### A Pluto.jl notebook ###
# v0.17.7

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 19e0c319-47f1-4c16-85e9-904938cdc74d
begin
	using Colors, ColorVectorSpace, ImageShow, FileIO, ImageIO
	using PlutoUI
	using HypertextLiteral, Plots, OffsetArrays
	using ImageMagick, ImageFiltering
	using StaticArrays, LinearAlgebra, ForwardDiff, NonlinearSolve
end

# ╔═╡ ac6d7ea0-8170-11ec-2320-63e980786867
md"""
### Image transformations
_We are going to play with an image in several ways!_
Don't forget that you can do so called indexing.
"""

# ╔═╡ c4e64bef-a72a-4c4d-a50a-4e3c217bfc6c
url ="https://images3.alphacoders.com/104/thumb-1920-1041183.jpg"

# ╔═╡ 0e4e01ec-7259-4cea-bb87-cb096a2b0031
dragon = download(url) # download to a local file

# ╔═╡ 2b16eaf3-acfb-42be-91f3-feb71eed8de2
dragons = load(dragon)

# ╔═╡ 660d3dbd-2417-499c-b4f4-6dea8a05f2d7
typeof(dragons)

# ╔═╡ 49193149-436d-40b8-9516-c46a51d55148
size(dragons) # number of pixels in rows and columns

# ╔═╡ fe9e36d0-dd60-4bea-83d7-330c6ae51b13
md"""
Now we want to transform this image whatever I want. It could be **linear** or **non-linear**.

FIrst, let me join the same image in different directions.
"""

# ╔═╡ f571be7e-c21c-47b6-b955-06f3ba9f2719
[
	dragons    dragons[:, end:-1:1]
	dragons[end:-1:1, :] dragons[end:-1:1, end:-1:1]
]

# ╔═╡ 379fb899-a120-4804-a201-cee9924265d0
[
	dragons reverse(dragons, dims=2)
	reverse(dragons, dims=1) rot180(dragons)
]

# ╔═╡ 05f0839f-a14c-4ccc-ac16-7be28a2400d7
[
	dragons                  reverse(dragons, dims=1)
	reverse(dragons, dims=2) rot180(dragons)
]

# ╔═╡ a6dd8a10-6538-4106-a768-845ceb06a516
upsidedown_dragon = dragons[end:-1:1, :]

# ╔═╡ 96bdc7fc-c7db-49aa-be61-1672a577949e
.7 * dragons .+ .3 * upsidedown_dragon

# ╔═╡ 91bfa0c0-eb1c-4e7f-b67e-ae42dd5a72f8
[
	[RGB(i, j, 0) for i in 0:0.1:1, j in 0:0.1:1]
	[RGB(i, 0, j) for i in 0:0.1:1, j in 0:0.1:1]
	[RGB(0, i, j) for i in 0:0.1:1, j in 0:0.1:1]
]

# ╔═╡ 9ad2cd7b-afdd-4cf3-9d20-9be21e9a974c
begin
	#plotly() # for interactivity
	x = [(i, j, k) for i in 0:0.1:1 for j in 0:0.1:1 for k in 0:0.1:1];
	plot(x; st=:scatter, color=[RGB(a...) for a in x], xguide="R", yguide="G", zguide="B", label=nothing)
	
end

# ╔═╡ f520720c-cfdf-4003-9bc6-5d1c6f7863d8
md"""
Some experimental codes for edge detection. You can see the little differences.
"""

# ╔═╡ 1033ad9f-6720-4e5b-b0dc-4e49f4e58d43
begin
	Δx = [1 0 -1; 1 0 -1; 1 0 -1]/2
	∇x = [-1 0 1;-1 0 1;-1 0 1]/2
	∇y = ∇x'
	Δy = Δx'
end

