Problem:
Score : 300 points

Problem Statement

We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1,~2,~...,~N)).

There are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|.

Notes

For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 \leq i < k) and X_k < Y_k.

Constraints

2 \leq N \leq 8

P and Q are permutations of size N.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 ... P_N
Q_1 Q_2 ... Q_N

Output

Print |a - b|.

Sample Input 1

3
1 3 2
3 1 2

Sample Output 1

3

There are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.

Sample Input 2

8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1

Sample Output 2

17517

Sample Input 3

3
1 2 3
1 2 3

Sample Output 3

0

Solution in Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
function permutation(a,n)
	ans = Array{Int,1}[copy(a)]
	c = ones(Int,n)
	i = 1
	while i<=n
		if c[i]<i
			if i%2==1
				tmp = a[1]
				a[1] = a[i]
				a[i] = tmp
			else
				tmp = a[c[i]]
				a[c[i]] = a[i]
				a[i] = tmp
			end
			c[i] += 1
			i = 1
			push!(ans,copy(a))
		else
			c[i] = 1
			i += 1
		end
	end
	ans
end

function calc(a::Array{Int,1})
	l = length(a)
	x = 0
	for i in 1:l
		x += a[i]*10^(l-i)
	end
	x
end

function main()
	n = readline() |> parseInt
	p = readline() |> split |> parseMap
	q = readline() |> split |> parseMap
	perm = permutation([i for i in 1:n],n)
	pb = [calc(perm[i]) for i in 1:length(perm)]
	pb = sort(pb)
	px = calc(p)
	qx = calc(q)
	a = 0
	b = 0
	for i in 1:length(perm)
		if pb[i]==px
			a = i
		end
		if pb[i]==qx
			b = i
		end
	end
	println(abs(a-b))
end

main()