By Legendre's three-square theorem, a positive integer can be expressed as $x^2 + y^2 + z^2$ (for non-negative integers) if and only if it is NOT of the form $4^a(8b+7)$. How many of the following integers CANNOT be written as a sum of three squares? (i) $7$ (ii) $15$ (iii) $20$ (iv) $31$