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;
	int a = 0,amax=0;
	long sum = 0;
	int down = 0;
	for (int i = 0; i < S.size(); i++)
	{

		if (S[i] == '<') {
			if (down > 0) {
				sum -= down * a;
				a = 0;
			}
			a++;
			down = 0;
			amax = a;
		}
		else {
			a--;
			down++;
			if (a < 0) {
				sum += down;//このフェーズではaをまだ足してない
				a++;
			}
		}
		sum += a;
	}
	sum -= down * a;
	cout << sum;
	return 0;
}


