
#include <bits/stdc++.h>
#define ll long long
#define eps 1e-7
using namespace std;
#define pi acos(-1)

struct Node { int key; Node* le, * ri, * p; };
Node* root, * NIL;
void insert(int k) {
	Node* y = NIL, * x = root;
	Node* z;
	z = new(Node);
	z->key = k;
	z->le = NIL, z->ri = NIL;
	while (x != NIL) {
		y = x;
		if (z->key < x->key) x = x->le;
		else x = x->ri;
	}
	z->p = y;
	if (y == NIL) root = z;
	else {
		if (z->key < y->key) y->le = z;
		else y->ri = z;
	}
}
bool find(int k) {
	Node* x = root;
	while (x != NIL) {
		if (x->key > k) x = x->le;
		else if (x->key == k) return true;
		else x = x->ri;
	}
	return false;
}
void preorder(Node* u) {
	if (u != NIL) {
		printf(" %d", u->key);
		preorder(u->le);
		preorder(u->ri);
	}
}
void inorder(Node* u) {
	if (u != NIL) {
		inorder(u->le);
		printf(" %d", u->key);
		inorder(u->ri);
	}
}

int main() {
	int n, i, k;
	string com;
	cin >> n;
	while (n--) {
		cin >> com;
		if (com == "insert") cin >> k, insert(k);
		else if (com == "print") inorder(root), cout << endl, preorder(root), cout << endl;
		else if (com == "find") {
			cin >> k;
			if (find(k)) cout << "yes" << endl;
			else cout << "no" << endl;
		}
	}
}

### 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 <bits/stdc++.h>
#define ll long long
#define eps 1e-7
using namespace std;
#define pi acos(-1)

struct Node { int key; Node* le, * ri, * p; };
Node* root, * NIL;
void insert(int k) {
	Node* y = NIL, * x = root;
	Node* z;
	z = new(Node);
	z->key = k;
	z->le = NIL, z->ri = NIL;
	while (x != NIL) {
		y = x;
		if (z->key < x->key) x = x->le;
		else x = x->ri;
	}
	z->p = y;
	if (y == NIL) root = z;
	else {
		if (z->key < y->key) y->le = z;
		else y->ri = z;
	}
}
bool find(int k) {
	Node* x = root;
	while (x != NIL) {
		if (x->key > k) x = x->le;
		else if (x->key == k) return true;
		else x = x->ri;
	}
	return false;
}
void preorder(Node* u) {
	if (u != NIL) {
		printf(" %d", u->key);
		preorder(u->le);
		preorder(u->ri);
	}
}
void inorder(Node* u) {
	if (u != NIL) {
		inorder(u->le);
		printf(" %d", u->key);
		inorder(u->ri);
	}
}

int main() {
	int n, i, k;
	string com;
	cin >> n;
	while (n--) {
		cin >> com;
		if (com == "insert") cin >> k, insert(k);
		else if (com == "print") inorder(root), cout << endl, preorder(root), cout << endl;
		else if (com == "find") {
			cin >> k;
			if (find(k)) cout << "yes" << endl;
			else cout << "no" << endl;
		}
	}
}

```