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 = STDIN.gets.to_i
matrix    = Array.new(n) { Array.new(n, false) }
distances = Array.new(n)

n.times do
	vertex, degree, *adj_list = STDIN.gets.split.map(&:to_i)
	degree.times do |i|
		matrix[vertex - 1][adj_list[i] - 1] = true
	end
end

queue = [].push(0)
distances[0] = 0
until queue.empty?
	v = queue.shift
	adj_list = matrix[v].each_index.
		select { |i| matrix[v][i] && distances[i].nil? }.
		each { |adj| distances[adj] = distances[v] + 1; queue << adj }
end

matrix.each_index { |i| puts "#{i + 1} #{distances[i] || -1}" }