Desk Disorder

有$N$ 个人和$2N$ 个座位。告诉你这$N$ 个人它们现在的座位。以及它们想去的座位。 每个人可以去它们想去的座位或者就坐在原来的座位上。 新的座位安排和旧的座位安排,都不允许一个座位被两个人占据的情况。 问你新的座位安排的方案数。 感谢@FakerS 提供的翻译

A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement. How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo $ 1000000007=10^{9}+7 $ .

Input will begin with a line containing $ N $ ( $ 1<=N<=100000 $ ), the number of engineers. $ N $ lines follow, each containing exactly two integers. The $ i $ -th line contains the number of the current desk of the $ i $ -th engineer and the number of the desk the $ i $ -th engineer wants to move to. Desks are numbered from $ 1 $ to $ 2·N $ . It is guaranteed that no two engineers sit at the same desk.

Print the number of possible assignments, modulo $ 1000000007=10^{9}+7 $ .

4
1 5
5 2
3 7
7 3

6

5
1 10
2 10
3 10
4 10
5 5

5

These are the possible assignments for the first example: - 1 5 3 7 - 1 2 3 7 - 5 2 3 7 - 1 5 7 3 - 1 2 7 3 - 5 2 7 3