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
graph = Array.new(n)

n.times do |i|
  input = gets.split().map(&:to_i)
  tmp = []
  input[1].times do |j|
    tmp << input[j+2]-1
  end
  graph[i] = tmp
end

dist = Array.new(n, -1)
queue = []

dist[0] = 0
queue << 0

while !queue.empty?
  v = queue.shift
  graph[v].each do |i|
    next if dist[i] != -1
    dist[i] = dist[v] + 1
    queue << i
  end
end

dist.each_with_index do |i, index|
  puts "#{index+1} #{i}"
end