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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  string s;
  cin >> s;
  int res = 0;
  int c = 0;
  int nr = 0;
  if (s[c] == '>')
  {
    while (s[c] == '>')
    {
      nr++;
      c++;
    }
  }
  res += nr*(nr+1)/2;
  for (int i = c; i < s.size(); ++i)
  {
    if (s[i] == '<')
    {
      int nr1 = 0, nr2 = 0;
      while (s[i] == '<')
      {
        nr1++;
        i++;
      }
      while (s[i] == '>')
      {
        nr2++;
        i++;
      }
      if (nr1 > nr2)
        res += nr1*(nr1+1)/2 + nr2*(nr2-1)/2;
      else 
        res += nr1 * (nr1-1)/2 + nr2*(nr2+1)/2;
      i--;
    }
  }
  cout << res << '\n';
}