Molecular Energy

This problem was long proposed in BIOCAD, and they expected it to be programmed for CUDA / OpenCL - however after testing it a bit I think it is good enough for any language.

The task is to calculate intra-molecular energy - simply as a sum of energy (electrostatic) between every pair of atoms in it, regarding atoms as a dimensionless charges. E.g. energy attracting two atoms, A and B is calculated like this:

                   Q(A) * Q(B)
E(A, B)   =   C * -------------
                     R(A, B)

Here Q(x) is the charge of the atom and R(m, n) is the distance between two atoms. You will be given charges and coordinates. Constant factor is C = 1389.38757.

However amendment to the calculated energy value should be made due to bonds between atoms:

• if there exists a chain of 3 bonds linking the two atoms, their energy should be halved;
• if there exists even a shorter chain, the energy of this atom pair is nullified at all.

Input: The first line gives Na - number of atoms in molecule.
Then Na lines follow, each with four values Xi Yi Zi Qi - coordinates and charge of i-th atom.
Next here comes line with single value Nb - number of bonds.
It is followed by Nb lines, each containing a pair of integers - indices of atoms which have a bond between them. Bonds are bi-directional, atom indices are zero-based.

Answer: resultant energy, rounded to nearest integer.