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?

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Can you provide 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:
.

# Tree - Rooted Trees
class Node:
    def __init__(self, idnty):
        self.id = idnty
        self.parent = None
        self.children = []
        self.depth = 0
    def __str__(self):
        prnt = self.parent.id if self.parent else -1
        typ = 'root'
        if self.depth > 0: typ = 'internal node'
        if self.depth > 0 and not self.children: typ = 'leaf'
        cld = [n.id for n in self.children]
        return 'node {0}: parent = {1}, depth = {2}, {3}, {4}'.format(self.id, prnt, self.depth, typ, cld)

n = int(input())
tr = [Node(i) for i in range(n)]
for _ in range(n):
    rl = list(map(int, input().split()))
    id, k = rl[0],rl[1]
    if k > 0:
        for i in rl[2:]:
            c = tr[i]
            c.parent = tr[id]
            c.depth += tr[id].depth + 1
            tr[id].children.append(c)
    else:
        p = tr[id].parent
        if p:
            tr[id].depth = p.depth + 1
for t in tr: print(t)