From d400599612869a491821b5e9595ae1bfb1068548 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sun, 20 Oct 2024 17:03:18 +0000 Subject: [PATCH] build based on 66c0584 --- dev/.documenter-siteinfo.json | 2 +- dev/API/index.html | 134 ++++++++++---------- dev/ECC_API/index.html | 14 +- dev/ECC_evaluating/10d3268d.png | Bin 42911 -> 0 bytes dev/ECC_evaluating/1eaca3f2.png | Bin 53769 -> 0 bytes dev/ECC_evaluating/a7799318.png | Bin 0 -> 55446 bytes dev/ECC_evaluating/de44a129.png | Bin 0 -> 42753 bytes dev/ECC_evaluating/index.html | 4 +- dev/allops/index.html | 2 +- dev/canonicalization/4d5f47ca.png | Bin 9515 -> 0 bytes dev/canonicalization/4fb90daa.png | Bin 0 -> 9671 bytes dev/canonicalization/50272d0d.png | Bin 0 -> 9868 bytes dev/canonicalization/7dc75468.png | Bin 9828 -> 0 bytes dev/canonicalization/989781e7.png | Bin 0 -> 9880 bytes dev/canonicalization/a55d1f39.png | Bin 9836 -> 0 bytes dev/canonicalization/b75b9e76.png | Bin 9772 -> 0 bytes dev/canonicalization/d717ca69.png | Bin 0 -> 9396 bytes dev/canonicalization/index.html | 8 +- dev/commonstates/index.html | 2 +- dev/datastructures/index.html | 2 +- dev/ecc_example_sim/index.html | 6 +- dev/graphs/index.html | 2 +- dev/index.html | 2 +- dev/mixed/index.html | 2 +- dev/noise/index.html | 2 +- dev/noisycircuits/index.html | 2 +- dev/noisycircuits_API/index.html | 2 +- dev/noisycircuits_mc/index.html | 2 +- dev/noisycircuits_ops/index.html | 2 +- dev/noisycircuits_perturb/index.html | 2 +- dev/plotting/{6b8d6d9d.svg => 304a0046.svg} | 12 +- dev/plotting/{87e11ca4.svg => 33d94897.svg} | 12 +- dev/plotting/{f0d2ac3a.svg => 4bea7805.svg} | 12 +- dev/plotting/{a994eba7.svg => 94a98303.svg} | 12 +- dev/plotting/{2d5ce333.svg => d31f8297.svg} | 12 +- dev/plotting/index.html | 12 +- dev/references/index.html | 2 +- dev/stab-algebra-manual/index.html | 2 +- dev/tutandpub/index.html | 2 +- 39 files changed, 135 insertions(+), 135 deletions(-) delete mode 100644 dev/ECC_evaluating/10d3268d.png delete mode 100644 dev/ECC_evaluating/1eaca3f2.png create mode 100644 dev/ECC_evaluating/a7799318.png create mode 100644 dev/ECC_evaluating/de44a129.png delete mode 100644 dev/canonicalization/4d5f47ca.png create mode 100644 dev/canonicalization/4fb90daa.png create mode 100644 dev/canonicalization/50272d0d.png delete mode 100644 dev/canonicalization/7dc75468.png create mode 100644 dev/canonicalization/989781e7.png delete mode 100644 dev/canonicalization/a55d1f39.png delete mode 100644 dev/canonicalization/b75b9e76.png create mode 100644 dev/canonicalization/d717ca69.png rename dev/plotting/{6b8d6d9d.svg => 304a0046.svg} (99%) rename dev/plotting/{87e11ca4.svg => 33d94897.svg} (98%) rename dev/plotting/{f0d2ac3a.svg => 4bea7805.svg} (98%) rename dev/plotting/{a994eba7.svg => 94a98303.svg} (98%) rename dev/plotting/{2d5ce333.svg => d31f8297.svg} (99%) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index fbc9db2ee..d9ee266ca 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-20T14:17:43","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-20T17:03:10","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/API/index.html b/dev/API/index.html index 937b92d85..2358dac3b 100644 --- a/dev/API/index.html +++ b/dev/API/index.html @@ -4,7 +4,7 @@ padding-top: 0 !important; padding-bottom: 0 !important; } -

States

Stabilizer states can be represented with the Stabilizer, Destabilizer, MixedStabilizer, and MixedDestabilizer tableau data structures. You probably want to use MixedDestabilizer which supports the widest set of operations.

Moreover, a MixedDestabilizer can be stored inside a Register together with a set of classical bits in which measurement results can be written.

Lastly, for Pauli frame simulations there is the PauliFrame type, a tableau in which each row represents a different Pauli frame.

There are convenience constructors for common types of states and operators.

Operations

Acting on quantum states can be performed either:

See the full list of operations for a list of implemented operations.

Autogenerated API list

QuantumClifford.QuantumClifford — Module

A module for using the Stabilizer formalism and simulating Clifford circuits.

source
QuantumClifford.continue_stat — Constant

Returned by applywstatus! if the circuit simulation should continue.

source
QuantumClifford.failure_stat — Constant

Returned by applywstatus! if the circuit reports a failure.

See also: VerifyOp, BellMeasurement.

source
QuantumClifford.false_success_stat — Constant

Returned by applywstatus! if the circuit reports a success, but it is a false positive (i.e., there was an undetected error).

See also: VerifyOp, BellMeasurement.

source
QuantumClifford.true_success_stat — Constant

Returned by applywstatus! if the circuit reports a success and there is no undetected error.

See also: VerifyOp, BellMeasurement.

source
QuantumClifford.AbstractSingleQubitOperator — Type

Supertype of all single-qubit symbolic operators.

source
QuantumClifford.AbstractSymbolicOperator — Type

Supertype of all symbolic operators. Subtype of AbstractCliffordOperator

source
QuantumClifford.AbstractTwoQubitOperator — Type

Supertype of all two-qubit symbolic operators.

source
QuantumClifford.BellMeasurement — Type

A Bell measurement performing the correlation measurement corresponding to the given pauli projections on the qubits at the selected indices.

source
QuantumClifford.CircuitStatus — Type

A convenience struct to represent the status of a circuit simulated by mctrajectories

source
QuantumClifford.ClassicalXOR — Type

Applies an XOR gate to classical bits. Currently only implemented for functionality with pauli frames.

source
QuantumClifford.CliffordOperator — Type

Clifford Operator specified by the mapping of the basis generators.

julia> tCNOT
+
States
Stabilizer states can be represented with the Stabilizer, Destabilizer, MixedStabilizer, and MixedDestabilizer tableau data structures. You probably want to use MixedDestabilizer which supports the widest set of operations.
Moreover, a MixedDestabilizer can be stored inside a Register together with a set of classical bits in which measurement results can be written.
Lastly, for Pauli frame simulations there is the PauliFrame type, a tableau in which each row represents a different Pauli frame.
There are convenience constructors for common types of states and operators.
Operations
Acting on quantum states can be performed either:
  • In a "linear algebra" language where unitaries, measurements, and other operations have separate interfaces. This is an explicitly deterministic lower-level interface, which provides a great deal of control over how tableaux are manipulated. See the Stabilizer Tableau Algebra Manual as a primer on these approaches.
  • Or in a "circuit" language, where the operators (and measurements and noise) are represented as circuit gates. This is a higher-level interface in which the outcome of an operation can be stochastic. The API for it is centered around the apply! function. Particularly useful for Monte Carlo simulations and Perturbative Expansion Symbolic Results.
See the full list of operations for a list of implemented operations.
Autogenerated API list
QuantumClifford.BellMeasurement — Type
A Bell measurement performing the correlation measurement corresponding to the given pauli projections on the qubits at the selected indices.
source
QuantumClifford.CliffordOperator — Type
Clifford Operator specified by the mapping of the basis generators.
julia> tCNOT
 X₁ ⟼ + XX
 X₂ ⟼ + _X
 Z₁ ⟼ + Z_
@@ -33,12 +33,12 @@
 
 julia> CliffordOperator(d)
 X₁ ⟼ + Z
-Z₁ ⟼ + Y
source
QuantumClifford.Destabilizer — Type
A tableau representation of a pure stabilizer state. The tableau tracks the destabilizers as well, for efficient projections. On initialization there are no checks that the provided state is indeed pure. This enables the use of this data structure for mixed stabilizer state, but a better choice would be to use MixedDestabilizer.
source
QuantumClifford.MixedDestabilizer — Type
A tableau representation for mixed stabilizer states that keeps track of the destabilizers in order to provide efficient projection operations.
The rank r of the n-qubit tableau is tracked, either so that it can be used to represent a mixed stabilizer state, or so that it can be used to represent an n-r logical-qubit code over n physical qubits. The "logical" operators are tracked as well.
When the constructor is called on an incomplete Stabilizer it automatically calculates the destabilizers and logical operators, following chapter 4 of (Gottesman, 1997). Under the hood the conversion uses the canonicalize_gott! canonicalization. That canonicalization permutes the columns of the tableau, but we automatically undo the column permutation in the preparation of a MixedDestabilizer so that qubits are not reindexed. The boolean keyword arguments undoperm and reportperm can be used to control this behavior and to report the permutations explicitly.
See also: stabilizerview, destabilizerview, logicalxview, logicalzview
source
QuantumClifford.PauliFrame — Type
struct PauliFrame{T, S} <: QuantumClifford.AbstractQCState
This is a wrapper around a tableau. This "frame" tableau is not to be viewed as a normal stabilizer tableau, although it does conjugate the same under Clifford operations. Each row in the tableau refers to a single frame. The row represents the Pauli operation by which the frame and the reference differ.
source
QuantumClifford.Destabilizer — Type
A tableau representation of a pure stabilizer state. The tableau tracks the destabilizers as well, for efficient projections. On initialization there are no checks that the provided state is indeed pure. This enables the use of this data structure for mixed stabilizer state, but a better choice would be to use MixedDestabilizer.
source
QuantumClifford.MixedDestabilizer — Type
A tableau representation for mixed stabilizer states that keeps track of the destabilizers in order to provide efficient projection operations.
The rank r of the n-qubit tableau is tracked, either so that it can be used to represent a mixed stabilizer state, or so that it can be used to represent an n-r logical-qubit code over n physical qubits. The "logical" operators are tracked as well.
When the constructor is called on an incomplete Stabilizer it automatically calculates the destabilizers and logical operators, following chapter 4 of (Gottesman, 1997). Under the hood the conversion uses the canonicalize_gott! canonicalization. That canonicalization permutes the columns of the tableau, but we automatically undo the column permutation in the preparation of a MixedDestabilizer so that qubits are not reindexed. The boolean keyword arguments undoperm and reportperm can be used to control this behavior and to report the permutations explicitly.
See also: stabilizerview, destabilizerview, logicalxview, logicalzview
source
QuantumClifford.PauliFrame — Type
struct PauliFrame{T, S} <: QuantumClifford.AbstractQCState
This is a wrapper around a tableau. This "frame" tableau is not to be viewed as a normal stabilizer tableau, although it does conjugate the same under Clifford operations. Each row in the tableau refers to a single frame. The row represents the Pauli operation by which the frame and the reference differ.
source
QuantumClifford.PauliFrame — Method
PauliFrame(
     frames,
     qubits,
     measurements
 ) -> PauliFrame{Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, LinearAlgebra.Adjoint{UInt64, Matrix{UInt64}}}}}
-
Prepare an empty set of Pauli frames with the given number of frames and qubits. Preallocates spaces for measurement number of measurements.
source
QuantumClifford.PauliOperator — Type
A multi-qubit Pauli operator ($±\{1,i\}\{I,Z,X,Y\}^{\otimes n}$).
A Pauli can be constructed with the P custom string macro or by building up one through products and tensor products of smaller operators.
julia> pauli3 = P"-iXYZ"
+
Prepare an empty set of Pauli frames with the given number of frames and qubits. Preallocates spaces for measurement number of measurements.
source
QuantumClifford.PauliOperator — Type
A multi-qubit Pauli operator ($±\{1,i\}\{I,Z,X,Y\}^{\otimes n}$).
A Pauli can be constructed with the P custom string macro or by building up one through products and tensor products of smaller operators.
julia> pauli3 = P"-iXYZ"
 -iXYZ
 
 julia> pauli4 = 1im * pauli3 ⊗ X
@@ -55,7 +55,7 @@
 (true, false)
 
 julia> p[1] = (true, true); p
-+ YYZ
source
QuantumClifford.Register — Type
A register, representing the state of a computer including both a tableaux and an array of classical bits (e.g. for storing measurement results)
source
QuantumClifford.Reset — Type
Reset the specified qubits to the given state.
Be careful, this operation implies first tracing out the qubits, which can lead to mixed states if these qubits were entangled with the rest of the system.
See also: sMRZ
source
QuantumClifford.SingleQubitOperator — Type
A "symbolic" general single-qubit operator which permits faster multiplication than an operator expressed as an explicit tableau.
julia> op = SingleQubitOperator(2, true, true, true, false, true, true) # Tableau components and phases
++ YYZ
source
QuantumClifford.Register — Type
A register, representing the state of a computer including both a tableaux and an array of classical bits (e.g. for storing measurement results)
source
QuantumClifford.Reset — Type
Reset the specified qubits to the given state.
Be careful, this operation implies first tracing out the qubits, which can lead to mixed states if these qubits were entangled with the rest of the system.
See also: sMRZ
source
QuantumClifford.SingleQubitOperator — Type
A "symbolic" general single-qubit operator which permits faster multiplication than an operator expressed as an explicit tableau.
julia> op = SingleQubitOperator(2, true, true, true, false, true, true) # Tableau components and phases
 SingleQubitOperator on qubit 2
 X₁ ⟼ - Y
 Z₁ ⟼ - X
@@ -76,7 +76,7 @@
 
 julia> CliffordOperator(op, 1, compact=true) # You can also extract just the non-trivial part of the tableau
 X₁ ⟼ - Y
-Z₁ ⟼ - X
See also: sHadamard, sPhase, sId1, sX, sY, sZ, CliffordOperator
Or simply consult subtypes(QuantumClifford.AbstractSingleQubitOperator) and subtypes(QuantumClifford.AbstractTwoQubitOperator) for a full list. You can think of the s prefix as "symbolic" or "sparse".
source
QuantumClifford.SparseGate — Type
A Clifford gate, applying the given cliff operator to the qubits at the selected indices.
apply!(state, cliff, indices) and apply!(state, SparseGate(cliff, indices)) give the same result.
source
QuantumClifford.StabMixture — Type
mutable struct StabMixture{T, F}
Represents mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is a pure stabilizer state.
julia> StabMixture(S"-X")
+Z₁ ⟼ - X
See also: sHadamard, sPhase, sId1, sX, sY, sZ, CliffordOperator
Or simply consult subtypes(QuantumClifford.AbstractSingleQubitOperator) and subtypes(QuantumClifford.AbstractTwoQubitOperator) for a full list. You can think of the s prefix as "symbolic" or "sparse".
source
QuantumClifford.SparseGate — Type
A Clifford gate, applying the given cliff operator to the qubits at the selected indices.
apply!(state, cliff, indices) and apply!(state, SparseGate(cliff, indices)) give the same result.
source
QuantumClifford.StabMixture — Type
mutable struct StabMixture{T, F}
Represents mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is a pure stabilizer state.
julia> StabMixture(S"-X")
 A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
 𝒟ℯ𝓈𝓉𝒶𝒷
 + Z
@@ -101,7 +101,7 @@
  0.0+0.353553im | + _ | + Z
  0.0-0.353553im | + Z | + _
  0.853553+0.0im | + _ | + _
- 0.146447+0.0im | + Z | + Z
See also: PauliChannel
source
QuantumClifford.Stabilizer — Type
Stabilizer, i.e. a list of commuting multi-qubit Hermitian Pauli operators.
Instances can be created with the S custom string macro or as direct sum of other stabilizers.
Stabilizers and Destabilizers
In many cases you probably would prefer to use the MixedDestabilizer data structure, as it caries a lot of useful additional information, like tracking rank and destabilizer operators. Stabilizer has mostly a pedagogical value, and it is also used for slightly faster simulation of a particular subset of Clifford operations.
julia> s = S"XXX
+ 0.146447+0.0im | + Z | + Z
See also: PauliChannel
source
QuantumClifford.Stabilizer — Type
Stabilizer, i.e. a list of commuting multi-qubit Hermitian Pauli operators.
Instances can be created with the S custom string macro or as direct sum of other stabilizers.
Stabilizers and Destabilizers
In many cases you probably would prefer to use the MixedDestabilizer data structure, as it caries a lot of useful additional information, like tracking rank and destabilizer operators. Stabilizer has mostly a pedagogical value, and it is also used for slightly faster simulation of a particular subset of Clifford operations.
julia> s = S"XXX
              ZZI
              IZZ"
 + XXX
@@ -134,7 +134,7 @@
 
 julia> s[1,1] = (true, false); s
 + X_
-+ __
There are no automatic checks for correctness (i.e. independence of all rows, commutativity of all rows, hermiticity of all rows). The rank (number of rows) is permitted to be less than the number of qubits (number of columns): canonilization, projection, etc. continue working in that case. To great extent this library uses the Stabilizer data structure simply as a tableau. This might be properly abstracted away in future versions.
See also: PauliOperator, canonicalize!
source
QuantumClifford.UnitaryPauliChannel — Type
A Pauli channel datastructure, mainly for use with StabMixture.
More convenient to use than PauliChannel when you know your Pauli channel is unitary.
julia> Tgate = UnitaryPauliChannel(
++ __
There are no automatic checks for correctness (i.e. independence of all rows, commutativity of all rows, hermiticity of all rows). The rank (number of rows) is permitted to be less than the number of qubits (number of columns): canonilization, projection, etc. continue working in that case. To great extent this library uses the Stabilizer data structure simply as a tableau. This might be properly abstracted away in future versions.
See also: PauliOperator, canonicalize!
source
QuantumClifford.UnitaryPauliChannel — Type
A Pauli channel datastructure, mainly for use with StabMixture.
More convenient to use than PauliChannel when you know your Pauli channel is unitary.
julia> Tgate = UnitaryPauliChannel(
            (I, Z),
            ((1+exp(im*π/4))/2, (1-exp(im*π/4))/2)
        )
@@ -149,7 +149,7 @@
  0.853553+0.0im | + _ | + _
  0.0+0.353553im | + _ | + Z
  0.0-0.353553im | + Z | + _
- 0.146447+0.0im | + Z | + Z
source
QuantumClifford.VerifyOp — Type
A "probe" to verify that the state of the qubits corresponds to a desired good_state, e.g. at the end of the execution of a circuit.
source
QuantumClifford.sMRZ — Type
Measure a qubit in the Z basis and reset to the |0⟩ state.
It does not trace out the qubit!
As described below there is a difference between measuring the qubit (followed by setting it to a given known state) and "tracing out" the qubit. By reset here we mean "measuring and setting to a known state", not "tracing out".
julia> s = MixedDestabilizer(S"XXX ZZI IZZ") # |000⟩+|111⟩
+ 0.146447+0.0im | + Z | + Z
source
QuantumClifford.VerifyOp — Type
A "probe" to verify that the state of the qubits corresponds to a desired good_state, e.g. at the end of the execution of a circuit.
source
QuantumClifford.sMRZ — Type
Measure a qubit in the Z basis and reset to the |0⟩ state.
It does not trace out the qubit!
As described below there is a difference between measuring the qubit (followed by setting it to a given known state) and "tracing out" the qubit. By reset here we mean "measuring and setting to a known state", not "tracing out".
julia> s = MixedDestabilizer(S"XXX ZZI IZZ") # |000⟩+|111⟩
 𝒟ℯ𝓈𝓉𝒶𝒷
 + Z__
 + _X_
@@ -199,7 +199,7 @@
 𝒮𝓉𝒶𝒷━
 + Z__
 - ZZ_
-- Z_Z
See also: Reset, sMZ
source
QuantumClifford.PauliError — Function
A convenient constructor for various types of Pauli errors, that can be used as circuit gates in simulations. Returns more specific types when necessary.
source
QuantumClifford.PauliError — Method
"Construct a gate operation that applies a biased Pauli error on all qubits independently, each with  probabilities px, py, pz. Note that the probability of any error occurring is px+py+pz. Because of this, PauliError(1, p) is equivalent to PauliError(1,p/3,p/3,p/3). Similarly, if one wanted to exclude Z errors from PauliError(1,p/3,p/3,p/3) while mainting the same rate of X errors, one could write PauliError(1, p*2/3, 0, 0) (in the sense that Y errors can be interpreted as an X and a Z happening at the same time).
source
QuantumClifford.PauliError — Method
"Construct a gate operation that applies a biased Pauli error on  qubit q with independent probabilities px, py, pz. Note that the probability of any error occurring is px+py+pz. Because of this, PauliError(1, p) is equivalent to PauliError(1,p/3,p/3,p/3). Similarly, if one wanted to exclude Z errors from PauliError(1,p/3,p/3,p/3) while mainting the same rate of X errors, one could write PauliError(1, p*2/3, 0, 0) (in the sense that Y errors can be interpreted as an X and a Z happening at the same time).
source
QuantumClifford.applybranches — Function
Compute all possible new states after the application of the given operator. Reports the probability of each one of them. Deterministic (as it reports all branches of potentially random processes), part of the Perturbative Expansion interface.
source
QuantumClifford.applynoise! — Function
A method modifying a given state by applying the corresponding noise model. It is non-deterministic, part of the Noise interface.
source
QuantumClifford.PauliError — Function
A convenient constructor for various types of Pauli errors, that can be used as circuit gates in simulations. Returns more specific types when necessary.
source
QuantumClifford.PauliError — Method
"Construct a gate operation that applies a biased Pauli error on all qubits independently, each with  probabilities px, py, pz. Note that the probability of any error occurring is px+py+pz. Because of this, PauliError(1, p) is equivalent to PauliError(1,p/3,p/3,p/3). Similarly, if one wanted to exclude Z errors from PauliError(1,p/3,p/3,p/3) while mainting the same rate of X errors, one could write PauliError(1, p*2/3, 0, 0) (in the sense that Y errors can be interpreted as an X and a Z happening at the same time).
source
QuantumClifford.PauliError — Method
"Construct a gate operation that applies a biased Pauli error on  qubit q with independent probabilities px, py, pz. Note that the probability of any error occurring is px+py+pz. Because of this, PauliError(1, p) is equivalent to PauliError(1,p/3,p/3,p/3). Similarly, if one wanted to exclude Z errors from PauliError(1,p/3,p/3,p/3) while mainting the same rate of X errors, one could write PauliError(1, p*2/3, 0, 0) (in the sense that Y errors can be interpreted as an X and a Z happening at the same time).
source
QuantumClifford.applybranches — Function
Compute all possible new states after the application of the given operator. Reports the probability of each one of them. Deterministic (as it reports all branches of potentially random processes), part of the Perturbative Expansion interface.
source
QuantumClifford.applynoise! — Function
A method modifying a given state by applying the corresponding noise model. It is non-deterministic, part of the Noise interface.
source
QuantumClifford.bell — Function
Prepare one or more Bell pairs (with optional phases).
julia> bell()
 + XX
 + ZZ
 
@@ -217,11 +217,11 @@
 - XX__
 + ZZ__
 - __XX
-- __ZZ
source
QuantumClifford.bigram — Method
bigram(
     state::QuantumClifford.AbstractStabilizer;
     clip
 ) -> Matrix{Int64}
-
Get the bigram of a tableau.
It is the list of endpoints of a tableau in the clipped gauge.
If clip=true (the default) the tableau is converted to the clipped gauge in-place before calculating the bigram. Otherwise, the clip gauge conversion is skipped (for cases where the input is already known to be in the correct gauge).
Introduced in (Nahum et al., 2017), with a more detailed explanation of the algorithm in (Li et al., 2019) and (Gullans et al., 2021).
See also: canonicalize_clip!
source
QuantumClifford.canonicalize! — Method
canonicalize!(
+
Get the bigram of a tableau.
It is the list of endpoints of a tableau in the clipped gauge.
If clip=true (the default) the tableau is converted to the clipped gauge in-place before calculating the bigram. Otherwise, the clip gauge conversion is skipped (for cases where the input is already known to be in the correct gauge).
Introduced in (Nahum et al., 2017), with a more detailed explanation of the algorithm in (Li et al., 2019) and (Gullans et al., 2021).
See also: canonicalize_clip!
source
QuantumClifford.canonicalize_clip! — Method
canonicalize_clip!(
     state::QuantumClifford.AbstractStabilizer;
     phases
 ) -> QuantumClifford.AbstractStabilizer
@@ -294,32 +294,32 @@
 + _XZX__
 - _ZYX_Z
 - __YZ_X
-- ____Z_
If phases=false is set, the canonicalization does not track the phases in the tableau, leading to a significant speedup.
Introduced in (Nahum et al., 2017), with a more detailed explanation of the algorithm in Appendix A of (Li et al., 2019)
See also: canonicalize!, canonicalize_rref!, canonicalize_gott!.
source
QuantumClifford.canonicalize_gott! — Method
Inplace Gottesman canonicalization of a tableau.
This uses different canonical form from canonicalize!. It is used in the computation of the logical X and Z operators of a MixedDestabilizer.
It returns the (in place) modified state, the indices of the last pivot of both Gaussian elimination steps, and the permutations that have been used to put the X and Z tableaux in standard form.
Based on (Gottesman, 1997).
See also: canonicalize!, canonicalize_rref!
source
QuantumClifford.canonicalize_gott! — Method
Inplace Gottesman canonicalization of a tableau.
This uses different canonical form from canonicalize!. It is used in the computation of the logical X and Z operators of a MixedDestabilizer.
It returns the (in place) modified state, the indices of the last pivot of both Gaussian elimination steps, and the permutations that have been used to put the X and Z tableaux in standard form.
Based on (Gottesman, 1997).
See also: canonicalize!, canonicalize_rref!
source
QuantumClifford.canonicalize_rref! — Method
canonicalize_rref!(
     state::QuantumClifford.AbstractStabilizer,
     colindices;
     phases
 ) -> Tuple{QuantumClifford.AbstractStabilizer, Any}
-
Canonicalize a stabilizer (in place) along only some columns.
This uses different canonical form from canonicalize!. It also indexes in reverse in order to make its use in traceout! more efficient. Its use in traceout! is its main application.
It returns the (in place) modified state and the index of the last pivot.
Based on (Audenaert and Plenio, 2005).
See also: canonicalize!, canonicalize_gott!
source
QuantumClifford.centralizer — Method
For a given set of Paulis (in the form of a Tableau), return the subset of Paulis that commute with all Paulis in set.
julia> centralizer(T"XX ZZ _Z")
-+ ZZ
source
QuantumClifford.clifford_cardinality — Method
The size of the Clifford group 𝒞 over a given number of qubits, possibly modulo the phases.
For n qubits, not accounting for phases is 2ⁿⁿΠⱼ₌₁ⁿ(4ʲ-1). There are 4ⁿ different phase configurations.
julia> clifford_cardinality(7)
+
source
QuantumClifford.centralizer — Method
For a given set of Paulis (in the form of a Tableau), return the subset of Paulis that commute with all Paulis in set.
julia> centralizer(T"XX ZZ _Z")
++ ZZ
source
QuantumClifford.clifford_cardinality — Method
The size of the Clifford group 𝒞 over a given number of qubits, possibly modulo the phases.
For n qubits, not accounting for phases is 2ⁿⁿΠⱼ₌₁ⁿ(4ʲ-1). There are 4ⁿ different phase configurations.
julia> clifford_cardinality(7)
 457620995529680351512370381586432000
When not accounting for phases (phases = false) the result is the same as the size of the Symplectic group Sp(2n) ≡ 𝒞ₙ/𝒫ₙ, where 𝒫ₙ is the Pauli group over n qubits.
julia> clifford_cardinality(7, phases=false)
-27930968965434591767112450048000
See also: enumerate_cliffords.
source
QuantumClifford.comm — Function
Check whether two operators commute.
0x0 if they commute, 0x1 if they anticommute.
julia> P"XX"*P"ZZ", P"ZZ"*P"XX"
 (- YY, - YY)
 
 julia> comm(P"ZZ", P"XX")
 0x00
 
 julia> comm(P"IZ", P"XX")
-0x01
See also: comm!
source
QuantumClifford.compactify_circuit — Method
Convert a list of gates to a more optimized "sum type" format which permits faster dispatch.
Generally, this should be called on a circuit before it is used in a simulation.
source
QuantumClifford.contractor — Method
Return the subset of Paulis in a Stabilizer that have identity operators on all qubits corresponding to  the given subset, without the entries corresponding to subset.
julia> contractor(S"_X X_", [1])
-+ X
source
QuantumClifford.delete_columns — Method
Return the given stabilizer without all the qubits in the given iterable.
The resulting tableaux is not guaranteed to be valid (to retain its commutation relationships).
julia> delete_columns(S"XYZ YZX ZXY", [1,3])
+0x01
See also: comm!
source
QuantumClifford.compactify_circuit — Method
Convert a list of gates to a more optimized "sum type" format which permits faster dispatch.
Generally, this should be called on a circuit before it is used in a simulation.
source
QuantumClifford.contractor — Method
Return the subset of Paulis in a Stabilizer that have identity operators on all qubits corresponding to  the given subset, without the entries corresponding to subset.
julia> contractor(S"_X X_", [1])
++ X
source
QuantumClifford.delete_columns — Method
Return the given stabilizer without all the qubits in the given iterable.
The resulting tableaux is not guaranteed to be valid (to retain its commutation relationships).
julia> delete_columns(S"XYZ YZX ZXY", [1,3])
 + Y
 + Z
-+ X
See also: traceout!
source
QuantumClifford.enumerate_single_qubit_gates — Method
Generate a symbolic single-qubit gate given its index. Optionally, set non-trivial phases.
julia> enumerate_single_qubit_gates(6)
 sPhase on qubit 1
 X₁ ⟼ + Y
 Z₁ ⟼ + Z
@@ -327,7 +327,7 @@
 julia> enumerate_single_qubit_gates(6, qubit=2, phases=(true, true))
 SingleQubitOperator on qubit 2
 X₁ ⟼ - Y
-Z₁ ⟼ - Z
See also: enumerate_cliffords.
source
QuantumClifford.fastcolumn — Function
Convert a tableau to a memory layout that is fast for column operations.
In this layout a column of the tableau is stored (mostly) contiguously in memory. Due to bitpacking, e.g., packing 64 bits into a single UInt64, the memory layout is not perfectly contiguous, but it is still optimal given that some bitwrangling is required to extract a given bit.
See also: fastrow
source
QuantumClifford.fastrow — Function
Convert a tableau to a memory layout that is fast for row operations.
In this layout a Pauli string (a row of the tableau) is stored contiguously in memory.
See also: fastrow
source
QuantumClifford.generate! — Method
Generate a Pauli operator by using operators from a given the Stabilizer.
It assumes the stabilizer is already canonicalized. It modifies the Pauli operator in place, generating it in reverse, up to a phase. That phase is left in the modified operator, which should be the identity up to a phase. Returns the new operator and the list of indices denoting the elements of stabilizer that were used for the generation.
julia> ghz = S"XXXX
+Z₁ ⟼ - Z
See also: enumerate_cliffords.
source
QuantumClifford.fastcolumn — Function
Convert a tableau to a memory layout that is fast for column operations.
In this layout a column of the tableau is stored (mostly) contiguously in memory. Due to bitpacking, e.g., packing 64 bits into a single UInt64, the memory layout is not perfectly contiguous, but it is still optimal given that some bitwrangling is required to extract a given bit.
See also: fastrow
source
QuantumClifford.fastrow — Function
Convert a tableau to a memory layout that is fast for row operations.
In this layout a Pauli string (a row of the tableau) is stored contiguously in memory.
See also: fastrow
source
QuantumClifford.generate! — Method
Generate a Pauli operator by using operators from a given the Stabilizer.
It assumes the stabilizer is already canonicalized. It modifies the Pauli operator in place, generating it in reverse, up to a phase. That phase is left in the modified operator, which should be the identity up to a phase. Returns the new operator and the list of indices denoting the elements of stabilizer that were used for the generation.
julia> ghz = S"XXXX
                ZZII
                IZZI
                IIZZ";
@@ -344,7 +344,7 @@
 true
 
 julia> generate!(P"XII",canonicalize!(S"XII")) === nothing
-false
source
QuantumClifford.ghz — Function
Prepare a GHZ state of n qubits.
julia> ghz()
 + XXX
 + ZZ_
 + _ZZ
@@ -357,7 +357,7 @@
 + XXXX
 + ZZ__
 + _ZZ_
-+ __ZZ
source
QuantumClifford.graphstate — Method
Convert any stabilizer state to a graph state
Graph states are a special type of entangled stabilizer states that can be represented by a graph. For a graph $G=(V,E)$ the corresponding stabilizers are $S_v = X_v \prod_{u ∈ N(v)} Z_u$. Notice that such tableau rows contain only a single X operator. There is a set of single qubit gates that converts any stabilizer state to a graph state.
This function returns the graph state corresponding to a stabilizer and the gates that might be necessary to convert the stabilizer into a state representable as a graph.
For a tableau stab you can convert it with:
graph, hadamard_idx, iphase_idx, flips_idx = graphstate()
where graph is the graph representation of stab, and the rest specifies the single-qubit gates converting stab to graph: hadamard_idx are the qubits that require a Hadamard gate (mapping X ↔ Z), iphase_idx are (different) qubits that require an inverse Phase gate (Y → X), and flips_idx are the qubits that require a phase flip (Pauli Z gate), after the previous two sets of gates.
julia> using Graphs
+true
See also: graph_gatesequence
source
QuantumClifford.graphstate — Method
Convert any stabilizer state to a graph state
Graph states are a special type of entangled stabilizer states that can be represented by a graph. For a graph $G=(V,E)$ the corresponding stabilizers are $S_v = X_v \prod_{u ∈ N(v)} Z_u$. Notice that such tableau rows contain only a single X operator. There is a set of single qubit gates that converts any stabilizer state to a graph state.
This function returns the graph state corresponding to a stabilizer and the gates that might be necessary to convert the stabilizer into a state representable as a graph.
For a tableau stab you can convert it with:
graph, hadamard_idx, iphase_idx, flips_idx = graphstate()
where graph is the graph representation of stab, and the rest specifies the single-qubit gates converting stab to graph: hadamard_idx are the qubits that require a Hadamard gate (mapping X ↔ Z), iphase_idx are (different) qubits that require an inverse Phase gate (Y → X), and flips_idx are the qubits that require a phase flip (Pauli Z gate), after the previous two sets of gates.
julia> using Graphs
 
 julia> s = S" XXX
               ZZ_
@@ -421,15 +421,15 @@
 1-element Vector{Int64}:
  3
The Graphs.jl library provides many graph-theory tools and the MakieGraphs.jl library provides plotting utilities for graphs.
You can directly call the graph constructor on a stabilizer, if you just want the graph and do not care about the Clifford operation necessary to convert an arbitrary state to a state representable as a graph:
julia> collect(edges( Graph(bell()) ))
 1-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
- Edge 1 => 2
For a version that does not copy the stabilizer, but rather performs transformations in-place, use graphstate!. It would perform canonicalize_gott! on its argument as it finds a way to convert it to a graph state.
source
QuantumClifford.groupify — Method
Return the full stabilizer group represented by the input generating set (a Stabilizer).
The returned object is exponentially long.
julia> groupify(S"XZ ZX")
+ Edge 1 => 2
For a version that does not copy the stabilizer, but rather performs transformations in-place, use graphstate!. It would perform canonicalize_gott! on its argument as it finds a way to convert it to a graph state.
source
QuantumClifford.groupify — Method
Return the full stabilizer group represented by the input generating set (a Stabilizer).
The returned object is exponentially long.
julia> groupify(S"XZ ZX")
 + __
 + XZ
 + ZX
-+ YY
source
QuantumClifford.logdot — Method
Logarithm of the inner product between to Stabilizer states.
If the result is nothing, the dot inner product is zero. Otherwise the inner product is 2^(-logdot/2).
The actual inner product can be computed with LinearAlgebra.dot.
Based on (Garcia et al., 2012).
source
QuantumClifford.minimal_generating_set — Method
For a not-necessarily-minimal generating set, return the minimal generating set.
The input has to have only real phases.
julia> minimal_generating_set(S"__ XZ ZX YY")
++ YY
source
QuantumClifford.logdot — Method
Logarithm of the inner product between to Stabilizer states.
If the result is nothing, the dot inner product is zero. Otherwise the inner product is 2^(-logdot/2).
The actual inner product can be computed with LinearAlgebra.dot.
Based on (Garcia et al., 2012).
source
QuantumClifford.minimal_generating_set — Method
For a not-necessarily-minimal generating set, return the minimal generating set.
The input has to have only real phases.
julia> minimal_generating_set(S"__ XZ ZX YY")
 + XZ
-+ ZX
source
QuantumClifford.normalizer — Method
Return all Pauli operators with the same number of qubits as the given Tableau t that commute with all operators in t.
julia> normalizer(T"X")
++ ZX
source
QuantumClifford.normalizer — Method
Return all Pauli operators with the same number of qubits as the given Tableau t that commute with all operators in t.
julia> normalizer(T"X")
 + _
-+ X
source
QuantumClifford.pauligroup — Method
Return the full Pauli group of a given length. Phases are ignored by default,  but can be included by setting phases=true.
julia> pauligroup(1)
++ X
source
QuantumClifford.pauligroup — Method
Return the full Pauli group of a given length. Phases are ignored by default,  but can be included by setting phases=true.
julia> pauligroup(1)
 + _
 + X
 + Z
@@ -451,32 +451,32 @@
 -i_
 -iX
 -iZ
--iY
source
QuantumClifford.pfmeasurements — Method
pfmeasurements(frame::PauliFrame) -> Any
-
Returns the measurement results for each frame in the PauliFrame instance.
Relative measurements
The return measurements are relative to the reference measurements, i.e. they only say whether the reference measurements have been flipped in the given frame.
source
QuantumClifford.pfmeasurements — Method
pfmeasurements(register::Register, frame::PauliFrame) -> Any
-
Takes the references measurements from the given Register and applies the flips as prescribed by the PauliFrame relative measurements. The result is the actual (non-relative) measurement results for each frame.
source
QuantumClifford.pfmeasurements — Method
pfmeasurements(frame::PauliFrame) -> Any
+
Returns the measurement results for each frame in the PauliFrame instance.
Relative measurements
The return measurements are relative to the reference measurements, i.e. they only say whether the reference measurements have been flipped in the given frame.
source
QuantumClifford.pfmeasurements — Method
pfmeasurements(register::Register, frame::PauliFrame) -> Any
+
Takes the references measurements from the given Register and applies the flips as prescribed by the PauliFrame relative measurements. The result is the actual (non-relative) measurement results for each frame.
source
QuantumClifford.pftrajectories — Method
pftrajectories(
     circuit;
     trajectories,
     threads
 ) -> PauliFrame{Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, LinearAlgebra.Adjoint{UInt64, Matrix{UInt64}}}}, Matrix{Bool}}
-
The main method for running Pauli frame simulations of circuits. See the other methods for lower level access.
Multithreading is enabled by default, but can be disabled by setting threads=false. Do not forget to launch Julia with multiple threads enabled, e.g. julia -t4, if you want to use multithreading.
See also: mctrajectories, petrajectories
source
QuantumClifford.pftrajectories — Method
pftrajectories(
+
The main method for running Pauli frame simulations of circuits. See the other methods for lower level access.
Multithreading is enabled by default, but can be disabled by setting threads=false. Do not forget to launch Julia with multiple threads enabled, e.g. julia -t4, if you want to use multithreading.
See also: mctrajectories, petrajectories
source
QuantumClifford.pftrajectories — Method
pftrajectories(
     register::Register,
     circuit;
     trajectories
 ) -> Tuple{Register, PauliFrame{Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, LinearAlgebra.Adjoint{UInt64, Matrix{UInt64}}}}, Matrix{Bool}}}
-
For a given Register and circuit, simulates the reference circuit acting on the register and then also simulate numerous PauliFrame trajectories. Returns the register and the PauliFrame instance.
Use pfmeasurements to get the measurement results.
source
QuantumClifford.phases — Method
The phases of a given tableau. It is a view, i.e. if you modify this array, the original tableau caries these changes.
source
QuantumClifford.prodphase — Method
Get the phase of the product of two Pauli operators.
Phase is encoded as F(4) in the low qubits of an UInt8.
julia> P"ZZZ"*P"XXX"
+
For a given Register and circuit, simulates the reference circuit acting on the register and then also simulate numerous PauliFrame trajectories. Returns the register and the PauliFrame instance.
Use pfmeasurements to get the measurement results.
source
QuantumClifford.phases — Method
The phases of a given tableau. It is a view, i.e. if you modify this array, the original tableau caries these changes.
source
QuantumClifford.prodphase — Method
Get the phase of the product of two Pauli operators.
Phase is encoded as F(4) in the low qubits of an UInt8.
julia> P"ZZZ"*P"XXX"
 -iYYY
 
 julia> prodphase(P"ZZZ", P"XXX")
 0x03
 
 julia> prodphase(P"XXX", P"ZZZ")
-0x01
source
QuantumClifford.random_brickwork_clifford_circuit — Method
Random brickwork Clifford circuit.
The connectivity of the random circuit is brickwork in some dimensions. Each gate in the circuit is a random 2-qubit Clifford gate.
The brickwork is defined as follows: The qubits are arranged as a lattice, and lattice_size contains side length in each dimension. For example, a chain of length five will have lattice_size = (5,), and a 5×5 lattice will have lattice_size = (5, 5).
In multi-dimensional cases, gate layers act alternatively along each direction. The nearest two layers along the same direction are offset by one qubit, forming a so-called brickwork. The boundary condition is chosen as open.
source
QuantumClifford.random_pauli — Function
A random Pauli operator on n qubits.
Use nophase=false to randomize the phase. Use realphase=false to get operators with phases including ±i.
Optionally, a "flip" probability p can be provided specified, in which case each bit is set to I with probability 1-p and to X or Y or Z with probability p. Useful for simulating unbiased Pauli noise.
See also random_pauli!
source
QuantumClifford.stabilizerplot — Function
A Makie.jl recipe for pictorial representation of a tableau.
Requires a Makie.jl backend to be loaded, e.g. using CairoMakie.
Alternatively, you can use the Plots.jl plotting ecosystem, e.g. using Plots; plot(S"XXX ZZZ").
Consult the documentation for more details on visualization options.
source
QuantumClifford.stabilizerplot_axis — Function
A Makie.jl recipe for pictorial representation of a tableau.
Requires a Makie.jl backend to be loaded, e.g. using CairoMakie.
Alternatively, you can use the Plots.jl plotting ecosystem, e.g. using Plots; plot(S"XXX ZZZ").
Consult the documentation for more details on visualization options.
source
QuantumClifford.random_brickwork_clifford_circuit — Method
Random brickwork Clifford circuit.
The connectivity of the random circuit is brickwork in some dimensions. Each gate in the circuit is a random 2-qubit Clifford gate.
The brickwork is defined as follows: The qubits are arranged as a lattice, and lattice_size contains side length in each dimension. For example, a chain of length five will have lattice_size = (5,), and a 5×5 lattice will have lattice_size = (5, 5).
In multi-dimensional cases, gate layers act alternatively along each direction. The nearest two layers along the same direction are offset by one qubit, forming a so-called brickwork. The boundary condition is chosen as open.
source
QuantumClifford.random_pauli — Function
A random Pauli operator on n qubits.
Use nophase=false to randomize the phase. Use realphase=false to get operators with phases including ±i.
Optionally, a "flip" probability p can be provided specified, in which case each bit is set to I with probability 1-p and to X or Y or Z with probability p. Useful for simulating unbiased Pauli noise.
See also random_pauli!
source
QuantumClifford.stabilizerplot — Function
A Makie.jl recipe for pictorial representation of a tableau.
Requires a Makie.jl backend to be loaded, e.g. using CairoMakie.
Alternatively, you can use the Plots.jl plotting ecosystem, e.g. using Plots; plot(S"XXX ZZZ").
Consult the documentation for more details on visualization options.
source
QuantumClifford.stabilizerplot_axis — Function
A Makie.jl recipe for pictorial representation of a tableau.
Requires a Makie.jl backend to be loaded, e.g. using CairoMakie.
Alternatively, you can use the Plots.jl plotting ecosystem, e.g. using Plots; plot(S"XXX ZZZ").
Consult the documentation for more details on visualization options.
source
QuantumClifford.xbit — Method
Extract as a new bit array the X part of the UInt array of packed qubits of a given Pauli operator.
source
QuantumClifford.zbit — Method
Extract as a new bit array the Z part of the UInt array of packed qubits of a given Pauli operator.
source
QuantumInterface.apply! — Function
In QuantumClifford the apply! function is used to apply any quantum operation to a stabilizer state, including unitary Clifford operations, Pauli measurements, and noise. Thus, this function may result in a random/stochastic result (e.g. with measurements or noise).
source
QuantumClifford.xbit — Method
Extract as a new bit array the X part of the UInt array of packed qubits of a given Pauli operator.
source
QuantumClifford.zbit — Method
Extract as a new bit array the Z part of the UInt array of packed qubits of a given Pauli operator.
source
QuantumInterface.apply! — Function
In QuantumClifford the apply! function is used to apply any quantum operation to a stabilizer state, including unitary Clifford operations, Pauli measurements, and noise. Thus, this function may result in a random/stochastic result (e.g. with measurements or noise).
source
QuantumInterface.embed — Method
Embed a Pauli operator in a larger Pauli operator.
julia> embed(5, 3, P"-Y")
 - __Y__
 
 julia> embed(5, (3,5), P"-YX")
-- __Y_X
source
QuantumInterface.entanglement_entropy — Function
Get bipartite entanglement entropy of a subsystem
Defined as entropy of the reduced density matrix.
It can be calculated with multiple different algorithms, the most performant one depending on the particular case.
Currently implemented are the :clip (clipped gauge), :graph (graph state), and :rref (Gaussian elimination) algorithms. Benchmark your particular case to choose the best one.
source
QuantumInterface.entanglement_entropy — Method
Get bipartite entanglement entropy by first converting the state to a graph and computing the rank of the adjacency matrix.
Based on "Entanglement in graph states and its applications".
source
QuantumInterface.expect — Method
expect(p::PauliOperator, st::AbstractStabilizer)
Compute the expectation value of a Pauli operator p on a stabilizer state st. This function will allocate a temporary copy of the stabilizer state st.
source
QuantumInterface.entanglement_entropy — Function
Get bipartite entanglement entropy of a subsystem
Defined as entropy of the reduced density matrix.
It can be calculated with multiple different algorithms, the most performant one depending on the particular case.
Currently implemented are the :clip (clipped gauge), :graph (graph state), and :rref (Gaussian elimination) algorithms. Benchmark your particular case to choose the best one.
source
QuantumInterface.entanglement_entropy — Method
Get bipartite entanglement entropy by first converting the state to a graph and computing the rank of the adjacency matrix.
Based on "Entanglement in graph states and its applications".
source
QuantumInterface.expect — Method
expect(p::PauliOperator, st::AbstractStabilizer)
Compute the expectation value of a Pauli operator p on a stabilizer state st. This function will allocate a temporary copy of the stabilizer state st.
source
QuantumInterface.project! — Method
project!(
     state::MixedStabilizer,
     pauli::PauliOperator;
     phases
@@ -611,25 +611,25 @@
 julia> project!(ms, P"IIY")[1]
 + X__
 + _Z_
-+ __Y
Similarly to project! on Stabilizer, this function has cubic complexity when the Pauli operator commutes with all rows of the tableau. Most of the time it is better to simply use MixedDestabilizer representation.
Unlike other project! methods, this one does not allow for keep_result=false, as the correct rank or anticommutation index can not be calculated without the expensive (cubic) canonicalization operation required by keep_result=true.
See the "Datastructure Choice" section in the documentation for more details.
See also: projectX!, projectY!, projectZ!.
source
QuantumInterface.reset_qubits! — Method
reset_qubits!(
++ __Y
Similarly to project! on Stabilizer, this function has cubic complexity when the Pauli operator commutes with all rows of the tableau. Most of the time it is better to simply use MixedDestabilizer representation.
Unlike other project! methods, this one does not allow for keep_result=false, as the correct rank or anticommutation index can not be calculated without the expensive (cubic) canonicalization operation required by keep_result=true.
See the "Datastructure Choice" section in the documentation for more details.
See also: projectX!, projectY!, projectZ!.
source
QuantumInterface.reset_qubits! — Method
reset_qubits!(
     s::Stabilizer,
     newstate,
     qubits;
     phases
 ) -> Union{PauliOperator, Stabilizer}
-
Reset a given set of qubits to be in the state newstate. These qubits are traced out first, which could lead to "nonlocal" changes in the tableau.
source
QuantumInterface.tensor — Function
Tensor product between operators or tableaux. 
Tensor product between CiffordOperators:
julia> tensor(CliffordOperator(sCNOT), CliffordOperator(sCNOT))
+
Reset a given set of qubits to be in the state newstate. These qubits are traced out first, which could lead to "nonlocal" changes in the tableau.
source
QuantumInterface.tensor — Function
Tensor product between operators or tableaux. 
Tensor product between CiffordOperators:
julia> tensor(CliffordOperator(sCNOT), CliffordOperator(sCNOT))
 X₁ ⟼ + XX__
 X₂ ⟼ + _X__
 X₃ ⟼ + __XX
@@ -656,7 +656,7 @@
 + XZ____
 - _Z____
 + ___XZ_
-- ____Z_
See also tensor_pow.
source
QuantumInterface.tensor_pow — Method
Repeated tensor product of an operators or a tableau.
For CliffordOperator:
julia> tensor_pow(CliffordOperator(sHadamard), 3)
 X₁ ⟼ + Z__
 X₂ ⟼ + _Z_
 X₃ ⟼ + __Z
@@ -678,21 +678,21 @@
 + ___XZ____
 + ____Z____
 + ______XZ_
-+ _______Z_
See also tensor.
source
QuantumInterface.traceout! — Method
traceout!(
     s::Union{MixedDestabilizer, MixedStabilizer},
     qubits;
     phases,
     rank
 ) -> Union{Tuple{Union{MixedDestabilizer, MixedStabilizer}, Int64}, MixedDestabilizer, MixedStabilizer}
-
source
Private API
Private Implementation Details
These functions are used internally by the library and might be drastically modified or deleted without warning or deprecation.
QuantumClifford.Tableau — Type
Internal Tableau type for storing a list of Pauli operators in a compact form. No special semantic meaning is attached to this type, it is just a convenient way to store a list of Pauli operators. E.g. it is not used to represent a stabilizer state, or a stabilizer group, or a Clifford circuit.
source
Base.hcat — Method
Horizontally concatenates tableaux.
julia> hcat(ghz(2), ghz(2))
+
source
Private API
Private Implementation Details
These functions are used internally by the library and might be drastically modified or deleted without warning or deprecation.
QuantumClifford.Tableau — Type
Internal Tableau type for storing a list of Pauli operators in a compact form. No special semantic meaning is attached to this type, it is just a convenient way to store a list of Pauli operators. E.g. it is not used to represent a stabilizer state, or a stabilizer group, or a Clifford circuit.
source
Base.hcat — Method
Horizontally concatenates tableaux.
julia> hcat(ghz(2), ghz(2))
 + XXXX
-+ ZZZZ
See also: vcat
source
Base.inv — Method
inv(
     c::CliffordOperator;
     phases
 ) -> CliffordOperator{QuantumClifford.Tableau{Vector{UInt8}, Matrix{UInt64}}}
@@ -710,28 +710,28 @@
 
 julia> inv(CliffordOperator(tHadamard))
 X₁ ⟼ + Z
-Z₁ ⟼ + X
source
Base.vcat — Method
Vertically concatenates tableaux.
julia> vcat(ghz(2), ghz(2))
+Z₁ ⟼ + X
source
Base.vcat — Method
Vertically concatenates tableaux.
julia> vcat(ghz(2), ghz(2))
 + XX
 + ZZ
 + XX
-+ ZZ
See also: hcat
source
QuantumClifford._remove_rowcol! — Method
Unexported low-level function that removes a row (by shifting all rows up as necessary)
Because MixedDestabilizer is not mutable we return a new MixedDestabilizer with the same (modified) xzs array.
Used on its own, this function will break invariants. Meant to be used with projectremove!.
source
QuantumClifford._rowmove! — Method
Unexported low-level function that moves row i to row j.
Used on its own, this function will break invariants. Meant to be used in _remove_rowcol!.
source
QuantumClifford.applynoise_branches — Function
Compute all possible new states after the application of the given noise model. Reports the probability of each one of them. Deterministic (as it reports all branches of potentially random processes), part of the Noise interface.
source
QuantumClifford.initZ! — Method
initZ!(frame::PauliFrame) -> PauliFrame
-
Inject random Z errors over all frames and qubits for the supplied PauliFrame with probability 0.5.
Calling this after initialization is essential for simulating any non-deterministic circuit. It is done automatically by most PauliFrame constructors.
source
QuantumClifford._remove_rowcol! — Method
Unexported low-level function that removes a row (by shifting all rows up as necessary)
Because MixedDestabilizer is not mutable we return a new MixedDestabilizer with the same (modified) xzs array.
Used on its own, this function will break invariants. Meant to be used with projectremove!.
source
QuantumClifford._rowmove! — Method
Unexported low-level function that moves row i to row j.
Used on its own, this function will break invariants. Meant to be used in _remove_rowcol!.
source
QuantumClifford.applynoise_branches — Function
Compute all possible new states after the application of the given noise model. Reports the probability of each one of them. Deterministic (as it reports all branches of potentially random processes), part of the Noise interface.
source
QuantumClifford.initZ! — Method
initZ!(frame::PauliFrame) -> PauliFrame
+
Inject random Z errors over all frames and qubits for the supplied PauliFrame with probability 0.5.
Calling this after initialization is essential for simulating any non-deterministic circuit. It is done automatically by most PauliFrame constructors.
source
QuantumClifford.make_sumtype_method — Function
``` julia> makesumtypemethod([sCNOT], :apply!, (:s,)) quote     function QuantumClifford.apply!(s, g::CompactifiedGate)         @cases g begin             sCNOT(q1, q2) => apply!(s, sCNOT(q1, q2))         end     end end
source
QuantumClifford.make_sumtype_method — Function
``` julia> makesumtypemethod([sCNOT], :apply!, (:s,)) quote     function QuantumClifford.apply!(s, g::CompactifiedGate)         @cases g begin             sCNOT(q1, q2) => apply!(s, sCNOT(q1, q2))         end     end end
source
QuantumClifford.projectremoverand! — Method
Unexported low-level function that projects a qubit and returns the result while making the tableau smaller by a qubit.
Because MixedDestabilizer is not mutable we return a new MixedDestabilizer with the same (modified) xzs array.
source
QuantumClifford.remove_column! — Method
Unexported low-level function that removes a column (by shifting all columns to the right of the target by one step to the left)
Because Tableau is not mutable we return a new Tableau with the same (modified) xzs array.
source
QuantumClifford.rowdecompose — Method
Decompose a Pauli $P$ in terms of stabilizer and destabilizer rows from a given tableaux.
For given tableaux of rows destabilizer rows $\{d_i\}$ and stabilizer rows $\{s_i\}$, there are boolean vectors $b$ and $c$ such that $P = i^p \prod_i d_i^{b_i} \prod_i s_i^{c_i}$.
This function returns p, b, c.
julia> s = MixedDestabilizer(ghz(2))
+end)
source
QuantumClifford.projectremoverand! — Method
Unexported low-level function that projects a qubit and returns the result while making the tableau smaller by a qubit.
Because MixedDestabilizer is not mutable we return a new MixedDestabilizer with the same (modified) xzs array.
source
QuantumClifford.remove_column! — Method
Unexported low-level function that removes a column (by shifting all columns to the right of the target by one step to the left)
Because Tableau is not mutable we return a new Tableau with the same (modified) xzs array.
source
QuantumClifford.rowdecompose — Method
Decompose a Pauli $P$ in terms of stabilizer and destabilizer rows from a given tableaux.
For given tableaux of rows destabilizer rows $\{d_i\}$ and stabilizer rows $\{s_i\}$, there are boolean vectors $b$ and $c$ such that $P = i^p \prod_i d_i^{b_i} \prod_i s_i^{c_i}$.
This function returns p, b, c.
julia> s = MixedDestabilizer(ghz(2))
 𝒟ℯ𝓈𝓉𝒶𝒷
 + Z_
 + _X
@@ -743,7 +743,7 @@
 (3, Bool[1, 0], Bool[1, 1])
 
 julia> im^3 * P"Z_" * P"XX" * P"ZZ"
-+ XY
source
QuantumClifford.to_cpu — Function
copies the memory content of the object to CPU
You can only use this function if CUDA.jl is imported
For more advanced users to_cpu(data, element_type) will reinterpret elements of data and converts them to element_type. For example based on your CPU architecture, if working with matrices of UInt32 is faster than UInt64, you can use to_cpu(data, UInt32)
julia> using QuantumClifford: to_cpu, to_gpu
++ XY
source
QuantumClifford.to_cpu — Function
copies the memory content of the object to CPU
You can only use this function if CUDA.jl is imported
For more advanced users to_cpu(data, element_type) will reinterpret elements of data and converts them to element_type. For example based on your CPU architecture, if working with matrices of UInt32 is faster than UInt64, you can use to_cpu(data, UInt32)
julia> using QuantumClifford: to_cpu, to_gpu
 
 julia> using CUDA # without this import, to_cpu, to_gpu are just function
 
@@ -766,7 +766,7 @@
 julia> pf_gpu = to_gpu(PauliFrame(1000, 2, 2));
 julia> circuit = [sMZ(1, 1), sHadamard(2), sMZ(2, 2)];
 julia> pftrajectories(pf_gpu, circuit);
-julia> measurements = to_cpu(pf_gpu.measurements);
See also: to_gpu
source
QuantumClifford.to_gpu — Function
copies the memory content of the object to GPU
You can only use this function if CUDA.jl is imported
For more advanced users to_gpu(data, element_type) will reinterpret elements of data and converts them to element_type. For example based on your GPU architecture, if working with matrices of UInt64 is faster than UInt32, you can use to_gpu(data, UInt64)
julia> using QuantumClifford: to_cpu, to_gpu
+julia> measurements = to_cpu(pf_gpu.measurements);
See also: to_gpu
source
QuantumClifford.to_gpu — Function
copies the memory content of the object to GPU
You can only use this function if CUDA.jl is imported
For more advanced users to_gpu(data, element_type) will reinterpret elements of data and converts them to element_type. For example based on your GPU architecture, if working with matrices of UInt64 is faster than UInt32, you can use to_gpu(data, UInt64)
julia> using QuantumClifford: to_cpu, to_gpu
 
 julia> using CUDA # without this import, to_cpu, to_gpu are just function
 
@@ -789,4 +789,4 @@
 julia> pf_gpu = to_gpu(PauliFrame(1000, 2, 2));
 julia> circuit = [sMZ(1, 1), sHadamard(2), sMZ(2, 2)];
 julia> pftrajectories(pf_gpu, circuit);
-julia> measurements = to_cpu(pf_gpu.measurements);
See also: to_cpu
source
+julia> measurements = to_cpu(pf_gpu.measurements);

See also: to_cpu

source
QuantumClifford.trusted_rank — Function

A "trusted" rank which returns rank(state) for Mixed[De]Stabilizer and length(state) for [De]Stabilizer.

source
QuantumClifford.zero! — Method

Zero-out a given row of a Tableau

source
QuantumClifford.zero! — Method

Zero-out the phases and single-qubit operators in a PauliOperator

source
QuantumClifford.@qubitop1 — Macro

Macro used to define single qubit symbolic gates and their qubit_kernel methods.

source
QuantumClifford.@qubitop2 — Macro

Macro used to define 2-qubit symbolic gates and their qubit_kernel methods.

source
QuantumClifford.@valbooldispatch — Macro

Turns f(Val(x)) into x ? f(Val(true)) : f(Val(false)) in order to avoid dynamic dispatch

See discourse discussion

source
diff --git a/dev/ECC_API/index.html b/dev/ECC_API/index.html index 815ce953a..1317bb64e 100644 --- a/dev/ECC_API/index.html +++ b/dev/ECC_API/index.html @@ -2,7 +2,7 @@ API · QuantumClifford.jl
GitHub

Full ECC API (autogenerated)

QuantumClifford.ECC.CSS — Type

An arbitrary CSS error correcting code defined by its X and Z checks.

julia> CSS([0 1 1 0; 1 1 0 0], [1 1 1 1]) |> parity_checks
 + _XX_
 + XX__
-+ ZZZZ
source
QuantumClifford.ECC.Concat — Type

Concat(c₁, c₂) is a code concatenation of two quantum codes (Knill and Laflamme, 1996).

The inner code c₁ and the outer code c₂. The construction is the following: replace each qubit in code c₂ with logical qubits encoded by code c₁. The resulting code will have n = n₁ × n₂ qubits and k = k₁ × k₂ logical qubits.

source
QuantumClifford.ECC.QuantumReedMuller — Type

The family of [[2ᵐ - 1, 1, 3]] CSS Quantum-Reed-Muller codes, as discovered by Steane in his 1999 paper (Steane, 1999).

Quantum codes are constructed from shortened Reed-Muller codes RM(1, m), by removing the first row and column of the generator matrix Gₘ. Similarly, we can define truncated dual codes RM(m - 2, m) using the generator matrix Hₘ (Anderson et al., 2014). The quantum Reed-Muller codes QRM(m) derived from RM(1, m) are CSS codes.

Given that the stabilizers of the quantum code are defined through the generator matrix of the classical code, the minimum distance of the quantum code corresponds to the minimum distance of the dual classical code, which is d = 3, thus it can correct any single qubit error. Since one stabilizer from the original and one from the dual code are removed in the truncation process, the code parameters are [[2ᵐ - 1, 1, 3]].

You might be interested in consulting (Anderson et al., 2014) and (Campbell et al., 2012) as well.

The ECC Zoo has an entry for this family.

source
QuantumClifford.ECC.ShorSyndromeECCSetup — Type

Configuration for ECC evaluators that simulate the Shor-style syndrome measurement (without a flag qubit).

The simulated circuit includes:

  • perfect noiseless encoding (encoding and its fault tolerance are not being studied here)
  • one round of "memory noise" after the encoding but before the syndrome measurement
  • perfect preparation of entangled ancillary qubits
  • noisy Shor-style syndrome measurement (only two-qubit gate noise)
  • noiseless "logical state measurement" (providing the comparison data when evaluating the decoder)

See also: CommutationCheckECCSetup, NaiveSyndromeECCSetup

source
QuantumClifford.ECC.Surface — Type

The planar surface code refers to the code (Kitaev, 2003) in a 2D lattice with open boundaries.

Illustration of a 3×2 surface code, where qubits are located on the edges:

|---1--(Z)--2---|---3---|
++ ZZZZ
source
QuantumClifford.ECC.Concat — Type

Concat(c₁, c₂) is a code concatenation of two quantum codes (Knill and Laflamme, 1996).

The inner code c₁ and the outer code c₂. The construction is the following: replace each qubit in code c₂ with logical qubits encoded by code c₁. The resulting code will have n = n₁ × n₂ qubits and k = k₁ × k₂ logical qubits.

source
QuantumClifford.ECC.QuantumReedMuller — Type

The family of [[2ᵐ - 1, 1, 3]] CSS Quantum-Reed-Muller codes, as discovered by Steane in his 1999 paper (Steane, 1999).

Quantum codes are constructed from shortened Reed-Muller codes RM(1, m), by removing the first row and column of the generator matrix Gₘ. Similarly, we can define truncated dual codes RM(m - 2, m) using the generator matrix Hₘ (Anderson et al., 2014). The quantum Reed-Muller codes QRM(m) derived from RM(1, m) are CSS codes.

Given that the stabilizers of the quantum code are defined through the generator matrix of the classical code, the minimum distance of the quantum code corresponds to the minimum distance of the dual classical code, which is d = 3, thus it can correct any single qubit error. Since one stabilizer from the original and one from the dual code are removed in the truncation process, the code parameters are [[2ᵐ - 1, 1, 3]].

You might be interested in consulting (Anderson et al., 2014) and (Campbell et al., 2012) as well.

The ECC Zoo has an entry for this family.

source
QuantumClifford.ECC.ShorSyndromeECCSetup — Type

Configuration for ECC evaluators that simulate the Shor-style syndrome measurement (without a flag qubit).

The simulated circuit includes:

  • perfect noiseless encoding (encoding and its fault tolerance are not being studied here)
  • one round of "memory noise" after the encoding but before the syndrome measurement
  • perfect preparation of entangled ancillary qubits
  • noisy Shor-style syndrome measurement (only two-qubit gate noise)
  • noiseless "logical state measurement" (providing the comparison data when evaluating the decoder)

See also: CommutationCheckECCSetup, NaiveSyndromeECCSetup

source
QuantumClifford.ECC.Surface — Type

The planar surface code refers to the code (Kitaev, 2003) in a 2D lattice with open boundaries.

Illustration of a 3×2 surface code, where qubits are located on the edges:

|---1--(Z)--2---|---3---|
 |  (X)  7       8       o
 |---4---|---5---|---6---|
 |       o       o       o
@@ -13,7 +13,7 @@
 + ZZ____Z_
 + _ZZ____Z
 + ___ZZ_Z_
-+ ____ZZ_Z

More information can be seen in (Fowler et al., 2012).

source
QuantumClifford.ECC.TableDecoder — Type

A simple look-up table decoder for error correcting codes.

The lookup table contains only weight=1 errors, thus it is small, but at best it provides only for distance=3 decoding.

The size of the lookup table would grow exponentially quickly for higher distances.

source
QuantumClifford.ECC.TableDecoder — Type

A simple look-up table decoder for error correcting codes.

The lookup table contains only weight=1 errors, thus it is small, but at best it provides only for distance=3 decoding.

The size of the lookup table would grow exponentially quickly for higher distances.

source
QuantumClifford.ECC.Toric — Type

The Toric code (Kitaev, 2003).

