Ill-Conditioned Nonlinear System Work-Precision Diagrams
Setup
Fetch required packages
using NonlinearSolve, SparseDiffTools, LinearAlgebra, SparseArrays, DiffEqDevTools,
CairoMakie, Symbolics, BenchmarkTools, PolyesterForwardDiff, LinearSolve, Sundials,
Enzyme, SparseConnectivityTracer, DifferentiationInterface
import NLsolve, MINPACK, PETSc
const RUS = RadiusUpdateSchemes;
BenchmarkTools.DEFAULT_PARAMETERS.seconds = 0.2;Define a utility to timeout the benchmark after a certain time.
# Taken from ReTestItems.jl
function timeout(f, timeout)
cond = Threads.Condition()
timer = Timer(timeout) do tm
close(tm)
ex = ErrorException("timed out after $timeout seconds")
@lock cond notify(cond, ex; error=false)
end
Threads.@spawn begin
try
ret = $f()
isopen(timer) && @lock cond notify(cond, ret)
catch e
isopen(timer) && @lock cond notify(cond, CapturedException(e, catch_backtrace()); error=true)
finally
close(timer)
end
end
return @lock cond wait(cond) # will throw if we timeout
endtimeout (generic function with 1 method)Define the Brussletor problem.
brusselator_f(x, y) = (((x - 3 // 10) ^ 2 + (y - 6 // 10) ^ 2) ≤ 0.01) * 5
limit(a, N) = ifelse(a == N + 1, 1, ifelse(a == 0, N, a))
function init_brusselator_2d(xyd, N)
N = length(xyd)
u = zeros(N, N, 2)
for I in CartesianIndices((N, N))
x = xyd[I[1]]
y = xyd[I[2]]
u[I, 1] = 22 * (y * (1 - y))^(3 / 2)
u[I, 2] = 27 * (x * (1 - x))^(3 / 2)
end
return u
end
function generate_brusselator_problem(N::Int; sparsity = nothing, kwargs...)
xyd_brusselator = range(0; stop = 1, length = N)
function brusselator_2d_loop(du_, u_, p)
A, B, α, δx = p
α = α / δx ^ 2
du = reshape(du_, N, N, 2)
u = reshape(u_, N, N, 2)
@inbounds @simd for I in CartesianIndices((N, N))
i, j = Tuple(I)
x, y = xyd_brusselator[I[1]], xyd_brusselator[I[2]]
ip1, im1 = limit(i + 1, N), limit(i - 1, N)
jp1, jm1 = limit(j + 1, N), limit(j - 1, N)
du[i, j, 1] = α * (u[im1, j, 1] + u[ip1, j, 1] + u[i, jp1, 1] + u[i, jm1, 1] -
4u[i, j, 1]) +
B + u[i, j, 1] ^ 2 * u[i, j, 2] - (A + 1) * u[i, j, 1] +
brusselator_f(x, y)
du[i, j, 2] = α * (u[im1, j, 2] + u[ip1, j, 2] + u[i, jp1, 2] + u[i, jm1, 2] -
4u[i, j, 2]) +
A * u[i, j, 1] - u[i, j, 1] ^ 2 * u[i, j, 2]
end
return nothing
end
return NonlinearProblem(
NonlinearFunction(brusselator_2d_loop; sparsity),
vec(init_brusselator_2d(xyd_brusselator, N)),
(3.4, 1.0, 10.0, step(xyd_brusselator));
kwargs...
)
endgenerate_brusselator_problem (generic function with 1 method)function get_ordering(x::AbstractMatrix)
idxs = Vector{Int}(undef, size(x, 1))
placed = zeros(Bool, size(x, 1))
idx = 1
for j in size(x, 2):-1:1
row = view(x, :, j)
idxs_row = sortperm(row; by = x -> isnan(x) ? Inf : (x == -1 ? Inf : x))
for i in idxs_row
if !placed[i] && !isnan(row[i]) && row[i] ≠ -1
idxs[idx] = i
placed[i] = true
idx += 1
idx > length(idxs) && break
end
end
idx > length(idxs) && break
end
return idxs
endget_ordering (generic function with 1 method)Scaling of Sparsity Detection Algorithm
We increase the problem size, and compute the jacobian 10 times similar to a real workload where the jacobian is computed several times and amortizes the cost for computing the sparsity pattern.
test_problem = generate_brusselator_problem(4)
bruss_f!, u0 = (du, u) -> test_problem.f(du, u, test_problem.p), test_problem.u0
y = similar(u0)
J = Float64.(ADTypes.jacobian_sparsity(bruss_f!, y, u0, TracerSparsityDetector()))
colors = matrix_colors(J)
begin
J_ = similar(J)
rows = rowvals(J)
vals = nonzeros(J)
for j in 1:size(J, 2)
for i in nzrange(J, j)
row = rows[i]
J_[j, row] = colors[j] # spy does a ordering I can't figure out. so transposing it here
end
end
end
function cache_and_compute_10_jacobians(adtype, f!::F, y, x, p) where {F}
prep = DifferentiationInterface.prepare_jacobian(f!, y, adtype, x, Constant(p))
J = DifferentiationInterface.jacobian(f!, y, prep, adtype, x, Constant(p))
for _ in 1:9
DifferentiationInterface.jacobian!(f!, y, J, prep, adtype, x, Constant(p))
end
return J
end
# XXX: run till 8 on CI
# Ns = [2^i for i in 1:8]
Ns = [2^i for i in 1:6]
adtypes = [
(
AutoSparse(AutoFiniteDiff(); sparsity_detector=TracerSparsityDetector()),
[:finitediff, :exact_sparse]
),
(
AutoSparse(
AutoPolyesterForwardDiff(; chunksize=8);
sparsity_detector=TracerSparsityDetector()
),
[:forwarddiff, :exact_sparse]
),
(
AutoSparse(
AutoEnzyme(; mode=Enzyme.Forward);
sparsity_detector=TracerSparsityDetector()
),
[:enzyme, :exact_sparse]
),
(
AutoSparse(
AutoFiniteDiff();
sparsity_detector=DenseSparsityDetector(AutoFiniteDiff(); atol=1e-5)
),
[:finitediff, :approx_sparse]
),
(
AutoSparse(
AutoPolyesterForwardDiff(; chunksize=8);
sparsity_detector=DenseSparsityDetector(
AutoPolyesterForwardDiff(; chunksize=8); atol=1e-5
)
),
[:polyester, :approx_sparse]
),
(
AutoSparse(
AutoEnzyme(; mode=Enzyme.Forward);
sparsity_detector=DenseSparsityDetector(
AutoEnzyme(; mode=Enzyme.Forward); atol=1e-5
)
),
[:enzyme, :approx_sparse]
),
(
AutoPolyesterForwardDiff(; chunksize=8),
[:polyester, :none]
),
]
times = Matrix{Float64}(undef, length(Ns), length(adtypes))
for (i, N) in enumerate(Ns)
@info N
test_problem = generate_brusselator_problem(N)
bruss_f! = test_problem.f
u0 = test_problem.u0
y = similar(u0)
for (j, (adtype, _)) in enumerate(adtypes)
times[i, j] = @belapsed begin
$(cache_and_compute_10_jacobians)(
$(adtype), $(bruss_f!), $(y), $(u0), $(test_problem.p)
)
end
@info times[i, j]
end
endPlotting the results.
symbol_to_adname = Dict(
:finitediff => "Finite Diff",
:forwarddiff => "Forward Mode AD",
:polyester => "Threaded Forward Mode AD",
:enzyme => "Forward Mode AD (Enzyme)",
)
fig = begin
cycle = Cycle([:marker], covary=true)
plot_theme = Theme(Lines=(; cycle), Scatter=(; cycle))
with_theme(plot_theme) do
fig = Figure(; size=(1400, 1400 * 0.5))
ax = Axis(fig[1, 1]; title="Sparsity Pattern for 2D Brusselator Jacobian",
titlesize=22, titlegap=10,
xticksize=20, yticksize=20, xticklabelsize=20, yticklabelsize=20,
xtickwidth=2.5, ytickwidth=2.5, spinewidth=2.5, yreversed=true)
spy!(ax, J_; markersize=1, marker=:circle, framecolor=:lightgray,
colormap=:seaborn_bright)
ax = Axis(fig[1, 2]; title="Scaling of Sparse Jacobian Computation",
titlesize=22, titlegap=10, xscale=log10, yscale=log10,
xticksize=20, yticksize=20, xticklabelsize=20, yticklabelsize=20,
xtickwidth=2.5, ytickwidth=2.5, spinewidth=2.5,
xlabel=L"Input Dimension ($\mathbf{N}$)", ylabel=L"Time $\mathbf{(s)}$", xlabelsize=22,
ylabelsize=22, yaxisposition=:right)
colors = cgrad(:seaborn_bright, length(adtypes); categorical=true)
line_list = []
scatter_list = []
Ns_ = Ns .^ 2 .* 2
linestyles = [:solid, :solid, :solid, :dash, :dash, :dash, :dot, :dot]
for (i, times) in enumerate(eachcol(times))
l = lines!(Ns_, times; linewidth=5, color=colors[i], linestyle=linestyles[i])
push!(line_list, l)
sc = scatter!(Ns_, times; markersize=16, strokewidth=2, color=colors[i])
push!(scatter_list, sc)
end
tracer_idxs = [idx for idx in 1:length(adtypes) if :exact_sparse ∈ adtypes[idx][2]]
group_tracer = [
[
LineElement(;
color=line_list[idx].color,
linestyle=line_list[idx].linestyle,
linewidth=line_list[idx].linewidth,
),
MarkerElement(;
color=scatter_list[idx].color,
marker=scatter_list[idx].marker,
strokewidth=scatter_list[idx].strokewidth,
markersize=scatter_list[idx].markersize,
),
] for idx in tracer_idxs
]
local_sparse_idxs = [idx for idx in 1:length(adtypes) if :approx_sparse ∈ adtypes[idx][2]]
group_local_sparse = [
[
LineElement(;
color=line_list[idx].color,
linestyle=line_list[idx].linestyle,
linewidth=line_list[idx].linewidth,
),
MarkerElement(;
color=scatter_list[idx].color,
marker=scatter_list[idx].marker,
strokewidth=scatter_list[idx].strokewidth,
markersize=scatter_list[idx].markersize,
),
] for idx in local_sparse_idxs
]
non_sparse_idxs = [idx for idx in 1:length(adtypes) if :none ∈ adtypes[idx][2]]
group_nonsparse = [
[
LineElement(;
color=line_list[idx].color,
linestyle=line_list[idx].linestyle,
linewidth=line_list[idx].linewidth,
),
MarkerElement(;
color=scatter_list[idx].color,
marker=scatter_list[idx].marker,
strokewidth=scatter_list[idx].strokewidth,
markersize=scatter_list[idx].markersize,
),
] for idx in non_sparse_idxs
]
axislegend(
ax,
[group_tracer, group_local_sparse, group_nonsparse],
[
[symbol_to_adname[adtypes[idx][2][1]] for idx in tracer_idxs],
[symbol_to_adname[adtypes[idx][2][1]] for idx in local_sparse_idxs],
[symbol_to_adname[adtypes[idx][2][1]] for idx in non_sparse_idxs],
],
["Exact Sparsity", "Approx. Local Sparsity", "No Sparsity"];
position=:rb, framevisible=true, framewidth=2.5, titlesize=18,
labelsize=16, patchsize=(40.0f0, 20.0f0)
)
fig
end
end
save("brusselator_sparse_jacobian_scaling.svg", fig)CairoMakie.Screen{SVG}Scaling with Problem Size
First, let us experiment the scaling of each algorithm with the problem size.
Ns = vcat(collect(2 .^ (2:7)), [150, 175, 200])
# XXX: PETSc just segfaults
solvers_scaling = [
(; pkg = :nonlinearsolve, sparsity = :none, name = "NR (No Sparsity)", alg = NewtonRaphson()),
# (; pkg = :nonlinearsolve, sparsity = :approx, name = "NR (Approx. Local Sparsity)", alg = NewtonRaphson()),
(; pkg = :nonlinearsolve, sparsity = :exact, name = "NR (Exact Sparsity)", alg = NewtonRaphson()),
(; pkg = :wrapper, sparsity = :none, name = "NR [NLsolve.jl]", alg = NLsolveJL(; method = :newton, autodiff = :forward)),
(; pkg = :wrapper, sparsity = :none, name = "Mod. NR [Sundials]", alg = KINSOL()),
# (; pkg = :wrapper, sparsity = :none, name = "NR [PETSc] (No Sparsity)", alg = PETScSNES(; snes_type = "newtonls")),
# (; pkg = :wrapper, sparsity = :none, name = "NR [PETSc] (Approx. Local Sparsity)", alg = PETScSNES(; snes_type = "newtonls")),
# (; pkg = :wrapper, sparsity = :none, name = "NR [PETSc] (Exact Sparsity)", alg = PETScSNES(; snes_type = "newtonls")),
(; pkg = :nonlinearsolve, sparsity = :none, name = "TR (No Sparsity)", alg = TrustRegion(; radius_update_scheme = RUS.NLsolve)),
# (; pkg = :nonlinearsolve, sparsity = :approx, name = "TR (Approx. Local Sparsity)", alg = TrustRegion(; radius_update_scheme = RUS.NLsolve)),
(; pkg = :nonlinearsolve, sparsity = :exact, name = "TR (Exact Sparsity)", alg = TrustRegion(; radius_update_scheme = RUS.NLsolve)),
(; pkg = :wrapper, sparsity = :none, name = "TR [NLsolve.jl]", alg = NLsolveJL(; autodiff = :forward)),
# (; pkg = :wrapper, sparsity = :none, name = "TR [PETSc] (No Sparsity)", alg = PETScSNES(; snes_type = "newtontr")),
# (; pkg = :wrapper, sparsity = :none, name = "TR [PETSc] (Approx. Local Sparsity)", alg = PETScSNES(; snes_type = "newtontr")),
# (; pkg = :wrapper, sparsity = :none, name = "TR [PETSc] (Exact Sparsity)", alg = PETScSNES(; snes_type = "newtontr")),
(; pkg = :wrapper, sparsity = :none, name = "Mod. Powell [MINPACK]", alg = CMINPACK()),
]
runtimes_scaling = fill(-1.0, length(solvers_scaling), length(Ns))
for (i, N) in enumerate(Ns)
prob_dense = generate_brusselator_problem(N)
prob_exact_sparse = generate_brusselator_problem(N;
sparsity = TracerSparsityDetector()
)
@info "Benchmarking N = $N"
for (j, solver) in enumerate(solvers_scaling)
ptype = solver.sparsity
alg = solver.alg
name = solver.name
prob = if ptype == :none
prob_dense
elseif ptype == :approx
# With Tracing based sparsity detection, we dont need this any more
error("Approximate Sparsity not implemented")
elseif ptype == :exact
prob_exact_sparse
end
if (j > 1 && runtimes_scaling[j - 1, i] == -1) ||
(alg isa CMINPACK && N > 32) ||
(alg isa KINSOL && N > 64) ||
(alg isa NLsolveJL && N > 64 && alg.method == :trust_region) ||
(alg isa GeneralizedFirstOrderAlgorithm && alg.name == :TrustRegion && N > 64) ||
(alg isa NLsolveJL && N > 128 && alg.method == :newton) ||
(alg isa GeneralizedFirstOrderAlgorithm && alg.name == :NewtonRaphson && N > 128 && ptype == :none) ||
(alg isa GeneralizedFirstOrderAlgorithm && alg.name == :NewtonRaphson && N > 150 && ptype == :approx)
# The last benchmark failed so skip this too
runtimes_scaling[j, i] = NaN
@warn "$(name): Would Have Timed out"
else
function benchmark_function()
termination_condition = (alg isa PETScSNES || alg isa KINSOL) ?
nothing :
NonlinearSolveBase.AbsNormTerminationMode(Base.Fix1(maximum, abs))
sol = solve(prob, alg; abstol=1e-6, reltol=1e-6, termination_condition)
runtimes_scaling[j, i] = @belapsed solve($prob, $alg; abstol=1e-6,
reltol=1e-6, termination_condition=$termination_condition)
@info "$(name): $(runtimes_scaling[j, i]) | $(norm(sol.resid, Inf)) | $(sol.retcode)"
end
timeout(benchmark_function, 600)
if runtimes_scaling[j, i] == -1
@warn "$(name): Timed out"
runtimes_scaling[j, i] = NaN
end
end
end
println()
endPlot the results.
fig = begin
ASPECT_RATIO = 0.7
WIDTH = 1200
HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
STROKEWIDTH = 2.5
cycle = Cycle([:marker], covary = true)
colors = cgrad(:seaborn_bright, length(solvers_scaling); categorical = true)
theme = Theme(Lines = (cycle = cycle,), Scatter = (cycle = cycle,))
LINESTYLES = Dict(
(:nonlinearsolve, :none) => :solid,
# (:nonlinearsolve, :approx) => :dash,
(:nonlinearsolve, :exact) => :dashdot,
# (:simplenonlinearsolve, :none) => :solid,
(:wrapper, :none) => :dot,
)
Ns_ = Ns .^ 2 .* 2
with_theme(theme) do
fig = Figure(; size = (WIDTH, HEIGHT))
ax = Axis(fig[1, 1:3], ylabel = L"Time ($s$)", xlabel = L"Problem Size ($N$)",
xscale = log10, yscale = log10, xlabelsize = 22, ylabelsize = 22,
xticklabelsize = 20, yticklabelsize = 20, xtickwidth = STROKEWIDTH,
ytickwidth = STROKEWIDTH, spinewidth = STROKEWIDTH)
idxs = get_ordering(runtimes_scaling)
ls, scs = [], []
for (i, solver) in zip(idxs, solvers_scaling[idxs])
linestyle = LINESTYLES[(solver.pkg, solver.sparsity)]
l = lines!(Ns_, runtimes_scaling[i, :]; linewidth = 5, color = colors[i],
linestyle)
sc = scatter!(Ns_, runtimes_scaling[i, :]; markersize = 16, strokewidth = 2,
color = colors[i])
push!(ls, l)
push!(scs, sc)
end
main_legend = [
[
LineElement(; color = ls[idx].color, linestyle = ls[idx].linestyle,
linewidth = ls[idx].linewidth),
MarkerElement(; color = scs[idx].color, marker = scs[idx].marker,
markersize = scs[idx].markersize, strokewidth = scs[idx].strokewidth)
]
for idx in 1:length(solvers_scaling)
]
sparsity_legend = [
LineElement(; linestyle = :solid, linewidth = 5),
# LineElement(; linestyle = :dash, linewidth = 5),
LineElement(; linestyle = :dashdot, linewidth = 5),
]
axislegend(ax, main_legend, [s.name for s in solvers_scaling[idxs]],
"Successful Solvers\n(Fastest to Slowest)";
framevisible=true, framewidth = STROKEWIDTH, orientation = :vertical,
titlesize = 20, nbanks = 1, labelsize = 16,
tellheight = true, tellwidth = false, patchsize = (60.0f0, 20.0f0),
position = :rb)
axislegend(ax, sparsity_legend,
[
"No Sparsity Detection",
# "Approx. Sparsity",
"Exact Sparsity"
],
"Sparsity Detection"; framevisible=true, framewidth = STROKEWIDTH,
orientation = :vertical, titlesize = 20, nbanks = 1, labelsize = 16,
tellheight = true, tellwidth = false, patchsize = (60.0f0, 20.0f0),
position = :lt)
fig[0, :] = Label(fig,
"Brusselator 2D: Scaling of First-Order Nonlinear Solvers with Problem Size",
fontsize = 24, tellwidth = false, font = :bold)
return fig
end
end
save("brusselator_scaling.svg", fig)CairoMakie.Screen{SVG}Jacobian-Free Newton / TR Krylov Methods
In this section, we will benchmark jacobian-free nonlinear solvers with Krylov methods. We will use preconditioning from AlgebraicMultigrid.jl and IncompleteLU.jl. Unfortunately, our ability to use 3rd party software is limited here, since only Sundials.jl supports jacobian-free methods via :GMRES.
using AlgebraicMultigrid, IncompleteLU
incompletelu(W, p = nothing) = ilu(W, τ = 50.0), LinearAlgebra.I
function algebraicmultigrid(W, p = nothing)
return aspreconditioner(ruge_stuben(convert(AbstractMatrix, W))), LinearAlgebra.I
end
function algebraicmultigrid_jacobi(W, p = nothing)
A = convert(AbstractMatrix, W)
Pl = AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(
A, presmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1))),
postsmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1)))
))
return Pl, LinearAlgebra.I
end
Ns = 2 .^ (2:7)
solvers_scaling_jacobian_free = [
(; pkg = :nonlinearsolve, name = "Newton Krylov", alg = NewtonRaphson(; linsolve = KrylovJL_GMRES())),
(; pkg = :nonlinearsolve, name = "Newton Krylov (ILU)", alg = NewtonRaphson(; linsolve = KrylovJL_GMRES(; precs = incompletelu), concrete_jac = true)),
(; pkg = :nonlinearsolve, name = "Newton Krylov (AMG)", alg = NewtonRaphson(; linsolve = KrylovJL_GMRES(; precs = algebraicmultigrid), concrete_jac = true)),
(; pkg = :nonlinearsolve, name = "Newton Krylov (AMG Jacobi)", alg = NewtonRaphson(; linsolve = KrylovJL_GMRES(; precs = algebraicmultigrid_jacobi), concrete_jac = true)),
(; pkg = :nonlinearsolve, name = "TR Krylov", alg = TrustRegion(; linsolve = KrylovJL_GMRES())),
(; pkg = :nonlinearsolve, name = "TR Krylov (ILU)", alg = TrustRegion(; linsolve = KrylovJL_GMRES(; precs = incompletelu), concrete_jac = true)),
(; pkg = :nonlinearsolve, name = "TR Krylov (AMG)", alg = TrustRegion(; linsolve = KrylovJL_GMRES(; precs = algebraicmultigrid), concrete_jac = true)),
(; pkg = :nonlinearsolve, name = "TR Krylov (AMG Jacobi)", alg = TrustRegion(; linsolve = KrylovJL_GMRES(; precs = algebraicmultigrid_jacobi), concrete_jac = true)),
(; pkg = :wrapper, name = "Newton Krylov [Sundials]", alg = KINSOL(; linear_solver = :GMRES)),
]
runtimes_scaling = zeros(length(solvers_scaling_jacobian_free), length(Ns)) .- 1
for (i, N) in enumerate(Ns)
prob = generate_brusselator_problem(
N; sparsity = TracerSparsityDetector()
)
@info "Benchmarking N = $N"
for (j, solver) in enumerate(solvers_scaling_jacobian_free)
alg = solver.alg
name = solver.name
if (j > 1 && runtimes_scaling[j - 1, i] == -1)
# The last benchmark failed so skip this too
runtimes_scaling[j, i] = NaN
@warn "$(name): Would Have Timed out"
else
function benchmark_function()
termination_condition = (alg isa PETScSNES || alg isa KINSOL) ?
nothing :
NonlinearSolveBase.AbsNormTerminationMode(Base.Fix1(maximum, abs))
sol = solve(prob, alg; abstol=1e-6, reltol=1e-6,
linsolve_kwargs = (; abstol = 1e-9, reltol = 1e-9),
termination_condition)
if SciMLBase.successful_retcode(sol) || norm(sol.resid, Inf) ≤ 1e-5
runtimes_scaling[j, i] = @belapsed solve($prob, $alg; abstol=1e-6,
reltol=1e-6,
linsolve_kwargs = (; abstol = 1e-9, reltol = 1e-9),
termination_condition=$termination_condition)
else
runtimes_scaling[j, i] = NaN
end
@info "$(name): $(runtimes_scaling[j, i]) | $(norm(sol.resid, Inf)) | $(sol.retcode)"
end
timeout(benchmark_function, 600)
if runtimes_scaling[j, i] == -1
@warn "$(name): Timed out"
runtimes_scaling[j, i] = NaN
end
end
end
println()
endPlot the results.
fig = begin
ASPECT_RATIO = 0.7
WIDTH = 1200
HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
STROKEWIDTH = 2.5
cycle = Cycle([:marker], covary = true)
colors = cgrad(:seaborn_bright, length(solvers_scaling_jacobian_free); categorical = true)
theme = Theme(Lines = (cycle = cycle,), Scatter = (cycle = cycle,))
LINESTYLES = Dict(
(:nonlinearsolve, :none) => :solid,
(:nonlinearsolve, :amg) => :dot,
(:nonlinearsolve, :amg_jacobi) => :dash,
(:nonlinearsolve, :ilu) => :dashdot,
)
Ns_ = Ns .^ 2 .* 2
with_theme(theme) do
fig = Figure(; size = (WIDTH, HEIGHT))
ax = Axis(fig[1, 1:2], ylabel = L"Time ($s$)", xlabel = L"Problem Size ($N$)",
xscale = log10, yscale = log10, xlabelsize = 22, ylabelsize = 22,
xticklabelsize = 20, yticklabelsize = 20, xtickwidth = STROKEWIDTH,
ytickwidth = STROKEWIDTH, spinewidth = STROKEWIDTH)
idxs = get_ordering(runtimes_scaling)
ls, scs, labels = [], [], []
for (i, solver) in zip(idxs, solvers_scaling_jacobian_free[idxs])
all(isnan, runtimes_scaling[i, :]) && continue
precon = occursin("AMG Jacobi", solver.name) ? :amg_jacobi : occursin("AMG", solver.name) ? :amg : occursin("ILU", solver.name) ? :ilu : :none
linestyle = LINESTYLES[(solver.pkg, precon)]
l = lines!(Ns_, runtimes_scaling[i, :]; linewidth = 5, color = colors[i],
linestyle)
sc = scatter!(Ns_, runtimes_scaling[i, :]; markersize = 16, strokewidth = 2,
color = colors[i])
push!(ls, l)
push!(scs, sc)
push!(labels, solver.name)
end
axislegend(ax, [[l, sc] for (l, sc) in zip(ls, scs)], labels,
"Successful Solvers\n(Fastest to Slowest)";
framevisible=true, framewidth = STROKEWIDTH, orientation = :vertical,
titlesize = 20, labelsize = 16, position = :rb,
tellheight = true, tellwidth = false, patchsize = (40.0f0, 20.0f0))
axislegend(ax, [
LineElement(; linestyle = :solid, linewidth = 5),
LineElement(; linestyle = :dot, linewidth = 5),
LineElement(; linestyle = :dash, linewidth = 5),
LineElement(; linestyle = :dashdot, linewidth = 5),
], ["No Preconditioning", "AMG", "AMG Jacobi", "Incomplete LU"],
"Preconditioning"; framevisible=true, framewidth = STROKEWIDTH,
orientation = :vertical, titlesize = 20, labelsize = 16,
tellheight = true, tellwidth = true, patchsize = (40.0f0, 20.0f0),
position = :lt)
fig[0, :] = Label(fig,
"Brusselator 2D: Scaling of Jacobian-Free Nonlinear Solvers with Problem Size",
fontsize = 24, tellwidth = false, font = :bold)
return fig
end
endError: BoundsError: attempt to access 9-element Vector{NamedTuple{(:pkg, :n
ame, :alg)}} at index [[3, 7, 1, 5, 8, 4, 6, 2, 140618801602960]]save("brusselator_krylov_methods_scaling.svg", fig)CairoMakie.Screen{SVG}Work-Precision Diagram
In this section, we will generate the work-precision of the solvers. All solvers that can exploit sparsity will automatically do so.
