#include<cstdio>
#include<cstdlib>
#include<string>
#include<iostream>
using namespace std;

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

Node *root, *NIL;

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

  return u;
}

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 inorder(Node*u) {
  if(u == NIL) return;
  inorder(u->left);
  printf(" %d", u->key);
  inorder(u->right);
}

void preorder(Node *u) {
  if(u == NIL) return;
  printf(" %d", u->key);
  preorder(u->left);
  preorder(u->right);
}

int main() {
  int n, i, x;
  string com;

  scanf("%d", &n);
  for(i = 0; i < n; i++) {
    cin >> com;
    if(com[0] == 'f') {
      scanf("%d", &x);
      Node *t = NIL;
      t = find(root, x);
      if(t != NIL) printf("yes\n");
      else printf("no\n");
    } else if(com == "insert") {
      scanf("%d",&x);
      insert(x);
    } else if(com == "print") {
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }

  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<cstdio>
#include<cstdlib>
#include<string>
#include<iostream>
using namespace std;

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

Node *root, *NIL;

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

  return u;
}

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 inorder(Node*u) {
  if(u == NIL) return;
  inorder(u->left);
  printf(" %d", u->key);
  inorder(u->right);
}

void preorder(Node *u) {
  if(u == NIL) return;
  printf(" %d", u->key);
  preorder(u->left);
  preorder(u->right);
}

int main() {
  int n, i, x;
  string com;

  scanf("%d", &n);
  for(i = 0; i < n; i++) {
    cin >> com;
    if(com[0] == 'f') {
      scanf("%d", &x);
      Node *t = NIL;
      t = find(root, x);
      if(t != NIL) printf("yes\n");
      else printf("no\n");
    } else if(com == "insert") {
      scanf("%d",&x);
      insert(x);
    } else if(com == "print") {
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }

  return 0;
}


```