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 sum=0;
  vector<int> a(s.size()+1);
  for(int i=0; i<s.size(); i++){
    if(s[i]=='<'){
      a[i+1]=max(a[i+1],a[i]+1);
    }
  }
  for(int i=0; i<s.size(); i++){
    if(s[s.size()-i-1]=='>'){
      a[s.size()-i-1]=max(a[s.size()-i]+1,a[s.size()-i-1]);
    }
  }
  for(int i=0; i<=s.size(); i++){
    sum+=a[i];
  }
  cout << sum << endl;
}