Suppose there are the following three sets of items $($i$.$e$.,$ three transactions$)$ in a dataset:

S$1$: $\{a1,a2,a3,a4,$dots,$a99,a100\}$

$S2$:$\{a1,b2,a3,b4,$dots,$a99,b100\}$ Note: $S2$ is formed from $S1$ by replacing ai with bi if i mod $2=0$

$S3$:$\{a1,a,c3,a4,$dots,$c99,a100\},$ Note: $S3$ is formed from $S1$ by replacing aj with cj if jod$3=0$

where ai $!=$ bi $!=$ ci for i from $1$ to $100.$

Let min support $=2.$

How many frequent patterns are there in this dataset?

$2^{90}+2^{33}-2^{16}-1$

$2^{90}+2^{67}-2^{33}-1$

None of the above

$2^{90}+2^{33}+2^{16}-3$