INMO 2015 Problem 6

From a set of 11 square integers, show that one can choose 6 numbers $a^{2}, b^{2}, c^{2}, d^{2}, e^{2}, f^{2}$ such that

$$a^{2}+b^{2}+c^{2} \equiv d^{2}+e^{2}+f^{2} (\bmod 12)$$