Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::str::FromStr;
use std::io::*;
use std::collections::*;
use std::cmp::*;
use std::ops::*;

struct Scanner<I: Iterator<Item = char>> {
    iter: std::iter::Peekable<I>,
}

macro_rules! exit {
    () => {{
        exit!(0)
    }};
    ($code:expr) => {{
        if cfg!(local) {
            writeln!(std::io::stderr(), "===== Terminated =====")
                .expect("failed printing to stderr");
        }
        std::process::exit($code);
    }}
}

impl<I: Iterator<Item = char>> Scanner<I> {
    pub fn new(iter: I) -> Scanner<I> {
        Scanner {
            iter: iter.peekable(),
        }
    }

    pub fn safe_get_token(&mut self) -> Option<String> {
        let token = self.iter
            .by_ref()
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            Some(token)
        }
    }

    pub fn token(&mut self) -> String {
        self.safe_get_token().unwrap_or_else(|| exit!())
    }

    pub fn get<T: FromStr>(&mut self) -> T {
        self.token().parse::<T>().unwrap_or_else(|_| exit!())
    }

    pub fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.get()).collect()
    }

    pub fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }

    pub fn char(&mut self) -> char {
        self.iter.next().unwrap_or_else(|| exit!())
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.get::<String>().chars().collect()
    }

    pub fn mat_chars(&mut self, row: usize) -> Vec<Vec<char>> {
        (0..row).map(|_| self.chars()).collect()
    }

    pub fn line(&mut self) -> String {
        if self.peek().is_some() {
            self.iter
                .by_ref()
                .take_while(|&c| !(c == '\n' || c == '\r'))
                .collect::<String>()
        } else {
            exit!();
        }
    }

    pub fn peek(&mut self) -> Option<&char> {
        self.iter.peek()
    }
}

use std::ops::*;
use std::fmt;

#[derive(Copy, Clone, PartialEq, Debug)]
struct ModInt(usize);

const MOD: usize = 1000000007;
impl ModInt {
    fn pow(self, power: usize) -> Self {
        if power == 0 {
            return ModInt(1);
        }
        if power % 2 == 0 {
            let t = self.pow(power/2);
            return t * t;
        }
        self * self.pow(power-1)
    }

    fn inv(self) -> Self {
        self.pow(MOD - 2)
    }
}

impl Add for ModInt {
    type Output = Self;

    fn add(self, rhs: Self) -> Self {
        let mut tmp = self;
        tmp.0 += rhs.0;
        if tmp.0 >= MOD {
            tmp.0 -= MOD;
        }
        tmp
    }
}

impl AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl Sub for ModInt {
    type Output = Self;

    fn sub(self, rhs: Self) -> Self {
        let mut ret = self;
        if ret.0 < rhs.0 {
            ret.0 += MOD;
        }
        ret.0 -= rhs.0;
        ret
    }
}

impl SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl Mul for ModInt {
    type Output = Self;

    fn mul(self, rhs: ModInt) -> Self {
        let mut ret = self;
        ret.0 *= rhs.0;
        ret.0 %= MOD;
        ret
    }
}

impl MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: ModInt) -> Self {
        let mut ret = self;
        ret.0 *= rhs.inv().0;
        ret.0 %= MOD;
        ret
    }
}

impl DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl fmt::Display for ModInt {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "{}", self.0)
    }
}

fn gcd<T>(v1: T, v2: T) -> T
where
    T: Rem<Output=T>
     + Copy
     + Default
     + PartialEq    
{
    let zero = T::default();
    match (v1, v2) {
        (v1, v2) if v2 == zero => v1,
        (v1, v2) => gcd(v2, v1 % v2)
    }
}

fn lcm<T>(v1: T, v2: T) -> T
where
    T: Rem<Output=T>
     + Mul<Output=T>
     + Div<Output=T>
     + Copy
     + Default
     + PartialEq
{
    v1 * v2 / gcd(v1, v2)
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin.bytes().map(|c| c.unwrap() as char));
    let N: usize = sc.get();
    let A: Vec<usize> = sc.vec(N);
    let mut l = HashMap::new();
    l.insert(1, 1);
    for i in 0..N {
        let mut rem = A[i];
        let mut p = HashMap::new();
        for j in (2..).take_while(|k| k * k <= A[i]) {
            while rem % j == 0 {
                let e = p.entry(j).or_insert(0usize);
                *e += 1;
                rem /= j;
            }
        }
        if rem != 1 {
            let e = p.entry(rem).or_insert(0usize);
            *e += 1;
        }
        for (k, v) in p {
            let e = l.entry(k).or_insert(0);
            *e = max(*e, v);
        }
    }
    let mut ans = ModInt(0);
    for i in 0..N {
        let mut rem = A[i];
        let mut p = HashMap::new();
        for j in (2..).take_while(|k| k * k <= A[i]) {
            while rem % j == 0 {
                let e = p.entry(j).or_insert(0usize);
                *e += 1;
                rem /= j;
            }
        }
        if rem != 1 {
            let e = p.entry(rem).or_insert(0usize);
            *e += 1;
        }
        let mut B = ModInt(1);
        for (&k, &v) in &l {
            if let Some(e) = p.get(&k) {
                B *= ModInt(k).pow(v - e);
            } else {
                B *= ModInt(k).pow(v);
            }
        }
        ans += B;
    }
    println!("{}", ans);
}