Problem:
Score : 300 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
function main()
    n=parseInt(readline())
    a=parseMap(split(readline()))
    l=[a[1] for i in 1:n]
    r=[a[n] for i in 1:n]
    for i in 2:n
        l[i]=gcd(l[i-1],a[i])
        r[i]=gcd(r[i-1],a[n-i+1])
    end
    ans=1
    for i in 1:n
        if i==1
            ans=max(ans,r[n-1])
        elseif i==n
            ans=max(ans,l[n-1])
        else
            ans=max(ans,gcd(r[i-1],l[i-1]))
        end
    end
    println(ans)
end
main()