Given $S_0\cup S_1=T_0\cup T_1=\{0,1\}^n$, $S_0\cap S_1=T_0\cap T_1=\emptyset$, with $|S_i|=|T_i|$ for both $i\in\{0,1\}$, what is degree of transformation that simultaneously maps $S_i$ to $T_i$ for both $i\in\{0,1\}$?
What is the maximum absolute value of any entry in the coefficient of transformation equations?
Note that transformation can be multilinear ($x_i^c=x_i\forall c\in\Bbb N$) since we seek to transform $\{0,1\}^n$. Hence total degree of transformation is at most $n$.