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>

int cou = 1;
int oya[500010];
int kodo[2][500010];
int ata[500010];

int ks(int x,int y){
  if(y==0)printf(" %d",ata[x]);
  if(kodo[0][x])ks(kodo[0][x],y);
  if(y==1)printf(" %d",ata[x]);
  if(kodo[1][x])ks(kodo[1][x],y);
  if(y==2)printf(" %d",ata[x]);
}

void pull(int x, int xa){
  if(cou==1){
    ata[cou]=xa;
    cou++;
    return;
  }
  if(kodo[ata[x]<xa][x])pull(kodo[ata[x]<xa][x],xa);
  else{
    kodo[ata[x]<xa][x] = cou;
    oya[cou]=x;
    ata[cou]=xa;
    cou++;
  }
}

int tanch(int x,int xa){
  if(ata[x]==xa)return 1;
  if (kodo[ata[x]<xa][x])return tanch(kodo[ata[x]<xa][x],xa);
  return 0;
}

int main(){
  int p;
  scanf("%d",&p);
  while(p--){
    char s[10];
    scanf("%s",s);
    if(s[0]=='p'){
      ks(1,1);
      puts("");
      ks(1,0);
      puts("");
    }else if(s[0]=='i'){
      int t;
      scanf("%d",&t);
      pull(1,t);
    }else{
      int t;
      scanf("%d",&t);
      puts(tanch(1,t)?"yes":"no");
      
    }
  }
}