Martial Arts Tournament

题意翻译

已有 $n$ 个人，每个人的权重为 $a_i$。 再让你加入 $k$ 个人，每个人也有各自的权重。对这 $n+k$ 个人分成三组，要求每组的人数都必须大于零且都是 $2$ 的非负次幂。 分组方法如下： 1. 选择两个数 $x,y$ 2. 将权重小于 $x$ 的人分为第一组；权重大于等于 $x$、小于 $y$ 的人分为第二组；权重大于等于 $y$ 的人分为第三组。 询问 $k$ 可能的最小值 翻译人： @[BFSDFS123](https://www.luogu.com.cn/user/358739)

题目描述

Monocarp is planning to host a martial arts tournament. There will be three divisions based on weight: lightweight, middleweight and heavyweight. The winner of each division will be determined by a single elimination system. In particular, that implies that the number of participants in each division should be a power of two. Additionally, each division should have a non-zero amount of participants. $ n $ participants have registered for the tournament so far, the $ i $ -th of them weighs $ a_i $ . To split participants into divisions, Monocarp is going to establish two integer weight boundaries $ x $ and $ y $ ( $ x < y $ ). All participants who weigh strictly less than $ x $ will be considered lightweight. All participants who weigh greater or equal to $ y $ will be considered heavyweight. The remaining participants will be considered middleweight. It's possible that the distribution doesn't make the number of participants in each division a power of two. It can also lead to empty divisions. To fix the issues, Monocarp can invite an arbitrary number of participants to each division. Note that Monocarp can't kick out any of the $ n $ participants who have already registered for the tournament. However, he wants to invite as little extra participants as possible. Help Monocarp to choose $ x $ and $ y $ in such a way that the total amount of extra participants required is as small as possible. Output that amount.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of testcases. The first line of each testcase contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of the registered participants. The second line of each testcase contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le n $ ) — the weights of the registered participants. The sum of $ n $ over all testcases doesn't exceed $ 2 \cdot 10^5 $ .

输出格式

For each testcase, print a single integer — the smallest number of extra participants Monocarp is required to invite after he chooses the weight boundaries $ x $ and $ y $ .

输入输出样例

输入样例 #1

4
4
3 1 2 1
1
1
6
2 2 2 1 1 1
8
6 3 6 3 6 3 6 6

输出样例 #1

0
2
3
2

说明

In the first testcase of the example, Monocarp can choose $ x=2 $ and $ y=3 $ . Lightweight, middleweight and heavyweight divisions will have $ 2 $ , $ 1 $ and $ 1 $ participants, respectively. They all are powers of two, so no extra participants are required. In the second testcase of the example, regardless of the choice of $ x $ and $ y $ , one division will have $ 1 $ participant, the rest will have $ 0 $ . Thus, Monocarp will have to invite $ 1 $ participant into both of the remaining divisions. In the third testcase of the example, Monocarp can choose $ x=1 $ and $ y=2 $ . Lightweight, middleweight and heavyweight divisions will have $ 0 $ , $ 3 $ and $ 3 $ participants, respectively. So an extra participant is needed in each division. In the fourth testcase of the example, Monocarp can choose $ x=8 $ and $ y=9 $ . Lightweight, middleweight and heavyweight divisions will have $ 8 $ , $ 0 $ and $ 0 $ participants, respectively. Middleweight and heavyweight division need an extra participant each.