### A Pluto.jl notebook ###
# v0.17.5

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

# ╔═╡ f9e8c9c0-86f6-4f27-938c-307f4fae7d52
using Plots

# ╔═╡ 0af2c481-e7c4-4ce5-a0f1-a940caeefed5
using PlutoUI

# ╔═╡ 2b72f685-7705-45f9-afa9-b38f8308e887
using OffsetArrays

# ╔═╡ 60d767b2-9d44-4fed-8564-6ec7d66d0a21
using ReinforcementLearning

# ╔═╡ 954cd93f-2c30-4826-944c-293deeba452e
using KernelDensity

# ╔═╡ 3ac7c63e-7423-11ec-1ae1-8f50247003da
md"""
# Notes on [Distributional Reinforcement Learning](https://www.distributional-rl.org/)
"""

# ╔═╡ ed570ba8-efcf-45ef-8db6-5a2ca58e8698
md"""
## Chapter 1

In Chapter 1, the [Kuhn Poker](https://en.wikipedia.org/wiki/Kuhn_poker) is introduced to explain the distribution of rewards after playing ``T`` rounds. We can calculate the probability when ``T = 1`` based on the given policy.

| First player holding a ... | Jack | Queen | King|
|:--------------------------:|:----:|:-----:|:----|
|Probability of raising      | 1/3  | 0     | 1   |
|Probability of calling      | 0    | 2/3   | 1   |

[![](https://juntian.me/reading/Notes_on_Distributional_Reinforcement_Learning/img/kuhn_poker.svg)](https://juntian.me/reading/Notes_on_Distributional_Reinforcement_Learning/img/kuhn_poker.svg)

(You can click to view the image.)
"""

# ╔═╡ e5b88be0-c50a-468e-bb64-6faa3832b600
md"""
Then we can get the initial reward distribution by some simple calculations:

$$\begin{alignedat}{4}

& p(r=-2) && = && \left( \frac{1}{6} * \frac{1}{3} * \frac{1}{2} \right) && + \\
& &&        && \left( \frac{1}{6} * \frac{1}{3} * \frac{1}{2} \right) && +  \\
& &&        && \left( \frac{1}{6} * 1 * \frac{1}{2} * \frac{2}{3} \right) \\
& && = && \frac{4}{36} \\

& p(r=-1) && = && \left( \frac{1}{6} * \frac{2}{3} * \frac{1}{2} \right) && + \\
& &&        && \left( \frac{1}{6} * \frac{2}{3} * \frac{1}{2} \right) &&  +  \\
& &&        && \left( \frac{1}{6} * \frac{2}{3} * \frac{1}{2} \right) &&  + \\ 
& &&        && \left( \frac{1}{6} * \frac{2}{3} * \frac{1}{2} \right) && + \\
& &&        && \left( \frac{1}{6} * 1 * \frac{1}{2} * \frac{1}{3} \right)&&  + \\
& &&        && \left( \frac{1}{6} * 1 * \frac{1}{2} \right) && + \\
& &&        && \left( \frac{1}{6} * 1 * \frac{1}{2} * \frac{1}{3} \right) \\
& && = && \frac{13}{36} \\

& p(r=+1) && = && \left( \frac{1}{6} * \frac{1}{3} * \frac{1}{2} \right) && + \\
& &&        &&  \left( \frac{1}{6} * \frac{1}{3} * \frac{1}{2} \right) && + \\
& &&        &&  \left( \frac{1}{6} * 1 * \frac{1}{2} \right) && + \\
& &&        &&  \left( \frac{1}{6} * 1 * \frac{1}{2} \right) && + \\
& &&        &&  \left( \frac{1}{6} * 1 * \frac{1}{2} \right)  \\
& && = && \frac{11}{36} \\


& p(r=+2) && = && \left( \frac{1}{6} * 1 * \frac{1}{2} * \frac{2}{3} \right)  && +\\
& &&        &&  \left( \frac{1}{6} * 1 * \frac{1}{2} \right) && + \\
& &&        &&  \left( \frac{1}{6} * 1 * \frac{1}{2} \right) \\
& && = && \frac{8}{36} \\

