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
from collections import deque
n=int(input())
edge=[[] for _ in range(n+1)]
for i in range(n):
  v,k,*u=map(int,input().split())
  edge[v]=u
p=[-1]*(n+1)
p[1]=0
q=deque([])
q.append(1)
v=[1]*(n+1)
v[1]=0
while q:
  now=q.popleft()
  for i in edge[now]:
    if v[i]:
      q.append(i)
      p[i]=p[now]+1
      v[i]=0
for i in range(1,n+1):
  print(i,p[i])
