Chinese Postman Problem

For a given weighted undirected graph G(V, E), find the distance of the shortest route that meets the following criteria:

• It is a closed cycle where it ends at the same point it starts.
• The route must go through every edge at least once.

Input

|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

s_i and t_i represent source and target verticess of i-th edge (undirected) and d_i represents the distance between s_i and t_i (the i-th edge).

Note that there can be multiple edges between a pair of vertices.

Output

Print the shortest distance in a line.

Constraints

• 2 ≤ |V| ≤ 15
• 0 ≤ |E| ≤ 1,000
• 0 ≤ d_i ≤ 1,000
• s_i ≠ t_i
• The graph is connected

Sample Input 1

4 4
0 1 1
0 2 2
1 3 3
2 3 4

Sample Output 1

10

Sample Input 2

4 5
0 1 1
0 2 2
1 3 3
2 3 4
1 2 5

Sample Output 2

18

Sample Input 3

2 3
0 1 1
0 1 2
0 1 3

Sample Output 3

7

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