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;
const int N=500005;
char s[N];
int l[N],r[N];
int main(){
	scanf("%s",s);
	int n=strlen(s)+1;
	l[n]=0;r[n]=n;
	for (int i=n-1;i;i--)
		if (s[i-1]=='<')l[i]=0,r[i]=r[i+1]-1;
		else l[i]=l[i+1]+1,r[i]=n;
	int now=l[1];long long ans=now;
	for (int i=2;i<=n;i++)
		if (s[i-2]=='<')now=max(now+1,l[i]),ans+=now;
		else now=l[i],ans+=now;
	printf("%lld\n",ans);
}