Problem Statement

Let S be a set composed of all integers from 1 through N.
f is a function from S to S. You are given the values $f(1), f(2), \cdots, f(N)$ as $f_1, f_2, \cdots, f_N$.
Find the number, modulo 998244353, of non-empty subsets T of S satisfying both of the following conditions:

• For every $a \in$ $T, f(a) \in$ T.

• For every $a, b \in$ $T, f(a) \neq f(b)$ if $a \neq b$.

Input

Input is given from Standard Input in the following format:
N
$f_1 f_2 \ldots f_N$

Output

Print the number of non-empty subsets of S satisfying both of the conditions, modulo 998244353.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq f_i \leq N$
• All values in input are integers.

Sample Input 1

2
2 1

Sample Output 1

1

We have $f(1) = 2, f(2) = 1. Since f(1) \neq f(2)$, the second condition is always satisfied, but the first condition requires T to contain 1 and 2 simultaneously.

Sample Input 2

2
1 1

Sample Output 2

1

We have f(1) = f(2) = 1. The first condition requires T to contain 1, and the second condition forbids T to contain 2.

Sample Input 3

3
1 2 3

Sample Output 3

7

We have f(1) = 1, f(2) = 2, f(3) = 3. Both of the conditions are always satisfied, so all non-empty subsets of T count.

见题面 Input 部分

见题面 Output 部分