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)

function f()
    n = parse(Int, chomp(readline()))
    a = map(x -> parse(Int, x), split(chomp(readline()), " "))

    if all(a .== a[1])
        print(a[1])
    else
        id = a % 2 .== 0
        if all(id .== false)
            print(findmax(a)[1])
        else
            gusu = a[id]
            min = findmin(gusu)[1]

            amari = gusu % min
            ret = 0
            while any(amari .!= 0)
                ret = findmax(amari)[1]
                amari = gusu % findmax(amari)[1]
            end
            print(ret)
        end
    end
end
f()