Common Divisors

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

Output

7