Let $w, x, y, z$ be integers from $0$ to $3$ inclusive. Find the number of ordered quadruples $(w, x, y, z)$ such that $5x^2 + 5y^2 + 5z^2 - 6wx - 6wy - 6wz$ is divisible by $4$.

Let's think step by step and output the final answer within \boxed{}.
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