human
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

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

Constraints

* 1 ≤ n ≤ 100000

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....
Solve the task in PYTHON3.
assistant
#Here is Python code to print the information of each node in the following format ordered by IDs:
.

#coding:utf-8
#1_7_A
class Node():
    def __init__(self, node_id, children):
        self.node_id = node_id
        self.parent = -1
        self.depth = 0
        self.typ = "root"
        self.children = children

    def set_child(self, child):
        """ Overwrite child's attribute """
        child.parent = self.node_id
        child.depth = self.depth + 1
        if child.children:
            child.typ = "internal node"
        else:
            child.typ = "leaf"

    def set_children(self, tree):
        """ Repeat set_child starting from root node """
        stack = []
        stack.append(self.node_id)

        while stack:
            node = tree[stack.pop()]
            for child_id in node.children:
                node.set_child(tree[child_id])
            stack.extend(node.children)

n = int(input())
tree = [None for i in range(n)]
children = []
for i in range(n):
    info = list(map(int, input().split()))
    tree[info[0]] = Node(info[0], info[2:])
    children.extend(info[2:])

root_id = (set([x for x in range(n)]) - set(children)).pop()

tree[root_id].set_children(tree)

for node in tree:
    print("node {}: parent = {}, depth = {}, {}, {}".format(node.node_id, node.parent, node.depth, node.typ, node.children))