\end{alignedat}$$
"""

# ╔═╡ 21cbc023-2ea2-48a3-b16c-285aba0737f8
INIT_WININGS = OffsetArray([zeros(8)..., 4/36, 13/36, 0, 11/36, 8/36, zeros(8)...], -10:10)

# ╔═╡ 85773172-ee70-45b8-96b2-51ea2a5b94bd
bar(-10:10, collect(INIT_WININGS), label="T=1")

# ╔═╡ acc2b47b-7857-40ac-b004-7e8ae416e9ba
fill!(similar(INIT_WININGS), 0.)

# ╔═╡ 8d13fbca-b1a3-4b3c-ae66-9da08ae0272b
firstindex(INIT_WININGS)

# ╔═╡ 5168b209-6cc1-49c1-afd1-784c4ce8ff77
function winings_after_step(T, init=INIT_WININGS)
	pre = copy(init)
	cur = fill!(similar(init), 0.)
	for _ in 1:T
		for (i, w) in zip(axes(pre,1), pre)
			if i == firstindex(pre) || i == lastindex(pre)
				cur[i] += pre[i]
			else
				for (j, v) in zip(axes(init,1), init)
					k = i + j
					cur[min(lastindex(init), max(firstindex(init), k))] += w * v
				end
			end
		end
		pre, cur = cur, pre
		fill!(cur, 0.)
	end
	pre
end

# ╔═╡ af2d315f-7ad5-4035-9408-e410d57cafbe
@bind T Slider(0:200, default=15)

# ╔═╡ 4a74562c-f16a-4b35-b4c1-d1f2a5636694
bar(-10:10, collect(winings_after_step(T)), label="T=$T")

# ╔═╡ af23ad49-346b-4e36-8784-87f05e3bc60b
md"""
# Chapter 2
"""

# ╔═╡ bf24b6c7-c606-44b3-aa59-55539dc88fef
md"""
### Figure 2.2
We'll use APIs in [ReinforcementLearning.jl](https://github.com/JuliaReinforcementLearning/ReinforcementLearning.jl) to define the Cliff World environment. Part of the code are borrowed from [Reinforcement Learning: An Introduction/Chapter06 Temporal-Difference Learning](https://juliareinforcementlearning.org/ReinforcementLearningAnIntroduction.jl/notebooks/Chapter06_Cliff_Walking.html)
"""

# ╔═╡ 0b27269d-0a9f-4a20-9b65-1f2ee092d536
begin
	NX = 4
	NY = 12
	Start = CartesianIndex(4, 1)
	Goal = CartesianIndex(4, 12)
	LRUD = [
		CartesianIndex(0, -1),  # left
		CartesianIndex(0, 1),   # right
		CartesianIndex(-1, 0),  # up
		CartesianIndex(1, 0),   # down
	]
	LinearInds = LinearIndices((NX, NY))
end

# ╔═╡ 2cacc2d3-89ed-47c1-b727-2c2a597ecc10
function iscliff(p::CartesianIndex{2})
    x, y = Tuple(p)
    x == 4 && y > 1 && y < NY
end

# ╔═╡ 8049593f-5b5a-4640-8699-e443a00a008b
heatmap((!iscliff).(CartesianIndices((NX, NY))); yflip = true)

# ╔═╡ 401ca430-dc57-4580-8b04-f7125f311e5f
begin
	Base.@kwdef mutable struct CliffWalkingEnv <: AbstractEnv
		position::CartesianIndex{2} = Start
	end
	function (env::CliffWalkingEnv)(a::Int)
		if rand() <= 0.25
			a_unintended = rand(1:4)
			while a == a_unintended
				a_unintended = rand(1:4)
			end
			a = a_unintended
		end
		x, y = Tuple(env.position + LRUD[a])
		env.position = CartesianIndex(min(max(x, 1), NX), min(max(y, 1), NY))
	end
end

