#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:11 ms
	Memory:1184 kb
****************************************************************/