### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# ╔═╡ 8e250d30-e1c2-11eb-0360-7dc2bf254c24
using Plots, Distributions, Measurements, StatsPlots, DataFrames, Gadfly, PlutoUI, Statistics, StatsBase, LaTeXStrings, Latexify

# ╔═╡ 49244122-c0b3-47eb-a2a7-4a6fa61bf683
md"# Máquinas de Fluxo - Labs1
\
**Alunos:**
* Alessandro Cappellini Portugal
* Rodrigo Kenji Kuroda
* Jean Carlos Reisdorfer
* Laís Tussi
* Stella Colferai"

# ╔═╡ 0cabd498-4112-4de3-a3fe-7971d0cb566e
html"""<p style="font-family: times; text-align: center; font-style:bold; font-size: 14.5pt"><a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png" /></a></p>This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License</a>."""

# ╔═╡ 4225646f-c459-454e-b238-bd369d20ef9d
y = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48]

# ╔═╡ 6789cfda-abe9-471f-86e2-209f3ccd7898
x = [-0.2, 1, 2, 3.1, 4, 5, 6.1, 7.3, 8.2, 9.25, 10.3, 11.3, 12.4, 13.45, 14.48, 15.1, 16.5, 17.5, 18.5, 19.6, 20.62, 21.7, 22.7, 23.7, 24.8, 25.9, 26.9, 28, 29.1, 30.1, 31.1, 32.1, 33.2, 34.2, 35.3, 36.3, 37.4, 38.5, 39.4, 40.5, 41.5, 42.5, 43.5, 44.5, 45.5, 46.6, 47.6, 48.7, 49.7]

# ╔═╡ 295a89c9-24e0-4be8-95b1-8bf60fa20c23
σx = [0.2, 0.1, 0.1, 0.1, 0.1, 0.05, 0.2, 0.1, 0.1, 0.05, 0.1, 0.1, 0.05, 0.05, 0.05, 0.1, 0.1, 0.1, 0.1, 0.1, 0.05, 0.1, 0.1, 0.1, 0.1, 0.15, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]


# ╔═╡ abba40bf-a742-4033-8ba5-9c10af910e32
md"## Sem filtrar dados espúrios"

# ╔═╡ 0a6f1d35-5be7-4192-8ca9-2dbf476bb5af
md"### Equação 1° grau"

# ╔═╡ 8e400648-232d-405c-a9dd-e9bc6380802b
begin
	scatter(x,y,
		title = "Medições",
		label = "Medições",
		ylabel = "Valores verdadeiros",
		xlabel = "Valores medidos",
		markersize = 2,
		markerstrokewidth = 0,
		legend = :bottomright,
		xerror = σx)
	plot!(x,y,
		label = "",
		linealpha = 0,
		xerror = σx)
end

# ╔═╡ fb4da8a1-2ca9-4056-abdb-ba4f8da9950a
begin
	A = [x[i]^j for i in 1:49, j in 0:1]
	x̂ = A\y
	ŷ(x) = x̂' * [1,x]
end

# ╔═╡ d8673d86-8642-44b6-91cb-2e31e1df2a25
plot!(ŷ, label = "Regressão linear")

# ╔═╡ 45a828ec-a47b-4dd8-94bb-8620969b74c3
L"""
f(x) =  %$(round(x̂[1],digits=4))  + %$(round(x̂[2],digits=4))x
"""

# ╔═╡ 44f43f20-e258-4d16-aaf3-f0654ecae258
x̂

# ╔═╡ 3407bbda-c149-4bc3-ae63-d8e09940573d
begin
	c1 = x̂[1] 
	c2 = x̂[2]
	eq1(x) = c1 + c2*x
	
	r1 = convert(Array{Float64},[])
	for i in 1:49
		append!(r1, eq1(x[i]))
	end
	d1 = y .- r1
	r1, d1
end

# ╔═╡ a34aeeea-00cf-42de-a8fc-d7270086a433
begin
	#Definição dos limites de aceitação para α = 95%
	
	limy = [2std(d1), 2*std(d1)]
	limx = [0, 50]
	limx, limy
end

# ╔═╡ 60a6e0d1-d222-44e7-9200-99742285adeb
begin
	histogram(d1,
		bins = 12,
		title = "Histograma das medições",
		label = "Histograma",
		ylabel = "Frequência normalizada",
		xlabel = "Desvio à média",
		normalize=true)
	plot!(Normal(mean(d1),std(d1)),
		lw=2,
		color=:orange,
		label = "Distribuição normal")
	plot!(limy,limx./7,
		label = "Limite superior",
		color=:red,
		ls=:dash,
		lw=1)
	plot!(-limy,limx./7,
		label = "Limite inferior",
		color=:red,
		ls=:dash,
		lw=1)
	plot!([mean(d1),mean(d1)],limx./7,
		label = "Média",
		color=:green,
		ls=:dash,
		lw=1)
end

