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
#!/usr/bin/env pypy3
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    mod=10**9+7
    N=I()
    s="<"+input()
    
    dp=[[0]*(N+1)for _ in range(N+1)]
    #dp[i][j]はi番目まで見て，Piよりも大きいものがj個ある時の通り数
    dp[0][-1]=1#0からスタートしたとみなす    
    
    for i in range(N):
        if s[i]==">":
            S=0
            for j in range(N-i+1):
                S=(S+dp[i][j])%mod
                dp[i+1][j]=S
        else:
            S=0
            for j in range(N-i,0,-1):
                S=(S+dp[i][j])%mod
                dp[i+1][j-1]=S
    print(dp[-1][0])
                
                
                    
            

main()
