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(a, b):
    if(a == 0):
        return b
    if(b == 0):
        return a

    if(a < b):
        a, b = b, a
    r = a % b
    while(r != 0):
        a, b = b, r
        r = a % b
    return b

def L(end_i, A):
    if(end_i == 0):
        return 0
    
    a = 0
    for i in range(end_i):
        a = gcd(a, A[i])
    return a


def R(start_i, A, N):
    if(start_i == N - 1):
        return 0

    a = 0
    for i in range(start_i + 1, N):
        a = gcd(a, A[i])
    return a


N = int(input())
A = list(map(int, input().split(' ')))

left = [0] * N
right = [0] * N

for i in range(1, N):
    left[i] = gcd(left[i - 1], A[i - 1])
#print(left)

for i in reversed(range(0, N - 1)):
    right[i] = gcd(A[i + 1], right[i + 1])
#print(right)

M = []
for i in range(N):
    M.append(gcd(left[i], right[i]))
#print(M)

print(max(M))