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: WA: Presentation Error)


import java.util.*;

/**
 * A_
 */
public class Main {

    public static void main(String[] args) {
        run();
    }

    public static void run() {
        
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        //node set
        Node[] node = new Node[n];
        boolean[] root = new boolean[n];

        Arrays.fill(root, true);

        for(int i=0; i<n; i++) {

            int id = sc.nextInt();
            int k = sc.nextInt();
            int[] c = new int[k];

            for(int j=0; j<k; j++) {

                c[j] = sc.nextInt();
                root[c[j]] = false;

            }

            node[id] = new Node(c);

        }

        for(int i=0; i<n; i++) {

            if(root[i]) {
                make(node, i, -1, 0);
            }

        }

        export(node, n);
        sc.close();

    }

    public static void make(Node[] nodes, int id, int parent, int depth) {

        StringBuilder sb = new StringBuilder();

        sb.append("node ").append(id).append(": parent = ").append(parent).append(", depth = ").append(depth).append(", ");
        if(parent == -1) {
            sb.append("root");
        } else if(nodes[id].c.length == 0) {
            sb.append("leaf");
        } else {
            sb.append("internal node");
        }
        sb.append(", [");
        for(int i=0; i < nodes[id].c.length; i++) {

            sb.append(nodes[id].c[i]);
            if(i != nodes[id].c.length-1) {
                sb.append(", ");
            }
            make(nodes, nodes[id].c[i], id, depth+1);

        }
        sb.append("]");
        nodes[id].tree = sb.toString();

    }

    public static void export(Node[] node, int n) {

        StringBuilder sb = new StringBuilder();
        for(int i=0; i<n; i++) {
            sb.append(node[i].tree).append("\n");
        }
        System.out.println(sb);

    }

}

class Node {

    public int[] c;
    public String tree; //retain tree information
    public Node(int[] c) {
        this.c = c;
    }

}