Dima and Two Sequences

题意翻译

给定两个整数点坐标序列：$(a_1, 1),(a_2,2),\dots,(a_n,n)$ 和 $(b_1, 1),(b_2,2),\dots,(b_n,n)$。请你计算出用这些点能组成多少个不同的长度为 $2\times n$ 的整数点坐标序列，并且这个序列中点的 $x$ 坐标不会减少。 一个序列 $(p_1,q_1),(p_2,q_2),\dots,(p_{2\times n},q_{2\times n})$ 与序列 $(x_1,y_1),(x_2,y_2),\dots,(x_{2\times n},y_{2\times n})$ 不同当且仅当有 $i(1\le i\le 2\times n)$，满足 $(p_i,q_i)\not=(x_i,y_i)$。 你只需要输出答案对 $m$ 取模的值。

题目描述

Little Dima has two sequences of points with integer coordinates: sequence $ (a_{1},1),(a_{2},2),...,(a_{n},n) $ and sequence $ (b_{1},1),(b_{2},2),...,(b_{n},n) $ . Now Dima wants to count the number of distinct sequences of points of length $ 2·n $ that can be assembled from these sequences, such that the $ x $ -coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence. Dima considers two assembled sequences $ (p_{1},q_{1}),(p_{2},q_{2}),...,(p_{2·n},q_{2·n}) $ and $ (x_{1},y_{1}),(x_{2},y_{2}),...,(x_{2·n},y_{2·n}) $ distinct, if there is such $ i $ $ (1<=i<=2·n) $ , that $ (p_{i},q_{i})≠(x_{i},y_{i}) $ . As the answer can be rather large, print the remainder from dividing the answer by number $ m $ .

输入输出格式

输入格式

The first line contains integer $ n $ $ (1<=n<=10^{5}) $ . The second line contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ $ (1<=a_{i}<=10^{9}) $ . The third line contains $ n $ integers $ b_{1},b_{2},...,b_{n} $ $ (1<=b_{i}<=10^{9}) $ . The numbers in the lines are separated by spaces. The last line contains integer $ m $ $ (2<=m<=10^{9}+7) $ .

输出格式

In the single line print the remainder after dividing the answer to the problem by number $ m $ .

输入输出样例

输入样例 #1

1
1
2
7

输出样例 #1

1

输入样例 #2

2
1 2
2 3
11

输出样例 #2

2

说明

In the first sample you can get only one sequence: $ (1,1),(2,1) $ . In the second sample you can get such sequences : $ (1,1),(2,2),(2,1),(3,2) $ ; $ (1,1),(2,1),(2,2),(3,2) $ . Thus, the answer is $ 2 $ .