A rooted binary tree is a tree with a root node in which every node has at most two children.

Your task is to write a program which reads a rooted binary tree T and prints the following information for each node u of T:

* node ID of u
* parent of u
* sibling of u
* the number of children of u
* depth of u
* height of u
* node type (root, internal node or leaf)



If two nodes have the same parent, they are siblings. Here, if u and v have the same parent, we say u is a sibling of v (vice versa).

The height of a node in a tree is the number of edges on the longest simple downward path from the node to a leaf.

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

Constraints

* 1 ≤ n ≤ 25

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 is given in the following format:

id left right

id is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1.

Output

Print the information of each node in the following format:

node id: parent = p, sibling = s, degree = deg, depth = dep, height = h, type


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

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

deg, dep and h are the number of children, depth and height of the node respectively.

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.

Please follow the format presented in a sample output below.

Example

Input

9
0 1 4
1 2 3
2 -1 -1
3 -1 -1
4 5 8
5 6 7
6 -1 -1
7 -1 -1
8 -1 -1


Output

node 0: parent = -1, sibling = -1, degree = 2, depth = 0, height = 3, root
node 1: parent = 0, sibling = 4, degree = 2, depth = 1, height = 1, internal node
node 2: parent = 1, sibling = 3, degree = 0, depth = 2, height = 0, leaf
node 3: parent = 1, sibling = 2, degree = 0, depth = 2, height = 0, leaf
node 4: parent = 0, sibling = 1, degree = 2, depth = 1, height = 2, internal node
node 5: parent = 4, sibling = 8, degree = 2, depth = 2, height = 1, internal node
node 6: parent = 5, sibling = 7, degree = 0, depth = 3, height = 0, leaf
node 7: parent = 5, sibling = 6, degree = 0, depth = 3, height = 0, leaf
node 8: parent = 4, sibling = 5, degree = 0, depth = 2, height = 0, leaf
import java.io.*;
import java.util.*;
public class Main{
    public static void main(String args[]){
		Scanner scan = new Scanner(System.in);
		int numNodes = scan.nextInt();
		TempNodeData tempNodeData = new TempNodeData(scan);
		AbsNode root = AbsNode.createRoot(tempNodeData);
		Iterator<AbsNode> iter = root.treeIter();
		while(iter.hasNext())
			System.out.println(iter.next());
	}
}

abstract class AbsNode implements Comparable<Object>{
	int id;
	int height = -1;
	AbsNode parent= null;
	AbsNode left=null;
	AbsNode right=null;
	public AbsNode(){
		left=null;
		right=null;
	}
	public static AbsNode createRoot(TempNodeData data) {
		return new Root(data);
	}
	public AbsNode createNode(TempNodeData data, int tempID) {
		if(tempID == -1)
			return new NullNode();
		else
			return (!data.isLeaf(tempID))?
				new InternalNode(data, tempID, this) : new Leaf(data, tempID, this);
	}
	public AbsNode(TempNodeData data, int id, AbsNode p){
		this.id = id;
		this.parent = p;
		this.left = createNode(data, data.getLeftNodeID(id));
		this.right = createNode(data, data.getRightNodeID(id));
	}

	@Override
	public int compareTo(Object other) {
		AbsNode n = (AbsNode) other;
		return this.id - n.id; 
	}
	public int getHeight(){
		int	leftHeight = left.getHeight() + 1;
		int	rightHeight = right.getHeight() + 1;
		return leftHeight > rightHeight ? leftHeight : rightHeight;
	}
	boolean isNull(){
		return false;
	}
	String getType(){
		return "";
	}
	int getDegree(){
		return (left.isNull()?0:1) + 
				(right.isNull()?0:1);
	}
	int getParentID(){
			return parent.id;
	}
	public int getSiblingID(){
		return parent.getSiblingID(this.id);
	}
	public int getSiblingID(int id){
		return (left.id == id)?
				right.id : left.id;
	}
	int getDepth(){
		return parent.getDepth()+1;
	}
	public void treeIter(ArrayList<AbsNode> tree){
			left.treeIter(tree);
			right.treeIter(tree);
			tree.add(this);
	}
	public Iterator<AbsNode> treeIter(){
		ArrayList<AbsNode> tree = new ArrayList<AbsNode>();
		treeIter(tree);
		Collections.sort(tree);
		return tree.iterator();
	}

	@Override
	public String toString(){
		String tmp = "";
		tmp += "node " + id;
			tmp += ": parent = " + getParentID();
			tmp += ", sibling = " + getSiblingID();
		tmp += ", degree = " + getDegree();
		tmp += ", depth = " + getDepth();
		tmp += ", height = "+ getHeight();
		tmp += ", " + getType();
		return tmp;
	}
}
class InternalNode extends AbsNode{
	public InternalNode(TempNodeData data, int id, AbsNode p){
		super(data,id,p);
	}
	String getType(){
			return "internal node";
	}
}
class NullNode extends AbsNode{
	public NullNode(){
		super();
		id = -1;
	}
	boolean isNull(){
		return true;
	}
	@Override
	public int getHeight(){
		return -1;
	}
	@Override
	public void treeIter(ArrayList<AbsNode> tree){
	}
	/*int getDegree(){
		return 0;
	}*/
}
class Leaf extends AbsNode{
	public Leaf(TempNodeData data, int id, AbsNode p){
		super(data, id, p);
	}
	@Override
	public int getHeight(){
		return 0;
	}
	@Override
	public void treeIter(ArrayList<AbsNode> tree){
		tree.add(this);
	}
	String getType(){
			return "leaf";
	}
	int getDegree(){
		return 0;
	}
}
class Root extends AbsNode{
	public Root(TempNodeData data){
		super(data, data.keyOfRoot(),null);
	}
	@Override
	int getParentID(){
		return -1;
	}
	@Override
	public int getSiblingID(){
			return -1;
	}
	String getType(){
			return "root";
	}
	@Override
	int getDepth(){
		return 0;
	}
}

class TempNodeData{
	HashMap<Integer,Integer> mapLeftID = new HashMap<Integer,Integer>();
	HashMap<Integer,Integer> mapRightID = new HashMap<Integer,Integer>();
	public TempNodeData(Scanner scan){
		while(scan.hasNext()){
			int key = scan.nextInt();
			mapLeftID.put(key,scan.nextInt());
			mapRightID.put(key,scan.nextInt());
		}
	}
	public int keyOfRoot(){
		int index = 0;
		for(int i=0; i<mapLeftID.size(); i++)
			if(!mapLeftID.containsValue(i) && !mapRightID.containsValue(i)){
				index = i;
				break;
			}
		return index;
	}
	public int getLeftNodeID(int nodeID){
		return mapLeftID.get(nodeID);
	}
	public int getRightNodeID(int nodeID){
		return mapRightID.get(nodeID);
	}
	boolean isLeaf(int nodeID){
		return (mapLeftID.get(nodeID) == -1 && mapRightID.get(nodeID) == -1);
	}
}
class NodeData{
	public Integer id;
	public int left;
	public int right;
	public NodeData(int i, int r, int l){
		id = i;
		right = r;
		left = l;
	}
	public boolean isLeaf(){
		return (left==-1 && right == -1);
	}
	public boolean isLeftNull(){
		return (left==-1 && right != -1);
	}
	public boolean isRightNull(){
		return (left!=-1 && right == -1);
	}
}