Problem:
Binary Search Tree II

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.

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.

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.

Sample Input 1

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

#define MAX


struct node{
  int key;
  struct node *right;
  struct node *left;
  struct node *parent;
};
  typedef struct node Node;
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){
    //leafのところまで探索
    y = x;
    if(z->key < x->key){
      x = x->left;
    }
    else{
      x = x->right;
    }
  }
  z->parent = y;
  //右に入るか左に入るかを考える
  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 print(Node *u){
  if(u == NIL)return;
  printf(" %d",u->key);
  print(u->left);
  print(u->right);
}

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;
}


int main(){
  int i,j,n,k;
  char s[10];
  Node *t;
  
  scanf("%d",&n);
  for(i=0; i<n; i++){
    scanf("%s",s);
    if(s[0]=='i'){
      scanf("%d",&k);
      insert(k);
    }
    else if(s[0]=='p'){
      //print
      inorder(root);
      printf("\n");
      print(root);
      printf("\n");
    }
    else if(s[0]=='f'){
      //find
      scanf("%d",&k);
      t = find(root,k);
      if(t != NIL)printf("yes\n");
      else printf("no\n");
    }
  }
  return 0;
}