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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            string[] sS = System.Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            sS = System.Console.ReadLine().Trim().Split(' ');
            List<int> lstM = new List<int>();
            for (int i = 0; i < sS.Length; i++)
            {
                lstM.Add(int.Parse(sS[i]));
            }

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            lstM.Sort();
            List<ClsSup> lstSup = new List<ClsSup>();
            for (int i = 0; i < lstM.Count; i++)
            {
                for (int j = i + 1; j < lstM.Count; j++)
                {
                    ClsSup oneUsr = new ClsSup();
                    oneUsr.iS = lstM[j] % lstM[i];
                    oneUsr.iD = j;
                    if (oneUsr.iS == 0) { oneUsr.iS = lstM[i]; }
                    if (!lstSup.Contains(oneUsr))
                    {
                        lstSup.Add(oneUsr);
                    }
                }
            }
            lstSup.Sort(delegate (ClsSup mca1, ClsSup mca2) { return (int)(mca1.iS - mca2.iS); });         // 剰余昇順
            if (lstSup[0].iS == 1) { }
            else if (lstSup[0].iS == 2)
            {
                for (int j = 0; j < lstM.Count; j++)
                {
                    ClsSup oneUsr = new ClsSup();
                    oneUsr.iS = lstM[j] % lstSup[0].iS;
                    oneUsr.iD = j;
                    if (oneUsr.iS == 1)
                    {
                        lstSup.Insert(0, oneUsr);
                        break;
                    }
                }
            }
            else if (lstSup[0].iS == 3)
            {
                for (int j = 0; j < lstM.Count; j++)
                {
                    ClsSup oneUsr = new ClsSup();
                    oneUsr.iS = lstM[j] % lstSup[0].iS;
                    oneUsr.iD = j;
                    if (oneUsr.iS == 1)
                    {
                        lstSup.Insert(0, oneUsr);
                        break;
                    }
                }
            }
            else if (lstSup[0].iS > 3)
            {
                for (int j = 0; j < lstM.Count; j++)
                {
                    ClsSup oneUsr = new ClsSup();
                    oneUsr.iS = lstM[j] % lstSup[0].iS;
                    oneUsr.iD = j;
                    if (oneUsr.iS != 0 && oneUsr.iS <= 3)
                    {
                        lstSup.Insert(0, oneUsr);
                        break;
                    }
                }
            }

            // 出力
            System.Console.WriteLine("{0}", lstSup[0].iS.ToString());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }

        // 剰余
        private class ClsSup
        {
            public int iS { get; set; } = 0;    // 剰余
            public int iD { get; set; } = 0;    // 相手Index

            public override bool Equals(object obj)                         // 重複排除用定義 .Distinct()用
            {
                var p = obj as ClsSup;
                if (p == null) { return false; }
                return (this.iS == p.iS);
            }
            public override int GetHashCode()                               // 重複排除用定義 .Distinct()用
            => iS.GetHashCode();                                            // 重複排除用定義 .Distinct()用
        }

}