CF288D Polo the Penguin and Trees

Little penguin Polo has got a tree — a non-directed connected acyclic graph, containing $ n $ nodes and $ n-1 $ edges. We will consider the tree nodes numbered by integers from 1 to $ n $ . Today Polo wonders, how to find the number of pairs of paths that don't have common nodes. More formally, he should find the number of groups of four integers $ a,b,c $ and $ d $ such that: - $ 1

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