Problem Statement

You are given a string $s$ of length $N-1$. $s$ consists of < and >.

How many permutations $(p_1,p_2,\ldots,p_N)$ of $(1,2,\ldots,N)$ satisfy all of the following conditions? Find the count modulo $998244353$.

• For each $i \ (1\le i\le N-1)$, if the $i$-th character of $s$ is <, then $p_i\lt p_{i+1}$, and if it is >, then $p_i\gt p_{i+1}$.
• The length of the longest increasing subsequence of $(p_1,p_2,\ldots,p_N)$ is $2$.

Constraints

• $N$ is an integer between $2$ and $2\times 10^5$, inclusive
• $s$ is a string of length $N-1$ consisting of < and >

Input

$N$
$s$

Output

Print the number of permutations satisfying all of the conditions, modulo $998244353$.

Sample

4
<><

2

5
<<<<

0

35
><>><>>><>>>><>>>>><>>>>>><>>>>>>>

592821357