ILL 1989 Problem 50

Let $a, b, c, d,m, n \in \mathbb{Z}^+$ such that $$a^2+b^2+c^2+d^2 = 1989,$$

$$a+b+c+d = m^2,$$ and the largest of $a, b, c, d$ is $n^2.$ Determine, with proof, the values of $m$ and $n.$