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())
graph = {}
d = [-1] * (n+1)
for i in range(n):
    t = list(map(int, input().split()))
    v = t[0]
    k = t[1]
    graph[v] = [t[i+2] for i in range(k)]

from queue import Queue

def bfs(s):
    d[s] = 0
    q=Queue()
    q.put(s)
    while not q.empty():
        v=q.get()
        for child in graph[v]:
            if d[child] != -1: continue
            d[child] = d[v] + 1
            q.put(child)
bfs(1)
for i in range(1, n+1):print(i,d[i])