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: Accepted)

function main()
  n = parse(Int, readline())
  a = map(x -> parse(Int, x), split(readline(), " "))
  
  lgcd = zeros(Int, n)
  rgcd = zeros(Int, n)

  for i in 1:n
    if i == 1
      lgcd[i] = a[i]
    else
      lgcd[i] = gcd(a[i], lgcd[i-1])
    end
  end

  for i in 1:n
    if i == 1
      rgcd[end-i+1] = a[end]
    else
      rgcd[end-i+1] = gcd(a[end-i+1], rgcd[end-i+2])
    end
  end

  ans = 0
  for i in 1:n
    if i == 1
      temp = rgcd[i+1]
    elseif i == n
      temp = lgcd[i-1]
    else
      temp = gcd(lgcd[i-1], rgcd[i+1])
    end
    ans = temp > ans ? temp : ans
  end
  println(ans)
end

main()