Equilateral \triangle A B C has side length 600 . Points P and Q lie outside the plane of \triangle A B C and are on the opposite sides of the plane. Furthermore, P A=P B= P C, and Q A=Q B=Q C, and the planes of \triangle P A B and \triangle Q A B form a 120^{\circ} dihedral angle (the angle between the two planes). There is a point O whose distance from each of A, B, C, P, and Q is d. Find d.