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: Accepted)

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
struct ModInt {
    value: usize,
}
impl ModInt {
    fn new(value: usize) -> Self {
        ModInt {
            value: value % Self::modulo(),
        }
    }
    fn value(&self) -> usize {
        self.value
    }
    fn modulo() -> usize {
        1_000_000_007
    }
}
impl From<usize> for ModInt {
    fn from(value: usize) -> Self {
        ModInt { value: value }
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        let mut value = self.value + other.value;
        if value > Self::modulo() {
            value -= Self::modulo();
        }
        ModInt { value: value }
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, other: Self) -> Self {
        let mut value = self.value;
        if value < other.value {
            value += Self::modulo();
        }
        value -= other.value;
        ModInt { value: value }
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, other: Self) -> Self {
        let value = self.value * other.value % Self::modulo();
        ModInt { value: value }
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, other: Self) -> Self {
        let mut exp = Self::modulo() - 2;
        let mut value = self.value;
        let mut ovalue = other.value;
        while exp > 0 {
            if exp % 2 == 1 {
                value = value * ovalue % Self::modulo();
            }
            ovalue = ovalue * ovalue % Self::modulo();
            exp /= 2;
        }
        ModInt { value: value }
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, other: Self) {
        *self = *self + other;
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, other: Self) {
        *self = *self - other;
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, other: Self) {
        *self = *self * other;
    }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, other: Self) {
        *self = *self / other;
    }
}
impl std::fmt::Debug for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.value)
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.value)
    }
}

fn prime_fact(m: usize) -> BTreeMap<usize, usize> {
#[doc = "O(sqrt(m))"]
    let mut m = m;
    let mx = (m as f64).sqrt() as usize;
    let mut map = BTreeMap::new();
    for i in 2..mx + 1 {
        while m % i == 0 {
            m /= i;
            *map.entry(i).or_insert(0) += 1;
        }
    }
    if m > 1 {
        map.insert(m, 1);
    }
    map
}

fn solve() {
    let n = get!(usize);
    let a = get!([usize]);

    let mut map = BTreeMap::new();
    for &e in &a {
        let em = prime_fact(e);
        for (k,v) in em {
            let entry = map.entry(k).or_insert(0);
            *entry = max!(*entry, v);
        }
    }

    let mut l = ModInt::new(1);
    for (k,v) in map {
        for i in 0..v {
            l *= ModInt::new(k);
        }
    }
    let mut sum = ModInt::new(0);
    for e in a {
        sum += l/ModInt::new(e);
    }
    println!("{}", sum);
}