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 JAVA (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
//Wrong Answer
public class Main {
    private static int[] A = new int[2000001];
    private static int heapSize = 0;
    
    private static void maxHeapify(int k){
        int l = 2*k;
        int r = 2*k+1;
        int largest;
    
        if ((l <= (heapSize - 1)) && (A[l] > A[k])){
            largest = l;
        }else{
            largest = k;
        }
        if ((r <= (heapSize - 1)) && (A[r] > A[largest])){
            largest = r;
        }
        if (largest != k){
            swap(k, largest);
            maxHeapify(largest);
        }
    }
    
    private static void swap(int i, int j) {
        int tmp = A[i];
        A[i] = A[j];
        A[j] = tmp;
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        while (true){
            String[] line = br.readLine().split(" ");
            String order = line[0];
            if (order.equals("insert")){
                heapSize++;
                //A[heapSize] = Integer.MIN_VALUE;
                int num = Integer.parseInt(line[1]);
                A[heapSize] = num;
                int i = heapSize;
                while (i > 1 && A[i/2] < A[i]) {
                    swap(i, i/2);
                    i = i/2;
                }
                
            }else if (order.equals("extract")){
                int max = A[1];
                A[1] = A[heapSize];
                heapSize--;
                maxHeapify(1);
                System.out.println(max);

            }else{ // end
                break;
            }
        }
    }
}