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

$1 \le N \le 10^5$