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;

typedef unsigned long long ull;
typedef long long ll;

int main(){
	string s;
	cin >> s;
	int n=s.length();
	s=s+'/';

	vector<ll> v;
	if(s[0]=='>') v.push_back(0);
	ll cnt=1;
	for(int i=1; i<=n; i++){
		if(s[i]!=s[i-1]){
			v.push_back(cnt);
			cnt=1;
		}else cnt++;
	}
	if(s[n-1]=='<') v.push_back(0);

	ll a=0;
	for(int i=0; i<v.size(); i+=2){
		a+=v[i]*v[i]+v[i+1]*v[i+1]+abs(v[i]-v[i+1]);
	}
	cout << a/2 << endl;
	return 0;
}