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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mfl, mce, mmi = math.floor, math.ceil, math.min
local SegTree = {}
SegTree.updateAll = function(self)
  for i = self.stagenum - 1, 1, -1 do
    for j = 1, self.cnt[i] do
      self.stage[i][j] = self.func(self.stage[i + 1][j * 2 - 1], self.stage[i + 1][j * 2])
    end
  end
end
SegTree.create = function(self, ary, func, emptyvalue)
  self.func, self.emptyvalue = func, emptyvalue
  local stagenum, mul = 1, 1
  self.cnt, self.stage, self.size = {1}, {{}}, {}
  while mul < #ary do
    mul, stagenum = mul * 2, stagenum + 1
    self.cnt[stagenum], self.stage[stagenum] = mul, {}
  end
  for i = 1, stagenum do self.size[i] = self.cnt[stagenum + 1 - i] end
  self.stagenum = stagenum
  for i = 1, #ary do self.stage[stagenum][i] = ary[i] end
  for i = #ary + 1, mul do self.stage[stagenum][i] = emptyvalue end
  self:updateAll()
end
SegTree.getRange = function(self, left, right)
  if left == right then return self.stage[self.stagenum][left] end
  local start_stage = 1
  while right - left + 1 < self.size[start_stage] do
    start_stage = start_stage + 1
  end
  local ret = self.emptyvalue
  local tasks = {{start_stage, left, right}}
  while 0 < #tasks do
    local task = tasks[#tasks]
    table.remove(tasks)
    local stage, l, r = task[1], task[2], task[3]
    if (l - 1) % self.size[stage] ~= 0 then
      local newr = mce((l - 1) / self.size[stage]) * self.size[stage]
      table.insert(tasks, {stage + 1, l, mmi(r, newr)})
      l = newr + 1
    end
    if self.size[stage] <= r + 1 - l then
      local pos = mce(l / self.size[stage])
      ret = self.func(ret, self.stage[stage][pos])
      l = l + self.size[stage]
    end
    if l <= r then
      table.insert(tasks, {stage + 1, l, r})
    end
  end
  return ret
end
SegTree.setValue = function(self, idx, value, silent)
  self.stage[self.stagenum][idx] = value
  if not silent then
    for i = self.stagenum - 1, 1, -1 do
      local dst = mce(idx / 2)
      local rem = dst * 4 - 1 - idx
      self.stage[i][dst] = self.func(self.stage[i + 1][idx], self.stage[i + 1][rem])
      idx = dst
    end
  end
end
SegTree.new = function(ary, func, emptyvalue)
  local obj = {}
  setmetatable(obj, {__index = SegTree})
  obj:create(ary, func, emptyvalue)
  return obj
end
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 mma = math.max
local st = SegTree.new(a, function(x, y) return getgcd(x, y) end, 0)
local ret = 1
for i = 1, n do
  local tmp = a[i]
  st:setValue(i, 0)
  ret = mma(ret, st:getRange(1, n))
  st:setValue(i, tmp)
end
print(ret)