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
#define loop(i, n) for (int i = 0; i < n; i++)
#define ll long long
#include <bits/stdc++.h>
using namespace std;
const ll m = 1e9 + 7;

ll exp_mod(ll a, ll n) {
	if (n == 0)
		return 1;
	else {
		ll res = exp_mod(a, n / 2);
		res = (res * res) % m;
		if (n % 2 != 0)
			res = (res * a) % m;
		return res;
	}
}

int main() {


	int n;	ll lcm = 1, final = 0;	cin >> n;
	vector <ll> v(n);		map <ll, ll> p;
	for (int i = 0; i < n; i++) {
		cin >> v[i];
		ll temp = v[i];
		for (int i = 2; i * i <= temp; i++) {
			ll cnt = 0;
			while (temp % i == 0) {
				temp /= i;
				cnt++;
			}
			if (cnt)
				p[i] = max(p[i], cnt);
			if (temp == 1)		break;
		}
		if (temp > 1)	p[temp] = max(p[temp], (ll)1);
	}
	for (auto &i : p) {
		lcm = (lcm * exp_mod(i.first, i.second)) % m;
	}
	for (int i = 0; i < n; i++) {
		final += (lcm * exp_mod(v[i], m - 2)) % m;
		final %= m;
	}
	cout << final << endl;
	return 0;
}