#include <cstdio>
#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

struct node{
	int num;
	node *parent,*left,*right;
};
node *root,*NIL;

void find(int a){
	node *x=root;
	while(x!=NIL){
		if(x->num < a) x=x->right;
		else if(x->num>a) x=x->left;
		else {
			printf("yes\n");
			return ;
		}
	}
	printf("no\n");
	return ;
}

void print_inorder(node *x){
	if(x==NIL) return ;
	print_inorder(x->left);
	printf(" %d",x->num);
	print_inorder(x->right);
	return ;
}

void print_preorder(node *x){
	if(x==NIL) return ;
	printf(" %d",x->num);
	print_preorder(x->left);
	print_preorder(x->right);
	return ;
}

void insert(int a){
	node *x=root,*y=NIL;
	node *z=new node();
	z->num=a;z->left=NIL;z->right=NIL;
	while(x!=NIL){
		y=x;
		if(z->num < x->num) x=x->left;
		else x=x->right;
	}
	z->parent=y;
	if(y==NIL) root=z;
	else {
		if(z->num < y->num) y->left=z;
		else y->right=z;
	}
	return ;
}

int main(){
	int n;
	cin>>n;
	string s;
	int a;
	for(int i=0;i<n;i++){
		cin>>s;
		if(s[0]=='i') cin>>a,insert(a);
		else if(s[0]=='p'){
			print_inorder(root);
			printf("\n");
			print_preorder(root);
			printf("\n");
		}
		else cin>>a,find(a);
	}
	return 0;
}

### Prompt

Your task is to create 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 <cstdio>
#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

struct node{
	int num;
	node *parent,*left,*right;
};
node *root,*NIL;

void find(int a){
	node *x=root;
	while(x!=NIL){
		if(x->num < a) x=x->right;
		else if(x->num>a) x=x->left;
		else {
			printf("yes\n");
			return ;
		}
	}
	printf("no\n");
	return ;
}

void print_inorder(node *x){
	if(x==NIL) return ;
	print_inorder(x->left);
	printf(" %d",x->num);
	print_inorder(x->right);
	return ;
}

void print_preorder(node *x){
	if(x==NIL) return ;
	printf(" %d",x->num);
	print_preorder(x->left);
	print_preorder(x->right);
	return ;
}

void insert(int a){
	node *x=root,*y=NIL;
	node *z=new node();
	z->num=a;z->left=NIL;z->right=NIL;
	while(x!=NIL){
		y=x;
		if(z->num < x->num) x=x->left;
		else x=x->right;
	}
	z->parent=y;
	if(y==NIL) root=z;
	else {
		if(z->num < y->num) y->left=z;
		else y->right=z;
	}
	return ;
}

int main(){
	int n;
	cin>>n;
	string s;
	int a;
	for(int i=0;i<n;i++){
		cin>>s;
		if(s[0]=='i') cin>>a,insert(a);
		else if(s[0]=='p'){
			print_inorder(root);
			printf("\n");
			print_preorder(root);
			printf("\n");
		}
		else cin>>a,find(a);
	}
	return 0;
}

```