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....
def g
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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:
.
etDepth(u):
    d = 0
    while node_list[u].parent != -1:
        u = node_list[u].parent
        d += 1
    return d
def getChildren(u):
    c = node_list[u].left
    child_list = []
    while c != -1:
        child_list.append(c)
        c = node_list[c].right
    return child_list

def getType(u):
    if node_list[u].parent == -1:
        return "root"
    if node_list[u].left == -1:
        return "leaf"
    return "internal node"
max_value = 10 ** 10
nil = -1

class Node():
    " node of the tree structure"
    def __init__(self, name = -1, parent = -1, left = -1, right = -1):
        self.name = name
        self.parent = parent
        self.left = left
        self.right = right
node_list = []
n = int(input())
for i in range(n):
    node = Node()
    node_list.append(node)

for i in range(n):
    a,b,*args = map(int, input().split())
    for j in range(b):
        if j == 0:
            node_list[a].left = args[j]
        else:
            node_list[l].right = args[j]
        l = args[j]
        node_list[args[j]].parent = a

#for i in range(n):

for i in range(n):
    print("node", str(i) + ":" , "parent =", str(node_list[i].parent) + ",", "depth =", str(getDepth(i)) + ",", getType(i) + ",", getChildren(i))