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 <iostream>
#include <vector>
using namespace std;
using ll=long long;

int main() {
  string S; cin>>S;
  int N=S.size();
  vector<int> A(N+1);
  for(int i=0; i<N; i++){
    if(S.at(i)=='<') A.at(i+1)=A.at(i)+1;
  }
  for (int i=N-1; i>=0; i--){
    if(S.at(i)=='>' && A.at(i)<=A.at(i+1)) A.at(i)=A.at(i+1)+1;
  }
  ll answer=0;
  for(int i=0; i<=N; i++) answer+=A.at(i);
  cout<<answer<<endl;
}
