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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    static long mod = 1000_000_007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        String s = sc.next();
        long[][] dp = new long[n + 1][n + 1];
        dp[1][1] = 1;
        long[][] pref = new long[n + 1][n + 1];
        pref[1][1] = 1;
        for (int i = 2; i <= n; i++) {
            char cc = s.charAt(i - 2);
            for (int a = 1; a <= i; a++) {
                if (cc == '<') {
                    dp[i][a] = (dp[i][a] + pref[i - 1][a - 1]) % mod;
                    pref[i][a] = (pref[i][a - 1] + dp[i][a]) % mod;
                } else {
                    dp[i][a] = (dp[i][a] + pref[i - 1][i - 1]) % mod;
                    dp[i][a] = (dp[i][a] - pref[i - 1][a - 1]) % mod;
                    pref[i][a] = (pref[i][a - 1] + dp[i][a]) % mod;
                }
            }
        }

        long ans = 0;
        for (int i = 0; i <= n; i++) {
            ans = (ans + dp[n][i]) % mod;
            if (ans < 0) {
                ans += mod;
            }
        }
        System.out.println(ans);
    }
}