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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

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

  public void run() {

    try(BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {

      int n = Integer.parseInt(br.readLine());
      int id,degree;
      int[] childId;
      String[] words;
      TreeNodeA[] tree = new TreeNodeA[n];
      for (int i=0; i<n; i++) {
        tree[i] = new TreeNodeA();
      }

      for(int i=0, k=0; i<n; i++, k=0){
        words = br.readLine().split(" ");
        id     = Integer.parseInt(words[k++]);
        degree = Integer.parseInt(words[k++]);
        childId = new int[degree];

        tree[id].setId(id).setDegree(degree).setChildId(childId);

        for (int j=0,l=0; j<degree; j++) {
          childId[j] = Integer.parseInt(words[k++]);
          if( j==0 ) tree[id].setLeftChild(childId[j]);
          else tree[l].setRightSibling(childId[j]);
          l = childId[j];
          tree[childId[j]].setParent(id);
        }
      }

      int root=0;
      for (TreeNodeA node : tree)
        if(node.getParent() == TreeNodeA.NIL) root = node.getId();
      calcDepth(tree, root, 0);

      StringBuilder s = new StringBuilder();
      for (TreeNodeA node : tree) {
        s.append(node).append("\n");
      }
      System.out.print(s);
    }
    catch(IOException e) {
      System.out.println("IOException!");
    }
  }

  void calcDepth(TreeNodeA[] tree, int u, int p) {
    tree[u].setDepth(p);

    if( tree[u].getRightSibling() != TreeNodeA.NIL ) {
      for (int i=tree[u].getRightSibling(); i!=TreeNodeA.NIL; i=tree[i].getRightSibling()) {
        tree[i].setDepth(p);
      }
    }

    if( tree[u].getLeftChild() != TreeNodeA.NIL )
      calcDepth(tree, tree[u].getLeftChild(), p+1);
  }
}

class TreeNodeA {
  static final int NIL = -1;
  private int id;
  private int degree;
  private int parent;
  private int depth;
  private int type;
  private int[] childId;
  private int leftChild;
  private int rightSibling;

  public TreeNodeA() {
    this.id = NIL;
    this.degree = NIL;
    this.parent = NIL;
    this.leftChild = NIL;
    this.rightSibling = NIL;
  }

  public int getId() {
    return id;
  }
  public int getDegree() {
    return degree;
  }
  /**
   * @return the parent
   */
  public int getParent() {
    return parent;
  }
  public int getDepth() {
    return depth;
  }
  public String getType() {
    switch(type) {
      case 0:
        return "root";
      case 1:
        return "internal node";
      default:
        return "leaf";
    }
  }
  public int getChildId(int k) {
    if(childId != null)
      return childId[k];
    else
      return NIL;
  }
  /**
   * @return the rightSibling
   */
  public int getRightSibling() {
    return rightSibling;
  }
  /**
   * @return the leftChild
   */
  public int getLeftChild() {
    return leftChild;
  }
  public TreeNodeA getNode(int id) {
    return this;
  }

  public TreeNodeA setId(int id) {
    this.id = id;
    return this;
  }
  public void setDepth(int d) {
    depth = d;
    if(depth > 0) {
      if(degree > 0)
        setType(1);
      else
        setType(2);
    }
  }
  public void setType(int t) {
    this.type = t;
  }
  /**
   * @param degree the degree to set
   */
  public TreeNodeA setDegree(int degree) {
    this.degree = degree;
    return this;
  }
  /**
   * @param parent the parent to set
   */
  public void setParent(int parent) {
    this.parent = parent;
  }
  /**
   * @param childId the childId to set
   */
  public TreeNodeA setChildId(int[] childId) {
    this.childId = childId;
    return this;
  }
  /**
   * @param rightChild the rightSibling to set
   */
  public void setRightSibling(int rightSibling) {
    this.rightSibling = rightSibling;
  }
  /**
   * @param leftSibling the leftSibling to set
   */
  public void setLeftChild(int leftChild) {
    this.leftChild = leftChild;
  }

  @Override
  public String toString() {
    return "node " + id + ": parent = " + parent + ", depth = " + depth + ", "
      + getType() +", " + Arrays.toString(childId);
  }
}