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 <cstdio>
#include <cstring>

inline void CMax(int &a,int b){a<b?a=b:0;}
int n,m,G[15][15],g[1<<15],f[1<<15][15],Sum;

int main()
{
    scanf("%d%d",&n,&m),memset(f,-1,sizeof f),f[1][0]=0;
    for(int i=1,x,y,z;i<=m;++i)
    {
        scanf("%d%d%d",&x,&y,&z),--x,--y,Sum+=z,G[x][y]=G[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)&&G[j][k])
                        CMax(f[1<<k|i][k],f[i][j]+G[j][k]);
                for(int U=((1<<n)-1)^i,k=U;k;k=(k-1)&U)
                    CMax(f[i|k][j],f[i][j]+g[1<<j|k]);
            }
    return printf("%d\n",Sum-f[(1<<n)-1][n-1]),0;
}