From 92d5ac363617cb054a2300cd9b1875d64c8b692f Mon Sep 17 00:00:00 2001
From: Simeon David Schaub <simeon@schaub.rocks>
Date: Wed, 6 Dec 2023 18:47:48 +0100
Subject: [PATCH] add RS algorithm notebook

---
 src/math/rs_algorithm.jl | 1443 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 1443 insertions(+)
 create mode 100644 src/math/rs_algorithm.jl

diff --git a/src/math/rs_algorithm.jl b/src/math/rs_algorithm.jl
new file mode 100644
index 0000000..7541f61
--- /dev/null
+++ b/src/math/rs_algorithm.jl
@@ -0,0 +1,1443 @@
+### A Pluto.jl notebook ###
+# v0.19.32
+
+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
+
+# ╔═╡ 087084fe-a3d8-4ef5-8819-22787e885844
+using Random
+
+# ╔═╡ e76fa719-b8a2-4a3d-bf29-bbac6b64808b
+using Plots, PlutoUI
+
+# ╔═╡ 4db253c8-6c3c-11ee-2921-45f9793427aa
+using YoungTableaux
+
+# ╔═╡ 50401b76-6c95-48c9-8ce6-a96281e911ff
+using HypertextLiteral, AbstractPlutoDingetjes.Bonds
+
+# ╔═╡ 322aec90-7ec6-4131-8625-bbd32afbe0b1
+using UUIDs
+
+# ╔═╡ 7b3aadec-4ec4-4f89-8ccb-c78c24bad000
+md"""
+# The RS algorithm visualized
+
+Try plugging in your own name:
+"""
+
+# ╔═╡ ef2fac57-ff72-400a-bc18-2e4eadafac11
+begin
+	s = collect("PLUTOROCKS");
+	Text(String(s))
+end
+
+# ╔═╡ b4fcb4ce-5474-49e5-81c6-0cf6a2024643
+@htl """
+Show Record $(@bind show_Q CheckBox())
+"""
+
+# ╔═╡ 0acd1cda-9a65-4730-a451-6369dfbb92f8
+function schensted_insert!(rows, k, i=1)
+	i > length(rows) && return push!(rows, [k]), i
+	row = rows[i]
+	for (j, m) in pairs(row)
+		k < m || continue
+		row[j] = k
+		return schensted_insert!(rows, m, i+1)
+	end
+	push!(row, k)
+	return rows, i
+end
+
+# ╔═╡ 47e58152-f784-40e6-9616-eb7d31fa606c
+function rs_pair(j)
+    T = eltype(j)
+	P, Q = Vector{eltype(j)}[], Vector{Int}[]
+	for (n, k) in enumerate(j)
+		P, i = schensted_insert!(P, k)
+		# record index for j in Q in the same row i
+		Q, _i = schensted_insert!(Q, n, i)
+		@assert i == _i
+	end
+	return YoungTableau(P), YoungTableau(Q)
+end
+
+# ╔═╡ a8ca7dae-72e6-4ff8-9171-8a22c48f0e49
+md"""
+What happens if we plug in a permutation of the numbers from ``1`` through ``N`` instead?
+"""
+
+# ╔═╡ 61851b37-4fdf-4702-82ab-9fdca6cf42d2
+π = randperm(16)
+
+# ╔═╡ 37dc5a55-8dc7-4dfa-854b-2463bc1863bc
+md"""
+Logan-Shepp limit shape on [-2,2] when rotated 45 degrees
+``\frac{2}{\pi}(x*\arcsin(x)/2 + \sqrt{4-x^2} )``
+
+**Reference:**
+
+Borodin, A., Okounkov, A., & Olshanski, G. (2000). Asymptotics of Plancherel measures for symmetric groups. Journal of the American Mathematical Society, 13(3), 481-515.
