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 JavaScript (judge verdict: Wrong Answer)

const input = require('fs').readFileSync('/dev/stdin', 'utf8');

const inputs = input.trim().split('\n');
const n = Number(inputs.shift());
const adj = inputs.map((s) => s.split(' ').map(Number));

class Node {
  constructor(id) {
    this.id = id;
    this.parentId = -1;
    this.children = [];
  }
  add(node) {
    node.parentId = node.id;
    this.children.push(node);
  }
  isRoot() {
    return this.parentId === -1;
  }
  getType() {
    return this.isRoot() ? 'root' : this.children.length ? 'internal node' : 'leaf';
  }
  calc(depth) {
    this.depth = depth++;
    this.children.sort((a, b) => a.id > b.id);
    this.children.forEach(child => child.calc(depth));
  }
  toString() {
    return 'node ' + this.id + ': ' + [
      'parent = ' + this.parentId,
      'depth = ' + this.depth,
      this.getType(),
      '[' + this.children.map(child => child.id).join(', ') + ']',
    ].join(', ');
  }
}

class Tree {
  constructor() {
    this.map = new Map();
  }
  getNode(id) {
    this.map.has(id) || this.map.set(id, new Node(id));
    return this.map.get(id);
  }
  getRoot() {
    for (let i = 0; i < this.map.size; i++) {
      const node = this.map.get(i);
      if (node.isRoot()) {
        return node;
      }
    }
  }
  calc() {
    const root = this.getRoot();
    root.calc(0);
  }
  print() {
    for (let i = 0; i < this.map.size; i++) {
      const node = this.map.get(i);
      console.log(node.toString());
    }
  }
}

const tree = new Tree();
adj.forEach(([u, k, ...vk]) => {
  const parent = tree.getNode(u);
  vk.forEach(v => {
    const node = tree.getNode(v);
    parent.add(node);
  });
});

tree.calc();
tree.print();