2rBhA23evJm+//57ndlrbq01ZcoU0Uua74uz9/PmzRPXNWvWTPw/duxY8TvSzxcvXhR/I/8N/Hd2796dtm/fXmEsvO2HH35ITz75pPg7mzRpQl9//XWFba5du0YTJkyggIAA8vHxoW7dutHBgwfV12/YsEH8HTyuFi1a0Jw5c0SbOUeCoBsAAAAAAOxeRkaGyBpzRpuDQ22c/WY8jZuDUd5+165dIgt+6dIleuCBB9Tb/vrrr2INNwekUVFRItjVDqh//vlnmjlzJn3wwQcUGxsrtp0xYwYtX77c4LEPGDCAOnbsSGvXrtV5/eeffy6y4Dyus2fPivuWguvDhw+L/zl7zlPSpZ9v3bpFI0aMENPqjx07JjLsPM2eDzho+uSTT0QgzdvwQYvJkyeL+5Buo3///pSQkCDu/8SJE/Tmm2+qp8Lv3r2bHn30UZGpP336NH311VfiwAE/Jo4E08tBp5LSMjoUl0Ep2flUz9eTejQPIBdnJ6O3k3ucAAAAAODYLly4QGVlZSLjXB0OQk+ePElxcXHUuHFjcdkPP/wgMuIcsHJGeNGiRSK7zSf2/vvviyyxZrZ71qxZImAdN26c+JmnskuB52OPPWbw+Hnc0dHROq/jQLl169bUp08fkc3mTLekbt266oMKmlPSOYjnk2Tu3Lm0bt06ETxz1lzCgTkH2+ytt96iTz/9lP755x9q27YtrVixglJTU8XjwpluxrMHJJzVnjZtmvrv5Uw33w8H5vz4OArFZboXL14sjsrw9IPIyEgx9aMqp06dEtNCeHt+cvGT39TbBKItMYnUZ8HfNGHpAXp55XHxP//MlxuzndzjBAAAAADggFsfnJXmYFsKuFloaKgIWvk6aRuOKzT17NlTfT4nJ0dM3+agnKduSycOzvlyY8dfVc9oLsB2/PhxEQi/9NJLtHXr1hpvj7PUr7/+upj+zn8bj4//Lu1Md0REhPo83z8H7ikpKeJnvs/OnTurA25tnPl+7733KjwGkyZNEhn33NxcchSKCrpXrVol1lPwUY+jR4+KIy9Dhw5V71RtvKP4aAmvp6iqkICht+noOGCd/NNRSsysuCYlKTNfXC4FtPpuJ/c4AQAAAAAYZ4I5aLRGsTQOaNnSpUtFYCqdYmJiKqwdNwQHxJwt14XXTHNmnrPIeXl5Yg36vffeW+3tccDNmW2e9s7TwHl84eHhYn24Jq6irokfQ2n6uJeXV42Pw5w5cyo8BjyL4Pz58yIh6igUFXQvXLhQHPl44oknxNGkJUuWkLe3tyiRrwtP7fjPf/5DDz74oCg4YI7bdGQ8VXvOxtOk6xigdBlfn19YQrN/r3k7vj05x2mp+wcAAAAA28PZWE6+8SxYzkRru3nzpvifM79Xr14VJwlPC+frOZ6QttEsFsY0g2kuTtagQQOxFpynW2ueqgqcq/P333+LYJVn+VaFC77xunMO9DnxuGbNGrEuXQqcuRq6pr1794oMORdY42Cbk5hc3d0QnAXnQFq6H10HA86ePVvpMeCTs7OiQlHHWNPNR1SOHDlC06dPV1/GO2LQoEG0f/9+q95mQUGBOEmysrLE/0VFReJkTdL9WeN+D8ZlVMoca+IQlq9vN3NLtbcjbbf/QgpFNg+QbZyWun+59g8YDvtH+bCPlA37R9mwf5TNkfYP/4089Zmzn9q9pJXmv//9L/Xt25d69OghCqHxrFlO3vE6bk7O8fJVLlrGQehDDz0kEnhcaZvXOHPBMA4i+W/kPt9c0Zt/5hZkvLaZf5dvT3oMeKbt1KlTRTDMwT7HF1x0jYP3V155Ref4+HHkdeHXr19Xtwz766+/xMzekSNH0sMPP1zhMZYec15nzUEzT/XmeIcLqvHPfN98PS+15TXnPAWe/946deqIwJcLs/Htcvaai77xttK+1ByT9n6VLuMgnzPlY8aMEcXRuKAcF1zjAw58X++++y7dc889Yqo+HzDgsfGUc36sOCuvz3IAXfdvTdJjws9zFxeXCtfp+/pWTNCdlpYmnlh8VEgT/2zsFBBjb5PL6/M0CG28NoKz5HLgqomWdiSN14hUfCKZYuvug5QeWybbOC11/3LtHzAe9o/yYR8pG/aPsmH/KJsj7B/uG80BHk8l1p6arDRBQUGiCBgXOHvttddEUMuX8RJUnkErJdu4cBoXDbvzzjtFoDhw4EDR11u6fvjw4WJ6Nm/DwTRX/eaZtZyRlrbhKd4czHKgz4XDOI7gTDlX/5a20cZBHAfZ3C6MH1deax0WFiaCbm7LpZ2h56nkfFu8LY+PM+s8Xj4YwNluaZo7xzYcAHMLMw6MuSAbX8YHE7j4Gs8C4ArjN27cEPtQGh8HnHwQQHO8HF/x3yxdtnr1alGVnYN3vo7XlUuPJQfeK1eupI8++kiceJxt2rShRx55pMrHQFt2djbJiR8Pfpz//fffSq3O9F2X7lSmb0UBC+OjOfzk2rdvX4UiBPwE5VL92tM3tPHRGz6SxCdTb1NXppuPznAQz0eLrIlfePxmPXjw4ErrKSyRQX54WVSN270ysCV9uqPmAhA/PdnNYplufcZpqfuXa/+A4bB/lA/7SNmwf5QN+0fZHGn/cFDGU7GlwsW2gsMgDui4/3RVBcpAPmUK2T/8/OZp9xwPaj+/OU7kgzaZmZnVxomKyXTzYDldr910nn+uqkiapW6Tp1zoWiPOb5hyvWla4757tqpH9f09RTEyXUdi+Kke4u9Jk+9qQyujEmrcjm/PEu279B2npe5fFzmfG1Az7B/lwz5SNuwfZcP+UTZH2D+c3eSgiDOstrROV5qyLI0dlKVUIfuH75vHoOu1rO9rWzHPLnd3d+ratatYT6H5QPPPmllquW/TnnGAOmtUeXEIbVLoyte7uzqrt3OqZjtLBbz6jhP9ugEAAAAAQG6KCboZt/bianvLly8XJfF5vQOvW+D1EezRRx+tUBSN59dLpef5fEJCgjjPje/1vU2oaFhYffry4S4isNbEmWO+nK/X3I4vr247S4/T18NVlvsHAAAAAADQh2KmlzOufpeamioq5yUlJVGnTp1oy5Yt6kJo3Khdc2oBr9nmCn2Sjz/+WJy4suDOnTv1uk2ojAPWIJ/TdD0zn14e2JruaBFIPZoHVMoc83aDQ0No9u+n6McDV6hny0D66alIq2WY+f5jrmfRF39fIBcnop+evkPnOAEAAAAAAOSiqKCbcQU9PukiBdISLtagTx246m4TKsspKBYBN3u8VzOq4+Ne5bYc4LYJriXO+3u6WT3gLSgq7zdYUkYIuAEAAAAAQHEUNb0clOFSankrgqBa7tUG3BI3l/KnUVGJ9fvn5amCblZYrOy+kAAAAAAA4HgQdEMlF1LLe+G1rFuewdY76C61fve5vMLbgXa+RgAOAAAAAACgBAi6oZILKbfE/63q6Rl0q4quFcmQadYMtAuQ6QYAAAAAAIVB0A0mB93uXMVMpunluYXF6vMFxch0AwAAAACAsiDohkrOG5rpVsiabmS6AQAAAEAJZs+eLbomWYuTkxOtX7+eHMHjjz9OY8aMIVuCoBsq4GJkV9JzjQq6C7mEuJXlFWFNNwAAAIA9KCkto/0X02nD8QTxP/9sacnJyfTSSy9RixYtyMPDgxo3bkyjRo2iHTt2kBKCSw6m+eTm5iZaHg8ePJiWLVtGpaUVk02JiYk0fPhwvW7XkQJ0Xe655x5q0qQJeXp6Uv369emRRx4RragdqmUYyOtKeo54g6vl4Uohfp56/Y6rjNPL8ypML0emGwAAAMAWbYlJpDkbT1Oiqm0tq+/vSbNGhdKwsPoWuc/Lly/TXXfdRXXq1KH//Oc/FB4eTkVFRfTXX3/RCy+8QGfOnCG5DRs2jL777jsqKSkRBwi2bNlCL7/8Mv3222/0+++/k6treTgXEhIi91Btxl133UVvv/22CLgTEhLo9ddfp3vvvZf27dtnsftEpht0ruduWa+WOAqmD3elTC/XyHoDAAAAgO0E3JN/Oloh4GZJmfnicr7eEjiw5u+7Bw4coPHjx1ObNm2oQ4cO9Oqrr4rLJPHx8TR69GiqVasW+fn50f333y8CYE3z588XmWhfX1966qmnKD+/4t/CvvnmG2rfvr3IsLZr147+97//1ThGzr5zQN2wYUPq0qWLCBY3bNhAmzdvpu+//15n9rqwsJCmTJkigkq+r6ZNm9K8efPEdc2aNRP/jx07VvyO9PPFixfF38h/A/+d3bt3p+3bt1cYC2/74Ycf0pNPPin+Ts4Wf/311xW2uXbtGk2YMIECAgLIx8eHunXrRgcPHlRfz2Pnv4PHxbML5syZQ8XFt5No2vhgw2uvvUa1a9emwMBAevPNN6mszLQZEK+88grdcccd4nHp1asXTZs2TexvPuBiKQi6QXcRNT3bhVVY0y1DplmzZRgKqQEAAADIj4MiLnarzyk7v4hm/X6KdIVR0mWzfz8tttPn9vQNyDIyMkRGmwNkDg61cZDHeBo3B6O8/a5du2jbtm106dIleuCBB9Tb/vrrr2INNwekUVFRItjVDqh//vlnmjlzJn3wwQcUGxsrtp0xYwYtX76cDDVgwADq2LEjrV27Vuf1n3/+uciC87jOnj0r7lsKrg8fPiz+5+w5T0mXfr516xaNGDFCTKs/duyYyLDzNHs+4KDpk08+EYE0b/P888/T5MmTxX1It9G/f3+RPeb7P3HihAiSS1VT4Xfv3k2PPvqoyNSfPn2avvrqK3HggB+TqnzxxRfiMeIp9Xv27BH7Yd26dRW24ceSDxRUd9L+OyR8e/z4cPDNU/gtBdPLoYILqYYVUZN7TTdahgEAAAAoC89EDJ35l1lui79dJmXlU/jsrXptf/q9oeTtXnOIc+HCBRGgc3a7OhyEnjx5kuLi4sR6b/bDDz+IjDgHrJwRXrRokQje+cTef/99kSXWzHbPmjVLBKzjxo0TPzdv3lwdeD722GNkKM6UR0dH67yOA8zWrVtTnz59RDabM7qSunXrqg8qaE5J5yCeT5K5c+eK4JaDZ86aSzgw52CbvfXWW/Tpp5/SP//8Q23btqUVK1ZQamqqeFw4081atWql/l3OanNWWfp7OdPN98OBOT8+uixZskT8jvS48c98sETTc889J2YfVKdBgwYVfuaxc0Cfm5srst5//PEHWRIy3VDB+WTDg2531/Jp6MVaBR2sdRRVgkJqAAAAAKAPfTPinJXmYFsKuFloaKgIWvk6aZvIyMgKv9ezZ0/1+ZycHDF9m4NyzewrB+d8ubHjr2opKBdgO378uAiEuUjc1q01H7DgLDWvbebp7/y38fj479LOEEdERKjP8/1z4J6SkiJ+5vvs3LmzOuDWduLECXrvvfcqPAaTJk0SGXcOfrVlZmZSUlIS9ejRQ30Zr2HnTLsmvj8O7qs7SWvfJW+88YbI1vNj4+LiIjLwpk5brw4y3aBWWlpGl9KMz3Rbe3p5YUkpaRa1RKYbAAAAQH5ebi4i46yPQ3EZ9Ph35VOcq/P9E92pR/MAve5bH5wJ5qDx3LlzZGkc0LKlS5dWCs454DMGB8ScLdeF10xzZp7XfXPGnbPAgwYNEsXXqsIBN0+d//jjj0WQ6uXlJYqL8fpwTdpTsPkxlKaP8+/U9DjMmTNHnbXWxGu8jcXTy/lUHZ5VwGvQJUFBQeLEMx34QAMfVOF13ZoHS8wJQTeoJdzMo/yiUlEYrXGd6l80uvt0W3d6eb7Gem5WgEw3AAAAgOw4ENNnijfr27quqFLORdN0fZPkXG6Iv6fYzsVZvyK/+uDs6JAhQ+jbb78VWU8uDKbp5s2bIuPLAdnVq1fFScp2cwDH13PGm/E2XCyMs6USzUJsXJyMpzfzWvCHHnrI5LH//fffYso7FwSrChd843XnfOLgmddo8/pl/rs5cOYCZZr27t0rMuRcYE0KkLm6uyE4C87F4qT70XUw4OzZsxWmnFfH399fZNIPHTpEd955p7iMi64dOXJE3JYp08s1SQcNCgoKyFIQdEOlImrNg3zIVRVIG7amu7TaqS7mlltUsdIhMt0AAAAAtoUDaW4LxlXK+RukZuAtfaPk680ZcEt4TS+ve+Y1vTztmYNGDuo44/vll1+KbDJniLmVGAfLvHabr+c1zVwwTJrmzIXBOGDln3v37i0Kc506dUqsWZZwhpenenMgyQEwB3hcdO3GjRuiWnpVeDueYq3ZMowrkd99990VgnxNCxcuFMXceKq3s7MzrV69WgSvUnE4LqrGa9V5rFwdnVumceafC7Nx8TT+Ls9F3rR7gdeEq5ZzxnnMmDFijDwGnsLdoEEDkUHmQnI8bs4484EAHhtPOY+JiRFT7XV59tlnacGCBSIjzevY+W/jAx6aOMCvakq7Nj44wmvOeb/z383T+/lvbdmypcWy3AxruqFy5fJg/aeWa7YMY8Wa870tLK+w4hE6ztIDAAAAgG3hPtxfPtxFZLQ18c98uaX6dHNQvHPnTpFF5bZUYWFhNHjwYBGQctDNOADlNlccoPXr108E4fx7q1atUt8OZ5M5cOOCYF27dqUrV66Iqt6ann76aZEF5qrhHMRz0M6Vu6uaIi7hIJuDVw6UOVjnomVcnZzHVNXUdM7af/TRR+IgABd644z1pk2bRJDLuKAbH1jgzD0H5oyDWf4buYo3B95Dhw6tkE3Wh7u7u1gjXa9ePVFwjf9ObqXmohon3yYXLONteFx8sIMLsWkWetPGRdwefvhhUXyNg2L+26RsvDG8vb3FwYWBAweKNe+8zp4PtnBlej4AYSlOZZZcMW4nsrKyxFEpXszPUzWsifvF8YuEn7iWLGPP3votmlZFXaWXB7amVwZXX8lRU05BMXWY9ZdBFSPN4dT1TBr5+R71z8/f2ZLeHNaO7HX/gOGwf5QP+0jZsH+UDftH2Rxp/3CVbl5DzAGkKWtzS0rLxBrvlOx8qufrKdZwWyLDLeFMLn/P5+/3UkAKylGqkP1T3fNb3zgR08vBpHZhmtPLWVFxGZE7WYV2tXJMLwcAAACwXRxg92wZKPcwAMwOh3RA4AkP55OzjQy6bx+B5HXd1pKrNb28oBiF1AAAAAAAQFkQdIOQequAsvKLiWfwcCE1Q/BaFynwtmavbqzpBgAAAAAApUPQDRWKqDUO8CZPPfsb6u7VbcVCapheDgAAAAAACoegG4SLqqC7tYFTy3W1DZMr040+3QAAAAAAoDQIuqFCpruliUF3kTWDbmS6AQAAABQDTZHAHpWaYfksqpdDxcrldY0Lut1Va7rlCLq93V1EUTUUUgMAAACwPm6JxjV+UlNTqW7duuK8rQRThYWFoiUUWoYpT6nM+4cPIvH98/Oa75/7kBsLQTcI55ONaxcmcZUh052vml5e28tNBN0opAYAAABgfS4uLtSoUSO6du0aXb58mWwFB1V5eXnk5eVlMwcKHEmZQvaPt7c3NWnSxKTAH0E3UFZ+EaVkF5g4vbz8hVBoxUJqUsuw2t7udD0zH9PLAQAAAGRSq1Ytat26NRUVFZGt4LH++++/1K9fP5GtB2UpUsD+4QNKrq6uJgf9CLpBvZ472M+D/DzdbG5Nd23v8jFjejkAAACAfDhA4ZOt4LEWFxeTp6cngm4FcrGj/YPFC6AOuo2dWs7cXZ2t36dbFXTX8S5fX1GA6eUAAAAAAKAwCLpBo12Yr9G3oW4ZZs0+3arp5f7IdAMAAAAAgEIh6AaT24VprumWY3p5HSnoRqYbAAAAAAAUBkE3mNwuTLY13erq5arp5SikBgAAAAAACoOg28HlF5VQfEau6Wu65WgZplVIrbCklEpLrTe9HQAAAAAAoCYIuh3cpdQcKisj8vdyo6BaJjR8l1qGlVi/ZZhUSI0h2w0AAAAAAEqCoNvBqaeW16tlUv859fTyYvlahjEUUwMAAAAAACVB0O3gpCJqrU2YWi739PJanq7k4lx+wACZbgAAAAAAUBIE3Q5OahdmynpuzUx3can1p5d7ubmQh6pPOCqYAwAAAACAkiDodnDmaBfG3FxVa7qtlGkuKytTTy/3cnchTzcXcR7TywEAAAAAQEkQdDuw4pJSupRmerswOVqG8TRyLgCnnenOR6YbAAAAAAAUBEG3A+NWYUUlZSJobVjby6bWdEvruStNL0emGwAAAAAAFARBtwOTppa3qOtDzqpCZKZnususup6bg31XF2fycJWmlyPTDQAAAAAAyoGg24Fptgsz1e0+3dYJeqX13J5uzhX+R6YbAAAAAACUBEG3AzNXuzA5+nTnSZXL3csz3FKmG2u6AQAAAABASRB0OzBztQuTY023lOn2dncV/3sg0w0AAAAAAAqEoNtBccutC2YMut1U08uttaZbynRLrcLQpxsAAAAAAJQIQbeDSszMp5zCEnJ1dqKmgT4m356bqzyZbi9VhttD3acbQTcAAAAAACgHgm4HJWW5mwZ6q9dj21Kfbqll2O013VKfbkwvBwAAAAAA5UDQ7aDMObW84ppu67YM83JTrelGyzAAAAAAAFAgBN0OypztwjQz3VZrGVapejkKqQEAAAAAgPIg6CZHbxfma5bbu11ITa413SikBgAAAAAAyoOg20GZs12YHGu6pUy31DLME9PLAQAAAABAgRB0O6CMnEJKzykU51vUNb1yeYWgu7jMqpludcswVaYbhdQAAAAAAEBJEHQ78NTyhrW91Jli251eLq3pRqYbAAAAAACUB0G3AzJ35fIKfbpLrdQyTF1ITbWmG4XUAAAAAABAgRB0OyBLBN3uVp5erm4ZJq3pVmW8kekGAAAAAAAlUVzQvXjxYmrWrBl5enpSZGQkHTp0qNrtV69eTe3atRPbh4eH06ZNmypcn5ycTI8//jg1aNCAvL29adiwYXT+/HlyVCWlZRR1JUOcd3Yq/9kmC6lVml6ONd0AAObEnw8H4zLoSJqT+N9cnxcAAACORlFB96pVq+jVV1+lWbNm0dGjR6ljx440dOhQSklJ0bn9vn37aMKECfTUU0/RsWPHaMyYMeIUExMjri8rKxM/X7p0iTZs2CC2adq0KQ0aNIhycnLI0WyJSaQ+C/6m6GuZ4uelu+PEz3y5udZ0F8ocdCPTDQBgvs+Lh5dF0Q/nXcT/5vq8AAAAcDSKCroXLlxIkyZNoieeeIJCQ0NpyZIlIju9bNkyndt/9tlnInP9xhtvUPv27Wnu3LnUpUsX+uKLL8T1nNE+cOAAffnll9S9e3dq27atOJ+Xl0e//PILORL+ojT5p6OUmJlf4fKkzHxxualfpORrGSZVL1dNL0efbgAARX9eAAAAOBrFBN2FhYV05MgRkYWWODs7i5/379+v83f4cs3tGWfGpe0LCgrE/zz1XPM2PTw8aM+ePeQoeErgnI2nSdfEQOkyvt6UqYO3g255WoZ5opAaAIBNfF4AAAA4GvP0izKDtLQ0KikpoeDg4AqX889nzpzR+TtJSUk6t+fLGa/1btKkCU2fPp2++uor8vHxoU8//ZSuXbtGiYlVH6nnYF0K2FlWVpb4v6ioSJysSbo/U+6X1+JpZyw08Vcnvn7/hRSKbB5g3J2UlQe7/EUsv6CQXHjBuAXlFRaL/92cy8Rj4+JUpl7Tbc19ZI79A5aD/aN82EfKYpXPCzAbvH6UDftH+bCPlK3IBvaPvmNTTNBtCW5ubrR27Vqx5jsgIIBcXFxEZnz48OFivXdV5s2bR3PmzKl0+datW8V0dzls27bN6N/lIjhE5Rnh6mzdfZDSY43LXuQV3346/bFpM7lZeA5F5i3+e5zo8IG9lOBNlCCW6LtSVk5epWJ6St8/YHnYP8qHfaQM1vi8APPD60fZsH+UD/tI2bYpeP/k5ubaVtAdFBQkgmKuNq6Jfw4JCdH5O3x5Tdt37dqVjh8/TpmZmWIKe926dUVV9G7dulU5Fs6Mc0E3zUx348aNaciQIeTn50fWPnrCT7TBgweLgwjGCIzLoB/OR9W43ZC+kUZnLjjDPO3wDnF+4OAhVMvDsk+taVHbiaiUhg68kxrX8aa4tBz6KHovkYsbjRgxlGxp/4DlYP8oH/aRsljj8wLMB68fZcP+UT7sI2UrsoH9I82Itpmg293dXQTIO3bsEBXHWWlpqfh5ypQpOn+nZ8+e4vqpU6eqL+Mdw5dr8/f3VxdXi4qKEkXXqsJrvvmkjXe2XDvclPvu2aoe1ff3FEVwdOUlOK8R4u8ptjN2Wrizi8ZTycnFoo8Tz1LIUxVM8/XyFPfl4+Whrl4uxz6S87kBNcP+UT7sI2WQPi+qmmJujs8LMD+8fpQN+0f5sI+UzU3B+0ffcSmmkBrj7PLSpUtp+fLlFBsbS5MnTxatvbiaOXv00UdFFlry8ssv05YtW+iTTz4R675nz54tAmrNIJ37eO/cuVPdNoyPlHBQz1lrR8FfjGaNCtV5nfSVia835QsU/67065auYK7ZFszLvWIhtcLi0mqXDgAAgHGfF6zMDJ8XAAAAjkYxmW72wAMPUGpqKs2cOVMUQ+vUqZMIqqViafHx8aL6uKRXr160YsUKevfdd+ntt9+m1q1b0/r16yksLEy9DRdM42Cep53Xr19fBO4zZswgRzMsrD59+XAXeu3XE5SjardFqowFf4Hi603FFcw5ILZ0r+5cjfGr+3Sr/mc8BqmqOQAAGKZZkE+V1/m4u1D3ZphWDgAAYLNBN+MsdVXTyTljre2+++4Tp6q89NJL4gTlgff+S+m0fN8VGty+Hj3ZpwX1aB5gtoyFuyrotnTbMKldmLurs3rsHqpMt9SrG0E3AIBxVhyMF/8PDwumh3o0FkXTBvTqTvO2nKOzybfovT9O02cPdpZ7mAAAADZDUdPLwfKk3qodGvpTz5aBZp0i6OriZJXp5XmqTLeU5Rb3rTG9Hb26AQCMk1tYTOuOJojzD0U2E8XSugaVUe9WQfSf+zqK99kNx6/T32cqFjEFAACAqiHodjC85lnKEpsbTy/XvA9L4Urp2kG3k5OTOrutueYbAAD098eJRMouKKamgd7Uq2VghesiGtWmp/o0F+ffXRdDtwpEr0gAAACoAYJuRw26VQGyJYLuIiut6fZWFVGTSFPMpaAcAAAM8/Oh8qnlE3o0IWcdM6FeHdyWmgR40/XMfPrPljMyjBAAAMD2IOh2MFKRM0tkuqXbLFZNYbf0mm7tddsersh0AwAY69T1TDpx9Sa5uTjRvV0b6dyGO0Z8ODZcnP/hwBU6ciXDyqMEAACwPQi6HYxlM92qNd3FVlrTrZ3pdiv/m7CmGwDA+AJqQzqEUFAtjyq369M6iO7r2oi4O+Nba07iPRcAAKAGCLodTIE11nRbupBaUbHO6eWeUqa7CJluAABD5BQUiwJp7KEeTWrc/p2R7UVgfiHlFi3+56IVRggAAGC7EHQ7GGsUUrN4y7DCUt3Ty1WZ7nxkXQAADLLxxHVRGK15kI/obFGT2t7uNOeeDuL8lzsv0NmkbCuMEgAAwDYh6HYwUpEzS0wvl27T4i3DdFQv1yykhkw3AIBhVqgLqDUW3SD0MSI8hAaHBosDrW+tiVa3pAQAAICKEHQ7GEsWUnNztU6fbl0twxgKqQEAGC4mIZOir2WKA6f3dm2s9+9xcD53dBj5erjS8as3afm+yxYdJwAAgK1C0O1gLFlIzdXZOn26cwuLdRdSkzLdmF4OAKC3n1UF1IaFhVCAj7tBvxvi70nTRrQT5z/eepauZuRaZIwAAAC2DEG3g7GnNd3aQbe0xhuZbgAA/fA67t+PJ4jzEyNrLqCmy4TuTahH8wDKLSyhd9bHUBmXNQcAAAA1BN0OxpJBt7uVppfXtKZbmn4OAADV23A8gXIKS6hFXR+KbB5g1G04OzvR/HHh4nPl33OptO5YeRAPAAAA5RB0OxiLrum2UiE1Kaj2rqpPNwqpAQDUiDPSUm/uiT2a6F1ATZcWdWvRywNbi/Pv/XGa0m4VmG2cAAAAtg5Bt6P26Xax3enl0pruSi3DUEgNAEBvXDzt1PUscRB2fJdGJt/eM/1aUPv6fnQzt4je23jaLGMEAACwBwi6HbVlmA1nuvNUmexK08ulTDcKqQEA1OgXVZuwEWEhVMfAAmpVfQYsGB9Ozk5Ev5+4Tn+fSTbDKAEAAGwfgm4HY9E13S5WahlWWFJF9fLyn/MxvRwAoFrZ+UUiMGYTI5ua7XYjGtWmp/u2EOffXRcjCrUBAAA4OgTdDqS4pJRKVTO/LTm9XFo3bim5RWgZBgBgivXHr4tq463q1aLuzeqY9bZfGdSGmgR40/XMfPpoyxmz3jYAAIAtQtDtQDSDYUtkul2l6eXFlm4ZVn31cqzpBgCwTgE1XfiA6Lxx4eL8jweuUNTlDLPePgAAgK1B0O2AU8stlem22vTyKtZ0q/t0Y3o5AECVjl+9SbGJWeJA5bguDS1yH71bBdF9XRsRt+yetvYkZiABAIBDQ9DtgEE3F7mRstK2WUitipZhUp9ufLkDAKiSlOUeGV6fanubXkCtKu+ODKWgWh50IeUWLf77gsXuBwAAQOkQdDtiuzALTC1nbq4ytwxDphsAoFqZeUW0MVoqoNbEovfl7+1G743uIM7/b+dFOpOUZdH7AwAAUCoE3Q64ptsSU8utlekuLS27Pb0chdQAAAyy/liCeA9tE1yLujY1bwE1XYaHhdDg0GAqLi2jaWtOUolUzRMAAMCBIOh2yB7dFYNVW1rTrVkkDYXUAAAMK6Am9ea2RAE1Xfg+5o4OI18PV7GWfPm+yxa/TwAAAKVB0O2IPbpVwbEtZrqlqeXVFlJD0A0AUMnR+Jt0JimbPN2caWyXRla73xB/T5o2op04/5+/ztLVjFyr3TcAAIASIOh2xKDbUmu61X26yyxeRI2z2s5cEU5XITXVNgAAULmA2t0RDcjfy82q9z2hexPq0TxAvIe/ve6kyLoDAAA4CgTdDsTSQberNL3cgplmKaDWXs/NPFTT5pHpBgCoKDO3iP6wUgE1Xfgg6fxx4eLzZ/f5NFp3LMHqYwAAAJALgm4HUqBe022Z3e5uhenleYXlt+2tNbWcebip1nQj0w0AUMHaY9fEAcl2Ib7UuXFtWcbQom4tenlga3H+vT9OU9qtAlnGAQAAYG0Iuh1yTbftVi9XtwvTkenGmm4AgMp4Krc0tfyhSOsUUKvKM/1aUPv6fnQzt4je23hatnEAAABYE4JuB1JoB326pTXd2kXUtKuXY70gAEC5qCs36HzKLfG+ObpzQ1nHwgdnF4wPJy7J8fuJ6/T3mWRZxwMAAGANCLodiKVbhrlZoWVYvh5BN0O2GwCgnJTlHtWxPvl5WreAmi4RjWrT031biPPvrIuh7PwiuYcEAABgUQi6HYilW4ZZY013bmHNhdQYgm4AAKIbOYX058lEcX5iZFNSilcGtaEmAd6UmJkv2ogBAADYMwTdDqTQwoXUbq/plmd6OWfapS5iBcUopgYAsPZYgjjgGlrfjzo28iel4AOn88aFi/M/HrhCUZcz5B4SAACAxSDodiDWKqQmBfeWkFdNppuLA6nbhhUh0w0Ajq28gNoVdZswOQuo6dK7VRDd360RcQmOt9ZE42ApAADYLQTdDkSacm25TLf11nR76wi6K7QNw5c3AHBwh+Iy6GJqjni/HN2pASnROyNCKaiWhxjn4r8vyD0cAAAAi0DQ7UAsXr1cml5ebPk13VJ7sKqKqeUj0w0ADm7FofICahxw+yqggJou/t5u9N7oDuL8/3ZepDNJWXIPCQAAwOwQdDvimm4XF7tsGcbU08tRSA0AHFhGTiFtPpkkzk/soZwCaroMDwuhIaHBVFxaRm+tOUklpWj5CAAA9gVBtwMpstL0cg7uLdUnu6bp5Z6YXg4AQGuOXBPvxWEN/ShcQQXUdOG15u+NDiNfD1c6cfUmfb/vstxDAgAAMCsE3Q6Z6bZsyzBmqUxFzdPLUUgNABwbH/T8RTW1XOlZbkmIvydNH9FenP/4r7N0NSNX7iEBAACYDYJuB2KtNd2WnGJeXfVyzTXdyHQDgKPafymdLqXlkI+7C92j0AJqujzYvTFFNg8Qy4jeXnfSYjOmAAAArA1BtwOxZtBtqbZhNa7pVk8vR6YbABzTL4euiv9Hd25ItTxcyVY4OzuJ3t38GbX7fBqtPZog95AAAADMAkG3AylQTy+37JpuS7YNq3FNN6aXA4ADS79VQFtiEsX5iT2akK1pUbcWTR3UWpyf++dpSrtVIPeQAAAATIag2yEz3S4WK4Zj6V7dNa7pVmW68zG9HAAc0G9HronlPR0b+VNYQ2UXUKvKpL4tKLS+H93MLaI5G0/LPRwAAACTIeh2IJaeXs5cnaVe3WXytgxDphsAHExpqUYBtUjby3JrLlVaMD6CnJ2INp64Tjtik+UeEgAAgEkQdDsQKftsyaBbs22YJeSrMt3e7rrXKaKQGgA4cgG1y+m5ovXWqI62U0BNF25zxhlv9u76GMrOL5J7SAAAAEZD0O2ImW4LtQwTt60Kei02vVzKdLvrfupK085RSA0AHM2Kg+VZ7jGdG1Z5YNKWTB3UhpoGelNiZj59tOWs3MMBAAAwGoJuR+zTbdFMd/ltF1u4ZVjVfbpVa7pVwTkAgCNIzS6gv04lifMTbLCAmi7cGnLe2HBx/scDVyjqcobcQwIAADAKgm6HzHRbppCaZtBtienlvF5RymBXvaYbLcMAwPGsPnKVikvLqFPj2hTawI/sRa9WQXR/t0bi/FtronFAFQAAbBKCbgdijUJqlqxerlmRvMo13dL0chRSAwAHwQckV6p6c9tyAbWqvDMilOr6etDF1Bxa/M8FuYcDAABgMATdDkTK/lpjerklgm6pXZhmRlsbCqkBgKPZezGN4jNyydfTlUZF2HYBNV38vd3ovXs6iPNf7rxIZ5Ky5B4SAACAQRB0O+KablVgbGuF1G6v53YmZ+4lU12mG9PLAcDBCqiN69xQrIO2R8PCQmhIaLCYQv/WmpNUUmqZuiEAAACWgKDbgVijZZirKhgutECfbmktX3VVeVFIDQAcSUp2Pm07Xd7HemJkU7JXTk5ONHdMmGiHduLqTfp+32W5hwQAAKA3BN0OWUjNtqeXV1VEjaGQGgA4ktVR10T2t2vTOtQ2xJfsWbCfJ00f0V6c//ivs3Q1I1fuIQEAAOgFQbcDsUYhNYtOLy+6Pb28Kh6umF4OAI5TQO2XQ+VTyyfaSZuwmjzYvTFFNg8QnwdvrztJZWWYZg4AAMqHoNuBvpxxNsSW+3RLQXd1axalgByF1ADA3v17PpWu3cgjP09XGhlRnxwB1/OYPz5CfI7tPp9Ga48myD0kAAAA2wu6Fy9eTM2aNSNPT0+KjIykQ4cOVbv96tWrqV27dmL78PBw2rRpU4Xrb926RVOmTKFGjRqRl5cXhYaG0pIlS8jRaPbNtkbLMEv06c5XTS/3dqtuTXd5QJ6PlmEA4CgF1Lo0Is9qlt3Ym+ZBPjR1UGtxfu6fpyntVoHcQwIAALCdoHvVqlX06quv0qxZs+jo0aPUsWNHGjp0KKWkpOjcft++fTRhwgR66qmn6NixYzRmzBhxiomJUW/Dt7dlyxb66aefKDY2lqZOnSqC8N9//50cieZ0a1tf0+1ZTabbA5luAHAAyVn5tONM+WfjQ3bYm7smk/q2oND6fnQzt4jmbDwt93AAAABsJ+heuHAhTZo0iZ544gl1Rtrb25uWLVumc/vPPvuMhg0bRm+88Qa1b9+e5s6dS126dKEvvviiQmD+2GOP0Z133iky6M8884wI5mvKoNvrem7NbLQlSAG9Jdd0e1W7plsVdCPTDQB27NfDV0XbrO7N6lDrYPsuoFbVAd4F4yOIG2ZsPHGddsSWV3AHAABQIsUE3YWFhXTkyBEaNGiQ+jJnZ2fx8/79+3X+Dl+uuT3jzLjm9r169RJZ7YSEBFFw5Z9//qFz587RkCFDyFHbhXHrFctnuuVpGSZNsUQhNQCwVxxsrzx8VZyf6IBZbkl4I3+R8Wbvro+h7PwiuYcEAACgU9XRi5WlpaVRSUkJBQcHV7icfz5z5ozO30lKStK5PV8u+e9//yuy27ym29XVVQTyS5cupX79+lU5loKCAnGSZGVlif+LiorEyZqk+zP1fnPzC9VZbkv+Dc5O5cF2fqH5H6vsvPK/wb2av8GFStUBujX2lbn2D1gG9o/yYR8Zbue5VEq4mUe1vdxocNsgiz52St8/L/RvTptjEik+I4/mb4ql2aPKW4o5CqXvH0eH/aN82EfKVmQD+0ffsSkm6LYUDroPHDggst1Nmzalf//9l1544QVq0KBBpSy5ZN68eTRnzpxKl2/dulVMd5fDtm3bTPr9RNHO1JWopLhSsTlzSrjKmW5nij13gTblnzPrbZ+6Un7bSQnxtGnTZZ3bZIm43FVkuv/8cxNZMKlv1v0DloX9o3zYR/pbeqb8vbBT7QLase0vcvT9MyrEiRZnuNDPh65SYE4ctfQjh6Pk/QPYP7YA+0jZtil4/+TmiiDLdoLuoKAgcnFxoeTkiuuy+OeQkBCdv8OXV7d9Xl4evf3227Ru3ToaOXKkuCwiIoKOHz9OH3/8cZVB9/Tp00UBNs1Md+PGjcWUdD8/P6sfPeEn2uDBg8nNzc3o2zl1PYvoxAGq5e1JI0b0J0uJ3nKW/k26Qk2bNacRw9qa9baP/HmG6Ho8hbZuSSMGl1eu1cbTC2cc+UecHzR0mHqNt9L3D1gG9o/yYR8ZJjEzn04f+Fecn3ZfX2pZ14ccff+MIKKU9ado9ZEE+iPZn34ffwd5OEg1d1vYP44M+0f5sI+UrcgG9o80I9pmgm53d3fq2rUr7dixQ1QgZ6WlpeJnrjauS8+ePcX1XJFcwjuGL9ecDs5TyjVxcM+3XRUPDw9x0sY7W64dbup9l6iW73NLLUv+DZ6q9dYlZU5mv59C1TrxWl7uVd62j9PtfV3q5Gy1/SXncwNqhv2jfNhH+ll7PI5Ky4h6NA+gdg1qW+1+lb5/3h3ZgXaeS6NLaTn01Z4r9NoQ8x70VTql7x9Hh/2jfNhHyuam4P2j77gUU0iNcXaZ11svX75ctPeaPHky5eTkiGrm7NFHHxVZaMnLL78s2oF98sknYt337NmzKSoqSh2kc1a6f//+orr5zp07KS4ujr7//nv64YcfaOzYseSI1cst2aPbai3DqslgcPV0aUo5KpgDgD0pLimlVaoCao7YJqw6/t5u9N49HcT5L3depNhE/TIPAAAA1qCYTDd74IEHKDU1lWbOnCmKoXXq1EkE1VKxtPj4+ApZa65MvmLFCnr33XfFNPLWrVvT+vXrKSwsTL3NypUrRaD+0EMPUUZGhljX/cEHH9Bzzz1HjqRQql5uwR7dlg66b7cMqzro5srsPKU8v6hUXe0cAMAe7DybKqaX1/F2o2FhupddObLh4fVpaIdg+utUMk1bE01rn+9NLtxTDAAAQGaKCroZZ6mrmk7O2Wpt9913nzhVhdd3f/fdd+ToiqyU6Xa3Ssuw6tfq8RR6DrrRNgwA7Mkvh+LF//d2bSTe56Cy90aH0b6L6XTiWiZ9tzeOnla1FAMAAJCToqaXgz1kup0q3J+1p5czqXhaQTEy3QBgH67fzKN/zqaI8xN6YGp5VYL9POntEeVtwz7Zeo6uZuhXVRYAAMCSEHQ7CGut6XaVMt0WyDLnqYJurxoy3VJQjkw3ANiLlYevigJqPVsEUou6teQejqI90K0xRTYPEEuS3l53ksrKzD/zCgAAwBAIuh1EodWnl5dabHp5dWu6NTPdWNMNAPZTQK18avlEFFCrkbOzE80fHyE+C3afT6M1RxPkHhIAADg4BN0OosBa08tdnSy2pjtP3zXdbtL0cmS6AcD2/X0mhZKzCijQx52GdkABNX00D/KhqYPaiPNz/zhNqdkFcg8JAAAcGIJuB2HtlmHyrulWTS9HyzAAsAMrpAJq3RpZ/D3cnjzdtzmF1vejzLwimrPxlNzDAQAAB4ZPbwdh7aCbp0NarGVYjWu6UUgNAOwDFwLbdS5VnJ/QHVPLDf08+ujeCNE27I/oRNp+OlnuIQEAgINC0O0gpDXWttoyrKS0TH3gwBuZbgBwEKsOXyWuA9a7VSA1C/KRezg2J6yhv8h4s3fXx1B2fpHcQwIAAAeEoNvRMt0WbxlmmUJqUpZbn0w3WoYBgD3g99FVUVfF+Yk9mso9HJs1dWAbahroTUlZ+bRgyxm5hwMAAA4IQbej9el2tc0+3VK7MM2guuagG5luALBdO2JTRAGwoFruNDg0WO7h2Cw+UDtvXLg4/9OBeDp8OUPuIQEAgINB0O0grJbpdrVMpluzXZiTU3lgX+P0cgTdAGAHBdTu69YYBdRM1KtlkOjfzd5aE42WkgAAYFX4FHcQUgBq8Uy3syroLi6TpV2YZiE1fKkCAFsuoLb7PAqomdPbI9pTXV8PupSaQ1/8fUHu4QAAgANB0O0grFa9XN2nu1SWdmHMQ7UNMt0AYKt+ORQvCqj1bR1ETQK95R6OXfD3dqO5ozuI80t2XaTYxCy5hwQAAA4CQbejrem2UiE1S63prqmIWoU13ch0A4AN4oOWv0ZdE+cfikSW25yGhdWnoR2Cqbi0jKatiRadMQAAACwNQbeDKLJSplsK6ovN3DIs34Dp5SikBgC2bNvpZEq7VSCmQg9sjwJq5vbe6DDy9XSlE9cy6bu9cXIPBwAAHACCbgdh7Uy3nNPLpW0QdAOALVpxsLyA2v3dGqnfU8F8gv08xfpu9snWc2L9PAAAgCXh09xBWG1Nt6plGE/dKzXjtL08jerl+ma6UUgNAGzN5bQc2nMhjbhJw4MooGYxD3ZvTHe0CBCfLdPXnqQyXkAPAABgIQi6HYT1Cqndvv2i0lKZgm5kugHANq08fFX83691XWocgAJqlsKtJ+eNixAHafkgx5qjCXIPCQAA7BiCbgdRYKXp5Zq3X2TGdd35hQas6Va1DCsoRqYbAGzr4OhvR8qD7okooGZxzYN8aOqgNuL83D9OU2p2gdxDAgAAO4Wg20FYK9Pt6lw+vVyzeJtZ13S7G5DpLkKmGwBsx9bTSZR2q5CC/TxoYLt6cg/HIUzq25w6NPCjzLwimrPxlNzDAQAAO2VSBFZQUED79++nDRs2UFpamvlGBWZXqMr6WjrodnF2EmsRzV1MzaDp5apMdz4y3QBggwXUHujWmFxRQM0q+HFeMD5CfHb9EZ1I208nyz0kAACwQ0Z/qn/++edUv3596tOnD40bN46io6PF5Rx8BwUF0bJly8w5TjCRNNXb0kE3r5OzRK9uo1qGIdMNADYiLi2H9l1MFwctH+iBqeXWFNbQn57u21ycf3d9DGXlF8k9JAAAsDNGRWDfffcdTZ06lYYNG0bffvtthaqfHHAPGDCAVq5cac5xgrmml1she2KJXt25hcV6twxDITUAsDW/HCrPct/Zpi41rO0l93AcziuD2lDTQG9Kysqnj7ackXs4AABgZ4yKwD755BMaPXo0rVixgkaNGlXp+q5du9KpU1gbpcg+3RbOdGu2DTPv9PJSg1uGoZAaANgCfq/67cg1cX5iZFO5h+OQ+IDuvHHh4vxPB+LpUFyG3EMCAAA7YlQEduHCBRo+fHiV1wcEBFB6erop4wIbznRbYnp5nqqQmpce08ulbHg+ppcDgA3YEpNEGTmFFOLnSXe1rSv3cBxWr5ZBon83m7Y2Wr2sCQAAwFRGRWC1a9eutnDa6dOnKSQkxJRxgY1WL9cMus3aMsyYNd3IdAOALRVQ644CanKbPrw91fX1oEupOfTF3xfkHg4AANgJoz7dR4wYQV9//TXdvHmz0nU8rXzp0qV0zz33mGN8YAa85t6a08ul+zDn9HKD1nSr+3SXVqg3AACgNBdTb9HBuAzibosP9ijPsoJ8/L3daO7oDuL8kl0XKTYxS+4hAQCAHTAqAnv//feppKSEwsLC6N133xUVq5cvX04PP/wwdevWjerVq0czZ840/2jBKJrTvK0RdEu9us3Zp9uwNd3l23C8bc5sOwCAuf2iynIPaFeP6vujgJoSDAurT8M6hFBxaRm9tSaaSkrxOQIAAKYxKgJr0KABHTlyRFQvX7Vqlcgm/vjjj7Rx40aaMGECHThwQFQxB2XQDDxtdU23IdPLPVWZboYp5gCgVPy+9ttRqYAa2oQpyZzRHcjX05Wir2XSd3vj5B4OAADYOKMjMM5mf/PNN5SRkUHJycmUmJhIN27cEP25+TpQ3npuqwXd6unl8rQM0/wbUUwNAJRcQO1mbpFoEda/DT43lSTYz5PeGdFenP9461mKT8+Ve0gAAGDDjIrAnnzySTp48KD657p161JwcDA5O5ff3KFDh8Q2oKygm6d9O6umfluSu6plWLFM1ct5uQOKqQGALRVQc7HCezMYhvfLHS0CxMHbt9edRI0QAACwbtD9/fff08WLF6u8Pi4uTqzxBserXG656eWlek8vZ7eDbmS6AUB5zidn06HLGSLYvr8bCqgpER/AnT8uQnye7LmQpu6lDgAAYCiLRGHXr18nLy8UhFGKwpISWYJuc00v54y5FMDrU0hNcxp6AaaXA4ACrTh0u4BaiL+n3MOBKjQL8qFXBrcR59//M5ZSswvkHhIAANggV3033LBhgzhJuGXY9u3bK23HbcT48u7du5tvlGASKdtrjfXcFYNu8wS8eaoiavqu6dZsG5aP6eUAoMACamtUWVMUUFO+p/s0p40nrtOp61k0e+MpWjyxi9xDAgAAew26T58+TatXr1ZPueI13VzBXBNf7uPjQ/369aOFCxeaf7RgE9PL3V2dLBJ0Ozndnjaub9swZLoBQGk2nUykrPxiUUCtX+u6cg8HauDq4kwLxkfQ6MV76c/oRBrTKZkGhwbLPSwAALAhekdh06dPp+zsbHHiYiLffvut+mfplJWVJaqY//HHH9SmTfl0LJCfNM3bWkG3q6qgnmbVdFPkF6rWc7u5iAM7+kAhNQBQegG1CT1QQM1WhDX0p0l9W4jz764/SVn5RXIPCQAAbIhRUVhpaSlNnDjR/KMBy2a6XWxzTXduUbHelcslKKQGAEp0Ljmboq7cEN0kUEDNtkwd1JqaBXpTclYBLdh8Ru7hAACADbFOFAYOVUjN7NPLVe3C9F3Prbktr50EAFBalntQ+2Cq54cCaraEP1c+HBcuzv98MJ4OxWXIPSQAALARRkdhmzdvpsGDB1NgYCC5urqSi4tLpRM4eqbbvGu69W0XxpDpBgCl4QOIa46igJot69UyiB7sXj5DYdqaaBzYBQAAvRgVha1Zs4buvvtuSk5OpgcffFBMN58wYYI4z63CIiIiaObMmcbcNFiyermNtgyTvtTo2y6sQiE1BN0AoBB/RF+n7PxiahzgRX1aBck9HDDS9BHtqZ6vB11Ky6H//n1e7uEAAIANMCoKmzdvHvXo0YOOHTtGc+bMEZc9+eST9PPPP1NMTIwopta8eXNzjxVspHq5uTPduUZML5dahhUgCwEACuvN/WD3JuSMAmo2y9/Ljd4bHSbOf7XrEp2+niX3kAAAQOGMisK4fRhntXkKOU8tZ0VF5ZU8mzVrRs8//zwtWLDAvCMFoxWWWHd6ubuLZdZ0G1JIzROZbgBQkNjELDoWf1MUULuvWyO5hwMmGhYWQsM6hFBxaRlNWxtNxWb6vAMAAPtkVBTm7e1N7u7u4nzt2rXJw8NDZLclwcHBFBcXZ75RgkmKbDzTnW/Mmm5kugFAQX5RZbmHdAimer4ooGYP3hvdgXw9XSn6WiZ9v++y3MMBAAAFMyoKa9u2rch2Szp16kQ//vgjFRcXU35+Pq1YsYKaNEGRGEfNdLupgvvC4jL5ppejkBoAKERuYTGtO5ogzk/s0VTu4YCZcPX5d0a0F+c/3nqW4tNz5R4SAAAolFFR2NixY2nDhg1UUFAgfn7nnXdo586dIutdt25d2r17N02bNs3cYwUbWdPN0yctUb0chdQAwBb9cSKRsguKqWmgN/VqGSj3cMCMHujemHq2CKT8olJ6e91JKiszz8FmAACwL0ZFYa+//jrFx8eLaeWMK5lz0D1p0iR69tlnaceOHfT444+be6xgI0G3dD9ytgzzlKaXF2N6OQDI62fV1PIJPVBAzd44OTnRvHHhYnbVngtp9NuR8pZwAAAAmsqroJlB3759xUmSnZ1Nvr6+5rp5MEGBtaeXm3tNd6HxmW7OPgAAyOXU9Uw6cfUmubk40b1dUUDNHjUL8qFXBreh+ZvP0Pt/xtKdbetRXd/ypAQAAAAzexSWkpJCb7/9NtZ0K4h8LcPMvKbbmEJqyHQDgIxWHCzPcg/tEEJBtRCI2aun+zSnDg38KDOviGZvPCX3cAAAQGGcDQ2oP/74Y5o8ebIIrI8cOaK+LiEhQbQK45Zh8+fPp86dO1tivGATQbcS1nRL1cuR6QYAeeQUFNOG49fF+Yk9cCDanrm6ONOC8RHk4uxEf0Yn0rbTyXIPCQAAbHF6+ZkzZ6hfv36Unp6uLhTy0Ucf0U8//STWND399NOicvn48ePpjTfeoK5du1py3GAAKfi12ppuJbQMQyE1AJDZ7yeu062CYmoe5EM9UUDN7oU19KdJfVvQkl0X6d31JymyRQD5ebrJPSwAAFAAvaOwGTNm0K1bt+h///sfxcTE0MaNG6lFixY0depUUTRt+PDhdPbsWVq5ciUCbqVmuq28prvQ3NPL3QwvpCYF7AAAck0tn9CjsTg4DfZv6qDW1CzQm5KzCmjB5jNyDwcAAGwt0/3vv/+KaeVcnZyFhoaSq6urCLYfe+wx+u677yw5TjBHn25rTS+XqpebKcuMlmEAYGtOXsukkwmZ4mDnvV0byz0csBI+ODxvXARNWHqAfj4YT/d0bECRLTDLAQDA0ekdhfG08oiIiAqXdezYUd23G5TL6pluc/fpVmW6vd1dDV/TjUJqACCDFao2YcPCQijAx13u4YAV8VICnt3Apq89iRlXAACgf9BdWlpKbm4V1yZJP9eqVcv8IwOzkbK9Vs90m3lNt5e7sxHVy5HpBgDr4nXcvx9PEOcnRqKAmiOaNrw91fP1oEtpOfTfv8/LPRwAALClPt1RUVHk6elZoRc3r1Pbs2cP3bx5s9L248aNM88owSR20zLMmOnlqF4OAFa24XgC5RSWUMu6PhTZPEDu4YAM/L3c6L3RYfTcT0foq12XaGR4Awpt4Cf3sAAAQCYGRWGLFi2ie++9V3164oknRCXz2bNnV7icT/fdd5/Rg1q8eLFoPcYBfmRkJB06dKja7VevXk3t2rUT24eHh9OmTZsqXM8HBnSd/vOf/5BDrel2cZyWYepCapheDgBWxJ+JtwuoNUEBNQfGSwuGh4VQcWkZTVsbTcVm+kwEAAA7znT/888/ZA2rVq2iV199lZYsWSICbg70hw4dKiqj16tXr9L2+/btowkTJtC8efPo7rvvphUrVtCYMWPo6NGjFBYWJrZJTEys8DubN2+mp556SrQ3cwT20zLMkDXdyHQDgPVFX8ukU9ezxPvt+C6N5B4OyGzOPR1o74U08bz4bu9lmtSvhdxDAgAAGegdxfTv35+sYeHChTRp0iSRRWccfP/555+0bNkymjZtWqXtP/vsMxo2bJjoDc7mzp1L27Ztoy+++EL8LgsJCanwOxs2bKC77rpLtDxzBHK1DDPH9HIO3KXbMax6+e1Capx5QrYJAKxBynKPCAuhOiig5vDq+XnSOyPb01trTtIn287S0A4h1CTQW+5hAQCAlVknCtNTYWEhHTlyhAYNGqS+zNnZWfy8f/9+nb/Dl2tuzzgzXtX2ycnJIojnTLejsPqabtX9SNPazTG1nHkaUkhNlekuLSMxtQ8AwNKy8ovo9xPXxfmJkU3lHg4oxP3dGlPPFoGUX1RKb687KQ4EAwCAYzGokJqlpaWlUUlJCQUHB1e4nH8+c+aMzt9JSkrSuT1frsvy5cvJ19e32iJvBQUF4iTJysoS/xcVFYmTNUn3Z8r9ShW8nanUKuN3Ki1RZ6n5QIopWebs3PL94OLsJG63SM/p4i5UUuE2fD1dFbt/wHKwf5TPnvbR2iNXxYFCLqDWqWEtu/ib7Gn/yGnuPe1p5Bf7aM+FNFp56Ard26WhWW4X+0fZsH+UD/tI2YpsYP/oOzZFBd3WwNPUH3rooQpV2LXx+vA5c+ZUunzr1q3k7S3PtDCeMm+s7FzO+jrRwX176aoPWVyOeO65Eh/M/2PTZlLVVTNKWn75bbk6lYq1+PoqTySUP703/bWVfCt2u1PU/gHLw/5RPlvfR/yeszS6/L02wifLoPcrW2Dr+0cJhjZwot/jXWju7zFUHH+C/My4+gD7R9mwf5QP+0jZtil4/+Tm5tpe0B0UFEQuLi5iCrgm/ll7XbaEL9d3+927d4uCbFysrTrTp08Xxdw0M92NGzemIUOGkJ+fn9WPnvATbfDgwZX6pOvr3WN/ExUV08C7+lPzIB+r9Kh9O+pvcX7Q4KHk5a7/WmxtZ5KyiY7tJ18vDxox4k6DfvfNqO1ian3f/ndRg9pepNT9A5aD/aN89rKPjl+9SQkHDol6Eu9MvEu0jLIH9rJ/lGBISSld/PognbqeTfvyG9LnYzqafJvYP8qG/aN82EfKVmQD+0eaEW1TQbe7uzt17dqVduzYISqQs9LSUvHzlClTdP5Oz549xfVTp05VX8Y7hy/X9u2334rb79ix+g86Dw8PcdLGO1uuHW7KfUtrur093a0yfm+n22uvy5xdTLrPorLyNDkH7obeDn/55b+9hJwt/nfL+dyAmmH/KJ+t76Nfj5Sv5R4ZUZ+C/OyvUJat7x8l4IdvwfiONHrxXtp8Kpn+OZdOQzqEmOm2sX+UDPtH+bCPlM1NwftH33E5G5NC58BVqgxubpxhXrp0qVh7HRsbS5MnT6acnBx1NfNHH31UZKIlL7/8Mm3ZsoU++eQTse6be4ZHRUVVCtL5KAT383766afJ0Vi7ZZib8+37MbUvaX6hql2Ym+HHhzxV1c65eA0AgKVk5hXRxujyoPuhyCZyDwcULKyhP03qW945ZcaGGFF8DwAA7J/BURivaY6Li7NYC6YHHniAPv74Y5o5cyZ16tSJjh8/LoJqqVhafHx8hb7bvXr1Er25v/76a5HB/u2332j9+vXqHt2SlStXioqh3NPbkXDQKxXvtlbLMGdnJ3J1djJL27BcVdDtacQUdc22YQAAlrL+WII4uNcmuBZ1aVJH7uGAwk0d1Fos9UrOKqD5m3UXiQUAAPtiVBTGfbH/+usvshTOUl+5ckVUED948CBFRkaqr9u5cyd9//33Fba/7777xFpt3j4mJoZGjBhR6TafeeYZkaX39/cnR6LZtstame6KvbpLzdIyzMvN2YSgG5luALAMPpgr9eae2KOJxQ5Ig/3gWVjzxoWL8/zcOXgpXe4hAQCAhRkVhc2YMYPOnTtHjzzyCO3Zs4cSEhIoIyOj0gnkJ63ntmamm7mpSpYXmino9nY3fHq51KsbQTcAWMrR+Bt0NjmbPN2caWyXRnIPB2zEHS0CaUKPxuL89LUnKV/1WQcAAPbJqEJqHTp0EP+fPn1aTO2uCvfcBmUE3Tzb29WKQbeUVTc10y19EfFSrc82BH8JZgX4MgMAFvKzKst9d0QDu6lYDtYxbXh72hGbQpfScujzHefpzWHt5B4SAAAoKejm9daYQmcbpCyvNaeWM1dVMbWiYjOt6TYi6JYy3fnIdAOABWTmFtGf0eU1RiaigBoYiA