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 rep(i,x,y) for (int i=(x);i<=(y);i++)
#define two(x) (1<<(x-1))
using namespace std;
#define N 20
int n,m,w[N][N],f[(1<<16)+10][N],p[(1<<16)+10],ans;
int main(){
	scanf("%d%d",&n,&m);int Max=(1<<n)-1;
	rep (i,1,m){
		int x,y,z;scanf("%d%d%d",&x,&y,&z);
		ans+=z;w[x][y]=w[y][x]=z;
	}
	p[0]=0;
	rep (i,1,Max){
		int now;
		rep (j,1,n) if (i>>j-1&1){now=j;break;}
		p[i]=p[i^(1<<now-1)];
		rep (j,1,n) if (i>>j-1&1) p[i]+=w[now][j];
	}
	memset(f,0xc0,sizeof(f));
	f[1][1]=0;
	int tmp=-1e9;
	rep (s,1,Max) rep (i,1,n){
		for (int t=s;t;t=(t-1)&s)
			if (t>>i-1&1)
				f[s][i]=max(f[s][i],f[(s-t)|(1<<i-1)][i]+p[t]);
        rep (j,1,n)
			if (!(s>>j-1&1)&&w[i][j])
				f[s|(1<<j-1)][j]=max(f[s|(1<<j-1)][j],f[s][i]+w[i][j]);
	}
	ans-=f[Max][n];
	printf("%d\n",ans);
	return 0;
}