Name the quadrilateral

You will write three functions that name a quadrilateral from its four corners. The checker uses a rectangle, a rhombus, a square, a plain parallelogram and a shape that is not a parallelogram.

The idea. In a parallelogram $ABCD$, $A + C = B + D$. A rectangle has equal diagonals. A rhombus has equal adjacent sides. A square has both. Squared lengths keep the numbers exact.

Your tasks.

1. Finish sq(p, q). Return the squared distance between two points.
2. Finish is_parallelogram(a, b, c, d). Return True if the diagonals have the same midpoint.
3. Finish classify(a, b, c, d). Return one of "not a parallelogram", "parallelogram", "rectangle", "rhombus" or "square".