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 Python3 (judge verdict: Accepted)

from sys import stdin
from collections import deque
n = int(stdin.readline())
d = [-1] * (n + 1)
def bfs(G):
    d[1] = 0
    queue = [1]
    dq = deque([1])
    while len(dq) > 0:
        v = dq.popleft()
        for c in G[v]:
            if d[c] < 0:
                d[c] = d[v] + 1
                dq.append(c)
    for i, x in enumerate(d[1:], start=1):
        print(i, x)
G = {}
for i in range(n):
    x = list(map(int, stdin.readline().split()))
    G[x[0]] = x[2:]
bfs(G)