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 Python3 (judge verdict: Accepted)

# copy
class Tree():
    def __init__(self):
        self.nodes = {}

    def add_node(self, id):
        if id not in self.nodes:
            self.nodes[id] = Node(id)

    def add_child(self, parent_id, child_id):
        self.add_node(parent_id)
        self.add_node(child_id)
        self.nodes[parent_id].add_child(self.nodes[child_id])


class Node():
    def __init__(self, id):
        self.id = id
        self.parent = None
        self.children = []
        self.depth = 0
        self.nodetype = 'root'

    def add_child(self, child):
        self.children.append(child)
        child.parent = self
        child.update_depth()
        child.update_nodetype()
        self.update_nodetype()
        if self.parent:
            self.parent.update_nodetype()

    def update_depth(self):
        depth = self.depth
        if self.parent:
            self.depth = self.parent.depth + 1
        if depth != self.depth:
            for child in self.children:
                child.update_depth()

    def update_nodetype(self):
        if self.parent:
            if len(self.children):
                self.nodetype = 'internal node'
            else:
                self.nodetype = 'leaf'
        else:
            self.nodetype = 'root'

    def walk(self):
        yield self
        for child in self.children:
            for node in child.walk():
                yield node

    def __str__(self):
        parent = self.parent.id if self.parent else -1
        children = ', '.join([str(node.id) for node in self.children])
        return 'node {}: parent = {}, depth = {}, {}, [{}]'.format(self.id,
                                                                   parent,
                                                                   self.depth,
                                                                   self.nodetype,
                                                                   children)


tree = Tree()

n = int(input())
for i in range(n):
    line = input().split()
    id = int(line[0])
    tree.add_node(id)
    for ci in map(int, line[2:]):
        tree.add_child(id, ci)

for id in sorted(tree.nodes):
    print(tree.nodes[id])