Binary Tree

A rooted binary tree is a tree with a root node in which every node has at most two children.

Your task is to write a program which reads a rooted binary tree T and prints the following information for each node u of T:

node ID of u

parent of u

sibling of u

the number of children of u

depth of u

height of u

node type (root, internal node or leaf)

If two nodes have the same parent, they are siblings. Here, if u and v have the same parent, we say u is a sibling of v (vice versa).

The height of a node in a tree is the number of edges on the longest simple downward path from the node to a leaf.

Here, the given binary tree consists of n nodes and evey node has a unique ID from 0 to n-1.

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 is given in the following format:

id left right

id is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1.

Output

Print the information of each node in the following format:

node id: parent = p , sibling = s , degree = deg, depth = dep, height = h, type

p is ID of its parent. If the node does not have a parent, print -1.

s is ID of its sibling. If the node does not have a sibling, print -1.

deg, dep and h are the number of children, depth and height of the node respectively.

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.

Please follow the format presented in a sample output below.

Constraints

1 ≤ n ≤ 25

Sample Input 1

90 1 41 2 32 -1 -13 -1 -14 5 85 6 76 -1 -17 -1 -18 -1 -1

Sample Output 1

node 0: parent = -1, sibling = -1, degree = 2, depth = 0, height = 3, rootnode 1: parent = 0, sibling = 4, degree = 2, depth = 1, height = 1, internal nodenode 2: parent = 1, sibling = 3, degree = 0, depth = 2, height = 0, leafnode 3: parent = 1, sibling = 2, degree = 0, depth = 2, height = 0, leafnode 4: parent = 0, sibling = 1, degree = 2, depth = 1, height = 2, internal nodenode 5: parent = 4, sibling = 8, degree = 2, depth = 2, height = 1, internal nodenode 6: parent = 5, sibling = 7, degree = 0, depth = 3, height = 0, leafnode 7: parent = 5, sibling = 6, degree = 0, depth = 3, height = 0, leafnode 8: parent = 4, sibling = 5, degree = 0, depth = 2, height = 0, leaf

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

求线段树的高度就是求左右子树的最大高度+1。

代码如下：

#include 
   
    #include 
    
     #include 
     
      #include 
      
       using namespace std;const int maxn=30;struct tree{    int height;  //节点高度    int depth;   //节点深度    int parent;  //节点的父节点    int sibling; //节点的兄弟节点    int left,right;//节点的左右孩子    int degree;  //节点子节点个数};tree node[maxn];int n;void init(){    memset (node,-1,sizeof(node));}//求节点深度int Sdepth (int x){    if(node[x].parent==-1)        node[x].depth=0;    if(node[x].depth!=-1)        return node[x].depth;    return Sdepth(node[x].parent)+1;}//求节点高度int Sheight(int x){    if(x==-1)       return -1;    return max(Sheight(node[x].left)+1,Sheight(node[x].right)+1);}int main(){    scanf("%d",&n);    init();    for (int i=0;i

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