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.

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Can you provide 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, parent=-1, child=[]):
        self.parent = parent
        self.child = child

def node_depth(u, id):
    if u[id].parent == -1:
        return 0
    else:
        return node_depth(u, u[id].parent) + 1

def node_type(u, id):
    if u[id].parent == -1:
        return "root"
    elif u[id].child == []:
        return "leaf"
    else:
        return "internal node"

def main():
    n = int(input())
    u = [Node() for _ in range(n)]

    for _ in range(n):
        id, _, *child = (int(x) for x in input().split())
        u[id].child = child
        for c in child:
            u[c].parent = id

    for id in range(n):
        print("node {}: parent = {}, depth = {}, {}, {}".
              format(id, u[id].parent,
                     node_depth(u, id), node_type(u, id),
                     u[id].child))

main()