Sets of 4 Integers a, b, c, d for which Every Integer is in form ax^2 + by^2 + cz^2 + du^2

Theorem
There are exactly $55$ sets of $4$ integers $\left\{ {a, b, c, d}\right\}$ such that all integers can be written in the form:
 * $n = a x^2 + b y^2 + c z^2 + d w^2$

for integer $x, y, z, w$.