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 Scanner sc = new Scanner(System.in);
	static final long MOD = 1_000_000_007;

	public static void main(String[] args) {
		int N = sc.nextInt();
		char[] S = sc.next().toCharArray();
		long[][] dp = new long[N][N];
		dp[0][0] = 1;
		for (int i = 0; i < N - 1; i++) {
			long sum = 0;
			if (S[i] == '<') {
				for (int j = 0; j <= i; j++) {
					sum += dp[i][j];
					if (sum >= MOD) sum -= MOD;
					dp[i + 1][j + 1] = sum;
				}
			} else {
				for (int j = i; j >= 0; j--) {
					sum += dp[i][j];
					if (sum >= MOD) sum -= MOD;
					dp[i + 1][j] = sum;
				}
			}
		}
		long ans = 0;
		for (int i = 0; i < N; i++) {
			ans += dp[N - 1][i];
		}
		System.out.println(ans % MOD);
	}
}