READ ALL INSTRUCTIONS AND TEST CASES CAREFULLY:

$10)$ Problem $5$: Construct an NFA to recognize strings from $\backslash$Sigma $=\{0,1,2\}$ having a substring

x$=10^($i$)1,$"where i is a mupltiple of $2,3,$ or $6,$i $>0$

in $8$ or fewer states $(-50(\%)/()$ extra state$).$For the test cases, the first six should ACCEPT, the last six should REJECT.

$1001$

$10001$

$10000001$

$21210012121$

$212100000001210001$

$21021011100011$

$111111$

$1000001$

$1210121000001212$

$212102012121$

$212100000001210000021$

$201021010101010000011$