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(void) {
  string S;
  cin >> S;
  int n = S.size();

  vector<int> A(n + 1, 0);
  for (int i = 0; i < n; ++i) {
    if (S[i] == '<') A[i + 1] = A[i] + 1;
  }
  for (int i = n; i >= 0; --i) {
    if (S[i] == '>' && A[i] <= A[i + 1]) A[i] = A[i + 1] + 1;
  }

  int64_t answer = 0;
  for (auto n : A) answer += n;
  cout << answer << endl;
  return 0;
}