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.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int32();
            var a = consoleReader.SplitInt32();

            var gcd = Gcd(a[0], a[1]);
            for (int i = 2; i < a.Length; i++)
            {
                gcd = Gcd(gcd, a[i]);
            }
            return gcd;
        }
        int Gcd(int a, int b)
        {
            if (a < b)
                return Gcd(b, a);
            while (b != 0)
            {
                var amari = a % b;
                a = b;
                b = amari;
            }
            return a;
        }

        const int mod = 1000000007;
        private readonly ConsoleReader consoleReader;
        public Program() : this(new ConsoleReader()) { }
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program().Calc());
        public static string MultiLine<T>(IEnumerable<T> source) => string.Join("\n", source);
    }

    public class ConsoleReader
    {
        public virtual string String() => Console.ReadLine();
        public int Int32() => int.Parse(String());
        public long Int64() => long.Parse(String());
        public ulong UInt64() => ulong.Parse(String());
        public double Double() => double.Parse(String());
        public string[] Split() => String().Split().ToArray();
        public int[] SplitInt32() => String().Split().Select(int.Parse).ToArray();
        public long[] SplitInt64() => String().Split().Select(long.Parse).ToArray();
        public ulong[] SplitUInt64() => String().Split().Select(ulong.Parse).ToArray();
        public double[] SplitDouble() => String().Split().Select(double.Parse).ToArray();

        public IEnumerable<string> Repeat(int count)
        {
            for (int i = 0; i < count; i++)
                yield return String();
        }
        public IEnumerable<int> RepeatInt32(int count)
        {
            for (int i = 0; i < count; i++)
                yield return Int32();
        }
        public IEnumerable<long> RepeatInt64(int count)
        {
            for (int i = 0; i < count; i++)
                yield return Int64();
        }
        public IEnumerable<string[]> RepeatSplit(int count)
        {
            for (int i = 0; i < count; i++)
                yield return Split();
        }
        public IEnumerable<int[]> RepeatSplitInt32(int count)
        {
            for (int i = 0; i < count; i++)
                yield return SplitInt32();
        }
    }
}