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 System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            IO io = new IO();

            //ここから
            int N = io.ReadLineToInt();
            List<int> lifes = io.ReadLineToIntList();

            while (lifes.Distinct().Count() != 1)
            {
                lifes.RemoveAll(l => l == 0);
                lifes = lifes.Distinct().ToList();
                int min = lifes.Min();

                for (int i = 0; i < lifes.Count(); i++)
                {
                    if (lifes[i] != min)
                    {
                        lifes[i] = lifes[i] % min;
                    }

                }

            }

            Console.Write(lifes.Min());

            Console.ReadKey();
        }
    }

    //IOを担う関数群
    public class IO
    {
        //stringの入力
        public string ReadLineToString()
        {
            return Console.ReadLine();
        }

        //intの入力
        public int ReadLineToInt()
        {
            return int.Parse(Console.ReadLine());
        }

        //空白区切りの複数の文字列の入力をstring[]にして返す
        public string[] ReadLineToStringArray()
        {
            return Console.ReadLine().Split(' ').ToArray();
        }


        //空白区切りの複数の整数の入力をint[]にして返す
        public int[] ReadLineToIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        //空白区切りの複数の文字列の入力をList<string>で受け取る
        public List<string> ReadLineToStringList()
        {
            return Console.ReadLine().Split(' ').ToList();
        }

        //空白区切りの複数の整数の入力をList<int>で受け取る
        public List<int> ReadLineToIntList()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToList();
        }

    }

}