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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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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