# ╔═╡ 193473e2-f977-4d3c-bdc8-69db6a54844e
Gray.(2 .* (imfilter(dragons, OffsetArray(Δx, -1:1, -1:1))))

# ╔═╡ 21743c4b-466c-4181-a11e-ce6cee3fa49b
Gray.(2 .* (imfilter(dragons, OffsetArray(∇x, -1:1, -1:1))))

# ╔═╡ fda2bdc1-84af-45e3-9bb1-310c791c698c
Gray.(2 .* (imfilter(dragons, OffsetArray(Δy, -1:1, -1:1))))

# ╔═╡ b5529ade-62f5-492a-91b8-5b10b4c9eb52
Gray.(2 .* (imfilter(dragons, OffsetArray(∇y, -1:1, -1:1))))

# ╔═╡ b58fdb86-34af-4d42-bc73-f4c0498aa3d6
md"""
###### Now let's play the image with filtering. (convolutions)
- Gaussian blur (probability of the center must be the highest.)
- Edge detect
- Sharpening
"""

# ╔═╡ e5d2a112-635c-4f76-a55a-3195b3352d37
gaussian_blur = round.(Kernel.gaussian(1), digits=3)

# ╔═╡ e2aab6c0-eab5-4a64-b4f0-93595145adb4
[dragons; imfilter(dragons, gaussian_blur)]

# ╔═╡ 74fd7029-b2f7-4c14-9fc2-90f1b9938783
begin
	identity_M = [0 0 0; 0 1 0; 0 0 0]
	edge_detect = [0 -1 0; -1 4 -1; 0 -1 0]
end

# ╔═╡ 3f7b0527-2429-4ff6-a5d4-febfd35a1bd9
2 .* abs.(imfilter(dragons, OffsetArray(edge_detect, -1:1, -1:1)))

# ╔═╡ dccd1c87-575a-4620-aa7f-f7b89f2b27db
sharpen_m = 1.5 .* identity_M .+ edge_detect

# ╔═╡ 4502e1bf-f36a-43f5-9b83-b4e55763c6aa
[dragons; imfilter(dragons, OffsetArray(sharpen_m, -1:1, -1:1))]

# ╔═╡ 50982109-86d1-4e28-bfab-c36669e82a6a
idkm = [-1 -1 -1; -1 9 -1; -1 -1 -1]

# ╔═╡ 42f0f92e-1b13-4f23-a5c3-c20dfdf3fa26
imfilter(dragons, OffsetArray(idkm, -1:1, -1:1))

# ╔═╡ 22b62dff-ba3e-4752-8dff-1008540a6cdb
md"""
###### Image transformations

Here are some transforming functions. (You are able to make your own function.)

- linear combinations
- rotate
- shear
- warp

etc

[Julia's  `∘` operator(composition)](https://docs.julialang.org/en/v1/manual/functions/#Function-composition-and-piping) 
follows the [mathematical typography](https://en.wikipedia.org/wiki/Function_composition#Typography) convention, as was
shown in the `sin ∘ cos` example above. We can type this symbol as `\circ<TAB>`.

"""

# ╔═╡ bc1373b7-b1ea-4c02-898c-7a9cba3644e2
begin
	white(c::RGB) = RGB(1,1,1)
	white(c::RGBA) = RGBA(1,1,1,0.75)
	black(c::RGB) = RGB(0,0,0)
	black(c::RGBA) = RGBA(0,0,0,0.75)
end

# ╔═╡ d1932e69-5e31-4ea9-88c6-780ccabdf2bc
begin
	pixels = 3000
	panx = 0
	pany = 0
	z = 1
	α = 10
	img = dragons
end

# ╔═╡ 78ea1f13-a9b1-435e-a173-29b7f2d5a940
begin
	 id((x, y)) = SA[x, y]
	
	 scalex(α) = ((x, y),) -> SA[α*x,  y]
	 scaley(α) = ((x, y),) -> SA[x,   α*y]
	 scale(α)  = ((x, y),) -> SA[α*x, α*y]
	
	 swap((x, y))  = SA[y, x]
	 flipy((x, y)) = SA[x, -y]
	
	 rotate(θ) = ((x, y),) -> SA[cos(θ)*x + sin(θ)*y, -sin(θ)*x + cos(θ)*y]
	 shear(α)  = ((x, y),) -> SA[x + α*y, y]
end

# ╔═╡ 29f5acb1-4dcc-4b97-bf10-d66fd34b4740
begin
	lin(a, b, c, d) = ((x, y),) -> (a*x + b*y, c*x + d*y)
	
	lin(A) = v-> A * [v...]  # linear algebra version using matrix multiplication
end

