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;
char p;
int l, lp;
long long r;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  string s;
  cin >> s;
  for(char c: s) {
    if(c != p) {
      if(c == '<')
        r -= l < lp ? l : lp;
      p = c; lp = l; l = 0;
    }
    r += ++l;
  }
  if(p == '>')
    r -= l < lp ? l : lp;
  cout << r << '\n';
  return 0;
}
