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....
Using python can you solve the prior task?

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What is a Python code to print the information of each node in the following format ordered by IDs:?
assistant
#Here is Python code to print the information of each node in the following format ordered by IDs:
.

# coding: utf-8
# Here your code !
from collections import deque 

class Node:
    def __init__(self):
        self.id = -1
        self.k = -1
        self.depth = -1
        self.parent = -1
        self.type = 'root'
        self.end = False
        self.children = []
        
def find_root_id(nodes):
    i = 0
    rootid = -1
    while nodes[i].parent != -1:
        nodes[i]
        i += 1
    else:
        rootid = nodes[i].id
        return rootid
        
def set_depth(rootid, nodes):
    que = deque()
    depth = 0
    node = nodes[rootid]
    que = deque(node.children)
    for i in que:
        nodes[i].depth = depth + 1
    depth += 1
    
    while que:
        for i in range(len(que)):
            for child in nodes[que.popleft()].children:
                que.append(child)
        for j in que:
            nodes[j].depth = depth + 1
        depth += 1

n = int(raw_input())
nodes = []
for i in range(n):
    node = Node()
    ls =  map(int, raw_input().split())
    node.id = ls[0]
    node.k = ls[1]
    if node.k == 0:
        pass
    else:
        node.children = ls[2:]
    nodes.append(node)
    
nodes = sorted(nodes, key=lambda node:node.id)
for node in nodes:
    for child in node.children:
        nodes[child].parent = node.id
        
for node in nodes:
    if node.children == []:
        if node.parent != -1:
            node.type = 'leaf'
    else:
        if node.parent != -1:
            node.type = 'internal node'

rootid = find_root_id(nodes)
nodes[rootid].depth = 0

def set_depth(rootid, nodes):
    que = deque()
    depth = 0
    node = nodes[rootid]
    que = deque(node.children)
    for i in que:
        nodes[i].depth = depth + 1
    depth += 1
    
    while que:
        for i in range(len(que)):
            for child in nodes[que.popleft()].children:
                que.append(child)
        for j in que:
            nodes[j].depth = depth + 1
        depth += 1

set_depth(rootid, nodes)
for node in nodes:#sorted(nodes, key=lambda node:node.id):
    print 'node %s: parent = %s,...