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 gcd(a,b)
    if b == 0 then
        return a
    else
        return gcd(b, a % b)
    end
end

local function gcdmany(tbl)
    local ans = tbl[1]
    for i=2,#tbl do
        ans = gcd(ans, tbl[i])
    end
    return ans
end

----

local N = io.read("n")
local A = {} for i=1,N do A[i] = io.read("n") end

local L, R = {}, {}
L[1] = A[1]
for i=2, N do
    L[i] = gcd(L[i-1], A[i])
end
R[N] = A[N]
for i=N-1, 1,-1 do
    R[i] = gcd(R[i+1], A[i])
end

local maxval = 0
maxval = math.max(maxval, R[2])
for i=2, N-1 do
    local g = gcd(L[i-1], R[i+1])
    maxval = math.max(maxval, g)
end
maxval = math.max(maxval, L[N-1])

print(maxval)