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Ali and Shayan are playing a turn-based game on an infinite grid. Initially, all cells are white. Ali starts the game, and in the first turn, he colors one unit square black. In the following turns, each player must color a white square that shares at least one side with a black square. The game continues for exactly 2808 turns, after which each player has made 1404 moves. Let
be the set of black cells at the end of the game. Ali and Shayan respectively aim to minimize and maximise the perimeter of the shape
by playing optimally. (The perimeter of shape
is defined as the total length of the boundary segments between a black and a white cell.)
What are the possible values of the perimeter of
, assuming both players play optimally?



What are the possible values of the perimeter of