Illustration of a 2x2 toric code, where qubits are located on the edges:

|--1-(Z)-2--|
 | (X) 5     6
 |--3--|--4--|
 |     7     8
@@ -23,7 +23,7 @@
 + X_X___XX
 + ZZ__Z_Z_
 + ZZ___Z_Z
-+ __ZZZ_Z_
source
QuantumClifford.ECC.code_k — Method

The number of logical qubits in a code.

Note that when redundant rows exist in the parity check matrix, the number of logical qubits code_k(c) will be greater than code_n(c) - code_s(c), where the difference equals the redundancy.

source
QuantumClifford.ECC.code_s — Function

The number of stabilizer checks in a code. They might not be all linearly independent, thus code_s >= code_n-code_k. For the number of linearly independent checks you can use LinearAlgebra.rank.

source
QuantumClifford.ECC.evaluate_decoder — Method

Evaluate the performance of an error-correcting circuit.

This method requires you give the circuit that performs both syndrome measurements and (probably noiseless) logical state measurements. The faults matrix that translates an error vector into corresponding logical errors is necessary as well.

This is a relatively barebones method that assumes the user prepares necessary circuits, etc. It is a method that is used internally by more user-frienly methods providing automatic conversion of codes and noise models to the necessary noisy circuits.

source
QuantumClifford.ECC.faults_matrix — Method

Error-to-logical-observable map (a.k.a. fault matrix) of a code.

For a code with n physical qubits and k logical qubits this function returns a 2k × 2n binary matrix O such that O[i,j] is true if the logical observable of index i is flipped by the single physical qubit error of index j. Indexing is such that:

  • O[1:k,:] is the error-to-logical-X-observable map (logical X observable, i.e. triggered by logical Z errors)
  • O[k+1:2k,:] is the error-to-logical-Z-observable map
  • O[:,1:n] is the X-physical-error-to-logical-observable map
  • O[n+1:2n,:] is the Z-physical-error-to-logical-observable map

E.g. for k=1, n=10, then if O[2,5] is true, then the logical Z observable is flipped by a X₅ error; and if O[1,12] is true, then the logical X observable is flipped by a Z₂ error.

Of note is that there is a lot of freedom in choosing the logical operations! A logical operator multiplied by a stabilizer operator is still a logical operator. Similarly there is a different fault matrix for each choice of logical operators. But once the logical operators are picked, the fault matrix is fixed.

Below we show an example that uses the Shor code. While it is not the smallest code, it is a convenient choice to showcase the importance of the fault matrix when dealing with degenerate codes where a correction operation and an error do not need to be the same.

First, consider a single-qubit error, potential correction operations, and their effect on the Shor code:

julia> using QuantumClifford.ECC: faults_matrix, Shor9
++ __ZZZ_Z_
source
QuantumClifford.ECC.code_k — Method

The number of logical qubits in a code.

Note that when redundant rows exist in the parity check matrix, the number of logical qubits code_k(c) will be greater than code_n(c) - code_s(c), where the difference equals the redundancy.

source
QuantumClifford.ECC.code_s — Function

The number of stabilizer checks in a code. They might not be all linearly independent, thus code_s >= code_n-code_k. For the number of linearly independent checks you can use LinearAlgebra.rank.

source
QuantumClifford.ECC.evaluate_decoder — Method

Evaluate the performance of an error-correcting circuit.

This method requires you give the circuit that performs both syndrome measurements and (probably noiseless) logical state measurements. The faults matrix that translates an error vector into corresponding logical errors is necessary as well.

This is a relatively barebones method that assumes the user prepares necessary circuits, etc. It is a method that is used internally by more user-frienly methods providing automatic conversion of codes and noise models to the necessary noisy circuits.

source
QuantumClifford.ECC.faults_matrix — Method

Error-to-logical-observable map (a.k.a. fault matrix) of a code.

For a code with n physical qubits and k logical qubits this function returns a 2k × 2n binary matrix O such that O[i,j] is true if the logical observable of index i is flipped by the single physical qubit error of index j. Indexing is such that:

  • O[1:k,:] is the error-to-logical-X-observable map (logical X observable, i.e. triggered by logical Z errors)
  • O[k+1:2k,:] is the error-to-logical-Z-observable map
  • O[:,1:n] is the X-physical-error-to-logical-observable map
  • O[n+1:2n,:] is the Z-physical-error-to-logical-observable map

E.g. for k=1, n=10, then if O[2,5] is true, then the logical Z observable is flipped by a X₅ error; and if O[1,12] is true, then the logical X observable is flipped by a Z₂ error.

Of note is that there is a lot of freedom in choosing the logical operations! A logical operator multiplied by a stabilizer operator is still a logical operator. Similarly there is a different fault matrix for each choice of logical operators. But once the logical operators are picked, the fault matrix is fixed.

Below we show an example that uses the Shor code. While it is not the smallest code, it is a convenient choice to showcase the importance of the fault matrix when dealing with degenerate codes where a correction operation and an error do not need to be the same.

First, consider a single-qubit error, potential correction operations, and their effect on the Shor code:

julia> using QuantumClifford.ECC: faults_matrix, Shor9
 
 julia> state = MixedDestabilizer(Shor9())
 𝒟ℯ𝓈𝓉𝒶𝒷━━━━━
@@ -146,7 +146,7 @@
 julia> O * stab_to_gf2(bad_Z₆Z₉)
 2-element Vector{Int64}:
  1
- 0

While its use in this situation is rather contrived, the fault matrix is incredibly useful when running large scale simulations in which we want a separate fast error sampling process, (e.g. with Pauli frames) and a syndrome decoding process, without coupling between them. We just gather all our syndrome measurement and logical observables from the Pauli frame simulations, and then use them with the fault matrix in the syndrome decoding simulation.

source
QuantumClifford.ECC.isdegenerate — Function

Check if the code is degenerate with respect to a given set of error or with respect to all "up to d physical-qubit" errors (defaulting to d=1).

julia> using QuantumClifford.ECC
+ 0

While its use in this situation is rather contrived, the fault matrix is incredibly useful when running large scale simulations in which we want a separate fast error sampling process, (e.g. with Pauli frames) and a syndrome decoding process, without coupling between them. We just gather all our syndrome measurement and logical observables from the Pauli frame simulations, and then use them with the fault matrix in the syndrome decoding simulation.

source
QuantumClifford.ECC.isdegenerate — Function

Check if the code is degenerate with respect to a given set of error or with respect to all "up to d physical-qubit" errors (defaulting to d=1).

julia> using QuantumClifford.ECC
 
 julia> isdegenerate(Shor9(), [single_z(9,1), single_z(9,2)])
 true
@@ -158,7 +158,7 @@
 false
 
 julia> isdegenerate(Steane7(), 2)
-true
source
QuantumClifford.ECC.naive_encoding_circuit — Method

Encoding physical qubits into a larger logical code.

The initial physical qubits to be encoded have to be at indices n-k+1:n.

Encoding circuits are not fault-tolerant

Encoding circuits are not fault-tolerant, and thus should not be used in practice. Instead, you should measure the stabilizers of the code and the logical observables, thus projecting into the code space (which can be fault-tolerant).

The canonicalization operation performed on the code may permute the qubits (see canonicalize_gott!). That permutation is corrected for with SWAP gates by default (controlled by the undoperm keyword argument).

Based on (Cleve and Gottesman, 1997) and (Gottesman, 1997), however it seems the published algorithm has some errors. Consult the erratum, as well as the more recent (Grassl, 2002) and (Grassl, 2011), and be aware that this implementation also uses H instead of Z gates.

source
QuantumClifford.ECC.naive_syndrome_circuit — Function

Generate the non-fault-tolerant stabilizer measurement cicuit for a given code instance or parity check tableau.

Use the ancillary_index and bit_index arguments to offset where the corresponding part the circuit starts.

Returns the circuit, the number of ancillary qubits that were added, and a list of bit indices that will store the measurement results.

See also: shor_syndrome_circuit

source
QuantumClifford.ECC.shor_syndrome_circuit — Function

Generate the Shor fault-tolerant stabilizer measurement cicuit for a given code instance or parity check tableau.

Use the ancillary_index and bit_index arguments to offset where the corresponding part the circuit starts. Ancillary qubits

Returns:

  • The ancillary cat state preparation circuit.
  • The Shor syndrome measurement circuit.
  • The number of ancillary qubits that were added.
  • The list of bit indices that store the final measurement results.

See also: naive_syndrome_circuit

source

Implemented in an extension requiring Hecke.jl

QuantumCliffordHeckeExt.LPCode — Type
struct LPCode <: QuantumClifford.ECC.AbstractECC

Lifted product codes ((Panteleev and Kalachev, 2021), (Panteleev and Kalachev, Jun 2022))

A lifted product code is defined by the hypergraph product of a base matrices A and the conjugate of another base matrix B'. Here, the hypergraph product is taken over a group algebra, of which the base matrices are consisting.

The binary parity check matrix is obtained by applying repr to each element of the matrix resulted from the hypergraph product, which is mathematically a linear map from each group algebra element to a binary matrix.

Constructors

Multiple constructors are available:

  1. Two base matrices of group algebra elements.

  2. Two lifted codes, whose base matrices are for quantum code construction.

  3. Two base matrices of group elements, where each group element will be considered as a group algebra element by assigning a unit coefficient.

  4. Two base matrices of integers, where each integer represent the shift of a cyclic permutation. The order of the cyclic permutation should be specified.

Examples

A [[882, 24, d ≤ 24]] code from Appendix B of (Roffe et al., 2023). We use the 1st constructor to generate the code and check its length and dimension. During the construction, we do arithmetic operations to get the group algebra elements in base matrices A and B. Here x is the generator of the group algebra, i.e., offset-1 cyclic permutation, and GA(1) is the unit element.

julia> import Hecke: group_algebra, GF, abelian_group, gens; import LinearAlgebra: diagind;
+true
source
QuantumClifford.ECC.naive_encoding_circuit — Method

Encoding physical qubits into a larger logical code.

The initial physical qubits to be encoded have to be at indices n-k+1:n.

Encoding circuits are not fault-tolerant

Encoding circuits are not fault-tolerant, and thus should not be used in practice. Instead, you should measure the stabilizers of the code and the logical observables, thus projecting into the code space (which can be fault-tolerant).

The canonicalization operation performed on the code may permute the qubits (see canonicalize_gott!). That permutation is corrected for with SWAP gates by default (controlled by the undoperm keyword argument).

Based on (Cleve and Gottesman, 1997) and (Gottesman, 1997), however it seems the published algorithm has some errors. Consult the erratum, as well as the more recent (Grassl, 2002) and (Grassl, 2011), and be aware that this implementation also uses H instead of Z gates.

source
QuantumClifford.ECC.naive_syndrome_circuit — Function

Generate the non-fault-tolerant stabilizer measurement cicuit for a given code instance or parity check tableau.

Use the ancillary_index and bit_index arguments to offset where the corresponding part the circuit starts.

Returns the circuit, the number of ancillary qubits that were added, and a list of bit indices that will store the measurement results.

See also: shor_syndrome_circuit

source
QuantumClifford.ECC.shor_syndrome_circuit — Function

Generate the Shor fault-tolerant stabilizer measurement cicuit for a given code instance or parity check tableau.

Use the ancillary_index and bit_index arguments to offset where the corresponding part the circuit starts. Ancillary qubits

Returns:

  • The ancillary cat state preparation circuit.
  • The Shor syndrome measurement circuit.
  • The number of ancillary qubits that were added.
  • The list of bit indices that store the final measurement results.

See also: naive_syndrome_circuit

source

Implemented in an extension requiring Hecke.jl

QuantumCliffordHeckeExt.LPCode — Type
struct LPCode <: QuantumClifford.ECC.AbstractECC

Lifted product codes ((Panteleev and Kalachev, 2021), (Panteleev and Kalachev, Jun 2022))

A lifted product code is defined by the hypergraph product of a base matrices A and the conjugate of another base matrix B'. Here, the hypergraph product is taken over a group algebra, of which the base matrices are consisting.

The binary parity check matrix is obtained by applying repr to each element of the matrix resulted from the hypergraph product, which is mathematically a linear map from each group algebra element to a binary matrix.

Constructors

Multiple constructors are available:

  1. Two base matrices of group algebra elements.

  2. Two lifted codes, whose base matrices are for quantum code construction.

  3. Two base matrices of group elements, where each group element will be considered as a group algebra element by assigning a unit coefficient.

  4. Two base matrices of integers, where each integer represent the shift of a cyclic permutation. The order of the cyclic permutation should be specified.

Examples

A [[882, 24, d ≤ 24]] code from Appendix B of (Roffe et al., 2023). We use the 1st constructor to generate the code and check its length and dimension. During the construction, we do arithmetic operations to get the group algebra elements in base matrices A and B. Here x is the generator of the group algebra, i.e., offset-1 cyclic permutation, and GA(1) is the unit element.

julia> import Hecke: group_algebra, GF, abelian_group, gens; import LinearAlgebra: diagind;
 
 julia> l = 63; GA = group_algebra(GF(2), abelian_group(l)); x = gens(GA)[];
 
@@ -184,7 +184,7 @@
 julia> c2 = LPCode(base_matrix, l .- base_matrix', l);
 
 julia> code_n(c2), code_k(c2)
-(175, 19)

Code subfamilies and convenience constructors for them

  • When the base matrices of the LPCode are 1×1, the code is called a two-block group-algebra code two_block_group_algebra_codes.
  • When the base matrices of the LPCode are 1×1 and their elements are sums of cyclic permutations, the code is called a generalized bicycle code generalized_bicycle_codes.
  • When the two matrices are adjoint to each other, the code is called a bicycle code bicycle_codes.

The representation function

We use the default representation function Hecke.representation_matrix to convert a GF(2)-group algebra element to a binary matrix. The default representation, provided by Hecke, is the permutation representation.

We also accept a custom representation function as detailed in LiftedCode.

See also: LiftedCode, two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes.

  • A::Union{LinearAlgebra.Adjoint{<:Hecke.GroupAlgebraElem, <:Matrix{<:Hecke.GroupAlgebraElem}}, Matrix{<:Hecke.GroupAlgebraElem}}: the first base matrix of the code, whose elements are in a group algebra.

  • B::Union{LinearAlgebra.Adjoint{<:Hecke.GroupAlgebraElem, <:Matrix{<:Hecke.GroupAlgebraElem}}, Matrix{<:Hecke.GroupAlgebraElem}}: the second base matrix of the code, whose elements are in the same group algebra as A.

  • GA::Hecke.GroupAlgebra: the group algebra for which elements in A and B are from.

  • repr::Function: a function that converts a group algebra element to a binary matrix; default to be the permutation representation for GF(2)-algebra.

source
QuantumCliffordHeckeExt.LiftedCode — Type
struct LiftedCode <: QuantumClifford.ECC.ClassicalCode

Classical codes lifted over a group algebra, used for lifted product code construction ((Panteleev and Kalachev, 2021), (Panteleev and Kalachev, Jun 2022))

The parity-check matrix is constructed by applying repr to each element of A, which is mathematically a linear map from a group algebra element to a binary matrix. The size of the parity check matrix will enlarged with each element of A being inflated into a matrix. The procedure is called a lift (Panteleev and Kalachev, Jun 2022).

Constructors

A lifted code can be constructed via the following approaches:

  1. A matrix of group algebra elements.

  2. A matrix of group elements, where a group element will be considered as a group algebra element by assigning a unit coefficient.

  3. A matrix of integers, where each integer represent the shift of a cyclic permutation. The order of the cyclic permutation should be specified.

The default GA is the group algebra of A[1, 1], the default representation repr is the permutation representation.

The representation function repr

We use the default representation function Hecke.representation_matrix to convert a GF(2)-group algebra element to a binary matrix. The default representation, provided by Hecke, is the permutation representation.

We also accept a custom representation function (the repr field of the constructor). Whatever the representation, the matrix elements need to be convertible to Integers (e.g. permit lift(ZZ, ...)). Such a customization would be useful to reduce the number of bits required by the code construction.

For example, if we use a D4 group for lifting, our default representation will be 8×8 permutation matrices, where 8 is the group's order. However, we can find a 4×4 matrix representation for the group, e.g. by using the typical 2×2 representation and converting it into binary representation by replacing "1" with the Pauli I, and "-1" with the Pauli X matrix.

See also: LPCode.

  • A::Union{LinearAlgebra.Adjoint{<:Hecke.GroupAlgebraElem, <:Matrix{<:Hecke.GroupAlgebraElem}}, Matrix{<:Hecke.GroupAlgebraElem}}: the base matrix of the code, whose elements are in a group algebra.

  • GA::Hecke.GroupAlgebra: the group algebra for which elements in A are from.

  • repr::Function: a function that converts a group algebra element to a binary matrix; default to be the permutation representation for GF(2)-algebra.

source
QuantumCliffordHeckeExt.LiftedCode — Method

LiftedCode constructor using the default GF(2) representation (coefficients converted to a permutation matrix by representation_matrix provided by Hecke).

source
QuantumClifford.ECC.generalized_bicycle_codes — Method

Generalized bicycle codes, which are a special case of 2GBA codes (and therefore of lifted product codes). Here the group is chosen as the cyclic group of order l, and the base matrices a and b are the sum of the group algebra elements corresponding to the shifts a_shifts and b_shifts.

See also: two_block_group_algebra_codes, bicycle_codes.

A [[254, 28, 14 ≤ d ≤ 20]] code from (A1) in Appendix B of (Panteleev and Kalachev, 2021).

julia> c = generalized_bicycle_codes([0, 15, 20, 28, 66], [0, 58, 59, 100, 121], 127);
+(175, 19)

Code subfamilies and convenience constructors for them

  • When the base matrices of the LPCode are 1×1, the code is called a two-block group-algebra code two_block_group_algebra_codes.
  • When the base matrices of the LPCode are 1×1 and their elements are sums of cyclic permutations, the code is called a generalized bicycle code generalized_bicycle_codes.
  • When the two matrices are adjoint to each other, the code is called a bicycle code bicycle_codes.

The representation function

We use the default representation function Hecke.representation_matrix to convert a GF(2)-group algebra element to a binary matrix. The default representation, provided by Hecke, is the permutation representation.

We also accept a custom representation function as detailed in LiftedCode.

See also: LiftedCode, two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes.

  • A::Union{LinearAlgebra.Adjoint{<:Hecke.GroupAlgebraElem, <:Matrix{<:Hecke.GroupAlgebraElem}}, Matrix{<:Hecke.GroupAlgebraElem}}: the first base matrix of the code, whose elements are in a group algebra.

  • B::Union{LinearAlgebra.Adjoint{<:Hecke.GroupAlgebraElem, <:Matrix{<:Hecke.GroupAlgebraElem}}, Matrix{<:Hecke.GroupAlgebraElem}}: the second base matrix of the code, whose elements are in the same group algebra as A.

  • GA::Hecke.GroupAlgebra: the group algebra for which elements in A and B are from.

  • repr::Function: a function that converts a group algebra element to a binary matrix; default to be the permutation representation for GF(2)-algebra.

source
QuantumCliffordHeckeExt.LiftedCode — Type
struct LiftedCode <: QuantumClifford.ECC.ClassicalCode

Classical codes lifted over a group algebra, used for lifted product code construction ((Panteleev and Kalachev, 2021), (Panteleev and Kalachev, Jun 2022))

The parity-check matrix is constructed by applying repr to each element of A, which is mathematically a linear map from a group algebra element to a binary matrix. The size of the parity check matrix will enlarged with each element of A being inflated into a matrix. The procedure is called a lift (Panteleev and Kalachev, Jun 2022).

Constructors

A lifted code can be constructed via the following approaches:

  1. A matrix of group algebra elements.

  2. A matrix of group elements, where a group element will be considered as a group algebra element by assigning a unit coefficient.

  3. A matrix of integers, where each integer represent the shift of a cyclic permutation. The order of the cyclic permutation should be specified.

The default GA is the group algebra of A[1, 1], the default representation repr is the permutation representation.

The representation function repr

We use the default representation function Hecke.representation_matrix to convert a GF(2)-group algebra element to a binary matrix. The default representation, provided by Hecke, is the permutation representation.

We also accept a custom representation function (the repr field of the constructor). Whatever the representation, the matrix elements need to be convertible to Integers (e.g. permit lift(ZZ, ...)). Such a customization would be useful to reduce the number of bits required by the code construction.

For example, if we use a D4 group for lifting, our default representation will be 8×8 permutation matrices, where 8 is the group's order. However, we can find a 4×4 matrix representation for the group, e.g. by using the typical 2×2 representation and converting it into binary representation by replacing "1" with the Pauli I, and "-1" with the Pauli X matrix.

See also: LPCode.

  • A::Union{LinearAlgebra.Adjoint{<:Hecke.GroupAlgebraElem, <:Matrix{<:Hecke.GroupAlgebraElem}}, Matrix{<:Hecke.GroupAlgebraElem}}: the base matrix of the code, whose elements are in a group algebra.

  • GA::Hecke.GroupAlgebra: the group algebra for which elements in A are from.

  • repr::Function: a function that converts a group algebra element to a binary matrix; default to be the permutation representation for GF(2)-algebra.

source
QuantumCliffordHeckeExt.LiftedCode — Method

LiftedCode constructor using the default GF(2) representation (coefficients converted to a permutation matrix by representation_matrix provided by Hecke).

source
QuantumClifford.ECC.generalized_bicycle_codes — Method

Generalized bicycle codes, which are a special case of 2GBA codes (and therefore of lifted product codes). Here the group is chosen as the cyclic group of order l, and the base matrices a and b are the sum of the group algebra elements corresponding to the shifts a_shifts and b_shifts.

See also: two_block_group_algebra_codes, bicycle_codes.

A [[254, 28, 14 ≤ d ≤ 20]] code from (A1) in Appendix B of (Panteleev and Kalachev, 2021).

julia> c = generalized_bicycle_codes([0, 15, 20, 28, 66], [0, 58, 59, 100, 121], 127);
 
 julia> code_n(c), code_k(c)
-(254, 28)
source
+(254, 28)source
QuantumClifford.ECC.two_block_group_algebra_codes — Method

Two-block group algebra (2GBA) codes, which are a special case of lifted product codes from two group algebra elements a and b, used as 1x1 base matrices.

See also: LPCode, generalized_bicycle_codes, bicycle_codes

source
QuantumCliffordHeckeExt.group_algebra_conj — Method

Compute the conjugate of a group algebra element. The conjugate is defined by inversing elements in the associated group.

