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 e[20][20];
int v[33333];
int f[33333][20];
int n,m,ans;
int main(){
	scanf("%d%d",&n,&m);
	for (int i=1;i<=m;i++){
		int x,y,v;
		scanf("%d%d%d",&x,&y,&v);
		e[--x][--y]=v; e[y][x]=v;
		ans+=v;
	}
	for (int i=0;i<1<<n;i++)
		for (int j=0;j<n;j++)
			if (i&(1<<j))
				for (int k=j+1;k<n;k++)
					if (i&(1<<k))
						v[i]+=e[j][k];
	memset(f,233,sizeof(f));
	for (int i=0;i<1<<n;i++)
		if (i&1) f[i][0]=v[i];
	for (int i=0;i<1<<n;i++)
		for (int j=0;j<n;j++)
			if (f[i][j]>=0){
				//printf("%d %d %d\n",i,j,f[i][j]);
				int res=(1<<n)-1-i;
				for (int ano=res;ano;ano=(ano-1)&res)
					for (int k=0;k<n;k++)
						if (e[j][k]&&!(i&(1<<k))&&(ano&(1<<k)))
							f[i|ano][k]=max(f[i|ano][k],f[i][j]+v[ano]+e[j][k]);
			}
	printf("%d\n",ans-f[(1<<n)-1][n-1]);
}