### A Pluto.jl notebook ###
# v0.17.2

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

# ╔═╡ 673b5f44-0db4-4848-95d7-24a31e7e86b1
begin
	#try
		using PlutoUI
		using Plots
		using Plots.PlotMeasures
		using LaTeXStrings
		using Markdown
		using StatsBase
		using Images
		using DelimitedFiles
		

		#using LinearAlgebra
		#using SparseArrays
		#using SpecialFunctions
		#using StatsBase
		using Random
		#using Distributions
		md""" 
		### Packages
		
		All needed Packages available :) """
	#=catch
		using Pkg;
		Pkg.activate(mktempdir())
		Pkg.add("PlutoUI")
		Pkg.add("Plots")
		Pkg.add("LaTeXStrings")
		Pkg.add("Markdown")
		Pkg.add("Images")
		Pkg.add("Random")
		Pkg.add("DelimitedFiles")
		Pkg.add("StatsBase")
		#Pkg.add("LinearAlgebra")
		#Pkg.add("SparseArrays")
		#Pkg.add("SpecialFunctions")
		#Pkg.add("StatsBase")
		#Pkg.add("Distributions")
		using PlutoUI, Plots, LaTeXStrings, Markdown, Images, Plots.PlotMeasures, Random, DelimitedFiles, StatsBase

		#using LinearAlgebra
		#using SparseArrays
		#using StatsBase

		md""" 
		### Packages
		
		Some Package sources not added, this will take approx. 3 minutes"""
	end
	=#
end

# ╔═╡ e342faf1-550f-4b6f-963e-ef53ac581c0b
#todo:
#scale invariance
#vdL im Video nix von multiple orders of magnitude erwähnt, also was jetzt?
#i am confused

# ╔═╡ 2dde8f33-1166-42b9-834f-7bcb54895992
md""" # Benford's Law"""

# ╔═╡ 245d5573-09f4-4536-b104-351a7669cd8b
md""" If you haven't already, you can watch the new episode here!"""

# ╔═╡ 9a4bc5f5-7acd-4640-a71b-82051b6d3db3
html"""<div style="display: flex; justify-content: center;">
<div  notthestyle="position: relative; right: 0; top: 0; z-index: 300;">
<iframe src="https://www.youtube.com/embed/ABbv9g5kTdI?start=394" width=600 height=375  frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div>
</div>"""

# ╔═╡ 27811f40-08a7-4da7-9788-db4b0c47153b
Markdown.MD(Markdown.Admonition("hint", string("Benford's law"), [md"""For a lot of naturally occurring datasets, the probability that the leading digit of a number in the set is the number  `` d \in \{1, 2, 3, .. 9\}`` can be calculated with

``P(d) = \log_{10}(d + 1) - \log_{10}(d)``"""]))

# ╔═╡ 0527804c-68b7-42f9-8830-c41d6b9036f4
md""" **Bayes:** 
...But to be sure, let's have a look at your data!"""

# ╔═╡ 91d8c001-c210-4c42-a7f2-5e84ee907ea6
md""" **Lyra:** I've collected data on different kinds of things - litter in the ocean, how many Frogfish are caught on a weekly basis, and the population of all organisms on the reefs! Which one do you want to see first?"""

# ╔═╡ fb1b6ea0-330c-4744-b3b8-19730b55e7e5
begin
	md"""
	Choose the **data** to compare 👉 $(@bind data_list Select(["Mass of marine litter in g", "Mass of marine litter in lbs", "Pieces of litter on the beach", "Frogfish caught weekly", "Reef population", "Random data"]))
	"""
	
end

# ╔═╡ 56b1302d-6a0e-4262-aa0e-9ae98c2167df
if data_list == "Random data"
md""" Choose a seed for the randomly generated data! $(@bind seed Scrubbable(0:1:20))"""
end

# ╔═╡ 64d6faa9-1564-4d7d-bf32-02f0720fa552
md"""
## Comparison with Benford's law
"""

# ╔═╡ c13206e8-ff41-405a-b9b8-50b589854901
md""" **Lyra:** You're right, it does coincide quite well! But there are some cases, where it does not work at all! Do you know why, Captain Bayes?

