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: Wrong Answer)

//--- pE ---//
import java.util.*;
import java.lang.*;
import java.io.*;

public class Main {
	public static void main (String[] args) throws java.lang.Exception {
		new Solution();
	}
}
class Solution {
	Scanner scanner;
	int inf = (int)1e9;
	int mod = (int)1e9 + 7;

	public Solution() {
		scanner = new Scanner(System.in);

		// scanner.nextLine();
		while (scanner.hasNext()) {
			run_case();
		}
	}
	private void run_case() {
		// scanner.nextLine();
		String line = scanner.nextLine();

		int N = Integer.parseInt(line.split("\\s+")[0]);
		// int N = Integer.parseInt(line.split("\\s+")[1]);

		int[] A = strToIntArray(scanner.nextLine());

		long L = 1;
		for (int u : A) {
			L = lcm(L, u);
		}

		long res = 0;
		for (int u : A) {
			res += L/u;
			res %= mod;
		}

		System.out.println(res);
		return ;
	}

	private long gcd(long a, long b) {
	    if (b == 0) return a;
	    else return gcd(b, a%b);
	}

	private long lcm(long a, long b) {
	    return (a / gcd(a, b) * b);
	}

	private int[] strToIntArray(String str) {
	    String[] vals = str.split("\\s+");
	    int sz = vals.length;
	    int[] res = new int[sz];
	    for (int i=0; i<sz; i++) {
	        res[i] = Integer.parseInt(vals[i]);
	    }
	    return res;
	}
}
class Spell {
	public int power, cost;
	public Spell(int power, int cost) {
		this.power = power;
		this.cost = cost;
	}
}