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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace ABC152 {
    class E {
        static void Main (string[] args) {
            int n = int.Parse (Console.ReadLine ());
            int[] a = Console.ReadLine ().Split ().Select (int.Parse).ToArray ();
            BigInteger ans = new BigInteger(0);
            if (n == 1) { ans = 1; } else {
                long sum = 0;
                BigInteger k = Lcm (a);
                for (int i = 0; i < n; i++) {
                    ans += k / a[i];
                    ans %= 1000000007;
                }
            }
            Console.WriteLine (ans);
        }
        public static BigInteger Lcm (BigInteger m, BigInteger n) {
            return m * n / Gcd (m, n);
        }
        public static BigInteger Gcd (BigInteger m, BigInteger n) {
            BigInteger temp;
            while (m % n != 0) {
                temp = n;
                n = m % n;
                m = temp;
            }
            return n;
        }
        public static BigInteger Gcd (int[] n) {
            if (n.Length == 2) { return Gcd (n[0], n[1]); }
            return Gcd (Gcd (n.Take (n.Length - 1).ToArray ()), n[n.Length - 1]);
        }
        public static BigInteger Lcm (int[] n) {
            if (n.Length == 2) { return Lcm (n[0], n[1]); }
            return Lcm (Lcm (n.Take (n.Length - 1).ToArray ()), n[n.Length - 1]);
        }
    }
}