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 $|a - b|$.

Note

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 $|a - b|$.