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....
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to print the information of each node in the following format ordered by IDs:
.

# coding: utf-8
import queue

class Node:
    def __init__(self, myNum, childNums):
        self.myNum = myNum
        self.parentNum = -1
        self.childNums = childNums
        self.nodeType = ""
        self.depth = -1
        
n = int(input().rstrip())
nodes = []
# 入力を使ってクラスに放り込む
for i in range(n):
    line = [int(i) for i in input().rstrip().split()]
    childNums = [i for i in line[2:]]
    nodes.append(Node(line[0],childNums))
# nodesを節点順にソートする
nodes = sorted(nodes,key=lambda x: x.myNum)
# 親を計算する
for node in nodes:
    for num in node.childNums:
        nodes[num].parentNum = node.myNum

# type を求める
for node in nodes:
    if node.parentNum == -1:
        node.nodeType = "root"
        rootNum = node.myNum
    elif not node.childNums:
        node.nodeType = "leaf"
    else:
        node.nodeType = "internal node"
        
# depth を計算する
q = queue.Queue()
q.put(nodes[rootNum])
nodes[rootNum].depth=0
while not q.empty():
    nd = q.get()
    for c in nd.childNums:
        nodes[c].depth = nd.depth + 1
        q.put(nodes[c])

#アウトプット
for node in nodes:
    print("node {0}: parent = {1}, depth = {2}, {3}, {4}".format(node.myNum,node.parentNum,node.depth,node.nodeType,node.childNums))