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;

long long ans;
int n; 
string s;
int num[500005];

int main()
{
	cin >> s;
	n=s.length()+1;
	for(int i=0;i<s.length();i++) if(s[i]=='<') num[i+2]=max(num[i+1]+1,num[i+2]);
	for(int i=s.length()-1;i>=0;i--) if(s[i]=='>') num[i+1]=max(num[i+2]+1,num[i+1]);
	for(int i=1;i<=n;i++) ans+=num[i];
	cout << ans << endl;
	return 0;
}
