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>
#define N 500100
using namespace std;
char s[N];
int a[N];
int main(){
	scanf("%s",s);
	int n=strlen(s)+1;
	long long ans=0;
	for(int i=0;i<n;i++){
		if((i<=0||s[i-1]=='>')&&(i>=n-1||s[i]=='<')){
			a[i]=0;
			for(int j=1;i-j>=0&&s[i-j]=='>';j++){
				a[i-j]=max(a[i-j],j);
			}
			for(int j=1;i+j<n&&s[i+j-1]=='<';j++){
				a[i+j]=max(a[i+j],j);
			}
		}
	}
	for(int i=0;i<n;i++) ans+=a[i];
	cout<<ans<<endl;
	return 0;
}