Problem Statement

There are n squares arranged in a row. Each square has a left- or right-pointing footprint or a hole.
The initial state of each square is described by a string s consisting of ., <, >. If the i-th character of s is ., the i-th square from the left has a hole; if that character is <, that square has a left-pointing footprint; if that character is >, that square has a right-pointing footprint.
Snuke, the cat, will repeat the following procedure until there is no more square with a hole.

• Step 1: Choose one square with a hole randomly with equal probability.
• Step 2: Fill the hole in the chosen square, stand there, and face to the left or right randomly with equal probability.
• Step 3: Keep walking in the direction Snuke is facing until he steps on a square with a hole or exits the row of squares.

Here, the choices of squares and directions are independent of each other.
When Snuke walks on a square (without a hole), that square gets a footprint in the direction he walks in.
If the square already has a footprint, it gets erased and replaced by a new one.
For example, in the situation >.<><.><, if Snuke chooses the 6-th square from the left and faces to the left, the 6-th, 5-th, 4-th, 3-rd squares get left-pointing footprints: >.<<<<><.
Find the expected value of the number of left-pointing footprints when Snuke finishes the procedures, modulo 998244353.

Input

Input is given from Standard Input in the following format:
n
s

Output

Print the expected value of the number of left-pointing footprints, modulo 998244353.

Constraints

• $1 \leq n \leq 10^5$
• s is a string of length n consisting of ., <, >.
• s contains at least one ..

Sample Input 1

5

<.<<

Sample Output 1

3

In Step 1, Snuke always chooses the only square with a hole.
If Snuke faces to the left in Step 2, the squares become <<<<<, where 5 squares have left-pointing footprints.
If Snuke faces to the right in Step 2, the squares become ><>>>, where 1 square has a left-pointing footprint.
Therefore, the answer is $\frac{5+1}{2}=3$.

Sample Input 2

20

.>.<>.<<.<>.<..<>><

Sample Output 2

848117770

见题面 Input 部分

见题面 Output 部分