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: Accepted)

#include <bits/stdc++.h>

using namespace std;

int main(){
  string s;
  char c;
  int64_t ans=0;
  cin >> s;
  vector<int> a(s.size()+1);
  vector<int> b(s.size()+1);
  a.front() = 0;
  b.back() = 0;

  for(int i=0;i<s.size();i++){
    if(s.at(i) == '<'){
      a.at(i+1) = a.at(i)+1;
    }
    else{
      a.at(i+1) = 0;
    }
  }

  for(int i=s.size()-1;i>=0;i--){
    if(s.at(i) == '>'){
      b.at(i) = b.at(i+1)+1;
    }
    else{
      b.at(i) = 0;
    }
  }

  for(int i=0;i<s.size()+1;i++){
    //cout << a.at(i) << "  " << b.at(i) << endl;
    ans = ans + max(a.at(i),b.at(i));
  }

  cout << ans << endl;

  return 0;
}