Net-Burn   (burning.X)

A fishing net is knit from N knots (3 <= N <= 100), labeled 1..N,
and M fibers (3 <= M <= 6,000), each with a positive integer length
Li (1 <= Li <= 1,000). Each fiber runs between two different knots.
Two or more fibers might run between the same pair of knots.

The net is to be set on fire starting at a knot of your choice. A
fire started at any knot will eventually spread throughout the net
and burn all of it. When set on fire, each fiber burns at the uniform
rate of one unit of length per second.

Each knot burns completely in D seconds, where D is the number of
fibers connected to it. A fiber starts burning at one of its ends
when the knot at that end has completely burned. A knot starts to
burn when any fiber attached to it has completely burned.

Find the minimum time to burn the entire net.

PROBLEM NAME: burning

INPUT FORMAT:

* Line 1: Two space-separated integers, N and M

* Lines 2..M+1: Each line describes a fiber using three
        space-delimited integers, respectively, the numbers of the two
        knots it connects and its length

SAMPLE INPUT:

3 4
1 2 6
1 3 4
2 1 2
3 2 5

OUTPUT FORMAT:

* Line 1: A single line with the minimum time-to-burn expressed as an
        number with exactly one decimal place.

SAMPLE OUTPUT:

11.0