/SzB0TRs/+eIS++veSOHAT2sC6bUkBAEDBQTdXCAfbIE3vtubUcubmaqbp5aqg28vdiDXdyHQDgAWtPXZNHNhsF+JLnRvXlns4YIOGdgih4WEhtDkmid5aE03rnu9l1VlpAABgHWZ5Z8/LyxMnUO70cndV1tfWCqnlm7SmG4XUAMDyBdS4TRhmf4Gx5ozuQH6ernQyIZO+23tZ7uEAAICSgm5u3cW9s7mVV61atcSJzz/55JOi8jgorEe3qrCZtbibKeg2x/RyBN0AYG5RV27Q+ZRbot7E6M4N5R4O2LB6vp70zsj24vwn287SlfQcuYcEAABKmF5+5swZ6tOnD928eZMGDx5M7du3V1/+ww8/0MaNG0VV87Zt25p7vGB0ptvK08tVQXexiX2688xQSA1VYQHA3KQs9z0dG5CfJwqogWnu79aYNhy/Tvsupotq5j8/HYnZEwAAjh50T5s2jZydnenYsWMUHl7ea1LCfbIHDhwotlm3bp25xgk2F3Sbu2UYMt0AoAw3cgrpz5PlBdQmoIAamAEH2Ny7e8in/4rAe/WRayIQBwAA+2BUJLZr1y566aWXKgXcLCwsjKZMmUI7d+40x/jARAUl8ma6TV7TLRVSM2p6ubSmG5luADCfNUeviQOaofX9qGMjf7mHA3aiaaAPvTq4jTj//h+nKSU7X+4hAQCAmRgViRUVFZGXl1eV13t7e4ttQEGZbitXQzVXn271mm5jMt3q6uXIdAOAGQuoHYpXtwnDFGAwp6f6NKewhn6UlV9Mc34/LfdwAADATIyKxDp37kzffPMNZWZmVrouKyuLvv32W+rSpYs5xgc2vqbb1D7dJq3pVk8vR6YbAMzjUFwGXUrNEUteRndqIPdwwM5wu7AF4yPIxdlJLGHYeipJ7iEBAIBca7rnzJlDw4YNo3bt2okK5m3alE+HOnv2LC1fvpzS09Np8eLF5hgf2GjLMFdn86zpvt0yDJluAJCflOXmgNsXBdTAAjo08Kdn+rWgL3depBkbYuiOloEo1gcA4IhB94ABA2jTpk30xhtv0Pz58ytc16lTJ/rxxx/prrvuMtcYwQZbhrmZe3o5WoYBgMwycgpp88nyzOPEHk3lHg7YsZcHtqYtMUkUl5ZD8zefoQ/HVq6hAwAAdhx081rt2NhYkeXm6uVJSUnqvtxNmzalkJAQS4wTjCRlmq09vdxcfbpNmV6OQmoAYE5rjlwT76nhDf0pHAXUwIL4QDNXM3/w6wOiPR23prujRaDcwwIAACMZHIlxq7CuXbvS2rVrxc8cZEdGRooTAm7lkauQmtQyrMjEPt1S9XJjppdL2XFkugHAHAXUftEooAZgaRxkT+hR/lzj3t3ScisAALA9BkdiLi4uIqNdUFBgmRGBWUkBp622DFNnuo3q010+BnxRAQBT7b+UTpfScsjH3YVGdUQBNbCOacPbUT1fDzHN/PMd5+UeDgAAGMmoSOzFF1+kr7/+mjIyMoy9X3CU6uUmBN089uLSMuPXdEuF1JDpBgAT8RRfNrpzQ6rlYVQ5FACD+Xu50dwxYeL8V/9eolPXK3eNAQAA5TPqm0NJSQl5eHhQy5Yt6d5776VmzZpV6tvNvUtfeeUVc40TTF3T7eIiU5/uMpOz3Mav6VZNL0f1cgAwQdqtAvpL1bppomq6L4C1DO0QQiPCQ2jTySSatuYkrXu+l2gtBgAAdh50v/766+rz3JNbFwTdjp7pVrUMMyHLLE0L5/ZjxowfhdQAwFwF1PgAYsdG/hTWEAXUwPpm39OB9pxPo5MJmbRsbxw906+l3EMCAABLB91xcXHG/Bo4UMswV2fTp5dL7cKMyXJrTknPR6YbAIxUWooCaiC/er6e9O7IUHpzTTQt3HZOZL+bBvrIPSwAALBU0J2Xl0efffaZ6MM9atQoQ38dHCTTfXt6ufEBb57Uo9uIImoMmW4AMEcBtcvpueTr4YoCaiCr+7o1ovXHE2jfxXRRzfznpyPlHhIAAOjJ4EiM125/9dVXlJycbOivggNOLzfHmm5j2oVVWNONQmoAYGIBtTGdG5K3OwqogXx42R737vZ0cxaB9+qoa3IPCQAA9GRUJMZ9umNiYoz5VbCyAvX0cturXi6t6TZ2ejmqlwOAKVKzbxdQk/olA8iJp5S/OriNOP/+n6fFcxQAAJTPqEhs0aJFtHLlSvrmm2+ouLjY/KMCC2S6XWwu6JbWdBvTLkz8nupvLiktM7lfOAA4ntVHroq2hZ0a16bQBn5yDwdAeLJ3cwpv6E9Z+cX03p9n5B4OAABYKuh+/PHHydnZmZ599lny8/Oj1q1bU0RERIVTx44djblpsJc13eqgW8bp5apMN0O2GwAMLaC28tBVcR4F1EBJuF3Y/PHh5OLsRFtOJVN0hnULpQIAgOGMWqAWEBBAgYGB1LZtW2N+HRxhTberk+nTy02sXq45pb6gqIRqeWA9JgDoZ8+FNIrPyCVfT1caFYECaqAsHRr40zP9WtCXOy/S6kvO9HxeEQW6uck9LAAAqIJRUcjOnTuN+TVwoJZh0vRyU/p0S5luY6uXO3N/bxdnKiwpRaYbAIwqoDauc0PyMvI9CMCSXh7YmjafTBTV9T/aep4W3IsZhgAASmXd9CdYHQeccmS6ldCnm6GYGgAYKiUrn7bHlnfomBjZVO7hAOjE9U7eHx0qzq+KukYHLqXLPSQAAKiC3pHY888/T1FRUeqfi4qK6Ndff6XU1NRK227fvp0GDBig702DNaaXu1g3U+Ounl4u35puzbZhUiV0AICarD5yTRRQ69q0DrUN8ZV7OABVimweQL3qlX/Oc+9ufNYBANh40L1kyRI6d+6c+uesrCyaMGECnTx5stK23MN7165d5hsl2GCfbvlbhjEP1d+NTDcA6FtA7ZdD5VPLJ6JNGNiAe5qWUj1fD4pLy6HPdpyXezgAAKCDSZFYWZnxWUywjgKZg25persxcguLTWoZVmF6OY7+A4Ae/j2fStdu5JG/lxuNjKgv93AAauTlSjT77vbi/Nf/XqJT1zPlHhIAAGjBmm5HWdOtUcnbmkF3sSnTywtLzTa9HJluADCogFqXhiYd8AOwpsGh9WhEeAiVlJbRW2uiqdiEA94AAGB+CLrtnPx9us0wvdyEoNtTlenGOjcAqElyVj7tOJMizmNqOdia2fd0ID9PV4pJyKJle+PkHg4AAGhA0O0wLcNsr0+3umUY1nQDgBWsOnxVZAq7N6tDrYNRQA1sSz1fT3p3ZHk184XbztGV9By5hwQAAMb06f7hhx/owIED4nx+fj45OTnRF198QevXr6+wnWbBNXDsQmqm9OmW1nSbVkgN08sBoGYcbK+UCqhFIssNtum+bo1ow4kE2nshXVQz//npSPFdDQAAbCjo3rp1qzhp0g64JXiTV0YVXm57I0vQre7TbUrLMHOs6ZYy3ZheDgBV+/dcKl3PzKfa3m40PAwF1MA28XevD8eG09BF/9K+i+m0Ouoa3d+9sdzDAgBweHpHYqWlpQadSkoQ5MhNs3K41YNuM0wvzy80vWWYNDU9XxXAAwDo8rOqgNr4Lo1QQA1sWtNAH3p1cBtx/v0/T1NKVr7cQwIAcHhY023HNKdUy1a9vLRMZNyNkVukahmGTDcAWFBiZh79fSZZnJ+AAmpgB57s3ZzCG/pTVn4xzd54Su7hAAA4PATddkxzPbWbi5MsQTcrKi2Vr2WYuk83Mt0AUHUBNT42GNk8gFrVqyX3cABM5uriTPPHh5OLsxNtOplEf51KkntIAAAODUG3I/TodnW2+hp7zcy6sb261S3DUEgNACyE+xlz0M1QQA3sSYcG/vRsvxbi/Iz1MZSZVyT3kAAAHBaCbjtWJFUut/LUcu3MujHrusvKytQtw0xb043p5QBQtZ1nUykxM5/qeLvRsLAQuYcDYFYvDWxNLYJ8KCW7gOZvPiP3cAAAHBaCbgfJdFsbT2mTkuuaBd30xb/DLXxMX9ONQmoAULUVqjZh93ZtpH6/ALAXXBRw3rhwcf6XQ/F04FK63EMCAHBICLodoUe3DJluns4ures2pm1Yvmo9t+nTy5HpBgDdEm7m0c6zKeI8CqiBvYpsEaheOsG9u6WlWwAAYD0Iuu2YtI5Zjky3uF8p6DZiPbU0tZynqWsWZTM+6EamGwB0F1Dr2SKQWtRFATWwX9OGt6NgPw+KS8uhz3acl3s4AAAOx1WfjZ588kmjMp3ffvutMWMCc2e6ZQq6XVXruo1Z051bqGoXZmK/XA/V76N6OQBULqBWPrUcBdTA3vl5utHc0WH0zI9H6Ot/L9HI8PoU1tBf7mEBADgMvYLuv//+2+Dq19aulg3VrOmWYXo5kzLUxqzpljLdprQLYyikBgC6/H0mhZKzCijQx52GdkABNbB/QzqEiGD7z5OJNG1tNK1/vrdoLQYAAAoJui9fvmz5kYDdZbrdTVnTbYbK5RVahiHTDQC6Cqh1ayTbeySAtc26J5T2XEijmIQs+nZPHD3bv6XcQwIAcAj4pmHHimTPdDupp3EaKk9VSM3k6eUopAYAWq5m5NKuc6ni/ITumFoOjqOerye9M7K9OL9w2zm6nJYj95AAABwCgm47Jnem25Tp5dKabi93M2W6UUgNADQKqJWVEfVpFUTNgnzkHg6AVd3XtRH1bhUoPhffXneSyvjFAAAAFmV0NLZ582YaPHgwBQYGkqurK7m4uFQ6gbyUEnQbM73c3Gu60SIFAKQZQKuirorzaBMGjohr7swbGyE+H/ddTKdfVa8HAACwHKOisTVr1tDdd99NycnJ9OCDD1JpaSlNmDBBnPfy8qKIiAiaOXOm+UcLBimQe3q5q/Etw8y+phuZbgAgoh2xyZSaXUBBtdxpcGiw3MMBkEWTQG96bXBbcf6DP2MpJStf7iEBANg1o6KxefPmUY8ePejYsWM0Z84cdVuxn3/+mWJiYigxMZGaN29u7rGCjWW63U1qGVZippZh6NMNALf9fLC8gNp93RqjgBo4tCd6N6Pwhv6UlV9Ms34/JfdwAADsmlHfOE6fPi2y2jyFnKeWs6KiIvF/s2bN6Pnnn6cFCxaYd6Rgc0G3q7P8LcPUhdQwvRzA4XEBtd3n08R5FFADR8ftwhaMjyAXZyfaHJNEW2KS5B4SAIDdMioa8/b2Jnd3d3G+du3a5OHhIbLbkuDgYIqLizPfKMEmg2719HID13SXlJbRheRscT4zt0j8bCwpU25Ippvvb//FdNpwPEH8X9X98+UH4zLoSJqT+N+UcQKA5f2iahPWt3WQmF4L4OhCG/jRs/1aiPMzN8RQZl55AgUAAMzLqGisbdu2Itst6dSpE/34449UXFxM+fn5tGLFCmrSxLgswuLFi0W23NPTkyIjI+nQoUPVbr969Wpq166d2D48PJw2bdpUaZvY2Fi65557yN/fn3x8fKh79+4UH1/+5cueyd0yzJjp5VtiEqnPgr9p7bHr4ue/TieLn/lyUzLdxaVlerUuk+5/wtID9PLK4+J/Xfcvbffwsij64byL+N+UcQKAZfH70K9R18T5hyKR5QaQvDSwNbUI8qGU7AKavzlW7uEAANglo6KxsWPH0oYNG6igoED8/M4779DOnTtF1rtu3bq0e/dumjZtmsG3u2rVKnr11Vdp1qxZdPToUerYsSMNHTqUUlJSdG6/b98+UcDtqaeeEuvLx4wZI068rlxy8eJF6tOnjwjMeYzR0dE0Y8YMEaTbO2lat9zVy/Xt080B6+SfjlJiZsWCLkmZ+eJyYwJaqZCaPtlufe/fEuMEAMvadjqZ0m4VUF1fDxrYHgXUADRnhM0bFy7O/3LoqpjhBQAA5mVUNPb666+LTDFPK2dcyZwD2kmTJtGzzz5LO3bsoMcff9zg2124cKG4jSeeeIJCQ0NpyZIlYir7smXLdG7/2Wef0bBhw+iNN96g9u3b09y5c6lLly70xRdfqLfhAwIjRoygjz76iDp37kwtW7YUWe969eqRw0wvd5G7T3fN0655avacjadJ15bSZXy9oVO4NQ84VBd063v//JhaYpwAYFkrVAXUHujWWP3eBADlIlsE0kTVDJDpa6PRZhMAwMzKq6CZQd++fcXJWIWFhXTkyBGaPn26+jJnZ2caNGgQ7d+/X+fv8OWcGdfEmfH169eL89zK7M8//6Q333xTXM7ZcK6qzvfBGfGqcAZfyuKzrKwsdbE4qWCctUj3Z8z95hUWi/9dnMqsPm5xv6rvtfmFNT9uvCZaO3OsiUNYvn7/hRSKbB5g0DjcXJzEuvJbeQXk6+5k0v0/+NVei40TlPX6AfvZR1fSc2nPhTRyciIa37k+ng8GwGtI2cy5f14f1JJ2nE6my+m5tHDrGXpjSBszjNCx4fWjfNhHylZkA/tH37EZFXRzkTSewj1q1Cid12/cuFGsr+a12fpKS0ujkpISUYRNE/985swZnb+TlJSkc3u+nPG09Fu3btH8+fPp/fffFxXVt2zZQuPGjaN//vmH+vfvX2VLNKkVmqatW7eKzLsctm3bZvDvxF3hqNeZ4i6co015Z8nakhLK7/9U7BnalF39OjEuRkZUc6XyrbsPUnqsYVlkF3KhInKiv7b/TfW8TLv/o1fLD8BYYpygrNcP2M8++l31XtjOv5Si9/9D0Ra7J/uF15Bj7J9RDZzom7Mu9M3uOPLPvECNfMxysw4Prx/lwz5Stm0K3j+5ubmWC7p5ejlnf6sKurkYGq/vXrlyJcmJM91s9OjR9Morr6iLvvFacJ66XlXQzZlwzQw6/62NGzemIUOGkJ+fH1n76Ak/0QYPHkxubm4G/e7WX6OJUpMoPCyURvRsStZ2+I9Y2p9ylZq3bE0jBraqdtvAuAz64XxUjbc5pG+kwRnk96J3Un5OIfXs3ZfahviadP99WwbSbj3WuxkzTlDW6wfsYx+JJSEf7+J7oheHd6HBofa/tMic8BpyrP0zgogSVp6gzaeSaVNaHfptXKRoLQbGwetH+bCPlK3IBvaPNCPaIkE3T+ueOnVqldcPHDiQFi1aZNBtBgUFib7fycnJFS7nn0NCQnT+Dl9e3fZ8m9xHnNeHa+L133v27KlyLLxWXVqvrol3tlw73Jj75ordzMtdnnG7q3q4l5Q51Xj/PVvVo/r+nqIYma78MOehQ/w9xXbcU9SYtmEl5FzlOPS9/2+f6EH9//OPRcYJliPnaxfk3Ud/xV6njJwiCvbzoCFh9RFAGAmvIcfZP++NCad9lzLo1PVs+uHgNXq2f0uz3K4jw+tH+bCPlM1NwftH33EZ9e3jxo0b5OurO2PIatWqRenphlW/5L7fXbt2FUXYNDPV/HPPnj11/g5frrk946Mh0vZ8m9we7OzZilOrz507R02bWj/za21Sf2zZCqm56t8yjAPUWaPKD45oh6rSz3y9MYGs1DasukJqmvdP1dw/F2az1DgBwLIF1BBwA9SMK/y/M7K9OL9w2zm6nJYj95AAAGyeUd9AuAf33r17q7yeW4Y1atTI4NvlKd1Lly6l5cuXi97akydPppycHFHNnD366KMVCq29/PLLYo32J598ItZ9z549m6KiomjKlCnqbbiyObci49u9cOGCqGzOa86ff/55cpjq5TK1DJOCfX37dA8Lq09fPtxFZIo18c98OV9vDA9Vprumaqx8+/NVbVOqu/+qxhlYy92kcQKAecWl5dC+i+nEx8Ae6IHe3AD6uq9rI+rdKlAcrJ6+9iSVlaFGCQCAKYyaXs69sbk9V48ePUSAy1XGGRdC46CWg1xu1WWoBx54gFJTU2nmzJmiGBqvv+agWiqWxm3KpPtivXr1ohUrVtC7775Lb7/9NrVu3VpULg8LC6vQU5zXb3NxtJdeeonatm1La9asEb277Z3cQbebgUE344B1UPtgavPuZuLZ8YsnchAbYlLmWJ9Mt6RxQHmhPJ6K+vaI9lTP15N6NA+odP88zsGhIaJK+bRVh+hajjM90bs5Am4ABfnlUHmW+8629ahh7SqqKAJAJU5OTjRvbAQNWbSL9l9Kp1+jrtID3XHgCgDAqkE3Z5t5TTSv6/7ggw9EIMt4GjcHzXfeeadRQTfjIF4zU62Je4Fru++++8SpOk8++aQ4OZqCEmX06ZamuRuyFl1qc92/bV2Tp2rfDrpr7jt6IfWW+D+8oT+N7tSw2m15XFwsLbJuGV3LIdp3MY1euKv6gnEAYB38ev/tyDVxfiKy3AAGaxLoTa8NbksfbIql9/+Mpbva1qN6fhVneAEAgH6Misa4yBi3z/r2229FtpvbffGJzy9btoy2b9+usxAZOFqmW/813ZpuFZT3F2feqqnhppCmlxcU1TyO88nlQXfLerX0vv22tcuPEBy+fKPGKewAYB1bYpIoI6eQQvw86c62deUeDoBNeqJ3M4po5E/Z+cU06/dTcg8HAMCxMt2Mp3nzWmtpvTUoT6Eqsyvbmm7V/RocdOeXB921PFzJ2QwFyTwNmF5+IaU86G5VV/+gu54nUYifByVlFdDhyxnUtzW+4AMopoBadxRQAzAWv3bmj4uge77YQ5tjksTBLF7yBQAAhsE3ETtWWKKMNd2FxWVGZbo56DYHfQupaU4vb2VAptvJiahXy0Bxfs/5NKPHCQDmwQfPDsZliAJqD/ZoLPdwAGxaaAM/erZ/C3F+5oYYyswrkntIAAA2R6+o5q677hKZ7b/++kv0vR4wYIBeRTi023mBdRWpgl251nS7Ops2vdzHw/Sp5YYUUuMvEqnZBQYH3ax3y0Bae+w67bmAoBtAKQXUBrSrR/X9UUANwFQvDmhNm08m0aW0HJq/OZbmjYuQe0gAADZFr2iMW0Vwz2wJn+fLqjtpbg+Omek2eXq5p37N5s1VSE2aWs5rQH0NvO9eLQPE/6euZ1H6rfLAHQCsj2e0rDmqKqAWiQJqAObg6eZC81QtNX85dJX2X0yXe0gAAPaX6dauGq6rijgouJCa7NXLjct0+5prermri16Z7ovSem4Ds9wsqJYHtQvxpTNJ2aIv8KiODYwcLQCYgtec3swtEi3C+repJ/dwAOxGZItAeiiyCf18MJ6mr42mLVP7iWAcAABqhjXddkz+6uWqNd0l8q7p9nRz1mtN9/mUbKODbta3dZD4H+u6AZRRQM3UdoMAUNFbw9tRsJ8HXU7PpUXbz8s9HAAAm2FUVBMfX/6lprr13J6enhQUFCTOg/XxFH+5p5dLLcOKjV7Tbd1MtzS93JB2YZp6twqipbvjxLpufvzx3AewrvPJ2XTocoYItjnoBgDz8vN0o/fHhNOkH6Jo6e5LdHdEfQpr6C/3sAAAFM+oqKZZs2Z6BRQcePft25dmzJhBvXv3NuauwEhSwC3rmm4X09Z0+3qaq3q5s159utWVyw1oF6apR/MA8Tcn3MwTWYDmQT5G3Q4AGGeFqoDawHb1KNjPU+7hANilwaHBNDKiPv0ZnUhvrYmmDS/0Rls+AIAaGPUu+e2331JERATVqVOHpkyZQosWLRKnF154QVzWqVMn+uyzz2jSpEkUFRUlqp3/888/xtwVmDi1XNY13epCajK3DNOjkBpPPb92I0+cbx1sXNDt7e5KXZrWFuf3nE816jYAwIQCakfKC6hNQAE1AIuaPaoD+Xu5ieKh3+yJk3s4AACKZ1Q0dv36dSosLKQLFy6I4PrFF18Up88//5zOnTtHeXl54sSB+NmzZ6l+/fo0Z84c848eqqQZ6MpdSE3zAIAc08ulQi/51WS6L6beorIyotrebhTo4270ffVtXVf8j9ZhANbFWbes/GJRQK2f6nUIAJZR19eD3h3ZXpz/dNs5ikvLkXtIAACKZlQ0tmTJEnr66aepdu3yrJ6mgIAAcd0XX3whfg4MDKQnn3ySjhw5YvpoQW9SoMu9sp1lKiYkrek2vmWY9TLd0npunlpuylpsXtfNuIK5oWvZAcD0qeUTeqCAGoA13Nu1EfVpFSTqpXA1c65lAgAAZgy609PTKTc3t8rrc3JyKDX19vTakJAQvBk7WOVyW2sZZkq7ME3hDf3FlLvs/GI6mZBp0m0BgH7OJmXTkSs3xEHG+7uhgBqANfAB6g/HhpOXmwsduJRBqw5flXtIAACKZVRE1r17dzGt/OTJk5Wui46Opv/+97/Uo0cP9WWxsbHUqFEj00YKBiksKVFQ0K2UNd1VB93nzRR0c4atV8tAcR6twwCs4xdVlntQ+2CqhwJqAFbTJNCbXhvSRpz/YFMspWTlyz0kAABFMioi46C6pKSEOnfuLKqTP/HEE+LE57t06ULFxcVifTfLz8+nnTt30r333mvusUM1pABTrvXcmtPLNSupy7mmu6CaPt2mtgvTNcV8N9Z1A1hcXmEJrTlaXkBtIgqoAVjd472aUUQjfzHDa+aGU3IPBwBAkYyKyLhyOWe5n3/+eUpJSaFffvlFnPg8X8bZbt5Gaht27Ngxev/99809dlD49HIp4C9WSsuwKjLdPL7L6TkmtQvT1Ld1edB9LP4G5agOIACAZfwRfV182W8S4C3WlwKAdXG7sPnjIsTyji2nkmhLTKLcQwIAUByjo5oGDRqos9mgPEoIuqXp5aVlRCWlZXoXN8qx1PTyKjLdVzJyxRR4XpfGlY9NxV/+G9XxEi3IDsVl0F3t6pl8mwBQfQG1B3s0lq1oJICjC23gR8/2b0GL/7lIMzacop4tg0R9EwAAKGdyRHbr1i2xZptPfB6UQVpHLev0co2AX99iaqWlZXSr0NzVy6svpHZ7armPWb60c3EZKduN1mEAlhObmEXH4m+KDBtXUgYA+bw4oDW1qOtDqdkFNG9TrNzDAQBQFKMjssOHD9Ndd91FderUobCwMHHi8wMGDKCoqCjzjhJstJDa7QBW33XduUUlol+2NQupabYLM5c+rVT9ulFMDcBiVhwsz3IP6RBM9XxRQA1ATlw/haeZs5WHr9K+i/j8AwCQGBXVHDx4kO68805yd3cXPbnbt28vLudsN6/t7tevnyieplnBHGSaXi5npttZI9NdTeVwXeu5OXMlBcvmKqSWX8X0cnO1C9PEFcy53ffZ5GxRzRUVlQHMK7ewmNYfSxDnJ/ZoKvdwAICIejQPoIcim9DPB+Pp7bUnacvUfurPYAAAR2ZU0P3OO+9Qw4YNac+ePaIHt6bZs2dT7969xTbbtm0z1zjB2OrlMma6eao2r+Pm9dz6tg1TtwvzdBXTtM1BCt6LS8tE0TQu+mKJdmGa6vi4U1gDf9Gre+/FNBrbGVNfAczpjxOJlF1QTE0DvdVt+gBAfm8Nb0c7YlPocnoufbr9HE0fXp6YAQBwZM7GZrqfffbZSgE3Cw4OpmeeeYYOHDhgjvGBDRdS05xiru+abnW7MHfzTC3XrF6ua5o7ryG/mGr+oLtC6zBMMQcwu59VBdQm9GiCAmoACuLn6UZzx4SJ89/sjqOYhEy5hwQAIDujIjJnZ2fRi7sq3MObtwH5SMGlnNPLNSuY67um29ztwjQLqbGCoorjSMzKp9zCEjGdvWmgD5mTVExt74U0KpMWqgOAyU5dz6QTV2+Kg3oooAagPINDg2lkRH0x0+2tNdEGtw4FALA3RkVkvXr1osWLF9OVK1cqXRcfH0//+9//xBRzkI9SMt23e3UbOL3cTEXUGE9xlzLu+cUlOouoNQvyUR8gMJeuTeuIqe3JWQXq+wEA8xVQG9ohhIJqecg9HADQYfaoDqJt2KnrWfTNnji5hwMAICujIpsPP/xQFEtr164djR07ltq0aSMuP3v2LG3YsIFcXV1p3rx55h4rGKBIYZluQ6eXm6tdmGa2u6ikuFKm2xKVyyVcPIaLyvD0cm4d1jrY1+z3AeBocgqKacPx6+L8xMgmcg8HAKpQ19eD3h3Znt74LZo+3XZOHCRrHmTeGWUAALbCqIisc+fOYl33sGHD6Pfff6f33ntPnDZu3Cgu4/XcHTt2NP9oweYy3W6uTgZOLy8S//uYMdNdXdswddBt5vXckj6qdd1oHQZgHr+fuC4OzvGX954tUEANQMl4+Qd/DvJn7/S10VhqBQAOy+iILDQ0lNatW0dZWVmUmJgoTnx+7dq11LRpU7p+vTwTAQ4edEuZ7mLDMt2+Fgu6SyzeLkxXMbUDl9L1zvYDQM1Tyyf0aGy2DgcAYBn8Gv1wbDh5ubnQgUsZtOrwVbmHBAAgC5MjMi6YxhXL+SQVT1u0aBE1btzYHOMDIxUoZHq5dP/6twwrMfua7oq9uisGvudTsi0adIfW96MAH3fKKSyh41dvWuQ+ABzFyWuZog0fv6/c2xWfMQC2oEmgN702pHwZ4gebYik5K1/uIQEAWB1KjNsppWS6XQ1uGWaZ6eXuOjLd6bcK6EZu+f21qGuZdWbcykjqIYzWYQCmWXGovHjnsLAQcTALAGzDE72bU8dG/pSdX0yzNpySezgAAFaHoNtOKSXoVkLLMOahynRrFlKT1nM3quNF3mbsC15d6zAAMA4vPUEBNQDbxF1E5o+PEO05t5xKoi0xiXIPCQDAqhB02ymlBd36Z7otM71cVyG1C6mWXc8t6dO6rvifp5dnqQrFAYBhNhxPoNzCEmpZ14cimwfIPRwAMFD7+n70XP+W4vyMDacoUzXTDADAESDotlNFilvTbdj0cvO3DKs8vdyS7cI0NaztJSotl5SW0YGL6Ra9LwB7xBWPbxdQa4ICagA2asqAVmI5V2p2Ac3bHCv3cAAArEbvyObo0aN63ygql8tPms4tf6bbycBCasUWWdOtq5CapduFaeKWKXFpOWKK+ZAOIRa/PwB7En0tk05dzxLvZ9yCCABsE38Wzx8XQfd/tZ9WHr5K93RqQL1ali/BAgCwZ3pHNt26ddM7u8BZCWQiFDK93MXGppfnW69lmKXbhWm3DvvxwBXajXXdAAaTstwjw+tTbW8UUAOwZT2aB9DDdzShnw7E0/S1J+mvqf3UB8YBAOyV3pHNd999Z9mRgFlJa5dlz3S7Gtqnu8RC08tVhdRU4+CM+vXMfKsF3T1bBpKzE9Gl1By6fjOPGtT2svh9AtgDroPw+4nr6qnlAGD73hrWjrafTqEr6bn06fZzNH14e7mHBABgUXpHNo899phlRwJ2WUjN8D7dqpZhZq4m7uGmynSrppdLWe6gWh5WyZz5e7lRx8a16Vj8TdpzIY3u74YewwD62HAsgfKKSsTBse7N6sg9HAAwA19PN3p/TBg9/UMUfbM7jkZFNKCwhv5yDwsAwGJQSM3e13TLPr3cSe+WYTwFXVpzbe6WYZ6qTHe+anr57fXclunPXdW6brYH/boB9F6q9LNqavlEFFADsCuDQoPp7oj6osjom79F670MDQDAFiHotlNKyXS7GrCmO0dVRM0ShdS0M93WahemK+jmYmqlpfpl/gEcGbfZO5OULWoyjO+CAmoA9mbWqA5iJtjpxCyR8QYAsFcIuu2ULbYMkyqXe7o5qwuwWaqQmrXahWnq3KQOebu7UHpOoQgkAEDPAmoR9cnf203u4QCAmdX19aAZd4eK84u2nxNdPgAA7BGCbjullEy3IS3DpKC7lpmz3LoKqd2uXO5L1sL7IrJ5gDrbDQBVy8wroo3R5QXUHopEATUAezW+S0Pq2zpIfD5PWxONmWAAYJcQdNsp5QTdBmS68y0XdHP2nOUXlYhs95WMXKtPL5dahzG0DgOo3vpjCaLGQ9tgX+rSBAXUAOwV12r4cGw4ebm50MG4DFoVdVXuIQEAmB2CbnsvpGZLQbeU6TZzETXtTPfltFxRuIWD+2A/D7Kmvq3riv8PxaVX6BkOABULqElTyydGooAagL1rHOBNrw1pI85/uCmWkrPKW3oCANgLBN323qdb7jXd6j7d+k8v9zFzu7CKa7pLNSqX17L6l/k2wbXEGjbO4B25csOq9w1gK47G36CzydlihsqYzg3lHg4AWMETvZtTx0b+lJ1fTDM3xMg9HAAAs0LQbaeUt6Zb/+nl5m4XVrF6eUmFoNvaOMhH6zCA6kltwu6OaCAqGwOA/XNxdqL54yPI1dmJ/jqVTJtPJso9JAAAs0HQbadTM5U2vVyfPt3WKqQmR7uwqlqHAUBFmblF9Gd0onpqOQA4jvb1/ei5/i3F+Zm/nxLvBwAA9gBBtx0qLi2jMtVsbrmnl7sqZE23ZiE1OdqF6SqmFp2QSTdzC2UZA4BSrTl6TRwcaxfiS50b15Z7OABgZVMGtKIWdX0oNbtArO8GALAHCLrtkGaAK3em292QlmGq6eU+Fsx05xWV0CWZM90h/p7Uul4tcWBk/8V0WcYAoNRZOr8cile3CUMBNQDH4+nmQgvGR4jzXMl8H2aFAYAdQNBtx+u5lZDpNqZ6ua9Fgu7ycVy7kSeyaHwwgqulyqVPa7QOA9AWdeUGnU+5JVoHjUYBNQCH1b1ZAD18R/nykunrTlJeIbp9AIBtQ9Btx0G3s9Pt6d021TLMEkG3ano5twpjLYJ8RNEWuaCYGkBlUpuwezo2ID9PFFADcGRvDWtHIX6edCU9lxZtPyf3cAAATIKg257bhck8tbxi0G1AyzALBN2equnlErmmlksiWwSKCq3xGbkUn54r61gAlOBGbiH9qapWjAJqAODr6UbvjwkT55fuvkQxCZlyDwkAwGjyR2VgdurK5TJnucUYXJXVMkwpQTdn8zs3KS8StQdTzAFo/fFEMUunQwM/imjkL/dwAEABBoUG090R9Yknqb35W7Re3yUAAJRI/qgMLNiju2J2V9aWYRrrzGueXu5msUJqSgm6WZ9WdcX/aB0Gjo6LCq48fFWcn9ADBdQA4LbZ93Sg2t5udDoxi77ZHSf3cAAAjIKg256DblXlcJtb022JTLfWVHtFBN2qYmp7L6ap15oDOKKLWUSX0nLJ292FRndqIPdwAEBBgmp50LsjQ8V5Xtsdl5Yj95AAAAyGoNsOSQGuMtZ0G9AyTJ3pNn+GntdPS/hcExkrl0s6NvIXldpv5hbRqetYqwaOhw82HYzLoI3x5e9VozrWF+s4AQA0je/SkPq2DhI1a6atiaZSHKgGABsjf1Smw+LFi6lZs2bk6elJkZGRdOjQoWq3X716NbVr105sHx4eTps2bapw/eOPPy6mK2qehg0bRvY/vdzZZjLd3J9XWtNt7unlW2IS6c6Pd96+LyIa+MkucbmcuLL8HS0DxXms6wZHw6+/Pgv+poeXRdHlW+XvE9tjU2R/XQKA8vD3tg/Hhot2gnygjvt3AwDYEvmjMi2rVq2iV199lWbNmkVHjx6ljh070tChQyklJUXn9vv27aMJEybQU089RceOHaMxY8aIU0xMTIXtOMhOTExUn3755ReyVwUlthd089HrYtWRa3NOL+cv8JN/OkqJmfkVLk/KzBeXy/0FH63DwBFV9brMuFWoiNclAChP4wBvem1IG3H+w02xlJxV8f0DAEDJ5I/KtCxcuJAmTZpETzzxBIWGhtKSJUvI29ubli1bpnP7zz77TATUb7zxBrVv357mzp1LXbp0oS+++KLCdh4eHhQSEqI+1alTh+x/TbfttAyTppYzbzcXs01dnbPxtMhsa5Mu4+vlXE8treuOunyD8gpLZBsHgLXYwusSAJTpid7NxdKs7PximrmhYnIFAEDJzF+xygSFhYV05MgRmj59uvoyZ2dnGjRoEO3fv1/n7/DlnBnXxJnx9evXV7hs586dVK9ePRFsDxgwgN5//30KDCyf2qutoKBAnCRZWVni/6KiInGyJun+DLnfvIIi9Xpqa49Xm1NZiTrTXd1Ybt4qP2Lt4+FCJSXFVGKG+JOnoGln0jTxV3q+fv+FFIpsHmC1/aOpsb87hfh5UFJWAe2/mEJ9VZlvMA9T9w+YnzVel2A+eA0pmyPun/dHh9LYLw/QX6eSaePxazSsQzAplSPuH1uDfaRsRTawf/Qdm6KC7rS0NCopKaHg4IpvoPzzmTNndP5OUlKSzu35cglnwseNG0fNmzenixcv0ttvv03Dhw8XAbuLS+Ws6rx582jOnDmVLt+6davIusth27Ztem97OJVLhblQZkZ6pfXt1nZTHLtwpYKi4mrHcvVW+XauZdVvZ4gjaeWPQ0227j5I6bFlVts/2pp6OFMSOdNPW6Mo+xx6kFqCKfsHzMuar0swH7yGlM3R9s+A+s60NcGZ3llznG5dLCFvRX2brczR9o8twj5Stm0K3j+5ubl6bafwtynzePDBB9XnudBaREQEtWzZUmS/Bw4cWGl7zrRrZs850924cWMaMmQI+fn5kbWPnvATbfDgweTmpl+Bseyoa0QXTlODkGAaMaIzySn9VgHNOrqLSsqcxIGOqvrvcvaLTkZRkH8tGjGit1nuOzAug344H1XjdkP6RpqU6TZ0/2griU6kg6tPUmKZP40Y0dOo2wDL7R8wH644fPyvs0Tn4y36ugTzwWtI2Rx1/wwsKqF7/rdftBo8WtqUPhzRgZTIUfePLcE+UrYiG9g/0oxomwq6g4KCROY5OTm5wuX8M6/D1oUvN2R71qJFC3FfFy5c0Bl08/pvPmnjnS3XDjfkvktFUywiT3cX2Z+gXp4aPzi7klsVxd1Uhcuplqf5HuOerepRfX9PUTRNV76MH6UQf0+xnYtGSzFjmPLc6NeWZ2qcpNikbMosKBU9ScG85HztQrkzSVn09tqTdDT+ZrXbmfN1CeaD15CyOdr+4b91wb0d6b4l+2n1kQQa27kR9VLw8ixH2z+2CPtI2dwUvH/0HZf8lbY0uLu7U9euXWnHjh3qy0pLS8XPPXvqzgDy5ZrbMz4iUtX27Nq1a5Senk7169cne6SsQmq3vzRXV8FcKqTGfavNhb+wzxoVKs5rf3WXfubr5f5iz0F2+/rlMyj2XUyXdSwA5pZbWEzzNsXSyM/3iIDbx92F7uvaSLwGlfy6BABl694sgB65o6k4P33dSRQjBQBFkz8q08LTupcuXUrLly+n2NhYmjx5MuXk5Ihq5uzRRx+tUGjt5Zdfpi1bttAnn3wi1n3Pnj2boqKiaMqUKeL6W7duicrmBw4coMuXL4sAffTo0dSqVStRcM0ecfstpbUM0zformXGoJsNC6tPXz7cRWTONPHPfDlfrwR9Wqn6dZ9PlXsoAGbz95lkGrzwX/rq30uiGvmwDiG0/bX+9J/7OtrE6xIAlO3NYW3FjLYr6bm0aPs5uYcDAGAb08vZAw88QKmpqTRz5kxRDK1Tp04iqJaKpcXHx4uK5pJevXrRihUr6N133xUF0lq3bi0ql4eFhYnrebp6dHS0COJv3rxJDRo0EGuzubWYrinkdpXpVkDQ7aqRrSrUJ+g2Y49uCX+BHxwaQofiMiglO5/q+XpSj+YBisqk9Wldl5bujhP9usvKyqpc+w5gC3hJx5yNp2hzTHlBy4a1vei90R1oYPvgSq9LrlLORdN4DTemlAOAIXw93ej9MWH01PIoWrr7Et0d0YDCG/nLPSwAAOUH3Yyz1FKmWhsXP9N23333iZMuXl5e9Ndff5EjkYJbdx2V2a2Ng0ee5s5jqq5X9618y2S6JfxFvmdL3S3ilKBHswDxOF3PzKe4tBxqUbeW3EMCMBhns3/cf5k+3npOHEjj191TfZrT1EGtydu98mubr+diaVylnP9HwA0AhuKDeXdH1Kc/ohPprTXRtGFK7wqz7AAAlADvSnZISZluzXXdxTJML7cVXu4u1LVpHXF+z4U0uYcDYLCYhEwa+7+9NHvjafF67tS4Nm2c0ofeHtFeZ8ANAGAus+/pQLW93eh0YpbIeAMAKI0yojKwUCE1ZWSNpIrlRTJNL7cVfVqXV17lKeYAtoJfu+9tPE33fLGHoq9lkq+nq5juuXZyLwptYN0WiwDgmLgg6YyR5YVTF20/T5dSb8k9JACAChB02yEpuFVOprt8HIXFNU8v93HQTDfro2p3sv9ierWzAgCUgGsPbIlJosELd9GyvXFUWkY0qmMD2vFaf3r4jqbkjKniAGBF47o0pL6tg0TiYfrak1TKb0oAAAqhjKgM7Hp6udS6zNotw2xNWEN/8vdyo+yCYopOyJR7OABVunYjlyb9EEXP/XSEEjPzqUmANy1/sgf9d0JnUagQAECOGjIfjg0nLzcXOhiXQSsPX5V7SAAAasqIysCsCtSF1JS1pluOlmG2hItI9Va3DsMUc1AenoGx9N9Log3Y9tgU8dp+4a6WtPWVftS/TV25hwcADq5xgDe9PrStOD9vUywlZ+XLPSQAAEEZURlYKNMtf/Vy5ipNL8ea7hr1Vk0xR9ANSnMs/gaN+mIvfbAplvKKSqh7szq06aW+9MbQduTppoz3GgCAx3s1o46Na4tZYzPWx4ilMAAAckPQbYeUNr1cWtMtZ8swW9G3VXm28Gj8DcpRHYgAkFNmXhG9u/4kjftyH8UmZokKwQvGh9OqZ3pS62BfuYcHAFBp1hi/R7k6O9HW08m0OSZJ7iEBACDotkdKC7qlKupFqnHpgunl5ZoEelPjAC8qLi2jg3Hpcg8HHBhnhzaeuE6DFu6inw7EEyeLuFDRjlf70wPdm6BQGgAoVrsQP5p8Z0txfuaGU5SZWyT3kADAwSkjKgOzkqZxK6ZlmCrTXVyqO+jmCqM5hZheLumjynbvOY+gG+QRn55Lj313mF785RilZhdQiyAfWvF0JC28vxMF1vKQe3gAADWaMqAVtazrQ2m3CuiDTaflHg4AODgE3XZIsS3DqphenltUIrJozNEz3Zqtw/ZcSJV7KOCAs2QW/3OBBn+6i/49lyqKMU4d1Jo2T+1LvVTPSwAAW+Dh6kILxkeI879GXaO9F1ArBQDko4yoDCwzvdxFGcWN3FTBf1XTy6X13Lz+ykMhBwrk1KtlIDk5EZ1LvoXKq2A1hy9n0MjPd9N//jpLBcWl4nm4ZWpfmjqojfjyCgBga7o1C6BH7mgqznPv7rzCErmHBAAOChGOHVLsmu4qqpdrVi7nPpuOro6PO4U39BfncWQeLO1mbiG99Vs03bdkP51PuUWBPu608P6O9PPTkdSibi25hwcAYJI3h7Wl+v6eFJ+RS59uPyf3cADAQSkjKgOz4iyVMquX1xB0Y2q5GlqHgTUKpa09eo0GfrKLVkVdFZc92L0x7XitP43r0ggHwADALvh6utH7Y8LE+W92X6KT1zLlHhIAOCBlRGVgoUJqzgrr0617TTfahVXWV72uOw09RsHsLqXeooe+OUiv/nqC0nMKqU1wLVr9XE+aPz6Canu7yz08AACzGtg+mEZ1bEClZURvromuMgkAAGApyojKwK6nl7vVOL28vJUHgu7bujStI9a3p2QXiCm/AOZQUFxCi7afo2GLdtO+i+niOfbG0Lb0x4t9qXuzALmHBwBgMbNGhVJtbzeKTcyipbsvyT0cAHAwyojKwEKF1JSxe6VxVFlIraC8sAnahd3m6eZCPZqXB0GYYg7msO9iGg1ftJsWbT8vZsP0b1OXtr3Sn164q5ViDtABAFhKUC0PmjEyVJzn90Ge8QMAYC34pmWHlNoyrIjndelwK7880+2DTHcFfVvfnmIOYKz0WwX06q/HaeLSg3QpLYfq+nrQFxM70/dPdKcmgd5yDw8AwGrGdWkoPls5OTFt7UkqreJ7CQCAuSkjKgOz4Q+QYtWHiK0VUvNF0K2zmNqBS+nq2QsAhrwXrDocTwMX7qK1RxNEGzpunbP91f50d0QDFEoDAIfD73sfjg0nLzcXOhSXQSsPlxeRBACwNGVEZWD2ImqKCrpdVWu6qwgcs1G9XKf2IX6ifVNuYQkdv3pT7uGADTmfnE0PfL2f3lpzkm7mFlH7+n60dnIvmjsmjPy93OQeHgCAbBoHeNPrQ9uK8/M2xVJSZr7cQwIAB6CMqAzM3i5MkWu6q8h052j06YbbnJ2dqJe6dViq3MMBG5BfVEL/+esMjfh8Nx2+fENkc94Z0Z42TulNnZvUkXt4AACK8HivZtSxcW1x0H/Ghhh0CQEAi1NGVAZmozkNWaoarpTp5WgZZlrrMIDq7DqXSkM+/ZcW/3ORikrKaFD7erT9tf40qV8Ldds+AAAgcnF2ogXjw8nV2Ym2nU6mzTFJcg8JAOwcvonZa49uV2fFrNl0rbFlGILuqvRWFVM7cS2TslQF5wA0pWTn04u/HKPHlh2i+IxcCvHzpCUPd6Wlj3ajhrW95B4eAIAitQvxo+fvbCnOz9xwim7mFso9JACwYwi67YzS2oXpM71cHXRjenklHDS1CPKhktIy2n8xXe7hgMIKpf144AoN/GQXbTxxnZydiJ7s3Vxkt4eFhSjmoBsAgFK9MKAVtazrQ2m3CujDTbFyDwcA7JhyIjOwy3ZhhlQvR8sw3fqost17McUcVE5fz6JxX+6jGetjKDu/mCIa+dPvU/rQzFGhmDECAKAnD1cXWjA+QnR3+DXqGj5nAcBilBOZgd1mum8H3dWv6UbLsOpbh+05jy8Dji63sFhkY0Z9sUdUtOcAe/aoUFr3fG8Ka+gv9/AAAGxOt2YBop0im772JOUVlsg9JACwQ8qJzMCs1cuVlenWc003ppfr1LNloJg6fCkthxJu5sk9HJDJ9tPJNHjhv/T1v5fEcoMR4SGi5/bjvZuLokAAAGCcN4a2pfr+nqIuxqfbz8k9HACwQ8qJzMC8mW4FBd3SWFBIzTh+nm6itQnbi2y3w0nMzKPnfjxCT/8QJQ668Dr/ZY93o/891JVC/D3lHh4AgM3z9XSj98eEifPf7L5E0dduyj0kALAzyonMwLzVy5U4vby48vRyDsTzi8rHjKC75tZhu7HezGFwNnvZnjga9Mku2nIqSWSzn+3fgra92o8GtAuWe3gAAHZlYPtgGtWxAZWWEb215mSViQIAAGMoJzIDu8103+7TXfkDLEeV5WYopFa1Pq3riv/3XUgTVavBvp28lkmjF++h9/44TTmFJdS5SW3648U+NH14e/J2x+sEAMASZo0KpdrebhSbmCWW8gAAmItyIjOw20Jq1fXplqaWe7o5q4NzqKxT49rk7e5C6TmFFJuUJfdwwEKy84to9u+nRMAdk5BFfp6u9MHYMFrzXC9qX99P7uEBANi1oFoeNPPuUHH+sx3n6WLqLbmHBAB2AlGOnVFiy7Dq+nRjPbd+eH/e0SJQnEdLE/tTVlZGW2ISadDCXfT9vstieuPoTg1ox2t30kORTckZhdIAAKxibOeG1Ld1kEhicDVzzC4DAHNQTmQGdj+9XFfLMKldGIJu/VuH7UYxNbty7UYuPb08ip776SglZxVQ00Bv+vGpHvTZg52prq+H3MMDAHAoTk5O9OHYcPJyc6FDcRn0y+F4uYcEAHZAOZEZmEWBIgupOVU4IKApG+3C9MZH3tnhyxmUX4Q+oraOZ358teuiaAO240yKeJ28OKAV/TW1H/VVreEHAADraxzgTa8PbSvOz990hpIy8+UeEgDYOOVEZmD3me7i0qoLqSHTXbPW9WpRPV8PUe396JUbcg8HTHA0/gaN+u8emrf5DOUVlVCP5gG0+eW+9NqQtuTp5iL38AAAHN7jvZqJeiqcHJixIUYsAwIAMJZyIjNwgD7dmF5u6pS3PmgdZtMy84ronXUnafyX++hMUjbV8Xajj+6NoFXP3EGt6vnKPTwAAFDhNo0LxkeQq7MTbTudTJtOJsk9JACwYcqJzMBug+7bfbpRSM1UfVRTzFFMzbZwhmTD8QQa+Mku+vlgPHHC5N6ujUShtPu7NRYHVAAAQFnahvjS83e2FOdn/R5DN3ML5R4SANgo5URmYBaFJSXKXdNdXfVyrOk2qJjayYRMupGDD39bcCU9hx5ddoheXnmc0m4VUIu6PvTLpDvo4/s6UoCPu9zDAwCAarwwoBW1qleL0m4V0gd/xso9HACwUcqJzMAspCncNtMyTDW93AeZbr0E+3lSm+BaIlO6/1K63MOBGmadfPH3eRry6b+i4jy/Jl8d3Eas3e7Zsrz9GwAAKJuHqwstGB9OPCFp9ZFrtAcdRADACMqJzMC808sVlOl2VY2FW12WaPW7lDLdvgi69YbWYcp38FI6jfh8N3289RwVFJdS71aBoir5SwNbiy9wAABgO7o2DaBH7mgqzr+97iTlFaKDCAAYRjmRGZgFf8FXWqZbml6uK9utbhmGoNvg1mF7LqTKPRTQwlP+3/ztBD3w9QG6kHKLgmq506IHOtFPT0VS8yAfuYcHAABGenNYO6rv70nxGbm0cNtZuYcDADZGOZEZ2H0hNV3rutUtwzzdrD4uWxXZPFBUU72akUfx6blyDwdUhdJ+O3KNBi7cRb9GXROXTejRhHa8eieN6dwQhdIAAGwcJwc+GBsmzn+7J46ir92Ue0gAYEOUE5mBWUhBrZKml2sG3cVabcNutwzDlFt98fr3Lk3qiPO7ke2W3cXUWzRh6QF6ffUJysgppLbBvvTbcz1p3rhw8vfGwSQAAHsxoF0w3dOxgVgu9+Zv0Tpr1QAA6KKcyAzMorC4RHGZbu51ySem/QF1u2UYghNDoHWY/PKLSmjhtnM0fNFuOnApgzzdnOmtYe3oj5f6ULdmAXIPDwAALGDWqFCq4+1GZ5Ky6et/L8k9HACwEcqJzMBuC6lVaBum1asbLcNMK6a290J6peJ0YHl8sGP4Z7vp8x3nxeySO9vWpW2v9KfJd7asMLMDAADsS2AtD5pxd6g4/9mO82K2EwBATfDt0M4osWUYkwKRqjPdmF5uiI6N/MnX05Uy84ooJiFT7uE4DO6z/cqq4/TQNwcpLi2H6vl60OKJXei7x7tT4wBvuYcHAABWMLZzQ+rXpq5IJExfc5JKcfAbAGqgrMgM7LKQWsVe3WUVik/dXtON6eWGtmHr2aK81/MeTDG3OP5CtfJQPA38ZBetO5Yg+rU+1rMpbX+tP42MqI9CaQAADoTf8z8YE0be7i506HIG/XI4Xu4hAYDCKSsyA5MVKLCQGnNVTS/XzHRze7Ni1dFhTC83fl33HvTrtqhzydl0/1f7adrak2JmQWh9P1r3fG+aMzqM/FB1HwDAIfHspteHtBXn5286Q0mZ+XIPCQAUTFmRGdhtpluaXq7ZMkyaWs5JQm83TC83VB/Vuu4jV25QXmF5AT0wH35MF2w5QyM+201RV26IjMa7I9vT71N6U6fGteUeHgAAyOyxXs3E50F2QTG9uz5GzOADANBFWZEZ2GX18grTyzUKqUlTy33cXclZVd0c9Nc8yIca+HuKAxk8vQ3MZ+fZFBqyaBd9ufOimI0xODSYtr3an57u20JM7QcAAODOLAvGR4hisdtjk2nTySS5hwQACoVvj/bap1uhmW5pOnnFImqYWm7smjK0DjOvlKx8emHFUXr8u8N0NSOP6vt70tePdKWlj3ajhrW95B4eAAAoTNsQX5p8ZytxftbvMXQzt1DuIQGAAikrMgP7bRnm6lTl9HKs5zZen9Z1xf+7sa7bJNx27Yf9l0WhtD+jE4knXjzVp7nIbg/pECL38AAAQMFeuKsltapXi9JuFdIHf8bKPRwAUCBlRWZg/y3DdEwvR6bbeL1allcwj03MotTsArmHY5NOXc+kcV/uo5kbTol1edyO7fcpfUQfVjw3AQCgJh6uLrRgfLioUbP6yDUUOAWASpQVmYH9Zrp1tAzD9HLTBdXyENW02b6L+JA3RE5BMb3/x2m654u9dOLqTfL1cKX3Rnegtc/3prCG/nIPDwAAbEjXpgH06B1Nxfnp66JR4BQAKlBWZAYO0Kf7dqabs4oMQbdp0Dqs6injB+My6Eiak/iff5ZsO51Mgxfuom/2xInLR4bXFz23H+3ZTBTGAQAAMNQbw9qJAqdcE+TjrWeq/AwCANO+x9kiZUVmKosXL6ZmzZqRp6cnRUZG0qFDh6rdfvXq1dSuXTuxfXh4OG3atKnKbZ977jlRgGrRokVkb7hVhVILqUl9ujXXdHOmkWFNt3lah3ExNbQrKbclJpH6LPibHl4WRT+cdxH/888rDl6hZ36Iokk/RNH1zHxqVMeLvnuiOy1+qAsF+3nKPWwAALBhnER4f2yYOP/tnsuVPoP4swkAjP8eZ8uvIWVFZkS0atUqevXVV2nWrFl09OhR6tixIw0dOpRSUlJ0br9v3z6aMGECPfXUU3Ts2DEaM2aMOMXExFTadt26dXTgwAFq0KAB2SPNgFZpQfft6eVY021u3ZsFiJkEHEReSsshR8dvyJN/OkqJmfkVLuef314XQ1tPJ5OrsxNNvrMlbXulP93Vtp5sYwUAAPuccagtKTNffDbZctAAIOf3uCQbfw0pKzIjooULF9KkSZPoiSeeoNDQUFqyZAl5e3vTsmXLdG7/2Wef0bBhw+iNN96g9u3b09y5c6lLly70xRdfVNguISGBXnzxRfr555/Jzc2N7P2NXmlrunX26cb0crPwcnehbs3qiPOOPsWcpx7N2Xiaqsv3cz9VLpT21rB24rEDAAAw52eQLtLnEl9v69NkAeT4Hldm468hRUU7hYWFdOTIEZo+fbr6MmdnZxo0aBDt379f5+/w5ZwZ18SZ8fXr16t/Li0tpUceeUQE5h06dKhxHAUFBeIkycrKEv8XFRWJkzVJ96fP/ebk3+4N6VRaQkVFuo+2ykE1u5zyi4rVf0tmXvl4vdycrP64yrF/LKlXiwDadzGddp9LoYndG5Kj4jU/2kdGtXExv4xbeVRUhL7bSqCU1xDohv2jbNg/tvUZxGECXx/5wTbycMNBXyXgVXn5+S604PS/ovo8yKugqITScopqfA3tv5BCkc0DSAn0ff9VVNCdlpZGJSUlFBwcXOFy/vnMmTM6fycpKUnn9ny5ZMGCBeTq6kovvfSSXuOYN28ezZkzp9LlW7duFVl3OWzbtq3GbW6K4wSu5OxURlu2bCYlSU7kTLczxZyOpU2Z5UeBL14pv+zy+TO0Kdu2+1rqs38sqewW/+tKe86n0MY/N6kPcjgaLrZBVPMXma3/b+9OwKMqz4aP39nDkgUSIOxb2BQBiYIgqFRA1GqtiggKrmittlaxr4oKqF/FBVyquOECqIhirVqlCC58BWWRTXZewEBESQh7IBBCct7rfsiZJmGAJGRmnpn5/65rmJlzzsw8Ofccztzn2eYulJ1rg+8qaSgL9DGEEyM+diM+wXUOOppUcKHEHhEiBSe+YA+7zLLod1x+fn7wJd2+oDXn2gRd+4frAGoVoTXtpWvPtaa7adOm0r9/f0lMPDo9kz+vnujJtF+/fidtFp+1K19k6TyJj4mWSy65SGwy/7M1sjB3q7RKbyuX9Gltln2wfbHIrl3SPaOLXNK5oQSjysTHl7SZzZsb58ieg4XS5IyecmazZAlHKZm7ZMqGxSfdrn/v7tZcIQ13thxD8I742I34BOc56NHLOkjHRv79PQnvjhw5IgsXLZTu3bqbCjoE1qpf98nof60Nqt9xbovok7Hq25WamipRUVGSk5NTZrk+T0tL8/oaXX6i7efOnWsGYWvWrJlnvdamjxgxwoxgvnnz5mPeMy4uztzK0xNaoE5qFflsJyLSM4iabSdfvRCgip0IT9kOHD7a/D25Zpx15a2sQH43zOdrE/P0FJmxMlvmZ+6Rbq3rSTjqkV5fGiTGSc6+/3YPKU0vu6UlxZvtmBrMLoE+hnBixMduxMcOem5pmBRvBnxyTnAOur5HS85BFl24yl4j0rVFCseQBbo0T5FX/5N50mPIpt9xFf3eWDXaVmxsrGRkZMjXX39dpj+2Pu/Ro4fX1+jy0tsrverrbq99uVesWCHLly/33