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 JAVA (judge verdict: Accepted)

import java.util.*;

public class Main {
    static long count = 0;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(); //節点の個数
        Node[] node = new Node[n];
        for(int i=0; i<n; i++) {
            int id = sc.nextInt();
            node[id] = new Node();
            node[id].id = id;
            node[id].k = sc.nextInt();
            node[id].parent = -1;
            node[id].type = "leaf"; //初期値：葉
            if(node[id].k>0) { //次元がある場合
                node[id].child = new int[node[id].k];
                for(int j=0; j<node[id].k; j++) { //子ノードをchild[]に詰める
                    node[id].child[j] = sc.nextInt();
                }
                //タイプを内部節点に書き換える
                node[id].type = "internal node";
            }
        }
        //子ノードの親=ノードid
        for(int i=0; i<n; i++) {
            for(int j=0; j<node[i].k; j++) {
                node[node[i].child[j]].parent = node[i].id;
            }
        }
        //親がない場合、タイプを根に書き換える
        for(int i=0; i<n; i++) {
            if(node[i].parent==-1) {
                node[i].type = "root";
                for(int j=0; j<node[i].k; j++) {
                    depth(node, node[i].child[j], 1);
                }
            }
        }
        //出力
        for(int i=0; i<n; i++) {
            System.out.print("node "+node[i].id+": parent = "+node[i].parent+", depth = "+node[i].depth+", "+node[i].type+", [");
            for(int j=0; j<node[i].k; j++) {
                if(j==0) System.out.print(node[i].child[j]);
                else System.out.print(", "+node[i].child[j]);
            }
            System.out.println("]");
        }
    }
    static void depth(Node[] node, int i, int d) {
        node[i].depth = d;
        d++;
        for(int j=0; j<node[i].k; j++) {
            depth(node, node[i].child[j], d);
        }
    }
}
/**
 * クラス
 */
class Node {
    int id;
    int k;
    int[] child;
    int parent;
    int depth;
    String type;
}