Count 'em All 22!

Hint:Let the numbers of rectangles in a $m\times n$ grid be $f(m,n)=\dfrac{mn(m+1)(n+1)}4$

Evaluate $f(20,40)+f(10,40)+f(50,18)+f(50,7)-f(20,18)-f(20,7)-f(10,18)-f(10,7)$ and get $418290$

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$\begin{array}{|c|c|c|}\hline a_1 & a_2 & a_3 \\ \hline b_1 & b_2 & b_3 \\ \hline c_1& c_2 & c_3 \\ \hline \end{array}$

Cut the rectangle into nine areas(notice that $b_2$ is the hole).

Count the rectangles in "row $a$ ( $a_1\cup a_2\cup a_3$ ,the $50 \times18$ rectangle)","row $c$ ","column $1$ ","column $3$ ".

But we counted the rectangles in $a_1,a_3,c_1,c_3$ twice,so we have to subtract it.