Problem:
Score : 300 points

Problem Statement

Given is a string S of length N-1.
Each character in S is < or >.

A sequence of N non-negative integers, a_1,a_2,\cdots,a_N, is said to be good when the following condition is satisfied for all i (1 \leq i \leq N-1):

If S_i= <: a_i<a_{i+1}

If S_i= >: a_i>a_{i+1}

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Constraints

2 \leq N \leq 5 \times 10^5

S is a string of length N-1 consisting of < and >.

Input

Input is given from Standard Input in the following format:

S

Output

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Sample Input 1

<>>

Sample Output 1

3

a=(0,2,1,0) is a good sequence whose sum is 3.
There is no good sequence whose sum is less than 3.

Sample Input 2

<>>><<><<<<<>>><

Sample Output 2

28

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let S: Vec<char> = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().chars().collect()
    };

    const INF: i64 = 1e15 as i64;
    let N = S.len() + 1;
    let mut R = S
        .iter()
        .rev()
        .scan(0, |state, &s| {
            *state = if s == '>' { *state + 1 } else { 0 };
            Some(*state)
        })
        .collect::<Vec<_>>();
    R.reverse();
    let mut res = vec![0; N];
    res[0] = R[0];
    for i in 0..(N - 2) {
        res[i + 1] = match (S[i], S[i + 1]) {
            ('<', '<') => res[i] + 1,
            ('<', '>') => std::cmp::max(res[i] + 1, R[i + 1]),
            ('>', '<') => 0,
            _ => R[i + 1],
        };
    }
    res[N - 1] = if S[N - 2] == '>' { 0 } else { res[N - 2] + 1 };
    let ans = res.iter().sum::<i64>();

    println!("{}", ans);
}