#include <iostream>
using namespace std;

struct Node{
	int key;
	Node *parent;
	Node *left;
	Node *right;
	
	Node(): left(NULL), right(NULL){}
	Node(int _k): key(_k), left(NULL), right(NULL){}
};

void Insert(Node *&T, int key)
{
	Node *z = new Node(key);
	
	Node *y = NULL;
	Node *x = T;

	while(x != NULL)
	{
		y = x;
		if (z->key < x->key)
		{
			x = x->left;
		}
		else
		{
			x = x->right;
		}
	}
	
	z->parent = y;
	 
	if (y == NULL)
	{
		T = z;
	}
	else if (z->key < y->key)
	{
		y->left = z;
	}
	else
	{
		y->right = z;
	}
}

void Find(Node *T, int key)
{
	Node *temp = T;
	while(temp != NULL)
	{
		if (temp->key < key)
		{
			temp = temp->right;
		}
		else if (temp->key > key)
		{
			temp = temp->left;
		}
		else
		{
			cout << "yes" << endl;
			return;
		}
	}
	cout << "no" << endl;
	return;
}

void Preorder(Node *T)
{
	if (T == NULL) return;
	
	cout << " " << T->key;
	Preorder(T->left);
	Preorder(T->right);
}

void Inorder(Node *T)
{
	if (T == NULL) return;
	
	Inorder(T->left);
	cout << " " << T->key;
	Inorder(T->right);
}

int main ()
{
	int n;
	cin >> n;
	string cmd;
	Node *Tree = NULL;
	while(n--)
	{
		cin >> cmd;
		if (cmd == "insert")
		{
			int k;
			cin >> k;
			Insert(Tree, k);
		}
		else if (cmd == "print")
		{
			Inorder(Tree);
			cout << endl;
			Preorder(Tree);
			cout << endl;
		}
		else if (cmd == "find")
		{
			int k;
			cin >> k;
			Find(Tree, k);
		}
	}
	
	return 0;
}

### Prompt

Please formulate 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>
using namespace std;

struct Node{
	int key;
	Node *parent;
	Node *left;
	Node *right;
	
	Node(): left(NULL), right(NULL){}
	Node(int _k): key(_k), left(NULL), right(NULL){}
};

void Insert(Node *&T, int key)
{
	Node *z = new Node(key);
	
	Node *y = NULL;
	Node *x = T;

	while(x != NULL)
	{
		y = x;
		if (z->key < x->key)
		{
			x = x->left;
		}
		else
		{
			x = x->right;
		}
	}
	
	z->parent = y;
	 
	if (y == NULL)
	{
		T = z;
	}
	else if (z->key < y->key)
	{
		y->left = z;
	}
	else
	{
		y->right = z;
	}
}

void Find(Node *T, int key)
{
	Node *temp = T;
	while(temp != NULL)
	{
		if (temp->key < key)
		{
			temp = temp->right;
		}
		else if (temp->key > key)
		{
			temp = temp->left;
		}
		else
		{
			cout << "yes" << endl;
			return;
		}
	}
	cout << "no" << endl;
	return;
}

void Preorder(Node *T)
{
	if (T == NULL) return;
	
	cout << " " << T->key;
	Preorder(T->left);
	Preorder(T->right);
}

void Inorder(Node *T)
{
	if (T == NULL) return;
	
	Inorder(T->left);
	cout << " " << T->key;
	Inorder(T->right);
}

int main ()
{
	int n;
	cin >> n;
	string cmd;
	Node *Tree = NULL;
	while(n--)
	{
		cin >> cmd;
		if (cmd == "insert")
		{
			int k;
			cin >> k;
			Insert(Tree, k);
		}
		else if (cmd == "print")
		{
			Inorder(Tree);
			cout << endl;
			Preorder(Tree);
			cout << endl;
		}
		else if (cmd == "find")
		{
			int k;
			cin >> k;
			Find(Tree, k);
		}
	}
	
	return 0;
}

```