\documentclass[lettersize,journal]{IEEEtran}
\usepackage{amsmath,amsfonts}
\usepackage{algorithmic}
\usepackage{algorithm}
\usepackage{array}
\usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
\usepackage{textcomp}
\usepackage{stfloats}
\usepackage{url}
\usepackage{verbatim}
\usepackage{graphicx}
\usepackage{cite}
\hyphenation{op-tical net-works semi-conduc-tor IEEE-Xplore}
% updated with editorial comments 8/9/2021

\begin{document}

\title{Non-ergodicity of Game 2048}

\author{Xingguo Chen,  Xinwen Li, Shangdong Yang, and Wenhao Wang
\thanks{Manuscript received XXXX; revised XXXX; accepted XXXX.
Date of publication XXXX; date of current version XXXX. The work was supported
by the National Natural Science Foundation, China (Nos. 62276142, 62206133, and 62202240).}
\IEEEcompsocitemizethanks{
\IEEEcompsocthanksitem X. Chen,  X. Li and S. Yang are
 with  the Jiangsu Key Laboratory of Big Data Security \&
Intelligent Processing, Nanjing University of Posts and Telecommunications,
 P.R., China \protect (e-mail:
chenxg@njupt.edu.cn).}%
\IEEEcompsocitemizethanks{
\IEEEcompsocthanksitem W. Wang is 
 with College of Electronic Engineering, National University of Defense Technology, 
 P.R., China \protect (e-mail:
wangwenhao11@nudt.edu.cn).
\emph{(Corresponding author: W. Wang.)}%
}

}

% The paper headers
\markboth{IEEE Transaction on Games,~Vol.~14, No.~8, August~202X}%
{Shell \MakeLowercase{\textit{et al.}}: A Sample Article Using IEEEtran.cls for IEEE Journals}

\IEEEpubid{0000--0000/00\$00.00~\copyright~2024 IEEE}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark.

\maketitle

\begin{abstract}

\end{abstract}

\begin{IEEEkeywords}

\end{IEEEkeywords}

\input{main/introduction}
\input{main/nonergodicity}

 
\bibliographystyle{IEEEtran.bst}
%\bibliography{bibliography/IEEEabrv,bibliography/IEEEexample}
\bibliography{references.bib} 


\end{document}


