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D. Polo the Penguin and Trees

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle 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 ≤
*a*<*b*≤*n*; - 1 ≤
*c*<*d*≤*n*; - there's no such node that lies on both the shortest path from node
*a*to node*b*and from node*c*to node*d*.

The shortest path betweem two nodes is the path that is shortest in the number of edges.

Help Polo solve this problem.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 80000) — the number of tree nodes. Each of the following *n* - 1 lines contains a pair of integers *u*_{i} and *v*_{i} (1 ≤ *u*_{i}, *v*_{i} ≤ *n*; *u*_{i} ≠ *v*_{i}) — the *i*-th edge of the tree.

It is guaranteed that the given graph is a tree.

Output

In a single line print a single integer — the answer to the problem.

Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is recommended to use the cin, cout streams or the %I64d specificator.

Examples

Input

4

1 2

2 3

3 4

Output

2

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