#include<bits/stdc++.h>
using namespace std;
struct Node{
	int key;
	Node *right,*left,*parent;
};
Node *root,*NIL;
void insert(int k){
	Node *x=root;
	Node *y =NULL;
	Node *z=(Node *)malloc(sizeof(Node));
	z->key=k;z->left=NULL;z->right=NULL;
	while(x!=NULL){
		y=x;
		if(x->key>z->key){
			x=x->left;
		}
		else x=x->right;
	}
	z->parent=y;
	if(y==NULL)root=z;
	else {
		if(y->key>z->key){
			y->left=z;
		}
		else y->right=z;
	} 
	
}
Node * find(Node *u,int k){
	while(u!=NULL&&u->key!=k){
		if(u->key>k)u=u->left;
		else u=u->right; 
	}
	return u; 
}
void inorder(Node *u){
	if(u==NIL)return ;
	inorder(u->left);
	printf(" %d",u->key);
	inorder(u->right);
} 

void preorder(Node *u){
	if(u==NIL)return ;
	printf(" %d",u->key);
	preorder(u->left);
	preorder(u->right);
}
int main(){
	int n,i,x,k;
	string com;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		cin>>com;
		if(com=="insert"){
			scanf("%d",&x);
			insert(x); 
		}else if(com=="print"){
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}
		else if(com=="find"){
			scanf("%d",&k);
			if(find(root,k)!=NULL)printf("yes\n");
			else printf("no\n");
		}
			} 
} 

### Prompt

Generate 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>
using namespace std;
struct Node{
	int key;
	Node *right,*left,*parent;
};
Node *root,*NIL;
void insert(int k){
	Node *x=root;
	Node *y =NULL;
	Node *z=(Node *)malloc(sizeof(Node));
	z->key=k;z->left=NULL;z->right=NULL;
	while(x!=NULL){
		y=x;
		if(x->key>z->key){
			x=x->left;
		}
		else x=x->right;
	}
	z->parent=y;
	if(y==NULL)root=z;
	else {
		if(y->key>z->key){
			y->left=z;
		}
		else y->right=z;
	} 
	
}
Node * find(Node *u,int k){
	while(u!=NULL&&u->key!=k){
		if(u->key>k)u=u->left;
		else u=u->right; 
	}
	return u; 
}
void inorder(Node *u){
	if(u==NIL)return ;
	inorder(u->left);
	printf(" %d",u->key);
	inorder(u->right);
} 

void preorder(Node *u){
	if(u==NIL)return ;
	printf(" %d",u->key);
	preorder(u->left);
	preorder(u->right);
}
int main(){
	int n,i,x,k;
	string com;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		cin>>com;
		if(com=="insert"){
			scanf("%d",&x);
			insert(x); 
		}else if(com=="print"){
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}
		else if(com=="find"){
			scanf("%d",&k);
			if(find(root,k)!=NULL)printf("yes\n");
			else printf("no\n");
		}
			} 
} 

```