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 competitive::prelude::*;
#[modtype::use_modtype]
type F = modtype::F<1_000_000_007u64>;

// 素因数分解O(√n)
fn prime_factor(mut n: u64) -> BTreeMap<u64, u32> {
    dbg!(n);
    let mut res = BTreeMap::<u64, u32>::new();
    let mut i = 2;
    while i * i <= n {
        while n % i == 0 {
            let count = res.entry(i).or_insert(0);
            *count += 1;
            n /= i;
        }
        i += 1;
    }
    if n != 1 {
        let count = res.entry(n).or_insert(0);
        *count = 1;
    }
    res
}

fn marge(mut x: BTreeMap<u64, u32>, y: BTreeMap<u64, u32>) -> BTreeMap<u64, u32> {
    for (k, v) in y {
        let count = x.entry(k).or_insert(0);
        *count = max(*count, v);
    }
    x
}

#[proconio::fastout]
fn main() {
    input! {
        n: usize,
        a: [u64; n],
    }
    let mut x = BTreeMap::<u64, u32>::new();
    for i in 0..n {
        let y = prime_factor(a[i]);
        x = marge(x, y);
    }
    let mut lcm = F(1);
    for (k, v) in x {
        for _ in 0..v {
            lcm *= F(k);
        }
    }
    let mut ans = F(0);
    for i in 0..n {
        ans += lcm / F(a[i]);
    }
    echo!(ans);
}
*/

fn main() {
    let exe = "/tmp/bin2384F682";
    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>";