The equidistant shell of a three-dimensional body is the set of points external to it,
within a distance of no more than a given δ.
Example of equidistant shell of cube with its cross section is presented on picture.

Given an arbitrary convex polyhedron aand a value of δ.
You program must calculate volume of the equidistant shell.

Input format

Input data contains original polyhedron presented in a following format.

First there is the integer V, followed by exactly 3 ⋅ V real numbers that are coordinates of the vertices.

Next, integer E, followed by exactly 2 ⋅ E numbers of the vertices, defining the edges pairwise.

Next is the integer F, followed by exactly F faces represented in the following format.

First integer number of edges N, followed by N indices of edges of this face in an arbitrary order.

Indices of the all elements start from zero.

The floating point value of δ is written at the end of the input data.

Output format

Output data must contain the volume with an accuracy of at least 5 digits after decimal point.

Constraints

All faces are non-degenerate and convex.

Vertex coordinates are in the range from − 10 to 10.

Count of elements of each kind does not exceed 100.