The greatest common divisor (GCD), also called highest common factor (HCF) of N numbers is the largest positve integer that divides all numbers without giving a remainder.

Write an algorithm to determine the GCD of N positive integers.

Input

The input to the function/method consists of two arguments -

num, an integer representing the number of positive integers (N).

arr, a list of positive integers.

Output

Return an integer representing the GCD of the given positive integers.

Example

Input

num = 5 arr = [2, 4, 6, 8, 10]

Output

2

Explanation: The largest positive integers that divides all the positive integers 2, 4, 6, 8, 10 without a remainder is 2. So, the output is 2.