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)

//Binary tree search 2

#include<stdio.h>
#include<stdlib.h>
#define N NULL

typedef struct node
{

  struct node *p, *l, *r;
  int w;

}*tree;

void prepare(tree *root, int w)
{
  (*root) = (tree)malloc(sizeof(struct node));
  (*root)->p = N;
  (*root)->l = N;
  (*root)->r = N;
  (*root)->w = w;
  
}

void ins(tree *root, tree imp)
{
  tree y = N;
  tree x = *root;

  while(x != N)
    {
      y = x;
      if(imp->w < x->w)
	{
	  x = x->l;
	} else {
	x = x->r;
      }
    }

  imp->p = y;


  if(y == N)
    {
      *root = imp;
    }
  else if(imp->w > y->w)
    {
      y->r = imp;
    }
  else y->l = imp;
}


tree find(tree root,int w)
{
  while(root != N && w != root->w)
    {
      if(w < root->w)
	{
	  root = root->l;
	}
      else root = root->r;
    }
  return root;
  }


void inorder(tree imp)
{
  if(imp != N)
    {
      inorder(imp->l);
      printf(" %d",imp->w);
      inorder(imp->r);
    }
}

void preorder(tree imp)
{
  if(imp != N)
    {
      printf(" %d",imp->w);
      preorder(imp->l);
      preorder(imp->r);
    }
}

void print(tree root)
{
  inorder(root);
  printf("\n");
  preorder(root);
  printf("\n");
}


int main()
{
  tree root, imp, f;

  root = N;

  int n,w,i;
  char arr[10];

  //input data
  scanf("%d",&n);
  for(i = 0; i < n; i++)
    {
      scanf("%s",arr);

      if(arr[0] == 'i')
	{
	  scanf("%d",&w);

	  prepare(&imp,w);

	  ins(&root,imp);
	}


      if(arr[0] == 'p')
	{	  
	  print(root);
	 
	}
      
      if(arr[0] == 'f')
	{
	  scanf("%d",&w);

	  f = find(root,w);

	  if(f != N)
	    {
	     
	      printf("yes\n");
	    }
	  else printf("no\n");
	}

    }

  return 0;
}