#include<bits/stdc++.h>
using namespace std;

struct Node{
	int key;
	Node *parent, *left, *right;
};

Node *root, *NIL;

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;
		}
	}
		
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 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, a;
	string status;
	
	cin >> n;
	
	for(int i = 0 ; i < n ; i++){
		cin >> status;
		if(status == "insert"){
			cin >> a;
			insert(a);
			}
		else if(status == "print"){
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
			}
		else if(status == "find"){
			cin >> a;
			if(find(root, a) != NIL) cout << "yes" <<endl;
			else cout << "no" <<endl;
			}
		}
	
	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<bits/stdc++.h>
using namespace std;

struct Node{
	int key;
	Node *parent, *left, *right;
};

Node *root, *NIL;

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;
		}
	}
		
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 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, a;
	string status;
	
	cin >> n;
	
	for(int i = 0 ; i < n ; i++){
		cin >> status;
		if(status == "insert"){
			cin >> a;
			insert(a);
			}
		else if(status == "print"){
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
			}
		else if(status == "find"){
			cin >> a;
			if(find(root, a) != NIL) cout << "yes" <<endl;
			else cout << "no" <<endl;
			}
		}
	
	return 0;
	
}
```