natemcintosh · May 21, 2025 03:15
diff --git a/fiddler_graph_pyramid.jl b/fiddler_graph_pyramid.jl
 ### A Pluto.jl notebook ###
 # v0.20.8

 using Markdown
 using InteractiveUtils

 # ╔═╡ 446b951f-049b-441a-a869-03529b1ef965
 using Graphs, GraphMakie, CairoMakie

 # ╔═╡ fc389c8e-771e-430d-866e-4188cd9d8c3f
 using Test, Chairmarks

 # ╔═╡ 6534f7c8-3321-11f0-1c07-a5f5efec77d4
 md"""
 # Can you permeate the pyramid?

 Consider the following figure, which shows 16 points arranged in a rhombus shape and connected to their neighbors by edges. How many distinct paths are there from the top point to the bottom along the edges such that:

 - You never visit the same point twice.
 - You only move downward or sideways—never upward.

 ![The Pyramid](https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5af6e222-c841-4b17-b05b-54bcb3d254ad_1336x1054.png)

 ## Answer

 I will label the nodes 1 - 16 starting going top to bottom, left to right, as if reading.
 """

 # ╔═╡ bf1174ac-98df-4a10-b3c0-9d6176a3a607
 const pyramid_edges = [
 	1 2
 	1 3
 	2 3
 	3 2
 	2 4 
 	2 5
 	3 5
 	3 6
 	4 5
 	5 4
 	5 6
 	6 5
 	4 7
 	4 8
 	5 8
 	5 9
 	6 9
 	6 10
 	7 8
 	8 7
 	8 9
 	9 8
 	9 10
 	10 9
 	7 11
 	8 11
 	8 12
 	9 12
 	9 13
 	10 13
 	11 12
 	12 11
 	12 13
 	13 12
 	11 14
 	12 14
 	12 15
 	13 15
 	14 15
 	15 14
 	14 16
 	15 16
 ]

 # ╔═╡ 1c103973-163d-4aab-8997-52b546526ca7
 function pyramid_graph(edges)
 	g = SimpleDiGraph([Edge(e[1], e[2]) for e in eachrow(edges)])
 	g
 end

 # ╔═╡ 9cef439c-9976-4952-8a3c-370d6a7f86d5
 g = pyramid_graph(pyramid_edges)

 # ╔═╡ d9b39ef9-7a7d-44f2-a29e-005d73c66343
 function draw_pyramid(g)
 	f, ax, p = graphplot(
 		g, 
 		arrow_shift=:end,
 		nlabels=repr.(1:nv(g)),
 	)
 	hidedecorations!(ax)
 	hidespines!(ax)

 	f
 end

 # ╔═╡ 353fca42-5db7-4d43-93a5-2bff0415d7d9
 draw_pyramid(g)

 # ╔═╡ 0c14dabb-f47c-4b9a-b32d-db04991d8a3a
 md"""
 Now that we have the graph, we can use the `all_simple_paths()` iterator to visit all of the paths.
 """

 # ╔═╡ 853d4628-9849-427c-8d96-10b873adf528
 function count_all_paths(g, u, v)
 	res = BigInt(0)
 	for _ in all_simple_paths(g, u, v)
 		res += 1
 	end
 	res
 end	

 # ╔═╡ 5e1c72b7-893e-4011-9915-462820e2d58f
 count_all_paths(g, 1, 16)

 # ╔═╡ 204c594f-e596-4b39-a238-b3d566180fb3
 md"""
 If viewing raw julia file, the answer is 2304
 """

 # ╔═╡ 2212380f-6c93-437a-a491-ffb760032e84
 md"""
 # 3D case

 Consider the following figure, which shows 30 points arranged in a three-dimensional triangular bipyramid. As before, points are connected to their neighbors by edges. How many distinct paths are there from the top point to the bottom along the edges such that:

 - You never visit the same point twice.
 - You only move downward or sideways—never upward.

 ![3D triangular bipyramid](https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0ee87243-ef32-458f-8577-f29d30508a99_720x790.png)

 ## Answer

 In this case, there are too many edges to write them all out by hand. Instead, we need a way to generate the nodes and edges automatically. For the top half of the structure, each parent node produces 3 child nodes. Once we have generated the top half, we can mirror it to produce the bottom half.

 ### Top Half
 #### Indexing the top half
 Let each "layer" of the 3D version be called the "layer index". Within in each layer, index the nodes the same as the 2D case, linearly from top to bottom, left to right. Within each 2D layer, we count the rows of nodes, starting with 1 for the single top node, 2 for the two nodes below, and so on. For convenience's sake, denote a node's index with `(layer, layer_index)`. 

 The children of node `(layer_n, n)` are (all in `layer_n + 1`) `[n, n+row, n+row+1]`. So we can create the edges from the parent to its children, and then the two-way edges between all of the children.

 ### Bottom Half
 """

 # ╔═╡ f80d45e5-dea0-4f53-ac6a-e511f78d219d
 """
    to_linear_ind(layer::Integer, index::Integer)::Int

 From a layer number, and an index inside that layer, what
 is the global linear index of that location?
 """
 function to_linear_ind(layer::Integer, index::Integer)::Int
  layer < 1 && error("layer must be >= 1")

  # How many total indices in the layers above?
  inds_above = layer == 1 ? 0 : sum(sum(1:n) for n in 1:(layer-1))
  
  index + inds_above
 end

 # ╔═╡ ea760191-eb6c-4423-a557-8bf96d3ea803
 @be to_linear_ind(4, 8)

 # ╔═╡ 35f7058e-e66c-41a0-bbc1-2a0b8fddb1d9
 @testset "generating linear indices" begin
 	# Columns are: layer, layer_index, want
 	cases = [
 		1 1 1
 		2 1 2
 		2 2 3
 		2 3 4
 		3 1 5
 		3 2 6
 		3 3 7
 		3 4 8
 		3 5 9
 		3 6 10
 		4 1 11
 		4 2 12
 		4 3 13
 		4 4 14
 		4 5 15
 		4 6 16
 		4 7 17
 		4 8 18
 		4 9 19
 		4 10 20
 	]
 	for row in eachrow(cases) 
 		@test row[3] == to_linear_ind(row[1], row[2])
 	end
 end

 # ╔═╡ d08f5aa8-a805-4651-bf55-51bf8ee88781
 """
    row_number(index::Integer, max_rows::Int = 100)::Int

 Calculate which row in the triangle this index is in.
 """
 function row_number(index::Integer, max_rows::Int = 100)::Int
 	index < 1 && error("index must be >= 1")

 	for n in 1:max_rows
 		# Each row ends at sum(1:n)
 		if index <= sum(1:n)
 			return n
 		end
 	end
 	error("more than $max_rows rows calculated")
 end

 # ╔═╡ 971cd3e3-53ef-49fd-803e-18ef9fa22bd2
 @be row_number(300)

 # ╔═╡ 1b6cc796-dd26-4cee-bd7a-5985c3b8624a
 @testset "row number determination" begin
 	# Columns are want, index
 	cases = [
 		(1:1, 1)
 		(2:3, 2)
 		(4:6, 3)
 		(7:10, 4)
 		(11:15, 5)
 		(16:21, 6)
 	]
 	for (idx_range, row) in cases
 		for idx in idx_range
 			@test row == row_number(idx)
 		end
 	end
 end

 # ╔═╡ a692c080-cf9d-4915-9840-2351605bc186
 md"""
 Now to generate the top half. I think we should start out by creating a graph with the total number of necessary nodes. Counting the points, that is 30.

