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: Wrong Answer)

import copy
ans = 1
N = int(input())
A = list(map(int, input().split()))
l = []

def gcd(a,b):
    x = max(a, b)
    y = min(a, b)
    if x % y == 0:
        return y
    else:
        while x % y != 0:
            z = x%y
            x = y
            y = z
        else:
            return z
    
def gcd_list(list):
    p = 1
    for i in range(len(list)-1):
        if i == 0:
            p = gcd(list[0], list[1])
        else:
            p = gcd(p,list[i+1]) 
    return p

if N == 2:
    print(gcd(A[0], A[1]))
else:
    for i in range(N):
        l = copy.copy(A)
        l.pop(i)
        ans = max(gcd_list(l), ans)
    print(ans)