human
What is a Python program to print the information of each node in the following format ordered by IDs: given the following:
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....
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.

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

def getdepth(u):
    for i in range(N):
        depth = 0
        j = i
        while trees[j].parent != -1:
            j = trees[j].parent
            depth += 1
        depths[i] = depth

N = int(input())
# ?????????
trees = [Tree(-1,-1,-1) for i in range(N)]
for i in range(N):
    l = list(map(int, input().split()))
    no = l[0]
    jisu = l[1]
    # 2???????????????????????§???????´??????????
    childs = l[2:]
    for j in range(jisu):
        child = childs[j]
        if j == 0:
            trees[no].left = child

        if j != len(childs)-1:
            trees[child].right = childs[j+1]

        trees[child].parent = no

r = 0
for i in range(N):
    if trees[i].parent == -1:
        r = i

depths = [-1] * N
getdepth(r)

for i in range(N):
    type = ""
    if trees[i].parent == -1: type = "root"
    elif trees[i].left == -1: type = "leaf"
    else: type = "internal node"
    childs = "["
    child = trees[i].left
    while child != -1:
        childs += str(child)
        child = trees[child].right
        if child != -1: childs += ", "
    childs += "]"

    print("node {0}: parent = {1}, depth = {2}, {3}, {4}".format(i, trees[i].parent, depths[i], type, childs))