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())

tree = [[] for _ in range(N)]

for _ in range(N):
    u, k, *v = map(int, input().split())
    tree[u-1] = v

ans = [float('inf') for _ in range(N)]
ans[0] = 0

from collections import deque

q = deque([(0, 0)])

while q:
    p, d = q.popleft()
    for c in tree[p]:
        if ans[c-1] > d+1:
            ans[c-1] = d+1
            q.append((c-1, d+1))

for i in range(N):
    if ans[i] == float('inf'):
        print(i+1, -1)
    else:
        print(i+1, ans[i])
