#define _CRT_SECURE_NO_WARNINGS
#define _SILENCE_CXX17_C_HEADER_DEPRECATION_WARNING
#include <bits/stdc++.h>
using namespace std;
const int N = 1005, M = 10050;
int n, m;
int adj[N], nxt[M << 1], to[M << 1], len[M << 1], ecnt;
int dis[N];
inline void addEdge(int f, int t, int l)
{
    ecnt++;
    to[ecnt] = t;
    len[ecnt] = l;
    nxt[ecnt] = adj[f];
    adj[f] = ecnt;
}
int inq[N], que[M];
void spfa(int s)
{
    memset(inq, 0, sizeof(inq));
	memset(dis, 0x3f3f3f3f, sizeof(dis));
    int h, t, x;
    h = t = x = 0;
    for (dis[s] = 0, que[t++] = s, inq[s] = true; h ^ t; inq[que[h++]] = false)
        for (int cur = adj[que[h]]; cur; cur = nxt[cur])
            if (dis[to[cur]] > dis[que[h]] + len[cur])
            {
                dis[to[cur]] = dis[que[h]] + len[cur];
                if (!inq[to[cur]]) que[t++] = to[cur], inq[to[cur]] = true;
            }
}
int main()
{
    while (scanf("%d%d", &n, &m), n | m)
    {
        memset(adj, 0, sizeof(adj)), ecnt = 0;
        for (int i = 0, a, b, c; i < m; i++)
        {
            scanf("%d%d%d", &a, &b, &c);
            addEdge(a, b, c);
            addEdge(b, a, c);
        }
        spfa(1);
        printf("%d\n", dis[n]);
    }
    return 0;
}