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)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

struct node {
  struct node *next;
  int val;
};

typedef struct node *Node;

Node head;

void insert(int num) {
  if (head->val == -1) {
    head->val = num;
    return;
  }

  Node temp;
  Node new = malloc(sizeof(struct node));
  new->val = num;
  new->next = NULL;

  if (num >= head->val) {
    temp = head;
    head = new;
    new->next = temp;
  }

  Node cur = head;

  while (1) {
    if (cur->next == NULL) {
      cur->next = new;
      break;
    } else if (num >= cur->next->val) {
      temp = cur->next;
      cur->next = new;
      new->next = temp;
      break;
    }

    cur = cur->next;
  }
}

void extract() {
  printf("%d\n", head->val);

  if (head->next != NULL) {
    Node temp = head->next;
    free(head);
    head = temp;
  }
}

int main() {
  head = malloc(sizeof(struct node));
  head->next = NULL;
  head->val = -1;

  char command[20];
  scanf("%s", command);

  while (strcmp(command, "end")) {
    if (!strcmp(command, "insert")) {
        int val;
        scanf("%d", &val);
        insert(val);
    } else {
      extract();
    }

    scanf("%s", command);
  }
}