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: Runtime Error)

'use strict'

const permutation = ({ result = [], pre = [], post, n = post.length }) => {
  if (n > 0) {
    post.forEach((_, i) => {
      const rest = [...post];
      const elem = rest.splice(i, 1);
      permutation({ result, pre: [...pre, ...elem], post: rest, n: n - 1});
    });
  } else {
    result.push(pre);
  }
  return result;
};

function Main(input) {

  input = input.trim().split('\n')
  const N = parseInt(input[0])
  let P = input[1].split(' ').map(s => parseInt(s))
  let Q = input[2].split(' ').map(s => parseInt(s))

  const a = []
  for(let i = 0; i < N; ++i){ 
    a.push(i + 1)
  }

  const results = permutation({ post: a });

  const strP = P.join('')
  const strQ = Q.join('')

  let indexP = 0
  let indexQ = 0

  results.forEach((d, index) => {
    const s = d.join('')
    if(strP === s) indexP = index
    if(strQ === s) indexQ = index
  })
  console.log(Math.abs(indexP - indexQ));

  
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));