Problem:
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Breadth First Search

Write a program which reads an directed graph $G = (V, E)$, and finds the shortest distance from vertex $1$ to each vertex (the number of edges in the shortest path). Vertices are identified by IDs $1, 2, ... n$.

Input

In the first line, an integer $n$ denoting the number of vertices, is given. In the next $n$ lines, adjacent lists of vertex $u$ are given in the following format:

$u$ $k$ $v_1$ $v_2$ ... $v_k$

$u$ is ID of the vertex and $k$ denotes its degree.$v_i$ are IDs of vertices adjacent to $u$.

Constraints

$1 \leq n \leq 100$

Output

For each vertex $u$, print $id$ and $d$ in a line. $id$ is ID of vertex $u$ and $d$ is the distance from vertex $1$ to vertex $u$. If there are no path from vertex $1$ to vertex $u$, print -1 as the shortest distance. Print in order of IDs.

Sample Input 1

4
1 2 2 4
2 1 4
3 0
4 1 3

Sample Output 1

1 0
2 1
3 2
4 1

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Ruby (judge verdict: Runtime Error)

N = gets.to_i
$adjacency_list = []
N.times{
  u, k, *v = gets.split.map &:to_i
  $adjacency_list[u] = v
}
$d = Array.new(N+1, -1)
$q = []
def calc_d v, distance
  $d[v] = distance if $d[v] == -1
  $adjacency_list[v].each{|e|
    $d[e] = distance + 1 if $d[e] == -1
  }
  $q += $adjacency_list[v] unless $adjacency_list.empty?
  until $q.empty?
    t_v = $q.shift
    calc_d t_v, distance + 1
  end
end
calc_d(1, 0)

(1..N).each{|i|
  puts "#{i} #{$d[i]}"
}