For \(p,q \in R\), consider the real valued function \(f(x) = (x - p)^{2} - q,x \in R\) and \(q > 0\). Let \(a_{1},a_{2},a_{3}\) and \(a_{4}\) be in an arithmetic progression with mean \(p\) and positive common difference. If \(\left| f\left( a_{i} \right) \right| = 500\) for all \(i = 1,2,3\), 4 , then the absolute difference between the roots of \(f(x) = 0\) is