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)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

const M: usize = 1_000_000_007;

struct SegmentTree {
    n: usize,
    data: Vec<i64>,
}

impl SegmentTree {
    fn f(&self, a: i64, b: i64) -> i64 {
        (a + b) % M as i64
    }

    pub fn initial() -> i64 {
        0
    }

    fn new(size: usize) -> Self {
        let n = {
            let mut res = 1;
            while res < size {
                res <<= 1
            }
            res
        };
        let data = vec![Self::initial(); n * 2 - 1];
        SegmentTree { n: n, data: data }
    }

    fn update(&mut self, k: usize, a: i64) {
        let mut index = k + self.n - 1;
        self.data[index] = a;
        while index > 0 {
            index = (index - 1) / 2;
            self.data[index] = self.f(self.data[index * 2 + 1], self.data[index * 2 + 2]);
        }
    }

    // [a, b)
    fn query(&mut self, a: usize, b: usize) -> i64 {
        let (l, r) = (0, self.n);
        self.query_iter(a, b, 0, l, r)
    }

    fn query_iter(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> i64 {
        if r <= a || b <= l {
            Self::initial()
        } else if a <= l && r <= b {
            self.data[k]
        } else {
            let vl = self.query_iter(a, b, k * 2 + 1, l, (l + r) / 2);
            let vr = self.query_iter(a, b, k * 2 + 2, (l + r) / 2, r);
            self.f(vl, vr)
        }
    }
}

fn main() {
    input! {
        n: usize,
        s: chars,
    }

    let mut dp = vec![vec![0; n + 1]; n + 1];
    for i in 0..n {
        dp[0][i] = 1;
    }

    for i in 1..n + 1 {
        let mut seg_tree = SegmentTree::new(n + 1);
        for j in 0..n - i + 1 {
            seg_tree.update(j, dp[i - 1][j]);
        }
        for j in 0..n - i {
            if s[i - 1] == '<' {
                dp[i][j] = seg_tree.query(0, j + 1);
            // for k in 0..j + 1 {
            //     dp[i][j] += dp[i - 1][k];
            //     dp[i][j] %= M;
            // }
            } else {
                dp[i][j] = seg_tree.query(j + 1, n - i + 1);
                // for k in j + 1..n - i + 1 {
                //     dp[i][j] += dp[i - 1][k];
                //     dp[i][j] %= M;
                // }
            }
        }
    }

    println!("{}", dp[n - 1][0]);
}