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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;


public class Main {

    public static String Y = "Yes";
    public static String N = "No";
    public static long MOD = (long) (Math.pow(10, 9) + 7);
    public static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {

        int n = ni();
        //long[] a = new long[n];

        long ans = nl();
        for (int i = 1; i < n; i++) {
            ans = gcd(ans, nl());
        }

        out(ans);

    }

    /*
     * 以下メソッド集
     */
    static char[][] same(char[][] c, int h, int w) {

        char[][] a = new char[h][w];
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                a[i][j] = c[i][j];
            }
        }
        return a;

    }

    static int countkuro(char[][] c) {

        int count = 0;
        for (char[] cc : c) {
            for (char ccc : cc) {
                if ('#' == ccc) {
                    count++;
                }
            }
        }
        return count;
    }

    static double[] sort(double[] r) {

        Arrays.sort(r);
        return r;
    }

    static void debug() {

        out("---");
    }

    static void debug(long a) {

        out("-------");
        out(a);
        out("-------");
    }

    static void debug(double a) {

        out("-------");
        out(a);
        out("-------");
    }

    static void debug(String a) {

        out("-------");
        out(a);
        out("-------");
    }

    static long[] sort(long[] n) {

        Arrays.sort(n);
        return n;
    }

    static int ketasuu(int n) {

        String str = "" + n;
        return str.length();
    }

    static int account(String str) {

        String target = "AC";
        int count = 0;
        int len = str.length();
        for (int i = 0; i < len - 1; i++) {
            if (target.equals(str.substring(i, i + target.length()))) {
                count++;
            }
        }
        return count;
    }

    static int ni() {

        return sc.nextInt();
    }

    static long nl() {

        return sc.nextLong();
    }

    static double nd() {

        return sc.nextDouble();
    }

    static String n() {

        return sc.next();
    }

    static char[] nc() {

        return sc.next().toCharArray();
    }

    static int kaijo(int n) {

        if (n == 0 || n == 1) {
            return 1;
        } else {
            return n * kaijo(n - 1);
        }
    }

    static int fib(int n) {

        return (n == 1 || n == 0) ? n : fib(n - 2) + fib(n - 1);
    }

    static long lcm(long m, long n) {

        return m * n / gcd(m, n);
    }

    static int lcm(int m, int n) {

        return m * n / gcd(m, n);
    }

    static long gcd(long a, long b) {

        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcd(int a, int b) {

        return (b == 0) ? a : gcd(b, a % b);
    }

    static void out(String info) {

        System.out.println(info);
    }

    static void out(int info) {

        System.out.println(info);
    }

    static void out(double info) {

        System.out.println(info);
    }

    static void out(long info) {

        System.out.println(info);
    }

    static void out(char info) {

        System.out.println(info);
    }

    static void out(Object obj) {

        System.out.println(obj.toString());
    }

    static void outn(String info) {

        System.out.print(info);
    }

    static void outn(int info) {

        System.out.print(info);
    }

    static void outn(double info) {

        System.out.print(info);
    }

    static void outn(long info) {

        System.out.print(info);
    }

    static void outn(char info) {

        System.out.print(info);
    }

    static double max(double d, double e) {

        return Math.max(d, e);
    }

    static long max(long a, long b) {

        return Math.max(a, b);
    }

    static long min(long d, long e) {

        return Math.min(d, e);
    }

    static int min(int a, int b) {

        return Math.min(a, b);
    }
}


class XY {

    int h;
    int c;

    XY(int h, int c) {
        this.h = h;
        this.c = c;
    }
}