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: Time Limit Exceeded)

use std::io;
use std::str::FromStr;
use std::collections::HashMap;

static MOD: u64 = 1_000_000_007;

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

fn input_vec() -> Vec<u64> {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.split_whitespace().map(|s| s.parse().unwrap()).collect()
}

fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
      a
    } else {
      gcd(b, a % b)
    }
}

fn binary_power(x: u64, n: u64) -> u64 {
    if n == 0 {
      return 1;
    }
    if n % 2 == 0 {
      return (binary_power(x, n / 2) % MOD).pow(2) % MOD;
    } else {
      return binary_power(x, n - 1) % MOD * x % MOD;
    }
}

fn prime_factors(n: u64) -> HashMap<u64, u64> {
  let limit = n;
  let mut n = n; 
  let mut prime_numbers: HashMap<u64, u64> = HashMap::new();
  let mut candidate = 2;
  while n > 1 {
      if candidate * candidate > limit {
          prime_numbers.insert(n, 1);
          return prime_numbers;
      }
      while n % candidate == 0 {
          let val = prime_numbers.entry(candidate).or_insert(0);
          *val += 1;
          n /= candidate;
      }
      candidate += 1;
  }
  return prime_numbers;
}

fn calc(lcm_factors: &HashMap<u64, u64>, target_factors: &HashMap<u64, u64>) -> u64 {
  let mut sum = 1;
  for (k, v) in lcm_factors {
    let n = target_factors.get(k).or(Some(&0)).unwrap();
    sum *= binary_power(*k, *v - n);
    sum %= MOD;
  }
  sum
}

fn main() {
    let n: usize = input();
    let a_vec = input_vec();
    let mut lcm_factors: HashMap<u64, u64> = HashMap::new();
    for a in &a_vec {
        for (k, v) in prime_factors(*a) {
          let n = lcm_factors.entry(k).or_insert(0);
          if *n < v {
             *n = v;
          }
        }
    }
    // println!("{:?}", lcm_factors);
    let mut sum = 0;
    for a in a_vec {
        let tmp = calc(&lcm_factors, &prime_factors(a));
        // println!("{}", tmp);
        sum += tmp;
        sum %= MOD;
    }
    println!("{}", sum);
}