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)

# Your code here!
n=STDIN.gets.to_i
as= STDIN.gets.split(' ').map(&:to_i)

# find min index gcd and max value gcd
min = 1000000000
max = 0
index_min = 0
def gcd(a,b)
    while b > 0
        a,b = b,a%b
    end
    return a
end

for i in 0..n-2 do
    for j in i+1..n-1
        t = gcd(as[i], as[j])
        if (t < min) 
            index_min = i
        end
        if (t > max)
            max = t;
        end
    end
end

as[index_min] = max;
def gcds(args)
    if args.length == 1
        return args
    end
    a = args.shift;
    b = args.shift
    args.push(gcd(a,b))
    gcds(args)
end    

puts gcds(as)