**Bayes:** Benford's law applies to many, albeit not all naturally occurring datasets. The data has to be scale invariant. But the question is how do we know if this is the case? 
A good hint for scale invariance is data that spans several magnitudes. In many cases this is a sufficient criteria.

We can examine our data in the histogram below, for some data you can observe a bias which is the reason why Benford's law is violated.


"""

# ╔═╡ a2a6d8c3-c9b7-458d-b5a7-6d3b3f68a926
md"""
## Data analysis and discussion
"""

# ╔═╡ 8a30e661-3057-4a30-a495-b1523b42207b
begin
	MarineLitter = html"<a href = 'https://catalogue.data.govt.nz/dataset/marine-litter-2018-2019' title = 'Hello' >Marine Litter</a>"
	ReefPopulation = html"<a href = 'https://data.world/gmoney/us-city-populations' title = 'Hello' >Reef Population</a>"
	Frogfish = html"<a href = https://datadryad.org/stash/dataset/doi:10.5061/dryad.ng8pf' title = 'Hello' >Frogfish</a>"
	
	md""" ## Did you know?
	
	The data analyzed here is acual scientific data! You can find our sources here:
	
	$(MarineLitter) (yes this is actual litter collected from beaches)
	
	
	$(ReefPopulation) (this is actually the population of US cities with more than 6000 inhabitants)
	
	
	$(Frogfish) (this is actually Pacific Salmon caught weekly) 
	
	
	
	"""
	
end

# ╔═╡ 4f48ef9a-05ea-41f9-a2a0-381865b8be6a
md""" # Derivation of Benford's Law using scale invariance"""

# ╔═╡ 601c53ed-ac2f-48fe-8afa-6b511a3ef369
html"""<div style="display: flex; justify-content: center;">
<div  notthestyle="position: relative; right: 0; top: 0; z-index: 300;">
<iframe src="https://www.youtube.com/embed/udDNi8yZH4o?start=1328" width=600 height=375  frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div>
</div>"""

# ╔═╡ a8d53828-ca73-4cb7-906f-ca2c94735a93
md"""
## About the creators

This notebook was created by **Johanna Moser** and **Gerhard Dorn** in the context of the course **Bayesian probability theory**.

The course is a free massive open online course (MOOC) available on the platform [`IMOOX`](https://imoox.at/mooc/local/landingpage/course.php?shortname=bayes&lang=en)

$(Resource("https://raw.githubusercontent.com/Captain-Bayes/images/main/adventure_map.gif"))
"""

# ╔═╡ 7b74d968-8591-49ba-81d8-9d8485676e93
TableOfContents()

# ╔═╡ 05d42951-063d-45d6-87ce-4d15b0472b84
begin
	
	# how to extract data from the non so csv csv file
	#=
	file_source = readdlm("data_marine_litter.csv", '\\')
		litter_count = []
		litter_mass = []
		for i in 3:986
			append!(litter_count, parse(Float64, reverse(split(file_source[i], ","))[8]))
		append!(litter_mass, parse(Float64, reverse(split(file_source[i], ","))[7]))
			end
		#a1 = convert(Array{Float64,1}, marine_numbers)
	
	writedlm("litter_beach.txt", [["count" "mass"]; [litter_count litter_mass]], "," )
	
	=#
end

# ╔═╡ a491e298-7a49-4cef-b269-886455538348
begin
	
	
	check_box_skip = @bind skip_low_gram CheckBox()
	select_counting = @bind count_in_pairs_dozens Select(["Single pieces", "Pairs", "Dozens"])
	
	md"""
	### define Checkboxes and Sliders """
end

# ╔═╡ 8368ba6c-cada-4caa-b37f-752034bfd571
begin 
	if data_list =="Mass of marine litter in g🚯" || data_list =="Mass of marine litter in lbs 🚯" 
		
		
		md""" See what happens if we **exclude objects** with **less than 10 grams** ⚖ from our analysis 👉 $(check_box_skip)
		
