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;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  string s;
  cin >> s;
  int n = (int)s.size();
  vector<int> v(n + 1, 0);
  for (int i = 0; i < n; i++) {
    if (s[i] == '<') v[i + 1] = v[i] + 1;
  }
  long long ans = v[n];
  for (int i = n - 1; ~i; i--) {
    if (s[i] == '>') v[i] = max(v[i], v[i + 1] + 1);
    ans += v[i];
  }
  cout << ans;
  return 0;
}
