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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

namespace AtCoder.DP
{
    class EDPC_T
    {
        public const int mod = 1000000007;

        public static void Main()
        {
            var n = int.Parse(Console.ReadLine());
            var s = Console.ReadLine();

            var dp = new long[n, n];
            var acc = new long[n];
            for (int i = 0; i < n; i++)
                dp[0, i] = 1;


            for (int i = 0; i < s.Length; i++)
            {
                acc[0] = dp[i, 0];
                for (int j = 1; j < n - i; j++)
                    acc[j] = (acc[j - 1] + dp[i, j]) % mod;

                if (s[i] == '<')
                {
                    for (int j = 0; j < n - i - 1; j++)
                        dp[i + 1, j] = acc[j];
                }
                else
                {
                    for (int j = 0; j < n - i - 1; j++)
                        dp[i + 1, j] = (acc[n - i - 1] - acc[j] + mod) % mod;
                }
            }
            Console.WriteLine(dp[n - 1, 0] % mod);
        }
    }
}