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())

adj = [0]*n # adjacent list
d = [-1]*n # distance from the source vertex
c = ['w']*n # the 'color' of each vertex

# receiving input (the structure of the graph)
for i in range(n):
    tmp = list(map( int, input().split() ) )
    adj[tmp[0]-1] = list(map(lambda x : x - 1, tmp[2:]))

# set the source vertex
s = 0
d[s] = 0
c[s] = 'g'


Q = deque()
Q.append(s)

while Q:
    u = Q.popleft()
    for v in adj[u]:
        if c[v] == 'w':
            c[v] = 'g'
            d[v] = d[u] + 1
            Q.append(v)
    c[u] = 'b'
    

for i in range(n):
    print(f'{i+1} {d[i]}')


