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.IO;
using System.Linq;

namespace Contest
{

    class Program
    {
        private const long Mod = (long)1e9 + 7;
        private Scanner sc;
        private int N;
        private string S;
        public void Solve()
        {
            sc = new Scanner();
            N = sc.NextInt();
            S = sc.Next();

            // i個まで見て最後がj dp[i,j]
            var dp = new long[N, N];
            dp[0, 0] = 1;


            for (int i = 1; i < N; i++)
            {
                if (S[i - 1] == '<')
                {
                    // j 除いて 0 ~ iのi-1個並び替える
                    // ..... j以下, j
                    long sum = 0;
                    for (int j = 0; j <= i; j++)
                    {
                        if (j != 0)
                        {
                            //Console.WriteLine($"aaa {sum} {j}");
                            // dp[i, j] += dp[i-1, 0 ~ j-1]
                            dp[i, j] += sum;
                            dp[i, j] %= Mod;
                        }

                        sum += dp[i - 1, j];
                        sum %= Mod;
                    }
                }
                else
                {
                    long sum = 0;
                    // j 除いて 0 ~ iのi-1個並び替える
                    // 
                    for (int j = i; j >= 0; j--)
                    {
                        if (j == i)
                        {
                            // dp[i,j] += 0
                            continue;
                        }

                        sum += dp[i - 1, j];
                        sum %= Mod;
                        dp[i, j] += sum;
                        dp[i, j] %= Mod;
                    }
                }
            }

            long ans = 0;
            //for (int i = 0; i < N; i++)
            //{
            //    for (int j = 0; j <= i; j++)
            //    {
            //        Console.Write($"{dp[i,j]} ");
            //    }
            //    Console.WriteLine();
            //}
            for (int i = 0; i < N; i++)
            {
                ans += dp[N - 1, i];
                ans %= Mod;
            }
            Console.WriteLine(ans);
        }


        static void Main() => new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _stream = new StreamReader(Console.OpenStandardInput());
        _pos = 0;
        _line = new string[0];
        _separator = ' ';
    }
    private readonly char _separator;
    private readonly StreamReader _stream;
    private int _pos;
    private string[] _line;
    #region get a element
    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = _stream.ReadLine().Split(_separator);
            _pos = 0;
        }
        return _line[_pos++];
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    #endregion
    #region convert array
    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }
    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }
    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }
    #endregion
    #region get array
    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = _stream.ReadLine().Split(_separator);
        _pos = _line.Length;
        return _line;
    }
    public int[] IntArray()
    {
        return ToIntArray(Array());
    }
    public long[] LongArray()
    {
        return ToLongArray(Array());
    }
    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }
    #endregion
}