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....
impor
What is a Python program to print the information of each node in the following format ordered by IDs:?
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.
t sys
sys.setrecursionlimit(10**9)

class Node:
    def __init__(self):
        self.p = -1
        self.l = -1
        self.r = -1

n = int(input())
T = [Node() for _ in range(n)]
D = [0]*n

def rec(u,p):
    D[u] = p
    if T[u].r != -1: rec(T[u].r,p)
    if T[u].l != -1: rec(T[u].l,p+1)

def printinfo(u):
    clst = []
    c = T[u].l
    while c != -1:
        clst.append(c)
        c = T[c].r
    if T[u].p == -1: ntype = "root"
    elif T[u].l == -1: ntype = "leaf"
    else: ntype = "internal node"
    print("node {}: parent = {}, depth = {}, {}, {}".format(u,T[u].p,D[u],ntype,clst))

for i in range(n):
    inp = [int(i) for i in input().split()]
    v = inp[0]
    d = inp[1]
    C = inp[2:]
    for j in range(d):
        c = C[j]
        if j == 0: T[v].l = c
        else: T[l].r = c
        l = c
        T[c].p = v
for i in range(n):
    if T[i].p == -1: r = i

rec(r,0)
for i in range(n): printinfo(i)