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,n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

int main(){
  string s; cin >>s;
  int n = s.size()+1;
  vector<int> a(n);
  rep(i,n){
    if(s[i]=='<'){
      a[i+1] = max(a[i+1], a[i]+1);
    }
  }
  for(int i = n-1; 0<=i; i--){
    if(s[i]=='>'){
      a[i] = max(a[i], a[i+1]+1);
    }
  }
  ll ans = 0;
  for(auto x : a){
    ans += x;
  }
  cout << ans << endl;
  return 0; 
}