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)

pub fn main() {
    use std::collections::HashMap;
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    let mut iter = input.split_whitespace().map(|w| w.parse().unwrap());
    let n: usize = iter.next().unwrap();
    let a: Vec<usize> = (0..n).map(|_| iter.next().unwrap()).collect();
    let b = *a.iter().max().unwrap() + 1;
    let divisors = {
        let mut divisors: Vec<usize> = (0..b).collect();
        let mut i = 2;
        while i * i < b {
            if divisors[i] == i {
                let mut j = i * i;
                while j < b {
                    divisors[j] = i;
                    j += i;
                }
            }
            i += 1;
        }
        divisors
    };
    let factors: Vec<HashMap<usize, u32>> = a
        .iter()
        .map(|&x| {
            let mut x = x;
            let mut map = HashMap::new();
            while x > 1 {
                let p = divisors[x];
                *map.entry(p).or_insert(0) += 1;
                x /= p;
            }
            map
        })
        .collect();
    let lcm_factors = {
        let mut map = HashMap::new();
        for i in 0..n {
            for (&p, &e) in &factors[i] {
                let k = map.entry(p).or_insert(0);
                *k = std::cmp::max(*k, e);
            }
        }
        map
    };
    const MODULO: usize = 1_000_000_007;
    let mut ans = 0;
    for i in 0..n {
        let mut b = 1;
        for (&p, &k) in &lcm_factors {
            let e = *factors[i].get(&p).unwrap_or(&0);
            b = (b * p.pow(k - e)) % MODULO;
        }
        ans = (ans + b) % MODULO;
    }
    println!("{}", ans);
}