# ╔═╡ 465ae4a5-2f6c-4a16-83bc-74bd58c896f8
begin
  translate(α,β)  = ((x, y),) -> SA[x+α, y+β]   # affine, but not linear
	
  nonlin_shear(α) = ((x, y),) -> SA[x, y + α*x^2]
	
  warp(α)    = ((x, y),) -> rotate(α*√(x^2+y^2))(SA[x, y])
  xy((r, θ)) = SA[ r*cos(θ), r*sin(θ) ]
  rθ(x)      = SA[norm(x), atan(x[2],x[1]) ] 
  
  # exponentialish =  ((x,y),) -> [log(x+1.2), log(y+1.2)]
  # merc = ((x,y),) ->  [ log(x^2+y^2)/2 , atan(y,x) ] # (reim(log(complex(y,x)) ))
end

# ╔═╡ 884e538f-f030-418e-98c6-a3d69b8dd818
# T⁻¹ = id
#  T⁻¹ = rotate(α)
#  T⁻¹ = shear(α)
#   T⁻¹ = lin(A)
#   T⁻¹ = shear(α) ∘ shear(-α) #this is equal to id.
#  T⁻¹ = nonlin_shear(α)  
#    T⁻¹ =   inverse(nonlin_shear(α))
#    T⁻¹ =  nonlin_shear(-α)
#  T⁻¹ =  xy 
 T⁻¹ = warp(α)
# T⁻¹ = ((x,y),)-> (x+α*y^2,y+α*x^2) # may be non-invertible

# T⁻¹ = ((x,y),)-> (x,y^2)  
# T⁻¹  = flipy ∘ ((x,y),) ->  ( (β*x - α*y)/(β - y)  , -h*y/ (β - y)   ) 

# ╔═╡ 3d5be741-4cf6-4760-b857-ae7955ae288b
begin
	function transform_xy_to_ij(img::AbstractMatrix, x::Float64, y::Float64)
	# convert coordinate system xy to ij 
	# center image, and use "white" when out of the boundary
		
		rows, cols = size(img)
		m = max(cols, rows)	
		
	    # function to take xy to ij
		xy_to_ij =  translate(rows/2, cols/2) ∘ swap ∘ flipy ∘ scale(m/2)
		
		# apply the function and "snap to grid"
		i, j = floor.(Int, xy_to_ij((x, y))) 
	
	end
	
	function getpixel(img,i::Int,j::Int; circular::Bool=false, r::Real=200)   
		#  grab image color or place default
		rows, cols = size(img)
		m = max(cols,rows)
		if circular
			c = (i-rows/2)^2 + (j-cols/2)^2 ≤ r*m^2/4
		else
			c = true
		end
		
		if 1 < i ≤ rows && 1 < j ≤ cols && c
			img[i, j]
		else
			# white(img[1, 1])
			black(img[1,1])
		end
		
	end
	
	
	# function getpixel(img,x::Float64,y::Float64)
	# 	i,j = transform_xy_to_ij(img,x,y)
	# 	getpixel(img,i,j)
	# end
	
	function transform_ij_to_xy(i::Int,j::Int,pixels)
	
	   ij_to_xy =  scale(2/pixels) ∘ flipy ∘ swap ∘ translate(-pixels/2,-pixels/2)
	   ij_to_xy([i,j])
	end

	    
end

# ╔═╡ b58460fc-e842-49dc-bb78-a265e7e41251
begin
		[			    
			begin
			
			 x, y = transform_ij_to_xy(i,j, pixels)
			 X, Y = ( T⁻¹ )([x,y])
			 i, j = transform_xy_to_ij(img,X,Y)
			 getpixel(img,i,j;)
			end	 
		
			for i = 1:pixels, j = 1:pixels
		]	
end

# ╔═╡ dcdf9472-d234-4352-92c0-1690e3de3b2b
brightness(c::AbstractRGB) = 0.3 * c.r + 0.59 * c.g + 0.11 * c.b

# ╔═╡ adee2556-a696-48fe-9671-ba4d9a6757ac
Gray.(brightness.(img))

# ╔═╡ 2c99a42e-11f7-43fb-81d8-e8df006767eb
Sy, Sx = Kernel.sobel()

# ╔═╡ 8e02a427-4595-4c2a-b42a-c381c79080b1
(collect(Int.(8 .* Sx)), collect(Int.(8 .* Sy)))

# ╔═╡ 921a01bf-6416-4fbb-abaf-946cb19e8d29
md"""
### Seam Carving

The idea of **seam carving** is to shrink an image by removing the "least interesting" parts of the image, but *without* resizing the objects within the image. We want to remove the "dead space" within the image.

