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Logic: 4b->4b LUT

There is nothing to enjoy. This is challenge for implementing complex logic.

Puzzle requires implementation of LookUpTable with 4 bit input and 4 bit output.
Map already contains sequence generator (numbers from 0-15, then random numbers, total of 50 numbers), one LUT to encode inputs (huge black box), comparator (to check your solution gives valid results) and clock.

Your task is to create circuit, that converts back numbers, that enter huge black box: you take output from black box, and have to convert them to signals that originally entered black box (conduits that go to black box are covered with invisible blocks, so you cant tap them). Your circuit must be fast: must produce output within 2 cycles after change of black box outputs.

Black box conversion is described by: {3,8,15,1,10,6,5,11,14,13,4,2,7,0,9,12} [serpent SBox 0]