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>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define int long long
#define mkp make_pair
#define pb push_back
#define ff first
#define ss second
#define debug1(a) cout<<a<<endl;
#define debug2(a,b) cout<<a<<' '<<b<<endl;
#define debug3(a,b,c) cout<<a<' '<<b<<' '<<c<<endl;
#define rep(i,n) for(int i=0;i<n;i++)
#define repre(i,a,b)for(int i=a;i<=b;i++)
#define clr1(arr) memset(arr,-1,sizeof(arr));
#define clr0(arr) memset(arr,0,sizeof(arr));
#define pi pair<int,int>
#define pii pair<int,pi>
#define aint(v) v.begin(),v.end()
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
using namespace __gnu_pbds;
using namespace std;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> orderedSet;
typedef tree<int,null_type,less_equal<int>,rb_tree_tag,tree_order_statistics_node_update> orderedMSet;
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};
#define ump gp_hash_table<int,int,custom_hash>
//*p.find_by_order(index) return value at index
//p.order_of_key(key) return index
/*int **dp,in main function,int row,col;dp=new int*[n];rep(i,n)dp[i]=new int[m]*/
//**** Maths Section*******/
int power(int x,int y);
bool isPrime(int n);
int modInv(int a,int b);
int gcdExtended(int a,int b,int *x,int* y);
int mpower(int a,int b,int p);
/***************************/
bool cmp(vector<int>a,vector<int>b)
{
  int flag=0;
  rep(i,a.size())
  {
    if(a[i]<b[i])
    {
      flag=1;
      break;
    }
  }
  if(flag)return a<b;
  else return b>a;
}
bool check(vector<int>a,vector<int>b){
  int flag=0;
  rep(i,a.size())
  {
    if(a[i]!=b[i])return false;
  }
  return true;
}
int32_t main()
{
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
  fastio
  int n;
  cin>>n;
  vector<int>a;
  vector<int>b;
  rep(i,n)
  {
    int a1;
    cin>>a1;
    a.pb(a1);
  }
  rep(i,n)
  {
    int a1;
    cin>>a1;
    b.pb(a1);
  }
  vector<int>v;
  vector<vector<int> >temp;
  repre(i,1,n)v.pb(i);
  int i=1;
  do {
    temp.pb(v);
  } while(next_permutation(v.begin(),v.end()));

  sort(temp.begin(),temp.end(),cmp);
  int index1=-1;
  int index2=-1;
  rep(i,temp.size())
  {
    if(check(a,temp[i]))
    {
      index1=i+1;
      break;
    }
  }
  rep(i,temp.size())
  {
    if(check(b,temp[i]))
    {
      index2=i+1;
      break;
    }
  }
//  cout<<index2<<" "<<index1<<endl;
  cout<<abs(index2-index1)<<endl;
  return 0;
}

int modInv(int a, int m)
{
int x, y;
int g = gcdExtended(a, m, &x, &y);
int res = (x%m + m) % m;
return res;
}

int gcdExtended(int a, int b, int *x, int *y)
{
if (a == 0){
    *x = 0, *y = 1;
    return b;
  }
  int x1, y1;
  int gcd = gcdExtended(b%a, a, &x1, &y1);
  *x = y1 - (b/a) * x1;
  *y = x1;
  return gcd;
}

int mpower(int x, int y, int p)
{
int res = 1;
x = x % p;
while(y > 0){
    if(y & 1) res = (res*x) % p;
      y = y>>1;
      x = (x*x) % p;
    }
    return res;
}
int power(int x, int y)
{
int res = 1;
while (y > 0){
    if (y & 1) res = res*x;
      y = y>>1;
      x = x*x;
    }
    return res;
}

bool isPrime(int n)
{
if (n <= 1)  return false;
  if (n <= 3)  return true;
    if (n%2 == 0 || n%3 == 0) return false;
      int p=sqrt(n);
      for(int i=5;i<=p;i=i+6)
        if (n%i == 0 || n%(i+2) == 0)
          return false;
      return true;
}