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 C# (judge verdict: Time Limit Exceeded)

using System;

class Program{
    static int H=0;
    static void MaxHeapify(int[] A, int i){
        var l=i*2+1;
        var r=(i+1)*2;
        int largest;
        if(l<H && A[l]>A[i]){
            largest=l;
        } else{
            largest=i;
        }
        if(r<H && A[r]>A[largest]){
            largest=r;
        }
        if(largest!=i){
            var tmp=A[largest];
            A[largest]=A[i];
            A[i]=tmp;
            MaxHeapify(A, largest);
        }
    }

    static void BuildMaxHeap(int[] A){
        for(var i=(H-1)/2; i>=0; i--){
            MaxHeapify(A, i);
        }
    }

    static void Insert(int[] A, int k){
        A[H]=k;
        H++;
    }

    static int ExtractMax(int[] A){
        BuildMaxHeap(A);
        var result=A[0];
        A[0]=A[H-1];
        H--;
        BuildMaxHeap(A);
        return result;
    }

    public static void Main(){
        var S=new int[2*1000*1000];
        var sout=new System.Text.StringBuilder();
        while (true) {
            var s=Console.ReadLine().Split(' ');
            if (s[0][0]=='i') {
                Insert(S, int.Parse(s[1]));
            } else if (s[0][1]=='x') {
                sout.Append(ExtractMax(S)+"\n");
            } else {
                break;
            }
        }
        Console.Write(sout);
    }
}