IMO 1989 - Shortlist problems Question 15

(IRE 1) Let $a,b,c,d,m,n$ be positive integers 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 $n$.