+Equation for ``\Omega(u)`` at the bottom of page 2 
+"""
+
+# ╔═╡ 2626db42-96cb-49c6-ab26-8053fa7fab66
+x = [1,3,3,2,2,1,2]
+
+# ╔═╡ 74b9394b-c57b-4d47-ac2e-0925cb46fac1
+rs_pair(x)
+
+# ╔═╡ f9536da7-8743-43d2-a9b8-b432ead8c99d
+md"""
+Recreation of [https://math.mit.edu/events/stanley70/savethedate/]():
+"""
+
+# ╔═╡ 877b720b-b96d-4316-b0d2-8cb65aef6304
+name = uppercase("richardpstanley")
+
+# ╔═╡ 65cbdc74-cec1-48cd-ae6a-a0cd5fca424e
+P, Q = rs_pair(name)
+
+# ╔═╡ 4e1a8c4a-b7bd-4e4d-a3ba-5b9493bfe769
+('A':'Z')[Q]
+
+# ╔═╡ f78d304e-9bc6-41cd-8cd4-62b88215ff19
+begin
+	log!(::Nothing, _...) = nothing
+	log!(x, rows, (i, j), k) = push!(x, (YoungTableau(copy.(rows)), (i, j), k))
+	sublog!(::Nothing) = nothing
+	sublog!(x) = (y = Any[]; push!(x, y); y)
+end
+
+# ╔═╡ 0f6bc3dd-505b-4000-80db-fa17d39ee47a
+function _schensted_insert!(rows, k, i=1; log=nothing)
+	if i > length(rows)
+		log!(log, rows, (i, 1), k)
+		return push!(rows, [k]), i
+	end
+	row = rows[i]
+	for (j, m) in pairs(row)
+		k < m || continue
+		log!(log, rows, (i, j), k)
+		row[j] = k
+		return _schensted_insert!(rows, m, i+1; log)
+	end
+	log!(log, rows, (i, lastindex(row)+1), k)
+	push!(row, k)
+	return rows, i
+end
+
+# ╔═╡ 20df36ae-9191-4700-b963-7f80cec971d8
+function _rs_pair(j; log_P=nothing, log_Q=nothing)
+    T = eltype(j)
+	P, Q = Vector{eltype(j)}[], Vector{Int}[]
+	for (n, k) in enumerate(j)
+		P, i = _schensted_insert!(P, k; log=sublog!(log_P))
+		Q, _i = _schensted_insert!(Q, n, i; log=sublog!(log_Q))
+		@assert i == _i
+	end
+	return YoungTableau(P), YoungTableau(Q)
+end
+
+# ╔═╡ d29210b7-f3fd-4a66-997a-9f19373290ec
+function calc_steps(s)
+	_STEPS_P, _STEPS_Q = Any[], Any[]
+	_rs_pair(s; log_P=_STEPS_P, log_Q=_STEPS_Q)
+	return (
+		[(idx, x, i == lastindex(y)) for (idx, y) in enumerate(_STEPS_P) for (i, x) in enumerate(y)],
+		[x for (idx, y) in enumerate(_STEPS_Q) for x in y],
+	)
+end
+
+# ╔═╡ 358b2401-9c0b-43aa-816a-7312db17f677
+STEPS_P_Π, STEPS_Q_Π = calc_steps(π);
+
+# ╔═╡ e455823e-62df-4b0d-a145-584d54557353
+STEPS_P, STEPS_Q = calc_steps(s);
+
+# ╔═╡ 9c7803cf-cf92-4573-a6b8-d88e51b5919e
+function visualize_insert((yt, to_replace, x); delete=true)
+	YoungTableaux.visualize_insert(yt, x, to_replace[1]; to_replace, delete)
+end
+
+# ╔═╡ 8e43cf19-0a50-486d-8220-3372ff41801f
+function visualize_step(STEP_P, s, STEPS_Q=nothing; show_Q=false)
+	idx = STEP_P[1]
+	@htl """
+	<br>
+	<div style="display: flex">
+	$(visualize_insert(STEP_P[2]))
+	$(if show_Q
+		visualize_insert(Base.setindex(STEPS_Q[idx], (STEP_P[2][2][1], STEP_P[3] ? STEPS_Q[idx][2][2] : 0), 2); delete=STEP_P[3])
+	end)
+	</div>
+	<br>
+	$(YoungTableau([collect(Iterators.flatten((' '^idx, s[idx+1:end])))]))
+	"""
+end
+
+# ╔═╡ ed00d350-b394-4db9-ad7a-c0a9db65b6a6
+begin
+	struct SeekingSlider
+		r::StepRange{Int, Int}
+		default::Int
+	end
+	function Base.show(io::IO, ::MIME"text/html", (; r, default)::SeekingSlider)
+		print(io, @htl("""
+		<span>
+		<input $((id="f", type="button", value="<<"))/>
+		<input $((id="m", type="button", value="<"))/>
+		<input $((id="s", type="range", min=r.start, max=r.stop, step=r.step)) style="vertical-align: middle"/>
+		<input $((id="p", type="button", value=">"))/>
+		<input $((id="l", type="button", value=">>"))/>
+		<span id="t" style="margin-left: 1em">$default</span>
+
+		<script>
+		const span = currentScript.parentElement
+		const slider = span.querySelector("#s")
+
+		function get() {