HT0cu3f/eWXX0ooKXDn6LZsEDV38Kryo5czZVj16pV+NNGetzFXwllKrWMvmCn3v+bRl51mzX/UAIDQoecWPceo8mcZzkFAeB9D1mVn2qx74sSJMnnyZFm7dq3ccccdcuDAATOauRo2bFiZgdbuvvtumTlzpowfP970+x4zZowsXrxY7rrrLrM+JSVFOnbsWOamVyS0Jrxdu3YSiqOX2zZdmIouuRBQelozpgyrXr3bHJ2ve1nWHs/I8OFm3Kz1smbbPnORJ7V2bJl1emX0leu7yoCOwdmVAQBgPz3H6LlGzzmlcQ4CwvsYsi7bGTRokOTm5sqoUaPMYGhdunQxSbU7WFpWVpYZ0dzVs2dPmTp1qjz88MMycuRIadOmjRm5XJPrcGNz0u11nm6mDKtWTevWlGZ1a5q+/Qt/2ikXdig7wGCo+3zFr/LKnE3m8fhrusilZzQ0o1vqYBva98empkgAgNClSUG/09I4BwFVNCAEjyErsx2tpXZrqsubM2fOMcsGDhxobhXlrR93KHBrkW1sXh7rNi8/crSHRnGx89+km+bl1aZXm1SZujBL5m3cEVZJ95pf98lfp68wj28/v5Vc3rmReayDbOjolnofzP9RAwCCi55zOAcBVRcVYseQfdkZqsytRQ6Gmu78wiLPOmq6q0+v9KNNzOdt2CHhYveBw3L7u4vlYGGRaWL/Pxe1D3SRAAAAAA/7sjOcevPyKIuT7mKnTH/u6MgIibPwIkGw6tk6RXRmvA3b95uRH0PdkaJi+dP7y+TnXQdN0/oXB58Z9FdCAQAAEFrIdkJx9HILk9iYkjIVlpRxf0Ghp2l5RedPx8kl14yVTo2TzOPvNoZ+bfdTM9eZpvQ1Y6Pk9WEZ5u8HAAAAbGJfdoaQHEjN06e7pHn5/oKjzctpWl79znWbmId40v3Jsl9k4txM83j8wM7SPi0x0EUCAAAAjmFfdoaQHEjNbV7ulpHpwnw7mJqbdDvO0eb8oWbVL3vl/n8cHTjtrj7pcvEZwTl9BAAAAEKffdkZQrKmu/xAap7m5STd1S6jeR2Jj4mU3LwC+d+c/RJqdu4vkNvfWWK6U/RpV0/u6dc20EUCAAAAjsu+7AwhOpCa27z8aM1rnlvTzXRh1S4uOkq6tUwJySbmetHmzqlL5Zc9B6Vlai15/loGTgMAAIDd7MvOEBZThh1w5+imptsneqWXJN0bciWU/O2LtbLgp13mezNxWIYk1YgJdJEAAACAE7IvO0NINy93y7ifpNuneqXXM/cLM3d59nmwm774Z5n0/Wbz+NlrOkt6/YRAFwkAAAA4KfuyM1RZQRAMpHakZJ7uPJJun2qfliCptWMl/3CRLMvaLcHux5/3yEOfrDKP776wjfQ/PS3QRQIAAAAqxL7sDCFZ0x0bHeG9eTl9un0iMjJCerYOjanDdEA4HThNv999OzQwSTcAAAAQLOzLzhCSSbenT7fbvJwpw/w6dVgwf6f/+N4Syd53SFrXqyXPDepsLigAAAAAwcK+7AwhnXQfLhm9nD7dvtcrPdXTNHvvwaNTtAWbxz5fLT9s3i0JZuC0syQhnoHTAAAAEFzsy85QZYeDoE+327ycKcN8r1FyDWlVr5ZoN/r5m3ZKsJm2KEveXZAlEREiLwzuIq3q1Q50kQAAAIBKsy87Q4hOGVauT/dharr9oXdJbfd3QdbEfMmW3TLq09Xm8Yh+beU37RsEukgAAABAldiXneHUm5cHQU03fbr949z04OvXnbPvkNzx7hLTcuPijmlyZ5/0QBcJAAAAqDL7sjNUWUEQ9OkuLHLEcZz/9ummeblPndM6RaIiIyRzxwHZujtfbFdwpEj+8O4S2Z5XIO0aJMi4gZ0lQtuXAwAAAEHKvuwMITmQWunad52rm4HU/CMxPkY6N0kKiibmejFm9KerZVnWHkmMj5bXh2VILb4fAAAACHL2ZWcIzYHUSubpVvmHi+RQ4dGyknT7Xq829cz93A12J93vLcySaT/8LDoj2ItDukrzlFqBLhIAAABwyuzLzhCSNd1u83K1J/+w5zE1mb7Xu2S+7u837ZRiHcrcQosyd8mYz44OnPY/A9rL+W2PXigAAAAAgp192RlCciC1aK2+LLHrwNGkOz4mskwyDt/o0jRZasVGmf2+Zts+sc22vQflj+8tMd0Oftupodx+XqtAFwkAAACoNmQ8IcTmKcN0MCz3YsCe/EJzXzsuJsClCg96YeOcVilW9us+VFgkf3hniezYf1japyXI01d3YuA0AAAAhBT7sjOEZPNyFV0yV7db0107LirAJQofNk4dpgOnPfTPVfLj1r2SXDNGJg47S2rG0t0AAAAAocXO7AynNpCapUm325R8d0mfbqYL83+/bu07rbXLNpj8/Wb5x9KtZuC0CUO6StO6NQNdJAAAAKDa2Zmd4dTm6Y4KkqSbQdT8Jr1+bWmQGGe+I0u27A50cWT+pp3y+BdrzeORl3Tw1MQDAAAAocbO7Awh2bw81tO83O3TTdLtL9pP2k1sAz112C97DsqdU5dKUbEjV3RpJLf0ahnQ8gAAAAC+ZGd2hir1j7W+eXlJudwpw0i6A9PEPJCDqR08XCS3TVls+vV3bJwoT17FwGkAAAAIbXZmZ6g0nW7JKZmC2fbm5Z6B1OjT7Vfntj6adK/6da/sLomBvy8MPfjxCln96z5JqRUrrw09S+JjGEwPAAAAoc3O7AxVblpudU03U4YFVP3EeGnXIMFcnPl+006/f/6b8zLlk+W/SlRkhEy4rqs0Tq7h9zIAAAAA/mZndoYqz9Ftc023p0+3p3k5tZyBmzos16+fO2/DDnlixtGB0x65tINn3nAAAAAg1NmZnaHKNd06/VK0pUm3Wy63aTN9ugPXr1sHU9Pm3v7w8658uev9pVLsiFyd0URu6NnCL58LAAAA2MDO7AxVny7M0qblKqakplv7n6va8TQv97duLeuaOGzdfVCyduX7/PPyDx+R4VMWmy4FnZskyf+7oiMDpwEAACCs2JuhoVI8I5dbWstduk+3i5pu/6sVFy1nNqvjl6nDtCb9rx+tkHXZeZJaO05eHZrBwGkAAAAIO/ZmaKjiHN32JjXlLwiQdAdG73T/TB322n9+ki9WbJPoyAh55fqu0jCJgdMAAAAQfki6Qy3pLmnCHRQ13UwZFhDnlvTr1hHMi0qa+le3Oeu3y1Mz15nHYy4/Xc5uUdcnnwMAAADYjqQ71JqX29ynu1zZqOkOjE6NkyQhPlr2HiyUlb/srfb337zjgPz5/WVmarLB3ZrKdd2bVftnAAAAAMHC3gwNlVIYRAOpuUi6AzeKfI+SKbuqu4n5/oIjcts7i2XfoSPStVmyqeVm4DQAAACEM3szNFRKQRDUdB/Tp5vm5RZMHZZbrQOn3ffhj/K/OfulfkKcvHp9hsRZPMYAAAAA4A/2ZmioYp/uyKDo062VnzUZyTpgerWpZ+6XbtljpvWqDhO+3SgzV2eb76COVF4/Mb5a3hcAAAAIZvZmaKji6OX2hjS6VPPy2rHREhlJs+NAaZFSUxon1zBjASzK3HXK7/f12hwZP/t/zePHfne6dC2ZlgwAAAAId/ZmaAjpKcN0vmgEjvaz7lVNU4dtyt0vf5m23AycNvSc5nJtNwZOAwAAAFwk3aE2enmQTBlGf257pg6bu6HqSXfeoUK5bcpiySs4Ime3qCOP/Pa0aiwhAAAAEPxIukNEMDQvL5N0U9MdcOe2PjqC+brsPMnNK6j064uLHbnngx9lU+4BSUuMl5evy7D6+wcAAAAEAr+QQ0Shp6bb3pDGRJfq003SHXAptePk9EaJ5vH3mypf2/3C1xvkq7U5JtF+bWiG1EuI80EpAQAAgOBmb4aGSikIgpru0hcESLrt4PbrrmwT8y9XZ5ukW439/RnSuWmyT8oHAAAABDt7MzSEdvNy+nRboVeb/w6mpvNsV8SGnDy594Pl5vGNPVvIVRlNfFpGAAAAIJjZm6GhigOp2Tt6OX267XN2i7rmQs22vYdM3+yT2XuwUG57Z4kcOFwk57SqKw9d2sEv5QQAAACCFUl3iAi6ebpJuq0QHxNlRh1X8zbknnDbomJH7p62TDJ3HDBzfE8Y0rXMhRQAAAAAx+IXc6gl3RZPGVamTzfNy63RK72euZ+3cecJt3t29nqZsz5X4mOODpymA7EBAAAAODGS7hARDDXdNC+3ezC1BT/t9IyCX96MldtkwrebzOOnruokHRsn+bWMAAAAQLCyN0ND1aYMszrppnm5jXTasOSaMbK/4Iis2LrnmPXrsvfJfdN/NI+H924pv+vSOAClBAAAAIKTvRkaKqUgKObppqbbRpGREXJua+9Th+3JPyy3TVki+YeLTI34/QPaB6iUAAAAQHCyN0NDFZuX2zt6OX267Z86bF6ppPtIUbH86f1lkrUrX5rWrSEvDj5Toi2+qAMAAADYiMwnBOio0tv3HTKPNUHS51GR9g2oFhXx3zL9lLvfTFdlYznDuV/30qzd8sEPWdKsbi35Zl2OqfmuERMlrw89S+rUig10MQEAAICgY2W11YQJE6RFixYSHx8v3bt3l0WLFp1w++nTp0v79u3N9meccYbMmDGjzPoxY8aY9bVq1ZI6depI3759ZeHChRIKZq7aJr2e+kZ+3LrXPH/1/28yz3W5TbQ8d05d6nk+8p+rrCxnuFr9615zAaTYEbn/Hytl8MQFMnFupln3zMBO0qFhYqCLCAAAAAQl65LuDz74QO69914ZPXq0LF26VDp37iwXXXSRbN++3ev233//vQwePFhuueUWWbZsmVxxxRXmtmrVKs82bdu2lZdeeklWrlwp8+bNMwl9//79JTf3xPMS204T1jveXSrb9h6t5XZl7z1kltuS0Lrl3HngsNXlDFdufLSFhDfRtEYAAAAAQifpfvbZZ2X48OFy0003yWmnnSavvvqq1KxZU9566y2v27/wwgsyYMAA+etf/yodOnSQxx9/XLp27WqSbNeQIUNM7XarVq3k9NNPN5+xb98+WbFihQQrTZAe/dca8ZYmuct0/fESKX8JlnKGqxPFR2m6TXwAAACAEOnTffjwYVmyZIk8+OCDnmWRkZEmYZ4/f77X1+hyrRkvTWvGP/nkk+N+xuuvvy5JSUmmFt2bgoICc3Npgq4KCwvNzZ/czyv/uQszdx1Tw12apki6fv7G7dK9ZV0JlGApZ3XHJ1gQHwQaMbIb8bEb8bEb8bEfMbJbYRDEp6Jlsyrp3rFjhxQVFUmDBg3KLNfn69at8/qa7Oxsr9vr8tI+//xzufbaayU/P18aNmwos2fPltTUo4NHlTd27Fh59NFHj1k+a9YsU+seCFre0pbs0DrIk49UPmvuQtm5NnC1lMFSzuqOT7AgPrAFMbIb8bEb8bEb8bEfMbLbbIvjo7ll0CXdvtSnTx9Zvny5SewnTpwo11xzjRlMrX79+sdsqzXtpWvPtaa7adOmph94YmKi36+e6BetX79+EhMT41mekrlLpmxYfNLX9+/dPaA1lMFSzuqOT7AgPgg0YmQ34mM34mM34mM/YmS3wiCIj9siOqiSbq15joqKkpycnDLL9XlaWprX1+jyimyvI5enp6eb2znnnCNt2rSRN998s0xTdldcXJy5lafBDlTAy392j/T60jAp3gxG5q3+Uesv05LizXaBnJYrWMp5qgL53TgVxAe2IEZ2Iz52Iz52Iz72I0Z2i7E4PhUtl1UDqcXGxkpGRoZ8/fXXnmXFxcXmeY8ePby+RpeX3l7pFZHjbV/6fUv32w42mgCNvuw087h8KuQ+1/WBTpSCpZzhivgAAAAAvmVV0q20Wbc2/548ebKsXbtW7rjjDjlw4IAZzVwNGzasTO303XffLTNnzpTx48ebft86J/fixYvlrrvuMuv1tSNHjpQFCxbIli1bzEBtN998s/zyyy8ycOBACWYDOjaUV67vamoiS9PnulzX2yBYyhmuiA8AAADgO1Y1L1eDBg0y82ePGjXKDIbWpUsXk1S7g6VlZWWZEc1dPXv2lKlTp8rDDz9skmttNq4jl3fs2NGs1+bqmoxrEq/9uVNSUuTss8+WuXPnmunDgp0mRP1OS5NFmbtke94hqZ8QL91a1rWuZjJYyhmuiA8AAAAQJkm30lpqt6a6vDlz5hyzTGusj1drHR8fLx9//LGEMk2MerROEdsFSznDFfEBAAAAwqB5OQAAAAAAoYKkGwAAAAAAHyHpBgAAAADAR0i6AQAAAADwEZJuAAAAAAB8hKQbAAAAAAAfIekGAAAAAMBHSLoBAAAAAPARkm4AAAAAAHyEpBsAAAAAAB8h6QYAAAAAwEdIugEAAAAA8BGSbgAAAAAAfISkGwAAAAAAHyHpBgAAAADAR6J99cahxHEcc79v3z6/f3ZhYaHk5+ebz46JifH75+PEiI/diI/9iJHdiI/diI/diI/9iJHdCoMgPm5+6OaLx0PSXQF5eXnmvmnTpoEuCgAAAADAsnwxKSnpuOsjnJOl5ZDi4mL59ddfJSEhQSIiIvx+9UST/Z9//lkSExP9+tk4OeJjN+JjP2JkN+JjN+JjN+JjP2Jkt31BEB9NpTXhbtSokURGHr/nNjXdFaA7sEmTJgEtg37RbP2ygfjYjvjYjxjZjfjYjfjYjfjYjxjZLdHy+JyohtvFQGoAAAAAAPgISTcAAAAAAD5C0m25uLg4GT16tLmHfYiP3YiP/YiR3YiP3YiP3YiP/YiR3eJCKD4MpAYAAAAAgI9Q0w0AAAAAgI+QdAMAAAAA4CMk3QAAAAAA+AhJt59NmDBBWrRoIfHx8dK9e3dZtGjRCbefPn26tG/f3mx/xhlnyIwZM8qs1y75o0aNkoYNG0qNGjWkb9++smHDBh//FaGtumN04403SkRERJnbgAEDfPxXhK7KxGf16tVy1VVXme11vz///POn/J7wb3zGjBlzzPGjxxt8H5+JEydK7969pU6dOuam55fy23MOsj9GnIMCF5+PP/5YzjrrLElOTpZatWpJly5d5J133imzDceQ3fHh+KleE6r4e2vatGlm319xxRXBe/zoQGrwj2nTpjmxsbHOW2+95axevdoZPny4k5yc7OTk5Hjd/rvvvnOioqKcp59+2lmzZo3z8MMPOzExMc7KlSs92zz55JNOUlKS88knnzg//vijc/nllzstW7Z0Dh486Me/LHT4IkY33HCDM2DAAGfbtm2e265du/z4V4VvfBYtWuTcd999zvvvv++kpaU5zz333Cm/J/wbn9GjRzunn356meMnNzfXD39N6KlsfIYMGeJMmDDBWbZsmbN27VrnxhtvNOebrVu3erbhHGR/jDgHBS4+3377rfPxxx+b3wcbN250nn/+efObYebMmZ5tOIbsjg/HT/WZVsXfW5mZmU7jxo2d3r17O7/73e/KrAum44ek24+6devm3HnnnZ7nRUVFTqNGjZyxY8d63f6aa65xLr300jLLunfv7tx+++3mcXFxsfmh+swzz3jW79mzx4mLizM/YhH4GLn/YZf/TwL+iU9pzZs395rUncp7wvfx0aS7c+fO1V7WcHSq3/UjR444CQkJzuTJk81zzkH2x0hxDqo+1XG+OPPMM80FesUxZHd8FMdPYONz5MgRp2fPns4bb7xxTCyC7fihebmfHD58WJYsWWKaPbgiIyPN8/nz53t9jS4vvb266KKLPNtnZmZKdnZ2mW2SkpJMc43jvSf8GyPXnDlzpH79+tKuXTu54447ZOfOnT76K0JXVeITiPcMV77cl9pUrFGjRtKqVSu57rrrJCsrqxpKHF6qIz75+flSWFgodevWNc85B9kfIxfnoMDHRyu6vv76a1m/fr2cd955ZhnHkN3xcXH8BC4+jz32mNn3t9xyyzHrgu34iQ50AcLFjh07pKioSBo0aFBmuT5ft26d19foF8nb9rrcXe8uO942CGyMlPb9ufLKK6Vly5ayadMmGTlypFx88cXmP4SoqCgf/TWhpyrxCcR7hitf7Us9eU6aNMn82Nm2bZs8+uijpg/rqlWrJCEhoRpKHh6qIz7333+/ufjh/sDhHGR/jBTnoMDGZ+/evdK4cWMpKCgw+/vll1+Wfv36mXUcQ3bHR3H8BC4+8+bNkzfffFOWL1/udX2wHT8k3YCPXXvttZ7HOtBap06dpHXr1ubK6YUXXhjQsgG20x83Lj12NAlv3ry5fPjhh16vfMM3nnzySTOQjf6/pQPgIHhixDkosPTioCYN+/fvNzWp9957r2m1c8EFFwS6aKhAfDh+AiMvL0+GDh1qBotMTU2VUEDzcj/RL4xeEcvJySmzXJ+npaV5fY0uP9H27n1l3hP+jZE3+p+5ftbGjRurqeThoSrxCcR7hit/7UsdZbZt27YcP36Mz7hx40xCN2vWLPOD08U5yP4YecM5yL/x0Sa06enpZmTsESNGyNVXXy1jx4416ziG7I6PNxw//onPpk2bZPPmzXLZZZdJdHS0uU2ZMkU+++wz81jXB9vxQ9LtJ7GxsZKRkWGuormKi4vN8x49enh9jS4vvb2aPXu2Z3tt6qJfqtLb7Nu3TxYuXHjc94R/Y+TN1q1bTX8gnd4Avo1PIN4zXPlrX2pthJ5sOX78E5+nn35aHn/8cZk5c6aZWqc0zkH2x8gbzkGB/T9OX6NNmRXHkN3x8Ybjxz/xad++vaxcudK0QnBvl19+ufTp08c8btq0afAdP4EeyS3chsrXEfUmTZpkpie47bbbzFD52dnZZv3QoUOdBx54oMx0VNHR0c64cePMVCA6iq+3KcP0PT799FNnxYoVZlQ/W4fKD8cY5eXlmSmR5s+fb6Y8+Oqrr5yuXbs6bdq0cQ4dOhSwvzNc4lNQUGCm0tFbw4YNTSz08YYNGyr8nghsfEaMGOHMmTPHHD96vPXt29dJTU11tm/fHpC/MZzio+cXnd7lo48+KjNdjv6/VnobzkH2xohzUGDj88QTTzizZs1yNm3aZLbX3wr6m2HixImebTiG7I0Px09g41Oet5Hkg+n4Ien2sxdffNFp1qyZOUnq0PkLFizwrDv//PPNF6q0Dz/80Gnbtq3ZXueq/eKLL8qs1+HyH3nkEadBgwbmi3zhhRc669ev99vfE4qqM0b5+flO//79nXr16plkXKdF0nkJSej8Ex89Seq1xfI33a6i74nAxmfQoEEmIdf303k69bnOpwrfx0f/v/IWH7246OIcZHeMOAcFNj4PPfSQk56e7sTHxzt16tRxevToYRKP0jiG7I0Px0/gf2OfLOkOpuMnQv8JdG07AAAAAAChiD7dAAAAAAD4CEk3AAAAAAA+QtINAAAAAICPkHQDAAAAAOAjJN0AAAAAAPgISTcAAAAAAD5C0g0AAAAAgI+QdAMAAAAA4CMk3QAAVMCkSZMkIiJCFi9e7LfP3Lx5s/lM/WxfmDNnjnl/vQcAAL5B0g0ACGtuMu3e4uPjpW3btnLXXXdJTk5OoItn5T4qf1uwYIHY6MYbbyxTzri4OBPbUaNGyaFDh6r0nmvWrJExY8aYCyIAAFREdIW2AgAgxD322GPSsmVLk4zNmzdPXnnlFZkxY4asWrVKatasGZAyNW/eXA4ePCgxMTFi0z4qLz09XWylifYbb7xhHu/du1c+/fRTefzxx2XTpk3y3nvvVSnpfvTRR+WCCy6QFi1a+KDEAIBQQ9INAICIXHzxxXLWWWeZx7feequkpKTIs88+a5K0wYMHB6RMbs27jfuooo4cOSLFxcUSGxt7zLoDBw5IrVq1qlwex3HMRZIaNWocd5vo6Gi5/vrrPc//+Mc/Ss+ePeX999838W3QoEGVPx8AgIqgeTkAAF785je/MfeZmZlllhcUFMi9994r9erVMwnj73//e8nNzfWsv+GGGyQ1NVUKCwuPec/+/ftLu3btPM9nz54tvXr1kuTkZKldu7ZZN3LkyJP26V63bp1cc801pgyacOrrHnroIc/6LVu2mORSl+t6vYAwcOBAnzeJdss7btw4ef7556V169amptltkq3r9PGQIUOkTp065m93E3OtfXa31xpk3Q+6r0vT5b/97W/lyy+/NMm//m2vvfZapcqoZdDP1YT9p59+qtQ+0zjoMtWnTx9Ps/XSfeL//e9/S+/evc13IyEhQS699FJZvXp1lfcpACD4UdMNAIAX2vxYafJV2p/+9CeTMI4ePdokZJpcav/vDz74wKwfOnSoTJkyxSSGmiC6srOz5ZtvvjGvU5qI6fpOnTqZZtuabG7cuFG+++67E5ZrxYoVJqnTJue33XabSUS1rP/617/kb3/7m9nmhx9+kO+//16uvfZaadKkiSmnNpfXJtGa9Fa1ubw2z96xY0eZZZp0lt9Hb7/9tqmB1vLp31W3bl3POk1a27RpI0888YRJfN2WBZMnT5arr75aRowYIQsXLpSxY8fK2rVr5Z///GeZ916/fr1peXD77bfL8OHDy1zEqCg3kdY4uiqyz8477zz585//LH//+9/NRYEOHTqY17r377zzjrnoctFFF8lTTz0l+fn55j00yV+2bBnN0QEgXDkAAISxt99+WzM/56uvvnJyc3Odn3/+2Zk2bZqTkpLi1KhRw9m6dWuZ7fr27esUFxd7Xn/PPfc4UVFRzp49e8zzoqIip0mTJs6gQYPKfM6zzz7rREREOD/99JN5/txzz5n30888nszMTLONfrbrvPPOcxISEpwtW7aU2bZ0mfLz8495r/nz55v3mjJlimfZt99+a5bpfUX2kbdbXFzcMeVNTEx0tm/fXuY9Ro8ebdYNHjy4zPLly5eb5bfeemuZ5ffdd59Z/s0333iWNW/e3CybOXOmUxE33HCDU6tWLbOP9bZx40Zn3LhxJg4dO3as0j6bPn26132Wl5fnJCcnO8OHDy+zPDs720lKSjpmOQAgfNC8HAAAEenbt69prt20aVNT26nNvbWWtXHjxmW209pbrd11aa1zUVGRaZ6sIiMj5brrrpPPPvtM8vLyPNvpoF3al9gdiEyblCvtM659nitCm7H/5z//kZtvvlmaNWtWZl3pMpXu46zN3Hfu3GkGO9PPXLp0qVTVhAkTTJP40jdtTl3eVVddZfalN3/4wx/KPNfB6pQ22S9Na7zVF198UWa57j+tSa4o7TeuZdGb7oP77rtPzj33XLPfq3Of6b7Ys2ePqYXX1gDuLSoqSrp37y7ffvtthcsMAAgtNC8HAKAkodTppHTgLR1cS5stawJdXvlk122ivHv3bs+yYcOGmebFmrTrY20SvWTJEnn11Vc92wwaNMiMqq1Nqx944AG58MIL5corrzRNrL19rnL7IHfs2PGEf4uOeK7Ns7WZ9y+//OJpxu02Ea+qbt26VWggNW8jnB9vnV6s0L+3/AjoaWlpJuF1L2ZU5L290YHotOm92rp1qzz99NOyffv2YwZfO9V9tmHDhjJjAZSXmJhYqXIDAEIHSTcAAJVIKLXm0pvSSdppp50mGRkZ8u6775qkW+919G4d/MylSZ/WWmsNqNbmzpw50/QL16Rt1qxZx/2citB+55o8/uUvf5EePXpIUlKSqdXVGvyK1qqfihONJn68daVrnav63t7oftRWDC6tJW/fvr3pE66tEaprn7nbaL9uvWBQnl7MAQCEJ84AAAD4gCbb2mR627ZtMnXqVDOKdemBu5TW8GoNt950+iodXExHIddEvHSi6GrVqpW517nDT+Sjjz4yA3qNHz/es0wHNtPmz7bRucg1YdWaYndAMpWTk2PKq+urU8OGDeWee+4xc20vWLBAzjnnnErts+NdHNCR11X9+vW9xg4AEL7o0w0AgA9o315N0O6++27TLLz0XNFq165dx7ymS5cu5r78VFku7ZesI2i/9dZbkpWVddyadq3dLf1cvfjii6bvuW0uueQSc6+jwJemFyGUXqyoblqrraORP/nkk5XeZ+684uWTca1B1ybkeuHE23RxpaeVAwCEF2q6AQDwAU2QBwwYINOnTzd9k8snjzpNmDYv1+Vam6v9jF9++WUzXZU7f7U3Ol2Vru/atasZ1E37OOv0VtpEffny5WYbnYpMmzlrE2lt6j5//nz56quvjpnaq7J00DSdI7w8HSDOrYWvrM6dO5sa5tdff90ksueff74sWrTITCF2xRVXmPmwq5vuh5tuusnsb52WTGvYK7rP9MKIJujaZ1/7euuUaNolQGu4dXownTJOY6PN0vU7oBdHNDY6eNtLL71U7X8LAMB+JN0AAPiwifnnn39u+nJrclba5ZdfbpJlrbXWUa5TU1NNwqnNnjXxO1GSqs2iH3nkEZPkaRNoTdpL9xd/4YUXTGKoI6brek34NIGszKjf3owaNcrrcu0LXdWkW+mAcvr6SZMmmcHntE/0gw8+6JnT3Be06b8ObKfJs35uRfeZlk1fp4Ou3XLLLaYmXLsDaNI9ZMgQadSokalBf+aZZ0yLBR39Xke41yQfABCeInTesEAXAgCAUKTTUmltrdZoa+IFAADCD0k3AAA+ok2Wtfnyxo0bKzw6NwAACC00LwcAoJpNmzZNVqxYYfryarNlEm4AAMIXNd0AAFQzTbJr164tgwYNMv1/maMZAIDwxa8AAACqGdezAQCAi3m6AQAAAADwEZJuAAAAAAB8hKQbAAAAAAAfIekGAAAAAMBHSLoBAAAAAPARkm4AAAAAAHyEpBsAAAAAAB8h6QYAAAAAwEdIugEAAAAAEN/4PwItqUaDKiZpAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "print(logical_errors)\n", + "plt.figure(figsize=(10, 6))\n", + "for d, errors in logical_errors.items():\n", + " plt.plot(physical_error_values, errors, marker='o', label=f'Code Distance d={d}')\n", + "\n", + "# Labels and title\n", + "plt.xlabel('Physical Error Rate', fontsize=12)\n", + "plt.ylabel('Logical Error Rate', fontsize=12)\n", + "plt.title('Rotated Surface Code: Logical v/s Physical Error Rates', fontsize=14)\n", + "plt.legend(title='Code Distance')\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "\n", + "# Save and show\n", + "plt.savefig('logical_vs_physical_error_rates.png', dpi=300)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3bdf5e74", + "metadata": {}, + "source": [ + "- The varying d values are not simulated due to the resource constraint of the machine as d=5 requires 49 qubits in total including ancillas\n", + "- We expect the logical error rate to decrease with increase in physical error rate.\n", + "- As we can see that the error distance decreases with increase in showing that the logical qubit is resilient to errors. " + ] + }, + { + "cell_type": "markdown", + "id": "c9044d97", + "metadata": {}, + "source": [ + "### Results of comparing with increase in Timesteps T\n", + "- The commonly used T values are d or d**d to know the relationship we simulate an experiment for varying timesteps\n", + "- The previous expereiment was run with T=3, 3 timesteps same as distance code, now we run varying time steps keeping the distance code (d) and physical error rate (p) as constant. " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "b2859fb1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running for code distance d=3, timesteps t=1\n", + "Physical error rate p=0.001\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Physical error rate p=0.300\n", + "Physical error rate p=0.400\n", + "Running for code distance d=3, timesteps t=2\n", + "Physical error rate p=0.001\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Physical error rate p=0.300\n", + "Physical error rate p=0.400\n", + "Running for code distance d=3, timesteps t=3\n", + "Physical error rate p=0.001\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Physical error rate p=0.300\n", + "Physical error rate p=0.400\n", + "Running for code distance d=3, timesteps t=9\n", + "Physical error rate p=0.001\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Physical error rate p=0.300\n", + "Physical error rate p=0.400\n", + "Running for code distance d=3, timesteps t=12\n", + "Physical error rate p=0.001\n", + "Physical error rate p=0.010\n", + "Physical error rate p=0.100\n", + "Physical error rate p=0.150\n", + "Physical error rate p=0.200\n", + "Physical error rate p=0.300\n", + "Physical error rate p=0.400\n" + ] + } + ], + "source": [ + "def isLogicalState(state):\n", + " # Anti-Diagonal Measurement\n", + " return qsharp.Result.Zero == state[2]\n", + "\n", + "\n", + "\n", + "def run_experiment_for_T(tValues, pValues):\n", + " SHOTS = 100\n", + " results = {}\n", + " for t in tValues:\n", + " logical_error_rates = []\n", + " print(f\"Running for code distance d=3, timesteps t={t}\")\n", + " \n", + " for p in pValues:\n", + " logical_errors = 0\n", + " print(f\"Physical error rate p={p:.3f}\")\n", + "\n", + " for i in range(SHOTS):\n", + " qubit = LogicalQubit(3, t)\n", + " qubit.encode(p//2, p//2)\n", + " qubit.decode(p//2, p//2)\n", + " state = qubit.getState()\n", + " logical_errors += int(not isLogicalState(state))\n", + " logical_error_rates.append(logical_errors / SHOTS)\n", + "\n", + " results[t] = logical_error_rates\n", + "\n", + " return results\n", + "\n", + "physical_error_values = [0.001, 0.01, 0.1, 0.15, 0.2, 0.3, 0.4]\n", + "logical_errors = run_experiment_for_T(tValues=[1,2,3,9,12], pValues=physical_error_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4ebe9223", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{1: [0.41, 0.36, 0.34, 0.35, 0.46, 0.39, 0.38], 2: [0.36, 0.43, 0.48, 0.5, 0.4, 0.44, 0.38], 3: [0.05, 0.04, 0.09, 0.02, 0.04, 0.12, 0.11], 9: [0.37, 0.42, 0.36, 0.5, 0.42, 0.34, 0.4], 12: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n" + ] + }, + { + "data": { + "image/png": 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+eXt7Gy644AKL+66ye/L111+vXv/0009Nnuc1EBUVZQgJCTHk5uaq5/744w+17QMPPGDxWmbfquPyyy9Xn8HxQYdjwIgRI9S1ZzyG6ePR119/Xe252rp1a9UsUdvrrDIyMjLUNdytW7cKr/3555/qcx555JFzPlacRyxbtqzC+2bPnq1e//LLL02e5zjbokULQ2hoqMl8wtJ8qbb7guME+8pr5dChQybfyeuA21e236ujuvdaOqb6tRsYGGhyTzl16pQ6f3gv6dSpkyEhIaHstQ0bNqj3cG5lDO9bfP6ZZ54xmXfyOHPs4+fp8zaOE9z20ksvrdBPHmee/+Z9NL6HGjN06FA1j+Cc2RjOf318fNT1YL4f+HkjR45Uc0TjMTg4ONjg5uZWdp7VZtxv6ojobiLoE4b27duX3fA50Oo3ak7y9u3bV7Y9LxJ3d3dDUFBQhYklGTt2rHrfqlWraiy6K+PNN9+sMJGsboLTq1cvNaDm5ORUeE0faB5++OGy5yg4OBiZTyoJJ0U1Fd1k27Zthu7du5fdBNg4aF500UWGX375pd5ENyfTlVGV6K6Me++9V73nxIkTZc/dddddVYr7c9nnldGlSxe17YEDB2rc99qej/r2vKHrky8dCjlOqM33+3333VfhnDZ+DydyvCno/P3332r7hx56qML2J0+eVK9xn5nDG52/v7/Fc8L4nKpJq+wGqQtLvfFmfOTIkUr2bvkNftq0aSbP82ZIYUAhUp+iu7bHkxME3qR5PM0nyZx48PtqIrp5/fPmznHQeKJXWyyNWbUV3fr5w+vSmEWLFlUqEjh54j4znphwnOB1mZKSUuffo48nvH45Jj399NNqMYmTdT7Pa8N8fOJkyhz9NfNrom/fvqqP6enpZc9xgskxeeDAgWXP8XW+f9iwYVUuZFYmZHSBb6lv5zpW1lV0V9V+/fXXGo/7+r3iwQcfrHS8obAy328cu/Qxl5N882POBbfaoPeTY6E+l2CfeBz5PMWDpftsZVBU8Dwwvh6rEt2JiYlq8m++iKDz3nvvqfdSUBqLbvPFvdrw/vvvmwg79oHjCBdjea5FR0dXWEwz3tfnIrprc51VxnXXXae237p1q8nzV199tcmi17kcq8suu8zie/TrfPjw4SbP//bbb+p9XBg2pirRXdN9QYFvPm7prFu3zmqi+4UXXqiwvb4I8NVXX1V4rV27dsrIY3wtBwQEqPuXpfFRP9d5vhrPy3j8q6Mq0c05r6X5gQ73PV/fvXu3yX7gc2vWrKmw/UsvvWRixKjNuN/UEffyJgZdRMzjZBlrsXr1ahWnoUNXS8ZY0I3H3CWI8Hm6BjIzMt2QagJdUZi0jS5KdG/RY/jMk4NVB93F6E5Elyi6g5qjx2TyNxC6OdHlizEtxkmCdNj/2mScpFsrv3/9+vXK9YXxa3TdYyZxNrpg6zGb54IlF66aQFcwZgClSxndJemOZL6f6VJE6IJKqnOxr+0+r29qez7SxZTb04XL3P2O7lV0tTIPEWBiPKK7SplDdzTj36cneTN2wdLRY5AsZS1mXBXdwiyV5qiv0kx00SZ006TbGhO9MdswXWYtuWIzlpXQ5csYuuQ1RPbvuhxPnseMzzMOOSC8zui2zG2qg6EC3Mf8/Jq4F9bXmGUJuhDSJZxuhIzP011ymbXfkms5v5vum3Rt112KCd23H3vsMRU6QLc9/jaed3SrrC2MqdP3Kd/P/U33RbpnmsPzyRzGEOvnnTF0BaULMN1M+T9hvCLdD41dS/mddGmlGyjDQZiLgC6NHAtrcrxqOp7VZaw812zM9TXuMxO2ObxOCMMmzO87HO/onsprjtsxTre6z6sJvO+Zx24z1Ib3QktZuvnddA3m6wx/MM6doI89NUmgRVdThifxWFmKf9bHdf5euuryt/NzeR1zXOZz3E+M6a7pPVoPR+L9ntcbx26OIxxLOY4x/Igx5oyt5TZ0qTbfz3WlNtdZZXAsYVgY5yW8rvR5EcMOGF9s7rpbl2NV2XnEsA2G03Cc4zHRE8rRtZwwwWd974uq7r90gTYPf2gsLIVK6PuxsteME/PyHseYdM7DzOfxhKElRJ+n8BynuzaPPd3C6RLO8ZTfxXGhpuhzo/j4eIvXnP59/N84hI37mSFk5uiaQc8RcK7jflNCRHcTg/EdTF6lX6BMVPb444+rck2csFAQ6AMyqSzmVh8o9O2qg3FCvIAYn0bBwzgPihVOHjnAMxbLfMJTGRx0eMPjJMnSwKPD+BHjPjI+1xLVxRVbQp/o6zGK7A9/AyenjJ1inBxjx86FuvSLibJ48+Nv5kSBsX0c0DjAcqLAmB3j/cwkG/wt1U12arvPq4ILHxyc+Vk1LStT2/NRT45Tm2POc5RwAlUT9BhUTrrMqcv3NwS8xnge8Jrnvub5yQUo8xuZLiYtCeCGoLbHs76uYf241KQcTX2OWZbg51AkU+hyoWfSpEkq9o0xilwg1CfHOlyE4OKXeZwxY1IZc8rYbn4WYyc52eHnsUJAbWJ0GQdtaWHSEpZEvT6ZpSgyhr+T/eREWxfdzKjP+w0T1ZnHhjKmmQJdrwrA72KcH5+v6hytzfGt7VjZWFR3Llt6/Vzu13Udi7iQwooHvC/wvOG5xnOPE2bmhzBeGGKcur7YxwUR5rfgsee9h+c7RVJN97U+TjOOmq26exEXDSkamDuBIpMTe0JRzMWQypJ8GcP4eI49ehw3/+e5QhHIsZP3RBou+Lt4X6uNkKzP66wyuM95nCl8eYx4bLgwy76bL+7V9VhVdR7xXOF38/rn93MxiwuZXPywlGfgXPdFVfcLXt/WKt1WVf8re41x9+bnPnMZsFV37vP9XFCkUGbsNfOV6AshjPvm+Gp8nVaG/r2MG9fzw1T1vTrcz5bEvX6uGCcxPJdxvykhorsJwwuPEyGe+C+//LLKYKon9tAHAK5sWYKrn8bbVQcnWJy8srYsv8cYrkDrZXBqgv6dvOFZyqhb2fa0Wlmist9YG3hD4ioiE5IxIzEHOl1064OO8eCpU1Xm1LpYyjnxoUDmirZej12Hk13zknAUEfqkqaqJam33eVVQwHBSS2tyTRNg1fZ81K2ztTnm+nt5w6bFoibXj/ENyZi6fD+pbeZgJkCpSRZW/jbW7uakiWKDK+DG6L9B/00NTW2PZ31dw7pXAifGjTlmVQYnvBTKtG5TJHNiRGFtPhEm/D56bRhn+tXHiWnTpqlG7wtO/mnZYFIaWv127dpVo4lVQ8LriR5ALCfFBQtOzpjUkOJEX+jV4eSK9yM2LhBR4FDcMeEjRQI/oz6Ob23HysaiunHf0uvncr8+V48svp+WNyZ44/fwXGYyJ+PkYFzIpFDjuWlufaQgrk12Yv03UEDUJHEnYXJQJoJkwkReD/QYYSJEJtJjojDzhR9L0PLGa4rnFu9ftKDzuuK4ygVYnqf6eVdZok5rwX7yN3J+xwURjiE87zk34YKYMXU9VlWdR9x3tHDTu4UCihm8KZJrmkCttlR1v+A5QEu9teuAn8vvolFH92arDi7I8nrk+U5jB+em/JuJ/Lj4zmShNf1e4yRtNYH7mfvbXHjr45SxF925jPtNCSkZ1gxgRkveND/88MOy0gscIDnBoyuXpVJJumussUuMPrGztPpKt3ZiKRssB3dzqvosTuAoGjhpq4l7FQcMWnsoNvTJR3XfX1fMJ5BEz2xtaSJoqQTHuVDZfqawtmQV0F3COAmpitru8+qEIo/v//73vzJ3qMrQV9Rrez5y9Zzbc4HA3BLNmwBX883RM2/qrlQ1sX7wZmLJrVl317NUvobWTN0d1BxaTGrTalo2xtgV2pK7lv4bjMtQNSS1PZ600tOtnO6s5lYWntsM9agJdJfmMeMN3dxl8lzHrLrA84T7nIKa7qkULJZKhfGcZegKre0spVLVBIuLfwsWLFALWqwoYKlMnDWgtYt8+umnZa6l1U26OW5zMYECmGOrpZI4dRnP6jJW2jL6dcLM0uYhKvxbL5NoyYW1PqFLMgUoJ848n433NUNYzEUcr32Wx6vN/Z/eJ7xGanrNG8Nrn/uA4Rh62aLqzikdXUjzfbyu9AVjjkv0eKOY0S3h5hnIK4O/s6bW6nNFX8jjGMOs0Lym+JvMxWdtj1VNYSZ+3u+58MvM4pwX1Vdlhcruv5auY3p0WjKA2AOcg3E+y3lNdfcvc3jN8P1caNLLwxmf+1Vdc/rcqLbXHPezpffo90+GatbHuN+UENHdDOBNki7mvIhp1SEsk8OVUa5UMSbNGLqq0h2SMeC0WprHhXJAN0ePizMXIXQl0d29jOGAzEHC0mfptSV5E+CkzZJLM1fKjAUJbziMHzQvz8PJWW3iuTlgc7XWkksxbyj6ZNL4hqXH6JmXXOJKZX1bUyrbz7TMWaqlSIsOB1ta8szreHKyZhyzWtt9Xhk8bzjp4bl14YUXqveZw/3LOFfd8lvb85ETIdZ35Eq3Hqeqw2PE8jrm0M2Q7lgsY2Gprq0eH21sVWO8FG+AFEXmlhVaQmhVYbiBMVzpr2zhojR5ZY2b8eSOk9zK4po5yeG5S1dB49wNOnrcGN39zD0xuDpOT4j6pC7Hk7HMXCHXvXF0eD3WNJcA3do40bOU24LwfNEnZLUds+oKxyau5NMSwYk7j4F5PCgnLuybpQUAPb7UGI7luvdCdSWFGgtOsDgW8nqgKyGvHfM4UI6hlsYpWqS52FLdb+Hns1FkUtybY7zwWdux0pbheEMBRZdTXuvGcHGTi6UUifUVZ1wZdGPnPYUeF8bXKfc1j6GxSywn9/S0s7TwWtVcguEPHNu5cErruqU8GBzP9MU8fqclDwD9uZpeH7ro5sICMfbS4mtcSOV8ggu+NGLUBP5OjoGW5hP1DcNVGLbCMoK0GnK/WfKoqe2xqiksCcV9TW9A5lLgdzfU2MRxkmKN3kr64hrh2P7MM8/AXuH8hKUmOVfj8bAkvDl26RZ+zscszcksnftVXXMcpym8ueDEBV1zOP+pbC5Lox7n3jqMLaf1mvd05keoj3G/KSHu5c0ErkIyQRYnsLxImAiEf/NC4qo1b3C86HgBc8JEVxC6CBm7jfAmRHcvfhYntrTIcADn4MrGz6Og4Wown6ebEgUvk2wwwZMxHDD1yRPfS7HA79LrCtJqQoskY9K5mkkLEG90HEw4AedNl5Nj3fWWIo/fwYkYbyYURBxc6C5Gt86q4lSMoQjlzYMuNvwMWuw4EHIQpCWKVkx+HuPajG8A3J8U3fxOTj45CeIEW08eUV9wwsPjwv3PiQktX9xPXKG29DtpZePkiIKalltaybh/6RHAfc/36JOn2u7zquA5xYkGXTxpxeS5wwQctMJShNMFjhM3bqdT2/ORk2eeX1xQ4MRa3+/c34xVM7eG8fvp7cGbGvvEY8PjRjHLSQK/m1Z6ujzpMISAblrcL+Y1iD/44AMlGhlHzdV9vU43rbtMJFKfHhaE+4sr2bTm8rykBYM3LX4fjz9XyHnszOHki/uJ7zWPr+MErS51uinS9dqf5jDOi+NEbY8nxTnPC8Zh8n16nW5ed6w/SrFek+QwPMa8wdONkucCzz3uAy7E8Jzg+cwFldqOWXWF7p38TVwE4OTF0kSY5w9/G+OOzeE1q4cPsI+ciNGSQWscFyrONRFYfcLxiYnZKrNyUxTzuNJSRVHOc5jnNT0B+LuMa2xXBkU9F6N4H6ILLRP5cKzhuM9FMz0BYm3HyrrCc7YyUUUBqce4nyuM6ediL/crY5cpsPibaSVi2Ahfbwy4gE9Rx0VTXju8lvg/ry32j/uak2guFvF481iZJ5XkMaMxgPcejmF62Ise5sFrmNc+7+v6Meb38P7KRVCGVXAM4jjCa+HRRx9VYzHHNx5nve40+0HLX03gPYGLCvxcfgbPT2PRzWuX5xavuZrCsYf95eIz7wlcjOS8wrguc33CsYXuxFw44L6xZGmu7bGqKRR1nBfxeJGGci0nPBd4/nEMYEgcxZ1ep5tij/OW2iQSsyV4n+AYxUVajlE8Vxi7zuPDZLe8R3GRls9xIYj3KopmPZEwt9PvJ1wAMT6Haeji/J/jBvcX96PuTk7BzW24L3ldchGH1ygNFPw+CmfzcY7XCw00vFZ479LrdPM6Yf91L4v6GPebDNZOny40fJ1u87IYrHuow9IYLLvA9P8uLi6qvh5rqxqXBjDmtddeU+WYuK15+RyWpRg3bpwqecC6fnyNtZorKw/C+n+sMczySizPYamcAesRs24kP5Pf2bJlS1UHmiV92HdjWIv0jjvuUKWfWK6IJU9Y4qu6mqDGsBYi6y5zH7FsGPvG2s78TJYeY41O8zqD+v5nuR/+bpbO4babN2+usmSYeXmRmpYM4/tZeoHfxf5xH7JUSFUlIfgcS56xjiTLe0RGRqqyU2vXrq2wbW32eXVwH7AMBWsyszwRy0K1adNG1WG1VPOztucjS+lcc801aj94enqquqorV66scl9s2rTJcO2116pavfp3sIzPjBkzTOrqEtbD5PFn6TVLsF/c/6wZyuNx4YUXqufqWl6vKrKyslSdbZZVYY1n9p3nGs9TlvQxr1Gsw7JX7Ms777xT4bW61umuqhmXU6nt8WRd5auuukqV6DM+ntOnT1efvX379hqVeGKJEtY5ZSklnnP8PNYr5v4zLodT2zGrNiXDjOH1xPdyXDIuq6XDMZV1Ui3x4YcfGi6++GK1D/UybIMGDTJ89NFHNS6LVlmdbktUNT5VV1aL5eG4v3mtW6q9yueef/55dQ6zhi/HIl6HEyZMMCxevLjG/WA95fvvv1+V3OFncFxjWae33nqrzmNlQ5QM6927d41+T03q6BKWOJs6daradxyX+D//Ni59di5lJ6ur063D0nPchteYzk8//aTGUV63vM5Zroo1iysbCxcuXKjKkOll68z7ytKVnG/wPs5xjtuxNCjvs6yRzZrMhKVQeS6wbB2vDZ5/PC/4vXv37q3Vb9frg/PeaAyvM47xxmXFLO0z82PL8pG33367Ok4sg2a8zblcZ5XBMmasp11dGanaHKvazJ84dnLbwYMHV7pNVSXDarsvfvzxR3Xc9XKTt912m5oH8lgZX3uNVTLM0rVb1VygsmuUc8xPPvlEjV2+vr7q97G0GMdJjvucCxDe8zlv4f7m7+dYyO1Yd379+vUVPpel1lhvm59n6XeyLCXLSfbo0UNdb9yPvDfxujAvl6vvB76H826WJebncr/Pnz+/zuN+U8eB/1hb+AuCINgqtB5wxZneDjVJwGZrMIkUM8nSDc9S+TN7gFYZrrbTHd5SXgV7ht4ZtFLQ6k7Lnj1Dqx49mHjN0KtKEITmAz2c6HVAt2/G7FoD5rig1xmt+JZcpYX6Qfd4rE3eGUFiugVBEKqE7tGMyWVmT3uDLtUs5UK3TXsQ3JZiy5kYSA93aGqCm+hZ0i3Fc9sbjMElDOEQBKH5QNfjOXPmqHw9eixvQ6LHAxvD+7TuUs2wHEGwNSSmWxAEoQoYM8tY6fooPdfYMKkJY9JrGtdobRh3z9gvWn71etmMMaSHQU3LB9kbjPdms1cY88dcD4wTZDwfyxUxBlcQhKYP86kwBweTY9IbjLk5GqPmMr+T+SOYv4WJBpmwjnl0aHllLP0111zT4H0QhNoi7uWCIAiCTfDUU0+pJFEUckzKwgRLTO7CjLRMHifYHlwU4TGiFwL/ZzZtJvQRBKHpwwokTP7FBJoMK2ESNyafbWiYTI/3BSbp1LOusyIGxTYTczWnjNjWQNzL64aIbkEQBEEQBEEQBEFoICSmWxAEQRAEQRAEQRAaCBHdgiAIgiAIgiAIgtBANPtEaiUlJYiNjVWJelg4XhAEQRAEQRAEQRCqg5HamZmZiIiIgKNj5fbsZi+6KbijoqKs3Q1BEARBEARBEATBDjl9+jQiIyMrfb3Zi25auPUd5evrC1ujsLAQS5cuVWURXFxcrN0dwQw5PraNHB/bRo6P7SPHyLaR42PbyPGxbeT42DaFdnJ8MjIylAFX15SV0exFt+5STsFtq6KbNQ/ZN1s+4ZorcnxsGzk+to0cH9tHjpFtI8fHtpHjY9vI8bFtCu3s+FQXpiyJ1ARBEARBEARBEAShgRDRLQiCIAiCIAiCIAgNhIhuQRAEQRAEQRAEQWggRHQLgiAIgiAIgiAIQgMholsQBEEQBEEQBEEQGggR3YIgCIIgCIIgCILQQIjoFgRBEARBEARBEIQGQkS3IAiCIAiCIAiCIDQQIroFQRAEQRAEQRAEoYEQ0S0IgiAIgiAIgiAIDYSIbkEQBEEQBEEQBEFoIER0C4IgCIIgCIIgCEIDIaJbEARBEARBEARBEBoIEd2CIAiCIAiCIAiC0ECI6BYEQRAEQRAEQRCEBkJEtyAIgtDoGAoLkPvnXLRa86P6n38LgiAIgiA0RWxSdH/wwQdo06YN3N3dER0djU2bNlW67ZdffgkHBweTxvcJgiAItknG3Jk4Mrg3Yp58B+5/blX/828+LwiCIAiC0NSwOdG9YMECPPTQQ3juueewbds29O7dG+PHj0dCQkKl7/H19cXZs2fL2smTJxu1z4IgCELNoLCOee1rFGUbTJ7n33xehLcgCIIgCE0NmxPdb731Fm6//XZMnToV3bp1w8cffwxPT0/MnTu30vfQuh0eHl7WwsLCGrXPgiAIQvXQhTz+g3