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;

namespace AtCoder
{
    class Program
    {
        static int n;
        static List<int> monsters;

        static void Main(string[] args)
        {
            //[summary]C - Monsters Battle Royale
            n = int.Parse(Console.ReadLine());

            //モンスターの体力を取得
            monsters = ReadLine();
            int minMonster = monsters.Min();

            //モンスターの体力を減らす
            int minDiff = GetMinDiff();

            //一番体力の少ないモンスターが初期状態と変わっていなかったら、
            //最後に生き残るのは一番体力の少ないモンスター
            if (monsters.Min() == minMonster)
            {
                Console.WriteLine(minMonster);
            }
            else
            {
                Console.WriteLine(minDiff);
            }            
        }

        static int  GetMinDiff()
        {
            //モンスターの体力が少ない順に並べる
            monsters = monsters.OrderBy(x => x).ToList();

            int minDiff = monsters[n - 1];

            for (int i = 1; i < n - 1; i++)
            {
                //モンスター1体ごとに、自分より体力の少ないモンスター総当たりで割っていき
                //余りの最小値を求める
                int index = n - i;
                int min = monsters[index];

                for (int j = 0; j < index; j++)
                {
                    int mod = monsters[index] % monsters[j];

                    if (mod == 1)
                    {
                        Console.WriteLine(1);
                        return minDiff;
                    }
                    else if (mod < min && mod != 0)
                    {
                        min = mod;
                    }

                    monsters[index] = min;
                }

                var clone = monsters.OrderByDescending(x => x).ToList();

                for(int j = 0; j < n - 1; j++)
                {
                    int diff = clone[j] - clone[j + 1];

                    if (diff == 1)
                    {
                        return 1;
                    }
                    else if (diff < minDiff && diff != 0)
                    {
                        minDiff = diff;
                    }
                }
            }

            return minDiff;
        }

        static List<int> ReadLine()
        {
            var line = Console.ReadLine().TrimEnd();
            var array = line.Split(' ');
            var numbers = new List<int>();

            foreach (var s in array)
            {
                int num = int.Parse(s);
                numbers.Add(num);
            }

            return numbers;
        }
    }
}