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.

Examples

Input

<>>


Output

3


Input

<>>><<><<<<<>>><


Output

28
#include <bits/stdc++.h>
using namespace std;

int main() {
  string S;
  cin>>S;
  int N=S.size();
  int64_t Z=0,l=0,r=0;
  for(int i=0;i<N;i++){
    if(S.at(i)=='<'){
      if(r!=0){
        Z+=r*(r+1)/2+l*(l+1)/2-min(l,r);
        l=0,r=0;
      }
      l++;
    }
    else{
      r++;
    }
  }
  Z+=r*(r+1)/2+l*(l+1)/2-min(l,r);
  cout<<Z<<endl;
}


