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:

• $1 ≤ *a* < *b* ≤ *n*$;
• $1 ≤ *c* < *d* ≤ *n*$;
• 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.