Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

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>


struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
  
};
typedef struct node * Node;
#define NIL NULL

Node root;

Node treeMinimum(Node x){
  while(x->left!=NIL)x=x->left;
  return x;

}

Node treeMaximum(Node x){
  while(x->right!=NIL)x=x->right;
  return x;


}

Node treeSearch(Node u, int k){
  while(u!=NIL&&k!=u->key){
    if(k<u->key)u=u->left;
    else u=u->right;
  }
  return u;
}


Node treeSuccessor(Node x){
  Node y;
  if(x->right!=NIL)return treeMinimum(x->right);

  y=x->parent;
  while(y!=NIL && x==y->right){
    x=y;
    y=y->parent;
  }
  return y;
}


void treeDelete(Node z){
  Node y; // node to be deleted
  Node x; // child of y
  if(z->left==NIL||z->right==NIL)y=z;
  else y=treeSuccessor(z);

  
  if(y->left!=NIL)x=y->left;
  else x=y->right;

  
  if(x!=NIL)x->parent=y->parent;

  
  if(y->parent!=NIL)root=x;
  else if(y==y->parent->left)y->parent->left=x;
  else y->parent->right=x;

  
  if(y!=z)z->key=y->key;
  
}

void insert(int k){
  Node y = NIL;
  Node x = root;
  Node z;

  
  z = malloc(sizeof(struct node));
  z->key = k;
  z->left = NIL;
  z->right = NIL;

  while(x!=NIL){
    y=x;
    if(z->key<x->key)
      x=x->left;
    else x=x->right;
  }

  
  z->parent=y;

  
  if(y==NIL)
    root=z;
  else if(z->key<y->key)
    y->left=z;
  else
    y->right=z;
    
}



void inorder(Node u){
  if(u==NIL)return;
  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);
}


void preorder(Node u){
  if(u==NIL)return;
  printf(" %d",u->key);
  preorder(u->left);
  preorder(u->right);
}


int main(){
  int n, i, x;
  char com[20];
  scanf("%d", &n);

  
  for ( i = 0; i < n; i++ ){
    scanf("%s", com);
    if ( com[0] == 'f' ){
      scanf("%d", &x);
      Node t = treeSearch(root, x);
      if ( t != NIL ) printf("yes\n");
      else printf("no\n");
    } else if ( com[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( com[0] == 'p' ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    } else if ( com[0] == 'd' ){
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }
  }

  return 0;
}