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>
#define N 16
#define oo (1<<29)
using namespace std;
int n,m,G[N][N],f[1<<N][N],S[1<<N],sum;
int main()
{
	int i,j,k,l,x,y,z;
	scanf("%d %d",&n,&m);
	for(i=1;i<=m;i++){
		scanf("%d %d %d",&x,&y,&z);
		x--,y--,G[x][y]=G[y][x]=z,sum+=z;
	  }
	for(i=0;i<(1<<n);i++)
		for(j=0;j<n;j++)
			if((i>>j)&1)
				for(k=j+1;k<n;k++)
					if((i>>k)&1)
						S[i]+=G[j][k];
	for(i=0;i<(1<<n);i++)
		for(j=0;j<n;j++) f[i][j]=-oo;
	for(i=0;i<(1<<n);i++)
		if(i&1) f[i][0]=S[i];
	for(i=1;i<(1<<n);i++)
		for(j=0;j<n;j++)
			if((i>>j)&1)
				for(k=i;k;k=(k-1)&i)
					if(k&1)
						for(l=0;l<n;l++)
							if(((k>>l)&1)&&((~k>>j)&1)&&G[l][j])
								f[i][j]=max(f[i][j],f[k][l]+G[l][j]+S[i^k]);
	cout<<sum-f[(1<<n)-1][n-1];
	return 0;
}