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.

Examples

Input

3
7 6 8


Output

2


Input

3
12 15 18


Output

6


Input

2
1000000000 1000000000


Output

1000000000
#-*- using:utf-8 -*-
def euclidean(a,b):
    if b == 0:
        return a
    else:
        return  euclidean(b,a%b)

def gcd(a,b):
#    print("gcd %d %d" %(a,b))
    n = 0
    if a == b:
        return a
    elif a > b:
        n = euclidean(a,b)

    elif a < b:
        n = euclidean(b,a)

    else:
        pass

    return n

def blackboard(n,a):
    candidate = 0
    maxnum = 0
    b = list(map(int,a))

    left = [0] * (n+1)
    right = [0] * (n+1)
    for i in range(n):
        left[i+1] = gcd(left[i],b[i])
        right[i+1] = gcd(right[i],b[n - i -1])

    for i in range(n):
        candidate = gcd(left[i],right[n-i-1])
        if candidate > maxnum:
            maxnum = candidate

    return maxnum


if __name__ == '__main__':
    n = raw_input()
    a = raw_input().split()
    m = int(n)
    print("%d" %(blackboard(m,a)))