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
import sys
#sys = stdin.buffer.readline

def main():
    N = int(input())
    s = input()
    MOD = 10**9+7
    base = [1]*N
    
    for i in range(N-1):
        imos = [0]*N
        if s[i] == "<":
            for j in range(N-i-1):
                imos[0] += base[1+j]
                imos[1+j] -= base[1+j]
        else:
            for j in range(N-i-1):
                imos[j] += base[j]
                imos[N-i-1] -= base[j]
        for k in range(N-1):
            imos[k+1] += imos[k]
            imos[k+1] %= MOD
        base = imos
    
    print(base[0]%MOD)
    
if __name__ == "__main__":
    main()
