Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)
typedef long long ll;
ll const M = 1000000007;


ll gcd(ll x, ll y){
	if (y == 0){
		return x;
	}
	return gcd(y,x%y);
}


ll lcm(ll x, ll y){
	return x*y/gcd(x,y);
}

int main(){
	int n;
	cin >> n;
	vector<ll> a(n);
	rep(i,n){
		cin >> a[i];
	}
	
	
	ll val = a[0];
	
	REP(i,n-1){
		val = lcm(val,a[i]);
	}
	
	vector<ll> b(n);
	ll ans = 0;
	
	rep(i,n){
		b[i] = val/a[i];
		ans += b[i];
		ans %= M;
	}
	
	cout << ans << endl;
}