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 \(x_1,x_2,…,x_n\): 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

Sample input

5
3 14 15 7 9

Sample output

7