Problem Desrcription
Shil likes to play with trees a lot.He is playing with an undirected tree containing N nodes.He wants to find out total number of unordered triplets (A,B,C) such that A is not connected to B, B is not connected to C and A is not connected to C by a direct edge (No two of A, B, C are mutually connected). Since he doesn't like to play with this alone , he asks for your help.

Input
The first line of each test case contains a single integer N denoting the number of nodes.
Next N - 1 lines consists of two integers u and v describing an edge from u to v

Output
Output a single line containing total number of triplets.

Constraints

1 ≤ N ≤ 10^5
1 ≤ u, v ≤ N

Example
Input:
5
1 2
1 3
3 4
2 5

Output:
1

Explanation
The only possible triplet is (1,4,5)

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