Score : $700$ points

Problem Statement

Given is a sequence of $N$ integers $A_1,A_2,\cdots,A_N$.

Find the number of non-empty subsequences $s$ of $A$ satisfying the following condition, modulo $998244353$.

• There is only one way to extract $s$ from $A$. Formally, there uniquely exists a sequence of indices $1 \leq idx(1) such that$A_{idx(i)}=s_i$ ($1 \leq i \leq k$), where $s=(s_1,s_2,\cdots,s_k)$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the answer.

3
1 2 1

5

The following five subsequences satisfy the condition.

• $(1,1)$
• $(1,2)$
• $(1,2,1)$
• $(2)$
• $(2,1)$

The subsequence $(1)$ does not satisfy the condition since there are two ways to extract it.

4
4 2 1 3

15

12
1 2 3 6 9 2 3 3 9 6 1 6

1178