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
INFTY = 1<<30
a = [None] * 2000001
h = 0
ret = [] 

def maxHeapify(i):
    global a, h
    l = 2 * i
    r = 2 * i + 1
    if l <= h and a[l] > a[i]:
        largest = l
    else:
        largest = i
    if r <= h and a[r] > a[largest]:
        largest = r
    if largest != i:
        a[i], a[largest] = a[largest], a[i]
        maxHeapify(largest)

def extract():
    global a, h
    if h < 1:
        return -INFTY
    maxv = a[1]
    a[1] = a[h]
    h -= 1
    maxHeapify(1)
    return maxv
    
def increaseKey(i, k):
    global a
    if k < a[i]:
        return
    a[i] = k
    while i > 1 and a[i//2] < a[i]:
        a[i], a[i//2] = a[i//2], a[i]
        i = i // 2

def insert(k):
    global a, h
    h += 1
    a[h] = -INFTY
    increaseKey(h, k)

for com in sys.stdin.readlines():
    if com[0] == "i":
        insert(int(com[7:]))
    elif com[1] == "x":
        ret.append(extract()) 
    else:
        print(*ret, sep="\n")