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

def BFS(s = 0):
    Q.pop(0)
    color[s] = 2
    for j in range(len(color)):
        if A[s][j] == 1 and color[j] == 0:
            Q.append(j)
            color[j] = 1
            d[j] = d[s] + 1
    if len(Q) != 0:
        BFS(Q[0])

n = int(raw_input())
A = [0] * n
for i in range(n):
    A[i] = [0] * n

for i in range(n):
    value = map(int, raw_input().split())
    u = value[0] - 1
    k = value[1]
    nodes = value[2:]
    for j in range(k):
        v = nodes[j] - 1
        A[u][v] = 1

color = [0] * n
Q = [0]
d = [-1] * n
d[0] = 0

BFS(0)

for i in range(n):
    print(str(i + 1) + " " + str(d[i]))