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.
 Can you provide 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(1000000)

class Node():
    def __init__(self, p, l, r):
        self.p = p
        self.l = l
        self.r = r

def rec(u, p):
    D[u] = p
    if T[u].r != -1:
        rec(T[u].r, p)
    if T[u].l != -1:
        rec(T[u].l, p + 1)

N = int(input())
T = [Node(-1, -1, -1) for _ in range(N)]
D = [-1] * N
for i in range(N):
    i, k, *cs = map(int, input().split())
    for j, c in enumerate(cs):
        if j == 0:
            T[i].l = c
        else:
            T[l].r = c
        l = c
        T[c].p = i
for i, t in enumerate(T):
    if t.p == -1:
        r = i
rec(r, 0)
for i, t in enumerate(T):
    cs = []
    c = t.l
    while c != -1:
        cs.append(c)
        c = T[c].r
    if t.p == -1:
        print('node {}: parent = {}, depth = {}, root, {}'
              .format(i, t.p, D[i], cs))
    elif t.l == -1:
        print('node {}: parent = {}, depth = {}, leaf, {}'
              .format(i, t.p, D[i], cs))
    else:
        print('node {}: parent = {}, depth = {}, internal node, {}'
              .format(i, t.p, D[i], cs))