Ninety-four bricks, each measuring \(4''\times10''\times19'',\) are to be stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes \(4''\,\) or \(10''\,\) or \(19''\,\) to the total height of the tower. How many different tower heights can be achieved using all 94 of the bricks?

(第十二届AIME1994 第11题)