Pat has made up a list of 5-digit perfect squares (all different) which use only the digits 0 through 4, none of them starting or ending with a zero. Each of the digits 0 through 4 is used a different number of times, those numbers of times being 5 through 9.

Mike has also chosen some 5-digit perfect squares, but using only the digits from 5 through 9. Each of his digits 5 through 9 is used a different number of times in his squares, those numbers of times being 0 through 4.

What were the eligible squares for each of Pat and Mike, based on their constituent digits? Which of them did each actually use?