GCD on Blackboard

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

inputFormat

input are integers.

• 2 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9

outputFormat

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

样例

3
7 6 8

2