#include<stdio.h>

const int inf=1000000000;
int g[101][101],mini[101];

void dijkstra(int n,int g[][101],int s,int* mini)
{
        int v[101],i,j,k;
        for(i=1;i<=n;i++)
        {
                mini[i]=inf;
                v[i]=0;
        }
        for(mini[s]=0,j=1;j<=n;j++)
        {
                for(k=-1,i=1;i<=n;i++)
                        if(!v[i]&&(k==-1||mini[i]<mini[k]))
                                k=i;
                for(v[k]=1,i=1;i<=n;i++)
                        if(!v[i]&&mini[k]+g[k][i]<mini[i])
                                mini[i]=mini[k]+g[k][i];
        }
}

int main()
{
        int n,m,a,b,c,i,j;
        while(scanf("%d%d",&n,&m)!=EOF,n||m)
        {
                for(i=1;i<=n;i++)
                        for(j=1;j<=n;j++)
                                g[i][j]=inf;
                while(m--)
                {
                        scanf("%d%d%d",&a,&b,&c);
                        if(g[a][b]>c)
                                g[a][b]=g[b][a]=c;
                }
                dijkstra(n,g,1,mini);
                printf("%d\n",mini[n]);
        }
        return 0;
}
/**************************************************************
	Problem: 2230
	User: admin
	Language: C
	Result: Accepted
	Time:14 ms
	Memory:1184 kb
****************************************************************/