# ╔═╡ 74e7d640-e932-4af4-be7d-d68c100e979f


# ╔═╡ 781e8b4a-a414-40f7-a25f-cee7410192bf
begin
	scatter(d1,
		title = "Desvio à média dos pontos (α = 95%)",
		label = "Desvios à média",
		ylabel = "Desvio à média",
		xlabel = "Valores verdadeiros",
		ylim = (-0.4,0.4),
		markersize = 2,
		markerstrokewidth = 0)
	plot!(d1,
		label = "",
		ylim = (-0.4,0.4),
		linealpha = 0,
		xerror = σx)
	plot!(limx,limy,
		label = "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,-limy,
		label = "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,[mean(d1),mean(d1)],
		label = "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ 623a27b7-c768-42e4-963e-97658e81693a


# ╔═╡ 68300505-e792-4b68-a703-6e32de110964
md"### Equação 5° grau"

# ╔═╡ 5c5ebaa0-2092-4344-8c80-4b6b92d4dbb3
begin
	scatter(x,y,
		title = "Medições",
		label = "Medições",
		ylabel = "Valores verdadeiros",
		xlabel = "Valores medidos",
		markersize = 2,
		markerstrokewidth = 0,
		legend=:bottomright,
		xerror=σx)
	plot!(x,y,
		label = "",
		linealpha = 0,
		xerror=σx)
end

# ╔═╡ d53f1bc4-7572-4b49-9019-cec3b585c38b
begin
	C = [x[i]^j for i in 1:49, j in 0:5]
	ẋ = C\y
	ẏ(x) = ẋ' * [1,x,x^2,x^3,x^4,x^5]
end

# ╔═╡ 764ab490-bc21-4f77-a93a-897212d75016
plot!(ẏ, label = "Regressão linear")

# ╔═╡ db8dcdb4-3f6b-490d-97e0-b5aff6f9d4f4
L"""
f(x) =  %$(round(ẋ[1],digits=4)) + %$(round(ẋ[2],digits=4))x + %$(round(ẋ[3],digits=4))x^2 %$(round(ẋ[4],digits=4))x^3 + %$(round(ẋ[5],digits=4))x^4 %$(round(ẋ[6],digits=4))x^5
"""

# ╔═╡ b64dd1cc-076d-4edb-b1bc-30bbd8707a01
ẋ

# ╔═╡ cdbcb0e9-2286-4066-a453-b27a25f2c884
begin
	ṫ0 = ẋ[1]
	ṫ1 = ẋ[2] 
	ṫ2 = ẋ[3]
	ṫ3 = ẋ[4]
	ṫ4 = ẋ[5]
	ṫ5 = ẋ[6]
	eq3(x) =ṫ0 + ṫ1*x + ṫ2*x^2 + ṫ3*x^3 + ṫ4*x^4 + ṫ5*x^5
	
	r3 = convert(Array{Float64},[])
	for i in 1:49
		append!(r3, eq3(x[i]))
	end
	d3 = y .- r3
	r3, d3
end

# ╔═╡ dcf76d4d-95e2-4acc-b5bd-55921968379c
begin
	histogram(d3,
		bins = 12,
		title = "Histograma das medições",
		label = "Histograma",
		ylabel = "Frequência normalizada",
		xlabel = "Desvio à média",
		normalize=true)
	plot!(Normal(mean(d3),std(d3)),
		lw=2,
		color=:orange,
		label = "Distribuição normal")
	plot!(limy,limx./7,
		label = "Limite superior",
		color=:red,
		ls=:dash,
		lw=1)
	plot!(-limy,limx./7,
		label = "Limite inferior",
		color=:red,
		ls=:dash,
		lw=1)
	plot!([mean(d3),mean(d3)],limx./7,
		label = "Média",
		color=:green,
		ls=:dash,
		lw=1)
end