 Then, we can generate the top half. For each layer, we use the above indexing and child generation knowledge to create the necessary edges.
 """

 # ╔═╡ df192b40-2c57-486e-8ade-fcbcd5fa773c
 const n_points = 30

 # ╔═╡ 701b3c25-4488-43bb-918b-88606ee8cd27
 """
    children(layer::Int, index::Int)

 Generate the three children of node at `layer` and `idx`
 """
 function children(layer::Int, idx::Int)
 	# Each child has a layer one greater
 	c_layer = layer + 1

 	# The layer indices are [idx, idx+row, idx+row+1]
 	c1 = to_linear_ind(c_layer, idx)
 	c2 = to_linear_ind(c_layer, idx + row_number(idx))
 	c3 = to_linear_ind(c_layer, idx + row_number(idx) + 1)
 	(c1, c2, c3)
 end

 # ╔═╡ 54b5ef56-0282-4d73-83fa-440ce8cc8b49
 @be children(3,6)

 # ╔═╡ 30e81a04-9355-46ab-975a-a8de8ca5285d
 @testset "Child Index Generation" begin
 	# The parent, and then the children
 	cases = [
 		((1,1), (2,3,4)),
 		((2,1), (5,6,7)),
 		((2,2), (6,8,9)),
 		((2,3), (7,9,10)),
 		((3,1), (11,12,13)),
 		((3,2), (12,14,15)),
 		((3,3), (13,15,16)),
 		((3,4), (14,17,18)),
 		((3,5), (15,18,19)),
 		((3,6), (16,19,20)),
 	]
 	for ((layer, idx), want) in cases
 		@test want == children(layer, idx)
 	end
 end

 # ╔═╡ 8592e23a-5da6-4e45-a0ea-c190f55e84a7
 """
    edges_to_add(p::Int, c1::Int, c2::Int, c3::Int)

 Return a tuple of the edges to add. One way edges from the parent to its
 children, and two way edges between all the children. 9 edges total
 """
 function edges_to_add(p::Int, c1::Int, c2::Int, c3::Int)::NTuple{9, Edge}
 	(
 		# Parent to all children
 		Edge(p, c1), Edge(p, c2), Edge(p, c3),
 		# Between c1 and c2
 		Edge(c1, c2), Edge(c2, c1),
 		# Between c1 and c3
 		Edge(c1, c3), Edge(c3, c1),
 		# Between c2 and c3
 		Edge(c2, c3), Edge(c3, c2)
 	)
 end

 # ╔═╡ d4e45003-554f-48e4-91dd-c7990ad94a19
 @be edges_to_add(1, 2, 3, 4)

 # ╔═╡ 4070bca5-feaa-4a22-ae31-8651029c47b9
 function flip(n::Number, mid_point::Number)
 	dist = n - mid_point
 	mid_point - dist
 end

 # ╔═╡ 617e45e8-2940-4753-90cb-84a61760db07
 @testset "get mirror layer" begin
 	# Columns are layer number, mid_point, and desired result
 	cases = [
 		1 4 7
 		2 4 6
 		3 4 5
 		4 4 4
 		5 4 3
 		6 4 2
 		7 4 1
 	]
 	for row in eachrow(cases)
 		@test row[3] == flip(row[1], row[2])
 	end
 end

 # ╔═╡ dd57e5b7-c27d-47ac-8659-53a67df31a4f
 function lookup_mirror_index(index::Int)::Int
 	lookup = (
 		1 => 30,
 		2 => 27,
 		3 => 28,
 		4 => 29,
 		5 => 21,
 		6 => 22,
 		7 => 23,
 		8 => 24,
 		9 => 25,
 		10 => 26,
 		11 => 11,
 		12 => 12,
 		13 => 13,
 		14 => 14,
 		15 => 15,
 		16 => 16,
 		17 => 17,
 		18 => 18,
 		19 => 19,
 		20 => 20,
 	)
 	for (i, val) in lookup
 		if i == index
 			return val
 		end
 	end
 	error("Could not find $index")
 end

 # ╔═╡ ffd5a55c-2e45-4536-b6bd-55e3cbee93c9
 @be lookup_mirror_index(6)

 # ╔═╡ 582c3dfa-e2f4-47fa-811c-c324fd6f1a41
 function generate_3d_triangular_bipyramid()::SimpleDiGraph
 	# Create the graph with the correct number of points
 	g = SimpleDiGraph(n_points)

 	# For each layer, 1:3
 	for layer in 1:3
 		# For each index in that layer
 		n_nodes_in_layer = sum(1:layer)
 		for idx in 1:n_nodes_in_layer
 			# Parent global index
 			gidx = to_linear_ind(layer, idx)
 			
 			# Generate the children
 			(c1, c2, c3) = children(layer, idx)

 			# Create the edges
 			for e in edges_to_add(gidx, c1, c2, c3)
 				# Add the edges
 				add_edge!(g, e)

 				# Add the mirror edges. The mirror edges
 				# use the mirror indices, but reversed
 				add_edge!(g, lookup_mirror_index(e.dst), lookup_mirror_index(e.src))
 			end
 		end
 	end

 	g
 end

 # ╔═╡ fed249af-d6bf-4e87-a884-8af551c2e895
 g2 = generate_3d_triangular_bipyramid()

 # ╔═╡ 4149be42-e68c-4a4c-94ec-bee69ab134aa
 g2

 # ╔═╡ d266874f-f48f-4b24-b10f-49b0eb4bf8fb
 neighbors(g2, 21)

 # ╔═╡ 38ddc0e6-3b0f-415d-8d90-ffb54beeca05
 draw_pyramid(g2)

 # ╔═╡ 22621f3f-7d75-49f6-b297-da97fea45320
 count_all_paths(g2, 1, 30)

 # ╔═╡ d1ba80c0-c77e-4dfe-95df-85f588700cf1
 md"""
 If you are reading the unrendered version of this notebook, the answer is: 

 $$\boxed{1,093,007,025}$$

 Took 680 seconds on my 5.4 GHz i7.
 """

 # ╔═╡ 00000000-0000-0000-0000-000000000001
 PLUTO_PROJECT_TOML_CONTENTS = """
 [deps]
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 Chairmarks = "0ca39b1e-fe0b-4e98-acfc-b1656634c4de"
 GraphMakie = "1ecd5474-83a3-4783-bb4f-06765db800d2"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

 [compat]
 CairoMakie = "~0.13.5"
 Chairmarks = "~1.3.1"
 GraphMakie = "~0.5.14"
 Graphs = "~1.12.1"
 """

 # ╔═╡ 00000000-0000-0000-0000-000000000002
 PLUTO_MANIFEST_TOML_CONTENTS = """
 # This file is machine-generated - editing it directly is not advised

 julia_version = "1.11.5"
 manifest_format = "2.0"
 project_hash = "18490c9b114d7b6a70b7e1b90cb3f43be0c9c636"

 [[deps.AbstractFFTs]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
 version = "1.5.0"
 weakdeps = ["ChainRulesCore", "Test"]

    [deps.AbstractFFTs.extensions]
    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
    AbstractFFTsTestExt = "Test"

 [[deps.AbstractTrees]]
 git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177"
 uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
 version = "0.4.5"

 [[deps.Adapt]]
 deps = ["LinearAlgebra", "Requires"]
 git-tree-sha1 = "f7817e2e585aa6d924fd714df1e2a84be7896c60"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 version = "4.3.0"
 weakdeps = ["SparseArrays", "StaticArrays"]

    [deps.Adapt.extensions]
    AdaptSparseArraysExt = "SparseArrays"
    AdaptStaticArraysExt = "StaticArrays"

 [[deps.AdaptivePredicates]]
 git-tree-sha1 = "7e651ea8d262d2d74ce75fdf47c4d63c07dba7a6"
 uuid = "35492f91-a3bd-45ad-95db-fcad7dcfedb7"
 version = "1.2.0"

 [[deps.AliasTables]]
 deps = ["PtrArrays", "Random"]
 git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
 uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
 version = "1.1.3"

 [[deps.Animations]]
 deps = ["Colors"]
 git-tree-sha1 = "e092fa223bf66a3c41f9c022bd074d916dc303e7"
 uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340"
 version = "0.4.2"

 [[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 version = "1.1.2"

 [[deps.ArnoldiMethod]]
 deps = ["LinearAlgebra", "Random", "StaticArrays"]
 git-tree-sha1 = "d57bd3762d308bded22c3b82d033bff85f6195c6"
 uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
 version = "0.4.0"

