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# Ghd

4000ms 262144K

## Description:

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.

## Input:

The first line contains an integer n (1 ≤ n ≤ 106) showing how many numbers are in set a. The second line contains space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1012). Please note, that given set can contain equal numbers.

Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the %I64d specifier.

## Output:

Print a single integer g — the Ghd of set a.

## Sample Input:

66 2 3 4 5 6

## Sample Output:

3

## Sample Input:

55 5 6 10 15

## Sample Output:

5

Info

Provider CodeForces

Code CF364D

Tags

brute forcemathprobabilities

Submitted 107

Passed 30

AC Rate 28.04%

Date 03/03/2019 21:48:41

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