A16084. Swaps

You are given an array of integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le n$ ). You can perform the following operation several (possibly, zero) times:

- pick an arbitrary $i$ and perform swap $(a_i, a_{a_i})$ .

How many distinct arrays is it possible to attain? Output the answer modulo $(10^9 + 7)$ .

The first line contains an integer $n$ ( $1 \le n \le 10^6$ ).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1\le a_i\le n$ ).

Output the number of attainable arrays modulo $(10^9 + 7)$ .

In the first example, the initial array is $[1, 1, 2]$ . If we perform the operation with $i = 3$ , we swap $a_3$ and $a_2$ , obtaining $[1, 2, 1]$ . One can show that there are no other attainable arrays.

In the second example, the four attainable arrays are $[2, 1, 4, 3]$ , $[1, 2, 4, 3]$ , $[1, 2, 3, 4]$ , $[2, 1, 3, 4]$ . One can show that there are no other attainable arrays.