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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program speedrun
implicit none
integer::N
integer,allocatable,dimension(:)::P,Q
integer,allocatable,dimension(:)::Perm,DID
integer::i
integer::a=0,b=0
read*,N
allocate(P(N),Q(N),Perm(0:N),DID(1:N))
read*,P
read*,Q
Perm=1
do i=1,N
    Perm(i)=Perm(i-1)*i
end do
DID=0
do i=1,N
    a=a+Perm(N-i)*(P(i)-sum(DID(1:P(i)))+1)
    DID(P(i))=1
end do
DID=0
do i=1,N
    b=b+Perm(N-i)*(Q(i)-sum(DID(1:Q(i)))+1)
    DID(Q(i))=1
end do
print"(i0)",abs(a-b)
end program speedrun