Let Q be the cube with the set of vertices $\{(x_1,x_2,x_3)\in R^3:x_1,x_2,x_3\in \{0,1\}\}.$ Let F be the set of all twelve lines containing the diagonals of the six faces of the cube Q. Let S be the set of all four lines containing the main diagonals of the cube $Q;$ for instance, the line passing through the vertices $(0,0,0)$ and $(1,1,1)$ is in S .For lines $l_1$ and $l_2,$ let $d(l_1,l_2)$ denote the shortest distance between them. Then the maximum value of $d(l_1,l_2),$ as $l_1$ varies over F and  $l_2$ varies over $S,$ is greater than or equal to