Let \(a\), \(b\), and \(c\) be the roots of the polynomial \(x^3 + 4x^2 - 7x - 1\). Find the polynomial that has roots \(ab\), \(bc\), and \(ac\). The original answer is in the form \(mx^3 + nx^2 + px + q\). Please give the value of \(m + n + p + q\).

Let's think step by step and output the final answer within \boxed{}.
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