Problem Statement

For a sequence $X = (X_1, \dots, X_n)$ of positive integers, we call $X$ a 221 sequence if and only if the length and value are equal for every (length, value) pair in its run-length encoding. More formally, a sequence satisfying the following condition is called a 221 sequence.

• For any integer pair $(l, r)$ satisfying $1 \leq l \leq r \leq n$, if all three of the following conditions hold, then $(r-l+1) = X_l$.
• $l = 1$ or ($l \geq 2$ and $X_{l-1} \neq X_l$)
  • $r = n$ or ($r \leq n-1$ and $X_{r+1} \neq X_r$)
  • $X_l = X_{l+1} = \dots = X_r$

For example, $(2,2,3,3,3,1,2,2)$ is a 221 sequence, but $(1,1)$ and $(4,4,1,4,4)$ are not 221 sequences.

You are given a sequence $A = (A_1, \dots, A_N)$ of positive integers of length $N$. Find the number, modulo $998244353$, of non-empty (not necessarily contiguous) subsequences of $A$ that are 221 sequences. Even if two subsequences are extracted from different positions, they are counted as one if they are equal as sequences.

Constraints

• $1 \leq N \leq 500\,000$
• $1 \leq A_i \leq N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Output the answer on one line.