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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::char::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

#[allow(unused_macros)]
macro_rules! debug {($($a:expr),*) => {println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);}}
#[allow(unused_macros)]
macro_rules! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules! input_inner { ( $ next : expr ) => { } ; ( $ next : expr , ) => { } ; ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules! read_value { ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) } ; ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 } ; ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) } ; }

#[derive(PartialEq, PartialOrd)]
pub struct Total<T>(pub T);
impl<T: PartialEq> Eq for Total<T> {}
impl<T: PartialOrd> Ord for Total<T> { fn cmp(&self, other: &Total<T>) -> std::cmp::Ordering { self.0.partial_cmp(&other.0).unwrap() }}

#[allow(dead_code)]
const MAX:usize = 100006;
#[allow(dead_code)]
const INF_U32:u32 = 1 << 31;
#[allow(dead_code)]
const INF_I32:i32 = 1 << 30;
#[allow(dead_code)]
const INF_U64:u64 = 1 << 63;
#[allow(dead_code)]
const INF_I64:i64 = 1 << 62;
#[allow(dead_code)]
const MOD:i64 = 1e9 as i64 + 7;

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}


#[allow(unused_imports)]
use std::f64;

fn gcd(a:i64, b:i64) -> i64 {
    if b == 0 { return a; }
    gcd(b, a%b)
}

fn main() {
    input!{n:usize, a:[i64;n]};

    let mut ans = a[0];
    for i in 1..n {
        ans = gcd(ans, a[i]);
    }
    println!("{}", ans);

}