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,N,f[15][1<<15],s[1<<15],e[15][15],ans;

void upd(int &x,int y){if (x<y)  x=y;}

void work()
{
	scanf("%d %d",&n,&m),N=1<<n;
	for (int i=1,u,v,w; i<=m; i++)
		scanf("%d %d %d",&u,&v,&w),u--,v--,e[u][v]=e[v][u]=w;
	for (int i=1; i<N; i++)
		for (int j=0; j<n; j++)
			for (int k=j; k<n; k++)
				if ((i&(1<<j))&&(i&(1<<k)))
					s[i]+=e[j][k];
	memset(f,128,sizeof(f));
	f[0][1]=0;
	for (int i=1; i<N; i+=2)
		for (int j=0; j<n; j++)
			if (i&(1<<j))
				{
					int x=N-1-i;
					for (int k=x; k; k-=x&-x,k&=x)
						upd(f[j][i|k],f[j][i]+s[k|(1<<j)]);
					for (int k=0; k<n; k++)
						if ((x&(1<<k))&&(e[j][k]))
							upd(f[k][i|(1<<k)],f[j][i]+e[j][k]);
					if (j==n-1)  upd(ans,f[j][i]);
				}
	printf("%d",s[N-1]-ans);
}

int main()
{
	work();
	return 0;
}