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: Accepted)

N = gets.to_i
G = (1..N).map{ Array.new(N, 0) }
N.times do
  u, k, *v = gets.split(' ').map(&:to_i)
  v.each do |vi|
    G[u - 1][vi - 1] = 1
  end
end

Q = [0] #?§????0?????\??£????????\???
D = Array.new(N, -1)
D[0] = 0 #?§???????????????¢???0??????????????¢???-1??¨????????????

while Q.size > 0
  cur = Q.shift
  (0..N-1).each do |dst|
    if G[cur][dst] == 1 && D[dst] == -1
      D[dst] = D[cur] + 1
      Q << dst
    end
  end
end

(0..N-1).each do |id|
  puts "#{id + 1} #{D[id]}"
end



# g.each do |r|
#   puts r.join(" ")
# end