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 Scala (judge verdict: Runtime Error)

import scala.io.StdIn.{readInt, readLine}
case class Node[T](value: T, parent: Node[T], var children: List[Node[T]], depth: Int) {
    override def toString(): String = {
        val p = if (parent == null) -1 else parent.value
        val t = if (parent == null) "root" else if (children == Nil) "leaf" else "internal node"
        val c = children.map(_.value).mkString(",")
        s"node ${value}: parent = ${p}, depth = ${depth}, ${t}, [${c}]"
    }
}
class IntTree() {
    var node: Node[Int] = null
    
    def add(target: Int, c: List[Int]): Unit = {
        if (node == null) {
            node = new Node[Int](target, null,  Nil, 0)
            node.children = c.map(new Node[Int](_, node, Nil, 1))
        } else search(target) match {
            case n => n.children = c.map(new Node[Int](_, n, Nil, n.depth + 1))
        }
    }

    def search(target: Int): Node[Int] = {
        def go(nodes: List[Node[Int]]): Node[Int] = nodes match {
            case Nil => null
            case x :: xs if x.value == target => x
            case x :: xs => go(x.children) match {
                case null => go(xs)
                case ret => ret
            }
        }
        if (node.value == target) node else go(node.children)
    }
}
object Main {
    def main(args: Array[String]): Unit = {
        val len = readInt
        val t = new IntTree()
        val l = (0 until len).foldLeft(Nil: List[Int]) { (list, i) =>
            val line = readLine.split(" ").map(_.toInt)
            val c = line.slice(2, line.length).toList
            val p = line.head
            t.add(p, c)
            if (i == 0) (p :: c) ::: list
            else c ::: list
        }
        println(l.sorted.map(t.search(_)).mkString("\n"))
    }
}