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).

Examples

Input

3
2 3 4


Output

13


Input

5
12 12 12 12 12


Output

5


Input

3
1000000 999999 999998


Output

996989508
#include <cstdio>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
 
using namespace std;
#define PB push_back
#define MP make_pair
#define REP(i,n) for(int i=0;i<(n);i++)
#define ll long long
map<int,ll>cnt;
const ll mod = 1000000007;
ll Pow(ll x, ll y){
	ll ans=1;
	for(; y; y>>=1, x=x*x%mod) if(y&1) ans=ans*x%mod;
	return ans;
}
int main(){
    int a[10010];
    int n;
    cin>>n;
    long long ans=0,p=1;
    REP(i,n){
        cin>>a[i];
        int num=a[i];
        for(int j=2;j*j<=num;j++)
        {
            int c=0;
            while(num%j==0)
            {
                num/=j;
                c++;
            }

            if(cnt[j]<c)
                cnt[j]=c;
        }
        if(num!=1&&cnt[num]==0)
            cnt[num]=1;
    }
    ll s = 1;
    for(int i=1;i<=1000000;i++)
    {
        s = (s * Pow(i,cnt[i])) % mod;
    }
    REP(i,n)
    {
        ans = (ans + (ll)s * Pow(a[i],mod-2)) % mod;
    }
    cout<<ans<<endl;
}