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)

class Heep
  def initialize
    @node = []
  end
  def insert(num) #upheap
    i = @node.size
    @node[i] = num
    while i > 0 && @node[i/2] < @node[i]
      @node[i], @node[i/2] = @node[i/2], @node[i]
      i /= 2
    end
  end
  def extract #downheap
    ret = @node[0]
    @node[0] = @node.pop()
    maxHeapify(@node, 0)
    return ret
  end
  def maxHeapify(a, i)
    h = a.size
    l = 2 * i + 1
    r = 2 * i + 2
    largest = i
    largest = l if l < h && a[l] > a[i]
    largest = r if r < h && a[r] > a[largest]

    if largest != i then
      a[i], a[largest] = a[largest], a[i]
      maxHeapify(a, largest)
    end
  end
end

heep = Heep.new()
loop do
  cmd, num = gets.split
  case cmd;
  when "insert";
    heep.insert(num.to_i)
  when "extract";
    puts heep.extract
  when "end";
    break
  end
end