Problem:
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Priority Queue

A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:

$insert(S, k)$: insert an element $k$ into the set $S$

$extractMax(S)$: remove and return the element of $S$ with the largest key

Write a program which performs the $insert(S, k)$ and $extractMax(S)$ operations to a priority queue $S$.
The priority queue manages a set of integers, which are also keys for the priority.

Input

Multiple operations to the priority queue $S$ are given. Each operation is given by "insert $k$", "extract" or "end" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.

The input ends with "end" operation.

Output

For each "extract" operation, print the element extracted from the priority queue $S$ in a line.

Constraints

The number of operations $\leq 2,000,000$

$0 \leq k \leq 2,000,000,000$

Sample Input 1

insert 8
insert 2
extract
insert 10
extract
insert 11
extract
extract
end

Sample Output 1

8
10
11
2

Solution in Ruby (judge verdict: Wrong Answer)

$heap = [nil]
def max_heapify(index)
  left = index * 2
  right = index * 2 + 1
  if left < $heap.length && $heap[left] > $heap[index]
    largest = left
  else
    largest = index
  end
  largest = right if right < $heap.length && $heap[right] > $heap[largest]

  unless largest == index
    $heap[index], $heap[largest] = $heap[largest], $heap[index]
    max_heapify largest
  end
end

def extract_max
  max = $heap[1]
  $heap[1] = $heap.pop
  max_heapify 1
  max
end

def insert(key)
  $heap << key
  i = $heap.length
  while i > 1 && !$heap[i / 2 - 1].nil? && $heap[i / 2 - 1] < $heap[i - 1]
    $heap[i / 2 - 1] , $heap[i - 1] = $heap[i - 1] , $heap[i / 2 - 1]
    i /= 2
  end
end

loop do
  input = gets.split ' '
  case input[0]
  when 'insert'
    insert input[1].to_i
  when 'extract'
    puts extract_max
  when 'end'
    break
  end
end