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)

///====================== TEMPLATE STARTS HERE =====================///
#include <bits/stdc++.h>
using namespace std;

//#include <ext/pb_ds/assoc_container.hpp> // Include for built in treap
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;

//#include <sys/resource.h>     // for linux stack memory increase
//#define gc getchar_unlocked   // for linux fast io
//#define gc getchar            // for windows fast io

#define pb push_back
#define MP make_pair
#define ff first
#define ss second
#define nl puts("")
#define sp printf(" ")
#define phl debug("Hello")
#define FOR(i,x,y) for(vlong i = (x) ; i <= (y) ; ++i)
#define ROF(i,x,y) for(vlong i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define ALL(x) (x).begin(),(x).end()
#define SZ(x) ((vlong)(x).size())
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x))
#define SQ(x) ((x)*(x))
#define LCM(x,y) (((x)/gcd((x),(y)))*(y))
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define NUMDIGIT(x,y) (((vlong)(log10((x))/log10((y))))+1)
#define NORM(x) if(x>=mod) x-=mod;if(x<0) x+=mod;
#define ODD(x) (((x)&1)==0?(0):(1))
#define Set(N,p) N=((N)|((1LL)<<(p)))
#define Reset(N,p) N=((N)&(~((1LL)<<(p))))
#define Check(N,p) (!(((N)&((1LL)<<(p)))==(0)))
#define fast_cin ios_base::sync_with_stdio(false);cin.tie(NULL)
#define arrayIndexPrint(A,i) cerr<<"~ At pos: "<<i<<" = "<<A[i]
#define dump(x) cerr<<"~ "<<#x<<" = "<<x<<endl
#define arrayPrint(A,st,ed) cerr<<"~ Array:";FOR(i,st,ed) cerr<<" "<<A[i];cerr<<endl
#define LINE cerr<<"\n"; FOR(i,0,50) cerr<<"=";cerr<<"\n\n"

#define LL long long
#define LLU long long unsigned int
typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<int> vi;
typedef vector<vlong> vl;
typedef vector<pll> vll;
//typedef tree <int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pb_ds;

#ifdef forthright48
     #include <ctime>
     clock_t tStart = clock();
     #define debug(args...) {dbg,args; cerr<<endl;}
     #define timeStamp debug ("Execution Time: ", (double)(clock() - tStart)/CLOCKS_PER_SEC)
     #define bug printf("%d\n",__LINE__);

#else
    #define debug(args...)  // Just strip off all debug tokens
    #define timeStamp
#endif

struct debugger{
    template<typename T> debugger& operator , (const T& v){
        cerr<<v<<" ";
        return *this;
    }
}dbg;

#ifdef forthright48
    #define line                    cout << "\n===================\n"
    #define trace(...)              __f( #__VA_ARGS__ , __VA_ARGS__ )
    template <typename Arg1>
    void __f(const char* name, Arg1&& arg1){
        cerr << name << " = " << arg1 << "\n";
    }
    template <typename Arg1, typename... Args>
    void __f(const char* names, Arg1&& arg1, Args&&... args){
        const char* comma = strchr(names + 1, ',');
        cerr.write(names, comma - names) << " = " << arg1 << " , ";
    __f(comma + 1, args...);
    }
#else
    #define line
    #define trace(...)
#endif

inline vlong gcd ( vlong a, vlong b ) {
    a = ABS ( a ); b = ABS ( b );
    while ( b ) { a = a % b; swap ( a, b ); } return a;
}

vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
    vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
    x2 = 1; y2 = 0;
    x1 = 0; y1 = 1;
    for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
        q = r2 / r1;
        r = r2 % r1;
        x = x2 - (q * x1);
        y = y2 - (q * y1);
    }
    *X = x2; *Y = y2;
    return r2;
}

inline vlong modInv ( vlong a, vlong m ) {
    vlong x, y;
    ext_gcd( a, m, &x, &y );
    x %= m;
    if ( x < 0 ) x += m;
    return x;
}

inline vlong bigmod ( vlong a, vlong p, vlong m ) {
    vlong res = 1 % m, x = a % m;
    while ( p ) {
        if ( p & 1 ) res = ( res * x ) % m;
        x = ( x * x ) % m; p >>= 1; /// For bigmod2 multiply here using mulmod
    }
    return res;
}


//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};
//int dir8[8][2] = {{-1,0},{0,1},{1,0},{0,-1},{-1,-1},{1,1},{1,-1},{-1,1}};
const vlong inf = 2147383647;
const vlong mod = 1000000007;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-11;
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); /// For generating random numbers

///======================  TEMPLATE ENDS HERE  =====================///

#define SIZE 1000002

vector<int> Prime; //Prime vector

int mark[SIZE]; //1 if not prime, 0 if prime

void sieve(int n) {
    int i, j, limit = sqrt(n*1.0) + 2;

    mark[1] = 1; //1 is not prime

    for(i=4; i<=n; i+=2) mark[i] = 1; //evens

    Prime.push_back(2); //2 is prime

    for(i=3; i<=n; i+=2) { //run loops only on odds
        if(!mark[i]) {
            Prime.push_back(i);

            //if we don't do it, following
            //i*i may overflow
            if(i<=limit) {
                for(j=i*i; j<=n; j += i*2) {
                    mark[j] = 1;
                }
            }
        }
    }
}

int mxx[1000000];
int N;
vector<int> V;
vector<map<int, int> > MV;

map<int, int> m;
//if d is large, it may require long long
void primeFact(int d)
{
    m.clear();
    int sq = sqrt(d);
    int temp = d;
    for(int i=0; i<Prime.size(); i++) {
        if(Prime[i]>sq) break;
        if(temp%Prime[i]==0) {
            int cnt=0;
            while(temp%Prime[i]==0) {
                temp /= Prime[i];
                cnt++;
            }
            m[Prime[i]] = cnt;
            mxx[Prime[i]] = max(mxx[Prime[i]], cnt);
        }
    }
    if(temp>1) {
        m[temp] = 1;
        mxx[temp] = max(mxx[temp], 1);
    }

    MV.push_back(m);
}

map<int, int> MMM;

int main () {
    #ifdef forthright48
    freopen ( "input.txt", "r", stdin );
    //freopen ( "output.txt", "w", stdout );
    #endif // forthright48

    fast_cin;

    sieve(1000000);

    cin >> N;
    for(int i=0; i<N; i++) {
        int a;
        cin >> a;
        V.push_back(a);
    }

    for(int i=0; i<V.size(); i++) {
        primeFact(V[i]);
    }

    for(int i=0; i<Prime.size(); i++) {
        if(mxx[Prime[i]]>0) {
            MMM[Prime[i]] = mxx[Prime[i]];
        }
    }

    LL sum = 0;
    for(int i=0; i<MV.size(); i++) {
        map<int, int>::iterator it;
        LL tempVal = 1;
        for(it=MMM.begin(); it!=MMM.end(); it++) {
            LL PR = it->first;
            LL mx = it->second;

            LL cnt = MV[i][PR];

            LL toMul = bigmod(PR, mx-cnt, mod);
            tempVal *= toMul;
            tempVal %= mod;

            //trace(i, PR, cnt, mx, toMul, tempVal, sum);
        }
        sum += tempVal;
        sum %= mod;
    }

    cout << sum << "\n";

    return 0;
}