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)

use std::str::FromStr;

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

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

fn gcd(mut x : u64, mut y : u64) -> u64 {
    while y != 0 {
        let tmp = y;
        y = x % y;
        x = tmp;
    }
    return x;
}

fn lcm(x : u64, y : u64) -> u64 {
    return (x / gcd(x,y)) * y
}

fn mod_pow(a : u64, b : u64, modd : u64) -> u64 {
    if b == 0 { return 1; }
    if b % 2 == 0 {
        let h = mod_pow(a, b/2, modd);
        return (h * h) % modd;
    }
    else {
        return (a * mod_pow(a, b-1, modd)) % modd;
    }
}

fn main() {
    let n : u64 = get_one();
    let v : Vec<u64> = get_vec();
    let mut v_lcm = 1;
    for vi in &v {
        v_lcm = lcm(*vi,v_lcm);
        v_lcm = v_lcm % 1000000007;
    }
    let mut ans = 0;
    //println!("{}", v_lcm);
    for vi in &v {
        let mut a = v_lcm * mod_pow(*vi, 1000000005,1000000007);
        a = a % 1000000007;
        ans += a;
        ans = ans % 1000000007
    }
    println!("{}", ans);
}