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 python3 can you solve the prior task?
 ... 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:
.

n = int(input())

tree_info = {}
for i in range(n):
    row = input().split()
    tree_info[int(row[0])] = (int(row[1]), list(map(int, row[2:])))
tree_info

Nodes = [None] * n

class Node:
    
    def __init__(self, id, parent, depth, child):
        self.id = id
        self.parent = parent
        self.depth = depth
        if (parent == -1):
            self.tree_type = "root"
        elif(len(child) == 0):
            self.tree_type = "leaf"
        else:
            self.tree_type = "internal node"
            
        self.child = child
        
        if(self.tree_type != "leaf"):
            self.make_child()
    
    def make_child(self):
        for ch_id in self.child:
            Nodes[ch_id] = Node(ch_id, self.id, self.depth + 1, tree_info[ch_id][1])
        
    
    def __str__(self):
        return "node {}: parent = {}, depth = {}, {}, {}".format(self.id, self.parent, self.depth, self.tree_type, self.child)

for i in range(n):
    if(Nodes[i] == None):
        Nodes[i] = Node(i, -1, 0, tree_info[i][1])
        Nodes[i].make_child()

for root in Nodes:
    print(root)