## Problem G: Jogging Trails

Gord is training for a marathon. Behind his house is a park with a large
network of jogging trails connecting water stations. Gord wants to find the
shortest jogging route that travels along every trail at least once.
Input consists of several test cases.
The first line of input for each case contains two positive integers:
*n <= 15*, the number of water stations, and *m < 1000*, the
number of trails. For each trail, there is one subsequent line of
input containing three positive integers: the first two, between
1 and *n*, indicating the water stations at the end points of the trail;
the third indicates the length of the trail, in cubits. There may be more
than one trail between any two stations; each different trail is given only
once in the input; each trail can be travelled in either direction.
It is possible to reach any trail from any other trail by visiting a
sequence of water stations connected by trails. Gord's route may start
at any water station, and must end at the same station. A single line containing 0 follows the last test
case.

For each case, there should be one line of output giving the length of
Gord's jogging route.

### Sample Input

4 5
1 2 3
2 3 4
3 4 5
1 4 10
1 3 12
0

### Output for Sample Input

41