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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
constexpr int MOD = 1e9 + 7;
int main()
{
    int N;
    std::cin >> N;
    std::string S;
    std::cin >> S;
    S = "<" + S;
    std::vector<int> dp(N + 1, 0), sum(N + 1, 0);
    dp[0] = 1, std::fill(sum.begin(), sum.end(), 1);
    for (int i = 0; i < N; i++) {
        if (S[i] == '<') {
            for (int j = 0; j < N - i; j++) { dp[j] = sum[j]; }
        } else {
            for (int j = 0; j < N - i; j++) { dp[j] = (sum[N - i] + MOD - sum[j]) % MOD; }
        }
        for (int j = 0; j <= N; j++) { sum[j] = (dp[j] + (j == 0 ? 0 : sum[j - 1])) % MOD; }
        std::fill(dp.begin(), dp.end(), 0);
    }
    std::cout << sum[N] << std::endl;
    return 0;
}