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 <string>

using namespace std;

int main(){
  string S;
  cin >> S;

  int n = S.size(), a[n+1];
  for (int i = 0; i < n+1; i++){
    a[i] = 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] == '>') a[i] = max(a[i], a[i+1] + 1);
  }

  long long ans = 0;
  for (int i = 0; i < n+1; i++){
    ans += a[i];
  }
  
  printf("%lld\n", ans);
}
