Problem:
Binary Tree

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.

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.

Constraints

1 ≤ n ≤ 25

Sample Input 1

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

Sample Output 1

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

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Ruby (judge verdict: Accepted)

class Node
  def initialize(id)
    @id = id
    @parent = -1
    @sibling = -1
    @depth = 0
    @height = 0
    @type = nil
    @children = []
  end

  attr_accessor :id, :parent, :sibling, :depth, :height, :type, :children

  def degree
    return @children.size
  end
end

def find_root(node_map)
  node_index = node_map.values.index {|item| item.degree == 0}
  parent_index = node_index
  while parent_index > -1 
    node_index = parent_index
    parent_index = $node_map[node_index].parent
  end
  return $node_map[node_index]
end

def assign(node, depth)
  if (node.parent == -1) then
    node.type = "root"
  else
    node.type = (node.children.size > 0) ? "internal node" : "leaf"
  end

  if (node.children.size == 2) then
    $node_map[node.children[0]].sibling = node.children[1]
    $node_map[node.children[1]].sibling = node.children[0]
  end

  node.depth = depth

  node.children.each do |index|
    assign($node_map[index], depth+1)
  end
end

def assign_height(node_map)
  node_map.values.each do |node|
    if node.type == "leaf" then
      height = 0
      parent_node = node
      while parent_node.parent > -1
        parent_node = node_map[parent_node.parent]
        height += 1
        parent_node.height = [parent_node.height, height].max
      end
    end
  end
end

n = gets.chomp.to_i
$node_map = {}
n.times do |index|
  $node_map[index] = Node.new(index)
end

n.times do
  array = gets.chomp.split.map(&:to_i)
  array[1..2].each do |item|
    if (item > -1) then
      $node_map[array[0]].children << item
      $node_map[item].parent = array[0]
    end
  end
end

root = find_root($node_map)
assign(root, 0)
assign_height($node_map)

$node_map.each do |key, node|
  puts "node #{node.id}: parent = #{node.parent}, sibling = #{node.sibling}, degree = #{node.degree}, depth = #{node.depth}, height = #{node.height}, #{node.type}"
end