Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4
<><

Sample Output 1

5

There are five permutations that satisfy the condition, as follows:

(1, 3, 2, 4)

(1, 4, 2, 3)

(2, 3, 1, 4)

(2, 4, 1, 3)

(3, 4, 1, 2)

Sample Input 2

5
<<<<

Sample Output 2

1

There is one permutation that satisfies the condition, as follows:

(1, 2, 3, 4, 5)

Sample Input 3

20
>>>><>>><>><>>><<>>

Sample Output 3

217136290

Be sure to print the number modulo 10^9 + 7.

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

n = int(input())
s = input()
M = 10**9 + 7

def mod(v):
    if v >= M:
        return v % M
    return v


dp = [[1] * n + [0] for _ in range(2)]
s = [v == "<" for v in s]
for i in reversed(range(n - 1)):
    for j in range(n - 1):
        dp[1][j + 1] = dp[1][j + 1] + dp[1][j]
        dp[0][j] = dp[1][j]
    dp[0][-2] = dp[1][-2]

    for zk in range(n - i):
        cnt = 0

        if s[i]:
            cnt = dp[0][zk - 1]
        else:
            zj = n - i - zk - 1
            cnt = dp[0][zk + zj - 1] - dp[0][zk - 1]
        dp[1][zk] = mod(cnt)

print(sum(dp[1]) % M)