#include <cstdio>
#include <cstdlib>
#include <string>
#include <iostream>
#define NILL 2000000010
using namespace std;

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

tree *root,*NIL;

void insert(int k){
	tree *x=root,*y=NULL,*z;
	z = (tree *)malloc(sizeof(tree));
	z->key = k;
	z->l=NULL,z->r=NULL;
	while( x != NULL ){
		y = x;
		if(z->key < x->key ){
			x = x->l;
		} else {
			x = x->r;
		}
	}
	z->p = y;
	if( y == NULL ){
		root = z;
	} else {
		if( z->key > y->key ){
			y->r = z;
			z->p = y;
		} else {
			y->l = z;
			z->p = y;
		}
	}
}

void inorder(tree *u){
	if( u == NULL ) return;
	inorder(u->l);
	printf(" %d",u->key);
	inorder(u->r);
}

void preorder(tree *u){
	if( u == NULL ) return;
	printf(" %d",u->key);
	preorder(u->l);
	preorder(u->r);
}

void find(int x){
	tree *u = root;
	while( u != NULL){
		if(u->key == x){
			printf("yes\n");
			return;
		}
		if(u->key > x) u=u->l;
		else u=u->r;
	}
	printf("no\n");
	return;
}

int main(){
	int i,n,j,x;
	string com;
	cin >> n;
	root = NULL;
	while(n--){
		cin >> com;
		if( com == "insert" ){
			cin >> x;
			insert(x);
		}else if( com == "print" ){
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		} else if( com == "find" ){
			cin >> x;
			find(x);
		}
	}
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 <cstdlib>
#include <string>
#include <iostream>
#define NILL 2000000010
using namespace std;

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

tree *root,*NIL;

void insert(int k){
	tree *x=root,*y=NULL,*z;
	z = (tree *)malloc(sizeof(tree));
	z->key = k;
	z->l=NULL,z->r=NULL;
	while( x != NULL ){
		y = x;
		if(z->key < x->key ){
			x = x->l;
		} else {
			x = x->r;
		}
	}
	z->p = y;
	if( y == NULL ){
		root = z;
	} else {
		if( z->key > y->key ){
			y->r = z;
			z->p = y;
		} else {
			y->l = z;
			z->p = y;
		}
	}
}

void inorder(tree *u){
	if( u == NULL ) return;
	inorder(u->l);
	printf(" %d",u->key);
	inorder(u->r);
}

void preorder(tree *u){
	if( u == NULL ) return;
	printf(" %d",u->key);
	preorder(u->l);
	preorder(u->r);
}

void find(int x){
	tree *u = root;
	while( u != NULL){
		if(u->key == x){
			printf("yes\n");
			return;
		}
		if(u->key > x) u=u->l;
		else u=u->r;
	}
	printf("no\n");
	return;
}

int main(){
	int i,n,j,x;
	string com;
	cin >> n;
	root = NULL;
	while(n--){
		cin >> com;
		if( com == "insert" ){
			cin >> x;
			insert(x);
		}else if( com == "print" ){
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		} else if( com == "find" ){
			cin >> x;
			find(x);
		}
	}
}

```