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.io.*;

public class Main {

	final static long MOD = 1000000007;
	public static void main(String[] args) throws Exception {
		// TODO 自動生成されたメソッド・スタブ

		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String S = in.readLine();
		int[] a = new int[S.length()+1];
		a[0]=0;
		int i=0;
		int cnt=0;

		long sum=0;
		while(i<S.length()){
			a[i]=0;
			while(i<S.length()&&S.charAt(i)=='<'){
				a[i+1]=a[i]+1;
				i++;
			}
			while(i<S.length()&&S.charAt(i)=='>'){
				a[i+1]=a[i]-1;
				cnt++;
				i++;
			}
			if(cnt>0){
				int dif=a[i]*-1;
				for(int k=i-cnt+1;k<=i;k++){
					a[k]+=dif;
				}
				a[i-cnt]=Math.max(a[i-cnt],a[i-cnt+1]+1);
			}
			cnt=0;

		}

		for(i=0;i<a.length;i++){
			sum+=a[i];
		}
		System.out.println(sum);
	}
}