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.

Sample Input 1

3
7 6 8

Output

Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N

Constraints

• All values in input are integers.
• $2 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$

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.

见题面 Input 部分

见题面 Output 部分