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 _GLIBCXX_DEBUG

using namespace std;
using ll = long long;

int		main(void)
{
	string S;

	cin >> S;
	int i = 0;
	ll sum = 0, s1, s2;

	while (S[i])
	{
		s1 = 0;
		while (S[i] == '<')
		{
			s1++;
			i++;
		}
		s2 = 0;
		while (S[i] == '>')
		{
			s2++;
			i++;
		}
		s1 < s2 ? s1-- : s2--;
		sum += ((1 + s1) * s1 / 2) + ((1 + s2) * s2 / 2);
	}
	cout << sum << endl;
}