mlfzmYvar9zdfF1VwQBEEQhKaEM2yIgoICbN26FU888UTZc46Ojrjggguwfv36St+XlZWF1q1bo6SkBP369cPMmTPRvXt3i9vm5+erppORkaH+LywsVM3W0Ptki30T5PjYOnJ8bIjiAuT+8CaKsi0Jbh0H9Xrmn1/AY/K0xu2fYBG5hmwbOT62jRwf20aOj21TaCfHp6b9czAYDKY+flYkNjYWLVu2xLp16zBkyJCy5x977DGsXLkSGzdurPAeivHDhw+jV69eSE9PxxtvvIFVq1Zh7969iIyMrLD9888/jxdeeKHC8/Pnz1cWdUEQBOEcMJTAsyAZvnmn4ZN7Br5seWfgnXcWmSddEbs+oNqPyJvcH6eGX9Uo3RUEQRAEQagrOTk5uP7665UOZcizXVi66wLFubFAHzp0KLp27YpPPvkEL730UoXtaUVnzLixpTsqKgrjxo2rckdZc/Vk2bJlGDt2LFxcXKzdHcEMOT62jRyfBiY7CQ6J++CQsB8OifsB/p90AA4FypxdASfvmt1y2g0Zjh4TJ9ZzZ4W6INeQbSPHx7aR42PbyPGxbQrt5PjoXtPVYVOiOzg4GE5OToiPjzd5nn8zVrsm8KD07dsXR44csfi6m5ubapbeZ8sH1Nb719yR42PbyPE5R/KzgMSDQMJeIH4fkFDashMtb+/kCgR3BsK6AaFdgdDu6n8vz1A4D+6DohxDFS7mQMby7fAakwXngOqt4kLjINeQbSPHx7aR42PbyPGxbVxs/PjUtG82JbpdXV3Rv39/rFixApdeeql6jnHa/Hv69Ok1+ozi4mLs3r0bE8VKIgiCUDuKC4HkI5qgNhbXqScqeYMDENAGCNNENUK7aY8D2wFOFW9ChoICOPoFAzlJ/MtMeJdGOjkAWf+swrGLJiHi1VnwHjmyYX6rIAiCIAhCI2FTopvQ9fvmm2/GgAEDMGjQILzzzjvIzs5W2czJTTfdpOK+X331VfX3iy++iMGDB6NDhw5IS0vD66+/rkqG3XbbbVb+JYIgCDYKU3mknzYV1nycdAgoqSQhiHeYidVaWbFDugCuXjX8SgPinnseBWeT4ODmCkfHAhTnlr/u7OWAsFsmwDV2CWJWFKIgORWn77gTAddfh9BHH4Wjh0c9/XhBEARBEIRmLrqvueYaJCYm4tlnn0VcXBz69OmDJUuWlJUBO3XqlMporpOamqpKjHHbgIAAZSlnIjaWGxMEQWj25KQA8XtNxXXCfqAg0/L2rj6l4rqrqQXbK/icupHy1VdI//VXlqRA5IcfwmvQQJWl/Oj61Wg/ZAR8Jk+Fg4srkP4I2kZchcRlp5FyyBup879D9rr1iHj9NXj07HlOfRAEQRAEQbAGNie6CV3JK3Mn/++//0z+fvvtt1UTBEFo1hTkAIkHKrqGZ5nmyCjD0QUI7lRutdYt2P6tAIfK463rQtbqNUh47XX1OGzG4/AeNkw9ZlmwU07hKmmagx4T5dcSjrcvQZj/zfBeuwaxGwNQcOIETlx7HYLvvgvBd94JB2ebvHUJgiAIgiBYRGYugiAI9kRxEZBytKK4TjleHhdtjn9rC3HX7QFn1wbvbv7x44h5+GEm6IDfFZcj4MYbq3+Tuy9w/Q/w8n0Q7QK+QdxWf2Sc8kDS+3OQtWoVWs6eDdc2bRq874IgCIIgCPWBiG5BEARbjbvOiDEV1myJh4DifMvv8Qoxi7vursVdu3nDGhRnZuLM3fegJCMDHn37Ivy55+BQUys6E7Fd/D6cAlqjpdvL8G6Zh7jtwcjbuQvHLrscYY8/Dv9rrq755wmCIAiCIFgJEd2CIAjWJje1YlIzxl3np1ve3sXLQtx1d8A7BLaCobhYWbgLjh+Hc3g4It9/D46utbSsU1CPfBTwawW/3++BZ3AMYne2Rs6pXMQ9/zyy/vsPLV5+Cc7B5xZvLgiCIAiC0JCI6BYEQWgsCnNL613vK01utl97nHnW8vaOzkBQxwr1rpW7uFFCSVsk4a23kL1qNRzc3RH5wZxzE8a9rwF8I+CyYApaDTmOlKjWSNwMJbqPTb4YLV56ET4XXFCf3RcEQRAEQag3RHQLgiDUNyXFQMoxC3HXxwBDieX3+LUyFdd8TMHdCHHX9U36778j5fO56nHEzFfg0b37uX9o2xHAtKVw+PYqBDmchFdoMGJ3dkD+sVM4M/1eFS8e9sSTcPKuWQkzQRAEQRCExkJEtyAIwrnEXdNKXSHu+iBQlGf5PR6BpS7h3Uzjrpk8rAmQu3Mnzj7zrHoc9H93wnfixPr78NAuwG3LgflXw/3sDrSJzkJS78uQ/NsqpP/8C3I2bkLEa7Ph2a9f/X2nIAiCIAjCOSKiWxCEpklJMRxOrkHLlPVwOOkLtBsJODrV/fNy00rdwUvdwnWhnZdmeXsXT01Mq2zhRhZs79B6L8llKxTGJyirs6GgAN7nn4+Q++6r/y/xCQOmLgJ+mgbHQ0sQ6vY9vGfcg9ivNqDwzBmcvOFGBN1+O0LuuRsOtY0hFwRBEARBaABEdAuC0PTY9wew5HE4Z8RiAP8++ZGKCcaE2UC3i6t+b2EekHSoYtw1M4lbwsEJCOpQKqz11hUIaGvzcdf1SUleHs5Mn46ixES4deyAiNmz4dBQv9/VC7jmW3WMsfkzeB6fg7bTpyF+00Ck//Y7kj/5BFmrV6Hla6/BrUOHhumDIAiCIAhCDRHRLQhC0xPcP9xUsWZ1xlnt+au/1oQ3465TTxjFXZcK7OSjTL1t+bN9I03FtR537eKO5ozBYMDZZ59F3u7dcPLzQ+SHHzZ8bLWTMzDxDS2p3LJn4LRrLiJ6T4T3iNmIe+lV5O/bj+NXXInQhx9GwA1TGm4BQBAEQRAEoRpEdAuC0HSgkKb101xwK0qf+/VOYPWbpXHXuZY/x92/PO66TGR3Bdz9GrT79krK3LnI+ONPwMkJLd99F65RUY3zxXTTH3Yf4B8F/HIncHARfCPi4PH9XJyd+bbKnh4/c6ZWWuzVmXAJC2ucfgmCIAiCIBgholsQhKbDyXVARmzV2xTmAGd3aI+d3S3HXfuEN9m46/oma+VKJLzxpnoc9uQT8Boc3fid6H4Z4NMC+O46IHYbXH67GlEv/4S0FWMQP/s1ZK9bh2MXX4IWzz1bv4ndBEEQBEEQaoCIbkEQ7JuCbOD0JuDUemDvbzV7z+C7gQG3AoFtzy25WjMn/+hRxDz8iMri7n/11Qi4/nrrdabVYC2z+TdXAKnH4TB3HAKunQ/PX35B7OOPK9f3mIceRuY//yL82Wfg5Ns0ssULgiAIgmD7iOgWBMG+yE0FTm0ETq7VLNu0WpcU1e4zOk8EgiXB1rlQnJ6O03ffjZKsLHgM6I/wp5+Cg7W9A4Laa8L7u2uBM5uBeZfC7dKP0Gb+t0j66GMkffIJMv76CzlbtiBi1qvwGjzYuv0VBEEQBKFZIKJbEATbJitBE9d6i99TMWabCc7aDNOsnf+9CmQlVhLX7aBlMW89tLF63yQxFBUh5sGHUHjyFFwiIhD53nu2U57LKxi4+U/glzuA/X8AP98Kh/NPIuTeh+A9cgRiHn9c9fvULVMReMstCHnwATi6uVm714IgCIIgNGFEdAuCYFuknS4V2KWW7OTDFbdhiS4K59bDtP/9W5W/5hlcmr3cwUx4l1phJ8wSl/JzJOH1N1SctIOHByI//ADOgYGwKVw8gKu+UlnNsX4OsOJFIPUkPCa9hXa//qrivNMWLEDKl18ie+1aRLz+Gty7dLF2rwVBEARBaKKI6BYEwXoYDFqJLl1gs6WfMtvIQcskrkT2UKDVUMCniizULAfGsmDMYm6cVE3V6Z5VfZ1uoUrSfv4FKV99pR5HzJplu2KVJcLGv6KVFOO5sO0rVWvd8aov0eKF5+E9ZjTOPvU08g8fxvGrrkbo/fchcOpUODjJgowgCIIgCPWLiG5BEBqPkhKtHvbJ9eVCOzvBdBsHJyCib7klu1U04BFQu++hsO4yCUXHVmHH6r/RZ8R4OLcbKRbucyRn23bEPf+8ehw8fTp8x4+DzRN9B+AXCfw0DTiyHPjiQuD6H+EzejQ8/vwDZ595FlkrVqgM7Fn/rUSLWbPgGtnS2r0WBEEQBKEJIaJbEISGo7gQOLuzXGAzw3heuuk2Tm5A5MBySzYfu3mf+3c7OsHQejhi9magd+vhIrjPkcKzZ3HmvvtgKCyEz7hxCL77LtgNXSYCtywEvrsGiNsNfHY+MOVHOId1R+Sc95H+yy+If2WmSrB2/JJLEPbM0/C75BLrJ4YTBEEQBKFJIKJbEIT6ozAXiNlaHpPNUl6si22MqzcQFV1uyW7ZD3CWRFa2TEluLs7cMx3FSUlw69wZEa/OhAPdt+2JyP6lJcWu1PIEzJ2gwhAc2o+B/xVXwHPQIMQ+PgO527bh7IwnkMXSYi88D+eAWnpZCIIgCIIgmCGiWxCEupOfCZzeWB6PTcFdXGC6DV3DGYetW7LDewFOMvTYCwaDAWefegp5+/bBKSAAkR98AEcvL9glAW2AW5cCC27QFoW+vRKY/B7Qdwpco6LQet7XSP7scyS+/z4yly5FzvZtiJg5E94jRli754IgCIIg2DEy8xUEoebkpGgu4rolm67jhhLTbbzDywU2LdkhXbSkVoJdkvzJ/5CxaDHg7IzI9961/3hnz0Dgxl+B3+8Bdv8I/H43kHYKGD1DJVELvvMOeA0fhtjHHkfB0aM4ffsdCLj+OoQ++igcPTys3XtBEARBEOwQEd2CIFROxlnglFGN7IR9Fbdhdmi9dBdbYDtAYmGbBJn//IPEd99Vj8OfeQaeAweiScBwhsv+p5WaW/0msHKWJrwnvws4u8Kje3e0/fknJLz5FlLnzUPq/O+QvW69Ki3m0bOntXsvCIIgCIKdIaJbEITy8l1pJ01rZKccq7gdLdd66a7WQ7TM0EKTg6W0Yh95VJ0XAddfj4BrrkaTgt4X5z8L+EUBCx8Gds4HMs4AV88DPPzh6O6O8KeehPfoUTj7xJMoOHECJ669TiWQC77zTjg4y+1TEARBEISaIbMGQWjOIjvxoGlm8YwY020cHIHwnuWW7FZDAK9ga/VYaCSKUlNx+u57UJKTA8/oaIQ9MQNNlgFTtYWjH28Bjq/SEqxN+RHwj1Ivew8bhnZ//I64F19UbvZJ789B1qpVaDl7NlzbtLF27wVBEARBsANEdAtCc6GkWCuXpFuyKbJzkk23cXTRsonr8dhRgwB3P2v1WLACLAkW88CDKDx9Gi6RkWj5zttwcHFBk6bjWGDqYmD+1UDifq2k2PU/ABF91MtO/v6IePNNeI85T4nvvJ27cOyyyxE2Ywb8r76qyZYWKy4xYOPxFGxNckDQ8RQM6RAKJ8em+VsFQRAEoSER0S0ITZWiAiB2e7klm1nG8zNMt3H2AKIGlluyWw4AXD2t1WPBBoifNRs5GzfC0dMTkR9+0HxKZrXopZUU+/YqLXfBFxOBq74EOo1TL1NY+02+CJ79+yH2iSfVPop77jlk/fsvWrz8EpyDm5YHyJI9Z/HCn/twNj2Pyw74+vAWtPBzx3OTu2FCjxbW7p4gCIIg2BUiugWhqVCQA5zZXG7JPrMFKMo13cbNF2g1uNyS3aKPShwlCCR1wQ9I/fZb9ZhJw9w7dUKzgm7m05YAP9wEHPsP+O5aYNIbwIBpZZu4RESg1RdzkfLV10h86y1k/fcfjk2+WAlvn/PPR1MR3Hd9sw0Gs+fj0vPU8x/d0E+EtyAIgiDUAhHdgmCv5KUDpzaWW7JjtwElRabbeAZryc50S3ZYD8DRyVo9FmyYnC1bEPfSS+pxyAP3NxkBWWsYTnH9j8BfDwA7vgX+ehBIPQmc/1xZ6TsHR0cETb0FXsOGIvbRx5B/8CDO3DMdfldegbAZT8DJ28uuXcpp4TYX3ITP0bmcr4/tFi6u5oIgCIJQQ0R0C4K9kJ1UXrqLQpvx2eZTY9+WRuW7hgHBHaV8l1AthTExOHPf/UBREXwnXoigO+9Es4beH5d8oJXD+28msPYdIP00cMmHgIt72Wb0BGjz4w9Ieu89JH8+F+k//YycjZsQMXs2PPv1hT2y6XhKqUu5ZTji8HVuN6R9UKP2TRAEQRDsFRHdgmCrpJ8xEtnrgKSDFbcJbF8usPk/6w6LyBZqATOUn75nOopTUuDWrStavPJKk00MViu4D0Y/rl1Tf0wH9vwMZMQC184HPAPLNnN0dUXoI4/Aa+RIxM6YoRLQnbzhBgTdfjtC7rkbDq72Fb6RkFm54DYmLt0sdEUQBEEQhEoR0S0ItlK+izWxdVdx/p92quJ2od1LRXZp8wm3Rm+FJoKhpASxM55A/oEDcAoKQtQHH8DRw8Pa3bIt+lwH+EYAC27UMv5/PhaY8hMQ2NZkM69Bg9Du998R/8pMpP/2G5I/+QTZq1er2Hi39u1hL4T6lFvyq+Lp3/dg9eEkXNAtDCM7hcDbTaYTgiAIglAZcpcUBGtQUqKVJtIFNv/PijfdxsEJaNG73JLNBGhGFjZBOFeSPvoImUuXAi4uiHz/fbi0kORYFmk3Crj1b+CbK4HkI8BnF2glxSL7m2zm5OODiFmvwnvMGMQ9+yzy9u3D8cuvQOjDDyPghikqFtzWcXZyUHHblmK6jZ0AsvOL8cv2GNVcnRwxuH0QxnYNxfldwxDhLws3giAIgmCMiG5BaAyKi4C4nabu4nlppts4uWolu3QrNmtku/lYq8dCEydj6VIkvT9HPW7x/HN2G4PcaIR21UqKsZZ33C7gy0nAFZ8BXS+qsKnv+HHw6NsHZ596Wlm742fOVFnOW7w6Ey5hYbBVNhxLxq1fbi4T3ObiWw86mHNdXwR7u2H5/ngs2xePE8k5WHUoUbVnft+L7hG+uKBrGMZ2C1OPJVxBEARBaO6I6BaEhqAwT8smXlYjexNQkGW6jYuXJqzLamT3N0nSJAgNRd6BA4h9fIZ6HHDTjfC/4gprd8k+8G0BTF0M/DQVOLwUWHADMOFVYPBdFTZ1CQ1F1P8+Qer8+Uh4/Q1kr1uHYxdfohY4fC+8ELbGykOJuOPrLcgvKsHwDsG4akAkZi0+YJJULdysTnd0uyA8ObErjiZmKwG+fF88tp5Kxd7YDNXeXXFY1fY+v2uoEuFMvObmLNUTBEEQhOaHiG5BqA8oqE9tL7dis0Z2cb7pNu7+pvHY4b0AJxdr9VhophSlpODM3ffAkJsLr6FDEPbYY9bukn3h5g1c+x2w6BFg6xfAkhlaSbHxr1Qox0cLb+CUKfAaMgSxjz2OvD17EPPgQ8j851+EP/M0nHx9YQv8vTcO987fjoLiEpzfJRQfTOkHdxcnXNQrAuuPJGDp6o0YNyIaQzqEVigTxt/YIdRbtf8b1R5JWfn490CCEuGrDiUp0f7NhlOqebk6YVTnECXAx3QORYCXfSWZEwRBEIS6IqJbEOpCTgpwagMcj6/GyINL4LzjJGAoNt3GKxRoM6zckh3StazOryBYA0NBAWLuux+FsbFwad0KLd96Cw7OchuoNU7OwEVvAwFtgOXPARs/0kqKXf4p4OpZYXO3du3Q5rv5KoY+6eNPkPHnn6ouesSrr8JrcDSsye87YvDQDztVfe5JPVvg7Wv6wNVZG6cosKPbBiJ5v0H9X5O63HQ7v2pAlGp5hcVYfzQZS/fFY8X+eCRk5mPR7jjV+FED2gRibNcwlYytbbD91jYXBEEQhOqQ2ZYg1ITMONN47IS96mnatQL0bVhayLhGdmA7Kd8l2BRxM2cqsefo5YWoDz+Ek7+/tbtkv/DaHv4A4B8F/Pp/wIG/gK8mA9d9D3iHVNzcxQUh990H75EjEfPY4yg8dQqnpk5F4C23IOSB++Ho5tboP+GHzafx+C+7VPGEy/u2xGtX9oKzU/0tDNJaPqZLqGolJT2wOya9LA78QFymqvXN9sqi/Wgf4qXEN0V431YBNRL4giAIgmAviOgWBHM4A2W5LuPM4ilHK24X3AnFUYOxI8UTvSb/H1yCTUsICYItkfrdd0j7foESixFvvmFXZaxsmh5XAD4tgO+uA2K2AJ9fAEz5GQjuYHFzjz590O7XXxA/+zWk/fADUr74Atlr1qjSYu5dujRat79adwLP/aEtHl4f3QovX9IDjg0odPnZvaP8VXt4XGecTslR1u/l+xNUAjfGhR9deQyfrDyGQC9XnNdFiwMf0TEYXlKOTBAEQbBz5E4mCBTZSYeNamSvAzLOmG3kAIT3KLdktxqqrFklhYU4s2gRevlFWqnzglA92Rs2Iu6Vmepx6MMPwWf0aGt3qWnBMYGZzb+5Akg9oQlvxn23HmJxc3oatHjxBXiPHo2zzzyD/MOHceKqq5XFm5ZvB6eGTTb28cqjKkkauXV4Wzw9qWujZxiPCvTELcPaqpaRV4iVBxOVFZzx4CnZBfhp6xnV6Oo+jOXIuoWrhGxhvpJsUhAEQbA/RHQLzY+SYiB+r6klOyfJdBtHZyCib7mreFQ04CGuuIL9UXD6NGIeeAAoKoLv5MkIvPVWa3epaRLcEbhtBfDdNUDMVuDrS4DLPtIs4ZXgc94YePT+HWefeRZZ//yjspxn/fsfImbPgkvLlvXeRYPBgHeWH1ZZxcm953XAQ2M7Wb2kl6+7Cyb3jlCtsLgEm0+kYPm+BCzbH4fTKbn492CiavgV6B3ppyzgdEXvEu5j9b4LgiAIQk0Q0S00fYoKgLM7ywX2qQ1AfrrpNs7uQOTAUkv2EO2xqyT2Eeyb4qxslam8OC0N7j16oMVLL4pIaUgYy33zX8Avt2sx3j9NA9JOA8PurzS/g3NQECI/mIP0n39G3MxXVcz9sUsuRdjTT8Hvkkvq7XhRcL+6+AD+t+qY+vuxCZ1x92jLLvDWxMXJEUPbB6v2zEVdcTghS8WAs+04nYadZ9JVe3PZIbT091C1wCnCB7UNLEsAJwiCIAi2hohuoelRkKPFVuqWbJbvKswx3cbVB2g1uNySHdEHcG78REaC0FAYSkoQ+/jjynXZKSRYCTtHd3HNbXCYvfzqr4G/n9KymjO7edpJ4MLXtaznFqCw9r/ySngOGqTqp+du346zM55AFkuLvfA8nAPK0jXWiZISg4rfnrfhpPqbtbanDrP9HBTcL53CfFS7Z0wHJGTm4Z/9Wjmy1YeTEJOWiy/XnVDNx81ZlSOjCB/dKRR+nlKOURAEQbAdRHQL9k9eBnB6Y7klO2YbUFJouo1HYLnA5v9hPSqdAAtCUyBpzhxkrVgBB1dXRM2ZA5ewMGt3qfnAet0XzgICWgNLngC2zAXSY4Ar52p1vivBtVUrtJ73NZI/+wyJcz5A5tKlSoC3mPkKvEeMqFNXWArs8Z93qfhoGs1fvawnrh3UCvZIqI+76jtbbkEx1hxJwnKWIzsQj6SsAvy166xqzo4OyvKt3NC7hqFVUMUyboIgCILQmIjqEOyP7GTglF6+ay0Qt5tmPdNtmE3YuHxXcCepkS00GzIWL0bShx+px+EvvgCP3r2t3aXmyeC7ACZZ/Pk24PDfwJcTget/AHzCK30L66YH/9//wWv4CMQ+9hgKjh3D6dvvQMD11yP00Ufg6OFR469nfPSDC3YoIcoSXG9e1RuX9q3/WHFr4OHqpKzabLTk7ziTpgQ43dDpkr7uaLJqL/61D53DfHBBNy0beu9I/wbN0i4IZZQUw+HkGrRMWQ+Hk75Au5HagpwgCM0SEd2C7ZMRa5r0LFHLumtCQFsjkT0UCGgjNbKFZknevn2IfeJJ9Thw2jT4X3qptbvUvOk6GbhlITD/Gi23xGcsKfYjENq1yrd59OiOtr/8jIQ33kTqN98gdf58ZK9fj4jXXoNHzx7Vfm1eYTGmz9+uXLFdnBzw/nV9MaFHCzRFKKL7tQpQ7bEJXXAiKVv9brbNJ1JxMD5TtQ/+PYpgbzdc0FUT4MM6BCvxLgj1zr4/gCWPwzkjFgP498mPAN8IYMJsoNvF1u6dIAhWQES3YHvlu1KPl5fuotBmCR5zQrqWC2w23swEoZlTlJSE0/dMhyEvD14jRqjyYIINEDkAuG0Z8O1VQPIR4PPxwDXzgHajqnwbY/DDn35KKy325JMoOH4cJ667DsF334XgO+5QVnFL0PX6jnlbVNyzm7MjPr6hP8Z0CUVzoU2wF24b0U61tJwC/HcwEcv2x6uyZElZ+fh+82nV3F0cMbwD48BDcV6XMIT4SF4PoZ4E9w83cUJj+nzGWe155nwQ4S0IzQ4R3YJ1KSkBkg6a1sjOPGu6jYMjEN7LqEb2EMAryFo9FgSbpKSgAGfuvQ9FZ8/CtW1btHzzjQav9yzUgsB2wK3LgO+vB06t12p6XzIH6H1ttW/1Hj4M7f74HWeffwGZS5Yg6b33kb1yFSJemw3X1q1Nts3KL8K0Lzdj0/EUeLo64bObBmBoh2A0V/w9XZVLPVtBUQk2Hk9WbujL9yeoRGy6RdzBYTf6RPkrCzhd1juGekumf6FuJUmXPF5RcCv4nAOwZAbQZZK4mgtCM0NEt9C4FBcBcbtKS3et1/7PTTHdxskVaNm/3IodOQhw97VWjwXB5mE5qLgXXlBJtxx9fBD54Qdw8pVrxubwDARu/A347S5g7y/Ar3cCaaeAkY9WGw7j5O+Plm+/hYzzz0Pciy8hd+dOHLvscoTNeBz+V12lBGJ6TiFu+mITdp5OU9m8v5w2EP1bBzbaz7N1WFJsRMcQ1Z6/2ID9ZzPLRPeuM+nYfipNtdf/PojWQZ5lidgGtgmAs5PkBBEskJsKxO8DEkrbyfVaSFylGICMGGDPz0Cvqxuxo4IgWBsR3ULDUpSvZRPXLdnMMl6QZbqNiycQNajckk3B7VLzZEGC0NxJnfcN0n/+RSULbPnWW3Bra/vloJotLu7AFZ8D/lHA2neBf18BUk8Ck98BnKouc0Vh7Td5Mjz790fsjCeQs2kT4p59TpUWc3/iGdz821HsO5sBf08XzJsWjZ6Rfo32s+wN7stuEb6q3Xd+R8Sl56ks6LSCrz2ajJPJOfh8zXHV/DxcMKZzCC7oFoZRnULg4y7lyJodhblA4sFyca0LbXPPvJryy+3APy8BbUcB7UYDbUcC3s0nBEQQmiMiuoX6pSAbOL2p3FX8zGagON90Gzc/oPWQ8sziLXpXO9kUBMEy2evWIX72bPU49NFH4T1iuLW7JFQHKymMfRHwbw0segTY8Q2QcUaL9XSvXii7RESg1ZdfIOXLr5D49tvI+u8/nN2wFT69r0Rwx3745rZB6BIung61IdzPHVOiW6uWnV+E1YcTsWxfAv45EI/UnEL8tiNWNSalG9wuSFnAz+8aisgAKUfW5NzDU44DCXtNLdgpxypWSdHxiwJCu2nJER2dgdVvVP89DJujl8v2eVoj/AyKbwrxNsNqNBYIgmA/iOgWzt216pRRjeyzO4CSItNtvEJMa2TzxiKxTIJwzhScPIkzDz4EFBfD79JLEXjLzdbuklAbBt6qTdh/vAU49h8w90Its7lf9WW9HBwdETRtKrJ69sOh+x5CZGosnt/4BRyDU9DBe0ijdL+p4uXmrDK9s7HO+bZTqVo5sv3xOJaYrRLUsT33x150beGLscyG3i0MPVv6SRy4PSVtpZXa2GrNRmt2UZ7l93gEAKHdgbBSgc3HoV1MxTFF+875WtI0i3HdDlri17vWA2c2adf98ZVa6VO9Dxs/BhycgIi+WrJFivCoaM1LRhAEu0VEt1A7shKMMouvA+L3VLyx+EZqq7S60A7qIOW7BKGeKc7Kwum770FJerqqwx3+wvMy4bdHOo0Dpi4C5l+tWdc+O1+r5d2iV7VvZWms65cnIXH4fbjnxHKM37MCJQt/x/Fd2xAxezY8+/VtlJ/QlGF984FtAlV7YmJXHE3MwgrGge9LwJaTKdh/NkO19/45gjBfliMLUwJ8SLsguLvI4rJNkJsGJOyv6Bqel2Z5e2cPTUwr63WpwA7rDniHVT+XoUGBZcFU9nIHs/lR6XsnzAI8/ICOY7VGspOBE6uAYys1EU7LeswWra1+E3B214S3EuGjgYg+YrwQBDtDRHdzg6uwFMtZ8doNhMK4qoGb7k9MDKJbspMPV9yGotrYku3fqkF/giA0dwzFxYh9+BEUHD0K57AwtHz/PTi6Sbkju4UT6NuWayXFEg8AX1wIXP0V0OGCSt9yOD4TUz7biITMfLQL98O1T78On4O7EDtjBgpPn8bJG25A0O23I+Seu+Hg6tqoP6cp0z7EW7U7RrZHSnYB/j2QoBKxrTyUiPiMfHy78ZRqzBw/sqMWB35el1AEeskxaJQcMhXirvdroRuVuXhz/qKLa2XB7gYEtDk3QctyYAwVYRZz46Rqqk73LMvlwliRpftlWiNppzXxrYtwztn4Pxte1ML02gwvFeEjgZAuYtwQBBtHRHdzqx1p8SYwW7sJ0N2KNWSNy3elnzb7EAcgrEd5ZnGW7/IJa+xfIgjNmsR33kXWypVwcHND5Jw5cAmVBDx2Dxcrp/0NLLgBOLEa+PZq4KK3gf4VQwb2xKTjprmblOjrEu6DebdGazWmBw1Cu99/R/zLLyP99z+Q/MknyF69GhGvvwa39u2t8rOaMhTSV/SPVC2vsBgbjiVjmSpHFq8E+JK9cao5OgD9WweUWcEp2oVzNB6knqjoGp58lCuSlt/j29JUWLMFd2o4l23OqbpMQtGxVdix+m/0GTEezu1G1lzMM9Fi3xu0xrlZ0qFyAX58NZCfDhxcqDVCI4oeD04hLsYPQbA5RHQ3J8Gt3J3MXMEpwH+4EYgcqN3EshNNX9fjinRLdqtoLa5JEASrkP7nX0j+9FP1uMUrr8CjZw9rd0moLzz8gRt+Af64F9j1PfDnfUDaSeC8Z8qsWIwvvmXuJmTkFaFXpB++njZI1aLWcfLxUa7l3mPGIO6555G3bx+OX34FQh95BAFTrlex4EL9Q1fy0Z1DVXv50h7YE5OhYsAZC86M8ptPpKr26uIDaBfspcQ3RTjFOF3YBQtQbNLCay6uEw4ARbmW38P46gpx1121a6uxcXSCofVwxOzNQO/Ww+tuPee1H9JZa9F3aIsOzJ+ji/BTG7T9tPtHrZGAtuXx4BTjXsH1+tMEQag9IrqbAxygaeG2mNSjFGYZJ05umgAvq5E9EHCTVXlBsAVyd+/B2aefVo/pOux30SRrd0mob5xdgcs+BgJaAytna/GcDPO55ANsOJWFW7/cjOyCYgxoHYC5UwfCt5LyVb4TJsCjbz+cffJJZK9di/hXXlFZzlvMfAUuYeKd1JAwtwLLtbE9NLYTYtJyVRw4reC0hh9Lysb/Vh1TLcDTBed1CcPYbqGqfjiTuDVL8jJM4675OH4vkJtieXvGOFOElsVdl1qxfVo0fTdrineWVmUb8RBQmFealK1UhLNMa+pxYCvbl9p7wnqWi3BWj3HzsfavEIRmRzMd3ZsZdBM3dimvDLqZD5gKOEtsqCDYGoUJCTgzfToM+fnwHj0aIQ/cb+0uCQ0FRcOYJzUX0T/vV9artPiTuDf2DmQXeWJYhyB8etMAeLpWfQt3CQtF1GefInX+fCS89roS38cuvgQtnn8Ovhde2Gg/p7nT0t8DNw1po1pmXiFWHUpSLuj/HEhQ5ch+3nZGNVcnRwztoJUjY2MZsyZHUYHmKm0ed51+qvK468B25VZr3T2cz0kiMQ26yCvX8pEAntEWMDjv02PCVfmz3VpbP0cra0bBrrui07gi8z5BaHBEdDcH6HZUE+h+JAOvINgcJfn5OHPvvSiKj4dr+/aIeON1ODjJhLPJw3hO35Yo+m4K/BM24TvHM/hf+9l48eaBNc6MTatr4JQp8BoyBLGPPoa8vXsR8+BDyPz3X4Q//TScfKWed2Pi4+6CSb1aqFZUXIItJ8vLkZ1MzsF/BxNVe/q3PaoEmRYHHopuLXztqzpBSYkWGmGeMZx5Y8zLiurQSm2cLZyPac128Wjs3ts37r5A5wla06vOHF9VLsJ5XE5v1Nqq17Rs7bR+6yI8vJcsaAhCAyCiuznABBv1uZ0gCI2GwWDQYnN37oKjnx+iPvwATt4S8tFc+COrMz7KfRafO89GB8dYzE57CA4JLTVLVS1wa9cObb7/DokffojkT/6HjD/+RM7mLYiYNQte0YMarP9C5Tg7OWJwuyDVnprUFUcSssriwLefTsPumHTV3l5+CBF+7mVx4Nze1dmGYvMp6izFXRdmW96embeVsDZyDeffnoGN3fPmgXco0PNKrRHm7ylLyrZKy+Vz9B+tEXd/oO2IUhE+Wsq+CkI9IaK7OcDYbGYpr9TF3EF7ndsJgmBTpHz5FdJ/+w1wckLkO2/DtXVra3dJaCR+2HIaj/+8CwZDFD7t+j88m/k8HOL3AF9eBFzxOdBlYq0+z8HFBaH33w/vkSMR+/gMFJ46hVO33ILAW25R4QpSds560IrdMcxHtbtHd0BiZr4qR0YRvvpwImLT8/D1+pOqebs5Y1SnEIztFoZh7RoxsWl+llncdanQzkmyvL2Tq+W4a2YSFxFnPVgSrT/bzVqyOh5Him8K8RNrtPrl+//UGvGJ0FzX9Zhwv5bW/gWCYJeI6G4O0E2I8drMUl6B0hsfa0eKO5Eg2BRZq1cj4fXX1eOwGTOUi7DQPPh6/Qk8+/te9fi6Qa3wzKU94FA4GPjxFuDIcmDBFODC14BBt9f6sz379kW7X39B/KzZSPvxR6R88YWK92ZpMffOnRvg1wi1hSXgrh4YpRrLka09osWBL9+foAT5wt1nVWPm87bejoj3P4nxPVqgdZDXuX95cSGQdLiiazjdki3iAAS2rVjvOrA94CTTTJuGix905WcbfBdQXATEbgeO/6eJcLqgZ8Zq1RTYCC3fuit6mxHioSAINURGw+ZCl0mAqzcMeVnISXRFUZ4TnN2L4dk+GA4TS+t0C4JgM+QfO46Yhx5WsZH+V12JgBumWLtLQiPxycqjqrQUmTasLZ65qKsWz8uMw9d9Dyx8GNj2FbDoEc1VdOxLQC1LgTl6eaHFSy/Ce8xonH36GeQfOoQTV16lLN60fDNngKG4GDmbN8Nnxw7khITANzpacglYAcbvn981TLVXSgzYFZOuXNApwg/EZeJIhiNmLj6oWsdQ7zI39D5R/lWXI2PcdfrpiuKagruksPIwNCWsS0tx6XHXrvUg9gXrw0WSqIFaG/koUJirlSTT48FZqoxx+WxbPtcWXFr0KhfhrYbIuSAIlSCiu7kQsw0ZR4sQvz0cRTnlkzPnfWEI6+UO325W7Z0gCEYUZ2TgzN13oyQzEx79+iH8mWfsK4mSUOf4/XdXHMY7yw+rv+89r4MqOWVy7J1cgMnvaiXFVryoZSOmcLrskzolnPI57zx4/NlbCe+sf/9FwutvIOu/lfCdNBFJH3+Corg4tAAQ+933SAgPR9iTT8B33Lj6/NlCLXB0dFBimu2R8Z1xND4dc35diTjHEGw6kYrDCVmqffTfUQR7u+K8LqFKgA9v6QDP1INmcdf7gYIsy1/k6mMh7rob4BXU2D9ZsCYcU9qP0RrJTQNOri2PCU88AJzdqbV17wGOLkDUoNJs6syMPkAbswRBENHdXMj44VPErGXsl+nEvSghATH3PwC8+45MpATBBqB1MebhR1Bw4gScW7RA5HvvwsHV1drdEhpBcM9afACfrDqm/n50fGfcM6aD5Y0pwkc8DPi1An6/G9j3O5BxFrjuO60KRS1xDgpC5IcfIO2nnxD/6ixl3WYzh9nz5X5hW7QK9MToFgZMnDgAOYXA6n0nsH/XFmSc3IE2eSfRaedpdNl9Gp4O6ZY/gCJJxV13NXUP94uSuGuhIh7+muckG8mMK48HpwjnAiBFOdt/rwIuXlq+ID0ePKxHrb1yBKGpIKK7mUzi479bW8mLBnVjjZ/5KnzOP19cBwXByiS8+RayV6+Gg7s7oj6YA+fg2osowb4oKTHg+T/3qiRZ5NmLumHa8LbVv7HXVYBvC+D764Ezm4DPxwJTfgKC2te6D7SmB1x1FTz798exSy4FCi24F8v9wnZg7G3yETic3Y0usX/A6cfv4Jd4ABelnsBF4HGqOMM7WRKKQ4YoHDBEIS+gMyI790e/vgPRKSJAPGmEuuETDvS6WmscH1KOlbuiU4znpgBHlmmNeAZpceC6CGe9dTn3hGaCiO5mQM7KJSjKKqlg5S7DYFAuhDlbtkrpGEGwImm//YaUuXPV44hZr8K9m8R9NHWKSwwqQ/lPW8+ouefMy3qqxGk1ps1w4NZlwLdXahPezy7Q4r5bRdepP0WJSZYFt47cLxoXCpn0Mxbirg8BxQVqEqdS38UbvccrxMRqbQjthkOGllh2mCXJErDzdBqQCCCxCFizHlGBHsoFfWzXMAxsGwgXJ7FECnWAAxgX/NgGTNNyBrDagl6a7MRaICcZ2Peb1gg9Kii+9ezoFPGC0EQR0d0MKNrzX422i581SyVs8h45Cq6RUhJCEBqT3B07EPfMs+px8N13wXfCBGt3SWhgCotL8OCCHfhrl5aF+o2reuGyvpG1/yC6B9+2Aph/tZZ5+KvJwOX/A7pfWuuPKkqkGquejIUL4d6tK5x8fGrfX8EyOSkW6l3vB/IzLG/v4oWSkC44le+NqH7j4NSipya0vUNMNnMoFeado4Dp53VEQkYeVrAc2b54rDmShNMpufhi7QnVfNydMaZzqErGxrJkfh4SjyvUEbqRM8ka29B7taz4MVvLXdFPb9Lc0Xd8ozUS3LncCs4FRbqzC0ITQUR3M8A5a3+Ntsvfvx/xL76EeLwE1w7tlfhmPVfP/v1UfVdBEBqGwvh4nL73XhgKC+F9wfkInj7d2l0SGpj8omJMn79dCR8XJwe8d21fXNiTKcvqiHcocMtC4KdbgUOLtdJi6S8BQ6bXyn3TOcRUsFVG2g8/qPrx3qNGwnfSJHiPHg1Hd/e69785UZADJJklNePjrDjL2zs6A8GdLMRdt0JxcTF2LlqEloMmwqmG9+lQX3flTcGWU1CE1YeTVDb0fw4kIDm7AH/sjFXN2dEB0e0ClRWcLSrQs373g9C8YEK1VoO1NvpxoCAbOLW+XISf3aVdF2yb/gc4ULT3KRfhfF8dkkUKgq0gorupU5gLz6ItcPbwRVFuJfF3Dg5wCgpCwI03qFjS3O07UHDkKFLY5s6Fo7c3vIYOVZMrrxEj4BIa2ti/QhCaLCV5eThzz3QUJybBrVMntJw9Gw6SaKZJk1tQjDvmbVFix9XZEZ/c0B9jutTDuMpSPdd+CyyZoU1alz4NpJ4ELpwNONYs/tpzQH84h4erpGnKtdkCvCc4hYai8NgxZC5brpqjp6daMPK76CJVT14WakvjrunyXyas92qWaz7HuGtL+LcCQkvLcelluYI6As6VJFMsLj6nLnq6OmN893DVGOqw43Qqlu1LUOXIjiRkYe2RZNVe+HMfuoT7YGxpObKeLf1UJnVBOKfxqsMFWtM9PU6sLo8HTz4MxG7T2pq3ASc3LTO6LsIj+kkdeMGukLO1qXNiDRxKchE8IABxqy28XmoBCX/2GZWNNuTOO1Gcno7stWuRtXIVslavRnFKCjKXLlWNMM7Ua9RI+IwaBfeePSWZjiCcQ8ZqlmrK27MHTv7+KoM06ycLTZes/CJM+3IzNh1PgYeLEz67eQCGdajHZHkU1xe+Bvi31kT35k+1mOArP69R/VyO5ywLprKU8/5gLLxL7xctZr4Cn7FjkX/woHIzz1i4CIWxscj440/VeC77TBgPv0mT4NG/f9NfROI+yoitGHedeBAozrf8HiaUMql33V0LE3D3hbVgiEP/1oGqzbiwC44nZWPF/njljbH5RIqqCc72/j9HEOrjpuqGj+0WiqHtg1UtcUE4JzwDgW6XaI2kx2jiW0/MlhmriXI2vKyVtWszrLxGOK8nScom2DAiuu2AEgOw8XgKknOKEOrjjkFtA9XNsUYcWqL+K3JrB+CYKj1kKCgoe9k5LKxC3VUnPz/4TpyomqGkRAkCJcBXrULe7t3I27dPteSPPoZTQAC8RgzXXNGHD1OTLUEQakbyZ58h46+/AGdntHz3XbhG1iGeV7Ab0nMKcfMXm7DjdBp83JzxxdSBGNAmsP6/iBPPodMB/yjglzs0d/MvJwHXLQB8wqp9u7ofvPuOylLOpGmV3S/cu3RRLeShh5SHlBLgixerhdq07xeoRqu5up9MmqgWbO0+S3Zuqmat1q3WutDOq6Qkl4snENLFtN41hTaTndn4vmgb7IXbRrRTLTW7AP8dSsDyfQn472ACEjLz8d2mU6px8WhEx2AVB8664MHebtbuutAU8GsJ9LlOa1zYSj4CHPuvNDHbaiAvTZvjls5z1TWl1wenCA9oY+1fIAgmiOi2cf7eG48XtjkhbcOWsuda+LnjucndMKFHNfF/HKQOLYWhGEjdqiXHaTHrVTgHBatkOYzdoythVZZqWig8evVSLeTe6ShKSkLW6jXIWrUS2WvWojg1tcy6waQZHn36qDhwuqK7deli/xMsQWggMv/7D4lvva0ehz/1pGSCbuIkZ+Xjxs83Yd/ZDPh7uuDraYPQK7KBFylpMfJpAXx3rZZgjZnNb/hJs6hWA4U1y4JlbNyIrcuWof/YsfCNjrZ4v+A479mvr2phT8xA9oaNSoBnLlumRDvDlNhc27SB70UXKQHu1rYGJdGsSWGe5bhrWtss4eAEBHcst1or9/BugH+bJlGXOMDLVSX5Y2M+gg3HUlQcON3Qz6bnYem+eNV4y+/XKkDLht4tFO1DvGUeIJw7PId4fbENuh0oKQbidpXHg59cD2QnAnt+1hqht4/uik4xzrwXgmBFHAz0b2zGZGRkwM/PD+np6fD1tZ5blyWW7DmLu77ZBoOK/Sq/aemPPrqhX9XCmxOEj4YgI8YXMau94RQSjI7//FNvsXZM+sSMy7SAZ/23EvmHD5u87hwaqsWBjxwJryFD4eTd9NxmCwsLsWjRIkycOBEuEsNoc9jq8ck/ehQnrr4GJdnZ8L/2GrR4/nk0R2z1+NQ3zBY95bONOJyQhWBvV3xzWzS6hDfi/Sb5aHlJMXc/4Nr5WmbgBj5GJfn56v6Q8ddCZP33Hwz55a7WtHozAZvvxAvh0uIcEsidK5y8pxw3yhZeKq5TjgIGltq0AMsc6UnNdPdwJjpzdmt21xCnkHtjM5T4ZtsTY5ppvU2QZ6kAD0P/1gFwbmblyKx9fJoNRfnAmS3lrugxW4CSItNteL3qVvDWw1Qohxwf26bQTo5PTbWkWLptFCY0YeISbUXEdJVYl+B8fWy38MpdzQ//rf5LPcXVvRwEXHV1vSa34Wd5DhyoWujDD6uYvqxVq5G1ciWyN2xAUUIC0n78STVw2wH9NTf0UaPg2raNrH4LzZLitDScvvtuJbh57YQ/+aS1uyQ0IGdSc5TgPpmcg3Bfd3x7e7Sy/jUqrJt763LN4n1mE/D1pcClHwK9rm7Qr3V0c4MvLeRjx6I4KwtZK1YgfeFCZK9dVxamlPD66/AcMAC+F02Cz/jxcA4IaJjO0L6QGQcklLqFG8ddF+Vafo9HgKnVWj3uoi1cCArex3u09FPtgQs6ITYtV5UjoxV8/dFknEjOwWdrjqtGD4/zSsuRjewUAm83mYIK9QQXvBjfzTbmSSA/U7N+6yI8fnf5otrGjzTPlJb94Nh6BIIzXYGi89Q8VRAaEhnxbBQm2aHLVmVQePN1bjekfZDljQ79jfx0Z+SczAGcnOB/9VUN12GGrkVEIODaa1SjhSNn8xYlwNkKT51CzvoNqiXMng2XqCjNDX30KCU8pNSM0BwwFBUh5qGHUHjyFFxatkTLd99ReRaEpsmJpGxc/+kGxKbnISrQA/NvG2y9skteQcDNfwC/3gns+x345XYg7SQw4pFGiS128vaG3yWXqFbE5Jx//60EeO6WrcjZskW1uJdfgdfQISoBm/f5F9TdO4rx1ZbirhmPbQlnD83lviypWakF2zvM5uOubY0Ifw/cOLi1akwauPpQIpbt18qRpeUU4pftMaq5OjlicPsgjO0aqhKy8X2CUG+4+QCdxmmNZCeVJmUrTcxGr58zm+F0ZjOG8d785jtaSTLdEs5SZTWs+CAINUVEt42SkJl3btux9MLpjUg9ollUfM4bA5fwcDQWtHAwsRobnnoSBSdOlArwVcjZvBmFp08j9dtvVXNwd4fX4MHKFZ1CnGJEEJoi8a+9hux16+Hg6akylTsHNkASLcEmOByfqSzcTDjVLthLWbhb+FlZWLDG7ZVfAsufBda9D/zzMpB2Cpj0llZDt5HgeR9w3XWqqaznixcrAZ6/bz+yV61WzYH3kDFjVPw37wu8p1h0KU06VGq1NrJgZ5yx/MWs+xvUwSzuuruWcEkm2PUOLdmsPc9WVFyCbafSlAs6s6EzM/qqQ4mqPfP7XnSP8C1zQ+dj8YQT6hWvYKDH5VojHPeOr0LJ0X9RcGAZ3IvStSRtbCso2v20EBw9JpyLcnJOCueIiG4bhVnKz2m7IytQUmBA+glNdHNyY02YQCeQ7eablVst3c/1jOhMtMN4Pza1bYf2ygWdruhMzCP1XoWmQNpPPyH163nqccTsWXDvXH0yK8E+2ROTjpvmbkJKdoGqbTzv1miE+NhIRmcm9Rr3spZkaPFjwLavtdI8V31plXJV9JAKuvVW1fKPHS8tQbZQLdRmLlmimqOPD3xGRsN3QFt4hRXAIfmAJq6ZzZiZQi3h27I0W7hRvevgzoCLeFVZA8Zys/IK25MTu6oa4CoOfF88tp5KVXHhbO+uOKySxZ7fNVSJcHryuTnLgohQz/i3AvregOIe1+Bv54WYOKgDXE6v1VzRT6wB8tOBgwu1RrzDtWRsughnZQhBqCUium0U3ph444lLzyuN6zaF623hflr5MIsc/hvpJz1QUqgJXs/Bg2ErsA4xs+KyMQlL/qFDmgBfuRK527ej4MhRpLB9PheO3t7wGjZMc0UfOUJlXBcEeyNn2zacfeFF9Tj43ukqxlVommw/lYqb525CRl4RekX64aupg1TmZ5uDGYD9IoGfpgFHVwBfTASm/AD4RlitS25t2yDklqsQfGFX5G1ehYx/1iNjewyKMjORvnA50hcCTm7F8G2VC9/WufAIKoaDh5/luGvGYws2S4dQb9X+b1R7ldmf7ucU4asOJanQuW82nFLNy9UJozqHKAE+pnOobV5Lgn1DCzYt2RE9gOg7geIi4OxO4DjLk60CTm0AsuKA3T9ojQS2K3dFbzNSC98RhGoQ0W2jMDkay4Ixe3l56jRT+LrFJGrFRTAcWobUI1o8XMB116rSX7YIXcho8WMLvuN2FKenI3vtWs0VfdVqVZKMsX9sxL17d80NfdQouPfoUWW5M0GwBeg+e+be+5iGUyWKCr7rLmt3SWggNhxLxq1fbkZ2QTEGtA7A3KkD4etuw546nS8EblkIzL9GSzTEkmLX/wCE92j472aiI0tx1znJ6m5HR3wPGqsjgNxEV6Sf8kbmGQ8U5zkh9bC3ai4twrUSZMMmw71zp4bvs9AgBHm74aoBUarlFRarBGzLSq3gDM9YtDtONU53WNd+bNcwlYyNdcQFod5xcgYi+2ttxMNa+UAmoNTLk8Vs02LC2bZ+ob0nrGe5Fbz1UMCtkZNlCnaBTYruDz74AK+//jri4uLQu3dvvP/++xg0qPoatt9//z2uu+46XHLJJfjtt99g77Ac2PvX9sbTv+xAWoHpoty71/SpvFzYmU3IjclGflqIipf2u/RS2AtOfn7wnThRNUNJCfL27FHlyOiGzsd5e/eqlvThR3AKCIDXiOGaK/qwYXDyb+Cat4JQS0pyc3F6+nQUJyeruvURr8602QUw4dxYeSgRd87bgrzCEgxtH4TPbh4AT1ebvMWa0rIfcNty4NurtLrUcycAV38FdDhfldNyOLkGLVPWw+GkL9BuZO1jn4sKgOTDFetdp5+qPO6aVqTSuGuH0K7wDOsOz4C2CC8xIHvdOhX/nbV8BQrPxiH5089Uc+vYQStBNmkSXKPE9dNecXdxwpguoaq9fEkP7IlNV+J72f4E7D+boZLHsr2yaD/ah3gp8U0R3rdVQOWVXAThXGBICl3L2fCMlqjx5LpyEa7GtN1aWz8HcHQGWg4oF+GRAwFn8dCoLYbiYpUDymfHDuSEhMA3OtruDW02NyNYsGABHnroIXz88ceIjo7GO++8g/Hjx+PgwYMIDa28sP2JEyfwyCOPYMSIEWhKjO8ehsITxQjpNhiJWYV4aeE+pGQXoriq8uqH/kbqYW0FmEloKGTtEYoTj169VAu5714UJSVpJclWrUL2mjXKCp7xx5+qMU7Ro08fTYCPGgm3zp0lEYtgVRg6Efvkkyo5lFNgIKI+mANHTytlrhYalKV74zB9/nYUFJdgTOcQfHRDfyUe7IaA1sCtfwPf3wCcXAPMvxrodwtwaBGcM2IxgNuc/EhzPZ8wG+h2ccXPKCnRsqErq7VRUjMKbvN6uTo+LSrWuw7poiV8swCr/Ghj/Ci1oMU8IKoE2cpVyD98BInvvKuae69e8GMJsgkT4FLFvEGwbRwdHdAr0l+1h8Z1VuX3VuxPUInY6FVyNDEbR1cewycrjyHQyxXnddHiwEd0DIaXlCMTGgqWDKSXEBvJStDc0JmEjSKcSdpOb9DaytmAiyfQaki5CA/vpeXWEColY+lSxM98VeV8onkx9rvvkRAejrAnn4DvuNKM9HaIg4EzQxuCQnvgwIGYM2eO+rukpARRUVG49957MWPGDIvvKS4uxsiRIzFt2jSsXr0aaWlpNbZ017Sgua0Uhn9/xWG8uewQ+rcOwM93DbX4nqLXB+HIFxkwlDigzU8/waNHdzQ1DIWFyNm+HdmrtFhwTriMcQ4L0+LAR42E15AhKo68MY6PYFtY8/gkffyxEgCs/dn6yy/g2b9/o36/PdAUrp8/d8bigQU7UFxiwIU9wvHutX3h6mynEypmA/99enncYgVKFzIvngP4R5q6hyceAAqyLL/NzdcsqVnpY8/6yd5fnJGBzGXLkbHwL2Rv2KgtABBHR3gOGqQWnzlRs9cF6KZ+DdWFjLxCrDyYqOLA/z2QoHIo6PD6G8ZyZN3CVUK2MF/rJc9rrsfHXmiQ45N6otwKTjGenWj6OvNNMDO6igkfrVVUECORieCOuf8BWi5gQuk+YqlVWxPeNdWSNrUUWFBQgK1bt+KJJ54oe87R0REXXHAB1q9fX+n7XnzxRWUFv/XWW5XobspcMyhKZffcepLZPtPRPcJsEpF6EmmbY2Ao8YV7j25NUnATZjT3GjRItdBHHkFhTAyyVq9WCdmYGb0oPh5pP/6oGrf1HDgAXkqEj1KJ5cQKLjQkmStWaIKbCQ+ffUYEdxPlxy2n8fjPu1BiAC7r2xKvX9lLZWm2W5zdgEs/Ag4uqkRAl06C/rjH8vudXLUM4SqhWWlZLj5mJvEGHHOdfH3hf8XlqhUlJiJjyd8qA3ou3RI3bFAt7sWX4D1ihBLgPmPGiNeJncNcCZN7R6hWWFyCzSdSsHxfApbtj8PplFz8ezBRNfwK9I70UxZwuqKzmoDc/4UGhSUI+7PdrAlHup/rIvzEWiA3Fdj/p9YIx0flvl6amM2KySxtwaU8fuarFQW3etGg7iN8nYmY7dHV3KZEd1JSkrJah4WFmTzPvw8cOGDxPWvWrMHnn3+OHTt21Og78vPzVTNendBXu9hsDb1P+v8B7k4Y1y0Ui/bE4+t1J/DyJd1MtnfYtxBpR7XJhO+119nkb2oQQkPhfcUVqpXk5yN3yxbkqHqvq1B05oyqjcyWMGs2XKKi4DliBDxHjoDHgAGW67/W8fgItoU1jg+z8cc8+ph67Hf99fC+9FI5P5rg9fPtxlN4/i/tvnTNgEi8OLkrDCXFKCyppISVncAYbufKLNZGGLzDYYjoB0NoVxhCusJA6zVjsRnPaE5RJe7lDYG/P3yuvUa1wjNnVMmxrEWLUXD4MLL++Uc1Bw8PeI0eDZ9JE+E5dKhdl6W052uoPhnYyk+1GeM74EhCNlYcSMCKg4nYcTodO89ojV6CLf3dlRv6+V1CMLB1QIN7pcjxsW0a5fgEdtLagNtVqI1D7HY4nFiltTOb4ZARA+z8TmscW4M6oKTNSBjYWg9rVpUYctavVy7llWIwqNczNm6E58CBsBVqev7YlHt5bGwsWrZsiXXr1mHIkCFlzz/22GNYuXIlNm7caLJ9ZmYmevXqhQ8//BAXXqjFVtxyyy1Vupc///zzeOGFFyo8P3/+fHjaycr3kXTg/X3OcHU04MX+xfAwmuP0+3cmspZkwODmjCPPPAeDHU8m6gWDAS5JSfA6cABeBw7C8/hxOBSXT4pLXFyQ06E9srt0QXbnLigKkGRsQt1xzM5GqzkfwDUlBTnt2+PMrdMAO1yNFapmRYwD/jilHddRLUpwWeuSJuMdyKRpAxi/XQ1bWt+FmMDy+7St4xoXD5+dO+CzY6e6PnWKPTyQ2bMnMvv0Rm7bthJr2cTIKAD2pjpgT6oDDqY7oLCk/EJ1dzKgq78BPQIM6BZggKdNmaGE5oBTST4Csw4jOGsfQjL3wT/nOByMCgUb4IB0j9ZI9OmORJ+uSPHujGLHuhuKbI6SErjGx8PzyBF4Hjmq/neswSLt2euuRWafPrAVcnJycP3111frXm5Topvu5RS+P/30Ey41yrh98803KyH9+++/m2xP63bfvn3hZDSpZQy47pbO5Gvt27ev1tLNmHFa2W01pnvZsmUYO3ZsWbwJD9nE99fhSGI2np3UBTcObqVtXJCNs5P7IzvWFf5XTUbws69Yt/M2SEl2NnI2bETO6tXIXr0axQkJJq+7dmgPzxEj4TViBNz79K7WAmLp+Ai2Q2MeH+YZiP2//0Pups1wjoxE1HfzJaN+Ndjb9cOxd86/x/Dev0fV33eNaosHz+/QpNxVlaX7m+orXhTd8BsMrYfD3uAxzN+9G5mLFyNryd8oTkoqe82JHlPjx8Nn4oVw697dLo6rvV1D1iS3oBjrjiYrC/g/BxKRnF1eFsbZ0QED2wTgvC4hOK9zCFoF1o8RRo6PbWNzxyc3DQ6n1ikruCMt4UmHTF42OLrAEDlAs4KzRfQDnGyg37Wg8PQZ5GzcgNyNm5C7aSOKU1Jr/RkRcz+3KUs3tWRwcLB9xXS7urqif//+WLFiRZnopojm39OnT6+wfZcuXbB7926T555++mllAX/33XeVmDbHzc1NNXN4sdnEBVcJ5v27aWgbPPv7XszffAZTh7dTk4OCdX8hO1bbJujWu23691gNf3+4TRiPgAnjtcnXwYMqDpwZ0XO3b0fBkaOqpX3xBRx9fOA1bJiWkG3EcDiHhFT6sbZ+/jR3GuP4xL06Swluxoq2+uhDuFVxvgj2d/1wvJi1+AA+WXVM/f3o+M64Z0wHNDlYFowxhRlny2O4TXBQrzvXpXyYjeDavz98+veH4YknVEma9L/+QubSZWoRNn3ePNVcWrdSpSv9LroIbmaL97aIPVxD1ob7Z0KvlqqVlBiw40yaKkfGZGyH4rOw/liKaq8sOojOYT64oJuWDb13pL/KpH6u3y3Hx3axmePjEgL0uERrhOMwk7ExHvzYSjhknIHDqfUA26rZgKu3VhdcjwdnHg0b89Zhng0muMzesF4ZvZiDyRiG+3gOGACvwYPhOWggzky/F0U0iFmyCTs4qETJtlY+rKbnjk2JbsJyYbRsDxgwQNXmZsmw7OxsTJ06Vb1+0003KRf0V199Fe7u7ujRo4fJ+/1LLUvmzzc1mLSHE8AjCVnYcCwFQ9oHIe27b9WEyKtziEoWJlQNFyrcu3RRLfjOO1CcloastWu1jOirVquSZIwHZCPuPXpoAnz0KPVY6i0LOqnfL0Dq/PnqhhDxxhtw69jR2l0S6hFO0J//cy++Xn9S/f3MRd1w6/C2aJJQSLMs2A83lWYrN574lAqPCbPsVnAbw0kbJ3psJc8+q0pRZvy1EJn//IPCk6eQ/NHHqrl16aISsPkxw3HLltbutlAPUET3axWg2mMTuuBkcjaW709QInzTiRQcjM9U7YN/jyLY2w0XdNUE+LAOwfBwtf9zX7ATfFsAva/RGkVoyrHS0mQU4quA3BTg8FKtEc8g06RsAW0bPTN6cWamWszMXs8klusrVBeCszM8evfWxt4hg1VZYAfX8jrmYU89qWUvZ7+NhXfp72DZMFsS3LXB5kT3Nddcg8TERDz77LOIi4tDnz59sGTJkrLkaqdOnVKu480dH3cXXNq3JeZvPIVvNpxEdEsvpG04oV4LuLJ610ChInQF9ps0STVmUMzbs0eVI6MlPG/vXvU3W9KHH6q6y7R+uw8fDsecHGt3XbAivLnEvfyyehzywAPwOW+Mtbsk1CMsBTbj5134cesZdc9/5dKeuD66NKSnqcI63Fd/DSx5HMiILX9e1emeZblOt53j6OoKn/POU41hSJn//KsyoGetWYP8AweQyPbmW/Do2xe+F02C74QJcA4Ksna3hXqidZCXWkhjS88pxH+HtHrgLEuWlJWP7zefVs3dxRHDO4RgbLdQnNclDCE+blWOHRuPp2BrkgOCjqdgSIdQOJ2jxVxoxvAGFNReawNv1Uojxu8ps4Lj5DogJxnY+6vWiF9UuQDn/z6miarrA5W8mCV8129Q1uy8PXtZy9mk325du8Br8BB4DY5W1VyqKuOryoG9+05ZnW4dWrilTredY291uo3ZF5uBie+tVrFIK9seRsabH8PZswQd1m6Fg4e31frcFKF7DK3fdEPPXrsWJVnl2X0NDg7w6NsHPqPHqLrgbp062UUsYHOgoWukFpyJwYmrrlJeEXRFjXjzDTn2TaiGLUsRPfTDTlWLm3PlN6/ujcv6RqLZUFKMomOrsGP13+gzYrxdu5TXFXpAsW4sLeBcYCuzvJRayX0nTYLP2Avg5ONjlf7Z+jVk7xQUlWDj8eRSN/QExKTllr3Gob5PlL+ygI/tFoaOod5l4/+SPWfxwp/7cDY9r2z7Fn7ueG5yN0zo0cIqv0Vo4tdPUQEQs7VchJ/ZDJSYZdUO6VIuwlVm9NrnnTEUFSlDlBLZjM3eth0Go1xZxLV1a3gOoRfREHhGD4JzQO0zsNP4xSzlW5ctQ/+xY23OpbwuWlJEtx2LbnLlR+uw5WQq/tz0CpxjUxEyJhzBH/1rlb42F5gwK2fbdmStohV8pYoBN8Y5PFxzQx81Uk3KqlrRE+z3hkpr2Inrp6i8AO7du6P1N/Pg6OFRr9/R1LHlCU9+UTGmz9+urF1c2Hzvur6Y2LP5TZZt+Rg1NoXx8chYvBgZCxchzyifDF0jvUeNUgKc4UeO7u6N1yc5Po0Gp8v7z2aqGHC2XWfSTV5vHeSpBDhriL+z/FCFjAj6cuxHN/QT4W0jNOnrpyAbOLleE+FsZ3eZhgs5OAIRfctFeFQ04OJh8bwvOHKk1JK9QS0+lmRmmmzDnEe6yKbLuEuLFs3q+GTUUEvanHu5UDtuHNIaKTv3KMENRwP8r7zC2l1q8jCjuVf0INUCH3gAS7/5BtEuLshds1YNSHSHSfvhB9W4LTMsKgE+ciTcWJJGsHsMJSWInfGEEtxOwcGI/GCOCO4mluX4zm+2YtWhRFXH9+Mb+ilXUqF54xIWhqBbblGt4ORJpC9cqAR4wdGjyFy2TDUusvpccIFyQeeiqz3XABdMoRW7W4Svaved3xFx6XlYcSBeWcHXHk3GyeQcfL7meKXvN5QKb1rAx3YLF1dzoWFx9QI6XqA1kpMCnFitWcEpwpOPaJZxtjVvAU5uQNQgJcALPXsg+3gWsjduUtbs4sTyKg/E0ddXzYE9o7W4bNd2WkJnoWpEdNs5E3qEI+HMavXYNzIPzgMvt3aXmh1FgYEqwU7wDTegJC9PrQKqjOgrV6Lw9Glkr1unGl6dpTLieo8cpSzhzNLoaCGTvmD7JH34kZpgc0Id+f57cAkPt3aXhHoiK78It365WcVierg44bObB6jkSYJg7j4ZcvfdCL7rLrX4xvhvivCi2LNI//131ZwCAuAzYbzKgM5YcEm+2bQI93PHlOjWqmXnF2H14STM33QSqw6ZChRz4U2X8/4vLUOAl6saYzxdnVRyNv7v6eqsHnup55xLn3Mq3c4Znm5O8Cx9XP4e7f2uTo4ifITK8QwEul2iNZIeU+aKXrRvJXKOpSJ7wy5kxx9EYZapPHRwc4Vn/wFl1mz3bl1t1tXblhHRbec45+Zg6Mkd6nFeF38t0Y1gNehW6D1ihGqGp55EwfETZW7oOVu2qoy4qfPmqcYyCbSE0ApOEe4SIcfOHsj4eymS5sxRj8Offx6efftau0tCPcEESrd8uQnbT6XB280ZX0wdiIFtAq3dLcFOqmCEPPggcnfsUPHfGUuWoDglBWnffa+ac4sW8J14oUrU6da1q4ijJoaXm7MygjAspSrRrZOWW6hafcIwGBPxXiroPd2cS4V6ubjXBb2xuFevGYt79bcm7unxIzQdirOykbP9MHLWn0L2hnjkH+R4ZHSvczDAI7AQnmH58ArLh0dwARx9cwCGZhe6ARk+QEBra/4Eu0REt52T/tvvcCwsgptfIf70GYTJiVloFyJJ1GwBTqrc2rVVje6IapDbsL4sIzrrEGb9+69qhGWmGA9IAe7Rp4+4JdogeQcOIHbGDPU48Oab4X+FeJY0FZKz8nHj55uw72wG/D1d8PW0QegVWfskM0LzhZZsz379VGOWXcZA0gKeuXw5is6eRcrnc1VzbdtWuZ9TgEt5z6ZFqE/N4vlnXtYDHUJ9kFNQpMJZctgKi5GTX6Qe5/JxQenjgmJkq//L/1bbl/5dVKLF6fL/zLwi1QDTxFb1Kei9jKzsSrCXiXszsV/6uibsS8W8sVXfRRP3Lk4i6BuakoICtSCYs2GDGpdymZOiiOdJOW6dO2u1slWG8X5wyjpW7orO2PDsBGDPT1ojAW20eHC9RJl3iHV+nB0hotuOYXKD1O/mq8f+HbLxb0k/ZGw8pWrICraHk7cW68fGY8cyNMoNfdUqNRjmHz6sWvKnn8HRxwdew4dprugjhsM5WNxbrU1RcjJO3303DLm58Bo2DKGPPmLtLgn1REJGHqZ8thGHE7IQ7O2Kb26LRpdw20usKdgPDs7OauxmK8l/Xi22Mv6bi6wFx48j6f05qjEJIxOw0QouYSr2z6C2gSpLOeO9LWUpdih1S79mYKt6i+lmhnUlxAtNRXm2kaDXBbsu6OkObyz2jQV9ttHjxhD0Lk4O5e7zpaLcy0TYm1rvvdxMxb6xoDd20efj5iroVdnb/QeUoUfVy966FYa88kz6xCUqqqxWtmd0dMUSiL59tURrwx8AivK1bOi6CGcceOoJrW37Sts+tHt5abLWQwF3uYeaI6LbjsnZuAkFx47D0bkEnp3csTO3HY5tOY1HxnVWA45g4y6JXbuqFvx/d6IoNRXZa9cpV/TsVatVmZrMxUtUI+49e5ZlRHfv0UNiAxsZQ0EBztx/v4rXZCxny7feVJNqwf5hCaApn27AieQchPu649vbo9FevIWEeoS5O1hblq04K0tZvinAmeuDpXfYEl5/HZ4DBmglyMaPq1OJHcH6UEizLNhd32xTAttYeOsSm6/XZxI1un6z+aEBymIaCfrsfF3QF5UK9XJBn20m7i0KfyPrPRvrmJPCYgMKi4uQoQQ9GkTQ0/3f2MKuP2bd9cRYR+z++xC83V1MrPdl4r4spt40rt7ZhgS9yjB+/Diy16/XrNmbNqMk3TS7PpO+ekVHayJ78BC4Rras+Rc4uwFthmsNTwH5meWZ0SnE43cDCXu1tuFDwMEJaNm/XIQzQZuz5DCSWaMdk/r99+p/3za5cOs1EZGHvXA6JVfVlL16YJS1uyfUAk6w/OhueNEkbYVy925lAc/6byXy9u1Tf7MlffABnAIDtbhxZkQfNgxOfn7W7n6ThjezuJdeRu6WrXD09kbkRx/KPm8inEjKVhZuCu/IAA98d/tgRAV6WrtbQhPGydsb/pdeqlpRSoqK/aYAz926VSXhZIt7+WV4DRuqErD5nHeelJ20M1gOjGXBzOt0h9thne6GEvRKJBaXCvoywW4qypXrvRLqpuLeeDtzV3ttgaC2gt4Ra+JP1Po3MHGdJWt8efI7U+u76XZVuN7XUNAXxsVpVmxaszdsRFF8vOmv8vZW1XM0kT1YhTDWWy4JNx+g0zitkewk4PiqchGeehw4s0lrq14HnD2AVoPLRXiL3oBj1cbB4qIiHNiwGAUnN+DABgd0GzIRTnZu7LDv3jdjCuMT1Go5CeiQDYdOEzAlsDVmLT6AbzaeFNFtxzAjJGO62ULuuw+FCQnIXr1GuSdmr12rkvPo2XHBbfv20dzQR42CW6d6HFQFRer8+Uj78Ue6JygLt1u7dtbuklAPHI7PVII7ITMf7YK9lIW7hZ+UfRMaD+fAQARef71qhbGxqgY4M6Dn79uP7JWrVHNgcs4xo1X8N8tOOrq6WrvbQg2gsGZZsPVHErB09UaMGxGNIR1CpUyYcc4bZyfV/Ot5nbOioDdyrTcT9Bk5Bdi97yBatm6LvGKDBeFvZr03EvT8joLcEqTXc0I8XdDrFnVdlAeW5KLz2UPocPoAok7shX/yWZP3lDi7ILdzdxT06g/0GwjXbl1R5OGGIldnFFHQ5xepz2mQc9ArGOhxudZI2qlyV3SK8ax44Ni/WiPufkCbEeU1woM7qTmWzva/v0LE+hfQE8noySdWfIj4FUGIHfIc+o6/GfaKiG47Je2nH1USBI/gfLgz4WD7Mbi6jQfeWnYIu86kY+fpNPSOkiRATQGX0FCVsIuNbs4523doydhWrUTBkaPKAsuW+NZbKkOu7oZONyKxkJwbrLseP/NV9Tj0kYfVvhXsn72x6SppWkp2ATqH+agY7hAfcX0TrAerVwTdeqtq+ceOaRnQFy5U9cD1UCPm+vAZN1YJcMZgSske24biJrptIJL3G9T/IrhtT9AXFhZiUdZ+TLywM1xqkLxW5eMpc7k3jZW3JO71100S4RlZ700t9kUo1fNK0Dtk5KJ98nH0STyM3olH0D49Fo5GAQvFcMDhgEjsCOmInSEdsS+wDQqcXIBcAGuzgLWbLf4Gei5obval8fN0vTdyn7dotTey3tPt3tySry8MlJ3j/q2AfjdqzWAAEg+UivBVwIk1QF46cOAvrRGfFmUJ2facTkTvrc+VHszyfocYkhGy7j5sB+xWeIvotkMMRUVI++FH9TigY05pwgI/lez/op4t8Mv2GMzbcFJEdxPEwdUVXtGDVAt77FEUnInR4sBpFdm4UWXITVuwQDVmP6drkZ4RXbLk1o6C06cRc/8DQHExfC+ejMBp06zdJaEe2H4qFTfP3aTcDXu29FNZylkvVxBsBXrThNx3L4LvnY68vfuU+M5YtEi5j6b//ItqjM/0nTABXhPGa5NaQRAaJx+PC2PBnVT1rPrOMJ6xfScy161H7sYNKN5TMcN4XsvWSOvSG4kde+Jsm67IcPZAQUEx2hQUIdRcyJeKez05nj5MME6fLQ31b6F30wW9cSK8spj6QfB0GQLvro+hTeFRdMzeitbpmxGevgNOmWeBXQtU61GaC8HcaZN6nosSLda/gOLzp9ilq7n99VhA5r//qpuvk6cTfCJzgY7jy167YUhrJboZ1/30pK7w95TJZFOGiTB098SSvDzkbNqkZURfuRKFZ86oRD1stNYyAZiXqgk+Cp6DBoqbYhWwvNuZu+9GcXo63Hv1QouXXhK3/SbAxmPJmPblZmV16N86QNXh9nWX0nyCbcIxx6NHd9VYLSFnyxYV/53JGuBJSUj95hvV2gQGIvnIEfhPvhjunTtZu9uCINQAQ0kJ8g8eVHHZ2RvWI2fLVhhycip4wHgOGQyvwUPgGT1IeT7W6btKLfRlrvUFlVvb9SR5KnFeaUZ8yzH3pdb7wuIyQc/vYEvNqU7QuwMYppobCtDP8TCGOe7BeMfN6OgYW0FwGwvvcCRj78a/0X3YJNgbIrrtkLTvvlP/+7fJ1PIQdJpQ9lrfKH90a+Gras3+tPUMbhsh8afNBUfG/tG1fORIGJ5+SmWy1AU4y0XQTbHg63lI/XoeHDw84DVkSJkruksL+0ns0hg3wtjHHkP+4SNwDglB5Pvvq+zDgn2z6lAi7pi3BXmFJRjaPgif3jRArb4Lgj3AihVegwapFv70U2oxNf0vrQa4a0oKUj/7XDW3jh3gO+ki+E6aCNcoye0iCLYChW/hyZMq6RlD13I2bkRxaqrJNk4BAapONkU2E6CxrFd9LPgbW+gD69mzy1jQq1J0Ze7zxiXrTEvRaZb4Utd7Je5bYEXBMCSmtMMLRW9X+525qTGwR2TGYWfkHzuO7HXrld9FQPtMILA9ENzB5MK6cUhrPPHLbnyz4SSmDWsLR4kjap4xTe3aqRY09RZVpoalJFQytpWrUJSYiKx//lGNuHXqpMQ3k7ExgVtzLoeV+N57ar/QlT/ygzlwCavbyrJgOyzbF497vt2m4uTGdA7BRzf0V5MPQbBHGDrEsZotPyMDa955Fx3j4pCzerVaLEx85x3V3Hv3UvHfPhMm1NlCJghC3WEiXFXCi9bsjRtU2VFjHD094TFwQJnI5lzM3krC1qeg37s2DVhW/XYeAbUod2ZDNN+ZtZ2StkArE+bdJQguXjFAp3LXcp1L+kRg5sL9qu7smiNJGNkpxAo9FWytTI3v2LGqqVXJAwe0ZGwrVyF3507kHzqkWvKnn8HR11eVq1GTuhEj4BwUhOYC4yaTP/5EPW7x8kvw6NXL2l0SzhGG2jywYIfKODuhezjeu66vSiQjCE0BRw8PZPXuhRZPzIBjbi4yly1TMeC0puXt3KVa/KzZyjVVCfCxY6XkoSA0EMUZGSrMT3MZ34CCo0dNN2CunT59Sl3GB8OjZ0+1iCZodIkej/hlQSppmiV7IWO6ExyC1Hb2iIhuO6IkNxdpv/6mHgdEldbjsyC6mcDgiv6R+HLdCZVQTUS3UGFVsmtX1YL/7/9QlJqK7DVrVV3w7NWrUZyWVpYtlx4V7j17lrmhu3fvbnersDUld+9exD75lHocdNut8Lv4Ymt3SThHftxyGo//vEvdqC/r2xKvX9mrRvVPBcEecfL1hf8VV6hGb6aMxawBvlAtrOawnu/6DYh74UVVesxv0kR4jxmjRLsgCHWDuXRyt20rE9l5e/cCJSXlG3AO1a1baa3sIfDs30+uuSpgcjSWBWOWct63jYW3ntn97JDnEG6n3pj22evmRkkJcjZvRs6SJSjJyIBzeDC8AnYBrj5Aq6EW33LD4FZKdK/YH4/YtFxE+MtFLljGOSAAfpMvUs1QXIzcXbs0Ab5yFfL27UPerl2qJc2ZA6egIGX9ViXJhg1Tk7ymQFFSEs7cMx2GvDyVbC7kwQet3SXhHJm3/gSe+X2venzdoCi8cmlPCbURmg3MRxF4042qFZw5oxKwZfz1F/IPH0bWihWqOXh6wue88+B70SR4Dx2qQmoEQai6elDu7t1lLuO527fDUGiaNMy1bdtSkT1Y5WBw8pdKQrWh7/ibVVkw1ukOQ3LZ87RwU3Dba7kwIqLbxslavhxtZ81GbHp62XMlaenIPOMO33FjAGfLN8kOoT4Y0i4I648l47tNp/DwuM6N2GvBXmHdV8++fVXD/fejMD4B2WtWI+u/lSpxT3FyMtJ/+001lG6rMqKPGgW3jh3tMsM3y3Scufc+FMXFwbVdO7R84w2pf2vn/G/VUcxcdEA9njqsDZ69qJtdnpuCUB+4RkYi+M47VMs7dEgT4AsXqgoXFOJsdDn3GT8evqwBPnBAk/VoEoTaoMLxDh1Gzob1SmTTAFaSnW2yjXNYmHIVVy7jQ4bAJSzMav1tKvQdf7MqC7Z7/SIc2L4eXfoOQbchE+3Wwq1j371v4mQsXYq4hx6Gs1kNzpK8QsSsDQAGtUZVdkYmVNNE92nce15HiWMUag2TiOnuioaCAuRs267Fgq9apWKVWMKGLfHNt+DcokWpG/ooeA2OVglC7OGGGvf8C2q1mrHsTJzm5ONj7W4J53A831txBG8vP6T+vmdMezwyrrMIbkEoxb1TJ9VCHrhfeTAxA3rG4sWqBFnaDz+o5hwaCt+JE5UAd+/RXa4foVlBzxAmnmU4RjYzjCeXW1sJF6g8o6PLrNmubdrINdJAruZdBl+IYykG9b891uU2x/5/QROFbr6srczid5VdyvHzV8PntuJKrXJju4Uh1McNCZn5+HtvHCb3jmjQPgtNG7oeUkyzhT3+mLox6QI8Z8NGFJ09i7QFC1RjYhDPQYNKM+yOVDXCbZHUefOQ/ssvgKMjWr71FtzatrV2l4RzENyzlhzAJyuPqb8fGdcJ08/raO1uCYLt1gDv3Vu1sBmPq+RP6QsXInPpMhQlJCDlyy9Vc2ndSiVgowB3a9/e2t0WhHrHKTMTmYsWIY9hnBs2Kg8QY1hi1bN//zKRzXw44gki1AUR3TZKzpatyt21chxQFJ+gtvOKHmRxCxcnR1w3qBXeXXFYlQ8T0S3Ut8ti4JQpqjGZCGtO6nXBC2NikL12rWrxM2eqlWAVBz5yJDwHDoSjDcQOZq1Zq7L6Ei4ieA8fZu0uCXWkpMSAF/7ci6/Wn1R/P3NRN9w6XBZQBKEmcOGebrFsJc8+qxJq0v08859/UXjyFJI+/Eg1t65dVQI2WsFdImQ+IdgnLKGas2kzsukyvm492h85gtLUxBrOzqpyCV3GKbS5MCX5DoT6QES3jcLMo/WxHUX3nH+PYOPxFByKz0SnMHGdFeofR3f3srqxBsPTKDh2TBPgtIJv2YKCEyeQwvbV1yp5Dyd3ekZ0l/DwRu8v+xPz0EMqSaHf5Zcj4KabGr0PQv3AUmBP/LILP2w5w0SxePnSHpgSbZueFYJg63BB1Of881Vj7CqFN2O+s9auRf7+/Uhge+NNePTrpxKw+U6YAOfAQGt3WxAqpSQ/H7nbdyiRTZfx3D17gOJik21cu3SBt1p4Gqys2o5eXlbrr9B0EdFtw5lH62O7cD93jO0ahiV745S1+8VLetRTDwWhcrdFuiGyBU2bqlaVmYRNz4jOhSI9ey5x69xZE+CjR2kryg0ct1OcmYnTd9+jKgF49OmD8Oefk3gsO6WwuAQP/7ATf+yMVaVF3riqNy7vF2ntbglCk4DCQ69swdKSdD2nBZzJpFgmiS3+lZlqEZXu5z5jL4CTt7e1uy00cxieydJdKvHZxg3I2boNhvx8k20YNuE1eAjcBw7Emox0TLjqKrhIvWyhgRHRbaN4DugP5/BwFMXHq7juCjg4qIyJ3K46mFCNovuXbTF4bEIXeLvJYRcaD07CfMeNU01lAt2/XwlwZkRn/dj8gwdVS/70U5XMjG7eKhnbiBH1bkHhzTj2kUeVJZ7XV+T779mEq7tQe/KLinHv/O1Yui8ezo4OePfavpjUq4W1uyUITba0ZMA1V6tWGB+PjEWLlQDP27MH2WvWqBb33HPwHj1aCXB6MdEDShAaGs4rmNhVr5XN/AQlmZkm2ziFBCuRrbuM6+ERhYWFKFm0yEo9F5obor5sOMYq7MknEHP/A6DktmSH4+s1KW00tH0Q2oV44VhiNn7bHoMbBovrpWAdaFF279ZNteD/+z9lPeFkja7ojCMsTk/XJnOLFquFJfeePdXkzXvkKLh373bOyUsS33lHxZw7uLkhcs6cGnuUCLZFbkEx7vxmK1YdSlRVGT6a0g/nd5UyLYLQGLAkUtDUW1RjqE76ItYAX6gWMzOXLlWNVnKfCy6A70UXKZHT0B5MQvOiMDa2XGRv2FAh1NLRxwee0YM0oT1ksCoHKh5tgrWRUdCGoWWw+K03cfr55+GSnlH2vHOQH8Kee1G9XhM40NwQ3Rov/rUP89afQPsQL5XRPNTHHYPaBsKJfpmCYCXrid/kyarRCp27cxeyVmkZ0fP37VclbdiS3p8Dp+BgeI8YoSVkGzoUTr6+1Vq16Qbps2MHckJCYEhMRPKnn6nXWsx8BR49ujfSrxTqk6z8Itz65WaVp8LDxQmf3jQAwzsGW7tbgtAsYZLMkLvvRvBddyH/wAFl/aYIL4o9i/Tff1fNKTAQvhO0GuAefftK5meh1nCBnuI6e8NGFZvNBH/GcCHds38/eJaKbC7s18QoJQiNiYhuG8cnMg8dLkqAITYLRXlOcHYvhmc7Axwi82r1OVf0j8Sri/fjYHwWrvt0Y9nzLfzc8dzkbpjQQ9wyBevCG6Rnv76qhT7wAArjE5C9mtnQV6mYcNaRTf/1V9Wgtu2nWcFHjYJrhw4mq9iscc+Se6wAwDM79rvvy14LuvNOVQJHsD/ScwtxyxebsP1UmgqT+WLqQAxsI0mcBMEmvJi6dlUt5KGHkLtjh0rAlrHkbxSnpCB1/neqOUe0gF9pDXC3Ll3E+ihYhEn8mIRVt2ZzQccEJyd49OgBzyGDlTXbo28fOLq5Wau7glAjRHTbMvv+gNPPU+EBAxyMPSez44AfbgKu/hrodnGNPmr90SQUFleMDY9Lz8Nd32zDRzf0E+Et2BQuYaHwv/JK1QwFBcjZtq2sJBndGGnFZmMmXU7ktGzoo1CSlY3Yxx6znAsBgHu3ro3+W4RzJyW7ADd+vhF7YzPg5+GCr6cNQu8of2t3SxAEM2jJ5qIoW9iTTyrhpEqQLVumLODJn32uGl1+fSdNVIugtJgLzRfe45njRRfZubt2AUVFJtu4depUViubpUclaZ9gb4jotlVKioElj3MoshDPXRrlvWQG0GUS4OhUbUmdF/7cZ/E1PV6cr4/tFi6u5oJNwhqZKgHK4MGqpnbB6dNaMraVK5GzcZOayKV9v0C16oh/dZaKNRTXM/shISMPUz7biMMJWQj2dsW8W6PRtUXV4QWCIFgfxnJ7jxiuWsnzz6mFUwrwrP/+U4unDB1ic+/RQ1m/fSdeqGLGhWaQYXz/AZVdXGUZ37oVhtxck21cIiPLRLZXdDScgyWMSLBvRHTbKifXARmxFhOoaRiAjBhtu7YjqvyoTcdTcDa9cnd0Cm++/t6Kwyo2MtTHTcV7e7iKKBFsE9eoKAROmaJaSW6uylZKAZ7x91IUJydX+V66nOds2Qqv6EGN1l+h7sSk5WLKpxtwIjkHYb5u+Pa2wegQKhYOQbA3mM3cd/w41VhKMnP5cpWALXv9epUFnS3htdeUFVOVIBs3VuX9EJpIhvHjJ8pqZWczw3h6usk2TkFBSlwrl/EhQ+AaKeUfhaaFiG5bJSu+3rZLyKxZ/Pe7Kw6rpsOYSQrwEIpwX3eEePN/tzJRzsd8zt/TReKyBKvh6OGh3MrZPPr1UyXBqsM806lgm5xMzsb1n25UwjsywAPzbxuMVkGe1u6WIAjnCF2D/S+9VLWi5GRk/P03MhYuQu7WrWoRlS3upZfgPWyYyoDuc94YlRFdsB9YWo4LKkpkM8M4S+AawePpOWiQZs2OHgy3Th1lLik0aUR02yreYfW2HQVyTegU5o28whIl0vk/swSzHUvKrvJ9rk6OSpjrzViUl4l2H3flFursJFlLhYbDOSS0httJqTBb50hCphLcrLTQLtgL39wWjQh/D2t3SxCEesY5KAiB11+vGktBZSxahPSFi5C/f7/yYFJlHt3dlfCmBdxrxAg4urpau9uCGcVpacqCrbKMr9+AguPHTV53cHFRC+MU2QwVY0iBlJITmhNyttsqrYcCvhEwZJyFg3IAN8dBva62qwaWBWOWciZNq+STEO7njsX3j1Qx3XQDyswvQmJmPhIy8pUIV48z80v/zyt9Pl9lEy4oLlGWKLaq4AJmkJcrQnzcjcS5LszLRbq4tgt1xXNAfziHh2sr6pYSqTk4wDksTG0n2C57Y9Nx0+ebkJxdgM5hPph326AaLx4KgmC/uEREIOi221TLP3pUWb/TF/6lSkRlLFqsmqOvr3I9ZwI2WkolP4d1KMnJQc7WbWUu43n795vedx0d4d69u5aPZchgJbgZYiAIzRUR3bYKk6NNmK2ylOvJzsop/WvCrGqTqBEKaZYFY5ZyvtNYiuify9f1JGp07/F1d1GtfUjVsZN5hcVIytIEOIV4IgV5mTgvF+jcpsQAJGUVqLb/bNV99nFzLrec+7obiXNTKzqzGIs7kqDDyVfYk08g5v4HtFUe4wlA6XnC12WSZrtsP5WKm+duQkZeEXq09MW8adEI8BKrliA0N9zat0fIffci+N7pyNuzVyVgoxW8KCEB6T/9rJpTSDB8J1wIv0kT4d67t8wHGhBDYSFyd+8ucxnP2bkTKCw02ca1Q3tVwstrcLRaEHHylYSXgqAjotuW6XYxiq/4AoV/PASPwpTy52nhpuCuYbkwwnJgLAvGLOXGSdXCz7FOt7uLEyIDPFWrLoM6S/4k6KKcAp1iPUP721ig5xeVKEt7Zi1d25UwV3HmplZzPqaFXVzbmwe+48YB775TVqdbhxZuCm71umB1OCZsPJ6CrUkOCDqegiEdQrHlRAqmfbkZ2QXF6NfKH19MHaQW1gRBaL5QSHv07KFa6KOPqESYqgTZ33+jODEJqfPmqeYSFQVfVQN8Itw7dbJ2t+0eQ0kJ8g8dKi3jtR65m7co67YxLNepRLaKy46GS2jNQrwEoTkiotvGMXS5CEuPApN6+MM5N1mL4aZLeQ0s3OZQWLMsGLOZU+BSkNL1vDHKhPE7dHHcvYrtdNd2Y7f2Mqt5qUDX/66ra3u5xVwX6sbPiWt7U4DC2uf885GxcSO2LluG/mPHwjc6WizcNsKSPWeNFgCd8PXhLQj0dEVmfiEKiw0Y0i4In908AF5ucosSBKEcjuGsPMEW/vRTyFq3TrmgZ65YgcLTp5H8ySequXXsqBKwUYBLFuyawflX4alTZbWyczZuRHFqqsk2Tv7+WgmvUpdxl1atxLtAEGqIzGjsAQdHGFoPB1xc6kX8DmkfBFvF2LW9urJAdG1XojzL1LVdPc46R9f20szsxq7t5lZ0scDZ/uSMpWcyExPV/yK4bUdwM9TFPOI+JadA/d89whdfTB2ovGgEQRAqw8HVFT6jR6tGCyxrfzMBW/aqVcg/fBiJb7+tmkfv3loN8AsnSBJNMwoTEpS41q3ZRbGmEyQHT094DhwAr2hNZLt17gwHR/EaFIS6IKJbsFs4KY8K9FStOjfW5OxyC3miWXI4i67tiUU4lliNa7uzI0KYkb3ICX+l7UCYHwW6cZI4cW0XBPNrkRZuSwkddZg8zUWuF0EQaoGjp6fmWj5xIorT05G5bBnSFy5EzsZNyN25U7X4WbNUrLGqAT52bLOMNy7OyEDO5s1lIrvgyFHTDVxc4Nm7d1mtbI+ePVXWcUEQzh0R3UKTh9Z9JYB93Gvt2p5gIfY8UXdtL6JrO91jHXByf0KNXdvLrebGlnRNrItru9CUyM4vQjI9TLLzkZSZj80nUkxySliCVRYYAmPLHjmCINguTn5+8L/yStWKEhORsXiJigGn8M5et161uOdfgNfIkfC7aBK8R4+Go0fTLEdYkpeH3G3bylzG8/buBUpKyjdwcIB7166ayB48BJ79+6kFDEEQ6h8R3YJwDq7tZ1OzsWTlerTq1B3JOeWCXRfndXVtNxbiukg3/luytgvWslSn5vBcztfEtNn/yqOE/5f+nVtYXKfv4TUkCIJwrtCdPPCmG1UrOH1axX9TgNP9PGvFCtUoMr3PP1/Ff3sPG2bXll1DURHy9uxRAptCO3f7dhgKtNAdHde2beE5OFoT2YMGwjkgwGr9FYTmhIhuQTgH1/ZwHxecDTJgYnQruFi4Ueuu7brFXHdttxR7XnvXdmOLeak7u1nsubi2C9WRU1Bqjc7iIlGpYM42+7v0dcZdWyp/XhXuLo4I9nZDkLcb6Mex7XRate+RmtyCINQ3rlFRCP6/O1XLO3RIE+B//YXCmBhk/PmnarSS+0yYoAS454ABNh+/TA89LiDklIpsuo6XZGWZbMPKHUx8plmzB8MlPNxq/RWE5oyIbkFoJNf26m6crEusxZmXu7ZXiD3PyFPbaa7tNc3abp6t3c1i7LkkrmoacKEnTVmjNcGclF36f5l4LrVMZ2t/5xTUzhrNcyrA01Ut6GhiuvR//u2j/U+BHVL6mqerU5lXBvs2fPY/yoXcknZ3KC1jyKoKgiAIDQVLirGFPHA/8nbuVAnYMhYvRnFSEtIWLFCNYtX3wgtVFnT37t1sxrus4MyZMpGdzQzjSUkmrzv6+cFr0KAyl3HXtm1spu+C0JwR0S0INgBviHQZZ6upa7vmwm5URs3Yip5JQaW7tmuCq1rXdndnUyGuW82N//Zxh6+Hs9zAG5ncguJSoVygYqMpmDVRbSqglTU6u0Ad99qge04Ee2uC2VhAU1Dr4pqNpb3q6j3BRajnJndT2ct5Bhl3Uz+j+HpjlDEUBEFQNcD79FEtbMbjKpM3E7BlLl2Govh4pHz5pWqurVtrGdAvmgS3du0atY9FyclaCa9SoV145ozpb3B3h2f//lqt7MFD4N61i1TrEAQbRES3IDTxrO1aOTUzq7luRS8tt6Zc2/OKVKuNa3tVsefWdm3n7994PAVbkxwQxMRcHUJtRsyV0BqdW1i2IKLioXV37lJBbfx8di2t0STA08VEQAeXWqDLrdO6pdoNXkbW6IZmQo8W+OiGfkZ1ujVo4abg5uuCIAhWqQE+dKhqJc89h+zVq1X8d+Y//6Lg5Ekkffiham7dusKPAnziRLi0qHy8MhQXK3dvnx07kBMSAt/o6BqJ4eKsLPU+XWTnHzpkuoGzMzx69Sqrle3euzccXV3rYxcIgtCAiOgWhCZK7V3btdhyXYhXiD2vpWs79W2gl3m29nKreUgDurazFnS5qHPC14e3oEUDizp6IFRIMGZkgTaOm2YyMi4K1AYudgSbuXBrVmhXIxdv7e8AL1ebLrvFYzC2WzjWH0nA0tUbMW5EtE0tigiC0LyhiPU5/3zVSrKzkfnPP8j4ayGy1q5F/r79SGB7/Q149O+vMqD7jB8P58DysJiMpUsRP/NVFMXFgXec2O++R0J4OMKefAK+48aZfFdJQQFyt+9QJbxymPxs926g2HSh1a1LlzKR7dF/AJy8vRptXwiCUD+I6BaEZo6pa7tPrV3bLcWem7u276uBa7uJEK8k9rwmru0U3HRfNpe0jCPm87Sy1kR40xrN0nBlCcWMBHRZvHSpyzefz8ovQm3xpzXaLAaawlkX0bq7N//3dmtabv0U2NFtA5G836D+F8EtCIIt4ujlBb/Jk1UrSk1F5t9LlQU8Z8sW5G7dqlrcy68oCzkTsMHREWcfn8EVbZPPobt6zP0PAG+/BZeWLbXEZxTaW7fBkJ9vsq1Lq1ZlItszOtpE0AuCYJ+I6BYEoVFc2y1a0TPzleVcd20/WgPX9nJxbmY1V9na3fDs73stJunic5R1fD3M17209JUmmI0FdJJRbHStrdFOjmWxz8aW5/KY6PK/mYyMv0cQBEGwD1heK+Daa1QrjI9HxqLFKgM661/THZ2tUkpFeMyDD1UQ5E4hwSrpmZcq5TVYiXJBEJoWIroFQbAZ1/aEymLPM/PLXNvPpOaqVhc4zeHnXvbhuhq/x9fduTQm2ihTd6mADjFLPObTxKzRgiAIgmVcwsIQNPUW1fKPH0fGokVI++lnFJ2txrXLYICDh4cWP15qzXZt317uHYLQxBHRLQiCnbm2Vx57fjo1R1nMq4PfFxngYVLyKriCa7cbAr3EGi0IgiBUjVvbtgi55x6V5Tz2kUer3b7FC8/D7+KLG6VvgiDYBiK6BUFoMq7t648m47pPN1T7WR/f0B9D2gfVcw8FQRCE5oxzSGjNtgsLb/C+CIJgW4gJRxCEJsOgtoEqS3llTnp8nq9zO0EQBEGoTzwH9IdzeDjduCxv4OCgXud2giA0L0R0C4LQpGLJWRaMmE959L/5umTKFgRBEOob1uFmWTDtD7P7TOnffL0m9boFQWhaiOgWBKFJwXJgLAsW7meaxI1/17RcmCAIgiDUBdbhbvnuO3AOCzN5nn/zefM63YIgNA8kplsQhCYHhfXYbuFYfyQBS1dvxLgR0RjSIVQs3IIgCEKDQ2Htc/75yNi4EVuXLUP/sWPhGx0tFm5BaMaI6BYEoUlCgR3dNhDJ+w3qfxHcgiAIQmNBge05cCAyExPV/yK4BaF5I+7lgiAIgiAIgiAIgtBAiOgWBEEQBEEQBEEQhAZCRLcgCIIgCIIgCIIg2GJMd35+PrZt24aEhAQMGzYMwcHB9dczQRAEQRAEQRAEQWiulu733nsPLVq0wPDhw3H55Zdj165d6vmkpCQlvufOnVuf/RQEQRAEQRAEQRCE5iG6v/jiCzzwwAOYMGECPv/8cxgMhrLXKLjPO+88fP/99/XZT0EQBEEQBEEQBEFoHqL7zTffxCWXXIL58+dj8uTJFV7v378/9u7dWx/9EwRBEARBEARBEITmJbqPHDmCCy+8sNLXAwMDkZycfC79EgRBEARBEARBEITmKbr9/f1V7HZl7Nu3D+Hh4efSL0EQBEEQBEEQBEFontnLJ06ciP/973+4++67K7xGt/JPP/0U06ZNq4/+CYIgCIIgCILQzCguLkZhYWGDfT4/29nZGXl5eeq7BNui0EaOj4uLC5ycnKwjul9++WVER0ejR48eKqbbwcEBX331lcpY/vPPP6us5s8+++w5d04QBEEQBEEQhOYDEzTHxcUhLS2twb+HnrmnT59WWkawLQw2dHzo5c2+nEs/6iS6IyIisHXrVjz55JNYsGCB2inz5s2Dj48PrrvuOsyaNUtqdguCIAiCIAiCUCt0wR0aGgpPT88GE1wlJSXIysqCt7c3HB3rXEVZaCBKbOD4UOPm5OQgISFB/U3DcqOKbsIL4bPPPlMtMTFR7ZiQkBA5aQVBEARBEARBqDV0I9YFd1BQUIN+F7VLQUEB3N3dRb/YICU2cnw8PDzU/xTePC/r6mpep1/AeO2NGzeW/U2xHRYWVrZDNm3aJDHdgiAIgiAIgiDUGD2GmxZuQbAV9PPxXHIM1El0f/nllzh69Gilrx8/flzFeAuCIAiCIAiCINQGa8fwCkJ9n48NYquPjY0tM8ULgiAIgiAIgiAIQnOlxjHdv//+u2o6LBm2fPnyCtsxDoPPDxw4sP56KQiCIAiCIAiCYOfccsstSi/99ttv1u6KYIuie9++ffjxxx/LTOyM6WYGc2P4vJeXF0aOHIm33nqr/nsrCIIgCIIgCIJgh27Izz33HN59912VFbuhYaJrlnBeuHAh4uPjERAQgN69e6vnhg0bVtbfX3/9FZdeemmD96e5U2PR/cQTT6hGmDDt888/x/XXX9+QfRMEQRAEQRAEQbALzp49W/aYZZUpcA8ePFj2HMtfsTUGV1xxhcr+zTxb7dq1U8J7xYoVSE5ObpTvF+ohppsp3EVwC4IgCIIgCIIgaISHh5c1Pz8/ZUk2fo6Cm+7lxpbl0aNH495778UDDzygrNGsCPXpp58iOzsbU6dOhY+PDzp06IDFixebfNeePXtw4YUXqs/ke2688UYkJSWp1+i+vnr1asyePRtjxoxB69atMWjQIGVAvfjii9U2bdq0Uf9fdtllqp/634Qhxf369VPluijYX3jhBRQVFZW9zu0/+ugj9f3M48Vtfvrpp7LXKfanT5+u6lrzM1q3bo1XX30VzRkpSicIgiAIgiAIgmAlaI0ODg5WZZcpwO+66y5cddVVGDp0KLZt24Zx48YpUZ2Tk1Mmqs877zz07dsXW7ZswZIlS5Ql++qrrzaxqDNuPD8/3+J3bt68Wf3/xRdfKAu9/jfF+k033YT7779fhRd/8sknqnLVK6+8YvL+Z555RlnTd+7ciSlTpuDaa6/F/v371Wvvvfce/vjjD/zwww/K0v/tt9+aiPrmSJ1FN1dbxo4dqwrXOzs7q0Lh5k0QBEEQBEEQBEGoHMZaP/300+jYsaOyRtM6TBF+++23q+fopk638F27dqnt58yZowT3zJkz0aVLF/V47ty5+Pfff3Ho0CGlzSiUKeb9/f1VDPeTTz5Z9n4SEhKi/ufrtMLrf9OqPWPGDNx8883Kgk2999JLLynxbQwXBW677TZ06tRJvT5gwAC8//776rVTp06pfg8fPlxZuYcPH47rrrsOzZk6ie6ff/4ZF110kVpR4aoG3c25I/mYLga9evVSJ4cgCIIgCIIgCIJQOdROOjRc0qjZs2fPsufoPk4SEhLU/7QuU2DrFm02im9y9OhR9T+t0CzjTIvzhAkT8N9//ymXcYrxquBnv/jiiyafTfFPa7huaSdDhgwxeR//1i3ddKHfsWMHOnfujPvuuw9Lly5Fc6fGidSMoU8+4wLWrFmD1NRU5dM/bdo05eZw4sQJDB48GG3btq3/3gqCIAiCIAiCIDQhXFxcTP5mzLTxc3pWdBo6SVZWFiZPnqxits1hHLUOLea0VLPRHZyWaWZQpyiuDH42rd2XX355hdf4eTWB4v748ePKM5qlpK+++mpccMEFJnHfzY06Wbrp30+rNldi6L5ACgsL1f/017/77rstngSCIAiCIAiCIAhC3aGo3bt3r9JdTLJm3Fi+uTK6deumErTpUNgXFxdX+GzGYZt/LhsrWOls2LDB5H38u2vXrmV/+/r64pprrlFJ4RYsWKA8pVNSUtBcqZPo9vT0hKura1kcgJubm0mKfLpAcHWjrnzwwQfqJOJqSnR0tEoqUBm//PKLiiFgP3iS9enTB/PmzavzdwuCIAiCIAiCINgq99xzjxKwDO9lAjS6lP/9998q2zlFNOO/6YH8zTffqDhu6rIff/wRr732Gi655JKyz6HeYhmxuLg45b1MGCL89ddfK2s3hT1dxr///nsVc24MP49x5Iwhp/Wceo0Zy8lbb72F7777DgcOHFCv//jjjypunHqtuVIn0U3/fFq7dXShy1TyeXl5mD9/Plq1alWnDnEl5KGHHlIHj9n6mFhg/PjxZTEM5gQGBuKpp57C+vXr1UnFk42NJ54gCIIgCIIgCEJTIiIiAmvXrlUCm5nNGf/NkmMUtbRGMw6bhsu3334bI0eORI8ePZR7OWOzmYRN580338SyZcsQFRWlkrER6q6//vpLxWEPHDhQhQ3zc5gQzRiKcopxxqNTpFNk05JOWOaMAp+GUX7GiRMnsGjRIhNLeXPDwWAwGGr7pjfe+P/27gM8qmpr4/iCQOgQEELvTRFBilFQEQQEe5erXsVy7eUqNmzYKYqIXa8NvfYOVxEpio0mIiCCNKlSEpQeICGZ73k33xknySQkIZM5k/x/zzMkmTmZOZkzQ/KevfbaI10r+KVLl7pRbh0YnTVREzXNOVDZgs585DVfIDd6gejgeC8IzV3QC0Ht89VJLz9UFnHyySe7Tnr7s23bNreO3tatW10ZhN+obF8v0pNOOinHfA9EH8fH3zg+/sbx8T+Okb9xfPyN41NwGrzTqKx6Q+V3/nBhKWMoB+jv/9IcBgtDee+TTz7Jst54ST4+u/N4XeY3SxbqJ7j11ltdK3gFblEnc3XE09mTq666ypUpFCZwayH1n376yU20D+5g2bLua41k74/OH+ixNQ9BZ3UAAAAAAIi57uXhHHvsse7i2b59uystKIhNmza5MgmvLb5HX2tOQG50ZqFhw4Zu8Xc1d3vuuedcl75wtE3oIvE6O+GdjfSawfmJt09+3DdwfPyO4+NvHB//4xj5G8fH3zg+BafnSoNoGuX0OnVHilfs6z0eCibSxyjgo+Ojx9d+6PWprBkqv+/vIgvdHs29Hj16tFtGzJuQH2kK91oLTi3uNdKtOeFazL1nz55hlzvTHITsNG9BDeL8SvMt4F8cH3/j+Pgbx8f/OEb+xvHxN45P/mlVJDXc0t/0qoAtDhooRMF4Gc8bvCzpxyctLc127dpl3377rethFip07fIiC90K1Joorw55NWvWdIuud+nSxd32xx9/2COPPOIWXFfde7jAuz+1a9d2Zw82btyY5Xp9rTdgblSCrjb2XlM3ddlTuA63D3feeacL5R69WDRnXE0I/DqnW/9Za+Se+UD+w/HxN46Pv3F8/I9j5G8cH3/j+BScMsSaNWtcI7BIz+nWyKVXmeutgw3/CPjo+Oh1qd5lmr4cbk53kYZulXfrgdSC3hvuV1c6taLXE6HF1rVDCuK33XZbMIwXhJYh0/dptNqbmK/hfH3ttaDPD31PaAl5KM1D9+aih9J/hn7+D9Hv+1facXz8jePjbxwf/+MY+RvHx984PvmnaabKFRpQi3TzLK9k2Xs8+Eumj46PHl/7Ee69nN/3dr5Dt9rMq9RD86U1d1sd3G6++WbXnl5zqk899VQbPny4K+s+EBqFHjhwoGsxn5SU5ErV1Q1dy4DJxRdf7OZvayRb9FHbtmzZ0gVtdYnU8mUqbwcAAAAAIJryHbpVw37NNde47uSiddg07+LEE090Ifm1114rkh0aMGCApaSkuIXZtVC7ysUnTJgQbK6mrumhZzsUyK+99lpbu3atG/Y/+OCD3ei77gcAAAAAgJgI3Sor1+LnoTp27Og+nnnmmUW6Uyolz62cXEuThXr44YfdBQAAAAAAvylbkLr63GrY1ewAAAAAAAAcQPfy2bNnZ+nYpo5ymlT+/fff25YtW3Jsf9ZZZxXk7gEAAACgRLnkkktcVvr000+jvSuIhdCtpma6ZHf//ffnuE5hXB0IAQAAAKC4ZGQGbNaKvyx5+25LrFbRkprXsriykVl2an/LWd1333325JNPBld/Km4vvfSSPfPMM27JZ/Xjat68uZ133nluGWU/nRCYOnWq9erVy60BnpCQUOj70RLWn3/+uc2dO9etjBVuYNjXofvrr7+O7J4AAAAAwAGYsGC9PfC/hbZ+6+7gdfVrVLT7Tm1n/dvXL/LHW79+ffDz9957zzWDXrx4cfA6TcON1lTcV1991a009dRTT9lxxx3nVnqaP3++LViwwEqqtLQ0O/fcc61bt272yiuvmF/kO3TrQAEAAACAXwP3NW/Osexjyhu27nbXP//PzkUevOvVqxf8vEaNGm7kO/S6cKPJPXv2tMMOO8zi4uLs9ddfdyOyagx9wQUXuGbSH374oVu56emnn3YrRXkUlm+77Tb77rvvrEqVKnbCCSfYE088YbVr1w67b+PGjXOj2pdffnnwukMPPTRLtbIeP3TEXgOt2r81a9bYLbfcYhMnTnQrR2nJaI3YN2vWLMvP1KlTJzeSrkCv/VfA188j+jkeeOABW7ZsmVWuXNltO3bsWLfvoVauXOlGuaVmzZrBZaL1eAWlx5MxY8aYn7ASPAAAAADfUUl2atrefF227063+8b9miNwu/v5/4/3j1votvO+Z1daRq73F+lycIVdheVZs2bZDTfc4JZm1ght9+7dbc6cOS5QX3TRRZaamuq2V8A9/vjjXXBVny0tqbxx40YXqnOj8D9jxgxbtWpV2NtvvfVW9/39+/d3I/a66PHT09OtX79+Vq1aNRfwf/jhBzdar+00kuyZMmWKLVq0yJWGv/POO/bxxx8HQ6/u6/zzz7fLLrssuI36fYV7Xhs3bmwfffSR+1xVAvpeb0rzsGHDgtUCuV20pHSJmtMNAAAAAMVhV3qGtRvyZZHcl6Lehm277bD7J+Zr+4UP9rPK8ZGLSlp6+Z577nGfa3718OHDXQi/4oor3HUqU3/++eddOfhRRx3lRpMVuIcOHZqlfFyBdcmSJdamTZuw88kVdDU6rdtVcn3SSSfZOeec40avFVgrVarkRqlDR+fffPNNt3LVyy+/HBwBf+2119xca4VnnRAQjWhrHzSKrRH0Bx980I3EP/TQQy4479271z1+06ZN3fYa3Q9HI/61atVynycmJrrH0eNv27bNrrrqKhswYECez2WDBg3M7wjdAAAAAFCMOnTokCV0HnTQQVlCqcrLJTk52X2cN2+eK/0ONz9cTdLChe769evb9OnTXVn6t99+a9OmTbOBAwe6MK2RcgXvcPRYKgnXSHeo3bt3u8cKPXGgwO1RqN+xY4crTddtvXv3dj9Tv379XFBX2PfKx/NLYTy38vlYQugGAAAA4DuVyse5Eef8ULfyS177cb/bjbn0CNfNXCOp27dtt2rVq4UNn3rsSCpfvnyWrzWiHHqdN8Ks/RSF2VNPPdVGjBgRNlznpX379u5y7bXX2tVXX+3mZ3/zzTfBedTZ6bG6dOlib731Vo7b6tSpk6+fTycSJk2a5IL+xIkT3fz0u+++22bOnOk6qOeXyst1ycvChQutSZMm5meEbgAAAAC+o+CZ3xLvY1vXcV3K1TQt3GxsRdh6NSq67bR8mMLs3vg4d/+5jfj6SefOnd28Z5WKa+mvwmrXrp37uHPnzmCJePZlnvVY6sSuUu/q1avnel8aEd+1a5crURfNH9dIvEreveN39NFHu4vK5VVm/sknn9igQYNy3JfXfC37vpSU8vICv8I0mV9nPl544YXI7BEAAAAAFICCtJYFk+wrZ3tf6/ZIrdcdadddd5399ddfrjnZjz/+6Mq8v/zyS7v00ktzBFWPmrNpfrUaoamZmkKxuoJrtFql4KIQr3njamC2adMm10TtwgsvdCXdp59+umuktmLFCjeX+8Ybb7S1a9cG719N1dQZXSPN48ePd3PI1X1dJzE0oq3552r6tnr1atdkLSUlxQ455JCw+6pArpD+2Wefue002u6Vl7dq1SrPS+hJCD2W1ujWRz0v+lwX7/5iJnSrbl9P/P4WggcAAACA4qLlwLQsmEa0Q+nrSCwXVpw0mqvwrCCp+dGaK601uNV0LLeR+j59+rigra7omvN99tlnW8WKFV3Xcc0hFzVua9u2rXXt2tWFcT2G8p7mgKtkW43QFJQVrjWnO3TkW3O2W7dubT169HCj0aeddppbhky0ne5DjdvatGnjmsY9/vjjWZZAC9WwYUPX+Xzw4MFuPrs6uheGRtTVcE4nABS09bnX8T2aygQK0Q9fa7DpSdcZi1inrnhaU2/r1q15lk9Ei8426cyRXrDZ534g+jg+/sbx8TeOj/9xjPyN4+NvHJ+CU77Q4J7m/CocFlZGZsDN8U7evtsSq1V0c7izj3B73bH1938slJf7Tfa1x4tapo+OT16vy/xmyUJNCLj33nvdGROtHac6e+2AV8sfymv9DgAAAADFQQG7W8t9I7mAHxQqdGsdNlH9/ttvv53rdrnNLwAAAAAAoDQoV9haeeZ0AwAAAEDpM2bMmGjvQskP3d4EeQAAAAAAkLsimZWu9dl0AQAAAAAARRC6tfaZ1oVTS3ctgq6LPr/sssvcOnAAAAAAAJR2hSov/+233+yYY45xbeL79u0bXORc17/xxhv2v//9z77//nu35hsAAAAAAKVVoUK3Fi3Xemk///yzW5g91IIFC9xC6drmk08+Kar9BAAAAACgdJSXf/PNN3bjjTfmCNzSvn17u/76623q1KlFsX8AAAAAAJSu0J2enm6VKlXK9fbKlSu7bQAAAACgNLvkkkvsjDPOiPZuINZCd6dOnezll1+2rVu35rht27Zt9sorr1jnzp2LYv8AAAAAIP8yM8xWfGf2y4f7PurrCClTpkyeFy21/OSTT0ZtXeuXXnrJOnbs6JpeJyQkuBw3bNgw350QmDp1qnu+1DOssFauXGmXX365NW/e3A0Qt2zZ0u677z5LS0uzmJzT/cADD1j//v3t4IMPdh3M27Rp465fvHixvf766/bnn3/as88+W9T7CgAAAAC5WzjObMIdZtvW/X1d9QZm/UeYtTutyB9u/fr1wc/fe+89GzJkiMtEHm+Vp2h49dVX7aabbrKnnnrKjjvuONuzZ4/Nnz/f9eAqiX777TfLzMy0F1980Vq1auV+ziuuuMJ27txpI0eOjL2R7uOPP97Gjx9v9erVs+HDh7tlwnQZMWKEu0639erVq+j3FgAAAAByC9zvX5w1cMu29fuu1+1FTNnHu9SoUcON1oZep8CdfTS5Z8+edsMNN7hAXLNmTbfsskakFQ41oFmtWjUXGr/44ossj6UQeeKJJwaXar7ooots06ZNue7buHHj7LzzznOjv7q/Qw891M4//3x75JFH3O0ahdeA6dixY4Mj815frjVr1rjv1eh4rVq17PTTT3cjyR7vZ9JgbJ06dax69ep29dVXZxlV/vDDD10PsEqVKtlBBx1kffr0cT9jdrpfLzvq+dB+6HkoKA0Kv/baa3bCCSdYixYt7LTTTrNbb73VPv74Y4u2AoduzdXWGRKNcqt7+bp162z69Onuos/nzJnjupcDAAAAQKEFAmZpO/N32b3N7Ivb9U3h7mjfB42Aazvve9JTc78/PXYEKezWrl3bZs2a5QL4NddcY+eee651797d5SkFR4Xq1NRUt73KrjXwqfLw2bNn24QJE2zjxo0uGOdGoX/GjBm2atWqsLcrkOr7FVY1Yq+LHl95r1+/fi78f/fdd/bDDz+4oK/tQkP1lClTbNGiRS6ov/POOy7cKoSL7ksBXwOzi/5/m7POOssCYZ7Xxo0b20cffeQ+V5WAvnf06NHua5XCe9UCuV1Wr16d63Og6dA6aRBz5eVaKqxLly72+OOPuw7m3lkcAAAAACgyCsVDGxTRnQX2jYAPbxwceUzIa/O71pnFV7FI0Tzre+65x31+5513uuphhXCVQ4vK1J9//nk32HnUUUfZM8884wL30KFDs5SPK7AuWbIkON03lOYzK+g2a9bM3d6tWzc76aST7JxzznGZToFVo9AqOw/Nc2+++aYr01YPL406i0aQNeqt8KwTAhIfH+/2QU20NYr+4IMP2m233WYPPfSQC8579+51j9+0aVO3fbiVryQuLi4YjBMTE93j6PHVK+yqq66yAQMG5PlcNmgQ/jWybNkye/rpp6NeWl6o0K0nRU+cDg4AAAAAoGA6dOiQJV+p/Do0lKp8XJKTk93HefPm2ddffx12fvjy5cvDhu769eu7amSVpX/77bc2bdo0GzhwoAvTGilX8A5Hj6XAqpHuULt373aPFXriQIHbo1C/Y8cOV5qu21T9rJ+pX79+Lqgr7Kt8vCAUxnUyoqD++OMPNzKv6gHvREbMNVJTCYTOtmh+gB+G6wEAAACUMOUr7xtxzo9V08zeOmf/2134oVnT7vtGUrdvt+rVqoUPn3rsCCpfvnyWrzWiHHqdN8Ks/RSF2VNPPdX10AoXrvPSvn17d7n22mvdvOtjjz3Wvvnmm1x7cOmxVNn81ltv5bhN87fzQycSJk2a5IL+xIkT3Yjz3XffbTNnznTdxfNL5eWh3dbDWbhwoTVp0iT4taY862dTqfx//vMf84NChe6MjAyrUKGCa8OuMxYqWci+brdeKDfffHNR7ScAAACA0kTBM78l3i2P39elXE3Tws7rLrPvdm1XNk5p1qx8xr77z2XE10+0HLPmPSt3lStXqAjntGvXzn30GpqpRFzZLvtjqRO7Sr3VIC03GhHftWtXMAdq/rhG4lXy7uXBo48+2l1ULq9q6U8++cQGDRqU4760H5J9XwpaXq4RbgVunTRQSXxuo/nFrVBHTJPuPVqTOxxCNwAAAIBioSCtZcHUpVwBO0vw3jdqbP2H79suBl133XWuw7mak91+++2u2lgl4O+++64rF9fIcnZqzqZAqgZsjRo1cvOsH374YTdarVJwUYj/8ssvXQMzlbirA/uFF15ojz32mOtYrnna+l41Y1OjND22vhY1VVPls+amqwO55pBff/31LuhqRFuN1lRWnpiY6L5OSUmxQw45JOzPp0Cu/PjZZ5+5eeca4C1oebkCtzrD6740j1uP54l2D7JChe4VK1YU/Z4AAAAAQGFpHe7z3shlne7hEVmnu7goPKuL+B133OGCrPprKVxq3nJuo7laokuNztSQ7c8//3ThVWFbYVgBWzTfWc3Runbt6srKNW9cwVVzwPVYaoS2fft2a9iwoZujHTryra9bt25tPXr0cPujEwJahky0ne5DXci3bdvm9lWNuLXkWTi6f3U+Hzx4sFsuTJ3bn3zyyQI9Rypn14kIXbwTA55wXdOLU5lAAfdAJQSqx9ewveYVxDq9CHRGR+3k8yqfiBa17Ne65zrjk33uB6KP4+NvHB9/4/j4H8fI3zg+/sbxKTg16tLgnub8VqxYsfB3lJmxb473jo1mVeu6OdzZR7i97tj6+98vJcixROt0axmzTz/9NCL3n+mj45PX6zK/WbLAI92q2X/xxReD8wEAAAAAwDcUsJsfG+29AIIKddpAE9PVeh4AAAAAABTxnG7V5qtURq3nVVpwIB30AAAAAACxY8yYMdHehZhSqLSsoK3aerVwv/HGG93E93BLhqmNPAAAAAAApVWhQrdat6vjXdu2bYt+jwAAAAAAKM2hW23lAQAAAABA3uiPDwAAAABAtEP3tddea7Nnz86y9uD7779vKSkpObadPHmyHX/88UW3lwAAAAAAlOTQ/cILL9iSJUuyLAR+/vnn2y+//JJj240bN9o333xTdHsJAAAAADFITajPOOOMaO8GYrW8PBAIFN2eAAAAAEAM0YpNeV3uv/9+e/LJJ6O2xNZLL71kHTt2tKpVq1pCQoJ16tTJhg0b5rsTAlOnTnXP15YtWw7ofk477TRr0qSJVaxY0erXr28XXXSRrVu3zqKNBbYBAAAAlBgZmRk2J3mOpaSmWJ3KdaxzYmeLKxsXkcdav3598PP33nvPhgwZYosXLw5ep7CrSzS8+uqrdtNNN9lTTz1lxx13nO3Zs8fmz59vCxYssJKqV69edtddd7nA/ccff9itt95q55xzjk2bNi2q+0UjNQAAAAAlwuRVk63fR/3ssi8vszu+u8N91Ne6PhLq1asXvNSoUcON1oZep8CdfTS5Z8+edsMNN7hAXLNmTatbt64bkd65c6ddeumlVq1aNWvVqpV98cUXWR5LYfnEE09096nv0Sjupk2bct23cePG2XnnnWeXX365u79DDz3UTQ9+5JFH3O0ahX/99ddt7NixwZF5b5WqNWvWuO/V6LiWiz799NNt5cqVwfv2fqYHHnjA6tSpY9WrV7err77a0tLSgtt8+OGHdthhh1mlSpXcctN9+vRxP2N2ul+FZdHzof3Q81AYN998sx111FHWtGlT6969uw0ePNhmzJjh+pFFE6EbAAAAQMxTsB40dZBtTN2Y5frk1GR3faSCd2Eo7NauXdtmzZrlAvg111xj5557rguKc+bMsRNOOMGF6tTUVLe9yq7VqFrl4WpuPWHCBNdHS8E4Nwr9CpyrVq0Ke7tGgfX9/fv3dyP2uujxFVD79evnwv93331nP/zwgwv62i40VE+ZMsUWLVrkgvo777xjH3/8sQvhovtSwL/sssuC25x11llhpyc3btzYPvroI/e5qgT0vaNHj3ZfqxTeqxbI7bJ69eqwP99ff/1lb731lvuZypcvbzFTXv7GG2+4Aye7d+92ZyGeeeYZ+/TTT7NsF9pwDQAAAAAKSgFt195d+S4pHzZrmAUsZ6jzrhs+a7gdWe9IV2qemZnp7rtcejkrWzbnOGSlcpVc1okUzbO+55573Od33nmnDR8+3IXwK664wl2nMvXnn3/elYNr5FaZS4F76NChWcrHFViVvdq0aZPjMe677z4XdJs1a+Zu79atm5100kmu3Fo/swKrRqFVdq6A7nnzzTfd8/Pyyy8Hn4PXXnvNjXorPOuEgMTHx7t9qFy5shtFf/DBB+22226zhx56yAXnvXv3usdv2rSp216j3uHExcW50XRJTEx0j6PHV+Puq666ygYMGJDnc9mgQYMsX99xxx3u+dIJCz13n332mUVbgUL3xIkT3SVU9sDtieSLFAAAAEDJplB85NtHFtn9aQS8+7vd87XtzAtmWuXylS1SOnTokCV0qvw6NJSqfFySk5Pdx3nz5tnXX38ddn748uXLw4ZuzWuePn26K0v/9ttv3bzmgQMHujCtkfJwJxu8x1q2bJkb6Q6lQVc9VuiJAwVuj0L9jh07XGm6buvdu7f7mfr16+eCusK+yscLQmFcJyMKQsFfJfUa4dfI+8UXX+yCdzTzab5Dt842AAAAAAAOTPZyZwXC0Ou8gOhlMIXZU0891UaMGBE2XOelffv27nLttde6edfHHnusW97Zm0ednR6rS5curjQ7O83fzg+dSJg0aZIL+hMnTrSnn37a7r77bps5c6Y1b97c8kvl5aHd1sNZuHCh61juUUjXRSciDjnkEFcNoGptnRSIFrqXAwAAAPAdlXhrxDk/ftr4k1075dr9bvdc7+esS90uLsxu377djebmVl7uJ507d3bznlUqXq5c4SNcu3bt3EevoZlKxDMyMnI8ljqxq9RbDdJyoxHxXbt2uRJ1UbDVSLxCrnfi4Oijj3YXlcurzPyTTz6xQYMG5bgv7Ydk35fClJeH8k5aqIQ+mgjdAAAAAHxHoS2/Jd7dG3S3upXruqZp4eZ1l7Ey7nZt583p3ltur7v/3Mqs/eS6665zHc7VnOz22293ZdcqAX/33XddubhGlrNTczYFUjVga9SokZtn/fDDD7vRam/UVyH+yy+/dA3MVOKuDuwXXnihPfbYY65jueZp63tVqq1GaXpsfS1qqqYybs1NVwdyzSG//vrr3fOpEW01WlNZeWJiovs6JSXFjTyHo0Cu460ycM07r1ChQoHLy/UYP/74ox1zzDGujF2l8Pfee6+1bNkyqqPc4v9XGAAAAADkQUF6cNLgYMAO5X19R9IdEVuvO9IUntVFXCPBCrKaK60lx9R0LLeTBlqiS6PP6oquUuuzzz7bKlas6MKwAraocVvbtm2ta9euLozrMTRPW3PAVbKtRmgKygrXmtMdOvKtOdutW7e2Hj16uNHo0047zS1DJtpO96EA3aZNGxfMH3/8cbfkWTgNGzZ086+1xJfms6uje0Fpv3ViQPuln0n7rLnzKqX3Qny0lAmE69teiqgrns7obN26Nc/yiWhRy/7x48e7F2y0W90jJ46Pv3F8/I3j438cI3/j+Pgbx6fgFOpWrFjh5vwqHBaGlgVTl/LQZcPqVa7nAnefpn2C13ndsfX3fyyMdPuN1unWMma5NdU+UJk+Oj55vS7zmyUpLwcAAABQIihY92rcy+Ykz7GU1BSrU7mOdU7sHLMj3CgZCN0AAAAASgwF7CPqHRHt3QCCCN0AAAAAgHwbM2ZMtHeh5IXuyy67rMB3rO5zr7zySmH2CQAAAACA0hO6v/rqq+AC7flV0O0BAAAAACiVoVvrrgEAAAAAgIKhPz4AAAAAABFC6AYAAAAAwG+h+4svvrC+ffvaQQcdZOXKlbO4uLgcFwAAAAAASrNChe6PPvrITjnlFNu4caP94x//sMzMTDv//PPd55UqVbIOHTrYkCFDin5vAQAAACCGXHLJJXbGGWdEezcQa6F72LBhlpSUZD///LM98MADwWXF3nrrLVuwYIGtX7/emjdvXtT7CgAAAAC+oRWb8rrcf//99uSTT0ZtXeuXXnrJOnbsaFWrVrWEhATr1KmTy3J+OyEwdepU93xt2bLlgO5nzpw5rhpbP6sqsq+88krbsWOHxWToXrhwoRvVVgm5SsslPT3dfWzWrJlde+21NmLEiKLdUwAAAADYj0BGhu2cOcu2fva5+6ivI0WDjd5l9OjRVr169SzX3XrrrVajRg0XAovbq6++ajfddJPdeOONNnfuXPvhhx/s9ttv90UIjYR169ZZnz59rFWrVjZz5kybMGGC/frrr+7EQkyG7sqVK1t8fLz7XC+gChUquBeVp27durZixYqi20sAAAAA2I9tEyfast59bPXAgbbu1lvdR32t6yOhXr16wYvCtUZrQ6/TCHP20eSePXvaDTfc4AJxzZo1XXbSiPTOnTvt0ksvtWrVqrngqB5aoVRRfOKJJ7r71PdcdNFFtmnTplz3bdy4cXbeeefZ5Zdf7u7v0EMPdVOCH3nkEXe7RuFff/11Gzt2bHBkXiPOsmbNGve9ynq1atWy008/Pcsy0t7PpKrnOnXquJMNV199taWlpQW3+fDDD+2www5z04816qxArJ8xO91vr1693Od6PrQfeh4K6rPPPrPy5cvbs88+a23btrUjjjjCXnjhBTc1etmyZRZzoVs/hEa7PYcffrj997//tb1799ru3bvt7bfftiZNmhTlfgIAAABArhSs//j3TbZ3w4Ys1+/duNFdH6ngXRgKu7Vr17ZZs2a5AH7NNdfYueeea927d3cl0ieccIIL1ampqW57lV0ff/zxrjx89uzZbhRX/bUUjHOj0D9jxgxbtWpV2Ns1Cq/v79+/f3BkXo+vCuZ+/fq58P/dd9+5EXIFfW0XGqqnTJliixYtckH9nXfesY8//jg49Vj3pYCvKciL/n+bs846ywKBQI79aNy4sQvGsnjx4mDVgKgUXo+d12X16tVu2z179riB4bJl/464Cvzy/fffWzTtqw0voDPPPNOeeuopGzlypBvlvvvuu93ZD50J0ZkJncFQOQMAAAAAFIYCWmDXrvxtm5FhGx9+RN8U7o7MyphtfGSoVenWzcrExblG0Jm7dlmmpsqGhDRPmUqVXK6JFM2zvueee9znd955pw0fPtyF8CuuuMJdp6bUzz//vM2fP9+OOuooe+aZZ1zgHjp0aPA+lLcUWJcsWWJt2rTJ8Rj33XefC7qa/qvbu3XrZieddJKdc845LpgqsCqUKqwqoHvefPNN9/y8/PLLwefgtddec1lP4VknBEQBV/ugKmiNoj/44IN222232UMPPeSCswZk9fhNmzZ122vUOxxNWdZouiQmJrrH0eNv27bNrrrqKhswYECez2WDBg3cR52UGDRokD322GP273//22XSwYMHu9tCq7JjJnTrrIguHnUy1wHQ2Q09aSeffHKwRAAAAAAACkqBe3HnLkV0Z/tGvJcckZTl6o25bN52zk9WpnJlixSt9uRRflL5dWgoVfm4JCcnu4/z5s2zr7/+2gXl7JYvXx42dNevX9+mT5/uytK//fZbmzZtmg0cONCFaY2Uh44Ih9JjqRxbI92hVNGsxwo9caDA7VGo13xxlabrtt69e7ufqV+/fi6oK+yrfLwgFMZ1MiI/FPxVQaDgrRMZel41n13PZW4/q69DdzjHHnusuwAAAAAAcqe5x6E0ohx6nTfCrBFfUZg99dRTwzarVrjOS/v27d1Fza4171qZ7Ztvvsl1kFSP1aVLF7cyVXaav50fCryTJk1yQX/ixIn29NNPu+poNTgryCpXKi8P7bYejqY9e1ObL7jgAndR6X2VKlXc8zhq1Chr0aKFxVzoVpM0nTHRgQ/nf//7nzuroVIGAAAAACgolXhrxDk/UmfPtjVXXrXf7Rr/50Wr3LXrvvLl7duterVqYUdB9dh+0rlzZzfvWfnKWz2qMNq1a+c+eg3NVCKeka27ux7rvffec6XeapCWG42I79q1KzhvWvPHNRKvkndR4D366KPdReXyKjP/5JNP3Eh0dl6T7uz7UpDy8lBepYDK3ytWrOiWEYvJ8nLV2OcWutUxTrX477777oHuHwAAAIBSyHXUzmeJd5Wjj7Zy9eq5EvKw87rLlLFydeu67TSn2zIzrezevVa2cuWolx7nx3XXXec6nKs5mZb9Utm1SsCVt1QurpHl7NScTYFUc50bNWrk5jU//PDDbrRapeCiEP/ll1+6BmYqcVcH9gsvvNDNi1bPLs3T1veqGZumEuux9bWoqZo6o2tuujqQaw759ddf755PjWir0ZrKyhMTE93XKSkpdsghh4T9+RTIdbzVgVzzztU3rKDl5aK572oGp/CvkXbNMdd8+Wgs2RaqUK8wzQ3I62yB6vfV6Q4AAAAAIk1Buu5dd/7/F9kaoP3/17rdBe4YpPCsLuIaCVaQVVWxlhxTmMztpIGW6NLos7qia8732Wef7UZ9FYYVsEWN27QyVdeuXV0Y12NonrbmgKtkW43QFJQVrjWnO3TkW5mvdevW1qNHDzcafdppp7llyETb6T4UoNu0aeOC+eOPP+6WPAunYcOGrvO5Gp9plFod3QtD3eCVU/X8/Oc//7EXX3zRzeuOtkKNdG/evDnHxPpQOrPw559/Hsh+AQAAAEC+VVdX7SdH28ahw7IsG6YRbgVud3sEae1qXbIbM2ZMlq+9tbBDha6B7cm+vJYCrkab80shW5e8KGhrznV26maupmT7o6DsLRMWSkFdzdoK4t5773UX8bqXF9Qbb7xhflSo0K2zHjoLopKFcDTK7ZUdAAAAAEBxULCu1ru3pc7+yfampFi5OnWsctcuMTvCjZKhUOXlmkugBdC1VrfXUU9U7vDkk0+6iffqGgcAAAAAxUkBu8qRSVbjlJPdRwI3YnKkW+ueff/9924ewSOPPOLmAYgm4GuCfM+ePV1LeAAAAABAyZK9ZB4RGOlWNznV/r/yyiuWlJRkmzZtchd9rrbskydPDnacAwAAAACgtCr0Im/qknfppZe6CwAAAAAAyMmXi9JpnW+tGaeW9kceeaRr/Z4brVd37LHHWs2aNd1FrfHz2h4AAAAAAF+NdPfq1cuNbGvh9HLlyrkF1vdHi5trDbiCUhO2QYMG2QsvvOAC9+jRo61fv35uvrgWVs9OLffV2E2LoCukjxgxwq1d9+uvv7r13gAAAAAA8PVIt9aIC+1Srs91XV6X0O0LYtSoUW6RdpWtt2vXzoVvLdCuueLhvPXWW3bttdfa4YcfbgcffLC9/PLL7rELE/gBAAAAACj2ke7sC7iHW9C9KKSlpdlPP/3kuqN7NMKukvHp06fn6z5SU1MtPT3datWqFfb2PXv2uIvHW3Rd36OL33j75Md9A8fH7zg+/sbx8T+Okb9xfPyN41Nweq68wbvCDuDllx7H+xjpx0JsHx9vwFmvz7hsy8/l9/1dJuD9RD6wbt06VxI+bdo069atW/D622+/3b755hubOXPmfu9Do94qg1d5ucrNs7v//vvtgQceyHH922+/7UbUAQAAABQ/TWOtV6+eNW7c2OLj462kUD7ZunWrq9BF7NHA8Jo1a2zDhg22d+/eHAO+F1xwgTu+1atXL9ru5atXr97vfG4F3tq1a7vPi8vw4cPt3XffdSPx4QK3aBRdc8ZDR7r1xtY88LyeqGjR2ZNJkyZZ3759rXz58tHeHWTD8fE3jo+/cXz8j2Pkbxwff+P4FNzu3btduKlatWquf8sXFY07bt++3apVq3ZAeSX7yGd2Q4YMcU2i9XjRyBpqOv3cc8/Z8uXL3UmN5s2b27nnnmuDBw92t2tK75YtW+yTTz6xaJo6dar17t3b/vzzT0tISCj08Rk6dKiNHz/e5s6d607c/PXXX1lunzdvnusB9sMPP7glr9W8+6qrrrIbb7wxz9dlpUqVrEePHjlel17V9P4UKnRr5/Lzw2un1Fn83nvvtaOPPnq/2yuk64W7cePGLNfra531ysvIkSNd6NYa4R06dMh1O60fHm4Ncf1n6Of/EP2+f6Udx8ffOD7+xvHxP46Rv3F8/I3jk38ZGRkuY2h6qS6FlZkZsPVLt9jObXusSvUKVr91gpUtmzW7eCXL3uMV1vr167M0hFbIVgNoj04g6BIN6omlwcannnrKjjvuODfFdv78+bZgwYLgz6yf/0Cfg6JQ9v8f3zv2hT0+Otmlkwqqmn7llVdyfO/PP/9sdevWtTfffNMNvKrC+sorr3QnJK6//vpc9037Ee69nN/3dqFCt34AHTydibrwwgutVatW7vqlS5e6Mu2mTZu6sybLli1zP5C6nU+YMMF1Qc+LzkZ06dLFNUE744wz3HVeU7TcngR59NFH7ZFHHnFl5V27di3MjwQAAAAgxi3/Odm+e2+p7dzydw+nKgkV7NgBra1lp5wrIR2o0IHBGjVquHCWfbDwkksucaPJn376qfu6Z8+edthhh7nBxtdff91loIcfftiVKSvzfPjhhy4YPv3003biiScG70dh+bbbbrPvvvvOqlSp4ip1n3jiCTdwGc64cePsvPPOs8svvzx43aGHHppl2q0eX7wB1a+//trtn3LeLbfcYhMnTnShUwOpTz75pBt8Df2ZOnXqZM8884wL9Np/ZURvaoB+Dk3rXbZsmZvGq23Hjh3r9j3UypUrgzlRS0DLxRdf7B6voLxpxGPGjAl7+2WXXZbl6xYtWrjeYR9//HGeefNAlS3s3GvVtusJ1JNxww03uIue5CVLltiuXbvcRct96UxP/fr1w86jDkdnY1QGoRfAokWL7JprrrGdO3e6EO8dgNBGayoP0Ei6zuToRaBae1127NhRmB8NAAAAQIwG7gkvLsgSuEVf63rd7hfKOgrLs2bNcjlKmUcjtFoGec6cOS5QX3TRRW7OsCjgaiBTwXX27NluQFPVwArVuVH4nzFjhq1atSrs7bfeeqv7/v79+7sRe130+Bot1pLNKu1WwFcptkbrtZ0yoEcDo8prKg1/5513XHD1Mp/uS8s6K+Qu+v9tzjrrrGCDtFAacf7oo4/c58qO+l7lSBk2bFiwWiC3y/6mPu+P5mPn1oS7qBRqpFvLeCkcq94+O+3wv/71LxfGdSbmoIMOck/2Y489lq/7HjBggKWkpLjSDIVnLQWmF5XO9oie1NAygeeff94d/HPOOSfL/dx3333u7A0AAACA2KOAtjctM98l5d+9tyTPbTQC3ujgWq7UXNW0e9MyLH1PhpUtmzMIlovfV1IcKR07drR77rnHfa4BRU2TVQjX0smiLKSco3Lwo446yo0mK3BrzrJHg44KrBr0bNOmTY7HUB5S0NXApG5XyfVJJ53kcpPylAKr5iprlDp0dF6Vynp+tBSz9xy89tprLvspPOuEgGhEW/ugUWyNoD/44IMu/z300EMuOKvpmB6/adOmbnuN7oejEX8v9CYmJrrH0eNrvrTmWysf5qVBgwZWWCov17SAzz//3HwXujXB3TvrEo5GphWcPTqIBWmSrqH93Ib3sy9XpnIEAAAAACWLAvd//v1Nkd2fRrxfvvnbfG175ZPHWfkKeTdJOxChPagUOjVQGRpKvQHH5OTkYAMwlX6Hmx+uJmnhQreqjVU6rbL0b7/91gXMgQMHujCtQc3c5krrsVTRrJHu7A3F9FihJw5CV39SqFe1sUrTdZsao+ln6tevnwvqCvte+Xh+KYznVj5/oPS8nH766e7khHciwVeh+4gjjnAj2aeddlqOMxY6G6P5B0lJScHrVFLQqFGjA99bAAAAAIhx2RtweY26Qr8Wr6GYwuypp57qptaGC9d5ad++vbto6bKrr77azc/Wcsy59dvSY6nPVrglzurUqZOvn08nEtS9X0F/4sSJLh/efffdbglodVDPL5WX65KXhQsXWpMmTfJ9n9736KSAmqh5FQe+C9160nSQVOKgMxpeIzWdEdHZFLXD1/xu74yIRqezl38DAAAAQG5U4q0R5/xYt3SLffbMvP1ud8r1Ha1B633ly9u3b7Nq1aqHHfHVY/tJ586d3bxnlYqr03ZhtWvXLliZ7JWIq2t89sdSybVKvfNa5kwj4urjpRJ10fxxjcSr5N07caAVrI4++mhXLq8ycy1NFrp8s8drvpZ9XyJRXv7rr7+6+fEa9Vcz7uJQrrDlEL/88oube6CO4T/++KO7Xk+kzqDcfvvtwZFtLRum1uwAAAAAkF9u9DefJd6N29VyXcqzN1ELVbVmBbfdvjndZazcnjh3/9FeLis/rrvuOtdsWs3JlLVUdq0Bz3fffdeVi4dbL1zN2RRIFTCVzTTPWl3SNVqtgVNRiFeeUwMzlbirA7tWp1I/LpVea562vlfN2NQoLTTnqa+WOqNrpFhTflWmrSnCej41oq1GayrbTkxMdF9r+vEhhxwS9udTjtTx/uyzz9y8c2+J54KWl6v/l9bm1kcFeK3XLRok1gkBlZTr+VDJu8K/eoiJnr/8juIXRqFfYTqAGs3WAdJoti76XNdRSg4AAACguChIa1mwvBxzXusc63XHCmUvdRFXkFSQ1RTfm266yTUdy+2kQZ8+fdzos7qia8732Wef7QZEFYYVsEWN29q2beuWXVbo1GNonrbmgKtkW43QFJQVrpX3Qke+VZ7dunVr69GjhxuN1tRjr5G1ttN9KEC3adPGBfPHH388yxJooRo2bOg6nw8ePNjNZ1dH98LQiLqqsXUCQGXy+tzr+O4tY6bwr2ZxKsv3Lpo+HUllAgXpcBaGN1leVEoQrcXfC0td8XRGR63i8yqfiBa17B8/frx7weZ38XUUH46Pv3F8/I3j438cI3/j+Pgbx6fgFOpWrFjh5vwqHBbVOt0a4VbgDl2n2+uOrb//Y2Gk22+yrz1e1DJ9dHzyel3mN0sWekKASspVXvD9998HJ/h7C6c/+uij7mwJAAAAABQXBevmHevY+qVbbOe2PValegWr3zohZke4UTIUKnSrJr9nz55uwrvW5PZq89WlXAujq8RAzdNCO5gDAAAAQKQpYDdsW7ClqQDfhW61e1fdvUa5QxdSF9Xxq0OdtlGbeAAAAABAyTFmzJho70JMKVvYkW61b88euEUT37XemSbtAwAAAABQmhUqdGvu9t69e3O9XV31oj3hHQAAAACAaCtUMu7evbs9++yzbr227LQm2nPPPedKzAEAAACgIA5wcSXAd6/HQs3pHjp0qGuWdvDBB9uZZ57p1l4TrdM9duxYK1eunA0bNuyAdw4AAABA6eAtrZaammqVKlWK9u4AwdejHMjSf4UK3VpgXPO61Sxt3LhxwR3RQur9+/e3hx9+2Nq1a1fonQIAAABQusTFxVlCQoIlJycHs0WZMpFZ6ktLHqelpbk1mJkW6z+ZPjg+GuFWztXrUa9LvT4Lq9DrdCtUf/LJJ+4JSUlJcdfVqVPHPSk7d+60devWWYMGDQq9YwAAAABKF69Rsxe8Ixmodu3a5UbUIxXsUTKOT0JCQtgG4sUSuj0K2epYHmr06NE2ZMgQ11ANAAAAAPJDAat+/fqWmJho6enpEXsc3fe3337rpsweSNkwSvbxKV++/AGNcBdZ6AYAAACAoqSgUxRhJ6/712pMFStWJHT7UFwJOz5MYAAAAAAAIEII3QAAAAAARAihGwAAAACACMn3nO45c+bk+07VuRwAAAAAgNIu36G7a9eu+W7Xrhbv0W7tDgAAAABAzITu1157LbJ7AgAAAABAaQ3dAwcOjOyeAAAAAABQwtBIDQAAAACACCF0AwAAAAAQIYRuAAAAAAAihNANAAAAAECEELoBAAAAAIgQQjcAAAAAABFC6AYAAAAAIEII3QAAAAAARAihGwAAAACACCF0AwAAAAAQIYRuAAAAAAAihNANAAAAAECEELoBAAAAAIgQQjcAAAAAABFC6AYAAAAAIEII3QAAAAAARAihGwAAAACACCF0AwAAAAAQIYRuAAAAAAAihNANAAAAAECEELoBAAAAAIgQQjcAAAAAABFC6AYAAAAAIEII3QAAAAAARAihGwAAAACACCF0AwAAAAAQIYRuAAAAAAAihNANAAAAAECEELoBAAAAAIgQQjcAAAAAABFC6AYAAAAAIEII3QAAAAAARAihGwAAAACACCF0AwAAAAAQIYRuAAAAAAAihNANAAAAAECEELoBAAAAAIgQQjcAAAAAABFC6AYAAACKUEZmhs3eONvmpc1zH/U1gNKrXLR3AAAAACgpJq+abMNnDbeNqRvd1x9M+cDqVq5rg5MGW5+mfaK9ewCigJFuAAAAoIgC96Cpg4KB25Ocmuyu1+0ASh9CNwAAAHCAVEKuEe6ABXLc5l03YtYISs2BUojycgAAAOAAzUmek2OEO3vw3pC6wf7x2T+sbpW6VqlcpeClcvnKWb7O6/rK5SpbxXIVrWwZxs6AWEHoBgAAAA7AHzv+sPcXv5+vbX/b/Ju7HKhwIT00mFcqn8v13tflw99GoAeKHqEbAAAAKKBNuzbZlyu/tC9WfGHzUubl+/uu6nCV1a9S33bt3ZXjkpqemvXrvVm/1sWT/euilGdYDwnsOa7fz8i9LmXKlInIPgN+RugGAAAA8mF72nbXDE1Be+aGmZYZyHTXl7EydkTdI9wI9ra0bWG/V9uoi/k1Ha+xuLJxhXp8Pd7uvbvDB/P0MCE+NLSn5x3mox7o8wjy+Sm/rxhXkUAP3yJ0AwAAALlQyP1m7TcuaH+79ltLz0wP3nZY7cPspOYnWb9m/axO5TrB7uUS2lBNgVvuSLqj0IFbVPatoKlLUfMCfdhAnp57UA83Qp/9+t0ZuyMe6PUcqzR+f/Phvc8rlK1gK/assLTlaVa1QtU8y+8J9DhQhG4AAAAghIL1jHUzbPyK8fbV6q9c4PS0rNHSTmpxkp3Y7ERrXL1xlu/TOtyjeo7Ksk63aIRbgdvP63QXd6DfX1DP721eoNdJjsIE+s9nfp6vQB+uvH5/I/P5Kb+vEFeBQJ+NOvzP3jjb5qXNs8SNiZbUIOmATlb5AaEbAAAApZ6C4ZyNc9yI9sRVE23Lni3B2xpWbWj9m/W3E5ufaG1qtskzJClY92rcy2atm2WTpk+yvt36lojQ4NdAr4Cm4J3biHxu5fc70nbY72t+t4Q6CbYnc0/Y8vs9GXuCgV7XhZ58KcrnRiPpBe1kHxroc/ueWAz0k1dNznLS6oMpH7iTVoOTBvv6pNX+ELoBAABQKgUCAVv01yIXtHUJHZ2uVbFWMGh3rNOxQOFFAbtr3a6WHJ/sPpbmwB1pem6rlK1iVcpXMauU/+9LT0+38X+Nt5N6nmTly5cvUKDPUWqfR/l9biP3XqDXyZ5IBvpCd7gvn3OkPvS2+LLxRR7oJ///9Izsa90npya761VFEqvBm9ANAACAUmXF1hXBoL1y28rg9dXKV7PeTXu7oJ1UL8nKleVP5dKssIE+PxTow4Z0hfdChPjQEf20zLRgoN+ZvtNdIhnow5bR59Xhvvzf13sf4+PibejMoTkCt+g6lfiPmDXCVZHE4kks/icBAABAibdh5wabsGKCm6et0W2PSnCPa3Scm6d9TMNj3NdApCk4Vo2v6i5FbW/m3ixd7rOX2GeZW59L+X1uDfWKI9CHo+C9IXWDzUmeY0fUO8JiDaEbAAAAJdLm3Ztt0qpJ9vnvn7s/1j3lypSzbg26uRHt45scv28kEyghVKERyUAfttFdHvPpU/PRHE/hPSOQsd/HT0lNsVhE6AYAAECJoT/e1XFcI9rqQL43sDd4W5e6XdwSX32b9rWaFWtGdT+BWA301eKruUtR+nHDj3bZl5ftdzstzReLCN0AAACIaWpK9f3a713Q1praXpMqOaTWIS5o92/e3+pVqRfV/QQQXufEzq5LuZqmhZvXrTndul3bxSJCNwAAAGKOylxnrZ/lgvaU1VNsR/qO4G3NqjdzQVvl481qNIvqfgLI3xx3LQumLuUK2KHBW1+L1rqPxSZqQugGAABAzCzxNS9lngvaX6780v7a/VfwNo2CKWTrotHtWFufGCjt+jTt45YFC12n23tvK3DH6nJhvgzdzz77rD322GO2YcMG69ixoz399NOWlJQUdttff/3VhgwZYj/99JOtWrXKnnjiCbvpppuKfZ8BAAAQuaC9ZPOS4BJf63auC96WUCHBTmh6gus83imxk1vGCEDs6tO0j1sWbNa6WTZp+iTr262vJTVIitkRbl+G7vfee88GDRpkL7zwgh155JE2evRo69evny1evNgSExNzbJ+ammotWrSwc889126++eao7DMAAACK3ppta9yItoL28q3Lg9drXd/eTfatpX1Ug6OsfNnyUd1PAEUrrmycda3b1ZLjk93HWA/cvgvdo0aNsiuuuMIuvfRS97XC9+eff26vvvqqDR48OMf2RxxxhLtIuNsBAAAQO7Qc0ISVE1zQ/mXTL8HrFax7NOrhgrbW1K5YrmJU9xMAYjJ0p6WluTLxO++8M3hd2bJlrU+fPjZ9+vQie5w9e/a4i2fbtm3uY3p6urv4jbdPftw3cHz8juPjbxwf/+MY+VtJOT7b0ra5RmhfrPrCftr4U7CBkkrFk+omWf9m/a1Xo15/L1EUiI2fuaQcn5KK4+Nv6TFyfPK7f74J3Zs2bbKMjAyrW7duluv19W+//VZkjzNs2DB74IEHclw/ceJEq1y5svnVpEmTor0LyAPHx984Pv7G8fE/jpG/xeLxSQuk2aL0RfZL2i+2dO9Sy7CM4G1N4ppYh/gO1r58e6u6u6rZb2bf/fadxapYPD6lCcfH3yb5/PhounNMhe7iopF0zRsPHelu3LixnXDCCVa9enXz49kTvdj69u1r5cszZ8lvOD7+xvHxN46P/3GM/C3Wjk96RrpNWz/Nvlz1pU1dO9V2Z+wO3tY6obX1b9rf+jXtZw2qNrCSINaOT2nD8fG39Bg5Pl7VdMyE7tq1a1tcXJxt3Ph3e3jR1/Xq1Suyx6lQoYK7ZKeD6ecD6vf9K+04Pv7G8fE3jo//cYz8zc/HJyMzw5WMqyHapFWTXCm5p1HVRq7ruNbTbpnQ0koqPx8fcHz8rrzPj09+9803oTs+Pt66dOliU6ZMsTPOOMNdl5mZ6b6+/vrro717AAAAyOcSXws2LQiupZ2yKyV4W51Kdaxfs34uaLev3Z61tAGUCr4J3aKy74EDB1rXrl3d2txaMmznzp3BbuYXX3yxNWzY0M3L9pqvLVy4MPj5H3/8YXPnzrWqVataq1atovqzAIj+6MrsjbNtXto8S9yYWCLWeAQAP1u+ZXlwia8129cEr68eX936Nu3rgnaXul34vxhAqeOr0D1gwABLSUmxIUOG2IYNG+zwww+3CRMmBJurrV692nU096xbt846deoU/HrkyJHuctxxx9nUqVOj8jMAiL7Jqybb8FnDbWPqvukqH0z5wOpWrmuDkwZbn6Z9or17AFBirNuxzoVshe0lm5cEr69UrpL1bNzTBe2jGxxt5eP8Wx4KAKUqdItKyXMrJ88epJs1a+ZKmAAgNHAPmjoouOSMJzk12V0/qucogjcAHIBNuzbZxJUTXdiemzI3eH25suXsmAbHuLW0Fbgrl/fvqjAAUKpDNwAcSEm5RrizB27RdWWsjI2YNcJ6Ne5FeSMAFMD2tO371tJe8YXNWD/DMgOZ7nr9v3pEvSNc0FYJeY0KNaK9qwDgO4RuACXGnOQ5wZLycBS8N6RucNvpj0QAQO52791t36z9xgXt79Z+Z2mZacHbDqt9mAvaaoqWWDkxqvsJAH5H6AYQ0zTFZOW2lW5JmnHLx+Xre1JS/+6kCwD4W3pmus1YN8MF7a/WfGU703cGb2tZo6UL2ro0qd4kqvsJALGE0A0gpqikcenmpa4zuYK2Ln/t/qtA91Gncp2I7R8AxOL/qz8n/+yCtuZqb96zOXhbgyoNrH/z/q4hWpuabVjiCwAKgdANwPejLov+XBQM2CoN19zCUPFl461DnQ7WKbGTfbjkwyx/MIbz1sK3rHG1xlavSr0I7z0A+LdK6Le/fnNdxyesnGAbdm4I3larYq3gWtod63QkaAPAASJ0A/DdHMJfNv0SDNnzUubZrr27smxTuVxlF7C13qsu7Wu3t/i4eHdbu4PauS7lEq6hWlkra1PWTLFp66fZNR2vsX+2+6eVL8tSNgBKh5VbVwaX+NLUHE/V8lWtd5PeLmgn1U9yncgBAEWD/1EBRJXmC85NnhsM2QrcGt0OpW64nRM7u4DdtW5Xa1urba5/EGo5MC0LFrpOt9SrXM/uSLrDzUN8eMbDrpRy1E+j3Dzwe466x903AJREGsX+cuWX9vnvn9uivxYFr68QV8F6NOphJzc/2Y5pdIz7GgBQ9AjdAIrV5t2bXYm4F7JV3ugtPeOpU6mOC9ed6+4L2i0TWlrZMmXz/RgK3loWbNa6WTZp+iTr262vJTVICi4TNqb/GBe2R80eZcu2LLNLJlxip7U8zQZ1GWQHVTqoyH9mAIjG/7WTVk1yI9pzNs4JVv7ElYmzbg26uRFt/T9ZNb5qtHcVAEo8QjeAiEpOTQ4GbF0UcrNrVLVRsFRcYbtRtUYHPIdQAVv3lRyf7D6GrsutAH9GqzPcH5xPznnSzQNXCP96zdd2U+eb7OzWZ7OON4CYrBz6avVXrnx8+rrptjewN3ibqoUUtPs26+vmbAMAig+hG0CRNuZZu2NtlpC9ZvuaHNtp2RkvZGs0O1oNzVS2PqTbEDu91en2yIxHXNnlQzMesk+XfWp3H3W3HXrQoVHZLwDILwVrnTCcuGaifbPmG9udsTt42yG1DnHLe/Vv1t/qV60f1f0EgNKM0A3ggEL271t/d+HaW8JLI9uhNKrctmbb4Ch2p7qdfDfKou68b5/8tr23+D175udn3LzyCz6/wAa0HWDXd7reqsdXj/YuAkDQ3sy9NmvDLPt8+ec2cetE2/3d30G7WfVmwbW0m9doHtX9BADsQ+gGkG8ZmRm2ePPiv5fv2jgnx/JcanDW/qD2wZHswxMPt2rx1czvtN8XHnKhndD0BBs5e6SbB/nOb++4NWtvPeJW12iIZXMARPMkp1ZzUOm4mqL9ufvP4G2JlRL3Be0WJ1q7Wu34vwoAfIbQDSBXaRlp9uufvwZDtjp+a85gqIpxFd1IsReyD6tzmFUqV8liVZ3KdWxEjxF2VuuzXJdzLalz53d32sdLP7Z7jrzHWiS0iPYuAihFlmxeYuN/37eW9h87/ghen1AhwXo37m0JGxLsmlOvsQrxdB4HAL8idAMISk1Ptfmb5gdD9vyU+bYnY0+WbbSWq9dVXBeNqpSPK3nrXB9Z/0j76LSP7I2Fb9iL8160Hzf8aGf/72wb2G6gXdnhSqtcvnK0dxFACaVeGBrR1iW0+WTlcpXt+CbHu1FtdSC3DLPx48cXaHUHAEDxI3QDpdi2tG1ujWxvPvbCTQuzdLsVzb/2ArYurRNal5rO3vFx8favw/7lmhBp3e9v1n5jryx4xZWeD04a7P74BYCikJKa4srGFbR18tNTvmx5O7bhsa50/LhGx2WpJErPSI/S3gIACoLQDZQif+76M8sa2Yv/Whxcu9VTt3Jd61qvazBkN6/evNTPD9QSZs/0fsa+Xv21DZs1zNbvXG///vrf1rNRTxt85GBrWLVhtHcRQAzaumerTV412QXtHzf+aJmBTHe9Rq6T6iW5Jb56N+1NM0cAiHGEbqAE27BzQ3AUW5cVW1fk2KZp9aZZRrIbVGlQ6kN2bno16eXKzl/65SUb8+sYm7p2qs1YP8OVmw88dKAbGQeA/U3jUdWMKma+/+N714nco/4YKh3v16yf1a5UO6r7CQAoOoRuoAR1tl29fXWWNbJDm+54WtdsbV0Su1iXel3cRzUOQ/5pLve/O//bTm1xqj0y8xG3bM9TPz9l45aPc2t7H1X/qGjvIgCfURn4tHXTXNDWmtq79u7K8n+yRrQ1jUVVNQCAkofQDcQolSEu3bw0S7n4pl2bsmwTVybODql1SHAUWw3QalSoEbV9LknUxfzlE162z1d8biN/HOm6nF8x8Qo3SnVb19s4mQGUclpiUf8vK2hPXj3ZlZJ7NCVFQVuXVjVbRXU/AQCRR+gGYkR6Zrr99udvf6+RnTzHNUILFV823i3ZFVwju87hdNmOIJXhn9LiFOvRqIc98/Mz9t7i99zczO/WfmfXd7reBrQd4Nb/BlB6Ko60zKKC9pcrvrTkXcnB21QurtFsnZg7rPZhTOMBgFKEvwYBn9JSXb+k/BIM2XNT5mYpSRR1se2U2CkYstvXbm8V4lirtbipydFdR95lp7c63R6e/rAt+HOB63Y+dtlYu+eoe6xDnQ7R3kUAEfT7lt9d0NZJN03z8VSLr2Z9m/Z1I9pd63YtNSs/AACyInQDPrEzfafNS54XbHz2y6Zf3Oh29nCnEnH98aaQ3bZWW7ecDPzh0IMOtTdPetM+WvqRjZ4z2hb9tcj+Of6fdnabs+2mzjdR2g+UIOt2rAuupb148+Lg9RXjKlqvxr3ciPbRDY+mwSIAgNANRIvm983Z+Pd8bAW0jEBGlm1UjhjaWbxVQiu3lAz8SyNZ57U9z3o36W2jfhrlGqx9uORDm7Jqit3c5WY3Gs4xBGJ32cWJqya6oP1z8s/B68uVKecCtoK2AjfTegAAoQjdQDFJSU2xn5J/sp82/OQ+qgladmquExqym1Rrwry/GHVQpYPskWMesTNbnem6nC/bssyGTBtiny771HU5b1OzTbR3EUA+7EjbYVNWT3Hl4zPXzwyeHC1jZaxrva4uaPdt0tcSKiZEe1cBAD5F6AYi1ExHy3WFLt8VOs/P07xG879DdmIXq1+1flT2F5GjP8rfP/V9e2vhW/bcvOdcA7zz/nee/fOQf9o1h19jVcpXifYuAshm997d9u3ab92Itj6mZaYFb2t/UPvgWtp1q9SN6n4CAGIDoRsoopCtRjrefGxdNqZuzLKNRkUOrnVwcOmuzomd3WgoSj7Nu7+k/SXWv3l/GzFrhFs+6PWFr9sXK7+wO464wzVaoqIBiC710NBItoK2RrbVZ8PTokYLF7R1aVq9aVT3EwAQewjdQCHXX12yeYnNWjfLxu8cb49//Lht3rM5yzaa43do7UP/Xr4r8XDXCA2lV70q9eyJXk+4kbNhM4fZ2h1r7ZZvbnFzQe9KusuaVG8S7V0ESpXMQKbNTZ7rSscnrpyY5f/x+lXquxNlJzc/2U0H4cQYAKCwCN1APqRnpLu1V71RbDXQ2ZG+I8s2WqqrY52OwZCtdVhppoNwtK53Ur0ke2XBK/bKL6/YD3/8YGeOPdP+ddi/7LLDLmPZNyDClUm//fXbvs7jK7+wDTs3BG+rVbGWndD0BDupxUnu/3OaHgIAigKhGwhD62GHrpE9L2We7c7YnWUbzcU9vPbhVnlzZbvg2AusQ90OLA2DfKtYrqJdd/h1dkqLU+yRGY/Y9PXT3Zzv//3+P7fm9zENj4n2LgIlyqptq4Jraa/YuiLL/+VabUBraR9Z/0grV5Y/jQAARYvfLICZbU/b7koMvZC94M8Ftjdzb5ZtEiokZOks3rZmW8vMyLTx48e7EZHycayXjYLT/NAX+77oliF6dNajtmb7Grtm8jVunvftR9zuStIBFI5Gsb9c+aUL2wv/XBi8Pr5svB3X+DgXtI9tdCzVJQCAiCJ0o1T6a/dfWdbIXrx5sZvbFyqxcqIL113rdnUf1Ugn+5w+hW7gQOl1pU7IRzc42o12v73obZu0apIrO7/28GvtgkMucM3YAOzflt1bgmtp6//3gAXc9XFl4uyoBke5oH184+OtanzVaO8qAKCUIHSj1Ix2hC7f9fvW33NsozWx1VXcG8luVLURjXNQrBQCNLp9esvT7aEZD7lpDSNnj7Sxy8faPUfe416fAHJKTU+1r9Z85YL2tD+m2d7A35VKWilCXcdPaHaCm7MNAEBxI3SjRDbJUYmuwrW3hJfWzM6uVUKr4Ei2woxGtgE/aFurrb1x4hs2dtlYG/XTKFu6eakNnDDQzmh1ht3c5WaCA2BmaRlp9t0f37mg/c2ab7L03dDyjBrR7t+sv9WvWj+q+wkAAKEbMU9l4cu3LM8ykp2yKyXLNupAe0itQ4Kj2Br5SKiYELV9BvZHr9kzW59pvRr3stFzRttHSz+yT5d9al+t/spu6nKTnd36bDoro1Qu1zhrwywXtCevmmzb07dn6Y/graWt6UAAAPgFoTtGQqVGbDenbbY6leu4wBhXNs5KKzU4W/zX4uAo9pzkObZ1z9Ys22j+q5bs8kK2Gp0xfw+xSCeH7u9+vxvlfnjGw67/wIPTH7RPl35q9xx1jx1y0CHR3kUg4tVL8zfNd0F7wooJ9ufuP4O3qUJJo9la4qtdrXZMCQIA+BKh2+emrJliI7eNtG1TtgWvq1u5rg1OGmx9mvax0mBPxh5bsGlBsPGZ1shO3ZuaZZtK5SrlWCNbSzIBJcXhiYfbu6e8a+/+9q49M/cZF0L+8fk/7B9t/2HXd7reqsVXi/YuAkVK0yq8Jb5CpwjVqFDDraWtEW39f0/FBwDA7wjdPqbSudu/uz3YedWTnJpsg6YOslE9R5XI4K2GOHNT/l6+S+tlp2WmZdlGAUMj/l7I1mgf3Z1R0mn94H+2+6drCDXyx5H2xcov7O3f3nadmm/repsLIYz0IZapH4dGsxW2l21ZluXE6vFNjnfztLvV78YSjQCAmELo9vG8teGzhucI3KLrylgZGzFrhJvvGeul5ioN1+i1F7K1lmpGICPLNmoc5S3dpUvrmq0Z3UCppZLaR4971M35HjpzqK3cttLu+O4O+3jpx3bXUXcxnxUxZdOuTfvW0v59vKvg8OhE6jENj3FBW2tqK3gDABCLCN0+pXnKG1M35nq7gveG1A1uuyPqHWGx9gdWaNMzlRBmP7nQoEqDYMDWRQ1yGMEDsurWoJt9dNpH9tqC1+ylX16ymRtm2tnjzrZLD73UruhwBSEFvj7ZOmX1FDei/eOGH13vEtHJ1KR6SS5o927a26rHV4/2rgIAcMAI3T6Vkpq1+3ZuVGrud+t2rMsSsjUql12z6s2yhOwGVRtEZV+BWBMfF29XdbzKNZIaNnOYW0JJAVxh5s6kO90IIeAHu/buckt76bX5/R/fW3pmevC2DnU6uKDdr1k/q12pdlT3EwCAokbo9il1Kc+P5+Y+ZxXiKri5bn4ot1aXWYXq0JC9fuf6LNuoNL5NzTZ/L99VtzN/ZAEHqHG1xvZs72ftqzVfuakpajx1/VfXuykoarzIiSxEQ3pGuk1fP90+//1z+3rN1y54e1oltNq3lnbz/u71CwBASUXo9ik1CVOXco1kh5vX7Vm9fbXdPPVma1mjpSsn1SiBmi0V59xzNbvxlu/S5a/df2XZJq5MnB160KHBkK0uzOo+C6BoaQpG7ya9XaOpF+a/YP/99b8u6ExfN92Nhg9sN5AGVIg4lYrrd4FGtCetmpRlSceGVRu6oK2mf+rNAQBAaUDo9ik1R9PolLqUZ6eRYnnw6Addp9e3F71ty7cut8HfDXYj3/867F92SotTIvLHtcoB1ejMC9g/b/zZtqdvz7JNfNl4VyoYukZ25fKVi3xfAISn99ugLoPstBan2cMzH3bv1SfnPGnjlo+ze468x5LqJ0V7F1HCqMpJvxsUtNV9PHnX31OfDqp4kBvNVtDuULsD/TkAAKUOodvHtBzYo8c+ag99/5BtC2Rdp/uOpDuCy4UNPHSgW7v3vwv/60a+h0wbYs/Pe94ubX+pndX6LFd+HjoyreZrmjOuEnaNqOfV/Xz33t32y6ZfgiPZ81PmZykPlMrlKlunup1cd3HdX/va7d08UwDR1apmK3ut32v22e+f2cjZI23F1hV2+cTL7eQWJ9utXW9lWgfypN8X+r9/Xto8S9yYaEkNknL8vvh9y+/BtbT1+8dTrXw19ztKvQaOqHtEzK+yAQDAgSB0+1zvxr1tV/VdVq9rPductjlsUFZ31ys7XGn/POSf9sGSD2zMr2PcPGotJfSf+f+xSw69xM5tc65NWzfNzfUM7YquAK8RdS/A70jbkXWN7E2/2N7MvVn2SaXhXRL/v+lZvS7WtmbbYi1pB5B/GlU8teWp1qNRD3v656ft/cXvu/m136751m7ofIOd1+Y8AhFymLxqcpbfFx9M+SD4+0LThbRGvIL2b3/9FvyeinEVrWfjnm5EW0t9cfIVAIB9SEoxQA3SNIpcvnz5/ZaUatR7QNsB9smyT+zVBa/ahp0b3AiXys5T96bm+B79QaU54cc1Os5SdqW4P6C8pVs8dSrVybJGdouEFr5o2gYg/3Sy7J6j7rEzWp1hD814yJUC68TcJ0s/sXuPutcOq3NYtHcRPgrcmtqUvZ+I9/siVLky5ax7w+4uaB/f+HimEgEAEAahuwSqWK6inX/w+XZO63NcWalGu9fuWJvn93yz9pvg542qNgoGbIXtRtUaMQcPKCE0/ePtk952VTFPzXnKFv21yC4cf6Grhrmx8400OSzlVFKuEe68GniKqugLZp4AAB+ESURBVJ1Obnmy9W3S1xIqJhTb/gEAEIsI3SWYGqmd2fpMq1+lvl0x6Yr9bn/lYVfauW3PtXpV6hXL/gGIDpWT/+Pgf7hpJaNmj7L//f4/e3/J+zZ59WS7pestdmqLUznRVooaoGk60tLNS23plqU2Y92MLFOQcnNdp+vsiHpHFMs+AgAQ6wjdpUD2Jbxy0zKhJYEbKEXUSG3osUPdybmHZzxsv2/93e7+/m77aMlHrhSdJZ1Kli27t7hgvWTzErfUo4K2Pu5M31ng+1IzTgAAkD+E7lJAzdeKcjsAJYtGLD889UP776L/2gvzXnArHJz3v/PsonYX2dUdr2aebozRChPqKh4arhW2N+3aFHZ7zctuVqOZO8lSKa6Sfbzs4/0+Br8vAADIP0J3KaBu5+o6m5yaHHaentb91u3aDkDpnY5yWfvL7MRmJ9qIH0fYlNVT7LVfX3PLQaljde8mvSk59xmtLLF622oXqL1Ra31cs31NrnOyG1ZtaK0TWruA3SqhlfvYrHozd/y9Od0/rPuB3xcAABQhQncpmb+pP5rVjVZ/MIX+IaWvRet+s2wQgPpV69voXqPtmzXf2LBZw+yPHX+4jtVaAuqupLuscfXG0d7FUjnvWvOsvRFrL2BrNDstMy3s99SsUNMFandJaO3WbFfIrlK+Sp6Pxe8LAACKHqG7lHANk3qOCrtOt/6A8tbpBgA5rvFxllQ/yV7+5WW3/OD3f3xvZ4470/512L/s0vaXWoW4CtHexRJp656tWUatFbKXbV5m29O3h92+UrlKLkx7o9beCLbm6xcWvy8AAChahO5SRH8o9Wrcy83XVBMczclTiSAjFgByC3Q3dLrBTmlxij0y8xGbuX6mPTv3WbcU4V1H3mXdG3SP9i7GrN17d7vGdVkC9uallrwrOez2cWXiXBl4aFm4LioXL1umbMR+X8xaN8smTZ9kfbv1taQGSfy+AACgEAjdpYz+YGKZFwAF0bxGc3up70s2YeUEe/THR23VtlV21aSrrF+zfnZb19usbpW60d5F39Icac2xzj7vevX21ZYZyAz7PVrmMbQsXB91DOLj4ov990XXul0tOT7ZfSRwAwBQOIRuAMB+qYnaic1PdHO7n5v7nL3929v25cov7bu139l1h19nFxxygZUrW65Uz7tW87HQsnB91Gj2now9Yb+nRoUawaZmXsjW0o3V4qsV+/4DAIDIKb1/IQEACkyBUPN6T291uj004yGbnzLfHpv9mI1dPtat7d0psZOVdNvStrl51grYWpbLG8HW9eFUjKvownSwLPz/g7bmXdMRHgCAko/QDQAosINrHWz/PfG/9vHSj+2Jn55w4fPiLy62M1udaTd3udlqVqxpsS4tIy047zq0PHzDzg1ht9fc6qbVmwbLwtsktHEfG1VtRGk2AAClGKEbAFAoCpnntDnHjm9yvI3+abR9suwTd/lqzVd2c+eb7czWZ0akyVck5l1raTSF6iVblrhRbIVsrYGdEcgI+z3q5B1aFq6PmndNV3cAAJAdoRsAcEBqVaxlDx79oAvZKjlXeL1/+v328bKP7d6j7nWj4n6Zd71p16bgqLU3cr18y3LbnbE713L64Lzr//+o0evq8dWLff8BAEBsInQDAIqE5nO/f8r79vait93SYprvPeCzAXbBwRe4ZmtV46sW277sSNuxr6lZtq7hW/ZsCbu9Rqhb1GiRo2t4YuVE5l0DAIADQugGABQZdTC/+NCL3XJiWl5s4qqJ9uaiN12n89uPuN1drxCrku7ZG2fbvLR5lrgxsdBrQKdnpO+bd71labAsXB/X7VwXdnuVuzep1iTLWtf6XNcx7xoAAEQCoRsAUOS0dvfjPR+3H/74wYbOHOrWpb7t29vso6UfWa/GvezVBa/axtSNbtsPpnzg5kgPThpsfZr2CXt/WtPam3cdXJZr81K3ZvjewN6w35NYKTEYqr2ArdHsiuUqRvRnBwAACEXoBgBEzNENj7aPT//YheyX579sM9bPcJfstMb1oKmDbFTPUXZ44uHBYB36cdfeXWEfo1r5asFycO+jArbWwQYAAIg2QjcAIKI0X/qajtfYic1OtLPHnW1pmWk5tglYwH1U8PY+z6582fJ/z7v+/xHsNjXbuFFy5l0DAAC/InQDAIpFyq6UsIE7lBe4s8+71uh1k+pN3JxxAACAWMJfLwCAYpGSmpKv7R7svm/5MQAAgJKgbLR3AABQOtSpXCdf2zWq1iji+wIAAFBcCN0AgGLRObHzvvnXFn7+ta6vV7me2w4AAKCkIHQDAIqF1sHWsmCSPXh7X9+RdAfrZQMAgBKF0A0AKDZah1vLgiVWTsxyvUbAdX1u63QDAADEKhqpAQCKlYJ1r8a9bNa6WTZp+iTr262vJTVIYoQbAACUSIRuAECxU8DuWrerJccnu48EbgAAUFJRXg4AAAAAQIQQugEAAAAAiBBCNwAAAAAAEULoBgAAAAAgQgjdAAAAAABECKEbAAAAAIAIIXTHgEDAbN3SLbbkxw32x+LNlpkZKPR96Xt1H0VxX4Cf6bWt903qunLuI691f+H4+B/HCCg83j9A4WWWwPePL9fpfvbZZ+2xxx6zDRs2WMeOHe3pp5+2pKSkXLf/4IMP7N5777WVK1da69atbcSIEXbSSSdZSbBi7ibbMLWKfTbhl+B1VRIq2LEDWlvLTokFuq/lPyfbd+8ttZ1b9hzwfQF+lvW1Xsk+m/cLr3Uf4fj4H8cIKDzeP0DhLS+h7x/fjXS/9957NmjQILvvvvtszpw5LnT369fPkpOTw24/bdo0O//88+3yyy+3n3/+2c444wx3WbBggZWEF92kVxZZxu4yWa7Xi3DCiwvc7QW5L31PaOAu7H0BfsZr3d84Pv7HMQIKj/cPUHjLS/D7x3cj3aNGjbIrrrjCLr30Uvf1Cy+8YJ9//rm9+uqrNnjw4BzbP/nkk9a/f3+77bbb3NcPPfSQTZo0yZ555hn3vbFKZRQ6y7NP1tDt0e2NDq5lZcuWycd9Lclzm/zeF7JKT8+wzL1m6XsyzDJ9dw6r1OG17m8cH//jGMUWfgf5C++f2ML7J/beP9+/v9Sad6wTk++fMoGAZgz7Q1pamlWuXNk+/PBDN1rtGThwoG3ZssXGjh2b43uaNGniRsZvuumm4HUaJf/0009t3rx5Obbfs2ePu3i2bdtmjRs3tk2bNln16tXNLzR/4bOn/i4pBwAAAIDS7JQbD7MGrRPML5Qla9eubVu3bs0zS/pqpFvBNyMjw+rWrZvlen3922+/hf0ezfsOt72uD2fYsGH2wAMP5Lh+4sSJLvD7hRoHaB4DAAAAAMBs2jezrPLSveYXqamp+drOV6G7ONx5551uZDz7SPcJJ5zgv5Huefsf6e5/9aFWv1WNPLdZv2yrTXjh1yK5L2SVnp5uX331lR1//PFWvnz5aO9Oqcdr3d84Pv7HMYot/A7yF94/sYX3T2y+f7ofl+S7ke6YC90amo+Li7ONGzdmuV5f16tXL+z36PqCbF+hQgV3yU5vNj+94RofXNt16sveSCBU1ZoVrHmHxP3Oa2jeoYJVSVhWJPeFrNLT46xsObPKVSv66vVTWvFa9zeOj/9xjGILv4P8hfdPbOH9E5vvn8YH1/bV+ye/rx1fdQ2Ij4+3Ll262JQpU4LXZWZmuq+7desW9nt0fej2okZquW0fK/RiUmv8fcJPuz/mvNb5etFlvS87oPsC/IzXur9xfPyPYwQUHu8foPDKlvD3j69Ct6j0+6WXXrLXX3/dFi1aZNdcc43t3Lkz2M384osvdiXinn//+982YcIEe/zxx9287/vvv99mz55t119/vcU6rUXX9/JDLK5iIMdZnv5XtS/QWnXaVt+j0fMDvS/Az3it+xvHx/84RkDh8f4BCq9lCX7/+Kq8XAYMGGApKSk2ZMgQ1wzt8MMPd6Haa5a2evVqK1v273MF3bt3t7ffftvuueceu+uuu6x169auc3n79u2tJGh+eG2r98dO69Smu+3ZmWFVqlew+q0TCnWWRy9Utdlfv3SL7dy254DuC/Az77W+5rdNruGG5v/4rRypNOP4+B/HCCg83j9A4bUsoe8f34Vu0Sh1biPVU6dOzXHdueee6y4lVZky5hoGFMV8E71gG7atWST7BfiZXut636jDpT7G+n/WJQ3Hx/84RkDh8f4BCq9sCXz/+K68HAAAAACAkoLQDQAAAABAhBC6AQAAAACIEEI3AAAAAAARQugGAAAAACBCCN0AAAAAAEQIoRsAAAAAgAghdAMAAAAAECGEbgAAAAAAIoTQDQAAAABAhBC6AQAAAACIEEI3AAAAAAARQugGAAAAACBCCN0AAAAAAEQIoRsAAAAAgAgpZ6VcIBBwH7dt22Z+lJ6ebqmpqW7/ypcvH+3dQTYcH3/j+Pgbx8f/OEb+xvHxN46Pv3F8/C09Ro6PlyG9TJmbUh+6t2/f7j42btw42rsCAAAAAIjBTFmjRo1cby8T2F8sL+EyMzNt3bp1Vq1aNStTpoz58eyJTgisWbPGqlevHu3dQTYcH3/j+Pgbx8f/OEb+xvHxN46Pv3F8/G1bjBwfRWkF7gYNGljZsrnP3C71I916cho1amR+pxebn19wpR3Hx984Pv7G8fE/jpG/cXz8jePjbxwff6seA8cnrxFuD43UAAAAAACIEEI3AAAAAAARQuj2uQoVKth9993nPsJ/OD7+xvHxN46P/3GM/I3j428cH3/j+PhbhRJ2fEp9IzUAAAAAACKFkW4AAAAAACKE0A0AAAAAQIQQugEAAAAAiBBCdzF79tlnrVmzZlaxYkU78sgjbdasWXlu/8EHH9jBBx/stj/ssMNs/PjxWW7XlPwhQ4ZY/fr1rVKlStanTx9bunRphH+Kkq2oj9Ell1xiZcqUyXLp379/hH+Kkqsgx+fXX3+1s88+222v53306NEHfJ8o3uNz//3353j/6P2GyB+fl156yY499lirWbOmu+j3S/bt+R3k7+PD75/oHqOPP/7YunbtagkJCValShU7/PDD7b///W+WbXgP+fv48B4qWs8W8u+td9991z33Z5xxRuy+f9RIDcXj3XffDcTHxwdeffXVwK+//hq44oorAgkJCYGNGzeG3f6HH34IxMXFBR599NHAwoULA/fcc0+gfPnygV9++SW4zfDhwwM1atQIfPrpp4F58+YFTjvttEDz5s0Du3btKsafrOSIxDEaOHBgoH///oH169cHL3/99Vcx/lSl9/jMmjUrcOuttwbeeeedQL169QJPPPHEAd8nivf43HfffYFDDz00y/snJSWlGH6akqegx+eCCy4IPPvss4Gff/45sGjRosAll1zift+sXbs2uA2/g/x9fPj9E91j9PXXXwc+/vhj9/fBsmXLAqNHj3Z/M0yYMCG4De8hfx8f3kNF591C/r21YsWKQMOGDQPHHnts4PTTT89yWyy9fwjdxSgpKSlw3XXXBb/OyMgINGjQIDBs2LCw25933nmBk08+Oct1Rx55ZOCqq65yn2dmZro/VB977LHg7Vu2bAlUqFDB/RGL6B8j7z/s7P9JoHiOT6imTZuGDXUHcp+I/PFR6O7YsWOR72tpdKCv9b179waqVasWeP31193X/A7y9/ERfv8UraL4fdGpUyd3gl54D/n7+Ajvoegen7179wa6d+8eePnll3Mci1h7/1BeXkzS0tLsp59+cmUPnrJly7qvp0+fHvZ7dH3o9tKvX7/g9itWrLANGzZk2aZGjRquXCO3+0TxHiPP1KlTLTEx0dq2bWvXXHON/fnnnxH6KUquwhyfaNxnaRXJ51KlYg0aNLAWLVrYhRdeaKtXry6CPS5diuL4pKamWnp6utWqVct9ze8gfx8fD79//HGMNNA1ZcoUW7x4sfXo0cNdx3vI38fHw3soesfnwQcfdM/95ZdfnuO2WHv/lIv2DpQWmzZtsoyMDKtbt26W6/X1b7/9FvZ79EIKt72u9273rsttG0T3GInm/px11lnWvHlzW758ud1111124oknuv8Q4uLiIvTTlDyFOT7RuM/SKlLPpX55jhkzxv2xs379envggQfcPNYFCxZYtWrVimDPS4eiOD533HGHO/nh/YHD7yB/Hx/h90/0j9HWrVutYcOGtmfPHvecP/fcc9a3b193G+8hfx8f4T0UvePz/fff2yuvvGJz584Ne3usvX8I3UCE/eMf/wh+rkZrHTp0sJYtW7ozp717947qvgF+pz9uPHrvKIQ3bdrU3n///bBnvhEZw4cPd41s9P+WGuAgNo4Pv3+iTycHFRp27NjhRlIHDRrkqnZ69uwZ7V1DPo4P76Ho2L59u1100UWuYWTt2rWtJKC8vJjoBaMzYhs3bsxyvb6uV69e2O/R9Xlt730syH2ieI9ROPrPXI+1bNmyItrz0qEwxyca91laFddzqS6zbdq04f1TjMdn5MiRLtRNnDjR/cHp4XeQv49POPz+Kf5jpBLaVq1auc7Yt9xyi51zzjk2bNgwdxvvIX8fn3B4DxXP8Vm+fLmtXLnSTj31VCtXrpy7vPHGGzZu3Dj3uW6PtfcPobuYxMfHW5cuXdxZNE9mZqb7ulu3bmG/R9eHbi+TJk0Kbq9SF72oQrfZtm2bzZw5M9f7RPEeo3DWrl3r5gNpeQNE9vhE4z5Lq+J6LjUaoV+2vH+K5/g8+uij9tBDD9mECRPc0jqh+B3k7+MTDr9/ov9/nL5HpczCe8jfxycc3kPFc3wOPvhg++WXX1wVgnc57bTTrFevXu7zxo0bx977J9qd3Epbq3x11BszZoxbnuDKK690rfI3bNjgbr/ooosCgwcPzrIcVbly5QIjR450y4Goi2+4JcN0H2PHjg3Mnz/fdfXza6v80niMtm/f7pZEmj59ulvyYPLkyYHOnTsHWrduHdi9e3fUfs7Scnz27NnjltPRpX79+u5Y6POlS5fm+z4R3eNzyy23BKZOnereP3q/9enTJ1C7du1AcnJyVH7G0nR89PtFy7t8+OGHWZbL0f9rodvwO8ifx4ffP9E/RkOHDg1MnDgxsHz5cre9/lbQ3wwvvfRScBveQ/49PryHont8sgvXST6W3j+E7mL29NNPB5o0aeJ+Uap1/owZM4K3HXfcce4FFer9998PtGnTxm2vtWo///zzLLerXf69994bqFu3rnsh9+7dO7B48eJi+3lKoqI8RqmpqYETTjghUKdOHRfGtSyS1iUk0BXP8dEvSZ1bzH7Rdvm9T0T3+AwYMMAFct2f1unU11pPFZE/Pvr/Ktzx0clFD7+D/Ht8+P0T/WN09913B1q1ahWoWLFioGbNmoFu3bq54BGK95B/jw/voej/jb2/0B1L758y+ifao+0AAAAAAJREzOkGAAAAACBCCN0AAAAAAEQIoRsAAAAAgAghdAMAAAAAECGEbgAAAAAAIoTQDQAAAABAhBC6AQAAAACIEEI3AAAAAAARQugGACCbMWPGWJkyZWz27NnF9pgrV650j6nHjoSpU6e6+9dHAABQfAjdAIBSF6a9S8WKFa1NmzZ2/fXX28aNG6O9e758jrJfZsyYYX50ySWXZNnPChUquGM7ZMgQ2717d6Huc+HChXb//fe7EyIAABRWuUJ/JwAAMerBBx+05s2buzD2/fff2/PPP2/jx4+3BQsWWOXKlaOyT02bNrVdu3ZZ+fLlzU/PUXatWrUyv1LQfvnll93nW7dutbFjx9pDDz1ky5cvt7feeqtQofuBBx6wnj17WrNmzSKwxwCA0oDQDQAodU488UTr2rWr+/xf//qXHXTQQTZq1CgX0s4///yo7JM38u7H5yi/9u7da5mZmRYfH5/jtp07d1qVKlUKvT+BQMCdJKlUqVKu25QrV87++c9/Br++9tprrXv37vbOO++441u3bt1CPz4AAIVFeTkAoNQ7/vjj3ccVK1ZkuX7Pnj02aNAgq1OnjguMZ555pqWkpARvHzhwoNWuXdvS09Nz3OcJJ5xgbdu2DX49adIkO+aYYywhIcGqVq3qbrvrrrv2O6f7t99+s/POO8/tgwKnvu/uu+8O3r5q1SoXLnW9btcJhHPPPTfiJdHe/o4cOdJGjx5tLVu2dCPNXkm2btPnF1xwgdWsWdP97F4w1+izt71GkPU86LkOpetPOeUU+/LLL13418/24osvFmgftQ96XAX233//vUDPmY6DrpNevXoFy9ZD58R/8cUXduyxx7rXRrVq1ezkk0+2X3/9tdDPKQCgZGKkGwBQ6qn8WBS+Qt1www0uMN53330ukClcav73e++9526/6KKL7I033nDBUAHRs2HDBvvqq6/c94mCmG7v0KGDK9tW2Fy2bJn98MMPee7X/PnzXahTyfmVV17pgqj29X//+5898sgjbpsff/zRpk2bZv/4xz+sUaNGbj9VLq+SaIXewpbLqzx706ZNWa5T6Mz+HL322mtuBFr7p5+rVq1awdsUWlu3bm1Dhw51wderLHj99dftnHPOsVtuucVmzpxpw4YNs0WLFtknn3yS5b4XL17sKg+uuuoqu+KKK7KcxMgvL0jrOHry85z16NHDbrzxRnvqqafcSYFDDjnEfa/38b///a876dKvXz8bMWKEpaamuvtQyP/5558pRwcA/C0AAEAp8dprryn5BSZPnhxISUkJrFmzJvDuu+8GDjrooEClSpUCa9euzbJdnz59ApmZmcHvv/nmmwNxcXGBLVu2uK8zMjICjRo1CgwYMCDL44waNSpQpkyZwO+//+6+fuKJJ9z96TFzs2LFCreNHtvTo0ePQLVq1QKrVq3Ksm3oPqWmpua4r+nTp7v7euONN4LXff311+46fczPcxTuUqFChRz7W7169UBycnKW+7jvvvvcbeeff36W6+fOneuu/9e//pXl+ltvvdVd/9VXXwWva9q0qbtuwoQJgfwYOHBgoEqVKu451mXZsmWBkSNHuuPQvn37Qj1nH3zwQdjnbPv27YGEhITAFVdckeX6DRs2BGrUqJHjegBA6UZ5OQCg1OnTp48r127cuLEb7VS5t0ZZGzZsmGU7jd5qdNejUeeMjAxXnixly5a1Cy+80MaNG2fbt28PbqemXZpL7DUiU0m5aM645jznh8rYv/32W7vsssusSZMmWW4L3afQOc4qc//zzz9dszM95pw5c6ywnn32WVcSH3pROXV2Z599tnsuw7n66quzfK1mdaKS/VAa8ZbPP/88y/V6/jSSnF+aN6590UXPwa233mpHH320e96L8jnTc7FlyxY3Cq9qAO8SFxdnRx55pH399df53mcAQMlHeTkAoNRRoNRyUmq8peZaKltWgM4ue9j1SpQ3b94cvO7iiy925cUK7fpcJdE//fSTvfDCC8FtBgwY4Lpqq7R68ODB1rt3bzvrrLNciXW4xxVvDnL79u3z/FnU8Vzl2Srz/uOPP4Jl3F6JeGElJSXlq5FauA7nud2mkxX6ebN3QK9Xr54LvN7JjPzcdzhqRKfSe1m7dq09+uijlpycnKP52oE+Z0uXLs3SCyC76tWrF2i/AQAlG6EbAFDq5DdQauQynNCQ1q5dO+vSpYu9+eabLnTro7p3q/mZR6FPo9YaAdVo7oQJE9y8cIW2iRMn5vo4+aF55wqPN910k3Xr1s1q1KjhRnU1gp/fUfUDkVc38dxuCx11Lux9h6PnUVUMHo2SH3zwwW5OuKoRiuo587bRvG6dMMhOJ3MAAPDwWwEAgAOksK2S6fXr19vbb7/tuliHNu4SjfBqhFsXLV+l5mLqQq4gHhoUPS1atHAftXZ4Xj788EPX0Ovxxx8PXqfGZip/9hutRa7AqpFiryGZbNy40e2vbi9K9evXt5tvvtmttT1jxgw76qijCvSc5XZyQJ3XJTExMeyxAwAgFHO6AQA4QJrbq4D273//25WFh64VLX/99VeO7zn88MPdx+xLZXk0L1kdtF999VVbvXp1riPtGt0N/VqefvppN/fcb0466ST3UV3gQ+kkhOhkRVHTqLa6kQ8fPrzAz5m3rnj2MK4RdJWQ68RJuOXiQpeVAwCAkW4AAA6QAnL//v3tgw8+cHOTs4dHLROm8nJdr9FczTN+7rnn3HJV3vrV4Wi5Kt3euXNn19RNc5y1vJVK1OfOneu20VJkKnNWibRK3adPn26TJ0/OsbRXQalpmtYIz04N4rxR+ILq2LGjG2H+z3/+44LscccdZ7NmzXJLiJ1xxhluPeyipufh0ksvdc+3liXTCHt+nzOdGFFA15x9zfXWkmiaEqARbi0PpiXjdGxUlq7XgE6O6NioedszzzxT5D8LACA2EboBACiiEvPPPvvMzeVWOAt12mmnubCsUWt1ua5du7YLnCp7VvDLK6SqLPree+91IU8l0ArtofPFn3zySRcM1TFdtyvwKUAWpOt3OEOGDAl7veZCFzZ0ixrK6fvHjBnjms9pTvSdd94ZXNM8ElT6r8Z2Cs963Pw+Z9o3fZ+arl1++eVuJFzTARS6L7jgAmvQoIEbQX/sscdcxYK636vDvUI+AACeMlo3LPgVAAAoFC1LpdFajWgreAEAAAihGwCAIqCSZZUvL1u2LN/duQEAQMlHeTkAAAfg3Xfftfnz57u5vCpbJnADAIBQjHQDAHAAFLKrVq1qAwYMcPN/WaMZAACE4i8DAAAOAOeuAQBAXlinGwAAAACACCF0AwAAAAAQIYRuAAAAAAAihNANAAAAAECEELoBAAAAAIgQQjcAAAAAABFC6AYAAAAAIEII3QAAAAAARAihGwAAAAAAi4z/A2GUxYKIyfCIAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "print(logical_errors)\n", + "plt.figure(figsize=(10, 6))\n", + "for t, errors in logical_errors.items():\n", + " plt.plot(physical_error_values, errors, marker='o', label=f'Time Steps t={t}')\n", + "\n", + "# Labels and title\n", + "plt.xlabel('Physical Error Rate', fontsize=12)\n", + "plt.ylabel('Logical Error Rate', fontsize=12)\n", + "plt.title('Rotated Surface Code(d=3): Logical v/s Physical Error Rates with varying Timesteps', fontsize=14)\n", + "plt.legend(title='TimeSteps')\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "\n", + "# Save and show\n", + "plt.savefig('logical_vs_physical_timesteps.png', dpi=300)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "441f968d", + "metadata": {}, + "source": [ + "- The logical errors tend to decrease with increase in timesteps.\n", + "- The correction is better for values with t=(d>3), except for t=9 where it seems to have higher error rate." + ] + }, + { + "cell_type": "markdown", + "id": "97ef9cd5", + "metadata": {}, + "source": [ + "### Visualization of matching graphs for error correction" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "5b6788d9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = 0.1\n", + "qubit = LogicalQubit(d=3, T=1)\n", + "qubit.encode(p//2, p//2)\n", + "qubit.decode(p//2, p//2)\n", + "qubit.decoder.graph_2D(qubit.decoder.S[X], \"distance\")\n", + "qubit.decoder.graph_2D(qubit.decoder.S[Z], \"distance\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "c4431403", + "metadata": {}, + "source": [ + "- The graphs shows the surfaces of stabilizer surfaces in 2D plane and their connection marking an event of detection. - The coordinates of the stabilizers are all factors of 0.5 as the data qubits lie between them.\n", + "- We use this matching graphs mapping the error detection zones to affected qubits to identify and correct errors\n", + "- The coordinates with -1 are virtual qubits which do not exits and are added to connect the boundaries for matching a concept of torus code\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "74d4ae6a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = 0.1\n", + "qubit = LogicalQubit(d=3, T=5)\n", + "qubit.encode(p//2, p//2)\n", + "qubit.decode(p//2, p//2)\n", + "\n", + "qubit.decoder.graph_3D(qubit.decoder.S[X], \"distance\")\n", + "# plt.show()\n", + "# qubit.decoder.graph_3D(qubit.decoder.S[Z], \"distance\")" + ] + }, + { + "cell_type": "markdown", + "id": "fe401d48", + "metadata": {}, + "source": [ + "### Conclusion:\n", + "- Successfully implemented a logical qubit using the surface code in Q#.\n", + "\n", + "- Applied Minimum-Weight Perfect Matching (MWPM) to correct quantum errors effectively.\n", + "\n", + "- Visualized error syndromes, aiding in understanding and debugging the error correction process.\n", + "\n", + "- Conducted a comparative analysis of logical qubit measurement outcomes to assess correction performance.\n", + "\n", + "- Simulated error correction across varying error rates, demonstrating the robustness and limitations of the surface code under different noise conditions.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "5f5e60fb", + "metadata": {}, + "source": [ + "### References: \n", + "https://www.nature.com/articles/s41586-022-05434-1 - d=3 Implementation
\n", + "https://www.nature.com/articles/s41586-022-04566-8 - More on implementation
\n", + "https://arxiv.org/html/2307.14989v4/#S5.F7 - Diagrams
\n", + "https://arxiv.org/pdf/2409.14765 Core Rotated circuit comparision
" + ] + }, + { + "cell_type": "markdown", + "id": "12270a6c", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From e16096c14fba19a8062bdef024f942a06bf1913d Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 19:28:22 -0400 Subject: [PATCH 10/19] Add instructions --- README.md | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 351aa93..266eb42 100644 --- a/README.md +++ b/README.md @@ -13,12 +13,29 @@ We build a logical qubit, identify errors using error syndromes at each timestep ## Workflow ![Workflow](/qec-highlevel.png) -# Components +## Components - Surface Code Architecture in Q# - Pauli Tracking Layer for syndrome measurements history - Error detection at each timestep using Minimum-weight perfect matching decoder with error graphs - Error correction on logical qubits +## Setup +- Clone repository +- Setup virtual environment in python +```bash +python3 -m virtualenv venv +``` +- Activate venv +```bash +source venv/bin/activate +``` +- Install Requirements +```bash +python3 -m pip install -r requirements.txt +``` +- Run Notebook and choose *venv* + + From 825f7c7ec0fa46c5900d1813941a2d814186a38f Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 19:29:04 -0400 Subject: [PATCH 11/19] Add supporting images --- logical_vs_physical_error_rates_d3.png | Bin 0 -> 217448 bytes logical_vs_physical_timesteps.png | Bin 0 -> 272698 bytes output.png | Bin 0 -> 28495 bytes qec-highlevel.png | Bin 0 -> 192448 bytes 4 files changed, 0 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BCvgA( literal 0 HcmV?d00001 From bea86c47921ff3e164a1b3876990e98f62c4bccb Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 19:29:16 -0400 Subject: [PATCH 12/19] Update requirements --- requirements.txt | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/requirements.txt b/requirements.txt index e4ce35d..ab6fcc6 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,3 +1,7 @@ -qsharp +qsharp==1.15.0 pytest matplotlib +qiskit==2.0.0 +matplotlib==3.10.1 +azure-quantum==3.1.0 +networkx \ No newline at end of file From 3b634e4b5da4eb32d7f74bc88fcfa41c6b134be7 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 19:29:30 -0400 Subject: [PATCH 13/19] Supporting image --- rotated_surface_code_measures.png | Bin 0 -> 29195 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 rotated_surface_code_measures.png diff --git a/rotated_surface_code_measures.png 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zy!2Y6R0y^N4#mw~_v770PnHN{OWmMXM4G13qULQ_ThH93OP^9;qNBTGvcGHGQ)YH> zy8^ZQhV+NH#R^50y8QK?^wm6MWA#xjGa(5M=RDQnZD5Wr!6xXVaQe9-wXFhF4ed*h^J-c zLLPV*?S6Yblm_22bER2^4a&97JIWUuXl zFYVgKldW7+VU&EwP%DqbZ6RF*7RnVsLg*WWtm9r9@=e7~>V_cbY_KP@=i1s!1tTk*G>>lzzBoIefLj_h?xUz%2lmBt@))PVm? zf-87d*Pk_HR34Ys*&)QdOeQ3JE&pNPuI=I-B0r&$UUYhNKY8@i;=|J0L9b{u)D*&X z^CS z&-ISciXb>*3QInBt{>+G)^H4+MLbz_$t3!12A>Un(9=ngx?ty!-mf$$QLxm!U8VuO zeYo_!4a>|NkC9~Tg$?!v-|Pr%cS{nU(yD!4&uMgLCiN`Rnn0RrGY^)0m2&awzNDiz_#@gj@__eee3vNAv`=KhpqSGfMwEK`(DH<%?fMg$ z+U~S1Y=Ta%(oYv9E5*Y-*>_iC{;hX)Kt6@79#_`*X@d8homG^&^nMLjk2q9*H_Urk SQwvWJFGX23nVOg8VgC Date: Sat, 19 Apr 2025 20:48:21 -0400 Subject: [PATCH 15/19] Add testcases --- src/Test.qs | 349 +++++++++++++++++++++++++++++++++++++++++++ test_surface_code.py | 89 +++++++++++ 2 files changed, 438 insertions(+) create mode 100644 src/Test.qs create mode 100644 test_surface_code.py diff --git a/src/Test.qs b/src/Test.qs new file mode 100644 index 0000000..56175c0 --- /dev/null +++ b/src/Test.qs @@ -0,0 +1,349 @@ +import RotatedSurfaceCode.XStabilizer; +import Std.Diagnostics.DumpMachine; +import Std.Diagnostics.CheckAllZero; +import Std.Arrays.All; +import Std.Arrays.ForEach; +import RotatedSurfaceCode.ZStabilizer; +import RotatedSurfaceCode.MeasureLogicalZTopDown; +import RotatedSurfaceCode.MeasureLogicalZ; +import Std.Random.DrawRandomDouble; + +import RotatedSurfaceCode.CorrectDataQubit; + +operation PrepareTestState(d : Int, onesAtIndices: Int[], dataQubits: Qubit[]) : Unit { + for idx in onesAtIndices { + X(dataQubits[idx]); + } + } + +operation PrepareState(indicesToFlip: Int[], qubits: Qubit[]) : Unit { + for idx in indicesToFlip { + X(qubits[idx]); + } + } + +operation TestMeasureLogicalZ_AllZero() : Bool { + use qs = Qubit[9]; + let d = 3; + let expected = Zero; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; +} + +operation TestMeasureLogicalZ_AllOne() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareTestState(d, [0, 3, 6], qs); // Logical Z line + let expected = One; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; +} + + operation TestMeasureLogicalZ_OneOneOne() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareTestState(d, [0, 3, 6], qs); + let expected = One; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + operation TestMeasureLogicalZ_TwoOnes() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareTestState(d, [0, 3], qs); + let expected = Zero; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + operation TestMeasureLogicalZ_OneOneZero() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareTestState(d, [3, 6], qs); + let expected = Zero; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation TestMeasureLogicalZ_OnlyMiddleOne() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareTestState(d, [3], qs); + let expected = One; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation TestMeasureLogicalZ_EmptyGrid() : Bool { + use qs = Qubit[1]; + let d = 1; + let expected = Zero; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation TestMeasureLogicalZ_Superposition() : Bool { + use qs = Qubit[9]; + let d = 3; + for i in [0, 3, 6] { + H(qs[i]); // Put logical line into superposition + } + let result = MeasureLogicalZ(d, qs); + // Result could be Zero or One; just check it's valid Result + ResetAll(qs); + return result == One or result == Zero; + } + + + operation TestMeasureLogicalZ_IrrelevantQubitsFlipped() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareTestState(d, [1, 2, 4, 5, 7, 8], qs); // Flip non-logical-Z qubits + let expected = Zero; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + operation TestMeasureLogicalZ_LargeGrid() : Bool { + let d = 5; + use qs = Qubit[d * d]; + // Flip every second qubit in logical Z line (indices 0, 5, 10, 15, 20) + PrepareTestState(d, [0, 10, 20], qs); + let expected = One; + let result = MeasureLogicalZ(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_AllZero() : Bool { + use qs = Qubit[9]; + let d = 3; + let expected = Zero; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_AllOne() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareState([0, 3, 6], qs); + let expected = One; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_OneQubitFlipped() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareState([3], qs); + let expected = One; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_TwoFlipped() : Bool { + use qs = Qubit[9]; + let d = 3; + PrepareState([0, 6], qs); + let expected = Zero; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_IgnoreNonColumnQubits() : Bool { + use qs = Qubit[9]; + let d = 3; + // Flip qubits not in first column + PrepareState([1, 2, 4, 5, 7, 8], qs); + let expected = Zero; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_ThreeFlipped_OddParity() : Bool { + use qs = Qubit[16]; + let d = 4; + PrepareState([0, 4, 8], qs); // Flip 3 qubits in logical Z + let expected = One; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_LargeGrid_ZeroParity() : Bool { + let d = 5; + use qs = Qubit[d * d]; + PrepareState([0, 10, 20], qs); // Indices = 0, 2, 4 in logical Z + let expected = One; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_SingleQubitGrid() : Bool { + use qs = Qubit[1]; + let d = 1; + PrepareState([0], qs); + let expected = One; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_AllFiveFlipped() : Bool { + use qs = Qubit[25]; + let d = 5; + PrepareState([0, 5, 10, 15, 20], qs); // Full logical Z column + let expected = One; // 5 is odd + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + + operation Test_MeasureLogicalZTopDown_AllFourFlipped() : Bool { + use qs = Qubit[16]; + let d = 4; + PrepareState([0, 4, 8, 12], qs); + let expected = Zero; + let result = MeasureLogicalZTopDown(d, qs); + ResetAll(qs); + return expected == result; + } + + operation Test_ZStabilizerApplyLater() : Bool { + use qs = Qubit[16]; + let indexes = [0,5,7]; + ResetAll(qs); + ZStabilizer(indexes, qs[0..Length(qs)-2], qs[Length(qs)-1]); + X(qs[Length(qs)-1]); + DumpMachine(); + let result = CheckAllZero(qs[0..Length(qs)-2]); + ResetAll(qs[0..Length(qs)-2]); + return (MResetEachZ([qs[Length(qs)-1]]) == [One] )and result; + } + + operation Test_ZStabilizer_ShouldNotActivate() : Bool { + use qs = Qubit[16]; + ResetAll(qs); + let indexes = [3,5,7]; + ZStabilizer(indexes, qs[0..Length(qs)-2], qs[Length(qs)-1]); + X(qs[Length(qs)-1]); + let result = CheckAllZero(qs[0..Length(qs)-2]); + ResetAll(qs); + return result; + } + operation Test_ZStabilizerShouldResetAncillaBeforeUse() : Bool { + use qs = Qubit[16]; + let indexes = []; + + X(qs[Length(qs)-1]); + ZStabilizer(indexes, qs[0..Length(qs)-2], qs[Length(qs)-1]); + let expected = Zero; + let res = M(qs[Length(qs)-1]); + ResetAll(qs); + return expected == res; + } + + + operation PrepareInXBasis(indicesToFlip : Int[], dataQubits : Qubit[]) : Unit { + // Prepare all qubits in |+⟩ + for q in dataQubits { + H(q); + } + // Flip selected qubits to |−⟩ + for i in indicesToFlip { + Z(dataQubits[i]); + } + } + + + operation Test_XStabilizer_EvenParity() : Bool { + use data = Qubit[4]; + use ancilla = Qubit(); + let indexes = [0, 1, 2, 3]; + + // Prepare even number of |−⟩: flip qubits 1 and 3 + PrepareInXBasis([1, 3], data); + + XStabilizer(indexes, data, ancilla); + let result = M(ancilla); + + ResetAll(data + [ancilla]); + return Zero == result; + } + + + operation Test_XStabilizer_OddParity() : Bool { + use data = Qubit[4]; + use ancilla = Qubit(); + let indexes = [0, 1, 2, 3]; + + // Prepare odd number of |−⟩: flip qubits 1, 2, and 3 + PrepareInXBasis([1, 2, 3], data); + + XStabilizer(indexes, data, ancilla); + let result = M(ancilla); + + ResetAll(data + [ancilla]); + return One == result; + } + + + operation Test_XStabilizer_SingleQubit() : Bool { + use data = Qubit[1]; + use ancilla = Qubit(); + let indexes = [0]; + + // Flip to |−⟩ + PrepareInXBasis([0], data); + + XStabilizer(indexes, data, ancilla); + let result = M(ancilla); + + + ResetAll(data + [ancilla]); + return One == result; + } + + + operation Test_XStabilizer_ZeroParity() : Bool { + use data = Qubit[3]; + use ancilla = Qubit(); + let indexes = [0, 1, 2]; + + // All in |+⟩ + PrepareInXBasis([], data); + + XStabilizer(indexes, data, ancilla); + let result = M(ancilla); + + ResetAll(data + [ancilla]); + return Zero == result + } diff --git a/test_surface_code.py b/test_surface_code.py new file mode 100644 index 0000000..ec8a533 --- /dev/null +++ b/test_surface_code.py @@ -0,0 +1,89 @@ +import qsharp +import pytest + +def test_2() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_AllZero()") + assert correct + +def test_3() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_AllOne()") + assert correct + +def test_4() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_OneOneOne()") + assert correct + +def test_5() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_TwoOnes()") + assert correct + +def test_6() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_OneOneZero()") + assert correct +def test_7() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_OnlyMiddleOne()") + assert correct +def test_8() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_EmptyGrid()") + assert correct +def test_9() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.TestMeasureLogicalZ_Superposition()") + assert correct +def test_10() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_MeasureLogicalZTopDown_AllFourFlipped()") + assert correct +def test_11() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_MeasureLogicalZTopDown_AllFiveFlipped()") + assert correct +def test_12() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_MeasureLogicalZTopDown_SingleQubitGrid()") + assert correct +def test_12() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_MeasureLogicalZTopDown_LargeGrid_ZeroParity()") + assert correct +def test_13() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_MeasureLogicalZTopDown_ThreeFlipped_OddParity()") + assert correct +def test_14() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_MeasureLogicalZTopDown_IgnoreNonColumnQubits()") + assert correct +def test_15() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_ZStabilizerApplyLater()") + assert correct +def test_16() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_ZStabilizer_ShouldNotActivate()") + assert correct +def test_17() -> None: + qsharp.init(project_root=".") + correct = qsharp.eval("Test.Test_ZStabilizerShouldResetAncillaBeforeUse()") + assert correct + +@pytest.mark.parametrize("functionName", [ + "Test_XStabilizer_EvenParity", + "Test_XStabilizer_OddParity", + "Test_XStabilizer_SingleQubit", + "Test_XStabilizer_ZeroParity" +]) +def test_runner(functionName): + print(functionName) + qsharp.init(project_root=".") + correct = qsharp.eval(f"Test.{functionName}()") + assert correct + + From dd098e0edb250e53c235d3374b5e7240ff7ebccc Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 20:51:04 -0400 Subject: [PATCH 16/19] Remove unused files --- surface-code.ipynb | 726 --------------------------------------------- 1 file changed, 726 deletions(-) delete mode 100644 surface-code.ipynb diff --git a/surface-code.ipynb b/surface-code.ipynb deleted file mode 100644 index 52103eb..0000000 --- a/surface-code.ipynb +++ /dev/null @@ -1,726 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "b2fb789e", - "metadata": {}, - "source": [ - "# Surface Code\n", - "\n", - "Ref: https://www.nature.com/articles/s41586-022-05434-1 - d=3 Implementation\n", - "https://www.nature.com/articles/s41586-022-04566-8 - More on implementation\n", - "https://arxiv.org/html/2307.14989v4/#S5.F7 - Diagrams\n", - "\n", - "\n", - "Core on roateted: https://arxiv.org/pdf/2409.14765\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4a8af2ee", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Logical Error without correction: 0.48\n", - "Logical Error with correction: 0.54\n" - ] - } - ], - "source": [ - "from collections import deque\n", - "import qsharp\n", - "from itertools import combinations\n", - "import pymatching\n", - "\n", - "import numpy as np\n", - "import random\n", - "import networkx as nx\n", - "\n", - "\n", - "def convert_syndrome(syndrome_results):\n", - " return np.array([1 if bit == qsharp.Result.One else 0 for bit in syndrome_results], dtype=np.uint8)\n", - "\n", - "\n", - "def getZCorrections(d, initMeasures, xMaps):\n", - " num_qubits = d*d\n", - " H_x = np.zeros((len(initMeasures), num_qubits), dtype=np.uint8)\n", - " for i, stabilizer in enumerate(xMaps):\n", - " for qubit_idx in stabilizer:\n", - " H_x[i, qubit_idx] = 1\n", - "\n", - "\n", - " z_decoder = pymatching.Matching(H_x) \n", - " z_correction = z_decoder.decode(initMeasures)\n", - " # print(z_correction)\n", - " z_error_qubits = np.where(z_correction == 1)[0] # Qubits needing phase flips\n", - " print(\"Apply phase flips (Z) to qubits:\", z_error_qubits)\n", - " return z_error_qubits\n", - "\n", - "\n", - "def flatten_syndrome_timeline(syndrome_matrix):\n", - " if syndrome_matrix.shape[0] == 1:\n", - " return syndrome_matrix[0]\n", - " return syndrome_matrix.flatten()\n", - "\n", - "def getSyndrome(a,b,c,d):\n", - " return [i!