Single Source Shortest Path
---------------------------

In this problem, you will have to find the distances from a single
node to each other node in a weighted, directed graph.

Input
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The input will consist of multiple instances.  The first line of each
instance will contain two integers n and m, representing the number of
nodes and edges in the graph, respectively.  These values will satisfy
1 <= n <= 10000 and 0 <= m <= 1000000.  Following this, there will be
m lines, each containing three integers i, j and w, where 1 <= i <= n,
1 <= j <= n and w >= 0, indicating that there is an edge from node i to 
node j with weight w.  The end of the input will be indicated by a line 
with m = n = 0.

Output
------

For each input graph, output the distance number of edges in the shortest
path from node 1 to each of the other nodes, in the format shown below.
If there is no path from node 1 to some other node, output "no path"
for that node.

Sample Input
------------
6 16
1 2 9
2 1 9
1 3 3
3 1 3
2 3 4
3 2 4
2 4 1
4 2 1
2 5 3
5 2 3
3 6 2
6 3 2
3 4 2
4 3 2
5 6 5
6 5 5
3 0
0 0

Sample Output
-------------
Graph #1
1: 0
2: 6
3: 3
4: 5
5: 9
6: 5
Graph #2
1: 0
2: no path
3: no path