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.util.InputMismatchException;
import java.util.StringTokenizer;

class Main {
	
	static class RootedTrees {
		public void rootedtrees (InputReader ir) {
			
			int n = ir.nextInt();
			Node[] node = new Node[n];
			
			for (int i = 0; i < n; i++) {
				int id = ir.nextInt();
				int k = ir.nextInt();
				node[id] = new Node (k);
				
				if ( k != 0) {
					for (int j = 0; j < k; j++) {
						node[id].type[j] = ir.nextInt();
					}
				}
			}
			
			Parent(node);
			Depth(node);
			
			StringBuilder sb = new StringBuilder();
			
			for (int i = 0; i < n; i++) {
				
				int k = node[i].type.length;
				
				sb.append("node ").append(Integer.toString(i))
				.append(": parent = ").append(node[i].parent)
				.append(", depth = ").append(node[i].depth);
				
				if (node[i].parent == -1) {
					sb.append(", root, [");
				} else if (k == 0){
					sb.append(", leaf, [");
				} else {
					sb.append(", internal node, [");
				}
				
				if (k != 0) {
					for (int j = 0; j < k; j++) {
						sb.append(node[i].type[j]);
						if (j != k - 1) {
							sb.append(", ");
						}
					}
				}
				sb.append("]\n");
				
			}
			
			System.out.print(sb);
			
			
		}
		
		static void Parent (Node[] node) {
			
			int n = node.length;
			
			for (int i = 0; i < n; i++) {
				int lentype = node[i].type.length;
				for (int j = 0; j < lentype; j++) {
					node[node[i].type[j]].parent = i;
				}
			}
			
		}
		
		static void Depth (Node[] node) {
			int n = node.length;
			
			for (int i = 0; i < n; i++) {
				int lentype = node[i].type.length;
				for (int j = 0; j < lentype; j++) {
					node[node[i].type[j]].depth += node[i].depth;
				}
			}
		}
		
		
		
	}
	
	static class Node {
		int parent;
		int depth;
		int[] type;
		public Node(int n) {
			parent = -1;
			depth = 0;
			type = new int[n];
		}
		
	}
	
	static class InputReader {
		BufferedReader br;
		StringTokenizer st;
		
		public String nextString() {
			
			 while (!st.hasMoreTokens()) {
	                try {
	                    st = new StringTokenizer(br.readLine(), " ");
	                } catch (IOException e) {
	                    throw new InputMismatchException();
	                }
	            }
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(nextString());
		}
					
		public InputReader (InputStream inputStream) {
			br = new BufferedReader (new InputStreamReader (inputStream));
			st = new StringTokenizer ("");
		}
		
	}
	
	public static void main (String[] args) {
		InputStream inputStream = System.in;
		InputReader in = new InputReader (inputStream);
		RootedTrees obj = new RootedTrees();
		obj.rootedtrees(in);
	}
	
}