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 cnt=1;
int oya[500010];
int ko[2][500010];
int val[500010];

int f(int v,int mode){
    if(mode==0)printf(" %d",val[v]);
    if(ko[0][v])f(ko[0][v],mode);
    if(mode==1)printf(" %d",val[v]);
    if(ko[1][v])f(ko[1][v],mode);
    if(mode==2)printf(" %d",val[v]);
}
void push(int v,int va){
	//初回
	if(cnt==1){
		val[cnt]=va;
		cnt++;
		return;
	}
	if(ko[val[v]<va][v])push(ko[val[v]<va][v],va);
	else{
		ko[val[v]<va][v]=cnt;
		oya[cnt]=v;
		val[cnt]=va;
		cnt++;
	}
}

int find(int v,int va){
	if(val[v]==va)return 1;
	if(ko[val[v]<va][v])return find(ko[val[v]<va][v],va);
	return 0;
}

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