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 Ruby (2.3.3) (judge verdict: Wrong Answer)

def s()
  gets().chomp
end
def i()
  gets.to_i
end
def li()
  gets.split.map(&:to_i)
end
def ili()
  n = gets.to_i
  as = gets.split.map(&:to_i)
  [n, as]
end
class Array
  def sum
    total = 0
    self.each do |item|
      total += item
    end
    total
  end
end

def eratosthenes(size)
  prime_list = []
  is_prime = Array.new(size, true)
  is_prime[0] = false
  is_prime[1] = false

  2.upto(size-1){|i|
    if is_prime[i]
      prime_list << i
      (2).upto((size.to_f/i).ceil-1){|j|
        is_prime[j*i] = false
      }
    end
  }
  [prime_list, is_prime]
end

def dijkstra(s, e, cost)
  size = cost.length
  if s==e
    return 0
  end
  dp = {}
  dp[s] = 0
  undefined_node = {}
  size.times{|i|
    if i != s
      undefined_node[i] = cost[s][i]
    end
  }
  while undefined_node.length != 0
    min = undefined_node.min_by{|_, v| v}
    stock = {}
    temp = undefined_node.clone
    temp.each{|k, v|
      if min[1] == v
        undefined_node.delete(k)
        if k == e
          return v
        end
        dp[k] = v
        stock[k] = v
      end
    }

    stock.each{|k, v|
      undefined_node.each{|k2, v2|
        undefined_node[k2] = v + cost[k][k2] < v2 ?  v + cost[k][k2] : v2
      }
    }
  end
end

def get_bits(len)
  res =  []
  (2**len).times{|i|
    res << i.to_s(2).rjust(len, '0')
  }
  res
end

def get_GCD(m, n)
  tmp = [n, m].max
  n = [n, m].min
  m = tmp
  while n != 0
    tmp = m % n
    m = n
    n = tmp
  end
  m
end


n = i()
an = li()
def solve(n, an)
  if an.size == 2
    return an.max
  end
  a1 = Array.new(n-1)

  (1..(n-1)).each{|i|
    a1[i-1] = get_GCD(an[0], an[i])
  }

  (2..(n-1)).each{|i|
    a1[i-1] = [get_GCD(an[1], an[i]), a1[i-1]].max
  }
  a1.sort[1]
end

p solve(n, an)