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 PHP (judge verdict: Runtime Error)

<?php
$n=trim(fgets(STDIN));
$tree=new Tree();
for($i=0;$i<$n;$i++) {
	$tree->insNode(trim(fgets(STDIN)));
}

for($i=0;$i<$n;$i++){
	$node=$tree->getNode($i);

	printf("node %d: parent = %d, depth = %d, %s, [%s]\n"
		,$node->id
		,$node->getParent()->id
		,$node->getDepth()
		,$node->getType()
		,implode(', ',$node->child)
	);
}

class Tree{
	public $node=array();

	function insNode($str){
		$this->node[]=new Node($this,$str);
	}
	function getNode($id){
		foreach($this->node as $node){
			if($node->id==$id){return $node;}
		}
		return new Node();
	}
}
class Node{
	public $tree;
	public $id=-1;
	public $parent;
	public $child=array();
	public $depth=-1;
	function __construct($tree='',$str=''){
		if(!$tree){return;}

		$this->tree=$tree;

		$in=explode(' ',$str);
		$this->id=(int)array_shift($in);

		$n=(int)array_shift($in);
		for($i=0;$i<$n;$i++){$this->child[]=(int)$in[$i];}
	}
	function getParent(){
		if(isset($this->parent)){return $this->parent;}
		foreach($this->tree->node as $node){
			if($node->id==$this->id){continue;}
			foreach($node->child as $child){
				if($child!=$this->id){return $this->parent=$node;}
			}
		}
		return $this->parent=new Node();
	}
	function getDepth(){
		if($this->id==-1){return -1;}
		if($this->depth>-1){return $this->depth;}

		return $this->depth=$this->getParent()->getDepth()+1;
	}
	function getType(){
		$isP=($this->getParent()->id!=-1)? 1:0;
		$isC=(count($this->child))? 1:0;
		if(!$isP){return 'root';}
		return ($isC)? 'internal node':'leaf';
	}
}