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;
typedef long long ll;
 
int main(){
  string a,x,y;
  ll l,ans,pl,i,z;
  cin >> a;
  x=a[0];
  y=a[1];
  l=1;
  pl=0;
  ans=0;
  for(i=2;i<=(ll)a.size()+1;i++){
    if(x==y){
      l+=1;
    }
    else if(x=="<"){
      pl=l;
      ans+=(l+1)*l/2;
      l=1;
      x=y;
    }
    else{
      ans+=(l+1)*l/2-min(l,pl);
      l=1;
      x=y;
    }
    y=a[i];
  }
  cout << ans << endl;
}