human
Give me a Python program to print the information of each node in the following format ordered by IDs: given the following:
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....
"""
根
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.
付き木を構成する
"""
class Node:
    def __init__(self):
        self.parent = -1
        self.depth = 0
        self.children = []

#空の木の構成
#node_idをインデックスに持たせる
n = int(input())
nodes = []
for _ in range(n):
    node = Node()
    nodes.append(node)

def getDepth(node_id):
    d = 0
    target = nodes[node_id]
    while target.parent != -1:
        d += 1
        tmp_num = target.parent
        target = nodes[tmp_num]
    return d

def getParent(node_id):
    target = nodes[node_id]
    return target.parent

def getChildren(node_id):
    target = nodes[node_id]
    return target.children

def getType(node_id):
    target = nodes[node_id]
    if target.parent == -1:
        return 'root'
    elif len(target.children) == 0:
        return 'leaf'
    else:
        return 'internal node'

#木の構成
for i in range(n):
    l = list(map(int, input().split()))
    node_id = l[0]
    num = l[1]

    for j in range(num):
        try:
            child = l[2+j] #l[2+j]というのは子供の番号
            nodes[node_id].children.append(child) 
            nodes[child].parent = node_id #子一人当たり親は必ず一人
        except:
            pass
    else:
        pass #子がいないとき

for i in range(n):
    ans = 'node '+str(i)+': parent = '+str(getParent(i))+', ' +\
    'depth = '+str(getDepth(i))+', '+getType(i)+', '+str(getChildren(i))
    print(ans)