#include<iostream>
#include<cstdio>
#include<cstdlib>
using namespace std;

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

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;
	}
}

int find(int k)
{
	Node *x=root;
	
	while(x!= NIL)
	{
		if(x->key == k) return 1;
		else if(x->key < k) x=x->right;
		else x=x->left;
	}
	return 0;
}

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 i,n,x;
	string com;
	
	scanf("%d",&n);
	
	for(i=0;i<=n-1;i++)
	{
		cin >> com;
		if(com=="insert")
		{
			scanf("%d",&x);
			insert(x);
		}
		else if(com=="find")
		{
			scanf("%d",&x);
			if(find(x)==1) printf("yes");
			else printf("no");
			printf("\n");
		}
		else if(com=="print")
		{
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}
	}
	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<iostream>
#include<cstdio>
#include<cstdlib>
using namespace std;

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

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;
	}
}

int find(int k)
{
	Node *x=root;
	
	while(x!= NIL)
	{
		if(x->key == k) return 1;
		else if(x->key < k) x=x->right;
		else x=x->left;
	}
	return 0;
}

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 i,n,x;
	string com;
	
	scanf("%d",&n);
	
	for(i=0;i<=n-1;i++)
	{
		cin >> com;
		if(com=="insert")
		{
			scanf("%d",&x);
			insert(x);
		}
		else if(com=="find")
		{
			scanf("%d",&x);
			if(find(x)==1) printf("yes");
			else printf("no");
			printf("\n");
		}
		else if(com=="print")
		{
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}
	}
	return 0;
}
```