Problem:
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Breadth First Search

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 $1, 2, ... n$.

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 $u$.

Constraints

$1 \leq n \leq 100$

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.

Sample Input 1

4
1 2 2 4
2 1 4
3 0
4 1 3

Sample Output 1

1 0
2 1
3 2
4 1

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C# (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
//using System.Threading.Tasks;

namespace Aoj.ALDS.Chapter11C
{
    class Program
    {
        public static void Solve()
        {
            int n = int.Parse(Console.ReadLine());
            var nodes = new List<Node>();
            var inputs = new List<int>[n];

            // Node????????????
            for (int i = 0; i < n; i++)
            {
                inputs[i] = new List<int>();
                inputs[i].AddRange(Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse));
                nodes.Add(new Node(inputs[i][0], inputs[i][1]));
            }

            // ???Node??????Node????¨????
            for (int i = 0; i < n; i++)
            {
                var childIds = inputs[i].Skip(2).ToArray();
                foreach (var childId in childIds)
                {
                    nodes[i].Children.Add(nodes[childId - 1]);
                }
            }

            // ???????????¢?´¢
            var queue = new Queue<Node>();
            nodes[0].D = 0;
            queue.Enqueue(nodes[0]);
            Bfs(queue);

            // ??????
            foreach (var node in nodes)
            {
                Console.WriteLine("{0} {1}", node.Id, node.D);
            }
        }


        public static void Bfs(Queue<Node> nodes)
        {
            while (nodes.Count > 0)
            {
                var current = nodes.Dequeue();
                foreach (var node in current.Children)
                {
                    if (node.D <= 0)
                    {
                        node.D = current.D + 1;
                    }
                    //Console.WriteLine("current:{0}, child{1}, child.D{2}", current.Id, node.Id, node.D);
                    if (!nodes.Contains(node))
                    {
                        //Console.WriteLine("id{0} was pushed", node.Id);
                        nodes.Enqueue(node);
                    }
                }
            }
        }

        public static void Main(string[] args)
        {
            Solve();
        }
    }

    class Node
    {
        // ???????????????
        public int Id { get; set; }

        // ????????°
        public int K { get; set; }

        // ????????????
        public int D { get; set; }

        // ?¨??????????????????°
        public bool Visited { get; set; }


        // ??£??\???????????????(???????????????)
        public List<Node> Children { get; set; }

        public Node(int id, int k)
        {
            Id = id;
            K = k;

            D = -1;
            Visited = false;
            Children = new List<Node>();
        }
    }
}