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.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.TreeMap;

/**
 * @author tutuz on 2020/04/05
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskX solver = new TaskX();
        solver.solve(1, in, out);
        out.close();
    }

    static int INF = 1 << 30;
    static long LINF = 1L << 55;
    static int MOD = 1000000007;
    static int[] mh4 = {0, -1, 1, 0};
    static int[] mw4 = {-1, 0, 0, 1};
    static int[] mh8 = {-1, -1, -1, 0, 0, 1, 1, 1};
    static int[] mw8 = {-1, 0, 1, -1, 1, -1, 0, 1};

    static class TaskX {
        Prime p = new Prime((int) Math.sqrt(1000010) + 1);

        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = in.nextIntArray(n);
            int[] ll = new int[1000010];
            for (int i = 0; i < n; i++) {
                TreeMap<Integer, Integer> map = primeFactorize(a[i]);
                for (int k : map.keySet()) {
                    int cnt = map.get(k);
                    if (ll[k] < cnt) {
                        ll[k] = cnt;
                    }
                }
            }

            long lcm = 1;
            for (int i = 0; i < 1000010; i++) {
                if (ll[i] > 0) {
                    lcm *= power(i, ll[i], MOD);
                    lcm %= MOD;
                }
            }

            long ans = 0;
            for (int i = 0; i < n; i++) {
                ans += lcm * power(a[i], MOD - 2, MOD);
                ans %= MOD;
            }

            out.println(ans);
        }

        TreeMap<Integer, Integer> primeFactorize(int n) {
            ArrayList<Integer> primes = p.getPrimes();
            TreeMap<Integer, Integer> ret = new TreeMap<>();
            for (int i = 0; i < primes.size(); i++) {
                int x = primes.get(i);
                if (n % x == 0) {
                    int cnt = 0;
                    while (n % x == 0) {
                        cnt++;
                        n /= x;
                    }
                    ret.put(x, cnt);
                }
            }
            if (n > 1) {
                ret.put(n, 1);
            }

            return ret;
        }

        class Prime {
            int n;
            boolean[] isPrime;
            ArrayList<Integer> primes;

            Prime(int n) {
                this.n = n;
                isPrime = new boolean[n + 1];
                primes = new ArrayList<>();
                sieve();
            }

            void sieve() {
                for (int i = 2; i < n; i++) {
                    if (!isPrime[i]) {
                        primes.add(i);
                        for (long j = (long) i * i; j < n; j += i) {
                            isPrime[(int) j] = true;
                        }
                    }
                }
            }

            ArrayList<Integer> getPrimes() {
                return primes;
            }
        }
    }


    /**
     * 累乗[a^e (mod modP)]
     *
     * @param a    : 被累乗数
     * @param e    : 累乗数
     * @param modP : mod数
     */
    static long power(long a, long e, long modP) {
        long ret = 1;
        for (; e > 0; e /= 2) {
            if (e % 2 != 0) {
                ret = (ret * a) % modP;
            }
            a = (a * a) % modP;
        }
        return ret;
    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++)
                ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public long nextLong() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            long ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++)
                ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        public String nextString() {
            return new String(nextChars());
        }

        public char[] nextChars() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            return Arrays.copyOf(str, len);
        }

        public char[][] next2DChars(int h, int w) {
            char[][] s = new char[h][w];
            for (int i = 0; i < h; i++) {
                s[i] = nextChars();
            }
            return s;
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (EndOfFileRuntimeException e) {
            }
            return len;
        }

        public int[] nextIntArray(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        public int[] nextIntArray1Index(final int n) {
            final int[] res = new int[n + 1];
            for (int i = 1; i < n + 1; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        public int[] nextIntArrayDec(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt() - 1;
            }
            return res;
        }

        public long[] nextLongArray(final int n) {
            final long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long[] nextLongArray1Index(final int n) {
            final long[] res = new long[n + 1];
            for (int i = 1; i < n + 1; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long[] nextLongArrayDec(final int n) {
            final long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong() - 1;
            }
            return res;
        }

        public double nextDouble() {
            return Double.parseDouble(nextString());
        }

        public double[] nextDoubleArray(int n) {
            double[] res = new double[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextDouble();
            }
            return res;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}
