#include <iostream>
#include <string>

using namespace std;

struct node {
  node *right,*left,*p;
  int key;
};

node *root;

void insert(int k) {
  node *y = NULL;
  node *x = root;
  node *z;

  z = (node*)malloc(sizeof(node));
  z->key = k;
  z->left = NULL;
  z->right = NULL;

  while(x!=NULL) {
    y = x;
    if(z->key < x->key) x = x->left;
    else x = x->right;
  }
  z->p = y;
  if(y==NULL) root = z;
  else {
    if(z->key < y->key) y->left = z;
    else y->right = z;
  }
}

node* find(int k) {
  node *x = root;
  while(x!=NULL) {
    if(x->key == k) return x;
    else if(x->key > k) x = x->left;
    else x = x->right;
  }
  return NULL;
}

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

void inorder(node *u) {
  if (u == NULL) return;
  inorder(u->left);
  cout << " " << u->key;
  inorder(u->right);
}
  
int main(){
  int n; cin >> n;
  while(n--) {
    string s;
    cin >> s;
    if(s=="insert") {
      int k; cin >> k;
      insert(k);
    } else if(s=="find") {
      int k; cin >> k;
      cout << (find(k)!=NULL?"yes":"no") << endl;
    } else {
      inorder(root);
      cout << endl;
      preorder(root);
      cout << endl;
    }
  }
  
  return 0;
}


### Prompt

Create a solution in Cpp for 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>
#include <string>

using namespace std;

struct node {
  node *right,*left,*p;
  int key;
};

node *root;

void insert(int k) {
  node *y = NULL;
  node *x = root;
  node *z;

  z = (node*)malloc(sizeof(node));
  z->key = k;
  z->left = NULL;
  z->right = NULL;

  while(x!=NULL) {
    y = x;
    if(z->key < x->key) x = x->left;
    else x = x->right;
  }
  z->p = y;
  if(y==NULL) root = z;
  else {
    if(z->key < y->key) y->left = z;
    else y->right = z;
  }
}

node* find(int k) {
  node *x = root;
  while(x!=NULL) {
    if(x->key == k) return x;
    else if(x->key > k) x = x->left;
    else x = x->right;
  }
  return NULL;
}

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

void inorder(node *u) {
  if (u == NULL) return;
  inorder(u->left);
  cout << " " << u->key;
  inorder(u->right);
}
  
int main(){
  int n; cin >> n;
  while(n--) {
    string s;
    cin >> s;
    if(s=="insert") {
      int k; cin >> k;
      insert(k);
    } else if(s=="find") {
      int k; cin >> k;
      cout << (find(k)!=NULL?"yes":"no") << endl;
    } else {
      inorder(root);
      cout << endl;
      preorder(root);
      cout << endl;
    }
  }
  
  return 0;
}


```