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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        n: usize,
        a: [u64; n]
    }
    let m = 1_000_000_007u64;

    let mut ap = Vec::new();
    for mut v in a {
        let mut vp = HashMap::new();
        for p in 2.. {
            if p * p > v {
                break;
            }
            let mut count = 0;
            while v % p == 0 {
                count += 1;
                v /= p;
            }
            if count > 0 {
                vp.insert(p, count);
            }
        }
        if v != 1 {
            vp.insert(v, 1);
        }
        ap.push(vp);
    }

    let mut lcm = HashMap::new();
    for vp in &ap {
        for (&p, &count) in vp.iter() {
            lcm.entry(p).and_modify(|c| *c = max(*c, count)).or_insert(count);
        }
    }

    let mut ans = 0;
    for vp in ap {
        let mut res = 1;
        for (&p, &count) in &lcm {
            let sub = *vp.get(&p).unwrap_or(&0);
            for _ in 0..count - sub {
                res *= p;
                res %= m;
            }
        }
        ans += res;
        ans %= m;
    }

    println!("{}", ans);
}