 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 version = "1.11.0"

 [[deps.Automa]]
 deps = ["PrecompileTools", "SIMD", "TranscodingStreams"]
 git-tree-sha1 = "a8f503e8e1a5f583fbef15a8440c8c7e32185df2"
 uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b"
 version = "1.1.0"

 [[deps.AxisAlgorithms]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
 git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712"
 uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
 version = "1.1.0"

 [[deps.AxisArrays]]
 deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
 git-tree-sha1 = "16351be62963a67ac4083f748fdb3cca58bfd52f"
 uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
 version = "0.4.7"

 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 version = "1.11.0"

 [[deps.Bzip2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "1b96ea4a01afe0ea4090c5c8039690672dd13f2e"
 uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
 version = "1.0.9+0"

 [[deps.CEnum]]
 git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
 version = "0.5.0"

 [[deps.CRC32c]]
 uuid = "8bf52ea8-c179-5cab-976a-9e18b702a9bc"
 version = "1.11.0"

 [[deps.CRlibm]]
 deps = ["CRlibm_jll"]
 git-tree-sha1 = "66188d9d103b92b6cd705214242e27f5737a1e5e"
 uuid = "96374032-68de-5a5b-8d9e-752f78720389"
 version = "1.0.2"

 [[deps.CRlibm_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "e329286945d0cfc04456972ea732551869af1cfc"
 uuid = "4e9b3aee-d8a1-5a3d-ad8b-7d824db253f0"
 version = "1.0.1+0"

 [[deps.Cairo]]
 deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
 git-tree-sha1 = "71aa551c5c33f1a4415867fe06b7844faadb0ae9"
 uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
 version = "1.1.1"

 [[deps.CairoMakie]]
 deps = ["CRC32c", "Cairo", "Cairo_jll", "Colors", "FileIO", "FreeType", "GeometryBasics", "LinearAlgebra", "Makie", "PrecompileTools"]
 git-tree-sha1 = "a5bbcd6f48d348f213f019a4dfd27c480e414ba9"
 uuid = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 version = "0.13.5"

 [[deps.Cairo_jll]]
 deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
 git-tree-sha1 = "2ac646d71d0d24b44f3f8c84da8c9f4d70fb67df"
 uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
 version = "1.18.4+0"

 [[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra"]
 git-tree-sha1 = "1713c74e00545bfe14605d2a2be1712de8fbcb58"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 version = "1.25.1"
 weakdeps = ["SparseArrays"]

    [deps.ChainRulesCore.extensions]
    ChainRulesCoreSparseArraysExt = "SparseArrays"

 [[deps.Chairmarks]]
 deps = ["Printf", "Random"]
 git-tree-sha1 = "9a49491e67e7a4d6f885c43d00bb101e6e5a434b"
 uuid = "0ca39b1e-fe0b-4e98-acfc-b1656634c4de"
 version = "1.3.1"
 weakdeps = ["Statistics"]

    [deps.Chairmarks.extensions]
    StatisticsChairmarksExt = ["Statistics"]

 [[deps.ColorBrewer]]
 deps = ["Colors", "JSON"]
 git-tree-sha1 = "e771a63cc8b539eca78c85b0cabd9233d6c8f06f"
 uuid = "a2cac450-b92f-5266-8821-25eda20663c8"
 version = "0.4.1"

 [[deps.ColorSchemes]]
 deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
 git-tree-sha1 = "403f2d8e209681fcbd9468a8514efff3ea08452e"
 uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
 version = "3.29.0"

 [[deps.ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
 git-tree-sha1 = "67e11ee83a43eb71ddc950302c53bf33f0690dfe"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
 version = "0.12.1"
 weakdeps = ["StyledStrings"]

    [deps.ColorTypes.extensions]
    StyledStringsExt = "StyledStrings"

 [[deps.ColorVectorSpace]]
 deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
 git-tree-sha1 = "8b3b6f87ce8f65a2b4f857528fd8d70086cd72b1"
 uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
 version = "0.11.0"
 weakdeps = ["SpecialFunctions"]

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

 [[deps.Colors]]
 deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
 git-tree-sha1 = "64e15186f0aa277e174aa81798f7eb8598e0157e"
 uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
 version = "0.13.0"

 [[deps.Compat]]
 deps = ["TOML", "UUIDs"]
 git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
 version = "4.16.0"
 weakdeps = ["Dates", "LinearAlgebra"]

    [deps.Compat.extensions]
    CompatLinearAlgebraExt = "LinearAlgebra"

 [[deps.CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 version = "1.1.1+0"

 [[deps.ConstructionBase]]
 git-tree-sha1 = "76219f1ed5771adbb096743bff43fb5fdd4c1157"
 uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 version = "1.5.8"
 weakdeps = ["IntervalSets", "LinearAlgebra", "StaticArrays"]

    [deps.ConstructionBase.extensions]
    ConstructionBaseIntervalSetsExt = "IntervalSets"
    ConstructionBaseLinearAlgebraExt = "LinearAlgebra"
    ConstructionBaseStaticArraysExt = "StaticArrays"

 [[deps.Contour]]
 git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8"
 uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
 version = "0.6.3"

 [[deps.DataAPI]]
 git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
 version = "1.16.0"

 [[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
 git-tree-sha1 = "4e1fe97fdaed23e9dc21d4d664bea76b65fc50a0"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 version = "0.18.22"

 [[deps.DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
 uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
 version = "1.0.0"

 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 version = "1.11.0"

 [[deps.DelaunayTriangulation]]
 deps = ["AdaptivePredicates", "EnumX", "ExactPredicates", "Random"]
 git-tree-sha1 = "5620ff4ee0084a6ab7097a27ba0c19290200b037"
 uuid = "927a84f5-c5f4-47a5-9785-b46e178433df"
 version = "1.6.4"

 [[deps.Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 version = "1.11.0"

 [[deps.Distributions]]
 deps = ["AliasTables", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"]
 git-tree-sha1 = "3e6d038b77f22791b8e3472b7c633acea1ecac06"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
 version = "0.25.120"

    [deps.Distributions.extensions]
    DistributionsChainRulesCoreExt = "ChainRulesCore"
    DistributionsDensityInterfaceExt = "DensityInterface"
    DistributionsTestExt = "Test"

    [deps.Distributions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

 [[deps.DocStringExtensions]]
 git-tree-sha1 = "e7b7e6f178525d17c720ab9c081e4ef04429f860"
 uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 version = "0.9.4"

 [[deps.Downloads]]
 deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 version = "1.6.0"

 [[deps.EarCut_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "e3290f2d49e661fbd94046d7e3726ffcb2d41053"
 uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
 version = "2.2.4+0"

 [[deps.EnumX]]
 git-tree-sha1 = "bddad79635af6aec424f53ed8aad5d7555dc6f00"
 uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
 version = "1.0.5"

 [[deps.ExactPredicates]]
 deps = ["IntervalArithmetic", "Random", "StaticArrays"]
 git-tree-sha1 = "b3f2ff58735b5f024c392fde763f29b057e4b025"
 uuid = "429591f6-91af-11e9-00e2-59fbe8cec110"
 version = "2.2.8"

 [[deps.Expat_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "d55dffd9ae73ff72f1c0482454dcf2ec6c6c4a63"
 uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
 version = "2.6.5+0"

 [[deps.Extents]]
 git-tree-sha1 = "b309b36a9e02fe7be71270dd8c0fd873625332b4"
 uuid = "411431e0-e8b7-467b-b5e0-f676ba4f2910"
 version = "0.1.6"

 [[deps.FFMPEG_jll]]
 deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
 git-tree-sha1 = "8cc47f299902e13f90405ddb5bf87e5d474c0d38"
 uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
 version = "6.1.2+0"

 [[deps.FFTW]]
 deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
 git-tree-sha1 = "7de7c78d681078f027389e067864a8d53bd7c3c9"
 uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 version = "1.8.1"

 [[deps.FFTW_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "6d6219a004b8cf1e0b4dbe27a2860b8e04eba0be"
 uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
 version = "3.3.11+0"

