Mole and Abandoned Mine

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.

Constraints

• 2 \leq N \leq 15
• N-1 \leq M \leq N(N-1)/2
• 1 \leq a_i, b_i \leq N
• 1 \leq c_i \leq 10^{6}
• There are neither multiple edges nor self-loops in the given graph.
• The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M a_1 b_1 c_1 : a_M b_M c_M

Output

Print the answer.

Examples

Input

4 6 1 2 100 3 1 100 2 4 100 4 3 100 1 4 100 3 2 100

Output

200

Input

2 1 1 2 1

Output

0

Input

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

Output

133677

inputFormat

Input

Input is given from Standard Input in the following format:

N M a_1 b_1 c_1 : a_M b_M c_M

outputFormat

Output

Print the answer.

Examples

Input

4 6 1 2 100 3 1 100 2 4 100 4 3 100 1 4 100 3 2 100

Output

200

Input

2 1 1 2 1

Output

0

Input

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

Output

133677

样例

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