solvers_all = [
(; pkg = :nonlinearsolve, name = "Default PolyAlg", solver = Dict(:alg => FastShortcutNonlinearPolyalg())),
(; pkg = :nonlinearsolve, name = "RobustMultiNewton (GMRES)", solver = Dict(:alg => RobustMultiNewton(; linsolve = KrylovJL_GMRES()))),
(; pkg = :nonlinearsolve, name = "Newton Raphson", solver = Dict(:alg => NewtonRaphson(; linsolve = nothing))),
(; pkg = :nonlinearsolve, name = "Newton Krylov", solver = Dict(:alg => NewtonRaphson(; linsolve = KrylovJL_GMRES()))),
(; pkg = :nonlinearsolve, name = "Trust Region", solver = Dict(:alg => TrustRegion())),
(; pkg = :nonlinearsolve, name = "TR Krylov", solver = Dict(:alg => TrustRegion(; linsolve = KrylovJL_GMRES()))),
(; pkg = :wrapper, name = "NR [NLsolve.jl]", solver = Dict(:alg => NLsolveJL(; method = :newton, autodiff = :forward))),
(; pkg = :wrapper, name = "TR [NLsolve.jl]", solver = Dict(:alg => NLsolveJL(; autodiff = :forward))),
(; pkg = :wrapper, name = "NR [Sundials]", solver = Dict(:alg => KINSOL())),
(; pkg = :wrapper, name = "Newton Krylov [Sundials]", solver = Dict(:alg => KINSOL(; linear_solver = :GMRES))),
(; pkg = :wrapper, name = "Mod. Powell [MINPACK]", solver = Dict(:alg => CMINPACK())),
];prob_wpd = generate_brusselator_problem(32; sparsity = TracerSparsityDetector())
abstols = 1.0 ./ 10 .^ (2:10)
reltols = 1.0 ./ 10 .^ (2:10)
function check_solver(prob, solver)
try
sol = solve(prob, solver.solver[:alg]; abstol = 1e-4, reltol = 1e-4,
maxiters = 10000)
err = norm(sol.resid, Inf)
if !SciMLBase.successful_retcode(sol.retcode)
Base.printstyled("[Warn] Solver $(solver.name) returned retcode $(sol.retcode) with an residual norm = $(norm(sol.resid)).\n";
color = :red)
return false
elseif err > 1e3
Base.printstyled("[Warn] Solver $(solver.name) had a very large residual (norm = $(norm(sol.resid))).\n";
color = :red)
return false
elseif isinf(err) || isnan(err)
Base.printstyled("[Warn] Solver $(solver.name) had a residual of $(err).\n";
color = :red)
return false
end
Base.printstyled("[Info] Solver $(solver.name) successfully solved the problem (norm = $(norm(sol.resid))).\n";
color = :green)
catch e
Base.printstyled("[Warn] Solver $(solver.name) threw an error: $e.\n"; color = :red)
return false
end
return true
end
function generate_wpset(prob, solvers)
# Finds the solvers that can solve the problem
successful_solvers = filter(solver -> check_solver(prob, solver), solvers)
return WorkPrecisionSet(prob, abstols, reltols,
getfield.(successful_solvers, :solver);
names = getfield.(successful_solvers, :name), numruns = 10, error_estimate = :l∞,
maxiters = 1000, verbose = true), successful_solvers
endgenerate_wpset (generic function with 1 method)wp_set, successful_solvers = generate_wpset(prob_wpd, solvers_all);[Warn] Solver Default PolyAlg threw an error: MethodError(Core.kwcall, ((fu
ll = false, alg = LinearAlgebra.DivideAndConquer()), LinearAlgebra.svd!, sp
arse([1, 2, 32, 33, 993, 1025, 1, 2, 3, 34, 994, 1026, 2, 3, 4, 35, 995, 10
27, 3, 4, 5, 36, 996, 1028, 4, 5, 6, 37, 997, 1029, 5, 6, 7, 38, 998, 1030,
6, 7, 8, 39, 999, 1031, 7, 8, 9, 40, 1000, 1032, 8, 9, 10, 41, 1001, 1033,
9, 10, 11, 42, 1002, 1034, 10, 11, 12, 43, 1003, 1035, 11, 12, 13, 44, 100
4, 1036, 12, 13, 14, 45, 1005, 1037, 13, 14, 15, 46, 1006, 1038, 14, 15, 16
, 47, 1007, 1039, 15, 16, 17, 48, 1008, 1040, 16, 17, 18, 49, 1009, 1041, 1
7, 18, 19, 50, 1010, 1042, 18, 19, 20, 51, 1011, 1043, 19, 20, 21, 52, 1012
, 1044, 20, 21, 22, 53, 1013, 1045, 21, 22, 23, 54, 1014, 1046, 22, 23, 24,
55, 1015, 1047, 23, 24, 25, 56, 1016, 1048, 24, 25, 26, 57, 1017, 1049, 25
, 26, 27, 58, 1018, 1050, 26, 27, 28, 59, 1019, 1051, 27, 28, 29, 60, 1020,
1052, 28, 29, 30, 61, 1021, 1053, 29, 30, 31, 62, 1022, 1054, 30, 31, 32,
63, 1023, 1055, 1, 31, 32, 64, 1024, 1056, 1, 33, 34, 64, 65, 1057, 2, 33,
34, 35, 66, 1058, 3, 34, 35, 36, 67, 1059, 4, 35, 36, 37, 68, 1060, 5, 36,
37, 38, 69, 1061, 6, 37, 38, 39, 70, 1062, 7, 38, 39, 40, 71, 1063, 8, 39,
40, 41, 72, 1064, 9, 40, 41, 42, 73, 1065, 10, 41, 42, 43, 74, 1066, 11, 42
, 43, 44, 75, 1067, 12, 43, 44, 45, 76, 1068, 13, 44, 45, 46, 77, 1069, 14,
45, 46, 47, 78, 1070, 15, 46, 47, 48, 79, 1071, 16, 47, 48, 49, 80, 1072,
17, 48, 49, 50, 81, 1073, 18, 49, 50, 51, 82, 1074, 19, 50, 51, 52, 83, 107
5, 20, 51, 52, 53, 84, 1076, 21, 52, 53, 54, 85, 1077, 22, 53, 54, 55, 86,
1078, 23, 54, 55, 56, 87, 1079, 24, 55, 56, 57, 88, 1080, 25, 56, 57, 58, 8
9, 1081, 26, 57, 58, 59, 90, 1082, 27, 58, 59, 60, 91, 1083, 28, 59, 60, 61
, 92, 1084, 29, 60, 61, 62, 93, 1085, 30, 61, 62, 63, 94, 1086, 31, 62, 63,
64, 95, 1087, 32, 33, 63, 64, 96, 1088, 33, 65, 66, 96, 97, 1089, 34, 65,
66, 67, 98, 1090, 35, 66, 67, 68, 99, 1091, 36, 67, 68, 69, 100, 1092, 37,
68, 69, 70, 101, 1093, 38, 69, 70, 71, 102, 1094, 39, 70, 71, 72, 103, 1095
, 40, 71, 72, 73, 104, 1096, 41, 72, 73, 74, 105, 1097, 42, 73, 74, 75, 106
, 1098, 43, 74, 75, 76, 107, 1099, 44, 75, 76, 77, 108, 1100, 45, 76, 77, 7
8, 109, 1101, 46, 77, 78, 79, 110, 1102, 47, 78, 79, 80, 111, 1103, 48, 79,
80, 81, 112, 1104, 49, 80, 81, 82, 113, 1105, 50, 81, 82, 83, 114, 1106, 5
1, 82, 83, 84, 115, 1107, 52, 83, 84, 85, 116, 1108, 53, 84, 85, 86, 117, 1
109, 54, 85, 86, 87, 118, 1110, 55, 86, 87, 88, 119, 1111, 56, 87, 88, 89,
120, 1112, 57, 88, 89, 90, 121, 1113, 58, 89, 90, 91, 122, 1114, 59, 90, 91
, 92, 123, 1115, 60, 91, 92, 93, 124, 1116, 61, 92, 93, 94, 125, 1117, 62,
93, 94, 95, 126, 1118, 63, 94, 95, 96, 127, 1119, 64, 65, 95, 96, 128, 1120
, 65, 97, 98, 128, 129, 1121, 66, 97, 98, 99, 130, 1122, 67, 98, 99, 100, 1
31, 1123, 68, 99, 100, 101, 132, 1124, 69, 100, 101, 102, 133, 1125, 70, 10
1, 102, 103, 134, 1126, 71, 102, 103, 104, 135, 1127, 72, 103, 104, 105, 13
6, 1128, 73, 104, 105, 106, 137, 1129, 74, 105, 106, 107, 138, 1130, 75, 10
6, 107, 108, 139, 1131, 76, 107, 108, 109, 140, 1132, 77, 108, 109, 110, 14
1, 1133, 78, 109, 110, 111, 142, 1134, 79, 110, 111, 112, 143, 1135, 80, 11
1, 112, 113, 144, 1136, 81, 112, 113, 114, 145, 1137, 82, 113, 114, 115, 14
6, 1138, 83, 114, 115, 116, 147, 1139, 84, 115, 116, 117, 148, 1140, 85, 11
6, 117, 118, 149, 1141, 86, 117, 118, 119, 150, 1142, 87, 118, 119, 120, 15
1, 1143, 88, 119, 120, 121, 152, 1144, 89, 120, 121, 122, 153, 1145, 90, 12
1, 122, 123, 154, 1146, 91, 122, 123, 124, 155, 1147, 92, 123, 124, 125, 15
6, 1148, 93, 124, 125, 126, 157, 1149, 94, 125, 126, 127, 158, 1150, 95, 12
6, 127, 128, 159, 1151, 96, 97, 127, 128, 160, 1152, 97, 129, 130, 160, 161
, 1153, 98, 129, 130, 131, 162, 1154, 99, 130, 131, 132, 163, 1155, 100, 13
1, 132, 133, 164, 1156, 101, 132, 133, 134, 165, 1157, 102, 133, 134, 135,
166, 1158, 103, 134, 135, 136, 167, 1159, 104, 135, 136, 137, 168, 1160, 10
5, 136, 137, 138, 169, 1161, 106, 137, 138, 139, 170, 1162, 107, 138, 139,
140, 171, 1163, 108, 139, 140, 141, 172, 1164, 109, 140, 141, 142, 173, 116
5, 110, 141, 142, 143, 174, 1166, 111, 142, 143, 144, 175, 1167, 112, 143,
144, 145, 176, 1168, 113, 144, 145, 146, 177, 1169, 114, 145, 146, 147, 178
, 1170, 115, 146, 147, 148, 179, 1171, 116, 147, 148, 149, 180, 1172, 117,
148, 149, 150, 181, 1173, 118, 149, 150, 151, 182, 1174, 119, 150, 151, 152
, 183, 1175, 120, 151, 152, 153, 184, 1176, 121, 152, 153, 154, 185, 1177,
122, 153, 154, 155, 186, 1178, 123, 154, 155, 156, 187, 1179, 124, 155, 156
, 157, 188, 1180, 125, 156, 157, 158, 189, 1181, 126, 157, 158, 159, 190, 1
182, 127, 158, 159, 160, 191, 1183, 128, 129, 159, 160, 192, 1184, 129, 161
, 162, 192, 193, 1185, 130, 161, 162, 163, 194, 1186, 131, 162, 163, 164, 1
95, 1187, 132, 163, 164, 165, 196, 1188, 133, 164, 165, 166, 197, 1189, 134
, 165, 166, 167, 198, 1190, 135, 166, 167, 168, 199, 1191, 136, 167, 168, 1
69, 200, 1192, 137, 168, 169, 170, 201, 1193, 138, 169, 170, 171, 202, 1194
, 139, 170, 171, 172, 203, 1195, 140, 171, 172, 173, 204, 1196, 141, 172, 1
73, 174, 205, 1197, 142, 173, 174, 175, 206, 1198, 143, 174, 175, 176, 207,
1199, 144, 175, 176, 177, 208, 1200, 145, 176, 177, 178, 209, 1201, 146, 1
77, 178, 179, 210, 1202, 147, 178, 179, 180, 211, 1203, 148, 179, 180, 181,
212, 1204, 149, 180, 181, 182, 213, 1205, 150, 181, 182, 183, 214, 1206, 1
51, 182, 183, 184, 215, 1207, 152, 183, 184, 185, 216, 1208, 153, 184, 185,
186, 217, 1209, 154, 185, 186, 187, 218, 1210, 155, 186, 187, 188, 219, 12
11, 156, 187, 188, 189, 220, 1212, 157, 188, 189, 190, 221, 1213, 158, 189,
190, 191, 222, 1214, 159, 190, 191, 192, 223, 1215, 160, 161, 191, 192, 22
4, 1216, 161, 193, 194, 224, 225, 1217, 162, 193, 194, 195, 226, 1218, 163,
194, 195, 196, 227, 1219, 164, 195, 196, 197, 228, 1220, 165, 196, 197, 19
8, 229, 1221, 166, 197, 198, 199, 230, 1222, 167, 198, 199, 200, 231, 1223,
168, 199, 200, 201, 232, 1224, 169, 200, 201, 202, 233, 1225, 170, 201, 20
2, 203, 234, 1226, 171, 202, 203, 204, 235, 1227, 172, 203, 204, 205, 236,
1228, 173, 204, 205, 206, 237, 1229, 174, 205, 206, 207, 238, 1230, 175, 20
6, 207, 208, 239, 1231, 176, 207, 208, 209, 240, 1232, 177, 208, 209, 210,
241, 1233, 178, 209, 210, 211, 242, 1234, 179, 210, 211, 212, 243, 1235, 18
0, 211, 212, 213, 244, 1236, 181, 212, 213, 214, 245, 1237, 182, 213, 214,
215, 246, 1238, 183, 214, 215, 216, 247, 1239, 184, 215, 216, 217, 248, 124
0, 185, 216, 217, 218, 249, 1241, 186, 217, 218, 219, 250, 1242, 187, 218,
219, 220, 251, 1243, 188, 219, 220, 221, 252, 1244, 189, 220, 221, 222, 253
, 1245, 190, 221, 222, 223, 254, 1246, 191, 222, 223, 224, 255, 1247, 192,
193, 223, 224, 256, 1248, 193, 225, 226, 256, 257, 1249, 194, 225, 226, 227
, 258, 1250, 195, 226, 227, 228, 259, 1251, 196, 227, 228, 229, 260, 1252,
197, 228, 229, 230, 261, 1253, 198, 229, 230, 231, 262, 1254, 199, 230, 231
, 232, 263, 1255, 200, 231, 232, 233, 264, 1256, 201, 232, 233, 234, 265, 1
257, 202, 233, 234, 235, 266, 1258, 203, 234, 235, 236, 267, 1259, 204, 235
, 236, 237, 268, 1260, 205, 236, 237, 238, 269, 1261, 206, 237, 238, 239, 2
70, 1262, 207, 238, 239, 240, 271, 1263, 208, 239, 240, 241, 272, 1264, 209
, 240, 241, 242, 273, 1265, 210, 241, 242, 243, 274, 1266, 211, 242, 243, 2
44, 275, 1267, 212, 243, 244, 245, 276, 1268, 213, 244, 245, 246, 277, 1269
, 214, 245, 246, 247, 278, 1270, 215, 246, 247, 248, 279, 1271, 216, 247, 2
48, 249, 280, 1272, 217, 248, 249, 250, 281, 1273, 218, 249, 250, 251, 282,
1274, 219, 250, 251, 252, 283, 1275, 220, 251, 252, 253, 284, 1276, 221, 2
52, 253, 254, 285, 1277, 222, 253, 254, 255, 286, 1278, 223, 254, 255, 256,
287, 1279, 224, 225, 255, 256, 288, 1280, 225, 257, 258, 288, 289, 1281, 2
26, 257, 258, 259, 290, 1282, 227, 258, 259, 260, 291, 1283, 228, 259, 260,
261, 292, 1284, 229, 260, 261, 262, 293, 1285, 230, 261, 262, 263, 294, 12
86, 231, 262, 263, 264, 295, 1287, 232, 263, 264, 265, 296, 1288, 233, 264,
265, 266, 297, 1289, 234, 265, 266, 267, 298, 1290, 235, 266, 267, 268, 29
9, 1291, 236, 267, 268, 269, 300, 1292, 237, 268, 269, 270, 301, 1293, 238,
269, 270, 271, 302, 1294, 239, 270, 271, 272, 303, 1295, 240, 271, 272, 27
3, 304, 1296, 241, 272, 273, 274, 305, 1297, 242, 273, 274, 275, 306, 1298,
243, 274, 275, 276, 307, 1299, 244, 275, 276, 277, 308, 1300, 245, 276, 27
7, 278, 309, 1301, 246, 277, 278, 279, 310, 1302, 247, 278, 279, 280, 311,
1303, 248, 279, 280, 281, 312, 1304, 249, 280, 281, 282, 313, 1305, 250, 28
1, 282, 283, 314, 1306, 251, 282, 283, 284, 315, 1307, 252, 283, 284, 285,
316, 1308, 253, 284, 285, 286, 317, 1309, 254, 285, 286, 287, 318, 1310, 25
5, 286, 287, 288, 319, 1311, 256, 257, 287, 288, 320, 1312, 257, 289, 290,
320, 321, 1313, 258, 289, 290, 291, 322, 1314, 259, 290, 291, 292, 323, 131
5, 260, 291, 292, 293, 324, 1316, 261, 292, 293, 294, 325, 1317, 262, 293,
294, 295, 326, 1318, 263, 294, 295, 296, 327, 1319, 264, 295, 296, 297, 328
, 1320, 265, 296, 297, 298, 329, 1321, 266, 297, 298, 299, 330, 1322, 267,
298, 299, 300, 331, 1323, 268, 299, 300, 301, 332, 1324, 269, 300, 301, 302
, 333, 1325, 270, 301, 302, 303, 334, 1326, 271, 302, 303, 304, 335, 1327,
272, 303, 304, 305, 336, 1328, 273, 304, 305, 306, 337, 1329, 274, 305, 306
, 307, 338, 1330, 275, 306, 307, 308, 339, 1331, 276, 307, 308, 309, 340, 1
332, 277, 308, 309, 310, 341, 1333, 278, 309, 310, 311, 342, 1334, 279, 310
, 311, 312, 343, 1335, 280, 311, 312, 313, 344, 1336, 281, 312, 313, 314, 3
45, 1337, 282, 313, 314, 315, 346, 1338, 283, 314, 315, 316, 347, 1339, 284
, 315, 316, 317, 348, 1340, 285, 316, 317, 318, 349, 1341, 286, 317, 318, 3
19, 350, 1342, 287, 318, 319, 320, 351, 1343, 288, 289, 319, 320, 352, 1344
, 289, 321, 322, 352, 353, 1345, 290, 321, 322, 323, 354, 1346, 291, 322, 3
23, 324, 355, 1347, 292, 323, 324, 325, 356, 1348, 293, 324, 325, 326, 357,
1349, 294, 325, 326, 327, 358, 1350, 295, 326, 327, 328, 359, 1351, 296, 3
27, 328, 329, 360, 1352, 297, 328, 329, 330, 361, 1353, 298, 329, 330, 331,
362, 1354, 299, 330, 331, 332, 363, 1355, 300, 331, 332, 333, 364, 1356, 3
01, 332, 333, 334, 365, 1357, 302, 333, 334, 335, 366, 1358, 303, 334, 335,
336, 367, 1359, 304, 335, 336, 337, 368, 1360, 305, 336, 337, 338, 369, 13
61, 306, 337, 338, 339, 370, 1362, 307, 338, 339, 340, 371, 1363, 308, 339,
340, 341, 372, 1364, 309, 340, 341, 342, 373, 1365, 310, 341, 342, 343, 37
4, 1366, 311, 342, 343, 344, 375, 1367, 312, 343, 344, 345, 376, 1368, 313,
344, 345, 346, 377, 1369, 314, 345, 346, 347, 378, 1370, 315, 346, 347, 34
8, 379, 1371, 316, 347, 348, 349, 380, 1372, 317, 348, 349, 350, 381, 1373,
318, 349, 350, 351, 382, 1374, 319, 350, 351, 352, 383, 1375, 320, 321, 35
1, 352, 384, 1376, 321, 353, 354, 384, 385, 1377, 322, 353, 354, 355, 386,
1378, 323, 354, 355, 356, 387, 1379, 324, 355, 356, 357, 388, 1380, 325, 35
6, 357, 358, 389, 1381, 326, 357, 358, 359, 390, 1382, 327, 358, 359, 360,
391, 1383, 328, 359, 360, 361, 392, 1384, 329, 360, 361, 362, 393, 1385, 33
0, 361, 362, 363, 394, 1386, 331, 362, 363, 364, 395, 1387, 332, 363, 364,
365, 396, 1388, 333, 364, 365, 366, 397, 1389, 334, 365, 366, 367, 398, 139
0, 335, 366, 367, 368, 399, 1391, 336, 367, 368, 369, 400, 1392, 337, 368,
369, 370, 401, 1393, 338, 369, 370, 371, 402, 1394, 339, 370, 371, 372, 403
, 1395, 340, 371, 372, 373, 404, 1396, 341, 372, 373, 374, 405, 1397, 342,
373, 374, 375, 406, 1398, 343, 374, 375, 376, 407, 1399, 344, 375, 376, 377
, 408, 1400, 345, 376, 377, 378, 409, 1401, 346, 377, 378, 379, 410, 1402,
347, 378, 379, 380, 411, 1403, 348, 379, 380, 381, 412, 1404, 349, 380, 381
, 382, 413, 1405, 350, 381, 382, 383, 414, 1406, 351, 382, 383, 384, 415, 1
407, 352, 353, 383, 384, 416, 1408, 353, 385, 386, 416, 417, 1409, 354, 385
, 386, 387, 418, 1410, 355, 386, 387, 388, 419, 1411, 356, 387, 388, 389, 4
20, 1412, 357, 388, 389, 390, 421, 1413, 358, 389, 390, 391, 422, 1414, 359
, 390, 391, 392, 423, 1415, 360, 391, 392, 393, 424, 1416, 361, 392, 393, 3
94, 425, 1417, 362, 393, 394, 395, 426, 1418, 363, 394, 395, 396, 427, 1419
, 364, 395, 396, 397, 428, 1420, 365, 396, 397, 398, 429, 1421, 366, 397, 3
98, 399, 430, 1422, 367, 398, 399, 400, 431, 1423, 368, 399, 400, 401, 432,
1424, 369, 400, 401, 402, 433, 1425, 370, 401, 402, 403, 434, 1426, 371, 4
02, 403, 404, 435, 1427, 372, 403, 404, 405, 436, 1428, 373, 404, 405, 406,
437, 1429, 374, 405, 406, 407, 438, 1430, 375, 406, 407, 408, 439, 1431, 3
76, 407, 408, 409, 440, 1432, 377, 408, 409, 410, 441, 1433, 378, 409, 410,
411, 442, 1434, 379, 410, 411, 412, 443, 1435, 380, 411, 412, 413, 444, 14
36, 381, 412, 413, 414, 445, 1437, 382, 413, 414, 415, 446, 1438, 383, 414,
415, 416, 447, 1439, 384, 385, 415, 416, 448, 1440, 385, 417, 418, 448, 44
9, 1441, 386, 417, 418, 419, 450, 1442, 387, 418, 419, 420, 451, 1443, 388,
419, 420, 421, 452, 1444, 389, 420, 421, 422, 453, 1445, 390, 421, 422, 42
3, 454, 1446, 391, 422, 423, 424, 455, 1447, 392, 423, 424, 425, 456, 1448,
393, 424, 425, 426, 457, 1449, 394, 425, 426, 427, 458, 1450, 395, 426, 42
7, 428, 459, 1451, 396, 427, 428, 429, 460, 1452, 397, 428, 429, 430, 461,
1453, 398, 429, 430, 431, 462, 1454, 399, 430, 431, 432, 463, 1455, 400, 43
1, 432, 433, 464, 1456, 401, 432, 433, 434, 465, 1457, 402, 433, 434, 435,
466, 1458, 403, 434, 435, 436, 467, 1459, 404, 435, 436, 437, 468, 1460, 40
5, 436, 437, 438, 469, 1461, 406, 437, 438, 439, 470, 1462, 407, 438, 439,
440, 471, 1463, 408, 439, 440, 441, 472, 1464, 409, 440, 441, 442, 473, 146
5, 410, 441, 442, 443, 474, 1466, 411, 442, 443, 444, 475, 1467, 412, 443,
444, 445, 476, 1468, 413, 444, 445, 446, 477, 1469, 414, 445, 446, 447, 478
, 1470, 415, 446, 447, 448, 479, 1471, 416, 417, 447, 448, 480, 1472, 417,
449, 450, 480, 481, 1473, 418, 449, 450, 451, 482, 1474, 419, 450, 451, 452
, 483, 1475, 420, 451, 452, 453, 484, 1476, 421, 452, 453, 454, 485, 1477,
422, 453, 454, 455, 486, 1478, 423, 454, 455, 456, 487, 1479, 424, 455, 456
, 457, 488, 1480, 425, 456, 457, 458, 489, 1481, 426, 457, 458, 459, 490, 1
482, 427, 458, 459, 460, 491, 1483, 428, 459, 460, 461, 492, 1484, 429, 460
, 461, 462, 493, 1485, 430, 461, 462, 463, 494, 1486, 431, 462, 463, 464, 4
95, 1487, 432, 463, 464, 465, 496, 1488, 433, 464, 465, 466, 497, 1489, 434
, 465, 466, 467, 498, 1490, 435, 466, 467, 468, 499, 1491, 436, 467, 468, 4
