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 extract(i)
  l = 2*i -1
  r = 2*i
  i -= 1

  if A[l] == nil
    return
  elsif A[r] == nil
    A[i], A[l] = A[l], A[i]
  elsif A[l] >= A[r] && A[l] > A[i]
    A[i], A[l] = A[l], A[i]
    extract(l+1)
  elsif A[l] < A[r] && A[r] > A[i]
    A[i], A[r] = A[r], A[i]
    extract(r+1)
  end
end

def insert(i)
  if i == 1
    return
  end

  parent = i/2 -1
  i -= 1

  if A[i] > A[parent]
    A[i], A[parent] = A[parent], A[i]
    insert(parent+1)
  end
end

A = Array.new

until (str=gets.chomp) == "end"
  if str == "extract"
    puts A.shift
    # A.shift
    A.unshift(A.pop)
    extract(1)
  else  # insert
    str = str.split(" ")
    A << str[1].to_i
    insert(A.length)
  end
  # p A
end