Problem:
Rooted Trees

A graph G = (V, E) is a data structure where V is a finite set of vertices and E is a binary relation on V represented by a set of edges. Fig. 1 illustrates an example of a graph (or graphs).

Fig. 1

A free tree is a connnected, acyclic, undirected graph. A rooted tree is a free tree in which one of the vertices is distinguished from the others. A vertex of a rooted tree is called "node."

Your task is to write a program which reports the following information for each node u of a given rooted tree T:

node ID of u

parent of u

depth of u

node type (root, internal node or leaf)

a list of chidlren of u

If the last edge on the path from the root r of a tree T to a node x is (p, x), then p is the parent of x, and x is a child of p. The root is the only node in T with no parent.

A node with no children is an external node or leaf. A nonleaf node is an internal node

The number of children of a node x in a rooted tree T is called the degree of x.

The length of the path from the root r to a node x is the depth of x in T.

Here, the given tree consists of n nodes and evey node has a unique ID from 0 to n-1.

Fig. 2 shows an example of rooted trees where ID of each node is indicated by a number in a circle (node). The example corresponds to the first sample input.

Fig. 2

Input

The first line of the input includes an integer n, the number of nodes of the tree.

In the next n lines, the information of each node u is given in the following format:

id k c1 c2 ... ck

where id is the node ID of u, k is the degree of u, c1 ... ck are node IDs of 1st, ... kth child of u. If the node does not have a child, the k is 0.

Output

Print the information of each node in the following format ordered by IDs:

node id: parent = p, depth = d, type, [c1...ck]

p is ID of its parent. If the node does not have a parent, print -1.

d is depth of the node.

type is a type of nodes represented by a string (root, internal node or leaf). If the root can be considered as a leaf or an internal node, print root.

c1...ck is the list of children as a ordered tree.

Please follow the format presented in a sample output below.

Constraints

1 ≤ n ≤ 100000

Sample Input 1

13
0 3 1 4 10
1 2 2 3
2 0
3 0
4 3 5 6 7
5 0
6 0
7 2 8 9
8 0
9 0
10 2 11 12
11 0
12 0

Sample Output 1

node 0: parent = -1, depth = 0, root, [1, 4, 10]
node 1: parent = 0, depth = 1, internal node, [2, 3]
node 2: parent = 1, depth = 2, leaf, []
node 3: parent = 1, depth = 2, leaf, []
node 4: parent = 0, depth = 1, internal node, [5, 6, 7]
node 5: parent = 4, depth = 2, leaf, []
node 6: parent = 4, depth = 2, leaf, []
node 7: parent = 4, depth = 2, internal node, [8, 9]
node 8: parent = 7, depth = 3, leaf, []
node 9: parent = 7, depth = 3, leaf, []
node 10: parent = 0, depth = 1, internal node, [11, 12]
node 11: parent = 10, depth = 2, leaf, []
node 12: parent = 10, depth = 2, leaf, []

Sample Input 2

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

Sample Output 2

node 0: parent = 1, depth = 1, leaf, []
node 1: parent = -1, depth = 0, root, [3, 2, 0]
node 2: parent = 1, depth = 1, leaf, []
node 3: parent = 1, depth = 1, leaf, []

Note

You can use a left-child, right-sibling representation to implement a tree which has the following data:

the parent of u

the leftmost child of u

the immediate right sibling of u

Reference

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

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ALDS1_7_A
{
    public class Program

    {

        public class Node
        {
            public int Parent;
            public int Depth;
            public string NodeTypes;
            public List<int> Children;

            public Node()
            {
                Parent = -1;
                Depth = -1;
                NodeTypes = "";
                Children = new List<int>();
            }
        }

        public static void Main(string[] args)
        {
            int n = ReadInt();
            SortedDictionary<int,Node> nodes = new SortedDictionary<int, Node>();

            for (int i = 0 ; i < n ; i++)
            {
                int[] line = ReadIntAr();
                nodes.Add(line[0],new Node());
                for (int j = 0 ; j < line[1] ; j++)
                { 
                    nodes[line[0]].Children.Add(line[j + 2]);
                }
            }

            foreach (var item in nodes)
            {
                for (int i = 0 ; i < item.Value.Children.Count ; i++)
                {
                    nodes[item.Value.Children[i]].Parent = item.Key;
                }

            }

            int rootNode = -1;
            foreach (var item in nodes)
            {
                if (item.Value.Parent == -1)
                {
                    item.Value.NodeTypes = "root";
                    item.Value.Depth = 0;
                    rootNode = item.Key;
                }
                else if (item.Value.Children.Count == 0)
                {
                    item.Value.NodeTypes = "leaf";
                }
                else
                {
                    item.Value.NodeTypes = "internal node";
                }
            }

            Queue<Node> nodeQ = new Queue<Node>();

            nodeQ.Enqueue(nodes[rootNode]);
            while (nodeQ.Count() != 0)
            {
                Node node = nodeQ.Dequeue();
                if (node.Depth == -1) { node.Depth = nodes[node.Parent].Depth + 1; }
                for (int i = 0 ; i < node.Children.Count ; i++) { nodeQ.Enqueue(nodes[node.Children[i]]); }
            }


            foreach (var item in nodes)
            {
                Console.WriteLine("node {0}: parent = {1}, depth = {2}, {3}, [{4}]",
                    item.Key, item.Value.Parent, item.Value.Depth, item.Value.NodeTypes, String.Join(", ", item.Value.Children.Select(x => x.ToString()).ToArray()));
            }

        }

        static string ReadSt() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Console.ReadLine()); }
        static long ReadLong() { return long.Parse(Console.ReadLine()); }
        static double ReadDouble() { return double.Parse(Console.ReadLine()); }
        static string[] ReadStAr(char sep = ' ') { return Console.ReadLine().Split(sep); }
        static int[] ReadIntAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => int.Parse(e)); }
        static long[] ReadLongAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => long.Parse(e)); }
        static double[] ReadDoubleAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => double.Parse(e)); }

    }

}