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
#!/usr/bin/python3

def find(id, V, d, dist):
    i = id - 1
    dist[i] = d
    for v in V[i]:
        if dist[v - 1] == -1 or dist[v - 1] > d + 1:
            find(v, V, d + 1, dist)
    
n = int(input())
# [isFind, d, f]
A = [[False, 0, 0] for i in range(n)]
U = []
V = []
dist = [-1] * n
for i in range(n):
    l = list(map(int, input().split()))
    U.append(l[0])
    V.append(l[2:])

find(1, V, 0, dist)

for u in U:
    print(u, dist[u - 1])