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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from fractions import gcd
from functools import reduce

def gcd_list(numbers):
    return reduce(gcd, numbers)

def main():
    n = int(input())
    A = list(map(int, input().split()))

    gcd_max = 1
    for i in range(n):
        if i == n-1:
            temp = A[i]
            A[i] = A[i-1]
            gcd_max = max(gcd_max, gcd_list(A))
            A[i] = temp
            break
        temp = A[i]
        A[i] = A[i+1]
        gcd_max = max(gcd_max, gcd_list(A))
        A[i] = temp
    print(gcd_max)


if __name__ == '__main__':
    main()