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: Runtime Error)

from math import gcd
N = int(input())
As = list(map(int, input().split()))

lis = [0]*N
ans = 0
for k in range(N):
    g = 10**20
    for i in range(N-1):
        if i==k: continue
        for j in range(i+1, N):
            if j==k: continue
            g = min(gcd(As[i], As[j]), g)
    ans = max(ans, g)
if N==2:
    print(max(As))
else:
    print(ans)