Draw structures corresponding to the following systematic names:
(a) $(4 E)-2,4$ -Dimethylhexa-1,4-diene
(b) cis-3,3-Dimethyl-4-propylocta-1,5-diene
(c) 4 -Methylpenta-1,2-diene
(d) $(3 E, 5 Z)-2,6$ -Dimethylocta- 1,3,5,7 -tetraene
(e) 3-Butylhept-2-ene
(f) trans-2,2,5,5-Tetramethylhex-3-ene