Soldering     (solder.X)

The cows are playing with wires! They have learned a technique
called soldering, in which they connect two pieces of wire together
by attaching the endpoint of one wire to a location along the length
of the other. (Soldering endpoint to endpoint is not allowed.) There
can be multiple solder junctions at the same point.

The cows have a plan for an Amazing Structure they would like to
build. It is in the form of a graph with N (1 <= N <= 50,000) nodes
and N-1 edges of unit length so that each pair of nodes is connected.
Each edge is described by a pair of integers, A and B (1 <= A <=
N; 1 <= B <= N; A != B).

The cows are able to buy wire from a local store; however longer
wire is more expensive. In particular the cows can buy a wire of
length L with cost L*L, but they cannot cut wires or join wires
together.

Given the plan, the cows would like solder wires together to build
their Amazing Structure. Please help them find the minimum possible
cost!


PROBLEM NAME: solder

INPUT FORMAT:

* Line 1: A single integer: N

* Lines 2..N: Two space-separated integers describing an edge: A and B

SAMPLE INPUT:

6
1 2
1 3
1 4
1 5
1 6

OUTPUT FORMAT:

* Line 1: A single integer, the cost of soldering the tree together.
        Note that this number may not always fit in a 32-bit integer.

SAMPLE OUTPUT:

7

OUTPUT DETAILS:

Since all nodes in the structure are connected to node 1, we only need to
buy one wire of length 2 and three of length 1, for a total cost of 2 * 2 +
1 * 1 + 1 * 1 + 1 * 1 = 7.