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 JAVA (judge verdict: Wrong Answer)



import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.Serializable;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;

import javax.swing.plaf.synth.SynthStyle;

public class Main {

	class Node {

		@Override
		public int hashCode() {
			// TODO Auto-generated method stub
			return super.hashCode();
		}

		private int id;
		private int parent;
		private int depth;
		private String type;
		private ArrayList<Integer> children = new ArrayList<>();

		public Node(int id) {
			this.id = id;
			this.parent = -1;
		}

		public int getId() {
			return id;
		}

		public int getDepth() {
			return depth;
		}

		public void setDepth(int depth) {
			this.depth = depth;
		}

		public String getType() {
			return type;
		}

		public void setType(String type) {
			this.type = type;
		}

		public int getParent() {
			return parent;
		}

		public void addChild(Integer child) {
			children.add(child);
		}

		public void setType() {
			if (parent == -1) {
				type = "root";
			} else if (children.size() == 0) {
				type = "leaf";
			} else {
				type = "internal node";
			}
		}

		public void setParent(int parent) {
			this.parent = parent;
		}

		@Override
		public boolean equals(Object obj) {
			Node node = (Node) obj;
			if (this.id == node.getId()) {
				return true;
			} else {
				return false;
			}

		}

		@Override
		public String toString() {
			setType();
			return "node " + id + ": " + "parent = " + parent + ", depth = " + depth + ", " + type + ", " + children;
		}

	}

	HashMap<Integer, Node> nodes = new HashMap<>();

	private void solv() {
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();

		for (int i = 0; i < n; i++) {
			Node parentNode;
			int parentId = input.nextInt();
			if (nodes.containsKey(parentId)) {
				parentNode = nodes.get(parentId);
			} else {
				parentNode = new Node(parentId);
			}

			int cn = input.nextInt();
			for (int j = 0; j < cn; j++) {
				Node childNode;
				int childId = input.nextInt();
				if (nodes.containsKey(childId)) {
					childNode = nodes.get(childId);
				} else {
					childNode = new Node(childId);
				}

				childNode.setParent(parentId);
				parentNode.addChild(childId);
				nodes.put(childId, childNode);
			}
			nodes.put(parentId, parentNode);
		}

		for (int key : nodes.keySet()) {
			nodes.get(key).setDepth(calcDepth(nodes.get(key), 0));
			System.out.println(nodes.get(key));
		}
	}

	public int calcDepth(Node parent, int depth) {
		if (parent.getParent() == -1) {
			return depth;
		} else {
			return calcDepth(nodes.get(parent.getParent()), ++depth);
		}
	}

	public class NodeComparator implements Comparator<Node> {
		@Override
		public int compare(Node n1, Node n2) {
			return n1.getId() < n2.getId() ? -1 : 1;
		}
	}

	public static void main(String[] args) {
		Main main = new Main();
		main.solv();
	}

	private void print(Object[] xs) {
		StringBuilder sb = new StringBuilder();
		for (Object x : xs)
			sb.append(x.toString()).append(' ');
		System.out.println(sb.toString().trim());
	}

	private void print(int[] xs) {
		StringBuilder sb = new StringBuilder();
		for (int i = 1; i < xs.length; i++) {
			sb.append(xs[i]).append(' ');
		}
		System.out.println(sb.toString().trim());
	}

	private static class Scanner {
		BufferedReader r;
		StreamTokenizer st;

		public Scanner(InputStream in) {
			r = new BufferedReader(new InputStreamReader(in));
			st = new StreamTokenizer(r);
		}

		public String next() {
			nextToken();
			return st.sval;
		}

		public Integer nextInt() {
			nextToken();
			return (int) st.nval;
		}

		private int nextToken() {
			int token = st.TT_EOF;
			try {
				token = st.nextToken();
			} catch (IOException e) {
			}
			return token;
		}
	}

}