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.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		Node[] nodes = input();
		StringBuilder stringBuilder = new StringBuilder();
		for (Node node : nodes) {
			stringBuilder.append("node " + node.getId());
			stringBuilder.append(": parent = " + node.getParent().getId());
			stringBuilder.append(", depth = " + node.getDepth());
			stringBuilder.append(", " + node.getType());
			stringBuilder.append(", [");
			for (int j = 0; j < node.getChildren().size(); j++) {
				if (j != 0) {
					stringBuilder.append(", ");
				}
				stringBuilder.append(node.getChildren().get(j).getId());
			}
			stringBuilder.append("]\n");
		}
		System.out.println(stringBuilder);
		
	}
	
	public static Node[] input() throws NumberFormatException, IOException {
		BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
		int num = Integer.parseInt(bufferedReader.readLine());
		Node[] nodes = new Node[num];
		for (int i = 0; i < num; i++) {
			nodes[i] = new Node(i);
		}
		for (int i = 0; i < num; i++) {
			String[] elements = bufferedReader.readLine().split(" ");
			int id = Integer.parseInt(elements[0]);
			int nextNum = Integer.parseInt(elements[1]);
			nodes[id].setId(id);
			List<Node> children = new ArrayList<>();
			for (int j = 0; j < nextNum; j++) {
				int element = Integer.parseInt(elements[j + 2]);
				children.add(nodes[element]);
				nodes[element].setParent(nodes[id]);
			}
			nodes[id].setChildren(children);
		}
		return nodes;
	}
}

class Node {
	/** ??????????????§??? */
	private int id = -1;
	/** ????????????????????§??? */
	private Node parent;
	/** ?????????????????????????????§??? */
	private List<Node> children = new ArrayList<>();
	public Node(int id) {
		this.id = id;
		if (id != -1) {
			parent = new Node(-1);
		}
	}
	
	public int getDepth() {
		if (id == -1) {
			return 0;
		} else {
			return parent.getDepth() + 1;
		}
	}
	
	public String getType() {
		if (parent.getId() == -1) {
			return "root";
		} else if (children.isEmpty()) {
			return "leaf";
		} else {
			return "internal node";
		}
	}

	/**
	 * ????????????????????????
	 * @return id
	 */
	public int getId() {
		return id;
	}

	/**
	 * ???????????????????????????
	 * @param id ??????????????? id
	 */
	public void setId(int id) {
		this.id = id;
	}

	/**
	 * ?????????????????????
	 * @return parent
	 */
	public Node getParent() {
		return parent;
	}

	/**
	 * ????????????????????????
	 * @param parent ??????????????? parent
	 */
	public void setParent(Node parent) {
		this.parent = parent;
	}

	/**
	 * ??????????????????????????????
	 * @return children
	 */
	public List<Node> getChildren() {
		return children;
	}

	/**
	 * ????????????????????????
	 * @param children ??????????????? children
	 */
	public void setChildren(List<Node> children) {
		this.children = children;
	}

}