In the diagram, four squares of side length $2$ are placed in the corners of a square of side length $6$. Each of the points $W$, $X$, $Y$,

In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points W, X, Y, Zand  is a vertex of one of the small squares. Square ABCD can be constructed with sides passing through W, X, Y, and Z. What is the maximum possible distance from A to P?

The answer is not sqrt34