CodeForces Round #521 (Div.3) E. Thematic Contests

http://codeforces.com/contest/1077/problem/E

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.

代码：

    #include <bits/stdc++.h>
    using namespace std;

    const int maxn = 2e5 + 10;
    const int N = 1e6 + 5;
    int n;
    int a[N];

    int main() {
        scanf("%d", &n);
        int cnt = 0;
        map<int, int> mp;
        for(int i = 1; i <= n; i ++) {
            int x;
            scanf("%d", &x);
            if(!mp[x]) {
                cnt ++;
                mp[x] = cnt;
            }
            a[mp[x]] ++;
        }
        sort(a + 1, a + 1 + cnt);
        int ans = 0;

        for(int i = 1; i <= n; i ++) {
            int st = 1;
            int m = 0;
            for(int k = i; k <= n; k *= 2) {
                int pos = lower_bound(a + st, a + 1 + cnt, k) - a;
                if(pos == cnt + 1) break;
                m += k;
                st = pos + 1;
            }
            ans = max(ans, m);
        }
        printf("%d\n", ans);
        return 0;
    }