Implement the following boolean function with $4 \times 1$ multiplexer and external gates, connect A and B to selection lines. The input requirement for the four lines will be a function of C and D. These values are obtained by expressing F as a function of C and D for each of the four cases when AB= 00,01,10 and 11. These functions may have to be implemented with the external gates.
$F(A,B,C,D) = \sum(1,3,4,11,12,13,14,15)$