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;

const int maxn = 3005, mod = 1e9+7;
int N, dp[maxn][maxn], sum[maxn][maxn];
string s;

int main(){
    cin>>N>>s;
    
    dp[1][1] =1;
    sum[1][1] = 1;
    for(int i = 2; i <= N; i++){
        for(int j = 1; j<= i; j++){
            if(s[i-2] == '<')
                (dp[i][j] = sum[i-1][j-1])%=mod;
            else 
                (dp[i][j] = 
                    sum[i-1][i-1] - sum[i-1][j-1]+mod)%=mod;
        }
        for(int j = 1;j<=i; j++)(sum[i][j] = sum[i][j-1] + dp[i][j])%=mod;
    }
    cout<<sum[N][N]<<endl;
    
    return 0;
}