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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....
impor
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.
t sys
sys.setrecursionlimit(10**7)

nodedict = {}

class Node:
    def __init__(self, id, jisu, children):
        self.id = id
        self.jisu = jisu
        self.children = children
        self.parent = -1
        self.depth = -1

    def __repr__(self):
        return "id:{}, jisu:{}, parent:{}, depth:{}, children:{}".format(self.id, self.jisu, self.parent, self.depth, self.children)

def assign_depth(node, current_depth):
    node.depth = current_depth
    for childid in node.children:
        assign_depth(nodedict[childid], current_depth+1)

def solve():
    n = int(input())

    # Node作成
    for i in range(n):
        input_list = list(map(int, input().split()))
        id = input_list[0]
        jisu = input_list[1]
        children = input_list[2:]
        nodedict[id] = Node(id, jisu, children)

    # 親番号の割り当て
    for i in range(n):
        node = nodedict[i]
        for childid in node.children:
            child = nodedict[childid]
            child.parent = node.id

    #print(nodedict)
    # 根探し
    neid = None
    for i in range(n):
        node = nodedict[i]
        if node.parent == -1:
            neid = node.id
            break

    # 深さを割り当てる
    assign_depth(nodedict[neid], 0)

    # 出力
    for i in range(n):
        node = nodedict[i]
        if node.depth == 0:
            type = "root"
        elif len(node.children) == 0:
            type = "leaf"
        else:
            type = "internal node"

        print("node {}: parent = {}, depth = {}, {}, {}".format(node.id, node.parent, node.depth, type, node.children))

solve()