201283: [AtCoder]ARC128 D - Neq Neq

Problem Statement

We have $N$ balls arranged in a row, numbered $1$ to $N$ from left to right. Ball $i$ has an integer $A_i$ written on it.

You can do the following operation any number of times.

• Choose three consecutive balls $x, y, z$ $(1 \leq x < y < z \leq N$). Here, $A_x \neq A_y$ and $A_y \neq A_z$ must hold. Then, eat Ball $y$. After this operation, Balls $x$ and $z$ are considered adjacent.

Find the number of possible sets of balls remaining in the end, modulo $998244353$.

Constraints

• $2 \leq N \leq 200000$
• $1 \leq A_i \leq N$
• 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

4
1 2 1 2

Sample Output 1

3

There are three possible sets of balls remaining in the end: $\{1,2,3,4\},\{1,2,4\},\{1,3,4\}$.

Sample Input 2

5
5 4 3 2 1

Sample Output 2

8

Different sequences of operations are not distinguished if they result in the same set of balls.

Sample Input 3

5
1 2 3 2 1

Sample Output 3

8

Different sets of remaining balls are distinguished even if they have the same sequence of integers written on them.

Sample Input 4

9
1 4 2 2 9 6 9 6 6

Sample Output 4

14