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 $a \neq b$.

Constraints

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

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 $998244353$.