A cubic trinomial $x^3 + px + q$ with integer coefficients $p$ and $q$ is said to be irrational if it has three pairwise distinct real irrational roots $a_1,a_2, a_3$ Find all irrational cubic trinomials for which the value of $|a_1| + [a_2| + |a_3|$ is the minimal possible. (E. Barabanov)