Contest Duration: - (local time) (100 minutes) Back to Home
C - Count Order /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 注記

2 つの数列 X,~Y について、ある整数 k が存在して X_i = Y_i~(1 \leq i < k) かつ X_k < Y_k が成り立つとき、XY より辞書順で小さいと定義されます。

### 制約

• 2 \leq N \leq 8
• P,~Q は大きさ N の順列である。
• 入力は全て整数である。

### 入力

N
P_1 P_2 ... P_N
Q_1 Q_2 ... Q_N


|a - b| を出力せよ。

### 入力例 1

3
1 3 2
3 1 2


### 出力例 1

3


### 入力例 2

8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1


### 出力例 2

17517


### 入力例 3

3
1 2 3
1 2 3


### 出力例 3

0


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


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