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<long long>aaa(S.size()+1,0);
 long long answer=0;
 for(long long i=0;i<S.size();i++){
     if(S.at(i)=='<'){
         aaa.at(i+1)=aaa.at(i)+1;
     }
 }
 for(long long i=S.size()-1;0<=i;i--){
     if(S.at(i)=='>'){
         if(aaa.at(i+1)>=aaa.at(i)){
             aaa.at(i)=aaa.at(i+1)+1;
         }
     }
 }
for(int i=0;i<=S.size();i++){
    answer+=aaa.at(i);
}
cout<<answer<<endl;
}