Soma has a tower of $63$ bricks , consisting of $6$ levels. On the $k$-th level from the top, there are $2k-1$ bricks (where $k = 1, 2, 3, 4, 5, 6$), and every brick which is not on the lowest level lies on precisely $2$ smaller bricks (which lie one level below) - see the figure. Soma takes away $7$ bricks from the tower, one by one. He can only remove a brick if there is no brick lying on it. In how many ways can he do this, if the order of removals is considered as well?