The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

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bitmasks

graph matchings

graphs

*2400

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D. Traveling Graph

time limit per test

0.5 secondmemory limit per test

64 megabytesinput

standard inputoutput

standard outputYou are given undirected weighted graph. Find the length of the shortest cycle which starts from the vertex 1 and passes throught all the edges at least once. Graph may contain multiply edges between a pair of vertices and loops (edges from the vertex to itself).

Input

The first line of the input contains two integers *n* and *m* (1 ≤ *n* ≤ 15, 0 ≤ *m* ≤ 2000), *n* is the amount of vertices, and *m* is the amount of edges. Following *m* lines contain edges as a triples *x*, *y*, *w* (1 ≤ *x*, *y* ≤ *n*, 1 ≤ *w* ≤ 10000), *x*, *y* are edge endpoints, and *w* is the edge length.

Output

Output minimal cycle length or -1 if it doesn't exists.

Examples

Input

3 3

1 2 1

2 3 1

3 1 1

Output

3

Input

3 2

1 2 3

2 3 4

Output

14

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