# ╔═╡ 915b66f4-6c35-47c0-9847-f73457f39106


# ╔═╡ f5dbcdc1-5aeb-461a-9e15-4239b0e4379c
begin
	scatter(d3,
		title = "Desvio à média dos pontos (α = 95%)",
		label = "Desvios à média",
		ylabel = "Desvio à média",
		xlabel = "Valores verdadeiros",
		ylim = (-0.4,0.4),
		markersize = 2,
		markerstrokewidth = 0)
	plot!(d3,
		label = "",
		ylim = (-0.4,0.4),
		linealpha = 0,
		xerror = σx)
	plot!(limx,limy,
		label = "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,-limy,
		label = "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,[mean(d3),mean(d3)],
		label = "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ 5b54a42f-8323-41ae-86b5-a7bda064d9b7
md"## Filtrando os dados espúrios"

# ╔═╡ b41a0cd0-7104-4520-9c3d-4069789b319d
md"### Encontrar Outliers"

# ╔═╡ 7e8643d2-1a95-4f98-addb-ef730cf77f12
md"""
A filtragem dos dados espúrios funciona pelo princípio de quartis
, onde se aplicam as seguintes equações e assim descobre-se os pontos a serem descartados:
\
\
``Lim_{mín} = Q_1 - 1.5(Q_3 - Q_1)``

``Lim_{máx} = Q_3 + 1.5(Q_3 - Q_1)``
"""

# ╔═╡ a909bac1-3c6c-4779-82a2-478a4eebb7d1
begin
	outliers = []
	valoresd1 = []
	indexd1 = []
	
	Q = quantile(d1)
	Q1 = Q[2]
	Q3 = Q[4]
	
	out_min = Q1-1.5*(Q3-Q1)
	out_max = Q3+1.5*(Q3 -Q1)
	
	for i in d1
		if i < out_min
			append!(valoresd1,i)
		elseif i > out_max
			append!(valoresd1,i)
		end
	end
	
	for i in 1:49
		for j in valoresd1
			if j == d1[i]
				append!(indexd1, i)
			end
		end
	end
	
	for i in indexd1
		append!(outliers,x[i])
	end
	
	outliers, indexd1
end

# ╔═╡ 7f29d513-03d1-4c64-90d9-61cc4fc94d29
md"### Filtrar Outliers"

# ╔═╡ 049c2a8d-e2de-4a95-b596-fc34acd48d9f
begin
	xx = convert(Array{Float64}, [])
	yy = convert(Array{Float64}, [])
	σxx = convert(Array{Float64}, [])
	for i in 1:49
		for j in outliers
			if x[i] != j
				append!(xx, x[i])
				append!(yy, y[i])
				append!(σxx, σx[i])
			end
		end
	end
	
	if size(outliers,1) == 0
		Print(size(outliers,1)," ponto foi removido!")
	elseif size(outliers,1) == 1
		Print(size(outliers,1)," ponto foi removido!")
	else
		Print(size(outliers,1)," pontos foram removidos!")
	end
end

# ╔═╡ 634c8ad1-bb47-450b-9143-2396810391f3
md"## Dados filtrados"

# ╔═╡ 18ab75fa-5a91-4817-b754-048bba299b59
md"### Equação 1° grau"

# ╔═╡ 595b3e0d-6e42-49c6-a479-85f32551bfff
yy

# ╔═╡ 5bf89139-715a-468d-a4ab-ce145d269175
xx

# ╔═╡ 95c8f96b-a35a-4b20-9c04-0f7e48aacada
σxx

# ╔═╡ 27ec07cb-f2fd-4a31-a3cf-c3bf82dd308d
begin
	scatter(xx,yy,
		title  =  "Medições",
		label  =  "Medições",
		ylabel  =  "Valores verdadeiros",
		xlabel  =  "Valores medidos",
		markersize = 2,
		markerstrokewidth = 0,
		legend = :bottomright)
	plot!(xx,yy,
		label  =  "",
		linealpha  =  0,
		xerror = σxx)
end

# ╔═╡ dd9463db-41f4-4c09-acac-9215d1c21229
begin
	B = [xx[i]^j for i in 1:48, j in 0:1]
	x̂f = B\yy
	ŷf(xx) = x̂f' * [1,xx]
end