69, 500, 1492, 437, 468, 469, 470, 501, 1493, 438, 469, 470, 471, 502, 1494
, 439, 470, 471, 472, 503, 1495, 440, 471, 472, 473, 504, 1496, 441, 472, 4
73, 474, 505, 1497, 442, 473, 474, 475, 506, 1498, 443, 474, 475, 476, 507,
1499, 444, 475, 476, 477, 508, 1500, 445, 476, 477, 478, 509, 1501, 446, 4
77, 478, 479, 510, 1502, 447, 478, 479, 480, 511, 1503, 448, 449, 479, 480,
512, 1504, 449, 481, 482, 512, 513, 1505, 450, 481, 482, 483, 514, 1506, 4
51, 482, 483, 484, 515, 1507, 452, 483, 484, 485, 516, 1508, 453, 484, 485,
486, 517, 1509, 454, 485, 486, 487, 518, 1510, 455, 486, 487, 488, 519, 15
11, 456, 487, 488, 489, 520, 1512, 457, 488, 489, 490, 521, 1513, 458, 489,
490, 491, 522, 1514, 459, 490, 491, 492, 523, 1515, 460, 491, 492, 493, 52
4, 1516, 461, 492, 493, 494, 525, 1517, 462, 493, 494, 495, 526, 1518, 463,
494, 495, 496, 527, 1519, 464, 495, 496, 497, 528, 1520, 465, 496, 497, 49
8, 529, 1521, 466, 497, 498, 499, 530, 1522, 467, 498, 499, 500, 531, 1523,
468, 499, 500, 501, 532, 1524, 469, 500, 501, 502, 533, 1525, 470, 501, 50
2, 503, 534, 1526, 471, 502, 503, 504, 535, 1527, 472, 503, 504, 505, 536,
1528, 473, 504, 505, 506, 537, 1529, 474, 505, 506, 507, 538, 1530, 475, 50
6, 507, 508, 539, 1531, 476, 507, 508, 509, 540, 1532, 477, 508, 509, 510,
541, 1533, 478, 509, 510, 511, 542, 1534, 479, 510, 511, 512, 543, 1535, 48
0, 481, 511, 512, 544, 1536, 481, 513, 514, 544, 545, 1537, 482, 513, 514,
515, 546, 1538, 483, 514, 515, 516, 547, 1539, 484, 515, 516, 517, 548, 154
0, 485, 516, 517, 518, 549, 1541, 486, 517, 518, 519, 550, 1542, 487, 518,
519, 520, 551, 1543, 488, 519, 520, 521, 552, 1544, 489, 520, 521, 522, 553
, 1545, 490, 521, 522, 523, 554, 1546, 491, 522, 523, 524, 555, 1547, 492,
523, 524, 525, 556, 1548, 493, 524, 525, 526, 557, 1549, 494, 525, 526, 527
, 558, 1550, 495, 526, 527, 528, 559, 1551, 496, 527, 528, 529, 560, 1552,
497, 528, 529, 530, 561, 1553, 498, 529, 530, 531, 562, 1554, 499, 530, 531
, 532, 563, 1555, 500, 531, 532, 533, 564, 1556, 501, 532, 533, 534, 565, 1
557, 502, 533, 534, 535, 566, 1558, 503, 534, 535, 536, 567, 1559, 504, 535
, 536, 537, 568, 1560, 505, 536, 537, 538, 569, 1561, 506, 537, 538, 539, 5
70, 1562, 507, 538, 539, 540, 571, 1563, 508, 539, 540, 541, 572, 1564, 509
, 540, 541, 542, 573, 1565, 510, 541, 542, 543, 574, 1566, 511, 542, 543, 5
44, 575, 1567, 512, 513, 543, 544, 576, 1568, 513, 545, 546, 576, 577, 1569
, 514, 545, 546, 547, 578, 1570, 515, 546, 547, 548, 579, 1571, 516, 547, 5
48, 549, 580, 1572, 517, 548, 549, 550, 581, 1573, 518, 549, 550, 551, 582,
1574, 519, 550, 551, 552, 583, 1575, 520, 551, 552, 553, 584, 1576, 521, 5
52, 553, 554, 585, 1577, 522, 553, 554, 555, 586, 1578, 523, 554, 555, 556,
587, 1579, 524, 555, 556, 557, 588, 1580, 525, 556, 557, 558, 589, 1581, 5
26, 557, 558, 559, 590, 1582, 527, 558, 559, 560, 591, 1583, 528, 559, 560,
561, 592, 1584, 529, 560, 561, 562, 593, 1585, 530, 561, 562, 563, 594, 15
86, 531, 562, 563, 564, 595, 1587, 532, 563, 564, 565, 596, 1588, 533, 564,
565, 566, 597, 1589, 534, 565, 566, 567, 598, 1590, 535, 566, 567, 568, 59
9, 1591, 536, 567, 568, 569, 600, 1592, 537, 568, 569, 570, 601, 1593, 538,
569, 570, 571, 602, 1594, 539, 570, 571, 572, 603, 1595, 540, 571, 572, 57
3, 604, 1596, 541, 572, 573, 574, 605, 1597, 542, 573, 574, 575, 606, 1598,
543, 574, 575, 576, 607, 1599, 544, 545, 575, 576, 608, 1600, 545, 577, 57
8, 608, 609, 1601, 546, 577, 578, 579, 610, 1602, 547, 578, 579, 580, 611,
1603, 548, 579, 580, 581, 612, 1604, 549, 580, 581, 582, 613, 1605, 550, 58
1, 582, 583, 614, 1606, 551, 582, 583, 584, 615, 1607, 552, 583, 584, 585,
616, 1608, 553, 584, 585, 586, 617, 1609, 554, 585, 586, 587, 618, 1610, 55
5, 586, 587, 588, 619, 1611, 556, 587, 588, 589, 620, 1612, 557, 588, 589,
590, 621, 1613, 558, 589, 590, 591, 622, 1614, 559, 590, 591, 592, 623, 161
5, 560, 591, 592, 593, 624, 1616, 561, 592, 593, 594, 625, 1617, 562, 593,
594, 595, 626, 1618, 563, 594, 595, 596, 627, 1619, 564, 595, 596, 597, 628
, 1620, 565, 596, 597, 598, 629, 1621, 566, 597, 598, 599, 630, 1622, 567,
598, 599, 600, 631, 1623, 568, 599, 600, 601, 632, 1624, 569, 600, 601, 602
, 633, 1625, 570, 601, 602, 603, 634, 1626, 571, 602, 603, 604, 635, 1627,
572, 603, 604, 605, 636, 1628, 573, 604, 605, 606, 637, 1629, 574, 605, 606
, 607, 638, 1630, 575, 606, 607, 608, 639, 1631, 576, 577, 607, 608, 640, 1
632, 577, 609, 610, 640, 641, 1633, 578, 609, 610, 611, 642, 1634, 579, 610
, 611, 612, 643, 1635, 580, 611, 612, 613, 644, 1636, 581, 612, 613, 614, 6
45, 1637, 582, 613, 614, 615, 646, 1638, 583, 614, 615, 616, 647, 1639, 584
, 615, 616, 617, 648, 1640, 585, 616, 617, 618, 649, 1641, 586, 617, 618, 6
19, 650, 1642, 587, 618, 619, 620, 651, 1643, 588, 619, 620, 621, 652, 1644
, 589, 620, 621, 622, 653, 1645, 590, 621, 622, 623, 654, 1646, 591, 622, 6
23, 624, 655, 1647, 592, 623, 624, 625, 656, 1648, 593, 624, 625, 626, 657,
1649, 594, 625, 626, 627, 658, 1650, 595, 626, 627, 628, 659, 1651, 596, 6
27, 628, 629, 660, 1652, 597, 628, 629, 630, 661, 1653, 598, 629, 630, 631,
662, 1654, 599, 630, 631, 632, 663, 1655, 600, 631, 632, 633, 664, 1656, 6
01, 632, 633, 634, 665, 1657, 602, 633, 634, 635, 666, 1658, 603, 634, 635,
636, 667, 1659, 604, 635, 636, 637, 668, 1660, 605, 636, 637, 638, 669, 16
61, 606, 637, 638, 639, 670, 1662, 607, 638, 639, 640, 671, 1663, 608, 609,
639, 640, 672, 1664, 609, 641, 642, 672, 673, 1665, 610, 641, 642, 643, 67
4, 1666, 611, 642, 643, 644, 675, 1667, 612, 643, 644, 645, 676, 1668, 613,
644, 645, 646, 677, 1669, 614, 645, 646, 647, 678, 1670, 615, 646, 647, 64
8, 679, 1671, 616, 647, 648, 649, 680, 1672, 617, 648, 649, 650, 681, 1673,
618, 649, 650, 651, 682, 1674, 619, 650, 651, 652, 683, 1675, 620, 651, 65
2, 653, 684, 1676, 621, 652, 653, 654, 685, 1677, 622, 653, 654, 655, 686,
1678, 623, 654, 655, 656, 687, 1679, 624, 655, 656, 657, 688, 1680, 625, 65
6, 657, 658, 689, 1681, 626, 657, 658, 659, 690, 1682, 627, 658, 659, 660,
691, 1683, 628, 659, 660, 661, 692, 1684, 629, 660, 661, 662, 693, 1685, 63
0, 661, 662, 663, 694, 1686, 631, 662, 663, 664, 695, 1687, 632, 663, 664,
665, 696, 1688, 633, 664, 665, 666, 697, 1689, 634, 665, 666, 667, 698, 169
0, 635, 666, 667, 668, 699, 1691, 636, 667, 668, 669, 700, 1692, 637, 668,
669, 670, 701, 1693, 638, 669, 670, 671, 702, 1694, 639, 670, 671, 672, 703
, 1695, 640, 641, 671, 672, 704, 1696, 641, 673, 674, 704, 705, 1697, 642,
673, 674, 675, 706, 1698, 643, 674, 675, 676, 707, 1699, 644, 675, 676, 677
, 708, 1700, 645, 676, 677, 678, 709, 1701, 646, 677, 678, 679, 710, 1702,
647, 678, 679, 680, 711, 1703, 648, 679, 680, 681, 712, 1704, 649, 680, 681
, 682, 713, 1705, 650, 681, 682, 683, 714, 1706, 651, 682, 683, 684, 715, 1
707, 652, 683, 684, 685, 716, 1708, 653, 684, 685, 686, 717, 1709, 654, 685
, 686, 687, 718, 1710, 655, 686, 687, 688, 719, 1711, 656, 687, 688, 689, 7
20, 1712, 657, 688, 689, 690, 721, 1713, 658, 689, 690, 691, 722, 1714, 659
, 690, 691, 692, 723, 1715, 660, 691, 692, 693, 724, 1716, 661, 692, 693, 6
94, 725, 1717, 662, 693, 694, 695, 726, 1718, 663, 694, 695, 696, 727, 1719
, 664, 695, 696, 697, 728, 1720, 665, 696, 697, 698, 729, 1721, 666, 697, 6
98, 699, 730, 1722, 667, 698, 699, 700, 731, 1723, 668, 699, 700, 701, 732,
1724, 669, 700, 701, 702, 733, 1725, 670, 701, 702, 703, 734, 1726, 671, 7
02, 703, 704, 735, 1727, 672, 673, 703, 704, 736, 1728, 673, 705, 706, 736,
737, 1729, 674, 705, 706, 707, 738, 1730, 675, 706, 707, 708, 739, 1731, 6
76, 707, 708, 709, 740, 1732, 677, 708, 709, 710, 741, 1733, 678, 709, 710,
711, 742, 1734, 679, 710, 711, 712, 743, 1735, 680, 711, 712, 713, 744, 17
36, 681, 712, 713, 714, 745, 1737, 682, 713, 714, 715, 746, 1738, 683, 714,
715, 716, 747, 1739, 684, 715, 716, 717, 748, 1740, 685, 716, 717, 718, 74
9, 1741, 686, 717, 718, 719, 750, 1742, 687, 718, 719, 720, 751, 1743, 688,
719, 720, 721, 752, 1744, 689, 720, 721, 722, 753, 1745, 690, 721, 722, 72
3, 754, 1746, 691, 722, 723, 724, 755, 1747, 692, 723, 724, 725, 756, 1748,
693, 724, 725, 726, 757, 1749, 694, 725, 726, 727, 758, 1750, 695, 726, 72
7, 728, 759, 1751, 696, 727, 728, 729, 760, 1752, 697, 728, 729, 730, 761,
1753, 698, 729, 730, 731, 762, 1754, 699, 730, 731, 732, 763, 1755, 700, 73
1, 732, 733, 764, 1756, 701, 732, 733, 734, 765, 1757, 702, 733, 734, 735,
766, 1758, 703, 734, 735, 736, 767, 1759, 704, 705, 735, 736, 768, 1760, 70
5, 737, 738, 768, 769, 1761, 706, 737, 738, 739, 770, 1762, 707, 738, 739,
740, 771, 1763, 708, 739, 740, 741, 772, 1764, 709, 740, 741, 742, 773, 176
5, 710, 741, 742, 743, 774, 1766, 711, 742, 743, 744, 775, 1767, 712, 743,
744, 745, 776, 1768, 713, 744, 745, 746, 777, 1769, 714, 745, 746, 747, 778
, 1770, 715, 746, 747, 748, 779, 1771, 716, 747, 748, 749, 780, 1772, 717,
748, 749, 750, 781, 1773, 718, 749, 750, 751, 782, 1774, 719, 750, 751, 752
, 783, 1775, 720, 751, 752, 753, 784, 1776, 721, 752, 753, 754, 785, 1777,
722, 753, 754, 755, 786, 1778, 723, 754, 755, 756, 787, 1779, 724, 755, 756
, 757, 788, 1780, 725, 756, 757, 758, 789, 1781, 726, 757, 758, 759, 790, 1
782, 727, 758, 759, 760, 791, 1783, 728, 759, 760, 761, 792, 1784, 729, 760
, 761, 762, 793, 1785, 730, 761, 762, 763, 794, 1786, 731, 762, 763, 764, 7
95, 1787, 732, 763, 764, 765, 796, 1788, 733, 764, 765, 766, 797, 1789, 734
, 765, 766, 767, 798, 1790, 735, 766, 767, 768, 799, 1791, 736, 737, 767, 7
68, 800, 1792, 737, 769, 770, 800, 801, 1793, 738, 769, 770, 771, 802, 1794
, 739, 770, 771, 772, 803, 1795, 740, 771, 772, 773, 804, 1796, 741, 772, 7
73, 774, 805, 1797, 742, 773, 774, 775, 806, 1798, 743, 774, 775, 776, 807,
1799, 744, 775, 776, 777, 808, 1800, 745, 776, 777, 778, 809, 1801, 746, 7
77, 778, 779, 810, 1802, 747, 778, 779, 780, 811, 1803, 748, 779, 780, 781,
812, 1804, 749, 780, 781, 782, 813, 1805, 750, 781, 782, 783, 814, 1806, 7
51, 782, 783, 784, 815, 1807, 752, 783, 784, 785, 816, 1808, 753, 784, 785,
786, 817, 1809, 754, 785, 786, 787, 818, 1810, 755, 786, 787, 788, 819, 18
11, 756, 787, 788, 789, 820, 1812, 757, 788, 789, 790, 821, 1813, 758, 789,
790, 791, 822, 1814, 759, 790, 791, 792, 823, 1815, 760, 791, 792, 793, 82
4, 1816, 761, 792, 793, 794, 825, 1817, 762, 793, 794, 795, 826, 1818, 763,
794, 795, 796, 827, 1819, 764, 795, 796, 797, 828, 1820, 765, 796, 797, 79
8, 829, 1821, 766, 797, 798, 799, 830, 1822, 767, 798, 799, 800, 831, 1823,
768, 769, 799, 800, 832, 1824, 769, 801, 802, 832, 833, 1825, 770, 801, 80
2, 803, 834, 1826, 771, 802, 803, 804, 835, 1827, 772, 803, 804, 805, 836,
1828, 773, 804, 805, 806, 837, 1829, 774, 805, 806, 807, 838, 1830, 775, 80
6, 807, 808, 839, 1831, 776, 807, 808, 809, 840, 1832, 777, 808, 809, 810,
841, 1833, 778, 809, 810, 811, 842, 1834, 779, 810, 811, 812, 843, 1835, 78
0, 811, 812, 813, 844, 1836, 781, 812, 813, 814, 845, 1837, 782, 813, 814,
815, 846, 1838, 783, 814, 815, 816, 847, 1839, 784, 815, 816, 817, 848, 184
0, 785, 816, 817, 818, 849, 1841, 786, 817, 818, 819, 850, 1842, 787, 818,
819, 820, 851, 1843, 788, 819, 820, 821, 852, 1844, 789, 820, 821, 822, 853
, 1845, 790, 821, 822, 823, 854, 1846, 791, 822, 823, 824, 855, 1847, 792,
823, 824, 825, 856, 1848, 793, 824, 825, 826, 857, 1849, 794, 825, 826, 827
, 858, 1850, 795, 826, 827, 828, 859, 1851, 796, 827, 828, 829, 860, 1852,
797, 828, 829, 830, 861, 1853, 798, 829, 830, 831, 862, 1854, 799, 830, 831
, 832, 863, 1855, 800, 801, 831, 832, 864, 1856, 801, 833, 834, 864, 865, 1
857, 802, 833, 834, 835, 866, 1858, 803, 834, 835, 836, 867, 1859, 804, 835
, 836, 837, 868, 1860, 805, 836, 837, 838, 869, 1861, 806, 837, 838, 839, 8
70, 1862, 807, 838, 839, 840, 871, 1863, 808, 839, 840, 841, 872, 1864, 809
, 840, 841, 842, 873, 1865, 810, 841, 842, 843, 874, 1866, 811, 842, 843, 8
44, 875, 1867, 812, 843, 844, 845, 876, 1868, 813, 844, 845, 846, 877, 1869
, 814, 845, 846, 847, 878, 1870, 815, 846, 847, 848, 879, 1871, 816, 847, 8
48, 849, 880, 1872, 817, 848, 849, 850, 881, 1873, 818, 849, 850, 851, 882,
1874, 819, 850, 851, 852, 883, 1875, 820, 851, 852, 853, 884, 1876, 821, 8
52, 853, 854, 885, 1877, 822, 853, 854, 855, 886, 1878, 823, 854, 855, 856,
887, 1879, 824, 855, 856, 857, 888, 1880, 825, 856, 857, 858, 889, 1881, 8
26, 857, 858, 859, 890, 1882, 827, 858, 859, 860, 891, 1883, 828, 859, 860,
861, 892, 1884, 829, 860, 861, 862, 893, 1885, 830, 861, 862, 863, 894, 18
86, 831, 862, 863, 864, 895, 1887, 832, 833, 863, 864, 896, 1888, 833, 865,
866, 896, 897, 1889, 834, 865, 866, 867, 898, 1890, 835, 866, 867, 868, 89
9, 1891, 836, 867, 868, 869, 900, 1892, 837, 868, 869, 870, 901, 1893, 838,
869, 870, 871, 902, 1894, 839, 870, 871, 872, 903, 1895, 840, 871, 872, 87
3, 904, 1896, 841, 872, 873, 874, 905, 1897, 842, 873, 874, 875, 906, 1898,
843, 874, 875, 876, 907, 1899, 844, 875, 876, 877, 908, 1900, 845, 876, 87
7, 878, 909, 1901, 846, 877, 878, 879, 910, 1902, 847, 878, 879, 880, 911,
1903, 848, 879, 880, 881, 912, 1904, 849, 880, 881, 882, 913, 1905, 850, 88
1, 882, 883, 914, 1906, 851, 882, 883, 884, 915, 1907, 852, 883, 884, 885,
916, 1908, 853, 884, 885, 886, 917, 1909, 854, 885, 886, 887, 918, 1910, 85
5, 886, 887, 888, 919, 1911, 856, 887, 888, 889, 920, 1912, 857, 888, 889,
890, 921, 1913, 858, 889, 890, 891, 922, 1914, 859, 890, 891, 892, 923, 191
5, 860, 891, 892, 893, 924, 1916, 861, 892, 893, 894, 925, 1917, 862, 893,
894, 895, 926, 1918, 863, 894, 895, 896, 927, 1919, 864, 865, 895, 896, 928
, 1920, 865, 897, 898, 928, 929, 1921, 866, 897, 898, 899, 930, 1922, 867,
898, 899, 900, 931, 1923, 868, 899, 900, 901, 932, 1924, 869, 900, 901, 902
, 933, 1925, 870, 901, 902, 903, 934, 1926, 871, 902, 903, 904, 935, 1927,
872, 903, 904, 905, 936, 1928, 873, 904, 905, 906, 937, 1929, 874, 905, 906
, 907, 938, 1930, 875, 906, 907, 908, 939, 1931, 876, 907, 908, 909, 940, 1
932, 877, 908, 909, 910, 941, 1933, 878, 909, 910, 911, 942, 1934, 879, 910
, 911, 912, 943, 1935, 880, 911, 912, 913, 944, 1936, 881, 912, 913, 914, 9
45, 1937, 882, 913, 914, 915, 946, 1938, 883, 914, 915, 916, 947, 1939, 884
, 915, 916, 917, 948, 1940, 885, 916, 917, 918, 949, 1941, 886, 917, 918, 9
19, 950, 1942, 887, 918, 919, 920, 951, 1943, 888, 919, 920, 921, 952, 1944
, 889, 920, 921, 922, 953, 1945, 890, 921, 922, 923, 954, 1946, 891, 922, 9
23, 924, 955, 1947, 892, 923, 924, 925, 956, 1948, 893, 924, 925, 926, 957,
1949, 894, 925, 926, 927, 958, 1950, 895, 926, 927, 928, 959, 1951, 896, 8
97, 927, 928, 960, 1952, 897, 929, 930, 960, 961, 1953, 898, 929, 930, 931,
962, 1954, 899, 930, 931, 932, 963, 1955, 900, 931, 932, 933, 964, 1956, 9
01, 932, 933, 934, 965, 1957, 902, 933, 934, 935, 966, 1958, 903, 934, 935,
936, 967, 1959, 904, 935, 936, 937, 968, 1960, 905, 936, 937, 938, 969, 19
61, 906, 937, 938, 939, 970, 1962, 907, 938, 939, 940, 971, 1963, 908, 939,
940, 941, 972, 1964, 909, 940, 941, 942, 973, 1965, 910, 941, 942, 943, 97
4, 1966, 911, 942, 943, 944, 975, 1967, 912, 943, 944, 945, 976, 1968, 913,
944, 945, 946, 977, 1969, 914, 945, 946, 947, 978, 1970, 915, 946, 947, 94
8, 979, 1971, 916, 947, 948, 949, 980, 1972, 917, 948, 949, 950, 981, 1973,
918, 949, 950, 951, 982, 1974, 919, 950, 951, 952, 983, 1975, 920, 951, 95
2, 953, 984, 1976, 921, 952, 953, 954, 985, 1977, 922, 953, 954, 955, 986,
1978, 923, 954, 955, 956, 987, 1979, 924, 955, 956, 957, 988, 1980, 925, 95
6, 957, 958, 989, 1981, 926, 957, 958, 959, 990, 1982, 927, 958, 959, 960,
991, 1983, 928, 929, 959, 960, 992, 1984, 929, 961, 962, 992, 993, 1985, 93
0, 961, 962, 963, 994, 1986, 931, 962, 963, 964, 995, 1987, 932, 963, 964,
965, 996, 1988, 933, 964, 965, 966, 997, 1989, 934, 965, 966, 967, 998, 199
0, 935, 966, 967, 968, 999, 1991, 936, 967, 968, 969, 1000, 1992, 937, 968,
969, 970, 1001, 1993, 938, 969, 970, 971, 1002, 1994, 939, 970, 971, 972,
1003, 1995, 940, 971, 972, 973, 1004, 1996, 941, 972, 973, 974, 1005, 1997,
942, 973, 974, 975, 1006, 1998, 943, 974, 975, 976, 1007, 1999, 944, 975,
976, 977, 1008, 2000, 945, 976, 977, 978, 1009, 2001, 946, 977, 978, 979, 1
010, 2002, 947, 978, 979, 980, 1011, 2003, 948, 979, 980, 981, 1012, 2004,
949, 980, 981, 982, 1013, 2005, 950, 981, 982, 983, 1014, 2006, 951, 982, 9
83, 984, 1015, 2007, 952, 983, 984, 985, 1016, 2008, 953, 984, 985, 986, 10
17, 2009, 954, 985, 986, 987, 1018, 2010, 955, 986, 987, 988, 1019, 2011, 9
56, 987, 988, 989, 1020, 2012, 957, 988, 989, 990, 1021, 2013, 958, 989, 99
0, 991, 1022, 2014, 959, 990, 991, 992, 1023, 2015, 960, 961, 991, 992, 102
4, 2016, 1, 961, 993, 994, 1024, 2017, 2, 962, 993, 994, 995, 2018, 3, 963,
994, 995, 996, 2019, 4, 964, 995, 996, 997, 2020, 5, 965, 996, 997, 998, 2
021, 6, 966, 997, 998, 999, 2022, 7, 967, 998, 999, 1000, 2023, 8, 968, 999
, 1000, 1001, 2024, 9, 969, 1000, 1001, 1002, 2025, 10, 970, 1001, 1002, 10
03, 2026, 11, 971, 1002, 1003, 1004, 2027, 12, 972, 1003, 1004, 1005, 2028,
13, 973, 1004, 1005, 1006, 2029, 14, 974, 1005, 1006, 1007, 2030, 15, 975,
1006, 1007, 1008, 2031, 16, 976, 1007, 1008, 1009, 2032, 17, 977, 1008, 10
09, 1010, 2033, 18, 978, 1009, 1010, 1011, 2034, 19, 979, 1010, 1011, 1012,
2035, 20, 980, 1011, 1012, 1013, 2036, 21, 981, 1012, 1013, 1014, 2037, 22
