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 Lua (5.3.2) (judge verdict: Accepted)

local function getgcd(x, y)
  while 0 < x do
    x, y = y % x, x
  end
  return y
end
local n = io.read("*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
end
local left = {a[1]}
for i = 2, n - 1 do
  left[i] = getgcd(left[i - 1], a[i])
end
local right = {a[n]}
for i = n - 1, 2, -1 do
  right[n - i + 1] = getgcd(right[n - i], a[i])
end
local mmi, mma = math.min, math.max
local ret = mma(left[n - 1], right[n - 1])
for i = 1, n - 2 do
  local cand = getgcd(left[i], right[n - 1 - i])
  ret = mma(ret, cand)
end
print(ret)