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....
assistant
#Here is Python code to print the information of each node in the following format ordered by IDs:
.

class Node():
    def __init__(self):
        self.parent = -1
        self.children = []

def cal_depth(node_id, d = 0):
    Tree[node_id].depth = d
    for child in Tree[node_id].children:
        cal_depth(child, d+1)
    
N = int(input())
Tree = [Node() for _ in range(N)]

#make_tree
for _ in range(N):
    #id, 子供の数k, c_0~c_k
    tree_info = list(map(int, input().split()))
    node_id = tree_info[0]
    k = tree_info[1]
    if k > 0:
        children = tree_info[2:]
        Tree[node_id].children = children
        Tree[node_id].type = "internal node"
    else:
        Tree[node_id].type = "leaf"
        
    for child in Tree[node_id].children:
        Tree[child].parent = node_id

#search_root
root_id =[i for i,t in enumerate(Tree) if t.parent == -1][0]
Tree[root_id].type = "root"
cal_depth(root_id)

#answer_output
for i, t in enumerate(Tree):
    print("node {}: parent = {}, depth = {}, {}, {}".format(i, t.parent, t.depth, t.type, t.children))