=j for i,j in zip(a,b)], [i!=j for i,j in zip(c,d)]\n", - "\n", - "\n", - "class PauliTracker:\n", - " '''Tracks the Pauli X&Z stabilizers measurements, Record \n", - " the stabilizer measurement outcomes in each round without\n", - " physically correcting the qubits'''\n", - "\n", - " def __init__(self):\n", - " self.XKEY = \"X\"\n", - " self.ZKEY = \"Z\"\n", - " self.tracker = {self.XKEY: [], self.ZKEY: []}\n", - "\n", - " def track(self, xMeasures, zMeasures):\n", - " self.tracker[self.XKEY].append(xMeasures)\n", - " self.tracker[self.ZKEY].append(zMeasures)\n", - " \n", - " def getX(self):\n", - " return self.tracker[self.XKEY]\n", - " def getZ(self):\n", - " return self.tracker[self.ZKEY]\n", - "\n", - "\n", - "def addTimeStep():\n", - " xMaps, initXMeasures, zMaps, initZMeasures = qsharp.eval(f\"RotatedSurfaceCode.GenerateLattice(d, qubits);\")\n", - " PAULI_TRACKER.track(initXMeasures, initZMeasures)\n", - " return xMaps, initXMeasures, zMaps, initZMeasures\n", - "\n", - "def convert_syndrome(syndrome_results):\n", - " return np.array([1 if bit == qsharp.Result.One else 0 for bit in syndrome_results], dtype=np.uint8)\n", - "\n", - "def getCorrections(d, p, syndrome, maps):\n", - " num_qubits = d*d\n", - " H = np.zeros((len(maps), num_qubits), dtype=np.uint8)\n", - " \n", - " for i, stabilizer in enumerate(maps):\n", - " for qubit_idx in stabilizer:\n", - " H[i, qubit_idx] = 1\n", - "\n", - " weights = np.ones(H.shape[1]) * np.log((1 - p) / p)\n", - " decoder = pymatching.Matching(H, weights=weights) \n", - " correction = decoder.decode(syndrome)\n", - " error_qubits = np.where(correction == 1)[0] # Qubits needing flips\n", - " # print(error_qubits)\n", - " # print(\"Apply flips to qubits:\", error_qubits)\n", - " return error_qubits\n", - "\n", - "from collections import defaultdict\n", - "def decode_surface_code(parity_checks, stabilizer_qubit_map):\n", - " \"\"\"\n", - " Args:\n", - " parity_checks (List[int]): List of 0 or 1 values for each stabilizer (1 = error detected)\n", - " stabilizer_qubit_map (List[List[int]]): List of lists, each with qubit indices for the stabilizer\n", - "\n", - " Returns:\n", - " Set[int]: Indices of qubits to apply correction to\n", - " \"\"\"\n", - "\n", - " # Count how many times each qubit appears in stabilizers with parity 1\n", - " qubit_votes = defaultdict(int)\n", - "\n", - " for stab_index, parity in enumerate(parity_checks):\n", - " if parity == 1:\n", - " for q in stabilizer_qubit_map[stab_index]:\n", - " qubit_votes[q] += 1\n", - "\n", - " # Apply correction to qubits that are involved in an odd number of violated stabilizers\n", - " corrections = {q for q, count in qubit_votes.items() if count % 2 == 1}\n", - " return corrections\n", - "\n", - "def applyCorrection(correct, zp, xp, zMeasures, zMaps, xMeasures, xMaps):\n", - " if correct:\n", - " x_correction = getCorrections(d, xp, convert_syndrome(zMeasures), zMaps)\n", - " z_correction = getCorrections(d, zp, convert_syndrome(xMeasures), xMaps)\n", - " print(x_correction)\n", - " for q in x_correction:\n", - " qsharp.eval(f\"X(qubits[{q}]);\")\n", - " for q in z_correction:\n", - " qsharp.eval(f\"Z(qubits[{q}]);\")\n", - "\n", - "\n", - "def runLogicalQubit(d, layers, xnoise, znoise, correct=False):\n", - " TOTAL_DATA_QUBITS = d*d\n", - " PAULI_TRACKER = PauliTracker()\n", - " qsharp.init(project_root=\".\")\n", - " qsharp.eval(f\"import Std.Diagnostics.ConfigurePauliNoise;\")\n", - " qsharp.eval(f\"import Std.Arrays.ForEach;\")\n", - " qsharp.eval(f\"let d = {d};\")\n", - " qsharp.eval(f\"let TOTAL_DATA_QUBITS = {TOTAL_DATA_QUBITS};\")\n", - " qsharp.eval(\"use qubits = Qubit[TOTAL_DATA_QUBITS];\")\n", - " qsharp.eval(\"ApplyToEach(X, qubits);\")\n", - " qsharp.eval(f\"ConfigurePauliNoise({xnoise}, 0.0, {znoise});\")\n", - " qsharp.eval(\"ResetAll(qubits);\")\n", - "\n", - " xMaps, initXMeasures, zMaps, initZMeasures = addTimeStep()\n", - "\n", - "\n", - " # x_correction = getCorrections(d, initZMeasures, zMaps)\n", - " # z_correction = getCorrections(d, initXMeasures, xMaps)\n", - " # # for q in x_correction:\n", - " # # qsharp.eval(f\"X(qubits[{q}]);\")\n", - " # # for q in z_correction:\n", - " # # qsharp.eval(f\"Z(qubits[{q}]);\")\n", - " # applyCorrection(correct, znoise, xnoise, initZMeasures, zMaps, initXMeasures, xMaps)\n", - " corrupt = False\n", - " for i in range(layers):\n", - " x , xMeasures, z, zMeasures = addTimeStep()\n", - " # applyCorrection(correct, znoise, xnoise, zMeasures, zMaps, xMeasures, xMaps)\n", - " xSyndrome, zSyndrome = getSyndrome(initXMeasures, xMeasures, initZMeasures, zMeasures)\n", - " # if any(zSyndrome):\n", - " # corrupt = True\n", - " \n", - " # x , xMeasures, z, zMeasures = addTimeStep()\n", - " \n", - " # print(f\"Visualize If any errors for time({i})\")\n", - " # print(\"X\", xSyndrome)\n", - " # print(\"Z\", zSyndrome)\n", - " \n", - " initXMeasures = xMeasures\n", - " initZMeasures = zMeasures\n", - " # xSyndrome, zSyndrome = getSyndrome(initXMeasures, xMeasures, initZMeasures, zMeasures)\n", - " \n", - " # results = qsharp.eval(\"ForEach(x => Measure([PauliZ], [x]), qubits);\")\n", - " results = []\n", - " re = []\n", - " s = d-1\n", - " for i in range(0, d*d):\n", - " # if ((i//d)*(d+1)) == i:\n", - " # re.append(i)\n", - " # s-=1\n", - " results.append(qsharp.eval(f\"Measure([PauliZ], [qubits[{i}]]);\"))\n", - " # print(re)\n", - " # print(results)\n", - " # for i in range(0, TOTAL_DATA_QUBITS, d):\n", - " # print(results[i:i+d])\n", - " # print(sum(convert_syndrome(results))%2)\n", - " # print(f\"Final Logical State: {sum(convert_syndrome(results))%2}\")\n", - " return int(not sum(convert_syndrome(results))%2)\n", - " \n", - "\n", - "qsharp.eval(\"ResetAll(qubits);\")\n", - "\n", - "d = 3\n", - "layers = 4\n", - "xnoise = 0.01\n", - "znoise = 0.0\n", - "SHOTS = 100\n", - "def failure(r):\n", - " return 1 - (sum(r)/SHOTS)\n", - "\n", - "r = []\n", - "for i in range(SHOTS):\n", - " r.append(runLogicalQubit(d, layers, xnoise, znoise, correct=False))\n", - "print(f\"Logical Error without correction: {failure(r)}\")\n", - "\n", - "r = []\n", - "for i in range(SHOTS):\n", - " r.append(runLogicalQubit(d, layers, xnoise, znoise, correct=True))\n", - "print(f\"Logical Error with correction: {failure(r)}\")\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "d9d451f0", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Running for code distance d=1\n", - "Physical error rate p=0.005\n", - "Physical error rate p=0.010\n", - "Physical error rate p=0.050\n", - "Physical error rate p=0.100\n", - "Physical error rate p=0.150\n", - "Physical error rate p=0.200\n", - "Running for code distance d=3\n", - "Physical error rate p=0.005\n", - "Physical error rate p=0.010\n", - "Physical error rate p=0.050\n", - "Physical error rate p=0.100\n", - "Physical error rate p=0.150\n", - "Physical error rate p=0.200\n", - "Running for code distance d=5\n", - "Physical error rate p=0.005\n", - "Physical error rate p=0.010\n", - "Physical error rate p=0.050\n", - "Physical error rate p=0.100\n", - "Physical error rate p=0.150\n", - "Physical error rate p=0.200\n", - "{1: [0.008, 0.014, 0.096, 0.179, 0.267, 0.299], 3: [0.073, 0.149, 0.422, 0.468, 0.474, 0.511], 5: [0.133, 0.22, 0.48, 0.505, 0.513, 0.493]}\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pymatching\n", - "import matplotlib.pyplot as plt\n", - "import qsharp\n", - "import pymatching\n", - "\n", - "import numpy as np\n", - "import networkx as nx\n", - "\n", - "def convert_syndrome(syndrome_results):\n", - " return np.array([1 if bit == qsharp.Result.One else 0 for bit in syndrome_results], dtype=np.uint8)\n", - "\n", - "\n", - "class Decoder:\n", - " def __init__(self, d,p, maps):\n", - " self.d = d\n", - " self.num_qubits = d*d\n", - " \n", - " self.H = np.zeros((len(maps), self.num_qubits), dtype=np.uint8)\n", - " for i, stabilizer in enumerate(maps):\n", - " for qubit_idx in stabilizer:\n", - " self.H[i, qubit_idx] = 1\n", - " \n", - " weights = np.ones(self.H.shape[1]) * np.log((1 - p) / p)\n", - " self.decoder = pymatching.Matching(self.H, weights=weights) \n", - "\n", - " def decode(self, syndrome):\n", - " return self.decoder.decode(syndrome)\n", - " \n", - " def decode_batch(self, syndromes):\n", - " return self.decoder.decode_batch(syndromes)\n", - "\n", - " def getErrorQubits(self, correction):\n", - " return np.where(correction == 1)[0]\n", - "\n", - "def qsharp_runner(d,p, shots):\n", - " qsharp.init(project_root=\".\")\n", - " # qsharp.eval(f\"import Std.Diagnostics.ConfigurePauliNoise;\")\n", - " # qsharp.eval(f\"import Std.Arrays.ForEach;\")\n", - " # qsharp.eval(f\"let d = {d};\")\n", - " # qsharp.eval(f\"let TOTAL_DATA_QUBITS = {TOTAL_DATA_QUBITS};\")\n", - " # qsharp.eval(\"use qubits = Qubit[TOTAL_DATA_QUBITS];\")\n", - " # # qsharp.eval(\"ApplyToEach(X, qubits);\")\n", - " # qsharp.eval(f\"ConfigurePauliNoise({p}, 0.0, 0.0);\")\n", - " # qsharp.eval(\"ResetAll(qubits);\")\n", - " xMaps, zMaps = qsharp.eval(f\"RotatedSurfaceCode.GetMaps({d});\")\n", - " \n", - "\n", - " results = qsharp.run(f\"RotatedSurfaceCode.RotatedSurfaceCode({d}, {d})\", shots=shots, noise=qsharp.BitFlipNoise(p))\n", - " zSyndromes = []\n", - " trueValues = []\n", - " for result in results:\n", - " zSyndromes.append(convert_syndrome(result[len(xMaps):len(xMaps)+len(zMaps)]))\n", - " trueValues.append(convert_syndrome(result[len(xMaps)+len(zMaps):]))\n", - "\n", - " # results = qsharp.eval(\"ForEach(x => Measure([PauliZ], [x]), qubits);\")\n", - " # results = []\n", - " # for i in range(0, d*d):\n", - " # # if (i%(d+1))== 0:\n", - " # results.append(1 if qsharp.eval(f\"Measure([PauliZ], [qubits[{i}]]);\") == qsharp.Result.One else 0)\n", - " # trueLogicalValue = int((sum(convert_syndrome(results))%2))\n", - " return zSyndromes, zMaps, trueValues\n", - "\n", - "\n", - "def is_logical_error(d, correction, true_logical):\n", - " def getParity(d, correction):\n", - " r = []\n", - " correctionParity = 0\n", - " for i in range(d):\n", - " # r.append((i+1)*(d-1))\n", - " # if correction[(d*d)-(i+1)]:\n", - " if correction[(i+1)*(d-1)]:\n", - " correctionParity = 0 if correctionParity else 1\n", - " # print(r)\n", - " return correctionParity\n", - " \n", - " return (int(getParity(d, true_logical))) != (int(getParity(d, true_logical)))\n", - " \n", - " \n", - "\n", - "def run_experiment_for_d(d_values, p_values, num_trials):\n", - " results = {}\n", - " for d in d_values:\n", - " logical_error_rates = []\n", - " print(f\"Running for code distance d={d}\")\n", - "\n", - " for p in p_values:\n", - " logical_errors = 0\n", - " print(f\"Physical error rate p={p:.3f}\")\n", - " syndrome, maps, true_logical = qsharp_runner(d, p, num_trials)\n", - " \n", - " decoder = Decoder(d,p, maps)\n", - " correction = decoder.decode_batch(syndrome)\n", - "\n", - " # Check if correction flips the logical qubit\n", - " logical_errors = sum(is_logical_error(d, c, true_logical[i]) for i,c in enumerate(correction))\n", - " logical_error_rates.append(logical_errors / num_trials)\n", - "\n", - " results[d] = logical_error_rates\n", - "\n", - " return results\n", - "\n", - "print(run_experiment_for_d(d_values=[1, 3, 5], p_values=[0.005, 0.01, 0.05, 0.1, 0.15, 0.2], num_trials=1000))\n", - "# print(run_experiment_for_d(d_values=[1, 3, 5], p_values=[0.005, 0.01, 0.05, 0.1, 0.15, 0.2], num_trials=11000))\n", - "#{1: [0.010181818181818183, 0.01818181818181818, 0.098, 0.1809090909090909, 0.2540909090909091, 0.31836363636363635], 3: [0.07636363636363637, 0.14945454545454545, 0.43618181818181817, 0.48918181818181816, 0.5086363636363637, 0.4979090909090909], 5: [0.15163636363636362, 0.2737272727272727, 0.49772727272727274, 0.5010909090909091, 0.49536363636363634, 0.5014545454545455]}\n", - "\n", - "# print(run_experiment_for_d(d_values=[3], p_values=[0.005, 0.01, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7], num_trials=2000))\n", - "# print(run_experiment_for_d(d_values=[3], p_values=[0.005], num_trials=2))" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "id": "08a20a62", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "MPS (Metal) is available!\n", - "mps\n", - "tensor([[1, 1, 1, 1, 1],\n", - " [1, 1, 1, 1, 1],\n", - " [1, 1, 1, 1, 1],\n", - " [1, 1, 1, 1, 1],\n", - " [1, 1, 1, 1, 1]], dtype=torch.uint8)\n" - ] - } - ], - "source": [ - "# !pip install torch torchvision torchaudio\n", - "import torch\n", - "\n", - "if torch.backends.mps.is_available():\n", - " print(\"MPS (Metal) is available!\")\n", - " device = torch.device(\"mps\")\n", - "else:\n", - " print(\"MPS not available, using CPU.\")\n", - " device = torch.device(\"cpu\")\n", - "\n", - "\n", - "import torch\n", - "\n", - "device = torch.device(\"mps\" if torch.backends.mps.is_available() else \"cpu\")\n", - "print(device)\n", - "\n", - "lattice = torch.zeros((5, 5), dtype=torch.uint8, device=device)\n", - "syndrome = torch.ones((5, 5), dtype=torch.uint8, device=device)\n", - "\n", - "lattice ^= syndrome\n", - "print(lattice.cpu())" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "fdd58514", - "metadata": {}, - "outputs": [], - "source": [ - "!pip install pyobjc\n", - "import numpy as np\n", - "import objc\n", - "from Cocoa import NSObject\n", - "import Metal\n", - "import MetalKit\n", - "\n", - "# 1. Create Metal device\n", - "device = Metal.MTLCreateSystemDefaultDevice()\n", - "\n", - "# 2. Load shader\n", - "source = open(\"my_shader.metal\").read()\n", - "options = {}\n", - "compile_error = None\n", - "library = device.newLibraryWithSource_options_error_(source, options, objc.nil)\n", - "function = library.newFunctionWithName_(\"add_one\")\n", - "\n", - "# 3. Create compute pipeline\n", - "pipeline_state, err = device.newComputePipelineStateWithFunction_error_(function, None)\n", - "\n", - "# 4. Input/output buffers\n", - "array = np.array([1.0, 2.0, 3.0, 4.0], dtype=np.float32)\n", - "buffer_size = array.nbytes\n", - "\n", - "input_buffer = device.newBufferWithBytes_length_options_(array.tobytes(), buffer_size, 0)\n", - "output_buffer = device.newBufferWithLength_options_(buffer_size, 0)\n", - "\n", - "# 5. Create command queue and encoder\n", - "command_queue = device.newCommandQueue()\n", - "command_buffer = command_queue.commandBuffer()\n", - "command_encoder = command_buffer.computeCommandEncoder()\n", - "\n", - "command_encoder.setComputePipelineState_(pipeline_state)\n", - "command_encoder.setBuffer_offset_atIndex_(input_buffer, 0, 0)\n", - "command_encoder.setBuffer_offset_atIndex_(output_buffer, 0, 1)\n", - "\n", - "# 6. Dispatch threads\n", - "thread_count = len(array)\n", - "thread_group_size = pipeline_state.maxTotalThreadsPerThreadgroup()\n", - "thread_groups = ((thread_count + thread_group_size - 1) // thread_group_size)\n", - "command_encoder.dispatchThreadgroups_threadsPerThreadgroup_(\n", - " (thread_groups, 1, 1),\n", - " (thread_group_size, 1, 1)\n", - ")\n", - "\n", - "command_encoder.endEncoding()\n", - "command_buffer.commit()\n", - "command_buffer.waitUntilCompleted()\n", - "\n", - "# 7. Get results\n", - "result_ptr = output_buffer.contents()\n", - "result = np.frombuffer(objc.pythonify(result_ptr), dtype=np.float32, count=len(array))\n", - "print(\"Result:\", result)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5fa4d0a0", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import itertools\n", - "from typing import List, Dict, Tuple\n", - "\n", - "def generate_all_single_pauli_errors(num_qubits: int) -> List[np.ndarray]:\n", - " \"\"\"Generates all single X/Z/Y errors on a code block.\"\"\"\n", - " errors = []\n", - " for q in range(num_qubits):\n", - " e = np.zeros(num_qubits, dtype=int)\n", - " e[q] = 1\n", - " errors.append((q, e)) # single-qubit X (or Z)\n", - " return errors\n", - "\n", - "def compute_syndrome(error: np.ndarray, stab_map: List[List[int]]) -> np.ndarray:\n", - " \"\"\"Compute syndrome based on parity check (mod 2) for each stabilizer.\"\"\"\n", - " syndrome = np.zeros(len(stab_map), dtype=int)\n", - " for i, qubits in enumerate(stab_map):\n", - " parity = sum(error[q] for q in qubits if q < len(error))\n", - " syndrome[i] = parity % 2\n", - " return syndrome\n", - "\n", - "def build_lookup_table(num_qubits: int, stab_map: List[List[int]]) -> Dict[str, np.ndarray]:\n", - " \"\"\"Precompute the syndrome → correction table for all single-qubit errors.\"\"\"\n", - " table = {}\n", - "\n", - " for q, error in generate_all_single_pauli_errors(num_qubits):\n", - " syndrome = compute_syndrome(error, stab_map)\n", - " key = ''.join(map(str, syndrome))\n", - " # Store only if not already stored — minimal weight correction\n", - " if key not in table:\n", - " table[key] = error.copy()\n", - " \n", - " # Add trivial correction for zero syndrome\n", - " table['0' * len(stab_map)] = np.zeros(num_qubits, dtype=int)\n", - " return table\n", - "\n", - "def lookup_decode(syndrome: np.ndarray, lookup_table: Dict[str, np.ndarray]) -> np.ndarray:\n", - " key = ''.join(map(str, syndrome))\n", - " return lookup_table.get(key, np.zeros_like(next(iter(lookup_table.values()))))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "f5aef0f2", - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "class SurfaceCodeDecoder:\n", - " def __init__(self, d):\n", - " self.d = d # code distance\n", - "\n", - " def _get_syndrome_graph(self, syndrome):\n", - " # Create a graph of syndrome nodes\n", - " G = nx.Graph()\n", - " for i, node1 in enumerate(syndrome):\n", - " for j, node2 in enumerate(syndrome):\n", - " if i >= j:\n", - " continue\n", - " weight = self._manhattan_distance(node1, node2)\n", - " G.add_edge(node1, node2, weight=weight)\n", - " return G\n", - "\n", - " def _manhattan_distance(self, a, b):\n", - " return abs(a[0] - b[0]) + abs(a[1] - b[1])\n", - "\n", - " def decode(self, syndrome):\n", - " G = self._get_syndrome_graph(syndrome)\n", - " matching = nx.algorithms.matching.min_weight_matching(G)\n", - " \n", - " # In real code, we would now apply the correction along the shortest paths\n", - " corrections = []\n", - " for u, v in matching:\n", - " corrections.append((u, v)) # paths to be corrected\n", - " return corrections\n", - " def getSyndrome(self, map, measures):\n", - " syndrome = []\n", - " syndromeMap = []\n", - " for i,measure in enumerate(measures):\n", - " if measure == qsharp.Result.One:\n", - " qubits = []\n", - " for qubit in map[i]:\n", - " qubits.append((qubit//self.d, qubit%self.d))\n", - " syndrome.append((sum(q[0] for q in qubits)/len(qubits),sum(q[1] for q in qubits)/len(qubits) ))\n", - " syndromeMap.append(i)\n", - " print(syndromeMap)\n", - " print(syndrome)\n", - " return syndrome, syndromeMap\n", - " \n", - " def getCoordQubits(self, coord):\n", - " return (coord[0]*self.d)+coord[1]\n", - " \n", - " \n", - "\n", - " def find_shortest_path(self, start, end):\n", - " # Round coordinates to integers\n", - " start_int = (round(start[0]), round(start[1]))\n", - " end_int = (round(end[0]), round(end[1]))\n", - " \n", - " # Calculate horizontal and vertical distances\n", - " x_diff = abs(end_int[0] - start_int[0])\n", - " y_diff = abs(end_int[1] - start_int[1])\n", - " \n", - " # Initialize the path with the starting point\n", - " path = [start_int]\n", - " \n", - " # Current position\n", - " current = start_int\n", - " \n", - " # Determine direction of movement\n", - " x_sign = 1 if end_int[0] > start_int[0] else -1 if end_int[0] < start_int[0] else 0\n", - " y_sign = 1 if end_int[1] > start_int[1] else -1 if end_int[1] < start_int[1] else 0\n", - " \n", - " # Move diagonally as much as possible\n", - " diagonal_steps = min(x_diff, y_diff)\n", - " for _ in range(diagonal_steps):\n", - " current = (current[0] + x_sign, current[1] + y_sign)\n", - " path.append(current)\n", - " \n", - " # Move remaining horizontal steps\n", - " remaining_x = x_diff - diagonal_steps\n", - " for _ in range(remaining_x):\n", - " current = (current[0] + x_sign, current[1])\n", - " path.append(current)\n", - " \n", - " # Move remaining vertical steps\n", - " remaining_y = y_diff - diagonal_steps\n", - " for _ in range(remaining_y):\n", - " current = (current[0], current[1] + y_sign)\n", - " path.append(current)\n", - " \n", - " # Return the path (excluding the starting point if it's already included)\n", - " return path[1:] if end_int != start_int else []\n", - "\n", - "\n", - "def correctErrors(errors):\n", - " for error, emap in errors.items():\n", - " for key, apply in emap.items():\n", - " # print(key, apply)\n", - " if apply:\n", - " # print(\"Applying\")\n", - " if error == \"x\":\n", - " qsharp.eval(f\"X(qubits[{key}]);\")\n", - " else:\n", - " qsharp.eval(f\"Z(qubits[{key}]);\")\n", - "\n", - "\n", - "\n", - "from collections import defaultdict\n", - "\n", - "def decode_surface_code(parity_checks, stabilizer_qubit_map):\n", - " \"\"\"\n", - " Args:\n", - " parity_checks (List[int]): List of 0 or 1 values for each stabilizer (1 = error detected)\n", - " stabilizer_qubit_map (List[List[int]]): List of lists, each with qubit indices for the stabilizer\n", - "\n", - " Returns:\n", - " Set[int]: Indices of qubits to apply correction to\n", - " \"\"\"\n", - "\n", - " # Count how many times each qubit appears in stabilizers with parity 1\n", - " qubit_votes = defaultdict(int)\n", - "\n", - " for stab_index, parity in enumerate(parity_checks):\n", - " if parity == 1:\n", - " for q in stabilizer_qubit_map[stab_index]:\n", - " qubit_votes[q] += 1\n", - "\n", - " # Apply correction to qubits that are involved in an odd number of violated stabilizers\n", - " corrections = {q for q, count in qubit_votes.items() if count % 2 == 1}\n", - " return corrections\n", - "\n", - "\n", - "def correct_surface_code(xcorrections, zcorrections):\n", - " for i in xcorrections:\n", - " qsharp.eval(f\"X(qubits[{i}]);\")\n", - " for i in zcorrections:\n", - " qsharp.eval(f\"Z(qubits[{i}]);\")\n", - "\n", - "\n", - "def getZCorrections(d, initMeasures, xMaps):\n", - " num_qubits = d*d\n", - " H_x = np.zeros((len(initMeasures), num_qubits), dtype=np.uint8)\n", - " for i, stabilizer in enumerate(xMaps):\n", - " for qubit_idx in stabilizer:\n", - " H_x[i, qubit_idx] = 1\n", - "\n", - "\n", - " z_decoder = pymatching.Matching(H_x) \n", - " z_correction = z_decoder.decode(initMeasures)\n", - " print(z_correction)\n", - " z_error_qubits = np.where(z_correction == 1)[0] # Qubits needing phase flips\n", - " print(\"Apply phase flips (Z) to qubits:\", z_error_qubits)\n", - " return z_error_qubits\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "04d0b9ab", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "venv", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} From b083b5cec56f23d4964903edba5d3793137972ca Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 20:51:30 -0400 Subject: [PATCH 17/19] Update gitignore --- .gitignore | 1 + 1 file changed, 1 insertion(+) diff --git a/.gitignore b/.gitignore index 0a19790..24aacf6 100644 --- a/.gitignore +++ b/.gitignore @@ -6,6 +6,7 @@ __pycache__/ # C extensions *.so +.DS_Store # Distribution / packaging .Python build/ From 15761cc13b6f82bd40df7181470606d6ac56f0ba Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 20:54:25 -0400 Subject: [PATCH 18/19] Update requirement.txt --- requirements.txt | 1 - 1 file changed, 1 deletion(-) diff --git a/requirements.txt b/requirements.txt index ab6fcc6..f56c92e 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,5 +1,4 @@ qsharp==1.15.0 -pytest matplotlib qiskit==2.0.0 matplotlib==3.10.1 From c223a409baddb877e9d3ed8a1279bc656e64fa40 Mon Sep 17 00:00:00 2001 From: Bhargav Chickmagalur Nanjundappa Date: Sat, 19 Apr 2025 20:54:41 -0400 Subject: [PATCH 19/19] Add CI pipeline --- .github/workflows/ci_pipeline.yml | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) create mode 100644 .github/workflows/ci_pipeline.yml diff --git a/.github/workflows/ci_pipeline.yml b/.github/workflows/ci_pipeline.yml new file mode 100644 index 0000000..4152b8e --- /dev/null +++ b/.github/workflows/ci_pipeline.yml @@ -0,0 +1,26 @@ +name: Run Pytest + +on: [push, pull_request] + +jobs: + test: + runs-on: ubuntu-latest + + steps: + - name: 📥 Checkout code + uses: actions/checkout@v3 + + - name: 🐍 Set up Python + uses: actions/setup-python@v4 + with: + python-version: '3.10' # or whatever version you need + + - name: 📦 Install dependencies + run: | + python -m pip install --upgrade pip + pip install -r requirements.txt + pip install pytest + + - name: 🧪 Run Pytest + run: | + pytest \ No newline at end of file

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