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

/*
 * 二叉树 
 * ALDS1_7_B
 * 
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;



public class Main {
	
	
	
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = "";
		while ((line = br.readLine()) != null && !line.isEmpty()) {

			int n = Integer.parseInt(line);
			Tree tree = new Tree();

			// ??????????則????
			for (int i = 0; i < n; i++) {
				tree.addNode(br.readLine());
			}
			// ??????????????賊??????
			for (int i = 0; i < n; i++) {
				System.out.println(tree.getNode(i).toString());
			}
		}
		
	}
	
	
	public static class Tree {
		ArrayList<Node> nodes = new ArrayList<Node>();
		
		void addNode(String info)
		{
			int pid, lid, rid;
			pid = Integer.parseInt(info.split(" ")[0]);
			lid = Integer.parseInt(info.split(" ")[1]);
			rid = Integer.parseInt(info.split(" ")[2]);
			
			Node parent, left = null, right = null;
			if((parent=getNode(pid))==null)
			{
				parent = new Node(pid,null);
			}
			
			
			
			if (lid != -1) 
			{
				if ((left = getNode(lid)) == null) 
				{
					left = new Node(lid, parent);
				} 
				else 
				{
					left.parent = parent;
					nodes.remove(left);
				}
			}
			//
			if (rid != -1) 
			{
				if ((right = getNode(rid)) == null)
				{
					right = new Node(rid, parent);
				} 
				else 
				{
					right.parent = parent;
					nodes.remove(right);
				}
			}
			
			parent.left = left;
			parent.right = right;
			
			if (parent.parent == null) 
			{
				nodes.add(parent);
			}
		}
			
			
			
			Node getNode(int id) 
			{
				Node result = null;
				for (Node n : nodes) {
					result = n.find(id);
					if (result != null)
						break;
				}
				return result;
			}
		
	}
	
	
	public static class Node {
		int id;  //节点编号
		Node parent; // 父节点 -1表示没有
		Node left; 
		Node right; //左右子节点 -1表示没有
		
		
		Node(int value, Node parent)
		{
			this.id = value;
			this.parent = parent;
		}
		
		//方法find 返回一个Node
		
		Node find(int id)
		{
			
			//就一直找
			Node result = null;
			if(this.id == id)
			{
				result = this;
			}
			
			if(result == null && left != null)
			{
				result = left.find(id);
			}
			
			if(result == null && right != null)
			{
				result = right.find(id);
			}
			
			return result;
		}
		
		//返回id
		int id()
		{
			return id;
		}
		
		//返回父节点 id
		int parentId()
		{
			if(parent != null)
				return parent.id();
			else
				return -1;
		}
		
		//返回兄弟节点
		int sibling()
		{
			int lid, rid;
			if(parent != null)
			{
				if(parent.left != null)
					lid = parent.left.id();
				else
					lid = -1;
				if(parent.right != null)
					rid = parent.right.id();
				else
					rid = -1;
			
				//这里的lid 和 rid 是父节点的 左子节点和右子节点
				//由于是二叉树
				//lid 和 rid 有一个是id
				//如果自己是lid 及左节点，返回右节点
				//如果自己是rid 及右节点，返回左节点
				return lid != id ? lid : rid;
			}
			else
			{
				//没有父节点，根节点
				return -1;
			}
		}
		
		
		//返回度数，即子节点的个数
		int degree()
		{
			int result = 0;
			if(left != null)
			{
				result++;
			}
			if(right != null)
			{
				result++;
			}
			
			return result;
		}
		
		
		//返回深度
		int depth()
		{
			int result = 0;
			Node p = parent;
			while(p != null)
			{
				result++;
				p = p.parent;
			}
			return result;
		}
		
		
		// 返回高
		int height()
		{
			int lh = 0;
			int rh = 0;
			if(left != null)
			{
				//一路往下，找到没有
				lh = left.height()+1;
			}
			if(right != null )
			{
				rh = right.height()+1;
			}
			return lh>rh ? lh: rh;
		}
		
		//
		String type()
		{
			String result = "";
			if(parent==null)
			{
				return "root";
			}
			if(left!=null||right!=null)
			{
				return "internal node";
			}
			if(left==null&&right==null)
			{
				return "leaf";
			}
			
			return result;
		}
		
		
		public String toString()
		{
			StringBuilder sb = new StringBuilder();
			sb.append("node " + id() + ": ");
			sb.append("parent = " + parentId() + ", ");
			sb.append("sibling = " + sibling() + ", ");
			sb.append("degree = " + degree() + ", ");
			sb.append("depth = " + depth() + ", ");
			sb.append("height = " + height() + ", ");
			sb.append(type());
			return sb.toString();
		}
		
		
	}
	
	
	
	
	
	
}

