There is a chip in one of the squares on the checkered board. In one move, she can move either $1$ square to the right, or diagonally $1$ to the left and $1$ up, or $1$ to the left and $3$ down (see Fig.). The chip made $n$ moves and returned to the starting square. Prove that a) $n$ is divisible by $2$, b) $n$ is divisible by $8$. K.A.Sukhov

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