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.util.*;
import java.io.*;
import java.math.BigInteger;

class FastReader {

    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException  e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}

public class Main {
    public static void main(String[] args) {
        FastReader fr = new FastReader();
        int N = fr.nextInt();
        BigInteger[] A = new BigInteger[N];
        for (int i = 0; i < N; i++) A[i] = new BigInteger("" + fr.nextInt());
        BigInteger mod = new BigInteger("1000000007");
        BigInteger ans = BigInteger.ZERO;
        BigInteger prev = A[0];
        for (BigInteger a : A) {
            BigInteger l = lcm(prev, a);
            BigInteger factor = l.divide(prev).mod(mod);
            ans = (ans.multiply(factor).add(l.divide(a))).mod(mod);
            prev = l;
        }
        System.out.println(ans);
    }

    private static BigInteger lcm(BigInteger a, BigInteger b) {
        return a.multiply(b).divide(gcd(a, b));
    }
    private static BigInteger gcd(BigInteger a, BigInteger b) {
        if (b.equals(BigInteger.ZERO)) return a;
        return gcd(b, a.mod(b));
    }
}