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: Time Limit Exceeded)

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

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

dp = [[None] * n for _ in range(n)]
def dfs(zk, i=0):
    if dp[zk][i] is not None:
        return dp[zk][i]

    if i == n - 1:
        dp[zk][i] = 1
        return 1

    zj = n - i - zk - 1
    cnt = 0

    if s[i] == "<":
        for v in range(zk):
            cnt += dfs(v, i + 1)
    else:
        for v in range(zj):
            cnt += dfs(zk + v, i + 1)
    dp[zk][i] = cnt
    return cnt

def cumsum(array):
    array = array[:]
    for i in range(len(array) - 1):
        array[i + 1] = mod(array[i + 1] + array[i])
    array.append(0)
    return array

for i in reversed(range(n)):
    for zk in range(n):
        if i == n - 1:
            dp[i][zk] = 1
            continue

        zj = n - i - zk - 1
        cnt = 0

        if s[i] == "<":
            # for v in range(zk):
            #     # cnt = mod(cnt + dp[i + 1][v])
            cnt = cs[zk - 1]
        else:
            # for v in range(zj):
            #     # cnt = mod(cnt + dp[i + 1][zk + v])
            cnt = cs[zk + zj - 1] - cs[zk - 1]
        dp[i][zk] = cnt
    cs = cumsum(dp[i])

print(sum(dp[0]) % M)