"""

# ╔═╡ 68d4a79c-2405-4337-aba2-804d1e2a321e
	function show_colored_array(array)
		pos_color = RGB(0.36, 0.82, 0.8)
		neg_color = RGB(0.99, 0.18, 0.13)
		to_rgb(x) = max(x, 0) * pos_color + max(-x, 0) * neg_color
		to_rgb.(array) / maximum(abs.(array))
	end

# ╔═╡ a00de352-63e2-4f43-bfc3-aacc080e14a0
function hbox(x, y, gap=16; sy=size(y), sx=size(x))
	w, h = (max(sx[1], sy[1]),
		   gap + sx[2] + sy[2])
	
	slate = fill(RGB(1,1,1), w,h)
	slate[1:size(x,1), 1:size(x,2)] .= RGB.(x)
	slate[1:size(y,1), size(x,2) + gap .+ (1:size(y,2))] .= RGB.(y)
	slate
end

# ╔═╡ b424e77e-fddb-4c6e-870b-4315bfe7e1b2
function convolve(M, kernel)
    height, width = size(kernel)
    
    half_height = height ÷ 2
    half_width = width ÷ 2
    
    new_image = similar(M)
	
    # (i, j) loop over the original image
	m, n = size(M)
    @inbounds for i in 1:m
        for j in 1:n
            # (k, l) loop over the neighbouring pixels
			accumulator = 0 * M[1, 1]
			for k in -half_height:-half_height + height - 1
				for l in -half_width:-half_width + width - 1
					Mi = i - k
					Mj = j - l
					# First index into M
					if Mi < 1
						Mi = 1
					elseif Mi > m
						Mi = m
					end
					# Second index into M
					if Mj < 1
						Mj = 1
					elseif Mj > n
						Mj = n
					end
					
					accumulator += kernel[k, l] * M[Mi, Mj]
				end
			end
			new_image[i, j] = accumulator
        end
    end
    
    return new_image
end

# ╔═╡ b716f0bf-002f-461d-8fc8-8340e44bd487
#            e[x,y] 
#          ↙   ↓   ↘       <-- pick the next path which gives the least overall energy
#  e[x-1,y+1] e[x,y+1]  e[x+1,y+1]     
#
# Basic calculation:   e[x,y] += min( e[x-1,y+1], e[x,y], e[x+1,y] )
#               `dirs` records which direction we take from (-1==SW, 0==S, 1==SE)

function least_edgy(E)
	least_E = zeros(size(E))
	dirs = zeros(Int, size(E))
	
	least_E[end, :] .= E[end, :] # the minimum energy on the last row is the energy
	                             # itself

	m, n = size(E)
	# Go from the last row up, finding the minimum energy
	
	for i in m-1:-1:1
		for j in 1:n
			
			j1, j2 = max(1, j-1), min(j+1, n)
			e, dir = findmin(least_E[i+1, j1:j2])
			least_E[i,j] += e
			least_E[i,j] += E[i,j]
			dirs[i, j] = (-1, 0, 1)[dir + (j==1)]
			
		end
	end
	
	return least_E, dirs
end

# ╔═╡ 0e8b20b6-9bb5-40e6-8dda-43d2bdec5c4d
function edgeness(img)
	Sy, Sx = Kernel.sobel()
	b = brightness.(img)

	∇y = convolve(b, Sy)
	∇x = convolve(b, Sx)

	sqrt.(∇x.^2 + ∇y.^2)
end

# ╔═╡ 0d720be1-b239-4d71-9d08-c9dc5c9c77cd
function get_seam_at(dirs, j)
	m = size(dirs, 1)
	js = fill(0, m)
	js[1] = j
	
	for i=2:m
		js[i] = js[i-1] + dirs[i-1, js[i-1]]
	end
	
	return tuple.(1:m, js)
end

# ╔═╡ 5e958841-b6ce-4a43-bd4f-b341d6e39d64
function rm_path(img, path)
	img′ = img[:, 1:end-1] # one less column
	for (i, j) in path
		img′[i, 1:j-1] .= img[i, 1:j-1]
		img′[i, j:end] .= img[i, j+1:end]
	end
	img′
end

