Problem:
Score : 300 points

Problem Statement

We have N clocks. The hand of the i-th clock (1≤i≤N) rotates through 360° in exactly T_i seconds.

Initially, the hand of every clock stands still, pointing directly upward.

Now, Dolphin starts all the clocks simultaneously.

In how many seconds will the hand of every clock point directly upward again?

Constraints

1≤N≤100

1≤T_i≤10^{18}

All input values are integers.

The correct answer is at most 10^{18} seconds.

Input

Input is given from Standard Input in the following format:

N
T_1
:
T_N

Output

Print the number of seconds after which the hand of every clock point directly upward again.

Sample Input 1

2
2
3

Sample Output 1

6

We have two clocks. The time when the hand of each clock points upward is as follows:

Clock 1: 2, 4, 6, ... seconds after the beginning

Clock 2: 3, 6, 9, ... seconds after the beginning

Therefore, it takes 6 seconds until the hands of both clocks point directly upward.

Sample Input 2

5
2
5
10
1000000000000000000
1000000000000000000

Sample Output 2

1000000000000000000

Solution in Rust (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules ! zero_one_impls {($ ({$ Trait : ident $ method : ident $ ($ t : ty ) *, $ e : expr } ) * ) => {$ ($ (impl $ Trait for $ t {# [inline ] fn $ method () -> Self {$ e } } ) * ) * } ; }
zero_one_impls ! ({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 0 } {Zero zero f32 f64 , 0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 1 } {One one f32 f64 , 1. } );
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn new(s: &'a str) -> Self {
            let iter = s.split_ascii_whitespace();
            Self { iter }
        }
        #[inline]
        pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
            <T as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    macro_rules ! iter_scan_impls {($ ($ t : ty ) * ) => {$ (impl IterScan for $ t {type Output = Self ; # [inline ] fn scan <'a , I : Iterator < Item = &'a str >> (iter : & mut I ) -> Option < Self > {iter . next () ?. parse ::<$ t > () . ok () } } ) * } ; }
    iter_scan_impls ! (char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String );
    macro_rules ! iter_scan_tuple_impl {($ ($ T : ident ) * ) => {impl <$ ($ T : IterScan ) ,*> IterScan for ($ ($ T , ) * ) {type Output = ($ (<$ T as IterScan >:: Output , ) * ) ; # [inline ] fn scan <'a , It : Iterator < Item = &'a str >> (_iter : & mut It ) -> Option < Self :: Output > {Some (($ (<$ T as IterScan >:: scan (_iter ) ?, ) * ) ) } } } ; }
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl ! (A B );
    iter_scan_tuple_impl ! (A B C );
    iter_scan_tuple_impl ! (A B C D );
    iter_scan_tuple_impl ! (A B C D E );
    iter_scan_tuple_impl ! (A B C D E F );
    iter_scan_tuple_impl ! (A B C D E F G );
    iter_scan_tuple_impl ! (A B C D E F G H );
    iter_scan_tuple_impl ! (A B C D E F G H I );
    iter_scan_tuple_impl ! (A B C D E F G H I J );
    iter_scan_tuple_impl ! (A B C D E F G H I J K );
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(pub char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[macro_export]
macro_rules ! min {($ e : expr ) => {$ e } ; ($ e : expr , $ ($ es : expr ) ,+ ) => {std :: cmp :: min ($ e , min ! ($ ($ es ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! chmin {($ dst : expr , $ ($ src : expr ) ,+ ) => {{let x = std :: cmp :: min ($ dst , min ! ($ ($ src ) ,+ ) ) ; $ dst = x ; } } ; }
#[macro_export]
macro_rules ! max {($ e : expr ) => {$ e } ; ($ e : expr , $ ($ es : expr ) ,+ ) => {std :: cmp :: max ($ e , max ! ($ ($ es ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! chmax {($ dst : expr , $ ($ src : expr ) ,+ ) => {{let x = std :: cmp :: max ($ dst , max ! ($ ($ src ) ,+ ) ) ; $ dst = x ; } } ; }
fn main() {
    #![allow(unused_imports, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut _in_buf = Vec::new();
    stdin().read_to_end(&mut _in_buf).expect("io error");
    let _in_buf = unsafe { String::from_utf8_unchecked(_in_buf) };
    let mut scanner = Scanner::new(&_in_buf);
    macro_rules ! scan {() => {scan ! (usize ) } ; (($ ($ t : tt ) ,* ) ) => {($ (scan ! ($ t ) ) ,* ) } ; ([$ t : tt ; $ len : expr ] ) => {(0 ..$ len ) . map (| _ | scan ! ($ t ) ) . collect ::< Vec < _ >> () } ; ([$ t : ty ; $ len : expr ] ) => {scanner . scan_vec ::<$ t > ($ len ) } ; ([$ t : ty ] ) => {scanner . iter ::<$ t > () } ; ({$ e : expr } ) => {scanner . mscan ($ e ) } ; ($ t : ty ) => {scanner . scan ::<$ t > () } ; }
    let _out = stdout();
    let mut _out = BufWriter::new(_out.lock());
    macro_rules ! print {($ ($ arg : tt ) * ) => (:: std :: write ! (_out , $ ($ arg ) * ) . expect ("io error" ) ) }
    macro_rules ! println {($ ($ arg : tt ) * ) => (:: std :: writeln ! (_out , $ ($ arg ) * ) . expect ("io error" ) ) }
    macro_rules! echo {
        ($ iter : expr ) => {
            echo!($iter, '\n')
        };
        ($ iter : expr , $ sep : expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!();
    let t = scan!([u64; n]);
    let ans = t.iter().fold(1, |x, y| lcm(x, *y));
    println!("{}", ans);
}
pub fn lcm(a: u64, b: u64) -> u64 {
    a / gcd_binary(a, b) * b
}
pub fn gcd_binary(mut a: u64, mut b: u64) -> u64 {
    if a == 0 {
        return b;
    }
    if b == 0 {
        return a;
    }
    let u = a.trailing_zeros();
    let v = b.trailing_zeros();
    a >>= u;
    b >>= v;
    let k = std::cmp::min(u, v);
    while a != b {
        if a < b {
            std::mem::swap(&mut a, &mut b);
        }
        a -= b;
        a >>= a.trailing_zeros();
    }
    a << k
}