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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

    #include <bits/stdc++.h>
    using namespace std;
    #define md 1000000007
    #define mk 1000001
    #define lld long long int  
    lld power(lld x, lld y) 
    { 
        lld temp; 
        
        if( y == 0) 
            return 1; 
        temp = power(x, y/2); 
        if (y%2 == 0) 
            return ((temp)*(temp)); 
        else
            return ((x)*(temp)*(temp)); 
    } 
     
    int main() {
        lld n,cnt = 0;
        lld mx = 0;
        lld a[10001];
        lld sm = 0 , gcd = 0 , k =1;
        cin>>n;
        for(int i = 0 ; i< n ; i++){
            cin>>a[i];
            mx = max(mx,a[i]);
        }
        // bool f = false;
        // lld p = 1;
        // gcd = a[0];
        // k = a[0];
        // for(int i=1 ; i<n ; i++){
        //     gcd = __gcd(k,a[i]);
        //     // k = ((k%md)*((power(gcd,mk)%md)*(a[i]%md))%md)%md;
        //     // k = ((k%md)*(a[i]%md))%md;
        //     // k = (k*(power(gcd,mk)%md))%md;
        //     // cout<<gcd<<" "<<k<<" "<<power(gcd,mk)<<endl;
        //     k = (k*a[i])/gcd;
        // }
        // for(int i=0 ; i<n ; i++){
        //     sm += (k/a[i])%md;
        //     sm %= md;
        // }
        mx = 1001;
        vector<lld>p;
        bool ch[mk];
        for(int i=0 ; i<mx ; i++)
            ch[i] = false;
        for(int i = 2 ; i*i < mx ; i++){
            if(!ch[i]){
                for(int j = 2 ; j*i < mx ; j++){
                    ch[j*i] = true;
                }
            }
        }
        for(int i = 2 ; i<mx ; i++){
            if(!ch[i])
                p.push_back(i);
        }
        // for(int i=0 ; i<p.size() ; i++)
        //     cout<<p[i]<<" ";
        // cout<<endl;
        lld ans  = 1;
        int tmp ;
        lld cc , mn = INT_MAX;
        // cout<<p.size()<<" "<<p[p.size()-1]<<endl;
        for(int i = 0 ; i<p.size() ; i++){
            cc = 0;
            mn = INT_MIN;
            for(int j=0 ; j< n ; j++){
                cc = 0;
                tmp = a[j];
                while(tmp % p[i] == 0){
                    cc++;
                    tmp /= p[i];
                }
                mn = max(mn,cc);
            }
            ans *= power(p[i],mn);
        }
        // cout<<ans<<endl;
        for(int i=0 ; i<n ; i++){
            sm += (ans/a[i])%md;
            sm %= md;
        }
        cout<<sm<<endl;
    }