, 982, 1013, 1014, 1015, 2038, 23, 983, 1014, 1015, 1016, 2039, 24, 984, 10
15, 1016, 1017, 2040, 25, 985, 1016, 1017, 1018, 2041, 26, 986, 1017, 1018,
1019, 2042, 27, 987, 1018, 1019, 1020, 2043, 28, 988, 1019, 1020, 1021, 20
44, 29, 989, 1020, 1021, 1022, 2045, 30, 990, 1021, 1022, 1023, 2046, 31, 9
91, 1022, 1023, 1024, 2047, 32, 992, 993, 1023, 1024, 2048, 1, 1025, 1026,
1056, 1057, 2017, 2, 1025, 1026, 1027, 1058, 2018, 3, 1026, 1027, 1028, 105
9, 2019, 4, 1027, 1028, 1029, 1060, 2020, 5, 1028, 1029, 1030, 1061, 2021,
6, 1029, 1030, 1031, 1062, 2022, 7, 1030, 1031, 1032, 1063, 2023, 8, 1031,
1032, 1033, 1064, 2024, 9, 1032, 1033, 1034, 1065, 2025, 10, 1033, 1034, 10
35, 1066, 2026, 11, 1034, 1035, 1036, 1067, 2027, 12, 1035, 1036, 1037, 106
8, 2028, 13, 1036, 1037, 1038, 1069, 2029, 14, 1037, 1038, 1039, 1070, 2030
, 15, 1038, 1039, 1040, 1071, 2031, 16, 1039, 1040, 1041, 1072, 2032, 17, 1
040, 1041, 1042, 1073, 2033, 18, 1041, 1042, 1043, 1074, 2034, 19, 1042, 10
43, 1044, 1075, 2035, 20, 1043, 1044, 1045, 1076, 2036, 21, 1044, 1045, 104
6, 1077, 2037, 22, 1045, 1046, 1047, 1078, 2038, 23, 1046, 1047, 1048, 1079
, 2039, 24, 1047, 1048, 1049, 1080, 2040, 25, 1048, 1049, 1050, 1081, 2041,
26, 1049, 1050, 1051, 1082, 2042, 27, 1050, 1051, 1052, 1083, 2043, 28, 10
51, 1052, 1053, 1084, 2044, 29, 1052, 1053, 1054, 1085, 2045, 30, 1053, 105
4, 1055, 1086, 2046, 31, 1054, 1055, 1056, 1087, 2047, 32, 1025, 1055, 1056
, 1088, 2048, 33, 1025, 1057, 1058, 1088, 1089, 34, 1026, 1057, 1058, 1059,
1090, 35, 1027, 1058, 1059, 1060, 1091, 36, 1028, 1059, 1060, 1061, 1092,
37, 1029, 1060, 1061, 1062, 1093, 38, 1030, 1061, 1062, 1063, 1094, 39, 103
1, 1062, 1063, 1064, 1095, 40, 1032, 1063, 1064, 1065, 1096, 41, 1033, 1064
, 1065, 1066, 1097, 42, 1034, 1065, 1066, 1067, 1098, 43, 1035, 1066, 1067,
1068, 1099, 44, 1036, 1067, 1068, 1069, 1100, 45, 1037, 1068, 1069, 1070,
1101, 46, 1038, 1069, 1070, 1071, 1102, 47, 1039, 1070, 1071, 1072, 1103, 4
8, 1040, 1071, 1072, 1073, 1104, 49, 1041, 1072, 1073, 1074, 1105, 50, 1042
, 1073, 1074, 1075, 1106, 51, 1043, 1074, 1075, 1076, 1107, 52, 1044, 1075,
1076, 1077, 1108, 53, 1045, 1076, 1077, 1078, 1109, 54, 1046, 1077, 1078,
1079, 1110, 55, 1047, 1078, 1079, 1080, 1111, 56, 1048, 1079, 1080, 1081, 1
112, 57, 1049, 1080, 1081, 1082, 1113, 58, 1050, 1081, 1082, 1083, 1114, 59
, 1051, 1082, 1083, 1084, 1115, 60, 1052, 1083, 1084, 1085, 1116, 61, 1053,
1084, 1085, 1086, 1117, 62, 1054, 1085, 1086, 1087, 1118, 63, 1055, 1086,
1087, 1088, 1119, 64, 1056, 1057, 1087, 1088, 1120, 65, 1057, 1089, 1090, 1
120, 1121, 66, 1058, 1089, 1090, 1091, 1122, 67, 1059, 1090, 1091, 1092, 11
23, 68, 1060, 1091, 1092, 1093, 1124, 69, 1061, 1092, 1093, 1094, 1125, 70,
1062, 1093, 1094, 1095, 1126, 71, 1063, 1094, 1095, 1096, 1127, 72, 1064,
1095, 1096, 1097, 1128, 73, 1065, 1096, 1097, 1098, 1129, 74, 1066, 1097, 1
098, 1099, 1130, 75, 1067, 1098, 1099, 1100, 1131, 76, 1068, 1099, 1100, 11
01, 1132, 77, 1069, 1100, 1101, 1102, 1133, 78, 1070, 1101, 1102, 1103, 113
4, 79, 1071, 1102, 1103, 1104, 1135, 80, 1072, 1103, 1104, 1105, 1136, 81,
1073, 1104, 1105, 1106, 1137, 82, 1074, 1105, 1106, 1107, 1138, 83, 1075, 1
106, 1107, 1108, 1139, 84, 1076, 1107, 1108, 1109, 1140, 85, 1077, 1108, 11
09, 1110, 1141, 86, 1078, 1109, 1110, 1111, 1142, 87, 1079, 1110, 1111, 111
2, 1143, 88, 1080, 1111, 1112, 1113, 1144, 89, 1081, 1112, 1113, 1114, 1145
, 90, 1082, 1113, 1114, 1115, 1146, 91, 1083, 1114, 1115, 1116, 1147, 92, 1
084, 1115, 1116, 1117, 1148, 93, 1085, 1116, 1117, 1118, 1149, 94, 1086, 11
17, 1118, 1119, 1150, 95, 1087, 1118, 1119, 1120, 1151, 96, 1088, 1089, 111
9, 1120, 1152, 97, 1089, 1121, 1122, 1152, 1153, 98, 1090, 1121, 1122, 1123
, 1154, 99, 1091, 1122, 1123, 1124, 1155, 100, 1092, 1123, 1124, 1125, 1156
, 101, 1093, 1124, 1125, 1126, 1157, 102, 1094, 1125, 1126, 1127, 1158, 103
, 1095, 1126, 1127, 1128, 1159, 104, 1096, 1127, 1128, 1129, 1160, 105, 109
7, 1128, 1129, 1130, 1161, 106, 1098, 1129, 1130, 1131, 1162, 107, 1099, 11
30, 1131, 1132, 1163, 108, 1100, 1131, 1132, 1133, 1164, 109, 1101, 1132, 1
133, 1134, 1165, 110, 1102, 1133, 1134, 1135, 1166, 111, 1103, 1134, 1135,
1136, 1167, 112, 1104, 1135, 1136, 1137, 1168, 113, 1105, 1136, 1137, 1138,
1169, 114, 1106, 1137, 1138, 1139, 1170, 115, 1107, 1138, 1139, 1140, 1171
, 116, 1108, 1139, 1140, 1141, 1172, 117, 1109, 1140, 1141, 1142, 1173, 118
, 1110, 1141, 1142, 1143, 1174, 119, 1111, 1142, 1143, 1144, 1175, 120, 111
2, 1143, 1144, 1145, 1176, 121, 1113, 1144, 1145, 1146, 1177, 122, 1114, 11
45, 1146, 1147, 1178, 123, 1115, 1146, 1147, 1148, 1179, 124, 1116, 1147, 1
148, 1149, 1180, 125, 1117, 1148, 1149, 1150, 1181, 126, 1118, 1149, 1150,
1151, 1182, 127, 1119, 1150, 1151, 1152, 1183, 128, 1120, 1121, 1151, 1152,
1184, 129, 1121, 1153, 1154, 1184, 1185, 130, 1122, 1153, 1154, 1155, 1186
, 131, 1123, 1154, 1155, 1156, 1187, 132, 1124, 1155, 1156, 1157, 1188, 133
, 1125, 1156, 1157, 1158, 1189, 134, 1126, 1157, 1158, 1159, 1190, 135, 112
7, 1158, 1159, 1160, 1191, 136, 1128, 1159, 1160, 1161, 1192, 137, 1129, 11
60, 1161, 1162, 1193, 138, 1130, 1161, 1162, 1163, 1194, 139, 1131, 1162, 1
163, 1164, 1195, 140, 1132, 1163, 1164, 1165, 1196, 141, 1133, 1164, 1165,
1166, 1197, 142, 1134, 1165, 1166, 1167, 1198, 143, 1135, 1166, 1167, 1168,
1199, 144, 1136, 1167, 1168, 1169, 1200, 145, 1137, 1168, 1169, 1170, 1201
, 146, 1138, 1169, 1170, 1171, 1202, 147, 1139, 1170, 1171, 1172, 1203, 148
, 1140, 1171, 1172, 1173, 1204, 149, 1141, 1172, 1173, 1174, 1205, 150, 114
2, 1173, 1174, 1175, 1206, 151, 1143, 1174, 1175, 1176, 1207, 152, 1144, 11
75, 1176, 1177, 1208, 153, 1145, 1176, 1177, 1178, 1209, 154, 1146, 1177, 1
178, 1179, 1210, 155, 1147, 1178, 1179, 1180, 1211, 156, 1148, 1179, 1180,
1181, 1212, 157, 1149, 1180, 1181, 1182, 1213, 158, 1150, 1181, 1182, 1183,
1214, 159, 1151, 1182, 1183, 1184, 1215, 160, 1152, 1153, 1183, 1184, 1216
, 161, 1153, 1185, 1186, 1216, 1217, 162, 1154, 1185, 1186, 1187, 1218, 163
, 1155, 1186, 1187, 1188, 1219, 164, 1156, 1187, 1188, 1189, 1220, 165, 115
7, 1188, 1189, 1190, 1221, 166, 1158, 1189, 1190, 1191, 1222, 167, 1159, 11
90, 1191, 1192, 1223, 168, 1160, 1191, 1192, 1193, 1224, 169, 1161, 1192, 1
193, 1194, 1225, 170, 1162, 1193, 1194, 1195, 1226, 171, 1163, 1194, 1195,
1196, 1227, 172, 1164, 1195, 1196, 1197, 1228, 173, 1165, 1196, 1197, 1198,
1229, 174, 1166, 1197, 1198, 1199, 1230, 175, 1167, 1198, 1199, 1200, 1231
, 176, 1168, 1199, 1200, 1201, 1232, 177, 1169, 1200, 1201, 1202, 1233, 178
, 1170, 1201, 1202, 1203, 1234, 179, 1171, 1202, 1203, 1204, 1235, 180, 117
2, 1203, 1204, 1205, 1236, 181, 1173, 1204, 1205, 1206, 1237, 182, 1174, 12
05, 1206, 1207, 1238, 183, 1175, 1206, 1207, 1208, 1239, 184, 1176, 1207, 1
208, 1209, 1240, 185, 1177, 1208, 1209, 1210, 1241, 186, 1178, 1209, 1210,
1211, 1242, 187, 1179, 1210, 1211, 1212, 1243, 188, 1180, 1211, 1212, 1213,
1244, 189, 1181, 1212, 1213, 1214, 1245, 190, 1182, 1213, 1214, 1215, 1246
, 191, 1183, 1214, 1215, 1216, 1247, 192, 1184, 1185, 1215, 1216, 1248, 193
, 1185, 1217, 1218, 1248, 1249, 194, 1186, 1217, 1218, 1219, 1250, 195, 118
7, 1218, 1219, 1220, 1251, 196, 1188, 1219, 1220, 1221, 1252, 197, 1189, 12
20, 1221, 1222, 1253, 198, 1190, 1221, 1222, 1223, 1254, 199, 1191, 1222, 1
223, 1224, 1255, 200, 1192, 1223, 1224, 1225, 1256, 201, 1193, 1224, 1225,
1226, 1257, 202, 1194, 1225, 1226, 1227, 1258, 203, 1195, 1226, 1227, 1228,
1259, 204, 1196, 1227, 1228, 1229, 1260, 205, 1197, 1228, 1229, 1230, 1261
, 206, 1198, 1229, 1230, 1231, 1262, 207, 1199, 1230, 1231, 1232, 1263, 208
, 1200, 1231, 1232, 1233, 1264, 209, 1201, 1232, 1233, 1234, 1265, 210, 120
2, 1233, 1234, 1235, 1266, 211, 1203, 1234, 1235, 1236, 1267, 212, 1204, 12
35, 1236, 1237, 1268, 213, 1205, 1236, 1237, 1238, 1269, 214, 1206, 1237, 1
238, 1239, 1270, 215, 1207, 1238, 1239, 1240, 1271, 216, 1208, 1239, 1240,
1241, 1272, 217, 1209, 1240, 1241, 1242, 1273, 218, 1210, 1241, 1242, 1243,
1274, 219, 1211, 1242, 1243, 1244, 1275, 220, 1212, 1243, 1244, 1245, 1276
, 221, 1213, 1244, 1245, 1246, 1277, 222, 1214, 1245, 1246, 1247, 1278, 223
, 1215, 1246, 1247, 1248, 1279, 224, 1216, 1217, 1247, 1248, 1280, 225, 121
7, 1249, 1250, 1280, 1281, 226, 1218, 1249, 1250, 1251, 1282, 227, 1219, 12
50, 1251, 1252, 1283, 228, 1220, 1251, 1252, 1253, 1284, 229, 1221, 1252, 1
253, 1254, 1285, 230, 1222, 1253, 1254, 1255, 1286, 231, 1223, 1254, 1255,
1256, 1287, 232, 1224, 1255, 1256, 1257, 1288, 233, 1225, 1256, 1257, 1258,
1289, 234, 1226, 1257, 1258, 1259, 1290, 235, 1227, 1258, 1259, 1260, 1291
, 236, 1228, 1259, 1260, 1261, 1292, 237, 1229, 1260, 1261, 1262, 1293, 238
, 1230, 1261, 1262, 1263, 1294, 239, 1231, 1262, 1263, 1264, 1295, 240, 123
2, 1263, 1264, 1265, 1296, 241, 1233, 1264, 1265, 1266, 1297, 242, 1234, 12
65, 1266, 1267, 1298, 243, 1235, 1266, 1267, 1268, 1299, 244, 1236, 1267, 1
268, 1269, 1300, 245, 1237, 1268, 1269, 1270, 1301, 246, 1238, 1269, 1270,
1271, 1302, 247, 1239, 1270, 1271, 1272, 1303, 248, 1240, 1271, 1272, 1273,
1304, 249, 1241, 1272, 1273, 1274, 1305, 250, 1242, 1273, 1274, 1275, 1306
, 251, 1243, 1274, 1275, 1276, 1307, 252, 1244, 1275, 1276, 1277, 1308, 253
, 1245, 1276, 1277, 1278, 1309, 254, 1246, 1277, 1278, 1279, 1310, 255, 124
7, 1278, 1279, 1280, 1311, 256, 1248, 1249, 1279, 1280, 1312, 257, 1249, 12
81, 1282, 1312, 1313, 258, 1250, 1281, 1282, 1283, 1314, 259, 1251, 1282, 1
283, 1284, 1315, 260, 1252, 1283, 1284, 1285, 1316, 261, 1253, 1284, 1285,
1286, 1317, 262, 1254, 1285, 1286, 1287, 1318, 263, 1255, 1286, 1287, 1288,
1319, 264, 1256, 1287, 1288, 1289, 1320, 265, 1257, 1288, 1289, 1290, 1321
, 266, 1258, 1289, 1290, 1291, 1322, 267, 1259, 1290, 1291, 1292, 1323, 268
, 1260, 1291, 1292, 1293, 1324, 269, 1261, 1292, 1293, 1294, 1325, 270, 126
2, 1293, 1294, 1295, 1326, 271, 1263, 1294, 1295, 1296, 1327, 272, 1264, 12
95, 1296, 1297, 1328, 273, 1265, 1296, 1297, 1298, 1329, 274, 1266, 1297, 1
298, 1299, 1330, 275, 1267, 1298, 1299, 1300, 1331, 276, 1268, 1299, 1300,
1301, 1332, 277, 1269, 1300, 1301, 1302, 1333, 278, 1270, 1301, 1302, 1303,
1334, 279, 1271, 1302, 1303, 1304, 1335, 280, 1272, 1303, 1304, 1305, 1336
, 281, 1273, 1304, 1305, 1306, 1337, 282, 1274, 1305, 1306, 1307, 1338, 283
, 1275, 1306, 1307, 1308, 1339, 284, 1276, 1307, 1308, 1309, 1340, 285, 127
7, 1308, 1309, 1310, 1341, 286, 1278, 1309, 1310, 1311, 1342, 287, 1279, 13
10, 1311, 1312, 1343, 288, 1280, 1281, 1311, 1312, 1344, 289, 1281, 1313, 1
314, 1344, 1345, 290, 1282, 1313, 1314, 1315, 1346, 291, 1283, 1314, 1315,
1316, 1347, 292, 1284, 1315, 1316, 1317, 1348, 293, 1285, 1316, 1317, 1318,
1349, 294, 1286, 1317, 1318, 1319, 1350, 295, 1287, 1318, 1319, 1320, 1351
, 296, 1288, 1319, 1320, 1321, 1352, 297, 1289, 1320, 1321, 1322, 1353, 298
, 1290, 1321, 1322, 1323, 1354, 299, 1291, 1322, 1323, 1324, 1355, 300, 129
2, 1323, 1324, 1325, 1356, 301, 1293, 1324, 1325, 1326, 1357, 302, 1294, 13
25, 1326, 1327, 1358, 303, 1295, 1326, 1327, 1328, 1359, 304, 1296, 1327, 1
328, 1329, 1360, 305, 1297, 1328, 1329, 1330, 1361, 306, 1298, 1329, 1330,
1331, 1362, 307, 1299, 1330, 1331, 1332, 1363, 308, 1300, 1331, 1332, 1333,
1364, 309, 1301, 1332, 1333, 1334, 1365, 310, 1302, 1333, 1334, 1335, 1366
, 311, 1303, 1334, 1335, 1336, 1367, 312, 1304, 1335, 1336, 1337, 1368, 313
, 1305, 1336, 1337, 1338, 1369, 314, 1306, 1337, 1338, 1339, 1370, 315, 130
7, 1338, 1339, 1340, 1371, 316, 1308, 1339, 1340, 1341, 1372, 317, 1309, 13
40, 1341, 1342, 1373, 318, 1310, 1341, 1342, 1343, 1374, 319, 1311, 1342, 1
343, 1344, 1375, 320, 1312, 1313, 1343, 1344, 1376, 321, 1313, 1345, 1346,
1376, 1377, 322, 1314, 1345, 1346, 1347, 1378, 323, 1315, 1346, 1347, 1348,
1379, 324, 1316, 1347, 1348, 1349, 1380, 325, 1317, 1348, 1349, 1350, 1381
, 326, 1318, 1349, 1350, 1351, 1382, 327, 1319, 1350, 1351, 1352, 1383, 328
, 1320, 1351, 1352, 1353, 1384, 329, 1321, 1352, 1353, 1354, 1385, 330, 132
2, 1353, 1354, 1355, 1386, 331, 1323, 1354, 1355, 1356, 1387, 332, 1324, 13
55, 1356, 1357, 1388, 333, 1325, 1356, 1357, 1358, 1389, 334, 1326, 1357, 1
358, 1359, 1390, 335, 1327, 1358, 1359, 1360, 1391, 336, 1328, 1359, 1360,
1361, 1392, 337, 1329, 1360, 1361, 1362, 1393, 338, 1330, 1361, 1362, 1363,
1394, 339, 1331, 1362, 1363, 1364, 1395, 340, 1332, 1363, 1364, 1365, 1396
, 341, 1333, 1364, 1365, 1366, 1397, 342, 1334, 1365, 1366, 1367, 1398, 343
, 1335, 1366, 1367, 1368, 1399, 344, 1336, 1367, 1368, 1369, 1400, 345, 133
7, 1368, 1369, 1370, 1401, 346, 1338, 1369, 1370, 1371, 1402, 347, 1339, 13
70, 1371, 1372, 1403, 348, 1340, 1371, 1372, 1373, 1404, 349, 1341, 1372, 1
373, 1374, 1405, 350, 1342, 1373, 1374, 1375, 1406, 351, 1343, 1374, 1375,
1376, 1407, 352, 1344, 1345, 1375, 1376, 1408, 353, 1345, 1377, 1378, 1408,
1409, 354, 1346, 1377, 1378, 1379, 1410, 355, 1347, 1378, 1379, 1380, 1411
, 356, 1348, 1379, 1380, 1381, 1412, 357, 1349, 1380, 1381, 1382, 1413, 358
, 1350, 1381, 1382, 1383, 1414, 359, 1351, 1382, 1383, 1384, 1415, 360, 135
2, 1383, 1384, 1385, 1416, 361, 1353, 1384, 1385, 1386, 1417, 362, 1354, 13
85, 1386, 1387, 1418, 363, 1355, 1386, 1387, 1388, 1419, 364, 1356, 1387, 1
388, 1389, 1420, 365, 1357, 1388, 1389, 1390, 1421, 366, 1358, 1389, 1390,
1391, 1422, 367, 1359, 1390, 1391, 1392, 1423, 368, 1360, 1391, 1392, 1393,
1424, 369, 1361, 1392, 1393, 1394, 1425, 370, 1362, 1393, 1394, 1395, 1426
, 371, 1363, 1394, 1395, 1396, 1427, 372, 1364, 1395, 1396, 1397, 1428, 373
, 1365, 1396, 1397, 1398, 1429, 374, 1366, 1397, 1398, 1399, 1430, 375, 136
7, 1398, 1399, 1400, 1431, 376, 1368, 1399, 1400, 1401, 1432, 377, 1369, 14
00, 1401, 1402, 1433, 378, 1370, 1401, 1402, 1403, 1434, 379, 1371, 1402, 1
403, 1404, 1435, 380, 1372, 1403, 1404, 1405, 1436, 381, 1373, 1404, 1405,
1406, 1437, 382, 1374, 1405, 1406, 1407, 1438, 383, 1375, 1406, 1407, 1408,
1439, 384, 1376, 1377, 1407, 1408, 1440, 385, 1377, 1409, 1410, 1440, 1441
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853, 1854, 1885, 830, 1822, 1853, 1854, 1855, 1886, 831, 1823, 1854, 1855,
1856, 1887, 832, 1824, 1825, 1855, 1856, 1888, 833, 1825, 1857, 1858, 1888,
1889, 834, 1826, 1857, 1858, 1859, 1890, 835, 1827, 1858, 1859, 1860, 1891
, 836, 1828, 1859, 1860, 1861, 1892, 837, 1829, 1860, 1861, 1862, 1893, 838
, 1830, 1861, 1862, 1863, 1894, 839, 1831, 1862, 1863, 1864, 1895, 840, 183
2, 1863, 1864, 1865, 1896, 841, 1833, 1864, 1865, 1866, 1897, 842, 1834, 18
65, 1866, 1867, 1898, 843, 1835, 1866, 1867, 1868, 1899, 844, 1836, 1867, 1
868, 1869, 1900, 845, 1837, 1868, 1869, 1870, 1901, 846, 1838, 1869, 1870,
1871, 1902, 847, 1839, 1870, 1871, 1872, 1903, 848, 1840, 1871, 1872, 1873,
1904, 849, 1841, 1872, 1873, 1874, 1905, 850, 1842, 1873, 1874, 1875, 1906
, 851, 1843, 1874, 1875, 1876, 1907, 852, 1844, 1875, 1876, 1877, 1908, 853
, 1845, 1876, 1877, 1878, 1909, 854, 1846, 1877, 1878, 1879, 1910, 855, 184
7, 1878, 1879, 1880, 1911, 856, 1848, 1879, 1880, 1881, 1912, 857, 1849, 18
80, 1881, 1882, 1913, 858, 1850, 1881, 1882, 1883, 1914, 859, 1851, 1882, 1
883, 1884, 1915, 860, 1852, 1883, 1884, 1885, 1916, 861, 1853, 1884, 1885,
1886, 1917, 862, 1854, 1885, 1886, 1887, 1918, 863, 1855, 1886, 1887, 1888,
1919, 864, 1856, 1857, 1887, 1888, 1920, 865, 1857, 1889, 1890, 1920, 1921
, 866, 1858, 1889, 1890, 1891, 1922, 867, 1859, 1890, 1891, 1892, 1923, 868
, 1860, 1891, 1892, 1893, 1924, 869, 1861, 1892, 1893, 1894, 1925, 870, 186
2, 1893, 1894, 1895, 1926, 871, 1863, 1894, 1895, 1896, 1927, 872, 1864, 18
95, 1896, 1897, 1928, 873, 1865, 1896, 1897, 1898, 1929, 874, 1866, 1897, 1
898, 1899, 1930, 875, 1867, 1898, 1899, 1900, 1931, 876, 1868, 1899, 1900,
1901, 1932, 877, 1869, 1900, 1901, 1902, 1933, 878, 1870, 1901, 1902, 1903,
1934, 879, 1871, 1902, 1903, 1904, 1935, 880, 1872, 1903, 1904, 1905, 1936
, 881, 1873, 1904, 1905, 1906, 1937, 882, 1874, 1905, 1906, 1907, 1938, 883
, 1875, 1906, 1907, 1908, 1939, 884, 1876, 1907, 1908, 1909, 1940, 885, 187
7, 1908, 1909, 1910, 1941, 886, 1878, 1909, 1910, 1911, 1942, 887, 1879, 19
10, 1911, 1912, 1943, 888, 1880, 1911, 1912, 1913, 1944, 889, 1881, 1912, 1
913, 1914, 1945, 890, 1882, 1913, 1914, 1915, 1946, 891, 1883, 1914, 1915,
1916, 1947, 892, 1884, 1915, 1916, 1917, 1948, 893, 1885, 1916, 1917, 1918,
1949, 894, 1886, 1917, 1918, 1919, 1950, 895, 1887, 1918, 1919, 1920, 1951
, 896, 1888, 1889, 1919, 1920, 1952, 897, 1889, 1921, 1922, 1952, 1953, 898
, 1890, 1921, 1922, 1923, 1954, 899, 1891, 1922, 1923, 1924, 1955, 900, 189
2, 1923, 1924, 1925, 1956, 901, 1893, 1924, 1925, 1926, 1957, 902, 1894, 19
25, 1926, 1927, 1958, 903, 1895, 1926, 1927, 1928, 1959, 904, 1896, 1927, 1
928, 1929, 1960, 905, 1897, 1928, 1929, 1930, 1961, 906, 1898, 1929, 1930,
1931, 1962, 907, 1899, 1930, 1931, 1932, 1963, 908, 1900, 1931, 1932, 1933,
1964, 909, 1901, 1932, 1933, 1934, 1965, 910, 1902, 1933, 1934, 1935, 1966
, 911, 1903, 1934, 1935, 1936, 1967, 912, 1904, 1935, 1936, 1937, 1968, 913
, 1905, 1936, 1937, 1938, 1969, 914, 1906, 1937, 1938, 1939, 1970, 915, 190
7, 1938, 1939, 1940, 1971, 916, 1908, 1939, 1940, 1941, 1972, 917, 1909, 19
40, 1941, 1942, 1973, 918, 1910, 1941, 1942, 1943, 1974, 919, 1911, 1942, 1
