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)

#!/usr/bin/ruby
def heappush(heap, item)
	heap.push(item)
	_siftdown(heap, 0, heap.size-1)
end

def heappop(heap)
	lastelt = heap.pop
	if !heap.empty?
		returnitem = heap[0]
		heap[0] = lastelt
		_siftup(heap, 0)
	else
		returnitem = lastelt
	end
	returnitem
end

def heappushpop(heap, item)
	if !heap.empty? && (heap[0]<=>item)<0
		item, heap[0] = heap[0], item
		_siftup(heap, 0)
	end
	item
end

def heapify(x)
	n = x.size
	(n/2-1).downto(0){|i|_siftup(x, i)}
end

def _siftdown(heap, startpos, pos)
	newitem = heap[pos]
	while pos > startpos
		parentpos = (pos - 1) >> 1
		parent = heap[parentpos]
		if (newitem<=>parent)<0
			heap[pos] = parent
			pos = parentpos
		else
			break
		end
	end
	heap[pos] = newitem
end

def _siftup(heap, pos)
	endpos = heap.size
	startpos = pos
	newitem = heap[pos]
	childpos = 2*pos + 1
	while childpos < endpos
		rightpos = childpos + 1
		if rightpos < endpos && (heap[childpos]<=>heap[rightpos])>=0
			childpos = rightpos
		end
		heap[pos] = heap[childpos]
		pos = childpos
		childpos = 2*pos + 1
	end
	heap[pos] = newitem
	_siftdown(heap, startpos, pos)
end

### main ###
q=[]
loop{
	a=gets.split
	break if a[0]=='end'
	if a[0]=='insert'
		heappush(q,a[1].to_i)
	else
		p heappop(q)
	end
}