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>
using namespace std;
string s;
long a[500050], b;
int main() {
  cin >> s;
  int n = s.size();
  for(int i = 0; i < n; ++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] == '>') a[i] = max(a[i], a[i+1] + 1);
  for(int c : a) b += c;
  cout << b;
  return 0;
}