#define _USE_MATH_DEFINES
#define INF 0x3f3f3f3f
#include <cstdio>
#include <iostream>
#include <sstream>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <limits>
#include <map>
#include <string>
#include <cstring>
#include <set>
#include <deque>
#include <bitset>
#include <list>
#include <cctype>
#include <utility>

using namespace std;

typedef long long ll;
typedef pair <int,int > P;
typedef pair <int,P > PP;

int tx[] = {0,1,0,-1};
int ty[] = {-1,0,1,0};

static const double EPS = 1e-8;

static const char RGB[]={'R','G','B'};

class Data{
public:
	int cost;
	int pos;
	int used;
	int m1;
	int m2;
	Data(int _cost,int _pos,int _used,int _m1,int _m2) 
		: cost(_cost), pos(_pos), used(_used),m1(_m1),m2(_m2){
	}

	Data(int _cost,int _pos,int _used) : cost(_cost), pos(_pos), used(_used),m1(-1),m2(-1){} 
	bool operator<(const Data& d) const{
		return cost < d.cost;
	}

	bool operator>(const Data& d) const{
		return cost > d.cost;
	}
};

int path[101][101];
int idx[101][101];


int main(){
	int n,m;
	while(~scanf("%d %d",&n,&m)){
		if(n==m && m==0) break;

		map<PP,int> cost;
		memset(path,0x3f,sizeof(path));
		vector<int> edge[101];

		for(int i=0;i<m;i++){
			int a,b,c;
			scanf("%d %d %d",&a,&b,&c);
			if(path[a][b] > c){
				edge[a].push_back(b);
				edge[b].push_back(a);
				path[b][a] = path[a][b] = c;
				idx[b][a] = idx[a][b] = i;
			}
		}

		priority_queue<Data,vector<Data>,greater<Data> > que;
		cost[PP(1,P(-1,-1))] = 0;

		que.push(Data(0,1,0,-1,-1));

		int minv;
		while(!que.empty()){
			Data d = que.top();
			que.pop();

			if(d.used !=1 && d.pos==n){
				minv = d.cost;
				break;
			}

			for(int i=0;i<edge[d.pos].size();i++){
				int to = edge[d.pos][i];
				if(to == d.pos) continue;
				if(path[d.pos][to] >= INF) continue;
				if(idx[d.pos][to] == d.m1) continue;

				if(d.used==0){
					//cost pos used path1 path2
					que.push(Data(d.cost,to,d.used+1,idx[d.pos][to],-1));
					
					map<PP,int>::iterator it = cost.find(PP(to,P(-1,-1)));
					if(it != cost.end() && it->second > d.cost + path[d.pos][to]){
						it->second = d.cost+path[d.pos][to];

						//cost pos used
						que.push(Data(d.cost+path[d.pos][to],to,d.used));
					}
					else if(it == cost.end()){
						cost[PP(to,P(-1,-1))] = d.cost+path[d.pos][to];

						//cost pos used
						que.push(Data(d.cost+path[d.pos][to],to,d.used));
					}
					
				}

				else if(0< d.used && d.used < 2){
					map<PP,int>::iterator it = cost.find(PP(to,P(min(d.m1,idx[d.pos][to]),max(d.m1,idx[d.pos][to]))));
					if(it != cost.end() && it->second > d.cost){
						it->second = d.cost;

						//cost pos used path1 path2
						que.push(Data(d.cost,to,d.used+1,min(d.m1,idx[d.pos][to]),max(d.m1,idx[d.pos][to])));
					}
					else if(it == cost.end()){
						cost[PP(to,P(min(d.m1,idx[d.pos][to]),max(d.m1,idx[d.pos][to])))] = d.cost;
						que.push(Data(d.cost,to,d.used+1,min(d.m1,idx[d.pos][to]),max(d.m1,idx[d.pos][to])));
					}
				}
				else{
					map<PP,int>::iterator it = cost.find(PP(to,P(d.m1,d.m2)));
					if(it != cost.end() && it->second > d.cost + path[d.pos][to]){
						it->second = d.cost + path[d.pos][to];
						que.push(Data(d.cost + path[d.pos][to],to,d.used,d.m1,d.m2));
					}
					else if(it == cost.end()){
						cost[PP(to,P(d.m1,d.m2))] = d.cost + path[d.pos][to];
						que.push(Data(d.cost + path[d.pos][to],to,d.used,d.m1,d.m2));
					}
				}
			}
		}

		//int minv = cost[PP(n,P(-1,-1))];
		//map<PP,int>::iterator it;
		//for(int m1=0;m1<m;m1++){
		//	for(int m2=m1+1;m2<m;m2++){
		//		if((it = cost.find(PP(n,P(m1,m2)))) != cost.end()){
		//			minv=min(it->second,minv);
		//		}
		//	}
		//}
		printf("%d\n",minv);
	}
}