local function makeset(self, x)
	if self.forest[x] == nil then
		self.forest[x] = { x, 1 }
	end
end

local function find(self, x)
	local x0, s0 = unpack(self.forest[x] or {})
	if x == x0 then
		return x0, s0
	else
		x0, s0 = self:find(x0)
		self.forest[x] = { x0, s0 }
		return x0, s0
	end
end

local function union(self, x, y)
	x0, xs = self:find(x)
	y0, ys = self:find(y)
	if x0 == y0 then return end
	if xs < ys then
		x0, y0 = y0, x0
	end
	self.forest[x0] = { x0, xs + ys }
	self.forest[y0] = { x0, xs + ys }
end

function unions(self)
	local index, item
	return function()
		repeat
			index, item = next(self.forest, index)
		until item == nil or index == item[1]
		if item ~= nil then
			return unpack(item)
		else
			return nil
		end
	end
end

function unionfind()
	local forest = {}
	return {
		forest = forest,
		makeset = makeset,
		find = find,
		union = union,
		unions = unions,
	}
end