On a $3\times3$ chess board, you must place seven knights according to the following rules:
- Immediately after placement, the knight must move to an unoccupied spot using a standard knight's move.
- Any placement where an immediate move is not possible is considered invalid.
- After being placed and moved once, the knight can never move again.
As an example, if your first placement is at A1, the knight must immediately move to either B3 or C2.
Find a series of placements and moves that allow you to place all seven knights.