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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

class Main{
    static Node[] nodes;
    static int n;

    static class Node{
        int id, parent, depth = 0;
        String type;
        ArrayList<Integer> children = new ArrayList<>();

        Node (int id){
            this.id = id;
            parent = -1;
        }
        Node (int id, int parent){
            this.id = id;
            this.parent = parent;
        }

        void addChild(int n){
            children.add(n);
            // update the parent of the child
            // if the child has already added into nodes, update parent
            // otherwise, create a new node, update its parent, then added into nodes
            if (nodes[n] != null) nodes[n].updateParent(this.id);
            else nodes[n] = new Node(n, this.id);

        }
        void updateParent(int p){
            parent = p;
        }
        void updateDepth(int d){
            depth = d;
        }

        String type(){
            if (parent == -1) return "root";
            if (children.isEmpty()) return "leaf";
            return "internal node";
        }

        String children(){
            if (children.isEmpty()) return "[]";
            StringBuilder sb = new StringBuilder("[").append(children.get(0));
            for (int i = 1; i < children.size(); i++)
                sb.append(", ").append(children.get(i));
            return sb.append("]").toString();
        }
    }

    static int root(){
        for (int i = 0; i < n; i++)
            if (nodes[i].parent == -1)
                return i;
        return -1;
    }
    // for all nodes, updating depth
    static void updateDepth(int p){
        for (int i = 0; i < nodes[p].children.size(); i++) {
            int c = nodes[p].children.get(i);
            nodes[c].updateDepth(nodes[p].depth+1);
            updateDepth(c);
        }
    }



    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        n = sc.nextInt();

        nodes = new Node[n];

        for (int i = 0; i < n; i++) {
            int id = sc.nextInt();
            int degree = sc.nextInt();

            Node node = new Node(id);
            if (nodes[id] != null) node = nodes[id];
            else nodes[id] = node;

            for (int j = 0; j < degree; j++)
                node.addChild(sc.nextInt());
        }
        updateDepth(root());
        for (Node node: nodes) {
            System.out.printf("node %d: parent = %d, depth = %d, %s, %s\n",
                    node.id, node.parent, node.depth, node.type(), node.children());
        }
    }


    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}