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>
using namespace std;
 
int main() {
  string a;
  cin >> a;
  int b = a.size();
  vector<int> c(b+1);
  vector<int> d(b+1);
  for(int i = 0;i < b;++i){
    if(a.at(i) == '<'){c.at(i+1) = c.at(i)+1;}
  }
  for(int i = 0;i < b;++i){
    if(a.at(b-i-1) == '>'){d.at(b-i-1) = d.at(b-i)+1;}}
    long long ans = 0;
     for(int i = 0;i < b+1;++i){
       ans += max(c.at(i),d.at(i));}
    cout << ans << endl;
    
       
  }