Coordinatewise Comparability in the Unit Square

Two independent random points $(X_1,Y_1)$ and $(X_2,Y_2)$ are drawn uniformly from the unit square. What is the probability that one point is coordinatewise less than the other, i.e. either $X_1<X_2$ and $Y_1<Y_2$, or $X_1>X_2$ and $Y_1>Y_2$?