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 N = 3100,mod=1e9+7;

typedef long long ll;

int f[N][N];

int main()
{
	int n;
	cin>>n;
	string s;
	cin>>s;
	s="#"+s;
	f[1][1]=1;
	for(int i=2;i<=n;i++)
	{
		if(s[i-1]=='<')
		for(int j=1;j<=i;j++)
		{
			f[i][j]=(f[i][j-1]+f[i-1][j-1])%mod;
		}
		else 
		for(int j=i;j>=1;j--)
		{
			f[i][j]=(f[i][j+1]+f[i-1][j])%mod; 
		}
	}
	ll ans=0;
	for(int i=1;i<=n;i++)
	{
		ans+=f[n][i];
		ans%=mod;
	}
	cout<<ans<<endl;
	
	
			
	
}