Integers $a, b, c, d$ satisfy $a+b+c+d=0$. Show that $$n=(ab-cd)\cdot(bc-ad)\cdot(ca-bd)$$is a perfect square.
Source: Moldova EGMO TST 2023
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Integers $a, b, c, d$ satisfy $a+b+c+d=0$. Show that $$n=(ab-cd)\cdot(bc-ad)\cdot(ca-bd)$$is a perfect square.