943, 1944, 1975, 920, 1912, 1943, 1944, 1945, 1976, 921, 1913, 1944, 1945,
1946, 1977, 922, 1914, 1945, 1946, 1947, 1978, 923, 1915, 1946, 1947, 1948,
1979, 924, 1916, 1947, 1948, 1949, 1980, 925, 1917, 1948, 1949, 1950, 1981
, 926, 1918, 1949, 1950, 1951, 1982, 927, 1919, 1950, 1951, 1952, 1983, 928
, 1920, 1921, 1951, 1952, 1984, 929, 1921, 1953, 1954, 1984, 1985, 930, 192
2, 1953, 1954, 1955, 1986, 931, 1923, 1954, 1955, 1956, 1987, 932, 1924, 19
55, 1956, 1957, 1988, 933, 1925, 1956, 1957, 1958, 1989, 934, 1926, 1957, 1
958, 1959, 1990, 935, 1927, 1958, 1959, 1960, 1991, 936, 1928, 1959, 1960,
1961, 1992, 937, 1929, 1960, 1961, 1962, 1993, 938, 1930, 1961, 1962, 1963,
1994, 939, 1931, 1962, 1963, 1964, 1995, 940, 1932, 1963, 1964, 1965, 1996
, 941, 1933, 1964, 1965, 1966, 1997, 942, 1934, 1965, 1966, 1967, 1998, 943
, 1935, 1966, 1967, 1968, 1999, 944, 1936, 1967, 1968, 1969, 2000, 945, 193
7, 1968, 1969, 1970, 2001, 946, 1938, 1969, 1970, 1971, 2002, 947, 1939, 19
70, 1971, 1972, 2003, 948, 1940, 1971, 1972, 1973, 2004, 949, 1941, 1972, 1
973, 1974, 2005, 950, 1942, 1973, 1974, 1975, 2006, 951, 1943, 1974, 1975,
1976, 2007, 952, 1944, 1975, 1976, 1977, 2008, 953, 1945, 1976, 1977, 1978,
2009, 954, 1946, 1977, 1978, 1979, 2010, 955, 1947, 1978, 1979, 1980, 2011
, 956, 1948, 1979, 1980, 1981, 2012, 957, 1949, 1980, 1981, 1982, 2013, 958
, 1950, 1981, 1982, 1983, 2014, 959, 1951, 1982, 1983, 1984, 2015, 960, 195
2, 1953, 1983, 1984, 2016, 961, 1953, 1985, 1986, 2016, 2017, 962, 1954, 19
85, 1986, 1987, 2018, 963, 1955, 1986, 1987, 1988, 2019, 964, 1956, 1987, 1
988, 1989, 2020, 965, 1957, 1988, 1989, 1990, 2021, 966, 1958, 1989, 1990,
1991, 2022, 967, 1959, 1990, 1991, 1992, 2023, 968, 1960, 1991, 1992, 1993,
2024, 969, 1961, 1992, 1993, 1994, 2025, 970, 1962, 1993, 1994, 1995, 2026
, 971, 1963, 1994, 1995, 1996, 2027, 972, 1964, 1995, 1996, 1997, 2028, 973
, 1965, 1996, 1997, 1998, 2029, 974, 1966, 1997, 1998, 1999, 2030, 975, 196
7, 1998, 1999, 2000, 2031, 976, 1968, 1999, 2000, 2001, 2032, 977, 1969, 20
00, 2001, 2002, 2033, 978, 1970, 2001, 2002, 2003, 2034, 979, 1971, 2002, 2
003, 2004, 2035, 980, 1972, 2003, 2004, 2005, 2036, 981, 1973, 2004, 2005,
2006, 2037, 982, 1974, 2005, 2006, 2007, 2038, 983, 1975, 2006, 2007, 2008,
2039, 984, 1976, 2007, 2008, 2009, 2040, 985, 1977, 2008, 2009, 2010, 2041
, 986, 1978, 2009, 2010, 2011, 2042, 987, 1979, 2010, 2011, 2012, 2043, 988
, 1980, 2011, 2012, 2013, 2044, 989, 1981, 2012, 2013, 2014, 2045, 990, 198
2, 2013, 2014, 2015, 2046, 991, 1983, 2014, 2015, 2016, 2047, 992, 1984, 19
85, 2015, 2016, 2048, 993, 1025, 1985, 2017, 2018, 2048, 994, 1026, 1986, 2
017, 2018, 2019, 995, 1027, 1987, 2018, 2019, 2020, 996, 1028, 1988, 2019,
2020, 2021, 997, 1029, 1989, 2020, 2021, 2022, 998, 1030, 1990, 2021, 2022,
2023, 999, 1031, 1991, 2022, 2023, 2024, 1000, 1032, 1992, 2023, 2024, 202
5, 1001, 1033, 1993, 2024, 2025, 2026, 1002, 1034, 1994, 2025, 2026, 2027,
1003, 1035, 1995, 2026, 2027, 2028, 1004, 1036, 1996, 2027, 2028, 2029, 100
5, 1037, 1997, 2028, 2029, 2030, 1006, 1038, 1998, 2029, 2030, 2031, 1007,
1039, 1999, 2030, 2031, 2032, 1008, 1040, 2000, 2031, 2032, 2033, 1009, 104
1, 2001, 2032, 2033, 2034, 1010, 1042, 2002, 2033, 2034, 2035, 1011, 1043,
2003, 2034, 2035, 2036, 1012, 1044, 2004, 2035, 2036, 2037, 1013, 1045, 200
5, 2036, 2037, 2038, 1014, 1046, 2006, 2037, 2038, 2039, 1015, 1047, 2007,
2038, 2039, 2040, 1016, 1048, 2008, 2039, 2040, 2041, 1017, 1049, 2009, 204
0, 2041, 2042, 1018, 1050, 2010, 2041, 2042, 2043, 1019, 1051, 2011, 2042,
2043, 2044, 1020, 1052, 2012, 2043, 2044, 2045, 1021, 1053, 2013, 2044, 204
5, 2046, 1022, 1054, 2014, 2045, 2046, 2047, 1023, 1055, 2015, 2046, 2047,
2048, 1024, 1056, 2016, 2017, 2047, 2048], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2
, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6
, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10,
10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13
, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 1
7, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20,
20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23,
23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26
, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29, 2
9, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32,
32, 32, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35,
35, 36, 36, 36, 36, 36, 36, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38
, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 41, 41, 4
2, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 44, 45,
45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 47, 48, 48,
48, 48, 48, 48, 49, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 51, 51, 51
, 51, 51, 51, 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 53, 54, 54, 54, 5
4, 54, 54, 55, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 57, 57, 57, 57,
57, 57, 58, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 59, 60, 60, 60, 60, 60,
60, 61, 61, 61, 61, 61, 61, 62, 62, 62, 62, 62, 62, 63, 63, 63, 63, 63, 63
, 64, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 6
7, 67, 67, 67, 67, 67, 68, 68, 68, 68, 68, 68, 69, 69, 69, 69, 69, 69, 70,
70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72, 72, 73, 73,
73, 73, 73, 73, 74, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 75, 76, 76, 76
, 76, 76, 76, 77, 77, 77, 77, 77, 77, 78, 78, 78, 78, 78, 78, 79, 79, 79, 7
9, 79, 79, 80, 80, 80, 80, 80, 80, 81, 81, 81, 81, 81, 81, 82, 82, 82, 82,
82, 82, 83, 83, 83, 83, 83, 83, 84, 84, 84, 84, 84, 84, 85, 85, 85, 85, 85,
85, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88
, 89, 89, 89, 89, 89, 89, 90, 90, 90, 90, 90, 90, 91, 91, 91, 91, 91, 91, 9
2, 92, 92, 92, 92, 92, 93, 93, 93, 93, 93, 93, 94, 94, 94, 94, 94, 94, 95,
95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 97, 98, 98,
98, 98, 98, 98, 99, 99, 99, 99, 99, 99, 100, 100, 100, 100, 100, 100, 101,
101, 101, 101, 101, 101, 102, 102, 102, 102, 102, 102, 103, 103, 103, 103,
103, 103, 104, 104, 104, 104, 104, 104, 105, 105, 105, 105, 105, 105, 106,
106, 106, 106, 106, 106, 107, 107, 107, 107, 107, 107, 108, 108, 108, 108,
108, 108, 109, 109, 109, 109, 109, 109, 110, 110, 110, 110, 110, 110, 111,
111, 111, 111, 111, 111, 112, 112, 112, 112, 112, 112, 113, 113, 113, 113,
113, 113, 114, 114, 114, 114, 114, 114, 115, 115, 115, 115, 115, 115, 116,
116, 116, 116, 116, 116, 117, 117, 117, 117, 117, 117, 118, 118, 118, 118,
118, 118, 119, 119, 119, 119, 119, 119, 120, 120, 120, 120, 120, 120, 121,
121, 121, 121, 121, 121, 122, 122, 122, 122, 122, 122, 123, 123, 123, 123,
123, 123, 124, 124, 124, 124, 124, 124, 125, 125, 125, 125, 125, 125, 126,
126, 126, 126, 126, 126, 127, 127, 127, 127, 127, 127, 128, 128, 128, 128,
128, 128, 129, 129, 129, 129, 129, 129, 130, 130, 130, 130, 130, 130, 131,
131, 131, 131, 131, 131, 132, 132, 132, 132, 132, 132, 133, 133, 133, 133,
133, 133, 134, 134, 134, 134, 134, 134, 135, 135, 135, 135, 135, 135, 136,
136, 136, 136, 136, 136, 137, 137, 137, 137, 137, 137, 138, 138, 138, 138,
138, 138, 139, 139, 139, 139, 139, 139, 140, 140, 140, 140, 140, 140, 141,
141, 141, 141, 141, 141, 142, 142, 142, 142, 142, 142, 143, 143, 143, 143,
143, 143, 144, 144, 144, 144, 144, 144, 145, 145, 145, 145, 145, 145, 146,
146, 146, 146, 146, 146, 147, 147, 147, 147, 147, 147, 148, 148, 148, 148,
148, 148, 149, 149, 149, 149, 149, 149, 150, 150, 150, 150, 150, 150, 151,
151, 151, 151, 151, 151, 152, 152, 152, 152, 152, 152, 153, 153, 153, 153,
153, 153, 154, 154, 154, 154, 154, 154, 155, 155, 155, 155, 155, 155, 156,
156, 156, 156, 156, 156, 157, 157, 157, 157, 157, 157, 158, 158, 158, 158,
158, 158, 159, 159, 159, 159, 159, 159, 160, 160, 160, 160, 160, 160, 161,
161, 161, 161, 161, 161, 162, 162, 162, 162, 162, 162, 163, 163, 163, 163,
163, 163, 164, 164, 164, 164, 164, 164, 165, 165, 165, 165, 165, 165, 166,
166, 166, 166, 166, 166, 167, 167, 167, 167, 167, 167, 168, 168, 168, 168,
168, 168, 169, 169, 169, 169, 169, 169, 170, 170, 170, 170, 170, 170, 171,
171, 171, 171, 171, 171, 172, 172, 172, 172, 172, 172, 173, 173, 173, 173,
173, 173, 174, 174, 174, 174, 174, 174, 175, 175, 175, 175, 175, 175, 176,
176, 176, 176, 176, 176, 177, 177, 177, 177, 177, 177, 178, 178, 178, 178,
178, 178, 179, 179, 179, 179, 179, 179, 180, 180, 180, 180, 180, 180, 181,
181, 181, 181, 181, 181, 182, 182, 182, 182, 182, 182, 183, 183, 183, 183,
183, 183, 184, 184, 184, 184, 184, 184, 185, 185, 185, 185, 185, 185, 186,
186, 186, 186, 186, 186, 187, 187, 187, 187, 187, 187, 188, 188, 188, 188,
188, 188, 189, 189, 189, 189, 189, 189, 190, 190, 190, 190, 190, 190, 191,
191, 191, 191, 191, 191, 192, 192, 192, 192, 192, 192, 193, 193, 193, 193,
193, 193, 194, 194, 194, 194, 194, 194, 195, 195, 195, 195, 195, 195, 196,
196, 196, 196, 196, 196, 197, 197, 197, 197, 197, 197, 198, 198, 198, 198,
198, 198, 199, 199, 199, 199, 199, 199, 200, 200, 200, 200, 200, 200, 201,
201, 201, 201, 201, 201, 202, 202, 202, 202, 202, 202, 203, 203, 203, 203,
203, 203, 204, 204, 204, 204, 204, 204, 205, 205, 205, 205, 205, 205, 206,
206, 206, 206, 206, 206, 207, 207, 207, 207, 207, 207, 208, 208, 208, 208,
208, 208, 209, 209, 209, 209, 209, 209, 210, 210, 210, 210, 210, 210, 211,
211, 211, 211, 211, 211, 212, 212, 212, 212, 212, 212, 213, 213, 213, 213,
213, 213, 214, 214, 214, 214, 214, 214, 215, 215, 215, 215, 215, 215, 216,
216, 216, 216, 216, 216, 217, 217, 217, 217, 217, 217, 218, 218, 218, 218,
218, 218, 219, 219, 219, 219, 219, 219, 220, 220, 220, 220, 220, 220, 221,
221, 221, 221, 221, 221, 222, 222, 222, 222, 222, 222, 223, 223, 223, 223,
223, 223, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 226,
226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228,
228, 228, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 231,
231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 232, 233, 233, 233, 233,
233, 233, 234, 234, 234, 234, 234, 234, 235, 235, 235, 235, 235, 235, 236,
236, 236, 236, 236, 236, 237, 237, 237, 237, 237, 237, 238, 238, 238, 238,
238, 238, 239, 239, 239, 239, 239, 239, 240, 240, 240, 240, 240, 240, 241,
241, 241, 241, 241, 241, 242, 242, 242, 242, 242, 242, 243, 243, 243, 243,
243, 243, 244, 244, 244, 244, 244, 244, 245, 245, 245, 245, 245, 245, 246,
246, 246, 246, 246, 246, 247, 247, 247, 247, 247, 247, 248, 248, 248, 248,
248, 248, 249, 249, 249, 249, 249, 249, 250, 250, 250, 250, 250, 250, 251,
251, 251, 251, 251, 251, 252, 252, 252, 252, 252, 252, 253, 253, 253, 253,
253, 253, 254, 254, 254, 254, 254, 254, 255, 255, 255, 255, 255, 255, 256,
256, 256, 256, 256, 256, 257, 257, 257, 257, 257, 257, 258, 258, 258, 258,
258, 258, 259, 259, 259, 259, 259, 259, 260, 260, 260, 260, 260, 260, 261,
261, 261, 261, 261, 261, 262, 262, 262, 262, 262, 262, 263, 263, 263, 263,
263, 263, 264, 264, 264, 264, 264, 264, 265, 265, 265, 265, 265, 265, 266,
266, 266, 266, 266, 266, 267, 267, 267, 267, 267, 267, 268, 268, 268, 268,
268, 268, 269, 269, 269, 269, 269, 269, 270, 270, 270, 270, 270, 270, 271,
271, 271, 271, 271, 271, 272, 272, 272, 272, 272, 272, 273, 273, 273, 273,
273, 273, 274, 274, 274, 274, 274, 274, 275, 275, 275, 275, 275, 275, 276,
276, 276, 276, 276, 276, 277, 277, 277, 277, 277, 277, 278, 278, 278, 278,
278, 278, 279, 279, 279, 279, 279, 279, 280, 280, 280, 280, 280, 280, 281,
281, 281, 281, 281, 281, 282, 282, 282, 282, 282, 282, 283, 283, 283, 283,
283, 283, 284, 284, 284, 284, 284, 284, 285, 285, 285, 285, 285, 285, 286,
286, 286, 286, 286, 286, 287, 287, 287, 287, 287, 287, 288, 288, 288, 288,
288, 288, 289, 289, 289, 289, 289, 289, 290, 290, 290, 290, 290, 290, 291,
291, 291, 291, 291, 291, 292, 292, 292, 292, 292, 292, 293, 293, 293, 293,
293, 293, 294, 294, 294, 294, 294, 294, 295, 295, 295, 295, 295, 295, 296,
296, 296, 296, 296, 296, 297, 297, 297, 297, 297, 297, 298, 298, 298, 298,
298, 298, 299, 299, 299, 299, 299, 299, 300, 300, 300, 300, 300, 300, 301,
301, 301, 301, 301, 301, 302, 302, 302, 302, 302, 302, 303, 303, 303, 303,
303, 303, 304, 304, 304, 304, 304, 304, 305, 305, 305, 305, 305, 305, 306,
306, 306, 306, 306, 306, 307, 307, 307, 307, 307, 307, 308, 308, 308, 308,
308, 308, 309, 309, 309, 309, 309, 309, 310, 310, 310, 310, 310, 310, 311,
311, 311, 311, 311, 311, 312, 312, 312, 312, 312, 312, 313, 313, 313, 313,
313, 313, 314, 314, 314, 314, 314, 314, 315, 315, 315, 315, 315, 315, 316,
316, 316, 316, 316, 316, 317, 317, 317, 317, 317, 317, 318, 318, 318, 318,
318, 318, 319, 319, 319, 319, 319, 319, 320, 320, 320, 320, 320, 320, 321,
321, 321, 321, 321, 321, 322, 322, 322, 322, 322, 322, 323, 323, 323, 323,
323, 323, 324, 324, 324, 324, 324, 324, 325, 325, 325, 325, 325, 325, 326,
326, 326, 326, 326, 326, 327, 327, 327, 327, 327, 327, 328, 328, 328, 328,
328, 328, 329, 329, 329, 329, 329, 329, 330, 330, 330, 330, 330, 330, 331,
331, 331, 331, 331, 331, 332, 332, 332, 332, 332, 332, 333, 333, 333, 333,
333, 333, 334, 334, 334, 334, 334, 334, 335, 335, 335, 335, 335, 335, 336,
336, 336, 336, 336, 336, 337, 337, 337, 337, 337, 337, 338, 338, 338, 338,
338, 338, 339, 339, 339, 339, 339, 339, 340, 340, 340, 340, 340, 340, 341,
341, 341, 341, 341, 341, 342, 342, 342, 342, 342, 342, 343, 343, 343, 343,
343, 343, 344, 344, 344, 344, 344, 344, 345, 345, 345, 345, 345, 345, 346,
346, 346, 346, 346, 346, 347, 347, 347, 347, 347, 347, 348, 348, 348, 348,
348, 348, 349, 349, 349, 349, 349, 349, 350, 350, 350, 350, 350, 350, 351,
351, 351, 351, 351, 351, 352, 352, 352, 352, 352, 352, 353, 353, 353, 353,
353, 353, 354, 354, 354, 354, 354, 354, 355, 355, 355, 355, 355, 355, 356,
356, 356, 356, 356, 356, 357, 357, 357, 357, 357, 357, 358, 358, 358, 358,
358, 358, 359, 359, 359, 359, 359, 359, 360, 360, 360, 360, 360, 360, 361,
361, 361, 361, 361, 361, 362, 362, 362, 362, 362, 362, 363, 363, 363, 363,
363, 363, 364, 364, 364, 364, 364, 364, 365, 365, 365, 365, 365, 365, 366,
366, 366, 366, 366, 366, 367, 367, 367, 367, 367, 367, 368, 368, 368, 368,
368, 368, 369, 369, 369, 369, 369, 369, 370, 370, 370, 370, 370, 370, 371,
371, 371, 371, 371, 371, 372, 372, 372, 372, 372, 372, 373, 373, 373, 373,
373, 373, 374, 374, 374, 374, 374, 374, 375, 375, 375, 375, 375, 375, 376,
376, 376, 376, 376, 376, 377, 377, 377, 377, 377, 377, 378, 378, 378, 378,
378, 378, 379, 379, 379, 379, 379, 379, 380, 380, 380, 380, 380, 380, 381,
381, 381, 381, 381, 381, 382, 382, 382, 382, 382, 382, 383, 383, 383, 383,
383, 383, 384, 384, 384, 384, 384, 384, 385, 385, 385, 385, 385, 385, 386,
386, 386, 386, 386, 386, 387, 387, 387, 387, 387, 387, 388, 388, 388, 388,
388, 388, 389, 389, 389, 389, 389, 389, 390, 390, 390, 390, 390, 390, 391,
391, 391, 391, 391, 391, 392, 392, 392, 392, 392, 392, 393, 393, 393, 393,
393, 393, 394, 394, 394, 394, 394, 394, 395, 395, 395, 395, 395, 395, 396,
396, 396, 396, 396, 396, 397, 397, 397, 397, 397, 397, 398, 398, 398, 398,
398, 398, 399, 399, 399, 399, 399, 399, 400, 400, 400, 400, 400, 400, 401,
401, 401, 401, 401, 401, 402, 402, 402, 402, 402, 402, 403, 403, 403, 403,
403, 403, 404, 404, 404, 404, 404, 404, 405, 405, 405, 405, 405, 405, 406,
406, 406, 406, 406, 406, 407, 407, 407, 407, 407, 407, 408, 408, 408, 408,
408, 408, 409, 409, 409, 409, 409, 409, 410, 410, 410, 410, 410, 410, 411,
411, 411, 411, 411, 411, 412, 412, 412, 412, 412, 412, 413, 413, 413, 413,
413, 413, 414, 414, 414, 414, 414, 414, 415, 415, 415, 415, 415, 415, 416,
416, 416, 416, 416, 416, 417, 417, 417, 417, 417, 417, 418, 418, 418, 418,
418, 418, 419, 419, 419, 419, 419, 419, 420, 420, 420, 420, 420, 420, 421,
421, 421, 421, 421, 421, 422, 422, 422, 422, 422, 422, 423, 423, 423, 423,
423, 423, 424, 424, 424, 424, 424, 424, 425, 425, 425, 425, 425, 425, 426,
426, 426, 426, 426, 426, 427, 427, 427, 427, 427, 427, 428, 428, 428, 428,
428, 428, 429, 429, 429, 429, 429, 429, 430, 430, 430, 430, 430, 430, 431,
431, 431, 431, 431, 431, 432, 432, 432, 432, 432, 432, 433, 433, 433, 433,
433, 433, 434, 434, 434, 434, 434, 434, 435, 435, 435, 435, 435, 435, 436,
436, 436, 436, 436, 436, 437, 437, 437, 437, 437, 437, 438, 438, 438, 438,
438, 438, 439, 439, 439, 439, 439, 439, 440, 440, 440, 440, 440, 440, 441,
441, 441, 441, 441, 441, 442, 442, 442, 442, 442, 442, 443, 443, 443, 443,
443, 443, 444, 444, 444, 444, 444, 444, 445, 445, 445, 445, 445, 445, 446,
446, 446, 446, 446, 446, 447, 447, 447, 447, 447, 447, 448, 448, 448, 448,
448, 448, 449, 449, 449, 449, 449, 449, 450, 450, 450, 450, 450, 450, 451,
451, 451, 451, 451, 451, 452, 452, 452, 452, 452, 452, 453, 453, 453, 453,
453, 453, 454, 454, 454, 454, 454, 454, 455, 455, 455, 455, 455, 455, 456,
456, 456, 456, 456, 456, 457, 457, 457, 457, 457, 457, 458, 458, 458, 458,
458, 458, 459, 459, 459, 459, 459, 459, 460, 460, 460, 460, 460, 460, 461,
461, 461, 461, 461, 461, 462, 462, 462, 462, 462, 462, 463, 463, 463, 463,
463, 463, 464, 464, 464, 464, 464, 464, 465, 465, 465, 465, 465, 465, 466,
466, 466, 466, 466, 466, 467, 467, 467, 467, 467, 467, 468, 468, 468, 468,
468, 468, 469, 469, 469, 469, 469, 469, 470, 470, 470, 470, 470, 470, 471,
471, 471, 471, 471, 471, 472, 472, 472, 472, 472, 472, 473, 473, 473, 473,
473, 473, 474, 474, 474, 474, 474, 474, 475, 475, 475, 475, 475, 475, 476,
476, 476, 476, 476, 476, 477, 477, 477, 477, 477, 477, 478, 478, 478, 478,
478, 478, 479, 479, 479, 479, 479, 479, 480, 480, 480, 480, 480, 480, 481,
481, 481, 481, 481, 481, 482, 482, 482, 482, 482, 482, 483, 483, 483, 483,
483, 483, 484, 484, 484, 484, 484, 484, 485, 485, 485, 485, 485, 485, 486,
486, 486, 486, 486, 486, 487, 487, 487, 487, 487, 487, 488, 488, 488, 488,
488, 488, 489, 489, 489, 489, 489, 489, 490, 490, 490, 490, 490, 490, 491,
491, 491, 491, 491, 491, 492, 492, 492, 492, 492, 492, 493, 493, 493, 493,
493, 493, 494, 494, 494, 494, 494, 494, 495, 495, 495, 495, 495, 495, 496,
496, 496, 496, 496, 496, 497, 497, 497, 497, 497, 497, 498, 498, 498, 498,
498, 498, 499, 499, 499, 499, 499, 499, 500, 500, 500, 500, 500, 500, 501,
501, 501, 501, 501, 501, 502, 502, 502, 502, 502, 502, 503, 503, 503, 503,
503, 503, 504, 504, 504, 504, 504, 504, 505, 505, 505, 505, 505, 505, 506,
506, 506, 506, 506, 506, 507, 507, 507, 507, 507, 507, 508, 508, 508, 508,
508, 508, 509, 509, 509, 509, 509, 509, 510, 510, 510, 510, 510, 510, 511,
511, 511, 511, 511, 511, 512, 512, 512, 512, 512, 512, 513, 513, 513, 513,
513, 513, 514, 514, 514, 514, 514, 514, 515, 515, 515, 515, 515, 515, 516,
516, 516, 516, 516, 516, 517, 517, 517, 517, 517, 517, 518, 518, 518, 518,
518, 518, 519, 519, 519, 519, 519, 519, 520, 520, 520, 520, 520, 520, 521,
521, 521, 521, 521, 521, 522, 522, 522, 522, 522, 522, 523, 523, 523, 523,
523, 523, 524, 524, 524, 524, 524, 524, 525, 525, 525, 525, 525, 525, 526,
526, 526, 526, 526, 526, 527, 527, 527, 527, 527, 527, 528, 528, 528, 528,
528, 528, 529, 529, 529, 529, 529, 529, 530, 530, 530, 530, 530, 530, 531,
531, 531, 531, 531, 531, 532, 532, 532, 532, 532, 532, 533, 533, 533, 533,
533, 533, 534, 534, 534, 534, 534, 534, 535, 535, 535, 535, 535, 535, 536,
536, 536, 536, 536, 536, 537, 537, 537, 537, 537, 537, 538, 538, 538, 538,
538, 538, 539, 539, 539, 539, 539, 539, 540, 540, 540, 540, 540, 540, 541,
541, 541, 541, 541, 541, 542, 542, 542, 542, 542, 542, 543, 543, 543, 543,
543, 543, 544, 544, 544, 544, 544, 544, 545, 545, 545, 545, 545, 545, 546,
546, 546, 546, 546, 546, 547, 547, 547, 547, 547, 547, 548, 548, 548, 548,
548, 548, 549, 549, 549, 549, 549, 549, 550, 550, 550, 550, 550, 550, 551,
551, 551, 551, 551, 551, 552, 552, 552, 552, 552, 552, 553, 553, 553, 553,
553, 553, 554, 554, 554, 554, 554, 554, 555, 555, 555, 555, 555, 555, 556,
556, 556, 556, 556, 556, 557, 557, 557, 557, 557, 557, 558, 558, 558, 558,
558, 558, 559, 559, 559, 559, 559, 559, 560, 560, 560, 560, 560, 560, 561,
561, 561, 561, 561, 561, 562, 562, 562, 562, 562, 562, 563, 563, 563, 563,
563, 563, 564, 564, 564, 564, 564, 564, 565, 565, 565, 565, 565, 565, 566,
566, 566, 566, 566, 566, 567, 567, 567, 567, 567, 567, 568, 568, 568, 568,
568, 568, 569, 569, 569, 569, 569, 569, 570, 570, 570, 570, 570, 570, 571,
571, 571, 571, 571, 571, 572, 572, 572, 572, 572, 572, 573, 573, 573, 573,
573, 573, 574, 574, 574, 574, 574, 574, 575, 575, 575, 575, 575, 575, 576,
576, 576, 576, 576, 576, 577, 577, 577, 577, 577, 577, 578, 578, 578, 578,
578, 578, 579, 579, 579, 579, 579, 579, 580, 580, 580, 580, 580, 580, 581,
581, 581, 581, 581, 581, 582, 582, 582, 582, 582, 582, 583, 583, 583, 583,
583, 583, 584, 584, 584, 584, 584, 584, 585, 585, 585, 585, 585, 585, 586,
586, 586, 586, 586, 586, 587, 587, 587, 587, 587, 587, 588, 588, 588, 588,
588, 588, 589, 589, 589, 589, 589, 589, 590, 590, 590, 590, 590, 590, 591,
591, 591, 591, 591, 591, 592, 592, 592, 592, 592, 592, 593, 593, 593, 593,
593, 593, 594, 594, 594, 594, 594, 594, 595, 595, 595, 595, 595, 595, 596,
596, 596, 596, 596, 596, 597, 597, 597, 597, 597, 597, 598, 598, 598, 598,
598, 598, 599, 599, 599, 599, 599, 599, 600, 600, 600, 600, 600, 600, 601,
601, 601, 601, 601, 601, 602, 602, 602, 602, 602, 602, 603, 603, 603, 603,
603, 603, 604, 604, 604, 604, 604, 604, 605, 605, 605, 605, 605, 605, 606,
606, 606, 606, 606, 606, 607, 607, 607, 607, 607, 607, 608, 608, 608, 608,
608, 608, 609, 609, 609, 609, 609, 609, 610, 610, 610, 610, 610, 610, 611,
611, 611, 611, 611, 611, 612, 612, 612, 612, 612, 612, 613, 613, 613, 613,
613, 613, 614, 614, 614, 614, 614, 614, 615, 615, 615, 615, 615, 615, 616,
616, 616, 616, 616, 616, 617, 617, 617, 617, 617, 617, 618, 618, 618, 618,
618, 618, 619, 619, 619, 619, 619, 619, 620, 620, 620, 620, 620, 620, 621,
621, 621, 621, 621, 621, 622, 622, 622, 622, 622, 622, 623, 623, 623, 623,
623, 623, 624, 624, 624, 624, 624, 624, 625, 625, 625, 625, 625, 625, 626,
626, 626, 626, 626, 626, 627, 627, 627, 627, 627, 627, 628, 628, 628, 628,
628, 628, 629, 629, 629, 629, 629, 629, 630, 630, 630, 630, 630, 630, 631,
631, 631, 631, 631, 631, 632, 632, 632, 632, 632, 632, 633, 633, 633, 633,
633, 633, 634, 634, 634, 634, 634, 634, 635, 635, 635, 635, 635, 635, 636,
636, 636, 636, 636, 636, 637, 637, 637, 637, 637, 637, 638, 638, 638, 638,
638, 638, 639, 639, 639, 639, 639, 639, 640, 640, 640, 640, 640, 640, 641,
641, 641, 641, 641, 641, 642, 642, 642, 642, 642, 642, 643, 643, 643, 643,
643, 643, 644, 644, 644, 644, 644, 644, 645, 645, 645, 645, 645, 645, 646,
646, 646, 646, 646, 646, 647, 647, 647, 647, 647, 647, 648, 648, 648, 648,
648, 648, 649, 649, 649, 649, 649, 649, 650, 650, 650, 650, 650, 650, 651,
651, 651, 651, 651, 651, 652, 652, 652, 652, 652, 652, 653, 653, 653, 653,
653, 653, 654, 654, 654, 654, 654, 654, 655, 655, 655, 655, 655, 655, 656,
656, 656, 656, 656, 656, 657, 657, 657, 657, 657, 657, 658, 658, 658, 658,
658, 658, 659, 659, 659, 659, 659, 659, 660, 660, 660, 660, 660, 660, 661,
661, 661, 661, 661, 661, 662, 662, 662, 662, 662, 662, 663, 663, 663, 663,
663, 663, 664, 664, 664, 664, 664, 664, 665, 665, 665, 665, 665, 665, 666,
666, 666, 666, 666, 666, 667, 667, 667, 667, 667, 667, 668, 668, 668, 668,
668, 668, 669, 669, 669, 669, 669, 669, 670, 670, 670, 670, 670, 670, 671,
671, 671, 671, 671, 671, 672, 672, 672, 672, 672, 672, 673, 673, 673, 673,
673, 673, 674, 674, 674, 674, 674, 674, 675, 675, 675, 675, 675, 675, 676,
676, 676, 676, 676, 676, 677, 677, 677, 677, 677, 677, 678, 678, 678, 678,
678, 678, 679, 679, 679, 679, 679, 679, 680, 680, 680, 680, 680, 680, 681,
681, 681, 681, 681, 681, 682, 682, 682, 682, 682, 682, 683, 683, 683, 683,
683, 683, 684, 684, 684, 684, 684, 684, 685, 685, 685, 685, 685, 685, 686,
686, 686, 686, 686, 686, 687, 687, 687, 687, 687, 687, 688, 688, 688, 688,
688, 688, 689, 689, 689, 689, 689, 689, 690, 690, 690, 690, 690, 690, 691,
691, 691, 691, 691, 691, 692, 692, 692, 692, 692, 692, 693, 693, 693, 693,
693, 693, 694, 694, 694, 694, 694, 694, 695, 695, 695, 695, 695, 695, 696,
696, 696, 696, 696, 696, 697, 697, 697, 697, 697, 697, 698, 698, 698, 698,
698, 698, 699, 699, 699, 699, 699, 699, 700, 700, 700, 700, 700, 700, 701,
701, 701, 701, 701, 701, 702, 702, 702, 702, 702, 702, 703, 703, 703, 703,
703, 703, 704, 704, 704, 704, 704, 704, 705, 705, 705, 705, 705, 705, 706,
706, 706, 706, 706, 706, 707, 707, 707, 707, 707, 707, 708, 708, 708, 708,
708, 708, 709, 709, 709, 709, 709, 709, 710, 710, 710, 710, 710, 710, 711,
711, 711, 711, 711, 711, 712, 712, 712, 712, 712, 712, 713, 713, 713, 713,
713, 713, 714, 714, 714, 714, 714, 714, 715, 715, 715, 715, 715, 715, 716,
716, 716, 716, 716, 716, 717, 717, 717, 717, 717, 717, 718, 718, 718, 718,
718, 718, 719, 719, 719, 719, 719, 719, 720, 720, 720, 720, 720, 720, 721,
721, 721, 721, 721, 721, 722, 722, 722, 722, 722, 722, 723, 723, 723, 723,
723, 723, 724, 724, 724, 724, 724, 724, 725, 725, 725, 725, 725, 725, 726,
726, 726, 726, 726, 726, 727, 727, 727, 727, 727, 727, 728, 728, 728, 728,
728, 728, 729, 729, 729, 729, 729, 729, 730, 730, 730, 730, 730, 730, 731,
731, 731, 731, 731, 731, 732, 732, 732, 732, 732, 732, 733, 733, 733, 733,
733, 733, 734, 734, 734, 734, 734, 734, 735, 735, 735, 735, 735, 735, 736,
736, 736, 736, 736, 736, 737, 737, 737, 737, 737, 737, 738, 738, 738, 738,
738, 738, 739, 739, 739, 739, 739, 739, 740, 740, 740, 740, 740, 740, 741,
741, 741, 741, 741, 741, 742, 742, 742, 742, 742, 742, 743, 743, 743, 743,
743, 743, 744, 744, 744, 744, 744, 744, 745, 745, 745, 745, 745, 745, 746,
746, 746, 746, 746, 746, 747, 747, 747, 747, 747, 747, 748, 748, 748, 748,
748, 748, 749, 749, 749, 749, 749, 749, 750, 750, 750, 750, 750, 750, 751,
751, 751, 751, 751, 751, 752, 752, 752, 752, 752, 752, 753, 753, 753, 753,
753, 753, 754, 754, 754, 754, 754, 754, 755, 755, 755, 755, 755, 755, 756,
756, 756, 756, 756, 756, 757, 757, 757, 757, 757, 757, 758, 758, 758, 758,
758, 758, 759, 759, 759, 759, 759, 759, 760, 760, 760, 760, 760, 760, 761,
761, 761, 761, 761, 761, 762, 762, 762, 762, 762, 762, 763, 763, 763, 763,
763, 763, 764, 764, 764, 764, 764, 764, 765, 765, 765, 765, 765, 765, 766,
766, 766, 766, 766, 766, 767, 767, 767, 767, 767, 767, 768, 768, 768, 768,
768, 768, 769, 769, 769, 769, 769, 769, 770, 770, 770, 770, 770, 770, 771,
771, 771, 771, 771, 771, 772, 772, 772, 772, 772, 772, 773, 773, 773, 773,
773, 773, 774, 774, 774, 774, 774, 774, 775, 775, 775, 775, 775, 775, 776,
776, 776, 776, 776, 776, 777, 777, 777, 777, 777, 777, 778, 778, 778, 778,
778, 778, 779, 779, 779, 779, 779, 779, 780, 780, 780, 780, 780, 780, 781,
781, 781, 781, 781, 781, 782, 782, 782, 782, 782, 782, 783, 783, 783, 783,
783, 783, 784, 784, 784, 784, 784, 784, 785, 785, 785, 785, 785, 785, 786,
786, 786, 786, 786, 786, 787, 787, 787, 787, 787, 787, 788, 788, 788, 788,
788, 788, 789, 789, 789, 789, 789, 789, 790, 790, 790, 790, 790, 790, 791,
791, 791, 791, 791, 791, 792, 792, 792, 792, 792, 792, 793, 793, 793, 793,
793, 793, 794, 794, 794, 794, 794, 794, 795, 795, 795, 795, 795, 795, 796,
796, 796, 796, 796, 796, 797, 797, 797, 797, 797, 797, 798, 798, 798, 798,
798, 798, 799, 799, 799, 799, 799, 799, 800, 800, 800, 800, 800, 800, 801,
801, 801, 801, 801, 801, 802, 802, 802, 802, 802, 802, 803, 803, 803, 803,
803, 803, 804, 804, 804, 804, 804, 804, 805, 805, 805, 805, 805, 805, 806,
806, 806, 806, 806, 806, 807, 807, 807, 807, 807, 807, 808, 808, 808, 808,
808, 808, 809, 809, 809, 809, 809, 809, 810, 810, 810, 810, 810, 810, 811,
811, 811, 811, 811, 811, 812, 812, 812, 812, 812, 812, 813, 813, 813, 813,
813, 813, 814, 814, 814, 814, 814, 814, 815, 815, 815, 815, 815, 815, 816,
816, 816, 816, 816, 816, 817, 817, 817, 817, 817, 817, 818, 818, 818, 818,
818, 818, 819, 819, 819, 819, 819, 819, 820, 820, 820, 820, 820, 820, 821,
821, 821, 821, 821, 821, 822, 822, 822, 822, 822, 822, 823, 823, 823, 823,
823, 823, 824, 824, 824, 824, 824, 824, 825, 825, 825, 825, 825, 825, 826,
826, 826, 826, 826, 826, 827, 827, 827, 827, 827, 827, 828, 828, 828, 828,
828, 828, 829, 829, 829, 829, 829, 829, 830, 830, 830, 830, 830, 830, 831,
831, 831, 831, 831, 831, 832, 832, 832, 832, 832, 832, 833, 833, 833, 833,
833, 833, 834, 834, 834, 834, 834, 834, 835, 835, 835, 835, 835, 835, 836,
836, 836, 836, 836, 836, 837, 837, 837, 837, 837, 837, 838, 838, 838, 838,
838, 838, 839, 839, 839, 839, 839, 839, 840, 840, 840, 840, 840, 840, 841,
841, 841, 841, 841, 841, 842, 842, 842, 842, 842, 842, 843, 843, 843, 843,
843, 843, 844, 844, 844, 844, 844, 844, 845, 845, 845, 845, 845, 845, 846,
846, 846, 846, 846, 846, 847, 847, 847, 847, 847, 847, 848, 848, 848, 848,
848, 848, 849, 849, 849, 849, 849, 849, 850, 850, 850, 850, 850, 850, 851,
851, 851, 851, 851, 851, 852, 852, 852, 852, 852, 852, 853, 853, 853, 853,
853, 853, 854, 854, 854, 854, 854, 854, 855, 855, 855, 855, 855, 855, 856,
856, 856, 856, 856, 856, 857, 857, 857, 857, 857, 857, 858, 858, 858, 858,
858, 858, 859, 859, 859, 859, 859, 859, 860, 860, 860, 860, 860, 860, 861,
861, 861, 861, 861, 861, 862, 862, 862, 862, 862, 862, 863, 863, 863, 863,
863, 863, 864, 864, 864, 864, 864, 864, 865, 865, 865, 865, 865, 865, 866,
866, 866, 866, 866, 866, 867, 867, 867, 867, 867, 867, 868, 868, 868, 868,
868, 868, 869, 869, 869, 869, 869, 869, 870, 870, 870, 870, 870, 870, 871,
871, 871, 871, 871, 871, 872, 872, 872, 872, 872, 872, 873, 873, 873, 873,
873, 873, 874, 874, 874, 874, 874, 874, 875, 875, 875, 875, 875, 875, 876,
876, 876, 876, 876, 876, 877, 877, 877, 877, 877, 877, 878, 878, 878, 878,
878, 878, 879, 879, 879, 879, 879, 879, 880, 880, 880, 880, 880, 880, 881,
881, 881, 881, 881, 881, 882, 882, 882, 882, 882, 882, 883, 883, 883, 883,
883, 883, 884, 884, 884, 884, 884, 884, 885, 885, 885, 885, 885, 885, 886,
886, 886, 886, 886, 886, 887, 887, 887, 887, 887, 887, 888, 888, 888, 888,
888, 888, 889, 889, 889, 889, 889, 889, 890, 890, 890, 890, 890, 890, 891,
891, 891, 891, 891, 891, 892, 892, 892, 892, 892, 892, 893, 893, 893, 893,
893, 893, 894, 894, 894, 894, 894, 894, 895, 895, 895, 895, 895, 895, 896,
896, 896, 896, 896, 896, 897, 897, 897, 897, 897, 897, 898, 898, 898, 898,
898, 898, 899, 899, 899, 899, 899, 899, 900, 900, 900, 900, 900, 900, 901,
901, 901, 901, 901, 901, 902, 902, 902, 902, 902, 902, 903, 903, 903, 903,
903, 903, 904, 904, 904, 904, 904, 904, 905, 905, 905, 905, 905, 905, 906,
906, 906, 906, 906, 906, 907, 907, 907, 907, 907, 907, 908, 908, 908, 908,
908, 908, 909, 909, 909, 909, 909, 909, 910, 910, 910, 910, 910, 910, 911,
911, 911, 911, 911, 911, 912, 912, 912, 912, 912, 912, 913, 913, 913, 913,
913, 913, 914, 914, 914, 914, 914, 914, 915, 915, 915, 915, 915, 915, 916,
916, 916, 916, 916, 916, 917, 917, 917, 917, 917, 917, 918, 918, 918, 918,
918, 918, 919, 919, 919, 919, 919, 919, 920, 920, 920, 920, 920, 920, 921,
921, 921, 921, 921, 921, 922, 922, 922, 922, 922, 922, 923, 923, 923, 923,
923, 923, 924, 924, 924, 924, 924, 924, 925, 925, 925, 925, 925, 925, 926,
926, 926, 926, 926, 926, 927, 927, 927, 927, 927, 927, 928, 928, 928, 928,
928, 928, 929, 929, 929, 929, 929, 929, 930, 930, 930, 930, 930, 930, 931,
931, 931, 931, 931, 931, 932, 932, 932, 932, 932, 932, 933, 933, 933, 933,
933, 933, 934, 934, 934, 934, 934, 934, 935, 935, 935, 935, 935, 935, 936,
936, 936, 936, 936, 936, 937, 937, 937, 937, 937, 937, 938, 938, 938, 938,
938, 938, 939, 939, 939, 939, 939, 939, 940, 940, 940, 940, 940, 940, 941,
941, 941, 941, 941, 941, 942, 942, 942, 942, 942, 942, 943, 943, 943, 943,
943, 943, 944, 944, 944, 944, 944, 944, 945, 945, 945, 945, 945, 945, 946,
946, 946, 946, 946, 946, 947, 947, 947, 947, 947, 947, 948, 948, 948, 948,
948, 948, 949, 949, 949, 949, 949, 949, 950, 950, 950, 950, 950, 950, 951,
951, 951, 951, 951, 951, 952, 952, 952, 952, 952, 952, 953, 953, 953, 953,
953, 953, 954, 954, 954, 954, 954, 954, 955, 955, 955, 955, 955, 955, 956,
956, 956, 956, 956, 956, 957, 957, 957, 957, 957, 957, 958, 958, 958, 958,
958, 958, 959, 959, 959, 959, 959, 959, 960, 960, 960, 960, 960, 960, 961,
961, 961, 961, 961, 961, 962, 962, 962, 962, 962, 962, 963, 963, 963, 963,
963, 963, 964, 964, 964, 964, 964, 964, 965, 965, 965, 965, 965, 965, 966,
966, 966, 966, 966, 966, 967, 967, 967, 967, 967, 967, 968, 968, 968, 968,
968, 968, 969, 969, 969, 969, 969, 969, 970, 970, 970, 970, 970, 970, 971,
971, 971, 971, 971, 971, 972, 972, 972, 972, 972, 972, 973, 973, 973, 973,
973, 973, 974, 974, 974, 974, 974, 974, 975, 975, 975, 975, 975, 975, 976,
976, 976, 976, 976, 976, 977, 977, 977, 977, 977, 977, 978, 978, 978, 978,
978, 978, 979, 979, 979, 979, 979, 979, 980, 980, 980, 980, 980, 980, 981,
981, 981, 981, 981, 981, 982, 982, 982, 982, 982, 982, 983, 983, 983, 983,
983, 983, 984, 984, 984, 984, 984, 984, 985, 985, 985, 985, 985, 985, 986,
986, 986, 986, 986, 986, 987, 987, 987, 987, 987, 987, 988, 988, 988, 988,
988, 988, 989, 989, 989, 989, 989, 989, 990, 990, 990, 990, 990, 990, 991,
991, 991, 991, 991, 991, 992, 992, 992, 992, 992, 992, 993, 993, 993, 993,
993, 993, 994, 994, 994, 994, 994, 994, 995, 995, 995, 995, 995, 995, 996,
996, 996, 996, 996, 996, 997, 997, 997, 997, 997, 997, 998, 998, 998, 998,
998, 998, 999, 999, 999, 999, 999, 999, 1000, 1000, 1000, 1000, 1000, 1000
, 1001, 1001, 1001, 1001, 1001, 1001, 1002, 1002, 1002, 1002, 1002, 1002, 1
003, 1003, 1003, 1003, 1003, 1003, 1004, 1004, 1004, 1004, 1004, 1004, 1005
, 1005, 1005, 1005, 1005, 1005, 1006, 1006, 1006, 1006, 1006, 1006, 1007, 1
007, 1007, 1007, 1007, 1007, 1008, 1008, 1008, 1008, 1008, 1008, 1009, 1009
, 1009, 1009, 1009, 1009, 1010, 1010, 1010, 1010, 1010, 1010, 1011, 1011, 1
011, 1011, 1011, 1011, 1012, 1012, 1012, 1012, 1012, 1012, 1013, 1013, 1013
, 1013, 1013, 1013, 1014, 1014, 1014, 1014, 1014, 1014, 1015, 1015, 1015, 1
015, 1015, 1015, 1016, 1016, 1016, 1016, 1016, 1016, 1017, 1017, 1017, 1017
, 1017, 1017, 1018, 1018, 1018, 1018, 1018, 1018, 1019, 1019, 1019, 1019, 1
019, 1019, 1020, 1020, 1020, 1020, 1020, 1020, 1021, 1021, 1021, 1021, 1021
, 1021, 1022, 1022, 1022, 1022, 1022, 1022, 1023, 1023, 1023, 1023, 1023, 1
023, 1024, 1024, 1024, 1024, 1024, 1024, 1025, 1025, 1025, 1025, 1025, 1025
, 1026, 1026, 1026, 1026, 1026, 1026, 1027, 1027, 1027, 1027, 1027, 1027, 1
028, 1028, 1028, 1028, 1028, 1028, 1029, 1029, 1029, 1029, 1029, 1029, 1030
, 1030, 1030, 1030, 1030, 1030, 1031, 1031, 1031, 1031, 1031, 1031, 1032, 1
032, 1032, 1032, 1032, 1032, 1033, 1033, 1033, 1033, 1033, 1033, 1034, 1034