# ╔═╡ c051daf8-d220-465d-9133-ec296a7cd48e
plot!(ŷf,label = "Regressão linear")

# ╔═╡ dc413f5f-e569-4458-9650-a6b064f6903d
L"""
f(x) =  %$(round(x̂f[1],digits=4))  + %$(round(x̂f[2],digits=4))x
"""

# ╔═╡ 072a675b-ef4c-47a0-8f26-64c84044a3bd
x̂f

# ╔═╡ ad1c1263-6967-4a28-bfc3-810c103382dd
begin
	c3 = x̂f[1] 
	c4 = x̂f[2]
	eq2(xx) = c3 + c4*xx
	
	r2 = convert(Array{Float64},[])
	for i in 1:48
		append!(r2, eq2(xx[i]))
	end
	d2 = yy .- r2
	r2, d2
end

# ╔═╡ c0bd8c32-462e-405f-87c6-09303edc7a8e
begin
	histogram(d2,
		bins  =  12,
		title  =  "Histograma das medições",
		label  =  "Histograma",
		ylabel  =  "Frequência normalizada",
		xlabel  =  "Desvio à média",
		normalize = true)
	plot!(Normal(mean(d2),std(d2)),
		color = :orange,
		lw = 2,
		label  =  "Distribuição normal")
	plot!(limy,limx./6,
		label  =  "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(-limy,limx./6,
		label  =  "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!([mean(d2),mean(d2)],limx./6,
		label  =  "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ 14ef3427-37ad-4dc3-86ec-eaf2f7e33cd7


# ╔═╡ 17f72af5-5adf-4903-acb4-b8e0fcbb6676
begin
	scatter(d2,
		title  =  "Desvio à média dos pontos (α = 95%)",
		label  =  "Desvios à média",
		ylabel  =  "Desvio à média",
		xlabel  =  "Valores verdadeiros",
		ylim = (-0.4,0.4),
		markersize = 2,
		markerstrokewidth  =  0)
	plot!(d2,
		label  =  "",
		ylim = (-0.4,0.4),
		linealpha  =  0,
		xerror = σx)
	plot!(limx,limy,
		label  =  "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,-limy,
		label  =  "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,[mean(d2),mean(d2)],
		label  =  "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ aab0c032-f169-4ff6-9052-2f5190510cb2


# ╔═╡ a5069b22-8962-4c12-8e2b-ff0c8681185b
md"### Equação 5° grau"

# ╔═╡ b8ab84f4-33f1-4231-9744-413132c9e279
begin
	scatter(xx,yy,
		title  =  "Medições",
		label  =  "Medições",
		ylabel  =  "Valores verdadeiros",
		xlabel  =  "Valores medidos",
		markersize = 2,
		markerstrokewidth = 0,
		legend = :bottomright)
	plot!(xx,yy,
		label  =  "",
		linealpha  =  0,
		xerror = σxx)
end

# ╔═╡ 0a367bcb-5700-48ad-b1dd-7c66e8dc789e
begin
	D = [xx[i]^j for i in 1:48, j in 0:5]
	ẋf = D\yy
	ẏf(xx) = ẋf' * [1,xx,xx^2,xx^3,xx^4,xx^5]
end

# ╔═╡ 9c92c27a-f4cb-424b-893c-321309ee93a6
plot!(ẏf, label = "Regressão linear")

# ╔═╡ b6e2adff-52f9-4b61-bc22-08c46478a0a3
L"""
f(x) =  %$(round(ẋf[1],digits=4)) + %$(round(ẋf[2],digits=4))x + %$(round(ẋf[3],digits=4))x^2 %$(round(ẋf[4],digits=4))x^3 + %$(round(ẋf[5],digits=4))x^4 %$(round(ẋf[6],digits=4))x^5
"""

# ╔═╡ 90c7e5f8-03f8-46a1-a2a4-35c861f84dfe
ẋf

# ╔═╡ af9eba14-0f5f-4941-b56b-eab68107b15a
begin
	t0 = ẋf[1]
	t1 = ẋf[2] 
	t2 = ẋf[3]
	t3 = ẋf[4]
	t4 = ẋf[5]
	t5 = ẋf[6]
	eq4(xx) =t0 + t1*xx + t2*xx^2 + t3*xx^3 + t4*xx^4 + t5*xx^5
	
	r4 = convert(Array{Float64},[])
	for i in 1:48
		append!(r4, eq4(xx[i]))
	end
	d4 = yy .- r4
	r4, d4
end

