#include <iostream> //第一道用Dijkstra解的题
#include <cstring>
using namespace std;
#ifndef ONLINE_JUDGE
#include <fstream>
ifstream fin("test.txt");
#define cin fin
#endif
int n,m;
const int INF = 1000010;
int vis[200],dis[200];
int graph[200][200];
int main()
{
ios::sync_with_stdio(false);
int a,c,b;
while(cin >> n >> m)
{
if(!n && !m)
break;
memset(vis,0,sizeof(vis));
for(int i = 1; i <= n; ++i)
for(int j = 1; j <= n; ++j)
{
if(i==j)
graph[i][j] = 0;
else
graph[i][j] = INF;
}
for(int i = 1; i <= m; ++i)
{
cin >> a >> b >> c;
graph[a][b] = graph[b][a] = c;
}
for(int i = 1; i <= n; ++i)
{
dis[i] = graph[i][1];
}
vis[1] = 1;
for(int i = 0; i < n; ++i)
{
int min = INF,t = 0;
for(int j = 2; j <= n; ++j)
if(!vis[j] && dis[j] < min)
{
min = dis[j];
t = j;
}
vis[t] = 1;
for(int j = 1; j <= n; ++j)
{
if(!vis[j] && dis[j] > dis[t] + graph[t][j])
dis[j] = dis[t] + graph[t][j];
}
}
cout << dis[n] << endl;
}
return 0;
}