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;
const int maxn=(1<<15)+5;
int n,m;
int dp[maxn][16];
int mp[16][16],val[maxn];
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int u,v,w;
		scanf("%d%d%d",&u,&v,&w);
		mp[v][u]=mp[u][v]=w;
	}
	memset(dp,-1,sizeof(dp));
	int all=(1<<n)-1;
	dp[1][1]=0;
	for(int s=0;s<=all;s++)
	{
		for(int i=1;i<=n;i++)
		if(s&(1<<i-1))
		{
			for(int j=i+1;j<=n;j++)
			if(s&(1<<j-1))val[s]+=mp[i][j];
		}
		for(int i=1;i<=n;i++)
		if(s&(1<<i-1))
		{
			for(int s0=s;s0;s0=(s0-1)&s)if(((s^s0)&(1<<i-1))&&dp[s^s0][i]!=-1)dp[s][i]=max(dp[s^s0][i]+val[s0|(1<<i-1)],dp[s][i]);
			for(int j=1;j<=n;j++)if((s&(1<<j-1))&&j!=i&&mp[j][i]&&dp[s^(1<<i-1)][j]!=-1)dp[s][i]=max(dp[s][i],dp[s^(1<<i-1)][j]+mp[j][i]);	
		}
	}
	printf("%d\n",val[all]-dp[all][n]);
}