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;
typedef long long ll;
ll read(){
	ll a=0,b=getchar(),c=1;
	while(!isdigit(b))c=b=='-'?-1:1,b=getchar();
	while(isdigit(b))a=a*10+b-'0',b=getchar();
	return a*c;
}
void gao(int &a,int b){
	if(a<b)a=b;
}
int n,m,sum,a[15][15],g[1<<15],f[1<<15][15];
int main(){
	n=read(),m=read();
	memset(f,-1,sizeof(f));
	f[1][0]=0;
	for(int i=1;i<=m;i++){
		int x=read()-1,y=read()-1,z=read();
		sum+=z,a[x][y]=a[y][x]=z;
		for(int j=0;j<(1<<n);j++)
			if((j>>x)&(j>>y)&1)
				g[j]+=z;
	}
	for(int i=1;i<(1<<n);i++)
		for(int j=0;j<n;j++)
			if(~f[i][j]){
				for(int k=0;k<n;k++)
					if(!(i>>k&1)and a[j][k])
						gao(f[1<<k|i][k],f[i][j]+a[j][k]);
				for(int U=((1<<n)-1)^i,k=U;k;k=(k-1)&U)
					gao(f[i|k][j],f[i][j]+g[1<<j|k]);
			}
	printf("%d",sum-f[(1<<n)-1][n-1]);
	return 0;
}