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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main() {
  int n;
  cin >> n;
  vector<int> p(n), q(n);
  rep(i, n) cin >> p[i];
  rep(i, n) cin >> q[i];
  int pv = 0, qv = 0;
  rep(i, n) {
    pv += p[i] * pow(10, n - 1 - i);
    qv += q[i] * pow(10, n - 1 - i);
  }
  vector<int> x(n, 0), y;
  int c = 0;
  for (int i = 0; i < n; i++) x[i] = i + 1;
  do {
    rep(i, n) {
      if (i == 0) {
        y.push_back(0);
        y[c] += x[i];
      } else {
        y[c] += x[i] * pow(10, i);
      }
    }
    c++;
  } while (next_permutation(x.begin(), x.end()));

  sort(y.begin(), y.end());
  int np, nq;

  auto itr1 = find(y.begin(), y.end(), pv);
  np = itr1 - y.begin();
  np++;
  auto itr2 = find(y.begin(), y.end(), qv);
  nq = itr2 - y.begin();
  nq++;

  cout << abs(np - nq) << endl;

  return 0;
}