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....
from  ... Write me a Python program to print the information of each node in the following format ordered by IDs:?
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.
collections import deque
from sys import stdin
input = stdin.readline

class Element:
    def __init__(self, node):
        self.node = node
        self.parent = -1
        self.depth = 0
        self.status = "internal node"
        self.children = None
    
    def display(self):
        print("node %d: parent = %d, depth = %d, %s, %s"
        %(self.node, self.parent, self.depth, self.status, str(self.children)))
        
N = int(input())

NODE_DICT = {}
ROOT_SEARCH = [True]*N

for loop in range(N):
    DATA = list(map(int, input().split()))
    node = DATA[0]    
    tmp = Element(node)
    tmp.children = DATA[2:]
    NODE_DICT[node] = tmp
    for i in tmp.children:
        ROOT_SEARCH[i] = False
    
#for node in NODE_DICT.keys():
#    for child in NODE_DICT[node].children:
#        ROOT_SEARCH[child] = False

for key in range(len(ROOT_SEARCH)):
    if ROOT_SEARCH[key]:
        root = key

def Process(parent):
    for child in parent.children:
        NODE_DICT[child].parent = parent.node
        NODE_DICT[child].depth = parent.depth + 1
    if parent.children == []:
        parent.status = "leaf"
    else:
        for child in parent.children:
            Process(NODE_DICT[child])
    

Process(NODE_DICT[root])
NODE_DICT[root].status = "root"

for i in range(N):
    NODE_DICT[i].display()

#for node in range(len(NODE_DICT)):
#    print("node %d: parent = %d, depth = %d, %s, %s"%(NODE_DICT[node].node, 
#    NODE_DICT[node].parent, NODE_DICT[node].depth, NODE_DICT[node].status, 
#   str(NODE_DICT[node].children)))