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>
 #define ll long long
 #define int long long
 #define MOD  1000000007
 #define MAX 500005
 #include<iomanip>
 #define Need_for_speed(activated) ios_base :: sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)
 #define satisfy ll t; cin>> t; while(t--)
 #define inp(n) int n;cin >> n
 #define mp make_pair
 #define pb push_back
 #define fore(i,a,b) for(ll i=a;i<b;i++)
 #define x first
 #define y second
using namespace std;

int gcd(int a, int b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
      
}
 int32_t main()
{
    Need_for_speed(activated);
//    satisfy
//    {
//
//    }
    ll n;cin>>n;
    ll a[10004]={0};
    ll k=1;
    fore(i,0,n)
    {cin>>a[i];
        k=(k*(a[i]/gcd(k,a[i])));
        
    }
    ll sum=0;
    fore(i,0,n)
    {
        sum+= (k/a[i])%MOD;
        sum=sum%MOD;
    }
    cout<<sum<<endl;
    return 0;
}