 [m]}$ satisfying the following conditions:  -   $a_{i,j} \in X_i$  -   $a_{i,j} \ne a_{i,j'}$ for $j \ne j'$.  -   For any $\eta : [n] \to [m]$ the tuple $(a_{0,\eta(0)},\ldots,a_{n,\eta(n)})$ lies in $Y$.  