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)

def gcd(x, y):
    while y != 0:
        x, y = y, x % y
    return x
 
N = int(input())
lst = [int(x) for x in input().split()]
 
l = [0] * N
r = [0] * N
 
l[0] = lst[0]
r[-1] = lst[-1]
 
for i in range(1, N):
    l[i] = gcd(l[i-1], lst[i])
 
for i in range(N-2, -1, -1):
    r[i] = gcd(r[i+1], lst[i])

ret = max(r[1], l[-2])
for i in range(1, N-1):
    ret = max(ret, gcd(l[i-1], r[i+1]))
print(ret)