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 <iostream>
#include <cstdio>
using namespace std;

string s;
long long sum, a[500005], b[500005];
int main() {
	int i;
	cin>> s;
	s = '.' + s;
	for(i=1; i<=s.size(); i++) {
		if(s[i]=='<') a[i] = a[i-1] + 1;
	}
	for(i=s.size(); i; i--) {
		if(s[i]=='>') b[i-1] = b[i] + 1;
	}
	for(i=0; i<=s.size(); i++) {
		sum += max(a[i], b[i]);
	}
	cout<< sum;
	return 0;
}