480 one-centimeter unit cubes are used to build a block measuring 6 cm by 8 cm by 10 cm. A tiny ant then chews its way in a straight line from one vertex of the block to the furthest vertex. How many cubes does the ant pass through? The ant is so tiny that it does not "pass through" cubes if it is merely passing through where their edges or vertices meet.

Let's think step by step and output the final answer within \boxed{}.
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