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There is a framework of a cuboid of length 6, breadth 5 and height 7. The cuboid is only composed of a skeleton of 210 cubes of side 1. An insect is on one corner of the cube and it wants to travel to the opposite end of the longest diagonal. It can only travel along the sides of the small cubes and it always takes the shortest possible route.
Find the number of choices the insect has.