def problem_331():
    """
    N×N disks are placed on a square game board.
    Each disk has a black side and white side.
    At each turn, you may choose a disk and flip all the disks in the same row and the same column as this disk: thus 2×N-1 disks are flipped.
    The game ends when all disks show their white side. The following example shows a game on a 5×5 board.

    It can be proven that 3 is the minimal number of turns to finish this game.

    The bottom left disk on the N×N board has coordinates (0,0);
    the bottom right disk has coordinates (N-1,0) and the top left disk has coordinates (0,N-1).

    Let C[N] be the following configuration of a board with N×N disks:
    A disk at (x,y) satisfying , shows its black side; otherwise, it shows its white side. C[5] is shown above.
    Let T(N) be the minimal number of turns to finish a game starting from configuration C[N] or 0 if configuration C[N] is unsolvable.
    We have shown that T(5)=3. You are also given that T(10)=29 and T(1000)=395253.

    Find .
    p_331_crossflips1.gif
    p_331_crossflips2.gif
    p_331_crossflips3.gif
    """

    pass

def problem_331():
    """
    N×N disks are placed on a square game board.
    Each disk has a black side and white side.
    At each turn, you may choose a disk and flip all the disks in the same row and the same column as this disk: thus 2×N-1 disks are flipped.
    The game ends when all disks show their white side. The following example shows a game on a 5×5 board.

    It can be proven that 3 is the minimal number of turns to finish this game.

    The bottom left disk on the N×N board has coordinates (0,0);
    the bottom right disk has coordinates (N-1,0) and the top left disk has coordinates (0,N-1).

    Let C[N] be the following configuration of a board with N×N disks:
    A disk at (x,y) satisfying , shows its black side; otherwise, it shows its white side. C[5] is shown above.
    Let T(N) be the minimal number of turns to finish a game starting from configuration C[N] or 0 if configuration C[N] is unsolvable.
    We have shown that T(5)=3. You are also given that T(10)=29 and T(1000)=395253.

    Find .
    p_331_crossflips1.gif
    p_331_crossflips2.gif
    p_331_crossflips3.gif
    """

    pass

N×N disks are placed on a square game board.     Each disk has a black side and white side.     At each turn, you may choose a disk and flip all the disks in the same row and the same column as this disk: thus 2×N-1 disks are flipped.     The game ends when all disks show their white side. The following example shows a game on a 5×5 board.      It can be proven that 3 is the minimal number of turns to finish this game.      The bottom left disk on the N×N board has coordinates (0,0);     the bottom right disk has coordinates (N-1,0) and the top left disk has coordinates (0,N-1).      Let C[N] be the following configuration of a board with N×N disks:     A disk at (x,y) satisfying , shows its black side; otherwise, it shows its white side. C[5] is shown above.     Let T(N) be the minimal number of turns to finish a game starting from configuration C[N] or 0 if configuration C[N] is unsolvable.     We have shown that T(5)=3. You are also given that T(10)=29 and T(1000)=395253.      Find .     p_331_crossflips1.gif     p_331_crossflips2.gif     p_331_crossflips3.gif