Number of shortest paths

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.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T11:56:14.974Z