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 $1, 2, ... n$.

Constraints

* $1 \leq n \leq 100$

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 $u$.

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.

Example

Input

4
1 2 2 4
2 1 4
3 0
4 1 3


Output

1 0
2 1
3 2
4 1
# https://onlinejudge.u-aizu.ac.jp/courses/lesson/1/ALDS1/11/ALDS1_11_C

from collections import deque

n = int(input())
graph = {}
res = [-1 for i in range(n + 1)]

for i in range(1, n + 1):
    data = input().split()
    graph[i] = [int(i) for i in data[2:]]

visited = set()
q = deque()
q.append((1, 0))  # node,distance
visited.add(1)

while q:
    node, dis = q.popleft()
    res[node] = dis
    for _next in graph[node]:
        if _next not in visited:
            visited.add(_next)
            q.append((_next, dis + 1))

for i in range(1, n + 1):
    print(i, res[i])

