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

def resolve():
    MOD = 10 ** 9 + 7
    N = int(input())
    S = input()

    # i番目の数字より大きい数字が残りj個の通り数
    dp = [[0] * (N + 1) for _ in range(N + 1)]
    for j in range(N):
        dp[0][j] = 1

    for i in range(N):
        cum = [0] * (N + 1)
        for j in range(N):
            cum[j+1] = (cum[j] + dp[i][j]) % MOD

        for j in range(N - i - 1):
            if S[i] == "<":
                dp[i+1][j] = (cum[N]-cum[j+1]) % MOD
            else:
                dp[i+1][j] = (cum[j+1] - cum[0]) % MOD

    print(dp[N - 1][0])


if __name__ == "__main__":
    resolve()