 [[deps.FileIO]]
 deps = ["Pkg", "Requires", "UUIDs"]
 git-tree-sha1 = "b66970a70db13f45b7e57fbda1736e1cf72174ea"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
 version = "1.17.0"

    [deps.FileIO.extensions]
    HTTPExt = "HTTP"

    [deps.FileIO.weakdeps]
    HTTP = "cd3eb016-35fb-5094-929b-558a96fad6f3"

 [[deps.FilePaths]]
 deps = ["FilePathsBase", "MacroTools", "Reexport", "Requires"]
 git-tree-sha1 = "919d9412dbf53a2e6fe74af62a73ceed0bce0629"
 uuid = "8fc22ac5-c921-52a6-82fd-178b2807b824"
 version = "0.8.3"

 [[deps.FilePathsBase]]
 deps = ["Compat", "Dates"]
 git-tree-sha1 = "3bab2c5aa25e7840a4b065805c0cdfc01f3068d2"
 uuid = "48062228-2e41-5def-b9a4-89aafe57970f"
 version = "0.9.24"
 weakdeps = ["Mmap", "Test"]

    [deps.FilePathsBase.extensions]
    FilePathsBaseMmapExt = "Mmap"
    FilePathsBaseTestExt = "Test"

 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 version = "1.11.0"

 [[deps.FillArrays]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "6a70198746448456524cb442b8af316927ff3e1a"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
 version = "1.13.0"
 weakdeps = ["PDMats", "SparseArrays", "Statistics"]

    [deps.FillArrays.extensions]
    FillArraysPDMatsExt = "PDMats"
    FillArraysSparseArraysExt = "SparseArrays"
    FillArraysStatisticsExt = "Statistics"

 [[deps.FixedPointNumbers]]
 deps = ["Statistics"]
 git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172"
 uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
 version = "0.8.5"

 [[deps.Fontconfig_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"]
 git-tree-sha1 = "301b5d5d731a0654825f1f2e906990f7141a106b"
 uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
 version = "2.16.0+0"

 [[deps.Format]]
 git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc"
 uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
 version = "1.3.7"

 [[deps.FreeType]]
 deps = ["CEnum", "FreeType2_jll"]
 git-tree-sha1 = "907369da0f8e80728ab49c1c7e09327bf0d6d999"
 uuid = "b38be410-82b0-50bf-ab77-7b57e271db43"
 version = "4.1.1"

 [[deps.FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
 git-tree-sha1 = "2c5512e11c791d1baed2049c5652441b28fc6a31"
 uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
 version = "2.13.4+0"

 [[deps.FreeTypeAbstraction]]
 deps = ["ColorVectorSpace", "Colors", "FreeType", "GeometryBasics"]
 git-tree-sha1 = "d52e255138ac21be31fa633200b65e4e71d26802"
 uuid = "663a7486-cb36-511b-a19d-713bb74d65c9"
 version = "0.10.6"

 [[deps.FriBidi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "7a214fdac5ed5f59a22c2d9a885a16da1c74bbc7"
 uuid = "559328eb-81f9-559d-9380-de523a88c83c"
 version = "1.0.17+0"

 [[deps.GeoFormatTypes]]
 git-tree-sha1 = "8e233d5167e63d708d41f87597433f59a0f213fe"
 uuid = "68eda718-8dee-11e9-39e7-89f7f65f511f"
 version = "0.4.4"

 [[deps.GeoInterface]]
 deps = ["DataAPI", "Extents", "GeoFormatTypes"]
 git-tree-sha1 = "294e99f19869d0b0cb71aef92f19d03649d028d5"
 uuid = "cf35fbd7-0cd7-5166-be24-54bfbe79505f"
 version = "1.4.1"

 [[deps.GeometryBasics]]
 deps = ["EarCut_jll", "Extents", "GeoInterface", "IterTools", "LinearAlgebra", "PrecompileTools", "Random", "StaticArrays"]
 git-tree-sha1 = "2670cf32dcf0229c9893b895a9afe725edb23545"
 uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
 version = "0.5.9"

 [[deps.Gettext_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
 git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
 uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
 version = "0.21.0+0"

 [[deps.Giflib_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "6570366d757b50fabae9f4315ad74d2e40c0560a"
 uuid = "59f7168a-df46-5410-90c8-f2779963d0ec"
 version = "5.2.3+0"

 [[deps.Glib_jll]]
 deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
 git-tree-sha1 = "b0036b392358c80d2d2124746c2bf3d48d457938"
 uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
 version = "2.82.4+0"

 [[deps.GraphMakie]]
 deps = ["DataStructures", "GeometryBasics", "Graphs", "LinearAlgebra", "Makie", "NetworkLayout", "PolynomialRoots", "SimpleTraits", "StaticArrays"]
 git-tree-sha1 = "707de559f03a9a9734039266d3563404460982a2"
 uuid = "1ecd5474-83a3-4783-bb4f-06765db800d2"
 version = "0.5.14"

 [[deps.Graphics]]
 deps = ["Colors", "LinearAlgebra", "NaNMath"]
 git-tree-sha1 = "a641238db938fff9b2f60d08ed9030387daf428c"
 uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
 version = "1.1.3"

 [[deps.Graphite2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "8a6dbda1fd736d60cc477d99f2e7a042acfa46e8"
 uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
 version = "1.3.15+0"

 [[deps.Graphs]]
 deps = ["ArnoldiMethod", "Compat", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
 git-tree-sha1 = "3169fd3440a02f35e549728b0890904cfd4ae58a"
 uuid = "86223c79-3864-5bf0-83f7-82e725a168b6"
 version = "1.12.1"

 [[deps.GridLayoutBase]]
 deps = ["GeometryBasics", "InteractiveUtils", "Observables"]
 git-tree-sha1 = "dc6bed05c15523624909b3953686c5f5ffa10adc"
 uuid = "3955a311-db13-416c-9275-1d80ed98e5e9"
 version = "0.11.1"

 [[deps.Grisu]]
 git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
 uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
 version = "1.0.2"

 [[deps.HarfBuzz_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
 git-tree-sha1 = "55c53be97790242c29031e5cd45e8ac296dadda3"
 uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
 version = "8.5.0+0"

 [[deps.HypergeometricFunctions]]
 deps = ["LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
 git-tree-sha1 = "68c173f4f449de5b438ee67ed0c9c748dc31a2ec"
 uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
 version = "0.3.28"

 [[deps.ImageAxes]]
 deps = ["AxisArrays", "ImageBase", "ImageCore", "Reexport", "SimpleTraits"]
 git-tree-sha1 = "e12629406c6c4442539436581041d372d69c55ba"
 uuid = "2803e5a7-5153-5ecf-9a86-9b4c37f5f5ac"
 version = "0.6.12"

 [[deps.ImageBase]]
 deps = ["ImageCore", "Reexport"]
 git-tree-sha1 = "eb49b82c172811fd2c86759fa0553a2221feb909"
 uuid = "c817782e-172a-44cc-b673-b171935fbb9e"
 version = "0.1.7"

 [[deps.ImageCore]]
 deps = ["ColorVectorSpace", "Colors", "FixedPointNumbers", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "PrecompileTools", "Reexport"]
 git-tree-sha1 = "8c193230235bbcee22c8066b0374f63b5683c2d3"
 uuid = "a09fc81d-aa75-5fe9-8630-4744c3626534"
 version = "0.10.5"

 [[deps.ImageIO]]
 deps = ["FileIO", "IndirectArrays", "JpegTurbo", "LazyModules", "Netpbm", "OpenEXR", "PNGFiles", "QOI", "Sixel", "TiffImages", "UUIDs", "WebP"]
 git-tree-sha1 = "696144904b76e1ca433b886b4e7edd067d76cbf7"
 uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
 version = "0.6.9"

 [[deps.ImageMetadata]]
 deps = ["AxisArrays", "ImageAxes", "ImageBase", "ImageCore"]
 git-tree-sha1 = "2a81c3897be6fbcde0802a0ebe6796d0562f63ec"
 uuid = "bc367c6b-8a6b-528e-b4bd-a4b897500b49"
 version = "0.9.10"

