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....
# cod
Give me 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:
.
ing: utf-8
# Your code here!
class Tree:
    def __init__(self, parent, left_child, right_sib):
        self.left_child = left_child
        self.right_sib = right_sib
        self.parent = parent
    

def getDepth(T, u):
    d = 0
    while T[u].parent is not None:
        u = T[u].parent
        d += 1
    return d

def getChildren(T, u):
    Children = []
    c = T[u].left_child
    while c is not None:
        Children.append(str(c))
        c = T[c].right_sib
    if len(Children) != 0:
        return "[" + ", ".join(Children) + "]"
    else:
        return "[]"

n = int(input().rstrip())

T = []
for _ in range(n):
    T.append(Tree(None, None, None))

for _ in range(n):
    inputs = list(map(int, input().rstrip().split(" ")))
    u = inputs[0]
    k = inputs[1]
    children = inputs[2:] if k > 0 else [None]
    T[u].left_child = children[0]
    if k > 0:
        for i, child in enumerate(children):
            T[child].parent = u
            T[child].right_sib = children[i+1] if i+1 < len(children) else None

def print_info(T, u):
    parent = T[u].parent
    if parent is None:
        parent = -1
    depth = getDepth(T, u)
    children = getChildren(T, u)
    type_ = "root" if parent == -1 else "leaf" if children == "[]" else "internal node"
    
    print("node {}: parent = {}, depth = {}, {}, {}".format(u, parent, depth, type_ ,children if type_ != "leaf" else "[]"))

for u in range(n):
    print_info(T, u)