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 \( \ell_1 \) and \( \ell_2 \), let \( d(\ell_1,\ell_2) \) denote the shortest distance between them. Then the maximum value of \( d(\ell_1,\ell_2) \), as \( \ell_1 \) varies over \( F \) and \( \ell_2 \) varies over \( S \), is:
