/*
 * ALDS1_8_B.cpp
 *
 *  Created on: May 3, 2018
 *      Author: 13743
 */

#include<cstdio>
#include<cstdlib>

struct Node {
	int key;
	Node *pa, *lc, *rc;
};

Node* root = NULL;

void insert(int k) {
	Node* y = NULL;
	Node* x = root;
	Node* z = new Node;
	while(x != NULL) {
		y = x;
		if(k < y->key) x = y->lc;
		else x = y->rc;
	}
	z->pa = y;
	z->lc = NULL;
	z->rc = NULL;
	z->key = k;
	if(y == NULL) {
		root = z;
	}
	else if(k < y->key) {
		y->lc = z;
	}
	else {
		y->rc = z;
	}
}

void preorder(Node* u) {
	if(u == NULL) return;
	printf(" %d", u->key);
	preorder(u->lc);
	preorder(u->rc);
}

void inorder(Node* u) {
	if(u == NULL) return;
	inorder(u->lc);
	printf(" %d", u->key);
	inorder(u->rc);
}

void print() {
	inorder(root);
	printf("\n");
	preorder(root);
	printf("\n");
}

void find(int k) {
	Node* x = root;
	while(x != NULL) {
		if(x->key == k) {
			printf("yes\n");
			return;
		}
		if(k < x->key) x = x->lc;
		else x = x->rc;
	}
	printf("no\n");
}

int main() {
	int m;
	scanf("%d", &m);
	char s[100];
	int ke;
	for(int i=0; i<m; i++) {
		scanf("%s", s);
		if(s[0] == 'i') {
			scanf("%d", &ke);
			insert(ke);
		}
		else if(s[0] == 'f') {
			scanf("%d", &ke);
			find(ke);
		}
		else {
			print();
		}
	}
}





### Prompt

Develop a solution in cpp to the problem described below:

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
/*
 * ALDS1_8_B.cpp
 *
 *  Created on: May 3, 2018
 *      Author: 13743
 */

#include<cstdio>
#include<cstdlib>

struct Node {
	int key;
	Node *pa, *lc, *rc;
};

Node* root = NULL;

void insert(int k) {
	Node* y = NULL;
	Node* x = root;
	Node* z = new Node;
	while(x != NULL) {
		y = x;
		if(k < y->key) x = y->lc;
		else x = y->rc;
	}
	z->pa = y;
	z->lc = NULL;
	z->rc = NULL;
	z->key = k;
	if(y == NULL) {
		root = z;
	}
	else if(k < y->key) {
		y->lc = z;
	}
	else {
		y->rc = z;
	}
}

void preorder(Node* u) {
	if(u == NULL) return;
	printf(" %d", u->key);
	preorder(u->lc);
	preorder(u->rc);
}

void inorder(Node* u) {
	if(u == NULL) return;
	inorder(u->lc);
	printf(" %d", u->key);
	inorder(u->rc);
}

void print() {
	inorder(root);
	printf("\n");
	preorder(root);
	printf("\n");
}

void find(int k) {
	Node* x = root;
	while(x != NULL) {
		if(x->key == k) {
			printf("yes\n");
			return;
		}
		if(k < x->key) x = x->lc;
		else x = x->rc;
	}
	printf("no\n");
}

int main() {
	int m;
	scanf("%d", &m);
	char s[100];
	int ke;
	for(int i=0; i<m; i++) {
		scanf("%s", s);
		if(s[0] == 'i') {
			scanf("%d", &ke);
			insert(ke);
		}
		else if(s[0] == 'f') {
			scanf("%d", &ke);
			find(ke);
		}
		else {
			print();
		}
	}
}





```