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.DataInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;


public class Main {
	
	public static void main(String[] args) throws IOException, InstantiationException, IllegalAccessException {
		new Main().exec();
	}
	
	public void exec() throws IOException, InstantiationException, IllegalAccessException {
		InputUtil in = new InputUtil();
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		BinaryTree bt = new BinaryTree(n);
		
		for(int i=0; i<n; i++){
			int id = in.nextInt();
			int leftId = in.nextInt();
			int rightId = in.nextInt();
			bt.setNode(id, leftId, rightId);
		}
		bt.refresh();
		out.print(bt);
		out.flush();
	}
}


class BinaryTree {
	
	private int[] left;
	private int[] right;
	private int[] parent;
	private int[] sibling;
	private int[] degree;
	private int[] depth;
	private int[] height;
	private int maxNodes;
	
	public BinaryTree(int maxNodes) {
		this.maxNodes=maxNodes;
		left = new int[maxNodes];
		right = new int[maxNodes];
		parent = new int[maxNodes];
		
		sibling = new int[maxNodes];
		degree = new int[maxNodes];
		depth = new int[maxNodes];
		height = new int[maxNodes];
		
		
		Arrays.fill(left, -1);
		Arrays.fill(right, -1);
		Arrays.fill(parent, -1);
		Arrays.fill(sibling, -1);
	}
	
	public void setNode(int id, int leftId, int rightId) {
		left[id] = leftId;
		if(leftId != -1) {
			parent[leftId] = id;
			sibling[leftId] = rightId;
		}
		right[id] = rightId;
		if(rightId != -1) {
			parent[rightId] = id;
			sibling[rightId] = leftId;
		}
	}
	
	public int getRootId() {
		int rootId = 0;
		while(parent[rootId] != -1)
			rootId = parent[rootId];
		return rootId;
	}
	
	public void refresh() throws InstantiationException, IllegalAccessException {
		refresh(getRootId(),0);
	}
	
	private int refresh(int id, int d) throws InstantiationException, IllegalAccessException {
		depth[id] = d;
		if(left[id] != -1) {
			degree[id] ++;
			height[id] = refresh(left[id], d+1);
		}
		if(right[id] != -1) {
			degree[id] ++;
			height[id] = Math.max(height[id], refresh(right[id], d+1));
		}
		return height[id]+1;
	}

	
	public String toString() {
		StringBuilder sb = new StringBuilder();
		for(int i=0; i<maxNodes; i++) {
			sb.append("node ").append(i)
				.append(": parent = ").append(parent[i])
				.append(", sibling = ").append(sibling[i])
				.append(", degree = ").append(degree[i])
				.append(", depth = ").append(depth[i])
				.append(", height = ").append(height[i])
				.append(", ");

			if(parent[i] == -1)
				sb.append("root");
			else if(left[i] == -1 && right[i] == -1)
				sb.append("leaf");
			else 
				sb.append("internal node");
			
			sb.append(System.lineSeparator());
		}
		return sb.toString();
	}
}


class InputUtil {
	//Static Fields
	private static final int BUFSIZ = 100000;
	
	//Fields
	protected InputStream in;
	private byte[] buf = null;
	private int ptr = 0;
	private int max = -1;
	private DataInputStream dis = null;
	//Constructors
	public InputUtil() {this(System.in,BUFSIZ);}
	public InputUtil(InputStream in, int bufsiz) {
		initBuf(bufsiz);
		initIn(in);
	}
	
	//Methods
	//Initializer
	protected void initIn(InputStream in) {dis = new DataInputStream(this.in = in);}
	protected void initBuf(int bufsiz) {buf = new byte[bufsiz];}
	
	//buffer operation
	private void next() throws IOException {ptr++; readBuf();}
	private void readBuf() throws IOException {
		if(ptr >= max && dis.available()>0) {
			if(max>0) Arrays.fill(buf,0,max,(byte)0);
			max = dis.read(buf);
			ptr = 0;
		}
	}
	
	//Number Input Reader/Parser
	private boolean isNum(byte b) {return '0' <= b && b <= '9'; }
	private boolean isMinus(byte b) {return b=='-'; }

	private int _nextInt() throws IOException {
		int sign = 1;
		int res = 0;
		byte c;
		while (!isNum(c=buf[ptr]) && !isMinus(c)) 
			next();
		if (isMinus(buf[ptr])) {
			sign = -1;
			next();
		}
		while (isNum(c=buf[ptr])) {
			res *= 10;
			res += c - '0' ;
			next();
		}
		next();
		return sign * res;
	}
	
	public int nextInt() throws IOException {
		readBuf();
		return _nextInt();
	}

	public int[] nextInt(int[] result) throws IOException {
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = _nextInt();
		}
		return result;
	}
	
	//Close 
	public void close() throws IOException {
		if(!this.in.equals(System.in)) 
			this.in.close();
	}

}