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 = input()
d = [99999 for i in range(n)]
G = [0 for i in range(n)]
v = [[0 for i in range(n)] for j in range(n)]
   
def bfs(u):
  for i in range(n):
    if v[u][i] == 1:
      if d[i] > d[u] + 1:
         d[i] = d[u] + 1
         bfs(i)
    else:
      continue        
def _(): 
 d[0] = 0
 for i in range(n):
   bfs(i)
 for i in range(n):
   if d[i] == 99999:
      d[i] = -1
 for i in range(n):
   print '{0} {1}'.format(i+1, d[i])


for i in range(n):
  G = map(int, raw_input().split())
  for j in range(G[1]):
    v[G[0]-1][G[2+j]-1] = 1

_()