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.chomp.to_i
ar = Array.new(N+1) { Array.new }
1.upto(N) do |i|
  arr = gets.chomp.split.map(&:to_i)
  arr.shift
  arr.shift
  ar[i] = arr
end

ans = Array.new(N+1, -1)
que = [[1,0]]
while !que.empty?
  n,c = que.shift
  next if ans[n] != -1 && ans[n] <= c
  ans[n] = c
  ar[n].each do |a|
    if ans[a] == -1 || ans[a] > c+1
      que.push([a,c+1])
    end
  end
end

1.upto(N) do |i|
  puts "#{i} #{ans[i]}"
end