source
diff --git a/dev/ECC_evaluating/10d3268d.png b/dev/ECC_evaluating/10d3268d.png deleted file mode 100644 index ed92ee8946067aba365ea59e8140f061cdde1b69..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 42911 zcmeFZcTiN@_Ac6z6@gY%l$=D#C@4q<5hUlFMRF90O;k`&1e72-OO8s;!GMC2lPDk= z8YDM4+_5~rbF1#HSFh^*|N5NTdv1F6Tr-aGjqe+Cy--t;BRfNV28BYA$={dJK%ofA zP$>Lh5ZjV{SAG#fXxZk<#)?ULN!IrL>%CU%$3!tU#Lm z3@>~3`UNgQk_!Y}UX1B#FJFeHa~9>1w3QHJS1?>0_1Kck>l_>;^dx68Ni?KZ$}7~+ z3byRe-d1hB+lk#fy0LWlML@oP>nqN?d6&iSX0&L6=qBI9_wSoFtn%lfBPi5-R;35w zztWHtBLPylcJKfH_x~{uvvz;apd^EgYh5kpyHcolO&Yw`r*KQdccrE4JpPW>d#;|Q zWUHyES>R5NiK+0}aoSr?mkN4L!7x6ByC@wh=ChqF=A+~9J8bOfjve^MF=#_>KUBod z%NxhgohC6+7u#Fzcd$)Jdg*JVbyxD-)H+*>*Z%x6p_Pr!V^n)<^re z&!0bUOnYz64LZ*J$gQZ@+U%ByV<09VP)ZYT{5(EdHz2Yce3}w^Ww6Sjvux+F@;f0a zidmwne`WT20{_AG-)II3XmOz@W2l(oj}a@Xj3FT*AyVSFCL|=JmAu%xJ2lO3TVGi@ z922W5aipdHC&4=Pz0MB?|6TKJY8Yvi&aK3|^&Wp6wohW5oAzY$f3ZZ0KIr0rS<%wD zBJS(;c({i)BO^m0wxhGtaHE*lw5g~87kCQaV57KLvGJq-&Y0(1(Sy$=Y;0^_#_QuQ za_U@Xm}EHF4XG@|7ozGyX#lUESfw^IiJ&!Zy^t#i$-N0%?@TbSp7~R&HxqSy^Z(NwJR4VqbP}FhPpS zwYY#I+_1X3dZg$^Xl%jhgV%|P23lII!8YGG`Felv8k|bcAPGh-f6Uj+t#bIuEaCC! zkvw8kdQr6#ADg!bD~fzyJpUX3m3jdh8x?S zMFsM+z%VF6$mulbC;WECumabE7X}N5-*OvDOG|fjbOfX2<>g`C*<^Ku0*()BAI~>5 zG%zzWW9b4X5BE0n^Ye#GO`ZF5l)b!a_Mh|Iv$UM8v>%>nA0Hn-K0cNXU0zrLCFSqb)cFe+1Z;ZJF`Akh8hy|$BO@c2XlobE z0r&N(&+p#7o0^(xX=#xPBHG*AODNZY4{Vjgn!6$7PEJl6)1#xKg}S93kz>Dq!zN2F z(oj=VGce$gaQao{Sg2E6P*|v_pfGd3SZ8T=*0RfRI5s+(l7YcgU;k&WY8t&5Mqumd z40OLUj@Pu#ja@=Q;`;ULLPA2UtTI`>dOBBvzT0Mpo8D6%n|p?ql9DPZDZ!R9^6{ya z-hs1u&;Jh=TW~0&p`-IQEsa-V8;5)@O0%-EzRSs}avH<51fKf)tJ+!Zvr;tcB6hIQ z*47pl0cNzdwbi)Z!`;)f)bsPk#>U4Giuu`D_vMjCa852AHZjWg!KUcz?=LJY6!BaU z^;$E_))u@EgNNDF*Vm7v7b7}**{q8LCgt?$)85|R{{H@c`&+Q}!WL&sO&T$C-xJ!} z+IWoXwpPaK$Ng@Lh#bIjLB(Q&$}?nS;h~{?V-1}h9TD_miAhN`unNArE|05%?iiMi z``3(no=T31T{R~_Z8mI=+AFl6tSoUX#y;iVX`VqzebT;%`htSLdA5U^mTn#&r_+pD{I^fRe6`&XBRVpdfVM zC#JpC#Kc5ZbY14rqxY@V_vPi)DU$PgZ8Ed69zTApe3m2n^=m$uHk@HiZSChzpNwi; zGR9Q}Z2MR(ijifIY#dY#F-E`c>9yvTN}Gr31zNhhS4#tq?7TVsH(tdXHUIehiakA8{@4L_%VIeEbs@QDbaizp+qdklT)Dy``-*Q{7@wG&i<486_v9mmM7+?_`Sa&L zI8TT-R)>a%#|AhJ^SjR6$Nj{|ajZ6MM!cuwg|k6SPRn6u2M?H|)+I-JbnIF=zTjo-M=h^Uw{uDe3*1C^rHYC0@s&9h6Oq%} zEbG!dTP)R%dY7#jm$>@})?#pQu%j>^e-eD>*^-T|e$_($$oG;@5D8GICHYcLvWnf?+jdO$go+cd$cokg>syusvL~vybjh{PWImN`p$aq$#ram~0 z2{+EhaT{7q&5SSfX7S&=InWsw7dPRv+DOEiHU1SVIg(y%ts-$Yod=Hzb?`bqK2Mz7 z#oaySw&N(Y13MyL{8gc%UrdhpaSx~W!QbjZd$G;${8;O;u`xI@`8%8kBC8EqT&3dZ zD|}{w`;6Z{J^6Z)P7d8y2}L$6q?^w!_CH1kadE1JzJ;MM9pS4*0T z9vvUoBJjH z*Z`Sb94Qe2!Pe5S>gs$3g~Xwn_bqout%1fFFC2ET0~UJH(77?&{~7$#ed^N-te*>5 z+Z>5RrPb=wu$h9)l}-m|XJ=z6M!+>K_U9Jz-f(~PNWJ9UYt}_L-dO%ggW@XPQWGp@ ze|MMl+BMG36W9RQok1G`G0av^{gB^ig)KI6t%I|4VQ|PyHIqD;Y!ver_YsA_g)c!A z;(9whQsVC}-*y<8j+AJ!?0g#)b-uB33(s6jOUu{S*WDclkA*#-7lWXI4h}fd+6?ks z#&ufaXL#A!_cqf`iejp5`(@?rvH0io)5QJg0rET}rAn-6PwE864*}rP~mNCtfjSeVRKwd zi)4Rn9BaO5v;RgL0t>DdMX_pYYv&6-z0;mggr7l(EIyW~jUnJr{j~8|z2~q<{oq&0 z>%nU~I}>&8_E6W~{}|w2oyR)53I#QdKmgq3eTX=M1UQRe8+G(N63}2!p?# zz6mc{Rz@aS=#g}8zj2-0VwcFOR)^2lLPoOMt&x#4XU@cEF2NLP;*AUz>c-Ax^xCL^ zrQLu0cjWzD??(V3cgB560lgO$EthwT_tz(>pAN=Ouw3FX%JZFp?^M|%U%XI<*^5{i z_gRg7?0@gxvwecG2Jg+8XPg`y;MZd|0RKO^26*1aKPp_?Ec_?8TAAmIChnZ?KFE5A*Jq0>ECF!XC#nTZ z!mf(@`%9NSO~kWA!ym@Hqy$++h6i1hM~J+I8EN>!w(w+RHnX6N9(&Lg@f3XRE>#L0616ES~X2yvIqBwlq8D# z)$Ip$KD(xxs->`{vV7s_GCl&U}rUsm0e8C_*nCbq7``Ijka>@ zZkgIV8ZX58&nN%c{l$5chrLZmCR|y?`8GpaG2*Gf>Yozd7t2F-V7#S9}?6|O359m2= zf8PbCblc*~EA@`SCq2J@8K(Hy+u1qQOcKrhENwnE;1L`d8TUVM%w7XWsiiAFX1h@N zy3VQo?`_M;VG|$aqk;O>ro!<+1xBrsTO?=C4%Fkc{1_^eKMee6vS^RMcJe4FD8%qK zf+=v#*rz@&F|NlNyOwrk0@RKpHTA=3XRmGla@OTdL(FtQAwk=7Co$4}b5s=TjYs^b z`pN0(O@I>ZpFeZMHvH4_gh=jvVNsFqQgJmi3rk@^0ao1Smt%E4F~6FrShkW1WAI45 zXX(Z+Z@^yIco>&SgPwPT^F&kKY9F|2Fd~B@=Ggylkp`jxu z^>Pe;16xbU5& zIZ3`@@!S{tXCPk_tN}K6W>Q zXg=Hs+vlsUsv7!Gr{AMM^RtYUloYlX04c7MTK^-AMfG3(A{Z}rhUIvq#sA>1V3;Wc zwm&vJ-vA6qV=Km9PPMF@r4@34)h=z?w*#y7g7O*|-bcG@lZ`$*bF;JToyh=T zi>t>m+dr*wLxVKS>V8#n%6B+32kiirZ>4H)yh2OgG0(0Jypxp&K+Vu9_5j%ksVnvWw7fJGQsbox^~{Xut4J8&dM0>Z32V=CNCCK-#PxON)hpVYp4!*2D}bL-`KzM4=gNjXK2cC z-y@Zp%QS|s&@(J$dNu!W0s^|ZAw($LgD{1ydAliR39Eg`I%5!YZi*HG$;k;^No z(<(ezjH#VIThdqOzEr2lhP_Hmsl+e^z?L)14NKVe_3Kwa_unETY45nsd_5;0H6x)+ zD^yhm=qsE?&It5>ywX5BG!+$_FJGQ%e6%(oM~~SgzO5xG*#gJ}NRws=ntmh+ zE*YQG1<&~4^BD#P23(^c2Dabf(b24T<6wC(O_q4|>x2Y-&nI8j2jEw z#63xA6*>E3pxCgQ-@1#0iBLi zr-zL1txDgTrDTtkdv*D}%cL|VPSCL}_;kS0lId*wYV%2xZ-hN;RT$pcNoY8hfz+vK z&&opcK}8v?7l*CO)fb-F$LX>Z_vE4HF#O4qmrnw-Fik?7DqvV~)QA{leNnOCnaZQcTtkQiGlT=qphu8aGod*lFvAKZN8he|g+b3wmFcq%3Ke{DO ziUjGO?{j5GMn;PMa!0z<1ZZ&u2pgT!%yH^7xF_|PwbMVrhHWpc4p60Dxp3~>x%20l zC3IvT#o(JuN(TCB0cTT?ockeV>E58+AmA9?wBNfc^{dn;`-PaCt+6k=PxRvHBZ>N~@&cRbo5|g0gn=$fyPG`>SbdXM0+#0sJ!bl)wVEb!}dP z*c8_2BJgh=;@2n0@>XOad`hQ(2#Cqyd;ASo!JCigl)M|RxEo^TQ#`kLD7}Eaja96H zNQb*L)0cqh)5dJ)pr8x=9oKg&ug+yIR>2zSIR|Q@Y*39S8^BaIxz2V>z!3rh6F{j5 zW@};UbJ*Zxjpl=u`i+-tZ1jA$$^8us5;4oK?>wG+mz%2?l9R?|ix5g|Z3 z3sp;qh=`8YK2iW^g6MN;s92Mtbst+;%HfQf{RT4BEHoYpeCE;z1|514Ba` zA1~VpBtm~VdENiCoSJ=5-qWMj|G2*sOK$UMYe9W4AHcwZnEUaeH?EGY$FpGgKb zl17R67FeVj6U&$-t!HSgeBF{ky+`qfhX}2dBAng72(0D+<V;BqGlc3Xt*2FxrvA#QQ{@V6%;=w_HaB00=`hqdY6n%6i%XZ6}3G$dfLciGv4 zboVtAJfy`W|3!h{&%Q}bEqTaataAVk;oB^>+!qe=eFcRm*2U3E``+GO1;if~449^L z0}4od{hHBqqHu*rfcnQ1eBv2xWG>>ERTFN`etJQ9=gu8~_Obh(1R04QnGl&h^}ihW zNfaXcP)z2X{{5ZRQraUuG|5$YgDQuFar+@U6Ib9=J2o!Sh8i{b>WeKuDJ-B}*Uq(X?NZ8yXr4tO@|A z{6)MB-$yx#t>+Ztc#I8JFY#R_$$nm~L8@~D3KCz8;c=Fli0o9#edQrDntBr`|(lIU4kZr;>zmbDG~@ZrNi`OBq*o0ba5w%G%FloT)J zwDzYJ>4{Gmgp-3QK~f|)oPG=8N{_MH<6hHb7HKMlgC%{z)tbg0u_O?!1U4nqEMx$Yi9;1T|XQkOiizjNi z{rR~jY5`|vQ&q*VwFj>V+v4Ld2TlJ}f?Wj$2j_JC+wSoGw`*yaiw66$6=Svf!30@u z7T`}pa7O0z{$ALn{CP3Kp%GBYlwUCo0NO+bvDsTVhU}&C|hAtN>2? zKgA1{Tm9%uQuBwkawjHxTj?}raMbYu2(g||Ee60-IGdYiVD>;=0&6y43~Ghu6$+)p z8|d3MOXo;Vb)o^(C4hp1d@E-6$laYz!rvDV=J>{2Lg}AyFd#@BY<~*Kxq8ea$@NWa z+Z6sA&=i25T`<0JHJF5gB4D*~M?q2Xhc8`<$_}`Z=OH1S^I|i#bGMy-+qmq(s^q5m z8}LrMul(LKJ=q85PfPa}2ZzEPjEARZ00d>Q+;Bj18=j7HAWXwVB~U(VYw@@2hXAR4 zpOA@SWsg=}@OuGKDApDqHU@FyMdg44M4sF~)Qcu=170CF6{B$Fr04Tz%f5H=z@+`? z>e7*$p?I;Ikda>IO%0y*7Uc4qkKk*w#i)C;aZ!KFjfC5}FDeNpPU0K;Nq85guQ0 zP0h&R9U=}64glQL{5@B(Ah<;XDoRMWf=0s*8wIVXZaDDP3t+LprfOK?pTpe#ze$~eVB3j!sQZS$f#kYYf`m{XwGC4VU zU_gtCDsFAfg};>LM|ZcXvT|`z(OGhGFaqUw;x1IZ`~CZOVj{JvscBestu1)RZ{NNF z-Ul455i*}+38Bu)bHBZfSqOy)2?&BiLXsBFA`WEscCU4+w=DfHHmJ?d-#TcHPF&-sP?OpO5-&v&Oa0~m#$fw+(TdnFhR(IiBr%Ya%ieWVr;G{X!+;MLgJ zI2&n&*#m?H4M7Byp3b;QjIxg^CPv77wMdvw9{mpw0eXOzOF=?{=vaUdt=2~G`~+(0 zEp(KDVRd?%^5R9rv)-OyVnmII1U*5cdLB3|SsSzrU7(_xaO+nFE*|kJAR|W5-r4At zW1s^85;hc3fH^=S(`(9!7cO0@^4;42RoHXf+Zy--;B9Vr=n_E^gV{X->6RF<4!r#Q zj{%Zy&{030`wm(`3k)5Yu12%gr*)mYhE?B(hj-#k{onA$FAkSZ6zP{EXL{{62HI$; zi;t)0n}tV$p9fJ|Q(ZY-Za6-b!~W)Q@lnRcrPLsFEDG;Ky( zs>4K+81P7+@F3jK%vFi)2QO!)r1VNOZ4gv8Hl=uoc!%RXB_NmpF~<{(Tz9~+rWjQM zv!I|Z$>jWeE{{WhPPj^LXLq;rcSHQZtc~q$@?$z!QUiKx5_1Ny&ElZCBC3;#1E79T zaL!48Pm>6k?TFpTPKE!h{af`5Ji`2sB+sc&r*Rwi?%e~Tg~-%yAWyv`Hj|K$5Vn;` zy@w-=8=^Z=AV-4=zp9s2RA?FN0kaltlasIna~1f75#2V_xHp#sz!PMn39!6MyzKIQ z5WF}u$vk{G^YS8RjF2D<1(+%O)~AH)>+A2|zpwu78umc}9J!WOOsg&@FYnIQ7VtxW zhS}J1YHD^XhfNGCY~C2zfUf@qpv0?Y|IayeEc%#eYQ*a2jtV+Kcyvt#;gQi=e zD{l2YK7rr*3=?3*G%yZeWu~T>gY`Z<{Du#sotHS-Tg*-C`u-hpG_+`ROVJiQuuPdi zS||c^TT-T{K|y5VoN;lnv9oh?)Jm`15u=zDRANwBuu|^I_#F&nSJzusd7k83_B!h7 zy_%|GI6xL8OklJ@!$pFde&>h&l90t!_R6&eFYg@5q!4h~!Rzayu^UrU5BTvj($Y*D zjdMkJ(nmq5IsVELnJntvH!+b`PYlau)=3iVLJQVU8k{^uP&dacnED^al%S0;-F+V4 z+^{&po+dG)D|UURHTrvP=|z>NY^THoPLnXX3IEeU6yKsKFKZD++@;4G81Z@+8ymZU z@9DYowvZC+Ko|>In=dk0onnI*!kcZJF_b~y&rzUIwDGL+h-;4`V!$jgEe#Rhj*uj2 z@2!1o%_L)GmD6esdTB5kl02-&B}t%{o~-g101@IKsqb}%&|?;0C{<3eX46RTfr^n1 zh0qIJ*s$L=7&qzAvNAsJ=ZFC#w%{YPtE64~cwv;7wmnZhD;O=DvI4n07*+WwR;rFp zs3UZ_kCE#x<&){lki&#*?kNa|2Yonh-`)l#RvKWp4d=jF6e|7B8zS=?2B&F5bPA0d zyxyaylAN1<0#eX0QBy0k>1Ae;k&*dC=lR>bav!Ev0KbosI>?)3QVsN^8sPjuXab)L z6!8u4%IxfmKmi@TrB?_B?9I9b5(aX zH|<*!;S>q*_Aw>~%SN%<51$HTrw*4TX)QT(4}+;gGqbXO8ol_WI9*gVz;!ZL zu2Yn|r;)Q=b}gAkhB9*uiYSjDfzX_L{m7q}@omw{5kvS;961H;;*&woP-X5g3d&J5 z6wUhY2ib@Vz|c@F9&dmRZ{y4@H!r47Chtx){>h?GS;`w^Gr_QFkD< zMRPybL2?sE(0z;s=gCN+Sa$K9R0ZGYB`BIvLc`tyyijb}zaLa~#^5sYSIc)&dZgj7 zRH!nxKE|R@55y1Zk=de$?r9>uED91JDa@)wo~9#79n78HiWIrS1xRS5l8_1p7i`g0 zK~}_2tf1{N| zRx;3V785dzAJ3p+IYT6~GLaA(j+{g0M?kEPaT$*rNx`&v01cB;Uxi{%3^dGA0T>XK z{_Qo9xv5Pe6ear^$=X(Wgpr2XpvPjFPmqSg?@c|PWhNlSw{Y4@dNq(C zkwVv2ZHk~2c=dje3#vjFis`LTJS(7&6wRS{xxxS`o`NE)fDsg1jNVBJT^{9uqS>WB zMp}v=R8Y)gutk%=z4 z!?#_q2-j_Ppya~*PD(O72U$^TDQbeP9^{n%xo|&7(s&vEhH~+JC)L8ZjdVjusE^U? zY&}w>y<&^zd-89Gl7|V9#DD2R>bA>J6JS3dBSm5;esASL>dM`P;wKZN7$ObD_J8x! z4iBRa_Cxj;`BMQBfeZD>{-Ql)i!MX?AUk529*Sp0P9sGcC|*AJSG;VCwmIu@5&k;D z*~i#(f0-MKWs2{l($`1Kp=cHWU5_?PgU1D?Fp=RYKN~})dpj7O!L&__{EiHMS25y^ zRAxXbTbv-3=@`lIempTo9$ggyl_|HGk;(#4*>~g(Qn?-~mp?FtnM4jN-jDDxq(@bu z0wfiv?dwQoI2}DVNAi)%hEO@oycwxX2HoI(VT_#CDi~@7-!`(DMhKwt#z-qt*$?KJ zW27A^!f9Pg<|U8~mVKF2 z^NUnSGo zqFoG@=izTEU|ogyJ=~!<56hKI>mvfckA@zYg}@rR!2F}0A};Mu@ckgv!{zP3+LvKr z#l|pKi6~oi;8QV%y!OvwR9RVBM~8>Letsb807#BYO0svD1c*jfG@ar(Zu{*FKFSOa z>L(Ufa-v2mAYl!NtNgOEHNZ>Dkbw)VvpBGupas)Q`2X(gEL_=u&_mRFV+PQGv5`@X z^l=;^YJ{YZ5heD222M9_+>j21pyBLgJ~POg0;FM5W+pW@3xE$)BzVwn_eGSMJ@g)% zNs3as<9}Ea8QEQ7+aD7JfK!!6u*TQb)wMfSZ12DI&Q6_WTK*0y0wk9m|9;&4EI2q` zkL$*bM-Y4hE#B1B6huUpDD)^3s8&K}Dmpqb?~RAyvRN_7BAzNFlS@nXE_;BRLAOVe ze4%APN_U^1O}OotxWAzehXJ;1;00PC(jQp&aNiw>oPc2jA(b9*5UALgZmgRys3P)F5JEs+Ii#l=YG~Ya7%794 za3(&!o+-iD>Ff0z7eI8DCh2c}(URZ8nl4u=|C*@vJ%Lg>Z=l#u2)CuBpS~c3^xs^S z6pq|h$Xkq$j|XUenhD{%%-ezi7JX?rfN%hEKN}&s3pn0PbMJ>-RWY$f;FTcKhseIp zYyAP>-{xanX_j21_})x(xVI?^#U)EkU`8GHs!cp5HrDTWZyu95MZ|f$ z!Mh`dok$lV5OyA(?TwA7(sP4$l>om7K%RkI%jXc7fBN__>j?ujDo_?qLmt%=bkz#v zpBO=IHRvNc+S-;FdHJa0qtyUXCScffi}W%+)xtQNa6^Wqm$*Vf-GRUY^ynCEh?TN3 zGtV{|K*~mLZZ3MNC*v+`J4pF2ZQLHsycaej9aLdZ48Jg$gzkd0&1+PHK6lRiOFJPd z-4;$@e2~hiD$pz~pvSlzDJB_T-v-~|Pw-PC0HQAoW(eE>p}vQG1){OLIrIme2`Msj{$^l!;3&5!ZIPC_bLte; z?AC)&-S;U95N9mID;hzSRd&b@hVd1|y|ERb)@7L?G=UsG$o>Nn>05FyHIf4jDX+fk zpQ#k&Aq@?kz-;YAH)_-GBlr>+%!^e+h67KKoQ{qa1w2)v($PQ{{ z5(^=tVKc2`myg0wpYFfyJiffTda}P%x)cl9pjMFnCmnixbTAJYiVq*c&QeMiT7ORC zq*vo&Zfm>v^$iPfapS(5KOlqYcy~I|stEu@IBRaJ`_j<2fGC(oS;pY$8es9z%tAsV zf686G|D_a^Bt%O>V$|&XJSh{zGTJ-(chGb23~TGoX(1mkFNd)@Tn5A?Q!lQ~SU!FF z6u3o!M^iEoo2f{~mOdv8M#HflD#3FgRmMBhDBuNoJBP3@nq6mKy4w@By!~(3hIS8e zf5Sct>uyCPEg{j2v0nZL;^fIs5LH2MG=j`{$S?(cii_*}VL7;J0ogGD=&oxQ86ICa zgiuTr6Av6bh_f3YiKN#4JT>yMJKo5#$fadZaHYoBobS0C?c%y|{U%mm7Z@BE@<5mq z-hacljz4LT`p2yct}HQaJU%m-hQLf5bLL+FcbW+ZU^4N-b4Lg7Kcq zDi54q0E&-Kyau^ofNld4N9p> z;n6d<@KNdV;G6_53X=`XUADsw|+?&qoCYFnPed{nRsBY@u!uuo6h0+?5n19())&a5z`GGGE!VR{@=ya`47 zj4Y%GaTba*vlJ;(Lvbk+0nKIPNZqVT>L-5Bd`VMZQR%^L zCMa|lS}|jSShJ_k(R%0IjDG#4G8#8M=+Ijji3@5=ABtq)=l)z?K*&|<=P)Sqp2x_b z03Y36Ig0le3?bC}_cH_t&Ot1?z2{wT#|JOjjp1F*| z%^beKL2wljT!9-s(t8-`QOvfzX!f_RW#|S46HJd7#H1p|qh54ILLBuq8inU1^y+Vx zS-L%hALc-inmc;nwY9WRkDD|fDj{*8_JiXZs1BPdB76l9B@zyzLgXR=QJNu8jz1lV z!g~OR|6yGihBl4?$+md+AOZQI1k}xyUWK}A63{}|b8=*#AaE>Kh5>-0B>d{#!W=vR z*$yrSTMz}d?NnY zxEMx%Z*zOCWo=trr-)*i1Xx;>5EX>3FIZm?PF%&*);8?fztq@W-Yq-I-&n zy0}DCFNtgi6^O6om~&fWiTk!XCiZVt7U*~`5r=qmMY2-13DikIU$~Hv`b%FrI<9eV1O zdbGZreRxy1_{#_$HItoNUyvzV#lvDV&jsRM0$|_3ea3O=-*oz20}gNEQ9GUMp024M zq~bmpt2+hL6@0hOL_Jzp$2cqc6*uE)bv=_5U7f+G%BN%IYF7l{{!$xo?$c9KF#zvQ za3Y)Y-KF{YdpkfAgN$#G?*UOVtQ3lpB-kbfzMOFFI(xHF;`~gD>nBjVN6(l_K z^KZUyrw85}(hKH`b(Q~N`!=hKZ*@&e^WHGnS0M5=MS5d;_u~ApICFOBL&v z&p{f;KLP$H+-lJ;w>r&a;=eZw3ip!MInn0EIQJ|mEsTlRnaWY_pwBQd*Y8WXS=^t-k`l|Mk#r*ZCTP&op^)|s7P@`~4-$yr z-X$msMFj;IV8sm^V4fi!33e<&9<4mEw`%bCExylW*-?7Y_rgj@- ze*+p{+fUI;GkwaaI9wOQ=PKn%MvXCZdG4;6Gs!?=sKtW^ueh@Y?U0L-OrL<_Gbpiw z#$}=LsQy21`}L(mD-LgFH&hf<$zHn{qdT$R%CyO!k(T>Qm*VWY+pWPe(^NG5&q_xN z?AZ{xZjw%r80ATB*z_>=he2dO!UWQrL8b}{l`BUb{KLSH)h`VD$;_B=c5qWLHA*RE z^C0L~8-DenZG3LwQ1>PUOOTuMJa@2{xAg9W(_c$l%SkR^Xy0ybZ(ou&YQzj~J@^OM zDJUY}=24%=dg2o6c@Jdwst4U(M^Mgfg*0@Z-Yg2>DVY|&-b`SZc&%bwC9U% zeV-yDuRl|bTv{wRM?o>aA~g^xNz#d1oiHVN1nFQPLxCQ7+0X&v80paQMxSaU2=7&1 z2#^@+XlEJv35;#syc$~xOBfPTaZ3Ug&WVCzKwe{AO#6oglL* zJv|+KGQ?e%lLGxA%z@;{3(~(Kw~yOU1Qqxg3|fNiE$RSg!C4@v=CX=gTtTA(&7mFQOD5=VtOx0l5-GHS$sKbKTL)CQwCb`;tZyKNlx^Wg`zUeFySFaQ_zLrf*ORGfT|$=z-%welM|o>fHzw1EPH+1_!lO3 zCYIVzGV5IQzFW`0oq1gYZJ&8;mXF4UfzRRO!V&C$0cs}s2a^j|idYI;b11ugZ(o&Q_owO6!HHP`*`EQ6VQKP2#tXSp3|yI~4{OcHvTC zwNf!yZ14yogW2K3C2}lTZFnnmBl_%Hu8+N0Z*EQd5Dh2?Nr$p55{C4hQEJFxeW4nW zqdT;a*i`3&m&_DA3koe!V;ZuY zm}Fpczy&aK2Son`U9n1S7PdHayWPbi?zW(ZtwmQKusW;b!Z`G(!0=4Ld_< z3(B5O@qcDuQp>I2fY4&!Q#8R_j4A8uNL#AYXp&C_&B)Kvdj&*tcNv3cAz1*{ySKKy z*C+iH%H})}!jXUHT?_2pJ^fsj*u9V6mfdQ9g~XTlDp!nD78~(JZUy}P6G#$VW(1ZN zqEfZh2OwL6NJ)D7^y0t^|1+o_Go%$q>&H2M9z~6j^>u5VlnEd`+=QDd=oOyP>Rj2H z`ZCRy^A$7#^=SdecW&O?fcupd9`_)~0B|_Zl-t@tJvQ4W@ro)j(UeU-N;V5}qc%3R zBxWZI+&z2!`K`YipOfM?&=o>=p)=n@oPuQO!Yy35@mbfcqooC+wk(Od)c#b6pNyt5D;d|mO zMU^1XZ614iHe+xF=uFUnAUy$ewv9AM20VrvXW&7KjC4_fM}RC~v>9H--7b7anc zTWL?(JaDTlGlJYPNcCfthiuw_nKyEf$QO)8f=u)j+ysRCssCj0Ke4(d=cFNd#jx@N z3Pl5y=R;SvhDzN((H6&i??0J-@nGn0gpl@!42yhDi58L4uX;~sH@6DWr#6rz1aQJ# zcr0Bi2tv`T!8Y)puvHu#i_yq8@MeVQ*h2fXnF+$5+8Os%RjH(dgM;+|%U|>uW4#~r zqqQW7z%44qyKw{jg~GRFntC_e>3qjeXSZk-TL}EEB(q*!;hzJN2zieIIfM8z7RwRb zV^?VkoD6bL1@g<1lWA*b;PkPQ;i0x(6FsS`pjIwRo1buAvi$q9MIU_5k4(s(fveWS z0mr_OdI5~r@8*C2`{Az<>xJ}NYriD6Mr@-Q$!;@YwO{8lheR(+>{spVXefKM&@WS`6a`)~MK+1r_)gPP^;^>*D6L zZpj7huL0X0Foue5=eg%7u>JSvbI&aAA1u)F(S32787U9$#j-0wb4 zv%M8kUR9E`f!w>Ajfxnly_rEdminrrwVtclYp&+C)k&R(n#_q<<3P673d*wIi~YF= z@V14ywv*j<2@_b3xuS@V5Atjl%q6`S-XF0^Q9GDdO|TYO_U9Mw6pN@E7uwIRXc%a7 zQtf-yyww`=s<9L7x+1*yob7AyBH^rHsi@bD=I>+oG_?y)CU&N7j2VhkB6{uugz}R7 z$dp{SRU^rG2ZmhUG8~=xK~~W3$2x<5r_)S5@{Kx@!EszJ=>F|3f4DDI`f134=kokW zCJ32HNwsD5^*-e~L@2W$0O@p8u8Ok)HcHyXJkvWgq}(2rHO!?&9a}f^_bhJ-e~Udh zZB7I3Az7yo2Z<&gpkUkv!S2`kIKc6M&Eyh(1oHkTa5#e_yyzwkJ6`DYnQ z2pQ>HaCq3=Lad;!M{2<0wo4c+kTeos_iVv~*(;+S3g@1N&`2X(rSH~?Z2e2>l*P^0 z!tz=}3k77x%4hTlk3jA~R8~|Ol^a0Of2vJOM2`smKh-AK@eHX=rI$msB!lMN--MOh zyPYE|DMt;|o3h>Et9RaorM)2hZ6r|ce3qVSsN}{fo&b}u4Ln@{o~{o@%9u01N#}vx zVRz9~M}YzRNO$=SXSch=X*Heq*e>Oj#FD?e^qcllPrT=;M6{p4|1b$Pp1C+W`o8Ue zfXj*N=5C%Ry4SXEpAcS^pNY}pH~}Co9qL2mfpPLxrL-s9uL;=cQJYH+{A(5i#Qs0J zL0m$$nlAEev)|yGtT<9>fOfNS-)0+s9VB9fYuTu-vYxy5*`7Hk|Ej)~U9qhW)~+(v(lO_!rRS!- z?XdAu?q96OBjq28I*HVF&uys_J!j94OM&f_K4^la;mym$IyqhX8&O2}X0pZ-STcW|U8SDN)Tpi5FqRq-A^*uY z1{YZhk0ycnuPP?^CzJ|h{Ae#dyLfqK(aJ$$b>cY3_zIy8=V=?Jh*7>VW6v=h(B+|D zA#JL#FxPQ$06u$zarul?0K`wjfFkq3o^`kqIlsy?JxP>igw$kRb+f*muZ2vV6Fa48^V# z`|J)B>Jo^OsH;rqHaE!of%}ow?x0pL!Orw@5wqtMd4Yqpw)8 z(PguncuY!E=gz%{8=q_{E0A1y4{VYiwJqA~u~(e&72QpRFzTfAbNQO~P4PYLiQ1>Q zr5J-3A(41eU7(eT`WP9Ri+>xhF4Fq)74}MAXQm5kV8N%UNyRfu6N-SdO#{@K z@M`$WRCm?+{b`dG9_GH>l#_^j{2*V^A`>bzW^txq@4P`Q$N+G!0X}bIVq|1x;hjmf zpdf+%R>ebx>VbTLmKL9^%)+Gsj#%HCr6Q-b&#iP6#$2Ooxxerl#~k%&dW;C9<6D6~ zw(3sx+nA9LdISy(5+nB@T@F%3%jL~Mr3S8(Y=4bnjMILQ&fvtu&c-M=o#MFX$MdVF za@0X8F&st_=jarktc6H`kf1F%H8(c|5>{WI#@Ky$kqEr(XZXE^oZ*E$g8!$TtLFqe zSNM9wc|J+rQ!GL`S@%F#%vBD8x6mN(lR_Z5zP>jAP{YRG zF0OQc5861)S0Mi%O6m9&2z-%Ly5iy#p+{4Y(n+1X2}y*AbV?m=1vENjftI^I>u9OR z@U{4y@R_|Zek!ogBc#xRY9x5|=PP;tRaREG&jQLKq?Q)FzXMt7YmlwQ!wj29hl>nl zCJehvh=P2DZw&IAWgfztc>vpHgO|PKeuh2E~hX*|J*saIyl{5 z;hEZ_LWCOOM}AL3zRqV17o$RHMZJ1<1^xzuZl|Bch6>CFB=IL$sNb%a?$r$r!{BA*B>t zJcR8P>IwhZP=WnZRg^YwKqdv@)#~BHP`IS5_@C<^)zzM0Otw>lN7n(DZl2EgR-+|w z)%(l{ji zD127OBU-p>7MxT}8Ym4W?ikV#tKe`3=D=P=1#8Ooo)0+qH31O>sBDgq36ky&^M>Lk zKjKR%Ep;|FhMTXw5R*GXDn~jpr6{_HW4g@sFy==?S{)oIBUg%U(o@$#R{n|#n9vc5a8lK|LOf@BzQIL+W(|F;S<_2BmS zel*CR@F_B71#JLAmb}PcDlKl1O}YdW9_6)e$g+g9`IbxW{r{fW4wzUs4%(|`fnbBn z&ZCqwbqe7&zfE&#X;;gp^fL zz}&pNrTd%k9vQKKfD>>z`S5NP<~~5naGfjwP%FHNDY#OR_zxf?X#atB;38aHI1q$u zFc6sJ7Zp{wbH9y(EPOh;V&xzM&)<*aU~M43Vo9~Ds|(pD|Est+56ALt+eR;v3{i;6 zkSLM4lCcoCCMlI9LljA784}?x$`mC;l&KYU*EBD$^(X^z1z!_MNluN}xUvT&K?c1TDKZb_*IXHG$)`@^t${~w8qzGBk zYzSBjz>l#8>SM2f<{Y%w5fZ=Odku|@V3OhrJv4_b3$X?6O^fzoC?Zsa6 zICjt_PkUa2Iz>!K=p5SfLCaqQA%y?hQ{&>(UeXX2Lo~#@-E6<391fWH*)w3hgYNMa zyFB1F=w91RjKia&#ROscHRX-}0S;}M6Q#S7>WpwBw9v5Y#g%wXe)Gl8qiYQtfvH-M zJd?dFA7fkFjJDvqd)mj3?*Q-j?OO^PdhMh!6&5Epg=f#7lVVxKXj7A3t!yD$%A~sh z{MhiVt5>hGeBLS|vO0uHC1y)OO*xRJyOxWKn@)qs1U<@xtDEV=M6A?Q)m7%akeplZ zaxY#Q`}^qfjW3x;-ZjGzvTW;~LodRc;tU10L${)t-v^-_zSRN8Vi0 zSS}nhJJ5dgjj~c_cklR{9m{44dt&27`m3ee5WXyfMfRvH%Wd=J&c0=+&D{>)JA6A9 z{Fc1DmdQgwd;dZO5m14^Tq~jfD9{nyfAAwBWo-axjsT{>@tWv<5U-IN@m$Hl9zE5_ z22J{DbZ+rWjcEoaRaV1pBw+v1qakx9h&jN(JO!J#5|L~m?=jnOKTSDdrxc!~665kO z%I~J(Md@$NG*=EY2%WLJ(F+c?@#U`YEr&PASlqr~pm1d}^G_|s8SaDN3Q)|-Z?3ns zEpC0m@7|w<2i;It_x9bpz7?-QE&u>XZ~W=gr!;J0f`Vu9lL&@%TSNEdHT1Q~<2Rdu zK$0pTxk$)F*RO95o1!T(Lrx*?c~ENI^L~5h2YFeH)1TJ{>tD2Qj9u~S)f4XMW%68P zeuRx>ey(Hw`KT_Jg#PF)uNn2}zYuC|IefpV=_3?zR$ec`En?XKM}u2|fvvDku?@a^ z@bPxP;3@3r*ucO*7=>j?-&6_?q`(Rsb^2bO2t!~DkatWr7}&ka%L~}Q==Fz1(Y#=*_*&4It@Vs=r-fAI8jfg8`fO^h)pyiER3|;!-mcg0xAFwT)O4U*LMWW)mw2t z+|9$aIs_PrK?LD`<~BXQ$7l@@pdCs|t+^*kf5{)zgUGE>FCuR((g00?)@AZs`5H5LNB&L|0fzO`LZl7eGLQT zahGEiG4~J&)9BdPZtPV2bHgig@@kk}?gfrFum-g~NPy$qv^UH~AEP55xcz0KNGuEO zuV;VWw<<3Gw=VW?e~I6DTVWP81-)G+dDu`5==@CKIq;d3rd>o$NSN5IhhvVU&cW-pmRVt1V zx+POIwI1+N0zyhdLqp!9e#$3gb2yMrP!KX^y>57b!a-i4bC7Ndl8N}JSS3L%{O0LR z)o80#ke^F#E%?ek8_iuOVBfc6*-J)&FdrehL}>KZhCt5OHhDq@M~=84)TmibyHRX$ zhCt~d=i0o^h6WoG*fn?4=?HNkj(VkjJ+eG81)n~A>MH7yo%-SNW*NOR!y#7}YOHW$ zCp95c{f!e89vmT^ohC?sUs#av@#DUlEk|v=pU~3!0Z!Ey%G=4^U7yY(`-Wrd zt5>hci)8RYx>4O8sd-8LGGV_FJ5{CNvcgTv3g??%JV;}v5f9FxOXQKYj`V}g&36R0 zwe{gMXTE`BM%gSW`T5Hj_Qa3(6^>KTnkF^zZLY{7fjCkgLAsA+o9(ooFgXn{hT4^R zzr+cVbp?beiW!VyAohOhW$KUg06fiKzkb29bLw%#>1S#Ou(g0D2S+y8KY`)(k)!}Z zS5t*e3d#E;U*C7AST4j9@?fkJB?&s^Lw+plNP|ic8;?>8|q0d@-Wm>Nhbv1txL zhKnXiOV}i`(O@3A^seaXf8DW=i;D{SuHqj=H_hAeqNAhmp-9q|Ph}l1Z^6Z`gDYlT zwcSnK=5*pi!^4HXUTjg2*~aorvxLZ}TUo7H!aysa{~JXWqWd4@&VA@SsI)-tg+&Y- zpK|e5QFuxmIKUQy_?|(GZ!8y4-kqlYGg^1>&zY+PXxhKm+*_oD{H$?t*h}O*R}d6?DPFutrmi z$XsEYD@g=z-numzhkbT8gv0oXezAeD*CtoOgN>^b*27`J83uN>F-iy6R|@h`2`POB{;D@all1F4tLrFySHpR@?WmquDwK4_2b| zyTzxZ3tjGf4TO7Gr+$71A3t-uK$y6bKe&6->I4l^Oa{XUIKgtq{(}D(&}{uA(o~uJ zi3boYI_2c#pjd{h1vW%JSTrOhork;*jy;)Y-oWt}V!w(0=1`dL4h_XdMYY7MuP|t2 zCUns;AevO}3PmEV{)SyhG~5!q0NLb)3LI60#v@Q-Nl**LIry<8G>ub%g-5n2Pmjo4 z`0xUm+e@8b(kXZmM+*EGk0@=26DM1Z=LKzwj%Yn3?+~o1fDnOBMr+F9MM77}(M($S(6cU7I-;_68 zr?9DFBgqRvjT*o(Awbu;l6-9MUb8Q+z3%H9xF4p@b0*;OQpjQ^kL}2jBW%csGi{v- z6C3g!-<%1*){D-+3!4JOiP%+~yipi)g+L?TvljwbK|xZZSkFvHLQJ#-FB>!Gp+*!w z@Iwr&K*Ye%6Jo6z5AzsZ`NqLSmvha)}l%l6DFsWE9}qo1>HVfTexy z2*a7J;9}ql*$Pf*vckY@MsT0-vm2=8{@iCVV}$}l!Sm9n;T9L z)W=N+uu|fL7<{C?!S*C=vSDltFR~QdVLU0QqOnysq1lr&q)9_POU6lM$(QR~H5M{R z!EOZvxcyE}!YWpp^@Tod7?mG3!$ERcgZ`Q(N=J}9D`JgzJ+s6JV(3TxN#nHSWQR+a zhTz>Zr;Zvrz~7%O1d*gNTCILRmsNE=`MibB(0G%cBkf-E9&Ds5xQoj;cIYvFcrG|0 z-Ng9{);ti9Ok|ln;f#bi2_lNDv|4xQ1=1C)^A#Ya8|CMsu4Var8GSa;GDQUqUfAZ4 zE5)2#DI=LTOPz4n1W|mgZsTL%k%2iZn}Wl4pYTdrf*D{IvBp1qWulmb1ZN0OyQ%i{ zKxsmPpj90m!9`*cBAkKiNeogz5axz*o~4m6U2zW^TfNvmJFXSJjDOp2)itouUm3Z~l(sW6n0HtJ$7usPru3!H*J$?TCd8DBh zD+&vCI@A66FD^g<`Mx+mTElyrbVS2vhEgM`erD&+`R@ldWMky_T0xupKaPv>mzkwk zaU@?s!h;Uq_3>#RXJ=;;MSwy};JLXC z2mp{MKu!39(A=e`S^ysdWu&NRWy5k>)xYGL`s}UB@E4gk*dq9Pj@^{RO$qApGuM|9 zoyFvmIRA#+xe?0?X%>$0zc__YLqQI!7R&FBV02@lN^9z_AS9qsA>;)>K8c6JJ>Vw6 zFB!%vZ11b8V&&{kbHu_sob<VOYP_^A5b1^s#i7<}|t7#K_YHeCLRj%WeS zA_*N%;_GU>GaX zuz=Tnx`yy1!$Q?}Y*k{QpC1&(2hcS48-OFS$?Dt0pLILHW zcHk1%vxn3H#{yIeGj|PaAzp})K64E=w_|ohNiX@ps*}E0$mFKe1Y-k)f#EP5{eT4H zMus1JoT73bRUD+ts`wAiKNOObpU9WsssbyAudr4^Yx?QwoF6rFzFkK+6+w;{BrO#T z)_!*li=uA^7-zJIJif`emKl$|fq$24CL$T>rJXcOKm`c`0+9g2?E<7UEg{eu>>h72 z6}$*%g1&mDlHRR55q;I{;y%)C$jd2axIE;{dlLb@`BxyXbl!yHcumO7n=6^uG7$6R zVHvmQ>2+zNQ>X6v0e9w(g-%*P5OVpv5K?u#9|{Jc)MeCpGODZB-Bpj2gp&*foA~)% zEpS&kP60LDc@vr!jl1~>aq{s~*`C6a9Xfwtov=wjmWh-jkG}f~JQo1HtPWYhe??pA zBFq>E2KwPIrwf#@1lnL4LONK3Es=TEs`hVmOgvTUykL>#1#@xo!8y#7B=d@7_I&oey*#obGsJ zz18u{`1C$F>^QX!w8nCUGyl2U+~3ahoRNW{2YCvV_twCaySsd_`l)x}M{pn1tf~h} zCyyN?aS(V07(^^9A?0?2h2-4>k)=qKvCFqW&JHjba%LFANz2I8AuUGM?9QP^WI~)s z5L-+hQ#3tb#)nFZq%eT*Hd>`6B_Yv<&1E+h7Ir#l>6)>3W>^A4VPg`woo~ZQdT*L^{wKF&MEcpE_%4Nm zqr^Sw4A@jcK>{a8K#R$q+-uk%l!p`oQ#o`ffb`Cc(b9%%h?Cr_q)q@3r|` zCZ<|M9Rxf_(sYjih$Sr#Qd4(C4&w!;6-;4ipa>!5S~kZvqYX&D`RT8|s}te-KMlJx zKuzd|0ByohSZPomPMXLoURXC@#O{aSxEm3%5A8fy z*UQSf0QVu8Gig?IolWH3(*xn#JnmRB@Ff+`8CQd~w5nGZzR$`mN|bn#ft)GQpo1)) z+%rrrU=5i=e57t`n|`6{0k$9fiBATrh~*2nb2*)wj5^3%2<{72aHH92w+-0?`B|J- zGt{gE+sFZ~(HE+^lzo6{LyK%+`FUqsmE5#@?w>K4MzNFiDMz}D8fTxYo1_v_mmCY_ z<8<(rZ;(b^oI|hPRy6h z&uV9+o~yU}+N$x`@|)GNgQRw$iTTUMI1`na&-~A405|G;4F{^PeXc25D{0(1`O_xG zHgP^nYIo#Vf1dGf&v_=hdDksNZYMtHR33RZwuOT>=u9{yk;|9f!^^%o9$jq3oV{MV z@*f?ec*=*%x%~T+8<8{Nk{Dc-5}A^yyDcp)CdSoh$XMXb4%T z9>NA%>+Z9r6?*J44EosH-e6~QFql!Q==*+`L;1w2#=S=vPb63B6!S+xI6dsQ@y6_4R&&mQk0R3B_dE=Fvo=sO_2n#QwY07wLH$IA zOr`{v5ka+Cc&X5Umn?YM&Gu`ke%jp2Zenk-`jcY^C~=oMh6#?-1*UPAZfSdMda=#P z;ixm~I4-QpXYGpnG@4RGNei&?bEWskw~Paj5U?>%d~SlSyAv zxV>9>ejiWW8KIf_D{}NZWVd6>2|Z4TW@T+9Q@U3;+i!ETn>2Vcvtln@)bRH`${UW1 z=9f+0|7N6?m-A=mw=$aZCA2Gv%neZ7-jC_``p|u=U0;QR-Yq|Hf5$L&;P?tlFWJ)8 zO?gEQc5B%jod31;O}pg(+$6I{FTLk+3ysP`E#qF5f z38eY>6r&?HI1p3n`jH+5-w=V^mk(Whrne_kE@E8f=y2EoY)QES`VcdDLGitUwP?zu1+&7&Vmq+KHbbOu8 z8!u|^s0}KdD*wVY_U9WFr(&VF`V!W(PcOq$^v5zHGCsArOzGJsyO^0d zMZY`yW`&EzK*F(m4(bb&h6r2iG(t5NW-T{N11F6AE_BD9(23_8wRiTPcI~(we6?eD zeMjIS3mvyT&DBT7FTcwFJ=f=7p~A5PEQZr#?;`!T4SakS{#$Wulh~~pS4EYXEmCba z?mX92R*4*=6dPa-L?2>^T>egpC_y~LZ{`jv$P^f;_2{nW);c!6v&|Ju9P9};Nq^so zE9sm{%{_D7<#05;RJcxzgh(xahgbZQ!)ceTwMI_9kI*k7|Iiz;U~6U1$0@oGF6S7^ zdCKR%Je+pQMWpXuPI1c4sJnIy#0LeU1ePpo%s=PW#ttfF%%0j*EW~7#*W{u&e=jGw zLF%JGm~Opgt%)he@46`AqJzy|MNh8txJ^aZfiGj>)llV;7aPG>8I?b9i1`JrDrPkh zoA!HaM)92He;M+$3+bI3HTXQU3 z9)6W0rXAKyBMz&EFN&o+x$yo5fs+GCbw*AY`BrWi(R0DoHcdGU($gecivme{uYDiR;p9q#;~VRm3C;l*)#}w4sR5vju1ed~`UP%yn~6 zSy1t<;MuJh_(OYH8ip3@yazx@^z zOqWbK_hb4{FpJ$c-G!SC5L*7;ACK3%M}G5s?{heB7H6C3=x3*sS+%se@idsv7wk5a z+g(2&^SN~5l3l9Y)2ZXdE;wHYu6SxsnpMErg2jI)xIE8t{l9=#Ia?<@ZW#%!VIPMb2~YicL?35TsSdMxv6=dB$w5Evq1H9 z*UR8?yBmWdPct=j>gtR#Ql>xL?HH7kKc_m~erC>mewCj7iTsV*{$4rrYCLw<_Eqm6 z&u^8J9cEgi?9wnh0N?Aov`M?}Etw|-o!Wl`Ja<+RpGooqHPp0z1!nPKt0Kf_7HmyO zDV)!uMFI#CUHrs-SmY2yPc;oeLL*65JFy zf?y)EVj?JB0DBdgy%3vv7ztIlQ{cDcTWASwQqD=d6i@_F7qn_H7MY@!#T}@#bVhlV zmP$lH`vz&S-yHE0-ALAz+%grdt*woXa^m9s$c@3Hu(Te59BsPpIZUIixK;`;{6Vd5 z^FCT4AG{Dx48ps9;|57dK#!muzDCf-{2dulh8ml`J1LR;8t<)rS6`1QTT-m4-06l3<2&$@!=uiW|C5LE4M4X)c2S5nX}YZR@{C`zX`!JZ2&f(MGumiC@*Zf;=bz?toSWMt2;UtByq)79#$dSjKD z^dOvp{l?zMH5S%J%c@tR-?nw@*8gfXaG*Jubm-nQSP#yUlY2<_cbGP9vAgs?*$c`* zMW-C=EOTDGc(M0ka(en8lF~hUN|B)h#wv#UH%gOGxwK=+6d#onJtQ#XH@KVa%f^*1 zj7w!X9p5tE190O5mp+7X=gytzsnjHvg0bQ7qZ|l?CS{StKpGB*%8?8PP*2RzJpu5l zi9U+ABaj8s48pn31%AnZ>oB*8d@yL9xb;4cIMgm_LKZMYHXR_8ZDIe-MvxK}We+J= z7MLOBh2I0E0?6S~6L99R=vbwB=nyYpLO@f84jlp^VQvOlKUfp=FXS;cY@l`w_xCq& zH`qx+i)4YD%(CG`YCSy5FoNQX%Dz$fXV0QGM%_8s+uPi4Y(N1SYOJSy8ok88Ti*W# zNzio&_!LIN5dtXbk^AyTjf`xrB<_9q50XR;GfZ)SPu-WYSHR0)2Y)D9RsvcI@Q+~s zR=ZmWuTcT86zRj2Z??}5>j~5{a`Xd;2C4iEun&PT2@5?se+8(;Ft-D;sjoekmPe6I z6hc3^fo6OVpf?`7+#zqlJNNHD^*G|R$SiPw{sa2S+S5E+;C=433;Os(HW1=abi;oW zrA&j@L0ENA9+kS`w&-S@wy|#|eVf@{0b+`toTk+xTQ-FGo(aPJg+)z*h7%bRwfAt51%>egoXP7I*b z#+bb18jIgv3YpumnnzH_0Tl~@D`P1Ndbpf`$%XFS7o&68=wbpQMNi-&Olfyo>cC?g z(*RHF>dImiAs{VO$FZnN#QZoBgM;?k=*j7*XlEg>;vZU=#SkO%wjx1 z!GnmJTdr2}>tzT2JyRqP|BjZF#!m=%VQ@aizuWQGO+Si;#)Tp6RZR<-d8Q0Ev&cI@ ziyD+PUCa|{>=Xcrfv@f}O+VC{sKIFpmxq}ycAo{G!N9`X7rR@0;mPR18zX42k!Mq1 zTp{)1|65D>l!t09ndwvO?fKP2D$xeQm0<)_4ZQPi!dV(&ixt(5B>`Lq>Na@196HIO zw6N(n06|WG+qMn-^)TE3&juV-e6{=mM-9H8Bg@sA6v$hW3C=R_0hsWDWhykEA7|mM zrmlVoT{lDr3F`d(2`Le#aVcZTq3;9u)oH5 zV4rr9zn|wnI!J}*iOg*aPbgRI4Gob?mOz9or3!U02?Z0m8m;*5LbS{7>&AD#TPMtGZ8!mviKtUc|91HimxUWeU7E#%bvkWc&Yg66tU1=D!xjt zRzF-SzNn`0S~QEr7vZa(M7vmg5y5`u%NL6;f_Kd<(^ByzFR9P9RD8+H_Yi5+Mqimx?cuWdnG*P<)Bd^Q~MezC;+c@N%K}5?Seim#|1A2$5B3D~YeLQo~F3 zHoSxp0bX*lun_AOZY$H?Bg+WVyy8z*vBN zRE`){B5!5qE(-^uQ*Pmf1tUQvFmjMRk1m%&>YsTUVtURP$Ml7?SM0t0m! zsq70c52?POEBUtY4u{m=(3NB@zT8_yS8{dXrT(>CM(V?bdz`)c0SDo`@X0I`qJ)WH zuvV}#xkir=yek(j($E5A4xkeF6zgj=Xh^vw?#$nW5ZcalRs z;YtYa>t3-Gt`>7k;Yx+Y{$jXNxg<6&g==*@Gu>ji5>pm*G^FPwo-d8to~3Zr<{#L& z7_NkjU-0V1a3#3ak25TWE3vnFE$w2sQXR5yEQPDRx|8oxxK^)`@mmVlYRahJQn*$- zW&1CMYqhvjz*4wY8_EPOg{ukelt$cor140SqPK(OdJGem^EOD3%a1su{((UTr`Ba; z^`w3J719oE#maS^Aar9kG2BK-VP+mlGa-MtkwK;&NfO4$$o_Ejgh(E#T5&5J-Ym$B)#W(u+4NYOu|69 zfw8)oSqs=bm>U9f!DJqCW&(_M@plikJ3;h_&o0f3oZurSkA|a10XBL$?HP<94%>Ph z#Ip>Qb(qKndoAwyD;e960g@h3pj5A0v&QU-Ir<2GbSqZ$t%63TySqEJ-qLaTLb^bF zyspZy?+(hbJ9o~SscC6_g2NQpjvAnzljD!qHo3y-X3-Y_M5zOsnjb!Y-mvZLTQF`Q z1&Pin0}tdpx>;cQuSZLrMR@I+HGcb5RjG5GT5@fVbW_3UVY!xY0UuyZT;AaaUWHR- zK^Lxf?Q99jDpcDy!4R}^G}q?LUHhWU87I%?4zGiaK~E#s{TLYJ{%$pOS*)A+!;Xx* z#f7ssZOwWo4Lo*#ZJD|(+voh5^KQn0yzJSJUUo@qYVzupAa8>LEbqyobQbCxXdM2d z6#SpWbdp(v&xmsP^wFb#U_!T9NT|08(+=_RtcD-cuiEfbHx&(UFx~#4(%boXzs(w% zmx&e^E+qR+PEE;nao)uKuT70o9GeW^cgs9Nr>=q1Fr$H$wDHOP_p`Ws)YVgaMYQgD zbCPOpc+p;)()adxaoe??TdAQ;A5t$Vs|=faNpYOsu{Hl^d)f5#jTJq`zkV1${u!Y= zF!eXig+|Nc(=C_tb2cB|U*)qsxXa)PU+=mekLlOOH=I@)?oQ6&xwqP$n@+7MALR-f z##68t1WBO$JO=t80JJF((7!|hV#B>AJx*FgVw&ayrN+*!plb>q!w?e{JslkkiLjEAIM(iQ+rY z6s6wruMOFKuQ=`0sj~1K%Q3mF3W91|= z-Bc^fYY^)6eoM~1lOvDsu+1yDrajBeVoVxIUuAqHE<2@$ag6VSL}B;y*}T8jeVS4t z`O~$tWt>5WtEZegF5~{Q<+RUV*U!a5NP&JgI-0TI&a#6 zsx)o(8#pSmt`&av?`?Ux`Aj?Zg!R0<_d`NzI{AL*JNI#Ma6AWs0?N<8 z5~Kd6adfu7(}iJ((XkWRQz9}>0PsID?_D~jc4fDrq0UZc%hVI+1RjSwA1zfb?;d^G zJT#J%l2~khKtn5ur_j7{HUE!{Q%8??clUDjoA&eE9F&xNaIN5PM#p5D9>Jt~gwcI1 z##wyx%I-Fk{e`ke@CydXVC$H=H4Zx-%J%KsW!#2t9H4>U{HRb`QPa$o7nZa*(LFF&z{MH7wX@h*cWI!x;|poy+8F4 zdUNI7S3>VU^vb%&moRzN=(=mti$lBF2QKg@wMGw&D zYKyiLB6_XMbJI)oi&p06+tHXzOx~xdbeNrTzA)n!ljksS zPDKlo=i>^S;|^oP-TSa+zViG3jzM3bfX%!l0S84T`pyD^F)=J1*AK`6g0byANLIei zZ`6OB&$3iekr}#|Zg0`gE?pu?7TVI)qmCh+KIAXP7v`v=+D=QE8j9%Oz3Wi%T4}s# z+-5p85np(A*5ykT1P^-edH!|N27F(e0C?~a4?qwaliJRQfIryTAidpj`Y0&4guMlR z?Z4}5meaB@wcN45$t+YS{qo4)HU%w45PCP@C04_?@!?o4yUBk-*$`%is=7s~QOdaJ zYiB&LQn=RyR-n~yqYWxAVG_aMqs0sb^Z4EW06TgA!>#+Q)sM&v-mXtE4xb4NpeLTYeP zQ$u3`eH(bq5YWhP+*lG2j#7$XrIMz5Bu#7RIBF2mYmBt}{y+HdMY1jT(Hi6@C2LUAx;!~2{xG^s49xqx5wU-#biJ*f)#PG262;&*d;`93mevsTVNIKY>UphQIQR!2b3{N%wSW-ddl?e+M5@+w<3J(|L zd6`!(WCr~jWXFx&1CR~3NDI0Ul^y_%7;VxygA5w&2dH1PDCwsQ^$iTHMiOhB#tSsk2*Ool&ZK#t<@_l_ z!x;#vkh7X#fH2GFs*fLaQtQzgVSyZzl@-cYK3QwM+0=a{H~X*PV$OKr4Y1ikT8FHC z$1K@X2;A>|{_4fBOl74GA^C$ML21fSbYZ_SgOZEXV{dXKT}r0BZitAKTCCY)(b2&f0;j^9ECpa~f{?vp zBo;aGc(zN*>q31>ILxz=NEtl4ufGARwJ!dBG2x-C&EM<3aw0%u3>J%A4K{fY0zh8T= zl6KhW;m~`dr_ck+kmHNM#LV}S@qgicQveP$gt5K{AG-nl<+=YH3BgHBUI!&GF9iFx ze+5WmTJ4fIGv~N|d<2%u`I0uKcK0GO(2aAU5Xh{w18JnVTu*HF|$da_aPd? z$Ba|J5d~0h2!s|}2#I!r{~xnU2t<~?da&}JVkOqQ4YA^ugzwx!rqon zj?h#%&q;6nQd35+3e|1vTP-an2q)`AJ$TR-Rawn#cXWT} z)|#Dl8`u$BSPUeS8&YyoX8-wqbK;*LTWfmT6K1CoTEj?c2kn zy~hQaU`80zNinmto5%BeYLqVv!9Q9}8PU-^mnx96Vdt*YYHn#^$FSO4ety%6e*Qt^ z*DS^+yLK$Q{aWsOzcIi6llb^O;#>v>1~1HKst;PO^hZYra!;?(ntcK8bg&MWf=mZd zns$f*HE{`7i1+6auIqF$>_+NA0(&U9dQfS>ktS8)2wqd00a+>0t4Wk3_dqq;BmNuc z83j~@5wE@=|?dT^BAeJ-+<*#)Km%#c`iN zLZ+@hk>>1){g)x!{PS;ptKH-ir8*MrI`ZD>u)qiA39o@WHAt8He-nS}Fa=+zyJ zc2bC8Z&Q_9#kfnzZQW)c;=$7{Ustp*{Vm|(EPCtN#2BOpirb0PY8ATl6C)$v58_sv zgQs}@{0nRyVBJFt5A4C^(LRe)jlL8dE5X6RuSFmuu4R>{S7v8dEuZBiju~!FL?1F;V z3~tlswMR4fmz1cUKi>_DOJqr=ra!P*`(D59FwHWorenwb$(qKan+>_k^>_4P?lx3yUKGH}0o zxKT@u{9Cf^l>Ml9vuFPC!1%Nn=f8<9W?&RMN>$wT+FBPy+I&RI6_MKYlI(HRZ$k!r6>No7o+l zRn-^YViyBr=brtl7(K^O{kZA7HTtQdw=f~f@qhmlIPU#>kY-i-;+ScE_POcz$%p@& zH-dMEAI!li{}eot`zGrgq(GB(>`jHL)@t?=@Bg~AI7a~ix}IZD?8k(MbFvLIKi`*S zxFvL;EkDBV2Am0DsWY~cwT?!BX7MVCRcf?~YuVMPlIP6KvLT!lR0Pi(78K2ab4c4j zK>*Q!LXLL&#dYV#2FCx}@7?1i6zj2O{GZ_T|8(N^doxfHzRr6?MESJ}vJZ`utekoD zYP7EZeT7a!B!wbdDwK{0$I-c&-CuR19_Cq9GQmO=(x4$s?L*0=CvHB?0PzE`F|YCF z^F~T~JxmKXmAqWMTXlH$&x^0}-eGRa+p`Y1PSCy&X=&B(=IY`4@4tly8s~j`Ax8(9 zL_}P48JWHlaq<7_dsuf1U))TL0t+vwH}KFFUj2XYV+T*Rk(Xo<4!4~wJ!`Ds^XHQW zvkDw=I3Rl?j}$u-leoce=%n1bzFv(WT$TFK&ung15E0pLw5+0{0wWbrp&G!7qTR_D zA~^VH;7cujSZe~#>QO6qkRLGZPI!0@2G$8OF*E<2m^e9MA16e5z2UGRy&JG3oNr+W zg29`W(~EA^yhnW=pI2Vmq-%$1YGPbZpQxt-?I;EG>TuxY{8|&x&0Cyl!c6Ysx$W zO@+2X$Rt?R*wH?I{D`r2e0+R7Jkfw#(XPko@QiOl`zYX0RB5i54~m8^tQQm&6>;WR zAipiJMC%r%FnH(DyDq~5_ZuP^O=tLPaIv!=)7B;#>-u_n09{X>JUP@+tOCOl)I0zr zzV;$*g}MO&CKystSLgKBj}6Jyed#l_84(RK^})yS=b@}iLgZsWXf$-1EiF@%lX$D* zzn_&1AHa)p|7JL7i@Ib%A_ONX+#cQjJ_IDt1RPD+zTh+iUJ|S{v2HH44k;2Ptw&h# zkXXSa7r-FJIEZ5)Zugyd7m9h(hYtszods`UHJk~$L9XWqW_x;;W*I%4_nt?=kmKxi zprO|3#vUHCBO@1eFXAbIaV0j-){EJL?EWt~P6h9wAh`@+X@_qnfPw-?aBEPmzwJ}p zwaaju^EV7S1db)zATB9s?hD*S-*E@#?O|t1|N0Em0zp?FvBA)KXxd+3a&0}?^p5!8 z^{;EKAosSjX!BoBN)lF*!HA2&ub7S3^^`=?$&b>v4WxRG4$@qm8%pP zuw)>vaU5WvqdmR+s%i#a#QBzz3;)S+3=78uztofz zWPZJUeXZ5iq~`%_E|IuErm1{ovKr@n)*Mc06g>D~q>Pswssi&$m`jlLIsjD9iTsYN zN3UyYNLOk^A`lepiUk`;(Fl7;ad9!G;IeVz;6|6@Y}QNE^LPfA92}A{O?Ll&c@*V) z_m;zg>vPQR*4L8&Ix!o)udfd$AQVyHlg#3DMI!m@=g2|E5bAaEj-MhO#-ZQna@c^(0 zWaQ+D6JXtt6fI1|ux>M2LG)~`dk_NF-i@<6oGF;#?hM&rnROg)dw%+F zx??`Z4;zi8rKO&K<$5*j&w}g>bl9s6&v$-UP;6Wy< zanKA6&qSLufK20G@%gi)m{_1#*n6|Dd~+X+=U(Rrfv0_2o~RQ$=O*#RP(jLsFFD`VAB((8x9kT3Pi$PTt7MNyG{7A&GAOc7FT9+6MM0pzsh3?