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+1,0);
  for(int i=0;i<n;i++){
    if(s[i]=='<'){
      a[i+1] = a[i]+1;
    }
  }

  for(int i=n-1;i>=0;i--){
    if(s[i]=='>'){
      int add = a[i+1]+1;
      if(a[i] < add){
        a[i] = add;
      }
    }
  }

  ll sum = 0;
  for(int i=0;i<n+1;i++){
    sum += a[i];
  }

  cout << sum << endl;
}
