We call a polynomial P square-friendly if it is monic, has integer coefficients, and there is a polynomial Q for which P\left(n^{2}\right)=P(n) Q(n) for all integers n. We say P is minimally square-friendly if it is square-friendly and cannot be written as the product of nonconstant, square-friendly polynomials. Determine the number of nonconstant, minimally square-friendly polynomials of degree at most 12.