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())
g = []
# ans = [[-1]*n for _ in range(n)]
ans = [-1] * n
done = set()
q = deque()

for i in range(n):
    temp = list(map(int, input().split()))
    g.append(temp[2:])

# print(g)

q.append(0)
# dis = 1
ans[0] = 0
done.add(1)

while q:
    idx = q.popleft()
    adj = g[idx]
    # print('node:', idx+1)

    for i in adj:
        if i not in done:
            ans[i-1] = ans[idx] + 1
            done.add(i)
            q.append(i-1)
    # if len(adj) > 0:
    #     dis += 1

# print(ans)

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