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 Aoj.ALDS.Chapter7A
{
    class Program
    {
        public static List<Node> RootedTree;

        public static void SetDepth(Node node, int depth)
        {
            node.Depth = depth;
         
            if (node.LeftChildId() > -1) {
                SetDepth(RootedTree[node.LeftChildId()], depth + 1);
            }

            if (node.RightSiblingId > -1) {
                SetDepth(RootedTree[node.RightSiblingId], depth);
            }
        }

        public class Node
        {
            public int Id { get; set; } 
            public int ParentId { get; set; }
            public int RightSiblingId { get; set; }
            public List<int> ChildIds { get; set; }
            public int Depth { get; set; }


            public Node(int id)
            {
                Id = id;

                ParentId = -1;
                RightSiblingId = -1;

                ChildIds = new List<int>();

                Depth = -1;
            }

            public bool IsRoot()
            {
                return ParentId <= -1;
            }

            public bool IsLeaf()
            {
                return ! IsRoot() && ChildIds.Count() == 0;
            }

            public int LeftChildId()
            {
                return (ChildIds.Count() > 0) ? ChildIds[0] : -1;
            }

            public override string ToString()
            {
                string type = "internal node";
                if (IsRoot()) {
                    type = "root";
                }
                if (IsLeaf()) {
                    type = "leaf";
                }

                string childIds = string.Join(", ", Array.ConvertAll(ChildIds.ToArray(), (i) => { return i.ToString(); }));

                return string.Format(
                    "node {0}: parent = {1}, depth = {2}, {3}, [{4}]", Id, ParentId, Depth, type, childIds
                );
            }
        }

        public static void Solve()
        {
            RootedTree = new List<Node>();

            int n = int.Parse(Console.ReadLine());


            for (int i = 0; i < n; i++)
            {
                RootedTree.Add(new Node(i));
            }

            for (int i = 0; i < n; i++)
            {
                int[] inputs = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                var parentNode = RootedTree[inputs[0]];

                parentNode.ChildIds = inputs.Skip(2).ToList();
                for (int j = 0; j < parentNode.ChildIds.Count(); j++)
                {
                    int childId = parentNode.ChildIds[j];
                    var childNode = RootedTree[childId];

                    childNode.ParentId = parentNode.Id;
                    if (childId != parentNode.ChildIds.Last()) {
                        childNode.RightSiblingId = parentNode.ChildIds[j + 1];
                    }
                }
            }

            Node rootNode = null;
            for (int i = 0; i < n; i++)
            {
                if (RootedTree[i].IsRoot()) {
                    rootNode = RootedTree[i];
                }
            }

            SetDepth(rootNode, 0);

            for (int i = 0; i < n; i++)
            {
                Console.WriteLine(RootedTree[i]);
            }
        }

        public static void Main()
        {
            Solve();
        }
    }
}