The door to Prof. Adams laboratory has one of those keypad locks that requires entering five digits to open. Unfortunately, he has a hard time remembering the combination, but he has figured out a way to determine it.

The five digits are all different, and he has observed that the first two digits form a perfect square, while the last two digits form a smaller perfect square. Also, the middle digit is the smallest. If he arranges the five digits to form all possible five-digit integers (leading zeros allowed) and adds all these numbers, the sum is a palindrome, with each of its digits a multiple of three.

What is the combination?