Find the minimum sum of products and the minimum product of sums for the function

f(a, b, c, d) = ?m(1, 3, 4, 11) + ?d(2, 7, 8, 12, 14, 15).

F(A, B, C, D, E) = ?m(0, 1, 2, 6, 7, 9, 10, 15, 16, 18, 20, 21, 27, 30) + ?d(3, 4, 11, 12, 19).

Find a minimum product-of-sums solution for f for the function and identify the essential prime implicants.

F(a, b, c, d, e) = ?m(2, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 27, 28, 29, 31) + ?d(1, 30)