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::vec::Vec;
use std::collections::HashMap;


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

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

const MOD: usize = 1_000_000_000 + 7;
fn main() {
    let n: usize = read();
    let a: Vec<usize> = read_vec();
    let mut map = HashMap::new();
    for &x in &a {
      let h = trial_division(x);
      for (key, val) in h.into_iter() {
        match map.get(&key) {
           Some(&v)  => {map.insert(key, if val > v { val } else { v });} ,
            _  => {map.insert(key, val);},
        }
      }
    }
    let mut p: usize = 1;
    for (key, val) in map.into_iter() {
      p *= key.pow(val as u32);
    }
    let mut ans = 0;
    for i in 0..n {
      ans += p / a[i];
      ans %= MOD;
    }
    println!("{}", ans);
}


// 試し割り
// O(√N)
fn trial_division(n :usize) -> HashMap<usize, usize>{
    let mut primes = HashMap::new();
    let mut i = 2;
    let mut n = n;

    //  n を root n 以下の整数で割り切れるまで割っていく
    while i * i <= n {
        while n % i == 0 {
            n /= i;
            // match primes.get_mut(&i) {
            //   None => { primes.insert(i, 1); },
            //   Some(x) => {
            //       *x += 1;
            //   },
            // }

            match primes.get(&i) {
              Some(&val) => {
                primes.insert(i, val + 1);
              },
              _  => { primes.insert(i, 1); },
            }
        }
        i+=1;
    }

    // 最後にnが素数になっている場合はそれ自身も素因数に含めて終了
    // match primes.get_mut(&n) {
    //   None => { primes.insert(n, 1); },
    //   Some(x) => {
    //     *x += 1;
    //   },
    // }

     match primes.get(&n) {
          Some(&val) => {
            primes.insert(n, val + 1);
          },
          _  => { primes.insert(n, 1); },
      }

    primes
}