Consider the lines L1 and L2 defined by
L1: x√2 + y − 1 = 0 and L2: x√2 − y + 1 = 0.
For a fixed constant λ, let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P from L2 is λ2. The line y = 2x + 1 meets C at two points R and S, where the distance between R and S is √270. Let the perpendicular bisector of RS meet C at two distinct points R′ and S′. Let D be the square of the distance between R′ and S′.
The value of λ² is ___.