, 1034, 1034, 1034, 1034, 1035, 1035, 1035, 1035, 1035, 1035, 1036, 1036, 1
036, 1036, 1036, 1036, 1037, 1037, 1037, 1037, 1037, 1037, 1038, 1038, 1038
, 1038, 1038, 1038, 1039, 1039, 1039, 1039, 1039, 1039, 1040, 1040, 1040, 1
040, 1040, 1040, 1041, 1041, 1041, 1041, 1041, 1041, 1042, 1042, 1042, 1042
, 1042, 1042, 1043, 1043, 1043, 1043, 1043, 1043, 1044, 1044, 1044, 1044, 1
044, 1044, 1045, 1045, 1045, 1045, 1045, 1045, 1046, 1046, 1046, 1046, 1046
, 1046, 1047, 1047, 1047, 1047, 1047, 1047, 1048, 1048, 1048, 1048, 1048, 1
048, 1049, 1049, 1049, 1049, 1049, 1049, 1050, 1050, 1050, 1050, 1050, 1050
, 1051, 1051, 1051, 1051, 1051, 1051, 1052, 1052, 1052, 1052, 1052, 1052, 1
053, 1053, 1053, 1053, 1053, 1053, 1054, 1054, 1054, 1054, 1054, 1054, 1055
, 1055, 1055, 1055, 1055, 1055, 1056, 1056, 1056, 1056, 1056, 1056, 1057, 1
057, 1057, 1057, 1057, 1057, 1058, 1058, 1058, 1058, 1058, 1058, 1059, 1059
, 1059, 1059, 1059, 1059, 1060, 1060, 1060, 1060, 1060, 1060, 1061, 1061, 1
061, 1061, 1061, 1061, 1062, 1062, 1062, 1062, 1062, 1062, 1063, 1063, 1063
, 1063, 1063, 1063, 1064, 1064, 1064, 1064, 1064, 1064, 1065, 1065, 1065, 1
065, 1065, 1065, 1066, 1066, 1066, 1066, 1066, 1066, 1067, 1067, 1067, 1067
, 1067, 1067, 1068, 1068, 1068, 1068, 1068, 1068, 1069, 1069, 1069, 1069, 1
069, 1069, 1070, 1070, 1070, 1070, 1070, 1070, 1071, 1071, 1071, 1071, 1071
, 1071, 1072, 1072, 1072, 1072, 1072, 1072, 1073, 1073, 1073, 1073, 1073, 1
073, 1074, 1074, 1074, 1074, 1074, 1074, 1075, 1075, 1075, 1075, 1075, 1075
, 1076, 1076, 1076, 1076, 1076, 1076, 1077, 1077, 1077, 1077, 1077, 1077, 1
078, 1078, 1078, 1078, 1078, 1078, 1079, 1079, 1079, 1079, 1079, 1079, 1080
, 1080, 1080, 1080, 1080, 1080, 1081, 1081, 1081, 1081, 1081, 1081, 1082, 1
082, 1082, 1082, 1082, 1082, 1083, 1083, 1083, 1083, 1083, 1083, 1084, 1084
, 1084, 1084, 1084, 1084, 1085, 1085, 1085, 1085, 1085, 1085, 1086, 1086, 1
086, 1086, 1086, 1086, 1087, 1087, 1087, 1087, 1087, 1087, 1088, 1088, 1088
, 1088, 1088, 1088, 1089, 1089, 1089, 1089, 1089, 1089, 1090, 1090, 1090, 1
090, 1090, 1090, 1091, 1091, 1091, 1091, 1091, 1091, 1092, 1092, 1092, 1092
, 1092, 1092, 1093, 1093, 1093, 1093, 1093, 1093, 1094, 1094, 1094, 1094, 1
094, 1094, 1095, 1095, 1095, 1095, 1095, 1095, 1096, 1096, 1096, 1096, 1096
, 1096, 1097, 1097, 1097, 1097, 1097, 1097, 1098, 1098, 1098, 1098, 1098, 1
098, 1099, 1099, 1099, 1099, 1099, 1099, 1100, 1100, 1100, 1100, 1100, 1100
, 1101, 1101, 1101, 1101, 1101, 1101, 1102, 1102, 1102, 1102, 1102, 1102, 1
103, 1103, 1103, 1103, 1103, 1103, 1104, 1104, 1104, 1104, 1104, 1104, 1105
, 1105, 1105, 1105, 1105, 1105, 1106, 1106, 1106, 1106, 1106, 1106, 1107, 1
107, 1107, 1107, 1107, 1107, 1108, 1108, 1108, 1108, 1108, 1108, 1109, 1109
, 1109, 1109, 1109, 1109, 1110, 1110, 1110, 1110, 1110, 1110, 1111, 1111, 1
111, 1111, 1111, 1111, 1112, 1112, 1112, 1112, 1112, 1112, 1113, 1113, 1113
, 1113, 1113, 1113, 1114, 1114, 1114, 1114, 1114, 1114, 1115, 1115, 1115, 1
115, 1115, 1115, 1116, 1116, 1116, 1116, 1116, 1116, 1117, 1117, 1117, 1117
, 1117, 1117, 1118, 1118, 1118, 1118, 1118, 1118, 1119, 1119, 1119, 1119, 1
119, 1119, 1120, 1120, 1120, 1120, 1120, 1120, 1121, 1121, 1121, 1121, 1121
, 1121, 1122, 1122, 1122, 1122, 1122, 1122, 1123, 1123, 1123, 1123, 1123, 1
123, 1124, 1124, 1124, 1124, 1124, 1124, 1125, 1125, 1125, 1125, 1125, 1125
, 1126, 1126, 1126, 1126, 1126, 1126, 1127, 1127, 1127, 1127, 1127, 1127, 1
128, 1128, 1128, 1128, 1128, 1128, 1129, 1129, 1129, 1129, 1129, 1129, 1130
, 1130, 1130, 1130, 1130, 1130, 1131, 1131, 1131, 1131, 1131, 1131, 1132, 1
132, 1132, 1132, 1132, 1132, 1133, 1133, 1133, 1133, 1133, 1133, 1134, 1134
, 1134, 1134, 1134, 1134, 1135, 1135, 1135, 1135, 1135, 1135, 1136, 1136, 1
136, 1136, 1136, 1136, 1137, 1137, 1137, 1137, 1137, 1137, 1138, 1138, 1138
, 1138, 1138, 1138, 1139, 1139, 1139, 1139, 1139, 1139, 1140, 1140, 1140, 1
140, 1140, 1140, 1141, 1141, 1141, 1141, 1141, 1141, 1142, 1142, 1142, 1142
, 1142, 1142, 1143, 1143, 1143, 1143, 1143, 1143, 1144, 1144, 1144, 1144, 1
144, 1144, 1145, 1145, 1145, 1145, 1145, 1145, 1146, 1146, 1146, 1146, 1146
, 1146, 1147, 1147, 1147, 1147, 1147, 1147, 1148, 1148, 1148, 1148, 1148, 1
148, 1149, 1149, 1149, 1149, 1149, 1149, 1150, 1150, 1150, 1150, 1150, 1150
, 1151, 1151, 1151, 1151, 1151, 1151, 1152, 1152, 1152, 1152, 1152, 1152, 1
153, 1153, 1153, 1153, 1153, 1153, 1154, 1154, 1154, 1154, 1154, 1154, 1155
, 1155, 1155, 1155, 1155, 1155, 1156, 1156, 1156, 1156, 1156, 1156, 1157, 1
157, 1157, 1157, 1157, 1157, 1158, 1158, 1158, 1158, 1158, 1158, 1159, 1159
, 1159, 1159, 1159, 1159, 1160, 1160, 1160, 1160, 1160, 1160, 1161, 1161, 1
161, 1161, 1161, 1161, 1162, 1162, 1162, 1162, 1162, 1162, 1163, 1163, 1163
, 1163, 1163, 1163, 1164, 1164, 1164, 1164, 1164, 1164, 1165, 1165, 1165, 1
165, 1165, 1165, 1166, 1166, 1166, 1166, 1166, 1166, 1167, 1167, 1167, 1167
, 1167, 1167, 1168, 1168, 1168, 1168, 1168, 1168, 1169, 1169, 1169, 1169, 1
169, 1169, 1170, 1170, 1170, 1170, 1170, 1170, 1171, 1171, 1171, 1171, 1171
, 1171, 1172, 1172, 1172, 1172, 1172, 1172, 1173, 1173, 1173, 1173, 1173, 1
173, 1174, 1174, 1174, 1174, 1174, 1174, 1175, 1175, 1175, 1175, 1175, 1175
, 1176, 1176, 1176, 1176, 1176, 1176, 1177, 1177, 1177, 1177, 1177, 1177, 1
178, 1178, 1178, 1178, 1178, 1178, 1179, 1179, 1179, 1179, 1179, 1179, 1180
, 1180, 1180, 1180, 1180, 1180, 1181, 1181, 1181, 1181, 1181, 1181, 1182, 1
182, 1182, 1182, 1182, 1182, 1183, 1183, 1183, 1183, 1183, 1183, 1184, 1184
, 1184, 1184, 1184, 1184, 1185, 1185, 1185, 1185, 1185, 1185, 1186, 1186, 1
186, 1186, 1186, 1186, 1187, 1187, 1187, 1187, 1187, 1187, 1188, 1188, 1188
, 1188, 1188, 1188, 1189, 1189, 1189, 1189, 1189, 1189, 1190, 1190, 1190, 1
190, 1190, 1190, 1191, 1191, 1191, 1191, 1191, 1191, 1192, 1192, 1192, 1192
, 1192, 1192, 1193, 1193, 1193, 1193, 1193, 1193, 1194, 1194, 1194, 1194, 1
194, 1194, 1195, 1195, 1195, 1195, 1195, 1195, 1196, 1196, 1196, 1196, 1196
, 1196, 1197, 1197, 1197, 1197, 1197, 1197, 1198, 1198, 1198, 1198, 1198, 1
198, 1199, 1199, 1199, 1199, 1199, 1199, 1200, 1200, 1200, 1200, 1200, 1200
, 1201, 1201, 1201, 1201, 1201, 1201, 1202, 1202, 1202, 1202, 1202, 1202, 1
203, 1203, 1203, 1203, 1203, 1203, 1204, 1204, 1204, 1204, 1204, 1204, 1205
, 1205, 1205, 1205, 1205, 1205, 1206, 1206, 1206, 1206, 1206, 1206, 1207, 1
207, 1207, 1207, 1207, 1207, 1208, 1208, 1208, 1208, 1208, 1208, 1209, 1209
, 1209, 1209, 1209, 1209, 1210, 1210, 1210, 1210, 1210, 1210, 1211, 1211, 1
211, 1211, 1211, 1211, 1212, 1212, 1212, 1212, 1212, 1212, 1213, 1213, 1213
, 1213, 1213, 1213, 1214, 1214, 1214, 1214, 1214, 1214, 1215, 1215, 1215, 1
215, 1215, 1215, 1216, 1216, 1216, 1216, 1216, 1216, 1217, 1217, 1217, 1217
, 1217, 1217, 1218, 1218, 1218, 1218, 1218, 1218, 1219, 1219, 1219, 1219, 1
219, 1219, 1220, 1220, 1220, 1220, 1220, 1220, 1221, 1221, 1221, 1221, 1221
, 1221, 1222, 1222, 1222, 1222, 1222, 1222, 1223, 1223, 1223, 1223, 1223, 1
223, 1224, 1224, 1224, 1224, 1224, 1224, 1225, 1225, 1225, 1225, 1225, 1225
, 1226, 1226, 1226, 1226, 1226, 1226, 1227, 1227, 1227, 1227, 1227, 1227, 1
228, 1228, 1228, 1228, 1228, 1228, 1229, 1229, 1229, 1229, 1229, 1229, 1230
, 1230, 1230, 1230, 1230, 1230, 1231, 1231, 1231, 1231, 1231, 1231, 1232, 1
232, 1232, 1232, 1232, 1232, 1233, 1233, 1233, 1233, 1233, 1233, 1234, 1234
, 1234, 1234, 1234, 1234, 1235, 1235, 1235, 1235, 1235, 1235, 1236, 1236, 1
236, 1236, 1236, 1236, 1237, 1237, 1237, 1237, 1237, 1237, 1238, 1238, 1238
, 1238, 1238, 1238, 1239, 1239, 1239, 1239, 1239, 1239, 1240, 1240, 1240, 1
240, 1240, 1240, 1241, 1241, 1241, 1241, 1241, 1241, 1242, 1242, 1242, 1242
, 1242, 1242, 1243, 1243, 1243, 1243, 1243, 1243, 1244, 1244, 1244, 1244, 1
244, 1244, 1245, 1245, 1245, 1245, 1245, 1245, 1246, 1246, 1246, 1246, 1246
, 1246, 1247, 1247, 1247, 1247, 1247, 1247, 1248, 1248, 1248, 1248, 1248, 1
248, 1249, 1249, 1249, 1249, 1249, 1249, 1250, 1250, 1250, 1250, 1250, 1250
, 1251, 1251, 1251, 1251, 1251, 1251, 1252, 1252, 1252, 1252, 1252, 1252, 1
253, 1253, 1253, 1253, 1253, 1253, 1254, 1254, 1254, 1254, 1254, 1254, 1255
, 1255, 1255, 1255, 1255, 1255, 1256, 1256, 1256, 1256, 1256, 1256, 1257, 1
257, 1257, 1257, 1257, 1257, 1258, 1258, 1258, 1258, 1258, 1258, 1259, 1259
, 1259, 1259, 1259, 1259, 1260, 1260, 1260, 1260, 1260, 1260, 1261, 1261, 1
261, 1261, 1261, 1261, 1262, 1262, 1262, 1262, 1262, 1262, 1263, 1263, 1263
, 1263, 1263, 1263, 1264, 1264, 1264, 1264, 1264, 1264, 1265, 1265, 1265, 1
265, 1265, 1265, 1266, 1266, 1266, 1266, 1266, 1266, 1267, 1267, 1267, 1267
, 1267, 1267, 1268, 1268, 1268, 1268, 1268, 1268, 1269, 1269, 1269, 1269, 1
269, 1269, 1270, 1270, 1270, 1270, 1270, 1270, 1271, 1271, 1271, 1271, 1271
, 1271, 1272, 1272, 1272, 1272, 1272, 1272, 1273, 1273, 1273, 1273, 1273, 1
273, 1274, 1274, 1274, 1274, 1274, 1274, 1275, 1275, 1275, 1275, 1275, 1275
, 1276, 1276, 1276, 1276, 1276, 1276, 1277, 1277, 1277, 1277, 1277, 1277, 1
278, 1278, 1278, 1278, 1278, 1278, 1279, 1279, 1279, 1279, 1279, 1279, 1280
, 1280, 1280, 1280, 1280, 1280, 1281, 1281, 1281, 1281, 1281, 1281, 1282, 1
282, 1282, 1282, 1282, 1282, 1283, 1283, 1283, 1283, 1283, 1283, 1284, 1284
, 1284, 1284, 1284, 1284, 1285, 1285, 1285, 1285, 1285, 1285, 1286, 1286, 1
286, 1286, 1286, 1286, 1287, 1287, 1287, 1287, 1287, 1287, 1288, 1288, 1288
, 1288, 1288, 1288, 1289, 1289, 1289, 1289, 1289, 1289, 1290, 1290, 1290, 1
290, 1290, 1290, 1291, 1291, 1291, 1291, 1291, 1291, 1292, 1292, 1292, 1292
, 1292, 1292, 1293, 1293, 1293, 1293, 1293, 1293, 1294, 1294, 1294, 1294, 1
294, 1294, 1295, 1295, 1295, 1295, 1295, 1295, 1296, 1296, 1296, 1296, 1296
, 1296, 1297, 1297, 1297, 1297, 1297, 1297, 1298, 1298, 1298, 1298, 1298, 1
298, 1299, 1299, 1299, 1299, 1299, 1299, 1300, 1300, 1300, 1300, 1300, 1300
, 1301, 1301, 1301, 1301, 1301, 1301, 1302, 1302, 1302, 1302, 1302, 1302, 1
303, 1303, 1303, 1303, 1303, 1303, 1304, 1304, 1304, 1304, 1304, 1304, 1305
, 1305, 1305, 1305, 1305, 1305, 1306, 1306, 1306, 1306, 1306, 1306, 1307, 1
307, 1307, 1307, 1307, 1307, 1308, 1308, 1308, 1308, 1308, 1308, 1309, 1309
, 1309, 1309, 1309, 1309, 1310, 1310, 1310, 1310, 1310, 1310, 1311, 1311, 1
311, 1311, 1311, 1311, 1312, 1312, 1312, 1312, 1312, 1312, 1313, 1313, 1313
, 1313, 1313, 1313, 1314, 1314, 1314, 1314, 1314, 1314, 1315, 1315, 1315, 1
315, 1315, 1315, 1316, 1316, 1316, 1316, 1316, 1316, 1317, 1317, 1317, 1317
, 1317, 1317, 1318, 1318, 1318, 1318, 1318, 1318, 1319, 1319, 1319, 1319, 1
319, 1319, 1320, 1320, 1320, 1320, 1320, 1320, 1321, 1321, 1321, 1321, 1321
, 1321, 1322, 1322, 1322, 1322, 1322, 1322, 1323, 1323, 1323, 1323, 1323, 1
323, 1324, 1324, 1324, 1324, 1324, 1324, 1325, 1325, 1325, 1325, 1325, 1325
, 1326, 1326, 1326, 1326, 1326, 1326, 1327, 1327, 1327, 1327, 1327, 1327, 1
328, 1328, 1328, 1328, 1328, 1328, 1329, 1329, 1329, 1329, 1329, 1329, 1330
, 1330, 1330, 1330, 1330, 1330, 1331, 1331, 1331, 1331, 1331, 1331, 1332, 1
332, 1332, 1332, 1332, 1332, 1333, 1333, 1333, 1333, 1333, 1333, 1334, 1334
, 1334, 1334, 1334, 1334, 1335, 1335, 1335, 1335, 1335, 1335, 1336, 1336, 1
336, 1336, 1336, 1336, 1337, 1337, 1337, 1337, 1337, 1337, 1338, 1338, 1338
, 1338, 1338, 1338, 1339, 1339, 1339, 1339, 1339, 1339, 1340, 1340, 1340, 1
340, 1340, 1340, 1341, 1341, 1341, 1341, 1341, 1341, 1342, 1342, 1342, 1342
, 1342, 1342, 1343, 1343, 1343, 1343, 1343, 1343, 1344, 1344, 1344, 1344, 1
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773, 1774, 1774, 1774, 1774, 1774, 1774, 1775, 1775, 1775, 1775, 1775, 1775
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778, 1778, 1778, 1778, 1778, 1778, 1779, 1779, 1779, 1779, 1779, 1779, 1780
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782, 1782, 1782, 1782, 1782, 1783, 1783, 1783, 1783, 1783, 1783, 1784, 1784
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786, 1786, 1786, 1786, 1787, 1787, 1787, 1787, 1787, 1787, 1788, 1788, 1788
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790, 1790, 1790, 1791, 1791, 1791, 1791, 1791, 1791, 1792, 1792, 1792, 1792
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794, 1794, 1795, 1795, 1795, 1795, 1795, 1795, 1796, 1796, 1796, 1796, 1796
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798, 1799, 1799, 1799, 1799, 1799, 1799, 1800, 1800, 1800, 1800, 1800, 1800
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803, 1803, 1803, 1803, 1803, 1803, 1804, 1804, 1804, 1804, 1804, 1804, 1805
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807, 1807, 1807, 1807, 1807, 1808, 1808, 1808, 1808, 1808, 1808, 1809, 1809
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811, 1811, 1811, 1811, 1812, 1812, 1812, 1812, 1812, 1812, 1813, 1813, 1813
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815, 1815, 1815, 1816, 1816, 1816, 1816, 1816, 1816, 1817, 1817, 1817, 1817
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819, 1819, 1820, 1820, 1820, 1820, 1820, 1820, 1821, 1821, 1821, 1821, 1821
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823, 1824, 1824, 1824, 1824, 1824, 1824, 1825, 1825, 1825, 1825, 1825, 1825
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828, 1828, 1828, 1828, 1828, 1828, 1829, 1829, 1829, 1829, 1829, 1829, 1830
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832, 1832, 1832, 1832, 1832, 1833, 1833, 1833, 1833, 1833, 1833, 1834, 1834
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836, 1836, 1836, 1836, 1837, 1837, 1837, 1837, 1837, 1837, 1838, 1838, 1838
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840, 1840, 1840, 1841, 1841, 1841, 1841, 1841, 1841, 1842, 1842, 1842, 1842
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844, 1844, 1845, 1845, 1845, 1845, 1845, 1845, 1846, 1846, 1846, 1846, 1846
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848, 1849, 1849, 1849, 1849, 1849, 1849, 1850, 1850, 1850, 1850, 1850, 1850
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853, 1853, 1853, 1853, 1853, 1853, 1854, 1854, 1854, 1854, 1854, 1854, 1855
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857, 1857, 1857, 1857, 1857, 1858, 1858, 1858, 1858, 1858, 1858, 1859, 1859
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861, 1861, 1861, 1861, 1862, 1862, 1862, 1862, 1862, 1862, 1863, 1863, 1863
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865, 1865, 1865, 1866, 1866, 1866, 1866, 1866, 1866, 1867, 1867, 1867, 1867
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873, 1874, 1874, 1874, 1874, 1874, 1874, 1875, 1875, 1875, 1875, 1875, 1875
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878, 1878, 1878, 1878, 1878, 1878, 1879, 1879, 1879, 1879, 1879, 1879, 1880
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882, 1882, 1882, 1882, 1882, 1883, 1883, 1883, 1883, 1883, 1883, 1884, 1884
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886, 1886, 1886, 1886, 1887, 1887, 1887, 1887, 1887, 1887, 1888, 1888, 1888
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890, 1890, 1890, 1891, 1891, 1891, 1891, 1891, 1891, 1892, 1892, 1892, 1892
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894, 1894, 1895, 1895, 1895, 1895, 1895, 1895, 1896, 1896, 1896, 1896, 1896
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928, 1928, 1928, 1928, 1928, 1928, 1929, 1929, 1929, 1929, 1929, 1929, 1930
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2, 0.014724445971058422, 9610.000000000002, -38440.01472444598, 9610.000000
000002, 9610.000000000002, 9610.000000000002, 0.014724445971058422, 9610.00
0000000002, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9610.
000000000002, 0.014724445971058422, 9610.000000000002, 9610.000000000002, -
38440.01472444598, 9610.000000000002, 9610.000000000002, 0.0147244459710584
22, 9610.000000000002, 9610.000000000002, -38440.01472444598, 9610.00000000
0002, 9610.000000000002, 0.014724445971058422, 9610.000000000002, 9610.0000
00000002, -38440.01472444598, 9610.000000000002, 9610.000000000002, 0.01472
4445971058422, 9610.000000000002, 9610.000000000002, -38440.01472444598, 96
10.000000000002, 9610.000000000002, 0.014724445971058422, 9610.000000000002
, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9610.0000000000
02, 0.014724445971058422, 9610.000000000002, 9610.000000000002, -38440.0147
2444598, 9610.000000000002, 9610.000000000002, 0.014724445971058422, 9610.0
00000000002, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9610
.000000000002, 0.014724445971058422, 9610.000000000002, 9610.000000000002,
-38440.01472444598, 9610.000000000002, 9610.000000000002, 0.014724445971058
422, 9610.000000000002, 9610.000000000002, -38440.01472444598, 9610.0000000
00002, 9610.000000000002, 0.014724445971058422, 9610.000000000002, 9610.000
000000002, -38440.01472444598, 9610.000000000002, 9610.000000000002, 0.0147
24445971058422, 9610.000000000002, 9610.000000000002, -38440.01472444598, 9
610.000000000002, 9610.000000000002, 0.014724445971058422, 9610.00000000000
2, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9610.000000000
002, 0.014724445971058422, 9610.000000000002, 9610.000000000002, -38440.014
72444598, 9610.000000000002, 9610.000000000002, 0.014724445971058422, 9610.
