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

v = int(input())
vlist = [0]*v
for num in range(v):
    temp = list(map(int,input().split()))
    if temp[1] != 0:
        vlist[num] = temp[2:]
deep = [0]+[-1]*(v-1)
waiting = [1]

while waiting:
    vertex = waiting.pop(0)
    if vlist[vertex-1]:
        for subv in vlist[vertex-1]:
            if deep[subv-1] == -1:
                deep[subv-1] = deep[vertex-1]+1
                waiting += [subv]

count = 0
for num in deep:
    count += 1
    print(count,num)

