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

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