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: Time Limit Exceeded)

function gcd(a :: Vector)
    sorted = sort(a)
    println(STDERR, "gcd: sorted: $(sorted)")
    a_diff = map(1:length(sorted)) do i
        i == 1 ? sorted[i] : sorted[i] - sorted[i-1]
    end
    println(STDERR, "gcd: a_diff: $(a_diff)")
    if any(a_diff .== 1)
        println(STDERR, "gcd: return 1")
        return 1
    end
    a_nonzero = a_diff[a_diff .!= 0]
    println(STDERR, "gcd: a_nonzero: $(a_nonzero)")
    if length(a_nonzero) == 1
        println(STDERR, "gcd: return $(a_nonzero[1])")
        return a_nonzero[1]
    else
        println(STDERR, "gcd: next gcd")
        return gcd(a_nonzero)
    end
end

function main()
    readline() # skip
    A = readdlm(STDIN, Int)
    
    result = maximum(map(1:length(A)) do i
        gcd(vcat(A[1:i-1], A[i+1:end]))
    end)
    println(result)
end

main()