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
MOD = 10**9 + 7

N = int(input())
s = input()

# dp[i][j] := i 番目まで決めて i 番目の数より大きいものが j 個のときの場合の数
dp = [[0]*N for _ in range(N)]
dp[0] = [1]*(N+1)
for i in range(N-1):
    # 累積和をとっておく
    for j in range(N-1):
        dp[i][j+1] += dp[i][j]
    for j in range(N-i-1):
        if s[i] == '<':
            dp[i+1][j] += dp[i][N-i-1]-dp[i][j]
        else:
            dp[i+1][j] += dp[i][j]
        dp[i+1][j] %= MOD

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