Description

There are n children in Johnny Johnny' s family.

And number i child wants to have a_i units of sugar.

But their PaPa don't want them eat too much sugar. Therefore he will randomly choose some children and only give them the great common divisor of a_i. 

 

For example, if there're n=5 children and a_i = { 1, 4, 6, 7, 18 }.

Suppose PaPa choose the children numbered 2,3,5.

Then all children will only get  gcd(a₂, a₃, a₅) = gcd(4,6,18) = 2 unit of sugar.

 

Now Johnny wants to know what's the maximum amount of sugar they can get.(PaPa will at least choose two child) 

If you can help him, he will laugh at you for you don't have any sugar " Ha Ha Ha!!! "

 

To calculate great common divisor, you can use the method 輾轉相除法(https://zh.wikipedia.org/wiki/%E8%BC%BE%E8%BD%89%E7%9B%B8%E9%99%A4%E6%B3%95)

Input

input contains two lines.

First line only contains one integer n ( 2 <= n <=  1000)

Second line contain n integers a₁ ~ a_n ( 1<= a_i <= 1000 )

Output

output contains only one integer the maximum amount of sugar they can get.

remember to print \n at the end of output.

Sample Input  Download

Sample Output  Download

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