#include<iostream>
#include<string>
#include<map>
#include<algorithm>
#include<vector>
#include<queue> 
#include<stack>
#include<cstdio>

using namespace std;

struct Node{
	int key;
	Node *parent, *left, *right;	
};

Node *root, *NIL;

void insert(int k){
	Node *y = NIL;
	Node *x = root;
	Node *z = (Node *)malloc(sizeof(Node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;
	
	while(x != NIL){
		y = x;
		if(z->key < x->key){
			x = x->left;
		}else{
			x = x->right;
		}
	}
	
	z->parent = y;
	
	if(y == NIL){
		root = z;
	}else{
		if(z->key < y->key){
			y->left = z;
		}else{
			y->right = z;
		}
	}
}

Node* find(Node *x, int k){
	while(x != NIL && k != x->key){
		if(k < x->key){
			x = x->left;
		}else{
			x = x->right;
		}
	}
	return x;
}

void inorder(Node *u){
	if(u == NIL) return;
	inorder(u->left);
	cout<<" "<<u->key;
	inorder(u->right);
}
void preorder(Node *u){
	if(u == NIL) return;
	cout<<" "<<u->key;
	preorder(u->left);
	preorder(u->right);
}

int main(){
	int n;
	cin>>n;
	
	string str;
	for(int i=0; i<n; i++ ){
		cin>>str;
		if(str[0] == 'i'){
			int k;
			scanf("%d",&k);
			insert(k);
		}else if(str[0] == 'f'){
			int k;
			scanf("%d",&k);
			if(find(root,k) != NIL){
				cout<<"yes"<<endl;
			}else{
				cout<<"no"<<endl;
			}
		}else{
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}
	}
	
	return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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>
#include<string>
#include<map>
#include<algorithm>
#include<vector>
#include<queue> 
#include<stack>
#include<cstdio>

using namespace std;

struct Node{
	int key;
	Node *parent, *left, *right;	
};

Node *root, *NIL;

void insert(int k){
	Node *y = NIL;
	Node *x = root;
	Node *z = (Node *)malloc(sizeof(Node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;
	
	while(x != NIL){
		y = x;
		if(z->key < x->key){
			x = x->left;
		}else{
			x = x->right;
		}
	}
	
	z->parent = y;
	
	if(y == NIL){
		root = z;
	}else{
		if(z->key < y->key){
			y->left = z;
		}else{
			y->right = z;
		}
	}
}

Node* find(Node *x, int k){
	while(x != NIL && k != x->key){
		if(k < x->key){
			x = x->left;
		}else{
			x = x->right;
		}
	}
	return x;
}

void inorder(Node *u){
	if(u == NIL) return;
	inorder(u->left);
	cout<<" "<<u->key;
	inorder(u->right);
}
void preorder(Node *u){
	if(u == NIL) return;
	cout<<" "<<u->key;
	preorder(u->left);
	preorder(u->right);
}

int main(){
	int n;
	cin>>n;
	
	string str;
	for(int i=0; i<n; i++ ){
		cin>>str;
		if(str[0] == 'i'){
			int k;
			scanf("%d",&k);
			insert(k);
		}else if(str[0] == 'f'){
			int k;
			scanf("%d",&k);
			if(find(root,k) != NIL){
				cout<<"yes"<<endl;
			}else{
				cout<<"no"<<endl;
			}
		}else{
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}
	}
	
	return 0;
}
```