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 python3
import sys
input = sys.stdin.readline
MOD = 10**9 + 7

n = int(input())
s = input().rstrip()

dp = [[0] * n for _ in range(n)]
dp[0] = [1] * n

used = 0
for i, ch in enumerate(s):
    if ch == "<":
        for j in range(n - used - 1, -1, -1):
            if j-1 >= 0:
                dp[i+1][j-1] = dp[i][j]
        for j in range(n - 1, 0, -1):
            dp[i+1][j-1] += dp[i+1][j]
            dp[i+1][j-1] %= MOD
    else:
        for j in range(n - used - 2, -1, -1):
            dp[i+1][j] = dp[i][j]
        for j in range(1, n - used - 1):
            dp[i+1][j] += dp[i+1][j-1]
            dp[i+1][j] %= MOD
    used += 1

# for line in dp:
#     print(line)
print(sum(dp[-1]) % MOD)