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 int long long
#define fast_io(); ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define loop(i,a,b) for(int i=a;i<b;i++)
#define all(x) x.begin(),x.end()
#define us unordered_set
#define um unordered_map
#define ms multiset
#define mm multimap
#define pb push_back
#define pf push_front
#define ins insert
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define _max max_element
#define _min min_element
#define tc(T) int T; cin>>T; while(T--)
#define q(q) int q; cin>>q; while(q--)

const int pinf=((int)2e18);
const int ninf=((int)-2e18);
const int mod=1000000007;

using namespace std;

int power(int x,int n,int M)
{
    if(n==0)
        return 1;
    else if(n%2 == 0)
        return power((x*x)%M,n/2,M);
    else
        return (x*power((x*x)%M,(n-1)/2,M))%M;
}

bool check_prime(int n)
{
    if(n<2)
        return false;
    for(int i=2;i<=sqrt(n);i++)
    {
        if(n%i==0)
            return false;
    }
    return true;
}

int setbits(int n)
{
    int count=0;
    while(n)
    {
        if(n%2==1)
            count++;
        n>>=1;
    }
    return count;
}

int lcm(int a,int b)
{
    return (a*b)/__gcd(a,b);
}

bool vowel(char c)
{
    return(c=='a' or c=='e' or c=='i' or c=='o' or c=='u' or c=='A' or c=='E' or c=='I' or c=='U' or c=='O');
}

int32_t main()
{
    fast_io();

    //FILE *fptr1=freopen("in.txt","r",stdin);
    //FILE *fptr2=freopen("out.txt","w",stdout);

    int n;
    cin>>n;
    vector <int> a(n),b(n);
    string sa,sb;
    vector <int> v(n);
    loop(i,0,n)
    {
        cin>>a[i];
        v[i]=i+1;
        sa+=to_string(a[i]);
    }
    loop(i,0,n)
    {
        cin>>b[i];
        sb+=to_string(b[i]);
    }
    int x=0,y=0;
    int c=0;
    do
    {
        c++;
        string str;
        for(auto x:v)
            str+=to_string(x);

        if(str==sa)
            x=c;
        if(str==sb)
            y=c;
    }
    while(next_permutation(all(v)));

    cout<<abs(x-y);


    return 0;
}