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 be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin>>n;
    int k=1;
    set<int> s;
    for(int i=1;i<n;i++){
        k*=i;
        s.insert(i);
    }
    s.insert(n);
    int pnum=0,qnum=0;
    int a;

    
    for(int i=n-1;i>0;i--){
        cin>>a;
        pnum+=(distance(s.begin(),s.find(a)))*k;
        s.erase(a);
        k/=i;
    }
    cin>>a;
    s.clear();
    for(int i=1;i<n;i++){
        k*=i;
        s.insert(i);
    }
    s.insert(n);
    for(int i=n-1;i>0;i--){
        cin>>a;
        qnum+=(distance(s.begin(),s.find(a)))*k;
        s.erase(a);
        k/=i;
    }
    cin>>a;
    cout << (abs(pnum-qnum))<<endl;
    return 0;
}