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 <string>

using namespace std;

using Int = long long;

const int MOD = 1000000007;

int N;
Int dp[3005][3005];
Int dp_sum[3005][3005];

int main()
{
	string s;
	cin >> N >> s;

	dp[0][0] = 1;

	for (int i = 1; i < N; ++i) {
		for (int j = 0; j <= i; ++j) {
			dp_sum[i - 1][j] = dp[i - 1][j];
			if (j - 1 >= 0) {
				dp_sum[i - 1][j] += dp_sum[i - 1][j - 1];
				dp_sum[i - 1][j] %= MOD;
			}
		}
		for (int j = 0; j <= i; ++j) {
			if (s[i - 1] == '<') {
				// [0, j) に対しての累積和
				if (j - 1 >= 0) {
					dp[i][j] += dp_sum[i - 1][j - 1];
					dp[i][j] %= MOD;
				}
			} else {
				// [j, i) に対しての累積和
				dp[i][j] += dp_sum[i - 1][i - 1];
				if (j - 1 >= 0) {
					dp[i][j] -= dp_sum[i - 1][j - 1];
					dp[i][j] += MOD;
				}
				dp[i][j] %= MOD;
			}
		}
	}

	Int ans = 0;
	for (int i = 0; i <= N - 1; ++i) (ans += dp[N - 1][i]) %= MOD;

	cout << ans << endl;
}