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 <cmath>
typedef long long int ll;
using namespace std;
const ll MOD = 1000000007;

ll modpow(int a, int b) {
  ll ans = 1;
  ll x = a;
  int y = b;
  while (y) {
    if (y & 1) {
      ans *= x;
      ans %= MOD;
    }
    x *= x;
    x %= MOD;
    y >>= 1;
  }
  return ans;
}

int main() {
  int N, A[10000], c[1000001] = {};
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    int x = A[i];
    for (int j = 2; j * j <= x; j++) {
      int e = 0;
      while (x % j == 0) {
        x /= j;
        e++;
      }
      c[j] = max(c[j], e);
    }
    if (x > 1) {
      c[x] = max(c[x], 1);
    }
  }
  ll lcm = 1;
  for (int i = 2; i <= 1000000; i++) {
    if (c[i] > 0) {
      lcm *= modpow(i, c[i]);
      lcm %= MOD;
    }
  }
  ll ans = 0;
  for (int i = 0; i < N; i++) {
    ans += modpow(A[i], MOD - 2);
    ans %= MOD;
  }
  ans *= lcm;
  ans %= MOD;
  cout << ans << endl;
  return 0;
}
