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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC118.C();
        }

        class ABC118
        {
            public static void A()
            {
                var A = Read.Int();
                var B = Read.Int();
                Console.WriteLine(B % A == 0 ? A + B : B - A);
            }
            public static void B()
            {
                var N = Read.Int();
                var M = Read.Int();
                var KA = Enumerable.Range(0, N).Select(i => Read.IntN()).ToArray();
                int[] count = new int[M + 1];
                foreach(var ka in KA)
                {
                    foreach(var v in ka.Skip(1))
                    {
                        count[v]++;
                    }
                }
                Console.WriteLine(count.Count(x => x == N));
            }
            public static void C()
            {
                var N = Read.Int();
                var A = Read.LongN();
                long gcd = A[0];
                for(int i = 1; i < N; ++i)
                {
                    gcd = Util.GCD(gcd, A[i]);
                }
                Console.WriteLine(gcd);
            }
            public static void D()
            {
                var N = Read.Int();
                var M = Read.Int();
                var A = Read.IntN();

                var table = new int[] { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };
                Dictionary<int, int> map = new Dictionary<int, int>();
                foreach(var a in A)
                {
                    var b = table[a];
                    if (map.ContainsKey(b))
                    {
                        map[b] = Math.Max(map[b], a);
                    }
                    else
                    {
                        map.Add(b, a);
                    }
                }
                var dp = Enumerable.Range(0, N + 1).Select(i => -1).ToArray();
                dp[0] = 0;
                for(int i = 2; i <= N; ++i)
                {
                    foreach(var k in map.Keys)
                    {
                        if (i >= k)
                        {
                            dp[i] = Math.Max(dp[i], dp[i - k] + 1);
                        }
                    }
                }
                List<int> keta = new List<int>();
                int idx = N;
                var cand = map.OrderBy(x => -x.Value).ToArray();
                while (idx > 0)
                {
                    foreach(var kvp in cand)
                    {
                        if (idx >= kvp.Key && dp[idx] == dp[idx - kvp.Key] + 1)
                        {
                            keta.Add(kvp.Value);
                            idx -= kvp.Key;
                            break;
                        }
                    }
                }
                Console.WriteLine(String.Join("", keta));
            }
        }

        class Util
        {
            public static long GCD(long a, long b)
            {
                while (b > 0)
                {
                    var c = a % b;
                    a = b;
                    b = c;
                }
                return a;
            }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
        }
    }
}