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Can you provide a Python program 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....
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.

class TreeNode():

  def __init__(self, val, parent=-1):
    self.val = val
    self.children = []
    self.parent_val = parent
    self.depth = None

  def node_type(self):
    if self.depth == 0:
      return "root"
    elif len(self.children) > 0:
      return "internal node"
    else:
      return "leaf"

  def children_values(self):
    return [ c.val for c in self.children ]

  def __str__(self):
    return "node {0}: parent = {1}, depth = {2}, {3}, {4}".format(str(self.val), str(self.parent_val), str(self.depth), self.node_type(), self.children_values())

def calc_depths(node, level):
  if node is None: return 
  node.depth = level
  for ch in node.children:
    calc_depths(ch, level+1)

num = int(input())
nodes = {}

for i in range(num):
  ins = list(map(int, input().split()))
  val = ins[0]

  if nodes.get(ins[0]) is None:
    nodes[val] = TreeNode(val)

  n = nodes[val]
  if ins[1] > 0:
    for j in ins[2:]:
      nodes.setdefault(j, TreeNode(j, n.val))
      n.children.append(nodes[j])
      nodes[j].parent_val = n.val

parent = [node for node in nodes.values() if node.parent_val == -1][0]
calc_depths(parent, 0)
sort_nodes = sorted(nodes.items(), key=lambda x:x[0] )

for _, node in sort_nodes:
  print(node)