Add lunar/moon days to calendar

Question

I want to display lunar days in normal calendar. Ex: 2018 : 5/12 = 29 (Lunar) ; 6/12 = 30 (lunar). See attached image: Red is lunar and black is gregorian. And attached code that i get in overlead (not include lunar calendar)

\documentclass[20pt,british,giant]{cdcalendar}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[utopia]{mathdesign}
\usepackage{ebgaramond}
\usepackage[defaultsans,osfigures,scale=0.94]{opensans}
\usepackage{graphicx}
\usepackage{wallpaper}
\usepackage{fontawesome}
\graphicspath{{img/}}
\usepackage[fleqn]{amsmath}

\tikzset{blue icon/.style={text=SkyBlue,font=\Large}}
\tikzset{pink icon/.style={text=Pink,font=\large}}
\tikzset{holiday/.style={rectangle,fill=orange!70}}

\geometry{a4paper}
\begin{document}
\clearpage
%%%%


%%%%%%
% Some settings for the monthly calendars
%%%%%%
\dayHeadingStyle{font=\sffamily\color{gray!90}}
\sundayColor{red!80!black}
\monthTitleStyle{font={\fontsize{40pt}{42pt}\bfseries\sffamily\itshape\selectfont}, red!50!RedViolet}
\eventStyle{\scriptsize\sffamily}

\setlength{\lessIllusSkip}{1ex}
\begin{monthCalendar}{2019}{01}
\end{monthCalendar}

\clearpage

\begin{monthCalendar}{2019}{02}

\end{monthCalendar}


\end{document}

Thank you very much