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
class Node():
    def __init__(self):
        self.parent = None
        self.left = None
        self.right = None
        self.depth = None
        self.height = None
        self.type = None

n = int(input())

# preparing the tree
tree = []
for _ in range(n):
    tree.append(Node())
for _ in range(n):
    id, left, right = map(int, input().split())
    if left > -1:
        tree[id].left = left
        tree[left].parent = id
    if right > -1:
        tree[id].right = right
        tree[right].parent = id
        
        
def get_type(id):
    if tree[id].parent is None:
        return 'root'
    elif (tree[id].left is None) and (tree[id].right is None):
        return 'leaf'
    else:
        return 'internal node'

# recursively set the depth of each node    
def set_depth(id, d):
    tree[id].depth = d
    if tree[id].left is not None:
        set_depth(tree[id].left, d+1)
    if tree[id].right is not None:
        set_depth(tree[id].right, d+1)

# recursively set the height of each node
def set_height(id):
    if id is None:
        pass
    elif tree[id].type == 'leaf':
        tree[id].height = 0
    else:
        left_id = tree[id].left
        right_id = tree[id].right
        set_height(left_id)
        set_height(right_id)
        
        
        tree[id].height = max(
                0 if left_id is None else tree[left_id].height + 1,  
                0 if right_id is None else tree[right_id].height + 1 
            )
         

def get_num_child(id):
    return (tree[id].left is not None)  + (tree[id].right is not None)

def get_sibling(id):
    if tree[id].type == 'root':
        out = None
    else:
        parent_node = tree[tree[id].parent]
        out = (parent_node.right if (parent_node.left == id) else parent_node.left)
    return (-1 if out is None else out)

# ==========

for id in range(n):
    tree[id].type = get_type(id)
    if tree[id].type == 'root':
        root_id = id
set_depth(root_id, 0)
set_height(root_id)

for id in range(n):
    print(f"node {id}: parent = {-1 if tree[id].parent is None else tree[id].parent}, sibling = {get_sibling(id)}, degree = {get_num_child(id)}, depth = {tree[id].depth}, height = {tree[id].height}, {tree[id].type}")

