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