#include<iostream>
#include<string>
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;
  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;
    }
  }
}

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

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

void find(Node *v, int x) {
  if (v==NIL) {
    cout << "no" << endl;
    return;
  } else if (v->key==x) {
    cout << "yes" << endl;
    return;
  }
  if (v->key < x) {
    find(v->right, x);
  } else{
    find(v->left, x);
  }
}

int main() {
  int n;
  cin >> n;
  int x;
  string com;
  for (int i=0; i<n; i++) {
    cin >> com;
    if (com=="insert") {
      cin >> x;
      insert(x);
    } else if (com=="print") {
      inorder(root);
      cout << endl;
      preorder(root);
      cout << endl;
    } else if (com=="find") {
      cin >> x;
      find(root, x);
    }
  }
  return 0;
}


### Prompt

Your challenge is to write 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<iostream>
#include<string>
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;
  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;
    }
  }
}

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

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

void find(Node *v, int x) {
  if (v==NIL) {
    cout << "no" << endl;
    return;
  } else if (v->key==x) {
    cout << "yes" << endl;
    return;
  }
  if (v->key < x) {
    find(v->right, x);
  } else{
    find(v->left, x);
  }
}

int main() {
  int n;
  cin >> n;
  int x;
  string com;
  for (int i=0; i<n; i++) {
    cin >> com;
    if (com=="insert") {
      cin >> x;
      insert(x);
    } else if (com=="print") {
      inorder(root);
      cout << endl;
      preorder(root);
      cout << endl;
    } else if (com=="find") {
      cin >> x;
      find(root, x);
    }
  }
  return 0;
}


```