#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<stack>
#include<stdlib.h>
#include<map>
#include<vector>
#include<queue>
#include<set>
#include<ctype.h>
#define zuida 100000
using namespace std;
#define INF 1e9
#define max 100005
struct node
{
    int to;
    int val;
    int next;
}bian[max];
int head[max],vis[max];
int n,m;
int tto=0;
void add(int a,int b,int c)
{
    bian[tto].to=b;
    bian[tto].val=c;
    bian[tto].next=head[a];
    head[a]=tto++;
}
int dis[max];
int que[max];
queue<int> qq;
void spfa(int start,int num)
{
    memset(vis,0,sizeof(vis));
    for(int i=0;i<=num;i++)
        dis[i]=INF;
    //int front=-1,tail=-1;
    //dis[start]=0;vis[start]=1;que[++tail]=start;
    qq.push(start);dis[start]=0;vis[start]=1;

    int top,to;
    int temp;
    /*while(front!=tail)
    {
        if(++front==n)front-=num;
        top=que[front];vis[top]=0;
        for(int p=head[top];p!=-1;p=bian[p].next)
        {
            to=bian[p].to;
            temp=dis[top]+bian[p].val;
            if(dis[to]>temp)
            {
                dis[to]=temp;
                if(!vis[to])
                {
                    if(++tail>num)tail-=num;
                    que[tail]=to;
                    vis[to]=1;
                }
            }
        }
    }
    */
    while(!qq.empty())
    {
        top=qq.front();qq.pop();vis[top]=0;
        for(int p=head[top];p!=-1;p=bian[p].next)
        {
            to=bian[p].to;
            temp=dis[top]+bian[p].val;
            if(dis[to]>temp)
            {
                dis[to]=temp;
                if(!vis[to])
                {
                   qq.push(to);
                    vis[to]=1;
                }
            }
        }
    }
}

int main()
{
    int b,w,m,k;
    while(cin>>n>>m&&n&&m)
    {
        int maxx=-100000;
        memset(head,-1,sizeof(head));
        for(int i=1;i<=m;i++)
        {
            cin>>k>>b>>w;
            if(k>maxx)maxx=k;
            if(b>maxx)maxx=b;
            add(k,b,w);
            add(b,k,w);
        }
        spfa(1,maxx);
        cout<<dis[n]<<endl;
    }
    return  0;
}