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)

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 factors: Vec<HashMap<usize, u32>> = a
        .iter()
        .map(|&x| {
            let mut map = HashMap::new();
            let mut x = x;
            let mut i = 2;
            while i * i <= x {
                if x % i == 0 {
                    *map.entry(i).or_insert(0) += 1;
                    x /= i;
                } else {
                    i += 1;
                }
            }
            if x > 0 {
                *map.entry(x).or_insert(0) += 1;
            }
            map
        })
        .collect();
    let mut lcm_factors: HashMap<usize, u32> = HashMap::new();
    for i in 0..n {
        for (&p, &e) in &factors[i] {
            let max_e = lcm_factors.entry(p).or_insert(0);
            *max_e = std::cmp::max(*max_e, e);
        }
    }
    const MODULO: usize = 1_000_000_007;
    let mut lcm = 1;
    for (&p, &e) in &lcm_factors {
        lcm = (lcm * p.pow(e)) % MODULO;
    }
    let mut ans = 0;
    for i in 0..n {
        let mut b = lcm;
        let mut base = a[i];
        let mut exponent = MODULO - 2;
        while exponent != 0 {
            if exponent & 1 == 1 {
                b = b * base % MODULO;
            }
            base = base * base % MODULO;
            exponent >>= 1;
        }
        ans = (ans + b) % MODULO;
    }
    println!("{}", ans);
}