Follow the Trace!

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Time limit1sMemory limit512 MB

Summary

Given n integers, build a nonempty square matrix using each value at most as many times as it appears, and maximize the diagonal sum.

Level: Easy3 of 10
Topics: Greedy, Sorting, Math, Array
Solved: No attempts yet

Problem

The trace of a square matrix $B_{ij}$ is the sum of the elements $B_{ii}$ on the main diagonal.

You are given a sequence of integers $a_i$ . You must place the numbers of the sequence into a non-empty square matrix $B_{ij}$ so that its trace is as large as possible. If a number $x$ occurs exactly $k$ times in the sequence $a_i$ , then it must occur at most $k$ times in the matrix $B_{ij}$ .

Input

The first line contains a single integer $n$ , the length of the sequence $a_i$ ( $1 \le n \le 10^5$ ).

The next $n$ lines each contain a single integer; the $i$ -th of them contains $a_i$ , the $i$ -th element of the sequence $a$ ( $-10^9 \le a_i \le 10^9$ ).

Output

Print a single integer: the largest possible value of the trace of the matrix $B$ .

Examples1

Example 1
Input
```
6
31
10
2021
-11
0
0
```
Expected output
```
2052
```