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<iostream>
#include<stdlib.h>
using namespace std;

struct node{
  int key;
  struct node *p;
  struct node *l;
  struct node *r;
};

typedef struct node *pointer;

node s;
pointer nil=&s;
pointer R=nil;


void insert(pointer z){
  pointer y=nil;
  pointer x=R;
  while(x!=nil){
    y=x;
    if(z->key < x->key)x=x->l;
    else x=x->r;
  }
  z->p=y;
  if(y==nil) R = z;
  else if(z->key < y->key) y->l= z;
  else y->r=z;
}


void print(pointer t,int pp){
  if(t==nil) return;
  if(pp)cout<<" "<<t->key;
  print(t->l,pp);
  if(!pp)cout<<" "<<t->key;
  print(t->r,pp);
}

pointer find(pointer x,int k){
  while(x!=nil && k!=x->key){
    if(k < x->key ) x=x->l;
    else x=x->r;
  }
    return x;
  }


int main(){
  int n;
  cin>>n;
  string str;
  for(int i=0;i<n;i++){
    cin>>str;
    if(str=="insert"){
      pointer   T=(pointer)malloc(sizeof(node));
      cin>>T->key;
      T->l=nil;
      T->r=nil;
      insert(T);
    }else if(str=="print"){
      print(R,0);
      cout<<endl;
      print(R,1);
      cout<<endl;
    }else if(str=="find"){
      int a;
        cin>>a;
	pointer point=find(R,a);
	if(point->key==a) cout<<"yes"<<endl;
	else cout<<"no"<<endl;
    }
  
  }
  return 0;
}