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.

Input

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

Output

Print the answer.

Constraints

• $2 \leq N \leq 200000$
• $1 \leq A_i \leq N$
• All values in input are integers.

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

见题面 Input 部分

见题面 Output 部分