Problem Statement

There is a permutation $P$ of $(1,2,\ldots,N)$ and an empty array $A$. Perform the following operation $N-1$ times on $P$:

• Choose two adjacent elements. Remove the smaller of the chosen elements from $P$ and concatenate the parts before and after the removed element. Append the removed element to the end of $A$.

Find the number, modulo $998244353$, of possible final sequences $A$ of length $N-1$.

Constraints

• $2 \le N \le 2\times 10^5$
• $1 \le P_i \le N$
• $P$ is a permutation of $(1,2,\ldots,N)$.
• All input values are integers.

Input

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

N
P_1 P_2 \ldots P_N

Output

Output the answer.