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)

// ---------- begin ModInt ----------
//https://github.com/kenkoooo/competitive-programming-rs/blob/master/src/math/mod_int.rs
//を参考にしています
#[allow(dead_code)]
mod modint {
    pub const MOD: u32 = 1_000_000_007;
    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
    #[derive(Clone, Copy)]
    pub struct ModInt<T: Copy + Clone>(pub T);
    type Num = u32;
    impl Add<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn add(self, other: ModInt<Num>) -> ModInt<Num> {
            let mut d = self.0 + other.0;
            if d >= MOD {
                d -= MOD;
            }
            ModInt(d)
        }
    }
    impl AddAssign<ModInt<Num>> for ModInt<Num> {
        fn add_assign(&mut self, other: ModInt<Num>) {
            *self = *self + other;
        }
    }
    impl Sub<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn sub(self, other: ModInt<Num>) -> ModInt<Num> {
            let mut d = self.0 + MOD - other.0;
            if d >= MOD {
                d -= MOD;
            }
            ModInt(d)
        }
    }
    impl SubAssign<ModInt<Num>> for ModInt<Num> {
        fn sub_assign(&mut self, other: ModInt<Num>) {
            *self = *self - other;
        }
    }
    impl Mul<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn mul(self, other: ModInt<Num>) -> ModInt<Num> {
            ModInt(((self.0 as u64) * (other.0 as u64) % (MOD as u64)) as u32)
        }
    }
    impl MulAssign<ModInt<Num>> for ModInt<Num> {
        fn mul_assign(&mut self, other: ModInt<Num>) {
            *self = *self * other;
        }
    }
    impl Div<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn div(self, other: ModInt<Num>) -> ModInt<Num> {
            self * other.pow(MOD - 2)
        }
    }
    impl DivAssign<ModInt<Num>> for ModInt<Num> {
        fn div_assign(&mut self, other: ModInt<Num>) {
            *self = *self / other;
        }
    }
    impl Neg for ModInt<Num> {
        type Output = ModInt<Num>;
        fn neg(self) -> ModInt<Num> {
            ModInt(if self.0 == 0 { 0 } else { MOD - self.0 })
        }
    }
    impl ModInt<Num> {
        pub fn new(v: u32) -> ModInt<Num> {
            ModInt(v % MOD)
        }
        pub fn pow(self, mut n: u32) -> ModInt<Num> {
            let mut t = ModInt::new(1);
            let mut s = self;
            while n > 0 {
                if (n & 1) == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
    }
    pub struct Precalc {
        n: usize,
        inv: Vec<ModInt<Num>>,
        fact: Vec<ModInt<Num>>,
        ifact: Vec<ModInt<Num>>,
    }
    impl Precalc {
        pub fn new(n: usize) -> Precalc {
            let mut inv = vec![ModInt(1); n + 1];
            let mut fact = vec![ModInt(1); n + 1];
            let mut ifact = vec![ModInt(1); n + 1];
            for i in 1..(n + 1) {
                if i >= 2 {
                    inv[i] = -inv[(MOD as usize) % i] * ModInt(MOD / (i as u32));
                }
                fact[i] = ModInt(i as u32) * fact[i - 1];
                ifact[i] = inv[i] * ifact[i - 1];
            }
            Precalc {
                n: n,
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        pub fn fact(&self, n: usize) -> ModInt<Num> {
            self.fact[n]
        }
        pub fn inv(&self, x: usize) -> ModInt<Num> {
            self.inv[x]
        }
        pub fn ifact(&self, x: usize) -> ModInt<Num> {
            self.ifact[x]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModInt<Num> {
            if !(k <= n) {
                return ModInt(0);
            }
            self.fact[n] * self.ifact[k] * self.ifact[n - k]
        }
    }
    use std;
    impl std::fmt::Display for ModInt<Num> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
}
// ---------- end ModInt ----------

use modint::*;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let n: usize = s.trim().parse().unwrap();
    s.clear();
    std::io::stdin().read_line(&mut s).unwrap();
    let s: Vec<char> = s.trim().chars().collect();
    let mut dp = vec![ModInt(1); n + 1];
    for (i, &c) in s.iter().enumerate() {
        let mut next = vec![ModInt(0); n + 1];
        if c == '>' {
            for j in 0..(n - i) {
                next[0] += dp[j];
                next[j] -= dp[j];
            }
        } else {
            for j in 0..(n - i) {
                next[j] += dp[j];
            }
        }
        for j in 1..(n - i) {
            let v = next[j - 1];
            next[j] += v;
        }
        dp = next;
    }
    println!("{}", dp[0]);
}

fn main() {
    run();
}