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;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static int H;

        static void Main(string[] args)
        {
            StringBuilder sb = new StringBuilder();
            List<int> A = new List<int>();
            A.Add(-1);
            
            while (true)
            {
                string[] input = Console.ReadLine().Split(' ');

                if (input[0] == "end") break;

                if (input[0][0] == 'i')
                {
                    Insert(A, int.Parse(input[1]));
                }
                else
                {
                    sb.AppendLine(Extract(A).ToString());
                }
            }
            Console.Write(sb);
        }

        static int Extract(List<int> A)
        {
            int ret;

            if (H < 1) return int.MinValue;

            ret = A[1];
            A[1] = A[H];
            A.RemoveAt(H);
            H--;

            MaxHeapify(A, 1);

            return ret;
        }

        static void Insert(List<int> A,int key)
        {
            H++;
            A.Add(int.MinValue);

            IncreaseKey(A, H, key);
        }

        static void IncreaseKey(List<int> A, int i, int key)
        {
            if (key < A[i]) return;
            A[i] = key;

            while (i > 1 && A[i / 2] < A[i])
            {
                int temp = A[i];
                A[i] = A[i / 2];
                A[i / 2] = temp;

                i /= 2;
            }
        }

        static void MaxHeapify(List<int> A, int i)
        {
            int l = i * 2;
            int r = i * 2 + 1;

            int largest = (l <= H && A[l] > A[i]) ? l : i;

            if (r <= H && A[r] > A[largest]) largest = r;

            if (largest != i)
            {
                int temp = A[i];
                A[i] = A[largest];
                A[largest] = temp;

                MaxHeapify(A, largest);
            }
        }
    }
}