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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict';
// JavaScript Array permutation generator
// (optimized from CoffeeScript output: see ArrayPermutation.coffee)
(function() {
  var generatePermutation = function(perm, pre, post, n) {
    var elem, i, rest, len;
    if (n > 0)
      for (i = 0, len = post.length; i < len; ++i) {
        rest = post.slice(0);
        elem = rest.splice(i, 1);
        generatePermutation(perm, pre.concat(elem), rest, n - 1);
      }
    else
      perm.push(pre);
  };

  /*
  extend Array.prototype
  e.g. [0, 1, 2].permutation(2)
  => [[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]]
  */
  Array.prototype.permutation = function(n) {
    if (n == null) n = this.length;
    var perm = [];
    generatePermutation(perm, [], this, n);
    return perm;
  };
})();
const main = input => {
  const n = parseInt(input[0]);
  const p = input[1].split(' ').map(val => parseInt(val));
  const q = input[2].split(' ').map(val => parseInt(val));
  let pStr = p.join('');
  let qStr = q.join('');
  // console.log(pStr, qStr);
  // console.log(p.permutation());
  let str = p.permutation().map(val => val.join(''));
  // console.log(str);
  str.sort();
  // console.log(str);
  let pId, qId;
  for(let i=0; i<str.length; i++) {
    if (pStr == str[i]) pId = i;
    if (qStr == str[i]) qId = i;
  }
  console.log(Math.abs(pId-qId));
  
}
main(require("fs").readFileSync("/dev/stdin", "utf8").split('\n'));