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 sys
input = lambda: sys.stdin.readline().rstrip() 
from collections import deque

def resolve():
    n = int(input())
    ukv = [list(map(int, input().split())) for _ in range(n)]

    dist = [-1]*n
    que = deque()

    que.append(0)
    dist[0] = 0
    while len(que)>0:
        v = que.popleft()
        for i in ukv[v][2:]:
            if dist[i-1]==-1:
                que.append(i-1)
                dist[i-1] = dist[v]+1

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

if __name__ == '__main__':
    resolve()
