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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.math.*;
import java.util.*;
import java.util.function.*;
 
public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    List<BigInteger> A = new ArrayList<>(N);
    for (int i = 0; i < N; i++) A.add(BigInteger.valueOf(sc.nextInt()));
    sc.close();

    BigInteger lcm = A.stream().parallel()
        .reduce(BigInteger.ONE, (a, b) -> a.divide(a.gcd(b)).multiply(b));

    BigInteger ans = A.stream().parallel()
      .map(a -> lcm.divide(a))
      .reduce(BigInteger.ZERO, (a, b) -> a.add(b));

    BigInteger mod = BigInteger.valueOf(1000000007);
    System.out.println(ans.mod(mod));
  }
}