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: Accepted)

import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		char c[] = sc.nextLine().toCharArray();
		sc.close();
		int n = c.length + 1;
		long sum = 0;
		int l=0,s=0;
		int start = 0;
		if(c[0]=='>') {
			for(int i=0; i<n-1 ;i++) {
				if(c[i]=='>') {
					start ++;
				}else {
					break;
				}
			}
		}
		sum += calc(start);

		for(int i=start; i<n-1; ) {
			l=0;
			s=0;
			while(i<n-1 && c[i]=='<') {
				s++;
				i++;
			}
			while(i<n-1 && c[i]=='>') {
				l++;
				i++;
			}
			sum += calc(s,l);
		}
		System.out.println(sum);
	}

	public static long calc(long a, long b) {
		if(a <= b) {
			return b*(b+1)/2 + a*(a-1)/2;
		}else {
			return a*(a+1)/2 + b*(b-1)/2;
		}
	}
	public static long calc(long a) {
		return a*(a+1)/2;
	}

}