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
# ALDS_11_C - 幅優先探索
import sys
import heapq

N = int(input())
G = []
for _ in range(N):
    u, k, *v = map(int, sys.stdin.readline().strip().split())
    v = [i - 1 for i in v]
    G.append(v)


distance = [-1] * N
q = []
fp = [True] * N  # 探索可能か記録する
heapq.heapify(q)
heapq.heappush(q, (0, 0))
fp[0] = False


while q:
    dist, u = heapq.heappop(q)
    distance[u] = dist
    for v in G[u]:
        if fp[v] is True:
            heapq.heappush(q, (dist + 1, v))
            fp[v] = False

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

