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: Accepted)

import fractions

integral_count = int(input())
blackboard_integers = list(map(int, input().split()))

gcd_integers = list(set(blackboard_integers))
gcds = [0] * len(gcd_integers)
for i in range(len(gcd_integers)):
    if blackboard_integers.count(gcd_integers[i]) >= 2:
        for n in gcd_integers:
            gcds[i] = fractions.gcd(gcds[i], n)
    else:
        for n in gcd_integers[:i]:
            gcds[i] = fractions.gcd(gcds[i], n)
        for n in gcd_integers[i+1:]:
            gcds[i] = fractions.gcd(gcds[i], n)

print(max(gcds))