You are given a rooted tree with \(N\) nodes and node 1 as a root. There is a unique path between any two nodes. Here, \(d(i,j)\) is defined as a number of edges in a unique path between nodes \(i\) and \(j\).

You have to find the number of pairs \((i,\ j)\) such that and \(d(i,j) = d(i,1)-d(j,1)\).

Input format

• The first line contains \(n\) denoting the integer.
• Next \(n - 1\) lines denote the edges of the tree.

Output format

Print a single integer denoting the number of pairs \((i,\ j)\) such that and \(d(i,j) = d(i,1)-d(j,1)\).

Constraints

\(1 \le N \le 10^5\)