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

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

• For each $i (1 \leq i \leq N - 1), p_i < p_{i + 1}$ 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.
• $2 \leq N \leq 3000$
• s is a string of length N - 1.
• s consists of < and >.

Input

Input is given from Standard Input in the following format:

N
s

Output

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

Examples

Input

4
<><

Output

5

Input

5
<<<<

Output

1

Input

20

<>>><>><>>><<>>

Output

217136290

见题面

见题面