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Given that $P_1(x) = x^2 + a_1 x + b_1$ and $P_2(x) = x^2 + a_2 x + b_2$ are two quadratic polynomials with integer coefficients such that $P_1(m) = P_2 (n)$ , $P_1(n)= P_2(m)$ , $a_1 \ne a_2$ , and $m$ and $n$ are distinct integers. What can be said about $a_1$ + $a_2$ ?