Algorithms and Data Structures

Deleting numbers

Given n numbers , you earn points by deleting numbers from the array. When deleting a number , you earn points. Yet, you must delete all the numbers equal to and from the array (those do not earn you points).
What would be the maximum possible points you can get?

Input

The input contains a single integer n (1 ≤ n ≤ ).
The next line contains n space-separated integers (1 ≤ ≤ ).

Output

The program should print the maximum possible points you can get.

Examples

Input
Output
3 2 4 3
6
6 3 2 3 2 3 4
9

Explanation

  1. Example 1:
    1. Delete 2 ⇒ earn 2 ⇒ also delete 3
    2. Delete 4 and earn 4
    3. In total, the score would be 6
  1. Example 2:
    1. Delete 3 ⇒ earn 3 ⇒ also delete all 2s and all 4s
    2. Delete 3 ⇒ earn 3 ⇒ nothing to delete
    3. Delete 3 ⇒ earn 3 ⇒ nothing to delete
    4. In total, the score would be 9
 

Constraints

Time limit: 3.5 seconds

Memory limit: 512 MB

Output limit: 1 MB

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