Let $S=(x,y):x\in 0,1,2,3,y\in 0,1,2,3,4,\text{ and }(x,y)\ne (0,0)$. Let $T$ be the set of all right triangles whose vertices are in $S$. For every right triangle $t=△ABC$ with vertices $A,B,$ and $C$ in counter-clockwise order and right angle at $A$, let $f(t)=\cot (\angle CBA)$. What is ${\prod }_{t\in T}f(t)$?