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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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:
.

class Tree:
    def __init__(self):
        self.id = 0
        self.p = -1
        self.depth = -1
        self.type = "leaf"
        self.len_c = 0
        self.c = []
    def __str__(self):
        return f"node {self.id}: parent = {self.p}, depth = {self.depth}, {self.type}, {self.c}"
n = int(input())
li = [Tree() for _ in range(n)]
for _ in range(n):
    id, k, *c = map(int, input().split())
    if k == 0:
        c = []
    else:
        li[id].type = "internal node"
    li[id].id = id
    li[id].c = c
    for j in c:
        li[j].p = id
root = 0
while True:
    a = li[root].p
    if a == -1:
        li[root].type = "root"
        li[root].depth = 0
        break
    root = a
dp = [(root, 0)]
while dp:
    id, d = dp.pop()
    for i in li[id].c:
        li[i].depth = d + 1
        dp.append((i, d + 1))
for i in range(n):
    print(li[i])