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: Runtime Error)

import java.util.*;

class Main {
    int heap[];
    int pos;
    int size;

    public Main() {
        this.heap = new int[100];
        this.size = 100;
        this.pos = 0;
    }

    void heapify(int i) {
        int leftchild = (2*i) + 1;
        int rightchild = (2*i) + 2;
        int parent = i;

        if (leftchild < this.pos && heap[parent] < heap[leftchild]) {
            parent = leftchild;
        }
        if (rightchild < this.pos && heap[parent] < heap[rightchild]) {
            parent = rightchild;
        }
        if(parent != i) {
            int temp = heap[i];
            heap[i] = heap[parent];
            heap[parent] = temp;
            heapify(parent);
        }

    }

    void insert(int value) {
        this.heap[pos] = value;
        boolean isHeap = false;
        int i = pos;
        while(i > 0 && !isHeap) {
            int j = (i-1)/2;
            if (heap[i] > heap[j]) {
                int temp = heap[i];
                heap[i] = heap[j];
                heap[j] = temp;
            } else {
                isHeap = true;
            }
            i = j;
        }
        pos++;
    }

    int remove() {
        if (pos > 0) {
            int removed = heap[0];
            heap[0] = heap[pos-1];
            heapify(0);
            pos--;
            return removed;
        }
        return 0;
    }


        public static void main(String[] args) {
            Scanner in = new Scanner(System.in);

            Main heap = new Main();

            String operation = in.next();

            while (!operation.equals("end")) {
                if (operation.charAt(0) == 'i') {
                    int number = in.nextInt();
                    heap.insert(number);
                } else {
                    int removed = heap.remove();
                    System.out.println(removed);
                }
                operation = in.next();
            }
        }
}