How to center the title, the author, and the date in Tufte handout?

I've copied the source code from the tufte-common.def and modified to meet the centered alignment, here are the modified tags:

%%%%%%%%%%%%%%%%%%%%
documentclass[]{tufte-handout}

usepackage{sectsty}
allsectionsfont{centering}

usepackage{lipsum}
%%%%%%%%%%%%%%%%%%%%
% How to center them?

makeatletter
renewcommand{maketitle}{%
  newpage
  global@topnumz@% prevent floats from being placed at the top of the page
  begingroup
    setlength{parindent}{0pt}%
    setlength{parskip}{4pt}%
    let@@title@empty
    let@@author@empty
    let@@date@empty
    ifthenelse{boolean{@tufte@sfsidenotes}}{%
      gdef@@title{sffamilyLARGEallcaps{@title}par}%
      gdef@@author{sffamilyLargeallcaps{@author}par}%
      gdef@@date{sffamilyLargeallcaps{@date}par}%
    }{%
      gdef@@title{LARGEitshapecentering@titlepar}%
      gdef@@author{Largeitshapecentering@authorpar}%
      gdef@@date{Largeitshapecentering@datepar}%
    }%
    @@title
    @@author
    @@date
  endgroup
  thispagestyle{plain}% suppress the running head
  tuftebreak% add some space before the text begins
  @afterindentfalse@afterheading% suppress indentation of the next paragraph
}
makeatother

title{Homework}
author{hengxin}
date{today}

%%%%%%%%%%%%%%%%%%%%
begin{document}
maketitle
%%%%%%%%%%%%%%%%%%%%
begin{abstract}
  Abstract here~footnote{footnote}.
  lipsum[10]
end{abstract}
%%%%%%%%%%%%%%%%%%%%
begin{center}
  fbox{begin{tabular}{@{}c@{}}
    Note 1: 123456789
    Note 2: 123456789
  end{tabular}}
end{center}
%%%%%%%%%%%%%%%%%%%%
part{Part I}

lipsum[2]~footnote{problems}

$a + b = c$

section{Section 1}
%%%%%%%%%%%%%%%%%%%%
end{document}

Output