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 len = s.size();
	vector<int> a(len + 1, 0);
	for(int i = 0, j = 0; i < len; i = j){
		while(j < len && s[i] == s[j]) j++;
		int sz = j - i;
		if(s[i] == '<'){
			for(int k = i; k <= j; k++) a[k] = max(a[k], k - i);
		} else {
			for(int k = j; k >= i; k--) a[k] = max(a[k], j - k);
		}
	}
	long long ans = 0;
	for(int i = 0; i <= len; i++) ans += a[i];
	cout << ans << endl;
	return 0;
}
