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())
g = [[0]*(n+1) for _ in range(n+1)]
for i in range(n):
    u, k, *v, = map(int, input().split())
    for vi in v:
        g[u][vi] = 1

d = [-1]*(n+1)
d[1] = 0

l = [1]
while len(l) > 0:
    u = l.pop(0)
    for i, v in enumerate(g[u]):
        if v == 1 and d[i] < 0:
            d[i] = d[u]+1
            l.append(i)

for i in range(1, n+1):
    print(f"{i} {d[i]}")

