Competitions

# Data Structures contest

# Binary Search Tree 1

Implement a balanced binary search tree.

#### Input

Contains the description of operations on the tree, their number is not greater than `10`

. Each line contains one of the next operations:^{5}

**insert x**- add the key**x**into the tree. If the key**x**is already in the tree, do nothing.**delete x**- delete the key**x**from the tree. If the tree does not contain the key**x**, do nothing.**exists x**- if the key**x**is in the tree, print "**true**", otherwise print "**false**".

All numbers are integers not greater than `10`

by absolute value.^{9}

#### Output

Print the result of all operations **exists** in format given in sample output.

Input example #1

insert 2 insert 5 insert 3 exists 2 exists 4 delete 5

Output example #1

true false