#include <iostream>
#include <cmath>
#include <iomanip>
#include<queue>
#include<algorithm>
#include<vector>
using namespace std;
#define inf 0x3f3f3f3f
#define ll long long
bool book[105];
struct node
{
    int c;
    int v;
    int nxt;
}e[20005];
struct node1
{
    int c;
    int v;
    friend bool operator <(node1 x, node1 y)
    {
        return x.c > y.c;//x成员小的优先级高，就越排在队首
    }
}a[20005];

int cnt=1;
int head[105];
priority_queue<node1>q;
void add(int u,int v,int z)
{
     e[cnt].v=v;
     e[cnt].c=z;
     e[cnt].nxt=head[u];
     head[u]=cnt++;
}
int d[105];
int main()
{
    int n,m;
    while(cin>>n>>m)
    {
        if(n==0&&m==0) break;
        while(!q.empty()) q.pop();
        memset(head,-1,sizeof(head));
        memset(d,inf,sizeof(d));
        memset(book,0,sizeof(book));
        for(int i=1;i<=m;i++)
        {
            int x,y,z;
            cin>>x>>y>>z;
            add(x,y,z);
            add(y,x,z);
        }
        for(int i=head[1];i!=-1;i=e[i].nxt)
        {
            node1 x;
            x.c=e[i].c;
            x.v=e[i].v;
            d[x.v]=x.c;
            book[x.v]=1;
            q.push(x);
        }
        while(!q.empty())
        {
            node1 x;
            x=q.top();
            book[x.v]=0;
            q.pop();
            for(int i=head[x.v];i!=-1;i=e[i].nxt)
            {
                if(d[e[i].v]>d[x.v]+e[i].c)
                {
                    d[e[i].v]=d[x.v]+e[i].c;
                    node1 y;
                    if(!book[e[i].v])
                    {
                        book[e[i].v]=1;
                        y.v=e[i].v;
                        y.c=d[e[i].v];
                        q.push(y);
                    }
                    
                }
            }
        }
        cout<<d[n]<<endl;
    }
    return 0;
}