		Check Benford's law now in the first plot 👆"""
	elseif data_list == "Pieces of litter on the beach"
			md""" Change the way of counting 👉 $(select_counting)"""
		
	end
	
end

# ╔═╡ 5dfa126f-754f-4d25-a191-6e5437df99da
begin 
	#read in data
	
	# population
	temp_population =  readdlm("data_city_population.csv", ';', skipblanks = true, skipstart = 1)[1:6889,3]
	
	population = parse.(Float64, filter.(x -> !isspace(x), temp_population))
	
	# litter
	litter_pieces = readdlm("litter_beach.txt",',', skipstart = 1)[:,1]
	litter_mass = readdlm("litter_beach.txt",',', skipstart = 1)[:,2]
	if skip_low_gram
		litter_mass = litter_mass[litter_mass .>= 10]
		
	end
	
	if count_in_pairs_dozens == "Pairs"
		litter_pieces = litter_pieces./2
	elseif count_in_pairs_dozens == "Dozens"
		litter_pieces = litter_pieces./12
	end
	
	
	
	# fish population
	
	fish_catches = readdlm("data_salmon.csv", ',', skipstart = 1)[:,5]
	
	md""" 
	## Load data"""
end

# ╔═╡ ea7c16d9-dd13-41c6-9c03-431d068fd105
begin
	claire = "https://raw.githubusercontent.com/Captain-Bayes/images/main/claire_100px.gif"
	lyra = "https://raw.githubusercontent.com/Captain-Bayes/images/main/lyra_50px.gif"
	bayes = "https://raw.githubusercontent.com/Captain-Bayes/images/main/bayes_100px.gif"
	bernoulli = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Bernoulli_wet.gif"
	island = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Turtle_island_with_ship.png"
	map = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Fishground_map.png"
	frogfish_image = "https://raw.githubusercontent.com/Captain-Bayes/images/main/frogfish_green_full.gif"
	venn = "https://raw.githubusercontent.com/Captain-Bayes/images/main/venn_100px.gif"
	angles_view = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Gipfel_angles.png"
	mountain_view = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Gipfel_view.png"
	image_of_data = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Daten_brett.png"
	diagram_of_data = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Diagram.png"
	treasure_map = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Treasure_map_2.png"
	
	md"""Images"""
end

# ╔═╡ 0615b18c-23b6-4f93-99ff-2044588dccf2
md""" $(Resource(lyra, :width=>180))

When strolling on the beach, I find all kinds of stuff getting washed up by the ocean!


I keep a statistic on my findings, and I have noticed a strange pattern regarding the distribution of the first digits of my data: 

I would have expected to find an equal distribution of all numbers as the first digit in my statistics, but it turns out that most entries in my datasets start with a 1, followed by 2, and decreasing - up to the point, that it is 6.6 times more likely to find an entry starting with a 1 than with a 9!


Weird, isn't it?"""

# ╔═╡ 468c679f-6a42-4801-a908-82ab5a4c9507
md"""$(Resource(bayes, :width=>180))

That's interesting. Your description does sound like we could apply Benford's law.
"""

# ╔═╡ 7959439c-f947-40b3-8d2a-7dc96e90bbdc
#commentaries
begin
	if data_list =="Mass of marine litter in g🚯"
		
		md"""
		The data's range spans 4 orders of magnitude and the comparison with Benford's law looks promising. However the data is **biased** 😨🤯, because so much data is in the one digit area and the values are **rounded** to integers in grams, so all 0.5 to 0.9 entries are mapped to one gram. Check the conversion to pound which actually should not alter the result.
		
		 $(Resource(bayes, :width=>180))"""
		
	elseif data_list =="Mass of marine litter in lbs 🚯"
		md"""
		**Bayes:** The data's range spans 4 orders of magnitude. Now you see the effect of the bias. We have converted the mass in gram to mass in pound by multiplying with 0.002something. This should not alter the result, but the bias due to rounding and having so many entries in the one digit range in grams has now a considerable effect.
		
		 $(Resource(bayes, :width=>180))"""	
	elseif data_list =="Pieces of litter on the beach"
		
		md"""
		
		**Bayes:** The data's range spans 3 orders of magnitude. At first glance the behaviour corresponds to the one predicted by Benford's law. 
		
