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
import collections
n= int(input())
g=[]
for _ in range(n):
    v,k,*varray= map(int,input().split())
    g.append(varray)
        

d= [-1]* (n+10)
d[0]=0
q= collections.deque()
q.append(0)
while len(q)>  0:
    cur = q.popleft()
    for next in g[cur]:
        if d[next-1]== -1:
            d[next-1]= d[cur]+1
            q.append(next-1)
            
for i in range(n):
    print(i+1,d[i])
    
