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.StringTokenizer;

class Main{
    static node[] t;
    public static void main(String[] args) throws IOException{
        final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        final int n = Integer.parseInt(br.readLine());
        t = new node[n];
        for(int i = 0; i<n; i++)
            t[i] = new node();

        for(int i = 0; i<n; i++){
            final StringTokenizer st = new StringTokenizer(br.readLine(), " ");
            final int id = Integer.parseInt(st.nextToken());
            final int m = Integer.parseInt(st.nextToken());
            int c0 = id;
            for(int j = 0; j<m; j++){
                final int c = Integer.parseInt(st.nextToken());
                t[c].parent = id;
                if(j==0) t[id].child = c;
                else t[c0].sibling = c;
                c0 = c;
            }
        }
        int root = 0;
        while(t[root].parent!=-1)
            root = t[root].parent;
        setdepth(root, 0);
        final StringBuilder sb = new StringBuilder();
        for(int i = 0; i<n; i++){
            sb.append("node ").append(i);
            sb.append(": parent = ").append(t[i].parent);
            sb.append(", depth = ").append(t[i].depth);
            if(t[i].parent==-1) sb.append(", root, [");
            else if(t[i].child==-1) sb.append(", leaf, [");
            else sb.append(", internal node, [");
            final int c = t[i].child;
            if(c!=-1){
                sb.append(c);
                int ch = c;
                while(true){
                    ch = t[ch].sibling;
                    if(ch==-1) break;
                    sb.append(", ").append(ch);
                }
            }
            sb.append("]\n");
        }
        System.out.print(sb);
    }
    static void setdepth(int root, int d){
        int n = root;
        do{
            t[n].depth = d;
            if(t[n].child!=-1){
                setdepth(t[n].child, d+1);
            }
            n = t[n].sibling;
        }while(n!=-1);
    }
}

class node{
    int parent;
    int child;
    int sibling;
    int depth;
    node(){
        parent = -1;
        child = -1;
        sibling = -1;
        depth = -1;
    }
}