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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use proconio::marker::Chars;

#[derive(Debug, Clone, Copy)]
enum Val {
    Less(usize),
    Greater(usize),
}

fn main() {
    input! {
        s: Chars,
    }

    let mut v = vec![];

    for &c in s.iter() {
        if let Some(p) = v.last_mut() {
            match (c, p) {
                ('<', Val::Less(n)) => {
                    *n += 1;
                },
                ('<', Val::Greater(_)) => {
                    v.push(Val::Less(1));
                },
                ('>', Val::Less(_)) => {
                    v.push(Val::Greater(1));
                },
                ('>', Val::Greater(n)) => {
                    *n += 1;
                }
                _ => {},
            }
        } else {
            match c {
                '<' => {
                    v.push(Val::Less(1));
                },
                '>' => {
                    v.push(Val::Greater(1));
                },
                _ => {},
            }
        }
    }
    let mut nums = vec![];
    for e in v.into_iter() {
        match e {
            Val::Less(n) => {
                if nums.is_empty() {
                    nums.push(0);
                }

                for i in 1..=n {
                    nums.push(i);
                }
            }
            Val::Greater(n) => {
                if nums.is_empty() {
                    nums.push(n);
                }
                if let Some(last) = nums.last_mut() {
                    if *last < n {
                        *last = n;
                    } 
                }
                for i in (0..n).rev() {
                    nums.push(i);
                }
            }
        }
    }
    let ans = nums.into_iter().sum::<usize>();
    println!("{}", ans);
}