# ╔═╡ 5a9b14cc-12f8-4e34-b2c6-90471137711f
function mark_path(img, path)
	img′ = copy(img)
	m = size(img, 2)
	
	for (i, j) in path
		# To make it easier to see, we'll color not just
		# the pixels of the seam, but also those adjacent to it
		
		for j′ in j-1:j+1
			img′[i, clamp(j′, 1, m)] = RGB(1,0,1)
		end
		
	end
	
	return img′
end

# ╔═╡ 1b77e7b5-6a0a-499a-9ec4-8ca6d3f2f9c8
function shrink_n(img, n)
	imgs = []
	marked_imgs = []

	e = edgeness(img)
	for i=1:n
		least_E, dirs = least_edgy(e)
		_, min_j = findmin(@view least_E[1, :])
		seam = get_seam_at(dirs, min_j)
		img = rm_path(img, seam)
		# Recompute the energy for the new image
		# Note, this currently involves rerunning the convolution
		# on the whole image, but in principle the only values that
		# need recomputation are those adjacent to the seam, so there
		# is room for a meanintful speedup here.
#		e = edgeness(img)
		e = rm_path(e, seam)

 		push!(imgs, img)
 		push!(marked_imgs, mark_path(img, seam))
	end
	imgs, marked_imgs
end

# ╔═╡ 32ddd79c-dcd2-45b7-b8c4-2da8b0063703
n_examples = min(200, size(img, 2))

# ╔═╡ d36396de-f641-44fe-a709-5c53f8071e34
# returns two vectors of n successively smaller images
# The second images have markings where the seam is cut out
carved, marked_carved = shrink_n(img, n_examples);

# ╔═╡ 5ba62566-6f23-4c6c-9b70-fb2ffcbe9ac5
@bind n Slider(1:length(carved))

# ╔═╡ 7a826725-2741-44da-b451-28dee60628b4
hbox(img, marked_carved[n], sy=size(img))

# ╔═╡ e870d3cc-79ea-4ae6-b276-8f5cb5ea8c10
least_e, dirs = least_edgy(edgeness(img))

# ╔═╡ fbd26ff9-fa99-41cd-a671-6792fdfb32ee
show_colored_array(least_e)

# ╔═╡ 8d9c9b99-b405-4bb7-ad4d-20330421212b
md"""
#### Reference
Some material on this website is based on:
Computational Thinking, a live online Julia/Pluto textbook. (computationalthinking.mit.edu)
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
ColorVectorSpace = "c3611d14-8923-5661-9e6a-0046d554d3a4"
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
ImageFiltering = "6a3955dd-da59-5b1f-98d4-e7296123deb5"
ImageIO = "82e4d734-157c-48bb-816b-45c225c6df19"
ImageMagick = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
ImageShow = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

[compat]
ColorVectorSpace = "~0.9.8"
Colors = "~0.12.8"
FileIO = "~1.12.0"
ForwardDiff = "~0.10.25"
HypertextLiteral = "~0.9.3"
ImageFiltering = "~0.7.1"
ImageIO = "~0.6.0"
ImageMagick = "~1.2.2"
ImageShow = "~0.3.3"
NonlinearSolve = "~0.3.14"
OffsetArrays = "~1.10.8"
Plots = "~1.25.7"
PlutoUI = "~0.7.32"
StaticArrays = "~1.3.3"
"""

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

[[AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.1.0"

