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

namespace Program
{
    public class ABC118C
    {
        static public void Main(string[] args)
        {
            var N = NextInt;
            var Alist = NextIntList(N);
            Alist.Sort();
            var ans = Alist.First();
            foreach (var item in Alist.Skip(1))
            {
                var tmp = item % ans;
                if (tmp != 0) ans = tmp;
            }

            Console.WriteLine(ans);
        }

        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static List<int> NextIntList(int N)
        {
            var ret = new List<int>(N);
            for (int i = 0; i < N; ++i) ret.Add(NextInt);
            return ret;
        }
        static long NextLong => long.Parse(Console_.NextString());
        static List<long> NextLongList(int N)
        {
            var ret = new List<long>(N);
            for (int i = 0; i < N; ++i) ret.Add(NextLong);
            return ret;
        }
        static string NextString => Console_.NextString();
        static void Sort<T>(List<T> l) where T : IComparable => l.Sort();
        static void RevSort<T>(List<T> l) where T : IComparable => l.Sort((x, y) => y.CompareTo(x));
        static IEnumerable<long> Prime(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i) if (!table[i]) yield return 2 * i + 1;
        }
        static IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i < max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        static long GCD(long a, long b)
        {
            long tmpa = a, tmpb = b;
            while (tmpb > 0) { var tmp = tmpb; tmpb = tmpa % tmpb; tmpa = tmp; }
            return tmpa;
        }
        class PQ<T> where T : IComparable
        {
            private List<T> h;
            private Comparison<T> c;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(T v)
            {
                var i = h.Count;
                h.Add(v);
                while (i > 0)
                {
                    var ni = (i - 1) / 2;
                    if (c(v, h[ni]) >= 0) break;
                    h[i] = h[ni]; i = ni;
                }
                h[i] = v;
            }
            public T Peek => h[0];
            public int Count => h.Count;
            public T Pop
            {
                get
                {
                    var r = h[0];
                    var v = h[h.Count - 1];
                    h.RemoveAt(h.Count - 1);
                    if (h.Count == 0) return r;
                    var i = 0;
                    while (i * 2 + 1 < h.Count)
                    {
                        var i1 = i * 2 + 1;
                        var i2 = i * 2 + 2;
                        if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2;
                        if (c(v, h[i1]) <= 0) break;
                        h[i] = h[i1]; i = i1;
                    }
                    h[i] = v;
                    return r;
                }
                private set { }
            }
        }
        class PQ<TKey, TValue> where TKey : IComparable
        {
            private PQ<Tuple<TKey, TValue>> q;
            public PQ(int cap, Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(TKey k, TValue v) => q.Push(Tuple.Create(k, v));
            public Tuple<TKey, TValue> Peek => q.Peek;
            public int Count => q.Count;
            public Tuple<TKey, TValue> Pop => q.Pop;
        }
        static class Mod
        {
            static public long _mod = 1000000007;
            static public long Add(long x, long y) => (x + y) % _mod;
            static public long Sub(long x, long y) => (x - y) % _mod;
            static public long Multi(long x, long y) => (x * y) % _mod;
            static public long Div(long x, long y) => (x * Inverse(y)) % _mod;
            static public long Pow(long x, long y)
            {
                var a = 1L;
                while (y != 0)
                {
                    if ((y & 1) == 1) a = Mod.Multi(a, x);
                    x = Mod.Multi(x, x);
                    y >>= 1;
                }
                return a;
            }
            static public long Inverse(long x)
            {
                var b = _mod;
                var r = 1L;
                var u = 0L;
                while (b > 0L)
                {
                    var q = x / b;
                    var t = u; u = r - q * u; r = t;
                    t = b; b = x - q * b; x = t;
                }
                return r < 0 ? r + _mod : r;
            }
            static private List<long> _fact = new List<long>();
            static private List<long> _ifact = new List<long>();
            static private void Build(int n)
            {
                if (n >= _fact.Count)
                    for (int i = _fact.Count; i <= n; ++i)
                        if (i == 0L) { _fact.Add(1); _ifact.Add(1); }
                        else { _fact.Add(Mod.Multi(_fact[i - 1], i)); _ifact.Add(Mod.Multi(_ifact[i - 1], Mod.Pow(i, _mod - 2))); }
            }
            static public long Comb(int n, int k)
            {
                Build(n);
                if (n == 0 && k == 0) return 1;
                if (n < k || n < 0) return 0;
                return Mod.Multi(Mod.Multi(_ifact[n - k], _ifact[k]), _fact[n]);
            }
        }
    }
}