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.io.DataInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Main {
	
	public static void main(String[] args) throws IOException {
		Main m = new Main();
		m.input();
		m.solve();
		m.output();
	}
	
//	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	InputUtil in = new InputUtil();
	PrintWriter out = new PrintWriter(System.out);
	
	int n = 0;
	ArrayGraph<Integer> g = new ArrayGraph<Integer>(){
		public Integer getInitValueInstance() {
			return new Integer(-1);
		}

	};
	
	public void input() throws IOException {
		n = in.nextInt();
		g.init(n);
		for(int i=0; i<n; i++) {
			int v = in.nextInt();
			int k = in.nextInt();
			int[] adj = in.nextInt(new int[k]);
			g.addVertice(v, adj, 0, k);
		}
	}

	public void solve() throws IOException {
		bfs();
	}
	
	public void output() {
		for(int i=1; i<=n; i++) {
			out.print(i);
			out.print(' ');
			out.println(g.getValue(i));
		}
		out.flush();
	}
	
	private void bfs() {
		ArrayDeque<Integer> q = new ArrayDeque<>();
		g.setValue(1, 0);
		q.add(1);
		while(!q.isEmpty()) {
			int id = q.pop();
			int d = g.getValue(id);
			for(int adjid: g.getAdjNode(id)){
				int nextd = g.getValue(adjid);
				if(nextd == -1 || d+1 < nextd){
					g.setValue(adjid, d+1);
					q.add(adjid);
				}
			}
		}
	}
	
}


abstract class ArrayGraph<T> {

	int[][] adj = null;
	List<T> value = null;
	
	public ArrayGraph() {}
	
	public abstract T getInitValueInstance() ;
	
	public void init(int nodeMax) {
		adj = new int[nodeMax+1][];
		value = new ArrayList<>(nodeMax+1);
		for(int i=0; i<=nodeMax; i++) {
			value.add(getInitValueInstance());
		}
	}
	
	public void addVertice (int nodeId, int[] adjNode, int adjNodeoffset, int adjNodeLen) {
		adj[nodeId] = Arrays.copyOfRange(adjNode, adjNodeoffset, adjNodeLen);
	}
	
	public int[] getAdjNode (int nodeId) {
		return (adj == null || adj.length <= nodeId ) ? null : adj[nodeId];
	}
	
	public T getValue(int nodeId) {
		return (value == null || value.size() <= nodeId) ? null : value.get(nodeId);
	}

	public void setValue(int nodeId, T v) {
		value.set(nodeId,v);
	}
}


class InputUtil {
	//Static Fields
	private static final int BUFSIZ = 100000;
	
	//Fields
	protected InputStream in;
	private byte[] buf = null;
	private int ptr = 0;
	private int max = -1;
	private DataInputStream dis = null;
	//Constructors
	public InputUtil() {this(System.in,BUFSIZ);}
	public InputUtil(InputStream in, int bufsiz) {
		initBuf(bufsiz);
		initIn(in);
	}
	
	//Methods
	//Initializer
	protected void initIn(InputStream in) {dis = new DataInputStream(this.in = in);}
	protected void initBuf(int bufsiz) {buf = new byte[bufsiz];}
	
	//buffer operation
	private void next() throws IOException {ptr++; readBuf();}
	private void readBuf() throws IOException {
		if(ptr >= max && dis.available()>0) {
			if(max>0) Arrays.fill(buf,0,max,(byte)0);
			max = dis.read(buf);
			ptr = 0;
		}
	}
	
	//Number Input Reader/Parser
	private boolean isNum(byte b) {return '0' <= b && b <= '9'; }
	private boolean isMinus(byte b) {return b=='-'; }

	private int _nextInt() throws IOException {
		int sign = 1;
		int res = 0;
		byte c;
		while (!isNum(c=buf[ptr]) && !isMinus(c)) 
			next();
		if (isMinus(buf[ptr])) {
			sign = -1;
			next();
		}
		while (isNum(c=buf[ptr])) {
			res *= 10;
			res += c - '0' ;
			next();
		}
		next();
		return sign * res;
	}
	
	public int nextInt() throws IOException {
		readBuf();
		return _nextInt();
	}

	public int[] nextInt(int[] result) throws IOException {
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = _nextInt();
		}
		return result;
	}
	
	//Close 
	public void close() throws IOException {
		if(!this.in.equals(System.in)) 
			this.in.close();
	}

}