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;

namespace E
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var MOD = 1000000007;

            var isPrime = new bool[1001];
            for (int i = 2; i < 1001; i++) isPrime[i] = true;
            for (int i = 2; i < 1001; i++)
            {
                if (isPrime[i])
                {
                    for (int j = i + 1; j < 1001; j++)
                    {
                        if ((j % i) == 0) isPrime[j] = false;
                    }
                }
            }
            var primeFactor = new int[N, 1001];
            for (int i = 0; i < N; i++)
            {
                var temp = A[i];
                for (int prime = 2; prime < 1001; prime++)
                {
                    if (temp == 1) break;
                    if (!isPrime[prime]) continue;
                    var count = 0;
                    while ((temp % prime) == 0)
                    {
                        temp /= prime;
                        count++;
                    }
                    primeFactor[i, prime] = count;
                }
            }

            var lcd = new int[1001];
            for (int prime = 2; prime < 1001; prime++)
            {
                if (!isPrime[prime]) continue;
                var max = 0;
                for (int i = 0; i < N; i++) if (max < primeFactor[i, prime]) max = primeFactor[i, prime];
                lcd[prime] = max;
            }

            var devide = new long[N];
            for (int i = 0; i < N; i++)
            {
                devide[i] = 1L;
                for (int prime = 2; prime < 1001; prime++)
                {
                    if (!isPrime[prime]) continue;
                    for (int j = 0; j < lcd[prime] - primeFactor[i, prime]; j++)
                    {
                        devide[i] *= prime;
                        devide[i] %= MOD;
                    }
                }
            }

            var result = 0L;
            for (int i = 0; i < N; i++)
            {
                result += devide[i];
                result %= MOD;
            }
            Console.WriteLine(result);
        }
    }
}