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)

#include <stdio.h>
#include <string.h>
#define INF 100000000
#define N 2000001

int h,A[N];

void exchange(int i,int j)
{
  int temp;
  temp=A[i];
  A[i]=A[j];
  A[j]=temp;
}

int left(int i){return 2*i;}
int right(int i){return 2*i+1;}

void maxHeapify(int i){
  int l,r,largest;
  l=left(i);
  r=right(i);
  if(l<=h&&A[l]>A[i])
    largest=l;
  else
    largest=i;
  if(r<=h&&A[r]>A[largest])
    largest=r;

  if(largest!=i){
    exchange(i,largest);
    maxHeapify(largest);
  }
  
}


int extract(){
  int max;
  if(h<1)return -INF;
  max=A[1];
  A[1]=A[h--];
  maxHeapify(1);
  return max;
}

void increaseKey(int i,int key){
  if(key<A[i])return;
  A[i]=key;
  while(i>1&&A[i/2]<A[i]){
    exchange(i,i/2);
    i/=2;
  }
}

void insert(int key){
  h++;
  A[h]=-INF;
  increaseKey(h,key);
}

int main(){
  int key;
  char c[10];

  while(1){

    scanf("%s",c);
    if(c[0]=='e'&&c[1]=='n')break;
    if(c[0]=='i'){
      scanf("%d",&key);
      insert(key);
    }else{
      printf("%d\n",extract());

    }

  }


  return 0;
}