Implementing a Priority Queue using a Binary Heap

In this problem, you are required to implement a priority queue with the following operations:

• insert <task> <priority>: Insert a task with a given integer priority.
• peek: Return the task with the maximum priority without removing it.
• extract: Remove and return the task with the maximum priority.

The priority queue must be implemented using a binary max-heap. In a binary heap, for a node at index \(i\), the parent's index is \(\lfloor (i-1)/2 \rfloor\) and its children are at indices \(2i+1\) and \(2i+2\).

If an operation that returns an element (i.e. peek or extract) is called on an empty queue, print "error".

inputFormat

The first line contains an integer n denoting the number of commands.

The following n lines each contain a command. Each command is one of the following formats:

• insert <task> <priority> where <task> is a string (with no spaces) and <priority> is an integer.
• peek
• extract

outputFormat

For every command peek or extract, output the resulting task in a new line. If the queue is empty when performing peek or extract, output "error" (without quotes).

## sample

7
insert task1 2
insert task2 5
insert task3 1
peek
extract
extract
extract

task2
task2
task1
task3

</p>