Question link : https://atcoder.jp/contests/abc150/tasks/abc150_c
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 ath and bth 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 Xi=Yi (1≤i<k) and Xk<Yk
.
Constraints

2≤N≤8

P and Q are permutations of size N

.
Input
Input is given from Standard Input in the following format:
N
P1 P2 …PN
Q1 Q2 …QN
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 2nd and 5th 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
Now one approach is to find all permutation and calculate which is the given permutation and return result , but how can it solved efficiently if the n is large say 10^5
@ssjgz @aryanc403 @anon55659401 @l_returns @nuttela @s5960r @akshay_1
Means the questions is just reduce to given a permutation find its no. of permutation.