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
from collections import deque
n = int(input())
M = [[0]*n for _ in range(n)]
d = [-1]*n
st = [0]*n
for _ in range(n):
    i = [int(i) for i in input().split()]
    u = i[0]
    k = i[1]
    V = i[2:]
    for v in V: M[u-1][v-1] = 1

def bfs(s):
    Q = deque()
    Q.append(s)
    st[s] = 1
    d[s] = 0
    while Q:
        u = Q.popleft()
        for v in range(n):
            if M[u][v] and st[v] == 0:
                st[v] = 1
                Q.append(v)
                d[v] = d[u]+1
        st[u] = 2
    return

bfs(0)
for i in range(n): print(i+1,d[i])
