Problems with order in crossings tikzcd

I need to draw the following diagram

but I don’t know how to use crossing over in order to make the arrow that goes from C to B cross over the rest.

• Is it possible to do so?

Here is my code. How should I modify it assuming it is possible?

documentclass{article}
usepackage{tikz-cd}
begin{document}
begin{tikzcd}
& A arrow{rr} arrow{d} & & B arrow{d} \
C arrow{ur} arrow[bend right = 50]{urrr} arrow{d} & D arrow{rr}& & E\
F arrow{ur} arrow[bend right = 50]{urrr} & & &
end{tikzcd}
end{document}

arrow[from=2-1,to=1-4,bend right = 50,crossing over]{urrr}

documentclass{article}
usepackage{tikz-cd}
begin{document}
begin{tikzcd}
& A arrow{rr} arrow{d} & & B arrow{d} \
C arrow[ur]  arrow{d} & D arrow[rr]& & E\
F arrow[ur] arrow[bend right = 50]{urrr} & & &
arrow[from=2-1,to=1-4,bend right = 50,crossing over]{urrr}
end{tikzcd}

end{document}