Denote by $x_1,\ x_2,\ x_3,\ x_4$ the roots of the polynomial $f(x)=x^4-4x^3-12x^2+1$. Denote $g(x)=x^2+2$. Find the value of the product $g(x_1)g(x_2)g(x_3)g(x_4) .$

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