# ╔═╡ 693116ed-d66c-4938-8916-51a1825490fe
begin
	histogram(d4,
		bins = 12,
		title  =  "Histograma das medições",
		label  =  "Histograma",
		ylabel  =  "Frequência normalizada",
		xlabel  =  "Desvio à média",
		normalize = true)
	plot!(Normal(mean(d4),std(d4)),
		color = :orange,
		lw = 2,
		label  =  "Distribuição normal")
	plot!(limy,limx./5,
		label  =  "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(-limy,limx./5,
		label  =  "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!([mean(d4),mean(d4)],limx./5,
		label  =  "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ e78f377e-0e61-40ed-995c-04e3197c0c09


# ╔═╡ 32ebe64e-703f-4f3c-a307-b0a43db5292a
begin
	scatter(d4,
		title  =  "Desvio à média dos pontos (α = 95%)",
		label  =  "Desvios à média",
		ylabel  =  "Desvio à média",
		xlabel  =  "Valores verdadeiros",
		ylim = (-0.4,0.4),
		markersize = 2,
		markerstrokewidth  =  0)
	plot!(d4,
		label  =  "",
		ylim = (-0.4,0.4),
		linealpha  =  0,
		xerror = σx)
	plot!(limx,limy,
		label  =  "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,-limy,
		label  =  "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,[mean(d4),mean(d4)],
		label  =  "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ bd9c53be-072a-4efe-9bf9-0f77ec96879e


# ╔═╡ 70ab5271-6b97-46d7-9d16-00366bdfc23d
md"## Comparação de desvios à média entre 5° grau e 1° grau"

# ╔═╡ 510901ce-a7f2-48d0-a483-5144db931be9
begin
	d5 = r2 .- r4
	
	scatter(d5,
		title  =  "Diferença entre desvios de 1° e 5° grau (α = 95%)",
		label  =  "Desvios à média",
		ylabel  =  "Desvio à média",
		xlabel  =  "Valores verdadeiros",
		ylim = (-0.4,0.4),
		markersize = 2,
		markerstrokewidth  =  0)
	plot!(limx,limy,
		label  =  "Limite superior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,-limy,
		label  =  "Limite inferior",
		color = :red,
		ls = :dash,
		lw = 1)
	plot!(limx,[mean(d5),mean(d5)],
		label  =  "Média",
		color = :green,
		ls = :dash,
		lw = 1)
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
Gadfly = "c91e804a-d5a3-530f-b6f0-dfbca275c004"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

[compat]
DataFrames = "~1.2.0"
Distributions = "~0.24.18"
Gadfly = "~1.3.3"
LaTeXStrings = "~1.2.1"
Latexify = "~0.15.6"
Measurements = "~2.6.0"
Plots = "~1.18.2"
PlutoUI = "~0.7.9"
StatsBase = "~0.33.8"
StatsPlots = "~0.14.25"
"""

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

[[AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.0.1"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

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

[[Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
git-tree-sha1 = "2ff92b71ba1747c5fdd541f8fc87736d82f40ec9"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.4.0"

[[Arpack_jll]]
deps = ["Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.0+3"

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

[[AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.0"

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

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.6+5"

[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.0+6"

[[Calculus]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
version = "0.5.1"

[[CategoricalArrays]]
deps = ["DataAPI", "Future", "JSON", "Missings", "Printf", "RecipesBase", "Statistics", "StructTypes", "Unicode"]
git-tree-sha1 = "1562002780515d2573a4fb0c3715e4e57481075e"
uuid = "324d7699-5711-5eae-9e2f-1d82baa6b597"
version = "0.10.0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "dcc25ff085cf548bc8befad5ce048391a7c07d40"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "0.10.11"

[[Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "75479b7df4167267d75294d14b58244695beb2ac"
uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
version = "0.14.2"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
git-tree-sha1 = "ed268efe58512df8c7e224d2e170afd76dd6a417"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.13.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.31.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[Compose]]
deps = ["Base64", "Colors", "DataStructures", "Dates", "IterTools", "JSON", "LinearAlgebra", "Measures", "Printf", "Random", "Requires", "Statistics", "UUIDs"]
git-tree-sha1 = "c6461fc7c35a4bb8d00905df7adafcff1fe3a6bc"
uuid = "a81c6b42-2e10-5240-aca2-a61377ecd94b"
version = "0.9.2"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[CoupledFields]]
deps = ["LinearAlgebra", "Statistics", "StatsBase"]
git-tree-sha1 = "6c9671364c68c1158ac2524ac881536195b7e7bc"
uuid = "7ad07ef1-bdf2-5661-9d2b-286fd4296dac"
version = "0.2.0"

