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 java.util.*;

public class Main {
	
    public static void main(String[] args){
    	
        final Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        boolean[][] ju = new boolean[n+1][n+1];
        
        for(int i=0;i<n+1;i++){
            Arrays.fill(ju[i],false);
        }
        
        ArrayList<ArrayList<Integer>> gr = new ArrayList<ArrayList<Integer>>();
        
        for(int i=0;i<2;i++){
            gr.add(new ArrayList<Integer>());
        }
        
        for(int i=0;i<n;i++){
            int u = sc.nextInt();
            int k = sc.nextInt();
            for(int j=0;j<k;j++){
                int v = sc.nextInt();
                ju[u][v] = true;
            }
        }
         
        int[] d = new int[n+1];
        Arrays.fill(d,-1);
        d[1] = 0;
         
        for(int i=0;i<n;i++){
            for(int k=1;k<=n;k++){
                if(d[k]==i){
                    for(int j=1;j<=n;j++){
                        if(ju[k][j] && d[j]==-1){
                            d[j] = d[k] + 1;
                        }
                    }
                }
            }
        }
         
        for(int i=1;i<=n;i++){
            System.out.println(i+" "+d[i]);
        }
    }
}