$!F^nOXcUXc1<*xM_@PMYQaJr0ZLeHwWooKUAwTFr{n*to z?YdWgX#aj~Wkt-TzAJW7=&KEGm2k#(&G&v5FlH!F$B&-(MTh3HFFrQPQB5-EvD7;L z>B6@#9GYmRVTbCn`Z=c#2Q4Hz=hT3ZXi!ia6g)j986hkr1h)mY8pNo+f(b#5p_xWH zK#g+P8jygzodY~Pz6sHd81MDQV55(pwT(^ls*A7g&u(1J&=mX=TuH;7uMFpqL~|Uq zx6e!;oS(J0mi7xqahEaavP>51stp6B05sZuTYt{FmmB8>JQx130(%?BOoG2?zP-8w zv!;;!*{1JUPirOX=wo@wPs*M#&3yhm8vD=4QCSbztyG+gyqTLj4vkTil_MCQ1?+b_ z++1BnGWbm`EG9ufDAZlNs0fuJMmF*BKU_7zUhO6OBy%jxN{Uw1>` zk4+6rk>d2DoaOG?tW$e_A+mO%;zMl$Q4l1a=*2?UZYFzf0`sCSQ)J+()TMDSJ0}NZ zyANESF+%$s?ml)fxLCb@JTnMNG8sIY5Vt{*>26AFbn)8{G!BZol^wQ3!k*B{d)@cd_VmL!;~=6v3mHGn!a1 zpVsz=D-F?ZyB`yORN>Yv9(L)*MnRn51_rIz`2k#t-F@NN91b%vXcIyFBTEyoq(+Oo z%|Z}$1LF14=cI>t}7pI&?z zFhaMov<#bwv$M7~%eaJ$DL4NQo&&g@u&8_-A1|P+TvSkC2*BeX2SxB%b~cWEe5K+T zJaB-V1;WS433wUqJ1Ve?N|~t)@k2eoVVA46p5A0j2u5N_oO(tP4TnBSJz z#>H)oWjyK_DXY2>Mr!~3;f#wY?M7KMVQXQVeR6jOWn$} zS74qg#`CRw+*f7hs$38wrl4j%fep!%W;h;%G2<|%Q0-gvc%n32gcK%?f(v0~i;${ro~jI9~J{tYRNKbWNl|1En3>9Nz# ze6%JK*=q1^RreJhUXc+Ow+4gVnzK6Cq;S`j$zg0Y1*CEj(s%(uq#Uf{UwB<6_TF3< zKQm|xxw06~w(Z-`mLh?p>7rAH#Z_6^IlKW5>Aqny;XrnI`TXSsqo!1+JyhF{oD61IPcWnhh?LjZ@9>zIcBDayO`48+jmY_} zy;u)BIgJ91F7wpAJaM|v?eV18bdoR5JTD~u{icWaigSVLotd2c9w;IL_JOh|K^c=gzn!Aga_%Ly}kWve+u~JXg8qpNBs%Z3at`&vw(ZDUdBQ@I{gn^NdQm6D!mzo z0U)fyl@q`k4&i2=7;MNeC$T*4U5VTZE|u$6uLiPOi_hie?p_Q)9N7i1X4893z$KJM za?XDsW##Zkd;MAsJwP}I>YX~p$;EXVBkFeUtcNKc3Y%xoM$m4ahMQ&4zh68q2a#r? z{3UaA&^^#F;a7C>^MgS6B|3>%rt|1)p>P4NnVXx7x(u6ZMoP+dX=zv`*xJ$v5Y!EQ zEOuAWn~ZBgF!=4?xEkUP(V_FwV8c9nw!Li1`rKNqsIJ795;Z7k)31aXc>V=yD!Ok3 z{i_pQ@9dDY7r9SJo(yUg5d`1<&nPA+;Am@qg}e%nT>Muz-o~8n%3#O;~YgG9uQIQlb|NBwyWOU^QteghrR_ z&YkC^E{mo-eG016rUdl+MC=U6L?7if))f~g=gt=zJ`_O(;LSK5QAynl3L3y7+qDZ& zM1o!tkWD;f3P|hangb|dU=F~+!BKWL3z!JF@F<^UNtLgryOV97AK{s%M4}x$CCaeQ9c%gg=^5v1j3CDu<+;+)2@J zOdFCxbGW(r9$%irj~m(|yt`b7VG;Lo3hqb!8x-Z`hl}h!R#mB>qC;)2uI{b6(HOC03faFI=_23P7LW(xR;d3s uHU=P>{9T+c{~zLI|G$8A|HprHN~K|So!Blqp&arC9nd&TNmnzu_J08af-|uI diff --git a/dev/ECC_evaluating/1eaca3f2.png b/dev/ECC_evaluating/1eaca3f2.png deleted file mode 100644 index 82d81cc7d3b38c6aa94e978b9ac9e5f1b2385c2e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 53769 zcmeEuWmJ@F6fPDbN*qN{kWwinq@`gHP>}9c=~g-fR6q~}lz!;^5HWJbNOh;vBa$YVwu@^`m*cn68!=?@F?d z-2BrkwfF9xcYJb@;zOHi;d}MfCX4)Ff3B-~6g2)wvIU8->--m=nkIXDlRRA=8gC5n0aRfY|# zI`G}UZ@BcQkXxJjp~YaH``=Ft{WG6#Fw`AjvIm8x_tvMh%PbWms~wlo+3NWZa`bN- z8X7Wdmvv;Vjk&FEudf$A7=cB;DQA|@$;NQq7IL-M(HS||UNoAVZVeqB9WAZ4LYFMS zYm9Ak5ar>{a`tFUbabWtf>NbxJ4?B@kB^awiRbR96VJn(z6Ej~%RgDF*%2(-RTULF z|3mG0^wQzQ?#gH` zVb8(%=?OzQ#=a_mjO~HH?QBQ%VqJ1ve7s3_LVRdws?hML)3{Zsb|kB=v|f9+$f?eT zw}8`1&RTF`#5mH({&2axJ^N3Qk&LYRWl@5pc19eWa2k60jG3E6f@`9(>X{>DHsjW+ zA)%pm(=GqS3i$f^mRk-f<*f`AOI4Q^6s)aH{xsk9r??g{Ys zAA7smDHqRgWMnin#KO`gQXv{uwn6 zVz_LxB~N78DN-@D#Lb+SQqZ}eqCz7tBQvvoCG~+7%^f~lLzirFGBRGb9ZLa$sLt7t zb(^`a_!)OvoYxoOnvB_BzI+Lw+dDjLr}WsHyquk@x?A$6dbKXr!>6o|EDLQ_K1%Po zLG7{k67H^dX}CNeiF~U4N{yr+iQ`~Cfe z*49>BFWSeCE5NVmF1HdR42_Ih<=%LBcu-MMA^dJI$iYobL!3C;**#=rgrHG%dTnP{ zyst&ZrYGpSWhyBtsiC1UTxKOhcw32-kB{$gcU4|ic6)c%27Z|;8Mw5X7#H_;y5(zo zB%7PFGZ%QexGy1^TJafafYErJ`&@V8?#>R_)kRq~uq5aXFJj)U*@$QsdyGjzvJ1TZuUD#Oj=qR zj=RqN@L+4 z?0$4!l#+~?nC3La`cFYaR|3RmjG#+VadGiZa6xSBaHza+bbP#3>1O@OHd|#kL*m$GyFMeVNarUxk-ym6#UV z&Pc}|N=ZrWf>9oXUc7XvGf`yxRpB2&!_g{-MNIlnui3YEtv}p}W@S$@2 zbYWrPZs9{qW8+ze{HFq>i}E7J_uEhRrie6G78kQ~b9rnn(Iw9cxe?E8ZEYd^hs$l) z+G}fSs+?AZ?dKJ?@2mO3Q4-vFtl)NK>Q|t$XRguL`1s>r6gC%eakY*;z;Uac*Z=l< z^lPbkwSA`GmD6=zt=%oDZk^<94yI;v8VDlhe7pBrv(9l@OLHtwSD^HDPl^Nv0c*{u zE&Fj8{QCTL20ogWnHiZ=x#L@7+H<#5K>+!=hSbK!rg(^%=xD1?9<`xuQ;T}>sO7l* zG4lB(>wc`OEe^=KNyy2`m5+NILcy@CYqY699>~$;Tt30|nw<2dhQF~^+P!(RPGM8? z@+RB1>v1RV_#HAblg%TDzTI)p`W>`@1IB*-H?08dAR}Y!O*180+?!a)ZD*v$r5M#( zx@%`|zXgFN;JC!-jYmYp)*ehI+6g$}I{}jc%@HJR6BGMGdf6C_K&dPOZ)*3guRNo= zyu@8_Iw%xs_Ui3xA7NKz%!AudK+HwXX*2Ov%`WEGTW3b+d7hqJxpGC#w`Od2Z>)4}^eM>60fq};NmnuD`vnwpwyc`gwV z1;e|W)M%Kk_J-cQ!`T)@i_^;|SQZOCx_dVTiJY&hkAzr0cL6tSN1PZ@bF|SuDD+8{ z<}K7ml+XH9bG!TW;}l3=rzgAhGhJxWy@t!wEgPptb0X$1)zl*N^2rbt)zx#evsvTs z9`o_d%*=cf=!h3kr`m31NNgz%rz7538d6>Q{e|S3Z zAKrWZ_o8?>ylKquA;q*}s*j+6Bqh;UJ%glcZJj6hgaXfPYd(3j&w~cCF|x;b`wdR5 z-Z)%sIor+EH9^p&_eA0*2?>|Yn9gB}Y%EVHhM?MVh@ zruu*L>rbk7#50zI^3mNx=)K9=S)R9hYdxt_7Hn3KO?UET1WKMI3cDLtmR)*|x4u27 zpFM*vl((+kRx4e@)y69oq00^l7Cvb4I1aby3nRYE%$#G;98_eH?uv#~e8^CU?_K0% z|Oy}|49>72;vR{@I)lYmbQ_x}_cpb&ghuj)OHNo2hb!J+yoOE$M#mvX~s ziDzeLUESO)vU4M}Fa3c1BHK6Tx+9y*%u&)TM{o>nH}M|6PF)!;mp^P@9zH*~P zh$WWWBEzFHDP$SBabz`IhH@lb1_&S~_P(mP=~a*8;!T9Jo0~Q_3ugP^!ev6!{8y0n z(UhMhQ#YW{pm=R7=+c!#b)Xdu2 z+VSBo!~OedX=#?jWwIWZsi~1$8K|8GL_tt}jy_Ojo7)yNJVLfO$V^1h7y1 z*ROAm_SUDT4R6!f+1loiH%cGWpB{?rFVwgn?qDl{+s;x`02vvp4&$!N{!Apw=f{s9 zkZ+YDg2}lbFflFke^ZW*jt(GY30c1XP(5#?;HB5d^8Q?6WP7daHoxPNhMwLSq!C;q zD$8Q&+qZA$*Y3nr-619}fH2)&9L(3N<>%p1TaKgm)~K@o=2+$xqE%+ebeVn#(9&B> zt9i?f$}E=p{n=O<0V_DSot4q-c$HefZ*Gw5D&C}a9$zM+dOPv`eM(BoJ*gnmSXXJ| z;1G|abt#92)>Z(HvQXbeAXiFD`&*t3=|1H*uf|6+)WXqTG9Kf>K-+OPu ziwLd>F$!kxE45HBUHhFZE^@pTT6HuNso$m_=U*Ze@h;HVF%9`we+P z+U`n^V^^1l{bY*zv|=v7P5O}O98$uZ|Lb|tQO8kIgq0_vR?i0In(FS_+1V*u zMq#Rr=fFS8R)6%$K`WNU8_g3T8AyJUjI8|_Jf^0mre8K!yS&U(aYMO|`0spADq2?j z!qv$A}rba2=@SOB)NMRB_$=jnfhg$ZRw1qJBE{otM&Qr zSBCD>d1Lpqq#v{6RfINnI5~20Pz|EHN9`O7^?yWDI7SuCym^`M4x>vt9nqDmSNrr< zXFFqOGW`7T4#T@UJFTD$!kNeNSeZMd>wD~{3wA%uuX%MUsK(+AcDHR&7~+30?4p*h zr>k`}IfXG;XeVkUZH&lioY1x~AD?)me- zlf6`{N46IFX5PcqY=3+rWzj+kv}BUnR4vd;D7K9uG~QEe!xc{8LpW)=pF4$fA_`AehwY|Gr-78Qovlx?PDj{G7p2w(- zhw4fJ;~OQu$8x3N{KvomJUr?~rsw8%G1>VMjxWlsNBg&Kk&$H*25ChM$i-T(NiGlM z#_mYU%E$x&4CbYyqxz6kG$|r>iXY&{(s;eTuCV9H+t%)JHG`XIS`lV^T7aG}OSivDQ8BeYlS>q~D%6k` zX#GMfUJ~g2*OhF3ZjOwcJge*n00Uh}iZ6eD1khJ*=hvASva>ECP|FMXz@Sj0Urg4r zS1uyyBlS=c$?e-NkjP6d21&`ts2{&h0$0P;6Wrvs(mtpky}1x6iKInC<2A@rXNys!E4GS>wvUOblQvHwnFYol}9D4`QO_ zbD{X~TK@Un<))U|R}0x3eSIi~#oH8?ZJon0ng|mx0otcF1g@#sBm$HPct%^j2p!u? zz~PQ{_+KeMm$sek;)}9~(SYlR$H%iomfje7hE6`3PW`BbwtlgrTk$&iywvE#vo_oJ z8(x6TjemY5C}mUJAdWSl$YP(W0$;yz{ko-Gc!sT$6ZNAP?+&<9RcV&`GP?m_VBwCp zpTED-T%iK*(5EES5>#pBjORmD4%w=e&y8;OWvjEL_Ly=+2i@Td2@j|9q)(T<&gkOe zA|WZ6C6u_kG;}Zaa_PN*t)-z&z`$gPClV5^q(6Wv4=0A%Kz%~fTg%IL2T=+D!d@QG zwn0S<_m|t~a}!&S*BzG)TZfiDu%XGRqEN+q0}QaGrNy>(^ubzl;|U#}wz^`T45OyT zWW6AcIsSWMoUDkQhc0|_UTO%$2c3xETdJRTignG+&9~zkG3QIINU}o6knz6}U3hF} z)SRK@T&6S>te|}unD9Fv+PPe%l?=M`4fjWXe}7cetx}gX$i%?y&?kW$an+TTnz9rc z%FLwg@lIn*Q?d#QzafMH;`M;PdwY8yu2kp$FmZHpS{LRdX5c|Bis;^G-$3p?ZY3)k$wwE6!}x z?v7cYrnIubYf~DBJ3YFm@sHSh^lV#Yh|BU2Zdbq`2fD`0Bx*0>I8gpGz>S1Xsf(q@ zr6sAAD(`lBD6MRGRi8ia0G^4O0joz2bo7F76EBy^6BI7^?A5DRz|N~iV6TAav#<6C zy`c4eDlHvCtpqs;)yh+{Jp!o=_K_{rm~|mG%VBWELPmXOnk~esW zKqNxiRzmUNH0feKl({3~p>t?=1F?iIm7(PN^YdpaKo;}@9o*Z-=4Ni)?Vb}K#nULj zli9kCKExQi&lsEyAfPx#080l~ zJRt%;62Afo!*;Qm+A}UTHhc6mw|p#wk`1Jo{JOk5^7?q|Lneve64g|(HQ3aRW%-35 z`lY1`@V`HRtp;+nOU3uXGC-CAuTYGfxfN`#g?H_m%BB?@THM8yoh>rd>}ImKuldjK zpwhkdVu-92k7Uu#_*I5IP4+LAn32ljxMI1n4z$32My$2c+>8LQ5v}XQ#J|CJC~^uY zPfkwEr&M3QOs=a77lzaZS(AT(^E`3XF$D`%o z;F#@B%pVnDXI}?=6_UO2pRCJG2?+@x;|V)oTsCLTs*|$-5l^S)Dk>`4I+E@`*tlNO zO>_ZSjpvP{Pzw4Gk}~i$L=Wh)tjx?E?d=dit60gV5?e8NOafS|*VbMSiAIKoazZWJ zUOWY^23C0H5l6{s{P}qEd7`i`t9%TX+2(Agad9Qk&(cA?P`lsd7K3t>+=h^8i)vY! zn6MI(FCk@-2J^RX-`HxmLhc+ZL8{$odx)_$G)z0PPY4f3LA8Sd3lb8b6u^ zPmrO(=5^~h$BQxH57i~5q#pW*L`3ia?ku|h^3aebtg!E7FGWjDB&DFBU}EA$C1!P% zZO%uXfLeH@>$^yJ%Jhs14YAsUWbHym>@@NLaEGIl!_}D#ND$a_s8s}&CS}K}ZYoHi z-`I|}ac6lrQ#LkZr%xCT)^Q*dqzhHu-*Qhk{|2yuxB3FNFfMih-4SS1m_cFCE%p?M z9L$DYw-5u7%VKW1p2z+SmIHyn8^}8r#c3kfD)W269*f7S;-aGVM(nyc62N=$A(|LBd*ADbDg~Ke%dsj zRhKxDu??z8Zr9Sn!nd++kJifRpuVS>K4Nqn zQy=R~?V)ja9sLZm{H3p&$v-8Yp!>xmKo9n-W4eb3z#q1+xDM6wbj(z>_kXI#zPisB z8LxsC^hVF#qiswQ^8%^F@RV3Wv80&E`{PG+ewpRVP)kB3ejxgXb4+|h$y(MZ1I;c? z6B8-~YGbCo^s-#kqXzTK%Vg9DKhV{~1V5n!y%!c1cJdKLF}?~c{U;qh!~hv>wYrMB z#gQuWlBM`_ow2;DeVM_i7rFZG+uZD)im-4v2-z2DmX$L8X47~d@cJuM#tUru7J?XJ;)-U;8_9zvB!fe@>d{*NwFG8 zc{z7@n=E;#K|Tl1-|#s)I^wY&(fFmv`jL<_tFv6lb?b}B+aUz9S1-f;+_`h;%iqha zM;~Y_Ka_zbN^>O*4kyP`1_9N_GHs#ddRYL!R3CgPt3$3}`lcDsb%EoW`d0 zNV%_ZlrDrXZKHNVz zVAZWs;n~c{$bhzk^01hFZ`w0xgp|4L<6!Qb2b=ps0f*2PIX&7`+syR&__1!YO8_Wh z87KKm7a<_1(24=Hhzg>b1aq(bBuW%?Q95i%q=cL*49ZMLG-qil3A8SVKp0;gtA*TL zgE|Qo+-QLySgn{M%r0vH#B;JUYy-;iL%!zkz+MZDJIR+h)j{Ehy$qB|nN?O*0Yxbn zIoV4^`Hp`7{+$e(JODZd1rwEX z38DACkzf0$ZC!~~^NUToBd!>3V^H-c2Nsv)@{Z4C74L_yi-I^kB&Miyh?6W$fp_oj z-Dyr=)lAiFHMH?Q{uWtyn_DVAEuha*lWwZz&7TN7Aju%kL#h{AZ@hty2bD83(W43k z0=-&SvvJ`-a&A}1DF6mjmOUSO;}H;m7%>G@BKbJz8Q$db@^Q<(U{Kpf9EYvcwy(gS z%dCdQiGIm)@HMmW?4+a#P%S{v1=u&>s3jSm^*t~qA_CZjx`xIdxYysme=n9PX)#9t zI02Ct;z8@sN6rkoRqzjB?F$z!XqTEhjBd_NPh)xL@(pV{s-_S?D)MoUzd|wkm$v>y zuU`_Sl%Tl?EmEAz5|N77pRX0L{jdL*KYzvK;k;XfbkD7O2?s}Ej>%uCPgT_F31lAl z=P{!e-utTeHrsc;q%cAUfj=HQmueDB}gO~$nY$vG8(6Zv< zDuFlPV>V8xeXkckc)NE&_d{J({Vu^k!>dAwfP0`m%n&48-lhV)ii3lEu0J+Pm)VlW zY9kWLGq?N4JP*f=*huQ^#vdq`{}Q(4yH{TkqpzzN1}I7=qXASiR?VWcn8kPe-XOu^ z;HZS2V>w@=^BLi1x8NcbQe?F6$0H`^TARWM414+f=)<=j5{kwhQH8H35e^REF^Qfh zeD8@JiSeKz|IYkNyD9Gfng!snK|E=e97FhB66osMW73N7^wclMAp-R{EGo*BOKt65 zRVNp6kkkME675;{UX||mPnQ?Y?{v29zhwoFr-`Xt`*&LpzIGm!clqUD)M*J)epJZ7 zKHu?w=JKNuJ2S1qsP$?;(#=4>5;HZcQn>jA_l*}IBNz{Gu$Wlr{oXf&D~}*=47_)? z3NI!Axmn$9f^4T1&O0UVL3eezNEkbrc$GC8Dl+>k<=vMef08~CgdH%j?#~E~Bwgjt zJUN_vkrFQ?pEg_O?$$o&#@2GZSi0x+xBc>x1`qO@R_8TxTl?zf}T=u zB~QHCiL#=9TPo7C39TKUcykvrIeFC9|IX3by$|odTlE<`ynv$Rp)+au5KmT&?@eqR zuraaWMJll`L~qoTT(3MbXs~k6k#l#+;I{BX%^a2%F4=s`(nbvxBz=0kx0cVjzrJvlOe8*YBD=I3>_ z6a7*c_Vg+F6V(aa^LYj!=-AY(OG2Rv4GGDs-UJaXBrL215HGm35oBXX^+!(Q?&Tm( zm?Ig$zvFlGTU5yEM%+()PMc;)Vrq0OOWH<8>89& zS3h*4dih3BC;IdiAD$Q=OE;uM-D zh+dj35~u5!D3b)2S*X)O?gu6D?jSjWLW71{1Js$|Hpl(@_owr!SEOZSb1_xl+@-}4 zh!P)KT3Tpss~-1a{f>LXQS+?{!+yTW4gE@{#^G(0qSf1xIKyYjt*=A~@M$|pXTDOW zdip;bB!#m^RYWU9#_>CtgOs_m>w@`~necX_6$$|DlNT?N^zwP5p96iIhnBUf34(i1 zlUw)T@R020&G7VQCO8W5w>t4u3!^G0SBciX#J(Mk)1w-59qjN3tjX`Ioez==j5(}s zSA`()oRi=a5;7x3y*s?(APMXldKS;=hf{68c>pN@Wc(EGKMA0iQ7xo#Ddq=&7@y z(#O_c!g=HJcuw4yOR%JmHh$?S^nemTABQ7yf_5Q4Kl-FAzwRK5I0b5NwpuO*n%u;9 zA3a(NSJ#VXHvpE2%2I{X?pZkn&$%U|sG(uHNwo zCeyw0@W_HfE`oV*(OWOGI$Ng2Y1e@h2M<}j&% zTs}D*KV{Xgt6_En{fqU%18F>V=$B+G8XAL}f{-Vn2+IC{|NTeX4qeU?Xu!srfDm4! zX)R@HiX{Gl+5ZJBBYOr;oodt034g~{G15ygzSO{9i(Qk1q1NNopaNfpX;l7j#)7+l zX9O($>C{35fG-gTfH?9Q16sU2JC;IRks+USa8X z1Y#9u>+}304^Xt{c#~68eJK(FA=*F`nZ5l219L|(LOXv9c1P@jn_m5gxOMHLFO{n) zuvSc?7wnZtXzPnyrrTDJ)Wcngb2y?_1BG9AtINwGvvbc2m38C>lhWrKc7|CIX-42$;s zxOBFnqycn%e46=#n_|DuMR(3ZPt2NIY!8K>1`CM_PaEY#Rr7NCI_Jh3+=Cd>5)h5ihUcP3pkTcMoKQud7P ztO*)%vr%=JOu7DDwdGaetw70Iy>6TFbKh27y&AsT)Rz@9`k$cX|D%(6 zAWErhzy7xggTdYq5WwtEiVLWBY*Y%KFnWSV3zXZ^I(#M}ApxZh1xkS}PNsYHWU>so zxlq(-shGhkuy=GCG}>a8YaHb~@&59d$DtJ(+^u3*!4qjmM9;u5Jd!0Gn%lQ<{`~o@ zQY{GRAc4pP5z~_(uPd7O$RxgD;RBV9$J$~o+1RLU)sN_c>9<}$YR<~t&*T%+zKlTP zyTZbHJA^2HyV=j!esss^Xl<1R05J?RH$j4I`wfI4DM_#nN$I9#RSYhQ5-xO5Io=k3 zCEA^;^y2OvOz_HR^;KGbe}6(47qPWaQ3)eXff*c>E(_dKq;5+~eVF!rbXxNyipqoZQ~E0tEHTWO#T}`uCn3L zg1E6#v)L7sMFlk{^?+wr-_D9Ytet+n#?WRLRP zuES0sw_-wo-W@OMpI%3Rj2%`c4_#lFLaA}t1o<&CDr$atc@z?9GnHG8&3GM3LmA8~ zk2G7Wcl&E)t=ddkYfXQjAZ4JJNtzG$$$5oin3N#?P@Z)`iG&VLIJ3{k#|LGvt1t?J zxX)FxEmwDdP!?6JNNeL_K3dv_7mq-g8L-!-@g^Q$mXF#R^{{IF67jxziqjTfwkS>Z zLU(F6!2>Iu=%P%q|B1rMm*4K{o_ibdj`A%F7V(CezZ(4Qxn)DE&H#tB)1!xeBSqm{ zb+jiMOd;SI7L$w-d>P0)P9^U%+o90h{ZMO3B}4vXxtSA-zTXL% z(=T1exa*f=Yti`ZNxew#!|$V&y5hqIQDAn4f1CjbQ)5_cPU8H^;7EPR@iQ;v!!z*y zUA5RlC?-Kahn2|e_Tz7EmCcTK2~r6EQ3Z7tp)bzt*`m6R+~jQ(c<>?Z3T`X|@mD4( z+_XFhpLu9jAa?a778UMHtzh^3;HhGxa{ZkJfz^BZMB8_3?WjYIUYD zv9a=5W*}=Z{*})pd^O>f(#JSCokeQ>_$$BBP{YiwQ+`p^1zvx8OW1bOT`J5_n!9*s z*cN~Mys%t`7_E13c3;l>Np1zsq>g_)M}lk1c4$k(Mue_;R*hOcbGy%V*YdA+XX*Ji zpMSK@JB86s-+M=Wt9w0hnCj&9ffYqtEUEtfba`|+_* zUYGd%lP7Ks(p=k&din)Ug4>XM*txNK-j^-xuX?}n_xxm+=k+-Z*CL)lkt8o zEcS;qm8~p!+?vhglG>}w>w9gcw2fOW#;U3|NgTh8NZ@0PzKa)galnfIRx z9oE!WhdTCgn<@Bx`^q9UI(}TYN*KlL59X0>zz^L`5sB zI_a@ix*<2?R#cLJ++zH3*0d`QR!7Id`L61gfUzka;U|!bKY;0y#ckJkIo_$vc@)vE zQZtFw{7jLHYa;Dc$FbhJ1_1+f zeUaxY!mM{Su>SEWF?G&Hq?(?m$!3l$z$#r#wRH*Tscu6&)(}#e84Z1rc0R;T?zOAF zt)n)J#7EQJJ)7l;HxW6H!x&keuhxobbkOy^7@CPcQi|F{&7@3=6Uyzry*bj+MZqet#u; z>n*Lf+`QJsipWLPqTSjTOcjQ1ePd+(muiWn|6EA9@SYg;Pfd{8Z5q|Z?H;Gi^kd}E z&U@yC@GCxKa3ZvPGuM|pj?N;TxBsy*mW$GsP1;~5I`b*rMVeq1&b#97I#xEq)t*JG zK6HsJy$kjzZMLMg|F9|pP7i;J!IXi!P9U8ymA)YR5Q9gnNx*}h5gLW|o-+?4_P;xO z?2z%@P>4FIPBHt9GQFBKx#jCavzfNHUi%F79lg(=k52?WjxSDZHH4X14*tm1o+lHM zX9;OyoJ>P|Y}3E&xZx_Cl6vsE9QOIWr&Ghlc{0dukc5de`LJ5`cM7AnoGz)7@Ig65UxL7H-aeJsmJT4qr*j&l6eCcW6c##mmJ-38m3z zT~nb?poN6{&Z~-^0G}N+A~xaE5%Z5%ghG2#_0BYy@Bf8A_ezX>>Lps+Oi2WH?<-Dz zQAJQ3D?l|XO>#Z1GkCp;l!m1Kw+$NJUYels_J1Tgf~lx$t!-x zcM^e@cg~v;Gk)TQS2!4vUYZv-Rj{x&6;cQbAPh zbBP~zmZbv(guz%-zdQKGlh*KIPrr|MlwMu;!{wXwRyPq*c2jKmly@GP%k-oR-S!+~ zW2UElva=F>FmO9%$P1+@{`m1(0>vbwzu?L|c)qX98VeuE4Jskg8{ndSaIn`c5&DT+ ziTCk8Q;HtHp)D5GNEgc&jm8b=hzN^A#QLgSveWxO>|fScy%>vFy|2!4i3v@Zj@z9v zn>T)?*5W4WGUKPSExP_4Ukq|`HfirFHdF6=p>Q?Qm+T-gHa(-Ex^8UHb8M$EC;Q6l z{f5Q}8_NR^Pei){m;Cd_Gwau)aswq{b#R6n|S?3-q_pNFTgd;KiB> zMnw{x)UND}Y%_QhdkOES&PTE!@c!%nVbm+&!#_uK;#Z9KX4ZC$O)3QbKDUZ>zs6w) zSnApMGOuP>s|*nyExqH_+_0EwN_~wus(4R~MN^n^RASnwiu0RdV#F;S??;-HGsCM7 zYo$29Mr$xR;Iuu3DUjxzZbUw%H=IoB~<~>0ukD)ftXy2 zZ?aLWrgC9AZrmV0k8Jjnl|Da_d&$#POS{uD0zv8kOa8?{1LOAb)1TzqRn*k;Z?vDR z1*+3;&pBpv{8?OeV)2rS0uwyb%#%!I2R-IjHto9RdB=Zs&0*~O8jg*+>^Lu(6Z_E> zD{_0Dd6Z6?zig|EIZ81aAO#4H@ras-=^Rx`N=WzFk-g6ZKkfJD9;6eB-aboh3cPR2 zMQDqYG_r6_z)>XGffWzW?+?N!4ovhi?5EHm73V5tTOyZMOGV2fFh-Uz}Q9x$pfr zA%xR@va936U;T`+tv=uU9IXlk?~(sY}1e~ z6TrvV!fNsp7W!;O$x?gC-FH2nr26Q{I;)fdlB-Y^Y|Ktd5)>sB1JA-1x!e!69OOqX(Sz(<$<>IA9A)tIbE##w1Y;=#V-K%g8Yl<(Fwlr|@K%!2Rc7munuS&D=PS8U9nSa+*OnU$7c#VoYR}PKr!z5fn;l zLQA=s&88shcGy$pwNDjew^+|%vXn((u)t18p#IgGS!%>B!I+DmM{=A9vdSKuOFzTo zNrd1}#T#o)Av5RhQMvAhUUIEH3GA^lA+mCCc&~wpqG}U#_0}=`yrxUEkp=9y!SvYUt@rPn)fS`1p-3BPZ0%;&Qcj5PpqOX2U}r9lqMG ziNCz2KIt^5iH4t(NS0eFxX5K^;*po^$j|o-6mCoXO5&iSlyAMwzMpZ*Teet9)Lyl3TqbzQj-|O%Str z-J5tNmulmaj-{%q04#$F{+C!$Hd`$sS)-XQ@2VHWTXC}kpL-$j zn&J}c%q+(~bsLeBAg1Gw?sA$Na}VM(lAVpw>+e0pS8t9Sb2O9aBt>ysvT2qZVTllWsP%jeo69Xl7VyE4>^wd=-y z&fjr8HzP^|a6oi9{S1_l!j!i+al0NU&;FoAJ&``slB|90ukL$+0UHugk z9&-gq-MxQVBpr(!q5P@t`(C;!Pk`)TqPCZGiXR)QQZVV~b5Z}Bjic&qg2jdk6yZ<3 zlw~p+$eoOyD=xw~g`LO2FYT*0cn6;5zAMVsU1bD667B!QWy*e&-bO~7b0S93kc$M~ zm7%>k74cy9$UKi+!Lf8f7RVqDypPeF=}-k7^M3Z|zQ7^l?1#@*H?DS_Dp>)w%66>H zhc``3V4jd)#1M>udV_;x0aU|1HHxK@TJO2=R75i3u`70F+nN2Ip!z#}T5rqE>nQdH zllL$dQCn3{%gc9pJ8z}!oRQ?2nF!#GKn?9S9Iqxat6#k_&?bts+v%}BZ_fGeV3jI+ zC$jE6A63}v)i*5~fpogdbB zzVzR2R2OlFalL?Q7u8p9a>v%_k{?#6sR^CCtg?un$1a=LAD)o%&fsq@7Q<7q`bSUr2qUAAp=M~)loq!)u{JA5l zYF=S+-4&9*$78w67G=VsR{wmp5{1T=cPCndpPy75D!&`%4YlEv>f}22VHYC&)@ep8 zTKOA+wXyB%X)cYoF8b@~Lh1wdD^?jOL#uaf|1yIns*5X1*_1yfjzyhwQ`VNR`ZtM# zux?(N#l+0A);iI5A2Kx)>b=2m*eK@0*=F0)96<70&7HWxjDQ#036lsW-D{jRAgC1 zViH+Kp%8mkU0-OIri)4ZM<3AC`noeZpmTsOef^C?FX7G2m4QCnp~21;MvixsrHjLq z*qFGEipD)H#I#sJ3z1U{u#xwrix>-*`FWru~dtFK#S7rt%oYh<7p!U*p^x9N``0Y=e{SPv{;ft&K&f0 zAm+K3{PBhpl!}~Bve5;G-8o{DQ;|!ptXx-UmF)aKMu^-fvzbq)V)gdJtLu5R(08a@ z8D}@IDofLE#(U0zqK18%G8_b)_R_i-Kg->64^kr3$CB$3b_yVsE^V=7C?pd2FQtGSX( zU0alq-I|3H?oEmS>q@B?7k8gJ&|58$Rp<655x?qdm6^(m4@mj7@R`cBeB$9L`GCE{ zJLxkId~M2|fQ!0KZ)vT2BbLMC*>an=sE|0;30~`P$Kta1Z~O`Nm67qvf}0khs?!kK zK6i&0Ymx6_C`&NuyhGJE^$P0l_t7rlZX#cW&voA(? z?2nGX1?_Ql!PVh=)Xe1@)2Sc+YtZ{IFt1BGe^AxfwNr7ct_`>MdG(fHok4-l@w!6Fg7n>*TIE#FU`u83?elm13>>ih{q^(GM+E1Q1n|rV zWTCmIUcf@^23oTh{WV#&Y`e*HN0`;)y)NU&C-X1j_A_HoT-03>E=>}rnNYgR7aI!% zyIZ7KCl7Z#GS_Y+2O^mJj9@F+pmMpK_lCs$_YQCWpdpHcsx?7#X4q}zQE9kmM*_2$ z3t8IB#{saBclb~~3wAh-sLCG{PV1}q7n`SXh#DpPz+olT(GqCAv0_&g7=M92nDl3o z*LAdbljt^l+cvao-g@)eB@^{Do7j1jQJzUApZO;`k^POTm#z%dr~g?v$c^y?pEnmd z+j%X5oVj&^>eXwa%BsBEQYx!df8W+tE`V&toUwGwc7;|@ptEqAL0^xzG3?EAysu>* zB+`^O61~%-s`y zY>v2**089|?9Vh6E0xw=W;1HzT)V&MXd`JBS zw_UV#WP5Lh`$9a$mYo@w$}t0T6O#zf!H1SzmFZhR?R&803?GkoB zzO=(Q6UU!8mRMCDuO~!?qr!hy4*Olw8aNaB>Oh$#`9116jayr+|MKs_mTWoG z?1wE`16_n9Y22wM_BNwV{Q_MFzo$&s_wod(`4<Qcwr$J`Ix7j@H@b>kc#xo=*y`jisYQ8_2G z5?$*VMC>0Ia2{#5XMkN^9hUDZp1P_xI{v^adyKn<^KYdR(ZFr*S4>t0J13F0g!ON{ zP#4VcJ=x$CF!y_3xP(Vs+0GL?caPU)+qwBLgGkyMbz8^*{ofM@*VWjua&o5pu9Y_VUVB~beu>PePd?qS?EG1NcN^8`%zN7v+a;TQ(h;q<+n-zyt?e)9P) zRFnzp)TI(Z0+{O@BR2DF&jsG|``2T~i5#w(6}-Z~F_>vX#gG{l>Cd)YTVrk7;4|LG z6QtPTqoyspAO+i98D6!BZ;%aQ%5vJ-rY>w?D)5cLb-*n*ufk0#Vn<$6P=lErS1m0x zJOpQBk{HS$4NCCq!s%iu{6QbsV1ToCg6YY!BnCw(^$I^HWTCeuU^tBs2 z<)r#!k#!3Ly;LO3aspvDj$OY;F*4K#6)CJPEsDI2@0yn+e-aOW5)2Q}|&1UN!rl=_{?RTjT!Dgd&5?(lbrk8W;4$BMka8n=?C`W~C(d*euG z0l+0mJv^;D7>d#!FDty+;IX2C9IJbjUC<_43Sam#SO^m_@C1k_JS+O_*|WjXeV8J2 ztrh0xMhy*VlA1@J!$B5+vbM+^KVE<`Ta*ItyO;O*uEEx#>6&Rw?W%+Wk(aui-Og=V z@2;U{&qn^t?+Liwvzl%Risi17f~#XY>oHkE*sk?=2SJ!yo$DTsa%#y?&Xj}aG&{x< zSFfJK3IELH?6uWZcXDqaGne{h7hg8EGh@^-FWO?(q~mHxPS7$EYw!+xej*n4U?q%Np8JG%-`9Sn`n!5EV(3^t>< z;0q&QTtJq-&;RB_*PW&4m>8{el#HBQS67#uyu5zJ>q!`GN=-?@ehm(h@ZLmjxn;-u zt2m;X{U5nB*kL1MJ2MFm&B{`qq~Y3zr2kszH5NZV^?waWN$JWQw7+x?PYjH6{l*Q> zmp?9swz{s+F*?oC9Tkeees*sH1~4&$;gx?u&+x7pEXJ>cK5F((~EP^ zDhTwy7h!z;+F~Hb1wISUz>LF_EA#WFhXUAf5QHC0pY4)WVG2>R`#u=Qrjp%ngJzn*UWYgD+5bBN>fH5&T?glRIEm-{jk&+njB?U>tHtUB?n9!5Xn;^JUN-r}l|prAJ~Oc2iq zQQ&<43S#|ZC&O4iaqVyI^a0n`Hc+QR`jn_y>SJwWJOAjo&+2D0eM>drgH6nCGWso& zYI`Z^^|_>s|NaMIUmlND|8~2j(4ds4gpv%IQX$Duw<1Z%l$j*6lzECmDWM1vDum24 znVTpw&r_tN2q9!XYxg_vIp_1ff1Lh!KKE1GzPIoG4%fA=wbn(a+M@&wdTX-k$aQP$ zUp-eNBz{a|muvM4$*m;)P*AxAoe1jH_--Hdq2Xa@2D55XMxa>O1LCId<~1jUPp(^g;2vGvt+MAQ%hU#bRj*GN9pKDRy@XT26t1j*D%kb8?@mD$g^2K-%-DT;vva(0;?z8J~3?#ZBkE)bE*3r{j3ietu0T0M)b+LbJF^(XPa@S6wh7`?5 z-z^vN?$g5<-L)=S7Qq(dtA!k*_ge||*G!b6Ekn{}*ooR)@<838_+!>U)c^`a*XU`u zCP6`2278G>IYwsY0_(0Em`Tl!wDAiIlZHZclN}W+B!Spb=I)Hmo&1lVKIJLDw`0o@ zFf%h#3`uCSY|B^|bVck52!Nt2f&5j3$ZdgIh>n^=xD+4tk;YWB-B#M#+9R48eoY?l zCEy?BC%XB<>99nF{^%kVJ?$4#^OrsSaQ=c6=A{693`aV-d_7_SC5 z&W5~G?x#Mm>qLALo{cp}V0GxAS9ZedlJR0I@R>Fjof4>xoBm}J-Zy;5!ELZOwSP`} zHMYRf*=1nVN2B?fK~lP~L9EslXSvDhJNG`9rR%<}adbYrx%H<*>D(9LwdA{BWUA?J zOF6Q0Q_bzmkyLdStu8GlOdjsedW)Klz5ey<7fUdo^Ebti z?aa*I8*`Au=+Dg1$jpCZ)Kd1jr+IThNiE}vv)RP&f!ct{S#vh=;aT=4Ne^hK%wE4Y zFA9bPhK}S4ZlaN$F&%=~T+rA5{{27G(`wJf2_og?wHa6K@X;IUU)eqhNP1-azCf?V zF7ZIS=(1sPPWrwUcZl(JoeaXbcj{#~7Z2C|bp9qVGn1-41XS74vuLe(^SS6C&WNulq>vK@~vB&dO ziQibZ2+BNowN&{+bblVpZt5>9_ixdLk7qVKmr}b*HtZeY^_A(7$_ zuYz934t>ioTEhF52wkPC-N;Q{aBAgX-GM23d(*BdQ0VqZy4cN64Z%JLHUWVQgJA4k zz6T4h;xj%(^oBWxH|f52?qurZTVjibh86VW+&smQKXVnUo`@~@+Gz;y(1h2+w;iG+ zv-)0y`2P4?b*1+Cj@xoFyZQ~f3S5Ui8y~7uUiExz>fC!viuTCCI^!dy_5sQhBR0pj zv;Q*bQ6#belItmeBX*@e`T%JTl$oyV;jsjo_v-Z1Rh$PLAdd6$@`{N$)jT=?OOWeE zFQAPW+7D>9=~G8)cTNW`6EBg?Y2SCiNT*0X7tuf<5Dsh~XevKVd^kaPdbr-M4&(3xYL1gX5_jkPc zNnR{XUc9;XJg(@ZvS@VOKIWM{HOOw-!~ZAh8I^r&I<4Im5;69!+D9+JBs+eyCM`X} z>2iEZK2aYu4RX(kcr1z{q4OHJLjn1979J!cqf##6BoD{#dz)PE2$X!U@ko{R3mbO6 z=u{Rp^QhE^O^0=$_g_k1u$Nw9i|qL8=sj1HXBvw~1xucDijBa-DMhGqon1Yi)?9e* zj8D?_vs+^L^K1{*PDRCcS+-GEPU`*21JLWtioN7c6trMa`>Jp8k_x%BYcx@o5|#e*u%18<}(DE?XHH6654EM`)~Bzt_1@(ZL~;u_0|3J%KO;E zJ_;7EE?%&RK{D+8$I{+CSkqG7Y~#n{oh362wHZ~%6AEOB6uUAtkl($(zEWaQ@9ll{ zendWVW~RB_a4D5yJnaA^Rvgir|riWcVTqY>}&Ci!nIR5)R8%Q z`OAf^OW2n!J?=k8UTV_gYt?Ezg63T-ZpD|7lL zOxim7Oex1tH_Tg{`W${O=cV4*0%7)TY8cyzcjDJ7i^juA=1k$P@~L@A-^1vaU4~yq zH&4H3I_gbx z=P&hg8;faPPHX5n9D9yVeRwMA2)UF7Z(69RN-?sW`~GBjLL$uG;u3lDx5Hymd6%Dt z&@dg$RMK(WpE_cH?Ch7=im;>`&KB}w!xJufMjfH9Jrhh<;+r)eW|!N|8Mg6lvC|Rq zl0#B&zG0jMCqf=9m1RCY|GnKd{l?j%`r;7VY-iV`RaJ@rM|D!VdpvzpQxDsSQML1oxVpj#j19K{Z+dJqfW^S-P*7% zhN+oD$<*e{oD_N6vVDvO*F+9mw`$rL@z83m6PG!9EE6-iGr&FRq#qZfPNwiRljQ-PdZ^muCb)d}ktX`(rNlT3%yG66R z=oNkCcvhm-T1#e(QX@~l7#Lmo+A(t=zlJ)RITS}Q5iG}&#>2(9fkP-{a-XIqoIJr4J%w4qvyZ+we2{ZhsCzN4X#1KwPihb9 zh+VcfU1>j_euTq&;cFT#K}c@4Xv|kP=zNiI(vM@#sQ&iz_J|Fp_NK27ZuuCtj*p41 zNcg-5cC*|EH2Oi#0Y%TO`txlMeP=tQ_3fe)SNhdlj#{n>qdO5aMUwTNxXuUHJ@N|v zsd4zZU&0LiuGumuqkR0Yyq_=aG$lvH)d)#iI z5{MOCJIpLzrlqNiL8*?soAgj3UC&;O5JYT{$Pb!4DmI5YH}xx5wVcAVFW+~)vvKZR z;h#y%&xXzGlGXPPyb<3Wr+PkG{1BYSxaj3hox0C@ta%~1qQXl-;UhHSGw^!Ebwp+S zLz+IHgy}71t})J|uisdnS6yXqxs~Cm{Bxkg^}1cJ2ghXSI+pu|^ejW!)$Fw&Kd#@r z*`UbI7;qt!&}qT!&|xER+d(Ns$_3XZ)udB|cM@JOqr&hWiC^xXPmDR?hv{k5RjUdwgkf?Rs%ex zJ)Sc78`E})>!Ia!!lQDlu?_30>li5)Qu!*|uIc!W0ci0f4IZO~jVU&sA}n<#!BX75 z;toF^eC4AiT*MH^v@)8>b&mh)%BA>2cHZ8X4k0qdAEGw-*0scMmxPleaF#RQAvr3@?*yB-v!pVz?`8zI7=Twb3XwSB0`}&?h)?+zv7J)Vm!Xp)%jg1Gjb1p+ZPw|H_Rdse76(PCNf`PEE)ZSLGk&f;w{Kr-#`|>$2}B~#K^Li$4xxB~Wyc!%BmZOFzt(67vtvilP5P$5s%CU( zNMlF^p>jDaD4|^lp`jv_-qm5O#UGy^TQjg(!r{m7HZ4OzoxC5A>I3hB4hudda7F!g zf;bV1K=IYR`+EX{OBvl-_&)NhSR9Hl{Lm*U#yh)Os=GxsUxbKYpff&-X9B(oZ0JG> z1K}-?K#=^g>4N(aN=&bI%isCD6#tD0N63R*|)zP~{UW4%fpG$|Orxa5{fAS8F=Jg(|~k69wENOuI)t zV;gakArMdeFeD`8;X_sDLP+}_J$m%^&X(hee0T?(^b!>{)5pU^{tk}^P4_z@JEn+* zvrGjgtFn0W{|-|XIp^dwJNP~zY%DEJfa8><<;d}gQZ-$#_@*KlL(nqO62Gx0L@;#D zIdYtueC?%gdw6$Rkm5<|?|+>a1LAAfsDOM;9~vG$3+bwEA=F}87B8D1U5`rR#X8$d zU;KdO@E5KNjo!yr`kp#^C=e-}3~|Pge?Tu4X5;hvL1g4lDCJ<6Ex|qrKnpInA47SL zC!F{M>Bl-;RLQqa_}~87mf8_{#O%=+Yz_a6v{}L6 z1ob0qeplG^Li8SDw=gn5WRCsRCw?~4 zx%GCEDD!@eg!KGh3y!XosSTFu&%Mn!8QwU-lo@Xp6HbGCvmm;PT-32(DKu*ES>_xM z4$Kk}k_yTFsovCmz~)c!!phOap$Msp?^|kZC&W&U&`|8>{d(!&rkg#?PW*J-QkPrg z+mb=i+*BE#G#j@$I3}D$ZzH!`LTq=;b?O_$L!;y2SlwXdVNf2YK*L>C)-qu8bhTje zo!^}Zwk*B=MF-~*e%d@eS-v zOFOk^=c49`%pHDhrSYEyX}df?pPq+&$bt<}7#GhrdmQEk5B@mF1aM%lkZzf97#r*Sh*r=th6_MTe2*pe}RI zA8$rJQ}h-N&ICqnXI)ib*kF|ZUt9o_Q5s1I`vb27RpYl1hFqT)a| zMhdJDC$Mx8{M2lifl13REF9$ip`oEL=?Mr3pr)QbPlwX6gZp{y2c|EA1&Di2V!p&p=?pnK2+F1cJYY zzY1(HkfdQeepiY-&Kgt+v})wH|3t@;*1?lDI4=FA!CuqA5yQMaw{OYtHQ&gRPM9qIBXe>`yRzRPu|s~Z?-*b@hBrNnQ+4Akfr;2w zNCRj-z8nuFQtM9fhX$DBkvRU&6M6hdf9YG{o%9x?InA3~VO6=V5w^ZZB8Pa&k2$EF zoBpj+ethAFw^R6-6gaCle`iyT$vIdw?RQM&cs9H-d@M)JP@DD*5+6(IxK`c`c8s>} zA%4_(Ha(hj*ncne?PO%+^!*EuOhG|G-Gc322Itoj&*Wmmkr*M#_PDNfweG3?O+Nd3 zwq9;3>OWrayBp}#Y0b@~3gV>HFPe5`R!WC!E5#oc0$lJSY3_`d-@@?@p5TIlIGZT` zI5F?+pd;+)*&ov|1#dQ=``K3}8q%6?>Wv+(grUD~JvFCKsUyozuPyI_CfanySg4AQ z&B?UI{oKSRk%zaOBLE{B0SNDTc;x90UH-tp@ecYvpx|7-A8Kpe0rMbKD0WcIzX+Ua zs#7G{#our zM4r^)El44>VTeOy35yhf%yg4*anl2a#1}Cd_5VHcEn`&PNx8VNq&@t2x#q)%M$7z~ z^j$NT!%au?X+6vGbOKw~wjHC&RTT@gLm3e(D88<@~lQuO$;@*}GcdvkT*ZXVy? zb8|A+2H(X8OY6x0*YKVUqavcn;q6_2lc9kB;6WK!xOF1{WW7WFJcLm_q`?1txM&zEx72B{V4<94IDX3Br+Lg-7ASrAu)`oa>0n`G++6{vQQo ziX2vfh_(k>h2~scy`=oADNR#@&|7Eb)M<;Z2XgV*sF)dgOrEy!Bz4-fdpuO=vfXAZ zX~SuVEH;ZqzsH}ZWDO?_OAjtLt+M4^eiL@5AKCvxUpnGlOOAKs7#(qk{$8b5816X8E$a*by>7y2t6EvaPblG42t~<=( zU3{pP*V;^Yr!NEC7ag6|G-FjHsEO!ZKo;}_UY?VDaLL!(PO za+LesLmH~qo4JzKNgg}k!kT-veEy1!=Vq)Kj9y3cE@B`WPt3Qk(`-~t>oO&v{pNz8 za+R|c)4<;pqKM)ApR7L74n2EBJ{vhuaX*B5ET8lG@UXDDnB&gyj6rh%)bMcLtGzt; zZ~E!$oXTqW^O`NSaCPQ37`@)9A(yo^OK6I+;6;98c>y8b1-j===CGWAbHc>%a70v8 zN}57)-qqfshy1=`q5CnCx@{=QMTduTD_nq0V|RXK)2A!;@J5!4zw7UBKGK04Z8x^g zhYz2(S&q6EzVA->wcc<%Jz32DzFbK8W0yMFj_Yf#aY6HRF+fzdbA`FIdteDmS6o{ksl+Liau{FKdV-2twZGj zOX^`%R56G=NVV_>)iW$9tgrV~RpcVDjQBqFH#N3;aKm#R`%g@i=4bXPt4we1-Ev*9+)e4?=c|3LQ*0yy{dc!i%`A=1s9JV(66@|N@AwrJx0HHj@#NTb zBDj)?(kZleZ{_8~;8ozYW`LMt89_}X?`VGZB(jr7Z(H2eQ+A)81}O7J+9^)Gr(HZc zpKxkc!)=h!Sd6cSrN4dQ!=aIOYL_+jEC2K88u1hP5k5Z7$ZkJ$!FTIxX`u)jq;gb5 zLBQR++F3?7HB&tSvmkyYw`e;i>}4mIP=hHr5_t|eo?iB)(m* zwmGDcSAD5#z4DbgQy$F!gy$PuO7aGMGIxx5XEjn(QFU zggXlk0qYK63Yf}nPP4PKw#_&gMRAM~BPS4)im)i1AgubIIr!^V{GI-M)t|^ z6@F3&4=1$}W}?!Rd~T^jVwFySXkaUX1S0yF8u=U%m_Ecz^>3obBEK8tnrmnV1TxSv z>ZBectq1b?*N_miuVTwWLHpl=;y=pO?;O23?Y3}OBVKuR^s`GmHhqM=5Ziu17W)>4 zuW#R?i&2U*+FPLR8Omn3pK#gSyjM@ZwxqdLi0ZfaTFf&Zo?#q=Da~jPrDie=``u#+ zyu@!6Jf=52d9H!du{v8=(UxnE-#V0;nuxuR^_T^~p}?xIcm_a4JeJ77Pn=%FlSBAD z2HxPKch$fKj$hm|GOKVXMIWNp(V4=}ZmHcvfCW(1BUtVpqISxH`EqAxC+q>?7o-fU z&+8_}Fh|6+h>VCxvUMc}!vEdMr1OM{5`GDkb1PO?O1i8wuK&QHh$am>sJX(7NaJOl z(0#eDI6H)aIpGgT3Zt;XO)2q`ldB3iSnl#Q@MsXs@i0(rtA)gguh@kNr`I2D%FUyZ zLrV6cNrc#myK-D&%WIBQ`6n|MAZDm1hOupSy%fC%Y@ zejoWWGVnA*ZFaRuevhB8FIq!Mf$j#J@>#%2A+?E|pHe-EaysQ+k2Z;t=)v zm0gYLVbW&|FC7?_*&~F2BPH4hrCf*%%t31%(wq;+ZXd$kTkAGrH$*3+ERXpqbWCXN zT*bfC)zpvx>quKFBO{|BnvTJj$`Y0yn}v3J?D|?d*QTj6b7e z)aq9YJa!>z<#-2K_(bQ(FOs-}W=NzXZ%%5HIZz5NU$UdvOg)G#pk3{Rv%EJI^`mgF zrLTM3%5EUw4NBSJ{p8^6La4}VtP+O=!n zRae8wyQM&jmarm+voHJCT5DK5^7@*CD%#hVr<2aGkB6sP=-@(w*UB_Hc9GOLr09Wc zuyW*4j$J}%sdE$vx5rGI7S@W1tl>BgT<5UxEiy|gbjC3Y0y#N3z6>}!+XL|*V3+1U zM%SG9xBaOZ?Y%kHU0}oS+gah|)z^p9TEN#Fp6_1`uOWm%qle^pIE(E(Y8xFwqnl@b z$oP#f3^>_V#cSvUf!Ns9-8~{KOlsxtSFs(x(XgZH-8&LR$5uhM^|M@J z{XRA(=qt<;*dACDp%_-1Kp2sk$g`iq(Und}**tzczvIgQGfA@B+RS^V*@=F{#Xr*0 z(qMOkL%VyH4}I0(4(|y&Ig}wT%(2XY%>f=F#UBJf#K~tv67oQZ`-|g3ZKNyDB6LRf z1|C&kkdKe=ku>_A?15=HXRu^5T#sS*-4J=Cy1F{4YR#k6XRltpY7fMJ5SQJ&d9z@7 znEJOJUjK>EL3WBrjr<pVDb$QyrOxhF^2R z5L!>>D{}XDlCj41p&Il}>d^O|V(UglU=)$Z_7`jf3z=A%Tdt*u+(WdE0|uOsc_czZ z-@o&9^ux3YZ2}S2QJRDK_=N&2+X>S5-xKp#M_T&-W{!!{y7#2d3Gtk;7?fYU*%rotc_ifZOI%7~LVv zg##W^T6A5|pYa=s6_9^jIdJov%w)?PuSNzvNoykyi0HMFce|`LKmT27lwy$a6o)tK zczjygIlAZAyCp3x4hjmU4>O_{6K>Vo$0IFWel|cZewPR={!jXh%=5){ze~{I?bu=y z8%CR`XpVNkzYR5O7A*q3~ycTwF=dBq>gC?x@t4F8Atc&&y zm1U}sqg8beNrKw%RGK+-<~ZmJ=Hbi9^Y3RF-j@FC5( z?7XFt&9o5wuIM-%B=n`O?p;gVd0GB>0FK6If#ir2KJ>lh;poeNUXlEKd?`2n;Dn+0 zBj_}J?@HKhOOxJ0sBHa8-+Sk9a6p&!=WG-CFxead{y_Su(RD-=3zFGqLbq9qg5f(z z8UfQ~8@;~8cSp>oJ0b1sQ8W`|;-mJCBBQVrlh&JyjpiaqqZlb<#~Z{1xp~7wL*zz7 z@n@HEyU#AAlfOVzZm?*is%Hv+`cY70CFWp;N(pP>B|d4Bd7j-HM#rs%j+_0o7Lu8G zyn(8fF;qLAiZrb3W_Bz}K_?*Ev=_5r#S0jgdtmp(p z?b+wcE3;?=#)hn|-dXOoArj03$+ z6IqsfPPIw8gBsWXwOe7N4~YaXx%~In5eWnUy&fR zPO~_8za8E%Y%OEjB^9Q7sY}`+<9E}le*Ml>9B%5#Ph|t_uML@1q@OWNwXV(ac>nxJ z|Kklo`rQvpZ+#u!J+(P(WwQK*&&$7gracebpBYuhhxd6~8PKzpiGhz!3vMpS1s~c`EsR2xH713W}V!$ zW9|`LW7>W;$hzab^Yw&i?qQYb*NfKCHB(cFn&GGrQg#)c*dt~+$`sjn&nwvCWJh^N z=Ll76&~rK^TTD9CgQpNYv>l!h{-%HEPmqG z4~dOs-@e`9_rPle*va~tsTYJYrv7^=JnOVc^RxelHlw5+|DT-52uH6`bR&hsEz&%)A%VUCA-=tX z=BC?2k#g10v(a= z$R~abHA;{QD1;!GEQ6tDDHH@KRA{80C+vi=XuNL3?Aa3ZgvWP3NK5Lw8#%xW<6<1S zRpJ}ioib_qh5y-0Ve!{aSj_*nV?{++TO!*)+LBhXJd^2_o}5fNOtb0lA(CNfAo9p? zxY{RkG1x1(Li_vnHW~*ywrtfs(vsG#pkOp6JXWVEn4XzoqQHRu;!(NNr`ceM%+H?+ zro>sYD}f&amPYDV{_x)d~=)JU-7n{~7+*ugcBwDgErE|-`czJZ3z0)l5 z)zYn;^qH$#CVMI}lr=1x)}6i+)Y<9JN7cF!Nvv9;gt*J^XO1Q~RkpB-XF+U&luyY5 zZlV-_$S5SrDTLkr=4ZLD@^w>Foo@;5@BeXUv|o46HLFmKHP5nlzA!2o%_uofN9OBf zQGx|Aso=jpfiFxENmA$%71j=XCevfBcPG~MUisA)trde3RwWfA8i3n(`6&G zLo&Lmc=oIgb}*D`1blzMX}7p-&50IpVFB32jLYNOzajBVYzbnRSj6rJz~-AJ+BBfI3&q$8Ak5i8p{ zB32FqN=-I)N(Ge@_6bB0)f$dpdqqVZk&5D{8l>i;UreH5C745GgKGTBnI86RL@$j+ z;}NzxK0e-~7Yow2uzlpqx$pQI=B33?8F0p=epjwEaitNz= zP-PNa@lxO;IP{Y*@(`U{EgDUv=Et5Jo*!y=F|WBN8$R~Dsjg6R*Kl$iAo-nTjl5UO zX4-*z10V*i1F4U(Codu{>>m_=7(|h6W6xQytCS++hH+o2O$Eo1e;~v@;JfqCrBiNh z3)o%LgMn(!BG<-Q|EjRi`O>99Xi(Jo82?jeu{(0#II9m?0`MUCrlXfSnKHC@4wG)( zXU;HCpq#4*8OS?^ge}JJxYHSz!1$Nr9XiCAYv0V01M40z;W&Q3FUiIK7~2dK58;d? z)3Vn-k$x>1dXLM8pE7>*{p*&h!b)@^((YkmVp`9UQC#)x`W)II#{#wX=03sV8+Wy* z){96#eAB6-;I&U2h0S0qA;Rpl%etf7)1BiT8dHtL3SU8DO@R`Njy7x^;RG@hQFN&4 zNauLCu5FXK2qrYpg5>lDvXLJkk@Xzt#5h#h{2y{SF<13~rUyvKGCDh=EiIa$V9NXj ze4@l1I`m_HdYI(6gGZ07^|ZXa@)I$ova?i`%<$KI9vR#*qxwADYuf(?R1td#g;OWh zUzcmWy19mk4t+ObXTAw!DD=C?K)a}}Hp_hE@dz%^F9smSS+tC3z-h{|dv~fqWQNi! zCBMQHgtNy41(iY)K72TnZ#8*pB=O{bF`oXGm(d>n|8kvf%Gk%L0uw}a80V zgYa;tKR;Bt=+A~YAZtS-KfJXf<_s)g$+fxnoA(h;U%JK zkD_g0P>^QH3Br6QmRqGgs7)l|g5wEkzb1-m=G)1?j~9MJMcA!JOgmsvMDeFV<|B_j zYYdkFlC3UuQ~(4R{uHU!P>n4DE9i@oHX9+b!GeJ=#MD^$NtjLO$4|X`2-e#t{Aqak z_|VomnIR6x0mUD*x=*oEC9%OXlasJ!BH^oKtL4e*LXYB}oW-|NF^hTYRkC9xc1~?x zZ}L(rU=%daS2;_q9pz11US4D(_X6YN;2bO{@3HLf3Z<$Hf}f4luBpvKwmZ3>@V%9@ zRyq6}ab3TYv+IbZ?C0m8WNP5orI*`#ih2{e-T=F#(4j3X$0@M6$WE$Gszf6%T=-%i ziGaSv>-%Be;&P`yeQ_4@g6)(?te(nrC%M<^A#$Q07#eCTb+yN)LX=>~oG}&qX0t0Z z0lHdi-cMcPHT-#o;HfJ{gv3v{7Wz;Bv`ae6wI*vF6cGc@&-kcxl*X8~Y^-@S_9*(o zsBFL%{iUDk#zsaD8R8Ucy=gCTswZb|2-M2m9r0~N? zqc(!EsWrM}VYeJib()@<+JNFSJw4e?7lmHURL2uGgv!z8z3OxGS6{lfOj$|(sfd3? zq2mDdROn#!bNfvdx(ViM&pF$5%_vqk4h7Rxd-3i6e9AijakLYTC?w%JKJ43=nVmZH zoy(xqL%p92`SXPu-VlrW@xS@=glelJDdED z$pnh%opJEcAXpSahElw~QjI8t4*^_)g1aBU2)-hG|4X;02=$>iOa!b5b>=4YQKX=Y zHrc(mwA2IeJBpN>GrMPaS4~|1J0tq&7m7urwHTU)T8TvY(sb|83_Fiq{|0yte(*^2o8O!QfanfKZ(jzqth3WgCnRGxzBpOA z%fg}fL2Nrc-u>;s744}F#l7!KBCC@8-ttp7@^13Y>I0ww43LH%$Wlst5B3E=hJX1f z%86=p*MRhM3o#HvnErt~Iw$J9KOf}p0T&(gF2A6QnU^W)UM0{y)qNB>5{Vbip`>BajwHisiI%&qCemMKcCCs@|% zF;5tD3hmoBh<2$s8WAgjU^74Awd#(26^c`!VAzPUB%DxE#dOUSs0D5{hP>5}fvj^u zlNRyhNl%5>D%#1bj;*dC#>pxO=-hq`fm7c?m1D)P4dOwS6%}O;E$0z0NoCu@PS^fwe-Fq^C+J= z(^=;3Y;B!pQoDBGBpE)oGHTHo(;`>K+vexxJp%*}H0`>&ziP|7negB+q-8tb{f0Mde4$)pZ`VlZ_iTpn3*)@P*T{|FDg{ zZ(n-s%Z7CdSuuE3?I2TNBBOs9a*@sdu*s|(Iu1gFr0Ni2MhT}(mQnf-3JO}mKp;9b z)h@_`e%l7|BrrS9e}b7+HRv9L55{8BezBVgdahR zJr7iC&}8!8w08dZ35IepJ>Zw=2cx?6cYmb5#QB+T(HsO43>OrO5GakQIBHI&rm-xMGJU-5*l z`=d=-pyGo8=qRD@;!?!+G`wM3GECniRhpn7N1LVrGy%p`fi9Fncko~)HZXJ*LAx6a zfkf#E!nR(&Wp8viNijalr(`1CQzpn&P0D>HuF8md&Zy?suJxudYV{pMSFe3!M++N7 zWBsClfl z(9OXY-z?kLhYsj4Y!(o3IH7tqRQ1d5c~p`hPdjO;N9=!iS?<=H!km;%8T;Nm)+*&#F2s+O{SePs-4&zqd0GhF@d z4!5%|ALFW?oFPt_Wc^ypGK9Pr=a!(55HrOAj2A@l_+NB*L&S=c3+xB2Vo&t_5jbsr zB=O$tMS8eR$08%U}sqx4hIR^mO6S9}H#~ z^70jwcm9#kN7TbekwRwa6oRf3oUZCDzAX}AY7!$YeeJm)M5bp#OjT8ERh$(0lnOmp zdcF+b5zgF1Xu%G`L>~b#792#h^JF>(Qh7+o1sxq0CZ;wNTu|Mt0FSON>YD62Z#fS7 zHwxsYH+wtzs2CSNDLT>#beJyHcQuVT{N>T#Su8mr#QVn|?6)8bay;kN5klJfi_j%a zWj5*iF`M|eOE+_QzJC(tqQ}JIS+cS z;}+ZZx0;8>R`SNRsyeU?Xb5_;FPiv)=DpGFpSH%N=54axaX3rgpYJ`!9q13iCgFgl zA~|E(NDDxby6rhiHBd!vXyV|_)2kpeR8=+ZF$t`SGW$W}J@W5gAX26OjpP9bQrB!J z*`K&@CoxVITD;$q_au3}C2I-WAo6cG54}SMfOb9T&1Ujw9U;Ds+?j%^Pi%yn5&5?o z!tHAabxbDWgy5z^Fa*dvN@Xjj5Ud2rJ*oBmGh9kbUfOnO9GBwAAS!nW|5-z@29n

