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)

def pq()
  q = []
  a = []
  loop{
    a = gets.split(' ')
    if a[0] == 'insert'
      n = a[1].to_i
      q.push(n)
      i = q.length-1
      until i == 0
        if q[i] > q[i/2]
          r = q[i]
          q[i] = q[i/2]
          q[i/2] = r
          i = i/2
        else
          break
        end
      end
    elsif a[0] == 'extract'
      n = q.shift
      puts n
    elsif a[0] == 'end'
      break
    end
  }
end

pq()