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;
#define int long
signed main(){
	string s;
	cin>>s;
	int pos=0,n=s.size(),i,j,b=0,r=0;
	while(pos<n){
		i=j=0;
		while(s[pos+i]=='>')++i;
		while(s[pos+i+j]=='<')++j;
		if(b<=i)r-=b;
		else r-=i;
		r+=i*(i+1)/2+j*(j+1)/2;
		b=j;
		pos+=i+j;
	}
	cout<<r<<"\n";
	return 0;
}