[[Crayons]]
git-tree-sha1 = "3f71217b538d7aaee0b69ab47d9b7724ca8afa0d"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.0.4"

[[DataAPI]]
git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.7.0"

[[DataFrames]]
deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
git-tree-sha1 = "1dadfca11c0e08e03ab15b63aaeda55266754bad"
uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
version = "1.2.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.9"

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

[[DataValues]]
deps = ["DataValueInterfaces", "Dates"]
git-tree-sha1 = "d88a19299eba280a6d062e135a43f00323ae70bf"
uuid = "e7dc6d0d-1eca-5fa6-8ad6-5aecde8b7ea5"
version = "0.4.13"

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

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distances]]
deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.3"

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

[[Distributions]]
deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
git-tree-sha1 = "a837fdf80f333415b69684ba8e8ae6ba76de6aaa"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.24.18"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.5"

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

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.1.5+1"

[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.2.10+0"

[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "3cc57ad0a213808473eafef4845a74766242e05f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.3.1+4"

[[FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "f985af3b9f4e278b1d24434cbb546d6092fca661"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.4.3"

[[FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3676abafff7e4ff07bbd2c42b3d8201f31653dcc"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.9+8"

[[FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays"]
git-tree-sha1 = "693210145367e7685d8604aee33d9bfb85db8b31"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.11.9"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "35895cf184ceaab11fd778b4590144034a167a2f"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.1+14"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.1+5"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[Future]]
deps = ["Random"]
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 = "dba1e8614e98949abfa60480b13653813d8f0157"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+0"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "b83e3125048a9c3158cbb7ca423790c7b1b57bea"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.57.5"

[[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 = "e14907859a1d3aee73a019e7b3c98e9e7b8b5b3e"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.57.3+0"

[[Gadfly]]
deps = ["Base64", "CategoricalArrays", "Colors", "Compose", "Contour", "CoupledFields", "DataAPI", "DataStructures", "Dates", "Distributions", "DocStringExtensions", "Hexagons", "IndirectArrays", "IterTools", "JSON", "Juno", "KernelDensity", "LinearAlgebra", "Loess", "Measures", "Printf", "REPL", "Random", "Requires", "Showoff", "Statistics"]
git-tree-sha1 = "96da4818e4d481a29aa7d66aac1eb778432fb89a"
uuid = "c91e804a-d5a3-530f-b6f0-dfbca275c004"
version = "1.3.3"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "15ff9a14b9e1218958d3530cc288cf31465d9ae2"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.3.13"

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

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "47ce50b742921377301e15005c96e979574e130b"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.1+0"

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

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "c6a1fff2fd4b1da29d3dccaffb1e1001244d844e"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.12"

[[Hexagons]]
deps = ["Test"]
git-tree-sha1 = "de4a6f9e7c4710ced6838ca906f81905f7385fd6"
uuid = "a1b4810d-1bce-5fbd-ac56-80944d57a21f"
version = "0.2.0"

[[IndirectArrays]]
git-tree-sha1 = "c2a145a145dc03a7620af1444e0264ef907bd44f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "0.5.1"

[[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"

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "1470c80592cf1f0a35566ee5e93c5f8221ebc33a"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.3"

[[InvertedIndices]]
deps = ["Test"]
git-tree-sha1 = "15732c475062348b0165684ffe28e85ea8396afc"
uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
version = "1.0.0"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

