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 = [[0 for i in range(n)] for j in range(n)]
d = [0] * n
f = [0] * n
queue = [0]


for i in range(n):
   a = list(map(int, input().split()))
   for j in range(0, a[1], 1):
       graph[a[0] - 1][a[2 + j] - 1] = 1

f[0] = 1
while len(queue) != 0:
    i = queue.pop(0)
    for j in range(n):
        if (graph[i][j] == 1) & (f[j] == 0):
            queue.append(j)
            f[j] = 1
            d[j] = d[i] + 1

[print(i+1, d[i] if (i == 0) | (d[i] != 0) else -1) for i in range(n)]
