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.LinkedList;
import java.util.Queue;
import java.util.Scanner;

class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		boolean[][] connected=new boolean[200][200];
		boolean[] visied=new boolean[200];

		for(int i=0; i<n; i++) {
			//polygon information
			int u=0,k=0,v=0;
			u=sc.nextInt();
			u--;

			k=sc.nextInt();

			for(int j=0; j<k; j++) {
				v=sc.nextInt();	//input polygon data
				v--;
				connected[u][v]=true;		//graph no renketu
			}
		}
		Queue<Integer> q1,q2;
		q1=new LinkedList<Integer>();
		q2=new LinkedList<Integer>();
		boolean[] visited=new boolean[200];
		int[] ans=new int[200];
		for(int i=0; i<n; i++) {
			ans[i]=-1;
		}
		q1.add(0);

		for(int i=0; i<n; i++) {
			while(q1.size()>0) {
				int p=q1.peek();
				q1.remove();
				if(visited[p]==true) {continue;}
				else {
					visited[p]=true;
					ans[p]=i;
				}

				for(int j=0; j<n; j++) {
					if(connected[p][j]==true) {
						q2.add(j);
					}
				}
			}
			q1=q2;
			q2=new LinkedList<Integer>();
		}

		for(int i=0; i<n; i++) {
			System.out.println(i+1+" "+ans[i]);
		}

	}
}
