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 $s=(s_1,s_2,\cdots,s_k)$.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分