#M`Kl;Vv{;V41D_e@oj8)sQR38-iDf$#@u4nepuH1B0K8jkF3dO9wY zBK$pKSGoH)ojoy$3C#{Y!xc7)ALrp&ljJ+PATOqdfwp75{~C{t_ekXw`;l$t<9OVL zc!o>M+0$Ql{Q4*;dVk(}uHX?X$0>tI<9AE%$}HwBBi0l3w~TlGrOZIEgWe zxV&bO@6-Kh{~_W7x+ON!Tp_%dAJRMz_hq_M5L;^AcU{Tl!OZxA$*|!9$H(l`RNm8< ztZ9f&5H0xJro%I0-Yf~0G|>Od^I9+(J$9wIV3Ui*#k>t+RNiWrTyPzu1;fZa>+dBq zFEO3L@zrTK-kq*d*`740ORE`km4=WEhvbAH#(hNS%ow^pIYZ%JyXA`X(S*?ExXW+E zZc4AeHU^)HR9$uuKglHkL9-n@D7S(ZDjW*8W`0mTlc=&FyxGW8-0t+Iw*L?ziGjGC z=~P4@31n0{9x|dPtmVm%FAiP7N0NwI*>=bp9|5t#Oi}ncHNip#5Z>-aziCK@5N2NC z>%a6^cjVL^_vK(ER1C?f*}ExToOotHE{dW(G}mz-a_-tG-UpK+buZ5HfsCE?z=uhE zXrO9m6BUt9p6~;oceYXyqGWx3V0LE*KK{FQ{myPGlJG)B{ATz!UB!1a@BKAiD`hc6 zlbh3bTvE7PHW_sVE@&pEa{G0hX11E-t!(9Mr>@i>`P&f>X^agGm%@vGzI#t!-7p-^ z@+e%Mw!qzWEc+n0e#?PRhJD?=_h0@!_d0`zlwM1;^Du<7x>l=4Z51&Jdh!0^1NAKX zv$?Mgt(MvnIf z4TPWFQVuv;VIgX9I-cwe67=CqlQ+IxZNb~5GZv71SaKuzrHEP^3zhg9PALLqjYVCr zU!@^5R`wZLODb0$z8!hZ^r>p<{+{&RXIETS2j@J)M3RNW5~4OJiTKxcJrcH67qrLj4U=pHvng!Qid70RcZKIIJb2Czd6Pv*F_kzYW}=Ho^WG@R zwHK3ms;>G{mmeBxMjCQ|a@0TdPUA8E^-re5md75syOu0bW;TbkAHCc;hiZwA*&CTH zKV@&HHOlu|R$rhJ7rgC3{MJLz9;zTwQF-Gk9fyWRhy48}`5@I7`>|stZz0&R$-0P} zoV+j|evP7Dc2@VsY|oqi#FrPg5!GM$ZhjsLd-IPr)HWZ()i|}inXXM_%g^odg4dN*ujP0Tl1xx zk&8*TOVFRy*`t3(`R)6%@NnF7&hlE!)z(wTchFaU6kekCHp7m3h`GO~Q0aj(8=LJ| z`^e;I_wh7#y_4})Vt>6@Jd<;HEM_=l%h&HN(?_@G=JyA`tM+epeyP5PsQ$wEzc=zk z!&w0 zwd!3^RXmb;B|J<=e^h5KaZIPZF5~Edx(lO8T6J8`*OcG09UOlamzEQ>Z?y8$L~u(? zVkFgVN2B`1nT}8PvB!oZU3dPyA>Q+S*uB%fGD67qE;oPAKziTffZzC!xoP_l!Dadh<^J*i&LMa%;H)I}U76x)eL0UZ$9TeX> ztbicw27)WNh4DJMffH?~U``jWnTiHch#s>+ws08lorhu(kW4osNksSeXGvDMmZ9g1 zjvoU9kRAk*8?g5XdR7dPDG#uD(#uRhC+`g1bInwe-u2@uTPuy zCWB}I`MX+(!0do)~j`hL!W$srOT4fH7i~zChKvzr+!7wm{fU?## zHL3PoP*K_I%PS-#)-3}Yt-X8qN=Ypv2Nn|(L%KXUJDULM z5;i4T#rf8YY=YMG;lqawlGEqr`;c=6lSvhP$J#+E#cTc3zq&Gq>VuP$6ENh1rN1d* zv?#;LtppQ0u>y6KuMCLA*H(PeW~OiQ}lI zs5JElwtv6*wt9|Jp3Yz$PHkaqD@Mi)B+ZWj41nzH`Id%RfK=!mnsnhMxJ=B<%!xMO z-c5t7aX&*zVsrvT9{}sWFkYi@VpyI5+Otb(6+B0!iL&f zMYre&4^+-K007*`ffk;LW0|QSGhiHn1hNFmxrH@WJ^o12X9Qi-$D9Cg02o4BQUbRU>QP}@#^jqY6mi+I$;C7&2^|U zH*ow3>TC_^o}Qit3=qgICktaSj8~hv$n6p?QtEJk!4}k6WHlsimyf^-lSf%odJ-0tn`<7Yj0;X=p(liTmXO2K+=Oni;{3lM|EgoMY=>d8ke z^Cd(@!=U=XXb7l9Gw#Eo?Tk< zVAL|ddQ}GI1yhUIR^&6^*VWlT4a03q35ki(ufJfiYOL)pZS0B)38-@U7IvV*fV9Nu ze(#%H%DVKlw3_+xRj1>}8+%^djZZH)t^KU{QFzZp)4eScCpXk<49m&0n7g%60_$U_4Q2}gZ6DhAAtWRA%RP3-Ccwe>u>EzWB zR?*Z#cTQc7cgvKvP<~~@bFNwQ^XzY_quR!dR71f)pU=%q`uq86O)`&-o=4x?_%v2Y zKZdA~(rDRu^`AUXd~F@fkL83{2Sif=Oc4FRpswZ zEQhnrB*@LEgn1rvH+)Y;S^ja1-avssVNJ{w?(6vZoHnH*G`Q!WY&0F8syxqz*m-*!CePZPJS^A4XAX(6H zTu@Vk?1(<%bI~% zZY4#!Lo%jPNT>{vsck4E^O&j3B*_%Q?hcL8K$D70ZL^XTp^*|o8`))OkRhauCA`OV z_1@q2ertX2TJQS)`mAR?&wglM)9?D7!*L$xaSq)3J+!cDdxvn#(0!Nrt?~BvgCLHr zmn3R&Es9q9T-xP~@h6^n1Y}*=UNx2aJ4?ja=W9m&zTdejUVpWcVI(~~R`Gc4FJH#D z^Giiv+5eht0*0c@#-5@Zd)w@uD30=@`fZwxQC52-C$udMk9y;W8rRi-6#`f+=v3v&D0f98~l zFR9yMao#5JPFGRI7R=YZY&ZFdt+B{7T>d;U{lrfGP_W}+M$BOWl zh6cG!o6egHj|0T8%Bsj>d{{LUyd8>h3X6u6^thLM7jCtmOrO_CHw}A~wq?r}1Td@D ztkKOh2anVbtm3Z2kj+1M=hm%W_%4iNr;cO2ODOT|!k+YNic%8G<}r9xw(9G^ab1Gn zIWgyG%9O$YYkU@k92qOS)sw8IdS+I?Fx)a~M`5naO{xa6-d zy&_w>YMZ7XUumn?;3c?8pa+7I#sCIw_o&3uFoP8&>1WGIv{t1yl}{1|NKmk#oH|pjtwz~*D!I%i3|NY!~>Tk+&MU+*ek`x^oLRw zV=L;$oPKLXnr>fF=AKnz+Hii4UVh%-=$*9sn2;NfS&DsFJ>InLF9{jj2!3-fMWMh1 zHtjGzu2|lG3UfFZ`-GTYiXg~x#gbjL!Aknf30XlUe1y;(J_@^Y6M`hBLI@<(&L>Wj(LSM?dOvRbvGl)O z05&3$ypNU3m@34`I_jf%;ud0L0eSyt`Ex{wDe5*}Kud=N3vjSIy7}yo*1(r661Nhc zNjQ;kJ9TmaJ&$}0^lN5g#94Xj>#74{#3qvKK%|bbt=vw2hrpPJl{(a?g&e#@7`Z5f zml-?T*`?%H=yJ6yiG$Q>8g(T9(iR|BhlrDkBWyLPzndw4!BASJ9Gdd%Z(3)c`sSNr z*RHhGn!6;=e7T2@`1*a<`C89-h%Bb7wVFl;veBh+1RsNdU*GdIZnAEPJ&h{%Wwo9D zl&u#3t211FX!E80;#)&!lUE#LPd#JC&sJnhUK{;~nIK!yPU<6W1*PbrQ3FwB%FG~^R@GG=Z3+y z`9ZGXy{V)>cq8-D}^jt#Vl$fLC zuag`0c5)*BjGEW@h};#(!6fNx~eC^k-CR^eVJQ)qzP`a$re51 zrn}e}aJG0uN@7lOX;)DDm!ZLDMGR0cpmu&5rmC1w7wIFM$xr`9B}=9Y7zG3qW)2Ho zw(ST662iIq2FPJB*89kp~WAxwOvcB-kkX%riS?8kvA`iE<=_H`0@B$(oS zdx!xZ>eNm*dDu<2Q>Py1&J?7V{Whmg@=Ab0{08=*9FSa;WQol`CUoa8bLJ zBQ>1e)SJ8{SUI)@sRya=2^ICgs`A)MRswL2yx-hZN}}Z?4POoCM}!WpHB-VSFV(&uEWcWW8NmpCD7%#wvl)f9z~rgQphXPR{`=r%jQIosNj z>b3srq#7(erYzlX0%Ncoe-xcf6WV^iDhY3sSNQTeiGyX=!=-)D=My zI%!JO)XDWGa_Xwzvl9a)AesOr3Xh0DnYsq4CtAa7A#Da`9|XVSC$#?X6Tx~Akas$a zI0$h9x&SeqtoG&0Y~?uWfoKQwavu3XW)S(-IAsx{E=tlM_SmuQ`ub4+Wj=oVxM&U? zO`it_!l9Ug<{vI{bopA78xJ9UfVyAn)Z0HdwAN>PsybRK$0jE)fm7^U6@{D+AxhkJ zAUi0;DtOchN~3zbcGtDO;o(_OC|jo}=!;-zP5`xO2LT_+ynw82BlMmQmZ4vIxV?Ct zq~!CK7JxzpWWHToocrVpqE|0p-`sZxKRn?uf#AKf^V0?hTZ7_xkOF`^ZK$ie|ib&O7yCbIAmXIU?MD({mwZ!Aii-n`ii3Ut18o2AR2_a_ULzq2^sy0vSwuJOnu`9S^y zjP#|nLt$auf(qRbfd@MRrCbE18dxPO#E+9>ZyRz;jV4WeeCjj9PPE30E#>;Eb(JZZ$&uZ=)5)R>xV)oOA^vP#_+DTzHxrjho2eKM{TavNt@1$_HB@e zQQs^va5-_l(Wr&tve^r(W5_$9-Bh1&c$}XS%WD@g-%54aJi48!aatw1V0PjsmekKe z6E)7uB>|Ys)phh%bjZ#toAk<*>i~)cy+gC3rTc*c2VOKZgaibHVL^hOS2=ED_8rPN zb#6eEDYR_aXkU85)hQ3GKuldl)weiuKwjAM%+)s6oubtDG^(r%oGmpO#KLTN8{Bf3 zJw`V1OGiCRqexLpFWmm}hHH$I(({yDZt2e?&e=>vQc%Zr}ODlj9^MQ8ruUEWzFPSEZ7NnrtJlb4Dn zM+OgChs=KaE?>&{oa8(k^sw~8^>N<0tS^H0j??}F>_azi&KZY|+|pAsN#4S$9XU)3 z4%lVTAg(1SWHl_FaO%#fZ!_Q5J!-AUebSnF=WFSH=99{wssHTO^4@*dY$QQRWyp7^ z&##tc*}nYlYT1_$GRk+Hi?EY8dD0KaiS>k-vay;~2!n801!QrnJoVEb08s)}4YW1O z#dx*mUAb3PfVL&jjGx!k_$ms;zTBQvfhPutbA?vaZ`cq=M@L}2cYuASrlx`vv_n)a zbQofXH?Ccim3#!X$w=sSLwDzzR&O4Gj(7k%F;|Z7-}jbPn&z`uFv-8uWnh=nfEtT1FH}81D1xQRe7k&FBUm-q1pG%n>WT?d(qTV{;ks2-@kCC z7IL0HK+0qBK(uBVjbSO{_o`}kTz>oZ?b*d>HEzkZS^wVfdQ>km9oZ{RbK2H#UlXss zk9^QEn;2Iw8ESUdGDbK1_~QlQZXO<(!7&R439v&z25%}j_QF!@r#EQ~2TcsNqrrDe z#Ka&NVxaQ;o|(!0;Q<#)XVplg7l{Bm$6Z#0mE9cz+@9nJdm9J?X#CCJ)zu(;H?bHMq~ zh9S+1LJzj9bA60yZVQ?e+IB<7Dnmb;9BPIrDn=6YJHX)rv^=K@dw(-a z%fz63SiqSW{A>5%rtcxHzY(C~VdtV0XYS;Z3Zqe=j3%cnW=N0?!{m-UIF{ct7eOUBPtW zKWj@O!ov&fisP1{qE8TxT=Dv@!yAb#bD1P)ZqklJ%%=SQ{lpgI^d=y~{|&T*FKV+> zv+oGv%E!admqLmyjXE`cUi=yMN4T9tNfAGrNP-Z4u27@o2>MQH)*+#tMV8_SrPTZP z524c%vtRDrxx=-1vB=htym;fVu3=17z@0sR_AIEcaSw=^2q1!$Etzpx@#|XAn(*l8 z>jI?+Dvfb8TCH}^CWUfqz5g(Jdv)6PzFyDk** z014mu1+HQ_8OMRdCod6`oD3FNkRy+v5+gO$1&z2gP8*vxG*j=;nvXL{=gvWL%x&tJ z3xbkhRS#xjZG$GL%cwlK`T9!2u5jBOvQ_6rfH7d{9eBrqocs zqlM84!2oD}dC383dlW)fahPuKDPg^Q>5W!}vUt=e(d(te(o$Bo=DdC21I_Oh*yFO4 z{KOCsU&+%h^2a&f+IROwd1twpwQT`S;k6?J*cH;5L#^+nVAUp zrTDn~(o0KAF?3P#c~LZ6FJ!QSKHGx$i^rR!!ks=aibq)J7pyu>JC0Jz8kFXgl_${L zoKpm4m502mR<6XT71&v8&vJzv&DXQoxn5r_J?^k1&z*h)`CO z7oO^>>kNxCc>VF0HoTqn_4SV*OQ@?q^r^ZE2iKOrd->9(5*k)AN#y9HGiPondY^Ba zHP7t(`Zd=NkN-B(4<8>N{(C$c!Rphv9vC0|%SONV55pkm*k_hny1&Cbw*@ymilQ0h zB|}1Z7A@NRuzGP$){WPiT{HGpHO2BVMI|NNi^-q71L>sf!xo8WwMpw89URax1-|Ac zoqR7(WoLDbKu}XnOm>Xq3$!~ zZYjk_%HRYmZx|B!(<$UW4)6W2q@-kcqX+6+U0qec!du!E*LYlujMuj?H{ayh0IHnb zf>@A=jX6II4n9PSH^O8HWpp72eECuuI(%1?v?sl3R(hi);pqwa{?=Bpq=pnRpY_7!W7!gsT!@>J$GMYlkD^J8yDIdJisR? zXxlSH+uPaRRqSa3`e+O<*ywVyvWl!;3`Qdd_Moxw?gl{Z=bg;)FU{vXQ@%wFZTvQv z{P#lCFh|jU@9E*;vm5=J8q~ATedxGjU~aJd!2@p0qAJxZV|z)4b3H>(o=7RSY(2h$ z&ifInrLei0P|QK3PSqUo^v{d+Nz2Im7#}y@wTo2sK-UW5Z03!#XL&_L5Fd47=ONqZ zuXIC90gJQI!3zE*bMtdx_ZcgQd9%=->q`o z{|h2V_C+q++&dLz1yr&Y_&kDCBs`s`;cNI9$#qz6Ql?`jcV&#%o2+`s?R;stPIlje z08oYIx>mU#-@k_e0pPZ2fiRB5Gb}P(iUwr!I)ry72r2o%wc>FqFOFgP?%FZe1bP1D z%RSxQp}O(@naUy!yrN|4vJ1jCxE<2s!x|NHOgVwJp{scmjX}^fkQh=j7B^mX=Opy9e#g*nINmu+AxMP9_~Km+z~hox??zEpr_c zk06N?oD$@&L&dy847)1!%gMFg|K3kr9^ zhpLQxOdlB7-1|AWlOH75amdC8?bWyI{d-4MG?c7P%O!D@fS%JjR*!jW2w#3pPkXw# z?brb6EAOT>Jv3LGI(ZVsR(KzkuEWJ(J9uY9l5=#_mrQx4CzXVZ@nV8NaO#v1%HI9L zdUgYcCQzRD^Yep5Pm&L^0Bu)=>Ew z=N4Y92D5Sr<598X*ft0l<*v#9II;qNh%uhIK9&j?mHbIXofnSe8NYH(K96 z0@M=wcu)&tC`~kfe(u5xjhjV05R9k_NiIUKh>3R3-04o!rNuCdk(+bAw-=u69E6}y zFBCh;KmnLd+!FCl1dn74wfkNjdP3%_aHZF2PGd6BFA(2b3!P!SUc+uqk_-y7Rwd4r zCL)`-nAwn*kkG|R;^mT9AUnvEG=RE5r_;fFf~WBG>?M;eq!6s#ria4A$!0MevUy_3 z!iB0)zo)=cf<+d@6IrpM9sM^lmExBA@vke96^x~L>olKp2`~0{cQ3&vhMgyYEVTP8 zDvqJMq_M(6)hD6d(|M#rC51IrU)b~M({UP;tuEo^N``u?tD zV)nU^CcVtGMZDTAgD+$$(Bn^6Qt!^|aqQwfv5XsN^4-|+vO5+WiZr$f%} zS_PU-?%-7@P|Tv`eTC!a{(fmu0Y+OiEL>6tS5CUJhjZD+09Db&o?X?|9$-M>p=^#^ z&!`OFH2u%FN>yg3f7FSDgoF>e!VOUV~{~_)AAAa54br|`f z%Xwrw7)!8ydkqXpa)fM20h-h_HJvz{ppmj*!Ggdgpl9BGs{;)zK}1g?yu1n+W*W%d z4XS`YDFo(URe{~f>I6Z@UYq&>#OCL}h*;@4C;>YB8iY{0L6YO$3oC#mMRD?g=?%zH z4bRR@!@dqSr5}4xGmjV-B4=sQGk*eCo5ik0#Paq%I~)Di8I2f%xSWADRPeh5XpoD$ z93hK@e=(VjuJs1f3PdjdVKWrZFOauBN-BgQKVp^oi;Icfz|;iLyJm5n(;Lo6G*}! zGRQ|$M>7&@(M171zQYjw0f_V^Dh3SFyZ zUo8=++Z3oH-39#+?Nyx^$qI`j+;Q$QSW7EbkPtcCiLbA(xOfVjF>>FhZ{8GhrQ9q) z=t?TIA-Vt%0Q?V5nY8LqM7z~CgdlRcoCB#q215?E$0)QAFu!&W?gV?p7_El4U13mb z5Iv!(R1=;83kFf?NYFM}m%#oC1=$htGXy?xXp+Q&t~|s8>81P@7@m0vAlWR`6&^-T zhd`ezH`f>bSVu=^o$*ySPtRLJ#rr$dGR?0fC$F!tgOkK$*_}7k?Lv3s!GIO(w{PD* zCnqPcXdw&jS$DY!NJwq;0MR&tSq2Kn;Ini&Nku()p7QeYuQOrLM}ttpo1r;Or{R>q zmjL8_{P5vso8&o_)daCLgwzF?JGWiTVCT-naFSx=^BY1&uUG{Y6_LP=nFk>X10?yW z);V-VaFs@v&uYFTTUs_LhH_A539XC*F zX->nozxrbj5?iu(5$7wm$?XNMk6Wu6vdT5p)!|`b1|1j)%nsZe2{4xgRG)*eHr?GW z-c2C5+>9IoU3js@1=`Ka02l)TZVy|_I3(Tt;f!(wq{3D_Re`i&Q`&P_k-J~fi`(+G z8#$Y!y}9`hc(DF2hfko8g?fkaPX^ngCq>72371_6vVaH&A%#U#AA%-4q$T2-51~{6 z<_Yf0>A}HF*vGON)QR)~egM_RosJK-k3wz%@7?5ctn@^uOfvsVJIzf8+CkQ5i;d=4P6@)|$pi_VAC|6NbR8&)A zwYFMMN>0n48taw3bnkes{~?>RCcsP1*% zH4!CbV;?M&22Pft5lrI*HwucM{c`ru5V^ag7c%m1lnu-8#qi>JW9Qx5KZj*pB!NU5 zJfzHvXh^i>Y=UEa_)xv$2C}0>>pR$=**%Dicxi|ZP&jlf?WI&^itgQm7T_iO)58*r z7cN{%oBH(&$da!xV(N@^sgC#W@9KmPKj_VP{B<}OI0-V;^Va3)#rAW}oZyX%ja?{V zU%DT8fRbOjeST}y6D-t~&KeXCzjk+zVC(rFyY;h6Q%zcJSBj=%wx!Q<=o%ZmRF{(K zLk3p%4XI&vvo-$aSDRC7K5LZW8U(ne0BQ;EGKG(DO5B}}kZgYZsLbCXz3DgXw0SS- z>?h;9fKniLq#Xx>ss#<7CpYKOC81eC)aeM@K(lereakYoilaw$V3e3?+%b@$YX15= zW$yQOdvvz1ErF`2(T4CEHlPE}oF9660I_6Tl(xv?lqd@s$|-GtJ`Lb4Qjl6gVw=y# z#W8qmlk7p-UtVzu7`o9Zd{MpxOxBvGPd}kceDmRAK$NuOcsU&2?G0avw5*C5h$K4B z=oq)~T6aCaQxmSFM;KQ#I=7Q^BUP&*Da3dCV4=fLp)Lq3C=(;7yzjDfu8fhY{L2?F zM#jd*Mn)74C$LUvMoi@GFK^O*OA;M*aoln9O#O6Bt;wL>gh-521?w3bJKeoo6HadP z8+|@UNY`BCO)DxgjgU%x2EgUpJPF!yq`8Jm6oul)9$_YM+3KHo;qP{UaXUBDHMdX# z#@WqvblPB9bBhC6LV-?VM=+UUkX;VYdz^T(IWEJf4cqXvkdmRl8Tt$6$nor>4O>|k zvGV{!fQ)Whc*`&oa$j#m4`=Rhg;eS|k{RwxhUMSjebS9DgMpii2K)TH;D%%slR~}P zQfSO=dKh&Ydl{vcSYD{2D7stmZ#sP9)-5v8_wdO25K;H?Gs z^mKnX!aE9|#Zu)C(%DkCeG;J&^eYB0jZJ`DA;SZ%fUOzy4(g2FV`Z{&7-!W0jT6|4 zCr@YyVI-bmoiiNP4DlzP7T1~u{Df*G88woN58ND*SUbuGWr9Y(7*nbwi{;JtBIkgC zKIoKu<3<#W7L=SId8D80le1DzZWrf=p`i*Sp-(f>TikpU$h5C(F>e|Gj2;KeVmR0E z4b5B8%CL#$?DP8NOEa0I<||iv@^WbWm0$>sR z5r?X%iu0d1=yCA?*A><+S+eBmRvip*0qgMIzAzxN$fCdAOO9$!LYjqs1n?6MV3EKY z6__i(wo_Z1zW*jwL*s-GR+@g*i3(|6jpZy+6xc@h=J&EP+3B>kRg1x78%Z6 z=n;Y55A7nm2*O9n;K&HfEpj30TgiY;BXdHt#WdoKGPU0#9!#Gp*=hzmhuXBw8x^;Y zt&%Vn5Ep1cVhBNb(5xNWTMWe$8D6(CI~Q<(%tzhD(@0V%EW76bAhTp!221KWFLYvIUdl5)7 zbiZ2#TPAwCUwBi%SK4uC2J4jlPT)<0;5-aB>OZ97Qfq#4kYfs$cMZ;M>78)f%&NR` zJ)!7;z?`n??&kKnw^z9HXk|u*uG+(5lr5~B!Z4%+ehV$$ZK#x?eAoN=v#p)oiW~n( z#bB#nL-+yM1fmS^PS9v7fgeT{8uGmfkTTMLeGo!{KYx;~;mEl7&wPgcw8+|NmTif@ zrX2oZU~79BK~7TFrA|R~`$R@YLJ8Px^?JqHwl)>)xxCP;XV0dJ?)2Li3E^UMArVOL zl7IkE4sVlrI}Hst1xT`P*I(JZ-Ct!b@nXet%*43dj+lm9*yOsJWus51QX2w1UyexRr16A%<6f}uu`4m$*=&@ZzZw;<;`)BG0K6hB;z0?#05 zDU}GPC7vOO0Y06S)PmrdwED^OTYQ26nfD!Jn^9iz)vY0x&6+arzh625pHCU zn?kXq(M3V!%DLHT8Ykcf7&)u3dN|Rfg2h zqapH;H8Tpbpa>~Eg3H!WP$bn3|q&M9~t?7Km~}|k)C|ziYjCPu+pdiL_uw#<-MU@hB4_*Cwm)N zz&P;MNNFhl>enEl{mSC=k{P zpBRMkBMYP#6B8XO!h=z!gJ4l-XD2`{InNoGcW!QOV-u4l_@9Lf`&lJl5$|J#&Agp9%7%a;)Um+v}+ZCjxRaIA4hx7`fCLQ(lDDIKi2z;i;YF8JiBE8gFKDZo&_)NXhRc{YVJ!u@>LI@ z+M2$a43pz;{3bi@;E=t`z5V&9RP2&7`Y-UC@Ipu^+vD^8QeegRkpcz_Z*tp#SvTaa zZoZ080Wm3S`h}6ndU)u1N7{lV{<+q<6cBsoQa442l^A|fLE=CDrI5ji&t3k&Z#=3A59UvV~L z$X4XP*02+@$u!pkv0hNwd4ww7FR;1lVPr{?n^rWCJzN%wsoQWtP@@tN6Dx=q!k{nU z3xLs3o69_^9;|U_q#G$F?KpZ#1v~FWAqT+w0V)E7qxRdC9tXk%IDyQn(fkF@1VS*B zrj!nJYjE&-e#04YI%ft%mgA{spmGynrG0UAIt z+Dios9}i$f5o1=MS&0Fq;K`WR4#An7u<=0~M>~*I3?jhDV0CqMyiF>=9iBwAx&SenOLSxrd7J;U$-)U?UAL`7K~ z?=J$7yM4eLKs6wxx=~BMI|DPnCNd5_HN01)vobOQ-W;8J5NeqiABS|>D9WGDE4L9p z(1A-_KDK{lUPV5@*HX;J+`M@do48rb1Vn>14rKfAOIQG4nbM~_5n z#`Px}MsR}HNO3Y1+|W=G4q9{<{cBk6=;%2BTcAr-r~>wCBsmMVYm*EmW4xG*CiMU1 zhK6B!`pOS!n*br*M@)pQ4dD#fDpsG?W7eG-qI2`?#XLL(U-F08h$5GN(K((K7%cyP oVL$v2VYvT}Jn{e4*R$sqys)b6KmE@A6?v})db@NBXfFT!2Q?E>-T(jq diff --git a/dev/ECC_evaluating/a7799318.png b/dev/ECC_evaluating/a7799318.png new file mode 100644 index 0000000000000000000000000000000000000000..9ab272a2a79b56b2790bb35b6a1649c0ca697aab GIT binary patch literal 55446 zcmdqJ=j^@q+G}0cwbq``^0JZy_~iIlSXczlpFMqvg>~sC78bTQ;v)P+ zh)_2hK5*VhNj}9o!~7p#l@@}9bsOvXQ&A6efe67Z!|rZ*6{%u;ki24(1Ar(n|z^`79!SkHmbM zFkYm^e4<}o62p9^ry#sBpYl@I5f|VyKKu?6GZzsS@!OZ+(^JFm|Hltl4YI((Dh)V3 zKDMkm+5KpLOUTvn>C>mm9J56OIw64v`_sW|cP-5uR8)eF>yydJ$$co*);dXQr~1Z5Nlo*ya=XSLD#eJAV)Kz~ zP41Qc<>h5@f70f@iq&$Is25IIS=kjb*21AzF|uUT)Z>*-TL$fsPEJnRC12a4xYq`9 zn{`BN%CSzx@ueG~9uh@3s2W_QZivNkfSXt8x&)5 zw71sT-d@BsT5PV#t9u#Cgaor+!s1Iy_v=ZTo123yItZAl5Du%O##~XYnZib0x6Nf% zQUzUhZw5+~MgI7~Xi1}Nj6Fr=F#0Y@M&`wfNFlfK7<_|*GTY-3SdPGIBo-P6_8vnn zIMPr_om9s^bZvn>Q*{-%Wf5$ z4JB%G{*WFfyNvbhDib!=Ov=EL)Wk??@4`Q8dHF6oOZV2!PPu2#o=HjB*x2~{`Wj7C zyDf;ac_Vpwc{fu_gv+gcPB{_Qu0{M#W;{({g{}Tczo?$tWYZ1i+w1=8g~ti;rH0MtlH)OmX=0f zhFs>uMjlU7)E|WJ@9(o4cI+P=IV_?x1Ok9np`;0~Hh$sQ7Hx*Vh?3%aT)5 zBc-k2cOYWtcTG-`WH7am z>)@+L;1j7A?>fP+3k*ABh1~e=-o1P0PNMtCVRv`;t_NB_L$hSn=L(shzyI{~bcOv2 zQ>(t;6+%KeDXD^Clw6#Uj*d=4LxY$v?AU;Ss|StOZy{ihqJ)e}%twmBJ}94zj0{Fb z#>M>H+}u7#_FtOxvparzm*e3-m>oHqYKG_kg^`CV5xTw>`lR&|X=C^|G$NlR-qOTB=U zMPu;T>Pwr!)_9dmNJxmkzyFgbPb{l;`eDJ28s%hU#tIDOL`6lx9i)VBnSrvL@O>^NR~8qiYi4Fv z<9>qnQd{{J8j41#K3rkEN+YCoQWP#}VX>-dSw%ulZnAS^-j~@oT4vLFs9>s2z{Kvl zZ)G=ivNtiH67t(}+@@17Ki}T_`vq*Arp+*B)t1fvY)zDp&1{553v8=x- zI=MAl9sD8RzL`-AKYVDpJ>NZS0|8mgi8^&Gbqb%M-LZ>bI@`8$Pq_BVa%%@u3w{d;$+mYoJK4*wHq9*5 z#vfiAg56_}V+wKmxr|Ja$ICd^&Cgk9+r4tFn|tFfaxUq2C4k85qIP)=SyJ~P?BslRgqW|Yj?+vzZXUk(*+HiV z+Q((JOtSy$wC~~J;pxQLNnBPIfj7HB+n1TM)4iI$y69-iDxHVk>l+)*ot>&@7ynL8 zDagymt2nL{4gAxAI20<$EO&buoe`4t$m7(tNS*?bCKE;Hvaq*0#_T}JX%ecjzdK?% zVRXB)`--wcC~SoKMLFS@A|k(L+oOuYWaxSa^WK`PkcwTx!J(t0Gg+bm*Ty6_RCRE0 z=kicNw(Jx-Lvdxeh*_JLgQM_mW018n1%lgbP`-Z!i!Vm@$X_vsz?)e$Cp6CPlGv~N z$n#a9N2aExYMihLv$3%~cp$CW6EEroak$K%3pwt7v@#sIi#=8Ag*!HuD|9V>U`eyk zD8X%q&u)>D-@fhiISB~~r^Tq+Q6d2aS7AAY{l?#h{8K*?=B(<65Qmkj+Lg&4zwzF^ zk6C%s8olA_4do+2O$yv58z($z6QUr_QgNaTB5 z+}he&u6ePB1qnhj;AR4AXC$Z8>PV%NO_9~~pFnP61hZAbpTP&=iG>pHx zy2^FtdKde(yL(zWWN!jkXhWo5>1Gr5o^!np`+vSY&XTAbFv#<@E?1&fh&)IS$vf;Dua}p_tYYCwz7=7uU*{Te<01F0Z9^{4YeV zWfKr#N@^+~N&$X;myT%O{5ZX#e0|gYtgn5sE~~s{5W?o3e7Z(LOiU^4UI}T8D=IWB zZ08S!WqKc3`sss!%|T?7WYjySi4oE;gGq5tU`K zV1i65pBW%jhn3-!7^N!3G+9WL8Wr~0?S}y6o1v*{9pOmF#s0r{e;Ls*qQwW9s0y9+pJ^9QwuTyUO{6y39)2C0x zPqG9ow#7)q1h(4PTf&UF!XfKHCZO>+-hgen=>Rb>1B{Z{3P^f0`=0mr$8ROq55Ovybakv^574Gk#9Vt6y$5G?b+td)!;ZE#0a%HJ-ZXvrLbV5qsnTB?wW^$p zDv8I&#)OZS3)vh$3JFhMm+-bJ;^??gujw=BpK^ z1FR1p<^q*Cou)Z+T(8A#J!HIKbtgzR8EbMlXXHtGRh)e8facD)QJfC@&8ztnBJi`` z1^3efL)7o#Wm@!Z9;B{LBaW6s!2a&;?u)4yOd!m7z@m$Iw>~Mll3ML{)FQK}9e;)N z!I%4ief_`GV$vOL3~%=uf?S?(iO9Rjz>%F zx-NQ@mU@zywW}V(Ya^i@_O`hRcbwYk-*t6$p-AQa2U~b}cqyHQ+pGlS99^+%hdWC% zso%ffJPPdW?6mAje*PO)k;}};E_G|RJ*3fTr%!c-rZMx=BW`ZhYqywOB=vibU8{Dks(< zbTZ%gHFl6Kc=WKF5>>v)vDhyUDky|*?jcns#l|Weavy|NwPY?Yn;lRG`1;CUDH`|# z**iD8#<-WRYyrZP>Xo8iVfT#&GL^=GU6R&{F5GLB3|A)HkIYwC6wK!z1AN$mGK=l5TEp!uyk607YRQ=D@{Nh^`uukdd__DTs)Ys)$}9 zHUQ|zREVwQbi13!@Y!YdWg9_$Nj^TUvRhKIvz0U#9{0v00vEokT2)zDc;6xz zY5+H~#^_vK-Q6c9jR!xU^Q(X0+lpN-a|YMyd&jo7GNP)alstyc*Ox-M7%`ho{(3*W z)i?ez;>QnT4_z9XI9P&o!z!chJ4KI}nN4Af5C777Ps@?*+=qYVO5dxb-i0g+`NG5) z4zU%AP(km-_Cysy@0qywR)8O(a(RFOyndZ9N=!_=4f!LY=q*HX^!E4A(Bx}D8nNTD zQ5KtGD_sd*yJGE4O}>DHxglz0n)g;47B#CNx&axI={SnI2-8~e5KY}Pnlo7C++OH>~I$`@TyKs}KhdBcZ;Z-c|; zZqv&~|5SURPnB#rQ9Udx_O6QPDn7oSpWjQDDSUi3Kvw~TLA-IY}?G%D9RTO5e0Y(K@;5qu@%?|zuRFU@(vG= zS`~kZdVxVgLIT-C9Ra&VB@K=5YENo!2@2bls!7CRhAVqDcf^xhMtBK z-7}73FaeR3>F0n9b+Q0GLrs%`p&^81Q{BXER<1@arMG|Vz}e~P=|`fOWM-zPdw~t? z7)zi;20<0^!X?bnDtn2@b33xPqrPGn5`)lamyHt=G-&${p+qgLRY~PBFnW6j2ksxz zuv?p&o4*Q&NAt%4GiR*8ExPLuL4ILx!h=lAY@%9w7iquH({P&X3Yo6Q z{@nm%Qvf8uDoc-6D~e{gAUntqct>$tQgfMoH|q<;smrX8_d$Y7`1<=-B$Q}g7Ls0$ z`|#6_l-m|ROmi6Br>Ae#Kk!v(Fsd0zNlR1h6wQ*AACXL8 za{Dlh$MP>={oC$i_6(3T@~8hckm(k(Q&panRr(-7Cip~-=ZjTvBtAT_?G_u~7z41{f;~X)7p3 z|Elt5p36IoJEdLq=C@ylxVQDhc6C%8M{MYc(V4pfZT;pEgFUO|c3ko9~QEvKZo zq@-!wA#<>wcDnUJ!YAtd@@Wl}GD;;8J<@&}(@e7es5{nrK@nNpA?AV)F}S;9+*n-j zGFDCyXoJd9M+BX-cRvgt6%{6xDS7U8Q>~0yWY*W$OGU6|w8HI-sHhZhTR^odl+12l zLLnq1-?J+Nn*;n%p--o(6+?WDjAW`wKHT3=4>30yxkW>B*7bzY*ded{y-Z)C_?4Zn z!nE~GU+rc{gpv|W)NN32!Lb1 z1;1vy>9IfciQ8!%te-J37tW$-F;CqJsHtkb?uwXiKtMo>R79qa%6ob3eTe1y0c94q zD{lc5S>&vA*|XrC?FzIf^z+k6w=RPj0pMXdlcMCcetKj>BxW{JEJMXHI51EG$Yyxq z{tY6cD_5>$pRy&Mcq<4?AD^7`Y1;cB7i|I-z49{ws;@i=NRdkbz@;BZhadmv95`wK zH~11Q08 zL$oC-6ZS4|VO6;OBkGk$T$vCo%mzV``A9HK>)O%-*=c^>$WA?IBR$opt4p49g6{tP z=I6Jg=iC*{g)kZ;*VSWSZrn~*P7d>+Z}tt6-nj9G6X%;u$+$Brx6*OYwbbvLdB>87u>YY6uF(XePyRB;R!{K{1HphnmP&(54P}7k*VrV zRjO>=EmG3dAlAFyO)V`TL4+5(zj)E2s_S-Nb>?p5=7Se6UW^0G`d_-{Qc?!j_?MIo z5H6yiph@*>TD+V4P0uBev_<;x2?+;+Bp^*qLWa*SEd^og6+m>bXLyv3>xOt#fp~;2 z_>DfUwvNvDWUW`9@EJ&G?*MgfE-indeX>kr2%yH=34X9Nkjov_e*gY`%gT+9(O%Wy z%8Ti=d!shN%ehiAGAn={fq1i!N;x|pN_n{&v z{p|p2Kpaqrh;!RjFKgvrtK4c~&W+}I_ZMb`k*xe5R;wKn+wzS~2Mg!0rX?o}0Gi(1 zKm)tKc8l$)pbuzt%_W3b1G7!M53zpjXgg4gi7SBKR}?&hpcN1l%s!mgD6zYxk#f)oICud&th& z;nKqusq~%f(~4Wbl6LPGhM-4i(;O6u#rY{>qoOpWrKQcxvUYtctEy(|jdo$Xv}G1; ze#*6PcxKJYpONK+C>oO#^Mz#(Cg*H9W%WxmGF0^S^UI$w8~RN*M44<0OSl`X=u9nE zG`bk1&ubVHS(~nsV3a)Dy&GkJIBG+`Pz7kJ#CJPt~8PY#}p!hU3bR zbpr#cvaRZ;PKYpk?R1r?%6HR$v@7h3$g_4(xz*oxviWd)ki!Qo-bjGH1MWOmZ$1*K z0KHv(tY>*;#hjDq6=)Z&Hl)_nb!~0ZD?B-nPR{=xWehsp=Kk;}v%VTdEGyb=*eqdJ zu3ptDHv2Igm&(M*s6a#T(r&&BQ{^aaUKQ%d4P3=vT z;-0BO7^!j@WwU_J=(TI4E6TV?W&$R{&^BIf46rM)7-L$SfEj=uggzBDJl@}cvPJ*t zbMcWapvDD|HB5vlXFKC2a&?8vG8z2%%u|^J1YAK@QDMITcyVx6upD3udYqIQbYNDE z!e{ndscC7JW97;&Ui0Y+NwXa>rd!(=N+~f|>J!*!WuoS+Y%aDSQkaE_X|ZZ=d?fGf zr?9sJ~H6c`WEx?1*&DMv&WmyFqe}ytCs${7pxXm&#Fc__lmJOdWuvl8I zUA{sJ*@aL=*B%7rI4JU9NV`MOrRIqV-6;FQ)|HWx0r!LIgj)zep{@hk4ntQ7!}K9G zbqXD2Q9kc$Z(qr&SoI4Ij)T&N^le!F5sd1FPpNf;tz@{xJQoD2^d^q@yA^D2CiB|? zpFe-?q*RFk;movRhS{nn-8P9V6ZrFMdzSF?xh^e);GeG!Irn*MK)s`s; z)nBX3(<7KbxS7Y_`(%W_O51O z3T&**_lXQ3$kqV$(8&$<_5CT_a@-CvA45za`&iiia?6g6j{g0L5ElmrWVP*b<1{E9 zf$jjIUPwp?N)0M|EyDnULce|cyS6p~%7nFhtANd{w6%49MMcHo4HfPzzVIQlYIsFO zg^P%Y=T+k{RC@Y6JOh|Mh)`YQg#k>;@2_w|0fUh-19BN`4Vc!zN($%_^m4J%a&ng4 zi9Wl8eEQF2G5@i$vR)$~FdwfxunUfhh;Z1RSJ;WQirQibS5Z@QgroyQhJi>(N{;;4 zxa{fwe?{O1mLw(o>_$ob?LPj*|~W-ctb=QgI`hbRRjL`gW&yiQF$yV56RhjR10H z|NFrATX)Y3=QBOGyM9i6E=|X>wA-n+-yuED{#`;?LPPRqy3y(XdI2{A&&oK0CItvs)g_({(>cNg~IN5IL{Fx1gNT*Jwhf6E9Y-nW|cL&#O69 zb;#r%E!K`mH1rd~V@}i>XKTlUOrqL3(g(JDXm;22*ukV$*pZ(OEnFT@RtHR5m5%Jnql6RdU8SUUhKAXyhU}Vi<+%cHxm6N?>5rJ%Y+4~G=f+cs=rka4tJ=yk zP&}Ex?bYz6xxL+-a#=BNIs`}I#8HU!_|li}K**@WN%h2HYr6x{P_&;uCUj#iDtodwIo5TXc3> zpNB_uDcWH-yuMH%X=w8o_eLvWatjB8w^}*(%+%!y8T%tVcq`sEvTi6_E$^n4X@V(G_+!Hdi;dljCEHd5BQI^4v#VPNh}emz!~DO1KjV z$BPeIepaQyRxjsHQM8?8uZkKTjp0D3ir)4vI0A*T=Ir!n6DIVT3B zL+$w`u|6!tu*e|bD5&iY3q*eU)ELOc$;9*m@p{K~`ZEzd+8Sbw*s29l_3^KRf6I65 zit5d}Q$=a(e}%tREaxsRduWVg^%g-GavS#~gV>PK3Y9PSy)lQ@Ovbb$3N}68zEn_q zChSMdU3Qn%p@8Cyn*l&99STojedxi#L4YwBFbX)xVIa#V9M zrJk1&P-lEakEG_aeTKLW-2lnYLwYoiVCFzK!NXN8w&-M|ze9}(NZ`VbGdFh$l;_rR zYfcZ354NB+NmEU2AJCO{TCX5&gHu!zJ<;BPZfzY7UUoV1UNzS#w+g-Bc zu2AkEd!QDd^9^U}7~!4H`|aB|ZzRAVt`aUNcOsw{NudneomID5fQ7}p_QT~x!;{vB zHLm;XQ$TSrYVMC8KS=%cyA#C$`uz0xk}6{^>>eNX?b}OUmXActOiTcPzrn`tHnPRQ zf&7Akt<6o)ZJ|6(HAbpbR#?bk*Yw!Iq1u@@!msKA(YJz{5o5_b*kuLjZLj-qbrrZ&EOf|e zoc_Wl1P1yfCg!G<`|;RC&QH)hgG@|MZ<>K;4dCWD=~lm@jOK zVakLJ0BB;q&@%(HQpuqea;aj^k}Znf_H#Ck)k!9KZyj0H&5ibNbPr4Rcn^W2;?oX4 z^^eopBp>9dHd<>{?tK}bi9{&a)c^T|PYb%$jT<*!SdLY@RUi|gINLXd8C?B`tJJ1+ z_C+yxc8SL6a-DRvu@}Sl*3x(zW-q4cqLA?86Nvv zk&{!59p)+G8<_+J-bMMu^OmyE@82DP6w%g$zDCu>_P;kw2#watSPCwWu5(>)OxqjT zf2ySx(|Wg_W4-bb*Ceib?L^Xi1>@y2mlns&{S$Cq z%=PqOZurLuvA7dl_#i<`z-ZJ-kpT0e6`ggOn=Gf>NtYD#!fBql8J@f|Zyx$qeubdG zznwb&-Y?agqq(V~F%`jOV*;;zb9!*F!+b@2$!BIFbgx~x0^Mk9pr1+7xD`Sn{k~K< zvsbo^dT)7X`MLHZO8Wy;v~D!kYf3d}CS?aNlO5$qKBakA zeTRJvJ4o!dH?uK1y}Rag=OOJ=$WQ8aP>%r0ezuSnm!na{bpL+C#Dp*xm;K-R&!GFE z{)7XJqz}`5Qyr?C$QsqwVt99WoZZ9lYx5oNu7!HZ-)|%)bUc2|X-;?QqwLB#uesa3 zx)PJPz_d@QVwroA4k`;5f=jgB+dlqcP5aXFe zqOdy7&gHeQ6wGWDe0PH=c)Dl2?0HN z2Fo%yiyJpvz;!D2fZxA8JosaS^h&oH;;Xum68r0tKef!%OInS+G95y>REmWhRfeyg zSLBX8;p<1K<_>qvm+!M);NMq*Ns451r7Mr61dqG3B~3Q32KIfs?bX=QSW&rsG)4Gv z{4eUc*UpprGo6i|pgV6HUVfXYp1Xd%L<2#O@9jx-4sg+W5(P8<=Bjh=2ScoPKG)tT z(C-hM!yB_LuVUmakvK%55~^cuRxN=;N_&as~xEhH3AC z=YNbsL`KD^P$19D<5pDLunf&r^Sjsy$T}trjk7n4yLV(Pk4R`8zc1TPQW8|P@DaQ3 zy)ivtXDri{-brx7450vA^u7OZH#t{tyiO;#AzDPMAMW_2oGglFI*00>k!=$rCp|T| z&3zu(e47ip^fRd;4|gJ>Tm{CK(`qN(&lDd>*bRNJW_i1!Z9OsRUgL-kWG4?aHa4b? z{m3MEH~z+XKeqhu%SVn)`j&erH#fe7UW;;ziTIA+a%t-Q)!y*AMv^r^;Uk%6wTJZd zzm4Ia@u|oNG98}9p zlV1iNb=&*D;o>wgvYo8G%50Y@YZx#iC!x6i%@vbJX=jEmkXvdsIBe( zm26nQIZUOE;O^!|g#Lluj)lcZV~qUyc@J}G!qanGo^%}3E}uU2%u7Vw@gov*NBfpr zWMEMCLvMNFnVJGa9a%5Yue8CHTiaVt^vO9iL-YLi>bVg6lEHM>%vdHx&JA1|t8G{i zPE*P^cD(K0?j|_)&*anL1*)f>&S~?Vsy*?YNi;e=6o;Kd)$T6`H0w^#9Q)?SWtS^D z@o1a8(__vT!b%XYdB`$HkWMvi*9h9y>K4mttg6-=lDCttue=27pUDO-ZA zZiTbIL}U3<_Vg=@x|+@1YKuzZxI7cjNW8#Xc(+i8QCpq*ITSDGp0@vD_XeX|5$xz_ z#)NB{*(lbZWmlJ5A6pj|M81CW%KvAnM6Cy9P5M~(Z<#X>hr+@z9Np%TqmSigm?zH4 zo?WxlKYbS$d6h&_bhbR9_QYc+U|tcA9*5_eAm+*G@3VU1&!wS8CIWog00XI-&JyYu ztwl@&WdmiY8i%`5s6*p5s>>!g=LaNAB72Ojmj4P4E9e!X-$`b(y^bk{^A^>L{Tp_x zLbim72LJi5gz->*3Ku*PfXT^9k?~K%5TslQiloQdU(zGu)y}Io>Oa14_(pmgVvbi# zlItuF2;|l$v##+)?ew0ah%#Qd+pJb1u zYf-_V-gPnWBPX{btD~Nz0O!7?h&coKHlJZJhqGDgS}LYJG?pYSX8-@(v zZvFoCOWy1?6i~TG2Fq22nY!y#rrWWiVUG5mPoNDE)IcINL2e`QcJG)ZZ2CW(-`@IN zv(Vmad|bj!uwkxT5~S>A_YqI(-N*K%3>$?ncna9-S7~7hw1WGjy$J=kzr=8)TlX%d z+FF`%{;t=~{wfYHZNJcQw4_}zY~RoGiPd??i0=MK z6k+YpN=U0H+*RSGlFa0k6z9q{#deRx92qx0l|u={7#gR(EGqgw^-Yy_FJ=E5PmZ|t99Ux@fm znvJf@yt|N_#q&T_&XBlihQ=X|sl}MpnVXE)xct{MafgG0Du~Lvi1sIL1JcXoyGDmU zzaz{KhLaYklCZHW1vB#xJf;2{GNV?@!yzZG*4flMQ?z#?QLTPR9gD*^1r3?9Tk;b{ zL>1NhE`RIBnk`3%7E?|mmL86HoYq=8l%VEH4Biaf#{PjU#W{~+th1*hcgX7F3Yd17= zA3iRM)`dw;&kpVz5LR^gIJE+?RiGy6(8gdcIDZ3 z%7F*ylEqGJtNYUYuy3*G6H{wDg=-9Qgkxmsz301m9F@#MADB@uR?IZ7wl>;r+t(b& z^n#jOEvE%~N;1JSB48%ja6y4tR+@AaSmoNBgvMFqAFWZApyN zdG8wxl+7kodq@ZQ%ew0`5f_UG=8@6?=l=L;ZP%S3>4>5^VVW|Bdj^Xa&py(J~dB=i;!Wv=!} zT6QwBIl0XDJrq|18M5_xvBndz0?*s_JMya?r?Jri&M!taK}8-Q4d_-(%?#+ z77nNR5;C@ATi5tIyN8?rjrebgU#2AgC-(>kFL9WS2i*y|U)O1Rl3dz9Wv3!H&t}z8 z9Aj8u%eT?I{+)4*LN(s!R9i?{`to9ag)nzaqQrmk`ZW_XK_*(7XX=w%P4L<%Uu6*T zPS<3fvseWGtOW&?X3ZN&2~$*pm2dbjcKlbBXiOjFNGBg;Tb{q-CNP>qeXnbBV<6OG z_y*Pu%d4==JR$%@l^2#J$uG6kxnRRj`mz^$ZhKPHRbaH?K0giw58=2YT&4>pi~h=3 zABTHHIB5wkc6=wIi24 zVtzY@Y*4yQ?4K}{B!*}Rjmz6z{Z=URCqPit&7-HxiN8EhMERW`HzxR-JTjE?GF?*& za1zVYGpAN{JT}Grfq~WYVLIBU?>1Z7c7BuCd`*hNQzA)oq&Y{j*0UT8#8Mr_^u%vt zwc3XTR{uWCGa*+Zq0eRFD?&eR$IgtksU!i%mM4Po5R1)ki=KGcY?(S2J|UKJN9GY8Je0Dw#dhw_N*`W0S*+)VK;BWx=8YWx8zYS7NN-_eqk7Sv z9g2gx8Yqdgt7dhdNXI<8gZ&v|>bk4x`mZAAwXPSg;=eKmk8FS+V98U5ar(72{(kF? zWIy9$lnOBL*Xm!W2W~4goL4JTvX_7CMe}dPO%ajM>w*_k@rJd$yj?54*9p>E+Cx)X zZ-fU!)%K%g5dx9(5M$92m|7c1&q`HV9Pu!%Y1{mmm)2XBUWl4{OK^ z5aWOGSNrrWF))%+Jxpr!P47=9{>_|wRm)<%Z>4rM`kdfz9~Q?6#V8nUAyC1|gmE=C z2ZKR4!7WbFop-bREu+$AOimMmz2AI|5?K19ot>FPbD5LqJo0g8T}*1)cPe{GPQrg4 zic+%pWW-#*v63_?SII)CYbt+Brr*4HcVR6{_;i?x#q#i~H?od7zeZKhqbxFxM-fLX zx9NiWif(SG>V@cA9*Z!}Ux69x-xIMlKb{EWgp^dQM0W0(7augQX8&GFM=gF&G^Mlc z3wq4{Q-AP^Th!S0EjUSgP7*1sLfECRf)c&+WJM}M&d+qaLp%HKab>@pU&Z}Vxgf?& zDhJzFtv_E>>JocShAY6ULMPgjYaRM&biX>*nkoF-Pt?%05U!e*PR&ho5%kFIBPu_( zV|)A0{OckeCsFaWT=rr`TlFe`ET)g=Z?rCJuCDz}w#jv0o5>W_omC&#N-D;2mF?+e z$5xJXaFXOw2@*4hGI4?LIlir11dF4UsKXg7!*c-kYiCRk{N;O_e$f3SeGYyze8(6= z&kluL0v?3hDh#eP2sX1AVsEq0;cm!DEEU(YL z{}t!Lr*kgyOQSDE6ie0zb2t{uD$wMa*Oa?XRO~#Rs%HOAcD)xigYY?m&B=_d76qUX zOjjG`BAuP6D15WvT6(L+_>@pKo${FJ1=hfGqqdr~#U%Qqg_Fi;B(hfEHXsr2^GnA^ zF#K6L;ZL$C)=VQmCHx~>5Or|nYQrobtLoAo*|IzKme_ynqoUA`LVUbk3 z6s%g6gIbKHZW!uMo0lqfLPCx`5f;mU`y6Dv$&ctJ4n%yN;}-k_O$rlIaXiCZ;=^Ui z28OeUw5yKvypmsA^VuKo&c@Ob2|OW&k$GkogQaI0alz0cG7{vMUg5@J3dEc$J889R z_Vk8iw~Fq6Hg*ESs%Dpqm^3)&Fea&sa$Yp%FAhiQ7VYvM|6eb_81VUahSF%fV6CR5 zvxEMM>e0MiBj>&H`IM3F8uoO-=IP> zpLx~L>lg{Y4Uu*b^WCoeHX=N{J+`W6S7c+`1(4L#;j?f=Or+)mRl%`sU13|z_}XcM z$P4j3=K_^U5Yr2)q?!skBB7zG zcMD!^F6&%9whQ;_ju@=pXh@m14f)S-G?)WA%D zwvp=cq|&)jSaTQu5Xamcuv$GSS+wJ8H`N}??EQ=pG#AFz5VVcNEN)1^r0pfRA~WaI zq_j9Q_VpXrxq05bl3oL`ut*%xVjg(&M8<;Fsf3tHtw}vywHb17&toYWR8r5rD9`xc zi?W<&DJX~O1ekt}WIn3vJbFKJr*Ed*P9Vwas&xpMVCefu_Mh*@l*@0|tx%&MFO)t% zj}NNKg2s;obCb{JMmh{gG{WLK8NXG1c#jjT9PF?_OvS+Q*3YDoipojz9}rHf0Zj+? zi&hUXCiIlbEaqT<3CJ9c#z*2+a9`{1c$8ou2F5BpA5l)4GbZwcg?%bAmQN!h93{>=REWSPpoRcp05sgjEs}+tM2h@U^m#)0)u5yayRz-(aH{T>yq!9g`0P=4 z-tap~c*CiYBZYbmx{F<(^r98!C_D6fyo|x1)aixYns+gWoP>Qrj7*JGEB!qCdyRZY zPGzdyC{>bbaU5@mZ>{EWf$yUu(DC^aWWL?XcL>A~aj67y;!YvB!odoW<+) zCD$zOPa<+Qs6hivpP~GY6BEL?^lIb4&blwH;VmEc6ZJ5u9=b5yn5G zC{ALV*F6p&Q3VeB+%{BYMMyC>d7UUOy38%+3vVwFrRqx=tc zM@F$n7G^9IFcx+Wnx(#1zFIqelt?~37m?8jHljrV?2F~De;AU|efISrW?J1zuFZ@G z(PigAq1`*yuHxvAfVuR=t{2NK$ z29=vZGFhqL4qh647)-pVUZT0+X6M`)KQ6VkTV?)uMlY*+%R0eOV<4UF@BYI zBNyn;S+x~@a_!Ql=~=lJE6<@17xK_T|_3$juJ)697L$>hM}sn>0G$Wb2TV%dC1=*86u!< z_YB%Dp%_@CYrY13#Cxk%@O>E2c%esomVu4cB1WF|=t-|+CB-W+@6zKXK+{S1%6 zalJBwkP-tE{P=Ky0RtOwuG0*92B6u-px~f9ESQRac4mfzhNkmu1`Ar@3C6F+L`8J8 zw_@@cbsWzxJNPyO_}T?R8lg&ovnMqC_E}C_v&XvEuu55B=7xa7wc4N~Lp4Y101ggd zIs{?4p+|vPHB&tYT0`N`&hGYh)*y2S9K+RK-vyC(2HO4`>g$i8)f5b2>);R^7)XUV zhr0_{@2QNO7YH(QYdm*Vbt{teeJwAak>%WM&`P&q*U}y+bLn4V;TLP;ZEQbKjZAac zySm26Tz)WoWPbtu?2=gN_W>Ojb136M1MEX)BpjO!q!B)aqnc>a{#;!TXy}L9cww28 zJ{+6DG(x_3aR`0O&^>AkZMo2!EE~gj0?i*#5>r0x!NMYYSpb3HuaWb(VU%2RUz!VN zc87?X>uSkzHj&rS*(xJmRW;SwJWq}I zS=a4&F10f28Tj6VWu-^tftW6e-dAdBgP0y(_$m?FdN>sY)nj5B8r_t3erWcD^CeKW zhhnYU=D%h*H3|pdEkV10mLR3DYF22yL+^9Ut2NBIw;oUH*qoMuJpF@h?+Wb$aWdBI zMZ*?>FBL~Am2Q^2ANK48>luyKMST5=o?7E zeT|X_n&8)=2NJ%Uqomj!zBvI-pqW!=YL-|muFjBAQN=_>nLfISc6qwvd{WRUQ~`|- zP=alX;_htq$DOzkUku)yk;pErZ*i0Hfds903d2cH=Ba2EnW3diPpF-IHVo^2%=qsF z^Gng!pyg!Mi%>}I=c`&c=L$vdv>FbE8WqbHumoqK}Mq1h_XoVB=^*ElUSzR5_8i8XXr|{)0 z#vJ6(5N&9Fdl?QkbQ={qaiH#oHbU-w{1S4};_snkOZ+zw{W3>MhN6$JlGK%^gAY*-CNtFm4qfbaUJDC@Q z;;UQP2MAT$#EXlUj`=;7M-HFcSbY0`jJ*j|jq%zx{xnD;qKQ(;kVK_PG}|gEDvg?z zqCq2R(m;bq85=c9np8B;6NwPgq|zXvIcXlh>v7)qUH|p2|F_n+*I8#d`|O^*pXWE- z_jO;_b-OL^M+P%5db^{sPA*7u{fF2ie}Aw-8J(+r>C4l1t36YrcGJHUKzr_iwS_%b zxO(a(;bUuJJi%@HoV=P)u^4tIqhVFv=c!eb*E#wC1;%>gu;GC#4+-rrxQf_$+wG0hI^YO(F{P0rzQDK0Y}qIyzflXHL(1_pPPF`JdBQ zfBc!~zNB$~6QwcQZ7l8*Hwx}0S#{Rp*`^gzutb66@R~3^F|k1}6FOis*IDu3Y)?+6 zrTskAJ3xXdYb0iGj$WGIRT?=QLd(J8v+sJ4kbpo#q2dMb>KJA3@W=}VKs1_u<-|vD zvQ+Ol7-qG0R33Rwhv!}lXQK1xpQ@&CNL{veahZfCmNwXIAZ|cdUJijDTv;H8PoEEo z1zj3niYdn`K%~|i$^@PVZkWzE!P}iDkO!55?+*5)< z%C^l>9ksHug2-IGi}rg{iW>Ox56>UX(j!+D#1wO&21I1Pe*N0#?*~cj`&siL`PQGm z2lepp-=8_w^7tC$UGwwv_E1%O9 zW>k#}1%M3%b-Gq&i)8d&s;^iCN3c)>nA(JfcfKeXp7yM#PO8!Tz_}&kid(nL`y%eu5Bfg^Hr{66Q=eIpcJOEVrrSkV7PM#!vU8{dm?#JDzpR)LW{p2) zSUKQXCf(lguAyP5>^|r^cs&|Vh&P>PkDhs=lKy3I$dHYrd~(vIz;F~Ch*yu=t)D|a zI_2pNqNt|k-L8T}Qx&^g5S!~raX~hRf%Cpm7@#yE~m1)CN#VTLZn=4T!{HKPVzR5~f=yasH}>=ZzV|-P*1SGjaYC2OdzImgenJpCkWHT4)ON8!}&#LPzmjZ`msUMq4%p-Ecnh0){{>{)aO* zn%|kfl=%!(b+KV#CgZ4~(1+CJB0Pa6rqc{d8w%Oy)8Nz&b_p>)9f;Uy^gPv#GMDQ0 z@r0mi;CDrJo6CtG%U*Ui7#V#yFu?v-a>K@x^Qn#x`g{uwLS|3C*eVp*U8uwF;k~|@ zTK?d~b})NLqamlhT6kz=(AMJ2jfdeGy@0ddqf7q>8z~OM)>czZ%?TI@fpS)8FKzjT>FW@_iGTJKxG<`J!-#OH z`|IT7dH++#mWMJchx2rP8VO8ZOx07fs(HG(*0bfhY{V_&%(^s9=Lby1`)DcdEM{gs z@aS+x!5Z<1Nr5fIyO~dB;FE?BWP*-D_+2VFhpcpJWqhM~R=PihzfvkHZu^6oj_Qb+ z(PZhNp`u*Q(>L;OZY`H^G?7>Hm>GDQ`6W@~{b&;(vnb2j;=R;}UFtHr^k?sa`a`v>`S&pU#I>uuqnzfjk%o)yvXIPQ+YsT3h$ zMkjrTLq14$-qeW!EwHG~3N;%`&^dM^YR9Og@1U{O$D2Xbsh_!OOuF;pY+c=gHW{;v zxMw!y+-rV3v2NY?D$V$AT8H>WMsxgv>|Y`_nv<=cTDAC2hONt&5D47auFu8%VzodT@?f<7dS3U*CFR$$hU%SBJUBa%@<+&h)1?97r71(N#ES|DcRjKt5fGt4YA( zlX7Od4)a%~?hc~p*bbonX*Z8QJ^Gd=?t1{!m(?zB)6c!!n=6ER&L?N)ryYA>l}_vA zM&|E+!;`(@*8R#ynEbwYG&=ze=vC~#OUKEVS<)3%Ri%1vASI4+#wva7#M#@{xYL#$ zj16_RLc((%?%f^T;p~SxIo>s~{an6m^f`O)n*hH{B5Ak@9VL#3ArI;H=N>XVWi`)v z<3#lH1NP>h8|wpFw5}|j19E44+YVRL=Vfe2bLymFHQ-D+mzjQG^;chAm7H0A|7t+X zPKgMv)#4u$(vz(8?i@jf@LTt*_)jv7Ot_^S>bhbp0aG;Zk1G+0QpG7|Avb>TGftem z?SP8{XRu1WSuAn2mu~T-wFXz0=+%ky;Z==wx>Ve^sesuk&^Mj+Pr@gb8eJJqoejU@ z>SXcit{}>SC0qM(0TqA75Ruiy79G8m&&Cl}0#bZxvVLpNMFA)64ij%re3&A5phMzo z;jP;r5{APZ?j`eApA%`qZRaR+T-3ZMeNx9O{3QKhE`O*iCQP5y1igMHZ%=_#J?#>jHGh$}z z3LbUQ4n}GP*76&mg}JY3O6*L3W9%rwrdFR(?S9Hq-(#3cW(!$_ahGdKlose-e3t&Z z`0_~GRm$(tcR#Y$PN>}WccR9rgP;%UmNA%P!u91P1m#a=SoiBe2l&Pam^v`$V(u}f z$JxlyCVnU1S%EyGFruMBb+8v25!hXU#cj0UVyL3>29o`caneN= zbqtG{q%r}_^8hAL{5_SGgJkyLZ&+VuXwdz6WryAlS0P@qCr>;=H9SL zt`1uV_8ta()-~>jgOmKet_s)YYdfECc%C zYqcvt<;02f5+f)z0+}EQ%uZWJ^iHez6Hb50AM|&2mYrgG;X+&2DE!qZFv%Rg1%#|S zRQz|V&b2>2>&{(F4f<=BrCc$3Uqi>Ob59CidrKV^H~ekup>94({{rdj$P+~-8)$e4a_B)4rbZx5gT}AX=31kI7mNW-yj*5slzv^cV zTZHRt)>{fN5xw&&{xfFg{xH75cF!P=cM*>^b z3?=h6vGX$UBr=uWPeTlG+C0DI{LV)>OI)p9_}jg?858>-S*b#`3#^h6 zRbUMrM+ln>J2f#u)>+b|=}sLM5)>2^5dn~PQ^L)t@~Q`nxS;3lkIBIB`C+1~*Kkn| zXG66wD_a305ec{b{QN2!8uIWxQoBX{Z{byZ^pTyd5l+3BI-ndf>i#+BS1VVQrS!Mu z_x6Sbkt=4@PO`L==0?DDNOlCc%wR%B?+nc{o+hjl-&z{xTHXw~g`uKqI?KvF&AL`J zB*$&=ab@il+ZTo=x-3M|(H)ATvC?i1z}992!PC_>%z$lgj^};`qE`^Ju-6!05T=(I zdgo4LSg7(jJ-vvW97o8{7!x4#mA8Cz7nJtqJy?!1Y*>!5VG6+=Ht;ybdb@lT!wwbF z>`;pxtc`Nn)({g{0aV&>aUIS$wySe+_P9_~&c%~F?LspRucri3YB6!GC%`s})yuTU z1H~T=2+-o){i3yNeTxop>N?H z*bnDD;Q;8ble6}ShI>!Mf?&Kg1qyo<5oe$001IIx6&D`8$lhjni7&L~2 zi+NgLKf>8Iz>b+M9oR82;=cyK0$G?D-5(Hzcozst0254SN%s<_$1wWIWm`{JC*n8l z*rjZASUpMeeVnwUj7<5nXCttYxp#$Y`(dZEP(L6?2K0K)!s7Ac$4@NhNas!yVIr}H zm(eq|sd*FQg~}I>BCK4(9m`LiNBt03H(|J;IPC#Y$z|+^-b3lBQf_0<^fCjPu+h&? z4#1Lb3&ptf^4p7t_J=p%BNb45xUl25oKf*drRB~na;$yrqEDBa*|kE_=M+~Kq#MG# zb)LIEd%kr*aMQ#ghRhZLH^vDCSh2uq7Td3)v9U206&#XwxG6cDOaj+u?({U>z`($f zBS+wy0F^um`sl;$vuzm8y4SB?|BS4w?;<{n7*cU($)E@wucqTDDjTx~55gDX36j={)&M%tV`nlz3);hGwd zYNnhTq9TeT^iz(up9!r?Io?wii}+seQs2x?)dbBD-ul+m?_IX%y2oSE#wH)qyYncU z9v(}HGzAcIfQNxdV{J-o)3Uz4D`@F4!^JBpZ!PjQ{25X-tb4){n}u(^+E-j%t&sQC zSW|O{;9eS{n(-c8MXbOqTyudt&5ZfA9k@q=;^VO>j?`UtBcnJR(BAK2IxA6CBh{ ziR-sF3N^kFt}3&?ot4sbF*FjEBKIPIm@8<^m<##-;wPa(}LU>`j1Pa-}MV4!<``hm+cTpuAVq`XUXTH4=Ys4)JQ- z^qVz5fPjBG_&=8$o3sA4#yjxy#cg?0v*R1ho~MB7*LEYfUbyo@?whK$aTI2j_CE;} z=XpmnLnXe+Y?B$g_j8B1`j|f}#V-&!uW(=q9XVo<)7E2o0ok&rARY0ExJPGFZOhsp zvFvlyj5kg-`nk68o3V`=`_lfK3m~?pP|l3&eQBQ6k5$(@k?F7ZFB!=R1n_rA7$j+S zwz7n7EkAAtvnT^CYVuuzK=%oA=e}3E~}@S zX+Ox7wV?q7AcPXx4_UT7pMM)4dhBXu#ez!P)4#{vGzEV6Zb}OE&8)Y#(R{p7eZ!bk zh&X*QcRwU%PNGeT!+VtIo_Reh8;S`(M^|{u*4l2^9EWH!lH8w zj-3Ddwp{nPP=nSMqNv&n+;YD!cj@A+>Iawn4eFX+Bq&ciwed+@E;Q55XRry~)@jN@ zXaZtIsd25%r+uQ6@3nP^6u^c;e$|tN6%U(+}CBjs>?C*;iLye$H%4 z)XREy(BMfwas!#J`Rqd?Z9Y<%z+0h~i1icy&9ZIYYFVyh`d#{x<3_7a4mE+3YCh7d z&2Be-jlC(J(Pm+A)_2KYeniVN*fG`n*L$Qb%7*3Hsjzh!^`%tBf`_dWb7rek%1p=a^ zTy3qaQo06^dqGf1#9uqEe0nc1d55mzKd^nml3s<;rR#s~7W#i1T?-7e^!|=B5;9aa z&*kPa!Zl_t&RjAa`xASAczRuP#<)HEr4XU^@W8KPk+Fqar<-1AaiuZX3hD15VguQK zJ9Xil8?Tr(B6Q%wG zDB75ilArTg4^Ys6i>W$_ir6Si##LLrD;W!0{@ z*3jGd4_D5!JZn$zsMsiSv_qr*@@1f=*>yt91=yS^34Yr1668a|VIfH$CI>SA}P&t`wg2kWRL$^8;X8jM%@+*pAr z?7&u_ntnz!`&`@8q}0C+7aZmHNGzm14B;MWKXfR~^>X5{n!u5z!iRJ@^~Nqwe|+lX zm6dlkI6=e)lN>MytPWLC7{H(X$5IhFAaLkKEUdUW>otdS})LeLd zX2X%E*Iy1jpUHm4=%>v@-?yDDWRI-uGW>6$;T3>#9xVn`Rc&#%XA?J6y`v=#Z?@57 zyJqN`sJGH)!*)!)E_&Rd`PbvVk=Ygd`1@7HL_xiVP%K%~^hU`@TU$Fbe=RMo3|!Wb z0j_6ondXF(i26~)Xdhqug-M}aMEWe7dW}l(zWOh-CZDA_*yv^G z2=FSRvVg!z|Jj*8D1!*F+#;hmQ!RqvkZanpJ7$8#zQ5-DF$YHP1FZ9Mp$m39%Q_6- zTSW)uWnSdb(>7SvXQ)1Ud&H>=S?NEkn;)qOKAshFa1-b`wn=t(z?lNu@bxgBI1E_8 ztMWtre!I$JznO<354KjOOx6}&KQ-GS2l#rZM41RX=X8Ty?t%fo5se~4Vf+T)jE%gs zj=N}yA_Wdb)|lrT`}}<(M3b~Q&Fvz?!sU|sXjW5ij_fq@CWeCkaD_pqNC^hY5L0$S zT0 z?W_`1#C9bPMMiORE{fx7`DD|^)mGnd!-tip%tW4?iJVH!nPny3T$c_=dw_u^^B`mzq@^@G5nQEA;8g~zT3jwg zcHO`D76uac?nwx0(h+ypBZ@EI_EL6eH;lG`cfdLNvuy#)i14Q=|#y%xyY>kq8dYZ)#dm1pC}wVwj?EG!zEHDiCgq+!-&INE)J;s%eMuF;2f;}Sz4h5p6Zi!nn9UulAa7MEw|w-MaPbACxH*6XL+3pBhB@u0B!e z9E_Nf=}b;KMae(qFM$BWb5oLP`rTATOqXj+uG2tbg^Y`zcc@_^kv*P3gDL@784y6r z&Q3>g-xhBtLdViLzn#7y&3M(r-X_IBsxno#J)c_ycDGqSQ`r520;6eMC($iJ&E`4q z7DR0AFu_@F!MTWtog3?atZY2Oft#8bB0*gzHoi@V)pOcNr+rE=e3CA}A`xciLqH$A zZ@_yV_JI=o{J&B6e-|knnSPR(;3pRvvxsjsIR*C#2r#T$XHe{vq?egh_z?}6q~J`) z`wH`;w_}K?26L@X1ZTk|UzHc$I1<(=LI+-<8nLj z5nSB|#4#|VV0-dLYd29W(X>P6#2`;zgN9J{O4DZpq`fBq_s{)a6gAdo>-`pWT5~Tb zRyHX2BFF$wij$Sq74)C=ykHIBd@Cl+1jf2NK;xqXqghscUEN!g14QvQa-vp>q$jFV zQ&R&a7RAtntHRr;%DG>eSMli48nojeJxgDlF)X||kK-K>iRzf@@RRcLtAI6tH_CZV z{r>Qb0qBJ!c5{GPd0$7aPZI9Cap~$cBuLE4%q#{_jKsp=463R|zV@SA$iMgtr^pw$ zJ2l(Ru3RWYffWUXozl`qQfN9h4FDN63fGDi(vp?*f>Nr12N4XJF2g%pseqb%(uAKK z|1;mQyEMIqSP^g*bZC9{6WWhPR2GEbNh!UwtIfRjmT4ci-Bvz#&OE-SH;8oIJh+vd zPw4ccOTU?ihlh>rkW+6pHpZ%jq0F`!l84!uZeNdC?7UCsoH6eiDENgB@1e^AOGJJ6v@ zgy{|<*#Oo_n0J|5kGC7TD$EF?D^Lj2PSDjl8ZjPh6yP`Ql4y?u2a>}x->BSK$!Rf- zX)*T7wg9}Qaf}GSu(sh#*hR6s)XVw9z-W}L2q4gw1*xvXr~bze%f&Cv&CQq`=!&um zx?ox1U--2JFd-h83B`W_JPZ#Hhn;1?@)%LR)`qEDIcf5*y=d2!3PTB=_YQqS8=niu3u`RzWj?Vr z5DZ`N&N;I`Cnl*uLonxkw@ze^q00p0r9p$mrw!|k-hGMG8%&)FMdi6+rjNO^Xk!nH zUw`p2dPz+kohdv4L68*(8p0)Jmw4&NoDqJ~d0aIA8W6%ufkZm(R z`l1=Ff(&)Q#L)HD{c==g1j1FNx{*?#Q;`eG8NjYT#7JazfI@&>k)_SDs^Qy%KZtWJ6_G+tU@R;pS(n4X!SyvHq+LT_H6 z!{)Hf{%~2w&P(2NiJ^#lcmsIPSpiN2DtKmmksstg5YP!uw%X?Ya~ z>PF|~H|51N1hjmQJpB2q??%E^X@}x5(v}Rqc2nm)(YMV9tCA9oRoaR2|6}aRB(5N8 zsRDi|`ZMRSQ7<{-*QNkAN7E2L#Eo7=ScHwh0sS2)n z^dTi0RdvJAJ(S>Dt~>NF(jbFfMTAS^SlPl{oEw4=@R*_?lx381;}8!}0fESc*>RpN zTeNg^^3l9zQ6cL7{anP29F>bm*y4Q_25)eCTCXh4OLoa*V0i$oUYr>%bTmKo2yJhy zs#Nw7?Ps!DNv}ej8%_IcK7BLD`aU=wredQh$LuDM7W+J#Bos$k1O{%+V zClPMykZX9$*V`0GZi+_QrIoEj>@|b6jNh;+h^^#X)ZOCnBzrYc=)+a_jBYU3NdCNm zLtKUa1qQ^>dv_~fX@W6fZRJ6G(OnXTu}o3=+HHLJod#DB5rQ9N#HBXqX3LKIhD}vi-us z!h(VYXAYnM0Q7&ss=yH8doIr3!KrI&x!rMcgDv&Qf` zNN+A04cEEsw$xjAG9>xXYacp(Nc~1iiSARBq`T_a7b~$gk-)klkphJs1!8afcE{qr zSICtd&z$t}S^3bsq3Ha#UEnRt#^YYqK==^Q5x0xX}oOe8JPR{+Y-aEy9W>J*eb~DK3LU`pHEZG zEBWxAVt3tI(|2hBzZYN9Y%9@us>TF(&k;l#brNNA?d=XFD&HKGot!4%BX2wQ7eoO) zo59wsPM}gK{s`{r)+{LF=uny6gfzFC+$=R*t|R5e0bSj9_opjF9M84rW!C+g3yF#E5fBfP>9l#< zY5)G&`FV%wx02$Y<5*YzY`l7E7Iv%4%gYiRjJuAI4Bdj~zNUJj-E}WV_)~^g^aIWt+uSf_HXDJ81BzJz8i;4x~B4Ni%jRffP&wNuH(O- zALV>f!S7&7?#y2G4B8TRR1M#OHGSv#s8U}I!WNKtm6OeP-zbCQ8k@u93AGZHSvvR} zW>na|yH+l}-tR!h$UzbF+5qg$54`;2U)i$0M8~SDlNldwP?p652b7I&q*lsq+17h$ zRZ!{(LwT)}gKJIepP9@z{N5D7aQ%3rLqC^IpF5vGDu;QA@7$L^Z&FL0ARw3DUb}rDjAJvj1oKoy&IhT6< zH>vn@Dn=CXd{OD2>lbEN@N<03 z<_~QXdcws=m))j#Wm;`3vuCI1K4!YYMI+5$Zm}yDs5Fnuh~6rdLI{Zwxr7!$$)DXv zb^U90jCN^e&Nd$*TRl;N5d%TzVVB?_i}o!{k8zj^rO^@>QR)1-Vsu$KZ~D!eWus$8 zYJxzLS!WBbTJ=Y3)VtZzqr@_`jJ$>*>WH6|C*sUMvPy*6sba^7Dw@uqLnF3j-2 zroH*&4Uf6*(C*e~QM?ktvApFqJ$!}cEJ2KF6yWw_-b{abFY4vXfF>P^PpaXeeOPZJ zrL?*dnV>Td5(f|J@QZ4w=;J)61f$zuv)eY}>@kih^?t{!(udX;6MsH1|L~ZGQ~wWrTB7HPS3?(x*W@fGKjX;C7O!tt#RgiFqobiFS>ODP9Su3+zuv8 z{dTt`yZJPC1 z5q=~Y%X%&1DTL<8AE6SsS_n9WP2-;`IE57CbDJ4O~+B0H?FlY5gKWG$OjF#hACdP5wB+`^vuPTWiVR zf!TF1A5^60t-t}8q{)vi#1*KWS57wU$A;>9^u+%Fu({B{ z)Fsh7lD+vKx67~WtjqO&98&+N&V_7f-MnRs%SgM(q5~O4DJj(fg!vJZ!6sxp2OnOP zPeDz`c+En)KnW(@?a?1fD(?NF9MuFJnTBzipWb#@y`!(9K^YXxbwE78!=iwO)ZCP9 zBF!71J;OVK8cVq3T2r+wz16=7t5^F1*+~Wg2n%@hU;>d`oUtA*!huY;orHm(sT+#@ zM6ZUKP_(y@!E`41V7Ny$K>#E4_Z~eOZs;JZ3mdtH8pi2K%9>xNdBpYpQa9)b4!it# zgGXy0+9Z{LK`AO&0_H&p#&{Q(D-cd3f>_NZa=OMD{R4OoJCSnu3-LB+v5EsOkg3VL z1d6gs^a{WYBh4j$=)W<2SY$|~krWiaM;6(XxC4gyX`p^kg3+x^g>xC^g}1kg)LOhK z$C#i!GjvxU-@k9REogeZiRkqJHb>0Xd13BL#W{d9fgYy)m~Y1@lqavzt>C@2INrF^ zWP@&3=n>d~eurN(X#G5o0p%)|sAFuqNW1+(1o=V->9(h*I75|pxgGhxvI-t)MT$c} z@IS$r9-K)1lHRf;)ctZ>=xYF{p~_#bqQQYm3uKLKE(bSTbX8en)Q=f*89){mC+?ZDP{BgDZy=wl*g@AM^=Ep+ zXd??n#@w4-cdlaM%tT@>{ROrM2*DPJ>esJdU39^vf-4OE?!0jGTXI83!^^zcsS6D+x;=*lVR3wo2KMEvK+!wRxZoNN z?`^Qf2mAZ;03X3L^{oz2Uq&FGz2;FbdyBFA!8BJ<7<42(+&`6Ysn8Cx8U>dpYp6=`X1!9 zL3Nz_06)Kz(kVg{rw>7B)LGKi*VWgr=Oqb+f3J%mao<9DRaaMnzjqQKAC|vJLX9){ zg}MUac)nz1DW~lMpcTM5n<*Q(W!eK%sQfO0$V0@3?qduC%#Q72g*U(*MF_Np0K9x9 z@9V`fPr&==(sK^fOQh3KFJL1H&(R{BV1iEc{$Ux}c%u{$Bw3L{(dLPExN6FmLD0+b z+{|=zc1xf!twT>G**}slzd0)!{>Zvf^+975e*QNG zX3UJp+#=puLfmItU^r%|S@r(|dH9)KdaV9XbpQnfxy2E&!Q}v`LQ$#0{uSPoNJ)x1 zXil-U6|iCQ^ZGaO)F$i%n!~ly$>uzWx{*nc`a~dRKf!jgYdruy2e>vOBB#fwsS>Y{ z&wLz)+Lx>gI{wq6==d0gNK_}^&#B$8mZ-KO$E>JtBZ6O?EVvFEg=}f;h^Da!|LUS+qdG?(Me5O2?(Na5*3H{#KD4>>*QW(kk613u^r4WoHF{&4a ziB2GE^?VTK$$+e2-hY$lXM4lxR=Rs4u zuAB^K*oS2dgcAojHQtH*q9Xan;1`Sm&qs!YeqR;llA+4XTeqV5UpFu=)E=O2y52z~ zp2sgGXn_$!$s&v6#?V_;QSlWHtX1sa=vI;zpFxen0M3;i=9B(pRTlcsW<-qwqqft! zRo2!34>9kcKN#!pe*m~0m>q5ta@tY|4~nnjSNbvj<=M{8!y^yNdjJQ#ikQymHV+(1~oO3~UfPVTLAu_GliOiU72MkaxR``@x+%DP)s2 zPb>rUf5%}vHS+b#fNmMjpzi_sjPAtpa+$q*>py-JMx}SmP)6Hd_5V9vRU)W+RsVY{ z)b$8{%FBObuGD9B>fK%jtK^&K4c<9>DJP2niA?@1p5|6RVMr~}>-N~G3poS8US=4@ z4@sJo8Tq2RGL`!%QD?k)al~ z8YNU<#?7`+KP3?Vb!iw^7ef8jyXW4!%rMc8YdQ&LhW^bg+ZTq=S%j8_qz&9mx0 zenfjlth0m`s(*8t$WE=1eX~*W{@uGf0@_P1UBD=y?l)Zu|9D9r2t>8~s9+ zXbLwJJJyxS#L;#gr@4kTnJp{#9hX#kp6)U>*h;jK^-UaC2@t-Tns%d|zy#zxx@G-K zfPmSAO%DVV17CO&0eDHJ^J|aGJHhN{Y*-nL)GY!UW>@0&>n*BfB(kA5bic^HT14Z{ zNc68UeaAzw`%mBUP24glJD)jy+8HYtDDDQ755Y3l%PhdO{wO;e%k&-Uq&NjTUGC7E8=*K5Sfcpydtec8o6 znkdHrq(wuxFnTOKw0I>&r9^YKtEXxlsiEk0Hxf0jh@>@zG2z+ zsP27Tdl+*?D)i0Id5+h-o^q0AbkMoJi1NoES&MIs11H9B)+G`vNr48tlo;q6u*7F) zW!!wlumr|Qj%Q+F6ki`LRulFoAQ3OnHUg&Bk4Hy*#9RQzrLI8Ei4iK222@qicb8SG~;G-f3?GS~l zRUQ8s6CmCM=_>aXBfP~u#Ky*=>y;Ju5@?xprM8B?u38>-1e3gyiEO!mbNoT_$)fs( zv)%r>%3QsbHg|QED^!n}TCp_N2_!p7I~=rnTw@3_y1IH8<}s>7PWB{{BOU{Yxd^Qn zD8bmL%MihFH+p~BK@g0zd3@X5kmK+wqV^nf$Q~yW@G%gWQI+pKKyHddVKz6?)O zg3o`5Y3a&>p8zHJ`*#cWhqTpdWYXc1iT+F}=485d~(YM?Xp6SG_SY zF+p~(M>KpdMTX!;3D(hEgzX~0-bL?$6fSdbJ(cKBcmL?t6#h|7m;mD0oMb;BwAl}a zuaC1){9guaon>4yi7*L$pZ+&HAl`E*9jyyW>}Y$tRs1K|*v{2Nhy>;JtmoZup;EA2 zO6b`~cKlEFi=4s-_(J-$x=W?s1Q4;Xd)}+b&q9*GQP=MZBqkJ4^tjX1|98WMs=PRk z#;XsCvK_6)OwC132(rCQsU5wexUqAW_BBF=G|~Lz1cQ^Fh!r27*=Xv);wQD1zBX?i z^@Wt?7R%*|b-me{KP{X%H|97nsCH2>Jn~A1o8}tvb;Eh(mC&N_bL6lVYAmZqI}&K0ox=< z1S-Qkk&z7u@%TyeGS;f?(@Cn3pT0S&U0^WCEN8t7;m#N58%zaf4{ilBY5St_gSVIa z)d`qVGuD=EYrJaYVRJlOIWt9Tb@83Kcjfb*5VAU}5NsGFc0t|4qvTw|JGlVD0ez6N zS%xxiGB&B!vt<_RxD3q3^Hy@me;Dv}|9s7`t$EkzL31OepBZWwD(|&&?O~>N+8GFW zbQv8Xahe~dS3WuwM-gUV?Sb>Iqw}z<;LU5Vrn6}IV4AZDMgoA4%Givr6egC(AA0%` zO%;nHg%eb~y{RJ59 z1G3m`BlsRaXjoOH)m`jx_=j){edMbi{GPay4TiGjK7A| z0_s_fxYJ{TsE5ObEN0hG)%@NbH#Saiz;-A3RJgh8QQE2 zwx=vgiQi9&|6ZZ3wmPRErDwa#;`Km-79DY?{uwUJ{^V%!z5kR!E-l7#`5HH?30j5! zEMp(zs`yc~$@hq$qdlRS6BR{8G#=*&;JnwASXq1dw3&1L@v@cTG~rC~O-99Tf8QEs z>Yg-kMZ2YH|37c|iR!m1{!Y8<=)O#7__pXrJ^2!{a7+5vr~}(rmDnyb+k2wssl|6q z*Y!f zsgbGf{J#I748aZFpFU>+zzcf(u%f3a)0=HV@^@L-}GZrq+3- zJ{OTC*w5C|{iDjcrRwf~6g2;}NCr1Bbi$-yX#eVMfA5x~hCVl7J0x;}hS;vi5wKQs zA8SJB=$u08;XxfkZ5=~5orZv{WEx5NuVRN(_S;1hnr3sZ>_qiul8La7nSmDymqH1p zl#_D}9nG$HT=z0kPn^Z`P{;!L!dyqS?z=Nr_^r%V=WQK)o=(GQ0--|5p`01bL2C8j zYaNgvCg{jdkAmQIFN4v?1?2MpJxR?>PX0ExwY{=YRa8WQ0%myigM)!Igaeri5u08f zfMpNKxgumXF&`m%Uz5R@`|h7E|JeRi#DvbtUoeL!=l#Ul_rL#n0Z|jZU!$6-h!zt5 z>irYdhJQlrNc1vBbx;wy))SopPcw7JjHccf4cuCxg*LMzsQg>Qk=-9 zH>0_Ue?Lr3rX z;p?s~{V&b9Rc>u)U$WHTiiXhf&P^Voe6tPHSW14A%*C2`!9fp7u(pR);mqH<0lmz_ z_q014#~Lx^udbo?E3+6|OXQ$0TIc+))i7{$1cnDz$xk-eBwF>!nZ9jJ6FWxL|(0`kiHX=VY_tLCy2{{WzCv8R%0i% zJ#}0n5SO778X+I+1Vq(fOvuA24vUcr>}kb`jzZ~t=p}&RrKGZM>mvaQNR~VXsTw4 zPTFhNu9a>1;o@O!Z4ErSqQV=4(1)6oYlL47!sAnAbkAx%^O6j zz(_er3`Io#kTnO{*)EhjNo6h?%A=q2NLNW-Y-gbJzZuz}Tu)t~Y-#xe?DQWlCGk?w z(k+1Y7r=y4!3rK53f15P$t_Q5^S%Nf4*B({sG}?lklNbZY6I2*1C#SvD!#0i6oG{A z$fciT^FB1Ojgj$~Ecf_JId%*hKAqK(KqdQ$kXbox;y@ zi>w8JJO{jK8DEZaJO(S{?>?Z*hA%7v&!0f^+t;C-MPQJDMgM_wGZnP-unM&{&{;>P84%sAjBP9|yJaV)r&|nv z3=MSvwg$BiesOC0cU3{FE5YStje0=32Jycf95_(fEgqEu?E-Yo1*R()A49d+7l5&e zvhu2`q-demG!CBa{gvJ1{-Ub1mqsG4sAzV0HAy{4>RY*oHvMT3gD^K)O^5pXcLkvD zw?IoPDmKF-BQnU1=T@gjzKW&Sf`S4Em9>M0deDRcEB}B>m9Vgep(k*e>gsBE2eP_` z?@K(9q9tfteD~itZn!{iei&@?{p6rUH>TjHuv4BqeTqiXZK#v%-mk;Y0>-9GNmomY zuH9#n!esK9#1b*2(D0EEVOg2)pE`DuvC zN|%kAFgjele}B8@`e~zyEZUd6aRvJYM$+Fweq&gx5cS|e-q{-JxRB<*OpVZ%iiv4^ zZ~O(V?bPIC2LN&aVX%CWwQ6{X3Tj^a%T;iZLhMgEI5?c>xNWE^C7Gt~54JLZs}CPP z=5*^NX$>r|U01X9$H2fomRn#0Un#12@NQt}o5?qOD%AkTJzK+&0r3Waq}G_y+S=OW zkE+*}>`$$&S1^YchM{lO&wN#1f4o$t;77BY{Lt<=`HSG;r?=iTRK$449?=$Kbm%UR z-mkiaiwx6{+C9`mgOgb97;)=Zw4j-S8kza zG(`eONjfMg`Kvm#<2ruK#zFo}P5#S5g8ckkV zP!zx}Ho*Re2cF@Vl41qk2YCY;vn}-+HylfcE;@R+C_7$|R^wH?Qfcx2W0G&T8h8yK zBc-JDJ-ki}p-_d10ko2q;(q}xBf+(IaA>^7S+J%`;iVH=N(Mg`&eDk-j@9N)V>1*x zSw7QY_bx)PziUUfoR8GpjS!n7YwoR!rfD+`{`lryqyFvotuCT`N6eC@dOTgnr{{*y zcC}jJ)2LtH-JjgxlYS}@myl&|@WNYs}T$fXSLC1`fiU{(LU%TOk_+k$>*k=73wkRaVGd;$%HNJf# z#_#K|(+`!eM1+`KO!lz%QtZn6;-)1&Ogm-s`Ln@n+zq&fGsJD$x)F#6uOc8!95;O_ zH8nMqV32@xUGw}XD*m6w{a3Oor-wD0mmBjIiWX*4HtKfnB>ZX~uTs72!%}73vjA|@ zPVm<4+vPsXrA)P$UL1yW);ky<@0R=BGxW}!JMbONLOvO-2{4&3ZQW>RHw@a83H=|; zUX=&UYB~Zf;8X@OfeQI6CQe9p_M7H+aH-%Rc6eUwe@R z%V38*WteaM0`z}gMX1d~GQOY|9vmDDt~~6`#19>6?e6aW^5qg#wP=Q#UK>HZ>MtIA zUwd7WPP(|-`Dw?N_cfj~m7GHsDXM8JMKF!A+SMOS-Rwke(o((!XWo7}iM2-jbW}h0$ zsApMD^xe<h(yJI zAD;LWPUZKV4B7mSK9-~*>d5&?98@1dVb69r2&v9~A1qNc@INIYH3fiN`6DcuRYq6_)H37+*F?x$X=w7({7>*MmQ&3?)t2|csK_q9 zDT+jkoubwbF)8sGvW#`v-;`FAi6O7g^fLd}Cs z1Gj`N-zEFzjIZLCCe3Dp!M-iU+>aeoI2q(u1%NTmG47DMzxeF-m{V3XdZ}NC_qos7 zbS?W*CHnLT5q|@ZTa-A!5h^}Gck8xMb;2=`J+NZ^A#;N_w`Gsb^|!dN9xsHvh%*(^ zvbS&S>QO&l>cElg6qP>r=!eFbL$TTL=8es!PG7E>Zg+m9z2dmH1ylFtKE{&uXT0pj zP3{@fBAiTfgfuF4Et_sjgS1io>D!iyhZ}6P*W5ZPZ?Tm-@B9Pj_N|*DJ-+r zn6YR4oAz+*pzu!DS>xYJhg3U-3>6+`Cj=X5A8V>)bd))?{88WPxo1t!JBbG&60|9z zW#KCR7FU#M48e#!$`3LOC!Fl;jq8>(7Dgno4aKrE@-jOJvQ9*D@io+O6rs@nQAKux3XA?Uy zV`Vez|8W5*&eWkas%|6iDctS+f*KX1ZbfmFhBBzSWs?tUsS0Z7^Gp-x&`=gtN1J?j zmxG|jFz;?L1V=0>E~)NOto*94Qw^iZiKgl=TQBf;Cg>`~vGypW7{a{Ml^y?m1`E=< zQ!u<|YQ7D{B_dK3>mrMvkEKg259K^t?I6V^_$tNPc~6p$6*&3qMfry)?o{5xd~vFL zteVMZOQ{{9WYM{fXP3q8|bE7pOT?vZTL{V!gYU&c~WM`S6PTqf|LBA2QUdK0M7( zp0^}TR}CcmAM%!@&UvVr3I$e#U(AW`_3-h$i$bbxl@zQL~-{}CnZYy>4@X6nNl_R5>LA7r%3az z|H*^ujA<+h^43p2Rp(A)P2+tlUiEkyixe6u+m&5yQ~pSjOQybTUoHH^kGBNZ1je>d zev{WGk?%vHW&s;6zRKqe#M z$!Vqh=f(xo#6@{mqkG+Tx$VZuR}=FI^gqx0jI6A#HB&DVK`0m@RxvH~vT@Rz@^V@4 zF(d$Cx~ATJ)jS8Q(O6|SJ@5n=I;d?oB$>Q;_bvySW9+#RCu{4Nm=P%dAnkaVn|r*9 z^%Q+{CdS6H+1|W$4vjGPRHZo8Xy4(VCI0E#w?c$t{QQ?dGGAj|xDg^%D5|RUBB}8~ zfw8~8AK^17Li_VhvU792+}s`n1?k%<^Gv4y0Krn$*c2T|VxZvt5aE{QWi*(9QAnzq zt-gan$ST@KY*k&f6f=SFP4LRjZ-M17yQ^ zQRq-#^S*nATR=2$`-(h`=#HVU{5H{Ugp3hbQ)KF}Y~jJl&m`$UGkQ&Od&oop$vJ_j zafosC@?|jgc25E{$W$*0N!TAeXmqin?|sHItY_v*W#u|RAQcs=EglpZu z|4xhmI8b1wZE^3oCQ^b_6jgUfZlay_G*W1^ok7#Cv%A|oM_*FSLt0T$am9*wu;j5K z4d$z%$3pUStBMkU6f$Aub#;tX*8UBUzTte(c@?=xJZ*ds@&03rjf}%*vOeflxSAJV zw|^Cqm}ihPfByZjf9%jX`O@lb*M{D|De`Rj*eiD=yZnPzL`2Y=Z+>Nz$&rt$*)B#+ zrb(ikxTA^Peg;M|C&%Tv>Iclyb47yW;@FhoO+@2M(2$FQ@-I;Hy3=!9ThwHP(2su> zjY1@#KGE?e0;~z7-GzTUqHtqsQzjsnarrVWI=Kgu=tCZ_h`3X_jii{^FqlR{n2z03 zpA5{V&L>cGM)rNVH!oj`XufZ1y8R=p2kzjSzJ1K+H_;OYRw1{dZGwWTAIh}14Moq1 zD%+-7U27`qedqRi+lm>%J9GRBKep7Q%q@;=?^Yf7GBKNpPa*cuz|QqhdG!Lg?RrU% z{r2O(RZo>=2WPsbrKoqY0y4c`?PD9av!fTqpFU-Ib4+VhJ=v+`c&p3&JChu&KIH>Z14)|E@t@oKTe&CEiBHGo_u?q+Q zztEzDbGnX>oZ#T#x7lCY+eMe|%EAed+m{CY^#(Lq3h-+>I5^O?(7S4X5Pu=(cuUvO zgZW~0ycZq#QPDbK%w?oc%$H)`>FSncKRuJw_}e&hmrLG(#)t=pbes%HYFR%OXvfcO@nG>jTl8;8@@Y!dp5`|;c*WpeyK17ZubbQ0AUR_c%IZA>Aqz7J<)uvr@si*EVF&$Ds|-U z6)JiIU-lxf%(cJbJ@(fARR8ld-J8RuDdX;%_rL#Z%({NnP=;x5Hr?O(`KowMH_%gj zCA@$&YA_iD9H)61q|T(?qdnE}FR!>(C0%-0Gjv`X}nKasi++1}KMA14A zV)+m{5%k2MWOf&1+xA!Uzz<0p2PO?}ETOtQFDom;p!)0AuZwMz8-oBz#34a_KdOdVfvnHjh&>uE&x!Di){gEv{{L=nE*2X$%ODjC`4Mtv9YHjk*?Zj)zcWx=E7612r#$n=&`{mq4*+U*S3>!2&ENTA z0?)zYf(&E5g`!a|M>3(DuUi3D`c^tRPw~Sh&#K*M-IRX%-z=RQ3*|FE`P?s3Q!XEjLXcSEM1d za~ZSkK}N=$fR2EDCb8lvH#U7n{7X%POhlVwO~MtC<-jmHYYwgN#VYb1q-!YZyvW6PLQ15ujlF@-r$Qn_S2nbV{77WF zruba6tr6>13Ky9@e~J3JQS4An+Awo~JcGtmTr4Fe1!q226WpgSaDF`lSy@?7v=pGD z%<&`GZ#2HC3EH+)o#LAvv_a}zBs_pGZwzYsxhsqOZG)K|ljE!MsWtE(gBwY*( zfK9MdTN~iGXJ1o2=!K;TFKvFKsVFuyG{KZJA;U2uAsZG3Xt*+fVG!Yf|JK;3uUy%V z0vk3bZ237fR2)$a>Zfl~T3{geds~~)pD6X!s}p6LuPHTW9}SO= zj=pk52kgSs)YJeG7-W#UwCg9J8qX8~U~KGgf(XOp70OCn8vu|FX4)b!hsT|vvnM@T z4UWHCz4BbKuh@Vc9UVA^^)`KoCV{NOBUD!#(W+5p0UeR+M87trSY%rEM=&s9OyQ!@ zIuU;3#sk!iNU1eey_hos6jE=`oRS0XL)?n=FKQ;LULUlzXH~p zI{N$3Mv$C2j(+oPC~+ac1~`t^cp$KDIFu-!qf@dk=0KmijyB!?Htb*kOj z8{da8az>w4z-~x`7W)-LDJkPcE6!KA&AB|p@}OHnuoDH%VuZ!0x>%|7F^xF=S^}&C zp}Op#pbBjEIP>?Zma6!Q9%i2_gZHRkRXmD*{X;N@Va)PBheAY9P|({EG#X*R_{a!X z548?^XJ;QUIF)jrzFZ|Gg_2Zwf<1ar!6PrvOhxxm^ZWOXEzY06eM@1;vQs#C&Q2QC z15nw6?9S^{eqbpLmB+;(tB?t|6sZYjvkFU5jXSFeM0br?edS_o22 zU`_VS#iRhxCShMf6Bq83+q@YZT5I|6@Pq;Id-e941f!k+O<8=2o|&z#pzs}7dCiPA zoY1eW%DUtF*5lK1d429RMdRqOxti*WPl4k(jJ(Q92@1(z>mzLlOBC|QY%Y$iY#0}% zry473A6QyqvQcT7J$p6|&W?+-WSUhAkiem6h6)Z_y|%WNOi94=F`3HR;cSvzcSpy4 z`6Sf0Q1rp^EPvpM4zXO^KveSUOcF7-2|69lpb#S;L}m!-71EsF)zzhREDeSSR*Ib0 zaMZd8QMS4|15rjmubyS&gM&cWqeDVWU|JyU9Es^L7xj10GCX_DaOmLPyOKg~+z=5F zsY1JvrKKfG7hvR8;0zv9pH5VY@X|;-Ou|1vF?IR!&sYkD1DjM-Q1ab37{7LWP^Yuj zY6F(k>%<9Y=hT{XBGbUq=450f?MshAg$gSCvBX=))~hr{GuJ-0pzhfb zFcPwS|3V0~V7{kCdV9&UXE-U2E-qvEZBc94=;gSTMfUfGR>$@$y?pcLL#9LUxLWb} z$Wg2kn$U#16EcjGW})g%qx~2hO#T*pXQ+A`5mkK^f@E<6qE8Gn@__$+A1~}7`zwB} zY~K^Bxj%pY#ERu{2YpPRd|J7BH5`Bi?cm|VCX8qhBXnc8DJZ0)->wzf#ux~PRS?sB zdF0{1wK=({bwebJ00~kdXCeQf)=Ts&VB9SNFj5Ix$A=?wk7l7`DK#a9DT3fif%_Ig zZbA!&d89AJGY~le{K(AC7Sr6gabwrQB@Fev1LNp_*{r690uY&Lq-{!c)S(V@=kDDU zdGjpCo4n34yXLfYn9B4$!RqgDgH3PB4Kx<^_hS-~ipm&T3?K=~1`!|n(FHY`IFzOx z`nWM@W~)VuOJn0-%>GjAWnQ`@NH6;HS+Jr6yN*VO+KzdLzCHHO*%B4?gy_J8^vF{< zRpPlYPld1YlWb{iS#h9*|Dv$Ktp5(j__ zU}MWO#o@I{4gd8MOmDf|Fm%!KhiPelDeW0KOC9J7SmLea)-;QebJ&KsS4l zau>o3OlxW3m-JoMC#rM$^dAsQJkolgl7p?xc6P>rQ8_Lzra4Pokp%~WPs6qdu9mG= z^Yeh3VF!?epc^fWA3ZiC$t5xX$zAeooali38-iPA`Q*{0L^~l9o)c(!ih~r zu-T)XmX<~Y#tXSHd;)Yt$R_{@0?u+WkSDsPeNd{vz6h9hFEcZfmma8v$S_}`kwr(R z?UAu2V!-;sOq*hOX;?}aX1s^d;QeKgltKQ5S3ZUi<$0i3qdEUahqpj>+VkzN`v{eym?C%$M&kBYm|lg_DiJub zdp$o@g9E$HG_R@}C}p4rurFANnr7hVFFtmVkNKQ@P3YeSR(^JTNnJ z5Ee*9?~h~rp*ghk0wmIcRFQ5lvIUQEd1<5~mqp^NAN!E=WuXk`ivb84+<5N;3pWy~ z*0ie@1Wr_+_`4S|ZiVC$wg-3c$(O#qwM(_1h zC8C-jq)5Vza3b-unxG>AUccQdw>F@a3Q7A?e5Umx&Bq$GLKLPDHhsnn$iEMDo1C{iZ=N+zphSo1vn0M z;PJWF7=_;T(2J4&ytD*#2^t;20D{jpHd;~di^PF?W%n`v?HQUMY#tIYWa9OHu1^2( zMr>{LH-R;zc^UgS+&jK(Po-)eckb*Dkscp+a6CVq`|;^KT6=t&ULkiw8X^o+bIfwO z01A zHJdo_Yoyoss1djnID)`hK-tT%efl5z-v#MrDfHQ zSxkYZn$oHt9NZDD#~wg0mvL%sYisMXXNM6`llH`%9GHpOG}?`RF;UHpYHIQpS-ah3 z*B?Lr9qWYly|r7m9LQJIIU48ApgGxGjq}P438_WYqnBL(?kL-&DnREZNfm4m#HeWk z5>VW-#TQo#zxlSJB3kia39cB^B^iO?=WkUP7t{yfHXu~KZE(Qxgoj7yQX)_Q|6$T< z>FDaZR9yTK3@|_y9FTLr8XdkD4jRnho68Ank2=6MX5YVmyKf9LN)EO?je}fWR78Y~ z)s|z24iQ8GHv#a?N*S3~FJ5#acN`ubUi&P^Fr|E>TXJ50KKWorPga-k_v4mhN(Q>j z&*Bu{L16~cpjQPr8Vf~e=eZ%6anW)ru1H_|s)sO<0CQ^ifba*2ZTErpt}baS-2_uV z#0%^e0bT9Kl5%cdASm^GAKZ%I#A3-+gk@kTK4_29Xx#m;8ikZj=8c}VRl3;)^(JPb zU&Ba4Ti8BjQZ0h5C#LAu@fmi@`gV;;x)|M8aKG}l5(HUyl?mnb>!XxF`;###&zTu& z_;tynRq(6OZ7SW+6QWCO34@dF?w)2ZU%#HG>G)RUa+BU;$;Os4ji%s}c?a@O zFs^2$&nRd%-2KmJVwdHE0->q=uDoAnCv@}Il!)>7n|#x+zhJp9^1>D8-OllI7` zZ%QscZECXka4eM#U~HO>)^-Op5Q#4bV_VBb$;93@J%UTTY!eVLAo+=*V+tJhlH$&!&UIoUtjLAWQ3eT5( z&yM4W-tn70%$k_`677Op1yzK}*AsZ-6QL*W7l=B|nXU>MLBq0y~DUUzpNbas-E zy_;1aEV*qls%+-x5J&y^;YKHtR>_ID7;wuFxru3}9LO_1T67*Wvw(vDt-L0onigqs zNucb!1YfWQjgf@ow`TtX4O#~9DfIv9{$8r3t*sxk^7)B~P#TiOlgZj;4v49J}Z=eK) z71E(qBZf!r$?%deI!M$N)~_d?`Z^>#M`kXg(+}eOpe0pAlSmi9*QfSxh&zPa(q=M+ zV~BaZb2UN96gAzR#JCQmU~Hj>o0}m~C<#t}m?W)!{P=NtDdO0xTp(OMZEf^E8@vIa zj_!!@hui@d; z^80b4g^$VC@ZG=N@cx*Kjhr3l6dwpZj!;GV=sQ>eKnFngK06a50~FaqPUWh#E!cqi z3zi+(MEMb=?x;fe6V%I}gVX-VJnNLquc*5?I#GMrM@x@TrYjJ#KmZ!R3j8Fg0?4zC zBW~Qd0ZWej7c+HxTxZMf15*@5@1!Ir+cJ;Su7JvX>+2)Nh7=0EJP~@vn;Qsf z9I8eHleSF&r|W<9-#6R>lo&#H8=%92Sw6im9shC2E zufhGJoG&4z_db0Zy&*aIi`;M@i6k^gsvmNX+t?kK+qUiFGxD`!&6<>lx!{x9-$er* zOAB=nq*+o-+9dGM-=PtUJW?I8D+sD!$oqQY$(r4asd#2#!BG(EFV%6M6C&dBZv^YeSJrv z=J2O8)(_Zh{-Z|_Fzl*OZA}4^Zd4g`^(r=9ODs@wl)wR9A+??{eL7CfZaqvK184(X z7QDQRi%WJ)6hP*~FJ{vbDXplRcDtj!{a900H(E0QC$3Xbae*iTk_plg#No&z)JJy%()pBRu9Y=I1$cPJq+5=cQvZ+oGe;Mo&oBXVTx})b2c zTzZMmCbfEXa;&u7EP5$|dzF2sfz1$^z^x6uCM<7@C~J~-dl+FHQ&WLgx_t$LYMra{ z)`k0TsSX0s!3R<(?0^#QPt*wlTFbDI;6}h-CN*Ibr5Pvv`re9JU6`;4-12c@VS=_o z;gA1D@{r61n1t++0^VT_UVVpIpq1&tk=QtfEa{diQ81)c1KvV~i`(!8c&+KviVFS5 z4Eb;c#8c}#^^Uo?czt_sbSrleH47~n=#!L@lCnn|6pS6b(-I__0KRcaP&US@R^xu) zov@)D-}#OH$%u`OjfiL@`oZ`C!d?V65Gjz}u;CO+6~-K*1%n*4q@)CimkRD(>ROWG zXwrZMAk>;k2f8>^E|(5<-@0_0i6GUF1fVl8cnd>#3KBiIIbc@|;v`koj-$T@VJ-An zkjLTYXxxxmxe{kV2I}wdNC-j^aRo945e{PG8%v8~KSLb-gqK(4>(|&c$Ym{e?kqz( zi0TZ`8OFumim(|#ERb9v#Q-+fkMskB){#CS$M75KGD15GHfcmu)X{CLKyAmmpg01| z48dx>KnU)H@a)-$!AZ4oWbqf^6M(B_nU3!t+=JEzK6!$>5A-Yvb_6WT*4DNyr~5$I zIkngUcp)Od40=JV-#LKGNY>HS0HBGCcgK~C0vfg{T2p^_>zPx|&OKO#keHZl0EiKD zI*xx(gm?*>sq|@WP*dvd?fv{2LwbQpzC)81)@B@?ZtyTNjRmu*i*fn$WKfONap+-+ zC`Eij*|_#Vmd~(r_u{wU=cmhu8o11)6Tu6V?}&W1;bSNHT4TiwqM}GC8!<;xWJYNQK84{51Pl` z`AAfNrj?R{tnQv`OpkhJS3=iDND>VVc?`!vH(MsctEa9T=Pfeb16nXOW)Q7}^@!{8 z3-k!;M~neL!ah%V&SeqJvqk%sTg^)OTVg6(54$U4YW=|We1{+ktOnQ@0U}s`;3#rA zNtEqwxJ3V+d)MV4$rKQ-JFg0<`t#?{byoFgz-aAEEiaxJFUXQcWkwe1@lD;Vv}t!$ zkH_$6TL?mBF^lw;NE~7{i{4p+f)d!_;NpQLrVu7Nn~75&rb}?~)I^(n4;>5Wz^WuA zU?E^D_h&g8wJqrF>5*mbN9$RBLi>3|420x*V}F3)fY~>8+MZWNTt-pd%#zi+xrern z$6`S&c4K}t#&I7tLcs~~Nq`9cl6%DsjO&!aeg$O%uP!~hsDASZ^5Mv@YSRuPcVUVk zDy-HG!*TXYnRQD?qS&q8NSs7L-@}Z;tB6KalCTxBn z2|k}XI;1Lg7hw@SRl;oD~)iwTb=7_6Xw9m}UP(PuqD1Vgyh(4xCQ% z80p91>|x3Pt0EPYs}`Mrk+O6Xe4CM!mV9}!-_o)eEEUbm&_=#}#PqrBs3^<@>P%b740OrK*wRmDjdAO0GW}fq1Lkr zJOLOxgtdB!-vT|+>q*ywSrrgAh7lS7o3Y2+6=OlMFrsFvy8o%@B^0>c;yP2 z=m3E<-A5MPkr*H4k>R^F)-DbP@Uk8^`@` z&2-qiHR?v%zPec!BcKGFM%;^Z86v+IN2b=DyfyV8M08&(6sIIw;F>yOEp`k$$`mpL zn2)WMSx`eRp|M&gBcs7W*PiPt)@dTsVcX-e@lkreQh z^>x+PSBs4|lrGQdK)C(8t9k`ucWgOa_M6Je@cWXXd|uVcs64@5@bmEjM(6~%hCGpA zKnP24GEjFd#0dxSDLM-A{)o+g_tCuwZYwqqjSk)nv9S1q8iX){JP4s1f0murZABzL z$JcGimiMh+zD6Cvp9t{?W!|EeT0mO)V4u2D+ zoVGWk&Ls-843Dz?i4TQ_1gPu<;Gh^rqj?sTO2NwQ3gNHWuQwxPwCV`^_wU~&Ci7cs zvAVkY1WX*f2G}wI$G7v~AHM123zs{cpI;K87i=5y&r$3%Sn-5G`CW8oLBT(iS1|d+ z@R;7xZN3{(l12813ddPA0i%-pFe_`#U~i4{4lONaR8%v9Z9}?T-K&ai401Ha^{KKTJl0qc>@t{s%RzxoKK0IS8MeqsyjKhs#(PckFx$t6LI4 zZ2sTefg`j0{QM&JAg#(oEn27H>d2ozjvpmC3|WYyB8p^#J&;t|)Z~LW9rem9fq}Pn zE=0}A&8RoL2{FjMLFEouR2;56GF_q+!52zNK%uWM-KvJCRVd@7z6(Iu zdpj>l6K1T`BRoJc_u|Eiw+kLqhEas9R8Qz-Fqmeo zpV@}e+b}X2i!qaq#AKDeppiWqR5dT-B08af|Ni~8rCTkMHIcqBMUXZ>@*ccz?~Sce zcM&nTSoQ!?4WwCnY3mS4JLyi-LGTZw!W1DXbVpH0$5tqwRjFfu(wOuPQ`+F4DmR)xbjWbzO%2~M>loE585h7HvF zYJjcaW&Y}I0Ofx>k{DyzFeH_U9sz_CkI1>gIQ4-dAb6sI2Pre~*1EAP(Bch;?1jXQ z&`NZUVdTNryk--U>mac0gNH@XatC1y5C$NCI9H42&aDCT1X>Ul;Tz=j&Hx65roLRa z4DPlcSSG~~U7gGfd{IZ%ybNfg2yM79T4P}RK*0b&L<@ETfFzjS)hkv!165d2@d0NF zlX_xnI#BwXqPl(|zY?IM9F9Ovpwi(}Z*Np&B-h+#QRDO1uakdp>rCP>az@OWyY$?8 zL`DvJDAb*aRxS4S@xkshwbI{e#7nXEvRm#t)WSx@jLW z{cAx%LV|)O!l~XUP#{K(*=0SFxgYuT&w+s&3v_6bv>f$Ky+0dt_tgu~A)4pmitJe{ zKf*8sFd7m&-2!fn>lh@@*028;Ym;H8)QAEtTz1 zKxG6z2Duc*gv9yGL)CU0#t~yPj*X7O_>uTNv>EyJ-0OAA!(R)7WPwY=Y-ofPS*|TU zsPUv)WY=)-ce?D+(YbONvG@>zVUDUS@+si5NRo674019vd(j{Q8Hq*Uc3m_L`z3?w z211eRSFXrlxLoc13T)`DTec)b}w0FD=9|N@P%^0+x zuHK5w0ZX}J=e18CmQi1{NT?%Rp|RiF64lS+gcNvk04KPJgW+|XP|xHA(BOo*mFPTF0eF5 zl-#LVCWrtq2RvF0C{X;nABv#cmJnaqgF_Ys;W`LEfW44ZvM(k)+zajzhaXtQNdp&Q w%6|$G3j{ z-e$7r{XF}8@5kf5f4KjH+voFmTt{zj=lMEc<2atr=W!h8!wZ@!bUT=LkVqst)pLs4 zBob9NiL}L^h7zC1(3@xAKh*!IsVI^*iT@>(y?#m}v5{02<#q2opXhay(;fP``P+)r zwN;5>9~GnjzFS&KPV6QP{7UJq>f^7j4tZyV50$y_iB4xsX|%*lKFf~^zxIghYQ!qF z9naB#<1}^TY#}FapXcTy9?bVCsH5iBS8m)He*Vnr>zT%y3p`^qGx;Fns-v{{R2|f6asATj#B$gio25igIprWIkdPGAq6Fdu4w7#fulFCAZ6d z+-Lb1%rY`DkzU~7=r}voTQXF;g?cBGl=GXeaXx5->R^efsu9l(>D|+MSiTF`?2K1-~@wyl#z{Q=dY%Y}qpS^QZA! z@8EYfEnFG;e6n$(R+_!aeeUPg)MPi7E-$~WsMrkS(P>y{k4T=%9{dDFU`>5 zO;_FxgX`B**E*FSM2cE{U0dj}pB=37+eUxnOlQtK#i2)3q2jB-ISIIq)B1r?L2@G^} zbS!or)7I7w)qMT*v+U;DpU%!s6;`iSg*JcNb82dQf`SJWqWMdh+mrt(BsMly{AQ=H*NXE{*PoHb%^@M5t^)h`wGp3jyPsrHrz< zc3u7X{^7lQ_htuIzKT(kDxd78q3FE7W!tXfA=5=8M_icqDJUu`-t5U25EIKyPgkdT z^8ESp@bIfwuHD0x<4?POt*PPQH&h#~2Ha;Ta_WH{F?a6K>W#v?%QEgp)eY29= z8r~CQV`C#D-2Qc+K1sUIS;xzGRaaMYsYhl1^I-?OVwPFiQ4WrI{jAJPO)V`g4ULSH zl(F^kRfe5X&Byn3bVeTa#v z^OXk6@-182$+k3up<3JS-0eGe>gx0G^YaS`gtHdd_xFANoK{?1oRp*}cngPQX2!a~ zq$4~gCMGJ%(8#DO%^>TDw7b~6|1UC`{5ev{yx2J)Mi+mfW&iize=l9S)M_p-C+BPCRO~nuxK{b$gVOTDr1bRkgakS7i9zCr!~fj* z^EfCsdh%^6yw{~}Pjn^)9^_X2hH!M1JN=nqL;uxZl>#r_Bj!_u@Ts)Ts2ubjLVjxk|= z*Va7E&HK&D++D`LeOQ_`$TE|58dkq}@nWQ)sa@fZ`_!v9H8sDEwY>iG=MNSJOZf8T z%OLUToSdAR2lOLDLtD3Qr8_K@E7J2q#3ZZgR$-MZ#i6i!S(a43AB~C}lTSE&iI?pk zIDrE_vH0MfRb%}Q{FvLUyo zyw-}hTU$s;NioX19$qS%G4uO3EWN8&ul5f8nVr4%^?6DG>%@;AB0d|Q8TvP71hjQ@ z+V*l^7mF?|EG#WO!|}A9^Vl&u%-Z?^Y>bB?Ar%fk6#U{xzn-4fZC{!FEEGN~?Xhrt zXtF!6Wz4x=hePGDZrsY)>-Z%1;pHeXn{Ns7eyy+f?P3o5)Z;=e*Ykub)^aK;D$Mwb;g$QmS8ZK}f`w&L)CWycwx_jMKQ z%nKBJe|g4bx@@t%z5RTs^XB>@-#yv28NZd}uoUZi3{_QC=a)}UmnLpJ{`y?9rNG`i z`F&TH+sB}TI4N{?#|F*QI92oV^5Q*bRdMF#WbQoJb$DZAv4ZiyfmCx1d+lf9{hm6# zsyzkvo9!m{V|tZKNhjicHj4UEh-2fk+S4ES=n>1Bbzo>{=(ZzwetJ?1kJ}An?!}Doi_O)g#v!r8^*%~bkjbVYE zsn-{ewp6{ozCQ9jar?fTp4!ip?aHWYElJdWy-+ZVIPc~dqDW)x>5jVnZ5}q*IAV9s zWNXFC=;`T^^Kd?R#W=U&XLWUT*#5jXZ1TE` zOJ46_WMt%6oxA?**|VDabZOHrD~r?S`ueZTHhSzUPCB+86BC;&==W~%c;xR-wLEfL z8hhG+Rr*3!j{7`$WmoCa%F0wvLF3W`<1+WWoVCznYGJcJ>*MC+$n%<-5uel2(xj!O zhZKZ_ge0k1zN<_(CqAe$j+Jsbzv9Gp=**pLsfFWb&YZy(V_7pxO-oY=X1+R8cEx9N zwV%avcglubXRH48YTo&+3iCW&munyEc{^KQV|y;?bWKi9uGe^ey1$~_+;-o`3Vqek z2mzC8zx--He$+QG;LCco%O9arw6OlEmQ2dmGxJ-k>+91&J*wDXAJFqKDo0Hw9~f`}u+n zeP@w$ymIZ@EBEEu+1b^pl17WGtt>`|X<~BcnMHSPdGkn)rt;KtJY^Z{z|Ws2+-85d zjJL;1+)^lGF^F^*(kR<}VKDoV#r{o)J2~ZbYa=`iG1VeSIz+rjC}PAq>3aQ&Bkm)D@8kmhtW;C#9r{0hP#+ zwhdY=nA%tQ+I#gym}szUo4ofBatgiIi*r0hx4g)S?fw3JF286tw!L<#W973@#T)ac z{(f00DdXvp7uZ=QZYN#XbX%o|mdY0Ubo5h%7|J(R#>obS^X(?JA*@+bel4%H#IaWH z6&e@<)6UE1*${;Ed@2J10(f*@z0neJxqVyzYtnz5V-3$l$s9j4H8pqd-c5FQ_waa~ zlyv;_=1dJed9lq}Oxk^}>2!w|00B8<24IKW);@6VYXY=O1_+IQ!Mb>8!ARr$*^|UaQ79y=hf` zlYI3)S|J`Dw_i_G!e$Zed2BSwIF63DrFGzmCCV6KjA?Gz>S`SWH(b~+98uHWcz^6we8>2+d@=P=**8U!>9hx=wS=aLt{y`k) zJ_Rr9WSj^BGGa)1H##Etjb1LMgzNot`Eq!*Q2COAVEUUk7b-k@x9oEdyDXELnYn-e ze#aMmnrnD2_Q))g0!^Mv*x#3|fAPy)jsMowWn`MkNKFS*J?Cu4c zA0s0LUaJeKsi}yhBk?|F>#a{XRG7c(&wFJ6CmEPoeF)q?yFD|MbA8%pQ>UKQd&%;u zTbUfw{{1d%OSfV*UB|v9mrNC_@eppqQLfG6G9N#`?yd~i(I)xr7Kp@p(GQdpC2#%o z|J|79G@?25!SvFl_Ds{Xw(Fnk>t)tv&X%Pe43~SeA^lI)zgz27fVwiYkFc_4mEK!n z>h)UeQ_{cV_6HcAdI3_{XiVs7SylN72h!tt_%V zS&eait0Um*yIEa;ys+7>cUF8ui~T+oW+z)Oj(lJ=52KyGtr#I_nmXa##w{wUV*=ht4-2?jHTySKS6EB)e>1k`f?Ar&dDXP8v?b|nypa%fN_wH%LO6je)u1;5E zmDb5_{H7mdkx%7jh;BNsVW=d;5C@mHyaH5axM_DE-sGz-9$&HrNq^KsH;(S^OB%=XJ_A?LAvCbybd!R z16673(Y*hP?Mfz3UHuWxXOJ52{^yH$8_R|5{`E!F6ciNhk#VV6i4i&x#a*uCR#mTV zB~{gjv&kxoigowMPD|L-sjl^9QjZ=VKCLh4xjYmZUX1`}TDF#=^SZUxJ{*B2!>U?h zr(7tf-S?f9*Y0?DY+_S_$93jh{fwY!?{J_55v0T1N1BW4754PhyMo@^G43a}%y;S3 zf7$NOP_eO+HoKJNv!2%Xh~KQ#&}|KOX!DA!tgPJ6r!OY4J9))*9cbOIxA;r!>BSiP zavmO@hk=3Js}E|Acr+}HKbQ3}bMpj{NsW)jhBV(~+dP$(Ipe>5@7(a|!=v2MY6GRwaJv%;py2?+^61G73^!26Pt$}-U_|K0P{ zdIHb$$p;KaPsW*GMa0h6nVm~jHp~A_oLW0hGcz+XZ5#MnQ2O}T*t6(pULUfS?7FVe z(Cc__?df3vtZ04ly~Z}8EVnOSY{tNHjWgCpUTMUTOKvt^L0rAa&H8(UdI9?*X06_& zz%IPv(XU@umW6GUls>$@T-zG?tZmWsyU*r2`O{5=)V3b-Xmg@+pFuC9`{Go_6fHYD zd;OE#q$JM4d0DsFq_xW4-gRJF1KIh=iZvzsQ#|a7c6OO3UIBgzpFVA}-cC-5`xS5B zT650RvvlSAMIoWA4l@spBg#|dt9EYIdIiZ_X%CFXmP!H44hhfR-LmZ$U79D=#n;Pl z;#L!#Z(U?vobt^$0I&Y-(IjO{uEVkSS8O6qUAl0=VQmR+H-z=fof)kAm&Qhe2uZ|p z0P&5v7OnA&H1V#)73+{_N8R_IJ|W7UpEf$yNW&hsMc15b;LWSPmX?-TvY#GQO!D1ew9B`lwnotnza&TjcB^jL4Pi%GV{T}L4qzt+Xx>kX^C4_y7p z>1uh!@tQ@h&#Uyh^KDHQBObbcs-hVzS%TlH=Z|&2E6l}pt?obe*+Cq!!&1)YLOGYU zI8Hylb{hc<=iCj8L8w3q3jc;u$5g~$SKzbtu4#VNtdphT)1E{ zQ|EIzEHYAdq4V;SCr=(75a=#;xnXP^{hXTRk7;Y{l5Ww%m)39c#B+qeRZ|<;J1&>f z2g>@mYPg&KR$hsuG0<1sfq}{QDmzQ^LxJqZ*ZM0W5J7sNs9h~2LV{JJ^X2p8E zJ;UAVeOqg5y3xCjJv}B~lfg&C#l>Z1WtYqQ$R++ADqc6)`S{YNC|zV@-F5g}{SCsx z!j6j{HFz^^BVyYvHow)t9n_h6aDVywLXYcY_c8xM049XRp&B;000Oq!1>PBLVn0@S z=gytcUaN1~&QiV7i{G7o)$Lwx^!4>Mu`hF(8K{CL1COd}e#43qZt0QOO>yx8XhMfi z->zeI=qq(Yq_h3Hty!l)1HNl`c(^{~vU14TE@*KRm4RZkSXud0SZteV?n(Hp{MY&}k4&2X2&*Y?g}u=uV+5^S>V zW6tgd&2_D(Z&POp-%LV8h?R6wreRmr{^y^UeR@vh9+o#&tHMT#itoWU^wSM*{iwc| z0e{+CtXFQPxd5uowB27JU}k0pe2kX8{_|%c^YZk#tgPHzF%glA-jE?j5VO-759#EEH6H3fWw&*!)ymc%PnC(Eq|? zh9febhRbg)8lptzd-v2dc(2bJ9HV=DNYZiSYi#}01VIFbE6TTLI3{&FD2Hb%Q}HLa`4k9~Re?A?1zRom5Ux%|ZJ9wBJe08cwzXd`vw=g)f;>KK2f+V3#N&*Gwx3+n{* z9Oxp!759o`(i$hjVx>LwCAob%vn>S$1>HFw_Jzm8;na6bj*aoK(nCKq*u}$o`nLM? zuYeWh&|!ON65Y?Ri==#c>4I9&P4nfbs5s0pZwTaFn^_Ogb7i+u$D#A{I#RJy;Ra?G zH%ga>V>G-Y!4Ta#S$~PL*VNQ(V&W!yOBOrdUao)gAC#i24?5ZA5*PfDFRb4k+788L{}XYFEHp!<#Et*58RpSZ77 zY;LRy`CN#E8{A1?0l-`LogHM4;)aC~0x{*_U0S}z1>#>-)l5MejQ zW17y#bY&+dCPF8JSdkSMF!YH#o}Y&Y)PLLlvi3aa&55k%XxJg3maomKxjbCyV0ijR z4j26PaAjdK?Qsd=K>gC}`$~G0`Ox=rbDhBw$UKJT-pf~q1X?K)z!O=$ z<}Tj8z3^}^HxSXa8K3jEwizdafv3B2ZJy3*Llx4|JVi@OE9!0UZq&P7U>Bh(hYbpRUmZ6zD$DZv7!tnj4kuLzvAe)3B!1KE96{#NRNR8vD?dkErK?e(jFgRWM=kdy&*?`>~ zVI9pS^p@7vqptm4k&%%F5b7*z?(+;GitA5#UC(}d_1ZOF#x81VYF<|nXp9&8C7rr+ zZ9d9It~_9Zr~;=;%P5%i`gKR_Ih~?OfA@dem;a3Lx!#8=bs^{3)2A)d6`O*QX(6+a zAowLEjY5;ax;}jPz%vvgy%44C<01nz=70=?r*1UbybgchYh{j1{NvE-o&5 zr#>J^&Uc5(D^pr}4L8R358MwWZyL`RheM@WS>!N+f-@`Sem7eNG$JnNyjSof=%sEw zu=eWQn5cCVn+v^*tE+)sk==U@@!r-bUY@(z+1VGQHS8d$;g9*nE+rqxeJLsRHH7MioxSLQMQwIRzRxPPMST^s9`ue=t<59o&YQ~f_lRpE(%)1o>pLt%O z1+JBd%p{%F(|;NPq@uI5$PT7n@5pE%bhp1n_ei7Pc?+swOgQsub1k&uA zeYI7gtK4gq*odqDLaHyC%)lCS`xW-%B36 zEO3MdcSkxUwZUg}VuEm1anc^AxVcphhZorPTw8M?)B5LpEP%#{H98-f3#rFt@ZzcR z@B7+R{LU&U^g+s5DUOk1kU@6y0X?gJe{eQ}uTa?>5{07W5BEWE3gs*V)+9T(B6z^Z zn1yn>u*j>Lt(6sm_!ryd8u-GZp(EOWSFXIZ8XnssjZ?@`a znU;GNJz>=dO@bowfYsa3D|#G}|J}QHh`8Z<$~q$=BgL_p^SsQ#T&GSgq-B+#pj>6s z_`hob3iVo`q=1;t2ed-!!%0r_xvKNIt}Y6KP2bz9(a}+`l#WFnGmpuW^AtTmcSO$d z-9~`ywrVb0X-akr=HR(ny$VtgQX|0?wQ@>I_hMp9oVbb={T!W~{!apIeZ8i-S_(SU z;-TyV7j<==fB#g<&>tTk?@3glpTBooU{w%mKeAFl$+}uJ&AM>%po*YL;@=(oo)~ps z{Tnvf#l<_oY9Sld^``AFDk_3%32_;uB=}57E|Pfy0vS0uCy>vRkSG*+y)Rk^WI{tD zI3y(GQ_uH8xHW)&q(lM&Xk6~t8FA%)Yq#q}Ca@fyq@u#-%9W%iRWlG8^#u2NK?MI* zWD7ov1fHj-CsGSnyEC|UdS_rz(CDG`O@2#O(|Jt;;EbsB8R)OYMH9Vf+ri8qRCr3tfU~-krD&o3g<+|zR!TVS%F->%G5j+E^}y@j1rc{6?7 z%DA!{wE##0rM!7#jo1RT3)1M0O%IIaGdFtCuOfQ`%-Xfj&FapbrBuB%FbN8CMm2+lJe5La6ja}9SFhT3K=>XvZ=W(2!Ou{hXIr#niLe`~ zr5-EQhWSnmkvXAdOM!Y4t{*h)HyePGTqinzH;6X+-@ngn1URmP$^CDHlS$a360(U# zOaz;tpk1~9b~0ZFa#h^^!V;19&&c<~BZTj_za;QbNao1dWiVN(S0UobV5w)w^>Nk>gZ^}e?D^Wr;Xn(M)U z@P+p0uCk85>M%SI()n*{LMhWquj&ZqfgD#VZBO2f*DYf^cI=4$(@wI;IwLK8c0-Ph ziu7j?vvC$F?^;%$(wki;1|MaZS9mwZNh<_^gJnWwmuYjtKOq*HxVbGOb@iB4Hq)%U zuy6@eMs0o_Ftq;JOGv9IMCr@6JnP^vgSmxJYVELJaz{i&L@I5baR$T7@Tp7NFk52V z?lQDbK@{!5un9+|r+3v;RW)=28agdId_A^7;`^fJL>1_f<9~*~sHv-~pF3AL6k!sk z2O4(y@@2YmV_2SD1r8CLful%qpF&$8oLzjTw9zT@QzG5@ig~<%;w3^#!4u zEkSvr`zp5uS2jHKI;gsPD;4om7Xl|4%>V59bAEpslr%&bu$;JZPC=pi9xWrMs&>C} zbs)~JPQw>uj2?= zT3vNAa3}7^P02n{i$a-u4A3&D_NfW$@Q@qP;aP99t6gG(MXa3f&_#gs6~ul zqeK!53-3TK!jhIV96fVp4FF&qg*m^)uY1aEC6R=Kb4n=R?544lg_}}b|Kr9xWSo)z zCys37TlCxh76F|E4i#r{RVtT1J#X7TO0p>D_iT ztqgNyq^F0m78VyrXKCU|ucUYb2PtE2{kGm{@;HNL-qUF6)#9(;V7Utbn}P+yK& z(aC{Tp)(vBGeE;KLef(%4Q5$yPh<*F6a%38^x3m9GPxMqFSQDWt98!LnhU!lu%u*_ z;9k(8P%42!BCtnW$08Jd-KS$I^ku*d?)}CV9U@0#@(toF4$LE2u6;=19JdB_APS$p z#-9FPtfZ!67Q0%%&)nQxw0$3ml;HA&y7{PBD5p{JE>cjlwU`1;G4DQ5VTFLErVDBY zRPFzAQAmqzS7}NTt1G7p8sH|%1}h^RZZZf2+$N4o=gx0z#s@SAUz1IjB%do`OvDO{ zEf_kT7#qyWZrtL$^;wv{dK`2w=bM6HlE#&o71LfG!=@wY2Z{x>D_nyK zd@2KTzcDr|$$|?e3o|QW?t;nQO_)t&Tuf6;9wsrVmU-6qV9N2~#?j3T7>;kd0<(X3 zq5v_-jDN*w##Nk%ximgv!*J^Ef$cDJg}<@g+#0+GrnPF4d?!QqF_=yN;KBl8fQ6)l zs~EeJbu3IdS~j}s1I=>8g@nZwwrGCB6oW};OnB}lDwunj1qss-=E3g2=5d&;(L%(h805qr0VbH%BpZf> zK;@kY>0V`ro1_f7(xy1>ydj6Rwd~h+aU@%W|&PX%>I4}8pKz9Fe8Hr zMufTfK#b;r!e;`jY{=rfbiu^3Fkqe@D6SHpp7V3KAa)CegcN>#AcI(+UBO~BD#~ZE z_k0I&*Q(}r+;t$~oFC~6v1X40#As+x)JGy6Vz6QOuX&XCt>HO8-+yltdvu!uGgYhg z3M>cAiX43gv5dR!iqW(x5xd!Uor8{&x|uL7M$Y-kd5sdo$hJz7ucUD&7IET$4TJFG zudqm~ip*5ZiaxM>4{1%rbVEidlqdN|-9Ogt^W}N2#IEPnfZUskBI#(lEIa z9>A;|enL&r(xeL0q6dThG|CM#+cHT$L2{IrF!f+Q8zojN8`~sdc~qD%rC};HS;4fp zjNz)i=z&=o@gMcw1B#7!a^Ekwg}|e)#BBG-F;f{ITHglql&=^~E_E?{2r2!r4TJTu zxuY-*Pkv)-avwbhGusRo)@vr7$RZgRzL9tuSF2>kC`A)g2$TFDHN~F<9l|Vz`R;`| zVFtoTnC^l(tPGQ?j4-b$!Q6J3Sk~dQFn4$n<~6KvI$iJIPl-Qc zkR~28<1sGAEyWJgm=U)yo;wRO_b6`sWi$|`wE%`w-^_wRHt}MR^NDA%-U&l^;uyJj z99lVAY>oVX?Qm#)Be3*0X{7h!?*#6P(R3b=B9_aT8W)zF(;_a6t#9#Y^d)g&L70i7 z$%J_TX36Lqn8KL$Y@0bfm{HiVol?cb@l=;*rkWs0AAqTW=bYFQ``5(7O;E4@HSt6f z+f5nqg=VU2Ll76llYrmfnqeiyRbR~0XVW$ zcdjAzE^Bm4L=TNo12HfYSAG zL)4Q=^6ez~?oN^?T^EeVBw4iO8c#yBf+n5|;)L=a(4jJDILLa+g2X&{pwc^}^;`lf z;KPme)zha>^W9sE+)6Us{*8?!P4)kzOUGnn%xFXaHj#lNa`7lVLS=+m?~snR_V@4K z!3I9c8jyVRaLC_0VkZd?BTJ2nJP5D)=b`O#MY3FyId&`=l|O4vxB&}p;3uI#!}1Oa zHCXkTKMkTNCRaW{1bAEwrJ!K7C?Oa2Ub|ypV6e9jISPUrF$XL25GBtHU}?1jvjEG; z`VyKA^baV}L~M7Py)r+Rh@Hf0!yxDNzrZfH7nfq=;TZ!SNA>rqLOEpPp~w+%*v0bP zxjKwdIheVv!Bt2=Ao$TEaF-60iGyaQE~aa~{xdfh#+iZ=21u)JZf?hp9Xoq}=Q2c@ zEtHh%-a3+xzv;bz9?PJ>w5dV0>mKley9WIB!Z8b~%M|~gWJ*Ovg_a%6@dUI~q|Hu_ z^oAUgJOM@pC8lido0>~Y0s{(~6EPX!^Pt_uSpQqMephVFXCa9tWSsj(a+;Rp`w3eo zXfW(z=Y4!LM0Vp2#L$n7CaCtsr1&$Su+0=jOKTpT_$TT?^08-7EOAKI`%;-FE{8<+ z&T>L|3=>r%U>l12p->MD3;@?_K9^`7;Kj-qXSCPUoRv{&1=0iNMh(^A@Ryi=pG`01 z54pUpNu=m|Vl)Zh*oGyjC$NRqkED!;o?iIxW5-likSG)I4|w>HsCM5oq8xH$ePukW zF-BYn#Te}DKO#)*F6yg7Obre`xpW=idunP*AplYiDCdp5ZfFI_`d<(fL*4f$q))RP zfLl=w0E7vAdHsDYniGHvD8#7!DARjUF$L<%tnQ}}@czBxa_U1cmEyv+vD(L|HBCU4 zO(6i_G3B#L$PrUhdda2aq@?d|Be5v4lmdR&(UQK(NwYSL8{_%N}FfV_O$rK?N zq#zrc+_RUW($c+kp?G?QfXYfaKOJ`z$12LW=!A04+j0i=6uYD$FGysE3}mjizCpDe zEj#j4C@zlyoSv9C19}H_SjaFt0eKkY){*GTDqA4(#}&vLDwhK*eBpdug;LpipHONF zCKWdSb(BHpFdXINd_VBc(ap%n2x1k7J>^B5vI`g3{0%F-y?U*NWcmsq=I|vfJs8ieb9Gx7ssdX$WZrc10VTlq#$6Eq?Q{Iy*?d0;wJk;4ghYUe5Mir`fgZz`R!Gf6t!r5X~7jzqa}# zipx%k(6fA^>5pQMC|6sN#*0ThVATW?2RU%>DBg`FJ5d3|Q5hlZB z!UVgbFg#F0n1oX@Jj8+U@4J;Sw@?$H+zFr{dk+zy@%d%Y6|wI6XurrEvXXHrVd;;@ z2Zw+DBC8MH9YcNXUohuyqj|-&!gjsNgkxR&@M?uzl!-Qv>d)~9cFs;OwpS^N5myx@ zF2tRa*+1KU_j_o)R)|%~=L*@F)taL3h4hbg+ei8J#5<*^+3-~-5GUfRAztHhW;Wpr z3f!tLj7vW*O_i}c*6Rq}Zn@(lzUHeBn(~SFhO=4b*N>6E9bI@+Qbn}9EUcLB;~E5R z{35cDvE|^sp^uTvVj|WM?msXYIV>EGMPC-8}CY$ZDyz(dB>r@NGZ7oV^#+J?_DM=Z7>iQjsR1 zE@cWlYu;ZOgbX4DC(rO3igZd5M2cXYFY|&&hs9sU^w*p{D`2|2b3Zi?#tRNgnSC*c z*jrx!K`ly{Qemp&*jltOWe_HCvc))4HemwVT5Mx_2QwPLvr4qLL<;ukib zH6>=sqj~_Fk07C>+xLId0)St{mYkqJ3v4R~W=WdZlSr6Q8b}lSw;aSEfNe>)gWh6y zCV;e%7J`4ktOQ{tmDC2ni&%iL`f^xY01O2Sr5a#k>cAK_{4s`G!nqj38Y{m0;O9SM zMDL~{?Kie`d3mGxxK_`h#wWe&Yh{-N3|TwHiJ9~JYR5mV+aCK>;g}K7I{p1;+2kdUqP$zFi$NExxPvQRkE@kvHyH6rP-e1Y=MbQK z{0Z7I=F@}9^q%zz4(i6qZPd=cJ)bVBnW7U3~AF`rnD#{;sl zjgPzKm-yFAdJ;BbHPzk0W6f0!`~7+^Phd`WVIs%pnu1LqoAIOy0Y*57Iyup97S0uDL-yLs*0o%zf@1seMT zS<|+mkuGJL-)oak8hZ~|K8vo(yhVrk&-Q^L;a~B1?8iis&B%}0CM)i+YM=hLl7#dX z`^)Zz+5co;rc%fy#cCoY+CSM>b{c3I0Zc+-38^>+1y7{>_j0MvEG*9LFB(UUI z>n`S`c2iVMhJ`x#2niWj(duts2$l;NhK3pq9>6|K7ZLgUScqMt3(i=&FQ- ziL@HgiZztFo#b#KNnRqrI5y1a(u=jR=^^qbc_p!3cNxCSq9I{qWMp+^B@?9ssCQIS zQX)D#;-oJ^@&>QcLofkfkNmm4E?cRilzrI zi=H}`N^8KC#NX|HZET@mK##AJ;l5JT6v{#s0%W{afLA*Tf)IJpF3RsOfr8v+2&E1; ziRYUBI{e<}PHv9!>x}e^k>)&^3<{+yYP`=F=>EClKL&Kq>5oj1@9z%^XV2baKq<)Z zo4usUA5W-%um$p^vUY|U8YPP6G~DpercYvw&N!c~wDYlWERt^wKgn%r9~qGrWgwEs z&k{9Bq*@4ngPo2)$pKT|w$I1y`3uV;jkVAMQt(B9T*lWOB0X)}S&s_iL=YvXas| z$UwNgR#wYc=+mbt`;bC`Fwq4@vzw7o9JM`a9gHN40=P5_X3c|2?}84WUT8BgH_g9k zq^$fAh-RodENtKW_Lpdyxr3c8pez4ZsHzs(dZ*}qu2W;PzJAAfYDR}|)>8Q{bie1% zi8_6;&|%_hzJz>{jO)~Q zrT609iV^Ez{=K~^wyv^T@AS6k2gn5+7@U~+j@zNr)3Ep`CK=3LzpqPe&p&OAi~u<) zkM|XqNEo!X_O*VQejs_athe*W1CgE4!lpQWNNu8gG)QOxHEQU($TH5WKa)pEl0c+j zGm$LsczLlmzCv2tv`{R+*1zxW=_3abK>e(b3Y+4jUB7-EPa7?qsvN@EpetiXD{f(OlfzBdEfQV70QcqGd;^rt?RmlJKgY)008ATzCHeOQJqkqk*g&QJ-+KWN zmU5BzjOLP(l9HA-_4Y)gIP(9yIh2u5H_XN5R}s*B+be~4v>@{|KiZ7!N$0oy6r@f` z;&1mnW~g??GL;g&myb~Jh21EKZe-BoYj5_GD!&4tCCm#)y=+@w8Vmt1MN>s7kmg@m zkz}oRh+WYsJR;%->g??YpqfFMR{@RbX=_DtmR{pZxDoks`AWF+GB*cI`0=`&|gvGPk6FnSf~ z7I+eqLLkH*%o*vAg~h!w)WJHS6^;EpDtW_EN){e|tp9~KvWcL<;8o{URS(K|-a)nz zR}e5Y`k&hA+a;V|?Til<0GXWLl;I^&rcQU{C)3{&33RY;O`0Dz)b^=M0#u zsJ%6O>aKrNJ)0Zr;i0HJcXeGvqb={TBS((l6n(9)HwKg6no2{;<{{3xsIp;{=IfTf z6<*mA3z^Jjnx6Ol=i zelPgc_HP#BZ=1R9w$~sZ<$!lHSj3l>l?}zTZXsO&EGMN?aR{j|g4UK477BYECncy7 zGcV2LX(?rIKi%EkU0toLuD1AOtTIJndG1KctVyq$O1nf@x*9FjWn4 zXx2bAQS1&4inrhE2+4N^zZ7jz{WkP+cK`N?q$(yNqFldm1I3;T=n*)B*+=zh93o<{ zcwc9cla-cMV=*nt`S24{5lSN6fahySFD+h}S`3-netosyyoKMC(eNZCySghHJ4Z*Y zhZ<4Pc(XJ6MftsW5A^58`}7@Zqa+y~gk*c|s$Sk+S&2}GjczTT4&o0_6NuDW2^wuf zed_gT@68!49ybLVJLv#40b3SB{D6+6EI5G{_tbC-k|8^;;tkr>@NtBKDXDFGZDf8^+RmLHuL4C^6LZVQ z1nw<|6dR>4ouxByHX(!?es8E^cU{=kN)rq}(o;zSCH$+3Q@{POAn`(B`e$6kzx1p!gf1M@-2e@;(OgpBgo}{E0;cM3ff+ZLqPXMkDA2sU^ZO^jAl_W@H#c*A<%JYM05Jj%+8|iXw7_MmXU*27QG9E3w{Ow zWqp!3rrcBtQJF7a{zTJiMCMjfr6)1-Ry6*?riO-{s2gM{a==R_()6iGP2I$=e28Dc z8FH&fS&SKzNDWAAk#0Y{g}j*W@!7VkJQD~gQlKuyPX1us8K-`trf1BT>XV?uvrp?qE*Uh|DcF z;Y5kBQ4Z-e`8}cvG}p8?-eY&~-i2fjuv&7A*P338Ihf(!%pG_)#(jpPVq&e|_TSC3 zF5{AC&b=74C*s)aDzb5GmDRTUOVP4>bA%{3m|B|o)ATb!TP)zs#cjKtp`W4HY`i0j zao@g)o`UJ})hQ=O$NEp7icm)nP|uI(A-5MteD8#M`L(}ls5#G(&95(*4|nZs|JU;H zs}fWc5zUP3?{jThP$Pp^BphL8CQnT8`&;*yucIATc6H(%(UzFlOmtUuB@;3j&RldL zxqIsHnPC2e=71_w&lcMH2K{4|63VyNWEZB+u%)_hZZ3Irx?a&y+;c(ql8y-7$%iKj zR-#|MGR?3vweS8SW>T>{8POXNv(Pg2C2cHEEHWYu9hp(DQc|Mo9dB(Dr&5$#@Orkq zE^@M&#If^TCiyCMAKOxM99^kgQAMRP~;RN?UCPJK*h($7b#$J3SuyF0toS_8IMU( zCshhyRnOkK<=7yY`AvF6!OSSTAkBtMVfT=wB~b&f3E8&mP*hx;;L%;Xc445XyhXrA zEd<$PPiifs*BWkr_rYs9P1ORgUnB>YP}wvsID`pjNi)tKx#U!ulW+FozmI8)rlxDI zUk?2oB44Qw9X*z?<$*`;!-4`=6b->AjF8Exy1b&IqV%jXrN{>%o~E@}Kvh;yKncVD zp0seac$=-q&t0xowVPvYFMcc?j_rANjE=JS_jdN3=(iSXSx=un#Tzw>Xemg!&Ojj9NGv1P8WuXd5c&Mp=+eQR#)aN&xw%&&+333WKi<=% zAVhK4aJ%n;i@f1Tun5GP>*;;4Wc0m<$U};*`G>SV4;GpG0V=S?l>2MELpn*6>@mh)K-6|@z=tn`h_~=_3QWMfpq$UL_ zg;9I7ixANVJBP)-^sU$G?UtK!s7Y7X)QrPxKb-Dnqih!XhDrWS8wu3%uAm1Ym`UVi zUJSB*I-A+Zz(Vs!HTo!c4Q^_ilZ8;Q`w6No!xJQGz|t-iI)@!8}W`86`~C?G4#zNU(JB}91rzyDHZB+!sP z0x>%4r2M*W`C(Po>`bgq>XC=r|9J3n@mKdJ{>c5jb-zm1zKzpAQmJV3 zeVaHTM&0-EpVze<^H<{gGBr2jzBTsOd}w=Ep&!M3mtmy@>1@2|rUj%P00J*~K);|1 zn&aX7;P`^M(bIvP;4^pow3jdc!Rua#cH=1<1XJzTRY;zpT3Er0r5)5Fi1}n{PR=YI z#R>9J%`##)6daB6)@;j~RxJY)!l}2Vp{jSW^KwWq^GPzQhmpB%b`O-=alJP)J2zKX z@#cnOI*A`aq)8(=)U8J|L-vWA$>~KM$z$ZIX!oItUFOT5n`V^g=X66nT?Ji#b`QF$ zP#-B=>M2W9&Qzbd?Xoh}c-HfKcekw1v#|Lk#!rjRtCRCy-=9ydbUdk(3$fMOb(>>v zbuNv6Q$M&$-c-2*s$GZeN`U8>*7I|&dW{4rbCDLkAmvc zZNp|mjx)NHlZV6vhS#JKOC7oHY@}H4I4(9QYqhV9Pw&y<>qm7jx4EabSh&PGE*5>i zuccLHcJ%0F1J*}A*Uy>AaIa}OE+octxAEweG!EHNe@-1&ORX2`edmAZOauzOHbY{96=&8EwR zMu=-j&U2{cjpf^|Vn2p*=se6Qbo_iE(lvP}-{g2*dit`>BPsDkk9>xcH@H09$#*Et z$ahZE(m8u|8T*9)QVv5Sqmj0`SqQY-8XL)3u+^KT_ui|k0RhUBDIP@$2^0;D(swVL zA7XX*)zMLmuo*@(xgIA`HGLl;=M3H1+?K6d$Fa0W-`alS^))EyBaeEJsw)cr>eUwk ziO}gpi}|6P??p>TKQrioCvEB_zppYo{Tn+VDXzgbQ*FMY>P8~<#KntA9A3Gw)KPEh zcoJ=0Lv1uLHGNyi8`dsN6)3|q!fON%1*QfY_C-IOJl>8yg#@oNLox&o9654V(O3OI z^|Prbv2wq@fB%h?4*LHM5)x}+p%oWLLy?*1?4_u%utbAY!5H@`$P=JKAvr-FEUNl(~g*OB(p3d|!7H%N@*mo_9SvtQe0^Pp%3`hNF&xis`Kl!VFt z{UO$PRtdR}`#U;Fws}O2yOYzIMjl?**jH(@(~M(_7WiA152ik*)GP4#{CTzN;ZDVu zhZ5rBf-OSz13Z*OL`2kQ|3(-!1}S3f6 z0qX!11t4kvV&^7BlAa_b@9Ey>ZFjYEaQ`7o%gosqSd*K>3HqVamWFp~Fl`IBR1I12 zj-GdSYuNOr{#DQ2_;$YhLbEEvO~-so3}bUTdwx8d{L{Tu#L^_>{6Wd1#ao@u%q>+v zDpJcE!Z~6BU4?BOg^zS+47+`Mb|hJYG}mhP--?G1LKfIh$ckpC|JGc$ya|+Ev2bHi zK&Ri%K|bEHG^LUX_R~wBiEFrb$t(yDSJ^0S2+x)yj~l$}R`G2QGZg&t!Sbfy8sX)X zV4+iuDxH#t(;E7c3bn;(rWqo&Z3y_yEiC%``u+h6R&-D3#QAKhqs1u@lqk5VqaJ^| zvvf}^5JC#jeYw(v#e}IKNC@2yf7ps+glFHcG8Jsqsr~aQ*6K#c^sn}>`5G6m-uPF} z%QN0K+9f*G;(w4TG2S=vdE`=WvdpjiRp%#0hn*5V*&TemmTndGm&*3n^u^$yI6;Kd zTN2!fU5@$-g_ze_$w0R$PLS0|Y!phAhdTgVl0K7tTqhQV{rP6EP>CGGW`0aHtO#&7zb3Cy>xAj4jEHOgB6k*VVmt=hv7u8DckBUzh2eiYvub;e-2PgZe)2kTI~- z1fQ>U9X65%J&#%E2EeGl|>4YmK!L%p1D zVZ6quR5TFR!sMh!kAedSJu8J?-V)Wul7%Fj^dwrb5ImOjl1-7F0mB4M2N+Mhos&qfqwg6W zJjj5AhA#-jDK~W_ZP?OQkt*_`FS+_#j+&ZoJKL(p*E27;zi!Dv2!OFm(A2!N7S6!W zr3+3mWKx2q8kgn~u7&{oGH7}~*C;Jml@vhlH=*5ZFy?O-iR zyXAmd0o*`CcDuObAd7Xb$M6B+&~2y{8sUMTKbHv$t0O9ap1`kx=CS5w{3~lS_3ozO z8jjE6aj%r!f*QF@Y`jOU!u7u0Uz65*r+25j&DBb?q^F4$kKQD_^Ow_QUWCFm+&}pi z=Ao#R6iL`>ARw))tAn4LyVH-VU&`(4mdNGR_3q3!ejrsT&myPH(9hWBb?QTtk+6Pj zNMc3jo5VNc63g-yB7KcByn1W|ZnmSJthTzZAZXkZt?T+NiVY4Y7wNd9nxrn0ITJ1& z&bIYD=a+y+RJgf;NW0xH*>v`+R7(@75w50PKf5$?Usey;>tY)#sefIP@i<5Cr6SbekUbXhp41BC58urh1`bVAZ z2F^jvg#rX5dqmk{%rZyh{HifUKfCO7&c2MTk$G&)JJ$PsbgVh$koskE7A{>_w+K$K z$Wo@%w<=J`d(ykH=9mri2ZMPG& zZ~#5T`xnEwj~+5#T6qP6(M6b4qobo!>YtF0GF}n%M(|__S*X7=YqL-2I)ho>1X2RQ z(9F` z%L&FgB$M#Ybwn%(c{27=h`As?C*xz7Q6bugN)|3R@awq)R^iW|*!B3=u5}#rU@3dZ zyz4hl*k@ircy{WP)be0#%4a`6>43hIv=h{M=sP!y>GcOVeoSa6tWu{@9EAMr%ePmo z^gS39gz=?tt|`d+SB1iH#||EAy`d=N1P4y(`{70;fvBon`28I@^!**)Uo2c%=|SXQ zHC=wiHTC|(hn1mFJyq}Cy&I|H5Ojos`#n)nL46T{zL?=BPNEa}BVo$dw4u8Of^aIV zGliDyqEbPe>-zP}b{DFNVw7)JmojAtL>ataoI?oe*P44IHIkozloQ`{MDuYN1H^uM3W|r~udwF{|`T=J-4JTv# zOXD2eR(?Wag-f@;{keV}K{&jCFf{_+)cC2btwlzmqN;lD`5Kwm&pm3(J?A1Sv_7uG z;Tbp!iJ~pj63}O+)qU23(nOi5?0P)4+Li2D0-C7j!|Q=eLRVRN9ojNcrz?UjlXT2M z)ZaUvM3h;RQz-9J61PKwK`QJT5j?}S>VV_dyv%lO@F-_censg(5xWQA?0e~2gu*sJ zI%U=jkNAB^nu>AY?7Y0D&z}q2hgx|=1c7oOJf@z+6NYGRX>ukTvwldIJI3NS3q^RF z_qZh=3VKG?)}5GUf;&_|orU27O8y1Uo}tog|Ls}b-czjf7vz;G2PiF`0&r{v5+jZF z9VGHEkkb9S50}lVXeE6r0E|;#dWo_!^38v(*vv6QdQHDYJzUX!oxK6L{DA-%UQd%85XZgL8*A0m{$1XLNNYtX zG-}Jj7Z4mI^wg}-w56N$Cqf_qoDd9OGiPU@^9a!8Dab-L0pF$xJOp3D;lv)lSqgH!J1;w34KU6%ico|~9oUF`oTy#atXGU6L9R-&}nIDG7e`ZMj z_hG1S(M;0;Zb+J2k@k5r-sMwMQ^2Ag?C>^wz_DV{tC5~o`HRq!%yR+i@%r?^ptHnb z$icL~Q=TxcdGVqh;X39}=kBi%l@V^#5VNN>)k zDugYRheX*Dl>Has^&;qB849Ur(C(v0TMb*gE|FYJk7L zK(4?%l1IxYcN7fRts6HUph8hWC2d@wX;yGQMASlV2Yr;-(u5WFA3Ok6qS|r+ApmU< zWLc(v3BrxsI|veX1RDDdvAA6Fc2!kRh^PPk!?0IJ5RNE-`_$CninQS4r$>XrepfrLUg^8~+zk_BZ782jX&e8)e! z8#hAQ7V#CFYroucW&v&7UWqvdWr3<;Ku}M@Pz#!8l}E2$zYcy2!xBX?0DXL+BO@+i zs}>TaB;H=Tz6o1xQIQ1|p6f0L(lauahr*qxIuH``K&W*DFsde??F6Zmu|~@mh6fZ3 zH@=oSM*#g4enG*s)!V(Nkf0JYBl2ar&~*G~U*8lNf)@x@Q!oe`K7HD{y^Azug!Cg& z4OH>oP!KZG&f56?8_2(xVML4tkuS?pHn`Rb?nD}JNaXtr<2-Pa;GPCY2m@S)rR9T| z7?R?>1LAGpi3$;fzM!-GK~fv?7We>cjy}Mt7NZ@2a{0GX7Q!4tEgWgEq~4_R)!dP|7L+g^%XSWkgy9uUE35M6nuOz zM;r%pMTL>~pNf_1(+b76h?@K7iy?@cIDYo^sgj=RejIn7FD1s_FJbO*JJfew#-TnE^P?LmfifB%Aaj5$P!DRP;QMkYf zf!kxn^2E9fx=oWmXdf_Qn}putYM>XaV0qPk)3;aVc+6LdXxa~V9*fiz`_HrKw|nP* zjHHZi+*nglL6!%uquQ}eRdwT$C+p?q_fuiGV1t;ZncQs&hnHzwGXNd*s0oRQu0@xD72+*Qg_Orbqp zNp1u5?DLh9W}>i&hZ_)5ld&&$hy$XJ^|8=M#yAm0An8Db>o6d(Hs`+H-o@sN2_bUU zmMM~35L_5cjE#H8Enxo@cZKAiq-2`J6dZaqX=9_|uHkO8rHM^b1Gz-`!#!bDmaK#j zSa%uaufy&xS#)>y$ZhMBJrhT-gu8O^{zE}eTSZv>c-yKk+r|t_v%4WOE&c>cF%iHq!Af^S`2+#E1CVrXTVZ0~qkPyF+%MsD441?IUML2d=Z-XCVeh?$ zy!5;iEF44>;uD73##gSE)0!Lk>Iz4T^3%ftuLYec9eDS`u{zdpQQ60HU%4P@$JF}z z+rZ+JS<=UrckPqHHi~{5-?*yBn#}&G$nTp75GA;&ps`0GS!alI4-Oa~F&7yeN?jea zWOSgv%klMXqWh{QQhKP#X`bI62yYnUQ3g`*CHR#9L9-y|hwRF}O+*N1Vjq zBBwLsTt+29B$68$ZPGM~g$Te9fUcRL%tkDRngKFU+C@N3{N((VDPP1xC_spT6!(gb z;C%dvtf^0tD1)LM2NsJsLui_lBb{N8(L~Ud$yJtCY|3CErpOG7)@b^ah45ew`2o{B z{44X!Y^DV)L?(0KDl;yy5oRPGk6uli;UIEIc!Dr5=U+nDN|9$)e*NwnAdU<+@<~XC zuPHJ3eYkQoGdU|=w{U@nyhof#&Dc?(1G~Q1?mz8%#I>bZ=H{7Q040mmU)o&oFAdGJ zRg2`7mbME&VY0z?SL z^gJ4z1QbJ{t&X~#rm}HW^8OM>mCk3Xs$+xSGsXVqG^O?>xx0_LyBzF}s#mX-d7NSP zhMoIQTc7wil|y=Yp-^=3RM#C_9T4(4mk2dv?c7zak5l7VCrYxAI@_+Sk3z zKIM9ei~FzoigMQ)u3?wYs;aLKnk&ZSzZr}2@(di@9zXD{bh4gS-@uk5Y^O$iM{%R9 zbNhD5JCISOf7+y*bi23EgLjp#wnIbxt3TEkuMcil8kOE?;^$CzLCx~MqO`SYmneQWHABtd*HyS;Z<^1Hj^CcLJ~de~Hz zeBQp>DM~4E{P5g{r{HIv8^^bl&}S;!?R|%DaC*4fPT!h3x_qG6!uNv8BNNWEVUZl& zLE&o&EN}hqANmNFMr~54t?!6=t65F!avLo6E5FLUER*?!BCcZPB+0i@woO0 zkp$J;ai7%@t30^6;WZ^I z%z55+ll}Ms!5kKLE!$%Nh4G8B+q}dWh9ul4PBd~7s^ktz$W9Zqo8)`f#6Cp3%KUV_ zLxkvu@d^l+wJh+pAQvWjfGsOgc9a}9^p#+BGq}ldQ%efGns<59(YJ4h2{|$wCFEeJ z@eRprIlw&d!$GUT|Fj}{L)y?OA)@Y)<12<95b;vn0T0Nfk{;o_*`0;119QOV;Ai;x z`H^@AYLz6{-QtMEFZCBXqX~fD3@ilj%a6{^rVBo>zl9p~UD$@xFOGRI@7_#t5nUd+7m9_wiYdy7 zaOTr@rR^GERRYA$`K~}xZ4eO0E-kMl`+)7(;R8EmTvyX3IRLJRoK;o70y{)&EojG` z&!4Y5;f&gio12^CHj?j+4qG5;NOUD9C6R>-D6O}j`%VuF1IjQ0|D%TABZuZQ2u+Pe z;d-YA1?k2pbZf#?2<&oB9>IoR{wPJ>-D2bT`AJec4JnUJthe&tV723W!4tl59SHB$J`SM3Rwm+b&Q@gHDKg~K!q zj2~F}3oipN8WhyH{eJi}*d6u4S3MBDaBi&L(g_xb$5{`s*WjzV4JjVd-_D^SAV|~kSuf_793bOH~QFD z9Sls$W)%OyAxvrGRXz8;Eagxl$VaeMxD^%Ee9i~fm-yc>^EJx$QByrUco~C8H}v=H zfoK0o^xeo=dssRg2ZtJ;r-rW>BrcML1q(v}C&qJMDCN&RY^i@+HBK)*+<*h{&o2&CJaXXp@gIPBavjY9>q$|NYudLDap$03iwK^*g-x~vbQt-$-jIzY zwVVEeyU;5_(m*q>BGW<?bQkY`B)2K1_%h zc^S#Yz$B^m9#~rIrTf8qv^qDIKWfXg}PgN#X5chtq%>5F_lSPa4J$w@Lqon)*DJ|s7Zj{`?ym&5oNOX)z#Ig*15Q>+3IKk z%%=0h0{}8R&Z&+xgN2I}%Ybo(X#^t+%+Ls5L9XtmZ9MX3Ie|6gU@>31 z@R({t&^5iT*Q^85!!a=3_P5kxFoXNRG_E7na{QG^OJCRa`HvS1;|1)t8ILTQ>VrBOQ0f z_zZrq&RE3of;GXCQAdNNQvuj zF-0_$nc`HFA>hla%A@h>aBiZpIQxY{FLz~=E#3Wb&Ca4{+v>GF-E61&MTzpmyN>Cj zqNDQ=o5VX^C6UF-?)#-^cLm#yA;WH#a}}(T&N>stp>y(I>iw5hKmHjD%cZ0!nK)QK z-0uhWmC{~6%9Hk!*85M7s*4D3_e`v^$YqJR8Nr&Dh@#TR>8(A`X;IO%Belb79edS{ ze>|+UyK6RCI zI=%5wijlPQCqi@86)jQ9bn2HpDT2|>7KW`Zq_W$OiA^2(u9I zZ({`lqNB@7>>_npM8vg6?8G$)&vD>2-duzLi3k&>JIt053Tn&)FLK#H&}hs9%h?_z z%5E_a99)|SWQrM~y2e8aT|wr{M7nk|E5Sh)lHh`2y#Q%GdEkuYGmD5EF6MzZnyn;i zVVZ<LvxDe|1><}o(9ev`HLr6loCklA z2(YotW6nqf{D@{4B)|z_C9Krkn0HkxP`#A+$~==T|IAV*I)$|dYazXw z`Kr5jonS9hCeM#VpmpIqs)s~i0N-WCj`D%0H}3R+(X!t1vnz^aCaEdypTMx zrd^#h3u6KK8VL1TITi*p94BUK6<8R|QV&sFw}pjqocsbkFV2CLmdU(F2Wl64nKbjv zUv6}A(MOpNQGk7B86m?wv%+#SNumj61{kuME{BK=QoBl&F>D_arku=Meo?2-!eC{d z`9$0UR$349z`L|`7nCJ14}9(Fqeb)%=8X!h@LoZ1GvBX*vY8AKK@t)O8mo&5Axl={ z06p3=V6MzO@VnX*ER1!`0~;n(v(luP2bS2Cyr7Iij%i}=O>1uYB=a0qmwmYDcjrG| ziQr~Ve(1acv$#nT3BFqu@|v4|asK0tR&M%g=0{nUfmQR>d%|>~iUJ|Qyfnrd#bd-? z5=A0thq^0>C?wptw2!sHED8&lm$o25h>hmLytMaJZH_WH1K`2042fAx=VM-k>}rSA z1RPy3xJd^lug^wPU>>+n zE0Lp2fq7u#t4De0EX*s;;2RL6=P@6qsg#QHe6bR~go+Nt2y?J8&WzwAbJ<|H!4ia!_6E*4u+i`_@2d3@CZ>gH z%0IJ)ZqA%p&C+Hn1Zi)Ge-*G4rdu=b*6)3ozy-(G5Hk`MLp?`EyAL?kHC4WtG3J?S*Q;oiy`KNLCR(d3g84Cy&0CcAbpBY^o0c;6G0*>vzeSWr zDw;97xdf?YP0Z&~t2Gix-^UyPaUHhHSeWWhTGk;dAfBqLBqo4XP4qfwo32TL3^)?Ly};DMfZjsyx^ z(Hq(WX=6)Ei|YYTkXVqy_(0u)AR%NoN{u#EQGdY2BW*f3HqQT{a)LX%V`fp&bg1sy z)nEXE%iyy2eO1*oh|3cD@2Bkdqija?7P$|y>eWTe@lAZWabV%GQ;1_$iinibUR(yV zq%SH0nIWvwm>jw-U+^qc0nj6MXx~=m#Swn%fG&_-hu~X<{*3nWOINN~Q4NX(l1?5@ZEbC+61TL( z4k_6np@f;?B;(a zyxGn}8W>5+agUDPH8K9%-_&q9*lhIe%aRvAJvntJJfogmgQg{RZK>P$9~(bi9$fot z(pT(xThoW?o$(5%ASpb`u4Q@^i3?=XBvGg^Inyi`Y9-XFi_s3949lRt0d`|_>QqPU z+;kUMECGKJiW(Xk-t$U@#UHdas1!rUfGV!4oRop^g4`@Abc>RvpinP&aX|}4x4ouA zu~Y9<*oG}3GJU;&-=AslbKJjVqqp-|>@p7xb;WOrr(|1WXFaATyAQUBnJj7)+p3q& zi8gdzL*E;D$HkVhGDL8lg-9^LocV)S39zToCe0`f!Y?b*6P=_?O}K8qdHp(BIm5d` z+K%l0>+h!}aJPpdSHgxG0Y(TzbQ?S z+?&nHY#slKNoOCyLpHlp?^nVfmsfhFhrX;hZruK3Le7 z1!>pF$cV(y!8UMCS=c!2TMBc*{87Ih6?I{9_*Ba$2?x=Af?k+`FviQM8@-+8BU~)( z>NC9ZSI3X}>I1P2t4zHrdiqp->oKcS{}X0WF~1H)+R) zr`zFbuqqU!LG}d;lzd!J_@>-O$Eh>Fea?MF76>~c(=Y;FaFdv@YUoCSueX)@&cW&* zL>Hb5CQ}d@I3bnCTxqhkJM%&4`NoDmwS{exnLZ~g-j!FHi8bDev6}rADfQ}b;nC8< z{gZ%#IXA8lNaaA}?R9l&-cP&>k~Hz7(Jj#Ii&mu)V;Qis!n!#kxvTUf!oC zDH2Q{F$y4Q$kPftW~7(P%|5C`sk!0tVnR8i!ob;N-SDji4Fn-k*0q=+3|p0t)1zui zKYQQ%^lpGbs`t~K*YDq714!n#Oh}E|-@SYGyn|2>^29q45m6Nx{TX*J(~ zV+Y@PS67GOL)911l_Xo{{D0R*)G}-e%hR&wnR=ko>A$bhxhzcn;gZozVE_oHU0rjh zIAJzX--r-{FjYWHh^zliW-xCnPcVRcH{XCmU(jwqsbM$K{30k2f>xHtl5FIk!EnKz z^rNBv0vTi9QRPm|B~qf2%Jd{82>kjDN$#hn8jS>{y|lY{Xg1=Vdu?Nj&$U5B!?+-=*oZB?-vR#eCvi|jthS6@K=9<_4nLr{~z zEKoA{Cck>6eTP3o3Q2Ga=-t4UftV^l5sDvB+R?j2OhyJE=&8oE!%LPFaUsAWrh!ZS zSLO`qiSV{_q?iS}q{&TA4vs9V(wL1XJQD#XGy8w>Uy_$bzXUz%LkMGh zr|M%}s?Z*00=o`g0hWXFfak9S1Vm@3MeW+RuNrMQU8hD)18snD#@=W}pe>)-W`R6_ z^pUOvuclgDuTa6>sQu|~T>#Xc(HVDToi79$WbW zGd4MTF{xk@&>npJ=Q_vn!uB26axIN{f_wR}G6p@X812q+)qo7iKG96hhZ%|*VSl&d zDw_uRar?mq%cO{k6fk{vcuhQTZ|#B1_UE$lh6W?PBhX1({{lIARVeBc(GT|uJTOSb znh1fPQ^gB#$M9%#3z8uN#2r*mB)w2Gd#-=(4uca&BYyOf47NP+nsnm(oNH$?e@f#4 z@|25Xm$C++k}@pZSjE9%KDd6!7jc($nib>utB| zx8kKlU6FDRLN7Ytxa4x*r-SzhL7C0gn3_Z7va%N=ze^rFvCyA>3E?CVp!5S7pN=8^ zft(dWwb8$Sot>T0Zm@y$2p!)ARsJ+^;JH4lxxx;&M%^(m*v{+%Ef{eU=2X^rQ~bRk zcP>m9ye>2hujuu~%9aTiWBB+YCOqvl3t%6x9HtTiF0A3jMMV&;e4gm#Q&`8{MqY0W z4gilJc(TIzRe8-f^vnuWytq4woWr$Fb_d0Ag?_~t&ITizd$ zM6Gzz@@usDIGhP8!Y-npoa_C~D(L0_ZFE4Fe~J<2cna8DJ=v#o{CnKFct-y{rwn6b zRNiWX#ewppqazpbCmAwL55GrU1N~@CvMf%&e-!U`We6{DZ_Tym{(4DZhm(!J0~Os3 z{?}Dq7sb210~vd!`PLTBKcs=Lcf(qEL7-ZI?$M;g7uaUX&7U3?IRglXmq1<}E1yt! zcpc<)3E+M;(Eu-^t6cq;fduiYC;GNtQ$5L~@Em>_;JA_+>R|6@{D%u1$TI@Uscg_a_-?kjlRP`zW05=LU25ylpLI!7KMwJ6tOoKfLw*pSp*a& zppV$5C~($Fo!zOAhIpto0m()8>X=)%zISycuPp_e4DuxGh6oogK;si|;0QSzNBe|I zjZh~b-!bL@+L*h7o$lV^8tDOYkrzbVC`pXKLkg{!J(@uEE5?CfHW6SY0+x~?F7T_< z2kD%s^O3esVxSuWPAZ0CVEgJFDtH3Pd3j^tpUU067Qsj$U-{`M??_3&s;EKXapGM) z2iFSbO*v^kH~2YhbjYG=Q~gg7<~>SEB0cTUC9rGB=PzFX^BNaO!AzY3RyrTwc`Hs-y~rORx_m>Pgu%qF z`!juFe0!1%vQ6zzoT!ifqb-xVY5ibZsmQ8T-~ub>m(&p z5)v-Y$Sz-mu6my=s!>Gb4=pH|#3p;;DoQ}m-Sn#e-jf+>p%@FxH^HD4bod|&$S;{XbIuE*Ym$ayR0+Ej%6e5$htKn?)T5n zst(=zVBvtfNKH(v&^x*Lh_P`5s>bPA{9nE^FR(B`Q2TNq*$WTx2TA)E*z_Y@`;}pW zUC~a_OUcv&iG%LOEFRI=p$-2I&3JlxE(?X_S7l=V3+OHrZY-vc^T3&Vk}RpAEH;+D zSHc;^Ei@-WG-V+lsh0%jXz0l>M}&Kpo7KJ&J!EKj0=ZCszlE7ur5-AOD1_2%Y~Z@F z(PR4btsh^tvxl==jq|$c9JOazm>UoaA2T1+~T=gH5^@9TYaFS zN9_kIHYR!h?whqwvUr0Kn}A1;)tIy(eZH` z->`)|JPw98Yb9FL*8jrQ72xXfE+^@clA$#Rf*j-SUG>L*V-`HV#_E!a?1^&xrqihm z3)z+K4@2NZ0d}}^so9Yu4#@Gr#kL57YXed-@Z`anMR*LFX2F8faec)%ZY^BA*oE2K zv*yDGQ);encW7f2*&ng7A5A~>e>f1bl647CSaozwU_%uY z6b!UQdU8f!bqbdj>xKXM2QKoM=a#*QZlH6KNI(%+GUENoCwPzibqL&HwVxUD;*!ez z&8jWr`o43wW|tP8KWU+!=h&i0MJoOI*?BR~It`cxLE*A}``ti@8(Y3_; z{N08yHqGQOCEluhtA&KNn(UMaTfoWbJjZKhYI;t?7ji4h?MB^#%ySUD%!{lIcR{D{ zx{|&8gi&QpP2}$Nte0ruLrcrpo<3b2t5J%56NU@Nv!e#Yezmushc!L6)rWSR+?Fh& zEc2%&4^?=?@>09$~Lu=}0aw z87#qVg&hmP4aObDHjHFUpNc36H00j3OLBgJ_pJ*RAL@NrZZik7AsVoYA|C=hrV}y& z(ggpp(?oy8i58-ZHBrpJp zxV4DZu{L7;eT(f~Ur&#eaUuG^;v*y^1PT(2d2szo?v7xcz{(UmIJATuOV)IEbgWpp z(%Rm>>V~zo_0a;SD}jK7tdAcrR~<*{138UE0`z=N+!1I<4`-l$P|uM|0LwrlkC@G; zDoOMwcW&rwa6mu+`2LjP@o|xD=i-jv;}7};?FPvC-m}vM*RNLtKQhTMjd!B_0iV0Q zy&VGx2?P$5mzO8D>zZkSQ&M>NVb#I-1gy8Dx(VqL#wTf6MU%hq zl6o07HESu@@(Pi(;PNl}s^J-)vaykAYGWK@!T z3H-E=A4VKkQRWxgHN1Rxcg+wAF zs_+~JG8;9Z^FYvgNrX;q7S3-N~DGS9C%Ja zwpa}CYviK+wFoE+oD&lg?mU%142f_Q!PBdwM?c?r5^*5(-ANE#j7l^qf@q|P?6Sa( zot5SBWzBWpZ@>{0k{QcQH8$w!xIcDBOSCx;QCmSHr%8j5>fe#8SG{{(nl(7zaj}0qBfHoB49e_cFQa>1CKs?|}lVO(I zi*__}*EGb%p`cAJDQT^<%M9s6^4gPs6R>6n)a6I*0xXS=EthXnD{nGb=Uq9rV7? zDc99y1HhA9j^3_NJ;|BnNFu>P-C*F^Rjv4QuqDA>gZVM?>bK)1nJxQ<^}`13PGu@eWB5+xZ_Oy{Sq<-fTS;X@T`Hh!0Cxszr1=$N`+eXK=dReF2?>O$7S6uB4=BpLK(v^-7aeW- z4$UZn5M!ml)GWIbi>#>_3M3i7KCY((btsZWE&cd;XCK!cwxA$v)i=y86Ij7wOlwYE6e(B0U8t^I~M;V z9Qr`UQMC9quQzfw+i|5hQ5BsJ@9uqM`azjhl;T(td2Az_%+Y5S@}=j0a-GLk2i)7<*^iBy0r8B`AstI{N?C1e6$0$ zXIA|O_w3=4LEYq-c+ofky9X*2>n--E4A?@6Qx%FuNM^7Ups&Vu(P#E^Cj&x7RCokirln^KDXX?^mAU)EOT3b^Tv(Nw09lDz`cS3;nv~mIyaukl^3lK zDKMy!%fEU7q5)qPKLuB8?qny~**iFZbN5D75h*$ZbT#1cb?9M#(4o{J3A~^r1fgDf z`U=iA3H!xkV`Eqr4R=&N8p1OCY;jm!Q`1oxr8+xc9^Wu2A2!FT(=mEtF%J(s$+amk z{64eK@bN>hVC+fgIJ0}bLCNdkVW+VQnISCnEvPC4*`f!n?6{#KRtNZVQ_u;lP}XgqPSk4${$4SC_cXR7mnnxW+PE{kB3W?AX37x zQVoAtN`07^c*4eJ92&2pBDGh;O&g!{3kW;|Bn;j2(V`2R)~%!anD2j$IBC-YVYCW> zs{m|RWI}i2T+Nk|$afJWLA{4Nc8KR5D@iz>(D($Y8L5)PhVa~XZpS$58P05f1#$5X z6rdd9qp6fb)8Y9>yf=prMJ!d>wk;*2W?w>QN5}Ow+n<{Phoi6TDj8rKqHo`}h>{TX-ZRKLiR*rxU40m3bm3L!L`6 z;^HE!Tt-F>2!_x;TRvRx@87@JTtTvKhcP22FotuurJ}NOo)=dzZb?g9+s@7|s5>*i zbr|uGlanB9lo69bYF4#5%Z=uK8ha{XF=0b0UKwoT zF7i&je!XkVBN@!>=R&-T7w_G-Zw9+L)Vzoy(MSui*6@Zv>d8~55cT25*xdZy?c2jc zzH_RZH$MTKfdJ^7v$Nr3xELQ`QAALsadF?n#iV3qEuNg*qpj@+WEH$4zfaE>!C_HvH^aUgJNZPw>eMv z9PLR(>xKF#^k7*W0!0%&8dewP1$fI>s!Lthzd`ET@bP0>M#i<9H*JPO0Io~>h)9OL zL)!xUAjCBdijQx{HdhLFvWyJbyvp6UN9Td3*-6RC>Gxk-Fla9zVHKlL0!eE{OhQtF zDQ}5B8hOW+aiEvS&p&@0Dqe-@BYjhEJ%9Ycw+?xAj`sQPt*jbwe>EaE+M9Rp9^q6q z2%5JR)Q_4ruI5As8_=Dj&*9s>KgPG zb>I5>r!8_{KYz}?Nni_q?WXj-cw<^-raDqTpw9pVuDfT&$BUZFBweX#e6;tj78QHt ziI7O?$`2n9;@IoyE&5mf8*`m{5?1EZm*CZ^rCVYSr&DP@br>X|tXruIcM#yb?~GXn z7B;;{?1ajAnJP9RH*{#HAj}w`ZLB`#einnTa%d1PpLtLCfE}z{4A}AD{_hyj-Mzgk zsFs7n;C7)1xeq@xv9N|?D4rtcc#sM91eEfA{`?ta3!6rJ^FTLlpc4+4{t*O+#~$iV zqxA_0r;x=XJw>lGy2%R+*+7JSGv8mZy&8rBTR8yttMrL%qyVzQZYpT=G;=`({0YF! z^%PK2^Tvh0jsuzOD(XpPvWID7&V3u6FW(ot1N6nq@i6^&f6al;IC*1>FKmPj62TY6$6m#fn#5AKbrRHP-c=s-xo#o3nnKaQ7jg zX~CsWd_A5axB+3KYDeeEm&gAgE<<>NjRkp6YtK(kqWi;dve`?@GV{JUlq;}F#V8!p z^7ftq4)@u38BCGBJUf4a^DCyBMX8Vadu7y5&mx&hCwqC}rtktFGKVa`_(tihz?{K&Ff|VYWyNvAY?JnI* z`SwLA90T}67>4*-|6#zjt3~^7CfJwc{u61H9lImPwDoaB( z*X`c7?{I4k4G}32_2ALZmGVeUD)*f?Pe2t`Mx-O6tq2|SDnqBCy*NDi=PTwZz{+AGANH8DiTuimZb>i2@k0+SQ=H=$PqBrIEcs_%1aIgc5EMhx0sCHf0bB|c zk8q}rp`o+Kj~iH7)jYA_<-KW~)$p;oc>=lF(NdpcAS53@enihoKxbHzIuF~mD+j;& zft7%Q9(M-LThs7_BqStI7GBQ}sS3gp5|#3un;o!C%S=Xu7z^bTQmOd(V<2Av9S3mR ze^5*7@+^4-4{Fv4)j*{b*N@d_-gtsfaluUN>A=nD(dt8eQF+y9^> z!CdWqeLB+NaN*Qk&rb%Wp0U_I2?1GY)Z^8Uz%ym{ddlH{b!2s(jN7{}HM`qlyZ=^n zaSI>%6Yzrd-r~oKU%1^`%1UVR=C}_X#e=i4>B18Qs&@X~GW;o>LN1=QTa*+PmtyAB z;q6~|Ux8l`ek3lYsg7!c@A#l4mQ<`0t{y*OPX+6mh~4WksD;0M!N8B>)Yc-Ya`+Vg zyHb+*i5>vx@IU`Xo}T=%l_XC^{s=B2;~M<@|LJQ}B9;kCYp+E0myvhAM`u4ZON(~- Fe*n~2d-wnV literal 0 HcmV?d00001 diff --git a/dev/ECC_evaluating/index.html b/dev/ECC_evaluating/index.html index 2dd45d617..470c3469a 100644 --- a/dev/ECC_evaluating/index.html +++ b/dev/ECC_evaluating/index.html @@ -38,7 +38,7 @@ end end -make_decoder_figure(mem_errors, results, "Shor's code with a lookup table decoder")Example block output

