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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

//#define FILE_IO

const int mod = 1e9 + 7;

int N;
int dp[3005][3005], sum[3005][3005];
char s[3005];

/// dp[i][j] = nr perm de lungime i care respecta [1, i] si au j pe ultima pozitie

int main()
{
    #ifdef FILE_IO
    freopen("1.in", "r", stdin);
    //freopen("1.out", "w", stdout);
    #endif

    scanf("%d\n", &N);
    scanf("%s", s + 1);

    dp[1][1] = 1;
    for(int i = 1; i <= N; i++) sum[1][i] = 1;
    for(int i = 2; i <= N; i++)
        for(int j = 1; j <= i; j++)
        {
            if(s[i - 1] == '<')
                dp[i][j] = sum[i - 1][j - 1];
            else if(s[i - 1] == '>')
                dp[i][j] = (sum[i - 1][i - 1] - sum[i - 1][j - 1] + mod) % mod;
            sum[i][j] = (sum[i][j - 1] + dp[i][j]) % mod;
        }

    cout << sum[N][N] << '\n';

    return 0;
}