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: Runtime Error)

import math
import copy
N = int(input())
ListA = list(map(int,input().split()))



Answer = 1
if N == 2:
    Answer = math.gcd(ListA[0],ListA[1])
else:
    for j in range(N):
        Lista = copy.deepcopy(ListA)
        Lista.pop(j)
        GCDa = math.gcd(Lista[0],Lista[1])
        proAnswer = GCDa
        for i in range(N-1):
            GCDa = math.gcd(Lista[i],GCDa)
            if GCDa == 1:
                break
            Answer = max(GCDa,proAnswer,Answer)

print(Answer)