Problem Statement

Railway company A has $N$ stations and $N−1$ tracks. The $i$-th track connects stations $u_i$ and $v_i$, and its length is $1$ km.

All stations can be reached from one another via the tracks. That is, the railway network is a tree.

In this railway company, you can ride at the initial fare if and only if the riding distance is at most $3$ km.

How many unordered pairs of $2$ distinct stations are there such that the fare between them is the initial fare?

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq u_i,v_i \leq N$ for each $i$ such that $1 \leq i \leq N-1$
• All inputs are integers
• The given graph is a tree

Input

$N$
$u_1\ v_1$
$\vdots$
$u_{N-1}\ v_{N-1}$

• $N$ is the number of stations
• For each $i$ such that $1 \leq i \leq N-1$, there is a track bidirectionally connecting station $u_i$ and station $v_i$

Output

Output the answer on one line.

Sample

5
1 2
2 3
3 4
4 5

9

8
1 2
2 3
2 4
2 5
5 6
6 7
6 8

22

2
1 2

1