C - GCD on Blackboard /

### 問題文

N 個の整数 A_1, A_2, ..., A_N が黒板に書かれています。

あなたはこの中から整数を 1 つ選んで、1 以上 10^9 以下の好きな整数に書き換えます。

### 制約

• 入力は全て整数である。
• 2 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9

### 入力

N
A_1 A_2 ... A_N


### 入力例 1

3
7 6 8


### 出力例 1

2


74 に書き換えると 3 つの整数の最大公約数は 2 となり、これが最大です。

### 入力例 2

3
12 15 18


### 出力例 2

6


### 入力例 3

2
1000000000 1000000000


### 出力例 3

1000000000


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.