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);
		Node root = new Node(tempNodeData, tempNodeData.keyOfRoot());
		for(int i=0; i<numNodes; i++)
			System.out.println(root.getNode(i));
	}

}
class Node{
	int id;
	Node parent = null;
	Node left = null;
	Node right = null;
	int depth;
	int height = -1;
	public Node(TempNodeData data, int id){//root??¨?????????????????????
		this.id = id;
		if(data.getLeftNodeID(id)!=-1)
			this.left = new Node(data, data.getLeftNodeID(id),this);
		if(data.getRightNodeID(id)!=-1)
			this.right = new Node(data, data.getRightNodeID(id),this);
	}
	public Node(TempNodeData data, int id, Node p){
		this.id = id;
		parent = p;
		if(data.getLeftNodeID(id)!=-1)
			this.left = new Node(data, data.getLeftNodeID(id),this);
		if(data.getRightNodeID(id)!=-1)
			this.right = new Node(data, data.getRightNodeID(id),this);
	
	}
	public int getSiblingID(int id){
		if(left!=null)
			if(left.id == id)
				return right == null ? -1 : right.id;
		if(right!=null)
			if(right.id == id)
				return left == null ? -1 : left.id;
		return -1;
	}
	public void getDepth(Node n, int depth){
		if(n.parent==null)
			this.depth = depth;
		else
			getDepth(n.parent,depth+1);
	}
	public int getDepth(){
		getDepth(this, 0);
		return this.depth;
		//getDepth(this, 0);
	}
	/*public void getDepth(Node node, int d){
		node.depth = d;
		if(node.left!=null)
			getDepth(node.left,d+1);
		if(node.right!=null)
			getDepth(node.right,d+1);
	}*/
	public Node getNode(int id){
		Node temp=null;
		if(this.id==id)
			return this;
		else{
			if(left!=null)
			if(left.getNode(id)!=null)
				return left.getNode(id);
			if(right!=null)
			if(right.getNode(id)!=null)
				return right.getNode(id);
		}
		return null;
	}
	public int getHeight(){
		getHeight(this);
		return this.height;
	}
	public int getHeight(Node n){
		int leftHeight = 0;
		int rightHeight = 0;
		if(n.left==null && n.right==null)
			return n.height = 0;
		if(n.left != null)
			leftHeight = getHeight(n.left) + 1;
		if(n.right != null)
			rightHeight = getHeight(n.right) + 1;
		return n.height =
			 leftHeight > rightHeight ? leftHeight : rightHeight;
	}
	int getDegree(){
		int temp=0;
		if(left!=null)
			temp++;
		if(right!=null)
			temp++;
		return temp;
	}
	String getType(){
		if(parent ==null)
			return "root";
		else if(left==null && right ==null)
			return "leaf";
		else
			return "internal node";
	}
	@Override
	public String toString(){
		String tmp = "";
		tmp += "node " + id;
		if(parent==null){
			tmp += ": parent = -1";
			tmp += ", sibling = -1";
		}else{
			tmp += ": parent = " + parent.id;
			tmp += ", sibling = "+ parent.getSiblingID(id);
		}
		
		tmp += ", degree = " + getDegree();
		tmp += ", depth = "+ getDepth();
		tmp += ", height = "+ getHeight();
		tmp += ", " + getType();
		return tmp;
	}
}
class TempNodeData{
	//ArrayList<Integer> leftIDList = new ArrayList<Integer>();
	//ArrayList<Integer> rightIDList = new ArrayList<Integer>();
	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);
	}
}
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);
	}

}