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.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        long mod = (long)Math.pow(10,9)+7;
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        HashMap<Long,Long> map = new HashMap<Long,Long>();
        ArrayList<Long> li = new ArrayList<Long>();
        for(int i = 0; i < n; i++){
            long l = sc.nextLong();
            li.add(l);
            map = fact(l,map);
        }
        long ans = 0;
        for(long v : li){
            long tmp = 1;
            for (Map.Entry<Long,Long> e : map.entrySet()) {
                long k = e.getKey();
                long ev = e.getValue();
                long cnt = 0;
                while(v % k == 0){
                    cnt++;
                    v /= k;
                }
                tmp *= rep2(k,ev-cnt, mod);
                tmp %= mod;
            }
            ans += tmp;
            ans %= mod;
        }
        System.out.println(ans%mod);
    }
    
    private static long rep2(long b, long n, long mod){
        if(n == 0) return 1;
        if(n == 1) return b;
        long bn = rep2(b,n/2,mod)%mod;
        if(n % 2 == 0){
            return (long)(bn%mod*bn%mod)%mod;
        }else{
            return (long)(bn%mod*bn%mod)%mod*b%mod;
        }
    }
    
    static HashMap<Long,Long> fact(long l, HashMap<Long,Long> map) {
        long cnt = 0;
        while (l % 2 == 0) {
            cnt++;
            l /= 2;
        }
        if(cnt != 0 &&(!map.containsKey(2L) || map.get(2L) < cnt)){
            map.put(2L,cnt);
        }
        long d = 3;
        long q = l / d;
        while (q >= d) {
            cnt = 0;
            while(l % d == 0) {
                cnt++;
                l /= d;
            }
            if(cnt != 0 && (!map.containsKey(d) || map.get(d) < cnt)){
                map.put(d,cnt);
            }
            d += 2;
            q = l / d;
        }
        if(l != 1 && (!map.containsKey(l))){
            map.put(l,1L);
        }
        return map;
    }
}