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

[[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 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.1"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
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[[Juno]]
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[[KernelDensity]]
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[[LAME_jll]]
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git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
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[[LZO_jll]]
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[[LaTeXStrings]]
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[[Latexify]]
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[[LazyArtifacts]]
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[[LibCURL]]
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[[LibCURL_jll]]
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[[LibGit2]]
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[[LibSSH2_jll]]
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uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[LibVPX_jll]]
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[[Libdl]]
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libglvnd_jll]]
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[[Libgpg_error_jll]]
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[[Libiconv_jll]]
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[[Libmount_jll]]
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[[Libtiff_jll]]
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[[Libuuid_jll]]
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[[LinearAlgebra]]
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[[Loess]]
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[[LogExpFunctions]]
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[[Logging]]
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[[MKL_jll]]
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[[MacroTools]]
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[[Markdown]]
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[[MbedTLS]]
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[[MbedTLS_jll]]
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[[Measurements]]
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[[Measures]]
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[[Media]]
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[[Missings]]
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[[Mmap]]
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[[MozillaCACerts_jll]]
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[[MultivariateStats]]
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[[NaNMath]]
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[[NearestNeighbors]]
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[[NetworkOptions]]
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[[Observables]]
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[[OffsetArrays]]
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[[Ogg_jll]]
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git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
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[[OpenBLAS_jll]]
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[[OpenSSL_jll]]
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[[OpenSpecFun_jll]]
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[[Opus_jll]]
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[[OrderedCollections]]
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[[PCRE_jll]]
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[[PDMats]]
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[[Parsers]]
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[[Pixman_jll]]
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[[PlotThemes]]
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[[Plots]]
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[[PlutoUI]]
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[[PooledArrays]]
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[[Preferences]]
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[[PrettyTables]]
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[[Printf]]
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[[Profile]]
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[[Qt5Base_jll]]
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[[QuadGK]]
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[[REPL]]
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[[Random]]
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[[Ratios]]
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[[RecipesBase]]
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[[RecipesPipeline]]
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[[Reexport]]
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[[Requires]]
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[[Rmath]]
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[[Rmath_jll]]
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[[SHA]]
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[[Scratch]]
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[[SentinelArrays]]
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[[Serialization]]
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[[SharedArrays]]
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[[Showoff]]
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[[Sockets]]
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[[SortingAlgorithms]]
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[[SparseArrays]]
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[[SpecialFunctions]]
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[[StaticArrays]]
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[[Statistics]]
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[[StatsAPI]]
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[[StatsBase]]
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[[StatsFuns]]
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version = "0.9.8"

[[StatsPlots]]
deps = ["Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "990daa9c943e7ee108a36ad17769bf3a51622875"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.14.25"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.0"

[[StructTypes]]
deps = ["Dates", "UUIDs"]
git-tree-sha1 = "e36adc471280e8b346ea24c5c87ba0571204be7a"
uuid = "856f2bd8-1eba-4b0a-8007-ebc267875bd4"
version = "1.7.2"

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

[[Suppressor]]
git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787"
uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
version = "0.2.0"

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

[[TableOperations]]
deps = ["SentinelArrays", "Tables", "Test"]
git-tree-sha1 = "a7cf690d0ac3f5b53dd09b5d613540b230233647"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.0.0"

[[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 = "8ed4a3ea724dac32670b062be3ef1c1de6773ae8"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.4.4"

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

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

[[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"

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

[[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", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "eae2fbbc34a79ffd57fb4c972b08ce50b8f6a00d"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.3"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

[[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", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+4"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+4"

[[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 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"

[[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:
# ╟─49244122-c0b3-47eb-a2a7-4a6fa61bf683
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# ╟─abba40bf-a742-4033-8ba5-9c10af910e32
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# ╟─764ab490-bc21-4f77-a93a-897212d75016
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# ╠═cdbcb0e9-2286-4066-a453-b27a25f2c884
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# ╠═5bf89139-715a-468d-a4ab-ce145d269175
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# ╠═dd9463db-41f4-4c09-acac-9215d1c21229
# ╟─c051daf8-d220-465d-9133-ec296a7cd48e
# ╟─dc413f5f-e569-4458-9650-a6b064f6903d
# ╠═072a675b-ef4c-47a0-8f26-64c84044a3bd
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# ╟─b8ab84f4-33f1-4231-9744-413132c9e279
# ╠═0a367bcb-5700-48ad-b1dd-7c66e8dc789e
# ╟─9c92c27a-f4cb-424b-893c-321309ee93a6
# ╟─b6e2adff-52f9-4b61-bc22-08c46478a0a3
# ╠═90c7e5f8-03f8-46a1-a2a4-35c861f84dfe
# ╠═af9eba14-0f5f-4941-b56b-eab68107b15a
# ╟─693116ed-d66c-4938-8916-51a1825490fe
# ╟─e78f377e-0e61-40ed-995c-04e3197c0c09
# ╟─32ebe64e-703f-4f3c-a307-b0a43db5292a
# ╟─bd9c53be-072a-4efe-9bf9-0f77ec96879e
# ╟─70ab5271-6b97-46d7-9d16-00366bdfc23d
# ╟─510901ce-a7f2-48d0-a483-5144db931be9
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
