template <class Item>
void fixDown (Item *pq, int k, int N) {
  int j; 

  while (2 * k <= N) {

    j = 2 * k;

    if (j < N) {
      if (pq[j] < pq[j+1]) { j = j+1; }
    }
    
    if (pq[k] < pq[j]) {
      exch (pq[k], pq[j]);
      k = j;
    } else {
      break;
    }

  }

  return;
}