Circles \omega_{1} and \omega_{2} with radii 961 and 625 , respectively, intersect at distinct points A and B. A third circle \omega is externally tangent to both \omega_{1} and \omega_{2}. Suppose line A B intersects \omega at two points P and Q such that the measure of minor arc \overparen{P Q} is 120^{\circ}. Find the distance between the centers of \omega_{1} and \omega_{2}.