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 <iostream>
#include <algorithm>

using namespace std;
typedef long long ll;
#define REP(i,n) for (int i = 0; i < n; ++i)
#define REPR(i,n) for (int i = n-1; i >= 0; --i)
#define FOR(i,m,n) for (int i = m; i < n; ++i)

const int MAX = 3e3+10;
const int MOD = 1e9+7;
int N;
string S;
ll dp[MAX][MAX];

ll solve(int n, int m) {
    if (n == 0) return 1;
    if (dp[n][m] >= 0) return dp[n][m];

}

int main () {
	cin >> N >> S;
    REP (j, N) dp[0][j] = 1;
    
    FOR (i, 1, N) {
        bool g = (S[i-1] == '<');
        if (g) {
            REPR (j, N-i)
                dp[i][j] = (dp[i][j+1] + dp[i-1][j+1]) % MOD;
        } else {
            dp[i][0] = dp[i-1][0];
            FOR (j, 1, N-i)
                dp[i][j] = (dp[i][j-1] + dp[i-1][j]) % MOD;
        }
    }
    cout << dp[N-1][0] << endl;
}