On every square of a chessboard, there are as many grains as shown on the picture. Starting from an arbitrary square, a knight starts a journey over the chessboard. After every move it eats up all the grains from the square it arrived to, but when it leaves, the same number of grains is put back on the square. After some time the knight returns to its initial square. Prove that the total number of grains the knight has eaten up during the journey is divisible by $3$.