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.BigInteger;

public class Main {
	BigInteger n;
	BigInteger a[];

	Main(BigInteger a[]) {
		this.a = a;
	}

	public static void main(String[] args) {
		java.util.Scanner s = new java.util.Scanner(System.in);
		int n = s.nextInt();
		BigInteger a[] = new BigInteger[n];
		for (int i = 0; i < n; i++) {
			a[i] = BigInteger.valueOf(s.nextInt());
		}

		System.out.println(new Main(a).calc());
	}

	public BigInteger calc() {
		BigInteger b = BigInteger.ONE;
		for (int i = 0; i < a.length; i++) {
            b = b.multiply(a[i]).divide(b.gcd(a[i]));
		}
        BigInteger c = BigInteger.ZERO;
        for (int i = 0; i < a.length; i++) {
            c = c.add(b.divide(a[i]));
		}
		return c.mod(BigInteger.valueOf(1000000007));
	}

}