 [[deps.Imath_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "0936ba688c6d201805a83da835b55c61a180db52"
 uuid = "905a6f67-0a94-5f89-b386-d35d92009cd1"
 version = "3.1.11+0"

 [[deps.IndirectArrays]]
 git-tree-sha1 = "012e604e1c7458645cb8b436f8fba789a51b257f"
 uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
 version = "1.0.0"

 [[deps.Inflate]]
 git-tree-sha1 = "d1b1b796e47d94588b3757fe84fbf65a5ec4a80d"
 uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
 version = "0.1.5"

 [[deps.IntelOpenMP_jll]]
 deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
 git-tree-sha1 = "0f14a5456bdc6b9731a5682f439a672750a09e48"
 uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
 version = "2025.0.4+0"

 [[deps.InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 version = "1.11.0"

 [[deps.Interpolations]]
 deps = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
 git-tree-sha1 = "88a101217d7cb38a7b481ccd50d21876e1d1b0e0"
 uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 version = "0.15.1"
 weakdeps = ["Unitful"]

    [deps.Interpolations.extensions]
    InterpolationsUnitfulExt = "Unitful"

 [[deps.IntervalArithmetic]]
 deps = ["CRlibm", "MacroTools", "OpenBLASConsistentFPCSR_jll", "Random", "RoundingEmulator"]
 git-tree-sha1 = "694c52705f8b23dc5b39eeac629dc3059a168a40"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 version = "0.22.35"

    [deps.IntervalArithmetic.extensions]
    IntervalArithmeticDiffRulesExt = "DiffRules"
    IntervalArithmeticForwardDiffExt = "ForwardDiff"
    IntervalArithmeticIntervalSetsExt = "IntervalSets"
    IntervalArithmeticLinearAlgebraExt = "LinearAlgebra"
    IntervalArithmeticRecipesBaseExt = "RecipesBase"
    IntervalArithmeticSparseArraysExt = "SparseArrays"

    [deps.IntervalArithmetic.weakdeps]
    DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
    RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

 [[deps.IntervalSets]]
 git-tree-sha1 = "5fbb102dcb8b1a858111ae81d56682376130517d"
 uuid = "8197267c-284f-5f27-9208-e0e47529a953"
 version = "0.7.11"

    [deps.IntervalSets.extensions]
    IntervalSetsRandomExt = "Random"
    IntervalSetsRecipesBaseExt = "RecipesBase"
    IntervalSetsStatisticsExt = "Statistics"

    [deps.IntervalSets.weakdeps]
    Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
    RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
    Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

 [[deps.InverseFunctions]]
 git-tree-sha1 = "a779299d77cd080bf77b97535acecd73e1c5e5cb"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
 version = "0.1.17"
 weakdeps = ["Dates", "Test"]

    [deps.InverseFunctions.extensions]
    InverseFunctionsDatesExt = "Dates"
    InverseFunctionsTestExt = "Test"

 [[deps.IrrationalConstants]]
 git-tree-sha1 = "e2222959fbc6c19554dc15174c81bf7bf3aa691c"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.2.4"

 [[deps.Isoband]]
 deps = ["isoband_jll"]
 git-tree-sha1 = "f9b6d97355599074dc867318950adaa6f9946137"
 uuid = "f1662d9f-8043-43de-a69a-05efc1cc6ff4"
 version = "0.1.1"

 [[deps.IterTools]]
 git-tree-sha1 = "42d5f897009e7ff2cf88db414a389e5ed1bdd023"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
 version = "1.10.0"

 [[deps.IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
 uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"

 [[deps.JLLWrappers]]
 deps = ["Artifacts", "Preferences"]
 git-tree-sha1 = "a007feb38b422fbdab534406aeca1b86823cb4d6"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
 version = "1.7.0"

 [[deps.JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
 git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.4"

 [[deps.JpegTurbo]]
 deps = ["CEnum", "FileIO", "ImageCore", "JpegTurbo_jll", "TOML"]
 git-tree-sha1 = "9496de8fb52c224a2e3f9ff403947674517317d9"
 uuid = "b835a17e-a41a-41e7-81f0-2f016b05efe0"
 version = "0.1.6"

 [[deps.JpegTurbo_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "eac1206917768cb54957c65a615460d87b455fc1"
 uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
 version = "3.1.1+0"

 [[deps.KernelDensity]]
 deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
 git-tree-sha1 = "7d703202e65efa1369de1279c162b915e245eed1"
 uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
 version = "0.6.9"

 [[deps.LAME_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd"
 uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
 version = "3.100.2+0"

 [[deps.LERC_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "aaafe88dccbd957a8d82f7d05be9b69172e0cee3"
 uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
 version = "4.0.1+0"

 [[deps.LLVMOpenMP_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "eb62a3deb62fc6d8822c0c4bef73e4412419c5d8"
 uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
 version = "18.1.8+0"

 [[deps.LZO_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "1c602b1127f4751facb671441ca72715cc95938a"
 uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
 version = "2.10.3+0"

 [[deps.LaTeXStrings]]
 git-tree-sha1 = "dda21b8cbd6a6c40d9d02a73230f9d70fed6918c"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 version = "1.4.0"

 [[deps.LazyArtifacts]]
 deps = ["Artifacts", "Pkg"]
 uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
 version = "1.11.0"

 [[deps.LazyModules]]
 git-tree-sha1 = "a560dd966b386ac9ae60bdd3a3d3a326062d3c3e"
 uuid = "8cdb02fc-e678-4876-92c5-9defec4f444e"
 version = "0.3.1"

 [[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
 version = "0.6.4"

 [[deps.LibCURL_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
 uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
 version = "8.6.0+0"

 [[deps.LibGit2]]
 deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 version = "1.11.0"

 [[deps.LibGit2_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
 uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
 version = "1.7.2+0"

 [[deps.LibSSH2_jll]]
 deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
 uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
 version = "1.11.0+1"

 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 version = "1.11.0"

 [[deps.Libffi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "27ecae93dd25ee0909666e6835051dd684cc035e"
 uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
 version = "3.2.2+2"

 [[deps.Libglvnd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll"]
 git-tree-sha1 = "d36c21b9e7c172a44a10484125024495e2625ac0"
 uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
 version = "1.7.1+1"

 [[deps.Libiconv_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "be484f5c92fad0bd8acfef35fe017900b0b73809"
 uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
 version = "1.18.0+0"

 [[deps.Libmount_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "a31572773ac1b745e0343fe5e2c8ddda7a37e997"
 uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
 version = "2.41.0+0"

 [[deps.Libtiff_jll]]
 deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
 git-tree-sha1 = "4ab7581296671007fc33f07a721631b8855f4b1d"
 uuid = "89763e89-9b03-5906-acba-b20f662cd828"
 version = "4.7.1+0"

 [[deps.Libuuid_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "321ccef73a96ba828cd51f2ab5b9f917fa73945a"
 uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
 version = "2.41.0+0"

 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 version = "1.11.0"

 [[deps.LogExpFunctions]]
 deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
 git-tree-sha1 = "13ca9e2586b89836fd20cccf56e57e2b9ae7f38f"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
 version = "0.3.29"

    [deps.LogExpFunctions.extensions]
    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

    [deps.LogExpFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 version = "1.11.0"

 [[deps.MKL_jll]]
 deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "oneTBB_jll"]
 git-tree-sha1 = "5de60bc6cb3899cd318d80d627560fae2e2d99ae"
 uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
 version = "2025.0.1+1"

 [[deps.MacroTools]]
 git-tree-sha1 = "1e0228a030642014fe5cfe68c2c0a818f9e3f522"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 version = "0.5.16"

