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 <algorithm>
#include <cstring>
#include <set>
#include <map>
#include <iostream>
#include <cstring>
#include <cmath>
#include <queue>
#define ull unsigned long long
#define ll long long
#define INF 0x3f3f3f3f
using namespace std;
void close(){
       std::ios::sync_with_stdio(false);
       std::cin.tie(0);
}
const ll mod=1e9+7;
ll qpow(ll a,ll b){
	ll ret=1;
	while(b) {
		if (b&1) ret=(ret*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return ret;
}
const int maxn=1e4+5;
const int N=1e6+5;
int n,a[maxn],num[N],lcm=1,ans=0;
int main(){
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i];
	for(int i=1;i<=n;i++) {
		int x=a[i];
		for(int j=2;j*j<=x;j++){
			if(x%j==0){
				int cnt=0;
				while(x%j==0){
					x/=j,cnt++;
				}
				num[j]=max(num[j],cnt);
			}
		}
		if(x!=1) num[x]=max(num[x],1);
	}
	for(int i=2;i<N;i++) 
		if(num[i]){
			lcm=1ll*lcm*qpow(i,num[i])%mod;
		}
	for(int i=1;i<=n;i++){
		ans=(ans+1ll*lcm*qpow(a[i],mod-2)%mod)%mod;
	}
	cout<<ans<<endl;
}