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....
class ... 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:
.
 Node:
    def __init__(self):
        self.parent = -1
        self.left = -1
        self.right = -1

#ノードの深さを求める関数
def getdepth(node,node_id):
    d = 0
    while node[node_id].parent != -1:
        node_id = node[node_id].parent
        d += 1
    return d

#子のリストを求める関数
def getchild(node,node_id):
    if node[node_id].left == -1:
        return []
    ret = [node[node_id].left]
    while node[ret[-1]].right != -1:
        ret.append(node[ret[-1]].right)
    return ret

N = int(input())
nodes = [Node() for i in range(N)]

#入力を木構造に入力する
for i in range(N):
    n,k,*child = map(int,input().split())
    if k != 0:
        nodes[n].left = child[0]
        for j in range(len(child)):
            nodes[child[j]].parent = n
            if j != len(child)-1:
                nodes[child[j]].right = child[j+1]

for i in range(N):
    depth = getdepth(nodes,i)
    children = getchild(nodes,i)
    if nodes[i].parent == -1:
        node_type = 'root'
    elif nodes[i].left == -1:
        node_type = 'leaf'
    else:
        node_type = 'internal node'
    print('node {}: parent = {}, depth = {}, {}, {}'.format(i,nodes[i].parent, depth, node_type, children))