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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)


def gcd(a,b):
    if b == 0: return a
    else: return(gcd(b, a % b))

def main2(N,A):
    if N == 2:
        return max(A)
    else:
        max_ = -1
        for i in range(N):
            L = 0
            R = 0

            for j in range(N):
                if i == j: continue
                if j < i:
                    L = gcd(L, A[j])
                else:
                    R = gcd(R, A[j])
            tmp = gcd(L,R)
            if tmp > max_:
                max_ = tmp
        return max_

N = int(input())
A = [int(i) for i in input().split(" ")]
print(main2(N,A))