CSES - Common Divisors
  • Time limit: 1.00 s
  • Memory limit: 512 MB

You are given an array of nn 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 nn: the size of the array.

The second line has nn integers x1,x2,,xnx_1,x_2,\ldots,x_n: the contents of the array.

Output

Print the maximum greatest common divisor.

Constraints

  • 2n21052 \le n \le 2 \cdot 10^5
  • 1xi1061 \le x_i \le 10^6

Example

Input:

5
3 14 15 7 9

Output:

7