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#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
using namespace std;

const int maxn=103;
const int maxm=23;
const int maxe=maxm*maxm*2;
const int INF=2e9;

int n,m,k,e,x,y,z,d,p,a,b;
int tot,point[maxm],nxt[maxe],v[maxe],c[maxe];
int dis[maxm];
bool vis[maxm],flag[maxm];
queue <int> q;

inline void addedge(int x,int y,int z)
{
    ++tot;
    nxt[tot]=point[x];
    point[x]=tot;
    v[tot]=y;
    c[tot]=z;
    ++tot;
    nxt[tot]=point[y];
    point[y]=tot;
    v[tot]=x;
    c[tot]=z;
}
inline int spfa()
{
    memset(dis,0x7f,sizeof(dis));
    dis[1]=0;
    memset(vis,0,sizeof(vis));
    vis[1]=true;
    while (!q.empty()) q.pop();
    q.push(1);

    while (!q.empty())
    {
        int now=q.front();
        q.pop();
        vis[now]=false;
        for (int i=point[now]; i; i=nxt[i])
            if (dis[v[i]]>dis[now]+c[i]&&!flag[v[i]])
            {
                dis[v[i]]=dis[now]+c[i];
                if (!vis[v[i]])
                {
                    vis[v[i]]=true;
                    q.push(v[i]);
                }
            }
    }
    return dis[m];
}

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//Dijkstra
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<queue>
using namespace std;
template<typename T>
void Swap(T& a,T& b){T t=a;a=b;b=t;}
template<typename T>
int read(T& w)
{
	char r=getchar();bool f=false;
	if(r==-1)return -1;
	for(;(r<48||r>57)&&r!='-';r=getchar());
	if(r=='-')r=getchar(),f=true;
	for(w=0;r>=48&&r<=57;r=getchar())w=w*10+r-48;
	if(f)w=-w;
	return 1;
}
const int maxn=103;
const int maxm=10003;
int n,m;
struct EDGE
{
	int to,nxt,w;
	void init(int too,int nxtt,int ww)
	{
		to=too;nxt=nxtt;w=ww;
	}
}edge[maxm<<1];
int ek=0;
int node[maxn];
struct p
{
	int d,id;
	p(){d=id=0;}
	p(int idd,int dd)
	{
		d=dd,id=idd;
	}
};
void addEdge(int from,int too,int ww)
{
	edge[++ek].init(too,node[from],ww);
	node[from]=ek;
}
bool operator<(const p& a,const p& b)
{
	return a.d<b.d;
}
int to[maxn]; 
//小根堆
const int maxnode=maxn;
template<typename T>
struct HEAP
{
	T ary[maxnode];
	int f;
	HEAP(){f=0;}
	void clear(){f=0;}
	bool empty(){return f==0;}
	void push(const T& w)
	{
		ary[++f]=w;
		for(int k=f;k!=1&&ary[k]<ary[k/2];k/=2)
		{
			Swap(ary[k],ary[k/2]);
			Swap(to[ary[k].id],to[ary[k/2].id]);
		}
	}
	void adjust(int k,int dd)
	{
		if(dd<ary[k].d)ary[k].d=dd;
		for(;k!=1&&ary[k]<ary[k/2];k/=2)
		{
			Swap(ary[k],ary[k/2]);
			Swap(to[ary[k].id],to[ary[k/2].id]);
		}
	}
	T top() {return ary[1];}
	void pop()
	{
		ary[1]=ary[f--];
		for(int k=1,son=k*2;son<=f;k=son,son=k*2)
		{
			if(son+1<=f&&ary[son+1]<ary[son])
				++son;
			if(ary[son]<ary[k])
				Swap(ary[son],ary[k]),
				Swap(to[ary[son].id],to[ary[k].id]);
			else break;
		}
	}
};
HEAP<p> q;
int s,t;
typedef unsigned int uint;
const uint uinf=4294967295u;
uint d[maxn];
bool ok[maxn];

void Dijkstra()
{
	memset(d+1,255,n*sizeof(uint));
	memset(ok+1,0,n*sizeof(bool));
	memset(to+1,0,n*sizeof(int));
	q.clear();
	if(!to[s])
		to[s]=q.f+1;
	q.push(p(s,0));
	for(int i=1;i<=n&&!q.empty();++i)
	{
		p tmp;
		do
		{	tmp=q.top();
			q.pop();
			to[tmp.id]=0;
		}while(ok[tmp.id]&&!q.empty());
		ok[tmp.id]=true;
		d[tmp.id]=tmp.d;
		for(int j=node[tmp.id];j;j=edge[j].nxt)
		{
			int v=edge[j].to;
			if(d[tmp.id]!=uinf&&!ok[v])
			if(d[tmp.id]+edge[j].w<d[v])
			{
				if(!to[v])
					to[v]=q.f+1,q.push(p(v,d[tmp.id]+edge[j].w));
				else q.adjust(to[v],d[tmp.id]+edge[j].w);			
			}
		}
		if(tmp.id==t)break;
	}
}
void input()
{
	ek=0;
	memset(node+1,0,n*sizeof(int));
	int x,y,l;
	for(int i=1;i<=m;++i)
	{
		read(x),read(y),read(l);
		if(x!=y)
		{
			addEdge(x,y,l);
			addEdge(y,x,l);
		}
	}
	s=1,t=n;
}
int main()
{
	freopen("hdu2544_1.in","r",stdin);
	//freopen("hdu2544.out","w",stdout);
	while(read(n),read(m),n!=0)
	{
		input();
		Dijkstra();
		printf("%u\n",d[t]);
	}
	return 0;
}