#include <cstdio>
#pragma warning(disable : 4996)
int Q, x, lc[500009], rc[500009], key[500009], cnt; char b[10];
void inorder(int pos) {
	if (lc[pos]) inorder(lc[pos]);
	printf(" %d", key[pos]);
	if (rc[pos]) inorder(rc[pos]);
}
void preorder(int pos) {
	printf(" %d", key[pos]);
	if (lc[pos]) preorder(lc[pos]);
	if (rc[pos]) preorder(rc[pos]);
}
int main() {
	scanf("%d", &Q);
	while (Q--) {
		scanf("%s", b);
		if (b[0] == 'i') {
			scanf("%d", &x);
			if (cnt == 0) key[cnt++] = x;
			else {
				int pos = 0;
				while (true) {
					if (x < key[pos]) {
						if (lc[pos]) pos = lc[pos];
						else {
							lc[pos] = cnt;
							key[cnt++] = x;
							break;
						}
					}
					else {
						if (rc[pos]) pos = rc[pos];
						else {
							rc[pos] = cnt;
							key[cnt++] = x;
							break;
						}
					}
				}
			}
		}
		else if (b[0] == 'f') {
			scanf("%d", &x);
			if (cnt == 0) puts("no");
			else {
				int pos = 0;
				while (key[pos] != x) {
					if (x < key[pos]) {
						if (lc[pos]) pos = lc[pos];
						else break;
					}
					else {
						if (rc[pos]) pos = rc[pos];
						else break;
					}
				}
				puts(x == key[pos] ? "yes" : "no");
			}
		}
		else {
			inorder(0); printf("\n");
			preorder(0); printf("\n");
		}
	}
	return 0;
}
### Prompt

Please provide a CPP coded solution 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
#include <cstdio>
#pragma warning(disable : 4996)
int Q, x, lc[500009], rc[500009], key[500009], cnt; char b[10];
void inorder(int pos) {
	if (lc[pos]) inorder(lc[pos]);
	printf(" %d", key[pos]);
	if (rc[pos]) inorder(rc[pos]);
}
void preorder(int pos) {
	printf(" %d", key[pos]);
	if (lc[pos]) preorder(lc[pos]);
	if (rc[pos]) preorder(rc[pos]);
}
int main() {
	scanf("%d", &Q);
	while (Q--) {
		scanf("%s", b);
		if (b[0] == 'i') {
			scanf("%d", &x);
			if (cnt == 0) key[cnt++] = x;
			else {
				int pos = 0;
				while (true) {
					if (x < key[pos]) {
						if (lc[pos]) pos = lc[pos];
						else {
							lc[pos] = cnt;
							key[cnt++] = x;
							break;
						}
					}
					else {
						if (rc[pos]) pos = rc[pos];
						else {
							rc[pos] = cnt;
							key[cnt++] = x;
							break;
						}
					}
				}
			}
		}
		else if (b[0] == 'f') {
			scanf("%d", &x);
			if (cnt == 0) puts("no");
			else {
				int pos = 0;
				while (key[pos] != x) {
					if (x < key[pos]) {
						if (lc[pos]) pos = lc[pos];
						else break;
					}
					else {
						if (rc[pos]) pos = rc[pos];
						else break;
					}
				}
				puts(x == key[pos] ? "yes" : "no");
			}
		}
		else {
			inorder(0); printf("\n");
			preorder(0); printf("\n");
		}
	}
	return 0;
}
```