		**BUT:** There might be a slight bias due to the fact that we can only have integer numbers and a lot of ONES in the data. We could check if the data is scale invariant if we count in pairs or in dozens. 
		
		$(Resource(bayes, :width=>180))"""
				
	elseif data_list =="Frogfish caught weekly"
		md""" 
		**Bayes:** The data spans several orders of magnitude, so this is a good hint for scale invariance and we see that the data behaves according to Benford's law.
$(Resource(bayes, :width=>180))"""
		
	elseif data_list =="Reef population"
		md""" **Bayes:** The data's range spans almost 3 orders of magnitude. But since there surely are populations at the Reef that have less inhabitants, I am guessing you have cut off the data at some point, is that correct?
		
$(Resource(bayes, :width=>180))
		
**Lyra:**  Oh my, yes that is correct! I got so bored with counting groups of only 10 fish! I decided to only count populations that are higher than 6000! Does that interfere with the analysis of the numbers?
		
$(Resource(lyra, :width=>180))

**Bayes:** I'm afraid so. But at least that can explain the peak at 6!"""
					
	elseif data_list == "Random data"
		md""" 
		This data was generated by generating 10000 random (equally distributed) numbers A in a range of (ln(10^-8), ln(10^+8")) and then calculating exp(A). This way, we can assure data spanning multiple orders of magnitude. This type of data is called **log uniform**
		""" 
	
					end
end

# ╔═╡ 1f8c2dfc-1f42-41f9-b18d-3f04df20e527
begin
almost(text, headline=md"Almost there!") = Markdown.MD(Markdown.Admonition("warning", string(headline), [text]));
#brown
	
correct(text=md"Great! You got the right answer!", headline=md"Got it!") = Markdown.MD(Markdown.Admonition("correct", string(headline), [text]));
#green
	
	
keep_working(text=md"The answer is not quite right.", headline=md"Keep working on it!") = Markdown.MD(Markdown.Admonition("danger", string(headline), [text]));
#red
	
hint(text, headline=md"Hint") = Markdown.MD(Markdown.Admonition("hint", string(headline), [text]));
#blue
	
md"definition of boxes"
end

# ╔═╡ ce366a2b-3933-4b4b-a01c-c0a1ed7da96a
#definition of get_firstdigit
function get_first_digit(data) #data must be array of numbers
	#get rounded number (to highest power of 10)
	rounded = floor.(log.(10, data))
	#get number between 0 and 10
	mantissa = data ./ (10 .^rounded)
	digit = floor.(mantissa)
	firstdigit = digit[0 .< digit .< 10]
	return firstdigit


end

# ╔═╡ deb756be-10ee-43c5-b466-9909b4431268
function normalize(array)
	#gets keys and values out of countmap and returns keys and normed values in 2D list
	dict_values = []
	key = sort(collect(keys(countmap(array))))
	for i in key
		append!(dict_values, countmap(array)[i])
		end
	if key[1] == 0
	normed_dict_values = dict_values/sum(dict_values[2:10])
	return [key[2:10], normed_dict_values[2:10]]
	else
		normed_dict_values = dict_values/sum(dict_values)
		return [key, normed_dict_values]
	end
end

# ╔═╡ ac233104-737c-4a92-843d-45042ba25cd1
begin
#data

	if data_list == "Random data"
		#generate data
		rng = MersenneTwister(seed)
		sample_size = 10000
		# parameters of random number generator fort scale invariant random numbers
		x0     = 10^(-10)   # smallest number
		x1     = 10^10      # largest number

		ln0    = log(x0)
		ln1    = log(x1)
		lsx    = rand(rng,ln0:ln1,sample_size)
		a1 = exp.(lsx)
		
		
		
	elseif data_list == "Reef population"
		a1 = population

		
	elseif data_list == "Frogfish caught weekly"
		#get data
		a1 = fish_catches
	
		
		
	elseif data_list == "Pieces of litter on the beach"
		a1 = litter_pieces
		
	
		
	elseif data_list == "Mass of marine litter in g"
		a1 = litter_mass
		
			
	elseif data_list == "Mass of marine litter in lbs"
		a1= litter_mass .* 0.00220462
		
	end
	
#get first digits
first_digits = get_first_digit(a1)
#plot
bar(normalize(first_digits)[1], normalize(first_digits)[2], label = "Data")

