Find the shortest path through a bidirection graph.

Input:
------

<Number of Nodes> <start node> <end node> <edges>
followed by a line for each edge:
<start> <end> <cost>

All are integers except cost, which can be a floating point number.

The nodes are numbered 0 to n-1 where n is the number of nodes.

Output:
-------

print the path and the cost.  If there is no path, print an error.


Sample Input:
-------------

5 1 4 5
1 2 10.0
1 3 1.0
2 3 1.0
2 4 1.0
3 4 10.0

5 1 4 0

0

Sample Output:
--------------

path = [1, 3, 2, 4] cost = 3.0
No path