Problem Statement

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 >.

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.

Constraints

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

Sample Input 1

4
<><

Sample Output 1

5

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

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

• (1, 2, 3, 4, 5)

Sample Input 3

20

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

Sample Output 3

217136290

Be sure to print the number modulo 10^9 + 7.

见题面 Input 部分

见题面 Output 部分