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;
using System.Collections.Generic;
using System.Text;
					
public class Program
{
	public static void Main()
	{
		List<int> S = new List<int>();
		string order;
		StringBuilder sb = new StringBuilder();
		
		order = Console.ReadLine();
		
		while(order != "end") {
			switch(order[0]) {
				case 'e':
					int[] s = S.ToArray();
					
					BuildMaxHeap(s);
					sb.AppendLine(s[0].ToString());
					
					S.Remove(s[0]);
					break;
				case 'i':
					S.Add( int.Parse(order.Split(" ".ToCharArray())[1]) );
					break;
			}
			
			order = Console.ReadLine();
		}
		
		Console.Write(sb);
	}
	
	public static string ConvertString(int[] heap, int i)
	{
		string result = "node " + (i + 1) ;
		
		result += ": key = " + heap[i];
		
		if(i > 0) {
			result += ", parent key = " + heap[(i-1)/2];
		}
		
		if( 2*i+1 < heap.Length) {
			result += ", left key = " + heap[2*i+1];
		}
		
		if( 2 * (i+1) < heap.Length) {
			result += ", right key = " + heap[2*i + 2];
		}
		
		return result + ", ";
	}
	
	public static void BuildMaxHeap(int[] A)
	{
		for(int i = A.Length / 2; i >= 0; i--){
			MaxHeapify(A, i);
		}
	}
	
	public static void MaxHeapify(int[] A, int i)
	{
		int l = Left(A, i);
		int r = Right(A, i);
		int largest = i;
		
		//l,r,i?£???????????£???§???????\???§?£???????????£???¶?£????
		if(l >= 0) {
			if(A[l] > A[largest]) largest = l;	
		}
		if(r >= 0) {
			if(A[r] > A[largest]) largest = r;
		}
		
		if(i != largest) {
			Swap(A, i, largest);
			MaxHeapify(A, largest);
		}
	}
	
	public static int Left(int[] A, int i)
	{	
		return ( (2*i + 1) < A.Length )? (2*i + 1) : -1;
	}
	
	public static int Right(int[] A, int i)
	{	
		return ( 2 * (i+1) < A.Length )? (2*i + 2) : -1;
	}
	
	public static void Swap(int[] A, int i, int j)
	{
		int tmp = A[i];
		A[i] = A[j];
		A[j] = tmp;
	}
}