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>
#define int long long
constexpr long long mod = 1000000007;
#define for0(i, n) for(int i = 0; i < (n); i++)
#define for1(i, n) for(int i = 1; i <= (n);i++)
#define puts(x) cout << x << "\n"
using namespace std;
int f1(int a, int p) {
	if (p == 1)return a;
	if (p % 2)return f1(a, p - 1) * a % mod;
	else return f1(a * a % mod, p / 2) % mod;
}
int n, a[10100], k[1010], ans, a1, K = 1;
set<int>s1;
signed main() {
	cin >> n;
	for1(i, n) {
		cin >> a[i]; a1 = a[i];
		for (int p = 2; p <= 997; p++) {
			int cnt = 0;
			while (a1 % p == 0) { cnt++; a1 /= p; }
			k[p] = max(k[p], cnt);
		}
		if (a1 > 1)s1.insert(a1);
	}
	for (int p = 2; p <= 997; p++)for0(valsqotch, k[p]) { K *= p; if (K > mod)K %= mod; }
	for (int p : s1) { K = K * p % mod; }
	for1(i, n) {
		a1 = a[i]; int e = K;
		for (int p = 2; p <= 997; p++)while (a1 % p == 0) {
			e *= f1(p, mod - 2); if (e > mod)e %= mod;
			a1 /= p;
		}
		if (a1 > 1)e *= f1(a1, mod - 2); if (e > mod)e %= mod;
		ans += e; ans %= mod;
	}
	puts(ans);
}