Problem Statement

You are given a sequence $A=(A_1, A_2, \cdots, A_N)$ of length $N$.

There are $2^{N-1}$ ways to split $A$ into some number of non-empty contiguous subarrays. Among them, find the number of splits satisfying the following condition, modulo $998244353$.

• If $A$ is split into $B_1, B_2, \cdots,B_K$, then $(\min{B_1}, \min{B_2}, \cdots, \min{B_K})$ is a non-decreasing sequence.

Here, for a non-empty sequence $B$, $\min{B}$ denotes the minimum value of its elements.

Constraints

• $1\leq N\leq 2\times{10}^5$
• $1\leq A_i\leq {10}^9$
• All input values are integers.

Input

$N$
$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the number of splits satisfying the condition, modulo $998244353$.

Sample

3
1 3 2

3

3
3 2 1

1

10
4 1 2 6 1 3 9 10 1 3

40