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: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using VI = vector<int>;
using VL = vector<ll>;
template<class T> using PQ = priority_queue<T, vector<T>, greater<T>>;
#define FOR(i,a,n) for(int (i)=(a);(i)<(n);++(i))
#define eFOR(i,a,n) for(int (i)=(a);(i)<=(n);++(i))
#define rFOR(i,a,n) for(int (i)=(n)-1;(i)>=(a);--(i))
#define erFOR(i,a,n) for(int (i)=(n);(i)>=(a);--(i))
#define each(i, a) for(auto &i : a)
#define SORT(i) sort((i).begin(),(i).end())
#define rSORT(i,a) sort((i).begin(),(i).end(),(a))
#define all(i) (i).begin(),(i).end()
#define out(y,x) ((y) < 0 || h <= (y) || (x) < 0 || w <= (x))
#define line cout << "------------------------\n" 
#define ENDL(i,n) ((i) == (n) - 1 ? "\n" : " ")
#define stop system("pause") //comment out this on AOJ.
constexpr ll INF = 1000000000;
constexpr ll LLINF = 1LL << 60;
constexpr ll mod = 1000000007;
constexpr ll MOD = 998244353;
constexpr ld eps = 1e-10; //1e-9?
constexpr ld pi = 3.1415926535897932;
template<class T>inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T>inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; }return false; }
inline void init() { cin.tie(nullptr); cout.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); }
template<class T>inline istream& operator>>(istream& is, vector<T>& v) { for (auto& elemnt : v)is >> elemnt; return is; }
template<class T, class U>inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template<class T>inline vector<T> vec(size_t a) { return vector<T>(a); }
template<class T>inline vector<T> defvec(T def, size_t a) { return vector<T>(a, def); }
template<class T, class... Ts>inline auto vec(size_t a, Ts... ts) { return vector<decltype(vec<T>(ts...))>(a, vec<T>(ts...)); }
template<class T, class... Ts>inline auto defvec(T def, size_t a, Ts... ts) { return vector<decltype(defvec<T>(def, ts...))>(a, defvec<T>(def, ts...)); }

template<int mod> struct ModInt {
    int x;

    ModInt() : x(0) {}
    ModInt(long long 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;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        return ModInt(u);
    }

    ModInt pow(int e) {
        long long a = 1, p = x;
        while (e > 0) {
            if (e % 2 == 0) { p = (p * p) % mod; e /= 2; }
            else { a = (a * p) % mod; e--; }
        }
        return ModInt(a);
    }

    friend ostream& operator<<(ostream& os, const ModInt<mod>& p) {
        return os << p.x;
    }
    friend istream& operator>>(istream& is, ModInt<mod>& a) {
        long long x;
        is >> x;
        a = ModInt<mod>(x);
        return (is);
    }
};
using modint = ModInt<mod>;

int main() {
    init();

    int n; cin >> n;
    VL a(n); cin >> a;

    unordered_map<ll, int> m;
    FOR(i, 0, n) {
        ll x = a[i];
        for (ll y = 2; y * y <= x; ++y) {
            int cnt = 0;
            while (x % y == 0) {
                x /= y;
                ++cnt;
            }
            chmax(m[y], cnt);
        }
        if (x != 1)chmax(m[x], 1);
    }

    modint lcm = 1, ans = 0;
    each(i, m)lcm = lcm * modint(i.first).pow(i.second);
    FOR(i, 0, n)ans += lcm / modint(a[i]);
    cout << ans << "\n";
}