#!/usr/bin/env luajit
require("utils")

local targets = { A=3, B=5, C=7, D=9 }
local costs = { A=1, B=10, C=100, D=1000 }

local f = io.open(arg[3])
local line = f:read("*l") -- #####
line = f:read("*l") -- #...#
local hall = {}
local length = #line - 2
line = f:read("*l") -- ##A#B##
local rooms = {}
local depth = 1
local ncorrect = 0
while line do
	local l = 0
	for char in chars(line) do
		if char ~= "#" and char ~= " " then
			if rooms[l] == nil then rooms[l] = {} end
			table.insert(rooms[l], char)
			if targets[char] == l then ncorrect = ncorrect + 1 end
		end
		l = l + 1
	end
	line = f:read("*l") -- ##A#B##
	depth = depth + 1
end

table.insert(rooms[3], 2, "D")
table.insert(rooms[3], 2, "D")
table.insert(rooms[5], 2, "B"); ncorrect = ncorrect + 1 -- this line
table.insert(rooms[5], 2, "C")
table.insert(rooms[7], 2, "A")
table.insert(rooms[7], 2, "B")
table.insert(rooms[9], 2, "C")
table.insert(rooms[9], 2, "A")

function printit()
	for l = 1, length do io.write(hall[l] or ".") end
	io.write("\n")
	for d = 1, depth do
		for l = 1, length do
			if rooms[l] then
				io.write(rooms[l][d] or ".")
			else
				io.write(" ")
			end
		end
		io.write("\n")
	end
end

printit()

function addtoroom(rooms, room, char)
	local room = rooms[room]
	for d = depth, 1, -1 do
		if room[d] == nil then
			room[d] = char
			return
		end
	end
end

function removefromroom(rooms, i)
	local room = rooms[i]
	local c, dst, complete = nil, nil, true
	for d = depth, 1, -1 do
		if room[d] ~= nil then
			c, dst = room[d], d
			if targets[c] ~= i then complete = false end
		end
	end
	if dst then room[dst] = nil end
	return c, dst, complete
end

function pathtoroom(l, c, hall, rooms)
	local t = targets[c]
	if rooms[t][1] ~= nil then return end
	for p = l + sign(t - l), t, sign(t - l) do
		if hall[p] ~= nil then return end
	end
	local room = rooms[t]
	for d = depth, 1, -1 do
		if room[d] == nil then
			return t, math.abs(t - l) + d
		elseif room[d] ~= c then
			return
		end
	end
end

local nhall = 0
local minscore = math.huge
-- global: length, depth, hall, rooms, ncorrect, nhall, minscore
-- returns: score
function backtrack(step, score)
	if step > 32 then
	elseif ncorrect == 16 and score < minscore then
		minscore = score
		print(minscore)
	elseif score > minscore then
	else
		-- move into rooms
		for l = 1, length do
			if hall[l] ~= nil then
				local c = hall[l]
				local room, distance = pathtoroom(l, c, hall, rooms)
				if room then
					hall[l] = nil
					addtoroom(rooms, room, c)
					ncorrect = ncorrect + 1
					backtrack(step + 1, score + distance * costs[c])
					ncorrect = ncorrect - 1
					removefromroom(rooms, room)
					hall[l] = c
				end
			end
		end
		-- remove from rooms
		for l, room in pairs(rooms) do
			local c, distance, complete = removefromroom(rooms, l)
			if c ~= nil then
				if not complete then
					if targets[c] == l then ncorrect = ncorrect - 1 end
					-- left
					local t = l - 1
					while t >= 1 and hall[t] == nil do
						if rooms[t] == nil then
							hall[t] = c
							backtrack(step + 1, score + (distance + l - t) * costs[c])
							hall[t] = nil
						end
						t = t - 1
					end
					-- right
					local t = l + 1
					while t <= length and hall[t] == nil do
						if rooms[t] == nil then
							hall[t] = c
							backtrack(step + 1, score + (distance + t - l) * costs[c])
							hall[t] = nil
						end
						t = t + 1
					end
					if targets[c] == l then ncorrect = ncorrect + 1 end
				end
				addtoroom(rooms, l, c)
			end
		end
	end
end

backtrack(0, 0)
print(minscore)