#include<iostream>
#include<cstdlib>
using namespace std;
struct Node{
	int key;
	Node *right, *left, *parent;
};
Node *root, *NIL;

Node *find(Node *u, int k){
	while(u!=NIL && k!=u->key){
		if(k<u->key)	u=u->left;
		else	u=u->right;
	}
	return u;
}
void insert(int k){
	Node *y=NIL;
	Node *x=root;
	Node *z;
	z=(Node *)malloc(sizeof(Node));
	z->key=k;
	z->left=NIL;
	z->right=NIL;

	while(x!=NIL){
		y=x;
		if(z->key < x->key){
			x=x->left;
		}
		else
			x=x->right;
	}
	z->parent=y;
	if(y==NIL){
		root=z;
	}else{
		if(z->key < y->key){
			y->left=z;
		}else{
			y->right=z;
		}
	}
}
void inorder(Node *u){
	if(u==NIL)	return ;
	inorder(u->left);
	cout<<" "<<u->key;
	inorder(u->right);
}
void preorder(Node *u){
	if(u==NIL)	return ;
	cout<<" "<<u->key;
	preorder(u->left);
	preorder(u->right);
}
int main(){
	int n, i, x;
	string com;
	cin>>n;
	while(n--){
		cin>>com;
		if(com=="insert"){
			cin>>x;
			insert(x);
		}
		else if(com=="print"){
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}
		else if(com=="find"){
			cin>>x;
			Node *t=find(root, x);
			if(t!=NIL)	cout<<"yes"<<endl;
			else	cout<<"no"<<endl;
		}
	}
	return 0;

}

### Prompt

Develop a solution in Cpp 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<iostream>
#include<cstdlib>
using namespace std;
struct Node{
	int key;
	Node *right, *left, *parent;
};
Node *root, *NIL;

Node *find(Node *u, int k){
	while(u!=NIL && k!=u->key){
		if(k<u->key)	u=u->left;
		else	u=u->right;
	}
	return u;
}
void insert(int k){
	Node *y=NIL;
	Node *x=root;
	Node *z;
	z=(Node *)malloc(sizeof(Node));
	z->key=k;
	z->left=NIL;
	z->right=NIL;

	while(x!=NIL){
		y=x;
		if(z->key < x->key){
			x=x->left;
		}
		else
			x=x->right;
	}
	z->parent=y;
	if(y==NIL){
		root=z;
	}else{
		if(z->key < y->key){
			y->left=z;
		}else{
			y->right=z;
		}
	}
}
void inorder(Node *u){
	if(u==NIL)	return ;
	inorder(u->left);
	cout<<" "<<u->key;
	inorder(u->right);
}
void preorder(Node *u){
	if(u==NIL)	return ;
	cout<<" "<<u->key;
	preorder(u->left);
	preorder(u->right);
}
int main(){
	int n, i, x;
	string com;
	cin>>n;
	while(n--){
		cin>>com;
		if(com=="insert"){
			cin>>x;
			insert(x);
		}
		else if(com=="print"){
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}
		else if(com=="find"){
			cin>>x;
			Node *t=find(root, x);
			if(t!=NIL)	cout<<"yes"<<endl;
			else	cout<<"no"<<endl;
		}
	}
	return 0;

}

```