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;
  
Node root;


Node Search(Node t,int k);

void Insert(int k);

void Inorder(Node t);

void Preorder(Node t);

  

  
main(){
  int i, a, n;
  char A[10];
    
  scanf("%d",&n);
  
  for ( i = 0; i < n; i++ ){
    scanf("%s",A);
  
    if (A[0]=='i'){
      scanf("%d",&a);
      Insert(a);
    } 
    else if (A[0]=='p'){
      Inorder(root);
      printf("\n");
        
      Preorder(root);
      printf("\n");
    }
    else if(A[0]=='f'){
      
      scanf("%d",&a);
      Node s=Search(root,a);
      if (s!= NULL ) printf("yes\n");
      else printf("no\n");
    }
  }
  return 0;
}


Node Search(Node t,int k){
  if(t==NULL || k==t->key){
    return t;
  }
  if(k<t->key){
    return Search(t->left,k);
  }
  else return Search(t->right,k);
}



void Insert(int k){
  Node y=NULL;
  Node x=root;
  Node z;
  
  z=malloc(sizeof(struct node));
  z->key=k;
  z->left=NULL;
  z->right=NULL;
    
  while(x!=NULL){
    y=x;
  
    if(z->key<x->key){
      x=x->left;
    }
    else x=x->right;
  }
  z->parent=y;
    
  if(y==NULL){
    root=z;
  }
  else if(z->key<y->key){
    y->left=z;
  }
  else y->right=z;
}



void Inorder(Node t){
    
  if(t!=NULL){
    if(t->left!=NULL){
      Inorder(t->left);
    }
    printf(" %d",t->key);
      
    if(t->right!=NULL){
      Inorder(t->right);
    }
  }
}



void Preorder(Node t){
  printf(" %d",t->key);
  if(t!=NULL){
    if(t->left!=NULL){
      Preorder(t->left);
    }
    if(t->right!=NULL){
      Preorder(t->right);
    }
  }
}