#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 100 + 10;
int mp[maxn][maxn],dis[maxn],book[maxn],node,edge;
void dijkstra(){
    for(int i = 1; i <= node; i++)
        dis[i] = mp[1][i];
    for(int i = 1; i <= node - 1; i++){
        int minn = INF,u;
        for(int j = 1; j <= node; j++){
            if(book[j]  == 0 && dis[j] < minn){
                minn = dis[j];
                u = j;
            }
        }
        book[u] = 1;
        for(int j = 1; j <= node; j++){
            if(book[j] == 0 && dis[u] + mp[u][j] < dis[j]){
                dis[j] = dis[u] + mp[u][j];
            }
        }
    }
    printf("%d\n",dis[node]);
}
int main(){
    while(~scanf("%d%d",&node,&edge) && node && edge){
        for(int i = 1; i <= node; i++){
            for(int j = 1; j <= node; j++){
                if(i==j)
                    mp[i][j] = 0;
                else
                    mp[i][j] = INF;
            }
        }
        int m,n,t;
        for(int i = 1; i <= edge; i++){
            scanf("%d%d%d",&m,&n,&t);
            if(t < mp[m][n])
                mp[m][n] = mp[n][m] = t;
        }
        dijkstra();
    }
    return 0;
}