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


//template code, C343, 2019
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

class Graph2 {
	int totalVertex;
	Queue<Integer> toVisit;
	int[] distance;
	public LinkedList<LinkedList<Integer>> adjList;
	//adjacency list of edges
	public Graph2() { totalVertex = 0; }
	public void loadAdjList() {
		Scanner in = new Scanner(System.in);
		totalVertex = in.nextInt();
		toVisit = new LinkedList<Integer>();
		distance = new int[totalVertex];
		adjList = new LinkedList<LinkedList<Integer>>();
		for(int i = 0; i < totalVertex; i ++) {
			LinkedList<Integer> tmp = new LinkedList<Integer>();
			int idx1 = in.nextInt() - 1;
			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);
		}
		
		for(int i = 1; i < totalVertex; i++) {
			distance[i] = Integer.MAX_VALUE;
		}
		
		in.close();
	}
	
	
	public void BFS(int v) {
		toVisit.add(v);
		while(!toVisit.isEmpty()) {
			int next = toVisit.remove();
			for(int neighbor : adjList.get(next)) {
				if(!toVisit.contains(neighbor)) {
					if(distance[neighbor] > distance[next] + 1) {
						toVisit.add(neighbor);
						distance[neighbor] = distance[next] + 1;
					}
				}
			}
		}
	}
	
	public void SearchGraph() {
		BFS(0);
		for(int i = 0; i < totalVertex; i++) {
			if(distance[i] == Integer.MAX_VALUE) {
				distance[i] = -1;
			}
			System.out.println(i+1 + " " + distance[i]);
		}
	}
	
}
//change class name GraphRepresentation to Main() for submission to AIZU
public class Main {

	
	public static void main(String argv[]) {
		Graph2 g = new Graph2();
		g.loadAdjList();
		g.SearchGraph();
	}
}
