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;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Linq;
using System.Numerics;

namespace AtCoderWorkspace
{
    public class Solver
    {
        public void Solve()
        {
            var cin = new Scanner();            
            var n = cin.nextInt();
            var a = cin.ArrayLong(n);

            var tmp = a[0];
            for (int i = 1; i < n; i++)
            {
                tmp = MathEx.GCD(tmp, a[i]);
            }            
            Console.WriteLine(tmp);
        }
    }
    public static partial class MathEx
    {
        public static int GCD(int n, int m) { return (int)GCD((long)n, m); }

        public static long GCD(long n, long m)
        {
            n = Math.Abs(n);
            m = Math.Abs(m);
            while (n != 0)
            {
                m %= n;
                if (m == 0) return n;
                n %= m;
            }
            return m;
        }

        public static long LCM(long n, long m) { return (n / GCD(n, m)) * m; }

        public static bool[] Sieve(int max, List<int> primes = null)
        {
            var isPrime = new bool[max + 1];
            for (int i = 2; i < isPrime.Length; i++) isPrime[i] = true;
            for (int i = 2; i * i <= max; i++)
                if (!isPrime[i]) continue;
                else for (int j = i * i; j <= max; j += i) isPrime[j] = false;
            if (primes != null) for (int i = 0; i <= max; i++) if (isPrime[i]) primes.Add(i);

            return isPrime;
        }
        public static bool IsPrime(int num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false;

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {
                    return false;
                }
            }

            return true;
        }

        private static readonly List<int> facs = new List<int> { 1 };
        public static int Fac(int n)
        {
            for (int i = facs.Count; i <= n; ++i)
            {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % 1000000007));
            }
            return facs[n];
        }

        public static int Ncr(int n, int r)
        {
            return (n < r) ? 0
            : (n == r) ? 1
            : Fac(n) / (Fac(r) * Fac(n - r));
        }

    }
    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public int[] DPArrayInt(int N, int ex)
        {
            int[] Array = new int[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt();
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public long[] DPArrayLong(int N, int ex)
        {
            long[] Array = new long[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong();
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }

    class Program
    {
        static void Main(string[] s) => new Solver().Solve();
    }
}