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 <cstring>

using namespace std;
const int maxn = 3010;
const int mod = 1000000007;

int n;
char niz[maxn];
int dp[maxn];
int sum[maxn];

int main() {
    scanf("%d%s", &n, niz);
    for (int i = 1; i <= n; i++) sum[i] = i;
    for (int i = 0; i < n - 1; i++) {
        memset(dp, 0, sizeof dp);
        for (int j = 1; j < n - i; j++) {
            if (niz[i] == '<') dp[j] = sum[j];
            else dp[j] = sum[n] - sum[j] + mod, dp[j] %= mod;
        }
        //memset(sum, 0, sizeof sum);
        for (int j = 1; j <= n; j++) sum[j] = sum[j - 1] + dp[j], sum[j] %= mod;
    }
    printf("%d\n", sum[n]);
    //system("pause");
    return 0;
}