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>
int main(){
    std::string s;std::cin>>s;
    int n=s.length();
    long long ans=0;
    for(int i=0,j=0;j<n;){
        for(;j<n&&s.at(j)=='<';j++);
        long long a=j-i;i=j;
        for(;j<n&&s.at(j)=='>';j++);
        long long b=j-i;i=j;
        ans+=a*(a+1)/2+b*(b+1)/2-std::min(a,b);
    }
    std::cout<<ans<<std::endl;
}