 [[deps.Makie]]
 deps = ["Animations", "Base64", "CRC32c", "ColorBrewer", "ColorSchemes", "ColorTypes", "Colors", "Contour", "Dates", "DelaunayTriangulation", "Distributions", "DocStringExtensions", "Downloads", "FFMPEG_jll", "FileIO", "FilePaths", "FixedPointNumbers", "Format", "FreeType", "FreeTypeAbstraction", "GeometryBasics", "GridLayoutBase", "ImageBase", "ImageIO", "InteractiveUtils", "Interpolations", "IntervalSets", "InverseFunctions", "Isoband", "KernelDensity", "LaTeXStrings", "LinearAlgebra", "MacroTools", "MakieCore", "Markdown", "MathTeXEngine", "Observables", "OffsetArrays", "PNGFiles", "Packing", "PlotUtils", "PolygonOps", "PrecompileTools", "Printf", "REPL", "Random", "RelocatableFolders", "Scratch", "ShaderAbstractions", "Showoff", "SignedDistanceFields", "SparseArrays", "Statistics", "StatsBase", "StatsFuns", "StructArrays", "TriplotBase", "UnicodeFun", "Unitful"]
 git-tree-sha1 = "f79702e65fa2d5dbcfdd7c1dffb953ef2df03a48"
 uuid = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 version = "0.22.5"

 [[deps.MakieCore]]
 deps = ["ColorTypes", "GeometryBasics", "IntervalSets", "Observables"]
 git-tree-sha1 = "733d910c70805e7114c82508bae99c6cdf004466"
 uuid = "20f20a25-4f0e-4fdf-b5d1-57303727442b"
 version = "0.9.3"

 [[deps.MappedArrays]]
 git-tree-sha1 = "2dab0221fe2b0f2cb6754eaa743cc266339f527e"
 uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
 version = "0.4.2"

 [[deps.Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 version = "1.11.0"

 [[deps.MathTeXEngine]]
 deps = ["AbstractTrees", "Automa", "DataStructures", "FreeTypeAbstraction", "GeometryBasics", "LaTeXStrings", "REPL", "RelocatableFolders", "UnicodeFun"]
 git-tree-sha1 = "f5a6805fb46c0285991009b526ec6fae43c6dec2"
 uuid = "0a4f8689-d25c-4efe-a92b-7142dfc1aa53"
 version = "0.6.3"

 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 version = "2.28.6+0"

 [[deps.Missings]]
 deps = ["DataAPI"]
 git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d"
 uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
 version = "1.2.0"

 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 version = "1.11.0"

 [[deps.MosaicViews]]
 deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
 git-tree-sha1 = "7b86a5d4d70a9f5cdf2dacb3cbe6d251d1a61dbe"
 uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
 version = "0.3.4"

 [[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2023.12.12"

 [[deps.NaNMath]]
 deps = ["OpenLibm_jll"]
 git-tree-sha1 = "9b8215b1ee9e78a293f99797cd31375471b2bcae"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 version = "1.1.3"

 [[deps.Netpbm]]
 deps = ["FileIO", "ImageCore", "ImageMetadata"]
 git-tree-sha1 = "d92b107dbb887293622df7697a2223f9f8176fcd"
 uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
 version = "1.1.1"

 [[deps.NetworkLayout]]
 deps = ["GeometryBasics", "LinearAlgebra", "Random", "Requires", "StaticArrays"]
 git-tree-sha1 = "f7466c23a7c5029dc99e8358e7ce5d81a117c364"
 uuid = "46757867-2c16-5918-afeb-47bfcb05e46a"
 version = "0.4.10"
 weakdeps = ["Graphs"]

    [deps.NetworkLayout.extensions]
    NetworkLayoutGraphsExt = "Graphs"

 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"

 [[deps.Observables]]
 git-tree-sha1 = "7438a59546cf62428fc9d1bc94729146d37a7225"
 uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
 version = "0.5.5"

 [[deps.OffsetArrays]]
 git-tree-sha1 = "117432e406b5c023f665fa73dc26e79ec3630151"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 version = "1.17.0"
 weakdeps = ["Adapt"]

    [deps.OffsetArrays.extensions]
    OffsetArraysAdaptExt = "Adapt"

 [[deps.Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
 uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
 version = "1.3.5+1"

 [[deps.OpenBLASConsistentFPCSR_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "567515ca155d0020a45b05175449b499c63e7015"
 uuid = "6cdc7f73-28fd-5e50-80fb-958a8875b1af"
 version = "0.3.29+0"

 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
 version = "0.3.27+1"

 [[deps.OpenEXR]]
 deps = ["Colors", "FileIO", "OpenEXR_jll"]
 git-tree-sha1 = "97db9e07fe2091882c765380ef58ec553074e9c7"
 uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
 version = "0.3.3"

 [[deps.OpenEXR_jll]]
 deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
 git-tree-sha1 = "8292dd5c8a38257111ada2174000a33745b06d4e"
 uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
 version = "3.2.4+0"

 [[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 version = "0.8.5+0"

 [[deps.OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "9216a80ff3682833ac4b733caa8c00390620ba5d"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
 version = "3.5.0+0"

 [[deps.OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "1346c9208249809840c91b26703912dff463d335"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 version = "0.5.6+0"

 [[deps.Opus_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575"
 uuid = "91d4177d-7536-5919-b921-800302f37372"
 version = "1.3.3+0"

 [[deps.OrderedCollections]]
 git-tree-sha1 = "cc4054e898b852042d7b503313f7ad03de99c3dd"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.8.0"

 [[deps.PCRE2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
 version = "10.42.0+1"

 [[deps.PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
 git-tree-sha1 = "f07c06228a1c670ae4c87d1276b92c7c597fdda0"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
 version = "0.11.35"

 [[deps.PNGFiles]]
 deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
 git-tree-sha1 = "cf181f0b1e6a18dfeb0ee8acc4a9d1672499626c"
 uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
 version = "0.4.4"

 [[deps.Packing]]
 deps = ["GeometryBasics"]
 git-tree-sha1 = "bc5bf2ea3d5351edf285a06b0016788a121ce92c"
 uuid = "19eb6ba3-879d-56ad-ad62-d5c202156566"
 version = "0.5.1"

 [[deps.PaddedViews]]
 deps = ["OffsetArrays"]
 git-tree-sha1 = "0fac6313486baae819364c52b4f483450a9d793f"
 uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
 version = "0.5.12"

 [[deps.Pango_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "3b31172c032a1def20c98dae3f2cdc9d10e3b561"
 uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
 version = "1.56.1+0"

 [[deps.Parsers]]
 deps = ["Dates", "PrecompileTools", "UUIDs"]
 git-tree-sha1 = "7d2f8f21da5db6a806faf7b9b292296da42b2810"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "2.8.3"

 [[deps.Pixman_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
 git-tree-sha1 = "db76b1ecd5e9715f3d043cec13b2ec93ce015d53"
 uuid = "30392449-352a-5448-841d-b1acce4e97dc"
 version = "0.44.2+0"

 [[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 version = "1.11.0"
 weakdeps = ["REPL"]

    [deps.Pkg.extensions]
    REPLExt = "REPL"

 [[deps.PkgVersion]]
 deps = ["Pkg"]
 git-tree-sha1 = "f9501cc0430a26bc3d156ae1b5b0c1b47af4d6da"
 uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
 version = "0.3.3"

 [[deps.PlotUtils]]
 deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "StableRNGs", "Statistics"]
 git-tree-sha1 = "3ca9a356cd2e113c420f2c13bea19f8d3fb1cb18"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
 version = "1.4.3"

 [[deps.PolygonOps]]
 git-tree-sha1 = "77b3d3605fc1cd0b42d95eba87dfcd2bf67d5ff6"
 uuid = "647866c9-e3ac-4575-94e7-e3d426903924"
 version = "0.1.2"

 [[deps.PolynomialRoots]]
 git-tree-sha1 = "5f807b5345093487f733e520a1b7395ee9324825"
 uuid = "3a141323-8675-5d76-9d11-e1df1406c778"
 version = "1.0.0"

 [[deps.PrecompileTools]]
 deps = ["Preferences"]
 git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
 uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 version = "1.2.1"