[[AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.3"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[ArrayInterface]]
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[[Artifacts]]
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[[Base64]]
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[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
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[[CEnum]]
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[[Cairo_jll]]
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git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
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[[CatIndices]]
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[[ChainRulesCore]]
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[[ChangesOfVariables]]
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[[ColorSchemes]]
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git-tree-sha1 = "6b6f04f93710c71550ec7e16b650c1b9a612d0b6"
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[[ColorTypes]]
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[[ColorVectorSpace]]
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[[Colors]]
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git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
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[[CommonSolve]]
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[[CommonSubexpressions]]
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[[Compat]]
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git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
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[[CompilerSupportLibraries_jll]]
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[[ComputationalResources]]
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[[ConstructionBase]]
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[[Contour]]
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[[CustomUnitRanges]]
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[[DataAPI]]
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[[DataStructures]]
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[[DataValueInterfaces]]
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[[Dates]]
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[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[DiffResults]]
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[[DiffRules]]
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[[Distributed]]
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[[DocStringExtensions]]
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[[Downloads]]
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[[EarCut_jll]]
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git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
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[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
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[[FFMPEG]]
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[[FFMPEG_jll]]
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git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
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[[FFTViews]]
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[[FFTW]]
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[[FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c6033cc3892d0ef5bb9cd29b7f2f0331ea5184ea"
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[[FileIO]]
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[[FillArrays]]
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[[FiniteDiff]]
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[[FixedPointNumbers]]
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[[Fontconfig_jll]]
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git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
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[[Formatting]]
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[[ForwardDiff]]
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[[FreeType2_jll]]
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git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
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[[FriBidi_jll]]
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[[Future]]
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uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
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[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "RelocatableFolders", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "4a740db447aae0fbeb3ee730de1afbb14ac798a1"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.63.1"

[[GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "aa22e1ee9e722f1da183eb33370df4c1aeb6c2cd"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
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[[GeometryBasics]]
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[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
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[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "a32d672ac2c967f3deb8a81d828afc739c838a06"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
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[[Graphics]]
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git-tree-sha1 = "1c5a84319923bea76fa145d49e93aa4394c73fc2"
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[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
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[[Grisu]]
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[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
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[[HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
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[[Hyperscript]]
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[[HypertextLiteral]]
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[[IOCapture]]
deps = ["Logging", "Random"]
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uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
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[[IfElse]]
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[[ImageBase]]
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[[ImageCore]]
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[[ImageFiltering]]
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git-tree-sha1 = "15bd05c1c0d5dbb32a9a3d7e0ad2d50dd6167189"
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[[ImageIO]]
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git-tree-sha1 = "816fc866edd8307a6e79a575e6585bfab8cef27f"
uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
version = "0.6.0"

[[ImageMagick]]
deps = ["FileIO", "ImageCore", "ImageMagick_jll", "InteractiveUtils"]
git-tree-sha1 = "ca8d917903e7a1126b6583a097c5cb7a0bedeac1"
uuid = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
version = "1.2.2"

[[ImageMagick_jll]]
deps = ["JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "1c0a2295cca535fabaf2029062912591e9b61987"
uuid = "c73af94c-d91f-53ed-93a7-00f77d67a9d7"
version = "6.9.10-12+3"

[[ImageShow]]
deps = ["Base64", "FileIO", "ImageBase", "ImageCore", "OffsetArrays", "StackViews"]
git-tree-sha1 = "d0ac64c9bee0aed6fdbb2bc0e5dfa9a3a78e3acc"
uuid = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
version = "0.3.3"

[[Imath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "87f7662e03a649cffa2e05bf19c303e168732d3e"
uuid = "905a6f67-0a94-5f89-b386-d35d92009cd1"
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[[IndirectArrays]]
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uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "1.0.0"

[[Inflate]]
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uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
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[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2018.0.3+2"

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

[[InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.2"

[[IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"

[[IterTools]]
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uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.4.0"

[[IterativeSolvers]]
deps = ["LinearAlgebra", "Printf", "Random", "RecipesBase", "SparseArrays"]
git-tree-sha1 = "1169632f425f79429f245113b775a0e3d121457c"
uuid = "42fd0dbc-a981-5370-80f2-aaf504508153"
version = "0.9.2"

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

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "22df5b96feef82434b07327e2d3c770a9b21e023"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
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[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
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[[LaTeXStrings]]
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uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.9"

