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; 
int main(){
string s;
cin>>s;
int n  = (int)s.size();
vector<int> a(n+1);
for(int i=0;i<n;i++){
if(s[i]=='<'){
a[i+1] = max(a[i+1],a[i]+1);
}
}
for(int i=n-1;i>=0;--i){
if(s[i]=='>'){
a[i] = max(a[i],a[i+1]+1);
}
}
long long ans=0;
for(int i=0;i<=n;i++){
ans+=a[i];
}
cout<<ans<<endl;


}