Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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)

def bfs(u)
	$q.push([u, 0])
	$d[u] = 0
	while $q != []
		f = $q.first
		distance = f[1] + 1
		$l[f[0]].each do |i|
			if $d[i] == nil
				$q.push([i, f[1]+1]) if i != u
				$d[i] = distance
			end
		end
		$q.shift
	end
end



n = gets.chomp.to_i
$l=[]
$q = []
$d = Array.new(n+1)
n.times do
	u, k, *v = gets.chomp.split(" ").map(&:to_i)
	$l[u] = v
end
bfs(1)
$d.each_with_index do |val,i|
	next if i == 0
	val = -1 if val == nil
	puts "#{i} #{val}"
end