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;int64_t ans=0;std::vector<int>A(S.size()+1);for(int i=0;i<S.size();i++)if(S.at(i)=='<')A[i+1]=std::max(A[i+1],A[i]+1);for(int i=S.size()-1;i>=0;i--)if(S.at(i)=='>')A[i]=std::max(A[i],A[i+1]+1);for(int i=0;i<=S.size();i++)ans+=A[i];std::cout<<ans<<std::endl;}