Codeforces Thematic Contests DP

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本文介绍了一个算法问题，目标是通过合理的比赛安排最大化使用的问题数量。文章详细解释了问题背景，输入输出格式，并提供了代码实现，利用动态规划解决该问题。

E. Thematic Contests

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Polycarp has prepared nn competitive programming problems. The topic of the ii-th problem is aiai, 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.

Input

The first line of the input contains one integer nn (1≤n≤2⋅1051≤n≤2⋅105) — the number of problems Polycarp has prepared.

The second line of the input contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤ai≤109) where aiai is the topic of the ii-th problem.

Output

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

Examples

input

Copy
18
2 1 2 10 2 10 10 2 2 1 10 10 10 10 1 1 10 10
output

Copy
14
input

Copy
10
6 6 6 3 6 1000000000 3 3 6 6
output

Copy
9
input

Copy
3
1337 1337 1337
output

Copy
3
Note

In the first example the optimal sequence of contests is: 22 problems of the topic 11, 44 problems of the topic 22, 88 problems of the topic 1010.

In the second example the optimal sequence of contests is: 33 problems of the topic 33, 66 problems of the topic 66.

In the third example you can take all the problems with the topic 13371337 (the number of such problems is 33 so the answer is 33) and host a single contest.

题目链接：http://codeforces.com/problemset/problem/1077/E

题目的意思非常好理解，所以在这里就不多说了，就是最大的问题的数量

又是强大的DP！

#include <bits/stdc++.h>
using namespace std ;
const int Maxn = 2e5 + 10 ;

int dp[Maxn << 1] ;
vector < int > ve ;
map < int, int> ma ;
int n ;

int main (){
    int n ;
    int x ;
    cin >> n ;
    for (int i = 0; i < n; i++){
        cin >> x ;
        ma[x]++ ;
    }
    for (auto i : ma) ve.push_back(i.second) ;
//    sort(ve.begin(), ve.end(), [] (int a, int b) {return a < b ;}) ;
    sort(ve.begin(), ve.end()) ;
    int ve_size = ve.size() ;
    int ans = 0;
    for (int i = ve_size - 1; i >= 0; i--){
        for (int j = 1; j <= ve[i]; j++){
            dp[j] = max(dp[j], j + dp[j << 1]) ;
            ans = max(ans, dp[j]) ;
        }
    }
    cout << ans << endl ;
    return 0 ;
}