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;
const int MAX_N = 500005;
int A[MAX_N];
string str;
long long ans;
int main(void)
{
	cin >> str;
	int n = str.size();
	for (int i = 0; i < n; i++)
	{
		if (str[i] == '<')
		{
			A[i + 1] = max(A[i + 1], A[i] + 1);
		}
	}
	for (int i = n - 1; i >= 0; i--)
	{
		if (str[i] == '>')
		{
			A[i] = max(A[i], A[i + 1] + 1);
		}
	}
	for (int i = 0; i <= n; i++)
	{
		ans += A[i];
	}
	cout << ans << endl;
	return 0;
}
