Draw structures corresponding to the following systematic names:
(a) $(4 E)-2,4-$ Dimethyl-1, 4 -hexadiene
(b) cis-3,3-Dimethyl-4-propyl-1,5-octadiene
(c) 4-Methyl-1,2-pentadiene
(d) $(3 E, 5 Z)-2,6$ -Dimethyl- 1,3,5,7 -octatetraene
(e) 3-Butyl-2-heptene
(f) trans-2,2,5,5 -Tetramethyl-3-hexene