#include <bits/stdc++.h>
#include<cstdio>
#include<cstdlib>
#include<string>
#include<iostream>
#include <math.h>
#include<algorithm>
using namespace std;
#define MAX 25

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

node *NIL,*root;

void insert(node * z){
  node * y=NIL;
  node * x=root;
  while(x!=NIL){
    y=x;
    if(z->key < x->key){
      x=x->l;
    }else{
      x=x->r;
    }
  }
  z->p=y;

  if(y==NIL){
    root=z;
  }else if(z->key < y->key){
    y->l=z;
  }else{
    y->r=z;
  }
}

void Preorder(node * x){
  if(x==NIL) return;
  cout<<" "<<x->key;
  Preorder(x->l);
  Preorder(x->r);
}

void Inorder(node * x){
  if(x==NIL) return;
  Inorder(x->l);
  cout<<" "<<x->key;
  Inorder(x->r);
}

int find(int k){
  node *x=root;
  while(x!=NIL && k!=x->key){
    if(x->key < k){
      x=x->r;
    }else{
      x=x->l;
    }
  }
  return x!=NIL;
}


int main(){
  int n,x;
  cin>>n;
  string s;
  for(int i=0;i<n;i++){
    cin>>s;
    if(s=="insert"){
      cin>>x;
      node * a=(node *)malloc(sizeof(node));
      a->key=x;
      a->l=a->r=NIL;
      insert(a);
    }else if(s=="print"){
      Inorder(root);
      cout<<endl;
      Preorder(root);
      cout<<endl;
    }else{
      cin>>x;
      if(find(x)) cout<<"yes"<<endl;
      else cout<<"no"<<endl;
    }
  }
  return 0;
}


### Prompt

Your challenge is to write a CPP solution to the following problem:

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.

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.

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.

Example

Input

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


Output

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

### Response

```cpp
#include <bits/stdc++.h>
#include<cstdio>
#include<cstdlib>
#include<string>
#include<iostream>
#include <math.h>
#include<algorithm>
using namespace std;
#define MAX 25

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

node *NIL,*root;

void insert(node * z){
  node * y=NIL;
  node * x=root;
  while(x!=NIL){
    y=x;
    if(z->key < x->key){
      x=x->l;
    }else{
      x=x->r;
    }
  }
  z->p=y;

  if(y==NIL){
    root=z;
  }else if(z->key < y->key){
    y->l=z;
  }else{
    y->r=z;
  }
}

void Preorder(node * x){
  if(x==NIL) return;
  cout<<" "<<x->key;
  Preorder(x->l);
  Preorder(x->r);
}

void Inorder(node * x){
  if(x==NIL) return;
  Inorder(x->l);
  cout<<" "<<x->key;
  Inorder(x->r);
}

int find(int k){
  node *x=root;
  while(x!=NIL && k!=x->key){
    if(x->key < k){
      x=x->r;
    }else{
      x=x->l;
    }
  }
  return x!=NIL;
}


int main(){
  int n,x;
  cin>>n;
  string s;
  for(int i=0;i<n;i++){
    cin>>s;
    if(s=="insert"){
      cin>>x;
      node * a=(node *)malloc(sizeof(node));
      a->key=x;
      a->l=a->r=NIL;
      insert(a);
    }else if(s=="print"){
      Inorder(root);
      cout<<endl;
      Preorder(root);
      cout<<endl;
    }else{
      cin>>x;
      if(find(x)) cout<<"yes"<<endl;
      else cout<<"no"<<endl;
    }
  }
  return 0;
}


```