Given two tetrahedrons $A_1A_2A_3A_4$ and $B_1B_2B_3B_4$. Consider six pairs of edges $A_iA_j$ and $B_kB_l$, where ($i, j, k, l$) is a transposition of numbers ($1, 2, 3, 4$) (for example $A_1A_2$ and $B_3B_4$). It is known that for all but one such pairs the edges are perpendicular. Prove that the edges in the remaining pair also are perpendicular.