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() {
  string S;
  cin >> S;
  int n = S.size();
  vector<int> a(n + 1), b(n + 1);
  for (int i = 0; i != n; ++i)
    if (S[i] == '<') a[i + 1] = a[i] + 1;
    else a[i + 1] = 0;
  for (int i = n; i; --i)
    if (S[i - 1] == '>') b[i - 1] = b[i] + 1;
    else b[i - 1] = 0;
  long long ans{};
  for (int i = 0; i <= n; ++i) ans += max(a[i], b[i]);
  cout << ans << endl;
}
