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()
# 配るDPの初期値を入れておく
dp = [1]*n
for i in range(n-1):
    nxt = [0]*(n+1)
    # 前の相対順位は
    # [0, n-1-i]
    # 次の相対順位は
    # [0, n-2-i]
    # 今の順位がjのとき、
    # < → [i, n-2-i]に加算
    # > → [0, j-1]に加算
    for j in range(n-i):
        if s[i] == "<":
            left = j
            right = n-1-i
        else:
            left = 0
            right = j
        if left >= right:
            continue
        nxt[left] += dp[j]
        nxt[right] -= dp[j]
    for j in range(n):
        nxt[j+1] += nxt[j]
        nxt[j+1] %= mod
    dp = nxt
ans = sum(dp)%mod
print(ans)
