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;
  long long int p=0,x=0;
  while(p<S.size()){
    long long int i=0,j=0;
    while(p+i<S.size()&&S.at(p+i)=='<')i++;
    while(p+i+j<S.size()&&S.at(p+i+j)=='>')j++;
    x+=i*(i+1)/2+j*(j+1)/2-min(i,j);
    p+=i+j;
  }
  cout<<x<<endl;
}