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
assistant
#Here is Python code to print the information of each node in the following format ordered by IDs:
.
 Node:
    def __init__(self, p, l, r):
        self.p, self.l, self.r = p, l, r

N = int(input())
T = [Node(None, None, None) for _ in range(N)]

def get_depth(i):
    depth = 0
    while T[i].p != None:
        depth += 1
        i = T[i].p
    return depth

def get_children(i):
    children = []
    child = T[i].l
    while child != None:
        children.append(child)
        child = T[child].r
    return children

for _ in range(N):
    node, num, *children = map(int, input().split())
    if len(children) > 0:
        T[node].l = children[0]
        for i, child in enumerate(children):
            if len(children) - 1 < i + 1:
                break
            T[child].r = children[i + 1]
        for child in children:
            T[child].p = node

for i, t in enumerate(T):
    parent = t.p if t.p != None else -1
    depth = get_depth(i)
    if t.p == None:
        node = 'root'
    elif t.l == None:
        node = 'leaf'
    else:
        node = 'internal node'
    children = get_children(i)
    print('node {}:'.format(i), end=' ')
    print('parent = {},'.format(parent), end=' ')
    print('depth = {},'.format(depth), end=' ')
    print('{},'.format(node), end=' ')
    print(children)