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 <iostream>
#include <cstdio>
#define N 1000005
using namespace std;
typedef long long ll;

ll n, num, lcm=1, ans, M=1e9+7, a[N], cnt[N];

ll pow(ll p, ll q) {
	ll re = 1;
	for(; q; q>>=1, p=p*p%M) {
		if(q&1) re = re * p % M;
	}
	return re;
}

int main() {
	ll i, j, c;
	cin >> n;
	for(i=0; i<n; i++) {
		cin >> a[i];
		num = a[i];
		for(j=2; j*j<=num; j++) {
			if(num%j == 0) {
				c = 0;
				while(num%j == 0) c++, num /= j;
				cnt[j] = max(c, cnt[j]);
			}
		}
		if(num>1 && cnt[num]==0) cnt[num] = 1;
	}
	for(i=2; i<=1000000; i++) {
		if(cnt[i]) lcm = lcm * pow(i, cnt[i]) % M;
	}
	for(i=0; i<n; i++) {
		ans = (ans + lcm * pow(a[i], M-2)) % M;
	}
	cout << ans;
	return 0;
}