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.Arrays;
import java.util.Scanner;

class Main
{
  static void do_left(String s, int[] v, int idx){
	while(idx > 0 && s.charAt(idx) == '>'){
      v[idx - 1] = Math.max(v[idx] + 1, v[idx - 1]);
      idx -= 1;
    }
  }

  static void do_right(String s, int[] v, int idx){
    while(idx < s.length() - 2 && s.charAt(idx + 1) == '<'){
      v[idx + 1] = Math.max(v[idx] + 1, v[idx + 1]);
      idx += 1;
    }
  }
  
  public static void main(String... args){
	Scanner scanner = new Scanner(System.in);
	String s = ">" + scanner.next() + "<";
    int[] v = new int[s.length() - 1];

    for(int i = 0; i < s.length() - 1; i++){
      if(s.charAt(i) == '>' && s.charAt(i + 1) == '<'){
        do_left(s, v, i);
        do_right(s, v, i);
      }
    }

    //Arrays.stream(v).forEach(x -> System.out.print(x + ","));
    //System.out.println();
	long[] sum = new long[1];
    Arrays.stream(v).forEach(x -> { sum[0] += x; });
    System.out.println(sum[0]);    
  }
}