OME 2019 Problem 5

We consider all pairs (x, y) of real numbers such that $0\leq x \leq y \leq 1$ .Let $M (x,y)$ the maximum value of the set $$A=\{xy, 1-x-y+xy, x+y-2xy\}.$$ Find the minimum value that $M(x,y)$ can take for all these pairs $(x,y)$ .