000000000002, 9610.000000000002, -38440.01472444598, 9610.000000000002, 961
0.000000000002, 0.014724445971058422, 9610.000000000002, 9610.000000000002,
-38440.01472444598, 9610.000000000002, 9610.000000000002, 0.01472444597105
8422, 9610.000000000002, 9610.000000000002, -38440.01472444598, 9610.000000
000002, 9610.000000000002, 0.014724445971058422, 9610.000000000002, 9610.00
0000000002, -38440.01472444598, 9610.000000000002, 9610.000000000002, 0.014
724445971058422, 9610.000000000002, 9610.000000000002, -38440.01472444598,
9610.000000000002, 9610.000000000002, 0.014724445971058422, 9610.0000000000
02, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9610.00000000
0002, 0.014724445971058422, 9610.000000000002, 9610.000000000002, -38440.01
472444598, 9610.000000000002, 9610.000000000002, 0.014724445971058422, 9610
.000000000002, 9610.000000000002, -38440.01472444598, 9610.000000000002, 96
10.000000000002, 0.014724445971058422, 9610.000000000002, 9610.000000000002
, -38440.01472444598, 9610.000000000002, 9610.000000000002, 0.0147244459710
58422, 9610.000000000002, 9610.000000000002, -38440.01472444598, 9610.00000
0000002, 9610.000000000002, 0.014724445971058422, 9610.000000000002, 9610.0
00000000002, -38440.01472444598, 9610.000000000002, 9610.000000000002, 0.01
4724445971058422, 9610.000000000002, 9610.000000000002, -38440.01472444598,
9610.000000000002, 9610.000000000002, 0.014724445971058422, 9610.000000000
002, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9610.0000000
00002, 0.014724445971058422, 9610.000000000002, 9610.000000000002, -38440.0
1472444598, 9610.000000000002, 9610.000000000002, 0.014724445971058422, 961
0.000000000002, 9610.000000000002, -38440.01472444598, 9610.000000000002, 9
610.000000000002, 0.014724445971058422, 9610.000000000002, 9610.00000000000
2, -38440.01472444598, 9610.000000000002, 9610.000000000002, 0.014724445971
058422, 9610.000000000002, 9610.000000000002, 9610.000000000002, -38440.014
72444598, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002, -38
440.00000000001, 9610.000000000002, 9610.000000000002, 0.0, 9610.0000000000
02, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610.00000000
0002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -38440.
00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002,
9610.000000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.0000000
00002, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610.00000
0000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -384
40.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.00000000000
2, 9610.000000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.0000
00000002, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610.00
0000000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -
38440.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.00000000
0002, 9610.000000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.0
00000000002, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610
.000000000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002
, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.00000
0000002, 9610.000000000002, -38440.00000000001, 9610.000000000002, 0.0, 961
0.000000000002, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9
610.000000000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000
002, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.00
0000000002, 9610.000000000002, -38440.00000000001, 9610.000000000002, 0.0,
9610.000000000002, 9610.000000000002, 9610.000000000002, -38440.00000000001
, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000
000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610
.000000000002, 9610.000000000002, -38440.00000000001, 9610.000000000002, 0.
0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -38440.00000000
001, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000
000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9
610.000000000002, 9610.000000000002, -38440.00000000001, 9610.000000000002,
0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -38440.00000
000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.
000000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000000002
, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610.0000000000
02, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -38440.00
000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002, 96
10.000000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000000
002, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610.0000000
00002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, -38440
.00000000001, 9610.000000000002, 0.0, 9610.000000000002, 9610.000000000002,
9610.000000000002, -38440.00000000001, 9610.000000000002, 0.0, 9610.000000
000002, 9610.000000000002, 9610.000000000002, -38440.00000000001, 9610.0000
00000002, 0.0, 9610.000000000002, 9610.000000000002, 9610.000000000002, 961
0.000000000002, -38440.00000000001], 2048, 2048)), 0x0000000000007dd8).
[Info] Solver RobustMultiNewton (GMRES) successfully solved the problem (no
rm = 1.1664069101655303e-8).
[Info] Solver Newton Raphson successfully solved the problem (norm = 2.6476
053818757766e-9).
[Info] Solver Newton Krylov successfully solved the problem (norm = 1.16640
69101655303e-8).
[Info] Solver Trust Region successfully solved the problem (norm = 2.647605
3818757766e-9).
[Info] Solver TR Krylov successfully solved the problem (norm = 1.166406910
1655303e-8).
[Info] Solver NR [NLsolve.jl] successfully solved the problem (norm = 2.629
767216137896e-9).
[Info] Solver TR [NLsolve.jl] successfully solved the problem (norm = 2.629
767216137896e-9).
[Info] Solver NR [Sundials] successfully solved the problem (norm = 5.94616
2345262808e-6).
[Warn] Solver Newton Krylov [Sundials] returned retcode Failure with an res
idual norm = 34.06162309153361.
[Info] Solver Mod. Powell [MINPACK] successfully solved the problem (norm =
1.962972484440553e-6).Plotting the Work-Precision Diagram.
fig = begin
LINESTYLES = Dict(:nonlinearsolve => :solid, :simplenonlinearsolve => :dash,
:wrapper => :dot)
ASPECT_RATIO = 0.7
WIDTH = 1200
HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
STROKEWIDTH = 2.5
colors = cgrad(:seaborn_bright, length(successful_solvers); categorical = true)
cycle = Cycle([:marker], covary = true)
plot_theme = Theme(Lines = (; cycle), Scatter = (; cycle))
with_theme(plot_theme) do
fig = Figure(; size = (WIDTH, HEIGHT))
# `textbf` doesn't work
ax = Axis(fig[1, 1], ylabel = L"Time $\mathbf{(s)}$",
xlabelsize = 22, ylabelsize = 22,
xlabel = L"Error: $\mathbf{||f(u^\ast)||_\infty}$",
xscale = log10, yscale = log10, xtickwidth = STROKEWIDTH,
ytickwidth = STROKEWIDTH, spinewidth = STROKEWIDTH,
xticklabelsize = 20, yticklabelsize = 20)
idxs = sortperm(median.(getfield.(wp_set.wps, :times)))
ls, scs = [], []
for (i, (wp, solver)) in enumerate(zip(wp_set.wps[idxs], successful_solvers[idxs]))
(; name, times, errors) = wp
errors = [err.l∞ for err in errors]
l = lines!(ax, errors, times; linestyle = LINESTYLES[solver.pkg], label = name,
linewidth = 5, color = colors[i])
sc = scatter!(ax, errors, times; label = name, markersize = 16, strokewidth = 2,
color = colors[i])
push!(ls, l)
push!(scs, sc)
end
xlims!(ax; high=1)
ylims!(ax; low=5e-3)
axislegend(ax, [[l, sc] for (l, sc) in zip(ls, scs)],
[solver.name for solver in successful_solvers[idxs]], "Successful Solvers";
framevisible=true, framewidth = STROKEWIDTH, position = :rb,
titlesize = 20, labelsize = 16, patchsize = (40.0f0, 20.0f0))
fig[0, :] = Label(fig, "Brusselator Steady State PDE: Work Precision Diagram",
fontsize = 24, tellwidth = false, font = :bold)
fig
end
end
save("brusselator_wpd.svg", fig)CairoMakie.Screen{SVG}Appendix
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/NonlinearProblem","bruss.jmd")Computer Information:
Julia Version 1.10.6
Commit 67dffc4a8ae (2024-10-28 12:23 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
JULIA_CPU_THREADS = 128
JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953
Package Information:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Project.toml`
[2169fc97] AlgebraicMultigrid v0.6.0
[6e4b80f9] BenchmarkTools v1.5.0
[13f3f980] CairoMakie v0.12.16
⌃ [2b5f629d] DiffEqBase v6.158.3
[f3b72e0c] DiffEqDevTools v2.45.1
⌃ [a0c0ee7d] DifferentiationInterface v0.6.22
⌃ [7da242da] Enzyme v0.13.14
[40713840] IncompleteLU v0.2.1
[b964fa9f] LaTeXStrings v1.4.0
[d3d80556] LineSearches v7.3.0
⌃ [7ed4a6bd] LinearSolve v2.36.2
[4854310b] MINPACK v1.3.0
[2774e3e8] NLsolve v4.5.1
[b7050fa9] NonlinearProblemLibrary v0.1.2
⌃ [8913a72c] NonlinearSolve v4.1.0
[ace2c81b] PETSc v0.3.1
[98d1487c] PolyesterForwardDiff v0.1.2
[08abe8d2] PrettyTables v2.4.0
[31c91b34] SciMLBenchmarks v0.1.3
[efcf1570] Setfield v1.1.1
[727e6d20] SimpleNonlinearSolve v2.0.0
[9f842d2f] SparseConnectivityTracer v0.6.8
[47a9eef4] SparseDiffTools v2.23.0
[f1835b91] SpeedMapping v0.3.0
[860ef19b] StableRNGs v1.0.2
[90137ffa] StaticArrays v1.9.8
[c3572dad] Sundials v4.26.1
⌃ [0c5d862f] Symbolics v6.18.3
Info Packages marked with ⌃ have new versions available and may be upgradable.
Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.And the full manifest:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Manifest.toml`
⌃ [47edcb42] ADTypes v1.9.0
[a4c015fc] ANSIColoredPrinters v0.0.1
[621f4979] AbstractFFTs v1.5.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.38
[22286c92] AccurateArithmetic v0.3.8
[79e6a3ab] Adapt v4.1.1
[35492f91] AdaptivePredicates v1.2.0
[2169fc97] AlgebraicMultigrid v0.6.0
[66dad0bd] AliasTables v1.1.3
⌃ [27a7e980] Animations v0.4.1
[4c88cf16] Aqua v0.8.9
[ec485272] ArnoldiMethod v0.4.0
⌃ [4fba245c] ArrayInterface v7.17.0
[4c555306] ArrayLayouts v1.10.4
[67c07d97] Automa v1.1.0
[13072b0f] AxisAlgorithms v1.1.0
[39de3d68] AxisArrays v0.4.7
[6e4b80f9] BenchmarkTools v1.5.0
[e2ed5e7c] Bijections v0.1.9
[d1d4a3ce] BitFlags v0.1.9
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
[8e7c35d0] BlockArrays v1.1.1
[70df07ce] BracketingNonlinearSolve v1.1.0
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.6
⌃ [159f3aea] Cairo v1.1.0
[13f3f980] CairoMakie v0.12.16
[7057c7e9] Cassette v0.3.14
[d360d2e6] ChainRulesCore v1.25.0
[fb6a15b2] CloseOpenIntervals v0.1.13
[944b1d66] CodecZlib v0.7.6
[a2cac450] ColorBrewer v0.4.0
[35d6a980] ColorSchemes v3.27.1
⌅ [3da002f7] ColorTypes v0.11.5
⌅ [c3611d14] ColorVectorSpace v0.10.0
⌅ [5ae59095] Colors v0.12.11
[861a8166] Combinatorics v1.0.2
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.1
[f70d9fcc] CommonWorldInvalidations v1.0.0
[34da2185] Compat v4.16.0
[b152e2b5] CompositeTypes v0.1.4
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.3
[f0e56b4a] ConcurrentUtilities v2.4.2
[8f4d0f93] Conda v1.10.2
[187b0558] ConstructionBase v1.5.8
[d38c429a] Contour v0.6.3
[a2441757] Coverage v1.6.1
[c36e975a] CoverageTools v1.3.2
[adafc99b] CpuId v0.3.1
[a8cc5b0e] Crayons v4.1.1
[9a962f9c] DataAPI v1.16.0
[864edb3b] DataStructures v0.18.20
[e2d170a0] DataValueInterfaces v1.0.0
⌃ [927a84f5] DelaunayTriangulation v1.6.1
⌃ [2b5f629d] DiffEqBase v6.158.3
[f3b72e0c] DiffEqDevTools v2.45.1
[77a26b50] DiffEqNoiseProcess v5.23.0
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
⌃ [a0c0ee7d] DifferentiationInterface v0.6.22
[b4f34e82] Distances v0.10.12
[31c24e10] Distributions v0.25.113
[ffbed154] DocStringExtensions v0.9.3
⌃ [e30172f5] Documenter v1.7.0
[35a29f4d] DocumenterTools v0.1.20
[5b8099bc] DomainSets v0.7.14
[7c1d4256] DynamicPolynomials v0.6.0
[4e289a0a] EnumX v1.0.4
⌃ [7da242da] Enzyme v0.13.14
⌃ [f151be2c] EnzymeCore v0.8.5
[429591f6] ExactPredicates v2.2.8
⌃ [460bff9d] ExceptionUnwrapping v0.1.10
[e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
[411431e0] Extents v0.1.4
[7a1cc6ca] FFTW v1.8.0
[7034ab61] FastBroadcast v0.3.5
[9aa1b823] FastClosures v0.3.2
[29a986be] FastLapackInterface v2.0.4
⌃ [5789e2e9] FileIO v1.16.4
[8fc22ac5] FilePaths v0.8.3
[48062228] FilePathsBase v0.9.22
[1a297f60] FillArrays v1.13.0
⌃ [6a86dc24] FiniteDiff v2.26.0
[53c48c17] FixedPointNumbers v0.8.5
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v0.10.38
[b38be410] FreeType v4.1.1
⌃ [663a7486] FreeTypeAbstraction v0.10.4
[f62d2435] FunctionProperties v0.1.2
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
⌅ [46192b85] GPUArraysCore v0.1.6
[61eb1bfa] GPUCompiler v1.0.1
[68eda718] GeoFormatTypes v0.4.2
[cf35fbd7] GeoInterface v1.3.8
⌅ [5c1252a2] GeometryBasics v0.4.11
[d7ba0133] Git v1.3.1
[a2bd30eb] Graphics v1.1.3
[86223c79] Graphs v1.12.0
⌃ [3955a311] GridLayoutBase v0.11.0
[42e2da0e] Grisu v1.0.2
[708ec375] Gumbo v0.8.2
[cd3eb016] HTTP v1.10.10
[eafb193a] Highlights v0.5.3
[3e5b6fbb] HostCPUFeatures v0.1.17
[34004b35] HypergeometricFunctions v0.3.25
[7073ff75] IJulia v1.26.0
[b5f81e59] IOCapture v0.2.5
[615f187c] IfElse v0.1.1
[2803e5a7] ImageAxes v0.6.12
[c817782e] ImageBase v0.1.7
⌃ [a09fc81d] ImageCore v0.10.4
[82e4d734] ImageIO v0.6.9
[bc367c6b] ImageMetadata v0.9.10
[40713840] IncompleteLU v0.2.1
[9b13fd28] IndirectArrays v1.0.0
[d25df0c9] Inflate v0.1.5
[18e54dd8] IntegerMathUtils v0.1.2
[a98d9a8b] Interpolations v0.15.1
[d1acc4aa] IntervalArithmetic v0.22.19
[8197267c] IntervalSets v0.7.10
[3587e190] InverseFunctions v0.1.17
[92d709cd] IrrationalConstants v0.2.2
[f1662d9f] Isoband v0.1.1
[c8e1da08] IterTools v1.10.0
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[692b3bcd] JLLWrappers v1.6.1
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[b835a17e] JpegTurbo v0.1.5
[ef3ab10e] KLU v0.6.0
[5ab0869b] KernelDensity v0.6.9
[ba0b0d4f] Krylov v0.9.8
[929cbde3] LLVM v9.1.3
[b964fa9f] LaTeXStrings v1.4.0
[23fbe1c1] Latexify v0.16.5
[10f19ff3] LayoutPointers v0.1.17
[0e77f7df] LazilyInitializedFields v1.3.0
⌃ [5078a376] LazyArrays v2.2.1
[8cdb02fc] LazyModules v0.3.1
[87fe0de2] LineSearch v0.1.4
[d3d80556] LineSearches v7.3.0
⌃ [7ed4a6bd] LinearSolve v2.36.2
[2ab3a3ac] LogExpFunctions v0.3.28
[e6f89c97] LoggingExtras v1.1.0
[bdcacae8] LoopVectorization v0.12.171
[4854310b] MINPACK v1.3.0
[d8e11817] MLStyle v0.4.17
[da04e1cc] MPI v0.20.22
[3da0fdf6] MPIPreferences v0.1.11
[1914dd2f] MacroTools v0.5.13
[ee78f7c6] Makie v0.21.16
[20f20a25] MakieCore v0.8.10
[d125e4d3] ManualMemory v0.1.8
[dbb5928d] MappedArrays v0.4.2
[d0879d2d] MarkdownAST v0.1.2
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[e94cdb99] MosaicViews v0.3.4
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[102ac46a] MultivariatePolynomials v0.5.7
[ffc61752] Mustache v1.0.20
⌃ [d8a4904e] MutableArithmetics v1.5.2
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[77ba4419] NaNMath v1.0.2
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[b7050fa9] NonlinearProblemLibrary v0.1.2
⌃ [8913a72c] NonlinearSolve v4.1.0
⌃ [be0214bd] NonlinearSolveBase v1.3.1
⌃ [5959db7a] NonlinearSolveFirstOrder v1.0.0
[9a2c21bd] NonlinearSolveQuasiNewton v1.0.0
[26075421] NonlinearSolveSpectralMethods v1.0.0
[d8793406] ObjectFile v0.4.2
[510215fc] Observables v0.5.5
[6fe1bfb0] OffsetArrays v1.14.1
[52e1d378] OpenEXR v0.3.3
[4d8831e6] OpenSSL v1.4.3
⌃ [429524aa] Optim v1.9.4
[bac558e1] OrderedCollections v1.6.3
[90014a1f] PDMats v0.11.31
[ace2c81b] PETSc v0.3.1
[f57f5aa1] PNGFiles v0.4.3
[65ce6f38] PackageExtensionCompat v1.0.2
⌃ [19eb6ba3] Packing v0.5.0
[5432bcbf] PaddedViews v0.5.12
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.8.1
[eebad327] PkgVersion v0.3.3
[995b91a9] PlotUtils v1.4.3
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.16
[98d1487c] PolyesterForwardDiff v0.1.2
[1d0040c9] PolyesterWeave v0.2.2
[647866c9] PolygonOps v0.1.2
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v0.4.24
[aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[08abe8d2] PrettyTables v2.4.0
[27ebfcd6] Primes v0.5.6
[92933f4c] ProgressMeter v1.10.2
[43287f4e] PtrArrays v1.2.1
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[1fd47b50] QuadGK v2.11.1
[74087812] Random123 v1.7.0
[e6cf234a] RandomNumbers v1.6.0
[b3c3ace0] RangeArrays v0.3.2
[c84ed2f1] Ratios v0.4.5
[3cdcf5f2] RecipesBase v1.3.4
⌃ [731186ca] RecursiveArrayTools v3.27.3
[f2c3362d] RecursiveFactorization v0.2.23
[189a3867] Reexport v1.2.2
[2792f1a3] RegistryInstances v0.1.0
[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.0
[ae5879a3] ResettableStacks v1.1.1
[79098fc4] Rmath v0.8.0
[47965b36] RootedTrees v2.23.1
[5eaf0fd0] RoundingEmulator v0.2.1
[7e49a35a] RuntimeGeneratedFunctions v0.5.13
[fdea26ae] SIMD v3.7.0
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.43
[322a6be2] Sass v0.2.0
⌃ [0bca4576] SciMLBase v2.59.2
[31c91b34] SciMLBenchmarks v0.1.3
[19f34311] SciMLJacobianOperators v0.1.1
[c0aeaf25] SciMLOperators v0.3.12
⌃ [53ae85a6] SciMLStructures v1.5.0
[6c6a2e73] Scratch v1.2.1
[efcf1570] Setfield v1.1.1
⌅ [65257c39] ShaderAbstractions v0.4.1
[992d4aef] Showoff v1.0.3
[73760f76] SignedDistanceFields v0.4.0
[777ac1f9] SimpleBufferStream v1.2.0
[727e6d20] SimpleNonlinearSolve v2.0.0
[699a6c99] SimpleTraits v0.9.4
[45858cf5] Sixel v0.1.3
[b85f4697] SoftGlobalScope v1.1.0
[a2af1166] SortingAlgorithms v1.2.1
[9f842d2f] SparseConnectivityTracer v0.6.8
[47a9eef4] SparseDiffTools v2.23.0
⌃ [0a514795] SparseMatrixColorings v0.4.9
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.4.0
[f1835b91] SpeedMapping v0.3.0
[860ef19b] StableRNGs v1.0.2
[cae243ae] StackViews v0.1.1
[aedffcd0] Static v1.1.1
[0d7ed370] StaticArrayInterface v1.8.0
[90137ffa] StaticArrays v1.9.8
[1e83bf80] StaticArraysCore v1.4.3
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.3
[4c63d2b9] StatsFuns v1.3.2
[7792a7ef] StrideArraysCore v0.5.7
[69024149] StringEncodings v0.3.7
[892a3eda] StringManipulation v0.4.0
⌅ [09ab397b] StructArrays v0.6.18
[53d494c1] StructIO v0.3.1
[c3572dad] Sundials v4.26.1
⌃ [2efcf032] SymbolicIndexingInterface v0.3.34
[19f23fe9] SymbolicLimits v0.2.2
[d1185830] SymbolicUtils v3.7.2
⌃ [0c5d862f] Symbolics v6.18.3
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.0
[62fd8b95] TensorCore v0.1.1
[8ea1fca8] TermInterface v2.0.0
[8290d209] ThreadingUtilities v0.5.2
[731e570b] TiffImages v0.11.1
[a759f4b9] TimerOutputs v0.5.25
[3bb67fe8] TranscodingStreams v0.11.3
[d5829a12] TriangularSolve v0.2.1
[981d1d27] TriplotBase v0.1.0
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.21.0
[a7c27f48] Unityper v0.1.6
[3d5dd08c] VectorizationBase v0.21.71
[81def892] VersionParsing v1.3.0
[19fa3120] VertexSafeGraphs v0.2.0
[44d3d7a6] Weave v0.10.12
[e3aaa7dc] WebP v0.1.3
[efce3f68] WoodburyMatrices v1.0.0
[ddb6d928] YAML v0.4.12
[c2297ded] ZMQ v1.3.0
[6e34b625] Bzip2_jll v1.0.8+2
[4e9b3aee] CRlibm_jll v1.0.1+0
[83423d85] Cairo_jll v1.18.2+1
[5ae413db] EarCut_jll v2.2.4+0
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⌃ [2e619515] Expat_jll v2.6.2+0
[b22a6f82] FFMPEG_jll v6.1.2+0
[f5851436] FFTW_jll v3.3.10+1
[a3f928ae] Fontconfig_jll v2.13.96+0
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[59f7168a] Giflib_jll v5.2.2+0
[f8c6e375] Git_jll v2.46.2+0
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[3b182d85] Graphite2_jll v1.3.14+0
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[2e76f6c2] HarfBuzz_jll v8.3.1+0
[e33a78d0] Hwloc_jll v2.11.2+1
[905a6f67] Imath_jll v3.1.11+0
[1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
[aacddb02] JpegTurbo_jll v3.0.4+0
[c1c5ebd0] LAME_jll v3.100.2+0
[88015f11] LERC_jll v4.0.0+0
[dad2f222] LLVMExtra_jll v0.0.34+0
[1d63c593] LLVMOpenMP_jll v18.1.7+0
[dd4b983a] LZO_jll v2.10.2+1
⌅ [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.11.0+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[7add5ba3] Libgpg_error_jll v1.50.0+0
[94ce4f54] Libiconv_jll v1.17.0+1
[4b2f31a3] Libmount_jll v2.40.1+0
[89763e89] Libtiff_jll v4.7.0+0
[38a345b3] Libuuid_jll v2.40.1+0
[856f044c] MKL_jll v2024.2.0+0
[7cb0a576] MPICH_jll v4.2.3+0
[f1f71cc9] MPItrampoline_jll v5.5.1+0
⌃ [9237b28f] MicrosoftMPI_jll v10.1.4+2
[e7412a2a] Ogg_jll v1.3.5+1
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
[18a262bb] OpenEXR_jll v3.2.4+0
[fe0851c0] OpenMPI_jll v5.0.5+0
[9bd350c2] OpenSSH_jll v9.9.1+1
[458c3c95] OpenSSL_jll v3.0.15+1
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.3+0
[8fa3689e] PETSc_jll v3.22.0+0
[36c8627f] Pango_jll v1.54.1+0
[30392449] Pixman_jll v0.43.4+0
[f50d1b31] Rmath_jll v0.5.1+0
[aabda75e] SCALAPACK32_jll v2.2.1+1
⌅ [fb77eaff] Sundials_jll v5.2.2+0
⌃ [02c8fc9c] XML2_jll v2.13.4+0
[aed1982a] XSLT_jll v1.1.41+0
[ffd25f8a] XZ_jll v5.6.3+0
[4f6342f7] Xorg_libX11_jll v1.8.6+0
[0c0b7dd1] Xorg_libXau_jll v1.0.11+0
[a3789734] Xorg_libXdmcp_jll v1.1.4+0
[1082639a] Xorg_libXext_jll v1.3.6+0
[ea2f1a96] Xorg_libXrender_jll v0.9.11+0
[14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
[c7cfdc94] Xorg_libxcb_jll v1.17.0+0
[c5fb5394] Xorg_xtrans_jll v1.5.0+0
[8f1865be] ZeroMQ_jll v4.3.5+1
[3161d3a3] Zstd_jll v1.5.6+1
[b792d7bf] cminpack_jll v1.3.8+0
[9a68df92] isoband_jll v0.2.3+0
[a4ae2306] libaom_jll v3.9.0+0
[0ac62f75] libass_jll v0.15.2+0
[f638f0a6] libfdk_aac_jll v2.0.3+0
[b53b4c65] libpng_jll v1.6.44+0
[47bcb7c8] libsass_jll v3.6.6+0
[075b6546] libsixel_jll v1.10.3+1
[a9144af2] libsodium_jll v1.0.20+1
[f27f6e37] libvorbis_jll v1.3.7+2
[c5f90fcd] libwebp_jll v1.4.0+0
[1317d2d5] oneTBB_jll v2021.12.0+0
[1270edf5] x264_jll v10164.0.0+0
⌅ [dfaa095f] x265_jll v3.6.0+0
[0dad84c5] ArgTools v1.1.1
[56f22d72] Artifacts
[2a0f44e3] Base64
[8bf52ea8] CRC32c
[ade2ca70] Dates
[8ba89e20] Distributed
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.10.0
[de0858da] Printf
[9abbd945] Profile
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays v1.10.0
[10745b16] Statistics v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.52.0+1
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.