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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
use std::collections::HashMap;

const MOD: i128 = 1000000007;

fn p_d(primes: &Vec<i128>, n: i128) -> (Vec<i128>, Vec<(i128, u32)>) {
    let mut ret = vec![];
    let mut tmp = n;
    for &p in primes.iter() {
        let mut cnt = 0;
        while tmp % p == 0 {
            tmp /= p;
            cnt += 1;
        }
        ret.push((p, cnt));
        if tmp == 1 {
            return (vec![], ret);
        }
    }
    let mut pt = 3;
    let mut np = vec![];
    while tmp != 1 && pt * pt <= n {
        if tmp % pt == 0 {
            let mut cnt = 0;
            while tmp % pt == 0 {
                tmp /= pt;
                cnt += 1;
            }
            np.push(pt);
            ret.push((pt, cnt));
        } else {
            pt += 2;
        }
    }

    if tmp != 1 {
        np.push(tmp);
        ret.push((tmp, 1));
    }

    return (np, ret);
}

fn modinv(aa: i128, m: i128) -> i128 {
    let mut a = aa;
    let mut b = m;
    let mut u = 1;
    let mut v = 0;
    while b != 0 {
        let t = a / b;
        a -= t * b;
        std::mem::swap(&mut a, &mut b);

        u -= t * v;
        std::mem::swap(&mut u, &mut v);
    }
    u %= m;
    if u < 0 {
        u += m;
    }
    u
}

fn main() {
    input!(n: usize, aa: [i128; n]);
    let mut lcmp = HashMap::new();
    let mut primes = vec![2, 3];
    for &a in aa.iter() {
        let (more, pp) = p_d(&primes, a);
        primes.append(&mut more.into_iter().collect());

        for (p, cnt) in pp {
            lcmp.entry(p)
                .and_modify(|e| {
                    if *e < cnt {
                        *e = cnt
                    }
                })
                .or_insert(cnt);
        }
    }
    let mut lcm = 1;
    for (p, cnt) in lcmp {
        lcm *= p.pow(cnt);
        lcm %= MOD;
    }
    let mut ans = 0;
    for &a in aa.iter() {
        let mi = modinv(a, MOD);
        let tmp = lcm * mi;
        ans += tmp;
        ans %= MOD;
    }
    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin5A4ADC42";
    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>";