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....
Solve the task in PYTHON3.
 ... 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:
.

class node():
    def __init__(self, id, parent, child, depth, type_t):
        self.id = id
        self.parent = parent
        self.child = child
        self.depth = depth
        self.type_t = type_t

def add(t, d, i, parent, depth):
    type_t = 'internal node'
    if d[i][1] == 0:
        type_t = 'leaf'
    if depth == 0:
        type_t = 'root'

    child = []
    if not d[i][1] == 0:
        child = d[i][2:]
    new_node = node(i, parent, d[i][2:], depth, type_t)
    t.append(new_node)
    for c in child:
        add(t, d, c, i, depth + 1)

N = int(input())
tree = []
data = [[] for i in range(N)]
for i in range(N):
    data[i] = [int(i) for i in input().split()]

data.sort(key=lambda x: x[0])

root = [True for i in range(N)]
for d in data:
    for c in d[2:]:
        root[c] = False

for i in range(N):
    if root[i]:
        add(tree, data, i, -1, 0)

tree.sort(key=lambda x: x.id)

for t in tree:
    print(f'node {t.id}: parent = {t.parent}, depth = {t.depth}, {t.type_t}, {t.child}')