Binary Search Tree 1

Implement a balanced binary search tree.

Input

Сontains a description of operations on the tree, with the total number of operations not exceeding $10^5$. Each line contains one of the following operations:

• insert $x$ — insert key $x$ into the tree. If key $x$ is already present in the tree, do nothing.

• delete $x$ — remove key $x$ from the tree. If key $x$ is not present in the tree, do nothing.

• exists $x$ — if key $x$ is present in the tree, output "true", otherwise "false".

All numbers are integers and do not exceed $10^9$ in absolute value.

Output

Print the results of all exists operations sequentially, following the format provided in the example.

Examples