[16.4] Divide an $8 \times 8$ chessboard with alternating black and white squares into $K$ rectangles, keeping the squares intact, and satisfying the following conditions:
(i) Each rectangle contains an equal number of white and black squares;
(ii) Let $a_{i}$ be the number of white squares in the $i$-th rectangle, then $a_{1}<a_{2}<\cdots<a_{K}$. Determine the maximum value of $K$ that satisfies these conditions, and for this maximum value of $K$, find all possible values of $a_{1}, a_{2}, \cdots, a_{K}$.