Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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)

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