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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.math.*;
import java.util.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 26).start();
    }

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static long modPow(long a, long p, long m) {
        if (a == 1) return 1;
        long ans = 1;
        while (p > 0) {
            if (p % 2 == 1) ans = (ans * a) % m;
            a = (a * a) % m;
            p >>= 1;
        }
        return ans;
    }

    static long modInv(long a, long m) {
        return modPow(a, m - 2, m);
    }


    static class Radix {


        static int getMax(int arr[], int n) {
            int mx = arr[0];
            for (int i = 1; i < n; i++)
                if (arr[i] > mx)
                    mx = arr[i];
            return mx;
        }

        static void countSort(int arr[], int n, int exp) {
            int output[] = new int[n];
            int i;
            int count[] = new int[10];
            Arrays.fill(count, 0);

            for (i = 0; i < n; i++)
                count[(arr[i] / exp) % 10]++;

            for (i = 1; i < 10; i++)
                count[i] += count[i - 1];

            for (i = n - 1; i >= 0; i--) {
                output[count[(arr[i] / exp) % 10] - 1] = arr[i];
                count[(arr[i] / exp) % 10]--;
            }

            for (i = 0; i < n; i++)
                arr[i] = output[i];
        }

        static void radixsort(int arr[], int n) {
            int m = getMax(arr, n);

            for (int exp = 1; m / exp > 0; exp *= 10)
                countSort(arr, n, exp);
        }

    }

    class DSU {
        int par[], size[], connectedComponent;

        DSU(int n) {
            par = new int[n];
            size = new int[n];
            for (int i = 0; i < n; i++) {
                size[i] = 1;
                par[i] = i;
            }
            connectedComponent = n;
        }

        int root(int n) {
            if (n == par[n]) return n;
            return par[n] = root(par[n]);
        }

        boolean union(int u, int v) {
            return f_union(root(u), root(v));
        }

        boolean f_union(int u, int v) {
            if (u == v) return false;
            if (size[u] > size[v]) {
                size[u] += size[v];
                par[v] = u;
            } else {
                size[v] += size[u];
                par[u] = v;
            }
            connectedComponent--;
            return true;
        }

        DSU clone_DSU() {
            DSU t = new DSU(par.length);
            t.connectedComponent = connectedComponent;
            for (int i = 0; i < par.length; i++) {
                t.par[i] = par[i];
                t.size[i] = size[i];
            }
            return t;
        }
    }


    class segmentTree {
        long query(int cur, int l, int r, int start, int end, long tree[], long a[], long[] lazy) {
            if (l > end || r < start) return 0;
            if (lazy[cur] != 0) {
                tree[cur] += lazy[cur];
                if (l != r) {
                    lazy[2 * cur + 1] += lazy[cur];
                    lazy[2 * cur + 2] += lazy[cur];
                }
                lazy[cur] = 0;
            }
            if (l >= start && r <= end) return tree[cur];
            int mid = (l + r) >> 1;
            long p1 = query(2 * cur + 1, l, mid, start, end, tree, a, lazy);
            long p2 = query(2 * cur + 2, mid + 1, r, start, end, tree, a, lazy);
            return p1 + p2;
        }

        void build(int cur, int l, int r, long tree[], long a[]) {
            if (l == r) {
                tree[cur] = a[l];
                return;
            }
            int mid = (l + r) >> 1;
            build(2 * cur + 1, l, mid, tree, a);
            build(2 * cur + 2, mid + 1, r, tree, a);
            tree[cur] = tree[2 * cur + 1] + tree[2 * cur + 2];
        }

        void update(int cur, int start, int end, long val, int l, int r, long tree[], long a[], long[] lazy) {
            if (l > end || r < start) return;
            if (lazy[cur] != 0) {
                tree[cur] += (r - l + 1) * lazy[cur];
                if (l != r) {
                    lazy[2 * cur + 1] += lazy[cur];
                    lazy[2 * cur + 2] += lazy[cur];
                }
                lazy[cur] = 0;
            }
            if (l >= start && r <= end) {
                tree[cur] += (r - l + 1) * val;
                if (l != r) {
                    lazy[cur * 2 + 1] += val;
                    lazy[cur * 2 + 2] += val;
                }
                return;
            }
            int mid = (l + r) >> 1;
            update(2 * cur + 1, start, end, val, l, mid, tree, a, lazy);
            update(2 * cur + 2, start, end, val, mid + 1, r, tree, a, lazy);
            tree[cur] = tree[2 * cur + 1] + tree[2 * cur + 2];
        }
    }


    public void run() {
        InputReader sc = new InputReader(System.in);
        // Scanner sc=new Scanner(System.in);
        //  Random sc=new Random();
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        int a[]=new int[n];
        for (int i = 0; i < n; i++) {
            a[i]=sc.nextInt();
        }
        ArrayList<Integer> l[]=new ArrayList[n];
        for (int i = 0; i <n ; i++) {
            l[i]=new ArrayList<>();
        }
        HashMap<Integer,Integer> h=new HashMap<>();
        long ans=0;
        for (int i = n-1; i >=0; i--) {
            int m=a[i];
            int d=2;
            while (d*d<=m){
                int c=0;
                while (m%d==0){
                    m/=d;
                    c++;
                }
                if(c>0){
                    l[i].add(d);
                    l[i].add(c);
                    h.put(d,Math.max(c,h.getOrDefault(d,0)));
                }
                if(d==2)d=3;
                else d+=2;
            }
            if(m!=1){
                l[i].add(m);
                l[i].add(1);
                h.put(m,Math.max(1,h.getOrDefault(m,0)));
            }

        }

        long lcm=1,mod=1000000007;
        for(int key:h.keySet()){
            lcm=(lcm*modPow(key,h.get(key),mod))%mod;
        }


        for (int i = 0; i <n ; i++) {
            ans=(ans+(lcm*modInv(a[i],mod))%mod)%mod;
        }

        out.println(ans);

        out.close();
    }




}