Chef and Lost Story

Once upon a time, in a land far, far away... nevermind, we don't recall the rest of the story. All we know is that Chef has a matrix of integers $M$ with $N$ rows and $N$ columns; he wants to take a single element from each row and a single element from each column ($N$ elements in total) and find their [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Find the set of all valu