Problem Statement

A sequence $X$ is called good when the following holds.

• $X$ can be emptied by repeating the following operation zero or more times.
• Delete two adjacent elements $x_i$ and $x_{i+1}$ of $X$ such that $x_i \neq x_{i+1}$.

You are given a sequence with $2N$ elements: $A=(a_1,\ldots,a_{2N})$. Among the $2^{2N-1}$ ways to divide $A$ into one or more contiguous subsequences, how many are such that all those contiguous subsequences are good? Find the count modulo $998244353$.

Constraints

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

Input

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

N
a_1 \ldots a_{2N}

Output

Print the answer.