#theory
	
d = range(1,stop = 9, length = 50)
p_benford = log.(10, (d .+ 1.0)) - log.(10, d)
	
d_discrete = range(1,stop = 9, length = 9)
p_benford_discrete = log.(10, (d_discrete .+ 1.0)) - log.(10, d_discrete )
	
plot!(d , p_benford, label = "Theory", 
	
	linewidth = 3)
plot!(d_discrete,p_benford_discrete, line = :scatter, label = :none,
		title = "Testing Benford's Law for " * String(data_list),
		xlabel = "first digit", 
		ylabel = "relative frequency",
		#xlim = [0,10],
		size = (600,400),
		labelfontsize = 15,
		tickfontsize = 13,
		bottom_margin =5mm,
		left_margin = 5mm,
		right_margin = 5mm,
		linewidth = 5,
		titlefontsize = 13,	
		#foreground_color_grid = :black,
		#foreground_color_xticks = :black,
		background_color = :transparent,
		#foreground_color_axis = :black,
		#foreground_color_text = :black,
		#foreground_color_border = :black,
		foreground_color = :black,
		fontfamily="Computer Modern")

	
end

# ╔═╡ d16680ec-541d-42f0-867e-4259b30adcdb
begin
#plot logarithmic histogram of data
a2 = a1[0 .< a1]
	bins_exp = range(log10(minimum(a2)), log10(maximum(a2)), step = 0.1)
		bins =  10 .^ bins_exp
	
	plot((histogram(a1; bins, xaxis=(:log10, [minimum(a2), :auto]))), 
		label = "", 
		title = "Frequency analysis of data \n(" * String(data_list) * ")",
		xlabel = "range", 
		ylabel = "frequencies",
		#xlim = [0,10],
		size = (600,400),
		labelfontsize = 15,
		tickfontsize = 13,
		bottom_margin =5mm,
		left_margin = 5mm,
		right_margin = 5mm,
		linewidth = 1,
		titlefontsize = 16,	
		#foreground_color_grid = :black,
		#foreground_color_xticks = :black,
		background_color = :transparent,
		#foreground_color_axis = :black,
		#foreground_color_text = :black,
		#foreground_color_border = :black,
		foreground_color = :black,
		fontfamily="Computer Modern")
	
	
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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[deps]
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[compat]
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LaTeXStrings = "~1.3.0"
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version = "0.1.2"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[IntegralArrays]]
deps = ["IntervalSets"]
git-tree-sha1 = "26c4df96fdf6127a92d53cb8ffb577104617adca"
uuid = "1d092043-8f09-5a30-832f-7509e371ab51"
version = "0.1.0"

[[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"

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "61aa005707ea2cebf47c8d780da8dc9bc4e0c512"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.4"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.3"

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

[[IrrationalConstants]]
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uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"

[[IterTools]]
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uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

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

[[JLD2]]
deps = ["DataStructures", "FileIO", "MacroTools", "Mmap", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
git-tree-sha1 = "46b7834ec8165c541b0b5d1c8ba63ec940723ffb"
uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
version = "0.4.15"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[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"
version = "2.10.1+0"

[[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"
version = "2.36.0+0"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.5"

[[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"]
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.9"

[[MappedArrays]]
git-tree-sha1 = "e8b359ef06ec72e8c030463fe02efe5527ee5142"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.1"

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

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[MetaGraphs]]
deps = ["Graphs", "JLD2", "Random"]
git-tree-sha1 = "2af69ff3c024d13bde52b34a2a7d6887d4e7b438"
uuid = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
version = "0.7.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.3"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "16baacfdc8758bc374882566c9187e785e85c2f0"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.9"

[[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"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "043017e0bdeff61cfbb7afeb558ab29536bbb5ed"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.8"

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+0"

[[OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
version = "0.3.2"

