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: Accepted)

using System;

class Program{
    static int H=0;

    static void Insert(int[] A, int k){
        H++;
        var i=H-1;
        while (i>0) {
            var p=(i-1)/2;
            if (A[p]>=k) {
                break;
            }
            A[i]=A[p];
            i=p;
        }
        A[i]=k;
    }

    static int ExtractMax(int[] A){
        var result=A[0];
        int k=A[H-1];
        H--;
        int i=0;
        while (i*2+1<H) {
            int l=i*2+1;
            int r=(i+1)*2;
            if (r<H && A[r]>A[l]) {
                l=r;
            }
            if (A[l]<=k) {
                break;
            }
            A[i]=A[l];
            i=l;
        }
        A[i]=k;
        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);
    }
}