Problem:
Score : 300 points

Problem Statement

There are N monsters, numbered 1, 2, ..., N.

Initially, the health of Monster i is A_i.

Below, a monster with at least 1 health is called alive.

Until there is only one alive monster, the following is repeated:

A random alive monster attacks another random alive monster.

As a result, the health of the monster attacked is reduced by the amount equal to the current health of the monster attacking.

Find the minimum possible final health of the last monster alive.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible final health of the last monster alive.

Sample Input 1

4
2 10 8 40

Sample Output 1

2

When only the first monster keeps on attacking, the final health of the last monster will be 2, which is minimum.

Sample Input 2

4
5 13 8 1000000000

Sample Output 2

1

Sample Input 3

3
1000000000 1000000000 1000000000

Sample Output 3

1000000000

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;

namespace ABC118C
{
    public partial class Program
    {
        void Solve(StreamScanner ss, StreamWriter sw)
        {
            //---------------------------------
            var N = ss.Next(int.Parse);
            var A = ss.Next(long.Parse, N);

            var ret = A[0];

            foreach (var a in A)
            {
                ret = MathX.Gcd(ret, a);
            }

            sw.WriteLine(ret);
            //---------------------------------
        }
    }

    public static partial class MathX
    {
        public static long Gcd(long a, long b)
        {
            return b == 0 ? a : Gcd(b, a % b);
        }

        public static long Lcm(long a, long b)
        {
            return a * (b / Gcd(a, b));
        }
    }

    public class StreamScanner
    {
        static readonly char[] Separator = { ' ' };
        readonly StreamReader streamReader;

        string[] line = new string[0];
        int index = 0;

        public bool EndOfStream { get { return streamReader.EndOfStream && index >= line.Length; } }

        public StreamScanner(Stream stream)
        {
            this.streamReader = new StreamReader(stream);
        }

        public string Next()
        {
            return Next(s => s);
        }

        public string[] Next(int x)
        {
            return Next(s => s, x);
        }

        public string[][] Next(int x, int y)
        {
            return Next(s => s, x, y);
        }

        public T Next<T>(Func<string, T> parser)
        {
            if (EndOfStream) throw new EndOfStreamException();
            if (index < line.Length) return parser(line[index++]);
            index = 0;
            line = streamReader.ReadLine()?.Split(Separator, StringSplitOptions.RemoveEmptyEntries);
            return Next(parser);
        }

        public T[] Next<T>(Func<string, T> parser, int x)
        {
            var ret = new T[x];
            for (var i = 0; i < x; ++i) ret[i] = Next(parser);
            return ret;
        }

        public T[][] Next<T>(Func<string, T> parser, int x, int y)
        {
            var ret = new T[y][];
            for (var i = 0; i < y; ++i) ret[i] = Next(parser, x);
            return ret;
        }
    }

    public partial class Program
    {
        static void Main()
        {
            Excute(Console.OpenStandardInput(), Console.OpenStandardOutput());
        }

        public static void Excute(Stream input, Stream output)
        {
            var ss = new StreamScanner(input);
            var sw = new StreamWriter(output);
            new Program().Solve(ss, sw);
            sw.Flush();
        }
    }
}