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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
  implicit none
  integer N
  integer(8) A(10**5), koyakusu_TOP, dai, sho, koyakusu, yakurow(10**5), yakurank(2)
  integer i, j, t
  
  read(*, *) N
  read(*, *) (A(i), i = 1,N)
  
  !yakurow = 10**9
  koyakusu_TOP = 10**9
  do i = 1,N
    koyakusu_TOP = 10**9
    do j = 1,N
      !do j = i+1,N
      
        dai = max(A(i),A(j))
        sho = min(A(i),A(j))
        koyakusu = yaku(dai,sho)
        if (koyakusu < koyakusu_TOP) then
          koyakusu_TOP = koyakusu
        end if
      !end do
    end do
    yakurow(i) = koyakusu_TOP
  end do
  if (N == 2) then
    write(* ,'(i0)') max(A(1),A(2))
  else
    yakurank = 10**9
    do i = 1,N
      if (yakurank(1) < yakurow(i)) then
        yakurank(2) = yakurank(1)
        yakurank(1) = yakurow(i)
      else if (yakurank(2) < yakurow(i)) then
        yakurank(2) = yakurow(i)
      end if
    end do
    write(* ,'(i0)') yakurank(2)
  end if


  
  stop
contains

  
  integer(8) function yaku(dai, sho)
    implicit none
    integer(8) dai, sho, ans, dai2
    do while (mod(dai,sho) /= 0)
      dai2 = mod(dai, sho)
      dai = sho
      sho = dai2
    end do
    yaku = sho
    return
  end function yaku
      
      
end program main