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: Time Limit Exceeded)

using System;
using System.Linq;
using System.IO;
using System.Collections.Generic;
using System.Text;

namespace AtCoder {
    public class Program {
        static int[] getKeys() {
            var Keys = Console.ReadLine().Split(' ');
            int N = Keys.Length;
            int[] Ns = new int[N];
            for (int i = 0; i < N; i++) {
                Ns[i] = int.Parse(Keys[i]);
            }
            return Ns;
        }
        static int[] getKeys(char delimiter) {
            var Keys = Console.ReadLine().Split(delimiter);
            int N = Keys.Length;
            int[] Ns = new int[N];
            for (int i = 0; i < N; i++) {
                Ns[i] = int.Parse(Keys[i]);
            }
            return Ns;
        }

        public static void Show<T>(T[,] map) {
            int H = map.GetLength(0);
            int W = map.GetLength(1);
            Console.WriteLine("-------------------------");
            for (int i = 0; i < H; i++) {
                for (int j = 0; j < W; j++) {
                    Console.Write(map[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine("-------------------------");
        }
        public static void Show<T>(T[,] map, string delimiter) {
            int H = map.GetLength(0);
            int W = map.GetLength(1);
            Console.WriteLine("-------------------------");
            for (int i = 0; i < H; i++) {
                for (int j = 0; j < W; j++) {
                    Console.Write(map[i, j] + delimiter);
                }
                Console.WriteLine();
            }
            Console.WriteLine("-------------------------");
        }
        public static void Show<T>(IEnumerable<T> ts) {
            foreach (var item in ts) {
                Console.Write(item + " ");
            }
            Console.WriteLine();
        }
        public static void Show<T>(IEnumerable<T> ts, string delimiter) {
            foreach (var item in ts) {
                Console.Write(item + delimiter);
            }
            Console.WriteLine();
        }
        static T[] getUniform<T>(int length, T value) {
            T[] Ts = new T[length];
            for (int i = 0; i < length; i++) {
                Ts[i] = value;
            }
            return Ts;
        }
        static void setUniform<T>(T[] ts, T value) {
            int length = ts.Length;
            for (int i = 0; i < length; i++) {
                ts[i] = value;
            }
        }
        static T[,] getUniform<T>(int row, int col, T value) {
            T[,] Ts = new T[row, col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    Ts[j, i] = value;
                }
            }
            return Ts;
        }
        static void setUniform<T>(T[,] ts, T value) {
            int N = ts.GetLength(0);
            int M = ts.GetLength(1);
            for (int i = 0; i < M; i++) {
                for (int j = 0; j < N; j++) {
                    ts[j, i] = value;
                }
            }
        }

        static int N;
        static List<int> HPs;
        static void Main() {
            N = int.Parse(Console.ReadLine());
            HPs = getKeys().ToList();
            Attack();
            while (HPs.Count > 1) {
                Attack();
            }
            if (HPs.Count > 0) {
                Console.WriteLine(HPs[0]);
            }
        }

        static void Attack() {
            int attacker = HPs.FindIndex(x => x == HPs.Min());
            int min = HPs.Min();
            N = HPs.Count();
            for (int i = 0; i < N; i++) {
                if (i != attacker) {
                    HPs[i] %= min;
                }
            }
            HPs = HPs.Where(x => x != 0).ToList();
        }

    }
}