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 JavaScript (judge verdict: Time Limit Exceeded)

const line = require('fs').readFileSync('/dev/stdin', 'utf-8').split('\n');

const maxHeapify = (arr, i) => {
    const l = i * 2;
    const r = l + 1;
    let max;

    if (l <= arr.length && arr[l-1] > arr[i-1]) {
        max = l;
    } else {
        max = i;
    }
    if (r <= arr.length && arr[r-1] > arr[max-1]) {
        max = r;
    }

    if (max !== i) {
        const tmp = arr[i-1];
        arr[i-1] = arr[max-1];
        arr[max-1] = tmp;
        maxHeapify(arr, max);
    }

};

const insert = (arr, n) => {
    arr.push(n);
    const helper = (i) => {
        if (i <= 1) return;
        const parentIndex = Math.floor(i/2);
        if (arr[i-1] > arr[parentIndex-1]) {
            const tmp = arr[i-1];
            arr[i-1] = arr[parentIndex-1];
            arr[parentIndex-1] = tmp;
            helper(parentIndex);
        }
    };
    helper(arr.length);
};

const extract = arr => {
    const n = arr.shift();
    arr.unshift(arr.pop());
    maxHeapify(arr, 1);
    return n;
};

const data = line.reduce((acc, x) => {
    const cmd = x.split(' ');
    switch(cmd[0]) {
        case 'insert':
            insert(acc, Number(cmd[1]));
            break;
        case 'extract':
            console.log(extract(acc));
            break;
    }
    return acc;
}, []);