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 MAX 2000000
#define INF 100000000
int heap[MAX+1],H;

void maxHeapify(int i){
  int temp;
  int l,r,largest;
  l = 2*i;
  r = 2*i+1;

  if(l<=H && heap[l] > heap[i]) largest = l;
  else largest = i;
  if(r<=H && heap[r]>heap[largest]) largest = r;
  if(largest != i){
    temp = heap[i];
    heap[i] = heap[largest];
    heap[largest] = temp;
    maxHeapify(largest);
  } 
}

void increaseKey(int i,int key){
  int temp;
  
  heap[i] = key;
  while(i>1 && heap[i/2]<heap[i]){
    temp = heap[i];
    heap[i] = heap[i/2];
    heap[i/2] = temp;
    i /= 2;
  }
}


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

void extract(){
  printf("%d\n",heap[1]);
  heap[1] = heap[H--];
  maxHeapify(1);
}

int main(){
  int k;
  char s[10];

  while(1){
    scanf("%s",s);
    if(s[0]=='e' && s[1]=='n') break;
    if(s[0]=='i'){
      scanf("%d",&k);
      insert(k);
    }
    if(s[0]=='e') extract();
  }

  return 0;
}