using static System.Math;
using System.Collections.Generic;
using System;

public class PriorityQueue<T> where T : IComparable
{
	private IComparer<T> _comparer = null;
	private int _type = 0;
	private T[] _heap;
	private int _sz = 0;
	private int _count = 0;
	public PriorityQueue(int maxSize, IComparer<T> comparer)
	{
		_heap = new T[maxSize];
		_comparer = comparer;
	}
	public PriorityQueue(int maxSize, int type = 0)
	{
		_heap = new T[maxSize];
		_type = type;
	}
	private int Compare(T x, T y)
	{
		if (_comparer != null) return _comparer.Compare(x, y);
		return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
	}
	public void Push(T x)
	{
		_count++;
		var i = _sz++;
		while (i > 0)
		{
			var p = (i - 1) / 2;
			if (Compare(_heap[p], x) <= 0) break;
			_heap[i] = _heap[p];
			i = p;
		}
		_heap[i] = x;
	}
	public T Pop()
	{
		_count--;
		T ret = _heap[0];
		T x = _heap[--_sz];
		int i = 0;
		while (i * 2 + 1 < _sz)
		{
			int a = i * 2 + 1;
			int b = i * 2 + 2;
			if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;
			if (Compare(_heap[a], x) >= 0) break;
			_heap[i] = _heap[a];
			i = a;
		}
		_heap[i] = x;
		return ret;
	}
	public int Count() => _count;
	public T Peek() => _heap[0];
	public bool Contains(T x)
	{
		for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
		return false;
	}
	public void Clear()
	{
		while (this.Count() > 0) this.Pop();
	}
	public IEnumerator<T> GetEnumerator()
	{
		var ret = new List<T>();
		while (this.Count() > 0)
		{
			ret.Add(this.Pop());
		}
		foreach (var r in ret)
		{
			this.Push(r);
			yield return r;
		}
	}
	public T[] ToArray()
	{
		T[] array = new T[_sz];
		int i = 0;
		foreach (var r in this)
		{
			array[i++] = r;
		}
		return array;
	}
}

public class Edge
{
	public int to1 { get; set; }
	public int to2 { get; set; }
	public int d { get; set; }
}
public class Node : IComparable
{
	public int id1 { get; set; }
	public int id2 { get; set; }
	public int d { get; set; }
	public int CompareTo(object obj)
	{
		var x = (Node)obj;
		if (this.d > x.d) return 1;
		else if (this.d == x.d) return 0;
		else return -1;
	}
}

public class hello
{
	public static int BIG = 99999999;

	public static void goDijk(List<Edge>[,] aa, int r1, int r2, int[,] mind)
	{
		var pq = new PriorityQueue<Node>(30000, 0);
		pq.Push(new Node { id1 = r1, id2 = r2, d = 0 });
		while (pq.Count() > 0)
		{
			var targ = pq.Pop();
			var nowd = targ.d;
			var nowid1 = targ.id1;
			var nowid2 = targ.id2;
			if (mind[nowid1, nowid2] < nowd) continue;
			mind[nowid1, nowid2] = nowd;
			foreach (var x in aa[nowid1, nowid2])
				if (nowd + x.d < mind[x.to1, x.to2])
				{
					mind[x.to1, x.to2] = nowd + x.d;
					pq.Push(new Node { id1 = x.to1, id2 = x.to2, d = nowd + x.d });
				}
		}
	}

	public static void Main()
	{
		while (true)
		{
			string[] line = Console.ReadLine().Trim().Split(' ');
			var n = int.Parse(line[0]);
			var m = int.Parse(line[1]);
			if (n == 0 && m == 0) break;
			var aa = setEdge(n, m);
			var mind = new int[n, 3];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < 3; j++) mind[i, j] = BIG;
			goDijk(aa, 0, 2, mind);
			Console.WriteLine(Min(mind[n - 1, 0], mind[n - 1, 2]));
		}
	}
	static List<Edge>[,] setEdge(int n, int m)
	{
		var aa = new List<Edge>[n, 3];
		for (int i = 0; i < n; i++)
			for (int j = 0; j < 3; j++) aa[i, j] = new List<Edge>();
		for (int i = 0; i < m; i++)
		{
			string[] line = Console.ReadLine().Trim().Split(' ');
			var a = int.Parse(line[0]) - 1;
			var b = int.Parse(line[1]) - 1;
			var c = int.Parse(line[2]);
			aa[a, 2].Add(new Edge { to1 = b, to2 = 2, d = c });
			aa[a, 2].Add(new Edge { to1 = b, to2 = 1, d = 0 });
			aa[a, 1].Add(new Edge { to1 = b, to2 = 0, d = 0 });
			aa[a, 0].Add(new Edge { to1 = b, to2 = 0, d = c });
			aa[b, 2].Add(new Edge { to1 = a, to2 = 2, d = c });
			aa[b, 2].Add(new Edge { to1 = a, to2 = 1, d = 0 });
			aa[b, 1].Add(new Edge { to1 = a, to2 = 0, d = 0 });
			aa[b, 0].Add(new Edge { to1 = a, to2 = 0, d = c });
		}
		return aa;
	}
}



Measured memory_bytes: 24300