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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod = (int)1e9+7;

ll power(ll a, ll b){
	ll ans = 1;
	while(b){
		if(b&1){
			ans = (ans * a) % mod;
		}
		a = (a * a) % mod;
		b = b>>1;
	}
	return ans;
}

ll inv(ll a){
	return power(a,mod-2);
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	int n;
	cin>>n;
	vector<int> a(n);
	for(int i=0;i<n;i++)
		cin>>a[i];
		
	vector<int> pf(1000006);
	for(int i=0;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){
					cnt++;
					x/=j;
				}
				pf[j] = max(pf[j],cnt);
			}
		}
		if(x>1){
			pf[x] = max(pf[x],1);
		}
	}		
	ll lcm = 1;
	for(int i=2;i<1000006;i++){
		if(pf[i]){
			lcm = (lcm * power(i,pf[i]) )%mod;
		}
	}
	//ctrl + /cout<<lcm<<"\n";
	ll ans = 0;
	for(int i=0;i<n;i++){
		ans = (ans + lcm * inv(a[i]) )%mod;
	}
	cout<<ans;
	return 0;
}
