Testing out the toric code with a decoder provided by the python package pymatching (provided in julia by the meta package PyQDecoders.jl).

import PyQDecoders
+make_decoder_figure(mem_errors, results, "Shor's code with a lookup table decoder")
Example block output

Testing out the toric code with a decoder provided by the python package pymatching (provided in julia by the meta package PyQDecoders.jl).

import PyQDecoders
 
 mem_errors = 0.001:0.005:0.1
 codes = [Toric(4,4), Toric(6,6)]
@@ -53,4 +53,4 @@
     end
 end
 
-make_decoder_figure(mem_errors, results, "Toric code with a MWPM decoder")
Example block output +make_decoder_figure(mem_errors, results, "Toric code with a MWPM decoder")Example block output diff --git a/dev/allops/index.html b/dev/allops/index.html index d683fc605..63f18759b 100644 --- a/dev/allops/index.html +++ b/dev/allops/index.html @@ -10,4 +10,4 @@ noise = UnbiasedUncorrelatedNoise(ε) noisy_gate = NoisyGate(SparseGate(tCNOT, [2,4]), noise)Example block output

In circuit diagrams the noise is not depicted, but after each application of the gate defined in noisy_gate, a noise operator will also be applied. The example above is of Pauli Depolarization implemented by UnbiasedUncorrelatedNoise.

One can also apply only the noise operator by using NoiseOp which acts only on specified qubits. Or alternatively, one can use NoiseOpAll in order to apply noise to all qubits.

[NoiseOp(noise, [4,5]), NoiseOpAll(noise)]
Example block output

The machinery behind noise processes and different types of noise is detailed in the section on noise

Coincidence Measurements

Global parity measurements involving single-qubit projections and classical communication are implemented with BellMeasurement. One needs to specify the axes of measurement and the qubits being measured. If the parity is trivial, the circuit continues, if the parity is non-trivial, the circuit ends and reports a detected failure. This operator is frequently used in the simulation of entanglement purification.

BellMeasurement([sMX(1), sMY(3), sMZ(4)])
Example block output

There is also NoisyBellMeasurement that takes the bit-flip probability of a single-qubit measurement as a third argument.

Stabilizer Measurements

A measurement over one or more qubits can also be performed, e.g., a direct stabilizer measurement on multiple qubits without the use of ancillary qubits. When applied to multiple qubits, this differs from BellMeasurement as it performs a single projection, unlike BellMeasurement which performs a separate projection for every single qubit involved. This measurement is implemented in PauliMeasurement which requires a Pauli operator on which to project and the index of the classical bit in which to store the result. Alternatively, there are sMX, sMZ, sMY if you are measuring a single qubit.

[PauliMeasurement(P"XYZ", 1), sMZ(2, 2)]
Example block output

Reset Operations

The Reset operations lets you trace out the specified qubits and set their state to a specific tableau.

new_state = random_stabilizer(3)
 qubit_indices = [1,2,3]
-Reset(new_state, qubit_indices)
Example block output

It can be done anywhere in a circuit, not just at the beginning.

+Reset(new_state, qubit_indices)Example block output

It can be done anywhere in a circuit, not just at the beginning.

diff --git a/dev/canonicalization/4d5f47ca.png b/dev/canonicalization/4d5f47ca.png deleted file mode 100644 index 790ae6b9a86289e38dc3940c6c8284ff13c69e79..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9515 zcmd6t2~?A3*2kl^;xb4_ii}%m%eVwoR78+fTg4g#Bmz-{pdx}qL}Z6RT(DFYsTxF( z5ENNMh%8|bC>CN-KqLteAnZ$kBtT>dfiTaT&~JLq_f2QMscn&ShCi=gBwst|Web`!?t0IlX5d(ypbn1GVP6vHL}l z+TWbqGm_x@_hTAqURdAItcTynDLm=hyJExFj25*J)dLqgencK2yw&80XZMV5q*3Pl ziNkY~hF1zJs_Uvmh8@D;V27SM$%sBNBO?Rc-oeD=cnr9`>lasi4gNoI^D}T~gfBjU z!B%Wpu>=PDdgUU!9Bi%yZugx!(ITxoAJ`DyxS?y!m%xzie&Bwu@4(ucTnklZw~O(a zm*49_*A|}*|MelWnm#PuCk%efW^bVRw3gT<4-Ks`XK!Gc>_36E&L}x`WF_NKl0ft* ziP+>;IlQOKjuO;Q%=sqw?8}>W$!ATkg)JKI0yiEM6gFG#+xlJ>j zh*o57U~P`i(#f=Th+IyaTuM$SMzDfE4KUiDLPVo80*^82C7gijA$ZSyehp`}{14eQf z`#re!$T${RHu`bx3hXv!Yp?C(FF-)QmpZm{e)qW`jH4aTchr_`6Pk&+NR z*+QCOrcF-0Ce6}|5ROEw3!d#!Bc%q}aD4mi9urh7hulSLa zhJ8!PXzH$%4-*sZ!Bg!-3zzuGzd}b&_mYYS90PeNDFhc%@Z?4jBmp>bXI;@RHV!NvZ2##RfP$WNxC#4ACK-EF5?nr%ib*t6iAV?r_a@S{Qp| zz~Gaxty{NpXCxi7{klCpJt>5GT)#H-72eb@p-?k<+cw>8XlPi5^8sgHVR0(&VyzN>`qgFw-?k75pCtW|Rx!h(K15jb3dwrlXw^QD^OTJt^9`MRsM)@7Cxb$botUhr>~c7r3cv50n2nlH z6SS`moY8FWd`=9R;pMs1OFI=zntOzrGVe^b3quO;35SoG{`uwG+Ocu zD`6~;$DHHX7@7(Xggq1RkVUqw88i^4jvQr|U1U8)J=o#_J&4hsJA&w=naZ*(lia<> z*4mHUH(?=_<&AklaTYthL<2+iAu)W*zvqZoWomW>^q!!J0=y}et%Su>F@}zto9ob* zDF*e&xd0DzfTACdxv^>?!$4x86ZU)d=Y}`B9rOQ`MK4)fcj^cqcd5{}l4Ub>KYe-^ zT_RGaneNf{)+eHB@?zC^Q90trQv}q-gU5@%`E7g#>KI6%FJ3!E8x;hI`fuSzqjb4N zfOL6hOl6o+msf8r>Aa-`@4bc2wnspX<>L3z!6Qy2N!!4h(d!lSbHXzPms=zQPInJn zw2S>G$dK?-v4a1L7&NAMN+}i-$UE&q)S+9JiEjUU*%_kEsl_$1U9*DwYL z2bYxV8yez%@PgxK$If`rX@qNSo(!Yu&RfC3^f&vUPrs_i&UOg8PK96i%ov~+WKN<{ z(9FzC$cJRL&3On7KunsP98|`vWTLuxdDxYdYg_) zNplb}@mmXHQ4fJRF;rYiH7cw+tOgjluTv@!I#z@PBb=qP;*GjjE?-daTal50zns*a zFM#TmiYmFt#=*xjDs)KjKMvpQpWHIoHrLnj-b-&z?+B!Nu z;K=8@l_sw=)y1HI=-Uh%fC6n2!h(2Y~^pD^S8bzHn{K;z;|;Y6oOt}w+zpiMz3N)@5ARLp#r1SNTy0)RGAnd#_zL>VZsjr&QMhT- zCc|k)g`{1WSneDS9ok^r18`q}v|Ixt=IdqW^t+BJ^1%a~cBAI;Qh+U~=;p%kZ6;lR z8|IX_J5a1P_8Zw_nd5f1kO+6W#t>$$N_4~U*bn)Wf75j1(>R!0*my1sRrDLP^W%+R z>E)@aNdcgqnp1c4<(0={<+h5a?8NMF)n>>JsIhUM=hC{f3Noh+x7w3eGMer9IQVd) z_)d7<^<|4_?1l2|3u_lQw@lt<*XDV8_u$V|i2}7%!vbKJOBPYXI9kOL-A*RcB5d-{ zabM9)cgir^XNx_V&*b=3`hp43X3EaNuqYLDbdp+zPI%mtMjio`NT2=IBeJ%mERC>t z+4-8q)8rxC8Ig~@lTScB;HgYfXn-g|+mqWSr!>$^?2?fzEUkMuN1&Nb^!VJTFw?)9 z6L5^lf*2+)U2pZI^H^uR`sSQ~{OYf2y%v?E@gnj)kYYUTzgpHFIPYCQMGcSfSO+6&T! z%2R`VEgx2SY@^U$Kw%o4BVe)Wsz4c$*OeOdE+E~|)^f}3B#Dg{K3aFSv@)&3tS{vf(AIs5?T`;Iw*UkX7pyXgE+ z_qRxbnjh{w69P1xSX7;Xuq;LsZPB<_1`&R{iaKvT_9!oI#3j zYiA09MMi63%8C>WrU_Qa`R0R-nq@@qu&tUFW_n_k`csuWH~t=5`z!$%eZv`gvU>FJ zvKmzSe2Rj3+7 zTEaC6zi{dzKp;SC@nbiXaA$=cG0nwZ1H3env^zqpE?#F?!DRa7NK0N&o?Ivha}wg0 zwvoEJx^At{Jzo_b1`ix;II1@H#!(8+5mK8B`1$&h&7a88PCD`GthDja@^c7h-uskj z;~7^(N+S<9nMa~LZ#kq4k!M&>=K~=OgBz>T!Lmo@L`)_V0$caig5?@*cXpe@pHpgM>qTYv?Uh!Z&?M9=pfB&i;mKFN-@9?*Xr*SH-><3h(Q67tfcm_ zF3GcceF}jZ%*R@q%z1mP`waS8MSp0Pf)8 zM78jdFQC&2bgxe|iggSTgDB(jy!T&e^Opt3x?T4EuM~9&DBqE0&qj0IiL;6_3d1@% zIRUD=fN%!VB&0Z=!Q*?Pba&YoJttgaZ1x)oevvPeJB%jSiZ7Ic2fr!o2$58TTw-UP z23%?g00DC+IKfan_{Q;nzEyr#sD0DDh7dtjlF(&pC@9BnxM`om6jnPC^E1nm`bd=CW$ z1uc+-9wDN~AW?zGb+5GP$^RJ}OQZ3#PVtjt5j^NDdV_%?rxh|5aVww~OdbB|J}XaBXpEypMz-KC=a4S-x45Puw7h%J!1Etm0mRKO?U8+v{B#^CCt@pd)y>sW*Q*w{>{Ej3sDLXpG5@V)AKMYXx)A%N-s85Q4-?+YwsC^*ArOF zkej~cR5pF2wYXU(YsH|Tb)Ki4fsLVf^|~GDKaV6(FZp@zrh$(MqO@nAEmY-!l=VO`4fJu4XO`YG8A{>!rl-{S`DLi8vG`%cRO zxVi)g48HJW^6-f*3A3P2thAGO9L16tU{^xp?%4%(Mr(xg)9xLe*FQ=a{PK2wqXaK| zMt}+|!CC{nrC9lZc02TTMM*UgAeUi}ks}Vx_xPo6Xv0-k)g8a(kq$aP}eRZqyf+Et0F`OEi+-+$Qpjn4T0JwwBa zi;s5;Q~*JW8T8gyNvpm7XhFM@H^0ReYQJjToYsrV{91*s&uPhqJ#vd-EUM Cjgjd9 diff --git a/dev/canonicalization/4fb90daa.png b/dev/canonicalization/4fb90daa.png new file mode 100644 index 0000000000000000000000000000000000000000..4ea8c0419d3aea34a1ded83c893d5cf1d218bc2f GIT binary patch literal 9671 zcmds72~<oxL_~-T5y;q9g;tcb z${>V6OT&;bs9_RFQjCIv5D`KMLsEu-1TcY+KnNjkpWt1q@4fb}yE@(a$XaBrlboHs z|NZ^{|9#&+Umx~#HF;yr8!#BmgsCKzOtJ)Z|>V!{MK{hR3j72 zVX%kWKhR0eXWp9Wpsl;=v1ZuxufCwae8m5sO>hA~>mMvKbGmg}$V4_ivd$s3c{q$4 z>O>gg_y7%oaZ7iMc^;CVfHV z^K(nz8PTtk8s^<}Gv9s!a>{;}ydd{^)j$&2N|0g45}wxc6UzOI#q8iTWOYrA0(??Z zQsSmt`XTtTX4iC2RK5q@$1QH`c0>4GSt@nrIvU5pHzZjylEFPRD+E`v9m-dA-Xa*R z_S{&F(B24gHUN1lGTzeL3!$GPN>tgwIb=;iZqlsGh8j0F(O^&q=a42JUGv->BFJ`b zu%gb{P$m+;-Qc=zutL{o%nUR~U5x9E!6|9fxdE<~i9R%HxTTjJ>;;!qbceJ2&mVwN zt4zvB!*q#6zHWDivx)ZMJu{P3!vu|5OHj*^jSViE+i>r^cFcy+%FE&UUPD~JnV_9+ z=*y>kf{TR*Dd1Lx4s*A#B%VZxjMH{8F_}r+?d3w3R8-tai}u!1agvM1pptrq5H9vP zo|xv@bM7fQEcIcbmM7PiqK17@>i%{Y6^bUK8)OCBtZVN|NT&CnGTcFkbp44o7`zbG zU5TUeEhM*M6q2LtlO`r6SJv*D)O6!;eAA2LmW-Mx z?y9a5`0g@UD2ouWd$zINN9X4wOAkBj$~);e+exj6xiPXL9@kZI$fNWFlD=ki9UXT? zau`oRp=>-6es+|nyl6Alc{^~T|AA^)fW7_cgIt=6zuVo3 zdJDsl)k>eME1+_k(D>bfM2$*(H)?pk?e#^A7D;D2Dl2eO?(w=WX{5moqJWqHcu-GO z1l3@+Z1Y>tE&OdbNv)ow+4JSu`(M2kBZ(VM56;%!TV|7q?>I`-jE%_U{?*YTF)?&E z4`|2UZ2028qzJo+{`+2Jxi?lX_np?CY;CgPk^1j{{Tf08dmX}FpI_D4zIW193>)%D zja2{K+soOGF!gMooeHL9F9$#CvBvIn`}J*sZg3p2yZaz*U2luc)}^n&U>_RqKl~-A zxa*VGzY2pbefKAq=Z)CndjeQ)NZQ$dVY%limB_es6J3{x+woAO-jEB1|3ljiNc0=U zB|3r5MfEU)ph^Q92chv`b6@eU^L7ns+3yaFnv`-#<60DoGs&2IF!F4(v~~AvXW0qL zFq0BgQBvYS1Y56;udKVA9w;}#r8El0CbQHhrxn>qFchOS=7vP+L0=`Zz_=Z?uV&Mn zE$b|yxc*XHej!}{-pfL}9Xr~mOvl-wq7snZB_mto70+dkAUmYa49VFw?HRUyc#7ca z1Zuc#X+z%LavKWjT4hN%NLG497*ePWZ3ruLsMSo`o=gJoa)Ttfu_>ku0Dl$~x==#m zl4v|W1-ay;l=w~5O6hDXvT<~MUe7!K8#MpkDEt(@zc7k| zU*DA{Q3f?Rv;z=~fQZRSm_r~~P{An2de>g=4LnJbHwFA z06SgM&vX?&$0%*jp_&9mjg}MJ71j{&WNPIO!Ec0;uy+a+0$7-kM{L~d=|}oV6Kir7 zqDViJu)nb4Uws++?J)JQYGs+rj5e<__KF;e%v?||6egm!BeRaFV#$wg=YsNDnwyrt z*VEH`BQ78SHE z*MDK>f8*GA2M(;rCQdl)xFVKS8fx(fc)HcgR*B)9uF}+X}$v z*iC@zDg7e=7bre<_fB%8yf7bh{j73cCUk48N9WkAb7YXi}-oeI+C)E9$sCT9Qk-# zLlL^Nq^5?Pz7bk;e4wN@PNyAvWl7(1FQ;u`U1c2N^tqTAs;*n=GITxAwDsI;`(F?g z=_1m*#Xh0(_CkS^>SK6N>vso&v+x}^J4aDQG0Kln8afqBR!LVi9zY#@FGtriZ2ACM znq-X5lh11uT;j-61|#{JmrLA(ODnF7t%oMj71mu5=6fvS06b{$;kQz-2?wvN5k6c4 zrSXm8Z0fvLB|sQ1uEM;>=)sEu@-rjdyy**MeD#_&)q_{vDQXrr1$nYL1K)aJm0i_~ z-8zuCGOY8~&E&~1%t$|`qQgVZt>y*&C!|KtjdgAVcpzKl#P)wJ!cz6~R*1m*%S^=K zO~wfgLTs%GJAX$pAY}O(+8VqvcYb0%X($_dv%^Bd{*1)wD;Hw8ydfo5@~=u7tpLH)cDY_rrzi0Tz=Ou?d@gWqF=R|2O3(&cqem*f@EG;uJ2f z2`%61ZPaYtnURffGv}$pZRj~FrSQ$axU&C=&SZw3I#n=Y*%d4*2>=;#jH7jSuZLJx z2q+V~c~SVO6hPdtiakOt-QK3ep*B}Q8V{}j<yis%k6J%8P3DEtZC z@^|S##+EB28}QDwq7Xu2-zey=5+&%g1b(87&Ia6rsY(l@AHmIBCgg@3apmQ8(&l@; zn{re1#mWH_0tU7PJjau z$g{T1Z(_$~EEl#VS>_HmGFFnYVWc7LJ+EVMvEvRGnAZ8ZX~Bryv*`hj;qD+b$>r$L zmK?x!IejSUCHHZMOysnmkMk}Rk9HV^Rs2ww6 z%qE%xVQx7vNa%sE=`gVx-#!yBOwFIEsqS zn@lNfN7vIX0}WIrsEQZ}uj-3OHbO+9*-kXaZ#Wk5UD5Dn{yXE;Gd0HK?+ z9AkhWcZ%(p8j(=`H$hRsN>Z>zuLxAwD-*>VlGY+DvF;X({8l&N|dJCM> zcv+iiGv&2C3v>=^*nXWC^Z8z2hwjG9$IOjvDDu2I8>XC?=*GNY6c4P zv)8=+cIWiOlP6Dt(gG^tR6~5z&^E;L-#*)S@4VGhsnh^@s<-&2HP60F>?k_Q z4r)q$khsd~YP*y90-Lc--HO)e6;xhwq*~|;ZNz2UmiHK>i9~EqMHrg6av_SbzzQwp z&H|?r^0??Yu2#u6gS@$~-rC?_+%YxMh9!(JUIel$Od;W<9gBRF?Mwt`3_eAE5rf~l zrXuT;EQ#agqEsaC=_q=&sPcq~(HjnTPu&s+VBijC1G=~)Gt+#xzsjjD_{br4F^Fl4nRanao{(%^M{QJgRG)GWu<h1lQUT(%b~ecOU~~8>ZR^8zzg_?9@tT!u|)${z(?I5J(VKfd4eF+LLFu|)mu1{ zRiwFHYoxI{N4@TdVh=~$ba0^)2M%2)@X?I(G+9}g`Xp$_gUE^A$pP!^bKMcE+UZ{T zf0hUIyRh1YL4M9FNPY_F9N;TWDPmez!yRUq;EXUaP^<6s)B0(IYq=q+{)~Z9%v=|4 zDKHR@WMKhQ1A3vY!h^Y+$E-pSA_ zBYp>O;z!h}=G9?jkBo9GmIDWn? z4AqcUK2Xta!37y$^x-EgZY9Z z+2G|gUP1Wn7Shk1sv~CxFT-Gq&qB`v{K4`Zg5Ez+Vibq_5vq(redzXHz|&8@b0)4gu?-s)3vvhuf#T=4v0Qe)5^(+MftywPpvMK= zp*HhJJ}yuuggDAFn_49}_L}Q6qjrvMeBtPjHDdf|2jsqqc=LGnf|v6z9KyV?$Sp&F z^#n|-p1V=q6_0Kidt2Xi2b_fBvKeZ$n9ALM*J`{Lc+S0x%K)a12QBWSw`i?gISQVT z&YP|pkeeu?6ZF$4$oS6|>kDQdcW@^y$y->FLl#HWewa?xJUD8E8-k{~MZ@?rolI+Xy%3y2o^{~NGOCGP+L literal 0 HcmV?d00001 diff --git a/dev/canonicalization/50272d0d.png b/dev/canonicalization/50272d0d.png new file mode 100644 index 0000000000000000000000000000000000000000..ddc710cf64d27d7db4e228ae4393bae77d35df4e GIT binary patch literal 9868 zcmeI2c~p~UzQ@x+#TJ3yaZafsq&-%dsnzHxB3n|&g*q;Ht1*=bu|`NAv0wS9VVKoU5AdrxR5JE!M`@F$f&bepi-ZPy$r=C0T2ZuLr z@;>>!zvc7&KJOQY4~4kCw)!;$0^z#vgWVq@5KHbN5Kf;j{{=XLb|MQ$>i)rxK8PYV{NeT7xHx%i-{#6cM%_PDyX(gFx`TJ#nLn`Q z)T2X>zFF~{TU&s17T4Kh9v=Lr_t`w1Q^fbq7Umai;ObfpC;AN2d1b-TF-b|)V117g zd%trBfA61M{yPNXv%?o(2TT0sttAM=@^#B!K_Gtj>d)+O<0Uk_+%>CKuMW6Gtf;7n zPKbMpw`(~9@%rPy&k>0CuXcDMgE}s&ke2bS=f1w6b9);c{Pj-wgx|jo?#$=E1ZN?x zFZuW3|EDoYbEbm?`0Q8i!E;aO1~CqMEh2SFRU>7LIt%5&nv}VxA!V^`S2yBLoZZus z0_O?HHZL!FOQ2*+aBw(w1CB$Jc}kOcAq-PDOHxlJV%Z_}2ooWwZ%srrn47=;u4 zrlrSEpv}bb71&Vp!q|eGWp}sFxPuSdFSM5s%!7TK>c+l~X3^*23wQ{PO_yCfiYGn| zy$_cRB2nSP81>2G`x!e(3|&9L)ylwEpGlb?h%Qs?LYfW}U9Z9&;ae(+uEe)AH$#e* zEaQ)3V`B!JnP3$WRN{sjh%t_1oYpHu;+99I-;_u#6MoqS?)D4v>s@GVZm;!PuwH6z zMuyMo1zIRoCL>IH+NGG3<5J@q<7Ff@MQS`wu$+=6V}mIJ1*T@Xex!jcP2fdkm+BuM z)pgHqATX*)yrB%{wB-hhs{JlBN6l$a*IQ=WgjN+vs4LRYj3epHu@J^soxFJH?#GSO z)6)+xyI?FM?p+U7m0z4`^D)I*M?8=m5*A&3@xR{<})?;q*@XWa`PUP_}Ms5 zJLs~+ljlywNsSj9NRysiDDPm1`M)ox#1Lx8q%_Pz8B0d)Tid%V?Qu2Y`9PsAFgs}W z(Y$Ji#Mk$V8z{^X7s4&bAhcWUBgi+lx4s6q)2*k6s^ff&lUFz5ZEcr33jCOJB}h70 zzNS`|<;R~osG)19Ww8V0r|k>iP5%Mkqtel<_;~*ZA))J+clpZ;8#Ds5qKs?ntr6(! z`}pdCXqMON)%8kFLt480R*xfVZ|}$(Go#?#^kc~UY?Ilx$^Otc=tD!2>Q9=!>}Cb; zgR^h==oxXn{;O$=L}Qf@EKP(Un^Cs^>U;i23Vd3*Mc~qJ{;((Gjg8^;l~Ba&*Vo=V zUVds5rV37ozds@tg5h;LC5`9eimB>46m_6&!l-iu;1#nBW0PH=MKDkQ>i>A&^vrbXFrJBC*kod0eqE{Q< z;N$0|@?@<#KI9jHy;3Bj-nCs z^!#|FEHv?B^D6%q-Di}45xl`T_Jnxme4^5JN^S)40iH48a>brazL@3P6e^i@=>SHycC~0cO6@kx^qJ$Ynv zvgGamu?7Ep;N8{TgxKu83f&J;3J z&PlQ477c*D>m~ISgUWMp^ObDGa}QwI0p&GhrXwm3N~_`e>s*(auBk57eJTYZV$ElG zpwynx-r9doSzQd8d$P+QrbzdpjlFmhy@MFhO?eYW=gkzs+znLl%zY=Hh2by0cojZ2 z^9yYS#$3@CP7%NAJ)?1x46ReI#)`xf9K0{T9gDgmP9ZFZDQ)kamdj;R_~N zFd(v{0Sb5I`-TQ-cVpv*s#RnzRh+k@&wVGnpu#V^?JW!qO&*xN#{WYs{GC)%n`-OX zTgWWryG|hR2XO?|cjHcN2p>Jv|5g#7D6%9-A!27K|X~>Gv1b z>~h5Yc64#d1kAU9nAlJ~Sm36H>GGXLyB)6<0k-yxuN`S4*v?_&`tOcxB&D<=+}Aoj zwiATGZOx9uSd3kVVakgrZu6TNkADpdgOstHka&Q4kxWL@hKRF6aWzFot+JO*w7T4I zuzgmL_Q#cWo5s$V?xGshRuoeBNz-dPmpg6WUSCJD3}08#WxUT+07B2w6^`DJHO@9G zw|m8%kUp&q$GQZd4ry|4OEM~=`_6;uvQb$?s9}66H6GA2PE!dL9o*YteIB2%Rh z&?twm9u?5DvZ1 zda(jLM_IsuAbN;fjhezNixpY(<3y=7(}Lf!)0t20d`@hr6s^1bubP_h&G^YK3p{!Y zUx_R!0EmL`^A{`)yjr8yC}|T1vhJt=%H3O=nT}+I4S?q9?9PrCO9xVHWaYK_Op1~b zrUui=Pe2+N0V8O0#Z-(m*&v>EBqJMlGoQ2^%MWdHa3G;>=6j;KHxKhNLR?gIv@<=e zPS+oq9c-QJzJ%U$3q;9~*>xsh&`-kFKmH~|_pmCl^@2c4Z*zlZ$=D-+`@PYf{gYrg zLjlP#R4~4KGrFyn13(&(g`#@>erNjUNBZbxtiI5;-VELMeG!xgLxwpOhUDt%iWTi? zs41N2#E5IzPy}MjxECz=e*U)FUuC3k(4^BJKLJQ5HJ*}gbMgh*p|m+j7|+HFE6?&) zw}1l5;j_&$SSW;My$5Go0HE9kv#+m!SWlvL9hD_x;hy$lQ1b)@s%hGTV>)8BIsRCY z-8@&utsUJ(SGFTxI*JJ*{J9DBS{I1TxvL5t0_w_IBEU7f?+|28yBi%_f0l-WgP^2^ zd7ohn-cec}S7YR*Zk3%}5JVD9&XF{R236IQc>2fZJwch)OHXJB-XrS4oBTF1w|xOyR-QdibngpYOJHTVUYOHfzw_pKG#7 z*8@-&G_jE0YPIfS<;j-WUaKRdvLhQ{0v^3B0vi^pEnum3+Q8{+!MgUXD26t}uGZMp4_#0}9Ztw>A&f+uDZsRu z7Z~_lNHAZ;71MMbn3*kp;`7~GyMm5jDPl5?@WL&N1RmP)d!OvVim4htYoR^b))=A@ z+HKBA+Fghvw3&Q~y_Lm__;I_U3vC9d7pURsAVnOBIwZ6yg$&Iu0zfjUonr zD&lLKJ>9(m&i5WqoXa*ZVrPFnSvi$`;J^V(o6ypBJi17KwT3rtGixw3;|#Ftx;}_4 zUV%Bf47jnIlhn@_T0oCs6_Ry2N% zU@JE8N+EBCabzgIA@W61zQy{YeS zaOjXyfnnJ&0N2?-b*;>dIS;NsE#ZU3blD{MKd^lq{$V0u?g^8U%gW0GTPK5ciE?0$ z+8doX^$MtfB&dVD>2psrJ^iZxBvTB04Lu~=n++Aj*H5{Uk{jJ=?XXMUy6)Oh5huLC zn>O=6(CD~P{G z_XIJ+s!cUb8P4=2#U3ve4#5_Y@$IiN4LN)i!)uYmg?D8>b5NlC*n*AR4)kV z!LA{^!9bR591@m`lC_{K&jT*{NSUg1sg9-X)8LY5P$K<@L|!ab-t>YmBTI^u9e{=! z#%GA!vKr0QP_*Eu+FJi`3jE`HeQ=l}4!;3>8erT2>Onhgk+r4LbSB@b;lrAdmOm$i z19!*_U_vNumMS33l(sQbbMzsD>&HOXC@UFtVAc{&_uG||y(!&A5Te*VK zFWvR*t<2=~e})M7D{lK6`?WC60b8N{c56;mXZjOin!r&=8?a2Kx}PHy6@+Awzu7Ghh^~3|!5cN14=Qy@{ZCdFyYY$BS!XAu;lGbn_K@ zH!oqML-H?r%3_b`b7(^0G0@5JhL*i}x!fSG1$O#kVnv2*|BHmtq?XXuTpOx;={o!Av_5Jm^T-x{`k;|VSB-&?D_H%b%3}gkoAvt`(**kgo z0`O>) zQo5{t?Jn?m#w9f9KKD-mB88xIB*VCkvPo!}g#yOEH5CA&%*n}dcya63uRo;QT-xZ^ zaQs^(o~tMNfL69F{^|F7N=izwq=*hF+E@f^ONJKk(T4d;BXYTJVh! O`}Q2#&H3HQi~j|UrRh`v literal 0 HcmV?d00001 diff --git a/dev/canonicalization/7dc75468.png b/dev/canonicalization/7dc75468.png deleted file mode 100644 index 27ff51f6202cc68f9c147f66676a47975116e62a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9828 zcmds-3s941*2iOMt1SYylu}C}b*+mQkX9<7Xi|$UZK+0!3MEK%t)j*xDuin;))rZ{ zz_u1BMM%{G3Wlf{0tpa>B9;3!;T8g<5JE^oAouG&Z{qHDreD8t)^B(8gBddO=FQ9V zoabDA=YMi`$M!I%=U;su27@_$^x@V|VX&ufz+etvEqMxDLAYS(;N{uBgokZ~S)tz_ z>q;-cV6VeI+PY;|@2IKi*F zzS*^8cc>>el)3a=O}PS|Uw!z>is}?vgjk(ya_bNCr>fK&yi+vN;LVPXj!rPxsZH() zMzBm+LdNS)!(dBREm;JEz4zRE;GG?(mx0xO_n2MoAC@^l%l#0A>f8{6j*1G-!0sJ) zUIBx>yE+Lh{*!B1HF4L%q!({#b_O! z>BFd%=)WpYOab|;>K{ZRycZkp*fC$?7Yfrepc{&W4YT%<;_(B@ZdefzVMiW-y z&{#T)rM&_-A4Z{2-6>B)o-2+?5)d038|h32MP05PO;co(+cJ=*@h~{~HnR#hT*bul zd7dS4`}beMd%|F2=^_=qN{Mqpb{3v>v3`KXb-%5a5va!XjFk2W)MlcjIL{(NT12fF z%RJmX&8k<^eJZLa`mROzQ}wOf`5cBXx@tD1NV9Zg1ql1;s~AHuW+Ry}#}S(45`vR? zXGr2~FmYxVR#tD6`_S+H8OjSA6@?0txT|XiRu(}s^r=)T7pqZdkqPBOE|;k(;OYws z0&!)C4|u5MW_c3V7(>OnMqPBQpO@g_EBY!U>zKn~QMH{&eI_2hUukLfuf3H({Rne0 z2&v3rD`&(cbxzU=cCl)`F_TeP=0Tv>&F@B{gGTxMB(Ni%EIv@qwOabiBasVj0j$wf zsZ!KTorb@_*$HDyKii_~i$IaZAwr2}%~)-Z_D;J1@!nOv zteH*zswqt|>kYjYc)hYlfa!4;|I)TqkgSfcH?(kq1)myzFzZ6SXYQe~=no?MGZ|4g z-&>X_D34W_g(zwlTr6WQUSw7G*|TRu`ddGl5&pJ6Q& z>I;$PUgT!;h4;ZZCNVHvi@vjH)s`hN*o{|0lH{AbL#V1Ss)|oF^HH0WTd7oQ&CsTB z%iwb$-{Yg}N&2$g<6ZZqcKE(?HR~BS3{p)_VF@M)xLTW+SetU)7me$a6`en zT?eH+I!8Bgo;n#xDQ=`iLN_N2(#(T2;^cxMcjte)oef-3MGk((7kRl?Co-E&cYvPH||UnGB;j+LEIRgZv zXa3+WHu4>`zU{M!>b)1 zLznR+it#2}c{JSMbP3oPGU4IlwRjUQ4?`Au2xD2+(;#4bqdkP0xrLE@-5lXIuj9+_ zPd*}*s1t3_=D9xcWbZ=E_rc!ccV0H97pxys1D?bilWv>rqtl`C{R{aRYhR&9M!Uemm<2~k^ z7Yb(XiO+Ly6{A{be2|+re##aGMWmcabVvGy^UvEdxl1SRs)xAEmVOwP7CdAd#I7JS zJd3vtxp1qTa5$1LtK3x$RiHnrPY+>>>fG4fO48iG!1u2MVhTo?W*C;4%%IWaGmAF?8p&|>+-R1DudVq>^%mq! zKgL&Z8?u$TXT0)KY)(Bi;UW=?we{a;9AWJ7SD?`cNYNcEeF~z zd(8z5^vf^5oOSh%#pOOeU1)A;>6&=yuvHJg>LpcDT$mR?f+#HUsTMA<~0aCip%`BOR!bUD>)*1yBpNJb7I&)BUFzIx+iY_Tv41y4 z*Wk`3pR;zl(hA)RnIl-NsW z@=6weFmo^RdeqLKju$8F`T^uUkB~=xL&Xn~b^h(UZ5cIw--BvXD6Tq~uv_N+{q;is z-v9|OdYF7UfinAR30paTJ^D}N2?Zq)?;n3}fi zV_GhOW12DUsjtJ+iW@wki`U$3lC#th8y#e6NOGo> z4sfI~ul;0vLR*0~XP#}A-Yb=sY+&>w{1)%&2U|UJ$kB!Rxt(6GC)6UoZ$2krqiS7tLEQ55@0h^U8w>4a}83uV$1mqreXUY)}K0Rg!TrIxVuzvjrwHi-4d;`y6^0L}K`A!ax ziocB~frbfR>xPVXUivaZjK(fLY(ukSAtcKz9rg;qA@d(p|;+VkoUCDB&D zmXY;D0qz66_36Qyc(KrG7P5Gw`i><0NVT%YD-nPR*HF$qN;exAR>QzRRQLX;S6KJ| zBQ-7b*-&p~06@J~OoRjI5?Qw!l)NF+oeu#B%K`V31E6kP8DN)Rd=MnHN5jDVhM=!N zM>X+@tYWh%w|h6JkRNkzNptH|XV}D!X+J_r>)s^6dL+`?G6EE1aK zNJ4^2QcAPvX;wW_e*t+d-&)XW7NQEulB#6ngm^!VdaE#$otgP!&DB#Yc zbRZDo4j;bi5Vs7HXZCjW_AZQl>9Q76PujnKKQM^08EzE_%>v#K7GO`Byrwk3eyc!v zF0yt)#eGvbeI>gB&61z>E~=iseBLteZ=Ihw?=Np#WD0?vdH#gKe-R=NC|MWVf0>@1 zE=8!Xb&{q6gcc3Uu6r@+4Kwla^_4b0ds!4leWi^`%-u2&JzSfz5QkXE=S2g_o?zw? z3ctKixc&hn(nxW0Kf9v7&d#P;)Bs&Mqw0$M{Cvl?(_I+3tL;DE1e_{Ht_uv*fHnEM z#~i;KGOEnV@JgMY?!Myc>MDL?edihYn_w!?nD+7@*p6)ImtP}&u?FSkSzI?gfqU8#|2(TYk znr1MLP_LhgDBZ4Bsb;}_--fR}LZ`>p8O#a@PIXEV;K8`XS+>L4h&y?5-gZDZpo)0} z9@C9exuUF)J&agEGzX}=DCCc}vC8yS_$Z7t>4Qn>+^jWCXRKvUU*4RiiAf$$N7klC zJ#eoL3kwTDf`nd^i3AMT*VhLmPD`&tMa|R?!*~vz3H0i0-~jZ0^c_&w0lb&V!`Dpa z2GvQnAvJF&3CUWw$e8Zv;kq;}@Zp%GS8T4kA{%MZ0ml$JIXl-+`VsVyXe>@0XmZEY z#&s6mwf&flTI<+it zf@-QjP6d+6iKvU9xbP^aYZ`N;%nV^LKp0XoJ`_?|Y-yQ?(d87Dy#~orYiffR`U&bB zRO``x_c$SxSNavX2Lf_LO@t+(l_H|35%(MyT|X_vAH!h;i12jVVt*@R{wIO$5ubf^ z6c0Z|Yk&kgU4q~pUmlQDBotxW5L@X$pL=FFI%HkI&LG4)Q7i%IXP(W0{bD3Q!EkM9 zIDb4HlEwvyh6&I7{M7=Qka8UmkKho9q+;U%?;y7d)XR7lFWNfJmObcO9dfuXS?zr| zR@KkK<5f#vs$cP4fdI3Sd-EjKPDF5vO#*FU{a+|F4{NL6O(*{S&;vAhDr?3(yVzjS zh7uvAvp+NR$MG7cVk0D*3;g?SsR{_-|IA4GmLySTrO`HBa43JC@9oISV*}UeG55rE zfIj4()1*jlzvV5W34A%g3HmNT-b}$7k`JEl6j|@Vkft3G1c(3iNlH);gg$6EIUF~A z5zS4WyMVDGfzhBYYuRDoMv!mW)N{Ki{7wE@Ho(B&2!Skkxd(#>ObQJMSD9}gX%ZuE zOdS>k@7-mHYXu>9J*MUs-ug^=X=y1l(WFy~YbsOKGrXacWfA|SF2hruNg#>Nc;KtY z&v;m-2$m9#w;dMMV9w~dDH#ZaUt+8VJ}1q_g%6`7Jdhq&9pP8(jnhqMd4_CE{Pul2 z_nZJ!NE^QbiHT#i%s0MOv_WBT=P$D(HI>6*$@RBR&z116!%32IsV36W(84~kB%v|W z2O4UkYv$v^wO0NrYbD-v%Lfw)IyufIg}T_7*RG&@P!lI#q?B{VSdNTOn08}Z31(>*_=ZNXjyvQup9uAnTt(>Io zKWk8g>sox(rQ0NWK691Hy5^L8zH>XsS-+na+T*dsu;vQHsVtIy9uNj^=sdJNj!3K@w1tuqG%9iV7%+VNKA;mJmXKkc5O}-gDy2bJtFvJJVjS{^4VClDzME zf6M3h{ho7s_XODe#_=~8490HP?{|KI!OSVcU~ImgKO4N_=Rhn4|I9nIJ76cqg8aQ& zTXYG7S&7-Tb9->&6;)5nO{tDx(dhOE?jYZcJA1#Mm1N?-&ie4=$BT~lUpx3>y(!1( ze3{Fgw&(HlsJR`T4^F@6%=!a9D`=myqALFqTk~-!?!pd_l;z7)BDRgLAN{lT)8h8M zqR+Vtjy&vGtu*xfHn`)3W1G%Xay&A#vGj*{jTcLq!jA8Ktb5bcs!)(-VK6@o;M4rT zGBIhZ=7ax!@-LrYFlY9DwFs>9$CYz1nE4;fu$S!|rjX?-4<9>rGnPW7a$_kgyH_DA z?XzD6_S4t$Kq2tn1^{Z)lqZb><-PwncwedNj2OpH_R%(+L_?JW)usBlS^^u^ zbavplaR(~NiU%(uB*9RAm`^89tef3+x1y8`!?X;S;ao3V53Njdaks^&(GPd9i(&Mx zkbFYr#hBje${jQ7^ht@Wwg*O+^3=*)FGl|fiRi32u@WXFJfq_AqGJ+K@x$wcAPBc< zqYQ`J;Ms}el7|jRf~myvbs5``s>Ak{?n%+7q8QU1a-0`>`DNVAGa=*mzQUz4o5|| z6qLgG-U((?i^WvpJLYbF?QW0ti-5do!}=VSAqVG`Nn9}(g9%+D8~2rs=d{rK`~1~1 zA@j(Qz8Z({{rf8o{dpy%#6k@YpY|v^%q!5j*vm8*T4nzvB$=dYIRL!rNwMy zB`b>ID)1RTrHe;Pe+S7^rNV4fGsp8}5s+})TR8r7QwzN@Kxo!-WbrM&ke0`afqTtfNT^E@@{`8J}Py+^5{;oop7Si>e z6DOY#l;LiKb5|U%IaE}AwxQ)NsDz-XQ6g;4c+5$dfsJ_--gCmY2Zt+9tt69lXr<1O zG&gW}OP@Y6UClhjSkR^8QYbOu@Q|Q*pVLGfmyzJ%*C=Iq<}bsZ+5Oeb>O{TJ+7mJf zj!K_AAql2X!aK`A+&UvC_26Y&n%{jxekjR1RQ`k^X}S3GH%Y_SMBnf;srMEi(Itv$M9Tn8dW46*(~xc?jus)@}x2spx(V4z2c3eoHy| zCLHF#D@!Fxg4Ja3MggyMh`f~wEJP-ax({9#F{g@{hHRz*=Q_%=7+7lp z3+RTHkjSLIT-Q%g!b14RJf-9?GiwV@C^HTeKJfBB%Qj!6X-OM~D~-AyCKOJbsqv!O=!9LEcQ$WyH{<)Y4jaf&LKW ztM5$r)xmF?mGC=W%5TCS93Jaccj}BdYeN8W0$Mdf@)Ygmc{omjn)Ie$Ubf*hi+OI z1zfmb;r-}>q@!R@H?kugU0uzW{0*1*HGOOGMb#_cqKMwNF67Sb+qV3 zq8cyQy;(T2=>AHS5^#PgJTmEE9LNa{{yeAz*0L-v9O9)td)l0U$1z=&WzyKV75;bb z#8NZNaONLxzI5C295?3&#nYTk9zCanAPPV`fWIvq06kwiTgy3BYZ`B1_S#_e zFZlup0w*;f)m%tesCXY)`GM(MY_{}Ny`5#$!Lk=J>eQCjbid7Y^(dff8LVm$J(x_Rycrkfu!434A^L=#P@iOxy zpJ*QM?(Vis>0P{O=-2MPr(>vf7cw#kdO1RNOqG2Q`jMU*xr;h+xV&**>UWlY{1I^H ze$hD}$(cozgGK?nxCaLc)uEx&l3=c1BO%JRx{y??ii5=W5y~qbq7Z`I#56ck9!;~K znm@oV*1Xo$zTXhtLc>F1QKc^>yp6JZ)9P_bIJEfE^$ap5+h^ur4?=br-#ti0LWgh| zM#F3=(*0GDxk|uy_%=#QEJ_DKsYNh+S#X~DC-rL&!ElN8wfkv1s&aZ{Wa9=;uff%r zH~(m*`bBVJBGj|28;8RoeWV@%_E<`YEO_AF(o7y6q9{_JD+)&ds5xq<61c6D?DYIx zsguUDAhh$_B6tM51mkpR1|eM-f#5Q+VtLt`g2Y3u0SBTwYBzfzh;x53^(~e|ViX)2 z&NE4xW1w!J5eq=)v-N+Q!^KK;VgVWj!gvn#bN)l~Nx$HdobPR+%P+!Ja}G8AO62!5 zlsY6Q>(1T*h#>DAxlw7il?sz@hRYwy#5j>k^!oXB>?_mJPy20Czs7kWa)b5AB`**z zoc=J^i(dp7$`~hEvdw+wWS~`>M7Q?ANt6^``RubFCP#E3fCTiEhLZ87z|Su5C?HA0 z!jMpgAV7tVk}ZWf9R^T=*w^fC>E_NW+c0zFq5s50b1GH>ECp;d9*)e*|4z#T@YB~> z_V&;cfZm6kAzF?U(_VY>yV`Ju z_Ez75Im~G#Uz)5;!p67ZJ$x;uaYzfan;LCt458ZEf~nNO)@z_~28#h;=`VBWecpak z-?-CXT?}w7h8>vt`V`#=;je-cwc|*(FObdvza4>6fmkx#4}QKW-3%6|l`y9zC5iyX zn*hJ*p+Jsy7m9$%DaI}t1N3<~xj!fRWVMPHVm3!%jqO0O^4Pq2!qCDr8wG0P%c;XDeBsU)Mj+ft26+5qH9(^NoVVWAm`8$5U~-EZO=INAk8fh@n| ziDSD-k@I8z)ds-u@=cpI5vN{c!-}l%lSzZu(xu}Cx?pjPWip248Gkg@ekB5B^LmGh zSc1N+a9B~qP!x?+4ir3DS3TTb9+gdG7(kE;QjL*x%|q(eG^?iQUOVx^&ZB$OD!_p# z8*Xyr+=9vM%KpVH{Z7c&td}Qr$2NL7qq^cP{?O16hoLQjxJ-)~h^>M#9bd*U;v^A4 zkgg{|_QWC73UY+nIGfQ%rm0a~tCLy`*PgfwO~^6`v<^4^BFV&G+4I&dy1pJ8xqtr( zN5|ZpoQ|5L@dTeV@U6T$0J0_`GLjAFova!HA?U4+8W9*r z_`+!wg!A?`K3bi5tLGpZ)?Nl=vOx~f#mOnfVw71P2QtRQt~4NvI(ySjSpS?nIU+PG zg)awv%u&f;u%M2Ch^|NGp`=xrHItoWY|3ys&hG-s2F3qta|W$06?*|0Qo`?0c8inC zdUnSXg5=ygAmq_8z7w?v3W1CWH`vqG;soy>Jvsmw^txc56OjPnJ_j1RTd6HsWT;>C z?ZC_$_|MGRTCP1U@7$R|!y|SFZ~$(Ri($osFS_0f-wIlpn0zh9+73V)%f|E9;utQO zEd_`XR2-k;D5-k-{ZkJ%Iys{_N-}AH2H>Q%og0yCbd8Rhi2(n@A0Qf0{*Z`tZ*B@ueo6IS+{C-FrJA{05K?)Fp@3-|;W-fP zFpTx04N^x;;~4?4;@xjQnu)N2iAh|;D;UYm4I2)Fb1oWqrSQ4OK+9Q-L@!WCsbKhd zdP4SIo^KcT?)nacvj;wg9HD$+45OGBKINhR~Dya66p;ZXCy);67UAR-!5 zNwI;5vv)HM$le^WJh~YSfyxC7>t+^2V@!OIT~&pkrB)Zh3V_atwQ8&?q^$)WBn$_g zPhH03sbBLME^9sv=;8s*(UJHr#BKH9R`*Xec%kN=rh}}-C4knl9eEZ2H1Jw4Vo4o& zMvj1W%y1<2sE0u6!LZ^fy-Nh#)f?YD2166XyXT>I#Qt1;(!fMmWL?9>)d7+6>*@9` zVf;%Go2|%$;H5-=6QPfa!?mmaP0dBcfb+2cyTMSP9YfW!pYaq#lLhe$%Gij#2OMBH z8F-0a?Qd;W#5eYzY>!Iw``u;K^ZoX}_79KCvnnrvQl`O!C~e z#2<~8h(yTa2(Tj-Jh;$#x1Cm&BM5@TJLUUW;6}2`LHf&6Ib!7Ae{{h2*D6~-_kj?U zIeP7S(Y(*uX?+`;)3}ia03(!eAbDkh;0KRfsIP*$(aH0( zsCXY$ESWj`dOL4|;5y(7{9;Hf&-6EYB>-5>onacrKSklPD`m6orxt>#RCy42gh=%_ nNU$Es4AN}={(eOk+l?ddyQB~PxBzSjv+H+zcCtS?@YP=cccqy7 literal 0 HcmV?d00001 diff --git a/dev/canonicalization/a55d1f39.png b/dev/canonicalization/a55d1f39.png deleted file mode 100644 index 77bc4be1a7ff3f93489740572ec1c8387e2fd754..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9836 zcmd6t2~bn#+Q(yEXsd|PqKF_hil~TG5y1jM3y6q-6)FM|yaKWWWK+TxP}^$QD+rXJ zphZHXEM?ybRD=phSOWw|Fvz}y2!W80QO4Y8!UQZV2bFuYI=V$AV4Po6Em9 zb;)x%@u^I&Td01jcgwYF@doWiTPQiXEuQqf1>yy z_@}VV-+=1|AANy9-27q9E^zOcw>KdWkM^DX5P>*%{~x@aZi5FaySdi|i#5jBU@&Jf z*pG1VlD+SO75?bxAP}m0{cCnkoZuZ3?*m<10jvHyA7KY$Y;|)$HnS|R!%(x5JSEB? z$Jy`5CDm$ebTl!jY0goxGLL*+l0g=3S#M>I^m;VzNo${Nbf&fE3ekJVCbzqAkx|(m z!REB~s>@EaPdrPli>_UI7L8~iYOSPGclF?|a;_LnY`LKDnkU;Q%tZg}wPAzr-mFM7 zxq71PFS21WpBE~69NbuQn%3@T$QV2$L?63y2syP``#`lEj#= zoUiEG9WtA$Fi9^^MjgA>%WJ|_`h+$OWJiD+a`dILEhkKCs(4^Q*Q2K}v&C6%{$G)& z>;-d^$QA}8xK19IUr?aZ;t!|A3?^VS4UfkoIbHVAeZD>Jb@;}~B4+UHNDHB>5-+$T z=|cH=UKg%Kq*CEr4;3w#An<#cZ+1Fl4@r+2`G$g5=a{RB}j3*Q{G(KZGh5 zDc}{>c4o1nnzA^kN)>lBhZNY?ML8w=??qLGSFW7i?pc#6> z!O+lZe=|O>CKURmCs*eoL%Jf1eCTYa(T*TM6)$JptI~krZsm+gHrM`#S%*2 z{H{)lh#Mbd8{+uMim2~US29%w8C+8US6#ijLI;yb9H>)agwvRYGR*3)A6l8;b@{{$?*%b8}OKRXxUU}AD(-pRxfU3Px3l7P58TCDd^_u4;nEsMZs zQV3Pok*@d*G9&q32AS~O-~6zS8c|)H;k6HYpc85+?YFw~!&7(@VeR1*Ov+s1F{&xa z{YILKL5&42gw`$!{WgP)3C%V{m`bgvTKu%4L*nMP4w>WzB5`NWcgtHs1q8N|NKW85 z)lrl6sx~FeI{gZr-B#x2eL_&FbB?eL?(@`5sS#IA4D{b*O1=^DKDenkxbb~4(~ol( z6hKZsBHxK}_YYm4x_|iMx?ZTB{3*_rH|$f4z{$D(Mge|?^!5|9bAh!e{ULtd2ROpVcvVJb zqLFBQyl@u?O24|t5JJRHN*lK);5dPSx$!8LCyRDs9z$!tK4gC7sK)`>=Pq^wL)|Yk z$mEP&2+f^;);#|a3WoTgs^P2$^)!nP=MXrp8qo3m?GxdH5GZZUC3%}bF{o&pbuo(? z*4sI7ozbZohvR5aO+jRiZ8^wcDT(&1=?{5-q4_RifxdOyHXHmp>xmXa1$QoTjINv0 zJhoe|4m5;NEPf^_m$Yu3RvyXQJ^5iHkvKL*CD!A8717Ehr&D<(c=PuHUc?U%hD|81 zQ(Zq!%fxb#7j5ZuI*OH}Y&RB}Qy@qVC$xP^`pc0D;V4M7kNx{^Nz6_5;9{gIMf~y3 zOq-(XcaczUeKiB|OCY;KX`%n|<6UrrCi>NBF*vWKLU?PWcs)#!?{t6lusDcj<)kwD zuixn>!8Ty@qn)1I4oh9}-O9?!^{VBbMp6SNj^JzK!^_x}fow(v(o3{3%)HTg$yhiF zx9QyJUv@{k^%Sb0Xc<;M;F~+1S*miKK7kgKIiId8bOFx;z>=H(L|+*WkeUha2^_yK zz(W@Z1lzW5MX^f9v&trN8;CRhYoU@A4uO=E_Vfw;^7#sOAK-vCbT)4L+W+7auNW;U zG_U`a22&0>{J^KFVxG~%V3eO-LX0cJO%IiLBS!09Z!yzu>Fk{E^`RCN6@?6IF^_}0 zV@z@9;pLMx7Xojpl3JYI`bxRv^yDxCSfw2Rm+ixR1(@H=Ij!OxrjqW$%kJ)OLRaaH zaVPXlVuYU1qnx|}EOz|_lOhH*7C|V$c20HYr7Jpl-rZz9dZP0+$YV$t-5O~G9eAWk zt|2$%$}X==)nkq(?olAiYs?MwnL#YNGp%{3JHJ61*%EiWP&-o&)P1-EeDI@7aIlDu z&5k61ry3#_FzxcLnixmDh6}s7j&Qau;gWB+9e^!DF!##!1f zJhKxXKmjcDeIad`Km8f}=>2`!4E#v*V}c(wkm1wgUQ{smnMe|P^09I{0kiz^><|&v z13zx#QT+PO7Tw^>moFQMzaT?`+c_pZIbcjd%&VITNq(@%W=9oz4V;3*>~p_CWxMXS zHlMfAA>3zn71!^61YK`FIt=JfPfDkK%zQCcBM!vxpLT`6r&hzox0O^X$Rk~da{q-W z%htTFE{y~@v?t4P`h(xYULb0Hyldr&{U3vXnpo z)Ry+x-lmmw6?9Kjzzm81`NqLWM|#RUKB7F^>uH%9_P}|&KK#A8R?|h!+A49qJS4$Z zig{E}#79)+wrNnv9flXZlbn>cbn;P?Vcg%i8|dh+JLNeo8INl~HE2_FkuW}r_S)x@ zrR=^`PvBD0Zi!==|8Q74L4EC$(>&c@D*Luexah1nSU@y10TO4?Vb-n%QmY+o4$%6@ zq*2mX67zmx$HT%;kiTQ>VXeet1#Xnua?5j1(A97z(jV~gXUln!HSFD0-Ybh4mP*wm zs1cq-t>zn=?pTz&%Rcx0s4Gv)bg{03jbN)X#x`LDGUS5A*#ok>4)B&ylbKbM`F-;C zS43IjOY1OBl%9(XS@nlgjJBPZyJ7cm#W;man@fUt$NG5QF6`4Hr#+B|^_H|*il#x? z4}Ra+2xL{7?V^60S}J6X9i*BMf(mmMvm-_GexZ8KcLnza>L2WRAN%@MgM4?X%vZ?T zMj;TMWtF5sbJvGL=ub-l{h#%JBM!E4I3`QLUxEaQiIXud^DKfmLhta zK$#dB;Zf@r=ZYxua&kfZ(R9e@Q4LvWFviI&34MQHe_Si))Dn1o>|k8qjZXRb!=1K) zlWk_Y@<<%Re;8{gpr>g?!0qy>yq2$9Z}DN&+*F^S|7$5xk0BcvH3Bw87lnR%FB)LS zjbH7bu|_p&Z;=Pn%ITprvJ>O;Dn-0FybV1oV2VZNDSQk4^4F3cyfI5kX}i)A?DL)vc4O$vZAP{=p(1;L#b5_wLqoF%~kTylvgy2RQBv_IHzxnQFQ{UEK5%7)HEv1woZ-+Nxk-PwaQ-`IUj+&ZJ?RFD> z9Uf}e{T37Sg7LKI4U&>VPIQR&K!jRWF)J((Jpbv}&r?%V_mlmPEb$;VB05^!FQH2y zn1%4$fZG@dB2OL(Z6AD+d=M}ceGsiH;sH7yCHM(?n86JyMGyRk5(DQZta7dxq_&K( z*&)ExOY&R?-|a@#neT;Y4nznrEhoG4hBNY-!U){)&XBphlt{vE!>C?h@R?}BLlo!2 zoSdAy3c;EX_!YXek+z8h+)g`i2z)~EWMNNoNL37sB_`aTC98_c2UUs~0ppZl=NDnp zU!yRx^ZCI6DyjNDglx+Jjk%H-7R`r@ z8rucr+y&?DN=?>T`ozY@Lgbq;q8)r#2SU_x5jR^54k74BbUAPu6#_;cE25*|Ao}Vr z%!;6DSM?GUuSTM*Y)=dTMi@F^rvbP}K))`T+$R`=V-MwD66-s9Vts$ATr!fFbr^}w zDGOU%jP>f`M}ft^^15;U3BZd(y%P?!R>=2UZpO}UD6AM zLvE9Weg-6qe|LDFMgR0>&g`Ir2{fTv>OpbOASRCEwMIdNY^=rc9$XqKR=sVd(Y7KD zqvZTUwZ=QMqyH8!=5H5vRl3|)9%p*SOaV2*ynG9?0x^2_HrDuW29{MH6Vi0FMrXRk znDmZcWa}$1UBy&4@!(3SPXx;xVcrF;6Q3NjsNJH-e{J(1@cycasx%|^INLc7^ zkO#$9T^%|(fqE3qt)BQfz-jDL4>Wc^iYw3r`UmT}54#U_-cBD#raTgVs4e+Y4u(<- znJfDrC9WhP+iU?wLfNX6#kURM4`3P@Va-|@bTg@{&D+7i)GHH0Xx9J;s?Gs5@HjD_ z%!z^qF`(DvXNH2=s)h1Q@?~g-TA|}_gIwJLdEkJrq(jY1s9#--7tN;YLiQfg>!o4> zCW!MwMLYDJ2j+wGOHc$Xu9W^%Fkf}18<{3ToT@3Ug`3i@HiYcADwlD`dqGNjAwo8N zk#(sIL|;OEQav#A-s!yzCR9P2EwHofuY>s&cL=YL4wIlTm ztIk+#IE1L>H4g!?8rHaMGG9>~@i)D5v^+*w-mx)8OY+LH|Fl%1R+bs{4yeo(ue$vu WlJI54?bRUp5k>~4`dMFGzWr}plU>gM diff --git a/dev/canonicalization/b75b9e76.png b/dev/canonicalization/b75b9e76.png deleted file mode 100644 index c6dc882311cbcca3df97d4d5c680ec8e09a2916c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9772 zcmeI24_MOozQ?&|Yt@?Cxt%jl!$0fpHdj`5PbBA4U!eB37fx%unHs?3s2+{|~20vc; zG$!f;m>c^0ov`8z4E82$(+BTw%VZi9)I4Qck#Wp;gZwgIDq|#`J!zf$yOdzB&AP43 z^=0!G)o#AXVwb;`ds_2oeO)oj?Q`K>TOxqmkFD`Sl4o*Ai69l4xN1B zjib>%dsbim_{1rnCv8mB`OLg%b~koXQQWDw#Rvgm5uxL z8fJl?!`|=Dfx+fS&j+hM_Rq(_k?&t#1cSZz&I@+9O58sWEROsk4yW3}T(f3P`tK^z zjt6-b9I@zS7_7c#N4n;>u{+Fl^vI>fiB?PSb`~|ABU<(ZPC-1e|i)WD2T6Cb(+*KYE6&2;ywQr1y zDqN0{CFqStx1|E5=9$>VFQ~xJ0SDX9XQEZ&9OghMNT~W!lzMo zZaHSn;h}r{B*&dQcXXFtg2DX4y^#knbt96um<>aF-SPx@#z)gm4T^p{7&~Trl3z;h z+Jv&*^ofnM_MoPR(R4?5cWk)f#*vpQSlPNsv3vT&f}j9(BjeFrsK%orjai-Hwq#SU z*k!#be#21#J^rH`M`ZF=lxwW(jpU>AVX*Ja%85o^M=^rKO>gzjNLGoa^WD?MD(BEp zM=^##%I+>6>MX?xH_Ffp6_fX$lw=1xFoUDi^r_x#|j?Y4m zb+uoz+6q3QhN4{RBYd@#=jh64tO#ij^mg+2YBrZ~$yq~o!2_mg3KNTlclV-7wji41 zUroCAYMou}<2{=?i>C8Ks){?+I|S(li?*9S)vv-c{VYLY!Xi@5i=oABEHqZamEA!ti_T)#uv}rV1nDVsIwN}X%mwOyRjJ;^OPCo= zPy9=5w}QM~pFQA-rwt&(){fUPHqD$>wY~au8`FnwYr#1m`vy`i50-p#$&X#cxXUSl z)Z)^nGjDG$Uc=^29QAG5-F9|KiL(bvk~hyn2|Z^qR5k17t^=j;@sADau-$kbnnjOJqe{1b=2!!uNb@=BftMRdyi^cn=MNqbVzqnhM z>yvk{298Z3+gU`;N}9BN(h`ngTTB$kQ_6I`pKj2TpIw8z5#=sK6Swhm<3N|4&8~zi zx)Ds>nLs5eOgOYWA1EJ_UkAHiG?{u@o0ZS2$AAS{Ua*VMrFe zmUnMi2})N&Js@Rteo`q~hG47W5ls%_&g`9Wr8$P)o<}E})$Ej_x@xlP{z!8RM^xNV z9pUs3C%7joE%h9v-4kXsE8;paH1gJh|C%7r$(tAFuvBH36;|c0t$syx5X0mBL9CuO z>vKE%g%^mKgp{d~+vVmMue^IB6R)<`vXIONgA~5-H;WtZJ=~7S$-HQa8_*AVy-o}6 zt2?||VTxJIi`&GSm?XM|>2 zfdwV?U0LpAC#rca;dEO-D-8YL7wFHp+mFimXPgZ_`@1ri{wRE-+pf|NJ*%%)$?9@* zub~8k$oc&4RnYoDWG4$r>{D?P z)m0i!VLA{=t%hoDV!?2lK$hR}~kSHqE6<4^f&%lyCB8~>l>$8*l60?Ae=zdsz1_4FH@YrIgQ z{M7l%#(n9O<9mCC$0N(lp2jniJmf7_-(+o)k!U7MyEEDkVD^nHEtyG~NNP)ETy|*W z^y=06nonNGlJ_Z`d*g689KmoT=CtMJLoK{CnH}l%Y1=RCL{M7*HFk7>I;nsoh!OXE zaX{%gG;6i~+;5@Tq{MvVC7%J>l!0M?tXA)VhAPv$V{P%G@e5zA2)i|p2FQh|;9DP+ zq9ev`btQS`6%8{(nWZVoP%grzYRd})oGlkNd?f)2-<9P2cp=c%y|-?LrXzRFIyG2R^+w3C@xIA%^HrWsvymgR{3b0 z3i{NP{#uHsF>uE@l}osYtE{+eo4yK71H{uORaG4DsTlt(VNCszM~)e$dwAqwFzA?Y z?g0&wM=Uz`I`qO4$#)jw2Pj6NLiyNjUY`UG{gmu}h7>%f)c=-;f%W3* zZH-;_^5~HE4HS*ciy<)``>Uw?;sgZhO{})foLlzIgw z{E?2vhRGbvwm4xZf z9{1hME=F^HRpFR|uk#CBiDR9WE_AfaSNgW4iLZ%$w zRURK}4Htk}q01hb0#XSCB`*OCgIeeERp|wi5H6Sn`055pSdw}JUe>W z<8w4lO?fqjfd1m!@n2KkJPT9?<;ZE>f9^nRE{GHW-R*(iimeXG=sThz&312Nti!D#V$x(|JGid?|y4>nme z9xLKSvm1ZHYBLLj1|)J1Ju$Uq80DrYoFE<$sCiln2P@i!4#BZ4^_6i#=R}*jSZ1vD zQvv$sz_HYEDXw93uA*L8C`K*b>h)=5;h%!E;j6>bYb)Vcwu7K^DvI^F#>;R;0wD!V5OVa&t)Y}| z2laS2rhlt_HCIR^6WF%gE1#1TBeIjKzMc4zdeeoe&MnIV+RvIE!P6~efo#kj+(H0$!_0-N_U)n=07jI$EERx>ZsVvO zNrj0Mw-%tU%4D^PQ^0)_6Bj~UcYjN8d@XYoK9*pRVMs!NLavcAo+7;;fLvdK!1nkn zfLLPwt!wVr70xFc?VmDF_--v|&7Is*j>Hvt;slI9qcukzbj;z;pNg z6(#9%ofI?_2%mucV{di4fS+WpYYour^;1B^%{BPQ>TEC1>9dTqNkM1imx_T`$CdsUqYE2tyC%5y+6C?eu(_9G8f(ZiIlHzO zOEIt_DG7wa#Pq)F8rD=i?yw@Q7v$Q0HrJ}}Re?byt=$s{Z%8yD==JjU#-`q!6=?q< zils{mVx~gtcx5*92SHLgftN1&JW%{?05BicUy3bpKm$=KHfy2}uL3xETc5cOl*`x8 zX|X@!Ffj69bjCB)29o1(Tbga#OLHK=fkRYdyJQ9SEtsdPLW)7p*cXp8m*X0wh+~EV z#;P!nI6cW|UtZ9gLr4Lx#PRMJhA-}1@x*8~TzQgYJrjhkg~$4g{hD+e;yqh<-U?N> z;rDk)yFc3p+;e0RaO^&DNaBJcnczR)KW-laEi^`B-d07LQ*InNT|$7OG($c@a&}$X zCyjs$fww};3>Gc(q$^d z(Hf6mr|fQzuSWW@qOD0Fg(fVkRVRJ$QDf?w{%{`AmZ}(*B|J+F&&(i`^Oy8TYYInk zz@1xKg4`M=gbZP#%_QOXvAO9UQ|o`z-~3xnkk7gIe+-sg_Giq;TK`TY*p#}o(^YA; zj7!bcKKRRrY)y*brLDXTl$h4uH$X9wY1)Fr&rH3qCM3&Q4};djV6&vqcLA8lB#hc5 zOX%N@$W9Ci@tOTgU*kVu%iFWFVpXL{Zy<=(#VAjK9XN+N<{1~Vmd3iYz@7+|7A9%c z$sS{Zkg~gi(^qlTvj-DC!2!E(3B`yVp-qnZWc@t653n^th1}(Wi~ShkrKu|nW)E)@crhu0P{y{k&qrL%pd1*ufW!yc6#`k!Y zI+$_-O}*iaJ{Mi$@PQh+``}|b2Ts#n)bw~&Frcr3q)}!A$1N6Y7ZTVCx_de*6c0Fs z%{|!K18olWHQ;$NV1u1gtJQDq8v4-2T>$#d^S&WcPcr~N>%CrJsqIfqy~3S<;8;-X zx#+!g@E@QC|NoIMkdrrK$^0b^!%udzUir7d8B<_p@8Vb05FK>= Yw%reZ<0p6*6bfw9hS(2k*X=&~@0UQO2mk;8 diff --git a/dev/canonicalization/d717ca69.png b/dev/canonicalization/d717ca69.png new file mode 100644 index 0000000000000000000000000000000000000000..43efe75dacb4146eed4077d0288c711b5e86e4bf GIT binary patch literal 9396 zcmdU#2~<R$C2&!PZ(GJ&c0EmOX&MmR?!81ROD6??D0oR(RT29)`)F-y8-h z6$aY|vpRghG2#xtCm_+yyS$;#r)~Ithoi&2RS}y;*BBmrvGT6f+Ba8L96DqwT59ys zS8=WX*!J+`xv0EPH>_NN2)lOp9x7)kWydG9jhBud@+5kCdhQ7RGUiSD(H)vrPTQ7! z{%Gw>ajSB24N4+->Hb3O!6sepEa$mnsEl|I=StFU1A`M_SU-n4wygpGTR%Rq5(e8~ zy#WmQ%El|;$lYb1!C?EpTx5p}sl&^`;G*ug4Ljc11LhEn-roJ$G8k;-;5sngAHADK z;*-xmo9mL6H113ajo$zsG+`U``Hqzz!C(hh9fZNYKYr=|>0!LB{(hl!bVQ4(MibQS zpjptI!+q)frP5ay(Yd?yoP)_5R%us{r+L`)v@x4`4>NtLidpU=6`IJ$@(6|D%xk*M zo?hMRH@;}X48_y8w^22{T@5=sri4k_<)li^kG+u7Upn3zK{=tKN`B(xwyL26jit_q zSwDHoiA1HxP>~TlXm|E89-&ua!z(e`ia55PN+EyIqYIQ1b|# zJ2IlB;TyG_Lqr(%POp}@OrdR!>l4tpid}`cA?4K}(X2x*d?RE2Sz={|BcbRhLA<+BQ&XcurH8a+nGp%QTTF$i+4BQkW`YK!bgBY7Y7JkbsyE-! zV7|vn@?IwwEIKnmayb2MGGe@Amghuv##Z($m=|^Ni`^L&gx73#c!Ngxm?U6J>H#Rb zrkl%oS-4k6RMSvdF>}MNK@4nlN;&^=SJ*_aoAoJ1)XdYTUq~B|L;BL{P}URHWzewI z!CKttQY9EGX{j0{x0ua#H|^z~wliFAw`B{e)$i+W>bhFP zv!&Cd^si2R(}`ILiNXs1jt6J!6Soiv4E8rxlm2)`ckHbql&Fzl_^^SwpUh zOU(s0QclM%%n%7ZmEly6>MFuFd-jN)E87!Lf#9mQDaa}%#CtO+GvmF^og098XlQCm z)0J68r-VHdG2!fDx3cb#7bNqU0)70j4UynrXEK;AJKOigCyHzM9GcSmk(yZw<@JZ%U(Z=TZ5b}Z@~+1bGv7M zxtHz{BL;_3qQ?%%6+PaorvmFV6g@-sSg2Va^B{bpx3k2Doe}wCbpFRc>r=mN$}sY2 zzJqGSaV5}4vjW#Of3BC@Lq~A|t`CY>`AzDxAk(Ak?x1rIUWl*1?S2+HXQ{Ny&ITko zP^a0KWx_~*3d=l&PZuaBKP=8@h?p2{4hoVL;o*KktPcJc~0-a^$%XOAG;;EubjY_;89#~-HCrO^6 zSupXMT?I6@UtJwXyt+`Q4^1Iwy2SB<{U%MHRl~yqYc zE6OaF&fMkyG9v~ZEZ_^dOKBF^_;xppZw*>J802PYUROB&ZF{taVu)$t7 zIq6ct&l-PTD4@J`z2htFB9xOPCfU+|e48 zD;|#F8R1Zq`X2u;i7&wk{{BTbG`c^#uc+*=fzn7UmHd(lBOoAGQSEZZ9ETGLb%-*+ z0QiPEbgr?ZivEKHeSQT;oaK=2bw>@26WqP0ogFPm&?yG@ykjDaN6z;Zohnf~RV&Y* ztf*mPdNWcs@8W@{5klB*;h7g+TiFIEXwJvev;QA9dSVc1SL;(WKW3b&d&ip(>0x1E zp&30{gKC8E70@QF(|cYW%1O;m25uJ1b}O4`(UMNaQ>&$OOOY{R!C>l~spsUO>cs^YP=?Qfxme-RlJ`BizUIgvegr_i}z zUSMIEC*_q2mq7iiN=k4f)2myKi&#|*iRFG~ax*{r`iiJu{+GJ>ZzReYBL<94`K>zd zIA4)>wW8&%Ad1?cSk>|#HbJM_M1{*A_2YZ0P?;>v?Z+O2I+1+gdEO1R>xM0hXFk}S zJ9lREUc9<6OKgL(Oi{13K=oE3Ihod1T&JbBVUI#=iURq6XHeN{b?vRg7p&njgFVq#LZ!S%H&Bh6t}P<|RipqEy{6H1No+MHa^G=`W6yUg zDFz36+MH$!eMzjUYn+09gFtc=C9wAiz^p-?p>{PU8dP&epVr2f?Qa&(TAIsn|9(i` zWijQV;OJI#ucD#D4%-rqXgP@iczAt>X$n?>i;BEtuyQzPoYfceV@HiGa(w5G}f$zd9 zk&@1q7|^7@%rcW?YY9Qc3a(2~(PvD*1|EoTh8l|(+?;Z;fE)}Sa0bfzuBuzZA&@a* zpDy7xoDQyoPDa7KYp<>arc3vL?smD|;TI7R0ZNw~NFaj1zi^qToT!S|jLIj3Ox3CC zyH#93?Ug$WW<~*=QV6sFED;GW^sDCwfn6Z9iJfc9u9}R~C!l&|(phedgrCazL5@;1 zWqZ@$bLRlK0DGp`ty0t^iy2IFF$c9X(~j4Ro4~UxdyRfIQ=+B9Y@}qY#0JilipsQN z=ciDO;Axcw_MqkF&%GnpqaGXr75$zP_v#+pNC7Fs{o-o5ZjQ*47_DOOaxK9nE;aV( z=C#EI#sQ!wRUy$F5Zsy(cM;#To|UmT$h}RcRWH+yL=b3s)mj?!V)fMF#I2FX7NoP) z*~nNam{;_(RoedCs)gw`dv0a;#4p;}^T7V_14fUf@%))5hameYaeefgrIHx(^YNZa zdj!7}0E1n&`2vC~whQum@WICM;UbqrBLJLXwL(C&)|*Z~tzD0t=OJa~gpjvMd$WMG zh7}=JLg4V`{QTSan)#B;A3sAiz9!me#k}uBS(DntFMZ4%&X!!>359E2Lyb1~qcLD0 zHD$;os&4@`rn`l8CTk#)_Z3>op4dY+$kt?#Pa5JM({x;{^vP$E@yZGC z&EmP4QS$wvn#sH00G4ff0uILlBu+yWSIv!p=w=a&6#3UQ0D#UmJL37{5X~H;Q|3RgopHUcGA2ilq}C`7sM2QxRlI50>4OjjSew zj8e+RaZm5d%_y^(p|wxfEd@y9pci_vtyu8}-Y;nTP{lEHmq%OXD^i*9>U|HL6 zH-5Hfw@-8Qi=}qRg=tK2c^*OVa(7FSJ0l8}F3)L3Xzkj)i76@RsNyI62@o6u#}PoZ zo$1tbRAYUTx>nS?yT7+4r2K|f{w zor2kF8U7!lsq4egVjRFv;JEfNg4D~A16zFVOm%pr*b4T^p-M5S|H+;Sgbin`hqW~F zjVZvy2u35EOug*bpB3OLM%=|)=~rIF;Fx60t2Y_w+{d~noiUDX{ODX?K8?dEqq4FL zZbkj)_3p2V=6^So!1|NP7qcJVz}a!?0+Y!}^$32*%9>xcDri&J=C8;`exT^mES$Ov zX=usoKt2sEOze?F(N27=QVuQ3MX?p7K)T-Z!Jxu5`S>>@lZjSIdD#C`5Cv4&<~2o`uC!AK zZs^8hW||X8SM9U|rai31D|BPb#sfBTsr;j;G?Eg5Se*h7A?%9sQ2LEsw+);BCK7~l z4u<{Elmc!rWIU77gag`lidmpRq6yIy430teRIDGSnxpl1qr!JHD`k0$CpL~y9URv1 z?QpO+V@|I==KY()M6)n)qaW$9`MeJuz+3(}f_F2a4NA3O4qgP@q$PfleQ~Pe)iNon(S&y=RMhFS_sI``u>1E<8}^M8(4M&QR$%ymZKTP`^DTQ! z{1s$U1kerUp#qVB1FQOoK;xFe3L0fmFi~;a2M>9JPyWh2Iakh34kh0)2L zcW~2(eK$YghNYN^PPVxc`l*mIJpbnr#y1}S;GllUc212-!<1*EJ(qeA)C%7+|C zxbD=Qu!1H+5B?aTsqQ#C;6j)*-8p}}OKu2wNajd>NuGZ1F6<)`+$zJsZm(F#OGoAH zKel-0nBV;T`QbJMNR8=(q&7Hlj6)k;$$JT5-8aiU8~-M)|GVDgP*?{5`Epc&y4HQ? suo=OtxlQ$;EFFTQjsl^k7y;><$+nJag&40A!yuB>(^b literal 0 HcmV?d00001 diff --git a/dev/canonicalization/index.html b/dev/canonicalization/index.html index ad3470a55..7947e26a8 100644 --- a/dev/canonicalization/index.html +++ b/dev/canonicalization/index.html @@ -2,13 +2,13 @@ Canonicalization · QuantumClifford.jl
GitHub

