You are given an array of ~n~ positive integers. Your task is to find two integers such that their greatest common divisor is as large as possible.

Input

• The first input line has an integer ~n~: the size of the array.

The second line has ~n~ integers ~x\_1,x\_2,\ldots,x\_n~: the contents of the array.

Output

• Print the maximum greatest common divisor.

Constraints

• ~2 \le n \le 2 \cdot 10^5~
• ~1 \le x\_i \le 10^6~

Example Input

5
3 14 15 7 9

Example Output

7