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;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		int n = int.Parse(Console.ReadLine());
		long mod = 1000000007;
		string s = Console.ReadLine();
		long[,] dp = new long[n+1,n];
    long[,] sums = new long[n+1,n+1];

    for(int i = 0; i < n; i++)
    {
      dp[1,i] = 1;
      sums[1,i+1] = i+1;
    }

    for(int i = 2; i <= n; i++)
    {
      for(int j = 0; j < n+1-i; j++)//左から0-indexで何番目を取るのか
      {
        if(s[i-2] == '>')
        {
          dp[i,j] = sums[i-1,n]-sums[i-1,j+1];
        }else
        {
          dp[i,j] = sums[i-1,j+1];
        }
        dp[i,j] += mod;
        dp[i,j] %= mod;
        sums[i,j+1] = sums[i,j] + dp[i,j];
        sums[i,j+1] %= mod;
        //Console.WriteLine(i+" "+j+" "+dp[i,j]);
      }
      for(int j = n+1-i; j < n; j++)
      {
        sums[i,j+1] = sums[i,j];
      }
    }

		Console.WriteLine(dp[n,0]);
	}
}