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;
using System.Text;
using System.Threading.Tasks;
using static ABC118.Util;
using static System.Console;

#if DEBUG
using System.Diagnostics;
#endif

namespace ABC118
{
    class Program
    {
        static void Main(string[] args)
        {
#if DEBUG
            while (true)
            {
#endif
                // AB(); // 2m
                // FoodsLovedByEveryone(); // 13m
                MonstersBattleRoyale();
#if DEBUG
            }
#endif
        }

        static void MonstersBattleRoyale()
        {
            int N = ReadInt();
            int[] M = ReadIntArray();

            int ans = M[0];
            for (int i = 1; i < N; i++)
            {
                ans = GCD(ans, M[i]);
            }

            WriteLine(ans);
        }

        static void FoodsLovedByEveryone()
        {
            int[] tmp = ReadIntArray();
            int N = tmp[0];
            int M = tmp[1];

            int[] buff = new int[M + 1];

            for (int i = 0; i < N; i++)
            {
                int[] line = ReadIntArray();
                for (int j = 1; j < line[0] + 1; j++)
                {
                    buff[line[j]]++;
                }
            }

            int ans = 0;
            for (int i = 1; i < M + 1; i++)
            {
                if (buff[i] == N)
                    ans++;
            }

            WriteLine(ans);
        }

        static void AB()
        {
            int[] tmp = ReadIntArray();
            int A = tmp[0];
            int B = tmp[1];

            if (B % A == 0)
            {
                WriteLine(A + B);
            }
            else
            {
                WriteLine(B - A);
            }
        }
    }

    #region ToolBox

    /// <summary>
    /// ユーティリティー
    /// </summary>
    public static class Util
    {
        // 10^10 * 2
        public static readonly long INF = 20000000000;

        public static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }

        public static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        public static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        public static string ReadString()
        {
            return Console.ReadLine();
        }

        /// <summary>
        /// "00101001010"という様な入力をintの配列にして返す
        /// </summary>
        /// <returns></returns>
        public static int[] ReadIntArrayFromBinaryString()
        {
            return Console.ReadLine().Select(c => int.Parse(c.ToString())).ToArray();
        }

        /// <summary>
        /// "00101001010"という様な入力をboolの配列にして返す
        /// </summary>
        /// <returns></returns>
        public static bool[] ReadBoolArrayFromBinaryString()
        {
            return Console.ReadLine().Select(c => c == '1').ToArray();
        }

        /// <summary>
        /// ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] Sort<T>(T[] array)
        {
            Array.Sort<T>(array);
            return array;
        }

        /// <summary>
        /// 逆順ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] ReverseSort<T>(T[] array)
        {
            Array.Sort<T>(array);
            Array.Reverse(array);
            return array;
        }

        /// <summary>
        /// Rubyにあるようなやつ
        /// ex) 5.Times(i => Console.WriteLine(i));
        /// </summary>
        /// <param name="times"></param>
        /// <param name="action"></param>
        public static void Times(this int times, Action<int> action)
        {
            for (int i = 0; i < times; i++)
            {
                action(i);
            }
        }

        /// <summary>
        /// 引数aと引数bの値を入れ替えます
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="a"></param>
        /// <param name="b"></param>
        public static void Swap<T>(ref T a, ref T b)
        {
            T _a = a;
            a = b;
            b = _a;
        }

        /// <summary>
        /// Console.WriteLineの自動フラッシュをしないようにする
        /// </summary>
        public static void DontAutoFlush()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
        }

        public static void Flush()
        {
            Console.Out.Flush();
        }

        /// <summary>
        /// 先頭と末尾に要素を増やした新しい配列を返します。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] AddHeadAndTail<T>(T[] array)
        {
            int len = array.Length;
            T[] res = new T[len + 2];
            Array.Copy(array, 0, res, 1, len);
            return res;
        }

        /// <summary>
        /// 昇順ソート済みの配列を2分探索します。
        /// 要素が見つからなかった場合はnより大きい数値の中で最小の数値のインデックスを返す。
        /// </summary>
        /// <param name="array"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static int BinarySearch(long[] array, long n)
        {
            int left = 0;
            int right = array.Length;

            while (left <= right)
            {
                int mid = (right - left) / 2 + left;

                if (array[mid] == n)
                {
                    return mid;
                }
                else if (n < array[mid])
                {
                    right = mid - 1;
                }
                else
                {
                    left = mid + 1;
                }
            }

            return left;
        }

        public static int GCD(int a, int b)
        {
            return (b == 0) ? a : GCD(b, a % b);
        }

#if DEBUG
        static void SampleGenerator()
        {
            int A = 1000;
            int B = 1000;
            int Q = 1000;

            Random r = new Random();
            StringBuilder sb = new StringBuilder();
            sb.AppendLine(string.Format("{0} {1} {2}", A, B, Q));
            A.Times(a => sb.AppendLine(((long)r.Next() * r.Next()).ToString()));
            B.Times(b => sb.AppendLine(((long)r.Next() * r.Next()).ToString()));
            Q.Times(q => sb.AppendLine(((long)r.Next() * r.Next()).ToString()));

            Debug.WriteLine(sb.ToString());
        }
#endif

    }

    /// <summary>
    /// HashSetにTupleを入れた時の、等値性判定方法の指定に使います。
    /// HashSetのコンストラクタに渡して使います。
    /// EqualsとGetHashCodeを提供します。
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class EqualityComparer<T> : IEqualityComparer<T>
    {
        private Func<T, T, bool> _equals;
        private Func<T, int> _getHashCode;

        public EqualityComparer(Func<T, T, bool> equals, Func<T, int> getHashCode)
        {
            _equals = equals;
            _getHashCode = getHashCode;
        }

        public bool Equals(T x, T y)
        {
            return _equals(x, y);
        }

        public int GetHashCode(T obj)
        {
            return _getHashCode(obj);
        }
    }

    /// <summary>
    /// UnionFindTree
    /// </summary>
    public class UnionFindTree
    {
        int[] Node;

        public UnionFindTree(int N)
        {
            Node = new int[N];
            for (int i = 0; i < N; i++)
            {
                Node[i] = -1;
            }
        }

        public bool IsSameGroup(int x, int y)
        {
            return GetRoot(x) == GetRoot(y);
        }

        public bool Merge(int x, int y)
        {
            int xr = GetRoot(x);
            int yr = GetRoot(y);

            if (xr == yr)
                return false;

            // xが、大きなグループを示すようにSwapする（値が小さい方が大きなグループ）
            if (Node[xr] > Node[yr])
                Swap(ref xr, ref yr);

            // グループの数を合算する
            Node[xr] += Node[yr];

            // 根を張り替える
            Node[yr] = xr;
            return true;
        }

        public int Size(int x)
        {
            return -Node[GetRoot(x)];
        }

        public int GetRoot(int n)
        {
            if (Node[n] < 0)
            {
                return n;
            }
            else
            {
                // 根を張りなおす。
                Node[n] = GetRoot(Node[n]);
                return Node[n];
            }
        }
    }

    /// <summary>
    /// PriorityQueue
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class PriorityQueue<T> where T : IComparable
    {
        private Comparison<T> _comparison = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        public PriorityQueue(int maxSize, Comparison<T> comparison)
        {
            _heap = new T[maxSize];
            _comparison = comparison;
        }

        private int Compare(T x, T y)
        {
            if (_comparison != null) return _comparison(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }

    #endregion
}