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: Wrong Answer)


import javax.xml.crypto.Data;
import java.util.*;
import java.io.*;

public class Main {
    public static int SENTINEL = 100000007;
    public static int MAX = 10007;
    public static int NIL = -1;

    public static int[] Depth = new int[MAX];
    public static Tree[] Node = new Tree[MAX];
    public static int n;

    public static void main(String[] args) throws IOException {

        //??\???
        /*
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");
        */

        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        for(int i = 0; i < n; i++) {
            Node[i] = new Tree(NIL, NIL, NIL);
        }
        int v, c, d, l;
        for (int i = 0; i < n; i++) {
            v = sc.nextInt();
            d = sc.nextInt();
            l = 0;
            for(int j = 0; j < d; j++) {
                c = sc.nextInt();
                if (j == 0) Node[v].left = c;
                else Node[l].right = c;
                l = c;
                Node[c].parent = v;
            }
        }
        int r = 0;
        for(int i = 0; i < n; i++) {
            if(Node[i].parent == NIL) r = i;
        }
        rec(r, 0);
        // ??????
        for(int i = 0; i < n; i++) print(i);
    }

    public static void rec(int u, int p) {
        Depth[u] = p;
        if(Node[u].right != NIL) rec(Node[u].right, p);
        if(Node[u].left != NIL) rec(Node[u].left, p + 1);
    }

    public static void print(int u) {
        System.out.printf("node  %d: parent = %d, depth = %d, ", u, Node[u].parent, Depth[u]);
        if(Node[u].parent != NIL) System.out.print("root, ");
        else if(Node[u].left == NIL) System.out.print("leaf, ");
        else System.out.print("internal node, ");

        System.out.print("[");
        int c = Node[u].left;
        for(int i = 0; c != NIL; c = Node[c].right) {
            if(i != 0) System.out.print(", ");
            System.out.print(c);
            i++;
        }
        System.out.println("]");
    }
}

class Tree {
    int parent;
    int left;
    int right;
    Tree(int p, int l, int r) {
        parent = p;
        left = l;
        right = r;
    }
}