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 $1 \\leq idx(1)<idx(2)<\\cdots<idx(k) \\leq N$ 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.

Sample Input 1

3
1 2 1

Sample Output 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.

Sample Input 2

4
4 2 1 3

Sample Output 2

15

Sample Input 3

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

Sample Output 3

1178