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

    let mut lcm_int = 1;
    for (&p, &count) in &lcm_map {
        for _ in 0..count {
            lcm_int *= p;
            lcm_int %= m;
        }
    }

    let mut ans = 0;
    for vp in ap {
        let mut res = lcm_int;
        for (&p, &count) in &vp {
            for _ in 0..count {
                res *= mod_inverse(p, m);
                res %= m;
            }
        }
        ans += res;
        ans %= m;
    }
    println!("{}", ans);
}
#[allow(dead_code)]
pub fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
#[allow(dead_code)]
/// (gcd, x, y)
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b == 0 {
        (a, 1, 0)
    } else {
        let (gcd, x, y) = extgcd(b, a % b);
        (gcd, y, x - (a / b) * y)
    }
}
#[allow(dead_code)]
pub fn mod_inverse(a: u64, m: u64) -> u64 {
    let (_, x, _) = extgcd(a as i64, m as i64);
    ((m as i64 + x) as u64 % m) % m
}