[[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 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.10+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"
version = "1.3.2+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
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"
version = "0.3.12"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "646eed6f6a5d8df6708f15ea7e02a7a2c4fe4800"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.10"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.3"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.1.2"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[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"
version = "0.1.1"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.15"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
git-tree-sha1 = "02a083caba3f73e42decb810b2e0740783022978"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.24.0"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "1e0cb51e0ccef0afc01aab41dc51a3e7f781e8cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.20"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

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

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.1"

[[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"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+0"

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

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

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

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.2"

[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.4.1"

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

[[RegionTrees]]
deps = ["IterTools", "LinearAlgebra", "StaticArrays"]
git-tree-sha1 = "4618ed0da7a251c7f92e869ae1a19c74a7d2a7f9"
uuid = "dee08c22-ab7f-5625-9660-a9af2021b33f"
version = "0.3.2"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[Rotations]]
deps = ["LinearAlgebra", "Random", "StaticArrays", "Statistics"]
git-tree-sha1 = "6a23472b6b097d66da87785b61137142ac104f94"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.4"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[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"

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

[[SimpleWeightedGraphs]]
deps = ["Graphs", "LinearAlgebra", "Markdown", "SparseArrays", "Test"]
git-tree-sha1 = "a6f404cc44d3d3b28c793ec0eb59af709d827e4e"
uuid = "47aef6b3-ad0c-573a-a1e2-d07658019622"
version = "1.2.1"

[[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 = "e08890d19787ec25029113e88c34ec20cac1c91e"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.0.0"

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

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.4.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.13"

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

[[StatsAPI]]
git-tree-sha1 = "0f2aa8e32d511f758a2ce49208181f7733a0936a"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.1.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.13"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.3"

[[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 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

[[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 = "c342ae2abf4902d65a0b0bf59b28506a6e17078a"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.5.2"

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

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[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"

[[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"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[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"

[[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"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[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"
"""

# ╔═╡ Cell order:
# ╟─e342faf1-550f-4b6f-963e-ef53ac581c0b
# ╟─2dde8f33-1166-42b9-834f-7bcb54895992
# ╟─245d5573-09f4-4536-b104-351a7669cd8b
# ╟─9a4bc5f5-7acd-4640-a71b-82051b6d3db3
# ╟─0615b18c-23b6-4f93-99ff-2044588dccf2
# ╟─468c679f-6a42-4801-a908-82ab5a4c9507
# ╟─27811f40-08a7-4da7-9788-db4b0c47153b
# ╟─0527804c-68b7-42f9-8830-c41d6b9036f4
# ╟─91d8c001-c210-4c42-a7f2-5e84ee907ea6
# ╟─fb1b6ea0-330c-4744-b3b8-19730b55e7e5
# ╟─56b1302d-6a0e-4262-aa0e-9ae98c2167df
# ╟─8368ba6c-cada-4caa-b37f-752034bfd571
# ╟─64d6faa9-1564-4d7d-bf32-02f0720fa552
# ╟─ac233104-737c-4a92-843d-45042ba25cd1
# ╟─c13206e8-ff41-405a-b9b8-50b589854901
# ╟─a2a6d8c3-c9b7-458d-b5a7-6d3b3f68a926
# ╟─d16680ec-541d-42f0-867e-4259b30adcdb
# ╟─7959439c-f947-40b3-8d2a-7dc96e90bbdc
# ╟─8a30e661-3057-4a30-a495-b1523b42207b
# ╟─4f48ef9a-05ea-41f9-a2a0-381865b8be6a
# ╟─601c53ed-ac2f-48fe-8afa-6b511a3ef369
# ╟─a8d53828-ca73-4cb7-906f-ca2c94735a93
# ╟─7b74d968-8591-49ba-81d8-9d8485676e93
# ╟─5dfa126f-754f-4d25-a191-6e5437df99da
# ╟─05d42951-063d-45d6-87ce-4d15b0472b84
# ╟─673b5f44-0db4-4848-95d7-24a31e7e86b1
# ╟─a491e298-7a49-4cef-b269-886455538348
# ╟─ea7c16d9-dd13-41c6-9c03-431d068fd105
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