Score : 900 points
Mole decided to live in an abandoned mine. The structure of the mine is represented by a simple connected undirected graph which consists of N vertices numbered 1 through N and M edges. The i-th edge connects Vertices a_i and b_i, and it costs c_i yen (the currency of Japan) to remove it.
Mole would like to remove some of the edges so that there is exactly one path from Vertex 1 to Vertex N that does not visit the same vertex more than once. Find the minimum budget needed to achieve this.
Input is given from Standard Input in the following format:
N M a_1 b_1 c_1 : a_M b_M c_M
Print the answer.
4 6 1 2 100 3 1 100 2 4 100 4 3 100 1 4 100 3 2 100
200
By removing the two edges represented by the red dotted lines in the figure below, the objective can be achieved for a cost of 200 yen.
2 1 1 2 1
0
It is possible that there is already only one path from Vertex 1 to Vertex N in the beginning.
15 22 8 13 33418 14 15 55849 7 10 15207 4 6 64328 6 9 86902 15 7 46978 8 14 53526 1 2 8720 14 12 37748 8 3 61543 6 5 32425 4 11 20932 3 12 55123 8 2 45333 9 12 77796 3 9 71922 12 15 70793 2 4 25485 11 6 1436 2 7 81563 7 11 97843 3 1 40491
133677