The game of Hex is played on an n times n board composed of hexagonal cells. Two players take placing black and white stones on the cells (see figure 1 for an illustration of a hex game in progress). If the upper left and lower right sides are connected to each other by a path of black stones, the black player wins. If the lower left and upper right sides are connected to each other by a path of white stones, the white player wins. Formalizer the problem of detecting when one of the players has won and show how union-find can help with this problem. Provide some details as to the resulting running-time of your approach