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)
N=int(input())
D=[0]*N
for i in range(N-1):
    a,b=map(int,raw_input().split())
    a-=1;b-=1;
    D[a]+=1
    D[b]+=1
ans=N*(N-1)*(N-2)
ans/=6
ans-=(N-1)*(N-2)
for i in D:
    if i>=2:
        ans+=(i*(i-1))/2
print ans