Normally, a yardstick (36 inches long) has 35 marks placed on it at one-inch intervals, numbered 1 to 35. But suppose you are given a yardstick that only has the 1", 4", 9", 16", and 25" marks on it. Using only these marks and/or the ends of the stick, how many distinct lengths can be measured with this yardstick?

For example, a length of 7" can be measured from the 9" mark to the 16" mark, and a length of 11" can be measured from the 25" mark to one end of the stick.

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