# ╔═╡ 96858c59-fc12-4ab1-b37a-cb94ffdd05bc
RLBase.state(env::CliffWalkingEnv) = LinearInds[env.position]

# ╔═╡ 8347f825-f739-4f3a-89e2-0d85d051cf6e
RLBase.state_space(env::CliffWalkingEnv) = Base.OneTo(length(LinearInds))

# ╔═╡ 0fe2ab3c-e2a4-4e8a-bfe7-14d963eb1c7b
RLBase.action_space(env::CliffWalkingEnv) = Base.OneTo(length(LRUD))

# ╔═╡ e2b0991d-ef04-4de9-87f8-402ef5460afa
RLBase.reward(env::CliffWalkingEnv) = env.position == Goal ? 1.0 : (iscliff(env.position) ? -1.0 : 0.)

# ╔═╡ f018cfeb-af07-44af-b022-2c2f9180ce34
RLBase.reset!(env::CliffWalkingEnv) = env.position = Start

# ╔═╡ 469496c5-6549-4616-814f-8ce80cb3bde6
RLBase.is_terminated(env::CliffWalkingEnv) = env.position == Goal || iscliff(env.position)

# ╔═╡ da8c59d6-4458-40d5-9640-77291daab666
safe_policy = TabularPolicy(
	Dict(
		i => if i > NX * (NY-1)
			4 # down
		elseif i % NX == 1
			2 # right
		else
			3
		end
			
		for i in LinearInds
	),
	4
)

# ╔═╡ b7580a82-3e5c-449f-80f2-be69712db36c
map(i -> safe_policy(i), LinearInds)

# ╔═╡ 476b82d9-f5f6-4a96-9351-e909f6408731
quick_policy = TabularPolicy(
	Dict(
		i => if i == NX
			3 # up
		elseif i % NX == 3 && i <= NX * (NY -1)
			2 # right
		else
			4
		end
			
		for i in LinearInds
	),
	4
)

# ╔═╡ e4eb00c0-0bb0-44b8-99f5-95b940c82d8f
map(i -> quick_policy(i), LinearInds)

# ╔═╡ e99571ee-1543-450b-b5a1-88a89a45d884
quick_policy_hook = ComposedHook(
	TotalRewardPerEpisode(),
	StepsPerEpisode()
)

# ╔═╡ df7371bc-25c9-46c5-868e-d29f9ea5128a
run(quick_policy, CliffWalkingEnv(), StopAfterEpisode(100_000), quick_policy_hook)

# ╔═╡ 6dc05c0e-61cd-482d-b6e2-1318a66a12a7
safe_policy_hook = ComposedHook(
	TotalRewardPerEpisode(),
	StepsPerEpisode()
)

# ╔═╡ 3017eb45-e96c-4713-bb14-c6e49e1cf32c
run(safe_policy, CliffWalkingEnv(), StopAfterEpisode(100_000), safe_policy_hook)

# ╔═╡ a03ffe02-b0bb-4d82-83c3-4bb4fc27142c
begin
	quick_policy_kde = kde(0.99 .^ (quick_policy_hook[2].steps[1:end-1] .- 1) .* quick_policy_hook[1].rewards, bandwidth=0.02)
	safe_policy_kde = kde(0.99 .^ (safe_policy_hook[2].steps[1:end-1] .- 1) .* safe_policy_hook[1].rewards, bandwidth=0.02)
	plot(safe_policy_kde.x, safe_policy_kde.density, label="safe policy", legend=:topleft)
	plot!(quick_policy_kde.x, quick_policy_kde.density, label="quick policy")
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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uuid = "b8865327-cd53-5732-bb35-84acbb429228"
version = "2.5.1"

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

[[deps.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"

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

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

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.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"

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "3593e69e469d2111389a9bd06bac1f3d730ac6de"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.9.4"

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

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

[[deps.Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "78da1a0a69bcc86b33f7cb07bc1566c926412de3"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.33"

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

[[deps.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"

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

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

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

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

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

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

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

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

[[deps.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:
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# ╟─00000000-0000-0000-0000-000000000002
