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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {
	static PrintWriter out;

	static HashMap<Integer, Integer> happyC;
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);

		int n = sc.nextInt();
		boolean eq = true;
		int f = sc.nextInt();
		boolean odd = false;
		int temp = 0;
		if(f%2 !=0)
			odd = true;
		
		for (int i = 1; i < n; i++) {
			int curr = sc.nextInt();
			temp = curr;
			if(curr%2 != 0)
				odd = true;
			
			if(eq) {
				if(curr != f)
					eq = false;
			}
			f = curr;
		}
		if(eq)
			out.println(temp);
		else {
			if(odd)
				out.println(1);
			else
				out.println(2);
		}
	
		out.flush();	
	}
	
}
	
class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream system) {
		br = new BufferedReader(new InputStreamReader(system));
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public char nextChar() throws IOException {
		return next().charAt(0);
	}

	public Long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	public boolean ready() throws IOException {
		return br.ready();
	}

	public void waitForInput() throws InterruptedException {
		Thread.sleep(3000);
	}

}