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

import sys
sys.setrecursionlimit(2**20)

class Node:
    def __init__(self, parent, left, right):
        self.parent = parent
        self.left = left
        self.right = right

d = {} # {id: depth}
def get_all_depth(t, u, p): # (Tree, id, depth)
    d[u] = p
    if t[u].right is not None:
        get_all_depth(t, t[u].right, p)
    if t[u].left is not None:
        get_all_depth(t, t[u].left, p+1)

def return_children(t, u):
    children = []
    c = t[u].left
    while c is not None:
        children.append(c)
        c = t[c].right
    return children

n = int(input())
t = {k: Node(None, None, None) for k in range(n)}
for _ in range(n):
    tmp = list(map(int, input().split()))
    if tmp[1] == 0: # 子なし
        continue
    t[tmp[0]].left = tmp[2] # 最も左の子
    t[tmp[2]].parent = tmp[0] # 親
    prev_sib = tmp[2]
    for sib in tmp[3:]:
        t[prev_sib].right = sib # すぐ右の子
        t[sib].parent = tmp[0] # 親
        prev_sib = sib

for node in range(n):
    if t[node].parent is None:
        get_all_depth(t, node, 0)
        break

for node in range(n):
    node_type = "internal node" if t[node].left is not None else "leaf"
    if t[node].parent is None:
        parent = -1
        node_type = "root"
    else:
        parent = t[node].parent
    children = return_children(t, node)
    print(f"node {node}: parent = {parent}, depth = {d[node]}, {node_type}, {children}")