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
import sys
from copy import deepcopy
def gcd(a, b):
    if b > a:
        a, b = b, a
    if b == 0:
        return a
    return gcd(b, a%b)

def process(arr):
    L = [0]*(n+1)
    for i in range(1, n+1):
        gcd1 = gcd(L[i-1], arr[i-1])
        L[i] = gcd1
    R = [0]*(n+1)
    for i in range(1, n+1):
        gcd2 = gcd(R[-1-i+1], arr[-1-i+1])
        R[-1-i] = gcd2
    return L, R
    
n = int(raw_input())
arr = map(int, raw_input().split())
if n <= 2:
    print max(arr)
    exit()
L, R = process(arr)
M = [-1] * (n+1)
for i in range(n):
    M[i] = gcd(L[i], R[i+1])

print max(M)
