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 12.16.1) (judge verdict: Accepted)

function permutation(n,k){
    var ret=[[]];
    var next;
    for(var i=0;i<k;i++){
        next=[];
        ret.forEach(e=>{
            for(var k=1;k<=n;k++){
                if(!e.includes(k)){
                    next.push(e.concat([k]));
                }
            }
        });
        ret=next.concat([]);
    }
    return ret;
}

function Main(input) {
  input=input.split("\n");
  if(input[input.length-1]===''){
    input.pop();
  }
  const N=input[0].split(' ')[0]-0;
  var a,b
  permutation(N,N).forEach((e,i)=>{
    if(e.join(' ')===input[1]){
      a=i;
    }
    if(e.join(' ')===input[2]){
      b=i;
    }
  });
  console.log(Math.abs(a-b));
}


//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));