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: Time Limit Exceeded)

//author:luckYrat(twitter:@luckYrat_)
//#include <bits/stdc++.h>

//def
#include <iostream>

#include <cmath>
#include <algorithm>
#include <iomanip>

//array
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <utility>
#include <climits>



using namespace std;

typedef pair<int,int> P;
typedef long long ll;

#define anyfill(n,s) setw(n) << setfill(s)
#define loop(s) for(int i = 0; s > i; i++)
#define rep(i,q) for(int i = 0; (q) > i; i++)
#define repp(i,n,q) for(int i = n; (q) > i; i++)
#define dep(i,q) for(int i = (q); 0 < i; i--)


#define MAX 1000000000
const int mod = 1000000007;
#define EPS (1e-10)

#define pb push_back
#define fir first
#define scn second
#define ednl endl

#define YesNo(a) (a?"Yes":"No")
#define YESNO(a) (a?"YES":"NO")
#define yesno(a) (a?"yes":"no")
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< mod >;


template <typename T>
T gcd(T a,T b){
  if(a%b==0)return b;
  else return gcd(b,a%b);
}
template <typename T>
T lcm(T a,T b){
  return a/gcd(a,b)*b;
}
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
vector.unique()は隣接した同じ要素を削除するので先にソートをする

計算量は変わらないが楽できるシリーズ
C++11以降でmin({a,b,c...})で複数個のmic,maxを処理できる
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる

*/
template <typename T>
T binaryPowerMethod(T z,T n){
  T ans = 1;
  while(n != 0){
    if(n%2){
      ans=(ans*z);
    }
    n = n/2;
    z= z*z;
  }
  return ans;
}
__attribute__((constructor))
void initial() {
 cin.tie(0);
 ios::sync_with_stdio(false);
}
int ya[1000000];
int main() { 
  //cout << (long long)(278784881LL*1000000LL)%mod << endl;
  int n;cin>>n;
  vector<int> A(n);
  modint sm = 1;
  for(int i = 0; n > i; i++){
    cin>>A[i];
    sm = sm*A[i];
    int t = A[i];
    int nw = 2;
    while(t > 1){
      int Z = 0;
      while(!(t%nw)){
        t/=nw;
        Z++;
      }
      ya[nw] = max(ya[nw],Z);
      nw++;
    }
  }
  modint ret = 1;
  for(int i = 0; 1000000 > i; i++){
    if(!ya[i])continue;
    modint nw = 1;
    nw = binaryPowerMethod(i,ya[i]);
    ret = (ret*nw);
  }
  modint ans = 0;
  for(int i = 0; n > i; i++){
    ans = ans+(ret/A[i]);
  }
  cout << ans << endl;

}