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.