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Problem

Read a natural number n followed by n positive natural numbers.

Print the greatest common divisor (GCD) of all n numbers, computed using a recursive function based on Euclid's algorithm.

Define a recursive function cmmdc(a, b) with the relation:

cmmdc(a, 0) = a
cmmdc(a, b) = cmmdc(b, a % b), for b > 0

Then compute the GCD of all n numbers by successive reduction: start with the first number and combine it one by one with each of the remaining numbers using cmmdc.

Input format

Input input.txt

The first line contains the natural number `n` (the count of values). The second line contains `n` positive natural numbers separated by spaces. - `1 <= n <= 50` - `1 <= valori <= 1.000.000` - The solution must use recursion.

Output format

Output output.txt

Print a single natural number: the GCD of all `n` numbers, followed by a newline.

Example

input
3

24 36 60
output
12

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