Binary Search Tree 1 - Problems

Implement a balanced binary search tree.

Contains the description of operations on the tree, their number is not greater than 10⁵. Each line contains one of the following operations:

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 10⁹ by absolute value.

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

Time limit 3 seconds

Memory limit 128 MiB

Input example #1

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

Output example #1

true
false