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 Python (judge verdict: Wrong Answer)

n = input()
  
d = [1000 for i in range(n)]
M = [[0 for i in range(n)] for j in range(n)]
  
def BFS(s):
  q = []
  q.append(s)
  d[s] = 0
  while len(q) != 0:
    u = q[0]
    q.pop(0)
    for v in range(n):
      if M[u][v] == 0 and d[v] != 1000:
        d[v] = d[u] + 1
        q.append(v)
  for i in range(n):
    print i+1, d[i]
  
for i in range(n):
  G = [0 for i in range(n)]
  G = map(int, raw_input().split())
  for j in range(G[1]):
    M[G[0]-1][G[2+j]-1] = 1
  
BFS(0)