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.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static System.Console;
using static System.Math;

namespace Atcoder
{
    class Program
    {
        static StreamWriter sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
        static void Main(string[] args)
        {
            try
            {
                SetOut(sw);
                Solve.Answer();
                Out.Flush();
            }
            catch (Exception ex)
            {
                WriteLine(ex.ToString());
            }
        }
    }

    public class Solve
    {
        public static void Answer()
        {
            var n = IO.RInt;
            var a = IO.RSInt;

            int minNum;

            while (a.Length > 1)
            {
                Array.Sort(a);
                minNum = a[0];
                for (int i = 1; i < a.Length; i++)
                {
                    a[i] %= minNum;
                }
                a = a.Where(x => x != 0).ToArray();
            }
            WriteLine(a[0]);
        }
    }

    public class IO
    {
        #region Input
        public static int RInt => int.Parse(ReadLine());
        public static long RLong => long.Parse(ReadLine());
        public static double RDouble => double.Parse(ReadLine());

        public static string[] RSString => ReadLine().Split();
        public static int[] RSInt => ReadLine().Split().Select(s => int.Parse(s)).ToArray();
        public static long[] RSLong => ReadLine().Split().Select(s => long.Parse(s)).ToArray();
        public static double[] RSDouble => ReadLine().Split().Select(s => double.Parse(s)).ToArray();
        #endregion

        #region Output
        public static void OutJoinSpace<T>(IEnumerable<T> list) => WriteLine(string.Join(" ", list));
        public static void WriteLineYes_or_No(bool flag) => WriteLine(flag ? "Yes" : "No");
        public static void WriteLineYES_or_NO(bool flag) => WriteLine(flag ? "YES" : "NO");
        #endregion
    }

    public class Mod
    {
        #region
        private readonly static long M = 1000000007;

        public static long Add(long a, long b) => (a * b) % M;
        public static long Sub(long a, long b) => (a - b) % M >= 0 ? (a - b) % M : (a - b) % M + M;
        public static long Multi(long a, long b) => (a * b) % M;
        #endregion
    }
}