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)

n = int(input())
a = list(map(int,input().split()))
a.sort()
def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    divisors.sort()
    return divisors
divs = make_divisors(a[0]) #list

divsTF = [0]*len(divs)
for i in range(len(divs)):
    j = [1 if a[_] % divs[i] else 0 for _ in range(n) ]

    if sum(j) <= 1:
        divsTF[i] = 1

ans = 1
for i in range(len(divs)):
    if divsTF[i] == 1:
        ans = max(ans,divs[i])


divs2 = make_divisors(a[1]) #list

divsTF2 = [0]*len(divs2)
for i in range(len(divs2)):
    j = [1 if a[_] % divs2[i] else 0 for _ in range(n) ]

    if sum(j) <= 1:
        divsTF2[i] = 1

aans = 1
for i in range(len(divs2)):
    if divsTF2[i] == 1:
        aans = max(aans,divs2[i])
print(max(aans,ans))