Thematic Contests

题意翻译

###### 题目描述 `Polycarp`有$n$个问题，问题的主题分别是$a_1,a_2,\cdots,a_n$，`Polycarp`需要组织一些专题比赛，同时要满足以下条件： - 一场专题比赛中的所有题目的主题相同 - 组织的所有专题比赛中主题互异 - 从第二场比赛开始，比赛中的题目数必须是前一场比赛题目数量的$2$倍，第一场比赛的题目数量可以是任意的 - 所有比赛使用的题目数量之和最大 求所有比赛使用的题目数量之和的最大值 注意：不需要使比赛的数量最大，不一定需要使用所有的题目，不一定需要使用所有的主题 ###### 输入格式 第一行一个整数$n(1\leq n\leq2\cdot10^5)$表示题目数量 第二行$n$个整数$a_1,a_2,\cdots,a_n(1\leq a_i\leq10^9)$表示问题的主题 ###### 输出格式 输出一个整数，表示所有比赛使用的题目数量之和的最大值

题目描述

Polycarp has prepared $ n $ competitive programming problems. The topic of the $ i $ -th problem is $ a_i $ , and some problems' topics may coincide. Polycarp has to host several thematic contests. All problems in each contest should have the same topic, and all contests should have pairwise distinct topics. He may not use all the problems. It is possible that there are no contests for some topics. Polycarp wants to host competitions on consecutive days, one contest per day. Polycarp wants to host a set of contests in such a way that: - number of problems in each contest is exactly twice as much as in the previous contest (one day ago), the first contest can contain arbitrary number of problems; - the total number of problems in all the contests should be maximized. Your task is to calculate the maximum number of problems in the set of thematic contests. Note, that you should not maximize the number of contests.

输入输出格式

输入格式

The first line of the input contains one integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of problems Polycarp has prepared. The second line of the input contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) where $ a_i $ is the topic of the $ i $ -th problem.

输出格式

Print one integer — the maximum number of problems in the set of thematic contests.

输入输出样例

输入样例 #1

18
2 1 2 10 2 10 10 2 2 1 10 10 10 10 1 1 10 10

输出样例 #1

14

输入样例 #2

10
6 6 6 3 6 1000000000 3 3 6 6

输出样例 #2

9

输入样例 #3

3
1337 1337 1337

输出样例 #3

3

说明

In the first example the optimal sequence of contests is: $ 2 $ problems of the topic $ 1 $ , $ 4 $ problems of the topic $ 2 $ , $ 8 $ problems of the topic $ 10 $ . In the second example the optimal sequence of contests is: $ 3 $ problems of the topic $ 3 $ , $ 6 $ problems of the topic $ 6 $ . In the third example you can take all the problems with the topic $ 1337 $ (the number of such problems is $ 3 $ so the answer is $ 3 $ ) and host a single contest.