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;
int G[20][20],U[110],V[110],W[110];
int Sum[(1<<15)+5],F[(1<<15)+5][20];

int main()
{
	int i,j,k,s;
	scanf("%d%d",&N,&M);
	for(i=1; i<=M; i++)
	{
		scanf("%d%d%d",&U[i],&V[i],&W[i]);
		U[i]--,V[i]--;
		G[U[i]][V[i]]=G[V[i]][U[i]]=W[i];
	}
	for(i=0; i<1<<N; i++)
		for(j=1; j<=M; j++)
			if(i>>U[j]&1&&i>>V[j]&1)
				Sum[i]+=W[j];
	memset(F,-0x3f,sizeof(F));
	F[1][0]=0;
	for(i=1; i<1<<N; i++)
		for(j=0; j<N; j++)
			if(F[i][j]>=0)
			{
				s=(1<<N)-1-i;
				for(k=s; k; k=(k-1)&s)
					F[i|k][j]=max(F[i|k][j],F[i][j]+Sum[k|1<<j]);
				if(~i>>N-1&1)
					for(k=0; k<N; k++)
						if(~i>>k&1&&G[j][k])
							F[i|1<<k][k]=max(F[i|1<<k][k],F[i][j]+G[j][k]);
			}
	printf("%d\n",Sum[(1<<N)-1]-F[(1<<N)-1][N-1]);
	return 0;
}