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(){
  int N;
  string S;
  cin >> S;
  N = S.size() + 1;
  
  vector<int> a(N, 0);
  for(int i = 0; i < N - 1; 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 - 1] == '>'){
      a[i - 1] = max(a[i] + 1, a[i - 1]);
    }
  }
  
  long long sum = 0;
  for(int x : a) sum += x;
  
  cout << sum << endl;
  
  return 0;
}