def delete_item(self, item: int) -> None:
        arr_len = len(self.arr)
        if arr_len == self.size:
            self.arr.append([item, self.key(item_value)])
        else:
            self.arr[self.size] = [item, self.key(item_value)]
        self.pos_map[item] = self.size
        self.size += 1
        self._heapify_up(self.size - 1)