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: Time Limit Exceeded)

class Heep
  def initialize
    @node = []
  end
  def insert(num) #upheap
    @node.push(num)
    i = @node.size - 1
    loop do
      p = (i + 1) / 2 - 1
      break if p < 0
      break if @node[p] > @node[i]
      tmp = @node[i]
      @node[i] = @node[p]
      @node[p] = tmp
      i = p
    end
  end
  def extract #downheap
    ret = @node.shift
    @node.unshift(@node.pop())
    p = 0
    loop do
      i = 2 * p + 1
      np = @node[p]
      break unless i < @node.size
      i += 1 if i < @node.size-1 && @node[i] < @node[i+1]
      ni = @node[i]
      break unless np < ni
      @node[p], @node[i] = ni, np
      p = i
    end
    return ret
  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