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;
  vector<int>v(s.size()+1,0);
   for( int i=0;i<s.size();i++)
   {
     if(s[i]=='<')
       v[i+1]=max(v[i+1],v[i]+1);
   }
  for( int i=s.size()-1;i>=0;i--)
    if(s[i]=='>')
      v[i]=max(v[i+1]+1,v[i]);
  long long sum=0;
  for( int i=0;i<v.size();i++)
    sum+=v[i];
  cout<<sum<<"\n";
  return 0;
}
