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)

pub trait FromFragments {
    #[doc = " Output type."]
    #[doc = ""]
    #[doc = " In almost all cases, `Output` should be `Self`."]
    #[doc = " This type field exists for implementing 1-origin to 0-origin conversion"]
    #[doc = " by `usize_` etc."]
    type Output;
    #[doc = " Returns how many words are read."]
    fn fragments_count() -> usize;
    #[doc = " Converts words into `Output`s."]
    #[doc = ""]
    #[doc = " If the conversion fails, returns `Err` with error message."]
    #[doc = ""]
    #[doc = " # Panics"]
    #[doc = ""]
    #[doc = " If `fragments.len()` differs from `fragments_count()`,"]
    #[doc = " the method may panic."]
    fn from_fragments(fragments: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $ t : ty , |$ fragments : ident | $ from_fragments : expr ) => {
        readable!($t, 1, |$fragments| $from_fragments);
    };
    ( $ t : ty , $ fragments_count : expr , |$ fragments : ident | $ from_fragments : expr ) => {
        impl FromFragments for $t {
            type Output = $t;
            fn fragments_count() -> usize {
                $fragments_count
            }
            fn from_fragments($fragments: &[&str]) -> Result<$t, String> {
                Ok($from_fragments)
            }
        }
    };
}
readable!((), |_ss| ());
readable!(String, |ss| ss[0].to_string());
macro_rules ! impl_from_fragments { ( $ ( $ t : ty ) * ) => { $ ( impl FromFragments for $ t { type Output = Self ; fn fragments_count ( ) -> usize { 1 } fn from_fragments ( fragments : & [ & str ] ) -> Result <$ t , String > { use std :: str :: FromStr ; <$ t >:: from_str ( fragments [ 0 ] ) . map_err ( | _ | { format ! ( "cannot parse \"{}\" as {}" , fragments [ 0 ] , stringify ! ( $ t ) ) } ) } } ) * } ; }
impl_from_fragments ! ( i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64 ) ;
macro_rules ! define_one_origin_int_types { ( $ new_t : ident $ int_t : ty ) => { # [ doc = " Convert 1-origin integer into 0-origin when read from input." ] # [ allow ( non_camel_case_types ) ] pub struct $ new_t ( ) ; impl FromFragments for $ new_t { type Output = $ int_t ; fn fragments_count ( ) -> usize { 1 } fn from_fragments ( fragments : & [ & str ] ) -> Result < Self :: Output , String > { <$ int_t >:: from_fragments ( fragments ) . map ( | n | n - 1 ) } } } ; ( $ new_t : ident $ int_t : ty ; $ ( $ inner_new_t : ident $ inner_int_t : ty ) ;* ) => { define_one_origin_int_types ! ( $ new_t $ int_t ) ; define_one_origin_int_types ! ( $ ( $ inner_new_t $ inner_int_t ) ;* ) ; } ; }
define_one_origin_int_types ! ( u64_ u64 ; usize_ usize ) ;
macro_rules ! impl_from_fragments_for_tuples { ( $ t : ident $ var : ident $ count : expr ) => ( ) ; ( $ t : ident $ var : ident $ count : expr ; $ ( $ inner_t : ident $ inner_var : ident $ inner_count : expr ) ;* ) => { impl_from_fragments_for_tuples ! ( $ ( $ inner_t $ inner_var $ inner_count ) ;* ) ; impl <$ t : FromFragments , $ ( $ inner_t : FromFragments ) ,*> FromFragments for ( $ t , $ ( $ inner_t ) ,* ) { type Output = ( <$ t >:: Output , $ ( <$ inner_t >:: Output ) ,* ) ; fn fragments_count ( ) -> usize { let mut n = <$ t >:: fragments_count ( ) ; $ ( n += <$ inner_t >:: fragments_count ( ) ; ) * n } # [ allow ( unused_assignments ) ] fn from_fragments ( fragments : & [ & str ] ) -> Result < Self :: Output , String > { let mut start = 0 ; let $ var = <$ t >:: from_fragments ( & fragments [ start .. start +<$ t >:: fragments_count ( ) ] ) ?; start += <$ t >:: fragments_count ( ) ; $ ( let $ inner_var = <$ inner_t >:: from_fragments ( & fragments [ start .. start +<$ inner_t >:: fragments_count ( ) ] ) ?; start += <$ inner_t >:: fragments_count ( ) ; ) * Ok ( ( $ var , $ ( $ inner_var ) ,* ) ) } } } ; }
impl_from_fragments_for_tuples ! ( T4 x4 4 ; T3 x3 3 ; T2 x2 2 ; T1 x1 1 ) ;
pub trait FromLine: Sized {
    type Output;
