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 maxHeapify a,i
  l = i*2
  r = l+1
  max = l<=$h && a[l-1] > a[i-1] ? l : i
  max = r if r <= $h && a[r-1] > a[max-1]
  unless max == i
    a[i-1],a[max-1] = a[max-1],a[i-1]
    maxHeapify a,max
  end
end
def makeMaxHeap a
  ($h/2).downto(1) {|i| maxHeapify a,i}
end
a=[]
$h=0
min=0
begin
  command, $key = gets.split
  $key = $key.to_i
  case command
  when 'insert'
    a<<$key
    $h+=1
    makeMaxHeap a
  when 'extract'
    puts a[0]
    $h-=1
    a = a[1..-1]
    makeMaxHeap a
  end
end while command != 'end'