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;
import java.util.Iterator;

public class Main {
	public static void main(String[] args) {
		Graph g = new Graph();
		g.loadAdjList();
		g.BFS(0);
		for(int i = 0; i < g.getDistance().length; i++) {
			if (i != 0 && g.getDistance()[i] == 0) {
				System.out.println(i+1 + " " + "-1");
			}else {
				System.out.println(i+1 + " " + g.getDistance()[i]);
			}
		}
	}
	
}

class Graph {
	
	private int totalVertex;
	private LinkedList<LinkedList<Integer>> adjList;
	private boolean[] if_visited;
	private int[] discover_time;
	private int[] complete_time;
	private int[] id;
	private static int timestamp = 1;
	private int[] dist;
	
	
	public boolean[] getVisited() {
		return if_visited;
	}
	
	public int[] getDistance() {
		return dist;
	}
	
	//adjacency list of edges
	public Graph() { totalVertex = 0; }
	public void loadAdjList() {
		Scanner in = new Scanner(System.in);
		
		totalVertex = in.nextInt();
		adjList = new LinkedList<LinkedList<Integer>>();
		if_visited = new boolean[totalVertex];
		discover_time = new int[totalVertex];
		complete_time = new int[totalVertex];
		id = new int[totalVertex];
		dist = new int[totalVertex];
		
		for(int i = 0; i < totalVertex; i ++) {
			LinkedList<Integer> tmp = new LinkedList<Integer>();
			int idx1 = in.nextInt() - 1;
			if_visited[idx1] = false;
			id[idx1] = i;
			dist[idx1] = 0;
			int degree = in.nextInt();
			//System.out.println("mark idx1 = " + idx1 + " degree = " + degree);
			for(int j = 0; j < degree; j ++) {
				int idx2 = in.nextInt() - 1;
				tmp.add(idx2);
			}	
			adjList.add(tmp);
		}
		in.close();
	}
	public void printAdjMatrix() {
		Integer[][] adjMatrix = new Integer[totalVertex][totalVertex];
		//complete the following
		for (int i = 0; i < totalVertex; i++) {
			for (int j = 0; j< totalVertex; j++) {
				if (adjList.get(i).contains(j)) {
					adjMatrix[i][j] = 1;
				}else {
					adjMatrix[i][j] = 0;				
				}
				if (j == totalVertex - 1) {
					System.out.println(adjMatrix[i][j]);
					
				}else {
					System.out.print(adjMatrix[i][j] + " ");
				}
			}
		}
	}
	
	public void DFS(int id) {
		if(!if_visited[id]) {
			if_visited[id] = true;
			discover_time[id] = timestamp;
			timestamp += 1;
			Iterator<Integer> i = adjList.get(id).listIterator();
			while(i.hasNext()) {
				int n = i.next();
				DFS(n);
			}
			complete_time[id] = timestamp++;
		}else {
			
		}
		
	}
	
	public void call_DFS(int id) {
		DFS(id);
	}
	
	
	public void show_result() {
		for (int i = 0; i < totalVertex; i++) {
			System.out.print(id[i] + 1 + " ");
			System.out.print(discover_time[id[i]] + " ");
			System.out.print(complete_time[id[i]] + " ");
			System.out.println();
		}
	}
	
	public void BFS(int src) {
		if_visited[src] = true;
		Queue<Integer> q = new LinkedList<>();
		q.add(src);
		while(!q.isEmpty()) {
			int u = q.remove();
			//if_visited[u] = true;
			LinkedList<Integer> tmp = adjList.get(u);
			for(int i = 0; i < tmp.size(); i++) {
				if(!if_visited[tmp.get(i)]) {
					if_visited[tmp.get(i)] = true;
					//if(!q.contains(tmp.get(i))){
					q.add(tmp.get(i));
					dist[tmp.get(i)] = dist[u] + 1;
					//}
				}
			}
		}
	}
	
}


