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 Python (3.4.3) (judge verdict: Wrong Answer)



def permutation(a):
    n = len(a)
    end = True
    for i in range(n-2, -1, -1):
        if a[i] < a[i + 1]:
            end = False
            break

    if end:
        return []

    pivot = i

    for i in range(n - 1, pivot, -1):
        if a[i] > a[pivot]:
            a[i], a[pivot] = a[pivot], a[i]
            break
    a[pivot + 1:] = a[:pivot:-1]
    return a


n = int(input())
f = list(map(int, input().split()))
e = list(map(int, input().split()))
a = sorted(f)
first = 0
end = 0

p = permutation(a)
i = 0
while p:
    if p == f:
        first = i
    if p == e:
        end = i

    i += 1
    p = permutation(p)

print(abs(end-first))