CF364D Ghd

John Doe offered his sister Jane Doe find the gcd of some set of numbers $ a $ . Gcd is a positive integer $ g $ , such that all number from the set are evenly divisible by $ g $ and there isn't such $ g' $ $ (g'>g) $ , that all numbers of the set are evenly divisible by $ g' $ . Unfortunately Jane couldn't cope with the task and John offered her to find the ghd of the same subset of numbers. Ghd is a positive integer $ g $ , such that at least half of numbers from the set are evenly divisible by $ g $ and there isn't such $ g' $ $ (g'>g) $ that at least half of the numbers from the set are evenly divisible by $ g' $ . Jane coped with the task for two hours. Please try it, too.

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