#include<iostream>
using namespace std;

struct Node {
	int key;
	Node *p, *l, *r;
};

Node *nil;
Node *root = nil;

void insert(int k) {
	Node *y = nil;
	Node *x = root;
	Node *z = new Node;
	z->key = k;
	z->l = nil;
	z->r = nil;
	while (x != nil) {
		y = x;
		if (z->key < x->key) x = x->l;
		else x = x->r;
	}
	z->p = y;
	if (y == nil) root = z;
	else {
		if (z->key < y->key) y->l = z;
		else y->r = z; 
	}
}

void inorder(Node *root) {
	if (root == nil) return;
	inorder(root->l);
	cout << ' ' << root->key;
	inorder(root->r);
}

void preorder(Node *root) {
	if (root == nil) return;
	cout << ' ' << root->key;
	preorder(root->l);
	preorder(root->r);
}

void print() {
	inorder(root);
	cout << endl;
	preorder(root);
	cout << endl;
}

void find(int key) {
	Node *x = root;
	while (x != nil) {
		if (key == x->key) {
			cout << "yes" << endl;
			return;
		} else if (key < x->key) {
			x = x->l;
		} else x = x->r;
	}
	cout << "no" << endl;
}

int main() {
	int n, key;
	char cmd[10];
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> cmd;
		if (cmd[0] == 'i') {
			cin >> key;
			insert(key);
		} else if (cmd[0] == 'f') {
			cin >> key;
			find(key);
		} else print();
	}

	return 0;
}
### Prompt

Your challenge is to write 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 *p, *l, *r;
};

Node *nil;
Node *root = nil;

void insert(int k) {
	Node *y = nil;
	Node *x = root;
	Node *z = new Node;
	z->key = k;
	z->l = nil;
	z->r = nil;
	while (x != nil) {
		y = x;
		if (z->key < x->key) x = x->l;
		else x = x->r;
	}
	z->p = y;
	if (y == nil) root = z;
	else {
		if (z->key < y->key) y->l = z;
		else y->r = z; 
	}
}

void inorder(Node *root) {
	if (root == nil) return;
	inorder(root->l);
	cout << ' ' << root->key;
	inorder(root->r);
}

void preorder(Node *root) {
	if (root == nil) return;
	cout << ' ' << root->key;
	preorder(root->l);
	preorder(root->r);
}

void print() {
	inorder(root);
	cout << endl;
	preorder(root);
	cout << endl;
}

void find(int key) {
	Node *x = root;
	while (x != nil) {
		if (key == x->key) {
			cout << "yes" << endl;
			return;
		} else if (key < x->key) {
			x = x->l;
		} else x = x->r;
	}
	cout << "no" << endl;
}

int main() {
	int n, key;
	char cmd[10];
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> cmd;
		if (cmd[0] == 'i') {
			cin >> key;
			insert(key);
		} else if (cmd[0] == 'f') {
			cin >> key;
			find(key);
		} else print();
	}

	return 0;
}
```