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)

-- SegTree
-- Ref: http://tsutaj.hatenablog.com/entry/2017/03/29/204841
local function SegTree(func, ident, vec)
    -- func: binary function
    -- ident: identity element
    -- vec: table

    -- private variables
    -- func, ident are also private variables
    local a = {}
    -- n is smallest power of 2 that is greater than or equal to #vec
    local n = 1
    -- end of private variables
    -- constructor
    do -- just make a scope
        while n < #vec do
            n = n << 1
        end
        local size = 2*n - 1
        for i=1, size do
            a[i] = ident
        end
        for i=1, #vec do
            a[i+n-1] = vec[i]
        end
        for i=n-1,1,-1 do
            a[i] = func(a[2*i], a[2*i+1])
        end
    end
    vec = nil
    -- public member functions
    local self = {}
    self.update = function(idx, val)
        idx = idx + n - 1
        a[idx] = val
        while true do
            idx = idx // 2
            a[idx] = func(a[idx*2], a[idx*2 + 1])
            if idx == 1 then
                break
            end
        end
    end
    self.query = function(left, right)
        -- query to [left, right)
        -- **be careful about right half open interval**
        local function q(k, l, r)
            if r <= left or l >= right then
                return ident
            end
            if l >= left and r <= right then
                return a[k]
            end
            local vl = q(2*k  , l, (l+r)//2)
            local vr = q(2*k+1, (l+r)//2, r)
            return func(vl, vr)
        end
        return q(1, 1, n + 1)
    end
    return self
end

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

local N = io.read("n")
local A = {}
for i=1,N do
    A[i] = io.read("n")
end
local st = SegTree(gcd, 0, A)
local maxval = 0
local mathmax = math.max
local query = st.query
for i=1, N do
    local left = query(1, i)
    local right = query(i+1, N+1)
    local g = gcd(left, right)
    maxval = mathmax(maxval, g)
end
print(maxval)