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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
    // 最小公倍数
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }

    // ユークリッドの互除法 
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        string[] input = Console.ReadLine().Split();
        long[] A = new long[N];
        for(int i = 0; i < N; i++)
        {
            A[i] = long.Parse(input[i]);
        }
        long lcm = 1;
        for (int i = 0; i < N; i++)
        {
            lcm=Lcm(lcm, A[i]);
        }
        Mint ans = 0;
        for(int i = 0; i < N; i++)
        {
            Mint LCM = lcm;
            Mint AI = A[i];
            Mint temp = LCM / AI;
            ans = ans+temp;
        }
        Console.WriteLine(ans);
    }
    public struct Mint
    {
        const int mod = (int)1e9 + 7;
        private long d;
        public Mint(long d) { this.d = d; }
        public static implicit operator Mint(long d) { return new Mint(d % mod); }
        public static explicit operator long(Mint d) { return d.d; }
        public override string ToString() { return d.ToString(); }
        public static Mint operator +(Mint a, long b) { a.d = (a.d + b) % mod; return a; }
        public static Mint operator +(Mint a, Mint b) { a.d = (a.d + b.d) % mod; return a; }
        public static Mint operator -(Mint a, long b) { a.d = (mod + a.d - b) % mod; return a; }
        public static Mint operator -(Mint a, Mint b) { a.d = (mod + a.d - b.d) % mod; return a; }
        public static Mint operator *(Mint a, long b) { a.d = (a.d * b) % mod; return a; }
        public static Mint operator *(Mint a, Mint b) { a.d = (a.d * b.d) % mod; return a; }
        public static Mint operator /(Mint a, long b) { a.d = (a.d * Mi(b)) % mod; return a; }
        public static Mint operator /(Mint a, Mint b) { a.d = (a.d * Mi(b.d)) % mod; return a; }
        private static long Mi(long a)
        {
            a = (a + mod) % mod;
            long b = mod, u = 1, v = 0;
            while (b > 0)
            {
                long t = a / b;
                a -= t * b; a ^= b; b ^= a; a ^= b;
                u -= t * v; u ^= v; v ^= u; u ^= v;
            }
            u %= mod;
            if (u < 0) { u += mod; }
            return u % mod;
        }
    }
}