 [[deps.Preferences]]
 deps = ["TOML"]
 git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
 version = "1.4.3"

 [[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 version = "1.11.0"

 [[deps.ProgressMeter]]
 deps = ["Distributed", "Printf"]
 git-tree-sha1 = "13c5103482a8ed1536a54c08d0e742ae3dca2d42"
 uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
 version = "1.10.4"

 [[deps.PtrArrays]]
 git-tree-sha1 = "1d36ef11a9aaf1e8b74dacc6a731dd1de8fd493d"
 uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d"
 version = "1.3.0"

 [[deps.QOI]]
 deps = ["ColorTypes", "FileIO", "FixedPointNumbers"]
 git-tree-sha1 = "8b3fc30bc0390abdce15f8822c889f669baed73d"
 uuid = "4b34888f-f399-49d4-9bb3-47ed5cae4e65"
 version = "1.0.1"

 [[deps.QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
 git-tree-sha1 = "9da16da70037ba9d701192e27befedefb91ec284"
 uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 version = "2.11.2"

    [deps.QuadGK.extensions]
    QuadGKEnzymeExt = "Enzyme"

    [deps.QuadGK.weakdeps]
    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"

 [[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "StyledStrings", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 version = "1.11.0"

 [[deps.Random]]
 deps = ["SHA"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 version = "1.11.0"

 [[deps.RangeArrays]]
 git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
 uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
 version = "0.3.2"

 [[deps.Ratios]]
 deps = ["Requires"]
 git-tree-sha1 = "1342a47bf3260ee108163042310d26f2be5ec90b"
 uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
 version = "0.4.5"
 weakdeps = ["FixedPointNumbers"]

    [deps.Ratios.extensions]
    RatiosFixedPointNumbersExt = "FixedPointNumbers"

 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"

 [[deps.RelocatableFolders]]
 deps = ["SHA", "Scratch"]
 git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
 uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
 version = "1.0.1"

 [[deps.Requires]]
 deps = ["UUIDs"]
 git-tree-sha1 = "62389eeff14780bfe55195b7204c0d8738436d64"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
 version = "1.3.1"

 [[deps.Rmath]]
 deps = ["Random", "Rmath_jll"]
 git-tree-sha1 = "852bd0f55565a9e973fcfee83a84413270224dc4"
 uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
 version = "0.8.0"

 [[deps.Rmath_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "58cdd8fb2201a6267e1db87ff148dd6c1dbd8ad8"
 uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
 version = "0.5.1+0"

 [[deps.RoundingEmulator]]
 git-tree-sha1 = "40b9edad2e5287e05bd413a38f61a8ff55b9557b"
 uuid = "5eaf0fd0-dfba-4ccb-bf02-d820a40db705"
 version = "0.2.1"

 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"

 [[deps.SIMD]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "fea870727142270bdf7624ad675901a1ee3b4c87"
 uuid = "fdea26ae-647d-5447-a871-4b548cad5224"
 version = "3.7.1"

 [[deps.Scratch]]
 deps = ["Dates"]
 git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
 uuid = "6c6a2e73-6563-6170-7368-637461726353"
 version = "1.2.1"

 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 version = "1.11.0"

 [[deps.ShaderAbstractions]]
 deps = ["ColorTypes", "FixedPointNumbers", "GeometryBasics", "LinearAlgebra", "Observables", "StaticArrays"]
 git-tree-sha1 = "818554664a2e01fc3784becb2eb3a82326a604b6"
 uuid = "65257c39-d410-5151-9873-9b3e5be5013e"
 version = "0.5.0"

 [[deps.SharedArrays]]
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 version = "1.11.0"

 [[deps.Showoff]]
 deps = ["Dates", "Grisu"]
 git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
 uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
 version = "1.0.3"

 [[deps.SignedDistanceFields]]
 deps = ["Random", "Statistics", "Test"]
 git-tree-sha1 = "d263a08ec505853a5ff1c1ebde2070419e3f28e9"
 uuid = "73760f76-fbc4-59ce-8f25-708e95d2df96"
 version = "0.4.0"

 [[deps.SimpleTraits]]
 deps = ["InteractiveUtils", "MacroTools"]
 git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
 uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
 version = "0.9.4"

 [[deps.Sixel]]
 deps = ["Dates", "FileIO", "ImageCore", "IndirectArrays", "OffsetArrays", "REPL", "libsixel_jll"]
 git-tree-sha1 = "2da10356e31327c7096832eb9cd86307a50b1eb6"
 uuid = "45858cf5-a6b0-47a3-bbea-62219f50df47"
 version = "0.1.3"

 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 version = "1.11.0"

 [[deps.SortingAlgorithms]]
 deps = ["DataStructures"]
 git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
 uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
 version = "1.2.1"

 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 version = "1.11.0"

 [[deps.SpecialFunctions]]
 deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
 git-tree-sha1 = "41852b8679f78c8d8961eeadc8f62cef861a52e3"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
 version = "2.5.1"
 weakdeps = ["ChainRulesCore"]

    [deps.SpecialFunctions.extensions]
    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"

 [[deps.StableRNGs]]
 deps = ["Random"]
 git-tree-sha1 = "95af145932c2ed859b63329952ce8d633719f091"
 uuid = "860ef19b-820b-49d6-a774-d7a799459cd3"
 version = "1.0.3"

 [[deps.StackViews]]
 deps = ["OffsetArrays"]
 git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
 uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
 version = "0.1.1"

 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
 git-tree-sha1 = "0feb6b9031bd5c51f9072393eb5ab3efd31bf9e4"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
 version = "1.9.13"
 weakdeps = ["ChainRulesCore", "Statistics"]

    [deps.StaticArrays.extensions]
    StaticArraysChainRulesCoreExt = "ChainRulesCore"
    StaticArraysStatisticsExt = "Statistics"

 [[deps.StaticArraysCore]]
 git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682"
 uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 version = "1.4.3"

 [[deps.Statistics]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 version = "1.11.1"
 weakdeps = ["SparseArrays"]

    [deps.Statistics.extensions]
    SparseArraysExt = ["SparseArrays"]

 [[deps.StatsAPI]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 version = "1.7.0"

 [[deps.StatsBase]]
 deps = ["AliasTables", "DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
 git-tree-sha1 = "b81c5035922cc89c2d9523afc6c54be512411466"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 version = "0.34.5"

 [[deps.StatsFuns]]
 deps = ["HypergeometricFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
 git-tree-sha1 = "8e45cecc66f3b42633b8ce14d431e8e57a3e242e"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
 version = "1.5.0"
 weakdeps = ["ChainRulesCore", "InverseFunctions"]

    [deps.StatsFuns.extensions]
    StatsFunsChainRulesCoreExt = "ChainRulesCore"
    StatsFunsInverseFunctionsExt = "InverseFunctions"

 [[deps.StructArrays]]
 deps = ["ConstructionBase", "DataAPI", "Tables"]
 git-tree-sha1 = "8ad2e38cbb812e29348719cc63580ec1dfeb9de4"
 uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
 version = "0.7.1"

    [deps.StructArrays.extensions]
    StructArraysAdaptExt = "Adapt"
    StructArraysGPUArraysCoreExt = ["GPUArraysCore", "KernelAbstractions"]
    StructArraysLinearAlgebraExt = "LinearAlgebra"
    StructArraysSparseArraysExt = "SparseArrays"
    StructArraysStaticArraysExt = "StaticArrays"

    [deps.StructArrays.weakdeps]
    Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
    KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

 [[deps.StyledStrings]]
 uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
 version = "1.11.0"

 [[deps.SuiteSparse]]
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
 uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

 [[deps.SuiteSparse_jll]]
 deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
 version = "7.7.0+0"

 [[deps.TOML]]
 deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 version = "1.0.3"

 [[deps.TableTraits]]
 deps = ["IteratorInterfaceExtensions"]
 git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
 uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
 version = "1.0.1"

 [[deps.Tables]]
 deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "OrderedCollections", "TableTraits"]
 git-tree-sha1 = "598cd7c1f68d1e205689b1c2fe65a9f85846f297"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 version = "1.12.0"

