Problem Statement

You are given an integer sequence a of length N.
How many permutations p of the integers 1 through N satisfy the following condition?

• For each 1 ≤ i ≤ N, at least one of the following holds: p_i = a_i and p_{p_i} = a_i.

Find the count modulo 10^9 + 7.

Input

The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N

Output

Print the number of the permutations p that satisfy the condition, modulo 10^9 + 7.

Constraints

• 1 ≤ N ≤ 10^5
• a_i is an integer.
• 1 ≤ a_i ≤ N

Sample Input 1

3
1 2 3

Sample Output 1

4

The following four permutations satisfy the condition:

• (1, 2, 3)
• (1, 3, 2)
• (3, 2, 1)
• (2, 1, 3)

For example, (1, 3, 2) satisfies the condition because p_1 = 1, p_{p_2} = 2 and p_{p_3} = 3.

Sample Input 2

2
1 1

Sample Output 2

1

The following one permutation satisfies the condition:

• (2, 1)

Sample Input 3

3
2 1 1

Sample Output 3

2

The following two permutations satisfy the condition:

• (2, 3, 1)
• (3, 1, 2)

Sample Input 4

3
1 1 1

Sample Output 4

0

Sample Input 5

13
2 1 4 3 6 7 5 9 10 8 8 9 11

Sample Output 5

6

见题面 Input 部分

见题面 Output 部分