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).

Examples

Input

3
2 3 4


Output

13


Input

5
12 12 12 12 12


Output

5


Input

3
1000000 999999 999998


Output

996989508
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.util.BitSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AnandOza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EFlatten solver = new EFlatten();
        solver.solve(1, in, out);
        out.close();
    }

    static class EFlatten {
        NumberTheory.Mod107 mod = new NumberTheory.Mod107();
        LinearSieve sieve = new LinearSieve(1_000_000);

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = in.readIntArray(n);

            HashMap<Integer, Integer> max = new HashMap<>();
            for (int v : a) {
                HashMap<Integer, Integer> c = new HashMap<>();
                while (v > 1) {
                    c.merge(sieve.leastPrimeDivisor[v], 1, Integer::sum);
                    v /= sieve.leastPrimeDivisor[v];
                }

                for (Map.Entry<Integer, Integer> e : c.entrySet()) {
                    max.merge(e.getKey(), e.getValue(), Math::max);
                }
            }

            long lcm = 1;
            for (Map.Entry<Integer, Integer> e : max.entrySet()) {
                lcm = mod.mult(lcm, mod.pow(e.getKey(), e.getValue()));
            }

            long answer = 0;
            for (long v : a) {
                answer = mod.add(answer, mod.div(lcm, v));
            }

            out.println(answer);
        }

    }

    static class NumberTheory {
        private static void ASSERT(boolean assertion) {
            if (!assertion)
                throw new AssertionError();
        }

        public abstract static class Modulus<M extends NumberTheory.Modulus<M>> {
            ArrayList<Long> factorial = new ArrayList<>();
            ArrayList<Long> invFactorial = new ArrayList<>();

            public abstract long modulus();

            public Modulus() {
                super();
                factorial.add(1L);
                invFactorial.add(1L);
            }

            public long normalize(long x) {
                x %= modulus();
                if (x < 0)
                    x += modulus();
                return x;
            }

            public long add(long a, long b) {
                long v = a + b;
                return v < modulus() ? v : v - modulus();
            }

            public long mult(long a, long b) {
                return (a * b) % modulus();
            }

            public long div(long a, long b) {
                return mult(a, inv(b));
            }

            public long pow(long x, int e) {
                if (e < 0) {
                    x = inv(x);
                    e *= -1;
                }
                if (e == 0)
                    return 1;
                if ((e & 1) > 0)
                    return mult(x, pow(x, e - 1));
                return pow(mult(x, x), e / 2);
            }

            public long inv(long value) {
                long g = modulus(), x = 0, y = 1;
                for (long r = value; r != 0; ) {
                    long q = g / r;
                    g %= r;

                    long temp = g;
                    g = r;
                    r = temp;

                    x -= q * y;

                    temp = x;
                    x = y;
                    y = temp;
                }

                ASSERT(g == 1);
                ASSERT(y == modulus() || y == -modulus());

                return normalize(x);
            }

        }

        public static class Mod107 extends NumberTheory.Modulus<NumberTheory.Mod107> {
            public long modulus() {
                return 1_000_000_007L;
            }

        }

    }

    static class LinearSieve {
        public final BitSet isComposite;
        public final int[] leastPrimeDivisor;
        public final int[] primes;

        public LinearSieve(int n) {
            double estimate;
            if (n < 10000) {
                estimate = n + 1;
            } else {
                estimate = ((double) n) / Math.log(n);
                estimate *= 1.1;
            }
            int[] primes = new int[(int) estimate];
            leastPrimeDivisor = new int[n + 1];
            int size = 0;

            if (n <= 1) {
                isComposite = new BitSet();
            } else {
                isComposite = new BitSet(n + 1);

                for (int i = 2; i <= n; i++) {
                    if (!isComposite.get(i)) {
                        if (size >= primes.length)
                            primes = resize(primes);
                        primes[size++] = i;
                        leastPrimeDivisor[i] = i;
                    }

                    for (int j = 0; j < size; j++) {
                        int p = primes[j];
                        if (i * p > n)
                            break;
                        isComposite.set(i * p);
                        leastPrimeDivisor[i * p] = p;
                        if (i % p == 0)
                            break;
                    }
                }
            }

            this.primes = new int[size];
            System.arraycopy(primes, 0, this.primes, 0, size);
        }

        private static int[] resize(int[] primes) {
            int newSize = 1 + ((primes.length * 11) / 10);
            int[] newPrimes = new int[newSize];
            System.arraycopy(primes, 0, newPrimes, 0, primes.length);
            return newPrimes;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] readIntArray(int n) {
            int[] x = new int[n];
            for (int i = 0; i < n; i++) {
                x[i] = nextInt();
            }
            return x;
        }

    }
}

