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_mut, unused_macros, unused_variables, unused_assignments, non_snake_case, unused_imports, dead_code, non_camel_case_types)]

use std::collections::{HashMap, BinaryHeap, BTreeMap};

// [Rustで競技プログラミングの入力をスッキリ記述するマクロ - Qiita]
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 から拝借
macro_rules! input {
    ($($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)*}
    };
}
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)*}
    };
}
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    // ABC128-C-Switches用に拡張
    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, $t);
        (0..len).map(|_| read_value!($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")
    };
}

// 可愛い可愛い、手塩にかけたライブラリ達
// 出力
macro_rules! p {
    ($t:expr) => {
        println!("{}", $t);
    };
}
macro_rules! debug {
    ($t:expr) => {
        println!("{:?}", $t);
    };
}
// 最大公約数 / 最小公倍数
fn gcd(a:isize, b:isize) -> isize {
    if b == 0 {return a};
    gcd(b, a % b)
}
fn lcm(a:isize, b:isize) -> isize {
    a / gcd(a, b) * b
}
// 置換
macro_rules! chmax {
    ($x:expr, $y:expr) => {
        if $x < $y {$x = $y;}
    }
}
macro_rules! chmin {
    ($x:expr, $y:expr) => {
        if $x > $y {$x = $y;}
    }
}
// Union-Find木
struct uft {
    g: Vec<isize>,
}
impl uft {
    fn new(n:usize) -> uft {
        uft {g:vec![-1; n]}
    }
    fn root(&mut self, a:usize) -> usize {
        let va = self.g[a];
        if va.is_negative() {a}
        else {
            let na = self.root(va as usize);
            self.g[a] = na as isize;
            na
        }
    }
    fn merge(&mut self, a:usize, b:usize) -> bool {
        let (na, nb) = (self.root(a), self.root(b));
        if na == nb {return false;}
        self.g[na] += self.g[nb];
        self.g[nb] = na as isize;
        true
    }
    fn size(&mut self, a:usize) -> usize {
        let na = self.root(a);
        (self.g[na] * -1) as usize
    }
}
// グラフ(深さ優先探索DFS/幅優先探索BFS)

// 検索(二分探索：右)
macro_rules! bsr {
    ($g:expr, $v:expr) => {
        bsr($g, $v, 0, $g.len() - 1)
    }
}
fn bsr(g:&[isize], v:isize, lo:usize, hi:usize) -> usize {
    if hi < lo {return lo;}
    let mi = (hi + lo) / 2;
    if g[mi] < v {
        return bsr(&g, v, mi + 1, hi);
    } else {
        return bsr(&g, v, lo, mi - 1);
    }
}

// エントリーポイント
fn main() {
    input! {
        N : usize,
        A : [isize; N]
    }
    let mut hp = A[0];
    for n in 1..N {
        hp = gcd(hp, A[n]);
    }
    p!(hp);
}