+			return slider.value
+		}
+		function set(val){
+		    val = Math.min(Math.max(val, $(r.start)), $(r.stop));
+			slider.value = val
+			span.querySelector("#t").textContent = val
+			span.value = val
+			span.dispatchEvent(new CustomEvent("input"))
+		}
+
+		span.querySelector("#f").onclick = () => set($(r.start))
+		span.querySelector("#l").onclick = () => set($(r.stop))
+		span.querySelector("#m").onclick = () => set(+get() - $(r.step))
+		span.querySelector("#p").onclick = () => set(+get() + $(r.step))
+		slider.oninput = () => set(get())
+		set($default)
+		</script>
+		</span>
+		"""))
+	end
+	Base.get((; default)::SeekingSlider) = default
+	Bonds.initial_value((; default)::SeekingSlider) = default
+	Bonds.possible_values((; r)::SeekingSlider) = r
+end
+
+# ╔═╡ 9f1c4744-b629-4bf8-b8b2-caf812efc496
+@bind i SeekingSlider(eachindex(STEPS_P), 1)
+
+# ╔═╡ e3c074b4-7d4e-4a02-8d14-ffdc54439ecb
+visualize_step(STEPS_P[i], s, STEPS_Q; show_Q)
+
+# ╔═╡ 7d3f7f83-5af3-4d4b-8299-2f429d026622
+@bind i_π SeekingSlider(eachindex(STEPS_P_Π), 1)
+
+# ╔═╡ 9bc40166-338b-4060-bb76-16e30e3f7086
+visualize_step(STEPS_P_Π[i_π], π, STEPS_Q_Π; show_Q)
+
+# ╔═╡ 3abc835b-2f8a-4553-92c2-41e47b3e32f4
+@bind N SeekingSlider(0:20:700, 0)
+
+# ╔═╡ 200c88f2-159a-4693-bee8-e3ccc271d781
+begin
+	Z, _ = rs_pair(randperm(N))
+	X = [j for i in 1:nrows(Z) for j in 1:length(row(Z, i))]
+	Y = [i for i in 1:nrows(Z) for j in 1:length(row(Z, i))]
+	# Logan-Shepp Limit
+	# -2 <= u <- 2
+	Ω(u) = [abs(ℓ/2) > 1 ? abs(ℓ) : 2/pi*(ℓ * asin(ℓ/2) + sqrt(4-ℓ^2)) for ℓ ∈ u ] 
+	u = (X - Y)/sqrt(N)#scale by cardinality of partition
+	v = (X + Y)/sqrt(N)
+  	p1 = scatter(u,v,markershape=:circle,markersize=:100/sqrt(N),
+		markercolor = :white,
+    	markerstrokewidth = 0.5,legend=false)
+	plot!(ℓ->2/pi*(ℓ * asin(ℓ/2) + sqrt(4-ℓ^2))   ,-2,2,linewidth=:3,ylims=(0,2.5),xlims=(-2.5,2.5),ratio=1,color=:red)
+	#plot!(p1, sort(u), Ω(sort(u)),linewidth=:5,ylims=(0,2.5),xlims=(-2.5,2.5),ratio=1)
+end
+
+# ╔═╡ 01059a74-a4e4-4962-8515-a8a333176a15
+function small_yt(yt)
+	class_yt = string("yt-", uuid1())
+	@htl """
+	<style>
+	td.$class_yt {
+		padding: 2px;
+	}
+	td.$class_yt div {
+		font-size: small;
+	}
+	</style>
+	$(HTML(repr("text/html", yt; context=:html_class => class_yt)))
+	"""
+end
+
+# ╔═╡ c0b78cdc-5702-44c4-8989-ab86587daa2b
+small_yt(Z)
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+AbstractPlutoDingetjes = "6e696c72-6542-2067-7265-42206c756150"
+HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
+YoungTableaux = "b7062236-b0aa-4473-bf76-66f344053691"
+
+[compat]
+AbstractPlutoDingetjes = "~1.2.2"
+HypertextLiteral = "~0.9.5"
+Plots = "~1.39.0"
+PlutoUI = "~0.7.54"
+YoungTableaux = "~1.1.0"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.9.4"
+manifest_format = "2.0"
+project_hash = "4f520b01b3ee163a7b5bac5e8d4929b787dae93f"
+
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+
+    [deps.ColorVectorSpace.weakdeps]
+    SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+
+[[deps.Colors]]
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+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", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.6+0"
+
+[[deps.Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.39.0+0"
+
+[[deps.Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.5.0+0"
+
+[[deps.YoungTableaux]]
+deps = ["HypertextLiteral", "MappedArrays", "UUIDs"]
+git-tree-sha1 = "1d57589902579bd5588a2bcd205f371e6d501e31"
