Unexpected problems with law enforcement have convinced Mirko to take up a less lucrative but less morally ambiguous career: he has become the chief organizer of a team computer science contest.
There are CS clubs that wish to participate in the contest. The presidents of the clubs are quite stubborn and will participate in the contest only if the contest team size makes it possible for all club members to participate.
The contest consists of two rounds: qualifications and finals. All teams that are competing must have an equal number of members and all members of one team must belong to the same club. Any number of teams from each club can participate in the qualification round, and the best team from each club earns a spot in the finals.
Mirko is aware that, with a new and unproven contest, he needs publicity. For that reason, he wants to set the team size such that the number of individual participants in the finals is as large as possible. Remember, each club that participates has a right to one team in the finals. Furthermore, at least two clubs must participate in the contest, otherwise the contest would be too boring to attract sponsors.
Determine the maximum possible number of participants in the finals so that Mirko can double check his team size choice.
Input
The first line of input contains the positive integer
, the number of clubs.
The second line of input contains space-separated integers from the interval
, the number of members of each club.
Output
The first and only line of output must contain the maximum possible number of finalists.
Scoring
In test data worth at least of total points,
will be less than
.
Sample Input 1
3
1 2 4
Sample Output 1
4
Explanation
Mirko decides on members per team, so clubs
and
participate.
Sample Input 2
2
1 5
Sample Output 2
2
Sample Input 3
5
4 6 3 8 9
Sample Output 3
9
Comments
Problem type
The problem type should be math instead of dynamic programming in my opinion.🤔
This comment is hidden due to too much negative feedback. Show it anyway.
Making a frequency array and naming it "dp" does not constitute a dp solution. This problem should be tagged as intermediate math.
An issue in the official test data was discovered by jeffreyxiao, and has been fixed. All submissions have been rejudged.
Congratulations to those who now have AC!