#include<iostream>
#include <cstring>
#define INF 0x3f3f3f3f
#define MAX_N 10001
using namespace std;
int g[MAX_N][MAX_N];
int dist[MAX_N];
int sure[MAX_N];
int n,m;
void dijkstra(int begin)
{
    dist[begin] = 0;
    while(1)
    {
        int i, u=-1, v;
        int min = INF;
        for(i=1;i<=n;i++)
        {
            if(!sure[i] && dist[i]<min)
            {
                min = dist[i];
                u = i;
            }
        }
        if(u==-1)
            break;
        sure[u] = 1;
        for(v=1;v<=n;v++)
            if(g[u][v]!=-1 && dist[v]>dist[u]+g[u][v])
                dist[v] = dist[u] + g[u][v] > dist[v] ? dist[v]: dist[u]+g[u][v];
    }
}
int main()
{
    while(cin>>n>>m&&m&&n)
    {
        int a,b,c;
        int i;
        memset(dist,0x3f3f3f,sizeof(dist));
        memset(sure,0,sizeof(sure));
        memset(g,-1,sizeof(g));
        for(i=0;i<m;i++)
        {
            cin>>a>>b>>c;
            g[a][b] = g[b][a] = c;
        }
        dijkstra(1);
        cout<<dist[n]<<endl;
    }
    return 0;
}