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>
#define NIL NULL

struct node{
  struct node *right;
    struct node*left;
    struct node *parent;
  int key;
};
  typedef struct node *Node;

Node root;

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

void preoder(Node u)
{
  if( u!= NIL )
    {
  printf(" %d", u->key);
  preoder(u->left);
  preoder(u->right);
    }
}
    
    
Node treeSearch(Node u, int k){
  if(u==NIL || k==u->key)
    {
      return u;
    }
  if(k<u->key)
    {
      return treeSearch(u->left,k);
    }
  else return  treeSearch(u->right,k);
}
    
  



int main()
{
  char com[20];
  int n,x,i;
  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')
	{
	  inoder(root);
	  printf("\n");
	  preoder(root);
	  printf("\n");
	}
    }
  return 0;
}