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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

use kyopro_lib::modint;
struct F;
impl modint::Modulation for F {
    const MOD: u64 = 1_000_000_000 + 7;
}
type Mint = modint::ModInt<F>;

fn main() {
    input! {
        n : usize,
        a : [u64; n]
    }

    let sieve = kyopro_lib::sieve::Sieve::new(*a.iter().max().unwrap());
    let mut fac = a
        .iter()
        .map(|x| sieve.factorization(*x).v)
        .collect::<Vec<_>>();

    let mut lcm = std::collections::BTreeMap::new();
    for f in &fac {
        for (p, n) in f {
            let r = lcm.entry(*p).or_insert(0);
            *r = std::cmp::max(*r, *n);
        }
    }
    // println!("{:?}", lcm);

    let mut res = Mint::new(0);
    for f in &mut fac {
        f.reverse();
        let mut r = Mint::new(1);
        for (p, n) in &lcm {
            let mut m = 0;
            if !f.is_empty() && f[f.len() - 1].0 == *p {
                m = f[f.len() - 1].1;
                f.pop();
            }
            r *= Mint::new(*p).pow((*n - m) as u64);
        }
        res += r;
    }
    println!("{}", res.val());
}
*/

fn main() {
    let exe = "/tmp/bin9D36CCF9";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";