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: Wrong Answer)

#include <iostream>
#include <vector>
#include <cstdint>
#include <unordered_map>
#include <algorithm>

// by noshi91
template <std::uint_fast64_t Modulus> class modint {
    using u64 = std::uint_fast64_t;

public:
    u64 a;

    constexpr modint(const u64 x = 0) noexcept : a(x% Modulus) {}
    constexpr u64& value() noexcept { return a; }
    constexpr const u64& value() const noexcept { return a; }
    constexpr modint operator+(const modint rhs) const noexcept {
        return modint(*this) += rhs;
    }
    constexpr modint operator-(const modint rhs) const noexcept {
        return modint(*this) -= rhs;
    }
    constexpr modint operator*(const modint rhs) const noexcept {
        return modint(*this) *= rhs;
    }
    constexpr modint operator/(const modint rhs) const noexcept {
        return modint(*this) /= rhs;
    }
    constexpr modint& operator+=(const modint rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    constexpr modint& operator-=(const modint rhs) noexcept {
        if (a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    constexpr modint& operator*=(const modint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr modint& operator/=(modint rhs) noexcept {
        u64 exp = Modulus - 2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
};

using Mint = modint<(int)1e9 + 7>;

int main() {
	int n;
	std::cin >> n;

    std::vector<int> a(n);
    for (auto&& e : a)
        std::cin >> e;

    std::unordered_map<int, int> factor;
    for (auto&& e : a) {
        bool isPrime = true;

        for (int x = e, i = 2; i * i <= e; ++i) {
            int cnt = 0;

            while (x % i == 0) {
                isPrime = false;

                x /= i;
                ++cnt;
            }

            if (factor.count(i) == 0)
                factor[i] = 0;
            if (cnt != 0)
                factor[i] = std::max(cnt, factor[i]);
        }

        if (factor.count(e) == 0)
            factor[e] = 0;
        if (isPrime)
            factor[e] = std::max(factor[e], 1);
    }

    Mint lcm = 1;
    for (auto&& p : factor)
        for (int i = 0; i < p.second; ++i)
            lcm *= p.first;

    Mint ans = 0;
    for (auto&& e : a)
        ans += lcm / e;

    std::cout << ans.a << std::endl;
}