Unable to fill color in the intersection region of $y =\sqrt{x}, y =x , using tikz by the given code. 
Please help, thanks

```
\documentclass{article}
\usepackage{tikz,pgfplots}
%\usepackage[x11names]{xcolor}
\usepackage{tikz}
\usetikzlibrary{intersections}
\pgfdeclarelayer{bg}    % declare background
\pgfsetlayers{bg,main}  % order of layers (main = standard layer)
\pgfplotsset{compat=1.13}
\usepackage{amsmath}
\usetikzlibrary{positioning}

\begin{document}

    \begin{tikzpicture}[domain=0:2, scale = 0.75, dot/.style={circle,fill,inner sep=1pt}]
    \draw(-4,0)--(4,0);
    \draw (0,-4)--(0,4);

    \draw(0,0)--(3,3);
    %\draw[black, line width = 0.50mm]   plot[smooth,domain=0:2] (\x, {\sqrt{\x}});

    \draw[blue,line width = 0.50mm]   plot[smooth,domain= 0:2,variable=\y]
    ( {3(\y)^2},\y);
    \draw(1,0)--(1,1);
    %\draw[black, line width = 0.50mm]   plot[smooth,domain= -2:2] (\y,  {(\y)^2});
    \draw(2,3)node($y=x^2$){$y=x$};
    \draw(5,2)node($x=y^2$){$\sqrt{x}=y$};
    \draw [left=.2cm](0,0)node(o){O};
    \draw[right=.1cm](1,1)node(a){A};

    \begin{pgfonlayer}{bg}    % select background
    \clip plot[smooth,domain=0:2] (\x, {\x});
    \fill[red]  plot[smooth,domain= 0:2,variable=\y] ({(\y)^2},\y);
    \end{pgfonlayer}
    \end{tikzpicture}

\end{document}

```