Find the minimum product of sums for the following function.

Each drop down menu has a number of choices. You must select an answer from each drop down menu. The choices include possible terms in the function. Another choice is "none", and should be used when none of the terms from that drop down menu are needed for the minimum solution. Finally, the choice "two or more" should be selected if more than one of the possible terms appearing in that drop down menu are required for the solution.

There are too many possible $3$ and $4$ literal terms for automatic checking, so just select how many of them are required.

$f(a,b,c,d)={\displaystyle \underset{?}{\overset{?}{}}}m(0,1,2,3,8,9,13)+{\displaystyle \underset{?}{\overset{?}{}}}d(7,12)$

Terms involving a and b:

Terms involving a and $c$ :

Terms involving a and d:

Terms involving $b$ and $c$ :

Terms involving $b$ and $d$ :

Terms involving $c$ and $d$ : $c+d$

Terms involving $3$ literals:

Terms involving $4$ literals: