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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>

using namespace std;

#define debug(n) cerr << #n << ':' << n << endl;
#define dline    cerr << __LINE__ << endl;

using ll = long long;
using ull = unsigned long long;
template<class T, class U> using P = pair<T,U>;
template<class T> using Heap = priority_queue<T>;
template<class T> using heaP = priority_queue<T,vector<T>,greater<T>>;
template<class T,class U> using umap = unordered_map<T,U>;
template<class T> using uset = unordered_set<T>;

template<class T>
bool ChangeMax(T&a,const T&b){
  if(a >= b) return false;
  a = b;    return true;
}

template<class T>
bool ChangeMin(T&a,const T&b){
  if(a <= b) return false;
  a = b;    return true;  
}

template<class T, size_t N, class U>
void Fill(T (&a)[N], const U&v){
    fill((U*)a,(U*)(a+N),v);
}

template<class T>
istream& operator >> (istream&is, vector<T>&v){
  for(auto&e:v)is >> e;
  return is;
}

template<long long mod>
class modint{
private:
  long long extgcd(long long a, long long b, long long&x, long long&y)const {
    long long d = a;
    if(b != 0){d = extgcd(b, a%b, y, x);  y -= (a/b) * x;}
    else{x = 1; y = 0;}
    return d;
  }
  long long modinverse()const{
    long long x, y;
    extgcd(num, mod, x, y);
    return (mod + x%mod)%mod;
  }
public:
  long long num;
  modint():num(0){}
  modint(const long long x):num((x < 0?(x+mod):x)%mod ){}
  friend modint operator+(const modint&a, const modint&b)
  {    return modint(a.num + b.num);  }
  friend modint operator-(const modint&a, const modint&b)
  {    return modint(a.num - b.num);  }
  friend modint operator*(const modint&a, const modint&b)
  {    return modint(a.num * b.num);  }
  friend modint operator/(const modint&a, const modint&b)
  {    return modint(a*b.modinverse());  }
  modint& operator+=(const modint&b)
  {    return (*this) = (*this) + b;  }
  modint& operator-=(const modint&b)
  {    return (*this) = (*this) - b;  }
  modint& operator*=(const modint&b)
  {    return (*this) = (*this) * b;  }
  modint& operator/=(const modint&b)
  {    return (*this) = (*this) / b;  }
  modint& operator++()
  {    (*this)+=1; return (*this);  }
  modint& operator--()
  {    (*this)-=1; return (*this);  }
  modint operator++(int){
    modint tmp(*this);
    ++(*this);
    return tmp;
  }
  modint operator--(int){
    modint tmp(*this);
    --(*this);
    return tmp;
  }    
  modint pow(unsigned long long i){
    if(i == 0) return 1;
    if(i & 1){
      return (*this) * (this->pow(i-1));
    }
    modint<mod>hpow = (this->pow(i>>1));
    return hpow * hpow;
  }
  friend ostream& operator<<(ostream&os, const modint&a){
    os << a.num;
    return os;
  }
  friend istream& operator>>(istream&is, modint&a){
    long long x; is >> x;
    a = x;
    return is;
  }
};

constexpr int mod = 1000000007;

using mint = modint<mod>;

vector<int> plist;
map<ll,int> mp;

void Update(int n){
  for(auto e:plist){
    int cnt = 0;
    while(n % e == 0){
      n /= e;
      cnt++;
    }
    ChangeMax(mp[e],cnt);
  }
}

map<ll,ll> sum;

ll F(int n){
  sum.clear();
  map<ll,int> mmp;
  for(auto e:plist){
    int cnt = 0;
    while(n % e == 0){
      n /= e;
      cnt++;
    }
    mmp[e] = cnt;
  }
  ll ret = 1;  
  for(auto e:mp){
    sum[e.first] = e.second - mmp[e.first];
  }
}

int main(){
  {
    set<int> st;
    for(int i = 2; i <= 1000000; ++i){
      if(st.find(i) != st.end())continue;
      plist.push_back(i);
      int x = i;
      while(x <= 1000000){
	x += i;
	st.insert(x);
      }
    }    
  }
  
  int n; cin >> n;
  vector<int> v(n); cin >> v;
  
  mint ans(0);
  for(auto e:v)Update(e);
  for(auto e:v){
    F(e);
    mint x(1);
    for(auto ee:sum){
      x *= mint(ee.first).pow(ee.second);      
    }
    ans += x;
  }
  cout << ans << endl;
}