Consider the following scoring scheme for DNA sequences. The score of a match is $+5,$ the score of a mismatch between A and G$,$ since they are both purines, is $-1,$ similarly the score of a mismatch between $C$ and $T$ is also $-1$ since they are both pyrimidines, and the score of other mismatches is $-4.$ The gap penalty is $-2.$

a$.$ Find an optimal semi$-$global alignment of the sequences:

Sequence $1$: AAGTTCGT

Sequence $2$: CAGTCCT

b$.$ Find an optimal local alignment of the sequences:

Sequence $1$: AGTGGCATT

Sequence $2$: TGTCACGT