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Give me a Python code 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....
class
assistant
#Here is Python code to print the information of each node in the following format ordered by IDs:
.
 node:
    def __init__(self, s):
        self.id = int(s.split()[0])
        self.dim = int(s.split()[1])
        self.child_ids = None
        if self.dim>0:
            self.child_ids = list(map(int, s.split()[2:]))
        
        self.pearent = None
        self.child = None
    
    def set_pearent(self, p):
        self.pearent = p
    
    def set_depth(self, d):
        self.depth = d
    
    def set_kind(self, k):
        self.kind = k
    
    def __repr__(self):
        str_node = 'node ' + str(self.id) + ': '
        str_pearent = 'parent = ' + str(self.pearent if self.pearent is not None else -1)
        str_depth = 'depth = ' + str(self.depth)
        str_kind = self.kind
        str_child = '[' + ', '.join([str(i) for i in self.child_ids] if self.child_ids is not None else '') + ']'
        return str_node + ', '.join([str_pearent, str_depth, str_kind, str_child])
        

n = int(input())
inputs = [input() for i in range(n)]
nodes = [0]*n

for i in inputs:
    nd = node(i)
    nodes[nd.id] = nd
    
for nd in nodes:
    if nd.child_ids:
        for i in nd.child_ids:
            nodes[i].set_pearent(nd.id)
            
def get_depth(idx):
    nd = nodes[idx]
    d = 0
    while nd.pearent is not None:
        nd = nodes[nd.pearent]
        d += 1
     
    nodes[idx].depth = d

def get_kind(idx):
    nd = nodes[idx]
    if nd.pearent is None:
        nd.kind = 'root'
    elif nd.child_ids:
        nd.kind = 'internal node'
    else:
        nd.kind = 'leaf'

for i in range(n):
    get_depth(i)
    get_kind(i)

for nd in nodes:
    print(nd)