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;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }

        static readonly long Mod = 1000000000 + 7;
        static void Main(string[] args)
        {
            var N = Sarray()[0];
            var s = ReadLine();
            var from = new long[N];
            for (var i = 0; i < N; ++i)
                from[i] = 1;
            //i個目まで決まっているとする。このとき、i個目に残りN-(i-1)個からm番目のものを選んだとする
            for (var i = 0; i < N - 1; ++i)
            {
                //[0,i)個
                var sum = new long[N + 1];
                for (var k = 1; k <= N - i; ++k)
                    sum[k] = sum[k - 1] + from[k - 1];
                var to = new long[N];
                for (var m = 0; m < N - i; ++m)
                {
                    if (s[i] == '<')
                        to[m] = (to[m] + sum[m + 1]) % Mod;
                    else
                        to[m] = (to[m] + sum[N - i] - sum[m + 1] + Mod) % Mod;
                }
                from = to;
            }
            WriteLine(from[0]);
        }
    }
}