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....
class
Write me 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:
.
 Node:
  def __init__(self, id, children):
    self.id = id
    self.children = children
    self.type = "root"
    self.parent = None
    self.depth = 0

  def set_parent(self, parent):
    self.parent = parent
    self.type = "leaf" if len(self.children) == 0 else "internal node"

  def get_depth(self):
    if self.depth: return self.depth
    if self.type == "root": return 0
    self.depth = self.parent.get_depth() + 1
    return self.depth

  def display(self):
    print("node {}: parent = {}, depth = {}, {}, {}".format(
      self.id,
      self.parent.id if self.parent else -1,
      self.get_depth(),
      self.type,
      self.children
      )
    )

nodelist = {}
for i in range(int(input())):
  p = input().split()
  id = int(p[0])
  nodelist[id] = Node(id, list(map(int, p[2:])) if len(p) >= 3 else [])

for i in nodelist:
  n = nodelist[i]
  for cid in n.children:
    nodelist[cid].set_parent(n)

for i in sorted(nodelist): nodelist[i].display()