In this problem we model a simple power grid. As input, we are given n houses, represented by n pairs of positive integers (x1, y1), (x2, y2), · · · , (xn, yn) which are their coordinates in the plane. We are also given a list of m power plants. Each power plant is represented by 

1. a) A pair of positive integers (a_i,b_i) representing their coordinates in the plane.
2. b) A positive integer r_i, representing the maximum distance to which the power plant
3. can send power (measured by standard Euclidean distance).
4. c) A positive integer c_i, representing the number of houses that power plant can simultaneously power.

Design an algorithm to solve the following problem: given a list of n houses and m power plants as described above, decide if it is possible to connect each house to each power plant such that all houses receive power and no power plant is over its capacity.