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

A = [0]*2000000
H = 0

def maxHeapify(i):
    global H, A
    l = (i+1)*2-1
    r = (i+1)*2
    # 左の子、自分、右の子で値が最大のノードを選ぶ
    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:  # i の子の方が値が大きい場合
        A[i], A[largest] = A[largest], A[i]
        maxHeapify(largest) #  再帰的に呼び出し


while True:
    com = sys.stdin.readline()
    if com[2] == 'd':   break
    if com[0] == 'i':
        _, arg = com.strip().split()
        A[H] = int(arg)
        H+=1
        i=H-1
        parent = (i-1)//2
        if parent<0: continue
        while A[parent]<A[i]:
            A[parent], A[i] = A[i], A[parent]
            if parent<=0: break
            i, parent = parent, (parent-1)//2
        
    else: # extract
        print(A[0])
        A[0] = A[H-1]
        maxHeapify(0)
        H-=1