+uuid = "b7062236-b0aa-4473-bf76-66f344053691"
+version = "1.1.0"
+
+[[deps.Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+version = "1.2.13+0"
+
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.5+0"
+
+[[deps.eudev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
+git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
+uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
+version = "3.2.9+0"
+
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.43.0+0"
+
+[[deps.gperf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
+uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
+version = "3.1.1+0"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.4.0+0"
+
+[[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"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.8.0+0"
+
+[[deps.libevdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
+uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
+version = "1.11.0+0"
+
+[[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.libinput_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
+git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
+uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
+version = "1.18.0+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "f7c281e9c61905521993a987d38b5ab1d4b53bef"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+1"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+1"
+
+[[deps.mtdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
+uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
+version = "1.1.6+0"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+version = "1.52.0+1"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+version = "17.4.0+0"
+
+[[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 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+1"
+"""
+
+# ╔═╡ Cell order:
+# ╟─7b3aadec-4ec4-4f89-8ccb-c78c24bad000
+# ╠═ef2fac57-ff72-400a-bc18-2e4eadafac11
+# ╟─9f1c4744-b629-4bf8-b8b2-caf812efc496
+# ╟─b4fcb4ce-5474-49e5-81c6-0cf6a2024643
+# ╠═e3c074b4-7d4e-4a02-8d14-ffdc54439ecb
+# ╠═0acd1cda-9a65-4730-a451-6369dfbb92f8
+# ╠═47e58152-f784-40e6-9616-eb7d31fa606c
+# ╟─a8ca7dae-72e6-4ff8-9171-8a22c48f0e49
+# ╠═087084fe-a3d8-4ef5-8819-22787e885844
+# ╠═61851b37-4fdf-4702-82ab-9fdca6cf42d2
+# ╠═358b2401-9c0b-43aa-816a-7312db17f677
+# ╟─7d3f7f83-5af3-4d4b-8299-2f429d026622
+# ╠═9bc40166-338b-4060-bb76-16e30e3f7086
+# ╠═e76fa719-b8a2-4a3d-bf29-bbac6b64808b
+# ╠═3abc835b-2f8a-4553-92c2-41e47b3e32f4
+# ╠═200c88f2-159a-4693-bee8-e3ccc271d781
+# ╟─37dc5a55-8dc7-4dfa-854b-2463bc1863bc
+# ╠═c0b78cdc-5702-44c4-8989-ab86587daa2b
+# ╠═2626db42-96cb-49c6-ab26-8053fa7fab66
+# ╠═74b9394b-c57b-4d47-ac2e-0925cb46fac1
+# ╟─f9536da7-8743-43d2-a9b8-b432ead8c99d
+# ╠═877b720b-b96d-4316-b0d2-8cb65aef6304
+# ╠═65cbdc74-cec1-48cd-ae6a-a0cd5fca424e
+# ╠═4e1a8c4a-b7bd-4e4d-a3ba-5b9493bfe769
+# ╠═f78d304e-9bc6-41cd-8cd4-62b88215ff19
+# ╠═0f6bc3dd-505b-4000-80db-fa17d39ee47a
+# ╠═20df36ae-9191-4700-b963-7f80cec971d8
+# ╠═d29210b7-f3fd-4a66-997a-9f19373290ec
+# ╠═e455823e-62df-4b0d-a145-584d54557353
+# ╠═9c7803cf-cf92-4573-a6b8-d88e51b5919e
+# ╠═8e43cf19-0a50-486d-8220-3372ff41801f
+# ╠═4db253c8-6c3c-11ee-2921-45f9793427aa
+# ╠═50401b76-6c95-48c9-8ce6-a96281e911ff
+# ╠═ed00d350-b394-4db9-ad7a-c0a9db65b6a6
+# ╠═322aec90-7ec6-4131-8625-bbd32afbe0b1
+# ╠═01059a74-a4e4-4962-8515-a8a333176a15
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002