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 = sys.stdin.readline
from collections import deque

def main():
	n = int(input().strip())
	v = [[] for _ in range(n)]
	for i in range(n):
		v[i] = list(map(int, input().strip().split()))
	l = [-1] * (n+1)
	q = deque()
	q.append((1, 0))
	while len(q) != 0:
		id, d = q.popleft()
		# print("id", id)
		if l[id] != -1:
			# print("b")
			continue
		l[id] = d
		# l[id] = min(d, l[id])
		# print(id, d)
		for i in range(v[id-1][1]):
			q.append((v[id-1][2+i], d+1))
			# if id == 8:
				# print("##", id, v[id-1][2+i])
				# print(repr(q))
	for i in range(1, n+1):
		print(i, l[i])

if __name__ == '__main__':
	main()

