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;

long inv(int a, int m) {
    long i = 1, j = 0;
    for(int b = m; a > 1; swap(i, j), swap(a, b)) {
        j = (j + b / a * (m - i)) % m;
        b %= a;
    }
    return i;
}
int main() {
    int n, p = 1e9 + 7;
    cin >> n;
    map<int, int> f;
    long x = 0;
    for(int j = 0; j < n; j++) {
        int m;
        cin >> m;
        (x += inv(m, p)) %= p;
        for(int i = 2; i * i <= m; i++) {
            if(m % i)
                continue;
            int c = 0;
            while(m % i == 0)
                m /= i, c++;
            f[i] = max(f[i], c);
        }
        if(m > 1)
            f[m] = max(f[m], 1);
    }
    for(auto i : f)
        for(int j = 0; j < i.second; j++)
            (x *= i.first) %= p;
    cout << x << endl;
    return 0;
}