Canonicalization operations

Different types of canonicalization operations are implemented. All of them are types of Gaussian elimination.

canonicalize!

First do elimination on all X components and only then perform elimination on the Z components. Based on (Garcia et al., 2012). It is used in logdot for inner products of stabilizer states.

The final tableaux, if square should look like the following

If the tableaux is shorter than a square, the diagonals might not reach all the way to the right.

using QuantumClifford, CairoMakie
 f=Figure()
 stabilizerplot_axis(f[1,1], canonicalize!(random_stabilizer(20,30)))
-f
Example block output

canonicalize_rref!

Cycle between elimination on X and Z for each qubit. Particularly useful for tracing out qubits. Based on (Audenaert and Plenio, 2005). For convenience reasons, the canonicalization starts from the bottom row, and you can specify as a second argument which columns to be canonicalized (useful for tracing out arbitrary qubits, e.g., in traceout!).

The tableau canonicalization is done in recursive steps, each one of which results in something akin to one of these three options 

using QuantumClifford, CairoMakie
+f
Example block output

canonicalize_rref!

Cycle between elimination on X and Z for each qubit. Particularly useful for tracing out qubits. Based on (Audenaert and Plenio, 2005). For convenience reasons, the canonicalization starts from the bottom row, and you can specify as a second argument which columns to be canonicalized (useful for tracing out arbitrary qubits, e.g., in traceout!).

The tableau canonicalization is done in recursive steps, each one of which results in something akin to one of these three options 

using QuantumClifford, CairoMakie
 f=Figure()
 stabilizerplot_axis(f[1,1], canonicalize_rref!(random_stabilizer(20,30),1:30)[1])
-f
Example block output

canonicalize_gott!

First do elimination on all X components and only then perform elimination on the Z components, but without touching the qubits that were eliminated during the X pass. Unlike other canonicalization operations, qubit columns are reordered, providing for a straight diagonal in each block. Particularly useful as certain blocks of the new created matrix are related to logical operations of the corresponding code, e.g. computing the logical X and Z operators of a MixedDestabilizer. Based on (Gottesman, 1997).

A canonicalized tableau would look like the following (the right-most block does not exist for square tableaux). 

using QuantumClifford, CairoMakie
+f
Example block output

canonicalize_gott!

First do elimination on all X components and only then perform elimination on the Z components, but without touching the qubits that were eliminated during the X pass. Unlike other canonicalization operations, qubit columns are reordered, providing for a straight diagonal in each block. Particularly useful as certain blocks of the new created matrix are related to logical operations of the corresponding code, e.g. computing the logical X and Z operators of a MixedDestabilizer. Based on (Gottesman, 1997).

A canonicalized tableau would look like the following (the right-most block does not exist for square tableaux). 

using QuantumClifford, CairoMakie
 f=Figure()
 stabilizerplot_axis(f[1,1], canonicalize_gott!(random_stabilizer(30))[1])
-f
Example block output

canonicalize_clip!

Convert to the "clipped" gauge of a stabilizer state resulting in a "river" of non-identity operators around the diagonal.

using QuantumClifford, CairoMakie
+f
Example block output

canonicalize_clip!

Convert to the "clipped" gauge of a stabilizer state resulting in a "river" of non-identity operators around the diagonal.

using QuantumClifford, CairoMakie
 f=Figure()
 stabilizerplot_axis(f[1,1], canonicalize_clip!(random_stabilizer(30)))
-f
Example block output

The properties of the clipped gauge are:

  1. Each qubit is the left/right "endpoint" of exactly two stabilizer rows.
  2. For the same qubit the two endpoints are always different Pauli operators.

This canonicalization is used to derive the bigram a stabilizer state, which is also related to entanglement entropy in the state.

Introduced in (Nahum et al., 2017), with a more detailed explanation of the algorithm in Appendix A of (Li et al., 2019).

+fExample block output

The properties of the clipped gauge are:

  1. Each qubit is the left/right "endpoint" of exactly two stabilizer rows.
  2. For the same qubit the two endpoints are always different Pauli operators.

This canonicalization is used to derive the bigram a stabilizer state, which is also related to entanglement entropy in the state.

Introduced in (Nahum et al., 2017), with a more detailed explanation of the algorithm in Appendix A of (Li et al., 2019).

diff --git a/dev/commonstates/index.html b/dev/commonstates/index.html index 637bf987c..60d6383e8 100644 --- a/dev/commonstates/index.html +++ b/dev/commonstates/index.html @@ -72,4 +72,4 @@ + XXXX + ZZ__ + _ZZ_ -+ __ZZ ++ __ZZ diff --git a/dev/datastructures/index.html b/dev/datastructures/index.html index 0c1c30ba9..17aafdbaa 100644 --- a/dev/datastructures/index.html +++ b/dev/datastructures/index.html @@ -1,2 +1,2 @@ -Datastructure Choice · QuantumClifford.jl
GitHub

Data Structures Options

Choosing Appropriate Tableau Data Structure

There are four different data structures used to represent stabilizer states. If you will never need projective measurements you probably would want to use Stabilizer. If you require projective measurements, but only on pure states, Destabilizer should be the appropriate data structure. If mixed stabilizer states are involved, MixedStabilizer would be necessary.

Stabilizer is simply a list of Pauli operators in a tableau form. As a data structure it does not enforce the requirements for a pure stabilizer state (the rows of the tableau do not necessarily commute, nor are they forced to be Hermitian; the tableau might be underdetermined, redundant, or contradictory). It is up to the user to ensure that the initial values in the tableau are meaningful and consistent.

canonicalize!, project!, and generate! can accept an under determined (mixed state) Stabilizer instance and operate correctly. canonicalize! can also accept a redundant Stabilizer (i.e. not all rows are independent), leaving as many identity rows at the bottom of the canonicalized tableau as the number of redundant stabilizers in the initial tableau.

canonicalize! takes $\mathcal{O}(n^3)$ steps. generate! expects a canonicalized input and then takes $\mathcal{O}(n^2)$ steps. project! takes $\mathcal{O}(n^3)$ for projecting on commuting operators due to the need to call canonicalize! and generate!. If the projections is on an anticommuting operator (or if keep_result=false) then it takes $\mathcal{O}(n^2)$ steps.

MixedStabilizer provides explicit tracking of the rank of the mixed state and works properly when the projection is on a commuting operator not in the stabilizer (see table below for details). Otherwise it has the same performance as Stabilizer.

The canonicalization can be made unnecessary if we track the destabilizer generators. There are two data structures capable of that.

Destabilizer stores both the destabilizer and stabilizer states. project! called on it never requires a stabilizer canonicalization, hence it runs in $\mathcal{O}(n^2)$. However, project! will raise an exception if you try to project on a commuting state that is not in the stabilizer as that would be an expensive $\mathcal{O}(n^3)$ operation.

MixedDestabilizer tracks both the destabilizer operators and the logical operators in addition to the stabilizer generators. It does not require canonicalization for measurements and its project! operations always takes $\mathcal{O}(n^2)$.

For the operation _, anticom_index, result = project!(...) we have the following behavior:

projectionStabilizerMixedStabilizerDestabilizerMixedDestabilizer
on anticommuting operator anticom_index>0 result===nothingcorrect result in $\mathcal{O}(n^2)$ stepssame as Stabilizersame as Stabilizersame as Stabilizer
on commuting operator in the stabilizer anticom_index==0 result!==nothing$\mathcal{O}(n^3)$; or $\mathcal{O}(n^2)$ if keep_result=false$\mathcal{O}(n^3)$$\mathcal{O}(n^2)$ if the state is pure, throws exception otherwise$\mathcal{O}(n^2)$
on commuting operator out of the stabilizer[1] anticom_index==rank result===nothing$\mathcal{O}(n^3)$, but the user needs to manually include the new operator to the stabilizer; or $\mathcal{O}(n^2)$ if keep_result=false but then result indistinguishable from cell above and anticom_index==0$\mathcal{O}(n^3)$ and rank goes up by onenot applicable if the state is pure, throws exception otherwise$\mathcal{O}(n^2)$ and rank goes up by one

Notice the results when the projection operator commutes with the state but is not generated by the stabilizers of the state (the last row of the table). In that case we have _, anticom_index, result = project!(...) where both anticom_index==rank and result===nothing, with rank being the new rank after projection, one more than the number of rows in the tableau before the measurement.

Bit Packing in Integers and Array Order

We do not use boolean arrays to store information about the qubits as this would be wasteful (7 out of 8 bits in the boolean would be unused). Instead, we use all 8 qubits in a byte and perform bitwise logical operations as necessary. Implementation details of the object in RAM can matter for performance. The library permits any of the standard UInt types to be used for packing the bits, and larger UInt types (like UInt64) are usually faster as they permit working on 64 qubits at a time (instead of 1 if we used a boolean, or 8 if we used a byte).

Moreover, how a tableau is stored in memory can affect performance, as a row-major storage usually permits more efficient use of the CPU cache (for the particular algorithms we use).

Both of these parameters are benchmarked (testing the application of a Pauli operator, which is an $\mathcal{O}(n^2)$ operation; and testing the canonicalization of a Stabilizer, which is an $\mathcal{O}(n^3)$ operation). Row-major UInt64 is the best performing and it is used by default in this library.

  • 1This can occur only if the state being projected is mixed. Both Stabilizer and Destabilizer can be used for mixed states by simply providing fewer stabilizer generators than qubits at initialization. This can be useful for low-level code that tries to avoid the extra memory cost of using MixedStabilizer and MixedDestabilizer but should be avoided otherwise. project! works correctly or raises an explicit warning on all 4 data structures.
+Datastructure Choice · QuantumClifford.jl
GitHub

Data Structures Options

Choosing Appropriate Tableau Data Structure

There are four different data structures used to represent stabilizer states. If you will never need projective measurements you probably would want to use Stabilizer. If you require projective measurements, but only on pure states, Destabilizer should be the appropriate data structure. If mixed stabilizer states are involved, MixedStabilizer would be necessary.

Stabilizer is simply a list of Pauli operators in a tableau form. As a data structure it does not enforce the requirements for a pure stabilizer state (the rows of the tableau do not necessarily commute, nor are they forced to be Hermitian; the tableau might be underdetermined, redundant, or contradictory). It is up to the user to ensure that the initial values in the tableau are meaningful and consistent.

canonicalize!, project!, and generate! can accept an under determined (mixed state) Stabilizer instance and operate correctly. canonicalize! can also accept a redundant Stabilizer (i.e. not all rows are independent), leaving as many identity rows at the bottom of the canonicalized tableau as the number of redundant stabilizers in the initial tableau.

canonicalize! takes $\mathcal{O}(n^3)$ steps. generate! expects a canonicalized input and then takes $\mathcal{O}(n^2)$ steps. project! takes $\mathcal{O}(n^3)$ for projecting on commuting operators due to the need to call canonicalize! and generate!. If the projections is on an anticommuting operator (or if keep_result=false) then it takes $\mathcal{O}(n^2)$ steps.

MixedStabilizer provides explicit tracking of the rank of the mixed state and works properly when the projection is on a commuting operator not in the stabilizer (see table below for details). Otherwise it has the same performance as Stabilizer.

The canonicalization can be made unnecessary if we track the destabilizer generators. There are two data structures capable of that.

Destabilizer stores both the destabilizer and stabilizer states. project! called on it never requires a stabilizer canonicalization, hence it runs in $\mathcal{O}(n^2)$. However, project! will raise an exception if you try to project on a commuting state that is not in the stabilizer as that would be an expensive $\mathcal{O}(n^3)$ operation.

MixedDestabilizer tracks both the destabilizer operators and the logical operators in addition to the stabilizer generators. It does not require canonicalization for measurements and its project! operations always takes $\mathcal{O}(n^2)$.

For the operation _, anticom_index, result = project!(...) we have the following behavior:

projectionStabilizerMixedStabilizerDestabilizerMixedDestabilizer
on anticommuting operator anticom_index>0 result===nothingcorrect result in $\mathcal{O}(n^2)$ stepssame as Stabilizersame as Stabilizersame as Stabilizer
on commuting operator in the stabilizer anticom_index==0 result!==nothing$\mathcal{O}(n^3)$; or $\mathcal{O}(n^2)$ if keep_result=false$\mathcal{O}(n^3)$$\mathcal{O}(n^2)$ if the state is pure, throws exception otherwise$\mathcal{O}(n^2)$
on commuting operator out of the stabilizer[1] anticom_index==rank result===nothing$\mathcal{O}(n^3)$, but the user needs to manually include the new operator to the stabilizer; or $\mathcal{O}(n^2)$ if keep_result=false but then result indistinguishable from cell above and anticom_index==0$\mathcal{O}(n^3)$ and rank goes up by onenot applicable if the state is pure, throws exception otherwise$\mathcal{O}(n^2)$ and rank goes up by one

Notice the results when the projection operator commutes with the state but is not generated by the stabilizers of the state (the last row of the table). In that case we have _, anticom_index, result = project!(...) where both anticom_index==rank and result===nothing, with rank being the new rank after projection, one more than the number of rows in the tableau before the measurement.

Bit Packing in Integers and Array Order

We do not use boolean arrays to store information about the qubits as this would be wasteful (7 out of 8 bits in the boolean would be unused). Instead, we use all 8 qubits in a byte and perform bitwise logical operations as necessary. Implementation details of the object in RAM can matter for performance. The library permits any of the standard UInt types to be used for packing the bits, and larger UInt types (like UInt64) are usually faster as they permit working on 64 qubits at a time (instead of 1 if we used a boolean, or 8 if we used a byte).

Moreover, how a tableau is stored in memory can affect performance, as a row-major storage usually permits more efficient use of the CPU cache (for the particular algorithms we use).

Both of these parameters are benchmarked (testing the application of a Pauli operator, which is an $\mathcal{O}(n^2)$ operation; and testing the canonicalization of a Stabilizer, which is an $\mathcal{O}(n^3)$ operation). Row-major UInt64 is the best performing and it is used by default in this library.

  • 1This can occur only if the state being projected is mixed. Both Stabilizer and Destabilizer can be used for mixed states by simply providing fewer stabilizer generators than qubits at initialization. This can be useful for low-level code that tries to avoid the extra memory cost of using MixedStabilizer and MixedDestabilizer but should be avoided otherwise. project! works correctly or raises an explicit warning on all 4 data structures.
diff --git a/dev/ecc_example_sim/index.html b/dev/ecc_example_sim/index.html index eb6006864..4dec76155 100644 --- a/dev/ecc_example_sim/index.html +++ b/dev/ecc_example_sim/index.html @@ -20,7 +20,7 @@ errors = [PauliError(i,errprob) for i in 1:code_n(code)] fullcircuit = [ecirc..., errors..., scirc...]Example block output

And running this noisy simulation:

frames = pftrajectories(fullcircuit; trajectories=nframes)
 pfmeasurements(frames)
4×6 Matrix{Bool}:
- 1  1  1  1  1  1
  0  0  0  0  0  0
- 1  1  0  0  0  0
- 0  1  0  0  1  0
+ 0 0 1 0 0 1 + 0 0 0 0 0 0 + 0 0 0 0 0 0 diff --git a/dev/graphs/index.html b/dev/graphs/index.html index 3b3a2c8dd..513e04d01 100644 --- a/dev/graphs/index.html +++ b/dev/graphs/index.html @@ -43,4 +43,4 @@ + XZZ_ + ZX_Z + Z_XZ -+ _ZZX

Graphs are represented with the Graphs.jl package and plotting can be done both in Plots.jl and Makie.jl (with GraphMakie).

++ _ZZX

Graphs are represented with the Graphs.jl package and plotting can be done both in Plots.jl and Makie.jl (with GraphMakie).

diff --git a/dev/index.html b/dev/index.html index 42e50b33e..920bb7f63 100644 --- a/dev/index.html +++ b/dev/index.html @@ -15,4 +15,4 @@ julia> tCNOT * S"-XX +ZZ" - X_ -+ _Z

Circuit Simulation

The circuit simulation component of QuantumClifford.jl enables Monte Carlo (or symbolic) simulations of noisy Clifford circuits. It provides three main simulation methods: mctrajectories, pftrajectories, and petrajectories. These methods offer varying levels of efficiency, accuracy, and insight.

Monte Carlo Simulations with Stabilizer Tableaux (mctrajectories)

The mctrajectories method runs Monte Carlo simulations using a Stabilizer tableau representation for the quantum states.

Monte Carlo Simulations with Pauli Frames (pftrajectories)

The pftrajectories method runs Monte Carlo simulations of Pauli frames over a single reference Stabilizer tableau simulation. This approach is much more efficient but supports a smaller class of circuits.

Symbolic Depth-First Traversal of Quantum Trajectories (petrajectories)

The petrajectories method performs a depth-first traversal of the most probable quantum trajectories, providing a fixed-order approximation of the circuit's behavior. This approach gives symbolic expressions for various figures of merit instead of just a numeric value.

++ _Z

Circuit Simulation

The circuit simulation component of QuantumClifford.jl enables Monte Carlo (or symbolic) simulations of noisy Clifford circuits. It provides three main simulation methods: mctrajectories, pftrajectories, and petrajectories. These methods offer varying levels of efficiency, accuracy, and insight.

Monte Carlo Simulations with Stabilizer Tableaux (mctrajectories)

The mctrajectories method runs Monte Carlo simulations using a Stabilizer tableau representation for the quantum states.

Monte Carlo Simulations with Pauli Frames (pftrajectories)

The pftrajectories method runs Monte Carlo simulations of Pauli frames over a single reference Stabilizer tableau simulation. This approach is much more efficient but supports a smaller class of circuits.

Symbolic Depth-First Traversal of Quantum Trajectories (petrajectories)

The petrajectories method performs a depth-first traversal of the most probable quantum trajectories, providing a fixed-order approximation of the circuit's behavior. This approach gives symbolic expressions for various figures of merit instead of just a numeric value.

diff --git a/dev/mixed/index.html b/dev/mixed/index.html index 51b7143e3..a4e67ecfb 100644 --- a/dev/mixed/index.html +++ b/dev/mixed/index.html @@ -57,4 +57,4 @@ + XXX + ZZ_ 𝒵ₗ━━━ -+ Z_Z

Destabilizer and MixedStabilizer do not use any column swaps on instantiation as they do not track the logical operators.

++ Z_Z

Destabilizer and MixedStabilizer do not use any column swaps on instantiation as they do not track the logical operators.

diff --git a/dev/noise/index.html b/dev/noise/index.html index 7940d93fe..7d5680825 100644 --- a/dev/noise/index.html +++ b/dev/noise/index.html @@ -1,2 +1,2 @@ -Noise Processes · QuantumClifford.jl
GitHub
+Noise Processes · QuantumClifford.jl
GitHub
diff --git a/dev/noisycircuits/index.html b/dev/noisycircuits/index.html index 5c0ad5d31..77ec320ad 100644 --- a/dev/noisycircuits/index.html +++ b/dev/noisycircuits/index.html @@ -1,2 +1,2 @@ -Simulation of Noisy Circuits · QuantumClifford.jl
GitHub

Simulation of Noisy Clifford Circuits

Unstable

This is unfinished experimental functionality that will change significantly.

We have experimental support for simulation of noisy Clifford circuits which can be imported with using QuantumClifford.Experimental.NoisyCircuits.

Both Monte Carlo and Perturbative Expansion approaches are supported. When performing a perturbative expansion in the noise parameter, the expansion can optionally be performed symbolically, to arbitrary high orders.

Multiple notebooks with examples are also available. For instance, see this tutorial on entanglement purification for many examples.

+Simulation of Noisy Circuits · QuantumClifford.jl
GitHub

Simulation of Noisy Clifford Circuits

Unstable

This is unfinished experimental functionality that will change significantly.

We have experimental support for simulation of noisy Clifford circuits which can be imported with using QuantumClifford.Experimental.NoisyCircuits.

Both Monte Carlo and Perturbative Expansion approaches are supported. When performing a perturbative expansion in the noise parameter, the expansion can optionally be performed symbolically, to arbitrary high orders.

Multiple notebooks with examples are also available. For instance, see this tutorial on entanglement purification for many examples.

diff --git a/dev/noisycircuits_API/index.html b/dev/noisycircuits_API/index.html index 661a655c3..6eb4bf2b5 100644 --- a/dev/noisycircuits_API/index.html +++ b/dev/noisycircuits_API/index.html @@ -1,2 +1,2 @@ -API · QuantumClifford.jl
GitHub

Full API (autogenerated)

Unstable

This is experimental functionality with an unstable API.

+API · QuantumClifford.jl
GitHub

Full API (autogenerated)

Unstable

This is experimental functionality with an unstable API.

diff --git a/dev/noisycircuits_mc/index.html b/dev/noisycircuits_mc/index.html index cb2a7ef33..152666a54 100644 --- a/dev/noisycircuits_mc/index.html +++ b/dev/noisycircuits_mc/index.html @@ -18,4 +18,4 @@ continue:CircuitStatus(0) => 0.0 failure:CircuitStatus(3) => 4.0 false_success:CircuitStatus(2) => 9.0 - true_success:CircuitStatus(1) => 487.0

For more examples, see the notebook comparing the Monte Carlo and Perturbative method or this tutorial on entanglement purification for many examples.

Interface for custom operations

If you want to create a custom gate type (e.g. calling it Operation), you need to definite the following methods.

applywstatus!(s::T, g::Operation)::Tuple{T,Symbol} where T is a tableaux type like Stabilizer or a Register. The Symbol is the status of the operation. Predefined statuses are kept in the registered_statuses list, but you can add more. Be sure to expand this list if you want the trajectory simulators using your custom statuses to output all trajectories.

There is also applynoise! which is convenient wait to create a noise model that can then be plugged into the NoisyGate struct, letting you reuse the predefined perfect gates and measurements. However, you can also just make up your own noise operator simply by implementing applywstatus! for it.

You can also consult the list of implemented operators.

+ true_success:CircuitStatus(1) => 487.0

For more examples, see the notebook comparing the Monte Carlo and Perturbative method or this tutorial on entanglement purification for many examples.

Interface for custom operations

If you want to create a custom gate type (e.g. calling it Operation), you need to definite the following methods.

applywstatus!(s::T, g::Operation)::Tuple{T,Symbol} where T is a tableaux type like Stabilizer or a Register. The Symbol is the status of the operation. Predefined statuses are kept in the registered_statuses list, but you can add more. Be sure to expand this list if you want the trajectory simulators using your custom statuses to output all trajectories.

There is also applynoise! which is convenient wait to create a noise model that can then be plugged into the NoisyGate struct, letting you reuse the predefined perfect gates and measurements. However, you can also just make up your own noise operator simply by implementing applywstatus! for it.

You can also consult the list of implemented operators.

diff --git a/dev/noisycircuits_ops/index.html b/dev/noisycircuits_ops/index.html index 680d5be0c..36ae20642 100644 --- a/dev/noisycircuits_ops/index.html +++ b/dev/noisycircuits_ops/index.html @@ -10,4 +10,4 @@ gate3 = SparseGate(tSWAP, [1,3]) cg = ConditionalGate(gate1, gate2, 2) dg = DecisionGate([gate1,gate2,gate3], bit_register->1) # it will always perform gate1 -[sMX(4,1), sMZ(5,2), cg, dg]Example block output

TODO: Split ConditionalGate into quantum conditional and classical conditional

+[sMX(4,1), sMZ(5,2), cg, dg]Example block output

TODO: Split ConditionalGate into quantum conditional and classical conditional

diff --git a/dev/noisycircuits_perturb/index.html b/dev/noisycircuits_perturb/index.html index cad0b37ec..e75765dda 100644 --- a/dev/noisycircuits_perturb/index.html +++ b/dev/noisycircuits_perturb/index.html @@ -20,4 +20,4 @@ petrajectories(initial_state, circuit)
Dict{CircuitStatus, Float64} with 3 entries:
   failure:CircuitStatus(3)       => 0.0129373
   false_success:CircuitStatus(2) => 0.019406
-  true_success:CircuitStatus(1)  => 0.967065

For more examples, see the notebook comparing the Monte Carlo and Perturbative method or this tutorial on entanglement purification.

Symbolic expansions

The perturbative expansion method works with symbolic variables as well. One can use any of the symbolic libraries available in Julia and simply plug symbolic parameters in lieu of numeric parameters. A detailed example is available as a Jupyter notebook.

Interface for custom operations

If you want to create a custom gate type (e.g. calling it Operation), you need to definite the following methods.

applyop_branches!(s::T, g::Operation; max_order=1)::Vector{Tuple{T,Symbol,Real,Int}} where T is a tableaux type like Stabilizer or a Register. The Symbol is the status of the operation, the Real is the probability for that branch, and the Int is the order of that branch.

There is also applynoise_branches! which is convenient for use in NoisyGate, but you can also just make up your own noise operator simply by implementing applyop_branches! for it.

You can also consult the list of implemented operators.

+ true_success:CircuitStatus(1) => 0.967065

For more examples, see the notebook comparing the Monte Carlo and Perturbative method or this tutorial on entanglement purification.

Symbolic expansions

The perturbative expansion method works with symbolic variables as well. One can use any of the symbolic libraries available in Julia and simply plug symbolic parameters in lieu of numeric parameters. A detailed example is available as a Jupyter notebook.

Interface for custom operations

If you want to create a custom gate type (e.g. calling it Operation), you need to definite the following methods.

applyop_branches!(s::T, g::Operation; max_order=1)::Vector{Tuple{T,Symbol,Real,Int}} where T is a tableaux type like Stabilizer or a Register. The Symbol is the status of the operation, the Real is the probability for that branch, and the Int is the order of that branch.

There is also applynoise_branches! which is convenient for use in NoisyGate, but you can also just make up your own noise operator simply by implementing applyop_branches! for it.

You can also consult the list of implemented operators.

diff --git a/dev/plotting/6b8d6d9d.svg b/dev/plotting/304a0046.svg similarity index 99% rename from dev/plotting/6b8d6d9d.svg rename to dev/plotting/304a0046.svg index 969f97132..223b01fd7 100644 --- a/dev/plotting/6b8d6d9d.svg +++ b/dev/plotting/304a0046.svg @@ -1,23 +1,23 @@ - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + Visualizations · QuantumClifford.jl
GitHub

Visualizations

Stabilizers have a plot recipe that can be used with Plots.jl or Makie.jl. It simply displays the corresponding parity check matrix (extracted with stab_to_gf2) as a bitmap image. Circuits can be visualized with Quantikz.jl.

Importing the aforementioned packages together with QuantumClifford is necessary to enable the plotting functionality (implemented as package extensions).

Plots.jl

In Plots.jl we have a simple recipe plot(s::Stabilizer; xzcomponents=...) where xzcomponents=:split plots the tableau heatmap in a wide form, X bits on the left, Z bits on the right; or xzcomponents=:together plots them overlapping, with different colors for I, X, Z, and Y.

using QuantumClifford, Plots
-plot(random_stabilizer(20,30), xzcomponents=:split)
Example block output
using QuantumClifford, Plots
-plot(canonicalize!(random_stabilizer(20,30)))
Example block output
using QuantumClifford, Plots
-plot(canonicalize_gott!(random_stabilizer(30))[1], xzcomponents=:split)
Example block output
using QuantumClifford, Plots
-plot(canonicalize_gott!(random_stabilizer(30))[1]; xzcomponents=:together)
Example block output
using QuantumClifford, Plots
-plot(canonicalize_rref!(random_stabilizer(20,30),1:30)[1]; xzcomponents=:together)
Example block output

Makie.jl

Makie's heatmap can be directly called on Stabilizer.

using QuantumClifford, CairoMakie
+plot(random_stabilizer(20,30), xzcomponents=:split)
Example block output
using QuantumClifford, Plots
+plot(canonicalize!(random_stabilizer(20,30)))
Example block output
using QuantumClifford, Plots
+plot(canonicalize_gott!(random_stabilizer(30))[1], xzcomponents=:split)
Example block output
using QuantumClifford, Plots
+plot(canonicalize_gott!(random_stabilizer(30))[1]; xzcomponents=:together)
Example block output
using QuantumClifford, Plots
+plot(canonicalize_rref!(random_stabilizer(20,30),1:30)[1]; xzcomponents=:together)
Example block output

Makie.jl

Makie's heatmap can be directly called on Stabilizer.

using QuantumClifford, CairoMakie
 s = S"IIXZ
       ZZIZ
       YYIZ
@@ -47,4 +47,4 @@
 f=Figure()
 stabilizerplot_axis(f[1,1],random_stabilizer(100))
 f
Example block output

Quantikz.jl

With the Quantikz library you can visualize gates or sequences of gates.

using QuantumClifford, Quantikz
-circuit = [sCNOT(1,2), SparseGate(random_clifford(4), [1,4,5,6]), sMZ(4)]
Example block output
+circuit = [sCNOT(1,2), SparseGate(random_clifford(4), [1,4,5,6]), sMZ(4)]Example block output diff --git a/dev/references/index.html b/dev/references/index.html index 7fadeb74b..bc50b97c6 100644 --- a/dev/references/index.html +++ b/dev/references/index.html @@ -1,2 +1,2 @@ -Suggested Readings & References · QuantumClifford.jl
GitHub

Suggested reading

For the basis of the tableaux methods first read (Gottesman, 1998) followed by the more efficient approach described in (Aaronson and Gottesman, 2004).

The tableaux can be canonicalized (i.e. Gaussian elimination can be performed on them) in a number of different ways, and considering the different approaches provides useful insight. The following methods are implemented in this library:

For the use of these methods in error correction and the subtle overlap between the two fields consider these resources. They are also useful in defining some of the specific constraints in commutation between rows in the tableaux:

These publications describe the uniform sampling of random stabilizer states:

For circuit construction routines (for stabilizer measurements for a given code):

For quantum code construction routines:

For classical code construction routines:

References

  • Aaronson, S. and Gottesman, D. (2004). Improved simulation of stabilizer circuits. Physical Review A 70, 052328.
  • Abbe, E.; Shpilka, A. and Ye, M. (2020). Reed–Muller codes: Theory and algorithms. IEEE Transactions on Information Theory 67, 3251–3277.
  • Anderson, J. T.; Duclos-Cianci, G. and Poulin, D. (2014). Fault-tolerant conversion between the steane and reed-muller quantum codes. Physical review letters 113, 080501.
  • Audenaert, K. M. and Plenio, M. B. (2005). Entanglement on mixed stabilizer states: normal forms and reduction procedures. New Journal of Physics 7, 170.
  • Bose, R. C. and Ray-Chaudhuri, D. K. (1960). Further results on error correcting binary group codes. Information and Control 3, 279–290.
  • Bose, R. C. and Ray-Chaudhuri, D. K. (1960). On a class of error correcting binary group codes. Information and control 3, 68–79.
  • Bravyi, S. and Maslov, D. (2021). Hadamard-free circuits expose the structure of the Clifford group. IEEE Transactions on Information Theory 67, 4546–4563.
  • Brown, W. and Fawzi, O. (Jul 2013). Short Random Circuits Define Good Quantum Error Correcting Codes. In: 2013 IEEE International Symposium on Information Theory; pp. 346–350.
  • Calderbank, A. R.; Rains, E. M.; Shor, P. and Sloane, N. J. (1998). Quantum error correction via codes over GF (4). IEEE Transactions on Information Theory 44, 1369–1387.
  • Campbell, E. T.; Anwar, H. and Browne, D. E. (2012). Magic-state distillation in all prime dimensions using quantum reed-muller codes. Physical Review X 2, 041021.
  • Chao, R. and Reichardt, B. W. (2017). Quantum Error Correction with Only Two Extra Qubits. Physical review letters 121 5, 050502.
  • Cleve, R. and Gottesman, D. (1997). Efficient computations of encodings for quantum error correction. Physical Review A 56, 76.
  • Djordjevic, I. B. (2021). Quantum information processing, quantum computing, and quantum error correction: an engineering approach (Academic Press).
  • Fowler, A. G.; Mariantoni, M.; Martinis, J. M. and Cleland, A. N. (2012). Surface codes: Towards practical large-scale quantum computation. Physical Review A 86, 032324.
  • Garcia, H. J.; Markov, I. L. and Cross, A. W. (2012). Efficient inner-product algorithm for stabilizer states, arXiv preprint arXiv:1210.6646.
  • Gottesman, D. (1996). Class of quantum error-correcting codes saturating the quantum Hamming bound. Physical Review A 54, 1862.
  • Gottesman, D. (1997). Stabilizer codes and quantum error correction. Ph.D. Thesis, California Institute of Technology.
  • Gottesman, D. (1998). The Heisenberg representation of quantum computers. In: International Conference on Group Theoretic Methods in Physics (Citeseer).
  • Grassl, M. (2002). Algorithmic aspects of quantum error-correcting codes. Mathematics of Quantum Computation, 223–252.
  • Grassl, M. (2011). Variations on encoding circuits for stabilizer quantum codes. In: International Conference on Coding and Cryptology (Springer); pp. 142–158.
  • Gullans, M. J.; Krastanov, S.; Huse, D. A.; Jiang, L. and Flammia, S. T. (2021). Quantum Coding with Low-Depth Random Circuits. Physical Review X 11, 031066.
  • Hocquenghem, A. (1959). Codes correcteurs d'erreurs. Chiffers 2, 147–156.
  • Knill, E. and Laflamme, R. (1996). Concatenated quantum codes, arXiv preprint quant-ph/9608012.
  • Koenig, R. and Smolin, J. A. (2014). How to efficiently select an arbitrary Clifford group element. Journal of Mathematical Physics 55, 122202.
  • Krastanov, S.; de la Cerda, A. S. and Narang, P. (2020). Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices, arXiv preprint arXiv:2011.11640.
  • Li, Y.; Chen, X. and Fisher, M. P. (2019). Measurement-driven entanglement transition in hybrid quantum circuits. Physical Review B 100, 134306.
  • Lin, S. and Costello, D. (2024). Error Control Coding (Pearson).
  • MacKay, D. J.; Mitchison, G. and McFadden, P. L. (2004). Sparse-graph codes for quantum error correction. IEEE Transactions on Information Theory 50, 2315–2330.
  • Muller, D. E. (1954). Application of Boolean algebra to switching circuit design and to error detection. Transactions of the IRE professional group on electronic computers, 6–12.
  • Nahum, A.; Ruhman, J.; Vijay, S. and Haah, J. (2017). Quantum Entanglement Growth under Random Unitary Dynamics. Physical Review X 7, 031016.
  • Panteleev, P. and Kalachev, G. (2021). Degenerate Quantum LDPC Codes With Good Finite Length Performance. Quantum 5, 585, arXiv:1904.02703 [quant-ph].
  • Panteleev, P. and Kalachev, G. (Jun 2022). Asymptotically Good Quantum and Locally Testable Classical LDPC Codes. In: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (ACM, Rome Italy); pp. 375–388.
  • Raaphorst, S. (2003). Reed-muller codes. Carleton University, May 9.
  • Raveendran, N.; Rengaswamy, N.; Rozpędek, F.; Raina, A.; Jiang, L. and Vasić, B. (2022). Finite Rate QLDPC-GKP Coding Scheme That Surpasses the CSS Hamming Bound. Quantum 6, 767.
  • Reed, I. S. (1954). A class of multiple-error-correcting codes and the decoding scheme. IEEE Transactions on Information Theory 4, 38–49.
  • Roffe, J.; Cohen, L. Z.; Quintavalle, A. O.; Chandra, D. and Campbell, E. T. (2023). Bias-Tailored Quantum LDPC Codes. Quantum 7, 1005.
  • Steane, A. M. (1999). Quantum reed-muller codes. IEEE Transactions on Information Theory 45, 1701–1703.
  • Steane, A. M. (2007). A tutorial on quantum error correction. In: PROCEEDINGS-INTERNATIONAL SCHOOL OF PHYSICS ENRICO FERMI, Vol. 162 (IOS Press; Ohmsha; 1999); p. 1.
  • Van Den Berg, E. (2021). A simple method for sampling random Clifford operators. In: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE); pp. 54–59.
  • Wilde, M. M. (2009). Logical operators of quantum codes. Physical Review A 79, 062322.
  • Yu, S.; Bierbrauer, J.; Dong, Y.; Chen, Q. and Oh, C. H. (2013). All the Stabilizer Codes of Distance 3. IEEE Transactions on Information Theory 59, 5179–5185.
+Suggested Readings & References · QuantumClifford.jl
GitHub

Suggested reading

For the basis of the tableaux methods first read (Gottesman, 1998) followed by the more efficient approach described in (Aaronson and Gottesman, 2004).

The tableaux can be canonicalized (i.e. Gaussian elimination can be performed on them) in a number of different ways, and considering the different approaches provides useful insight. The following methods are implemented in this library:

For the use of these methods in error correction and the subtle overlap between the two fields consider these resources. They are also useful in defining some of the specific constraints in commutation between rows in the tableaux:

These publications describe the uniform sampling of random stabilizer states:

For circuit construction routines (for stabilizer measurements for a given code):

For quantum code construction routines:

For classical code construction routines:

References

  • Aaronson, S. and Gottesman, D. (2004). Improved simulation of stabilizer circuits. Physical Review A 70, 052328.
  • Abbe, E.; Shpilka, A. and Ye, M. (2020). Reed–Muller codes: Theory and algorithms. IEEE Transactions on Information Theory 67, 3251–3277.
  • Anderson, J. T.; Duclos-Cianci, G. and Poulin, D. (2014). Fault-tolerant conversion between the steane and reed-muller quantum codes. Physical review letters 113, 080501.
  • Audenaert, K. M. and Plenio, M. B. (2005). Entanglement on mixed stabilizer states: normal forms and reduction procedures. New Journal of Physics 7, 170.
  • Bose, R. C. and Ray-Chaudhuri, D. K. (1960). Further results on error correcting binary group codes. Information and Control 3, 279–290.
  • Bose, R. C. and Ray-Chaudhuri, D. K. (1960). On a class of error correcting binary group codes. Information and control 3, 68–79.
  • Bravyi, S. and Maslov, D. (2021). Hadamard-free circuits expose the structure of the Clifford group. IEEE Transactions on Information Theory 67, 4546–4563.
  • Brown, W. and Fawzi, O. (Jul 2013). Short Random Circuits Define Good Quantum Error Correcting Codes. In: 2013 IEEE International Symposium on Information Theory; pp. 346–350.
  • Calderbank, A. R.; Rains, E. M.; Shor, P. and Sloane, N. J. (1998). Quantum error correction via codes over GF (4). IEEE Transactions on Information Theory 44, 1369–1387.
  • Campbell, E. T.; Anwar, H. and Browne, D. E. (2012). Magic-state distillation in all prime dimensions using quantum reed-muller codes. Physical Review X 2, 041021.
  • Chao, R. and Reichardt, B. W. (2017). Quantum Error Correction with Only Two Extra Qubits. Physical review letters 121 5, 050502.
  • Cleve, R. and Gottesman, D. (1997). Efficient computations of encodings for quantum error correction. Physical Review A 56, 76.
  • Djordjevic, I. B. (2021). Quantum information processing, quantum computing, and quantum error correction: an engineering approach (Academic Press).
  • Fowler, A. G.; Mariantoni, M.; Martinis, J. M. and Cleland, A. N. (2012). Surface codes: Towards practical large-scale quantum computation. Physical Review A 86, 032324.
  • Garcia, H. J.; Markov, I. L. and Cross, A. W. (2012). Efficient inner-product algorithm for stabilizer states, arXiv preprint arXiv:1210.6646.
  • Gottesman, D. (1996). Class of quantum error-correcting codes saturating the quantum Hamming bound. Physical Review A 54, 1862.
  • Gottesman, D. (1997). Stabilizer codes and quantum error correction. Ph.D. Thesis, California Institute of Technology.
  • Gottesman, D. (1998). The Heisenberg representation of quantum computers. In: International Conference on Group Theoretic Methods in Physics (Citeseer).
  • Grassl, M. (2002). Algorithmic aspects of quantum error-correcting codes. Mathematics of Quantum Computation, 223–252.
  • Grassl, M. (2011). Variations on encoding circuits for stabilizer quantum codes. In: International Conference on Coding and Cryptology (Springer); pp. 142–158.
  • Gullans, M. J.; Krastanov, S.; Huse, D. A.; Jiang, L. and Flammia, S. T. (2021). Quantum Coding with Low-Depth Random Circuits. Physical Review X 11, 031066.
  • Hocquenghem, A. (1959). Codes correcteurs d'erreurs. Chiffers 2, 147–156.
  • Knill, E. and Laflamme, R. (1996). Concatenated quantum codes, arXiv preprint quant-ph/9608012.
  • Koenig, R. and Smolin, J. A. (2014). How to efficiently select an arbitrary Clifford group element. Journal of Mathematical Physics 55, 122202.
  • Krastanov, S.; de la Cerda, A. S. and Narang, P. (2020). Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices, arXiv preprint arXiv:2011.11640.
  • Li, Y.; Chen, X. and Fisher, M. P. (2019). Measurement-driven entanglement transition in hybrid quantum circuits. Physical Review B 100, 134306.
  • Lin, S. and Costello, D. (2024). Error Control Coding (Pearson).
  • MacKay, D. J.; Mitchison, G. and McFadden, P. L. (2004). Sparse-graph codes for quantum error correction. IEEE Transactions on Information Theory 50, 2315–2330.
  • Muller, D. E. (1954). Application of Boolean algebra to switching circuit design and to error detection. Transactions of the IRE professional group on electronic computers, 6–12.
  • Nahum, A.; Ruhman, J.; Vijay, S. and Haah, J. (2017). Quantum Entanglement Growth under Random Unitary Dynamics. Physical Review X 7, 031016.
  • Panteleev, P. and Kalachev, G. (2021). Degenerate Quantum LDPC Codes With Good Finite Length Performance. Quantum 5, 585, arXiv:1904.02703 [quant-ph].
  • Panteleev, P. and Kalachev, G. (Jun 2022). Asymptotically Good Quantum and Locally Testable Classical LDPC Codes. In: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (ACM, Rome Italy); pp. 375–388.
  • Raaphorst, S. (2003). Reed-muller codes. Carleton University, May 9.
  • Raveendran, N.; Rengaswamy, N.; Rozpędek, F.; Raina, A.; Jiang, L. and Vasić, B. (2022). Finite Rate QLDPC-GKP Coding Scheme That Surpasses the CSS Hamming Bound. Quantum 6, 767.
  • Reed, I. S. (1954). A class of multiple-error-correcting codes and the decoding scheme. IEEE Transactions on Information Theory 4, 38–49.
  • Roffe, J.; Cohen, L. Z.; Quintavalle, A. O.; Chandra, D. and Campbell, E. T. (2023). Bias-Tailored Quantum LDPC Codes. Quantum 7, 1005.
  • Steane, A. M. (1999). Quantum reed-muller codes. IEEE Transactions on Information Theory 45, 1701–1703.
  • Steane, A. M. (2007). A tutorial on quantum error correction. In: PROCEEDINGS-INTERNATIONAL SCHOOL OF PHYSICS ENRICO FERMI, Vol. 162 (IOS Press; Ohmsha; 1999); p. 1.
  • Van Den Berg, E. (2021). A simple method for sampling random Clifford operators. In: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE); pp. 54–59.
  • Wilde, M. M. (2009). Logical operators of quantum codes. Physical Review A 79, 062322.
  • Yu, S.; Bierbrauer, J.; Dong, Y.; Chen, Q. and Oh, C. H. (2013). All the Stabilizer Codes of Distance 3. IEEE Transactions on Information Theory 59, 5179–5185.
diff --git a/dev/stab-algebra-manual/index.html b/dev/stab-algebra-manual/index.html index 5ae6f7d0d..ec528b456 100644 --- a/dev/stab-algebra-manual/index.html +++ b/dev/stab-algebra-manual/index.html @@ -302,4 +302,4 @@ 𝒮𝓉𝒶𝒷━ + _ZX - _Z_ -- Z_X

Mixed States

Both the Stabilizer and Destabilizer structures have more general forms that enable work with mixed stabilizer states. They are the MixedStabilizer and MixedDestabilizer structures, described in Mixed States. More information that can be seen in the data structures page, which expands upon the algorithms available for each structure.

Random States and Circuits

random_clifford, random_stabilizer, and enumerate_cliffords can be used for the generation of random states.

+- Z_X

Mixed States

Both the Stabilizer and Destabilizer structures have more general forms that enable work with mixed stabilizer states. They are the MixedStabilizer and MixedDestabilizer structures, described in Mixed States. More information that can be seen in the data structures page, which expands upon the algorithms available for each structure.

Random States and Circuits

random_clifford, random_stabilizer, and enumerate_cliffords can be used for the generation of random states.

diff --git a/dev/tutandpub/index.html b/dev/tutandpub/index.html index 79019da8d..e68537263 100644 --- a/dev/tutandpub/index.html +++ b/dev/tutandpub/index.html @@ -1,2 +1,2 @@ -Tutorials and Publications · QuantumClifford.jl
GitHub

Tutorials and Publications

This list has a number of notebooks with tutorials, examples, and reproduction of published results (some of these results originally obtained with this very library).

On the topic of explicit use of the Tableaux formalism for Stabilizer states

On the Monte Carlo and Perturbative Expansions for Noisy Clifford circuits

+Tutorials and Publications · QuantumClifford.jl
GitHub

Tutorials and Publications

This list has a number of notebooks with tutorials, examples, and reproduction of published results (some of these results originally obtained with this very library).

On the topic of explicit use of the Tableaux formalism for Stabilizer states

On the Monte Carlo and Perturbative Expansions for Noisy Clifford circuits