    fn from_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_fragments(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: FromFragments> FromLine for T {
    type Output = T::Output;
    fn from_line(line: &str) -> Result<T::Output, String> {
        let fragments = split_into_fragments(line);
        if fragments.len() != T::fragments_count() {
            return Err(format!(
                "line \"{}\" has {} fragments, expected {}",
                line,
                fragments.len(),
                T::fragments_count()
            ));
        }
        T::from_fragments(&fragments)
    }
}
impl<T: FromFragments> FromLine for Vec<T> {
    type Output = Vec<T::Output>;
    fn from_line(line: &str) -> Result<Self::Output, String> {
        let n = T::fragments_count();
        let fragments = split_into_fragments(line);
        if fragments.len() % n != 0 {
            return Err(format!(
                "line \"{}\" has {} fragments, expected multiple of {}",
                line,
                fragments.len(),
                n
            ));
        }
        let mut result = Vec::new();
        for chunk in fragments.chunks(n) {
            match T::from_fragments(chunk) {
                Ok(v) => result.push(v),
                Err(msg) => {
                    let flagment_msg = if n == 1 {
                        format!("fragment {}", result.len())
                    } else {
                        let l = result.len();
                        format!("fragments {}-{}", n * l + 1, (n + 1) * l)
                    };
                    return Err(format!("{} of line \"{}\": {}", flagment_msg, line, msg));
                }
            }
        }
        Ok(result)
    }
}
pub fn read<T: FromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::from_line(&line).unwrap()
}
#[macro_export]
macro_rules ! read { ( ) => { let mut line = String :: new ( ) ; std :: io :: stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; } ; ( $ pat : pat = $ t : ty ) => { let $ pat = read ::<$ t > ( ) ; } ; ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { read ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ) ; } ; }
#[macro_export]
macro_rules ! readls { ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { $ ( read ! ( $ pat = $ t ) ; ) * } ; }
pub fn readx<T: FromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin
        .lock()
        .lines()
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::from_line(&line).unwrap()
        }).collect();
    result
}
#[macro_export]
macro_rules ! readx_loop { ( $ pat : pat = $ t : ty ; $ block : block ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; for line in stdin . lock ( ) . lines ( ) { let line = line . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; $ block } } ; ( $ ( $ pat : pat = $ t : ty ) ,* ; $ block : block ) => { readx_loop ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ; $ block ) ; } ; }
#[macro_export]
macro_rules ! readn_loop { ( $ n : expr ; $ pat : pat = $ t : ty ; $ block : block ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; { let lock = stdin . lock ( ) ; for _ in 0 ..$ n { let line = String :: new ( ) ; lock . read_line ( & mut line ) . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; $ block } } } ; ( $ n : expr ; $ ( $ pat : pat = $ t : ty ) ,* ; $ block : block ) => { read_times_loop ! ( $ n ; ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ; $ block ) ; } ; }
pub trait ReadExt {
    fn read<T: FromFragments>(&self) -> T::Output;
}
impl<'a> ReadExt for [&'a str] {
    fn read<T: FromFragments>(&self) -> T::Output {
        T::from_fragments(self).unwrap()
    }
}
impl<'a> ReadExt for &'a str {
    fn read<T: FromFragments>(&self) -> T::Output {
        T::from_fragments(&[self]).unwrap()
    }
}

fn gcd(a: u32, b: u32) -> u32 {
    if b == 0 { a } else { gcd(b, a%b) }
}

fn main() {
    read!();
    read!(aa = Vec<u32>);
    println!("{}", aa.into_iter().fold(0, gcd));
}