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
from fractions import gcd

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

M = [0]*N

#漸化式を作る
L = [0]*N
R = [0]*N

for i in range(1,N):
    L[i] = gcd(L[i-1],A[i-1])
    R[N-1-i] = gcd(R[N-i],A[N-i])

for j in range(N):
    M[j] = gcd(L[j],R[j])

print(max(M))