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;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
constexpr int MX = 10005, MOD = 1e9+7;
int n;
map<int,int> mp;
ll a, x, y, ac = 1, ac2;
void exgcd(ll a, ll b, ll &x, ll &y){
	if(b){
		exgcd(b, a%b, y, x);
		y -= a/b*x;
	}else{
		x = 1; y = 0;
	}
}
int main(){
	scanf("%d", &n);
	rep(i,n){
		scanf("%lld", &a);
		exgcd(a,MOD,x,y);
		ac2 += x;
		for(int t=2; t*t<=a; t++) if(a%t == 0){
			int k=0;
			for(; a%t == 0; a/=t) k++;
			mp[t] = max(mp[t],k);
		}
		if(a>1) mp[a] = max(mp[a],1);
	}
	ac2 %= MOD; ac2 += MOD;
	for(pair<int,int> it: mp){
		tie(x,y) = it;
		rep(i,y) (ac *= x) %= MOD;
	}
	printf("%lld\n",ac*ac2%MOD);
}