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
import sys

n = int(sys.stdin.readline())
dist = [0] + [-1] * (n-1)
vv=[list(map(int, sys.stdin.readline().split()))[2:] for _ in range(n)]


def walk(k, d):
    for i in vv[k]:
        if dist[i-1]<0 or (dist[i-1]>0 and dist[i-1]>d):
            dist[i-1]=d
        else: continue
        walk(i-1, d+1)

walk(0, 1)

for i, d in enumerate(dist):
    print(i+1, d)
