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For every $i \in \{0,\ldots,n\}$ (where $n$ is the length of the array) and for every $a,b,c \in \{0,\ldots,15\}$, we determine whether it is possible to partition the first $i$ elements of the array into four subsets, the first three of which XOR to $a,b,c$, respectively. We also compute the XOR of the entire array. Using the information for $i = n$, we can ...

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