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 <bits/stdc++.h>
using namespace std;
using vi = vector<int>;

const int MOD = 1e9 + 7;
const int N = 3030;

int main() {
    ios_base::sync_with_stdio(false);
    int n;
    string s;
    cin >> n >> s;
    vi dp(n), tmp(n);
    dp[0] = 1;
    for (int i=0; i+1<n; i++) {
        if (s[i] == '<') {
            tmp[0] = 0;
            for (int j=1; j<=i+1; j++) {
                tmp[j] = (tmp[j-1] + dp[j-1]) % MOD;
            }
        }
        else {
            tmp[i+1] = dp[i+1];
            for (int j=i; j>=0; j--) {
                tmp[j] = (tmp[j+1] + dp[j]) % MOD;
            }
        }
        swap(dp, tmp);
    }
    int ans = 0;
    for (int x : dp) {
        ans = (ans + x) % MOD;
    }
    cout << ans << '\n';
}