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.Scanner;
import java.util.Arrays;
import java.util.Iterator;
import java.util.Queue;

class Graph {
	private int totalVertex;
	private LinkedList<LinkedList<Integer>> adjList;
	//adjacency list of edges
	public Graph() { totalVertex = 0; }
	public void loadAdjList() {
		Scanner in = new Scanner(System.in);
		totalVertex = in.nextInt();   //4
		adjList = new LinkedList<LinkedList<Integer>>();
		for(int i = 0; i < totalVertex; i ++) {
			LinkedList<Integer> tmp = new LinkedList<Integer>();
			int idx1 = in.nextInt() - 1;  //2-1=0
			int degree = in.nextInt();//1
			//System.out.println("mark idx1 = " + idx1 + " degree = " + degree);
			for(int j = 0; j < degree; j ++) {
				int idx2 = in.nextInt() - 1; //4-1=3
				tmp.add(idx2);// adds 3
			}	
			adjList.add(tmp);
		}
		in.close();
	}
	
	public void printAdjMatrix() {
		Integer[][] adjMatrix = new Integer[totalVertex][totalVertex];
		System.out.println(adjList);
		adjMatrix[0][0] = (adjList.get(0).get(0));
		
		//Assign the matrix 0's
		for (int i=0; i<totalVertex;i++) {
			for (int j =0; j < totalVertex; j++) {
				adjMatrix[i][j] = 0;
			}
		}
		// uses index to change 0 to 1
		for (int i=0; i <totalVertex;i++) {
			for (int j=0; j< adjList.get(i).size(); j++) {
				adjMatrix[i][adjList.get(i).get(j)] = 1;
			}
		}
		System.out.println(Arrays.deepToString(adjMatrix));
		
		for(int i =0; i < totalVertex;i++) {
			for (int j =0; j < totalVertex; j++) {
				System.out.print(adjMatrix[i][j]);
				if(j == totalVertex-1) {
					
				}
				else {
					System.out.print(" ");
				}
			}
			System.out.println();
		}
		//complete the following
	}
	int visited[];
	int distance[];
	public void bfs() {
		
		visited = new int[totalVertex];
		distance = new int[totalVertex];
		Queue<Integer> q = new LinkedList<>();
		q.add(0); // start at node 1
		//set distance to -1
		for(int i=0; i<distance.length;i++) {
			distance[i] = -1;
		}
		distance[0] = 0;
		
		while (!q.isEmpty()) {
			//if visited
			int v = q.remove();
			
			// if not visited
				// adding links to q and updating distance
				for(int i=0; i<adjList.get(v).size();i++) {
					int u = adjList.get(v).get(i);
					if(distance[u]!=-1) continue;
					distance[u] = distance[v] + 1;
					q.add(u);
				}
			
	    }
		for (int i=0; i<totalVertex; i++) {
			System.out.println(i+1 + " " + distance[i]);		
		}
    }
	public int checkVisited(int node) {
		for(int i=0; i<visited.length;i++) {
			if (visited[i]==node) {
				return 1;
			}
		}
		return 0;
	}
}
//change class name GraphRepresentation to Main() for submission to AIZU
public class Main{
	
	public static void main(String argv[]) {
		Graph g = new Graph();
		g.loadAdjList();
		//g.printAdjMatrix();
		g.bfs();
	}
}