 [[deps.Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 version = "1.10.0"

 [[deps.TensorCore]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
 uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
 version = "0.1.1"

 [[deps.Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 version = "1.11.0"

 [[deps.TiffImages]]
 deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "ProgressMeter", "SIMD", "UUIDs"]
 git-tree-sha1 = "f21231b166166bebc73b99cea236071eb047525b"
 uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
 version = "0.11.3"

 [[deps.TranscodingStreams]]
 git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.11.3"

 [[deps.TriplotBase]]
 git-tree-sha1 = "4d4ed7f294cda19382ff7de4c137d24d16adc89b"
 uuid = "981d1d27-644d-49a2-9326-4793e63143c3"
 version = "0.1.0"

 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 version = "1.11.0"

 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 version = "1.11.0"

 [[deps.UnicodeFun]]
 deps = ["REPL"]
 git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
 uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
 version = "0.4.1"

 [[deps.Unitful]]
 deps = ["Dates", "LinearAlgebra", "Random"]
 git-tree-sha1 = "d62610ec45e4efeabf7032d67de2ffdea8344bed"
 uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
 version = "1.22.1"
 weakdeps = ["ConstructionBase", "InverseFunctions"]

    [deps.Unitful.extensions]
    ConstructionBaseUnitfulExt = "ConstructionBase"
    InverseFunctionsUnitfulExt = "InverseFunctions"

 [[deps.WebP]]
 deps = ["CEnum", "ColorTypes", "FileIO", "FixedPointNumbers", "ImageCore", "libwebp_jll"]
 git-tree-sha1 = "aa1ca3c47f119fbdae8770c29820e5e6119b83f2"
 uuid = "e3aaa7dc-3e4b-44e0-be63-ffb868ccd7c1"
 version = "0.1.3"

 [[deps.WoodburyMatrices]]
 deps = ["LinearAlgebra", "SparseArrays"]
 git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
 uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
 version = "1.0.0"

 [[deps.XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
 git-tree-sha1 = "b8b243e47228b4a3877f1dd6aee0c5d56db7fcf4"
 uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
 version = "2.13.6+1"

 [[deps.XZ_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "fee71455b0aaa3440dfdd54a9a36ccef829be7d4"
 uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
 version = "5.8.1+0"

 [[deps.Xorg_libX11_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
 git-tree-sha1 = "b5899b25d17bf1889d25906fb9deed5da0c15b3b"
 uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
 version = "1.8.12+0"

 [[deps.Xorg_libXau_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "aa1261ebbac3ccc8d16558ae6799524c450ed16b"
 uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
 version = "1.0.13+0"

 [[deps.Xorg_libXdmcp_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "52858d64353db33a56e13c341d7bf44cd0d7b309"
 uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
 version = "1.1.6+0"

 [[deps.Xorg_libXext_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
 git-tree-sha1 = "a4c0ee07ad36bf8bbce1c3bb52d21fb1e0b987fb"
 uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
 version = "1.3.7+0"

 [[deps.Xorg_libXrender_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
 git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d"
 uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
 version = "0.9.12+0"

 [[deps.Xorg_libxcb_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
 git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
 uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
 version = "1.17.1+0"

 [[deps.Xorg_xtrans_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
 uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
 version = "1.6.0+0"

 [[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 version = "1.2.13+1"

 [[deps.Zstd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
 uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
 version = "1.5.7+1"

 [[deps.isoband_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
 uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
 version = "0.2.3+0"

 [[deps.libaom_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "522c1df09d05a71785765d19c9524661234738e9"
 uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
 version = "3.11.0+0"

 [[deps.libass_jll]]
 deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
 git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
 uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
 version = "0.15.2+0"

 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
 version = "5.11.0+0"

 [[deps.libfdk_aac_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
 uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
 version = "2.0.3+0"

 [[deps.libpng_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
 git-tree-sha1 = "002748401f7b520273e2b506f61cab95d4701ccf"
 uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
 version = "1.6.48+0"

 [[deps.libsixel_jll]]
 deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "libpng_jll"]
 git-tree-sha1 = "c1733e347283df07689d71d61e14be986e49e47a"
 uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
 version = "1.10.5+0"

 [[deps.libvorbis_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
 git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
 uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
 version = "1.3.7+2"

 [[deps.libwebp_jll]]
 deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"]
 git-tree-sha1 = "d2408cac540942921e7bd77272c32e58c33d8a77"
 uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2"
 version = "1.5.0+0"

 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
 version = "1.59.0+0"

 [[deps.oneTBB_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
 uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
 version = "2022.0.0+0"

 [[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 version = "17.4.0+2"

 [[deps.x264_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
 uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
 version = "10164.0.1+0"

 [[deps.x265_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "dcc541bb19ed5b0ede95581fb2e41ecf179527d2"
 uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
 version = "3.6.0+0"
 """

 # ╔═╡ Cell order:
 # ╟─6534f7c8-3321-11f0-1c07-a5f5efec77d4
 # ╠═446b951f-049b-441a-a869-03529b1ef965
 # ╟─bf1174ac-98df-4a10-b3c0-9d6176a3a607
 # ╠═1c103973-163d-4aab-8997-52b546526ca7
 # ╠═9cef439c-9976-4952-8a3c-370d6a7f86d5
 # ╠═d9b39ef9-7a7d-44f2-a29e-005d73c66343
 # ╠═353fca42-5db7-4d43-93a5-2bff0415d7d9
 # ╟─0c14dabb-f47c-4b9a-b32d-db04991d8a3a
 # ╠═853d4628-9849-427c-8d96-10b873adf528
 # ╠═5e1c72b7-893e-4011-9915-462820e2d58f
 # ╟─204c594f-e596-4b39-a238-b3d566180fb3
 # ╟─2212380f-6c93-437a-a491-ffb760032e84
 # ╠═fc389c8e-771e-430d-866e-4188cd9d8c3f
 # ╠═f80d45e5-dea0-4f53-ac6a-e511f78d219d
 # ╠═ea760191-eb6c-4423-a557-8bf96d3ea803
 # ╟─35f7058e-e66c-41a0-bbc1-2a0b8fddb1d9
 # ╠═d08f5aa8-a805-4651-bf55-51bf8ee88781
 # ╠═971cd3e3-53ef-49fd-803e-18ef9fa22bd2
 # ╠═1b6cc796-dd26-4cee-bd7a-5985c3b8624a
 # ╟─a692c080-cf9d-4915-9840-2351605bc186
 # ╠═df192b40-2c57-486e-8ade-fcbcd5fa773c
 # ╠═701b3c25-4488-43bb-918b-88606ee8cd27
 # ╠═54b5ef56-0282-4d73-83fa-440ce8cc8b49
 # ╠═30e81a04-9355-46ab-975a-a8de8ca5285d
 # ╠═8592e23a-5da6-4e45-a0ea-c190f55e84a7
 # ╠═d4e45003-554f-48e4-91dd-c7990ad94a19
 # ╠═4070bca5-feaa-4a22-ae31-8651029c47b9
 # ╟─617e45e8-2940-4753-90cb-84a61760db07
 # ╠═dd57e5b7-c27d-47ac-8659-53a67df31a4f
 # ╠═ffd5a55c-2e45-4536-b6bd-55e3cbee93c9
 # ╠═582c3dfa-e2f4-47fa-811c-c324fd6f1a41
 # ╠═fed249af-d6bf-4e87-a884-8af551c2e895
 # ╠═4149be42-e68c-4a4c-94ec-bee69ab134aa
 # ╠═d266874f-f48f-4b24-b10f-49b0eb4bf8fb
 # ╠═38ddc0e6-3b0f-415d-8d90-ffb54beeca05
 # ╠═22621f3f-7d75-49f6-b297-da97fea45320
 # ╠═d1ba80c0-c77e-4dfe-95df-85f588700cf1
 # ╟─00000000-0000-0000-0000-000000000001
 # ╟─00000000-0000-0000-0000-000000000002
No results found