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Let $k \geq 2$ and $N_1, N_2, ..., N_k$ be positive integers. Let $S=\{(a_1,a_2,...,a_k) \in \mathbb{Z}^k:1 \leq a_i \leq N_i\}$ and $A=\{1,2,...,\prod_{i=1}^{k} N_{i}\}$. Given a bijective map $f:...