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 C (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

#if 1
#define gc() getchar_unlocked()
#define pc(c) putchar_unlocked(c)
#else
#define gc() getchar()
#define pc(c) putchar(c)
#endif
int in()
{
	int n = 0, c = gc();
	do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
	return n;
}

void out(int n)
{
	int i;
	char ob[20];

	if (!n) { pc('0'); return; }
	i = 0; while (n) ob[i++] = n%10 + '0', n/=10;
	while (i--) pc(ob[i]); 
}

void sout(char *s) { while (*s) pc(*s++); }

typedef struct { int parent; int depth; int k; int *c; } TREE;
TREE tbl[100002];

void calc_depth(int node, int d)
{
	int i;
	tbl[node].depth = d;
	for (i = 0; i < tbl[node].k; i++) calc_depth(tbl[node].c[i], d+1);
}

int main()
{
	int n, i, j, k, id;
	int root;

	n = in();
	for (i = 0; i < n; i++) {
		id = in(), tbl[id].k = k = in();
		tbl[id].c = malloc(k << 2);
		for (j = 0; j < k; j++) {
			int _c = in();
			tbl[_c].parent = id+1;
			tbl[id].c[j] = _c;
		}
	}
	for (root = 0; root < n; root++) {
		if (tbl[root].parent == 0) break;
	}
	calc_depth(root, 0);

	for (i = 0; i < n; i++) {
		sout("node "), out(i);
		sout(": parent = ");
		if (i == root) sout("-1");
		else out(tbl[i].parent - 1);
		sout(", depth = "), out(tbl[i].depth);
		sout(", ");
		if (i == root)          sout("root");
		else if (tbl[i].k == 0) sout("leaf");
		else                    sout("internal node");
		sout(", [");
		if (tbl[i].k > 0) {
			out(tbl[i].c[0]);
			for (j = 1; j < tbl[i].k; j++) {
				pc(','), pc(' '), out(tbl[i].c[j]);
			}
		}
		sout("]\n");
	}
	return 0;
}