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)

def exchange i
  unless i==0
    pr=(i-1)/2
    if $a[i]>$a[pr]
      $a[i],$a[pr]=$a[pr],$a[i]
      exchange pr
    end
  end
end
def delete i
  l = i*2+1
  r = l+1
  max = l < $h && $a[l] > $a[i] ? l : i
  max = r if r < $h && $a[r] > $a[max]
  unless max == i
    $a[i],$a[max] = $a[max],$a[i]
    delete max
  end
end
$a=Array.new(2000000)
$h=0
begin
  command, $key = gets.split
  $key = $key.to_i
  case command
  when 'insert'
    $a[$h]=$key
    exchange $h
    $h+=1
  when 'extract'
    puts $a[0]
    $h-=1
    $a[0]=$a[$h]
    $a[$h]=nil
    delete 0
  end
end while command != 'end'