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 <bits/stdc++.h>
#define rep(i,cc,n) for(int i=cc;i<=n;++i)
using namespace std;
using ll = long long;

int main() {
  string S;
  cin >> S;

  ll ans = 0, last = 0;
  rep(i,0,S.size()-1) {
    ll cnt = 0;
    while (S[i] == S[i+cnt]) {
      cnt++;
      ans += cnt;
    }
    if (S[i] == '>') ans -= min(cnt, last);
    i += cnt - 1;
    last = cnt;
  }

  cout << ans << endl;
  return 0;
}
