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

def main():
    n = int(input())
    _next = [[] for _ in range(n)]
    for _ in range(n):
        u, k, *v = map(lambda s: int(s) - 1, input().split())
        _next[u] = v
    queue = deque()
    queue.append(0)
    d = [-1] * n
    d[0] = 0
    while queue:
        u = queue.popleft()
        for v in _next[u]:
            if d[v] == -1:
                d[v] = d[u] + 1
                queue.append(v)
    for i, v in enumerate(d, start=1):
        print(i, v)


if __name__ == '__main__':
    main()

