#include<iostream>
#include<cstring>
#include<cstdio>
#define INF 0xfffffff  //十六进制
#define N 105
using namespace std;
int map[N][N],vis[N],dis[N];
int n;

void Dijkstra()
{
    int i,j;
    for(i=1; i<=n; i++)
        {
            dis[i]=map[1][i];///给出出发点到各个地点的距离
            vis[i]=false;///路径指示为还未走
            //cout<<dis[i]<<' ';
        }

    for(i=1; i<=n; i++)
        {
            int tmp=INF;
            int k;          ///假设一变量表示两地之间所花时间
            for(j=1; j<=n; j++)
                {
                    if(!vis[j]&&dis[j]<tmp)     ///找出花时间最短的一条路径k
                        tmp=dis[k=j];
                }
            vis[k]=true;
            for(j=1; j<=n; j++)
                {
                    if(!vis[j]&&dis[j]>dis[k]+map[k][j])    ///判断从出发点到j的时间 是否大于 经过k而到j的距离
                        dis[j]=dis[k]+map[k][j];
                }
        }
    cout<<dis[n]<<endl;
}

int main()
{
    int i,j,m;
    while(cin>>n>>m&&(n||m))
        {
            for(i=0; i<N; i++)
                for(j=0; j<N; j++)
                    map[i][j]=INF;
            int a,b,time;
            for(i=1; i<=m; i++)
                {
                    cin>>a>>b>>time;
                    if(time<map[a][b]) map[a][b]=map[b][a]=time; ///判断并给出两地间最短距离
                }
            Dijkstra();
        }
    return 0;
}

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<set>
#include<queue>
#include<stack>
#include<vector>
#include<map>

#define N 100010
#define Mod 10000007
#define lson l,mid,idx<<1
#define rson mid+1,r,idx<<1|1
#define lc idx<<1
#define rc idx<<1|1
typedef long long ll;

const int INF=1000010;

using namespace std;

int d[110][110];

int main()
{
    int i,j,k,n,m,p,q,s;
    while(scanf("%d%d",&n,&m)!=EOF,n+m)
        {
            for (i=1; i<=n; i++)
                {
                    for(j=1; j<=n; j++)
                        {
                            d[i][j]=INF;
                        }
                }
            for (i=0; i<m; i++)
                {
                    scanf("%d%d%d",&p,&q,&s);
                    d[p][q]=d[q][p]=s;
                }
            for (k=1; k<=n; k++)
                {
                    for (i=1; i<=n; i++)
                        {
                            for (j=1; j<=n; j++)
                                {
                                    if (d[i][j]>d[i][k]+d[k][j])
                                        {
                                            d[i][j]=d[i][k]+d[k][j];
                                        }
                                }
                        }
                }
            printf("%d\n",d[1][n]);
        }
    return 0;
}