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 <cmath>
#include<iostream>
#include <functional>
#include <string>
#include <sstream>
#include <vector>
#include <algorithm>
#include <stdio.h>
#include <iomanip>
using namespace std;
 
int main(){    
  string S;
  char s,s0;
  cin >> S;
  int N = S.length(); 
  int A[N+1];
  int i = 0,count = 0;
  vector<int> vec;
  vector<int> vec2;

  s0 = S[0];
  s = S[0];
  for(int i=0;i<N;i++){
    if(s == S[i]){     
      count++;
      if(i==N-1){
	vec.push_back(count);
      }
    }
    else{
      s = S[i];
       vec.push_back(count);
       count = 1;
       if(i==N-1){
	 vec.push_back(count);
       }
     }
  }

  //cout << s0 << endl;
  //for(int i=0;i<vec.size();i++){
  //  cout << vec[i] << endl;
  //}

  if(s0 == '>' && S.length() == 1){
    cout << 1 << endl;
    return 0;
  }

  if(s0 == '<'){
    for(int i=0;i<vec.size()/2;i++){
      if(vec[2*i] < vec[2*i+1]){
	vec2.push_back(vec[2*i]-1);
	vec2.push_back(vec[2*i+1]);
      }
      else{
	vec2.push_back(vec[2*i]);
	vec2.push_back(vec[2*i+1]-1);
      }
    }
    if(vec.size()%2 == 1){
      vec2.push_back(vec[vec.size()-1]);
    }
  }
  else{
    if(vec.size()%2 == 1){
       vec2.push_back(vec[0]);
      for(int i=0;i<vec.size()/2;i++){
	if(vec[2*i+1] < vec[2*i+2]){
	vec2.push_back(vec[2*i+1]-1);
	vec2.push_back(vec[2*i+2]);
	}
	else{
	  vec2.push_back(vec[2*i+1]);
	  vec2.push_back(vec[2*i+2]-1);
	}
      }
    }
    else{
      vec2.push_back(vec[0]);
      for(int i=0;i<vec.size()/2 - 1;i++){
	if(vec[2*i+1] < vec[2*i+2]){
	  vec2.push_back(vec[2*i+1]-1);
	  vec2.push_back(vec[2*i+2]);
	}
	else{
	  vec2.push_back(vec[2*i+1]);
	  vec2.push_back(vec[2*i+2]-1);
	}
      }
      vec2.push_back(vec[vec.size()-1]);
    }
  }


  long long k;
  int sum=0;
  for(int i=0;i<vec2.size();i++){
    k = vec2[i];
    sum += (k*(k+1))/2;
  }

  cout << sum << endl;
  
}