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)

// inputに入力データ全体が入る
function Main(input) {
	// 1行目がinput[0], 2行目がinput[1], …に入る
	input = input.split("\n");
    
	//文字列から10進数に変換するときはparseIntを使います
	var a = parseInt(input[0],10);
    var b = input[1].replace(/ /g,"");
    var c = input[2].replace(/ /g,"");
    
    
    var str ="1";
    for(i=2;i<=a;i++){
        str=str+","+i;
    }

    const arr =str.split(",");

    const n = arr.length;
arr2 = [];
    function recursivef(p){
        if (p.length == n){
            //console.log(p.map(i => arr[i]));
            //console.log(arr[i]);
            arr2.push((p.map(i => arr[i])).join(""));
            return;
        }
        for (let i = 0; i < n; ++i){
            if (p.includes(i)) continue;
            p.push(i);
            recursivef(p);
            p.pop();
        }
    }
    recursivef([]);

    var p1 = 0;
    for(i=0;i<arr2.length;i++){
        if(arr2[i]==b){
            p1=i;
        }
    }

    var p2 = 0;
    for(i=0;i<arr2.length;i++){
        if(arr2[i]==c){
            p2=i;
        }
    }

    var res = p1-p2;

    if(res<0){
        res=res*-1;

    }

    //出力
	console.log('%d',res);
}

//*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"));
//Main("3\n1 3 2\n3 1 2");