Dijkstra? P26855

Write a program that, given a directed multigraph with arcs with positive costs, computes the cost of the second cheapest walk from vertex 0 to every other vertex. Remember that a multigraph may have arcs from $x$ to $x$, and more than one arc from $x$ to $y$. Also remember that a walk can repeat vertices and arcs.

Input

Input consists of several cases. Every case begins with the number of vertices $n$ and the number of arcs $m$, followed by $m$ triples $x$ $y$ $c$ to indicate an arc from $x$ to $y$ with cost $c$. Assume $2 \le n \le 10^4$, $0 \le m \le 5n$, that vertices are numbered from 0 to $n - 1$, and that every cost $c$ is an integer number between 1 and $10^4$.

Output

For every case, print the second minimum cost of walking from 0 to the rest of vertices, ordered from 1 to $n - 1$. If there is no second best walk to some vertex, just print “no”. Print a line with ten dashes at the end of every case.