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(void){
   string S;
   cin>>S;
   int N=S.size();
   vector<int> A(N+1,0);
   for(int i=0;i<N;i++){
      if(S[i]=='<'){
         A[i+1]=max(A[i+1],A[i]+1);
      }
   }
   for(int i=N-1;i>=0;i--){
      if(S[i]=='>'){
         A[i]=max(A[i+1]+1,A[i]);
      }
   }
   long long ans=0;
   for(int i=0;i<N+1;i++){
      ans+=A[i];
   }
   cout<<ans<<endl;
   return 0;
}
