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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
//これは嘘
$s=trim(fgets(STDIN)).">";
$n=strlen($s);
$key=array_keys(str_split($s),"<");
if($key != null){
  $ans=array_fill(0,$n,0);
  $m=count($key);
  $c=0;
  $i=0;
  $key=array_flip($key);
  while($i<$n){
    if(isset($key[$i])){
      if(isset($key[$i-1])){
        $ans[$i]=$ans[$i-1]+1;
      }
      ++$i;
    }else{
      $c=$i;
      while($i<$n && !isset($key[$i])){
        ++$i;
      }
      $ans[$c]=max($ans[$c-1]+1,$i-$c);
      ++$c;
      while($c<$i){
        $ans[$c]=$i-$c;
        ++$c;
      }
    }
  }
  echo array_sum($ans);
}else{
  echo (int)($n-1)*$n/2;
}