You are given a tree with n vertices numbered 1,… ,n. A tree is an associated basic diagram without cycles. Let dist(u,v) be the number of edges in the novel basic way interfacing vertices u and v. Let diam(l,r)=maxdist(u,v) over all sets u,v with the end goal that l≤u,v≤r. Figure ∑1≤l≤r≤ndiam(l,r
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You are given a tree with n vertices numbered 1,… ,n. A tree is an associated basic diagram without cycles.
Let dist(u,v) be the number of edges in the novel basic way interfacing vertices u and v.
Let diam(l,r)=maxdist(u,v) over all sets u,v with the end goal that l≤u,v≤r.
Figure ∑1≤l≤r≤ndiam(l,r).
Input
The main line contains a solitary integer n (1≤n≤105) — the number of vertices in the tree.
The following n−1 lines depict the tree edges. Every one of these lines contains two integers u,v (1≤u,v≤n) — endpoint files of the particular tree edge. It is ensured that the edge list for sure portrays a tree.
Output
Print a solitary integer — ∑1≤l≤r≤ndiam(l,r).
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