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 functools import lru_cache

@lru_cache(maxsize=None)
def solve(i, count):
    global ans
    global a
    if count >= N:
        return
    if ans[i][0] == -1:
        ans[i][0] = count
    elif ans[i][0] > count:
        ans[i][0] = count

    for x in range(a[i][1]):
        solve(a[i][2 + x] - 1, count + 1)


N = int(input())
a = []
for _ in range(N):
    a.append([int(x) for x in input().split()])

ans = [[-1 for i in range(1)] for j in range(N)]

solve(0, 0)

for i, x in enumerate(ans):
    print(i + 1, *x)




