Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n,m,sum=0,f[40010][20],b[40010],dis[20][20];
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=m;i++)
	{
		int xx,yy,zz;
		scanf("%d%d%d",&xx,&yy,&zz);
		dis[xx][yy]=zz;
		dis[yy][xx]=zz;
		sum+=zz;
    }
    for (int i=1;i<(1<<n);i++)
	  for (int j=1;j<=n;j++)
	    if (i>>(j-1)&1)
	      for (int k=j+1;k<=n;k++)
	        if ((i>>(k-1))&1) b[i]+=dis[j][k];
	memset(f,-10,sizeof(f));
	f[1][1]=0;
	int N=(1<<n)-1;
	for (int i=1;i<=N;i++)
	  for (int j=1;j<=n;j++)
	    if ((i>>(j-1))&1)
	    {
	    	for (int k=1;k<=n;k++)
	    	  if (!((i>>(k-1))&1)&&dis[j][k]) f[i|(1<<(k-1))][k]=max(f[i|(1<<(k-1))][k],f[i][j]+dis[j][k]);
	    	for (int k=N^i;k;k=(k-1)&(N^i))
	    	  f[i|k][j]=max(f[i|k][j],f[i][j]+b[k|(1<<(j-1))]);
	    }
	cout<<sum-f[N][n];
}