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)

g = []

n = STDIN.gets.to_i
n.times.each {
  as = STDIN.gets.split(' ').map{|x| x.to_i }
  g[as[0]] = as.drop(2)
}

queue = []
mode = [] # nil: ????¨????, 1: ?¨??????????, 2: ??£??\?????¨????¨??????????
d = []

v = 1
mode[v] = 1
queue.push(v)
d[v] = 0
for i in 1..n
  while queue.size != 0
    v = queue.shift
    adjacencies = g[v]
    for a in adjacencies
      if mode[a] == nil
        # ????¨????
        mode[a] = 1
        queue.push(a)
        d[a] = d[v] + 1
      end
    end
  end
end

for i in 1..n
  puts "#{i} #{if d[i].nil? then -1 else d[i] end}"
end