#include<iostream>
#include<cstring>
#define INF 0x3f3f3f3f
using namespace std;
int edge[105][105],d[105];
int Dijstra(int st,int n)
{
int mark[105],minn,minn_num;
memset(mark,0,sizeof(mark));
for(int i=1;i<n;i++)
{
d[i]=edge[0][i];
}
d[0]=0;
mark[0]=1;
for(int i=1;i<n;i++)
{
int minn=INF;
for(int j=0;j<n;j++)
{
if(mark[j]==0&&d[j]<=minn)
{
minn=d[j];
minn_num=j;
}
}
mark[minn_num]=1;
for(int j=0;j<n;j++)
{
if(d[j]>minn+edge[minn_num][j])
{
d[j]=minn+edge[minn_num][j];
}
}
}
}
int main()
{
int n,m,x,y,val;
while(cin>>n>>m)
{
if(n==0&&m==0)
break;
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
if(i==j)
edge[i][j]=0;
else
edge[i][j]=INF;
}
}
for(int i=0;i<m;i++)
{
cin>>x>>y>>val;
edge[x-1][y-1]=val;
edge[y-1][x-1]=val;
}
Dijstra(0,n);
cout<<d[n-1]<<endl;
}
}