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
n=int(input())
ps=[0 for j in range(n+1)]

for i in range(n):
    p,d,*vs=[int(j) for j in input().split()]
    ps[p]=vs
    
dist=[-1 for i in range(n+1)]    
    
d=0
queue=[1]

while queue:
    pos=queue.pop(0)
    if dist[pos] == -1:
        dist[pos]=d
    for i in ps[pos]:
        if dist[i]==-1:
            queue.append(i)
            dist[i]=dist[pos]+1

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