Problem:
Rooted Trees

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

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. If the node does not have a parent, print -1.

d is depth of the node.

type is a type of nodes represented by a string (root, internal node or leaf). If the root can be considered as a leaf or an internal node, print root.

c1...ck is the list of children as a ordered tree.

Please follow the format presented in a sample output below.

Constraints

1 ≤ n ≤ 100000

Sample Input 1

13
0 3 1 4 10
1 2 2 3
2 0
3 0
4 3 5 6 7
5 0
6 0
7 2 8 9
8 0
9 0
10 2 11 12
11 0
12 0

Sample Output 1

node 0: parent = -1, depth = 0, root, [1, 4, 10]
node 1: parent = 0, depth = 1, internal node, [2, 3]
node 2: parent = 1, depth = 2, leaf, []
node 3: parent = 1, depth = 2, leaf, []
node 4: parent = 0, depth = 1, internal node, [5, 6, 7]
node 5: parent = 4, depth = 2, leaf, []
node 6: parent = 4, depth = 2, leaf, []
node 7: parent = 4, depth = 2, internal node, [8, 9]
node 8: parent = 7, depth = 3, leaf, []
node 9: parent = 7, depth = 3, leaf, []
node 10: parent = 0, depth = 1, internal node, [11, 12]
node 11: parent = 10, depth = 2, leaf, []
node 12: parent = 10, depth = 2, leaf, []

Sample Input 2

4
1 3 3 2 0
0 0
3 0
2 0

Sample Output 2

node 0: parent = 1, depth = 1, leaf, []
node 1: parent = -1, depth = 0, root, [3, 2, 0]
node 2: parent = 1, depth = 1, leaf, []
node 3: parent = 1, depth = 1, leaf, []

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

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Python3 (judge verdict: Runtime Error)

#coding:utf-8

n = int(input())
T = [list(map(int, input().split())) for i in range(n)]
A = []
def parentSearch():
    numList = []
    for t in T:
        if t[1] != 0:
            for num in t[2:]:
                numList.append(num)
    numList.sort()
    for i in range(n-1):
        if numList[i] != i:
            return i
            break


def rootedTrees(node, parent, depth):
    t = T[node]
    if t[1] != 0:
        if parent == -1:
            kind = "root"
        else:
            kind = "internal node"
        A.append([t[0], parent, depth, kind, t[2:]])
        parent = node
        for i in t[2:]:
            rootedTrees(i, parent, depth+1)
    else:
        if parent == -1:
            kind = "root"
        else:
            kind = "leaf"
        A.append([t[0], parent, depth, kind, []])


def Merge(A, left, mid, right):
    L = A[left:mid]
    R = A[mid:right]
    L.append([510000])
    R.append([510000])
    i,j = 0,0
    for k in range(left,right):
        if L[i][0] <= R[j][0]:
            A[k] = L[i]
            i += 1
        else:
            A[k] = R[j]
            j += 1

def MergeSort(A, left, right):
    if left+1 < right:
        mid = (left + right)//2
        MergeSort(A, left, mid)
        MergeSort(A, mid, right)
        Merge(A, left, mid, right)

node = parentSearch()
if node == None:
    node = 0
depth = 0
parent = -1
rootedTrees(node, parent, depth)
MergeSort(A, 0, n)

for t in A:
    print("node {}: parent = {}, depth = {}, {}, {}".format(t[0],t[1],t[2],t[3],t[4]))