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 execute_order(orders)
  output = []
  length = orders.length
  for i in 0..(length-1)
    if orders[i][0] == "insert"
      output.push(orders[i][1].to_i)
    elsif orders[i][0] == "extract"
      max = output.max
      count = output.count(max)
      output.delete(max)
      if count != 1
        (count-1).times do
          output.push(max)
        end
      end
      puts max
    else
      puts "error!"
    end
  end
end

input_orders = []
while true
  input_order = gets.chomp.split
  if input_order == ["end"]
    break
  else
    input_orders.push(input_order)
  end
end

execute_order(input_orders)