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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)


import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		String s = sc.next();
		int n = s.length();
		
		int []a = new int [n+1];
		Arrays.fill(a, 1000000000);
		a[0] = 0;
		a[n] = 0;
		List <Integer> l = new ArrayList<Integer>();
		
		for(int i = 0  ; i < n-1 ;i++) {
			if(s.charAt(i) == '>' && s.charAt(i+1) == '<') {
				a[i+1] = 0;
			}
			if(s.charAt(i) == '<' && s.charAt(i+1) == '>') {
				l.add(i+1);
			}
		}
		
		for(int i = 0 ; i < n ;i++) {
			if(s.charAt(i) == '<') {
				a[i+1] = a[i] + 1;
			}
		}
		
		for(int i = n-1 ; i >= 0 ; i--) {
			if(l.contains(i)) {
				a[i] = Math.max(a[i+1] + 1 ,a[i]);
				continue;
			}
			if(s.charAt(i) == '>') {
				a[i] = a[i+1] + 1;
			}
		}
		
		long ans = 0;
		
		for(int i = 0 ; i <= n ;i++) {
			ans += (long)a[i];
		}
		
		System.out.println(ans);
	}
}