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Write me 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
input = sys.stdin.readline
sys.setrecursionlimit(100000)

tree = []
root_index = []
depths = []

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

    # 初期化
    for i in range(n):
        tree.append(Node(i, None, None))
        root_index.append(i)
        depths.append(0)

    for i in range(n):
        node_number, _, *c_list = list(map(int, input().split()))
        tree[node_number].child = c_list

        for c in c_list:
            tree[c].parent = tree[node_number]
            root_index.remove(c)

    root = tree[root_index[0]]
    root.parent = Node(-1, None, None)

    setDepth(root, 0)
    showTree(root)

def setDepth(node, d):
    depths[node.number] = d
    for c in node.child:
        setDepth(tree[c], d + 1)

def getDepth(node_number):
    return depths[node_number]

def showTree(root):
    for node in tree:
        type = ""
        if node.parent.number == -1:
            type = "root"
        elif len(node.child) == 0:
            type = "leaf"
        else:
            type = "internal node"

        print("node {0}: parent = {1}, depth = {2}, {3}, {4}".format(str(node.number), str(node.parent.number), str(depths[node.number]), type, node.child))

class Node():
    def __init__(self, number, parent, child):
        self.number = number
        self.parent = parent
        self.child = child

if __name__ == '__main__':
    main()