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: Wrong Answer)

const MOD: u64 = 1_000_000_007;


fn gcd(a: u64, b: u64) -> u64 {
    let (mut a, mut b) = (a, b);
    while b != 0 {
        let tmp = a - (a / b) * b;
        a = b;
        b = tmp;
    }
    a
}


fn lcm(iterable: &Vec<u64>) -> u64 {
    let mut a = iterable[0];

    for b in iterable.iter() {
        a = (a * b) / gcd(a, *b);
    }
    a

}


fn main() {
    let _n: u64 = read();
    let an: Vec<u64> = read_vec();

    let lcm_an = lcm(&an);

    let mut ans: u64 = 0;
    for a in an.iter() {
        ans = (ans + lcm_an / a) % MOD;
    }

    println!("{}", ans);

}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}