# Two Kinds Of Partitions

Let $$p(n)$$ be the number of partitions of $$n$$. Let $$q(n)$$ be the number of partitions of $$2n$$ into exactly $$n$$ parts. For example, $$q(3) = 3$$ because $6 = 4+1+1 = 3+2+1 = 2+2+2.$ Compute $$p(12)-q(12).$$

Definition: A partition of an integer is an expression of the integer as a sum of one or more positive integers, called parts. Two expressions consisting of the same parts written in a different order are considered the same partition ("order does not matter").

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