Number of shortest paths P77353

Given a directed graph, compute in how many ways every vertex is reachable from the vertex 0 making the minim number of steps.

Input

Input consists of several cases, each one with the number of vertices $n$ (between 1 and $10^4$), the number of arcs $m$ (between 0 and $10n$), and $m$ pairs $x \enspace y$ to indicate an arc from $x$ to $y$. There are no repeated arcs, nor of the kind $x \enspace x$. Vertices are numbered from 0 to $n - 1$.

Output

For every case, and for every vertex $x$, print its number, the minimum number of steps to reach $x$ starting from 0, and in how many different ways this can be done. Print a -1 if a vertex is unreachable from 0. Print an empty line after every case.