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;

template<typename T>
void out(T x) { cout << x << endl; exit(0); }
#define watch(x) cout << (#x) << " is " << (x) << endl




typedef long long ll;
const ll mod = 1e9+7;
const int maxn = 3003;





ll dp[maxn][maxn];
int n;
string s;


void add(ll &x, ll y) {
    x %= mod;
    y %= mod;
    x += y;
    x %= mod;
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0);  cout.tie(0);
    cin>>n>>s;

    s="*"+s;
    dp[1][1]=1;

    for (int i=2; i<=n; i++) {
	
	for (int j=1; j<=i; j++) {
	    dp[i-1][j] += dp[i-1][j-1];
	    dp[i-1][j] %= mod;
	}

	
	for (int j=1; j<=i; j++) {
	    if (s[i-1]=='<') {
		ll acc=dp[i-1][j-1];
		dp[i][j] += acc;
	    }
	    if (s[i-1]=='>') {
		ll acc=dp[i-1][i]-dp[i-1][j-1];
		dp[i][j] += acc;
	    }
	    dp[i][j] %= mod;
	}
	// for (int b=1; b<=i; b++) {
	//     for (int a=1; a<=i-1; a++) {
	// 	//...a,b
	// 	int real_a = a;
	// 	if (a>=b) real_a++;
	// 	assert(real_a!=b);
	// 	if ((real_a<b) != (s[i-1]=='<')) {
	// 	    continue;
	// 	}
	// 	add(dp[i][b], dp[i-1][a]);
	//     }
	// }
    }


    ll res = 0;
    for (int j=1; j<=n; j++) {
	add(res, dp[n][j]);
    }
    res %= mod;
    res += mod;
    res %= mod;
    cout<<res<<endl;

    return 0;
}