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)

import sys

def max_heapify(A, i):
  l = i * 2
  r = l + 1
  largest = i
  H = len(A) -1
  if l <= H and A[l] > A[i]:
      largest = l
  if r <= H and A[r] > A[largest]:
      largest = r
  if largest != i:
    A[i], A[largest] = A[largest], A[i]
    max_heapify(A, largest)

def build_max_heap(A):
    for i in range(len(A)-1 // 2, 0, -1):
        max_heapify(A, i)

#@profile
def extract(A):
    out = A[1]
    A[1] = A[-1]
    del A[-1]
    max_heapify(A, 1)
    return out

_input = sys.stdin.readlines()
A = [0]

#@profile
def main():
    out = []
    for l in _input:
        if l[0] == "e":
            if l[1] == "n":
                #end
                print(*out, sep = "\n")
                return
            else:
                build_max_heap(A)
                #print(A)
                out.append(extract(A))
        else:
            #insert k
            k = int(l.split()[1])
            A.append(k)
            #build_max_heap(A)
        #print(A)

if __name__ == "__main__":
    main()