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 s;
  cin >> s;
  ll l=0,m=0,n=s.size(),ans=0;
  s += '0';
  for(int i=0;i<n;i++){
    if(s.at(i)=='<') l++;
    else if(s.at(i)=='>') m++;
    if((s.at(i)=='>'&&s.at(i+1)=='<')||i==n-1){
      ll j=max(l,m),k= min(l,m);
      ans += j*(j+1)/2+k*(k-1)/2;
      l=0;m=0;
    }
  }
  cout << ans << endl;
}