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, 88problems 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.

題意：有n個問題，每個問題都屬於某個話題，現在要舉行一系列比賽，每個比賽只能用同種類的問題而且問題數是前一場比賽的2倍（第一場比賽問題數可以任意），要你安排比賽使比賽總問題數最大

#include <bits/stdc++.h>
using namespace std;
#define ll long long
//#define mp make_pair
#define CL(a, b) memset(a, b, sizeof(a))
#define debug(x) cout<<"debug"<<x<<"\n"
//#define sc scanf
//#define pr printf

const int N = 1e6 + 7;
const int M = 1e9 + 7;

int a[N], b[N], c[N], d[N];

map<int, int> mp;




int main() {
	
	int n;
	scanf ("%d", &n);
	int cnt = 0, x;
	for(int i = 1; i <= n; ++i) {
		scanf ("%d", &x);
		if (!mp[x]) {
			mp[x] = ++cnt;
		}
		++a[mp[x]]; //x這個話題的問題數加一 
	}
	//for (int i = 1; i <= cnt; ++i) printf("%d ", a[i]);
	//puts("");
	sort(a+1, a+cnt+1); 
	//for (int i = 1; i <= cnt; ++i) printf("%d ", a[i]);
	//puts("");
	int ans = 0;
	
	for(int j = 1; j <= n; ++j) { //j為列舉第一次contest可能的問題數 
								//j的最大值為當每個問題的topic一樣的時候，取n 
		int m = 0;
		// 暴力做法
		/*for (int i = 1, k = j; i <= cnt; ++i) { 
			if (a[i] >= k) {
				m += k;
				k *= 2;
			}
		}*/ 
		// 二分加速 
		int la = 1; 
		for (int k = j; k <= n; k *= 2) {  //k為每次contest的問題數 
			int pos = lower_bound(a+la, a+cnt+1, k) - a;
			if (pos == cnt+1) break; //如果沒有比k大的話題相同的問題就break 
			m += k;                 //否則繼續舉行比賽 
			la = pos + 1;
		}
		
		
		ans = max(ans, m); //更新答案 
		
		
	}
	
	
	printf ("%d\n", ans);
	
	return 0;
}