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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let s: Vec<char> = it.next().unwrap().chars().collect();
    const MOD: u64 = 1_000_000_007;
    let mut dp = vec![1; n];
    for (i, c) in s.iter().enumerate() {
        let mut next = vec![0; n - i];
        if *c == '>' {
            for j in 1..(n - i) {
                next[0] += dp[j];
                next[j] += MOD - dp[j];
            }
        } else {
            for j in 0..(n - i) {
                next[j] += dp[j];
                *next.last_mut().unwrap() += MOD - dp[j];
            }
        }
        next[0] %= MOD;
        for j in 1..(n - i) {
            next[j] = (next[j] + next[j - 1]) % MOD;
        }
        next.pop();
        dp = next;
    }
    println!("{}", dp[0]);
}

fn main() {
    run();
}