Let $N$ be a positive integer. You are given a string $s$ of length $N-1$, consisting of < and >.

Find the number of permutations $(p_1,p_2,\dots ,p_N)$ of $(1,2,\dots ,N)$ that satisfy the following condition, modulo ${10}^9+7$:

• For each $i$ $(1\le i\le N-1)$, $p_i<p_{i+1}$ if the $i$-th character in $s$ is < and $p_i>p_{i+1}$ if the $i$-th character in $s$ is >.

Constraints

• $N$ is an integer.
• $2\le N\le 3000$
• $s$ is a string of length $N-1$.
• $s$ consists of < and >.

Input Specification

The first line will contain the integer $N$.

The second line will contain the string $s$.

Output Specification

Print the number of permutations that satisfy the condition, modulo ${10}^9+7$.

Note: Be sure to print the number modulo ${10}^9+7$.

Sample Input 1

4
<><

Sample Output 1

5

Explanation For Sample 1

There are five permutations that satisfy the condition, as follows:

• $(1,3,2,4)$
• $(1,4,2,3)$
• $(2,3,1,4)$
• $(2,4,1,3)$
• $(3,4,1,2)$

Sample Input 2

5
<<<<

Sample Output 2

1

Explanation For Sample 2

There is one permutation that satisfies the condition, as follows:

• $(1,2,3,4,5)$

Sample Input 3

20
>>>><>>><>><>>><<>>

Sample Output 3

217136290