\(1^{st}\) round, September \(28^{th}\), 2013

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 N 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.

In test data worth at least 30% of total points, N will be less than 1000.

The first line of input contains the positive integer N (\(2 \le N \le 200\,000\)), the number of clubs.
The second line of input contains N spa\(ce-se\)parated integers from the interval [1, 2 000 000], the
number of members of each club.

The first and only line of output must contain the maximum possible number of finalists.

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출처 COCI 2013/2014 Contest 1