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)

#include <bits/stdc++.h>
using namespace std;

using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for (lint i = (begin), i##_end_ = (end); i < i##_end_; i++)
#define IFOR(i, begin, end) for (lint i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)

#include <cstdint>

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;
    }
};

#define M 1000000007
long long modinv(long long a, long long m)
{
    long long b = m, u = 1, v = 0;
    while (b)
    {
        long long t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= m;
    if (u < 0)
        u += m;
    return u;
}
lint gcd(lint a, lint b)
{
    if (a % b == 0)
    {
        return (b);
    }
    else
    {
        return (gcd(b, a % b));
    }
}
lint lcm(lint a, lint b)
{
   // return (a * b / gcd(a, b));
    return (a * b *modinv(gcd(a, b), M))%M;
}

int main()
{
    lint n;cin >> n;
    vector<lint> a(n),b;
    REP(i, n) { cin >> a[i]; }
    lint ans=0;
    //modint<M> x=1,y,z;
    lint x=1;
    b = a;

    REP(i,n){
        lint aa = a[i];
        //x = lcm(x, aa) % M;
        x = x*aa % M;
        FOR(j, i+1, n)
        {
            a[j] /= gcd(a[i], a[j]);
        }
    }
    REP(i, n)
    {
        lint aa = b[i];
        //ans += x / aa;
        lint tmp = (x * modinv(aa, M))%M;
        //cout << tmp << " ";
        ans += tmp;
    }
    
   // cout << x << "\n";

    cout << ans%M <<"\n";


    return 0;
}