Statement

Alessandro and Giorgio are having an argument about who is better at the popular game Colorpoints and, to prevent the situation from escalating, Giorgio posed Alessandro a challenge: if he manages to beat it, Giorgio will admit his superiority. The challenge is obviously nothing but an insidious game of Colorpoints. Colorpoints is a solitaire game where there are N blue points on the cartesian plane. The points are indexed from 0 to N-1, with the i-th point located at (x_i, y_i). In order to win, Alessandro must select some of the blue points and color them red so that, for each column and row, the number of blue points is double the number of red points. Note that some games are unwinnable, which means that a winning coloring does not exist. Given the coordinates of the points, help Alessandro find a winning coloring or determine that the game is unwinnable.