P3540 [POI 2012] SQU-Squarks

A famous Byteotian physicist Byteasar is studying a new constituent of matter - squarks. These are quite exotic particles that never exist alone but always in pairs. Moreover, squarks of a particular kind form pairs only with squarks of different kinds. After years of studies Byteasar has established that there are  different kinds of squarks. Squarks of each kind have a unique mass, which is a positive integer multiple of (an appropriate) unit. Byteasar has also measured the total mass of each of the  possible pairs of squarks. According to standard Byteotian model of physics, the mass of a pair of squarks equals the sum of the masses of the two squarks forming it. Now Byteasar desires to determine the individual masses of squarks of every kind. He has asked your help in writing a program that will determine all solutions to this puzzle, i.e., will reconstruct all configurations of squark masses that are consistent with his previous measurements.

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