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;

namespace ABC118C
{
    class Program
    {
        static void Main(string[] args)
        {
            if (args.Length > 0)
            {
                Console.SetIn(new StreamReader(args[0]));
            }

            new Program().calc();
        }

        void calc()
        {
            var n = int.Parse(Console.ReadLine()); // 使わない
            var hpList = Console.ReadLine().Split(' ').Select(int.Parse); // モンスターの体力
            Console.WriteLine(attack(hpList));
        }

        int attack(IEnumerable<int> hpList)
        {
            Console.Error.WriteLine(string.Join(",", hpList));

            // 最も体力の少ないモンスターが、周りを攻撃する
            var min = hpList.Min();

            // 体力をちょうどゼロにできるかどうかを確かめる
            hpList = hpList.Select(hp => hp % min).Where(hp => hp > 0);

            if (hpList.Count() == 0)
            {
                // 全モンスターの体力をちょうどゼロにできたら終了
                return min;
            }
            else
            {
                // そうでない場合は自分の体力を元に戻して攻撃を繰り返す
                // Enumerable.Appendは.NET Framework 4.7.1/.NET Core 1.0以降が必要なので、Concatを使う
                return attack(hpList.Concat(new[] { min }));
            }
        }
    }
}