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
N=int(input())
S=input()
mod=10**9+7

#DP[i]#最後においた数の右にある残っている個数
rest=N-1
DP=[1]*(N)

for s in S:
    NDP=[0]*(N)
    if s=="<":
        for i in range(rest+1):
            if i>=1:
                NDP[i-1]=(DP[i]+NDP[i-1])%mod

        DP=NDP
        for i in range(N-2,-1,-1):
            DP[i]=(DP[i+1]+DP[i])%mod

    else:
        DP=[DP[rest-i] for i in range(N)]#左右逆にして考える

        #print(DP)
        for i in range(rest+1):
            if i>=1:
                NDP[i-1]=(DP[i]+NDP[i-1])%mod

        DP=NDP
        for i in range(N-2,-1,-1):
            DP[i]=(DP[i+1]+DP[i])%mod


        DP=[DP[rest-1-i] for i in range(N)]

    rest-=1
    #print(DP,rest)

print(DP[0])