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 s;
	cin>>s;
	long long l = s.length();
	long long res = 0,i = 0;
	while(i<l)
	{
		long long p = 0, q = 0;
		while(s[i]=='<' && i<l)
		{
			i++;
			p++;
		}
		while(s[i]=='>' && i<l)
		{
			i++;
			q++;
		}
		if(p<q)
			swap(p,q);
		p = p*(p+1)/2;
		q = q*(q-1)/2;
		res+= p + q;
	}
	cout<<res<<'\n';
}