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())
G=[[] for i in range(n)]
#G=[]
Q=[1]
d=[-1]*n
d[0]=0
visited=[False]*n
visited[0]=True

for i in range(n):
    arr=[int(x) for x in input().split()[2:]]
    for l in arr:
        G[i].append(l)
        #G[l-1].append(i+1)
    

kyori=0
while len(Q)!=0:
    
    #print(Q)
    #print(visited)
    v=Q.pop(0)
    
    for j in G[v-1]:
        if visited[j-1]:#次に行くところがすでに踏破済みだったら
            continue#更新しない
        else:
            d[j-1]=d[v-1]+1
            Q.append(j)
            visited[j-1]=True
for a in range(n):
    print(a+1,d[a])
    
        
