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....
The above is tricky. Write me a correct solution in PYTHON.

Write 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:
.

import sys

class Node:
    def __init__(self):
        self.id = -1
        self.parent = -1
        self.type = "leaf"

    def printInfo(self):
        print "node {0.id}: parent = {0.parent}, depth = {0.depth}, {0.type}, {0.children}".format(self)

def setTree(id, tree, depth):
    tree[id].depth = depth
    if not tree[id].children:
        return

    for child in tree[id].children:
        tree[child].parent = id
        setTree(child, tree, depth + 1)
    tree[id].type = "internal node"

if __name__ == "__main__":
    lines = sys.stdin.readlines()
    N = int(lines[0])
    del lines[0]

    tree = []
    for i in range(N):
        tree.append(Node())

    root = N * (N - 1) / 2
    for line in lines:
        info = map(int, line.split())
        tree[info[0]].children = info[2:]
        tree[info[0]].id = info[0]
        for i in tree[info[0]].children:
            root -= i

    setTree(root, tree, 0)
    tree[root].type = "root"

    for node in tree:
        node.printInfo()