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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;

public class Main {
	static int[] arr;
	static int N;

	public static void main(String[] args) throws NumberFormatException, IOException {
		read();
	}

	private static void read() throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		N = Integer.parseInt(br.readLine());
		String[] wrods = br.readLine().split(" ");
		arr = new int[wrods.length];
		BigInteger t = BigInteger.ONE;
		for (int i = 0; i < N; i++) {
			arr[i ] = Integer.parseInt(wrods[i ]);
			BigInteger tmp = BigInteger.valueOf(arr[i]);
			BigInteger A = t.gcd(tmp);
			t = t.multiply( tmp ).divide(A);
		}
		BigInteger sum = BigInteger.ZERO;
		for(int i=0;i<N;i++) {
			BigInteger s  = t.divide(BigInteger.valueOf(arr[i]));
			sum = s.add(sum);
		}
		System.out.println(sum.mod(BigInteger.valueOf(1000000007)).longValue());
		br.close();
	}
}