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

def main():

    inf = 1000000007
    n = int(input())
    e = [[] for _ in range(n)]
    d = [inf]*n

    for i in range(n):
        m = list(map(int,input().split()))
        for j in range(2,len(m)):
            e[m[0]-1].append(m[j]-1)

    d[0] = 0
    dq = deque([])
    dq.append([0,0])
    while dq:
        c,v = dq.popleft()
        for u in e[v]:
            if d[u]==inf:
                d[u] = c+1
                dq.append([c+1,u])

    for i in range(n):
        if d[i]==inf:print (i+1,-1)
        else        :print (i+1,d[i])

if __name__ == '__main__':
    main()


