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 Python3 (judge verdict: Time Limit Exceeded)

def insert(k):
    a.append(-1)
    heap_increasekey(a, len(a) - 1, k)
def heap_increasekey(a, i, k):
    a[i] = k
    while i > 1 and a[int(i / 2)] < a[i]:
        a[i], a[int(i / 2)] = a[int(i / 2)], a[i]
        i = int(i / 2)
def heap_extractmax(a):
    m = a[1]
    a[1] = a[-1]
    a.pop()
    max_heapify(a, 1)
    return m

def max_heapify(a, i):
    l = 2 * i
    r = 2 * i + 1
    largest = l if l < len(a) and a[l] > a[i] else i
    if r < len(a) and a[r] > a[largest]:
        largest = r
    if largest != i:
        a[largest], a[i] = a[i], a[largest]
        max_heapify(a, largest)
        
a = [0]
while True:
    s = input()
    if s[2] == "d":
        break
    elif s[0] == "i":
        insert(int(s[7:]))
    else:
        print(heap_extractmax(a))