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

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

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

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

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

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
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[[LinearAlgebra]]
deps = ["Libdl"]
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[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.6"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "5455aef09b40e5020e1520f551fa3135040d4ed0"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+2"

[[MacroTools]]
deps = ["Markdown", "Random"]
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[[MappedArrays]]
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version = "0.4.1"

[[Markdown]]
deps = ["Base64"]
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[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
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[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
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[[Missings]]
deps = ["DataAPI"]
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version = "1.0.2"

[[Mmap]]
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[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d"
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version = "0.3.3"

[[MozillaCACerts_jll]]
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[[NaNMath]]
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uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
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[[Netpbm]]
deps = ["FileIO", "ImageCore"]
git-tree-sha1 = "18efc06f6ec36a8b801b23f076e3c6ac7c3bf153"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.0.2"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[NonlinearSolve]]
deps = ["ArrayInterface", "FiniteDiff", "ForwardDiff", "IterativeSolvers", "LinearAlgebra", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "SciMLBase", "Setfield", "StaticArrays", "UnPack"]
git-tree-sha1 = "b61c51cd5b9d8b197dfcbbf2077a0a4e1505278d"
uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
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[[OffsetArrays]]
deps = ["Adapt"]
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uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.8"

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

[[OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
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[[OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "923319661e9a22712f24596ce81c54fc0366f304"
uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
version = "3.1.1+0"

[[OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.13+0"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
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[[OrderedCollections]]
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uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "6d105d40e30b635cfed9d52ec29cf456e27d38f8"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
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[[PaddedViews]]
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[[Parsers]]
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uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.2.1"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
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[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
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[[PlotThemes]]
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[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
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[[Plots]]
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git-tree-sha1 = "7e4920a7d4323b8ffc3db184580598450bde8a8e"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.25.7"

[[PlutoUI]]
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git-tree-sha1 = "ae6145ca68947569058866e443df69587acc1806"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
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[[Preferences]]
deps = ["TOML"]
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[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
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[[QOI]]
deps = ["ColorTypes", "FileIO", "FixedPointNumbers"]
git-tree-sha1 = "18e8f4d1426e965c7b532ddd260599e1510d26ce"
uuid = "4b34888f-f399-49d4-9bb3-47ed5cae4e65"
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[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
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[[REPL]]
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uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RecipesBase]]
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[[RecipesPipeline]]
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[[RecursiveArrayTools]]
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[[RecursiveFactorization]]
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[[Reexport]]
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[[RelocatableFolders]]
deps = ["SHA", "Scratch"]
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[[Requires]]
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version = "1.3.0"

[[SHA]]
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[[SciMLBase]]
deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "RecipesBase", "RecursiveArrayTools", "StaticArrays", "Statistics", "Tables", "TreeViews"]
git-tree-sha1 = "f4862c0cb4e34ed182718221028ba1bf50742108"
uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
version = "1.26.1"

[[Scratch]]
deps = ["Dates"]
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uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[Serialization]]
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[[Setfield]]
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git-tree-sha1 = "0afd9e6c623e379f593da01f20590bacc26d1d14"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
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[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

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

[[Sixel]]
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git-tree-sha1 = "8fb59825be681d451c246a795117f317ecbcaa28"
uuid = "45858cf5-a6b0-47a3-bbea-62219f50df47"
version = "0.1.2"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "e6bf188613555c78062842777b116905a9f9dd49"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.0"

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

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "b4912cd034cdf968e06ca5f943bb54b17b97793a"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.5.1"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "2884859916598f974858ff01df7dfc6c708dd895"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.3.3"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.2.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.14"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "d21f2c564b21a202f4677c0fba5b5ee431058544"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.4"

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

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

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

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

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

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

[[TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "991d34bbff0d9125d93ba15887d6594e8e84b305"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.5.3"

[[TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "5683455224ba92ef59db72d10690690f4a8dc297"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
version = "0.3.1"

[[TreeViews]]
deps = ["Test"]
git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
version = "0.3.0"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

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

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

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

[[Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

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

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "78736dab31ae7a53540a6b752efc61f77b304c5b"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.8.6+1"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

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